LMFDB - Embedded newform 23.19.d.a.5.1

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			5.1
Character	$\chi$	$=$	23.5
Dual form			23.19.d.a.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-972.723 - 285.617i) q^{2} +(-21289.0 + 24568.8i) q^{3} +(644082. + 413927. i) q^{4} +(-2.61874e6 - 376518. i) q^{5} +(2.77256e7 - 1.78182e7i) q^{6} +(3.10489e7 - 1.41796e7i) q^{7} +(-3.34254e8 - 3.85750e8i) q^{8} +(-9.52698e7 - 6.62616e8i) q^{9} +(2.43977e9 + 1.11420e9i) q^{10} +(-4.23069e8 - 1.44084e9i) q^{11} +(-2.38816e10 + 7.01227e9i) q^{12} +(-1.15159e9 + 2.52164e9i) q^{13} +(-3.42519e10 + 4.92468e9i) q^{14} +(6.50010e10 - 5.63237e10i) q^{15} +(1.31585e11 + 2.88130e11i) q^{16} +(-7.40776e10 - 1.15267e11i) q^{17} +(-9.65834e10 + 6.71752e11i) q^{18} +(1.38137e11 - 2.14946e11i) q^{19} +(-1.53083e12 - 1.32647e12i) q^{20} +(-3.12625e11 + 1.06470e12i) q^{21} +1.52237e12i q^{22} +(1.74380e12 - 4.50903e11i) q^{23} +1.65934e13 q^{24} +(3.05585e12 + 8.97278e11i) q^{25} +(1.84041e12 - 2.12394e12i) q^{26} +(7.71254e12 + 4.95655e12i) q^{27} +(2.58673e13 + 3.71916e12i) q^{28} +(3.51289e12 - 2.25760e12i) q^{29} +(-7.93149e13 + 3.62219e13i) q^{30} +(1.58931e13 + 1.83416e13i) q^{31} +(-2.66582e13 - 1.85412e14i) q^{32} +(4.44065e13 + 2.02798e13i) q^{33} +(3.91347e13 + 1.33281e14i) q^{34} +(-8.66478e13 + 2.54421e13i) q^{35} +(2.12913e14 - 4.66214e14i) q^{36} +(-1.23672e14 + 1.77813e13i) q^{37} +(-1.95762e14 + 1.69628e14i) q^{38} +(-3.74375e13 - 8.19766e13i) q^{39} +(7.30083e14 + 1.13603e15i) q^{40} +(-7.11150e13 + 4.94616e14i) q^{41} +(6.08195e14 - 9.46371e14i) q^{42} +(-6.40239e13 - 5.54770e13i) q^{43} +(3.23911e14 - 1.10314e15i) q^{44} +1.77109e15i q^{45} +(-1.82502e15 - 5.94555e13i) q^{46} +1.65674e15 q^{47} +(-9.88034e15 - 2.90113e15i) q^{48} +(-3.03410e14 + 3.50154e14i) q^{49} +(-2.71621e15 - 1.74560e15i) q^{50} +(4.40902e15 + 6.33921e14i) q^{51} +(-1.78550e15 + 1.14747e15i) q^{52} +(-3.17162e15 + 1.44843e15i) q^{53} +(-6.08649e15 - 7.02418e15i) q^{54} +(5.65405e14 + 3.93248e15i) q^{55} +(-1.58480e16 - 7.23753e15i) q^{56} +(2.34016e15 + 7.96986e15i) q^{57} +(-4.06188e15 + 1.19268e15i) q^{58} +(2.20758e15 - 4.83392e15i) q^{59} +(6.51799e16 - 9.37145e15i) q^{60} +(9.73075e15 - 8.43174e15i) q^{61} +(-1.02209e16 - 2.23806e16i) q^{62} +(-1.23536e16 - 1.92226e16i) q^{63} +(-1.52086e16 + 1.05778e17i) q^{64} +(3.96517e15 - 6.16992e15i) q^{65} +(-3.74030e16 - 3.24098e16i) q^{66} +(7.54401e15 - 2.56925e16i) q^{67} -1.04904e17i q^{68} +(-2.60456e16 + 5.24424e16i) q^{69} +9.15509e16 q^{70} +(6.48341e15 + 1.90370e15i) q^{71} +(-2.23760e17 + 2.58233e17i) q^{72} +(-2.88880e16 - 1.85652e16i) q^{73} +(1.25377e17 + 1.80265e16i) q^{74} +(-8.71011e16 + 5.59765e16i) q^{75} +(1.77944e17 - 8.12642e16i) q^{76} +(-3.35663e16 - 3.87376e16i) q^{77} +(1.30023e16 + 9.04333e16i) q^{78} +(-1.77335e15 - 8.09864e14i) q^{79} +(-2.36100e17 - 8.04082e17i) q^{80} +(-3.71238e16 + 1.09005e16i) q^{81} +(2.10446e17 - 4.60812e17i) q^{82} +(2.14434e16 - 3.08309e15i) q^{83} +(-6.42066e17 + 5.56353e17i) q^{84} +(1.50590e17 + 3.29745e17i) q^{85} +(4.64323e16 + 7.22500e16i) q^{86} +(-1.93195e16 + 1.34370e17i) q^{87} +(-4.14392e17 + 6.44806e17i) q^{88} +(1.80263e17 + 1.56199e17i) q^{89} +(5.05853e17 - 1.72278e18i) q^{90} +9.46232e16i q^{91} +(1.30979e18 + 4.31386e17i) q^{92} -7.88979e17 q^{93} +(-1.61155e18 - 4.73194e17i) q^{94} +(-4.42676e17 + 5.10876e17i) q^{95} +(5.12288e18 + 3.29228e18i) q^{96} +(-4.96499e17 - 7.13858e16i) q^{97} +(3.95144e17 - 2.53944e17i) q^{98} +(-9.14419e17 + 4.17601e17i) 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 $

$2$	−972.723	−	285.617i	−1.89985	−	0.557846i	−0.989613	−	0.143755i	$-0.954082\pi$
$2$	−972.723	−	285.617i	−1.89985	−	0.557846i	−0.910235	−	0.414091i	$-0.864099\pi$
$3$	−21289.0	+	24568.8i	−1.08159	+	1.24823i	−0.114605	+	0.993411i	$0.536560\pi$
$3$	−21289.0	+	24568.8i	−1.08159	+	1.24823i	−0.966990	+	0.254815i	$0.917985\pi$
$4$	644082.	+	413927.i	2.45698	+	1.57900i
$5$	−2.61874e6	−	376518.i	−1.34079	−	0.192777i	−0.565694	−	0.824615i	$-0.691392\pi$
$5$	−2.61874e6	−	376518.i	−1.34079	−	0.192777i	−0.775100	+	0.631838i	$0.782301\pi$
$6$	2.77256e7	−	1.78182e7i	2.75118	−	1.76808i
$7$	3.10489e7	−	1.41796e7i	0.769420	−	0.351383i	0.00827669	−	0.999966i	$-0.497365\pi$
$7$	3.10489e7	−	1.41796e7i	0.769420	−	0.351383i	0.761144	+	0.648583i	$0.224638\pi$
$8$	−3.34254e8	−	3.85750e8i	−2.49039	−	2.87406i
$9$	−9.52698e7	−	6.62616e8i	−0.245908	−	1.71033i
$10$	2.43977e9	+	1.11420e9i	2.43977	+	1.11420i
$11$	−4.23069e8	−	1.44084e9i	−0.179423	−	0.611057i	−0.999260	−	0.0384608i	$-0.987755\pi$
$11$	−4.23069e8	−	1.44084e9i	−0.179423	−	0.611057i	0.819838	−	0.572596i	$-0.194064\pi$
$12$	−2.38816e10	+	7.01227e9i	−4.62841	+	1.35902i
$13$	−1.15159e9	+	2.52164e9i	−0.108595	+	0.237790i	−0.956126	−	0.292956i	$-0.905361\pi$
$13$	−1.15159e9	+	2.52164e9i	−0.108595	+	0.237790i	0.847531	+	0.530746i	$0.178088\pi$
$14$	−3.42519e10	+	4.92468e9i	−1.65780	+	0.238356i
$15$	6.50010e10	−	5.63237e10i	1.69082	−	1.46511i
$16$	1.31585e11	+	2.88130e11i	1.91481	+	4.19285i
$17$	−7.40776e10	−	1.15267e11i	−0.624664	−	0.971996i	−0.999000	−	0.0447032i	$-0.985766\pi$
$17$	−7.40776e10	−	1.15267e11i	−0.624664	−	0.971996i	0.374336	−	0.927293i	$-0.377871\pi$
$18$	−9.65834e10	+	6.71752e11i	−0.486912	+	3.38654i
$19$	1.38137e11	−	2.14946e11i	0.428084	−	0.666111i	−0.558474	−	0.829522i	$-0.688613\pi$
$19$	1.38137e11	−	2.14946e11i	0.428084	−	0.666111i	0.986558	+	0.163410i	$0.0522495\pi$
$20$	−1.53083e12	−	1.32647e12i	−2.98991	−	2.59077i
$21$	−3.12625e11	+	1.06470e12i	−0.393596	+	1.34046i
$22$			1.52237e12i			1.26101i
$23$	1.74380e12	−	4.50903e11i	0.968158	−	0.250341i
$23$	1.74380e12	−	4.50903e11i	0.968158	−	0.250341i
$24$	1.65934e13			6.28107
$25$	3.05585e12	+	8.97278e11i	0.801072	+	0.235216i
$26$	1.84041e12	−	2.12394e12i	0.338964	−	0.391185i
$27$	7.71254e12	+	4.95655e12i	1.01140	+	0.649988i
$28$	2.58673e13	+	3.71916e12i	2.44529	+	0.351579i
$29$	3.51289e12	−	2.25760e12i	0.242149	−	0.155620i	−0.413938	−	0.910305i	$-0.635847\pi$
$29$	3.51289e12	−	2.25760e12i	0.242149	−	0.155620i	0.656087	+	0.754685i	$0.272210\pi$
$30$	−7.93149e13	+	3.62219e13i	−4.02962	+	1.84026i
$31$	1.58931e13	+	1.83416e13i	0.601108	+	0.693715i	0.972005	−	0.234958i	$-0.0754954\pi$
$31$	1.58931e13	+	1.83416e13i	0.601108	+	0.693715i	−0.370898	+	0.928674i	$0.620950\pi$
$32$	−2.66582e13	−	1.85412e14i	−0.757672	−	5.26972i
$33$	4.44065e13	+	2.02798e13i	0.956800	+	0.436956i
$34$	3.91347e13	+	1.33281e14i	0.644543	+	2.19511i
$35$	−8.66478e13	+	2.54421e13i	−1.09937	+	0.322805i
$36$	2.12913e14	−	4.66214e14i	2.09643	−	4.59053i
$37$	−1.23672e14	+	1.77813e13i	−0.951602	+	0.136820i	−0.600595	−	0.799553i	$-0.705070\pi$
$37$	−1.23672e14	+	1.77813e13i	−0.951602	+	0.136820i	−0.351007	+	0.936373i	$0.614161\pi$
$38$	−1.95762e14	+	1.69628e14i	−1.18488	+	1.02671i
$39$	−3.74375e13	−	8.19766e13i	−0.179360	−	0.392743i
$40$	7.30083e14	+	1.13603e15i	2.78504	+	4.33361i
$41$	−7.11150e13	+	4.94616e14i	−0.217223	+	1.51082i	0.530999	+	0.847373i	$0.321817\pi$
$41$	−7.11150e13	+	4.94616e14i	−0.217223	+	1.51082i	−0.748222	+	0.663449i	$0.769092\pi$
$42$	6.08195e14	−	9.46371e14i	1.49555	−	2.32711i
$43$	−6.40239e13	−	5.54770e13i	−0.127387	−	0.110382i	0.588837	−	0.808252i	$-0.299586\pi$
$43$	−6.40239e13	−	5.54770e13i	−0.127387	−	0.110382i	−0.716224	+	0.697870i	$0.754131\pi$
$44$	3.23911e14	−	1.10314e15i	0.524024	−	1.78466i
$45$			1.77109e15i			2.34060i
$46$	−1.82502e15	−	5.94555e13i	−1.97900	−	0.0644721i
$47$	1.65674e15			1.48038			0.740191	−	0.672396i	$-0.234735\pi$
$47$	1.65674e15			1.48038			0.740191	+	0.672396i	$0.234735\pi$
$48$	−9.88034e15	−	2.90113e15i	−7.30467	−	2.14484i
$49$	−3.03410e14	+	3.50154e14i	−0.186323	+	0.215028i
$50$	−2.71621e15	−	1.74560e15i	−1.39070	−	0.893750i
$51$	4.40902e15	+	6.33921e14i	1.88890	+	0.271583i
$52$	−1.78550e15	+	1.14747e15i	−0.642287	+	0.412772i
$53$	−3.17162e15	+	1.44843e15i	−0.961166	+	0.438950i	−0.833287	−	0.552840i	$-0.813544\pi$
$53$	−3.17162e15	+	1.44843e15i	−0.961166	+	0.438950i	−0.127879	+	0.991790i	$0.540817\pi$
$54$	−6.08649e15	−	7.02418e15i	−1.55892	−	1.79909i
$55$	5.65405e14	+	3.93248e15i	0.122771	+	0.853890i
$56$	−1.58480e16	−	7.23753e15i	−2.92605	−	1.33628i
$57$	2.34016e15	+	7.96986e15i	0.368445	+	1.25481i
$58$	−4.06188e15	+	1.19268e15i	−0.546859	+	0.160572i
$59$	2.20758e15	−	4.83392e15i	0.254828	−	0.557996i	−0.738375	−	0.674391i	$-0.764406\pi$
$59$	2.20758e15	−	4.83392e15i	0.254828	−	0.557996i	0.993203	+	0.116395i	$0.0371337\pi$
$60$	6.51799e16	−	9.37145e15i	6.46773	−	0.929920i
$61$	9.73075e15	−	8.43174e15i	0.832104	−	0.721022i	−0.130642	−	0.991430i	$-0.541704\pi$
$61$	9.73075e15	−	8.43174e15i	0.832104	−	0.721022i	0.962746	+	0.270407i	$0.0871584\pi$
$62$	−1.02209e16	−	2.23806e16i	−0.755028	−	1.65328i
$63$	−1.23536e16	−	1.92226e16i	−0.790186	−	1.22955i
$64$	−1.52086e16	+	1.05778e17i	−0.844248	+	5.87187i
$65$	3.96517e15	−	6.16992e15i	0.191444	−	0.297892i
$66$	−3.74030e16	−	3.24098e16i	−1.57402	−	1.36390i
$67$	7.54401e15	−	2.56925e16i	0.277287	−	0.944351i	−0.696627	−	0.717433i	$-0.745317\pi$
$67$	7.54401e15	−	2.56925e16i	0.277287	−	0.944351i	0.973914	−	0.226918i	$-0.0728650\pi$
$68$		−	1.04904e17i		−	3.37452i
$69$	−2.60456e16	+	5.24424e16i	−0.734671	+	1.47925i
$70$	9.15509e16			2.26872
$71$	6.48341e15	+	1.90370e15i	0.141409	+	0.0415216i	0.351671	−	0.936124i	$-0.385613\pi$
$71$	6.48341e15	+	1.90370e15i	0.141409	+	0.0415216i	−0.210262	+	0.977645i	$0.567432\pi$
$72$	−2.23760e17	+	2.58233e17i	−4.30318	+	4.96614i
$73$	−2.88880e16	−	1.85652e16i	−0.490695	−	0.315351i	0.271790	−	0.962357i	$-0.412385\pi$
$73$	−2.88880e16	−	1.85652e16i	−0.490695	−	0.315351i	−0.762485	+	0.647006i	$0.776021\pi$
$74$	1.25377e17	+	1.80265e16i	1.88422	+	0.270910i
$75$	−8.71011e16	+	5.59765e16i	−1.16004	+	0.745511i
$76$	1.77944e17	−	8.12642e16i	2.10359	−	0.960676i
$77$	−3.35663e16	−	3.87376e16i	−0.352766	−	0.407114i
$78$	1.30023e16	+	9.04333e16i	0.121666	+	0.846207i
$79$	−1.77335e15	−	8.09864e14i	−0.0147963	−	0.00675722i	0.408003	−	0.912981i	$-0.366225\pi$
$79$	−1.77335e15	−	8.09864e14i	−0.0147963	−	0.00675722i	−0.422799	+	0.906223i	$0.638953\pi$
$80$	−2.36100e17	−	8.04082e17i	−1.75908	−	5.99088i
$81$	−3.71238e16	+	1.09005e16i	−0.247336	+	0.0726244i
$82$	2.10446e17	−	4.60812e17i	1.25550	−	2.74915i
$83$	2.14434e16	−	3.08309e15i	0.114707	−	0.0164924i	−0.0847221	−	0.996405i	$-0.527000\pi$
$83$	2.14434e16	−	3.08309e15i	0.114707	−	0.0164924i	0.199429	+	0.979912i	$0.436091\pi$
$84$	−6.42066e17	+	5.56353e17i	−3.08366	+	2.67200i
$85$	1.50590e17	+	3.29745e17i	0.650167	+	1.42367i
$86$	4.64323e16	+	7.22500e16i	0.180440	+	0.280771i
$87$	−1.93195e16	+	1.34370e17i	−0.0676584	+	0.470575i
$88$	−4.14392e17	+	6.44806e17i	−1.30938	+	2.03744i
$89$	1.80263e17	+	1.56199e17i	0.514514	+	0.445829i	0.873010	−	0.487702i	$-0.162165\pi$
$89$	1.80263e17	+	1.56199e17i	0.514514	+	0.445829i	−0.358496	+	0.933531i	$0.616710\pi$
$90$	5.05853e17	−	1.72278e18i	1.30570	−	4.44679i
$91$			9.46232e16i			0.221119i
$92$	1.30979e18	+	4.31386e17i	2.77403	+	0.913642i
$93$	−7.88979e17			−1.51607
$94$	−1.61155e18	−	4.73194e17i	−2.81250	−	0.825825i
$95$	−4.42676e17	+	5.10876e17i	−0.702383	+	0.810593i
$96$	5.12288e18	+	3.29228e18i	7.39730	+	4.75396i
$97$	−4.96499e17	−	7.13858e16i	−0.653089	−	0.0939001i	−0.192197	−	0.981356i	$-0.561561\pi$
$97$	−4.96499e17	−	7.13858e16i	−0.653089	−	0.0939001i	−0.460892	+	0.887456i	$0.652470\pi$
$98$	3.95144e17	−	2.53944e17i	0.473937	−	0.304581i
$99$	−9.14419e17	+	4.17601e17i	−1.00099	+	0.457135i
$100$	1.59681e18	+	1.84282e18i	1.59681	+	1.84282i
$101$	−7.45635e16	−	5.18601e17i	−0.0681764	−	0.474177i	−0.995096	−	0.0989167i	$-0.968462\pi$
$101$	−7.45635e16	−	5.18601e17i	−0.0681764	−	0.474177i	0.926919	−	0.375261i	$-0.122447\pi$
$102$	−4.10769e18	−	1.87592e18i	−3.43713	−	1.56969i
$103$	−5.28758e17	−	1.80079e18i	−0.405249	−	1.38015i	−0.869274	−	0.494330i	$-0.835413\pi$
$103$	−5.28758e17	−	1.80079e18i	−0.405249	−	1.38015i	0.464025	−	0.885822i	$-0.346405\pi$
$104$	1.35765e18	−	3.98641e17i	0.953865	−	0.280080i
$105$	1.21956e18	−	2.67047e18i	0.786142	−	1.72141i
$106$	3.49880e18	−	5.03052e17i	2.07094	−	0.297756i
$107$	−5.57346e17	+	4.82943e17i	−0.303159	+	0.262689i	−0.793133	−	0.609048i	$-0.791552\pi$
$107$	−5.57346e17	+	4.82943e17i	−0.303159	+	0.262689i	0.489974	+	0.871737i	$0.337006\pi$
$108$	2.91587e18	+	6.38485e18i	1.45866	+	3.19402i
$109$	3.41544e16	+	5.31453e16i	0.0157256	+	0.0244696i	0.849027	−	0.528349i	$-0.177189\pi$
$109$	3.41544e16	+	5.31453e16i	0.0157256	+	0.0244696i	−0.833302	+	0.552818i	$0.813552\pi$
$110$	5.73201e17	−	3.98670e18i	0.243093	−	1.69075i
$111$	2.19599e18	−	3.41702e18i	0.858465	−	1.33580i
$112$	8.17112e18	+	7.08031e18i	2.94659	+	2.55323i
$113$	−4.44820e17	+	1.51492e18i	−0.148074	+	0.504293i	−0.999806	−	0.0196840i	$-0.993734\pi$
$113$	−4.44820e17	+	1.51492e18i	−0.148074	+	0.504293i	0.851733	+	0.523977i	$0.175552\pi$
$114$		−	8.42086e18i		−	2.58948i
$115$	−4.73633e18	+	5.24225e17i	−1.34636	+	0.149018i
$116$	3.19707e18			0.840680
$117$	1.78059e18	+	5.22829e17i	0.433403	+	0.127259i
$118$	−3.52801e18	+	4.07154e18i	−0.795411	+	0.917953i
$119$	−3.93446e18	−	2.52852e18i	−0.822172	−	0.528378i
$120$	−4.34537e19	−	6.24770e18i	−8.42162	−	1.21085i
$121$	2.78027e18	−	1.78677e18i	0.500055	−	0.321366i
$122$	−1.18736e19	+	5.42248e18i	−1.98309	+	0.905647i
$123$	−1.06382e19	−	1.22771e19i	−1.65090	−	1.90524i
$124$	2.64438e18	+	1.83920e19i	0.381530	+	2.65360i
$125$	1.51576e18	+	6.92226e17i	0.203442	+	0.0929090i
$126$	6.52634e18	+	2.22267e19i	0.815333	+	2.77677i
$127$	2.61161e18	−	7.66837e17i	0.303861	−	0.0892215i	−0.126248	−	0.991999i	$-0.540293\pi$
$127$	2.61161e18	−	7.66837e17i	0.303861	−	0.0892215i	0.430109	+	0.902777i	$0.358475\pi$
$128$	2.46071e19	−	5.38821e19i	2.66791	−	5.84191i
$129$	2.72601e18	−	3.91941e17i	0.275563	−	0.0396199i
$130$	−5.61924e18	+	4.86910e18i	−0.529892	+	0.459154i
$131$	−2.73894e18	−	5.99743e18i	−0.241068	−	0.527866i	0.749966	−	0.661477i	$-0.230070\pi$
$131$	−2.73894e18	−	5.99743e18i	−0.241068	−	0.527866i	−0.991034	+	0.133611i	$0.957343\pi$
$132$	2.02071e19	+	3.14429e19i	1.66088	+	2.58438i
$133$	1.24117e18	−	8.63256e18i	0.0953165	−	0.662941i
$134$	−1.46765e19	+	2.28370e19i	−1.05361	+	1.63944i
$135$	−1.83309e19	−	1.58838e19i	−1.23078	−	1.06648i
$136$	−1.97035e19	+	6.71039e19i	−1.23792	+	4.21597i
$137$		−	2.04512e19i		−	1.20291i	−0.798907	−	0.601455i	$-0.794588\pi$
$137$		−	2.04512e19i		−	1.20291i	0.798907	−	0.601455i	$-0.205412\pi$
$138$	4.03136e19	−	4.35729e19i	2.22096	−	2.40051i
$139$	3.04783e19			1.57347			0.786734	−	0.617292i	$-0.211770\pi$
$139$	3.04783e19			1.57347			0.786734	+	0.617292i	$0.211770\pi$
$140$	−6.63395e19	−	1.94790e19i	−3.21085	−	0.942790i
$141$	−3.52704e19	+	4.07042e19i	−1.60117	+	1.84785i
$142$	−5.76283e18	−	3.70355e18i	−0.245494	−	0.157769i
$143$	4.12048e18	+	5.92436e17i	0.164787	+	0.0236928i
$144$	1.78384e20	−	1.14640e20i	6.70028	−	4.30601i
$145$	−1.00494e19	+	4.58940e18i	−0.354672	+	0.161973i
$146$	2.27975e19	+	2.63097e19i	0.756330	+	0.872851i
$147$	−2.14357e18	−	1.49089e19i	−0.0668778	−	0.465146i
$148$	−8.70150e19	−	3.97384e19i	−2.55411	−	1.16642i
$149$	1.22617e19	+	4.17595e19i	0.338746	+	1.15366i	0.936114	+	0.351696i	$0.114395\pi$
$149$	1.22617e19	+	4.17595e19i	0.338746	+	1.15366i	−0.597368	+	0.801967i	$0.703787\pi$
$150$	1.00713e20	−	2.95720e19i	2.61978	−	0.769236i
$151$	−8.63432e18	+	1.89065e19i	−0.211561	+	0.463254i	−0.985428	−	0.170094i	$-0.945593\pi$
$151$	−8.63432e18	+	1.89065e19i	−0.211561	+	0.463254i	0.773867	+	0.633349i	$0.218320\pi$
$152$	−1.29088e20	+	1.85601e19i	−2.98054	+	0.428537i
$153$	−6.93204e19	+	6.00665e19i	−1.50882	+	1.30740i
$154$	2.15866e19	+	4.72680e19i	0.443095	+	0.970244i
$155$	−3.47138e19	−	5.40158e19i	−0.672229	−	1.04601i
$156$	9.81949e18	−	6.82961e19i	0.179460	−	1.24817i
$157$	3.39275e19	−	5.27922e19i	0.585403	−	0.910905i	−0.414597	−	0.910005i	$-0.636077\pi$
$157$	3.39275e19	−	5.27922e19i	0.585403	−	0.910905i	1.00000		0.000899405i	$-0.000286290\pi$
$158$	1.49367e18	+	1.29427e18i	0.0243412	+	0.0210917i
$159$	3.19345e19	−	1.08759e20i	0.491683	−	1.67452i
$160$			4.95583e20i			7.21168i
$161$	4.77494e19	−	3.87263e19i	0.656955	−	0.532811i
$162$	3.92246e19			0.510414
$163$	1.30478e20	+	3.83119e19i	1.60639	+	0.471678i	0.957314	−	0.289049i	$-0.0933392\pi$
$163$	1.30478e20	+	3.83119e19i	1.60639	+	0.471678i	0.649072	+	0.760727i	$0.275157\pi$
$164$	−2.50539e20	+	2.89137e20i	−2.91931	+	3.36906i
$165$	−1.08653e20	−	6.98272e19i	−1.19864	−	0.770317i
$166$	−2.17391e19	−	3.12561e18i	−0.227127	−	0.0326559i
$167$	2.65303e19	−	1.70500e19i	0.262599	−	0.168762i	−0.402716	−	0.915325i	$-0.631934\pi$
$167$	2.65303e19	−	1.70500e19i	0.262599	−	0.168762i	0.665315	+	0.746563i	$0.268297\pi$
$168$	5.15206e20	−	2.35287e20i	4.83278	−	2.20706i
$169$	6.86101e19	+	7.91803e19i	0.610110	+	0.704104i
$170$	−5.23011e19	−	3.63762e20i	−0.441032	−	3.06745i
$171$	−1.55587e20	−	7.10542e19i	−1.24454	−	0.568362i
$172$	−1.82732e19	−	6.22330e19i	−0.138695	−	0.472351i
$173$	−1.84446e20	+	5.41584e19i	−1.32879	+	0.390167i	−0.867656	−	0.497165i	$-0.834374\pi$
$173$	−1.84446e20	+	5.41584e19i	−1.32879	+	0.390167i	−0.461131	+	0.887332i	$0.652556\pi$
$174$	5.71708e19	−	1.25187e20i	0.391049	−	0.856278i
$175$	1.07604e20	−	1.54711e19i	0.699012	−	0.100503i
$176$	3.59480e20	−	3.11491e20i	2.21851	−	1.92235i
$177$	7.17666e19	+	1.57147e20i	0.420885	+	0.921609i
$178$	−1.30733e20	−	2.03424e20i	−0.728795	−	1.13403i
$179$	−1.17896e19	+	8.19988e19i	−0.0624918	+	0.434640i	0.934424	+	0.356163i	$0.115915\pi$
$179$	−1.17896e19	+	8.19988e19i	−0.0624918	+	0.434640i	−0.996916	+	0.0784778i	$0.974994\pi$
$180$	−7.33101e20	+	1.14073e21i	−3.69582	+	5.75081i
$181$	−2.03106e20	−	1.75992e20i	−0.974126	−	0.844085i	0.0136595	−	0.999907i	$-0.495652\pi$
$181$	−2.03106e20	−	1.75992e20i	−0.974126	−	0.844085i	−0.987785	+	0.155822i	$0.950197\pi$
$182$	2.70260e19	−	9.20422e19i	0.123350	−	0.420092i
$183$			4.18577e20i			1.81851i
$184$	−7.56808e20	−	5.21954e20i	−3.13058	−	2.15910i
$185$	3.30559e20			1.30228
$186$	7.67458e20	+	2.25346e20i	2.88030	+	0.845733i
$187$	−1.34741e20	+	1.55500e20i	−0.481866	+	0.556103i
$188$	1.06708e21	+	6.85769e20i	3.63727	+	2.33753i
$189$	3.09748e20	+	4.45350e19i	1.00659	+	0.144725i
$190$	5.76516e20	−	3.70505e20i	1.78661	−	1.14818i
$191$	−1.35604e20	+	6.19282e19i	−0.400841	+	0.183058i	−0.605627	−	0.795749i	$-0.707077\pi$
$191$	−1.35604e20	+	6.19282e19i	−0.400841	+	0.183058i	0.204786	+	0.978807i	$0.434350\pi$
$192$	−2.27507e21	−	2.62557e21i	−6.41629	−	7.40480i
$193$	4.18866e19	+	2.91327e20i	0.112735	+	0.784089i	0.965239	+	0.261369i	$0.0841738\pi$
$193$	4.18866e19	+	2.91327e20i	0.112735	+	0.784089i	−0.852504	+	0.522721i	$0.824917\pi$
$194$	4.62567e20	+	2.11247e20i	1.18839	+	0.542719i
$195$	6.71733e19	+	2.28771e20i	0.164773	+	0.561164i
$196$	−3.40359e20	+	9.99385e19i	−0.797321	+	0.234114i
$197$	−3.07228e20	+	6.72735e20i	−0.687487	+	1.50539i	0.167024	+	0.985953i	$0.446584\pi$
$197$	−3.07228e20	+	6.72735e20i	−0.687487	+	1.50539i	−0.854511	+	0.519433i	$0.826143\pi$
$198$	1.00875e21	−	1.45036e20i	2.15673	−	0.310092i
$199$	5.52233e20	−	4.78512e20i	1.12835	−	0.977722i	0.128449	−	0.991716i	$-0.459000\pi$
$199$	5.52233e20	−	4.78512e20i	1.12835	−	0.977722i	0.999902	+	0.0139941i	$0.00445462\pi$
$200$	−6.75305e20	−	1.47871e21i	−1.31896	−	2.88811i
$201$	4.70631e20	+	7.32316e20i	0.878853	+	1.36752i
$202$	−7.55916e19	+	5.25751e20i	−0.134993	+	0.938897i
$203$	7.70597e19	−	1.19907e20i	0.131632	−	0.204824i
$204$	2.57737e21	+	2.23331e21i	4.21217	+	3.64986i
$205$	3.72463e20	−	1.26849e21i	0.582503	−	1.98382i
$206$			1.90269e21i			2.84815i
$207$	−4.64907e20	−	1.11251e21i	−0.666244	−	1.59431i
$208$	−8.78093e20			−1.20495
$209$	−3.68144e20	−	1.08097e20i	−0.483840	−	0.142068i
$210$	−1.94903e21	+	2.24930e21i	−2.45383	+	2.83187i
$211$	−8.21040e20	−	5.27650e20i	−0.990427	−	0.636508i	−0.0581701	−	0.998307i	$-0.518527\pi$
$211$	−8.21040e20	−	5.27650e20i	−0.990427	−	0.636508i	−0.932256	+	0.361798i	$0.882163\pi$
$212$	−2.64233e21	−	3.79910e20i	−3.05467	−	0.439195i
$213$	−1.84797e20	+	1.18762e20i	−0.204776	+	0.131602i
$214$	6.80080e20	−	3.10582e20i	0.722497	−	0.329953i
$215$	1.46774e20	+	1.69386e20i	0.149521	+	0.172556i
$216$	−6.65961e20	−	4.63186e21i	−0.650676	−	4.52555i
$217$	7.53537e20	+	3.44129e20i	0.706264	+	0.322540i
$218$	−1.80436e19	−	6.14507e19i	−0.0162261	−	0.0552610i
$219$	1.07112e21	−	3.14510e20i	0.924363	−	0.271417i
$220$	−1.26359e21	+	2.76688e21i	−1.04665	+	2.29185i
$221$	3.75969e20	−	5.40562e19i	0.298966	−	0.0429848i
$222$	−3.11204e21	+	2.69660e21i	−2.37612	+	2.05892i
$223$	−4.90198e20	−	1.07338e21i	−0.359441	−	0.787066i	−0.999819	−	0.0190064i	$-0.993950\pi$
$223$	−4.90198e20	−	1.07338e21i	−0.359441	−	0.787066i	0.640378	−	0.768060i	$-0.278778\pi$
$224$	−3.45677e21	−	5.37883e21i	−2.43466	−	3.78840i
$225$	3.03421e20	−	2.11034e21i	0.205306	−	1.42794i
$226$	8.65372e20	−	1.34655e21i	0.562635	−	0.875478i
$227$	−1.18988e21	−	1.03104e21i	−0.743482	−	0.644231i	0.198420	−	0.980117i	$-0.436419\pi$
$227$	−1.18988e21	−	1.03104e21i	−0.743482	−	0.644231i	−0.941903	+	0.335886i	$0.890964\pi$
$228$	−1.79168e21	+	6.10191e21i	−1.07609	+	3.66481i
$229$		−	1.25791e21i		−	0.726327i	−0.931726	−	0.363163i	$-0.881697\pi$
$229$		−	1.25791e21i		−	0.726327i	0.931726	−	0.363163i	$-0.118303\pi$
$230$	4.75686e21	+	8.42850e20i	2.64101	+	0.467950i
$231$	1.66633e21			0.889720
$232$	−2.04507e21	−	6.00486e20i	−1.05031	−	0.308398i
$233$	4.67946e20	−	5.40038e20i	0.231202	−	0.266822i	−0.628280	−	0.777987i	$-0.716241\pi$
$233$	4.67946e20	−	5.40038e20i	0.231202	−	0.266822i	0.859482	+	0.511166i	$0.170786\pi$
$234$	−1.58269e21	−	1.01714e21i	−0.752409	−	0.483544i
$235$	−4.33857e21	−	6.23792e20i	−1.98489	−	0.285384i
$236$	3.42275e21	−	2.19967e21i	1.50719	−	0.968610i
$237$	5.76504e19	−	2.63281e19i	0.0244381	−	0.0111605i
$238$	3.10495e21	+	3.58330e21i	1.26725	+	1.46248i
$239$	−1.83043e20	−	1.27309e21i	−0.0719404	−	0.500356i	−0.993654	−	0.112484i	$-0.964119\pi$
$239$	−1.83043e20	−	1.27309e21i	−0.0719404	−	0.500356i	0.921713	−	0.387872i	$-0.126790\pi$
$240$	2.47817e22	+	1.13174e22i	9.38058	+	4.28397i
$241$	−1.27314e20	−	4.33592e20i	−0.0464219	−	0.158098i	0.933020	−	0.359824i	$-0.117163\pi$
$241$	−1.27314e20	−	4.33592e20i	−0.0464219	−	0.158098i	−0.979442	+	0.201726i	$0.935345\pi$
$242$	−3.21476e21	+	9.43939e20i	−1.12930	+	0.331593i
$243$	−9.52971e20	+	2.08672e21i	−0.322569	+	0.706329i
$244$	9.75752e21	−	1.40292e21i	3.18296	−	0.457641i
$245$	9.26391e20	−	8.02723e20i	0.291273	−	0.252389i
$246$	6.84143e21	+	1.49807e22i	2.07363	+	4.54062i
$247$	3.82938e20	+	5.95863e20i	0.111907	+	0.174130i
$248$	1.76294e21	−	1.22615e22i	0.496789	−	3.45524i
$249$	−3.80761e20	+	5.92476e20i	−0.103480	+	0.161019i
$250$	−1.27671e21	−	1.10627e21i	−0.334681	−	0.290003i
$251$	−1.46442e21	+	4.98736e21i	−0.370342	+	1.26127i	0.537966	+	0.842966i	$0.319193\pi$
$251$	−1.46442e21	+	4.98736e21i	−0.370342	+	1.26127i	−0.908308	+	0.418302i	$0.862625\pi$
$252$		−	1.74944e22i		−	4.26870i
$253$	−1.38743e21	−	2.32177e21i	−0.326682	−	0.546683i
$254$	−2.75939e21			−0.627061
$255$	−1.13074e22	−	3.32014e21i	−2.48028	−	0.728275i
$256$	−2.09801e22	+	2.42123e22i	−4.44271	+	5.12716i
$257$	1.27069e20	+	8.16621e19i	0.0259801	+	0.0166964i	0.553566	−	0.832805i	$-0.313267\pi$
$257$	1.27069e20	+	8.16621e19i	0.0259801	+	0.0166964i	−0.527586	+	0.849501i	$0.676903\pi$
$258$	−2.76360e21	−	3.97345e20i	−0.545629	−	0.0784496i
$259$	−3.58774e21	+	2.30570e21i	−0.684106	+	0.439648i
$260$	5.10779e21	−	2.33265e21i	0.940747	−	0.429625i
$261$	−1.83060e21	−	2.11262e21i	−0.325708	−	0.375887i
$262$	9.51255e20	+	6.61613e21i	0.163525	+	1.13734i
$263$	−2.61229e21	−	1.19299e21i	−0.433930	−	0.198169i	0.186460	−	0.982463i	$-0.440299\pi$
$263$	−2.61229e21	−	1.19299e21i	−0.433930	−	0.198169i	−0.620390	+	0.784293i	$0.713026\pi$
$264$	−7.02014e21	−	2.39084e22i	−1.12697	−	3.83809i
$265$	8.85101e21	−	2.59889e21i	1.37335	−	0.403251i
$266$	−3.67292e21	+	8.04258e21i	−0.550906	+	1.20632i
$267$	−7.67525e21	+	1.10354e21i	−1.11299	+	0.160024i
$268$	1.54938e22	−	1.34254e22i	2.17242	−	1.88242i
$269$	−2.64441e21	−	5.79045e21i	−0.358557	−	0.785130i	−0.999841	−	0.0178266i	$-0.994325\pi$
$269$	−2.64441e21	−	5.79045e21i	−0.358557	−	0.785130i	0.641284	−	0.767303i	$-0.278402\pi$
$270$	1.32942e22	+	2.06862e22i	1.74336	+	2.71273i
$271$	−2.78595e20	+	1.93767e21i	−0.0353386	+	0.245786i	−0.999832	−	0.0183209i	$-0.994168\pi$
$271$	−2.78595e20	+	1.93767e21i	−0.0353386	+	0.245786i	0.964494	+	0.264106i	$0.0850770\pi$
$272$	2.34644e22	−	3.65114e22i	2.87932	−	4.48031i
$273$	−2.32478e21	−	2.01444e21i	−0.276006	−	0.239161i
$274$	−5.84121e21	+	1.98933e22i	−0.671039	+	2.28535i
$275$		−	4.78260e21i		−	0.531704i
$276$	−3.84829e22	+	2.29963e22i	−4.14081	+	2.47443i
$277$	−3.48796e21			−0.363290			−0.181645	−	0.983364i	$-0.558142\pi$
$277$	−3.48796e21			−0.363290			−0.181645	+	0.983364i	$0.558142\pi$
$278$	−2.96470e22	−	8.70513e21i	−2.98935	−	0.877753i
$279$	1.06393e22	−	1.22784e22i	1.03866	−	1.19868i
$280$	3.87767e22	+	2.49202e22i	3.66563	+	2.35575i
$281$	2.91315e21	+	4.18848e20i	0.266689	+	0.0383442i	0.274362	−	0.961626i	$-0.411533\pi$
$281$	2.91315e21	+	4.18848e20i	0.266689	+	0.0383442i	−0.00767279	+	0.999971i	$0.502442\pi$
$282$	4.59341e22	−	2.95201e22i	4.07281	−	2.61743i
$283$	−1.68354e22	+	7.68846e21i	−1.44592	+	0.660330i	−0.975073	−	0.221884i	$-0.928779\pi$
$283$	−1.68354e22	+	7.68846e21i	−1.44592	+	0.660330i	−0.470848	+	0.882214i	$0.656052\pi$
$284$	3.38786e21	+	3.90980e21i	0.281877	+	0.325304i
$285$	−3.12748e21	−	2.17521e22i	−0.252110	−	1.75347i
$286$	−3.83888e21	−	1.75316e21i	−0.299854	−	0.136939i
$287$	4.80539e21	+	1.63656e22i	0.363740	+	1.23879i
$288$	−1.20317e23	+	3.53283e22i	−8.82664	+	2.59174i
$289$	−1.95697e21	+	4.28516e21i	−0.139156	+	0.304710i
$290$	1.10861e22	−	1.59394e21i	0.764180	−	0.109872i
$291$	1.23238e22	−	1.06787e22i	0.823586	−	0.713642i
$292$	−1.09216e22	−	2.39150e22i	−0.707688	−	1.54962i
$293$	−1.18778e22	−	1.84823e22i	−0.746326	−	1.16131i	−0.981891	−	0.189448i	$-0.939330\pi$
$293$	−1.18778e22	−	1.84823e22i	−0.746326	−	1.16131i	0.235564	−	0.971859i	$-0.424306\pi$
$294$	−2.17313e21	+	1.51144e22i	−0.132422	+	0.921014i
$295$	−7.60112e21	+	1.18276e22i	−0.449241	+	0.699032i
$296$	4.81970e22	+	4.17629e22i	2.76309	+	2.39423i
$297$	3.87866e21	−	1.32095e22i	0.215712	−	0.734647i
$298$		−	4.41226e22i		−	2.38075i
$299$	−8.71135e20	+	4.91649e21i	−0.0456084	+	0.257404i
$300$	−7.92704e22			−4.02736
$301$	−2.77451e21	−	8.14669e20i	−0.136801	−	0.0401683i
$302$	1.37988e22	−	1.59247e22i	0.660359	−	0.762094i
$303$	1.43288e22	+	9.20857e21i	0.665620	+	0.427768i
$304$	8.01092e22	+	1.15180e22i	3.61260	+	0.519414i
$305$	−2.86570e22	+	1.84167e22i	−1.25468	+	0.806332i
$306$	8.45855e22	−	3.86289e22i	3.59586	−	1.64218i
$307$	−7.39576e20	−	8.53516e20i	−0.0305308	−	0.0352344i	0.740279	−	0.672300i	$-0.234693\pi$
$307$	−7.39576e20	−	8.53516e20i	−0.0305308	−	0.0352344i	−0.770810	+	0.637066i	$0.780148\pi$
$308$	−5.58495e21	−	3.88442e22i	−0.223904	−	1.55729i
$309$	5.55000e22	+	2.53460e22i	2.16106	+	0.986922i
$310$	1.83391e22	+	6.24572e22i	0.693622	+	2.36226i
$311$	4.32477e22	−	1.26987e22i	1.58898	−	0.466568i	0.636531	−	0.771251i	$-0.280369\pi$
$311$	4.32477e22	−	1.26987e22i	1.58898	−	0.466568i	0.952454	+	0.304683i	$0.0985505\pi$
$312$	−1.91088e22	+	4.18425e22i	−0.682092	+	1.49357i
$313$	−2.89987e22	+	4.16938e21i	−1.00573	+	0.144601i	−0.625444	−	0.780269i	$-0.715082\pi$
$313$	−2.89987e22	+	4.16938e21i	−1.00573	+	0.144601i	−0.380281	+	0.924871i	$0.624173\pi$
$314$	−4.80804e22	+	4.16619e22i	−1.62032	+	1.40402i
$315$	2.51133e22	+	5.49904e22i	0.822447	+	1.80091i
$316$	−8.06963e20	−	1.25566e21i	−0.0256844	−	0.0399657i
$317$	6.75798e21	−	4.70028e22i	0.209066	−	1.45409i	−0.567147	−	0.823616i	$-0.691953\pi$
$317$	6.75798e21	−	4.70028e22i	0.209066	−	1.45409i	0.776213	−	0.630470i	$-0.217138\pi$
$318$	−6.21267e22	+	9.66711e22i	−1.86825	+	2.90705i
$319$	−4.73904e21	−	4.10640e21i	−0.138540	−	0.120045i
$320$	7.96548e22	−	2.71279e23i	2.26392	−	7.71022i
$321$		−	2.39747e22i		−	0.662534i
$322$	−5.75079e22	+	2.40319e22i	−1.54534	+	0.645782i
$323$	−3.50090e22			−0.914866
$324$	−2.84228e22	−	8.34570e21i	−0.722374	−	0.212108i
$325$	−5.78171e21	+	6.67245e21i	−0.142924	+	0.164943i
$326$	−1.15977e23	−	7.45337e22i	−2.78877	−	1.79223i
$327$	−2.03283e21	−	2.92277e20i	−0.0475524	−	0.00683700i
$328$	2.14568e23	−	1.37895e23i	4.88316	−	3.13822i
$329$	5.14400e22	−	2.34919e22i	1.13904	−	0.520181i
$330$	8.57457e22	+	9.89558e22i	1.84751	+	2.13214i
$331$	8.51805e21	+	5.92444e22i	0.178603	+	1.24221i	0.859999	+	0.510296i	$0.170464\pi$
$331$	8.51805e21	+	5.92444e22i	0.178603	+	1.24221i	−0.681396	+	0.731915i	$0.738627\pi$
$332$	1.50875e22	+	6.89023e21i	0.307875	+	0.140602i
$333$	2.35644e22	+	8.02529e22i	0.468013	+	1.59391i
$334$	−3.06763e22	+	9.00739e21i	−0.593042	+	0.174133i
$335$	−2.94295e22	+	6.44416e22i	−0.553833	+	1.21273i
$336$	−3.47910e23	+	5.00219e22i	−6.37402	+	0.916446i
$337$	4.35127e22	−	3.77039e22i	0.776152	−	0.672539i	−0.173854	−	0.984771i	$-0.555622\pi$
$337$	4.35127e22	−	3.77039e22i	0.776152	−	0.672539i	0.950006	+	0.312232i	$0.101077\pi$
$338$	−4.41234e22	−	9.66167e22i	−0.766334	−	1.67804i
$339$	−2.77500e22	−	4.31798e22i	−0.469316	−	0.730270i
$340$	−3.94983e22	+	2.74716e23i	−0.650531	+	4.52454i
$341$	1.97034e22	−	3.06591e22i	0.316047	−	0.491779i
$342$	1.31049e23	+	1.13554e23i	2.04738	+	1.77406i
$343$	−2.01152e22	+	6.85060e22i	−0.306109	+	1.04251i
$344$			4.32406e22i			0.641012i
$345$	8.79522e22	−	1.27526e23i	1.27021	−	1.84174i
$346$	1.94884e23			2.74215
$347$	−6.37998e22	−	1.87333e22i	−0.874690	−	0.256832i	−0.186581	−	0.982440i	$-0.559741\pi$
$347$	−6.37998e22	−	1.87333e22i	−0.874690	−	0.256832i	−0.688109	+	0.725607i	$0.741559\pi$
$348$	−6.80626e22	+	7.85484e22i	−0.909275	+	1.04936i
$349$	−6.90671e22	−	4.43867e22i	−0.899171	−	0.577862i	0.00737325	−	0.999973i	$-0.497653\pi$
$349$	−6.90671e22	−	4.43867e22i	−0.899171	−	0.577862i	−0.906544	+	0.422111i	$0.861289\pi$
$350$	−1.09087e23	−	1.56844e22i	−1.38408	−	0.199001i
$351$	−2.13804e22	+	1.37403e22i	−0.264394	+	0.169915i
$352$	−2.55871e23	+	1.16852e23i	−3.08416	+	1.40849i
$353$	3.76558e22	+	4.34571e22i	0.442445	+	0.510609i	0.932543	−	0.361058i	$-0.117584\pi$
$353$	3.76558e22	+	4.34571e22i	0.442445	+	0.510609i	−0.490098	+	0.871667i	$0.663039\pi$
$354$	−2.49251e22	−	1.73358e23i	−0.285501	−	1.98571i
$355$	−1.62616e22	−	7.42642e21i	−0.181597	−	0.0829324i
$356$	5.14495e22	+	1.75221e23i	0.560184	+	1.90781i
$357$	1.45884e23	−	4.28353e22i	1.54879	−	0.454766i
$358$	3.48883e22	−	7.63947e22i	0.361187	−	0.790890i
$359$	−8.32179e22	+	1.19649e22i	−0.840169	+	0.120798i	−0.548947	−	0.835857i	$-0.684971\pi$
$359$	−8.32179e22	+	1.19649e22i	−0.840169	+	0.120798i	−0.291222	+	0.956655i	$0.594062\pi$
$360$	6.83198e23	−	5.91994e23i	6.72704	−	5.82901i
$361$	1.61362e22	+	3.53334e22i	0.154966	+	0.339329i
$362$	1.47299e23	+	2.29202e23i	1.37982	+	2.14705i
$363$	−1.52903e22	+	1.06346e23i	−0.139719	+	0.971770i
$364$	−3.91671e22	+	6.09452e22i	−0.349147	+	0.543284i
$365$	6.86600e22	+	5.94942e22i	0.597129	+	0.517415i
$366$	1.19553e23	−	4.07159e23i	1.01445	−	3.45489i
$367$		−	1.01337e23i		−	0.839020i	−0.907751	−	0.419510i	$-0.862202\pi$
$367$		−	1.01337e23i		−	0.839020i	0.907751	−	0.419510i	$-0.137798\pi$
$368$	3.59376e23	+	4.43110e23i	2.90348	+	3.57998i
$369$	3.34515e23			2.63742
$370$	−3.21542e23	−	9.44133e22i	−2.47413	−	0.726470i
$371$	−7.79372e22	+	8.99443e22i	−0.585302	+	0.675474i
$372$	−5.08168e23	−	3.26579e23i	−3.72495	−	2.39388i
$373$	−2.03896e23	−	2.93158e22i	−1.45891	−	0.209760i	−0.633259	−	0.773940i	$-0.718283\pi$
$373$	−2.03896e23	−	2.93158e22i	−1.45891	−	0.209760i	−0.825652	+	0.564180i	$0.809192\pi$
$374$	1.75479e23	−	1.12774e23i	1.22569	−	0.787705i
$375$	−4.92763e22	+	2.25037e22i	−0.336014	+	0.153452i
$376$	−5.53773e23	−	6.39088e23i	−3.68673	−	4.25471i
$377$	1.64743e21	+	1.14581e22i	0.0107086	+	0.0744801i
$378$	−2.88579e23	−	1.31789e23i	−1.83163	−	0.836477i
$379$	4.90792e22	+	1.67148e23i	0.304190	+	1.03598i	0.959755	+	0.280837i	$0.0906122\pi$
$379$	4.90792e22	+	1.67148e23i	0.304190	+	1.03598i	−0.655565	+	0.755138i	$0.727570\pi$
$380$	−4.96585e23	+	1.45811e23i	−3.00567	+	0.882545i
$381$	−3.67583e22	+	8.04894e22i	−0.217285	+	0.475788i
$382$	1.49593e23	−	2.15082e22i	0.863655	−	0.124175i
$383$	−8.38124e22	+	7.26238e22i	−0.472628	+	0.409534i	−0.858337	−	0.513086i	$-0.828502\pi$
$383$	−8.38124e22	+	7.26238e22i	−0.472628	+	0.409534i	0.385710	+	0.922620i	$0.373957\pi$
$384$	7.99959e23	+	1.75167e24i	4.40643	+	9.64873i
$385$	7.33159e22	+	1.14082e23i	0.394504	+	0.613861i
$386$	4.24641e22	−	2.95344e23i	0.223222	−	1.55254i
$387$	−3.06604e22	+	4.77085e22i	−0.157463	+	0.245018i
$388$	−2.90238e23	−	2.51492e23i	−1.45636	−	1.26194i
$389$	9.36940e22	−	3.19092e23i	0.459373	−	1.56448i	−0.325946	−	0.945388i	$-0.605683\pi$
$389$	9.36940e22	−	3.19092e23i	0.459373	−	1.56448i	0.785319	−	0.619091i	$-0.212499\pi$
$390$		−	2.41717e23i		−	1.15804i
$391$	−1.81151e23	−	1.67601e23i	−0.848104	−	0.784666i
$392$	2.36488e23			1.08202
$393$	2.05659e23	+	6.03870e22i	0.919635	+	0.270029i
$394$	4.90992e23	−	5.66635e23i	2.14589	−	2.47649i
$395$	4.33902e21	+	2.78852e21i	0.0185361	+	0.0119124i
$396$	−7.61817e23	−	1.09533e23i	−3.18122	−	0.457391i
$397$	−3.45918e23	+	2.22308e23i	−1.41208	+	0.907486i	−0.999993	−	0.00366058i	$-0.998835\pi$
$397$	−3.45918e23	+	2.22308e23i	−1.41208	+	0.907486i	−0.412082	+	0.911147i	$0.635198\pi$
$398$	−6.73840e23	+	3.07733e23i	−2.68912	+	1.22808i
$399$	1.85669e23	+	2.14273e23i	0.724407	+	0.836010i
$400$	1.43570e23	+	9.98550e23i	0.547676	+	3.80917i
$401$	1.09540e23	+	5.00253e22i	0.408577	+	0.186591i	0.609092	−	0.793100i	$-0.291534\pi$
$401$	1.09540e23	+	5.00253e22i	0.408577	+	0.186591i	−0.200515	+	0.979691i	$0.564261\pi$
$402$	−2.48631e23	−	8.46761e23i	−0.906821	−	3.08835i
$403$	−6.45532e22	+	1.89545e22i	−0.230236	+	0.0676033i
$404$	1.66638e23	−	3.64886e23i	0.581220	−	1.27270i
$405$	1.01322e23	−	1.45679e22i	0.345627	−	0.0496937i
$406$	−1.09205e23	+	9.46269e22i	−0.364342	+	0.315704i
$407$	7.79417e22	+	1.70669e23i	0.254343	+	0.556934i
$408$	−1.22920e24	−	1.91267e24i	−3.92356	−	6.10518i
$409$	−2.05135e22	+	1.42675e23i	−0.0640517	+	0.445489i	0.932407	+	0.361409i	$0.117704\pi$
$409$	−2.05135e22	+	1.42675e23i	−0.0640517	+	0.445489i	−0.996459	+	0.0840800i	$0.973205\pi$
$410$	−7.24606e23	+	1.12751e24i	−2.21334	+	3.44402i
$411$	5.02462e23	+	4.35386e23i	1.50150	+	1.30106i
$412$	4.04829e23	−	1.37872e24i	1.18358	−	4.03090i
$413$		−	1.81390e23i		−	0.518876i
$414$	1.34473e23	+	1.21495e24i	0.376385	+	3.40060i
$415$	−5.73155e22			−0.156978
$416$	4.98242e23	+	1.46297e23i	1.33537	+	0.392099i
$417$	−6.48854e23	+	7.48817e23i	−1.70185	+	1.96404i
$418$	3.27228e23	+	2.10297e23i	0.839970	+	0.539816i
$419$	3.67415e22	+	5.28263e21i	0.0923062	+	0.0132716i	0.188313	−	0.982109i	$-0.439698\pi$
$419$	3.67415e22	+	5.28263e21i	0.0923062	+	0.0132716i	−0.0960070	+	0.995381i	$0.530607\pi$
$420$	1.89088e24	−	1.21519e24i	4.64965	−	2.98815i
$421$	−5.53334e23	+	2.52699e23i	−1.33183	+	0.608226i	−0.948907	−	0.315555i	$-0.897809\pi$
$421$	−5.53334e23	+	2.52699e23i	−1.33183	+	0.608226i	−0.382922	+	0.923781i	$0.625082\pi$
$422$	6.47938e23	+	7.47761e23i	1.52659	+	1.76178i
$423$	−1.57837e23	−	1.09778e24i	−0.364038	−	2.53194i
$424$	1.61886e24	+	7.39309e23i	3.65525	+	1.66929i
$425$	−1.22943e23	−	4.18706e23i	−0.271772	−	0.925570i
$426$	2.13677e23	−	6.27412e22i	0.462457	−	0.135790i
$427$	1.82571e23	−	3.99774e23i	0.386883	−	0.847156i
$428$	−5.58880e23	+	8.03548e22i	−1.15964	+	0.166732i
$429$	−1.02277e23	+	8.86232e22i	−0.207807	+	0.180066i
$430$	−9.43906e22	−	2.06687e23i	−0.187807	−	0.411241i
$431$	−2.45622e23	−	3.82196e23i	−0.478600	−	0.744716i	0.515059	−	0.857155i	$-0.327770\pi$
$431$	−2.45622e23	−	3.82196e23i	−0.478600	−	0.744716i	−0.993659	+	0.112439i	$0.964134\pi$
$432$	−4.13280e23	+	2.87442e24i	−0.788661	+	5.48526i
$433$	1.51259e23	−	2.35364e23i	0.282703	−	0.439895i	−0.670640	−	0.741783i	$-0.733980\pi$
$433$	1.51259e23	−	2.35364e23i	0.282703	−	0.439895i	0.953343	+	0.301888i	$0.0976169\pi$
$434$	−6.34694e23	−	5.49965e23i	−1.16187	−	1.00676i
$435$	1.01185e23	−	3.44605e23i	0.181432	−	0.617901i
$436$			4.83674e22i			0.0849521i
$437$	1.43964e23	−	4.37109e23i	0.247697	−	0.752068i
$438$	−1.13174e24			−1.90756
$439$	1.31854e23	+	3.87157e22i	0.217726	+	0.0639303i	0.388777	−	0.921332i	$-0.372898\pi$
$439$	1.31854e23	+	3.87157e22i	0.217726	+	0.0639303i	−0.171050	+	0.985262i	$0.554716\pi$
$440$	1.32796e24	−	1.53255e24i	2.14838	−	2.47937i
$441$	2.60924e23	+	1.67685e23i	0.413586	+	0.265796i
$442$	−3.81153e23	−	5.48015e22i	−0.591969	−	0.0851123i
$443$	9.78556e22	−	6.28880e22i	0.148920	−	0.0957049i	−0.464059	−	0.885804i	$-0.653607\pi$
$443$	9.78556e22	−	6.28880e22i	0.148920	−	0.0957049i	0.612979	+	0.790099i	$0.289971\pi$
$444$	2.82879e24	−	1.29187e24i	4.21846	−	1.92651i
$445$	−4.13250e23	−	4.76916e23i	−0.603911	−	0.696951i
$446$	1.70250e23	+	1.18411e24i	0.243822	+	1.69582i
$447$	−1.28702e24	−	5.87764e23i	−1.80642	−	0.824964i
$448$	1.02768e24	+	3.49995e24i	1.41369	+	4.81459i
$449$	−5.00402e23	+	1.46931e23i	−0.674687	+	0.198106i	−0.601089	−	0.799182i	$-0.705266\pi$
$449$	−5.00402e23	+	1.46931e23i	−0.674687	+	0.198106i	−0.0735977	+	0.997288i	$0.523448\pi$
$450$	−8.97893e23	+	1.96611e24i	−1.18662	+	2.59834i
$451$	7.42749e23	−	1.06791e23i	0.962173	−	0.138340i
$452$	−9.13565e23	+	7.91609e23i	−1.16010	+	1.00523i
$453$	−2.80695e23	−	6.14637e23i	−0.349423	−	0.765129i
$454$	8.62942e23	+	1.34276e24i	1.05312	+	1.63869i
$455$	3.56273e22	−	2.47793e23i	0.0426266	−	0.296474i
$456$	2.29217e24	−	3.56668e24i	2.68882	−	4.18389i
$457$	8.07244e23	+	6.99481e23i	0.928452	+	0.804508i	0.980979	−	0.194112i	$-0.0621824\pi$
$457$	8.07244e23	+	6.99481e23i	0.928452	+	0.804508i	−0.0525279	+	0.998619i	$0.516728\pi$
$458$	−3.59282e23	+	1.22360e24i	−0.405178	+	1.37991i
$459$		−	1.25617e24i		−	1.38910i
$460$	−3.26758e24	−	1.62285e24i	−3.54328	−	1.75978i
$461$	−1.13710e24			−1.20918			−0.604589	−	0.796538i	$-0.706663\pi$
$461$	−1.13710e24			−1.20918			−0.604589	+	0.796538i	$0.706663\pi$
$462$	−1.62088e24	−	4.75933e23i	−1.69033	−	0.496327i
$463$	−7.12798e22	+	8.22612e22i	−0.0729016	+	0.0841330i	−0.791029	−	0.611779i	$-0.790454\pi$
$463$	−7.12798e22	+	8.22612e22i	−0.0729016	+	0.0841330i	0.718127	+	0.695912i	$0.245000\pi$
$464$	1.11273e24	+	7.15106e23i	1.11616	+	0.717313i
$465$	2.06613e24	+	2.97065e23i	2.03274	+	0.292263i
$466$	−6.09425e23	+	3.91654e23i	−0.588095	+	0.377946i
$467$	1.35405e24	−	6.18374e23i	1.28169	−	0.585328i	0.346027	−	0.938224i	$-0.387530\pi$
$467$	1.35405e24	−	6.18374e23i	1.28169	−	0.585328i	0.935662	+	0.352896i	$0.114803\pi$
$468$	9.30435e23	+	1.07378e24i	0.863920	+	0.997017i
$469$	−1.30076e23	−	9.04695e23i	−0.118479	−	0.824037i
$470$	4.04206e24	+	1.84595e24i	3.61179	+	1.64945i
$471$	5.74760e23	+	1.95745e24i	0.503847	+	1.71594i
$472$	−2.60257e24	+	7.64185e23i	−2.23834	+	0.657235i
$473$	−5.28470e22	+	1.15719e23i	−0.0445933	+	0.0976458i
$474$	−6.35976e22	+	9.14396e21i	−0.0526545	+	0.00757058i
$475$	6.14993e23	−	5.32894e23i	0.499606	−	0.432911i
$476$	−1.48749e24	−	3.25716e24i	−1.18575	−	2.59643i
$477$	1.26191e24	+	1.96358e24i	0.987107	+	1.53597i
$478$	−1.85567e23	+	1.29065e24i	−0.142446	+	0.990733i
$479$	−1.19602e24	+	1.86104e24i	−0.900986	+	1.40196i	0.0146236	+	0.999893i	$0.495345\pi$
$479$	−1.19602e24	+	1.86104e24i	−0.900986	+	1.40196i	−0.915610	+	0.402068i	$0.868291\pi$
$480$	−1.21759e25	−	1.05505e25i	−9.00181	−	7.80011i
$481$	9.75817e22	−	3.32333e23i	0.0708048	−	0.241139i
$482$			4.58128e23i			0.326259i
$483$	−6.50777e22	+	1.99759e24i	−0.0454892	+	1.39631i
$484$	2.53031e24			1.73606
$485$	1.27332e24	+	3.73881e23i	0.857556	+	0.251801i
$486$	1.52298e24	−	1.75761e24i	1.00686	−	1.16197i
$487$	2.43560e24	+	1.56527e24i	1.58069	+	1.01585i	0.975564	+	0.219713i	$0.0705122\pi$
$487$	2.43560e24	+	1.56527e24i	1.58069	+	1.01585i	0.605122	+	0.796132i	$0.293124\pi$
$488$	−6.50509e24	−	9.35290e23i	−4.14452	−	0.595893i
$489$	−3.71904e24	+	2.39008e24i	−2.32622	+	1.49497i
$490$	−1.13039e24	+	5.16233e23i	−0.694168	+	0.317016i
$491$	−1.20548e23	−	1.39119e23i	−0.0726817	−	0.0838791i	0.718244	−	0.695791i	$-0.244946\pi$
$491$	−1.20548e23	−	1.39119e23i	−0.0726817	−	0.0838791i	−0.790926	+	0.611912i	$0.790401\pi$
$492$	−1.77004e24	−	1.23109e25i	−1.04784	−	7.28791i
$493$	−5.20453e23	−	2.37683e23i	−0.302524	−	0.138158i
$494$	−2.02304e23	−	6.88983e23i	−0.115468	−	0.393248i
$495$	2.55186e24	−	7.49293e23i	1.43024	−	0.419957i
$496$	−3.19348e24	+	6.99274e24i	−1.75764	+	3.84869i
$497$	2.28296e23	−	3.28241e22i	0.123393	−	0.0177413i
$498$	5.39596e23	−	4.67562e23i	0.286421	−	0.248185i
$499$	−1.20379e24	−	2.63594e24i	−0.627548	−	1.37414i	−0.909900	−	0.414828i	$-0.863842\pi$
$499$	−1.20379e24	−	2.63594e24i	−0.627548	−	1.37414i	0.282351	−	0.959311i	$-0.408886\pi$
$500$	6.89746e23	+	1.07327e24i	0.353150	+	0.549512i
$501$	−1.45905e23	+	1.01479e24i	−0.0733723	+	0.510315i
$502$	2.84895e24	−	4.43306e24i	1.40719	−	2.18963i
$503$	9.11935e23	+	7.90196e23i	0.442437	+	0.383374i	0.847396	−	0.530961i	$-0.178169\pi$
$503$	9.11935e23	+	7.90196e23i	0.442437	+	0.383374i	−0.404959	+	0.914335i	$0.632714\pi$
$504$	−3.28587e24	+	1.11907e25i	−1.56594	+	5.33311i
$505$			1.38615e24i			0.648917i
$506$	6.86443e23	+	2.65471e24i	0.315682	+	1.22085i
$507$	−3.40601e24			−1.53877
$508$	1.99951e24	+	5.87108e23i	0.887461	+	0.260582i
$509$	−6.58109e23	+	7.59498e23i	−0.286971	+	0.331182i	−0.880871	−	0.473357i	$-0.843042\pi$
$509$	−6.58109e23	+	7.59498e23i	−0.286971	+	0.331182i	0.593900	+	0.804539i	$0.297588\pi$
$510$	1.00506e25	+	6.45916e24i	4.30589	+	2.76722i
$511$	−1.16019e24	−	1.66810e23i	−0.488360	−	0.0702155i
$512$	1.42602e25	−	9.16447e24i	5.89788	−	3.79034i
$513$	2.13078e24	−	9.73095e23i	0.865929	−	0.395457i
$514$	−1.00278e23	−	1.15728e23i	−0.0400442	−	0.0462135i
$515$	7.06652e23	+	4.91487e24i	0.277294	+	1.92862i
$516$	1.91801e24	+	8.75926e23i	0.739612	+	0.337769i
$517$	−7.00916e23	−	2.38710e24i	−0.265614	−	0.904598i
$518$	4.14842e24	−	1.21809e24i	1.54495	−	0.453639i
$519$	2.59608e24	−	5.68461e24i	0.950192	−	2.08063i
$520$	−3.70542e24	+	5.32759e23i	−1.33293	+	0.191646i
$521$	−1.04042e24	+	9.01526e23i	−0.367847	+	0.318742i	−0.819096	−	0.573657i	$-0.805524\pi$
$521$	−1.04042e24	+	9.01526e23i	−0.367847	+	0.318742i	0.451248	+	0.892398i	$0.350979\pi$
$522$	1.17726e24	+	2.57784e24i	0.409108	+	0.895822i
$523$	−2.70234e24	−	4.20492e24i	−0.923047	−	1.43629i	−0.899674	−	0.436563i	$-0.856196\pi$
$523$	−2.70234e24	−	4.20492e24i	−0.923047	−	1.43629i	−0.0233738	−	0.999727i	$-0.507441\pi$
$524$	7.18397e23	−	4.99656e24i	0.241203	−	1.67760i
$525$	−1.91067e24	+	2.97306e24i	−0.630597	+	0.981229i
$526$	2.20030e24	+	1.90657e24i	0.713854	+	0.618558i
$527$	9.36858e23	−	3.19064e24i	0.298798	−	1.01761i
$528$			1.54634e25i			4.84840i
$529$	2.83752e24	−	1.57257e24i	0.874658	−	0.484740i
$530$	−9.35186e24			−2.83410
$531$	−3.41335e24	−	1.00225e24i	−1.01702	−	0.298624i
$532$	4.37266e24	−	5.04632e24i	1.28098	−	1.47833i
$533$	−1.16535e24	−	7.48923e23i	−0.335668	−	0.215721i
$534$	7.78108e24	+	1.11875e24i	2.20378	+	0.316856i
$535$	1.64138e24	−	1.05485e24i	0.457114	−	0.293770i
$536$	−1.24325e25	+	5.67774e24i	−3.40468	+	1.55486i
$537$	−1.76362e24	−	2.03533e24i	−0.474939	−	0.548109i
$538$	9.18425e23	+	6.38779e24i	0.243222	+	1.69165i
$539$	6.32880e23	+	2.89026e23i	0.164825	+	0.0752729i
$540$	−5.23188e24	−	1.78181e25i	−1.34003	−	4.56371i
$541$	−1.80979e24	+	5.31402e23i	−0.455882	+	0.133859i	−0.501608	−	0.865095i	$-0.667258\pi$
$541$	−1.80979e24	+	5.31402e23i	−0.455882	+	0.133859i	0.0457260	+	0.998954i	$0.485440\pi$
$542$	8.24428e23	−	1.80524e24i	0.204249	−	0.447242i
$543$	8.64784e24	−	1.24337e24i	2.10722	−	0.302972i
$544$	−1.93971e25	+	1.68077e25i	−4.64886	+	4.02826i
$545$	−6.94313e22	−	1.52033e23i	−0.0163677	−	0.0358402i
$546$	1.68601e24	+	2.62349e24i	0.390955	+	0.608338i
$547$	−1.95407e23	+	1.35909e24i	−0.0445713	+	0.310000i	0.955324	+	0.295559i	$0.0955060\pi$
$547$	−1.95407e23	+	1.35909e24i	−0.0445713	+	0.310000i	−0.999896	+	0.0144410i	$0.995403\pi$
$548$	8.46529e24	−	1.31722e25i	1.89940	−	2.95553i
$549$	−6.51405e24	−	5.64446e24i	−1.43781	−	1.24587i
$550$	−1.36599e24	+	4.65214e24i	−0.296609	+	1.01016i
$551$		−	1.06694e24i		−	0.227917i
$552$	2.89355e25	−	7.48200e24i	6.08107	−	1.57241i
$553$	−6.65442e22			−0.0137589
$554$	3.39282e24	+	9.96222e23i	0.690197	+	0.202660i
$555$	−7.03728e24	+	8.12145e24i	−1.40854	+	1.62554i
$556$	1.96306e25	+	1.26158e25i	3.86598	+	2.48451i
$557$	−6.35284e24	−	9.13400e23i	−1.23104	−	0.176996i	−0.504066	−	0.863665i	$-0.668163\pi$
$557$	−6.35284e24	−	9.13400e23i	−1.23104	−	0.176996i	−0.726970	+	0.686669i	$0.759072\pi$
$558$	−1.38560e25	+	8.90471e24i	−2.64198	+	1.69790i
$559$	2.13623e23	−	9.75582e22i	0.0400812	−	0.0183045i
$560$	−1.87322e25	−	2.16181e25i	−3.45856	−	3.99139i
$561$	−9.51939e23	−	6.62088e24i	−0.172959	−	1.20296i
$562$	−2.71406e24	−	1.23947e24i	−0.485280	−	0.221620i
$563$	8.24853e23	+	2.80919e24i	0.145145	+	0.494318i	0.999686	−	0.0250663i	$-0.00797969\pi$
$563$	8.24853e23	+	2.80919e24i	0.145145	+	0.494318i	−0.854541	+	0.519384i	$0.826162\pi$
$564$	−3.95656e25	+	1.16175e25i	−6.85182	+	2.01188i
$565$	1.73526e24	−	3.79969e24i	0.295752	−	0.647608i
$566$	1.85721e25	−	2.67026e24i	3.11539	−	0.447926i
$567$	−9.98089e23	+	8.64849e23i	−0.164787	+	0.142788i
$568$	−1.43276e24	−	3.13730e24i	−0.232829	−	0.509824i
$569$	−4.48361e24	−	6.97664e24i	−0.717163	−	1.11593i	−0.988172	−	0.153350i	$-0.950994\pi$
$569$	−4.48361e24	−	6.97664e24i	−0.717163	−	1.11593i	0.271009	−	0.962577i	$-0.412643\pi$
$570$	−3.17060e24	+	2.20520e25i	−0.499192	+	3.47196i
$571$	−4.10681e24	+	6.39031e24i	−0.636472	+	0.990370i	0.361837	+	0.932241i	$0.382150\pi$
$571$	−4.10681e24	+	6.39031e24i	−0.636472	+	0.990370i	−0.998309	+	0.0581282i	$0.981487\pi$
$572$	2.40871e24	+	2.08716e24i	0.367468	+	0.318413i
$573$	1.36537e24	−	4.65002e24i	0.205049	−	0.698334i
$574$		−	1.72917e25i		−	2.55642i
$575$	5.73337e24	+	1.86782e23i	0.834448	+	0.0271847i
$576$	7.15393e25			10.2504
$577$	3.23185e24	+	9.48956e23i	0.455899	+	0.133864i	0.501616	−	0.865090i	$-0.332739\pi$
$577$	3.23185e24	+	9.48956e23i	0.455899	+	0.133864i	−0.0457170	+	0.998954i	$0.514557\pi$
$578$	3.12750e24	−	3.60933e24i	0.434358	−	0.501275i
$579$	−8.04930e24	−	5.17297e24i	−1.10065	−	0.707348i
$580$	−8.37230e24	−	1.20376e24i	−1.12718	−	0.162064i
$581$	6.22077e23	−	3.99784e23i	0.0824629	−	0.0529957i
$582$	−1.50377e25	+	6.86748e24i	−1.96279	+	0.896377i
$583$	3.42877e24	+	3.95701e24i	0.440678	+	0.508570i
$584$	2.49442e24	+	1.73490e25i	0.315685	+	2.19563i
$585$	−4.46605e24	−	2.03958e24i	−0.556571	−	0.254178i
$586$	6.27499e24	+	2.13706e25i	0.770077	+	2.62264i
$587$	5.33307e24	−	1.56593e24i	0.644517	−	0.189247i	0.0568918	−	0.998380i	$-0.481881\pi$
$587$	5.33307e24	−	1.56593e24i	0.644517	−	0.189247i	0.587626	+	0.809133i	$0.300063\pi$
$588$	4.79054e24	−	1.04898e25i	0.570150	−	1.24845i
$589$	6.13787e24	−	8.82493e23i	0.719416	−	0.103436i
$590$	1.07719e25	−	9.33393e24i	1.24344	−	1.07745i
$591$	−9.98774e24	−	2.18701e25i	−1.13548	−	2.48636i
$592$	−2.13967e25	−	3.32938e25i	−2.39580	−	3.72794i
$593$	1.82134e24	−	1.26677e25i	0.200863	−	1.39703i	−0.600869	−	0.799347i	$-0.705179\pi$
$593$	1.82134e24	−	1.26677e25i	0.200863	−	1.39703i	0.801732	−	0.597684i	$-0.203912\pi$
$594$	−7.54572e24	+	1.17414e25i	−0.819639	+	1.27538i
$595$	9.35129e24	+	8.10294e24i	1.00050	+	0.866941i
$596$	−9.38783e24	+	3.19720e25i	−0.989348	+	3.36941i
$597$			2.37548e25i			2.46594i
$598$	2.25161e24	−	4.53357e24i	0.230241	−	0.463586i
$599$	8.04624e24			0.810498			0.405249	−	0.914206i	$-0.367185\pi$
$599$	8.04624e24			0.810498			0.405249	+	0.914206i	$0.367185\pi$
$600$	5.07068e25	+	1.48889e25i	5.03159	+	1.47741i
$601$	−3.56657e24	+	4.11604e24i	−0.348642	+	0.402355i	−0.902803	−	0.430055i	$-0.858494\pi$
$601$	−3.56657e24	+	4.11604e24i	−0.348642	+	0.402355i	0.554160	+	0.832410i	$0.313040\pi$
$602$	2.46614e24	+	1.58489e24i	0.237493	+	0.152627i
$603$	−1.77430e25	−	2.55106e24i	−1.68334	−	0.242027i
$604$	−1.33871e25	+	8.60339e24i	−1.25128	+	0.804150i
$605$	−7.95354e24	+	3.63226e24i	−0.732423	+	0.334486i
$606$	−1.13078e25	−	1.30499e25i	−1.02595	−	1.18401i
$607$	−8.71337e23	−	6.06028e24i	−0.0778911	−	0.541744i	−0.990983	−	0.133990i	$-0.957221\pi$
$607$	−8.71337e23	−	6.06028e24i	−0.0778911	−	0.541744i	0.913092	−	0.407755i	$-0.133688\pi$
$608$	−4.35360e25	−	1.98822e25i	−3.83457	−	1.75119i
$609$	1.30546e24	+	4.44598e24i	0.113294	+	0.385844i
$610$	3.31354e25	−	9.72944e24i	2.83350	−	0.831992i
$611$	−1.90789e24	+	4.17771e24i	−0.160762	+	0.352020i
$612$	−6.95112e25	+	9.99420e24i	−5.77154	+	0.829822i
$613$	−3.49825e24	+	3.03125e24i	−0.286224	+	0.248015i	−0.786124	−	0.618068i	$-0.787916\pi$
$613$	−3.49825e24	+	3.03125e24i	−0.286224	+	0.248015i	0.499900	+	0.866083i	$0.333370\pi$
$614$	4.75624e23	+	1.04147e24i	0.0383485	+	0.0839714i
$615$	2.32360e25	+	3.61560e25i	1.84623	+	2.87279i
$616$	−3.72334e24	+	2.58964e25i	−0.291545	+	2.02774i
$617$	3.14177e23	−	4.88869e23i	0.0242442	−	0.0377247i	−0.828920	−	0.559367i	$-0.811044\pi$
$617$	3.14177e23	−	4.88869e23i	0.0242442	−	0.0377247i	0.853164	+	0.521643i	$0.174681\pi$
$618$	−4.67468e25	−	4.05064e25i	−3.55513	−	3.08054i
$619$	7.22588e24	−	2.46091e25i	0.541596	−	1.84451i	0.00607722	−	0.999982i	$-0.498066\pi$
$619$	7.22588e24	−	2.46091e25i	0.541596	−	1.84451i	0.535518	−	0.844524i	$-0.320116\pi$
$620$		−	4.91596e25i		−	3.63148i
$621$	1.56841e25	+	5.16562e24i	1.14192	+	0.376096i
$622$	−4.56950e25			−3.27910
$623$	7.81180e24	+	2.29375e24i	0.552534	+	0.162239i
$624$	1.86937e25	−	2.15737e25i	1.30327	−	1.50406i
$625$	−1.39294e25	−	8.95186e24i	−0.957219	−	0.615167i
$626$	2.93985e25	+	4.22687e24i	1.99139	+	0.286319i
$627$	1.04933e25	−	6.74360e24i	0.700652	−	0.450282i
$628$	4.37042e25	−	1.99590e25i	2.87665	−	1.31372i
$629$	1.12109e25	+	1.29381e25i	0.727420	+	0.839487i
$630$	−8.72204e24	−	6.06631e25i	−0.557896	−	3.88025i
$631$	−1.65931e25	−	7.57781e24i	−1.04632	−	0.477837i	−0.183324	−	0.983053i	$-0.558686\pi$
$631$	−1.65931e25	−	7.57781e24i	−1.04632	−	0.477837i	−0.862993	+	0.505216i	$0.831413\pi$
$632$	2.80346e23	+	9.54772e23i	0.0174277	+	0.0593535i
$633$	3.04429e25	−	8.93884e24i	1.86575	−	0.547833i
$634$	−1.99984e25	+	4.37905e25i	−1.20835	+	2.64592i
$635$	−7.12784e24	+	1.02483e24i	−0.424614	+	0.0610503i
$636$	6.55866e25	−	5.68311e25i	3.85213	−	3.33789i
$637$	−5.33557e23	−	1.16833e24i	−0.0308977	−	0.0676565i
$638$	3.43691e24	+	5.34794e24i	0.196238	+	0.305352i
$639$	6.43750e23	−	4.47738e24i	0.0362418	−	0.252067i
$640$	−8.47272e25	+	1.31838e26i	−4.70330	+	7.31848i
$641$	−9.08639e24	−	7.87340e24i	−0.497358	−	0.430963i	0.369714	−	0.929145i	$-0.379456\pi$
$641$	−9.08639e24	−	7.87340e24i	−0.497358	−	0.430963i	−0.867072	+	0.498182i	$0.834001\pi$
$642$	−6.84759e24	+	2.33208e25i	−0.369592	+	1.25872i
$643$			6.80847e24i			0.362369i	0.983449	+	0.181184i	$0.0579931\pi$
$643$			6.80847e24i			0.362369i	−0.983449	+	0.181184i	$0.942007\pi$
$644$	4.67844e25	−	5.17819e24i	2.45544	−	0.271772i
$645$	−7.28628e24			−0.377110
$646$	3.40541e25	+	9.99918e24i	1.73811	+	0.510354i
$647$	6.01048e23	−	6.93646e23i	0.0302531	−	0.0349140i	−0.740421	−	0.672143i	$-0.765374\pi$
$647$	6.01048e23	−	6.93646e23i	0.0302531	−	0.0349140i	0.770674	+	0.637229i	$0.219919\pi$
$648$	1.66137e25	+	1.06770e25i	0.824690	+	0.529996i
$649$	−7.89886e24	−	1.13568e24i	−0.386689	−	0.0555975i
$650$	7.52976e24	−	4.83909e24i	0.363548	−	0.233638i
$651$	−2.44969e25	+	1.11874e25i	−1.16649	+	0.532720i
$652$	6.81805e25	+	7.86845e25i	3.20208	+	3.69539i
$653$	−1.39999e24	−	9.73714e24i	−0.0648494	−	0.451038i	−0.996213	−	0.0869471i	$-0.972289\pi$
$653$	−1.39999e24	−	9.73714e24i	−0.0648494	−	0.451038i	0.931363	−	0.364091i	$-0.118620\pi$
$654$	1.89390e24	+	8.64917e23i	0.0865283	+	0.0395161i
$655$	4.91442e24	+	1.67370e25i	0.221462	+	0.754232i
$656$	−1.51871e26	+	4.45935e25i	−6.75058	+	1.98215i
$657$	−9.54945e24	+	2.09104e25i	−0.418687	+	0.916797i
$658$	−5.67465e25	+	8.15892e24i	−2.45418	+	0.352858i
$659$	−5.24260e24	+	4.54274e24i	−0.223655	+	0.193798i	−0.759479	−	0.650531i	$-0.774546\pi$
$659$	−5.24260e24	+	4.54274e24i	−0.223655	+	0.193798i	0.535825	+	0.844329i	$0.320001\pi$
$660$	−4.10783e25	−	8.99490e25i	−1.72869	−	3.78531i
$661$	7.22284e24	+	1.12390e25i	0.299843	+	0.466566i	0.958183	−	0.286155i	$-0.0923773\pi$
$661$	7.22284e24	+	1.12390e25i	0.299843	+	0.466566i	−0.658340	+	0.752721i	$0.728741\pi$
$662$	8.63550e24	−	6.00612e25i	0.353643	−	2.45964i
$663$	−6.67592e24	+	1.03879e25i	−0.269705	+	0.419669i
$664$	−8.35685e24	−	7.24125e24i	−0.333066	−	0.288603i
$665$	−6.50062e24	+	2.21391e25i	−0.255600	+	0.870492i
$666$		−	8.47942e25i		−	3.28926i
$667$	5.10783e24	−	5.52078e24i	0.195481	−	0.211285i
$668$	2.41451e25			0.911677
$669$	3.68076e25	+	1.08077e25i	1.37121	+	0.402622i
$670$	4.70323e25	−	5.42782e25i	1.72871	−	1.99504i
$671$	−1.62656e25	−	1.04532e25i	−0.589884	−	0.379095i
$672$	2.05743e26	+	2.95814e25i	7.36210	+	1.05851i
$673$	−8.46738e24	+	5.44166e24i	−0.298960	+	0.192130i	−0.681518	−	0.731802i	$-0.738680\pi$
$673$	−8.46738e24	+	5.44166e24i	−0.298960	+	0.192130i	0.382557	+	0.923932i	$0.375043\pi$
$674$	−5.30946e25	+	2.42475e25i	−1.84974	+	0.844750i
$675$	1.91210e25	+	2.20668e25i	0.657318	+	0.758586i
$676$	1.14157e25	+	7.93982e25i	0.387243	+	2.69334i
$677$	8.42405e24	+	3.84713e24i	0.281983	+	0.128777i	0.551386	−	0.834250i	$-0.314099\pi$
$677$	8.42405e24	+	3.84713e24i	0.281983	+	0.128777i	−0.269403	+	0.963027i	$0.586826\pi$
$678$	1.46601e25	+	4.99278e25i	0.484251	+	1.64921i
$679$	−1.64280e25	+	4.82368e24i	−0.535495	+	0.157236i
$680$	7.68641e25	−	1.68309e26i	2.47254	−	5.41410i
$681$	5.06628e25	−	7.28421e24i	1.60829	−	0.231238i
$682$	−2.79227e25	+	2.41952e25i	−0.874779	+	0.758001i
$683$	1.79273e25	+	3.92553e25i	0.554278	+	1.21370i	0.954755	+	0.297393i	$0.0961173\pi$
$683$	1.79273e25	+	3.92553e25i	0.554278	+	1.21370i	−0.400477	+	0.916307i	$0.631155\pi$
$684$	−7.07996e25	−	1.10166e26i	−2.16036	−	3.36159i
$685$	−7.70023e24	+	5.35563e25i	−0.231893	+	1.61285i
$686$	3.91330e25	−	6.08921e25i	1.16312	−	1.80986i
$687$	3.09055e25	+	2.67798e25i	0.906620	+	0.785591i
$688$	7.56004e24	−	2.57471e25i	0.218891	−	0.745475i
$689$		−	9.66569e24i		−	0.276223i
$690$	−1.21977e26	+	9.89271e25i	−3.44061	+	2.79044i
$691$	1.82089e25			0.506968			0.253484	−	0.967340i	$-0.418423\pi$
$691$	1.82089e25			0.506968			0.253484	+	0.967340i	$0.418423\pi$
$692$	−1.41216e26	−	4.14648e25i	−3.88088	−	1.13953i
$693$	−2.24703e25	+	2.59321e25i	−0.609550	+	0.703458i
$694$	5.67090e25	+	3.64446e25i	1.51851	+	0.975885i
$695$	−7.98148e25	−	1.14756e25i	−2.10970	−	0.303329i
$696$	5.82908e25	−	3.74612e25i	1.52096	−	0.977459i
$697$	6.22809e25	−	2.84427e25i	1.60420	−	0.732616i
$698$	5.45055e25	+	6.29027e25i	1.38593	+	1.59945i
$699$	3.30600e24	+	2.29938e25i	0.0829868	+	0.577186i
$700$	7.57095e25	+	3.45754e25i	1.87615	+	0.856810i
$701$	1.81496e25	+	6.18119e25i	0.444023	+	1.51220i	0.812720	+	0.582654i	$0.197986\pi$
$701$	1.81496e25	+	6.18119e25i	0.444023	+	1.51220i	−0.368697	+	0.929550i	$0.620196\pi$
$702$	2.47216e25	−	7.25893e24i	0.597095	−	0.175323i
$703$	−1.32617e25	+	2.90390e25i	−0.316228	+	0.692443i
$704$	1.58844e26	−	2.28383e25i	3.73953	−	0.537663i
$705$	1.07690e26	−	9.33138e25i	2.50307	−	2.16892i
$706$	−2.42166e25	−	5.30268e25i	−0.555738	−	1.21690i
$707$	−9.66864e24	−	1.50447e25i	−0.219074	−	0.340886i
$708$	−1.88237e25	+	1.30922e26i	−0.421120	+	2.92895i
$709$	4.32653e25	−	6.73221e25i	0.955704	−	1.48710i	0.0843577	−	0.996436i	$-0.473116\pi$
$709$	4.32653e25	−	6.73221e25i	0.955704	−	1.48710i	0.871346	−	0.490669i	$-0.163247\pi$
$710$	1.36969e25	+	1.18684e25i	0.298743	+	0.258862i
$711$	−3.67682e23	+	1.25221e24i	−0.00791855	+	0.0269681i
$712$		−	1.21747e26i		−	2.58903i
$713$	3.59846e25	+	2.48178e25i	0.755633	+	0.521144i
$714$	−1.54139e26			−3.19616
$715$	−1.05674e25	−	3.10287e24i	−0.216378	−	0.0635345i
$716$	−4.15350e25	+	4.79339e25i	−0.839840	+	0.969227i
$717$	3.51753e25	+	2.26058e25i	0.702368	+	0.451385i
$718$	8.43653e25	+	1.21299e25i	1.66358	+	0.239187i
$719$	−2.62363e25	+	1.68610e25i	−0.510908	+	0.328341i	−0.770566	−	0.637360i	$-0.780026\pi$
$719$	−2.62363e25	+	1.68610e25i	−0.510908	+	0.328341i	0.259658	+	0.965701i	$0.416390\pi$
$720$	−5.10304e26	+	2.33048e26i	−9.81379	+	4.48181i
$721$	−4.19517e25	−	4.84148e25i	−0.796769	−	0.919520i
$722$	−5.60425e24	−	3.89784e25i	−0.105119	−	0.731122i
$723$	1.33632e25	+	6.10279e24i	0.247552	+	0.113053i
$724$	−5.79690e25	−	1.97424e26i	−1.06059	−	3.61205i
$725$	1.27606e25	−	3.74684e24i	0.230583	−	0.0677054i
$726$	4.52476e25	−	9.90785e25i	0.807544	−	1.76827i
$727$	−2.12373e25	+	3.05346e24i	−0.374360	+	0.0538248i	−0.326927	−	0.945050i	$-0.606013\pi$
$727$	−2.12373e25	+	3.05346e24i	−0.374360	+	0.0538248i	−0.0474328	+	0.998874i	$0.515104\pi$
$728$	3.65009e25	−	3.16282e25i	0.635508	−	0.550671i
$729$	−3.72073e25	−	8.14727e25i	−0.639854	−	1.40108i
$730$	−4.97946e25	−	7.74819e25i	−0.845817	−	1.31612i
$731$	−1.65193e24	+	1.14894e25i	−0.0277163	+	0.192771i
$732$	−1.73260e26	+	2.69598e26i	−2.87143	+	4.46804i
$733$	−5.95266e25	−	5.15801e25i	−0.974485	−	0.844396i	0.0133487	−	0.999911i	$-0.495751\pi$
$733$	−5.95266e25	−	5.15801e25i	−0.974485	−	0.844396i	−0.987834	+	0.155515i	$0.950296\pi$
$734$	−2.89435e25	+	9.85725e25i	−0.468044	+	1.59401i
$735$			3.98495e25i			0.636557i
$736$	−1.30089e26	−	3.11301e26i	−2.05278	−	4.91225i
$737$	−4.02105e25			−0.626804
$738$	−3.25391e26	−	9.55433e25i	−5.01069	−	1.47127i
$739$	−3.48945e24	+	4.02704e24i	−0.0530832	+	0.0612613i	−0.781670	−	0.623692i	$-0.785632\pi$
$739$	−3.48945e24	+	4.02704e24i	−0.0530832	+	0.0612613i	0.728587	+	0.684953i	$0.240177\pi$
$740$	2.12907e26	+	1.36827e26i	3.19967	+	2.05630i
$741$	−2.27920e25	−	3.27700e24i	−0.338392	−	0.0486534i
$742$	1.01501e26	−	6.52307e25i	1.48880	−	0.956790i
$743$	−1.13472e26	+	5.18210e25i	−1.64433	+	0.750942i	−0.999906	−	0.0137232i	$-0.995632\pi$
$743$	−1.13472e26	+	5.18210e25i	−1.64433	+	0.750942i	−0.644428	+	0.764665i	$0.722904\pi$
$744$	2.63720e26	+	3.04349e26i	3.77560	+	4.35727i
$745$	−1.63870e25	−	1.13974e26i	−0.231789	−	1.61213i
$746$	1.89961e26	+	8.67522e25i	2.65470	+	1.21236i
$747$	−4.08582e24	−	1.39150e25i	−0.0564149	−	0.192131i
$748$	−1.51150e26	+	4.43817e25i	−2.06203	+	0.605465i
$749$	−1.04571e25	+	2.28978e25i	−0.140953	+	0.308643i
$750$	5.43597e25	−	7.81574e24i	0.723978	−	0.104092i
$751$	4.24056e25	−	3.67447e25i	0.558039	−	0.483543i	−0.329577	−	0.944129i	$-0.606906\pi$
$751$	4.24056e25	−	3.67447e25i	0.558039	−	0.483543i	0.887615	+	0.460586i	$0.152361\pi$
$752$	2.18002e26	+	4.77357e26i	2.83465	+	6.20702i
$753$	−9.13576e25	−	1.42155e26i	−1.17379	−	1.82645i
$754$	1.67014e24	−	1.16161e25i	0.0212037	−	0.147475i
$755$	2.97297e25	−	4.62603e25i	0.372965	−	0.580344i
$756$	1.81069e26	+	1.56897e26i	2.24464	+	1.94499i
$757$	5.84052e24	−	1.98910e25i	0.0715466	−	0.243665i	−0.915953	−	0.401285i	$-0.868564\pi$
$757$	5.84052e24	−	1.98910e25i	0.0715466	−	0.243665i	0.987500	+	0.157620i	$0.0503820\pi$
$758$		−	1.76607e26i		−	2.13789i
$759$	8.65803e25	+	1.53408e25i	1.03572	+	0.183516i
$760$	3.45037e26			4.07890
$761$	−1.01890e26	−	2.99175e25i	−1.19033	−	0.349514i	−0.374184	−	0.927354i	$-0.622077\pi$
$761$	−1.01890e26	−	2.99175e25i	−1.19033	−	0.349514i	−0.816149	+	0.577841i	$0.803895\pi$
$762$	5.87448e25	−	6.77951e25i	0.678226	−	0.782714i
$763$	1.81403e24	+	1.16581e24i	0.0206978	+	0.0133017i
$764$	−1.12974e26	−	1.62432e25i	−1.27391	−	0.183160i
$765$	2.04148e26	−	1.31198e26i	2.27506	−	1.46209i
$766$	1.02269e26	−	4.67046e25i	1.12638	−	0.514400i
$767$	9.64717e24	+	1.11334e25i	0.105013	+	0.121191i
$768$	−1.48223e26	−	1.03091e27i	−1.59465	−	11.0910i
$769$	−9.55126e25	−	4.36191e25i	−1.01560	−	0.463810i	−0.163142	−	0.986603i	$-0.552163\pi$
$769$	−9.55126e25	−	4.36191e25i	−1.01560	−	0.463810i	−0.852460	+	0.522793i	$0.824890\pi$
$770$	−3.87323e25	−	1.31910e26i	−0.407059	−	1.38632i
$771$	−4.71151e24	+	1.38342e24i	−0.0489408	+	0.0143703i
$772$	−9.36098e25	+	2.04977e26i	−0.961093	+	2.10450i
$773$	−1.80807e26	+	2.59962e25i	−1.83485	+	0.263812i	−0.970851	−	0.239683i	$-0.922956\pi$
$773$	−1.80807e26	+	2.59962e25i	−1.83485	+	0.263812i	−0.863998	+	0.503495i	$0.832047\pi$
$774$	4.34505e25	−	3.76500e25i	0.435839	−	0.377656i
$775$	3.21093e25	+	7.03095e25i	0.318358	+	0.697106i
$776$	1.38420e26	+	2.15385e26i	1.35657	+	2.11087i
$777$	1.97311e25	−	1.37233e26i	0.191145	−	1.32944i
$778$	−1.82276e26	+	2.83628e26i	−1.74548	+	2.71602i
$779$	9.64920e25	+	8.36108e25i	0.913385	+	0.791453i
$780$	−5.14293e25	+	1.75152e26i	−0.481238	+	1.63894i
$781$		−	1.01470e25i		−	0.0938592i
$782$	1.28340e26	+	2.14769e26i	1.17355	+	1.96386i
$783$	3.82833e25			0.346061
$784$	−1.40814e26	−	4.13468e25i	−1.25835	−	0.369485i
$785$	−1.08724e26	+	1.25475e26i	−0.960506	+	1.10848i
$786$	−1.82802e26	−	1.17480e26i	−1.59653	−	1.02603i
$787$	−2.38178e25	−	3.42448e24i	−0.205650	−	0.0295680i	0.0387198	−	0.999250i	$-0.487672\pi$
$787$	−2.38178e25	−	3.42448e24i	−0.205650	−	0.0295680i	−0.244370	+	0.969682i	$0.578581\pi$
$788$	−4.76343e26	+	3.06127e26i	−4.06615	+	2.61316i
$789$	8.49236e25	−	3.87833e25i	0.716697	−	0.327304i
$790$	−3.42422e24	−	3.95176e24i	−0.0285705	−	0.0329721i
$791$	7.66969e24	+	5.33438e25i	0.0632687	+	0.440044i
$792$	4.66738e26	+	2.13152e26i	3.80668	+	1.73845i
$793$	1.00559e25	+	3.42474e25i	0.0810894	+	0.276165i
$794$	3.99977e26	−	1.17444e26i	3.18897	−	0.936365i
$795$	−1.24578e26	+	2.72787e26i	−0.982055	+	2.15040i
$796$	5.53752e26	−	7.96176e25i	4.31616	−	0.620571i
$797$	−7.56856e25	+	6.55819e25i	−0.583295	+	0.505428i	−0.895782	−	0.444494i	$-0.853383\pi$
$797$	−7.56856e25	+	6.55819e25i	−0.583295	+	0.505428i	0.312487	+	0.949922i	$0.398838\pi$
$798$	−1.19404e26	−	2.61458e26i	−0.909898	−	1.99240i
$799$	−1.22727e26	−	1.90968e26i	−0.924742	−	1.43893i
$800$	8.49026e25	−	5.90511e26i	0.632574	−	4.39965i
$801$	8.63263e25	−	1.34326e26i	0.635990	−	0.989620i
$802$	−9.22641e25	−	7.99473e25i	−0.672145	−	0.582417i
$803$	−1.45279e25	+	4.94774e25i	−0.104655	+	0.356424i
$804$			6.66479e26i			4.74769i
$805$	−1.39624e26	+	8.34356e25i	−0.983555	+	0.587745i
$806$	6.82061e25			0.475125
$807$	1.98561e26	+	5.83029e25i	1.36783	+	0.401632i
$808$	−1.75127e26	+	2.02107e26i	−1.19303	+	1.37683i
$809$	9.11155e24	+	5.85564e24i	0.0613841	+	0.0394491i	0.570973	−	0.820969i	$-0.306566\pi$
$809$	9.11155e24	+	5.85564e24i	0.0613841	+	0.0394491i	−0.509589	+	0.860418i	$0.670202\pi$
$810$	−1.02719e26	−	1.47687e25i	−0.684361	−	0.0983962i
$811$	−8.09070e25	+	5.19958e25i	−0.533087	+	0.342594i	−0.779330	−	0.626614i	$-0.784440\pi$
$811$	−8.09070e25	+	5.19958e25i	−0.533087	+	0.342594i	0.246243	+	0.969208i	$0.420804\pi$
$812$	9.92656e25	−	4.53331e25i	0.646837	−	0.295400i
$813$	−4.16753e25	−	4.80959e25i	−0.268574	−	0.309951i
$814$	−2.70698e25	−	1.88275e26i	−0.172530	−	1.19998i
$815$	−3.27263e26	−	1.49456e26i	−2.06290	−	0.942097i
$816$	3.97507e26	+	1.35379e27i	2.47818	+	8.43992i
$817$	−2.07686e25	+	6.09822e24i	−0.128059	+	0.0376015i
$818$	6.07043e25	−	1.32924e26i	0.370203	−	0.810631i
$819$	6.26989e25	−	9.01474e24i	0.378185	−	0.0543748i
$820$	7.64960e26	−	6.62841e26i	4.56367	−	3.95444i
$821$	1.04982e25	+	2.29879e25i	0.0619480	+	0.135647i	0.938074	−	0.346435i	$-0.112608\pi$
$821$	1.04982e25	+	2.29879e25i	0.0619480	+	0.135647i	−0.876126	+	0.482082i	$0.839881\pi$
$822$	−3.64402e26	−	5.67021e26i	−2.12684	−	3.30943i
$823$	−2.99509e25	+	2.08313e26i	−0.172906	+	1.20259i	0.699798	+	0.714341i	$0.253273\pi$
$823$	−2.99509e25	+	2.08313e26i	−0.172906	+	1.20259i	−0.872704	+	0.488249i	$0.837636\pi$
$824$	−5.17913e26	+	8.05889e26i	−2.95741	+	4.60183i
$825$	1.17503e26	+	1.01817e26i	0.663687	+	0.575088i
$826$	−5.18081e25	+	1.76442e26i	−0.289453	+	0.985785i
$827$		−	7.04751e25i		−	0.389481i	−0.980855	−	0.194740i	$-0.937614\pi$
$827$		−	7.04751e25i		−	0.389481i	0.980855	−	0.194740i	$-0.0623865\pi$
$828$	1.61060e26	−	9.08987e26i	0.880471	−	4.96918i
$829$	−3.40403e25			−0.184078			−0.0920391	−	0.995755i	$-0.529338\pi$
$829$	−3.40403e25			−0.184078			−0.0920391	+	0.995755i	$0.529338\pi$
$830$	5.57521e25	+	1.63703e25i	0.298235	+	0.0875696i
$831$	7.42553e25	−	8.56952e25i	0.392933	−	0.453469i
$832$	−2.49221e26	−	1.60164e26i	−1.30459	−	0.838409i
$833$	6.28371e25	+	9.03461e24i	0.325395	+	0.0467848i
$834$	8.45030e26	−	5.43068e26i	4.32890	−	2.78202i
$835$	−7.58954e25	+	3.46603e25i	−0.384625	+	0.175652i
$836$	−1.92371e26	−	2.22008e26i	−0.964458	−	1.11304i
$837$	3.16650e25	+	2.20235e26i	0.157055	+	1.09234i
$838$	−3.42305e25	−	1.56325e25i	−0.167964	−	0.0767067i
$839$	−5.04046e25	−	1.71662e26i	−0.244688	−	0.833331i	−0.986645	−	0.162884i	$-0.947920\pi$
$839$	−5.04046e25	−	1.71662e26i	−0.244688	−	0.833331i	0.741957	−	0.670447i	$-0.233898\pi$
$840$	−1.43778e27	+	4.22170e26i	−6.90524	+	2.02756i
$841$	−8.01834e25	+	1.75577e26i	−0.380996	+	0.834266i
$842$	6.10416e26	−	8.77645e25i	2.86957	−	0.412582i
$843$	−7.23087e25	+	6.26559e25i	−0.336312	+	0.291416i
$844$	−3.10409e26	−	6.79701e26i	−1.42841	−	3.12778i
$845$	−1.49859e26	−	2.33185e26i	−0.682296	−	1.06167i
$846$	−1.60014e26	+	1.11292e27i	−0.720815	+	5.01338i
$847$	6.09886e25	−	9.49001e25i	0.271830	−	0.422976i
$848$	−8.34674e26	−	7.23249e26i	−3.68090	−	3.18952i
$849$	1.69512e26	−	5.77305e26i	0.739659	−	2.51905i
$850$			4.42400e26i			1.91005i
$851$	−2.07641e26	+	8.67711e25i	−0.887049	+	0.370688i
$852$	−1.68183e26			−0.710930
$853$	1.44416e26	+	4.24043e25i	0.604050	+	0.177365i	0.569436	−	0.822036i	$-0.307162\pi$
$853$	1.44416e26	+	4.24043e25i	0.604050	+	0.177365i	0.0346141	+	0.999401i	$0.488980\pi$
$854$	−2.91773e26	+	3.36724e26i	−1.20760	+	1.39365i
$855$	3.80688e26	+	2.44654e26i	1.55910	+	1.00197i
$856$	3.72590e26	+	5.35704e25i	1.50997	+	0.217101i
$857$	3.57486e26	−	2.29742e26i	1.43361	−	0.921327i	0.433820	−	0.901000i	$-0.357165\pi$
$857$	3.57486e26	−	2.29742e26i	1.43361	−	0.921327i	0.999793	−	0.0203275i	$-0.00647088\pi$
$858$	1.24799e26	−	5.69938e25i	0.495251	−	0.226174i
$859$	−3.91851e24	−	4.52220e24i	−0.0153880	−	0.0177587i	0.748003	−	0.663695i	$-0.231013\pi$
$859$	−3.91851e24	−	4.52220e24i	−0.0153880	−	0.0177587i	−0.763391	+	0.645936i	$0.776467\pi$
$860$	2.44210e25	+	1.69852e26i	0.0949026	+	0.660062i
$861$	−5.04387e26	−	2.30346e26i	−1.93970	−	0.885833i
$862$	1.29761e26	+	4.41925e26i	0.493831	+	1.68183i
$863$	3.75885e26	−	1.10370e26i	1.41566	−	0.415674i	0.517625	−	0.855607i	$-0.326816\pi$
$863$	3.75885e26	−	1.10370e26i	1.41566	−	0.415674i	0.898030	+	0.439933i	$0.144998\pi$
$864$	7.13401e26	−	1.56213e27i	2.65895	−	5.82229i
$865$	5.03408e26	−	7.23792e25i	1.85684	−	0.266974i
$866$	−2.14357e26	+	1.85742e26i	−0.782487	+	0.678029i
$867$	−6.36196e25	−	1.39307e26i	−0.229836	−	0.503272i
$868$	3.42896e26	+	5.33557e26i	1.22598	+	1.90767i
$869$	−4.16633e23	+	2.89775e24i	−0.00147427	+	0.0102538i
$870$	−1.96850e26	+	3.06305e26i	−0.689387	+	1.07271i
$871$	5.60997e25	+	4.86107e25i	0.194445	+	0.168488i
$872$	9.08454e24	−	3.09391e25i	0.0311641	−	0.106135i
$873$			3.35789e26i			1.14009i
$874$	−2.64883e26	+	3.84067e26i	−0.890125	+	1.29064i
$875$	5.68782e25			0.189179
$876$	8.20076e26	+	2.40796e26i	2.69971	+	0.792706i
$877$	−3.15096e26	+	3.63640e26i	−1.02671	+	1.18488i	−0.0441285	+	0.999026i	$0.514051\pi$
$877$	−3.15096e26	+	3.63640e26i	−1.02671	+	1.18488i	−0.982577	+	0.185856i	$0.940494\pi$
$878$	−1.17199e26	−	7.53193e25i	−0.377984	−	0.242916i
$879$	7.06956e26	+	1.01645e26i	2.25680	+	0.324478i
$880$	−1.05867e27	+	6.80364e26i	−3.34515	+	2.14980i
$881$	−4.02423e26	+	1.83781e26i	−1.25864	+	0.574800i	−0.929270	−	0.369402i	$-0.879562\pi$
$881$	−4.02423e26	+	1.83781e26i	−1.25864	+	0.574800i	−0.329366	+	0.944202i	$0.606835\pi$
$882$	−2.05912e26	−	2.37636e26i	−0.637478	−	0.735689i
$883$	2.53227e25	+	1.76123e26i	0.0776004	+	0.539722i	0.991124	+	0.132938i	$0.0424410\pi$
$883$	2.53227e25	+	1.76123e26i	0.0776004	+	0.539722i	−0.913524	+	0.406785i	$0.866650\pi$
$884$	2.64530e26	+	1.20807e26i	0.802427	+	0.366456i
$885$	−1.28769e26	−	4.38548e26i	−0.386654	−	1.31682i
$886$	−1.13148e26	+	3.32233e25i	−0.336313	+	0.0987505i
$887$	−1.02141e26	+	2.23658e26i	−0.300530	+	0.658069i	−0.998302	−	0.0582510i	$-0.981448\pi$
$887$	−1.02141e26	+	2.23658e26i	−0.300530	+	0.658069i	0.697772	+	0.716320i	$0.254175\pi$
$888$	−2.05213e27	+	2.95052e26i	−5.97708	+	0.859374i
$889$	7.02141e25	−	6.08409e25i	0.202446	−	0.175420i
$890$	2.65763e26	+	5.81939e26i	0.758549	+	1.66099i
$891$	3.14119e25	+	4.88778e25i	0.0887553	+	0.138106i
$892$	1.28574e26	−	8.94253e26i	0.359642	−	2.50136i
$893$	2.28858e26	−	3.56110e26i	0.633728	−	0.986100i
$894$	1.08404e27	+	9.39327e26i	2.97172	+	2.57501i
$895$	6.17480e25	−	2.10294e26i	0.167577	−	0.570716i
$896$		−	2.02190e27i		−	5.43234i
$897$	−1.02247e26	−	1.26070e26i	−0.271968	−	0.335336i
$898$	5.28719e26			1.39232
$899$	9.72386e25	+	2.85518e25i	0.253514	+	0.0744383i
$900$	1.06895e27	−	1.23364e27i	2.75915	−	3.18423i
$901$	4.01902e26	+	2.58287e26i	1.02706	+	0.660054i
$902$	−7.52990e26	−	1.08264e26i	−1.90515	−	0.273920i
$903$	7.90821e25	−	5.08230e25i	0.198102	−	0.127312i
$904$	7.33062e26	−	3.34778e26i	1.81813	−	0.830312i
$905$	4.65616e26	+	5.37350e26i	1.14338	+	1.31953i
$906$	9.74878e25	+	6.78043e26i	0.237026	+	1.64855i
$907$	−4.96438e26	−	2.26716e26i	−1.19509	−	0.545778i	−0.284333	−	0.958726i	$-0.591772\pi$
$907$	−4.96438e26	−	2.26716e26i	−1.19509	−	0.545778i	−0.910755	+	0.412947i	$0.864499\pi$
$908$	−3.39607e26	−	1.15660e27i	−0.809477	−	2.75683i
$909$	−3.36530e26	+	9.88140e25i	−0.794234	+	0.233208i
$910$	−1.05430e26	+	2.30858e26i	−0.246371	+	0.539478i
$911$	1.67159e26	−	2.40338e25i	0.386779	−	0.0556105i	0.0538176	−	0.998551i	$-0.482861\pi$
$911$	1.67159e26	−	2.40338e25i	0.386779	−	0.0556105i	0.332962	+	0.942940i	$0.391952\pi$
$912$	−1.98843e27	+	1.72298e27i	−4.55572	+	3.94755i
$913$	−1.35143e25	−	2.95921e25i	−0.0306589	−	0.0671335i
$914$	−5.85441e26	−	9.10964e26i	−1.31513	−	2.04638i
$915$	1.57602e26	−	1.09614e27i	0.350567	−	2.43824i
$916$	5.20685e26	−	8.10201e26i	1.14687	−	1.78457i
$917$	−1.70082e26	−	1.47377e26i	−0.370966	−	0.321444i
$918$	−3.58784e26	+	1.22191e27i	−0.774906	+	2.63909i
$919$			1.45560e26i			0.311318i	0.987811	+	0.155659i	$0.0497500\pi$
$919$			1.45560e26i			0.311318i	−0.987811	+	0.155659i	$0.950250\pi$
$920$	1.78536e27	+	1.65181e27i	3.78124	+	3.49841i
$921$	3.67148e25			0.0770024
$922$	1.10608e27	+	3.24775e26i	2.29726	+	0.674535i
$923$	−1.22667e25	+	1.41565e25i	−0.0252298	+	0.0291167i
$924$	1.07325e27	+	6.89739e26i	2.18602	+	1.40487i
$925$	−3.93877e26	−	5.66310e25i	−0.794484	−	0.114230i
$926$	9.28307e25	−	5.96586e25i	0.185435	−	0.119172i
$927$	−1.14286e27	+	5.21925e26i	−2.26086	+	1.03250i
$928$	−5.12234e26	−	5.91149e26i	−1.00354	−	1.15815i
$929$	8.52488e25	+	5.92918e26i	0.165404	+	1.15041i	0.888236	+	0.459388i	$0.151931\pi$
$929$	8.52488e25	+	5.92918e26i	0.165404	+	1.15041i	−0.722832	+	0.691024i	$0.757160\pi$
$930$	−1.92492e27	−	8.79083e26i	−3.69885	−	1.68921i
$931$	3.33519e25	+	1.13586e26i	0.0634707	+	0.216161i
$932$	5.24932e26	−	1.54134e26i	0.989372	−	0.290506i
$933$	−6.08710e26	+	1.33289e27i	−1.13625	+	2.48805i
$934$	−1.49373e27	+	2.14766e26i	−2.76154	+	0.397049i
$935$	4.11401e26	−	3.56481e26i	0.753287	−	0.652727i
$936$	−3.93489e26	−	8.61621e26i	−0.713592	−	1.56255i
$937$	−3.99410e26	−	6.21495e26i	−0.717403	−	1.11630i	−0.988126	−	0.153643i	$-0.950899\pi$
$937$	−3.99410e26	−	6.21495e26i	−0.717403	−	1.11630i	0.270724	−	0.962657i	$-0.412737\pi$
$938$	−1.31869e26	+	9.17169e26i	−0.234594	+	1.63164i
$939$	5.14917e26	−	8.01226e26i	0.907291	−	1.41177i
$940$	−2.53619e27	−	2.19762e27i	−4.42621	−	3.83533i
$941$	−2.60711e26	+	8.87900e26i	−0.450664	+	1.53482i	0.350610	+	0.936522i	$0.385974\pi$
$941$	−2.60711e26	+	8.87900e26i	−0.450664	+	1.53482i	−0.801273	+	0.598298i	$0.795844\pi$
$942$		−	2.06822e27i		−	3.54110i
$943$	9.90134e25	+	8.94577e26i	0.167915	+	1.51709i
$944$	1.68328e27			2.82754
$945$	−7.94380e26	−	2.33251e26i	−1.32173	−	0.388094i
$946$	8.44567e25	−	9.74683e25i	0.139192	−	0.160636i
$947$	5.24470e26	+	3.37056e26i	0.856191	+	0.550241i	0.893500	−	0.449063i	$-0.148242\pi$
$947$	5.24470e26	+	3.37056e26i	0.856191	+	0.550241i	−0.0373089	+	0.999304i	$0.511879\pi$
$948$	4.80295e25	+	6.90560e24i	0.0776664	+	0.0111667i
$949$	8.00820e25	−	5.14656e25i	0.128274	−	0.0824368i
$950$	−7.50421e26	+	3.42706e26i	−1.19067	+	0.543762i
$951$	1.01093e27	+	1.16668e27i	1.58890	+	1.83369i
$952$	3.39732e26	+	2.36289e27i	0.528937	+	3.67884i
$953$	−3.14394e26	−	1.43579e26i	−0.484884	−	0.221439i	0.157946	−	0.987448i	$-0.449513\pi$
$953$	−3.14394e26	−	1.43579e26i	−0.484884	−	0.221439i	−0.642830	+	0.766009i	$0.722240\pi$
$954$	−6.66661e26	−	2.27044e27i	−1.01852	−	3.46876i
$955$	3.78428e26	−	1.11117e26i	0.572734	−	0.168170i
$956$	4.09073e26	−	8.95744e26i	0.613309	−	1.34296i
$957$	2.01779e26	−	2.90114e25i	0.299687	−	0.0430885i
$958$	1.69494e27	−	1.46867e27i	2.49382	−	2.16090i
$959$	−2.89989e26	−	6.34986e26i	−0.422682	−	0.925544i
$960$	4.96924e27	+	7.73230e27i	7.17545	+	11.1652i
$961$	1.56619e25	−	1.08931e26i	0.0224044	−	0.155826i
$962$	−1.89840e26	+	2.95397e26i	−0.269037	+	0.418629i
$963$	3.73104e26	+	3.23297e26i	0.523834	+	0.453904i
$964$	9.74745e25	−	3.31968e26i	0.135581	−	0.461745i
$965$		−	7.78681e26i		−	1.07303i
$966$	6.33850e26	−	1.92452e27i	0.865351	−	2.62741i
$967$	1.71852e26			0.232443			0.116222	−	0.993223i	$-0.462922\pi$
$967$	1.71852e26			0.232443			0.116222	+	0.993223i	$0.462922\pi$
$968$	−1.61856e27	−	4.75253e26i	−2.16896	−	0.636863i
$969$	7.45308e26	−	8.60132e26i	0.989514	−	1.14196i
$970$	−1.13180e27	−	7.27365e26i	−1.48876	−	0.956769i
$971$	−9.08510e26	−	1.30624e26i	−1.18401	−	0.170235i	−0.477952	−	0.878386i	$-0.658621\pi$
$971$	−9.08510e26	−	1.30624e26i	−1.18401	−	0.170235i	−0.706061	+	0.708151i	$0.749530\pi$
$972$	−1.47754e27	+	9.49557e26i	−1.90784	+	1.22610i
$973$	9.46318e26	−	4.32169e26i	1.21066	−	0.552889i
$974$	−1.92210e27	−	2.21822e27i	−2.43638	−	2.81173i
$975$	−4.08474e25	−	2.84100e26i	−0.0513006	−	0.356804i
$976$	3.70986e27	+	1.69423e27i	4.61646	+	2.10827i
$977$	1.29441e26	+	4.40836e26i	0.159596	+	0.543534i	0.999999	+	0.00157148i	$0.000500217\pi$
$977$	1.29441e26	+	4.40836e26i	0.159596	+	0.543534i	−0.840403	+	0.541962i	$0.817682\pi$
$978$	4.30024e27	−	1.26266e27i	5.25343	−	1.54255i
$979$	1.48794e26	−	3.25813e26i	0.180111	−	0.394389i
$980$	9.28941e26	−	1.33561e26i	1.11417	−	0.160194i
$981$	3.19611e25	−	2.76944e25i	0.0379840	−	0.0329133i
$982$	7.75245e25	+	1.69755e26i	0.0912926	+	0.199903i
$983$	−8.78927e25	−	1.36764e26i	−0.102558	−	0.159584i	0.786182	−	0.617995i	$-0.212055\pi$
$983$	−8.78927e25	−	1.36764e26i	−0.102558	−	0.159584i	−0.888740	+	0.458411i	$0.848419\pi$
$984$	−1.18004e27	+	8.20734e27i	−1.36439	+	9.48957i
$985$	1.05785e27	−	1.64604e27i	1.21198	−	1.88588i
$986$	4.38370e26	+	3.79850e26i	0.497679	+	0.431241i
$987$	−5.17939e26	+	1.76394e27i	−0.582673	+	1.98440i
$988$			5.42293e26i			0.604535i
$989$	−1.36660e26	−	6.78722e25i	−0.150964	−	0.0749765i
$990$	−2.69626e27			−2.95151
$991$	−2.64060e26	−	7.75350e25i	−0.286444	−	0.0841076i	0.135354	−	0.990797i	$-0.456783\pi$
$991$	−2.64060e26	−	7.75350e25i	−0.286444	−	0.0841076i	−0.421798	+	0.906690i	$0.638601\pi$
$992$	2.97707e27	−	3.43572e27i	3.20025	−	3.69328i
$993$	−1.63691e27	−	1.05198e27i	−1.74374	−	1.12063i
$994$	−2.31444e26	−	3.32767e25i	−0.244326	−	0.0351287i
$995$	−1.62632e27	+	1.04517e27i	−1.70137	+	1.09340i
$996$	−4.90483e26	+	2.23996e26i	−0.508499	+	0.232224i
$997$	9.44871e26	+	1.09044e27i	0.970769	+	1.12033i	0.992705	+	0.120568i	$0.0384716\pi$
$997$	9.44871e26	+	1.09044e27i	0.970769	+	1.12033i	−0.0219357	+	0.999759i	$0.506983\pi$
$998$	4.18088e26	+	2.90786e27i	0.425689	+	2.96073i
$999$	−1.04196e27	−	4.75846e26i	−1.05138	−	0.480150i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.19.d.a.5.1	✓	350
23.14	odd	22	inner	23.19.d.a.14.1	yes	350

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.19.d.a.5.1	✓	350	1.1	even	1	trivial
23.19.d.a.14.1	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+(-972.723 - 285.617i) q^{2} +(-21289.0 + 24568.8i) q^{3} +(644082. + 413927. i) q^{4} +(-2.61874e6 - 376518. i) q^{5} +(2.77256e7 - 1.78182e7i) q^{6} +(3.10489e7 - 1.41796e7i) q^{7} +(-3.34254e8 - 3.85750e8i) q^{8} +(-9.52698e7 - 6.62616e8i) q^{9} +(2.43977e9 + 1.11420e9i) q^{10} +(-4.23069e8 - 1.44084e9i) q^{11} +(-2.38816e10 + 7.01227e9i) q^{12} +(-1.15159e9 + 2.52164e9i) q^{13} +(-3.42519e10 + 4.92468e9i) q^{14} +(6.50010e10 - 5.63237e10i) q^{15} +(1.31585e11 + 2.88130e11i) q^{16} +(-7.40776e10 - 1.15267e11i) q^{17} +(-9.65834e10 + 6.71752e11i) q^{18} +(1.38137e11 - 2.14946e11i) q^{19} +(-1.53083e12 - 1.32647e12i) q^{20} +(-3.12625e11 + 1.06470e12i) q^{21} +1.52237e12i q^{22} +(1.74380e12 - 4.50903e11i) q^{23} +1.65934e13 q^{24} +(3.05585e12 + 8.97278e11i) q^{25} +(1.84041e12 - 2.12394e12i) q^{26} +(7.71254e12 + 4.95655e12i) q^{27} +(2.58673e13 + 3.71916e12i) q^{28} +(3.51289e12 - 2.25760e12i) q^{29} +(-7.93149e13 + 3.62219e13i) q^{30} +(1.58931e13 + 1.83416e13i) q^{31} +(-2.66582e13 - 1.85412e14i) q^{32} +(4.44065e13 + 2.02798e13i) q^{33} +(3.91347e13 + 1.33281e14i) q^{34} +(-8.66478e13 + 2.54421e13i) q^{35} +(2.12913e14 - 4.66214e14i) q^{36} +(-1.23672e14 + 1.77813e13i) q^{37} +(-1.95762e14 + 1.69628e14i) q^{38} +(-3.74375e13 - 8.19766e13i) q^{39} +(7.30083e14 + 1.13603e15i) q^{40} +(-7.11150e13 + 4.94616e14i) q^{41} +(6.08195e14 - 9.46371e14i) q^{42} +(-6.40239e13 - 5.54770e13i) q^{43} +(3.23911e14 - 1.10314e15i) q^{44} +1.77109e15i q^{45} +(-1.82502e15 - 5.94555e13i) q^{46} +1.65674e15 q^{47} +(-9.88034e15 - 2.90113e15i) q^{48} +(-3.03410e14 + 3.50154e14i) q^{49} +(-2.71621e15 - 1.74560e15i) q^{50} +(4.40902e15 + 6.33921e14i) q^{51} +(-1.78550e15 + 1.14747e15i) q^{52} +(-3.17162e15 + 1.44843e15i) q^{53} +(-6.08649e15 - 7.02418e15i) q^{54} +(5.65405e14 + 3.93248e15i) q^{55} +(-1.58480e16 - 7.23753e15i) q^{56} +(2.34016e15 + 7.96986e15i) q^{57} +(-4.06188e15 + 1.19268e15i) q^{58} +(2.20758e15 - 4.83392e15i) q^{59} +(6.51799e16 - 9.37145e15i) q^{60} +(9.73075e15 - 8.43174e15i) q^{61} +(-1.02209e16 - 2.23806e16i) q^{62} +(-1.23536e16 - 1.92226e16i) q^{63} +(-1.52086e16 + 1.05778e17i) q^{64} +(3.96517e15 - 6.16992e15i) q^{65} +(-3.74030e16 - 3.24098e16i) q^{66} +(7.54401e15 - 2.56925e16i) q^{67} -1.04904e17i q^{68} +(-2.60456e16 + 5.24424e16i) q^{69} +9.15509e16 q^{70} +(6.48341e15 + 1.90370e15i) q^{71} +(-2.23760e17 + 2.58233e17i) q^{72} +(-2.88880e16 - 1.85652e16i) q^{73} +(1.25377e17 + 1.80265e16i) q^{74} +(-8.71011e16 + 5.59765e16i) q^{75} +(1.77944e17 - 8.12642e16i) q^{76} +(-3.35663e16 - 3.87376e16i) q^{77} +(1.30023e16 + 9.04333e16i) q^{78} +(-1.77335e15 - 8.09864e14i) q^{79} +(-2.36100e17 - 8.04082e17i) q^{80} +(-3.71238e16 + 1.09005e16i) q^{81} +(2.10446e17 - 4.60812e17i) q^{82} +(2.14434e16 - 3.08309e15i) q^{83} +(-6.42066e17 + 5.56353e17i) q^{84} +(1.50590e17 + 3.29745e17i) q^{85} +(4.64323e16 + 7.22500e16i) q^{86} +(-1.93195e16 + 1.34370e17i) q^{87} +(-4.14392e17 + 6.44806e17i) q^{88} +(1.80263e17 + 1.56199e17i) q^{89} +(5.05853e17 - 1.72278e18i) q^{90} +9.46232e16i q^{91} +(1.30979e18 + 4.31386e17i) q^{92} -7.88979e17 q^{93} +(-1.61155e18 - 4.73194e17i) q^{94} +(-4.42676e17 + 5.10876e17i) q^{95} +(5.12288e18 + 3.29228e18i) q^{96} +(-4.96499e17 - 7.13858e16i) q^{97} +(3.95144e17 - 2.53944e17i) q^{98} +(-9.14419e17 + 4.17601e17i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more