LMFDB - Embedded newform 820.2.bk.c.43.75

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(43,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.43"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$120$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			43.75
Character	$\chi$	$=$	820.43
Dual form			820.2.bk.c.267.75

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.525554 + 1.31293i) q^{2} -1.83316i q^{3} +(-1.44759 + 1.38003i) q^{4} +(2.14699 - 0.624854i) q^{5} +(2.40682 - 0.963425i) q^{6} +(1.07901 - 3.32085i) q^{7} +(-2.57268 - 1.17530i) q^{8} -0.360477 q^{9} +(1.94875 + 2.49046i) q^{10} +(0.282507 + 1.78368i) q^{11} +(2.52982 + 2.65366i) q^{12} +(1.79872 + 5.53588i) q^{13} +(4.92713 - 0.328618i) q^{14} +(-1.14546 - 3.93577i) q^{15} +(0.191011 - 3.99544i) q^{16} +(-5.75762 - 4.18315i) q^{17} +(-0.189450 - 0.473282i) q^{18} +(5.03222 - 2.56405i) q^{19} +(-2.24563 + 3.86745i) q^{20} +(-6.08764 - 1.97799i) q^{21} +(-2.19338 + 1.30833i) q^{22} +(-4.00584 - 2.04108i) q^{23} +(-2.15451 + 4.71613i) q^{24} +(4.21912 - 2.68311i) q^{25} +(-6.32292 + 5.27100i) q^{26} -4.83867i q^{27} +(3.02092 + 6.29628i) q^{28} +(2.41555 + 0.382585i) q^{29} +(4.56541 - 3.57237i) q^{30} +(3.51404 - 4.83666i) q^{31} +(5.34613 - 1.84903i) q^{32} +(3.26977 - 0.517881i) q^{33} +(2.46626 - 9.75784i) q^{34} +(0.241575 - 7.80404i) q^{35} +(0.521821 - 0.497470i) q^{36} +(0.0414266 - 0.261557i) q^{37} +(6.01113 + 5.25943i) q^{38} +(10.1482 - 3.29734i) q^{39} +(-6.25790 - 0.915810i) q^{40} +(6.30138 + 1.13693i) q^{41} +(-0.602410 - 9.03221i) q^{42} +(-3.73931 + 7.33880i) q^{43} +(-2.87049 - 2.19216i) q^{44} +(-0.773939 + 0.225245i) q^{45} +(0.574513 - 6.33210i) q^{46} +(0.238419 - 0.0774669i) q^{47} +(-7.32428 - 0.350153i) q^{48} +(-4.20064 - 3.05194i) q^{49} +(5.74011 + 4.12930i) q^{50} +(-7.66839 + 10.5546i) q^{51} +(-10.2435 - 5.53138i) q^{52} +(-5.27985 + 3.83604i) q^{53} +(6.35285 - 2.54298i) q^{54} +(1.72108 + 3.65302i) q^{55} +(-6.67893 + 7.27530i) q^{56} +(-4.70031 - 9.22487i) q^{57} +(0.767192 + 3.37252i) q^{58} +(-2.97884 - 9.16792i) q^{59} +(7.08965 + 4.11660i) q^{60} +(0.363458 + 0.118095i) q^{61} +(8.19703 + 2.07177i) q^{62} +(-0.388957 + 1.19709i) q^{63} +(5.23734 + 6.04734i) q^{64} +(7.32094 + 10.7615i) q^{65} +(2.39839 + 4.02082i) q^{66} +(8.48529 + 11.6790i) q^{67} +(14.1075 - 1.89023i) q^{68} +(-3.74163 + 7.34335i) q^{69} +(10.3731 - 3.78427i) q^{70} +(0.342417 + 2.16194i) q^{71} +(0.927390 + 0.423669i) q^{72} +(-11.3074 + 11.3074i) q^{73} +(0.365179 - 0.0830721i) q^{74} +(-4.91857 - 7.73432i) q^{75} +(-3.74611 + 10.6563i) q^{76} +(6.22816 + 0.986443i) q^{77} +(9.66259 + 11.5909i) q^{78} +(1.78734 - 1.78734i) q^{79} +(-2.08647 - 8.69751i) q^{80} -9.95149 q^{81} +(1.81900 + 8.87081i) q^{82} +(0.302351 - 0.302351i) q^{83} +(11.5421 - 5.53784i) q^{84} +(-14.9754 - 5.38351i) q^{85} +(-11.6006 - 1.05252i) q^{86} +(0.701340 - 4.42808i) q^{87} +(1.36956 - 4.92087i) q^{88} +(13.6784 - 6.96948i) q^{89} +(-0.702479 - 0.897752i) q^{90} +20.3246 q^{91} +(8.61556 - 2.57356i) q^{92} +(-8.86638 - 6.44180i) q^{93} +(0.227011 + 0.272315i) q^{94} +(9.20197 - 8.64938i) q^{95} +(-3.38957 - 9.80031i) q^{96} +(-1.50476 + 1.09328i) q^{97} +(1.79933 - 7.11912i) q^{98} +(-0.101837 - 0.642975i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) $ 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.525554	+	1.31293i	0.371623	+	0.928384i
$2$	0.525554	+	1.31293i	0.371623	+	0.928384i
$3$		−	1.83316i		−	1.05838i	−0.848505	−	0.529188i	$-0.822497\pi$
$3$		−	1.83316i		−	1.05838i	0.848505	−	0.529188i	$-0.177503\pi$
$4$	−1.44759	+	1.38003i	−0.723793	+	0.690017i
$5$	2.14699	−	0.624854i	0.960162	−	0.279443i
$5$	2.14699	−	0.624854i	0.960162	−	0.279443i
$6$	2.40682	−	0.963425i	0.982579	−	0.393316i
$7$	1.07901	−	3.32085i	0.407827	−	1.25516i	−0.510685	−	0.859768i	$-0.670608\pi$
$7$	1.07901	−	3.32085i	0.407827	−	1.25516i	0.918512	−	0.395394i	$-0.129392\pi$
$8$	−2.57268	−	1.17530i	−0.909579	−	0.415532i
$9$	−0.360477			−0.120159
$10$	1.94875	+	2.49046i	0.616249	+	0.787552i
$11$	0.282507	+	1.78368i	0.0851792	+	0.537800i	0.992969	+	0.118375i	$0.0377684\pi$
$11$	0.282507	+	1.78368i	0.0851792	+	0.537800i	−0.907790	+	0.419425i	$0.862232\pi$
$12$	2.52982	+	2.65366i	0.730297	+	0.766045i
$13$	1.79872	+	5.53588i	0.498874	+	1.53538i	0.810830	+	0.585281i	$0.199016\pi$
$13$	1.79872	+	5.53588i	0.498874	+	1.53538i	−0.311956	+	0.950097i	$0.600984\pi$
$14$	4.92713	−	0.328618i	1.31683	−	0.0878269i
$15$	−1.14546	−	3.93577i	−0.295756	−	1.01621i
$16$	0.191011	−	3.99544i	0.0477527	−	0.998859i
$17$	−5.75762	−	4.18315i	−1.39643	−	1.01456i	−0.995125	−	0.0986182i	$-0.968558\pi$
$17$	−5.75762	−	4.18315i	−1.39643	−	1.01456i	−0.401302	−	0.915946i	$-0.631442\pi$
$18$	−0.189450	−	0.473282i	−0.0446538	−	0.111554i
$19$	5.03222	−	2.56405i	1.15447	−	0.588232i	0.231399	−	0.972859i	$-0.425670\pi$
$19$	5.03222	−	2.56405i	1.15447	−	0.588232i	0.923072	+	0.384626i	$0.125670\pi$
$20$	−2.24563	+	3.86745i	−0.502138	+	0.864787i
$21$	−6.08764	−	1.97799i	−1.32843	−	0.431634i
$22$	−2.19338	+	1.30833i	−0.467630	+	0.278938i
$23$	−4.00584	−	2.04108i	−0.835276	−	0.425594i	−0.0166085	−	0.999862i	$-0.505287\pi$
$23$	−4.00584	−	2.04108i	−0.835276	−	0.425594i	−0.818668	+	0.574268i	$0.805287\pi$
$24$	−2.15451	+	4.71613i	−0.439789	+	0.962676i
$25$	4.21912	−	2.68311i	0.843823	−	0.536621i
$26$	−6.32292	+	5.27100i	−1.24003	+	1.03373i
$27$		−	4.83867i		−	0.931202i
$28$	3.02092	+	6.29628i	0.570901	+	1.18988i
$29$	2.41555	+	0.382585i	0.448556	+	0.0710442i	0.376626	−	0.926365i	$-0.377084\pi$
$29$	2.41555	+	0.382585i	0.448556	+	0.0710442i	0.0719298	+	0.997410i	$0.477084\pi$
$30$	4.56541	−	3.57237i	0.833525	−	0.652222i
$31$	3.51404	−	4.83666i	0.631141	−	0.868690i	−0.366964	−	0.930235i	$-0.619603\pi$
$31$	3.51404	−	4.83666i	0.631141	−	0.868690i	0.998104	+	0.0615448i	$0.0196027\pi$
$32$	5.34613	−	1.84903i	0.945071	−	0.326866i
$33$	3.26977	−	0.517881i	0.569195	−	0.0901516i
$34$	2.46626	−	9.75784i	0.422960	−	1.67346i
$35$	0.241575	−	7.80404i	0.0408336	−	1.31912i
$36$	0.521821	−	0.497470i	0.0869702	−	0.0829117i
$37$	0.0414266	−	0.261557i	0.00681049	−	0.0429997i	−0.984049	−	0.177897i	$-0.943071\pi$
$37$	0.0414266	−	0.261557i	0.00681049	−	0.0429997i	0.990860	+	0.134898i	$0.0430705\pi$
$38$	6.01113	+	5.25943i	0.975133	+	0.853192i
$39$	10.1482	−	3.29734i	1.62501	−	0.527997i
$40$	−6.25790	−	0.915810i	−0.989461	−	0.144802i
$41$	6.30138	+	1.13693i	0.984110	+	0.177559i
$41$	6.30138	+	1.13693i	0.984110	+	0.177559i
$42$	−0.602410	−	9.03221i	−0.0929539	−	1.39370i
$43$	−3.73931	+	7.33880i	−0.570239	+	1.11916i	0.408253	+	0.912869i	$0.366138\pi$
$43$	−3.73931	+	7.33880i	−0.570239	+	1.11916i	−0.978491	+	0.206288i	$0.933862\pi$
$44$	−2.87049	−	2.19216i	−0.432743	−	0.330481i
$45$	−0.773939	+	0.225245i	−0.115372	+	0.0335776i
$46$	0.574513	−	6.33210i	0.0847074	−	0.933617i
$47$	0.238419	−	0.0774669i	0.0347769	−	0.0112997i	−0.291577	−	0.956547i	$-0.594180\pi$
$47$	0.238419	−	0.0774669i	0.0347769	−	0.0112997i	0.326354	+	0.945248i	$0.394180\pi$
$48$	−7.32428	−	0.350153i	−1.05717	−	0.0505402i
$49$	−4.20064	−	3.05194i	−0.600091	−	0.435992i
$50$	5.74011	+	4.12930i	0.811775	+	0.583971i
$51$	−7.66839	+	10.5546i	−1.07379	+	1.47794i
$52$	−10.2435	−	5.53138i	−1.42052	−	0.767064i
$53$	−5.27985	+	3.83604i	−0.725244	+	0.526920i	−0.888055	−	0.459737i	$-0.847944\pi$
$53$	−5.27985	+	3.83604i	−0.725244	+	0.526920i	0.162812	+	0.986657i	$0.447944\pi$
$54$	6.35285	−	2.54298i	0.864513	−	0.346056i
$55$	1.72108	+	3.65302i	0.232070	+	0.492573i
$56$	−6.67893	+	7.27530i	−0.892510	+	0.972203i
$57$	−4.70031	−	9.22487i	−0.622571	−	1.22186i
$58$	0.767192	+	3.37252i	0.100737	+	0.442834i
$59$	−2.97884	−	9.16792i	−0.387812	−	1.19356i	−0.934420	−	0.356173i	$-0.884081\pi$
$59$	−2.97884	−	9.16792i	−0.387812	−	1.19356i	0.546609	−	0.837388i	$-0.315919\pi$
$60$	7.08965	+	4.11660i	0.915270	+	0.531451i
$61$	0.363458	+	0.118095i	0.0465360	+	0.0151205i	0.332193	−	0.943212i	$-0.392212\pi$
$61$	0.363458	+	0.118095i	0.0465360	+	0.0151205i	−0.285656	+	0.958332i	$0.592212\pi$
$62$	8.19703	+	2.07177i	1.04102	+	0.263115i
$63$	−0.388957	+	1.19709i	−0.0490040	+	0.150819i
$64$	5.23734	+	6.04734i	0.654667	+	0.755917i
$65$	7.32094	+	10.7615i	0.908051	+	1.33480i
$66$	2.39839	+	4.02082i	0.295221	+	0.494929i
$67$	8.48529	+	11.6790i	1.03664	+	1.42682i	0.899841	+	0.436219i	$0.143683\pi$
$67$	8.48529	+	11.6790i	1.03664	+	1.42682i	0.136803	+	0.990598i	$0.456317\pi$
$68$	14.1075	−	1.89023i	1.71079	−	0.229225i
$69$	−3.74163	+	7.34335i	−0.450439	+	0.884036i
$70$	10.3731	−	3.78427i	1.23983	−	0.452307i
$71$	0.342417	+	2.16194i	0.0406375	+	0.256575i	0.999640	−	0.0268219i	$-0.00853869\pi$
$71$	0.342417	+	2.16194i	0.0406375	+	0.256575i	−0.959003	+	0.283397i	$0.908539\pi$
$72$	0.927390	+	0.423669i	0.109294	+	0.0499298i
$73$	−11.3074	+	11.3074i	−1.32343	+	1.32343i	−0.412445	+	0.910982i	$0.635325\pi$
$73$	−11.3074	+	11.3074i	−1.32343	+	1.32343i	−0.910982	+	0.412445i	$0.864675\pi$
$74$	0.365179	−	0.0830721i	0.0424512	−	0.00965693i
$75$	−4.91857	−	7.73432i	−0.567947	−	0.893082i
$76$	−3.74611	+	10.6563i	−0.429708	+	1.22236i
$77$	6.22816	+	0.986443i	0.709764	+	0.112416i
$78$	9.66259	+	11.5909i	1.09407	+	1.31241i
$79$	1.78734	−	1.78734i	0.201091	−	0.201091i	−0.599376	−	0.800467i	$-0.704585\pi$
$79$	1.78734	−	1.78734i	0.201091	−	0.201091i	0.800467	+	0.599376i	$0.204585\pi$
$80$	−2.08647	−	8.69751i	−0.233274	−	0.972411i
$81$	−9.95149			−1.10572
$82$	1.81900	+	8.87081i	0.200875	+	0.979617i
$83$	0.302351	−	0.302351i	0.0331874	−	0.0331874i	−0.690318	−	0.723506i	$-0.742530\pi$
$83$	0.302351	−	0.302351i	0.0331874	−	0.0331874i	0.723506	+	0.690318i	$0.242530\pi$
$84$	11.5421	−	5.53784i	1.25934	−	0.604228i
$85$	−14.9754	−	5.38351i	−1.62431	−	0.583924i
$86$	−11.6006	−	1.05252i	−1.25092	−	0.113496i
$87$	0.701340	−	4.42808i	0.0751915	−	0.474740i
$88$	1.36956	−	4.92087i	0.145996	−	0.524566i
$89$	13.6784	−	6.96948i	1.44991	−	0.738764i	0.461012	−	0.887394i	$-0.347486\pi$
$89$	13.6784	−	6.96948i	1.44991	−	0.738764i	0.988893	+	0.148630i	$0.0474863\pi$
$90$	−0.702479	−	0.897752i	−0.0740478	−	0.0946313i
$91$	20.3246			2.13060
$92$	8.61556	−	2.57356i	0.898234	−	0.268313i
$93$	−8.86638	−	6.44180i	−0.919401	−	0.667984i
$94$	0.227011	+	0.272315i	0.0234144	+	0.0280871i
$95$	9.20197	−	8.64938i	0.944102	−	0.887408i
$96$	−3.38957	−	9.80031i	−0.345947	−	1.00024i
$97$	−1.50476	+	1.09328i	−0.152786	+	0.111005i	−0.661552	−	0.749900i	$-0.730102\pi$
$97$	−1.50476	+	1.09328i	−0.152786	+	0.111005i	0.508766	+	0.860905i	$0.330102\pi$
$98$	1.79933	−	7.11912i	0.181760	−	0.719140i
$99$	−0.101837	−	0.642975i	−0.0102350	−	0.0646215i
$100$	−2.40475	+	9.70655i	−0.240475	+	0.970655i
$101$	−6.79231	+	3.46086i	−0.675860	+	0.344368i	−0.758002	−	0.652253i	$-0.773824\pi$
$101$	−6.79231	+	3.46086i	−0.675860	+	0.344368i	0.0821413	+	0.996621i	$0.473824\pi$
$102$	−17.8877	−	4.52105i	−1.77114	−	0.447651i
$103$	−0.993032	+	0.505975i	−0.0978464	+	0.0498552i	−0.502229	−	0.864735i	$-0.667486\pi$
$103$	−0.993032	+	0.505975i	−0.0978464	+	0.0498552i	0.404382	+	0.914590i	$0.367486\pi$
$104$	1.87881	−	16.3561i	0.184232	−	1.60385i
$105$	−14.3061	−	0.442845i	−1.39613	−	0.0432173i
$106$	−7.81131	−	4.91605i	−0.758701	−	0.477489i
$107$	−3.25945	+	1.66077i	−0.315103	+	0.160553i	−0.604388	−	0.796690i	$-0.706582\pi$
$107$	−3.25945	+	1.66077i	−0.315103	+	0.160553i	0.289285	+	0.957243i	$0.406582\pi$
$108$	6.67753	+	7.00439i	0.642546	+	0.673998i
$109$	−9.10287	+	9.10287i	−0.871897	+	0.871897i	−0.992679	−	0.120782i	$-0.961460\pi$
$109$	−9.10287	+	9.10287i	−0.871897	+	0.871897i	0.120782	+	0.992679i	$0.461460\pi$
$110$	−3.89165	+	4.17952i	−0.371054	+	0.398502i
$111$	−0.479476	−	0.0759416i	−0.0455099	−	0.00720805i
$112$	−13.0621	−	4.94543i	−1.23426	−	0.467299i
$113$	−0.806991	−	5.09514i	−0.0759153	−	0.479310i	−0.996130	−	0.0878956i	$-0.971986\pi$
$113$	−0.806991	−	5.09514i	−0.0759153	−	0.479310i	0.920214	−	0.391415i	$-0.128014\pi$
$114$	9.64137	−	11.0194i	0.902997	−	1.03206i
$115$	−9.87587	−	1.87911i	−0.920930	−	0.175228i
$116$	−4.02469	+	2.77971i	−0.373683	+	0.258090i
$117$	−0.648396	−	1.99556i	−0.0599442	−	0.184489i
$118$	10.4713	−	8.72925i	0.963963	−	0.803592i
$119$	−20.1041	+	14.6065i	−1.84294	+	1.33898i
$120$	−1.67883	+	11.4717i	−0.153255	+	1.04722i
$121$	7.35991	−	2.39138i	0.669083	−	0.217398i
$122$	0.0359664	+	0.539261i	0.00325625	+	0.0488224i
$123$	2.08418	−	11.5514i	0.187924	−	1.04156i
$124$	1.58788	+	11.8510i	0.142596	+	1.06425i
$125$	7.38184	−	8.39693i	0.660252	−	0.751044i
$126$	−1.77611	+	0.118459i	−0.158229	+	0.0105532i
$127$	−10.8815	−	1.72345i	−0.965573	−	0.152932i	−0.346314	−	0.938119i	$-0.612567\pi$
$127$	−10.8815	−	1.72345i	−0.965573	−	0.152932i	−0.619259	+	0.785187i	$0.712567\pi$
$128$	−5.18725	+	10.0545i	−0.458492	+	0.888698i
$129$	13.4532	+	6.85475i	1.18449	+	0.603527i
$130$	−10.2816	+	15.2677i	−0.901759	+	1.33906i
$131$	11.9181	+	8.65902i	1.04129	+	0.756542i	0.970537	−	0.240952i	$-0.0774596\pi$
$131$	11.9181	+	8.65902i	1.04129	+	0.756542i	0.0707535	+	0.997494i	$0.477460\pi$
$132$	−4.01858	+	5.26208i	−0.349773	+	0.458005i
$133$	−3.08499	−	19.4779i	−0.267503	−	1.68895i
$134$	−10.8743	+	17.2786i	−0.939394	+	1.49264i
$135$	−3.02346	−	10.3886i	−0.260218	−	0.894105i
$136$	9.89603	+	17.5288i	0.848577	+	1.50309i
$137$	−3.24368			−0.277126			−0.138563	−	0.990354i	$-0.544248\pi$
$137$	−3.24368			−0.277126			−0.138563	+	0.990354i	$0.544248\pi$
$138$	−11.6078	−	1.05317i	−0.988118	−	0.0896522i
$139$	0.289512	−	0.891025i	0.0245561	−	0.0755758i	−0.938027	−	0.346561i	$-0.887349\pi$
$139$	0.289512	−	0.891025i	0.0245561	−	0.0755758i	0.962584	+	0.270985i	$0.0873494\pi$
$140$	10.4201	+	11.6304i	0.880663	+	0.982948i
$141$	−0.142009	−	0.437059i	−0.0119593	−	0.0368070i
$142$	−2.65852	+	1.58579i	−0.223098	+	0.133076i
$143$	−9.36610	+	4.77227i	−0.783233	+	0.399077i
$144$	−0.0688549	+	1.44026i	−0.00573791	+	0.120022i
$145$	5.42521	−	0.687958i	0.450539	−	0.0571318i
$146$	−20.7885	−	8.90319i	−1.72046	−	0.736833i
$147$	−5.59470	+	7.70044i	−0.461443	+	0.635122i
$148$	0.300989	+	0.435797i	0.0247412	+	0.0358223i
$149$	−2.00618	+	12.6665i	−0.164353	+	1.03768i	0.758259	+	0.651953i	$0.226050\pi$
$149$	−2.00618	+	12.6665i	−0.164353	+	1.03768i	−0.922612	+	0.385729i	$0.873950\pi$
$150$	7.56967	−	10.5225i	0.618061	−	0.859162i
$151$	−8.21940	+	16.1315i	−0.668885	+	1.31276i	0.268100	+	0.963391i	$0.413604\pi$
$151$	−8.21940	+	16.1315i	−0.668885	+	1.31276i	−0.936985	+	0.349370i	$0.886396\pi$
$152$	−15.9598	+	0.682085i	−1.29451	+	0.0553244i
$153$	2.07549	+	1.50793i	0.167793	+	0.121909i
$154$	1.97810	+	8.69558i	0.159400	+	0.700710i
$155$	4.52240	−	12.5800i	0.363248	−	1.01045i
$156$	−10.1399	+	18.7780i	−0.811842	+	1.50344i
$157$	21.1913	+	6.88548i	1.69125	+	0.549521i	0.987041	−	0.160470i	$-0.0513011\pi$
$157$	21.1913	+	6.88548i	1.69125	+	0.549521i	0.704211	+	0.709991i	$0.251301\pi$
$158$	3.28600	+	1.40731i	0.261420	+	0.111960i
$159$	7.03207	+	9.67882i	0.557680	+	0.767580i
$160$	10.3227	−	7.31040i	0.816081	−	0.577938i
$161$	−11.1004	+	11.1004i	−0.874838	+	0.874838i
$162$	−5.23004	−	13.0656i	−0.410911	−	1.02653i
$163$	−4.15115	+	4.15115i	−0.325143	+	0.325143i	−0.850736	−	0.525593i	$-0.823844\pi$
$163$	−4.15115	+	4.15115i	−0.325143	+	0.325143i	0.525593	+	0.850736i	$0.323844\pi$
$164$	−10.6908	+	7.05031i	−0.834811	+	0.550537i
$165$	6.69656	−	3.15502i	0.521327	−	0.245618i
$166$	0.555869	+	0.238065i	0.0431438	+	0.0184774i
$167$	−10.3090			−0.797736			−0.398868	−	0.917008i	$-0.630597\pi$
$167$	−10.3090			−0.797736			−0.398868	+	0.917008i	$0.630597\pi$
$168$	13.3368	+	12.2436i	1.02896	+	0.944611i
$169$	−16.8934	+	12.2738i	−1.29949	+	0.944136i
$170$	−0.802187	−	22.4910i	−0.0615250	−	1.72498i
$171$	−1.81400	+	0.924279i	−0.138720	+	0.0706814i
$172$	−4.71483	−	15.7839i	−0.359502	−	1.20351i
$173$	12.1066	−	12.1066i	0.920451	−	0.920451i	−0.0766104	−	0.997061i	$-0.524410\pi$
$173$	12.1066	−	12.1066i	0.920451	−	0.920451i	0.997061	+	0.0766104i	$0.0244098\pi$
$174$	6.18237	−	1.40639i	0.468684	−	0.106618i
$175$	−4.35772	−	16.9061i	−0.329413	−	1.27798i
$176$	7.18055	−	0.788038i	0.541254	−	0.0594006i
$177$	−16.8063	+	5.46069i	−1.26324	+	0.410450i
$178$	16.3392	+	14.2960i	1.22467	+	1.07153i
$179$	−17.1633	−	2.71840i	−1.28284	−	0.203182i	−0.522464	−	0.852661i	$-0.674987\pi$
$179$	−17.1633	−	2.71840i	−1.28284	−	0.203182i	−0.760380	+	0.649479i	$0.774987\pi$
$180$	0.809497	−	1.39412i	0.0603364	−	0.103912i
$181$	2.35106	+	14.8440i	0.174753	+	1.10335i	0.906635	+	0.421917i	$0.138642\pi$
$181$	2.35106	+	14.8440i	0.174753	+	1.10335i	−0.731881	+	0.681432i	$0.761358\pi$
$182$	10.6817	+	26.6849i	0.791780	+	1.97802i
$183$	0.216486	−	0.666277i	0.0160031	−	0.0492526i
$184$	7.90686	+	9.95911i	0.582901	+	0.734195i
$185$	−0.0744926	−	0.587446i	−0.00547680	−	0.0431899i
$186$	3.79789	−	15.0265i	0.278475	−	1.10179i
$187$	5.83484	−	11.4515i	0.426686	−	0.837419i
$188$	−0.238224	+	0.441166i	−0.0173743	+	0.0321753i
$189$	−16.0685	−	5.22096i	−1.16881	−	0.379769i
$190$	16.1922	+	7.53585i	1.17470	+	0.546708i
$191$	−5.03260	+	5.03260i	−0.364146	+	0.364146i	−0.865337	−	0.501191i	$-0.832896\pi$
$191$	−5.03260	+	5.03260i	−0.364146	+	0.364146i	0.501191	+	0.865337i	$0.332896\pi$
$192$	11.0857	−	9.60088i	0.800045	−	0.692884i
$193$	−10.9463	+	7.95298i	−0.787934	+	0.572468i	−0.907350	−	0.420377i	$-0.861898\pi$
$193$	−10.9463	+	7.95298i	−0.787934	+	0.572468i	0.119415	+	0.992844i	$0.461898\pi$
$194$	−2.22623	−	1.40108i	−0.159834	−	0.100592i
$195$	19.7276	−	13.4205i	1.41272	−	0.961059i
$196$	10.2926	−	1.37908i	0.735184	−	0.0985054i
$197$	0.0744019	+	0.469755i	0.00530092	+	0.0334687i	0.990197	−	0.139678i	$-0.0446066\pi$
$197$	0.0744019	+	0.469755i	0.00530092	+	0.0334687i	−0.984896	+	0.173146i	$0.944607\pi$
$198$	0.790663	−	0.471624i	0.0561900	−	0.0335169i
$199$	−3.40628	+	6.68519i	−0.241464	+	0.473901i	−0.979654	−	0.200692i	$-0.935681\pi$
$199$	−3.40628	+	6.68519i	−0.241464	+	0.473901i	0.738190	+	0.674593i	$0.235681\pi$
$200$	−14.0079	+	1.94404i	−0.990507	+	0.137464i
$201$	21.4095	−	15.5549i	1.51011	−	1.09716i
$202$	−8.11360	−	7.09899i	−0.570871	−	0.499483i
$203$	3.87690	−	7.60885i	0.272105	−	0.534036i
$204$	−3.46510	−	25.8614i	−0.242606	−	1.81066i
$205$	14.2394	−	1.49646i	0.994523	−	0.104517i
$206$	−1.18620	−	1.03787i	−0.0826467	−	0.0723116i
$207$	1.44401	+	0.735761i	0.100366	+	0.0511390i
$208$	22.4618	−	6.12925i	1.55745	−	0.424987i
$209$	5.99508	+	8.25152i	0.414688	+	0.570770i
$210$	−6.93718	−	19.0156i	−0.478711	−	1.31220i
$211$	−14.8419	−	7.56235i	−1.02176	−	0.520613i	−0.138929	−	0.990302i	$-0.544366\pi$
$211$	−14.8419	−	7.56235i	−1.02176	−	0.520613i	−0.882832	+	0.469689i	$0.844366\pi$
$212$	2.34918	−	12.8394i	0.161342	−	0.881812i
$213$	3.96318	−	0.627706i	0.271553	−	0.0430097i
$214$	−3.89350	−	3.40661i	−0.266154	−	0.232871i
$215$	−3.44257	+	18.0928i	−0.234781	+	1.23392i
$216$	−5.68689	+	12.4483i	−0.386944	+	0.847002i
$217$	−12.2701	−	16.8884i	−0.832951	−	1.14646i
$218$	−16.7355	−	7.16741i	−1.13347	−	0.485438i
$219$	20.7282	+	20.7282i	1.40068	+	1.40068i
$220$	−7.53270	−	2.91291i	−0.507854	−	0.196388i
$221$	12.8011	−	39.3978i	0.861097	−	2.65018i
$222$	−0.152284	−	0.669431i	−0.0102207	−	0.0449293i
$223$	−2.43859	−	1.24252i	−0.163300	−	0.0832055i	0.370430	−	0.928860i	$-0.379210\pi$
$223$	−2.43859	−	1.24252i	−0.163300	−	0.0832055i	−0.533730	+	0.845655i	$0.679210\pi$
$224$	−0.371840	−	19.7488i	−0.0248446	−	1.31952i
$225$	−1.52089	+	0.967198i	−0.101393	+	0.0644798i
$226$	6.26546	−	3.73730i	0.416772	−	0.248601i
$227$	−16.8347	−	5.46993i	−1.11736	−	0.363052i	−0.308600	−	0.951192i	$-0.599861\pi$
$227$	−16.8347	−	5.46993i	−1.11736	−	0.363052i	−0.808759	+	0.588140i	$0.799861\pi$
$228$	19.5347	+	6.86721i	1.29372	+	0.454792i
$229$	4.37280	−	0.692584i	0.288963	−	0.0457672i	−0.0102702	−	0.999947i	$-0.503269\pi$
$229$	4.37280	−	0.692584i	0.288963	−	0.0457672i	0.299233	+	0.954180i	$0.403269\pi$
$230$	−2.72316	−	13.9539i	−0.179560	−	0.920095i
$231$	1.80831	−	11.4172i	0.118978	−	0.751197i
$232$	−5.76477	−	3.82326i	−0.378476	−	0.251009i
$233$	5.10606	+	15.7148i	0.334509	+	1.02951i	0.966963	+	0.254915i	$0.0820475\pi$
$233$	5.10606	+	15.7148i	0.334509	+	1.02951i	−0.632455	+	0.774597i	$0.717952\pi$
$234$	2.27927	−	1.90007i	0.149000	−	0.124212i
$235$	0.463476	−	0.315297i	0.0302339	−	0.0205677i
$236$	16.9642	+	9.16045i	1.10427	+	0.596295i
$237$	−3.27648	−	3.27648i	−0.212830	−	0.212830i
$238$	−29.7432	−	18.7189i	−1.92796	−	1.21336i
$239$	6.65160	+	13.0545i	0.430256	+	0.844425i	0.999748	+	0.0224284i	$0.00713978\pi$
$239$	6.65160	+	13.0545i	0.430256	+	0.844425i	−0.569492	+	0.821997i	$0.692860\pi$
$240$	−15.9439	+	3.82483i	−1.02918	+	0.246892i
$241$	−2.40231	−	3.30650i	−0.154746	−	0.212990i	0.724604	−	0.689166i	$-0.242023\pi$
$241$	−2.40231	−	3.30650i	−0.154746	−	0.212990i	−0.879350	+	0.476175i	$0.842023\pi$
$242$	7.00775	+	8.40627i	0.450476	+	0.540376i
$243$			3.72666i			0.239065i
$244$	−0.689112	+	0.330632i	−0.0441158	+	0.0211666i
$245$	−10.9257	−	3.92770i	−0.698020	−	0.250932i
$246$	16.2616	−	3.33452i	1.03680	−	0.212601i
$247$	23.2458	+	23.2458i	1.47910	+	1.47910i
$248$	−14.7250	+	8.31312i	−0.935040	+	0.527883i
$249$	−0.554258	−	0.554258i	−0.0351247	−	0.0351247i
$250$	14.9042	+	5.27882i	0.942622	+	0.333862i
$251$	−20.1452	+	14.6364i	−1.27156	+	0.923839i	−0.999263	−	0.0383758i	$-0.987782\pi$
$251$	−20.1452	+	14.6364i	−1.27156	+	0.923839i	−0.272292	+	0.962215i	$0.587782\pi$
$252$	−1.08897	−	2.26966i	−0.0685988	−	0.142975i
$253$	2.50895	−	7.72177i	0.157737	−	0.485463i
$254$	−3.45601	−	15.1924i	−0.216850	−	0.953255i
$255$	−9.86884	+	27.4523i	−0.618011	+	1.71913i
$256$	−15.9270	−	1.52634i	−0.995439	−	0.0953964i
$257$	−2.91868	+	4.01722i	−0.182063	+	0.250588i	−0.890287	−	0.455400i	$-0.849496\pi$
$257$	−2.91868	+	4.01722i	−0.182063	+	0.250588i	0.708225	+	0.705987i	$0.249496\pi$
$258$	−1.92944	+	21.2657i	−0.120122	+	1.32394i
$259$	−0.823891	−	0.419794i	−0.0511941	−	0.0260847i
$260$	−25.4490	−	5.47510i	−1.57828	−	0.339551i
$261$	−0.870748	−	0.137913i	−0.0538980	−	0.00853660i
$262$	−5.10510	+	20.1985i	−0.315394	+	1.24787i
$263$	19.6515	+	14.2776i	1.21176	+	0.880396i	0.995390	−	0.0959150i	$-0.0305777\pi$
$263$	19.6515	+	14.2776i	1.21176	+	0.880396i	0.216372	+	0.976311i	$0.430578\pi$
$264$	−9.02074	−	2.51063i	−0.555188	−	0.154518i
$265$	−8.93882	+	11.5351i	−0.549107	+	0.708593i
$266$	23.9518	−	14.2871i	1.46858	−	0.875996i
$267$	−12.7762	−	25.0747i	−0.781889	−	1.53454i
$268$	−28.4006	−	5.19637i	−1.73484	−	0.317419i
$269$	17.8811	−	5.80994i	1.09023	−	0.354238i	0.291896	−	0.956450i	$-0.405714\pi$
$269$	17.8811	−	5.80994i	1.09023	−	0.354238i	0.798336	+	0.602212i	$0.205714\pi$
$270$	12.0505	−	9.42935i	0.733370	−	0.573852i
$271$	2.78691	+	0.905521i	0.169293	+	0.0550065i	0.392437	−	0.919779i	$-0.371632\pi$
$271$	2.78691	+	0.905521i	0.169293	+	0.0550065i	−0.223144	+	0.974785i	$0.571632\pi$
$272$	−17.8133	+	22.2052i	−1.08009	+	1.34639i
$273$		−	37.2583i		−	2.25498i
$274$	−1.70473	−	4.25874i	−0.102986	−	0.257280i
$275$	5.97774	+	6.76756i	0.360471	+	0.408099i
$276$	−4.71775	−	15.7937i	−0.283975	−	0.950669i
$277$	29.9381	−	4.74173i	1.79881	−	0.284903i	0.834757	−	0.550619i	$-0.185608\pi$
$277$	29.9381	−	4.74173i	1.79881	−	0.284903i	0.964051	+	0.265716i	$0.0856083\pi$
$278$	1.32201	−	0.0881725i	0.0792889	−	0.00528823i
$279$	−1.26673	+	1.74350i	−0.0758371	+	0.104381i
$280$	−9.79359	+	19.7933i	−0.585279	+	1.18288i
$281$	1.11825	−	2.19468i	0.0667089	−	0.130924i	−0.855244	−	0.518225i	$-0.826593\pi$
$281$	1.11825	−	2.19468i	0.0667089	−	0.130924i	0.921953	+	0.387302i	$0.126593\pi$
$282$	0.499196	−	0.416147i	0.0297267	−	0.0247812i
$283$	1.09404	−	6.90747i	0.0650337	−	0.410606i	−0.933599	−	0.358321i	$-0.883349\pi$
$283$	1.09404	−	6.90747i	0.0650337	−	0.410606i	0.998632	−	0.0522856i	$-0.0166506\pi$
$284$	−3.47923	−	2.65704i	−0.206454	−	0.157667i
$285$	−15.8557	−	16.8687i	−0.939211	−	0.999215i
$286$	−11.1881	−	9.78898i	−0.661564	−	0.578834i
$287$	10.5748	−	19.6992i	0.624212	−	1.16280i
$288$	−1.92715	+	0.666533i	−0.113559	+	0.0392759i
$289$	10.3981	+	32.0020i	0.611653	+	1.88247i
$290$	3.75448	+	6.76138i	0.220471	+	0.397042i
$291$	2.00415	+	2.75847i	0.117485	+	0.161705i
$292$	0.763832	−	31.9730i	0.0446999	−	1.87108i
$293$	−1.55681	+	0.505839i	−0.0909500	+	0.0295514i	−0.354139	−	0.935193i	$-0.615226\pi$
$293$	−1.55681	+	0.505839i	−0.0909500	+	0.0295514i	0.263189	+	0.964744i	$0.415226\pi$
$294$	−13.0505	−	3.29847i	−0.761120	−	0.192371i
$295$	−12.1241	−	17.8221i	−0.705894	−	1.03764i
$296$	−0.413986	+	0.624213i	−0.0240624	+	0.0362817i
$297$	8.63064	−	1.36696i	0.500801	−	0.0793190i
$298$	−17.6846	+	4.02296i	−1.02444	+	0.233044i
$299$	4.09380	−	25.8472i	0.236750	−	1.49478i
$300$	17.7937	+	4.40830i	1.02732	+	0.254513i
$301$	20.3363	+	20.3363i	1.17216	+	1.17216i
$302$	−25.4993	−	2.31356i	−1.46732	−	0.133130i
$303$	6.34430	+	12.4514i	0.364471	+	0.715314i
$304$	−9.28328	−	20.5957i	−0.532432	−	1.18124i
$305$	0.854132	+	0.0264397i	0.0489075	+	0.00151393i
$306$	−0.889030	+	3.51747i	−0.0508225	+	0.201081i
$307$	−4.93736	−	9.69011i	−0.281790	−	0.553044i	0.706116	−	0.708096i	$-0.250446\pi$
$307$	−4.93736	−	9.69011i	−0.281790	−	0.553044i	−0.987906	+	0.155052i	$0.950446\pi$
$308$	−10.3771	+	7.16711i	−0.591291	+	0.408384i
$309$	0.927534	+	1.82039i	0.0527655	+	0.103558i
$310$	18.8935	−	0.673874i	1.07308	−	0.0382735i
$311$	3.14255	−	0.497731i	0.178198	−	0.0282237i	−0.0666978	−	0.997773i	$-0.521246\pi$
$311$	3.14255	−	0.497731i	0.178198	−	0.0282237i	0.244895	+	0.969549i	$0.421246\pi$
$312$	−29.9833	−	3.44416i	−1.69747	−	0.194987i
$313$	−1.29355	−	1.78042i	−0.0731159	−	0.100635i	0.770893	−	0.636965i	$-0.219810\pi$
$313$	−1.29355	−	1.78042i	−0.0731159	−	0.100635i	−0.844009	+	0.536330i	$0.819810\pi$
$314$	2.09701	+	31.4415i	0.118341	+	1.77434i
$315$	−0.0870821	+	2.81317i	−0.00490652	+	0.158504i
$316$	−0.120738	+	5.05391i	−0.00679203	+	0.284305i
$317$	10.2109	−	14.0541i	0.573500	−	0.789356i	−0.419464	−	0.907772i	$-0.637782\pi$
$317$	10.2109	−	14.0541i	0.573500	−	0.789356i	0.992964	+	0.118416i	$0.0377818\pi$
$318$	−9.01190	+	14.3194i	−0.505362	+	0.802991i
$319$			4.41665i			0.247285i
$320$	15.0232	+	9.71100i	0.839822	+	0.542861i
$321$	3.04446	+	5.97510i	0.169925	+	0.333497i
$322$	−20.4080	−	8.74026i	−1.13729	−	0.487076i
$323$	−39.6994	−	6.28777i	−2.20893	−	0.349861i
$324$	14.4056	−	13.7334i	0.800313	−	0.762966i
$325$	22.4424	+	18.5304i	1.24488	+	1.02788i
$326$	−7.63184	−	3.26853i	−0.422688	−	0.181027i
$327$	16.6870	+	16.6870i	0.922794	+	0.922794i
$328$	−14.8752	−	10.3310i	−0.821344	−	0.570433i
$329$		−	0.875339i		−	0.0482590i
$330$	7.66173	+	7.13401i	0.421764	+	0.392714i
$331$	−8.70785	−	8.70785i	−0.478627	−	0.478627i	0.426066	−	0.904692i	$-0.359899\pi$
$331$	−8.70785	−	8.70785i	−0.478627	−	0.478627i	−0.904692	+	0.426066i	$0.859899\pi$
$332$	−0.0204243	+	0.854935i	−0.00112093	+	0.0469206i
$333$	−0.0149333	+	0.0942852i	−0.000818341	+	0.00516680i
$334$	−5.41795	−	13.5351i	−0.296457	−	0.740605i
$335$	25.5155	+	19.7726i	1.39406	+	1.08029i
$336$	−9.06576	+	23.9450i	−0.494578	+	1.30631i
$337$	−11.2369	−	11.2369i	−0.612111	−	0.612111i	0.331384	−	0.943496i	$-0.392484\pi$
$337$	−11.2369	−	11.2369i	−0.612111	−	0.612111i	−0.943496	+	0.331384i	$0.892484\pi$
$338$	−24.9930	−	15.7294i	−1.35944	−	0.855565i
$339$	−9.34021	+	1.47934i	−0.507290	+	0.0803469i
$340$	29.1076	−	12.8735i	1.57858	−	0.698162i
$341$	9.61981	+	4.90154i	0.520942	+	0.265433i
$342$	−2.16687	−	1.89590i	−0.117171	−	0.102519i
$343$	5.10661	−	3.71017i	0.275731	−	0.200330i
$344$	18.2453	−	14.4856i	0.983722	−	0.781009i
$345$	−3.44470	+	18.1041i	−0.185457	+	0.974690i
$346$	22.2579	+	9.53251i	1.19659	+	0.512471i
$347$	−2.11146	−	0.686054i	−0.113349	−	0.0368293i	0.251793	−	0.967781i	$-0.418980\pi$
$347$	−2.11146	−	0.686054i	−0.113349	−	0.0368293i	−0.365142	+	0.930952i	$0.618980\pi$
$348$	5.09566	+	7.37791i	0.273156	+	0.395497i
$349$	−1.89793	+	5.84123i	−0.101594	+	0.312674i	−0.988916	−	0.148476i	$-0.952563\pi$
$349$	−1.89793	+	5.84123i	−0.101594	+	0.312674i	0.887322	+	0.461150i	$0.152563\pi$
$350$	19.9064	−	14.6065i	1.06404	−	0.780749i
$351$	26.7863	−	8.70340i	1.42975	−	0.464553i
$352$	4.80841	+	9.01342i	0.256289	+	0.480417i
$353$	−9.12471	+	4.64927i	−0.485659	+	0.247456i	−0.679635	−	0.733551i	$-0.737862\pi$
$353$	−9.12471	+	4.64927i	−0.485659	+	0.247456i	0.193975	+	0.981006i	$0.437862\pi$
$354$	−16.0021	−	19.1956i	−0.850503	−	1.02024i
$355$	2.08606	+	4.42769i	0.110717	+	0.234998i
$356$	−10.1825	+	28.9656i	−0.539672	+	1.53517i
$357$	26.7761	+	36.8541i	1.41714	+	1.95053i
$358$	−5.45116	−	23.9629i	−0.288103	−	1.26648i
$359$	−24.6873	−	17.9364i	−1.30295	−	0.946645i	−0.302966	−	0.953001i	$-0.597977\pi$
$359$	−24.6873	−	17.9364i	−1.30295	−	0.946645i	−0.999980	+	0.00635591i	$0.997977\pi$
$360$	2.25583	+	0.330128i	0.118892	+	0.0173993i
$361$	7.58102	−	10.4344i	0.399001	−	0.549178i
$362$	−18.2536	+	10.8881i	−0.959389	+	0.572268i
$363$	−4.38378	−	13.4919i	−0.230089	−	0.708141i
$364$	−29.4217	+	28.0487i	−1.54211	+	1.47015i
$365$	−17.2113	+	31.3422i	−0.900883	+	1.64053i
$366$	0.988552	−	0.0659322i	0.0516725	−	0.00344633i
$367$	20.5641	+	10.4779i	1.07344	+	0.546944i	0.899101	−	0.437742i	$-0.144222\pi$
$367$	20.5641	+	10.4779i	1.07344	+	0.546944i	0.174337	+	0.984686i	$0.444222\pi$
$368$	−8.92016	+	15.6152i	−0.464996	+	0.814000i
$369$	−2.27150	−	0.409838i	−0.118250	−	0.0213353i
$370$	0.732127	−	0.406538i	0.0380615	−	0.0211349i
$371$	7.04188	+	21.6727i	0.365596	+	1.12519i
$372$	21.7248	−	2.91085i	1.12638	−	0.150920i
$373$	18.0088	+	2.85231i	0.932461	+	0.147687i	0.604139	−	0.796879i	$-0.293517\pi$
$373$	18.0088	+	2.85231i	0.932461	+	0.147687i	0.328321	+	0.944566i	$0.393517\pi$
$374$	18.1016	+	1.64236i	0.936012	+	0.0849246i
$375$	−15.3929	−	13.5321i	−0.794887	−	0.698795i
$376$	−0.704421	−	0.0809163i	−0.0363277	−	0.00417294i
$377$	2.22694	+	14.0603i	0.114693	+	0.724145i
$378$	−1.59008	−	23.8407i	−0.0817846	−	1.22623i
$379$	25.5051	+	18.5305i	1.31011	+	0.951850i	0.999999	+	0.00114865i	$0.000365628\pi$
$379$	25.5051	+	18.5305i	1.31011	+	0.951850i	0.310109	+	0.950701i	$0.399634\pi$
$380$	−1.38420	+	25.2198i	−0.0710081	+	1.29375i
$381$	−3.15937	+	19.9475i	−0.161859	+	1.02194i
$382$	−9.25237	−	3.96256i	−0.473392	−	0.202742i
$383$	−26.4491			−1.35148			−0.675742	−	0.737138i	$-0.736177\pi$
$383$	−26.4491			−1.35148			−0.675742	+	0.737138i	$0.736177\pi$
$384$	18.4315	+	9.50906i	0.940577	+	0.485257i
$385$	13.9882	−	1.77381i	0.712903	−	0.0904015i
$386$	−16.1946	−	10.1921i	−0.824284	−	0.518763i
$387$	1.34793	−	2.64547i	0.0685193	−	0.134477i
$388$	0.669518	−	3.65924i	0.0339896	−	0.185770i
$389$	6.91042	−	21.2681i	0.350372	−	1.07834i	−0.608272	−	0.793729i	$-0.708137\pi$
$389$	6.91042	−	21.2681i	0.350372	−	1.07834i	0.958644	−	0.284607i	$-0.0918630\pi$
$390$	27.9881	+	18.8479i	1.41723	+	0.954399i
$391$	14.5260	+	28.5088i	0.734610	+	1.44175i
$392$	7.21994	+	12.7887i	0.364662	+	0.645926i
$393$	15.8734	−	21.8478i	0.800705	−	1.10208i
$394$	−0.577655	+	0.344566i	−0.0291018	+	0.0173590i
$395$	2.72057	−	4.95422i	0.136887	−	0.249274i
$396$	1.03475	+	0.790223i	0.0519980	+	0.0397102i
$397$	18.7831	−	6.10301i	0.942698	−	0.306301i	0.202953	−	0.979188i	$-0.434946\pi$
$397$	18.7831	−	6.10301i	0.942698	−	0.306301i	0.739745	+	0.672887i	$0.234946\pi$
$398$	−10.5674	−	0.958782i	−0.529695	−	0.0480594i
$399$	−35.7060	+	5.65528i	−1.78754	+	0.283118i
$400$	−9.91429	−	17.3697i	−0.495714	−	0.868486i
$401$		−	21.3625i		−	1.06679i	−0.845865	−	0.533397i	$-0.820915\pi$
$401$		−	21.3625i		−	1.06679i	0.845865	−	0.533397i	$-0.179085\pi$
$402$	31.6744	+	19.9343i	1.57977	+	0.994231i
$403$	33.0960	+	10.7535i	1.64863	+	0.535672i
$404$	5.05636	−	14.3835i	0.251563	−	0.715606i
$405$	−21.3657	+	6.21822i	−1.06167	+	0.308986i
$406$	12.0274	+	1.09125i	0.596911	+	0.0541579i
$407$	0.478238			0.0237054
$408$	32.1332	−	18.1410i	1.59083	−	0.898114i
$409$			3.71678i			0.183783i	0.995769	+	0.0918914i	$0.0292913\pi$
$409$			3.71678i			0.183783i	−0.995769	+	0.0918914i	$0.970709\pi$
$410$	9.44833	+	17.9089i	0.466620	+	0.884458i
$411$			5.94619i			0.293304i
$412$	0.739236	−	2.10286i	0.0364196	−	0.103601i
$413$	−33.6594			−1.65627
$414$	−0.207099	+	2.28257i	−0.0101783	+	0.112182i
$415$	0.460219	−	0.838070i	0.0225913	−	0.0411392i
$416$	19.8522	+	26.2696i	0.973334	+	1.28798i
$417$	−1.63339	−	0.530721i	−0.0799876	−	0.0259895i
$418$	−7.68296	+	12.2078i	−0.375786	+	0.597101i
$419$			4.42574i			0.216211i	0.994139	+	0.108106i	$0.0344785\pi$
$419$			4.42574i			0.216211i	−0.994139	+	0.108106i	$0.965522\pi$
$420$	21.3204	−	19.1018i	1.04033	−	0.932072i
$421$	19.7068	−	3.12125i	0.960451	−	0.152121i	0.343527	−	0.939143i	$-0.388378\pi$
$421$	19.7068	−	3.12125i	0.960451	−	0.152121i	0.616924	+	0.787022i	$0.288378\pi$
$422$	2.12861	−	23.4609i	0.103619	−	1.14206i
$423$	−0.0859443	+	0.0279250i	−0.00417876	+	0.00135776i
$424$	18.0919	−	3.66347i	0.878618	−	0.177914i
$425$	−35.5159	−	2.20091i	−1.72277	−	0.106760i
$426$	2.90700	+	4.87350i	0.140845	+	0.236122i
$427$	0.784348	−	1.07956i	0.0379573	−	0.0522437i
$428$	2.42641	−	6.90227i	0.117285	−	0.333634i
$429$	8.74833	+	17.1696i	0.422373	+	0.828954i
$430$	−25.5639	+	4.98890i	−1.23280	+	0.240586i
$431$	3.85606	−	11.8677i	0.185740	−	0.571648i	−0.814220	−	0.580556i	$-0.802835\pi$
$431$	3.85606	−	11.8677i	0.185740	−	0.571648i	0.999960	+	0.00890729i	$0.00283532\pi$
$432$	−19.3326	−	0.924237i	−0.930140	−	0.0444674i
$433$	−12.4625	+	24.4590i	−0.598909	+	1.17543i	0.370237	+	0.928937i	$0.379277\pi$
$433$	−12.4625	+	24.4590i	−0.598909	+	1.17543i	−0.969146	+	0.246488i	$0.920723\pi$
$434$	15.7247	−	24.9856i	0.754810	−	1.19935i
$435$	−1.26114	−	9.94528i	−0.0604669	−	0.476840i
$436$	0.614915	−	25.7395i	0.0294491	−	1.23270i
$437$	−25.3917			−1.21465
$438$	−16.3210	+	38.1086i	−0.779846	+	1.82090i
$439$	−2.64801	+	16.7189i	−0.126383	+	0.797949i	0.840328	+	0.542078i	$0.182362\pi$
$439$	−2.64801	+	16.7189i	−0.126383	+	0.797949i	−0.966711	+	0.255871i	$0.917638\pi$
$440$	−0.134389	−	11.4208i	−0.00640675	−	0.544466i
$441$	1.51423	+	1.10015i	0.0721063	+	0.0523883i
$442$	58.4544	−	3.89866i	2.78039	−	0.185440i
$443$	3.23678	+	20.4362i	0.153784	+	0.970955i	0.937032	+	0.349245i	$0.113562\pi$
$443$	3.23678	+	20.4362i	0.153784	+	0.970955i	−0.783247	+	0.621710i	$0.786438\pi$
$444$	0.798885	−	0.551762i	0.0379134	−	0.0261854i
$445$	25.0124	−	23.5104i	1.18570	−	1.11450i
$446$	0.349739	−	3.85472i	0.0165606	−	0.182526i
$447$	23.2198	+	3.67765i	1.09826	+	0.173947i
$448$	25.7334	−	10.8673i	1.21579	−	0.513430i
$449$	−1.16583	−	3.58805i	−0.0550189	−	0.169331i	0.919771	−	0.392455i	$-0.128374\pi$
$449$	−1.16583	−	3.58805i	−0.0550189	−	0.169331i	−0.974790	+	0.223125i	$0.928374\pi$
$450$	−2.06918	−	1.48852i	−0.0975419	−	0.0701693i
$451$	−0.247739	+	11.5608i	−0.0116656	+	0.544379i
$452$	8.19966	+	6.26198i	0.385679	+	0.294539i
$453$	29.5716	+	15.0675i	1.38939	+	0.707932i
$454$	−1.66590	−	24.9776i	−0.0781846	−	1.17226i
$455$	43.6368	−	12.6999i	2.04572	−	0.595382i
$456$	1.25037	+	29.2569i	0.0585540	+	1.37008i
$457$	−7.68610	−	23.6554i	−0.359541	−	1.10655i	−0.953330	−	0.301932i	$-0.902369\pi$
$457$	−7.68610	−	23.6554i	−0.359541	−	1.10655i	0.593789	−	0.804621i	$-0.297631\pi$
$458$	3.20746	+	5.37721i	0.149875	+	0.251260i
$459$	−20.2409	+	27.8592i	−0.944764	+	1.30036i
$460$	16.8894	−	10.9089i	0.787473	−	0.508629i
$461$	−19.2313	−	13.9724i	−0.895693	−	0.650759i	0.0416630	−	0.999132i	$-0.486734\pi$
$461$	−19.2313	−	13.9724i	−0.895693	−	0.650759i	−0.937356	+	0.348373i	$0.886734\pi$
$462$	15.9404	−	3.62617i	0.741614	−	0.168705i
$463$	4.77677	+	6.57466i	0.221995	+	0.305550i	0.905459	−	0.424435i	$-0.139527\pi$
$463$	4.77677	+	6.57466i	0.221995	+	0.305550i	−0.683463	+	0.729985i	$0.739527\pi$
$464$	1.98999	−	9.57809i	0.0923829	−	0.444651i
$465$	−23.0612	−	8.29028i	−1.06944	−	0.384453i
$466$	−17.9490	+	14.9629i	−0.831472	+	0.693143i
$467$	−6.19273	+	3.15536i	−0.286566	+	0.146012i	−0.591365	−	0.806404i	$-0.701411\pi$
$467$	−6.19273	+	3.15536i	−0.286566	+	0.146012i	0.304799	+	0.952417i	$0.401411\pi$
$468$	3.69255	+	1.99393i	0.170688	+	0.0921695i
$469$	47.9399	−	15.5766i	2.21366	−	0.719261i
$470$	0.657546	+	0.442808i	0.0303303	+	0.0204252i
$471$	12.6222	−	38.8471i	0.581599	−	1.78998i
$472$	−3.11148	+	27.0871i	−0.143217	+	1.24679i
$473$	−14.1465	−	4.59646i	−0.650455	−	0.211346i
$474$	2.57983	−	6.02376i	0.118495	−	0.276680i
$475$	14.3519	−	24.3200i	0.658511	−	1.11588i
$476$	8.94498	−	48.8886i	0.409992	−	2.24080i
$477$	1.90326	−	1.38280i	0.0871445	−	0.0633142i
$478$	−13.6439	+	15.5939i	−0.624058	+	0.713250i
$479$	3.40813	+	1.73653i	0.155721	+	0.0793441i	0.530115	−	0.847926i	$-0.322149\pi$
$479$	3.40813	+	1.73653i	0.155721	+	0.0793441i	−0.374393	+	0.927270i	$0.622149\pi$
$480$	−13.4011	−	18.9232i	−0.611675	−	0.863720i
$481$	1.52246	−	0.241135i	0.0694184	−	0.0109948i
$482$	3.07866	−	4.89181i	0.140229	−	0.222816i
$483$	20.3489	+	20.3489i	0.925907	+	0.925907i
$484$	−7.35392	+	13.6187i	−0.334269	+	0.619030i
$485$	−2.54757	+	3.28751i	−0.115679	+	0.149278i
$486$	−4.89286	+	1.95856i	−0.221945	+	0.0888422i
$487$	1.86870	−	11.7985i	0.0846787	−	0.534640i	−0.908486	−	0.417916i	$-0.862761\pi$
$487$	1.86870	−	11.7985i	0.0846787	−	0.534640i	0.993164	−	0.116724i	$-0.0372393\pi$
$488$	−0.796263	−	0.730992i	−0.0360452	−	0.0330905i
$489$	7.60973	+	7.60973i	0.344124	+	0.344124i
$490$	−0.585259	−	16.4090i	−0.0264393	−	0.741282i
$491$		−	20.0629i		−	0.905428i	−0.891656	−	0.452714i	$-0.850456\pi$
$491$		−	20.0629i		−	0.905428i	0.891656	−	0.452714i	$-0.149544\pi$
$492$	12.9244	+	19.5979i	0.582675	+	0.883543i
$493$	−12.3074	−	12.3074i	−0.554297	−	0.554297i
$494$	−18.3033	+	42.7371i	−0.823503	+	1.92283i
$495$	−0.620409	−	1.31683i	−0.0278853	−	0.0591870i
$496$	−18.6534	−	14.9640i	−0.837561	−	0.671903i
$497$	7.54893	+	1.19563i	0.338616	+	0.0536315i
$498$	0.436411	−	1.01900i	0.0195561	−	0.0456623i
$499$	−11.2176	−	22.0158i	−0.502169	−	0.985562i	−0.993418	−	0.114543i	$-0.963460\pi$
$499$	−11.2176	−	22.0158i	−0.502169	−	0.985562i	0.491250	−	0.871019i	$-0.336540\pi$
$500$	0.902201	+	22.3425i	0.0403476	+	0.999186i
$501$			18.8981i			0.844304i
$502$	−29.8040	−	18.7571i	−1.33022	−	0.837172i
$503$	1.72212	−	2.37030i	0.0767857	−	0.105686i	−0.768896	−	0.639373i	$-0.779194\pi$
$503$	1.72212	−	2.37030i	0.0767857	−	0.105686i	0.845682	+	0.533687i	$0.179194\pi$
$504$	2.40760	−	2.62258i	0.107243	−	0.116819i
$505$	−12.4205	+	11.6746i	−0.552704	+	0.519514i
$506$	11.4568	−	0.764117i	0.509315	−	0.0339691i
$507$	22.4998	+	30.9683i	0.999251	+	1.37535i
$508$	18.1303	−	12.5219i	0.804401	−	0.555571i
$509$	−34.0352	+	5.39065i	−1.50859	+	0.238937i	−0.855283	−	0.518161i	$-0.826617\pi$
$509$	−34.0352	+	5.39065i	−1.50859	+	0.238937i	−0.653302	+	0.757097i	$0.726617\pi$
$510$	−41.2296	+	1.47054i	−1.82568	+	0.0651165i
$511$	25.3493	+	49.7508i	1.12139	+	2.20085i
$512$	−6.36653	−	21.7133i	−0.281364	−	0.959601i
$513$	−12.4066	−	24.3493i	−0.547763	−	1.07505i
$514$	−6.80827	−	1.72077i	−0.300300	−	0.0758998i
$515$	−1.81587	+	1.70682i	−0.0800167	+	0.0752116i
$516$	−28.9345	+	8.64304i	−1.27377	+	0.380489i
$517$	0.205531	+	0.403378i	0.00903925	+	0.0177405i
$518$	0.118161	−	1.30234i	0.00519172	−	0.0572215i
$519$	−22.1934	−	22.1934i	−0.974183	−	0.974183i
$520$	−6.18637	−	36.2903i	−0.271290	−	1.59143i
$521$	−3.16970	+	20.0127i	−0.138867	+	0.876773i	0.815635	+	0.578567i	$0.196388\pi$
$521$	−3.16970	+	20.0127i	−0.138867	+	0.876773i	−0.954502	+	0.298205i	$0.903612\pi$
$522$	−0.276555	−	1.21571i	−0.0121045	−	0.0532104i
$523$	21.5684	−	3.41609i	0.943119	−	0.149375i	0.334106	−	0.942536i	$-0.391566\pi$
$523$	21.5684	−	3.41609i	0.943119	−	0.149375i	0.609013	+	0.793160i	$0.291566\pi$
$524$	−29.2022	+	3.91274i	−1.27571	+	0.170929i
$525$	−30.9916	+	7.98841i	−1.35259	+	0.348643i
$526$	−8.41766	+	33.3047i	−0.367027	+	1.45215i
$527$	−40.4650	+	13.1479i	−1.76268	+	0.572731i
$528$	−1.44460	−	13.1631i	−0.0628682	−	0.572850i
$529$	−1.63828	−	2.25490i	−0.0712297	−	0.0980393i
$530$	−19.8426	−	5.67377i	−0.861907	−	0.246453i
$531$	1.07380	+	3.30482i	0.0465990	+	0.143417i
$532$	31.3459	+	23.9385i	1.35902	+	1.03787i
$533$	5.04048	+	36.9287i	0.218327	+	1.59956i
$534$	26.2068	−	29.9524i	1.13408	−	1.29617i
$535$	−5.96026	+	5.60234i	−0.257685	+	0.242210i
$536$	−8.10357	−	40.0191i	−0.350021	−	1.72856i
$537$	−4.98325	+	31.4630i	−0.215043	+	1.35773i
$538$	17.0256	+	20.4233i	0.734024	+	0.880512i
$539$	4.25698	−	8.35480i	0.183361	−	0.359867i
$540$	18.7133	+	10.8659i	0.805292	+	0.467592i
$541$	11.5734	−	15.9294i	0.497579	−	0.684859i	−0.484184	−	0.874966i	$-0.660883\pi$
$541$	11.5734	−	15.9294i	0.497579	−	0.684859i	0.981763	+	0.190107i	$0.0608835\pi$
$542$	0.275782	+	4.13492i	0.0118458	+	0.177610i
$543$	27.2115	−	4.30988i	1.16776	−	0.184955i
$544$	−38.5157	−	11.7176i	−1.65135	−	0.502390i
$545$	−13.8558	+	25.2317i	−0.593517	+	1.08081i
$546$	48.9177	−	19.5813i	2.09348	−	0.838001i
$547$			17.8977i			0.765251i	0.923904	+	0.382625i	$0.124980\pi$
$547$			17.8977i			0.765251i	−0.923904	+	0.382625i	$0.875020\pi$
$548$	4.69551	−	4.47639i	0.200582	−	0.191222i
$549$	−0.131018	−	0.0425704i	−0.00559172	−	0.00181686i
$550$	−5.74373	+	11.4051i	−0.244913	+	0.486315i
$551$	13.1365	−	4.26832i	0.559635	−	0.181837i
$552$	18.2566	−	14.4945i	0.777054	−	0.616929i
$553$	−4.00692	−	7.86403i	−0.170392	−	0.334412i
$554$	21.9597	+	36.8147i	0.932978	+	1.56411i
$555$	−1.07688	+	0.136557i	−0.0457111	+	0.00579652i
$556$	0.810552	+	1.68937i	0.0343751	+	0.0716453i
$557$	−26.8888	−	19.5359i	−1.13932	−	0.827762i	−0.152293	−	0.988335i	$-0.548666\pi$
$557$	−26.8888	−	19.5359i	−1.13932	−	0.827762i	−0.987024	+	0.160574i	$0.948666\pi$
$558$	−2.95484	−	0.746826i	−0.125088	−	0.0316157i
$559$	−47.3527	−	7.49993i	−2.00281	−	0.317213i
$560$	−31.1344	−	2.45585i	−1.31567	−	0.103779i
$561$	−20.9925	−	10.6962i	−0.886303	−	0.451594i
$562$	3.46917	+	0.314758i	0.146338	+	0.0132773i
$563$	16.5404	−	22.7659i	0.697094	−	0.959467i	−0.302885	−	0.953027i	$-0.597950\pi$
$563$	16.5404	−	22.7659i	0.697094	−	0.959467i	0.999979	−	0.00644034i	$-0.00205004\pi$
$564$	0.808728	+	0.436704i	0.0340536	+	0.0183885i
$565$	−4.91632	−	10.4350i	−0.206831	−	0.439002i
$566$	9.64402	−	2.19385i	0.405368	−	0.0922145i
$567$	−10.7377	+	33.0474i	−0.450943	+	1.38786i
$568$	1.66000	−	5.96441i	0.0696520	−	0.250261i
$569$	29.0354	−	21.0955i	1.21723	−	0.884368i	0.221362	−	0.975192i	$-0.428950\pi$
$569$	29.0354	−	21.0955i	1.21723	−	0.884368i	0.995867	+	0.0908234i	$0.0289499\pi$
$570$	13.8144	−	29.6829i	0.578623	−	1.24328i
$571$	−23.4461	−	23.4461i	−0.981189	−	0.981189i	0.0186378	−	0.999826i	$-0.494067\pi$
$571$	−23.4461	−	23.4461i	−0.981189	−	0.981189i	−0.999826	+	0.0186378i	$0.994067\pi$
$572$	6.97234	−	19.8338i	0.291528	−	0.829293i
$573$	9.22556	+	9.22556i	0.385403	+	0.385403i
$574$	31.4213	+	3.53106i	1.31150	+	0.147384i
$575$	−22.3776	+	2.13656i	−0.933208	+	0.0891006i
$576$	−1.88794	−	2.17992i	−0.0786641	−	0.0908302i
$577$		−	18.8675i		−	0.785466i	−0.919653	−	0.392733i	$-0.871530\pi$
$577$		−	18.8675i		−	0.785466i	0.919653	−	0.392733i	$-0.128470\pi$
$578$	−36.5518	+	30.4708i	−1.52035	+	1.26742i
$579$	14.5791	+	20.0664i	0.605886	+	0.833931i
$580$	−6.90405	+	8.48285i	−0.286675	+	0.352231i
$581$	−0.677822	−	1.33030i	−0.0281208	−	0.0551902i
$582$	−2.56840	+	4.08104i	−0.106464	+	0.169165i
$583$	−8.33387	−	8.33387i	−0.345153	−	0.345153i
$584$	42.3798	−	15.8007i	1.75369	−	0.653836i
$585$	−2.63903	−	3.87928i	−0.109110	−	0.160389i
$586$	−1.48232	−	1.77815i	−0.0612342	−	0.0734545i
$587$	−12.8303	−	39.4875i	−0.529561	−	1.62982i	−0.755116	−	0.655592i	$-0.772419\pi$
$587$	−12.8303	−	39.4875i	−0.529561	−	1.62982i	0.225554	−	0.974231i	$-0.427581\pi$
$588$	−2.52807	−	18.8679i	−0.104256	−	0.778101i
$589$	5.28202	−	33.3493i	0.217642	−	1.37414i
$590$	17.0273	−	25.2846i	0.701003	−	1.04095i
$591$	0.861137	−	0.136391i	0.0354224	−	0.00561036i
$592$	−1.03712	−	0.215477i	−0.0426255	−	0.00885607i
$593$	27.1163	+	8.81061i	1.11353	+	0.361808i	0.807295	−	0.590147i	$-0.200930\pi$
$593$	27.1163	+	8.81061i	1.11353	+	0.361808i	0.306236	+	0.951956i	$0.400930\pi$
$594$	6.33060	+	10.6130i	0.259747	+	0.435459i
$595$	−34.0364	+	43.9221i	−1.39536	+	1.80063i
$596$	−14.5761	−	21.1045i	−0.597061	−	0.864473i
$597$	12.2550	+	6.24425i	0.501565	+	0.255560i
$598$	36.0872	−	8.20922i	1.47571	−	0.335700i
$599$	−1.44408	+	4.44442i	−0.0590036	+	0.181594i	−0.976214	−	0.216808i	$-0.930435\pi$
$599$	−1.44408	+	4.44442i	−0.0590036	+	0.181594i	0.917211	+	0.398403i	$0.130435\pi$
$600$	3.56373	+	25.6787i	0.145489	+	1.04833i
$601$	−9.63733	−	9.63733i	−0.393115	−	0.393115i	0.482681	−	0.875796i	$-0.339663\pi$
$601$	−9.63733	−	9.63733i	−0.393115	−	0.393115i	−0.875796	+	0.482681i	$0.839663\pi$
$602$	−16.0124	+	37.3880i	−0.652615	+	1.52382i
$603$	−3.05875	−	4.21001i	−0.124562	−	0.171445i
$604$	−10.3637	−	34.6947i	−0.421693	−	1.41171i
$605$	14.3074	−	9.73314i	0.581678	−	0.395708i
$606$	−13.0136	+	14.8735i	−0.528640	+	0.604196i
$607$	28.0676	−	4.44548i	1.13923	−	0.180436i	0.441817	−	0.897105i	$-0.354334\pi$
$607$	28.0676	−	4.44548i	1.13923	−	0.180436i	0.697413	+	0.716669i	$0.254334\pi$
$608$	22.1619	−	23.0125i	0.898784	−	0.933279i
$609$	−13.9482	−	7.10698i	−0.565211	−	0.287989i
$610$	0.414179	+	1.13531i	0.0167696	+	0.0459675i
$611$	0.857695	+	1.18052i	0.0346986	+	0.0477586i
$612$	−5.08544	+	0.681385i	−0.205567	+	0.0275434i
$613$	14.9736	+	7.62943i	0.604778	+	0.308150i	0.729435	−	0.684050i	$-0.239783\pi$
$613$	14.9736	+	7.62943i	0.604778	+	0.308150i	−0.124657	+	0.992200i	$0.539783\pi$
$614$	10.1276	−	11.5751i	0.408717	−	0.467133i
$615$	−2.74325	−	26.1031i	−0.110619	−	1.05258i
$616$	−14.8637	−	9.85776i	−0.598874	−	0.397180i
$617$	12.6839	−	24.8936i	0.510636	−	1.00218i	−0.481433	−	0.876483i	$-0.659884\pi$
$617$	12.6839	−	24.8936i	0.510636	−	1.00218i	0.992069	−	0.125696i	$-0.0401164\pi$
$618$	−1.90258	+	2.17450i	−0.0765329	+	0.0874713i
$619$	22.8939	−	16.6334i	0.920185	−	0.668553i	−0.0233854	−	0.999727i	$-0.507444\pi$
$619$	22.8939	−	16.6334i	0.920185	−	0.668553i	0.943570	+	0.331173i	$0.107444\pi$
$620$	10.8143	+	24.4517i	0.434313	+	0.982005i
$621$	−9.87611	+	19.3830i	−0.396315	+	0.777811i
$622$	2.30507	+	3.86437i	0.0924248	+	0.154947i
$623$	−8.38549	−	52.9439i	−0.335958	−	2.12115i
$624$	−11.2359	−	41.1762i	−0.449796	−	1.64837i
$625$	10.6019	−	22.6407i	0.424075	−	0.905627i
$626$	1.65774	−	2.63405i	0.0662567	−	0.105278i
$627$	15.1264	−	10.9899i	0.604089	−	0.438896i
$628$	−40.1785	+	19.2774i	−1.60329	+	0.769253i
$629$	−1.33265	+	1.33265i	−0.0531363	+	0.0531363i
$630$	−3.73928	+	1.36414i	−0.148976	+	0.0543487i
$631$	−10.5638	−	3.43239i	−0.420539	−	0.136641i	0.0911003	−	0.995842i	$-0.470962\pi$
$631$	−10.5638	−	3.43239i	−0.420539	−	0.136641i	−0.511639	+	0.859200i	$0.670962\pi$
$632$	−6.69890	+	2.49758i	−0.266468	+	0.0993485i
$633$	−13.8630	+	27.2077i	−0.551004	+	1.08141i
$634$	23.8184	+	6.02003i	0.945951	+	0.239086i
$635$	−24.4393	+	3.09909i	−0.969843	+	0.122983i
$636$	−23.5366	−	4.30642i	−0.933288	−	0.170761i
$637$	9.33944	−	28.7438i	0.370042	−	1.13887i
$638$	−5.79876	+	2.32119i	−0.229575	+	0.0918967i
$639$	−0.123433	−	0.779328i	−0.00488295	−	0.0308298i
$640$	−4.85439	+	24.8281i	−0.191886	+	0.981417i
$641$	−30.7397	−	4.86869i	−1.21414	−	0.192302i	−0.483675	−	0.875248i	$-0.660698\pi$
$641$	−30.7397	−	4.86869i	−1.21414	−	0.192302i	−0.730469	+	0.682946i	$0.760698\pi$
$642$	−6.24487	+	7.13741i	−0.246465	+	0.281691i
$643$	8.92695	−	2.90054i	0.352044	−	0.114386i	−0.127656	−	0.991819i	$-0.540745\pi$
$643$	8.92695	−	2.90054i	0.352044	−	0.114386i	0.479700	+	0.877432i	$0.340745\pi$
$644$	0.749854	−	31.3879i	0.0295484	−	1.23685i
$645$	33.1671	+	6.31078i	1.30595	+	0.248487i
$646$	−12.6088	−	55.4272i	−0.496085	−	2.18076i
$647$	−23.7150	+	23.7150i	−0.932333	+	0.932333i	−0.997851	−	0.0655181i	$-0.979130\pi$
$647$	−23.7150	+	23.7150i	−0.932333	+	0.932333i	0.0655181	+	0.997851i	$0.479130\pi$
$648$	25.6020	+	11.6960i	1.00574	+	0.459462i
$649$	15.5111	−	7.90330i	0.608864	−	0.310232i
$650$	−12.5345	+	39.2040i	−0.491642	+	1.53771i
$651$	−30.9591	+	22.4931i	−1.21338	+	0.881575i
$652$	0.280417	−	11.7379i	0.0109820	−	0.459691i
$653$	−18.3622			−0.718568			−0.359284	−	0.933228i	$-0.616979\pi$
$653$	−18.3622			−0.718568			−0.359284	+	0.933228i	$0.616979\pi$
$654$	−13.1390	+	30.6789i	−0.513776	+	1.19964i
$655$	30.9987	+	11.1437i	1.21122	+	0.435421i
$656$	5.74617	−	24.9596i	0.224350	−	0.974509i
$657$	4.07604	−	4.07604i	0.159022	−	0.159022i
$658$	1.14926	−	0.460038i	0.0448029	−	0.0179341i
$659$	−14.5947	+	14.5947i	−0.568528	+	0.568528i	−0.931716	−	0.363188i	$-0.881688\pi$
$659$	−14.5947	+	14.5947i	−0.568528	+	0.568528i	0.363188	+	0.931716i	$0.381688\pi$
$660$	−5.33982	+	13.8086i	−0.207852	+	0.537501i
$661$	13.9041	+	19.1374i	0.540808	+	0.744358i	0.988729	−	0.149715i	$-0.0478355\pi$
$661$	13.9041	+	19.1374i	0.540808	+	0.744358i	−0.447921	+	0.894073i	$0.647836\pi$
$662$	6.85638	−	16.0093i	0.266481	−	0.622218i
$663$	−72.2225	−	23.4665i	−2.80489	−	0.911364i
$664$	−1.13321	+	0.422498i	−0.0439769	+	0.0163961i
$665$	−18.7943	−	39.8911i	−0.728810	−	1.54691i
$666$	−0.131638	+	0.0299455i	−0.00510089	+	0.00116037i
$667$	−8.89541	−	6.46290i	−0.344432	−	0.250244i
$668$	14.9232	−	14.2268i	0.577396	−	0.550451i
$669$	−2.27774	+	4.47032i	−0.0880626	+	0.172833i
$670$	−12.5503	+	43.8917i	−0.484862	+	1.69568i
$671$	−0.107964	+	0.681656i	−0.00416789	+	0.0263150i
$672$	−36.2027	+	0.681643i	−1.39655	+	0.0262949i
$673$	−9.67896	+	13.3219i	−0.373097	+	0.513523i	−0.953739	−	0.300635i	$-0.902801\pi$
$673$	−9.67896	+	13.3219i	−0.373097	+	0.513523i	0.580643	+	0.814159i	$0.302801\pi$
$674$	8.84768	−	20.6588i	0.340800	−	0.795749i
$675$	−12.9827	−	20.4149i	−0.499703	−	0.785770i
$676$	7.51642	−	41.0808i	0.289093	−	1.58003i
$677$	−0.126498	+	0.0644541i	−0.00486172	+	0.00247717i	−0.456420	−	0.889765i	$-0.650868\pi$
$677$	−0.126498	+	0.0644541i	−0.00486172	+	0.00247717i	0.451558	+	0.892242i	$0.350868\pi$
$678$	−6.85106	−	11.4856i	−0.263113	−	0.441101i
$679$	2.00695	+	6.17674i	0.0770195	+	0.237042i
$680$	32.1996	+	31.4506i	1.23480	+	1.20608i
$681$	−10.0273	+	30.8607i	−0.384246	+	1.18259i
$682$	−1.37966	+	15.2062i	−0.0528300	+	0.582275i
$683$	30.2820			1.15871			0.579355	−	0.815075i	$-0.303304\pi$
$683$	30.2820			1.15871			0.579355	+	0.815075i	$0.303304\pi$
$684$	1.35038	−	3.84135i	0.0516332	−	0.146878i
$685$	−6.96414	+	2.02683i	−0.266086	+	0.0774410i
$686$	7.55500	+	4.75474i	0.288451	+	0.181537i
$687$	−1.26962	−	8.01605i	−0.0484389	−	0.305831i
$688$	28.6075	+	16.3420i	1.09065	+	0.623031i
$689$	−30.7328	−	22.3287i	−1.17083	−	0.850656i
$690$	−25.5798	+	4.99200i	−0.973806	+	0.190042i
$691$	−32.5585	−	16.5894i	−1.23858	−	0.631089i	−0.292888	−	0.956147i	$-0.594616\pi$
$691$	−32.5585	−	16.5894i	−1.23858	−	0.631089i	−0.945694	+	0.325058i	$0.894616\pi$
$692$	−0.817824	+	34.2330i	−0.0310890	+	1.30134i
$693$	−2.24511	−	0.355590i	−0.0852845	−	0.0135077i
$694$	−0.208942	−	3.13276i	−0.00793133	−	0.118918i
$695$	0.0648176	−	2.09392i	0.00245867	−	0.0794270i
$696$	−7.00865	+	10.5677i	−0.265662	+	0.400569i
$697$	−31.5250	−	32.9057i	−1.19409	−	1.24639i
$698$	−8.66661	+	0.578026i	−0.328036	+	0.0218786i
$699$	28.8078	−	9.36022i	1.08961	−	0.354036i
$700$	29.6392	+	18.4593i	1.12026	+	0.697695i
$701$	13.8279	−	10.0466i	0.522274	−	0.379455i	−0.295186	−	0.955440i	$-0.595381\pi$
$701$	13.8279	−	10.0466i	0.522274	−	0.379455i	0.817460	+	0.575985i	$0.195381\pi$
$702$	25.5046	+	30.5945i	0.962610	+	1.15472i
$703$	−0.462177	−	1.42243i	−0.0174313	−	0.0536481i
$704$	−9.30694	+	11.0502i	−0.350769	+	0.416468i
$705$	−0.577990	−	0.849626i	−0.0217684	−	0.0319988i
$706$	−10.8997	−	9.53669i	−0.410216	−	0.358918i
$707$	4.16401	+	26.2905i	0.156604	+	0.988757i
$708$	16.7926	−	31.0980i	0.631104	−	1.16874i
$709$	31.7974	+	5.03622i	1.19418	+	0.189139i	0.721702	−	0.692204i	$-0.243360\pi$
$709$	31.7974	+	5.03622i	1.19418	+	0.189139i	0.472476	+	0.881343i	$0.343360\pi$
$710$	−4.71693	+	5.06585i	−0.177023	+	0.190118i
$711$	−0.644294	+	0.644294i	−0.0241629	+	0.0241629i
$712$	−43.3813	+	1.85402i	−1.62578	+	0.0694822i
$713$	−23.9487	+	12.2025i	−0.896886	+	0.456986i
$714$	−34.3147	+	54.5240i	−1.28419	+	2.04051i
$715$	−17.1269	+	16.0984i	−0.640511	+	0.602048i
$716$	28.5968	−	19.7508i	1.06871	−	0.738122i
$717$	23.9310	−	12.1934i	0.893719	−	0.455372i
$718$	10.5747	−	41.8393i	0.394646	−	1.56143i
$719$	7.50369	−	3.82332i	0.279840	−	0.142586i	−0.308438	−	0.951245i	$-0.599806\pi$
$719$	7.50369	−	3.82332i	0.279840	−	0.142586i	0.588278	+	0.808659i	$0.299806\pi$
$720$	0.752122	+	3.13525i	0.0280299	+	0.116844i
$721$	0.608776	+	3.84366i	0.0226720	+	0.143145i
$722$	17.6839	+	4.46954i	0.658126	+	0.166339i
$723$	−6.06134	+	4.40382i	−0.225423	+	0.163780i
$724$	−23.8886	−	18.2435i	−0.887815	−	0.678013i
$725$	11.2180	−	4.86700i	0.416626	−	0.180756i
$726$	15.4100	−	12.8463i	0.571920	−	0.476772i
$727$	10.5943	+	7.69722i	0.392922	+	0.285474i	0.766652	−	0.642063i	$-0.221921\pi$
$727$	10.5943	+	7.69722i	0.392922	+	0.285474i	−0.373730	+	0.927537i	$0.621921\pi$
$728$	−52.2888	−	23.8876i	−1.93795	−	0.885332i
$729$	−23.0229			−0.852700
$730$	−50.1958	−	6.12529i	−1.85783	−	0.226707i
$731$	52.2288	−	26.6119i	1.93175	−	0.984277i
$732$	0.606102	+	1.26325i	0.0224022	+	0.0466911i
$733$	1.82653	−	11.5323i	0.0674644	−	0.425953i	−0.930721	−	0.365731i	$-0.880819\pi$
$733$	1.82653	−	11.5323i	0.0674644	−	0.425953i	0.998185	−	0.0602224i	$-0.0191810\pi$
$734$	−2.94928	+	32.5060i	−0.108860	+	1.19982i
$735$	−7.20010	+	20.0286i	−0.265580	+	0.738767i
$736$	−25.1898	−	3.50493i	−0.928507	−	0.129193i
$737$	−18.4345	+	18.4345i	−0.679042	+	0.679042i
$738$	−0.655707	−	3.19772i	−0.0241369	−	0.117710i
$739$	−44.4781			−1.63615			−0.818076	−	0.575110i	$-0.804959\pi$
$739$	−44.4781			−1.63615			−0.818076	+	0.575110i	$0.804959\pi$
$740$	0.918529	+	0.747576i	0.0337658	+	0.0274814i
$741$	42.6133	−	42.6133i	1.56544	−	1.56544i
$742$	−24.7539	+	20.6357i	−0.908744	+	0.757560i
$743$	11.0508	+	1.75027i	0.405414	+	0.0642113i	0.355812	−	0.934558i	$-0.384205\pi$
$743$	11.0508	+	1.75027i	0.405414	+	0.0642113i	0.0496026	+	0.998769i	$0.484205\pi$
$744$	15.2393	+	26.9933i	0.558699	+	0.989624i
$745$	3.60748	+	28.4484i	0.132168	+	1.04227i
$746$	5.71970	+	25.1434i	0.209413	+	0.920565i
$747$	−0.108991	+	0.108991i	−0.00398776	+	0.00398776i
$748$	7.35706	+	24.6294i	0.269001	+	0.900538i
$749$	1.99820	+	12.6161i	0.0730125	+	0.460983i
$750$	9.67693	−	27.3217i	0.353351	−	0.997648i
$751$	2.99731	−	5.88255i	0.109373	−	0.214657i	−0.829832	−	0.558013i	$-0.811564\pi$
$751$	2.99731	−	5.88255i	0.109373	−	0.214657i	0.939205	+	0.343356i	$0.111564\pi$
$752$	−0.263974	−	0.967383i	−0.00962613	−	0.0352768i
$753$	26.8308	+	36.9294i	0.977769	+	1.34578i
$754$	−17.2899	+	10.3133i	−0.629662	+	0.375588i
$755$	−7.56713	+	39.7700i	−0.275396	+	1.44738i
$756$	30.4656	−	14.6173i	1.10802	−	0.531624i
$757$	−12.5882	+	38.7424i	−0.457525	+	1.40812i	0.410621	+	0.911806i	$0.365312\pi$
$757$	−12.5882	+	38.7424i	−0.457525	+	1.40812i	−0.868146	+	0.496310i	$0.834688\pi$
$758$	−10.9250	+	43.2253i	−0.396816	+	1.57001i
$759$	−14.1552	−	4.59932i	−0.513803	−	0.166945i
$760$	−33.8393	+	11.4370i	−1.22748	+	0.414863i
$761$	−6.00726	−	18.4884i	−0.217763	−	0.670205i	−0.998946	−	0.0459032i	$-0.985383\pi$
$761$	−6.00726	−	18.4884i	−0.217763	−	0.670205i	0.781183	−	0.624302i	$-0.214617\pi$
$762$	−27.8501	+	6.33543i	−1.00890	+	0.229508i
$763$	20.4072	+	40.0513i	0.738789	+	1.44995i
$764$	0.339961	−	14.2303i	0.0122993	−	0.514834i
$765$	5.39828	+	1.94063i	0.195175	+	0.0701637i
$766$	−13.9004	−	34.7259i	−0.502243	−	1.25470i
$767$	45.3944	−	32.9810i	1.63910	−	1.19087i
$768$	−2.79803	+	29.1968i	−0.100965	+	1.05355i
$769$	8.04878	−	11.0782i	0.290247	−	0.399490i	−0.638848	−	0.769333i	$-0.720589\pi$
$769$	8.04878	−	11.0782i	0.290247	−	0.399490i	0.929094	+	0.369843i	$0.120589\pi$
$770$	9.68042	+	17.4333i	0.348858	+	0.628252i
$771$	7.36422	+	5.35042i	0.265216	+	0.192691i
$772$	4.87038	−	26.6189i	0.175289	−	0.958037i
$773$	27.1808	−	8.83157i	0.977625	−	0.317650i	0.223735	−	0.974650i	$-0.428175\pi$
$773$	27.1808	−	8.83157i	0.977625	−	0.317650i	0.753890	+	0.657001i	$0.228175\pi$
$774$	4.18173	+	0.379410i	0.150309	+	0.0136376i
$775$	1.84886	−	29.8350i	0.0664131	−	1.07170i
$776$	5.15620	−	1.04409i	0.185097	−	0.0374808i
$777$	−0.769549	+	1.51032i	−0.0276074	+	0.0541826i
$778$	31.5554	−	2.10461i	1.13132	−	0.0754539i
$779$	34.6251	−	10.4357i	1.24057	−	0.373899i
$780$	−10.0367	+	46.6521i	−0.359373	+	1.67041i
$781$	−3.75947	+	1.22153i	−0.134525	+	0.0437097i
$782$	−29.7960	+	34.0545i	−1.06550	+	1.21779i
$783$	1.85120	−	11.6880i	0.0661566	−	0.417696i
$784$	−12.9962	+	16.2004i	−0.464150	+	0.578587i
$785$	49.7999	+	1.54156i	1.77744	+	0.0550207i
$786$	37.0270	+	9.35846i	1.32071	+	0.333805i
$787$	−48.7442	+	7.72033i	−1.73754	+	0.275200i	−0.943190	−	0.332254i	$-0.892191\pi$
$787$	−48.7442	+	7.72033i	−1.73754	+	0.275200i	−0.794355	+	0.607454i	$0.792191\pi$
$788$	−0.755982	−	0.577334i	−0.0269307	−	0.0205667i
$789$	26.1732	−	36.0243i	0.931790	−	1.28250i
$790$	7.93436	+	0.968215i	0.282292	+	0.0344475i
$791$	−17.7909	−	2.81780i	−0.632572	−	0.100190i
$792$	−0.493695	+	1.77386i	−0.0175427	+	0.0630313i
$793$			2.22448i			0.0789936i
$794$	17.8844	+	21.4535i	0.634693	+	0.761357i
$795$	21.1456	+	16.3863i	0.749958	+	0.581162i
$796$	−4.29492	−	14.3782i	−0.152229	−	0.509621i
$797$	−4.33972	−	2.21120i	−0.153721	−	0.0783246i	0.375438	−	0.926848i	$-0.377492\pi$
$797$	−4.33972	−	2.21120i	−0.153721	−	0.0783246i	−0.529159	+	0.848523i	$0.677492\pi$
$798$	−26.1905	−	43.9075i	−0.927132	−	1.55431i
$799$	−1.69678	−	0.551317i	−0.0600277	−	0.0195042i
$800$	17.5948	−	22.1455i	0.622069	−	0.782962i
$801$	−4.93074	+	2.51234i	−0.174219	+	0.0887690i
$802$	28.0476	−	11.2272i	0.990395	−	0.396445i
$803$	−23.3632	−	16.9743i	−0.824468	−	0.599011i
$804$	−9.52577	+	52.0629i	−0.335948	+	1.83612i
$805$	−16.8964	+	30.7687i	−0.595519	+	1.08445i
$806$	3.27505	+	49.1044i	0.115359	+	1.72963i
$807$	−10.6505	−	32.7790i	−0.374917	−	1.15388i
$808$	21.5420	−	0.920654i	0.757844	−	0.0323885i
$809$	7.11568	+	44.9267i	0.250174	+	1.57954i	0.718209	+	0.695827i	$0.244962\pi$
$809$	7.11568	+	44.9267i	0.250174	+	1.57954i	−0.468035	+	0.883710i	$0.655038\pi$
$810$	−19.3930	−	24.7838i	−0.681399	−	0.870812i
$811$	34.8310			1.22308			0.611542	−	0.791212i	$-0.290550\pi$
$811$	34.8310			1.22308			0.611542	+	0.791212i	$0.290550\pi$
$812$	4.88832	+	16.3647i	0.171546	+	0.574289i
$813$	1.65997	−	5.10885i	0.0582175	−	0.179175i
$814$	0.251340	+	0.627894i	0.00880946	+	0.0220077i
$815$	−6.31861	+	11.5063i	−0.221331	+	0.403049i
$816$	40.7056	+	32.6546i	1.42498	+	1.14314i
$817$			46.5182i			1.62747i
$818$	−4.87988	+	1.95337i	−0.170621	+	0.0682979i
$819$	−7.32656			−0.256011
$820$	−18.5476	+	21.8171i	−0.647710	+	0.761887i
$821$	38.9031			1.35773			0.678863	−	0.734265i	$-0.262473\pi$
$821$	38.9031			1.35773			0.678863	+	0.734265i	$0.262473\pi$
$822$	−7.80694	+	3.12504i	−0.272298	+	0.108998i
$823$			3.65930i			0.127555i	0.997964	+	0.0637776i	$0.0203148\pi$
$823$			3.65930i			0.127555i	−0.997964	+	0.0637776i	$0.979685\pi$
$824$	3.14942	−	0.134599i	0.109715	−	0.00468898i
$825$	12.4060	−	10.9582i	0.431922	−	0.381514i
$826$	−17.6898	−	44.1926i	−0.615508	−	1.53766i
$827$	−6.54846	+	20.1541i	−0.227712	+	0.700826i	0.770293	+	0.637690i	$0.220110\pi$
$827$	−6.54846	+	20.1541i	−0.227712	+	0.700826i	−0.998005	+	0.0631355i	$0.979890\pi$
$828$	−3.10571	+	0.927710i	−0.107931	+	0.0322401i
$829$	3.38666			0.117624			0.0588118	−	0.998269i	$-0.481269\pi$
$829$	3.38666			0.117624			0.0588118	+	0.998269i	$0.481269\pi$
$830$	1.34220	+	0.163786i	0.0465884	+	0.00568510i
$831$	−8.69236	−	54.8814i	−0.301535	−	1.90381i
$832$	−24.0569	+	39.8707i	−0.834022	+	1.38227i
$833$	11.4189	+	35.1438i	0.395642	+	1.21766i
$834$	−0.161634	−	2.42346i	−0.00559694	−	0.0839175i
$835$	−22.1333	+	6.44163i	−0.765956	+	0.222922i
$836$	−20.0658	−	3.67137i	−0.693989	−	0.126977i
$837$	−23.4030	−	17.0033i	−0.808927	−	0.587720i
$838$	−5.81069	+	2.32596i	−0.200727	+	0.0803490i
$839$	−17.0028	+	8.66338i	−0.587003	+	0.299093i	−0.722154	−	0.691732i	$-0.756848\pi$
$839$	−17.0028	+	8.66338i	−0.587003	+	0.299093i	0.135151	+	0.990825i	$0.456848\pi$
$840$	36.2844	+	17.9532i	1.25193	+	0.619445i
$841$	−21.8921	−	7.11319i	−0.754902	−	0.245282i
$842$	14.4550	+	24.2333i	0.498152	+	0.835136i
$843$	−4.02320	−	2.04992i	−0.138566	−	0.0706031i
$844$	31.9213	−	9.53524i	1.09878	−	0.328216i
$845$	−28.6006	+	36.9075i	−0.983891	+	1.26966i
$846$	−0.0818320	−	0.0981630i	−0.00281344	−	0.00337492i
$847$		−	27.0215i		−	0.928468i
$848$	14.3181	+	21.8280i	0.491687	+	0.749578i
$849$	−12.6625	−	2.00554i	−0.434576	−	0.0688300i
$850$	−15.7759	−	47.7867i	−0.541108	−	1.63907i
$851$	−0.699807	+	0.963202i	−0.0239891	+	0.0330181i
$852$	−4.87079	+	6.37798i	−0.166870	+	0.218506i
$853$	−32.3985	+	5.13142i	−1.10930	+	0.175697i	−0.684091	−	0.729397i	$-0.739801\pi$
$853$	−32.3985	+	5.13142i	−1.10930	+	0.175697i	−0.425213	+	0.905093i	$0.639801\pi$
$854$	1.82961	+	0.462428i	0.0626080	+	0.0158240i
$855$	−3.31710	+	3.11790i	−0.113442	+	0.106630i
$856$	10.3374	−	0.441798i	0.353326	−	0.0151003i
$857$	0.723726	−	4.56943i	0.0247220	−	0.156089i	−0.972239	−	0.233990i	$-0.924822\pi$
$857$	0.723726	−	4.56943i	0.0247220	−	0.156089i	0.996961	+	0.0779010i	$0.0248218\pi$
$858$	−17.9448	+	20.5095i	−0.612624	+	0.700183i
$859$	−19.4300	+	6.31319i	−0.662943	+	0.215403i	−0.621112	−	0.783722i	$-0.713319\pi$
$859$	−19.4300	+	6.31319i	−0.662943	+	0.215403i	−0.0418303	+	0.999125i	$0.513319\pi$
$860$	−19.9853	−	30.9418i	−0.681494	−	1.05511i
$861$	−36.1117	−	19.3853i	−1.23068	−	0.660651i
$862$	17.6081	−	1.17439i	0.599734	−	0.0399997i
$863$	16.4881	−	32.3598i	0.561263	−	1.10154i	−0.419758	−	0.907636i	$-0.637885\pi$
$863$	16.4881	−	32.3598i	0.561263	−	1.10154i	0.981021	−	0.193904i	$-0.0621150\pi$
$864$	−8.94686	−	25.8681i	−0.304378	−	0.880052i
$865$	18.4279	−	33.5577i	0.626568	−	1.14100i
$866$	−38.6628	−	3.50788i	−1.31381	−	0.119203i
$867$	58.6649	−	19.0614i	1.99236	−	0.647358i
$868$	41.0686	+	7.51419i	1.39396	+	0.255048i
$869$	3.69298	+	2.68311i	0.125276	+	0.0910181i
$870$	12.3947	−	6.88257i	0.420219	−	0.233341i
$871$	−49.3910	+	67.9808i	−1.67355	+	2.30344i
$872$	34.1174	−	12.7201i	1.15536	−	0.430758i
$873$	0.542432	−	0.394100i	0.0183586	−	0.0133383i
$874$	−13.3447	−	33.3376i	−0.451392	−	1.12766i
$875$	−19.9198	−	33.5743i	−0.673414	−	1.13502i
$876$	−58.6115	−	1.40023i	−1.98030	−	0.0473093i
$877$	14.4332	+	28.3268i	0.487375	+	0.956527i	0.995456	+	0.0952184i	$0.0303549\pi$
$877$	14.4332	+	28.3268i	0.487375	+	0.956527i	−0.508081	+	0.861309i	$0.669645\pi$
$878$	−23.3425	+	5.31002i	−0.787770	+	0.179204i
$879$	0.927285	+	2.85389i	0.0312765	+	0.0962593i
$880$	14.9241	−	6.17870i	0.503093	−	0.208284i
$881$	−23.0742	−	7.49727i	−0.777391	−	0.252590i	−0.106665	−	0.994295i	$-0.534017\pi$
$881$	−23.0742	−	7.49727i	−0.777391	−	0.252590i	−0.670726	+	0.741705i	$0.734017\pi$
$882$	−0.648618	+	2.56628i	−0.0218401	+	0.0864110i
$883$	7.45492	−	22.9439i	0.250878	−	0.772123i	−0.743736	−	0.668474i	$-0.766948\pi$
$883$	7.45492	−	22.9439i	0.250878	−	0.772123i	0.994614	−	0.103650i	$-0.0330520\pi$
$884$	35.8396	+	74.6977i	1.20542	+	2.51236i
$885$	−32.6707	+	22.2255i	−1.09821	+	0.747101i
$886$	−25.1303	+	14.9900i	−0.844269	+	0.503600i
$887$	33.9978	+	46.7940i	1.14154	+	1.57119i	0.764028	+	0.645183i	$0.223219\pi$
$887$	33.9978	+	46.7940i	1.14154	+	1.57119i	0.377507	+	0.926007i	$0.376781\pi$
$888$	1.14428	+	0.758902i	0.0383996	+	0.0254671i
$889$	−17.4645	+	34.2760i	−0.585741	+	1.14958i
$890$	44.0129	+	20.4836i	1.47532	+	0.686613i
$891$	−2.81137	−	17.7503i	−0.0941844	−	0.594657i
$892$	5.24479	−	1.56668i	0.175609	−	0.0524562i
$893$	1.00115	−	1.00115i	0.0335021	−	0.0335021i
$894$	7.37473	+	32.4188i	0.246648	+	1.08425i
$895$	−38.5479	+	4.88817i	−1.28852	+	0.163394i
$896$	27.7923	+	28.0749i	0.928475	+	0.937917i
$897$	−47.3821	−	7.50458i	−1.58204	−	0.250571i
$898$	4.09817	−	3.41637i	0.136758	−	0.114006i
$899$	10.3388	−	10.3388i	0.344817	−	0.344817i
$900$	0.866857	−	3.49899i	0.0288952	−	0.116633i
$901$	46.4461			1.54734
$902$	−15.3088	+	5.75058i	−0.509728	+	0.191473i
$903$	37.2797	−	37.2797i	1.24059	−	1.24059i
$904$	−3.91219	+	14.0566i	−0.130118	+	0.467516i
$905$	14.3231	+	30.4009i	0.476115	+	1.01056i
$906$	−4.24112	+	46.7443i	−0.140902	+	1.55297i
$907$	−0.401042	+	2.53208i	−0.0133164	+	0.0840764i	−0.993452	−	0.114255i	$-0.963552\pi$
$907$	−0.401042	+	2.53208i	−0.0133164	+	0.0840764i	0.980135	+	0.198331i	$0.0635521\pi$
$908$	31.9184	−	15.3143i	1.05925	−	0.508223i
$909$	2.44847	−	1.24756i	0.0812106	−	0.0413789i
$910$	39.6076	+	50.6177i	1.31298	+	1.67796i
$911$	−3.00148			−0.0994435			−0.0497217	−	0.998763i	$-0.515833\pi$
$911$	−3.00148			−0.0994435			−0.0497217	+	0.998763i	$0.515833\pi$
$912$	−37.7552	+	17.0177i	−1.25020	+	0.563513i
$913$	0.624715	+	0.453882i	0.0206750	+	0.0150213i
$914$	27.0185	−	22.5235i	0.893692	−	0.745012i
$915$	0.0484683	−	1.56576i	0.00160231	−	0.0517625i
$916$	−5.37422	+	7.03719i	−0.177569	+	0.232515i
$917$	41.6150	−	30.2351i	1.37425	−	0.998450i
$918$	−47.2150	−	11.9334i	−1.55833	−	0.393862i
$919$	−4.68253	−	29.5644i	−0.154463	−	0.975238i	−0.936158	−	0.351578i	$-0.885645\pi$
$919$	−4.68253	−	29.5644i	−0.154463	−	0.975238i	0.781696	−	0.623660i	$-0.214355\pi$
$920$	23.1989	+	16.4415i	0.764846	+	0.542059i
$921$	−17.7635	+	9.05097i	−0.585328	+	0.298240i
$922$	8.23770	−	32.5927i	0.271294	−	1.07338i
$923$	−11.3523	+	5.78430i	−0.373666	+	0.190393i
$924$	13.1385	+	19.0229i	0.432224	+	0.625808i
$925$	−0.527002	−	1.21469i	−0.0173277	−	0.0399388i
$926$	−6.12164	+	9.72692i	−0.201169	+	0.319646i
$927$	0.357965	−	0.182392i	0.0117571	−	0.00599055i
$928$	13.6212	−	2.42108i	0.447139	−	0.0794758i
$929$	−3.16367	+	3.16367i	−0.103797	+	0.103797i	−0.757098	−	0.653301i	$-0.773383\pi$
$929$	−3.16367	+	3.16367i	−0.103797	+	0.103797i	0.653301	+	0.757098i	$0.273383\pi$
$930$	−1.23532	−	34.6348i	−0.0405077	−	1.13572i
$931$	−28.9639	−	4.58743i	−0.949253	−	0.150347i
$932$	−29.0785	−	15.7020i	−0.952497	−	0.514337i
$933$	−0.912421	−	5.76080i	−0.0298713	−	0.188600i
$934$	−7.39739	−	6.47233i	−0.242050	−	0.211781i
$935$	5.37181	−	28.2322i	0.175677	−	0.923292i
$936$	−0.677267	+	5.89598i	−0.0221372	+	0.192716i
$937$	−9.53825	−	29.3557i	−0.311601	−	0.959009i	−0.977131	−	0.212638i	$-0.931794\pi$
$937$	−9.53825	−	29.3557i	−0.311601	−	0.959009i	0.665530	−	0.746371i	$-0.268206\pi$
$938$	45.6460	+	54.7555i	1.49040	+	1.78783i
$939$	−3.26380	+	2.37129i	−0.106510	+	0.0773841i
$940$	−0.235801	+	1.09603i	−0.00769098	+	0.0357487i
$941$	−15.1303	+	4.91615i	−0.493235	+	0.160262i	−0.545064	−	0.838394i	$-0.683495\pi$
$941$	−15.1303	+	4.91615i	−0.493235	+	0.160262i	0.0518293	+	0.998656i	$0.483495\pi$
$942$	57.6373	−	3.84416i	1.87792	−	0.125249i
$943$	−22.9218	−	17.4160i	−0.746436	−	0.567143i
$944$	−37.1988	+	10.1506i	−1.21072	+	0.330373i
$945$	−37.7612	−	1.16890i	−1.22837	−	0.0380243i
$946$	−1.39988	−	20.9890i	−0.0455140	−	0.682413i
$947$	37.3086	+	5.90911i	1.21237	+	0.192020i	0.729690	−	0.683778i	$-0.239664\pi$
$947$	37.3086	+	5.90911i	1.21237	+	0.192020i	0.482678	+	0.875798i	$0.339664\pi$
$948$	9.26463	+	0.221332i	0.300901	+	0.00718852i
$949$	−82.9351	−	42.2575i	−2.69219	−	1.37174i
$950$	39.4732	+	6.06164i	1.28068	+	0.196666i
$951$	−25.7634	−	18.7182i	−0.835435	−	0.606979i
$952$	68.8885	−	13.9494i	2.23269	−	0.452103i
$953$	−3.86006	−	24.3715i	−0.125040	−	0.789470i	−0.967900	−	0.251337i	$-0.919130\pi$
$953$	−3.86006	−	24.3715i	−0.125040	−	0.789470i	0.842860	−	0.538133i	$-0.180870\pi$
$954$	2.81579	+	1.77212i	0.0911647	+	0.0573745i
$955$	−7.66029	+	13.9496i	−0.247881	+	0.451397i
$956$	−27.6444	−	9.71807i	−0.894084	−	0.314305i
$957$	8.09642			0.261720
$958$	−0.488790	+	5.38729i	−0.0157921	+	0.174055i
$959$	−3.49996	+	10.7718i	−0.113020	+	0.347838i
$960$	17.8018	−	27.5399i	0.574551	−	0.888848i
$961$	−1.46530	−	4.50972i	−0.0472677	−	0.145475i
$962$	1.11673	+	1.87216i	0.0360048	+	0.0603610i
$963$	1.17496	−	0.598670i	0.0378624	−	0.0192919i
$964$	8.04063	+	1.47117i	0.258971	+	0.0473831i
$965$	−18.5322	+	23.9148i	−0.596573	+	0.769845i
$966$	−16.0223	+	37.4112i	−0.515509	+	1.20369i
$967$	22.6718	−	31.2050i	0.729075	−	1.00349i	−0.270098	−	0.962833i	$-0.587056\pi$
$967$	22.6718	−	31.2050i	0.729075	−	1.00349i	0.999173	−	0.0406532i	$-0.0129439\pi$
$968$	−21.7453	−	2.49786i	−0.698920	−	0.0802843i
$969$	−11.5265	+	72.7754i	−0.370284	+	2.33788i
$970$	−5.65516	−	1.61703i	−0.181576	−	0.0519198i
$971$	13.8294	−	27.1418i	0.443808	−	0.871022i	−0.555414	−	0.831574i	$-0.687440\pi$
$971$	13.8294	−	27.1418i	0.443808	−	0.871022i	0.999222	−	0.0394482i	$-0.0125600\pi$
$972$	−5.14292	−	5.39466i	−0.164959	−	0.173034i
$973$	−2.64657	−	1.92285i	−0.0848452	−	0.0616437i
$974$	16.4727	−	3.74727i	0.527820	−	0.120070i
$975$	33.9692	−	41.1405i	1.08788	−	1.31755i
$976$	0.541264	−	1.42962i	0.0173254	−	0.0457609i
$977$	−49.2991	−	16.0183i	−1.57722	−	0.512470i	−0.615881	−	0.787839i	$-0.711200\pi$
$977$	−49.2991	−	16.0183i	−1.57722	−	0.512470i	−0.961338	+	0.275370i	$0.911200\pi$
$978$	−5.99174	+	13.9904i	−0.191595	+	0.447363i
$979$	16.2956	+	22.4289i	0.520809	+	0.716832i
$980$	21.2363	−	9.39221i	0.678369	−	0.300023i
$981$	3.28137	−	3.28137i	0.104766	−	0.104766i
$982$	26.3413	−	10.5442i	0.840585	−	0.336478i
$983$	8.60633	−	8.60633i	0.274499	−	0.274499i	−0.556409	−	0.830908i	$-0.687821\pi$
$983$	8.60633	−	8.60633i	0.274499	−	0.274499i	0.830908	+	0.556409i	$0.187821\pi$
$984$	−18.9383	+	27.2686i	−0.603732	+	0.869291i
$985$	0.453268	+	0.962069i	0.0144423	+	0.0306541i
$986$	9.69057	−	22.6270i	0.308611	−	0.720589i
$987$	−1.60464			−0.0510761
$988$	−65.7303	−	1.57029i	−2.09116	−	0.0499577i
$989$	29.9581	−	21.7659i	0.952614	−	0.692114i
$990$	1.40285	−	1.50662i	0.0445854	−	0.0478835i
$991$	2.91636	−	1.48596i	0.0926414	−	0.0472031i	−0.407056	−	0.913403i	$-0.633445\pi$
$991$	2.91636	−	1.48596i	0.0926414	−	0.0472031i	0.499697	+	0.866200i	$0.333445\pi$
$992$	9.84336	−	32.3550i	0.312527	−	1.02727i
$993$	−15.9629	+	15.9629i	−0.506567	+	0.506567i
$994$	2.39759	+	10.5396i	0.0760468	+	0.334296i
$995$	−3.13597	+	16.4815i	−0.0994168	+	0.522497i
$996$	1.56723	+	0.0374411i	0.0496597	+	0.00118637i
$997$	14.3447	−	4.66089i	0.454303	−	0.147612i	−0.0729223	−	0.997338i	$-0.523233\pi$
$997$	14.3447	−	4.66089i	0.454303	−	0.147612i	0.527225	+	0.849726i	$0.323233\pi$
$998$	23.0098	−	26.2984i	0.728362	−	0.832462i
$999$	−1.26559	−	0.200450i	−0.0400414	−	0.00634194i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bk.c.43.75	yes	960
4.3	odd	2	inner	820.2.bk.c.43.9	✓	960
5.2	odd	4		820.2.bv.c.207.15	yes	960
20.7	even	4		820.2.bv.c.207.53	yes	960
41.21	even	20		820.2.bv.c.103.53	yes	960
164.103	odd	20		820.2.bv.c.103.15	yes	960
205.62	odd	20	inner	820.2.bk.c.267.9	yes	960
820.267	even	20	inner	820.2.bk.c.267.75	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bk.c.43.9	✓	960	4.3	odd	2	inner
820.2.bk.c.43.75	yes	960	1.1	even	1	trivial
820.2.bk.c.267.9	yes	960	205.62	odd	20	inner
820.2.bk.c.267.75	yes	960	820.267	even	20	inner
820.2.bv.c.103.15	yes	960	164.103	odd	20
820.2.bv.c.103.53	yes	960	41.21	even	20
820.2.bv.c.207.15	yes	960	5.2	odd	4
820.2.bv.c.207.53	yes	960	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.525554 + 1.31293i) q^{2} -1.83316i q^{3} +(-1.44759 + 1.38003i) q^{4} +(2.14699 - 0.624854i) q^{5} +(2.40682 - 0.963425i) q^{6} +(1.07901 - 3.32085i) q^{7} +(-2.57268 - 1.17530i) q^{8} -0.360477 q^{9} +(1.94875 + 2.49046i) q^{10} +(0.282507 + 1.78368i) q^{11} +(2.52982 + 2.65366i) q^{12} +(1.79872 + 5.53588i) q^{13} +(4.92713 - 0.328618i) q^{14} +(-1.14546 - 3.93577i) q^{15} +(0.191011 - 3.99544i) q^{16} +(-5.75762 - 4.18315i) q^{17} +(-0.189450 - 0.473282i) q^{18} +(5.03222 - 2.56405i) q^{19} +(-2.24563 + 3.86745i) q^{20} +(-6.08764 - 1.97799i) q^{21} +(-2.19338 + 1.30833i) q^{22} +(-4.00584 - 2.04108i) q^{23} +(-2.15451 + 4.71613i) q^{24} +(4.21912 - 2.68311i) q^{25} +(-6.32292 + 5.27100i) q^{26} -4.83867i q^{27} +(3.02092 + 6.29628i) q^{28} +(2.41555 + 0.382585i) q^{29} +(4.56541 - 3.57237i) q^{30} +(3.51404 - 4.83666i) q^{31} +(5.34613 - 1.84903i) q^{32} +(3.26977 - 0.517881i) q^{33} +(2.46626 - 9.75784i) q^{34} +(0.241575 - 7.80404i) q^{35} +(0.521821 - 0.497470i) q^{36} +(0.0414266 - 0.261557i) q^{37} +(6.01113 + 5.25943i) q^{38} +(10.1482 - 3.29734i) q^{39} +(-6.25790 - 0.915810i) q^{40} +(6.30138 + 1.13693i) q^{41} +(-0.602410 - 9.03221i) q^{42} +(-3.73931 + 7.33880i) q^{43} +(-2.87049 - 2.19216i) q^{44} +(-0.773939 + 0.225245i) q^{45} +(0.574513 - 6.33210i) q^{46} +(0.238419 - 0.0774669i) q^{47} +(-7.32428 - 0.350153i) q^{48} +(-4.20064 - 3.05194i) q^{49} +(5.74011 + 4.12930i) q^{50} +(-7.66839 + 10.5546i) q^{51} +(-10.2435 - 5.53138i) q^{52} +(-5.27985 + 3.83604i) q^{53} +(6.35285 - 2.54298i) q^{54} +(1.72108 + 3.65302i) q^{55} +(-6.67893 + 7.27530i) q^{56} +(-4.70031 - 9.22487i) q^{57} +(0.767192 + 3.37252i) q^{58} +(-2.97884 - 9.16792i) q^{59} +(7.08965 + 4.11660i) q^{60} +(0.363458 + 0.118095i) q^{61} +(8.19703 + 2.07177i) q^{62} +(-0.388957 + 1.19709i) q^{63} +(5.23734 + 6.04734i) q^{64} +(7.32094 + 10.7615i) q^{65} +(2.39839 + 4.02082i) q^{66} +(8.48529 + 11.6790i) q^{67} +(14.1075 - 1.89023i) q^{68} +(-3.74163 + 7.34335i) q^{69} +(10.3731 - 3.78427i) q^{70} +(0.342417 + 2.16194i) q^{71} +(0.927390 + 0.423669i) q^{72} +(-11.3074 + 11.3074i) q^{73} +(0.365179 - 0.0830721i) q^{74} +(-4.91857 - 7.73432i) q^{75} +(-3.74611 + 10.6563i) q^{76} +(6.22816 + 0.986443i) q^{77} +(9.66259 + 11.5909i) q^{78} +(1.78734 - 1.78734i) q^{79} +(-2.08647 - 8.69751i) q^{80} -9.95149 q^{81} +(1.81900 + 8.87081i) q^{82} +(0.302351 - 0.302351i) q^{83} +(11.5421 - 5.53784i) q^{84} +(-14.9754 - 5.38351i) q^{85} +(-11.6006 - 1.05252i) q^{86} +(0.701340 - 4.42808i) q^{87} +(1.36956 - 4.92087i) q^{88} +(13.6784 - 6.96948i) q^{89} +(-0.702479 - 0.897752i) q^{90} +20.3246 q^{91} +(8.61556 - 2.57356i) q^{92} +(-8.86638 - 6.44180i) q^{93} +(0.227011 + 0.272315i) q^{94} +(9.20197 - 8.64938i) q^{95} +(-3.38957 - 9.80031i) q^{96} +(-1.50476 + 1.09328i) q^{97} +(1.79933 - 7.11912i) q^{98} +(-0.101837 - 0.642975i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} - 22 q^{8} - 960 q^{9} + 20 q^{12} + 12 q^{13} + 8 q^{14} - 28 q^{16} - 52 q^{17} + 12 q^{18} + 14 q^{20} - 40 q^{21} + 18 q^{22} + 48 q^{24} - 4 q^{25} - 20 q^{26}+ \cdots + 42 q^{98}+O(q^{100}) \) 960 * q - 10 * q^2 - 20 * q^5 - 16 * q^6 - 22 * q^8 - 960 * q^9 + 20 * q^12 + 12 * q^13 + 8 * q^14 - 28 * q^16 - 52 * q^17 + 12 * q^18 + 14 * q^20 - 40 * q^21 + 18 * q^22 + 48 * q^24 - 4 * q^25 - 20 * q^26 - 2 * q^28 + 30 * q^30 + 16 * q^33 + 20 * q^34 - 100 * q^36 - 112 * q^37 - 36 * q^38 - 16 * q^40 - 24 * q^41 - 104 * q^42 + 20 * q^45 - 20 * q^46 + 12 * q^48 - 224 * q^49 + 12 * q^50 + 190 * q^52 + 12 * q^53 + 52 * q^54 + 96 * q^56 + 48 * q^57 - 10 * q^58 + 14 * q^60 - 40 * q^61 - 10 * q^62 + 120 * q^64 - 92 * q^65 - 12 * q^66 + 104 * q^69 - 120 * q^70 + 36 * q^72 + 72 * q^73 + 28 * q^74 - 40 * q^76 + 36 * q^77 + 16 * q^78 - 130 * q^80 + 592 * q^81 + 146 * q^82 + 92 * q^84 + 112 * q^85 - 12 * q^86 + 100 * q^88 - 136 * q^89 - 136 * q^90 + 160 * q^92 - 24 * q^93 + 32 * q^94 - 44 * q^96 - 72 * q^97 + 42 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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