LMFDB - Embedded newform 13.10.c.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(3,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("13.3");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$N$	$=$	$13$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	13.c (of order $3$ , degree $2$ , 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:	$6.69546587013$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{18} - 3 x^{17} + 3193 x^{16} + 896 x^{15} + 6827472 x^{14} + 3327136 x^{13} + 8054385232 x^{12} + \cdots + 15\!\cdots\!00$ x^18 - 3x^17 + 3193x^16 + 896x^15 + 6827472x^14 + 3327136x^13 + 8054385232x^12 + 694281600x^11 + 6899832636736x^10 - 1285276575488x^9 + 3495304064394496x^8 - 764853454571520x^7 + 1234658135287256064x^6 + 1254918535240499200x^5 + 146439647836867215360x^4 + 1052079877442940928000x^3 + 12856821885420326502400x^2 + 44600611845158952960000*x + 152210992401321984000000
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$2^{16}\cdot 3^{3}\cdot 13^{4}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.5
Root			$-2.19214 + 3.79690i$ of defining polynomial
Character	$\chi$	$=$	13.3
Dual form			13.10.c.a.9.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.19214 + 5.52895i) q^{2} +(2.91217 + 5.04403i) q^{3} +(235.621 - 408.107i) q^{4} -1063.81 q^{5} +(-18.5921 + 32.2025i) q^{6} +(3237.60 - 5607.69i) q^{7} +6277.28 q^{8} +(9824.54 - 17016.6i) q^{9} +(-3395.82 - 5881.73i) q^{10} +(-9318.25 - 16139.7i) q^{11} +2744.67 q^{12} +(76359.2 - 69092.5i) q^{13} +41339.5 q^{14} +(-3097.99 - 5365.87i) q^{15} +(-100600. - 174244. i) q^{16} +(-260981. + 452032. i) q^{17} +125445. q^{18} +(-136989. + 237271. i) q^{19} +(-250655. + 434146. i) q^{20} +37713.8 q^{21} +(59490.3 - 103040. i) q^{22} +(442891. + 767110. i) q^{23} +(18280.5 + 31662.8i) q^{24} -821442. q^{25} +(625758. + 201633. i) q^{26} +229084. q^{27} +(-1.52569e6 - 2.64257e6i) q^{28} +(-1.89328e6 - 3.27926e6i) q^{29} +(19778.4 - 34257.2i) q^{30} +9.87395e6 q^{31} +(2.24924e6 - 3.89580e6i) q^{32} +(54272.7 - 94003.1i) q^{33} -3.33235e6 q^{34} +(-3.44418e6 + 5.96549e6i) q^{35} +(-4.62973e6 - 8.01892e6i) q^{36} +(5.10467e6 + 8.84155e6i) q^{37} -1.74915e6 q^{38} +(570876. + 183949. i) q^{39} -6.67781e6 q^{40} +(6.37138e6 + 1.10356e7i) q^{41} +(120388. + 208518. i) q^{42} +(-2.01903e6 + 3.49706e6i) q^{43} -8.78228e6 q^{44} +(-1.04514e7 + 1.81024e7i) q^{45} +(-2.82754e6 + 4.89744e6i) q^{46} +1.84794e6 q^{47} +(585928. - 1.01486e6i) q^{48} +(-787309. - 1.36366e6i) q^{49} +(-2.62216e6 - 4.54171e6i) q^{50} -3.04009e6 q^{51} +(-1.02053e7 - 4.74423e7i) q^{52} +5.32516e7 q^{53} +(731267. + 1.26659e6i) q^{54} +(9.91281e6 + 1.71695e7i) q^{55} +(2.03233e7 - 3.52010e7i) q^{56} -1.59574e6 q^{57} +(1.20872e7 - 2.09357e7i) q^{58} +(8.32220e6 - 1.44145e7i) q^{59} -2.91980e6 q^{60} +(4.50235e7 - 7.79829e7i) q^{61} +(3.15190e7 + 5.45925e7i) q^{62} +(-6.36159e7 - 1.10186e8i) q^{63} -7.42946e7 q^{64} +(-8.12314e7 + 7.35010e7i) q^{65} +692984. q^{66} +(-1.30131e7 - 2.25394e7i) q^{67} +(1.22985e8 + 2.13016e8i) q^{68} +(-2.57955e6 + 4.46791e6i) q^{69} -4.39772e7 q^{70} +(-1.40020e8 + 2.42522e8i) q^{71} +(6.16714e7 - 1.06818e8i) q^{72} +1.22891e8 q^{73} +(-3.25897e7 + 5.64469e7i) q^{74} +(-2.39218e6 - 4.14338e6i) q^{75} +(6.45547e7 + 1.11812e8i) q^{76} -1.20675e8 q^{77} +(805272. + 3.74353e6i) q^{78} -4.73173e8 q^{79} +(1.07019e8 + 1.85362e8i) q^{80} +(-1.92709e8 - 3.33782e8i) q^{81} +(-4.06766e7 + 7.04540e7i) q^{82} +7.61296e8 q^{83} +(8.88615e6 - 1.53913e7i) q^{84} +(2.77633e8 - 4.80875e8i) q^{85} -2.57801e7 q^{86} +(1.10271e7 - 1.90996e7i) q^{87} +(-5.84933e7 - 1.01313e8i) q^{88} +(-6.13268e7 - 1.06221e8i) q^{89} -1.33449e8 q^{90} +(-1.40229e8 - 6.51892e8i) q^{91} +4.17417e8 q^{92} +(2.87546e7 + 4.98045e7i) q^{93} +(5.89889e6 + 1.02172e7i) q^{94} +(1.45729e8 - 2.52411e8i) q^{95} +2.62007e7 q^{96} +(-1.54470e8 + 2.67549e8i) q^{97} +(5.02640e6 - 8.70598e6i) q^{98} -3.66190e8 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$18 q + 15 q^{2} + 161 q^{3} - 1793 q^{4} - 2280 q^{5} + 2118 q^{6} - 1939 q^{7} - 14478 q^{8} - 33654 q^{9} + 46923 q^{10} - 5433 q^{11} + 8712 q^{12} - 212524 q^{13} - 9900 q^{14} - 347428 q^{15} + 400127 q^{16}+ \cdots + 2262149268 q^{99}+O(q^{100})$ 18 * q + 15 * q^2 + 161 * q^3 - 1793 * q^4 - 2280 * q^5 + 2118 * q^6 - 1939 * q^7 - 14478 * q^8 - 33654 * q^9 + 46923 * q^10 - 5433 * q^11 + 8712 * q^12 - 212524 * q^13 - 9900 * q^14 - 347428 * q^15 + 400127 * q^16 + 248589 * q^17 - 38738 * q^18 - 311001 * q^19 + 927069 * q^20 + 1553030 * q^21 + 1857242 * q^22 + 591609 * q^23 - 4492800 * q^24 + 7008998 * q^25 - 3801525 * q^26 - 11603482 * q^27 + 2697168 * q^28 + 11014155 * q^29 - 6597836 * q^30 - 23148076 * q^31 - 11868417 * q^32 + 14131427 * q^33 + 21859862 * q^34 + 21112794 * q^35 + 10792871 * q^36 - 29215749 * q^37 + 14572188 * q^38 - 71569875 * q^39 + 27322222 * q^40 + 3328377 * q^41 + 39828306 * q^42 + 6074381 * q^43 + 31824624 * q^44 + 32857342 * q^45 + 36693338 * q^46 - 45575052 * q^47 - 30270064 * q^48 + 10293266 * q^49 - 49601730 * q^50 - 136587494 * q^51 - 35278230 * q^52 - 29480016 * q^53 + 152965386 * q^54 - 18710998 * q^55 - 7665444 * q^56 + 523363230 * q^57 - 163479359 * q^58 - 32715855 * q^59 - 188638416 * q^60 - 220502845 * q^61 - 59980476 * q^62 + 166572574 * q^63 - 924604030 * q^64 + 128091756 * q^65 - 48128076 * q^66 + 112659045 * q^67 - 238942419 * q^68 + 86003951 * q^69 + 2040150992 * q^70 - 236450709 * q^71 + 995206683 * q^72 - 211881220 * q^73 - 455580507 * q^74 + 968954813 * q^75 - 365789708 * q^76 - 2399230890 * q^77 - 441111970 * q^78 - 817519096 * q^79 + 580424625 * q^80 + 176914851 * q^81 + 941792217 * q^82 + 2225691456 * q^83 - 1819004068 * q^84 + 1812284636 * q^85 + 291320076 * q^86 + 69564799 * q^87 + 3178375740 * q^88 - 1154379039 * q^89 - 10225809510 * q^90 - 1658338903 * q^91 - 4545506592 * q^92 + 3136878060 * q^93 + 2755131560 * q^94 + 1779441012 * q^95 + 5906965568 * q^96 - 3616470111 * q^97 + 8263323501 * q^98 + 2262149268 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	3.19214	+	5.52895i	0.141074	+	0.244347i	0.927901	−	0.372826i	$-0.121611\pi$
$2$	3.19214	+	5.52895i	0.141074	+	0.244347i	−0.786827	+	0.617173i	$0.788278\pi$
$3$	2.91217	+	5.04403i	0.0207573	+	0.0359527i	0.876217	−	0.481916i	$-0.160059\pi$
$3$	2.91217	+	5.04403i	0.0207573	+	0.0359527i	−0.855460	+	0.517869i	$0.826726\pi$
$4$	235.621	−	408.107i	0.460196	−	0.797083i
$5$	−1063.81			−0.761198			−0.380599	−	0.924740i	$-0.624282\pi$
$5$	−1063.81			−0.761198			−0.380599	+	0.924740i	$0.624282\pi$
$6$	−18.5921	+	32.2025i	−0.00585664	+	0.0101440i
$7$	3237.60	−	5607.69i	0.509662	−	0.882760i	−0.490276	−	0.871567i	$-0.663104\pi$
$7$	3237.60	−	5607.69i	0.509662	−	0.882760i	0.999937	−	0.0111926i	$-0.00356280\pi$
$8$	6277.28			0.541835
$9$	9824.54	−	17016.6i	0.499138	−	0.864533i
$10$	−3395.82	−	5881.73i	−0.107385	−	0.185997i
$11$	−9318.25	−	16139.7i	−0.191897	−	0.332375i	0.753982	−	0.656895i	$-0.228130\pi$
$11$	−9318.25	−	16139.7i	−0.191897	−	0.332375i	−0.945879	+	0.324520i	$0.894797\pi$
$12$	2744.67			0.0382098
$13$	76359.2	−	69092.5i	0.741509	−	0.670943i
$13$	76359.2	−	69092.5i	0.741509	−	0.670943i
$14$	41339.5			0.287600
$15$	−3097.99	−	5365.87i	−0.0158004	−	0.0273671i
$16$	−100600.	−	174244.i	−0.383758	−	0.664688i
$17$	−260981.	+	452032.i	−0.757859	+	1.31265i	0.186081	+	0.982534i	$0.440421\pi$
$17$	−260981.	+	452032.i	−0.757859	+	1.31265i	−0.943940	+	0.330117i	$0.892912\pi$
$18$	125445.			0.281662
$19$	−136989.	+	237271.i	−0.241154	+	0.417690i	−0.961043	−	0.276398i	$-0.910859\pi$
$19$	−136989.	+	237271.i	−0.241154	+	0.417690i	0.719890	+	0.694089i	$0.244192\pi$
$20$	−250655.	+	434146.i	−0.350300	+	0.606738i
$21$	37713.8			0.0423169
$22$	59490.3	−	103040.i	0.0541432	−	0.0937788i
$23$	442891.	+	767110.i	0.330006	+	0.571587i	0.982513	−	0.186196i	$-0.0596159\pi$
$23$	442891.	+	767110.i	0.330006	+	0.571587i	−0.652507	+	0.757783i	$0.726283\pi$
$24$	18280.5	+	31662.8i	0.0112470	+	0.0194804i
$25$	−821442.			−0.420578
$26$	625758.	+	201633.i	0.268551	+	0.0865329i
$27$	229084.			0.0829578
$28$	−1.52569e6	−	2.64257e6i	−0.469089	−	0.812486i
$29$	−1.89328e6	−	3.27926e6i	−0.497078	−	0.860965i	0.502916	−	0.864335i	$-0.332260\pi$
$29$	−1.89328e6	−	3.27926e6i	−0.497078	−	0.860965i	−0.999994	+	0.00337053i	$0.998927\pi$
$30$	19778.4	−	34257.2i	0.00445806	−	0.00772158i
$31$	9.87395e6			1.92027			0.960137	−	0.279529i	$-0.0901782\pi$
$31$	9.87395e6			1.92027			0.960137	+	0.279529i	$0.0901782\pi$
$32$	2.24924e6	−	3.89580e6i	0.379194	−	0.656783i
$33$	54272.7	−	94003.1i	0.00796652	−	0.0137984i
$34$	−3.33235e6			−0.427657
$35$	−3.44418e6	+	5.96549e6i	−0.387953	+	0.671955i
$36$	−4.62973e6	−	8.01892e6i	−0.459403	−	0.795710i
$37$	5.10467e6	+	8.84155e6i	0.447775	+	0.775570i	0.998241	−	0.0592881i	$-0.0188831\pi$
$37$	5.10467e6	+	8.84155e6i	0.447775	+	0.775570i	−0.550465	+	0.834858i	$0.685550\pi$
$38$	−1.74915e6			−0.136082
$39$	570876.	+	183949.i	0.0395140	+	0.0127323i
$40$	−6.67781e6			−0.412443
$41$	6.37138e6	+	1.10356e7i	0.352132	+	0.609911i	0.986623	−	0.163019i	$-0.0521233\pi$
$41$	6.37138e6	+	1.10356e7i	0.352132	+	0.609911i	−0.634490	+	0.772931i	$0.718790\pi$
$42$	120388.	+	208518.i	0.00596981	+	0.0103400i
$43$	−2.01903e6	+	3.49706e6i	−0.0900604	+	0.155989i	−0.907536	−	0.419974i	$-0.862039\pi$
$43$	−2.01903e6	+	3.49706e6i	−0.0900604	+	0.155989i	0.817476	+	0.575963i	$0.195373\pi$
$44$	−8.78228e6			−0.353240
$45$	−1.04514e7	+	1.81024e7i	−0.379943	+	0.658080i
$46$	−2.82754e6	+	4.89744e6i	−0.0931105	+	0.161272i
$47$	1.84794e6			0.0552394			0.0276197	−	0.999619i	$-0.491207\pi$
$47$	1.84794e6			0.0552394			0.0276197	+	0.999619i	$0.491207\pi$
$48$	585928.	−	1.01486e6i	0.0159316	−	0.0275943i
$49$	−787309.	−	1.36366e6i	−0.0195102	−	0.0337927i
$50$	−2.62216e6	−	4.54171e6i	−0.0593326	−	0.102767i
$51$	−3.04009e6			−0.0629246
$52$	−1.02053e7	−	4.74423e7i	−0.193558	−	0.899810i
$53$	5.32516e7			0.927024			0.463512	−	0.886091i	$-0.346589\pi$
$53$	5.32516e7			0.927024			0.463512	+	0.886091i	$0.346589\pi$
$54$	731267.	+	1.26659e6i	0.0117032	+	0.0202705i
$55$	9.91281e6	+	1.71695e7i	0.146071	+	0.253003i
$56$	2.03233e7	−	3.52010e7i	0.276152	−	0.478310i
$57$	−1.59574e6			−0.0200228
$58$	1.20872e7	−	2.09357e7i	0.140250	−	0.242919i
$59$	8.32220e6	−	1.44145e7i	0.0894137	−	0.154869i	−0.817850	−	0.575432i	$-0.804834\pi$
$59$	8.32220e6	−	1.44145e7i	0.0894137	−	0.154869i	0.907263	+	0.420563i	$0.138167\pi$
$60$	−2.91980e6			−0.0290852
$61$	4.50235e7	−	7.79829e7i	0.416346	−	0.721133i	−0.579223	−	0.815169i	$-0.696644\pi$
$61$	4.50235e7	−	7.79829e7i	0.416346	−	0.721133i	0.995569	+	0.0940368i	$0.0299771\pi$
$62$	3.15190e7	+	5.45925e7i	0.270901	+	0.469214i
$63$	−6.36159e7	−	1.10186e8i	−0.508783	−	0.881239i
$64$	−7.42946e7			−0.553538
$65$	−8.12314e7	+	7.35010e7i	−0.564435	+	0.510721i
$66$	692984.			0.00449547
$67$	−1.30131e7	−	2.25394e7i	−0.0788941	−	0.136649i	0.823879	−	0.566766i	$-0.191806\pi$
$67$	−1.30131e7	−	2.25394e7i	−0.0788941	−	0.136649i	−0.902773	+	0.430117i	$0.858472\pi$
$68$	1.22985e8	+	2.13016e8i	0.697528	+	1.20815i
$69$	−2.57955e6	+	4.46791e6i	−0.0137001	+	0.0237292i
$70$	−4.39772e7			−0.218920
$71$	−1.40020e8	+	2.42522e8i	−0.653926	+	1.13263i	0.328236	+	0.944596i	$0.393546\pi$
$71$	−1.40020e8	+	2.42522e8i	−0.653926	+	1.13263i	−0.982162	+	0.188038i	$0.939787\pi$
$72$	6.16714e7	−	1.06818e8i	0.270450	−	0.468434i
$73$	1.22891e8			0.506484			0.253242	−	0.967403i	$-0.418503\pi$
$73$	1.22891e8			0.506484			0.253242	+	0.967403i	$0.418503\pi$
$74$	−3.25897e7	+	5.64469e7i	−0.126339	+	0.218825i
$75$	−2.39218e6	−	4.14338e6i	−0.00873008	−	0.0151209i
$76$	6.45547e7	+	1.11812e8i	0.221956	+	0.384439i
$77$	−1.20675e8			−0.391210
$78$	805272.	+	3.74353e6i	0.00246330	+	0.0114513i
$79$	−4.73173e8			−1.36678			−0.683389	−	0.730054i	$-0.739495\pi$
$79$	−4.73173e8			−1.36678			−0.683389	+	0.730054i	$0.739495\pi$
$80$	1.07019e8	+	1.85362e8i	0.292115	+	0.505959i
$81$	−1.92709e8	−	3.33782e8i	−0.497416	−	0.861550i
$82$	−4.06766e7	+	7.04540e7i	−0.0993534	+	0.172085i
$83$	7.61296e8			1.76077			0.880384	−	0.474262i	$-0.157285\pi$
$83$	7.61296e8			1.76077			0.880384	+	0.474262i	$0.157285\pi$
$84$	8.88615e6	−	1.53913e7i	0.0194741	−	0.0337301i
$85$	2.77633e8	−	4.80875e8i	0.576881	−	0.999187i
$86$	−2.57801e7			−0.0508207
$87$	1.10271e7	−	1.90996e7i	0.0206360	−	0.0357427i
$88$	−5.84933e7	−	1.01313e8i	−0.103976	−	0.180092i
$89$	−6.13268e7	−	1.06221e8i	−0.103609	−	0.179455i	0.809560	−	0.587037i	$-0.199706\pi$
$89$	−6.13268e7	−	1.06221e8i	−0.103609	−	0.179455i	−0.913169	+	0.407581i	$0.866372\pi$
$90$	−1.33449e8			−0.214400
$91$	−1.40229e8	−	6.51892e8i	−0.214363	−	0.996528i
$92$	4.17417e8			0.607470
$93$	2.87546e7	+	4.98045e7i	0.0398598	+	0.0690391i
$94$	5.89889e6	+	1.02172e7i	0.00779283	+	0.0134976i
$95$	1.45729e8	−	2.52411e8i	0.183566	−	0.317945i
$96$	2.62007e7			0.0314842
$97$	−1.54470e8	+	2.67549e8i	−0.177162	+	0.306853i	−0.940907	−	0.338664i	$-0.890025\pi$
$97$	−1.54470e8	+	2.67549e8i	−0.177162	+	0.306853i	0.763746	+	0.645517i	$0.223358\pi$
$98$	5.02640e6	−	8.70598e6i	0.00550477	−	0.00953455i
$99$	−3.66190e8			−0.383132
$100$	−1.93548e8	+	3.35236e8i	−0.193548	+	0.335236i
$101$	9.05623e8	+	1.56859e9i	0.865967	+	1.49990i	0.866084	+	0.499899i	$0.166630\pi$
$101$	9.05623e8	+	1.56859e9i	0.865967	+	1.49990i	−0.000116750		1.00000i	$0.500037\pi$
$102$	−9.70438e6	−	1.68085e7i	−0.00887701	−	0.0153754i
$103$	−1.85827e9			−1.62683			−0.813415	−	0.581684i	$-0.802394\pi$
$103$	−1.85827e9			−1.62683			−0.813415	+	0.581684i	$0.802394\pi$
$104$	4.79328e8	−	4.33713e8i	0.401775	−	0.363540i
$105$	−4.01202e7			−0.0322115
$106$	1.69986e8	+	2.94425e8i	0.130779	+	0.226516i
$107$	1.49338e8	+	2.58661e8i	0.110139	+	0.190767i	0.915826	−	0.401574i	$-0.131537\pi$
$107$	1.49338e8	+	2.58661e8i	0.110139	+	0.190767i	−0.805687	+	0.592342i	$0.798204\pi$
$108$	5.39768e7	−	9.34905e7i	0.0381769	−	0.0661243i
$109$	1.36395e9			0.925507			0.462753	−	0.886487i	$-0.346862\pi$
$109$	1.36395e9			0.925507			0.462753	+	0.886487i	$0.346862\pi$
$110$	−6.32861e7	+	1.09615e8i	−0.0412137	+	0.0713842i
$111$	−2.97314e7	+	5.14963e7i	−0.0185892	+	0.0321975i
$112$	−1.30281e9			−0.782346
$113$	−1.16972e9	+	2.02602e9i	−0.674884	+	1.16893i	0.301618	+	0.953429i	$0.402473\pi$
$113$	−1.16972e9	+	2.02602e9i	−0.674884	+	1.16893i	−0.976503	+	0.215505i	$0.930860\pi$
$114$	−5.09382e6	−	8.82276e6i	−0.00282470	−	0.00489252i
$115$	−4.71150e8	−	8.16056e8i	−0.251200	−	0.435091i
$116$	−1.78439e9			−0.915014
$117$	−4.25526e8	−	1.97818e9i	−0.209937	−	0.975952i
$118$	1.06262e8			0.0504558
$119$	1.68990e9	+	2.92700e9i	0.772504	+	1.33802i
$120$	−1.94469e7	−	3.36831e7i	−0.00856122	−	0.0148285i
$121$	1.00531e9	−	1.74126e9i	0.426351	−	0.738462i
$122$	5.74884e8			0.234942
$123$	−3.71091e7	+	6.42749e7i	−0.0146187	+	0.0253203i
$124$	2.32651e9	−	4.02963e9i	0.883703	−	1.53062i
$125$	2.95160e9			1.08134
$126$	4.06141e8	−	7.03457e8i	0.143552	−	0.248640i
$127$	1.16688e9	+	2.02110e9i	0.398026	+	0.689401i	0.993482	−	0.113987i	$-0.0363621\pi$
$127$	1.16688e9	+	2.02110e9i	0.398026	+	0.689401i	−0.595457	+	0.803387i	$0.703029\pi$
$128$	−1.38877e9	−	2.40542e9i	−0.457283	−	0.792038i
$129$	−2.35190e7			−0.00747766
$130$	−6.65685e8	−	2.14498e8i	−0.204420	−	0.0658687i
$131$	−4.55953e9			−1.35269			−0.676347	−	0.736583i	$-0.736438\pi$
$131$	−4.55953e9			−1.35269			−0.676347	+	0.736583i	$0.736438\pi$
$132$	−2.55755e7	−	4.42981e7i	−0.00733233	−	0.0127000i
$133$	8.87030e8	+	1.53638e9i	0.245813	+	0.425761i
$134$	8.30793e7	−	1.43898e8i	0.0222598	−	0.0385551i
$135$	−2.43701e8			−0.0631473
$136$	−1.63825e9	+	2.83753e9i	−0.410634	+	0.711240i
$137$	3.73122e9	−	6.46265e9i	0.904915	−	1.56736i	0.0838835	−	0.996476i	$-0.473268\pi$
$137$	3.73122e9	−	6.46265e9i	0.904915	−	1.56736i	0.821031	−	0.570883i	$-0.193399\pi$
$138$	−3.29371e7			−0.00773090
$139$	−1.36478e7	+	2.36387e7i	−0.00310096	+	0.00537101i	−0.867572	−	0.497312i	$-0.834320\pi$
$139$	−1.36478e7	+	2.36387e7i	−0.00310096	+	0.00537101i	0.864471	+	0.502683i	$0.167654\pi$
$140$	1.62304e9	+	2.81118e9i	0.357069	+	0.618462i
$141$	5.38153e6	+	9.32109e6i	0.00114662	+	0.00198601i
$142$	−1.78786e9			−0.369008
$143$	−1.82667e9	−	5.88592e8i	−0.365298	−	0.117707i
$144$	−3.95338e9			−0.766192
$145$	2.01409e9	+	3.48850e9i	0.378375	+	0.655364i
$146$	3.92284e8	+	6.79456e8i	0.0714517	+	0.123758i
$147$	4.58556e6	−	7.94242e6i	0.000809961	−	0.00140289i
$148$	4.81106e9			0.824258
$149$	−1.62135e9	+	2.80826e9i	−0.269488	+	0.466766i	−0.968730	−	0.248119i	$-0.920188\pi$
$149$	−1.62135e9	+	2.80826e9i	−0.269488	+	0.466766i	0.699242	+	0.714885i	$0.253521\pi$
$150$	1.52723e7	−	2.64525e7i	0.00246317	−	0.00426634i
$151$	−5.80126e9			−0.908084			−0.454042	−	0.890980i	$-0.650018\pi$
$151$	−5.80126e9			−0.908084			−0.454042	+	0.890980i	$0.650018\pi$
$152$	−8.59917e8	+	1.48942e9i	−0.130665	+	0.226319i
$153$	5.12804e9	+	8.88202e9i	0.756553	+	1.31039i
$154$	−3.85212e8	−	6.67206e8i	−0.0551895	−	0.0955909i
$155$	−1.05040e10			−1.46171
$156$	2.09581e8	−	1.89636e8i	0.0283329	−	0.0256366i
$157$	1.92250e9			0.252533			0.126267	−	0.991996i	$-0.459700\pi$
$157$	1.92250e9			0.252533			0.126267	+	0.991996i	$0.459700\pi$
$158$	−1.51043e9	−	2.61615e9i	−0.192817	−	0.333969i
$159$	1.55078e8	+	2.68603e8i	0.0192425	+	0.0333291i
$160$	−2.39276e9	+	4.14438e9i	−0.288641	+	0.499941i
$161$	5.73562e9			0.672766
$162$	1.23031e9	−	2.13096e9i	0.140345	−	0.243085i
$163$	2.85625e9	−	4.94716e9i	0.316921	−	0.548924i	−0.662923	−	0.748688i	$-0.730684\pi$
$163$	2.85625e9	−	4.94716e9i	0.316921	−	0.548924i	0.979844	+	0.199764i	$0.0640176\pi$
$164$	6.00491e9			0.648200
$165$	−5.77356e7	+	1.00001e8i	−0.00606410	+	0.0105033i
$166$	2.43016e9	+	4.20916e9i	0.248398	+	0.430239i
$167$	−7.71200e9	−	1.33576e10i	−0.767261	−	1.32893i	−0.939043	−	0.343800i	$-0.888286\pi$
$167$	−7.71200e9	−	1.33576e10i	−0.767261	−	1.32893i	0.171782	−	0.985135i	$-0.445047\pi$
$168$	2.36740e8			0.0229287
$169$	1.05695e9	−	1.05517e10i	0.0996700	−	0.995021i
$170$	3.54497e9			0.325531
$171$	2.69170e9	+	4.66217e9i	0.240738	+	0.416970i
$172$	9.51448e8	+	1.64796e9i	0.0828910	+	0.143571i
$173$	6.98195e9	−	1.20931e10i	0.592611	−	1.02643i	−0.401269	−	0.915960i	$-0.631431\pi$
$173$	6.98195e9	−	1.20931e10i	0.592611	−	1.02643i	0.993879	−	0.110471i	$-0.0352360\pi$
$174$	1.40801e8			0.0116448
$175$	−2.65950e9	+	4.60639e9i	−0.214353	+	0.371270i
$176$	−1.87483e9	+	3.24730e9i	−0.147284	+	0.255103i
$177$	9.69427e7			0.00742396
$178$	3.91528e8	−	6.78146e8i	0.0292329	−	0.0506329i
$179$	−8.38612e9	−	1.45252e10i	−0.610552	−	1.05751i	−0.991148	−	0.132765i	$-0.957614\pi$
$179$	−8.38612e9	−	1.45252e10i	−0.610552	−	1.05751i	0.380596	−	0.924742i	$-0.375719\pi$
$180$	4.92513e9	+	8.53058e9i	0.349697	+	0.605692i
$181$	−9.40427e9			−0.651286			−0.325643	−	0.945493i	$-0.605581\pi$
$181$	−9.40427e9			−0.651286			−0.325643	+	0.945493i	$0.605581\pi$
$182$	3.15665e9	−	2.85625e9i	0.213258	−	0.192963i
$183$	5.24464e8			0.0345689
$184$	2.78015e9	+	4.81537e9i	0.178809	+	0.309706i
$185$	−5.43038e9	−	9.40570e9i	−0.340846	−	0.590362i
$186$	−1.83578e8	+	3.17966e8i	−0.0112463	+	0.0194792i
$187$	9.72754e9			0.581723
$188$	4.35414e8	−	7.54159e8i	0.0254209	−	0.0440304i
$189$	7.41681e8	−	1.28463e9i	0.0422804	−	0.0732318i
$190$	1.86075e9			0.103585
$191$	−1.17835e10	+	2.04097e10i	−0.640657	+	1.10965i	0.344629	+	0.938739i	$0.388005\pi$
$191$	−1.17835e10	+	2.04097e10i	−0.640657	+	1.10965i	−0.985286	+	0.170912i	$0.945329\pi$
$192$	−2.16359e8	−	3.74744e8i	−0.0114900	−	0.0199012i
$193$	1.48767e10	+	2.57672e10i	0.771788	+	1.33678i	0.936582	+	0.350449i	$0.113971\pi$
$193$	1.48767e10	+	2.57672e10i	0.771788	+	1.33678i	−0.164794	+	0.986328i	$0.552696\pi$
$194$	−1.97235e9			−0.0999716
$195$	−6.07301e8	−	1.95686e8i	−0.0300780	−	0.00969178i
$196$	−7.42024e8			−0.0359142
$197$	1.93122e9	+	3.34498e9i	0.0913554	+	0.158232i	0.908082	−	0.418793i	$-0.137547\pi$
$197$	1.93122e9	+	3.34498e9i	0.0913554	+	0.158232i	−0.816726	+	0.577025i	$0.804213\pi$
$198$	−1.16893e9	−	2.02465e9i	−0.0540499	−	0.0936172i
$199$	−8.44339e9	+	1.46244e10i	−0.381661	+	0.661057i	−0.991300	−	0.131623i	$-0.957981\pi$
$199$	−8.44339e9	+	1.46244e10i	−0.381661	+	0.661057i	0.609639	+	0.792679i	$0.291315\pi$
$200$	−5.15642e9			−0.227884
$201$	7.57929e7	−	1.31277e8i	0.00327526	−	0.00567292i
$202$	−5.78175e9	+	1.00143e10i	−0.244331	+	0.423193i
$203$	−2.45188e10			−1.01337
$204$	−7.16307e8	+	1.24068e9i	−0.0289576	+	0.0501561i
$205$	−6.77791e9	−	1.17397e10i	−0.268042	−	0.464263i
$206$	−5.93186e9	−	1.02743e10i	−0.229503	−	0.397511i
$207$	1.74048e10			0.658874
$208$	−1.97207e10	−	6.35443e9i	−0.730527	−	0.235392i
$209$	5.10598e9			0.185106
$210$	−1.28069e8	−	2.21822e8i	−0.00454420	−	0.00787079i
$211$	1.70685e10	+	2.95635e10i	0.592822	+	1.02680i	0.993850	+	0.110733i	$0.0353197\pi$
$211$	1.70685e10	+	2.95635e10i	0.592822	+	1.02680i	−0.401028	+	0.916066i	$0.631347\pi$
$212$	1.25472e10	−	2.17323e10i	0.426613	−	0.738915i
$213$	−1.63105e9			−0.0542950
$214$	−9.53415e8	+	1.65136e9i	−0.0310756	+	0.0538246i
$215$	2.14785e9	−	3.72019e9i	0.0685538	−	0.118739i
$216$	1.43802e9			0.0449494
$217$	3.19679e10	−	5.53700e10i	0.978691	−	1.69514i
$218$	4.35392e9	+	7.54121e9i	0.130565	+	0.226145i
$219$	3.57879e8	+	6.19864e8i	0.0105133	+	0.0182095i
$220$	9.34265e9			0.268886
$221$	1.13038e10	+	5.25486e10i	0.318755	+	1.48182i
$222$	−3.79627e8			−0.0104898
$223$	−2.81037e10	−	4.86770e10i	−0.761011	−	1.31811i	−0.942330	−	0.334686i	$-0.891370\pi$
$223$	−2.81037e10	−	4.86770e10i	−0.761011	−	1.31811i	0.181319	−	0.983424i	$-0.441963\pi$
$224$	−1.45643e10	−	2.52261e10i	−0.386521	−	0.669474i
$225$	−8.07028e9	+	1.39781e10i	−0.209927	+	0.363604i
$226$	−1.49357e10			−0.380834
$227$	6.84082e9	−	1.18486e10i	0.170998	−	0.296178i	−0.767771	−	0.640725i	$-0.778634\pi$
$227$	6.84082e9	−	1.18486e10i	0.170998	−	0.296178i	0.938769	+	0.344547i	$0.111967\pi$
$228$	−3.75989e8	+	6.51232e8i	−0.00921442	+	0.0159599i
$229$	4.60243e10			1.10593			0.552965	−	0.833204i	$-0.313496\pi$
$229$	4.60243e10			1.10593			0.552965	+	0.833204i	$0.313496\pi$
$230$	3.00795e9	−	5.20993e9i	0.0708755	−	0.122760i
$231$	−3.51427e8	−	6.08689e8i	−0.00812046	−	0.0140651i
$232$	−1.18847e10	−	2.05849e10i	−0.269334	−	0.466500i
$233$	4.15225e10			0.922957			0.461478	−	0.887151i	$-0.347319\pi$
$233$	4.15225e10			0.922957			0.461478	+	0.887151i	$0.347319\pi$
$234$	9.57889e9	−	8.66732e9i	0.208854	−	0.188979i
$235$	−1.96585e9			−0.0420481
$236$	−3.92176e9	−	6.79269e9i	−0.0822957	−	0.142540i
$237$	−1.37796e9	−	2.38670e9i	−0.0283707	−	0.0491394i
$238$	−1.07888e10	+	1.86868e10i	−0.217960	+	0.377518i
$239$	−3.15824e10			−0.626116			−0.313058	−	0.949734i	$-0.601353\pi$
$239$	−3.15824e10			−0.626116			−0.313058	+	0.949734i	$0.601353\pi$
$240$	−6.23313e8	+	1.07961e9i	−0.0121271	+	0.0210047i
$241$	−4.30413e10	+	7.45497e10i	−0.821880	+	1.42354i	0.0824008	+	0.996599i	$0.473741\pi$
$241$	−4.30413e10	+	7.45497e10i	−0.821880	+	1.42354i	−0.904281	+	0.426938i	$0.859592\pi$
$242$	1.28364e10			0.240588
$243$	3.37693e9	−	5.84902e9i	0.0621289	−	0.107610i
$244$	−2.12169e10	−	3.67487e10i	−0.383202	−	0.663725i
$245$	8.37544e8	+	1.45067e9i	0.0148512	+	0.0257230i
$246$	−4.73830e8			−0.00824924
$247$	5.93333e9	+	2.75827e10i	0.101429	+	0.471521i
$248$	6.19816e10			1.04047
$249$	2.21702e9	+	3.84000e9i	0.0365488	+	0.0633044i
$250$	9.42192e9	+	1.63192e10i	0.152549	+	0.264223i
$251$	−3.36390e10	+	5.82644e10i	−0.534948	+	0.926556i	0.464218	+	0.885721i	$0.346335\pi$
$251$	−3.36390e10	+	5.82644e10i	−0.534948	+	0.926556i	−0.999166	+	0.0408356i	$0.986998\pi$
$252$	−5.99568e10			−0.936561
$253$	8.25394e9	−	1.42962e10i	0.126654	−	0.219371i
$254$	−7.44971e9	+	1.29033e10i	−0.112302	+	0.194513i
$255$	3.23406e9			0.0478980
$256$	−1.01531e10	+	1.75857e10i	−0.147747	+	0.255906i
$257$	−1.83888e10	−	3.18503e10i	−0.262939	−	0.455423i	0.704083	−	0.710118i	$-0.251358\pi$
$257$	−1.83888e10	−	3.18503e10i	−0.262939	−	0.455423i	−0.967021	+	0.254695i	$0.918025\pi$
$258$	−7.50760e7	−	1.30035e8i	−0.00105490	−	0.00182714i
$259$	6.61076e10			0.912856
$260$	1.08565e10	+	5.04694e10i	0.147336	+	0.684933i
$261$	−7.44026e10			−0.992443
$262$	−1.45547e10	−	2.52094e10i	−0.190830	−	0.330527i
$263$	−3.04287e9	−	5.27040e9i	−0.0392177	−	0.0679271i	0.845750	−	0.533579i	$-0.179153\pi$
$263$	−3.04287e9	−	5.27040e9i	−0.0392177	−	0.0679271i	−0.884968	+	0.465652i	$0.845820\pi$
$264$	3.40685e8	−	5.90084e8i	0.00431654	−	0.00747646i
$265$	−5.66493e10			−0.705649
$266$	−5.66304e9	+	9.80868e9i	−0.0693557	+	0.120128i
$267$	3.57189e8	−	6.18669e8i	0.00430127	−	0.00745002i
$268$	−1.22646e10			−0.145227
$269$	2.53390e9	−	4.38885e9i	0.0295056	−	0.0511053i	−0.850896	−	0.525335i	$-0.823940\pi$
$269$	2.53390e9	−	4.38885e9i	0.0295056	−	0.0511053i	0.880401	+	0.474230i	$0.157273\pi$
$270$	−7.77926e8	−	1.34741e9i	−0.00890843	−	0.0154299i
$271$	4.11352e10	+	7.12483e10i	0.463289	+	0.802440i	0.999122	−	0.0418837i	$-0.0133359\pi$
$271$	4.11352e10	+	7.12483e10i	0.463289	+	0.802440i	−0.535834	+	0.844324i	$0.680003\pi$
$272$	1.05018e11			1.16334
$273$	2.87980e9	−	2.60574e9i	0.0313783	−	0.0283922i
$274$	4.76422e10			0.510640
$275$	7.65440e9	+	1.32578e10i	0.0807075	+	0.139790i
$276$	1.21559e9	+	2.10546e9i	0.0126095	+	0.0218402i
$277$	6.86879e10	−	1.18971e11i	0.701006	−	1.21418i	−0.267108	−	0.963667i	$-0.586068\pi$
$277$	6.86879e10	−	1.18971e11i	0.701006	−	1.21418i	0.968114	−	0.250511i	$-0.0805986\pi$
$278$	−1.74262e8			−0.00174986
$279$	9.70070e10	−	1.68021e11i	0.958483	−	1.66014i
$280$	−2.16201e10	+	3.74471e10i	−0.210207	+	0.364088i
$281$	−1.18897e11			−1.13761			−0.568805	−	0.822473i	$-0.692594\pi$
$281$	−1.18897e11			−1.13761			−0.568805	+	0.822473i	$0.692594\pi$
$282$	−3.43572e7	+	5.95084e7i	−0.000323517	+	0.000560347i
$283$	−7.20944e10	−	1.24871e11i	−0.668132	−	1.15724i	−0.978426	−	0.206598i	$-0.933761\pi$
$283$	−7.20944e10	−	1.24871e11i	−0.668132	−	1.15724i	0.310294	−	0.950641i	$-0.399573\pi$
$284$	6.59834e10	+	1.14287e11i	0.601869	+	1.04247i
$285$	1.69756e9			0.0152413
$286$	−2.57668e9	−	1.19784e10i	−0.0227726	−	0.105865i
$287$	8.25119e10			0.717874
$288$	−4.41955e10	−	7.65489e10i	−0.378540	−	0.655651i
$289$	−7.69282e10	−	1.33244e11i	−0.648702	−	1.12358i
$290$	−1.28585e10	+	2.22716e10i	−0.106758	+	0.184910i
$291$	−1.79937e9			−0.0147096
$292$	2.89555e10	−	5.01525e10i	0.233082	−	0.403710i
$293$	−6.91406e10	+	1.19755e11i	−0.548061	+	0.949270i	0.450346	+	0.892854i	$0.351301\pi$
$293$	−6.91406e10	+	1.19755e11i	−0.548061	+	0.949270i	−0.998407	+	0.0564156i	$0.982033\pi$
$294$	5.85509e7			0.000457058
$295$	−8.85321e9	+	1.53342e10i	−0.0680615	+	0.117886i
$296$	3.20435e10	+	5.55009e10i	0.242620	+	0.420231i
$297$	−2.13466e9	−	3.69734e9i	−0.0159193	−	0.0275731i
$298$	−2.07023e10			−0.152071
$299$	8.68204e10	+	2.79754e10i	0.628205	+	0.202421i
$300$	−2.25459e9			−0.0160702
$301$	1.30736e10	+	2.26441e10i	0.0918007	+	0.159004i
$302$	−1.85184e10	−	3.20748e10i	−0.128107	−	0.221888i
$303$	−5.27466e9	+	9.13598e9i	−0.0359503	+	0.0622678i
$304$	5.51241e10			0.370178
$305$	−4.78962e10	+	8.29587e10i	−0.316922	+	0.548924i
$306$	−3.27388e10	+	5.67053e10i	−0.213460	+	0.369723i
$307$	2.16461e10			0.139077			0.0695387	−	0.997579i	$-0.477847\pi$
$307$	2.16461e10			0.139077			0.0695387	+	0.997579i	$0.477847\pi$
$308$	−2.84335e10	+	4.92483e10i	−0.180033	+	0.311827i
$309$	−5.41161e9	−	9.37319e9i	−0.0337686	−	0.0584890i
$310$	−3.35301e10	−	5.80759e10i	−0.206209	−	0.357164i
$311$	1.38827e11			0.841497			0.420749	−	0.907177i	$-0.361767\pi$
$311$	1.38827e11			0.841497			0.420749	+	0.907177i	$0.361767\pi$
$312$	3.58355e9	+	1.15470e9i	0.0214100	+	0.00689879i
$313$	−6.48779e10			−0.382074			−0.191037	−	0.981583i	$-0.561185\pi$
$313$	−6.48779e10			−0.382074			−0.191037	+	0.981583i	$0.561185\pi$
$314$	6.13690e9	+	1.06294e10i	0.0356259	+	0.0617058i
$315$	6.76749e10	+	1.17216e11i	0.387285	+	0.670797i
$316$	−1.11489e11	+	1.93105e11i	−0.628986	+	1.08944i
$317$	−1.58646e11			−0.882395			−0.441197	−	0.897410i	$-0.645446\pi$
$317$	−1.58646e11			−0.882395			−0.441197	+	0.897410i	$0.645446\pi$
$318$	−9.90059e8	+	1.71483e9i	−0.00542924	+	0.00940372i
$319$	−3.52842e10	+	6.11140e10i	−0.190775	+	0.330432i
$320$	7.90350e10			0.421352
$321$	−8.69796e8	+	1.50653e9i	−0.00457240	+	0.00791963i
$322$	1.83089e10	+	3.17119e10i	0.0949097	+	0.164388i
$323$	−7.15029e10	−	1.23847e11i	−0.365521	−	0.633101i
$324$	−1.81625e11			−0.915637
$325$	−6.27246e10	+	5.67555e10i	−0.311862	+	0.282184i
$326$	3.64701e10			0.178837
$327$	3.97206e9	+	6.87981e9i	0.0192110	+	0.0332745i
$328$	3.99949e10	+	6.92733e10i	0.190798	+	0.330471i
$329$	5.98291e9	−	1.03627e10i	0.0281534	−	0.0487631i
$330$	−7.37201e8			−0.00342194
$331$	−7.80524e10	+	1.35191e11i	−0.357405	+	0.619043i	−0.987526	−	0.157453i	$-0.949672\pi$
$331$	−7.80524e10	+	1.35191e11i	−0.357405	+	0.619043i	0.630122	+	0.776496i	$0.283005\pi$
$332$	1.79377e11	−	3.10690e11i	0.810299	−	1.40348i
$333$	2.00604e11			0.894007
$334$	4.92355e10	−	8.52785e10i	0.216481	−	0.374956i
$335$	1.38434e10	+	2.39775e10i	0.0600540	+	0.104017i
$336$	−3.79400e9	−	6.57140e9i	−0.0162394	−	0.0281275i
$337$	−4.95762e10			−0.209382			−0.104691	−	0.994505i	$-0.533385\pi$
$337$	−4.95762e10			−0.209382			−0.104691	+	0.994505i	$0.533385\pi$
$338$	6.17137e10	−	2.78386e10i	0.257191	−	0.116017i
$339$	−1.36257e10			−0.0560352
$340$	−1.30832e11	−	2.26608e11i	−0.530957	−	0.919644i
$341$	−9.20080e10	−	1.59362e11i	−0.368494	−	0.638251i
$342$	−1.71846e10	+	2.97646e10i	−0.0679237	+	0.117647i
$343$	2.51102e11			0.979549
$344$	−1.26740e10	+	2.19520e10i	−0.0487979	+	0.0845204i
$345$	2.74414e9	−	4.75299e9i	0.0104285	−	0.0180626i
$346$	8.91494e10			0.334408
$347$	1.47050e11	−	2.54699e11i	0.544482	−	0.943071i	−0.454157	−	0.890922i	$-0.650060\pi$
$347$	1.47050e11	−	2.54699e11i	0.544482	−	0.943071i	0.998639	−	0.0521492i	$-0.0166071\pi$
$348$	−5.19644e9	−	9.00050e9i	−0.0189932	−	0.0328973i
$349$	−1.03964e10	−	1.80071e10i	−0.0375119	−	0.0649725i	0.846660	−	0.532134i	$-0.178610\pi$
$349$	−1.03964e10	−	1.80071e10i	−0.0375119	−	0.0649725i	−0.884172	+	0.467162i	$0.845277\pi$
$350$	−3.39580e10			−0.120958
$351$	1.74926e10	−	1.58280e10i	0.0615139	−	0.0556600i
$352$	−8.38360e10			−0.291064
$353$	1.52463e11	+	2.64074e11i	0.522611	+	0.905188i	0.999654	+	0.0263083i	$0.00837515\pi$
$353$	1.52463e11	+	2.64074e11i	0.522611	+	0.905188i	−0.477043	+	0.878880i	$0.658292\pi$
$354$	3.09455e8	+	5.35991e8i	0.00104733	+	0.00181402i
$355$	1.48955e11	−	2.57997e11i	0.497767	−	0.862158i
$356$	−5.77994e10			−0.190721
$357$	−9.84258e9	+	1.70479e10i	−0.0320702	+	0.0555473i
$358$	5.35393e10	−	9.27328e10i	0.172266	−	0.298373i
$359$	−4.70632e11			−1.49540			−0.747698	−	0.664039i	$-0.768841\pi$
$359$	−4.70632e11			−1.49540			−0.747698	+	0.664039i	$0.768841\pi$
$360$	−6.56064e10	+	1.13634e11i	−0.205866	+	0.356571i
$361$	1.23812e11	+	2.14449e11i	0.383690	+	0.664570i
$362$	−3.00197e10	−	5.19957e10i	−0.0918794	−	0.159140i
$363$	1.17106e10			0.0353997
$364$	−2.99082e11	−	9.63709e10i	−0.892965	−	0.287733i
$365$	−1.30732e11			−0.385535
$366$	1.67416e9	+	2.89973e9i	0.00487677	+	0.00844682i
$367$	3.26246e11	+	5.65075e11i	0.938745	+	1.62595i	0.767815	+	0.640672i	$0.221344\pi$
$367$	3.26246e11	+	5.65075e11i	0.938745	+	1.62595i	0.170931	+	0.985283i	$0.445323\pi$
$368$	8.91095e10	−	1.54342e11i	0.253285	−	0.438702i
$369$	2.50383e11			0.703051
$370$	3.46691e10	−	6.00486e10i	0.0961689	−	0.166569i
$371$	1.72407e11	−	2.98618e11i	0.472469	−	0.818340i
$372$	2.71007e10			0.0733733
$373$	−6.11421e10	+	1.05901e11i	−0.163550	+	0.283277i	−0.936139	−	0.351629i	$-0.885628\pi$
$373$	−6.11421e10	+	1.05901e11i	−0.163550	+	0.283277i	0.772589	+	0.634906i	$0.218961\pi$
$374$	3.10517e10	+	5.37831e10i	0.0820659	+	0.142142i
$375$	8.59557e9	+	1.48880e10i	0.0224457	+	0.0388772i
$376$	1.16001e10			0.0299306
$377$	−3.71142e11	−	1.19590e11i	−0.946246	−	0.304901i
$378$	9.47019e9			0.0238586
$379$	2.27772e11	+	3.94514e11i	0.567055	+	0.982167i	0.996855	+	0.0792435i	$0.0252505\pi$
$379$	2.27772e11	+	3.94514e11i	0.567055	+	0.982167i	−0.429801	+	0.902924i	$0.641416\pi$
$380$	−6.86737e10	−	1.18946e11i	−0.168952	−	0.292634i
$381$	−6.79634e9	+	1.17716e10i	−0.0165239	+	0.0286202i
$382$	−1.50459e11			−0.361520
$383$	−2.96947e11	+	5.14327e11i	−0.705154	+	1.22136i	0.261481	+	0.965209i	$0.415789\pi$
$383$	−2.96947e11	+	5.14327e11i	−0.705154	+	1.22136i	−0.966636	+	0.256155i	$0.917544\pi$
$384$	8.08868e9	−	1.40100e10i	0.0189840	−	0.0328812i
$385$	1.28375e11			0.297788
$386$	−9.49769e10	+	1.64505e11i	−0.217758	+	0.377169i
$387$	3.96720e10	+	6.87140e10i	0.0899052	+	0.155720i
$388$	7.27924e10	+	1.26080e11i	0.163058	+	0.282425i
$389$	−8.62301e11			−1.90935			−0.954675	−	0.297650i	$-0.903797\pi$
$389$	−8.62301e11			−1.90935			−0.954675	+	0.297650i	$0.903797\pi$
$390$	−8.56653e8	−	3.98239e9i	−0.00187506	−	0.00871672i
$391$	−4.62345e11			−1.00039
$392$	−4.94216e9	−	8.56007e9i	−0.0105713	−	0.0183101i
$393$	−1.32782e10	−	2.29984e10i	−0.0280783	−	0.0486331i
$394$	−1.23295e10	+	2.13553e10i	−0.0257757	+	0.0446449i
$395$	5.03364e11			1.04039
$396$	−8.62819e10	+	1.49445e11i	−0.176316	+	0.305388i
$397$	8.91115e10	−	1.54346e11i	0.180043	−	0.311844i	−0.761852	−	0.647751i	$-0.775710\pi$
$397$	8.91115e10	−	1.54346e11i	0.180043	−	0.311844i	0.941895	+	0.335907i	$0.109043\pi$
$398$	−1.07810e11			−0.215370
$399$	−5.16637e9	+	8.94841e9i	−0.0102049	+	0.0176753i
$400$	8.26368e10	+	1.43131e11i	0.161400	+	0.279553i
$401$	−1.79515e11	−	3.10929e11i	−0.346698	−	0.600499i	0.638963	−	0.769238i	$-0.279364\pi$
$401$	−1.79515e11	−	3.10929e11i	−0.346698	−	0.600499i	−0.985661	+	0.168739i	$0.946030\pi$
$402$	9.67765e8			0.00184822
$403$	7.53967e11	−	6.82216e11i	1.42390	−	1.28840i
$404$	8.53534e11			1.59406
$405$	2.05005e11	+	3.55080e11i	0.378632	+	0.655810i
$406$	−7.82674e10	−	1.35563e11i	−0.142960	−	0.247613i
$407$	9.51333e10	−	1.64776e11i	0.171853	−	0.297658i
$408$	−1.90835e10			−0.0340947
$409$	2.71317e11	−	4.69935e11i	0.479427	−	0.830391i	−0.520295	−	0.853987i	$-0.674178\pi$
$409$	2.71317e11	−	4.69935e11i	0.479427	−	0.830391i	0.999722	+	0.0235953i	$0.00751130\pi$
$410$	4.32721e10	−	7.49494e10i	0.0756276	−	0.130991i
$411$	4.34638e10			0.0751345
$412$	−4.37847e11	+	7.58374e11i	−0.748661	+	1.29672i
$413$	−5.38879e10	−	9.33366e10i	−0.0911415	−	0.157862i
$414$	5.55586e10	+	9.62302e10i	0.0929500	+	0.160994i
$415$	−8.09871e11			−1.34029
$416$	−9.74204e10	−	4.52886e11i	−0.159489	−	0.741428i
$417$	−1.58979e8			−0.000257470
$418$	1.62990e10	+	2.82307e10i	0.0261137	+	0.0452302i
$419$	−1.88542e11	−	3.26565e11i	−0.298845	−	0.517614i	0.677027	−	0.735958i	$-0.263268\pi$
$419$	−1.88542e11	−	3.26565e11i	−0.298845	−	0.517614i	−0.975872	+	0.218344i	$0.929935\pi$
$420$	−9.45314e9	+	1.63733e10i	−0.0148236	+	0.0256753i
$421$	7.14406e11			1.10835			0.554173	−	0.832402i	$-0.313035\pi$
$421$	7.14406e11			1.10835			0.554173	+	0.832402i	$0.313035\pi$
$422$	−1.08970e11	+	1.88742e11i	−0.167264	+	0.289709i
$423$	1.81552e10	−	3.14457e10i	0.0275721	−	0.0477562i
$424$	3.34275e11			0.502294
$425$	2.14381e11	−	3.71318e11i	0.318739	−	0.552072i
$426$	−5.20655e9	−	9.01801e9i	−0.00765962	−	0.0132668i
$427$	−2.91536e11	−	5.04955e11i	−0.424391	−	0.735067i
$428$	1.40748e11			0.202743
$429$	−2.35069e9	−	1.09278e10i	−0.00335071	−	0.0155767i
$430$	2.74250e10			0.0386846
$431$	−2.13211e11	−	3.69292e11i	−0.297620	−	0.515493i	0.677971	−	0.735089i	$-0.262859\pi$
$431$	−2.13211e11	−	3.69292e11i	−0.297620	−	0.515493i	−0.975591	+	0.219596i	$0.929526\pi$
$432$	−2.30458e10	−	3.99164e10i	−0.0318357	−	0.0551410i
$433$	−2.30953e11	+	4.00022e11i	−0.315739	+	0.546876i	−0.979594	−	0.200985i	$-0.935586\pi$
$433$	−2.30953e11	+	4.00022e11i	−0.315739	+	0.546876i	0.663855	+	0.747861i	$0.268919\pi$
$434$	4.08184e11			0.552271
$435$	−1.17307e10	+	2.03182e10i	−0.0157081	+	0.0272072i
$436$	3.21375e11	−	5.56638e11i	0.425915	−	0.737706i
$437$	−2.42684e11			−0.318328
$438$	−2.28480e9	+	3.95738e9i	−0.00296629	+	0.00513777i
$439$	3.57047e11	+	6.18423e11i	0.458812	+	0.794686i	0.998898	−	0.0469238i	$-0.0149418\pi$
$439$	3.57047e11	+	6.18423e11i	0.458812	+	0.794686i	−0.540086	+	0.841610i	$0.681608\pi$
$440$	6.22255e10	+	1.07778e11i	0.0791465	+	0.137086i
$441$	−3.09398e10			−0.0389532
$442$	−2.54455e11	+	2.30240e11i	−0.317111	+	0.286934i
$443$	−1.21811e12			−1.50269			−0.751346	−	0.659908i	$-0.770595\pi$
$443$	−1.21811e12			−1.50269			−0.751346	+	0.659908i	$0.770595\pi$
$444$	1.40106e10	+	2.42672e10i	0.0171094	+	0.0296344i
$445$	6.52399e10	+	1.12999e11i	0.0788666	+	0.136601i
$446$	1.79422e11	−	3.10767e11i	0.214718	−	0.371902i
$447$	−1.88866e10			−0.0223754
$448$	−2.40536e11	+	4.16621e11i	−0.282117	+	0.488641i
$449$	−1.54894e10	+	2.68284e10i	−0.0179856	+	0.0311520i	−0.874878	−	0.484343i	$-0.839059\pi$
$449$	−1.54894e10	+	2.68284e10i	−0.0179856	+	0.0311520i	0.856893	+	0.515495i	$0.172392\pi$
$450$	−1.03046e11			−0.118461
$451$	1.18740e11	−	2.05664e11i	0.135146	−	0.234080i
$452$	5.51221e11	+	9.54742e11i	0.621159	+	1.07588i
$453$	−1.68943e10	−	2.92617e10i	−0.0188494	−	0.0326481i
$454$	8.73474e10			0.0964936
$455$	1.49176e11	+	6.93487e11i	0.163173	+	0.758555i
$456$	−1.00169e10			−0.0108491
$457$	3.10463e11	+	5.37738e11i	0.332956	+	0.576697i	0.983090	−	0.183123i	$-0.0586206\pi$
$457$	3.10463e11	+	5.37738e11i	0.332956	+	0.576697i	−0.650134	+	0.759820i	$0.725287\pi$
$458$	1.46916e11	+	2.54466e11i	0.156018	+	0.270231i
$459$	−5.97865e10	+	1.03553e11i	−0.0628703	+	0.108895i
$460$	−4.44051e11			−0.462405
$461$	1.44948e11	−	2.51057e11i	0.149471	−	0.258892i	−0.781561	−	0.623829i	$-0.785576\pi$
$461$	1.44948e11	−	2.51057e11i	0.149471	−	0.258892i	0.931032	+	0.364937i	$0.118909\pi$
$462$	2.24361e9	−	3.88604e9i	0.00229117	−	0.00396843i
$463$	−1.30746e12			−1.32225			−0.661126	−	0.750275i	$-0.729921\pi$
$463$	−1.30746e12			−1.32225			−0.661126	+	0.750275i	$0.729921\pi$
$464$	−3.80928e11	+	6.59786e11i	−0.381515	+	0.660803i
$465$	−3.05894e10	−	5.29823e10i	−0.0303412	−	0.0525524i
$466$	1.32545e11	+	2.29575e11i	0.130205	+	0.225522i
$467$	−1.73341e11			−0.168645			−0.0843227	−	0.996439i	$-0.526873\pi$
$467$	−1.73341e11			−0.168645			−0.0843227	+	0.996439i	$0.526873\pi$
$468$	−9.07569e11	−	2.92439e11i	−0.874527	−	0.281792i
$469$	−1.68525e11			−0.160837
$470$	−6.27528e9	−	1.08691e10i	−0.00593189	−	0.0102743i
$471$	5.59866e9	+	9.69717e9i	0.00524192	+	0.00907927i
$472$	5.22408e10	−	9.04837e10i	0.0484474	−	0.0839134i
$473$	7.52552e10			0.0691292
$474$	8.79729e9	−	1.52374e10i	0.00800472	−	0.0138646i
$475$	1.12528e11	−	1.94905e11i	0.101424	−	0.175671i
$476$	1.59270e12			1.42201
$477$	5.23172e11	−	9.06161e11i	0.462713	−	0.801443i
$478$	−1.00815e11	−	1.74617e11i	−0.0883286	−	0.152990i
$479$	2.60090e11	+	4.50489e11i	0.225743	+	0.390998i	0.956542	−	0.291594i	$-0.0941858\pi$
$479$	2.60090e11	+	4.50489e11i	0.225743	+	0.390998i	−0.730799	+	0.682592i	$0.760852\pi$
$480$	−2.78725e10			−0.0239657
$481$	1.00067e12	+	3.22439e11i	0.852393	+	0.274660i
$482$	−5.49575e11			−0.463783
$483$	1.67031e10	+	2.89306e10i	0.0139648	+	0.0241878i
$484$	−4.73745e11	−	8.20551e11i	−0.392411	−	0.679675i
$485$	1.64326e11	−	2.84620e11i	0.134855	−	0.233576i
$486$	4.31185e10			0.0350591
$487$	−1.49647e11	+	2.59196e11i	−0.120555	+	0.208808i	−0.919987	−	0.391949i	$-0.871801\pi$
$487$	−1.49647e11	+	2.59196e11i	−0.120555	+	0.208808i	0.799431	+	0.600757i	$0.205134\pi$
$488$	2.82625e11	−	4.89521e11i	0.225591	−	0.390735i
$489$	3.32715e10			0.0263138
$490$	−5.34711e9	+	9.26147e9i	−0.00419022	+	0.00725768i
$491$	−5.86260e11	−	1.01543e12i	−0.455223	−	0.788469i	0.543478	−	0.839423i	$-0.317107\pi$
$491$	−5.86260e11	−	1.01543e12i	−0.455223	−	0.788469i	−0.998701	+	0.0509545i	$0.983774\pi$
$492$	1.74873e10	+	3.02889e10i	0.0134549	+	0.0233046i
$493$	1.97644e12			1.50686
$494$	−1.33564e11	+	1.20853e11i	−0.100906	+	0.0913033i
$495$	3.89555e11			0.291639
$496$	−9.93317e11	−	1.72048e12i	−0.736920	−	1.27638i
$497$	9.06660e11	+	1.57038e12i	0.666562	+	1.15452i
$498$	−1.41541e10	+	2.45156e10i	−0.0103122	+	0.0178612i
$499$	−2.19097e12			−1.58192			−0.790959	−	0.611869i	$-0.790418\pi$
$499$	−2.19097e12			−1.58192			−0.790959	+	0.611869i	$0.790418\pi$
$500$	6.95458e11	−	1.20457e12i	0.497629	−	0.861919i
$501$	4.49174e10	−	7.77991e10i	0.0318526	−	0.0551703i
$502$	−4.29521e11			−0.301869
$503$	−7.74097e10	+	1.34078e11i	−0.0539187	+	0.0933900i	−0.891725	−	0.452578i	$-0.850505\pi$
$503$	−7.74097e10	+	1.34078e11i	−0.0539187	+	0.0933900i	0.837806	+	0.545968i	$0.183838\pi$
$504$	−3.99335e11	−	6.91668e11i	−0.275676	−	0.477486i
$505$	−9.63407e11	−	1.66867e12i	−0.659172	−	1.14172i
$506$	1.05391e11			0.0714703
$507$	5.63011e10	−	2.53971e10i	0.0378426	−	0.0170706i
$508$	1.09977e12			0.732680
$509$	1.15953e12	+	2.00837e12i	0.765690	+	1.32621i	0.939881	+	0.341503i	$0.110936\pi$
$509$	1.15953e12	+	2.00837e12i	0.765690	+	1.32621i	−0.174190	+	0.984712i	$0.555731\pi$
$510$	1.03236e10	+	1.78810e10i	0.00675716	+	0.0117037i
$511$	3.97871e11	−	6.89132e11i	0.258136	−	0.447104i
$512$	−1.55174e12			−0.997940
$513$	−3.13819e10	+	5.43550e10i	−0.0200056	+	0.0346506i
$514$	1.17399e11	−	2.03341e11i	0.0741876	−	0.128497i
$515$	1.97684e12			1.23834
$516$	−5.54156e9	+	9.59827e9i	−0.00344119	+	0.00596032i
$517$	−1.72196e10	−	2.98252e10i	−0.0106002	−	0.0183602i
$518$	2.11025e11	+	3.65505e11i	0.128780	+	0.223054i
$519$	8.13306e10			0.0492041
$520$	−5.09912e11	+	4.61387e11i	−0.305830	+	0.276726i
$521$	1.22218e12			0.726717			0.363358	−	0.931649i	$-0.381630\pi$
$521$	1.22218e12			0.726717			0.363358	+	0.931649i	$0.381630\pi$
$522$	−2.37503e11	−	4.11368e11i	−0.140008	−	0.242501i
$523$	−5.36634e10	−	9.29477e10i	−0.0313632	−	0.0543227i	0.849918	−	0.526915i	$-0.176652\pi$
$523$	−5.36634e10	−	9.29477e10i	−0.0313632	−	0.0543227i	−0.881281	+	0.472593i	$0.843318\pi$
$524$	−1.07432e12	+	1.86078e12i	−0.622505	+	1.07821i
$525$	−3.09797e10			−0.0177975
$526$	1.94265e10	−	3.36477e10i	0.0110652	−	0.0191655i
$527$	−2.57691e12	+	4.46334e12i	−1.45530	+	2.52065i
$528$	−2.18393e10			−0.0122289
$529$	5.08271e11	−	8.80351e11i	0.282192	−	0.488771i
$530$	−1.80833e11	−	3.13211e11i	−0.0995486	−	0.172423i
$531$	−1.63524e11	−	2.83231e11i	−0.0892596	−	0.154602i
$532$	8.36009e11			0.452490
$533$	1.24899e12	+	4.02451e11i	0.670325	+	0.215994i
$534$	4.56078e9			0.00242719
$535$	−1.58867e11	−	2.75165e11i	−0.0838379	−	0.145212i
$536$	−8.16870e10	−	1.41486e11i	−0.0427476	−	0.0740410i
$537$	4.88437e10	−	8.45997e10i	0.0253469	−	0.0439020i
$538$	3.23543e10			0.0166499
$539$	−1.46727e10	+	2.54138e10i	−0.00748790	+	0.0129694i
$540$	−5.74208e10	+	9.94558e10i	−0.0290601	+	0.0503336i
$541$	−2.98856e12			−1.49994			−0.749971	−	0.661471i	$-0.769933\pi$
$541$	−2.98856e12			−1.49994			−0.749971	+	0.661471i	$0.769933\pi$
$542$	−2.62619e11	+	4.54869e11i	−0.130716	+	0.226407i
$543$	−2.73869e10	−	4.74354e10i	−0.0135190	−	0.0234155i
$544$	1.17402e12	+	2.03346e12i	0.574751	+	0.995498i
$545$	−1.45098e12			−0.704493
$546$	2.35997e10	+	7.60435e9i	0.0113642	+	0.00366180i
$547$	2.62920e11			0.125569			0.0627844	−	0.998027i	$-0.480002\pi$
$547$	2.62920e11			0.125569			0.0627844	+	0.998027i	$0.480002\pi$
$548$	−1.75830e12	−	3.04547e12i	−0.832877	−	1.44259i
$549$	−8.84669e11	−	1.53229e12i	−0.415629	−	0.719890i
$550$	−4.88678e10	+	8.46415e10i	−0.0227715	+	0.0394413i
$551$	1.03743e12			0.479489
$552$	−1.61926e10	+	2.80464e10i	−0.00742318	+	0.0128573i
$553$	−1.53195e12	+	2.65341e12i	−0.696595	+	1.20654i
$554$	8.77046e11			0.395575
$555$	3.16284e10	−	5.47820e10i	0.0141501	−	0.0245087i
$556$	6.43140e9	+	1.11395e10i	0.00285410	+	0.00494344i
$557$	1.53719e12	+	2.66250e12i	0.676675	+	1.17204i	0.975976	+	0.217877i	$0.0699130\pi$
$557$	1.53719e12	+	2.66250e12i	0.676675	+	1.17204i	−0.299302	+	0.954159i	$0.596754\pi$
$558$	1.23864e12			0.540868
$559$	8.74492e10	+	4.06532e11i	0.0378794	+	0.176093i
$560$	1.38593e12			0.595520
$561$	2.83283e10	+	4.90660e10i	0.0120750	+	0.0209145i
$562$	−3.79536e11	−	6.57376e11i	−0.160487	−	0.277972i
$563$	6.65130e11	−	1.15204e12i	0.279009	−	0.483258i	−0.692130	−	0.721773i	$-0.743327\pi$
$563$	6.65130e11	−	1.15204e12i	0.279009	−	0.483258i	0.971139	+	0.238515i	$0.0766607\pi$
$564$	5.07200e9			0.00211068
$565$	1.24436e12	−	2.15529e12i	0.513721	−	0.889790i
$566$	4.60270e11	−	7.97212e11i	0.188512	−	0.326512i
$567$	−2.49566e12			−1.01406
$568$	−8.78948e11	+	1.52238e12i	−0.354320	+	0.613700i
$569$	−2.13431e12	−	3.69674e12i	−0.853598	−	1.47847i	−0.877940	−	0.478771i	$-0.841082\pi$
$569$	−2.13431e12	−	3.69674e12i	−0.853598	−	1.47847i	0.0243419	−	0.999704i	$-0.492251\pi$
$570$	5.41884e9	+	9.38570e9i	0.00215015	+	0.00372417i
$571$	4.57651e12			1.80166			0.900828	−	0.434175i	$-0.142960\pi$
$571$	4.57651e12			1.80166			0.900828	+	0.434175i	$0.142960\pi$
$572$	−6.70608e11	+	6.06790e11i	−0.261931	+	0.237004i
$573$	−1.37263e11			−0.0531933
$574$	2.63389e11	+	4.56204e11i	0.101273	+	0.175410i
$575$	−3.63809e11	−	6.30136e11i	−0.138793	−	0.240397i
$576$	−7.29910e11	+	1.26424e12i	−0.276292	+	0.478552i
$577$	9.52517e11			0.357752			0.178876	−	0.983872i	$-0.442754\pi$
$577$	9.52517e11			0.357752			0.178876	+	0.983872i	$0.442754\pi$
$578$	4.91131e11	−	8.50664e11i	0.183030	−	0.317017i
$579$	−8.66469e10	+	1.50077e11i	−0.0320405	+	0.0554958i
$580$	1.89824e12			0.696507
$581$	2.46477e12	−	4.26911e12i	0.897396	−	1.55434i
$582$	−5.74383e9	−	9.94860e9i	−0.00207514	−	0.00359425i
$583$	−4.96212e11	−	8.59464e11i	−0.177893	−	0.308119i
$584$	7.71419e11			0.274431
$585$	4.52677e11	+	2.10440e12i	0.159804	+	0.742892i
$586$	−8.82826e11			−0.309268
$587$	−1.21432e12	−	2.10327e12i	−0.422146	−	0.731179i	0.574003	−	0.818853i	$-0.305390\pi$
$587$	−1.21432e12	−	2.10327e12i	−0.422146	−	0.731179i	−0.996149	+	0.0876746i	$0.972056\pi$
$588$	−2.16090e9	−	3.74279e9i	−0.000745482	−	0.00129121i
$589$	−1.35262e12	+	2.34281e12i	−0.463081	+	0.802080i
$590$	−1.13043e11			−0.0384068
$591$	−1.12481e10	+	1.94823e10i	−0.00379259	+	0.00656896i
$592$	1.02706e12	−	1.77892e12i	0.343674	−	0.595262i
$593$	1.36233e12			0.452415			0.226207	−	0.974079i	$-0.427367\pi$
$593$	1.36233e12			0.452415			0.226207	+	0.974079i	$0.427367\pi$
$594$	1.36283e10	−	2.36048e10i	0.00449160	−	0.00777968i
$595$	−1.79773e12	−	3.11376e12i	−0.588028	−	1.01849i
$596$	7.64047e11	+	1.32337e12i	0.248034	+	0.429608i
$597$	−9.83544e10			−0.0316891
$598$	1.22468e11	+	5.69327e11i	0.0391622	+	0.182056i
$599$	−2.94102e12			−0.933420			−0.466710	−	0.884410i	$-0.654561\pi$
$599$	−2.94102e12			−0.933420			−0.466710	+	0.884410i	$0.654561\pi$
$600$	−1.50164e10	−	2.60091e10i	−0.00473026	−	0.00819305i
$601$	1.33023e11	+	2.30403e11i	0.0415904	+	0.0720367i	0.886071	−	0.463549i	$-0.153424\pi$
$601$	1.33023e11	+	2.30403e11i	0.0415904	+	0.0720367i	−0.844481	+	0.535586i	$0.820091\pi$
$602$	−8.34655e10	+	1.44567e11i	−0.0259014	+	0.0448625i
$603$	−5.11391e11			−0.157516
$604$	−1.36690e12	+	2.36753e12i	−0.417897	+	0.723818i
$605$	−1.06946e12	+	1.85236e12i	−0.324538	+	0.562116i
$606$	−6.73498e10			−0.0202866
$607$	6.04558e11	−	1.04712e12i	0.180754	−	0.313076i	−0.761383	−	0.648302i	$-0.775479\pi$
$607$	6.04558e11	−	1.04712e12i	0.180754	−	0.313076i	0.942138	+	0.335226i	$0.108813\pi$
$608$	6.16241e11	+	1.06736e12i	0.182888	+	0.316771i
$609$	−7.14029e10	−	1.23674e11i	−0.0210348	−	0.0364333i
$610$	−6.11565e11			−0.178838
$611$	1.41108e11	−	1.27679e11i	0.0409605	−	0.0370625i
$612$	4.83308e12			1.39265
$613$	−2.01039e11	−	3.48210e11i	−0.0575054	−	0.0996022i	0.835840	−	0.548974i	$-0.184981\pi$
$613$	−2.01039e11	−	3.48210e11i	−0.0575054	−	0.0996022i	−0.893345	+	0.449371i	$0.851648\pi$
$614$	6.90972e10	+	1.19680e11i	0.0196202	+	0.0339832i
$615$	3.94769e10	−	6.83760e10i	0.0111277	−	0.0192737i
$616$	−7.57512e11			−0.211971
$617$	2.80041e11	−	4.85045e11i	0.0777925	−	0.134741i	−0.824505	−	0.565855i	$-0.808546\pi$
$617$	2.80041e11	−	4.85045e11i	0.0777925	−	0.134741i	0.902297	+	0.431114i	$0.141879\pi$
$618$	3.45492e10	−	5.98410e10i	0.00952775	−	0.0165025i
$619$	3.82193e12			1.04634			0.523172	−	0.852227i	$-0.324749\pi$
$619$	3.82193e12			1.04634			0.523172	+	0.852227i	$0.324749\pi$
$620$	−2.47495e12	+	4.28674e12i	−0.672673	+	1.16510i
$621$	1.01459e11	+	1.75732e11i	0.0273766	+	0.0474176i
$622$	4.43155e11	+	7.67568e11i	0.118713	+	0.205617i
$623$	−7.94207e11			−0.211221
$624$	−2.53780e10	−	1.17977e11i	−0.00670081	−	0.0311506i
$625$	−1.53555e12			−0.402536
$626$	−2.07099e11	−	3.58706e11i	−0.0539007	−	0.0933587i
$627$	1.48695e10	+	2.57547e10i	0.00384231	+	0.00665508i
$628$	4.52981e11	−	7.84587e11i	0.116215	−	0.201290i
$629$	−5.32889e12			−1.35740
$630$	−4.32056e11	+	7.48342e11i	−0.109272	+	0.189264i
$631$	−2.65464e12	+	4.59798e12i	−0.666614	+	1.15461i	0.312231	+	0.950006i	$0.398924\pi$
$631$	−2.65464e12	+	4.59798e12i	−0.666614	+	1.15461i	−0.978845	+	0.204603i	$0.934410\pi$
$632$	−2.97024e12			−0.740568
$633$	−9.94129e10	+	1.72188e11i	−0.0246108	+	0.0426272i
$634$	−5.06421e11	−	8.77146e11i	−0.124483	−	0.215611i
$635$	−1.24134e12	−	2.15006e12i	−0.302976	−	0.524770i
$636$	1.46158e11			0.0354214
$637$	−1.54337e11	−	4.97307e10i	−0.0371400	−	0.0119673i
$638$	−4.50528e11			−0.107654
$639$	2.75127e12	+	4.76534e12i	0.652799	+	1.13068i
$640$	1.47738e12	+	2.55890e12i	0.348083	+	0.602898i
$641$	7.40710e11	−	1.28295e12i	0.173295	−	0.300156i	−0.766275	−	0.642513i	$-0.777892\pi$
$641$	7.40710e11	−	1.28295e12i	0.173295	−	0.300156i	0.939570	+	0.342357i	$0.111225\pi$
$642$	−1.11060e10			−0.00258019
$643$	−8.07901e11	+	1.39933e12i	−0.186384	+	0.322827i	−0.944042	−	0.329825i	$-0.893010\pi$
$643$	−8.07901e11	+	1.39933e12i	−0.186384	+	0.322827i	0.757658	+	0.652652i	$0.226344\pi$
$644$	1.35143e12	−	2.34074e12i	0.309604	−	0.536250i
$645$	2.50197e10			0.00569198
$646$	4.56494e11	−	7.90671e11i	0.103131	−	0.178628i
$647$	3.12449e12	+	5.41178e12i	0.700987	+	1.21415i	0.968120	+	0.250486i	$0.0805903\pi$
$647$	3.12449e12	+	5.41178e12i	0.700987	+	1.21415i	−0.267133	+	0.963660i	$0.586076\pi$
$648$	−1.20969e12	−	2.09525e12i	−0.269517	−	0.466818i
$649$	−3.10193e11			−0.0686328
$650$	−5.14023e11	−	1.65630e11i	−0.112947	−	0.0363939i
$651$	3.72384e11			0.0812600
$652$	−1.34598e12	−	2.33131e12i	−0.291692	−	0.505225i
$653$	1.16833e12	+	2.02361e12i	0.251453	+	0.435529i	0.963926	−	0.266170i	$-0.0857583\pi$
$653$	1.16833e12	+	2.02361e12i	0.251453	+	0.435529i	−0.712473	+	0.701699i	$0.752425\pi$
$654$	−2.53587e10	+	4.39226e10i	−0.00542035	+	0.00938833i
$655$	4.85046e12			1.02967
$656$	1.28192e12	−	2.22035e12i	0.270267	−	0.468116i
$657$	1.20734e12	−	2.09118e12i	0.252806	−	0.437872i
$658$	7.63931e10			0.0158868
$659$	4.28438e12	−	7.42076e12i	0.884919	−	1.53272i	0.0391117	−	0.999235i	$-0.487547\pi$
$659$	4.28438e12	−	7.42076e12i	0.884919	−	1.53272i	0.845807	−	0.533489i	$-0.179119\pi$
$660$	2.72074e10	+	4.71246e10i	0.00558135	+	0.00966718i
$661$	−1.96292e12	−	3.39987e12i	−0.399940	−	0.692717i	0.593778	−	0.804629i	$-0.297636\pi$
$661$	−1.96292e12	−	3.39987e12i	−0.399940	−	0.692717i	−0.993718	+	0.111912i	$0.964302\pi$
$662$	−9.96616e11			−0.201682
$663$	−2.32139e11	+	2.10047e11i	−0.0466591	+	0.0422188i
$664$	4.77887e12			0.954045
$665$	−9.43627e11	−	1.63441e12i	−0.187113	−	0.324089i
$666$	6.40357e11	+	1.10913e12i	0.126121	+	0.218448i
$667$	1.67704e12	−	2.90471e12i	0.328078	−	0.568247i
$668$	−7.26842e12			−1.41236
$669$	1.63685e11	−	2.83511e11i	0.0315931	−	0.0547209i
$670$	−8.83803e10	+	1.53079e11i	−0.0169441	+	0.0293481i
$671$	−1.67816e12			−0.319582
$672$	8.48274e10	−	1.46925e11i	0.0160463	−	0.0277930i
$673$	1.33513e12	+	2.31251e12i	0.250874	+	0.434526i	0.963767	−	0.266747i	$-0.0859488\pi$
$673$	1.33513e12	+	2.31251e12i	0.250874	+	0.434526i	−0.712893	+	0.701273i	$0.752616\pi$
$674$	−1.58254e11	−	2.74104e11i	−0.0295383	−	0.0511618i
$675$	−1.88179e11			−0.0348902
$676$	−4.05718e12	−	2.91754e12i	−0.747247	−	0.537350i
$677$	−3.61891e12			−0.662107			−0.331054	−	0.943612i	$-0.607404\pi$
$677$	−3.61891e12			−0.662107			−0.331054	+	0.943612i	$0.607404\pi$
$678$	−4.34952e10	−	7.53359e10i	−0.00790510	−	0.0136920i
$679$	1.00022e12	+	1.73243e12i	0.180585	+	0.312783i
$680$	1.74278e12	−	3.01859e12i	0.312574	−	0.541394i
$681$	7.96866e10			0.0141979
$682$	5.87404e11	−	1.01741e12i	0.103970	−	0.180081i
$683$	4.07016e12	−	7.04972e12i	0.715679	−	1.23959i	−0.247018	−	0.969011i	$-0.579451\pi$
$683$	4.07016e12	−	7.04972e12i	0.715679	−	1.23959i	0.962697	−	0.270581i	$-0.0872159\pi$
$684$	2.53688e12			0.443147
$685$	−3.96929e12	+	6.87501e12i	−0.688819	+	1.19307i
$686$	8.01551e11	+	1.38833e12i	0.138189	+	0.239350i
$687$	1.34031e11	+	2.32148e11i	0.0229562	+	0.0397612i
$688$	8.12454e11			0.138246
$689$	4.06625e12	−	3.67928e12i	0.687396	−	0.621981i
$690$	3.50387e10			0.00588474
$691$	4.32097e12	+	7.48413e12i	0.720991	+	1.24879i	0.960603	+	0.277924i	$0.0896464\pi$
$691$	4.32097e12	+	7.48413e12i	0.720991	+	1.24879i	−0.239612	+	0.970869i	$0.577020\pi$
$692$	−3.29018e12	−	5.69876e12i	−0.545434	−	0.944720i
$693$	−1.18558e12	+	2.05348e12i	−0.195268	+	0.338213i
$694$	1.87762e12			0.307249
$695$	1.45186e10	−	2.51470e10i	0.00236044	−	0.00408840i
$696$	6.92205e10	−	1.19893e11i	0.0111813	−	0.0193666i
$697$	−6.65123e12			−1.06747
$698$	6.63736e10	−	1.14962e11i	0.0105839	−	0.0183319i
$699$	1.20921e11	+	2.09441e11i	0.0191581	+	0.0331828i
$700$	1.25327e12	+	2.17072e12i	0.197289	+	0.341714i
$701$	−7.04350e12			−1.10168			−0.550842	−	0.834609i	$-0.685693\pi$
$701$	−7.04350e12			−1.10168			−0.550842	+	0.834609i	$0.685693\pi$
$702$	1.43351e11	+	4.61908e10i	0.0222784	+	0.00717858i
$703$	−2.79713e12			−0.431931
$704$	6.92296e11	+	1.19909e12i	0.106222	+	0.183982i
$705$	−5.72491e9	−	9.91583e9i	−0.000872806	−	0.00151174i
$706$	−9.73366e11	+	1.68592e12i	−0.147453	+	0.255397i
$707$	1.17282e13			1.76540
$708$	2.28417e10	−	3.95630e10i	0.00341648	−	0.00591751i
$709$	3.59267e12	−	6.22269e12i	0.533961	−	0.924848i	−0.465252	−	0.885178i	$-0.654036\pi$
$709$	3.59267e12	−	6.22269e12i	0.533961	−	0.924848i	0.999213	−	0.0396695i	$-0.0126305\pi$
$710$	1.90193e12			0.280888
$711$	−4.64871e12	+	8.05180e12i	−0.682211	+	1.18162i
$712$	−3.84966e11	−	6.66780e11i	−0.0561387	−	0.0972351i
$713$	4.37309e12	+	7.57441e12i	0.633702	+	1.09760i
$714$	−1.25676e11			−0.0180971
$715$	1.94322e12	+	6.26148e11i	0.278064	+	0.0895982i
$716$	−7.90377e12			−1.12389
$717$	−9.19734e10	−	1.59303e11i	−0.0129965	−	0.0225106i
$718$	−1.50232e12	−	2.60210e12i	−0.210961	−	0.365396i
$719$	−1.04301e12	+	1.80655e12i	−0.145549	+	0.252099i	−0.929578	−	0.368626i	$-0.879828\pi$
$719$	−1.04301e12	+	1.80655e12i	−0.145549	+	0.252099i	0.784028	+	0.620725i	$0.213162\pi$
$720$	4.20563e12			0.583224
$721$	−6.01635e12	+	1.04206e13i	−0.829133	+	1.43610i
$722$	−7.90450e11	+	1.36910e12i	−0.108257	+	0.187507i
$723$	−5.01374e11			−0.0682401
$724$	−2.21584e12	+	3.83795e12i	−0.299719	+	0.519129i
$725$	1.55522e12	+	2.69372e12i	0.209060	+	0.362103i
$726$	3.73818e10	+	6.47472e10i	0.00499397	+	0.00864981i
$727$	−5.89084e12			−0.782119			−0.391059	−	0.920365i	$-0.627891\pi$
$727$	−5.89084e12			−0.782119			−0.391059	+	0.920365i	$0.627891\pi$
$728$	−8.80255e11	−	4.09211e12i	−0.116150	−	0.539954i
$729$	−7.54686e12			−0.989674
$730$	−4.17314e11	−	7.22809e11i	−0.0543889	−	0.0942043i
$731$	−1.05386e12	−	1.82533e12i	−0.136506	−	0.236436i
$732$	1.23575e11	−	2.14037e11i	0.0159085	−	0.0275543i
$733$	5.76840e12			0.738052			0.369026	−	0.929419i	$-0.379691\pi$
$733$	5.76840e12			0.738052			0.369026	+	0.929419i	$0.379691\pi$
$734$	−2.08284e12	+	3.60759e12i	−0.264865	+	0.458760i
$735$	−4.87814e9	+	8.44919e9i	−0.000616541	+	0.00106788i
$736$	3.98468e12			0.500545
$737$	−2.42519e11	+	4.20055e11i	−0.0302790	+	0.0524448i
$738$	7.99258e11	+	1.38436e12i	0.0991822	+	0.171789i
$739$	−5.80701e12	−	1.00580e13i	−0.716230	−	1.24055i	−0.962483	−	0.271341i	$-0.912533\pi$
$739$	−5.80701e12	−	1.00580e13i	−0.716230	−	1.24055i	0.246254	−	0.969205i	$-0.420800\pi$
$740$	−5.11804e12			−0.627424
$741$	−1.21849e11	+	1.10254e11i	−0.0148471	+	0.0134342i
$742$	2.20139e12			0.266612
$743$	4.83615e12	+	8.37646e12i	0.582171	+	1.00835i	0.995222	+	0.0976413i	$0.0311298\pi$
$743$	4.83615e12	+	8.37646e12i	0.582171	+	1.00835i	−0.413051	+	0.910708i	$0.635537\pi$
$744$	1.80501e11	+	3.12637e11i	0.0215974	+	0.0374078i
$745$	1.72480e12	−	2.98745e12i	0.205133	−	0.355301i
$746$	−7.80696e11			−0.0922905
$747$	7.47938e12	−	1.29547e13i	0.878867	−	1.52224i
$748$	2.29201e12	−	3.96988e12i	0.267707	−	0.463681i
$749$	1.93399e12			0.224536
$750$	−5.48765e10	+	9.50489e10i	−0.00633302	+	0.0109691i
$751$	1.16497e12	+	2.01779e12i	0.133640	+	0.231471i	0.925077	−	0.379779i	$-0.124000\pi$
$751$	1.16497e12	+	2.01779e12i	0.133640	+	0.231471i	−0.791437	+	0.611251i	$0.790667\pi$
$752$	−1.85903e11	−	3.21993e11i	−0.0211985	−	0.0367169i
$753$	−3.91850e11			−0.0444163
$754$	−5.23530e11	−	2.43377e12i	−0.0589889	−	0.274226i
$755$	6.17141e12			0.691231
$756$	−3.49511e11	−	6.05370e11i	−0.0389146	−	0.0674020i
$757$	1.56250e11	+	2.70632e11i	0.0172937	+	0.0299535i	0.874543	−	0.484948i	$-0.161162\pi$
$757$	1.56250e11	+	2.70632e11i	0.0172937	+	0.0299535i	−0.857249	+	0.514902i	$0.827828\pi$
$758$	−1.45416e12	+	2.51868e12i	−0.159993	+	0.277116i
$759$	9.61476e10			0.0105160
$760$	9.14785e11	−	1.58445e12i	0.0994622	−	0.172274i
$761$	2.50004e12	−	4.33020e12i	0.270220	−	0.468034i	−0.698698	−	0.715416i	$-0.746237\pi$
$761$	2.50004e12	−	4.33020e12i	0.270220	−	0.468034i	0.968918	+	0.247382i	$0.0795704\pi$
$762$	−8.67794e10			−0.00932437
$763$	4.41593e12	−	7.64861e12i	0.471695	−	0.817000i
$764$	5.55289e12	+	9.61789e12i	0.589656	+	1.02131i
$765$	−5.45523e12	−	9.44874e12i	−0.575887	−	0.997465i
$766$	−3.79158e12			−0.397916
$767$	−3.60456e11	−	1.67568e12i	−0.0376074	−	0.174828i
$768$	−1.18271e11			−0.0122674
$769$	−3.87008e12	−	6.70317e12i	−0.399072	−	0.691213i	0.594540	−	0.804066i	$-0.297334\pi$
$769$	−3.87008e12	−	6.70317e12i	−0.399072	−	0.691213i	−0.993612	+	0.112853i	$0.964001\pi$
$770$	4.09790e11	+	7.09778e11i	0.0420101	+	0.0727636i
$771$	1.07103e11	−	1.85507e11i	0.0109158	−	0.0189067i
$772$	1.40210e13			1.42070
$773$	−5.08245e12	+	8.80306e12i	−0.511995	+	0.886801i	0.487909	+	0.872895i	$0.337760\pi$
$773$	−5.08245e12	+	8.80306e12i	−0.511995	+	0.886801i	−0.999903	+	0.0139061i	$0.995573\pi$
$774$	−2.53277e11	+	4.38689e11i	−0.0253666	+	0.0439362i
$775$	−8.11087e12			−0.807625
$776$	−9.69649e11	+	1.67948e12i	−0.0959924	+	0.166264i
$777$	1.92517e11	+	3.33449e11i	0.0189485	+	0.0328197i
$778$	−2.75258e12	−	4.76761e12i	−0.269360	−	0.466544i
$779$	−3.49123e12			−0.339672
$780$	−2.22953e11	+	2.01736e11i	−0.0215669	+	0.0195145i
$781$	5.21898e12			0.501945
$782$	−1.47587e12	−	2.55628e12i	−0.141129	−	0.244443i
$783$	−4.33720e11	−	7.51225e11i	−0.0412365	−	0.0714237i
$784$	−1.58406e11	+	2.74367e11i	−0.0149744	+	0.0259364i
$785$	−2.04517e12			−0.192228
$786$	8.47714e10	−	1.46828e11i	0.00792224	−	0.0137217i
$787$	1.86304e12	−	3.22687e12i	0.173115	−	0.299844i	−0.766392	−	0.642373i	$-0.777950\pi$
$787$	1.86304e12	−	3.22687e12i	0.173115	−	0.299844i	0.939507	+	0.342529i	$0.111283\pi$
$788$	1.82014e12			0.168166
$789$	1.77227e10	−	3.06966e10i	0.00162811	−	0.00281997i
$790$	1.60681e12	+	2.78307e12i	0.146772	+	0.254216i
$791$	7.57418e12	+	1.31189e13i	0.687926	+	1.19152i
$792$	−2.29868e12			−0.207594
$793$	−1.95008e12	−	9.06549e12i	−0.175115	−	0.814071i
$794$	1.13783e12			0.101598
$795$	−1.64973e11	−	2.85741e11i	−0.0146474	−	0.0253700i
$796$	3.97887e12	+	6.89161e12i	0.351278	+	0.608432i
$797$	8.94511e12	−	1.54934e13i	0.785277	−	1.36014i	−0.143556	−	0.989642i	$-0.545854\pi$
$797$	8.94511e12	−	1.54934e13i	0.785277	−	1.36014i	0.928833	−	0.370498i	$-0.120813\pi$
$798$	−6.59670e10			−0.00575856
$799$	−4.82278e11	+	8.35331e11i	−0.0418637	+	0.0725100i
$800$	−1.84762e12	+	3.20017e12i	−0.159481	+	0.276228i
$801$	−2.41003e12			−0.206860
$802$	1.14607e12	−	1.98506e12i	0.0978201	−	0.169429i
$803$	−1.14513e12	−	1.98342e12i	−0.0971926	−	0.168343i
$804$	−3.57167e10	−	6.18632e10i	−0.00301453	−	0.00522131i
$805$	−6.10159e12			−0.512108
$806$	6.17870e12	+	1.99091e12i	0.515691	+	0.166167i
$807$	2.95167e10			0.00244983
$808$	5.68485e12	+	9.84645e12i	0.469211	+	0.812697i
$809$	3.04044e12	+	5.26620e12i	0.249556	+	0.432244i	0.963403	−	0.268058i	$-0.0863819\pi$
$809$	3.04044e12	+	5.26620e12i	0.249556	+	0.432244i	−0.713846	+	0.700302i	$0.753049\pi$
$810$	−1.30881e12	+	2.26693e12i	−0.106830	+	0.185035i
$811$	−1.71492e13			−1.39204			−0.696018	−	0.718024i	$-0.745047\pi$
$811$	−1.71492e13			−1.39204			−0.696018	+	0.718024i	$0.745047\pi$
$812$	−5.77713e12	+	1.00063e13i	−0.466348	+	0.807738i
$813$	−2.39586e11	+	4.14975e11i	−0.0192333	+	0.0333130i
$814$	1.21471e12			0.0969760
$815$	−3.03849e12	+	5.26282e12i	−0.241240	+	0.417840i
$816$	3.05832e11	+	5.29716e11i	0.0241478	+	0.0418252i
$817$	−5.53168e11	−	9.58115e11i	−0.0434368	−	0.0752347i
$818$	3.46433e12			0.270538
$819$	−1.24707e13	−	4.01833e12i	−0.968529	−	0.312081i
$820$	−6.38806e12			−0.493408
$821$	6.24433e12	+	1.08155e13i	0.479669	+	0.830811i	0.999728	−	0.0233192i	$-0.00742340\pi$
$821$	6.24433e12	+	1.08155e13i	0.479669	+	0.830811i	−0.520059	+	0.854130i	$0.674090\pi$
$822$	1.38742e11	+	2.40309e11i	0.0105995	+	0.0183589i
$823$	−7.50367e12	+	1.29967e13i	−0.570131	+	0.987496i	0.426421	+	0.904525i	$0.359774\pi$
$823$	−7.50367e12	+	1.29967e13i	−0.570131	+	0.987496i	−0.996552	+	0.0829708i	$0.973559\pi$
$824$	−1.16649e13			−0.881472
$825$	−4.45819e10	+	7.72180e10i	−0.00335054	+	0.00580331i
$826$	3.44035e11	−	5.95887e11i	0.0257154	−	0.0445403i
$827$	1.07749e12			0.0801009			0.0400504	−	0.999198i	$-0.487248\pi$
$827$	1.07749e12			0.0801009			0.0400504	+	0.999198i	$0.487248\pi$
$828$	4.10093e12	−	7.10302e12i	0.303212	−	0.525178i
$829$	−4.71112e12	−	8.15990e12i	−0.346441	−	0.600053i	0.639174	−	0.769062i	$-0.279276\pi$
$829$	−4.71112e12	−	8.15990e12i	−0.346441	−	0.600053i	−0.985614	+	0.169009i	$0.945943\pi$
$830$	−2.58522e12	−	4.47773e12i	−0.189080	−	0.327497i
$831$	8.00125e11			0.0582040
$832$	−5.67307e12	+	5.13320e12i	−0.410453	+	0.371393i
$833$	8.21890e11			0.0591441
$834$	−5.07482e8	−	8.78985e8i	−3.63223e−5	−	6.29121e-5i
$835$	8.20407e12	+	1.42099e13i	0.584037	+	1.01158i
$836$	1.20307e12	−	2.08379e12i	0.0851852	−	0.147545i
$837$	2.26196e12			0.159302
$838$	1.20371e12	−	2.08488e12i	0.0843184	−	0.146044i
$839$	6.57680e12	−	1.13913e13i	0.458232	−	0.793681i	−0.540636	−	0.841257i	$-0.681816\pi$
$839$	6.57680e12	−	1.13913e13i	0.458232	−	0.793681i	0.998868	+	0.0475756i	$0.0151495\pi$
$840$	−2.51846e11			−0.0174533
$841$	8.45263e10	−	1.46404e11i	0.00582653	−	0.0100918i
$842$	2.28048e12	+	3.94991e12i	0.156359	+	0.270821i
$843$	−3.46249e11	−	5.99721e11i	−0.0236137	−	0.0409002i
$844$	1.60868e13			1.09126
$845$	−1.12439e12	+	1.12250e13i	−0.0758686	+	0.757407i
$846$	2.31816e11			0.0155588
$847$	−6.50961e12	−	1.12750e13i	−0.434590	−	0.752732i
$848$	−5.35709e12	−	9.27876e12i	−0.355753	−	0.616181i
$849$	4.19902e11	−	7.27292e11i	0.0277373	−	0.0480424i
$850$	2.73733e12			0.179863
$851$	−4.52163e12	+	7.83169e12i	−0.295537	+	0.511885i
$852$	−3.84310e11	+	6.65644e11i	−0.0249864	+	0.0432777i
$853$	2.15314e13			1.39252			0.696260	−	0.717790i	$-0.254846\pi$
$853$	2.15314e13			1.39252			0.696260	+	0.717790i	$0.254846\pi$
$854$	1.86125e12	−	3.22377e12i	0.119741	−	0.207398i
$855$	−2.86345e12	−	4.95964e12i	−0.183249	−	0.317397i
$856$	9.37436e11	+	1.62369e12i	0.0596774	+	0.103364i
$857$	1.14978e13			0.728118			0.364059	−	0.931376i	$-0.381391\pi$
$857$	1.14978e13			0.728118			0.364059	+	0.931376i	$0.381391\pi$
$858$	5.29157e10	−	4.78800e10i	0.00333343	−	0.00301621i
$859$	−7.28288e12			−0.456388			−0.228194	−	0.973616i	$-0.573282\pi$
$859$	−7.28288e12			−0.456388			−0.228194	+	0.973616i	$0.573282\pi$
$860$	−1.01216e12	−	1.75311e12i	−0.0630964	−	0.109286i
$861$	2.40289e11	+	4.16193e11i	0.0149011	+	0.0258095i
$862$	1.36120e12	−	2.35766e12i	0.0839728	−	0.145445i
$863$	−2.42399e12			−0.148759			−0.0743794	−	0.997230i	$-0.523698\pi$
$863$	−2.42399e12			−0.148759			−0.0743794	+	0.997230i	$0.523698\pi$
$864$	5.15264e11	−	8.92464e11i	0.0314571	−	0.0544852i
$865$	−7.42744e12	+	1.28647e13i	−0.451094	+	0.781317i
$866$	−2.94894e12			−0.178170
$867$	4.48056e11	−	7.76056e11i	0.0269306	−	0.0466452i
$868$	−1.50646e13	−	2.60926e13i	−0.900780	−	1.56020i
$869$	4.40915e12	+	7.63687e12i	0.262280	+	0.454283i
$870$	−1.49785e11			−0.00886401
$871$	−2.55097e12	−	8.21980e11i	−0.150184	−	0.0483926i
$872$	8.56191e12			0.501472
$873$	3.03518e12	+	5.25709e12i	0.176856	+	0.306324i
$874$	−7.74682e11	−	1.34179e12i	−0.0449078	−	0.0777827i
$875$	9.55610e12	−	1.65517e13i	0.551118	−	0.954564i
$876$	3.37294e11			0.0193526
$877$	1.45117e13	−	2.51349e13i	0.828359	−	1.43476i	−0.0709652	−	0.997479i	$-0.522608\pi$
$877$	1.45117e13	−	2.51349e13i	0.828359	−	1.43476i	0.899325	−	0.437282i	$-0.144059\pi$
$878$	−2.27949e12	+	3.94818e12i	−0.129453	+	0.224219i
$879$	−8.05398e11			−0.0455051
$880$	1.99445e12	−	3.45449e12i	0.112112	−	0.194184i
$881$	−2.75303e12	−	4.76839e12i	−0.153964	−	0.266673i	0.778717	−	0.627375i	$-0.215871\pi$
$881$	−2.75303e12	−	4.76839e12i	−0.153964	−	0.266673i	−0.932681	+	0.360701i	$0.882537\pi$
$882$	−9.87641e10	−	1.71064e11i	−0.00549529	−	0.00951812i
$883$	−3.59261e12			−0.198878			−0.0994391	−	0.995044i	$-0.531705\pi$
$883$	−3.59261e12			−0.198878			−0.0994391	+	0.995044i	$0.531705\pi$
$884$	2.41088e13	+	7.76840e12i	1.32783	+	0.427855i
$885$	−1.03128e11			−0.00565110
$886$	−3.88838e12	−	6.73487e12i	−0.211991	−	0.367179i
$887$	−1.07572e13	−	1.86320e13i	−0.583501	−	1.01065i	−0.995060	−	0.0992704i	$-0.968349\pi$
$887$	−1.07572e13	−	1.86320e13i	−0.583501	−	1.01065i	0.411560	−	0.911383i	$-0.364984\pi$
$888$	−1.86632e11	+	3.23257e11i	−0.0100723	+	0.0174457i
$889$	1.51116e13			0.811434
$890$	−4.16509e11	+	7.21415e11i	−0.0222520	+	0.0385417i
$891$	−3.59143e12	+	6.22053e12i	−0.190905	+	0.330657i
$892$	−2.64872e13			−1.40086
$893$	−2.53148e11	+	4.38464e11i	−0.0133212	+	0.0230729i
$894$	−6.02887e10	−	1.04423e11i	−0.00315658	−	0.00546736i
$895$	8.92121e12	+	1.54520e13i	0.464751	+	0.804972i
$896$	−1.79851e13			−0.932240
$897$	1.11727e11	+	5.19394e11i	0.00576225	+	0.0267874i
$898$	−1.97777e11			−0.0101492
$899$	−1.86942e13	−	3.23793e13i	−0.954527	−	1.65329i
$900$	3.80305e12	+	6.58707e12i	0.193215	+	0.334658i
$901$	−1.38976e13	+	2.40714e13i	−0.702554	+	1.21686i
$902$	1.51614e12			0.0762623
$903$	−7.61452e10	+	1.31887e11i	−0.00381108	+	0.00660098i
$904$	−7.34267e12	+	1.27179e13i	−0.365676	+	0.633369i
$905$	1.00043e13			0.495757
$906$	1.07858e11	−	1.86815e11i	0.00531831	−	0.00921159i
$907$	1.39586e13	+	2.41770e13i	0.684870	+	1.18623i	0.973478	+	0.228782i	$0.0734744\pi$
$907$	1.39586e13	+	2.41770e13i	0.684870	+	1.18623i	−0.288608	+	0.957447i	$0.593192\pi$
$908$	−3.22367e12	−	5.58357e12i	−0.157386	−	0.272600i
$909$	3.55893e13			1.72895
$910$	−3.35806e12	+	3.03849e12i	−0.162331	+	0.146883i
$911$	2.21733e13			1.06659			0.533296	−	0.845929i	$-0.320953\pi$
$911$	2.21733e13			1.06659			0.533296	+	0.845929i	$0.320953\pi$
$912$	1.60531e11	+	2.78048e11i	0.00768391	+	0.0133089i
$913$	−7.09395e12	−	1.22871e13i	−0.337885	−	0.585235i
$914$	−1.98208e12	+	3.43307e12i	−0.0939428	+	0.162714i
$915$	−5.57928e11			−0.0263138
$916$	1.08443e13	−	1.87828e13i	0.508945	−	0.881519i
$917$	−1.47620e13	+	2.55685e13i	−0.689417	+	1.19410i
$918$	−7.63387e11			−0.0354775
$919$	−5.97810e12	+	1.03544e13i	−0.276467	+	0.478855i	−0.970504	−	0.241084i	$-0.922497\pi$
$919$	−5.97810e12	+	1.03544e13i	−0.276467	+	0.478855i	0.694037	+	0.719939i	$0.255830\pi$
$920$	−2.95754e12	−	5.12262e12i	−0.136109	−	0.235747i
$921$	6.30371e10	+	1.09183e11i	0.00288687	+	0.00500021i
$922$	1.85078e12			0.0843461
$923$	6.06464e12	+	2.81932e13i	0.275041	+	1.27860i
$924$	−3.31213e11			−0.0149480
$925$	−4.19319e12	−	7.26282e12i	−0.188325	−	0.326188i
$926$	−4.17360e12	−	7.22888e12i	−0.186535	−	0.323089i
$927$	−1.82567e13	+	3.16215e13i	−0.812013	+	1.40645i
$928$	−1.70338e13			−0.753956
$929$	−1.30064e13	+	2.25278e13i	−0.572911	+	0.992312i	0.423354	+	0.905964i	$0.360853\pi$
$929$	−1.30064e13	+	2.25278e13i	−0.572911	+	0.992312i	−0.996265	+	0.0863471i	$0.972481\pi$
$930$	1.95291e11	−	3.38254e11i	0.00856069	−	0.0148276i
$931$	4.31410e11			0.0188199
$932$	9.78354e12	−	1.69456e13i	0.424741	−	0.735673i
$933$	4.04289e11	+	7.00248e11i	0.0174672	+	0.0302541i
$934$	−5.53327e11	−	9.58391e11i	−0.0237915	−	0.0412080i
$935$	−1.03482e13			−0.442806
$936$	−2.67115e12	−	1.24176e13i	−0.113751	−	0.528805i
$937$	4.61864e12			0.195743			0.0978714	−	0.995199i	$-0.468797\pi$
$937$	4.61864e12			0.195743			0.0978714	+	0.995199i	$0.468797\pi$
$938$	−5.37955e11	−	9.31766e11i	−0.0226899	−	0.0393001i
$939$	−1.88936e11	−	3.27246e11i	−0.00793083	−	0.0137366i
$940$	−4.63196e11	+	8.02278e11i	−0.0193504	+	0.0335158i
$941$	−2.25674e13			−0.938269			−0.469134	−	0.883127i	$-0.655434\pi$
$941$	−2.25674e13			−0.938269			−0.469134	+	0.883127i	$0.655434\pi$
$942$	−3.57434e10	+	6.19094e10i	−0.00147900	+	0.00256170i
$943$	−5.64365e12	+	9.77510e12i	−0.232412	+	0.402549i
$944$	−3.34884e12			−0.137253
$945$	−7.89005e11	+	1.36660e12i	−0.0321837	+	0.0557439i
$946$	2.40225e11	+	4.16082e11i	0.00975232	+	0.0168915i
$947$	8.09763e12	+	1.40255e13i	0.327177	+	0.566688i	0.981951	−	0.189138i	$-0.0605693\pi$
$947$	8.09763e12	+	1.40255e13i	0.327177	+	0.566688i	−0.654773	+	0.755825i	$0.727236\pi$
$948$	−1.29870e12			−0.0522243
$949$	9.38383e12	−	8.49082e12i	0.375562	−	0.339822i
$950$	1.43682e12			0.0572331
$951$	−4.62005e11	−	8.00216e11i	−0.0183162	−	0.0317245i
$952$	1.06080e13	+	1.83736e13i	0.418569	+	0.724983i
$953$	7.67583e12	−	1.32949e13i	0.301444	−	0.522117i	−0.675019	−	0.737800i	$-0.735865\pi$
$953$	7.67583e12	−	1.32949e13i	0.301444	−	0.522117i	0.976463	+	0.215683i	$0.0691979\pi$
$954$	6.68015e12			0.261107
$955$	1.25354e13	−	2.17120e13i	0.487667	−	0.844664i
$956$	−7.44146e12	+	1.28890e13i	−0.288136	+	0.499066i
$957$	−4.11015e11			−0.0158399
$958$	−1.66049e12	+	2.87605e12i	−0.0636929	+	0.110319i
$959$	−2.41604e13	−	4.18470e13i	−0.922401	−	1.59765i
$960$	2.30164e11	+	3.98655e11i	0.00874614	+	0.0151488i
$961$	7.10553e13			2.68745
$962$	1.41154e12	+	6.56194e12i	0.0531381	+	0.247027i
$963$	5.86870e12			0.219899
$964$	2.02828e13	+	3.51309e13i	0.756452	+	1.31021i
$965$	−1.58259e13	−	2.74113e13i	−0.587483	−	1.01755i
$966$	−1.06637e11	+	1.84701e11i	−0.00394014	+	0.00682453i
$967$	−3.04215e13			−1.11882			−0.559412	−	0.828890i	$-0.688973\pi$
$967$	−3.04215e13			−1.11882			−0.559412	+	0.828890i	$0.688973\pi$
$968$	6.31064e12	−	1.09304e13i	0.231012	−	0.400124i
$969$	4.16458e11	−	7.21326e11i	0.0151745	−	0.0262830i
$970$	2.09820e12			0.0760982
$971$	3.53291e11	−	6.11918e11i	0.0127540	−	0.0220906i	−0.859578	−	0.511005i	$-0.829273\pi$
$971$	3.53291e11	−	6.11918e11i	0.0127540	−	0.0220906i	0.872332	+	0.488914i	$0.162607\pi$
$972$	−1.59135e12	−	2.75630e12i	−0.0571830	−	0.0990439i
$973$	8.83722e10	+	1.53065e11i	0.00316088	+	0.00547480i
$974$	−1.91077e12			−0.0680289
$975$	−4.68941e11	−	1.51103e11i	−0.0166187	−	0.00535492i
$976$	−1.81174e13			−0.639104
$977$	−2.11715e13	−	3.66700e13i	−0.743405	−	1.28761i	−0.950936	−	0.309386i	$-0.899876\pi$
$977$	−2.11715e13	−	3.66700e13i	−0.743405	−	1.28761i	0.207532	−	0.978228i	$-0.433457\pi$
$978$	1.06207e11	+	1.83956e11i	0.00371218	+	0.00642969i
$979$	−1.14292e12	+	1.97959e12i	−0.0397643	+	0.0688737i
$980$	7.89370e11			0.0273378
$981$	1.34002e13	−	2.32098e13i	0.461956	−	0.800131i
$982$	3.74285e12	−	6.48280e12i	0.128440	−	0.222465i
$983$	8.38353e12			0.286376			0.143188	−	0.989696i	$-0.454265\pi$
$983$	8.38353e12			0.286376			0.143188	+	0.989696i	$0.454265\pi$
$984$	−2.32944e11	+	4.03471e11i	−0.00792089	+	0.0137194i
$985$	−2.05445e12	−	3.55841e12i	−0.0695395	−	0.120446i
$986$	6.30908e12	+	1.09277e13i	0.212579	+	0.368197i
$987$	6.96930e10			0.00233756
$988$	1.26547e13	+	4.07763e12i	0.422519	+	0.136145i
$989$	−3.57684e12			−0.118882
$990$	1.24351e12	+	2.15383e12i	0.0411427	+	0.0712612i
$991$	−1.26874e13	−	2.19753e13i	−0.417871	−	0.723773i	0.577855	−	0.816140i	$-0.303890\pi$
$991$	−1.26874e13	−	2.19753e13i	−0.417871	−	0.723773i	−0.995725	+	0.0923668i	$0.970557\pi$
$992$	2.22089e13	−	3.84669e13i	0.728156	−	1.26120i
$993$	−9.09208e11			−0.0296751
$994$	−5.78837e12	+	1.00258e13i	−0.188069	+	0.325745i
$995$	8.98213e12	−	1.55575e13i	0.290520	−	0.503195i
$996$	2.08951e12			0.0672786
$997$	−6.55918e12	+	1.13608e13i	−0.210243	+	0.364152i	−0.951791	−	0.306749i	$-0.900759\pi$
$997$	−6.55918e12	+	1.13608e13i	−0.210243	+	0.364152i	0.741548	+	0.670900i	$0.234092\pi$
$998$	−6.99388e12	−	1.21138e13i	−0.223167	−	0.386537i
$999$	1.16940e12	+	2.02546e12i	0.0371464	+	0.0643395i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.c.a.3.5	✓	18
13.3	even	3		169.10.a.c.1.5		9
13.9	even	3	inner	13.10.c.a.9.5	yes	18
13.10	even	6		169.10.a.d.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.c.a.3.5	✓	18	1.1	even	1	trivial
13.10.c.a.9.5	yes	18	13.9	even	3	inner
169.10.a.c.1.5		9	13.3	even	3
169.10.a.d.1.5		9	13.10	even	6

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	13.10.c.a.3.5

Level	$13$
Weight	$10$
Character	13.3
Analytic conductor	$6.695$
Analytic rank	$0$
Dimension	$18$
Inner twists	$2$