LMFDB - Embedded newform 13.14.e.a.10.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [13,14,Mod(4,13)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("13.4"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(13, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 13 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	13.e (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$13.9400207637$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.8
Character	$\chi$	$=$	13.10
Dual form			13.14.e.a.4.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.65944 + 3.26748i) q^{2} +(865.700 + 1499.44i) q^{3} +(-4074.65 + 7057.50i) q^{4} +60806.7i q^{5} +(-9798.77 - 5657.32i) q^{6} +(-175141. - 101118. i) q^{7} -106790. i q^{8} +(-701713. + 1.21540e6i) q^{9} +(-198685. - 344132. i) q^{10} +(7.21178e6 - 4.16372e6i) q^{11} -1.41097e7 q^{12} +(1.46292e7 - 9.42660e6i) q^{13} +1.32160e6 q^{14} +(-9.11757e7 + 5.26403e7i) q^{15} +(-3.30306e7 - 5.72106e7i) q^{16} +(-5.79744e7 + 1.00415e8i) q^{17} -9.17134e6i q^{18} +(3.26857e7 + 1.88711e7i) q^{19} +(-4.29143e8 - 2.47766e8i) q^{20} -3.50151e8i q^{21} +(-2.72098e7 + 4.71287e7i) q^{22} +(3.90588e8 + 6.76518e8i) q^{23} +(1.60125e8 - 9.24479e7i) q^{24} -2.47675e9 q^{25} +(-5.19921e7 + 1.01150e8i) q^{26} +3.30520e8 q^{27} +(1.42728e9 - 8.24038e8i) q^{28} +(1.79866e9 + 3.11538e9i) q^{29} +(3.44003e8 - 5.95830e8i) q^{30} -4.16316e9i q^{31} +(1.13149e9 + 6.53265e8i) q^{32} +(1.24865e10 + 7.20907e9i) q^{33} -7.57722e8i q^{34} +(6.14863e9 - 1.06497e10i) q^{35} +(-5.71846e9 - 9.90467e9i) q^{36} +(-7.24645e9 + 4.18374e9i) q^{37} -2.46644e8 q^{38} +(2.67991e10 + 1.37750e10i) q^{39} +6.49353e9 q^{40} +(-3.76924e10 + 2.17617e10i) q^{41} +(1.14411e9 + 1.98166e9i) q^{42} +(4.01899e9 - 6.96110e9i) q^{43} +6.78628e10i q^{44} +(-7.39045e10 - 4.26688e10i) q^{45} +(-4.42102e9 - 2.55248e9i) q^{46} -6.97104e10i q^{47} +(5.71892e10 - 9.90545e10i) q^{48} +(-2.79949e10 - 4.84886e10i) q^{49} +(1.40170e10 - 8.09272e9i) q^{50} -2.00754e11 q^{51} +(6.91923e9 + 1.41656e11i) q^{52} -1.25080e11 q^{53} +(-1.87056e9 + 1.07997e9i) q^{54} +(2.53182e11 + 4.38524e11i) q^{55} +(-1.07983e10 + 1.87033e10i) q^{56} +6.53468e10i q^{57} +(-2.03589e10 - 1.17542e10i) q^{58} +(4.64945e10 + 2.68436e10i) q^{59} -8.57963e11i q^{60} +(1.61205e11 - 2.79216e11i) q^{61} +(1.36030e10 + 2.35612e10i) q^{62} +(2.45798e11 - 1.41911e11i) q^{63} +5.32635e11 q^{64} +(5.73200e11 + 8.89554e11i) q^{65} -9.42220e10 q^{66} +(2.32265e11 - 1.34098e11i) q^{67} +(-4.72451e11 - 8.18309e11i) q^{68} +(-6.76264e11 + 1.17132e12i) q^{69} +8.03622e10i q^{70} +(1.03736e12 + 5.98918e11i) q^{71} +(1.29793e11 + 7.49357e10i) q^{72} +1.43783e12i q^{73} +(2.73406e10 - 4.73553e10i) q^{74} +(-2.14412e12 - 3.71372e12i) q^{75} +(-2.66365e11 + 1.53786e11i) q^{76} -1.68410e12 q^{77} +(-1.96678e11 + 9.60680e9i) q^{78} -3.07554e12 q^{79} +(3.47879e12 - 2.00848e12i) q^{80} +(1.40489e12 + 2.43334e12i) q^{81} +(1.42212e11 - 2.46318e11i) q^{82} +1.31800e12i q^{83} +(2.47119e12 + 1.42674e12i) q^{84} +(-6.10588e12 - 3.52523e12i) q^{85} +5.25280e10i q^{86} +(-3.11421e12 + 5.39396e12i) q^{87} +(-4.44643e11 - 7.70144e11i) q^{88} +(6.49621e12 - 3.75059e12i) q^{89} +5.57678e11 q^{90} +(-3.51538e12 + 1.71710e11i) q^{91} -6.36603e12 q^{92} +(6.24239e12 - 3.60405e12i) q^{93} +(2.27777e11 + 3.94522e11i) q^{94} +(-1.14749e12 + 1.98751e12i) q^{95} +2.26213e12i q^{96} +(1.09190e13 + 6.30408e12i) q^{97} +(3.16871e11 + 1.82946e11i) q^{98} +1.16869e13i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 730 q^{3} + 65535 q^{4} - 382584 q^{6} + 438984 q^{7} - 9117071 q^{9} + 3893475 q^{10} - 5364528 q^{11} + 27694876 q^{12} - 1794135 q^{13} + 61125588 q^{14} - 113380170 q^{15} - 350182521 q^{16}+ \cdots + 86959564160763 q^{98}+O(q^{100}) $ 30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−5.65944	+	3.26748i	−0.0625286	+	0.0361009i	−0.530938	−	0.847410i	$-0.678160\pi$
$2$	−5.65944	+	3.26748i	−0.0625286	+	0.0361009i	0.468410	+	0.883511i	$0.344827\pi$
$3$	865.700	+	1499.44i	0.685614	+	1.18752i	0.973244	+	0.229776i	$0.0737994\pi$
$3$	865.700	+	1499.44i	0.685614	+	1.18752i	−0.287630	+	0.957742i	$0.592867\pi$
$4$	−4074.65	+	7057.50i	−0.497393	+	0.861511i
$5$			60806.7i			1.74039i	0.492709	+	0.870194i	$0.336007\pi$
$5$			60806.7i			1.74039i	−0.492709	+	0.870194i	$0.663993\pi$
$6$	−9798.77	−	5657.32i	−0.0857410	−	0.0495026i
$7$	−175141.	−	101118.i	−0.562666	−	0.324855i	0.191549	−	0.981483i	$-0.438649\pi$
$7$	−175141.	−	101118.i	−0.562666	−	0.324855i	−0.754215	+	0.656628i	$0.771982\pi$
$8$		−	106790.i		−	0.144027i
$9$	−701713.	+	1.21540e6i	−0.440132	+	0.762331i
$10$	−198685.	−	344132.i	−0.0628296	−	0.108824i
$11$	7.21178e6	−	4.16372e6i	1.22741	−	0.708646i	0.260923	−	0.965360i	$-0.415973\pi$
$11$	7.21178e6	−	4.16372e6i	1.22741	−	0.708646i	0.966487	+	0.256714i	$0.0826398\pi$
$12$	−1.41097e7			−1.36408
$13$	1.46292e7	−	9.42660e6i	0.840601	−	0.541656i
$13$	1.46292e7	−	9.42660e6i	0.840601	−	0.541656i
$14$	1.32160e6			0.0469103
$15$	−9.11757e7	+	5.26403e7i	−2.06674	+	1.19323i
$16$	−3.30306e7	−	5.72106e7i	−0.492194	−	0.852505i
$17$	−5.79744e7	+	1.00415e8i	−0.582530	+	1.00897i	0.412648	+	0.910891i	$0.364604\pi$
$17$	−5.79744e7	+	1.00415e8i	−0.582530	+	1.00897i	−0.995178	+	0.0980815i	$0.968729\pi$
$18$		−	9.17134e6i		−	0.0635567i
$19$	3.26857e7	+	1.88711e7i	0.159389	+	0.0920234i	0.577573	−	0.816339i	$-0.304000\pi$
$19$	3.26857e7	+	1.88711e7i	0.159389	+	0.0920234i	−0.418184	+	0.908362i	$0.637333\pi$
$20$	−4.29143e8	−	2.47766e8i	−1.49936	−	0.865658i
$21$		−	3.50151e8i		−	0.890901i
$22$	−2.72098e7	+	4.71287e7i	−0.0511655	+	0.0886213i
$23$	3.90588e8	+	6.76518e8i	0.550158	+	0.952902i	0.998263	+	0.0589210i	$0.0187660\pi$
$23$	3.90588e8	+	6.76518e8i	0.550158	+	0.952902i	−0.448104	+	0.893981i	$0.647901\pi$
$24$	1.60125e8	−	9.24479e7i	0.171035	−	0.0987471i
$25$	−2.47675e9			−2.02895
$26$	−5.19921e7	+	1.01150e8i	−0.0330073	+	0.0642154i
$27$	3.30520e8			0.164185
$28$	1.42728e9	−	8.24038e8i	0.559733	−	0.323162i
$29$	1.79866e9	+	3.11538e9i	0.561517	+	0.972576i	0.997364	+	0.0725553i	$0.0231154\pi$
$29$	1.79866e9	+	3.11538e9i	0.561517	+	0.972576i	−0.435847	+	0.900021i	$0.643551\pi$
$30$	3.44003e8	−	5.95830e8i	0.0861537	−	0.149223i
$31$		−	4.16316e9i		−	0.842504i	−0.906944	−	0.421252i	$-0.861591\pi$
$31$		−	4.16316e9i		−	0.842504i	0.906944	−	0.421252i	$-0.138409\pi$
$32$	1.13149e9	+	6.53265e8i	0.186284	+	0.107551i
$33$	1.24865e10	+	7.20907e9i	1.68306	+	0.971714i
$34$		−	7.57722e8i		−	0.0841195i
$35$	6.14863e9	−	1.06497e10i	0.565375	−	0.979258i
$36$	−5.71846e9	−	9.90467e9i	−0.437838	−	0.758357i
$37$	−7.24645e9	+	4.18374e9i	−0.464316	+	0.268073i	−0.713857	−	0.700291i	$-0.753054\pi$
$37$	−7.24645e9	+	4.18374e9i	−0.464316	+	0.268073i	0.249541	+	0.968364i	$0.419720\pi$
$38$	−2.46644e8			−0.0132885
$39$	2.67991e10	+	1.37750e10i	1.21955	+	0.626862i
$40$	6.49353e9			0.250663
$41$	−3.76924e10	+	2.17617e10i	−1.23925	+	0.715481i	−0.968941	−	0.247293i	$-0.920459\pi$
$41$	−3.76924e10	+	2.17617e10i	−1.23925	+	0.715481i	−0.270308	+	0.962774i	$0.587126\pi$
$42$	1.14411e9	+	1.98166e9i	0.0321624	+	0.0557068i
$43$	4.01899e9	−	6.96110e9i	0.0969555	−	0.167932i	−0.813468	−	0.581610i	$-0.802423\pi$
$43$	4.01899e9	−	6.96110e9i	0.0969555	−	0.167932i	0.910423	+	0.413678i	$0.135756\pi$
$44$			6.78628e10i			1.40990i
$45$	−7.39045e10	−	4.26688e10i	−1.32675	−	0.766001i
$46$	−4.42102e9	−	2.55248e9i	−0.0688013	−	0.0397224i
$47$		−	6.97104e10i		−	0.943325i	−0.881779	−	0.471662i	$-0.843654\pi$
$47$		−	6.97104e10i		−	0.943325i	0.881779	−	0.471662i	$-0.156346\pi$
$48$	5.71892e10	−	9.90545e10i	0.674910	−	1.16898i
$49$	−2.79949e10	−	4.84886e10i	−0.288938	−	0.500455i
$50$	1.40170e10	−	8.09272e9i	0.126867	−	0.0732470i
$51$	−2.00754e11			−1.59756
$52$	6.91923e9	+	1.41656e11i	0.0485329	+	0.993602i
$53$	−1.25080e11			−0.775165			−0.387582	−	0.921835i	$-0.626690\pi$
$53$	−1.25080e11			−0.775165			−0.387582	+	0.921835i	$0.626690\pi$
$54$	−1.87056e9	+	1.07997e9i	−0.0102663	+	0.00592723i
$55$	2.53182e11	+	4.38524e11i	1.23332	+	2.13617i
$56$	−1.07983e10	+	1.87033e10i	−0.0467881	+	0.0810393i
$57$			6.53468e10i			0.252370i
$58$	−2.03589e10	−	1.17542e10i	−0.0702218	−	0.0405426i
$59$	4.64945e10	+	2.68436e10i	0.143504	+	0.0828520i	0.570033	−	0.821622i	$-0.306930\pi$
$59$	4.64945e10	+	2.68436e10i	0.143504	+	0.0828520i	−0.426529	+	0.904474i	$0.640264\pi$
$60$		−	8.57963e11i		−	2.37403i
$61$	1.61205e11	−	2.79216e11i	0.400623	−	0.693899i	−0.593178	−	0.805071i	$-0.702127\pi$
$61$	1.61205e11	−	2.79216e11i	0.400623	−	0.693899i	0.993801	+	0.111172i	$0.0354604\pi$
$62$	1.36030e10	+	2.35612e10i	0.0304152	+	0.0526806i
$63$	2.45798e11	−	1.41911e11i	0.495295	−	0.285959i
$64$	5.32635e11			0.968857
$65$	5.73200e11	+	8.89554e11i	0.942691	+	1.46297i
$66$	−9.42220e10			−0.140319
$67$	2.32265e11	−	1.34098e11i	0.313688	−	0.181108i	−0.334888	−	0.942258i	$-0.608698\pi$
$67$	2.32265e11	−	1.34098e11i	0.313688	−	0.181108i	0.648576	+	0.761150i	$0.275365\pi$
$68$	−4.72451e11	−	8.18309e11i	−0.579493	−	1.00371i
$69$	−6.76264e11	+	1.17132e12i	−0.754392	+	1.30665i
$70$			8.03622e10i			0.0816422i
$71$	1.03736e12	+	5.98918e11i	0.961056	+	0.554866i	0.896498	−	0.443048i	$-0.146103\pi$
$71$	1.03736e12	+	5.98918e11i	0.961056	+	0.554866i	0.0645583	+	0.997914i	$0.479436\pi$
$72$	1.29793e11	+	7.49357e10i	0.109796	+	0.0633910i
$73$			1.43783e12i			1.11201i	0.831178	+	0.556006i	$0.187667\pi$
$73$			1.43783e12i			1.11201i	−0.831178	+	0.556006i	$0.812333\pi$
$74$	2.73406e10	−	4.73553e10i	0.0193554	−	0.0335245i
$75$	−2.14412e12	−	3.71372e12i	−1.39108	−	2.40941i
$76$	−2.66365e11	+	1.53786e11i	−0.158558	+	0.0915436i
$77$	−1.68410e12			−0.920830
$78$	−1.96678e11	+	9.60680e9i	−0.0988872	+	0.00483018i
$79$	−3.07554e12			−1.42346			−0.711729	−	0.702454i	$-0.752088\pi$
$79$	−3.07554e12			−1.42346			−0.711729	+	0.702454i	$0.752088\pi$
$80$	3.47879e12	−	2.00848e12i	1.48369	−	0.856608i
$81$	1.40489e12	+	2.43334e12i	0.552700	+	0.957304i
$82$	1.42212e11	−	2.46318e11i	0.0516590	−	0.0894760i
$83$			1.31800e12i			0.442495i	0.975218	+	0.221247i	$0.0710128\pi$
$83$			1.31800e12i			0.442495i	−0.975218	+	0.221247i	$0.928987\pi$
$84$	2.47119e12	+	1.42674e12i	0.767521	+	0.443129i
$85$	−6.10588e12	−	3.52523e12i	−1.75600	−	1.01383i
$86$			5.25280e10i			0.0140007i
$87$	−3.11421e12	+	5.39396e12i	−0.769967	+	1.33362i
$88$	−4.44643e11	−	7.70144e11i	−0.102064	−	0.176781i
$89$	6.49621e12	−	3.75059e12i	1.38556	−	0.799952i	0.392747	−	0.919646i	$-0.371525\pi$
$89$	6.49621e12	−	3.75059e12i	1.38556	−	0.799952i	0.992811	+	0.119694i	$0.0381914\pi$
$90$	5.57678e11			0.110613
$91$	−3.51538e12	+	1.71710e11i	−0.648937	+	0.0316976i
$92$	−6.36603e12			−1.09458
$93$	6.24239e12	−	3.60405e12i	1.00049	−	0.577632i
$94$	2.27777e11	+	3.94522e11i	0.0340549	+	0.0589848i
$95$	−1.14749e12	+	1.98751e12i	−0.160156	+	0.277399i
$96$			2.26213e12i			0.294954i
$97$	1.09190e13	+	6.30408e12i	1.33096	+	0.768432i	0.985447	−	0.169980i	$-0.0543704\pi$
$97$	1.09190e13	+	6.30408e12i	1.33096	+	0.768432i	0.345517	+	0.938413i	$0.387704\pi$
$98$	3.16871e11	+	1.82946e11i	0.0361338	+	0.0208618i
$99$			1.16869e13i			1.24759i
$100$	1.00919e13	−	1.74796e13i	1.00919	−	1.74796i
$101$	−1.52422e12	−	2.64002e12i	−0.142876	−	0.247468i	0.785703	−	0.618604i	$-0.212302\pi$
$101$	−1.52422e12	−	2.64002e12i	−0.142876	−	0.247468i	−0.928578	+	0.371136i	$0.878968\pi$
$102$	1.13616e12	−	6.55960e11i	0.0998934	−	0.0576735i
$103$	−3.98736e10			−0.00329036			−0.00164518	−	0.999999i	$-0.500524\pi$
$103$	−3.98736e10			−0.00329036			−0.00164518	+	0.999999i	$0.500524\pi$
$104$	−1.00666e12	−	1.56225e12i	−0.0780132	−	0.121069i
$105$	2.12915e13			1.55051
$106$	7.07882e11	−	4.08696e11i	0.0484700	−	0.0279842i
$107$	−6.97803e12	−	1.20863e13i	−0.449509	−	0.778573i	0.548845	−	0.835924i	$-0.315068\pi$
$107$	−6.97803e12	−	1.20863e13i	−0.449509	−	0.778573i	−0.998354	+	0.0573516i	$0.981734\pi$
$108$	−1.34675e12	+	2.33264e12i	−0.0816645	+	0.141447i
$109$			7.88326e12i			0.450229i	0.974332	+	0.225115i	$0.0722757\pi$
$109$			7.88326e12i			0.450229i	−0.974332	+	0.225115i	$0.927724\pi$
$110$	−2.86574e12	−	1.65453e12i	−0.154235	−	0.0890479i
$111$	−1.25465e13	−	7.24373e12i	−0.636683	−	0.367589i
$112$			1.33599e13i			0.639568i
$113$	8.39243e11	−	1.45361e12i	0.0379208	−	0.0656808i	−0.846442	−	0.532481i	$-0.821260\pi$
$113$	8.39243e11	−	1.45361e12i	0.0379208	−	0.0656808i	0.884363	+	0.466800i	$0.154593\pi$
$114$	−2.13519e11	−	3.69826e11i	−0.00911078	−	0.0157803i
$115$	−4.11368e13	+	2.37503e13i	−1.65842	+	0.957489i
$116$	−2.93157e13			−1.11718
$117$	1.19159e12	+	2.43952e13i	0.0429456	+	0.879216i
$118$	−3.50844e11			−0.0119641
$119$	2.03074e13	−	1.17245e13i	0.655540	−	0.378476i
$120$	5.62145e12	+	9.73664e12i	0.171858	+	0.297667i
$121$	1.74118e13	−	3.01581e13i	0.504357	−	0.873573i
$122$			2.10694e12i			0.0578514i
$123$	−6.52606e13	−	3.76782e13i	−1.69929	−	0.981087i
$124$	2.93815e13	+	1.69634e13i	0.725826	+	0.419056i
$125$		−	7.63758e13i		−	1.79077i
$126$	−9.27385e11	+	1.60628e12i	−0.0206467	+	0.0357612i
$127$	1.76868e13	+	3.06345e13i	0.374047	+	0.647868i	0.990184	−	0.139771i	$-0.0446366\pi$
$127$	1.76868e13	+	3.06345e13i	0.374047	+	0.647868i	−0.616137	+	0.787639i	$0.711303\pi$
$128$	−1.22836e13	+	7.09192e12i	−0.246865	+	0.142528i
$129$	1.39170e13			0.265896
$130$	−6.15060e12	−	3.16146e12i	−0.111760	−	0.0574456i
$131$	6.42186e13			1.11019			0.555095	−	0.831787i	$-0.312682\pi$
$131$	6.42186e13			1.11019			0.555095	+	0.831787i	$0.312682\pi$
$132$	−1.01756e14	+	5.87488e13i	−1.67428	+	0.966649i
$133$	−3.81640e12	−	6.61020e12i	−0.0597886	−	0.103557i
$134$	−8.76328e11	+	1.51784e12i	−0.0130763	+	0.0226489i
$135$			2.00978e13i			0.285745i
$136$	1.07233e13	+	6.19108e12i	0.145319	+	0.0839002i
$137$	4.37661e13	+	2.52684e13i	0.565529	+	0.326508i	0.755362	−	0.655308i	$-0.227461\pi$
$137$	4.37661e13	+	2.52684e13i	0.565529	+	0.326508i	−0.189833	+	0.981816i	$0.560795\pi$
$138$		−	8.83872e12i		−	0.108937i
$139$	3.91378e11	−	6.77887e11i	0.00460257	−	0.00797189i	−0.863715	−	0.503981i	$-0.831868\pi$
$139$	3.91378e11	−	6.77887e11i	0.00460257	−	0.00797189i	0.868318	+	0.496009i	$0.165202\pi$
$140$	5.01070e13	+	8.67879e13i	0.562427	+	0.974153i
$141$	1.04526e14	−	6.03483e13i	1.12021	−	0.646756i
$142$	−7.82782e12			−0.0801247
$143$	6.62530e13	−	1.28895e14i	0.647920	−	1.26052i
$144$	9.27119e13			0.866521
$145$	−1.89436e14	+	1.09371e14i	−1.69266	+	0.977257i
$146$	−4.69809e12	−	8.13733e12i	−0.0401446	−	0.0695325i
$147$	4.84704e13	−	8.39532e13i	0.396199	−	0.686238i
$148$		−	6.81890e13i		−	0.533351i
$149$	1.36828e14	+	7.89976e13i	1.02439	+	0.591430i	0.915371	−	0.402610i	$-0.131897\pi$
$149$	1.36828e14	+	7.89976e13i	1.02439	+	0.591430i	0.109015	+	0.994040i	$0.465230\pi$
$150$	2.42691e13	+	1.40117e13i	0.173964	+	0.100438i
$151$			5.94563e13i			0.408176i	0.978953	+	0.204088i	$0.0654229\pi$
$151$			5.94563e13i			0.408176i	−0.978953	+	0.204088i	$0.934577\pi$
$152$	2.01524e12	−	3.49049e12i	0.0132539	−	0.0229564i
$153$	−8.13628e13	−	1.40925e14i	−0.512781	−	0.888162i
$154$	9.53110e12	−	5.50278e12i	0.0575782	−	0.0332428i
$155$	2.53148e14			1.46628
$156$	−2.06414e14	+	1.33006e14i	−1.14665	+	0.738861i
$157$	−3.48627e14			−1.85786			−0.928930	−	0.370256i	$-0.879270\pi$
$157$	−3.48627e14			−1.85786			−0.928930	+	0.370256i	$0.879270\pi$
$158$	1.74058e13	−	1.00493e13i	0.0890069	−	0.0513881i
$159$	−1.08282e14	−	1.87549e14i	−0.531463	−	0.920522i
$160$	−3.97228e13	+	6.88020e13i	−0.187180	+	0.324206i
$161$		−	1.57981e14i		−	0.714888i
$162$	−1.59018e13	−	9.18089e12i	−0.0691191	−	0.0399059i
$163$	3.02182e14	+	1.74465e14i	1.26197	+	0.728598i	0.973455	−	0.228878i	$-0.0735057\pi$
$163$	3.02182e14	+	1.74465e14i	1.26197	+	0.728598i	0.288513	+	0.957476i	$0.406839\pi$
$164$		−	3.54685e14i		−	1.42350i
$165$	−4.38359e14	+	7.59261e14i	−1.69116	+	2.92917i
$166$	−4.30654e12	−	7.45915e12i	−0.0159745	−	0.0276686i
$167$	−3.37811e14	+	1.95036e14i	−1.20508	+	0.695756i	−0.961681	−	0.274170i	$-0.911597\pi$
$167$	−3.37811e14	+	1.95036e14i	−1.20508	+	0.695756i	−0.243403	+	0.969925i	$0.578264\pi$
$168$	−3.73925e13			−0.128314
$169$	1.25154e14	−	2.75808e14i	0.413219	−	0.910632i
$170$	4.60745e13			0.146401
$171$	−4.58719e13	+	2.64841e13i	−0.140305	+	0.0810049i
$172$	3.27520e13	+	5.67281e13i	0.0964500	+	0.167056i
$173$	1.68948e14	−	2.92626e14i	0.479129	−	0.829876i	−0.520584	−	0.853810i	$-0.674286\pi$
$173$	1.68948e14	−	2.92626e14i	0.479129	−	0.829876i	0.999714	+	0.0239340i	$0.00761915\pi$
$174$		−	4.07025e13i		−	0.111186i
$175$	4.33780e14	+	2.50443e14i	1.14162	+	0.659116i
$176$	−4.76418e14	−	2.75060e14i	−1.20825	−	0.697582i
$177$			9.29541e13i			0.227218i
$178$	−2.45099e13	+	4.24525e13i	−0.0577580	+	0.100040i
$179$	−1.88456e14	−	3.26416e14i	−0.428219	−	0.741697i	0.568496	−	0.822686i	$-0.307525\pi$
$179$	−1.88456e14	−	3.26416e14i	−0.428219	−	0.741697i	−0.996715	+	0.0809893i	$0.974192\pi$
$180$	6.02270e14	−	3.47721e14i	1.31984	−	0.762007i
$181$	−2.76542e14			−0.584588			−0.292294	−	0.956329i	$-0.594419\pi$
$181$	−2.76542e14			−0.584588			−0.292294	+	0.956329i	$0.594419\pi$
$182$	1.93340e13	−	1.24582e13i	0.0394328	−	0.0254092i
$183$	5.58222e14			1.09869
$184$	7.22452e13	−	4.17108e13i	0.137244	−	0.0792378i
$185$	−2.54399e14	−	4.40632e14i	−0.466551	−	0.808090i
$186$	−2.35523e13	+	4.07938e13i	−0.0417061	+	0.0722371i
$187$			9.65557e14i			1.65123i
$188$	4.91981e14	+	2.84045e14i	0.812684	+	0.469204i
$189$	−5.78876e13	−	3.34214e13i	−0.0923813	−	0.0533364i
$190$		−	1.49976e13i		−	0.0231272i
$191$	4.75666e14	−	8.23878e14i	0.708901	−	1.22785i	−0.256365	−	0.966580i	$-0.582525\pi$
$191$	4.75666e14	−	8.23878e14i	0.708901	−	1.22785i	0.965265	−	0.261272i	$-0.0841419\pi$
$192$	4.61102e14	+	7.98652e14i	0.664262	+	1.15053i
$193$	−4.21240e14	+	2.43203e14i	−0.586688	+	0.338724i	−0.763787	−	0.645469i	$-0.776662\pi$
$193$	−4.21240e14	+	2.43203e14i	−0.586688	+	0.338724i	0.177099	+	0.984193i	$0.443329\pi$
$194$	−8.23939e13			−0.110964
$195$	−8.37612e14	+	1.62956e15i	−1.09098	+	2.12249i
$196$	4.56277e14			0.574863
$197$	5.63116e14	−	3.25115e14i	0.686385	−	0.396284i	−0.115871	−	0.993264i	$-0.536966\pi$
$197$	5.63116e14	−	3.25115e14i	0.686385	−	0.396284i	0.802256	+	0.596980i	$0.203633\pi$
$198$	−3.81869e13	−	6.61416e13i	−0.0450392	−	0.0780101i
$199$	2.33149e14	−	4.03826e14i	0.266127	−	0.460946i	−0.701731	−	0.712442i	$-0.747589\pi$
$199$	2.33149e14	−	4.03826e14i	0.266127	−	0.460946i	0.967858	+	0.251496i	$0.0809226\pi$
$200$			2.64491e14i			0.292224i
$201$	4.02144e14	+	2.32178e14i	0.430138	+	0.248340i
$202$	1.72525e13	+	9.96071e12i	0.0178676	+	0.0103159i
$203$		−	7.27507e14i		−	0.729647i
$204$	8.18001e14	−	1.41682e15i	0.794617	−	1.37632i
$205$	−1.32326e15	−	2.29195e15i	−1.24521	−	2.15677i
$206$	2.25662e11	−	1.30286e11i	0.000205742	−	0.000118785i
$207$	−1.09632e15			−0.968570
$208$	−1.02251e15	−	5.25582e14i	−0.875502	−	0.450016i
$209$	3.14295e14			0.260848
$210$	−1.20498e14	+	6.95696e13i	−0.0969515	+	0.0559750i
$211$	1.00243e15	+	1.73625e15i	0.782018	+	1.35449i	0.930764	+	0.365620i	$0.119143\pi$
$211$	1.00243e15	+	1.73625e15i	0.782018	+	1.35449i	−0.148746	+	0.988875i	$0.547524\pi$
$212$	5.09656e14	−	8.82750e14i	0.385562	−	0.667813i
$213$			2.07393e15i			1.52170i
$214$	7.89836e13	+	4.56012e13i	0.0562144	+	0.0324554i
$215$	4.23281e14	+	2.44382e14i	0.292266	+	0.168740i
$216$		−	3.52962e13i		−	0.0236471i
$217$	−4.20969e14	+	7.29140e14i	−0.273692	+	0.474048i
$218$	−2.57584e13	−	4.46149e13i	−0.0162537	−	0.0281522i
$219$	−2.15594e15	+	1.24473e15i	−1.32053	+	0.762410i
$220$	−4.12651e15			−2.45378
$221$	9.84474e13	+	2.01549e15i	0.0568401	+	1.16367i
$222$	9.46750e13			0.0530812
$223$	−3.11033e14	+	1.79575e14i	−0.169366	+	0.0977832i	−0.582287	−	0.812984i	$-0.697842\pi$
$223$	−3.11033e14	+	1.79575e14i	−0.169366	+	0.0977832i	0.412921	+	0.910767i	$0.364509\pi$
$224$	−1.32113e14	−	2.28827e14i	−0.0698770	−	0.121031i
$225$	1.73796e15	−	3.01024e15i	0.893006	−	1.54673i
$226$			1.09689e13i			0.00547591i
$227$	5.50555e14	+	3.17863e14i	0.267075	+	0.154196i	0.627557	−	0.778570i	$-0.284055\pi$
$227$	5.50555e14	+	3.17863e14i	0.267075	+	0.154196i	−0.360483	+	0.932766i	$0.617388\pi$
$228$	−4.61185e14	−	2.66265e14i	−0.217419	−	0.125527i
$229$		−	2.49234e14i		−	0.114203i	−0.998368	−	0.0571014i	$-0.981814\pi$
$229$		−	2.49234e14i		−	0.114203i	0.998368	−	0.0571014i	$-0.0181858\pi$
$230$	1.55208e14	−	2.68827e14i	0.0691325	−	0.119741i
$231$	−1.45793e15	−	2.52521e15i	−0.631333	−	1.09350i
$232$	3.32690e14	−	1.92079e14i	0.140077	−	0.0808738i
$233$	1.94204e15			0.795143			0.397572	−	0.917571i	$-0.369853\pi$
$233$	1.94204e15			0.795143			0.397572	+	0.917571i	$0.369853\pi$
$234$	−8.64545e13	−	1.34170e14i	−0.0344258	−	0.0534258i
$235$	4.23885e15			1.64175
$236$	−3.78897e14	+	2.18756e14i	−0.142756	+	0.0824201i
$237$	−2.66249e15	−	4.61157e15i	−0.975942	−	1.69038i
$238$	−7.66191e13	+	1.32708e14i	−0.0273267	+	0.0473312i
$239$			9.55722e14i			0.331700i	0.986151	+	0.165850i	$0.0530367\pi$
$239$			9.55722e14i			0.331700i	−0.986151	+	0.165850i	$0.946963\pi$
$240$	6.02317e15	+	3.47748e15i	2.03448	+	1.17460i
$241$	−1.10104e14	−	6.35686e13i	−0.0361987	−	0.0208993i	0.481791	−	0.876286i	$-0.339986\pi$
$241$	−1.10104e14	−	6.35686e13i	−0.0361987	−	0.0208993i	−0.517990	+	0.855387i	$0.673320\pi$
$242$			2.27571e14i			0.0728311i
$243$	−2.16895e15	+	3.75673e15i	−0.675784	+	1.17049i
$244$	1.31371e15	+	2.27541e15i	0.398534	+	0.690282i
$245$	2.94843e15	−	1.70228e15i	0.870986	−	0.502864i
$246$	4.92452e14			0.141672
$247$	6.56056e14	−	3.20453e13i	0.183828	−	0.00897913i
$248$	−4.44583e14			−0.121344
$249$	−1.97626e15	+	1.14099e15i	−0.525470	+	0.303380i
$250$	2.49556e14	+	4.32244e14i	0.0646485	+	0.111975i
$251$	3.42389e14	−	5.93035e14i	0.0864253	−	0.149693i	−0.819572	−	0.572976i	$-0.805789\pi$
$251$	3.42389e14	−	5.93035e14i	0.0864253	−	0.149693i	0.905998	+	0.423283i	$0.139122\pi$
$252$			2.31295e15i			0.568936i
$253$	5.63366e15	+	3.25260e15i	1.35054	+	0.779735i
$254$	−2.00195e14	−	1.15583e14i	−0.0467773	−	0.0270069i
$255$		−	1.22072e16i		−	2.78038i
$256$	−2.13533e15	+	3.69849e15i	−0.474138	+	0.821231i
$257$	−1.25380e15	−	2.17164e15i	−0.271433	−	0.470135i	0.697796	−	0.716296i	$-0.254164\pi$
$257$	−1.25380e15	−	2.17164e15i	−0.271433	−	0.470135i	−0.969229	+	0.246161i	$0.920831\pi$
$258$	−7.87624e13	+	4.54735e13i	−0.0166261	+	0.00959909i
$259$	1.69220e15			0.348340
$260$	−8.61361e15	+	4.20735e14i	−1.72925	+	0.0844660i
$261$	−5.04858e15			−0.988567
$262$	−3.63441e14	+	2.09833e14i	−0.0694186	+	0.0400789i
$263$	1.37088e14	+	2.37443e14i	0.0255438	+	0.0442432i	0.878515	−	0.477715i	$-0.158535\pi$
$263$	1.37088e14	+	2.37443e14i	0.0255438	+	0.0442432i	−0.852971	+	0.521958i	$0.825202\pi$
$264$	7.69855e14	−	1.33343e15i	0.139953	−	0.242406i
$265$		−	7.60568e15i		−	1.34909i
$266$	4.31974e13	+	2.49400e13i	0.00747700	+	0.00431685i
$267$	1.12475e16	+	6.49377e15i	1.89992	+	1.09692i
$268$			2.18561e15i			0.360327i
$269$	−5.34703e15	+	9.26133e15i	−0.860445	+	1.49033i	0.0110550	+	0.999939i	$0.496481\pi$
$269$	−5.34703e15	+	9.26133e15i	−0.860445	+	1.49033i	−0.871500	+	0.490396i	$0.836852\pi$
$270$	−6.56692e13	−	1.13742e14i	−0.0103157	−	0.0178673i
$271$	−7.55772e13	+	4.36345e13i	−0.0115902	+	0.00669160i	−0.505784	−	0.862660i	$-0.668797\pi$
$271$	−7.55772e13	+	4.36345e13i	−0.0115902	+	0.00669160i	0.494194	+	0.869352i	$0.335463\pi$
$272$	7.65972e15			1.14687
$273$	−3.30073e15	−	5.12244e15i	−0.482562	−	0.748892i
$274$	−3.30256e14			−0.0471490
$275$	−1.78617e16	+	1.03125e16i	−2.49035	+	1.43781i
$276$	−5.51107e15	−	9.54546e15i	−0.750460	−	1.29983i
$277$	6.65210e15	−	1.15218e16i	0.884790	−	1.53250i	0.0388361	−	0.999246i	$-0.487635\pi$
$277$	6.65210e15	−	1.15218e16i	0.884790	−	1.53250i	0.845954	−	0.533256i	$-0.179032\pi$
$278$			5.11529e12i			0.000664628i
$279$	5.05991e15	+	2.92134e15i	0.642267	+	0.370813i
$280$	−1.13728e15	−	6.56611e14i	−0.141040	−	0.0814294i
$281$		−	4.26462e15i		−	0.516760i	−0.966043	−	0.258380i	$-0.916811\pi$
$281$		−	4.26462e15i		−	0.516760i	0.966043	−	0.258380i	$-0.0831886\pi$
$282$	−3.94374e14	+	6.83076e14i	−0.0466970	+	0.0808816i
$283$	−7.45909e14	−	1.29195e15i	−0.0863126	−	0.149498i	0.819637	−	0.572883i	$-0.194175\pi$
$283$	−7.45909e14	−	1.29195e15i	−0.0863126	−	0.149498i	−0.905950	+	0.423385i	$0.860842\pi$
$284$	−8.45372e15	+	4.88076e15i	−0.956046	+	0.551974i
$285$	−3.97352e15			−0.439222
$286$	4.62054e13	+	9.45952e14i	0.00499245	+	0.102209i
$287$	8.80198e15			0.929711
$288$	−1.58796e15	+	9.16808e14i	−0.163979	+	0.0946732i
$289$	−1.76978e15	−	3.06535e15i	−0.178683	−	0.309488i
$290$	7.14734e14	−	1.23795e15i	0.0705598	−	0.122213i
$291$			2.18298e16i			2.10739i
$292$	−1.01475e16	−	5.85865e15i	−0.958010	−	0.553107i
$293$	−4.62699e15	−	2.67139e15i	−0.427227	−	0.246660i	0.270937	−	0.962597i	$-0.412666\pi$
$293$	−4.62699e15	−	2.67139e15i	−0.427227	−	0.246660i	−0.698165	+	0.715937i	$0.746000\pi$
$294$			6.33504e14i			0.0572126i
$295$	−1.63227e15	+	2.82717e15i	−0.144195	+	0.249752i
$296$	4.46780e14	+	7.73846e14i	0.0386098	+	0.0668742i
$297$	2.38364e15	−	1.37619e15i	0.201522	−	0.116349i
$298$	−1.03249e15			−0.0854046
$299$	1.20913e16	+	6.21502e15i	0.978608	+	0.503014i
$300$	3.49461e16			2.76765
$301$	−1.40778e15	+	8.12783e14i	−0.109107	+	0.0629930i
$302$	−1.94272e14	−	3.36489e14i	−0.0147355	−	0.0255227i
$303$	2.63903e15	−	4.57094e15i	0.195915	−	0.339335i
$304$		−	2.49329e15i		−	0.181173i
$305$	1.69782e16	+	9.80236e15i	1.20765	+	0.697239i
$306$	9.20937e14	+	5.31703e14i	0.0641269	+	0.0370237i
$307$		−	2.33136e16i		−	1.58931i	−0.607058	−	0.794657i	$-0.707651\pi$
$307$		−	2.33136e16i		−	1.58931i	0.607058	−	0.794657i	$-0.292349\pi$
$308$	6.86213e15	−	1.18856e16i	0.458015	−	0.793305i
$309$	−3.45186e13	−	5.97880e13i	−0.00225592	−	0.00390736i
$310$	−1.43268e15	+	8.27156e14i	−0.0916847	+	0.0529342i
$311$	−2.77730e16			−1.74052			−0.870261	−	0.492590i	$-0.836050\pi$
$311$	−2.77730e16			−1.74052			−0.870261	+	0.492590i	$0.836050\pi$
$312$	1.47103e15	−	2.86187e15i	0.0902852	−	0.175649i
$313$	−1.23145e16			−0.740250			−0.370125	−	0.928982i	$-0.620685\pi$
$313$	−1.23145e16			−0.740250			−0.370125	+	0.928982i	$0.620685\pi$
$314$	1.97303e15	−	1.13913e15i	0.116169	−	0.0670704i
$315$	8.62915e15	+	1.49461e16i	0.497679	+	0.862005i
$316$	1.25317e16	−	2.17056e16i	0.708019	−	1.22632i
$317$		−	8.56515e15i		−	0.474078i	−0.971500	−	0.237039i	$-0.923823\pi$
$317$		−	8.56515e15i		−	0.474078i	0.971500	−	0.237039i	$-0.0761769\pi$
$318$	1.22563e15	+	7.07616e14i	0.0664633	+	0.0383726i
$319$	2.59431e16	+	1.49783e16i	1.37842	+	0.795833i
$320$			3.23877e16i			1.68619i
$321$	1.20818e16	−	2.09262e16i	0.616379	−	1.06760i
$322$	5.16202e14	+	8.94087e14i	0.0258081	+	0.0447010i
$323$	−3.78986e15	+	2.18808e15i	−0.185698	+	0.107213i
$324$	−2.28977e16			−1.09964
$325$	−3.62329e16	+	2.33473e16i	−1.70554	+	1.09899i
$326$	−2.28024e15			−0.105212
$327$	−1.18205e16	+	6.82454e15i	−0.534655	+	0.308683i
$328$	2.32393e15	+	4.02516e15i	0.103049	+	0.178486i
$329$	−7.04896e15	+	1.22091e16i	−0.306444	+	0.530777i
$330$		−	5.72933e15i		−	0.244210i
$331$	−7.23331e15	−	4.17615e15i	−0.302312	−	0.174540i	0.341169	−	0.940002i	$-0.389177\pi$
$331$	−7.23331e15	−	4.17615e15i	−0.302312	−	0.174540i	−0.643481	+	0.765462i	$0.722510\pi$
$332$	−9.30178e15	−	5.37039e15i	−0.381214	−	0.220094i
$333$		−	1.17431e16i		−	0.471950i
$334$	1.27455e15	−	2.20759e15i	0.0502348	−	0.0870093i
$335$	8.15407e15	+	1.41233e16i	0.315198	+	0.545939i
$336$	−2.00323e16	+	1.15657e16i	−0.759498	+	0.438496i
$337$	1.85768e16			0.690837			0.345418	−	0.938449i	$-0.387737\pi$
$337$	1.85768e16			0.690837			0.345418	+	0.938449i	$0.387737\pi$
$338$	1.92897e14	+	1.96986e15i	0.00703666	+	0.0718581i
$339$	2.90613e15			0.103996
$340$	4.97586e16	−	2.87281e16i	1.74685	−	1.00854i
$341$	−1.73342e16	−	3.00238e16i	−0.597037	−	1.03410i
$342$	1.73073e14	−	2.99771e14i	0.00584870	−	0.0101302i
$343$			3.09175e16i			1.02516i
$344$	−7.43374e14	−	4.29187e14i	−0.0241868	−	0.0139642i
$345$	−7.12243e16	−	4.11214e16i	−2.27407	−	1.31294i
$346$			2.20814e15i			0.0691880i
$347$	1.57590e15	−	2.72954e15i	0.0484604	−	0.0839359i	−0.840778	−	0.541380i	$-0.817902\pi$
$347$	1.57590e15	−	2.72954e15i	0.0484604	−	0.0839359i	0.889238	+	0.457445i	$0.151235\pi$
$348$	−2.53786e16	−	4.39570e16i	−0.765953	−	1.32667i
$349$	1.92674e16	−	1.11240e16i	0.570766	−	0.329532i	−0.186689	−	0.982419i	$-0.559776\pi$
$349$	1.92674e16	−	1.11240e16i	0.570766	−	0.329532i	0.757455	+	0.652887i	$0.226442\pi$
$350$	−3.27327e15			−0.0951787
$351$	4.83525e15	−	3.11568e15i	0.138014	−	0.0889317i
$352$	1.08800e16			0.304862
$353$	1.25191e16	−	7.22793e15i	0.344381	−	0.198828i	−0.317827	−	0.948149i	$-0.602953\pi$
$353$	1.25191e16	−	7.22793e15i	0.344381	−	0.198828i	0.662208	+	0.749320i	$0.269620\pi$
$354$	−3.03726e14	−	5.26069e14i	−0.00820277	−	0.0142076i
$355$	−3.64182e16	+	6.30782e16i	−0.965682	+	1.67261i
$356$			6.11293e16i			1.59156i
$357$	3.51603e16	+	2.02998e16i	0.898895	+	0.518977i
$358$	2.13311e15	+	1.23155e15i	0.0535519	+	0.0309182i
$359$			2.78139e16i			0.685721i	0.939386	+	0.342861i	$0.111396\pi$
$359$			2.78139e16i			0.685721i	−0.939386	+	0.342861i	$0.888604\pi$
$360$	−4.55659e15	+	7.89225e15i	−0.110325	+	0.191088i
$361$	−2.03143e16	−	3.51853e16i	−0.483063	−	0.836690i
$362$	1.56507e15	−	9.03595e14i	0.0365535	−	0.0211042i
$363$	6.02936e16			1.38318
$364$	1.31121e16	−	2.55094e16i	0.295469	−	0.574833i
$365$	−8.74297e16			−1.93533
$366$	−3.15923e15	+	1.82398e15i	−0.0686996	+	0.0396637i
$367$	1.88547e16	+	3.26572e16i	0.402800	+	0.697670i	0.994063	−	0.108809i	$-0.0347038\pi$
$367$	1.88547e16	+	3.26572e16i	0.402800	+	0.697670i	−0.591263	+	0.806479i	$0.701370\pi$
$368$	2.58027e16	−	4.46916e16i	0.541569	−	0.938026i
$369$		−	6.10819e16i		−	1.25962i
$370$	2.87952e15	+	1.66249e15i	0.0583456	+	0.0336859i
$371$	2.19066e16	+	1.26478e16i	0.436159	+	0.251816i
$372$			5.87409e16i			1.14924i
$373$	−3.18570e16	+	5.51780e16i	−0.612489	+	1.06086i	0.378331	+	0.925670i	$0.376498\pi$
$373$	−3.18570e16	+	5.51780e16i	−0.612489	+	1.06086i	−0.990820	+	0.135191i	$0.956835\pi$
$374$	−3.15494e15	−	5.46452e15i	−0.0596109	−	0.103249i
$375$	1.14521e17	−	6.61185e16i	2.12657	−	1.22778i
$376$	−7.44435e15			−0.135864
$377$	5.56805e16	+	2.86203e16i	0.998813	+	0.513399i
$378$	4.36816e14			0.00770197
$379$	9.05952e16	−	5.23052e16i	1.57018	−	0.906546i	0.574038	−	0.818829i	$-0.305376\pi$
$379$	9.05952e16	−	5.23052e16i	1.57018	−	0.906546i	0.996145	−	0.0877170i	$-0.0279571\pi$
$380$	−9.35121e15	−	1.61968e16i	−0.159321	−	0.275953i
$381$	−3.06230e16	+	5.30406e16i	−0.512903	+	0.888375i
$382$			6.21692e15i			0.102368i
$383$	3.26567e16	+	1.88544e16i	0.528665	+	0.305225i	0.740473	−	0.672086i	$-0.234602\pi$
$383$	3.26567e16	+	1.88544e16i	0.528665	+	0.305225i	−0.211807	+	0.977311i	$0.567935\pi$
$384$	−2.12678e16	−	1.22790e16i	−0.338508	−	0.195438i
$385$		−	1.02405e17i		−	1.60260i
$386$	1.58932e15	−	2.75279e15i	0.0244565	−	0.0423599i
$387$	5.64036e15	+	9.76939e15i	0.0853464	+	0.147824i
$388$	−8.89821e16	+	5.13738e16i	−1.32403	+	0.764427i
$389$	2.42017e16			0.354139			0.177069	−	0.984198i	$-0.443338\pi$
$389$	2.42017e16			0.354139			0.177069	+	0.984198i	$0.443338\pi$
$390$	−5.84157e14	−	1.19593e16i	−0.00840639	−	0.172102i
$391$	−9.05764e16			−1.28194
$392$	−5.17809e15	+	2.98957e15i	−0.0720792	+	0.0416149i
$393$	5.55940e16	+	9.62917e16i	0.761161	+	1.31837i
$394$	−2.12462e15	+	3.67995e15i	−0.0286125	+	0.0495582i
$395$		−	1.87013e17i		−	2.47737i
$396$	−8.24806e16	−	4.76202e16i	−1.07481	−	0.620544i
$397$	4.33078e16	+	2.50037e16i	0.555172	+	0.320529i	0.751205	−	0.660069i	$-0.229473\pi$
$397$	4.33078e16	+	2.50037e16i	0.555172	+	0.320529i	−0.196034	+	0.980597i	$0.562806\pi$
$398$			3.04724e15i			0.0384297i
$399$	6.60772e15	−	1.14449e16i	0.0819837	−	0.142000i
$400$	8.18083e16	+	1.41696e17i	0.998637	+	1.72969i
$401$	1.54752e16	−	8.93461e15i	0.185865	−	0.107309i	−0.404180	−	0.914679i	$-0.632443\pi$
$401$	1.54752e16	−	8.93461e15i	0.185865	−	0.107309i	0.590045	+	0.807370i	$0.299110\pi$
$402$	−3.03455e15			−0.0358612
$403$	−3.92444e16	−	6.09038e16i	−0.456347	−	0.708209i
$404$	2.48426e16			0.284262
$405$	−1.47963e17	+	8.54265e16i	−1.66608	+	0.961912i
$406$	2.37712e15	+	4.11729e15i	0.0263409	+	0.0456239i
$407$	−3.48398e16	+	6.03444e16i	−0.379938	+	0.658071i
$408$			2.14385e16i			0.230093i
$409$	−1.36405e17	−	7.87534e16i	−1.44088	−	0.831894i	−0.442974	−	0.896535i	$-0.646077\pi$
$409$	−1.36405e17	−	7.87534e16i	−1.44088	−	0.831894i	−0.997909	+	0.0646407i	$0.979410\pi$
$410$	1.49778e16	+	8.64743e15i	0.155723	+	0.0899067i
$411$			8.74994e16i			0.895434i
$412$	1.62471e14	−	2.81408e14i	0.00163660	−	0.00283468i
$413$	−5.42873e15	−	9.40284e15i	−0.0538298	−	0.0932360i
$414$	6.20457e15	−	3.58221e15i	0.0605633	−	0.0349663i
$415$	−8.01432e16			−0.770112
$416$	2.27109e16	−	1.10932e15i	0.214846	−	0.0104942i
$417$	1.35527e15			0.0126223
$418$	−1.77874e15	+	1.02695e15i	−0.0163105	+	0.00941685i
$419$	−6.37443e16	−	1.10408e17i	−0.575507	−	0.996807i	−0.995986	−	0.0895051i	$-0.971471\pi$
$419$	−6.37443e16	−	1.10408e17i	−0.575507	−	0.996807i	0.420479	−	0.907302i	$-0.361862\pi$
$420$	−8.67553e16	+	1.50265e17i	−0.771216	+	1.33578i
$421$		−	5.77093e16i		−	0.505141i	−0.967579	−	0.252570i	$-0.918724\pi$
$421$		−	5.77093e16i		−	0.505141i	0.967579	−	0.252570i	$-0.0812759\pi$
$422$	−1.13464e16	−	6.55082e15i	−0.0977970	−	0.0564631i
$423$	8.47261e16	+	4.89166e16i	0.719126	+	0.415188i
$424$			1.33572e16i			0.111645i
$425$	1.43588e17	−	2.48702e17i	1.18193	−	2.04715i
$426$	−6.77654e15	−	1.17373e16i	−0.0549346	−	0.0951495i
$427$	−5.64674e16	+	3.26015e16i	−0.450834	+	0.260289i
$428$	1.13732e17			0.894332
$429$	2.50625e17	−	1.22418e16i	1.94111	−	0.0948145i
$430$	−3.19405e15			−0.0243667
$431$	−1.45630e17	+	8.40797e16i	−1.09433	+	0.631813i	−0.934727	−	0.355367i	$-0.884356\pi$
$431$	−1.45630e17	+	8.40797e16i	−1.09433	+	0.631813i	−0.159606	+	0.987181i	$0.551022\pi$
$432$	−1.09173e16	−	1.89093e16i	−0.0808108	−	0.139968i
$433$	9.98631e16	−	1.72968e17i	0.728171	−	1.26123i	−0.229484	−	0.973312i	$-0.573704\pi$
$433$	9.98631e16	−	1.72968e17i	0.728171	−	1.26123i	0.957655	−	0.287917i	$-0.0929629\pi$
$434$		−	5.50204e15i		−	0.0395221i
$435$	−3.27989e17	−	1.89365e17i	−2.32102	−	1.34004i
$436$	−5.56361e16	−	3.21215e16i	−0.387877	−	0.223941i
$437$			2.94832e16i			0.202510i
$438$	8.13427e15	−	1.40890e16i	0.0550474	−	0.0953449i
$439$	1.09481e17	+	1.89626e17i	0.729993	+	1.26439i	0.956885	+	0.290466i	$0.0938103\pi$
$439$	1.09481e17	+	1.89626e17i	0.729993	+	1.26439i	−0.226892	+	0.973920i	$0.572856\pi$
$440$	4.68299e16	−	2.70372e16i	0.307667	−	0.177631i
$441$	7.85775e16			0.508683
$442$	−7.14274e15	−	1.10849e16i	−0.0455638	−	0.0707109i
$443$	1.63645e17			1.02868			0.514339	−	0.857587i	$-0.328037\pi$
$443$	1.63645e17			1.02868			0.514339	+	0.857587i	$0.328037\pi$
$444$	1.02245e17	−	5.90313e16i	0.633364	−	0.365673i
$445$	2.28061e17	+	3.95013e17i	1.39223	+	2.41141i
$446$	1.17352e15	−	2.03259e15i	0.00706013	−	0.0122285i
$447$			2.73553e17i			1.62197i
$448$	−9.32863e16	−	5.38588e16i	−0.545143	−	0.314739i
$449$	−1.07867e16	−	6.22772e15i	−0.0621281	−	0.0358697i	0.468614	−	0.883403i	$-0.344753\pi$
$449$	−1.07867e16	−	6.22772e15i	−0.0621281	−	0.0358697i	−0.530742	+	0.847533i	$0.678087\pi$
$450$			2.27151e16i			0.128953i
$451$	−1.81219e17	+	3.13881e17i	−1.01404	+	1.75638i
$452$	6.83924e15	+	1.18459e16i	0.0377232	+	0.0653384i
$453$	−8.91509e16	+	5.14713e16i	−0.484716	+	0.279851i
$454$	−4.15445e15			−0.0222664
$455$	−1.04411e16	−	2.13758e17i	−0.0551661	−	1.12940i
$456$	6.97837e15			0.0363481
$457$	2.75869e17	−	1.59273e17i	1.41660	−	0.817876i	0.420605	−	0.907244i	$-0.361818\pi$
$457$	2.75869e17	−	1.59273e17i	1.41660	−	0.817876i	0.995999	+	0.0893676i	$0.0284846\pi$
$458$	8.14368e14	+	1.41053e15i	0.00412282	+	0.00714094i
$459$	−1.91617e16	+	3.31891e16i	−0.0956427	+	0.165658i
$460$		−	3.87097e17i		−	1.90500i
$461$	−1.81634e17	−	1.04867e17i	−0.881337	−	0.508840i	−0.0102382	−	0.999948i	$-0.503259\pi$
$461$	−1.81634e17	−	1.04867e17i	−0.881337	−	0.508840i	−0.871099	+	0.491107i	$0.836592\pi$
$462$	1.65021e16	+	9.52752e15i	0.0789528	+	0.0455834i
$463$			9.71559e15i			0.0458345i	0.999737	+	0.0229173i	$0.00729543\pi$
$463$			9.71559e15i			0.0458345i	−0.999737	+	0.0229173i	$0.992705\pi$
$464$	1.18822e17	−	2.05805e17i	0.552750	−	0.957392i
$465$	2.19150e17	+	3.79579e17i	1.00530	+	1.74124i
$466$	−1.09909e16	+	6.34559e15i	−0.0497192	+	0.0287054i
$467$	3.34629e17			1.49281			0.746403	−	0.665494i	$-0.231779\pi$
$467$	3.34629e17			1.49281			0.746403	+	0.665494i	$0.231779\pi$
$468$	−1.77024e17	−	9.09920e16i	−0.778815	−	0.400318i
$469$	−5.42389e16			−0.235336
$470$	−2.39896e16	+	1.38504e16i	−0.102656	+	0.0592687i
$471$	−3.01806e17	−	5.22744e17i	−1.27377	−	2.20624i
$472$	2.86662e15	−	4.96514e15i	0.0119329	−	0.0206685i
$473$		−	6.69359e16i		−	0.274828i
$474$	3.01365e16	+	1.73993e16i	0.122049	+	0.0704648i
$475$	−8.09541e16	−	4.67388e16i	−0.323393	−	0.186711i
$476$			1.91093e17i			0.753007i
$477$	8.77701e16	−	1.52022e17i	0.341175	−	0.590932i
$478$	−3.12281e15	−	5.40886e15i	−0.0119747	−	0.0207407i
$479$	−2.13778e17	+	1.23425e17i	−0.808689	+	0.466897i	−0.846500	−	0.532388i	$-0.821295\pi$
$479$	−2.13778e17	+	1.23425e17i	−0.808689	+	0.466897i	0.0378115	+	0.999285i	$0.487961\pi$
$480$	−1.37552e17			−0.513334
$481$	−6.65715e16	+	1.29514e17i	−0.245101	+	0.476842i
$482$	8.30837e14			0.00301794
$483$	2.36883e17	−	1.36765e17i	0.848942	−	0.490137i
$484$	1.41894e17	+	2.45767e17i	0.501728	+	0.869019i
$485$	−3.83330e17	+	6.63947e17i	−1.33737	+	2.31639i
$486$		−	2.83480e16i		−	0.0975857i
$487$	1.63345e17	+	9.43074e16i	0.554841	+	0.320337i	0.751072	−	0.660220i	$-0.229537\pi$
$487$	1.63345e17	+	9.43074e16i	0.554841	+	0.320337i	−0.196232	+	0.980558i	$0.562870\pi$
$488$	−2.98174e16	−	1.72151e16i	−0.0999404	−	0.0577006i
$489$			6.04136e17i			1.99815i
$490$	−1.11243e16	+	1.92679e16i	−0.0363077	+	0.0628868i
$491$	−2.42801e17	−	4.20543e17i	−0.782025	−	1.35451i	−0.930760	−	0.365630i	$-0.880854\pi$
$491$	−2.42801e17	−	4.20543e17i	−0.782025	−	1.35451i	0.148736	−	0.988877i	$-0.452480\pi$
$492$	5.31828e17	−	3.07051e17i	1.69043	−	0.975972i
$493$	−4.17106e17			−1.30840
$494$	−3.60820e15	+	2.32501e15i	−0.0111703	+	0.00719780i
$495$	−7.10644e17			−2.17129
$496$	−2.38177e17	+	1.37511e17i	−0.718239	+	0.414675i
$497$	−1.21123e17	−	2.09790e17i	−0.360503	−	0.624409i
$498$	7.45635e15	−	1.29148e16i	0.0219046	−	0.0379399i
$499$		−	1.99000e17i		−	0.577032i	−0.957475	−	0.288516i	$-0.906838\pi$
$499$		−	1.99000e17i		−	0.577032i	0.957475	−	0.288516i	$-0.0931618\pi$
$500$	5.39022e17	+	3.11204e17i	1.54277	+	0.890719i
$501$	−5.84887e17	−	3.37685e17i	−1.65244	−	0.954039i
$502$			4.47500e15i			0.0124801i
$503$	−7.23610e16	+	1.25333e17i	−0.199211	+	0.345043i	−0.948273	−	0.317457i	$-0.897171\pi$
$503$	−7.23610e16	+	1.25333e17i	−0.199211	+	0.345043i	0.749062	+	0.662500i	$0.230504\pi$
$504$	−1.51547e16	−	2.62487e16i	−0.0411858	−	0.0713360i
$505$	1.60531e17	−	9.26826e16i	0.430690	−	0.248659i
$506$	−4.25112e16			−0.112597
$507$	5.21902e17	−	5.11069e16i	1.36470	−	0.133637i
$508$	−2.88271e17			−0.744194
$509$	4.22730e17	−	2.44063e17i	1.07745	−	0.622066i	0.147243	−	0.989100i	$-0.452960\pi$
$509$	4.22730e17	−	2.44063e17i	1.07745	−	0.622066i	0.930207	+	0.367034i	$0.119627\pi$
$510$	3.98867e16	+	6.90858e16i	0.100374	+	0.173853i
$511$	1.45390e17	−	2.51823e17i	0.361243	−	0.625691i
$512$		−	1.44103e17i		−	0.353522i
$513$	1.08033e16	+	6.23727e15i	0.0261693	+	0.0151088i
$514$	1.41916e16	+	8.19352e15i	0.0339446	+	0.0195979i
$515$		−	2.42458e15i		−	0.00572650i
$516$	−5.67068e16	+	9.82190e16i	−0.132255	+	0.229072i
$517$	−2.90254e17	−	5.02735e17i	−0.668483	−	1.15785i
$518$	−9.57692e15	+	5.52924e15i	−0.0217812	+	0.0125754i
$519$	5.85033e17			1.31399
$520$	9.49953e16	−	6.12119e16i	0.210708	−	0.135773i
$521$	4.60598e17			1.00897			0.504484	−	0.863421i	$-0.331683\pi$
$521$	4.60598e17			1.00897			0.504484	+	0.863421i	$0.331683\pi$
$522$	2.85722e16	−	1.64961e16i	0.0618137	−	0.0356882i
$523$	3.89975e17	+	6.75456e17i	0.833250	+	1.44323i	0.895447	+	0.445168i	$0.146856\pi$
$523$	3.89975e17	+	6.75456e17i	0.833250	+	1.44323i	−0.0621964	+	0.998064i	$0.519811\pi$
$524$	−2.61668e17	+	4.53222e17i	−0.552201	+	0.956440i
$525$			8.67235e17i			1.80759i
$526$	−1.55168e15	−	8.95863e14i	−0.00319444	−	0.00184431i
$527$	4.18042e17	+	2.41357e17i	0.850063	+	0.490784i
$528$		−	9.52479e17i		−	1.91309i
$529$	−5.30995e16	+	9.19711e16i	−0.105349	+	0.182469i
$530$	2.48514e16	+	4.30439e16i	0.0487033	+	0.0843566i
$531$	−6.52516e16	+	3.76730e16i	−0.126321	+	0.0729316i
$532$	6.22019e16			0.118954
$533$	−3.46272e17	+	6.73668e17i	−0.654169	+	1.27268i
$534$	−8.48731e16			−0.158399
$535$	7.34928e17	−	4.24311e17i	1.35502	−	0.782320i
$536$	−1.43203e16	−	2.48036e16i	−0.0260845	−	0.0451796i
$537$	3.26293e17	−	5.65156e17i	0.587185	−	1.01703i
$538$		−	6.98853e16i		−	0.124251i
$539$	−4.03786e17	−	2.33126e17i	−0.709291	−	0.409509i
$540$	−1.41840e17	−	8.18915e16i	−0.246173	−	0.142128i
$541$			1.46895e17i			0.251898i	0.992037	+	0.125949i	$0.0401976\pi$
$541$			1.46895e17i			0.251898i	−0.992037	+	0.125949i	$0.959802\pi$
$542$	2.85150e14	−	4.93894e14i	0.000483146	−	0.000836833i
$543$	−2.39402e17	−	4.14657e17i	−0.400801	−	0.694209i
$544$	−1.31195e17	+	7.57453e16i	−0.217032	+	0.125303i
$545$	−4.79355e17			−0.783574
$546$	3.54178e16	+	1.82051e16i	0.0572096	+	0.0294063i
$547$	1.59096e17			0.253946			0.126973	−	0.991906i	$-0.459474\pi$
$547$	1.59096e17			0.253946			0.126973	+	0.991906i	$0.459474\pi$
$548$	−3.56663e17	+	2.05920e17i	−0.562581	+	0.324806i
$549$	2.26240e17	+	3.91859e17i	0.352654	+	0.610815i
$550$	6.73917e16	−	1.16726e17i	0.103812	−	0.179808i
$551$			1.35771e17i			0.206691i
$552$	1.25085e17	+	7.22181e16i	0.188193	+	0.108653i
$553$	5.38653e17	+	3.10991e17i	0.800932	+	0.462418i
$554$			8.69425e16i			0.127767i
$555$	4.40467e17	−	7.62911e17i	0.639748	−	1.10808i
$556$	3.18946e15	+	5.52430e15i	0.00457858	+	0.00793033i
$557$	2.76612e17	−	1.59702e17i	0.392475	−	0.226595i	−0.290757	−	0.956797i	$-0.593907\pi$
$557$	2.76612e17	−	1.59702e17i	0.392475	−	0.226595i	0.683232	+	0.730202i	$0.260574\pi$
$558$	−3.81817e16			−0.0535468
$559$	−6.82472e15	−	1.39721e17i	−0.00946037	−	0.193680i
$560$	−8.12372e17			−1.11310
$561$	−1.44779e18	+	8.35883e17i	−1.96087	+	1.13211i
$562$	1.39346e16	+	2.41354e16i	0.0186555	+	0.0323123i
$563$	2.30802e17	−	3.99760e17i	0.305446	−	0.529048i	−0.671915	−	0.740629i	$-0.734528\pi$
$563$	2.30802e17	−	3.99760e17i	0.305446	−	0.529048i	0.977360	+	0.211581i	$0.0678612\pi$
$564$			9.83592e17i			1.28677i
$565$	8.83893e16	+	5.10316e16i	0.114310	+	0.0659970i
$566$	8.44287e15	+	4.87449e15i	0.0107940	+	0.00623193i
$567$		−	5.68237e17i		−	0.718190i
$568$	6.39583e16	−	1.10779e17i	0.0799159	−	0.138418i
$569$	7.49948e16	+	1.29895e17i	0.0926406	+	0.160458i	0.908621	−	0.417621i	$-0.137136\pi$
$569$	7.49948e16	+	1.29895e17i	0.0926406	+	0.160458i	−0.815981	+	0.578079i	$0.803803\pi$
$570$	2.24879e16	−	1.29834e16i	0.0274639	−	0.0158563i
$571$	−1.08693e18			−1.31241			−0.656203	−	0.754584i	$-0.727839\pi$
$571$	−1.08693e18			−1.31241			−0.656203	+	0.754584i	$0.727839\pi$
$572$	6.39715e17	+	9.92780e17i	0.763682	+	1.18517i
$573$	1.64714e18			1.94413
$574$	−4.98143e16	+	2.87603e16i	−0.0581336	+	0.0335634i
$575$	−9.67387e17	−	1.67556e18i	−1.11624	−	1.93339i
$576$	−3.73757e17	+	6.47366e17i	−0.426425	+	0.738590i
$577$		−	9.15693e17i		−	1.03302i	−0.856282	−	0.516508i	$-0.827232\pi$
$577$		−	9.15693e17i		−	1.03302i	0.856282	−	0.516508i	$-0.172768\pi$
$578$	2.00319e16	+	1.15655e16i	0.0223456	+	0.0129012i
$579$	−7.29335e17	−	4.21082e17i	−0.804482	−	0.464468i
$580$		−	1.78259e18i		−	1.94433i
$581$	1.33273e17	−	2.30836e17i	0.143747	−	0.248977i
$582$	−7.13284e16	−	1.23544e17i	−0.0760787	−	0.131772i
$583$	−9.02047e17	+	5.20797e17i	−0.951445	+	0.549317i
$584$	1.53546e17			0.160160
$585$	−1.48339e18	+	7.24566e16i	−1.53018	+	0.0747421i
$586$	3.49149e16			0.0356186
$587$	−9.99108e17	+	5.76835e17i	−1.00801	+	0.581975i	−0.910608	−	0.413271i	$-0.864386\pi$
$587$	−9.99108e17	+	5.76835e17i	−1.00801	+	0.581975i	−0.0974014	+	0.995245i	$0.531053\pi$
$588$	3.94999e17	+	6.84159e17i	0.394134	+	0.682660i
$589$	7.85632e16	−	1.36076e17i	0.0775300	−	0.134286i
$590$		−	2.13337e16i		−	0.0208222i
$591$	9.74980e17	+	5.62905e17i	0.941190	+	0.543396i
$592$	4.78709e17	+	2.76383e17i	0.457067	+	0.263888i
$593$			5.73888e17i			0.541966i	0.962584	+	0.270983i	$0.0873487\pi$
$593$			5.73888e17i			0.541966i	−0.962584	+	0.270983i	$0.912651\pi$
$594$	−8.99337e15	+	1.55770e16i	−0.00840061	+	0.0145503i
$595$	7.12927e17	+	1.23483e18i	0.658696	+	1.14089i
$596$	−1.11505e18	+	6.43775e17i	−1.01905	+	0.588346i
$597$	8.07349e17			0.729841
$598$	−8.87373e16	+	4.33441e15i	−0.0793503	+	0.00387589i
$599$	6.12606e17			0.541884			0.270942	−	0.962596i	$-0.412665\pi$
$599$	6.12606e17			0.541884			0.270942	+	0.962596i	$0.412665\pi$
$600$	−3.96588e17	+	2.28970e17i	−0.347021	+	0.200353i
$601$	−8.44580e17	−	1.46286e18i	−0.731066	−	1.26624i	−0.956428	−	0.291969i	$-0.905690\pi$
$601$	−8.44580e17	−	1.46286e18i	−0.731066	−	1.26624i	0.225362	−	0.974275i	$-0.427644\pi$
$602$	5.31151e15	−	9.19980e15i	0.00454821	−	0.00787774i
$603$			3.76394e17i			0.318846i
$604$	−4.19612e17	−	2.42263e17i	−0.351648	−	0.203024i
$605$	1.83381e18	+	1.05875e18i	1.52036	+	0.877778i
$606$			3.44920e16i			0.0282908i
$607$	−6.86677e17	+	1.18936e18i	−0.557220	+	0.965132i	0.440508	+	0.897749i	$0.354798\pi$
$607$	−6.86677e17	+	1.18936e18i	−0.557220	+	0.965132i	−0.997727	+	0.0673836i	$0.978535\pi$
$608$	2.46556e16	+	4.27048e16i	0.0197944	+	0.0342849i
$609$	1.09085e18	−	6.29803e17i	0.866469	−	0.500256i
$610$	−1.28116e17			−0.100684
$611$	−6.57132e17	−	1.01981e18i	−0.510957	−	0.792959i
$612$	1.32610e18			1.02021
$613$	1.48043e18	−	8.54728e17i	1.12693	−	0.650631i	0.183766	−	0.982970i	$-0.441171\pi$
$613$	1.48043e18	−	8.54728e17i	1.12693	−	0.650631i	0.943160	+	0.332339i	$0.107838\pi$
$614$	7.61768e16	+	1.31942e17i	0.0573757	+	0.0993777i
$615$	2.29109e18	−	3.96828e18i	1.70747	−	2.95743i
$616$			1.79845e17i			0.132625i
$617$	1.21572e18	+	7.01897e17i	0.887116	+	0.512177i	0.872998	−	0.487724i	$-0.162173\pi$
$617$	1.21572e18	+	7.01897e17i	0.887116	+	0.512177i	0.0141181	+	0.999900i	$0.495506\pi$
$618$	3.90712e14	+	2.25578e14i	0.000282119	+	0.000162881i
$619$			8.50368e17i			0.607600i	0.952736	+	0.303800i	$0.0982555\pi$
$619$			8.50368e17i			0.607600i	−0.952736	+	0.303800i	$0.901745\pi$
$620$	−1.03149e18	+	1.78659e18i	−0.729320	+	1.26322i
$621$	1.29097e17	+	2.23603e17i	0.0903277	+	0.156452i
$622$	1.57180e17	−	9.07477e16i	0.108832	−	0.0628345i
$623$	−1.51700e18			−1.03948
$624$	−9.71139e16	−	1.98819e18i	−0.0658539	−	1.34821i
$625$	1.62078e18			1.08769
$626$	6.96932e16	−	4.02374e16i	0.0462868	−	0.0267237i
$627$	2.72086e17	+	4.71266e17i	0.178841	+	0.309761i
$628$	1.42053e18	−	2.46043e18i	0.924087	−	1.60057i
$629$		−	9.70199e17i		−	0.624643i
$630$	−9.76724e16	−	5.63912e16i	−0.0622384	−	0.0359333i
$631$	−1.33557e18	−	7.71093e17i	−0.842319	−	0.486313i	0.0157330	−	0.999876i	$-0.494992\pi$
$631$	−1.33557e18	−	7.71093e17i	−0.842319	−	0.486313i	−0.858052	+	0.513563i	$0.828325\pi$
$632$			3.28436e17i			0.205017i
$633$	−1.73560e18	+	3.00615e18i	−1.07232	+	1.85732i
$634$	2.79865e16	+	4.84740e16i	0.0171146	+	0.0296434i
$635$	−1.86278e18	+	1.07548e18i	−1.12754	+	0.650987i
$636$	1.76484e18			1.05739
$637$	−8.66626e17	−	4.45454e17i	−0.513955	−	0.264178i
$638$	−1.95765e17			−0.114921
$639$	−1.45585e18	+	8.40537e17i	−0.845984	+	0.488429i
$640$	−4.31236e17	−	7.46922e17i	−0.248053	−	0.429641i
$641$	−8.90600e17	+	1.54256e18i	−0.507114	+	0.878347i	0.492852	+	0.870113i	$0.335954\pi$
$641$	−8.90600e17	+	1.54256e18i	−0.507114	+	0.878347i	−0.999966	+	0.00823418i	$0.997379\pi$
$642$			1.57908e17i			0.0890074i
$643$	1.86575e18	+	1.07719e18i	1.04108	+	0.601065i	0.920138	−	0.391595i	$-0.128077\pi$
$643$	1.86575e18	+	1.07719e18i	1.04108	+	0.601065i	0.120938	+	0.992660i	$0.461410\pi$
$644$	1.11495e18	+	6.43719e17i	0.615884	+	0.355581i
$645$			8.46245e17i			0.462762i
$646$	1.42990e16	−	2.47666e16i	0.00774096	−	0.0134077i
$647$	4.05186e17	+	7.01803e17i	0.217158	+	0.376130i	0.953938	−	0.300003i	$-0.0969878\pi$
$647$	4.05186e17	+	7.01803e17i	0.217158	+	0.376130i	−0.736780	+	0.676133i	$0.763654\pi$
$648$	2.59856e17	−	1.50028e17i	0.137878	−	0.0796038i
$649$	4.47077e17			0.234851
$650$	1.28771e17	−	2.50523e17i	0.0669702	−	0.130290i
$651$	−1.45773e18			−0.750588
$652$	−2.46257e18	+	1.42176e18i	−1.25539	+	0.724800i
$653$	−1.12473e18	−	1.94808e18i	−0.567690	−	0.983267i	−0.996794	−	0.0800122i	$-0.974504\pi$
$653$	−1.12473e18	−	1.94808e18i	−0.567690	−	0.983267i	0.429104	−	0.903255i	$-0.358829\pi$
$654$	4.45981e16	−	7.72463e16i	0.0222875	−	0.0386031i
$655$			3.90492e18i			1.93216i
$656$	2.49000e18	+	1.43760e18i	1.21990	+	0.704310i
$657$	−1.74754e18	−	1.00894e18i	−0.847721	−	0.489432i
$658$		−	9.21293e16i		−	0.0442517i
$659$	2.00792e18	−	3.47782e18i	0.954973	−	1.65406i	0.220542	−	0.975377i	$-0.429217\pi$
$659$	2.00792e18	−	3.47782e18i	0.954973	−	1.65406i	0.734431	−	0.678684i	$-0.237449\pi$
$660$	−3.57232e18	−	6.18744e18i	−1.68234	−	2.91390i
$661$	2.37416e18	−	1.37072e18i	1.10714	−	0.639205i	0.169050	−	0.985608i	$-0.445930\pi$
$661$	2.37416e18	−	1.37072e18i	1.10714	−	0.639205i	0.938086	+	0.346402i	$0.112597\pi$
$662$	5.45820e16			0.0252042
$663$	−2.93688e18	+	1.89243e18i	−1.34291	+	0.865329i
$664$	1.40749e17			0.0637313
$665$	4.01944e17	−	2.32063e17i	0.180229	−	0.104055i
$666$	3.83705e16	+	6.64596e16i	0.0170378	+	0.0295104i
$667$	−1.40507e18	+	2.43366e18i	−0.617847	+	1.07014i
$668$		−	3.17880e18i		−	1.38426i
$669$	−5.38523e17	−	3.10916e17i	−0.232239	−	0.134083i
$670$	−9.22951e16	−	5.32866e16i	−0.0394178	−	0.0227579i
$671$		−	2.68486e18i		−	1.13560i
$672$	2.28741e17	−	3.96191e17i	0.0958173	−	0.165960i
$673$	1.25563e18	+	2.17482e18i	0.520913	+	0.902248i	0.999704	+	0.0243192i	$0.00774181\pi$
$673$	1.25563e18	+	2.17482e18i	0.520913	+	0.902248i	−0.478791	+	0.877929i	$0.658925\pi$
$674$	−1.05134e17	+	6.06992e16i	−0.0431971	+	0.0249398i
$675$	−8.18614e17			−0.333123
$676$	1.43656e18	+	2.00709e18i	0.578987	+	0.808935i
$677$	−1.13187e18			−0.451825			−0.225912	−	0.974148i	$-0.572536\pi$
$677$	−1.13187e18			−0.451825			−0.225912	+	0.974148i	$0.572536\pi$
$678$	−1.64471e16	+	9.49574e15i	−0.00650274	+	0.00375436i
$679$	−1.27491e18	−	2.20821e18i	−0.499259	−	0.864742i
$680$	−3.76459e17	+	6.52045e17i	−0.146019	+	0.252912i
$681$			1.10070e18i			0.422874i
$682$	1.96204e17	+	1.13279e17i	0.0746638	+	0.0431071i
$683$	2.60100e18	+	1.50169e18i	0.980407	+	0.566038i	0.902393	−	0.430914i	$-0.141809\pi$
$683$	2.60100e18	+	1.50169e18i	0.980407	+	0.566038i	0.0780140	+	0.996952i	$0.475142\pi$
$684$		−	4.31654e17i		−	0.161165i
$685$	−1.53649e18	+	2.66127e18i	−0.568251	+	0.984239i
$686$	−1.01022e17	−	1.74976e17i	−0.0370093	−	0.0641020i
$687$	3.73711e17	−	2.15762e17i	0.135618	−	0.0782990i
$688$	−5.30999e17			−0.190884
$689$	−1.82982e18	+	1.17908e18i	−0.651604	+	0.419872i
$690$	5.37453e17			0.189593
$691$	1.32391e18	−	7.64362e17i	0.462650	−	0.267111i	−0.250508	−	0.968115i	$-0.580598\pi$
$691$	1.32391e18	−	7.64362e17i	0.462650	−	0.267111i	0.713158	+	0.701003i	$0.247264\pi$
$692$	1.37681e18	+	2.38470e18i	0.476632	+	0.825550i
$693$	1.18176e18	−	2.04686e18i	0.405287	−	0.701977i
$694$			2.05969e16i			0.00699786i
$695$	4.12201e16	+	2.37984e16i	0.0138742	+	0.00801026i
$696$	5.76020e17	+	3.32565e17i	0.192078	+	0.110896i
$697$		−	5.04649e18i		−	1.66716i
$698$	−7.26953e16	+	1.25912e17i	−0.0237928	+	0.0412104i
$699$	1.68123e18	+	2.91197e18i	0.545161	+	0.944246i
$700$	−3.53500e18	+	2.04093e18i	−1.13567	+	0.655680i
$701$	−3.18684e18			−1.01436			−0.507181	−	0.861839i	$-0.669313\pi$
$701$	−3.18684e18			−1.01436			−0.507181	+	0.861839i	$0.669313\pi$
$702$	−1.71844e16	+	3.34321e16i	−0.00541931	+	0.0105432i
$703$	−3.15806e17			−0.0986760
$704$	3.84124e18	−	2.21774e18i	1.18919	−	0.686576i
$705$	3.66958e18	+	6.35589e18i	1.12561	+	1.94961i
$706$	−4.72343e16	+	8.18122e16i	−0.0143558	+	0.0248649i
$707$			6.16502e17i			0.185656i
$708$	−6.56023e17	−	3.78755e17i	−0.195751	−	0.113017i
$709$	−3.05438e18	−	1.76345e18i	−0.903072	−	0.521389i	−0.0248762	−	0.999691i	$-0.507919\pi$
$709$	−3.05438e18	−	1.76345e18i	−0.903072	−	0.521389i	−0.878195	+	0.478302i	$0.841252\pi$
$710$		−	4.75983e17i		−	0.139448i
$711$	2.15814e18	−	3.73801e18i	0.626510	−	1.08515i
$712$	−4.00524e17	−	6.93728e17i	−0.115215	−	0.199558i
$713$	2.81645e18	−	1.62608e18i	0.802824	−	0.463511i
$714$	−2.65317e17			−0.0749422
$715$	7.83765e18	+	4.02862e18i	2.19380	+	1.12763i
$716$	3.07157e18			0.851973
$717$	−1.43305e18	+	8.27369e17i	−0.393899	+	0.227418i
$718$	−9.08814e16	−	1.57411e17i	−0.0247552	−	0.0428772i
$719$	2.89471e18	−	5.01379e18i	0.781390	−	1.35341i	−0.149742	−	0.988725i	$-0.547844\pi$
$719$	2.89471e18	−	5.01379e18i	0.781390	−	1.35341i	0.931132	−	0.364682i	$-0.118822\pi$
$720$			5.63750e18i			1.50808i
$721$	6.98351e15	+	4.03193e15i	0.00185137	+	0.00106889i
$722$	2.29935e17	+	1.32753e17i	0.0604106	+	0.0348781i
$723$		−	2.20126e17i		−	0.0573154i
$724$	1.12681e18	−	1.95169e18i	0.290770	−	0.503629i
$725$	−4.45483e18	−	7.71600e18i	−1.13929	−	1.97331i
$726$	−3.41228e17	+	1.97008e17i	−0.0864882	+	0.0499340i
$727$	−3.36915e18			−0.846344			−0.423172	−	0.906049i	$-0.639083\pi$
$727$	−3.36915e18			−0.846344			−0.423172	+	0.906049i	$0.639083\pi$
$728$	1.83369e16	+	3.75406e17i	0.00456532	+	0.0934647i
$729$	−3.03094e18			−0.747908
$730$	4.94804e17	−	2.85675e17i	0.121014	−	0.0698672i
$731$	4.65998e17	+	8.07132e17i	0.112959	+	0.195651i
$732$	−2.27456e18	+	3.93965e18i	−0.546481	+	0.946533i
$733$		−	4.66042e18i		−	1.10981i	−0.831913	−	0.554906i	$-0.812754\pi$
$733$		−	4.66042e18i		−	1.10981i	0.831913	−	0.554906i	$-0.187246\pi$
$734$	−2.13414e17	−	1.23215e17i	−0.0503730	−	0.0290829i
$735$	5.10491e18	+	2.94732e18i	1.19432	+	0.689541i
$736$			1.02063e18i			0.236680i
$737$	1.11670e18	−	1.93418e18i	0.256683	−	0.444587i
$738$	1.99584e17	+	3.45689e17i	0.0454736	+	0.0787626i
$739$	−2.70836e17	+	1.56367e17i	−0.0611671	+	0.0353148i	−0.530272	−	0.847828i	$-0.677910\pi$
$739$	−2.70836e17	+	1.56367e17i	−0.0611671	+	0.0353148i	0.469105	+	0.883143i	$0.344577\pi$
$740$	4.14635e18			0.928238
$741$	6.15998e17	+	9.55973e17i	0.136698	+	0.212142i
$742$	−1.65306e17			−0.0363632
$743$	1.96738e18	−	1.13587e18i	0.429004	−	0.247686i	−0.269918	−	0.962883i	$-0.586997\pi$
$743$	1.96738e18	−	1.13587e18i	0.429004	−	0.247686i	0.698922	+	0.715198i	$0.253663\pi$
$744$	−3.84875e17	−	6.66624e17i	−0.0831948	−	0.144098i
$745$	−4.80358e18	+	8.32004e18i	−1.02932	+	1.78283i
$746$		−	4.16369e17i		−	0.0884456i
$747$	−1.60190e18	−	9.24858e17i	−0.337327	−	0.194756i
$748$	−6.81442e18	−	3.93431e18i	−1.42255	−	0.821311i
$749$			2.82241e18i			0.584102i
$750$	−4.32082e17	+	7.48388e17i	−0.0886479	+	0.153543i
$751$	−2.29380e18	−	3.97298e18i	−0.466548	−	0.808084i	0.532722	−	0.846290i	$-0.321169\pi$
$751$	−2.29380e18	−	3.97298e18i	−0.466548	−	0.808084i	−0.999270	+	0.0382058i	$0.987836\pi$
$752$	−3.98817e18	+	2.30257e18i	−0.804189	+	0.464299i
$753$	1.18563e18			0.237017
$754$	−4.08637e17	+	1.99600e16i	−0.0809886	+	0.00395592i
$755$	−3.61534e18			−0.710384
$756$	4.71743e17	−	2.72361e17i	0.0918997	−	0.0530583i
$757$	−2.32151e18	−	4.02097e18i	−0.448380	−	0.776617i	0.549901	−	0.835230i	$-0.314666\pi$
$757$	−2.32151e18	−	4.02097e18i	−0.448380	−	0.776617i	−0.998281	+	0.0586127i	$0.981332\pi$
$758$	−3.41812e17	+	5.92036e17i	−0.0654543	+	0.113370i
$759$			1.12631e19i			2.13839i
$760$	2.12245e17	+	1.22540e17i	0.0399530	+	0.0230669i
$761$	−3.43898e18	−	1.98549e18i	−0.641843	−	0.370568i	0.143481	−	0.989653i	$-0.454170\pi$
$761$	−3.43898e18	−	1.98549e18i	−0.641843	−	0.370568i	−0.785324	+	0.619085i	$0.787504\pi$
$762$		−	4.00241e17i		−	0.0740651i
$763$	7.97138e17	−	1.38068e18i	0.146259	−	0.253329i
$764$	3.87634e18	+	6.71402e18i	0.705205	+	1.22145i
$765$	8.56915e18	−	4.94740e18i	1.54575	−	0.892437i
$766$	−2.46425e17			−0.0440756
$767$	9.33223e17	−	4.55836e16i	0.165507	−	0.00808423i
$768$	−7.39421e18			−1.30030
$769$	−6.20823e18	+	3.58432e18i	−1.08255	+	0.625008i	−0.931582	−	0.363531i	$-0.881571\pi$
$769$	−6.20823e18	+	3.58432e18i	−1.08255	+	0.625008i	−0.150964	+	0.988539i	$0.548238\pi$
$770$	3.34606e17	+	5.79554e17i	0.0578554	+	0.100208i
$771$	2.17083e18	−	3.75998e18i	0.372196	−	0.644662i
$772$		−	3.96387e18i		−	0.673917i
$773$	−7.01876e18	−	4.05228e18i	−1.18330	−	0.683177i	−0.226522	−	0.974006i	$-0.572735\pi$
$773$	−7.01876e18	−	4.05228e18i	−1.18330	−	0.683177i	−0.956775	+	0.290830i	$0.906069\pi$
$774$	−6.38426e16	−	3.68595e16i	−0.0106732	−	0.00616217i
$775$			1.03111e19i			1.70940i
$776$	6.73212e17	−	1.16604e18i	0.110675	−	0.191695i
$777$	1.46494e18	+	2.53735e18i	0.238827	+	0.413660i
$778$	−1.36968e17	+	7.90786e16i	−0.0221438	+	0.0127847i
$779$	−1.64267e18			−0.263364
$780$	−8.08768e18	−	1.25513e19i	−1.28590	−	1.99561i
$781$	9.97491e18			1.57281
$782$	5.12612e17	−	2.95957e17i	0.0801577	−	0.0462791i
$783$	5.94494e17	+	1.02969e18i	0.0921926	+	0.159682i
$784$	−1.84938e18	+	3.20321e18i	−0.284427	+	0.492642i
$785$		−	2.11988e19i		−	3.23340i
$786$	−6.29263e17	−	3.63305e17i	−0.0951887	−	0.0549572i
$787$	5.53991e18	+	3.19847e18i	0.831126	+	0.479851i	0.854238	−	0.519882i	$-0.174024\pi$
$787$	5.53991e18	+	3.19847e18i	0.831126	+	0.479851i	−0.0231119	+	0.999733i	$0.507357\pi$
$788$			5.29892e18i			0.788437i
$789$	−2.37354e17	+	4.11109e17i	−0.0350264	+	0.0606675i
$790$	6.11062e17	+	1.05839e18i	0.0894353	+	0.154906i
$791$	−2.93972e17	+	1.69725e17i	−0.0426736	+	0.0246376i
$792$	1.24805e18			0.179687
$793$	−2.73746e17	−	5.60433e18i	−0.0390905	−	0.800292i
$794$	−3.26797e17			−0.0462855
$795$	1.14042e19	−	6.58424e18i	1.60206	−	0.924953i
$796$	1.90000e18	+	3.29090e18i	0.264740	+	0.458543i
$797$	1.68991e18	−	2.92701e18i	0.233553	−	0.404525i	−0.725298	−	0.688435i	$-0.758298\pi$
$797$	1.68991e18	−	2.92701e18i	0.233553	−	0.404525i	0.958851	+	0.283910i	$0.0916316\pi$
$798$			8.63624e16i			0.0118388i
$799$	6.99994e18	+	4.04142e18i	0.951788	+	0.549515i
$800$	−2.80241e18	−	1.61797e18i	−0.377960	−	0.218216i
$801$			1.05273e19i			1.40834i
$802$	−5.83874e16	+	1.01130e17i	−0.00774793	+	0.0134198i
$803$	5.98673e18	+	1.03693e19i	0.788022	+	1.36489i
$804$	−3.27719e18	+	1.89209e18i	−0.427895	+	0.247045i
$805$	9.60633e18			1.24418
$806$	4.21104e17	+	2.16451e17i	0.0541017	+	0.0278088i
$807$	−1.85157e19			−2.35973
$808$	−2.81928e17	+	1.62771e17i	−0.0356421	+	0.0205780i
$809$	−1.12327e17	−	1.94555e17i	−0.0140870	−	0.0243993i	0.858896	−	0.512150i	$-0.171151\pi$
$809$	−1.12327e17	−	1.94555e17i	−0.0140870	−	0.0243993i	−0.872983	+	0.487751i	$0.837818\pi$
$810$	5.58259e17	−	9.66934e17i	0.0694518	−	0.120294i
$811$		−	2.69842e18i		−	0.333022i	−0.986040	−	0.166511i	$-0.946750\pi$
$811$		−	2.69842e18i		−	0.333022i	0.986040	−	0.166511i	$-0.0532502\pi$
$812$	5.13438e18	+	2.96434e18i	0.628599	+	0.362922i
$813$	−1.30854e17	−	7.55488e16i	−0.0158928	−	0.00917570i
$814$		−	4.55354e17i		−	0.0548644i
$815$	−1.06086e19	+	1.83746e19i	−1.26804	+	2.19631i
$816$	6.63102e18	+	1.14853e19i	0.786311	+	1.36193i
$817$	2.62727e17	−	1.51685e17i	0.0309073	−	0.0178443i
$818$	1.02930e18			0.120129
$819$	2.25809e18	−	4.39309e18i	0.261454	−	0.508656i
$820$	2.15672e19			2.47744
$821$	2.75775e18	−	1.59219e18i	0.314286	−	0.181453i	−0.334557	−	0.942375i	$-0.608587\pi$
$821$	2.75775e18	−	1.59219e18i	0.314286	−	0.181453i	0.648843	+	0.760923i	$0.275253\pi$
$822$	−2.85903e17	−	4.95198e17i	−0.0323260	−	0.0559902i
$823$	−7.93033e18	+	1.37357e19i	−0.889595	+	1.54082i	−0.0492400	+	0.998787i	$0.515680\pi$
$823$	−7.93033e18	+	1.37357e19i	−0.889595	+	1.54082i	−0.840355	+	0.542037i	$0.817653\pi$
$824$			4.25809e15i			0.000473902i
$825$	−3.09258e19	−	1.78550e19i	−3.41484	−	1.97156i
$826$	6.14472e16	+	3.54766e16i	0.00673181	+	0.00388661i
$827$		−	1.18926e19i		−	1.29268i	−0.763051	−	0.646338i	$-0.776300\pi$
$827$		−	1.18926e19i		−	1.29268i	0.763051	−	0.646338i	$-0.223700\pi$
$828$	4.46712e18	−	7.73729e18i	0.481760	−	0.834433i
$829$	−8.01205e17	−	1.38773e18i	−0.0857312	−	0.148491i	0.819971	−	0.572405i	$-0.193989\pi$
$829$	−8.01205e17	−	1.38773e18i	−0.0857312	−	0.148491i	−0.905703	+	0.423914i	$0.860656\pi$
$830$	4.53566e17	−	2.61866e17i	0.0481541	−	0.0278018i
$831$	2.30349e19			2.42650
$832$	7.79204e18	−	5.02093e18i	0.814422	−	0.524787i
$833$	6.49195e18			0.673260
$834$	−7.67005e15	+	4.42831e15i	−0.000789258	+	0.000455678i
$835$	−1.18595e19	−	2.05412e19i	−1.21088	−	2.09731i
$836$	−1.28064e18	+	2.21814e18i	−0.129744	+	0.224723i
$837$		−	1.37601e18i		−	0.138326i
$838$	7.21515e17	+	4.16567e17i	0.0719713	+	0.0415527i
$839$	−7.47292e16	−	4.31449e16i	−0.00739669	−	0.00427048i	0.496297	−	0.868153i	$-0.334693\pi$
$839$	−7.47292e16	−	4.31449e16i	−0.00739669	−	0.00427048i	−0.503694	+	0.863882i	$0.668026\pi$
$840$		−	2.27371e18i		−	0.223316i
$841$	−1.34006e18	+	2.32106e18i	−0.130603	+	0.226210i
$842$	1.88564e17	+	3.26603e17i	0.0182360	+	0.0315858i
$843$	6.39452e18	−	3.69188e18i	0.613662	−	0.354298i
$844$	−1.63381e19			−1.55588
$845$	1.67709e19	+	7.61017e18i	1.58485	+	0.719161i
$846$	−6.39337e17			−0.0599546
$847$	−6.09904e18	+	3.52128e18i	−0.567570	+	0.327687i
$848$	4.13146e18	+	7.15589e18i	0.381531	+	0.660832i
$849$	1.29147e18	−	2.23689e18i	0.118354	−	0.204995i
$850$			1.87668e18i			0.170674i
$851$	−5.66075e18	−	3.26823e18i	−0.510895	−	0.294965i
$852$	−1.46368e19	−	8.45055e18i	−1.31096	−	0.756881i
$853$			1.54314e19i			1.37163i	0.727775	+	0.685816i	$0.240554\pi$
$853$			1.54314e19i			1.37163i	−0.727775	+	0.685816i	$0.759446\pi$
$854$	2.13049e17	−	3.69012e17i	0.0187933	−	0.0325510i
$855$	−1.61041e18	−	2.78932e18i	−0.140980	−	0.244184i
$856$	−1.29069e18	+	7.45183e17i	−0.112136	+	0.0647416i
$857$	−7.95277e17			−0.0685714			−0.0342857	−	0.999412i	$-0.510916\pi$
$857$	−7.95277e17			−0.0685714			−0.0342857	+	0.999412i	$0.510916\pi$
$858$	−1.37840e18	+	8.88193e17i	−0.117952	+	0.0760046i
$859$	−2.25924e19			−1.91870			−0.959350	−	0.282220i	$-0.908929\pi$
$859$	−2.25924e19			−1.91870			−0.959350	+	0.282220i	$0.908929\pi$
$860$	−3.44944e18	+	1.99154e18i	−0.290743	+	0.167860i
$861$	7.61988e18	+	1.31980e19i	0.637423	+	1.10405i
$862$	5.49458e17	−	9.51689e17i	0.0456181	−	0.0790128i
$863$			6.44533e18i			0.531098i	0.964097	+	0.265549i	$0.0855532\pi$
$863$			6.44533e18i			0.531098i	−0.964097	+	0.265549i	$0.914447\pi$
$864$	3.73979e17	+	2.15917e17i	0.0305850	+	0.0176582i
$865$	1.77936e19	+	1.02731e19i	1.44431	+	0.833871i
$866$			1.30520e18i			0.105151i
$867$	3.06420e18	−	5.30735e18i	0.245015	−	0.424379i
$868$	−3.43060e18	−	5.94198e18i	−0.272265	−	0.471577i
$869$	−2.21801e19	+	1.28057e19i	−1.74717	+	1.00873i
$870$	2.47498e18			0.193507
$871$	2.13377e18	−	4.15123e18i	0.165588	−	0.322150i
$872$	8.41852e17			0.0648453
$873$	−1.53240e19	+	8.84731e18i	−1.17160	+	0.676424i
$874$	−9.63360e16	−	1.66859e17i	−0.00731079	−	0.0126627i
$875$	−7.72295e18	+	1.33765e19i	−0.581742	+	1.00761i
$876$		−	2.02874e19i		−	1.51687i
$877$	−1.60906e19	−	9.28988e18i	−1.19419	−	0.689466i	−0.234936	−	0.972011i	$-0.575488\pi$
$877$	−1.60906e19	−	9.28988e18i	−1.19419	−	0.689466i	−0.959254	+	0.282545i	$0.908821\pi$
$878$	−1.23920e18	−	7.15454e17i	−0.0912910	−	0.0527069i
$879$		−	9.25051e18i		−	0.676453i
$880$	1.67255e19	−	2.89694e19i	1.21406	−	2.10282i
$881$	7.56702e18	+	1.31065e19i	0.545232	+	0.944370i	0.998592	+	0.0530424i	$0.0168918\pi$
$881$	7.56702e18	+	1.31065e19i	0.545232	+	0.944370i	−0.453360	+	0.891327i	$0.649775\pi$
$882$	−4.44705e17	+	2.56751e17i	−0.0318073	+	0.0183639i
$883$	−7.28807e18			−0.517450			−0.258725	−	0.965951i	$-0.583302\pi$
$883$	−7.28807e18			−0.517450			−0.258725	+	0.965951i	$0.583302\pi$
$884$	−1.46255e19	−	7.51762e18i	−1.03079	−	0.529835i
$885$	−5.65223e18			−0.395447
$886$	−9.26141e17	+	5.34708e17i	−0.0643218	+	0.0371362i
$887$	3.96105e18	+	6.86075e18i	0.273091	+	0.473007i	0.969652	−	0.244490i	$-0.0786207\pi$
$887$	3.96105e18	+	6.86075e18i	0.273091	+	0.473007i	−0.696561	+	0.717498i	$0.745287\pi$
$888$	−7.73556e17	+	1.33984e18i	−0.0529429	+	0.0916997i
$889$		−	7.15382e18i		−	0.486045i
$890$	−2.58139e18	−	1.49037e18i	−0.174108	−	0.100521i
$891$	2.02635e19	+	1.16991e19i	1.35678	+	0.783336i
$892$		−	2.92682e18i		−	0.194547i
$893$	1.31551e18	−	2.27853e18i	0.0868079	−	0.150356i
$894$	−8.93829e17	−	1.54816e18i	−0.0585546	−	0.101419i
$895$	1.98482e19	−	1.14594e19i	1.29084	−	0.745267i
$896$	2.86848e18			0.185203
$897$	1.14838e18	+	2.35104e19i	0.0736094	+	1.50699i
$898$	8.13958e16			0.00517971
$899$	1.29698e19	−	7.48812e18i	0.819399	−	0.473080i
$900$	1.41632e19	+	2.45314e19i	0.888351	+	1.53867i
$901$	7.25143e18	−	1.25598e19i	0.451557	−	0.782119i
$902$		−	2.36852e18i		−	0.146432i
$903$	−2.43743e18	−	1.40725e18i	−0.149611	−	0.0863778i
$904$	−1.55231e17	−	8.96226e16i	−0.00945983	−	0.00546164i
$905$		−	1.68156e19i		−	1.01741i
$906$	3.36363e17	−	5.82598e17i	0.0202058	−	0.0349974i
$907$	−3.46377e16	−	5.99942e16i	−0.00206586	−	0.00357818i	0.864991	−	0.501788i	$-0.167324\pi$
$907$	−3.46377e16	−	5.99942e16i	−0.00206586	−	0.00357818i	−0.867056	+	0.498210i	$0.833991\pi$
$908$	−4.48663e18	+	2.59036e18i	−0.265682	+	0.153392i
$909$	4.27825e18			0.251537
$910$	7.57542e17	+	1.17564e18i	0.0442219	+	0.0686285i
$911$	−2.17182e19			−1.25879			−0.629397	−	0.777084i	$-0.716698\pi$
$911$	−2.17182e19			−1.25879			−0.629397	+	0.777084i	$0.716698\pi$
$912$	3.73853e18	−	2.15844e18i	0.215147	−	0.124215i
$913$	5.48779e18	+	9.50512e18i	0.313572	+	0.543122i
$914$	−1.04085e18	+	1.80280e18i	−0.0590522	+	0.102281i
$915$			3.39436e19i			1.91215i
$916$	1.75897e18	+	1.01554e18i	0.0983869	+	0.0568037i
$917$	−1.12473e19	−	6.49364e18i	−0.624666	−	0.360651i
$918$		−	2.50442e17i		−	0.0138112i
$919$	−1.11528e18	+	1.93173e18i	−0.0610710	+	0.105778i	−0.894944	−	0.446178i	$-0.852785\pi$
$919$	−1.11528e18	+	1.93173e18i	−0.0610710	+	0.105778i	0.833873	+	0.551956i	$0.186118\pi$
$920$	2.53629e18	+	4.39299e18i	0.137905	+	0.238858i
$921$	3.49573e19	−	2.01826e19i	1.88734	−	1.08966i
$922$	1.37060e18			0.0734784
$923$	2.08215e19	−	1.01703e18i	1.10841	−	0.0541407i
$924$	2.37622e19			1.25608
$925$	1.79476e19	−	1.03621e19i	0.942075	−	0.543907i
$926$	−3.17455e16	−	5.49849e16i	−0.00165467	−	0.00286597i
$927$	2.79798e16	−	4.84625e16i	0.00144819	−	0.00250834i
$928$			4.70001e18i			0.241567i
$929$	1.77616e19	+	1.02546e19i	0.906523	+	0.523381i	0.879311	−	0.476248i	$-0.158004\pi$
$929$	1.77616e19	+	1.02546e19i	0.906523	+	0.523381i	0.0272121	+	0.999630i	$0.491337\pi$
$930$	−2.48054e18	−	1.43214e18i	−0.125721	−	0.0725848i
$931$		−	2.11317e18i		−	0.106356i
$932$	−7.91314e18	+	1.37060e19i	−0.395499	+	0.685024i
$933$	−2.40431e19	−	4.16438e19i	−1.19333	−	2.06690i
$934$	−1.89381e18	+	1.09339e18i	−0.0933432	+	0.0538917i
$935$	−5.87123e19			−2.87378
$936$	2.60515e18	−	1.27250e17i	0.126631	−	0.00618534i
$937$	−1.64549e19			−0.794305			−0.397153	−	0.917753i	$-0.630002\pi$
$937$	−1.64549e19			−0.794305			−0.397153	+	0.917753i	$0.630002\pi$
$938$	3.06962e17	−	1.77225e17i	0.0147152	−	0.00849583i
$939$	−1.06607e19	−	1.84648e19i	−0.507526	−	0.879060i
$940$	−1.72718e19	+	2.99157e19i	−0.816596	+	1.41439i
$941$			4.57647e18i			0.214881i	0.994212	+	0.107441i	$0.0342655\pi$
$941$			4.57647e18i			0.214881i	−0.994212	+	0.107441i	$0.965734\pi$
$942$	3.41611e18	+	1.97229e18i	0.159295	+	0.0919688i
$943$	−2.94444e19	−	1.69997e19i	−1.36357	−	0.787255i
$944$		−	3.54664e18i		−	0.163117i
$945$	2.03225e18	−	3.51995e18i	0.0928260	−	0.160779i
$946$	2.18712e17	+	3.78820e17i	0.00992155	+	0.0171846i
$947$	7.71316e18	−	4.45320e18i	0.347502	−	0.200630i	−0.316082	−	0.948732i	$-0.602368\pi$
$947$	7.71316e18	−	4.45320e18i	0.347502	−	0.200630i	0.663585	+	0.748101i	$0.269034\pi$
$948$	4.33949e19			1.94171
$949$	1.35539e19	+	2.10344e19i	0.602327	+	0.934757i
$950$	6.10873e17			0.0269617
$951$	1.28429e19	−	7.41485e18i	0.562976	−	0.325034i
$952$	−1.25206e18	−	2.16862e18i	−0.0545109	−	0.0944157i
$953$	8.51044e17	−	1.47405e18i	0.0368000	−	0.0637395i	−0.847039	−	0.531531i	$-0.821617\pi$
$953$	8.51044e17	−	1.47405e18i	0.0368000	−	0.0637395i	0.883839	+	0.467792i	$0.154950\pi$
$954$			1.14715e18i			0.0492669i
$955$	5.00973e19	+	2.89237e19i	2.13694	+	1.23376i
$956$	−6.74501e18	−	3.89423e18i	−0.285763	−	0.164985i
$957$			5.18668e19i			2.18254i
$958$	8.06575e17	−	1.39703e18i	0.0337108	−	0.0583888i
$959$	−5.11017e18	−	8.85107e18i	−0.212136	−	0.367430i
$960$	−4.85634e19	+	2.80381e19i	−2.00238	+	1.15607i
$961$	7.08567e18			0.290187
$962$	−4.64275e16	−	9.50500e17i	−0.00188859	−	0.0386646i
$963$	1.95863e19			0.791374
$964$	8.97271e17	−	5.18039e17i	0.0360100	−	0.0207904i
$965$	−1.47884e19	−	2.56142e19i	−0.589512	−	1.02106i
$966$	−8.93752e17	+	1.54802e18i	−0.0353888	+	0.0612952i
$967$		−	2.87503e19i		−	1.13076i	−0.824831	−	0.565379i	$-0.808730\pi$
$967$		−	2.87503e19i		−	1.13076i	0.824831	−	0.565379i	$-0.191270\pi$
$968$	−3.22058e18	−	1.85940e18i	−0.125818	−	0.0726412i
$969$	−6.56177e18	−	3.78844e18i	−0.254634	−	0.147013i
$970$		−	5.01010e18i		−	0.193121i
$971$	−1.02386e19	+	1.77338e19i	−0.392028	+	0.679012i	−0.992717	−	0.120471i	$-0.961560\pi$
$971$	−1.02386e19	+	1.77338e19i	−0.392028	+	0.679012i	0.600689	+	0.799483i	$0.294893\pi$
$972$	−1.76754e19	−	3.06147e19i	−0.672261	−	1.16439i
$973$	−1.37093e17	+	7.91506e16i	−0.00517943	+	0.00299034i
$974$	−1.23259e18			−0.0462579
$975$	−6.63746e19	−	3.41172e19i	−2.47441	−	1.27187i
$976$	−2.12988e19			−0.788737
$977$	1.99494e19	−	1.15178e19i	0.733864	−	0.423696i	−0.0859702	−	0.996298i	$-0.527399\pi$
$977$	1.99494e19	−	1.15178e19i	0.733864	−	0.423696i	0.819834	+	0.572601i	$0.194066\pi$
$978$	−1.97400e18	−	3.41908e18i	−0.0721349	−	0.124941i
$979$	3.12328e19	−	5.40968e19i	1.13377	−	1.96374i
$980$			2.77447e19i			1.00048i
$981$	−9.58133e18	−	5.53179e18i	−0.343224	−	0.198160i
$982$	2.74824e18	+	1.58669e18i	0.0977979	+	0.0564636i
$983$			1.61799e19i			0.571977i	0.958233	+	0.285988i	$0.0923219\pi$
$983$			1.61799e19i			0.571977i	−0.958233	+	0.285988i	$0.907678\pi$
$984$	−4.02365e18	+	6.96917e18i	−0.141303	+	0.244744i
$985$	1.97692e19	+	3.42412e19i	0.689689	+	1.19458i
$986$	2.36059e18	−	1.36289e18i	0.0818126	−	0.0472345i
$987$	−2.44091e19			−0.840409
$988$	−2.44704e18	+	4.76068e18i	−0.0836990	+	0.162836i
$989$	6.27908e18			0.213363
$990$	4.02185e18	−	2.32202e18i	0.135768	−	0.0783856i
$991$	−9.59941e18	−	1.66267e19i	−0.321933	−	0.557605i	0.658954	−	0.752183i	$-0.270999\pi$
$991$	−9.59941e18	−	1.66267e19i	−0.321933	−	0.557605i	−0.980887	+	0.194579i	$0.937666\pi$
$992$	2.71964e18	−	4.71056e18i	0.0906121	−	0.156945i
$993$		−	1.44612e19i		−	0.478667i
$994$	1.37097e18	+	7.91531e17i	0.0450835	+	0.0260290i
$995$	2.45553e19	+	1.41770e19i	0.802224	+	0.463164i
$996$		−	1.85966e19i		−	0.603598i
$997$	−2.23097e19	+	3.86415e19i	−0.719407	+	1.24605i	0.241828	+	0.970319i	$0.422253\pi$
$997$	−2.23097e19	+	3.86415e19i	−0.719407	+	1.24605i	−0.961235	+	0.275731i	$0.911080\pi$
$998$	6.50229e17	+	1.12623e18i	0.0208314	+	0.0360810i
$999$	−2.39510e18	+	1.38281e18i	−0.0762337	+	0.0440136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.e.a.10.8	yes	30
13.2	odd	12		169.14.a.f.1.14		30
13.4	even	6	inner	13.14.e.a.4.8	✓	30
13.11	odd	12		169.14.a.f.1.17		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.e.a.4.8	✓	30	13.4	even	6	inner
13.14.e.a.10.8	yes	30	1.1	even	1	trivial
169.14.a.f.1.14		30	13.2	odd	12
169.14.a.f.1.17		30	13.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 13 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	13.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.65944 + 3.26748i) q^{2} +(865.700 + 1499.44i) q^{3} +(-4074.65 + 7057.50i) q^{4} +60806.7i q^{5} +(-9798.77 - 5657.32i) q^{6} +(-175141. - 101118. i) q^{7} -106790. i q^{8} +(-701713. + 1.21540e6i) q^{9} +(-198685. - 344132. i) q^{10} +(7.21178e6 - 4.16372e6i) q^{11} -1.41097e7 q^{12} +(1.46292e7 - 9.42660e6i) q^{13} +1.32160e6 q^{14} +(-9.11757e7 + 5.26403e7i) q^{15} +(-3.30306e7 - 5.72106e7i) q^{16} +(-5.79744e7 + 1.00415e8i) q^{17} -9.17134e6i q^{18} +(3.26857e7 + 1.88711e7i) q^{19} +(-4.29143e8 - 2.47766e8i) q^{20} -3.50151e8i q^{21} +(-2.72098e7 + 4.71287e7i) q^{22} +(3.90588e8 + 6.76518e8i) q^{23} +(1.60125e8 - 9.24479e7i) q^{24} -2.47675e9 q^{25} +(-5.19921e7 + 1.01150e8i) q^{26} +3.30520e8 q^{27} +(1.42728e9 - 8.24038e8i) q^{28} +(1.79866e9 + 3.11538e9i) q^{29} +(3.44003e8 - 5.95830e8i) q^{30} -4.16316e9i q^{31} +(1.13149e9 + 6.53265e8i) q^{32} +(1.24865e10 + 7.20907e9i) q^{33} -7.57722e8i q^{34} +(6.14863e9 - 1.06497e10i) q^{35} +(-5.71846e9 - 9.90467e9i) q^{36} +(-7.24645e9 + 4.18374e9i) q^{37} -2.46644e8 q^{38} +(2.67991e10 + 1.37750e10i) q^{39} +6.49353e9 q^{40} +(-3.76924e10 + 2.17617e10i) q^{41} +(1.14411e9 + 1.98166e9i) q^{42} +(4.01899e9 - 6.96110e9i) q^{43} +6.78628e10i q^{44} +(-7.39045e10 - 4.26688e10i) q^{45} +(-4.42102e9 - 2.55248e9i) q^{46} -6.97104e10i q^{47} +(5.71892e10 - 9.90545e10i) q^{48} +(-2.79949e10 - 4.84886e10i) q^{49} +(1.40170e10 - 8.09272e9i) q^{50} -2.00754e11 q^{51} +(6.91923e9 + 1.41656e11i) q^{52} -1.25080e11 q^{53} +(-1.87056e9 + 1.07997e9i) q^{54} +(2.53182e11 + 4.38524e11i) q^{55} +(-1.07983e10 + 1.87033e10i) q^{56} +6.53468e10i q^{57} +(-2.03589e10 - 1.17542e10i) q^{58} +(4.64945e10 + 2.68436e10i) q^{59} -8.57963e11i q^{60} +(1.61205e11 - 2.79216e11i) q^{61} +(1.36030e10 + 2.35612e10i) q^{62} +(2.45798e11 - 1.41911e11i) q^{63} +5.32635e11 q^{64} +(5.73200e11 + 8.89554e11i) q^{65} -9.42220e10 q^{66} +(2.32265e11 - 1.34098e11i) q^{67} +(-4.72451e11 - 8.18309e11i) q^{68} +(-6.76264e11 + 1.17132e12i) q^{69} +8.03622e10i q^{70} +(1.03736e12 + 5.98918e11i) q^{71} +(1.29793e11 + 7.49357e10i) q^{72} +1.43783e12i q^{73} +(2.73406e10 - 4.73553e10i) q^{74} +(-2.14412e12 - 3.71372e12i) q^{75} +(-2.66365e11 + 1.53786e11i) q^{76} -1.68410e12 q^{77} +(-1.96678e11 + 9.60680e9i) q^{78} -3.07554e12 q^{79} +(3.47879e12 - 2.00848e12i) q^{80} +(1.40489e12 + 2.43334e12i) q^{81} +(1.42212e11 - 2.46318e11i) q^{82} +1.31800e12i q^{83} +(2.47119e12 + 1.42674e12i) q^{84} +(-6.10588e12 - 3.52523e12i) q^{85} +5.25280e10i q^{86} +(-3.11421e12 + 5.39396e12i) q^{87} +(-4.44643e11 - 7.70144e11i) q^{88} +(6.49621e12 - 3.75059e12i) q^{89} +5.57678e11 q^{90} +(-3.51538e12 + 1.71710e11i) q^{91} -6.36603e12 q^{92} +(6.24239e12 - 3.60405e12i) q^{93} +(2.27777e11 + 3.94522e11i) q^{94} +(-1.14749e12 + 1.98751e12i) q^{95} +2.26213e12i q^{96} +(1.09190e13 + 6.30408e12i) q^{97} +(3.16871e11 + 1.82946e11i) q^{98} +1.16869e13i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 730 q^{3} + 65535 q^{4} - 382584 q^{6} + 438984 q^{7} - 9117071 q^{9} + 3893475 q^{10} - 5364528 q^{11} + 27694876 q^{12} - 1794135 q^{13} + 61125588 q^{14} - 113380170 q^{15} - 350182521 q^{16}+ \cdots + 86959564160763 q^{98}+O(q^{100}) \) 30 * q - 3 * q^2 - 730 * q^3 + 65535 * q^4 - 382584 * q^6 + 438984 * q^7 - 9117071 * q^9 + 3893475 * q^10 - 5364528 * q^11 + 27694876 * q^12 - 1794135 * q^13 + 61125588 * q^14 - 113380170 * q^15 - 350182521 * q^16 - 23524899 * q^17 + 92116746 * q^19 + 959687745 * q^20 - 128185362 * q^22 + 417086886 * q^23 - 4232784354 * q^24 - 11926991364 * q^25 + 5442553119 * q^26 + 5605403288 * q^27 + 22569369732 * q^28 - 8810189577 * q^29 - 9936679242 * q^30 + 9137241117 * q^32 + 12085621392 * q^33 + 1059240720 * q^35 + 55900963715 * q^36 - 72651649419 * q^37 - 45168847944 * q^38 - 41492436530 * q^39 + 137282090274 * q^40 - 3909896103 * q^41 - 34124964786 * q^42 + 138326640480 * q^43 - 259122942393 * q^45 - 288578831832 * q^46 + 630595691198 * q^48 + 114277635303 * q^49 - 553717814136 * q^50 - 178343342508 * q^51 - 1243882821894 * q^52 + 938994404670 * q^53 + 1180281528282 * q^54 - 140610123120 * q^55 + 932974200720 * q^56 - 768032047215 * q^58 - 1420851272556 * q^59 + 284498233437 * q^61 + 2574083847030 * q^62 - 3219361289664 * q^63 - 4989806279958 * q^64 - 931161533727 * q^65 + 12037245084948 * q^66 + 2624227676622 * q^67 - 3124046642277 * q^68 + 1206986427996 * q^69 - 1317657850698 * q^71 - 2571404508735 * q^72 + 1723434230073 * q^74 + 1909848151684 * q^75 - 5741418039246 * q^76 - 8153714196816 * q^77 - 13064083856250 * q^78 + 10732970056200 * q^79 + 11699811454875 * q^80 + 26873856445 * q^81 - 924448017327 * q^82 + 5758359493380 * q^84 - 14711656818213 * q^85 - 6442966126134 * q^87 - 11094606812688 * q^88 + 18293004024660 * q^89 + 53932182551466 * q^90 + 2271787574784 * q^91 - 48706576133844 * q^92 - 50634402753492 * q^93 + 3529466920146 * q^94 + 11308314514950 * q^95 - 4972913690148 * q^97 + 86959564160763 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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