LMFDB - Embedded newform 23.19.d.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,19,Mod(5,23)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 19, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("23.5");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	23.d (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$47.2388116732$
Analytic rank:	$0$
Dimension:	$350$
Relative dimension:	$35$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	23.5
Dual form			23.19.d.a.14.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-591.122 - 173.569i) q^{2} +(18020.4 - 20796.7i) q^{3} +(98769.1 + 63475.1i) q^{4} +(2.99880e6 + 431163. i) q^{5} +(-1.42619e7 + 9.16557e6i) q^{6} +(-5.80033e7 + 2.64892e7i) q^{7} +(5.83933e7 + 6.73895e7i) q^{8} +(-5.26303e7 - 3.66052e8i) q^{9} +(-1.69782e9 - 7.75369e8i) q^{10} +(-2.18679e8 - 7.44752e8i) q^{11} +(3.09993e9 - 9.10221e8i) q^{12} +(-2.38134e9 + 5.21441e9i) q^{13} +(3.88847e10 - 5.59078e9i) q^{14} +(6.30064e10 - 5.45954e10i) q^{15} +(-3.56063e10 - 7.79669e10i) q^{16} +(4.21734e10 + 6.56232e10i) q^{17} +(-3.24243e10 + 2.25516e11i) q^{18} +(1.09827e11 - 1.70895e11i) q^{19} +(2.68821e11 + 2.32935e11i) q^{20} +(-4.94356e11 + 1.68362e12i) q^{21} +4.78195e11i q^{22} +(-8.82154e11 - 1.57034e12i) q^{23} +2.45375e12 q^{24} +(5.14675e12 + 1.51122e12i) q^{25} +(2.31272e12 - 2.66902e12i) q^{26} +(4.07539e11 + 2.61909e11i) q^{27} +(-7.41034e12 - 1.06545e12i) q^{28} +(-1.09342e13 + 7.02700e12i) q^{29} +(-4.67205e13 + 2.13366e13i) q^{30} +(2.82866e13 + 3.26445e13i) q^{31} +(4.18839e12 + 2.91309e13i) q^{32} +(-1.94290e13 - 8.87295e12i) q^{33} +(-1.35395e13 - 4.61113e13i) q^{34} +(-1.85362e14 + 5.44271e13i) q^{35} +(1.80369e13 - 3.94953e13i) q^{36} +(1.49799e14 - 2.15379e13i) q^{37} +(-9.45834e13 + 8.19570e13i) q^{38} +(6.55296e13 + 1.43490e14i) q^{39} +(1.46054e14 + 2.27265e14i) q^{40} +(7.50179e13 - 5.21761e14i) q^{41} +(5.84449e14 - 9.09421e14i) q^{42} +(5.61929e14 + 4.86914e14i) q^{43} +(2.56745e13 - 8.74392e13i) q^{44} -1.12041e15i q^{45} +(2.48899e14 + 1.08137e15i) q^{46} +1.39549e15 q^{47} +(-2.26309e15 - 6.64504e14i) q^{48} +(1.59632e15 - 1.84225e15i) q^{49} +(-2.78006e15 - 1.78663e15i) q^{50} +(2.12473e15 + 3.05489e14i) q^{51} +(-5.66188e14 + 3.63867e14i) q^{52} +(5.28477e15 - 2.41348e15i) q^{53} +(-1.95446e14 - 2.25557e14i) q^{54} +(-3.34666e14 - 2.32765e15i) q^{55} +(-5.17210e15 - 2.36202e15i) q^{56} +(-1.57491e15 - 5.36364e15i) q^{57} +(7.68313e15 - 2.25597e15i) q^{58} +(-2.57689e15 + 5.64260e15i) q^{59} +(9.68854e15 - 1.39300e15i) q^{60} +(4.41468e15 - 3.82534e15i) q^{61} +(-1.10548e16 - 2.42066e16i) q^{62} +(1.27492e16 + 1.98381e16i) q^{63} +(-6.17309e14 + 4.29348e15i) q^{64} +(-9.38944e15 + 1.46103e16i) q^{65} +(9.94486e15 + 8.61727e15i) q^{66} +(-3.21463e14 + 1.09480e15i) q^{67} +9.15850e15i q^{68} +(-4.85545e16 - 9.95223e15i) q^{69} +1.19018e17 q^{70} +(3.05839e16 + 8.98025e15i) q^{71} +(2.15948e16 - 2.49217e16i) q^{72} +(-4.03359e16 - 2.59223e16i) q^{73} +(-9.22880e16 - 1.32690e16i) q^{74} +(1.24175e17 - 7.98024e16i) q^{75} +(2.16951e16 - 9.90783e15i) q^{76} +(3.24120e16 + 3.74055e16i) q^{77} +(-1.38306e16 - 9.61939e16i) q^{78} +(-3.51478e16 - 1.60515e16i) q^{79} +(-7.31599e16 - 2.49160e17i) q^{80} +(1.50261e17 - 4.41208e16i) q^{81} +(-1.34906e17 + 2.95404e17i) q^{82} +(-1.76287e17 + 2.53463e16i) q^{83} +(-1.55695e17 + 1.34911e17i) q^{84} +(9.81757e16 + 2.14975e17i) q^{85} +(-2.47655e17 - 3.85359e17i) q^{86} +(-5.09011e16 + 3.54025e17i) q^{87} +(3.74191e16 - 5.82253e16i) q^{88} +(-2.04638e16 - 1.77320e16i) q^{89} +(-1.94468e17 + 6.62299e17i) q^{90} -3.65533e17i q^{91} +(1.25475e16 - 2.11096e17i) q^{92} +1.18863e18 q^{93} +(-8.24903e17 - 2.42213e17i) q^{94} +(4.03035e17 - 4.65127e17i) q^{95} +(6.81302e17 + 4.37846e17i) q^{96} +(7.76136e17 + 1.11592e17i) q^{97} +(-1.26338e18 + 8.11923e17i) q^{98} +(-2.61109e17 + 1.19244e17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 350 q - 179 q^{2} + 20119 q^{3} - 4092083 q^{4} - 11 q^{5} - 2318126 q^{6} - 11 q^{7} - 18825206 q^{8} - 4214797052 q^{9} - 11 q^{10} - 11 q^{11} + 5321755786 q^{12} + 655768935 q^{13} - 11 q^{14} + 253448904621 q^{15}+ \cdots - 95\!\cdots\!51 q^{99}+O(q^{100}) $ 350 * q - 179 * q^2 + 20119 * q^3 - 4092083 * q^4 - 11 * q^5 - 2318126 * q^6 - 11 * q^7 - 18825206 * q^8 - 4214797052 * q^9 - 11 * q^10 - 11 * q^11 + 5321755786 * q^12 + 655768935 * q^13 - 11 * q^14 + 253448904621 * q^15 - 121059691035 * q^16 - 296340696091 * q^17 + 845128269786 * q^18 + 34950057109 * q^19 - 4104516534283 * q^20 + 5306405877949 * q^21 - 8788512317886 * q^23 + 16248757876058 * q^24 + 15898871892338 * q^25 - 12820353995934 * q^26 - 13015455785135 * q^27 + 105657239863285 * q^28 + 24125383566071 * q^29 - 190975720579083 * q^30 + 21755707682535 * q^31 - 243907502265099 * q^32 + 261034241184453 * q^33 - 129972082436273 * q^34 - 266152601718391 * q^35 + 559915831168033 * q^36 + 428874756612181 * q^37 - 1776255039233686 * q^38 + 549617987179705 * q^39 + 3407519671874989 * q^40 + 453667246412903 * q^41 - 6199000632151481 * q^42 + 1284249744062989 * q^43 + 7033574851458386 * q^44 - 11529170898896835 * q^46 - 2752011365749412 * q^47 + 7346362951210082 * q^48 + 14923872408166082 * q^49 - 8729688416622456 * q^50 - 15827415309093971 * q^51 - 11781732119049248 * q^52 + 10327001802201029 * q^53 + 16483884134652258 * q^54 - 6495140540052155 * q^55 - 112789689088256488 * q^56 + 79316406647596261 * q^57 + 80750695224012275 * q^58 - 103310090431970893 * q^59 + 56789760614471819 * q^60 + 64312558011025621 * q^61 + 78525812725681666 * q^62 - 56271156969207411 * q^63 - 224715274461002686 * q^64 - 45304722356970395 * q^65 + 206405045580983832 * q^66 + 65297330513632789 * q^67 - 143603139268291161 * q^69 - 403103996477716918 * q^70 - 7242816485765057 * q^71 + 620604439361873263 * q^72 + 69596528836762215 * q^73 + 102815849039067692 * q^74 + 116102034703195999 * q^75 - 930398829208773122 * q^76 - 693643966535804563 * q^77 + 2957501787035331408 * q^78 + 960132297145477093 * q^79 - 2513912900105850122 * q^80 - 3453140773055113594 * q^81 + 841776961191439844 * q^82 + 2134251156441149669 * q^83 + 1875963344476894475 * q^84 - 2497986830714303135 * q^85 - 709961756623859245 * q^86 - 2620179835179103895 * q^87 + 746914657235259645 * q^88 + 2323216414828777369 * q^89 + 6947866797842083322 * q^90 - 2374143188353425254 * q^92 - 8687469182791611658 * q^93 - 3156566639060022579 * q^94 + 1273876168349301101 * q^95 + 19129033188570894661 * q^96 + 2956262222729055625 * q^97 - 5708307230013551083 * q^98 - 9593810550169008251 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{1}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−591.122	−	173.569i	−1.15453	−	0.339002i	−0.352228	−	0.935914i	$-0.614576\pi$
$2$	−591.122	−	173.569i	−1.15453	−	0.339002i	−0.802307	+	0.596912i	$0.796394\pi$
$3$	18020.4	−	20796.7i	0.915532	−	1.05658i	−0.0826665	−	0.996577i	$-0.526344\pi$
$3$	18020.4	−	20796.7i	0.915532	−	1.05658i	0.998198	−	0.0600026i	$-0.0191109\pi$
$4$	98769.1	+	63475.1i	0.376774	+	0.242138i
$5$	2.99880e6	+	431163.i	1.53539	+	0.220755i	0.857529	−	0.514436i	$-0.171999\pi$
$5$	2.99880e6	+	431163.i	1.53539	+	0.220755i	0.677859	+	0.735192i	$0.262908\pi$
$6$	−1.42619e7	+	9.16557e6i	−1.41520	+	0.909491i
$7$	−5.80033e7	+	2.64892e7i	−1.43738	+	0.656428i	−0.973335	−	0.229386i	$-0.926328\pi$
$7$	−5.80033e7	+	2.64892e7i	−1.43738	+	0.656428i	−0.464041	+	0.885814i	$0.653601\pi$
$8$	5.83933e7	+	6.73895e7i	0.435064	+	0.502091i
$9$	−5.26303e7	−	3.66052e8i	−0.135848	−	0.944843i
$10$	−1.69782e9	−	7.75369e8i	−1.69782	−	0.775369i
$11$	−2.18679e8	−	7.44752e8i	−0.0927413	−	0.315848i	0.900037	−	0.435814i	$-0.143539\pi$
$11$	−2.18679e8	−	7.44752e8i	−0.0927413	−	0.315848i	−0.992778	+	0.119966i	$0.961721\pi$
$12$	3.09993e9	−	9.10221e8i	0.600787	−	0.176407i
$13$	−2.38134e9	+	5.21441e9i	−0.224560	+	0.491717i	−0.988056	−	0.154095i	$-0.950754\pi$
$13$	−2.38134e9	+	5.21441e9i	−0.224560	+	0.491717i	0.763496	+	0.645812i	$0.223481\pi$
$14$	3.88847e10	−	5.59078e9i	1.88203	−	0.270595i
$15$	6.30064e10	−	5.45954e10i	1.63894	−	1.42015i
$16$	−3.56063e10	−	7.79669e10i	−0.518140	−	1.13457i
$17$	4.21734e10	+	6.56232e10i	0.355630	+	0.553372i	0.972266	−	0.233877i	$-0.0751413\pi$
$17$	4.21734e10	+	6.56232e10i	0.355630	+	0.553372i	−0.616636	+	0.787248i	$0.711505\pi$
$18$	−3.24243e10	+	2.25516e11i	−0.163463	+	1.13691i
$19$	1.09827e11	−	1.70895e11i	0.340352	−	0.529598i	−0.628316	−	0.777959i	$-0.716255\pi$
$19$	1.09827e11	−	1.70895e11i	0.340352	−	0.529598i	0.968668	+	0.248360i	$0.0798917\pi$
$20$	2.68821e11	+	2.32935e11i	0.525041	+	0.454951i
$21$	−4.94356e11	+	1.68362e12i	−0.622395	+	2.11968i
$22$			4.78195e11i			0.396097i
$23$	−8.82154e11	−	1.57034e12i	−0.489772	−	0.871850i
$23$	−8.82154e11	−	1.57034e12i	−0.489772	−	0.871850i
$24$	2.45375e12			0.928814
$25$	5.14675e12	+	1.51122e12i	1.34919	+	0.396158i
$26$	2.31272e12	−	2.66902e12i	0.425955	−	0.491578i
$27$	4.07539e11	+	2.61909e11i	0.0534436	+	0.0343461i
$28$	−7.41034e12	−	1.06545e12i	−0.700513	−	0.100718i
$29$	−1.09342e13	+	7.02700e12i	−0.753713	+	0.484382i	−0.860216	−	0.509930i	$-0.829671\pi$
$29$	−1.09342e13	+	7.02700e12i	−0.753713	+	0.484382i	0.106502	+	0.994312i	$0.466035\pi$
$30$	−4.67205e13	+	2.13366e13i	−2.37365	+	1.08401i
$31$	2.82866e13	+	3.26445e13i	1.06986	+	1.23468i	0.970874	+	0.239592i	$0.0770138\pi$
$31$	2.82866e13	+	3.26445e13i	1.06986	+	1.23468i	0.0989839	+	0.995089i	$0.468441\pi$
$32$	4.18839e12	+	2.91309e13i	0.119041	+	0.827949i
$33$	−1.94290e13	−	8.87295e12i	−0.418626	−	0.191180i
$34$	−1.35395e13	−	4.61113e13i	−0.222993	−	0.759446i
$35$	−1.85362e14	+	5.44271e13i	−2.35184	+	0.690563i
$36$	1.80369e13	−	3.94953e13i	0.177599	−	0.388887i
$37$	1.49799e14	−	2.15379e13i	1.15264	−	0.165725i	0.460618	−	0.887599i	$-0.347628\pi$
$37$	1.49799e14	−	2.15379e13i	1.15264	−	0.165725i	0.692025	+	0.721874i	$0.256719\pi$
$38$	−9.45834e13	+	8.19570e13i	−0.572483	+	0.496059i
$39$	6.55296e13	+	1.43490e14i	0.313947	+	0.687448i
$40$	1.46054e14	+	2.27265e14i	0.557153	+	0.866947i
$41$	7.50179e13	−	5.21761e14i	0.229145	−	1.59374i	−0.472578	−	0.881289i	$-0.656677\pi$
$41$	7.50179e13	−	5.21761e14i	0.229145	−	1.59374i	0.701723	−	0.712450i	$-0.252414\pi$
$42$	5.84449e14	−	9.09421e14i	1.43715	−	2.23625i
$43$	5.61929e14	+	4.86914e14i	1.11806	+	0.968805i	0.999708	−	0.0241669i	$-0.00769332\pi$
$43$	5.61929e14	+	4.86914e14i	1.11806	+	0.968805i	0.118352	+	0.992972i	$0.462239\pi$
$44$	2.56745e13	−	8.74392e13i	0.0415363	−	0.141459i
$45$		−	1.12041e15i		−	1.48069i
$46$	2.48899e14	+	1.08137e15i	0.269900	+	1.17262i
$47$	1.39549e15			1.24694			0.623469	−	0.781848i	$-0.285723\pi$
$47$	1.39549e15			1.24694			0.623469	+	0.781848i	$0.285723\pi$
$48$	−2.26309e15	−	6.64504e14i	−1.67314	−	0.491277i
$49$	1.59632e15	−	1.84225e15i	0.980292	−	1.13132i
$50$	−2.78006e15	−	1.78663e15i	−1.42339	−	0.914757i
$51$	2.12473e15	+	3.05489e14i	0.910272	+	0.130877i
$52$	−5.66188e14	+	3.63867e14i	−0.203672	+	0.130892i
$53$	5.28477e15	−	2.41348e15i	1.60156	−	0.731409i	0.603728	−	0.797191i	$-0.293681\pi$
$53$	5.28477e15	−	2.41348e15i	1.60156	−	0.731409i	0.997834	+	0.0657820i	$0.0209542\pi$
$54$	−1.95446e14	−	2.25557e14i	−0.0500591	−	0.0577712i
$55$	−3.34666e14	−	2.32765e15i	−0.0726687	−	0.505422i
$56$	−5.17210e15	−	2.36202e15i	−0.954937	−	0.436105i
$57$	−1.57491e15	−	5.36364e15i	−0.247960	−	0.844473i
$58$	7.68313e15	−	2.25597e15i	1.03439	−	0.303726i
$59$	−2.57689e15	+	5.64260e15i	−0.297459	+	0.651345i	−0.998063	−	0.0622051i	$-0.980187\pi$
$59$	−2.57689e15	+	5.64260e15i	−0.297459	+	0.651345i	0.700604	+	0.713550i	$0.252914\pi$
$60$	9.68854e15	−	1.39300e15i	0.961384	−	0.138226i
$61$	4.41468e15	−	3.82534e15i	0.377512	−	0.327116i	−0.445351	−	0.895356i	$-0.646921\pi$
$61$	4.41468e15	−	3.82534e15i	0.377512	−	0.327116i	0.822863	+	0.568240i	$0.192376\pi$
$62$	−1.10548e16	−	2.42066e16i	−0.816628	−	1.78817i
$63$	1.27492e16	+	1.98381e16i	0.815486	+	1.26892i
$64$	−6.17309e14	+	4.29348e15i	−0.0342675	+	0.238336i
$65$	−9.38944e15	+	1.46103e16i	−0.453335	+	0.705404i
$66$	9.94486e15	+	8.61727e15i	0.418508	+	0.362639i
$67$	−3.21463e14	+	1.09480e15i	−0.0118157	+	0.0402404i	−0.965190	−	0.261550i	$-0.915766\pi$
$67$	−3.21463e14	+	1.09480e15i	−0.0118157	+	0.0402404i	0.953374	+	0.301791i	$0.0975844\pi$
$68$			9.15850e15i			0.294608i
$69$	−4.85545e16	−	9.95223e15i	−1.36958	−	0.280723i
$70$	1.19018e17			2.94938
$71$	3.05839e16	+	8.98025e15i	0.667065	+	0.195868i	0.597696	−	0.801723i	$-0.296083\pi$
$71$	3.05839e16	+	8.98025e15i	0.667065	+	0.195868i	0.0693692	+	0.997591i	$0.477901\pi$
$72$	2.15948e16	−	2.49217e16i	0.415295	−	0.479276i
$73$	−4.03359e16	−	2.59223e16i	−0.685151	−	0.440320i	0.151208	−	0.988502i	$-0.451684\pi$
$73$	−4.03359e16	−	2.59223e16i	−0.685151	−	0.440320i	−0.836359	+	0.548182i	$0.815320\pi$
$74$	−9.22880e16	−	1.32690e16i	−1.38695	−	0.199413i
$75$	1.24175e17	−	7.98024e16i	1.65380	−	1.06283i
$76$	2.16951e16	−	9.90783e15i	0.256472	−	0.117127i
$77$	3.24120e16	+	3.74055e16i	0.340635	+	0.393114i
$78$	−1.38306e16	−	9.61939e16i	−0.129416	−	0.900111i
$79$	−3.51478e16	−	1.60515e16i	−0.293261	−	0.133928i	0.263352	−	0.964700i	$-0.415172\pi$
$79$	−3.51478e16	−	1.60515e16i	−0.293261	−	0.133928i	−0.556613	+	0.830772i	$0.687899\pi$
$80$	−7.31599e16	−	2.49160e17i	−0.545084	−	1.85638i
$81$	1.50261e17	−	4.41208e16i	1.00111	−	0.293953i
$82$	−1.34906e17	+	2.95404e17i	−0.804836	+	1.76235i
$83$	−1.76287e17	+	2.53463e16i	−0.943015	+	0.135585i	−0.596638	−	0.802510i	$-0.703497\pi$
$83$	−1.76287e17	+	2.53463e16i	−0.943015	+	0.135585i	−0.346377	+	0.938095i	$0.612588\pi$
$84$	−1.55695e17	+	1.34911e17i	−0.747759	+	0.647936i
$85$	9.81757e16	+	2.14975e17i	0.423871	+	0.928148i
$86$	−2.47655e17	−	3.85359e17i	−0.962413	−	1.49754i
$87$	−5.09011e16	+	3.54025e17i	−0.178260	+	1.23983i
$88$	3.74191e16	−	5.82253e16i	0.118236	−	0.183979i
$89$	−2.04638e16	−	1.77320e16i	−0.0584084	−	0.0506112i	0.625167	−	0.780491i	$-0.285031\pi$
$89$	−2.04638e16	−	1.77320e16i	−0.0584084	−	0.0506112i	−0.683576	+	0.729880i	$0.739576\pi$
$90$	−1.94468e17	+	6.62299e17i	−0.501957	+	1.70951i
$91$		−	3.65533e17i		−	0.854189i
$92$	1.25475e16	−	2.11096e17i	0.0265747	−	0.447083i
$93$	1.18863e18			2.28403
$94$	−8.24903e17	−	2.42213e17i	−1.43963	−	0.422715i
$95$	4.03035e17	−	4.65127e17i	0.639484	−	0.738004i
$96$	6.81302e17	+	4.37846e17i	0.983781	+	0.632237i
$97$	7.76136e17	+	1.11592e17i	1.02092	+	0.146786i	0.632391	−	0.774650i	$-0.282074\pi$
$97$	7.76136e17	+	1.11592e17i	1.02092	+	0.146786i	0.388530	+	0.921436i	$0.372983\pi$
$98$	−1.26338e18	+	8.11923e17i	−1.51530	+	0.973824i
$99$	−2.61109e17	+	1.19244e17i	−0.285828	+	0.130533i
$100$	4.12415e17	+	4.75953e17i	0.412415	+	0.475953i
$101$	1.83556e15	+	1.27666e16i	0.00167833	+	0.0116730i	0.990643	−	0.136476i	$-0.0435776\pi$
$101$	1.83556e15	+	1.27666e16i	0.00167833	+	0.0116730i	−0.988965	+	0.148149i	$0.952669\pi$
$102$	−1.20295e18	−	5.49368e17i	−1.00657	−	0.459686i
$103$	4.30235e17	+	1.46525e18i	0.329740	+	1.12299i	0.942912	+	0.333041i	$0.108075\pi$
$103$	4.30235e17	+	1.46525e18i	0.329740	+	1.12299i	−0.613173	+	0.789949i	$0.710107\pi$
$104$	−4.90451e17	+	1.44009e17i	−0.344585	+	0.101179i
$105$	−2.20839e18	+	4.83571e18i	−1.42355	+	3.11714i
$106$	−3.54285e18	+	5.09385e17i	−2.09701	+	0.301504i
$107$	2.24156e17	−	1.94232e17i	0.121926	−	0.105649i	−0.591764	−	0.806111i	$-0.701568\pi$
$107$	2.24156e17	−	1.94232e17i	0.121926	−	0.105649i	0.713690	+	0.700462i	$0.247023\pi$
$108$	2.36276e16	+	5.17371e16i	0.0118197	+	0.0258815i
$109$	−1.72066e18	−	2.67739e18i	−0.792237	−	1.23275i	−0.968650	−	0.248429i	$-0.920086\pi$
$109$	−1.72066e18	−	2.67739e18i	−0.792237	−	1.23275i	0.176413	−	0.984316i	$-0.443551\pi$
$110$	−2.06180e17	+	1.43401e18i	−0.0874405	+	0.608162i
$111$	2.25153e18	−	3.50345e18i	0.880179	−	1.36959i
$112$	4.13057e18	+	3.57916e18i	1.48952	+	1.29068i
$113$	5.87210e17	−	1.99985e18i	0.195473	−	0.665721i	−0.802169	−	0.597097i	$-0.796321\pi$
$113$	5.87210e17	−	1.99985e18i	0.195473	−	0.665721i	0.997643	−	0.0686242i	$-0.0218610\pi$
$114$			3.44392e18i			1.05903i
$115$	−1.96834e18	−	5.08948e18i	−0.559525	−	1.44675i
$116$	−1.52600e18			−0.401267
$117$	2.03407e18	+	5.97258e17i	0.495101	+	0.145375i
$118$	2.50264e18	−	2.88820e18i	0.564235	−	0.651161i
$119$	−4.18451e18	−	2.68922e18i	−0.874423	−	0.561957i
$120$	7.35831e18	+	1.05797e18i	1.42609	+	0.205041i
$121$	4.17046e18	−	2.68019e18i	0.750095	−	0.482057i
$122$	−3.27357e18	+	1.49499e18i	−0.546743	+	0.249689i
$123$	−9.49904e18	−	1.09625e19i	−1.47412	−	1.70123i
$124$	7.21733e17	+	5.01976e18i	0.104131	+	0.724250i
$125$	4.26976e18	+	1.94993e18i	0.573077	+	0.261716i
$126$	−4.09303e18	−	1.39396e19i	−0.511340	−	1.74146i
$127$	8.16990e18	−	2.39890e18i	0.950568	−	0.279112i	0.230544	−	0.973062i	$-0.425949\pi$
$127$	8.16990e18	−	2.39890e18i	0.950568	−	0.279112i	0.720023	+	0.693950i	$0.244131\pi$
$128$	4.31505e18	−	9.44864e18i	0.467839	−	1.02442i
$129$	2.02524e19	−	2.91185e18i	2.04724	−	0.294349i
$130$	8.08619e18	−	7.00672e18i	0.762525	−	0.660731i
$131$	1.60223e18	+	3.50839e18i	0.141021	+	0.308792i	0.966943	−	0.254991i	$-0.0820726\pi$
$131$	1.60223e18	+	3.50839e18i	0.141021	+	0.308792i	−0.825923	+	0.563783i	$0.809345\pi$
$132$	−1.35578e18	−	2.10963e18i	−0.111436	−	0.173397i
$133$	−1.84348e18	+	1.28217e19i	−0.141571	+	0.984648i
$134$	3.80048e17	−	5.91366e17i	0.0272832	−	0.0424534i
$135$	1.10920e18	+	9.61131e17i	0.0744745	+	0.0645325i
$136$	−1.95966e18	+	6.67400e18i	−0.123121	+	0.419311i
$137$			2.03766e19i			1.19852i	0.800554	+	0.599261i	$0.204539\pi$
$137$			2.03766e19i			1.19852i	−0.800554	+	0.599261i	$0.795461\pi$
$138$	2.69742e19	+	1.43105e19i	1.48606	+	0.788396i
$139$	−2.30559e19			−1.19028			−0.595140	−	0.803622i	$-0.702903\pi$
$139$	−2.30559e19			−1.19028			−0.595140	+	0.803622i	$0.702903\pi$
$140$	−2.17628e19	−	6.39013e18i	−1.05332	−	0.309284i
$141$	2.51473e19	−	2.90215e19i	1.14161	−	1.31749i
$142$	−1.65201e19	−	1.06168e19i	−0.703750	−	0.452273i
$143$	4.40420e18	+	6.33228e17i	0.176134	+	0.0253242i
$144$	−2.66660e19	+	1.71372e19i	−1.00160	+	0.643690i
$145$	−3.58194e19	+	1.63582e19i	−1.26417	+	0.577328i
$146$	1.93441e19	+	2.23243e19i	0.641761	+	0.740632i
$147$	−9.54634e18	−	6.63963e19i	−0.297839	−	2.07151i
$148$	1.61627e19	+	7.38125e18i	0.474415	+	0.216658i
$149$	−6.44248e18	−	2.19411e19i	−0.177982	−	0.606152i	−0.999360	−	0.0357677i	$-0.988612\pi$
$149$	−6.44248e18	−	2.19411e19i	−0.177982	−	0.606152i	0.821378	−	0.570385i	$-0.193206\pi$
$150$	−8.72538e19	+	2.56200e19i	−2.26967	+	0.666436i
$151$	−2.80165e19	+	6.13476e19i	−0.686470	+	1.50316i	0.169170	+	0.985587i	$0.445891\pi$
$151$	−2.80165e19	+	6.13476e19i	−0.686470	+	1.50316i	−0.855639	+	0.517572i	$0.826836\pi$
$152$	1.79297e19	−	2.57790e18i	0.413982	−	0.0595216i
$153$	2.18019e19	−	1.88914e19i	0.474538	−	0.411189i
$154$	−1.26670e19	−	2.77369e19i	−0.260009	−	0.569340i
$155$	7.07510e19	+	1.10091e20i	1.37008	+	2.13189i
$156$	−2.63572e18	+	1.83319e19i	−0.0481702	+	0.335031i
$157$	3.56140e19	−	5.54164e19i	0.614502	−	0.956185i	−0.384945	−	0.922940i	$-0.625780\pi$
$157$	3.56140e19	−	5.54164e19i	0.614502	−	0.956185i	0.999447	−	0.0332449i	$-0.0105841\pi$
$158$	1.79906e19	+	1.55889e19i	0.293178	+	0.254041i
$159$	4.50416e19	−	1.53397e20i	0.693489	−	2.36181i
$160$			8.91637e19i			1.29750i
$161$	9.27648e19	+	6.77171e19i	1.27629	+	0.931677i
$162$	−9.64808e19			−1.25547
$163$	7.74558e18	+	2.27431e18i	0.0953599	+	0.0280002i	0.329064	−	0.944307i	$-0.393267\pi$
$163$	7.74558e18	+	2.27431e18i	0.0953599	+	0.0280002i	−0.233705	+	0.972308i	$0.575085\pi$
$164$	4.05283e19	−	4.67721e19i	0.472241	−	0.544995i
$165$	−5.44382e19	−	3.49853e19i	−0.600549	−	0.385950i
$166$	1.08607e20	+	1.56153e19i	1.13471	+	0.163146i
$167$	−1.52608e20	+	9.80752e19i	−1.51053	+	0.970758i	−0.517147	+	0.855896i	$0.673006\pi$
$167$	−1.52608e20	+	9.80752e19i	−1.51053	+	0.970758i	−0.993382	+	0.114862i	$0.963358\pi$
$168$	−1.42326e20	+	6.49979e19i	−1.33506	+	0.609699i
$169$	5.21233e19	+	6.01535e19i	0.463502	+	0.534910i
$170$	−2.07208e19	−	1.44116e20i	−0.174730	−	1.21527i
$171$	−6.83366e19	−	3.12083e19i	−0.546623	−	0.249635i
$172$	2.45943e19	+	8.37605e19i	0.186672	+	0.635746i
$173$	1.36797e20	−	4.01674e19i	0.985515	−	0.289373i	0.251016	−	0.967983i	$-0.419235\pi$
$173$	1.36797e20	−	4.01674e19i	0.985515	−	0.289373i	0.734499	+	0.678610i	$0.237417\pi$
$174$	9.15365e19	−	2.00437e20i	0.626111	−	1.37099i
$175$	−3.38560e20	+	4.86776e19i	−2.19934	+	0.316218i
$176$	−5.02797e19	+	4.35676e19i	−0.310298	+	0.268875i
$177$	7.09107e19	+	1.55273e20i	0.415865	+	0.910617i
$178$	9.01886e18	+	1.40336e19i	0.0502773	+	0.0782329i
$179$	−9.84127e18	+	6.84475e19i	−0.0521644	+	0.362811i	0.946974	+	0.321310i	$0.104123\pi$
$179$	−9.84127e18	+	6.84475e19i	−0.0521644	+	0.362811i	−0.999138	+	0.0415012i	$0.986786\pi$
$180$	7.11181e19	−	1.10662e20i	0.358532	−	0.557886i
$181$	2.29513e19	+	1.98874e19i	0.110078	+	0.0953829i	0.708161	−	0.706051i	$-0.249525\pi$
$181$	2.29513e19	+	1.98874e19i	0.110078	+	0.0953829i	−0.598083	+	0.801434i	$0.704071\pi$
$182$	−6.34452e19	+	2.16075e20i	−0.289572	+	0.986191i
$183$		−	1.60745e20i		−	0.698356i
$184$	5.43122e19	−	1.51145e20i	0.224666	−	0.625221i
$185$	4.58506e20			1.80634
$186$	−7.02627e20	−	2.06310e20i	−2.63699	−	0.774290i
$187$	3.96506e19	−	4.57592e19i	0.141800	−	0.163645i
$188$	1.37831e20	+	8.85786e19i	0.469814	+	0.301931i
$189$	−3.05764e19	−	4.39622e18i	−0.0993642	−	0.0142864i
$190$	−3.18974e20	+	2.04992e20i	−0.988492	+	0.635265i
$191$	9.71037e18	−	4.43458e18i	0.0287035	−	0.0131085i	−0.401012	−	0.916073i	$-0.631341\pi$
$191$	9.71037e18	−	4.43458e18i	0.0287035	−	0.0131085i	0.429715	+	0.902965i	$0.358614\pi$
$192$	7.81658e19	+	9.02081e19i	0.220448	+	0.254410i
$193$	7.47661e19	+	5.20009e20i	0.201228	+	1.39957i	0.800647	+	0.599137i	$0.204489\pi$
$193$	7.47661e19	+	5.20009e20i	0.201228	+	1.39957i	−0.599419	+	0.800436i	$0.704601\pi$
$194$	−4.39422e20	−	2.00677e20i	−1.12893	−	0.515564i
$195$	1.34643e20	+	4.58552e20i	0.330272	+	1.12480i
$196$	2.74604e20	−	8.06311e19i	0.643284	−	0.188885i
$197$	−5.76044e19	+	1.26136e20i	−0.128902	+	0.282256i	−0.963068	−	0.269257i	$-0.913222\pi$
$197$	−5.76044e19	+	1.26136e20i	−0.128902	+	0.282256i	0.834166	+	0.551513i	$0.185949\pi$
$198$	1.75044e20	−	2.51675e19i	0.374249	−	0.0538089i
$199$	−1.26594e20	+	1.09694e20i	−0.258664	+	0.224133i	−0.774532	−	0.632534i	$-0.782015\pi$
$199$	−1.26594e20	+	1.09694e20i	−0.258664	+	0.224133i	0.515869	+	0.856668i	$0.327469\pi$
$200$	1.98696e20	+	4.35083e20i	0.388077	+	0.849771i
$201$	1.69753e19	+	2.64142e19i	0.0316996	+	0.0493256i
$202$	1.13085e18	−	7.86521e18i	0.00201949	−	0.0140458i
$203$	4.48082e20	−	6.97229e20i	0.765408	−	1.19100i
$204$	1.90466e20	+	1.65040e20i	0.311277	+	0.269723i
$205$	4.49928e20	−	1.53232e21i	0.703653	−	2.39642i
$206$		−	9.40815e20i		−	1.40831i
$207$	−5.28396e20	+	4.05561e20i	−0.757228	+	0.581197i
$208$	4.91343e20			0.674240
$209$	−1.51291e20	−	4.44231e19i	−0.198837	−	0.0583838i
$210$	2.14476e21	−	2.47518e21i	2.70025	−	3.11626i
$211$	−9.06684e19	−	5.82690e19i	−0.109374	−	0.0702904i	0.484810	−	0.874619i	$-0.338889\pi$
$211$	−9.06684e19	−	5.82690e19i	−0.109374	−	0.0702904i	−0.594184	+	0.804329i	$0.702525\pi$
$212$	6.75168e20	+	9.70745e19i	0.780529	+	0.112223i
$213$	7.37894e20	−	4.74216e20i	0.817669	−	0.525484i
$214$	−1.66216e20	+	7.59083e19i	−0.176583	+	0.0806428i
$215$	1.47518e21	+	1.70244e21i	1.50279	+	1.73431i
$216$	6.14762e18	+	4.27576e19i	0.00600652	+	0.0417763i
$217$	−2.50545e21	−	1.14420e21i	−2.34827	−	1.07242i
$218$	5.52404e20	+	1.88132e21i	0.496762	+	1.69182i
$219$	−1.26597e21	+	3.71722e20i	−1.09251	+	0.320790i
$220$	1.14693e20	−	2.51143e20i	0.0950022	−	0.208026i
$221$	−4.42616e20	+	6.36385e19i	−0.351962	+	0.0506046i
$222$	−1.93902e21	+	1.68017e21i	−1.48049	+	1.28285i
$223$	−7.82340e20	−	1.71308e21i	−0.573656	−	1.25613i	−0.944828	−	0.327567i	$-0.893771\pi$
$223$	−7.82340e20	−	1.71308e21i	−0.573656	−	1.25613i	0.371172	−	0.928564i	$-0.378956\pi$
$224$	−1.01459e21	−	1.57874e21i	−0.714596	−	1.11193i
$225$	2.82311e20	−	1.96351e21i	0.191023	−	1.32859i
$226$	−6.94225e20	+	1.08024e21i	−0.451361	+	0.702332i
$227$	−1.23936e21	−	1.07391e21i	−0.774400	−	0.671021i	0.175183	−	0.984536i	$-0.443948\pi$
$227$	−1.23936e21	−	1.07391e21i	−0.774400	−	0.671021i	−0.949583	+	0.313514i	$0.898494\pi$
$228$	1.84905e20	−	6.29729e20i	0.111054	−	0.378216i
$229$			1.86928e21i			1.07933i	0.841879	+	0.539667i	$0.181450\pi$
$229$			1.86928e21i			1.07933i	−0.841879	+	0.539667i	$0.818550\pi$
$230$	2.80151e20	+	3.35015e21i	0.155540	+	1.86000i
$231$	1.36199e21			0.727219
$232$	−1.11203e21	−	3.26522e20i	−0.571118	−	0.167695i
$233$	1.37903e21	−	1.59148e21i	0.681348	−	0.786317i	−0.304759	−	0.952430i	$-0.598576\pi$
$233$	1.37903e21	−	1.59148e21i	0.681348	−	0.786317i	0.986107	+	0.166112i	$0.0531213\pi$
$234$	−1.09872e21	−	7.06105e20i	−0.522329	−	0.335681i
$235$	4.18479e21	+	6.01682e20i	1.91453	+	0.275269i
$236$	−6.12682e20	+	3.93747e20i	−0.269791	+	0.173384i
$237$	−9.67195e20	+	4.41703e20i	−0.409996	+	0.187239i
$238$	2.00679e21	+	2.31596e21i	0.819047	+	0.945230i
$239$	6.14156e20	+	4.27155e21i	0.241378	+	1.67882i	0.645224	+	0.763993i	$0.276764\pi$
$239$	6.14156e20	+	4.27155e21i	0.241378	+	1.67882i	−0.403847	+	0.914827i	$0.632327\pi$
$240$	−6.50006e21	−	2.96848e21i	−2.46046	−	1.12365i
$241$	8.18844e20	+	2.78873e21i	0.298571	+	1.01684i	0.963003	+	0.269491i	$0.0868554\pi$
$241$	8.18844e20	+	2.78873e21i	0.298571	+	1.01684i	−0.664432	+	0.747349i	$0.731326\pi$
$242$	−2.93045e21	+	8.60458e20i	−1.02943	+	0.302267i
$243$	1.71224e21	−	3.74929e21i	0.579574	−	1.26909i
$244$	6.78848e20	−	9.76036e19i	0.221444	−	0.0318388i
$245$	5.58136e21	−	4.83628e21i	1.75487	−	1.52061i
$246$	3.71234e21	+	8.12889e21i	1.12521	+	2.46386i
$247$	6.29579e20	+	9.79644e20i	0.183983	+	0.286283i
$248$	−5.48147e20	+	3.81244e21i	−0.154466	+	1.07433i
$249$	−2.64965e21	+	4.12294e21i	−0.720104	+	1.12050i
$250$	−2.18550e21	−	1.89375e21i	−0.572915	−	0.496434i
$251$	1.45112e21	−	4.94206e21i	0.366978	−	1.24981i	−0.544604	−	0.838693i	$-0.683320\pi$
$251$	1.45112e21	−	4.94206e21i	0.366978	−	1.24981i	0.911582	−	0.411118i	$-0.134862\pi$
$252$			2.76864e21i			0.675557i
$253$	−9.76603e20	+	1.00039e21i	−0.229950	+	0.235550i
$254$	−5.24578e21			−1.19208
$255$	6.23992e21	+	1.83221e21i	1.36873	+	0.401895i
$256$	−3.44608e21	+	3.97699e21i	−0.729736	+	0.842160i
$257$	−5.91571e21	−	3.80180e21i	−1.20951	−	0.777304i	−0.228932	−	0.973442i	$-0.573523\pi$
$257$	−5.91571e21	−	3.80180e21i	−1.20951	−	0.777304i	−0.980576	+	0.196138i	$0.937160\pi$
$258$	−1.24770e22	−	1.79393e21i	−2.46339	−	0.354182i
$259$	−8.11834e21	+	5.21734e21i	−1.54799	+	0.994836i
$260$	−1.85477e21	+	8.47047e20i	−0.341610	+	0.156008i
$261$	3.14772e21	+	3.63266e21i	0.560056	+	0.646339i
$262$	−3.38164e20	−	2.35198e21i	−0.0581320	−	0.404317i
$263$	5.05040e21	+	2.30644e21i	0.838926	+	0.383125i	0.788073	−	0.615581i	$-0.211079\pi$
$263$	5.05040e21	+	2.30644e21i	0.838926	+	0.383125i	0.0508528	+	0.998706i	$0.483806\pi$
$264$	−5.36583e20	−	1.82744e21i	−0.0861394	−	0.293364i
$265$	1.68886e22	−	4.95894e21i	2.62048	−	0.769443i
$266$	3.31517e21	−	7.25922e21i	0.497246	−	1.08882i
$267$	−7.37531e20	+	1.06041e20i	−0.106950	+	0.0153770i
$268$	−1.01243e20	+	8.77278e19i	−0.0141956	+	0.0123005i
$269$	2.29397e21	+	5.02310e21i	0.311041	+	0.681085i	0.999002	−	0.0446628i	$-0.0142213\pi$
$269$	2.29397e21	+	5.02310e21i	0.311041	+	0.681085i	−0.687961	+	0.725748i	$0.741494\pi$
$270$	−4.88852e20	−	7.60669e20i	−0.0641068	−	0.0997521i
$271$	3.06216e20	−	2.12978e21i	0.0388423	−	0.270154i	−0.961140	−	0.276060i	$-0.910971\pi$
$271$	3.06216e20	−	2.12978e21i	0.0388423	−	0.270154i	0.999983	+	0.00590655i	$0.00188012\pi$
$272$	3.61480e21	−	5.62473e21i	0.443572	−	0.690211i
$273$	−7.60187e21	−	6.58706e21i	−0.902519	−	0.782037i
$274$	3.53674e21	−	1.20450e22i	0.406301	−	1.38373i
$275$		−	4.16353e21i		−	0.462879i
$276$	−4.16397e21	−	4.06497e21i	−0.448049	−	0.437397i
$277$	−1.30731e21			−0.136164			−0.0680819	−	0.997680i	$-0.521688\pi$
$277$	−1.30731e21			−0.136164			−0.0680819	+	0.997680i	$0.521688\pi$
$278$	1.36289e22	+	4.00179e21i	1.37422	+	0.403507i
$279$	1.04608e22	−	1.20725e22i	1.02124	−	1.17858i
$280$	−1.44917e22	−	9.31326e21i	−1.36993	−	0.880399i
$281$	1.48340e22	+	2.13281e21i	1.35801	+	0.195252i	0.782555	−	0.622582i	$-0.213916\pi$
$281$	1.48340e22	+	2.13281e21i	1.35801	+	0.195252i	0.575454	+	0.817834i	$0.304825\pi$
$282$	−1.99023e22	+	1.27904e22i	−1.76466	+	1.13408i
$283$	−5.80929e21	+	2.65301e21i	−0.498936	+	0.227856i	−0.648955	−	0.760827i	$-0.724794\pi$
$283$	−5.80929e21	+	2.65301e21i	−0.498936	+	0.227856i	0.150019	+	0.988683i	$0.452066\pi$
$284$	2.45073e21	+	2.82829e21i	0.203906	+	0.235320i
$285$	−2.41023e21	−	1.67635e22i	−0.194292	−	1.35133i
$286$	−2.49351e21	−	1.13875e21i	−0.194767	−	0.0889473i
$287$	9.46976e21	+	3.22510e22i	0.716806	+	2.44122i
$288$	1.04430e22	−	3.06633e21i	0.766111	−	0.224950i
$289$	3.31422e21	−	7.25712e21i	0.235668	−	0.516041i
$290$	2.40129e22	−	3.45253e21i	1.65525	−	0.237989i
$291$	1.63070e22	−	1.41301e22i	1.08978	−	0.944297i
$292$	−2.33852e21	−	5.12065e21i	−0.151529	−	0.331802i
$293$	−1.34270e22	−	2.08928e22i	−0.843667	−	1.31277i	−0.948013	−	0.318230i	$-0.896911\pi$
$293$	−1.34270e22	−	2.08928e22i	−0.843667	−	1.31277i	0.104347	−	0.994541i	$-0.466725\pi$
$294$	−5.88128e21	+	4.09052e22i	−0.358382	+	2.49260i
$295$	−1.01605e22	+	1.58100e22i	−0.600504	+	0.934402i
$296$	1.01987e22	+	8.83724e21i	0.584683	+	0.506631i
$297$	1.05937e20	−	3.60790e20i	0.00589171	−	0.0200653i
$298$			1.40881e22i			0.760160i
$299$	1.02891e22	−	8.60410e20i	0.538687	−	0.0450469i
$300$	1.73301e22			0.880461
$301$	−4.54917e22	−	1.33576e22i	−2.24302	−	0.658611i
$302$	2.72092e22	−	3.14011e22i	1.30213	−	1.50273i
$303$	2.98580e20	+	1.91886e20i	0.0138700	+	0.00891372i
$304$	−1.72347e22	−	2.47797e21i	−0.777215	−	0.111747i
$305$	1.48881e22	−	9.56801e21i	0.651840	−	0.418912i
$306$	−1.61665e22	+	7.38300e21i	−0.687264	+	0.313863i
$307$	−4.53410e21	−	5.23263e21i	−0.187174	−	0.216011i	0.654405	−	0.756144i	$-0.272919\pi$
$307$	−4.53410e21	−	5.23263e21i	−0.187174	−	0.216011i	−0.841579	+	0.540134i	$0.818374\pi$
$308$	8.26993e20	+	5.75186e21i	0.0331547	+	0.230596i
$309$	3.82253e22	+	1.74569e22i	1.48842	+	0.679737i
$310$	−2.27141e22	−	7.73572e22i	−0.859094	−	2.92580i
$311$	3.39857e22	−	9.97909e21i	1.24868	−	0.366647i	0.410412	−	0.911900i	$-0.365385\pi$
$311$	3.39857e22	−	9.97909e21i	1.24868	−	0.366647i	0.838271	+	0.545254i	$0.183567\pi$
$312$	−5.84322e21	+	1.27949e22i	−0.208574	+	0.456714i
$313$	−3.45834e22	+	4.97234e21i	−1.19941	+	0.172449i	−0.712926	−	0.701239i	$-0.752631\pi$
$313$	−3.45834e22	+	4.97234e21i	−1.19941	+	0.172449i	−0.486486	+	0.873688i	$0.661721\pi$
$314$	−3.06708e22	+	2.65764e22i	−1.03361	+	0.895631i
$315$	2.96788e22	+	6.49875e22i	0.971966	+	2.12831i
$316$	−2.45265e21	−	3.81640e21i	−0.0780642	−	0.121470i
$317$	1.48202e21	−	1.03077e22i	0.0458482	−	0.318881i	−0.953972	−	0.299897i	$-0.903048\pi$
$317$	1.48202e21	−	1.03077e22i	0.0458482	−	0.318881i	0.999820	−	0.0189842i	$-0.00604321\pi$
$318$	−5.32501e22	+	8.28588e22i	−1.60131	+	2.49169i
$319$	7.62446e21	+	6.60664e21i	0.222891	+	0.193136i
$320$	−3.70238e21	+	1.26091e22i	−0.105228	+	0.358373i
$321$		−	8.16184e21i		−	0.225550i
$322$	−4.30817e22	−	5.61301e22i	−1.15768	−	1.50832i
$323$	1.58465e22			0.414104
$324$	1.76418e22	+	5.18009e21i	0.448370	+	0.131653i
$325$	−2.01363e22	+	2.32386e22i	−0.497771	+	0.574459i
$326$	−4.18383e21	−	2.68879e21i	−0.100604	−	0.0646544i
$327$	−8.66877e22	−	1.24638e22i	−2.02781	−	0.291555i
$328$	3.95418e22	−	2.54120e22i	0.899895	−	0.578327i
$329$	−8.09429e22	+	3.69654e22i	−1.79232	+	0.818525i
$330$	2.61073e22	+	3.01294e22i	0.562517	+	0.649179i
$331$	5.64627e21	+	3.92707e22i	0.118388	+	0.823410i	0.959331	+	0.282285i	$0.0910924\pi$
$331$	5.64627e21	+	3.92707e22i	0.118388	+	0.823410i	−0.840942	+	0.541125i	$0.817999\pi$
$332$	−1.90206e22	−	8.68643e21i	−0.388134	−	0.177255i
$333$	−1.57680e22	−	5.37008e22i	−0.313168	−	1.06655i
$334$	1.07233e23	−	3.14864e22i	2.07305	−	0.608701i
$335$	−1.43604e21	+	3.14450e21i	−0.0270249	+	0.0591763i
$336$	1.48869e23	−	2.14041e22i	2.72741	−	0.392143i
$337$	1.03161e22	−	8.93899e21i	0.184013	−	0.159448i	−0.557983	−	0.829852i	$-0.688425\pi$
$337$	1.03161e22	−	8.93899e21i	0.184013	−	0.159448i	0.741996	+	0.670404i	$0.233879\pi$
$338$	−2.03704e22	−	4.46051e22i	−0.353794	−	0.774700i
$339$	−3.10085e22	−	4.82502e22i	−0.524425	−	0.816022i
$340$	−3.94881e21	+	2.74646e22i	−0.0650363	+	0.452337i
$341$	1.81264e22	−	2.82052e22i	0.290751	−	0.452418i
$342$	3.49784e22	+	3.03090e22i	0.546469	+	0.473518i
$343$	−1.45378e22	+	4.95112e22i	−0.221234	+	0.753453i
$344$			6.63007e22i			0.982860i
$345$	−1.41315e23	−	5.07797e22i	−2.04087	−	0.733362i
$346$	−8.78358e22			−1.23591
$347$	1.53404e22	+	4.50434e21i	0.210315	+	0.0617541i	0.385193	−	0.922836i	$-0.374135\pi$
$347$	1.53404e22	+	4.50434e21i	0.210315	+	0.0617541i	−0.174878	+	0.984590i	$0.555953\pi$
$348$	−2.74992e22	+	3.17358e22i	−0.367373	+	0.423971i
$349$	5.01625e22	+	3.22375e22i	0.653056	+	0.419694i	0.824782	−	0.565451i	$-0.191298\pi$
$349$	5.01625e22	+	3.22375e22i	0.653056	+	0.419694i	−0.171726	+	0.985145i	$0.554934\pi$
$350$	2.08579e23	+	2.99891e22i	2.64642	+	0.380497i
$351$	−2.33619e21	+	1.50138e21i	−0.0288898	+	0.0185664i
$352$	2.07794e22	−	9.48962e21i	0.250466	−	0.114384i
$353$	1.77810e22	+	2.05204e22i	0.208922	+	0.241109i	0.850534	−	0.525921i	$-0.176279\pi$
$353$	1.77810e22	+	2.05204e22i	0.208922	+	0.241109i	−0.641611	+	0.767030i	$0.721734\pi$
$354$	−1.49663e22	−	1.04093e23i	−0.171429	−	1.19232i
$355$	8.78433e22	+	4.01167e22i	0.980964	+	0.447991i
$356$	−8.95651e20	−	3.05031e21i	−0.00975189	−	0.0332119i
$357$	−1.31333e23	+	3.85629e22i	−1.39431	+	0.409408i
$358$	1.76978e22	−	3.87527e22i	0.183219	−	0.401194i
$359$	−5.79615e22	+	8.33361e21i	−0.585180	+	0.0841362i	−0.428545	−	0.903520i	$-0.640974\pi$
$359$	−5.79615e22	+	8.33361e21i	−0.585180	+	0.0841362i	−0.156635	+	0.987657i	$0.550065\pi$
$360$	7.55039e22	−	6.54245e22i	0.743441	−	0.644196i
$361$	2.61131e22	+	5.71797e22i	0.250780	+	0.549132i
$362$	−1.01152e22	−	1.57395e22i	−0.0947535	−	0.147439i
$363$	1.94144e22	−	1.35030e23i	0.177404	−	1.23387i
$364$	2.32022e22	−	3.61034e22i	0.206832	−	0.321837i
$365$	−1.09783e23	−	9.51274e22i	−0.954770	−	0.827313i
$366$	−2.79003e22	+	9.50197e22i	−0.236744	+	0.806277i
$367$			1.50888e23i			1.24928i	0.780913	+	0.624639i	$0.214754\pi$
$367$			1.50888e23i			1.24928i	−0.780913	+	0.624639i	$0.785246\pi$
$368$	−9.10240e22	+	1.24693e23i	−0.735403	+	1.00742i
$369$	−1.94940e23			−1.53696
$370$	−2.71033e23	−	7.95824e22i	−2.08548	−	0.612352i
$371$	−2.42603e23	+	2.79979e23i	−1.82193	+	2.10262i
$372$	1.17400e23	+	7.54486e22i	0.860563	+	0.553050i
$373$	9.53835e22	+	1.37141e22i	0.682486	+	0.0981266i	0.474833	−	0.880076i	$-0.342508\pi$
$373$	9.53835e22	+	1.37141e22i	0.682486	+	0.0981266i	0.207653	+	0.978203i	$0.433418\pi$
$374$	−3.13807e22	+	2.01671e22i	−0.219189	+	0.140864i
$375$	1.17495e23	−	5.36581e22i	0.801194	−	0.365893i
$376$	8.14872e22	+	9.40412e22i	0.542499	+	0.626077i
$377$	−1.06035e22	−	7.37493e22i	−0.0689254	−	0.479386i
$378$	1.73113e22	+	7.90582e21i	0.109876	+	0.0501788i
$379$	8.33749e22	+	2.83949e23i	0.516752	+	1.75990i	0.640891	+	0.767632i	$0.278565\pi$
$379$	8.33749e22	+	2.83949e23i	0.516752	+	1.75990i	−0.124139	+	0.992265i	$0.539617\pi$
$380$	6.93313e22	−	2.03575e22i	0.419640	−	0.123217i
$381$	9.73358e22	−	2.13136e23i	0.575371	−	1.25989i
$382$	−6.50971e21	+	9.35956e20i	−0.0375830	+	0.00540362i
$383$	2.05184e23	−	1.77793e23i	1.15706	−	1.00260i	0.157169	−	0.987572i	$-0.449763\pi$
$383$	2.05184e23	−	1.77793e23i	1.15706	−	1.00260i	0.999887	−	0.0150233i	$-0.00478225\pi$
$384$	−1.18741e23	−	2.60007e23i	−0.654065	−	1.43220i
$385$	8.10695e22	+	1.26147e23i	0.436225	+	0.678780i
$386$	4.60617e22	−	3.20366e23i	0.242133	−	1.68407i
$387$	1.48661e23	−	2.31321e23i	0.763483	−	1.18800i
$388$	6.95750e22	+	6.02871e22i	0.349114	+	0.302509i
$389$	−3.46958e22	+	1.18163e23i	−0.170110	+	0.579342i	0.829668	+	0.558258i	$0.188530\pi$
$389$	−3.46958e22	+	1.18163e23i	−0.170110	+	0.579342i	−0.999778	+	0.0210840i	$0.993288\pi$
$390$		−	2.94430e23i		−	1.41059i
$391$	6.58469e22	−	1.24116e23i	0.308279	−	0.581082i
$392$	2.17363e23			0.994514
$393$	1.01836e23	+	2.99016e22i	0.455372	+	0.133709i
$394$	5.59445e22	−	6.45634e22i	0.244507	−	0.282176i
$395$	−9.84807e22	−	6.32897e22i	−0.420705	−	0.270370i
$396$	−3.33585e22	−	4.79623e21i	−0.139300	−	0.0200283i
$397$	2.65726e23	−	1.70771e23i	1.08472	−	0.697109i	0.129079	−	0.991634i	$-0.458798\pi$
$397$	2.65726e23	−	1.70771e23i	1.08472	−	0.697109i	0.955644	+	0.294525i	$0.0951616\pi$
$398$	9.38721e22	−	4.28699e22i	0.374618	−	0.171082i
$399$	2.33428e23	+	2.69391e23i	0.910747	+	1.05106i
$400$	−6.54314e22	−	4.55086e23i	−0.249601	−	1.73601i
$401$	−1.84401e23	−	8.42131e22i	−0.687803	−	0.314109i	0.0406809	−	0.999172i	$-0.487047\pi$
$401$	−1.84401e23	−	8.42131e22i	−0.687803	−	0.314109i	−0.728484	+	0.685063i	$0.759775\pi$
$402$	−5.44982e21	−	1.85604e22i	−0.0198768	−	0.0676943i
$403$	−2.37582e23	+	6.97604e22i	−0.847360	+	0.248807i
$404$	−6.29064e20	+	1.37746e21i	−0.00219413	+	0.00480448i
$405$	4.69628e23	−	6.75223e22i	1.60199	−	0.230331i
$406$	−3.85888e23	+	3.34374e23i	−1.28744	+	1.11557i
$407$	−4.87984e22	−	1.06854e23i	−0.159241	−	0.348690i
$408$	1.03483e23	+	1.61023e23i	0.330315	+	0.513980i
$409$	8.34802e22	−	5.80618e23i	0.260660	−	1.81293i	−0.267249	−	0.963627i	$-0.586115\pi$
$409$	8.34802e22	−	5.80618e23i	0.260660	−	1.81293i	0.527909	−	0.849301i	$-0.322976\pi$
$410$	−5.31925e23	+	8.27691e23i	−1.62478	+	2.52821i
$411$	4.23764e23	+	3.67194e23i	1.26633	+	1.09728i
$412$	−5.05127e22	+	1.72030e23i	−0.147681	+	0.502956i
$413$		−	3.95549e23i		−	1.13149i
$414$	3.82739e23	−	1.48023e23i	1.07127	−	0.414311i
$415$	−5.39580e23			−1.47783
$416$	−1.61874e23	−	4.75306e22i	−0.433849	−	0.127389i
$417$	−4.15477e23	+	4.79486e23i	−1.08974	+	1.25763i
$418$	8.17211e22	+	5.25189e22i	0.209772	+	0.134812i
$419$	1.33676e23	+	1.92198e22i	0.335837	+	0.0482861i	0.308171	−	0.951331i	$-0.400283\pi$
$419$	1.33676e23	+	1.92198e22i	0.335837	+	0.0482861i	0.0276666	+	0.999617i	$0.491192\pi$
$420$	−5.25068e23	+	3.37441e23i	−1.29114	+	0.829762i
$421$	−3.07074e21	+	1.40236e21i	−0.00739102	+	0.00337536i	−0.419107	−	0.907937i	$-0.637657\pi$
$421$	−3.07074e21	+	1.40236e21i	−0.00739102	+	0.00337536i	0.411716	+	0.911312i	$0.364930\pi$
$422$	4.34824e22	+	5.01813e22i	0.102447	+	0.118231i
$423$	−7.34449e22	−	5.10820e23i	−0.169394	−	1.17816i
$424$	4.71239e23	+	2.15207e23i	1.06402	+	0.485920i
$425$	1.17885e23	+	4.01480e23i	0.260590	+	0.887490i
$426$	−5.18494e23	+	1.52244e23i	−1.12217	+	0.329498i
$427$	−1.54736e23	+	3.38824e23i	−0.327899	+	0.717998i
$428$	3.44686e22	−	4.95583e21i	0.0715203	−	0.0102831i
$429$	9.25344e22	−	8.01815e22i	0.188013	−	0.162914i
$430$	−5.76517e23	−	1.26240e24i	−1.14709	−	2.51177i
$431$	−3.75196e23	−	5.83816e23i	−0.731076	−	1.13758i	−0.985367	−	0.170448i	$-0.945478\pi$
$431$	−3.75196e23	−	5.83816e23i	−0.731076	−	1.13758i	0.254291	−	0.967128i	$-0.418158\pi$
$432$	5.90932e21	−	4.11002e22i	0.0112767	−	0.0784315i
$433$	−2.86934e23	+	4.46478e23i	−0.536279	+	0.834467i	−0.998635	−	0.0522277i	$-0.983368\pi$
$433$	−2.86934e23	+	4.46478e23i	−0.536279	+	0.834467i	0.462356	+	0.886694i	$0.347004\pi$
$434$	1.28243e24	+	1.11123e24i	2.34760	+	2.03421i
$435$	−3.05285e23	+	1.03971e24i	−0.547397	+	1.86426i
$436$		−	3.73662e23i		−	0.656298i
$437$	−3.65247e23	−	2.17103e22i	−0.628425	−	0.0373537i
$438$	8.12860e23			1.37009
$439$	−4.79904e23	−	1.40912e23i	−0.792453	−	0.232685i	−0.139638	−	0.990203i	$-0.544594\pi$
$439$	−4.79904e23	−	1.40912e23i	−0.792453	−	0.232685i	−0.652815	+	0.757517i	$0.726412\pi$
$440$	1.37317e23	−	1.58472e23i	0.222152	−	0.256377i
$441$	−7.58374e23	−	4.87378e23i	−1.20209	−	0.772535i
$442$	2.72685e23	+	3.92062e22i	0.423508	+	0.0608912i
$443$	−9.25694e23	+	5.94908e23i	−1.40875	+	0.905349i	−0.999973	−	0.00728561i	$-0.997681\pi$
$443$	−9.25694e23	+	5.94908e23i	−1.40875	+	0.905349i	−0.408777	+	0.912634i	$0.634045\pi$
$444$	4.44764e23	−	2.03117e23i	0.663258	−	0.302900i
$445$	−5.37215e22	−	6.19979e22i	−0.0785069	−	0.0906018i
$446$	1.65120e23	+	1.14843e24i	0.236475	+	1.64472i
$447$	−5.72398e23	−	2.61405e23i	−0.803397	−	0.366899i
$448$	−7.79249e22	−	2.65388e23i	−0.107195	−	0.365072i
$449$	−6.57767e23	+	1.93138e23i	−0.886860	+	0.260405i	−0.693271	−	0.720677i	$-0.743831\pi$
$449$	−6.57767e23	+	1.93138e23i	−0.886860	+	0.260405i	−0.193589	+	0.981083i	$0.562013\pi$
$450$	−5.07685e23	+	1.11168e24i	−0.670937	+	1.46915i
$451$	−4.04988e23	+	5.82284e22i	−0.524630	+	0.0754304i
$452$	1.84939e23	−	1.60251e23i	0.234846	−	0.203495i
$453$	7.70956e23	+	1.68816e24i	0.959723	+	2.10150i
$454$	5.46216e23	+	8.49928e23i	0.666594	+	1.03724i
$455$	1.57604e23	−	1.09616e24i	0.188567	−	1.31151i
$456$	2.69489e23	−	4.19333e23i	0.316124	−	0.491898i
$457$	3.46526e22	+	3.00266e22i	0.0398556	+	0.0345351i	0.674561	−	0.738219i	$-0.264333\pi$
$457$	3.46526e22	+	3.00266e22i	0.0398556	+	0.0345351i	−0.634705	+	0.772754i	$0.718878\pi$
$458$	3.24450e23	−	1.10497e24i	0.365896	−	1.24613i
$459$			3.77896e22i			0.0417887i
$460$	1.28644e23	−	6.27624e23i	0.139499	−	0.680580i
$461$	1.64286e24			1.74699			0.873497	−	0.486830i	$-0.161847\pi$
$461$	1.64286e24			1.74699			0.873497	+	0.486830i	$0.161847\pi$
$462$	−8.05100e23	−	2.36399e23i	−0.839599	−	0.246529i
$463$	4.14246e23	−	4.78066e23i	0.423672	−	0.488944i	−0.503280	−	0.864123i	$-0.667874\pi$
$463$	4.14246e23	−	4.78066e23i	0.423672	−	0.488944i	0.926952	+	0.375180i	$0.122419\pi$
$464$	9.37202e23	+	6.02303e23i	0.940094	+	0.604162i
$465$	3.56448e24	+	5.12495e23i	3.50687	+	0.504212i
$466$	−1.09140e24	+	7.01402e23i	−1.05320	+	0.676852i
$467$	−1.73764e24	+	7.93554e23i	−1.64478	+	0.751147i	−0.999914	−	0.0131474i	$-0.995815\pi$
$467$	−1.73764e24	+	7.93554e23i	−1.64478	+	0.751147i	−0.644868	+	0.764294i	$0.723088\pi$
$468$	1.62993e23	+	1.88104e23i	0.151341	+	0.174656i
$469$	−1.03546e22	−	7.20175e22i	−0.00943139	−	0.0655968i
$470$	−2.36929e24	−	1.08202e24i	−2.11708	−	0.966838i
$471$	−5.10698e23	−	1.73928e24i	−0.447689	−	1.52469i
$472$	−5.30725e23	+	1.55835e23i	−0.456449	+	0.134025i
$473$	2.39748e23	−	5.24976e23i	0.202304	−	0.442985i
$474$	6.48396e23	−	9.32253e22i	0.536828	−	0.0771843i
$475$	8.23515e23	−	7.13580e23i	0.669004	−	0.579696i
$476$	−2.42602e23	−	5.31224e23i	−0.193389	−	0.423462i
$477$	−1.16160e24	−	1.80748e24i	−0.908636	−	1.41386i
$478$	3.78367e23	−	2.63160e24i	0.290444	−	2.02008i
$479$	2.29933e23	−	3.57783e23i	0.173214	−	0.269526i	−0.743782	−	0.668422i	$-0.766970\pi$
$479$	2.29933e23	−	3.57783e23i	0.173214	−	0.269526i	0.916996	+	0.398896i	$0.130607\pi$
$480$	1.85431e24	+	1.60677e24i	1.37092	+	1.18790i
$481$	−2.44416e23	+	8.32405e23i	−0.177347	+	0.603989i
$482$		−	1.79060e24i		−	1.27519i
$483$	3.07995e24	−	7.08910e23i	2.15288	−	0.495526i
$484$	5.82039e23			0.399341
$485$	2.27937e24	+	6.69282e23i	1.53511	+	0.450748i
$486$	−1.66290e24	+	1.91909e24i	−1.09936	+	1.26873i
$487$	−1.05139e24	−	6.75687e23i	−0.682343	−	0.438515i	0.153013	−	0.988224i	$-0.451102\pi$
$487$	−1.05139e24	−	6.75687e23i	−0.682343	−	0.438515i	−0.835356	+	0.549709i	$0.814739\pi$
$488$	5.15576e23	+	7.41286e22i	0.328484	+	0.0472289i
$489$	1.86877e23	−	1.20098e23i	0.116889	−	0.0751203i
$490$	−4.13869e24	+	1.89008e24i	−2.54155	+	1.16069i
$491$	−7.84461e23	−	9.05316e23i	−0.472974	−	0.545842i	0.468262	−	0.883590i	$-0.344880\pi$
$491$	−7.84461e23	−	9.05316e23i	−0.472974	−	0.545842i	−0.941237	+	0.337748i	$0.890335\pi$
$492$	−2.42368e23	−	1.68571e24i	−0.143479	−	0.997920i
$493$	−9.22268e23	−	4.21186e23i	−0.536087	−	0.244823i
$494$	−2.02122e23	−	6.88365e23i	−0.115364	−	0.392895i
$495$	−8.34428e23	+	2.45010e23i	−0.467673	+	0.137321i
$496$	1.53801e24	−	3.36777e24i	0.846494	−	1.85356i
$497$	−2.01185e24	+	2.89260e23i	−1.08740	+	0.156344i
$498$	2.28188e24	−	1.97726e24i	1.21124	−	1.04954i
$499$	−5.23974e23	−	1.14734e24i	−0.273152	−	0.598120i	0.722489	−	0.691382i	$-0.242998\pi$
$499$	−5.23974e23	−	1.14734e24i	−0.273152	−	0.598120i	−0.995642	+	0.0932620i	$0.970271\pi$
$500$	2.97948e23	+	4.63616e23i	0.152549	+	0.237372i
$501$	−7.10422e23	+	4.94109e24i	−0.357254	+	2.48475i
$502$	−1.71558e24	+	2.66949e24i	−0.847377	+	1.31854i
$503$	7.66529e23	+	6.64202e23i	0.371892	+	0.322246i	0.820676	−	0.571394i	$-0.193597\pi$
$503$	7.66529e23	+	6.64202e23i	0.371892	+	0.322246i	−0.448784	+	0.893640i	$0.648143\pi$
$504$	−5.92412e23	+	2.01757e24i	−0.282325	+	0.961510i
$505$			3.90760e22i			0.0182931i
$506$	7.50927e23	−	4.21842e23i	0.345337	−	0.193997i
$507$	2.19028e24			0.989526
$508$	9.59204e23	+	2.81648e23i	0.425733	+	0.125007i
$509$	3.41585e23	−	3.94210e23i	0.148949	−	0.171897i	−0.676372	−	0.736561i	$-0.736449\pi$
$509$	3.41585e23	−	3.94210e23i	0.148949	−	0.171897i	0.825321	+	0.564664i	$0.190994\pi$
$510$	−3.37054e24	−	2.16611e24i	−1.44400	−	0.928004i
$511$	3.02628e24	+	4.35113e23i	1.27386	+	0.183153i
$512$	4.36623e23	−	2.80601e23i	0.180583	−	0.116054i
$513$	8.95179e22	−	4.08815e22i	0.0363793	−	0.0166139i
$514$	2.83703e24	+	3.27411e24i	1.13291	+	1.30745i
$515$	6.58432e23	+	4.57949e24i	0.258372	+	1.79702i
$516$	2.18514e24	+	9.97920e23i	0.842620	+	0.384812i
$517$	−3.05164e23	−	1.03929e24i	−0.115643	−	0.393843i
$518$	5.70450e24	−	1.67499e24i	2.12446	−	0.623799i
$519$	1.62980e24	−	3.56876e24i	0.596524	−	1.30621i
$520$	−1.53286e24	+	2.20392e23i	−0.551407	+	0.0792803i
$521$	3.19922e24	−	2.77214e24i	1.13111	−	0.980113i	0.131174	−	0.991359i	$-0.458125\pi$
$521$	3.19922e24	−	2.77214e24i	1.13111	−	0.980113i	0.999937	+	0.0112464i	$0.00357992\pi$
$522$	−1.23017e24	−	2.69369e24i	−0.427494	−	0.936081i
$523$	−1.60210e24	−	2.49292e24i	−0.547236	−	0.851515i	0.451943	−	0.892047i	$-0.350731\pi$
$523$	−1.60210e24	−	2.49292e24i	−0.547236	−	0.851515i	−0.999178	+	0.0405316i	$0.987095\pi$
$524$	−6.44446e22	+	4.48222e23i	−0.0216374	+	0.150491i
$525$	−5.08866e24	+	7.91810e24i	−1.67946	+	2.61329i
$526$	−2.58507e24	−	2.23998e24i	−0.838689	−	0.726728i
$527$	−9.49291e23	+	3.23299e24i	−0.302764	+	1.03112i
$528$			1.83076e24i			0.574018i
$529$	−1.68776e24	+	2.77056e24i	−0.520246	+	0.854016i
$530$	−1.08439e25			−3.28628
$531$	2.20111e24	+	6.46303e23i	0.655829	+	0.192569i
$532$	−9.95938e23	+	1.14937e24i	−0.291761	+	0.336710i
$533$	2.54203e24	+	1.63367e24i	0.732211	+	0.470564i
$534$	4.54376e23	+	6.53294e22i	0.128690	+	0.0185028i
$535$	7.55945e23	−	4.85817e23i	0.210526	−	0.135297i
$536$	−9.25495e22	+	4.22660e22i	−0.0253449	+	0.0115746i
$537$	1.24614e24	+	1.43812e24i	0.335581	+	0.387281i
$538$	−4.84163e23	−	3.36742e24i	−0.128219	−	0.891779i
$539$	−1.72110e24	−	7.86002e23i	−0.448237	−	0.204703i
$540$	4.85473e22	+	1.65337e23i	0.0124343	+	0.0423473i
$541$	3.18694e23	−	9.35771e22i	0.0802785	−	0.0235719i	−0.241347	−	0.970439i	$-0.577589\pi$
$541$	3.18694e23	−	9.35771e22i	0.0802785	−	0.0235719i	0.321625	+	0.946867i	$0.395771\pi$
$542$	−5.50675e23	+	1.20581e24i	−0.136427	+	0.298734i
$543$	8.27182e23	−	1.18931e23i	0.201559	−	0.0289798i
$544$	−1.73502e24	+	1.50340e24i	−0.415829	+	0.360318i
$545$	−4.00552e24	−	8.77086e24i	−0.944257	−	2.06763i
$546$	3.35032e24	+	5.21320e24i	0.776877	+	1.20884i
$547$	1.11589e24	−	7.76115e24i	0.254527	−	1.77027i	−0.315772	−	0.948835i	$-0.602263\pi$
$547$	1.11589e24	−	7.76115e24i	0.254527	−	1.77027i	0.570298	−	0.821438i	$-0.306828\pi$
$548$	−1.29340e24	+	2.01258e24i	−0.290208	+	0.451572i
$549$	−1.63262e24	−	1.41467e24i	−0.360358	−	0.312252i
$550$	−7.22660e23	+	2.46115e24i	−0.156917	+	0.534410i
$551$			2.64036e24i			0.564026i
$552$	−2.16459e24	−	3.85321e24i	−0.454907	−	0.809787i
$553$	2.46388e24			0.509441
$554$	7.72781e23	+	2.26909e23i	0.157206	+	0.0461598i
$555$	8.26246e24	−	9.53539e24i	1.65376	−	1.90854i
$556$	−2.27721e24	−	1.46348e24i	−0.448467	−	0.288212i
$557$	−2.44651e24	−	3.51754e23i	−0.474078	−	0.0681621i	−0.0988650	−	0.995101i	$-0.531521\pi$
$557$	−2.44651e24	−	3.51754e23i	−0.474078	−	0.0681621i	−0.375213	+	0.926939i	$0.622430\pi$
$558$	−8.27904e24	+	5.32061e24i	−1.57860	+	1.01450i
$559$	−3.87712e24	+	1.77062e24i	−0.727449	+	0.332215i
$560$	1.08436e25	+	1.25141e25i	2.00207	+	2.31051i
$561$	−2.37119e23	−	1.64920e24i	−0.0430825	−	0.299645i
$562$	−8.39854e24	−	3.83548e24i	−1.50168	−	0.685793i
$563$	1.65408e24	+	5.63329e24i	0.291060	+	0.991259i	0.967101	+	0.254394i	$0.0818761\pi$
$563$	1.65408e24	+	5.63329e24i	0.291060	+	0.991259i	−0.676041	+	0.736864i	$0.736306\pi$
$564$	4.32591e24	−	1.27020e24i	0.749145	−	0.219969i
$565$	2.62319e24	−	5.74399e24i	0.447089	−	0.978988i
$566$	3.89448e24	−	5.59941e23i	0.653283	−	0.0939279i
$567$	−7.54694e24	+	6.53946e24i	−1.24602	+	1.07968i
$568$	1.18072e24	+	2.58542e24i	0.191873	+	0.420142i
$569$	2.69172e24	+	4.18839e24i	0.430545	+	0.669942i	0.986960	−	0.160963i	$-0.0514599\pi$
$569$	2.69172e24	+	4.18839e24i	0.430545	+	0.669942i	−0.556415	+	0.830904i	$0.687824\pi$
$570$	−1.48489e24	+	1.03276e25i	−0.233787	+	1.62603i
$571$	−2.87223e24	+	4.46927e24i	−0.445137	+	0.692647i	−0.989229	−	0.146379i	$-0.953238\pi$
$571$	−2.87223e24	+	4.46927e24i	−0.445137	+	0.692647i	0.544092	+	0.839026i	$0.316874\pi$
$572$	3.94804e23	+	3.42100e23i	0.0602307	+	0.0521902i
$573$	8.27604e22	−	2.81856e23i	0.0124289	−	0.0423288i
$574$		−	2.07079e25i		−	3.06147i
$575$	−2.16710e24	−	9.41526e24i	−0.315405	−	1.37032i
$576$	1.60412e24			0.229845
$577$	−7.67754e24	−	2.25433e24i	−1.08303	−	0.318006i	−0.308939	−	0.951082i	$-0.599974\pi$
$577$	−7.67754e24	−	2.25433e24i	−1.08303	−	0.318006i	−0.774090	+	0.633076i	$0.781792\pi$
$578$	−3.21872e24	+	3.71460e24i	−0.447025	+	0.515895i
$579$	1.21618e25	+	7.81590e24i	1.66299	+	1.06874i
$580$	−4.57619e24	−	6.57957e23i	−0.616101	−	0.0885820i
$581$	9.55385e24	−	6.13989e24i	1.26647	−	0.813908i
$582$	−1.20920e25	+	5.52222e24i	−1.57830	+	0.720787i
$583$	−2.95311e24	−	3.40807e24i	−0.379545	−	0.438018i
$584$	−6.08457e23	−	4.23191e24i	−0.0770042	−	0.535576i
$585$	5.84228e24	+	2.66808e24i	0.728081	+	0.332503i
$586$	4.31065e24	+	1.46807e25i	0.529011	+	1.80164i
$587$	3.85664e24	−	1.13241e24i	0.466086	−	0.136855i	−0.0402534	−	0.999190i	$-0.512817\pi$
$587$	3.85664e24	−	1.13241e24i	0.466086	−	0.136855i	0.506339	+	0.862334i	$0.330998\pi$
$588$	3.27162e24	−	7.16386e24i	0.389374	−	0.852611i
$589$	8.68542e24	−	1.24878e24i	1.01801	−	0.146368i
$590$	8.75020e24	−	7.58209e24i	1.01007	−	0.875228i
$591$	1.58515e24	+	3.47100e24i	0.180212	+	0.394610i
$592$	−7.01305e24	−	1.09125e25i	−0.785257	−	1.22188i
$593$	−9.48252e23	+	6.59524e24i	−0.104576	+	0.727341i	0.868304	+	0.496032i	$0.165210\pi$
$593$	−9.48252e23	+	6.59524e24i	−0.104576	+	0.727341i	−0.972880	+	0.231309i	$0.925699\pi$
$594$	−1.25244e23	+	1.94883e23i	−0.0136044	+	0.0211688i
$595$	−1.13890e25	−	9.86865e24i	−1.21852	−	1.05586i
$596$	7.56393e23	−	2.57604e24i	0.0797134	−	0.271479i
$597$			4.60947e24i			0.478500i
$598$	−6.23144e24	−	1.27726e24i	−0.637203	−	0.130608i
$599$	1.25198e25			1.26112			0.630558	−	0.776142i	$-0.282826\pi$
$599$	1.25198e25			1.26112			0.630558	+	0.776142i	$0.282826\pi$
$600$	1.26288e25	+	3.70816e24i	1.25315	+	0.367957i
$601$	−2.46419e24	+	2.84383e24i	−0.240882	+	0.277993i	−0.863299	−	0.504694i	$-0.831606\pi$
$601$	−2.46419e24	+	2.84383e24i	−0.240882	+	0.277993i	0.622417	+	0.782686i	$0.286151\pi$
$602$	2.45727e25	+	1.57919e25i	2.36638	+	1.52078i
$603$	4.17673e23	+	6.00523e22i	0.0396260	+	0.00569736i
$604$	−6.66121e24	+	4.28090e24i	−0.622616	+	0.400131i
$605$	1.36620e25	−	6.23923e24i	1.25810	−	0.574556i
$606$	−1.43192e23	−	1.65252e23i	−0.0129917	−	0.0149932i
$607$	1.97229e23	+	1.37176e24i	0.0176308	+	0.122625i	0.996736	−	0.0807291i	$-0.0257249\pi$
$607$	1.97229e23	+	1.37176e24i	0.0176308	+	0.122625i	−0.979105	+	0.203354i	$0.934816\pi$
$608$	5.43832e24	+	2.48360e24i	0.478996	+	0.218750i
$609$	−6.42541e24	−	2.18830e25i	−0.557629	−	1.89911i
$610$	−1.04614e25	+	3.07174e24i	−0.894584	+	0.262673i
$611$	−3.32313e24	+	7.27664e24i	−0.280012	+	0.613141i
$612$	3.35249e24	−	4.82015e23i	0.278358	−	0.0400219i
$613$	−8.34814e24	+	7.23370e24i	−0.683039	+	0.591856i	−0.925702	−	0.378254i	$-0.876524\pi$
$613$	−8.34814e24	+	7.23370e24i	−0.683039	+	0.591856i	0.242663	+	0.970111i	$0.421979\pi$
$614$	1.77198e24	+	3.88010e24i	0.142871	+	0.312844i
$615$	−2.37591e25	−	3.69700e25i	−1.88779	−	2.93747i
$616$	−6.28090e23	+	4.36846e24i	−0.0491808	+	0.342060i
$617$	−8.89761e24	+	1.38450e25i	−0.686605	+	1.06838i	0.306582	+	0.951844i	$0.400815\pi$
$617$	−8.89761e24	+	1.38450e25i	−0.686605	+	1.06838i	−0.993187	+	0.116534i	$0.962822\pi$
$618$	−1.95658e25	−	1.69539e25i	−1.48800	−	1.28936i
$619$	−6.38108e24	+	2.17320e25i	−0.478276	+	1.62886i	0.268141	+	0.963380i	$0.413591\pi$
$619$	−6.38108e24	+	2.17320e25i	−0.478276	+	1.62886i	−0.746417	+	0.665478i	$0.768228\pi$
$620$			1.53645e25i			1.13499i
$621$	5.17734e22	−	8.71018e23i	0.00376949	−	0.0634166i
$622$	−2.18217e25			−1.56594
$623$	1.65667e24	+	4.86443e23i	0.117177	+	0.0344064i
$624$	8.85419e24	−	1.02183e25i	0.617288	−	0.712388i
$625$	−5.25044e24	−	3.37425e24i	−0.360808	−	0.231877i
$626$	2.13060e25	+	3.06334e24i	1.44322	+	0.207504i
$627$	−3.65018e24	+	2.34583e24i	−0.243729	+	0.156635i
$628$	7.03512e24	−	3.21283e24i	0.463058	−	0.211471i
$629$	7.73095e24	+	8.92199e24i	0.501622	+	0.578903i
$630$	−6.26396e24	−	4.35668e25i	−0.400668	−	2.78670i
$631$	−5.59481e24	−	2.55506e24i	−0.352794	−	0.161115i	0.231132	−	0.972922i	$-0.425757\pi$
$631$	−5.59481e24	−	2.55506e24i	−0.352794	−	0.161115i	−0.583926	+	0.811807i	$0.698484\pi$
$632$	−9.70698e23	−	3.30589e24i	−0.0603435	−	0.205511i
$633$	−2.84568e24	+	8.35568e23i	−0.174403	+	0.0512093i
$634$	−2.66516e24	+	5.83588e24i	−0.161035	+	0.352617i
$635$	2.55342e25	−	3.67127e24i	1.52111	−	0.218702i
$636$	1.41856e25	−	1.22919e25i	0.833172	−	0.721948i
$637$	5.80488e24	+	1.27109e25i	0.336154	+	0.736074i
$638$	−3.36028e24	−	5.22870e24i	−0.191862	−	0.298543i
$639$	1.67759e24	−	1.16679e25i	0.0944451	−	0.656880i
$640$	1.70139e25	−	2.64741e25i	0.944461	−	1.46961i
$641$	−1.25990e25	−	1.09171e25i	−0.689628	−	0.597566i	0.237913	−	0.971286i	$-0.423537\pi$
$641$	−1.25990e25	−	1.09171e25i	−0.689628	−	0.597566i	−0.927542	+	0.373720i	$0.878082\pi$
$642$	−1.41664e24	+	4.82464e24i	−0.0764619	+	0.260405i
$643$			8.37644e24i			0.445821i	0.974839	+	0.222911i	$0.0715558\pi$
$643$			8.37644e24i			0.445821i	−0.974839	+	0.222911i	$0.928444\pi$
$644$	4.86396e24	+	1.25766e25i	0.255280	+	0.660071i
$645$	6.19884e25			3.20829
$646$	−9.36719e24	−	2.75045e24i	−0.478098	−	0.140382i
$647$	5.22766e24	−	6.03304e24i	0.263129	−	0.303667i	−0.608776	−	0.793342i	$-0.708339\pi$
$647$	5.22766e24	−	6.03304e24i	0.263129	−	0.303667i	0.871905	+	0.489675i	$0.162885\pi$
$648$	1.17475e25	+	7.54969e24i	0.583139	+	0.374761i
$649$	4.76585e24	+	6.85226e23i	0.233313	+	0.0335453i
$650$	1.59365e25	−	1.02418e25i	0.769437	−	0.494487i
$651$	−6.89447e25	+	3.14860e25i	−3.28301	+	1.49930i
$652$	6.20663e23	+	7.16283e23i	0.0291492	+	0.0336400i
$653$	−4.51579e24	−	3.14080e25i	−0.209177	−	1.45486i	−0.775850	−	0.630918i	$-0.782679\pi$
$653$	−4.51579e24	−	3.14080e25i	−0.209177	−	1.45486i	0.566672	−	0.823943i	$-0.308230\pi$
$654$	4.90797e25	+	2.24139e25i	2.24234	+	1.02404i
$655$	3.29208e24	+	1.12118e25i	0.148354	+	0.505246i
$656$	−4.33512e25	+	1.27291e25i	−1.92693	+	0.565799i
$657$	−7.36602e24	+	1.61293e25i	−0.322957	+	0.707177i
$658$	5.42631e25	−	7.80186e24i	2.34678	−	0.337416i
$659$	−2.34682e25	+	2.03354e25i	−1.00118	+	0.867527i	−0.991193	−	0.132423i	$-0.957724\pi$
$659$	−2.34682e25	+	2.03354e25i	−1.00118	+	0.867527i	−0.00998614	+	0.999950i	$0.503179\pi$
$660$	−3.15612e24	−	6.91094e24i	−0.132818	−	0.290832i
$661$	−5.28766e24	−	8.22776e24i	−0.219508	−	0.341561i	0.713982	−	0.700164i	$-0.246890\pi$
$661$	−5.28766e24	−	8.22776e24i	−0.219508	−	0.341561i	−0.933490	+	0.358603i	$0.883253\pi$
$662$	3.47854e24	−	2.41938e25i	0.142454	−	0.990789i
$663$	−6.65265e24	+	1.03517e25i	−0.268765	+	0.418206i
$664$	−1.20021e25	−	1.03999e25i	−0.478348	−	0.414491i
$665$	−1.10565e25	+	3.76550e25i	−0.434733	+	1.48056i
$666$			3.44805e25i			1.33754i
$667$	2.06804e25	+	1.09715e25i	0.791457	+	0.419888i
$668$	−2.12983e25			−0.804186
$669$	−4.97245e25	−	1.46004e25i	−1.85240	−	0.543915i
$670$	1.39466e24	−	1.60953e24i	0.0512621	−	0.0591596i
$671$	−3.81433e24	−	2.45132e24i	−0.138330	−	0.0888991i
$672$	−5.11159e25	−	7.34936e24i	−1.82908	−	0.262982i
$673$	2.55656e25	−	1.64300e25i	0.902654	−	0.580100i	−0.00492231	−	0.999988i	$-0.501567\pi$
$673$	2.55656e25	−	1.64300e25i	0.902654	−	0.580100i	0.907576	+	0.419887i	$0.137930\pi$
$674$	−7.64963e24	+	3.49347e24i	−0.266503	+	0.121708i
$675$	1.70170e24	+	1.96387e24i	0.0584991	+	0.0675115i
$676$	1.32993e24	+	9.24984e24i	0.0451136	+	0.313772i
$677$	−1.96685e23	−	8.98232e22i	−0.00658376	−	0.00300670i	0.412120	−	0.911129i	$-0.364788\pi$
$677$	−1.96685e23	−	8.98232e22i	−0.00658376	−	0.00300670i	−0.418704	+	0.908123i	$0.637516\pi$
$678$	9.95507e24	+	3.39039e25i	0.328834	+	1.11991i
$679$	−4.79744e25	+	1.40866e25i	−1.56380	+	0.459174i
$680$	−8.75424e24	+	1.91691e25i	−0.281603	+	0.616626i
$681$	−4.46676e25	+	6.42223e24i	−1.41798	+	0.203874i
$682$	−1.56104e25	+	1.35265e25i	−0.489053	+	0.423767i
$683$	−1.18606e24	−	2.59711e24i	−0.0366708	−	0.0802978i	0.890410	−	0.455159i	$-0.150418\pi$
$683$	−1.18606e24	−	2.59711e24i	−0.0366708	−	0.0802978i	−0.927081	+	0.374861i	$0.877690\pi$
$684$	−4.76860e24	−	7.42008e24i	−0.145508	−	0.226414i
$685$	−8.78562e24	+	6.11053e25i	−0.264580	+	1.84020i
$686$	1.71872e25	−	2.67438e25i	0.510844	−	0.794889i
$687$	3.88748e25	+	3.36852e25i	1.14040	+	0.988164i
$688$	1.79550e25	−	6.11491e25i	0.519863	−	1.77049i
$689$			3.33043e25i			0.951760i
$690$	7.47203e25	+	5.45448e25i	2.10764	+	1.53855i
$691$	−3.28473e25			−0.914529			−0.457264	−	0.889331i	$-0.651171\pi$
$691$	−3.28473e25			−0.914529			−0.457264	+	0.889331i	$0.651171\pi$
$692$	1.60610e25	+	4.71593e24i	0.441385	+	0.129602i
$693$	1.19865e25	−	1.38331e25i	0.325157	−	0.375251i
$694$	−8.28622e24	−	5.32523e24i	−0.221881	−	0.142595i
$695$	−6.91402e25	−	9.94086e24i	−1.82754	−	0.262761i
$696$	−2.68299e25	+	1.72425e25i	−0.700060	+	0.449901i
$697$	3.74034e25	−	1.70816e25i	0.963421	−	0.439979i
$698$	−2.40567e25	−	2.77629e25i	−0.611699	−	0.705938i
$699$	−8.24687e24	−	5.73582e25i	−0.207012	−	1.43980i
$700$	−3.65291e25	−	1.66823e25i	−0.905225	−	0.413402i
$701$	2.02447e25	+	6.89470e25i	0.495278	+	1.68676i	0.705172	+	0.709036i	$0.250870\pi$
$701$	2.02447e25	+	6.89470e25i	0.495278	+	1.68676i	−0.209894	+	0.977724i	$0.567312\pi$
$702$	1.64157e24	−	4.82008e23i	0.0396483	−	0.0116418i
$703$	1.27714e25	−	2.79654e25i	0.304537	−	0.666842i
$704$	3.33257e24	−	4.79151e23i	0.0784558	−	0.0112802i
$705$	8.79247e25	−	7.61872e25i	2.04366	−	1.77084i
$706$	−6.94905e24	−	1.52163e25i	−0.159472	−	0.349194i
$707$	−4.44646e23	−	6.91882e23i	−0.0100749	−	0.0156768i
$708$	−2.85216e24	+	1.98372e25i	−0.0638079	+	0.443794i
$709$	−2.99224e25	+	4.65601e25i	−0.660967	+	1.02849i	0.335295	+	0.942113i	$0.391164\pi$
$709$	−2.99224e25	+	4.65601e25i	−0.660967	+	1.02849i	−0.996263	+	0.0863724i	$0.972473\pi$
$710$	−4.49630e25	−	3.89607e25i	−0.980687	−	0.849770i
$711$	−4.02583e24	+	1.37107e25i	−0.0867020	+	0.295280i
$712$		−	2.41447e24i		−	0.0513455i
$713$	2.63097e25	−	7.32170e25i	0.552471	−	1.53747i
$714$	8.43273e25			1.74857
$715$	1.29343e25	+	3.79785e24i	0.264843	+	0.0777649i
$716$	−5.31673e24	+	6.13583e24i	−0.107505	+	0.124067i
$717$	9.99013e25	+	6.42026e25i	1.99480	+	1.28198i
$718$	3.57088e25	+	5.13415e24i	0.704133	+	0.101239i
$719$	3.40317e25	−	2.18709e25i	0.662710	−	0.425898i	−0.165581	−	0.986196i	$-0.552950\pi$
$719$	3.40317e25	−	2.18709e25i	0.662710	−	0.425898i	0.828291	+	0.560298i	$0.189313\pi$
$720$	−8.73549e25	+	3.98937e25i	−1.67994	+	0.767205i
$721$	−6.37683e25	−	7.35926e25i	−1.21112	−	1.39771i
$722$	−5.51139e24	−	3.83326e25i	−0.103378	−	0.719007i
$723$	7.27521e25	+	3.32248e25i	1.34772	+	0.615485i
$724$	1.00452e24	+	3.42109e24i	0.0183786	+	0.0625918i
$725$	−6.68952e25	+	1.96422e25i	−1.20880	+	0.354934i
$726$	−3.49133e25	+	7.64494e25i	−0.623105	+	1.36441i
$727$	−9.15884e25	+	1.31684e25i	−1.61447	+	0.232126i	−0.889595	−	0.456751i	$-0.849013\pi$
$727$	−9.15884e25	+	1.31684e25i	−1.61447	+	0.232126i	−0.724878	+	0.688877i	$0.758104\pi$
$728$	2.46331e25	−	2.13447e25i	0.428881	−	0.371627i
$729$	−2.19133e25	−	4.79835e25i	−0.376843	−	0.825171i
$730$	4.83839e25	+	7.52867e25i	0.821854	+	1.27883i
$731$	−8.25437e24	+	5.74104e25i	−0.138493	+	0.963239i
$732$	1.02033e25	−	1.58766e25i	0.169099	−	0.263123i
$733$	−6.48742e25	−	5.62139e25i	−1.06203	−	0.920254i	−0.0650470	−	0.997882i	$-0.520720\pi$
$733$	−6.48742e25	−	5.62139e25i	−1.06203	−	0.920254i	−0.996982	+	0.0776285i	$0.975265\pi$
$734$	2.61894e25	−	8.91930e25i	0.423508	−	1.44234i
$735$		−	2.03225e26i		−	3.24633i
$736$	4.20505e25	−	3.22751e25i	0.663545	−	0.509293i
$737$	8.85654e23			0.0138056
$738$	1.15233e26	+	3.38355e25i	1.77448	+	0.521033i
$739$	1.76921e25	−	2.04177e25i	0.269140	−	0.310604i	−0.605050	−	0.796187i	$-0.706847\pi$
$739$	1.76921e25	−	2.04177e25i	0.269140	−	0.310604i	0.874191	+	0.485583i	$0.161393\pi$
$740$	4.52862e25	+	2.91037e25i	0.680582	+	0.437384i
$741$	3.17186e25	+	4.56045e24i	0.470923	+	0.0677086i
$742$	1.92004e26	−	1.23393e26i	2.81627	−	1.80991i
$743$	9.18292e25	−	4.19370e25i	1.33070	−	0.607712i	0.382083	−	0.924128i	$-0.375207\pi$
$743$	9.18292e25	−	4.19370e25i	1.33070	−	0.607712i	0.948621	+	0.316416i	$0.102479\pi$
$744$	6.94083e25	+	8.01014e25i	0.993699	+	1.14679i
$745$	−9.85957e24	−	6.85748e25i	−0.139461	−	0.969970i
$746$	−5.40029e25	−	2.46623e25i	−0.754688	−	0.344655i
$747$	1.85561e25	+	6.31963e25i	0.256213	+	0.872583i
$748$	6.82082e24	−	2.00277e24i	0.0930512	−	0.0273223i
$749$	−7.85672e24	+	1.72038e25i	−0.105902	+	0.231894i
$750$	−7.87672e25	+	1.13250e25i	−1.04904	+	0.150830i
$751$	3.06016e25	−	2.65165e25i	0.402703	−	0.348944i	−0.429839	−	0.902905i	$-0.641430\pi$
$751$	3.06016e25	−	2.65165e25i	0.402703	−	0.348944i	0.832543	+	0.553961i	$0.186884\pi$
$752$	−4.96881e25	−	1.08802e26i	−0.646089	−	1.41474i
$753$	−7.66286e25	−	1.19236e26i	−0.984546	−	1.53198i
$754$	−6.53260e24	+	4.54353e25i	−0.0829362	+	0.576834i
$755$	−1.10467e26	+	1.71890e26i	−1.38583	+	2.15639i
$756$	−2.74095e24	−	2.37505e24i	−0.0339786	−	0.0294426i
$757$	1.67935e25	−	5.71935e25i	0.205721	−	0.700622i	−0.790397	−	0.612595i	$-0.790126\pi$
$757$	1.67935e25	−	5.71935e25i	0.205721	−	0.700622i	0.996118	−	0.0880269i	$-0.0280561\pi$
$758$		−	1.82320e26i		−	2.20704i
$759$	3.20591e24	+	3.83374e25i	0.0383509	+	0.458614i
$760$	5.48792e25			0.648762
$761$	−1.50393e24	−	4.41594e23i	−0.0175698	−	0.00515895i	0.272936	−	0.962032i	$-0.412005\pi$
$761$	−1.50393e24	−	4.41594e23i	−0.0175698	−	0.00515895i	−0.290506	+	0.956873i	$0.593823\pi$
$762$	−9.45311e25	+	1.09095e26i	−1.09139	+	1.25953i
$763$	1.70726e26	+	1.09719e26i	1.94795	+	1.25187i
$764$	1.24057e24	+	1.78367e23i	0.0139888	+	0.00201129i
$765$	7.35248e25	−	4.72515e25i	0.819372	−	0.526578i
$766$	−1.52148e26	+	6.94837e25i	−1.67574	+	0.765286i
$767$	−2.32864e25	−	2.68739e25i	−0.253480	−	0.292532i
$768$	2.06083e25	+	1.43334e26i	0.221713	+	1.54205i
$769$	−4.41463e25	−	2.01610e25i	−0.469416	−	0.214375i	0.166640	−	0.986018i	$-0.446708\pi$
$769$	−4.41463e25	−	2.01610e25i	−0.469416	−	0.214375i	−0.636056	+	0.771643i	$0.719435\pi$
$770$	−2.60268e25	−	8.86391e25i	−0.273529	−	0.931556i
$771$	−1.85668e26	+	5.45171e25i	−1.92863	+	0.566296i
$772$	−2.56230e25	+	5.61067e25i	−0.263072	+	0.576048i
$773$	−1.79883e26	+	2.58633e25i	−1.82547	+	0.262463i	−0.967797	−	0.251733i	$-0.918999\pi$
$773$	−1.79883e26	+	2.58633e25i	−1.82547	+	0.262463i	−0.857673	+	0.514196i	$0.828090\pi$
$774$	−1.28027e26	+	1.10936e26i	−1.28420	+	1.11277i
$775$	9.62512e25	+	2.10761e26i	0.954313	+	2.08965i
$776$	3.78011e25	+	5.88196e25i	0.370466	+	0.576457i
$777$	−3.77926e25	+	2.62853e26i	−0.366115	+	2.54638i
$778$	4.10188e25	−	6.38266e25i	0.392796	−	0.611202i
$779$	−8.09273e25	−	7.01239e25i	−0.766051	−	0.663787i
$780$	−1.58080e25	+	5.38372e25i	−0.147920	+	0.503769i
$781$		−	2.47412e25i		−	0.228856i
$782$	−6.04663e25	+	6.19388e25i	−0.552907	+	0.566372i
$783$	−6.29657e24			−0.0569178
$784$	−2.00474e26	−	5.88644e25i	−1.79148	−	0.526027i
$785$	1.30693e26	−	1.50828e26i	1.15458	−	1.33246i
$786$	−5.50072e25	−	3.53510e25i	−0.480415	−	0.308744i
$787$	1.27366e26	+	1.83125e25i	1.09972	+	0.158116i	0.668196	−	0.743986i	$-0.267067\pi$
$787$	1.27366e26	+	1.83125e25i	1.09972	+	0.158116i	0.431524	+	0.902101i	$0.357976\pi$
$788$	−1.36960e25	+	8.80191e24i	−0.116912	+	0.0751347i
$789$	1.38976e26	−	6.34684e25i	1.17287	−	0.535630i
$790$	4.72289e25	+	5.45051e25i	0.394062	+	0.454772i
$791$	1.89144e25	+	1.31553e26i	0.156029	+	1.08521i
$792$	−2.32828e25	−	1.06329e25i	−0.189893	−	0.0867213i
$793$	9.43404e24	+	3.21294e25i	0.0760745	+	0.259086i
$794$	−1.86717e26	+	5.48250e25i	−1.48867	+	0.437113i
$795$	2.01210e26	−	4.40589e26i	1.58616	−	3.47320i
$796$	−1.94664e25	+	2.79885e24i	−0.151729	+	0.0218154i
$797$	6.65522e25	−	5.76678e25i	0.512906	−	0.444435i	−0.359552	−	0.933125i	$-0.617070\pi$
$797$	6.65522e25	−	5.76678e25i	0.512906	−	0.444435i	0.872458	+	0.488690i	$0.162525\pi$
$798$	−9.12267e25	−	1.99759e26i	−0.695178	−	1.52223i
$799$	5.88525e25	+	9.15763e25i	0.443449	+	0.690020i
$800$	−2.24667e25	+	1.56259e26i	−0.167390	+	1.16422i
$801$	−5.41380e24	+	8.42403e24i	−0.0398850	+	0.0620622i
$802$	9.43866e25	+	8.17865e25i	0.687608	+	0.595816i
$803$	−1.04851e25	+	3.57089e25i	−0.0755322	+	0.257239i
$804$			3.68641e24i			0.0262603i
$805$	2.48987e26	+	2.43067e26i	1.75393	+	1.71223i
$806$	1.52548e26			1.06265
$807$	1.45802e26	+	4.28113e25i	1.00439	+	0.294915i
$808$	−7.53150e23	+	8.69182e23i	−0.00513073	+	0.00592118i
$809$	−1.00997e26	−	6.49070e25i	−0.680413	−	0.437275i	0.154253	−	0.988031i	$-0.450703\pi$
$809$	−1.00997e26	−	6.49070e25i	−0.680413	−	0.437275i	−0.834666	+	0.550756i	$0.814339\pi$
$810$	−2.89327e26	−	4.15990e25i	−1.92763	−	0.277152i
$811$	1.19205e26	−	7.66084e25i	0.785429	−	0.504764i	−0.0854025	−	0.996347i	$-0.527218\pi$
$811$	1.19205e26	−	7.66084e25i	0.785429	−	0.504764i	0.870831	+	0.491582i	$0.163581\pi$
$812$	8.85133e25	−	4.04227e25i	0.576772	−	0.263403i
$813$	−3.87742e25	−	4.47478e25i	−0.249878	−	0.288374i
$814$	1.02993e25	+	7.16334e25i	0.0656431	+	0.456558i
$815$	2.22469e25	+	1.01598e25i	0.140233	+	0.0640424i
$816$	−5.18356e25	−	1.76536e26i	−0.323159	−	1.10058i
$817$	1.44926e26	−	4.25542e25i	0.893611	−	0.262388i
$818$	−1.50124e26	+	3.28726e26i	−0.915527	+	2.00472i
$819$	−1.33804e26	+	1.92381e25i	−0.807075	+	0.116040i
$820$	1.41703e26	−	1.22786e26i	0.845384	−	0.732529i
$821$	4.25757e25	+	9.32278e25i	0.251231	+	0.550119i	0.992664	−	0.120908i	$-0.0385806\pi$
$821$	4.25757e25	+	9.32278e25i	0.251231	+	0.550119i	−0.741433	+	0.671027i	$0.765853\pi$
$822$	−1.86763e26	−	2.90609e26i	−1.09004	−	1.69614i
$823$	3.05857e25	−	2.12728e26i	0.176571	−	1.22808i	−0.688053	−	0.725661i	$-0.741534\pi$
$823$	3.05857e25	−	2.12728e26i	0.176571	−	1.22808i	0.864624	−	0.502420i	$-0.167557\pi$
$824$	−7.36194e25	+	1.14554e26i	−0.420385	+	0.654132i
$825$	−8.65875e25	−	7.50285e25i	−0.489069	−	0.423780i
$826$	−6.86551e25	+	2.33818e26i	−0.383577	+	1.30634i
$827$		−	7.80607e25i		−	0.431403i	−0.976459	−	0.215701i	$-0.930796\pi$
$827$		−	7.80607e25i		−	0.431403i	0.976459	−	0.215701i	$-0.0692038\pi$
$828$	−7.79322e25	+	6.51697e24i	−0.426034	+	0.0356265i
$829$	−1.44971e26			−0.783951			−0.391976	−	0.919976i	$-0.628208\pi$
$829$	−1.44971e26			−0.783951			−0.391976	+	0.919976i	$0.628208\pi$
$830$	3.18958e26	+	9.36544e25i	1.70620	+	0.500986i
$831$	−2.35583e25	+	2.71877e25i	−0.124662	+	0.143868i
$832$	−2.09179e25	−	1.34431e25i	−0.109499	−	0.0703705i
$833$	1.88217e26	+	2.70615e25i	0.974660	+	0.140135i
$834$	3.28821e26	−	2.11321e26i	1.68448	−	1.08255i
$835$	−4.99928e26	+	2.28309e26i	−2.53355	+	1.15703i
$836$	−1.21231e25	−	1.39909e25i	−0.0607797	−	0.0701436i
$837$	2.97800e24	+	2.07125e25i	0.0147705	+	0.102731i
$838$	−7.56831e25	−	3.45633e25i	−0.371367	−	0.169597i
$839$	−5.25479e25	−	1.78962e26i	−0.255093	−	0.868765i	−0.983080	−	0.183175i	$-0.941362\pi$
$839$	−5.25479e25	−	1.78962e26i	−0.255093	−	0.868765i	0.727988	−	0.685590i	$-0.240456\pi$
$840$	−4.54831e26	+	1.33551e26i	−2.18442	+	0.641404i
$841$	−1.72485e25	+	3.77689e25i	−0.0819572	+	0.179461i
$842$	2.05859e24	−	2.95980e23i	0.00967744	−	0.00139141i
$843$	3.11671e26	−	2.70064e26i	1.44960	−	1.25609i
$844$	−5.25661e24	−	1.15104e25i	−0.0241893	−	0.0529672i
$845$	1.30372e26	+	2.02862e26i	0.593571	+	0.923615i
$846$	−4.52477e25	+	3.14705e26i	−0.203828	+	1.41765i
$847$	−1.70904e26	+	2.65933e26i	−0.761733	+	1.18528i
$848$	−3.76343e26	−	3.26103e26i	−1.65967	−	1.43811i
$849$	−4.95119e25	+	1.68622e26i	−0.216043	+	0.735776i
$850$		−	2.57785e26i		−	1.11298i
$851$	−1.65968e26	−	2.16236e26i	−0.709020	−	0.923765i
$852$	1.02982e26			0.435316
$853$	3.59581e26	+	1.05583e26i	1.50403	+	0.441623i	0.926987	−	0.375093i	$-0.122389\pi$
$853$	3.59581e26	+	1.05583e26i	1.50403	+	0.441623i	0.577041	+	0.816715i	$0.304207\pi$
$854$	1.50277e26	−	1.73429e26i	0.621973	−	0.717795i
$855$	−1.91472e26	−	1.23052e26i	−0.784171	−	0.503956i
$856$	2.61784e25	+	3.76389e24i	0.106091	+	0.0152536i
$857$	−2.44358e26	+	1.57039e26i	−0.979940	+	0.629769i	−0.929447	−	0.368955i	$-0.879716\pi$
$857$	−2.44358e26	+	1.57039e26i	−0.979940	+	0.629769i	−0.0504927	+	0.998724i	$0.516079\pi$
$858$	−6.86161e25	+	3.13359e25i	−0.272296	+	0.124353i
$859$	−2.53491e26	−	2.92544e26i	−0.995459	−	1.14882i	−0.988861	−	0.148843i	$-0.952445\pi$
$859$	−2.53491e26	−	2.92544e26i	−0.995459	−	1.14882i	−0.00659816	−	0.999978i	$-0.502100\pi$
$860$	3.76391e25	+	2.61786e26i	0.146269	+	1.01733i
$861$	8.41363e26	+	3.84238e26i	3.23560	+	1.47765i
$862$	1.20454e26	+	4.10229e26i	0.458412	+	1.56121i
$863$	1.24178e26	−	3.64618e25i	0.467677	−	0.137322i	−0.0393994	−	0.999224i	$-0.512544\pi$
$863$	1.24178e26	−	3.64618e25i	0.467677	−	0.137322i	0.507076	+	0.861901i	$0.330726\pi$
$864$	−5.92272e24	+	1.29690e25i	−0.0220748	+	0.0483372i
$865$	4.27548e26	−	6.14721e25i	1.57703	−	0.226742i
$866$	2.47108e26	−	2.14120e26i	0.902039	−	0.781621i
$867$	−9.12004e25	−	1.99701e26i	−0.329477	−	0.721453i
$868$	−1.74833e26	−	2.72045e26i	−0.625093	−	0.972664i
$869$	−4.26828e24	+	2.96865e25i	−0.0151034	+	0.105047i
$870$	3.60921e26	−	5.61604e26i	1.26398	−	1.96679i
$871$	−4.94324e24	−	4.28334e24i	−0.0171336	−	0.0148463i
$872$	7.99533e25	−	2.72296e26i	0.274276	−	0.934099i
$873$		−	2.89979e26i		−	0.984551i
$874$	2.12137e26	+	7.62290e25i	0.712876	+	0.256164i
$875$	−2.99312e26			−0.995525
$876$	−1.48634e26	−	4.36428e25i	−0.489305	−	0.143673i
$877$	−9.58183e25	+	1.10580e26i	−0.312214	+	0.360314i	−0.890069	−	0.455825i	$-0.849344\pi$
$877$	−9.58183e25	+	1.10580e26i	−0.312214	+	0.360314i	0.577856	+	0.816139i	$0.303890\pi$
$878$	2.59224e26	+	1.66593e26i	0.836034	+	0.537286i
$879$	−6.76462e26	−	9.72605e25i	−2.15945	−	0.310482i
$880$	−1.69564e26	+	1.08972e26i	−0.535783	+	0.344327i
$881$	−3.67353e26	+	1.67764e26i	−1.14895	+	0.524707i	−0.896561	−	0.442920i	$-0.853943\pi$
$881$	−3.67353e26	+	1.67764e26i	−1.14895	+	0.524707i	−0.252386	+	0.967627i	$0.581215\pi$
$882$	3.63698e26	+	4.19730e26i	1.12596	+	1.29943i
$883$	−7.99297e25	−	5.55923e26i	−0.244941	−	1.70360i	−0.626634	−	0.779314i	$-0.715568\pi$
$883$	−7.99297e25	−	5.55923e26i	−0.244941	−	1.70360i	0.381693	−	0.924289i	$-0.375341\pi$
$884$	−4.77562e25	−	2.18095e25i	−0.144864	−	0.0661570i
$885$	1.45699e26	+	4.96207e26i	0.437490	+	1.48995i
$886$	6.50455e26	−	1.90991e26i	1.93337	−	0.567687i
$887$	4.97356e25	−	1.08906e26i	0.146337	−	0.320434i	−0.822242	−	0.569137i	$-0.807277\pi$
$887$	4.97356e25	−	1.08906e26i	0.146337	−	0.320434i	0.968580	+	0.248704i	$0.0800045\pi$
$888$	3.67570e26	−	5.28486e25i	1.07059	−	0.153928i
$889$	−4.10336e26	+	3.55558e26i	−1.18311	+	1.02517i
$890$	2.09950e25	+	4.59727e25i	0.0599247	+	0.131217i
$891$	−6.57181e25	−	1.02259e26i	−0.185689	−	0.288937i
$892$	3.14672e25	−	2.18859e26i	0.0880185	−	0.612182i
$893$	1.53263e26	−	2.38482e26i	0.424398	−	0.660376i
$894$	2.92985e26	+	2.53873e26i	0.803170	+	0.695951i
$895$	−5.90241e25	+	2.01018e26i	−0.160185	+	0.545540i
$896$			6.62355e26i			1.77958i
$897$	1.67520e26	−	2.29484e26i	0.445589	−	0.610407i
$898$	4.22343e26			1.11219
$899$	−5.38686e26	−	1.58172e26i	−1.40442	−	0.412376i
$900$	1.52518e26	−	1.76015e26i	0.393675	−	0.454325i
$901$	3.81257e26	+	2.45019e26i	0.974305	+	0.626148i
$902$	2.49504e26	+	3.58732e25i	0.631274	+	0.0907635i
$903$	−1.09757e27	+	7.05367e26i	−2.74943	+	1.76695i
$904$	1.69058e26	−	7.72063e25i	0.419296	−	0.191486i
$905$	6.02516e25	+	6.95341e25i	0.147956	+	0.170750i
$906$	−1.62717e26	−	1.13172e27i	−0.395621	−	2.75160i
$907$	3.10701e26	+	1.41892e26i	0.747957	+	0.341580i	0.752661	−	0.658409i	$-0.228770\pi$
$907$	3.10701e26	+	1.41892e26i	0.747957	+	0.341580i	−0.00470409	+	0.999989i	$0.501497\pi$
$908$	−5.42440e25	−	1.84738e26i	−0.129294	−	0.440335i
$909$	4.57663e24	−	1.34382e24i	0.0108012	−	0.00317151i
$910$	−2.83423e26	+	6.20610e26i	−0.662312	+	1.45026i
$911$	3.83044e26	−	5.50734e25i	0.886305	−	0.127431i	0.315897	−	0.948793i	$-0.397694\pi$
$911$	3.83044e26	−	5.50734e25i	0.886305	−	0.127431i	0.570407	+	0.821362i	$0.306785\pi$
$912$	−3.62110e26	+	3.13770e26i	−0.829635	+	0.718882i
$913$	5.74271e25	+	1.25748e26i	0.130281	+	0.285275i
$914$	−1.52722e25	−	2.37640e25i	−0.0343072	−	0.0533831i
$915$	6.93072e25	−	4.82042e26i	0.154166	−	1.07225i
$916$	−1.18653e26	+	1.84627e26i	−0.261348	+	0.406665i
$917$	−1.85869e26	−	1.61056e26i	−0.405399	−	0.351280i
$918$	6.55911e24	−	2.23383e25i	0.0141664	−	0.0482465i
$919$			1.24244e26i			0.265728i	0.991134	+	0.132864i	$0.0424173\pi$
$919$			1.24244e26i			0.265728i	−0.991134	+	0.132864i	$0.957583\pi$
$920$	2.28040e26	−	4.29837e26i	0.482970	−	0.910361i
$921$	−1.90528e26			−0.399596
$922$	−9.71128e26	−	2.85149e26i	−2.01696	−	0.592234i
$923$	−1.19657e26	+	1.38092e26i	−0.246107	+	0.284023i
$924$	1.34522e26	+	8.64522e25i	0.273997	+	0.176087i
$925$	8.03530e26	+	1.15530e26i	1.62079	+	0.233034i
$926$	−3.27847e26	+	2.10695e26i	−0.654897	+	0.420877i
$927$	5.13713e26	−	2.34605e26i	1.01626	−	0.464108i
$928$	−2.50500e26	−	2.89092e26i	−0.490767	−	0.566375i
$929$	2.99450e24	+	2.08272e25i	0.00581009	+	0.0404101i	0.992520	−	0.122080i	$-0.0389565\pi$
$929$	2.99450e24	+	2.08272e25i	0.00581009	+	0.0404101i	−0.986710	+	0.162490i	$0.948047\pi$
$930$	−2.01809e27	−	9.21630e26i	−3.87787	−	1.77097i
$931$	−1.39512e26	−	4.75133e26i	−0.265499	−	0.904207i
$932$	2.37224e26	−	6.96554e25i	0.447112	−	0.131284i
$933$	4.04904e26	−	8.86616e26i	0.755818	−	1.65501i
$934$	1.16489e27	−	1.67486e26i	2.15360	−	0.309641i
$935$	1.38634e26	−	1.20127e26i	0.253843	−	0.219956i
$936$	7.85275e25	+	1.71951e26i	0.142410	+	0.311833i
$937$	1.37603e26	+	2.14115e26i	0.247157	+	0.384583i	0.942560	−	0.334036i	$-0.108411\pi$
$937$	1.37603e26	+	2.14115e26i	0.247157	+	0.384583i	−0.695404	+	0.718619i	$0.744774\pi$
$938$	−6.37920e24	+	4.43683e25i	−0.0113486	+	0.0789310i
$939$	−5.19799e26	+	8.08822e26i	−0.915893	+	1.42516i
$940$	3.75137e26	+	3.25058e26i	0.654695	+	0.567296i
$941$	2.04980e26	−	6.98098e26i	0.354327	−	1.20673i	−0.568878	−	0.822422i	$-0.692622\pi$
$941$	2.04980e26	−	6.98098e26i	0.354327	−	1.20673i	0.923206	−	0.384307i	$-0.125559\pi$
$942$			1.11677e27i			1.91207i
$943$	−8.85518e26	+	3.42471e26i	−1.50173	+	0.580789i
$944$	5.31690e26			0.893121
$945$	−8.97972e25	−	2.63668e25i	−0.149409	−	0.0438704i
$946$	−2.32840e26	+	2.68712e26i	−0.383740	+	0.442860i
$947$	−9.68933e25	−	6.22695e25i	−0.158177	−	0.101654i	0.459158	−	0.888355i	$-0.348151\pi$
$947$	−9.68933e25	−	6.22695e25i	−0.158177	−	0.101654i	−0.617335	+	0.786700i	$0.711788\pi$
$948$	−1.23566e26	−	1.77661e25i	−0.199813	−	0.0287288i
$949$	2.31223e26	−	1.48598e26i	0.370370	−	0.238022i
$950$	−6.10653e26	+	2.78876e26i	−0.968907	+	0.442485i
$951$	−1.87659e26	−	2.16570e26i	−0.294948	−	0.340388i
$952$	−6.31222e25	−	4.39024e26i	−0.0982764	−	0.683528i
$953$	5.30108e26	+	2.42092e26i	0.817576	+	0.373374i	0.779891	−	0.625915i	$-0.215274\pi$
$953$	5.30108e26	+	2.42092e26i	0.817576	+	0.373374i	0.0376848	+	0.999290i	$0.488002\pi$
$954$	3.72922e26	+	1.27006e27i	0.569748	+	1.94038i
$955$	3.10315e25	−	9.11168e24i	0.0469648	−	0.0137901i
$956$	−2.10477e26	+	4.60881e26i	−0.315561	+	0.690983i
$957$	2.74792e26	−	3.95091e25i	0.408128	−	0.0586800i
$958$	−1.98019e26	+	1.71584e26i	−0.291351	+	0.252457i
$959$	−5.39759e26	−	1.18191e27i	−0.786743	−	1.72273i
$960$	1.95510e26	+	3.04219e26i	0.282310	+	0.439284i
$961$	−1.66045e26	+	1.15487e27i	−0.237528	+	1.65204i
$962$	2.88960e26	−	4.49630e26i	0.409507	−	0.637205i
$963$	−8.28964e25	−	7.18301e25i	−0.116386	−	0.100849i
$964$	−9.61381e25	+	3.27416e26i	−0.133722	+	0.455415i
$965$			1.59164e27i			2.19331i
$966$	−1.94367e27	−	1.15532e26i	−2.65356	−	0.157728i
$967$	6.65790e26			0.900532			0.450266	−	0.892894i	$-0.351329\pi$
$967$	6.65790e26			0.900532			0.450266	+	0.892894i	$0.351329\pi$
$968$	4.24144e26	+	1.24540e26i	0.568376	+	0.166890i
$969$	2.85560e26	−	3.29553e26i	0.379125	−	0.437534i
$970$	−1.23122e27	−	7.91255e26i	−1.61953	−	1.04081i
$971$	−3.69926e26	−	5.31874e25i	−0.482105	−	0.0693163i	−0.103023	−	0.994679i	$-0.532851\pi$
$971$	−3.69926e26	−	5.31874e25i	−0.482105	−	0.0693163i	−0.379083	+	0.925363i	$0.623760\pi$
$972$	4.07103e26	−	2.61629e26i	0.525664	−	0.337824i
$973$	1.33732e27	−	6.10733e26i	1.71088	−	0.781333i
$974$	5.04221e26	+	5.81902e26i	0.639131	+	0.737597i
$975$	1.20420e26	+	8.37537e26i	0.151236	+	1.05187i
$976$	−4.55441e26	−	2.07993e26i	−0.566739	−	0.258821i
$977$	−9.21099e25	−	3.13697e26i	−0.113568	−	0.386776i	0.883018	−	0.469339i	$-0.155508\pi$
$977$	−9.21099e25	−	3.13697e26i	−0.113568	−	0.386776i	−0.996586	+	0.0825626i	$0.973690\pi$
$978$	−1.31312e26	+	3.85567e25i	−0.160419	+	0.0471032i
$979$	−8.73092e24	+	1.91180e25i	−0.0105686	+	0.0231419i
$980$	8.58250e26	−	1.23398e26i	1.02939	−	0.148004i
$981$	−8.89505e26	+	7.70761e26i	−1.05713	+	0.916006i
$982$	3.06577e26	+	6.71310e26i	0.361024	+	0.790532i
$983$	2.27998e26	+	3.54772e26i	0.266041	+	0.413968i	0.948413	−	0.317037i	$-0.102688\pi$
$983$	2.27998e26	+	3.54772e26i	0.266041	+	0.413968i	−0.682372	+	0.731005i	$0.739052\pi$
$984$	1.84075e26	−	1.28027e27i	0.212833	−	1.48029i
$985$	−2.27130e26	+	3.53421e26i	−0.260224	+	0.404917i
$986$	4.72068e26	+	4.09049e26i	0.535935	+	0.464391i
$987$	−6.89867e26	+	2.34947e27i	−0.776088	+	2.64311i
$988$			1.36721e26i			0.152413i
$989$	2.68911e26	−	1.31195e27i	0.297058	−	1.44927i
$990$	5.35775e26			0.586496
$991$	−9.18854e26	−	2.69800e26i	−0.996744	−	0.292671i	−0.257625	−	0.966245i	$-0.582940\pi$
$991$	−9.18854e26	−	2.69800e26i	−0.996744	−	0.292671i	−0.739119	+	0.673574i	$0.764758\pi$
$992$	−8.32488e26	+	9.60742e26i	−0.894897	+	1.03277i
$993$	9.18447e26	+	5.90250e26i	0.978387	+	0.628771i
$994$	1.23945e27	+	1.78207e26i	1.30844	+	0.188125i
$995$	−4.26927e26	+	2.74369e26i	−0.446628	+	0.287030i
$996$	−5.23408e26	+	2.39032e26i	−0.542633	+	0.247812i
$997$	−5.09854e26	−	5.88403e26i	−0.523829	−	0.604531i	0.430756	−	0.902468i	$-0.358247\pi$
$997$	−5.09854e26	−	5.88403e26i	−0.523829	−	0.604531i	−0.954585	+	0.297937i	$0.903701\pi$
$998$	1.10589e26	+	7.69165e26i	0.112600	+	0.783149i
$999$	6.66901e25	+	3.04564e25i	0.0672934	+	0.0307318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.19.d.a.5.9	✓	350
23.14	odd	22	inner	23.19.d.a.14.9	yes	350

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.19.d.a.5.9	✓	350	1.1	even	1	trivial
23.19.d.a.14.9	yes	350	23.14	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	23.d (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-591.122 - 173.569i) q^{2} +(18020.4 - 20796.7i) q^{3} +(98769.1 + 63475.1i) q^{4} +(2.99880e6 + 431163. i) q^{5} +(-1.42619e7 + 9.16557e6i) q^{6} +(-5.80033e7 + 2.64892e7i) q^{7} +(5.83933e7 + 6.73895e7i) q^{8} +(-5.26303e7 - 3.66052e8i) q^{9} +(-1.69782e9 - 7.75369e8i) q^{10} +(-2.18679e8 - 7.44752e8i) q^{11} +(3.09993e9 - 9.10221e8i) q^{12} +(-2.38134e9 + 5.21441e9i) q^{13} +(3.88847e10 - 5.59078e9i) q^{14} +(6.30064e10 - 5.45954e10i) q^{15} +(-3.56063e10 - 7.79669e10i) q^{16} +(4.21734e10 + 6.56232e10i) q^{17} +(-3.24243e10 + 2.25516e11i) q^{18} +(1.09827e11 - 1.70895e11i) q^{19} +(2.68821e11 + 2.32935e11i) q^{20} +(-4.94356e11 + 1.68362e12i) q^{21} +4.78195e11i q^{22} +(-8.82154e11 - 1.57034e12i) q^{23} +2.45375e12 q^{24} +(5.14675e12 + 1.51122e12i) q^{25} +(2.31272e12 - 2.66902e12i) q^{26} +(4.07539e11 + 2.61909e11i) q^{27} +(-7.41034e12 - 1.06545e12i) q^{28} +(-1.09342e13 + 7.02700e12i) q^{29} +(-4.67205e13 + 2.13366e13i) q^{30} +(2.82866e13 + 3.26445e13i) q^{31} +(4.18839e12 + 2.91309e13i) q^{32} +(-1.94290e13 - 8.87295e12i) q^{33} +(-1.35395e13 - 4.61113e13i) q^{34} +(-1.85362e14 + 5.44271e13i) q^{35} +(1.80369e13 - 3.94953e13i) q^{36} +(1.49799e14 - 2.15379e13i) q^{37} +(-9.45834e13 + 8.19570e13i) q^{38} +(6.55296e13 + 1.43490e14i) q^{39} +(1.46054e14 + 2.27265e14i) q^{40} +(7.50179e13 - 5.21761e14i) q^{41} +(5.84449e14 - 9.09421e14i) q^{42} +(5.61929e14 + 4.86914e14i) q^{43} +(2.56745e13 - 8.74392e13i) q^{44} -1.12041e15i q^{45} +(2.48899e14 + 1.08137e15i) q^{46} +1.39549e15 q^{47} +(-2.26309e15 - 6.64504e14i) q^{48} +(1.59632e15 - 1.84225e15i) q^{49} +(-2.78006e15 - 1.78663e15i) q^{50} +(2.12473e15 + 3.05489e14i) q^{51} +(-5.66188e14 + 3.63867e14i) q^{52} +(5.28477e15 - 2.41348e15i) q^{53} +(-1.95446e14 - 2.25557e14i) q^{54} +(-3.34666e14 - 2.32765e15i) q^{55} +(-5.17210e15 - 2.36202e15i) q^{56} +(-1.57491e15 - 5.36364e15i) q^{57} +(7.68313e15 - 2.25597e15i) q^{58} +(-2.57689e15 + 5.64260e15i) q^{59} +(9.68854e15 - 1.39300e15i) q^{60} +(4.41468e15 - 3.82534e15i) q^{61} +(-1.10548e16 - 2.42066e16i) q^{62} +(1.27492e16 + 1.98381e16i) q^{63} +(-6.17309e14 + 4.29348e15i) q^{64} +(-9.38944e15 + 1.46103e16i) q^{65} +(9.94486e15 + 8.61727e15i) q^{66} +(-3.21463e14 + 1.09480e15i) q^{67} +9.15850e15i q^{68} +(-4.85545e16 - 9.95223e15i) q^{69} +1.19018e17 q^{70} +(3.05839e16 + 8.98025e15i) q^{71} +(2.15948e16 - 2.49217e16i) q^{72} +(-4.03359e16 - 2.59223e16i) q^{73} +(-9.22880e16 - 1.32690e16i) q^{74} +(1.24175e17 - 7.98024e16i) q^{75} +(2.16951e16 - 9.90783e15i) q^{76} +(3.24120e16 + 3.74055e16i) q^{77} +(-1.38306e16 - 9.61939e16i) q^{78} +(-3.51478e16 - 1.60515e16i) q^{79} +(-7.31599e16 - 2.49160e17i) q^{80} +(1.50261e17 - 4.41208e16i) q^{81} +(-1.34906e17 + 2.95404e17i) q^{82} +(-1.76287e17 + 2.53463e16i) q^{83} +(-1.55695e17 + 1.34911e17i) q^{84} +(9.81757e16 + 2.14975e17i) q^{85} +(-2.47655e17 - 3.85359e17i) q^{86} +(-5.09011e16 + 3.54025e17i) q^{87} +(3.74191e16 - 5.82253e16i) q^{88} +(-2.04638e16 - 1.77320e16i) q^{89} +(-1.94468e17 + 6.62299e17i) q^{90} -3.65533e17i q^{91} +(1.25475e16 - 2.11096e17i) q^{92} +1.18863e18 q^{93} +(-8.24903e17 - 2.42213e17i) q^{94} +(4.03035e17 - 4.65127e17i) q^{95} +(6.81302e17 + 4.37846e17i) q^{96} +(7.76136e17 + 1.11592e17i) q^{97} +(-1.26338e18 + 8.11923e17i) q^{98} +(-2.61109e17 + 1.19244e17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 350 q - 179 q^{2} + 20119 q^{3} - 4092083 q^{4} - 11 q^{5} - 2318126 q^{6} - 11 q^{7} - 18825206 q^{8} - 4214797052 q^{9} - 11 q^{10} - 11 q^{11} + 5321755786 q^{12} + 655768935 q^{13} - 11 q^{14} + 253448904621 q^{15}+ \cdots - 95\!\cdots\!51 q^{99}+O(q^{100}) \) 350 * q - 179 * q^2 + 20119 * q^3 - 4092083 * q^4 - 11 * q^5 - 2318126 * q^6 - 11 * q^7 - 18825206 * q^8 - 4214797052 * q^9 - 11 * q^10 - 11 * q^11 + 5321755786 * q^12 + 655768935 * q^13 - 11 * q^14 + 253448904621 * q^15 - 121059691035 * q^16 - 296340696091 * q^17 + 845128269786 * q^18 + 34950057109 * q^19 - 4104516534283 * q^20 + 5306405877949 * q^21 - 8788512317886 * q^23 + 16248757876058 * q^24 + 15898871892338 * q^25 - 12820353995934 * q^26 - 13015455785135 * q^27 + 105657239863285 * q^28 + 24125383566071 * q^29 - 190975720579083 * q^30 + 21755707682535 * q^31 - 243907502265099 * q^32 + 261034241184453 * q^33 - 129972082436273 * q^34 - 266152601718391 * q^35 + 559915831168033 * q^36 + 428874756612181 * q^37 - 1776255039233686 * q^38 + 549617987179705 * q^39 + 3407519671874989 * q^40 + 453667246412903 * q^41 - 6199000632151481 * q^42 + 1284249744062989 * q^43 + 7033574851458386 * q^44 - 11529170898896835 * q^46 - 2752011365749412 * q^47 + 7346362951210082 * q^48 + 14923872408166082 * q^49 - 8729688416622456 * q^50 - 15827415309093971 * q^51 - 11781732119049248 * q^52 + 10327001802201029 * q^53 + 16483884134652258 * q^54 - 6495140540052155 * q^55 - 112789689088256488 * q^56 + 79316406647596261 * q^57 + 80750695224012275 * q^58 - 103310090431970893 * q^59 + 56789760614471819 * q^60 + 64312558011025621 * q^61 + 78525812725681666 * q^62 - 56271156969207411 * q^63 - 224715274461002686 * q^64 - 45304722356970395 * q^65 + 206405045580983832 * q^66 + 65297330513632789 * q^67 - 143603139268291161 * q^69 - 403103996477716918 * q^70 - 7242816485765057 * q^71 + 620604439361873263 * q^72 + 69596528836762215 * q^73 + 102815849039067692 * q^74 + 116102034703195999 * q^75 - 930398829208773122 * q^76 - 693643966535804563 * q^77 + 2957501787035331408 * q^78 + 960132297145477093 * q^79 - 2513912900105850122 * q^80 - 3453140773055113594 * q^81 + 841776961191439844 * q^82 + 2134251156441149669 * q^83 + 1875963344476894475 * q^84 - 2497986830714303135 * q^85 - 709961756623859245 * q^86 - 2620179835179103895 * q^87 + 746914657235259645 * q^88 + 2323216414828777369 * q^89 + 6947866797842083322 * q^90 - 2374143188353425254 * q^92 - 8687469182791611658 * q^93 - 3156566639060022579 * q^94 + 1273876168349301101 * q^95 + 19129033188570894661 * q^96 + 2956262222729055625 * q^97 - 5708307230013551083 * q^98 - 9593810550169008251 * q^99

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