LMFDB - Embedded newform 462.2.bf.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(5,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 25, 12]))

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

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

chi := DirichletCharacter("462.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bf (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	462.5
Dual form			462.2.bf.a.185.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207912 + 0.978148i) q^{2} +(0.665114 - 1.59926i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.17526 + 1.30525i) q^{5} +(1.42602 + 0.983084i) q^{6} +(-1.84250 - 1.89873i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.11525 - 2.12738i) q^{9} +O(q^{10})$	\(q+(-0.207912 + 0.978148i) q^{2} +(0.665114 - 1.59926i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.17526 + 1.30525i) q^{5} +(1.42602 + 0.983084i) q^{6} +(-1.84250 - 1.89873i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.11525 - 2.12738i) q^{9} +(-1.52108 + 0.878197i) q^{10} +(3.24434 + 0.688659i) q^{11} +(-1.25809 + 1.19047i) q^{12} +(1.96328 - 0.637908i) q^{13} +(2.24032 - 1.40747i) q^{14} +(2.86912 - 1.01139i) q^{15} +(0.669131 + 0.743145i) q^{16} +(7.46145 - 1.58598i) q^{17} +(2.52067 - 1.62672i) q^{18} +(-1.28445 - 2.88492i) q^{19} +(-0.542755 - 1.67043i) q^{20} +(-4.26203 + 1.68376i) q^{21} +(-1.34815 + 3.03026i) q^{22} +(-2.42141 - 1.39800i) q^{23} +(-0.902882 - 1.47811i) q^{24} +(0.200181 - 1.90459i) q^{25} +(0.215779 + 2.05300i) q^{26} +(-4.80910 + 1.96787i) q^{27} +(0.910927 + 2.48399i) q^{28} +(-1.43437 - 1.97424i) q^{29} +(0.392769 + 3.01670i) q^{30} +(-1.32776 - 1.19552i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.25920 - 4.73050i) q^{33} +7.62815i q^{34} +(0.312913 - 4.63643i) q^{35} +(1.06709 + 2.80380i) q^{36} +(-0.174549 - 1.66073i) q^{37} +(3.08893 - 0.656572i) q^{38} +(0.285626 - 3.56407i) q^{39} +(1.74677 - 0.183593i) q^{40} +(9.98409 + 7.25387i) q^{41} +(-0.760843 - 4.51897i) q^{42} +3.77132 q^{43} +(-2.68375 - 1.94871i) q^{44} +(0.290812 - 5.26115i) q^{45} +(1.87089 - 2.07784i) q^{46} +(-4.41911 + 1.96751i) q^{47} +(1.63353 - 0.575836i) q^{48} +(-0.210360 + 6.99684i) q^{49} +(1.82135 + 0.591793i) q^{50} +(2.42633 - 12.9876i) q^{51} +(-2.05300 - 0.215779i) q^{52} +(5.09424 + 4.58688i) q^{53} +(-0.925001 - 5.11316i) q^{54} +(2.91406 + 5.04404i) q^{55} +(-2.61910 + 0.374571i) q^{56} +(-5.46804 + 0.135363i) q^{57} +(2.22932 - 0.992557i) q^{58} +(-11.9328 - 5.31283i) q^{59} +(-3.03244 - 0.243021i) q^{60} +(-6.11377 + 5.50487i) q^{61} +(1.44546 - 1.05019i) q^{62} +(-0.141969 + 7.93598i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(3.13999 + 1.81287i) q^{65} +(3.94950 + 4.17150i) q^{66} +(4.96070 + 8.59218i) q^{67} +(-7.46145 - 1.58598i) q^{68} +(-3.84628 + 2.94263i) q^{69} +(4.47006 + 1.27004i) q^{70} +(-4.43154 - 1.43989i) q^{71} +(-2.96439 + 0.460829i) q^{72} +(-2.80651 + 6.30352i) q^{73} +(1.66073 + 0.174549i) q^{74} +(-2.91279 - 1.58691i) q^{75} +3.15794i q^{76} +(-4.67013 - 7.42899i) q^{77} +(3.42680 + 1.02040i) q^{78} +(6.86683 + 1.45959i) q^{79} +(-0.183593 + 1.74677i) q^{80} +(-0.0514691 + 8.99985i) q^{81} +(-9.17116 + 8.25775i) q^{82} +(0.468282 - 1.44122i) q^{83} +(4.57841 + 0.195331i) q^{84} +(10.8392 + 7.87516i) q^{85} +(-0.784102 + 3.68891i) q^{86} +(-4.11134 + 0.980830i) q^{87} +(2.46411 - 2.21994i) q^{88} +(-1.63930 + 2.83935i) q^{89} +(5.08572 + 1.37831i) q^{90} +(-4.82856 - 2.55239i) q^{91} +(1.64345 + 2.26202i) q^{92} +(-2.79506 + 1.32828i) q^{93} +(-1.00573 - 4.73161i) q^{94} +(2.25600 - 5.06705i) q^{95} +(0.223623 + 1.71755i) q^{96} +(-1.51318 + 0.491661i) q^{97} +(-6.80020 - 1.66049i) q^{98} +(-5.39754 - 8.35862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	$ 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) $ 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$2$	−0.207912	+	0.978148i	−0.147016	+	0.691655i
$3$	0.665114	−	1.59926i	0.384004	−	0.923331i
$3$	0.665114	−	1.59926i	0.384004	−	0.923331i
$4$	−0.913545	−	0.406737i	−0.456773	−	0.203368i
$5$	1.17526	+	1.30525i	0.525591	+	0.583728i	0.946228	−	0.323501i	$-0.104860\pi$
$5$	1.17526	+	1.30525i	0.525591	+	0.583728i	−0.420637	+	0.907229i	$0.638193\pi$
$6$	1.42602	+	0.983084i	0.582172	+	0.401342i
$7$	−1.84250	−	1.89873i	−0.696401	−	0.717653i
$7$	−1.84250	−	1.89873i	−0.696401	−	0.717653i
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$	−2.11525	−	2.12738i	−0.705082	−	0.709126i
$10$	−1.52108	+	0.878197i	−0.481008	+	0.277710i
$11$	3.24434	+	0.688659i	0.978206	+	0.207638i
$11$	3.24434	+	0.688659i	0.978206	+	0.207638i
$12$	−1.25809	+	1.19047i	−0.363179	+	0.343658i
$13$	1.96328	−	0.637908i	0.544515	−	0.176924i	−0.0238267	−	0.999716i	$-0.507585\pi$
$13$	1.96328	−	0.637908i	0.544515	−	0.176924i	0.568342	+	0.822792i	$0.307585\pi$
$14$	2.24032	−	1.40747i	0.598750	−	0.376163i
$15$	2.86912	−	1.01139i	0.740803	−	0.261141i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	7.46145	−	1.58598i	1.80967	−	0.384657i	0.825859	−	0.563877i	$-0.190691\pi$
$17$	7.46145	−	1.58598i	1.80967	−	0.384657i	0.983809	+	0.179220i	$0.0573574\pi$
$18$	2.52067	−	1.62672i	0.594128	−	0.383421i
$19$	−1.28445	−	2.88492i	−0.294673	−	0.661846i	0.704165	−	0.710036i	$-0.251321\pi$
$19$	−1.28445	−	2.88492i	−0.294673	−	0.661846i	−0.998838	+	0.0481899i	$0.984655\pi$
$20$	−0.542755	−	1.67043i	−0.121364	−	0.373519i
$21$	−4.26203	+	1.68376i	−0.930052	+	0.367427i
$22$	−1.34815	+	3.03026i	−0.287426	+	0.646055i
$23$	−2.42141	−	1.39800i	−0.504899	−	0.291504i	0.225835	−	0.974166i	$-0.427489\pi$
$23$	−2.42141	−	1.39800i	−0.504899	−	0.291504i	−0.730735	+	0.682662i	$0.760822\pi$
$24$	−0.902882	−	1.47811i	−0.184300	−	0.301718i
$25$	0.200181	−	1.90459i	0.0400361	−	0.380918i
$26$	0.215779	+	2.05300i	0.0423178	+	0.402627i
$27$	−4.80910	+	1.96787i	−0.925512	+	0.378717i
$28$	0.910927	+	2.48399i	0.172149	+	0.469430i
$29$	−1.43437	−	1.97424i	−0.266356	−	0.366607i	0.654800	−	0.755803i	$-0.272753\pi$
$29$	−1.43437	−	1.97424i	−0.266356	−	0.366607i	−0.921155	+	0.389196i	$0.872753\pi$
$30$	0.392769	+	3.01670i	0.0717095	+	0.550772i
$31$	−1.32776	−	1.19552i	−0.238473	−	0.214722i	0.541225	−	0.840878i	$-0.317961\pi$
$31$	−1.32776	−	1.19552i	−0.238473	−	0.214722i	−0.779698	+	0.626156i	$0.784627\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.25920	−	4.73050i	0.567354	−	0.823474i
$34$			7.62815i			1.30822i
$35$	0.312913	−	4.63643i	0.0528919	−	0.783700i
$36$	1.06709	+	2.80380i	0.177848	+	0.467301i
$37$	−0.174549	−	1.66073i	−0.0286957	−	0.273022i	−0.999456	−	0.0329718i	$-0.989503\pi$
$37$	−0.174549	−	1.66073i	−0.0286957	−	0.273022i	0.970761	−	0.240050i	$-0.0771638\pi$
$38$	3.08893	−	0.656572i	0.501091	−	0.106510i
$39$	0.285626	−	3.56407i	0.0457368	−	0.570708i
$40$	1.74677	−	0.183593i	0.276189	−	0.0290286i
$41$	9.98409	+	7.25387i	1.55925	+	1.13286i	0.936618	+	0.350352i	$0.113938\pi$
$41$	9.98409	+	7.25387i	1.55925	+	1.13286i	0.622635	+	0.782512i	$0.286062\pi$
$42$	−0.760843	−	4.51897i	−0.117401	−	0.697293i
$43$	3.77132			0.575121			0.287560	−	0.957762i	$-0.407156\pi$
$43$	3.77132			0.575121			0.287560	+	0.957762i	$0.407156\pi$
$44$	−2.68375	−	1.94871i	−0.404591	−	0.293780i
$45$	0.290812	−	5.26115i	0.0433518	−	0.784286i
$46$	1.87089	−	2.07784i	0.275848	−	0.306360i
$47$	−4.41911	+	1.96751i	−0.644593	+	0.286991i	−0.702880	−	0.711308i	$-0.748103\pi$
$47$	−4.41911	+	1.96751i	−0.644593	+	0.286991i	0.0582867	+	0.998300i	$0.481436\pi$
$48$	1.63353	−	0.575836i	0.235779	−	0.0831147i
$49$	−0.210360	+	6.99684i	−0.0300514	+	0.999548i
$50$	1.82135	+	0.591793i	0.257578	+	0.0836922i
$51$	2.42633	−	12.9876i	0.339754	−	1.81863i
$52$	−2.05300	−	0.215779i	−0.284701	−	0.0299232i
$53$	5.09424	+	4.58688i	0.699748	+	0.630056i	0.940207	−	0.340603i	$-0.110631\pi$
$53$	5.09424	+	4.58688i	0.699748	+	0.630056i	−0.240459	+	0.970659i	$0.577298\pi$
$54$	−0.925001	−	5.11316i	−0.125877	−	0.695813i
$55$	2.91406	+	5.04404i	0.392931	+	0.680138i
$56$	−2.61910	+	0.374571i	−0.349992	+	0.0500541i
$57$	−5.46804	+	0.135363i	−0.724259	+	0.0179292i
$58$	2.22932	−	0.992557i	0.292724	−	0.130329i
$59$	−11.9328	−	5.31283i	−1.55352	−	0.691671i	−0.562674	−	0.826679i	$-0.690227\pi$
$59$	−11.9328	−	5.31283i	−1.55352	−	0.691671i	−0.990845	+	0.135008i	$0.956894\pi$
$60$	−3.03244	−	0.243021i	−0.391486	−	0.0313739i
$61$	−6.11377	+	5.50487i	−0.782789	+	0.704826i	−0.960201	−	0.279311i	$-0.909894\pi$
$61$	−6.11377	+	5.50487i	−0.782789	+	0.704826i	0.177412	+	0.984137i	$0.443227\pi$
$62$	1.44546	−	1.05019i	0.183573	−	0.133374i
$63$	−0.141969	+	7.93598i	−0.0178864	+	0.999840i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	3.13999	+	1.81287i	0.389467	+	0.224859i
$66$	3.94950	+	4.17150i	0.486150	+	0.513477i
$67$	4.96070	+	8.59218i	0.606046	+	1.04970i	0.991885	+	0.127136i	$0.0405785\pi$
$67$	4.96070	+	8.59218i	0.606046	+	1.04970i	−0.385840	+	0.922566i	$0.626088\pi$
$68$	−7.46145	−	1.58598i	−0.904834	−	0.192328i
$69$	−3.84628	+	2.94263i	−0.463038	+	0.354251i
$70$	4.47006	+	1.27004i	0.534274	+	0.151799i
$71$	−4.43154	−	1.43989i	−0.525927	−	0.170884i	0.0340067	−	0.999422i	$-0.489173\pi$
$71$	−4.43154	−	1.43989i	−0.525927	−	0.170884i	−0.559933	+	0.828538i	$0.689173\pi$
$72$	−2.96439	+	0.460829i	−0.349357	+	0.0543092i
$73$	−2.80651	+	6.30352i	−0.328477	+	0.737771i	−0.999995	−	0.00321722i	$-0.998976\pi$
$73$	−2.80651	+	6.30352i	−0.328477	+	0.737771i	0.671518	+	0.740988i	$0.265643\pi$
$74$	1.66073	+	0.174549i	0.193056	+	0.0202910i
$75$	−2.91279	−	1.58691i	−0.336340	−	0.183241i
$76$			3.15794i			0.362240i
$77$	−4.67013	−	7.42899i	−0.532211	−	0.846612i
$78$	3.42680	+	1.02040i	0.388009	+	0.115537i
$79$	6.86683	+	1.45959i	0.772579	+	0.164217i	0.577301	−	0.816531i	$-0.304106\pi$
$79$	6.86683	+	1.45959i	0.772579	+	0.164217i	0.195278	+	0.980748i	$0.437439\pi$
$80$	−0.183593	+	1.74677i	−0.0205263	+	0.195295i
$81$	−0.0514691	+	8.99985i	−0.00571879	+	0.999984i
$82$	−9.17116	+	8.25775i	−1.01279	+	0.911916i
$83$	0.468282	−	1.44122i	0.0514006	−	0.158195i	−0.922061	−	0.387044i	$-0.873496\pi$
$83$	0.468282	−	1.44122i	0.0514006	−	0.158195i	0.973462	+	0.228849i	$0.0734962\pi$
$84$	4.57841	+	0.195331i	0.499546	+	0.0213124i
$85$	10.8392	+	7.87516i	1.17568	+	0.854181i
$86$	−0.784102	+	3.68891i	−0.0845519	+	0.397785i
$87$	−4.11134	+	0.980830i	−0.440781	+	0.105156i
$88$	2.46411	−	2.21994i	0.262675	−	0.236647i
$89$	−1.63930	+	2.83935i	−0.173766	+	0.300971i	−0.939733	−	0.341908i	$-0.888927\pi$
$89$	−1.63930	+	2.83935i	−0.173766	+	0.300971i	0.765968	+	0.642879i	$0.222260\pi$
$90$	5.08572	+	1.37831i	0.536082	+	0.145287i
$91$	−4.82856	−	2.55239i	−0.506171	−	0.267563i
$92$	1.64345	+	2.26202i	0.171342	+	0.235832i
$93$	−2.79506	+	1.32828i	−0.289835	+	0.137736i
$94$	−1.00573	−	4.73161i	−0.103734	−	0.488028i
$95$	2.25600	−	5.06705i	0.231461	−	0.519869i
$96$	0.223623	+	1.71755i	0.0228234	+	0.175297i
$97$	−1.51318	+	0.491661i	−0.153640	+	0.0499206i	−0.384827	−	0.922989i	$-0.625739\pi$
$97$	−1.51318	+	0.491661i	−0.153640	+	0.0499206i	0.231187	+	0.972909i	$0.425739\pi$
$98$	−6.80020	−	1.66049i	−0.686924	−	0.167735i
$99$	−5.39754	−	8.35862i	−0.542473	−	0.840073i
$100$	−0.957542	+	1.65851i	−0.0957542	+	0.165851i
$101$	0.0789716	−	0.0877068i	0.00785796	−	0.00872715i	−0.739203	−	0.673483i	$-0.764798\pi$
$101$	0.0789716	−	0.0877068i	0.00785796	−	0.00872715i	0.747061	+	0.664755i	$0.231464\pi$
$102$	12.1994	+	5.07359i	1.20792	+	0.502360i
$103$	−14.2055	+	1.49306i	−1.39971	+	0.147116i	−0.774123	−	0.633035i	$-0.781809\pi$
$103$	−14.2055	+	1.49306i	−1.39971	+	0.147116i	−0.625591	+	0.780151i	$0.715142\pi$
$104$	0.637908	−	1.96328i	0.0625520	−	0.192515i
$105$	−7.20672	−	3.58419i	−0.703304	−	0.349781i
$106$	−5.54579	+	4.02925i	−0.538655	+	0.391356i
$107$	6.30139	+	14.1532i	0.609178	+	1.36824i	0.910021	+	0.414563i	$0.136066\pi$
$107$	6.30139	+	14.1532i	0.609178	+	1.36824i	−0.300842	+	0.953674i	$0.597268\pi$
$108$	5.19374	+	0.158297i	0.499768	+	0.0152322i
$109$	−9.01121	−	15.6079i	−0.863117	−	1.49496i	−0.868905	−	0.494979i	$-0.835176\pi$
$109$	−9.01121	−	15.6079i	−0.863117	−	1.49496i	0.00578752	−	0.999983i	$-0.498158\pi$
$110$	−5.53968	+	1.80166i	−0.528188	+	0.171782i
$111$	−2.77202	−	0.825424i	−0.263109	−	0.0783457i
$112$	0.178157	−	2.63975i	0.0168342	−	0.249433i
$113$	−9.22714	+	12.7001i	−0.868017	+	1.19472i	0.111581	+	0.993755i	$0.464408\pi$
$113$	−9.22714	+	12.7001i	−0.868017	+	1.19472i	−0.979598	+	0.200967i	$0.935592\pi$
$114$	1.00446	−	5.37669i	0.0940766	−	0.503573i
$115$	−1.02103	−	4.80357i	−0.0952116	−	0.447935i
$116$	0.507366	+	2.38697i	0.0471077	+	0.221624i
$117$	−5.50989	−	2.82730i	−0.509389	−	0.261384i
$118$	7.67770	−	10.5674i	0.706789	−	0.972812i
$119$	−16.7591	−	11.2451i	−1.53630	−	1.03084i
$120$	0.868190	−	2.91565i	0.0792545	−	0.266161i
$121$	10.0515	+	4.46849i	0.913773	+	0.406226i
$122$	−4.11345	−	7.12470i	−0.372414	−	0.645040i
$123$	18.2414	−	11.1425i	1.64477	−	1.00468i
$124$	0.726709	+	1.63222i	0.0652604	+	0.146577i
$125$	9.82600	−	7.13901i	0.878864	−	0.638532i
$126$	−7.73305	−	1.78885i	−0.688915	−	0.159363i
$127$	3.99770	−	12.3037i	0.354738	−	1.09177i	−0.601423	−	0.798931i	$-0.705399\pi$
$127$	3.99770	−	12.3037i	0.354738	−	1.09177i	0.956161	−	0.292841i	$-0.0946008\pi$
$128$	0.994522	−	0.104528i	0.0879041	−	0.00923910i
$129$	2.50836	−	6.03131i	0.220849	−	0.531027i
$130$	−2.42610	+	2.69445i	−0.212783	+	0.236319i
$131$	−3.75324	+	6.50081i	−0.327922	+	0.567978i	−0.982099	−	0.188363i	$-0.939682\pi$
$131$	−3.75324	+	6.50081i	−0.327922	+	0.567978i	0.654177	+	0.756341i	$0.273015\pi$
$132$	−4.90149	+	2.99589i	−0.426620	+	0.260759i
$133$	−3.11109	+	7.75430i	−0.269765	+	0.672383i
$134$	−9.43581	+	3.06588i	−0.815130	+	0.264852i
$135$	−8.22050	−	3.96435i	−0.707508	−	0.341197i
$136$	3.10265	−	6.96866i	0.266050	−	0.597557i
$137$	−0.175047	−	0.823532i	−0.0149553	−	0.0703591i	0.970037	−	0.242957i	$-0.0781173\pi$
$137$	−0.175047	−	0.823532i	−0.0149553	−	0.0703591i	−0.984992	+	0.172598i	$0.944784\pi$
$138$	−2.07864	−	4.37404i	−0.176945	−	0.372343i
$139$	−4.24464	−	5.84224i	−0.360025	−	0.495532i	0.590130	−	0.807308i	$-0.299076\pi$
$139$	−4.24464	−	5.84224i	−0.360025	−	0.495532i	−0.950156	+	0.311775i	$0.899076\pi$
$140$	−2.17167	+	4.10832i	−0.183539	+	0.347216i
$141$	0.207348	+	8.37591i	0.0174619	+	0.705379i
$142$	2.32980	−	4.03533i	0.195512	−	0.338637i
$143$	6.80885	−	0.717562i	0.569384	−	0.0600056i
$144$	0.165574	−	2.99543i	0.0137978	−	0.249619i
$145$	0.891134	−	4.19245i	0.0740046	−	0.348164i
$146$	−5.58227	−	4.05575i	−0.461992	−	0.335657i
$147$	11.0498	+	4.99012i	0.911375	+	0.411578i
$148$	−0.516020	+	1.58814i	−0.0424165	+	0.130545i
$149$	2.26341	−	2.03798i	0.185426	−	0.166958i	−0.571190	−	0.820818i	$-0.693518\pi$
$149$	2.26341	−	2.03798i	0.185426	−	0.166958i	0.756616	+	0.653860i	$0.226851\pi$
$150$	2.15784	−	2.51920i	0.176187	−	0.205692i
$151$	−1.89053	+	17.9871i	−0.153849	+	1.46377i	0.596437	+	0.802660i	$0.296582\pi$
$151$	−1.89053	+	17.9871i	−0.153849	+	1.46377i	−0.750286	+	0.661113i	$0.770084\pi$
$152$	−3.08893	−	0.656572i	−0.250545	−	0.0532551i
$153$	−19.1568	−	12.5186i	−1.54873	−	1.01207i
$154$	8.23762	−	3.02351i	0.663806	−	0.243641i
$155$		−	3.13812i		−	0.252060i
$156$	−1.71057	+	3.13976i	−0.136955	+	0.251382i
$157$	−12.9602	−	1.36217i	−1.03433	−	0.108713i	−0.427883	−	0.903834i	$-0.640741\pi$
$157$	−12.9602	−	1.36217i	−1.03433	−	0.108713i	−0.606451	+	0.795121i	$0.707407\pi$
$158$	−2.85539	+	6.41331i	−0.227163	+	0.510216i
$159$	10.7238	−	5.09620i	0.850456	−	0.404155i
$160$	−1.67043	−	0.542755i	−0.132059	−	0.0429086i
$161$	1.80703	+	7.17344i	0.142414	+	0.565346i
$162$	−8.79248	−	1.92152i	−0.690803	−	0.150969i
$163$	10.9986	+	2.33783i	0.861479	+	0.183113i	0.617407	−	0.786644i	$-0.288183\pi$
$163$	10.9986	+	2.33783i	0.861479	+	0.183113i	0.244072	+	0.969757i	$0.421517\pi$
$164$	−6.17051	−	10.6876i	−0.481836	−	0.834564i
$165$	10.0049	−	1.30546i	0.778880	−	0.101630i
$166$	1.31237	+	0.757696i	0.101860	+	0.0588086i
$167$	4.36891	+	13.4461i	0.338076	+	1.04049i	0.965187	+	0.261562i	$0.0842374\pi$
$167$	4.36891	+	13.4461i	0.338076	+	1.04049i	−0.627111	+	0.778930i	$0.715763\pi$
$168$	−1.14297	+	4.43775i	−0.0881819	+	0.342380i
$169$	−7.06969	+	5.13643i	−0.543822	+	0.395110i
$170$	−9.95667	+	8.96503i	−0.763642	+	0.687586i
$171$	−3.42039	+	8.83483i	−0.261564	+	0.675616i
$172$	−3.44527	−	1.53393i	−0.262700	−	0.116961i
$173$	7.13118	−	3.17501i	0.542174	−	0.241391i	−0.117329	−	0.993093i	$-0.537433\pi$
$173$	7.13118	−	3.17501i	0.542174	−	0.241391i	0.659503	+	0.751702i	$0.270767\pi$
$174$	−0.104601	−	4.22542i	−0.00792982	−	0.320328i
$175$	−3.98514	+	3.12913i	−0.301248	+	0.236540i
$176$	1.65911	+	2.87182i	0.125060	+	0.216471i
$177$	−16.4333	+	15.5500i	−1.23520	+	1.16881i
$178$	−2.43648	−	2.19381i	−0.182622	−	0.164433i
$179$	14.6435	+	1.53909i	1.09451	+	0.115037i	0.634533	−	0.772896i	$-0.281192\pi$
$179$	14.6435	+	1.53909i	1.09451	+	0.115037i	0.459973	+	0.887933i	$0.347859\pi$
$180$	−2.40557	+	4.68801i	−0.179301	+	0.349424i
$181$	−20.1100	−	6.53415i	−1.49477	−	0.485680i	−0.556281	−	0.830994i	$-0.687772\pi$
$181$	−20.1100	−	6.53415i	−1.49477	−	0.485680i	−0.938487	+	0.345315i	$0.887772\pi$
$182$	3.50053	−	4.19238i	0.259476	−	0.310760i
$183$	4.73734	+	13.4389i	0.350194	+	0.993429i
$184$	−2.55428	+	1.13724i	−0.188304	+	0.0838383i
$185$	1.96253	−	2.17961i	0.144288	−	0.160248i
$186$	−0.718123	−	3.01015i	−0.0526553	−	0.220715i
$187$	25.2997	−	0.00706955i	1.85010	−	0.000516977i
$188$	4.83732			0.352798
$189$	12.5973	+	5.50538i	0.916315	+	0.400458i
$190$	4.48728	+	3.26020i	0.325541	+	0.236520i
$191$	−3.39031	+	0.356336i	−0.245314	+	0.0257836i	−0.226388	−	0.974037i	$-0.572692\pi$
$191$	−3.39031	+	0.356336i	−0.245314	+	0.0257836i	−0.0189268	+	0.999821i	$0.506025\pi$
$192$	−1.72652	−	0.138364i	−0.124601	−	0.00998554i
$193$	21.2518	−	4.51720i	1.52974	−	0.325155i	0.635270	−	0.772290i	$-0.280889\pi$
$193$	21.2518	−	4.51720i	1.52974	−	0.325155i	0.894467	+	0.447135i	$0.147556\pi$
$194$	−0.166310	−	1.58233i	−0.0119403	−	0.113605i
$195$	4.98770	−	3.81588i	0.357177	−	0.273261i
$196$	3.03804	−	6.30637i	0.217003	−	0.450455i
$197$			12.3413i			0.879279i	0.898174	+	0.439640i	$0.144894\pi$
$197$			12.3413i			0.879279i	−0.898174	+	0.439640i	$0.855106\pi$
$198$	9.29818	−	3.54174i	0.660793	−	0.251700i
$199$	12.8749	−	7.43333i	0.912678	−	0.526935i	0.0313864	−	0.999507i	$-0.490008\pi$
$199$	12.8749	−	7.43333i	0.912678	−	0.526935i	0.881292	+	0.472572i	$0.156674\pi$
$200$	−1.42318	−	1.28144i	−0.100634	−	0.0906116i
$201$	17.0405	−	2.21865i	1.20195	−	0.156491i
$202$	0.0693711	+	0.0954811i	0.00488093	+	0.00671803i
$203$	−1.10572	+	6.36102i	−0.0776063	+	0.446456i
$204$	−7.49911	+	10.8779i	−0.525043	+	0.761607i
$205$	2.26573	+	21.5569i	0.158245	+	1.50560i
$206$	1.49306	−	14.2055i	0.104027	−	0.989747i
$207$	2.14780	+	8.10838i	0.149283	+	0.563571i
$208$	1.78775	+	1.03216i	0.123958	+	0.0715672i
$209$	−2.18047	−	10.2442i	−0.150826	−	0.708607i
$210$	5.00422	−	6.30405i	0.345324	−	0.435020i
$211$	−7.44005	−	22.8981i	−0.512194	−	1.57637i	−0.788330	−	0.615253i	$-0.789054\pi$
$211$	−7.44005	−	22.8981i	−0.512194	−	1.57637i	0.276136	−	0.961119i	$-0.410946\pi$
$212$	−2.78817	−	6.26233i	−0.191492	−	0.430099i
$213$	−5.25024	+	6.12947i	−0.359740	+	0.419985i
$214$	−15.1540	+	3.22108i	−1.03591	+	0.220189i
$215$	4.43227	+	4.92253i	0.302278	+	0.335714i
$216$	−1.23468	+	5.04733i	−0.0840092	+	0.343428i
$217$	0.176431	+	4.72382i	0.0119769	+	0.320674i
$218$	17.1403	−	5.56923i	1.16089	−	0.377196i
$219$	8.21430	+	8.68089i	0.555071	+	0.586600i
$220$	−0.610528	−	5.79321i	−0.0411618	−	0.390578i
$221$	13.6372	−	7.87344i	0.917337	−	0.529625i
$222$	1.38372	−	2.53983i	0.0928694	−	0.170462i
$223$	−2.28476	+	3.14470i	−0.152999	+	0.210584i	−0.878635	−	0.477494i	$-0.841545\pi$
$223$	−2.28476	+	3.14470i	−0.152999	+	0.210584i	0.725637	+	0.688078i	$0.241545\pi$
$224$	2.54502	+	0.723098i	0.170046	+	0.0483140i
$225$	−4.47522	+	3.60282i	−0.298348	+	0.240188i
$226$	−10.5041	−	11.6660i	−0.698723	−	0.776011i
$227$	5.29782	+	2.35874i	0.351629	+	0.156555i	0.574948	−	0.818190i	$-0.305022\pi$
$227$	5.29782	+	2.35874i	0.351629	+	0.156555i	−0.223319	+	0.974745i	$0.571689\pi$
$228$	5.05036	+	2.10039i	0.334468	+	0.139102i
$229$	−4.11662	+	19.3672i	−0.272034	+	1.27982i	0.603773	+	0.797156i	$0.293663\pi$
$229$	−4.11662	+	19.3672i	−0.272034	+	1.27982i	−0.875807	+	0.482662i	$0.839670\pi$
$230$	4.91089			0.323814
$231$	−14.9870	+	2.52762i	−0.986074	+	0.166305i
$232$	−2.44029			−0.160213
$233$	3.00453	−	14.1352i	0.196833	−	0.926028i	−0.763204	−	0.646157i	$-0.776375\pi$
$233$	3.00453	−	14.1352i	0.196833	−	0.926028i	0.960038	−	0.279871i	$-0.0902916\pi$
$234$	3.91109	−	4.80165i	0.255676	−	0.313894i
$235$	−7.76169	−	3.45573i	−0.506317	−	0.225427i
$236$	8.74024	+	9.70702i	0.568941	+	0.631873i
$237$	6.90149	−	10.0110i	0.448300	−	0.650287i
$238$	14.4838	−	14.0549i	0.938845	−	0.911043i
$239$	8.26463	−	11.3753i	0.534594	−	0.735806i	−0.453228	−	0.891395i	$-0.649728\pi$
$239$	8.26463	−	11.3753i	0.534594	−	0.735806i	0.987822	+	0.155589i	$0.0497275\pi$
$240$	2.67143	+	1.45542i	0.172440	+	0.0939466i
$241$	3.34779	−	1.93285i	0.215650	−	0.124506i	−0.388284	−	0.921540i	$-0.626932\pi$
$241$	3.34779	−	1.93285i	0.215650	−	0.124506i	0.603935	+	0.797034i	$0.293599\pi$
$242$	−6.46066	+	8.90280i	−0.415307	+	0.572294i
$243$	14.3588	+	6.06824i	0.921120	+	0.389278i
$244$	7.82424	−	2.54225i	0.500896	−	0.162751i
$245$	−9.37988	+	7.94851i	−0.599259	+	0.507811i
$246$	7.10640	+	20.1594i	0.453087	+	1.28532i
$247$	−4.36205	−	4.84454i	−0.277550	−	0.308251i
$248$	−1.74764	+	0.371472i	−0.110975	+	0.0235885i
$249$	−1.99343	−	1.70748i	−0.126328	−	0.108207i
$250$	4.94006	+	11.0956i	0.312437	+	0.701745i
$251$	0.616222	+	1.89654i	0.0388956	+	0.119708i	0.968619	−	0.248550i	$-0.0799541\pi$
$251$	0.616222	+	1.89654i	0.0388956	+	0.119708i	−0.929723	+	0.368259i	$0.879954\pi$
$252$	3.35755	−	7.19214i	0.211506	−	0.453062i
$253$	−6.89314	−	6.20313i	−0.433368	−	0.389987i
$254$	11.2036	+	6.46841i	0.702978	+	0.405864i
$255$	19.8037	−	12.0968i	1.24016	−	0.757533i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	−0.199638	−	1.89943i	−0.0124531	−	0.118483i	0.986529	−	0.163584i	$-0.0523056\pi$
$257$	−0.199638	−	1.89943i	−0.0124531	−	0.118483i	−0.998982	+	0.0451013i	$0.985639\pi$
$258$	5.37799	+	3.70753i	0.334819	+	0.230820i
$259$	−2.83167	+	3.39132i	−0.175951	+	0.210726i
$260$	−2.13116	−	2.93329i	−0.132169	−	0.181915i
$261$	−1.16591	+	7.22745i	−0.0721680	+	0.447368i
$262$	−5.57840	−	5.02282i	−0.344635	−	0.310311i
$263$	2.86830	−	1.65601i	0.176867	−	0.102114i	−0.408953	−	0.912555i	$-0.634106\pi$
$263$	2.86830	−	1.65601i	0.176867	−	0.102114i	0.585820	+	0.810441i	$0.300773\pi$
$264$	−1.91134	−	5.41727i	−0.117635	−	0.333410i
$265$			12.0400i			0.739613i
$266$	−6.93802	−	4.65531i	−0.425397	−	0.285435i
$267$	3.45053	+	4.51016i	0.211169	+	0.276017i
$268$	−1.03707	−	9.86704i	−0.0633490	−	0.602726i
$269$	22.9418	−	4.87642i	1.39878	−	0.297321i	0.554039	−	0.832490i	$-0.313086\pi$
$269$	22.9418	−	4.87642i	1.39878	−	0.297321i	0.844745	+	0.535170i	$0.179752\pi$
$270$	5.58686	−	7.21663i	0.340005	−	0.439190i
$271$	12.4386	−	1.30735i	0.755593	−	0.0794160i	0.281104	−	0.959677i	$-0.409299\pi$
$271$	12.4386	−	1.30735i	0.755593	−	0.0794160i	0.474489	+	0.880261i	$0.342633\pi$
$272$	6.17130	+	4.48371i	0.374190	+	0.271865i
$273$	−7.29347	+	6.02448i	−0.441421	+	0.364618i
$274$	0.841930			0.0508629
$275$	1.96107	−	6.04129i	0.118257	−	0.364304i
$276$	4.71063	−	1.12380i	0.283547	−	0.0676449i
$277$	−3.38871	+	3.76355i	−0.203608	+	0.226130i	−0.836297	−	0.548276i	$-0.815284\pi$
$277$	−3.38871	+	3.76355i	−0.203608	+	0.226130i	0.632689	+	0.774406i	$0.281951\pi$
$278$	6.59708	−	2.93721i	0.395667	−	0.176162i
$279$	0.265216	+	5.35348i	0.0158781	+	0.320504i
$280$	−3.56703	−	2.97838i	−0.213171	−	0.177992i
$281$	8.52642	+	2.77040i	0.508644	+	0.165268i	0.552085	−	0.833788i	$-0.313832\pi$
$281$	8.52642	+	2.77040i	0.508644	+	0.165268i	−0.0434416	+	0.999056i	$0.513832\pi$
$282$	−8.23599	−	1.53863i	−0.490446	−	0.0916243i
$283$	−19.9940	−	2.10145i	−1.18852	−	0.124918i	−0.510444	−	0.859911i	$-0.670519\pi$
$283$	−19.9940	−	2.10145i	−1.18852	−	0.124918i	−0.678075	+	0.734992i	$0.737186\pi$
$284$	3.46275	+	3.11788i	0.205477	+	0.185012i
$285$	−6.60303	−	6.97809i	−0.391129	−	0.413346i
$286$	−0.713757	+	6.80925i	−0.0422053	+	0.402639i
$287$	−4.62258	−	32.3224i	−0.272862	−	1.90793i
$288$	2.89555	+	0.784740i	0.170622	+	0.0462412i
$289$	37.6277	−	16.7529i	2.21339	−	0.985465i
$290$	3.91556	+	1.74332i	0.229930	+	0.102371i
$291$	−0.220143	+	2.74697i	−0.0129050	+	0.161030i
$292$	5.12774	−	4.61704i	0.300079	−	0.270192i
$293$	−24.9419	+	18.1213i	−1.45712	+	1.05866i	−0.473019	+	0.881052i	$0.656836\pi$
$293$	−24.9419	+	18.1213i	−1.45712	+	1.05866i	−0.984101	+	0.177607i	$0.943164\pi$
$294$	−7.17846	+	9.77086i	−0.418656	+	0.569848i
$295$	−7.08951	−	21.8193i	−0.412767	−	1.27037i
$296$	−1.44615	−	0.834937i	−0.0840560	−	0.0485297i
$297$	−16.9576	+	3.07262i	−0.983978	+	0.178292i
$298$	1.52286	+	2.63767i	0.0882168	+	0.152796i
$299$	−5.64570	−	1.20003i	−0.326499	−	0.0693996i
$300$	2.01551	+	2.63445i	0.116366	+	0.152100i
$301$	−6.94867	−	7.16072i	−0.400515	−	0.412737i
$302$	−17.2010	−	5.58895i	−0.989808	−	0.321608i
$303$	−0.0877406	−	0.184631i	−0.00504057	−	0.0106068i
$304$	1.28445	−	2.88492i	0.0736682	−	0.165462i
$305$	−14.3705	−	1.51040i	−0.822853	−	0.0864853i
$306$	16.2279	−	16.1354i	0.927690	−	0.922400i
$307$		−	30.1267i		−	1.71942i	−0.510782	−	0.859710i	$-0.670644\pi$
$307$		−	30.1267i		−	1.71942i	0.510782	−	0.859710i	$-0.329356\pi$
$308$	1.24474	+	8.68623i	0.0709255	+	0.494944i
$309$	−7.06052	+	23.7114i	−0.401659	+	1.34889i
$310$	3.06954	+	0.652451i	0.174338	+	0.0370567i
$311$	1.17500	−	11.1794i	0.0666281	−	0.633924i	−0.909347	−	0.416039i	$-0.863418\pi$
$311$	1.17500	−	11.1794i	0.0666281	−	0.633924i	0.975975	−	0.217884i	$-0.0699155\pi$
$312$	−2.71551	−	2.32598i	−0.153735	−	0.131683i
$313$	−2.16025	+	1.94510i	−0.122105	+	0.109944i	−0.727921	−	0.685661i	$-0.759513\pi$
$313$	−2.16025	+	1.94510i	−0.122105	+	0.109944i	0.605816	+	0.795605i	$0.292847\pi$
$314$	4.02697	−	12.3937i	0.227255	−	0.699419i
$315$	−10.5253	+	9.14151i	−0.593035	+	0.515066i
$316$	−5.67950	−	4.12640i	−0.319497	−	0.232128i
$317$	−3.82570	+	17.9985i	−0.214873	+	1.01090i	0.729997	+	0.683450i	$0.239521\pi$
$317$	−3.82570	+	17.9985i	−0.214873	+	1.01090i	−0.944870	+	0.327446i	$0.893812\pi$
$318$	2.75523	+	11.5491i	0.154505	+	0.647639i
$319$	−3.29401	−	7.39290i	−0.184429	−	0.413923i
$320$	0.878197	−	1.52108i	0.0490927	−	0.0850310i
$321$	26.8257	−	0.664077i	1.49726	−	0.0370652i
$322$	−7.39238	+	0.276100i	−0.411961	+	0.0153865i
$323$	−14.1593	−	19.4886i	−0.787844	−	1.08437i
$324$	3.70759	−	8.20084i	0.205977	−	0.455602i
$325$	−0.821944	−	3.86694i	−0.0455932	−	0.214499i
$326$	−4.57349	+	10.2722i	−0.253302	+	0.568926i
$327$	−30.9545	+	4.03022i	−1.71179	+	0.222872i
$328$	11.7370	−	3.81358i	0.648068	−	0.210570i
$329$	11.8780	+	4.76555i	0.654856	+	0.262733i
$330$	−0.803199	+	10.0577i	−0.0442147	+	0.553658i
$331$	−8.94313	+	15.4900i	−0.491559	+	0.851405i	−0.999953	−	0.00971973i	$-0.996906\pi$
$331$	−8.94313	+	15.4900i	−0.491559	+	0.851405i	0.508394	+	0.861125i	$0.330239\pi$
$332$	−1.01400	+	1.12616i	−0.0556502	+	0.0618059i
$333$	−3.16378	+	3.88418i	−0.173374	+	0.212852i
$334$	−14.0606	+	1.47783i	−0.769364	+	0.0808634i
$335$	−5.38489	+	16.5730i	−0.294208	+	0.905479i
$336$	−4.10314	−	2.04065i	−0.223845	−	0.111327i
$337$	−0.860610	+	0.625270i	−0.0468804	+	0.0340606i	−0.610979	−	0.791647i	$-0.709224\pi$
$337$	−0.860610	+	0.625270i	−0.0468804	+	0.0340606i	0.564098	+	0.825708i	$0.309224\pi$
$338$	−3.55431	−	7.98312i	−0.193329	−	0.434224i
$339$	14.1736	+	23.2036i	0.769803	+	1.26025i
$340$	−6.69901	−	11.6030i	−0.363305	−	0.629262i
$341$	−3.48441	−	4.79306i	−0.188691	−	0.259559i
$342$	−7.93062	−	5.18251i	−0.428839	−	0.280238i
$343$	13.6727	−	12.4923i	0.738257	−	0.674520i
$344$	2.21673	−	3.05106i	0.119518	−	0.164502i
$345$	−8.36125	−	1.56203i	−0.450154	−	0.0840971i
$346$	1.62297	+	7.63547i	0.0872514	+	0.410485i
$347$	7.06311	+	33.2293i	0.379168	+	1.78384i	0.591142	+	0.806568i	$0.298677\pi$
$347$	7.06311	+	33.2293i	0.379168	+	1.78384i	−0.211974	+	0.977275i	$0.567989\pi$
$348$	4.15483	+	0.776198i	0.222722	+	0.0416086i
$349$	−13.8776	+	19.1008i	−0.742849	+	1.02244i	0.255601	+	0.966782i	$0.417727\pi$
$349$	−13.8776	+	19.1008i	−0.742849	+	1.02244i	−0.998450	+	0.0556614i	$0.982273\pi$
$350$	−2.23219	−	4.54864i	−0.119316	−	0.243135i
$351$	−8.18629	+	6.93125i	−0.436952	+	0.369963i
$352$	−3.15401	+	1.02577i	−0.168109	+	0.0546740i
$353$	12.7211	+	22.0336i	0.677075	+	1.17273i	0.975858	+	0.218407i	$0.0700859\pi$
$353$	12.7211	+	22.0336i	0.677075	+	1.17273i	−0.298783	+	0.954321i	$0.596581\pi$
$354$	−11.7935	−	19.3072i	−0.626818	−	1.02616i
$355$	−3.32876	−	7.47653i	−0.176672	−	0.396813i
$356$	2.65244	−	1.92711i	0.140579	−	0.102137i
$357$	−29.1306	+	19.3228i	−1.54175	+	1.02267i
$358$	−4.55002	+	14.0035i	−0.240476	+	0.740108i
$359$	9.80042	−	1.03007i	0.517246	−	0.0543648i	0.157691	−	0.987489i	$-0.449595\pi$
$359$	9.80042	−	1.03007i	0.517246	−	0.0543648i	0.359555	+	0.933124i	$0.382928\pi$
$360$	−4.08542	−	3.32770i	−0.215321	−	0.175385i
$361$	6.04052	−	6.70868i	0.317922	−	0.353089i
$362$	10.5725	−	18.3121i	0.555677	−	0.962461i
$363$	13.8317	−	13.1029i	0.725974	−	0.687723i
$364$	3.37296	+	4.29568i	0.176791	+	0.225155i
$365$	−11.5261	+	3.74504i	−0.603302	+	0.196025i
$366$	−14.1301	+	1.83972i	−0.738594	+	0.0961637i
$367$	7.49749	−	16.8396i	0.391366	−	0.879022i	−0.605189	−	0.796082i	$-0.706902\pi$
$367$	7.49749	−	16.8396i	0.391366	−	0.879022i	0.996555	−	0.0829401i	$-0.0264310\pi$
$368$	−0.581322	−	2.73491i	−0.0303035	−	0.142567i
$369$	−5.68710	−	36.5837i	−0.296058	−	1.90447i
$370$	1.72395	+	2.37281i	0.0896238	+	0.123357i
$371$	−0.676915	−	18.1239i	−0.0351437	−	0.940948i
$372$	3.09368	−	0.0765848i	0.160400	−	0.00397074i
$373$	−6.11015	+	10.5831i	−0.316372	+	0.547972i	−0.979728	−	0.200332i	$-0.935798\pi$
$373$	−6.11015	+	10.5831i	−0.316372	+	0.547972i	0.663356	+	0.748304i	$0.269131\pi$
$374$	−5.25319	+	24.7483i	−0.271636	+	1.27970i
$375$	−4.88169	−	20.4626i	−0.252090	−	1.05668i
$376$	−1.00573	+	4.73161i	−0.0518668	+	0.244014i
$377$	−4.07545	−	2.96099i	−0.209896	−	0.152499i
$378$	−8.00419	+	11.1773i	−0.411691	+	0.574900i
$379$	0.254613	−	0.783617i	0.0130786	−	0.0402517i	−0.944304	−	0.329074i	$-0.893264\pi$
$379$	0.254613	−	0.783617i	0.0130786	−	0.0402517i	0.957383	+	0.288822i	$0.0932636\pi$
$380$	−4.12191	+	3.71139i	−0.211450	+	0.190390i
$381$	−17.0178	−	14.5767i	−0.871847	−	0.746786i
$382$	0.356336	−	3.39031i	0.0182317	−	0.173463i
$383$	−21.0764	−	4.47993i	−1.07696	−	0.228914i	−0.364907	−	0.931044i	$-0.618899\pi$
$383$	−21.0764	−	4.47993i	−1.07696	−	0.228914i	−0.712049	+	0.702130i	$0.752232\pi$
$384$	0.494303	−	1.66002i	0.0252248	−	0.0847125i
$385$	4.20811	−	14.8267i	0.214465	−	0.755637i
$386$			21.7266i			1.10585i
$387$	−7.97727	−	8.02302i	−0.405507	−	0.407833i
$388$	1.58233	+	0.166310i	0.0803307	+	0.00844310i
$389$	13.7309	−	30.8400i	0.696183	−	1.56365i	−0.124469	−	0.992224i	$-0.539723\pi$
$389$	13.7309	−	30.8400i	0.696183	−	1.56365i	0.820652	−	0.571429i	$-0.193611\pi$
$390$	2.69549	+	5.67207i	0.136492	+	0.287217i
$391$	−20.2845	−	6.59082i	−1.02583	−	0.333312i
$392$	5.53691	+	4.28282i	0.279656	+	0.216315i
$393$	7.90012	+	10.3262i	0.398509	+	0.520887i
$394$	−12.0716	−	2.56590i	−0.608158	−	0.129268i
$395$	6.16515	+	10.6784i	0.310202	+	0.537286i
$396$	1.53114	+	9.83136i	0.0769429	+	0.494044i
$397$	15.1872	+	8.76834i	0.762224	+	0.440070i	0.830094	−	0.557624i	$-0.188287\pi$
$397$	15.1872	+	8.76834i	0.762224	+	0.440070i	−0.0678698	+	0.997694i	$0.521620\pi$
$398$	4.59405	+	14.1390i	0.230279	+	0.708726i
$399$	10.3319	+	10.1329i	0.517242	+	0.507281i
$400$	1.54934	−	1.12566i	0.0774668	−	0.0562829i
$401$	0.389909	−	0.351076i	0.0194711	−	0.0175319i	−0.659338	−	0.751847i	$-0.729163\pi$
$401$	0.389909	−	0.351076i	0.0194711	−	0.0175319i	0.678809	+	0.734315i	$0.262497\pi$
$402$	−1.37276	+	17.1294i	−0.0684671	+	0.854339i
$403$	−3.36940	−	1.50015i	−0.167842	−	0.0747280i
$404$	−0.107818	+	0.0480035i	−0.00536413	+	0.00238826i
$405$	−11.8076	+	10.5100i	−0.586724	+	0.522244i
$406$	−5.99213	−	2.40409i	−0.297384	−	0.119313i
$407$	0.577376	−	5.50817i	0.0286195	−	0.273030i
$408$	−9.08106	−	9.59688i	−0.449579	−	0.475116i
$409$	−18.9092	−	17.0259i	−0.935000	−	0.841878i	0.0526407	−	0.998614i	$-0.483236\pi$
$409$	−18.9092	−	17.0259i	−0.935000	−	0.841878i	−0.987641	+	0.156736i	$0.949903\pi$
$410$	−21.5569	−	2.26573i	−1.06462	−	0.111896i
$411$	−1.43347	−	0.267798i	−0.0707077	−	0.0132095i
$412$	13.5847	+	4.41393i	0.669270	+	0.217459i
$413$	11.8986	+	32.4461i	0.585492	+	1.59657i
$414$	−8.37774	+	0.415041i	−0.411744	+	0.0203982i
$415$	2.43152	−	1.08258i	0.119358	−	0.0531418i
$416$	−1.38130	+	1.53408i	−0.0677236	+	0.0752146i
$417$	−12.1664	+	2.90251i	−0.595792	+	0.142136i
$418$	10.4737	−	0.00292669i	0.512285	−	0.000143149i
$419$	9.61588			0.469766			0.234883	−	0.972024i	$-0.424529\pi$
$419$	9.61588			0.469766			0.234883	+	0.972024i	$0.424529\pi$
$420$	5.12585	+	6.20555i	0.250116	+	0.302800i
$421$	23.7929	+	17.2865i	1.15959	+	0.842495i	0.989727	−	0.142972i	$-0.0456659\pi$
$421$	23.7929	+	17.2865i	1.15959	+	0.842495i	0.169868	+	0.985467i	$0.445666\pi$
$422$	23.9446	−	2.51668i	1.16561	−	0.122510i
$423$	13.5331	+	5.23934i	0.658004	+	0.254745i
$424$	6.70518	−	1.42523i	0.325632	−	0.0692153i
$425$	−1.52701	−	14.5285i	−0.0740708	−	0.704736i
$426$	−4.90394	−	6.40990i	−0.237597	−	0.310561i
$427$	21.7169	+	1.46568i	1.05096	+	0.0709290i
$428$		−	15.4926i		−	0.748861i
$429$	3.38109	−	11.3664i	0.163241	−	0.548773i
$430$	−5.73648	+	3.31196i	−0.276638	+	0.159717i
$431$	−27.1656	−	24.4600i	−1.30852	−	1.17820i	−0.971591	−	0.236668i	$-0.923945\pi$
$431$	−27.1656	−	24.4600i	−1.30852	−	1.17820i	−0.336930	−	0.941530i	$-0.609389\pi$
$432$	−4.68033	−	2.25710i	−0.225183	−	0.108595i
$433$	−20.4538	−	28.1522i	−0.982946	−	1.35291i	−0.935227	−	0.354048i	$-0.884805\pi$
$433$	−20.4538	−	28.1522i	−0.982946	−	1.35291i	−0.0477188	−	0.998861i	$-0.515195\pi$
$434$	−4.65728	−	0.809562i	−0.223556	−	0.0388602i
$435$	−6.11211	−	4.21361i	−0.293053	−	0.202027i
$436$	1.88386	+	17.9237i	0.0902203	+	0.858389i
$437$	−0.922946	+	8.78125i	−0.0441505	+	0.420064i
$438$	−10.1990	+	6.22994i	−0.487329	+	0.297678i
$439$	13.1671	+	7.60202i	0.628430	+	0.362824i	0.780144	−	0.625600i	$-0.215146\pi$
$439$	13.1671	+	7.60202i	0.628430	+	0.362824i	−0.151714	+	0.988425i	$0.548479\pi$
$440$	5.79356	+	0.607290i	0.276197	+	0.0289514i
$441$	15.3299	−	14.3525i	0.729994	−	0.683453i
$442$	4.86605	+	14.9762i	0.231455	+	0.712344i
$443$	2.50670	+	5.63014i	0.119097	+	0.267496i	0.963250	−	0.268606i	$-0.0865629\pi$
$443$	2.50670	+	5.63014i	0.119097	+	0.267496i	−0.844153	+	0.536102i	$0.819896\pi$
$444$	2.19664	+	1.88155i	0.104248	+	0.0892942i
$445$	−5.63268	+	1.19726i	−0.267014	+	0.0567557i
$446$	−2.60095	−	2.88865i	−0.123159	−	0.136781i
$447$	−1.75383	−	4.97526i	−0.0829534	−	0.235322i
$448$	−1.23644	+	2.33907i	−0.0584161	+	0.110510i
$449$	10.5156	−	3.41672i	0.496260	−	0.161245i	−0.0501843	−	0.998740i	$-0.515981\pi$
$449$	10.5156	−	3.41672i	0.496260	−	0.161245i	0.546445	+	0.837495i	$0.315981\pi$
$450$	−2.59364	−	5.12649i	−0.122265	−	0.241665i
$451$	27.3964	+	30.4097i	1.29004	+	1.43193i
$452$	13.5950	−	7.84908i	0.639455	−	0.369190i
$453$	27.5087	+	14.9869i	1.29247	+	0.704148i
$454$	−3.40868	+	4.69164i	−0.159977	+	0.220190i
$455$	−2.34328	−	9.30222i	−0.109855	−	0.436095i
$456$	−3.10452	+	4.50330i	−0.145382	+	0.210886i
$457$	8.26880	+	9.18343i	0.386798	+	0.429583i	0.904826	−	0.425781i	$-0.140001\pi$
$457$	8.26880	+	9.18343i	0.386798	+	0.429583i	−0.518028	+	0.855363i	$0.673334\pi$
$458$	−18.0880	−	8.05332i	−0.845199	−	0.376307i
$459$	−32.7619	+	22.3103i	−1.52919	+	1.04136i
$460$	−1.02103	+	4.80357i	−0.0476058	+	0.223968i
$461$	−23.7294			−1.10519			−0.552594	−	0.833450i	$-0.686362\pi$
$461$	−23.7294			−1.10519			−0.552594	+	0.833450i	$0.686362\pi$
$462$	0.643596	−	15.1851i	0.0299428	−	0.706473i
$463$	22.2057			1.03199			0.515993	−	0.856593i	$-0.327423\pi$
$463$	22.2057			1.03199			0.515993	+	0.856593i	$0.327423\pi$
$464$	0.507366	−	2.38697i	0.0235539	−	0.110812i
$465$	−5.01865	−	2.08721i	−0.232734	−	0.0967918i
$466$	13.2016	+	5.87775i	0.611554	+	0.272281i
$467$	16.1361	+	17.9210i	0.746692	+	0.829285i	0.990060	−	0.140649i	$-0.0449189\pi$
$467$	16.1361	+	17.9210i	0.746692	+	0.829285i	−0.243368	+	0.969934i	$0.578252\pi$
$468$	3.88357	+	4.82394i	0.179518	+	0.222987i
$469$	7.17414	−	25.2502i	0.331271	−	1.16594i
$470$	4.99396	−	6.87359i	0.230354	−	0.317055i
$471$	−10.7984	+	19.8206i	−0.497566	+	0.913287i
$472$	−11.3121	+	6.53104i	−0.520681	+	0.300615i
$473$	12.2355	+	2.59715i	0.562587	+	0.119417i
$474$	8.35737	+	8.83209i	0.383867	+	0.405671i
$475$	−5.75172	+	1.86885i	−0.263907	+	0.0857486i
$476$	10.7364	+	17.0895i	0.492102	+	0.783294i
$477$	−1.01756	−	20.5397i	−0.0465908	−	0.940450i
$478$	9.40839	+	10.4491i	0.430330	+	0.477930i
$479$	−37.1960	+	7.90625i	−1.69953	+	0.361246i	−0.952733	−	0.303809i	$-0.901742\pi$
$479$	−37.1960	+	7.90625i	−1.69953	+	0.361246i	−0.746795	+	0.665055i	$0.768408\pi$
$480$	−1.97903	+	2.31045i	−0.0903300	+	0.105457i
$481$	−1.40208	−	3.14912i	−0.0639293	−	0.143588i
$482$	1.19457	+	3.67650i	0.0544110	+	0.167460i
$483$	12.6741	+	1.88125i	0.576689	+	0.0855999i
$484$	−7.36500	−	8.17048i	−0.334773	−	0.371385i
$485$	−2.42011	−	1.39725i	−0.109892	−	0.0634459i
$486$	−8.92101	+	12.7834i	−0.404665	+	0.579867i
$487$	−3.44337	+	32.7615i	−0.156034	+	1.48457i	0.583867	+	0.811850i	$0.301539\pi$
$487$	−3.44337	+	32.7615i	−0.156034	+	1.48457i	−0.739901	+	0.672716i	$0.765128\pi$
$488$	0.859945	+	8.18183i	0.0389279	+	0.370374i
$489$	11.0541	−	16.0347i	0.499885	−	0.725115i
$490$	−5.82462	−	10.8275i	−0.263130	−	0.489136i
$491$	−15.5236	−	21.3664i	−0.700571	−	0.964253i	−0.999949	−	0.0101181i	$-0.996779\pi$
$491$	−15.5236	−	21.3664i	−0.700571	−	0.964253i	0.299378	−	0.954135i	$-0.403221\pi$
$492$	−21.1964	+	2.75973i	−0.955606	+	0.124418i
$493$	−13.8336	−	12.4558i	−0.623033	−	0.560982i
$494$	5.64560	−	3.25949i	0.254007	−	0.146651i
$495$	4.56663	−	16.8687i	0.205255	−	0.758191i
$496$		−	1.78668i		−	0.0802244i
$497$	5.43115	+	11.0673i	0.243620	+	0.496437i
$498$	2.08463	−	1.59486i	0.0934143	−	0.0714674i
$499$	0.637085	+	6.06146i	0.0285198	+	0.271348i	0.999484	+	0.0321228i	$0.0102268\pi$
$499$	0.637085	+	6.06146i	0.0285198	+	0.271348i	−0.970964	+	0.239225i	$0.923107\pi$
$500$	−11.8802	+	2.52521i	−0.531298	+	0.112931i
$501$	24.4096	+	1.95620i	1.09054	+	0.0873965i
$502$	−1.98321	+	0.208444i	−0.0885151	+	0.00930331i
$503$	−3.02374	−	2.19688i	−0.134822	−	0.0979539i	0.518330	−	0.855181i	$-0.326554\pi$
$503$	−3.02374	−	2.19688i	−0.134822	−	0.0979539i	−0.653152	+	0.757227i	$0.726554\pi$
$504$	6.33690	+	4.77951i	0.282268	+	0.212896i
$505$	0.207292			0.00922435
$506$	7.50074	−	5.45281i	0.333448	−	0.242407i
$507$	3.51232	+	14.7226i	0.155988	+	0.653852i
$508$	−8.65643	+	9.61393i	−0.384067	+	0.426549i
$509$	−28.6496	+	12.7556i	−1.26987	+	0.565383i	−0.927374	−	0.374136i	$-0.877939\pi$
$509$	−28.6496	+	12.7556i	−1.26987	+	0.565383i	−0.342497	+	0.939519i	$0.611273\pi$
$510$	7.71506	+	21.8860i	0.341628	+	0.969130i
$511$	17.1397	−	6.28545i	0.758215	−	0.278052i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$	11.8542	+	11.3462i	0.523376	+	0.500949i
$514$	1.89943	+	0.199638i	0.0837802	+	0.00880565i
$515$	−18.6440	−	16.7871i	−0.821552	−	0.739729i
$516$	−4.74466	+	4.48963i	−0.208872	+	0.197645i
$517$	−15.6920	+	3.34003i	−0.690135	+	0.146894i
$518$	−2.72847	−	3.47488i	−0.119882	−	0.152678i
$519$	−0.334601	−	13.5163i	−0.0146873	−	0.593301i
$520$	3.31228	−	1.47472i	0.145253	−	0.0646709i
$521$	−6.12123	−	2.72535i	−0.268176	−	0.119400i	0.268243	−	0.963351i	$-0.413557\pi$
$521$	−6.12123	−	2.72535i	−0.268176	−	0.119400i	−0.536420	+	0.843951i	$0.680224\pi$
$522$	−6.82710	−	2.64310i	−0.298814	−	0.115685i
$523$	−29.9229	+	26.9427i	−1.30844	+	1.17812i	−0.336816	+	0.941570i	$0.609350\pi$
$523$	−29.9229	+	26.9427i	−1.30844	+	1.17812i	−0.971619	+	0.236550i	$0.923983\pi$
$524$	6.07287	−	4.41220i	0.265295	−	0.192748i
$525$	2.35371	+	8.45450i	0.102724	+	0.368984i
$526$	1.02347	+	3.14992i	0.0446255	+	0.137343i
$527$	−11.8031	−	6.81453i	−0.514152	−	0.296846i
$528$	5.69628	−	0.743264i	0.247899	−	0.0323464i
$529$	−7.59117	−	13.1483i	−0.330051	−	0.571665i
$530$	−11.7769	−	2.50326i	−0.511557	−	0.108735i
$531$	13.9384	+	36.6235i	0.604876	+	1.58933i
$532$	5.99608	−	5.81851i	0.259963	−	0.252265i
$533$	24.2289	+	7.87243i	1.04947	+	0.340993i
$534$	−5.12900	+	2.43741i	−0.221954	+	0.105477i
$535$	−11.0677	+	24.8585i	−0.478499	+	1.07473i
$536$	9.86704	+	1.03707i	0.426191	+	0.0447945i
$537$	12.2010	−	22.3950i	0.526512	−	0.966417i
$538$			23.4543i			1.01119i
$539$	−5.50091	+	22.5553i	−0.236941	+	0.971524i
$540$	5.89736	+	6.96519i	0.253782	+	0.299734i
$541$	0.988281	+	0.210066i	0.0424895	+	0.00903142i	0.229107	−	0.973401i	$-0.426419\pi$
$541$	0.988281	+	0.210066i	0.0424895	+	0.00903142i	−0.186618	+	0.982433i	$0.559753\pi$
$542$	−1.30735	+	12.4386i	−0.0561556	+	0.534285i
$543$	−23.8253	+	27.8152i	−1.02244	+	1.19366i
$544$	−5.66882	+	5.10423i	−0.243049	+	0.218842i
$545$	9.78176	−	30.1052i	0.419005	−	1.28956i
$546$	−4.37643	−	8.38665i	−0.187294	−	0.358916i
$547$	−8.66797	−	6.29765i	−0.370615	−	0.269268i	0.386851	−	0.922142i	$-0.373563\pi$
$547$	−8.66797	−	6.29765i	−0.370615	−	0.269268i	−0.757466	+	0.652874i	$0.773563\pi$
$548$	−0.175047	+	0.823532i	−0.00747764	+	0.0351796i
$549$	24.6431	+	1.36216i	1.05174	+	0.0581355i
$550$	5.50155	+	3.17427i	0.234587	+	0.135351i
$551$	−3.85315	+	6.67385i	−0.164150	+	0.284316i
$552$	0.119849	+	4.84134i	0.00510110	+	0.206061i
$553$	−9.88080	−	15.7276i	−0.420174	−	0.668804i
$554$	−2.97675	−	4.09715i	−0.126470	−	0.174071i
$555$	−2.18045	−	4.58828i	−0.0925550	−	0.194762i
$556$	1.50142	+	7.06360i	0.0636742	+	0.299563i
$557$	−6.35699	+	14.2780i	−0.269354	+	0.604979i	−0.996689	−	0.0813030i	$-0.974092\pi$
$557$	−6.35699	+	14.2780i	−0.269354	+	0.604979i	0.727335	+	0.686282i	$0.240759\pi$
$558$	−5.29164	−	0.853630i	−0.224013	−	0.0361371i
$559$	7.40415	−	2.40575i	0.313162	−	0.101753i
$560$	3.65492	−	2.86984i	0.154449	−	0.121273i
$561$	16.8159	−	40.4654i	0.709967	−	1.70845i
$562$	−4.48261	+	7.76410i	−0.189087	+	0.327509i
$563$	4.78889	−	5.31861i	0.201828	−	0.224153i	−0.633731	−	0.773554i	$-0.718477\pi$
$563$	4.78889	−	5.31861i	0.201828	−	0.224153i	0.835559	+	0.549401i	$0.185144\pi$
$564$	3.21737	−	7.73611i	0.135476	−	0.325749i
$565$	−27.4211	+	2.88207i	−1.15361	+	0.121250i
$566$	6.21252	−	19.1202i	0.261132	−	0.803680i
$567$	17.1831	−	16.4845i	0.721624	−	0.692285i
$568$	−3.76969	+	2.73884i	−0.158173	+	0.114919i
$569$	−9.80805	−	22.0292i	−0.411175	−	0.923514i	−0.993842	−	0.110803i	$-0.964658\pi$
$569$	−9.80805	−	22.0292i	−0.411175	−	0.923514i	0.582668	−	0.812711i	$-0.302009\pi$
$570$	8.19845	−	5.00791i	0.343395	−	0.209758i
$571$	−3.98910	−	6.90932i	−0.166938	−	0.289146i	0.770404	−	0.637557i	$-0.220055\pi$
$571$	−3.98910	−	6.90932i	−0.166938	−	0.289146i	−0.937342	+	0.348411i	$0.886721\pi$
$572$	−6.51205	−	2.11388i	−0.272282	−	0.0883858i
$573$	−1.68507	+	5.65898i	−0.0703949	+	0.236407i
$574$	32.5772	+	2.19863i	1.35974	+	0.0917692i
$575$	−3.14735	+	4.33195i	−0.131253	+	0.180655i
$576$	−1.36961	+	2.66911i	−0.0570670	+	0.111213i
$577$	−6.66169	−	31.3408i	−0.277330	−	1.30473i	−0.867493	−	0.497450i	$-0.834270\pi$
$577$	−6.66169	−	31.3408i	−0.277330	−	1.30473i	0.590163	−	0.807284i	$-0.299063\pi$
$578$	8.56359	+	40.2885i	0.356198	+	1.67578i
$579$	6.91069	−	36.9915i	0.287198	−	1.53731i
$580$	−2.51932	+	3.46754i	−0.104609	+	0.143982i
$581$	−3.59931	+	1.76632i	−0.149324	+	0.0732793i
$582$	−2.64117	−	0.786459i	−0.109480	−	0.0325998i
$583$	13.3687	+	18.3896i	0.553674	+	0.761619i
$584$	3.45003	+	5.97563i	0.142763	+	0.247273i
$585$	−2.78518	−	10.5146i	−0.115153	−	0.434726i
$586$	−12.5396	−	28.1645i	−0.518007	−	1.16346i
$587$	−5.55536	+	4.03621i	−0.229294	+	0.166592i	−0.696500	−	0.717556i	$-0.745261\pi$
$587$	−5.55536	+	4.03621i	−0.229294	+	0.166592i	0.467206	+	0.884148i	$0.345261\pi$
$588$	−8.06486	−	9.05307i	−0.332589	−	0.373342i
$589$	−1.74355	+	5.36608i	−0.0718415	+	0.221106i
$590$	22.8165	−	2.39811i	0.939339	−	0.0987285i
$591$	19.7369	+	8.20836i	0.811866	+	0.337647i
$592$	1.11736	−	1.24096i	0.0459234	−	0.0510031i
$593$	−3.40206	+	5.89254i	−0.139706	+	0.241977i	−0.927385	−	0.374108i	$-0.877949\pi$
$593$	−3.40206	+	5.89254i	−0.139706	+	0.241977i	0.787679	+	0.616085i	$0.211282\pi$
$594$	0.520199	−	17.2258i	0.0213440	−	0.706785i
$595$	−5.01851	−	35.0908i	−0.205739	−	1.43858i
$596$	−2.89665	+	0.941178i	−0.118651	+	0.0385521i
$597$	−3.32452	−	25.5343i	−0.136064	−	1.04505i
$598$	2.34762	−	5.27283i	0.0960011	−	0.215622i
$599$	−4.55960	−	21.4512i	−0.186300	−	0.876473i	−0.967634	−	0.252360i	$-0.918793\pi$
$599$	−4.55960	−	21.4512i	−0.186300	−	0.876473i	0.781333	−	0.624114i	$-0.214540\pi$
$600$	−2.99593	+	1.42373i	−0.122308	+	0.0581237i
$601$	11.6482	+	16.0324i	0.475141	+	0.653975i	0.977562	−	0.210648i	$-0.0675574\pi$
$601$	11.6482	+	16.0324i	0.475141	+	0.653975i	−0.502421	+	0.864623i	$0.667557\pi$
$602$	8.44895	−	5.30803i	0.344354	−	0.216339i
$603$	7.78571	−	28.7279i	0.317059	−	1.16989i
$604$	9.04311	−	15.6631i	0.367959	−	0.637324i
$605$	5.98058	+	18.3714i	0.243145	+	0.746903i
$606$	0.198839	−	0.0474363i	0.00807726	−	0.00192697i
$607$	−8.30363	+	39.0655i	−0.337034	+	1.58562i	0.404393	+	0.914585i	$0.367483\pi$
$607$	−8.30363	+	39.0655i	−0.337034	+	1.58562i	−0.741427	+	0.671034i	$0.765850\pi$
$608$	2.55483	+	1.85619i	0.103612	+	0.0752784i
$609$	9.43748	+	5.99914i	0.382426	+	0.243097i
$610$	4.46519	−	13.7424i	0.180790	−	0.556415i
$611$	−7.42085	+	6.68176i	−0.300215	+	0.270315i
$612$	12.4088	+	19.2281i	0.501597	+	0.777248i
$613$	2.76972	−	26.3522i	0.111868	−	1.06435i	−0.784222	−	0.620481i	$-0.786937\pi$
$613$	2.76972	−	26.3522i	0.111868	−	1.06435i	0.896090	−	0.443873i	$-0.146396\pi$
$614$	29.4683	+	6.26369i	1.18925	+	0.252782i
$615$	35.9820	+	10.7143i	1.45094	+	0.432044i
$616$	−8.75521	−	0.588432i	−0.352758	−	0.0237086i
$617$		−	7.45338i		−	0.300062i	−0.988681	−	0.150031i	$-0.952063\pi$
$617$		−	7.45338i		−	0.300062i	0.988681	−	0.150031i	$-0.0479373\pi$
$618$	−21.7253	−	11.8361i	−0.873918	−	0.476118i
$619$	−10.9633	−	1.15229i	−0.440653	−	0.0463145i	−0.118395	−	0.992967i	$-0.537775\pi$
$619$	−10.9633	−	1.15229i	−0.440653	−	0.0463145i	−0.322257	+	0.946652i	$0.604442\pi$
$620$	−1.27639	+	2.86681i	−0.0512609	+	0.115134i
$621$	14.3959	+	1.95811i	0.577688	+	0.0785763i
$622$	10.6908	+	3.47364i	0.428661	+	0.139280i
$623$	8.41158	−	2.11893i	0.337003	−	0.0848930i
$624$	2.83974	−	2.17257i	0.113681	−	0.0869722i
$625$	11.5001	+	2.44443i	0.460005	+	0.0977770i
$626$	−1.45345	−	2.51746i	−0.0580917	−	0.100618i
$627$	−17.8334	−	3.32645i	−0.712197	−	0.132845i
$628$	11.2857	+	6.51578i	0.450347	+	0.260008i
$629$	−3.93627	−	12.1146i	−0.156949	−	0.483041i
$630$	−6.75341	−	12.1960i	−0.269062	−	0.485898i
$631$	−1.68837	+	1.22667i	−0.0672129	+	0.0488330i	−0.620884	−	0.783902i	$-0.713226\pi$
$631$	−1.68837	+	1.22667i	−0.0672129	+	0.0488330i	0.553671	+	0.832735i	$0.313226\pi$
$632$	5.21706	−	4.69746i	0.207523	−	0.186855i
$633$	−41.5685	−	3.33131i	−1.65220	−	0.132408i
$634$	−16.8098	−	7.48419i	−0.667601	−	0.297235i
$635$	20.7577	−	9.24193i	0.823745	−	0.366755i
$636$	−11.8695	+	0.293834i	−0.470658	+	0.0116513i
$637$	4.05034	+	13.8709i	0.160480	+	0.549586i
$638$	7.91621	−	1.68495i	0.313406	−	0.0667080i
$639$	6.31059	+	12.4733i	0.249643	+	0.493435i
$640$	1.30525	+	1.17526i	0.0515947	+	0.0464561i
$641$	−29.8782	−	3.14033i	−1.18012	−	0.124035i	−0.505916	−	0.862582i	$-0.668846\pi$
$641$	−29.8782	−	3.14033i	−1.18012	−	0.124035i	−0.674202	+	0.738547i	$0.735512\pi$
$642$	−4.92780	+	26.3775i	−0.194485	+	1.04104i
$643$	5.34550	+	1.73686i	0.210806	+	0.0684951i	0.412516	−	0.910950i	$-0.364650\pi$
$643$	5.34550	+	1.73686i	0.210806	+	0.0684951i	−0.201710	+	0.979445i	$0.564650\pi$
$644$	1.26690	−	7.28825i	0.0499227	−	0.287197i
$645$	10.8204	−	3.81429i	0.426051	−	0.150187i
$646$	22.0066	−	9.79797i	0.865838	−	0.385496i
$647$	−9.47242	+	10.5202i	−0.372399	+	0.413591i	−0.899992	−	0.435906i	$-0.856428\pi$
$647$	−9.47242	+	10.5202i	−0.372399	+	0.413591i	0.527593	+	0.849497i	$0.323095\pi$
$648$	7.25078	+	5.33162i	0.284838	+	0.209446i
$649$	−35.0554	−	25.4542i	−1.37604	−	0.999167i
$650$	3.95333			0.155062
$651$	7.67195	+	2.85972i	0.300688	+	0.112081i
$652$	−9.09687	−	6.60926i	−0.356261	−	0.258839i
$653$	−27.7549	+	2.91715i	−1.08613	+	0.114157i	−0.630634	−	0.776080i	$-0.717205\pi$
$653$	−27.7549	+	2.91715i	−1.08613	+	0.114157i	−0.455497	+	0.890237i	$0.650539\pi$
$654$	2.49365	−	31.1160i	0.0975093	−	1.21673i
$655$	−12.8962	+	2.74118i	−0.503897	+	0.107107i
$656$	1.28999	+	12.2734i	0.0503656	+	0.479196i
$657$	19.3464	−	7.36299i	0.754776	−	0.287258i
$658$	−7.13098	+	10.6276i	−0.277995	+	0.414308i
$659$			5.95736i			0.232066i	0.993245	+	0.116033i	$0.0370178\pi$
$659$			5.95736i			0.232066i	−0.993245	+	0.116033i	$0.962982\pi$
$660$	−9.67091	−	2.87676i	−0.376440	−	0.111978i
$661$	9.21798	−	5.32200i	0.358538	−	0.207002i	−0.309901	−	0.950769i	$-0.600296\pi$
$661$	9.21798	−	5.32200i	0.358538	−	0.207002i	0.668439	+	0.743767i	$0.266963\pi$
$662$	−13.2921	−	11.9682i	−0.516611	−	0.465159i
$663$	−3.52136	−	27.0461i	−0.136758	−	1.05038i
$664$	−0.890726	−	1.22598i	−0.0345669	−	0.0475772i
$665$	−13.7777	+	5.05253i	−0.534275	+	0.195929i
$666$	−3.14151	−	3.90221i	−0.121731	−	0.151207i
$667$	0.713206	+	6.78570i	0.0276154	+	0.262743i
$668$	1.47783	−	14.0606i	0.0571790	−	0.544022i
$669$	3.50955	+	5.74549i	0.135687	+	0.222134i
$670$	−15.0912	−	8.71293i	−0.583026	−	0.336610i
$671$	−23.6261	+	13.6494i	−0.912077	+	0.526928i
$672$	2.84915	−	3.58920i	0.109908	−	0.138456i
$673$	−8.07714	−	24.8589i	−0.311351	−	0.958240i	−0.977230	−	0.212181i	$-0.931943\pi$
$673$	−8.07714	−	24.8589i	−0.311351	−	0.958240i	0.665879	−	0.746059i	$-0.268057\pi$
$674$	−0.432675	−	0.971804i	−0.0166660	−	0.0374325i
$675$	2.78531	+	9.55331i	0.107206	+	0.367707i
$676$	8.54765	−	1.81686i	0.328756	−	0.0698792i
$677$	26.2875	+	29.1952i	1.01031	+	1.12206i	0.992503	+	0.122222i	$0.0390019\pi$
$677$	26.2875	+	29.1952i	1.01031	+	1.12206i	0.0178075	+	0.999841i	$0.494331\pi$
$678$	−25.6434	+	9.03956i	−0.984828	+	0.347162i
$679$	3.72156	+	1.96723i	0.142820	+	0.0754953i
$680$	12.7423	−	4.14022i	0.488644	−	0.158770i
$681$	7.29589	−	6.90374i	0.279579	−	0.264552i
$682$	5.41277	−	2.41173i	0.207266	−	0.0923501i
$683$	−15.3366	+	8.85460i	−0.586839	+	0.338812i	−0.763847	−	0.645398i	$-0.776692\pi$
$683$	−15.3366	+	8.85460i	−0.586839	+	0.338812i	0.177008	+	0.984209i	$0.443358\pi$
$684$	6.71813	−	6.67982i	0.256874	−	0.255409i
$685$	0.869194	−	1.19634i	0.0332102	−	0.0457099i
$686$	9.37658	+	15.9712i	0.358000	+	0.609784i
$687$	28.2350	+	19.4649i	1.07723	+	0.742632i
$688$	2.52351	+	2.80264i	0.0962078	+	0.106850i
$689$	12.9274	+	5.75566i	0.492495	+	0.219273i
$690$	3.26630	−	7.85377i	0.124346	−	0.298988i
$691$	−1.27941	+	6.01916i	−0.0486711	+	0.228980i	−0.995760	−	0.0919927i	$-0.970676\pi$
$691$	−1.27941	+	6.01916i	−0.0486711	+	0.228980i	0.947089	+	0.320972i	$0.104010\pi$
$692$	−7.80605			−0.296742
$693$	−5.92578	+	25.6493i	−0.225102	+	0.974335i
$694$	−33.9717			−1.28955
$695$	2.63708	−	12.4065i	0.100030	−	0.470604i
$696$	−1.62307	+	3.90266i	−0.0615225	+	0.147930i
$697$	86.0003	+	38.2898i	3.25749	+	1.45033i
$698$	−15.7981	−	17.5456i	−0.597968	−	0.664110i
$699$	−20.6075	−	14.2065i	−0.779446	−	0.537341i
$700$	4.91334	−	1.23770i	0.185707	−	0.0467806i
$701$	21.9213	−	30.1720i	0.827955	−	1.13958i	−0.160345	−	0.987061i	$-0.551261\pi$
$701$	21.9213	−	30.1720i	0.827955	−	1.13958i	0.988300	−	0.152521i	$-0.0487392\pi$
$702$	−5.07776	−	9.44848i	−0.191648	−	0.356610i
$703$	−4.56686	+	2.63668i	−0.172243	+	0.0994443i
$704$	−0.347603	−	3.29836i	−0.0131008	−	0.124312i
$705$	−10.6890	+	10.1145i	−0.402571	+	0.380934i
$706$	−24.1969	+	7.86206i	−0.910663	+	0.295892i
$707$	−0.312037	+	0.0116544i	−0.0117354	+	0.000438307i
$708$	21.3373	−	7.52161i	0.801904	−	0.282679i
$709$	−13.8914	−	15.4280i	−0.521702	−	0.579409i	0.423499	−	0.905896i	$-0.360802\pi$
$709$	−13.8914	−	15.4280i	−0.521702	−	0.579409i	−0.945202	+	0.326487i	$0.894135\pi$
$710$	8.00524	−	1.70157i	0.300431	−	0.0638586i
$711$	−11.4199	−	17.6957i	−0.428281	−	0.663642i
$712$	1.33353	+	2.99515i	0.0499760	+	0.112248i
$713$	1.54372	+	4.75107i	0.0578127	+	0.177929i
$714$	−12.8440	−	32.5114i	−0.480674	−	1.21671i
$715$	8.93874	+	8.04396i	0.334290	+	0.300827i
$716$	−12.7515	−	7.36208i	−0.476546	−	0.275134i
$717$	−12.6951	−	20.7831i	−0.474106	−	0.776160i
$718$	−1.03007	+	9.80042i	−0.0384417	+	0.365749i
$719$	−2.88333	−	27.4331i	−0.107530	−	1.02308i	−0.906643	−	0.421899i	$-0.861364\pi$
$719$	−2.88333	−	27.4331i	−0.107530	−	1.02308i	0.799113	−	0.601181i	$-0.205303\pi$
$720$	4.10439	−	3.30428i	0.152961	−	0.123143i
$721$	29.0087	+	24.2215i	1.08034	+	0.902057i
$722$	5.30619	+	7.30334i	0.197476	+	0.271802i
$723$	−0.864458	−	6.63955i	−0.0321495	−	0.246927i
$724$	15.7138	+	14.1487i	0.583997	+	0.525834i
$725$	−4.04725	+	2.33668i	−0.150311	+	0.0867823i
$726$	9.94078	+	16.2536i	0.368937	+	0.603229i
$727$			3.01014i			0.111640i	0.998441	+	0.0558200i	$0.0177773\pi$
$727$			3.01014i			0.111640i	−0.998441	+	0.0558200i	$0.982223\pi$
$728$	−4.90309	+	2.40613i	−0.181720	+	0.0891772i
$729$	19.2550	−	18.9274i	0.713146	−	0.701015i
$730$	−1.26680	−	12.0528i	−0.0468865	−	0.446095i
$731$	28.1395	−	5.98124i	1.04078	−	0.221224i
$732$	1.13830	−	14.2039i	0.0420729	−	0.524990i
$733$	11.1998	−	1.17715i	0.413674	−	0.0434789i	0.104594	−	0.994515i	$-0.466646\pi$
$733$	11.1998	−	1.17715i	0.413674	−	0.0434789i	0.309080	+	0.951036i	$0.399979\pi$
$734$	14.9128	+	10.8348i	0.550443	+	0.399920i
$735$	6.47301	+	20.2875i	0.238761	+	0.748316i
$736$	2.79601			0.103062
$737$	10.1771	+	31.2922i	0.374879	+	1.15266i
$738$	36.9666	+	2.04335i	1.36076	+	0.0752167i
$739$	−6.46389	+	7.17888i	−0.237778	+	0.264079i	−0.850210	−	0.526444i	$-0.823525\pi$
$739$	−6.46389	+	7.17888i	−0.237778	+	0.264079i	0.612432	+	0.790524i	$0.290192\pi$
$740$	−2.67939	+	1.19294i	−0.0984963	+	0.0438534i
$741$	−10.6489	+	3.75386i	−0.391198	+	0.137901i
$742$	17.8686	+	3.10605i	0.655978	+	0.114027i
$743$	49.2830	+	16.0130i	1.80802	+	0.587461i	0.999999	−	0.00169422i	$-0.000539288\pi$
$743$	49.2830	+	16.0130i	1.80802	+	0.587461i	0.808020	+	0.589155i	$0.200539\pi$
$744$	−0.568300	+	3.04199i	−0.0208349	+	0.111525i
$745$	5.32017	+	0.559172i	0.194916	+	0.0204865i
$746$	−9.08146	−	8.17698i	−0.332496	−	0.299381i
$747$	−4.05656	+	2.05233i	−0.148422	+	0.0750909i
$748$	−23.1153	−	10.2839i	−0.845179	−	0.376015i
$749$	15.2627	−	38.0419i	0.557687	−	1.39002i
$750$	21.0304	−	0.520613i	0.767920	−	0.0190101i
$751$	34.6892	−	15.4446i	1.26583	−	0.563582i	0.339607	−	0.940568i	$-0.389706\pi$
$751$	34.6892	−	15.4446i	1.26583	−	0.563582i	0.926219	+	0.376985i	$0.123039\pi$
$752$	−4.41911	−	1.96751i	−0.161148	−	0.0717478i
$753$	3.44291	+	0.275916i	0.125467	+	0.0100549i
$754$	3.74362	−	3.37077i	0.136334	−	0.122756i
$755$	−25.6997	+	18.6719i	−0.935306	+	0.679540i
$756$	−9.26892	−	10.1532i	−0.337107	−	0.369268i
$757$	3.09580	+	9.52789i	0.112519	+	0.346297i	0.991421	−	0.130704i	$-0.0417238\pi$
$757$	3.09580	+	9.52789i	0.112519	+	0.346297i	−0.878903	+	0.477001i	$0.841724\pi$
$758$	0.713557	+	0.411972i	0.0259175	+	0.0149635i
$759$	−14.5051	+	6.89812i	−0.526502	+	0.250386i
$760$	−2.77329	−	4.80348i	−0.100598	−	0.174241i
$761$	39.6370	+	8.42511i	1.43684	+	0.305410i	0.859518	−	0.511106i	$-0.170764\pi$
$761$	39.6370	+	8.42511i	1.43684	+	0.305410i	0.577323	+	0.816516i	$0.304097\pi$
$762$	17.7963	−	13.6152i	0.644693	−	0.493228i
$763$	−13.0320	+	45.8674i	−0.471789	+	1.66051i
$764$	3.24214	+	1.05343i	0.117296	+	0.0381119i
$765$	−6.17420	−	39.7170i	−0.223228	−	1.43597i
$766$	8.76407	−	19.6844i	0.316659	−	0.711227i
$767$	−26.8165	−	2.81853i	−0.968288	−	0.101771i
$768$	1.52097	+	0.828639i	0.0548834	+	0.0299009i
$769$			31.1077i			1.12177i	0.827893	+	0.560887i	$0.189540\pi$
$769$			31.1077i			1.12177i	−0.827893	+	0.560887i	$0.810460\pi$
$770$	13.6278	+	7.19880i	0.491110	+	0.259427i
$771$	−3.17046	−	0.944064i	−0.114181	−	0.0339996i
$772$	−21.2518	−	4.51720i	−0.764868	−	0.162578i
$773$	−0.943858	+	8.98021i	−0.0339482	+	0.322996i	0.964348	+	0.264639i	$0.0852528\pi$
$773$	−0.943858	+	8.98021i	−0.0339482	+	0.322996i	−0.998296	+	0.0583568i	$0.981414\pi$
$774$	9.50627	−	6.13487i	0.341696	−	0.220513i
$775$	−2.54278	+	2.28953i	−0.0913393	+	0.0822423i
$776$	−0.491661	+	1.51318i	−0.0176496	+	0.0543198i
$777$	3.54021	+	6.78417i	0.127004	+	0.243381i
$778$	27.3113	+	19.8428i	0.979158	+	0.711400i
$779$	8.10277	−	38.1205i	0.290312	−	1.36581i
$780$	−6.10855	+	1.45730i	−0.218721	+	0.0521797i
$781$	−13.3858	−	7.72332i	−0.478982	−	0.276362i
$782$	10.6642	−	18.4709i	0.381350	−	0.660518i
$783$	10.7831	+	6.67167i	0.385356	+	0.238426i
$784$	−5.34042	+	4.52547i	−0.190729	+	0.161624i
$785$	−13.4535	−	18.5172i	−0.480177	−	0.660908i
$786$	−11.7431	+	5.58055i	−0.418861	+	0.199052i
$787$	4.55072	+	21.4095i	0.162216	+	0.763165i	0.981756	+	0.190144i	$0.0608955\pi$
$787$	4.55072	+	21.4095i	0.162216	+	0.763165i	−0.819540	+	0.573021i	$0.805771\pi$
$788$	5.01965	−	11.2743i	0.178818	−	0.401631i
$789$	−0.740644	−	5.68858i	−0.0263676	−	0.202519i
$790$	−11.7268	+	3.81027i	−0.417221	+	0.135563i
$791$	41.1151	−	5.88007i	1.46188	−	0.209071i
$792$	−9.93486	−	0.546370i	−0.353020	−	0.0194144i
$793$	−8.49144	+	14.7076i	−0.301540	+	0.522283i
$794$	−11.7343	+	13.0323i	−0.416436	+	0.462499i
$795$	19.2551	+	8.00800i	0.682908	+	0.284014i
$796$	−14.7852	+	1.55399i	−0.524049	+	0.0550797i
$797$	6.81936	−	20.9878i	0.241554	−	0.743427i	−0.754630	−	0.656150i	$-0.772184\pi$
$797$	6.81936	−	20.9878i	0.241554	−	0.743427i	0.996184	−	0.0872765i	$-0.0278164\pi$
$798$	−12.0596	+	7.99936i	−0.426906	+	0.283174i
$799$	−29.8525	+	21.6891i	−1.05611	+	0.767306i
$800$	0.778935	+	1.74952i	0.0275395	+	0.0618547i
$801$	9.50790	−	2.51852i	0.335945	−	0.0889874i
$802$	0.262337	+	0.454381i	0.00926345	+	0.0160448i
$803$	−13.4462	+	18.5180i	−0.474507	+	0.653487i
$804$	−16.4697	−	4.90417i	−0.580842	−	0.172957i
$805$	−7.23944	+	10.7893i	−0.255157	+	0.380271i
$806$	2.16791	−	2.98387i	0.0763614	−	0.105102i
$807$	7.46024	−	39.9332i	0.262613	−	1.40571i
$808$	−0.0245380	−	0.115442i	−0.000863243	−	0.00406124i
$809$	−5.61244	−	26.4045i	−0.197323	−	0.928332i	−0.959663	−	0.281154i	$-0.909283\pi$
$809$	−5.61244	−	26.4045i	−0.197323	−	0.928332i	0.762340	−	0.647177i	$-0.224051\pi$
$810$	−7.82535	−	13.7347i	−0.274955	−	0.482588i
$811$	8.48731	−	11.6818i	0.298030	−	0.410203i	−0.633572	−	0.773684i	$-0.718412\pi$
$811$	8.48731	−	11.6818i	0.298030	−	0.410203i	0.931602	+	0.363481i	$0.118412\pi$
$812$	3.59739	−	5.36135i	0.126244	−	0.188146i
$813$	6.18232	−	20.7621i	0.216823	−	0.728159i
$814$	5.26776	+	1.70997i	0.184635	+	0.0599345i
$815$	9.87475	+	17.1036i	0.345897	+	0.599112i
$816$	11.2752	−	6.88731i	0.394712	−	0.241104i
$817$	−4.84407	−	10.8800i	−0.169473	−	0.380642i
$818$	20.5853	−	14.9561i	0.719748	−	0.522928i
$819$	4.78370	+	15.6711i	0.167156	+	0.547593i
$820$	6.69815	−	20.6148i	0.233910	−	0.719900i
$821$	34.8163	−	3.65934i	1.21510	−	0.127712i	0.524792	−	0.851231i	$-0.324143\pi$
$821$	34.8163	−	3.65934i	1.21510	−	0.127712i	0.690305	+	0.723519i	$0.257476\pi$
$822$	0.559980	−	1.34646i	0.0195315	−	0.0469633i
$823$	−27.0396	+	30.0305i	−0.942542	+	1.04680i	0.0562869	+	0.998415i	$0.482074\pi$
$823$	−27.0396	+	30.0305i	−0.942542	+	1.04680i	−0.998829	+	0.0483842i	$0.984593\pi$
$824$	−7.14190	+	12.3701i	−0.248800	+	0.430934i
$825$	−8.35724	−	7.15440i	−0.290962	−	0.249084i
$826$	−34.2109	+	4.89267i	−1.19035	+	0.170238i
$827$	−1.84462	+	0.599352i	−0.0641436	+	0.0208415i	−0.340913	−	0.940095i	$-0.610736\pi$
$827$	−1.84462	+	0.599352i	−0.0641436	+	0.0208415i	0.276769	+	0.960936i	$0.410736\pi$
$828$	1.33586	−	8.28096i	0.0464243	−	0.287783i
$829$	−11.9087	+	26.7474i	−0.413606	+	0.928975i	0.579846	+	0.814726i	$0.303113\pi$
$829$	−11.9087	+	26.7474i	−0.413606	+	0.928975i	−0.993452	+	0.114249i	$0.963554\pi$
$830$	0.553383	+	2.60346i	0.0192082	+	0.0903675i
$831$	3.76500	+	7.92261i	0.130606	+	0.274832i
$832$	−1.21337	−	1.67006i	−0.0420661	−	0.0578991i
$833$	9.52726	+	52.5402i	0.330100	+	1.82041i
$834$	−0.309540	−	12.5040i	−0.0107185	−	0.432979i
$835$	−12.4160	+	21.5052i	−0.429674	+	0.744217i
$836$	−2.17474	+	10.2454i	−0.0752150	+	0.354346i
$837$	8.73799	+	3.13653i	0.302029	+	0.108414i
$838$	−1.99925	+	9.40575i	−0.0690631	+	0.324916i
$839$	−11.0584	−	8.03441i	−0.381779	−	0.277379i	0.380299	−	0.924863i	$-0.375821\pi$
$839$	−11.0584	−	8.03441i	−0.381779	−	0.277379i	−0.762078	+	0.647485i	$0.775821\pi$
$840$	−7.13567	+	3.72363i	−0.246204	+	0.128477i
$841$	7.12129	−	21.9171i	0.245562	−	0.755761i
$842$	−21.8556	+	19.6789i	−0.753194	+	0.678179i
$843$	10.1016	−	11.7933i	0.347919	−	0.406183i
$844$	−2.51668	+	23.9446i	−0.0866277	+	0.824208i
$845$	−15.0130	−	3.19112i	−0.516464	−	0.109778i
$846$	−7.93854	+	12.1481i	−0.272933	+	0.417660i
$847$	−10.0355	−	27.3183i	−0.344823	−	0.938668i
$848$			6.85498i			0.235401i
$849$	−16.6591	+	30.5778i	−0.571737	+	1.04943i
$850$	14.5285	+	1.52701i	0.498324	+	0.0523759i
$851$	−1.89905	+	4.26532i	−0.0650984	+	0.146213i
$852$	7.28941	−	3.46409i	0.249731	−	0.118678i
$853$	33.1425	+	10.7687i	1.13478	+	0.368712i	0.815390	−	0.578912i	$-0.196523\pi$
$853$	33.1425	+	10.7687i	1.13478	+	0.368712i	0.319389	+	0.947624i	$0.396523\pi$
$854$	−5.94885	+	20.9376i	−0.203565	+	0.716470i
$855$	−15.5515	+	5.91871i	−0.531851	+	0.202416i
$856$	15.1540	+	3.22108i	0.517953	+	0.110094i
$857$	−3.51494	−	6.08806i	−0.120068	−	0.207964i	0.799726	−	0.600365i	$-0.204978\pi$
$857$	−3.51494	−	6.08806i	−0.120068	−	0.207964i	−0.919794	+	0.392401i	$0.871645\pi$
$858$	10.4150	+	5.67041i	0.355562	+	0.193585i
$859$	−8.70847	−	5.02784i	−0.297129	−	0.171548i	0.344023	−	0.938961i	$-0.388210\pi$
$859$	−8.70847	−	5.02784i	−0.297129	−	0.171548i	−0.641153	+	0.767413i	$0.721543\pi$
$860$	−2.04690	−	6.29972i	−0.0697989	−	0.214819i
$861$	−54.7664	−	14.1054i	−1.86643	−	0.480710i
$862$	29.5735	−	21.4864i	1.00728	−	0.731831i
$863$	−35.3151	+	31.7978i	−1.20214	+	1.08241i	−0.207582	+	0.978218i	$0.566559\pi$
$863$	−35.3151	+	31.7978i	−1.20214	+	1.08241i	−0.994557	+	0.104193i	$0.966774\pi$
$864$	3.18087	−	4.10878i	0.108215	−	0.139784i
$865$	12.5252	+	5.57656i	0.425868	+	0.189609i
$866$	31.7896	−	14.1536i	1.08025	−	0.480960i
$867$	−1.76552	−	71.3189i	−0.0599602	−	2.42212i
$868$	1.76017	−	4.38719i	0.0597442	−	0.148911i
$869$	21.2732	+	9.46431i	0.721644	+	0.321055i
$870$	5.39231	−	5.10248i	0.182817	−	0.172990i
$871$	15.2202	+	13.7044i	0.515718	+	0.464355i
$872$	−17.9237	−	1.88386i	−0.606973	−	0.0637954i
$873$	4.24669	+	2.17911i	0.143729	+	0.0737518i
$874$	−8.39746	−	2.72850i	−0.284048	−	0.0922929i
$875$	−31.6595	−	5.50329i	−1.07029	−	0.186045i
$876$	−3.97330	−	11.2714i	−0.134245	−	0.380827i
$877$	21.3435	−	9.50272i	0.720717	−	0.320884i	−0.0133968	−	0.999910i	$-0.504264\pi$
$877$	21.3435	−	9.50272i	0.720717	−	0.320884i	0.734114	+	0.679026i	$0.237598\pi$
$878$	−10.1735	+	11.2988i	−0.343338	+	0.381316i
$879$	12.3915	+	51.9412i	0.417954	+	1.75193i
$880$	−1.79857	+	5.54069i	−0.0606297	+	0.186777i
$881$	−0.924139			−0.0311350			−0.0155675	−	0.999879i	$-0.504955\pi$
$881$	−0.924139			−0.0311350			−0.0155675	+	0.999879i	$0.504955\pi$
$882$	10.8516	+	17.9789i	0.365393	+	0.605382i
$883$	−1.76779	−	1.28437i	−0.0594908	−	0.0432226i	0.557642	−	0.830081i	$-0.311706\pi$
$883$	−1.76779	−	1.28437i	−0.0594908	−	0.0432226i	−0.617133	+	0.786859i	$0.711706\pi$
$884$	−15.6606	+	1.64600i	−0.526724	+	0.0553609i
$885$	−39.6100	−	3.17436i	−1.33147	−	0.106705i
$886$	−6.02828	+	1.28135i	−0.202524	+	0.0430478i
$887$	−0.666829	−	6.34446i	−0.0223899	−	0.213026i	−0.999997	−	0.00258576i	$-0.999177\pi$
$887$	−0.666829	−	6.34446i	−0.0223899	−	0.213026i	0.977607	−	0.210440i	$-0.0674897\pi$
$888$	−2.29714	+	1.75744i	−0.0770869	+	0.0589759i
$889$	−30.7271	+	15.0790i	−1.03055	+	0.505732i
$890$		−	5.75851i		−	0.193026i
$891$	−6.36481	+	29.1631i	−0.213229	+	0.977002i
$892$	3.36629	−	1.94353i	0.112712	−	0.0650742i
$893$	11.3522	+	10.2216i	0.379888	+	0.342053i
$894$	5.23118	−	0.681091i	0.174957	−	0.0227791i
$895$	15.2010	+	20.9223i	0.508112	+	0.699356i
$896$	−2.03088	−	1.69574i	−0.0678470	−	0.0566506i
$897$	−5.67420	+	8.23077i	−0.189456	+	0.274818i
$898$	1.15574	+	10.9962i	0.0385676	+	0.366946i
$899$	−0.455747	+	4.33614i	−0.0152000	+	0.144619i
$900$	5.55371	−	1.47111i	0.185124	−	0.0490369i
$901$	45.2851	+	26.1454i	1.50867	+	0.871029i
$902$	−35.4412	+	20.4752i	−1.18006	+	0.681749i
$903$	−16.0735	+	6.35001i	−0.534893	+	0.211315i
$904$	4.85100	+	14.9298i	0.161342	+	0.496559i
$905$	−15.1057	−	33.9280i	−0.502132	−	1.12781i
$906$	−20.3788	+	23.7916i	−0.677041	+	0.790422i
$907$	1.02406	−	0.217671i	0.0340034	−	0.00722764i	−0.190879	−	0.981614i	$-0.561134\pi$
$907$	1.02406	−	0.217671i	0.0340034	−	0.00722764i	0.224882	+	0.974386i	$0.427800\pi$
$908$	−3.88041	−	4.30963i	−0.128776	−	0.143020i
$909$	−0.353630	+	0.0175191i	−0.0117292	+	0.000581073i
$910$	9.58614	−	0.358035i	0.317777	−	0.0118687i
$911$	−28.1658	+	9.15164i	−0.933176	+	0.303207i	−0.735861	−	0.677133i	$-0.763222\pi$
$911$	−28.1658	+	9.15164i	−0.933176	+	0.303207i	−0.197315	+	0.980340i	$0.563222\pi$
$912$	−3.75942	−	3.97297i	−0.124487	−	0.131558i
$913$	2.51178	−	4.35334i	0.0831277	−	0.144074i
$914$	−10.7019	+	6.17876i	−0.353988	+	0.204375i
$915$	−11.9735	+	21.9775i	−0.395833	+	0.726555i
$916$	11.6380	−	16.0184i	0.384532	−	0.529263i
$917$	19.2586	−	4.85136i	0.635976	−	0.160206i
$918$	−15.0112	−	36.6845i	−0.495444	−	1.21077i
$919$	−9.03890	−	10.0387i	−0.298166	−	0.331147i	0.575382	−	0.817885i	$-0.304853\pi$
$919$	−9.03890	−	10.0387i	−0.298166	−	0.331147i	−0.873548	+	0.486738i	$0.838187\pi$
$920$	−4.48632	−	1.99744i	−0.147910	−	0.0658536i
$921$	−48.1803	−	20.0377i	−1.58759	−	0.660264i
$922$	4.93362	−	23.2109i	0.162480	−	0.764409i
$923$	−9.61886			−0.316609
$924$	14.7194	+	3.78668i	0.484233	+	0.124573i
$925$	−3.19795			−0.105148
$926$	−4.61683	+	21.7205i	−0.151718	+	0.713779i
$927$	33.2245	+	27.0624i	1.09124	+	0.888844i
$928$	2.22932	+	0.992557i	0.0731810	+	0.0325823i
$929$	−21.5307	−	23.9122i	−0.706399	−	0.784535i	0.277982	−	0.960586i	$-0.410334\pi$
$929$	−21.5307	−	23.9122i	−0.706399	−	0.784535i	−0.984381	+	0.176051i	$0.943668\pi$
$930$	3.08503	−	4.47503i	0.101162	−	0.146742i
$931$	20.4555	−	8.38021i	0.670403	−	0.274650i
$932$	−8.49408	+	11.6911i	−0.278233	+	0.382955i
$933$	−17.0972	−	9.31468i	−0.559736	−	0.304949i
$934$	−20.8843	+	12.0575i	−0.683355	+	0.394535i
$935$	29.7429	+	33.0142i	0.972695	+	1.07968i
$936$	−5.52597	+	2.79575i	−0.180622	+	0.0913818i
$937$	43.4794	−	14.1273i	1.42041	−	0.461520i	0.504679	−	0.863307i	$-0.331611\pi$
$937$	43.4794	−	14.1273i	1.42041	−	0.461520i	0.915733	+	0.401788i	$0.131611\pi$
$938$	23.2068	+	12.2672i	0.757729	+	0.400537i
$939$	1.67390	+	4.74851i	0.0546257	+	0.154962i
$940$	5.68509	+	6.31393i	0.185427	+	0.205938i
$941$	1.22799	−	0.261016i	0.0400312	−	0.00850889i	−0.187853	−	0.982197i	$-0.560153\pi$
$941$	1.22799	−	0.261016i	0.0400312	−	0.00850889i	0.227884	+	0.973688i	$0.426819\pi$
$942$	−17.1424	−	14.6834i	−0.558529	−	0.478412i
$943$	−14.0347	−	31.5224i	−0.457032	−	1.02651i
$944$	−4.03640	−	12.4228i	−0.131374	−	0.404327i
$945$	7.61908	+	22.9129i	0.247849	+	0.745355i
$946$	−5.08429	+	11.4281i	−0.165305	+	0.371560i
$947$	−23.6815	−	13.6725i	−0.769546	−	0.444298i	0.0631664	−	0.998003i	$-0.479880\pi$
$947$	−23.6815	−	13.6725i	−0.769546	−	0.444298i	−0.832713	+	0.553705i	$0.813213\pi$
$948$	−10.3767	+	6.33845i	−0.337019	+	0.205863i
$949$	−1.48889	+	14.1659i	−0.0483315	+	0.459843i
$950$	−0.632158	−	6.01459i	−0.0205099	−	0.195139i
$951$	26.2397	+	18.0893i	0.850880	+	0.586586i
$952$	−18.9482	+	6.94869i	−0.614116	+	0.225208i
$953$	3.01400	+	4.14842i	0.0976332	+	0.134381i	0.855039	−	0.518564i	$-0.173533\pi$
$953$	3.01400	+	4.14842i	0.0976332	+	0.134381i	−0.757405	+	0.652945i	$0.773533\pi$
$954$	20.3025	+	3.27513i	0.657316	+	0.106036i
$955$	−4.44960	−	4.00643i	−0.143986	−	0.129645i
$956$	−12.1769	+	7.03031i	−0.393828	+	0.227377i
$957$	−14.0140	+	0.350840i	−0.453009	+	0.0113410i
$958$		−	38.0270i		−	1.22860i
$959$	−1.24114	+	1.84973i	−0.0400785	+	0.0597309i
$960$	−1.84850	−	2.41615i	−0.0596600	−	0.0779811i
$961$	−2.90670	−	27.6554i	−0.0937646	−	0.892111i
$962$	3.37182	−	0.716701i	0.108712	−	0.0231074i
$963$	16.7801	−	43.3428i	0.540731	−	1.39670i
$964$	−3.84452	+	0.404076i	−0.123824	+	0.0130144i
$965$	30.8724	+	22.4301i	0.993817	+	0.722051i
$966$	−4.47522	+	12.0060i	−0.143988	+	0.386285i
$967$	−9.22297			−0.296591			−0.148295	−	0.988943i	$-0.547379\pi$
$967$	−9.22297			−0.296591			−0.148295	+	0.988943i	$0.547379\pi$
$968$	9.52320	−	5.50532i	0.306087	−	0.176948i
$969$	−40.5848	+	9.68220i	−1.30377	+	0.311037i
$970$	1.86989	−	2.07672i	0.0600385	−	0.0666795i
$971$	7.69577	−	3.42638i	0.246969	−	0.109958i	−0.279519	−	0.960140i	$-0.590175\pi$
$971$	7.69577	−	3.42638i	0.246969	−	0.109958i	0.526488	+	0.850182i	$0.323508\pi$
$972$	−10.6493	−	11.3839i	−0.341576	−	0.365138i
$973$	−3.27209	+	18.8238i	−0.104898	+	0.603463i
$974$	−31.3297	−	10.1796i	−1.00387	−	0.326176i
$975$	−6.73092	−	1.25746i	−0.215562	−	0.0402709i
$976$	−8.18183	−	0.859945i	−0.261894	−	0.0275262i
$977$	−4.62650	−	4.16572i	−0.148015	−	0.133273i	0.591797	−	0.806087i	$-0.298419\pi$
$977$	−4.62650	−	4.16572i	−0.148015	−	0.133273i	−0.739812	+	0.672814i	$0.765085\pi$
$978$	13.3860	+	14.1464i	0.428038	+	0.452351i
$979$	−7.27379	+	8.08291i	−0.232471	+	0.258331i
$980$	11.8019	−	3.44618i	0.376998	−	0.110084i
$981$	−14.1429	+	52.1847i	−0.451548	+	1.66613i
$982$	24.1270	−	10.7421i	0.769925	−	0.342793i
$983$	−11.7355	−	5.22496i	−0.374303	−	0.166650i	0.210958	−	0.977495i	$-0.432342\pi$
$983$	−11.7355	−	5.22496i	−0.374303	−	0.166650i	−0.585262	+	0.810845i	$0.699008\pi$
$984$	1.70755	−	21.3070i	0.0544347	−	0.679241i
$985$	−16.1085	+	14.5042i	−0.513260	+	0.462141i
$986$	15.0598	−	10.9416i	0.479601	−	0.348451i
$987$	15.5216	−	15.8263i	0.494057	−	0.503758i
$988$	2.01447	+	6.19991i	0.0640889	+	0.197246i
$989$	−9.13192	−	5.27232i	−0.290378	−	0.167650i
$990$	15.5506	+	7.97403i	0.494231	+	0.253431i
$991$	−19.7148	−	34.1470i	−0.626260	−	1.08471i	−0.988296	−	0.152550i	$-0.951251\pi$
$991$	−19.7148	−	34.1470i	−0.626260	−	1.08471i	0.362036	−	0.932164i	$-0.382082\pi$
$992$	1.74764	+	0.371472i	0.0554876	+	0.0117942i
$993$	18.8242	+	24.6050i	0.597368	+	0.780815i
$994$	−11.9547	+	3.01145i	−0.379179	+	0.0955173i
$995$	24.8337	+	8.06896i	0.787282	+	0.255803i
$996$	1.12659	+	2.37066i	0.0356974	+	0.0751173i
$997$	14.7241	−	33.0709i	0.466318	−	1.04737i	−0.515387	−	0.856958i	$-0.672352\pi$
$997$	14.7241	−	33.0709i	0.466318	−	1.04737i	0.981705	−	0.190409i	$-0.0609815\pi$
$998$	−6.06146	−	0.637085i	−0.191872	−	0.0201666i
$999$	4.10752	+	7.64312i	0.129956	+	0.241817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bf.a.5.10	✓	256
3.2	odd	2	inner	462.2.bf.a.5.26	yes	256
7.3	odd	6	inner	462.2.bf.a.269.16	yes	256
11.9	even	5	inner	462.2.bf.a.383.21	yes	256
21.17	even	6	inner	462.2.bf.a.269.21	yes	256
33.20	odd	10	inner	462.2.bf.a.383.16	yes	256
77.31	odd	30	inner	462.2.bf.a.185.26	yes	256
231.185	even	30	inner	462.2.bf.a.185.10	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bf.a.5.10	✓	256	1.1	even	1	trivial
462.2.bf.a.5.26	yes	256	3.2	odd	2	inner
462.2.bf.a.185.10	yes	256	231.185	even	30	inner
462.2.bf.a.185.26	yes	256	77.31	odd	30	inner
462.2.bf.a.269.16	yes	256	7.3	odd	6	inner
462.2.bf.a.269.21	yes	256	21.17	even	6	inner
462.2.bf.a.383.16	yes	256	33.20	odd	10	inner
462.2.bf.a.383.21	yes	256	11.9	even	5	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bf (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.665114 - 1.59926i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.17526 + 1.30525i) q^{5} +(1.42602 + 0.983084i) q^{6} +(-1.84250 - 1.89873i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.11525 - 2.12738i) q^{9} +O(q^{10})\)	\(q+(-0.207912 + 0.978148i) q^{2} +(0.665114 - 1.59926i) q^{3} +(-0.913545 - 0.406737i) q^{4} +(1.17526 + 1.30525i) q^{5} +(1.42602 + 0.983084i) q^{6} +(-1.84250 - 1.89873i) q^{7} +(0.587785 - 0.809017i) q^{8} +(-2.11525 - 2.12738i) q^{9} +(-1.52108 + 0.878197i) q^{10} +(3.24434 + 0.688659i) q^{11} +(-1.25809 + 1.19047i) q^{12} +(1.96328 - 0.637908i) q^{13} +(2.24032 - 1.40747i) q^{14} +(2.86912 - 1.01139i) q^{15} +(0.669131 + 0.743145i) q^{16} +(7.46145 - 1.58598i) q^{17} +(2.52067 - 1.62672i) q^{18} +(-1.28445 - 2.88492i) q^{19} +(-0.542755 - 1.67043i) q^{20} +(-4.26203 + 1.68376i) q^{21} +(-1.34815 + 3.03026i) q^{22} +(-2.42141 - 1.39800i) q^{23} +(-0.902882 - 1.47811i) q^{24} +(0.200181 - 1.90459i) q^{25} +(0.215779 + 2.05300i) q^{26} +(-4.80910 + 1.96787i) q^{27} +(0.910927 + 2.48399i) q^{28} +(-1.43437 - 1.97424i) q^{29} +(0.392769 + 3.01670i) q^{30} +(-1.32776 - 1.19552i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.25920 - 4.73050i) q^{33} +7.62815i q^{34} +(0.312913 - 4.63643i) q^{35} +(1.06709 + 2.80380i) q^{36} +(-0.174549 - 1.66073i) q^{37} +(3.08893 - 0.656572i) q^{38} +(0.285626 - 3.56407i) q^{39} +(1.74677 - 0.183593i) q^{40} +(9.98409 + 7.25387i) q^{41} +(-0.760843 - 4.51897i) q^{42} +3.77132 q^{43} +(-2.68375 - 1.94871i) q^{44} +(0.290812 - 5.26115i) q^{45} +(1.87089 - 2.07784i) q^{46} +(-4.41911 + 1.96751i) q^{47} +(1.63353 - 0.575836i) q^{48} +(-0.210360 + 6.99684i) q^{49} +(1.82135 + 0.591793i) q^{50} +(2.42633 - 12.9876i) q^{51} +(-2.05300 - 0.215779i) q^{52} +(5.09424 + 4.58688i) q^{53} +(-0.925001 - 5.11316i) q^{54} +(2.91406 + 5.04404i) q^{55} +(-2.61910 + 0.374571i) q^{56} +(-5.46804 + 0.135363i) q^{57} +(2.22932 - 0.992557i) q^{58} +(-11.9328 - 5.31283i) q^{59} +(-3.03244 - 0.243021i) q^{60} +(-6.11377 + 5.50487i) q^{61} +(1.44546 - 1.05019i) q^{62} +(-0.141969 + 7.93598i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(3.13999 + 1.81287i) q^{65} +(3.94950 + 4.17150i) q^{66} +(4.96070 + 8.59218i) q^{67} +(-7.46145 - 1.58598i) q^{68} +(-3.84628 + 2.94263i) q^{69} +(4.47006 + 1.27004i) q^{70} +(-4.43154 - 1.43989i) q^{71} +(-2.96439 + 0.460829i) q^{72} +(-2.80651 + 6.30352i) q^{73} +(1.66073 + 0.174549i) q^{74} +(-2.91279 - 1.58691i) q^{75} +3.15794i q^{76} +(-4.67013 - 7.42899i) q^{77} +(3.42680 + 1.02040i) q^{78} +(6.86683 + 1.45959i) q^{79} +(-0.183593 + 1.74677i) q^{80} +(-0.0514691 + 8.99985i) q^{81} +(-9.17116 + 8.25775i) q^{82} +(0.468282 - 1.44122i) q^{83} +(4.57841 + 0.195331i) q^{84} +(10.8392 + 7.87516i) q^{85} +(-0.784102 + 3.68891i) q^{86} +(-4.11134 + 0.980830i) q^{87} +(2.46411 - 2.21994i) q^{88} +(-1.63930 + 2.83935i) q^{89} +(5.08572 + 1.37831i) q^{90} +(-4.82856 - 2.55239i) q^{91} +(1.64345 + 2.26202i) q^{92} +(-2.79506 + 1.32828i) q^{93} +(-1.00573 - 4.73161i) q^{94} +(2.25600 - 5.06705i) q^{95} +(0.223623 + 1.71755i) q^{96} +(-1.51318 + 0.491661i) q^{97} +(-6.80020 - 1.66049i) q^{98} +(-5.39754 - 8.35862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9}+O(q^{10}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9	\( 256 q - 32 q^{4} + 4 q^{7} - 12 q^{9} + 12 q^{10} + 24 q^{15} + 32 q^{16} - 8 q^{18} - 16 q^{21} - 12 q^{22} + 48 q^{25} + 6 q^{28} + 18 q^{31} - 132 q^{33} + 16 q^{36} + 4 q^{37} - 18 q^{40} - 4 q^{42} + 64 q^{43} - 48 q^{45} + 8 q^{46} + 76 q^{49} - 8 q^{51} - 88 q^{57} + 46 q^{58} - 8 q^{60} - 12 q^{63} + 64 q^{64} - 120 q^{66} - 32 q^{67} - 58 q^{70} - 12 q^{72} - 96 q^{73} - 204 q^{75} - 32 q^{78} - 4 q^{79} - 64 q^{81} + 24 q^{82} - 36 q^{84} + 232 q^{85} - 228 q^{87} - 6 q^{88} + 40 q^{91} - 2 q^{93} - 144 q^{94} + 160 q^{99}+O(q^{100}) \) 256 * q - 32 * q^4 + 4 * q^7 - 12 * q^9 + 12 * q^10 + 24 * q^15 + 32 * q^16 - 8 * q^18 - 16 * q^21 - 12 * q^22 + 48 * q^25 + 6 * q^28 + 18 * q^31 - 132 * q^33 + 16 * q^36 + 4 * q^37 - 18 * q^40 - 4 * q^42 + 64 * q^43 - 48 * q^45 + 8 * q^46 + 76 * q^49 - 8 * q^51 - 88 * q^57 + 46 * q^58 - 8 * q^60 - 12 * q^63 + 64 * q^64 - 120 * q^66 - 32 * q^67 - 58 * q^70 - 12 * q^72 - 96 * q^73 - 204 * q^75 - 32 * q^78 - 4 * q^79 - 64 * q^81 + 24 * q^82 - 36 * q^84 + 232 * q^85 - 228 * q^87 - 6 * q^88 + 40 * q^91 - 2 * q^93 - 144 * q^94 + 160 * q^99

Introduction

L-functions

Modular forms

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