LMFDB - Embedded newform 620.2.k.d.63.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [620,2,Mod(63,620)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("620.63"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(620, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 620 = 2^{2} \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	620.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.95072492532$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			63.1
Character	$\chi$	$=$	620.63
Dual form			620.2.k.d.187.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41272 + 0.0649557i) q^{2} +(1.92422 - 1.92422i) q^{3} +(1.99156 - 0.183528i) q^{4} +(0.843724 + 2.07078i) q^{5} +(-2.59339 + 2.84337i) q^{6} +(0.570845 + 0.570845i) q^{7} +(-2.80160 + 0.388638i) q^{8} -4.40523i q^{9} +(-1.32646 - 2.87063i) q^{10} +5.77153i q^{11} +(3.47905 - 4.18535i) q^{12} +(-0.713084 - 0.713084i) q^{13} +(-0.843524 - 0.769365i) q^{14} +(5.60814 + 2.36112i) q^{15} +(3.93263 - 0.731016i) q^{16} +(1.64853 - 1.64853i) q^{17} +(0.286144 + 6.22336i) q^{18} +7.91202 q^{19} +(2.06038 + 3.96924i) q^{20} +2.19686 q^{21} +(-0.374893 - 8.15356i) q^{22} +(-0.387048 + 0.387048i) q^{23} +(-4.64306 + 6.13871i) q^{24} +(-3.57626 + 3.49433i) q^{25} +(1.05371 + 0.961070i) q^{26} +(-2.70396 - 2.70396i) q^{27} +(1.24164 + 1.03211i) q^{28} -1.56984i q^{29} +(-8.07611 - 2.97133i) q^{30} +1.00000i q^{31} +(-5.50823 + 1.28817i) q^{32} +(11.1057 + 11.1057i) q^{33} +(-2.22184 + 2.43600i) q^{34} +(-0.700458 + 1.66373i) q^{35} +(-0.808485 - 8.77328i) q^{36} +(1.74890 - 1.74890i) q^{37} +(-11.1775 + 0.513930i) q^{38} -2.74426 q^{39} +(-3.16856 - 5.47359i) q^{40} -6.81909 q^{41} +(-3.10355 + 0.142698i) q^{42} +(1.60483 - 1.60483i) q^{43} +(1.05924 + 11.4943i) q^{44} +(9.12226 - 3.71680i) q^{45} +(0.521650 - 0.571932i) q^{46} +(-5.22661 - 5.22661i) q^{47} +(6.16061 - 8.97388i) q^{48} -6.34827i q^{49} +(4.82528 - 5.16882i) q^{50} -6.34428i q^{51} +(-1.55102 - 1.28928i) q^{52} +(1.24465 + 1.24465i) q^{53} +(3.99559 + 3.64431i) q^{54} +(-11.9516 + 4.86958i) q^{55} +(-1.82113 - 1.37743i) q^{56} +(15.2244 - 15.2244i) q^{57} +(0.101970 + 2.21774i) q^{58} +11.2881 q^{59} +(11.6023 + 3.67307i) q^{60} -4.80140 q^{61} +(-0.0649557 - 1.41272i) q^{62} +(2.51470 - 2.51470i) q^{63} +(7.69792 - 2.17761i) q^{64} +(0.874994 - 2.07829i) q^{65} +(-16.4106 - 14.9678i) q^{66} +(-2.59782 - 2.59782i) q^{67} +(2.98061 - 3.58571i) q^{68} +1.48953i q^{69} +(0.881483 - 2.39588i) q^{70} +16.2104i q^{71} +(1.71204 + 12.3417i) q^{72} +(-8.09201 - 8.09201i) q^{73} +(-2.35711 + 2.58431i) q^{74} +(-0.157639 + 13.6054i) q^{75} +(15.7573 - 1.45208i) q^{76} +(-3.29464 + 3.29464i) q^{77} +(3.87687 - 0.178255i) q^{78} -14.6923 q^{79} +(4.83183 + 7.52684i) q^{80} +2.80965 q^{81} +(9.63347 - 0.442938i) q^{82} +(10.8426 - 10.8426i) q^{83} +(4.37518 - 0.403186i) q^{84} +(4.80466 + 2.02284i) q^{85} +(-2.16294 + 2.37142i) q^{86} +(-3.02071 - 3.02071i) q^{87} +(-2.24303 - 16.1695i) q^{88} +8.16496i q^{89} +(-12.6458 + 5.84334i) q^{90} -0.814120i q^{91} +(-0.699796 + 0.841864i) q^{92} +(1.92422 + 1.92422i) q^{93} +(7.72324 + 7.04424i) q^{94} +(6.67556 + 16.3840i) q^{95} +(-8.12032 + 13.0778i) q^{96} +(9.73234 - 9.73234i) q^{97} +(0.412356 + 8.96834i) q^{98} +25.4249 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) $ 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/620\mathbb{Z}\right)^\times$.

$n$	$311$	$497$	$561$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.41272	+	0.0649557i	−0.998945	+	0.0459306i
$2$	−1.41272	+	0.0649557i	−0.998945	+	0.0459306i
$3$	1.92422	−	1.92422i	1.11095	−	1.11095i	0.117925	−	0.993022i	$-0.462376\pi$
$3$	1.92422	−	1.92422i	1.11095	−	1.11095i	0.993022	−	0.117925i	$-0.0376243\pi$
$4$	1.99156	−	0.183528i	0.995781	−	0.0917642i
$5$	0.843724	+	2.07078i	0.377325	+	0.926081i
$5$	0.843724	+	2.07078i	0.377325	+	0.926081i
$6$	−2.59339	+	2.84337i	−1.05875	+	1.16080i
$7$	0.570845	+	0.570845i	0.215759	+	0.215759i	0.806709	−	0.590950i	$-0.201247\pi$
$7$	0.570845	+	0.570845i	0.215759	+	0.215759i	−0.590950	+	0.806709i	$0.701247\pi$
$8$	−2.80160	+	0.388638i	−0.990515	+	0.137404i
$9$		−	4.40523i		−	1.46841i
$10$	−1.32646	−	2.87063i	−0.419462	−	0.907773i
$11$			5.77153i			1.74018i	0.492892	+	0.870090i	$0.335940\pi$
$11$			5.77153i			1.74018i	−0.492892	+	0.870090i	$0.664060\pi$
$12$	3.47905	−	4.18535i	1.00432	−	1.20821i
$13$	−0.713084	−	0.713084i	−0.197774	−	0.197774i	0.601271	−	0.799045i	$-0.294661\pi$
$13$	−0.713084	−	0.713084i	−0.197774	−	0.197774i	−0.799045	+	0.601271i	$0.794661\pi$
$14$	−0.843524	−	0.769365i	−0.225441	−	0.205621i
$15$	5.60814	+	2.36112i	1.44802	+	0.609639i
$16$	3.93263	−	0.731016i	0.983159	−	0.182754i
$17$	1.64853	−	1.64853i	0.399828	−	0.399828i	−0.478344	−	0.878173i	$-0.658763\pi$
$17$	1.64853	−	1.64853i	0.399828	−	0.399828i	0.878173	+	0.478344i	$0.158763\pi$
$18$	0.286144	+	6.22336i	0.0674449	+	1.46686i
$19$	7.91202			1.81514			0.907571	−	0.419899i	$-0.137935\pi$
$19$	7.91202			1.81514			0.907571	+	0.419899i	$0.137935\pi$
$20$	2.06038	+	3.96924i	0.460714	+	0.887549i
$21$	2.19686			0.479394
$22$	−0.374893	−	8.15356i	−0.0799275	−	1.73834i
$23$	−0.387048	+	0.387048i	−0.0807051	+	0.0807051i	−0.746307	−	0.665602i	$-0.768175\pi$
$23$	−0.387048	+	0.387048i	−0.0807051	+	0.0807051i	0.665602	+	0.746307i	$0.268175\pi$
$24$	−4.64306	+	6.13871i	−0.947762	+	1.25306i
$25$	−3.57626	+	3.49433i	−0.715252	+	0.698867i
$26$	1.05371	+	0.961070i	0.206649	+	0.188481i
$27$	−2.70396	−	2.70396i	−0.520378	−	0.520378i
$28$	1.24164	+	1.03211i	0.234648	+	0.195050i
$29$		−	1.56984i		−	0.291511i	−0.989321	−	0.145756i	$-0.953439\pi$
$29$		−	1.56984i		−	0.291511i	0.989321	−	0.145756i	$-0.0465614\pi$
$30$	−8.07611	−	2.97133i	−1.47449	−	0.542488i
$31$			1.00000i			0.179605i
$31$			1.00000i			0.179605i
$32$	−5.50823	+	1.28817i	−0.973727	+	0.227718i
$33$	11.1057	+	11.1057i	1.93325	+	1.93325i
$34$	−2.22184	+	2.43600i	−0.381042	+	0.417771i
$35$	−0.700458	+	1.66373i	−0.118399	+	0.281221i
$36$	−0.808485	−	8.77328i	−0.134747	−	1.46221i
$37$	1.74890	−	1.74890i	0.287517	−	0.287517i	−0.548581	−	0.836098i	$-0.684832\pi$
$37$	1.74890	−	1.74890i	0.287517	−	0.287517i	0.836098	+	0.548581i	$0.184832\pi$
$38$	−11.1775	+	0.513930i	−1.81323	+	0.0833705i
$39$	−2.74426			−0.439433
$40$	−3.16856	−	5.47359i	−0.500993	−	0.865451i
$41$	−6.81909			−1.06496			−0.532481	−	0.846442i	$-0.678740\pi$
$41$	−6.81909			−1.06496			−0.532481	+	0.846442i	$0.678740\pi$
$42$	−3.10355	+	0.142698i	−0.478888	+	0.0220188i
$43$	1.60483	−	1.60483i	0.244735	−	0.244735i	−0.574071	−	0.818806i	$-0.694637\pi$
$43$	1.60483	−	1.60483i	0.244735	−	0.244735i	0.818806	+	0.574071i	$0.194637\pi$
$44$	1.05924	+	11.4943i	0.159686	+	1.73284i
$45$	9.12226	−	3.71680i	1.35987	−	0.554068i
$46$	0.521650	−	0.571932i	0.0769131	−	0.0843267i
$47$	−5.22661	−	5.22661i	−0.762379	−	0.762379i	0.214373	−	0.976752i	$-0.431229\pi$
$47$	−5.22661	−	5.22661i	−0.762379	−	0.762379i	−0.976752	+	0.214373i	$0.931229\pi$
$48$	6.16061	−	8.97388i	0.889208	−	1.29527i
$49$		−	6.34827i		−	0.906896i
$50$	4.82528	−	5.16882i	0.682397	−	0.730981i
$51$		−	6.34428i		−	0.888377i
$52$	−1.55102	−	1.28928i	−0.215088	−	0.178791i
$53$	1.24465	+	1.24465i	0.170966	+	0.170966i	0.787404	−	0.616438i	$-0.211425\pi$
$53$	1.24465	+	1.24465i	0.170966	+	0.170966i	−0.616438	+	0.787404i	$0.711425\pi$
$54$	3.99559	+	3.64431i	0.543730	+	0.495928i
$55$	−11.9516	+	4.86958i	−1.61155	+	0.656614i
$56$	−1.82113	−	1.37743i	−0.243359	−	0.184066i
$57$	15.2244	−	15.2244i	2.01653	−	2.01653i
$58$	0.101970	+	2.21774i	0.0133893	+	0.291204i
$59$	11.2881			1.46958			0.734791	−	0.678293i	$-0.237280\pi$
$59$	11.2881			1.46958			0.734791	+	0.678293i	$0.237280\pi$
$60$	11.6023	+	3.67307i	1.49785	+	0.474191i
$61$	−4.80140			−0.614756			−0.307378	−	0.951587i	$-0.599452\pi$
$61$	−4.80140			−0.614756			−0.307378	+	0.951587i	$0.599452\pi$
$62$	−0.0649557	−	1.41272i	−0.00824938	−	0.179416i
$63$	2.51470	−	2.51470i	0.316822	−	0.316822i
$64$	7.69792	−	2.17761i	0.962240	−	0.272202i
$65$	0.874994	−	2.07829i	0.108530	−	0.257780i
$66$	−16.4106	−	14.9678i	−2.02000	−	1.84241i
$67$	−2.59782	−	2.59782i	−0.317374	−	0.317374i	0.530384	−	0.847758i	$-0.322048\pi$
$67$	−2.59782	−	2.59782i	−0.317374	−	0.317374i	−0.847758	+	0.530384i	$0.822048\pi$
$68$	2.98061	−	3.58571i	0.361452	−	0.434831i
$69$			1.48953i			0.179318i
$70$	0.881483	−	2.39588i	0.105357	−	0.286363i
$71$			16.2104i			1.92382i	0.273369	+	0.961909i	$0.411862\pi$
$71$			16.2104i			1.92382i	−0.273369	+	0.961909i	$0.588138\pi$
$72$	1.71204	+	12.3417i	0.201766	+	1.45448i
$73$	−8.09201	−	8.09201i	−0.947098	−	0.947098i	0.0515717	−	0.998669i	$-0.483577\pi$
$73$	−8.09201	−	8.09201i	−0.947098	−	0.947098i	−0.998669	+	0.0515717i	$0.983577\pi$
$74$	−2.35711	+	2.58431i	−0.274008	+	0.300420i
$75$	−0.157639	+	13.6054i	−0.0182026	+	1.57101i
$76$	15.7573	−	1.45208i	1.80748	−	0.166565i
$77$	−3.29464	+	3.29464i	−0.375460	+	0.375460i
$78$	3.87687	−	0.178255i	0.438969	−	0.0201834i
$79$	−14.6923			−1.65301			−0.826507	−	0.562926i	$-0.809676\pi$
$79$	−14.6923			−1.65301			−0.826507	+	0.562926i	$0.809676\pi$
$80$	4.83183	+	7.52684i	0.540215	+	0.841527i
$81$	2.80965			0.312183
$82$	9.63347	−	0.442938i	1.06384	−	0.0489144i
$83$	10.8426	−	10.8426i	1.19013	−	1.19013i	0.213098	−	0.977031i	$-0.431645\pi$
$83$	10.8426	−	10.8426i	1.19013	−	1.19013i	0.977031	−	0.213098i	$-0.0683554\pi$
$84$	4.37518	−	0.403186i	0.477371	−	0.0439912i
$85$	4.80466	+	2.02284i	0.521139	+	0.219408i
$86$	−2.16294	+	2.37142i	−0.233235	+	0.255717i
$87$	−3.02071	−	3.02071i	−0.323854	−	0.323854i
$88$	−2.24303	−	16.1695i	−0.239108	−	1.72367i
$89$			8.16496i			0.865484i	0.901518	+	0.432742i	$0.142454\pi$
$89$			8.16496i			0.865484i	−0.901518	+	0.432742i	$0.857546\pi$
$90$	−12.6458	+	5.84334i	−1.33298	+	0.615942i
$91$		−	0.814120i		−	0.0853430i
$92$	−0.699796	+	0.841864i	−0.0729587	+	0.0877704i
$93$	1.92422	+	1.92422i	0.199532	+	0.199532i
$94$	7.72324	+	7.04424i	0.796591	+	0.726558i
$95$	6.67556	+	16.3840i	0.684898	+	1.68097i
$96$	−8.12032	+	13.0778i	−0.828777	+	1.33474i
$97$	9.73234	−	9.73234i	0.988170	−	0.988170i	−0.0117609	−	0.999931i	$-0.503744\pi$
$97$	9.73234	−	9.73234i	0.988170	−	0.988170i	0.999931	+	0.0117609i	$0.00374371\pi$
$98$	0.412356	+	8.96834i	0.0416543	+	0.905939i
$99$	25.4249			2.55530
$100$	−6.48103	+	7.61553i	−0.648103	+	0.761553i
$101$	−11.9264			−1.18673			−0.593363	−	0.804935i	$-0.702200\pi$
$101$	−11.9264			−1.18673			−0.593363	+	0.804935i	$0.702200\pi$
$102$	0.412097	+	8.96270i	0.0408037	+	0.887439i
$103$	3.59865	−	3.59865i	0.354586	−	0.354586i	−0.507227	−	0.861813i	$-0.669329\pi$
$103$	3.59865	−	3.59865i	0.354586	−	0.354586i	0.861813	+	0.507227i	$0.169329\pi$
$104$	2.27491	+	1.72064i	0.223073	+	0.168723i
$105$	1.85354	+	4.54921i	0.180887	+	0.443957i
$106$	−1.83919	−	1.67749i	−0.178638	−	0.162933i
$107$	0.702759	+	0.702759i	0.0679383	+	0.0679383i	0.740260	−	0.672321i	$-0.234703\pi$
$107$	0.702759	+	0.702759i	0.0679383	+	0.0679383i	−0.672321	+	0.740260i	$0.734703\pi$
$108$	−5.88137	−	4.88886i	−0.565935	−	0.470431i
$109$		−	3.99213i		−	0.382377i	−0.981553	−	0.191188i	$-0.938766\pi$
$109$		−	3.99213i		−	0.382377i	0.981553	−	0.191188i	$-0.0612341\pi$
$110$	16.5679	−	7.65567i	1.57969	−	0.729940i
$111$		−	6.73052i		−	0.638833i
$112$	2.66222	+	1.82763i	0.251556	+	0.172694i
$113$	−3.53030	−	3.53030i	−0.332102	−	0.332102i	0.521282	−	0.853384i	$-0.325454\pi$
$113$	−3.53030	−	3.53030i	−0.332102	−	0.332102i	−0.853384	+	0.521282i	$0.825454\pi$
$114$	−20.5190	+	22.4968i	−1.92178	+	2.10702i
$115$	−1.12805	−	0.474929i	−0.105191	−	0.0442874i
$116$	−0.288110	−	3.12643i	−0.0267503	−	0.290281i
$117$	−3.14130	+	3.14130i	−0.290413	+	0.290413i
$118$	−15.9469	+	0.733225i	−1.46803	+	0.0674988i
$119$	1.88211			0.172533
$120$	−16.6294	−	4.43538i	−1.51805	−	0.404893i
$121$	−22.3105			−2.02823
$122$	6.78304	−	0.311878i	0.614107	−	0.0282361i
$123$	−13.1214	+	13.1214i	−1.18312	+	1.18312i
$124$	0.183528	+	1.99156i	0.0164813	+	0.178848i
$125$	−10.2534	−	4.45739i	−0.917090	−	0.398681i
$126$	−3.38923	+	3.71591i	−0.301936	+	0.331040i
$127$	8.45871	+	8.45871i	0.750589	+	0.750589i	0.974589	−	0.224000i	$-0.0719115\pi$
$127$	8.45871	+	8.45871i	0.750589	+	0.750589i	−0.224000	+	0.974589i	$0.571912\pi$
$128$	−10.7336	+	3.57639i	−0.948722	+	0.316111i
$129$		−	6.17609i		−	0.543775i
$130$	−1.10113	+	2.99287i	−0.0965751	+	0.262492i
$131$		−	7.99008i		−	0.698097i	−0.937105	−	0.349048i	$-0.886505\pi$
$131$		−	7.99008i		−	0.698097i	0.937105	−	0.349048i	$-0.113495\pi$
$132$	24.1558	+	20.0794i	2.10250	+	1.74769i
$133$	4.51653	+	4.51653i	0.391633	+	0.391633i
$134$	3.83873	+	3.50125i	0.331616	+	0.302462i
$135$	3.31791	−	7.88072i	0.285561	−	0.678264i
$136$	−3.97785	+	5.25922i	−0.341098	+	0.450974i
$137$	−0.481044	+	0.481044i	−0.0410984	+	0.0410984i	−0.727357	−	0.686259i	$-0.759252\pi$
$137$	−0.481044	+	0.481044i	−0.0410984	+	0.0410984i	0.686259	+	0.727357i	$0.259252\pi$
$138$	−0.0967533	−	2.10429i	−0.00823619	−	0.179129i
$139$	−17.7945			−1.50931			−0.754654	−	0.656123i	$-0.772195\pi$
$139$	−17.7945			−1.50931			−0.754654	+	0.656123i	$0.772195\pi$
$140$	−1.08966	+	3.44197i	−0.0920934	+	0.290900i
$141$	−20.1143			−1.69393
$142$	−1.05296	−	22.9007i	−0.0883621	−	1.92179i
$143$	4.11558	−	4.11558i	0.344162	−	0.344162i
$144$	−3.22029	−	17.3242i	−0.268358	−	1.44368i
$145$	3.25079	−	1.32451i	0.269963	−	0.109995i
$146$	11.9574	+	10.9061i	0.989599	+	0.902597i
$147$	−12.2155	−	12.2155i	−1.00751	−	1.00751i
$148$	3.16207	−	3.80401i	0.259920	−	0.312688i
$149$		−	7.76657i		−	0.636263i	−0.948047	−	0.318131i	$-0.896945\pi$
$149$		−	7.76657i		−	0.636263i	0.948047	−	0.318131i	$-0.103055\pi$
$150$	−0.661045	−	19.2308i	−0.0539741	−	1.57019i
$151$		−	9.75804i		−	0.794098i	−0.917797	−	0.397049i	$-0.870034\pi$
$151$		−	9.75804i		−	0.794098i	0.917797	−	0.397049i	$-0.129966\pi$
$152$	−22.1663	+	3.07491i	−1.79793	+	0.249408i
$153$	−7.26217	−	7.26217i	−0.587112	−	0.587112i
$154$	4.44041	−	4.86842i	0.357818	−	0.392308i
$155$	−2.07078	+	0.843724i	−0.166329	+	0.0677696i
$156$	−5.46536	+	0.503649i	−0.437579	+	0.0403242i
$157$	−7.54907	+	7.54907i	−0.602482	+	0.602482i	−0.940970	−	0.338489i	$-0.890084\pi$
$157$	−7.54907	+	7.54907i	−0.602482	+	0.602482i	0.338489	+	0.940970i	$0.390084\pi$
$158$	20.7561	−	0.954349i	1.65127	−	0.0759239i
$159$	4.78995			0.379868
$160$	−7.31494	−	10.3195i	−0.578297	−	0.815826i
$161$	−0.441888			−0.0348257
$162$	−3.96925	+	0.182503i	−0.311854	+	0.0143388i
$163$	−16.4926	+	16.4926i	−1.29180	+	1.29180i	−0.358126	+	0.933673i	$0.616584\pi$
$163$	−16.4926	+	16.4926i	−1.29180	+	1.29180i	−0.933673	+	0.358126i	$0.883416\pi$
$164$	−13.5806	+	1.25150i	−1.06047	+	0.0977255i
$165$	−13.6273	+	32.3675i	−1.06088	+	2.51981i
$166$	−14.6133	+	16.0218i	−1.13421	+	1.24354i
$167$	−0.678472	−	0.678472i	−0.0525017	−	0.0525017i	0.680368	−	0.732870i	$-0.261820\pi$
$167$	−0.678472	−	0.678472i	−0.0525017	−	0.0525017i	−0.732870	+	0.680368i	$0.761820\pi$
$168$	−6.15472	+	0.853782i	−0.474847	+	0.0658707i
$169$		−	11.9830i		−	0.921771i
$170$	−6.91904	−	2.54562i	−0.530666	−	0.195240i
$171$		−	34.8542i		−	2.66537i
$172$	2.90159	−	3.49065i	0.221244	−	0.266160i
$173$	−14.0628	−	14.0628i	−1.06918	−	1.06918i	−0.997422	−	0.0717560i	$-0.977140\pi$
$173$	−14.0628	−	14.0628i	−1.06918	−	1.06918i	−0.0717560	−	0.997422i	$-0.522860\pi$
$174$	4.46363	+	4.07121i	0.338387	+	0.308637i
$175$	−4.03621	−	0.0467658i	−0.305109	−	0.00353516i
$176$	4.21908	+	22.6973i	0.318025	+	1.71087i
$177$	21.7207	−	21.7207i	1.63263	−	1.63263i
$178$	−0.530360	−	11.5348i	−0.0397522	−	0.864571i
$179$	−1.53767			−0.114931			−0.0574654	−	0.998348i	$-0.518302\pi$
$179$	−1.53767			−0.114931			−0.0574654	+	0.998348i	$0.518302\pi$
$180$	17.4854	−	9.07643i	1.30328	−	0.676517i
$181$	14.0096			1.04132			0.520662	−	0.853763i	$-0.325685\pi$
$181$	14.0096			1.04132			0.520662	+	0.853763i	$0.325685\pi$
$182$	0.0528817	+	1.15012i	0.00391985	+	0.0852529i
$183$	−9.23894	+	9.23894i	−0.682962	+	0.682962i
$184$	0.933932	−	1.23477i	0.0688504	−	0.0910288i
$185$	5.09717	+	2.14600i	0.374752	+	0.157777i
$186$	−2.84337	−	2.59339i	−0.208486	−	0.190157i
$187$	9.51456	+	9.51456i	0.695774	+	0.695774i
$188$	−11.3683	−	9.44988i	−0.829122	−	0.689204i
$189$		−	3.08709i		−	0.224553i
$190$	−10.4949	−	22.7125i	−0.761383	−	1.64774i
$191$			12.4139i			0.898240i	0.893472	+	0.449120i	$0.148262\pi$
$191$			12.4139i			0.898240i	−0.893472	+	0.449120i	$0.851738\pi$
$192$	10.6223	−	19.0027i	0.766597	−	1.37140i
$193$	5.73823	+	5.73823i	0.413047	+	0.413047i	0.882798	−	0.469752i	$-0.155657\pi$
$193$	5.73823	+	5.73823i	0.413047	+	0.413047i	−0.469752	+	0.882798i	$0.655657\pi$
$194$	−13.1169	+	14.3813i	−0.941740	+	1.03251i
$195$	−2.31540	−	5.68275i	−0.165809	−	0.406950i
$196$	−1.16509	−	12.6430i	−0.0832206	−	0.903070i
$197$	−12.1546	+	12.1546i	−0.865982	+	0.865982i	−0.992025	−	0.126043i	$-0.959772\pi$
$197$	−12.1546	+	12.1546i	−0.865982	+	0.865982i	0.126043	+	0.992025i	$0.459772\pi$
$198$	−35.9183	+	1.65149i	−2.55260	+	0.117366i
$199$	16.1213			1.14281			0.571403	−	0.820670i	$-0.306399\pi$
$199$	16.1213			1.14281			0.571403	+	0.820670i	$0.306399\pi$
$200$	8.66121	−	11.1796i	0.612440	−	0.790517i
$201$	−9.99753			−0.705172
$202$	16.8487	−	0.774690i	1.18547	−	0.0545070i
$203$	0.896133	−	0.896133i	0.0628962	−	0.0628962i
$204$	−1.16436	−	12.6350i	−0.0815212	−	0.884629i
$205$	−5.75343	−	14.1208i	−0.401837	−	0.986242i
$206$	−4.85014	+	5.31765i	−0.337925	+	0.370498i
$207$	1.70503	+	1.70503i	0.118508	+	0.118508i
$208$	−3.32557	−	2.28302i	−0.230587	−	0.158299i
$209$			45.6644i			3.15867i
$210$	−2.91404	−	6.30637i	−0.201088	−	0.435181i
$211$			8.77754i			0.604271i	0.953265	+	0.302135i	$0.0976995\pi$
$211$			8.77754i			0.604271i	−0.953265	+	0.302135i	$0.902301\pi$
$212$	2.70722	+	2.25037i	0.185933	+	0.154556i
$213$	31.1923	+	31.1923i	2.13726	+	2.13726i
$214$	−1.03845	−	0.947154i	−0.0709870	−	0.0647461i
$215$	4.67729	+	1.96922i	0.318989	+	0.134300i
$216$	8.62629	+	6.52456i	0.586945	+	0.443940i
$217$	−0.570845	+	0.570845i	−0.0387515	+	0.0387515i
$218$	0.259311	+	5.63976i	0.0175628	+	0.381973i
$219$	−31.1416			−2.10435
$220$	−22.9086	+	11.8915i	−1.54449	+	0.801726i
$221$	−2.35109			−0.158151
$222$	0.437186	+	9.50835i	0.0293420	+	0.638159i
$223$	2.34959	−	2.34959i	0.157340	−	0.157340i	−0.624047	−	0.781387i	$-0.714513\pi$
$223$	2.34959	−	2.34959i	0.157340	−	0.157340i	0.781387	+	0.624047i	$0.214513\pi$
$224$	−3.87969	−	2.40900i	−0.259223	−	0.160958i
$225$	15.3933	+	15.7542i	1.02622	+	1.05028i
$226$	5.21664	+	4.75801i	0.347006	+	0.316498i
$227$	−3.08839	−	3.08839i	−0.204984	−	0.204984i	0.597148	−	0.802131i	$-0.296301\pi$
$227$	−3.08839	−	3.08839i	−0.204984	−	0.204984i	−0.802131	+	0.597148i	$0.796301\pi$
$228$	27.5263	−	33.1145i	1.82297	−	2.19306i
$229$			15.3125i			1.01188i	0.862570	+	0.505938i	$0.168854\pi$
$229$			15.3125i			1.01188i	−0.862570	+	0.505938i	$0.831146\pi$
$230$	1.62447	+	0.597669i	0.107115	+	0.0394091i
$231$			12.6792i			0.834232i
$232$	0.610098	+	4.39806i	0.0400549	+	0.288746i
$233$	13.1656	+	13.1656i	0.862509	+	0.862509i	0.991629	−	0.129120i	$-0.0412152\pi$
$233$	13.1656	+	13.1656i	0.862509	+	0.862509i	−0.129120	+	0.991629i	$0.541215\pi$
$234$	4.23373	−	4.64182i	0.276768	−	0.303445i
$235$	6.41334	−	15.2330i	0.418360	−	0.993690i
$236$	22.4809	−	2.07168i	1.46338	−	0.134855i
$237$	−28.2712	+	28.2712i	−1.83641	+	1.83641i
$238$	−2.65890	+	0.122254i	−0.172351	+	0.00792455i
$239$	−17.5054			−1.13233			−0.566165	−	0.824292i	$-0.691573\pi$
$239$	−17.5054			−1.13233			−0.566165	+	0.824292i	$0.691573\pi$
$240$	23.7808	+	5.18579i	1.53504	+	0.334741i
$241$	9.30302			0.599260			0.299630	−	0.954055i	$-0.403137\pi$
$241$	9.30302			0.599260			0.299630	+	0.954055i	$0.403137\pi$
$242$	31.5185	−	1.44919i	2.02609	−	0.0931577i
$243$	13.5183	−	13.5183i	0.867198	−	0.867198i
$244$	−9.56228	+	0.881193i	−0.612162	+	0.0564126i
$245$	13.1459	−	5.35619i	0.839859	−	0.342195i
$246$	17.6846	−	19.3892i	1.12753	−	1.23621i
$247$	−5.64193	−	5.64193i	−0.358988	−	0.358988i
$248$	−0.388638	−	2.80160i	−0.0246785	−	0.177902i
$249$		−	41.7270i		−	2.64434i
$250$	14.7747	+	5.63103i	0.934433	+	0.356138i
$251$			7.97091i			0.503120i	0.967842	+	0.251560i	$0.0809435\pi$
$251$			7.97091i			0.503120i	−0.967842	+	0.251560i	$0.919056\pi$
$252$	4.54666	−	5.46970i	0.286413	−	0.344559i
$253$	−2.23386	−	2.23386i	−0.140441	−	0.140441i
$254$	−12.4992	−	11.4004i	−0.784272	−	0.715322i
$255$	13.1376	−	5.35282i	0.822709	−	0.335207i
$256$	14.9312	−	5.74964i	0.933202	−	0.359353i
$257$	−1.63005	+	1.63005i	−0.101680	+	0.101680i	−0.756117	−	0.654437i	$-0.772906\pi$
$257$	−1.63005	+	1.63005i	−0.101680	+	0.101680i	0.654437	+	0.756117i	$0.272906\pi$
$258$	0.401172	+	8.72510i	0.0249759	+	0.543201i
$259$	1.99670			0.124069
$260$	1.36118	−	4.29962i	0.0844167	−	0.266651i
$261$	−6.91549			−0.428058
$262$	0.519001	+	11.2878i	0.0320640	+	0.697360i
$263$	8.23883	−	8.23883i	0.508028	−	0.508028i	−0.405893	−	0.913921i	$-0.633039\pi$
$263$	8.23883	−	8.23883i	0.508028	−	0.508028i	0.913921	+	0.405893i	$0.133039\pi$
$264$	−35.4297	−	26.7976i	−2.18055	−	1.64928i
$265$	−1.52725	+	3.62753i	−0.0938184	+	0.222838i
$266$	−6.67398	−	6.08723i	−0.409208	−	0.373232i
$267$	15.7112	+	15.7112i	0.961508	+	0.961508i
$268$	−5.65049	−	4.69694i	−0.345158	−	0.286911i
$269$		−	1.13704i		−	0.0693268i	−0.999399	−	0.0346634i	$-0.988964\pi$
$269$		−	1.13704i		−	0.0693268i	0.999399	−	0.0346634i	$-0.0110359\pi$
$270$	−4.17539	+	11.3488i	−0.254106	+	0.690664i
$271$			0.607340i			0.0368933i	0.999830	+	0.0184466i	$0.00587208\pi$
$271$			0.607340i			0.0368933i	−0.999830	+	0.0184466i	$0.994128\pi$
$272$	5.27798	−	7.68819i	0.320025	−	0.466165i
$273$	−1.56654	−	1.56654i	−0.0948116	−	0.0948116i
$274$	0.648335	−	0.710828i	0.0391673	−	0.0429427i
$275$	−20.1676	−	20.6405i	−1.21615	−	1.24467i
$276$	0.273371	+	2.96649i	0.0164550	+	0.178562i
$277$	−15.9870	+	15.9870i	−0.960569	+	0.960569i	−0.999252	−	0.0386828i	$-0.987684\pi$
$277$	−15.9870	+	15.9870i	−0.960569	+	0.960569i	0.0386828	+	0.999252i	$0.487684\pi$
$278$	25.1386	−	1.15585i	1.50771	−	0.0693234i
$279$	4.40523			0.263734
$280$	1.31582	−	4.93333i	0.0786350	−	0.294823i
$281$	−1.60858			−0.0959598			−0.0479799	−	0.998848i	$-0.515278\pi$
$281$	−1.60858			−0.0959598			−0.0479799	+	0.998848i	$0.515278\pi$
$282$	28.4159	−	1.30654i	1.69214	−	0.0778031i
$283$	12.4198	−	12.4198i	0.738280	−	0.738280i	−0.233965	−	0.972245i	$-0.575170\pi$
$283$	12.4198	−	12.4198i	0.738280	−	0.738280i	0.972245	+	0.233965i	$0.0751701\pi$
$284$	2.97507	+	32.2840i	0.176538	+	1.91570i
$285$	44.3717	+	18.6812i	2.62835	+	1.10658i
$286$	−5.54684	+	6.08150i	−0.327991	+	0.359607i
$287$	−3.89264	−	3.89264i	−0.229775	−	0.229775i
$288$	5.67468	+	24.2650i	0.334384	+	1.42983i
$289$			11.5647i			0.680274i
$290$	−4.50642	+	2.08232i	−0.264626	+	0.122278i
$291$		−	37.4543i		−	2.19561i
$292$	−17.6008	−	14.6306i	−1.03001	−	0.856192i
$293$	−1.45781	−	1.45781i	−0.0851663	−	0.0851663i	0.663240	−	0.748407i	$-0.269181\pi$
$293$	−1.45781	−	1.45781i	−0.0851663	−	0.0851663i	−0.748407	+	0.663240i	$0.769181\pi$
$294$	18.0505	+	16.4636i	1.05273	+	0.960175i
$295$	9.52403	+	23.3751i	0.554510	+	1.36095i
$296$	−4.22003	+	5.57940i	−0.245284	+	0.324296i
$297$	15.6060	−	15.6060i	0.905552	−	0.905552i
$298$	0.504483	+	10.9720i	0.0292239	+	0.635591i
$299$	0.551995			0.0319227
$300$	2.18302	+	27.1248i	0.126037	+	1.56605i
$301$	1.83222			0.105607
$302$	0.633840	+	13.7854i	0.0364734	+	0.793260i
$303$	−22.9491	+	22.9491i	−1.31839	+	1.31839i
$304$	31.1151	−	5.78382i	1.78457	−	0.331725i
$305$	−4.05106	−	9.94264i	−0.231963	−	0.569314i
$306$	10.7311	+	9.78770i	0.613459	+	0.559526i
$307$	0.498041	+	0.498041i	0.0284247	+	0.0284247i	0.721176	−	0.692752i	$-0.243602\pi$
$307$	0.498041	+	0.498041i	0.0284247	+	0.0284247i	−0.692752	+	0.721176i	$0.743602\pi$
$308$	−5.95683	+	7.16615i	−0.339422	+	0.408329i
$309$		−	13.8492i		−	0.787853i
$310$	2.87063	−	1.32646i	0.163041	−	0.0753376i
$311$		−	7.92378i		−	0.449317i	−0.974438	−	0.224658i	$-0.927873\pi$
$311$		−	7.92378i		−	0.449317i	0.974438	−	0.224658i	$-0.0721266\pi$
$312$	7.68831	−	1.06652i	0.435265	−	0.0603799i
$313$	−12.5847	−	12.5847i	−0.711328	−	0.711328i	0.255485	−	0.966813i	$-0.417765\pi$
$313$	−12.5847	−	12.5847i	−0.711328	−	0.711328i	−0.966813	+	0.255485i	$0.917765\pi$
$314$	10.1744	−	11.1551i	0.574174	−	0.629518i
$315$	7.32910	+	3.08568i	0.412948	+	0.173858i
$316$	−29.2606	+	2.69646i	−1.64604	+	0.151688i
$317$	−14.6083	+	14.6083i	−0.820486	+	0.820486i	−0.986178	−	0.165692i	$-0.947014\pi$
$317$	−14.6083	+	14.6083i	−0.820486	+	0.820486i	0.165692	+	0.986178i	$0.447014\pi$
$318$	−6.76687	+	0.311134i	−0.379467	+	0.0174476i
$319$	9.06036			0.507282
$320$	11.0043	+	14.1034i	0.615158	+	0.788404i
$321$	2.70452			0.150952
$322$	0.624265	−	0.0287032i	0.0347889	−	0.00159956i
$323$	13.0432	−	13.0432i	0.725745	−	0.725745i
$324$	5.59559	−	0.515651i	0.310866	−	0.0286473i
$325$	5.04193	+	0.0584186i	0.279676	+	0.00324048i
$326$	22.2281	−	24.3707i	1.23110	−	1.34977i
$327$	−7.68172	−	7.68172i	−0.424800	−	0.424800i
$328$	19.1044	−	2.65015i	1.05486	−	0.146330i
$329$		−	5.96716i		−	0.328980i
$330$	17.1491	−	46.6115i	0.944026	−	2.56588i
$331$			18.2803i			1.00478i	0.864642	+	0.502389i	$0.167545\pi$
$331$			18.2803i			1.00478i	−0.864642	+	0.502389i	$0.832455\pi$
$332$	19.6038	−	23.5836i	1.07590	−	1.29432i
$333$	−7.70430	−	7.70430i	−0.422193	−	0.422193i
$334$	1.00256	+	0.914421i	0.0548578	+	0.0500349i
$335$	3.18767	−	7.57135i	0.174161	−	0.413667i
$336$	8.63944	−	1.60594i	0.471320	−	0.0876112i
$337$	−15.8360	+	15.8360i	−0.862644	+	0.862644i	−0.991645	−	0.129001i	$-0.958823\pi$
$337$	−15.8360	+	15.8360i	−0.862644	+	0.862644i	0.129001	+	0.991645i	$0.458823\pi$
$338$	0.778365	+	16.9287i	0.0423375	+	0.920798i
$339$	−13.5861			−0.737897
$340$	9.94003	+	3.14683i	0.539074	+	0.170661i
$341$	−5.77153			−0.312546
$342$	2.26398	+	49.2393i	0.122422	+	2.66256i
$343$	7.61979	−	7.61979i	0.411430	−	0.411430i
$344$	−3.87240	+	5.11979i	−0.208786	+	0.276041i
$345$	−3.08449	+	1.25675i	−0.166063	+	0.0676613i
$346$	20.7803	+	18.9534i	1.11716	+	1.01894i
$347$	−17.4554	−	17.4554i	−0.937057	−	0.937057i	0.0610758	−	0.998133i	$-0.480547\pi$
$347$	−17.4554	−	17.4554i	−0.937057	−	0.937057i	−0.998133	+	0.0610758i	$0.980547\pi$
$348$	−6.57031	−	5.46154i	−0.352206	−	0.292769i
$349$		−	18.8225i		−	1.00755i	−0.863836	−	0.503773i	$-0.831945\pi$
$349$		−	18.8225i		−	1.00755i	0.863836	−	0.503773i	$-0.168055\pi$
$350$	5.70508	−	0.196108i	0.304949	−	0.0104824i
$351$			3.85631i			0.205834i
$352$	−7.43470	−	31.7909i	−0.396271	−	1.69446i
$353$	−16.8358	−	16.8358i	−0.896081	−	0.896081i	0.0990059	−	0.995087i	$-0.468434\pi$
$353$	−16.8358	−	16.8358i	−0.896081	−	0.896081i	−0.995087	+	0.0990059i	$0.968434\pi$
$354$	−29.2744	+	32.0962i	−1.55592	+	1.70589i
$355$	−33.5681	+	13.6771i	−1.78161	+	0.725905i
$356$	1.49850	+	16.2610i	0.0794205	+	0.861832i
$357$	3.62160	−	3.62160i	0.191675	−	0.191675i
$358$	2.17230	−	0.0998802i	0.114809	−	0.00527883i
$359$	32.8028			1.73126			0.865632	−	0.500681i	$-0.166917\pi$
$359$	32.8028			1.73126			0.865632	+	0.500681i	$0.166917\pi$
$360$	−24.1124	+	13.9582i	−1.27084	+	0.735663i
$361$	43.6000			2.29474
$362$	−19.7916	+	0.910002i	−1.04023	+	0.0478286i
$363$	−42.9303	+	42.9303i	−2.25326	+	2.25326i
$364$	−0.149414	−	1.62137i	−0.00783143	−	0.0849829i
$365$	9.92934	−	23.5842i	0.519725	−	1.23445i
$366$	12.4519	−	13.6522i	0.650872	−	0.713610i
$367$	−15.9151	−	15.9151i	−0.830764	−	0.830764i	0.156857	−	0.987621i	$-0.449864\pi$
$367$	−15.9151	−	15.9151i	−0.830764	−	0.830764i	−0.987621	+	0.156857i	$0.949864\pi$
$368$	−1.23918	+	1.80506i	−0.0645967	+	0.0940951i
$369$			30.0396i			1.56380i
$370$	−7.34028	−	2.70060i	−0.381603	−	0.140398i
$371$			1.42100i			0.0737748i
$372$	4.18535	+	3.47905i	0.217000	+	0.180380i
$373$	−1.84038	−	1.84038i	−0.0952914	−	0.0952914i	0.657854	−	0.753145i	$-0.271464\pi$
$373$	−1.84038	−	1.84038i	−0.0952914	−	0.0952914i	−0.753145	+	0.657854i	$0.771464\pi$
$374$	−14.0594	−	12.8234i	−0.726997	−	0.663082i
$375$	−28.3067	+	11.1527i	−1.46175	+	0.575925i
$376$	16.6741	+	12.6116i	0.859902	+	0.650394i
$377$	−1.11943	+	1.11943i	−0.0576533	+	0.0576533i
$378$	0.200524	+	4.36119i	0.0103138	+	0.224316i
$379$	26.2916			1.35051			0.675255	−	0.737585i	$-0.264034\pi$
$379$	26.2916			1.35051			0.675255	+	0.737585i	$0.264034\pi$
$380$	16.3017	+	31.4047i	0.836261	+	1.61103i
$381$	32.5528			1.66773
$382$	−0.806354	−	17.5374i	−0.0412567	−	0.897292i
$383$	−13.6201	+	13.6201i	−0.695953	+	0.695953i	−0.963535	−	0.267582i	$-0.913775\pi$
$383$	−13.6201	+	13.6201i	−0.695953	+	0.695953i	0.267582	+	0.963535i	$0.413775\pi$
$384$	−13.7720	+	27.5355i	−0.702798	+	1.40516i
$385$	−9.60225	−	4.04271i	−0.489376	−	0.206036i
$386$	−8.47924	−	7.73378i	−0.431582	−	0.393639i
$387$	−7.06965	−	7.06965i	−0.359371	−	0.359371i
$388$	17.5964	−	21.1687i	0.893322	−	1.07468i
$389$		−	37.4917i		−	1.90091i	−0.310869	−	0.950453i	$-0.600620\pi$
$389$		−	37.4917i		−	1.90091i	0.310869	−	0.950453i	$-0.399380\pi$
$390$	3.64014	+	7.87775i	0.184325	+	0.398905i
$391$			1.27612i			0.0645364i
$392$	2.46718	+	17.7853i	0.124611	+	0.898294i
$393$	−15.3747	−	15.3747i	−0.775549	−	0.775549i
$394$	16.3816	−	17.9606i	0.825293	−	0.904843i
$395$	−12.3963	−	30.4246i	−0.623724	−	1.53083i
$396$	50.6352	−	4.66619i	2.54452	−	0.234485i
$397$	25.2608	−	25.2608i	1.26780	−	1.26780i	0.320584	−	0.947220i	$-0.396121\pi$
$397$	25.2608	−	25.2608i	1.26780	−	1.26780i	0.947220	−	0.320584i	$-0.103879\pi$
$398$	−22.7748	+	1.04717i	−1.14160	+	0.0524897i
$399$	17.3816			0.870168
$400$	−11.5097	+	16.3562i	−0.575485	+	0.817812i
$401$	20.2238			1.00993			0.504964	−	0.863140i	$-0.331506\pi$
$401$	20.2238			1.00993			0.504964	+	0.863140i	$0.331506\pi$
$402$	14.1237	−	0.649396i	0.704427	−	0.0323889i
$403$	0.713084	−	0.713084i	0.0355212	−	0.0355212i
$404$	−23.7522	+	2.18884i	−1.18172	+	0.108899i
$405$	2.37057	+	5.81817i	0.117795	+	0.289107i
$406$	−1.20778	+	1.32419i	−0.0599410	+	0.0657187i
$407$	10.0938	+	10.0938i	0.500332	+	0.500332i
$408$	2.46563	+	17.7741i	0.122067	+	0.879951i
$409$		−	29.5740i		−	1.46234i	−0.682195	−	0.731170i	$-0.738975\pi$
$409$		−	29.5740i		−	1.46234i	0.682195	−	0.731170i	$-0.261025\pi$
$410$	9.04522	+	19.5751i	0.446712	+	0.966744i
$411$			1.85127i			0.0913163i
$412$	6.50648	−	7.82740i	0.320552	−	0.385628i
$413$	6.44374	+	6.44374i	0.317076	+	0.317076i
$414$	−2.51949	−	2.29799i	−0.123826	−	0.112940i
$415$	31.6008	+	13.3045i	1.55122	+	0.653090i
$416$	4.84640	+	3.00926i	0.237615	+	0.147541i
$417$	−34.2404	+	34.2404i	−1.67676	+	1.67676i
$418$	−2.96616	−	64.5111i	−0.145080	−	3.15534i
$419$	−14.9740			−0.731527			−0.365764	−	0.930708i	$-0.619192\pi$
$419$	−14.9740			−0.731527			−0.365764	+	0.930708i	$0.619192\pi$
$420$	4.52635	+	8.71985i	0.220863	+	0.425485i
$421$	2.29931			0.112062			0.0560308	−	0.998429i	$-0.482155\pi$
$421$	2.29931			0.112062			0.0560308	+	0.998429i	$0.482155\pi$
$422$	−0.570151	−	12.4002i	−0.0277545	−	0.603633i
$423$	−23.0244	+	23.0244i	−1.11948	+	1.11948i
$424$	−3.97073	−	3.00329i	−0.192836	−	0.145853i
$425$	−0.135054	+	11.6561i	−0.00655110	+	0.565405i
$426$	−46.0921	−	42.0399i	−2.23317	−	2.03684i
$427$	−2.74085	−	2.74085i	−0.132639	−	0.132639i
$428$	1.52856	+	1.27061i	0.0738859	+	0.0614173i
$429$		−	15.8386i		−	0.764692i
$430$	−6.73562	−	2.47814i	−0.324820	−	0.119506i
$431$			3.41984i			0.164728i	0.996602	+	0.0823639i	$0.0262470\pi$
$431$			3.41984i			0.164728i	−0.996602	+	0.0823639i	$0.973753\pi$
$432$	−12.6103	−	8.65706i	−0.606716	−	0.416513i
$433$	4.47928	+	4.47928i	0.215260	+	0.215260i	0.806498	−	0.591237i	$-0.201360\pi$
$433$	4.47928	+	4.47928i	0.215260	+	0.215260i	−0.591237	+	0.806498i	$0.701360\pi$
$434$	0.769365	−	0.843524i	0.0369307	−	0.0404904i
$435$	3.70658	−	8.80387i	0.177717	−	0.422113i
$436$	−0.732669	−	7.95057i	−0.0350885	−	0.380763i
$437$	−3.06233	+	3.06233i	−0.146491	+	0.146491i
$438$	43.9943	−	2.02282i	2.10213	−	0.0966541i
$439$	−1.89748			−0.0905617			−0.0452808	−	0.998974i	$-0.514418\pi$
$439$	−1.89748			−0.0905617			−0.0452808	+	0.998974i	$0.514418\pi$
$440$	31.5910	−	18.2874i	1.50604	−	0.871819i
$441$	−27.9656			−1.33169
$442$	3.32143	−	0.152716i	0.157984	−	0.00726398i
$443$	27.0862	−	27.0862i	1.28690	−	1.28690i	0.350245	−	0.936658i	$-0.386098\pi$
$443$	27.0862	−	27.0862i	1.28690	−	1.28690i	0.936658	−	0.350245i	$-0.113902\pi$
$444$	−1.23524	−	13.4043i	−0.0586220	−	0.636138i
$445$	−16.9078	+	6.88898i	−0.801508	+	0.326569i
$446$	−3.16669	+	3.47193i	−0.149947	+	0.164401i
$447$	−14.9446	−	14.9446i	−0.706854	−	0.706854i
$448$	5.63740	+	3.15124i	0.266342	+	0.148882i
$449$		−	1.80479i		−	0.0851734i	−0.999093	−	0.0425867i	$-0.986440\pi$
$449$		−	1.80479i		−	0.0851734i	0.999093	−	0.0425867i	$-0.0135599\pi$
$450$	−22.7698	−	21.2565i	−1.07338	−	1.00204i
$451$		−	39.3565i		−	1.85323i
$452$	−7.67872	−	6.38290i	−0.361176	−	0.300226i
$453$	−18.7766	−	18.7766i	−0.882201	−	0.882201i
$454$	4.56364	+	4.16243i	0.214182	+	0.195352i
$455$	1.68586	−	0.686893i	0.0790345	−	0.0322020i
$456$	−36.7360	+	48.5696i	−1.72032	+	2.27448i
$457$	−7.87258	+	7.87258i	−0.368264	+	0.368264i	−0.866844	−	0.498580i	$-0.833855\pi$
$457$	−7.87258	+	7.87258i	−0.368264	+	0.368264i	0.498580	+	0.866844i	$0.333855\pi$
$458$	−0.994631	−	21.6322i	−0.0464761	−	1.01081i
$459$	−8.91516			−0.416124
$460$	−2.33375	−	0.738821i	−0.108812	−	0.0344477i
$461$	−18.4461			−0.859119			−0.429559	−	0.903039i	$-0.641331\pi$
$461$	−18.4461			−0.859119			−0.429559	+	0.903039i	$0.641331\pi$
$462$	−0.823587	−	17.9122i	−0.0383168	−	0.833351i
$463$	−20.5816	+	20.5816i	−0.956509	+	0.956509i	−0.999093	−	0.0425842i	$-0.986441\pi$
$463$	−20.5816	+	20.5816i	−0.956509	+	0.956509i	0.0425842	+	0.999093i	$0.486441\pi$
$464$	−1.14758	−	6.17360i	−0.0532749	−	0.286602i
$465$	−2.36112	+	5.60814i	−0.109494	+	0.260071i
$466$	−19.4545	−	17.7442i	−0.901214	−	0.821983i
$467$	2.49139	+	2.49139i	0.115288	+	0.115288i	0.762397	−	0.647110i	$-0.224022\pi$
$467$	2.49139	+	2.49139i	0.115288	+	0.115288i	−0.647110	+	0.762397i	$0.724022\pi$
$468$	−5.67957	+	6.83260i	−0.262538	+	0.315837i
$469$		−	2.96590i		−	0.136953i
$470$	−8.07079	+	21.9365i	−0.372278	+	1.01186i
$471$			29.0521i			1.33865i
$472$	−31.6247	+	4.38697i	−1.45564	+	0.201927i
$473$	9.26233	+	9.26233i	0.425882	+	0.425882i
$474$	38.1030	−	41.7757i	1.75013	−	1.91882i
$475$	−28.2954	+	27.6472i	−1.29828	+	1.26854i
$476$	3.74835	−	0.345422i	0.171805	−	0.0158324i
$477$	5.48296	−	5.48296i	0.251048	−	0.251048i
$478$	24.7302	−	1.13707i	1.13113	−	0.0520085i
$479$	40.5740			1.85388			0.926938	−	0.375215i	$-0.122431\pi$
$479$	40.5740			1.85388			0.926938	+	0.375215i	$0.122431\pi$
$480$	−33.9325	−	5.78138i	−1.54880	−	0.263882i
$481$	−2.49422			−0.113727
$482$	−13.1426	+	0.604284i	−0.598628	+	0.0275244i
$483$	−0.850290	+	0.850290i	−0.0386895	+	0.0386895i
$484$	−44.4327	+	4.09461i	−2.01967	+	0.186119i
$485$	28.3650	+	11.9421i	1.28799	+	0.542264i
$486$	−18.2195	+	19.9756i	−0.826452	+	0.906113i
$487$	24.2618	+	24.2618i	1.09941	+	1.09941i	0.994480	+	0.104927i	$0.0334610\pi$
$487$	24.2618	+	24.2618i	1.09941	+	1.09941i	0.104927	+	0.994480i	$0.466539\pi$
$488$	13.4516	−	1.86600i	0.608925	−	0.0844700i
$489$			63.4707i			2.87024i
$490$	−18.2235	+	8.42070i	−0.823256	+	0.380409i
$491$		−	27.6204i		−	1.24649i	−0.782026	−	0.623246i	$-0.785814\pi$
$491$		−	27.6204i		−	1.24649i	0.782026	−	0.623246i	$-0.214186\pi$
$492$	−23.7239	+	28.5403i	−1.06956	+	1.28669i
$493$	−2.58793	−	2.58793i	−0.116555	−	0.116555i
$494$	8.33695	+	7.60400i	0.375097	+	0.342120i
$495$	21.4516	+	52.6493i	0.964177	+	2.36641i
$496$	0.731016	+	3.93263i	0.0328236	+	0.176581i
$497$	−9.25361	+	9.25361i	−0.415081	+	0.415081i
$498$	2.71041	+	58.9486i	0.121456	+	2.64155i
$499$	7.12618			0.319012			0.159506	−	0.987197i	$-0.449010\pi$
$499$	7.12618			0.319012			0.159506	+	0.987197i	$0.449010\pi$
$500$	−21.2383	−	6.99538i	−0.949805	−	0.312843i
$501$	−2.61106			−0.116653
$502$	−0.517756	−	11.2607i	−0.0231086	−	0.502589i
$503$	5.42450	−	5.42450i	0.241866	−	0.241866i	−0.575755	−	0.817622i	$-0.695292\pi$
$503$	5.42450	−	5.42450i	0.241866	−	0.241866i	0.817622	+	0.575755i	$0.195292\pi$
$504$	−6.06788	+	8.02249i	−0.270285	+	0.357350i
$505$	−10.0626	−	24.6970i	−0.447781	−	1.09900i
$506$	3.30092	+	3.01072i	0.146744	+	0.133843i
$507$	−23.0579	−	23.0579i	−1.02404	−	1.02404i
$508$	18.3985	+	15.2936i	0.816300	+	0.678545i
$509$		−	27.6014i		−	1.22341i	−0.791086	−	0.611705i	$-0.790484\pi$
$509$		−	27.6014i		−	1.22341i	0.791086	−	0.611705i	$-0.209516\pi$
$510$	−18.2121	+	8.41541i	−0.806444	+	0.372641i
$511$		−	9.23855i		−	0.408690i
$512$	−20.7202	+	9.09251i	−0.915712	+	0.401836i
$513$	−21.3938	−	21.3938i	−0.944560	−	0.944560i
$514$	2.19693	−	2.40869i	0.0969023	−	0.106243i
$515$	10.4883	+	4.41575i	0.462169	+	0.194581i
$516$	−1.13349	−	12.3001i	−0.0498991	−	0.541480i
$517$	30.1655	−	30.1655i	1.32668	−	1.32668i
$518$	−2.82078	+	0.129697i	−0.123938	+	0.00569855i
$519$	−54.1199			−2.37560
$520$	−1.64368	+	6.16258i	−0.0720802	+	0.270247i
$521$	−18.7144			−0.819892			−0.409946	−	0.912110i	$-0.634452\pi$
$521$	−18.7144			−0.819892			−0.409946	+	0.912110i	$0.634452\pi$
$522$	9.76966	−	0.449200i	0.427606	−	0.0196610i
$523$	−27.1070	+	27.1070i	−1.18531	+	1.18531i	−0.206955	+	0.978351i	$0.566355\pi$
$523$	−27.1070	+	27.1070i	−1.18531	+	1.18531i	−0.978351	+	0.206955i	$0.933645\pi$
$524$	−1.46641	−	15.9127i	−0.0640603	−	0.695151i
$525$	−7.85653	+	7.67656i	−0.342887	+	0.335032i
$526$	−11.1040	+	12.1743i	−0.484158	+	0.530826i
$527$	1.64853	+	1.64853i	0.0718113	+	0.0718113i
$528$	51.7930	+	35.5561i	2.25400	+	1.54738i
$529$			22.7004i			0.986973i
$530$	1.92195	−	5.22390i	0.0834844	−	0.226912i
$531$		−	49.7266i		−	2.15795i
$532$	9.82387	+	8.16604i	0.425919	+	0.354043i
$533$	4.86258	+	4.86258i	0.210622	+	0.210622i
$534$	−23.2160	−	21.1750i	−1.00466	−	0.916330i
$535$	−0.862324	+	2.04819i	−0.0372815	+	0.0885511i
$536$	8.28766	+	6.26844i	0.357972	+	0.270755i
$537$	−2.95881	+	2.95881i	−0.127682	+	0.127682i
$538$	0.0738574	+	1.60633i	0.00318422	+	0.0692536i
$539$	36.6392			1.57816
$540$	5.16150	−	16.3039i	0.222115	−	0.701607i
$541$	−22.6922			−0.975616			−0.487808	−	0.872951i	$-0.662203\pi$
$541$	−22.6922			−0.975616			−0.487808	+	0.872951i	$0.662203\pi$
$542$	−0.0394502	−	0.858002i	−0.00169453	−	0.0368543i
$543$	26.9575	−	26.9575i	1.15686	−	1.15686i
$544$	−6.95692	+	11.2041i	−0.298276	+	0.480372i
$545$	8.26682	−	3.36826i	0.354112	−	0.144280i
$546$	2.31485	+	2.11133i	0.0990663	+	0.0903568i
$547$	−1.02488	−	1.02488i	−0.0438209	−	0.0438209i	0.684857	−	0.728678i	$-0.259865\pi$
$547$	−1.02488	−	1.02488i	−0.0438209	−	0.0438209i	−0.728678	+	0.684857i	$0.759865\pi$
$548$	−0.869744	+	1.04631i	−0.0371536	+	0.0446963i
$549$			21.1513i			0.902714i
$550$	29.8320	+	27.8492i	1.27204	+	1.18749i
$551$		−	12.4206i		−	0.529135i
$552$	−0.578887	−	4.17306i	−0.0246391	−	0.177617i
$553$	−8.38703	−	8.38703i	−0.356653	−	0.356653i
$554$	21.5468	−	23.6237i	0.915435	−	1.00367i
$555$	13.9374	−	5.67871i	0.591611	−	0.241048i
$556$	−35.4388	+	3.26579i	−1.50294	+	0.138500i
$557$	−31.4338	+	31.4338i	−1.33189	+	1.33189i	−0.428214	+	0.903678i	$0.640857\pi$
$557$	−31.4338	+	31.4338i	−1.33189	+	1.33189i	−0.903678	+	0.428214i	$0.859143\pi$
$558$	−6.22336	+	0.286144i	−0.263456	+	0.0121135i
$559$	−2.28876			−0.0968042
$560$	−1.53843	+	7.05488i	−0.0650106	+	0.298123i
$561$	36.6162			1.54594
$562$	2.27247	−	0.104486i	0.0958585	−	0.00440749i
$563$	12.5958	−	12.5958i	0.530849	−	0.530849i	−0.389976	−	0.920825i	$-0.627517\pi$
$563$	12.5958	−	12.5958i	0.530849	−	0.530849i	0.920825	+	0.389976i	$0.127517\pi$
$564$	−40.0588	+	3.69154i	−1.68678	+	0.155442i
$565$	4.33187	−	10.2891i	0.182243	−	0.432864i
$566$	−16.7390	+	18.3524i	−0.703591	+	0.771411i
$567$	1.60387	+	1.60387i	0.0673564	+	0.0673564i
$568$	−6.29996	−	45.4150i	−0.264341	−	1.90557i
$569$		−	0.320753i		−	0.0134467i	−0.999977	−	0.00672334i	$-0.997860\pi$
$569$		−	0.320753i		−	0.0134467i	0.999977	−	0.00672334i	$-0.00214012\pi$
$570$	−63.8983	−	23.5092i	−2.67641	−	0.984692i
$571$		−	7.32105i		−	0.306376i	−0.988197	−	0.153188i	$-0.951046\pi$
$571$		−	7.32105i		−	0.306376i	0.988197	−	0.153188i	$-0.0489540\pi$
$572$	7.44111	−	8.95176i	0.311128	−	0.374292i
$573$	23.8871	+	23.8871i	0.997897	+	0.997897i
$574$	5.75206	+	5.24636i	0.240086	+	0.218979i
$575$	0.0317085	−	2.73666i	0.00132234	−	0.114127i
$576$	−9.59289	−	33.9111i	−0.399704	−	1.41296i
$577$	15.8657	−	15.8657i	0.660499	−	0.660499i	−0.294998	−	0.955498i	$-0.595319\pi$
$577$	15.8657	−	15.8657i	0.660499	−	0.660499i	0.955498	+	0.294998i	$0.0953191\pi$
$578$	−0.751190	−	16.3376i	−0.0312454	−	0.679556i
$579$	22.0832			0.917746
$580$	6.23106	−	3.23445i	0.258731	−	0.134303i
$581$	12.3789			0.513562
$582$	2.43287	+	52.9125i	0.100846	+	2.19329i
$583$	−7.18352	+	7.18352i	−0.297511	+	0.297511i
$584$	25.8154	+	19.5257i	1.06825	+	0.807979i
$585$	−9.15532	−	3.85455i	−0.378526	−	0.159366i
$586$	2.15418	+	1.96479i	0.0889881	+	0.0811647i
$587$	12.0192	+	12.0192i	0.496085	+	0.496085i	0.910217	−	0.414132i	$-0.135915\pi$
$587$	12.0192	+	12.0192i	0.496085	+	0.496085i	−0.414132	+	0.910217i	$0.635915\pi$
$588$	−26.5697	−	22.0860i	−1.09572	−	0.910809i
$589$			7.91202i			0.326009i
$590$	−14.9731	−	32.4039i	−0.616434	−	1.33405i
$591$			46.7763i			1.92412i
$592$	5.59931	−	8.15625i	0.230130	−	0.335220i
$593$	−25.0685	−	25.0685i	−1.02944	−	1.02944i	−0.999553	−	0.0298876i	$-0.990485\pi$
$593$	−25.0685	−	25.0685i	−1.02944	−	1.02944i	−0.0298876	−	0.999553i	$-0.509515\pi$
$594$	−21.0332	+	23.0606i	−0.863004	+	0.946189i
$595$	1.58799	+	3.89744i	0.0651011	+	0.159780i
$596$	−1.42539	−	15.4676i	−0.0583861	−	0.633578i
$597$	31.0208	−	31.0208i	1.26960	−	1.26960i
$598$	−0.779815	+	0.0358552i	−0.0318890	+	0.00146623i
$599$	9.04727			0.369661			0.184831	−	0.982770i	$-0.440826\pi$
$599$	9.04727			0.369661			0.184831	+	0.982770i	$0.440826\pi$
$600$	−4.84591	−	38.1780i	−0.197834	−	1.55861i
$601$	9.82298			0.400688			0.200344	−	0.979726i	$-0.435794\pi$
$601$	9.82298			0.400688			0.200344	+	0.979726i	$0.435794\pi$
$602$	−2.58841	+	0.119013i	−0.105496	+	0.00485061i
$603$	−11.4440	+	11.4440i	−0.466035	+	0.466035i
$604$	−1.79088	−	19.4337i	−0.0728698	−	0.790748i
$605$	−18.8239	−	46.2002i	−0.765301	−	1.87830i
$606$	30.9300	−	33.9113i	1.25644	−	1.37755i
$607$	−1.58518	−	1.58518i	−0.0643404	−	0.0643404i	0.674204	−	0.738545i	$-0.264487\pi$
$607$	−1.58518	−	1.58518i	−0.0643404	−	0.0643404i	−0.738545	+	0.674204i	$0.764487\pi$
$608$	−43.5812	+	10.1920i	−1.76745	+	0.413341i
$609$		−	3.44871i		−	0.139749i
$610$	6.36884	+	13.7830i	0.257867	+	0.558059i
$611$			7.45402i			0.301557i
$612$	−15.7959	−	13.1302i	−0.638511	−	0.530759i
$613$	14.3058	+	14.3058i	0.577808	+	0.577808i	0.934299	−	0.356491i	$-0.116027\pi$
$613$	14.3058	+	14.3058i	0.577808	+	0.577808i	−0.356491	+	0.934299i	$0.616027\pi$
$614$	−0.735944	−	0.671243i	−0.0297003	−	0.0270892i
$615$	−38.2424	−	16.1007i	−1.54208	−	0.649243i
$616$	7.94985	−	10.5107i	0.320309	−	0.423488i
$617$	1.55856	−	1.55856i	0.0627452	−	0.0627452i	−0.675038	−	0.737783i	$-0.735873\pi$
$617$	1.55856	−	1.55856i	0.0627452	−	0.0627452i	0.737783	+	0.675038i	$0.235873\pi$
$618$	0.899583	+	19.5650i	0.0361865	+	0.787021i
$619$	9.24077			0.371418			0.185709	−	0.982605i	$-0.440542\pi$
$619$	9.24077			0.371418			0.185709	+	0.982605i	$0.440542\pi$
$620$	−3.96924	+	2.06038i	−0.159408	+	0.0827467i
$621$	2.09313			0.0839943
$622$	0.514695	+	11.1941i	0.0206374	+	0.448842i
$623$	−4.66092	+	4.66092i	−0.186736	+	0.186736i
$624$	−10.7922	+	2.00610i	−0.432032	+	0.0803082i
$625$	0.579251	−	24.9933i	0.0231700	−	0.999732i
$626$	18.5961	+	16.9612i	0.743249	+	0.677905i
$627$	87.8683	+	87.8683i	3.50912	+	3.50912i
$628$	−13.6490	+	16.4199i	−0.544653	+	0.655226i
$629$		−	5.76624i		−	0.229915i
$630$	−10.5544	−	3.88313i	−0.420498	−	0.154708i
$631$		−	35.9843i		−	1.43251i	−0.697838	−	0.716256i	$-0.745854\pi$
$631$		−	35.9843i		−	1.43251i	0.697838	−	0.716256i	$-0.254146\pi$
$632$	41.1620	−	5.70999i	1.63734	−	0.227131i
$633$	16.8899	+	16.8899i	0.671313	+	0.671313i
$634$	19.6886	−	21.5864i	0.781935	−	0.857305i
$635$	−10.3793	+	24.6529i	−0.411890	+	0.978322i
$636$	9.53948	−	0.879092i	0.378265	−	0.0348583i
$637$	−4.52685	+	4.52685i	−0.179360	+	0.179360i
$638$	−12.7998	+	0.588521i	−0.506747	+	0.0232998i
$639$	71.4104			2.82495
$640$	−16.4621	−	19.2094i	−0.650721	−	0.759317i
$641$	−18.0264			−0.712000			−0.356000	−	0.934486i	$-0.615860\pi$
$641$	−18.0264			−0.712000			−0.356000	+	0.934486i	$0.615860\pi$
$642$	−3.82074	+	0.175674i	−0.150792	+	0.00693330i
$643$	0.295089	−	0.295089i	0.0116372	−	0.0116372i	−0.701264	−	0.712901i	$-0.747381\pi$
$643$	0.295089	−	0.295089i	0.0116372	−	0.0116372i	0.712901	+	0.701264i	$0.247381\pi$
$644$	−0.880048	+	0.0810991i	−0.0346788	+	0.00319575i
$645$	12.7893	−	5.21092i	0.503579	−	0.205180i
$646$	−17.5792	+	19.2737i	−0.691645	+	0.758313i
$647$	−17.7724	−	17.7724i	−0.698705	−	0.698705i	0.265427	−	0.964131i	$-0.414487\pi$
$647$	−17.7724	−	17.7724i	−0.698705	−	0.698705i	−0.964131	+	0.265427i	$0.914487\pi$
$648$	−7.87151	+	1.09194i	−0.309222	+	0.0428953i
$649$			65.1494i			2.55734i
$650$	−7.12663	+	0.244972i	−0.279529	+	0.00960861i
$651$			2.19686i			0.0861017i
$652$	−29.8191	+	35.8729i	−1.16781	+	1.40489i
$653$	6.58870	+	6.58870i	0.257836	+	0.257836i	0.824173	−	0.566338i	$-0.191640\pi$
$653$	6.58870	+	6.58870i	0.257836	+	0.257836i	−0.566338	+	0.824173i	$0.691640\pi$
$654$	11.3511	+	10.3532i	0.443863	+	0.404841i
$655$	16.5457	−	6.74143i	0.646494	−	0.263409i
$656$	−26.8170	+	4.98487i	−1.04703	+	0.194626i
$657$	−35.6471	+	35.6471i	−1.39073	+	1.39073i
$658$	0.387601	+	8.42994i	0.0151103	+	0.328633i
$659$	7.54389			0.293868			0.146934	−	0.989146i	$-0.453059\pi$
$659$	7.54389			0.293868			0.146934	+	0.989146i	$0.453059\pi$
$660$	−21.1992	+	66.9629i	−0.825178	+	2.60653i
$661$	34.1151			1.32692			0.663462	−	0.748210i	$-0.269086\pi$
$661$	34.1151			1.32692			0.663462	+	0.748210i	$0.269086\pi$
$662$	−1.18741	−	25.8250i	−0.0461500	−	1.00372i
$663$	−4.52400	+	4.52400i	−0.175698	+	0.175698i
$664$	−26.1628	+	34.5904i	−1.01531	+	1.34237i
$665$	−5.54204	+	13.1635i	−0.214911	+	0.510457i
$666$	11.3845	+	10.3836i	0.441139	+	0.402356i
$667$	0.607602	+	0.607602i	0.0235265	+	0.0235265i
$668$	−1.47574	−	1.22670i	−0.0570980	−	0.0474624i
$669$		−	9.04223i		−	0.349593i
$670$	−4.01148	+	10.9033i	−0.154977	+	0.421230i
$671$		−	27.7114i		−	1.06979i
$672$	−12.1008	+	2.82993i	−0.466799	+	0.109167i
$673$	22.8808	+	22.8808i	0.881991	+	0.881991i	0.993737	−	0.111746i	$-0.0356443\pi$
$673$	22.8808	+	22.8808i	0.881991	+	0.881991i	−0.111746	+	0.993737i	$0.535644\pi$
$674$	21.3433	−	23.4005i	0.822112	−	0.901355i
$675$	19.1186	+	0.221519i	0.735877	+	0.00852629i
$676$	−2.19923	−	23.8649i	−0.0845856	−	0.917882i
$677$	−10.2566	+	10.2566i	−0.394195	+	0.394195i	−0.876180	−	0.481985i	$-0.839916\pi$
$677$	−10.2566	+	10.2566i	−0.394195	+	0.394195i	0.481985	+	0.876180i	$0.339916\pi$
$678$	19.1934	−	0.882496i	0.737118	−	0.0338920i
$679$	11.1113			0.426413
$680$	−14.2469	−	3.79993i	−0.546343	−	0.145721i
$681$	−11.8855			−0.455452
$682$	8.15356	−	0.374893i	0.312216	−	0.0143554i
$683$	−7.00563	+	7.00563i	−0.268063	+	0.268063i	−0.828319	−	0.560256i	$-0.810703\pi$
$683$	−7.00563	+	7.00563i	−0.268063	+	0.268063i	0.560256	+	0.828319i	$0.310703\pi$
$684$	−6.39675	−	69.4144i	−0.244586	−	2.65413i
$685$	−1.40201	−	0.590268i	−0.0535679	−	0.0225530i
$686$	−10.2697	+	11.2596i	−0.392098	+	0.429893i
$687$	29.4645	+	29.4645i	1.12414	+	1.12414i
$688$	5.13806	−	7.48438i	0.195887	−	0.285339i
$689$		−	1.77508i		−	0.0676251i
$690$	4.27589	−	1.97579i	0.162780	−	0.0752172i
$691$			26.9193i			1.02406i	0.858968	+	0.512029i	$0.171106\pi$
$691$			26.9193i			1.02406i	−0.858968	+	0.512029i	$0.828894\pi$
$692$	−30.5880	−	25.4261i	−1.16278	−	0.966555i
$693$	14.5137	+	14.5137i	0.551328	+	0.551328i
$694$	25.7935	+	23.5258i	0.979108	+	0.893029i
$695$	−15.0136	−	36.8484i	−0.569500	−	1.39774i
$696$	9.63678	+	7.28885i	0.365281	+	0.276283i
$697$	−11.2415	+	11.2415i	−0.425802	+	0.425802i
$698$	1.22263	+	26.5909i	0.0462771	+	1.00648i
$699$	50.6671			1.91640
$700$	−8.04694	+	0.647622i	−0.304146	+	0.0244778i
$701$	29.9874			1.13261			0.566303	−	0.824197i	$-0.308373\pi$
$701$	29.9874			1.13261			0.566303	+	0.824197i	$0.308373\pi$
$702$	−0.250489	−	5.44789i	−0.00945410	−	0.205617i
$703$	13.8373	−	13.8373i	0.521884	−	0.521884i
$704$	12.5682	+	44.4288i	0.473680	+	1.67447i
$705$	−16.9709	−	41.6522i	−0.639161	−	1.56871i
$706$	24.8779	+	22.6908i	0.936293	+	0.853978i
$707$	−6.80814	−	6.80814i	−0.256047	−	0.256047i
$708$	39.2718	−	47.2445i	1.47592	−	1.77556i
$709$		−	7.06581i		−	0.265362i	−0.991159	−	0.132681i	$-0.957641\pi$
$709$		−	7.06581i		−	0.265362i	0.991159	−	0.132681i	$-0.0423586\pi$
$710$	46.5340	−	21.5024i	1.74639	−	0.806969i
$711$			64.7230i			2.42730i
$712$	−3.17321	−	22.8750i	−0.118921	−	0.857275i
$713$	−0.387048	−	0.387048i	−0.0144951	−	0.0144951i
$714$	−4.88106	+	5.35155i	−0.182669	+	0.200277i
$715$	11.9949	+	5.05005i	0.448583	+	0.188861i
$716$	−3.06236	+	0.282206i	−0.114446	+	0.0105465i
$717$	−33.6842	+	33.6842i	−1.25796	+	1.25796i
$718$	−46.3412	+	2.13073i	−1.72944	+	0.0795180i
$719$	−9.12924			−0.340463			−0.170232	−	0.985404i	$-0.554452\pi$
$719$	−9.12924			−0.340463			−0.170232	+	0.985404i	$0.554452\pi$
$720$	33.1575	−	21.2853i	1.23571	−	0.793257i
$721$	4.10854			0.153010
$722$	−61.5947	+	2.83207i	−2.29232	+	0.105399i
$723$	17.9010	−	17.9010i	0.665746	−	0.665746i
$724$	27.9009	−	2.57116i	1.03693	−	0.0955563i
$725$	5.48554	+	5.61414i	0.203728	+	0.208504i
$726$	57.8599	−	63.4371i	2.14738	−	2.35437i
$727$	13.3459	+	13.3459i	0.494973	+	0.494973i	0.909869	−	0.414896i	$-0.136182\pi$
$727$	13.3459	+	13.3459i	0.494973	+	0.494973i	−0.414896	+	0.909869i	$0.636182\pi$
$728$	0.316398	+	2.28084i	0.0117265	+	0.0845335i
$729$		−	43.5953i		−	1.61464i
$730$	−12.4955	+	33.9628i	−0.462478	+	1.25702i
$731$		−	5.29124i		−	0.195704i
$732$	−16.7043	+	20.0955i	−0.617409	+	0.742752i
$733$	29.1980	+	29.1980i	1.07845	+	1.07845i	0.996649	+	0.0818028i	$0.0260678\pi$
$733$	29.1980	+	29.1980i	1.07845	+	1.07845i	0.0818028	+	0.996649i	$0.473932\pi$
$734$	23.5174	+	21.4499i	0.868045	+	0.791730i
$735$	14.9890	−	35.6020i	0.552879	−	1.31320i
$736$	1.63337	−	2.63053i	0.0602067	−	0.0969627i
$737$	14.9934	−	14.9934i	0.552288	−	0.552288i
$738$	−1.95124	−	42.4376i	−0.0718263	−	1.56215i
$739$	−8.10178			−0.298029			−0.149014	−	0.988835i	$-0.547610\pi$
$739$	−8.10178			−0.298029			−0.149014	+	0.988835i	$0.547610\pi$
$740$	10.5452	+	3.33841i	0.387649	+	0.122722i
$741$	−21.7126			−0.797633
$742$	−0.0923021	−	2.00748i	−0.00338852	−	0.0736969i
$743$	−30.4992	+	30.4992i	−1.11891	+	1.11891i	−0.127006	+	0.991902i	$0.540537\pi$
$743$	−30.4992	+	30.4992i	−1.11891	+	1.11891i	−0.991902	+	0.127006i	$0.959463\pi$
$744$	−6.13871	−	4.64306i	−0.225056	−	0.170223i
$745$	16.0829	−	6.55285i	0.589231	−	0.240078i
$746$	2.71949	+	2.48041i	0.0995677	+	0.0908141i
$747$	−47.7641	−	47.7641i	−1.74760	−	1.74760i
$748$	20.6950	+	17.2026i	0.756685	+	0.628991i
$749$			0.802332i			0.0293166i
$750$	39.2651	−	17.5944i	1.43376	−	0.642456i
$751$			10.0092i			0.365241i	0.983183	+	0.182621i	$0.0584580\pi$
$751$			10.0092i			0.365241i	−0.983183	+	0.182621i	$0.941542\pi$
$752$	−24.3751	−	16.7336i	−0.888868	−	0.610212i
$753$	15.3378	+	15.3378i	0.558940	+	0.558940i
$754$	1.50872	−	1.65415i	0.0549445	−	0.0602406i
$755$	20.2068	−	8.23310i	0.735399	−	0.299633i
$756$	−0.566568	−	6.14812i	−0.0206059	−	0.223605i
$757$	5.65390	−	5.65390i	0.205495	−	0.205495i	−0.596855	−	0.802349i	$-0.703583\pi$
$757$	5.65390	−	5.65390i	0.205495	−	0.205495i	0.802349	+	0.596855i	$0.203583\pi$
$758$	−37.1427	+	1.70779i	−1.34908	+	0.0620297i
$759$	−8.59686			−0.312046
$760$	−25.0697	−	43.3072i	−0.909374	−	1.57092i
$761$	26.6805			0.967167			0.483583	−	0.875298i	$-0.339335\pi$
$761$	26.6805			0.967167			0.483583	+	0.875298i	$0.339335\pi$
$762$	−45.9880	+	2.11449i	−1.66597	+	0.0765998i
$763$	2.27888	−	2.27888i	0.0825012	−	0.0825012i
$764$	2.27831	+	24.7231i	0.0824263	+	0.894450i
$765$	8.91109	−	21.1656i	0.322181	−	0.765245i
$766$	18.3567	−	20.1261i	0.663253	−	0.727184i
$767$	−8.04935	−	8.04935i	−0.290645	−	0.290645i
$768$	17.6674	−	39.7945i	0.637517	−	1.43596i
$769$			54.0128i			1.94775i	0.227079	+	0.973876i	$0.427082\pi$
$769$			54.0128i			1.94775i	−0.227079	+	0.973876i	$0.572918\pi$
$770$	13.8279	+	5.08750i	0.498323	+	0.183341i
$771$			6.27315i			0.225922i
$772$	12.4812	+	10.3749i	0.449207	+	0.373401i
$773$	−24.9518	−	24.9518i	−0.897456	−	0.897456i	0.0977549	−	0.995211i	$-0.468834\pi$
$773$	−24.9518	−	24.9518i	−0.897456	−	0.897456i	−0.995211	+	0.0977549i	$0.968834\pi$
$774$	10.4467	+	9.52823i	0.375497	+	0.342485i
$775$	−3.49433	−	3.57626i	−0.125520	−	0.128463i
$776$	−23.4838	+	31.0485i	−0.843019	+	1.11458i
$777$	3.84208	−	3.84208i	0.137834	−	0.137834i
$778$	2.43530	+	52.9653i	0.0873097	+	1.89890i
$779$	−53.9528			−1.93306
$780$	−5.65420	−	10.8926i	−0.202453	−	0.390018i
$781$	−93.5586			−3.34779
$782$	−0.0828915	−	1.80281i	−0.00296419	−	0.0644683i
$783$	−4.24478	+	4.24478i	−0.151696	+	0.151696i
$784$	−4.64069	−	24.9654i	−0.165739	−	0.891623i
$785$	−22.0018	−	9.26313i	−0.785278	−	0.330615i
$786$	22.7188	+	20.7214i	0.810352	+	0.739109i
$787$	−15.2521	−	15.2521i	−0.543677	−	0.543677i	0.380928	−	0.924605i	$-0.375605\pi$
$787$	−15.2521	−	15.2521i	−0.543677	−	0.543677i	−0.924605	+	0.380928i	$0.875605\pi$
$788$	−21.9760	+	26.4374i	−0.782862	+	0.941794i
$789$		−	31.7066i		−	1.12879i
$790$	19.4887	+	42.1762i	0.693377	+	1.50056i
$791$		−	4.03050i		−	0.143308i
$792$	−71.2304	+	9.88107i	−2.53106	+	0.351108i
$793$	3.42380	+	3.42380i	0.121583	+	0.121583i
$794$	−34.0457	+	37.3273i	−1.20824	+	1.32470i
$795$	4.04140	+	9.91894i	0.143334	+	0.351788i
$796$	32.1065	−	2.95871i	1.13798	−	0.104869i
$797$	26.2613	−	26.2613i	0.930224	−	0.930224i	−0.0674956	−	0.997720i	$-0.521501\pi$
$797$	26.2613	−	26.2613i	0.930224	−	0.930224i	0.997720	+	0.0674956i	$0.0215009\pi$
$798$	−24.5553	+	1.12903i	−0.869249	+	0.0399673i
$799$	−17.2325			−0.609642
$800$	15.1976	−	23.8544i	0.537315	−	0.843382i
$801$	35.9685			1.27088
$802$	−28.5706	+	1.31365i	−1.00886	+	0.0463866i
$803$	46.7032	−	46.7032i	1.64812	−	1.64812i
$804$	−19.9107	+	1.83483i	−0.702196	+	0.0647095i
$805$	−0.372832	−	0.915054i	−0.0131406	−	0.0322514i
$806$	−0.961070	+	1.05371i	−0.0338522	+	0.0371153i
$807$	−2.18792	−	2.18792i	−0.0770185	−	0.0770185i
$808$	33.4131	−	4.63506i	1.17547	−	0.163061i
$809$		−	22.4441i		−	0.789091i	−0.918876	−	0.394546i	$-0.870902\pi$
$809$		−	22.4441i		−	0.789091i	0.918876	−	0.394546i	$-0.129098\pi$
$810$	−3.72688	−	8.06547i	−0.130949	−	0.283392i
$811$		−	23.8916i		−	0.838947i	−0.907768	−	0.419474i	$-0.862215\pi$
$811$		−	23.8916i		−	0.838947i	0.907768	−	0.419474i	$-0.137785\pi$
$812$	1.62024	−	1.94917i	0.0568592	−	0.0684024i
$813$	1.16865	+	1.16865i	0.0409865	+	0.0409865i
$814$	−14.9154	−	13.6041i	−0.522784	−	0.476823i
$815$	−48.0677	−	20.2373i	−1.68374	−	0.708883i
$816$	−4.63777	−	24.9497i	−0.162355	−	0.873415i
$817$	12.6975	−	12.6975i	0.444228	−	0.444228i
$818$	1.92100	+	41.7798i	0.0671661	+	1.46080i
$819$	−3.58638			−0.125318
$820$	−14.0499	−	27.0666i	−0.490643	−	0.945206i
$821$	0.521133			0.0181877			0.00909383	−	0.999959i	$-0.497105\pi$
$821$	0.521133			0.0181877			0.00909383	+	0.999959i	$0.497105\pi$
$822$	−0.120250	−	2.61533i	−0.00419421	−	0.0912199i
$823$	17.6172	−	17.6172i	0.614095	−	0.614095i	−0.329915	−	0.944011i	$-0.607020\pi$
$823$	17.6172	−	17.6172i	0.614095	−	0.614095i	0.944011	+	0.329915i	$0.107020\pi$
$824$	−8.68341	+	11.4806i	−0.302501	+	0.399944i
$825$	−78.5237	−	0.909820i	−2.73384	−	0.0316759i
$826$	−9.52176	−	8.68465i	−0.331304	−	0.302178i
$827$	−39.5828	−	39.5828i	−1.37643	−	1.37643i	−0.850576	−	0.525852i	$-0.823746\pi$
$827$	−39.5828	−	39.5828i	−1.37643	−	1.37643i	−0.525852	−	0.850576i	$-0.676254\pi$
$828$	3.70860	+	3.08276i	0.128883	+	0.107133i
$829$		−	43.2723i		−	1.50291i	−0.659785	−	0.751454i	$-0.729353\pi$
$829$		−	43.2723i		−	1.50291i	0.659785	−	0.751454i	$-0.270647\pi$
$830$	−45.5073	−	16.7428i	−1.57958	−	0.581153i
$831$			61.5251i			2.13428i
$832$	−7.04209	−	3.93644i	−0.244140	−	0.136472i
$833$	−10.4653	−	10.4653i	−0.362603	−	0.362603i
$834$	46.1481	−	50.5963i	1.59798	−	1.75201i
$835$	0.832523	−	1.97741i	0.0288106	−	0.0684311i
$836$	8.38072	+	90.9435i	0.289853	+	3.14535i
$837$	2.70396	−	2.70396i	0.0934627	−	0.0934627i
$838$	21.1541	−	0.972645i	0.730755	−	0.0335995i
$839$	−34.0631			−1.17599			−0.587995	−	0.808865i	$-0.700083\pi$
$839$	−34.0631			−1.17599			−0.587995	+	0.808865i	$0.700083\pi$
$840$	−6.96088	−	12.0247i	−0.240173	−	0.414892i
$841$	26.5356			0.915021
$842$	−3.24829	+	0.149353i	−0.111943	+	0.00514706i
$843$	−3.09526	+	3.09526i	−0.106606	+	0.106606i
$844$	1.61093	+	17.4810i	0.0554505	+	0.601721i
$845$	24.8142	−	10.1104i	0.853635	−	0.347807i
$846$	31.0315	−	34.0226i	1.06688	−	1.16972i
$847$	−12.7358	−	12.7358i	−0.437608	−	0.437608i
$848$	5.80461	+	3.98489i	0.199331	+	0.136842i
$849$		−	47.7968i		−	1.64038i
$850$	−0.566337	−	16.4756i	−0.0194252	−	0.565109i
$851$			1.35382i			0.0464082i
$852$	67.8461	+	56.3967i	2.32437	+	1.93212i
$853$	37.5786	+	37.5786i	1.28667	+	1.28667i	0.936799	+	0.349867i	$0.113773\pi$
$853$	37.5786	+	37.5786i	1.28667	+	1.28667i	0.349867	+	0.936799i	$0.386227\pi$
$854$	4.05009	+	3.69403i	0.138591	+	0.126407i
$855$	72.1755	−	29.4074i	2.46835	−	1.00571i
$856$	−2.24197	−	1.69573i	−0.0766289	−	0.0579589i
$857$	1.63596	−	1.63596i	0.0558833	−	0.0558833i	−0.678613	−	0.734496i	$-0.737419\pi$
$857$	1.63596	−	1.63596i	0.0558833	−	0.0558833i	0.734496	+	0.678613i	$0.237419\pi$
$858$	1.02880	+	22.3755i	0.0351228	+	0.763885i
$859$	−29.3026			−0.999790			−0.499895	−	0.866086i	$-0.666628\pi$
$859$	−29.3026			−0.999790			−0.499895	+	0.866086i	$0.666628\pi$
$860$	9.67652	+	3.06340i	0.329967	+	0.104461i
$861$	−14.9806			−0.510537
$862$	−0.222138	−	4.83128i	−0.00756604	−	0.164554i
$863$	−23.5108	+	23.5108i	−0.800318	+	0.800318i	−0.983145	−	0.182827i	$-0.941475\pi$
$863$	−23.5108	+	23.5108i	−0.800318	+	0.800318i	0.182827	+	0.983145i	$0.441475\pi$
$864$	18.3772	+	11.4109i	0.625206	+	0.388207i
$865$	17.2559	−	40.9862i	0.586718	−	1.39357i
$866$	−6.61893	−	6.03702i	−0.224920	−	0.205146i
$867$	22.2529	+	22.2529i	0.755749	+	0.755749i
$868$	−1.03211	+	1.24164i	−0.0350320	+	0.0421439i
$869$		−	84.7971i		−	2.87654i
$870$	−4.66450	+	12.6782i	−0.158141	+	0.429830i
$871$			3.70492i			0.125537i
$872$	1.55149	+	11.1843i	0.0525401	+	0.378750i
$873$	−42.8732	−	42.8732i	−1.45104	−	1.45104i
$874$	4.12730	−	4.52513i	0.139608	−	0.153065i
$875$	−3.30861	−	8.39756i	−0.111851	−	0.283889i
$876$	−62.0203	+	5.71536i	−2.09547	+	0.193104i
$877$	−16.4466	+	16.4466i	−0.555362	+	0.555362i	−0.927983	−	0.372622i	$-0.878459\pi$
$877$	−16.4466	+	16.4466i	−0.555362	+	0.555362i	0.372622	+	0.927983i	$0.378459\pi$
$878$	2.68061	−	0.123252i	0.0904661	−	0.00415955i
$879$	−5.61030			−0.189231
$880$	−43.4414	+	27.8871i	−1.46441	+	0.940072i
$881$	17.3225			0.583610			0.291805	−	0.956478i	$-0.405744\pi$
$881$	17.3225			0.583610			0.291805	+	0.956478i	$0.405744\pi$
$882$	39.5076	−	1.81652i	1.33029	−	0.0611655i
$883$	−9.06110	+	9.06110i	−0.304930	+	0.304930i	−0.842939	−	0.538009i	$-0.819177\pi$
$883$	−9.06110	+	9.06110i	−0.304930	+	0.304930i	0.538009	+	0.842939i	$0.319177\pi$
$884$	−4.68234	+	0.431491i	−0.157484	+	0.0145126i
$885$	63.3051	+	26.6525i	2.12798	+	0.895915i
$886$	−36.5058	+	40.0246i	−1.22644	+	1.34465i
$887$	22.9682	+	22.9682i	0.771198	+	0.771198i	0.978316	−	0.207118i	$-0.0664084\pi$
$887$	22.9682	+	22.9682i	0.771198	+	0.771198i	−0.207118	+	0.978316i	$0.566408\pi$
$888$	2.61574	+	18.8562i	0.0877783	+	0.632774i
$889$			9.65722i			0.323893i
$890$	23.4386	−	10.8305i	0.785663	−	0.363038i
$891$			16.2160i			0.543255i
$892$	4.24813	−	5.11056i	0.142238	−	0.171114i
$893$	−41.3530	−	41.3530i	−1.38383	−	1.38383i
$894$	22.0833	+	20.1418i	0.738575	+	0.673642i
$895$	−1.29737	−	3.18417i	−0.0433662	−	0.106435i
$896$	−8.16876	−	4.08564i	−0.272899	−	0.136492i
$897$	1.06216	−	1.06216i	0.0354645	−	0.0354645i
$898$	0.117231	+	2.54967i	0.00391207	+	0.0850835i
$899$	1.56984			0.0523570
$900$	33.5481	+	28.5504i	1.11827	+	0.951680i
$901$	4.10369			0.136714
$902$	2.55643	+	55.5998i	0.0851198	+	1.85127i
$903$	3.52559	−	3.52559i	0.117324	−	0.117324i
$904$	11.2625	+	8.51847i	0.374585	+	0.283320i
$905$	11.8202	+	29.0108i	0.392918	+	0.964350i
$906$	27.7457	+	25.3064i	0.921790	+	0.840750i
$907$	4.09551	+	4.09551i	0.135989	+	0.135989i	0.771825	−	0.635835i	$-0.219344\pi$
$907$	4.09551	+	4.09551i	0.135989	+	0.135989i	−0.635835	+	0.771825i	$0.719344\pi$
$908$	−6.71753	−	5.58391i	−0.222929	−	0.185309i
$909$			52.5387i			1.74260i
$910$	−2.33704	+	1.07989i	−0.0774720	+	0.0357982i
$911$			50.0242i			1.65738i	0.559710	+	0.828688i	$0.310912\pi$
$911$			50.0242i			1.65738i	−0.559710	+	0.828688i	$0.689088\pi$
$912$	48.7429	−	71.0015i	1.61404	−	2.35109i
$913$	62.5783	+	62.5783i	2.07104	+	2.07104i
$914$	10.6104	−	11.6331i	0.350961	−	0.384790i
$915$	−26.9269	−	11.3367i	−0.890176	−	0.374779i
$916$	2.81027	+	30.4957i	0.0928540	+	1.00761i
$917$	4.56109	−	4.56109i	0.150621	−	0.150621i
$918$	12.5946	−	0.579090i	0.415685	−	0.0191128i
$919$	−33.9052			−1.11843			−0.559214	−	0.829023i	$-0.688897\pi$
$919$	−33.9052			−1.11843			−0.559214	+	0.829023i	$0.688897\pi$
$920$	3.34493	+	0.892158i	0.110279	+	0.0294136i
$921$	1.91668			0.0631567
$922$	26.0591	−	1.19818i	0.858212	−	0.0394598i
$923$	11.5594	−	11.5594i	0.380481	−	0.380481i
$924$	2.32700	+	25.2515i	0.0765526	+	0.830712i
$925$	−0.143277	+	12.3658i	−0.00471091	+	0.406583i
$926$	27.7392	−	30.4130i	0.911566	−	0.999432i
$927$	−15.8529	−	15.8529i	−0.520677	−	0.520677i
$928$	2.02222	+	8.64703i	0.0663825	+	0.283853i
$929$			26.6304i			0.873714i	0.899531	+	0.436857i	$0.143908\pi$
$929$			26.6304i			0.873714i	−0.899531	+	0.436857i	$0.856092\pi$
$930$	2.97133	−	8.07611i	0.0974336	−	0.264826i
$931$		−	50.2277i		−	1.64614i
$932$	28.6364	+	23.8039i	0.938017	+	0.779722i
$933$	−15.2471	−	15.2471i	−0.499167	−	0.499167i
$934$	−3.68146	−	3.35780i	−0.120461	−	0.109871i
$935$	−11.6749	+	27.7302i	−0.381810	+	0.906875i
$936$	7.57983	−	10.0215i	0.247755	−	0.327562i
$937$	23.8508	−	23.8508i	0.779173	−	0.779173i	−0.200517	−	0.979690i	$-0.564262\pi$
$937$	23.8508	−	23.8508i	0.779173	−	0.779173i	0.979690	+	0.200517i	$0.0642622\pi$
$938$	0.192652	+	4.18999i	0.00629031	+	0.136808i
$939$	−48.4313			−1.58050
$940$	9.97688	−	31.5144i	0.325410	−	1.02789i
$941$	37.2557			1.21450			0.607250	−	0.794511i	$-0.292273\pi$
$941$	37.2557			1.21450			0.607250	+	0.794511i	$0.292273\pi$
$942$	−1.88710	−	41.0426i	−0.0614850	−	1.33724i
$943$	2.63931	−	2.63931i	0.0859479	−	0.0859479i
$944$	44.3919	−	8.25177i	1.44483	−	0.268572i
$945$	6.39268	−	2.60465i	0.207954	−	0.0847293i
$946$	−13.6867	−	12.4834i	−0.444994	−	0.405872i
$947$	18.5108	+	18.5108i	0.601520	+	0.601520i	0.940716	−	0.339196i	$-0.110155\pi$
$947$	18.5108	+	18.5108i	0.601520	+	0.601520i	−0.339196	+	0.940716i	$0.610155\pi$
$948$	−51.1153	+	61.4924i	−1.66015	+	1.99718i
$949$			11.5406i			0.374622i
$950$	38.1777	−	40.8958i	1.23865	−	1.32683i
$951$			56.2192i			1.82303i
$952$	−5.27293	+	0.731461i	−0.170897	+	0.0237068i
$953$	27.4631	+	27.4631i	0.889616	+	0.889616i	0.994486	−	0.104870i	$-0.0334427\pi$
$953$	27.4631	+	27.4631i	0.889616	+	0.889616i	−0.104870	+	0.994486i	$0.533443\pi$
$954$	−7.38975	+	8.10205i	−0.239252	+	0.262313i
$955$	−25.7065	+	10.4739i	−0.831843	+	0.338928i
$956$	−34.8630	+	3.21274i	−1.12755	+	0.103907i
$957$	17.4341	−	17.4341i	0.563564	−	0.563564i
$958$	−57.3198	+	2.63551i	−1.85192	+	0.0851496i
$959$	−0.549203			−0.0177347
$960$	48.3126	+	5.96336i	1.55928	+	0.192467i
$961$	−1.00000			−0.0322581
$962$	3.52364	−	0.162014i	0.113607	−	0.00522354i
$963$	3.09581	−	3.09581i	0.0997612	−	0.0997612i
$964$	18.5275	−	1.70737i	0.596732	−	0.0549906i
$965$	−7.04112	+	16.7241i	−0.226662	+	0.538367i
$966$	1.14599	−	1.25645i	0.0368717	−	0.0404257i
$967$	−10.9166	−	10.9166i	−0.351054	−	0.351054i	0.509448	−	0.860502i	$-0.329850\pi$
$967$	−10.9166	−	10.9166i	−0.351054	−	0.351054i	−0.860502	+	0.509448i	$0.829850\pi$
$968$	62.5051	−	8.67070i	2.00899	−	0.278687i
$969$		−	50.1961i		−	1.61253i
$970$	−40.8475	−	15.0284i	−1.31153	−	0.482534i
$971$			27.6505i			0.887348i	0.896188	+	0.443674i	$0.146325\pi$
$971$			27.6505i			0.887348i	−0.896188	+	0.443674i	$0.853675\pi$
$972$	24.4415	−	29.4035i	0.783961	−	0.943116i
$973$	−10.1579	−	10.1579i	−0.325647	−	0.325647i
$974$	−35.8511	−	32.6992i	−1.14874	−	1.04775i
$975$	9.81417	−	9.58935i	0.314305	−	0.307105i
$976$	−18.8821	+	3.50990i	−0.604403	+	0.112349i
$977$	−23.9125	+	23.9125i	−0.765027	+	0.765027i	−0.977226	−	0.212199i	$-0.931937\pi$
$977$	−23.9125	+	23.9125i	−0.765027	+	0.765027i	0.212199	+	0.977226i	$0.431937\pi$
$978$	−4.12278	−	89.6664i	−0.131832	−	2.86721i
$979$	−47.1243			−1.50610
$980$	25.1978	−	13.0798i	0.804914	−	0.417820i
$981$	−17.5862			−0.561485
$982$	1.79410	+	39.0200i	0.0572521	+	1.24518i
$983$	−14.3807	+	14.3807i	−0.458675	+	0.458675i	−0.898220	−	0.439546i	$-0.855139\pi$
$983$	−14.3807	+	14.3807i	−0.458675	+	0.458675i	0.439546	+	0.898220i	$0.355139\pi$
$984$	31.6615	−	41.8604i	1.00933	−	1.33446i
$985$	−35.4247	−	14.9144i	−1.12873	−	0.475213i
$986$	3.82413	+	3.48792i	0.121785	+	0.111078i
$987$	−11.4821	−	11.4821i	−0.365480	−	0.365480i
$988$	−12.2717	−	10.2008i	−0.390415	−	0.324531i
$989$			1.24229i			0.0395026i
$990$	−33.7250	−	72.9854i	−1.07185	−	2.31963i
$991$			28.8433i			0.916239i	0.888891	+	0.458120i	$0.151477\pi$
$991$			28.8433i			0.916239i	−0.888891	+	0.458120i	$0.848523\pi$
$992$	−1.28817	−	5.50823i	−0.0408994	−	0.174887i
$993$	35.1753	+	35.1753i	1.11625	+	1.11625i
$994$	12.4717	−	13.6738i	0.395578	−	0.433708i
$995$	13.6019	+	33.3836i	0.431209	+	1.05833i
$996$	−7.65809	−	83.1019i	−0.242656	−	2.63318i
$997$	−22.6198	+	22.6198i	−0.716377	+	0.716377i	−0.967861	−	0.251484i	$-0.919081\pi$
$997$	−22.6198	+	22.6198i	−0.716377	+	0.716377i	0.251484	+	0.967861i	$0.419081\pi$
$998$	−10.0673	+	0.462886i	−0.318675	+	0.0146524i
$999$	−9.45792			−0.299235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	620.2.k.d.63.1	yes	88
4.3	odd	2		620.2.k.c.63.21	✓	88
5.2	odd	4		620.2.k.c.187.21	yes	88
20.7	even	4	inner	620.2.k.d.187.1	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
620.2.k.c.63.21	✓	88	4.3	odd	2
620.2.k.c.187.21	yes	88	5.2	odd	4
620.2.k.d.63.1	yes	88	1.1	even	1	trivial
620.2.k.d.187.1	yes	88	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 620 = 2^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	620.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41272 + 0.0649557i) q^{2} +(1.92422 - 1.92422i) q^{3} +(1.99156 - 0.183528i) q^{4} +(0.843724 + 2.07078i) q^{5} +(-2.59339 + 2.84337i) q^{6} +(0.570845 + 0.570845i) q^{7} +(-2.80160 + 0.388638i) q^{8} -4.40523i q^{9} +(-1.32646 - 2.87063i) q^{10} +5.77153i q^{11} +(3.47905 - 4.18535i) q^{12} +(-0.713084 - 0.713084i) q^{13} +(-0.843524 - 0.769365i) q^{14} +(5.60814 + 2.36112i) q^{15} +(3.93263 - 0.731016i) q^{16} +(1.64853 - 1.64853i) q^{17} +(0.286144 + 6.22336i) q^{18} +7.91202 q^{19} +(2.06038 + 3.96924i) q^{20} +2.19686 q^{21} +(-0.374893 - 8.15356i) q^{22} +(-0.387048 + 0.387048i) q^{23} +(-4.64306 + 6.13871i) q^{24} +(-3.57626 + 3.49433i) q^{25} +(1.05371 + 0.961070i) q^{26} +(-2.70396 - 2.70396i) q^{27} +(1.24164 + 1.03211i) q^{28} -1.56984i q^{29} +(-8.07611 - 2.97133i) q^{30} +1.00000i q^{31} +(-5.50823 + 1.28817i) q^{32} +(11.1057 + 11.1057i) q^{33} +(-2.22184 + 2.43600i) q^{34} +(-0.700458 + 1.66373i) q^{35} +(-0.808485 - 8.77328i) q^{36} +(1.74890 - 1.74890i) q^{37} +(-11.1775 + 0.513930i) q^{38} -2.74426 q^{39} +(-3.16856 - 5.47359i) q^{40} -6.81909 q^{41} +(-3.10355 + 0.142698i) q^{42} +(1.60483 - 1.60483i) q^{43} +(1.05924 + 11.4943i) q^{44} +(9.12226 - 3.71680i) q^{45} +(0.521650 - 0.571932i) q^{46} +(-5.22661 - 5.22661i) q^{47} +(6.16061 - 8.97388i) q^{48} -6.34827i q^{49} +(4.82528 - 5.16882i) q^{50} -6.34428i q^{51} +(-1.55102 - 1.28928i) q^{52} +(1.24465 + 1.24465i) q^{53} +(3.99559 + 3.64431i) q^{54} +(-11.9516 + 4.86958i) q^{55} +(-1.82113 - 1.37743i) q^{56} +(15.2244 - 15.2244i) q^{57} +(0.101970 + 2.21774i) q^{58} +11.2881 q^{59} +(11.6023 + 3.67307i) q^{60} -4.80140 q^{61} +(-0.0649557 - 1.41272i) q^{62} +(2.51470 - 2.51470i) q^{63} +(7.69792 - 2.17761i) q^{64} +(0.874994 - 2.07829i) q^{65} +(-16.4106 - 14.9678i) q^{66} +(-2.59782 - 2.59782i) q^{67} +(2.98061 - 3.58571i) q^{68} +1.48953i q^{69} +(0.881483 - 2.39588i) q^{70} +16.2104i q^{71} +(1.71204 + 12.3417i) q^{72} +(-8.09201 - 8.09201i) q^{73} +(-2.35711 + 2.58431i) q^{74} +(-0.157639 + 13.6054i) q^{75} +(15.7573 - 1.45208i) q^{76} +(-3.29464 + 3.29464i) q^{77} +(3.87687 - 0.178255i) q^{78} -14.6923 q^{79} +(4.83183 + 7.52684i) q^{80} +2.80965 q^{81} +(9.63347 - 0.442938i) q^{82} +(10.8426 - 10.8426i) q^{83} +(4.37518 - 0.403186i) q^{84} +(4.80466 + 2.02284i) q^{85} +(-2.16294 + 2.37142i) q^{86} +(-3.02071 - 3.02071i) q^{87} +(-2.24303 - 16.1695i) q^{88} +8.16496i q^{89} +(-12.6458 + 5.84334i) q^{90} -0.814120i q^{91} +(-0.699796 + 0.841864i) q^{92} +(1.92422 + 1.92422i) q^{93} +(7.72324 + 7.04424i) q^{94} +(6.67556 + 16.3840i) q^{95} +(-8.12032 + 13.0778i) q^{96} +(9.73234 - 9.73234i) q^{97} +(0.412356 + 8.96834i) q^{98} +25.4249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 2 q^{2} + 2 q^{3} - 2 q^{5} + 4 q^{7} - 4 q^{8} - 10 q^{10} - 12 q^{12} - 6 q^{13} + 22 q^{14} - 2 q^{15} + 8 q^{16} - 2 q^{17} - 24 q^{18} + 8 q^{19} + 8 q^{20} - 16 q^{21} - 16 q^{22} + 10 q^{23}+ \cdots - 8 q^{99}+O(q^{100}) \) 88 * q + 2 * q^2 + 2 * q^3 - 2 * q^5 + 4 * q^7 - 4 * q^8 - 10 * q^10 - 12 * q^12 - 6 * q^13 + 22 * q^14 - 2 * q^15 + 8 * q^16 - 2 * q^17 - 24 * q^18 + 8 * q^19 + 8 * q^20 - 16 * q^21 - 16 * q^22 + 10 * q^23 - 44 * q^24 - 4 * q^25 - 8 * q^26 + 8 * q^27 + 46 * q^28 + 16 * q^30 - 8 * q^32 - 8 * q^33 + 40 * q^34 - 12 * q^35 - 20 * q^36 + 10 * q^37 - 64 * q^38 + 8 * q^39 + 8 * q^41 + 28 * q^42 + 10 * q^43 - 16 * q^44 + 6 * q^45 - 24 * q^46 - 64 * q^47 + 88 * q^48 - 14 * q^50 + 20 * q^52 + 18 * q^53 + 36 * q^54 + 40 * q^55 - 24 * q^56 - 24 * q^57 - 52 * q^58 - 32 * q^60 + 20 * q^61 + 2 * q^62 - 4 * q^63 - 150 * q^64 - 18 * q^65 + 8 * q^66 + 116 * q^67 + 68 * q^68 - 6 * q^70 - 26 * q^72 + 38 * q^73 + 36 * q^74 - 70 * q^75 - 8 * q^76 + 40 * q^77 - 152 * q^78 + 32 * q^79 + 68 * q^80 - 60 * q^81 + 14 * q^82 - 14 * q^83 - 120 * q^84 + 6 * q^85 + 4 * q^86 - 44 * q^87 + 52 * q^88 - 68 * q^90 - 92 * q^92 + 2 * q^93 + 112 * q^94 + 104 * q^95 - 20 * q^96 + 16 * q^97 - 62 * q^98 - 8 * q^99

Introduction

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