LMFDB - Embedded newform 409.2.g.a.360.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(49,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.49"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.g (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			360.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	409.360
Dual form			409.2.g.a.217.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.633975 - 0.366025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205 q^{5} +1.26795 q^{6} +(-1.00000 + 0.267949i) q^{7} -1.73205i q^{8} +(-1.23205 - 2.13397i) q^{9} +(-2.59808 + 1.50000i) q^{10} +(-3.00000 + 3.00000i) q^{11} +(-0.633975 + 0.366025i) q^{12} +(-0.366025 + 0.366025i) q^{13} +(1.26795 - 1.26795i) q^{14} +(-1.09808 - 0.633975i) q^{15} +(2.50000 + 4.33013i) q^{16} +(0.232051 + 0.401924i) q^{17} +(3.69615 + 2.13397i) q^{18} +(-2.73205 + 2.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} +(0.732051 + 0.196152i) q^{21} +(1.90192 - 7.09808i) q^{22} +(-1.09808 + 0.633975i) q^{23} +(-0.633975 + 1.09808i) q^{24} -2.00000 q^{25} +(0.232051 - 0.866025i) q^{26} +4.00000i q^{27} +(-0.267949 + 1.00000i) q^{28} +(-1.90192 - 7.09808i) q^{29} +2.19615 q^{30} +(-5.73205 - 5.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 - 0.803848i) q^{33} +(-0.696152 - 0.401924i) q^{34} +(-1.73205 + 0.464102i) q^{35} -2.46410 q^{36} +(-8.09808 - 2.16987i) q^{37} +(1.73205 - 6.46410i) q^{38} +(0.366025 - 0.0980762i) q^{39} -3.00000i q^{40} +(-8.19615 - 4.73205i) q^{41} +(-1.26795 + 0.339746i) q^{42} +(2.00000 + 2.00000i) q^{43} +(1.09808 + 4.09808i) q^{44} +(-2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +(3.00000 + 11.1962i) q^{47} -3.66025i q^{48} +(-5.13397 + 2.96410i) q^{49} +(3.00000 - 1.73205i) q^{50} -0.339746i q^{51} +(0.133975 + 0.500000i) q^{52} +(6.46410 - 11.1962i) q^{53} +(-3.46410 - 6.00000i) q^{54} +(-5.19615 + 5.19615i) q^{55} +(0.464102 + 1.73205i) q^{56} +(2.73205 - 0.732051i) q^{57} +(9.00000 + 9.00000i) q^{58} +(7.73205 - 7.73205i) q^{59} +(-1.09808 + 0.633975i) q^{60} +(5.63397 + 5.63397i) q^{61} +(13.5622 + 3.63397i) q^{62} +(1.80385 + 1.80385i) q^{63} -1.00000 q^{64} +(-0.633975 + 0.633975i) q^{65} +(-3.80385 + 3.80385i) q^{66} +(-12.1962 + 3.26795i) q^{67} +0.464102 q^{68} +0.928203 q^{69} +(2.19615 - 2.19615i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-3.69615 + 2.13397i) q^{72} +(2.43782 + 9.09808i) q^{73} +(14.0263 - 3.75833i) q^{74} +(1.26795 + 0.732051i) q^{75} +(1.00000 + 3.73205i) q^{76} +(2.19615 - 3.80385i) q^{77} +(-0.464102 + 0.464102i) q^{78} +(5.00000 - 5.00000i) q^{79} +(4.33013 + 7.50000i) q^{80} +(-2.23205 + 3.86603i) q^{81} +16.3923 q^{82} -4.73205 q^{83} +(0.535898 - 0.535898i) q^{84} +(0.401924 + 0.696152i) q^{85} +(-4.73205 - 1.26795i) q^{86} +(-1.39230 + 5.19615i) q^{87} +(5.19615 + 5.19615i) q^{88} +0.928203 q^{89} +(6.40192 + 3.69615i) q^{90} +(0.267949 - 0.464102i) q^{91} +1.26795i q^{92} +(1.53590 + 5.73205i) q^{93} +(-14.1962 - 14.1962i) q^{94} +(-4.73205 + 4.73205i) q^{95} +(1.90192 + 3.29423i) q^{96} +(0.794229 + 2.96410i) q^{97} +(5.13397 - 8.89230i) q^{98} +(10.0981 + 2.70577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{2} - 6 q^{3} + 2 q^{4} + 12 q^{6} - 4 q^{7} + 2 q^{9} - 12 q^{11} - 6 q^{12} + 2 q^{13} + 12 q^{14} + 6 q^{15} + 10 q^{16} - 6 q^{17} - 6 q^{18} - 4 q^{19} - 4 q^{21} + 18 q^{22} + 6 q^{23} - 6 q^{24}+ \cdots + 30 q^{99}+O(q^{100}) $ 4 * q - 6 * q^2 - 6 * q^3 + 2 * q^4 + 12 * q^6 - 4 * q^7 + 2 * q^9 - 12 * q^11 - 6 * q^12 + 2 * q^13 + 12 * q^14 + 6 * q^15 + 10 * q^16 - 6 * q^17 - 6 * q^18 - 4 * q^19 - 4 * q^21 + 18 * q^22 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 6 * q^26 - 8 * q^28 - 18 * q^29 - 12 * q^30 - 16 * q^31 - 18 * q^32 + 12 * q^33 + 18 * q^34 + 4 * q^36 - 22 * q^37 - 2 * q^39 - 12 * q^41 - 12 * q^42 + 8 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 + 12 * q^47 - 24 * q^49 + 12 * q^50 + 4 * q^52 + 12 * q^53 - 12 * q^56 + 4 * q^57 + 36 * q^58 + 24 * q^59 + 6 * q^60 + 26 * q^61 + 30 * q^62 + 28 * q^63 - 4 * q^64 - 6 * q^65 - 36 * q^66 - 28 * q^67 - 12 * q^68 - 24 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 + 34 * q^73 + 18 * q^74 + 12 * q^75 + 4 * q^76 - 12 * q^77 + 12 * q^78 + 20 * q^79 - 2 * q^81 + 24 * q^82 - 12 * q^83 + 16 * q^84 + 12 * q^85 - 12 * q^86 + 36 * q^87 - 24 * q^89 + 36 * q^90 + 8 * q^91 + 20 * q^93 - 36 * q^94 - 12 * q^95 + 18 * q^96 - 28 * q^97 + 24 * q^98 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.925615	−	0.378467i	$-0.876451\pi$
$2$	−1.50000	+	0.866025i	−1.06066	+	0.612372i	−0.135045	+	0.990839i	$0.543118\pi$
$3$	−0.633975	−	0.366025i	−0.366025	−	0.211325i	0.305695	−	0.952129i	$-0.401111\pi$
$3$	−0.633975	−	0.366025i	−0.366025	−	0.211325i	−0.671721	+	0.740805i	$0.734444\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.73205			0.774597			0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205			0.774597			0.387298	+	0.921954i	$0.373408\pi$
$6$	1.26795			0.517638
$7$	−1.00000	+	0.267949i	−0.377964	+	0.101275i	−0.442799	−	0.896621i	$-0.646015\pi$
$7$	−1.00000	+	0.267949i	−0.377964	+	0.101275i	0.0648349	+	0.997896i	$0.479348\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−1.23205	−	2.13397i	−0.410684	−	0.711325i
$10$	−2.59808	+	1.50000i	−0.821584	+	0.474342i
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	−0.995824	−	0.0912903i	$-0.970901\pi$
$11$	−3.00000	+	3.00000i	−0.904534	+	0.904534i	0.0912903	+	0.995824i	$0.470901\pi$
$12$	−0.633975	+	0.366025i	−0.183013	+	0.105662i
$13$	−0.366025	+	0.366025i	−0.101517	+	0.101517i	−0.756041	−	0.654524i	$-0.772869\pi$
$13$	−0.366025	+	0.366025i	−0.101517	+	0.101517i	0.654524	+	0.756041i	$0.272869\pi$
$14$	1.26795	−	1.26795i	0.338874	−	0.338874i
$15$	−1.09808	−	0.633975i	−0.283522	−	0.163692i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	0.892793	−	0.450467i	$-0.148743\pi$
$17$	0.232051	+	0.401924i	0.0562806	+	0.0974808i	−0.836512	+	0.547948i	$0.815409\pi$
$18$	3.69615	+	2.13397i	0.871191	+	0.502983i
$19$	−2.73205	+	2.73205i	−0.626775	+	0.626775i	−0.947255	−	0.320480i	$-0.896156\pi$
$19$	−2.73205	+	2.73205i	−0.626775	+	0.626775i	0.320480	+	0.947255i	$0.396156\pi$
$20$	0.866025	−	1.50000i	0.193649	−	0.335410i
$21$	0.732051	+	0.196152i	0.159747	+	0.0428040i
$22$	1.90192	−	7.09808i	0.405492	−	1.51331i
$23$	−1.09808	+	0.633975i	−0.228965	+	0.132193i	−0.610094	−	0.792329i	$-0.708868\pi$
$23$	−1.09808	+	0.633975i	−0.228965	+	0.132193i	0.381130	+	0.924522i	$0.375535\pi$
$24$	−0.633975	+	1.09808i	−0.129410	+	0.224144i
$25$	−2.00000			−0.400000
$26$	0.232051	−	0.866025i	0.0455089	−	0.169842i
$27$			4.00000i			0.769800i
$28$	−0.267949	+	1.00000i	−0.0506376	+	0.188982i
$29$	−1.90192	−	7.09808i	−0.353178	−	1.31808i	−0.882761	−	0.469822i	$-0.844318\pi$
$29$	−1.90192	−	7.09808i	−0.353178	−	1.31808i	0.529583	−	0.848258i	$-0.322348\pi$
$30$	2.19615			0.400961
$31$	−5.73205	−	5.73205i	−1.02951	−	1.02951i	−0.999551	−	0.0299555i	$-0.990463\pi$
$31$	−5.73205	−	5.73205i	−1.02951	−	1.02951i	−0.0299555	−	0.999551i	$-0.509537\pi$
$32$	−4.50000	−	2.59808i	−0.795495	−	0.459279i
$33$	3.00000	−	0.803848i	0.522233	−	0.139932i
$34$	−0.696152	−	0.401924i	−0.119389	−	0.0689294i
$35$	−1.73205	+	0.464102i	−0.292770	+	0.0784475i
$36$	−2.46410			−0.410684
$37$	−8.09808	−	2.16987i	−1.33132	−	0.356725i	−0.478110	−	0.878300i	$-0.658678\pi$
$37$	−8.09808	−	2.16987i	−1.33132	−	0.356725i	−0.853205	+	0.521575i	$0.825345\pi$
$38$	1.73205	−	6.46410i	0.280976	−	1.04862i
$39$	0.366025	−	0.0980762i	0.0586110	−	0.0157048i
$40$		−	3.00000i		−	0.474342i
$41$	−8.19615	−	4.73205i	−1.28002	−	0.739022i	−0.303171	−	0.952936i	$-0.598045\pi$
$41$	−8.19615	−	4.73205i	−1.28002	−	0.739022i	−0.976853	+	0.213914i	$0.931379\pi$
$42$	−1.26795	+	0.339746i	−0.195649	+	0.0524239i
$43$	2.00000	+	2.00000i	0.304997	+	0.304997i	0.842965	−	0.537968i	$-0.180808\pi$
$43$	2.00000	+	2.00000i	0.304997	+	0.304997i	−0.537968	+	0.842965i	$0.680808\pi$
$44$	1.09808	+	4.09808i	0.165541	+	0.617808i
$45$	−2.13397	−	3.69615i	−0.318114	−	0.550990i
$46$	1.09808	−	1.90192i	0.161903	−	0.280423i
$47$	3.00000	+	11.1962i	0.437595	+	1.63313i	0.734779	+	0.678306i	$0.237286\pi$
$47$	3.00000	+	11.1962i	0.437595	+	1.63313i	−0.297184	+	0.954820i	$0.596048\pi$
$48$		−	3.66025i		−	0.528312i
$49$	−5.13397	+	2.96410i	−0.733425	+	0.423443i
$50$	3.00000	−	1.73205i	0.424264	−	0.244949i
$51$		−	0.339746i		−	0.0475740i
$52$	0.133975	+	0.500000i	0.0185789	+	0.0693375i
$53$	6.46410	−	11.1962i	0.887913	−	1.53791i	0.0455742	−	0.998961i	$-0.485488\pi$
$53$	6.46410	−	11.1962i	0.887913	−	1.53791i	0.842338	−	0.538949i	$-0.181178\pi$
$54$	−3.46410	−	6.00000i	−0.471405	−	0.816497i
$55$	−5.19615	+	5.19615i	−0.700649	+	0.700649i
$56$	0.464102	+	1.73205i	0.0620182	+	0.231455i
$57$	2.73205	−	0.732051i	0.361869	−	0.0969625i
$58$	9.00000	+	9.00000i	1.18176	+	1.18176i
$59$	7.73205	−	7.73205i	1.00663	−	1.00663i	0.00664938	−	0.999978i	$-0.497883\pi$
$59$	7.73205	−	7.73205i	1.00663	−	1.00663i	0.999978	−	0.00664938i	$-0.00211658\pi$
$60$	−1.09808	+	0.633975i	−0.141761	+	0.0818458i
$61$	5.63397	+	5.63397i	0.721357	+	0.721357i	0.968882	−	0.247525i	$-0.0796172\pi$
$61$	5.63397	+	5.63397i	0.721357	+	0.721357i	−0.247525	+	0.968882i	$0.579617\pi$
$62$	13.5622	+	3.63397i	1.72240	+	0.461515i
$63$	1.80385	+	1.80385i	0.227263	+	0.227263i
$64$	−1.00000			−0.125000
$65$	−0.633975	+	0.633975i	−0.0786349	+	0.0786349i
$66$	−3.80385	+	3.80385i	−0.468221	+	0.468221i
$67$	−12.1962	+	3.26795i	−1.49000	+	0.399244i	−0.909736	−	0.415187i	$-0.863716\pi$
$67$	−12.1962	+	3.26795i	−1.49000	+	0.399244i	−0.580261	+	0.814431i	$0.697049\pi$
$68$	0.464102			0.0562806
$69$	0.928203			0.111743
$70$	2.19615	−	2.19615i	0.262490	−	0.262490i
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−3.69615	+	2.13397i	−0.435596	+	0.251491i
$73$	2.43782	+	9.09808i	0.285326	+	1.06485i	0.948601	+	0.316474i	$0.102499\pi$
$73$	2.43782	+	9.09808i	0.285326	+	1.06485i	−0.663276	+	0.748375i	$0.730834\pi$
$74$	14.0263	−	3.75833i	1.63052	−	0.436897i
$75$	1.26795	+	0.732051i	0.146410	+	0.0845299i
$76$	1.00000	+	3.73205i	0.114708	+	0.428096i
$77$	2.19615	−	3.80385i	0.250275	−	0.433489i
$78$	−0.464102	+	0.464102i	−0.0525492	+	0.0525492i
$79$	5.00000	−	5.00000i	0.562544	−	0.562544i	−0.367485	−	0.930029i	$-0.619781\pi$
$79$	5.00000	−	5.00000i	0.562544	−	0.562544i	0.930029	+	0.367485i	$0.119781\pi$
$80$	4.33013	+	7.50000i	0.484123	+	0.838525i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	16.3923			1.81023
$83$	−4.73205			−0.519410			−0.259705	−	0.965688i	$-0.583625\pi$
$83$	−4.73205			−0.519410			−0.259705	+	0.965688i	$0.583625\pi$
$84$	0.535898	−	0.535898i	0.0584713	−	0.0584713i
$85$	0.401924	+	0.696152i	0.0435948	+	0.0755083i
$86$	−4.73205	−	1.26795i	−0.510270	−	0.136726i
$87$	−1.39230	+	5.19615i	−0.149271	+	0.557086i
$88$	5.19615	+	5.19615i	0.553912	+	0.553912i
$89$	0.928203			0.0983893			0.0491947	−	0.998789i	$-0.484335\pi$
$89$	0.928203			0.0983893			0.0491947	+	0.998789i	$0.484335\pi$
$90$	6.40192	+	3.69615i	0.674822	+	0.389609i
$91$	0.267949	−	0.464102i	0.0280887	−	0.0486511i
$92$			1.26795i			0.132193i
$93$	1.53590	+	5.73205i	0.159265	+	0.594386i
$94$	−14.1962	−	14.1962i	−1.46422	−	1.46422i
$95$	−4.73205	+	4.73205i	−0.485498	+	0.485498i
$96$	1.90192	+	3.29423i	0.194114	+	0.336216i
$97$	0.794229	+	2.96410i	0.0806417	+	0.300959i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	0.794229	+	2.96410i	0.0806417	+	0.300959i	−0.913812	+	0.406138i	$0.866875\pi$
$98$	5.13397	−	8.89230i	0.518610	−	0.898258i
$99$	10.0981	+	2.70577i	1.01489	+	0.271940i
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	−2.19615	−	3.80385i	−0.218525	−	0.378497i	0.735832	−	0.677164i	$-0.236791\pi$
$101$	−2.19615	−	3.80385i	−0.218525	−	0.378497i	−0.954357	+	0.298667i	$0.903458\pi$
$102$	0.294229	+	0.509619i	0.0291330	+	0.0504598i
$103$			12.1962i			1.20172i	0.799353	+	0.600861i	$0.205176\pi$
$103$			12.1962i			1.20172i	−0.799353	+	0.600861i	$0.794824\pi$
$104$	0.633975	+	0.633975i	0.0621663	+	0.0621663i
$105$	1.26795	+	0.339746i	0.123739	+	0.0331558i
$106$			22.3923i			2.17493i
$107$	6.46410	+	1.73205i	0.624908	+	0.167444i	0.557358	−	0.830272i	$-0.311815\pi$
$107$	6.46410	+	1.73205i	0.624908	+	0.167444i	0.0675502	+	0.997716i	$0.478482\pi$
$108$	3.46410	+	2.00000i	0.333333	+	0.192450i
$109$	−4.16025	+	2.40192i	−0.398480	+	0.230063i	−0.685828	−	0.727764i	$-0.740560\pi$
$109$	−4.16025	+	2.40192i	−0.398480	+	0.230063i	0.287348	+	0.957826i	$0.407226\pi$
$110$	3.29423	−	12.2942i	0.314092	−	1.17221i
$111$	4.33975	+	4.33975i	0.411910	+	0.411910i
$112$	−3.66025	−	3.66025i	−0.345861	−	0.345861i
$113$	−4.09808	+	15.2942i	−0.385515	+	1.43876i	0.451840	+	0.892099i	$0.350768\pi$
$113$	−4.09808	+	15.2942i	−0.385515	+	1.43876i	−0.837354	+	0.546661i	$0.815899\pi$
$114$	−3.46410	+	3.46410i	−0.324443	+	0.324443i
$115$	−1.90192	+	1.09808i	−0.177355	+	0.102396i
$116$	−7.09808	−	1.90192i	−0.659040	−	0.176589i
$117$	1.23205	+	0.330127i	0.113903	+	0.0305203i
$118$	−4.90192	+	18.2942i	−0.451259	+	1.68412i
$119$	−0.339746	−	0.339746i	−0.0311445	−	0.0311445i
$120$	−1.09808	+	1.90192i	−0.100240	+	0.173621i
$121$		−	7.00000i		−	0.636364i
$122$	−13.3301	−	3.57180i	−1.20685	−	0.323375i
$123$	3.46410	+	6.00000i	0.312348	+	0.541002i
$124$	−7.83013	+	2.09808i	−0.703166	+	0.188413i
$125$	−12.1244			−1.08444
$126$	−4.26795	−	1.14359i	−0.380219	−	0.101879i
$127$	1.00000	+	3.73205i	0.0887357	+	0.331166i	0.995995	−	0.0894049i	$-0.0284965\pi$
$127$	1.00000	+	3.73205i	0.0887357	+	0.331166i	−0.907260	+	0.420571i	$0.861830\pi$
$128$	10.5000	−	6.06218i	0.928078	−	0.535826i
$129$	−0.535898	−	2.00000i	−0.0471832	−	0.176090i
$130$	0.401924	−	1.50000i	0.0352510	−	0.131559i
$131$	13.0981	+	7.56218i	1.14438	+	0.660711i	0.947513	−	0.319719i	$-0.103588\pi$
$131$	13.0981	+	7.56218i	1.14438	+	0.660711i	0.196872	+	0.980429i	$0.436922\pi$
$132$	0.803848	−	3.00000i	0.0699660	−	0.261116i
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	15.4641	−	15.4641i	1.33589	−	1.33589i
$135$			6.92820i			0.596285i
$136$	0.696152	−	0.401924i	0.0596946	−	0.0344647i
$137$	10.7942	−	18.6962i	0.922213	−	1.59732i	0.126230	−	0.992001i	$-0.459712\pi$
$137$	10.7942	−	18.6962i	0.922213	−	1.59732i	0.795983	−	0.605319i	$-0.206955\pi$
$138$	−1.39230	+	0.803848i	−0.118521	+	0.0684280i
$139$	−4.09808	−	7.09808i	−0.347594	−	0.602051i	0.638227	−	0.769848i	$-0.279668\pi$
$139$	−4.09808	−	7.09808i	−0.347594	−	0.602051i	−0.985822	+	0.167797i	$0.946335\pi$
$140$	−0.464102	+	1.73205i	−0.0392237	+	0.146385i
$141$	2.19615	−	8.19615i	0.184949	−	0.690241i
$142$	9.00000	+	5.19615i	0.755263	+	0.436051i
$143$		−	2.19615i		−	0.183651i
$144$	6.16025	−	10.6699i	0.513355	−	0.889156i
$145$	−3.29423	−	12.2942i	−0.273571	−	1.02098i
$146$	−11.5359	−	11.5359i	−0.954718	−	0.954718i
$147$	4.33975			0.357936
$148$	−5.92820	+	5.92820i	−0.487295	+	0.487295i
$149$	−4.66987	−	17.4282i	−0.382571	−	1.42777i	−0.841961	−	0.539539i	$-0.818598\pi$
$149$	−4.66987	−	17.4282i	−0.382571	−	1.42777i	0.459390	−	0.888235i	$-0.348068\pi$
$150$	−2.53590			−0.207055
$151$	5.39230	+	5.39230i	0.438820	+	0.438820i	0.891615	−	0.452795i	$-0.149573\pi$
$151$	5.39230	+	5.39230i	0.438820	+	0.438820i	−0.452795	+	0.891615i	$0.649573\pi$
$152$	4.73205	+	4.73205i	0.383820	+	0.383820i
$153$	0.571797	−	0.990381i	0.0462270	−	0.0800676i
$154$			7.60770i			0.613046i
$155$	−9.92820	−	9.92820i	−0.797452	−	0.797452i
$156$	0.0980762	−	0.366025i	0.00785238	−	0.0293055i
$157$	−7.06218	+	1.89230i	−0.563623	+	0.151022i	−0.529370	−	0.848391i	$-0.677572\pi$
$157$	−7.06218	+	1.89230i	−0.563623	+	0.151022i	−0.0342528	+	0.999413i	$0.510905\pi$
$158$	−3.16987	+	11.8301i	−0.252182	+	0.941154i
$159$	−8.19615	+	4.73205i	−0.649997	+	0.375276i
$160$	−7.79423	−	4.50000i	−0.616188	−	0.355756i
$161$	0.928203	−	0.928203i	0.0731527	−	0.0731527i
$162$		−	7.73205i		−	0.607487i
$163$	3.12436	+	1.80385i	0.244718	+	0.141288i	0.617343	−	0.786694i	$-0.288209\pi$
$163$	3.12436	+	1.80385i	0.244718	+	0.141288i	−0.372625	+	0.927982i	$0.621542\pi$
$164$	−8.19615	+	4.73205i	−0.640012	+	0.369511i
$165$	5.19615	−	1.39230i	0.404520	−	0.108391i
$166$	7.09808	−	4.09808i	0.550918	−	0.318072i
$167$	−0.633975	−	1.09808i	−0.0490584	−	0.0849717i	0.840453	−	0.541884i	$-0.182289\pi$
$167$	−0.633975	−	1.09808i	−0.0490584	−	0.0849717i	−0.889512	+	0.456912i	$0.848955\pi$
$168$	0.339746	−	1.26795i	0.0262120	−	0.0978244i
$169$			12.7321i			0.979389i
$170$	−1.20577	−	0.696152i	−0.0924784	−	0.0533925i
$171$	9.19615	+	2.46410i	0.703247	+	0.188435i
$172$	2.73205	−	0.732051i	0.208317	−	0.0558184i
$173$	3.75833	+	14.0263i	0.285741	+	1.06640i	0.948296	+	0.317386i	$0.102805\pi$
$173$	3.75833	+	14.0263i	0.285741	+	1.06640i	−0.662556	+	0.749012i	$0.730528\pi$
$174$	−2.41154	−	9.00000i	−0.182819	−	0.682288i
$175$	2.00000	−	0.535898i	0.151186	−	0.0405101i
$176$	−20.4904	−	5.49038i	−1.54452	−	0.413853i
$177$	−7.73205	+	2.07180i	−0.581177	+	0.155726i
$178$	−1.39230	+	0.803848i	−0.104358	+	0.0602509i
$179$	−1.90192	+	3.29423i	−0.142156	+	0.246222i	−0.928308	−	0.371811i	$-0.878737\pi$
$179$	−1.90192	+	3.29423i	−0.142156	+	0.246222i	0.786152	+	0.618033i	$0.212070\pi$
$180$	−4.26795			−0.318114
$181$	2.69615	−	10.0622i	0.200403	−	0.747916i	−0.790398	−	0.612593i	$-0.790126\pi$
$181$	2.69615	−	10.0622i	0.200403	−	0.747916i	0.990802	−	0.135322i	$-0.0432070\pi$
$182$			0.928203i			0.0688030i
$183$	−1.50962	−	5.63397i	−0.111594	−	0.416475i
$184$	1.09808	+	1.90192i	0.0809513	+	0.140212i
$185$	−14.0263	−	3.75833i	−1.03123	−	0.276318i
$186$	−7.26795	−	7.26795i	−0.532912	−	0.532912i
$187$	−1.90192	−	0.509619i	−0.139082	−	0.0372670i
$188$	11.1962	+	3.00000i	0.816563	+	0.218797i
$189$	−1.07180	−	4.00000i	−0.0779617	−	0.290957i
$190$	3.00000	−	11.1962i	0.217643	−	0.812254i
$191$	4.09808	−	7.09808i	0.296526	−	0.513599i	−0.678812	−	0.734312i	$-0.737505\pi$
$191$	4.09808	−	7.09808i	0.296526	−	0.513599i	0.975339	+	0.220713i	$0.0708384\pi$
$192$	0.633975	+	0.366025i	0.0457532	+	0.0264156i
$193$	11.1962			0.805917			0.402958	−	0.915218i	$-0.367982\pi$
$193$	11.1962			0.805917			0.402958	+	0.915218i	$0.367982\pi$
$194$	−3.75833	−	3.75833i	−0.269832	−	0.269832i
$195$	0.633975	−	0.169873i	0.0453999	−	0.0121649i
$196$			5.92820i			0.423443i
$197$	3.46410	+	6.00000i	0.246807	+	0.427482i	0.962638	−	0.270791i	$-0.0872853\pi$
$197$	3.46410	+	6.00000i	0.246807	+	0.427482i	−0.715831	+	0.698273i	$0.753952\pi$
$198$	−17.4904	+	4.68653i	−1.24299	+	0.333057i
$199$	−4.63397	+	1.24167i	−0.328494	+	0.0880196i	−0.419297	−	0.907849i	$-0.637723\pi$
$199$	−4.63397	+	1.24167i	−0.328494	+	0.0880196i	0.0908030	+	0.995869i	$0.471057\pi$
$200$			3.46410i			0.244949i
$201$	8.92820	+	2.39230i	0.629747	+	0.168740i
$202$	6.58846	+	3.80385i	0.463562	+	0.267638i
$203$	3.80385	+	6.58846i	0.266978	+	0.462419i
$204$	−0.294229	−	0.169873i	−0.0206001	−	0.0118935i
$205$	−14.1962	−	8.19615i	−0.991502	−	0.572444i
$206$	−10.5622	−	18.2942i	−0.735902	−	1.27462i
$207$	2.70577	+	1.56218i	0.188064	+	0.108579i
$208$	−2.50000	−	0.669873i	−0.173344	−	0.0464473i
$209$		−	16.3923i		−	1.13388i
$210$	−2.19615	+	0.588457i	−0.151549	+	0.0406074i
$211$	−10.6603	+	2.85641i	−0.733882	+	0.196643i	−0.606357	−	0.795192i	$-0.707370\pi$
$211$	−10.6603	+	2.85641i	−0.733882	+	0.196643i	−0.127525	+	0.991835i	$0.540703\pi$
$212$	−6.46410	−	11.1962i	−0.443956	−	0.768955i
$213$			4.39230i			0.300956i
$214$	−11.1962	+	3.00000i	−0.765353	+	0.205076i
$215$	3.46410	+	3.46410i	0.236250	+	0.236250i
$216$	6.92820			0.471405
$217$	7.26795	+	4.19615i	0.493381	+	0.284853i
$218$	4.16025	−	7.20577i	0.281768	−	0.488036i
$219$	1.78461	−	6.66025i	0.120593	−	0.450058i
$220$	1.90192	+	7.09808i	0.128228	+	0.478552i
$221$	−0.232051	−	0.0621778i	−0.0156094	−	0.00418253i
$222$	−10.2679	−	2.75129i	−0.689140	−	0.184654i
$223$	−16.3205	−	16.3205i	−1.09290	−	1.09290i	−0.995217	−	0.0976846i	$-0.968856\pi$
$223$	−16.3205	−	16.3205i	−1.09290	−	1.09290i	−0.0976846	−	0.995217i	$-0.531144\pi$
$224$	5.19615	+	1.39230i	0.347183	+	0.0930273i
$225$	2.46410	+	4.26795i	0.164273	+	0.284530i
$226$	−7.09808	−	26.4904i	−0.472157	−	1.76211i
$227$			2.87564i			0.190863i	0.995436	+	0.0954316i	$0.0304231\pi$
$227$			2.87564i			0.190863i	−0.995436	+	0.0954316i	$0.969577\pi$
$228$	0.732051	−	2.73205i	0.0484812	−	0.180934i
$229$	−0.464102			−0.0306687			−0.0153343	−	0.999882i	$-0.504881\pi$
$229$	−0.464102			−0.0306687			−0.0153343	+	0.999882i	$0.504881\pi$
$230$	1.90192	−	3.29423i	0.125409	−	0.217215i
$231$	−2.78461	+	1.60770i	−0.183214	+	0.105779i
$232$	−12.2942	+	3.29423i	−0.807156	+	0.216277i
$233$	28.6244	+	7.66987i	1.87524	+	0.502470i	0.999817	+	0.0191191i	$0.00608618\pi$
$233$	28.6244	+	7.66987i	1.87524	+	0.502470i	0.875427	+	0.483351i	$0.160580\pi$
$234$	−2.13397	+	0.571797i	−0.139502	+	0.0373795i
$235$	5.19615	+	19.3923i	0.338960	+	1.26501i
$236$	−2.83013	−	10.5622i	−0.184226	−	0.687539i
$237$	−5.00000	+	1.33975i	−0.324785	+	0.0870259i
$238$	0.803848	+	0.215390i	0.0521057	+	0.0139617i
$239$	−21.2942	−	12.2942i	−1.37741	−	0.795248i	−0.385562	−	0.922682i	$-0.625992\pi$
$239$	−21.2942	−	12.2942i	−1.37741	−	0.795248i	−0.991847	+	0.127434i	$0.959326\pi$
$240$		−	6.33975i		−	0.409229i
$241$	1.57180	−	5.86603i	0.101248	−	0.377864i	−0.896644	−	0.442752i	$-0.854002\pi$
$241$	1.57180	−	5.86603i	0.101248	−	0.377864i	0.997893	+	0.0648878i	$0.0206690\pi$
$242$	6.06218	+	10.5000i	0.389692	+	0.674966i
$243$	13.2224	−	7.63397i	0.848219	−	0.489720i
$244$	7.69615	−	2.06218i	0.492696	−	0.132017i
$245$	−8.89230	+	5.13397i	−0.568109	+	0.327998i
$246$	−10.3923	−	6.00000i	−0.662589	−	0.382546i
$247$		−	2.00000i		−	0.127257i
$248$	−9.92820	+	9.92820i	−0.630442	+	0.630442i
$249$	3.00000	+	1.73205i	0.190117	+	0.109764i
$250$	18.1865	−	10.5000i	1.15022	−	0.664078i
$251$	2.24167	−	8.36603i	0.141493	−	0.528059i	−0.858394	−	0.512992i	$-0.828537\pi$
$251$	2.24167	−	8.36603i	0.141493	−	0.528059i	0.999886	−	0.0150671i	$-0.00479619\pi$
$252$	2.46410	−	0.660254i	0.155224	−	0.0415921i
$253$	1.39230	−	5.19615i	0.0875335	−	0.326679i
$254$	−4.73205	−	4.73205i	−0.296915	−	0.296915i
$255$		−	0.588457i		−	0.0368506i
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−19.0981	−	19.0981i	−1.19131	−	1.19131i	−0.976701	−	0.214604i	$-0.931154\pi$
$257$	−19.0981	−	19.0981i	−1.19131	−	1.19131i	−0.214604	−	0.976701i	$-0.568846\pi$
$258$	2.53590	+	2.53590i	0.157878	+	0.157878i
$259$	8.67949			0.539317
$260$	0.232051	+	0.866025i	0.0143912	+	0.0537086i
$261$	−12.8038	+	12.8038i	−0.792538	+	0.792538i
$262$	−26.1962			−1.61840
$263$	10.3923	+	10.3923i	0.640817	+	0.640817i	0.950756	−	0.309939i	$-0.100309\pi$
$263$	10.3923	+	10.3923i	0.640817	+	0.640817i	−0.309939	+	0.950756i	$0.600309\pi$
$264$	−1.39230	−	5.19615i	−0.0856904	−	0.319801i
$265$	11.1962	−	19.3923i	0.687774	−	1.19126i
$266$			6.92820i			0.424795i
$267$	−0.588457	−	0.339746i	−0.0360130	−	0.0207921i
$268$	−3.26795	+	12.1962i	−0.199622	+	0.744999i
$269$	−8.25833	+	30.8205i	−0.503519	+	1.87916i	−0.0277004	+	0.999616i	$0.508818\pi$
$269$	−8.25833	+	30.8205i	−0.503519	+	1.87916i	−0.475819	+	0.879543i	$0.657848\pi$
$270$	−6.00000	−	10.3923i	−0.365148	−	0.632456i
$271$	17.3205	−	10.0000i	1.05215	−	0.607457i	0.128897	−	0.991658i	$-0.458856\pi$
$271$	17.3205	−	10.0000i	1.05215	−	0.607457i	0.923249	+	0.384201i	$0.125523\pi$
$272$	−1.16025	+	2.00962i	−0.0703507	+	0.121851i
$273$	−0.339746	+	0.196152i	−0.0205624	+	0.0118717i
$274$			37.3923i			2.25895i
$275$	6.00000	−	6.00000i	0.361814	−	0.361814i
$276$	0.464102	−	0.803848i	0.0279356	−	0.0483859i
$277$	4.83013	−	18.0263i	0.290214	−	1.08309i	−0.654730	−	0.755863i	$-0.727218\pi$
$277$	4.83013	−	18.0263i	0.290214	−	1.08309i	0.944944	−	0.327231i	$-0.106116\pi$
$278$	12.2942	+	7.09808i	0.737359	+	0.425714i
$279$	−5.16987	+	19.2942i	−0.309512	+	1.15512i
$280$	0.803848	+	3.00000i	0.0480391	+	0.179284i
$281$	−5.59808	+	3.23205i	−0.333953	+	0.192808i	−0.657595	−	0.753372i	$-0.728426\pi$
$281$	−5.59808	+	3.23205i	−0.333953	+	0.192808i	0.323642	+	0.946180i	$0.395093\pi$
$282$	3.80385	+	14.1962i	0.226516	+	0.845369i
$283$	−13.2942	−	3.56218i	−0.790260	−	0.211749i	−0.158957	−	0.987286i	$-0.550813\pi$
$283$	−13.2942	−	3.56218i	−0.790260	−	0.211749i	−0.631303	+	0.775536i	$0.717480\pi$
$284$	−6.00000			−0.356034
$285$	4.73205	−	1.26795i	0.280302	−	0.0751068i
$286$	1.90192	+	3.29423i	0.112463	+	0.194792i
$287$	9.46410	+	2.53590i	0.558648	+	0.149689i
$288$			12.8038i			0.754474i
$289$	8.39230	−	14.5359i	0.493665	−	0.855053i
$290$	15.5885	+	15.5885i	0.915386	+	0.915386i
$291$	0.581416	−	2.16987i	0.0340832	−	0.127200i
$292$	9.09808	+	2.43782i	0.532425	+	0.142663i
$293$	9.06218	+	2.42820i	0.529418	+	0.141857i	0.513620	−	0.858018i	$-0.328304\pi$
$293$	9.06218	+	2.42820i	0.529418	+	0.141857i	0.0157985	+	0.999875i	$0.494971\pi$
$294$	−6.50962	+	3.75833i	−0.379649	+	0.219190i
$295$	13.3923	−	13.3923i	0.779730	−	0.779730i
$296$	−3.75833	+	14.0263i	−0.218449	+	0.815261i
$297$	−12.0000	−	12.0000i	−0.696311	−	0.696311i
$298$	22.0981	+	22.0981i	1.28011	+	1.28011i
$299$	0.169873	−	0.633975i	0.00982401	−	0.0366637i
$300$	1.26795	−	0.732051i	0.0732051	−	0.0422650i
$301$	−2.53590	−	1.46410i	−0.146167	−	0.0843894i
$302$	−12.7583	−	3.41858i	−0.734159	−	0.196717i
$303$			3.21539i			0.184719i
$304$	−18.6603	−	5.00000i	−1.07024	−	0.286770i
$305$	9.75833	+	9.75833i	0.558760	+	0.558760i
$306$			1.98076i			0.113233i
$307$	0.0980762	+	0.169873i	0.00559751	+	0.00969516i	0.868811	−	0.495145i	$-0.164885\pi$
$307$	0.0980762	+	0.169873i	0.00559751	+	0.00969516i	−0.863213	+	0.504840i	$0.831552\pi$
$308$	−2.19615	−	3.80385i	−0.125137	−	0.216744i
$309$	4.46410	−	7.73205i	0.253954	−	0.439861i
$310$	23.4904	+	6.29423i	1.33416	+	0.357488i
$311$	−12.9282	+	22.3923i	−0.733091	+	1.26975i	0.222465	+	0.974941i	$0.428590\pi$
$311$	−12.9282	+	22.3923i	−0.733091	+	1.26975i	−0.955556	+	0.294810i	$0.904744\pi$
$312$	−0.169873	−	0.633975i	−0.00961716	−	0.0358917i
$313$	1.00000	+	1.73205i	0.0565233	+	0.0979013i	0.892903	−	0.450250i	$-0.148665\pi$
$313$	1.00000	+	1.73205i	0.0565233	+	0.0979013i	−0.836379	+	0.548151i	$0.815332\pi$
$314$	8.95448	−	8.95448i	0.505331	−	0.505331i
$315$	3.12436	+	3.12436i	0.176037	+	0.176037i
$316$	−1.83013	−	6.83013i	−0.102953	−	0.384225i
$317$		−	6.80385i		−	0.382142i	−0.981576	−	0.191071i	$-0.938804\pi$
$317$		−	6.80385i		−	0.382142i	0.981576	−	0.191071i	$-0.0611961\pi$
$318$	8.19615	−	14.1962i	0.459617	−	0.796081i
$319$	27.0000	+	15.5885i	1.51171	+	0.872786i
$320$	−1.73205			−0.0968246
$321$	−3.46410	−	3.46410i	−0.193347	−	0.193347i
$322$	−0.588457	+	2.19615i	−0.0327934	+	0.122387i
$323$	−1.73205	−	0.464102i	−0.0963739	−	0.0258233i
$324$	2.23205	+	3.86603i	0.124003	+	0.214779i
$325$	0.732051	−	0.732051i	0.0406069	−	0.0406069i
$326$	−6.24871			−0.346084
$327$	3.51666			0.194472
$328$	−8.19615	+	14.1962i	−0.452557	+	0.783851i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$	−6.58846	+	6.58846i	−0.362683	+	0.362683i
$331$	−15.1962	+	15.1962i	−0.835256	+	0.835256i	−0.988230	−	0.152974i	$-0.951115\pi$
$331$	−15.1962	+	15.1962i	−0.835256	+	0.835256i	0.152974	+	0.988230i	$0.451115\pi$
$332$	−2.36603	+	4.09808i	−0.129853	+	0.224911i
$333$	5.34679	+	19.9545i	0.293002	+	1.09350i
$334$	1.90192	+	1.09808i	0.104069	+	0.0600841i
$335$	−21.1244	+	5.66025i	−1.15415	+	0.309253i
$336$	0.980762	+	3.66025i	0.0535050	+	0.199683i
$337$	27.5885	−	15.9282i	1.50284	−	0.867665i	0.502844	−	0.864377i	$-0.332287\pi$
$337$	27.5885	−	15.9282i	1.50284	−	0.867665i	0.999995	−	0.00328759i	$-0.00104647\pi$
$338$	−11.0263	−	19.0981i	−0.599751	−	1.03880i
$339$	8.19615	−	8.19615i	0.445154	−	0.445154i
$340$	0.803848			0.0435948
$341$	34.3923			1.86245
$342$	−15.9282	+	4.26795i	−0.861299	+	0.230784i
$343$	9.46410	−	9.46410i	0.511013	−	0.511013i
$344$	3.46410	−	3.46410i	0.186772	−	0.186772i
$345$	1.60770			0.0865554
$346$	−17.7846	−	17.7846i	−0.956107	−	0.956107i
$347$	−14.1962	−	3.80385i	−0.762089	−	0.204201i	−0.143215	−	0.989692i	$-0.545744\pi$
$347$	−14.1962	−	3.80385i	−0.762089	−	0.204201i	−0.618874	+	0.785490i	$0.712411\pi$
$348$	3.80385	+	3.80385i	0.203908	+	0.203908i
$349$	9.69615	−	5.59808i	0.519023	−	0.299658i	−0.217512	−	0.976058i	$-0.569794\pi$
$349$	9.69615	−	5.59808i	0.519023	−	0.299658i	0.736535	+	0.676400i	$0.236461\pi$
$350$	−2.53590	+	2.53590i	−0.135549	+	0.135549i
$351$	−1.46410	−	1.46410i	−0.0781480	−	0.0781480i
$352$	21.2942	−	5.70577i	1.13499	−	0.304119i
$353$	0.571797	+	2.13397i	0.0304337	+	0.113580i	0.979472	−	0.201581i	$-0.0646080\pi$
$353$	0.571797	+	2.13397i	0.0304337	+	0.113580i	−0.949038	+	0.315161i	$0.897941\pi$
$354$	9.80385	−	9.80385i	0.521069	−	0.521069i
$355$	−5.19615	−	9.00000i	−0.275783	−	0.477670i
$356$	0.464102	−	0.803848i	0.0245973	−	0.0426038i
$357$	0.0910347	+	0.339746i	0.00481806	+	0.0179813i
$358$		−	6.58846i		−	0.348211i
$359$	−7.39230	+	4.26795i	−0.390151	+	0.225254i	−0.682226	−	0.731142i	$-0.738988\pi$
$359$	−7.39230	+	4.26795i	−0.390151	+	0.225254i	0.292075	+	0.956396i	$0.405654\pi$
$360$	−6.40192	+	3.69615i	−0.337411	+	0.194804i
$361$			4.07180i			0.214305i
$362$	4.66987	+	17.4282i	0.245443	+	0.916006i
$363$	−2.56218	+	4.43782i	−0.134479	+	0.232925i
$364$	−0.267949	−	0.464102i	−0.0140444	−	0.0243255i
$365$	4.22243	+	15.7583i	0.221012	+	0.824829i
$366$	7.14359	+	7.14359i	0.373402	+	0.373402i
$367$	7.19615	−	1.92820i	0.375636	−	0.100651i	−0.0660611	−	0.997816i	$-0.521043\pi$
$367$	7.19615	−	1.92820i	0.375636	−	0.100651i	0.441697	+	0.897164i	$0.354377\pi$
$368$	−5.49038	−	3.16987i	−0.286206	−	0.165241i
$369$			23.3205i			1.21402i
$370$	24.2942	−	6.50962i	1.26300	−	0.338419i
$371$	−3.46410	+	12.9282i	−0.179847	+	0.671199i
$372$	5.73205	+	1.53590i	0.297193	+	0.0796326i
$373$	1.05256			0.0544994			0.0272497	−	0.999629i	$-0.491325\pi$
$373$	1.05256			0.0544994			0.0272497	+	0.999629i	$0.491325\pi$
$374$	3.29423	−	0.882686i	0.170341	−	0.0456426i
$375$	7.68653	+	4.43782i	0.396931	+	0.229168i
$376$	19.3923	−	5.19615i	1.00008	−	0.267971i
$377$	3.29423	+	1.90192i	0.169661	+	0.0979541i
$378$	5.07180	+	5.07180i	0.260865	+	0.260865i
$379$	−24.1962			−1.24287			−0.621436	−	0.783465i	$-0.713451\pi$
$379$	−24.1962			−1.24287			−0.621436	+	0.783465i	$0.713451\pi$
$380$	1.73205	+	6.46410i	0.0888523	+	0.331601i
$381$	0.732051	−	2.73205i	0.0375041	−	0.139967i
$382$			14.1962i			0.726338i
$383$	−4.39230	+	16.3923i	−0.224436	+	0.837608i	0.758193	+	0.652030i	$0.226082\pi$
$383$	−4.39230	+	16.3923i	−0.224436	+	0.837608i	−0.982630	+	0.185578i	$0.940584\pi$
$384$	−8.87564			−0.452933
$385$	3.80385	−	6.58846i	0.193862	−	0.335779i
$386$	−16.7942	+	9.69615i	−0.854804	+	0.493521i
$387$	1.80385	−	6.73205i	0.0916947	−	0.342209i
$388$	2.96410	+	0.794229i	0.150479	+	0.0403208i
$389$	10.3301	−	17.8923i	0.523758	−	0.907176i	−0.475859	−	0.879521i	$-0.657863\pi$
$389$	10.3301	−	17.8923i	0.523758	−	0.907176i	0.999618	−	0.0276545i	$-0.00880381\pi$
$390$	−0.803848	+	0.803848i	−0.0407044	+	0.0407044i
$391$	−0.509619	−	0.294229i	−0.0257725	−	0.0148798i
$392$	5.13397	+	8.89230i	0.259305	+	0.449129i
$393$	−5.53590	−	9.58846i	−0.279249	−	0.483674i
$394$	−10.3923	−	6.00000i	−0.523557	−	0.302276i
$395$	8.66025	−	8.66025i	0.435745	−	0.435745i
$396$	7.39230	−	7.39230i	0.371477	−	0.371477i
$397$	−9.40192	+	5.42820i	−0.471869	+	0.272434i	−0.717022	−	0.697051i	$-0.754495\pi$
$397$	−9.40192	+	5.42820i	−0.471869	+	0.272434i	0.245153	+	0.969484i	$0.421162\pi$
$398$	5.87564	−	5.87564i	0.294519	−	0.294519i
$399$	−2.53590	+	1.46410i	−0.126954	+	0.0732968i
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$			11.1962i			0.559109i	0.960130	+	0.279555i	$0.0901868\pi$
$401$			11.1962i			0.559109i	−0.960130	+	0.279555i	$0.909813\pi$
$402$	−15.4641	+	4.14359i	−0.771279	+	0.206664i
$403$	4.19615			0.209025
$404$	−4.39230			−0.218525
$405$	−3.86603	+	6.69615i	−0.192104	+	0.332734i
$406$	−11.4115	−	6.58846i	−0.566345	−	0.326980i
$407$	30.8038	−	17.7846i	1.52689	−	0.881550i
$408$	−0.588457			−0.0291330
$409$	−3.00000	−	20.0000i	−0.148340	−	0.988936i
$409$	−3.00000	−	20.0000i	−0.148340	−	0.988936i
$410$	28.3923			1.40220
$411$	−13.6865	+	7.90192i	−0.675107	+	0.389773i
$412$	10.5622	+	6.09808i	0.520361	+	0.300431i
$413$	−5.66025	+	9.80385i	−0.278523	+	0.482416i
$414$	−5.41154			−0.265963
$415$	−8.19615			−0.402333
$416$	2.59808	−	0.696152i	0.127381	−	0.0341317i
$417$			6.00000i			0.293821i
$418$	14.1962	+	24.5885i	0.694357	+	1.20266i
$419$	−16.3923	+	9.46410i	−0.800816	+	0.462352i	−0.843757	−	0.536726i	$-0.819661\pi$
$419$	−16.3923	+	9.46410i	−0.800816	+	0.462352i	0.0429401	+	0.999078i	$0.486328\pi$
$420$	0.928203	−	0.928203i	0.0452917	−	0.0452917i
$421$	14.7224	−	8.50000i	0.717527	−	0.414265i	−0.0963145	−	0.995351i	$-0.530705\pi$
$421$	14.7224	−	8.50000i	0.717527	−	0.414265i	0.813842	+	0.581086i	$0.197372\pi$
$422$	13.5167	−	13.5167i	0.657981	−	0.657981i
$423$	20.1962	−	20.1962i	0.981971	−	0.981971i
$424$	−19.3923	−	11.1962i	−0.941774	−	0.543733i
$425$	−0.464102	−	0.803848i	−0.0225122	−	0.0389923i
$426$	−3.80385	−	6.58846i	−0.184297	−	0.319212i
$427$	−7.14359	−	4.12436i	−0.345703	−	0.199592i
$428$	4.73205	−	4.73205i	0.228732	−	0.228732i
$429$	−0.803848	+	1.39230i	−0.0388101	+	0.0672211i
$430$	−8.19615	−	2.19615i	−0.395254	−	0.105908i
$431$	4.05256	−	15.1244i	0.195205	−	0.728515i	−0.797009	−	0.603968i	$-0.793586\pi$
$431$	4.05256	−	15.1244i	0.195205	−	0.728515i	0.992214	−	0.124547i	$-0.0397477\pi$
$432$	−17.3205	+	10.0000i	−0.833333	+	0.481125i
$433$	−3.86603	+	6.69615i	−0.185789	+	0.321797i	−0.943842	−	0.330397i	$-0.892818\pi$
$433$	−3.86603	+	6.69615i	−0.185789	+	0.321797i	0.758053	+	0.652193i	$0.226151\pi$
$434$	−14.5359			−0.697745
$435$	−2.41154	+	9.00000i	−0.115625	+	0.431517i
$436$			4.80385i			0.230063i
$437$	1.26795	−	4.73205i	0.0606542	−	0.226365i
$438$	3.09103	+	11.5359i	0.147695	+	0.551207i
$439$	−18.9808			−0.905902			−0.452951	−	0.891535i	$-0.649629\pi$
$439$	−18.9808			−0.905902			−0.452951	+	0.891535i	$0.649629\pi$
$440$	9.00000	+	9.00000i	0.429058	+	0.429058i
$441$	12.6506	+	7.30385i	0.602411	+	0.347802i
$442$	0.401924	−	0.107695i	0.0191176	−	0.00512254i
$443$	−15.2942	−	8.83013i	−0.726651	−	0.419532i	0.0905449	−	0.995892i	$-0.471139\pi$
$443$	−15.2942	−	8.83013i	−0.726651	−	0.419532i	−0.817196	+	0.576360i	$0.804472\pi$
$444$	5.92820	−	1.58846i	0.281340	−	0.0753848i
$445$	1.60770			0.0762121
$446$	38.6147	+	10.3468i	1.82846	+	0.489935i
$447$	−3.41858	+	12.7583i	−0.161693	+	0.603448i
$448$	1.00000	−	0.267949i	0.0472456	−	0.0126594i
$449$		−	9.33975i		−	0.440770i	−0.975413	−	0.220385i	$-0.929269\pi$
$449$		−	9.33975i		−	0.440770i	0.975413	−	0.220385i	$-0.0707313\pi$
$450$	−7.39230	−	4.26795i	−0.348477	−	0.201193i
$451$	38.7846	−	10.3923i	1.82630	−	0.489355i
$452$	11.1962	+	11.1962i	0.526623	+	0.526623i
$453$	−1.44486	−	5.39230i	−0.0678856	−	0.253353i
$454$	−2.49038	−	4.31347i	−0.116879	−	0.202441i
$455$	0.464102	−	0.803848i	0.0217574	−	0.0376850i
$456$	−1.26795	−	4.73205i	−0.0593772	−	0.221599i
$457$			21.1962i			0.991514i	0.868461	+	0.495757i	$0.165109\pi$
$457$			21.1962i			0.991514i	−0.868461	+	0.495757i	$0.834891\pi$
$458$	0.696152	−	0.401924i	0.0325291	−	0.0187807i
$459$	−1.60770	+	0.928203i	−0.0750408	+	0.0433248i
$460$			2.19615i			0.102396i
$461$	0.169873	+	0.633975i	0.00791177	+	0.0295271i	0.969769	−	0.244025i	$-0.0784680\pi$
$461$	0.169873	+	0.633975i	0.00791177	+	0.0295271i	−0.961857	+	0.273552i	$0.911801\pi$
$462$	2.78461	−	4.82309i	0.129552	−	0.224390i
$463$	−13.1962	−	22.8564i	−0.613277	−	1.06223i	−0.990684	−	0.136180i	$-0.956518\pi$
$463$	−13.1962	−	22.8564i	−0.613277	−	1.06223i	0.377407	−	0.926048i	$-0.376816\pi$
$464$	25.9808	−	25.9808i	1.20613	−	1.20613i
$465$	2.66025	+	9.92820i	0.123366	+	0.460409i
$466$	−49.5788	+	13.2846i	−2.29670	+	0.615398i
$467$	−15.4641	−	15.4641i	−0.715593	−	0.715593i	0.252106	−	0.967700i	$-0.418877\pi$
$467$	−15.4641	−	15.4641i	−0.715593	−	0.715593i	−0.967700	+	0.252106i	$0.918877\pi$
$468$	0.901924	−	0.901924i	0.0416914	−	0.0416914i
$469$	11.3205	−	6.53590i	0.522732	−	0.301800i
$470$	−24.5885	−	24.5885i	−1.13418	−	1.13418i
$471$	5.16987	+	1.38526i	0.238215	+	0.0638296i
$472$	−13.3923	−	13.3923i	−0.616431	−	0.616431i
$473$	−12.0000			−0.551761
$474$	6.33975	−	6.33975i	0.291194	−	0.291194i
$475$	5.46410	−	5.46410i	0.250710	−	0.250710i
$476$	−0.464102	+	0.124356i	−0.0212721	+	0.00569983i
$477$	−31.8564			−1.45860
$478$	42.5885			1.94795
$479$	−18.5885	+	18.5885i	−0.849328	+	0.849328i	−0.990049	−	0.140721i	$-0.955058\pi$
$479$	−18.5885	+	18.5885i	−0.849328	+	0.849328i	0.140721	+	0.990049i	$0.455058\pi$
$480$	3.29423	+	5.70577i	0.150360	+	0.260432i
$481$	3.75833	−	2.16987i	0.171365	−	0.0989377i
$482$	2.72243	+	10.1603i	0.124003	+	0.462787i
$483$	−0.928203	+	0.248711i	−0.0422347	+	0.0113168i
$484$	−6.06218	−	3.50000i	−0.275554	−	0.159091i
$485$	1.37564	+	5.13397i	0.0624648	+	0.233122i
$486$	−13.2224	+	22.9019i	−0.599782	+	1.03885i
$487$	−6.73205	+	6.73205i	−0.305058	+	0.305058i	−0.842989	−	0.537931i	$-0.819206\pi$
$487$	−6.73205	+	6.73205i	−0.305058	+	0.305058i	0.537931	+	0.842989i	$0.319206\pi$
$488$	9.75833	−	9.75833i	0.441739	−	0.441739i
$489$	−1.32051	−	2.28719i	−0.0597154	−	0.103430i
$490$	8.89230	−	15.4019i	0.401713	−	0.695788i
$491$	−21.8038			−0.983994			−0.491997	−	0.870597i	$-0.663733\pi$
$491$	−21.8038			−0.983994			−0.491997	+	0.870597i	$0.663733\pi$
$492$	6.92820			0.312348
$493$	2.41154	−	2.41154i	0.108610	−	0.108610i
$494$	1.73205	+	3.00000i	0.0779287	+	0.134976i
$495$	17.4904	+	4.68653i	0.786134	+	0.210644i
$496$	10.4904	−	39.1506i	0.471032	−	1.75792i
$497$	4.39230	+	4.39230i	0.197022	+	0.197022i
$498$	−6.00000			−0.268866
$499$	−12.9737	−	7.49038i	−0.580783	−	0.335316i	0.180661	−	0.983545i	$-0.442176\pi$
$499$	−12.9737	−	7.49038i	−0.580783	−	0.335316i	−0.761445	+	0.648230i	$0.775510\pi$
$500$	−6.06218	+	10.5000i	−0.271109	+	0.469574i
$501$			0.928203i			0.0414691i
$502$	3.88269	+	14.4904i	0.173293	+	0.646737i
$503$	20.6603	+	20.6603i	0.921195	+	0.921195i	0.997114	−	0.0759188i	$-0.0241890\pi$
$503$	20.6603	+	20.6603i	0.921195	+	0.921195i	−0.0759188	+	0.997114i	$0.524189\pi$
$504$	3.12436	−	3.12436i	0.139170	−	0.139170i
$505$	−3.80385	−	6.58846i	−0.169269	−	0.293183i
$506$	2.41154	+	9.00000i	0.107206	+	0.400099i
$507$	4.66025	−	8.07180i	0.206969	−	0.358481i
$508$	3.73205	+	1.00000i	0.165583	+	0.0443678i
$509$	15.3564	−	26.5981i	0.680661	−	1.17894i	−0.294119	−	0.955769i	$-0.595026\pi$
$509$	15.3564	−	26.5981i	0.680661	−	1.17894i	0.974780	−	0.223170i	$-0.0716405\pi$
$510$	0.509619	+	0.882686i	0.0225663	+	0.0390860i
$511$	−4.87564	−	8.44486i	−0.215686	−	0.373579i
$512$		−	8.66025i		−	0.382733i
$513$	−10.9282	−	10.9282i	−0.482492	−	0.482492i
$514$	45.1865	+	12.1077i	1.99309	+	0.534048i
$515$			21.1244i			0.930850i
$516$	−2.00000	−	0.535898i	−0.0880451	−	0.0235916i
$517$	−42.5885	−	24.5885i	−1.87304	−	1.08140i
$518$	−13.0192	+	7.51666i	−0.572032	+	0.330263i
$519$	2.75129	−	10.2679i	0.120768	−	0.450713i
$520$	1.09808	+	1.09808i	0.0481538	+	0.0481538i
$521$	−26.6603	−	26.6603i	−1.16801	−	1.16801i	−0.982676	−	0.185331i	$-0.940664\pi$
$521$	−26.6603	−	26.6603i	−1.16801	−	1.16801i	−0.185331	−	0.982676i	$-0.559336\pi$
$522$	8.11731	−	30.2942i	0.355285	−	1.32594i
$523$	−4.00000	+	4.00000i	−0.174908	+	0.174908i	−0.789132	−	0.614224i	$-0.789469\pi$
$523$	−4.00000	+	4.00000i	−0.174908	+	0.174908i	0.614224	+	0.789132i	$0.289469\pi$
$524$	13.0981	−	7.56218i	0.572192	−	0.330355i
$525$	−1.46410	−	0.392305i	−0.0638986	−	0.0171216i
$526$	−24.5885	−	6.58846i	−1.07211	−	0.287270i
$527$	0.973721	−	3.63397i	0.0424159	−	0.158298i
$528$	10.9808	+	10.9808i	0.477876	+	0.477876i
$529$	−10.6962	+	18.5263i	−0.465050	+	0.805490i
$530$			38.7846i			1.68470i
$531$	−26.0263	−	6.97372i	−1.12944	−	0.302634i
$532$	−2.00000	−	3.46410i	−0.0867110	−	0.150188i
$533$	4.73205	−	1.26795i	0.204968	−	0.0549210i
$534$	1.17691			0.0509301
$535$	11.1962	+	3.00000i	0.484052	+	0.129701i
$536$	5.66025	+	21.1244i	0.244486	+	0.912433i
$537$	2.41154	−	1.39230i	0.104066	−	0.0600824i
$538$	−14.3038	−	53.3827i	−0.616683	−	2.30149i
$539$	6.50962	−	24.2942i	0.280389	−	1.04643i
$540$	6.00000	+	3.46410i	0.258199	+	0.149071i
$541$	2.54552	−	9.50000i	0.109440	−	0.408437i	−0.889371	−	0.457187i	$-0.848857\pi$
$541$	2.54552	−	9.50000i	0.109440	−	0.408437i	0.998811	+	0.0487499i	$0.0155237\pi$
$542$	−17.3205	+	30.0000i	−0.743980	+	1.28861i
$543$	−5.39230	+	5.39230i	−0.231406	+	0.231406i
$544$		−	2.41154i		−	0.103394i
$545$	−7.20577	+	4.16025i	−0.308661	+	0.178206i
$546$	0.339746	−	0.588457i	0.0145398	−	0.0251836i
$547$	−19.3923	+	11.1962i	−0.829155	+	0.478713i	−0.853563	−	0.520989i	$-0.825563\pi$
$547$	−19.3923	+	11.1962i	−0.829155	+	0.478713i	0.0244082	+	0.999702i	$0.492230\pi$
$548$	−10.7942	−	18.6962i	−0.461107	−	0.798660i
$549$	5.08142	−	18.9641i	0.216870	−	0.809368i
$550$	−3.80385	+	14.1962i	−0.162197	+	0.605326i
$551$	24.5885	+	14.1962i	1.04750	+	0.604776i
$552$		−	1.60770i		−	0.0684280i
$553$	−3.66025	+	6.33975i	−0.155650	+	0.269593i
$554$	8.36603	+	31.2224i	0.355438	+	1.32651i
$555$	7.51666	+	7.51666i	0.319064	+	0.319064i
$556$	−8.19615			−0.347594
$557$	−22.9019	+	22.9019i	−0.970386	+	0.970386i	−0.999574	−	0.0291883i	$-0.990708\pi$
$557$	−22.9019	+	22.9019i	−0.970386	+	0.970386i	0.0291883	+	0.999574i	$0.490708\pi$
$558$	−8.95448	−	33.4186i	−0.379073	−	1.41472i
$559$	−1.46410			−0.0619249
$560$	−6.33975	−	6.33975i	−0.267903	−	0.267903i
$561$	1.01924	+	1.01924i	0.0430323	+	0.0430323i
$562$	5.59808	−	9.69615i	0.236141	−	0.409008i
$563$		−	10.7321i		−	0.452302i	−0.974092	−	0.226151i	$-0.927386\pi$
$563$		−	10.7321i		−	0.452302i	0.974092	−	0.226151i	$-0.0726143\pi$
$564$	−6.00000	−	6.00000i	−0.252646	−	0.252646i
$565$	−7.09808	+	26.4904i	−0.298618	+	1.11446i
$566$	23.0263	−	6.16987i	0.967867	−	0.259339i
$567$	1.19615	−	4.46410i	0.0502337	−	0.187475i
$568$	−9.00000	+	5.19615i	−0.377632	+	0.218026i
$569$	−3.00000	−	1.73205i	−0.125767	−	0.0726113i	0.435797	−	0.900045i	$-0.356467\pi$
$569$	−3.00000	−	1.73205i	−0.125767	−	0.0726113i	−0.561563	+	0.827434i	$0.689800\pi$
$570$	−6.00000	+	6.00000i	−0.251312	+	0.251312i
$571$			26.5885i			1.11269i	0.830951	+	0.556346i	$0.187797\pi$
$571$			26.5885i			1.11269i	−0.830951	+	0.556346i	$0.812203\pi$
$572$	−1.90192	−	1.09808i	−0.0795234	−	0.0459129i
$573$	−5.19615	+	3.00000i	−0.217072	+	0.125327i
$574$	−16.3923	+	4.39230i	−0.684202	+	0.183331i
$575$	2.19615	−	1.26795i	0.0915859	−	0.0528771i
$576$	1.23205	+	2.13397i	0.0513355	+	0.0889156i
$577$	−1.89230	+	7.06218i	−0.0787777	+	0.294002i	−0.994063	−	0.108803i	$-0.965298\pi$
$577$	−1.89230	+	7.06218i	−0.0787777	+	0.294002i	0.915286	+	0.402805i	$0.131965\pi$
$578$			29.0718i			1.20923i
$579$	−7.09808	−	4.09808i	−0.294986	−	0.170310i
$580$	−12.2942	−	3.29423i	−0.510490	−	0.136785i
$581$	4.73205	−	1.26795i	0.196319	−	0.0526034i
$582$	1.00704	+	3.75833i	0.0417432	+	0.155788i
$583$	14.1962	+	52.9808i	0.587945	+	2.19424i
$584$	15.7583	−	4.22243i	0.652084	−	0.174725i
$585$	2.13397	+	0.571797i	0.0882290	+	0.0236409i
$586$	−15.6962	+	4.20577i	−0.648402	+	0.173739i
$587$	−9.50962	+	5.49038i	−0.392504	+	0.226612i	−0.683245	−	0.730190i	$-0.739432\pi$
$587$	−9.50962	+	5.49038i	−0.392504	+	0.226612i	0.290741	+	0.956802i	$0.406098\pi$
$588$	2.16987	−	3.75833i	0.0894841	−	0.154991i
$589$	31.3205			1.29054
$590$	−8.49038	+	31.6865i	−0.349543	+	1.30451i
$591$		−	5.07180i		−	0.208626i
$592$	−10.8494	−	40.4904i	−0.445906	−	1.66414i
$593$	−10.1603	−	17.5981i	−0.417232	−	0.722666i	0.578428	−	0.815733i	$-0.303666\pi$
$593$	−10.1603	−	17.5981i	−0.417232	−	0.722666i	−0.995660	+	0.0930669i	$0.970333\pi$
$594$	28.3923	+	7.60770i	1.16495	+	0.312148i
$595$	−0.588457	−	0.588457i	−0.0241244	−	0.0241244i
$596$	−17.4282	−	4.66987i	−0.713887	−	0.191285i
$597$	3.39230	+	0.908965i	0.138838	+	0.0372015i
$598$	0.294229	+	1.09808i	0.0120319	+	0.0449037i
$599$	−1.05256	+	3.92820i	−0.0430064	+	0.160502i	−0.984090	−	0.177673i	$-0.943143\pi$
$599$	−1.05256	+	3.92820i	−0.0430064	+	0.160502i	0.941083	+	0.338175i	$0.109810\pi$
$600$	1.26795	−	2.19615i	0.0517638	−	0.0896575i
$601$	8.13397	+	4.69615i	0.331792	+	0.191560i	0.656636	−	0.754207i	$-0.271979\pi$
$601$	8.13397	+	4.69615i	0.331792	+	0.191560i	−0.324845	+	0.945767i	$0.605312\pi$
$602$	5.07180			0.206711
$603$	22.0000	+	22.0000i	0.895909	+	0.895909i
$604$	7.36603	−	1.97372i	0.299719	−	0.0803096i
$605$		−	12.1244i		−	0.492925i
$606$	−2.78461	−	4.82309i	−0.113117	−	0.195924i
$607$	34.9545	−	9.36603i	1.41876	−	0.380155i	0.533715	−	0.845664i	$-0.320795\pi$
$607$	34.9545	−	9.36603i	1.41876	−	0.380155i	0.885043	+	0.465509i	$0.154129\pi$
$608$	19.3923	−	5.19615i	0.786462	−	0.210732i
$609$		−	5.56922i		−	0.225676i
$610$	−23.0885	−	6.18653i	−0.934824	−	0.250485i
$611$	−5.19615	−	3.00000i	−0.210214	−	0.121367i
$612$	−0.571797	−	0.990381i	−0.0231135	−	0.0400338i
$613$	−9.69615	−	5.59808i	−0.391624	−	0.226104i	0.291240	−	0.956650i	$-0.405932\pi$
$613$	−9.69615	−	5.59808i	−0.391624	−	0.226104i	−0.682864	+	0.730546i	$0.739266\pi$
$614$	−0.294229	−	0.169873i	−0.0118741	−	0.00685552i
$615$	6.00000	+	10.3923i	0.241943	+	0.419058i
$616$	−6.58846	−	3.80385i	−0.265457	−	0.153261i
$617$	−27.1865	−	7.28461i	−1.09449	−	0.293267i	−0.333970	−	0.942584i	$-0.608388\pi$
$617$	−27.1865	−	7.28461i	−1.09449	−	0.293267i	−0.760518	+	0.649316i	$0.775055\pi$
$618$			15.4641i			0.622057i
$619$	−0.366025	+	0.0980762i	−0.0147118	+	0.00394202i	−0.266167	−	0.963927i	$-0.585757\pi$
$619$	−0.366025	+	0.0980762i	−0.0147118	+	0.00394202i	0.251456	+	0.967869i	$0.419091\pi$
$620$	−13.5622	+	3.63397i	−0.544670	+	0.145944i
$621$	−2.53590	−	4.39230i	−0.101762	−	0.176257i
$622$		−	44.7846i		−	1.79570i
$623$	−0.928203	+	0.248711i	−0.0371877	+	0.00996441i
$624$	1.33975	+	1.33975i	0.0536328	+	0.0536328i
$625$	−11.0000			−0.440000
$626$	−3.00000	−	1.73205i	−0.119904	−	0.0692267i
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$	−1.89230	+	7.06218i	−0.0755112	+	0.281812i
$629$	−1.00704	−	3.75833i	−0.0401534	−	0.149854i
$630$	−7.39230	−	1.98076i	−0.294516	−	0.0789155i
$631$	−37.3205	−	10.0000i	−1.48571	−	0.398094i	−0.577421	−	0.816446i	$-0.695941\pi$
$631$	−37.3205	−	10.0000i	−1.48571	−	0.398094i	−0.908285	+	0.418353i	$0.862608\pi$
$632$	−8.66025	−	8.66025i	−0.344486	−	0.344486i
$633$	7.80385	+	2.09103i	0.310175	+	0.0831112i
$634$	5.89230	+	10.2058i	0.234013	+	0.405323i
$635$	1.73205	+	6.46410i	0.0687343	+	0.256520i
$636$			9.46410i			0.375276i
$637$	0.794229	−	2.96410i	0.0314685	−	0.117442i
$638$	−54.0000			−2.13788
$639$	−7.39230	+	12.8038i	−0.292435	+	0.506512i
$640$	18.1865	−	10.5000i	0.718886	−	0.415049i
$641$	43.6865	−	11.7058i	1.72551	−	0.462350i	0.746373	−	0.665528i	$-0.231794\pi$
$641$	43.6865	−	11.7058i	1.72551	−	0.462350i	0.979142	+	0.203178i	$0.0651271\pi$
$642$	8.19615	+	2.19615i	0.323476	+	0.0866752i
$643$	27.6603	−	7.41154i	1.09081	−	0.292283i	0.331795	−	0.943351i	$-0.392346\pi$
$643$	27.6603	−	7.41154i	1.09081	−	0.292283i	0.759019	+	0.651069i	$0.225679\pi$
$644$	−0.339746	−	1.26795i	−0.0133879	−	0.0499642i
$645$	−0.928203	−	3.46410i	−0.0365480	−	0.136399i
$646$	3.00000	−	0.803848i	0.118033	−	0.0316270i
$647$	30.5885	+	8.19615i	1.20256	+	0.322224i	0.803837	−	0.594849i	$-0.202788\pi$
$647$	30.5885	+	8.19615i	1.20256	+	0.322224i	0.398719	+	0.917073i	$0.369455\pi$
$648$	6.69615	+	3.86603i	0.263050	+	0.151872i
$649$			46.3923i			1.82106i
$650$	−0.464102	+	1.73205i	−0.0182036	+	0.0679366i
$651$	−3.07180	−	5.32051i	−0.120393	−	0.208527i
$652$	3.12436	−	1.80385i	0.122359	−	0.0706441i
$653$	−21.2942	+	5.70577i	−0.833308	+	0.223284i	−0.650156	−	0.759801i	$-0.725297\pi$
$653$	−21.2942	+	5.70577i	−0.833308	+	0.223284i	−0.183151	+	0.983085i	$0.558630\pi$
$654$	−5.27499	+	3.04552i	−0.206268	+	0.119089i
$655$	22.6865	+	13.0981i	0.886436	+	0.511784i
$656$		−	47.3205i		−	1.84756i
$657$	16.4115	−	16.4115i	0.640275	−	0.640275i
$658$	18.0000	+	10.3923i	0.701713	+	0.405134i
$659$	−40.6865	+	23.4904i	−1.58492	+	0.915055i	−0.590797	+	0.806820i	$0.701187\pi$
$659$	−40.6865	+	23.4904i	−1.58492	+	0.915055i	−0.994125	+	0.108235i	$0.965480\pi$
$660$	1.39230	−	5.19615i	0.0541954	−	0.202260i
$661$	18.6244	−	4.99038i	0.724403	−	0.194103i	0.122268	−	0.992497i	$-0.460983\pi$
$661$	18.6244	−	4.99038i	0.724403	−	0.194103i	0.602136	+	0.798394i	$0.294317\pi$
$662$	9.63397	−	35.9545i	0.374435	−	1.39741i
$663$	0.124356	+	0.124356i	0.00482957	+	0.00482957i
$664$			8.19615i			0.318072i
$665$	3.46410	−	6.00000i	0.134332	−	0.232670i
$666$	−25.3013	−	25.3013i	−0.980404	−	0.980404i
$667$	6.58846	+	6.58846i	0.255106	+	0.255106i
$668$	−1.26795			−0.0490584
$669$	4.37307	+	16.3205i	0.169073	+	0.630987i
$670$	26.7846	−	26.7846i	1.03478	−	1.03478i
$671$	−33.8038			−1.30498
$672$	−2.78461	−	2.78461i	−0.107419	−	0.107419i
$673$	7.06218	+	26.3564i	0.272227	+	1.01596i	0.957677	+	0.287845i	$0.0929388\pi$
$673$	7.06218	+	26.3564i	0.272227	+	1.01596i	−0.685450	+	0.728120i	$0.740394\pi$
$674$	−27.5885	+	47.7846i	−1.06267	+	1.84059i
$675$		−	8.00000i		−	0.307920i
$676$	11.0263	+	6.36603i	0.424088	+	0.244847i
$677$	−4.11474	+	15.3564i	−0.158142	+	0.590195i	0.840674	+	0.541542i	$0.182159\pi$
$677$	−4.11474	+	15.3564i	−0.158142	+	0.590195i	−0.998816	+	0.0486525i	$0.984507\pi$
$678$	−5.19615	+	19.3923i	−0.199557	+	0.744757i
$679$	−1.58846	−	2.75129i	−0.0609594	−	0.105585i
$680$	1.20577	−	0.696152i	0.0462392	−	0.0266962i
$681$	1.05256	−	1.82309i	0.0403341	−	0.0698608i
$682$	−51.5885	+	29.7846i	−1.97542	+	1.14051i
$683$		−	40.9808i		−	1.56809i	−0.620707	−	0.784043i	$-0.713154\pi$
$683$		−	40.9808i		−	1.56809i	0.620707	−	0.784043i	$-0.286846\pi$
$684$	6.73205	−	6.73205i	0.257406	−	0.257406i
$685$	18.6962	−	32.3827i	0.714343	−	1.23728i
$686$	−6.00000	+	22.3923i	−0.229081	+	0.854942i
$687$	0.294229	+	0.169873i	0.0112255	+	0.00648106i
$688$	−3.66025	+	13.6603i	−0.139546	+	0.520792i
$689$	1.73205	+	6.46410i	0.0659859	+	0.246263i
$690$	−2.41154	+	1.39230i	−0.0918059	+	0.0530041i
$691$	8.75833	+	32.6865i	0.333183	+	1.24345i	0.905826	+	0.423650i	$0.139251\pi$
$691$	8.75833	+	32.6865i	0.333183	+	1.24345i	−0.572643	+	0.819805i	$0.694082\pi$
$692$	14.0263	+	3.75833i	0.533199	+	0.142870i
$693$	−10.8231			−0.411135
$694$	24.5885	−	6.58846i	0.933365	−	0.250094i
$695$	−7.09808	−	12.2942i	−0.269245	−	0.466347i
$696$	9.00000	+	2.41154i	0.341144	+	0.0914093i
$697$		−	4.39230i		−	0.166370i
$698$	−9.69615	+	16.7942i	−0.367005	+	0.635671i
$699$	−15.3397	−	15.3397i	−0.580202	−	0.580202i
$700$	0.535898	−	2.00000i	0.0202551	−	0.0755929i
$701$	−28.2224	−	7.56218i	−1.06595	−	0.285620i	−0.317120	−	0.948385i	$-0.602716\pi$
$701$	−28.2224	−	7.56218i	−1.06595	−	0.285620i	−0.748827	+	0.662766i	$0.769382\pi$
$702$	3.46410	+	0.928203i	0.130744	+	0.0350328i
$703$	28.0526	−	16.1962i	1.05802	−	0.610849i
$704$	3.00000	−	3.00000i	0.113067	−	0.113067i
$705$	3.80385	−	14.1962i	0.143261	−	0.534658i
$706$	−2.70577	−	2.70577i	−0.101833	−	0.101833i
$707$	3.21539	+	3.21539i	0.120927	+	0.120927i
$708$	−2.07180	+	7.73205i	−0.0778629	+	0.290588i
$709$	−30.3109	+	17.5000i	−1.13835	+	0.657226i	−0.946021	−	0.324104i	$-0.894937\pi$
$709$	−30.3109	+	17.5000i	−1.13835	+	0.657226i	−0.192328	+	0.981331i	$0.561604\pi$
$710$	15.5885	+	9.00000i	0.585024	+	0.337764i
$711$	−16.8301	−	4.50962i	−0.631179	−	0.169124i
$712$		−	1.60770i		−	0.0602509i
$713$	9.92820	+	2.66025i	0.371814	+	0.0996273i
$714$	−0.430781	−	0.430781i	−0.0161216	−	0.0161216i
$715$		−	3.80385i		−	0.142256i
$716$	1.90192	+	3.29423i	0.0710782	+	0.123111i
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	7.39230	−	12.8038i	0.275878	−	0.477835i
$719$	5.36603	+	1.43782i	0.200119	+	0.0536217i	0.357486	−	0.933918i	$-0.383634\pi$
$719$	5.36603	+	1.43782i	0.200119	+	0.0536217i	−0.157367	+	0.987540i	$0.550301\pi$
$720$	10.6699	−	18.4808i	0.397643	−	0.688737i
$721$	−3.26795	−	12.1962i	−0.121705	−	0.454208i
$722$	−3.52628	−	6.10770i	−0.131235	−	0.227305i
$723$	−3.14359	+	3.14359i	−0.116912	+	0.116912i
$724$	−7.36603	−	7.36603i	−0.273756	−	0.273756i
$725$	3.80385	+	14.1962i	0.141271	+	0.527232i
$726$		−	8.87564i		−	0.329406i
$727$	14.5885	−	25.2679i	0.541056	−	0.937136i	−0.457788	−	0.889061i	$-0.651358\pi$
$727$	14.5885	−	25.2679i	0.541056	−	0.937136i	0.998844	−	0.0480749i	$-0.0153086\pi$
$728$	−0.803848	−	0.464102i	−0.0297926	−	0.0172008i
$729$	2.21539			0.0820515
$730$	−19.9808	−	19.9808i	−0.739521	−	0.739521i
$731$	−0.339746	+	1.26795i	−0.0125660	+	0.0468968i
$732$	−5.63397	−	1.50962i	−0.208238	−	0.0557971i
$733$	1.96410	+	3.40192i	0.0725457	+	0.125653i	0.900016	−	0.435856i	$-0.143554\pi$
$733$	1.96410	+	3.40192i	0.0725457	+	0.125653i	−0.827471	+	0.561509i	$0.810221\pi$
$734$	−9.12436	+	9.12436i	−0.336786	+	0.336786i
$735$	7.51666			0.277256
$736$	6.58846			0.242854
$737$	26.7846	−	46.3923i	0.986624	−	1.70888i
$738$	−20.1962	−	34.9808i	−0.743431	−	1.28766i
$739$	17.2487	−	17.2487i	0.634504	−	0.634504i	−0.314690	−	0.949194i	$-0.601901\pi$
$739$	17.2487	−	17.2487i	0.634504	−	0.634504i	0.949194	+	0.314690i	$0.101901\pi$
$740$	−10.2679	+	10.2679i	−0.377457	+	0.377457i
$741$	−0.732051	+	1.26795i	−0.0268926	+	0.0465793i
$742$	−6.00000	−	22.3923i	−0.220267	−	0.822047i
$743$	−10.0981	−	5.83013i	−0.370462	−	0.213887i	0.303198	−	0.952928i	$-0.401946\pi$
$743$	−10.0981	−	5.83013i	−0.370462	−	0.213887i	−0.673660	+	0.739041i	$0.735279\pi$
$744$	9.92820	−	2.66025i	0.363986	−	0.0975296i
$745$	−8.08846	−	30.1865i	−0.296338	−	1.10595i
$746$	−1.57884	+	0.911543i	−0.0578054	+	0.0333740i
$747$	5.83013	+	10.0981i	0.213313	+	0.369469i
$748$	−1.39230	+	1.39230i	−0.0509077	+	0.0509077i
$749$	−6.92820			−0.253151
$750$	−15.3731			−0.561345
$751$	−13.8301	+	3.70577i	−0.504669	+	0.135226i	−0.502166	−	0.864771i	$-0.667463\pi$
$751$	−13.8301	+	3.70577i	−0.504669	+	0.135226i	−0.00250268	+	0.999997i	$0.500797\pi$
$752$	−40.9808	+	40.9808i	−1.49441	+	1.49441i
$753$	−4.48334	+	4.48334i	−0.163382	+	0.163382i
$754$	−6.58846			−0.239937
$755$	9.33975	+	9.33975i	0.339908	+	0.339908i
$756$	−4.00000	−	1.07180i	−0.145479	−	0.0389809i
$757$	20.3468	+	20.3468i	0.739517	+	0.739517i	0.972484	−	0.232968i	$-0.0748437\pi$
$757$	20.3468	+	20.3468i	0.739517	+	0.739517i	−0.232968	+	0.972484i	$0.574844\pi$
$758$	36.2942	−	20.9545i	1.31827	−	0.761101i
$759$	−2.78461	+	2.78461i	−0.101075	+	0.101075i
$760$	8.19615	+	8.19615i	0.297306	+	0.297306i
$761$	30.7583	−	8.24167i	1.11499	−	0.298760i	0.346135	−	0.938185i	$-0.387494\pi$
$761$	30.7583	−	8.24167i	1.11499	−	0.298760i	0.768854	+	0.639425i	$0.220827\pi$
$762$	1.26795	+	4.73205i	0.0459330	+	0.171424i
$763$	3.51666	−	3.51666i	0.127312	−	0.127312i
$764$	−4.09808	−	7.09808i	−0.148263	−	0.256799i
$765$	0.990381	−	1.71539i	0.0358073	−	0.0620201i
$766$	−7.60770	−	28.3923i	−0.274877	−	1.02586i
$767$			5.66025i			0.204380i
$768$	12.0455	−	6.95448i	0.434655	−	0.250948i
$769$	−13.7942	+	7.96410i	−0.497433	+	0.287193i	−0.727653	−	0.685946i	$-0.759389\pi$
$769$	−13.7942	+	7.96410i	−0.497433	+	0.287193i	0.230220	+	0.973139i	$0.426055\pi$
$770$			13.1769i			0.474863i
$771$	5.11731	+	19.0981i	0.184296	+	0.687800i
$772$	5.59808	−	9.69615i	0.201479	−	0.348972i
$773$	16.2846	+	28.2058i	0.585717	+	1.01449i	0.994786	+	0.101988i	$0.0325202\pi$
$773$	16.2846	+	28.2058i	0.585717	+	1.01449i	−0.409069	+	0.912503i	$0.634146\pi$
$774$	3.12436	+	11.6603i	0.112303	+	0.419119i
$775$	11.4641	+	11.4641i	0.411803	+	0.411803i
$776$	5.13397	−	1.37564i	0.184299	−	0.0493828i
$777$	−5.50258	−	3.17691i	−0.197404	−	0.113971i
$778$			35.7846i			1.28294i
$779$	35.3205	−	9.46410i	1.26549	−	0.339087i
$780$	0.169873	−	0.633975i	0.00608243	−	0.0226999i
$781$	24.5885	+	6.58846i	0.879844	+	0.235754i
$782$	1.01924			0.0364479
$783$	28.3923	−	7.60770i	1.01466	−	0.271877i
$784$	−25.6699	−	14.8205i	−0.916781	−	0.529304i
$785$	−12.2321	+	3.27757i	−0.436581	+	0.116981i
$786$	16.6077	+	9.58846i	0.592377	+	0.342009i
$787$	−38.7321	−	38.7321i	−1.38065	−	1.38065i	−0.843466	−	0.537182i	$-0.819489\pi$
$787$	−38.7321	−	38.7321i	−1.38065	−	1.38065i	−0.537182	−	0.843466i	$-0.680511\pi$
$788$	6.92820			0.246807
$789$	−2.78461	−	10.3923i	−0.0991347	−	0.369976i
$790$	−5.49038	+	20.4904i	−0.195339	+	0.729015i
$791$		−	16.3923i		−	0.582843i
$792$	4.68653	−	17.4904i	0.166529	−	0.621494i
$793$	−4.12436			−0.146460
$794$	9.40192	−	16.2846i	0.333662	−	0.577919i
$795$	−14.1962	+	8.19615i	−0.503486	+	0.290688i
$796$	−1.24167	+	4.63397i	−0.0440098	+	0.164247i
$797$	−32.2583	−	8.64359i	−1.14265	−	0.306172i	−0.362633	−	0.931932i	$-0.618122\pi$
$797$	−32.2583	−	8.64359i	−1.14265	−	0.306172i	−0.780016	+	0.625760i	$0.784789\pi$
$798$	2.53590	−	4.39230i	0.0897698	−	0.155486i
$799$	−3.80385	+	3.80385i	−0.134570	+	0.134570i
$800$	9.00000	+	5.19615i	0.318198	+	0.183712i
$801$	−1.14359	−	1.98076i	−0.0404069	−	0.0699868i
$802$	−9.69615	−	16.7942i	−0.342383	−	0.593025i
$803$	−34.6077	−	19.9808i	−1.22128	−	0.705106i
$804$	6.53590	−	6.53590i	0.230503	−	0.230503i
$805$	1.60770	−	1.60770i	0.0566638	−	0.0566638i
$806$	−6.29423	+	3.63397i	−0.221705	+	0.128001i
$807$	16.5167	−	16.5167i	0.581414	−	0.581414i
$808$	−6.58846	+	3.80385i	−0.231781	+	0.133819i
$809$	1.26795	+	2.19615i	0.0445787	+	0.0772126i	0.887454	−	0.460897i	$-0.152472\pi$
$809$	1.26795	+	2.19615i	0.0445787	+	0.0772126i	−0.842875	+	0.538109i	$0.819139\pi$
$810$		−	13.3923i		−	0.470558i
$811$	31.1506	−	8.34679i	1.09385	−	0.293095i	0.333590	−	0.942718i	$-0.391740\pi$
$811$	31.1506	−	8.34679i	1.09385	−	0.293095i	0.760257	+	0.649623i	$0.225073\pi$
$812$	7.60770			0.266978
$813$	−14.6410			−0.513483
$814$	−30.8038	+	53.3538i	−1.07967	+	1.87005i
$815$	5.41154	+	3.12436i	0.189558	+	0.109441i
$816$	1.47114	−	0.849365i	0.0515003	−	0.0297337i
$817$	−10.9282			−0.382329
$818$	21.8205	+	27.4019i	0.762936	+	0.958086i
$819$	−1.32051			−0.0461423
$820$	−14.1962	+	8.19615i	−0.495751	+	0.286222i
$821$	2.89230	+	1.66987i	0.100942	+	0.0582790i	0.549621	−	0.835414i	$-0.314772\pi$
$821$	2.89230	+	1.66987i	0.100942	+	0.0582790i	−0.448679	+	0.893693i	$0.648105\pi$
$822$	13.6865	−	23.7058i	0.477373	−	0.826834i
$823$	−21.1244			−0.736349			−0.368174	−	0.929757i	$-0.620017\pi$
$823$	−21.1244			−0.736349			−0.368174	+	0.929757i	$0.620017\pi$
$824$	21.1244			0.735902
$825$	−6.00000	+	1.60770i	−0.208893	+	0.0559728i
$826$		−	19.6077i		−	0.682239i
$827$	−15.1699	−	26.2750i	−0.527508	−	0.913671i	−0.999486	−	0.0320605i	$-0.989793\pi$
$827$	−15.1699	−	26.2750i	−0.527508	−	0.913671i	0.471978	−	0.881610i	$-0.343540\pi$
$828$	2.70577	−	1.56218i	0.0940321	−	0.0542894i
$829$	−34.0263	+	34.0263i	−1.18178	+	1.18178i	−0.202499	+	0.979282i	$0.564906\pi$
$829$	−34.0263	+	34.0263i	−1.18178	+	1.18178i	−0.979282	+	0.202499i	$0.935094\pi$
$830$	12.2942	−	7.09808i	0.426739	−	0.246378i
$831$	−9.66025	+	9.66025i	−0.335110	+	0.335110i
$832$	0.366025	−	0.366025i	0.0126896	−	0.0126896i
$833$	−2.38269	−	1.37564i	−0.0825552	−	0.0476633i
$834$	−5.19615	−	9.00000i	−0.179928	−	0.311645i
$835$	−1.09808	−	1.90192i	−0.0380005	−	0.0658188i
$836$	−14.1962	−	8.19615i	−0.490984	−	0.283470i
$837$	22.9282	−	22.9282i	0.792515	−	0.792515i
$838$	16.3923	−	28.3923i	0.566263	−	0.980796i
$839$	0.169873	+	0.0455173i	0.00586467	+	0.00157143i	0.261750	−	0.965136i	$-0.415700\pi$
$839$	0.169873	+	0.0455173i	0.00586467	+	0.00157143i	−0.255886	+	0.966707i	$0.582367\pi$
$840$	0.588457	−	2.19615i	0.0203037	−	0.0757745i
$841$	−21.6506	+	12.5000i	−0.746574	+	0.431034i
$842$	−14.7224	+	25.5000i	−0.507369	+	0.878788i
$843$	4.73205			0.162980
$844$	−2.85641	+	10.6603i	−0.0983216	+	0.366941i
$845$			22.0526i			0.758631i
$846$	−12.8038	+	47.7846i	−0.440205	+	1.64287i
$847$	1.87564	+	7.00000i	0.0644479	+	0.240523i
$848$	64.6410			2.21978
$849$	7.12436	+	7.12436i	0.244507	+	0.244507i
$850$	1.39230	+	0.803848i	0.0477557	+	0.0275717i
$851$	10.2679	−	2.75129i	0.351981	−	0.0943130i
$852$	3.80385	+	2.19615i	0.130318	+	0.0752389i
$853$	7.13397	−	1.91154i	0.244263	−	0.0654500i	−0.134611	−	0.990899i	$-0.542978\pi$
$853$	7.13397	−	1.91154i	0.244263	−	0.0654500i	0.378873	+	0.925449i	$0.376312\pi$
$854$	14.2872			0.488897
$855$	15.9282	+	4.26795i	0.544733	+	0.145961i
$856$	3.00000	−	11.1962i	0.102538	−	0.382677i
$857$	20.8923	−	5.59808i	0.713668	−	0.191227i	0.116323	−	0.993211i	$-0.462889\pi$
$857$	20.8923	−	5.59808i	0.713668	−	0.191227i	0.597344	+	0.801985i	$0.296223\pi$
$858$		−	2.78461i		−	0.0950650i
$859$	−23.1962	−	13.3923i	−0.791443	−	0.456940i	0.0490276	−	0.998797i	$-0.484388\pi$
$859$	−23.1962	−	13.3923i	−0.791443	−	0.456940i	−0.840470	+	0.541858i	$0.817721\pi$
$860$	4.73205	−	1.26795i	0.161362	−	0.0432367i
$861$	−5.07180	−	5.07180i	−0.172846	−	0.172846i
$862$	7.01924	+	26.1962i	0.239076	+	0.892244i
$863$	17.1962	+	29.7846i	0.585364	+	1.01388i	0.994830	+	0.101555i	$0.0323817\pi$
$863$	17.1962	+	29.7846i	0.585364	+	1.01388i	−0.409466	+	0.912325i	$0.634285\pi$
$864$	10.3923	−	18.0000i	0.353553	−	0.612372i
$865$	6.50962	+	24.2942i	0.221334	+	0.826029i
$866$		−	13.3923i		−	0.455089i
$867$	−10.6410	+	6.14359i	−0.361388	+	0.208647i
$868$	7.26795	−	4.19615i	0.246690	−	0.142427i
$869$			30.0000i			1.01768i
$870$	−4.17691	−	15.5885i	−0.141611	−	0.528498i
$871$	3.26795	−	5.66025i	0.110730	−	0.191790i
$872$	4.16025	+	7.20577i	0.140884	+	0.244018i
$873$	5.34679	−	5.34679i	0.180961	−	0.180961i
$874$	2.19615	+	8.19615i	0.0742860	+	0.277239i
$875$	12.1244	−	3.24871i	0.409878	−	0.109826i
$876$	−4.87564	−	4.87564i	−0.164733	−	0.164733i
$877$	11.3397	−	11.3397i	0.382916	−	0.382916i	−0.489236	−	0.872152i	$-0.662724\pi$
$877$	11.3397	−	11.3397i	0.382916	−	0.382916i	0.872152	+	0.489236i	$0.162724\pi$
$878$	28.4711	−	16.4378i	0.960855	−	0.554750i
$879$	−4.85641	−	4.85641i	−0.163803	−	0.163803i
$880$	−35.4904	−	9.50962i	−1.19638	−	0.320569i
$881$	6.97372	+	6.97372i	0.234951	+	0.234951i	0.814755	−	0.579805i	$-0.196871\pi$
$881$	6.97372	+	6.97372i	0.234951	+	0.234951i	−0.579805	+	0.814755i	$0.696871\pi$
$882$	−25.3013			−0.851938
$883$	−23.2487	+	23.2487i	−0.782381	+	0.782381i	−0.980232	−	0.197851i	$-0.936604\pi$
$883$	−23.2487	+	23.2487i	−0.782381	+	0.782381i	0.197851	+	0.980232i	$0.436604\pi$
$884$	−0.169873	+	0.169873i	−0.00571345	+	0.00571345i
$885$	−13.3923	+	3.58846i	−0.450177	+	0.120625i
$886$	30.5885			1.02764
$887$	2.78461			0.0934980			0.0467490	−	0.998907i	$-0.485114\pi$
$887$	2.78461			0.0934980			0.0467490	+	0.998907i	$0.485114\pi$
$888$	7.51666	−	7.51666i	0.252243	−	0.252243i
$889$	−2.00000	−	3.46410i	−0.0670778	−	0.116182i
$890$	−2.41154	+	1.39230i	−0.0808351	+	0.0466702i
$891$	−4.90192	−	18.2942i	−0.164221	−	0.612880i
$892$	−22.2942	+	5.97372i	−0.746466	+	0.200015i
$893$	−38.7846	−	22.3923i	−1.29788	−	0.749330i
$894$	−5.92116	−	22.0981i	−0.198033	−	0.739070i
$895$	−3.29423	+	5.70577i	−0.110114	+	0.190723i
$896$	−8.87564	+	8.87564i	−0.296514	+	0.296514i
$897$	−0.339746	+	0.339746i	−0.0113438	+	0.0113438i
$898$	8.08846	+	14.0096i	0.269915	+	0.467507i
$899$	−29.7846	+	51.5885i	−0.993372	+	1.72057i
$900$	4.92820			0.164273
$901$	6.00000			0.199889
$902$	−49.1769	+	49.1769i	−1.63741	+	1.63741i
$903$	1.07180	+	1.85641i	0.0356672	+	0.0617773i
$904$	26.4904	+	7.09808i	0.881057	+	0.236079i
$905$	4.66987	−	17.4282i	0.155232	−	0.579333i
$906$	6.83717	+	6.83717i	0.227150	+	0.227150i
$907$	−32.9808			−1.09511			−0.547554	−	0.836770i	$-0.684441\pi$
$907$	−32.9808			−1.09511			−0.547554	+	0.836770i	$0.684441\pi$
$908$	2.49038	+	1.43782i	0.0826462	+	0.0477158i
$909$	−5.41154	+	9.37307i	−0.179490	+	0.310885i
$910$			1.60770i			0.0532946i
$911$	−0.633975	−	2.36603i	−0.0210045	−	0.0783899i	0.954628	−	0.297801i	$-0.0962531\pi$
$911$	−0.633975	−	2.36603i	−0.0210045	−	0.0783899i	−0.975633	+	0.219411i	$0.929586\pi$
$912$	10.0000	+	10.0000i	0.331133	+	0.331133i
$913$	14.1962	−	14.1962i	0.469824	−	0.469824i
$914$	−18.3564	−	31.7942i	−0.607176	−	1.05166i
$915$	−2.61474	−	9.75833i	−0.0864405	−	0.322600i
$916$	−0.232051	+	0.401924i	−0.00766717	+	0.0132799i
$917$	−15.1244	−	4.05256i	−0.499450	−	0.133827i
$918$	1.60770	−	2.78461i	0.0530618	−	0.0919058i
$919$	15.1699	+	26.2750i	0.500408	+	0.866732i	1.00000		0.000471108i	$0.000149958\pi$
$919$	15.1699	+	26.2750i	0.500408	+	0.866732i	−0.499592	+	0.866261i	$0.666517\pi$
$920$	1.90192	+	3.29423i	0.0627046	+	0.108608i
$921$		−	0.143594i		−	0.00473157i
$922$	−0.803848	−	0.803848i	−0.0264733	−	0.0264733i
$923$	3.00000	+	0.803848i	0.0987462	+	0.0264590i
$924$			3.21539i			0.105779i
$925$	16.1962	+	4.33975i	0.532526	+	0.142690i
$926$	39.5885	+	22.8564i	1.30096	+	0.751108i
$927$	26.0263	−	15.0263i	0.854815	−	0.493528i
$928$	−9.88269	+	36.8827i	−0.324415	+	1.21073i
$929$	27.0788	+	27.0788i	0.888428	+	0.888428i	0.994372	−	0.105944i	$-0.0337865\pi$
$929$	27.0788	+	27.0788i	0.888428	+	0.888428i	−0.105944	+	0.994372i	$0.533786\pi$
$930$	−12.5885	−	12.5885i	−0.412792	−	0.412792i
$931$	5.92820	−	22.1244i	0.194289	−	0.725096i
$932$	20.9545	−	20.9545i	0.686387	−	0.686387i
$933$	16.3923	−	9.46410i	0.536660	−	0.309841i
$934$	36.5885	+	9.80385i	1.19721	+	0.320792i
$935$	−3.29423	−	0.882686i	−0.107733	−	0.0288669i
$936$	0.571797	−	2.13397i	0.0186898	−	0.0697511i
$937$	15.6147	+	15.6147i	0.510111	+	0.510111i	0.914560	−	0.404449i	$-0.132537\pi$
$937$	15.6147	+	15.6147i	0.510111	+	0.510111i	−0.404449	+	0.914560i	$0.632537\pi$
$938$	−11.3205	+	19.6077i	−0.369628	+	0.640214i
$939$		−	1.46410i		−	0.0477792i
$940$	19.3923	+	5.19615i	0.632507	+	0.169480i
$941$	−29.7846	−	51.5885i	−0.970951	−	1.68174i	−0.692698	−	0.721228i	$-0.743578\pi$
$941$	−29.7846	−	51.5885i	−0.970951	−	1.68174i	−0.278252	−	0.960508i	$-0.589755\pi$
$942$	−8.95448	+	2.39935i	−0.291753	+	0.0781749i
$943$	12.0000			0.390774
$944$	52.8109	+	14.1506i	1.71885	+	0.460564i
$945$	−1.85641	−	6.92820i	−0.0603889	−	0.225374i
$946$	18.0000	−	10.3923i	0.585230	−	0.337883i
$947$	1.85641	+	6.92820i	0.0603251	+	0.225136i	0.989507	−	0.144487i	$-0.0461533\pi$
$947$	1.85641	+	6.92820i	0.0603251	+	0.225136i	−0.929182	+	0.369624i	$0.879487\pi$
$948$	−1.33975	+	5.00000i	−0.0435129	+	0.162392i
$949$	−4.22243	−	2.43782i	−0.137066	−	0.0791351i
$950$	−3.46410	+	12.9282i	−0.112390	+	0.419446i
$951$	−2.49038	+	4.31347i	−0.0807561	+	0.139874i
$952$	−0.588457	+	0.588457i	−0.0190720	+	0.0190720i
$953$			17.1051i			0.554089i	0.960857	+	0.277045i	$0.0893550\pi$
$953$			17.1051i			0.554089i	−0.960857	+	0.277045i	$0.910645\pi$
$954$	47.7846	−	27.5885i	1.54708	−	0.893209i
$955$	7.09808	−	12.2942i	0.229688	−	0.397832i
$956$	−21.2942	+	12.2942i	−0.688705	+	0.397624i
$957$	−11.4115	−	19.7654i	−0.368883	−	0.638924i
$958$	11.7846	−	43.9808i	0.380743	−	1.42095i
$959$	−5.78461	+	21.5885i	−0.186795	+	0.697128i
$960$	1.09808	+	0.633975i	0.0354403	+	0.0204614i
$961$			34.7128i			1.11977i
$962$	−3.75833	+	6.50962i	−0.121173	+	0.209879i
$963$	−4.26795	−	15.9282i	−0.137533	−	0.513279i
$964$	−4.29423	−	4.29423i	−0.138308	−	0.138308i
$965$	19.3923			0.624260
$966$	1.17691	−	1.17691i	0.0378666	−	0.0378666i
$967$	12.1506	+	45.3468i	0.390738	+	1.45825i	0.828920	+	0.559368i	$0.188956\pi$
$967$	12.1506	+	45.3468i	0.390738	+	1.45825i	−0.438181	+	0.898887i	$0.644377\pi$
$968$	−12.1244			−0.389692
$969$	0.928203	+	0.928203i	0.0298182	+	0.0298182i
$970$	−6.50962	−	6.50962i	−0.209011	−	0.209011i
$971$	24.8827	−	43.0981i	0.798523	−	1.38308i	−0.122054	−	0.992523i	$-0.538948\pi$
$971$	24.8827	−	43.0981i	0.798523	−	1.38308i	0.920578	−	0.390560i	$-0.127718\pi$
$972$		−	15.2679i		−	0.489720i
$973$	6.00000	+	6.00000i	0.192351	+	0.192351i
$974$	4.26795	−	15.9282i	0.136754	−	0.510373i
$975$	−0.732051	+	0.196152i	−0.0234444	+	0.00628191i
$976$	−10.3109	+	38.4808i	−0.330044	+	1.23174i
$977$	−31.7942	+	18.3564i	−1.01719	+	0.587273i	−0.913288	−	0.407314i	$-0.866465\pi$
$977$	−31.7942	+	18.3564i	−1.01719	+	0.587273i	−0.103899	+	0.994588i	$0.533132\pi$
$978$	3.96152	+	2.28719i	0.126676	+	0.0731362i
$979$	−2.78461	+	2.78461i	−0.0889965	+	0.0889965i
$980$			10.2679i			0.327998i
$981$	10.2513	+	5.91858i	0.327298	+	0.188966i
$982$	32.7058	−	18.8827i	1.04368	−	0.602571i
$983$	−40.0526	+	10.7321i	−1.27748	+	0.342299i	−0.832891	−	0.553436i	$-0.813316\pi$
$983$	−40.0526	+	10.7321i	−1.27748	+	0.342299i	−0.444587	+	0.895736i	$0.646649\pi$
$984$	10.3923	−	6.00000i	0.331295	−	0.191273i
$985$	6.00000	+	10.3923i	0.191176	+	0.331126i
$986$	−1.52886	+	5.70577i	−0.0486887	+	0.181709i
$987$			8.78461i			0.279617i
$988$	−1.73205	−	1.00000i	−0.0551039	−	0.0318142i
$989$	−3.46410	−	0.928203i	−0.110152	−	0.0295151i
$990$	−30.2942	+	8.11731i	−0.962814	+	0.257985i
$991$	13.9545	+	52.0788i	0.443279	+	1.65434i	0.720441	+	0.693516i	$0.243939\pi$
$991$	13.9545	+	52.0788i	0.443279	+	1.65434i	−0.277163	+	0.960823i	$0.589394\pi$
$992$	10.9019	+	40.6865i	0.346136	+	1.29180i
$993$	15.1962	−	4.07180i	0.482235	−	0.129215i
$994$	−10.3923	−	2.78461i	−0.329624	−	0.0883225i
$995$	−8.02628	+	2.15064i	−0.254450	+	0.0681797i
$996$	3.00000	−	1.73205i	0.0950586	−	0.0548821i
$997$	−0.928203	+	1.60770i	−0.0293965	+	0.0509162i	−0.880349	−	0.474326i	$-0.842692\pi$
$997$	−0.928203	+	1.60770i	−0.0293965	+	0.0509162i	0.850953	+	0.525242i	$0.176025\pi$
$998$	25.9474			0.821352
$999$	8.67949	−	32.3923i	0.274607	−	1.02485i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.g.a.360.1	yes	4
409.217	even	12	inner	409.2.g.a.217.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.g.a.217.1	✓	4	409.217	even	12	inner
409.2.g.a.360.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.g (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{2} +(-0.633975 - 0.366025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205 q^{5} +1.26795 q^{6} +(-1.00000 + 0.267949i) q^{7} -1.73205i q^{8} +(-1.23205 - 2.13397i) q^{9} +(-2.59808 + 1.50000i) q^{10} +(-3.00000 + 3.00000i) q^{11} +(-0.633975 + 0.366025i) q^{12} +(-0.366025 + 0.366025i) q^{13} +(1.26795 - 1.26795i) q^{14} +(-1.09808 - 0.633975i) q^{15} +(2.50000 + 4.33013i) q^{16} +(0.232051 + 0.401924i) q^{17} +(3.69615 + 2.13397i) q^{18} +(-2.73205 + 2.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} +(0.732051 + 0.196152i) q^{21} +(1.90192 - 7.09808i) q^{22} +(-1.09808 + 0.633975i) q^{23} +(-0.633975 + 1.09808i) q^{24} -2.00000 q^{25} +(0.232051 - 0.866025i) q^{26} +4.00000i q^{27} +(-0.267949 + 1.00000i) q^{28} +(-1.90192 - 7.09808i) q^{29} +2.19615 q^{30} +(-5.73205 - 5.73205i) q^{31} +(-4.50000 - 2.59808i) q^{32} +(3.00000 - 0.803848i) q^{33} +(-0.696152 - 0.401924i) q^{34} +(-1.73205 + 0.464102i) q^{35} -2.46410 q^{36} +(-8.09808 - 2.16987i) q^{37} +(1.73205 - 6.46410i) q^{38} +(0.366025 - 0.0980762i) q^{39} -3.00000i q^{40} +(-8.19615 - 4.73205i) q^{41} +(-1.26795 + 0.339746i) q^{42} +(2.00000 + 2.00000i) q^{43} +(1.09808 + 4.09808i) q^{44} +(-2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +(3.00000 + 11.1962i) q^{47} -3.66025i q^{48} +(-5.13397 + 2.96410i) q^{49} +(3.00000 - 1.73205i) q^{50} -0.339746i q^{51} +(0.133975 + 0.500000i) q^{52} +(6.46410 - 11.1962i) q^{53} +(-3.46410 - 6.00000i) q^{54} +(-5.19615 + 5.19615i) q^{55} +(0.464102 + 1.73205i) q^{56} +(2.73205 - 0.732051i) q^{57} +(9.00000 + 9.00000i) q^{58} +(7.73205 - 7.73205i) q^{59} +(-1.09808 + 0.633975i) q^{60} +(5.63397 + 5.63397i) q^{61} +(13.5622 + 3.63397i) q^{62} +(1.80385 + 1.80385i) q^{63} -1.00000 q^{64} +(-0.633975 + 0.633975i) q^{65} +(-3.80385 + 3.80385i) q^{66} +(-12.1962 + 3.26795i) q^{67} +0.464102 q^{68} +0.928203 q^{69} +(2.19615 - 2.19615i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-3.69615 + 2.13397i) q^{72} +(2.43782 + 9.09808i) q^{73} +(14.0263 - 3.75833i) q^{74} +(1.26795 + 0.732051i) q^{75} +(1.00000 + 3.73205i) q^{76} +(2.19615 - 3.80385i) q^{77} +(-0.464102 + 0.464102i) q^{78} +(5.00000 - 5.00000i) q^{79} +(4.33013 + 7.50000i) q^{80} +(-2.23205 + 3.86603i) q^{81} +16.3923 q^{82} -4.73205 q^{83} +(0.535898 - 0.535898i) q^{84} +(0.401924 + 0.696152i) q^{85} +(-4.73205 - 1.26795i) q^{86} +(-1.39230 + 5.19615i) q^{87} +(5.19615 + 5.19615i) q^{88} +0.928203 q^{89} +(6.40192 + 3.69615i) q^{90} +(0.267949 - 0.464102i) q^{91} +1.26795i q^{92} +(1.53590 + 5.73205i) q^{93} +(-14.1962 - 14.1962i) q^{94} +(-4.73205 + 4.73205i) q^{95} +(1.90192 + 3.29423i) q^{96} +(0.794229 + 2.96410i) q^{97} +(5.13397 - 8.89230i) q^{98} +(10.0981 + 2.70577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{2} - 6 q^{3} + 2 q^{4} + 12 q^{6} - 4 q^{7} + 2 q^{9} - 12 q^{11} - 6 q^{12} + 2 q^{13} + 12 q^{14} + 6 q^{15} + 10 q^{16} - 6 q^{17} - 6 q^{18} - 4 q^{19} - 4 q^{21} + 18 q^{22} + 6 q^{23} - 6 q^{24}+ \cdots + 30 q^{99}+O(q^{100}) \) 4 * q - 6 * q^2 - 6 * q^3 + 2 * q^4 + 12 * q^6 - 4 * q^7 + 2 * q^9 - 12 * q^11 - 6 * q^12 + 2 * q^13 + 12 * q^14 + 6 * q^15 + 10 * q^16 - 6 * q^17 - 6 * q^18 - 4 * q^19 - 4 * q^21 + 18 * q^22 + 6 * q^23 - 6 * q^24 - 8 * q^25 - 6 * q^26 - 8 * q^28 - 18 * q^29 - 12 * q^30 - 16 * q^31 - 18 * q^32 + 12 * q^33 + 18 * q^34 + 4 * q^36 - 22 * q^37 - 2 * q^39 - 12 * q^41 - 12 * q^42 + 8 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 + 12 * q^47 - 24 * q^49 + 12 * q^50 + 4 * q^52 + 12 * q^53 - 12 * q^56 + 4 * q^57 + 36 * q^58 + 24 * q^59 + 6 * q^60 + 26 * q^61 + 30 * q^62 + 28 * q^63 - 4 * q^64 - 6 * q^65 - 36 * q^66 - 28 * q^67 - 12 * q^68 - 24 * q^69 - 12 * q^70 - 12 * q^71 + 6 * q^72 + 34 * q^73 + 18 * q^74 + 12 * q^75 + 4 * q^76 - 12 * q^77 + 12 * q^78 + 20 * q^79 - 2 * q^81 + 24 * q^82 - 12 * q^83 + 16 * q^84 + 12 * q^85 - 12 * q^86 + 36 * q^87 - 24 * q^89 + 36 * q^90 + 8 * q^91 + 20 * q^93 - 36 * q^94 - 12 * q^95 + 18 * q^96 - 28 * q^97 + 24 * q^98 + 30 * q^99

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