LMFDB - Embedded newform 13.14.e.a.10.6

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			10.6
Character	$\chi$	$=$	13.10
Dual form			13.14.e.a.4.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-55.2505 + 31.8989i) q^{2} +(924.809 + 1601.82i) q^{3} +(-2060.92 + 3569.63i) q^{4} -57759.0i q^{5} +(-102192. - 59000.7i) q^{6} +(-148669. - 85833.9i) q^{7} -785596. i q^{8} +(-913381. + 1.58202e6i) q^{9} +(1.84245e6 + 3.19121e6i) q^{10} +(3.30476e6 - 1.90800e6i) q^{11} -7.62384e6 q^{12} +(-1.69104e7 - 4.11257e6i) q^{13} +1.09520e7 q^{14} +(9.25192e7 - 5.34160e7i) q^{15} +(8.17652e6 + 1.41621e7i) q^{16} +(6.56843e7 - 1.13769e8i) q^{17} -1.16543e8i q^{18} +(2.87039e7 + 1.65722e7i) q^{19} +(2.06178e8 + 1.19037e8i) q^{20} -3.17520e8i q^{21} +(-1.21726e8 + 2.10836e8i) q^{22} +(2.37925e8 + 4.12097e8i) q^{23} +(1.25838e9 - 7.26526e8i) q^{24} -2.11539e9 q^{25} +(1.06549e9 - 3.12202e8i) q^{26} -4.29922e8 q^{27} +(6.12790e8 - 3.53794e8i) q^{28} +(-2.91981e9 - 5.05726e9i) q^{29} +(-3.40782e9 + 5.90251e9i) q^{30} +1.32980e9i q^{31} +(4.66988e9 + 2.69616e9i) q^{32} +(6.11253e9 + 3.52907e9i) q^{33} +8.38102e9i q^{34} +(-4.95768e9 + 8.58695e9i) q^{35} +(-3.76482e9 - 6.52086e9i) q^{36} +(-1.02373e10 + 5.91052e9i) q^{37} -2.11454e9 q^{38} +(-9.05131e9 - 3.08907e10i) q^{39} -4.53752e10 q^{40} +(3.16158e10 - 1.82534e10i) q^{41} +(1.01285e10 + 1.75431e10i) q^{42} +(9.93451e9 - 1.72071e10i) q^{43} +1.57290e10i q^{44} +(9.13759e10 + 5.27559e10i) q^{45} +(-2.62909e10 - 1.51790e10i) q^{46} -3.84473e10i q^{47} +(-1.51234e10 + 2.61945e10i) q^{48} +(-3.37096e10 - 5.83867e10i) q^{49} +(1.16876e11 - 6.74787e10i) q^{50} +2.42982e11 q^{51} +(4.95314e10 - 5.18881e10i) q^{52} -2.53422e11 q^{53} +(2.37534e10 - 1.37140e10i) q^{54} +(-1.10204e11 - 1.90879e11i) q^{55} +(-6.74307e10 + 1.16793e11i) q^{56} +6.13045e10i q^{57} +(3.22642e11 + 1.86277e11i) q^{58} +(-5.56951e11 - 3.21556e11i) q^{59} +4.40345e11i q^{60} +(-1.78695e11 + 3.09508e11i) q^{61} +(-4.24191e10 - 7.34721e10i) q^{62} +(2.71582e11 - 1.56798e11i) q^{63} -4.77981e11 q^{64} +(-2.37538e11 + 9.76727e11i) q^{65} -4.50294e11 q^{66} +(9.13162e11 - 5.27214e11i) q^{67} +(2.70741e11 + 4.68937e11i) q^{68} +(-4.40069e11 + 7.62223e11i) q^{69} -6.32577e11i q^{70} +(-1.89033e11 - 1.09138e11i) q^{71} +(1.24283e12 + 7.17548e11i) q^{72} -1.49484e12i q^{73} +(3.77078e11 - 6.53118e11i) q^{74} +(-1.95633e12 - 3.38847e12i) q^{75} +(-1.18313e11 + 6.83082e10i) q^{76} -6.55085e11 q^{77} +(1.48547e12 + 1.41800e12i) q^{78} +3.07835e12 q^{79} +(8.17991e11 - 4.72267e11i) q^{80} +(1.05863e12 + 1.83360e12i) q^{81} +(-1.16453e12 + 2.01702e12i) q^{82} +4.85189e12i q^{83} +(1.13343e12 + 6.54384e11i) q^{84} +(-6.57115e12 - 3.79386e12i) q^{85} +1.26760e12i q^{86} +(5.40054e12 - 9.35400e12i) q^{87} +(-1.49892e12 - 2.59620e12i) q^{88} +(4.51726e12 - 2.60804e12i) q^{89} -6.73142e12 q^{90} +(2.16105e12 + 2.06290e12i) q^{91} -1.96138e12 q^{92} +(-2.13010e12 + 1.22981e12i) q^{93} +(1.22642e12 + 2.12423e12i) q^{94} +(9.57194e11 - 1.65791e12i) q^{95} +9.97372e12i q^{96} +(1.41866e11 + 8.19065e10i) q^{97} +(3.72494e12 + 2.15060e12i) q^{98} +6.97093e12i 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 $

$2$	−55.2505	+	31.8989i	−0.610437	+	0.352436i	−0.773137	−	0.634240i	$-0.781313\pi$
$2$	−55.2505	+	31.8989i	−0.610437	+	0.352436i	0.162699	+	0.986676i	$0.447980\pi$
$3$	924.809	+	1601.82i	0.732426	+	1.26860i	0.955843	+	0.293876i	$0.0949453\pi$
$3$	924.809	+	1601.82i	0.732426	+	1.26860i	−0.223417	+	0.974723i	$0.571721\pi$
$4$	−2060.92	+	3569.63i	−0.251578	+	0.435745i
$5$		−	57759.0i		−	1.65316i	−0.562821	−	0.826579i	$-0.690284\pi$
$5$		−	57759.0i		−	1.65316i	0.562821	−	0.826579i	$-0.309716\pi$
$6$	−102192.	−	59000.7i	−0.894200	−	0.516267i
$7$	−148669.	−	85833.9i	−0.477620	−	0.275754i	0.241804	−	0.970325i	$-0.422261\pi$
$7$	−148669.	−	85833.9i	−0.477620	−	0.275754i	−0.719424	+	0.694571i	$0.755594\pi$
$8$		−	785596.i		−	1.05953i
$9$	−913381.	+	1.58202e6i	−0.572896	+	0.992284i
$10$	1.84245e6	+	3.19121e6i	0.582632	+	1.00915i
$11$	3.30476e6	−	1.90800e6i	0.562454	−	0.324733i	−0.191676	−	0.981458i	$-0.561392\pi$
$11$	3.30476e6	−	1.90800e6i	0.562454	−	0.324733i	0.754130	+	0.656725i	$0.228059\pi$
$12$	−7.62384e6			−0.737048
$13$	−1.69104e7	−	4.11257e6i	−0.971678	−	0.236310i
$13$	−1.69104e7	−	4.11257e6i	−0.971678	−	0.236310i
$14$	1.09520e7			0.388742
$15$	9.25192e7	−	5.34160e7i	2.09719	−	1.21082i
$16$	8.17652e6	+	1.41621e7i	0.121840	+	0.211032i
$17$	6.56843e7	−	1.13769e8i	0.660000	−	1.14315i	−0.320616	−	0.947209i	$-0.603890\pi$
$17$	6.56843e7	−	1.13769e8i	0.660000	−	1.14315i	0.980615	−	0.195943i	$-0.0627769\pi$
$18$		−	1.16543e8i		−	0.807636i
$19$	2.87039e7	+	1.65722e7i	0.139973	+	0.0808132i	0.568351	−	0.822786i	$-0.307582\pi$
$19$	2.87039e7	+	1.65722e7i	0.139973	+	0.0808132i	−0.428378	+	0.903599i	$0.640915\pi$
$20$	2.06178e8	+	1.19037e8i	0.720356	+	0.415898i
$21$		−	3.17520e8i		−	0.807877i
$22$	−1.21726e8	+	2.10836e8i	−0.228895	+	0.396458i
$23$	2.37925e8	+	4.12097e8i	0.335126	+	0.580456i	0.983509	−	0.180859i	$-0.0578877\pi$
$23$	2.37925e8	+	4.12097e8i	0.335126	+	0.580456i	−0.648383	+	0.761314i	$0.724554\pi$
$24$	1.25838e9	−	7.26526e8i	1.34412	−	0.776029i
$25$	−2.11539e9			−1.73293
$26$	1.06549e9	−	3.12202e8i	0.676432	−	0.198202i
$27$	−4.29922e8			−0.213563
$28$	6.12790e8	−	3.53794e8i	0.240317	−	0.138747i
$29$	−2.91981e9	−	5.05726e9i	−0.911524	−	1.57881i	−0.811913	−	0.583779i	$-0.801574\pi$
$29$	−2.91981e9	−	5.05726e9i	−0.911524	−	1.57881i	−0.0996108	−	0.995026i	$-0.531760\pi$
$30$	−3.40782e9	+	5.90251e9i	−0.853470	+	1.47825i
$31$			1.32980e9i			0.269114i	0.990906	+	0.134557i	$0.0429611\pi$
$31$			1.32980e9i			0.269114i	−0.990906	+	0.134557i	$0.957039\pi$
$32$	4.66988e9	+	2.69616e9i	0.768831	+	0.443885i
$33$	6.11253e9	+	3.52907e9i	0.823912	+	0.475686i
$34$			8.38102e9i			0.930431i
$35$	−4.95768e9	+	8.58695e9i	−0.455865	+	0.789581i
$36$	−3.76482e9	−	6.52086e9i	−0.288256	−	0.499273i
$37$	−1.02373e10	+	5.91052e9i	−0.655956	+	0.378717i	−0.790734	−	0.612159i	$-0.790301\pi$
$37$	−1.02373e10	+	5.91052e9i	−0.655956	+	0.378717i	0.134778	+	0.990876i	$0.456968\pi$
$38$	−2.11454e9			−0.113926
$39$	−9.05131e9	−	3.08907e10i	−0.411900	−	1.40575i
$40$	−4.53752e10			−1.75157
$41$	3.16158e10	−	1.82534e10i	1.03946	−	0.600135i	0.119782	−	0.992800i	$-0.461780\pi$
$41$	3.16158e10	−	1.82534e10i	1.03946	−	0.600135i	0.919681	+	0.392666i	$0.128447\pi$
$42$	1.01285e10	+	1.75431e10i	0.284725	+	0.493158i
$43$	9.93451e9	−	1.72071e10i	0.239663	−	0.415109i	−0.720954	−	0.692983i	$-0.756296\pi$
$43$	9.93451e9	−	1.72071e10i	0.239663	−	0.415109i	0.960618	+	0.277874i	$0.0896296\pi$
$44$			1.57290e10i			0.326782i
$45$	9.13759e10	+	5.27559e10i	1.64040	+	0.947087i
$46$	−2.62909e10	−	1.51790e10i	−0.409147	−	0.236221i
$47$		−	3.84473e10i		−	0.520271i	−0.965572	−	0.260135i	$-0.916233\pi$
$47$		−	3.84473e10i		−	0.520271i	0.965572	−	0.260135i	$-0.0837672\pi$
$48$	−1.51234e10	+	2.61945e10i	−0.178477	+	0.309131i
$49$	−3.37096e10	−	5.83867e10i	−0.347920	−	0.602615i
$50$	1.16876e11	−	6.74787e10i	1.05784	−	0.610747i
$51$	2.42982e11			1.93360
$52$	4.95314e10	−	5.18881e10i	0.347423	−	0.363954i
$53$	−2.53422e11			−1.57055			−0.785273	−	0.619149i	$-0.787477\pi$
$53$	−2.53422e11			−1.57055			−0.785273	+	0.619149i	$0.787477\pi$
$54$	2.37534e10	−	1.37140e10i	0.130367	−	0.0752672i
$55$	−1.10204e11	−	1.90879e11i	−0.536835	−	0.929825i
$56$	−6.74307e10	+	1.16793e11i	−0.292170	+	0.506053i
$57$			6.13045e10i			0.236759i
$58$	3.22642e11	+	1.86277e11i	1.11286	+	0.642507i
$59$	−5.56951e11	−	3.21556e11i	−1.71901	−	0.992471i	−0.920744	−	0.390167i	$-0.872417\pi$
$59$	−5.56951e11	−	3.21556e11i	−1.71901	−	0.992471i	−0.798267	−	0.602304i	$-0.794249\pi$
$60$			4.40345e11i			1.21846i
$61$	−1.78695e11	+	3.09508e11i	−0.444086	+	0.769180i	−0.997988	−	0.0634019i	$-0.979805\pi$
$61$	−1.78695e11	+	3.09508e11i	−0.444086	+	0.769180i	0.553902	+	0.832582i	$0.313138\pi$
$62$	−4.24191e10	−	7.34721e10i	−0.0948453	−	0.164277i
$63$	2.71582e11	−	1.56798e11i	0.547252	−	0.315956i
$64$	−4.77981e11			−0.869443
$65$	−2.37538e11	+	9.76727e11i	−0.390657	+	1.60634i
$66$	−4.50294e11			−0.670595
$67$	9.13162e11	−	5.27214e11i	1.23328	−	0.712034i	0.265568	−	0.964092i	$-0.414441\pi$
$67$	9.13162e11	−	5.27214e11i	1.23328	−	0.712034i	0.967712	+	0.252058i	$0.0811073\pi$
$68$	2.70741e11	+	4.68937e11i	0.332082	+	0.575184i
$69$	−4.40069e11	+	7.62223e11i	−0.490910	+	0.850281i
$70$		−	6.32577e11i		−	0.642652i
$71$	−1.89033e11	−	1.09138e11i	−0.175129	−	0.101111i	0.409873	−	0.912143i	$-0.365573\pi$
$71$	−1.89033e11	−	1.09138e11i	−0.175129	−	0.101111i	−0.585002	+	0.811032i	$0.698906\pi$
$72$	1.24283e12	+	7.17548e11i	1.05136	+	0.607001i
$73$		−	1.49484e12i		−	1.15610i	−0.816001	−	0.578051i	$-0.803814\pi$
$73$		−	1.49484e12i		−	1.15610i	0.816001	−	0.578051i	$-0.196186\pi$
$74$	3.77078e11	−	6.53118e11i	0.266947	−	0.462365i
$75$	−1.95633e12	−	3.38847e12i	−1.26924	−	2.19839i
$76$	−1.18313e11	+	6.83082e10i	−0.0704280	+	0.0406616i
$77$	−6.55085e11			−0.358185
$78$	1.48547e12	+	1.41800e12i	0.746876	+	0.712953i
$79$	3.07835e12			1.42476			0.712381	−	0.701793i	$-0.247617\pi$
$79$	3.07835e12			1.42476			0.712381	+	0.701793i	$0.247617\pi$
$80$	8.17991e11	−	4.72267e11i	0.348870	−	0.201420i
$81$	1.05863e12	+	1.83360e12i	0.416477	+	0.721359i
$82$	−1.16453e12	+	2.01702e12i	−0.423018	+	0.732689i
$83$			4.85189e12i			1.62893i	0.580210	+	0.814467i	$0.302970\pi$
$83$			4.85189e12i			1.62893i	−0.580210	+	0.814467i	$0.697030\pi$
$84$	1.13343e12	+	6.54384e11i	0.352029	+	0.203244i
$85$	−6.57115e12	−	3.79386e12i	−1.88981	−	1.09108i
$86$			1.26760e12i			0.337864i
$87$	5.40054e12	−	9.35400e12i	1.33525	−	2.31272i
$88$	−1.49892e12	−	2.59620e12i	−0.344065	−	0.595938i
$89$	4.51726e12	−	2.60804e12i	0.963473	−	0.556262i	0.0662330	−	0.997804i	$-0.478902\pi$
$89$	4.51726e12	−	2.60804e12i	0.963473	−	0.556262i	0.897240	+	0.441543i	$0.145569\pi$
$90$	−6.73142e12			−1.33515
$91$	2.16105e12	+	2.06290e12i	0.398929	+	0.380810i
$92$	−1.96138e12			−0.337241
$93$	−2.13010e12	+	1.22981e12i	−0.341397	+	0.197106i
$94$	1.22642e12	+	2.12423e12i	0.183362	+	0.317593i
$95$	9.57194e11	−	1.65791e12i	0.133597	−	0.231397i
$96$			9.97372e12i			1.30045i
$97$	1.41866e11	+	8.19065e10i	0.0172927	+	0.00998395i	0.508621	−	0.860990i	$-0.330155\pi$
$97$	1.41866e11	+	8.19065e10i	0.0172927	+	0.00998395i	−0.491329	+	0.870974i	$0.663489\pi$
$98$	3.72494e12	+	2.15060e12i	0.424766	+	0.245239i
$99$			6.97093e12i			0.744152i
$100$	4.35967e12	−	7.55116e12i	0.435967	−	0.755116i
$101$	1.60422e12	+	2.77859e12i	0.150375	+	0.260457i	0.931365	−	0.364086i	$-0.118619\pi$
$101$	1.60422e12	+	2.77859e12i	0.150375	+	0.260457i	−0.780991	+	0.624543i	$0.785285\pi$
$102$	−1.34248e13	+	7.75084e12i	−1.18034	+	0.681471i
$103$	−5.82223e12			−0.480449			−0.240225	−	0.970717i	$-0.577221\pi$
$103$	−5.82223e12			−0.480449			−0.240225	+	0.970717i	$0.577221\pi$
$104$	−3.23082e12	+	1.32847e13i	−0.250378	+	1.02952i
$105$	−1.83396e13			−1.33555
$106$	1.40017e13	−	8.08387e12i	0.958720	−	0.553517i
$107$	−6.47401e12	−	1.12133e13i	−0.417041	−	0.722337i	0.578599	−	0.815612i	$-0.303600\pi$
$107$	−6.47401e12	−	1.12133e13i	−0.417041	−	0.722337i	−0.995640	+	0.0932754i	$0.970266\pi$
$108$	8.86038e11	−	1.53466e12i	0.0537276	−	0.0930590i
$109$			4.82941e12i			0.275818i	0.990445	+	0.137909i	$0.0440381\pi$
$109$			4.82941e12i			0.275818i	−0.990445	+	0.137909i	$0.955962\pi$
$110$	1.21777e13	+	7.03078e12i	0.655408	+	0.378400i
$111$	−1.89351e13	−	1.09322e13i	−0.960879	−	0.554764i
$112$		−	2.80729e12i		−	0.134391i
$113$	−5.38815e12	+	9.33255e12i	−0.243461	+	0.421687i	−0.961698	−	0.274112i	$-0.911616\pi$
$113$	−5.38815e12	+	9.33255e12i	−0.243461	+	0.421687i	0.718237	+	0.695799i	$0.244950\pi$
$114$	−1.95555e12	−	3.38710e12i	−0.0834423	−	0.144526i
$115$	2.38023e13	−	1.37423e13i	0.959585	−	0.554016i
$116$	2.40700e13			0.917276
$117$	2.19518e13	−	2.29963e13i	0.791156	−	0.828800i
$118$	4.10290e13			1.39913
$119$	−1.95304e13	+	1.12759e13i	−0.630458	+	0.363995i
$120$	−4.19634e13	−	7.26827e13i	−1.28290	−	2.22204i
$121$	−9.98042e12	+	1.72866e13i	−0.289097	+	0.500731i
$122$		−	2.28006e13i		−	0.626048i
$123$	5.84772e13	+	3.37618e13i	1.52266	+	0.879108i
$124$	−4.74689e12	−	2.74062e12i	−0.117265	−	0.0677030i
$125$			5.16764e13i			1.21165i
$126$	−1.00034e13	+	1.73263e13i	−0.222709	+	0.385743i
$127$	1.19035e12	+	2.06175e12i	0.0251740	+	0.0436026i	0.878338	−	0.478040i	$-0.158653\pi$
$127$	1.19035e12	+	2.06175e12i	0.0251740	+	0.0436026i	−0.853164	+	0.521643i	$0.825319\pi$
$128$	−1.18470e13	+	6.83985e12i	−0.238091	+	0.137462i
$129$	3.67501e13			0.702143
$130$	−1.80324e13	−	6.15418e13i	−0.327659	−	1.11825i
$131$	7.77983e13			1.34495			0.672476	−	0.740119i	$-0.265231\pi$
$131$	7.77983e13			1.34495			0.672476	+	0.740119i	$0.265231\pi$
$132$	−2.51949e13	+	1.45463e13i	−0.414556	+	0.239344i
$133$	−2.84492e12	−	4.92754e12i	−0.0445691	−	0.0771959i
$134$	−3.36351e13	+	5.82577e13i	−0.501893	+	0.869304i
$135$			2.48319e13i			0.353053i
$136$	−8.93761e13	−	5.16013e13i	−1.21121	−	0.699291i
$137$	−3.13217e13	−	1.80836e13i	−0.404727	−	0.233669i	0.283795	−	0.958885i	$-0.408407\pi$
$137$	−3.13217e13	−	1.80836e13i	−0.404727	−	0.233669i	−0.688521	+	0.725216i	$0.741740\pi$
$138$		−	5.61509e13i		−	0.692058i
$139$	−6.15152e13	+	1.06547e14i	−0.723413	+	1.25299i	0.236211	+	0.971702i	$0.424094\pi$
$139$	−6.15152e13	+	1.06547e14i	−0.723413	+	1.25299i	−0.959624	+	0.281286i	$0.909239\pi$
$140$	−2.04348e13	−	3.53941e13i	−0.229371	−	0.397282i
$141$	6.15854e13	−	3.55564e13i	0.660015	−	0.381060i
$142$	1.39255e13			0.142540
$143$	−6.37316e13	+	1.86740e13i	−0.623261	+	0.182622i
$144$	−2.98731e13			−0.279206
$145$	−2.92102e14	+	1.68645e14i	−2.61001	+	1.50689i
$146$	4.76837e13	+	8.25906e13i	0.407452	+	0.705727i
$147$	6.23498e13	−	1.07993e14i	0.509651	−	0.882741i
$148$		−	4.87245e13i		−	0.381107i
$149$	6.89434e13	+	3.98045e13i	0.516157	+	0.298003i	0.735361	−	0.677676i	$-0.237013\pi$
$149$	6.89434e13	+	3.98045e13i	0.516157	+	0.298003i	−0.219204	+	0.975679i	$0.570346\pi$
$150$	2.16177e14	+	1.24810e14i	1.54959	+	0.894654i
$151$		−	6.67560e13i		−	0.458289i	−0.973392	−	0.229145i	$-0.926407\pi$
$151$		−	6.67560e13i		−	0.458289i	0.973392	−	0.229145i	$-0.0735929\pi$
$152$	1.30191e13	−	2.25497e13i	0.0856242	−	0.148305i
$153$	1.19990e14	+	2.07828e14i	0.756222	+	1.30981i
$154$	3.61937e13	−	2.08965e13i	0.218650	−	0.126237i
$155$	7.68079e13			0.444887
$156$	1.28922e14	+	3.13536e13i	0.716173	+	0.174172i
$157$	6.13387e13			0.326879			0.163439	−	0.986553i	$-0.447741\pi$
$157$	6.13387e13			0.326879			0.163439	+	0.986553i	$0.447741\pi$
$158$	−1.70080e14	+	9.81960e13i	−0.869728	+	0.502138i
$159$	−2.34367e14	−	4.05935e14i	−1.15031	−	1.99239i
$160$	1.55727e14	−	2.69727e14i	0.733812	−	1.27100i
$161$		−	8.16880e13i		−	0.369649i
$162$	−1.16979e14	−	6.75381e13i	−0.508466	−	0.293563i
$163$	−9.58066e12	−	5.53139e12i	−0.0400107	−	0.0231002i	0.479861	−	0.877344i	$-0.340687\pi$
$163$	−9.58066e12	−	5.53139e12i	−0.0400107	−	0.0231002i	−0.519872	+	0.854244i	$0.674020\pi$
$164$			1.50476e14i			0.603922i
$165$	2.03836e14	−	3.53054e14i	0.786383	−	1.36206i
$166$	−1.54770e14	−	2.68069e14i	−0.574095	−	0.994361i
$167$	−2.52237e14	+	1.45629e14i	−0.899811	+	0.519506i	−0.877139	−	0.480237i	$-0.840551\pi$
$167$	−2.52237e14	+	1.45629e14i	−0.899811	+	0.519506i	−0.0226720	+	0.999743i	$0.507217\pi$
$168$	−2.49442e14			−0.855972
$169$	2.69049e14	+	1.39090e14i	0.888316	+	0.459234i
$170$	4.84079e14			1.53815
$171$	−5.24352e13	+	3.02735e13i	−0.160379	+	0.0925951i
$172$	4.09486e13	+	7.09250e13i	0.120588	+	0.208864i
$173$	−2.61132e13	+	4.52294e13i	−0.0740561	+	0.128269i	−0.900675	−	0.434493i	$-0.856928\pi$
$173$	−2.61132e13	+	4.52294e13i	−0.0740561	+	0.128269i	0.826619	+	0.562761i	$0.190261\pi$
$174$			6.89084e14i			1.88236i
$175$	3.14493e14	+	1.81572e14i	0.827682	+	0.477862i
$176$	5.40428e13	+	3.12016e13i	0.137058	+	0.0791307i
$177$		−	1.18951e15i		−	2.90765i
$178$	−1.66387e14	+	2.88191e14i	−0.392093	+	0.679125i
$179$	2.86666e14	+	4.96520e14i	0.651376	+	1.12822i	0.982789	+	0.184730i	$0.0591412\pi$
$179$	2.86666e14	+	4.96520e14i	0.651376	+	1.12822i	−0.331413	+	0.943486i	$0.607525\pi$
$180$	−3.76638e14	+	2.17452e14i	−0.825377	+	0.476532i
$181$	−3.11633e14			−0.658768			−0.329384	−	0.944196i	$-0.606841\pi$
$181$	−3.11633e14			−0.658768			−0.329384	+	0.944196i	$0.606841\pi$
$182$	−1.85203e14	−	4.50409e13i	−0.377732	−	0.0918636i
$183$	−6.61033e14			−1.30104
$184$	3.23742e14	−	1.86912e14i	0.615011	−	0.355077i
$185$	3.41385e14	+	5.91297e14i	0.626078	+	1.08440i
$186$	7.84592e13	−	1.35895e14i	0.138934	−	0.240641i
$187$		−	5.01303e14i		−	0.857294i
$188$	1.37242e14	+	7.92369e13i	0.226706	+	0.130889i
$189$	6.39160e13	+	3.69019e13i	0.102002	+	0.0588908i
$190$			1.22134e14i			0.188338i
$191$	−6.65509e13	+	1.15270e14i	−0.0991829	+	0.171790i	−0.911347	−	0.411640i	$-0.864956\pi$
$191$	−6.65509e13	+	1.15270e14i	−0.0991829	+	0.171790i	0.812164	+	0.583430i	$0.198290\pi$
$192$	−4.42041e14	−	7.65638e14i	−0.636803	−	1.10297i
$193$	1.79755e14	−	1.03782e14i	0.250357	−	0.144544i	−0.369571	−	0.929203i	$-0.620495\pi$
$193$	1.79755e14	−	1.03782e14i	0.250357	−	0.144544i	0.619928	+	0.784659i	$0.287162\pi$
$194$	−1.04509e13			−0.0140748
$195$	−1.78421e15	+	5.22794e14i	−2.32392	+	0.680935i
$196$	2.77892e14			0.350115
$197$	6.78921e14	−	3.91975e14i	0.827540	−	0.477780i	−0.0254697	−	0.999676i	$-0.508108\pi$
$197$	6.78921e14	−	3.91975e14i	0.827540	−	0.477780i	0.853010	+	0.521895i	$0.174775\pi$
$198$	−2.22365e14	−	3.85147e14i	−0.262266	−	0.454258i
$199$	4.12311e13	−	7.14143e13i	0.0470630	−	0.0815155i	−0.841534	−	0.540204i	$-0.818347\pi$
$199$	4.12311e13	−	7.14143e13i	0.0470630	−	0.0815155i	0.888597	+	0.458688i	$0.151681\pi$
$200$			1.66184e15i			1.83610i
$201$	1.68900e15	+	9.75145e14i	1.80657	+	1.04303i
$202$	−1.77268e14	−	1.02346e14i	−0.183589	−	0.105995i
$203$			1.00248e15i			1.00542i
$204$	−5.00767e14	+	8.67354e14i	−0.486452	+	0.842559i
$205$	−1.05430e15	−	1.82610e15i	−0.992117	−	1.71840i
$206$	3.21681e14	−	1.85723e14i	0.293284	−	0.169328i
$207$	−8.69263e14			−0.767969
$208$	−8.00254e13	−	2.73114e14i	−0.0685199	−	0.233847i
$209$	1.26479e14			0.104971
$210$	1.01327e15	−	5.85013e14i	0.815268	−	0.470695i
$211$	−7.00392e13	−	1.21311e14i	−0.0546393	−	0.0946380i	0.837412	−	0.546572i	$-0.184068\pi$
$211$	−7.00392e13	−	1.21311e14i	−0.0546393	−	0.0946380i	−0.892051	+	0.451934i	$0.850734\pi$
$212$	5.22283e14	−	9.04621e14i	0.395114	−	0.684358i
$213$		−	4.03728e14i		−	0.296224i
$214$	7.15384e14	+	4.13027e14i	0.509155	+	0.293961i
$215$	−9.93863e14	−	5.73807e14i	−0.686241	−	0.396201i
$216$			3.37745e14i			0.226277i
$217$	1.14142e14	−	1.97700e14i	0.0742091	−	0.128534i
$218$	−1.54053e14	−	2.66827e14i	−0.0972080	−	0.168369i
$219$	2.39446e15	−	1.38244e15i	1.46663	−	0.846759i
$220$	9.08490e14			0.540223
$221$	−1.57863e15	+	1.65374e15i	−0.911445	+	0.954812i
$222$	1.39490e15			0.782075
$223$	4.28339e13	−	2.47302e13i	0.0233242	−	0.0134662i	−0.488293	−	0.872680i	$-0.662380\pi$
$223$	4.28339e13	−	2.47302e13i	0.0233242	−	0.0134662i	0.511617	+	0.859214i	$0.329047\pi$
$224$	−4.62843e14	−	8.01668e14i	−0.244806	−	0.424016i
$225$	1.93216e15	−	3.34660e15i	0.992788	−	1.71956i
$226$		−	6.87504e14i		−	0.343218i
$227$	2.32860e15	+	1.34442e15i	1.12961	+	0.652179i	0.943836	−	0.330414i	$-0.107188\pi$
$227$	2.32860e15	+	1.34442e15i	1.12961	+	0.652179i	0.185771	+	0.982593i	$0.440522\pi$
$228$	−2.18834e14	−	1.26344e14i	−0.103167	−	0.0595632i
$229$		−	1.94880e15i		−	0.892969i	−0.894791	−	0.446485i	$-0.852676\pi$
$229$		−	1.94880e15i		−	0.892969i	0.894791	−	0.446485i	$-0.147324\pi$
$230$	−8.76726e14	+	1.51853e15i	−0.390511	+	0.676384i
$231$	−6.05828e14	−	1.04933e15i	−0.262344	−	0.454394i
$232$	−3.97296e15	+	2.29379e15i	−1.67279	+	0.965789i
$233$	−2.66531e15			−1.09128			−0.545638	−	0.838021i	$-0.683713\pi$
$233$	−2.66531e15			−1.09128			−0.545638	+	0.838021i	$0.683713\pi$
$234$	−4.79292e14	+	1.97079e15i	−0.190852	+	0.784762i
$235$	−2.22067e15			−0.860090
$236$	2.29567e15	−	1.32540e15i	0.864930	−	0.499367i
$237$	2.84689e15	+	4.93096e15i	1.04353	+	1.80745i
$238$	7.19376e14	−	1.24600e15i	0.256570	−	0.444392i
$239$			1.09559e14i			0.0380242i	0.999819	+	0.0190121i	$0.00605210\pi$
$239$			1.09559e14i			0.0380242i	−0.999819	+	0.0190121i	$0.993948\pi$
$240$	1.51297e15	+	8.73513e14i	0.511043	+	0.295051i
$241$	3.49770e15	+	2.01940e15i	1.14993	+	0.663913i	0.948870	−	0.315666i	$-0.102228\pi$
$241$	3.49770e15	+	2.01940e15i	1.14993	+	0.663913i	0.201061	+	0.979579i	$0.435561\pi$
$242$		−	1.27346e15i		−	0.407553i
$243$	−2.30077e15	+	3.98506e15i	−0.716858	+	1.24163i
$244$	−7.36552e14	−	1.27575e15i	−0.223444	−	0.387017i
$245$	−3.37236e15	+	1.94703e15i	−0.996217	+	0.575166i
$246$	−4.30785e15			−1.23932
$247$	−4.17241e14	−	3.98290e14i	−0.116911	−	0.111601i
$248$	1.04469e15			0.285135
$249$	−7.77183e15	+	4.48707e15i	−2.06646	+	1.19307i
$250$	−1.64842e15	−	2.85514e15i	−0.427029	−	0.739636i
$251$	5.43307e14	−	9.41036e14i	0.137141	−	0.237535i	−0.789273	−	0.614043i	$-0.789542\pi$
$251$	5.43307e14	−	9.41036e14i	0.137141	−	0.237535i	0.926413	+	0.376509i	$0.122875\pi$
$252$			1.29260e15i			0.317950i
$253$	1.57257e15	+	9.07921e14i	0.376986	+	0.217653i
$254$	−1.31535e14	−	7.59419e13i	−0.0307343	−	0.0177444i
$255$		−	1.40344e16i		−	3.19655i
$256$	2.39418e15	−	4.14684e15i	0.531614	−	0.920783i
$257$	3.47423e15	+	6.01754e15i	0.752130	+	1.30273i	0.946788	+	0.321857i	$0.104307\pi$
$257$	3.47423e15	+	6.01754e15i	0.752130	+	1.30273i	−0.194658	+	0.980871i	$0.562360\pi$
$258$	−2.03046e15	+	1.17229e15i	−0.428614	+	0.247460i
$259$	2.02929e15			0.417730
$260$	−2.99700e15	−	2.86088e15i	−0.601673	−	0.574346i
$261$	1.06676e16			2.08883
$262$	−4.29839e15	+	2.48168e15i	−0.821008	+	0.474009i
$263$	−4.00058e15	−	6.92921e15i	−0.745436	−	1.29113i	−0.949991	−	0.312278i	$-0.898908\pi$
$263$	−4.00058e15	−	6.92921e15i	−0.745436	−	1.29113i	0.204554	−	0.978855i	$-0.434425\pi$
$264$	2.77242e15	−	4.80198e15i	0.504004	−	0.872961i
$265$			1.46374e16i			2.59636i
$266$	3.14366e14	+	1.81499e14i	0.0544133	+	0.0314155i
$267$	8.35519e15	+	4.82387e15i	1.41135	+	0.814841i
$268$			4.34620e15i			0.716528i
$269$	2.96061e15	−	5.12792e15i	0.476421	−	0.825186i	−0.523214	−	0.852201i	$-0.675267\pi$
$269$	2.96061e15	−	5.12792e15i	0.476421	−	0.825186i	0.999635	+	0.0270156i	$0.00860039\pi$
$270$	−7.92108e14	−	1.37197e15i	−0.124429	−	0.215517i
$271$	5.51666e15	−	3.18504e15i	0.846010	−	0.488444i	−0.0132923	−	0.999912i	$-0.504231\pi$
$271$	5.51666e15	−	3.18504e15i	0.846010	−	0.488444i	0.859303	+	0.511467i	$0.170898\pi$
$272$	2.14828e15			0.321656
$273$	−1.30582e15	+	5.36939e15i	−0.190909	+	0.784996i
$274$	2.30739e15			0.329414
$275$	−6.99086e15	+	4.03617e15i	−0.974693	+	0.562740i
$276$	−1.81390e15	−	3.14177e15i	−0.247004	−	0.427824i
$277$	1.74705e14	−	3.02598e14i	0.0232374	−	0.0402484i	−0.854173	−	0.519989i	$-0.825936\pi$
$277$	1.74705e14	−	3.02598e14i	0.0232374	−	0.0402484i	0.877410	+	0.479741i	$0.159269\pi$
$278$		−	7.84906e15i		−	1.01983i
$279$	−2.10377e15	−	1.21461e15i	−0.267037	−	0.154174i
$280$	6.74587e15	+	3.89473e15i	0.836586	+	0.483003i
$281$		−	1.27899e16i		−	1.54981i	−0.632080	−	0.774903i	$-0.717799\pi$
$281$		−	1.27899e16i		−	1.54981i	0.632080	−	0.774903i	$-0.282201\pi$
$282$	−2.26842e15	+	3.92901e15i	−0.268598	+	0.465226i
$283$	−4.42784e15	−	7.66925e15i	−0.512366	−	0.887444i	−0.999897	−	0.0143385i	$-0.995436\pi$
$283$	−4.42784e15	−	7.66925e15i	−0.512366	−	0.887444i	0.487531	−	0.873106i	$-0.337898\pi$
$284$	7.79165e14	−	4.49851e14i	0.0881170	−	0.0508744i
$285$	3.54089e15			0.391400
$286$	2.92552e15	−	3.06471e15i	0.316099	−	0.331139i
$287$	−6.26704e15			−0.661958
$288$	−8.53076e15	+	4.92524e15i	−0.880920	+	0.508599i
$289$	−3.67657e15	−	6.36800e15i	−0.371199	−	0.642935i
$290$	1.07592e16	−	1.86355e16i	1.06217	−	1.83973i
$291$			3.02991e14i			0.0292500i
$292$	5.33602e15	+	3.08075e15i	0.503766	+	0.290849i
$293$	−3.30203e15	−	1.90643e15i	−0.304889	−	0.176028i	0.339748	−	0.940516i	$-0.389658\pi$
$293$	−3.30203e15	−	1.90643e15i	−0.304889	−	0.176028i	−0.644637	+	0.764489i	$0.722991\pi$
$294$			7.95556e15i			0.718477i
$295$	−1.85727e16	+	3.21689e16i	−1.64071	+	2.84180i
$296$	4.64328e15	+	8.04239e15i	0.401262	+	0.695007i
$297$	−1.42079e15	+	8.20293e14i	−0.120119	+	0.0693509i
$298$	−5.07887e15			−0.420109
$299$	−2.32862e15	−	7.94722e15i	−0.188467	−	0.643209i
$300$	1.61274e16			1.27725
$301$	−2.95390e15	+	1.70544e15i	−0.228936	+	0.132176i
$302$	2.12944e15	+	3.68830e15i	0.161518	+	0.279757i
$303$	−2.96719e15	+	5.13932e15i	−0.220277	+	0.381530i
$304$			5.42012e14i			0.0393850i
$305$	1.78769e16	+	1.03212e16i	1.27158	+	0.734145i
$306$	−1.32590e16	−	7.65506e15i	−0.923252	−	0.533040i
$307$			9.30984e15i			0.634662i	0.948315	+	0.317331i	$0.102787\pi$
$307$			9.30984e15i			0.634662i	−0.948315	+	0.317331i	$0.897213\pi$
$308$	1.35008e15	−	2.33841e15i	0.0901114	−	0.156078i
$309$	−5.38445e15	−	9.32614e15i	−0.351893	−	0.609497i
$310$	−4.24367e15	+	2.45009e15i	−0.271576	+	0.156794i
$311$	2.93757e15			0.184097			0.0920483	−	0.995755i	$-0.470659\pi$
$311$	2.93757e15			0.184097			0.0920483	+	0.995755i	$0.470659\pi$
$312$	−2.42676e16	+	7.11067e15i	−1.48944	+	0.436421i
$313$	1.42368e16			0.855804			0.427902	−	0.903825i	$-0.359253\pi$
$313$	1.42368e16			0.855804			0.427902	+	0.903825i	$0.359253\pi$
$314$	−3.38899e15	+	1.95664e15i	−0.199539	+	0.115204i
$315$	−9.05649e15	−	1.56863e16i	−0.522326	−	0.904695i
$316$	−6.34426e15	+	1.09886e16i	−0.358438	+	0.620834i
$317$		−	2.01984e16i		−	1.11798i	−0.829176	−	0.558988i	$-0.811190\pi$
$317$		−	2.01984e16i		−	1.11798i	0.829176	−	0.558988i	$-0.188810\pi$
$318$	2.58977e16	+	1.49521e16i	1.40438	+	0.810821i
$319$	−1.92985e16	−	1.11420e16i	−1.02538	−	0.592003i
$320$			2.76077e16i			1.43733i
$321$	1.19744e16	−	2.07404e16i	0.610904	−	1.05812i
$322$	2.60575e15	+	4.51330e15i	0.130278	+	0.225648i
$323$	3.77080e15	−	2.17707e15i	0.184764	−	0.106673i
$324$	−8.72701e15			−0.419105
$325$	3.57722e16	+	8.69970e15i	1.68385	+	0.409508i
$326$	7.05781e14			0.0325653
$327$	−7.73582e15	+	4.46628e15i	−0.349902	+	0.202016i
$328$	−1.43398e16	−	2.48372e16i	−0.635862	−	1.10135i
$329$	−3.30008e15	+	5.71590e15i	−0.143467	+	0.248492i
$330$			2.60085e16i			1.10860i
$331$	1.52372e16	+	8.79720e15i	0.636829	+	0.367674i	0.783392	−	0.621528i	$-0.213488\pi$
$331$	1.52372e16	+	8.79720e15i	0.636829	+	0.367674i	−0.146563	+	0.989201i	$0.546821\pi$
$332$	−1.73194e16	−	9.99938e15i	−0.709800	−	0.409803i
$333$		−	2.15942e16i		−	0.867860i
$334$	9.29079e15	−	1.60921e16i	0.366185	−	0.634251i
$335$	−3.04513e16	−	5.27433e16i	−1.17711	−	2.03881i
$336$	4.49676e15	−	2.59621e15i	0.170488	−	0.0984314i
$337$	1.72716e16			0.642301			0.321151	−	0.947028i	$-0.395930\pi$
$337$	1.72716e16			0.642301			0.321151	+	0.947028i	$0.395930\pi$
$338$	−1.93019e16	+	8.97536e14i	−0.704111	+	0.0327411i
$339$	−1.99320e16			−0.713270
$340$	2.70853e16	−	1.56377e16i	0.950869	−	0.548985i
$341$	2.53726e15	+	4.39467e15i	0.0873900	+	0.151364i
$342$	1.93138e15	−	3.34525e15i	0.0652677	−	0.113047i
$343$			2.82064e16i			0.935268i
$344$	−1.35178e16	−	7.80451e15i	−0.439821	−	0.253931i
$345$	4.40252e16	+	2.54179e16i	1.40565	+	0.811552i
$346$		−	3.33193e15i		−	0.104400i
$347$	−7.85519e15	+	1.36056e16i	−0.241555	+	0.418385i	−0.961157	−	0.276001i	$-0.910991\pi$
$347$	−7.85519e15	+	1.36056e16i	−0.241555	+	0.418385i	0.719603	+	0.694386i	$0.244324\pi$
$348$	2.22602e16	+	3.85558e16i	0.671837	+	1.16366i
$349$	2.07448e16	−	1.19770e16i	0.614532	−	0.354800i	−0.160205	−	0.987084i	$-0.551215\pi$
$349$	2.07448e16	−	1.19770e16i	0.614532	−	0.354800i	0.774737	+	0.632283i	$0.217882\pi$
$350$	−2.31678e16			−0.673663
$351$	7.27016e15	+	1.76809e15i	0.207514	+	0.0504669i
$352$	2.05771e16			0.576576
$353$	4.87259e16	−	2.81319e16i	1.34037	−	0.773862i	0.353507	−	0.935432i	$-0.384989\pi$
$353$	4.87259e16	−	2.81319e16i	1.34037	−	0.773862i	0.986861	+	0.161570i	$0.0516558\pi$
$354$	3.79440e16	+	6.57209e16i	1.02476	+	1.77494i
$355$	−6.30370e15	+	1.09183e16i	−0.167152	+	0.289516i
$356$			2.14999e16i			0.559772i
$357$	−3.61238e16	−	2.08561e16i	−0.923527	−	0.533199i
$358$	−3.16769e16	−	1.82886e16i	−0.795248	−	0.459137i
$359$		−	1.74373e16i		−	0.429898i	−0.976625	−	0.214949i	$-0.931042\pi$
$359$		−	1.74373e16i		−	0.429898i	0.976625	−	0.214949i	$-0.0689585\pi$
$360$	4.14448e16	−	7.17845e16i	1.00347	−	1.73806i
$361$	−2.04772e16	−	3.54676e16i	−0.486938	−	0.843402i
$362$	1.72179e16	−	9.94073e15i	0.402136	−	0.232174i
$363$	−3.69199e16			−0.846969
$364$	−1.18175e16	+	3.46267e15i	−0.266298	+	0.0780282i
$365$	−8.63404e16			−1.91122
$366$	3.65224e16	−	2.10862e16i	0.794204	−	0.458534i
$367$	−1.72754e16	−	2.99219e16i	−0.369062	−	0.639234i	0.620357	−	0.784319i	$-0.286988\pi$
$367$	−1.72754e16	−	2.99219e16i	−0.369062	−	0.639234i	−0.989419	+	0.145086i	$0.953654\pi$
$368$	−3.89079e15	+	6.73904e15i	−0.0816633	+	0.141445i
$369$			6.66892e16i			1.37526i
$370$	−3.77234e16	−	2.17796e16i	−0.764363	−	0.441305i
$371$	3.76759e16	+	2.17522e16i	0.750124	+	0.433084i
$372$		−	1.01382e16i		−	0.198350i
$373$	1.95038e14	−	3.37816e14i	0.00374983	−	0.00649490i	−0.864144	−	0.503244i	$-0.832140\pi$
$373$	1.95038e14	−	3.37816e14i	0.00374983	−	0.00649490i	0.867894	+	0.496749i	$0.165473\pi$
$374$	1.59910e16	+	2.76972e16i	0.302141	+	0.523324i
$375$	−8.27760e16	+	4.77908e16i	−1.53710	+	0.887444i
$376$	−3.02040e16			−0.551244
$377$	2.85769e16	+	9.75283e16i	0.512620	+	1.74949i
$378$	−4.70852e15			−0.0830209
$379$	−6.36727e16	+	3.67614e16i	−1.10357	+	0.637144i	−0.937155	−	0.348913i	$-0.886551\pi$
$379$	−6.36727e16	+	3.67614e16i	−1.10357	+	0.637144i	−0.166410	+	0.986057i	$0.553218\pi$
$380$	3.94541e15	+	6.83365e15i	0.0672200	+	0.116429i
$381$	−2.20170e15	+	3.81346e15i	−0.0368762	+	0.0638714i
$382$		−	8.49159e15i		−	0.139823i
$383$	−1.38529e16	−	7.99797e15i	−0.224258	−	0.129476i	0.383662	−	0.923474i	$-0.374663\pi$
$383$	−1.38529e16	−	7.99797e15i	−0.224258	−	0.129476i	−0.607920	+	0.793998i	$0.707996\pi$
$384$	−2.19124e16	−	1.26511e16i	−0.348768	−	0.201361i
$385$			3.78370e16i			0.592137i
$386$	−6.62105e15	+	1.14680e16i	−0.101885	+	0.176470i
$387$	1.81480e16	+	3.14332e16i	0.274604	+	0.475628i
$388$	−5.84751e14	+	3.37606e14i	−0.00870092	+	0.00502348i
$389$	9.24178e16			1.35233			0.676166	−	0.736749i	$-0.263640\pi$
$389$	9.24178e16			1.35233			0.676166	+	0.736749i	$0.263640\pi$
$390$	8.19021e16	−	8.57990e16i	1.17862	−	1.23470i
$391$	6.25116e16			0.884733
$392$	−4.58684e16	+	2.64821e16i	−0.638490	+	0.368632i
$393$	7.19486e16	+	1.24619e17i	0.985078	+	1.70620i
$394$	−2.50071e16	+	4.33136e16i	−0.336774	+	0.583310i
$395$		−	1.77802e17i		−	2.35536i
$396$	−2.48836e16	−	1.43666e16i	−0.324261	−	0.187212i
$397$	−7.71196e16	−	4.45250e16i	−0.988614	−	0.570776i	−0.0837541	−	0.996486i	$-0.526691\pi$
$397$	−7.71196e16	−	4.45250e16i	−0.988614	−	0.570776i	−0.904860	+	0.425710i	$0.860024\pi$
$398$			5.26090e15i			0.0663468i
$399$	5.26201e15	−	9.11406e15i	0.0652871	−	0.113081i
$400$	−1.72966e16	−	2.99585e16i	−0.211140	−	0.365704i
$401$	3.67394e16	−	2.12115e16i	0.441259	−	0.254761i	−0.262873	−	0.964831i	$-0.584670\pi$
$401$	3.67394e16	−	2.12115e16i	0.441259	−	0.254761i	0.704131	+	0.710070i	$0.251337\pi$
$402$	−1.24424e17			−1.47040
$403$	5.46890e15	−	2.24875e16i	0.0635941	−	0.261492i
$404$	−1.32247e16			−0.151324
$405$	1.05907e17	−	6.11452e16i	1.19252	−	0.688502i
$406$	−3.19778e16	−	5.53872e16i	−0.354348	−	0.613748i
$407$	−2.25546e16	+	3.90656e16i	−0.245963	+	0.426021i
$408$		−	1.90885e17i		−	2.04872i
$409$	1.68226e16	+	9.71251e15i	0.177701	+	0.102596i	0.586212	−	0.810158i	$-0.300618\pi$
$409$	1.68226e16	+	9.71251e15i	0.177701	+	0.102596i	−0.408511	+	0.912753i	$0.633952\pi$
$410$	1.16501e17	+	6.72618e16i	1.21125	+	0.699316i
$411$		−	6.68955e16i		−	0.684581i
$412$	1.19992e16	−	2.07832e16i	0.120870	−	0.209354i
$413$	5.52007e16	+	9.56105e16i	0.547355	+	0.948048i
$414$	4.80272e16	−	2.77285e16i	0.468797	−	0.270660i
$415$	2.80240e17			2.69288
$416$	−6.78814e16	−	6.47983e16i	−0.642162	−	0.612995i
$417$	−2.27559e17			−2.11939
$418$	−6.98804e15	+	4.03455e15i	−0.0640781	+	0.0369955i
$419$	9.24301e16	+	1.60094e17i	0.834492	+	1.44538i	0.894443	+	0.447181i	$0.147572\pi$
$419$	9.24301e16	+	1.60094e17i	0.834492	+	1.44538i	−0.0599512	+	0.998201i	$0.519094\pi$
$420$	3.77965e16	−	6.54655e16i	0.335994	−	0.581959i
$421$		−	1.34165e17i		−	1.17437i	−0.809452	−	0.587186i	$-0.800236\pi$
$421$		−	1.34165e17i		−	1.17437i	0.809452	−	0.587186i	$-0.199764\pi$
$422$	7.73939e15	+	4.46834e15i	0.0667077	+	0.0385137i
$423$	6.08244e16	+	3.51170e16i	0.516257	+	0.298061i
$424$			1.99087e17i			1.66404i
$425$	−1.38948e17	+	2.40665e17i	−1.14373	+	1.98100i
$426$	1.28784e16	+	2.23061e16i	0.104400	+	0.180826i
$427$	5.31326e16	−	3.06761e16i	0.424209	−	0.244917i
$428$	5.33698e16			0.419673
$429$	−8.88519e16	−	8.48163e16i	−0.688168	−	0.656911i
$430$	7.32152e16			0.558542
$431$	5.81835e16	−	3.35922e16i	0.437217	−	0.252427i	−0.265199	−	0.964194i	$-0.585438\pi$
$431$	5.81835e16	−	3.35922e16i	0.437217	−	0.252427i	0.702417	+	0.711766i	$0.252104\pi$
$432$	−3.51527e15	−	6.08862e15i	−0.0260204	−	0.0450687i
$433$	−3.92303e16	+	6.79489e16i	−0.286055	+	0.495463i	−0.972865	−	0.231375i	$-0.925678\pi$
$433$	−3.92303e16	+	6.79489e16i	−0.286055	+	0.495463i	0.686809	+	0.726838i	$0.259011\pi$
$434$			1.45640e16i			0.104616i
$435$	−5.40277e17	−	3.11929e17i	−3.82328	−	2.20737i
$436$	−1.72392e16	−	9.95305e15i	−0.120186	−	0.0693895i
$437$			1.57718e16i			0.108330i
$438$	−8.81966e16	+	1.52761e17i	−0.596857	+	1.03379i
$439$	1.34482e17	+	2.32930e17i	0.896698	+	1.55313i	0.831689	+	0.555241i	$0.187374\pi$
$439$	1.34482e17	+	2.32930e17i	0.896698	+	1.55313i	0.0650085	+	0.997885i	$0.479293\pi$
$440$	−1.49954e17	+	8.65759e16i	−0.985180	+	0.568794i
$441$	1.23159e17			0.797287
$442$	3.44675e16	−	1.41726e17i	0.219870	−	0.904079i
$443$	−5.44678e15			−0.0342385			−0.0171193	−	0.999853i	$-0.505449\pi$
$443$	−5.44678e15			−0.0342385			−0.0171193	+	0.999853i	$0.505449\pi$
$444$	7.80477e16	−	4.50609e16i	0.483471	−	0.279132i
$445$	−1.50638e17	−	2.60912e17i	−0.919588	−	1.59277i
$446$	−1.57773e15	+	2.73271e15i	−0.00949196	+	0.0164406i
$447$			1.47246e17i			0.873062i
$448$	7.10609e16	+	4.10270e16i	0.415263	+	0.239752i
$449$	−8.93492e16	−	5.15858e16i	−0.514623	−	0.297118i	0.220109	−	0.975475i	$-0.429359\pi$
$449$	−8.93492e16	−	5.15858e16i	−0.514623	−	0.297118i	−0.734732	+	0.678358i	$0.762692\pi$
$450$			2.46535e17i			1.39958i
$451$	6.96550e16	−	1.20646e17i	0.389767	−	0.675096i
$452$	−2.22092e16	−	3.84674e16i	−0.122499	−	0.212174i
$453$	1.06931e17	−	6.17365e16i	0.581386	−	0.335663i
$454$	−1.71542e17			−0.919406
$455$	1.19151e17	−	1.24820e17i	0.629539	−	0.659493i
$456$	4.81606e16			0.250854
$457$	−1.74293e17	+	1.00628e17i	−0.895003	+	0.516730i	−0.875576	−	0.483081i	$-0.839518\pi$
$457$	−1.74293e17	+	1.00628e17i	−0.895003	+	0.516730i	−0.0194276	+	0.999811i	$0.506184\pi$
$458$	6.21645e16	+	1.07672e17i	0.314715	+	0.545102i
$459$	−2.82392e16	+	4.89116e16i	−0.140951	+	0.244135i
$460$			1.13287e17i			0.557513i
$461$	1.42308e17	+	8.21616e16i	0.690515	+	0.398669i	0.803805	−	0.594893i	$-0.202806\pi$
$461$	1.42308e17	+	8.21616e16i	0.690515	+	0.398669i	−0.113290	+	0.993562i	$0.536139\pi$
$462$	6.69446e16	+	3.86505e16i	0.320289	+	0.184919i
$463$		−	1.29114e17i		−	0.609113i	−0.952494	−	0.304556i	$-0.901492\pi$
$463$		−	1.29114e17i		−	0.609113i	0.952494	−	0.304556i	$-0.0985082\pi$
$464$	4.77478e16	−	8.27016e16i	0.222119	−	0.384722i
$465$	7.10326e16	+	1.23032e17i	0.325847	+	0.564384i
$466$	1.47260e17	−	8.50204e16i	0.666155	−	0.384605i
$467$	−6.26250e16			−0.279375			−0.139688	−	0.990196i	$-0.544610\pi$
$467$	−6.26250e16			−0.279375			−0.139688	+	0.990196i	$0.544610\pi$
$468$	3.68471e16	+	1.25753e17i	0.162108	+	0.553250i
$469$	−1.81011e17			−0.785385
$470$	1.22693e17	−	7.08370e16i	0.525031	−	0.303127i
$471$	5.67266e16	+	9.82533e16i	0.239415	+	0.414678i
$472$	−2.52613e17	+	4.37538e17i	−1.05156	+	1.82135i
$473$		−	7.58203e16i		−	0.311306i
$474$	−3.14584e17	−	1.81625e17i	−1.27402	−	0.735557i
$475$	−6.07201e16	−	3.50568e16i	−0.242563	−	0.140044i
$476$		−	9.29550e16i		−	0.366292i
$477$	2.31471e17	−	4.00919e17i	0.899759	−	1.55843i
$478$	−3.49479e15	−	6.05316e15i	−0.0134011	−	0.0232114i
$479$	−2.87595e17	+	1.66043e17i	−1.08793	+	0.628117i	−0.933025	−	0.359812i	$-0.882841\pi$
$479$	−2.87595e17	+	1.66043e17i	−1.08793	+	0.628117i	−0.154906	+	0.987929i	$0.549507\pi$
$480$	5.76071e17			2.14985
$481$	1.97425e17	−	5.78476e16i	0.726873	−	0.212982i
$482$	−2.57666e17			−0.935947
$483$	1.30849e17	−	7.55457e16i	0.468937	−	0.270741i
$484$	−4.11378e16	−	7.12527e16i	−0.145461	−	0.251945i
$485$	4.73083e15	−	8.19405e15i	0.0165050	−	0.0285876i
$486$		−	2.93568e17i		−	1.01059i
$487$	1.64803e17	+	9.51493e16i	0.559794	+	0.323197i	0.753063	−	0.657949i	$-0.228576\pi$
$487$	1.64803e17	+	9.51493e16i	0.559794	+	0.323197i	−0.193269	+	0.981146i	$0.561909\pi$
$488$	2.43148e17	+	1.40382e17i	0.814971	+	0.470524i
$489$		−	2.04619e16i		−	0.0676767i
$490$	1.24216e17	−	2.15149e17i	0.405418	−	0.702205i
$491$	9.35349e16	+	1.62007e17i	0.301262	+	0.521801i	0.976422	−	0.215870i	$-0.0692588\pi$
$491$	9.35349e16	+	1.62007e17i	0.301262	+	0.521801i	−0.675160	+	0.737671i	$0.735926\pi$
$492$	−2.41034e17	+	1.39161e17i	−0.766135	+	0.442328i
$493$	−7.67143e17			−2.40642
$494$	3.57577e16	+	8.69619e15i	0.110699	+	0.0269218i
$495$	4.02634e17			1.23020
$496$	−1.88328e16	+	1.08731e16i	−0.0567917	+	0.0327887i
$497$	1.87355e16	+	3.24508e16i	0.0557633	+	0.0965849i
$498$	2.86265e17	−	4.95825e17i	0.840964	−	1.45659i
$499$		−	1.06867e17i		−	0.309878i	−0.987924	−	0.154939i	$-0.950482\pi$
$499$		−	1.06867e17i		−	0.309878i	0.987924	−	0.154939i	$-0.0495180\pi$
$500$	−1.84465e17	−	1.06501e17i	−0.527971	−	0.304824i
$501$	−4.66541e17	−	2.69358e17i	−1.31809	−	0.760999i
$502$			6.93235e16i			0.193333i
$503$	2.12283e17	−	3.67684e17i	0.584416	−	1.01224i	−0.410532	−	0.911846i	$-0.634657\pi$
$503$	2.12283e17	−	3.67684e17i	0.584416	−	1.01224i	0.994948	−	0.100392i	$-0.0320098\pi$
$504$	−1.23180e17	−	2.13354e17i	−0.334766	−	0.579832i
$505$	1.60488e17	−	9.26580e16i	0.430576	−	0.248593i
$506$	−1.15847e17			−0.306835
$507$	2.60213e16	+	5.59598e17i	0.0680420	+	1.46327i
$508$	−9.81292e15			−0.0253329
$509$	5.70740e17	−	3.29517e17i	1.45470	−	0.839869i	0.455954	−	0.890003i	$-0.349298\pi$
$509$	5.70740e17	−	3.29517e17i	1.45470	−	0.839869i	0.998742	+	0.0501340i	$0.0159648\pi$
$510$	4.47680e17	+	7.75405e17i	1.12658	+	1.95129i
$511$	−1.28308e17	+	2.22236e17i	−0.318799	+	0.552177i
$512$			1.93422e17i			0.474517i
$513$	−1.23405e16	−	7.12477e15i	−0.0298929	−	0.0172587i
$514$	−3.83905e17	−	2.21648e17i	−0.918256	−	0.530156i
$515$			3.36286e17i			0.794258i
$516$	−7.57392e16	+	1.31184e17i	−0.176643	+	0.305955i
$517$	−7.33575e16	−	1.27059e17i	−0.168949	−	0.292628i
$518$	−1.12119e17	+	6.47321e16i	−0.254998	+	0.147223i
$519$	−9.65989e16			−0.216962
$520$	7.67313e17	+	1.86609e17i	1.70197	+	0.413914i
$521$	7.26801e16			0.159210			0.0796050	−	0.996826i	$-0.474634\pi$
$521$	7.26801e16			0.159210			0.0796050	+	0.996826i	$0.474634\pi$
$522$	−5.89390e17	+	3.40284e17i	−1.27510	+	0.736180i
$523$	−1.62435e17	−	2.81346e17i	−0.347072	−	0.601146i	0.638656	−	0.769492i	$-0.279491\pi$
$523$	−1.62435e17	−	2.81346e17i	−0.347072	−	0.601146i	−0.985728	+	0.168346i	$0.946157\pi$
$524$	−1.60336e17	+	2.77711e17i	−0.338360	+	0.586057i
$525$			6.71679e17i			1.39999i
$526$	4.42068e17	+	2.55228e17i	0.910084	+	0.525437i
$527$	1.51290e17	+	8.73471e16i	0.307638	+	0.177615i
$528$			1.15422e17i			0.231829i
$529$	1.38802e17	−	2.40412e17i	0.275381	−	0.476974i
$530$	−4.66916e17	−	8.08722e17i	−0.915051	−	1.58491i
$531$	1.01742e18	−	5.87405e17i	1.96963	−	1.13717i
$532$	2.34526e16			0.0448504
$533$	−6.09705e17	+	1.78650e17i	−1.15184	+	0.337502i
$534$	−6.15504e17			−1.14872
$535$	−6.47670e17	+	3.73932e17i	−1.19414	+	0.689435i
$536$	−4.14177e17	−	7.17376e17i	−0.754423	−	1.30670i
$537$	−5.30223e17	+	9.18372e17i	−0.954169	+	1.65267i
$538$			3.77760e17i			0.671632i
$539$	−2.22804e17	−	1.28636e17i	−0.391378	−	0.225962i
$540$	−8.86405e16	−	5.11766e16i	−0.153841	−	0.0888202i
$541$			1.59618e17i			0.273716i	0.990591	+	0.136858i	$0.0437004\pi$
$541$			1.59618e17i			0.273716i	−0.990591	+	0.136858i	$0.956300\pi$
$542$	−2.03199e17	+	3.51950e17i	−0.344291	+	0.596329i
$543$	−2.88201e17	−	4.99178e17i	−0.482499	−	0.835712i
$544$	6.13476e17	−	3.54190e17i	1.01486	−	0.585928i
$545$	2.78942e17			0.455970
$546$	−9.91301e16	−	3.38315e17i	−0.160123	−	0.546474i
$547$	6.93963e17			1.10769			0.553846	−	0.832619i	$-0.313160\pi$
$547$	6.93963e17			1.10769			0.553846	+	0.832619i	$0.313160\pi$
$548$	1.29103e17	−	7.45379e16i	0.203640	−	0.117572i
$549$	−3.26432e17	−	5.65398e17i	−0.508830	−	0.881320i
$550$	2.57499e17	−	4.46001e17i	0.396659	−	0.687034i
$551$		−	1.93551e17i		−	0.294653i
$552$	5.98799e17	+	3.45717e17i	0.900901	+	0.520135i
$553$	−4.57655e17	−	2.64227e17i	−0.680494	−	0.392884i
$554$			2.22916e16i			0.0327588i
$555$	−6.31432e17	+	1.09367e18i	−0.917112	+	1.58848i
$556$	−2.53556e17	−	4.39173e17i	−0.363989	−	0.630448i
$557$	−2.87956e17	+	1.66252e17i	−0.408571	+	0.235889i	−0.690176	−	0.723642i	$-0.742467\pi$
$557$	−2.87956e17	+	1.66252e17i	−0.408571	+	0.235889i	0.281605	+	0.959531i	$0.409133\pi$
$558$	1.54979e17			0.217346
$559$	−2.38762e17	+	2.50122e17i	−0.330970	+	0.346718i
$560$	−1.62146e17			−0.222169
$561$	8.02995e17	−	4.63609e17i	1.08756	−	0.627905i
$562$	4.07985e17	+	7.06650e17i	0.546208	+	0.946059i
$563$	1.00022e17	−	1.73242e17i	0.132370	−	0.229271i	−0.792220	−	0.610236i	$-0.791075\pi$
$563$	1.00022e17	−	1.73242e17i	0.132370	−	0.229271i	0.924590	+	0.380965i	$0.124408\pi$
$564$			2.93116e17i			0.383465i
$565$	5.39039e17	+	3.11214e17i	0.697116	+	0.402480i
$566$	4.89281e17	+	2.82486e17i	0.625535	+	0.361153i
$567$		−	3.63465e17i		−	0.459380i
$568$	−8.57384e16	+	1.48503e17i	−0.107130	+	0.185555i
$569$	5.46163e17	+	9.45982e17i	0.674672	+	1.16857i	0.976565	+	0.215224i	$0.0690482\pi$
$569$	5.46163e17	+	9.45982e17i	0.674672	+	1.16857i	−0.301893	+	0.953342i	$0.597618\pi$
$570$	−1.95636e17	+	1.12950e17i	−0.238925	+	0.137943i
$571$	1.29812e18			1.56740			0.783702	−	0.621137i	$-0.213329\pi$
$571$	1.29812e18			1.56740			0.783702	+	0.621137i	$0.213329\pi$
$572$	6.46866e16	−	2.65984e17i	0.0772218	−	0.317527i
$573$	−2.46187e17			−0.290577
$574$	3.46257e17	−	1.99912e17i	0.404084	−	0.233298i
$575$	−5.03304e17	−	8.71748e17i	−0.580750	−	1.00589i
$576$	4.36579e17	−	7.56177e17i	0.498100	−	0.862735i
$577$		−	6.88840e16i		−	0.0777097i	−0.999245	−	0.0388549i	$-0.987629\pi$
$577$		−	6.88840e16i		−	0.0777097i	0.999245	−	0.0388549i	$-0.0123710\pi$
$578$	4.06264e17	+	2.34557e17i	0.453187	+	0.261648i
$579$	3.32479e17	+	1.91957e17i	0.366736	+	0.211735i
$580$		−	1.39026e18i		−	1.51640i
$581$	4.16457e17	−	7.21324e17i	0.449185	−	0.778011i
$582$	−9.66508e15	−	1.67404e16i	−0.0103088	−	0.0178553i
$583$	−8.37497e17	+	4.83529e17i	−0.883360	+	0.510008i
$584$	−1.17434e18			−1.22493
$585$	−1.32824e18	−	1.26791e18i	−1.37014	−	1.30791i
$586$	2.43251e17			0.248154
$587$	2.51849e17	−	1.45405e17i	0.254093	−	0.146701i	−0.367544	−	0.930006i	$-0.619801\pi$
$587$	2.51849e17	−	1.45405e17i	0.254093	−	0.146701i	0.621637	+	0.783305i	$0.286468\pi$
$588$	2.56997e17	+	4.45131e17i	0.256434	+	0.444156i
$589$	−2.20378e16	+	3.81705e16i	−0.0217479	+	0.0376685i
$590$		−	2.36979e18i		−	2.31298i
$591$	1.25574e18	+	7.25004e17i	1.21222	+	0.699878i
$592$	−1.67411e17	−	9.66549e16i	−0.159843	−	0.0922853i
$593$		−	8.15618e16i		−	0.0770249i	−0.999258	−	0.0385124i	$-0.987738\pi$
$593$		−	8.15618e16i		−	0.0770249i	0.999258	−	0.0385124i	$-0.0122619\pi$
$594$	5.23328e16	−	9.06431e16i	0.0488835	−	0.0846687i
$595$	6.51283e17	+	1.12806e18i	0.601741	+	1.04225i
$596$	−2.84174e17	+	1.64068e17i	−0.259707	+	0.149942i
$597$	1.52523e17			0.137881
$598$	3.82165e17	+	3.64807e17i	0.341738	+	0.326216i
$599$	1.87817e18			1.66135			0.830676	−	0.556757i	$-0.187954\pi$
$599$	1.87817e18			1.66135			0.830676	+	0.556757i	$0.187954\pi$
$600$	−2.66197e18	+	1.53689e18i	−2.32927	+	1.34480i
$601$	−7.80165e17	−	1.35129e18i	−0.675309	−	1.16967i	−0.976378	−	0.216067i	$-0.930677\pi$
$601$	−7.80165e17	−	1.35129e18i	−0.675309	−	1.16967i	0.301070	−	0.953602i	$-0.402656\pi$
$602$	1.08803e17	−	1.88452e17i	0.0931673	−	0.161370i
$603$			1.92619e18i			1.63169i
$604$	2.38294e17	+	1.37579e17i	0.199698	+	0.115295i
$605$	9.98455e17	+	5.76458e17i	0.827787	+	0.477923i
$606$		−	3.78600e17i		−	0.310534i
$607$	−1.05078e18	+	1.82000e18i	−0.852676	+	1.47688i	0.0261081	+	0.999659i	$0.491689\pi$
$607$	−1.05078e18	+	1.82000e18i	−0.852676	+	1.47688i	−0.878784	+	0.477219i	$0.841645\pi$
$608$	8.93626e16	+	1.54781e17i	0.0717435	+	0.124263i
$609$	−1.60578e18	+	9.27098e17i	−1.27548	+	0.736399i
$610$	−1.31694e18			−1.03496
$611$	−1.58117e17	+	6.50159e17i	−0.122945	+	0.505536i
$612$	−9.89158e17			−0.760994
$613$	−1.08429e18	+	6.26015e17i	−0.825377	+	0.476532i	−0.852267	−	0.523107i	$-0.824773\pi$
$613$	−1.08429e18	+	6.26015e17i	−0.825377	+	0.476532i	0.0268902	+	0.999638i	$0.491440\pi$
$614$	−2.96973e17	−	5.14373e17i	−0.223678	−	0.387421i
$615$	1.95005e18	−	3.37758e18i	1.45330	−	2.51720i
$616$			5.14632e17i			0.379509i
$617$	−1.27017e18	−	7.33332e17i	−0.926847	−	0.535115i	−0.0410337	−	0.999158i	$-0.513065\pi$
$617$	−1.27017e18	−	7.33332e17i	−0.926847	−	0.535115i	−0.885813	+	0.464043i	$0.846398\pi$
$618$	5.94987e17	+	3.43516e17i	0.429618	+	0.248040i
$619$			1.72495e18i			1.23250i	0.787551	+	0.616250i	$0.211349\pi$
$619$			1.72495e18i			1.23250i	−0.787551	+	0.616250i	$0.788651\pi$
$620$	−1.58295e17	+	2.74176e17i	−0.111924	+	0.193858i
$621$	−1.02289e17	−	1.77170e17i	−0.0715705	−	0.123964i
$622$	−1.62302e17	+	9.37052e16i	−0.112379	+	0.0648823i
$623$	−8.95432e17			−0.613565
$624$	3.63470e17	−	3.80764e17i	0.246473	−	0.258200i
$625$	4.02506e17			0.270117
$626$	−7.86590e17	+	4.54138e17i	−0.522415	+	0.301616i
$627$	1.16969e17	+	2.02597e17i	0.0768834	+	0.133166i
$628$	−1.26414e17	+	2.18956e17i	−0.0822355	+	0.142436i
$629$			1.55291e18i			0.999811i
$630$	1.00075e18	+	5.77784e17i	0.637694	+	0.368173i
$631$	−1.13496e16	−	6.55272e15i	−0.00715799	−	0.00413267i	0.496417	−	0.868084i	$-0.334649\pi$
$631$	−1.13496e16	−	6.55272e15i	−0.00715799	−	0.00413267i	−0.503575	+	0.863952i	$0.667982\pi$
$632$		−	2.41834e18i		−	1.50958i
$633$	1.29546e17	−	2.24380e17i	0.0800385	−	0.138631i
$634$	6.44307e17	+	1.11597e18i	0.394015	+	0.682454i
$635$	1.19085e17	−	6.87536e16i	0.0720820	−	0.0416166i
$636$	1.93205e18			1.15757
$637$	3.29923e17	+	1.12598e18i	0.195662	+	0.667764i
$638$	1.42167e18			0.834573
$639$	3.45318e17	−	1.99369e17i	0.200661	−	0.115852i
$640$	3.95063e17	+	6.84268e17i	0.227246	+	0.393601i
$641$	1.45058e18	−	2.51247e18i	0.825969	−	1.43062i	−0.0752071	−	0.997168i	$-0.523962\pi$
$641$	1.45058e18	−	2.51247e18i	0.825969	−	1.43062i	0.901176	−	0.433453i	$-0.142705\pi$
$642$			1.52789e18i			0.861218i
$643$	−2.46567e18	−	1.42356e18i	−1.37583	−	0.794335i	−0.384174	−	0.923261i	$-0.625514\pi$
$643$	−2.46567e18	−	1.42356e18i	−1.37583	−	0.794335i	−0.991654	+	0.128926i	$0.958847\pi$
$644$	2.91595e17	+	1.68353e17i	0.161073	+	0.0929955i
$645$		−	2.12265e18i		−	1.16075i
$646$	−1.38892e17	+	2.40568e17i	−0.0751911	+	0.130235i
$647$	−1.19975e18	−	2.07802e18i	−0.643001	−	1.11371i	−0.984759	−	0.173923i	$-0.944356\pi$
$647$	−1.19975e18	−	2.07802e18i	−0.643001	−	1.11371i	0.341758	−	0.939788i	$-0.388978\pi$
$648$	1.44047e18	−	8.31654e17i	0.764303	−	0.441271i
$649$	−2.45411e18			−1.28915
$650$	−2.25394e18	+	6.60429e17i	−1.17221	+	0.343470i
$651$	4.22238e17			0.217411
$652$	3.94900e16	−	2.27996e16i	0.0201316	−	0.0116230i
$653$	1.17705e18	+	2.03871e18i	0.594098	+	1.02901i	0.993673	+	0.112308i	$0.0358243\pi$
$653$	1.17705e18	+	2.03871e18i	0.594098	+	1.02901i	−0.399575	+	0.916700i	$0.630842\pi$
$654$	2.84939e17	−	4.93528e17i	0.142395	−	0.246636i
$655$		−	4.49355e18i		−	2.22342i
$656$	5.17015e17	+	2.98498e17i	0.253296	+	0.146240i
$657$	2.36487e18	+	1.36536e18i	1.14718	+	0.662326i
$658$		−	4.21075e17i		−	0.202251i
$659$	3.14375e17	−	5.44514e17i	0.149518	−	0.258972i	−0.781532	−	0.623866i	$-0.785561\pi$
$659$	3.14375e17	−	5.44514e17i	0.149518	−	0.258972i	0.931049	+	0.364893i	$0.118895\pi$
$660$	8.40179e17	+	1.45523e18i	0.395673	+	0.685326i
$661$	−1.25720e18	+	7.25842e17i	−0.586264	+	0.338480i	−0.763619	−	0.645667i	$-0.776579\pi$
$661$	−1.25720e18	+	7.25842e17i	−0.586264	+	0.338480i	0.177355	+	0.984147i	$0.443246\pi$
$662$	−1.12248e18			−0.518326
$663$	−4.10892e18	−	9.99279e17i	−1.87884	−	0.456929i
$664$	3.81162e18			1.72591
$665$	−2.84610e17	+	1.64319e17i	−0.127617	+	0.0736797i
$666$	6.88831e17	+	1.19309e18i	0.305865	+	0.529774i
$667$	1.38939e18	−	2.40649e18i	0.610951	−	1.05820i
$668$		−	1.20052e18i		−	0.522784i
$669$	7.92263e16	+	4.57413e16i	0.0341664	+	0.0197260i
$670$	3.36490e18	+	1.94273e18i	1.43710	+	0.829709i
$671$			1.36380e18i			0.576838i
$672$	8.56083e17	−	1.48278e18i	0.358604	−	0.621121i
$673$	−9.21422e17	−	1.59595e18i	−0.382262	−	0.662097i	0.609123	−	0.793075i	$-0.291521\pi$
$673$	−9.21422e17	−	1.59595e18i	−0.382262	−	0.662097i	−0.991385	+	0.130979i	$0.958188\pi$
$674$	−9.54265e17	+	5.50945e17i	−0.392084	+	0.226370i
$675$	9.09455e17			0.370089
$676$	−1.05099e18	+	6.73748e17i	−0.423589	+	0.271546i
$677$	−7.60696e17			−0.303658			−0.151829	−	0.988407i	$-0.548516\pi$
$677$	−7.60696e17			−0.303658			−0.151829	+	0.988407i	$0.548516\pi$
$678$	1.10125e18	−	6.35810e17i	0.435406	−	0.251382i
$679$	−1.40607e16	−	2.43539e16i	−0.00550622	−	0.00953706i
$680$	−2.98044e18	+	5.16227e18i	−1.15604	+	2.00232i
$681$			4.97333e18i			1.91069i
$682$	−2.80370e17	−	1.61872e17i	−0.106692	−	0.0615988i
$683$	−2.14930e18	−	1.24090e18i	−0.810144	−	0.467737i	0.0368617	−	0.999320i	$-0.488264\pi$
$683$	−2.14930e18	−	1.24090e18i	−0.810144	−	0.467737i	−0.847006	+	0.531583i	$0.821597\pi$
$684$		−	2.49566e17i		−	0.0931794i
$685$	−1.04449e18	+	1.80911e18i	−0.386292	+	0.669077i
$686$	−8.99753e17	−	1.55842e18i	−0.329622	−	0.570922i
$687$	3.12162e18	−	1.80227e18i	1.13282	−	0.654034i
$688$	3.24919e17			0.116802
$689$	4.28547e18	+	1.04221e18i	1.52606	+	0.371135i
$690$	−3.24321e18			−1.14408
$691$	3.83031e18	−	2.21143e18i	1.33853	−	0.772799i	0.351937	−	0.936024i	$-0.385523\pi$
$691$	3.83031e18	−	2.21143e18i	1.33853	−	0.772799i	0.986589	+	0.163225i	$0.0521897\pi$
$692$	−1.07635e17	−	1.86429e17i	−0.0372617	−	0.0645392i
$693$	5.98342e17	−	1.03636e18i	0.205203	−	0.355422i
$694$		−	1.00229e18i		−	0.340530i
$695$	6.15407e18	+	3.55305e18i	2.07139	+	1.19592i
$696$	−7.34846e18	−	4.24264e18i	−2.45040	−	1.41474i
$697$		−	4.79585e18i		−	1.58435i
$698$	−7.64108e17	+	1.32347e18i	−0.250089	+	0.433167i
$699$	−2.46490e18	−	4.26934e18i	−0.799279	−	1.38439i
$700$	−1.29629e18	+	7.48414e17i	−0.416452	+	0.240439i
$701$	−3.69572e17			−0.117634			−0.0588168	−	0.998269i	$-0.518733\pi$
$701$	−3.69572e17			−0.117634			−0.0588168	+	0.998269i	$0.518733\pi$
$702$	−4.58080e17	+	1.34222e17i	−0.144461	+	0.0423286i
$703$	−3.91802e17			−0.122421
$704$	−1.57961e18	+	9.11989e17i	−0.489022	+	0.282337i
$705$	−2.05370e18	−	3.55711e18i	−0.629952	−	1.09111i
$706$	−1.79475e18	+	3.10860e18i	−0.545474	+	0.944788i
$707$		−	5.50785e17i		−	0.165866i
$708$	4.24610e18	+	2.45149e18i	1.26699	+	0.731499i
$709$	−9.16366e16	−	5.29064e16i	−0.0270937	−	0.0156426i	0.486392	−	0.873741i	$-0.338313\pi$
$709$	−9.16366e16	−	5.29064e16i	−0.0270937	−	0.0156426i	−0.513486	+	0.858098i	$0.671646\pi$
$710$		−	8.04324e17i		−	0.235641i
$711$	−2.81171e18	+	4.87002e18i	−0.816240	+	1.41377i
$712$	−2.04886e18	−	3.54874e18i	−0.589377	−	1.02083i
$713$	−5.48008e17	+	3.16392e17i	−0.156208	+	0.0901870i
$714$	2.66114e18			0.751673
$715$	1.07859e18	+	3.68107e18i	0.301904	+	1.03035i
$716$	−2.36319e18			−0.655487
$717$	−1.75493e17	+	1.01321e17i	−0.0482374	+	0.0278499i
$718$	5.56230e17	+	9.63418e17i	0.151511	+	0.262425i
$719$	−1.75018e18	+	3.03139e18i	−0.472437	+	0.818285i	−0.999503	−	0.0315396i	$-0.989959\pi$
$719$	−1.75018e18	+	3.03139e18i	−0.472437	+	0.818285i	0.527065	+	0.849825i	$0.323292\pi$
$720$			1.72544e18i			0.461571i
$721$	8.65583e17	+	4.99745e17i	0.229472	+	0.132486i
$722$	2.26275e18	+	1.30640e18i	0.594491	+	0.343229i
$723$			7.47023e18i			1.94507i
$724$	6.42252e17	−	1.11241e18i	0.165731	−	0.287055i
$725$	6.17655e18	+	1.06981e19i	1.57961	+	2.73596i
$726$	2.03984e18	−	1.17770e18i	0.517021	−	0.298502i
$727$	−1.59670e18			−0.401098			−0.200549	−	0.979684i	$-0.564273\pi$
$727$	−1.59670e18			−0.401098			−0.200549	+	0.979684i	$0.564273\pi$
$728$	1.62060e18	−	1.69771e18i	0.403480	−	0.422678i
$729$	−5.13551e18			−1.26723
$730$	4.77034e18	−	2.75416e18i	1.16668	−	0.673582i
$731$	−1.30508e18	−	2.26047e18i	−0.316355	−	0.547944i
$732$	1.36234e18	−	2.35964e18i	0.327313	−	0.566923i
$733$		−	4.43036e17i		−	0.105503i	−0.998608	−	0.0527513i	$-0.983201\pi$
$733$		−	4.43036e17i		−	0.105503i	0.998608	−	0.0527513i	$-0.0167991\pi$
$734$	1.90895e18	+	1.10213e18i	0.450578	+	0.260141i
$735$	−6.23757e18	−	3.60126e18i	−1.45931	−	0.842533i
$736$			2.56593e18i			0.595030i
$737$	2.01185e18	−	3.48463e18i	0.462442	−	0.800973i
$738$	−2.12731e18	−	3.68461e18i	−0.484691	−	0.839509i
$739$	−3.05496e18	+	1.76378e18i	−0.689948	+	0.398342i	−0.803593	−	0.595180i	$-0.797081\pi$
$739$	−3.05496e18	+	1.76378e18i	−0.689948	+	0.398342i	0.113644	+	0.993522i	$0.463748\pi$
$740$	−2.81428e18			−0.630029
$741$	2.52119e17	−	1.03668e18i	0.0559484	−	0.230053i
$742$	−2.77548e18			−0.610538
$743$	1.54531e18	−	8.92186e17i	0.336968	−	0.194549i	−0.321962	−	0.946752i	$-0.604342\pi$
$743$	1.54531e18	−	8.92186e17i	0.336968	−	0.194549i	0.658931	+	0.752204i	$0.271009\pi$
$744$	9.66135e17	+	1.67339e18i	0.208840	+	0.361721i
$745$	2.29907e18	−	3.98210e18i	0.492647	−	0.853289i
$746$			2.48860e16i			0.00528631i
$747$	−7.67580e18	−	4.43162e18i	−1.61637	−	0.933209i
$748$	1.78946e18	+	1.03315e18i	0.373562	+	0.215676i
$749$			2.22276e18i			0.460003i
$750$	3.04894e18	−	5.28092e18i	0.625534	−	1.08346i
$751$	−2.43770e18	−	4.22222e18i	−0.495816	−	0.858779i	0.504172	−	0.863603i	$-0.331798\pi$
$751$	−2.43770e18	−	4.22222e18i	−0.495816	−	0.858779i	−0.999988	+	0.00482400i	$0.998464\pi$
$752$	5.44496e17	−	3.14365e17i	0.109794	−	0.0633896i
$753$	2.00982e18			0.401782
$754$	−4.68993e18	−	4.47691e18i	−0.929506	−	0.887289i
$755$	−3.85575e18			−0.757625
$756$	−2.63452e17	+	1.52104e17i	−0.0513227	+	0.0296312i
$757$	1.15198e18	+	1.99529e18i	0.222496	+	0.385374i	0.955565	−	0.294780i	$-0.0952464\pi$
$757$	1.15198e18	+	1.99529e18i	0.222496	+	0.385374i	−0.733070	+	0.680154i	$0.761913\pi$
$758$	2.34530e18	−	4.06217e18i	0.449105	−	0.777872i
$759$			3.35861e18i			0.637659i
$760$	−1.30245e18	−	7.51968e17i	−0.245172	−	0.141550i
$761$	6.10886e18	+	3.52695e18i	1.14015	+	0.658263i	0.946467	−	0.322802i	$-0.104625\pi$
$761$	6.10886e18	+	3.52695e18i	1.14015	+	0.658263i	0.193679	+	0.981065i	$0.437958\pi$
$762$		−	2.80927e17i		−	0.0519859i
$763$	4.14527e17	−	7.17982e17i	0.0760577	−	0.131736i
$764$	−2.74313e17	−	4.75124e17i	−0.0499044	−	0.0864370i
$765$	1.20039e19	−	6.93047e18i	2.16533	−	1.25015i
$766$	1.02051e18			0.182527
$767$	8.09584e18	+	7.72813e18i	1.43579	+	1.37058i
$768$	8.85663e18			1.55747
$769$	4.17752e18	−	2.41189e18i	0.728446	−	0.420568i	−0.0894074	−	0.995995i	$-0.528497\pi$
$769$	4.17752e18	−	2.41189e18i	0.728446	−	0.420568i	0.817853	+	0.575427i	$0.195164\pi$
$770$	−1.20696e18	−	2.09051e18i	−0.208690	−	0.361462i
$771$	−6.42599e18	+	1.11301e19i	−1.10176	+	1.90830i
$772$			8.55546e17i			0.145456i
$773$	2.34860e17	+	1.35597e17i	0.0395952	+	0.0228603i	0.519667	−	0.854369i	$-0.326056\pi$
$773$	2.34860e17	+	1.35597e17i	0.0395952	+	0.0228603i	−0.480072	+	0.877229i	$0.659389\pi$
$774$	−2.00537e18	−	1.15780e18i	−0.335257	−	0.193561i
$775$		−	2.81305e18i		−	0.466355i
$776$	6.43454e16	−	1.11450e17i	0.0105783	−	0.0183222i
$777$	1.87671e18	+	3.25055e18i	0.305956	+	0.529932i
$778$	−5.10613e18	+	2.94802e18i	−0.825514	+	0.476611i
$779$	1.21000e18			0.193995
$780$	1.81095e18	−	7.44642e18i	0.287933	−	1.18395i
$781$	−8.32943e17			−0.131336
$782$	−3.45380e18	+	1.99405e18i	−0.540074	+	0.311812i
$783$	1.25529e18	+	2.17423e18i	0.194668	+	0.337174i
$784$	5.51254e17	−	9.54800e17i	0.0847808	−	0.146845i
$785$		−	3.54286e18i		−	0.540382i
$786$	−7.95038e18	−	4.59015e18i	−1.20266	−	0.694354i
$787$	1.18857e17	+	6.86219e16i	0.0178315	+	0.0102950i	0.508889	−	0.860832i	$-0.330056\pi$
$787$	1.18857e17	+	6.86219e16i	0.0178315	+	0.0102950i	−0.491058	+	0.871127i	$0.663390\pi$
$788$			3.23133e18i			0.480796i
$789$	7.39954e18	−	1.28164e19i	1.09195	−	1.89132i
$790$	5.67170e18	+	9.82367e18i	0.830113	+	1.43780i
$791$	1.60210e18	−	9.24972e17i	0.232564	−	0.134271i
$792$	5.47633e18			0.788453
$793$	4.29467e18	−	4.49901e18i	0.613274	−	0.642453i
$794$	5.68119e18			0.804649
$795$	−2.34464e19	+	1.35368e19i	−3.29374	+	1.90164i
$796$	1.69948e17	+	2.94359e17i	0.0236800	+	0.0410150i
$797$	−6.95241e18	+	1.20419e19i	−0.960851	+	1.66424i	−0.240481	+	0.970654i	$0.577305\pi$
$797$	−6.95241e18	+	1.20419e19i	−0.960851	+	1.66424i	−0.720370	+	0.693590i	$0.756028\pi$
$798$			6.71408e17i			0.0920381i
$799$	−4.37409e18	−	2.52538e18i	−0.594749	−	0.343378i
$800$	−9.87863e18	−	5.70343e18i	−1.33233	−	0.769221i
$801$			9.52853e18i			1.27472i
$802$	−1.35324e18	+	2.34389e18i	−0.179574	+	0.311031i
$803$	−2.85216e18	−	4.94008e18i	−0.375424	−	0.650254i
$804$	−6.96180e18	+	4.01940e18i	−0.908987	+	0.524804i
$805$	−4.71821e18			−0.611089
$806$	4.15166e17	+	1.41690e18i	0.0533389	+	0.182037i
$807$	1.09520e19			1.39577
$808$	2.18285e18	−	1.26027e18i	0.275962	−	0.159327i
$809$	−5.37385e18	−	9.30777e18i	−0.673938	−	1.16729i	−0.976778	−	0.214253i	$-0.931268\pi$
$809$	−5.37385e18	−	9.30777e18i	−0.673938	−	1.16729i	0.302840	−	0.953041i	$-0.402065\pi$
$810$	−3.90093e18	+	6.75661e18i	−0.485306	+	0.840574i
$811$		−	1.23664e19i		−	1.52618i	−0.646290	−	0.763092i	$-0.723680\pi$
$811$		−	1.23664e19i		−	1.52618i	0.646290	−	0.763092i	$-0.276320\pi$
$812$	−3.57846e18	−	2.06603e18i	−0.438109	−	0.252942i
$813$	1.02037e19	+	5.89111e18i	1.23928	+	0.715499i
$814$		−	2.87786e18i		−	0.346745i
$815$	−3.19488e17	+	5.53369e17i	−0.0381882	+	0.0661439i
$816$	1.98674e18	+	3.44114e18i	0.235589	+	0.408053i
$817$	5.70319e17	−	3.29274e17i	0.0670926	−	0.0387359i
$818$	−1.23927e18			−0.144634
$819$	−5.23741e18	+	1.53462e18i	−0.606417	+	0.177687i
$820$	8.69131e18			0.998378
$821$	−1.76468e18	+	1.01884e18i	−0.201111	+	0.116111i	−0.597174	−	0.802112i	$-0.703710\pi$
$821$	−1.76468e18	+	1.01884e18i	−0.201111	+	0.116111i	0.396063	+	0.918223i	$0.370376\pi$
$822$	2.13389e18	+	3.69601e18i	0.241271	+	0.417894i
$823$	5.34394e17	−	9.25598e17i	0.0599464	−	0.103830i	−0.834495	−	0.551016i	$-0.814240\pi$
$823$	5.34394e17	−	9.25598e17i	0.0599464	−	0.103830i	0.894441	+	0.447186i	$0.147574\pi$
$824$			4.57392e18i			0.509051i
$825$	−1.29304e19	−	7.46538e18i	−1.42778	−	0.824330i
$826$	−6.09973e18	−	3.52168e18i	−0.668252	−	0.385816i
$827$		−	1.16347e19i		−	1.26465i	−0.774705	−	0.632323i	$-0.782101\pi$
$827$		−	1.16347e19i		−	1.26465i	0.774705	−	0.632323i	$-0.217899\pi$
$828$	1.79149e18	−	3.10294e18i	0.193204	−	0.334639i
$829$	5.94079e18	+	1.02897e19i	0.635681	+	1.10103i	0.986370	+	0.164540i	$0.0526141\pi$
$829$	5.94079e18	+	1.02897e19i	0.635681	+	1.10103i	−0.350689	+	0.936492i	$0.614053\pi$
$830$	−1.54834e19	+	8.93934e18i	−1.64384	+	0.949069i
$831$	6.46276e17			0.0680787
$832$	8.08286e18	+	1.96573e18i	0.844819	+	0.205458i
$833$	−8.85677e18			−0.918507
$834$	1.25728e19	−	7.25888e18i	1.29375	−	0.746948i
$835$	8.41137e18	+	1.45689e19i	0.858825	+	1.48753i
$836$	−2.60664e17	+	4.51484e17i	−0.0264083	+	0.0457405i
$837$		−	5.71711e17i		−	0.0574726i
$838$	−1.02136e19	−	5.89683e18i	−1.01881	−	0.588210i
$839$	6.61517e18	+	3.81927e18i	0.654770	+	0.378031i	0.790281	−	0.612744i	$-0.209934\pi$
$839$	6.61517e18	+	3.81927e18i	0.654770	+	0.378031i	−0.135512	+	0.990776i	$0.543268\pi$
$840$			1.44075e19i			1.41506i
$841$	−1.19203e19	+	2.06465e19i	−1.16175	+	2.01221i
$842$	4.27971e18	+	7.41268e18i	0.413891	+	0.716880i
$843$	2.04871e19	−	1.18283e19i	1.96608	−	1.13512i
$844$	5.77382e17			0.0549841
$845$	8.03372e18	−	1.55400e19i	0.759186	−	1.46853i
$846$	−4.48077e18			−0.420190
$847$	2.96755e18	−	1.71332e18i	0.276157	−	0.159439i
$848$	−2.07211e18	−	3.58900e18i	−0.191355	−	0.331436i
$849$	8.18982e18	−	1.41852e19i	0.750540	−	1.29997i
$850$		−	1.77292e19i		−	1.61237i
$851$	−4.87142e18	−	2.81251e18i	−0.439656	−	0.253836i
$852$	1.44116e18	+	8.32052e17i	0.129078	+	0.0745235i
$853$			1.25220e19i			1.11303i	0.830839	+	0.556513i	$0.187861\pi$
$853$			1.25220e19i			1.11303i	−0.830839	+	0.556513i	$0.812139\pi$
$854$	−1.95707e18	+	3.38974e18i	−0.172635	+	0.299013i
$855$	1.74857e18	+	3.02860e18i	0.153074	+	0.265132i
$856$	−8.80914e18	+	5.08596e18i	−0.765339	+	0.441869i
$857$	1.12470e19			0.969754			0.484877	−	0.874582i	$-0.338864\pi$
$857$	1.12470e19			0.969754			0.484877	+	0.874582i	$0.338864\pi$
$858$	7.61465e18	+	1.85186e18i	0.651602	+	0.158468i
$859$	−7.24801e18			−0.615550			−0.307775	−	0.951459i	$-0.599584\pi$
$859$	−7.24801e18			−0.615550			−0.307775	+	0.951459i	$0.599584\pi$
$860$	4.09655e18	−	2.36515e18i	0.345286	−	0.199351i
$861$	−5.79581e18	−	1.00386e19i	−0.484835	−	0.839759i
$862$	−2.14311e18	+	3.71197e18i	−0.177929	+	0.308182i
$863$		−	1.97250e19i		−	1.62535i	−0.582716	−	0.812676i	$-0.698010\pi$
$863$		−	1.97250e19i		−	1.62535i	0.582716	−	0.812676i	$-0.301990\pi$
$864$	−2.00769e18	−	1.15914e18i	−0.164194	−	0.0947973i
$865$	2.61240e18	+	1.50827e18i	0.212049	+	0.122426i
$866$		−	5.00561e18i		−	0.403265i
$867$	6.80025e18	−	1.17784e19i	0.543751	−	0.941805i
$868$	4.70476e17	+	8.14888e17i	0.0373387	+	0.0646725i
$869$	1.01732e19	−	5.87350e18i	0.801363	−	0.462667i
$870$	3.98008e19			3.11183
$871$	−1.76101e19	+	5.15997e18i	−1.36661	+	0.400432i
$872$	3.79396e18			0.292238
$873$	−2.59156e17	+	1.49624e17i	−0.0198138	+	0.0114395i
$874$	−5.03101e17	−	8.71397e17i	−0.0381796	−	0.0661289i
$875$	4.43558e18	−	7.68266e18i	0.334117	−	0.578708i
$876$			1.13964e19i			0.852103i
$877$	1.60928e19	+	9.29117e18i	1.19436	+	0.689562i	0.959291	−	0.282418i	$-0.0911365\pi$
$877$	1.60928e19	+	9.29117e18i	1.19436	+	0.689562i	0.235064	+	0.971980i	$0.424470\pi$
$878$	−1.48604e19	−	8.57967e18i	−1.09476	−	0.632057i
$879$		−	7.05232e18i		−	0.515709i
$880$	1.80217e18	−	3.12145e18i	0.130815	−	0.226579i
$881$	3.59685e18	+	6.22993e18i	0.259167	+	0.448890i	0.966019	−	0.258471i	$-0.0832187\pi$
$881$	3.59685e18	+	6.22993e18i	0.259167	+	0.448890i	−0.706852	+	0.707361i	$0.749885\pi$
$882$	−6.80458e18	+	3.92863e18i	−0.486693	+	0.280993i
$883$	−2.17963e19			−1.54753			−0.773763	−	0.633476i	$-0.781628\pi$
$883$	−2.17963e19			−1.54753			−0.773763	+	0.633476i	$0.781628\pi$
$884$	−2.64980e18	−	9.04335e18i	−0.186756	−	0.637367i
$885$	−6.87048e19			−4.80680
$886$	3.00937e17	−	1.73746e17i	0.0209005	−	0.0120669i
$887$	−3.73952e18	−	6.47704e18i	−0.257818	−	0.446553i	0.707839	−	0.706373i	$-0.249670\pi$
$887$	−3.73952e18	−	6.47704e18i	−0.257818	−	0.446553i	−0.965657	+	0.259820i	$0.916337\pi$
$888$	−8.58828e18	+	1.48753e19i	−0.587790	+	1.01808i
$889$		−	4.08691e17i		−	0.0277673i
$890$	1.66456e19	+	9.61034e18i	1.12270	+	0.648192i
$891$	6.99701e18	+	4.03973e18i	0.468498	+	0.270487i
$892$			2.03868e17i			0.0135512i
$893$	6.37157e17	−	1.10359e18i	0.0420447	−	0.0728236i
$894$	−4.69698e18	−	8.13542e18i	−0.307698	−	0.532949i
$895$	2.86785e19	−	1.65575e19i	1.86512	−	1.07683i
$896$	2.34836e18			0.151622
$897$	1.05764e19	−	1.10797e19i	0.677936	−	0.710193i
$898$	6.58211e18			0.418860
$899$	6.72515e18	−	3.88277e18i	0.424878	−	0.245303i
$900$	7.96407e18	+	1.37942e19i	0.499527	+	0.865206i
$901$	−1.66458e19	+	2.88314e19i	−1.03656	+	1.79537i
$902$			8.88767e18i			0.549472i
$903$	−5.46359e18	−	3.15440e18i	−0.335357	−	0.193619i
$904$	7.33161e18	+	4.23291e18i	0.446791	+	0.257955i
$905$			1.79996e19i			1.08905i
$906$	−3.93865e18	+	6.82194e18i	−0.236600	+	0.409802i
$907$	−8.17972e18	−	1.41677e19i	−0.487855	−	0.844990i	0.512047	−	0.858957i	$-0.328887\pi$
$907$	−8.17972e18	−	1.41677e19i	−0.487855	−	0.844990i	−0.999902	+	0.0139671i	$0.995554\pi$
$908$	−9.59816e18	+	5.54150e18i	−0.568368	+	0.328148i
$909$	−5.86105e18			−0.344596
$910$	−2.60152e18	+	1.06971e19i	−0.151865	+	0.624451i
$911$	1.16478e19			0.675108			0.337554	−	0.941306i	$-0.390400\pi$
$911$	1.16478e19			0.675108			0.337554	+	0.941306i	$0.390400\pi$
$912$	−8.68204e17	+	5.01258e17i	−0.0499638	+	0.0288466i
$913$	9.25742e18	+	1.60343e19i	0.528968	+	0.916200i
$914$	6.41985e18	−	1.11195e19i	0.364229	−	0.630863i
$915$			3.81806e19i			2.15083i
$916$	6.95649e18	+	4.01633e18i	0.389107	+	0.224651i
$917$	−1.15662e19	−	6.67773e18i	−0.642375	−	0.370876i
$918$		−	3.60319e18i		−	0.198705i
$919$	−6.95909e18	+	1.20535e19i	−0.381067	+	0.660028i	−0.991215	−	0.132260i	$-0.957777\pi$
$919$	−6.95909e18	+	1.20535e19i	−0.381067	+	0.660028i	0.610148	+	0.792288i	$0.291110\pi$
$920$	−1.07959e19	−	1.86990e19i	−0.586998	−	1.01671i
$921$	−1.49126e19	+	8.60982e18i	−0.805132	+	0.464843i
$922$	−1.04834e19			−0.562022
$923$	2.74778e18	+	2.62298e18i	0.146275	+	0.139632i
$924$	4.99426e18			0.264000
$925$	2.16560e19	−	1.25031e19i	1.13673	−	0.656289i
$926$	4.11860e18	+	7.13362e18i	0.214673	+	0.371825i
$927$	5.31791e18	−	9.21090e18i	0.275247	−	0.476742i
$928$		−	3.14891e19i		−	1.61845i
$929$	−1.62776e19	−	9.39787e18i	−0.830784	−	0.479653i	0.0233371	−	0.999728i	$-0.492571\pi$
$929$	−1.62776e19	−	9.39787e18i	−0.830784	−	0.479653i	−0.854121	+	0.520074i	$0.825904\pi$
$930$	−7.84917e18	−	4.53172e18i	−0.397818	−	0.229680i
$931$		−	2.23457e18i		−	0.112466i
$932$	5.49301e18	−	9.51417e18i	0.274541	−	0.475518i
$933$	2.71669e18	+	4.70545e18i	0.134837	+	0.233545i
$934$	3.46006e18	−	1.99767e18i	0.170541	−	0.0984619i
$935$	−2.89547e19			−1.41724
$936$	−1.80658e19	−	1.72453e19i	−0.878140	−	0.838256i
$937$	4.02408e17			0.0194249			0.00971245	−	0.999953i	$-0.496908\pi$
$937$	4.02408e17			0.0194249			0.00971245	+	0.999953i	$0.496908\pi$
$938$	1.00010e19	−	5.77406e18i	0.479428	−	0.276798i
$939$	1.31663e19	+	2.28047e19i	0.626813	+	1.08567i
$940$	4.57664e18	−	7.92698e18i	0.216379	−	0.374780i
$941$		−	5.28505e18i		−	0.248151i	−0.992273	−	0.124076i	$-0.960403\pi$
$941$		−	5.28505e18i		−	0.248151i	0.992273	−	0.124076i	$-0.0395965\pi$
$942$	−6.26834e18	−	3.61903e18i	−0.292295	−	0.168757i
$943$	1.50444e19	+	8.68586e18i	0.696703	+	0.402242i
$944$		−	1.05168e19i		−	0.483689i
$945$	2.13142e18	−	3.69172e18i	0.0973557	−	0.168625i
$946$	2.41858e18	+	4.18910e18i	0.109716	+	0.190033i
$947$	−2.52549e18	+	1.45809e18i	−0.113781	+	0.0656916i	−0.555811	−	0.831309i	$-0.687592\pi$
$947$	−2.52549e18	+	1.45809e18i	−0.113781	+	0.0656916i	0.442029	+	0.897001i	$0.354259\pi$
$948$	−2.34689e19			−1.05012
$949$	−6.14763e18	+	2.52783e19i	−0.273198	+	1.12336i
$950$	4.47308e18			0.197426
$951$	3.23542e19	−	1.86797e19i	1.41826	−	0.818834i
$952$	8.85828e18	+	1.53430e19i	0.385664	+	0.667990i
$953$	−2.77981e18	+	4.81478e18i	−0.120202	+	0.208196i	−0.919847	−	0.392277i	$-0.871688\pi$
$953$	−2.77981e18	+	4.81478e18i	−0.120202	+	0.208196i	0.799645	+	0.600473i	$0.205021\pi$
$954$			2.95346e19i			1.26843i
$955$	6.65785e18	+	3.84391e18i	0.283996	+	0.163965i
$956$	−3.91083e17	−	2.25792e17i	−0.0165689	−	0.00956603i
$957$		−	4.12169e19i		−	1.73439i
$958$	1.05932e19	−	1.83479e19i	0.442742	−	0.766852i
$959$	3.10437e18	+	5.37693e18i	0.128870	+	0.223210i
$960$	−4.42225e19	+	2.55318e19i	−1.82339	+	1.05274i
$961$	2.26492e19			0.927578
$962$	−9.06253e18	+	9.49373e18i	−0.368648	+	0.386188i
$963$	2.36530e19			0.955685
$964$	−1.44170e19	+	8.32365e18i	−0.578594	+	0.334051i
$965$	−5.99433e18	−	1.03825e19i	−0.238953	−	0.413879i
$966$	−4.81965e18	+	8.34787e18i	−0.190838	+	0.330540i
$967$		−	3.47397e19i		−	1.36632i	−0.730267	−	0.683162i	$-0.760604\pi$
$967$		−	3.47397e19i		−	1.36632i	0.730267	−	0.683162i	$-0.239396\pi$
$968$	1.35803e19	+	7.84057e18i	0.530540	+	0.306308i
$969$	6.97453e18	+	4.02675e18i	0.270651	+	0.156261i
$970$			6.03633e17i			0.0232679i
$971$	−1.81601e19	+	3.14543e19i	−0.695335	+	1.20436i	0.274733	+	0.961521i	$0.411411\pi$
$971$	−1.81601e19	+	3.14543e19i	−0.695335	+	1.20436i	−0.970068	+	0.242835i	$0.921923\pi$
$972$	−9.48344e18	−	1.64258e19i	−0.360691	−	0.624735i
$973$	1.82908e19	−	1.05602e19i	0.691033	−	0.398968i
$974$	−1.21406e19			−0.455625
$975$	1.91471e19	+	6.53460e19i	0.713794	+	2.43606i
$976$	−5.84440e18			−0.216429
$977$	2.69907e19	−	1.55831e19i	0.992887	−	0.573244i	0.0867510	−	0.996230i	$-0.472352\pi$
$977$	2.69907e19	−	1.55831e19i	0.992887	−	0.573244i	0.906136	+	0.422986i	$0.139018\pi$
$978$	6.52712e17	+	1.13053e18i	0.0238517	+	0.0413123i
$979$	9.95228e18	−	1.72379e19i	0.361273	−	0.625743i
$980$		−	1.60507e19i		−	0.578796i
$981$	−7.64023e18	−	4.41109e18i	−0.273689	−	0.158015i
$982$	−1.03357e19	−	5.96732e18i	−0.367803	−	0.212351i
$983$			3.51180e19i			1.24146i	0.784025	+	0.620729i	$0.213163\pi$
$983$			3.51180e19i			1.24146i	−0.784025	+	0.620729i	$0.786837\pi$
$984$	2.65231e19	−	4.59394e19i	0.931444	−	1.61331i
$985$	−2.26401e19	−	3.92138e19i	−0.789846	−	1.36805i
$986$	4.23850e19	−	2.44710e19i	1.46897	−	0.848109i
$987$	−1.22078e19			−0.420315
$988$	2.28165e18	−	6.68548e17i	0.0780420	−	0.0228672i
$989$	9.45466e18			0.321270
$990$	−2.22457e19	+	1.28436e19i	−0.750960	+	0.433567i
$991$	−2.57722e19	−	4.46387e19i	−0.864316	−	1.49704i	−0.867725	−	0.497045i	$-0.834418\pi$
$991$	−2.57722e19	−	4.46387e19i	−0.864316	−	1.49704i	0.00340909	−	0.999994i	$-0.498915\pi$
$992$	−3.58535e18	+	6.21001e18i	−0.119455	+	0.206903i
$993$			3.25429e19i			1.07717i
$994$	−2.07029e18	−	1.19528e18i	−0.0680800	−	0.0393060i
$995$	−4.12482e18	−	2.38146e18i	−0.134758	−	0.0778026i
$996$		−	3.69901e19i		−	1.20060i
$997$	4.69042e18	−	8.12405e18i	0.151249	−	0.261972i	−0.780438	−	0.625234i	$-0.785004\pi$
$997$	4.69042e18	−	8.12405e18i	0.151249	−	0.261972i	0.931687	+	0.363262i	$0.118337\pi$
$998$	3.40894e18	+	5.90445e18i	0.109212	+	0.189161i
$999$	4.40125e18	−	2.54106e18i	0.140088	−	0.0808798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.14.e.a.10.6	yes	30
13.2	odd	12		169.14.a.f.1.12		30
13.4	even	6	inner	13.14.e.a.4.6	✓	30
13.11	odd	12		169.14.a.f.1.19		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.14.e.a.4.6	✓	30	13.4	even	6	inner
13.14.e.a.10.6	yes	30	1.1	even	1	trivial
169.14.a.f.1.12		30	13.2	odd	12
169.14.a.f.1.19		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+(-55.2505 + 31.8989i) q^{2} +(924.809 + 1601.82i) q^{3} +(-2060.92 + 3569.63i) q^{4} -57759.0i q^{5} +(-102192. - 59000.7i) q^{6} +(-148669. - 85833.9i) q^{7} -785596. i q^{8} +(-913381. + 1.58202e6i) q^{9} +(1.84245e6 + 3.19121e6i) q^{10} +(3.30476e6 - 1.90800e6i) q^{11} -7.62384e6 q^{12} +(-1.69104e7 - 4.11257e6i) q^{13} +1.09520e7 q^{14} +(9.25192e7 - 5.34160e7i) q^{15} +(8.17652e6 + 1.41621e7i) q^{16} +(6.56843e7 - 1.13769e8i) q^{17} -1.16543e8i q^{18} +(2.87039e7 + 1.65722e7i) q^{19} +(2.06178e8 + 1.19037e8i) q^{20} -3.17520e8i q^{21} +(-1.21726e8 + 2.10836e8i) q^{22} +(2.37925e8 + 4.12097e8i) q^{23} +(1.25838e9 - 7.26526e8i) q^{24} -2.11539e9 q^{25} +(1.06549e9 - 3.12202e8i) q^{26} -4.29922e8 q^{27} +(6.12790e8 - 3.53794e8i) q^{28} +(-2.91981e9 - 5.05726e9i) q^{29} +(-3.40782e9 + 5.90251e9i) q^{30} +1.32980e9i q^{31} +(4.66988e9 + 2.69616e9i) q^{32} +(6.11253e9 + 3.52907e9i) q^{33} +8.38102e9i q^{34} +(-4.95768e9 + 8.58695e9i) q^{35} +(-3.76482e9 - 6.52086e9i) q^{36} +(-1.02373e10 + 5.91052e9i) q^{37} -2.11454e9 q^{38} +(-9.05131e9 - 3.08907e10i) q^{39} -4.53752e10 q^{40} +(3.16158e10 - 1.82534e10i) q^{41} +(1.01285e10 + 1.75431e10i) q^{42} +(9.93451e9 - 1.72071e10i) q^{43} +1.57290e10i q^{44} +(9.13759e10 + 5.27559e10i) q^{45} +(-2.62909e10 - 1.51790e10i) q^{46} -3.84473e10i q^{47} +(-1.51234e10 + 2.61945e10i) q^{48} +(-3.37096e10 - 5.83867e10i) q^{49} +(1.16876e11 - 6.74787e10i) q^{50} +2.42982e11 q^{51} +(4.95314e10 - 5.18881e10i) q^{52} -2.53422e11 q^{53} +(2.37534e10 - 1.37140e10i) q^{54} +(-1.10204e11 - 1.90879e11i) q^{55} +(-6.74307e10 + 1.16793e11i) q^{56} +6.13045e10i q^{57} +(3.22642e11 + 1.86277e11i) q^{58} +(-5.56951e11 - 3.21556e11i) q^{59} +4.40345e11i q^{60} +(-1.78695e11 + 3.09508e11i) q^{61} +(-4.24191e10 - 7.34721e10i) q^{62} +(2.71582e11 - 1.56798e11i) q^{63} -4.77981e11 q^{64} +(-2.37538e11 + 9.76727e11i) q^{65} -4.50294e11 q^{66} +(9.13162e11 - 5.27214e11i) q^{67} +(2.70741e11 + 4.68937e11i) q^{68} +(-4.40069e11 + 7.62223e11i) q^{69} -6.32577e11i q^{70} +(-1.89033e11 - 1.09138e11i) q^{71} +(1.24283e12 + 7.17548e11i) q^{72} -1.49484e12i q^{73} +(3.77078e11 - 6.53118e11i) q^{74} +(-1.95633e12 - 3.38847e12i) q^{75} +(-1.18313e11 + 6.83082e10i) q^{76} -6.55085e11 q^{77} +(1.48547e12 + 1.41800e12i) q^{78} +3.07835e12 q^{79} +(8.17991e11 - 4.72267e11i) q^{80} +(1.05863e12 + 1.83360e12i) q^{81} +(-1.16453e12 + 2.01702e12i) q^{82} +4.85189e12i q^{83} +(1.13343e12 + 6.54384e11i) q^{84} +(-6.57115e12 - 3.79386e12i) q^{85} +1.26760e12i q^{86} +(5.40054e12 - 9.35400e12i) q^{87} +(-1.49892e12 - 2.59620e12i) q^{88} +(4.51726e12 - 2.60804e12i) q^{89} -6.73142e12 q^{90} +(2.16105e12 + 2.06290e12i) q^{91} -1.96138e12 q^{92} +(-2.13010e12 + 1.22981e12i) q^{93} +(1.22642e12 + 2.12423e12i) q^{94} +(9.57194e11 - 1.65791e12i) q^{95} +9.97372e12i q^{96} +(1.41866e11 + 8.19065e10i) q^{97} +(3.72494e12 + 2.15060e12i) q^{98} +6.97093e12i 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more