LMFDB - Embedded newform 600.2.v.b.43.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(43,600)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("600.43"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.v (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.8
Character	$\chi$	$=$	600.43
Dual form			600.2.v.b.307.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.804501 - 1.16309i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.705556 - 1.87141i) q^{4} +(1.39130 - 0.253561i) q^{6} +(3.43671 + 3.43671i) q^{7} +(-2.74424 - 0.684930i) q^{8} +1.00000i q^{9} +3.48120 q^{11} +(0.824386 - 1.82219i) q^{12} +(-2.05033 + 2.05033i) q^{13} +(6.76204 - 1.23237i) q^{14} +(-3.00438 + 2.64077i) q^{16} +(1.64963 - 1.64963i) q^{17} +(1.16309 + 0.804501i) q^{18} -0.642023i q^{19} +4.86024i q^{21} +(2.80063 - 4.04895i) q^{22} +(2.31024 - 2.31024i) q^{23} +(-1.45615 - 2.42479i) q^{24} +(0.735225 + 4.03421i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.00672 - 8.85630i) q^{28} -0.699613 q^{29} -1.56863i q^{31} +(0.654430 + 5.61887i) q^{32} +(2.46158 + 2.46158i) q^{33} +(-0.591537 - 3.24579i) q^{34} +(1.87141 - 0.705556i) q^{36} +(-5.31751 - 5.31751i) q^{37} +(-0.746731 - 0.516509i) q^{38} -2.89960 q^{39} +4.92316 q^{41} +(5.65290 + 3.91007i) q^{42} +(-3.56519 - 3.56519i) q^{43} +(-2.45618 - 6.51477i) q^{44} +(-0.828427 - 4.54561i) q^{46} +(-6.85586 - 6.85586i) q^{47} +(-3.99173 - 0.257109i) q^{48} +16.6220i q^{49} +2.33292 q^{51} +(5.28364 + 2.39039i) q^{52} +(1.94008 - 1.94008i) q^{53} +(0.253561 + 1.39130i) q^{54} +(-7.07726 - 11.7851i) q^{56} +(0.453979 - 0.453979i) q^{57} +(-0.562839 + 0.813713i) q^{58} -2.74121i q^{59} -5.20943i q^{61} +(-1.82446 - 1.26196i) q^{62} +(-3.43671 + 3.43671i) q^{63} +(7.06174 + 3.75923i) q^{64} +(4.84339 - 0.882696i) q^{66} +(-6.92316 + 6.92316i) q^{67} +(-4.25104 - 1.92323i) q^{68} +3.26718 q^{69} +11.1548i q^{71} +(0.684930 - 2.74424i) q^{72} +(6.56519 + 6.56519i) q^{73} +(-10.4627 + 1.90680i) q^{74} +(-1.20149 + 0.452983i) q^{76} +(11.9639 + 11.9639i) q^{77} +(-2.33274 + 3.37250i) q^{78} -2.09702 q^{79} -1.00000 q^{81} +(3.96069 - 5.72608i) q^{82} +(-6.64648 - 6.64648i) q^{83} +(9.09553 - 3.42917i) q^{84} +(-7.01483 + 1.27844i) q^{86} +(-0.494701 - 0.494701i) q^{87} +(-9.55327 - 2.38438i) q^{88} -0.733690i q^{89} -14.0928 q^{91} +(-5.95343 - 2.69342i) q^{92} +(1.10919 - 1.10919i) q^{93} +(-13.4895 + 2.45843i) q^{94} +(-3.51039 + 4.43589i) q^{96} +(-8.79083 + 8.79083i) q^{97} +(19.3328 + 13.3724i) q^{98} +3.48120i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{6} + 12 q^{8} + 8 q^{12} - 20 q^{16} - 8 q^{17} + 28 q^{22} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{36} - 40 q^{38} - 20 q^{42} + 32 q^{43} + 48 q^{46} - 16 q^{48} - 16 q^{51} + 48 q^{52}+ \cdots + 88 q^{98}+O(q^{100}) $ 24 * q + 4 * q^6 + 12 * q^8 + 8 * q^12 - 20 * q^16 - 8 * q^17 + 28 * q^22 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^36 - 40 * q^38 - 20 * q^42 + 32 * q^43 + 48 * q^46 - 16 * q^48 - 16 * q^51 + 48 * q^52 - 32 * q^56 + 12 * q^58 + 16 * q^62 - 24 * q^66 - 48 * q^67 - 72 * q^68 - 12 * q^72 + 40 * q^73 + 48 * q^76 + 24 * q^78 - 24 * q^81 - 24 * q^82 - 80 * q^83 - 32 * q^86 - 12 * q^88 + 64 * q^91 - 16 * q^92 - 44 * q^96 + 24 * q^97 + 88 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.804501	−	1.16309i	0.568868	−	0.822429i
$2$	0.804501	−	1.16309i	0.568868	−	0.822429i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−0.705556	−	1.87141i	−0.352778	−	0.935707i
$5$		0			0
$5$		0			0
$6$	1.39130	−	0.253561i	0.567995	−	0.103516i
$7$	3.43671	+	3.43671i	1.29895	+	1.29895i	0.929083	+	0.369871i	$0.120598\pi$
$7$	3.43671	+	3.43671i	1.29895	+	1.29895i	0.369871	+	0.929083i	$0.379402\pi$
$8$	−2.74424	−	0.684930i	−0.970237	−	0.242159i
$9$			1.00000i			0.333333i
$10$		0			0
$11$	3.48120			1.04962			0.524811	−	0.851219i	$-0.324136\pi$
$11$	3.48120			1.04962			0.524811	+	0.851219i	$0.324136\pi$
$12$	0.824386	−	1.82219i	0.237980	−	0.526022i
$13$	−2.05033	+	2.05033i	−0.568659	+	0.568659i	−0.931753	−	0.363093i	$-0.881721\pi$
$13$	−2.05033	+	2.05033i	−0.568659	+	0.568659i	0.363093	+	0.931753i	$0.381721\pi$
$14$	6.76204	−	1.23237i	1.80723	−	0.329364i
$15$		0			0
$16$	−3.00438	+	2.64077i	−0.751095	+	0.660194i
$17$	1.64963	−	1.64963i	0.400093	−	0.400093i	−0.478173	−	0.878266i	$-0.658701\pi$
$17$	1.64963	−	1.64963i	0.400093	−	0.400093i	0.878266	+	0.478173i	$0.158701\pi$
$18$	1.16309	+	0.804501i	0.274143	+	0.189623i
$19$		−	0.642023i		−	0.147290i	−0.997285	−	0.0736451i	$-0.976537\pi$
$19$		−	0.642023i		−	0.147290i	0.997285	−	0.0736451i	$-0.0234632\pi$
$20$		0			0
$21$			4.86024i			1.06059i
$22$	2.80063	−	4.04895i	0.597097	−	0.863239i
$23$	2.31024	−	2.31024i	0.481719	−	0.481719i	−0.423961	−	0.905680i	$-0.639361\pi$
$23$	2.31024	−	2.31024i	0.481719	−	0.481719i	0.905680	+	0.423961i	$0.139361\pi$
$24$	−1.45615	−	2.42479i	−0.297236	−	0.494958i
$25$		0			0
$26$	0.735225	+	4.03421i	0.144190	+	0.791174i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	4.00672	−	8.85630i	0.757198	−	1.67368i
$29$	−0.699613			−0.129915			−0.0649574	−	0.997888i	$-0.520691\pi$
$29$	−0.699613			−0.129915			−0.0649574	+	0.997888i	$0.520691\pi$
$30$		0			0
$31$		−	1.56863i		−	0.281734i	−0.990029	−	0.140867i	$-0.955011\pi$
$31$		−	1.56863i		−	0.281734i	0.990029	−	0.140867i	$-0.0449890\pi$
$32$	0.654430	+	5.61887i	0.115688	+	0.993286i
$33$	2.46158	+	2.46158i	0.428506	+	0.428506i
$34$	−0.591537	−	3.24579i	−0.101448	−	0.556648i
$35$		0			0
$36$	1.87141	−	0.705556i	0.311902	−	0.117593i
$37$	−5.31751	−	5.31751i	−0.874193	−	0.874193i	0.118733	−	0.992926i	$-0.462117\pi$
$37$	−5.31751	−	5.31751i	−0.874193	−	0.874193i	−0.992926	+	0.118733i	$0.962117\pi$
$38$	−0.746731	−	0.516509i	−0.121136	−	0.0837888i
$39$	−2.89960			−0.464308
$40$		0			0
$41$	4.92316			0.768869			0.384435	−	0.923152i	$-0.374396\pi$
$41$	4.92316			0.768869			0.384435	+	0.923152i	$0.374396\pi$
$42$	5.65290	+	3.91007i	0.872261	+	0.603337i
$43$	−3.56519	−	3.56519i	−0.543686	−	0.543686i	0.380921	−	0.924607i	$-0.375607\pi$
$43$	−3.56519	−	3.56519i	−0.543686	−	0.543686i	−0.924607	+	0.380921i	$0.875607\pi$
$44$	−2.45618	−	6.51477i	−0.370284	−	0.982139i
$45$		0			0
$46$	−0.828427	−	4.54561i	−0.122145	−	0.670214i
$47$	−6.85586	−	6.85586i	−1.00003	−	1.00003i	−1.00000		2.93703e-5i	$-0.999991\pi$
$47$	−6.85586	−	6.85586i	−1.00003	−	1.00003i	−2.93703e−5	−	1.00000i	$-0.500009\pi$
$48$	−3.99173	−	0.257109i	−0.576156	−	0.0371105i
$49$			16.6220i			2.37457i
$50$		0			0
$51$	2.33292			0.326675
$52$	5.28364	+	2.39039i	0.732709	+	0.331488i
$53$	1.94008	−	1.94008i	0.266490	−	0.266490i	−0.561194	−	0.827684i	$-0.689658\pi$
$53$	1.94008	−	1.94008i	0.266490	−	0.266490i	0.827684	+	0.561194i	$0.189658\pi$
$54$	0.253561	+	1.39130i	0.0345052	+	0.189332i
$55$		0			0
$56$	−7.07726	−	11.7851i	−0.945739	−	1.57485i
$57$	0.453979	−	0.453979i	0.0601310	−	0.0601310i
$58$	−0.562839	+	0.813713i	−0.0739044	+	0.106846i
$59$		−	2.74121i		−	0.356876i	−0.983951	−	0.178438i	$-0.942896\pi$
$59$		−	2.74121i		−	0.356876i	0.983951	−	0.178438i	$-0.0571043\pi$
$60$		0			0
$61$		−	5.20943i		−	0.666999i	−0.942750	−	0.333500i	$-0.891770\pi$
$61$		−	5.20943i		−	0.666999i	0.942750	−	0.333500i	$-0.108230\pi$
$62$	−1.82446	−	1.26196i	−0.231706	−	0.160269i
$63$	−3.43671	+	3.43671i	−0.432985	+	0.432985i
$64$	7.06174	+	3.75923i	0.882718	+	0.469903i
$65$		0			0
$66$	4.84339	−	0.882696i	0.596180	−	0.108652i
$67$	−6.92316	+	6.92316i	−0.845799	+	0.845799i	−0.989606	−	0.143807i	$-0.954066\pi$
$67$	−6.92316	+	6.92316i	−0.845799	+	0.845799i	0.143807	+	0.989606i	$0.454066\pi$
$68$	−4.25104	−	1.92323i	−0.515514	−	0.233226i
$69$	3.26718			0.393322
$70$		0			0
$71$			11.1548i			1.32384i	0.749576	+	0.661918i	$0.230257\pi$
$71$			11.1548i			1.32384i	−0.749576	+	0.661918i	$0.769743\pi$
$72$	0.684930	−	2.74424i	0.0807197	−	0.323412i
$73$	6.56519	+	6.56519i	0.768397	+	0.768397i	0.977824	−	0.209427i	$-0.0671599\pi$
$73$	6.56519	+	6.56519i	0.768397	+	0.768397i	−0.209427	+	0.977824i	$0.567160\pi$
$74$	−10.4627	+	1.90680i	−1.21626	+	0.221661i
$75$		0			0
$76$	−1.20149	+	0.452983i	−0.137821	+	0.0519608i
$77$	11.9639	+	11.9639i	1.36341	+	1.36341i
$78$	−2.33274	+	3.37250i	−0.264130	+	0.381860i
$79$	−2.09702			−0.235933			−0.117966	−	0.993018i	$-0.537637\pi$
$79$	−2.09702			−0.235933			−0.117966	+	0.993018i	$0.537637\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	3.96069	−	5.72608i	0.437385	−	0.632340i
$83$	−6.64648	−	6.64648i	−0.729546	−	0.729546i	0.240984	−	0.970529i	$-0.422530\pi$
$83$	−6.64648	−	6.64648i	−0.729546	−	0.729546i	−0.970529	+	0.240984i	$0.922530\pi$
$84$	9.09553	−	3.42917i	0.992403	−	0.374153i
$85$		0			0
$86$	−7.01483	+	1.27844i	−0.756429	+	0.137857i
$87$	−0.494701	−	0.494701i	−0.0530375	−	0.0530375i
$88$	−9.55327	−	2.38438i	−1.01838	−	0.254176i
$89$		−	0.733690i		−	0.0777710i	−0.999244	−	0.0388855i	$-0.987619\pi$
$89$		−	0.733690i		−	0.0777710i	0.999244	−	0.0388855i	$-0.0123808\pi$
$90$		0			0
$91$	−14.0928			−1.47732
$92$	−5.95343	−	2.69342i	−0.620688	−	0.280808i
$93$	1.10919	−	1.10919i	0.115017	−	0.115017i
$94$	−13.4895	+	2.45843i	−1.39134	+	0.253568i
$95$		0			0
$96$	−3.51039	+	4.43589i	−0.358278	+	0.452737i
$97$	−8.79083	+	8.79083i	−0.892574	+	0.892574i	−0.994765	−	0.102191i	$-0.967415\pi$
$97$	−8.79083	+	8.79083i	−0.892574	+	0.892574i	0.102191	+	0.994765i	$0.467415\pi$
$98$	19.3328	+	13.3724i	1.95291	+	1.35081i
$99$			3.48120i			0.349874i
$100$		0			0
$101$		−	1.40933i		−	0.140233i	−0.997539	−	0.0701167i	$-0.977663\pi$
$101$		−	1.40933i		−	0.140233i	0.997539	−	0.0701167i	$-0.0223372\pi$
$102$	1.87684	−	2.71340i	0.185835	−	0.268667i
$103$	2.41334	−	2.41334i	0.237793	−	0.237793i	−0.578143	−	0.815936i	$-0.696222\pi$
$103$	2.41334	−	2.41334i	0.237793	−	0.237793i	0.815936	+	0.578143i	$0.196222\pi$
$104$	7.03094	−	4.22227i	0.689440	−	0.414028i
$105$		0			0
$106$	−0.695690	−	3.81728i	−0.0675714	−	0.370767i
$107$	−1.56073	+	1.56073i	−0.150882	+	0.150882i	−0.778512	−	0.627630i	$-0.784025\pi$
$107$	−1.56073	+	1.56073i	−0.150882	+	0.150882i	0.627630	+	0.778512i	$0.284025\pi$
$108$	1.82219	+	0.824386i	0.175341	+	0.0793266i
$109$	−14.6177			−1.40012			−0.700060	−	0.714084i	$-0.746843\pi$
$109$	−14.6177			−1.40012			−0.700060	+	0.714084i	$0.746843\pi$
$110$		0			0
$111$		−	7.52009i		−	0.713775i
$112$	−19.4008	−	1.24961i	−1.83320	−	0.118077i
$113$	4.55758	+	4.55758i	0.428742	+	0.428742i	0.888199	−	0.459458i	$-0.151956\pi$
$113$	4.55758	+	4.55758i	0.428742	+	0.428742i	−0.459458	+	0.888199i	$0.651956\pi$
$114$	−0.162792	−	0.893245i	−0.0152469	−	0.0836601i
$115$		0			0
$116$	0.493616	+	1.30927i	0.0458311	+	0.121562i
$117$	−2.05033	−	2.05033i	−0.189553	−	0.189553i
$118$	−3.18828	−	2.20531i	−0.293505	−	0.203015i
$119$	11.3386			1.03941
$120$		0			0
$121$	1.11877			0.101707
$122$	−6.05904	−	4.19099i	−0.548559	−	0.379435i
$123$	3.48120	+	3.48120i	0.313889	+	0.313889i
$124$	−2.93555	+	1.10675i	−0.263620	+	0.0993895i
$125$		0			0
$126$	1.23237	+	6.76204i	0.109788	+	0.602410i
$127$	−9.62582	−	9.62582i	−0.854154	−	0.854154i	0.136488	−	0.990642i	$-0.456418\pi$
$127$	−9.62582	−	9.62582i	−0.854154	−	0.854154i	−0.990642	+	0.136488i	$0.956418\pi$
$128$	10.0535	−	5.18914i	0.888612	−	0.458659i
$129$		−	5.04194i		−	0.443918i
$130$		0			0
$131$	1.26769			0.110759			0.0553794	−	0.998465i	$-0.482363\pi$
$131$	1.26769			0.110759			0.0553794	+	0.998465i	$0.482363\pi$
$132$	2.86986	−	6.34342i	0.249789	−	0.552124i
$133$	2.20645	−	2.20645i	0.191323	−	0.191323i
$134$	2.48257	+	13.6220i	0.214461	+	1.17676i
$135$		0			0
$136$	−5.65685	+	3.39710i	−0.485071	+	0.291299i
$137$	12.2296	−	12.2296i	1.04485	−	1.04485i	0.0459032	−	0.998946i	$-0.485383\pi$
$137$	12.2296	−	12.2296i	1.04485	−	1.04485i	0.998946	−	0.0459032i	$-0.0146166\pi$
$138$	2.62845	−	3.80002i	0.223748	−	0.323479i
$139$		−	8.13630i		−	0.690112i	−0.938582	−	0.345056i	$-0.887860\pi$
$139$		−	8.13630i		−	0.690112i	0.938582	−	0.345056i	$-0.112140\pi$
$140$		0			0
$141$		−	9.69564i		−	0.816521i
$142$	12.9741	+	8.97408i	1.08876	+	0.753088i
$143$	−7.13761	+	7.13761i	−0.596877	+	0.596877i
$144$	−2.64077	−	3.00438i	−0.220065	−	0.250365i
$145$		0			0
$146$	12.9176	−	2.35420i	1.06907	−	0.194835i
$147$	−11.7535	+	11.7535i	−0.969412	+	0.969412i
$148$	−6.19946	+	13.7031i	−0.509592	+	1.12638i
$149$	−2.75071			−0.225347			−0.112674	−	0.993632i	$-0.535941\pi$
$149$	−2.75071			−0.225347			−0.112674	+	0.993632i	$0.535941\pi$
$150$		0			0
$151$		−	10.2020i		−	0.830226i	−0.909770	−	0.415113i	$-0.863742\pi$
$151$		−	10.2020i		−	0.830226i	0.909770	−	0.415113i	$-0.136258\pi$
$152$	−0.439741	+	1.76187i	−0.0356677	+	0.142906i
$153$	1.64963	+	1.64963i	0.133364	+	0.133364i
$154$	23.5400	−	4.29011i	1.89691	−	0.345707i
$155$		0			0
$156$	2.04583	+	5.42636i	0.163798	+	0.434457i
$157$	1.29115	+	1.29115i	0.103045	+	0.103045i	0.756750	−	0.653705i	$-0.226786\pi$
$157$	1.29115	+	1.29115i	0.103045	+	0.103045i	−0.653705	+	0.756750i	$0.726786\pi$
$158$	−1.68705	+	2.43902i	−0.134215	+	0.194038i
$159$	2.74369			0.217588
$160$		0			0
$161$	15.8793			1.25146
$162$	−0.804501	+	1.16309i	−0.0632076	+	0.0913810i
$163$	−9.30787	−	9.30787i	−0.729049	−	0.729049i	0.241382	−	0.970430i	$-0.422399\pi$
$163$	−9.30787	−	9.30787i	−0.729049	−	0.729049i	−0.970430	+	0.241382i	$0.922399\pi$
$164$	−3.47357	−	9.21328i	−0.271240	−	0.719436i
$165$		0			0
$166$	−13.0775	+	2.38335i	−1.01501	+	0.184984i
$167$	11.8845	+	11.8845i	0.919652	+	0.919652i	0.997004	−	0.0773515i	$-0.0246464\pi$
$167$	11.8845	+	11.8845i	0.919652	+	0.919652i	−0.0773515	+	0.997004i	$0.524646\pi$
$168$	3.32892	−	13.3377i	0.256832	−	1.02902i
$169$			4.59229i			0.353253i
$170$		0			0
$171$	0.642023			0.0490968
$172$	−4.15650	+	9.18738i	−0.316930	+	0.700531i
$173$	−13.2536	+	13.2536i	−1.00765	+	1.00765i	−0.00768426	+	0.999970i	$0.502446\pi$
$173$	−13.2536	+	13.2536i	−1.00765	+	1.00765i	−0.999970	+	0.00768426i	$0.997554\pi$
$174$	−0.973369	+	0.177394i	−0.0737909	+	0.0134482i
$175$		0			0
$176$	−10.4589	+	9.19307i	−0.788366	+	0.692954i
$177$	1.93833	−	1.93833i	0.145694	−	0.145694i
$178$	−0.853348	−	0.590255i	−0.0639611	−	0.0442414i
$179$		−	3.61084i		−	0.269887i	−0.990853	−	0.134943i	$-0.956915\pi$
$179$		−	3.61084i		−	0.269887i	0.990853	−	0.134943i	$-0.0430853\pi$
$180$		0			0
$181$			21.8993i			1.62776i	0.581032	+	0.813881i	$0.302649\pi$
$181$			21.8993i			1.62776i	−0.581032	+	0.813881i	$0.697351\pi$
$182$	−11.3377	+	16.3912i	−0.840403	+	1.21499i
$183$	3.68362	−	3.68362i	0.272301	−	0.272301i
$184$	−7.92222	+	4.75751i	−0.584034	+	0.350729i
$185$		0			0
$186$	−0.397742	−	2.18243i	−0.0291639	−	0.160023i
$187$	5.74268	−	5.74268i	0.419947	−	0.419947i
$188$	−7.99296	+	17.6673i	−0.582946	+	1.28852i
$189$	−4.86024			−0.353531
$190$		0			0
$191$		−	10.1309i		−	0.733045i	−0.930409	−	0.366522i	$-0.880548\pi$
$191$		−	10.1309i		−	0.733045i	0.930409	−	0.366522i	$-0.119452\pi$
$192$	2.33523	+	7.65158i	0.168531	+	0.552205i
$193$	14.3560	+	14.3560i	1.03337	+	1.03337i	0.999424	+	0.0339453i	$0.0108072\pi$
$193$	14.3560	+	14.3560i	1.03337	+	1.03337i	0.0339453	+	0.999424i	$0.489193\pi$
$194$	3.15229	+	17.2968i	0.226321	+	1.24184i
$195$		0			0
$196$	31.1066	−	11.7277i	2.22190	−	0.837694i
$197$	−14.6884	−	14.6884i	−1.04650	−	1.04650i	−0.998865	−	0.0476396i	$-0.984830\pi$
$197$	−14.6884	−	14.6884i	−1.04650	−	1.04650i	−0.0476396	−	0.998865i	$-0.515170\pi$
$198$	4.04895	+	2.80063i	0.287746	+	0.199032i
$199$	5.08593			0.360532			0.180266	−	0.983618i	$-0.442304\pi$
$199$	5.08593			0.360532			0.180266	+	0.983618i	$0.442304\pi$
$200$		0			0
$201$	−9.79083			−0.690592
$202$	−1.63918	−	1.13381i	−0.115332	−	0.0797744i
$203$	−2.40437	−	2.40437i	−0.168753	−	0.168753i
$204$	−1.64601	−	4.36587i	−0.115244	−	0.305672i
$205$		0			0
$206$	−0.865395	−	4.74846i	−0.0602950	−	0.330841i
$207$	2.31024	+	2.31024i	0.160573	+	0.160573i
$208$	0.745514	−	11.5744i	0.0516921	−	0.802543i
$209$		−	2.23501i		−	0.154599i
$210$		0			0
$211$	−21.7932			−1.50030			−0.750151	−	0.661266i	$-0.770019\pi$
$211$	−21.7932			−1.50030			−0.750151	+	0.661266i	$0.770019\pi$
$212$	−4.99952	−	2.26186i	−0.343369	−	0.155345i
$213$	−7.88766	+	7.88766i	−0.540454	+	0.540454i
$214$	0.559662	+	3.07089i	0.0382577	+	0.209921i
$215$		0			0
$216$	2.42479	−	1.45615i	0.164986	−	0.0990788i
$217$	5.39092	−	5.39092i	0.365959	−	0.365959i
$218$	−11.7599	+	17.0017i	−0.796484	+	1.15150i
$219$			9.28458i			0.627394i
$220$		0			0
$221$			6.76456i			0.455033i
$222$	−8.74654	−	6.04992i	−0.587029	−	0.406044i
$223$	7.63273	−	7.63273i	0.511126	−	0.511126i	−0.403746	−	0.914871i	$-0.632292\pi$
$223$	7.63273	−	7.63273i	0.511126	−	0.511126i	0.914871	+	0.403746i	$0.132292\pi$
$224$	−17.0613	+	21.5595i	−1.13996	+	1.44051i
$225$		0			0
$226$	8.96746	−	1.63430i	0.596507	−	0.108712i
$227$	8.84363	−	8.84363i	0.586973	−	0.586973i	−0.349838	−	0.936810i	$-0.613763\pi$
$227$	8.84363	−	8.84363i	0.586973	−	0.586973i	0.936810	+	0.349838i	$0.113763\pi$
$228$	−1.16989	−	0.529275i	−0.0774779	−	0.0350521i
$229$	23.9520			1.58279			0.791397	−	0.611302i	$-0.209354\pi$
$229$	23.9520			1.58279			0.791397	+	0.611302i	$0.209354\pi$
$230$		0			0
$231$			16.9195i			1.11322i
$232$	1.91991	+	0.479186i	0.126048	+	0.0314601i
$233$	−4.38332	−	4.38332i	−0.287161	−	0.287161i	0.548796	−	0.835956i	$-0.315086\pi$
$233$	−4.38332	−	4.38332i	−0.287161	−	0.287161i	−0.835956	+	0.548796i	$0.815086\pi$
$234$	−4.03421	+	0.735225i	−0.263725	+	0.0480632i
$235$		0			0
$236$	−5.12995	+	1.93408i	−0.333931	+	0.125898i
$237$	−1.48281	−	1.48281i	−0.0963191	−	0.0963191i
$238$	9.12190	−	13.1878i	0.591285	−	0.854837i
$239$	−16.7993			−1.08666			−0.543328	−	0.839521i	$-0.682836\pi$
$239$	−16.7993			−1.08666			−0.543328	+	0.839521i	$0.682836\pi$
$240$		0			0
$241$	3.47277			0.223701			0.111850	−	0.993725i	$-0.464322\pi$
$241$	3.47277			0.223701			0.111850	+	0.993725i	$0.464322\pi$
$242$	0.900054	−	1.30123i	0.0578576	−	0.0836464i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	−9.74900	+	3.67555i	−0.624116	+	0.235303i
$245$		0			0
$246$	6.84958	−	1.24832i	0.436713	−	0.0795900i
$247$	1.31636	+	1.31636i	0.0837580	+	0.0837580i
$248$	−1.07440	+	4.30470i	−0.0682245	+	0.273348i
$249$		−	9.39954i		−	0.595672i
$250$		0			0
$251$	10.6116			0.669797			0.334898	−	0.942254i	$-0.391298\pi$
$251$	10.6116			0.669797			0.334898	+	0.942254i	$0.391298\pi$
$252$	8.85630	+	4.00672i	0.557894	+	0.252399i
$253$	8.04242	−	8.04242i	0.505623	−	0.505623i
$254$	−18.9397	+	3.45171i	−1.18838	+	0.216580i
$255$		0			0
$256$	2.05262	−	15.8678i	0.128289	−	0.991737i
$257$	16.4495	−	16.4495i	1.02609	−	1.02609i	0.0264382	−	0.999650i	$-0.491583\pi$
$257$	16.4495	−	16.4495i	1.02609	−	1.02609i	0.999650	−	0.0264382i	$-0.00841653\pi$
$258$	−5.86423	−	4.05624i	−0.365091	−	0.252531i
$259$		−	36.5495i		−	2.27107i
$260$		0			0
$261$		−	0.699613i		−	0.0433050i
$262$	1.01986	−	1.47444i	0.0630072	−	0.0910913i
$263$	17.3101	−	17.3101i	1.06739	−	1.06739i	0.0698281	−	0.997559i	$-0.477755\pi$
$263$	17.3101	−	17.3101i	1.06739	−	1.06739i	0.997559	−	0.0698281i	$-0.0222451\pi$
$264$	−5.06917	−	8.44119i	−0.311986	−	0.519519i
$265$		0			0
$266$	−0.791208	−	4.34139i	−0.0485121	−	0.266188i
$267$	0.518797	−	0.518797i	0.0317499	−	0.0317499i
$268$	17.8408	+	8.07143i	1.08980	+	0.493041i
$269$	17.2178			1.04979			0.524895	−	0.851167i	$-0.324105\pi$
$269$	17.2178			1.04979			0.524895	+	0.851167i	$0.324105\pi$
$270$		0			0
$271$			8.37293i			0.508619i	0.967123	+	0.254310i	$0.0818482\pi$
$271$			8.37293i			0.508619i	−0.967123	+	0.254310i	$0.918152\pi$
$272$	−0.599815	+	9.31240i	−0.0363691	+	0.564647i
$273$	−9.96510	−	9.96510i	−0.603115	−	0.603115i
$274$	−4.38541	−	24.0629i	−0.264932	−	1.45370i
$275$		0			0
$276$	−2.30518	−	6.11424i	−0.138755	−	0.368034i
$277$	11.2504	+	11.2504i	0.675971	+	0.675971i	0.959086	−	0.283115i	$-0.0913678\pi$
$277$	11.2504	+	11.2504i	0.675971	+	0.675971i	−0.283115	+	0.959086i	$0.591368\pi$
$278$	−9.46325	−	6.54566i	−0.567568	−	0.392583i
$279$	1.56863			0.0939113
$280$		0			0
$281$	−25.9447			−1.54773			−0.773864	−	0.633352i	$-0.781679\pi$
$281$	−25.9447			−1.54773			−0.773864	+	0.633352i	$0.781679\pi$
$282$	−11.2769	−	7.80016i	−0.671530	−	0.464493i
$283$	−0.0392414	−	0.0392414i	−0.00233266	−	0.00233266i	0.705939	−	0.708272i	$-0.250525\pi$
$283$	−0.0392414	−	0.0392414i	−0.00233266	−	0.00233266i	−0.708272	+	0.705939i	$0.750525\pi$
$284$	20.8753	−	7.87036i	1.23872	−	0.467020i
$285$		0			0
$286$	2.55947	+	14.0439i	0.151345	+	0.830434i
$287$	16.9195	+	16.9195i	0.998726	+	0.998726i
$288$	−5.61887	+	0.654430i	−0.331095	+	0.0385627i
$289$			11.5575i			0.679851i
$290$		0			0
$291$	−12.4321			−0.728783
$292$	7.65408	−	16.9183i	0.447921	−	0.990068i
$293$	21.6367	−	21.6367i	1.26403	−	1.26403i	0.314905	−	0.949123i	$-0.398027\pi$
$293$	21.6367	−	21.6367i	1.26403	−	1.26403i	0.949123	−	0.314905i	$-0.101973\pi$
$294$	4.21467	+	23.1261i	0.245805	+	1.34874i
$295$		0			0
$296$	10.9504	+	18.2347i	0.636480	+	1.05987i
$297$	−2.46158	+	2.46158i	−0.142835	+	0.142835i
$298$	−2.21295	+	3.19933i	−0.128193	+	0.185332i
$299$			9.47352i			0.547868i
$300$		0			0
$301$		−	24.5050i		−	1.41245i
$302$	−11.8658	−	8.20751i	−0.682802	−	0.472289i
$303$	0.996546	−	0.996546i	0.0572501	−	0.0572501i
$304$	1.69544	+	1.92888i	0.0972401	+	0.110629i
$305$		0			0
$306$	3.24579	−	0.591537i	0.185549	−	0.0338159i
$307$	18.1166	−	18.1166i	1.03397	−	1.03397i	0.0345669	−	0.999402i	$-0.488995\pi$
$307$	18.1166	−	18.1166i	1.03397	−	1.03397i	0.999402	−	0.0345669i	$-0.0110052\pi$
$308$	13.9482	−	30.8306i	0.794772	−	1.75674i
$309$	3.41297			0.194157
$310$		0			0
$311$		−	9.63648i		−	0.546435i	−0.961952	−	0.273217i	$-0.911912\pi$
$311$		−	9.63648i		−	0.546435i	0.961952	−	0.273217i	$-0.0880878\pi$
$312$	7.95722	+	1.98603i	0.450489	+	0.112437i
$313$	−18.2372	−	18.2372i	−1.03083	−	1.03083i	−0.999509	−	0.0313208i	$-0.990029\pi$
$313$	−18.2372	−	18.2372i	−1.03083	−	1.03083i	−0.0313208	−	0.999509i	$-0.509971\pi$
$314$	2.54046	−	0.462992i	0.143366	−	0.0261282i
$315$		0			0
$316$	1.47956	+	3.92439i	0.0832319	+	0.220764i
$317$	0.866839	+	0.866839i	0.0486865	+	0.0486865i	0.731031	−	0.682344i	$-0.239040\pi$
$317$	0.866839	+	0.866839i	0.0486865	+	0.0486865i	−0.682344	+	0.731031i	$0.739040\pi$
$318$	2.20730	−	3.19115i	0.123779	−	0.178951i
$319$	−2.43549			−0.136362
$320$		0			0
$321$	−2.20721			−0.123195
$322$	12.7749	−	18.4690i	0.711917	−	1.02924i
$323$	−1.05910	−	1.05910i	−0.0589298	−	0.0589298i
$324$	0.705556	+	1.87141i	0.0391976	+	0.103967i
$325$		0			0
$326$	−18.3141	+	3.33770i	−1.01432	+	0.184858i
$327$	−10.3363	−	10.3363i	−0.571596	−	0.571596i
$328$	−13.5104	−	3.37202i	−0.745985	−	0.186189i
$329$		−	47.1232i		−	2.59799i
$330$		0			0
$331$	14.4884			0.796352			0.398176	−	0.917309i	$-0.369643\pi$
$331$	14.4884			0.796352			0.398176	+	0.917309i	$0.369643\pi$
$332$	−7.74885	+	17.1278i	−0.425273	+	0.940009i
$333$	5.31751	−	5.31751i	0.291398	−	0.291398i
$334$	23.3839	−	4.26166i	1.27951	−	0.233188i
$335$		0			0
$336$	−12.8348	−	14.6020i	−0.700196	−	0.796606i
$337$	−21.9977	+	21.9977i	−1.19829	+	1.19829i	−0.223611	+	0.974679i	$0.571784\pi$
$337$	−21.9977	+	21.9977i	−1.19829	+	1.19829i	−0.974679	+	0.223611i	$0.928216\pi$
$338$	5.34125	+	3.69451i	0.290526	+	0.200955i
$339$			6.44540i			0.350066i
$340$		0			0
$341$		−	5.46071i		−	0.295714i
$342$	0.516509	−	0.746731i	0.0279296	−	0.0403786i
$343$	−33.0679	+	33.0679i	−1.78550	+	1.78550i
$344$	7.34184	+	12.2256i	0.395845	+	0.659163i
$345$		0			0
$346$	4.75260	+	26.0777i	0.255501	+	1.40195i
$347$	−3.52917	+	3.52917i	−0.189456	+	0.189456i	−0.795461	−	0.606005i	$-0.792771\pi$
$347$	−3.52917	+	3.52917i	−0.189456	+	0.189456i	0.606005	+	0.795461i	$0.292771\pi$
$348$	−0.576751	+	1.27483i	−0.0309171	+	0.0683380i
$349$	3.26043			0.174527			0.0872635	−	0.996185i	$-0.472188\pi$
$349$	3.26043			0.174527			0.0872635	+	0.996185i	$0.472188\pi$
$350$		0			0
$351$		−	2.89960i		−	0.154769i
$352$	2.27820	+	19.5604i	0.121429	+	1.04257i
$353$	−22.6567	−	22.6567i	−1.20589	−	1.20589i	−0.972346	−	0.233547i	$-0.924967\pi$
$353$	−22.6567	−	22.6567i	−1.20589	−	1.20589i	−0.233547	−	0.972346i	$-0.575033\pi$
$354$	−0.695064	−	3.81384i	−0.0369422	−	0.202703i
$355$		0			0
$356$	−1.37304	+	0.517659i	−0.0727709	+	0.0274359i
$357$	8.01758	+	8.01758i	0.424336	+	0.424336i
$358$	−4.19973	−	2.90492i	−0.221963	−	0.153530i
$359$	−16.9181			−0.892903			−0.446451	−	0.894808i	$-0.647312\pi$
$359$	−16.9181			−0.892903			−0.446451	+	0.894808i	$0.647312\pi$
$360$		0			0
$361$	18.5878			0.978306
$362$	25.4708	+	17.6180i	1.33872	+	0.925982i
$363$	0.791092	+	0.791092i	0.0415215	+	0.0415215i
$364$	9.94325	+	26.3734i	0.521168	+	1.38234i
$365$		0			0
$366$	−1.32091	−	7.24787i	−0.0690449	−	0.378852i
$367$	2.82093	+	2.82093i	0.147252	+	0.147252i	0.776889	−	0.629637i	$-0.216797\pi$
$367$	2.82093	+	2.82093i	0.147252	+	0.147252i	−0.629637	+	0.776889i	$0.716797\pi$
$368$	−0.840020	+	13.0417i	−0.0437891	+	0.679845i
$369$			4.92316i			0.256290i
$370$		0			0
$371$	13.3350			0.692318
$372$	−2.85834	−	1.29316i	−0.148198	−	0.0670470i
$373$	−22.7300	+	22.7300i	−1.17691	+	1.17691i	−0.196388	+	0.980526i	$0.562921\pi$
$373$	−22.7300	+	22.7300i	−1.17691	+	1.17691i	−0.980526	+	0.196388i	$0.937079\pi$
$374$	−2.05926	−	11.2993i	−0.106482	−	0.584270i
$375$		0			0
$376$	14.1184	+	23.5099i	0.728099	+	1.21243i
$377$	1.43444	−	1.43444i	0.0738773	−	0.0738773i
$378$	−3.91007	+	5.65290i	−0.201112	+	0.290754i
$379$		−	2.55793i		−	0.131392i	−0.997840	−	0.0656959i	$-0.979073\pi$
$379$		−	2.55793i		−	0.131392i	0.997840	−	0.0656959i	$-0.0209267\pi$
$380$		0			0
$381$		−	13.6130i		−	0.697414i
$382$	−11.7831	−	8.15030i	−0.602877	−	0.417006i
$383$	−5.48289	+	5.48289i	−0.280163	+	0.280163i	−0.833174	−	0.553011i	$-0.813479\pi$
$383$	−5.48289	+	5.48289i	−0.280163	+	0.280163i	0.553011	+	0.833174i	$0.313479\pi$
$384$	10.7782	+	3.43962i	0.550021	+	0.175527i
$385$		0			0
$386$	28.2468	−	5.14791i	1.43772	−	0.262022i
$387$	3.56519	−	3.56519i	0.181229	−	0.181229i
$388$	22.6537	+	10.2489i	1.15007	+	0.520307i
$389$	−5.02529			−0.254792			−0.127396	−	0.991852i	$-0.540662\pi$
$389$	−5.02529			−0.254792			−0.127396	+	0.991852i	$0.540662\pi$
$390$		0			0
$391$		−	7.62208i		−	0.385465i
$392$	11.3849	−	45.6147i	0.575023	−	2.30389i
$393$	0.896394	+	0.896394i	0.0452171	+	0.0452171i
$394$	−28.9007	+	5.26709i	−1.45600	+	0.265352i
$395$		0			0
$396$	6.51477	−	2.45618i	0.327380	−	0.123428i
$397$	8.56361	+	8.56361i	0.429795	+	0.429795i	0.888558	−	0.458763i	$-0.151707\pi$
$397$	8.56361	+	8.56361i	0.429795	+	0.429795i	−0.458763	+	0.888558i	$0.651707\pi$
$398$	4.09163	−	5.91539i	0.205095	−	0.296512i
$399$	3.12039			0.156215
$400$		0			0
$401$	−12.5710			−0.627763			−0.313882	−	0.949462i	$-0.601630\pi$
$401$	−12.5710			−0.627763			−0.313882	+	0.949462i	$0.601630\pi$
$402$	−7.87674	+	11.3876i	−0.392856	+	0.567963i
$403$	3.21620	+	3.21620i	0.160211	+	0.160211i
$404$	−2.63744	+	0.994361i	−0.131217	+	0.0494713i
$405$		0			0
$406$	−4.73081	+	0.862179i	−0.234786	+	0.0427892i
$407$	−18.5113	−	18.5113i	−0.917572	−	0.917572i
$408$	−6.40211	−	1.59789i	−0.316952	−	0.0791073i
$409$		−	9.94711i		−	0.491853i	−0.969288	−	0.245927i	$-0.920908\pi$
$409$		−	9.94711i		−	0.491853i	0.969288	−	0.245927i	$-0.0790922\pi$
$410$		0			0
$411$	17.2953			0.853116
$412$	−6.21910	−	2.81361i	−0.306393	−	0.138617i
$413$	9.42076	−	9.42076i	0.463565	−	0.463565i
$414$	4.54561	−	0.828427i	0.223405	−	0.0407150i
$415$		0			0
$416$	−12.8623	−	10.1787i	−0.630628	−	0.499054i
$417$	5.75323	−	5.75323i	0.281737	−	0.281737i
$418$	−2.59952	−	1.79807i	−0.127147	−	0.0879465i
$419$		−	1.92920i		−	0.0942475i	−0.998889	−	0.0471238i	$-0.984994\pi$
$419$		−	1.92920i		−	0.0942475i	0.998889	−	0.0471238i	$-0.0150055\pi$
$420$		0			0
$421$			0.454084i			0.0221307i	0.999939	+	0.0110654i	$0.00352229\pi$
$421$			0.454084i			0.0221307i	−0.999939	+	0.0110654i	$0.996478\pi$
$422$	−17.5326	+	25.3474i	−0.853474	+	1.23389i
$423$	6.85586	−	6.85586i	0.333343	−	0.333343i
$424$	−6.65287	+	3.99523i	−0.323092	+	0.194026i
$425$		0			0
$426$	2.82843	+	15.5197i	0.137038	+	0.751932i
$427$	17.9033	−	17.9033i	0.866402	−	0.866402i
$428$	4.02196	+	1.81959i	0.194409	+	0.0879534i
$429$	−10.0941			−0.487348
$430$		0			0
$431$			7.07961i			0.341013i	0.985357	+	0.170506i	$0.0545403\pi$
$431$			7.07961i			0.341013i	−0.985357	+	0.170506i	$0.945460\pi$
$432$	0.257109	−	3.99173i	0.0123702	−	0.192052i
$433$	15.1484	+	15.1484i	0.727987	+	0.727987i	0.970219	−	0.242231i	$-0.0778793\pi$
$433$	15.1484	+	15.1484i	0.727987	+	0.727987i	−0.242231	+	0.970219i	$0.577879\pi$
$434$	−1.93312	−	10.6071i	−0.0927929	−	0.509158i
$435$		0			0
$436$	10.3136	+	27.3557i	0.493931	+	1.31010i
$437$	−1.48323	−	1.48323i	−0.0709525	−	0.0709525i
$438$	10.7988	+	7.46945i	0.515987	+	0.356904i
$439$	25.2936			1.20720			0.603599	−	0.797288i	$-0.293733\pi$
$439$	25.2936			1.20720			0.603599	+	0.797288i	$0.293733\pi$
$440$		0			0
$441$	−16.6220			−0.791522
$442$	7.86779	+	5.44209i	0.374232	+	0.258854i
$443$	26.9275	+	26.9275i	1.27936	+	1.27936i	0.941024	+	0.338341i	$0.109866\pi$
$443$	26.9275	+	26.9275i	1.27936	+	1.27936i	0.338341	+	0.941024i	$0.390134\pi$
$444$	−14.0732	+	5.30584i	−0.667885	+	0.251804i
$445$		0			0
$446$	−2.73701	−	15.0181i	−0.129601	−	0.711127i
$447$	−1.94505	−	1.94505i	−0.0919976	−	0.0919976i
$448$	11.3498	+	37.1885i	0.536227	+	1.75699i
$449$			22.4863i			1.06120i	0.847624	+	0.530598i	$0.178033\pi$
$449$			22.4863i			1.06120i	−0.847624	+	0.530598i	$0.821967\pi$
$450$		0			0
$451$	17.1385			0.807022
$452$	5.31350	−	11.7448i	0.249926	−	0.552427i
$453$	7.21389	−	7.21389i	0.338938	−	0.338938i
$454$	−3.17123	−	17.4007i	−0.148833	−	0.816653i
$455$		0			0
$456$	−1.55677	+	0.934885i	−0.0729026	+	0.0437800i
$457$	0.0735546	−	0.0735546i	0.00344074	−	0.00344074i	−0.705384	−	0.708825i	$-0.749226\pi$
$457$	0.0735546	−	0.0735546i	0.00344074	−	0.00344074i	0.708825	+	0.705384i	$0.249226\pi$
$458$	19.2694	−	27.8584i	0.900401	−	1.30174i
$459$			2.33292i			0.108892i
$460$		0			0
$461$			33.7901i			1.57376i	0.617105	+	0.786881i	$0.288305\pi$
$461$			33.7901i			1.57376i	−0.617105	+	0.786881i	$0.711695\pi$
$462$	19.6789	+	13.6117i	0.915545	+	0.633276i
$463$	27.4189	−	27.4189i	1.27427	−	1.27427i	0.330439	−	0.943827i	$-0.392803\pi$
$463$	27.4189	−	27.4189i	1.27427	−	1.27427i	0.943827	−	0.330439i	$-0.107197\pi$
$464$	2.10190	−	1.84752i	0.0975784	−	0.0857690i
$465$		0			0
$466$	−8.62457	+	1.57181i	−0.399526	+	0.0728126i
$467$	−11.8191	+	11.8191i	−0.546923	+	0.546923i	−0.925550	−	0.378626i	$-0.876397\pi$
$467$	−11.8191	+	11.8191i	−0.546923	+	0.546923i	0.378626	+	0.925550i	$0.376397\pi$
$468$	−2.39039	+	5.28364i	−0.110496	+	0.244236i
$469$	−47.5858			−2.19731
$470$		0			0
$471$			1.82596i			0.0841359i
$472$	−1.87754	+	7.52256i	−0.0864207	+	0.346254i
$473$	−12.4111	−	12.4111i	−0.570665	−	0.570665i
$474$	−2.91757	+	0.531720i	−0.134009	+	0.0244227i
$475$		0			0
$476$	−8.00000	−	21.2192i	−0.366679	−	0.972579i
$477$	1.94008	+	1.94008i	0.0888301	+	0.0888301i
$478$	−13.5150	+	19.5391i	−0.618164	+	0.893697i
$479$	39.9242			1.82418			0.912091	−	0.409988i	$-0.134467\pi$
$479$	39.9242			1.82418			0.912091	+	0.409988i	$0.134467\pi$
$480$		0			0
$481$	21.8053			0.994236
$482$	2.79385	−	4.03914i	0.127256	−	0.183978i
$483$	11.2283	+	11.2283i	0.510907	+	0.510907i
$484$	−0.789357	−	2.09369i	−0.0358798	−	0.0951676i
$485$		0			0
$486$	−1.39130	+	0.253561i	−0.0631105	+	0.0115017i
$487$	10.5650	+	10.5650i	0.478745	+	0.478745i	0.904730	−	0.425985i	$-0.140072\pi$
$487$	10.5650	+	10.5650i	0.478745	+	0.478745i	−0.425985	+	0.904730i	$0.640072\pi$
$488$	−3.56809	+	14.2959i	−0.161520	+	0.647147i
$489$		−	13.1633i		−	0.595266i
$490$		0			0
$491$	−27.7875			−1.25403			−0.627016	−	0.779006i	$-0.715724\pi$
$491$	−27.7875			−1.25403			−0.627016	+	0.779006i	$0.715724\pi$
$492$	4.05859	−	8.97096i	0.182975	−	0.404442i
$493$	−1.15410	+	1.15410i	−0.0519780	+	0.0519780i
$494$	2.59006	−	0.472032i	0.116532	−	0.0212377i
$495$		0			0
$496$	4.14239	+	4.71276i	0.185999	+	0.211609i
$497$	−38.3360	+	38.3360i	−1.71960	+	1.71960i
$498$	−10.9325	−	7.56194i	−0.489897	−	0.338859i
$499$			19.6133i			0.878014i	0.898484	+	0.439007i	$0.144670\pi$
$499$			19.6133i			0.878014i	−0.898484	+	0.439007i	$0.855330\pi$
$500$		0			0
$501$			16.8073i			0.750893i
$502$	8.53703	−	12.3422i	0.381026	−	0.550860i
$503$	−24.2004	+	24.2004i	−1.07904	+	1.07904i	−0.0824469	+	0.996595i	$0.526273\pi$
$503$	−24.2004	+	24.2004i	−1.07904	+	1.07904i	−0.996595	+	0.0824469i	$0.973727\pi$
$504$	11.7851	−	7.07726i	0.524949	−	0.315246i
$505$		0			0
$506$	−2.88392	−	15.8242i	−0.128206	−	0.703472i
$507$	−3.24724	+	3.24724i	−0.144215	+	0.144215i
$508$	−11.2223	+	24.8055i	−0.497911	+	1.10056i
$509$	10.8167			0.479444			0.239722	−	0.970842i	$-0.422944\pi$
$509$	10.8167			0.479444			0.239722	+	0.970842i	$0.422944\pi$
$510$		0			0
$511$			45.1253i			1.99623i
$512$	−16.8043	−	15.1530i	−0.742654	−	0.669676i
$513$	0.453979	+	0.453979i	0.0200437	+	0.0200437i
$514$	−5.89859	−	32.3658i	−0.260176	−	1.42759i
$515$		0			0
$516$	−9.43555	+	3.55737i	−0.415377	+	0.156604i
$517$	−23.8666	−	23.8666i	−1.04965	−	1.04965i
$518$	−42.5103	−	29.4041i	−1.86780	−	1.29194i
$519$	−18.7435			−0.822747
$520$		0			0
$521$	−29.5691			−1.29544			−0.647722	−	0.761877i	$-0.724278\pi$
$521$	−29.5691			−1.29544			−0.647722	+	0.761877i	$0.724278\pi$
$522$	−0.813713	−	0.562839i	−0.0356152	−	0.0246348i
$523$	26.2357	+	26.2357i	1.14721	+	1.14721i	0.987100	+	0.160106i	$0.0511835\pi$
$523$	26.2357	+	26.2357i	1.14721	+	1.14721i	0.160106	+	0.987100i	$0.448816\pi$
$524$	−0.894429	−	2.37238i	−0.0390733	−	0.103638i
$525$		0			0
$526$	−6.20721	−	34.0592i	−0.270647	−	1.48505i
$527$	−2.58765	−	2.58765i	−0.112720	−	0.112720i
$528$	−13.8960	−	0.895048i	−0.604746	−	0.0389520i
$529$			12.3256i			0.535894i
$530$		0			0
$531$	2.74121			0.118959
$532$	−5.68595	−	2.57241i	−0.246517	−	0.111528i
$533$	−10.0941	+	10.0941i	−0.437224	+	0.437224i
$534$	−0.186035	−	1.02078i	−0.00805052	−	0.0441735i
$535$		0			0
$536$	23.7407	−	14.2570i	1.02544	−	0.615807i
$537$	2.55325	−	2.55325i	0.110181	−	0.110181i
$538$	13.8518	−	20.0259i	0.597192	−	0.863378i
$539$			57.8644i			2.49240i
$540$		0			0
$541$			9.66967i			0.415731i	0.978157	+	0.207866i	$0.0666517\pi$
$541$			9.66967i			0.415731i	−0.978157	+	0.207866i	$0.933348\pi$
$542$	9.73847	+	6.73603i	0.418303	+	0.289337i
$543$	−15.4851	+	15.4851i	−0.664531	+	0.664531i
$544$	10.3486	+	8.18947i	0.443693	+	0.351121i
$545$		0			0
$546$	−19.6072	+	3.57337i	−0.839112	+	0.152926i
$547$	−4.45632	+	4.45632i	−0.190538	+	0.190538i	−0.795929	−	0.605390i	$-0.793017\pi$
$547$	−4.45632	+	4.45632i	−0.190538	+	0.190538i	0.605390	+	0.795929i	$0.293017\pi$
$548$	−31.5154	−	14.2580i	−1.34627	−	0.609073i
$549$	5.20943			0.222333
$550$		0			0
$551$			0.449168i			0.0191352i
$552$	−8.96593	−	2.23779i	−0.381615	−	0.0952465i
$553$	−7.20684	−	7.20684i	−0.306466	−	0.306466i
$554$	22.1362	−	4.03427i	0.940476	−	0.171400i
$555$		0			0
$556$	−15.2264	+	5.74061i	−0.645743	+	0.243456i
$557$	−7.10582	−	7.10582i	−0.301083	−	0.301083i	0.540354	−	0.841438i	$-0.318290\pi$
$557$	−7.10582	−	7.10582i	−0.301083	−	0.301083i	−0.841438	+	0.540354i	$0.818290\pi$
$558$	1.26196	−	1.82446i	0.0534231	−	0.0772353i
$559$	14.6196			0.618344
$560$		0			0
$561$	8.12138			0.342885
$562$	−20.8725	+	30.1760i	−0.880453	+	1.27290i
$563$	−12.1395	−	12.1395i	−0.511620	−	0.511620i	0.403403	−	0.915023i	$-0.367827\pi$
$563$	−12.1395	−	12.1395i	−0.511620	−	0.511620i	−0.915023	+	0.403403i	$0.867827\pi$
$564$	−18.1446	+	6.84082i	−0.764024	+	0.288050i
$565$		0			0
$566$	−0.0772109	+	0.0140715i	−0.00324542	+	0.000591470i
$567$	−3.43671	−	3.43671i	−0.144328	−	0.144328i
$568$	7.64028	−	30.6116i	0.320579	−	1.28443i
$569$			9.17667i			0.384706i	0.981326	+	0.192353i	$0.0616118\pi$
$569$			9.17667i			0.384706i	−0.981326	+	0.192353i	$0.938388\pi$
$570$		0			0
$571$	14.1460			0.591990			0.295995	−	0.955190i	$-0.404349\pi$
$571$	14.1460			0.591990			0.295995	+	0.955190i	$0.404349\pi$
$572$	18.3934	+	8.32145i	0.769067	+	0.347937i
$573$	7.16361	−	7.16361i	0.299264	−	0.299264i
$574$	33.2906	−	6.06714i	1.38952	−	0.253237i
$575$		0			0
$576$	−3.75923	+	7.06174i	−0.156634	+	0.294239i
$577$	−6.88789	+	6.88789i	−0.286747	+	0.286747i	−0.835792	−	0.549046i	$-0.814991\pi$
$577$	−6.88789	+	6.88789i	−0.286747	+	0.286747i	0.549046	+	0.835792i	$0.314991\pi$
$578$	13.4424	+	9.29799i	0.559129	+	0.386746i
$579$			20.3025i			0.843742i
$580$		0			0
$581$		−	45.6840i		−	1.89529i
$582$	−10.0016	+	14.4597i	−0.414582	+	0.599372i
$583$	6.75381	−	6.75381i	0.279714	−	0.279714i
$584$	−13.5198	−	22.5132i	−0.559452	−	0.931601i
$585$		0			0
$586$	−7.75867	−	42.5721i	−0.320508	−	1.75864i
$587$	−5.90740	+	5.90740i	−0.243824	+	0.243824i	−0.818430	−	0.574606i	$-0.805155\pi$
$587$	−5.90740	+	5.90740i	−0.243824	+	0.243824i	0.574606	+	0.818430i	$0.305155\pi$
$588$	30.2884	+	13.7029i	1.24907	+	0.565098i
$589$	−1.00710			−0.0414967
$590$		0			0
$591$		−	20.7725i		−	0.854467i
$592$	30.0182	+	1.93348i	1.23374	+	0.0794656i
$593$	22.6480	+	22.6480i	0.930042	+	0.930042i	0.997708	−	0.0676664i	$-0.0215554\pi$
$593$	22.6480	+	22.6480i	0.930042	+	0.930042i	−0.0676664	+	0.997708i	$0.521555\pi$
$594$	0.882696	+	4.84339i	0.0362174	+	0.198727i
$595$		0			0
$596$	1.94078	+	5.14772i	0.0794975	+	0.210859i
$597$	3.59629	+	3.59629i	0.147186	+	0.147186i
$598$	11.0186	+	7.62146i	0.450582	+	0.311665i
$599$	−17.4493			−0.712958			−0.356479	−	0.934303i	$-0.616023\pi$
$599$	−17.4493			−0.712958			−0.356479	+	0.934303i	$0.616023\pi$
$600$		0			0
$601$	−26.2079			−1.06904			−0.534521	−	0.845155i	$-0.679508\pi$
$601$	−26.2079			−1.06904			−0.534521	+	0.845155i	$0.679508\pi$
$602$	−28.5016	−	19.7143i	−1.16164	−	0.803496i
$603$	−6.92316	−	6.92316i	−0.281933	−	0.281933i
$604$	−19.0921	+	7.19807i	−0.776848	+	0.292885i
$605$		0			0
$606$	−0.357350	−	1.96080i	−0.0145164	−	0.0796519i
$607$	8.79177	+	8.79177i	0.356847	+	0.356847i	0.862649	−	0.505802i	$-0.168804\pi$
$607$	8.79177	+	8.79177i	0.356847	+	0.356847i	−0.505802	+	0.862649i	$0.668804\pi$
$608$	3.60745	−	0.420160i	0.146301	−	0.0170397i
$609$		−	3.40029i		−	0.137787i
$610$		0			0
$611$	28.1135			1.13735
$612$	1.92323	−	4.25104i	0.0777420	−	0.171838i
$613$	10.9270	−	10.9270i	0.441339	−	0.441339i	−0.451123	−	0.892462i	$-0.648976\pi$
$613$	10.9270	−	10.9270i	0.441339	−	0.441339i	0.892462	+	0.451123i	$0.148976\pi$
$614$	−6.49641	−	35.6461i	−0.262174	−	1.43856i
$615$		0			0
$616$	−24.6374	−	41.0262i	−0.992669	−	1.65299i
$617$	−13.6319	+	13.6319i	−0.548799	+	0.548799i	−0.926093	−	0.377294i	$-0.876855\pi$
$617$	−13.6319	+	13.6319i	−0.548799	+	0.548799i	0.377294	+	0.926093i	$0.376855\pi$
$618$	2.74574	−	3.96959i	0.110450	−	0.159681i
$619$		−	1.50796i		−	0.0606100i	−0.999541	−	0.0303050i	$-0.990352\pi$
$619$		−	1.50796i		−	0.0606100i	0.999541	−	0.0303050i	$-0.00964785\pi$
$620$		0			0
$621$			3.26718i			0.131107i
$622$	−11.2081	−	7.75256i	−0.449404	−	0.310849i
$623$	2.52148	−	2.52148i	0.101021	−	0.101021i
$624$	8.71152	−	7.65720i	0.348740	−	0.306533i
$625$		0			0
$626$	−35.8834	+	6.53967i	−1.43419	+	0.261378i
$627$	1.58039	−	1.58039i	0.0631148	−	0.0631148i
$628$	1.50530	−	3.32726i	0.0600679	−	0.132772i
$629$	−17.5438			−0.699517
$630$		0			0
$631$		−	42.8319i		−	1.70511i	−0.522638	−	0.852555i	$-0.675052\pi$
$631$		−	42.8319i		−	1.70511i	0.522638	−	0.852555i	$-0.324948\pi$
$632$	5.75472	+	1.43631i	0.228911	+	0.0571333i
$633$	−15.4101	−	15.4101i	−0.612496	−	0.612496i
$634$	1.70558	−	0.310839i	0.0677374	−	0.0123450i
$635$		0			0
$636$	−1.93582	−	5.13457i	−0.0767604	−	0.203599i
$637$	−34.0805	−	34.0805i	−1.35032	−	1.35032i
$638$	−1.95936	+	2.83270i	−0.0775717	+	0.112148i
$639$	−11.1548			−0.441279
$640$		0			0
$641$	9.93597			0.392447			0.196224	−	0.980559i	$-0.437132\pi$
$641$	9.93597			0.392447			0.196224	+	0.980559i	$0.437132\pi$
$642$	−1.77570	+	2.56718i	−0.0700814	+	0.101319i
$643$	20.3751	+	20.3751i	0.803517	+	0.803517i	0.983643	−	0.180127i	$-0.0576508\pi$
$643$	20.3751	+	20.3751i	0.803517	+	0.803517i	−0.180127	+	0.983643i	$0.557651\pi$
$644$	−11.2037	−	29.7167i	−0.441488	−	1.17100i
$645$		0			0
$646$	−2.08387	+	0.379781i	−0.0819889	+	0.0149423i
$647$	−25.4648	−	25.4648i	−1.00112	−	1.00112i	−0.999999	−	0.00112374i	$-0.999642\pi$
$647$	−25.4648	−	25.4648i	−1.00112	−	1.00112i	−0.00112374	−	0.999999i	$-0.500358\pi$
$648$	2.74424	+	0.684930i	0.107804	+	0.0269066i
$649$		−	9.54272i		−	0.374585i
$650$		0			0
$651$	7.62391			0.298805
$652$	−10.8517	+	23.9861i	−0.424984	+	0.939368i
$653$	−16.9677	+	16.9677i	−0.663999	+	0.663999i	−0.956320	−	0.292321i	$-0.905572\pi$
$653$	−16.9677	+	16.9677i	−0.663999	+	0.663999i	0.292321	+	0.956320i	$0.405572\pi$
$654$	−20.3375	+	3.70647i	−0.795260	+	0.144934i
$655$		0			0
$656$	−14.7911	+	13.0010i	−0.577494	+	0.507603i
$657$	−6.56519	+	6.56519i	−0.256132	+	0.256132i
$658$	−54.8085	−	37.9107i	−2.13666	−	1.47791i
$659$		−	0.958005i		−	0.0373186i	−0.999826	−	0.0186593i	$-0.994060\pi$
$659$		−	0.958005i		−	0.0373186i	0.999826	−	0.0186593i	$-0.00593978\pi$
$660$		0			0
$661$		−	5.22656i		−	0.203289i	−0.994821	−	0.101645i	$-0.967590\pi$
$661$		−	5.22656i		−	0.203289i	0.994821	−	0.101645i	$-0.0324105\pi$
$662$	11.6559	−	16.8513i	0.453019	−	0.654943i
$663$	−4.78326	+	4.78326i	−0.185767	+	0.185767i
$664$	13.6872	+	22.7919i	0.531166	+	0.884498i
$665$		0			0
$666$	−1.90680	−	10.4627i	−0.0738869	−	0.405421i
$667$	−1.61628	+	1.61628i	−0.0625824	+	0.0625824i
$668$	13.8557	−	30.6261i	0.536092	−	1.18496i
$669$	10.7943			0.417332
$670$		0			0
$671$		−	18.1351i		−	0.700097i
$672$	−27.3091	+	3.18069i	−1.05347	+	0.122698i
$673$	−16.3145	−	16.3145i	−0.628876	−	0.628876i	0.318909	−	0.947785i	$-0.396684\pi$
$673$	−16.3145	−	16.3145i	−0.628876	−	0.628876i	−0.947785	+	0.318909i	$0.896684\pi$
$674$	7.88812	+	43.2824i	0.303839	+	1.66718i
$675$		0			0
$676$	8.59408	−	3.24012i	0.330542	−	0.124620i
$677$	21.9712	+	21.9712i	0.844423	+	0.844423i	0.989431	−	0.145008i	$-0.0463207\pi$
$677$	21.9712	+	21.9712i	0.844423	+	0.844423i	−0.145008	+	0.989431i	$0.546321\pi$
$678$	7.49658	+	5.18533i	0.287904	+	0.199141i
$679$	−60.4231			−2.31883
$680$		0			0
$681$	12.5068			0.479261
$682$	−6.35130	−	4.39315i	−0.243204	−	0.168222i
$683$	27.9871	+	27.9871i	1.07090	+	1.07090i	0.997287	+	0.0736087i	$0.0234516\pi$
$683$	27.9871	+	27.9871i	1.07090	+	1.07090i	0.0736087	+	0.997287i	$0.476548\pi$
$684$	−0.452983	−	1.20149i	−0.0173203	−	0.0459402i
$685$		0			0
$686$	11.8578	+	65.0640i	0.452732	+	2.48416i
$687$	16.9366	+	16.9366i	0.646173	+	0.646173i
$688$	20.1260	+	1.29633i	0.767298	+	0.0494220i
$689$			7.95560i			0.303084i
$690$		0			0
$691$	−39.3415			−1.49662			−0.748310	−	0.663349i	$-0.769134\pi$
$691$	−39.3415			−1.49662			−0.748310	+	0.663349i	$0.769134\pi$
$692$	34.1542	+	15.4519i	1.29835	+	0.587391i
$693$	−11.9639	+	11.9639i	−0.454470	+	0.454470i
$694$	1.26552	+	6.94397i	0.0480386	+	0.263590i
$695$		0			0
$696$	1.01874	+	1.69642i	0.0386154	+	0.0643025i
$697$	8.12138	−	8.12138i	0.307619	−	0.307619i
$698$	2.62302	−	3.79218i	0.0992829	−	0.143536i
$699$		−	6.19895i		−	0.234466i
$700$		0			0
$701$		−	10.3150i		−	0.389594i	−0.980844	−	0.194797i	$-0.937595\pi$
$701$		−	10.3150i		−	0.389594i	0.980844	−	0.194797i	$-0.0624048\pi$
$702$	−3.37250	−	2.33274i	−0.127287	−	0.0880434i
$703$	−3.41396	+	3.41396i	−0.128760	+	0.128760i
$704$	24.5834	+	13.0866i	0.926520	+	0.493221i
$705$		0			0
$706$	−44.5790	+	8.12442i	−1.67775	+	0.305767i
$707$	4.84346	−	4.84346i	0.182157	−	0.182157i
$708$	−4.99502	−	2.25982i	−0.187724	−	0.0849292i
$709$	45.3404			1.70279			0.851397	−	0.524522i	$-0.175756\pi$
$709$	45.3404			1.70279			0.851397	+	0.524522i	$0.175756\pi$
$710$		0			0
$711$		−	2.09702i		−	0.0786442i
$712$	−0.502526	+	2.01342i	−0.0188330	+	0.0754563i
$713$	−3.62391	−	3.62391i	−0.135717	−	0.135717i
$714$	15.7753	−	2.87502i	0.590377	−	0.107595i
$715$		0			0
$716$	−6.75738	+	2.54765i	−0.252535	+	0.0952101i
$717$	−11.8789	−	11.8789i	−0.443625	−	0.443625i
$718$	−13.6106	+	19.6773i	−0.507944	+	0.734349i
$719$	−43.8494			−1.63531			−0.817653	−	0.575711i	$-0.804725\pi$
$719$	−43.8494			−1.63531			−0.817653	+	0.575711i	$0.804725\pi$
$720$		0			0
$721$	16.5879			0.617765
$722$	14.9539	−	21.6193i	0.556527	−	0.804587i
$723$	2.45562	+	2.45562i	0.0913255	+	0.0913255i
$724$	40.9826	−	15.4512i	1.52311	−	0.574238i
$725$		0			0
$726$	1.55654	−	0.283677i	0.0577688	−	0.0105282i
$727$	2.07567	+	2.07567i	0.0769824	+	0.0769824i	0.744550	−	0.667567i	$-0.232664\pi$
$727$	2.07567	+	2.07567i	0.0769824	+	0.0769824i	−0.667567	+	0.744550i	$0.732664\pi$
$728$	38.6740	+	9.65256i	1.43335	+	0.357748i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−11.7625			−0.435050
$732$	−9.49259	−	4.29458i	−0.350856	−	0.158732i
$733$	−2.13221	+	2.13221i	−0.0787549	+	0.0787549i	−0.745387	−	0.666632i	$-0.767735\pi$
$733$	−2.13221	+	2.13221i	−0.0787549	+	0.0787549i	0.666632	+	0.745387i	$0.267735\pi$
$734$	5.55045	−	1.01156i	0.204871	−	0.0373372i
$735$		0			0
$736$	14.4929	+	11.4691i	0.534214	+	0.422755i
$737$	−24.1009	+	24.1009i	−0.887769	+	0.887769i
$738$	5.72608	+	3.96069i	0.210780	+	0.145795i
$739$			32.9512i			1.21213i	0.795416	+	0.606064i	$0.207253\pi$
$739$			32.9512i			1.21213i	−0.795416	+	0.606064i	$0.792747\pi$
$740$		0			0
$741$			1.86161i			0.0683881i
$742$	10.7280	−	15.5098i	0.393837	−	0.569382i
$743$	17.0344	−	17.0344i	0.624931	−	0.624931i	−0.321857	−	0.946788i	$-0.604307\pi$
$743$	17.0344	−	17.0344i	0.624931	−	0.624931i	0.946788	+	0.321857i	$0.104307\pi$
$744$	−3.80360	+	2.28416i	−0.139447	+	0.0837415i
$745$		0			0
$746$	8.15072	+	44.7233i	0.298419	+	1.63744i
$747$	6.64648	−	6.64648i	0.243182	−	0.243182i
$748$	−14.7987	−	6.69515i	−0.541095	−	0.244799i
$749$	−10.7276			−0.391977
$750$		0			0
$751$			38.0634i			1.38895i	0.719515	+	0.694477i	$0.244364\pi$
$751$			38.0634i			1.38895i	−0.719515	+	0.694477i	$0.755636\pi$
$752$	38.7024	+	2.49284i	1.41133	+	0.0909043i
$753$	7.50352	+	7.50352i	0.273443	+	0.273443i
$754$	−0.514373	−	2.82239i	−0.0187324	−	0.102785i
$755$		0			0
$756$	3.42917	+	9.09553i	0.124718	+	0.330801i
$757$	31.5125	+	31.5125i	1.14534	+	1.14534i	0.987458	+	0.157885i	$0.0504674\pi$
$757$	31.5125	+	31.5125i	1.14534	+	1.14534i	0.157885	+	0.987458i	$0.449533\pi$
$758$	−2.97510	−	2.05786i	−0.108060	−	0.0747447i
$759$	11.3737			0.412839
$760$		0			0
$761$	36.1731			1.31128			0.655638	−	0.755076i	$-0.272400\pi$
$761$	36.1731			1.31128			0.655638	+	0.755076i	$0.272400\pi$
$762$	−15.8331	−	10.9516i	−0.573573	−	0.396736i
$763$	−50.2367	−	50.2367i	−1.81869	−	1.81869i
$764$	−18.9591	+	7.14790i	−0.685915	+	0.258602i
$765$		0			0
$766$	1.96610	+	10.7881i	0.0710382	+	0.389789i
$767$	5.62039	+	5.62039i	0.202941	+	0.202941i
$768$	12.6716	−	9.76880i	0.457248	−	0.352501i
$769$			29.7981i			1.07455i	0.843408	+	0.537273i	$0.180546\pi$
$769$			29.7981i			1.07455i	−0.843408	+	0.537273i	$0.819454\pi$
$770$		0			0
$771$	23.2630			0.837798
$772$	16.7371	−	36.9950i	0.602381	−	1.33148i
$773$	4.11081	−	4.11081i	0.147856	−	0.147856i	−0.629304	−	0.777159i	$-0.716660\pi$
$773$	4.11081	−	4.11081i	0.147856	−	0.147856i	0.777159	+	0.629304i	$0.216660\pi$
$774$	−1.27844	−	7.01483i	−0.0459524	−	0.252143i
$775$		0			0
$776$	30.1453	−	18.1031i	1.08215	−	0.649863i
$777$	25.8444	−	25.8444i	0.927162	−	0.927162i
$778$	−4.04285	+	5.84487i	−0.144943	+	0.209549i
$779$		−	3.16079i		−	0.113247i
$780$		0			0
$781$			38.8323i			1.38953i
$782$	−8.86516	−	6.13197i	−0.317017	−	0.219279i
$783$	0.494701	−	0.494701i	0.0176792	−	0.0176792i
$784$	−43.8948	−	49.9387i	−1.56767	−	1.78352i
$785$		0			0
$786$	1.76374	−	0.321437i	0.0629104	−	0.0114653i
$787$	−14.4907	+	14.4907i	−0.516537	+	0.516537i	−0.916522	−	0.399985i	$-0.869015\pi$
$787$	−14.4907	+	14.4907i	−0.516537	+	0.516537i	0.399985	+	0.916522i	$0.369015\pi$
$788$	−17.1246	+	37.8515i	−0.610038	+	1.34840i
$789$	24.4802			0.871518
$790$		0			0
$791$			31.3262i			1.11383i
$792$	2.38438	−	9.55327i	0.0847252	−	0.339461i
$793$	10.6811	+	10.6811i	0.379295	+	0.379295i
$794$	16.8497	−	3.07081i	0.597973	−	0.108979i
$795$		0			0
$796$	−3.58841	−	9.51788i	−0.127188	−	0.337352i
$797$	−3.99359	−	3.99359i	−0.141460	−	0.141460i	0.632830	−	0.774291i	$-0.281893\pi$
$797$	−3.99359	−	3.99359i	−0.141460	−	0.141460i	−0.774291	+	0.632830i	$0.781893\pi$
$798$	2.51036	−	3.62929i	0.0888657	−	0.128476i
$799$	−22.6192			−0.800210
$800$		0			0
$801$	0.733690			0.0259237
$802$	−10.1133	+	14.6211i	−0.357115	+	0.516291i
$803$	22.8547	+	22.8547i	0.806527	+	0.806527i
$804$	6.90798	+	18.3227i	0.243626	+	0.646192i
$805$		0			0
$806$	6.32818	−	1.15329i	0.222900	−	0.0406231i
$807$	12.1749	+	12.1749i	0.428575	+	0.428575i
$808$	−0.965291	+	3.86754i	−0.0339588	+	0.136060i
$809$			1.83726i			0.0645947i	0.999478	+	0.0322974i	$0.0102824\pi$
$809$			1.83726i			0.0645947i	−0.999478	+	0.0322974i	$0.989718\pi$
$810$		0			0
$811$	19.2559			0.676166			0.338083	−	0.941116i	$-0.390222\pi$
$811$	19.2559			0.676166			0.338083	+	0.941116i	$0.390222\pi$
$812$	−2.80315	+	6.19598i	−0.0983713	+	0.217436i
$813$	−5.92055	+	5.92055i	−0.207643	+	0.207643i
$814$	−36.4227	+	6.63795i	−1.27662	+	0.232660i
$815$		0			0
$816$	−7.00899	+	6.16073i	−0.245364	+	0.215669i
$817$	−2.28893	+	2.28893i	−0.0800797	+	0.0800797i
$818$	−11.5694	−	8.00246i	−0.404514	−	0.279800i
$819$		−	14.0928i		−	0.492442i
$820$		0			0
$821$		−	29.3331i		−	1.02373i	−0.859066	−	0.511865i	$-0.828955\pi$
$821$		−	29.3331i		−	1.02373i	0.859066	−	0.511865i	$-0.171045\pi$
$822$	13.9141	−	20.1160i	0.485310	−	0.701627i
$823$	−11.8788	+	11.8788i	−0.414067	+	0.414067i	−0.883153	−	0.469085i	$-0.844584\pi$
$823$	−11.8788	+	11.8788i	−0.414067	+	0.414067i	0.469085	+	0.883153i	$0.344584\pi$
$824$	−8.27575	+	4.96982i	−0.288299	+	0.173132i
$825$		0			0
$826$	−3.37818	−	18.5362i	−0.117542	−	0.644957i
$827$	−24.1429	+	24.1429i	−0.839530	+	0.839530i	−0.988797	−	0.149267i	$-0.952309\pi$
$827$	−24.1429	+	24.1429i	−0.839530	+	0.839530i	0.149267	+	0.988797i	$0.452309\pi$
$828$	2.69342	−	5.95343i	0.0936027	−	0.206896i
$829$	30.6528			1.06462			0.532309	−	0.846550i	$-0.321325\pi$
$829$	30.6528			1.06462			0.532309	+	0.846550i	$0.321325\pi$
$830$		0			0
$831$			15.9105i			0.551928i
$832$	−22.1866	+	6.77125i	−0.769181	+	0.234751i
$833$	27.4200	+	27.4200i	0.950047	+	0.950047i
$834$	−2.06304	−	11.3200i	−0.0714374	−	0.391980i
$835$		0			0
$836$	−4.18264	+	1.57693i	−0.144660	+	0.0545392i
$837$	1.10919	+	1.10919i	0.0383391	+	0.0383391i
$838$	−2.24383	−	1.55204i	−0.0775119	−	0.0536144i
$839$	−2.59796			−0.0896914			−0.0448457	−	0.998994i	$-0.514280\pi$
$839$	−2.59796			−0.0896914			−0.0448457	+	0.998994i	$0.514280\pi$
$840$		0			0
$841$	−28.5105			−0.983122
$842$	0.528141	+	0.365311i	0.0182009	+	0.0125895i
$843$	−18.3456	−	18.3456i	−0.631858	−	0.631858i
$844$	15.3763	+	40.7840i	0.529274	+	1.40384i
$845$		0			0
$846$	−2.45843	−	13.4895i	−0.0845227	−	0.463779i
$847$	3.84490	+	3.84490i	0.132112	+	0.132112i
$848$	−0.705426	+	10.9520i	−0.0242244	+	0.376095i
$849$		−	0.0554957i		−	0.00190461i
$850$		0			0
$851$	−24.5695			−0.842230
$852$	20.3263	+	9.19590i	0.696367	+	0.315046i
$853$	20.7909	−	20.7909i	0.711866	−	0.711866i	−0.255059	−	0.966925i	$-0.582095\pi$
$853$	20.7909	−	20.7909i	0.711866	−	0.711866i	0.966925	+	0.255059i	$0.0820949\pi$
$854$	−6.41992	−	35.2264i	−0.219685	−	1.20542i
$855$		0			0
$856$	5.35203	−	3.21404i	0.182929	−	0.109854i
$857$	33.7632	−	33.7632i	1.15333	−	1.15333i	0.167446	−	0.985881i	$-0.446448\pi$
$857$	33.7632	−	33.7632i	1.15333	−	1.15333i	0.985881	−	0.167446i	$-0.0535521\pi$
$858$	−8.12072	+	11.7404i	−0.277237	+	0.400809i
$859$		−	31.9834i		−	1.09126i	−0.838027	−	0.545629i	$-0.816291\pi$
$859$		−	31.9834i		−	1.09126i	0.838027	−	0.545629i	$-0.183709\pi$
$860$		0			0
$861$			23.9278i			0.815456i
$862$	8.23422	+	5.69555i	0.280459	+	0.193991i
$863$	2.78203	−	2.78203i	0.0947013	−	0.0947013i	−0.658169	−	0.752870i	$-0.728669\pi$
$863$	2.78203	−	2.78203i	0.0947013	−	0.0947013i	0.752870	+	0.658169i	$0.228669\pi$
$864$	−4.43589	−	3.51039i	−0.150912	−	0.119426i
$865$		0			0
$866$	29.8059	−	5.43206i	1.01285	−	0.184589i
$867$	−8.17236	+	8.17236i	−0.277548	+	0.277548i
$868$	−13.8922	−	6.28505i	−0.471533	−	0.213328i
$869$	−7.30014			−0.247640
$870$		0			0
$871$		−	28.3895i		−	0.961943i
$872$	40.1145	+	10.0121i	1.35845	+	0.339052i
$873$	−8.79083	−	8.79083i	−0.297525	−	0.297525i
$874$	−2.91839	+	0.531870i	−0.0987160	+	0.0179908i
$875$		0			0
$876$	17.3753	−	6.55079i	0.587057	−	0.221331i
$877$	−3.46500	−	3.46500i	−0.117005	−	0.117005i	0.646180	−	0.763185i	$-0.276365\pi$
$877$	−3.46500	−	3.46500i	−0.117005	−	0.117005i	−0.763185	+	0.646180i	$0.776365\pi$
$878$	20.3487	−	29.4187i	0.686736	−	0.992834i
$879$	30.5989			1.03207
$880$		0			0
$881$	11.9117			0.401316			0.200658	−	0.979661i	$-0.435692\pi$
$881$	11.9117			0.401316			0.200658	+	0.979661i	$0.435692\pi$
$882$	−13.3724	+	19.3328i	−0.450271	+	0.650970i
$883$	−14.6270	−	14.6270i	−0.492237	−	0.492237i	0.416774	−	0.909010i	$-0.363161\pi$
$883$	−14.6270	−	14.6270i	−0.492237	−	0.492237i	−0.909010	+	0.416774i	$0.863161\pi$
$884$	12.6593	−	4.77277i	0.425778	−	0.160526i
$885$		0			0
$886$	52.9823	−	9.65590i	1.77998	−	0.324396i
$887$	−5.84575	−	5.84575i	−0.196281	−	0.196281i	0.602123	−	0.798404i	$-0.294322\pi$
$887$	−5.84575	−	5.84575i	−0.196281	−	0.196281i	−0.798404	+	0.602123i	$0.794322\pi$
$888$	−5.15073	+	20.6370i	−0.172847	+	0.692531i
$889$		−	66.1623i		−	2.21901i
$890$		0			0
$891$	−3.48120			−0.116625
$892$	−19.6693	−	8.89868i	−0.658578	−	0.297950i
$893$	−4.40162	+	4.40162i	−0.147295	+	0.147295i
$894$	−3.82706	+	0.697472i	−0.127996	+	0.0233270i
$895$		0			0
$896$	52.3845	+	16.7174i	1.75004	+	0.558489i
$897$	−6.69879	+	6.69879i	−0.223666	+	0.223666i
$898$	26.1536	+	18.0903i	0.872758	+	0.603681i
$899$			1.09743i			0.0366014i
$900$		0			0
$901$		−	6.40081i		−	0.213242i
$902$	13.7880	−	19.9337i	0.459089	−	0.663718i
$903$	17.3277	−	17.3277i	0.576629	−	0.576629i
$904$	−9.38550	−	15.6287i	−0.312157	−	0.519804i
$905$		0			0
$906$	−2.58682	−	14.1940i	−0.0859414	−	0.471564i
$907$	19.5550	−	19.5550i	0.649314	−	0.649314i	−0.303513	−	0.952827i	$-0.598160\pi$
$907$	19.5550	−	19.5550i	0.649314	−	0.649314i	0.952827	+	0.303513i	$0.0981597\pi$
$908$	−22.7898	−	10.3104i	−0.756305	−	0.342163i
$909$	1.40933			0.0467445
$910$		0			0
$911$			20.2174i			0.669832i	0.942248	+	0.334916i	$0.108708\pi$
$911$			20.2174i			0.669832i	−0.942248	+	0.334916i	$0.891292\pi$
$912$	−0.165070	+	2.56278i	−0.00546601	+	0.0848622i
$913$	−23.1377	−	23.1377i	−0.765747	−	0.765747i
$914$	−0.0263758	−	0.144725i	−0.000872435	−	0.00478709i
$915$		0			0
$916$	−16.8995	−	44.8242i	−0.558375	−	1.48103i
$917$	4.35669	+	4.35669i	0.143871	+	0.143871i
$918$	2.71340	+	1.87684i	0.0895556	+	0.0619449i
$919$	58.3013			1.92318			0.961591	−	0.274485i	$-0.0885074\pi$
$919$	58.3013			1.92318			0.961591	+	0.274485i	$0.0885074\pi$
$920$		0			0
$921$	25.6207			0.844232
$922$	39.3009	+	27.1842i	1.29431	+	0.895263i
$923$	−22.8711	−	22.8711i	−0.752812	−	0.752812i
$924$	31.6634	−	11.9376i	1.04165	−	0.392720i
$925$		0			0
$926$	−9.83212	−	53.9493i	−0.323104	−	1.77288i
$927$	2.41334	+	2.41334i	0.0792644	+	0.0792644i
$928$	−0.457848	−	3.93104i	−0.0150296	−	0.129043i
$929$		−	5.05985i		−	0.166008i	−0.996549	−	0.0830041i	$-0.973549\pi$
$929$		−	5.05985i		−	0.166008i	0.996549	−	0.0830041i	$-0.0264515\pi$
$930$		0			0
$931$	10.6717			0.349750
$932$	−5.11033	+	11.2957i	−0.167394	+	0.370002i
$933$	6.81402	−	6.81402i	0.223081	−	0.223081i
$934$	4.23820	+	23.2552i	0.138678	+	0.760933i
$935$		0			0
$936$	4.22227	+	7.03094i	0.138009	+	0.229813i
$937$	10.0055	−	10.0055i	0.326864	−	0.326864i	−0.524529	−	0.851393i	$-0.675758\pi$
$937$	10.0055	−	10.0055i	0.326864	−	0.326864i	0.851393	+	0.524529i	$0.175758\pi$
$938$	−38.2828	+	55.3466i	−1.24998	+	1.80713i
$939$		−	25.7914i		−	0.841669i
$940$		0			0
$941$			23.9169i			0.779667i	0.920885	+	0.389834i	$0.127468\pi$
$941$			23.9169i			0.779667i	−0.920885	+	0.389834i	$0.872532\pi$
$942$	2.12376	+	1.46899i	0.0691958	+	0.0478622i
$943$	11.3737	−	11.3737i	0.370379	−	0.370379i
$944$	7.23893	+	8.23565i	0.235607	+	0.268048i
$945$		0			0
$946$	−24.4200	+	4.45050i	−0.793964	+	0.144698i
$947$	24.5395	−	24.5395i	0.797426	−	0.797426i	−0.185263	−	0.982689i	$-0.559314\pi$
$947$	24.5395	−	24.5395i	0.797426	−	0.797426i	0.982689	+	0.185263i	$0.0593136\pi$
$948$	−1.72875	+	3.82117i	−0.0561472	+	0.124106i
$949$	−26.9216			−0.873912
$950$		0			0
$951$			1.22590i			0.0397524i
$952$	−31.1158	−	7.76613i	−1.00847	−	0.251702i
$953$	0.855191	+	0.855191i	0.0277023	+	0.0277023i	0.720822	−	0.693120i	$-0.243764\pi$
$953$	0.855191	+	0.855191i	0.0277023	+	0.0277023i	−0.693120	+	0.720822i	$0.743764\pi$
$954$	3.81728	−	0.695690i	0.123589	−	0.0225238i
$955$		0			0
$956$	11.8528	+	31.4384i	0.383348	+	1.01679i
$957$	−1.72215	−	1.72215i	−0.0556694	−	0.0556694i
$958$	32.1190	−	46.4354i	1.03772	−	1.50026i
$959$	84.0595			2.71442
$960$		0			0
$961$	28.5394			0.920626
$962$	17.5424	−	25.3615i	0.565589	−	0.817688i
$963$	−1.56073	−	1.56073i	−0.0502939	−	0.0502939i
$964$	−2.45023	−	6.49899i	−0.0789167	−	0.209318i
$965$		0			0
$966$	22.0928	−	4.02636i	0.710824	−	0.129546i
$967$	−15.5174	−	15.5174i	−0.499007	−	0.499007i	0.412122	−	0.911129i	$-0.364788\pi$
$967$	−15.5174	−	15.5174i	−0.499007	−	0.499007i	−0.911129	+	0.412122i	$0.864788\pi$
$968$	−3.07018	−	0.766281i	−0.0986795	−	0.0246292i
$969$		−	1.49779i		−	0.0481160i
$970$		0			0
$971$	−11.2086			−0.359701			−0.179851	−	0.983694i	$-0.557561\pi$
$971$	−11.2086			−0.359701			−0.179851	+	0.983694i	$0.557561\pi$
$972$	−0.824386	+	1.82219i	−0.0264422	+	0.0584469i
$973$	27.9621	−	27.9621i	0.896424	−	0.896424i
$974$	20.7876	−	3.78848i	0.666076	−	0.121391i
$975$		0			0
$976$	13.7569	+	15.6511i	0.440349	+	0.500980i
$977$	19.3780	−	19.3780i	0.619957	−	0.619957i	−0.325563	−	0.945520i	$-0.605554\pi$
$977$	19.3780	−	19.3780i	0.619957	−	0.619957i	0.945520	+	0.325563i	$0.105554\pi$
$978$	−15.3101	−	10.5899i	−0.489564	−	0.338628i
$979$		−	2.55412i		−	0.0816302i
$980$		0			0
$981$		−	14.6177i		−	0.466707i
$982$	−22.3551	+	32.3194i	−0.713379	+	1.03135i
$983$	−14.1500	+	14.1500i	−0.451314	+	0.451314i	−0.895791	−	0.444476i	$-0.853390\pi$
$983$	−14.1500	+	14.1500i	−0.451314	+	0.451314i	0.444476	+	0.895791i	$0.353390\pi$
$984$	−7.16889	−	11.9376i	−0.228536	−	0.380558i
$985$		0			0
$986$	0.413847	+	2.27080i	0.0131796	+	0.0723169i
$987$	33.3211	−	33.3211i	1.06062	−	1.06062i
$988$	1.53469	−	3.39222i	0.0488250	−	0.107921i
$989$	−16.4729			−0.523808
$990$		0			0
$991$		−	45.3242i		−	1.43977i	−0.694093	−	0.719885i	$-0.744195\pi$
$991$		−	45.3242i		−	1.43977i	0.694093	−	0.719885i	$-0.255805\pi$
$992$	8.81392	−	1.02656i	0.279842	−	0.0325932i
$993$	10.2448	+	10.2448i	0.325109	+	0.325109i
$994$	13.7468	+	75.4295i	0.436023	+	2.39248i
$995$		0			0
$996$	−17.5904	+	6.63190i	−0.557374	+	0.210140i
$997$	14.5950	+	14.5950i	0.462228	+	0.462228i	0.899385	−	0.437157i	$-0.144015\pi$
$997$	14.5950	+	14.5950i	0.462228	+	0.462228i	−0.437157	+	0.899385i	$0.644015\pi$
$998$	22.8121	+	15.7790i	0.722104	+	0.499474i
$999$	7.52009			0.237925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.v.b.43.8		24
4.3	odd	2		2400.2.bh.b.943.5		24
5.2	odd	4	inner	600.2.v.b.307.10		24
5.3	odd	4		120.2.v.a.67.3	yes	24
5.4	even	2		120.2.v.a.43.5	yes	24
8.3	odd	2	inner	600.2.v.b.43.10		24
8.5	even	2		2400.2.bh.b.943.6		24
15.8	even	4		360.2.w.e.307.10		24
15.14	odd	2		360.2.w.e.163.8		24
20.3	even	4		480.2.bh.a.367.8		24
20.7	even	4		2400.2.bh.b.1807.6		24
20.19	odd	2		480.2.bh.a.463.11		24
40.3	even	4		120.2.v.a.67.5	yes	24
40.13	odd	4		480.2.bh.a.367.11		24
40.19	odd	2		120.2.v.a.43.3	✓	24
40.27	even	4	inner	600.2.v.b.307.8		24
40.29	even	2		480.2.bh.a.463.8		24
40.37	odd	4		2400.2.bh.b.1807.5		24
60.23	odd	4		1440.2.bi.e.847.10		24
60.59	even	2		1440.2.bi.e.1423.3		24
120.29	odd	2		1440.2.bi.e.1423.10		24
120.53	even	4		1440.2.bi.e.847.3		24
120.59	even	2		360.2.w.e.163.10		24
120.83	odd	4		360.2.w.e.307.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.3	✓	24	40.19	odd	2
120.2.v.a.43.5	yes	24	5.4	even	2
120.2.v.a.67.3	yes	24	5.3	odd	4
120.2.v.a.67.5	yes	24	40.3	even	4
360.2.w.e.163.8		24	15.14	odd	2
360.2.w.e.163.10		24	120.59	even	2
360.2.w.e.307.8		24	120.83	odd	4
360.2.w.e.307.10		24	15.8	even	4
480.2.bh.a.367.8		24	20.3	even	4
480.2.bh.a.367.11		24	40.13	odd	4
480.2.bh.a.463.8		24	40.29	even	2
480.2.bh.a.463.11		24	20.19	odd	2
600.2.v.b.43.8		24	1.1	even	1	trivial
600.2.v.b.43.10		24	8.3	odd	2	inner
600.2.v.b.307.8		24	40.27	even	4	inner
600.2.v.b.307.10		24	5.2	odd	4	inner
1440.2.bi.e.847.3		24	120.53	even	4
1440.2.bi.e.847.10		24	60.23	odd	4
1440.2.bi.e.1423.3		24	60.59	even	2
1440.2.bi.e.1423.10		24	120.29	odd	2
2400.2.bh.b.943.5		24	4.3	odd	2
2400.2.bh.b.943.6		24	8.5	even	2
2400.2.bh.b.1807.5		24	40.37	odd	4
2400.2.bh.b.1807.6		24	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.804501 - 1.16309i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-0.705556 - 1.87141i) q^{4} +(1.39130 - 0.253561i) q^{6} +(3.43671 + 3.43671i) q^{7} +(-2.74424 - 0.684930i) q^{8} +1.00000i q^{9} +3.48120 q^{11} +(0.824386 - 1.82219i) q^{12} +(-2.05033 + 2.05033i) q^{13} +(6.76204 - 1.23237i) q^{14} +(-3.00438 + 2.64077i) q^{16} +(1.64963 - 1.64963i) q^{17} +(1.16309 + 0.804501i) q^{18} -0.642023i q^{19} +4.86024i q^{21} +(2.80063 - 4.04895i) q^{22} +(2.31024 - 2.31024i) q^{23} +(-1.45615 - 2.42479i) q^{24} +(0.735225 + 4.03421i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(4.00672 - 8.85630i) q^{28} -0.699613 q^{29} -1.56863i q^{31} +(0.654430 + 5.61887i) q^{32} +(2.46158 + 2.46158i) q^{33} +(-0.591537 - 3.24579i) q^{34} +(1.87141 - 0.705556i) q^{36} +(-5.31751 - 5.31751i) q^{37} +(-0.746731 - 0.516509i) q^{38} -2.89960 q^{39} +4.92316 q^{41} +(5.65290 + 3.91007i) q^{42} +(-3.56519 - 3.56519i) q^{43} +(-2.45618 - 6.51477i) q^{44} +(-0.828427 - 4.54561i) q^{46} +(-6.85586 - 6.85586i) q^{47} +(-3.99173 - 0.257109i) q^{48} +16.6220i q^{49} +2.33292 q^{51} +(5.28364 + 2.39039i) q^{52} +(1.94008 - 1.94008i) q^{53} +(0.253561 + 1.39130i) q^{54} +(-7.07726 - 11.7851i) q^{56} +(0.453979 - 0.453979i) q^{57} +(-0.562839 + 0.813713i) q^{58} -2.74121i q^{59} -5.20943i q^{61} +(-1.82446 - 1.26196i) q^{62} +(-3.43671 + 3.43671i) q^{63} +(7.06174 + 3.75923i) q^{64} +(4.84339 - 0.882696i) q^{66} +(-6.92316 + 6.92316i) q^{67} +(-4.25104 - 1.92323i) q^{68} +3.26718 q^{69} +11.1548i q^{71} +(0.684930 - 2.74424i) q^{72} +(6.56519 + 6.56519i) q^{73} +(-10.4627 + 1.90680i) q^{74} +(-1.20149 + 0.452983i) q^{76} +(11.9639 + 11.9639i) q^{77} +(-2.33274 + 3.37250i) q^{78} -2.09702 q^{79} -1.00000 q^{81} +(3.96069 - 5.72608i) q^{82} +(-6.64648 - 6.64648i) q^{83} +(9.09553 - 3.42917i) q^{84} +(-7.01483 + 1.27844i) q^{86} +(-0.494701 - 0.494701i) q^{87} +(-9.55327 - 2.38438i) q^{88} -0.733690i q^{89} -14.0928 q^{91} +(-5.95343 - 2.69342i) q^{92} +(1.10919 - 1.10919i) q^{93} +(-13.4895 + 2.45843i) q^{94} +(-3.51039 + 4.43589i) q^{96} +(-8.79083 + 8.79083i) q^{97} +(19.3328 + 13.3724i) q^{98} +3.48120i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{6} + 12 q^{8} + 8 q^{12} - 20 q^{16} - 8 q^{17} + 28 q^{22} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{36} - 40 q^{38} - 20 q^{42} + 32 q^{43} + 48 q^{46} - 16 q^{48} - 16 q^{51} + 48 q^{52}+ \cdots + 88 q^{98}+O(q^{100}) \) 24 * q + 4 * q^6 + 12 * q^8 + 8 * q^12 - 20 * q^16 - 8 * q^17 + 28 * q^22 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^36 - 40 * q^38 - 20 * q^42 + 32 * q^43 + 48 * q^46 - 16 * q^48 - 16 * q^51 + 48 * q^52 - 32 * q^56 + 12 * q^58 + 16 * q^62 - 24 * q^66 - 48 * q^67 - 72 * q^68 - 12 * q^72 + 40 * q^73 + 48 * q^76 + 24 * q^78 - 24 * q^81 - 24 * q^82 - 80 * q^83 - 32 * q^86 - 12 * q^88 + 64 * q^91 - 16 * q^92 - 44 * q^96 + 24 * q^97 + 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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