LMFDB - Embedded newform 403.2.bg.a.123.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [403,2,Mod(123,403)] 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("403.123"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(403, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bg (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			123.11
Character	$\chi$	$=$	403.123
Dual form			403.2.bg.a.154.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.359643 - 1.34220i) q^{2} +(-2.72479 - 1.57316i) q^{3} +(0.0598795 - 0.0345714i) q^{4} +(1.15466 - 1.15466i) q^{5} +(-1.13155 + 4.22301i) q^{6} +(-1.21090 + 4.51915i) q^{7} +(-2.03306 - 2.03306i) q^{8} +(3.44967 + 5.97500i) q^{9} +(-1.96506 - 1.13453i) q^{10} +(1.19523 + 4.46066i) q^{11} -0.217546 q^{12} +(-2.59320 + 2.50506i) q^{13} +6.50112 q^{14} +(-4.96269 + 1.32975i) q^{15} +(-1.92847 + 3.34020i) q^{16} +(-1.22836 - 2.12759i) q^{17} +(6.77903 - 6.77903i) q^{18} +(-3.15936 - 0.846549i) q^{19} +(0.0292223 - 0.109059i) q^{20} +(10.4088 - 10.4088i) q^{21} +(5.55727 - 3.20849i) q^{22} +(-1.22565 + 2.12288i) q^{23} +(2.34134 + 8.73801i) q^{24} +2.33351i q^{25} +(4.29493 + 2.57968i) q^{26} -12.2686i q^{27} +(0.0837253 + 0.312467i) q^{28} +(4.31093 + 2.48892i) q^{29} +(3.56959 + 6.18271i) q^{30} +(-5.29000 - 1.73664i) q^{31} +(-0.377632 - 0.101186i) q^{32} +(3.76058 - 14.0347i) q^{33} +(-2.41388 + 2.41388i) q^{34} +(3.81991 + 6.61628i) q^{35} +(0.413129 + 0.238520i) q^{36} +(-1.09529 - 4.08767i) q^{37} +4.54497i q^{38} +(11.0068 - 2.74624i) q^{39} -4.69500 q^{40} +(-0.673782 - 2.51459i) q^{41} +(-17.7142 - 10.2273i) q^{42} +(4.14220 + 7.17450i) q^{43} +(0.225781 + 0.225781i) q^{44} +(10.8823 + 2.91591i) q^{45} +(3.29014 + 0.881589i) q^{46} +(-4.24420 - 4.24420i) q^{47} +(10.5094 - 6.06758i) q^{48} +(-12.8943 - 7.44451i) q^{49} +(3.13205 - 0.839229i) q^{50} +7.72964i q^{51} +(-0.0686761 + 0.239652i) q^{52} +1.79623i q^{53} +(-16.4670 + 4.41231i) q^{54} +(6.53065 + 3.77047i) q^{55} +(11.6496 - 6.72587i) q^{56} +(7.27686 + 7.27686i) q^{57} +(1.79024 - 6.68127i) q^{58} +(-3.58528 + 13.3804i) q^{59} +(-0.251192 + 0.251192i) q^{60} +(-1.02243 + 0.590303i) q^{61} +(-0.428419 + 7.72483i) q^{62} +(-31.1792 + 8.35443i) q^{63} +8.25712i q^{64} +(-0.101777 + 5.88677i) q^{65} -20.1899 q^{66} +(-3.71837 - 13.8772i) q^{67} +(-0.147107 - 0.0849325i) q^{68} +(6.67927 - 3.85628i) q^{69} +(7.50660 - 7.50660i) q^{70} +(-0.723569 - 0.193880i) q^{71} +(5.13416 - 19.1609i) q^{72} +(-4.08817 + 4.08817i) q^{73} +(-5.09257 + 2.94020i) q^{74} +(3.67098 - 6.35833i) q^{75} +(-0.218448 + 0.0585328i) q^{76} -21.6057 q^{77} +(-7.64454 - 13.7857i) q^{78} +1.76712i q^{79} +(1.63008 + 6.08354i) q^{80} +(-8.95144 + 15.5044i) q^{81} +(-3.13277 + 1.80871i) q^{82} +(8.36517 + 8.36517i) q^{83} +(0.263427 - 0.983123i) q^{84} +(-3.87499 - 1.03830i) q^{85} +(8.13994 - 8.13994i) q^{86} +(-7.83093 - 13.5636i) q^{87} +(6.63883 - 11.4988i) q^{88} +(-2.51809 - 9.39764i) q^{89} -15.6550i q^{90} +(-8.18062 - 14.7525i) q^{91} +0.169489i q^{92} +(11.6821 + 13.0540i) q^{93} +(-4.17019 + 7.22298i) q^{94} +(-4.62548 + 2.67052i) q^{95} +(0.869789 + 0.869789i) q^{96} +(6.29497 + 1.68673i) q^{97} +(-5.35473 + 19.9841i) q^{98} +(-22.5293 + 22.5293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 8 q^{2} - 12 q^{4} - 8 q^{5} - 16 q^{7} - 28 q^{8} + 64 q^{9} - 12 q^{10} + 68 q^{16} - 52 q^{18} - 4 q^{19} - 44 q^{20} - 64 q^{28} - 4 q^{31} - 28 q^{32} + 36 q^{33} + 28 q^{35} - 12 q^{36} - 28 q^{39}+ \cdots - 160 q^{98}+O(q^{100}) $ 144 * q - 8 * q^2 - 12 * q^4 - 8 * q^5 - 16 * q^7 - 28 * q^8 + 64 * q^9 - 12 * q^10 + 68 * q^16 - 52 * q^18 - 4 * q^19 - 44 * q^20 - 64 * q^28 - 4 * q^31 - 28 * q^32 + 36 * q^33 + 28 * q^35 - 12 * q^36 - 28 * q^39 - 48 * q^40 - 8 * q^41 + 12 * q^45 - 24 * q^47 + 48 * q^49 + 40 * q^50 + 48 * q^56 + 8 * q^59 + 42 * q^62 - 84 * q^63 - 80 * q^66 + 4 * q^67 - 24 * q^69 - 96 * q^70 - 80 * q^71 + 104 * q^72 - 116 * q^76 + 24 * q^78 - 112 * q^80 + 16 * q^81 + 108 * q^82 - 92 * q^87 + 64 * q^93 + 4 * q^94 - 132 * q^95 + 120 * q^97 - 160 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	−0.359643	−	1.34220i	−0.254306	−	0.949082i	−0.968475	−	0.249109i	$-0.919862\pi$
$2$	−0.359643	−	1.34220i	−0.254306	−	0.949082i	0.714170	−	0.699973i	$-0.246805\pi$
$3$	−2.72479	−	1.57316i	−1.57316	−	0.908265i	−0.995778	−	0.0917912i	$-0.970741\pi$
$3$	−2.72479	−	1.57316i	−1.57316	−	0.908265i	−0.577383	−	0.816474i	$-0.695926\pi$
$4$	0.0598795	−	0.0345714i	0.0299397	−	0.0172857i
$5$	1.15466	−	1.15466i	0.516381	−	0.516381i	−0.400093	−	0.916474i	$-0.631022\pi$
$5$	1.15466	−	1.15466i	0.516381	−	0.516381i	0.916474	+	0.400093i	$0.131022\pi$
$6$	−1.13155	+	4.22301i	−0.461954	+	1.72404i
$7$	−1.21090	+	4.51915i	−0.457678	+	1.70808i	0.222414	+	0.974952i	$0.428606\pi$
$7$	−1.21090	+	4.51915i	−0.457678	+	1.70808i	−0.680092	+	0.733127i	$0.738060\pi$
$8$	−2.03306	−	2.03306i	−0.718796	−	0.718796i
$9$	3.44967	+	5.97500i	1.14989	+	1.99167i
$10$	−1.96506	−	1.13453i	−0.621407	−	0.358769i
$11$	1.19523	+	4.46066i	0.360376	+	1.34494i	0.873583	+	0.486676i	$0.161791\pi$
$11$	1.19523	+	4.46066i	0.360376	+	1.34494i	−0.513207	+	0.858265i	$0.671543\pi$
$12$	−0.217546			−0.0628001
$13$	−2.59320	+	2.50506i	−0.719225	+	0.694778i
$13$	−2.59320	+	2.50506i	−0.719225	+	0.694778i
$14$	6.50112			1.73750
$15$	−4.96269	+	1.32975i	−1.28136	+	0.343340i
$16$	−1.92847	+	3.34020i	−0.482117	+	0.835051i
$17$	−1.22836	−	2.12759i	−0.297922	−	0.516015i	0.677739	−	0.735303i	$-0.262960\pi$
$17$	−1.22836	−	2.12759i	−0.297922	−	0.516015i	−0.975660	+	0.219288i	$0.929627\pi$
$18$	6.77903	−	6.77903i	1.59783	−	1.59783i
$19$	−3.15936	−	0.846549i	−0.724808	−	0.194212i	−0.122492	−	0.992470i	$-0.539089\pi$
$19$	−3.15936	−	0.846549i	−0.724808	−	0.194212i	−0.602316	+	0.798258i	$0.705755\pi$
$20$	0.0292223	−	0.109059i	0.00653430	−	0.0243863i
$21$	10.4088	−	10.4088i	2.27139	−	2.27139i
$22$	5.55727	−	3.20849i	1.18481	−	0.684052i
$23$	−1.22565	+	2.12288i	−0.255565	+	0.442651i	−0.965049	−	0.262070i	$-0.915595\pi$
$23$	−1.22565	+	2.12288i	−0.255565	+	0.442651i	0.709484	+	0.704722i	$0.248928\pi$
$24$	2.34134	+	8.73801i	0.477925	+	1.78364i
$25$			2.33351i			0.466702i
$26$	4.29493	+	2.57968i	0.842304	+	0.505917i
$27$		−	12.2686i		−	2.36109i
$28$	0.0837253	+	0.312467i	0.0158226	+	0.0590508i
$29$	4.31093	+	2.48892i	0.800519	+	0.462180i	0.843653	−	0.536889i	$-0.180401\pi$
$29$	4.31093	+	2.48892i	0.800519	+	0.462180i	−0.0431333	+	0.999069i	$0.513734\pi$
$30$	3.56959	+	6.18271i	0.651715	+	1.12880i
$31$	−5.29000	−	1.73664i	−0.950112	−	0.311910i
$31$	−5.29000	−	1.73664i	−0.950112	−	0.311910i
$32$	−0.377632	−	0.101186i	−0.0667566	−	0.0178874i
$33$	3.76058	−	14.0347i	0.654633	−	2.44312i
$34$	−2.41388	+	2.41388i	−0.413978	+	0.413978i
$35$	3.81991	+	6.61628i	0.645683	+	1.11836i
$36$	0.413129	+	0.238520i	0.0688549	+	0.0397534i
$37$	−1.09529	−	4.08767i	−0.180064	−	0.672008i	−0.995633	−	0.0933490i	$-0.970243\pi$
$37$	−1.09529	−	4.08767i	−0.180064	−	0.672008i	0.815569	−	0.578659i	$-0.196424\pi$
$38$			4.54497i			0.737291i
$39$	11.0068	−	2.74624i	1.76250	−	0.439751i
$40$	−4.69500			−0.742345
$41$	−0.673782	−	2.51459i	−0.105227	−	0.392713i	0.893144	−	0.449771i	$-0.148494\pi$
$41$	−0.673782	−	2.51459i	−0.105227	−	0.392713i	−0.998371	+	0.0570586i	$0.981828\pi$
$42$	−17.7142	−	10.2273i	−2.73336	−	1.57811i
$43$	4.14220	+	7.17450i	0.631679	+	1.09410i	0.987208	+	0.159436i	$0.0509674\pi$
$43$	4.14220	+	7.17450i	0.631679	+	1.09410i	−0.355529	+	0.934665i	$0.615699\pi$
$44$	0.225781	+	0.225781i	0.0340378	+	0.0340378i
$45$	10.8823	+	2.91591i	1.62224	+	0.434678i
$46$	3.29014	+	0.881589i	0.485104	+	0.129983i
$47$	−4.24420	−	4.24420i	−0.619080	−	0.619080i	0.326215	−	0.945296i	$-0.394227\pi$
$47$	−4.24420	−	4.24420i	−0.619080	−	0.619080i	−0.945296	+	0.326215i	$0.894227\pi$
$48$	10.5094	−	6.06758i	1.51689	−	0.875779i
$49$	−12.8943	−	7.44451i	−1.84204	−	1.06350i
$50$	3.13205	−	0.839229i	0.442938	−	0.118685i
$51$			7.72964i			1.08237i
$52$	−0.0686761	+	0.239652i	−0.00952367	+	0.0332338i
$53$			1.79623i			0.246732i	0.992361	+	0.123366i	$0.0393689\pi$
$53$			1.79623i			0.246732i	−0.992361	+	0.123366i	$0.960631\pi$
$54$	−16.4670	+	4.41231i	−2.24087	+	0.600439i
$55$	6.53065	+	3.77047i	0.880593	+	0.508410i
$56$	11.6496	−	6.72587i	1.55674	−	0.898783i
$57$	7.27686	+	7.27686i	0.963844	+	0.963844i
$58$	1.79024	−	6.68127i	0.235070	−	0.877294i
$59$	−3.58528	+	13.3804i	−0.466763	+	1.74198i	0.184214	+	0.982886i	$0.441026\pi$
$59$	−3.58528	+	13.3804i	−0.466763	+	1.74198i	−0.650977	+	0.759098i	$0.725640\pi$
$60$	−0.251192	+	0.251192i	−0.0324287	+	0.0324287i
$61$	−1.02243	+	0.590303i	−0.130909	+	0.0755805i	−0.564024	−	0.825758i	$-0.690748\pi$
$61$	−1.02243	+	0.590303i	−0.130909	+	0.0755805i	0.433115	+	0.901339i	$0.357414\pi$
$62$	−0.428419	+	7.72483i	−0.0544092	+	0.981055i
$63$	−31.1792	+	8.35443i	−3.92821	+	1.05256i
$64$			8.25712i			1.03214i
$65$	−0.101777	+	5.88677i	−0.0126239	+	0.730164i
$66$	−20.1899			−2.48520
$67$	−3.71837	−	13.8772i	−0.454272	−	1.69536i	−0.690220	−	0.723599i	$-0.742486\pi$
$67$	−3.71837	−	13.8772i	−0.454272	−	1.69536i	0.235948	−	0.971766i	$-0.424180\pi$
$68$	−0.147107	−	0.0849325i	−0.0178394	−	0.0102996i
$69$	6.67927	−	3.85628i	0.804089	−	0.464241i
$70$	7.50660	−	7.50660i	0.897211	−	0.897211i
$71$	−0.723569	−	0.193880i	−0.0858718	−	0.0230093i	0.215627	−	0.976476i	$-0.430820\pi$
$71$	−0.723569	−	0.193880i	−0.0858718	−	0.0230093i	−0.301499	+	0.953466i	$0.597487\pi$
$72$	5.13416	−	19.1609i	0.605067	−	2.25814i
$73$	−4.08817	+	4.08817i	−0.478484	+	0.478484i	−0.904647	−	0.426162i	$-0.859865\pi$
$73$	−4.08817	+	4.08817i	−0.478484	+	0.478484i	0.426162	+	0.904647i	$0.359865\pi$
$74$	−5.09257	+	2.94020i	−0.592000	+	0.341791i
$75$	3.67098	−	6.35833i	0.423889	−	0.734197i
$76$	−0.218448	+	0.0585328i	−0.0250577	+	0.00671418i
$77$	−21.6057			−2.46220
$78$	−7.64454	−	13.7857i	−0.865573	−	1.56092i
$79$			1.76712i			0.198816i	0.995047	+	0.0994082i	$0.0316950\pi$
$79$			1.76712i			0.198816i	−0.995047	+	0.0994082i	$0.968305\pi$
$80$	1.63008	+	6.08354i	0.182248	+	0.680160i
$81$	−8.95144	+	15.5044i	−0.994605	+	1.72271i
$82$	−3.13277	+	1.80871i	−0.345957	+	0.199738i
$83$	8.36517	+	8.36517i	0.918197	+	0.918197i	0.996898	−	0.0787011i	$-0.0250773\pi$
$83$	8.36517	+	8.36517i	0.918197	+	0.918197i	−0.0787011	+	0.996898i	$0.525077\pi$
$84$	0.263427	−	0.983123i	0.0287422	−	0.107267i
$85$	−3.87499	−	1.03830i	−0.420301	−	0.112619i
$86$	8.13994	−	8.13994i	0.877752	−	0.877752i
$87$	−7.83093	−	13.5636i	−0.839564	−	1.45417i
$88$	6.63883	−	11.4988i	0.707701	−	1.22577i
$89$	−2.51809	−	9.39764i	−0.266917	−	0.996148i	−0.961066	−	0.276317i	$-0.910886\pi$
$89$	−2.51809	−	9.39764i	−0.266917	−	0.996148i	0.694149	−	0.719831i	$-0.255781\pi$
$90$		−	15.6550i		−	1.65018i
$91$	−8.18062	−	14.7525i	−0.857562	−	1.54648i
$92$			0.169489i			0.0176705i
$93$	11.6821	+	13.0540i	1.21138	+	1.35364i
$94$	−4.17019	+	7.22298i	−0.430122	+	0.744994i
$95$	−4.62548	+	2.67052i	−0.474564	+	0.273990i
$96$	0.869789	+	0.869789i	0.0887724	+	0.0887724i
$97$	6.29497	+	1.68673i	0.639157	+	0.171262i	0.563822	−	0.825897i	$-0.309331\pi$
$97$	6.29497	+	1.68673i	0.639157	+	0.171262i	0.0753355	+	0.997158i	$0.475997\pi$
$98$	−5.35473	+	19.9841i	−0.540909	+	2.01870i
$99$	−22.5293	+	22.5293i	−2.26428	+	2.26428i
$100$	0.0806728	+	0.139729i	0.00806728	+	0.0139729i
$101$	5.21989	+	3.01370i	0.519398	+	0.299875i	0.736688	−	0.676232i	$-0.236388\pi$
$101$	5.21989	+	3.01370i	0.519398	+	0.299875i	−0.217290	+	0.976107i	$0.569722\pi$
$102$	10.3748	−	2.77991i	1.02725	−	0.275252i
$103$			13.8657i			1.36623i	0.730312	+	0.683114i	$0.239375\pi$
$103$			13.8657i			1.36623i	−0.730312	+	0.683114i	$0.760625\pi$
$104$	10.3651	+	0.179203i	1.01638	+	0.0175723i
$105$		−	24.0373i		−	2.34580i
$106$	2.41091	−	0.646002i	0.234169	−	0.0627453i
$107$	−3.68084	+	6.37540i	−0.355840	+	0.616333i	−0.987261	−	0.159107i	$-0.949138\pi$
$107$	−3.68084	+	6.37540i	−0.355840	+	0.616333i	0.631421	+	0.775440i	$0.282472\pi$
$108$	−0.424143	−	0.734637i	−0.0408131	−	0.0706904i
$109$	−1.60060	+	1.60060i	−0.153310	+	0.153310i	−0.779595	−	0.626285i	$-0.784575\pi$
$109$	−1.60060	+	1.60060i	−0.153310	+	0.153310i	0.626285	+	0.779595i	$0.284575\pi$
$110$	2.71205	−	10.1215i	0.258583	−	0.965047i
$111$	−3.44613	+	12.8611i	−0.327092	+	1.22072i
$112$	−12.7597	−	12.7597i	−1.20568	−	1.20568i
$113$	−4.51503	−	7.82026i	−0.424738	−	0.735668i	0.571658	−	0.820492i	$-0.306301\pi$
$113$	−4.51503	−	7.82026i	−0.424738	−	0.735668i	−0.996396	+	0.0848240i	$0.972967\pi$
$114$	7.14997	−	12.3841i	0.669656	−	1.15988i
$115$	1.03600	+	3.86642i	0.0966079	+	0.360545i
$116$	0.344182			0.0319565
$117$	−23.9134	−	6.85277i	−2.21080	−	0.633539i
$118$	19.2487			1.77199
$119$	11.1023	−	2.97485i	1.01775	−	0.272704i
$120$	12.7929	+	7.38599i	1.16783	+	0.674246i
$121$	−8.94266	+	5.16305i	−0.812969	+	0.469368i
$122$	1.16002	+	1.16002i	0.105023	+	0.105023i
$123$	−2.11993	+	7.91170i	−0.191148	+	0.713374i
$124$	−0.376801	+	0.0788937i	−0.0338377	+	0.00708486i
$125$	8.46773	+	8.46773i	0.757377	+	0.757377i
$126$	22.4267	+	38.8442i	1.99793	+	3.46052i
$127$	−2.65908	+	4.60567i	−0.235956	+	0.408687i	−0.959550	−	0.281538i	$-0.909155\pi$
$127$	−2.65908	+	4.60567i	−0.235956	+	0.408687i	0.723594	+	0.690225i	$0.242489\pi$
$128$	10.3275	−	2.76724i	0.912829	−	0.244592i
$129$		−	26.0654i		−	2.29493i
$130$	7.93785	−	1.98053i	0.696196	−	0.173704i
$131$	5.07578			0.443473			0.221736	−	0.975107i	$-0.428828\pi$
$131$	5.07578			0.443473			0.221736	+	0.975107i	$0.428828\pi$
$132$	−0.260018	−	0.970399i	−0.0226316	−	0.0844624i
$133$	7.65137	−	13.2526i	0.663458	−	1.14914i
$134$	−17.2887	+	9.98164i	−1.49352	+	0.862282i
$135$	−14.1661	−	14.1661i	−1.21922	−	1.21922i
$136$	−1.82818	+	6.82285i	−0.156765	+	0.585054i
$137$	2.54640	+	0.682307i	0.217554	+	0.0582934i	0.365950	−	0.930635i	$-0.380744\pi$
$137$	2.54640	+	0.682307i	0.217554	+	0.0582934i	−0.148396	+	0.988928i	$0.547411\pi$
$138$	−7.57806	−	7.57806i	−0.645088	−	0.645088i
$139$	12.3594	−	7.13571i	1.04831	−	0.605243i	0.126136	−	0.992013i	$-0.459743\pi$
$139$	12.3594	−	7.13571i	1.04831	−	0.605243i	0.922176	+	0.386770i	$0.126409\pi$
$140$	0.457469	+	0.264120i	0.0386632	+	0.0223222i
$141$	4.88777	+	18.2414i	0.411624	+	1.53620i
$142$			1.04091i			0.0873508i
$143$	−14.2737	−	8.57327i	−1.19363	−	0.716933i
$144$	−26.6103			−2.21753
$145$	7.85153	−	2.10381i	0.652034	−	0.174712i
$146$	6.95744	+	4.01688i	0.575802	+	0.332440i
$147$	23.4228	+	40.5695i	1.93188	+	3.34612i
$148$	−0.206902	−	0.206902i	−0.0170072	−	0.0170072i
$149$	20.8877	+	5.59683i	1.71118	+	0.458510i	0.975714	−	0.219047i	$-0.0702948\pi$
$149$	20.8877	+	5.59683i	1.71118	+	0.458510i	0.735470	+	0.677557i	$0.236961\pi$
$150$	−9.85443	−	2.64049i	−0.804611	−	0.215595i
$151$	−2.24565	+	2.24565i	−0.182748	+	0.182748i	−0.792552	−	0.609804i	$-0.791248\pi$
$151$	−2.24565	+	2.24565i	−0.182748	+	0.182748i	0.609804	+	0.792552i	$0.291248\pi$
$152$	4.70210	+	8.14427i	0.381390	+	0.660587i
$153$	8.47489	−	14.6789i	0.685154	−	1.18672i
$154$	7.77034	+	28.9993i	0.626152	+	2.33683i
$155$	−8.11340	+	4.10293i	−0.651684	+	0.329555i
$156$	0.564140	−	0.544965i	0.0451673	−	0.0436321i
$157$	8.28232			0.661001			0.330500	−	0.943806i	$-0.392782\pi$
$157$	8.28232			0.661001			0.330500	+	0.943806i	$0.392782\pi$
$158$	2.37184	−	0.635532i	0.188693	−	0.0505602i
$159$	2.82576	−	4.89437i	0.224098	−	0.388149i
$160$	−0.552874	+	0.319202i	−0.0437085	+	0.0252351i
$161$	−8.10949	−	8.10949i	−0.639117	−	0.639117i
$162$	24.0293	+	6.43864i	1.88792	+	0.505868i
$163$	−1.19078	+	4.44403i	−0.0932687	+	0.348084i	−0.996751	−	0.0805413i	$-0.974335\pi$
$163$	−1.19078	+	4.44403i	−0.0932687	+	0.348084i	0.903483	+	0.428625i	$0.141002\pi$
$164$	−0.127279	−	0.127279i	−0.00993879	−	0.00993879i
$165$	−11.8631	−	20.5475i	−0.923543	−	1.59962i
$166$	8.21930	−	14.2363i	0.637942	−	1.10495i
$167$	−4.94354	−	18.4495i	−0.382542	−	1.42767i	−0.842005	−	0.539470i	$-0.818624\pi$
$167$	−4.94354	−	18.4495i	−0.382542	−	1.42767i	0.459462	−	0.888197i	$-0.348042\pi$
$168$	−42.3235			−3.26533
$169$	0.449383	−	12.9922i	0.0345679	−	0.999402i
$170$			5.57444i			0.427540i
$171$	−5.84063	−	21.7975i	−0.446644	−	1.66690i
$172$	0.496066	+	0.286404i	0.0378246	+	0.0218381i
$173$	6.97955	−	4.02965i	0.530646	−	0.306368i	−0.210634	−	0.977565i	$-0.567553\pi$
$173$	6.97955	−	4.02965i	0.530646	−	0.306368i	0.741279	+	0.671197i	$0.234219\pi$
$174$	−15.3888	+	15.3888i	−1.16662	+	1.16662i
$175$	−10.5455	−	2.82565i	−0.797163	−	0.213599i
$176$	−17.2045	−	4.60993i	−1.29684	−	0.347486i
$177$	30.8187	−	30.8187i	2.31648	−	2.31648i
$178$	−11.7080	+	6.75959i	−0.877548	+	0.506653i
$179$	−3.25954	+	5.64570i	−0.243630	+	0.421979i	−0.961745	−	0.273945i	$-0.911672\pi$
$179$	−3.25954	+	5.64570i	−0.243630	+	0.421979i	0.718116	+	0.695924i	$0.245005\pi$
$180$	0.752435	−	0.201614i	0.0560832	−	0.0150274i
$181$	0.245726			0.0182647			0.00913234	−	0.999958i	$-0.497093\pi$
$181$	0.245726			0.0182647			0.00913234	+	0.999958i	$0.497093\pi$
$182$	−16.8587	+	16.2857i	−1.24965	+	1.20717i
$183$	3.71456			0.274588
$184$	6.80776	−	1.82413i	0.501875	−	0.134477i
$185$	−5.98456	−	3.45519i	−0.439994	−	0.254031i
$186$	13.3198	−	20.3746i	0.976652	−	1.49394i
$187$	8.02226	−	8.02226i	0.586646	−	0.586646i
$188$	−0.400869	−	0.107412i	−0.0292364	−	0.00783386i
$189$	55.4436	+	14.8561i	4.03293	+	1.08062i
$190$	5.24791	+	5.24791i	0.380723	+	0.380723i
$191$	−3.90719	−	6.76746i	−0.282715	−	0.489676i	0.689338	−	0.724440i	$-0.257902\pi$
$191$	−3.90719	−	6.76746i	−0.282715	−	0.489676i	−0.972052	+	0.234764i	$0.924568\pi$
$192$	12.9898	−	22.4990i	0.937456	−	1.62372i
$193$	−19.7583	+	5.29423i	−1.42224	+	0.381087i	−0.886276	−	0.463157i	$-0.846717\pi$
$193$	−19.7583	+	5.29423i	−1.42224	+	0.381087i	−0.535959	+	0.844244i	$0.680050\pi$
$194$		−	9.05576i		−	0.650166i
$195$	9.53815	−	15.8801i	0.683041	−	1.13720i
$196$	−1.02947			−0.0735336
$197$	−19.8970	+	5.33138i	−1.41760	+	0.379845i	−0.884632	−	0.466289i	$-0.845591\pi$
$197$	−19.8970	+	5.33138i	−1.41760	+	0.379845i	−0.532970	+	0.846134i	$0.678924\pi$
$198$	38.3415	+	22.1365i	2.72481	+	1.57317i
$199$	−5.50402	−	9.53324i	−0.390170	−	0.675794i	0.602302	−	0.798268i	$-0.294250\pi$
$199$	−5.50402	−	9.53324i	−0.390170	−	0.675794i	−0.992472	+	0.122475i	$0.960917\pi$
$200$	4.74417	−	4.74417i	0.335463	−	0.335463i
$201$	−11.6992	+	43.6620i	−0.825198	+	3.07968i
$202$	2.16771	−	8.09002i	0.152520	−	0.569212i
$203$	−16.4679	+	16.4679i	−1.15582	+	1.15582i
$204$	0.267225	+	0.462847i	0.0187095	+	0.0324058i
$205$	−3.68149	−	2.12551i	−0.257126	−	0.148452i
$206$	18.6106	−	4.98670i	1.29666	−	0.347440i
$207$	−16.9123			−1.17549
$208$	−3.36649	−	13.4927i	−0.233424	−	0.935553i
$209$		−	15.1047i		−	1.04481i
$210$	−32.2630	+	8.64486i	−2.22636	+	0.596552i
$211$	4.76593	−	8.25483i	0.328100	−	0.568286i	−0.654035	−	0.756465i	$-0.726925\pi$
$211$	4.76593	−	8.25483i	0.328100	−	0.568286i	0.982135	+	0.188178i	$0.0602583\pi$
$212$	0.0620984	+	0.107558i	0.00426494	+	0.00738708i
$213$	1.66657	+	1.66657i	0.114192	+	0.114192i
$214$	9.88087	+	2.64757i	0.675443	+	0.180984i
$215$	13.0670	+	3.50128i	0.891160	+	0.238786i
$216$	−24.9428	+	24.9428i	−1.69714	+	1.69714i
$217$	14.2538	−	21.8034i	0.967612	−	1.48011i
$218$	2.72398	+	1.57269i	0.184492	+	0.106516i
$219$	17.5708	−	4.70808i	1.18732	−	0.318142i
$220$	0.521403			0.0351530
$221$	8.51511	+	2.44014i	0.572788	+	0.164142i
$222$	18.5016			1.24175
$223$	−18.1644	+	4.86714i	−1.21638	+	0.325928i	−0.809262	−	0.587448i	$-0.800133\pi$
$223$	−18.1644	+	4.86714i	−1.21638	+	0.325928i	−0.407118	+	0.913376i	$0.633466\pi$
$224$	0.914553	−	1.58405i	0.0611061	−	0.105839i
$225$	−13.9427	+	8.04984i	−0.929515	+	0.536656i
$226$	−8.87260	+	8.87260i	−0.590196	+	0.590196i
$227$	−2.48201	−	0.665052i	−0.164737	−	0.0441411i	0.175508	−	0.984478i	$-0.443843\pi$
$227$	−2.48201	−	0.665052i	−0.164737	−	0.0441411i	−0.340245	+	0.940337i	$0.610510\pi$
$228$	0.687306	+	0.184163i	0.0455180	+	0.0121965i
$229$	−9.97373	+	9.97373i	−0.659082	+	0.659082i	−0.955163	−	0.296081i	$-0.904320\pi$
$229$	−9.97373	+	9.97373i	−0.659082	+	0.659082i	0.296081	+	0.955163i	$0.404320\pi$
$230$	4.81694	−	2.78106i	0.317619	−	0.183378i
$231$	58.8712	+	33.9893i	3.87344	+	2.23633i
$232$	−3.70427	−	13.8245i	−0.243197	−	0.907623i
$233$			10.6149i			0.695405i	0.937605	+	0.347703i	$0.113038\pi$
$233$			10.6149i			0.695405i	−0.937605	+	0.347703i	$0.886962\pi$
$234$	−0.597534	+	34.5613i	−0.0390620	+	2.25934i
$235$	−9.80124			−0.639363
$236$	0.247896	+	0.925162i	0.0161367	+	0.0602229i
$237$	2.77996	−	4.81504i	0.180578	−	0.312770i
$238$	−7.98573	−	13.8317i	−0.517638	−	0.896575i
$239$	2.81051	+	2.81051i	0.181797	+	0.181797i	0.792138	−	0.610342i	$-0.208968\pi$
$239$	2.81051	+	2.81051i	0.181797	+	0.181797i	−0.610342	+	0.792138i	$0.708968\pi$
$240$	5.12875	−	19.1408i	0.331059	−	1.23553i
$241$	−18.8637	−	5.05451i	−1.21512	−	0.325589i	−0.406349	−	0.913718i	$-0.633198\pi$
$241$	−18.8637	−	5.05451i	−1.21512	−	0.325589i	−0.808767	+	0.588129i	$0.799865\pi$
$242$	10.1460	+	10.1460i	0.652212	+	0.652212i
$243$	16.9070	−	9.76125i	1.08458	−	0.626184i
$244$	−0.0408152	+	0.0706940i	−0.00261293	+	0.00452572i
$245$	−23.4844	+	6.29264i	−1.50037	+	0.402022i
$246$	11.3815			0.725661
$247$	10.3135	−	5.71911i	0.656233	−	0.363898i
$248$	7.22419	+	14.2856i	0.458737	+	0.907136i
$249$	−9.63362	−	35.9531i	−0.610506	−	2.27844i
$250$	8.32007	−	14.4108i	0.526207	−	0.911418i
$251$	−1.78510	−	3.09188i	−0.112674	−	0.195157i	0.804173	−	0.594395i	$-0.202608\pi$
$251$	−1.78510	−	3.09188i	−0.112674	−	0.195157i	−0.916848	+	0.399237i	$0.869275\pi$
$252$	−1.57817	+	1.57817i	−0.0994153	+	0.0994153i
$253$	−10.9344	−	2.92986i	−0.687439	−	0.184199i
$254$	7.13807	+	1.91264i	0.447882	+	0.120010i
$255$	8.92513	+	8.92513i	0.558913	+	0.558913i
$256$	0.828712	+	1.43537i	0.0517945	+	0.0897107i
$257$	19.5544	+	11.2898i	1.21977	+	0.704236i	0.964869	−	0.262731i	$-0.0846231\pi$
$257$	19.5544	+	11.2898i	1.21977	+	0.704236i	0.254903	+	0.966967i	$0.417956\pi$
$258$	−34.9851	+	9.37423i	−2.17808	+	0.583614i
$259$	19.7991			1.23025
$260$	0.197420	+	0.356015i	0.0122435	+	0.0220791i
$261$			34.3438i			2.12583i
$262$	−1.82547	−	6.81273i	−0.112778	−	0.420892i
$263$	23.9227	+	13.8118i	1.47514	+	0.851670i	0.999607	−	0.0280305i	$-0.00892354\pi$
$263$	23.9227	+	13.8118i	1.47514	+	0.851670i	0.475528	+	0.879700i	$0.342257\pi$
$264$	−36.1789	+	20.8879i	−2.22666	+	1.28556i
$265$	2.07404	+	2.07404i	0.127408	+	0.127408i
$266$	−20.5394	−	5.50352i	−1.25935	−	0.337442i
$267$	−7.92272	+	29.5680i	−0.484863	+	1.80953i
$268$	−0.702408	−	0.702408i	−0.0429064	−	0.0429064i
$269$	−4.72311	+	2.72689i	−0.287973	+	0.166261i	−0.637028	−	0.770841i	$-0.719836\pi$
$269$	−4.72311	+	2.72689i	−0.287973	+	0.166261i	0.349054	+	0.937103i	$0.386503\pi$
$270$	−13.9191	+	24.1085i	−0.847086	+	1.46720i
$271$	−4.69486	−	17.5215i	−0.285192	−	1.06435i	−0.948699	−	0.316182i	$-0.897599\pi$
$271$	−4.69486	−	17.5215i	−0.285192	−	1.06435i	0.663506	−	0.748171i	$-0.269068\pi$
$272$	9.47542			0.574532
$273$	−0.917479	+	53.0668i	−0.0555283	+	3.21175i
$274$		−	3.66318i		−	0.221301i
$275$	−10.4090	+	2.78908i	−0.627686	+	0.168188i
$276$	0.266634	−	0.461824i	0.0160495	−	0.0277985i
$277$	2.02710	+	3.51104i	0.121797	+	0.210958i	0.920476	−	0.390798i	$-0.127801\pi$
$277$	2.02710	+	3.51104i	0.121797	+	0.210958i	−0.798680	+	0.601757i	$0.794468\pi$
$278$	−14.0226	−	14.0226i	−0.841017	−	0.841017i
$279$	−7.87231	−	37.5986i	−0.471303	−	2.25097i
$280$	5.68519	−	21.2174i	0.339755	−	1.26798i
$281$	−1.25080	−	1.25080i	−0.0746165	−	0.0746165i	0.668814	−	0.743430i	$-0.266802\pi$
$281$	−1.25080	−	1.25080i	−0.0746165	−	0.0746165i	−0.743430	+	0.668814i	$0.766802\pi$
$282$	22.7258	−	13.1208i	1.35330	−	0.781330i
$283$	−6.12816	−	3.53809i	−0.364281	−	0.210318i	0.306676	−	0.951814i	$-0.400783\pi$
$283$	−6.12816	−	3.53809i	−0.364281	−	0.210318i	−0.670957	+	0.741496i	$0.734117\pi$
$284$	−0.0500297	+	0.0134054i	−0.00296871	+	0.000795464i
$285$	16.8046			0.995421
$286$	−6.37366	+	22.2415i	−0.376883	+	1.31517i
$287$	12.1797			0.718944
$288$	−0.698119	−	2.60542i	−0.0411371	−	0.153526i
$289$	5.48225	−	9.49554i	0.322486	−	0.558561i
$290$	−5.64749	−	9.78174i	−0.331632	−	0.574404i
$291$	−14.4990	−	14.4990i	−0.849946	−	0.849946i
$292$	−0.103464	+	0.386132i	−0.00605475	+	0.0225966i
$293$	0.731319	−	2.72932i	0.0427241	−	0.159449i	−0.941268	−	0.337660i	$-0.890365\pi$
$293$	0.731319	−	2.72932i	0.0427241	−	0.159449i	0.983992	+	0.178212i	$0.0570312\pi$
$294$	46.0288	−	46.0288i	2.68445	−	2.68445i
$295$	11.3101	+	19.5897i	0.658500	+	1.14055i
$296$	−6.08369	+	10.5373i	−0.353607	+	0.612466i
$297$	54.7260	−	14.6638i	3.17553	−	0.850880i
$298$		−	30.0484i		−	1.74066i
$299$	−2.13959	−	8.57537i	−0.123736	−	0.495927i
$300$		−	0.507645i		−	0.0293089i
$301$	−37.4385	+	10.0316i	−2.15792	+	0.578212i
$302$	3.82175	+	2.20649i	0.219917	+	0.126969i
$303$	−9.48208	−	16.4235i	−0.544731	−	0.943503i
$304$	8.92037	−	8.92037i	0.511618	−	0.511618i
$305$	−0.498966	+	1.86217i	−0.0285707	+	0.106627i
$306$	−22.7501	−	6.09586i	−1.30054	−	0.348477i
$307$	16.9188	+	16.9188i	0.965607	+	0.965607i	0.999428	−	0.0338210i	$-0.0107676\pi$
$307$	16.9188	+	16.9188i	0.965607	+	0.965607i	−0.0338210	+	0.999428i	$0.510768\pi$
$308$	−1.29374	+	0.746941i	−0.0737177	+	0.0425609i
$309$	21.8130	−	37.7812i	1.24090	−	2.14930i
$310$	8.42490	+	9.41425i	0.478502	+	0.534694i
$311$		−	10.9868i		−	0.623003i	−0.950246	−	0.311501i	$-0.899168\pi$
$311$		−	10.9868i		−	0.623003i	0.950246	−	0.311501i	$-0.100832\pi$
$312$	−27.9608	−	16.7942i	−1.58297	−	0.950785i
$313$			17.6631i			0.998375i	0.866494	+	0.499188i	$0.166368\pi$
$313$			17.6631i			0.998375i	−0.866494	+	0.499188i	$0.833632\pi$
$314$	−2.97868	−	11.1166i	−0.168096	−	0.627344i
$315$	−26.3549	+	45.6480i	−1.48493	+	2.57197i
$316$	0.0610919	+	0.105814i	0.00343669	+	0.00595252i
$317$	6.01496	−	6.01496i	0.337834	−	0.337834i	−0.517718	−	0.855551i	$-0.673218\pi$
$317$	6.01496	−	6.01496i	0.337834	−	0.337834i	0.855551	+	0.517718i	$0.173218\pi$
$318$	−7.58551	−	2.03253i	−0.425374	−	0.113979i
$319$	−5.94966	+	22.2044i	−0.333117	+	1.24321i
$320$	9.53419	+	9.53419i	0.532977	+	0.532977i
$321$	20.0590	−	11.5811i	1.11959	−	0.646394i
$322$	−7.96807	+	13.8011i	−0.444043	+	0.769106i
$323$	2.07974	+	7.76168i	0.115720	+	0.431872i
$324$			1.23786i			0.0687699i
$325$	−5.84557	−	6.05126i	−0.324254	−	0.335663i
$326$	6.39306			0.354079
$327$	6.87933	−	1.84331i	0.380428	−	0.101935i
$328$	−3.74247	+	6.48215i	−0.206643	+	0.357917i
$329$	24.3195	−	14.0409i	1.34078	−	0.774099i
$330$	−23.3125	+	23.3125i	−1.28331	+	1.28331i
$331$	0.698756	−	2.60779i	0.0384071	−	0.143337i	−0.944060	−	0.329774i	$-0.893027\pi$
$331$	0.698756	−	2.60779i	0.0384071	−	0.143337i	0.982467	+	0.186437i	$0.0596940\pi$
$332$	0.790099	+	0.211706i	0.0433623	+	0.0116189i
$333$	20.6454	−	20.6454i	1.13136	−	1.13136i
$334$	−22.9851	+	13.2705i	−1.25769	+	0.726128i
$335$	−20.3169	−	11.7300i	−1.11003	−	0.640877i
$336$	14.6945	+	54.8406i	0.801651	+	2.99180i
$337$	−6.38727			−0.347937			−0.173968	−	0.984751i	$-0.555659\pi$
$337$	−6.38727			−0.347937			−0.173968	+	0.984751i	$0.555659\pi$
$338$	−17.5999	+	4.06940i	−0.957306	+	0.221346i
$339$			28.4115i			1.54310i
$340$	−0.267928	+	0.0717910i	−0.0145304	+	0.00389342i
$341$	1.42380	−	25.6726i	0.0771031	−	1.39025i
$342$	−27.1562	+	15.6786i	−1.46844	+	0.847804i
$343$	26.0989	−	26.0989i	1.40921	−	1.40921i
$344$	6.16485	−	23.0075i	0.332387	−	1.24048i
$345$	3.25960	−	12.1650i	0.175491	−	0.654942i
$346$	−7.91876	−	7.91876i	−0.425715	−	0.425715i
$347$	12.0218	−	6.94076i	0.645361	−	0.372600i	−0.141315	−	0.989965i	$-0.545133\pi$
$347$	12.0218	−	6.94076i	0.645361	−	0.372600i	0.786677	+	0.617365i	$0.211800\pi$
$348$	−0.937825	−	0.541453i	−0.0502727	−	0.0290249i
$349$	−20.3458	+	5.45164i	−1.08908	+	0.291819i	−0.758312	−	0.651891i	$-0.773976\pi$
$349$	−20.3458	+	5.45164i	−1.08908	+	0.291819i	−0.330772	+	0.943711i	$0.607309\pi$
$350$			15.1704i			0.810893i
$351$	30.7335	+	31.8149i	1.64043	+	1.69815i
$352$		−	1.80543i		−	0.0962299i
$353$	5.76832	−	1.54562i	0.307017	−	0.0822649i	−0.102021	−	0.994782i	$-0.532531\pi$
$353$	5.76832	−	1.54562i	0.307017	−	0.0822649i	0.409038	+	0.912517i	$0.365864\pi$
$354$	−52.4488	−	30.2813i	−2.78762	−	1.60943i
$355$	−1.05934	+	0.611612i	−0.0562241	+	0.0324610i
$356$	−0.475672	−	0.475672i	−0.0252106	−	0.0252106i
$357$	−34.9314	−	9.35985i	−1.84877	−	0.495376i
$358$	8.74995	+	2.34454i	0.462449	+	0.123913i
$359$	−10.9877	−	10.9877i	−0.579909	−	0.579909i	0.354969	−	0.934878i	$-0.384491\pi$
$359$	−10.9877	−	10.9877i	−0.579909	−	0.579909i	−0.934878	+	0.354969i	$0.884491\pi$
$360$	−16.1962	−	28.0527i	−0.853615	−	1.47850i
$361$	−7.18955	−	4.15089i	−0.378397	−	0.218468i
$362$	−0.0883736	−	0.329815i	−0.00464481	−	0.0173347i
$363$	32.4892			1.70524
$364$	−0.999865	−	0.600554i	−0.0524072	−	0.0314776i
$365$			9.44092i			0.494160i
$366$	−1.33592	−	4.98571i	−0.0698294	−	0.260607i
$367$	−16.0538	−	9.26868i	−0.838003	−	0.483821i	0.0185818	−	0.999827i	$-0.494085\pi$
$367$	−16.0538	−	9.26868i	−0.838003	−	0.483821i	−0.856585	+	0.516006i	$0.827418\pi$
$368$	−4.72724	−	8.18781i	−0.246424	−	0.426819i
$369$	12.7003	−	12.7003i	0.661154	−	0.661154i
$370$	−2.48527	+	9.27514i	−0.129203	+	0.482192i
$371$	−8.11745	−	2.17507i	−0.421437	−	0.112924i
$372$	1.15082	+	0.377799i	0.0596671	+	0.0195880i
$373$	6.92116	+	11.9878i	0.358364	+	0.620705i	0.987688	−	0.156439i	$-0.0500013\pi$
$373$	6.92116	+	11.9878i	0.358364	+	0.620705i	−0.629324	+	0.777143i	$0.716668\pi$
$374$	−13.6527	−	7.88237i	−0.705963	−	0.407588i
$375$	−9.75172	−	36.3939i	−0.503577	−	1.87937i
$376$			17.2574i			0.889985i
$377$	−17.4140	+	4.34486i	−0.896866	+	0.223772i
$378$		−	79.7595i		−	4.10239i
$379$	3.79631	+	14.1680i	0.195003	+	0.727762i	0.992266	+	0.124129i	$0.0396138\pi$
$379$	3.79631	+	14.1680i	0.195003	+	0.727762i	−0.797263	+	0.603632i	$0.793720\pi$
$380$	−0.184648	+	0.319819i	−0.00947222	+	0.0164064i
$381$	14.4909	−	8.36633i	0.742392	−	0.428620i
$382$	−7.67812	+	7.67812i	−0.392847	+	0.392847i
$383$	3.84136	−	14.3362i	0.196284	−	0.732543i	−0.795646	−	0.605762i	$-0.792869\pi$
$383$	3.84136	−	14.3362i	0.196284	−	0.732543i	0.991931	−	0.126782i	$-0.0404648\pi$
$384$	−32.4936	−	8.70663i	−1.65818	−	0.444308i
$385$	−24.9473	+	24.9473i	−1.27143	+	1.27143i
$386$	14.2119	+	24.6157i	0.723365	+	1.25291i
$387$	−28.5784	+	49.4993i	−1.45272	+	2.51619i
$388$	0.435252	−	0.116625i	0.0220966	−	0.00592076i
$389$	−28.7586			−1.45812			−0.729058	−	0.684452i	$-0.760042\pi$
$389$	−28.7586			−1.45812			−0.729058	+	0.684452i	$0.760042\pi$
$390$	−24.7447	−	7.09099i	−1.25300	−	0.359066i
$391$	6.02215			0.304553
$392$	11.0797	+	41.3500i	0.559609	+	2.08849i
$393$	−13.8305	−	7.98501i	−0.697654	−	0.402791i
$394$	14.3116	+	24.7885i	0.721009	+	1.24882i
$395$	2.04043	+	2.04043i	0.102665	+	0.102665i
$396$	−0.570174	+	2.12792i	−0.0286523	+	0.106932i
$397$	2.48384	−	9.26982i	0.124660	−	0.465239i	−0.875167	−	0.483821i	$-0.839249\pi$
$397$	2.48384	−	9.26982i	0.124660	−	0.465239i	0.999827	+	0.0185822i	$0.00591523\pi$
$398$	−10.8161	+	10.8161i	−0.542161	+	0.542161i
$399$	−41.6968	+	24.0737i	−2.08745	+	1.20519i
$400$	−7.79439	−	4.50009i	−0.389720	−	0.225005i
$401$	10.0172	+	37.3848i	0.500236	+	1.86691i	0.498469	+	0.866908i	$0.333896\pi$
$401$	10.0172	+	37.3848i	0.500236	+	1.86691i	0.00176746	+	0.999998i	$0.499437\pi$
$402$	62.8109			3.13272
$403$	18.0684	−	8.74829i	0.900052	−	0.435783i
$404$	0.416752			0.0207342
$405$	7.56640	+	28.2382i	0.375978	+	1.40317i
$406$	28.0259	+	16.1807i	1.39090	+	0.803037i
$407$	16.9246	−	9.77141i	0.838920	−	0.484351i
$408$	15.7148	−	15.7148i	0.778001	−	0.778001i
$409$	−8.09438	+	30.2087i	−0.400242	+	1.49372i	0.412424	+	0.910992i	$0.364682\pi$
$409$	−8.09438	+	30.2087i	−0.400242	+	1.49372i	−0.812666	+	0.582730i	$0.801985\pi$
$410$	−1.52885	+	5.70574i	−0.0755044	+	0.281786i
$411$	−5.86505	−	5.86505i	−0.289301	−	0.289301i
$412$	0.479357	+	0.830271i	0.0236162	+	0.0409045i
$413$	−56.1268	−	32.4048i	−2.76182	−	1.59454i
$414$	6.08239	+	22.6998i	0.298933	+	1.11563i
$415$	19.3179			0.948279
$416$	1.23275	−	0.683594i	0.0604408	−	0.0335160i
$417$	−44.9025			−2.19888
$418$	−20.2736	+	5.43229i	−0.991613	+	0.265702i
$419$	−0.584740	+	1.01280i	−0.0285664	+	0.0494785i	−0.879955	−	0.475057i	$-0.842428\pi$
$419$	−0.584740	+	1.01280i	−0.0285664	+	0.0494785i	0.851389	+	0.524535i	$0.175761\pi$
$420$	−0.831006	−	1.43934i	−0.0405489	−	0.0702328i
$421$	−23.2939	+	23.2939i	−1.13527	+	1.13527i	−0.145988	+	0.989286i	$0.546636\pi$
$421$	−23.2939	+	23.2939i	−1.13527	+	1.13527i	−0.989286	+	0.145988i	$0.953364\pi$
$422$	−12.7937	−	3.42806i	−0.622788	−	0.166876i
$423$	10.7180	−	40.0002i	0.521128	−	1.94488i
$424$	3.65185	−	3.65185i	0.177350	−	0.177350i
$425$	4.96474	−	2.86639i	0.240825	−	0.139040i
$426$	1.63751	−	2.83625i	0.0793377	−	0.137417i
$427$	−1.42960	−	5.33533i	−0.0691831	−	0.258195i
$428$			0.509007i			0.0246038i
$429$	25.4057	+	45.8152i	1.22660	+	2.21198i
$430$		−	18.7978i		−	0.906509i
$431$	−2.55921	−	9.55109i	−0.123273	−	0.460060i	0.876500	−	0.481403i	$-0.159873\pi$
$431$	−2.55921	−	9.55109i	−0.123273	−	0.460060i	−0.999772	+	0.0213428i	$0.993206\pi$
$432$	40.9796	+	23.6596i	1.97163	+	1.13832i
$433$	15.2032	+	26.3327i	0.730619	+	1.26547i	0.956619	+	0.291343i	$0.0941019\pi$
$433$	15.2032	+	26.3327i	0.730619	+	1.26547i	−0.225999	+	0.974127i	$0.572565\pi$
$434$	−34.3909	−	11.2901i	−1.65082	−	0.541943i
$435$	−24.7034	−	6.61927i	−1.18444	−	0.317369i
$436$	−0.0405082	+	0.151179i	−0.00193999	+	0.00724014i
$437$	5.66938	−	5.66938i	0.271203	−	0.271203i
$438$	−12.6384	−	21.8904i	−0.603886	−	1.04596i
$439$	25.4674	+	14.7036i	1.21549	+	0.701766i	0.963951	−	0.266080i	$-0.0857284\pi$
$439$	25.4674	+	14.7036i	1.21549	+	0.701766i	0.251544	+	0.967846i	$0.419062\pi$
$440$	−5.61161	−	20.9428i	−0.267523	−	0.998410i
$441$		−	102.724i		−	4.89164i
$442$	0.212770	−	12.3066i	0.0101205	−	0.585365i
$443$	8.87972			0.421888			0.210944	−	0.977498i	$-0.432346\pi$
$443$	8.87972			0.421888			0.210944	+	0.977498i	$0.432346\pi$
$444$	0.238275	+	0.889255i	0.0113080	+	0.0422022i
$445$	−13.7587	−	7.94356i	−0.652223	−	0.376561i
$446$	13.0654	+	22.6299i	0.618665	+	1.07156i
$447$	−48.1099	−	48.1099i	−2.27552	−	2.27552i
$448$	−37.3152	−	9.99857i	−1.76298	−	0.472388i
$449$	30.3762	+	8.13929i	1.43354	+	0.384117i	0.890268	−	0.455437i	$-0.150517\pi$
$449$	30.3762	+	8.13929i	1.43354	+	0.384117i	0.543276	+	0.839554i	$0.317184\pi$
$450$	15.8189	+	15.8189i	0.745711	+	0.745711i
$451$	10.4114	−	6.01103i	0.490254	−	0.283048i
$452$	−0.540715	−	0.312182i	−0.0254331	−	0.0146838i
$453$	9.65168	−	2.58616i	0.453476	−	0.121508i
$454$			3.57055i			0.167574i
$455$	−26.4800	−	7.58825i	−1.24140	−	0.355743i
$456$		−	29.5886i		−	1.38561i
$457$	38.5136	−	10.3197i	1.80159	−	0.482735i	0.807365	−	0.590052i	$-0.200893\pi$
$457$	38.5136	−	10.3197i	1.80159	−	0.482735i	0.994225	+	0.107318i	$0.0342262\pi$
$458$	16.9738	+	9.79981i	0.793132	+	0.457915i
$459$	−26.1025	+	15.0703i	−1.21836	+	0.703420i
$460$	0.195703	+	0.195703i	0.00912470	+	0.00912470i
$461$	6.09586	−	22.7500i	0.283912	−	1.05958i	−0.665718	−	0.746203i	$-0.731875\pi$
$461$	6.09586	−	22.7500i	0.283912	−	1.05958i	0.949630	−	0.313372i	$-0.101459\pi$
$462$	24.4480	−	91.2412i	1.13742	−	4.24492i
$463$	17.6096	−	17.6096i	0.818386	−	0.818386i	−0.167488	−	0.985874i	$-0.553566\pi$
$463$	17.6096	−	17.6096i	0.818386	−	0.818386i	0.985874	+	0.167488i	$0.0535656\pi$
$464$	−16.6270	+	9.59958i	−0.771888	+	0.445650i
$465$	28.5619	+	1.58404i	1.32453	+	0.0734582i
$466$	14.2474	−	3.81757i	0.659997	−	0.176846i
$467$		−	22.7745i		−	1.05388i	−0.849903	−	0.526939i	$-0.823340\pi$
$467$		−	22.7745i		−	1.05388i	0.849903	−	0.526939i	$-0.176660\pi$
$468$	−1.66883	+	0.416381i	−0.0771419	+	0.0192472i
$469$	67.2156			3.10373
$470$	3.52495	+	13.1553i	0.162594	+	0.606808i
$471$	−22.5676	−	13.0294i	−1.03986	−	0.600364i
$472$	34.4923	−	19.9142i	1.58764	−	0.916623i
$473$	−27.0521	+	27.0521i	−1.24386	+	1.24386i
$474$	−7.46256	−	1.99959i	−0.342767	−	0.0918441i
$475$	1.97543	−	7.37240i	0.0906389	−	0.338269i
$476$	0.561956	−	0.561956i	0.0257572	−	0.0257572i
$477$	−10.7325	+	6.19641i	−0.491408	+	0.283714i
$478$	2.76150	−	4.78306i	0.126308	−	0.218772i
$479$	−32.0790	+	8.59553i	−1.46572	+	0.392740i	−0.901463	−	0.432856i	$-0.857506\pi$
$479$	−32.0790	+	8.59553i	−1.46572	+	0.392740i	−0.564262	+	0.825596i	$0.690839\pi$
$480$	2.00862			0.0916808
$481$	13.0801	+	7.85639i	0.596403	+	0.358220i
$482$			27.1367i			1.23604i
$483$	9.33916	+	34.8542i	0.424946	+	1.58592i
$484$	−0.356988	+	0.618321i	−0.0162267	+	0.0281055i
$485$	9.21617	−	5.32096i	0.418485	−	0.241612i
$486$	−19.1821	−	19.1821i	−0.870116	−	0.870116i
$487$	−6.95368	+	25.9515i	−0.315101	+	1.17597i	0.608794	+	0.793328i	$0.291654\pi$
$487$	−6.95368	+	25.9515i	−0.315101	+	1.17597i	−0.923895	+	0.382646i	$0.875013\pi$
$488$	3.27879	+	0.878550i	0.148424	+	0.0397701i
$489$	10.2358	−	10.2358i	0.462879	−	0.462879i
$490$	16.8920	+	29.2578i	0.763103	+	1.32173i
$491$	19.8660	−	34.4089i	0.896540	−	1.55285i	0.0646535	−	0.997908i	$-0.479406\pi$
$491$	19.8660	−	34.4089i	0.896540	−	1.55285i	0.831887	−	0.554945i	$-0.187261\pi$
$492$	0.146578	+	0.547038i	0.00660826	+	0.0246624i
$493$		−	12.2292i		−	0.550774i
$494$	−11.3854	−	11.7860i	−0.512254	−	0.530278i
$495$			52.0276i			2.33846i
$496$	16.0023	−	14.3206i	0.718525	−	0.643014i
$497$	1.75234	−	3.03515i	0.0786034	−	0.136145i
$498$	−44.7918	+	25.8606i	−2.00717	+	1.15884i
$499$	−11.7947	−	11.7947i	−0.528004	−	0.528004i	0.391973	−	0.919977i	$-0.371793\pi$
$499$	−11.7947	−	11.7947i	−0.528004	−	0.528004i	−0.919977	+	0.391973i	$0.871793\pi$
$500$	0.799785	+	0.214302i	0.0357675	+	0.00958386i
$501$	−15.5540	+	58.0482i	−0.694900	+	2.59340i
$502$	−3.50793	+	3.50793i	−0.156567	+	0.156567i
$503$	−11.5500	−	20.0052i	−0.514988	−	0.891986i	−0.999849	−	0.0173944i	$-0.994463\pi$
$503$	−11.5500	−	20.0052i	−0.514988	−	0.891986i	0.484860	−	0.874592i	$-0.338870\pi$
$504$	80.3743	+	46.4041i	3.58015	+	2.06700i
$505$	9.50702	−	2.54740i	0.423057	−	0.113358i
$506$			15.7299i			0.699279i
$507$	−21.6633	+	34.6942i	−0.962103	+	1.54082i
$508$			0.367713i			0.0163146i
$509$	24.8006	−	6.64531i	1.09927	−	0.294548i	0.336802	−	0.941575i	$-0.390655\pi$
$509$	24.8006	−	6.64531i	1.09927	−	0.294548i	0.762467	+	0.647027i	$0.223988\pi$
$510$	8.76950	−	15.1892i	0.388320	−	0.672590i
$511$	−13.5247	−	23.4254i	−0.598297	−	1.03628i
$512$	16.7490	−	16.7490i	0.740208	−	0.740208i
$513$	−10.3860	+	38.7609i	−0.458551	+	1.71134i
$514$	8.12056	−	30.3063i	0.358183	−	1.33676i
$515$	16.0102	+	16.0102i	0.705494	+	0.705494i
$516$	−0.901118	−	1.56078i	−0.0396695	−	0.0687096i
$517$	13.8592	−	24.0048i	0.609525	−	1.05573i
$518$	−7.12059	−	26.5744i	−0.312861	−	1.16761i
$519$	−25.3571			−1.11305
$520$	12.1751	−	11.7612i	0.533913	−	0.515765i
$521$	−22.9033			−1.00341			−0.501706	−	0.865038i	$-0.667294\pi$
$521$	−22.9033			−1.00341			−0.501706	+	0.865038i	$0.667294\pi$
$522$	46.0964	−	12.3515i	2.01758	−	0.540610i
$523$	23.8326	+	13.7597i	1.04213	+	0.601671i	0.920434	−	0.390897i	$-0.127835\pi$
$523$	23.8326	+	13.7597i	1.04213	+	0.601671i	0.121691	+	0.992568i	$0.461168\pi$
$524$	0.303935	−	0.175477i	0.0132775	−	0.00766575i
$525$	24.2891	+	24.2891i	1.06006	+	1.06006i
$526$	9.93460	−	37.0764i	0.433169	−	1.61661i
$527$	2.80318	+	13.3881i	0.122108	+	0.583197i
$528$	39.6265	+	39.6265i	1.72452	+	1.72452i
$529$	8.49558	+	14.7148i	0.369373	+	0.639773i
$530$	2.03788	−	3.52971i	0.0885197	−	0.153321i
$531$	−92.3162	+	24.7360i	−4.00618	+	1.07345i
$532$		−	1.05808i		−	0.0458734i
$533$	8.04644	+	4.83297i	0.348530	+	0.209339i
$534$	42.5357			1.84070
$535$	3.11131	+	11.6116i	0.134514	+	0.502011i
$536$	−20.6534	+	35.7728i	−0.892093	+	1.54515i
$537$	17.7632	−	10.2556i	0.766538	−	0.442561i
$538$	5.35868	+	5.35868i	0.231029	+	0.231029i
$539$	17.7958	−	66.4149i	0.766520	−	2.86069i
$540$	−1.33800	−	0.358516i	−0.0575783	−	0.0154281i
$541$	30.5016	+	30.5016i	1.31136	+	1.31136i	0.920410	+	0.390955i	$0.127855\pi$
$541$	30.5016	+	30.5016i	1.31136	+	1.31136i	0.390955	+	0.920410i	$0.372145\pi$
$542$	−21.8289	+	12.6029i	−0.937632	+	0.541342i
$543$	−0.669553	−	0.386567i	−0.0287333	−	0.0165892i
$544$	0.248587	+	0.927739i	0.0106581	+	0.0397765i
$545$			3.69632i			0.158333i
$546$	71.5565	−	17.8537i	3.06234	−	0.764066i
$547$	2.34227			0.100148			0.0500741	−	0.998746i	$-0.484054\pi$
$547$	2.34227			0.100148			0.0500741	+	0.998746i	$0.484054\pi$
$548$	0.176066	−	0.0471767i	0.00752115	−	0.00201529i
$549$	−7.05412	−	4.07270i	−0.301063	−	0.173819i
$550$	7.48704	+	12.9679i	0.319248	+	0.552954i
$551$	−11.5128	−	11.5128i	−0.490462	−	0.490462i
$552$	−21.4194	−	5.73931i	−0.911671	−	0.244281i
$553$	−7.98588	−	2.13981i	−0.339594	−	0.0909940i
$554$	3.98351	−	3.98351i	0.169243	−	0.169243i
$555$	10.8711	+	18.8294i	0.461454	+	0.799262i
$556$	0.493384	−	0.854566i	0.0209241	−	0.0362417i
$557$	−3.06069	−	11.4226i	−0.129685	−	0.483993i	0.870278	−	0.492561i	$-0.163939\pi$
$557$	−3.06069	−	11.4226i	−0.129685	−	0.483993i	−0.999963	+	0.00856843i	$0.997273\pi$
$558$	−47.6338	+	24.0883i	−2.01650	+	1.01974i
$559$	−28.7141	−	8.22848i	−1.21448	−	0.348027i
$560$	−29.4663			−1.24518
$561$	−34.4793	+	9.23871i	−1.45572	+	0.390059i
$562$	−1.22899	+	2.12867i	−0.0518418	+	0.0897927i
$563$	16.7240	−	9.65560i	0.704832	−	0.406935i	−0.104312	−	0.994545i	$-0.533264\pi$
$563$	16.7240	−	9.65560i	0.704832	−	0.406935i	0.809145	+	0.587609i	$0.199931\pi$
$564$	0.923308	+	0.923308i	0.0388783	+	0.0388783i
$565$	−14.2431	−	3.81643i	−0.599212	−	0.160558i
$566$	−2.54490	+	9.49769i	−0.106970	+	0.399218i
$567$	−59.2272	−	59.2272i	−2.48731	−	2.48731i
$568$	1.07689	+	1.86523i	0.0451853	+	0.0782633i
$569$	−11.6649	+	20.2042i	−0.489017	+	0.847003i	−0.999920	−	0.0126358i	$-0.995978\pi$
$569$	−11.6649	+	20.2042i	−0.489017	+	0.847003i	0.510903	+	0.859638i	$0.329311\pi$
$570$	−6.04367	−	22.5553i	−0.253141	−	0.944736i
$571$	−10.8562			−0.454316			−0.227158	−	0.973858i	$-0.572943\pi$
$571$	−10.8562			−0.454316			−0.227158	+	0.973858i	$0.572943\pi$
$572$	−1.15109	−	0.0199014i	−0.0481296	−	0.000832118i
$573$			24.5866i			1.02712i
$574$	−4.38034	−	16.3476i	−0.182832	−	0.682337i
$575$	−4.95376	−	2.86006i	−0.206586	−	0.119273i
$576$	−49.3363	+	28.4843i	−2.05568	+	1.18685i
$577$	−10.1372	+	10.1372i	−0.422018	+	0.422018i	−0.885898	−	0.463880i	$-0.846457\pi$
$577$	−10.1372	+	10.1372i	−0.422018	+	0.422018i	0.463880	+	0.885898i	$0.346457\pi$
$578$	−14.7166	−	3.94331i	−0.612131	−	0.164020i
$579$	62.1660	+	16.6573i	2.58353	+	0.692255i
$580$	0.397414	−	0.397414i	0.0165017	−	0.0165017i
$581$	−47.9329	+	27.6741i	−1.98859	+	1.14811i
$582$	−14.2462	+	24.6751i	−0.590523	+	1.02282i
$583$	−8.01239	+	2.14691i	−0.331839	+	0.0889161i
$584$	16.6230			0.687865
$585$	−35.5246	+	19.6993i	−1.46876	+	0.814465i
$586$	−3.92632			−0.162195
$587$	35.9281	−	9.62690i	1.48291	−	0.397345i	0.575574	−	0.817750i	$-0.304779\pi$
$587$	35.9281	−	9.62690i	1.48291	−	0.397345i	0.907337	+	0.420405i	$0.138112\pi$
$588$	2.80509	+	1.61952i	0.115680	+	0.0667880i
$589$	15.2429	+	9.96492i	0.628072	+	0.410597i
$590$	22.2258	−	22.2258i	0.915020	−	0.915020i
$591$	62.6023	+	16.7742i	2.57512	+	0.690000i
$592$	15.7659	+	4.22445i	0.647973	+	0.173624i
$593$	−0.701785	−	0.701785i	−0.0288188	−	0.0288188i	0.692551	−	0.721369i	$-0.256487\pi$
$593$	−0.701785	−	0.701785i	−0.0288188	−	0.0288188i	−0.721369	+	0.692551i	$0.756487\pi$
$594$	−39.3636	−	68.1798i	−1.61511	−	2.79745i
$595$	9.38447	−	16.2544i	0.384726	−	0.666364i
$596$	1.44423	−	0.386981i	0.0591581	−	0.0158514i
$597$			34.6348i			1.41751i
$598$	−10.7404	+	5.95584i	−0.439208	+	0.243552i
$599$	0.708023			0.0289290			0.0144645	−	0.999895i	$-0.495396\pi$
$599$	0.708023			0.0289290			0.0144645	+	0.999895i	$0.495396\pi$
$600$	−20.3902	+	5.46354i	−0.832427	+	0.223048i
$601$	18.7924	+	10.8498i	0.766557	+	0.442572i	0.831645	−	0.555307i	$-0.187399\pi$
$601$	18.7924	+	10.8498i	0.766557	+	0.442572i	−0.0650878	+	0.997880i	$0.520733\pi$
$602$	26.9289	+	46.6423i	1.09754	+	1.90100i
$603$	70.0889	−	70.0889i	2.85424	−	2.85424i
$604$	−0.0568329	+	0.212103i	−0.00231250	+	0.00863036i
$605$	−4.36418	+	16.2873i	−0.177429	+	0.662174i
$606$	−18.6335	+	18.6335i	−0.756933	+	0.756933i
$607$	6.75487	+	11.6998i	0.274172	+	0.474879i	0.969926	−	0.243401i	$-0.0782630\pi$
$607$	6.75487	+	11.6998i	0.274172	+	0.474879i	−0.695754	+	0.718280i	$0.744930\pi$
$608$	1.10742	+	0.639369i	0.0449118	+	0.0259298i
$609$	70.7783	−	18.9650i	2.86808	−	0.768501i
$610$	2.67886			0.108464
$611$	21.6380	+	0.374103i	0.875381	+	0.0151346i
$612$		−	1.17196i		−	0.0473735i
$613$	−3.97544	+	1.06522i	−0.160566	+	0.0430237i	−0.338207	−	0.941072i	$-0.609820\pi$
$613$	−3.97544	+	1.06522i	−0.160566	+	0.0430237i	0.177640	+	0.984095i	$0.443154\pi$
$614$	16.6238	−	28.7932i	0.670881	−	1.16200i
$615$	6.68754	+	11.5832i	0.269668	+	0.467078i
$616$	43.9258	+	43.9258i	1.76982	+	1.76982i
$617$	10.9312	+	2.92902i	0.440075	+	0.117918i	0.472052	−	0.881571i	$-0.343514\pi$
$617$	10.9312	+	2.92902i	0.440075	+	0.117918i	−0.0319767	+	0.999489i	$0.510180\pi$
$618$	−58.5550	−	15.6898i	−2.35543	−	0.631135i
$619$	−13.7532	+	13.7532i	−0.552788	+	0.552788i	−0.927245	−	0.374456i	$-0.877829\pi$
$619$	−13.7532	+	13.7532i	−0.552788	+	0.552788i	0.374456	+	0.927245i	$0.377829\pi$
$620$	−0.343982	+	0.526173i	−0.0138146	+	0.0211316i
$621$	26.0447	+	15.0369i	1.04514	+	0.603412i
$622$	−14.7465	+	3.95131i	−0.591281	+	0.158433i
$623$	45.5185			1.82366
$624$	−12.0532	+	42.0610i	−0.482516	+	1.68379i
$625$	7.88720			0.315488
$626$	23.7075	−	6.35239i	0.947540	−	0.253893i
$627$	−23.7621	+	41.1572i	−0.948967	+	1.64366i
$628$	0.495941	−	0.286332i	0.0197902	−	0.0114259i
$629$	−7.35145	+	7.35145i	−0.293122	+	0.293122i
$630$	70.7473	+	18.9567i	2.81864	+	0.755252i
$631$	−38.0506	−	10.1956i	−1.51477	−	0.405882i	−0.596755	−	0.802424i	$-0.703543\pi$
$631$	−38.0506	−	10.1956i	−1.51477	−	0.405882i	−0.918017	+	0.396542i	$0.870210\pi$
$632$	3.59266	−	3.59266i	0.142908	−	0.142908i
$633$	−25.9724	+	14.9951i	−1.03231	+	0.596004i
$634$	−10.2365	−	5.91007i	−0.406545	−	0.234719i
$635$	2.24765	+	8.38834i	0.0891952	+	0.332881i
$636$		−	0.390763i		−	0.0154948i
$637$	52.0864	−	12.9958i	2.06374	−	0.514911i
$638$	31.9427			1.26462
$639$	−1.33764	−	4.99215i	−0.0529163	−	0.197486i
$640$	8.72953	−	15.1200i	0.345065	−	0.597670i
$641$	12.0722	+	20.9097i	0.476825	+	0.825885i	0.999647	−	0.0265564i	$-0.00845416\pi$
$641$	12.0722	+	20.9097i	0.476825	+	0.825885i	−0.522822	+	0.852442i	$0.675121\pi$
$642$	−22.7583	−	22.7583i	−0.898198	−	0.898198i
$643$	−11.3818	+	42.4773i	−0.448853	+	1.67514i	0.256706	+	0.966490i	$0.417363\pi$
$643$	−11.3818	+	42.4773i	−0.448853	+	1.67514i	−0.705558	+	0.708652i	$0.749304\pi$
$644$	−0.765949	−	0.205235i	−0.0301826	−	0.00808740i
$645$	−30.0967	−	30.0967i	−1.18506	−	1.18506i
$646$	9.66981	−	5.58287i	0.380454	−	0.219655i
$647$	−0.850529	+	1.47316i	−0.0334377	+	0.0579158i	−0.882260	−	0.470762i	$-0.843979\pi$
$647$	−0.850529	+	1.47316i	−0.0334377	+	0.0579158i	0.848822	+	0.528678i	$0.177312\pi$
$648$	49.7201	−	13.3225i	1.95319	−	0.523356i
$649$	−63.9708			−2.51107
$650$	−6.01971	+	10.0222i	−0.236112	+	0.393105i
$651$	−73.1390	+	36.9862i	−2.86654	+	1.44961i
$652$	0.0823336	+	0.307273i	0.00322443	+	0.0120338i
$653$	2.59754	−	4.49908i	0.101650	−	0.176063i	−0.810715	−	0.585441i	$-0.800921\pi$
$653$	2.59754	−	4.49908i	0.101650	−	0.176063i	0.912364	+	0.409379i	$0.134255\pi$
$654$	−4.94820	−	8.57053i	−0.193490	−	0.335134i
$655$	5.86081	−	5.86081i	0.229001	−	0.229001i
$656$	9.69860	+	2.59873i	0.378667	+	0.101463i
$657$	−38.5297	−	10.3240i	−1.50319	−	0.402778i
$658$	−27.5921	−	27.5921i	−1.07565	−	1.07565i
$659$	−9.96262	−	17.2558i	−0.388089	−	0.672189i	0.604104	−	0.796906i	$-0.293531\pi$
$659$	−9.96262	−	17.2558i	−0.388089	−	0.672189i	−0.992192	+	0.124717i	$0.960198\pi$
$660$	−1.42072	−	0.820250i	−0.0553013	−	0.0319282i
$661$	10.2648	−	2.75043i	0.399253	−	0.106979i	−0.0536052	−	0.998562i	$-0.517071\pi$
$661$	10.2648	−	2.75043i	0.399253	−	0.106979i	0.452858	+	0.891583i	$0.350405\pi$
$662$	−3.75149			−0.145806
$663$	−19.3632	−	20.0445i	−0.752004	−	0.778465i
$664$		−	34.0138i		−	1.31999i
$665$	−6.46748	−	24.1370i	−0.250798	−	0.935992i
$666$	−35.1354	−	20.2854i	−1.36147	−	0.786045i
$667$	−10.5673	+	6.10106i	−0.409169	+	0.236234i
$668$	−0.933844	−	0.933844i	−0.0361315	−	0.0361315i
$669$	57.1511	+	15.3136i	2.20959	+	0.592058i
$670$	−8.43720	+	31.4881i	−0.325957	+	1.21649i
$671$	−3.85519	−	3.85519i	−0.148828	−	0.148828i
$672$	−4.98394	+	2.87748i	−0.192260	+	0.111001i
$673$	3.79175	−	6.56751i	0.146161	−	0.253159i	−0.783644	−	0.621210i	$-0.786641\pi$
$673$	3.79175	−	6.56751i	0.146161	−	0.253159i	0.929806	+	0.368051i	$0.119975\pi$
$674$	2.29714	+	8.57303i	0.0884824	+	0.330221i
$675$	28.6288			1.10192
$676$	−0.422251	−	0.793504i	−0.0162404	−	0.0305194i
$677$			22.4056i			0.861119i	0.902562	+	0.430560i	$0.141684\pi$
$677$			22.4056i			0.861119i	−0.902562	+	0.430560i	$0.858316\pi$
$678$	38.1340	−	10.2180i	1.46453	−	0.392419i
$679$	−15.2452	+	26.4054i	−0.585057	+	1.01335i
$680$	5.76716	+	9.98901i	0.221160	+	0.383061i
$681$	5.71673	+	5.71673i	0.219066	+	0.219066i
$682$	−34.9699	+	7.32193i	−1.33907	+	0.280371i
$683$	2.30455	−	8.60070i	0.0881812	−	0.329097i	−0.907716	−	0.419584i	$-0.862176\pi$
$683$	2.30455	−	8.60070i	0.0881812	−	0.329097i	0.995898	+	0.0904876i	$0.0288425\pi$
$684$	−1.10331	−	1.10331i	−0.0421860	−	0.0421860i
$685$	3.72807	−	2.15240i	0.142442	−	0.0822391i
$686$	−44.4163	−	25.6437i	−1.69582	−	0.979083i
$687$	42.8666	−	11.4861i	1.63546	−	0.438221i
$688$	−31.9524			−1.21817
$689$	−4.49967	−	4.65799i	−0.171424	−	0.177455i
$690$	−17.5002			−0.666222
$691$	2.30765	+	8.61228i	0.0877872	+	0.327626i	0.995827	−	0.0912567i	$-0.0290884\pi$
$691$	2.30765	+	8.61228i	0.0877872	+	0.327626i	−0.908040	+	0.418883i	$0.862422\pi$
$692$	0.278621	−	0.482586i	0.0105916	−	0.0183452i
$693$	−74.5326	−	129.094i	−2.83126	−	4.90389i
$694$	−13.6395	−	13.6395i	−0.517747	−	0.517747i
$695$	6.03162	−	22.5103i	0.228792	−	0.853864i
$696$	−11.6548	+	43.4963i	−0.441774	+	1.64872i
$697$	−4.52235	+	4.52235i	−0.171296	+	0.171296i
$698$	14.6344	+	25.3476i	0.553921	+	0.959420i
$699$	16.6989	−	28.9234i	0.631612	−	1.09398i
$700$	−0.729145	+	0.195374i	−0.0275591	+	0.00738444i
$701$		−	2.91512i		−	0.110103i	−0.998484	−	0.0550513i	$-0.982468\pi$
$701$		−	2.91512i		−	0.110103i	0.998484	−	0.0550513i	$-0.0175322\pi$
$702$	31.6490	−	52.6927i	1.19452	−	1.98876i
$703$			13.8416i			0.522047i
$704$	−36.8322	+	9.86916i	−1.38817	+	0.371958i
$705$	26.7064	+	15.4189i	1.00582	+	0.580711i
$706$	−4.14907	−	7.18640i	−0.156152	−	0.270464i
$707$	−19.9402	+	19.9402i	−0.749927	+	0.749927i
$708$	0.779962	−	2.91086i	0.0293128	−	0.109397i
$709$	−17.5832	−	4.71139i	−0.660349	−	0.176940i	−0.0869457	−	0.996213i	$-0.527711\pi$
$709$	−17.5832	−	4.71139i	−0.660349	−	0.176940i	−0.573404	+	0.819273i	$0.694377\pi$
$710$	1.20189	+	1.20189i	0.0451063	+	0.0451063i
$711$	−10.5585	+	6.09598i	−0.395977	+	0.228617i
$712$	−13.9866	+	24.2254i	−0.524168	+	0.907886i
$713$	10.1703	−	9.10153i	0.380883	−	0.340855i
$714$			50.2514i			1.88061i
$715$	−26.3805	+	6.58205i	−0.986576	+	0.246155i
$716$			0.450749i			0.0168453i
$717$	−3.23668	−	12.0794i	−0.120876	−	0.451115i
$718$	−10.7961	+	18.6994i	−0.402907	+	0.697856i
$719$	−20.5824	−	35.6498i	−0.767594	−	1.32951i	−0.938864	−	0.344288i	$-0.888120\pi$
$719$	−20.5824	−	35.6498i	−0.767594	−	1.32951i	0.171270	−	0.985224i	$-0.445213\pi$
$720$	−30.7259	+	30.7259i	−1.14509	+	1.14509i
$721$	−62.6612	−	16.7900i	−2.33363	−	0.625293i
$722$	−2.98567	+	11.1427i	−0.111115	+	0.414688i
$723$	43.4481	+	43.4481i	1.61585	+	1.61585i
$724$	0.0147140	−	0.00849511i	0.000546840	−	0.000315718i
$725$	−5.80791	+	10.0596i	−0.215700	+	0.373604i
$726$	−11.6845	−	43.6072i	−0.433653	−	1.61841i
$727$			11.5640i			0.428886i	0.976737	+	0.214443i	$0.0687936\pi$
$727$			11.5640i			0.428886i	−0.976737	+	0.214443i	$0.931206\pi$
$728$	−13.3609	+	46.6243i	−0.495190	+	1.72801i
$729$	−7.71540			−0.285756
$730$	12.6716	−	3.39536i	0.468999	−	0.125668i
$731$	10.1762	−	17.6258i	0.376382	−	0.651912i
$732$	0.222426	−	0.128418i	0.00822111	−	0.00474646i
$733$	−4.98204	+	4.98204i	−0.184016	+	0.184016i	−0.793103	−	0.609087i	$-0.791536\pi$
$733$	−4.98204	+	4.98204i	−0.184016	+	0.184016i	0.609087	+	0.793103i	$0.291536\pi$
$734$	−6.66683	+	24.8809i	−0.246077	+	0.918372i
$735$	73.8896	+	19.7987i	2.72546	+	0.730284i
$736$	0.677650	−	0.677650i	0.0249785	−	0.0249785i
$737$	57.4570	−	33.1728i	2.11646	−	1.22194i
$738$	−21.6141	−	12.4789i	−0.795625	−	0.459354i
$739$	−0.798449	−	2.97985i	−0.0293714	−	0.109616i	0.949684	−	0.313210i	$-0.101404\pi$
$739$	−0.798449	−	2.97985i	−0.0293714	−	0.109616i	−0.979055	+	0.203594i	$0.934738\pi$
$740$	−0.477804			−0.0175644
$741$	−37.0993	−	0.641414i	−1.36288	−	0.0235629i
$742$			11.6775i			0.428696i
$743$	20.9774	−	5.62088i	0.769586	−	0.206210i	0.147397	−	0.989077i	$-0.452910\pi$
$743$	20.9774	−	5.62088i	0.769586	−	0.206210i	0.622189	+	0.782867i	$0.286244\pi$
$744$	2.78909	−	50.2901i	0.102253	−	1.84373i
$745$	30.5807	−	17.6558i	1.12039	−	0.646857i
$746$	13.6009	−	13.6009i	0.497966	−	0.497966i
$747$	−21.1249	+	78.8391i	−0.772918	+	2.88457i
$748$	0.203028	−	0.757711i	0.00742344	−	0.0277046i
$749$	−24.3542	−	24.3542i	−0.889885	−	0.889885i
$750$	−45.3410	+	26.1776i	−1.65562	+	0.955871i
$751$	16.6870	+	9.63426i	0.608918	+	0.351559i	0.772542	−	0.634964i	$-0.218985\pi$
$751$	16.6870	+	9.63426i	0.608918	+	0.351559i	−0.163624	+	0.986523i	$0.552318\pi$
$752$	22.3613	−	5.99169i	0.815432	−	0.218494i
$753$			11.2330i			0.409352i
$754$	12.0945	+	21.8105i	0.440456	+	0.794293i
$755$			5.18593i			0.188735i
$756$	3.83353	−	1.02719i	0.139424	−	0.0373586i
$757$	18.1229	+	10.4632i	0.658687	+	0.380293i	0.791777	−	0.610811i	$-0.209156\pi$
$757$	18.1229	+	10.4632i	0.658687	+	0.380293i	−0.133089	+	0.991104i	$0.542490\pi$
$758$	17.6511	−	10.1908i	0.641115	−	0.370148i
$759$	25.1848	+	25.1848i	0.914151	+	0.914151i
$760$	14.8332	+	3.97455i	0.538057	+	0.144172i
$761$	37.5369	+	10.0580i	1.36071	+	0.364601i	0.864077	−	0.503359i	$-0.167903\pi$
$761$	37.5369	+	10.0580i	1.36071	+	0.364601i	0.496634	+	0.867960i	$0.334569\pi$
$762$	−16.4409	−	16.4409i	−0.595590	−	0.595590i
$763$	−5.29520	−	9.17155i	−0.191699	−	0.332032i
$764$	−0.467922	−	0.270155i	−0.0169288	−	0.00977385i
$765$	−7.16358	−	26.7349i	−0.259000	−	0.966601i
$766$	−20.6236			−0.745160
$767$	−24.2214	−	43.6795i	−0.874584	−	1.57717i
$768$		−	5.21479i		−	0.188172i
$769$	12.0172	+	44.8487i	0.433351	+	1.61729i	0.744983	+	0.667084i	$0.232458\pi$
$769$	12.0172	+	44.8487i	0.433351	+	1.61729i	−0.311632	+	0.950203i	$0.600876\pi$
$770$	42.4565	+	24.5123i	1.53003	+	0.883362i
$771$	−35.5212	−	61.5245i	−1.27927	−	2.21575i
$772$	−1.00009	+	1.00009i	−0.0359940	+	0.0359940i
$773$	0.710456	−	2.65146i	0.0255533	−	0.0953663i	−0.951972	−	0.306187i	$-0.900947\pi$
$773$	0.710456	−	2.65146i	0.0255533	−	0.0953663i	0.977525	+	0.210820i	$0.0676135\pi$
$774$	76.7163	+	20.5561i	2.75751	+	0.738872i
$775$	4.05247	−	12.3443i	0.145569	−	0.443419i
$776$	−9.36883	−	16.2273i	−0.336321	−	0.582526i
$777$	−53.9484	−	31.1471i	−1.93539	−	1.11740i
$778$	10.3428	+	38.5999i	0.370808	+	1.38387i
$779$			8.51489i			0.305077i
$780$	0.0221412	−	1.28064i	0.000792781	−	0.0458543i
$781$		−	3.45933i		−	0.123785i
$782$	−2.16582	−	8.08296i	−0.0774496	−	0.289046i
$783$	30.5355	−	52.8890i	1.09125	−	1.89010i
$784$	49.7324	−	28.7130i	1.77616	−	1.02546i
$785$	9.56328	−	9.56328i	0.341328	−	0.341328i
$786$	−5.74350	+	21.4351i	−0.204864	+	0.764563i
$787$	−17.9380	−	4.80648i	−0.639422	−	0.171333i	−0.0754804	−	0.997147i	$-0.524049\pi$
$787$	−17.9380	−	4.80648i	−0.639422	−	0.171333i	−0.563942	+	0.825815i	$0.690716\pi$
$788$	−1.00711	+	1.00711i	−0.0358768	+	0.0358768i
$789$	−43.4563	−	75.2684i	−1.54708	−	2.67963i
$790$	2.00485	−	3.47250i	0.0713292	−	0.123546i
$791$	40.8082	−	10.9345i	1.45097	−	0.388787i
$792$	91.6070			3.25511
$793$	1.17264	−	4.09203i	0.0416415	−	0.145312i
$794$	−13.3353			−0.473252
$795$	−2.38854	−	8.91415i	−0.0847127	−	0.316152i
$796$	−0.659156	−	0.380564i	−0.0233632	−	0.0134887i
$797$	4.68469	+	8.11412i	0.165940	+	0.287417i	0.936989	−	0.349359i	$-0.113601\pi$
$797$	4.68469	+	8.11412i	0.165940	+	0.287417i	−0.771049	+	0.636776i	$0.780267\pi$
$798$	47.3077	+	47.3077i	1.67468	+	1.67468i
$799$	−3.81648	+	14.2433i	−0.135018	+	0.503892i
$800$	0.236119	−	0.881209i	0.00834807	−	0.0311554i
$801$	47.4644	−	47.4644i	1.67707	−	1.67707i
$802$	46.5754	−	26.8903i	1.64463	−	0.949530i
$803$	−23.1223	−	13.3496i	−0.815967	−	0.471099i
$804$	0.808917	+	3.01892i	0.0285283	+	0.106469i
$805$	−18.7274			−0.660055
$806$	−18.2402	−	21.1053i	−0.642482	−	0.743401i
$807$	17.1594			0.604038
$808$	−4.48531	−	16.7394i	−0.157793	−	0.588890i
$809$	−27.2985	−	15.7608i	−0.959765	−	0.554121i	−0.0636643	−	0.997971i	$-0.520279\pi$
$809$	−27.2985	−	15.7608i	−0.959765	−	0.554121i	−0.896101	+	0.443851i	$0.853612\pi$
$810$	35.1802	−	20.3113i	1.23611	−	0.713667i
$811$	−1.02573	+	1.02573i	−0.0360182	+	0.0360182i	−0.724887	−	0.688868i	$-0.758108\pi$
$811$	−1.02573	+	1.02573i	−0.0360182	+	0.0360182i	0.688868	+	0.724887i	$0.258108\pi$
$812$	−0.416771	+	1.55541i	−0.0146258	+	0.0545842i
$813$	−14.7715	+	55.1281i	−0.518061	+	1.93343i
$814$	−19.2020	−	19.2020i	−0.673031	−	0.673031i
$815$	3.75642	+	6.50630i	0.131582	+	0.227906i
$816$	−25.8186	−	14.9064i	−0.903831	−	0.521827i
$817$	−7.01315	−	26.1734i	−0.245359	−	0.915692i
$818$	43.4573			1.51945
$819$	59.9255	−	99.7703i	2.09397	−	3.48626i
$820$	−0.293928			−0.0102644
$821$	12.5957	−	3.37501i	0.439593	−	0.117789i	−0.0322329	−	0.999480i	$-0.510262\pi$
$821$	12.5957	−	3.37501i	0.439593	−	0.117789i	0.471826	+	0.881692i	$0.343595\pi$
$822$	−5.76277	+	9.98142i	−0.201000	+	0.348142i
$823$	9.16406	+	15.8726i	0.319439	+	0.553285i	0.980371	−	0.197161i	$-0.0631722\pi$
$823$	9.16406	+	15.8726i	0.319439	+	0.553285i	−0.660932	+	0.750446i	$0.729839\pi$
$824$	28.1898	−	28.1898i	0.982039	−	0.982039i
$825$	32.7501	+	8.77535i	1.14021	+	0.305518i
$826$	−23.3083	+	86.9878i	−0.811000	+	3.02669i
$827$	−14.0831	+	14.0831i	−0.489719	+	0.489719i	−0.908217	−	0.418499i	$-0.862556\pi$
$827$	−14.0831	+	14.0831i	−0.489719	+	0.489719i	0.418499	+	0.908217i	$0.362556\pi$
$828$	−1.01270	+	0.584683i	−0.0351938	+	0.0203191i
$829$	5.55440	−	9.62051i	0.192912	−	0.334134i	−0.753302	−	0.657675i	$-0.771540\pi$
$829$	5.55440	−	9.62051i	0.192912	−	0.334134i	0.946214	+	0.323541i	$0.104873\pi$
$830$	−6.94755	−	25.9286i	−0.241153	−	0.899995i
$831$		−	12.7558i		−	0.442495i
$832$	−20.6845	−	21.4124i	−0.717108	−	0.742340i
$833$			36.5782i			1.26736i
$834$	16.1489	+	60.2683i	0.559189	+	2.08692i
$835$	−27.0111	−	15.5949i	−0.934758	−	0.539683i
$836$	−0.522191	−	0.904461i	−0.0180603	−	0.0312814i
$837$	−21.3061	+	64.9008i	−0.736447	+	2.24330i
$838$	1.56968	+	0.420595i	0.0542237	+	0.0145292i
$839$	9.66917	−	36.0858i	0.333817	−	1.24582i	−0.571329	−	0.820721i	$-0.693572\pi$
$839$	9.66917	−	36.0858i	0.333817	−	1.24582i	0.905146	−	0.425101i	$-0.139761\pi$
$840$	−48.8694	+	48.8694i	−1.68615	+	1.68615i
$841$	−2.11059	−	3.65565i	−0.0727790	−	0.126057i
$842$	39.6427	+	22.8877i	1.36618	+	0.788762i
$843$	1.44046	+	5.37589i	0.0496122	+	0.185155i
$844$		−	0.659060i		−	0.0226858i
$845$	−14.4828	−	15.5205i	−0.498222	−	0.533922i
$846$	−57.5432			−1.97837
$847$	−12.5039	−	46.6652i	−0.429639	−	1.60344i
$848$	−5.99978	−	3.46398i	−0.206033	−	0.118953i
$849$	11.1320	+	19.2812i	0.382048	+	0.661727i
$850$	−5.63282	−	5.63282i	−0.193204	−	0.193204i
$851$	10.0201	+	2.68487i	0.343483	+	0.0920361i
$852$	0.157409	+	0.0421777i	0.00539276	+	0.00144498i
$853$	26.7514	+	26.7514i	0.915952	+	0.915952i	0.996732	−	0.0807800i	$-0.0257411\pi$
$853$	26.7514	+	26.7514i	0.915952	+	0.915952i	−0.0807800	+	0.996732i	$0.525741\pi$
$854$	−6.64697	+	3.83763i	−0.227455	+	0.131321i
$855$	−31.9128	−	18.4248i	−1.09139	−	0.630116i
$856$	20.4449	−	5.47821i	0.698794	−	0.187241i
$857$			45.3683i			1.54975i	0.632113	+	0.774877i	$0.282188\pi$
$857$			45.3683i			1.54975i	−0.632113	+	0.774877i	$0.717812\pi$
$858$	52.3564	−	50.5768i	1.78742	−	1.72666i
$859$		−	53.3187i		−	1.81921i	−0.415474	−	0.909605i	$-0.636384\pi$
$859$		−	53.3187i		−	1.81921i	0.415474	−	0.909605i	$-0.363616\pi$
$860$	0.903488	−	0.242089i	0.0308087	−	0.00825516i
$861$	−33.1872	−	19.1606i	−1.13102	−	0.652992i
$862$	−11.8991	+	6.86996i	−0.405286	+	0.233992i
$863$	29.3979	+	29.3979i	1.00072	+	1.00072i	1.00000		0.000715439i	$0.000227731\pi$
$863$	29.3979	+	29.3979i	1.00072	+	1.00072i	0.000715439		1.00000i	$0.499772\pi$
$864$	−1.24141	+	4.63302i	−0.0422337	+	0.157618i
$865$	3.40615	−	12.7119i	0.115812	−	0.432218i
$866$	29.8762	−	29.8762i	1.01523	−	1.01523i
$867$	−29.8760	+	17.2489i	−1.01464	+	0.585805i
$868$	0.0997365	−	1.79835i	0.00338528	−	0.0610400i
$869$	−7.88253	+	2.11212i	−0.267396	+	0.0716486i
$870$			35.5376i			1.20484i
$871$	44.4056	+	26.6715i	1.50463	+	0.903730i
$872$	6.50825			0.220397
$873$	11.6373	+	43.4311i	0.393864	+	1.46992i
$874$	−9.64843	−	5.57052i	−0.326363	−	0.188426i
$875$	−48.5206	+	28.0134i	−1.64029	+	0.947024i
$876$	0.889364	−	0.889364i	0.0300488	−	0.0300488i
$877$	−20.8719	−	5.59260i	−0.704793	−	0.188849i	−0.111417	−	0.993774i	$-0.535539\pi$
$877$	−20.8719	−	5.59260i	−0.704793	−	0.188849i	−0.593377	+	0.804925i	$0.702205\pi$
$878$	10.5761	−	39.4706i	0.356927	−	1.33207i
$879$	−6.28636	+	6.28636i	−0.212034	+	0.212034i
$880$	−25.1883	+	14.5425i	−0.849097	+	0.490226i
$881$	−1.88082	+	3.25767i	−0.0633664	+	0.109754i	−0.895968	−	0.444118i	$-0.853517\pi$
$881$	−1.88082	+	3.25767i	−0.0633664	+	0.109754i	0.832602	+	0.553872i	$0.186850\pi$
$882$	−137.877	+	36.9441i	−4.64257	+	1.24397i
$883$	0.613207			0.0206360			0.0103180	−	0.999947i	$-0.496716\pi$
$883$	0.613207			0.0206360			0.0103180	+	0.999947i	$0.496716\pi$
$884$	0.594240	−	0.148265i	0.0199864	−	0.00498670i
$885$		−	71.1704i		−	2.39237i
$886$	−3.19353	−	11.9184i	−0.107289	−	0.400407i
$887$	−5.20849	+	9.02137i	−0.174884	+	0.302908i	−0.940121	−	0.340841i	$-0.889288\pi$
$887$	−5.20849	+	9.02137i	−0.174884	+	0.302908i	0.765237	+	0.643748i	$0.222622\pi$
$888$	33.1536	−	19.1413i	1.11256	−	0.642338i
$889$	−17.5938	−	17.5938i	−0.590078	−	0.590078i
$890$	−5.71369	+	21.3238i	−0.191523	+	0.714775i
$891$	−79.8588	−	21.3981i	−2.67537	−	0.716863i
$892$	−0.919412	+	0.919412i	−0.0307842	+	0.0307842i
$893$	9.81605	+	17.0019i	0.328482	+	0.568947i
$894$	−47.2710	+	81.8757i	−1.58098	+	2.73833i
$895$	2.75520	+	10.2825i	0.0920962	+	0.343708i
$896$			50.0223i			1.67113i
$897$	−7.66049	+	26.7320i	−0.255776	+	0.892557i
$898$		−	43.6984i		−	1.45823i
$899$	−18.4825	−	20.6529i	−0.616424	−	0.688813i
$900$	−0.556589	+	0.964040i	−0.0185530	+	0.0321347i
$901$	3.82164	−	2.20642i	0.127317	−	0.0735067i
$902$	−11.8124	−	11.8124i	−0.393310	−	0.393310i
$903$	117.793	+	31.5627i	3.91992	+	1.05034i
$904$	−6.71974	+	25.0784i	−0.223495	+	0.834095i
$905$	0.283731	−	0.283731i	0.00943153	−	0.00943153i
$906$	−6.94232	−	12.0244i	−0.230643	−	0.399485i
$907$	−32.0996	−	18.5327i	−1.06585	−	0.615369i	−0.138805	−	0.990320i	$-0.544326\pi$
$907$	−32.0996	−	18.5327i	−1.06585	−	0.615369i	−0.927045	+	0.374951i	$0.877660\pi$
$908$	−0.171613	+	0.0459836i	−0.00569519	+	0.00152602i
$909$			41.5851i			1.37929i
$910$	−0.661665	+	38.2706i	−0.0219340	+	1.26866i
$911$		−	14.1251i		−	0.467986i	−0.972238	−	0.233993i	$-0.924821\pi$
$911$		−	14.1251i		−	0.467986i	0.972238	−	0.233993i	$-0.0751793\pi$
$912$	−38.3394	+	10.2730i	−1.26954	+	0.340173i
$913$	−27.3159	+	47.3125i	−0.904025	+	1.56582i
$914$	−27.7023	−	47.9817i	−0.916310	−	1.58709i
$915$	4.28907	−	4.28907i	0.141792	−	0.141792i
$916$	−0.252416	+	0.942028i	−0.00834005	+	0.0311255i
$917$	−6.14627	+	22.9382i	−0.202968	+	0.757486i
$918$	29.6149	+	29.6149i	0.977439	+	0.977439i
$919$	2.23667	+	3.87403i	0.0737810	+	0.127792i	0.900556	−	0.434741i	$-0.143160\pi$
$919$	2.23667	+	3.87403i	0.0737810	+	0.127792i	−0.826775	+	0.562533i	$0.809827\pi$
$920$	5.75441	−	9.96693i	0.189717	−	0.328600i
$921$	−19.4843	−	72.7163i	−0.642028	−	2.39608i
$922$	−32.7276			−1.07782
$923$	2.36204	−	1.30981i	0.0777475	−	0.0431130i
$924$	4.70023			0.154626
$925$	9.53860	−	2.55586i	0.313627	−	0.0840362i
$926$	−29.9688	−	17.3025i	−0.984836	−	0.568595i
$927$	−82.8476	+	47.8321i	−2.72107	+	1.57101i
$928$	−1.37610	−	1.37610i	−0.0451728	−	0.0451728i
$929$	1.94203	−	7.24776i	0.0637160	−	0.237791i	−0.926722	−	0.375747i	$-0.877386\pi$
$929$	1.94203	−	7.24776i	0.0637160	−	0.237791i	0.990438	+	0.137955i	$0.0440530\pi$
$930$	−8.14598	−	38.9056i	−0.267117	−	1.27577i
$931$	34.4356	+	34.4356i	1.12858	+	1.12858i
$932$	0.366972	+	0.635615i	0.0120206	+	0.0208203i
$933$	−17.2840	+	29.9367i	−0.565852	+	0.980084i
$934$	−30.5680	+	8.19068i	−1.00022	+	0.268007i
$935$		−	18.5260i		−	0.605866i
$936$	34.6853	+	62.5495i	1.13373	+	2.04450i
$937$	−51.2735			−1.67503			−0.837517	−	0.546412i	$-0.815993\pi$
$937$	−51.2735			−1.67503			−0.837517	+	0.546412i	$0.815993\pi$
$938$	−24.1736	−	90.2171i	−0.789296	−	2.94569i
$939$	27.7868	−	48.1282i	0.906789	−	1.57061i
$940$	−0.586893	+	0.338843i	−0.0191424	+	0.0110518i
$941$	0.0509394	+	0.0509394i	0.00166058	+	0.00166058i	0.707937	−	0.706276i	$-0.249626\pi$
$941$	0.0509394	+	0.0509394i	0.00166058	+	0.00166058i	−0.706276	+	0.707937i	$0.749626\pi$
$942$	−9.37187	+	34.9763i	−0.305352	+	1.13959i
$943$	6.16399	+	1.65164i	0.200727	+	0.0537847i
$944$	−37.7793	−	37.7793i	−1.22961	−	1.22961i
$945$	81.1724	−	46.8649i	2.64054	−	1.52452i
$946$	46.0386	+	26.5804i	1.49684	+	0.864204i
$947$	−4.26449	−	15.9153i	−0.138577	−	0.517178i	−0.999958	−	0.00921679i	$-0.997066\pi$
$947$	−4.26449	−	15.9153i	−0.138577	−	0.517178i	0.861380	−	0.507961i	$-0.169601\pi$
$948$		−	0.384429i		−	0.0124857i
$949$	0.360349	−	20.8426i	0.0116974	−	0.676578i
$950$	−10.6057			−0.344095
$951$	−25.8520	+	6.92703i	−0.838309	+	0.224624i
$952$	−28.6197	−	16.5236i	−0.927571	−	0.535533i
$953$	−9.42835	−	16.3304i	−0.305414	−	0.528993i	0.671939	−	0.740606i	$-0.265462\pi$
$953$	−9.42835	−	16.3304i	−0.305414	−	0.528993i	−0.977353	+	0.211613i	$0.932128\pi$
$954$	12.1767	+	12.1767i	0.394236	+	0.394236i
$955$	−12.3256	−	3.30264i	−0.398848	−	0.106871i
$956$	0.265455	+	0.0711285i	0.00858543	+	0.00230046i
$957$	51.1428	−	51.1428i	1.65321	−	1.65321i
$958$	23.0739	+	39.9652i	0.745485	+	1.29122i
$959$	−6.16690	+	10.6814i	−0.199139	+	0.344920i
$960$	−10.9799	−	40.9775i	−0.354374	−	1.32254i
$961$	24.9682	+	18.3737i	0.805424	+	0.592698i
$962$	5.84070	−	20.3817i	0.188312	−	0.657133i
$963$	−50.7907			−1.63671
$964$	−1.30429	+	0.349483i	−0.0420083	+	0.0112561i
$965$	−16.7012	+	28.9272i	−0.537629	+	0.931201i
$966$	43.4227	−	25.0701i	1.39710	−	0.806618i
$967$	27.0315	+	27.0315i	0.869275	+	0.869275i	0.992392	−	0.123117i	$-0.0392891\pi$
$967$	27.0315	+	27.0315i	0.869275	+	0.869275i	−0.123117	+	0.992392i	$0.539289\pi$
$968$	28.6778	+	7.68419i	0.921739	+	0.246979i
$969$	6.54352	−	24.4208i	0.210208	−	0.784508i
$970$	−10.4563	−	10.4563i	−0.335733	−	0.335733i
$971$	−3.21514	−	5.56878i	−0.103179	−	0.178711i	0.809814	−	0.586687i	$-0.199568\pi$
$971$	−3.21514	−	5.56878i	−0.103179	−	0.178711i	−0.912993	+	0.407976i	$0.866235\pi$
$972$	0.674921	−	1.16900i	0.0216481	−	0.0374956i
$973$	17.2813	+	64.4947i	0.554013	+	2.06761i
$974$	37.3330			1.19623
$975$	6.40838	+	25.6845i	0.205232	+	0.822561i
$976$		−	4.55352i		−	0.145754i
$977$	−2.57711	−	9.61791i	−0.0824491	−	0.307704i	0.912370	−	0.409367i	$-0.134250\pi$
$977$	−2.57711	−	9.61791i	−0.0824491	−	0.307704i	−0.994819	+	0.101663i	$0.967584\pi$
$978$	−17.4198	−	10.0573i	−0.557023	−	0.321597i
$979$	38.9100	−	22.4647i	1.24357	−	0.717975i
$980$	−1.18869	+	1.18869i	−0.0379713	+	0.0379713i
$981$	−15.0852	−	4.04206i	−0.481633	−	0.129053i
$982$	−53.3285	−	14.2893i	−1.70178	−	0.455991i
$983$	−39.3331	+	39.3331i	−1.25453	+	1.25453i	−0.300862	+	0.953668i	$0.597274\pi$
$983$	−39.3331	+	39.3331i	−1.25453	+	1.25453i	−0.953668	+	0.300862i	$0.902726\pi$
$984$	20.3949	−	11.7750i	0.650167	−	0.375374i
$985$	−16.8184	+	29.1303i	−0.535878	+	0.928167i
$986$	−16.4140	+	4.39813i	−0.522729	+	0.140065i
$987$	−88.3542			−2.81235
$988$	0.419850	−	0.699011i	0.0133572	−	0.0222385i
$989$	−20.3075			−0.645740
$990$	69.8316	−	18.7113i	2.21940	−	0.594685i
$991$	21.8841	+	12.6348i	0.695171	+	0.401357i	0.805546	−	0.592533i	$-0.201872\pi$
$991$	21.8841	+	12.6348i	0.695171	+	0.401357i	−0.110375	+	0.993890i	$0.535205\pi$
$992$	1.82195	+	1.19109i	0.0578470	+	0.0378171i
$993$	−6.00644	+	6.00644i	−0.190609	+	0.190609i
$994$	−4.70401	−	1.26044i	−0.149202	−	0.0399786i
$995$	−17.3630	−	4.65239i	−0.550443	−	0.147491i
$996$	−1.81981	−	1.81981i	−0.0576628	−	0.0576628i
$997$	−28.3485	−	49.1011i	−0.897808	−	1.55505i	−0.830291	−	0.557330i	$-0.811826\pi$
$997$	−28.3485	−	49.1011i	−0.897808	−	1.55505i	−0.0675165	−	0.997718i	$-0.521508\pi$
$998$	−11.5891	+	20.0728i	−0.366845	+	0.635394i
$999$	−50.1499	+	13.4376i	−1.58667	+	0.425147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bg.a.123.11	✓	144
13.11	odd	12	inner	403.2.bg.a.154.12	yes	144
31.30	odd	2	inner	403.2.bg.a.123.12	yes	144
403.154	even	12	inner	403.2.bg.a.154.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bg.a.123.11	✓	144	1.1	even	1	trivial
403.2.bg.a.123.12	yes	144	31.30	odd	2	inner
403.2.bg.a.154.11	yes	144	403.154	even	12	inner
403.2.bg.a.154.12	yes	144	13.11	odd	12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.359643 - 1.34220i) q^{2} +(-2.72479 - 1.57316i) q^{3} +(0.0598795 - 0.0345714i) q^{4} +(1.15466 - 1.15466i) q^{5} +(-1.13155 + 4.22301i) q^{6} +(-1.21090 + 4.51915i) q^{7} +(-2.03306 - 2.03306i) q^{8} +(3.44967 + 5.97500i) q^{9} +(-1.96506 - 1.13453i) q^{10} +(1.19523 + 4.46066i) q^{11} -0.217546 q^{12} +(-2.59320 + 2.50506i) q^{13} +6.50112 q^{14} +(-4.96269 + 1.32975i) q^{15} +(-1.92847 + 3.34020i) q^{16} +(-1.22836 - 2.12759i) q^{17} +(6.77903 - 6.77903i) q^{18} +(-3.15936 - 0.846549i) q^{19} +(0.0292223 - 0.109059i) q^{20} +(10.4088 - 10.4088i) q^{21} +(5.55727 - 3.20849i) q^{22} +(-1.22565 + 2.12288i) q^{23} +(2.34134 + 8.73801i) q^{24} +2.33351i q^{25} +(4.29493 + 2.57968i) q^{26} -12.2686i q^{27} +(0.0837253 + 0.312467i) q^{28} +(4.31093 + 2.48892i) q^{29} +(3.56959 + 6.18271i) q^{30} +(-5.29000 - 1.73664i) q^{31} +(-0.377632 - 0.101186i) q^{32} +(3.76058 - 14.0347i) q^{33} +(-2.41388 + 2.41388i) q^{34} +(3.81991 + 6.61628i) q^{35} +(0.413129 + 0.238520i) q^{36} +(-1.09529 - 4.08767i) q^{37} +4.54497i q^{38} +(11.0068 - 2.74624i) q^{39} -4.69500 q^{40} +(-0.673782 - 2.51459i) q^{41} +(-17.7142 - 10.2273i) q^{42} +(4.14220 + 7.17450i) q^{43} +(0.225781 + 0.225781i) q^{44} +(10.8823 + 2.91591i) q^{45} +(3.29014 + 0.881589i) q^{46} +(-4.24420 - 4.24420i) q^{47} +(10.5094 - 6.06758i) q^{48} +(-12.8943 - 7.44451i) q^{49} +(3.13205 - 0.839229i) q^{50} +7.72964i q^{51} +(-0.0686761 + 0.239652i) q^{52} +1.79623i q^{53} +(-16.4670 + 4.41231i) q^{54} +(6.53065 + 3.77047i) q^{55} +(11.6496 - 6.72587i) q^{56} +(7.27686 + 7.27686i) q^{57} +(1.79024 - 6.68127i) q^{58} +(-3.58528 + 13.3804i) q^{59} +(-0.251192 + 0.251192i) q^{60} +(-1.02243 + 0.590303i) q^{61} +(-0.428419 + 7.72483i) q^{62} +(-31.1792 + 8.35443i) q^{63} +8.25712i q^{64} +(-0.101777 + 5.88677i) q^{65} -20.1899 q^{66} +(-3.71837 - 13.8772i) q^{67} +(-0.147107 - 0.0849325i) q^{68} +(6.67927 - 3.85628i) q^{69} +(7.50660 - 7.50660i) q^{70} +(-0.723569 - 0.193880i) q^{71} +(5.13416 - 19.1609i) q^{72} +(-4.08817 + 4.08817i) q^{73} +(-5.09257 + 2.94020i) q^{74} +(3.67098 - 6.35833i) q^{75} +(-0.218448 + 0.0585328i) q^{76} -21.6057 q^{77} +(-7.64454 - 13.7857i) q^{78} +1.76712i q^{79} +(1.63008 + 6.08354i) q^{80} +(-8.95144 + 15.5044i) q^{81} +(-3.13277 + 1.80871i) q^{82} +(8.36517 + 8.36517i) q^{83} +(0.263427 - 0.983123i) q^{84} +(-3.87499 - 1.03830i) q^{85} +(8.13994 - 8.13994i) q^{86} +(-7.83093 - 13.5636i) q^{87} +(6.63883 - 11.4988i) q^{88} +(-2.51809 - 9.39764i) q^{89} -15.6550i q^{90} +(-8.18062 - 14.7525i) q^{91} +0.169489i q^{92} +(11.6821 + 13.0540i) q^{93} +(-4.17019 + 7.22298i) q^{94} +(-4.62548 + 2.67052i) q^{95} +(0.869789 + 0.869789i) q^{96} +(6.29497 + 1.68673i) q^{97} +(-5.35473 + 19.9841i) q^{98} +(-22.5293 + 22.5293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 8 q^{2} - 12 q^{4} - 8 q^{5} - 16 q^{7} - 28 q^{8} + 64 q^{9} - 12 q^{10} + 68 q^{16} - 52 q^{18} - 4 q^{19} - 44 q^{20} - 64 q^{28} - 4 q^{31} - 28 q^{32} + 36 q^{33} + 28 q^{35} - 12 q^{36} - 28 q^{39}+ \cdots - 160 q^{98}+O(q^{100}) \) 144 * q - 8 * q^2 - 12 * q^4 - 8 * q^5 - 16 * q^7 - 28 * q^8 + 64 * q^9 - 12 * q^10 + 68 * q^16 - 52 * q^18 - 4 * q^19 - 44 * q^20 - 64 * q^28 - 4 * q^31 - 28 * q^32 + 36 * q^33 + 28 * q^35 - 12 * q^36 - 28 * q^39 - 48 * q^40 - 8 * q^41 + 12 * q^45 - 24 * q^47 + 48 * q^49 + 40 * q^50 + 48 * q^56 + 8 * q^59 + 42 * q^62 - 84 * q^63 - 80 * q^66 + 4 * q^67 - 24 * q^69 - 96 * q^70 - 80 * q^71 + 104 * q^72 - 116 * q^76 + 24 * q^78 - 112 * q^80 + 16 * q^81 + 108 * q^82 - 92 * q^87 + 64 * q^93 + 4 * q^94 - 132 * q^95 + 120 * q^97 - 160 * q^98

Introduction

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