LMFDB - Embedded newform 230.2.l.a.57.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,2,Mod(7,230)] 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("230.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			57.12
Character	$\chi$	$=$	230.57
Dual form			230.2.l.a.113.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.977147 + 0.212565i) q^{2} +(2.02042 + 2.69897i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.81692 - 1.30338i) q^{5} +(1.40054 + 3.06676i) q^{6} +(-1.60647 - 0.114897i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-2.35713 + 8.02765i) q^{9} +(-1.49834 - 1.65981i) q^{10} +(2.59443 - 4.03702i) q^{11} +(0.716649 + 3.29438i) q^{12} +(-0.267263 - 3.73682i) q^{13} +(-1.54534 - 0.453752i) q^{14} +(-0.153151 - 7.53719i) q^{15} +(0.654861 + 0.755750i) q^{16} +(2.83053 + 1.05573i) q^{17} +(-4.00966 + 7.34315i) q^{18} +(0.432881 - 0.947878i) q^{19} +(-1.11128 - 1.94037i) q^{20} +(-2.93565 - 4.56796i) q^{21} +(3.39327 - 3.39327i) q^{22} +(-4.79083 + 0.218958i) q^{23} +3.37143i q^{24} +(1.60238 + 4.73628i) q^{25} +(0.533163 - 3.70823i) q^{26} +(-16.9522 + 6.32284i) q^{27} +(-1.41357 - 0.771867i) q^{28} +(4.46522 - 2.03920i) q^{29} +(1.45250 - 7.39750i) q^{30} +(-0.275290 - 1.91468i) q^{31} +(0.479249 + 0.877679i) q^{32} +(16.1376 - 1.15419i) q^{33} +(2.54143 + 1.63328i) q^{34} +(2.76907 + 2.30261i) q^{35} +(-5.47893 + 6.32302i) q^{36} +(-5.72807 + 3.12776i) q^{37} +(0.624475 - 0.834200i) q^{38} +(9.54558 - 8.27129i) q^{39} +(-0.673429 - 2.13225i) q^{40} +(5.94139 - 1.74455i) q^{41} +(-1.89757 - 5.08759i) q^{42} +(-4.07183 + 3.04813i) q^{43} +(4.03702 - 2.59443i) q^{44} +(14.7458 - 11.5133i) q^{45} +(-4.72789 - 0.804410i) q^{46} +(1.23406 + 1.23406i) q^{47} +(-0.716649 + 3.29438i) q^{48} +(-4.36120 - 0.627045i) q^{49} +(0.558994 + 4.96865i) q^{50} +(2.86948 + 9.77254i) q^{51} +(1.30922 - 3.51016i) q^{52} +(-0.363668 + 5.08474i) q^{53} +(-17.9088 + 2.57490i) q^{54} +(-9.97566 + 3.95339i) q^{55} +(-1.21719 - 1.05470i) q^{56} +(3.43290 - 0.746781i) q^{57} +(4.79663 - 1.04344i) q^{58} +(-6.22131 - 5.39080i) q^{59} +(2.99175 - 6.91969i) q^{60} +(-6.21156 + 0.893088i) q^{61} +(0.137997 - 1.92944i) q^{62} +(4.70902 - 12.6254i) q^{63} +(0.281733 + 0.959493i) q^{64} +(-4.38492 + 7.13784i) q^{65} +(16.0142 + 2.30249i) q^{66} +(1.82251 - 8.37794i) q^{67} +(2.13617 + 2.13617i) q^{68} +(-10.2705 - 12.4879i) q^{69} +(2.21634 + 2.83860i) q^{70} +(2.20559 - 1.41744i) q^{71} +(-6.69777 + 5.01389i) q^{72} +(-0.0961803 - 0.257869i) q^{73} +(-6.26202 + 1.83869i) q^{74} +(-9.54559 + 13.8941i) q^{75} +(0.787525 - 0.682395i) q^{76} +(-4.63173 + 6.18727i) q^{77} +(11.0856 - 6.05321i) q^{78} +(-6.22707 + 7.18643i) q^{79} +(-0.204797 - 2.22667i) q^{80} +(-30.2006 - 19.4088i) q^{81} +(6.17644 - 0.441748i) q^{82} +(1.41645 + 2.59404i) q^{83} +(-0.772762 - 5.37468i) q^{84} +(-3.76681 - 5.60744i) q^{85} +(-4.62670 + 2.11294i) q^{86} +(14.5254 + 7.93145i) q^{87} +(4.49625 - 1.67701i) q^{88} +(-0.560355 + 3.89736i) q^{89} +(16.8562 - 8.11577i) q^{90} +6.03381i q^{91} +(-4.44885 - 1.79101i) q^{92} +(4.61147 - 4.61147i) q^{93} +(0.943540 + 1.46818i) q^{94} +(-2.02196 + 1.15801i) q^{95} +(-1.40054 + 3.06676i) q^{96} +(3.14313 - 5.75621i) q^{97} +(-4.12824 - 1.53975i) q^{98} +(26.2923 + 30.3430i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) $ 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$3$	2.02042	+	2.69897i	1.16649	+	1.55825i	0.767174	+	0.641439i	$0.221662\pi$
$3$	2.02042	+	2.69897i	1.16649	+	1.55825i	0.399318	+	0.916813i	$0.369247\pi$
$4$	0.909632	+	0.415415i	0.454816	+	0.207708i
$5$	−1.81692	−	1.30338i	−0.812550	−	0.582891i
$5$	−1.81692	−	1.30338i	−0.812550	−	0.582891i
$6$	1.40054	+	3.06676i	0.571769	+	1.25200i
$7$	−1.60647	−	0.114897i	−0.607190	−	0.0434271i	−0.235640	−	0.971840i	$-0.575719\pi$
$7$	−1.60647	−	0.114897i	−0.607190	−	0.0434271i	−0.371549	+	0.928413i	$0.621173\pi$
$8$	0.800541	+	0.599278i	0.283034	+	0.211877i
$9$	−2.35713	+	8.02765i	−0.785710	+	2.67588i
$10$	−1.49834	−	1.65981i	−0.473817	−	0.524878i
$11$	2.59443	−	4.03702i	0.782251	−	1.21721i	−0.189658	−	0.981850i	$-0.560738\pi$
$11$	2.59443	−	4.03702i	0.782251	−	1.21721i	0.971909	−	0.235357i	$-0.0756258\pi$
$12$	0.716649	+	3.29438i	0.206879	+	0.951007i
$13$	−0.267263	−	3.73682i	−0.0741253	−	1.03641i	−0.889339	−	0.457248i	$-0.848835\pi$
$13$	−0.267263	−	3.73682i	−0.0741253	−	1.03641i	0.815214	−	0.579160i	$-0.196619\pi$
$14$	−1.54534	−	0.453752i	−0.413009	−	0.121270i
$15$	−0.153151	−	7.53719i	−0.0395434	−	1.94610i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	2.83053	+	1.05573i	0.686504	+	0.256053i	0.668420	−	0.743784i	$-0.266971\pi$
$17$	2.83053	+	1.05573i	0.686504	+	0.256053i	0.0180837	+	0.999836i	$0.494243\pi$
$18$	−4.00966	+	7.34315i	−0.945086	+	1.73080i
$19$	0.432881	−	0.947878i	0.0993098	−	0.217458i	−0.853455	−	0.521166i	$-0.825497\pi$
$19$	0.432881	−	0.947878i	0.0993098	−	0.217458i	0.952765	+	0.303708i	$0.0982246\pi$
$20$	−1.11128	−	1.94037i	−0.248490	−	0.433881i
$21$	−2.93565	−	4.56796i	−0.640612	−	0.996811i
$22$	3.39327	−	3.39327i	0.723448	−	0.723448i
$23$	−4.79083	+	0.218958i	−0.998957	+	0.0456558i
$23$	−4.79083	+	0.218958i	−0.998957	+	0.0456558i
$24$			3.37143i			0.688191i
$25$	1.60238	+	4.73628i	0.320476	+	0.947256i
$26$	0.533163	−	3.70823i	0.104562	−	0.727244i
$27$	−16.9522	+	6.32284i	−3.26245	+	1.21683i
$28$	−1.41357	−	0.771867i	−0.267139	−	0.145869i
$29$	4.46522	−	2.03920i	0.829170	−	0.378669i	0.0448255	−	0.998995i	$-0.485727\pi$
$29$	4.46522	−	2.03920i	0.829170	−	0.378669i	0.784344	+	0.620326i	$0.213000\pi$
$30$	1.45250	−	7.39750i	0.265188	−	1.35059i
$31$	−0.275290	−	1.91468i	−0.0494435	−	0.343887i	−0.999494	−	0.0317926i	$-0.989878\pi$
$31$	−0.275290	−	1.91468i	−0.0494435	−	0.343887i	0.950051	−	0.312095i	$-0.101031\pi$
$32$	0.479249	+	0.877679i	0.0847201	+	0.155153i
$33$	16.1376	−	1.15419i	2.80920	−	0.200918i
$34$	2.54143	+	1.63328i	0.435852	+	0.280105i
$35$	2.76907	+	2.30261i	0.468059	+	0.389212i
$36$	−5.47893	+	6.32302i	−0.913154	+	1.05384i
$37$	−5.72807	+	3.12776i	−0.941689	+	0.514201i	−0.875293	−	0.483592i	$-0.839332\pi$
$37$	−5.72807	+	3.12776i	−0.941689	+	0.514201i	−0.0663955	+	0.997793i	$0.521150\pi$
$38$	0.624475	−	0.834200i	0.101303	−	0.135325i
$39$	9.54558	−	8.27129i	1.52852	−	1.32447i
$40$	−0.673429	−	2.13225i	−0.106478	−	0.337138i
$41$	5.94139	−	1.74455i	0.927889	−	0.272453i	0.217336	−	0.976097i	$-0.430263\pi$
$41$	5.94139	−	1.74455i	0.927889	−	0.272453i	0.710553	+	0.703644i	$0.248445\pi$
$42$	−1.89757	−	5.08759i	−0.292802	−	0.785032i
$43$	−4.07183	+	3.04813i	−0.620948	+	0.464836i	−0.862847	−	0.505466i	$-0.831321\pi$
$43$	−4.07183	+	3.04813i	−0.620948	+	0.464836i	0.241899	+	0.970301i	$0.422230\pi$
$44$	4.03702	−	2.59443i	0.608603	−	0.391126i
$45$	14.7458	−	11.5133i	2.19818	−	1.71631i
$46$	−4.72789	−	0.804410i	−0.697089	−	0.118604i
$47$	1.23406	+	1.23406i	0.180006	+	0.180006i	0.791359	−	0.611352i	$-0.209374\pi$
$47$	1.23406	+	1.23406i	0.180006	+	0.180006i	−0.611352	+	0.791359i	$0.709374\pi$
$48$	−0.716649	+	3.29438i	−0.103439	+	0.475503i
$49$	−4.36120	−	0.627045i	−0.623028	−	0.0895779i
$50$	0.558994	+	4.96865i	0.0790536	+	0.702674i
$51$	2.86948	+	9.77254i	0.401807	+	1.36843i
$52$	1.30922	−	3.51016i	0.181556	−	0.486771i
$53$	−0.363668	+	5.08474i	−0.0499536	+	0.698443i	0.909344	+	0.416045i	$0.136584\pi$
$53$	−0.363668	+	5.08474i	−0.0499536	+	0.698443i	−0.959297	+	0.282398i	$0.908870\pi$
$54$	−17.9088	+	2.57490i	−2.43708	+	0.350399i
$55$	−9.97566	+	3.95339i	−1.34512	+	0.533075i
$56$	−1.21719	−	1.05470i	−0.162654	−	0.140941i
$57$	3.43290	−	0.746781i	0.454698	−	0.0989136i
$58$	4.79663	−	1.04344i	0.629829	−	0.137011i
$59$	−6.22131	−	5.39080i	−0.809946	−	0.701822i	0.147932	−	0.988998i	$-0.452738\pi$
$59$	−6.22131	−	5.39080i	−0.809946	−	0.701822i	−0.957878	+	0.287175i	$0.907284\pi$
$60$	2.99175	−	6.91969i	0.386234	−	0.893329i
$61$	−6.21156	+	0.893088i	−0.795309	+	0.114348i	−0.527980	−	0.849257i	$-0.677050\pi$
$61$	−6.21156	+	0.893088i	−0.795309	+	0.114348i	−0.267329	+	0.963605i	$0.586141\pi$
$62$	0.137997	−	1.92944i	0.0175256	−	0.245040i
$63$	4.70902	−	12.6254i	0.593281	−	1.59065i
$64$	0.281733	+	0.959493i	0.0352166	+	0.119937i
$65$	−4.38492	+	7.13784i	−0.543882	+	0.885340i
$66$	16.0142	+	2.30249i	1.97121	+	0.283417i
$67$	1.82251	−	8.37794i	0.222655	−	1.02353i	−0.721087	−	0.692845i	$-0.756357\pi$
$67$	1.82251	−	8.37794i	0.222655	−	1.02353i	0.943742	−	0.330684i	$-0.107279\pi$
$68$	2.13617	+	2.13617i	0.259049	+	0.259049i
$69$	−10.2705	−	12.4879i	−1.23642	−	1.50337i
$70$	2.21634	+	2.83860i	0.264903	+	0.339277i
$71$	2.20559	−	1.41744i	0.261755	−	0.168220i	−0.403181	−	0.915120i	$-0.632095\pi$
$71$	2.20559	−	1.41744i	0.261755	−	0.168220i	0.664936	+	0.746901i	$0.268459\pi$
$72$	−6.69777	+	5.01389i	−0.789340	+	0.590892i
$73$	−0.0961803	−	0.257869i	−0.0112571	−	0.0301813i	0.931200	−	0.364510i	$-0.118763\pi$
$73$	−0.0961803	−	0.257869i	−0.0112571	−	0.0301813i	−0.942457	+	0.334328i	$0.891491\pi$
$74$	−6.26202	+	1.83869i	−0.727945	+	0.213744i
$75$	−9.54559	+	13.8941i	−1.10223	+	1.60435i
$76$	0.787525	−	0.682395i	0.0903354	−	0.0782760i
$77$	−4.63173	+	6.18727i	−0.527835	+	0.705105i
$78$	11.0856	−	6.05321i	1.25520	−	0.685391i
$79$	−6.22707	+	7.18643i	−0.700601	+	0.808536i	−0.988834	−	0.149024i	$-0.952387\pi$
$79$	−6.22707	+	7.18643i	−0.700601	+	0.808536i	0.288233	+	0.957560i	$0.406932\pi$
$80$	−0.204797	−	2.22667i	−0.0228970	−	0.248949i
$81$	−30.2006	−	19.4088i	−3.35562	−	2.15653i
$82$	6.17644	−	0.441748i	0.682074	−	0.0487829i
$83$	1.41645	+	2.59404i	0.155476	+	0.284733i	0.943794	−	0.330536i	$-0.107229\pi$
$83$	1.41645	+	2.59404i	0.155476	+	0.284733i	−0.788317	+	0.615269i	$0.789048\pi$
$84$	−0.772762	−	5.37468i	−0.0843153	−	0.586426i
$85$	−3.76681	−	5.60744i	−0.408568	−	0.608213i
$86$	−4.62670	+	2.11294i	−0.498910	+	0.227844i
$87$	14.5254	+	7.93145i	1.55728	+	0.850340i
$88$	4.49625	−	1.67701i	0.479302	−	0.178770i
$89$	−0.560355	+	3.89736i	−0.0593976	+	0.413119i	0.938330	+	0.345741i	$0.112372\pi$
$89$	−0.560355	+	3.89736i	−0.0593976	+	0.413119i	−0.997728	+	0.0673780i	$0.978537\pi$
$90$	16.8562	−	8.11577i	1.77680	−	0.855477i
$91$			6.03381i			0.632515i
$92$	−4.44885	−	1.79101i	−0.463825	−	0.186726i
$93$	4.61147	−	4.61147i	0.478187	−	0.478187i
$94$	0.943540	+	1.46818i	0.0973187	+	0.151431i
$95$	−2.02196	+	1.15801i	−0.207449	+	0.118809i
$96$	−1.40054	+	3.06676i	−0.142942	+	0.313000i
$97$	3.14313	−	5.75621i	0.319137	−	0.584455i	−0.668033	−	0.744132i	$-0.732863\pi$
$97$	3.14313	−	5.75621i	0.319137	−	0.584455i	0.987169	+	0.159677i	$0.0510452\pi$
$98$	−4.12824	−	1.53975i	−0.417015	−	0.155539i
$99$	26.2923	+	30.3430i	2.64248	+	3.04958i
$100$	−0.509945	+	4.97393i	−0.0509945	+	0.497393i
$101$	12.1610	+	3.57078i	1.21006	+	0.355306i	0.823691	−	0.567038i	$-0.191911\pi$
$101$	12.1610	+	3.57078i	1.21006	+	0.355306i	0.386369	+	0.922344i	$0.373729\pi$
$102$	0.726597	+	10.1592i	0.0719438	+	1.00591i
$103$	1.18018	+	5.42518i	0.116286	+	0.534559i	0.998025	+	0.0628207i	$0.0200096\pi$
$103$	1.18018	+	5.42518i	0.116286	+	0.534559i	−0.881739	+	0.471738i	$0.843627\pi$
$104$	2.02544	−	3.15164i	0.198611	−	0.309044i
$105$	−0.619970	+	12.1259i	−0.0605029	+	1.18337i
$106$	−1.43620	+	4.89124i	−0.139496	+	0.475079i
$107$	−1.86446	−	1.39572i	−0.180244	−	0.134929i	0.505346	−	0.862917i	$-0.331365\pi$
$107$	−1.86446	−	1.39572i	−0.180244	−	0.134929i	−0.685590	+	0.727988i	$0.740456\pi$
$108$	−18.0469	−	1.29074i	−1.73656	−	0.124201i
$109$	−4.89062	−	10.7090i	−0.468437	−	1.02573i	−0.985483	−	0.169775i	$-0.945696\pi$
$109$	−4.89062	−	10.7090i	−0.468437	−	1.02573i	0.517046	−	0.855957i	$-0.327032\pi$
$110$	−10.5880	+	1.74256i	−1.00953	+	0.166147i
$111$	−20.0149	−	9.14048i	−1.89973	−	0.867576i
$112$	−0.965182	−	1.28933i	−0.0912012	−	0.121830i
$113$	11.9822	+	2.60658i	1.12719	+	0.245206i	0.737242	−	0.675629i	$-0.236128\pi$
$113$	11.9822	+	2.60658i	1.12719	+	0.245206i	0.389952	+	0.920835i	$0.372491\pi$
$114$	3.51319			0.329040
$115$	8.98993	+	5.84646i	0.838316	+	0.545185i
$116$	4.90882			0.455772
$117$	30.6278	+	6.66268i	2.83155	+	0.615965i
$118$	−4.93324	−	6.59004i	−0.454142	−	0.606662i
$119$	−4.42587	−	2.02123i	−0.405718	−	0.185285i
$120$	4.39427	−	6.12562i	0.401140	−	0.559190i
$121$	−4.99686	−	10.9416i	−0.454260	−	0.994691i
$122$	−6.25945	−	0.447685i	−0.566704	−	0.0405315i
$123$	16.7126	+	12.5109i	1.50692	+	1.12807i
$124$	0.544976	−	1.85602i	0.0489403	−	0.166675i
$125$	3.26180	−	10.6940i	0.291744	−	0.956496i
$126$	7.28512	−	11.3359i	0.649010	−	1.00988i
$127$	2.65635	+	12.2110i	0.235713	+	1.08355i	0.931056	+	0.364877i	$0.118889\pi$
$127$	2.65635	+	12.2110i	0.235713	+	1.08355i	−0.695343	+	0.718678i	$0.744747\pi$
$128$	0.0713392	+	0.997452i	0.00630555	+	0.0881631i
$129$	−16.4536	−	4.83122i	−1.44866	−	0.425365i
$130$	−5.80196	+	6.04264i	−0.508866	+	0.529974i
$131$	4.51626	+	5.21204i	0.394587	+	0.455378i	0.917929	−	0.396745i	$-0.129860\pi$
$131$	4.51626	+	5.21204i	0.394587	+	0.455378i	−0.523342	+	0.852123i	$0.675315\pi$
$132$	15.1588	+	5.65394i	1.31940	+	0.492112i
$133$	−0.804321	+	1.47300i	−0.0697434	+	0.127726i
$134$	3.56172	−	7.79908i	0.307686	−	0.673738i
$135$	39.0418	+	10.6071i	3.36019	+	0.912916i
$136$	1.63328	+	2.54143i	0.140052	+	0.217926i
$137$	−10.9066	+	10.9066i	−0.931816	+	0.931816i	−0.997819	−	0.0660030i	$-0.978975\pi$
$137$	−10.9066	+	10.9066i	−0.931816	+	0.931816i	0.0660030	+	0.997819i	$0.478975\pi$
$138$	−7.38126	−	14.3857i	−0.628334	−	1.22459i
$139$		−	15.5890i		−	1.32224i	−0.750279	−	0.661121i	$-0.770081\pi$
$139$		−	15.5890i		−	1.32224i	0.750279	−	0.661121i	$-0.229919\pi$
$140$	1.56230	+	3.24484i	0.132038	+	0.274239i
$141$	−0.837367	+	5.82402i	−0.0705191	+	0.490471i
$142$	2.45648	−	0.916220i	0.206143	−	0.0768875i
$143$	−15.7790	−	8.61599i	−1.31951	−	0.720505i
$144$	−7.61048	+	3.47559i	−0.634207	+	0.289633i
$145$	−10.7708	−	2.11484i	−0.894465	−	0.175628i
$146$	−0.0391682	−	0.272421i	−0.00324158	−	0.0225457i
$147$	−7.11909	−	13.0376i	−0.587173	−	1.07533i
$148$	−6.50976	+	0.465587i	−0.535099	+	0.0382710i
$149$	9.33018	+	5.99614i	0.764358	+	0.491223i	0.863809	−	0.503819i	$-0.168072\pi$
$149$	9.33018	+	5.99614i	0.764358	+	0.491223i	−0.0994508	+	0.995042i	$0.531709\pi$
$150$	−12.2808	+	11.5475i	−1.00273	+	0.942849i
$151$	−10.8327	+	12.5016i	−0.881552	+	1.01737i	0.118151	+	0.992996i	$0.462303\pi$
$151$	−10.8327	+	12.5016i	−0.881552	+	1.01737i	−0.999703	+	0.0243698i	$0.992242\pi$
$152$	0.914582	−	0.499399i	0.0741824	−	0.0405066i
$153$	−15.1470	+	20.2340i	−1.22456	+	1.63582i
$154$	−5.84108	+	5.06132i	−0.470688	+	0.407853i
$155$	−1.99539	+	3.83763i	−0.160273	+	0.308246i
$156$	12.1190	−	3.55846i	0.970295	−	0.284904i
$157$	0.395547	+	1.06050i	0.0315681	+	0.0846373i	0.951778	−	0.306789i	$-0.0992546\pi$
$157$	0.395547	+	1.06050i	0.0315681	+	0.0846373i	−0.920210	+	0.391426i	$0.871982\pi$
$158$	−7.61235	+	5.69853i	−0.605606	+	0.453351i
$159$	−14.4583	+	9.29180i	−1.14662	+	0.736888i
$160$	0.273196	−	2.21932i	0.0215981	−	0.175452i
$161$	7.72150	+	0.198703i	0.608539	+	0.0156600i
$162$	−25.3848	−	25.3848i	−1.99442	−	1.99442i
$163$	−3.11194	+	14.3054i	−0.243746	+	1.12048i	0.678718	+	0.734399i	$0.262536\pi$
$163$	−3.11194	+	14.3054i	−0.243746	+	1.12048i	−0.922464	+	0.386083i	$0.873828\pi$
$164$	6.12919	+	0.881244i	0.478609	+	0.0688136i
$165$	−30.8251	−	18.9365i	−2.39973	−	1.47420i
$166$	0.832680	+	2.83585i	0.0646285	+	0.220105i
$167$	−3.32429	+	8.91277i	−0.257241	+	0.689691i	0.742560	+	0.669779i	$0.233611\pi$
$167$	−3.32429	+	8.91277i	−0.257241	+	0.689691i	−0.999802	+	0.0199116i	$0.993662\pi$
$168$	0.387368	−	5.41611i	0.0298861	−	0.417862i
$169$	−1.02471	+	0.147332i	−0.0788241	+	0.0113332i
$170$	−2.48878	−	6.27999i	−0.190881	−	0.481653i
$171$	6.58887	+	5.70929i	0.503864	+	0.436600i
$172$	−4.97010	+	1.08118i	−0.378967	+	0.0824392i
$173$	20.7693	−	4.51808i	1.57906	−	0.343504i	0.664289	−	0.747476i	$-0.268734\pi$
$173$	20.7693	−	4.51808i	1.57906	−	0.343504i	0.914771	+	0.403972i	$0.132371\pi$
$174$	12.5075	+	10.8378i	0.948188	+	0.821610i
$175$	−2.03000	−	7.79282i	−0.153453	−	0.589082i
$176$	4.74997	−	0.682942i	0.358042	−	0.0514787i
$177$	1.97992	−	27.6828i	0.148820	−	2.08077i
$178$	−1.37599	+	3.68918i	−0.103135	+	0.276516i
$179$	1.35032	+	4.59878i	0.100928	+	0.343729i	0.994439	−	0.105312i	$-0.0335840\pi$
$179$	1.35032	+	4.59878i	0.100928	+	0.343729i	−0.893511	+	0.449041i	$0.851766\pi$
$180$	18.1961	−	4.34726i	1.35626	−	0.324026i
$181$	23.0409	+	3.31278i	1.71261	+	0.246237i	0.927689	−	0.373354i	$-0.121792\pi$
$181$	23.0409	+	3.31278i	1.71261	+	0.246237i	0.784925	+	0.619591i	$0.212701\pi$
$182$	−1.28258	+	5.89592i	−0.0950710	+	0.437034i
$183$	−14.9604	−	14.9604i	−1.10590	−	1.10590i
$184$	−3.96647	−	2.69575i	−0.292412	−	0.198734i
$185$	14.4841	+	1.78298i	1.06489	+	0.131088i
$186$	5.48633	−	3.52585i	0.402277	−	0.258528i
$187$	11.6056	−	8.68787i	0.848688	−	0.635320i
$188$	0.609894	+	1.63519i	0.0444811	+	0.119258i
$189$	27.9597	−	8.20971i	2.03377	−	0.597169i
$190$	−2.22190	+	0.701744i	−0.161194	+	0.0509098i
$191$	8.21279	−	7.11642i	0.594256	−	0.514926i	−0.304998	−	0.952353i	$-0.598656\pi$
$191$	8.21279	−	7.11642i	0.594256	−	0.514926i	0.899254	+	0.437427i	$0.144110\pi$
$192$	−2.02042	+	2.69897i	−0.145812	+	0.194781i
$193$	−13.4073	+	7.32092i	−0.965077	+	0.526972i	−0.882857	−	0.469642i	$-0.844383\pi$
$193$	−13.4073	+	7.32092i	−0.965077	+	0.526972i	−0.0822199	+	0.996614i	$0.526201\pi$
$194$	4.29487	−	4.95655i	0.308354	−	0.355859i
$195$	−28.1242	+	2.58671i	−2.01402	+	0.185238i
$196$	−3.70660	−	2.38209i	−0.264757	−	0.170149i
$197$	−4.75648	+	0.340190i	−0.338885	+	0.0242375i	−0.239745	−	0.970836i	$-0.577064\pi$
$197$	−4.75648	+	0.340190i	−0.338885	+	0.0242375i	−0.0991401	+	0.995073i	$0.531609\pi$
$198$	19.2416	+	35.2384i	1.36744	+	2.50428i
$199$	−1.43619	−	9.98893i	−0.101809	−	0.708096i	−0.975240	−	0.221149i	$-0.929019\pi$
$199$	−1.43619	−	9.98893i	−0.101809	−	0.708096i	0.873431	−	0.486948i	$-0.161890\pi$
$200$	−1.55558	+	4.75186i	−0.109996	+	0.336007i
$201$	26.2941	−	12.0081i	1.85464	−	0.846986i
$202$	11.1240	+	6.07417i	0.782683	+	0.427377i
$203$	−7.40755	+	2.76287i	−0.519908	+	0.193916i
$204$	−1.44949	+	10.0814i	−0.101485	+	0.705842i
$205$	−13.0688	−	4.57421i	−0.912767	−	0.319476i
$206$			5.55206i			0.386831i
$207$	9.53489	−	38.9752i	0.662721	−	2.70896i
$208$	2.64908	−	2.64908i	0.183681	−	0.183681i
$209$	−2.70352	−	4.20676i	−0.187006	−	0.290987i
$210$	−3.18335	+	11.7170i	−0.219672	+	0.808550i
$211$	−6.45464	+	14.1337i	−0.444355	+	0.973003i	0.546423	+	0.837509i	$0.315989\pi$
$211$	−6.45464	+	14.1337i	−0.444355	+	0.973003i	−0.990778	+	0.135493i	$0.956738\pi$
$212$	−2.44308	+	4.47417i	−0.167792	+	0.307287i
$213$	8.28186	+	3.08897i	0.567464	+	0.211653i
$214$	−1.52517	−	1.76014i	−0.104259	−	0.120321i
$215$	11.3711	−	0.231053i	0.775500	−	0.0157577i
$216$	−17.3601	−	5.09738i	−1.18120	−	0.346833i
$217$	0.222254	+	3.10752i	0.0150876	+	0.210952i
$218$	−2.50250	−	11.5038i	−0.169491	−	0.779136i
$219$	0.501657	−	0.780593i	0.0338988	−	0.0527476i
$220$	−10.7165	−	0.547909i	−0.722505	−	0.0369400i
$221$	3.18859	−	10.8593i	0.214488	−	0.730478i
$222$	−17.6145	−	13.1861i	−1.18221	−	0.884990i
$223$	−1.07759	−	0.0770710i	−0.0721610	−	0.00516105i	0.0352120	−	0.999380i	$-0.488789\pi$
$223$	−1.07759	−	0.0770710i	−0.0721610	−	0.00516105i	−0.107373	+	0.994219i	$0.534244\pi$
$224$	−0.669058	−	1.46503i	−0.0447033	−	0.0978866i
$225$	−41.7982	+	1.69933i	−2.78655	+	0.113288i
$226$	11.1543	+	5.09402i	0.741976	+	0.338849i
$227$	1.25870	+	1.68143i	0.0835430	+	0.111600i	0.840366	−	0.542020i	$-0.182340\pi$
$227$	1.25870	+	1.68143i	0.0835430	+	0.111600i	−0.756823	+	0.653620i	$0.773249\pi$
$228$	3.43290	+	0.746781i	0.227349	+	0.0494568i
$229$	−1.90049			−0.125588			−0.0627939	−	0.998027i	$-0.520001\pi$
$229$	−1.90049			−0.125588			−0.0627939	+	0.998027i	$0.520001\pi$
$230$	7.54173	+	7.62380i	0.497287	+	0.502698i
$231$	−26.0573			−1.71444
$232$	4.79663	+	1.04344i	0.314915	+	0.0685055i
$233$	0.838591	+	1.12023i	0.0549379	+	0.0733885i	0.827169	−	0.561954i	$-0.189950\pi$
$233$	0.838591	+	1.12023i	0.0549379	+	0.0733885i	−0.772231	+	0.635342i	$0.780859\pi$
$234$	28.5116	+	13.0208i	1.86386	+	0.851198i
$235$	−0.633733	−	3.85064i	−0.0413402	−	0.251188i
$236$	−3.41969	−	7.48807i	−0.222603	−	0.487432i
$237$	−31.9773	−	2.28706i	−2.07715	−	0.148561i
$238$	−3.89508	−	2.91582i	−0.252480	−	0.189005i
$239$	5.80506	−	19.7702i	0.375498	−	1.27883i	−0.527637	−	0.849470i	$-0.676922\pi$
$239$	5.80506	−	19.7702i	0.375498	−	1.27883i	0.903134	−	0.429358i	$-0.141260\pi$
$240$	5.59594	−	5.05156i	0.361216	−	0.326077i
$241$	−6.22601	+	9.68786i	−0.401053	+	0.624050i	−0.981774	−	0.190052i	$-0.939134\pi$
$241$	−6.22601	+	9.68786i	−0.401053	+	0.624050i	0.580721	+	0.814102i	$0.302771\pi$
$242$	−2.55686	−	11.7537i	−0.164361	−	0.755558i
$243$	−4.76217	−	66.5838i	−0.305493	−	4.27136i
$244$	−6.02124	−	1.76799i	−0.385470	−	0.113184i
$245$	7.10666	+	6.82360i	0.454028	+	0.435944i
$246$	13.6713	+	15.7775i	0.871649	+	1.00594i
$247$	−3.65774	−	1.36427i	−0.232737	−	0.0868063i
$248$	0.927046	−	1.69776i	0.0588675	−	0.107808i
$249$	−4.13940	+	9.06403i	−0.262324	+	0.574410i
$250$	5.46042	−	9.75622i	0.345347	−	0.617038i
$251$	−3.31309	−	5.15526i	−0.209120	−	0.325397i	0.720811	−	0.693132i	$-0.243770\pi$
$251$	−3.31309	−	5.15526i	−0.209120	−	0.325397i	−0.929931	+	0.367735i	$0.880133\pi$
$252$	9.52824	−	9.52824i	0.600223	−	0.600223i
$253$	−11.5456	+	19.9087i	−0.725863	+	1.25165i
$254$			12.4966i			0.784108i
$255$	7.52376	−	21.4959i	0.471156	−	1.34613i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	25.2311	−	9.41072i	1.57387	−	0.587025i	0.597265	−	0.802044i	$-0.296254\pi$
$257$	25.2311	−	9.41072i	1.57387	−	0.587025i	0.976610	+	0.215019i	$0.0689815\pi$
$258$	−15.0507	−	8.21828i	−0.937013	−	0.511648i
$259$	9.56136	−	4.36653i	0.594114	−	0.271323i
$260$	−6.95383	+	4.67125i	−0.431258	+	0.289699i
$261$	5.84485	+	40.6518i	0.361787	+	2.51629i
$262$	3.30515	+	6.05293i	0.204193	+	0.373951i
$263$	−12.4570	+	0.890943i	−0.768132	+	0.0549379i	−0.449905	−	0.893076i	$-0.648542\pi$
$263$	−12.4570	+	0.890943i	−0.768132	+	0.0549379i	−0.318227	+	0.948014i	$0.603088\pi$
$264$	13.6105	+	8.74696i	0.837670	+	0.538338i
$265$	7.28812	−	8.76456i	0.447706	−	0.538403i
$266$	−1.09905	+	1.26837i	−0.0673870	+	0.0777687i
$267$	−11.6510	+	6.36193i	−0.713030	+	0.389344i
$268$	5.13814	−	6.86375i	0.313862	−	0.419270i
$269$	20.3565	−	17.6390i	1.24116	−	1.07547i	0.246833	−	0.969058i	$-0.420610\pi$
$269$	20.3565	−	17.6390i	1.24116	−	1.07547i	0.994322	−	0.106409i	$-0.0339352\pi$
$270$	35.8949	+	18.6637i	2.18449	+	1.13583i
$271$	−4.27589	+	1.25551i	−0.259742	+	0.0762670i	−0.409011	−	0.912530i	$-0.634126\pi$
$271$	−4.27589	+	1.25551i	−0.259742	+	0.0762670i	0.149269	+	0.988797i	$0.452308\pi$
$272$	1.05573	+	2.83053i	0.0640132	+	0.171626i
$273$	−16.2851	+	12.1908i	−0.985617	+	0.737824i
$274$	−12.9758	+	8.33901i	−0.783894	+	0.503778i
$275$	23.2777	+	5.81913i	1.40370	+	0.350907i
$276$	−4.15468	−	15.6259i	−0.250082	−	0.940570i
$277$	7.15110	+	7.15110i	0.429668	+	0.429668i	0.888515	−	0.458847i	$-0.151738\pi$
$277$	7.15110	+	7.15110i	0.429668	+	0.429668i	−0.458847	+	0.888515i	$0.651738\pi$
$278$	3.31368	−	15.2328i	0.198741	−	0.913600i
$279$	16.0193	+	2.30323i	0.959051	+	0.137891i
$280$	0.836856	+	3.50278i	0.0500117	+	0.209331i
$281$	−8.37990	−	28.5393i	−0.499903	−	1.70251i	−0.692659	−	0.721265i	$-0.743561\pi$
$281$	−8.37990	−	28.5393i	−0.499903	−	1.70251i	0.192756	−	0.981247i	$-0.438257\pi$
$282$	−2.05622	+	5.51293i	−0.122446	+	0.328290i
$283$	2.19883	−	30.7436i	0.130707	−	1.82752i	−0.334589	−	0.942364i	$-0.608598\pi$
$283$	2.19883	−	30.7436i	0.130707	−	1.82752i	0.465296	−	0.885155i	$-0.345948\pi$
$284$	2.59510	−	0.373119i	0.153991	−	0.0221405i
$285$	−7.21064	−	3.11754i	−0.427121	−	0.184667i
$286$	−13.5869	−	11.7732i	−0.803413	−	0.696161i
$287$	−9.74512	+	2.11992i	−0.575236	+	0.125135i
$288$	−8.17535	+	1.77844i	−0.481737	+	0.104795i
$289$	−5.95042	−	5.15607i	−0.350025	−	0.303298i
$290$	−10.0751	−	4.35600i	−0.591630	−	0.255793i
$291$	21.8863	−	3.14678i	1.28300	−	0.184467i
$292$	0.0196341	−	0.274521i	0.00114900	−	0.0160651i
$293$	−0.0229980	+	0.0616599i	−0.00134355	+	0.00360221i	−0.937620	−	0.347662i	$-0.886976\pi$
$293$	−0.0229980	+	0.0616599i	−0.00134355	+	0.00360221i	0.936276	+	0.351265i	$0.114248\pi$
$294$	−4.18505	−	14.2530i	−0.244077	−	0.831249i
$295$	4.27734	+	17.9034i	0.249036	+	1.04238i
$296$	−6.45995	−	0.928801i	−0.375477	−	0.0539855i
$297$	−18.4559	+	84.8405i	−1.07092	+	4.92295i
$298$	7.84239	+	7.84239i	0.454297	+	0.454297i
$299$	2.09862	+	17.8440i	0.121366	+	1.03194i
$300$	−14.4548	+	8.67312i	−0.834547	+	0.500743i
$301$	6.89150	−	4.42890i	0.397219	−	0.255277i
$302$	−13.2425	+	9.91324i	−0.762023	+	0.570443i
$303$	14.9329	+	40.0366i	0.857871	+	2.30004i
$304$	0.999835	−	0.293578i	0.0573445	−	0.0168379i
$305$	12.4499	+	6.47338i	0.712881	+	0.370665i
$306$	−19.1019	+	16.5519i	−1.09198	+	0.946207i
$307$	3.74258	−	4.99950i	0.213600	−	0.285337i	−0.680926	−	0.732352i	$-0.738422\pi$
$307$	3.74258	−	4.99950i	0.213600	−	0.285337i	0.894526	+	0.447016i	$0.147513\pi$
$308$	−6.78345	+	3.70405i	−0.386523	+	0.211058i
$309$	−12.2579	+	14.1464i	−0.697330	+	0.804762i
$310$	−2.76554	+	3.32578i	−0.157072	+	0.188892i
$311$	−15.7976	−	10.1525i	−0.895801	−	0.575696i	0.00974118	−	0.999953i	$-0.496899\pi$
$311$	−15.7976	−	10.1525i	−0.895801	−	0.575696i	−0.905542	+	0.424256i	$0.860536\pi$
$312$	12.5984	−	0.901058i	0.713246	−	0.0510123i
$313$	−11.0572	−	20.2497i	−0.624988	−	1.14458i	−0.977930	−	0.208934i	$-0.933001\pi$
$313$	−11.0572	−	20.2497i	−0.624988	−	1.14458i	0.352942	−	0.935645i	$-0.385181\pi$
$314$	0.161081	+	1.12035i	0.00909035	+	0.0632248i
$315$	−25.0116	+	16.8016i	−1.40924	+	0.946663i
$316$	−8.64970	+	3.95018i	−0.486583	+	0.222215i
$317$	21.0904	+	11.5162i	1.18455	+	0.646816i	0.945954	−	0.324302i	$-0.105129\pi$
$317$	21.0904	+	11.5162i	1.18455	+	0.646816i	0.238601	+	0.971118i	$0.423311\pi$
$318$	−16.1030	+	6.00612i	−0.903013	+	0.336806i
$319$	3.35244	−	23.3167i	0.187701	−	1.30549i
$320$	0.738702	−	2.11053i	0.0412947	−	0.117982i
$321$		−	7.85208i		−	0.438260i
$322$	7.50280	+	1.83548i	0.418115	+	0.102288i
$323$	2.22599	−	2.22599i	0.123857	−	0.123857i
$324$	−19.4088	−	30.2006i	−1.07826	−	1.67781i
$325$	17.2704	−	7.25365i	0.957988	−	0.402360i
$326$	−6.08165	+	13.3169i	−0.336831	+	0.737557i
$327$	19.0221	−	34.8363i	1.05192	−	1.92645i
$328$	5.80180	+	2.16396i	0.320351	+	0.119485i
$329$	−1.84069	−	2.12427i	−0.101481	−	0.117115i
$330$	−26.0954	−	25.0561i	−1.43651	−	1.37929i
$331$	3.45235	+	1.01370i	0.189758	+	0.0557180i	0.375231	−	0.926931i	$-0.377563\pi$
$331$	3.45235	+	1.01370i	0.189758	+	0.0557180i	−0.185473	+	0.982649i	$0.559382\pi$
$332$	0.210848	+	2.94804i	0.0115718	+	0.161795i
$333$	−11.6068	−	53.3555i	−0.636047	−	2.92386i
$334$	−5.14287	+	8.00245i	−0.281405	+	0.437875i
$335$	−14.2310	+	12.8466i	−0.777524	+	0.701885i
$336$	1.52979	−	5.21000i	0.0834571	−	0.284229i
$337$	8.67560	+	6.49447i	0.472590	+	0.353777i	0.808872	−	0.587985i	$-0.200079\pi$
$337$	8.67560	+	6.49447i	0.472590	+	0.353777i	−0.336282	+	0.941761i	$0.609169\pi$
$338$	−1.03261	−	0.0738540i	−0.0561668	−	0.00401713i
$339$	17.1741	+	37.6061i	0.932771	+	2.04248i
$340$	−1.09700	−	6.66550i	−0.0594931	−	0.361488i
$341$	−8.44384	−	3.85617i	−0.457259	−	0.208823i
$342$	5.22470	+	6.97938i	0.282519	+	0.377402i
$343$	17.9505	+	3.90489i	0.969235	+	0.210844i
$344$	−5.08634			−0.274237
$345$	2.38405	+	36.0759i	0.128353	+	1.94226i
$346$	21.2550			1.14268
$347$	−32.9574	−	7.16945i	−1.76925	−	0.384876i	−0.794338	−	0.607476i	$-0.792182\pi$
$347$	−32.9574	−	7.16945i	−1.76925	−	0.384876i	−0.974910	+	0.222599i	$0.928546\pi$
$348$	9.91789	+	13.2487i	0.531655	+	0.710208i
$349$	0.657562	+	0.300298i	0.0351985	+	0.0160746i	0.432936	−	0.901424i	$-0.357477\pi$
$349$	0.657562	+	0.300298i	0.0351985	+	0.0160746i	−0.397738	+	0.917499i	$0.630205\pi$
$350$	−0.327124	−	8.04623i	−0.0174855	−	0.430089i
$351$	28.1580	+	61.6574i	1.50296	+	3.29103i
$352$	4.78659	+	0.342343i	0.255126	+	0.0182470i
$353$	−1.62738	−	1.21824i	−0.0866165	−	0.0648403i	0.555092	−	0.831789i	$-0.312683\pi$
$353$	−1.62738	−	1.21824i	−0.0866165	−	0.0648403i	−0.641708	+	0.766949i	$0.721774\pi$
$354$	7.81908	−	26.6293i	0.415579	−	1.41533i
$355$	−5.85484	−	0.299345i	−0.310743	−	0.0158876i
$356$	−2.12874	+	3.31238i	−0.112823	+	0.175556i
$357$	−3.48690	−	16.0290i	−0.184546	−	0.848345i
$358$	0.341924	+	4.78072i	0.0180712	+	0.252669i
$359$	−6.13505	−	1.80141i	−0.323795	−	0.0950749i	0.115795	−	0.993273i	$-0.463058\pi$
$359$	−6.13505	−	1.80141i	−0.323795	−	0.0950749i	−0.439591	+	0.898198i	$0.644877\pi$
$360$	18.7043	−	0.380060i	0.985804	−	0.0200309i
$361$	11.7313	+	13.5386i	0.617435	+	0.712558i
$362$	21.8101	+	8.13476i	1.14631	+	0.427553i
$363$	19.4353	−	35.5931i	1.02009	−	1.86815i
$364$	−2.50653	+	5.48854i	−0.131378	+	0.287678i
$365$	−0.161351	+	0.593887i	−0.00844549	+	0.0310855i
$366$	−11.4384	−	17.7986i	−0.597897	−	0.930346i
$367$	−3.75744	+	3.75744i	−0.196137	+	0.196137i	−0.798342	−	0.602205i	$-0.794289\pi$
$367$	−3.75744	+	3.75744i	−0.196137	+	0.196137i	0.602205	+	0.798342i	$0.294289\pi$
$368$	−3.30280	−	3.47728i	−0.172171	−	0.181266i
$369$			51.8075i			2.69699i
$370$	13.7741	+	4.82106i	0.716081	+	0.250635i
$371$	1.16845	−	8.12672i	0.0606627	−	0.421918i
$372$	6.11042	−	2.27907i	0.316810	−	0.118164i
$373$	18.8367	+	10.2856i	0.975326	+	0.532568i	0.886126	−	0.463445i	$-0.153387\pi$
$373$	18.8367	+	10.2856i	0.975326	+	0.532568i	0.0892008	+	0.996014i	$0.471569\pi$
$374$	13.1871	−	6.02237i	0.681891	−	0.311409i
$375$	35.4529	−	12.8028i	1.83078	−	0.661135i
$376$	0.248371	+	1.72746i	0.0128088	+	0.0890870i
$377$	−8.81349	−	16.1407i	−0.453918	−	0.831289i
$378$	29.0659	−	2.07883i	1.49499	−	0.106924i
$379$	26.1992	+	16.8372i	1.34576	+	0.864869i	0.997370	−	0.0724790i	$-0.0230910\pi$
$379$	26.1992	+	16.8372i	1.34576	+	0.864869i	0.348393	+	0.937348i	$0.386727\pi$
$380$	−2.32029	+	0.213407i	−0.119028	+	0.0109476i
$381$	−27.5903	+	31.8409i	−1.41349	+	1.63126i
$382$	9.53780	−	5.20803i	0.487996	−	0.266466i
$383$	−19.6375	+	26.2327i	−1.00343	+	1.34043i	−0.0639030	+	0.997956i	$0.520355\pi$
$383$	−19.6375	+	26.2327i	−1.00343	+	1.34043i	−0.939528	+	0.342471i	$0.888736\pi$
$384$	−2.54796	+	2.20782i	−0.130025	+	0.112667i
$385$	16.4799	−	5.20484i	0.839891	−	0.265263i
$386$	−14.6570	+	4.30370i	−0.746024	+	0.219052i
$387$	−14.8715	−	39.8720i	−0.755961	−	2.02681i
$388$	5.25031	−	3.93033i	0.266544	−	0.199532i
$389$	−17.1761	+	11.0384i	−0.870863	+	0.559669i	−0.898016	−	0.439962i	$-0.854992\pi$
$389$	−17.1761	+	11.0384i	−0.870863	+	0.559669i	0.0271539	+	0.999631i	$0.491356\pi$
$390$	−28.0313	−	3.45064i	−1.41942	−	0.174730i
$391$	−13.7917	−	4.43807i	−0.697478	−	0.224443i
$392$	−3.11554	−	3.11554i	−0.157359	−	0.157359i
$393$	−4.94239	+	22.7198i	−0.249310	+	1.14606i
$394$	−4.72009	−	0.678646i	−0.237795	−	0.0341897i
$395$	20.6808	−	4.94088i	1.04056	−	0.248603i
$396$	11.3114	+	38.5232i	0.568421	+	1.93586i
$397$	4.55279	−	12.2065i	0.228498	−	0.612627i	−0.771215	−	0.636574i	$-0.780351\pi$
$397$	4.55279	−	12.2065i	0.228498	−	0.612627i	0.999713	+	0.0239477i	$0.00762352\pi$
$398$	0.719930	−	10.0659i	0.0360868	−	0.504560i
$399$	−5.60066	+	0.805253i	−0.280384	+	0.0403131i
$400$	−2.53011	+	4.31261i	−0.126505	+	0.215630i
$401$	6.40698	+	5.55168i	0.319949	+	0.277238i	0.799996	−	0.600005i	$-0.204835\pi$
$401$	6.40698	+	5.55168i	0.319949	+	0.277238i	−0.480047	+	0.877243i	$0.659380\pi$
$402$	28.2457	−	6.14447i	1.40877	−	0.306458i
$403$	−7.08126	+	1.54043i	−0.352742	+	0.0767344i
$404$	9.57864	+	8.29994i	0.476555	+	0.412938i
$405$	29.5750	+	74.6271i	1.46959	+	3.70825i
$406$	−7.82555	+	1.12514i	−0.388376	+	0.0558400i
$407$	−2.23426	+	31.2391i	−0.110748	+	1.54846i
$408$	−3.55933	+	9.54293i	−0.176213	+	0.472446i
$409$	−4.19886	−	14.3000i	−0.207620	−	0.707090i	−0.995793	−	0.0916356i	$-0.970791\pi$
$409$	−4.19886	−	14.3000i	−0.207620	−	0.707090i	0.788172	−	0.615455i	$-0.211028\pi$
$410$	−11.7979	−	7.24765i	−0.582654	−	0.357936i
$411$	−51.4727	−	7.40066i	−2.53896	−	0.365047i
$412$	−1.18018	+	5.42518i	−0.0581431	+	0.267279i
$413$	9.37498	+	9.37498i	0.461313	+	0.461313i
$414$	17.6018	−	36.0577i	0.865080	−	1.77214i
$415$	0.807451	−	6.55935i	0.0396362	−	0.321986i
$416$	3.15164	−	2.02544i	0.154522	−	0.0993053i
$417$	42.0743	−	31.4964i	2.06039	−	1.54239i
$418$	−1.74752	−	4.68529i	−0.0854742	−	0.229165i
$419$	−2.82030	+	0.828115i	−0.137781	+	0.0404561i	−0.349896	−	0.936789i	$-0.613783\pi$
$419$	−2.82030	+	0.828115i	−0.137781	+	0.0404561i	0.212115	+	0.977245i	$0.431965\pi$
$420$	−5.60122	+	10.7726i	−0.273312	+	0.525647i
$421$	−4.54989	+	3.94250i	−0.221748	+	0.192146i	−0.758649	−	0.651499i	$-0.774140\pi$
$421$	−4.54989	+	3.94250i	−0.221748	+	0.192146i	0.536901	+	0.843645i	$0.319595\pi$
$422$	−9.31146	+	12.4386i	−0.453275	+	0.605504i
$423$	−12.8154	+	6.99776i	−0.623108	+	0.340243i
$424$	−3.33830	+	3.85261i	−0.162122	+	0.187099i
$425$	−0.464659	+	15.0979i	−0.0225393	+	0.732354i
$426$	7.43598	+	4.77882i	0.360275	+	0.231534i
$427$	10.0813	−	0.721030i	0.487869	−	0.0348931i
$428$	−1.11617	−	2.04412i	−0.0539522	−	0.0988062i
$429$	−8.62598	−	59.9950i	−0.416466	−	2.89659i
$430$	11.1603	+	2.19132i	0.538198	+	0.105675i
$431$	23.7645	−	10.8529i	1.14470	−	0.522765i	0.249472	−	0.968382i	$-0.419743\pi$
$431$	23.7645	−	10.8529i	1.14470	−	0.522765i	0.895224	+	0.445617i	$0.147016\pi$
$432$	−15.8798	−	8.67103i	−0.764018	−	0.417185i
$433$	32.7560	−	12.2174i	1.57415	−	0.587129i	0.597485	−	0.801880i	$-0.296167\pi$
$433$	32.7560	−	12.2174i	1.57415	−	0.587129i	0.976669	+	0.214751i	$0.0688941\pi$
$434$	−0.443376	+	3.08375i	−0.0212827	+	0.148025i
$435$	−16.0537	−	33.3429i	−0.769715	−	1.59867i
$436$		−	11.7729i		−	0.563818i
$437$	−1.86632	+	4.63591i	−0.0892780	+	0.221765i
$438$	0.656119	−	0.656119i	0.0313506	−	0.0313506i
$439$	−4.50680	−	7.01272i	−0.215098	−	0.334699i	0.716891	−	0.697185i	$-0.245564\pi$
$439$	−4.50680	−	7.01272i	−0.215098	−	0.334699i	−0.931989	+	0.362486i	$0.881928\pi$
$440$	−10.3551	−	2.81334i	−0.493660	−	0.134121i
$441$	15.3136	−	33.5321i	0.729219	−	1.59677i
$442$	5.42404	−	9.93338i	0.257995	−	0.472483i
$443$	−34.0505	−	12.7002i	−1.61779	−	0.603404i	−0.632540	−	0.774528i	$-0.717987\pi$
$443$	−34.0505	−	12.7002i	−1.61779	−	0.603404i	−0.985250	+	0.171124i	$0.945260\pi$
$444$	−14.4091	−	16.6290i	−0.683824	−	0.789175i
$445$	6.09787	−	6.35082i	0.289067	−	0.301058i
$446$	−1.03658	−	0.304369i	−0.0490837	−	0.0144123i
$447$	2.66751	+	37.2966i	0.126169	+	1.76407i
$448$	−0.342353	−	1.57377i	−0.0161746	−	0.0743536i
$449$	17.8186	−	27.7263i	0.840911	−	1.30848i	−0.108387	−	0.994109i	$-0.534569\pi$
$449$	17.8186	−	27.7263i	0.840911	−	1.30848i	0.949299	−	0.314375i	$-0.101795\pi$
$450$	−41.2042	−	7.22436i	−1.94239	−	0.340560i
$451$	8.37176	−	28.5116i	0.394211	−	1.34256i
$452$	9.81662	+	7.34863i	0.461735	+	0.345650i
$453$	−55.6281	−	3.97860i	−2.61363	−	0.186931i
$454$	0.872523	+	1.91056i	0.0409496	+	0.0896670i
$455$	7.86436	−	10.9629i	0.368687	−	0.513950i
$456$	3.19571	+	1.45943i	0.149653	+	0.0683441i
$457$	2.13493	+	2.85193i	0.0998677	+	0.133408i	0.847691	−	0.530490i	$-0.177992\pi$
$457$	2.13493	+	2.85193i	0.0998677	+	0.133408i	−0.747824	+	0.663898i	$0.768901\pi$
$458$	−1.85706	−	0.403978i	−0.0867746	−	0.0188767i
$459$	−54.6589			−2.55126
$460$	5.74882	+	9.05268i	0.268040	+	0.422083i
$461$	12.0071			0.559224			0.279612	−	0.960113i	$-0.409794\pi$
$461$	12.0071			0.559224			0.279612	+	0.960113i	$0.409794\pi$
$462$	−25.4618	−	5.53888i	−1.18459	−	0.257692i
$463$	−13.8901	−	18.5551i	−0.645530	−	0.862327i	0.351745	−	0.936096i	$-0.385588\pi$
$463$	−13.8901	−	18.5551i	−0.645530	−	0.862327i	−0.997275	+	0.0737687i	$0.976497\pi$
$464$	4.46522	+	2.03920i	0.207292	+	0.0946673i
$465$	−14.3892	+	2.36815i	−0.667283	+	0.109820i
$466$	0.581305	+	1.27288i	0.0269284	+	0.0589651i
$467$	−4.57078	−	0.326909i	−0.211511	−	0.0151275i	−0.0348182	−	0.999394i	$-0.511085\pi$
$467$	−4.57078	−	0.326909i	−0.211511	−	0.0151275i	−0.176692	+	0.984266i	$0.556540\pi$
$468$	25.0923	+	18.7839i	1.15989	+	0.868284i
$469$	−3.89041	+	13.2495i	−0.179643	+	0.611807i
$470$	0.199263	−	3.89735i	0.00919131	−	0.179771i
$471$	−2.06309	+	3.21023i	−0.0950622	+	0.147920i
$472$	−1.74983	−	8.04385i	−0.0805426	−	0.370248i
$473$	1.74128	+	24.3462i	0.0800639	+	1.11944i
$474$	−30.7604	−	9.03205i	−1.41287	−	0.414856i
$475$	5.18306	+	0.531386i	0.237815	+	0.0243816i
$476$	−3.18626	−	3.67714i	−0.146042	−	0.168542i
$477$	−39.9613	−	14.9048i	−1.82970	−	0.682444i
$478$	9.87485	−	18.0844i	0.451665	−	0.827163i
$479$	−4.80171	+	10.5143i	−0.219396	+	0.480410i	−0.987042	−	0.160465i	$-0.948701\pi$
$479$	−4.80171	+	10.5143i	−0.219396	+	0.480410i	0.767646	+	0.640874i	$0.221428\pi$
$480$	6.54184	−	3.74661i	0.298593	−	0.171009i
$481$	13.2188	+	20.5688i	0.602725	+	0.937858i
$482$	−8.14303	+	8.14303i	−0.370905	+	0.370905i
$483$	15.0644	+	21.2416i	0.685454	+	0.966524i
$484$		−	12.0286i		−	0.546755i
$485$	−13.2134	+	6.36186i	−0.599988	+	0.288877i
$486$	9.50007	−	66.0745i	0.430932	−	2.99720i
$487$	−38.9920	+	14.5432i	−1.76689	+	0.659018i	−0.767046	+	0.641592i	$0.778274\pi$
$487$	−38.9920	+	14.5432i	−1.76689	+	0.659018i	−0.999848	+	0.0174257i	$0.994453\pi$
$488$	−5.50782	−	3.00750i	−0.249327	−	0.136143i
$489$	−44.8972	+	20.5039i	−2.03032	+	0.927216i
$490$	5.49379	+	8.17829i	0.248184	+	0.369457i
$491$	−5.74739	−	39.9740i	−0.259376	−	1.80400i	−0.537294	−	0.843395i	$-0.680554\pi$
$491$	−5.74739	−	39.9740i	−0.259376	−	1.80400i	0.277918	−	0.960605i	$-0.410356\pi$
$492$	10.0051	+	18.3230i	0.451065	+	0.826064i
$493$	14.7918	−	1.05793i	0.666188	−	0.0476467i
$494$	−3.28416	−	2.11060i	−0.147761	−	0.0949603i
$495$	−8.22249	−	89.3997i	−0.369573	−	4.01822i
$496$	1.26675	−	1.46190i	0.0568785	−	0.0656413i
$497$	−3.70608	+	2.02367i	−0.166240	+	0.0907740i
$498$	−5.97151	+	7.97700i	−0.267590	+	0.357458i
$499$	10.7412	−	9.30729i	0.480842	−	0.416652i	−0.380420	−	0.924814i	$-0.624220\pi$
$499$	10.7412	−	9.30729i	0.480842	−	0.416652i	0.861261	+	0.508162i	$0.169675\pi$
$500$	7.40946	−	8.37257i	0.331361	−	0.374433i
$501$	−30.7718	+	9.03541i	−1.37478	+	0.403672i
$502$	−2.14154	−	5.74169i	−0.0955817	−	0.256264i
$503$	3.95812	−	2.96301i	0.176484	−	0.132114i	−0.507384	−	0.861720i	$-0.669387\pi$
$503$	3.95812	−	2.96301i	0.176484	−	0.132114i	0.683868	+	0.729606i	$0.260297\pi$
$504$	11.3359	−	7.28512i	0.504940	−	0.324505i
$505$	−17.4414	−	22.3382i	−0.776131	−	0.994037i
$506$	−15.5136	+	16.9996i	−0.689664	+	0.755724i
$507$	−2.46800	−	2.46800i	−0.109608	−	0.109608i
$508$	−2.65635	+	12.2110i	−0.117856	+	0.541777i
$509$	−19.2081	−	2.76171i	−0.851384	−	0.122411i	−0.297211	−	0.954812i	$-0.596056\pi$
$509$	−19.2081	−	2.76171i	−0.851384	−	0.122411i	−0.554173	+	0.832401i	$0.686965\pi$
$510$	11.9211	−	19.4054i	0.527876	−	0.859285i
$511$	0.124883	+	0.425311i	0.00552448	+	0.0188146i
$512$	−0.349464	+	0.936950i	−0.0154443	+	0.0414077i
$513$	−1.34501	+	18.8057i	−0.0593835	+	0.830290i
$514$	26.6549	−	3.83240i	1.17570	−	0.169040i
$515$	4.92681	−	11.3953i	0.217101	−	0.502138i
$516$	−12.9598	−	11.2297i	−0.570523	−	0.494361i
$517$	8.18362	−	1.78024i	0.359915	−	0.0782947i
$518$	10.2710	−	2.23432i	0.451283	−	0.0981706i
$519$	54.1570	+	46.9273i	2.37723	+	2.05988i
$520$	−7.78785	+	3.08635i	−0.341520	+	0.135346i
$521$	−38.7729	+	5.57471i	−1.69867	+	0.244232i	−0.922420	−	0.386189i	$-0.873791\pi$
$521$	−38.7729	+	5.57471i	−1.69867	+	0.244232i	−0.776253	+	0.630421i	$0.782882\pi$
$522$	−2.92989	+	40.9652i	−0.128238	+	1.79300i
$523$	−9.24043	+	24.7746i	−0.404056	+	1.08332i	0.562486	+	0.826807i	$0.309845\pi$
$523$	−9.24043	+	24.7746i	−0.404056	+	1.08332i	−0.966542	+	0.256509i	$0.917428\pi$
$524$	1.94297	+	6.61716i	0.0848792	+	0.289072i
$525$	16.9311	−	21.2237i	0.738935	−	0.926278i
$526$	−12.3617	−	1.77735i	−0.538996	−	0.0774960i
$527$	1.24218	−	5.71020i	0.0541101	−	0.248740i
$528$	11.4402	+	11.4402i	0.497870	+	0.497870i
$529$	22.9041	−	2.09798i	0.995831	−	0.0912165i
$530$	8.98461	−	7.01506i	0.390266	−	0.304715i
$531$	57.9399	−	37.2357i	2.51438	−	1.61589i
$532$	−1.34354	+	1.00576i	−0.0582500	+	0.0436054i
$533$	−8.10698	−	21.7356i	−0.351152	−	0.941475i
$534$	−12.7371	+	3.73994i	−0.551187	+	0.161843i
$535$	1.56842	+	4.96602i	0.0678087	+	0.214700i
$536$	6.47971	−	5.61470i	0.279881	−	0.242518i
$537$	−9.68374	+	12.9360i	−0.417884	+	0.558228i
$538$	23.6407	−	12.9088i	1.01922	−	0.556537i
$539$	−13.8462	+	15.9794i	−0.596399	+	0.688282i
$540$	31.1073	+	25.8671i	1.33865	+	1.11314i
$541$	18.5364	+	11.9126i	0.796944	+	0.512165i	0.874617	−	0.484814i	$-0.161113\pi$
$541$	18.5364	+	11.9126i	0.796944	+	0.512165i	−0.0776734	+	0.996979i	$0.524749\pi$
$542$	−4.44505	+	0.317916i	−0.190931	+	0.0136557i
$543$	37.6112	+	68.8798i	1.61405	+	2.95592i
$544$	0.429934	+	2.99025i	0.0184333	+	0.128206i
$545$	−5.07203	+	25.8317i	−0.217262	+	1.10651i
$546$	−18.5043	+	8.45061i	−0.791909	+	0.361653i
$547$	7.12062	+	3.88815i	0.304456	+	0.166245i	0.624213	−	0.781254i	$-0.285420\pi$
$547$	7.12062	+	3.88815i	0.304456	+	0.166245i	−0.319758	+	0.947499i	$0.603601\pi$
$548$	−14.4518	+	5.39024i	−0.617350	+	0.230260i
$549$	7.47206	−	51.9694i	0.318900	−	2.21800i
$550$	21.5088	+	10.6342i	0.917139	+	0.453443i
$551$		−	5.11521i		−	0.217915i
$552$	−0.738201	−	16.1520i	−0.0314199	−	0.687473i
$553$	10.8293	−	10.8293i	0.460510	−	0.460510i
$554$	5.46760	+	8.50775i	0.232296	+	0.361460i
$555$	24.4518	+	42.6946i	1.03792	+	1.81228i
$556$	6.47591	−	14.1803i	0.274640	−	0.601377i
$557$	0.00537883	−	0.00985060i	0.000227908	−	0.000417383i	−0.877565	−	0.479458i	$-0.840833\pi$
$557$	0.00537883	−	0.00985060i	0.000227908	−	0.000417383i	0.877793	+	0.479040i	$0.159015\pi$
$558$	15.1636	+	5.65574i	0.641928	+	0.239427i
$559$	12.4786	+	14.4010i	0.527787	+	0.609099i
$560$	0.0731621	+	3.60061i	0.00309166	+	0.152154i
$561$	46.8966	+	13.7701i	1.97998	+	0.581373i
$562$	−2.12192	−	29.6684i	−0.0895079	−	1.25148i
$563$	−7.32165	−	33.6571i	−0.308571	−	1.41848i	−0.826444	−	0.563019i	$-0.809640\pi$
$563$	−7.32165	−	33.6571i	−0.308571	−	1.41848i	0.517873	−	0.855457i	$-0.326724\pi$
$564$	−3.18108	+	4.94986i	−0.133948	+	0.208427i
$565$	−18.3734	−	20.3534i	−0.772974	−	0.856274i
$566$	8.68361	−	29.5737i	0.364999	−	1.24307i
$567$	46.2864	+	34.6496i	1.94385	+	1.45515i
$568$	2.61511	+	0.187036i	0.109727	+	0.00784786i
$569$	5.73880	+	12.5662i	0.240583	+	0.526803i	0.990952	−	0.134216i	$-0.0428515\pi$
$569$	5.73880	+	12.5662i	0.240583	+	0.526803i	−0.750369	+	0.661019i	$0.770124\pi$
$570$	−6.38317	−	4.57903i	−0.267362	−	0.191794i
$571$	36.7892	+	16.8011i	1.53958	+	0.703103i	0.991107	−	0.133066i	$-0.0424821\pi$
$571$	36.7892	+	16.8011i	1.53958	+	0.703103i	0.548473	+	0.836168i	$0.315209\pi$
$572$	−10.7739	−	14.3922i	−0.450478	−	0.601769i
$573$	35.8003	+	7.78788i	1.49558	+	0.325343i
$574$	−9.97304			−0.416267
$575$	−8.71379	−	22.3399i	−0.363390	−	0.931637i
$576$	−8.36655			−0.348606
$577$	−29.3290	−	6.38013i	−1.22098	−	0.265608i	−0.444518	−	0.895770i	$-0.646625\pi$
$577$	−29.3290	−	6.38013i	−1.22098	−	0.265608i	−0.776464	+	0.630162i	$0.782989\pi$
$578$	−4.71843	−	6.30309i	−0.196261	−	0.262174i
$579$	−46.8473	−	21.3945i	−1.94691	−	0.889123i
$580$	−8.91892	−	6.39807i	−0.370338	−	0.265665i
$581$	−1.97745	−	4.33000i	−0.0820383	−	0.179639i
$582$	22.0550	+	1.57741i	0.914210	+	0.0653856i
$583$	19.5837	+	14.6602i	0.811073	+	0.607162i
$584$	0.0775390	−	0.264074i	0.00320859	−	0.0109274i
$585$	−46.9643	−	52.0254i	−1.94173	−	2.15098i
$586$	−0.0355791	+	0.0553622i	−0.00146976	+	0.00228699i
$587$	1.32725	+	6.10126i	0.0547814	+	0.251826i	0.996391	−	0.0848801i	$-0.0270507\pi$
$587$	1.32725	+	6.10126i	0.0547814	+	0.251826i	−0.941610	+	0.336706i	$0.890687\pi$
$588$	−1.05972	−	14.8168i	−0.0437021	−	0.611036i
$589$	−1.93405	−	0.567890i	−0.0796913	−	0.0233995i
$590$	0.373946	+	18.4035i	0.0153951	+	0.757659i
$591$	−10.5283	−	12.1503i	−0.433075	−	0.499795i
$592$	−6.11489	−	2.28074i	−0.251321	−	0.0937377i
$593$	−1.62944	+	2.98410i	−0.0669131	+	0.122542i	−0.908994	−	0.416809i	$-0.863149\pi$
$593$	−1.62944	+	2.98410i	−0.0669131	+	0.122542i	0.842081	+	0.539351i	$0.181330\pi$
$594$	−36.0683	+	78.9786i	−1.47990	+	3.24053i
$595$	5.40700	+	9.44100i	0.221666	+	0.387043i
$596$	5.99614	+	9.33018i	0.245612	+	0.382179i
$597$	24.0581	−	24.0581i	0.984633	−	0.984633i
$598$	−1.74235	+	17.8823i	−0.0712499	+	0.731260i
$599$			9.69171i			0.395993i	0.980203	+	0.197996i	$0.0634434\pi$
$599$			9.69171i			0.395993i	−0.980203	+	0.197996i	$0.936557\pi$
$600$	−15.9681	+	5.40232i	−0.651893	+	0.220549i
$601$	−4.97998	+	34.6365i	−0.203138	+	1.41285i	0.591762	+	0.806113i	$0.298432\pi$
$601$	−4.97998	+	34.6365i	−0.203138	+	1.41285i	−0.794900	+	0.606741i	$0.792477\pi$
$602$	7.67544	−	2.86279i	0.312827	−	0.116679i
$603$	62.9593	+	34.3784i	2.56390	+	1.40000i
$604$	−15.0471	+	6.87179i	−0.612258	+	0.279609i
$605$	−5.18222	+	26.3928i	−0.210687	+	1.07302i
$606$	6.08122	+	42.2958i	0.247033	+	1.71815i
$607$	−3.35529	−	6.14476i	−0.136187	−	0.249408i	0.800681	−	0.599091i	$-0.204471\pi$
$607$	−3.35529	−	6.14476i	−0.136187	−	0.249408i	−0.936868	+	0.349683i	$0.886289\pi$
$608$	1.03939	−	0.0743387i	0.0421529	−	0.00301483i
$609$	−22.4233	−	14.4106i	−0.908638	−	0.583946i
$610$	10.7894	+	8.97187i	0.436850	+	0.363260i
$611$	4.28164	−	4.94128i	0.173217	−	0.199903i
$612$	−22.1837	+	12.1132i	−0.896722	+	0.489647i
$613$	−2.30016	+	3.07265i	−0.0929025	+	0.124103i	−0.844584	−	0.535423i	$-0.820152\pi$
$613$	−2.30016	+	3.07265i	−0.0929025	+	0.124103i	0.751682	+	0.659526i	$0.229243\pi$
$614$	4.71977	−	4.08970i	0.190474	−	0.165047i
$615$	−14.0589	−	44.5142i	−0.566911	−	1.79499i
$616$	−7.41578	+	2.17747i	−0.298790	+	0.0877328i
$617$	−2.40006	−	6.43481i	−0.0966228	−	0.259056i	0.879642	−	0.475637i	$-0.157782\pi$
$617$	−2.40006	−	6.43481i	−0.0966228	−	0.259056i	−0.976265	+	0.216581i	$0.930510\pi$
$618$	−14.9849	+	11.2175i	−0.602779	+	0.451235i
$619$	−7.21076	+	4.63407i	−0.289825	+	0.186259i	−0.677472	−	0.735549i	$-0.736924\pi$
$619$	−7.21076	+	4.63407i	−0.289825	+	0.186259i	0.387647	+	0.921808i	$0.373288\pi$
$620$	−3.40928	+	2.66192i	−0.136920	+	0.106905i
$621$	79.8307	−	34.0035i	3.20349	−	1.36451i
$622$	−13.2785	−	13.2785i	−0.532420	−	0.532420i
$623$	1.34799	−	6.19662i	0.0540061	−	0.248262i
$624$	12.5021	+	1.79752i	0.500483	+	0.0719585i
$625$	−19.8647	+	15.1787i	−0.794590	+	0.607147i
$626$	−6.50009	−	22.1373i	−0.259796	−	0.884783i
$627$	5.89166	−	15.7961i	0.235290	−	0.630837i
$628$	−0.0807464	+	1.12898i	−0.00322213	+	0.0450513i
$629$	−19.5155	+	2.80591i	−0.778136	+	0.111879i
$630$	−28.0114	+	11.1010i	−1.11600	+	0.442276i
$631$	9.20398	+	7.97529i	0.366405	+	0.317491i	0.818531	−	0.574463i	$-0.194789\pi$
$631$	9.20398	+	7.97529i	0.366405	+	0.317491i	−0.452126	+	0.891954i	$0.649334\pi$
$632$	−9.29170	+	2.02128i	−0.369604	+	0.0804024i
$633$	−51.1875	+	11.1352i	−2.03452	+	0.442583i
$634$	18.1605	+	15.7361i	0.721244	+	0.624961i
$635$	11.0893	−	25.6487i	0.440066	−	1.01784i
$636$	−17.0117	+	2.44592i	−0.674558	+	0.0969869i
$637$	−1.17757	+	16.4646i	−0.0466571	+	0.652351i
$638$	8.23215	−	22.0713i	0.325914	−	0.873809i
$639$	6.17989	+	21.0468i	0.244473	+	0.832597i
$640$	1.17045	−	1.90527i	0.0462659	−	0.0753125i
$641$	−21.8939	−	3.14786i	−0.864756	−	0.124333i	−0.304359	−	0.952557i	$-0.598442\pi$
$641$	−21.8939	−	3.14786i	−0.864756	−	0.124333i	−0.560397	+	0.828224i	$0.689351\pi$
$642$	1.66908	−	7.67263i	0.0658733	−	0.302815i
$643$	7.78056	+	7.78056i	0.306835	+	0.306835i	0.843681	−	0.536845i	$-0.180384\pi$
$643$	7.78056	+	7.78056i	0.306835	+	0.306835i	−0.536845	+	0.843681i	$0.680384\pi$
$644$	6.94118	+	3.38837i	0.273521	+	0.133521i
$645$	23.5980	+	30.2233i	0.929169	+	1.19004i
$646$	2.64829	−	1.70195i	0.104195	−	0.0669623i
$647$	−5.37378	+	4.02276i	−0.211265	+	0.158151i	−0.699670	−	0.714466i	$-0.746670\pi$
$647$	−5.37378	+	4.02276i	−0.211265	+	0.158151i	0.488405	+	0.872617i	$0.337579\pi$
$648$	−12.5456	−	33.6361i	−0.492838	−	1.32135i
$649$	−37.9035	+	11.1295i	−1.48784	+	0.436871i
$650$	18.4176	−	3.41679i	0.722396	−	0.134018i
$651$	−7.93805	+	6.87836i	−0.311117	+	0.269584i
$652$	−8.77338	+	11.7199i	−0.343592	+	0.458985i
$653$	−3.38925	+	1.85067i	−0.132631	+	0.0724223i	−0.544195	−	0.838959i	$-0.683165\pi$
$653$	−3.38925	+	1.85067i	−0.132631	+	0.0724223i	0.411563	+	0.911381i	$0.364983\pi$
$654$	25.9923	−	29.9967i	1.01638	−	1.17297i
$655$	−1.41238	−	15.3563i	−0.0551864	−	0.600019i
$656$	5.20922	+	3.34776i	0.203386	+	0.130708i
$657$	2.29679	−	0.164270i	0.0896064	−	0.00640878i
$658$	−1.34708	−	2.46700i	−0.0525147	−	0.0961735i
$659$	6.93213	+	48.2140i	0.270038	+	1.87815i	0.447880	+	0.894094i	$0.352179\pi$
$659$	6.93213	+	48.2140i	0.270038	+	1.87815i	−0.177843	+	0.984059i	$0.556912\pi$
$660$	−20.1730	−	30.0305i	−0.785234	−	1.16893i
$661$	13.0297	−	5.95046i	0.506797	−	0.231446i	−0.145573	−	0.989348i	$-0.546502\pi$
$661$	13.0297	−	5.95046i	0.506797	−	0.231446i	0.652369	+	0.757901i	$0.273775\pi$
$662$	3.15797	+	1.72438i	0.122738	+	0.0670201i
$663$	35.7513	−	13.3346i	1.38847	−	0.517871i
$664$	−0.420622	+	2.92549i	−0.0163233	+	0.113531i
$665$	3.38127	−	1.62799i	0.131120	−	0.0631307i
$666$		−	54.6033i		−	2.11584i
$667$	−20.9456	+	10.7471i	−0.811017	+	0.416131i
$668$	−6.72638	+	6.72638i	−0.260251	+	0.260251i
$669$	−1.96918	−	3.06411i	−0.0761330	−	0.118465i
$670$	−16.6365	+	9.52800i	−0.642726	+	0.368099i
$671$	−12.5101	+	27.3932i	−0.482946	+	1.05750i
$672$	2.60230	−	4.76575i	0.100386	−	0.183843i
$673$	−32.3446	−	12.0639i	−1.24679	−	0.465030i	−0.362510	−	0.931980i	$-0.618080\pi$
$673$	−32.3446	−	12.0639i	−1.24679	−	0.465030i	−0.884284	+	0.466950i	$0.845353\pi$
$674$	7.09684	+	8.19019i	0.273360	+	0.315474i
$675$	−57.1107	−	70.1588i	−2.19819	−	2.70041i
$676$	−0.993316	−	0.291664i	−0.0382045	−	0.0112178i
$677$	1.94403	+	27.1810i	0.0747150	+	1.04465i	0.887114	+	0.461550i	$0.152707\pi$
$677$	1.94403	+	27.1810i	0.0747150	+	1.04465i	−0.812399	+	0.583102i	$0.801839\pi$
$678$	8.78790	+	40.3973i	0.337497	+	1.55145i
$679$	−5.71073	+	8.88606i	−0.219158	+	0.341016i
$680$	0.344926	−	6.74636i	0.0132273	−	0.258711i
$681$	−1.99502	+	6.79440i	−0.0764492	+	0.260362i
$682$	−7.43118	−	5.56291i	−0.284555	−	0.213015i
$683$	34.3993	+	2.46028i	1.31625	+	0.0941402i	0.711733	−	0.702451i	$-0.247911\pi$
$683$	34.3993	+	2.46028i	1.31625	+	0.0941402i	0.604519	+	0.796591i	$0.293365\pi$
$684$	3.62172	+	7.93047i	0.138480	+	0.303229i
$685$	34.0320	−	5.60093i	1.30030	−	0.214001i
$686$	16.7102	+	7.63130i	0.637999	+	0.291364i
$687$	−3.83979	−	5.12937i	−0.146497	−	0.195697i
$688$	−4.97010	−	1.08118i	−0.189483	−	0.0412196i
$689$	19.0980			0.727574
$690$	−5.33892	+	35.7582i	−0.203249	+	1.36129i
$691$	−19.5208			−0.742608			−0.371304	−	0.928511i	$-0.621089\pi$
$691$	−19.5208			−0.742608			−0.371304	+	0.928511i	$0.621089\pi$
$692$	20.7693	+	4.51808i	0.789530	+	0.171752i
$693$	−38.7516	−	51.7661i	−1.47205	−	1.96643i
$694$	−30.6803	−	14.0112i	−1.16461	−	0.531859i
$695$	−20.3185	+	28.3240i	−0.770723	+	1.07439i
$696$	6.87501	+	15.0542i	0.260597	+	0.570627i
$697$	18.6590	+	1.33452i	0.706762	+	0.0505486i
$698$	0.578701	+	0.433210i	0.0219042	+	0.0163973i
$699$	−1.32915	+	4.52666i	−0.0502730	+	0.171214i
$700$	1.39070	−	7.93189i	0.0525636	−	0.299797i
$701$	−20.9034	+	32.5263i	−0.789511	+	1.22850i	0.180051	+	0.983657i	$0.442374\pi$
$701$	−20.9034	+	32.5263i	−0.789511	+	1.22850i	−0.969562	+	0.244846i	$0.921263\pi$
$702$	14.4083	+	66.2338i	0.543805	+	2.49983i
$703$	0.485163	+	6.78346i	0.0182983	+	0.255843i
$704$	4.60443	+	1.35198i	0.173536	+	0.0509547i
$705$	9.11236	−	9.49035i	0.343191	−	0.357427i
$706$	−1.33123	−	1.53632i	−0.0501015	−	0.0578202i
$707$	−19.1260	−	7.13362i	−0.719306	−	0.268287i
$708$	13.3009	−	24.3587i	0.499877	−	0.915456i
$709$	−4.80799	+	10.5280i	−0.180568	+	0.395388i	−0.978173	−	0.207791i	$-0.933373\pi$
$709$	−4.80799	+	10.5280i	−0.180568	+	0.395388i	0.797605	+	0.603180i	$0.206100\pi$
$710$	−5.65741	−	1.53704i	−0.212319	−	0.0576841i
$711$	−43.0121	−	66.9281i	−1.61308	−	2.51000i
$712$	−2.78419	+	2.78419i	−0.104342	+	0.104342i
$713$	1.73810	+	9.11265i	0.0650925	+	0.341271i
$714$		−	16.4039i		−	0.613900i
$715$	17.4392	+	36.2206i	0.652190	+	1.35458i
$716$	−0.682105	+	4.74414i	−0.0254914	+	0.177297i
$717$	65.0879	−	24.2765i	2.43075	−	0.906623i
$718$	−5.61192	−	3.06434i	−0.209435	−	0.114360i
$719$	−2.15282	+	0.983161i	−0.0802867	+	0.0366657i	−0.455154	−	0.890413i	$-0.650416\pi$
$719$	−2.15282	+	0.983161i	−0.0802867	+	0.0366657i	0.374867	+	0.927079i	$0.377688\pi$
$720$	18.3577	+	3.60451i	0.684149	+	0.134332i
$721$	−1.27258	−	8.85100i	−0.0473934	−	0.329629i
$722$	8.58533	+	15.7229i	0.319513	+	0.585144i
$723$	−38.7264	+	2.76977i	−1.44025	+	0.103009i
$724$	19.5825	+	12.5849i	0.727779	+	0.467715i
$725$	16.8132	+	17.8810i	0.624426	+	0.664082i
$726$	26.5570	−	30.6484i	0.985622	−	1.13747i
$727$	−0.348223	+	0.190144i	−0.0129149	+	0.00705206i	−0.485693	−	0.874129i	$-0.661433\pi$
$727$	−0.348223	+	0.190144i	−0.0129149	+	0.00705206i	0.472779	+	0.881181i	$0.343251\pi$
$728$	−3.61593	+	4.83031i	−0.134015	+	0.179023i
$729$	88.6930	−	76.8530i	3.28493	−	2.84641i
$730$	−0.283903	+	0.546017i	−0.0105077	+	0.0202090i
$731$	−14.7434	+	4.32906i	−0.545306	+	0.160116i
$732$	−7.39369	−	19.8232i	−0.273278	−	0.732688i
$733$	−22.6243	+	16.9363i	−0.835647	+	0.625557i	−0.929002	−	0.370076i	$-0.879332\pi$
$733$	−22.6243	+	16.9363i	−0.835647	+	0.625557i	0.0933549	+	0.995633i	$0.470241\pi$
$734$	−4.47028	+	2.87287i	−0.165001	+	0.106040i
$735$	−4.05824	+	32.9672i	−0.149691	+	1.21601i
$736$	−2.48818	−	4.09988i	−0.0917154	−	0.151123i
$737$	−29.0935	−	29.0935i	−1.07167	−	1.07167i
$738$	−11.0125	+	50.6235i	−0.405375	+	1.86348i
$739$	−16.4525	−	2.36551i	−0.605214	−	0.0870166i	−0.167106	−	0.985939i	$-0.553442\pi$
$739$	−16.4525	−	2.36551i	−0.605214	−	0.0870166i	−0.438108	+	0.898922i	$0.644351\pi$
$740$	12.4345	+	7.63878i	0.457102	+	0.280807i
$741$	−3.70807	−	12.6285i	−0.136219	−	0.463921i
$742$	2.86920	−	7.69262i	0.105332	−	0.282405i
$743$	3.32183	−	46.4452i	0.121866	−	1.70391i	−0.457799	−	0.889056i	$-0.651362\pi$
$743$	3.32183	−	46.4452i	0.121866	−	1.70391i	0.579665	−	0.814855i	$-0.303183\pi$
$744$	6.45523	−	0.928122i	0.236660	−	0.0340266i
$745$	−9.13690	−	23.0553i	−0.334750	−	0.844681i
$746$	16.2198	+	14.0546i	0.593851	+	0.514574i
$747$	−24.1628	+	5.25630i	−0.884071	+	0.192318i
$748$	14.1659	−	3.08161i	0.517958	−	0.112675i
$749$	2.83485	+	2.45641i	0.103583	+	0.0897552i
$750$	37.3641	−	4.97420i	1.36434	−	0.181632i
$751$	−42.0589	+	6.04715i	−1.53475	+	0.220664i	−0.857266	−	0.514874i	$-0.827839\pi$
$751$	−42.0589	+	6.04715i	−1.53475	+	0.220664i	−0.677484	+	0.735538i	$0.736930\pi$
$752$	−0.124503	+	1.74078i	−0.00454016	+	0.0634797i
$753$	7.22006	−	19.3577i	0.263114	−	0.705435i
$754$	−5.18112	−	17.6453i	−0.188685	−	0.642603i
$755$	35.9765	−	8.59522i	1.30932	−	0.312812i
$756$	28.8435	+	4.14707i	1.04903	+	0.150827i
$757$	2.91909	−	13.4189i	0.106096	−	0.487717i	−0.893181	−	0.449698i	$-0.851532\pi$
$757$	2.91909	−	13.4189i	0.106096	−	0.487717i	0.999277	−	0.0380188i	$-0.0121047\pi$
$758$	22.0215	+	22.0215i	0.799856	+	0.799856i
$759$	−77.0600	+	9.06298i	−2.79710	+	0.328965i
$760$	−2.31263	−	0.284683i	−0.0838879	−	0.0103265i
$761$	−26.4072	+	16.9709i	−0.957261	+	0.615194i	−0.923239	−	0.384227i	$-0.874468\pi$
$761$	−26.4072	+	16.9709i	−0.957261	+	0.615194i	−0.0340225	+	0.999421i	$0.510832\pi$
$762$	−33.7280	+	25.2485i	−1.22184	+	0.914656i
$763$	6.62622	+	17.7656i	0.239885	+	0.643157i
$764$	10.4269	−	3.06161i	0.377231	−	0.110765i
$765$	53.8935	−	17.0212i	1.94852	−	0.615402i
$766$	−24.7649	+	21.4589i	−0.894793	+	0.775342i
$767$	−18.4817	+	24.6887i	−0.667336	+	0.891457i
$768$	−2.95903	+	1.61576i	−0.106775	+	0.0583035i
$769$	3.69926	−	4.26917i	0.133399	−	0.153950i	−0.685120	−	0.728430i	$-0.740250\pi$
$769$	3.69926	−	4.26917i	0.133399	−	0.153950i	0.818519	+	0.574480i	$0.194796\pi$
$770$	17.2096	−	1.58284i	0.620191	−	0.0570417i
$771$	76.3768	+	49.0844i	2.75064	+	1.76773i
$772$	−15.2369	+	1.08977i	−0.548388	+	0.0392215i
$773$	9.95969	+	18.2398i	0.358225	+	0.656040i	0.993191	−	0.116500i	$-0.0371676\pi$
$773$	9.95969	+	18.2398i	0.358225	+	0.656040i	−0.634966	+	0.772540i	$0.718986\pi$
$774$	−6.05623	−	42.1220i	−0.217687	−	1.51404i
$775$	8.62737	−	4.37191i	0.309904	−	0.157044i
$776$	5.96578	−	2.72448i	0.214159	−	0.0978031i
$777$	31.1031	+	16.9836i	1.11582	+	0.609283i
$778$	−19.1299	+	7.13510i	−0.685842	+	0.255806i
$779$	0.918297	−	6.38689i	0.0329014	−	0.228834i
$780$	−26.6572	−	9.33027i	−0.954482	−	0.334077i
$781$		−	12.5815i		−	0.450200i
$782$	−12.5332	−	7.26829i	−0.448186	−	0.259914i
$783$	−62.8017	+	62.8017i	−2.24435	+	2.24435i
$784$	−2.38209	−	3.70660i	−0.0850745	−	0.132379i
$785$	0.663565	−	2.44239i	0.0236836	−	0.0871728i
$786$	−9.65887	+	21.1500i	−0.344521	+	0.754395i
$787$	8.76446	−	16.0509i	0.312419	−	0.572153i	−0.673538	−	0.739153i	$-0.735226\pi$
$787$	8.76446	−	16.0509i	0.312419	−	0.572153i	0.985957	+	0.167000i	$0.0534079\pi$
$788$	−4.46796	−	1.66646i	−0.159165	−	0.0593653i
$789$	−27.5731	−	31.8210i	−0.981627	−	1.13286i
$790$	21.2584	−	0.431957i	0.756340	−	0.0153683i
$791$	−18.9497	−	5.56412i	−0.673772	−	0.197837i
$792$	2.86423	+	40.0472i	0.101776	+	1.42302i
$793$	4.99743	+	22.9728i	0.177464	+	0.815788i
$794$	7.04342	−	10.9598i	0.249962	−	0.388948i
$795$	38.3804	+	1.96230i	1.36121	+	0.0695957i
$796$	2.84315	−	9.68287i	0.100773	−	0.343200i
$797$	−40.8770	−	30.6002i	−1.44794	−	1.08391i	−0.979736	−	0.200293i	$-0.935811\pi$
$797$	−40.8770	−	30.6002i	−1.44794	−	1.08391i	−0.468203	−	0.883621i	$-0.655098\pi$
$798$	−5.64384	−	0.403655i	−0.199790	−	0.0142892i
$799$	2.19021	+	4.79588i	0.0774839	+	0.169666i
$800$	−3.38900	+	3.67624i	−0.119819	+	0.129975i
$801$	−29.9658	−	13.6849i	−1.05879	−	0.483533i
$802$	5.08047	+	6.78671i	0.179398	+	0.239647i
$803$	−1.29056	−	0.280743i	−0.0455428	−	0.00990722i
$804$	28.9063			1.01944
$805$	−13.7703	−	10.4251i	−0.485341	−	0.367436i
$806$	−7.24687			−0.255260
$807$	88.7357	+	19.3033i	3.12365	+	0.679507i
$808$	7.59546	+	10.1463i	0.267207	+	0.356947i
$809$	29.6396	+	13.5360i	1.04207	+	0.475899i	0.861551	−	0.507671i	$-0.169494\pi$
$809$	29.6396	+	13.5360i	1.04207	+	0.475899i	0.180524	+	0.983571i	$0.442221\pi$
$810$	13.0360	+	79.2082i	0.458037	+	2.78309i
$811$	−0.725354	−	1.58830i	−0.0254706	−	0.0557729i	0.896469	−	0.443106i	$-0.146124\pi$
$811$	−0.725354	−	1.58830i	−0.0254706	−	0.0557729i	−0.921940	+	0.387333i	$0.873396\pi$
$812$	−7.88588	−	0.564009i	−0.276740	−	0.0197928i
$813$	−12.0277	−	9.00382i	−0.421830	−	0.315778i
$814$	−8.82355	+	30.0503i	−0.309265	+	1.05326i
$815$	24.2995	−	21.9356i	0.851175	−	0.768371i
$816$	−5.50648	+	8.56826i	−0.192766	+	0.299949i
$817$	1.12664	+	5.17907i	0.0394161	+	0.181193i
$818$	−1.06322	−	14.8658i	−0.0371746	−	0.519769i
$819$	−48.4373	−	14.2225i	−1.69254	−	0.496973i
$820$	−9.98763	−	9.58983i	−0.348783	−	0.334891i
$821$	2.83306	+	3.26952i	0.0988743	+	0.114107i	0.803030	−	0.595938i	$-0.203220\pi$
$821$	2.83306	+	3.26952i	0.0988743	+	0.114107i	−0.704156	+	0.710046i	$0.748674\pi$
$822$	−48.7233	−	18.1728i	−1.69942	−	0.633850i
$823$	14.9632	−	27.4031i	0.521586	−	0.955213i	−0.475558	−	0.879684i	$-0.657754\pi$
$823$	14.9632	−	27.4031i	0.521586	−	0.955213i	0.997144	−	0.0755284i	$-0.0240644\pi$
$824$	−2.30641	+	5.05033i	−0.0803476	+	0.175937i
$825$	31.3252	+	74.5830i	1.09060	+	2.59665i
$826$	7.16794	+	11.1535i	0.249405	+	0.388081i
$827$	−10.6741	+	10.6741i	−0.371176	+	0.371176i	−0.867905	−	0.496730i	$-0.834534\pi$
$827$	−10.6741	+	10.6741i	−0.371176	+	0.371176i	0.496730	+	0.867905i	$0.334534\pi$
$828$	24.8641	−	31.4922i	0.864088	−	1.09443i
$829$		−	1.45658i		−	0.0505890i	−0.999680	−	0.0252945i	$-0.991948\pi$
$829$		−	1.45658i		−	0.0505890i	0.999680	−	0.0252945i	$-0.00805235\pi$
$830$	2.18329	−	6.23781i	0.0757830	−	0.216517i
$831$	−4.85235	+	33.7488i	−0.168326	+	1.17073i
$832$	3.51016	−	1.30922i	0.121693	−	0.0453891i
$833$	−11.6825	−	6.37913i	−0.404775	−	0.221024i
$834$	47.8078	−	21.8331i	1.65545	−	0.756018i
$835$	17.6567	−	11.8609i	0.611036	−	0.410465i
$836$	−0.711657	−	4.94968i	−0.0246132	−	0.171188i
$837$	16.7730	+	30.7175i	0.579760	+	1.06175i
$838$	−2.93188	+	0.209692i	−0.101280	+	0.00724369i
$839$	−45.0080	−	28.9249i	−1.55385	−	0.998599i	−0.984272	−	0.176662i	$-0.943470\pi$
$839$	−45.0080	−	28.9249i	−1.55385	−	0.998599i	−0.569579	−	0.821937i	$-0.692894\pi$
$840$	−7.76309	+	9.33574i	−0.267852	+	0.322114i
$841$	−3.21112	+	3.70583i	−0.110728	+	0.127787i
$842$	−5.28395	+	2.88526i	−0.182097	+	0.0994325i
$843$	60.0958	−	80.2786i	2.06981	−	2.76494i
$844$	−11.7427	+	10.1751i	−0.404200	+	0.350241i
$845$	2.05385	+	1.06791i	0.0706546	+	0.0367371i
$846$	−14.0101	+	4.11372i	−0.481676	+	0.141433i
$847$	6.77017	+	18.1515i	0.232626	+	0.623694i
$848$	−4.08094	+	3.05496i	−0.140140	+	0.104908i
$849$	87.4187	−	56.1806i	3.00020	−	1.92811i
$850$	−3.66332	+	14.6541i	−0.125651	+	0.502630i
$851$	26.7574	−	16.2388i	0.917231	−	0.556658i
$852$	6.25024	+	6.25024i	0.214130	+	0.214130i
$853$	4.45957	−	20.5003i	0.152693	−	0.701918i	−0.835599	−	0.549340i	$-0.814879\pi$
$853$	4.45957	−	20.5003i	0.152693	−	0.701918i	0.988292	−	0.152577i	$-0.0487573\pi$
$854$	10.0042	+	1.43839i	0.342336	+	0.0492206i
$855$	−4.53005	−	18.9611i	−0.154924	−	0.648457i
$856$	−0.656156	−	2.23466i	−0.0224270	−	0.0763792i
$857$	7.44944	−	19.9727i	0.254468	−	0.682255i	−0.745409	−	0.666607i	$-0.767746\pi$
$857$	7.44944	−	19.9727i	0.254468	−	0.682255i	0.999878	−	0.0156485i	$-0.00498128\pi$
$858$	4.32401	−	60.4575i	0.147619	−	2.06399i
$859$	38.4185	−	5.52374i	1.31082	−	0.188468i	0.548764	−	0.835977i	$-0.315098\pi$
$859$	38.4185	−	5.52374i	1.31082	−	0.188468i	0.762057	+	0.647509i	$0.224189\pi$
$860$	10.4395	+	4.51354i	0.355983	+	0.153910i
$861$	−25.4109	−	22.0187i	−0.866000	−	0.750394i
$862$	25.5283	−	5.55335i	0.869499	−	0.189148i
$863$	28.0234	−	6.09612i	0.953929	−	0.207514i	0.291442	−	0.956588i	$-0.405865\pi$
$863$	28.0234	−	6.09612i	0.953929	−	0.207514i	0.662486	+	0.749074i	$0.269501\pi$
$864$	−13.6737	−	11.8484i	−0.465190	−	0.403090i
$865$	−43.6249	−	18.8614i	−1.48329	−	0.641306i
$866$	34.6044	−	4.97536i	1.17591	−	0.169070i
$867$	1.89371	−	26.4775i	0.0643136	−	0.899222i
$868$	−1.08874	+	2.91903i	−0.0369543	+	0.0990782i
$869$	12.8560	+	43.7835i	0.436110	+	1.48525i
$870$	−8.59925	−	35.9934i	−0.291542	−	1.22029i
$871$	−31.7939	−	4.57128i	−1.07730	−	0.154892i
$872$	2.50250	−	11.5038i	0.0847454	−	0.389568i
$873$	38.8001	+	38.8001i	1.31318	+	1.31318i
$874$	−2.80910	+	4.13325i	−0.0950191	+	0.139809i
$875$	−6.46869	+	16.8048i	−0.218682	+	0.568105i
$876$	0.780593	−	0.501657i	0.0263738	−	0.0169494i
$877$	30.0454	−	22.4917i	1.01456	−	0.759492i	0.0436792	−	0.999046i	$-0.486092\pi$
$877$	30.0454	−	22.4917i	1.01456	−	0.759492i	0.970883	+	0.239554i	$0.0770011\pi$
$878$	−2.91314	−	7.81044i	−0.0983139	−	0.263590i
$879$	−0.212884	+	0.0625083i	−0.00718039	+	0.00210835i
$880$	−9.52044	−	4.95018i	−0.320934	−	0.166871i
$881$	19.1281	−	16.5746i	0.644444	−	0.558414i	−0.270135	−	0.962823i	$-0.587068\pi$
$881$	19.1281	−	16.5746i	0.644444	−	0.558414i	0.914578	+	0.404409i	$0.132523\pi$
$882$	22.0914	−	29.5107i	0.743856	−	0.993676i
$883$	−4.08014	+	2.22792i	−0.137308	+	0.0749756i	−0.546434	−	0.837502i	$-0.684015\pi$
$883$	−4.08014	+	2.22792i	−0.137308	+	0.0749756i	0.409127	+	0.912478i	$0.365833\pi$
$884$	7.41157	−	8.55341i	0.249278	−	0.287682i
$885$	−39.6787	+	47.7169i	−1.33379	+	1.60398i
$886$	−30.5727	−	19.6479i	−1.02711	−	0.660084i
$887$	3.24929	−	0.232393i	0.109100	−	0.00780301i	−0.0166823	−	0.999861i	$-0.505310\pi$
$887$	3.24929	−	0.232393i	0.109100	−	0.00780301i	0.125783	+	0.992058i	$0.459856\pi$
$888$	−10.5450	−	19.3118i	−0.353868	−	0.648061i
$889$	−2.86434	−	19.9219i	−0.0960668	−	0.668160i
$890$	7.30848	−	4.90949i	0.244981	−	0.164566i
$891$	−156.707	+	71.5657i	−5.24988	+	2.39754i
$892$	−0.948197	−	0.517754i	−0.0317480	−	0.0173357i
$893$	1.70394	−	0.635537i	0.0570202	−	0.0212674i
$894$	−5.32142	+	37.0113i	−0.177975	+	1.23784i
$895$	3.54055	−	10.1156i	0.118347	−	0.338127i
$896$		−	1.61058i		−	0.0538056i
$897$	−43.9202	+	41.7164i	−1.46645	+	1.39287i
$898$	23.3050	−	23.3050i	0.777699	−	0.777699i
$899$	−5.13365	−	7.98811i	−0.171217	−	0.266418i
$900$	−38.7269	−	15.8178i	−1.29090	−	0.527262i
$901$	−6.39750	+	14.0086i	−0.213132	+	0.466693i
$902$	14.2410	−	26.0805i	0.474174	−	0.868385i
$903$	25.8772	+	9.65170i	0.861140	+	0.321189i
$904$	8.03021	+	9.26736i	0.267081	+	0.308228i
$905$	−37.5455	−	36.0501i	−1.24806	−	1.19835i
$906$	−53.5111	−	15.7123i	−1.77779	−	0.522005i
$907$	0.574645	+	8.03459i	0.0190808	+	0.266784i	0.998033	+	0.0626937i	$0.0199691\pi$
$907$	0.574645	+	8.03459i	0.0190808	+	0.266784i	−0.978952	+	0.204090i	$0.934576\pi$
$908$	0.446465	+	2.05237i	0.0148165	+	0.0681101i
$909$	−57.3299	+	89.2071i	−1.90151	+	2.95881i
$910$	10.0150	−	9.04070i	0.331993	−	0.299696i
$911$	−2.70385	+	9.20846i	−0.0895825	+	0.305090i	−0.992080	−	0.125604i	$-0.959913\pi$
$911$	−2.70385	+	9.20846i	−0.0895825	+	0.305090i	0.902498	+	0.430694i	$0.141731\pi$
$912$	2.81245	+	2.10537i	0.0931295	+	0.0697159i
$913$	14.1471	+	1.01182i	0.468200	+	0.0334864i
$914$	1.47992	+	3.24056i	0.0489513	+	0.107188i
$915$	7.68268	+	46.6810i	0.253982	+	1.54323i
$916$	−1.72875	−	0.789492i	−0.0571194	−	0.0260855i
$917$	−6.65640	−	8.89191i	−0.219814	−	0.293637i
$918$	−53.4098	−	11.6186i	−1.76279	−	0.383470i
$919$	−8.90819			−0.293854			−0.146927	−	0.989147i	$-0.546938\pi$
$919$	−8.90819			−0.293854			−0.146927	+	0.989147i	$0.546938\pi$
$920$	3.69316	+	10.0678i	0.121760	+	0.331926i
$921$	21.0551			0.693789
$922$	11.7327	+	2.55228i	0.386394	+	0.0840550i
$923$	−5.88621	−	7.86305i	−0.193747	−	0.258815i
$924$	−23.7026	−	10.8246i	−0.779757	−	0.356103i
$925$	−23.9925	−	22.1179i	−0.788869	−	0.727232i
$926$	−9.62855	−	21.0836i	−0.316414	−	0.692850i
$927$	−46.3333	−	3.31382i	−1.52178	−	0.108840i
$928$	3.92971	+	2.94174i	0.128999	+	0.0965675i
$929$	−3.50617	+	11.9409i	−0.115034	+	0.391769i	−0.996802	−	0.0799144i	$-0.974535\pi$
$929$	−3.50617	+	11.9409i	−0.115034	+	0.391769i	0.881768	+	0.471683i	$0.156353\pi$
$930$	−14.5637	−	0.744611i	−0.477564	−	0.0244168i
$931$	−2.48224	+	3.86245i	−0.0813522	+	0.126587i
$932$	0.297450	+	1.36736i	0.00974331	+	0.0447893i
$933$	−4.51656	−	63.1497i	−0.147865	−	2.06743i
$934$	−4.39684	−	1.29103i	−0.143869	−	0.0422437i
$935$	−32.4101	+	0.658552i	−1.05992	+	0.0215370i
$936$	20.5261	+	23.6883i	0.670915	+	0.774277i
$937$	−26.5588	−	9.90592i	−0.867639	−	0.323612i	−0.124071	−	0.992273i	$-0.539595\pi$
$937$	−26.5588	−	9.90592i	−0.867639	−	0.323612i	−0.743568	+	0.668661i	$0.766868\pi$
$938$	−6.61790	+	12.1198i	−0.216082	+	0.395725i
$939$	32.3131	−	70.7559i	1.05450	−	2.30903i
$940$	1.02315	−	3.76593i	0.0333715	−	0.122831i
$941$	22.3133	+	34.7201i	0.727392	+	1.13184i	0.986143	+	0.165900i	$0.0530528\pi$
$941$	22.3133	+	34.7201i	0.727392	+	1.13184i	−0.258751	+	0.965944i	$0.583311\pi$
$942$	−2.69833	+	2.69833i	−0.0879162	+	0.0879162i
$943$	−28.0822	+	9.65875i	−0.914482	+	0.314532i
$944$		−	8.23198i		−	0.267928i
$945$	−61.5009	−	21.5259i	−2.00063	−	0.700236i
$946$	−3.47368	+	24.1600i	−0.112939	+	0.785508i
$947$	−41.6516	+	15.5352i	−1.35349	+	0.504827i	−0.918434	−	0.395574i	$-0.870546\pi$
$947$	−41.6516	+	15.5352i	−1.35349	+	0.504827i	−0.435060	+	0.900401i	$0.643273\pi$
$948$	−28.1375	−	15.3642i	−0.913863	−	0.499007i
$949$	−0.937906	+	0.428327i	−0.0304457	+	0.0139041i
$950$	4.95166	+	1.62098i	0.160653	+	0.0525915i
$951$	11.5296	+	80.1900i	0.373872	+	2.60034i
$952$	−2.33181	−	4.27040i	−0.0755745	−	0.138404i
$953$	−23.4149	+	1.67467i	−0.758483	+	0.0542478i	−0.445223	−	0.895420i	$-0.646876\pi$
$953$	−23.4149	+	1.67467i	−0.758483	+	0.0542478i	−0.313260	+	0.949667i	$0.601421\pi$
$954$	−35.8798	−	23.0586i	−1.16165	−	0.746548i
$955$	−24.1974	+	2.22554i	−0.783009	+	0.0720168i
$956$	13.4933	−	15.5721i	0.436405	−	0.503638i
$957$	69.7045	−	38.0615i	2.25323	−	1.23035i
$958$	−6.92695	+	9.25332i	−0.223800	+	0.298961i
$959$	18.7743	−	16.2681i	0.606255	−	0.525323i
$960$	7.18874	−	2.27042i	0.232016	−	0.0732775i
$961$	26.1541	−	7.67952i	0.843679	−	0.247727i
$962$	8.54447	+	22.9086i	0.275485	+	0.738604i
$963$	15.5991	−	11.6774i	0.502675	−	0.376298i
$964$	−9.68786	+	6.22601i	−0.312025	+	0.200526i
$965$	33.9019	+	4.17330i	1.09134	+	0.134343i
$966$	10.2049	+	23.9583i	0.328338	+	0.770845i
$967$	0.662148	+	0.662148i	0.0212932	+	0.0212932i	0.717673	−	0.696380i	$-0.245207\pi$
$967$	0.662148	+	0.662148i	0.0212932	+	0.0212932i	−0.696380	+	0.717673i	$0.745207\pi$
$968$	2.55686	−	11.7537i	0.0821807	−	0.377779i
$969$	10.5053	+	1.51044i	0.337479	+	0.0485222i
$970$	−14.2637	+	3.40777i	−0.457980	+	0.109417i
$971$	−4.84343	−	16.4952i	−0.155433	−	0.529356i	0.844548	−	0.535479i	$-0.179869\pi$
$971$	−4.84343	−	16.4952i	−0.155433	−	0.529356i	−0.999981	+	0.00612341i	$0.998051\pi$
$972$	23.3281	−	62.5451i	0.748249	−	2.00613i
$973$	−1.79113	+	25.0433i	−0.0574211	+	0.802852i
$974$	−41.1923	+	5.92255i	−1.31989	+	0.189771i
$975$	54.4709	+	31.9568i	1.74446	+	1.02344i
$976$	−4.74266	−	4.10954i	−0.151809	−	0.131543i
$977$	44.3433	−	9.64629i	1.41867	−	0.308612i	0.563137	−	0.826364i	$-0.309594\pi$
$977$	44.3433	−	9.64629i	1.41867	−	0.308612i	0.855531	+	0.517752i	$0.173231\pi$
$978$	−48.2295	+	10.4917i	−1.54221	+	0.335487i
$979$	14.2799	+	12.3736i	0.456388	+	0.395462i
$980$	3.62982	+	9.15918i	0.115950	+	0.292579i
$981$	97.4956	−	14.0178i	3.11280	−	0.447553i
$982$	2.88103	−	40.2821i	0.0919375	−	1.28545i
$983$	13.6404	−	36.5712i	0.435060	−	1.16644i	−0.515770	−	0.856727i	$-0.672494\pi$
$983$	13.6404	−	36.5712i	0.435060	−	1.16644i	0.950830	−	0.309713i	$-0.100233\pi$
$984$	5.88163	+	20.0310i	0.187499	+	0.638564i
$985$	9.08552	+	5.58141i	0.289489	+	0.177839i
$986$	14.6786	+	2.11047i	0.467462	+	0.0672109i
$987$	2.01437	−	9.25992i	0.0641181	−	0.294746i
$988$	−2.76046	−	2.76046i	−0.0878220	−	0.0878220i
$989$	18.8400	−	15.4946i	0.599078	−	0.492701i
$990$	10.9687	−	89.1045i	0.348608	−	2.83193i
$991$	18.4994	−	11.8888i	0.587651	−	0.377661i	−0.212766	−	0.977103i	$-0.568247\pi$
$991$	18.4994	−	11.8888i	0.587651	−	0.377661i	0.800418	+	0.599442i	$0.204611\pi$
$992$	1.54855	−	1.15923i	0.0491664	−	0.0368055i
$993$	4.23926	+	11.3659i	0.134529	+	0.360686i
$994$	−4.05154	+	1.18964i	−0.128507	+	0.0377331i
$995$	−10.4100	+	20.0210i	−0.330018	+	0.634708i
$996$	−7.53067	+	6.52536i	−0.238618	+	0.206764i
$997$	25.8009	−	34.4660i	0.817122	−	1.09155i	−0.177098	−	0.984193i	$-0.556671\pi$
$997$	25.8009	−	34.4660i	0.817122	−	1.09155i	0.994221	−	0.107355i	$-0.0342380\pi$
$998$	12.4741	−	6.81139i	0.394861	−	0.215611i
$999$	77.3270	−	89.2401i	2.44652	−	2.82343i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.l.a.57.12	✓	240
5.3	odd	4	inner	230.2.l.a.103.7	yes	240
23.21	odd	22	inner	230.2.l.a.67.7	yes	240
115.113	even	44	inner	230.2.l.a.113.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.l.a.57.12	✓	240	1.1	even	1	trivial
230.2.l.a.67.7	yes	240	23.21	odd	22	inner
230.2.l.a.103.7	yes	240	5.3	odd	4	inner
230.2.l.a.113.12	yes	240	115.113	even	44	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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.977147 + 0.212565i) q^{2} +(2.02042 + 2.69897i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.81692 - 1.30338i) q^{5} +(1.40054 + 3.06676i) q^{6} +(-1.60647 - 0.114897i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-2.35713 + 8.02765i) q^{9} +(-1.49834 - 1.65981i) q^{10} +(2.59443 - 4.03702i) q^{11} +(0.716649 + 3.29438i) q^{12} +(-0.267263 - 3.73682i) q^{13} +(-1.54534 - 0.453752i) q^{14} +(-0.153151 - 7.53719i) q^{15} +(0.654861 + 0.755750i) q^{16} +(2.83053 + 1.05573i) q^{17} +(-4.00966 + 7.34315i) q^{18} +(0.432881 - 0.947878i) q^{19} +(-1.11128 - 1.94037i) q^{20} +(-2.93565 - 4.56796i) q^{21} +(3.39327 - 3.39327i) q^{22} +(-4.79083 + 0.218958i) q^{23} +3.37143i q^{24} +(1.60238 + 4.73628i) q^{25} +(0.533163 - 3.70823i) q^{26} +(-16.9522 + 6.32284i) q^{27} +(-1.41357 - 0.771867i) q^{28} +(4.46522 - 2.03920i) q^{29} +(1.45250 - 7.39750i) q^{30} +(-0.275290 - 1.91468i) q^{31} +(0.479249 + 0.877679i) q^{32} +(16.1376 - 1.15419i) q^{33} +(2.54143 + 1.63328i) q^{34} +(2.76907 + 2.30261i) q^{35} +(-5.47893 + 6.32302i) q^{36} +(-5.72807 + 3.12776i) q^{37} +(0.624475 - 0.834200i) q^{38} +(9.54558 - 8.27129i) q^{39} +(-0.673429 - 2.13225i) q^{40} +(5.94139 - 1.74455i) q^{41} +(-1.89757 - 5.08759i) q^{42} +(-4.07183 + 3.04813i) q^{43} +(4.03702 - 2.59443i) q^{44} +(14.7458 - 11.5133i) q^{45} +(-4.72789 - 0.804410i) q^{46} +(1.23406 + 1.23406i) q^{47} +(-0.716649 + 3.29438i) q^{48} +(-4.36120 - 0.627045i) q^{49} +(0.558994 + 4.96865i) q^{50} +(2.86948 + 9.77254i) q^{51} +(1.30922 - 3.51016i) q^{52} +(-0.363668 + 5.08474i) q^{53} +(-17.9088 + 2.57490i) q^{54} +(-9.97566 + 3.95339i) q^{55} +(-1.21719 - 1.05470i) q^{56} +(3.43290 - 0.746781i) q^{57} +(4.79663 - 1.04344i) q^{58} +(-6.22131 - 5.39080i) q^{59} +(2.99175 - 6.91969i) q^{60} +(-6.21156 + 0.893088i) q^{61} +(0.137997 - 1.92944i) q^{62} +(4.70902 - 12.6254i) q^{63} +(0.281733 + 0.959493i) q^{64} +(-4.38492 + 7.13784i) q^{65} +(16.0142 + 2.30249i) q^{66} +(1.82251 - 8.37794i) q^{67} +(2.13617 + 2.13617i) q^{68} +(-10.2705 - 12.4879i) q^{69} +(2.21634 + 2.83860i) q^{70} +(2.20559 - 1.41744i) q^{71} +(-6.69777 + 5.01389i) q^{72} +(-0.0961803 - 0.257869i) q^{73} +(-6.26202 + 1.83869i) q^{74} +(-9.54559 + 13.8941i) q^{75} +(0.787525 - 0.682395i) q^{76} +(-4.63173 + 6.18727i) q^{77} +(11.0856 - 6.05321i) q^{78} +(-6.22707 + 7.18643i) q^{79} +(-0.204797 - 2.22667i) q^{80} +(-30.2006 - 19.4088i) q^{81} +(6.17644 - 0.441748i) q^{82} +(1.41645 + 2.59404i) q^{83} +(-0.772762 - 5.37468i) q^{84} +(-3.76681 - 5.60744i) q^{85} +(-4.62670 + 2.11294i) q^{86} +(14.5254 + 7.93145i) q^{87} +(4.49625 - 1.67701i) q^{88} +(-0.560355 + 3.89736i) q^{89} +(16.8562 - 8.11577i) q^{90} +6.03381i q^{91} +(-4.44885 - 1.79101i) q^{92} +(4.61147 - 4.61147i) q^{93} +(0.943540 + 1.46818i) q^{94} +(-2.02196 + 1.15801i) q^{95} +(-1.40054 + 3.06676i) q^{96} +(3.14313 - 5.75621i) q^{97} +(-4.12824 - 1.53975i) q^{98} +(26.2923 + 30.3430i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 8 q^{6} - 8 q^{12} + 16 q^{13} + 24 q^{16} - 72 q^{18} - 80 q^{23} - 8 q^{26} + 16 q^{27} - 44 q^{28} + 24 q^{31} - 44 q^{33} - 8 q^{35} - 32 q^{36} - 88 q^{37} - 24 q^{41} - 8 q^{46}+ \cdots + 24 q^{98}+O(q^{100}) \) 240 * q - 8 * q^3 - 8 * q^6 - 8 * q^12 + 16 * q^13 + 24 * q^16 - 72 * q^18 - 80 * q^23 - 8 * q^26 + 16 * q^27 - 44 * q^28 + 24 * q^31 - 44 * q^33 - 8 * q^35 - 32 * q^36 - 88 * q^37 - 24 * q^41 - 8 * q^46 - 80 * q^47 + 8 * q^48 + 8 * q^50 + 16 * q^52 - 44 * q^56 - 88 * q^57 - 176 * q^61 - 32 * q^62 - 176 * q^66 + 24 * q^70 - 336 * q^71 + 16 * q^72 - 88 * q^73 - 36 * q^75 - 24 * q^77 + 40 * q^78 - 136 * q^81 + 40 * q^82 - 100 * q^85 - 44 * q^86 + 40 * q^87 + 8 * q^92 + 56 * q^93 + 52 * q^95 + 8 * q^96 + 132 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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