LMFDB - Embedded newform 230.2.j.a.119.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(9,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 10]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("230.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.j (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$12$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			119.3
Character	$\chi$	$=$	230.119
Dual form			230.2.j.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909632 + 0.415415i) q^{2} +(0.0359844 + 0.122552i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.96836 - 1.06092i) q^{5} +(-0.0836423 - 0.0965284i) q^{6} +(-0.277941 + 0.0399619i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.51004 - 1.61310i) q^{9} +O(q^{10})$	\(q+(-0.909632 + 0.415415i) q^{2} +(0.0359844 + 0.122552i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.96836 - 1.06092i) q^{5} +(-0.0836423 - 0.0965284i) q^{6} +(-0.277941 + 0.0399619i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.51004 - 1.61310i) q^{9} +(2.23121 + 0.147361i) q^{10} +(2.07071 - 4.53422i) q^{11} +(0.116183 + 0.0530590i) q^{12} +(-3.69726 - 0.531586i) q^{13} +(0.236223 - 0.151811i) q^{14} +(0.0591873 - 0.279402i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(5.80355 - 5.02880i) q^{17} +(-1.61310 + 2.51004i) q^{18} +(-2.73415 + 3.15538i) q^{19} +(-2.09079 + 0.792833i) q^{20} +(-0.0148989 - 0.0326241i) q^{21} +4.98467i q^{22} +(0.919072 - 4.70694i) q^{23} -0.127725 q^{24} +(2.74889 + 4.17655i) q^{25} +(3.58398 - 1.05235i) q^{26} +(0.577595 + 0.500489i) q^{27} +(-0.151811 + 0.236223i) q^{28} +(-1.53549 - 1.77205i) q^{29} +(0.0622293 + 0.278741i) q^{30} +(3.18900 + 0.936376i) q^{31} +(0.540641 + 0.841254i) q^{32} +(0.630188 + 0.0906074i) q^{33} +(-3.19005 + 6.98524i) q^{34} +(0.589484 + 0.216214i) q^{35} +(0.424623 - 2.95332i) q^{36} +(-4.55996 - 7.09543i) q^{37} +(1.17628 - 4.00604i) q^{38} +(-0.0678970 - 0.472234i) q^{39} +(1.57250 - 1.58973i) q^{40} +(1.35119 + 0.868354i) q^{41} +(0.0271051 + 0.0234867i) q^{42} +(2.28629 + 7.78640i) q^{43} +(-2.07071 - 4.53422i) q^{44} +(-6.65203 + 0.512218i) q^{45} +(1.11932 + 4.66338i) q^{46} +5.98632i q^{47} +(0.116183 - 0.0530590i) q^{48} +(-6.64080 + 1.94991i) q^{49} +(-4.23548 - 2.65719i) q^{50} +(0.825125 + 0.530276i) q^{51} +(-2.82294 + 2.44609i) q^{52} +(-10.5552 + 1.51760i) q^{53} +(-0.733310 - 0.215319i) q^{54} +(-8.88634 + 6.72812i) q^{55} +(0.0399619 - 0.277941i) q^{56} +(-0.485083 - 0.221530i) q^{57} +(2.13286 + 0.974046i) q^{58} +(-1.46074 + 10.1597i) q^{59} +(-0.172399 - 0.227700i) q^{60} +(10.4089 + 3.05634i) q^{61} +(-3.28980 + 0.473003i) q^{62} +(-0.633179 + 0.548653i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(6.71358 + 4.96886i) q^{65} +(-0.610879 + 0.179370i) q^{66} +(8.30299 - 3.79185i) q^{67} -7.67920i q^{68} +(0.609915 - 0.0567427i) q^{69} +(-0.626032 + 0.0482056i) q^{70} +(-1.57188 - 3.44193i) q^{71} +(0.840602 + 2.86283i) q^{72} +(-7.70105 - 6.67300i) q^{73} +(7.09543 + 4.55996i) q^{74} +(-0.412926 + 0.487172i) q^{75} +(0.594188 + 4.13267i) q^{76} +(-0.394338 + 1.34299i) q^{77} +(0.257934 + 0.401354i) q^{78} +(0.687186 - 4.77948i) q^{79} +(-0.769995 + 2.09931i) q^{80} +(3.67785 - 8.05337i) q^{81} +(-1.58981 - 0.228580i) q^{82} +(6.83669 + 10.6381i) q^{83} +(-0.0344123 - 0.0101044i) q^{84} +(-16.7586 + 3.74140i) q^{85} +(-5.31428 - 6.13300i) q^{86} +(0.161914 - 0.251942i) q^{87} +(3.76716 + 3.26427i) q^{88} +(-5.36601 + 1.57560i) q^{89} +(5.83812 - 3.22928i) q^{90} +1.04886 q^{91} +(-2.95541 - 3.77698i) q^{92} +0.424512i q^{93} +(-2.48681 - 5.44534i) q^{94} +(8.72941 - 3.31021i) q^{95} +(-0.0836423 + 0.0965284i) q^{96} +(2.46614 - 3.83739i) q^{97} +(5.23066 - 4.53239i) q^{98} +(-2.11660 - 14.7213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	$ 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) $ 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{2}{11}\right)$

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 $

$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$2$	−0.909632	+	0.415415i	−0.643207	+	0.293743i
$3$	0.0359844	+	0.122552i	0.0207756	+	0.0707552i	0.969228	−	0.246163i	$-0.0791700\pi$
$3$	0.0359844	+	0.122552i	0.0207756	+	0.0707552i	−0.948453	+	0.316919i	$0.897352\pi$
$4$	0.654861	−	0.755750i	0.327430	−	0.377875i
$5$	−1.96836	−	1.06092i	−0.880278	−	0.474458i
$5$	−1.96836	−	1.06092i	−0.880278	−	0.474458i
$6$	−0.0836423	−	0.0965284i	−0.0341468	−	0.0394075i
$7$	−0.277941	+	0.0399619i	−0.105052	+	0.0151042i	−0.194640	−	0.980875i	$-0.562354\pi$
$7$	−0.277941	+	0.0399619i	−0.105052	+	0.0151042i	0.0895884	+	0.995979i	$0.471445\pi$
$8$	−0.281733	+	0.959493i	−0.0996075	+	0.339232i
$9$	2.51004	−	1.61310i	0.836679	−	0.537701i
$10$	2.23121	+	0.147361i	0.705570	+	0.0465996i
$11$	2.07071	−	4.53422i	0.624342	−	1.36712i	−0.287977	−	0.957637i	$-0.592983\pi$
$11$	2.07071	−	4.53422i	0.624342	−	1.36712i	0.912319	−	0.409480i	$-0.134290\pi$
$12$	0.116183	+	0.0530590i	0.0335392	+	0.0153168i
$13$	−3.69726	−	0.531586i	−1.02544	−	0.147435i	−0.390984	−	0.920397i	$-0.627865\pi$
$13$	−3.69726	−	0.531586i	−1.02544	−	0.147435i	−0.634452	+	0.772962i	$0.718774\pi$
$14$	0.236223	−	0.151811i	0.0631333	−	0.0405733i
$15$	0.0591873	−	0.279402i	0.0152821	−	0.0721414i
$16$	−0.142315	−	0.989821i	−0.0355787	−	0.247455i
$17$	5.80355	−	5.02880i	1.40757	−	1.21966i	0.465147	−	0.885233i	$-0.346001\pi$
$17$	5.80355	−	5.02880i	1.40757	−	1.21966i	0.942420	−	0.334431i	$-0.108544\pi$
$18$	−1.61310	+	2.51004i	−0.380212	+	0.591621i
$19$	−2.73415	+	3.15538i	−0.627258	+	0.723894i	−0.977068	−	0.212927i	$-0.931700\pi$
$19$	−2.73415	+	3.15538i	−0.627258	+	0.723894i	0.349811	+	0.936820i	$0.386246\pi$
$20$	−2.09079	+	0.792833i	−0.467516	+	0.177283i
$21$	−0.0148989	−	0.0326241i	−0.00325121	−	0.00711916i
$22$			4.98467i			1.06274i
$23$	0.919072	−	4.70694i	0.191640	−	0.981465i
$23$	0.919072	−	4.70694i	0.191640	−	0.981465i
$24$	−0.127725			−0.0260718
$25$	2.74889	+	4.17655i	0.549779	+	0.835310i
$26$	3.58398	−	1.05235i	0.702876	−	0.206383i
$27$	0.577595	+	0.500489i	0.111158	+	0.0963192i
$28$	−0.151811	+	0.236223i	−0.0286897	+	0.0446420i
$29$	−1.53549	−	1.77205i	−0.285133	−	0.329061i	0.595056	−	0.803684i	$-0.297130\pi$
$29$	−1.53549	−	1.77205i	−0.285133	−	0.329061i	−0.880189	+	0.474623i	$0.842584\pi$
$30$	0.0622293	+	0.278741i	0.0113615	+	0.0508908i
$31$	3.18900	+	0.936376i	0.572762	+	0.168178i	0.555272	−	0.831669i	$-0.312614\pi$
$31$	3.18900	+	0.936376i	0.572762	+	0.168178i	0.0174902	+	0.999847i	$0.494432\pi$
$32$	0.540641	+	0.841254i	0.0955727	+	0.148714i
$33$	0.630188	+	0.0906074i	0.109702	+	0.0157727i
$34$	−3.19005	+	6.98524i	−0.547090	+	1.19796i
$35$	0.589484	+	0.216214i	0.0996410	+	0.0365468i
$36$	0.424623	−	2.95332i	0.0707705	−	0.492219i
$37$	−4.55996	−	7.09543i	−0.749652	−	1.16648i	−0.981075	−	0.193628i	$-0.937974\pi$
$37$	−4.55996	−	7.09543i	−0.749652	−	1.16648i	0.231423	−	0.972853i	$-0.425662\pi$
$38$	1.17628	−	4.00604i	0.190818	−	0.649866i
$39$	−0.0678970	−	0.472234i	−0.0108722	−	0.0756180i
$40$	1.57250	−	1.58973i	0.248634	−	0.251359i
$41$	1.35119	+	0.868354i	0.211020	+	0.135614i	0.641882	−	0.766804i	$-0.278154\pi$
$41$	1.35119	+	0.868354i	0.211020	+	0.135614i	−0.430862	+	0.902418i	$0.641790\pi$
$42$	0.0271051	+	0.0234867i	0.00418240	+	0.00362407i
$43$	2.28629	+	7.78640i	0.348657	+	1.18742i	0.928078	+	0.372387i	$0.121461\pi$
$43$	2.28629	+	7.78640i	0.348657	+	1.18742i	−0.579421	+	0.815028i	$0.696721\pi$
$44$	−2.07071	−	4.53422i	−0.312171	−	0.683559i
$45$	−6.65203	+	0.512218i	−0.991627	+	0.0763570i
$46$	1.11932	+	4.66338i	0.165034	+	0.687578i
$47$			5.98632i			0.873194i	0.899657	+	0.436597i	$0.143816\pi$
$47$			5.98632i			0.873194i	−0.899657	+	0.436597i	$0.856184\pi$
$48$	0.116183	−	0.0530590i	0.0167696	−	0.00765841i
$49$	−6.64080	+	1.94991i	−0.948685	+	0.278559i
$50$	−4.23548	−	2.65719i	−0.598988	−	0.375784i
$51$	0.825125	+	0.530276i	0.115541	+	0.0742534i
$52$	−2.82294	+	2.44609i	−0.391471	+	0.339212i
$53$	−10.5552	+	1.51760i	−1.44986	+	0.208459i	−0.821832	−	0.569731i	$-0.807048\pi$
$53$	−10.5552	+	1.51760i	−1.44986	+	0.208459i	−0.628030	+	0.778189i	$0.716138\pi$
$54$	−0.733310	−	0.215319i	−0.0997909	−	0.0293012i
$55$	−8.88634	+	6.72812i	−1.19823	+	0.907219i
$56$	0.0399619	−	0.277941i	0.00534013	−	0.0371414i
$57$	−0.485083	−	0.221530i	−0.0642509	−	0.0293424i
$58$	2.13286	+	0.974046i	0.280059	+	0.127899i
$59$	−1.46074	+	10.1597i	−0.190173	+	1.32268i	0.641375	+	0.767227i	$0.278364\pi$
$59$	−1.46074	+	10.1597i	−0.190173	+	1.32268i	−0.831548	+	0.555453i	$0.812545\pi$
$60$	−0.172399	−	0.227700i	−0.0222566	−	0.0293960i
$61$	10.4089	+	3.05634i	1.33273	+	0.391325i	0.869070	−	0.494689i	$-0.164718\pi$
$61$	10.4089	+	3.05634i	1.33273	+	0.391325i	0.463659	+	0.886014i	$0.346536\pi$
$62$	−3.28980	+	0.473003i	−0.417806	+	0.0600714i
$63$	−0.633179	+	0.548653i	−0.0797731	+	0.0691238i
$64$	−0.841254	−	0.540641i	−0.105157	−	0.0675801i
$65$	6.71358	+	4.96886i	0.832717	+	0.616311i
$66$	−0.610879	+	0.179370i	−0.0751940	+	0.0220790i
$67$	8.30299	−	3.79185i	1.01437	−	0.463248i	0.162338	−	0.986735i	$-0.448097\pi$
$67$	8.30299	−	3.79185i	1.01437	−	0.463248i	0.852033	+	0.523487i	$0.175369\pi$
$68$		−	7.67920i		−	0.931239i
$69$	0.609915	−	0.0567427i	0.0734252	−	0.00683102i
$70$	−0.626032	+	0.0482056i	−0.0748252	+	0.00576167i
$71$	−1.57188	−	3.44193i	−0.186547	−	0.408482i	0.793133	−	0.609049i	$-0.208449\pi$
$71$	−1.57188	−	3.44193i	−0.186547	−	0.408482i	−0.979680	+	0.200567i	$0.935721\pi$
$72$	0.840602	+	2.86283i	0.0990658	+	0.337387i
$73$	−7.70105	−	6.67300i	−0.901340	−	0.781015i	0.0750167	−	0.997182i	$-0.476099\pi$
$73$	−7.70105	−	6.67300i	−0.901340	−	0.781015i	−0.976356	+	0.216167i	$0.930644\pi$
$74$	7.09543	+	4.55996i	0.824827	+	0.530084i
$75$	−0.412926	+	0.487172i	−0.0476806	+	0.0562537i
$76$	0.594188	+	4.13267i	0.0681580	+	0.474050i
$77$	−0.394338	+	1.34299i	−0.0449390	+	0.153048i
$78$	0.257934	+	0.401354i	0.0292053	+	0.0454444i
$79$	0.687186	−	4.77948i	0.0773145	−	0.537734i	−0.913948	−	0.405831i	$-0.866982\pi$
$79$	0.687186	−	4.77948i	0.0773145	−	0.537734i	0.991263	−	0.131903i	$-0.0421087\pi$
$80$	−0.769995	+	2.09931i	−0.0860881	+	0.234710i
$81$	3.67785	−	8.05337i	0.408650	−	0.894819i
$82$	−1.58981	−	0.228580i	−0.175565	−	0.0252424i
$83$	6.83669	+	10.6381i	0.750425	+	1.16768i	0.980882	+	0.194601i	$0.0623412\pi$
$83$	6.83669	+	10.6381i	0.750425	+	1.16768i	−0.230458	+	0.973082i	$0.574022\pi$
$84$	−0.0344123	−	0.0101044i	−0.00375469	−	0.00110248i
$85$	−16.7586	+	3.74140i	−1.81773	+	0.405811i
$86$	−5.31428	−	6.13300i	−0.573053	−	0.661339i
$87$	0.161914	−	0.251942i	0.0173590	−	0.0270111i
$88$	3.76716	+	3.26427i	0.401581	+	0.347972i
$89$	−5.36601	+	1.57560i	−0.568796	+	0.167014i	−0.553470	−	0.832869i	$-0.686697\pi$
$89$	−5.36601	+	1.57560i	−0.568796	+	0.167014i	−0.0153257	+	0.999883i	$0.504879\pi$
$90$	5.83812	−	3.22928i	0.615392	−	0.340396i
$91$	1.04886			0.109951
$92$	−2.95541	−	3.77698i	−0.308122	−	0.393777i
$93$			0.424512i			0.0440199i
$94$	−2.48681	−	5.44534i	−0.256494	−	0.561644i
$95$	8.72941	−	3.31021i	0.895618	−	0.339620i
$96$	−0.0836423	+	0.0965284i	−0.00853671	+	0.00985188i
$97$	2.46614	−	3.83739i	0.250398	−	0.389628i	−0.693186	−	0.720758i	$-0.743794\pi$
$97$	2.46614	−	3.83739i	0.250398	−	0.389628i	0.943585	+	0.331131i	$0.107430\pi$
$98$	5.23066	−	4.53239i	0.528376	−	0.457841i
$99$	−2.11660	−	14.7213i	−0.212727	−	1.47955i
$100$	4.95657	+	0.657585i	0.495657	+	0.0657585i
$101$	1.61923	−	1.04062i	0.161119	−	0.103545i	−0.457596	−	0.889160i	$-0.651290\pi$
$101$	1.61923	−	1.04062i	0.161119	−	0.103545i	0.618716	+	0.785615i	$0.287653\pi$
$102$	−0.970844	−	0.139586i	−0.0961279	−	0.0138211i
$103$	13.7653	+	6.28640i	1.35633	+	0.619417i	0.955025	−	0.296525i	$-0.0958279\pi$
$103$	13.7653	+	6.28640i	1.35633	+	0.619417i	0.401310	+	0.915943i	$0.368555\pi$
$104$	1.55169	−	3.39773i	0.152156	−	0.333175i
$105$	−0.00528512	+	0.0800225i	−0.000515775	+	0.00780940i
$106$	8.97087	−	5.76523i	0.871328	−	0.559968i
$107$	2.00341	−	6.82299i	0.193677	−	0.659603i	−0.804193	−	0.594368i	$-0.797402\pi$
$107$	2.00341	−	6.82299i	0.193677	−	0.659603i	0.997870	−	0.0652348i	$-0.0207796\pi$
$108$	0.756489	−	0.108767i	0.0727932	−	0.0104661i
$109$	6.96543	+	8.03854i	0.667167	+	0.769952i	0.983930	−	0.178553i	$-0.0571415\pi$
$109$	6.96543	+	8.03854i	0.667167	+	0.769952i	−0.316763	+	0.948505i	$0.602596\pi$
$110$	5.28834	−	9.81163i	0.504224	−	0.935503i
$111$	0.705469	−	0.814154i	0.0669601	−	0.0772761i
$112$	0.0791102	+	0.269425i	0.00747521	+	0.0254582i
$113$	11.3093	−	5.16480i	1.06389	−	0.485864i	0.194969	−	0.980809i	$-0.437539\pi$
$113$	11.3093	−	5.16480i	1.06389	−	0.485864i	0.868924	+	0.494946i	$0.164812\pi$
$114$	0.533274			0.0499457
$115$	−6.80276	+	8.28990i	−0.634361	+	0.773037i
$116$	−2.34475			−0.217705
$117$	−10.1378	+	4.62976i	−0.937237	+	0.428022i
$118$	−2.89175	−	9.84840i	−0.266207	−	0.906619i
$119$	−1.41208	+	1.62963i	−0.129445	+	0.149388i
$120$	0.251410	+	0.135506i	0.0229504	+	0.0123700i
$121$	−9.06782	−	10.4648i	−0.824347	−	0.951347i
$122$	−10.7380	+	1.54389i	−0.972170	+	0.139777i
$123$	−0.0577966	+	0.196837i	−0.00521134	+	0.0177482i
$124$	2.79602	−	1.79689i	0.251090	−	0.161366i
$125$	−0.979823	−	11.1373i	−0.0876380	−	0.996152i
$126$	0.348041	−	0.762104i	0.0310060	−	0.0678936i
$127$	16.4027	+	7.49084i	1.45550	+	0.664705i	0.976972	−	0.213368i	$-0.0684432\pi$
$127$	16.4027	+	7.49084i	1.45550	+	0.664705i	0.478528	+	0.878072i	$0.341170\pi$
$128$	0.989821	+	0.142315i	0.0874887	+	0.0125790i
$129$	−0.871965	+	0.560378i	−0.0767722	+	0.0493385i
$130$	−8.17103	−	1.73091i	−0.716646	−	0.151811i
$131$	−0.239081	−	1.66284i	−0.0208886	−	0.145283i	0.976708	−	0.214573i	$-0.0688359\pi$
$131$	−0.239081	−	1.66284i	−0.0208886	−	0.145283i	−0.997597	+	0.0692895i	$0.977927\pi$
$132$	0.481162	−	0.416929i	0.0418798	−	0.0362890i
$133$	0.633838	−	0.986271i	0.0549607	−	0.0855205i
$134$	−5.97747	+	6.89837i	−0.516375	+	0.595929i
$135$	−0.605937	−	1.59793i	−0.0521507	−	0.137528i
$136$	3.19005	+	6.98524i	0.273545	+	0.598980i
$137$			0.809274i			0.0691410i	0.999402	+	0.0345705i	$0.0110063\pi$
$137$			0.809274i			0.0691410i	−0.999402	+	0.0345705i	$0.988994\pi$
$138$	−0.531227	+	0.304983i	−0.0452210	+	0.0259619i
$139$	14.9861			1.27111			0.635554	−	0.772057i	$-0.280772\pi$
$139$	14.9861			1.27111			0.635554	+	0.772057i	$0.280772\pi$
$140$	0.549434	−	0.303913i	0.0464356	−	0.0256853i
$141$	−0.733632	+	0.215414i	−0.0617830	+	0.0181411i
$142$	2.85966	+	2.47791i	0.239977	+	0.207941i
$143$	−10.0663	+	15.6634i	−0.841784	+	1.30984i
$144$	−1.95390	−	2.25492i	−0.162825	−	0.187910i
$145$	1.14239	+	5.11706i	0.0948705	+	0.424949i
$146$	9.77718	+	2.87084i	0.809166	+	0.237592i
$147$	−0.477930	−	0.743673i	−0.0394190	−	0.0613372i
$148$	−8.34850	−	1.20033i	−0.686243	−	0.0986668i
$149$	4.53178	−	9.92321i	0.371258	−	0.812941i	−0.628135	−	0.778104i	$-0.716182\pi$
$149$	4.53178	−	9.92321i	0.371258	−	0.812941i	0.999393	−	0.0348367i	$-0.0110911\pi$
$150$	0.173232	−	0.614683i	0.0141443	−	0.0501886i
$151$	−1.99528	+	13.8775i	−0.162374	+	1.12933i	0.731770	+	0.681552i	$0.238695\pi$
$151$	−1.99528	+	13.8775i	−0.162374	+	1.12933i	−0.894143	+	0.447781i	$0.852214\pi$
$152$	−2.25727	−	3.51237i	−0.183088	−	0.284891i
$153$	6.45514	−	21.9842i	0.521868	−	1.77732i
$154$	−0.199197	−	1.38544i	−0.0160517	−	0.111642i
$155$	−5.28369	−	5.22641i	−0.424396	−	0.419795i
$156$	−0.401354	−	0.257934i	−0.0321340	−	0.0206513i
$157$	2.38154	+	2.06362i	0.190068	+	0.164695i	0.744696	−	0.667403i	$-0.232594\pi$
$157$	2.38154	+	2.06362i	0.190068	+	0.164695i	−0.554629	+	0.832098i	$0.687140\pi$
$158$	1.36038	+	4.63304i	0.108226	+	0.368585i
$159$	−0.565805	−	1.23894i	−0.0448713	−	0.0982543i
$160$	−0.171673	−	2.22947i	−0.0135719	−	0.176255i
$161$	−0.0673495	+	1.34498i	−0.00530788	+	0.105999i
$162$			8.85344i			0.695592i
$163$	−10.4484	+	4.77165i	−0.818386	+	0.373744i	−0.780203	−	0.625527i	$-0.784884\pi$
$163$	−10.4484	+	4.77165i	−0.818386	+	0.373744i	−0.0381828	+	0.999271i	$0.512157\pi$
$164$	1.54110	−	0.452507i	0.120339	−	0.0353348i
$165$	−1.14431	−	0.846928i	−0.0890845	−	0.0659333i
$166$	−10.6381	−	6.83669i	−0.825677	−	0.530630i
$167$	−10.4103	+	9.02060i	−0.805575	+	0.698035i	−0.956890	−	0.290451i	$-0.906195\pi$
$167$	−10.4103	+	9.02060i	−0.805575	+	0.698035i	0.151315	+	0.988486i	$0.451649\pi$
$168$	0.0355001	−	0.00510414i	0.00273889	−	0.000393793i
$169$	0.913765	+	0.268306i	0.0702896	+	0.0206389i
$170$	13.6900	−	10.3651i	1.04997	−	0.794966i
$171$	−1.77287	+	12.3306i	−0.135575	+	0.942944i
$172$	7.38178	+	3.37114i	0.562855	+	0.257047i
$173$	5.24943	+	2.39734i	0.399107	+	0.182266i	0.604849	−	0.796340i	$-0.293233\pi$
$173$	5.24943	+	2.39734i	0.399107	+	0.182266i	−0.205742	+	0.978606i	$0.565961\pi$
$174$	−0.0426211	+	0.296436i	−0.00323110	+	0.0224728i
$175$	−0.930932	−	1.05098i	−0.0703719	−	0.0794469i
$176$	−4.78276	−	1.40434i	−0.360514	−	0.105856i
$177$	−1.29765	+	0.186574i	−0.0975374	+	0.0140238i
$178$	4.22656	−	3.66234i	0.316794	−	0.274504i
$179$	−6.13268	−	3.94123i	−0.458378	−	0.294582i	0.291001	−	0.956723i	$-0.406012\pi$
$179$	−6.13268	−	3.94123i	−0.458378	−	0.294582i	−0.749379	+	0.662141i	$0.769648\pi$
$180$	−3.96905	+	5.36270i	−0.295835	+	0.399712i
$181$	−6.47102	+	1.90006i	−0.480987	+	0.141231i	−0.513233	−	0.858249i	$-0.671552\pi$
$181$	−6.47102	+	1.90006i	−0.480987	+	0.141231i	0.0322457	+	0.999480i	$0.489734\pi$
$182$	−0.954080	+	0.435714i	−0.0707211	+	0.0322972i
$183$			1.38561i			0.102427i
$184$	4.25735	+	2.20794i	0.313856	+	0.162772i
$185$	1.44795	+	18.8041i	0.106455	+	1.38251i
$186$	−0.176349	−	0.386150i	−0.0129305	−	0.0283139i
$187$	−10.7842	−	36.7277i	−0.788621	−	2.68580i
$188$	4.52416	+	3.92020i	0.329958	+	0.285910i
$189$	−0.180538	−	0.116025i	−0.0131322	−	0.00843955i
$190$	−6.56544	+	6.63740i	−0.476307	+	0.481527i
$191$	−1.27458	−	8.86490i	−0.0922254	−	0.641442i	−0.982534	−	0.186084i	$-0.940420\pi$
$191$	−1.27458	−	8.86490i	−0.0922254	−	0.641442i	0.890309	−	0.455358i	$-0.150489\pi$
$192$	0.0359844	−	0.122552i	0.00259695	−	0.00884440i
$193$	1.38166	+	2.14990i	0.0994540	+	0.154753i	0.887415	−	0.460972i	$-0.152499\pi$
$193$	1.38166	+	2.14990i	0.0994540	+	0.154753i	−0.787960	+	0.615726i	$0.788863\pi$
$194$	−0.649171	+	4.51508i	−0.0466077	+	0.324164i
$195$	−0.367357	+	1.00156i	−0.0263070	+	0.0717233i
$196$	−2.87515	+	6.29570i	−0.205368	+	0.449693i
$197$	6.50936	+	0.935904i	0.463773	+	0.0666804i	0.370241	−	0.928936i	$-0.379275\pi$
$197$	6.50936	+	0.935904i	0.463773	+	0.0666804i	0.0935319	+	0.995616i	$0.470184\pi$
$198$	8.04079	+	12.5117i	0.571434	+	0.889168i
$199$	8.55843	+	2.51298i	0.606691	+	0.178140i	0.570627	−	0.821209i	$-0.306700\pi$
$199$	8.55843	+	2.51298i	0.606691	+	0.178140i	0.0360633	+	0.999350i	$0.488518\pi$
$200$	−4.78183	+	1.46087i	−0.338126	+	0.103299i
$201$	0.763475	+	0.881097i	0.0538514	+	0.0621478i
$202$	−1.04062	+	1.61923i	−0.0732175	+	0.113929i
$203$	0.497589	+	0.431163i	0.0349239	+	0.0302617i
$204$	0.941097	−	0.276331i	0.0658900	−	0.0193470i
$205$	−1.73837	−	3.14274i	−0.121413	−	0.219498i
$206$	−15.1328			−1.05435
$207$	−5.28588	−	13.2972i	−0.367394	−	0.924216i
$208$			3.73528i			0.258995i
$209$	8.64555	+	18.9311i	0.598025	+	1.30949i
$210$	−0.0284351	−	0.0749866i	−0.00196221	−	0.00517457i
$211$	−9.02200	+	10.4119i	−0.621100	+	0.716788i	−0.975916	−	0.218149i	$-0.929998\pi$
$211$	−9.02200	+	10.4119i	−0.621100	+	0.716788i	0.354815	+	0.934936i	$0.384544\pi$
$212$	−5.76523	+	8.97087i	−0.395957	+	0.616122i
$213$	0.365251	−	0.316492i	0.0250266	−	0.0216856i
$214$	1.01201	+	7.03865i	0.0691793	+	0.481152i
$215$	3.76051	−	17.7520i	0.256464	−	1.21068i
$216$	−0.642943	+	0.413195i	−0.0437468	+	0.0281143i
$217$	−0.923774	−	0.132819i	−0.0627098	−	0.00901631i
$218$	−9.67531	−	4.41856i	−0.655294	−	0.299263i
$219$	0.540669	−	1.18390i	0.0365350	−	0.0800005i
$220$	−0.734545	+	11.1218i	−0.0495230	+	0.749834i
$221$	−24.1305	+	15.5077i	−1.62319	+	1.04316i
$222$	−0.303505	+	1.03364i	−0.0203699	+	0.0693736i
$223$	0.341892	−	0.0491567i	0.0228948	−	0.00329177i	−0.130858	−	0.991401i	$-0.541773\pi$
$223$	0.341892	−	0.0491567i	0.0228948	−	0.00329177i	0.153753	+	0.988109i	$0.450864\pi$
$224$	−0.183884	−	0.212214i	−0.0122863	−	0.0141791i
$225$	13.6370	+	6.04905i	0.909135	+	0.403270i
$226$	−8.14180	+	9.39614i	−0.541584	+	0.625022i
$227$	2.18901	+	7.45510i	0.145290	+	0.494812i	0.999692	−	0.0247995i	$-0.00789474\pi$
$227$	2.18901	+	7.45510i	0.145290	+	0.494812i	−0.854402	+	0.519612i	$0.826077\pi$
$228$	−0.485083	+	0.221530i	−0.0321254	+	0.0146712i
$229$	−7.14024			−0.471841			−0.235920	−	0.971772i	$-0.575810\pi$
$229$	−7.14024			−0.471841			−0.235920	+	0.971772i	$0.575810\pi$
$230$	2.74426	−	10.3667i	0.180951	−	0.683562i
$231$	−0.178776			−0.0117626
$232$	2.13286	−	0.974046i	0.140029	−	0.0639493i
$233$	−2.52146	−	8.58730i	−0.165186	−	0.562573i	−0.999929	−	0.0119323i	$-0.996202\pi$
$233$	−2.52146	−	8.58730i	−0.165186	−	0.562573i	0.834743	−	0.550640i	$-0.185616\pi$
$234$	7.29837	−	8.42276i	0.477109	−	0.550613i
$235$	6.35101	−	11.7832i	0.414294	−	0.768653i
$236$	6.72160	+	7.75714i	0.437539	+	0.504947i
$237$	0.610461	−	0.0877711i	0.0396537	−	0.00570134i
$238$	0.607503	−	2.06896i	0.0393786	−	0.134111i
$239$	−16.1199	+	10.3596i	−1.04271	+	0.670107i	−0.945655	−	0.325172i	$-0.894578\pi$
$239$	−16.1199	+	10.3596i	−1.04271	+	0.670107i	−0.0970521	+	0.995279i	$0.530941\pi$
$240$	−0.284982	−	0.0188217i	−0.0183955	−	0.00121494i
$241$	−6.46276	+	14.1515i	−0.416303	+	0.911576i	0.579051	+	0.815291i	$0.303423\pi$
$241$	−6.46276	+	14.1515i	−0.416303	+	0.911576i	−0.995354	+	0.0962849i	$0.969304\pi$
$242$	12.5956	+	5.75223i	0.809677	+	0.369767i
$243$	3.38877	+	0.487231i	0.217389	+	0.0312559i
$244$	9.12624	−	5.86508i	0.584248	−	0.375473i
$245$	15.1402	+	3.20723i	0.967271	+	0.204902i
$246$	−0.0291954	−	0.203059i	−0.00186143	−	0.0129466i
$247$	11.7862	−	10.2128i	0.749940	−	0.649827i
$248$	−1.79689	+	2.79602i	−0.114103	+	0.177547i
$249$	−1.05770	+	1.22065i	−0.0670291	+	0.0773557i
$250$	5.51789	+	9.72383i	0.348982	+	0.614989i
$251$	−8.44330	−	18.4883i	−0.532937	−	1.16697i	−0.964305	−	0.264793i	$-0.914697\pi$
$251$	−8.44330	−	18.4883i	−0.532937	−	1.16697i	0.431369	−	0.902176i	$-0.358031\pi$
$252$			0.837816i			0.0527774i
$253$	−19.4392	−	13.9140i	−1.22213	−	0.874764i
$254$	−18.0322			−1.13144
$255$	−1.06156	−	1.91917i	−0.0664777	−	0.120183i
$256$	−0.959493	+	0.281733i	−0.0599683	+	0.0176083i
$257$	11.5971	+	10.0489i	0.723405	+	0.626834i	0.936692	−	0.350155i	$-0.113871\pi$
$257$	11.5971	+	10.0489i	0.723405	+	0.626834i	−0.213286	+	0.976990i	$0.568417\pi$
$258$	0.560378	−	0.871965i	0.0348876	−	0.0542862i
$259$	1.55094	+	1.78989i	0.0963710	+	0.111218i
$260$	8.15167	−	1.81987i	0.505545	−	0.112864i
$261$	−6.71262	−	1.97100i	−0.415501	−	0.122002i
$262$	0.908245	+	1.41326i	0.0561116	+	0.0873113i
$263$	−14.7581	−	2.12189i	−0.910024	−	0.130842i	−0.328625	−	0.944460i	$-0.606585\pi$
$263$	−14.7581	−	2.12189i	−0.910024	−	0.130842i	−0.581399	+	0.813619i	$0.697494\pi$
$264$	−0.264482	+	0.579134i	−0.0162777	+	0.0356432i
$265$	22.3864	+	8.21099i	1.37519	+	0.504397i
$266$	−0.166847	+	1.16045i	−0.0102301	+	0.0711517i
$267$	−0.386185	−	0.600916i	−0.0236341	−	0.0367754i
$268$	2.57161	−	8.75811i	0.157086	−	0.534987i
$269$	−1.18916	−	8.27078i	−0.0725043	−	0.504279i	−0.993421	−	0.114519i	$-0.963467\pi$
$269$	−1.18916	−	8.27078i	−0.0725043	−	0.504279i	0.920917	−	0.389759i	$-0.127442\pi$
$270$	1.21498	+	1.20181i	0.0739415	+	0.0731398i
$271$	1.99805	+	1.28407i	0.121373	+	0.0780015i	0.599919	−	0.800061i	$-0.295200\pi$
$271$	1.99805	+	1.28407i	0.121373	+	0.0780015i	−0.478546	+	0.878063i	$0.658836\pi$
$272$	−5.80355	−	5.02880i	−0.351892	−	0.304916i
$273$	0.0377427	+	0.128540i	0.00228429	+	0.00777959i
$274$	−0.336185	−	0.736142i	−0.0203097	−	0.0444720i
$275$	24.6295	−	3.81566i	1.48522	−	0.230093i
$276$	0.356526	−	0.498102i	0.0214604	−	0.0299822i
$277$			9.82954i			0.590600i	0.955405	+	0.295300i	$0.0954196\pi$
$277$			9.82954i			0.590600i	−0.955405	+	0.295300i	$0.904580\pi$
$278$	−13.6319	+	6.22546i	−0.817585	+	0.373379i
$279$	9.51499	−	2.79385i	0.569647	−	0.167264i
$280$	−0.373533	+	0.504692i	−0.0223228	+	0.0301611i
$281$	14.1872	+	9.11754i	0.846336	+	0.543907i	0.890430	−	0.455120i	$-0.150404\pi$
$281$	14.1872	+	9.11754i	0.846336	+	0.543907i	−0.0440942	+	0.999027i	$0.514040\pi$
$282$	0.577849	−	0.500709i	0.0344104	−	0.0298168i
$283$	−3.63199	+	0.522201i	−0.215899	+	0.0310416i	−0.249416	−	0.968397i	$-0.580238\pi$
$283$	−3.63199	+	0.522201i	−0.215899	+	0.0310416i	0.0335164	+	0.999438i	$0.489329\pi$
$284$	−3.63060	−	1.06604i	−0.215436	−	0.0632578i
$285$	0.719793	+	0.950687i	0.0426369	+	0.0563138i
$286$	2.64978	−	18.4296i	0.156685	−	1.08977i
$287$	−0.410251	−	0.187355i	−0.0242163	−	0.0110592i
$288$	2.71406	+	1.23947i	0.159927	+	0.0730364i
$289$	5.97296	−	41.5429i	0.351351	−	2.44370i
$290$	−3.16486	−	4.18007i	−0.185847	−	0.245462i
$291$	0.559020	+	0.164143i	0.0327703	+	0.00962224i
$292$	−10.0862	+	1.45018i	−0.590252	+	0.0848654i
$293$	12.8772	−	11.1581i	0.752293	−	0.651866i	−0.191842	−	0.981426i	$-0.561446\pi$
$293$	12.8772	−	11.1581i	0.752293	−	0.651866i	0.944134	+	0.329560i	$0.106901\pi$
$294$	0.743673	+	0.477930i	0.0433719	+	0.0278734i
$295$	13.6539	−	18.4482i	0.794961	−	1.07410i
$296$	8.09270	−	2.37623i	0.470379	−	0.138116i
$297$	3.46536	−	1.58258i	0.201080	−	0.0918303i
$298$			10.9090i			0.631943i
$299$	−5.90020	+	16.9142i	−0.341217	+	0.978176i
$300$	0.0977710	+	0.631098i	0.00564481	+	0.0364365i
$301$	−0.946614	−	2.07279i	−0.0545619	−	0.119474i
$302$	−3.94994	−	13.4523i	−0.227294	−	0.774091i
$303$	0.185796	+	0.160993i	0.0106737	+	0.00924882i
$304$	3.51237	+	2.25727i	0.201448	+	0.129463i
$305$	−17.2460	−	17.0591i	−0.987505	−	0.976799i
$306$	3.26076	+	22.6791i	0.186405	+	1.29648i
$307$	−0.588388	+	2.00387i	−0.0335811	+	0.114367i	−0.974578	−	0.224048i	$-0.928073\pi$
$307$	−0.588388	+	2.00387i	−0.0335811	+	0.114367i	0.940997	+	0.338415i	$0.109891\pi$
$308$	0.756730	+	1.17749i	0.0431187	+	0.0670940i
$309$	−0.275072	+	1.91317i	−0.0156483	+	0.108836i
$310$	6.97734	+	2.55918i	0.396286	+	0.145352i
$311$	−5.77456	+	12.6445i	−0.327445	+	0.717005i	−0.999729	−	0.0232890i	$-0.992586\pi$
$311$	−5.77456	+	12.6445i	−0.327445	+	0.717005i	0.672284	+	0.740294i	$0.265313\pi$
$312$	0.472234	+	0.0678970i	0.0267350	+	0.00384391i
$313$	5.59660	+	8.70847i	0.316338	+	0.492232i	0.962616	−	0.270870i	$-0.0873115\pi$
$313$	5.59660	+	8.70847i	0.316338	+	0.492232i	−0.646277	+	0.763103i	$0.723675\pi$
$314$	−3.02358	−	0.887804i	−0.170631	−	0.0501017i
$315$	1.82840	−	0.408194i	0.103019	−	0.0229991i
$316$	−3.16208	−	3.64924i	−0.177881	−	0.205286i
$317$	−0.919290	+	1.43044i	−0.0516325	+	0.0803417i	−0.866110	−	0.499853i	$-0.833387\pi$
$317$	−0.919290	+	1.43044i	−0.0516325	+	0.0803417i	0.814478	+	0.580195i	$0.197024\pi$
$318$	1.02935	+	0.891936i	0.0577230	+	0.0500173i
$319$	−11.2144	+	3.29284i	−0.627885	+	0.184364i
$320$	1.08231	+	1.95668i	0.0605032	+	0.109382i
$321$	0.908259			0.0506941
$322$	−0.497461	−	1.25141i	−0.0277224	−	0.0697386i
$323$			32.0619i			1.78397i
$324$	−3.67785	−	8.05337i	−0.204325	−	0.447410i
$325$	−7.94318	−	16.9031i	−0.440609	−	0.937615i
$326$	7.52203	−	8.68088i	0.416607	−	0.480790i
$327$	−0.734488	+	1.14289i	−0.0406173	+	0.0632017i
$328$	−1.21385	+	1.05181i	−0.0670238	+	0.0580764i
$329$	−0.239224	−	1.66384i	−0.0131889	−	0.0917306i
$330$	1.39273	+	0.295029i	0.0766672	+	0.0162408i
$331$	−1.82523	+	1.17300i	−0.100324	+	0.0644741i	−0.589841	−	0.807520i	$-0.700809\pi$
$331$	−1.82523	+	1.17300i	−0.100324	+	0.0644741i	0.489517	+	0.871994i	$0.337173\pi$
$332$	12.5168	+	1.79965i	0.686950	+	0.0987685i
$333$	−22.8913	−	10.4541i	−1.25444	−	0.572882i
$334$	5.72228	−	12.5300i	0.313109	−	0.685613i
$335$	−20.3661	−	1.34509i	−1.11272	−	0.0734900i
$336$	−0.0301717	+	0.0193902i	−0.00164600	+	0.00105782i
$337$	−4.43691	+	15.1107i	−0.241694	+	0.823134i	0.745894	+	0.666065i	$0.232023\pi$
$337$	−4.43691	+	15.1107i	−0.241694	+	0.823134i	−0.987588	+	0.157069i	$0.949795\pi$
$338$	−0.942648	+	0.135532i	−0.0512733	+	0.00737199i
$339$	1.03991	+	1.20012i	0.0564804	+	0.0651818i
$340$	−8.14702	+	15.1154i	−0.441834	+	0.819750i
$341$	10.8492	−	12.5207i	0.587518	−	0.678032i
$342$	−3.50965	−	11.9528i	−0.189780	−	0.646332i
$343$	3.55579	−	1.62388i	0.191995	−	0.0876811i
$344$	−8.11512			−0.437538
$345$	−1.26073	−	0.535382i	−0.0678756	−	0.0288240i
$346$	−5.77094			−0.310248
$347$	−7.23170	+	3.30261i	−0.388218	+	0.177293i	−0.599956	−	0.800033i	$-0.704815\pi$
$347$	−7.23170	+	3.30261i	−0.388218	+	0.177293i	0.211738	+	0.977327i	$0.432088\pi$
$348$	−0.0843745	−	0.287353i	−0.00452295	−	0.0154037i
$349$	8.39969	−	9.69375i	0.449625	−	0.518895i	−0.485008	−	0.874510i	$-0.661183\pi$
$349$	8.39969	−	9.69375i	0.449625	−	0.518895i	0.934632	+	0.355615i	$0.115729\pi$
$350$	1.28340	+	0.569285i	0.0686006	+	0.0304296i
$351$	−1.86947	−	2.15748i	−0.0997849	−	0.115158i
$352$	4.93393	−	0.709393i	0.262980	−	0.0378108i
$353$	2.41739	−	8.23286i	0.128665	−	0.438191i	−0.869811	−	0.493385i	$-0.835759\pi$
$353$	2.41739	−	8.23286i	0.128665	−	0.438191i	0.998476	+	0.0551937i	$0.0175776\pi$
$354$	1.10288	−	0.708777i	0.0586174	−	0.0376711i
$355$	−0.557594	+	8.44260i	−0.0295940	+	0.448087i
$356$	−2.32323	+	5.08716i	−0.123131	+	0.269619i
$357$	−0.250527	−	0.114412i	−0.0132593	−	0.00605531i
$358$	7.21573	+	1.03747i	0.381363	+	0.0548318i
$359$	23.6966	−	15.2289i	1.25066	−	0.803749i	0.263681	−	0.964610i	$-0.415063\pi$
$359$	23.6966	−	15.2289i	1.25066	−	0.803749i	0.986977	+	0.160861i	$0.0514271\pi$
$360$	1.38262	−	6.52689i	0.0728707	−	0.343997i
$361$	0.223148	+	1.55203i	0.0117447	+	0.0816858i
$362$	5.09693	−	4.41652i	0.267889	−	0.232127i
$363$	0.956180	−	1.48785i	0.0501864	−	0.0780916i
$364$	0.686860	−	0.792678i	0.0360012	−	0.0415476i
$365$	8.07893	+	21.3051i	0.422870	+	1.11516i
$366$	−0.575605	−	1.26040i	−0.0300873	−	0.0658821i
$367$		−	7.72825i		−	0.403411i	−0.979446	−	0.201706i	$-0.935352\pi$
$367$		−	7.72825i		−	0.403411i	0.979446	−	0.201706i	$-0.0646484\pi$
$368$	−4.78983	−	0.239849i	−0.249687	−	0.0125030i
$369$	4.79227			0.249476
$370$	−9.12862	−	16.5033i	−0.474574	−	0.857967i
$371$	2.87306	−	0.843607i	0.149162	−	0.0437979i
$372$	0.320825	+	0.277996i	0.0166340	+	0.0144134i
$373$	−10.5439	+	16.4067i	−0.545944	+	0.849505i	−0.999121	−	0.0419151i	$-0.986654\pi$
$373$	−10.5439	+	16.4067i	−0.545944	+	0.849505i	0.453177	+	0.891420i	$0.350290\pi$
$374$	25.0669	+	28.9288i	1.29618	+	1.49587i
$375$	1.32964	−	0.520848i	0.0686622	−	0.0268965i
$376$	−5.74383	−	1.68654i	−0.296215	−	0.0869767i
$377$	4.73511	+	7.36797i	0.243870	+	0.379470i
$378$	0.212421	+	0.0305416i	0.0109258	+	0.00157089i
$379$	10.7155	−	23.4636i	0.550417	−	1.20525i	−0.406169	−	0.913798i	$-0.633136\pi$
$379$	10.7155	−	23.4636i	0.550417	−	1.20525i	0.956587	−	0.291448i	$-0.0941371\pi$
$380$	3.21486	−	8.76497i	0.164919	−	0.449634i
$381$	−0.327775	+	2.27972i	−0.0167924	+	0.116794i
$382$	4.84201	+	7.53432i	0.247739	+	0.385489i
$383$	6.97756	−	23.7634i	0.356537	−	1.21425i	−0.564715	−	0.825286i	$-0.691014\pi$
$383$	6.97756	−	23.7634i	0.356537	−	1.21425i	0.921252	−	0.388966i	$-0.127168\pi$
$384$	0.0181772	+	0.126425i	0.000927602	+	0.00645161i
$385$	2.20101	−	2.22513i	0.112174	−	0.113403i
$386$	−2.14990	−	1.38166i	−0.109427	−	0.0703246i
$387$	18.2990	+	15.8561i	0.930188	+	0.806012i
$388$	−1.28513	−	4.37674i	−0.0652424	−	0.222195i
$389$	15.0325	+	32.9167i	0.762180	+	1.66894i	0.743153	+	0.669122i	$0.233330\pi$
$389$	15.0325	+	32.9167i	0.762180	+	1.66894i	0.0190271	+	0.999819i	$0.493943\pi$
$390$	−0.0819035	−	1.06366i	−0.00414734	−	0.0538604i
$391$	−18.3364	−	31.9388i	−0.927312	−	1.61521i
$392$		−	6.92115i		−	0.349571i
$393$	0.195181	−	0.0891361i	0.00984557	−	0.00449632i
$394$	−6.30991	+	1.85276i	−0.317889	+	0.0933405i
$395$	−6.42329	+	8.67870i	−0.323191	+	0.436673i
$396$	−12.5117	−	8.04079i	−0.628737	−	0.404065i
$397$	−3.78090	+	3.27617i	−0.189758	+	0.164426i	−0.744559	−	0.667557i	$-0.767340\pi$
$397$	−3.78090	+	3.27617i	−0.189758	+	0.164426i	0.554801	+	0.831983i	$0.312795\pi$
$398$	−8.82895	+	1.26941i	−0.442555	+	0.0636298i
$399$	0.143677	+	0.0421874i	0.00719286	+	0.00211201i
$400$	3.74283	−	3.31530i	0.187142	−	0.165765i
$401$	0.918153	−	6.38589i	0.0458504	−	0.318896i	−0.953969	−	0.299904i	$-0.903045\pi$
$401$	0.918153	−	6.38589i	0.0458504	−	0.318896i	0.999820	−	0.0189919i	$-0.00604568\pi$
$402$	−1.06050	−	0.484315i	−0.0528930	−	0.0241554i
$403$	−11.2928	−	5.15726i	−0.562536	−	0.256901i
$404$	0.273925	−	1.90519i	0.0136283	−	0.0947868i
$405$	−15.7833	+	11.9500i	−0.784280	+	0.593802i
$406$	−0.631734	−	0.185494i	−0.0313525	−	0.00920591i
$407$	−41.6145	+	5.98327i	−2.06276	+	0.296580i
$408$	−0.741260	+	0.642306i	−0.0366978	+	0.0317989i
$409$	−10.3948	−	6.68035i	−0.513991	−	0.330322i	0.257800	−	0.966198i	$-0.417003\pi$
$409$	−10.3948	−	6.68035i	−0.513991	−	0.330322i	−0.771791	+	0.635876i	$0.780639\pi$
$410$	2.88681	+	2.13659i	0.142570	+	0.105519i
$411$	−0.0991778	+	0.0291212i	−0.00489208	+	0.00143644i
$412$	13.7653	−	6.28640i	0.678167	−	0.309709i
$413$		−	2.88217i		−	0.141822i
$414$	10.3320	+	9.89969i	0.507792	+	0.486543i
$415$	−2.17090	−	28.1928i	−0.106565	−	1.38393i
$416$	−1.55169	−	3.39773i	−0.0760780	−	0.166588i
$417$	0.539267	+	1.83657i	0.0264080	+	0.0899374i
$418$	−15.7285	−	13.6288i	−0.769307	−	0.666609i
$419$	−14.1760	−	9.11038i	−0.692544	−	0.445071i	0.146445	−	0.989219i	$-0.453217\pi$
$419$	−14.1760	−	9.11038i	−0.692544	−	0.445071i	−0.838989	+	0.544148i	$0.816853\pi$
$420$	0.0570160	+	0.0563978i	0.00278210	+	0.00275193i
$421$	−2.79809	−	19.4611i	−0.136371	−	0.948478i	−0.937003	−	0.349322i	$-0.886412\pi$
$421$	−2.79809	−	19.4611i	−0.136371	−	0.948478i	0.800632	−	0.599156i	$-0.204497\pi$
$422$	3.88142	−	13.2189i	0.188945	−	0.643486i
$423$	9.65654	+	15.0259i	0.469517	+	0.730583i
$424$	1.51760	−	10.5552i	0.0737012	−	0.512603i
$425$	36.9564	+	10.4152i	1.79265	+	0.505211i
$426$	−0.200768	+	0.439621i	−0.00972726	+	0.0212997i
$427$	−3.01521	−	0.433522i	−0.145916	−	0.0209796i
$428$	−3.84451	−	5.98218i	−0.185832	−	0.289160i
$429$	−2.28181	−	0.669999i	−0.110167	−	0.0323478i
$430$	3.95379	+	17.7100i	0.190668	+	0.854052i
$431$	16.5280	+	19.0744i	0.796127	+	0.918780i	0.998162	−	0.0605987i	$-0.0193010\pi$
$431$	16.5280	+	19.0744i	0.796127	+	0.918780i	−0.202035	+	0.979378i	$0.564756\pi$
$432$	0.413195	−	0.642943i	0.0198798	−	0.0309336i
$433$	15.8328	+	13.7192i	0.760877	+	0.659304i	0.946276	−	0.323360i	$-0.104812\pi$
$433$	15.8328	+	13.7192i	0.760877	+	0.659304i	−0.185399	+	0.982663i	$0.559358\pi$
$434$	0.895469	−	0.262933i	0.0429839	−	0.0126212i
$435$	−0.585995	+	0.324136i	−0.0280963	+	0.0155411i
$436$	10.6365			0.509396
$437$	12.3393	+	15.7695i	0.590269	+	0.754358i
$438$			1.30151i			0.0621888i
$439$	2.96603	+	6.49469i	0.141561	+	0.309975i	0.967111	−	0.254353i	$-0.0818626\pi$
$439$	2.96603	+	6.49469i	0.141561	+	0.309975i	−0.825551	+	0.564328i	$0.809135\pi$
$440$	−3.95201	−	10.4219i	−0.188405	−	0.496845i
$441$	−13.5232	+	15.6066i	−0.643963	+	0.743173i
$442$	15.5077	−	24.1305i	0.737627	−	1.14777i
$443$	26.6438	−	23.0870i	1.26588	−	1.09689i	0.275103	−	0.961415i	$-0.411288\pi$
$443$	26.6438	−	23.0870i	1.26588	−	1.09689i	0.990780	−	0.135479i	$-0.0432575\pi$
$444$	−0.153313	−	1.06632i	−0.00727591	−	0.0506051i
$445$	12.2338	+	2.59156i	0.579939	+	0.122852i
$446$	−0.290576	+	0.186742i	−0.0137591	+	0.00884247i
$447$	1.37918	+	0.198296i	0.0652329	+	0.00937907i
$448$	0.255424	+	0.116648i	0.0120676	+	0.00551110i
$449$	−14.0161	+	30.6909i	−0.661460	+	1.44839i	0.219696	+	0.975568i	$0.429493\pi$
$449$	−14.0161	+	30.6909i	−0.661460	+	1.44839i	−0.881156	+	0.472826i	$0.843234\pi$
$450$	−14.9175	+	0.162615i	−0.703220	+	0.00766575i
$451$	6.73521	−	4.32846i	0.317149	−	0.203819i
$452$	3.50274	−	11.9292i	0.164755	−	0.561105i
$453$	−1.77251	+	0.254848i	−0.0832796	+	0.0119738i
$454$	−5.08816	−	5.87205i	−0.238799	−	0.275589i
$455$	−2.06454	−	1.11276i	−0.0967873	−	0.0521671i
$456$	0.349220	−	0.403022i	0.0163537	−	0.0188732i
$457$	1.02884	+	3.50389i	0.0481269	+	0.163905i	0.980050	−	0.198750i	$-0.0636883\pi$
$457$	1.02884	+	3.50389i	0.0481269	+	0.163905i	−0.931923	+	0.362656i	$0.881870\pi$
$458$	6.49499	−	2.96616i	0.303491	−	0.138600i
$459$	5.86897			0.273940
$460$	1.81023	+	10.5699i	0.0844023	+	0.492825i
$461$	28.5065			1.32768			0.663839	−	0.747875i	$-0.268926\pi$
$461$	28.5065			1.32768			0.663839	+	0.747875i	$0.268926\pi$
$462$	0.162620	−	0.0742662i	0.00756578	−	0.00345518i
$463$	8.58203	+	29.2277i	0.398841	+	1.35833i	0.877184	+	0.480154i	$0.159419\pi$
$463$	8.58203	+	29.2277i	0.398841	+	1.35833i	−0.478344	+	0.878173i	$0.658763\pi$
$464$	−1.53549	+	1.77205i	−0.0712832	+	0.0822652i
$465$	0.450374	−	0.835594i	0.0208856	−	0.0387497i
$466$	5.86089	+	6.76383i	0.271501	+	0.313328i
$467$	−35.9205	+	5.16459i	−1.66220	+	0.238989i	−0.908397	−	0.418109i	$-0.862693\pi$
$467$	−35.9205	+	5.16459i	−1.66220	+	0.238989i	−0.753805	+	0.657098i	$0.771784\pi$
$468$	−3.13988	+	10.6935i	−0.145141	+	0.494306i
$469$	−2.15621	+	1.38571i	−0.0995645	+	0.0639862i
$470$	−0.882149	+	13.3567i	−0.0406905	+	0.616099i
$471$	−0.167201	+	0.366120i	−0.00770422	+	0.0168699i
$472$	−9.33662	−	4.26389i	−0.429753	−	0.196262i
$473$	40.0395	+	5.75681i	1.84102	+	0.264698i
$474$	−0.518834	+	0.333434i	−0.0238308	+	0.0153151i
$475$	−20.6945	−	2.74553i	−0.949529	−	0.125973i
$476$	0.306875	+	2.13436i	0.0140656	+	0.0978283i
$477$	−24.0458	+	20.8358i	−1.10098	+	0.954005i
$478$	10.3596	−	16.1199i	0.473837	−	0.737305i
$479$	−16.1276	+	18.6122i	−0.736889	+	0.850415i	−0.993229	−	0.116172i	$-0.962938\pi$
$479$	−16.1276	+	18.6122i	−0.736889	+	0.850415i	0.256340	+	0.966587i	$0.417483\pi$
$480$	0.267047	−	0.101265i	0.0121890	−	0.00462209i
$481$	13.0875	+	28.6577i	0.596740	+	1.30668i
$482$		−	15.5574i		−	0.708618i
$483$	−0.167253	+	0.0401445i	−0.00761027	+	0.00182664i
$484$	−13.8469			−0.629406
$485$	−8.92542	+	4.93699i	−0.405282	+	0.224177i
$486$	−3.28493	+	0.964543i	−0.149008	+	0.0437526i
$487$	−23.0853	−	20.0035i	−1.04610	−	0.906447i	−0.0503631	−	0.998731i	$-0.516038\pi$
$487$	−23.0853	−	20.0035i	−1.04610	−	0.906447i	−0.995733	+	0.0922838i	$0.970583\pi$
$488$	−5.86508	+	9.12624i	−0.265500	+	0.413126i
$489$	−0.960754	−	1.10877i	−0.0434468	−	0.0501403i
$490$	−15.1043	+	3.37207i	−0.682344	+	0.152334i
$491$	−1.21049	−	0.355433i	−0.0546289	−	0.0160405i	0.254304	−	0.967124i	$-0.418154\pi$
$491$	−1.21049	−	0.355433i	−0.0546289	−	0.0160405i	−0.308933	+	0.951084i	$0.599972\pi$
$492$	0.110911	+	0.172581i	0.00500024	+	0.00778053i
$493$	−17.8226	−	2.56250i	−0.802687	−	0.115409i
$494$	−6.47857	+	14.1861i	−0.291485	+	0.638263i
$495$	−11.4519	+	31.2224i	−0.514725	+	1.40334i
$496$	0.473003	−	3.28980i	0.0212384	−	0.147717i
$497$	0.574434	+	0.893837i	0.0257669	+	0.0400941i
$498$	0.455042	−	1.54973i	0.0203909	−	0.0694451i
$499$	0.500048	+	3.47791i	0.0223852	+	0.155693i	0.997948	−	0.0640277i	$-0.0203946\pi$
$499$	0.500048	+	3.47791i	0.0223852	+	0.155693i	−0.975563	+	0.219720i	$0.929486\pi$
$500$	−9.05867	−	6.55289i	−0.405116	−	0.293054i
$501$	−1.48010	−	0.951201i	−0.0661259	−	0.0424965i
$502$	15.3606	+	13.3100i	0.685577	+	0.594056i
$503$	−2.11631	−	7.20748i	−0.0943615	−	0.321366i	0.898762	−	0.438437i	$-0.144468\pi$
$503$	−2.11631	−	7.20748i	−0.0943615	−	0.321366i	−0.993124	+	0.117071i	$0.962649\pi$
$504$	−0.348041	−	0.762104i	−0.0155030	−	0.0339468i
$505$	−4.29124	+	0.330433i	−0.190958	+	0.0147041i
$506$	23.4626	+	4.58127i	1.04304	+	0.203662i
$507$			0.121638i			0.00540214i
$508$	16.4027	−	7.49084i	0.727750	−	0.332352i
$509$	−32.3869	+	9.50966i	−1.43552	+	0.421508i	−0.904727	−	0.425991i	$-0.859926\pi$
$509$	−32.3869	+	9.50966i	−1.43552	+	0.421508i	−0.530797	+	0.847499i	$0.678107\pi$
$510$	1.76288	+	1.30475i	0.0780618	+	0.0577751i
$511$	2.40710	+	1.54695i	0.106484	+	0.0684330i
$512$	0.755750	−	0.654861i	0.0333997	−	0.0289410i
$513$	−3.15847	+	0.454119i	−0.139450	+	0.0200498i
$514$	−14.7235	−	4.32322i	−0.649427	−	0.190689i
$515$	−20.4257	−	26.9778i	−0.900064	−	1.18878i
$516$	−0.147510	+	1.02596i	−0.00649378	+	0.0451652i
$517$	27.1432	+	12.3959i	1.19376	+	0.545171i
$518$	−2.15433	−	0.983851i	−0.0946560	−	0.0432279i
$519$	−0.104900	+	0.729593i	−0.00460458	+	0.0320256i
$520$	−6.65902	+	5.04174i	−0.292017	+	0.221095i
$521$	−35.8966	−	10.5402i	−1.57266	−	0.461774i	−0.624884	−	0.780718i	$-0.714854\pi$
$521$	−35.8966	−	10.5402i	−1.57266	−	0.461774i	−0.947774	+	0.318944i	$0.896672\pi$
$522$	6.92480	−	0.995636i	0.303090	−	0.0435778i
$523$	16.7895	−	14.5482i	0.734156	−	0.636150i	−0.205348	−	0.978689i	$-0.565833\pi$
$523$	16.7895	−	14.5482i	0.734156	−	0.636150i	0.939503	+	0.342540i	$0.111287\pi$
$524$	−1.41326	−	0.908245i	−0.0617384	−	0.0396769i
$525$	0.0953006	−	0.151906i	0.00415926	−	0.00662973i
$526$	14.3059	−	4.20059i	0.623767	−	0.183155i
$527$	23.2164	−	10.6026i	1.01132	−	0.461855i
$528$		−	0.636669i		−	0.0277074i
$529$	−21.3106	−	8.65204i	−0.926548	−	0.376176i
$530$	−23.7744	+	1.83067i	−1.03269	+	0.0795191i
$531$	12.7221	+	27.8575i	0.552093	+	1.20891i
$532$	−0.330298	−	1.12489i	−0.0143202	−	0.0487703i
$533$	−4.53408	−	3.92881i	−0.196393	−	0.170175i
$534$	0.600916	+	0.386185i	0.0260042	+	0.0167119i
$535$	−11.1821	+	11.3046i	−0.483444	+	0.488742i
$536$	1.29903	+	9.03495i	0.0561095	+	0.390250i
$537$	0.262324	−	0.893392i	0.0113201	−	0.0385527i
$538$	4.51751	+	7.02938i	0.194763	+	0.303058i
$539$	−4.90981	+	34.1485i	−0.211481	+	1.47088i
$540$	−1.60444	−	0.588483i	−0.0690440	−	0.0253243i
$541$	7.77132	−	17.0168i	0.334115	−	0.731610i	−0.665779	−	0.746149i	$-0.731901\pi$
$541$	7.77132	−	17.0168i	0.334115	−	0.731610i	0.999894	+	0.0145386i	$0.00462794\pi$
$542$	−2.35091	−	0.338010i	−0.100980	−	0.0145188i
$543$	−0.465711	−	0.724661i	−0.0199856	−	0.0310982i
$544$	7.36814	+	2.16348i	0.315906	+	0.0927584i
$545$	−5.18223	−	23.2125i	−0.221982	−	0.994315i
$546$	−0.0877294	−	0.101245i	−0.00375447	−	0.00433289i
$547$	−10.4448	+	16.2524i	−0.446587	+	0.694903i	−0.989443	−	0.144923i	$-0.953707\pi$
$547$	−10.4448	+	16.2524i	−0.446587	+	0.694903i	0.542856	+	0.839826i	$0.317343\pi$
$548$	0.611609	+	0.529962i	0.0261266	+	0.0226389i
$549$	31.0570	−	9.11917i	1.32548	−	0.389197i
$550$	−20.8187	+	13.7023i	−0.887714	+	0.584269i
$551$	9.78974			0.417057
$552$	−0.117389	+	0.601196i	−0.00499640	+	0.0255886i
$553$			1.35587i			0.0576577i
$554$	−4.08334	−	8.94126i	−0.173484	−	0.379878i
$555$	−2.25237	+	0.854103i	−0.0956078	+	0.0362547i
$556$	9.81383	−	11.3258i	0.416199	−	0.480319i
$557$	0.377707	−	0.587724i	0.0160040	−	0.0249027i	−0.833159	−	0.553033i	$-0.813470\pi$
$557$	0.377707	−	0.587724i	0.0160040	−	0.0249027i	0.849163	+	0.528130i	$0.177107\pi$
$558$	−7.49453	+	6.49405i	−0.317269	+	0.274915i
$559$	−4.31389	−	30.0038i	−0.182458	−	1.26902i
$560$	0.130121	−	0.614255i	0.00549861	−	0.0259570i
$561$	4.11298	−	2.64325i	0.173650	−	0.111598i
$562$	−16.6927	−	2.40004i	−0.704138	−	0.101240i
$563$	−42.9535	−	19.6162i	−1.81027	−	0.826724i	−0.946386	−	0.323037i	$-0.895296\pi$
$563$	−42.9535	−	19.6162i	−1.81027	−	0.826724i	−0.863886	−	0.503687i	$-0.831977\pi$
$564$	−0.317628	+	0.695508i	−0.0133746	+	0.0292862i
$565$	−27.7403	−	1.83212i	−1.16704	−	0.0770778i
$566$	3.08684	−	1.98379i	0.129750	−	0.0833850i
$567$	−0.700398	+	2.38534i	−0.0294139	+	0.100175i
$568$	3.74536	−	0.538501i	0.157152	−	0.0225950i
$569$	9.95551	+	11.4893i	0.417357	+	0.481655i	0.925030	−	0.379894i	$-0.124040\pi$
$569$	9.95551	+	11.4893i	0.417357	+	0.481655i	−0.507673	+	0.861550i	$0.669494\pi$
$570$	−1.04968	−	0.565762i	−0.0439661	−	0.0236972i
$571$	24.3482	−	28.0993i	1.01894	−	1.17592i	0.0346409	−	0.999400i	$-0.488971\pi$
$571$	24.3482	−	28.0993i	1.01894	−	1.17592i	0.984297	−	0.176518i	$-0.0564833\pi$
$572$	5.24562	+	17.8650i	0.219331	+	0.746971i
$573$	1.04054	−	0.475200i	0.0434693	−	0.0198517i
$574$	0.451007			0.0188247
$575$	22.1852	−	9.10033i	0.925188	−	0.379510i
$576$	−2.98369			−0.124320
$577$	2.45018	−	1.11896i	0.102002	−	0.0465829i	−0.363760	−	0.931493i	$-0.618507\pi$
$577$	2.45018	−	1.11896i	0.102002	−	0.0465829i	0.465763	+	0.884910i	$0.345780\pi$
$578$	11.8243	+	40.2700i	0.491827	+	1.67501i
$579$	−0.213756	+	0.246687i	−0.00888339	+	0.0102520i
$580$	4.61532	+	2.48760i	0.191641	+	0.103292i
$581$	−2.32531	−	2.68356i	−0.0964703	−	0.111333i
$582$	−0.576690	+	0.0829155i	−0.0239046	+	0.00343696i
$583$	−14.9755	+	51.0018i	−0.620221	+	2.11228i
$584$	8.57233	−	5.50910i	0.354726	−	0.227968i
$585$	24.8666	+	1.64232i	1.02811	+	0.0679017i
$586$	−7.07824	+	15.4992i	−0.292399	+	0.640265i
$587$	2.43392	+	1.11153i	0.100458	+	0.0458778i	0.465010	−	0.885305i	$-0.346051\pi$
$587$	2.43392	+	1.11153i	0.100458	+	0.0458778i	−0.364552	+	0.931183i	$0.618778\pi$
$588$	−0.875008	−	0.125807i	−0.0360847	−	0.00518820i
$589$	−11.6738	+	7.50232i	−0.481012	+	0.309128i
$590$	−4.75636	+	22.4531i	−0.195816	+	0.924381i
$591$	0.119539	+	0.831410i	0.00491716	+	0.0341996i
$592$	−6.37426	+	5.52333i	−0.261980	+	0.227007i
$593$	6.82295	−	10.6167i	0.280185	−	0.435976i	−0.672428	−	0.740163i	$-0.734748\pi$
$593$	6.82295	−	10.6167i	0.280185	−	0.435976i	0.952612	+	0.304187i	$0.0983847\pi$
$594$	−2.49477	+	2.87912i	−0.102362	+	0.118132i
$595$	4.50840	−	1.70959i	0.184826	−	0.0700865i
$596$	−4.53178	−	9.92321i	−0.185629	−	0.406470i
$597$			1.13928i			0.0466275i
$598$	−1.65942	−	17.8368i	−0.0678588	−	0.729400i
$599$	16.1949			0.661704			0.330852	−	0.943683i	$-0.392664\pi$
$599$	16.1949			0.661704			0.330852	+	0.943683i	$0.392664\pi$
$600$	−0.351103	−	0.533451i	−0.0143337	−	0.0217781i
$601$	40.2708	−	11.8246i	1.64268	−	0.482334i	0.675698	−	0.737179i	$-0.263843\pi$
$601$	40.2708	−	11.8246i	1.64268	−	0.482334i	0.966982	+	0.254845i	$0.0820243\pi$
$602$	1.72214	+	1.49224i	0.0701892	+	0.0608193i
$603$	14.7242	−	22.9112i	0.599614	−	0.933018i
$604$	9.18127	+	10.5957i	0.373580	+	0.431135i
$605$	6.74640	+	30.2188i	0.274280	+	1.22857i
$606$	−0.235885	−	0.0692621i	−0.00958218	−	0.00281358i
$607$	0.896532	+	1.39503i	0.0363891	+	0.0566225i	0.858972	−	0.512023i	$-0.171104\pi$
$607$	0.896532	+	1.39503i	0.0363891	+	0.0566225i	−0.822582	+	0.568646i	$0.807467\pi$
$608$	−4.13267	−	0.594188i	−0.167602	−	0.0240975i
$609$	−0.0349343	+	0.0764954i	−0.00141561	+	0.00309975i
$610$	22.7741	+	8.35321i	0.922098	+	0.338211i
$611$	3.18224	−	22.1330i	0.128740	−	0.895405i
$612$	−12.3873	−	19.2751i	−0.500728	−	0.779148i
$613$	7.58275	−	25.8245i	0.306264	−	1.04304i	−0.652252	−	0.758003i	$-0.726175\pi$
$613$	7.58275	−	25.8245i	0.306264	−	1.04304i	0.958516	−	0.285039i	$-0.0920064\pi$
$614$	−0.297219	−	2.06721i	−0.0119948	−	0.0834257i
$615$	0.322593	−	0.326129i	0.0130082	−	0.0131508i
$616$	−1.17749	−	0.756730i	−0.0474426	−	0.0304895i
$617$	−26.1497	−	22.6589i	−1.05275	−	0.912211i	−0.0564697	−	0.998404i	$-0.517984\pi$
$617$	−26.1497	−	22.6589i	−1.05275	−	0.912211i	−0.996278	+	0.0861928i	$0.972530\pi$
$618$	−0.544545	−	1.85455i	−0.0219048	−	0.0746009i
$619$	−12.1489	−	26.6024i	−0.488305	−	1.06924i	−0.980096	−	0.198525i	$-0.936385\pi$
$619$	−12.1489	−	26.6024i	−0.488305	−	1.06924i	0.491791	−	0.870713i	$-0.336343\pi$
$620$	−7.40994	+	0.570578i	−0.297590	+	0.0229150i
$621$	2.88663	−	2.25872i	0.115836	−	0.0906394i
$622$		−	13.9007i		−	0.557367i
$623$	1.42847	−	0.652360i	0.0572304	−	0.0261362i
$624$	−0.457765	+	0.134412i	−0.0183253	+	0.00538078i
$625$	−9.88717	+	22.9618i	−0.395487	+	0.918472i
$626$	−8.70847	−	5.59660i	−0.348061	−	0.223685i
$627$	−2.00893	+	1.74075i	−0.0802290	+	0.0695188i
$628$	3.11916	−	0.448467i	0.124468	−	0.0178958i
$629$	−62.1455	−	18.2476i	−2.47790	−	0.727578i
$630$	−1.49360	+	1.13085i	−0.0595066	+	0.0450542i
$631$	−2.97986	+	20.7254i	−0.118626	+	0.825063i	0.840445	+	0.541897i	$0.182294\pi$
$631$	−2.97986	+	20.7254i	−0.118626	+	0.825063i	−0.959071	+	0.283166i	$0.908615\pi$
$632$	4.39228	+	2.00589i	0.174715	+	0.0797899i
$633$	−1.60065	−	0.730993i	−0.0636202	−	0.0290544i
$634$	0.241988	−	1.68306i	0.00961057	−	0.0668430i
$635$	−24.3392	−	32.1466i	−0.965870	−	1.27570i
$636$	−1.30685	−	0.383726i	−0.0518200	−	0.0152157i
$637$	25.5893	−	3.67919i	1.01389	−	0.145775i
$638$	8.83307	−	7.65390i	0.349705	−	0.303021i
$639$	−9.49765	−	6.10377i	−0.375721	−	0.241461i
$640$	−1.79734	−	1.33025i	−0.0710462	−	0.0525827i
$641$	7.35104	−	2.15846i	0.290349	−	0.0852540i	−0.133315	−	0.991074i	$-0.542562\pi$
$641$	7.35104	−	2.15846i	0.290349	−	0.0852540i	0.423663	+	0.905820i	$0.360744\pi$
$642$	−0.826181	+	0.377304i	−0.0326068	+	0.0148910i
$643$			39.1290i			1.54310i	0.636170	+	0.771549i	$0.280518\pi$
$643$			39.1290i			1.54310i	−0.636170	+	0.771549i	$0.719482\pi$
$644$	0.972363	+	0.931673i	0.0383165	+	0.0367131i
$645$	2.31086	−	0.177940i	0.0909900	−	0.00700639i
$646$	−13.3190	−	29.1645i	−0.524029	−	1.14746i
$647$	6.68277	+	22.7594i	0.262727	+	0.894766i	0.980172	+	0.198150i	$0.0634935\pi$
$647$	6.68277	+	22.7594i	0.262727	+	0.894766i	−0.717445	+	0.696616i	$0.754688\pi$
$648$	6.69099	+	5.79777i	0.262847	+	0.227758i
$649$	43.0415	+	27.6611i	1.68953	+	1.08579i
$650$	14.2472	+	12.0759i	0.558820	+	0.473655i
$651$	−0.0169643	−	0.117989i	−0.000664883	−	0.00462436i
$652$	−3.23611	+	11.0212i	−0.126736	+	0.431622i
$653$	−12.9480	−	20.1475i	−0.506695	−	0.788433i	0.489822	−	0.871823i	$-0.337062\pi$
$653$	−12.9480	−	20.1475i	−0.506695	−	0.788433i	−0.996517	+	0.0833895i	$0.973425\pi$
$654$	0.193342	−	1.34472i	0.00756027	−	0.0525828i
$655$	−1.29355	+	3.52672i	−0.0505431	+	0.137800i
$656$	0.667222	−	1.46101i	0.0260506	−	0.0570429i
$657$	−30.0941	−	4.32688i	−1.17408	−	0.168808i
$658$	0.908791	+	1.41411i	0.0354284	+	0.0551276i
$659$	25.4360	+	7.46869i	0.990847	+	0.290939i	0.736695	−	0.676225i	$-0.236385\pi$
$659$	25.4360	+	7.46869i	0.990847	+	0.290939i	0.254152	+	0.967164i	$0.418204\pi$
$660$	−1.38943	+	0.310193i	−0.0540835	+	0.0120742i
$661$	−1.73503	−	2.00233i	−0.0674849	−	0.0778817i	0.721003	−	0.692932i	$-0.243681\pi$
$661$	−1.73503	−	2.00233i	−0.0674849	−	0.0778817i	−0.788488	+	0.615050i	$0.789136\pi$
$662$	1.17300	−	1.82523i	0.0455901	−	0.0709395i
$663$	−2.76882	−	2.39919i	−0.107532	−	0.0931770i
$664$	−12.1333	+	3.56266i	−0.470863	+	0.138258i
$665$	−2.29398	+	1.26889i	−0.0889566	+	0.0492053i
$666$	25.1655			0.975142
$667$	−9.75215	+	5.59881i	−0.377605	+	0.216787i
$668$			13.7748i			0.532965i
$669$	0.0183270	+	0.0401305i	0.000708563	+	0.00155154i
$670$	19.0845	−	7.23686i	0.737297	−	0.279584i
$671$	35.4120	−	40.8676i	1.36707	−	1.57768i
$672$	0.0193902	−	0.0301717i	0.000747991	−	0.00116390i
$673$	18.7465	−	16.2439i	0.722623	−	0.626156i	−0.213862	−	0.976864i	$-0.568604\pi$
$673$	18.7465	−	16.2439i	0.722623	−	0.626156i	0.936485	+	0.350708i	$0.114059\pi$
$674$	−2.24127	−	15.5884i	−0.0863305	−	0.600442i
$675$	−0.502571	+	3.78815i	−0.0193440	+	0.145806i
$676$	0.801161	−	0.514875i	0.0308139	−	0.0198029i
$677$	14.8204	+	2.13086i	0.569595	+	0.0818954i	0.421094	−	0.907017i	$-0.361646\pi$
$677$	14.8204	+	2.13086i	0.569595	+	0.0818954i	0.148501	+	0.988912i	$0.452555\pi$
$678$	−1.44449	−	0.659676i	−0.0554752	−	0.0253347i
$679$	−0.532092	+	1.16512i	−0.0204198	+	0.0447131i
$680$	1.13161	−	17.1339i	0.0433954	−	0.657054i
$681$	−0.834864	+	0.536534i	−0.0319920	+	0.0205600i
$682$	−4.66753	+	15.8961i	−0.178729	+	0.608694i
$683$	21.5081	−	3.09240i	0.822986	−	0.118327i	0.282059	−	0.959397i	$-0.408983\pi$
$683$	21.5081	−	3.09240i	0.822986	−	0.118327i	0.540927	+	0.841070i	$0.318074\pi$
$684$	8.15785	+	9.41466i	0.311923	+	0.359979i
$685$	0.858576	−	1.59294i	0.0328045	−	0.0608633i
$686$	−2.55988	+	2.95426i	−0.0977367	+	0.112794i
$687$	−0.256937	−	0.875048i	−0.00980277	−	0.0333852i
$688$	7.38178	−	3.37114i	0.281428	−	0.128524i
$689$	39.8319			1.51747
$690$	1.36921	−	0.0367271i	0.0521249	−	0.00139818i
$691$	−44.9009			−1.70811			−0.854056	−	0.520181i	$-0.825865\pi$
$691$	−44.9009			−1.70811			−0.854056	+	0.520181i	$0.825865\pi$
$692$	5.24943	−	2.39734i	0.199553	−	0.0911330i
$693$	1.17658	+	4.00707i	0.0446946	+	0.152216i
$694$	5.20623	−	6.00831i	0.197626	−	0.228072i
$695$	−29.4981	−	15.8991i	−1.11893	−	0.603087i
$696$	0.196121	+	0.226335i	0.00743393	+	0.00857922i
$697$	12.2085	−	1.75531i	0.462428	−	0.0664871i
$698$	−3.61369	+	12.3071i	−0.136780	+	0.465831i
$699$	0.961654	−	0.618017i	0.0363731	−	0.0233756i
$700$	−1.40391	+	0.0153039i	−0.0530629	+	0.000578435i
$701$	17.1355	−	37.5215i	0.647198	−	1.41717i	−0.246788	−	0.969070i	$-0.579375\pi$
$701$	17.1355	−	37.5215i	0.647198	−	1.41717i	0.893985	−	0.448096i	$-0.147898\pi$
$702$	2.59678	+	1.18591i	0.0980091	+	0.0447593i
$703$	34.8564	+	5.01159i	1.31463	+	0.189016i
$704$	−4.19337	+	2.69492i	−0.158044	+	0.101568i
$705$	1.67259	+	0.354314i	0.0629934	+	0.0133442i
$706$	1.22112	+	8.49310i	0.0459576	+	0.319642i
$707$	−0.408465	+	0.353937i	−0.0153619	+	0.0133112i
$708$	−0.708777	+	1.10288i	−0.0266375	+	0.0414487i
$709$	15.1105	−	17.4385i	0.567488	−	0.654916i	−0.397379	−	0.917655i	$-0.630080\pi$
$709$	15.1105	−	17.4385i	0.567488	−	0.654916i	0.964867	+	0.262738i	$0.0846256\pi$
$710$	−2.99998	−	7.91129i	−0.112587	−	0.296905i
$711$	−5.98494	−	13.1052i	−0.224453	−	0.491483i
$712$		−	5.59255i		−	0.209590i
$713$	7.33839	−	14.1499i	0.274825	−	0.529916i
$714$	0.275415			0.0103072
$715$	36.4317	−	20.1518i	1.36247	−	0.753633i
$716$	−6.99464	+	2.05381i	−0.261402	+	0.0767545i
$717$	−1.84965	−	1.60273i	−0.0690764	−	0.0598550i
$718$	−15.2289	+	23.6966i	−0.568336	+	0.884349i
$719$	−20.6369	−	23.8163i	−0.769628	−	0.888198i	0.226687	−	0.973968i	$-0.427211\pi$
$719$	−20.6369	−	23.8163i	−0.769628	−	0.888198i	−0.996315	+	0.0857693i	$0.972665\pi$
$720$	1.45369	+	6.51143i	0.0541757	+	0.242667i
$721$	−4.07715	−	1.19716i	−0.151841	−	0.0445846i
$722$	−0.847720	−	1.31908i	−0.0315489	−	0.0490910i
$723$	−1.96684	−	0.282789i	−0.0731477	−	0.0105170i
$724$	−2.80165	+	6.13475i	−0.104122	+	0.227996i
$725$	3.18016	−	11.2842i	0.118108	−	0.419085i
$726$	−0.251699	+	1.75060i	−0.00934142	+	0.0649710i
$727$	−5.62176	−	8.74764i	−0.208500	−	0.324432i	0.721216	−	0.692710i	$-0.243584\pi$
$727$	−5.62176	−	8.74764i	−0.208500	−	0.324432i	−0.929715	+	0.368279i	$0.879947\pi$
$728$	−0.295499	+	1.00638i	−0.0109519	+	0.0372988i
$729$	−3.71770	−	25.8571i	−0.137692	−	0.957672i
$730$	−16.1993	−	16.0237i	−0.599563	−	0.593063i
$731$	52.4249	+	33.6915i	1.93901	+	1.24612i
$732$	1.04718	+	0.907384i	0.0387048	+	0.0335379i
$733$	−10.6777	−	36.3650i	−0.394391	−	1.34317i	−0.882468	−	0.470373i	$-0.844120\pi$
$733$	−10.6777	−	36.3650i	−0.394391	−	1.34317i	0.488077	−	0.872801i	$-0.337699\pi$
$734$	3.21043	+	7.02986i	0.118499	+	0.259477i
$735$	0.151760	+	1.97086i	0.00559775	+	0.0726964i
$736$	4.45662	−	1.77159i	0.164273	−	0.0653018i
$737$		−	45.4993i		−	1.67599i
$738$	−4.35920	+	1.99078i	−0.160464	+	0.0732816i
$739$	−46.3361	+	13.6055i	−1.70450	+	0.500487i	−0.981678	−	0.190545i	$-0.938974\pi$
$739$	−46.3361	+	13.6055i	−1.70450	+	0.500487i	−0.722824	+	0.691032i	$0.757156\pi$
$740$	15.1594	+	11.2198i	0.557271	+	0.412448i
$741$	1.67572	+	1.07692i	0.0615591	+	0.0395616i
$742$	−2.26298	+	1.96088i	−0.0830767	+	0.0719863i
$743$	14.8177	−	2.13047i	0.543609	−	0.0781592i	0.134961	−	0.990851i	$-0.456909\pi$
$743$	14.8177	−	2.13047i	0.543609	−	0.0781592i	0.408649	+	0.912692i	$0.366000\pi$
$744$	−0.407317	−	0.119599i	−0.0149329	−	0.00438471i
$745$	−19.4479	+	14.7246i	−0.712516	+	0.539468i
$746$	2.77552	−	19.3041i	0.101619	−	0.706775i
$747$	34.3207	+	15.6737i	1.25573	+	0.573472i
$748$	−34.8191	−	15.9014i	−1.27311	−	0.581412i
$749$	−0.284170	+	1.97645i	−0.0103833	+	0.0722178i
$750$	−0.993113	+	1.02613i	−0.0362634	+	0.0374690i
$751$	19.9134	+	5.84711i	0.726651	+	0.213364i	0.624079	−	0.781361i	$-0.285474\pi$
$751$	19.9134	+	5.84711i	0.726651	+	0.213364i	0.102573	+	0.994726i	$0.467293\pi$
$752$	5.92538	−	0.851942i	0.216077	−	0.0310671i
$753$	1.96194	−	1.70003i	0.0714970	−	0.0619525i
$754$	−7.36797	−	4.73511i	−0.268326	−	0.172442i
$755$	18.6503	−	25.1991i	0.678755	−	0.917087i
$756$	−0.205913	+	0.0604614i	−0.00748897	+	0.00219896i
$757$	−20.9559	+	9.57022i	−0.761654	+	0.347836i	−0.758083	−	0.652158i	$-0.773864\pi$
$757$	−20.9559	+	9.57022i	−0.761654	+	0.347836i	−0.00357061	+	0.999994i	$0.501137\pi$
$758$			25.7946i			0.936904i
$759$	1.00567	−	2.88299i	0.0365036	−	0.104646i
$760$	0.716763	+	9.30840i	0.0259997	+	0.337651i
$761$	−1.72489	−	3.77698i	−0.0625271	−	0.136915i	0.875789	−	0.482695i	$-0.160342\pi$
$761$	−1.72489	−	3.77698i	−0.0625271	−	0.136915i	−0.938316	+	0.345779i	$0.887615\pi$
$762$	−0.648877	−	2.20987i	−0.0235063	−	0.0800552i
$763$	−2.25721	−	1.95589i	−0.0817166	−	0.0708078i
$764$	−7.53432	−	4.84201i	−0.272582	−	0.175178i
$765$	−36.0296	+	36.4245i	−1.30265	+	1.31693i
$766$	3.52465	+	24.5145i	0.127351	+	0.885745i
$767$	10.8015	−	36.7866i	0.390020	−	1.32829i
$768$	−0.0690535	−	0.107449i	−0.00249175	−	0.00387725i
$769$	1.75312	−	12.1932i	0.0632190	−	0.439698i	−0.933488	−	0.358609i	$-0.883251\pi$
$769$	1.75312	−	12.1932i	0.0632190	−	0.439698i	0.996707	−	0.0810887i	$-0.0258397\pi$
$770$	−1.07776	+	2.93839i	−0.0388396	+	0.105892i
$771$	−0.814197	+	1.78284i	−0.0293226	+	0.0642075i
$772$	2.52958	+	0.363699i	0.0910417	+	0.0130898i
$773$	10.6268	+	16.5355i	0.382218	+	0.594742i	0.978051	−	0.208366i	$-0.0668145\pi$
$773$	10.6268	+	16.5355i	0.382218	+	0.594742i	−0.595833	+	0.803108i	$0.703178\pi$
$774$	−23.2322	−	6.82159i	−0.835064	−	0.245197i
$775$	4.85541	+	15.8930i	0.174411	+	0.570895i
$776$	2.98715	+	3.44736i	0.107233	+	0.123753i
$777$	−0.163543	+	0.254479i	−0.00586709	+	0.00912937i
$778$	−27.3481	−	23.6973i	−0.980479	−	0.849590i
$779$	−6.43433	+	1.88929i	−0.230534	+	0.0676909i
$780$	0.516361	+	0.933513i	0.0184887	+	0.0334251i
$781$	−18.8613			−0.674912
$782$	29.9472	+	21.4353i	1.07091	+	0.766526i
$783$		−	1.79202i		−	0.0640416i
$784$	2.87515	+	6.29570i	0.102684	+	0.224846i
$785$	−2.49840	−	6.58857i	−0.0891717	−	0.235156i
$786$	−0.140514	+	0.162162i	−0.00501198	+	0.00578413i
$787$	4.63405	−	7.21072i	0.165186	−	0.257034i	−0.748786	−	0.662812i	$-0.769363\pi$
$787$	4.63405	−	7.21072i	0.165186	−	0.257034i	0.913972	+	0.405778i	$0.132999\pi$
$788$	4.97003	−	4.30656i	0.177050	−	0.153415i
$789$	−0.271020	−	1.88498i	−0.00964856	−	0.0671072i
$790$	2.23756	−	10.5628i	0.0796089	−	0.375806i
$791$	−2.93693	+	1.88745i	−0.104425	+	0.0671100i
$792$	14.7213	+	2.11660i	0.523099	+	0.0752103i
$793$	−36.8599	−	16.8334i	−1.30893	−	0.597770i
$794$	2.07826	−	4.55075i	0.0737547	−	0.161500i
$795$	−0.200709	+	3.03896i	−0.00711841	+	0.107781i
$796$	7.50376	−	4.82237i	0.265964	−	0.170925i
$797$	−10.8307	+	36.8861i	−0.383644	+	1.30657i	0.510918	+	0.859629i	$0.329306\pi$
$797$	−10.8307	+	36.8861i	−0.383644	+	1.30657i	−0.894562	+	0.446943i	$0.852513\pi$
$798$	−0.148219	+	0.0213106i	−0.00524689	+	0.000754388i
$799$	30.1040	+	34.7419i	1.06500	+	1.22908i
$800$	−2.02738	+	4.57053i	−0.0716785	+	0.161593i
$801$	−10.9273	+	12.6107i	−0.386096	+	0.445579i
$802$	1.81761	+	6.19023i	0.0641822	+	0.218585i
$803$	−46.2034	+	21.1004i	−1.63048	+	0.744617i
$804$	1.16586			0.0411166
$805$	1.55948	−	2.57595i	0.0549646	−	0.0907904i
$806$	12.4147			0.437290
$807$	0.970806	−	0.443352i	0.0341740	−	0.0156067i
$808$	0.542274	+	1.84682i	0.0190771	+	0.0649707i
$809$	−12.8412	+	14.8196i	−0.451474	+	0.521028i	−0.935166	−	0.354210i	$-0.884750\pi$
$809$	−12.8412	+	14.8196i	−0.451474	+	0.521028i	0.483692	+	0.875238i	$0.339295\pi$
$810$	9.39280	−	17.4268i	0.330029	−	0.612314i
$811$	15.8211	+	18.2585i	0.555554	+	0.641143i	0.962168	−	0.272457i	$-0.0878361\pi$
$811$	15.8211	+	18.2585i	0.555554	+	0.641143i	−0.406614	+	0.913600i	$0.633291\pi$
$812$	0.651703	−	0.0937007i	0.0228703	−	0.00328825i
$813$	−0.0854659	+	0.291070i	−0.00299742	+	0.0102083i
$814$	35.3684	−	22.7299i	1.23966	−	0.796682i
$815$	25.6287	+	1.69265i	0.897733	+	0.0592911i
$816$	0.407451	−	0.892192i	0.0142636	−	0.0312330i
$817$	−30.8201	−	14.0751i	−1.07826	−	0.492425i
$818$	12.2306	+	1.75849i	0.427633	+	0.0614843i
$819$	2.63269	−	1.69192i	0.0919935	−	0.0591206i
$820$	−3.51351	−	0.744285i	−0.122697	−	0.0259916i
$821$	3.79085	+	26.3660i	0.132302	+	0.920178i	0.942544	+	0.334083i	$0.108427\pi$
$821$	3.79085	+	26.3660i	0.132302	+	0.920178i	−0.810242	+	0.586095i	$0.800664\pi$
$822$	0.0781179	−	0.0676896i	0.00272468	−	0.00236095i
$823$	−2.59683	+	4.04075i	−0.0905200	+	0.140852i	−0.883560	−	0.468317i	$-0.844860\pi$
$823$	−2.59683	+	4.04075i	−0.0905200	+	0.140852i	0.793040	+	0.609169i	$0.208497\pi$
$824$	−9.90989	+	11.4366i	−0.345227	+	0.398413i
$825$	1.35389	+	2.88108i	0.0471365	+	0.100306i
$826$	1.19730	+	2.62171i	0.0416593	+	0.0912211i
$827$		−	3.63332i		−	0.126343i	−0.998003	−	0.0631715i	$-0.979878\pi$
$827$		−	3.63332i		−	0.126343i	0.998003	−	0.0631715i	$-0.0201215\pi$
$828$	−13.5108	−	4.71299i	−0.469534	−	0.163788i
$829$	4.44615			0.154421			0.0772106	−	0.997015i	$-0.475399\pi$
$829$	4.44615			0.154421			0.0772106	+	0.997015i	$0.475399\pi$
$830$	13.6864	+	24.7433i	0.475063	+	0.858851i
$831$	−1.20463	+	0.353710i	−0.0417880	+	0.0122701i
$832$	2.82294	+	2.44609i	0.0978678	+	0.0848029i
$833$	−28.7345	+	44.7117i	−0.995590	+	1.54917i
$834$	−1.25347	−	1.44659i	−0.0434043	−	0.0500912i
$835$	30.0614	−	6.71127i	1.04032	−	0.232253i
$836$	19.9688	+	5.86337i	0.690635	+	0.202789i
$837$	1.37331	+	2.13691i	0.0474685	+	0.0738624i
$838$	16.6796	+	2.39816i	0.576186	+	0.0828430i
$839$	−19.4575	+	42.6060i	−0.671748	+	1.47092i	0.199408	+	0.979916i	$0.436098\pi$
$839$	−19.4575	+	42.6060i	−0.671748	+	1.47092i	−0.871156	+	0.491006i	$0.836629\pi$
$840$	−0.0752921	−	0.0276160i	−0.00259782	−	0.000952842i
$841$	3.34470	−	23.2629i	0.115335	−	0.802169i
$842$	10.6297	+	16.5401i	0.366323	+	0.570010i
$843$	−0.606852	+	2.06675i	−0.0209011	+	0.0711826i
$844$	1.96067	+	13.6367i	0.0674890	+	0.469396i
$845$	−1.51397	−	1.49755i	−0.0520821	−	0.0515175i
$846$	−15.0259	−	9.65654i	−0.516600	−	0.331999i
$847$	2.93851	+	2.54623i	0.100968	+	0.0874896i
$848$	3.00431	+	10.2317i	0.103168	+	0.351359i
$849$	−0.194691	−	0.426314i	−0.00668179	−	0.0146311i
$850$	−37.9433	+	5.87826i	−1.30145	+	0.201623i
$851$	−37.5887	+	14.9422i	−1.28852	+	0.512213i
$852$		−	0.483296i		−	0.0165574i
$853$	−17.3122	+	7.90622i	−0.592759	+	0.270704i	−0.689125	−	0.724642i	$-0.742005\pi$
$853$	−17.3122	+	7.90622i	−0.592759	+	0.270704i	0.0963667	+	0.995346i	$0.469278\pi$
$854$	2.92282	−	0.858218i	0.100017	−	0.0293676i
$855$	16.5714	−	22.3902i	0.566731	−	0.765728i
$856$	5.98218	+	3.84451i	0.204467	+	0.131403i
$857$	7.18356	−	6.22459i	0.245386	−	0.212628i	−0.523480	−	0.852038i	$-0.675367\pi$
$857$	7.18356	−	6.22459i	0.245386	−	0.212628i	0.768866	+	0.639410i	$0.220821\pi$
$858$	2.35393	−	0.338444i	0.0803619	−	0.0115543i
$859$	42.4560	+	12.4662i	1.44858	+	0.425341i	0.909072	−	0.416639i	$-0.136792\pi$
$859$	42.4560	+	12.4662i	1.44858	+	0.425341i	0.539508	+	0.841981i	$0.318610\pi$
$860$	−10.9535	−	14.4671i	−0.373511	−	0.493324i
$861$	0.00819805	−	0.0570187i	0.000279389	−	0.00194319i
$862$	−22.9582	−	10.4847i	−0.781959	−	0.357109i
$863$	−43.6356	−	19.9277i	−1.48537	−	0.678347i	−0.502830	−	0.864385i	$-0.667708\pi$
$863$	−43.6356	−	19.9277i	−1.48537	−	0.678347i	−0.982542	+	0.186039i	$0.940435\pi$
$864$	−0.108767	+	0.756489i	−0.00370032	+	0.0257363i
$865$	−7.78940	−	10.2881i	−0.264847	−	0.349804i
$866$	−20.1012	−	5.90225i	−0.683067	−	0.200567i
$867$	5.30608	−	0.762899i	0.180204	−	0.0259094i
$868$	−0.705321	+	0.611164i	−0.0239401	+	0.0207443i
$869$	−20.2483	−	13.0128i	−0.686875	−	0.441428i
$870$	0.398389	−	0.538276i	0.0135067	−	0.0182493i
$871$	−32.7140	+	9.60571i	−1.10847	+	0.325477i
$872$	−9.67531	+	4.41856i	−0.327647	+	0.149631i
$873$		−	13.6101i		−	0.460633i
$874$	−17.7751	−	9.21852i	−0.601253	−	0.311821i
$875$	0.717401	+	3.05636i	0.0242526	+	0.103324i
$876$	−0.540669	−	1.18390i	−0.0182675	−	0.0400002i
$877$	5.75302	+	19.5930i	0.194266	+	0.661609i	0.997797	+	0.0663456i	$0.0211340\pi$
$877$	5.75302	+	19.5930i	0.194266	+	0.661609i	−0.803531	+	0.595263i	$0.797048\pi$
$878$	−5.39598	−	4.67565i	−0.182106	−	0.157795i
$879$	1.83082	+	1.17660i	0.0617522	+	0.0396857i
$880$	7.92429	+	7.83838i	0.267128	+	0.264232i
$881$	−1.18784	−	8.26160i	−0.0400193	−	0.278340i	0.959979	−	0.280071i	$-0.0903581\pi$
$881$	−1.18784	−	8.26160i	−0.0400193	−	0.278340i	−0.999999	+	0.00173092i	$0.999449\pi$
$882$	5.81793	−	19.8141i	0.195900	−	0.667174i
$883$	26.7301	+	41.5929i	0.899540	+	1.39971i	0.916577	+	0.399857i	$0.130940\pi$
$883$	26.7301	+	41.5929i	0.899540	+	1.39971i	−0.0170371	+	0.999855i	$0.505423\pi$
$884$	−4.08216	+	28.3920i	−0.137298	+	0.954927i
$885$	2.75219	+	1.00946i	0.0925137	+	0.0339326i
$886$	−14.6454	+	32.0688i	−0.492020	+	1.07737i
$887$	−16.3948	−	2.35721i	−0.550483	−	0.0791475i	−0.138539	−	0.990357i	$-0.544241\pi$
$887$	−16.3948	−	2.35721i	−0.550483	−	0.0791475i	−0.411943	+	0.911209i	$0.635150\pi$
$888$	0.582422	+	0.906266i	0.0195448	+	0.0304123i
$889$	−4.85831	−	1.42653i	−0.162943	−	0.0478443i
$890$	−12.2049	+	2.72476i	−0.409108	+	0.0913340i
$891$	−28.9000	−	33.3524i	−0.968186	−	1.11735i
$892$	0.186742	−	0.290576i	0.00625257	−	0.00972919i
$893$	−18.8891	−	16.3675i	−0.632100	−	0.547717i
$894$	−1.33692	+	0.392555i	−0.0447133	+	0.0131290i
$895$	7.88999	+	14.2641i	0.263733	+	0.476795i
$896$	−0.280799			−0.00938083
$897$	−2.28518	−	0.114430i	−0.0763000	−	0.00382070i
$898$		−	33.7399i		−	1.12592i
$899$	−3.23737	−	7.08886i	−0.107972	−	0.236427i
$900$	13.5019	−	6.34489i	0.450064	−	0.211496i
$901$	−53.6256	+	61.8873i	−1.78653	+	2.06176i
$902$	−4.32846	+	6.73521i	−0.144122	+	0.224258i
$903$	0.219961	−	0.190597i	0.00731984	−	0.00634268i
$904$	1.76938	+	12.3063i	0.0588488	+	0.409302i
$905$	14.7531	+	3.12523i	0.490410	+	0.103886i
$906$	1.50646	−	0.968143i	0.0500488	−	0.0321644i
$907$	4.60154	+	0.661601i	0.152791	+	0.0219681i	0.218286	−	0.975885i	$-0.429953\pi$
$907$	4.60154	+	0.661601i	0.152791	+	0.0219681i	−0.0654946	+	0.997853i	$0.520863\pi$
$908$	7.06769	+	3.22771i	0.234549	+	0.107115i
$909$	2.38571	−	5.22397i	0.0791289	−	0.173268i
$910$	2.34023	+	0.154561i	0.0775779	+	0.00512366i
$911$	−26.4234	+	16.9813i	−0.875446	+	0.562615i	−0.899414	−	0.437098i	$-0.856006\pi$
$911$	−26.4234	+	16.9813i	−0.875446	+	0.562615i	0.0239679	+	0.999713i	$0.492370\pi$
$912$	−0.150241	+	0.511673i	−0.00497497	+	0.0169432i
$913$	62.3922	−	8.97065i	2.06488	−	0.296885i
$914$	−2.39143	−	2.75986i	−0.0791016	−	0.0912881i
$915$	1.47003	−	2.72739i	0.0485976	−	0.0901647i
$916$	−4.67586	+	5.39624i	−0.154495	+	0.178297i
$917$	0.132901	+	0.452618i	0.00438876	+	0.0149468i
$918$	−5.33860	+	2.43806i	−0.176200	+	0.0804679i
$919$	−5.49271			−0.181188			−0.0905939	−	0.995888i	$-0.528877\pi$
$919$	−5.49271			−0.181188			−0.0905939	+	0.995888i	$0.528877\pi$
$920$	−6.03754	−	8.86274i	−0.199052	−	0.292196i
$921$	−0.266750			−0.00878970
$922$	−25.9304	+	11.8420i	−0.853972	+	0.389996i
$923$	3.98196	+	13.5613i	0.131068	+	0.446376i
$924$	−0.117073	+	0.135110i	−0.00385143	+	0.00444479i
$925$	17.0996	−	38.5495i	0.562231	−	1.26750i
$926$	−19.9481	−	23.0214i	−0.655536	−	0.756529i
$927$	44.6920	−	6.42574i	1.46788	−	0.211049i
$928$	0.660594	−	2.24977i	0.0216850	−	0.0738525i
$929$	7.02870	−	4.51707i	0.230604	−	0.148200i	−0.420237	−	0.907415i	$-0.638053\pi$
$929$	7.02870	−	4.51707i	0.230604	−	0.148200i	0.650841	+	0.759214i	$0.274417\pi$
$930$	−0.0625565	+	0.947175i	−0.00205131	+	0.0310591i
$931$	12.0042	−	26.2856i	0.393423	−	0.861476i
$932$	−8.14105	−	3.71789i	−0.266669	−	0.121784i
$933$	−1.75740	−	0.252676i	−0.0575346	−	0.00827223i
$934$	30.5290	−	19.6198i	0.998939	−	0.641979i
$935$	−17.7380	+	83.7347i	−0.580093	+	2.73842i
$936$	−1.58609	−	11.0315i	−0.0518429	−	0.360575i
$937$	−35.1166	+	30.4287i	−1.14721	+	0.994063i	−0.147222	+	0.989103i	$0.547033\pi$
$937$	−35.1166	+	30.4287i	−1.14721	+	0.994063i	−0.999988	+	0.00495980i	$0.998421\pi$
$938$	1.38571	−	2.15621i	0.0452451	−	0.0704028i
$939$	−0.865847	+	0.999241i	−0.0282558	+	0.0326090i
$940$	−4.74615	−	12.5161i	−0.154802	−	0.408232i
$941$	9.97888	+	21.8507i	0.325302	+	0.712312i	0.999660	−	0.0260927i	$-0.00830651\pi$
$941$	9.97888	+	21.8507i	0.325302	+	0.712312i	−0.674357	+	0.738405i	$0.735579\pi$
$942$		−	0.402492i		−	0.0131139i
$943$	5.32913	−	5.56187i	0.173540	−	0.181119i
$944$	10.2642			0.334070
$945$	0.232271	+	0.419915i	0.00755577	+	0.0136598i
$946$	−38.8127	+	11.3964i	−1.26191	+	0.370530i
$947$	40.9726	+	35.5030i	1.33143	+	1.15369i	0.975702	+	0.219103i	$0.0703129\pi$
$947$	40.9726	+	35.5030i	1.33143	+	1.15369i	0.355729	+	0.934589i	$0.384233\pi$
$948$	0.333434	−	0.518834i	0.0108294	−	0.0168509i
$949$	24.9255	+	28.7656i	0.809117	+	0.933771i
$950$	19.9649	−	6.09939i	0.647747	−	0.197890i
$951$	−0.208383	−	0.0611868i	−0.00675729	−	0.00198412i
$952$	−1.16579	−	1.81400i	−0.0377835	−	0.0587922i
$953$	−30.8033	−	4.42885i	−0.997817	−	0.143464i	−0.375994	−	0.926622i	$-0.622699\pi$
$953$	−30.8033	−	4.42885i	−0.997817	−	0.143464i	−0.621823	+	0.783158i	$0.713608\pi$
$954$	13.2173	−	28.9419i	0.427926	−	0.937027i
$955$	−6.89612	+	18.8016i	−0.223153	+	0.608404i
$956$	−2.72700	+	18.9667i	−0.0881974	+	0.613426i
$957$	−0.807086	−	1.25585i	−0.0260894	−	0.0405959i
$958$	6.93838	−	23.6299i	0.224169	−	0.763449i
$959$	−0.0323401	−	0.224930i	−0.00104432	−	0.00726338i
$960$	−0.200848	+	0.203049i	−0.00648233	+	0.00655338i
$961$	−16.7859	−	10.7877i	−0.541481	−	0.347989i
$962$	−23.8097	−	20.6312i	−0.767654	−	0.665176i
$963$	−5.97755	−	20.3577i	−0.192624	−	0.656016i
$964$	6.46276	+	14.1515i	0.208151	+	0.455788i
$965$	−0.438727	−	5.69762i	−0.0141231	−	0.183413i
$966$	0.135462	−	0.105996i	0.00435842	−	0.00341037i
$967$			5.75671i			0.185123i	0.995707	+	0.0925617i	$0.0295055\pi$
$967$			5.75671i			0.185123i	−0.995707	+	0.0925617i	$0.970494\pi$
$968$	12.5956	−	5.75223i	0.404839	−	0.184884i
$969$	−3.92924	+	1.15373i	−0.126225	+	0.0370631i
$970$	6.06795	−	8.19859i	0.194830	−	0.263241i
$971$	−26.5964	−	17.0925i	−0.853520	−	0.548524i	0.0391508	−	0.999233i	$-0.487535\pi$
$971$	−26.5964	−	17.0925i	−0.853520	−	0.548524i	−0.892671	+	0.450709i	$0.851171\pi$
$972$	2.58739	−	2.24199i	0.0829907	−	0.0719119i
$973$	−4.16526	+	0.598874i	−0.133532	+	0.0191990i
$974$	29.3089	+	8.60588i	0.939118	+	0.275750i
$975$	1.78567	−	1.58170i	0.0571872	−	0.0506548i
$976$	1.54389	−	10.7380i	0.0494186	−	0.343714i
$977$	−19.1808	−	8.75957i	−0.613648	−	0.280244i	0.0842458	−	0.996445i	$-0.473152\pi$
$977$	−19.1808	−	8.75957i	−0.613648	−	0.280244i	−0.697894	+	0.716201i	$0.745879\pi$
$978$	1.33453	+	0.609460i	0.0426736	+	0.0194884i
$979$	−3.96731	+	27.5933i	−0.126796	+	0.881884i
$980$	12.3386	−	9.34191i	0.394141	−	0.298416i
$981$	30.4505	+	8.94106i	0.972209	+	0.285466i
$982$	1.24876	−	0.179544i	0.0398494	−	0.00572948i
$983$	−31.8138	+	27.5668i	−1.01470	+	0.879245i	−0.992712	−	0.120513i	$-0.961546\pi$
$983$	−31.8138	+	27.5668i	−1.01470	+	0.879245i	−0.0219910	+	0.999758i	$0.507001\pi$
$984$	−0.172581	−	0.110911i	−0.00550167	−	0.00353571i
$985$	−11.8198	−	8.74811i	−0.376612	−	0.278738i
$986$	17.2765	−	5.07283i	0.550195	−	0.161552i
$987$	0.195298	−	0.0891896i	0.00621640	−	0.00283894i
$988$		−	15.5954i		−	0.496157i
$989$	38.7514	−	3.60519i	1.23222	−	0.114638i
$990$	−2.55324	−	33.1582i	−0.0811473	−	1.05384i
$991$	8.62386	+	18.8836i	0.273946	+	0.599858i	0.995735	−	0.0922549i	$-0.0294075\pi$
$991$	8.62386	+	18.8836i	0.273946	+	0.599858i	−0.721790	+	0.692113i	$0.756680\pi$
$992$	0.936376	+	3.18900i	0.0297300	+	0.101251i
$993$	−0.209433	−	0.181475i	−0.00664616	−	0.00575893i
$994$	−0.893837	−	0.574434i	−0.0283508	−	0.0182200i
$995$	−14.1800	−	14.0263i	−0.449536	−	0.444663i
$996$	0.229861	+	1.59872i	0.00728341	+	0.0506572i
$997$	1.16846	−	3.97941i	0.0370055	−	0.126029i	−0.938919	−	0.344139i	$-0.888171\pi$
$997$	1.16846	−	3.97941i	0.0370055	−	0.126029i	0.975924	+	0.218110i	$0.0699891\pi$
$998$	−1.89964	−	2.95589i	−0.0601319	−	0.0935671i
$999$	0.917377	−	6.38050i	0.0290245	−	0.201870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.j.a.119.3	yes	120
5.4	even	2	inner	230.2.j.a.119.10	yes	120
23.6	even	11	inner	230.2.j.a.29.10	yes	120
115.29	even	22	inner	230.2.j.a.29.3	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.j.a.29.3	✓	120	115.29	even	22	inner
230.2.j.a.29.10	yes	120	23.6	even	11	inner
230.2.j.a.119.3	yes	120	1.1	even	1	trivial
230.2.j.a.119.10	yes	120	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.j (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909632 + 0.415415i) q^{2} +(0.0359844 + 0.122552i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.96836 - 1.06092i) q^{5} +(-0.0836423 - 0.0965284i) q^{6} +(-0.277941 + 0.0399619i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.51004 - 1.61310i) q^{9} +O(q^{10})\)	\(q+(-0.909632 + 0.415415i) q^{2} +(0.0359844 + 0.122552i) q^{3} +(0.654861 - 0.755750i) q^{4} +(-1.96836 - 1.06092i) q^{5} +(-0.0836423 - 0.0965284i) q^{6} +(-0.277941 + 0.0399619i) q^{7} +(-0.281733 + 0.959493i) q^{8} +(2.51004 - 1.61310i) q^{9} +(2.23121 + 0.147361i) q^{10} +(2.07071 - 4.53422i) q^{11} +(0.116183 + 0.0530590i) q^{12} +(-3.69726 - 0.531586i) q^{13} +(0.236223 - 0.151811i) q^{14} +(0.0591873 - 0.279402i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(5.80355 - 5.02880i) q^{17} +(-1.61310 + 2.51004i) q^{18} +(-2.73415 + 3.15538i) q^{19} +(-2.09079 + 0.792833i) q^{20} +(-0.0148989 - 0.0326241i) q^{21} +4.98467i q^{22} +(0.919072 - 4.70694i) q^{23} -0.127725 q^{24} +(2.74889 + 4.17655i) q^{25} +(3.58398 - 1.05235i) q^{26} +(0.577595 + 0.500489i) q^{27} +(-0.151811 + 0.236223i) q^{28} +(-1.53549 - 1.77205i) q^{29} +(0.0622293 + 0.278741i) q^{30} +(3.18900 + 0.936376i) q^{31} +(0.540641 + 0.841254i) q^{32} +(0.630188 + 0.0906074i) q^{33} +(-3.19005 + 6.98524i) q^{34} +(0.589484 + 0.216214i) q^{35} +(0.424623 - 2.95332i) q^{36} +(-4.55996 - 7.09543i) q^{37} +(1.17628 - 4.00604i) q^{38} +(-0.0678970 - 0.472234i) q^{39} +(1.57250 - 1.58973i) q^{40} +(1.35119 + 0.868354i) q^{41} +(0.0271051 + 0.0234867i) q^{42} +(2.28629 + 7.78640i) q^{43} +(-2.07071 - 4.53422i) q^{44} +(-6.65203 + 0.512218i) q^{45} +(1.11932 + 4.66338i) q^{46} +5.98632i q^{47} +(0.116183 - 0.0530590i) q^{48} +(-6.64080 + 1.94991i) q^{49} +(-4.23548 - 2.65719i) q^{50} +(0.825125 + 0.530276i) q^{51} +(-2.82294 + 2.44609i) q^{52} +(-10.5552 + 1.51760i) q^{53} +(-0.733310 - 0.215319i) q^{54} +(-8.88634 + 6.72812i) q^{55} +(0.0399619 - 0.277941i) q^{56} +(-0.485083 - 0.221530i) q^{57} +(2.13286 + 0.974046i) q^{58} +(-1.46074 + 10.1597i) q^{59} +(-0.172399 - 0.227700i) q^{60} +(10.4089 + 3.05634i) q^{61} +(-3.28980 + 0.473003i) q^{62} +(-0.633179 + 0.548653i) q^{63} +(-0.841254 - 0.540641i) q^{64} +(6.71358 + 4.96886i) q^{65} +(-0.610879 + 0.179370i) q^{66} +(8.30299 - 3.79185i) q^{67} -7.67920i q^{68} +(0.609915 - 0.0567427i) q^{69} +(-0.626032 + 0.0482056i) q^{70} +(-1.57188 - 3.44193i) q^{71} +(0.840602 + 2.86283i) q^{72} +(-7.70105 - 6.67300i) q^{73} +(7.09543 + 4.55996i) q^{74} +(-0.412926 + 0.487172i) q^{75} +(0.594188 + 4.13267i) q^{76} +(-0.394338 + 1.34299i) q^{77} +(0.257934 + 0.401354i) q^{78} +(0.687186 - 4.77948i) q^{79} +(-0.769995 + 2.09931i) q^{80} +(3.67785 - 8.05337i) q^{81} +(-1.58981 - 0.228580i) q^{82} +(6.83669 + 10.6381i) q^{83} +(-0.0344123 - 0.0101044i) q^{84} +(-16.7586 + 3.74140i) q^{85} +(-5.31428 - 6.13300i) q^{86} +(0.161914 - 0.251942i) q^{87} +(3.76716 + 3.26427i) q^{88} +(-5.36601 + 1.57560i) q^{89} +(5.83812 - 3.22928i) q^{90} +1.04886 q^{91} +(-2.95541 - 3.77698i) q^{92} +0.424512i q^{93} +(-2.48681 - 5.44534i) q^{94} +(8.72941 - 3.31021i) q^{95} +(-0.0836423 + 0.0965284i) q^{96} +(2.46614 - 3.83739i) q^{97} +(5.23066 - 4.53239i) q^{98} +(-2.11660 - 14.7213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9}+O(q^{10}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9	\( 120 q + 12 q^{4} - 4 q^{6} + 8 q^{9} + 8 q^{11} - 6 q^{15} - 12 q^{16} - 16 q^{19} - 22 q^{20} + 4 q^{24} - 52 q^{25} - 4 q^{26} - 8 q^{29} - 44 q^{30} + 12 q^{31} + 16 q^{35} - 8 q^{36} - 36 q^{39} - 28 q^{41} - 8 q^{44} + 16 q^{45} - 4 q^{46} - 58 q^{49} + 12 q^{50} - 24 q^{51} - 6 q^{54} - 36 q^{55} + 22 q^{56} - 102 q^{59} - 38 q^{60} + 72 q^{61} + 12 q^{64} - 138 q^{65} + 80 q^{66} - 212 q^{69} - 108 q^{70} + 176 q^{71} - 88 q^{74} - 100 q^{75} + 16 q^{76} - 104 q^{79} - 22 q^{80} - 28 q^{81} - 22 q^{84} + 2 q^{85} + 62 q^{86} + 48 q^{89} + 24 q^{90} - 56 q^{91} + 24 q^{94} + 18 q^{95} - 4 q^{96} + 188 q^{99}+O(q^{100}) \) 120 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 8 * q^11 - 6 * q^15 - 12 * q^16 - 16 * q^19 - 22 * q^20 + 4 * q^24 - 52 * q^25 - 4 * q^26 - 8 * q^29 - 44 * q^30 + 12 * q^31 + 16 * q^35 - 8 * q^36 - 36 * q^39 - 28 * q^41 - 8 * q^44 + 16 * q^45 - 4 * q^46 - 58 * q^49 + 12 * q^50 - 24 * q^51 - 6 * q^54 - 36 * q^55 + 22 * q^56 - 102 * q^59 - 38 * q^60 + 72 * q^61 + 12 * q^64 - 138 * q^65 + 80 * q^66 - 212 * q^69 - 108 * q^70 + 176 * q^71 - 88 * q^74 - 100 * q^75 + 16 * q^76 - 104 * q^79 - 22 * q^80 - 28 * q^81 - 22 * q^84 + 2 * q^85 + 62 * q^86 + 48 * q^89 + 24 * q^90 - 56 * q^91 + 24 * q^94 + 18 * q^95 - 4 * q^96 + 188 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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