LMFDB - Embedded newform 475.2.bb.b.143.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [475,2,Mod(32,475)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(475, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("475.32"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bb (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			143.6
Character	$\chi$	$=$	475.143
Dual form			475.2.bb.b.382.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.983828 - 1.40505i) q^{2} +(0.215709 - 2.46557i) q^{3} +(-0.322212 - 0.885271i) q^{4} +(-3.25203 - 2.72877i) q^{6} +(-0.0743036 - 0.277305i) q^{7} +(1.75276 + 0.469650i) q^{8} +(-3.07806 - 0.542745i) q^{9} +(-2.29500 - 3.97505i) q^{11} +(-2.25220 + 0.603475i) q^{12} +(-2.46682 + 0.215819i) q^{13} +(-0.462730 - 0.168420i) q^{14} +(3.82765 - 3.21178i) q^{16} +(-3.94756 - 2.76411i) q^{17} +(-3.79086 + 3.79086i) q^{18} +(1.73832 + 3.99728i) q^{19} +(-0.699742 + 0.123383i) q^{21} +(-7.84303 - 0.686176i) q^{22} +(6.88562 + 3.21082i) q^{23} +(1.53604 - 4.22023i) q^{24} +(-2.12369 + 3.67833i) q^{26} +(-0.0804202 + 0.300132i) q^{27} +(-0.221548 + 0.155130i) q^{28} +(0.000506761 - 0.00287398i) q^{29} +(2.87440 + 1.65954i) q^{31} +(-0.430665 - 4.92252i) q^{32} +(-10.2958 + 4.80101i) q^{33} +(-7.76743 + 2.82711i) q^{34} +(0.511312 + 2.89980i) q^{36} +(5.46158 + 5.46158i) q^{37} +(7.32659 + 1.49020i) q^{38} +6.12865i q^{39} +(0.132829 + 0.158299i) q^{41} +(-0.515065 + 1.10456i) q^{42} +(-0.0847905 - 0.181834i) q^{43} +(-2.77952 + 3.31250i) q^{44} +(11.2856 - 6.51576i) q^{46} +(2.89119 + 4.12905i) q^{47} +(-7.09320 - 10.1301i) q^{48} +(5.99080 - 3.45879i) q^{49} +(-7.66662 + 9.13672i) q^{51} +(0.985897 + 2.11426i) q^{52} +(1.11603 - 2.39334i) q^{53} +(0.342582 + 0.408273i) q^{54} -0.520945i q^{56} +(10.2305 - 3.42370i) q^{57} +(-0.00353953 - 0.00353953i) q^{58} +(0.369926 + 2.09795i) q^{59} +(-3.76621 + 1.37079i) q^{61} +(5.15965 - 2.40598i) q^{62} +(0.0782052 + 0.893889i) q^{63} +(1.31435 + 0.758840i) q^{64} +(-3.38362 + 19.1895i) q^{66} +(-7.42839 + 5.20141i) q^{67} +(-1.17503 + 4.38529i) q^{68} +(9.40177 - 16.2843i) q^{69} +(4.33266 - 11.9039i) q^{71} +(-5.14019 - 2.39691i) q^{72} +(10.7580 + 0.941200i) q^{73} +(13.0471 - 2.30055i) q^{74} +(2.97856 - 2.82686i) q^{76} +(-0.931774 + 0.931774i) q^{77} +(8.61107 + 6.02954i) q^{78} +(-4.20092 + 3.52499i) q^{79} +(-8.08850 - 2.94397i) q^{81} +(0.353099 - 0.0308922i) q^{82} +(-15.4419 + 4.13763i) q^{83} +(0.334693 + 0.579705i) q^{84} +(-0.338905 - 0.0597581i) q^{86} +(-0.00697668 - 0.00186940i) q^{87} +(-2.15569 - 8.04514i) q^{88} +(-12.1125 - 10.1636i) q^{89} +(0.243141 + 0.668024i) q^{91} +(0.623812 - 7.13020i) q^{92} +(4.71173 - 6.72905i) q^{93} +8.64596 q^{94} -12.2297 q^{96} +(3.42156 - 4.88649i) q^{97} +(1.03414 - 11.8202i) q^{98} +(4.90670 + 13.4810i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) $ 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.983828	−	1.40505i	0.695671	−	0.993521i	−0.303501	−	0.952831i	$-0.598155\pi$
$2$	0.983828	−	1.40505i	0.695671	−	0.993521i	0.999172	−	0.0406901i	$-0.0129556\pi$
$3$	0.215709	−	2.46557i	0.124540	−	1.42349i	−0.634738	−	0.772728i	$-0.718892\pi$
$3$	0.215709	−	2.46557i	0.124540	−	1.42349i	0.759277	−	0.650767i	$-0.225553\pi$
$4$	−0.322212	−	0.885271i	−0.161106	−	0.442635i
$5$		0			0
$5$		0			0
$6$	−3.25203	−	2.72877i	−1.32763	−	1.11402i
$7$	−0.0743036	−	0.277305i	−0.0280841	−	0.104811i	0.950461	−	0.310844i	$-0.100612\pi$
$7$	−0.0743036	−	0.277305i	−0.0280841	−	0.104811i	−0.978545	+	0.206032i	$0.933945\pi$
$8$	1.75276	+	0.469650i	0.619693	+	0.166046i
$9$	−3.07806	−	0.542745i	−1.02602	−	0.180915i
$10$		0			0
$11$	−2.29500	−	3.97505i	−0.691967	−	1.19852i	−0.971192	−	0.238297i	$-0.923411\pi$
$11$	−2.29500	−	3.97505i	−0.691967	−	1.19852i	0.279225	−	0.960226i	$-0.409922\pi$
$12$	−2.25220	+	0.603475i	−0.650153	+	0.174208i
$13$	−2.46682	+	0.215819i	−0.684172	+	0.0598573i	−0.423942	−	0.905689i	$-0.639354\pi$
$13$	−2.46682	+	0.215819i	−0.684172	+	0.0598573i	−0.260230	+	0.965547i	$0.583798\pi$
$14$	−0.462730	−	0.168420i	−0.123670	−	0.0450121i
$15$		0			0
$16$	3.82765	−	3.21178i	0.956913	−	0.802946i
$17$	−3.94756	−	2.76411i	−0.957423	−	0.670395i	−0.0132738	−	0.999912i	$-0.504225\pi$
$17$	−3.94756	−	2.76411i	−0.957423	−	0.670395i	−0.944150	+	0.329517i	$0.893114\pi$
$18$	−3.79086	+	3.79086i	−0.893515	+	0.893515i
$19$	1.73832	+	3.99728i	0.398799	+	0.917038i
$19$	1.73832	+	3.99728i	0.398799	+	0.917038i
$20$		0			0
$21$	−0.699742	+	0.123383i	−0.152696	+	0.0269244i
$22$	−7.84303	−	0.686176i	−1.67214	−	0.146293i
$23$	6.88562	+	3.21082i	1.43575	+	0.669501i	0.975845	−	0.218466i	$-0.0701053\pi$
$23$	6.88562	+	3.21082i	1.43575	+	0.669501i	0.459906	+	0.887968i	$0.347883\pi$
$24$	1.53604	−	4.22023i	0.313543	−	0.861451i
$25$		0			0
$26$	−2.12369	+	3.67833i	−0.416489	+	0.721380i
$27$	−0.0804202	+	0.300132i	−0.0154769	+	0.0577605i
$28$	−0.221548	+	0.155130i	−0.0418687	+	0.0293168i
$29$	0.000506761	−	0.00287398i	9.41031e−5	−	0.000533685i	−0.984761	−	0.173915i	$-0.944358\pi$
$29$	0.000506761	−	0.00287398i	9.41031e−5	−	0.000533685i	0.984855	+	0.173381i	$0.0554693\pi$
$30$		0			0
$31$	2.87440	+	1.65954i	0.516258	+	0.298062i	0.735402	−	0.677631i	$-0.236993\pi$
$31$	2.87440	+	1.65954i	0.516258	+	0.298062i	−0.219144	+	0.975692i	$0.570327\pi$
$32$	−0.430665	−	4.92252i	−0.0761315	−	0.870187i
$33$	−10.2958	+	4.80101i	−1.79227	+	0.835748i
$34$	−7.76743	+	2.82711i	−1.33210	+	0.484846i
$35$		0			0
$36$	0.511312	+	2.89980i	0.0852187	+	0.483299i
$37$	5.46158	+	5.46158i	0.897878	+	0.897878i	0.995248	−	0.0973701i	$-0.0310431\pi$
$37$	5.46158	+	5.46158i	0.897878	+	0.897878i	−0.0973701	+	0.995248i	$0.531043\pi$
$38$	7.32659	+	1.49020i	1.18853	+	0.241742i
$39$			6.12865i			0.981370i
$40$		0			0
$41$	0.132829	+	0.158299i	0.0207444	+	0.0247222i	0.776317	−	0.630343i	$-0.217086\pi$
$41$	0.132829	+	0.158299i	0.0207444	+	0.0247222i	−0.755573	+	0.655065i	$0.772641\pi$
$42$	−0.515065	+	1.10456i	−0.0794763	+	0.170437i
$43$	−0.0847905	−	0.181834i	−0.0129304	−	0.0277294i	0.899737	−	0.436433i	$-0.143759\pi$
$43$	−0.0847905	−	0.181834i	−0.0129304	−	0.0277294i	−0.912667	+	0.408704i	$0.865981\pi$
$44$	−2.77952	+	3.31250i	−0.419028	+	0.499379i
$45$		0			0
$46$	11.2856	−	6.51576i	1.66397	−	0.960696i
$47$	2.89119	+	4.12905i	0.421724	+	0.602284i	0.972652	−	0.232269i	$-0.0746150\pi$
$47$	2.89119	+	4.12905i	0.421724	+	0.602284i	−0.550928	+	0.834553i	$0.685726\pi$
$48$	−7.09320	−	10.1301i	−1.02382	−	1.46216i
$49$	5.99080	−	3.45879i	0.855829	−	0.494113i
$50$		0			0
$51$	−7.66662	+	9.13672i	−1.07354	+	1.27940i
$52$	0.985897	+	2.11426i	0.136719	+	0.293195i
$53$	1.11603	−	2.39334i	0.153299	−	0.328751i	−0.814627	−	0.579985i	$-0.803058\pi$
$53$	1.11603	−	2.39334i	0.153299	−	0.328751i	0.967926	+	0.251234i	$0.0808363\pi$
$54$	0.342582	+	0.408273i	0.0466194	+	0.0555589i
$55$		0			0
$56$		−	0.520945i		−	0.0696142i
$57$	10.2305	−	3.42370i	1.35507	−	0.453481i
$58$	−0.00353953	−	0.00353953i	−0.000464763	−	0.000464763i
$59$	0.369926	+	2.09795i	0.0481602	+	0.273130i	0.999373	−	0.0354053i	$-0.0112722\pi$
$59$	0.369926	+	2.09795i	0.0481602	+	0.273130i	−0.951213	+	0.308536i	$0.900161\pi$
$60$		0			0
$61$	−3.76621	+	1.37079i	−0.482214	+	0.175511i	−0.571677	−	0.820479i	$-0.693707\pi$
$61$	−3.76621	+	1.37079i	−0.482214	+	0.175511i	0.0894634	+	0.995990i	$0.471485\pi$
$62$	5.15965	−	2.40598i	0.655276	−	0.305560i
$63$	0.0782052	+	0.893889i	0.00985293	+	0.112619i
$64$	1.31435	+	0.758840i	0.164294	+	0.0948550i
$65$		0			0
$66$	−3.38362	+	19.1895i	−0.416495	+	2.36206i
$67$	−7.42839	+	5.20141i	−0.907522	+	0.635454i	−0.931296	−	0.364263i	$-0.881321\pi$
$67$	−7.42839	+	5.20141i	−0.907522	+	0.635454i	0.0237737	+	0.999717i	$0.492432\pi$
$68$	−1.17503	+	4.38529i	−0.142494	+	0.531794i
$69$	9.40177	−	16.2843i	1.13184	−	1.96040i
$70$		0			0
$71$	4.33266	−	11.9039i	0.514192	−	1.41273i	−0.362639	−	0.931930i	$-0.618124\pi$
$71$	4.33266	−	11.9039i	0.514192	−	1.41273i	0.876830	−	0.480800i	$-0.159654\pi$
$72$	−5.14019	−	2.39691i	−0.605778	−	0.282479i
$73$	10.7580	+	0.941200i	1.25912	+	0.110159i	0.697108	−	0.716967i	$-0.254470\pi$
$73$	10.7580	+	0.941200i	1.25912	+	0.110159i	0.562017	+	0.827126i	$0.310026\pi$
$74$	13.0471	−	2.30055i	1.51669	−	0.267433i
$75$		0			0
$76$	2.97856	−	2.82686i	0.341665	−	0.324263i
$77$	−0.931774	+	0.931774i	−0.106186	+	0.106186i
$78$	8.61107	+	6.02954i	0.975012	+	0.682711i
$79$	−4.20092	+	3.52499i	−0.472641	+	0.396592i	−0.847757	−	0.530385i	$-0.822047\pi$
$79$	−4.20092	+	3.52499i	−0.472641	+	0.396592i	0.375116	+	0.926978i	$0.377603\pi$
$80$		0			0
$81$	−8.08850	−	2.94397i	−0.898723	−	0.327108i
$82$	0.353099	−	0.0308922i	0.0389933	−	0.00341147i
$83$	−15.4419	+	4.13763i	−1.69496	+	0.454164i	−0.971664	−	0.236368i	$-0.924043\pi$
$83$	−15.4419	+	4.13763i	−1.69496	+	0.454164i	−0.723301	+	0.690533i	$0.757376\pi$
$84$	0.334693	+	0.579705i	0.0365180	+	0.0632510i
$85$		0			0
$86$	−0.338905	−	0.0597581i	−0.0365451	−	0.00644388i
$87$	−0.00697668	−	0.00186940i	−0.000747978	−	0.000200420i
$88$	−2.15569	−	8.04514i	−0.229797	−	0.857615i
$89$	−12.1125	−	10.1636i	−1.28392	−	1.07734i	−0.992691	−	0.120683i	$-0.961492\pi$
$89$	−12.1125	−	10.1636i	−1.28392	−	1.07734i	−0.291228	−	0.956654i	$-0.594064\pi$
$90$		0			0
$91$	0.243141	+	0.668024i	0.0254881	+	0.0700280i
$92$	0.623812	−	7.13020i	0.0650369	−	0.743375i
$93$	4.71173	−	6.72905i	0.488584	−	0.697770i
$94$	8.64596			0.891763
$95$		0			0
$96$	−12.2297			−1.24819
$97$	3.42156	−	4.88649i	0.347407	−	0.496148i	−0.606982	−	0.794716i	$-0.707620\pi$
$97$	3.42156	−	4.88649i	0.347407	−	0.496148i	0.954389	+	0.298567i	$0.0965088\pi$
$98$	1.03414	−	11.8202i	0.104464	−	1.19402i
$99$	4.90670	+	13.4810i	0.493142	+	1.35490i
$100$		0			0
$101$	8.53219	+	7.15936i	0.848985	+	0.712383i	0.959566	−	0.281484i	$-0.0908267\pi$
$101$	8.53219	+	7.15936i	0.848985	+	0.712383i	−0.110581	+	0.993867i	$0.535271\pi$
$102$	5.29493	+	19.7609i	0.524276	+	1.95663i
$103$	0.797004	+	0.213557i	0.0785312	+	0.0210424i	0.297871	−	0.954606i	$-0.403724\pi$
$103$	0.797004	+	0.213557i	0.0785312	+	0.0210424i	−0.219340	+	0.975649i	$0.570390\pi$
$104$	−4.42509	−	0.780263i	−0.433916	−	0.0765111i
$105$		0			0
$106$	−2.26479	−	3.92272i	−0.219975	−	0.381009i
$107$	15.0602	−	4.03536i	1.45592	−	0.390113i	0.557842	−	0.829947i	$-0.311630\pi$
$107$	15.0602	−	4.03536i	1.45592	−	0.390113i	0.898079	+	0.439835i	$0.144963\pi$
$108$	0.291611	−	0.0255126i	0.0280602	−	0.00245495i
$109$	−8.88129	−	3.23252i	−0.850673	−	0.309620i	−0.120358	−	0.992731i	$-0.538404\pi$
$109$	−8.88129	−	3.23252i	−0.850673	−	0.309620i	−0.730315	+	0.683111i	$0.760627\pi$
$110$		0			0
$111$	14.6440	−	12.2878i	1.38995	−	1.16630i
$112$	−1.17505	−	0.822780i	−0.111032	−	0.0777454i
$113$	−1.30423	+	1.30423i	−0.122692	+	0.122692i	−0.765787	−	0.643095i	$-0.777650\pi$
$113$	−1.30423	+	1.30423i	−0.122692	+	0.122692i	0.643095	+	0.765787i	$0.277650\pi$
$114$	5.25459	−	17.7427i	0.492137	−	1.66176i
$115$		0			0
$116$	−0.00270754		0.000477412i	−0.000251389		4.43266e-5i
$117$	7.71014	+	0.674550i	0.712803	+	0.0623622i
$118$	3.31168	+	1.54426i	0.304864	+	0.142161i
$119$	−0.473183	+	1.30006i	−0.0433767	+	0.119176i
$120$		0			0
$121$	−5.03401	+	8.71916i	−0.457637	+	0.792651i
$122$	−1.77927	+	6.64034i	−0.161088	+	0.601188i
$123$	0.418950	−	0.293352i	0.0377754	−	0.0264506i
$124$	0.542972	−	3.07935i	0.0487603	−	0.276534i
$125$		0			0
$126$	1.33290	+	0.769551i	0.118744	+	0.0685570i
$127$	0.878208	+	10.0380i	0.0779284	+	0.890725i	0.930062	+	0.367402i	$0.119753\pi$
$127$	0.878208	+	10.0380i	0.0779284	+	0.890725i	−0.852134	+	0.523324i	$0.824692\pi$
$128$	11.3160	−	5.27675i	1.00020	−	0.466403i
$129$	−0.466613	+	0.169833i	−0.0410830	+	0.0149530i
$130$		0			0
$131$	3.39696	+	19.2651i	0.296794	+	1.68320i	0.659820	+	0.751423i	$0.270632\pi$
$131$	3.39696	+	19.2651i	0.296794	+	1.68320i	−0.363026	+	0.931779i	$0.618256\pi$
$132$	7.56763	+	7.56763i	0.658677	+	0.658677i
$133$	0.979301	−	0.779058i	0.0849162	−	0.0675529i
$134$			15.5546i			1.34371i
$135$		0			0
$136$	−5.62095	−	6.69879i	−0.481992	−	0.574416i
$137$	4.50418	−	9.65926i	0.384818	−	0.825246i	−0.614521	−	0.788901i	$-0.710651\pi$
$137$	4.50418	−	9.65926i	0.384818	−	0.825246i	0.999339	−	0.0363453i	$-0.0115716\pi$
$138$	−13.6306	−	29.2309i	−1.16031	−	2.48830i
$139$	−9.87278	+	11.7659i	−0.837399	+	0.997973i	0.162538	+	0.986702i	$0.448032\pi$
$139$	−9.87278	+	11.7659i	−0.837399	+	0.997973i	−0.999936	+	0.0112706i	$0.996412\pi$
$140$		0			0
$141$	10.8041	−	6.23775i	0.909869	−	0.525313i
$142$	−12.4630	−	17.7990i	−1.04587	−	1.49366i
$143$	6.51922	+	9.31042i	0.545165	+	0.778576i
$144$	−13.5249	+	7.80862i	−1.12708	+	0.650718i
$145$		0			0
$146$	11.9064	−	14.1895i	0.985382	−	1.17433i
$147$	−7.23560	−	15.5168i	−0.596783	−	1.27980i
$148$	3.07519	−	6.59477i	0.252779	−	0.542086i
$149$	6.22102	+	7.41392i	0.509646	+	0.607372i	0.958100	−	0.286434i	$-0.0924698\pi$
$149$	6.22102	+	7.41392i	0.509646	+	0.607372i	−0.448454	+	0.893806i	$0.648025\pi$
$150$		0			0
$151$			3.10459i			0.252648i	0.991989	+	0.126324i	$0.0403179\pi$
$151$			3.10459i			0.252648i	−0.991989	+	0.126324i	$0.959682\pi$
$152$	1.16954	+	7.82266i	0.0948623	+	0.634502i
$153$	10.6506	+	10.6506i	0.861051	+	0.861051i
$154$	0.392486	+	2.22590i	0.0316274	+	0.179368i
$155$		0			0
$156$	5.42552	−	1.97473i	0.434389	−	0.158105i
$157$	−14.6336	+	6.82378i	−1.16789	+	0.544597i	−0.907148	−	0.420811i	$-0.861746\pi$
$157$	−14.6336	+	6.82378i	−1.16789	+	0.544597i	−0.260744	+	0.965408i	$0.583968\pi$
$158$	0.819812	+	9.37049i	0.0652207	+	0.745476i
$159$	−5.66021	−	3.26792i	−0.448884	−	0.259163i
$160$		0			0
$161$	0.378749	−	2.14799i	0.0298496	−	0.169285i
$162$	−12.0941	+	8.46840i	−0.950204	+	0.665340i
$163$	−0.0214015	+	0.0798713i	−0.00167629	+	0.00625600i	−0.966759	−	0.255690i	$-0.917697\pi$
$163$	−0.0214015	+	0.0798713i	−0.00167629	+	0.00625600i	0.965083	+	0.261946i	$0.0843641\pi$
$164$	0.0973387	−	0.168596i	0.00760088	−	0.0131651i
$165$		0			0
$166$	−9.37854	+	25.7673i	−0.727916	+	1.99993i
$167$	−7.81520	−	3.64429i	−0.604758	−	0.282003i	0.0960237	−	0.995379i	$-0.469388\pi$
$167$	−7.81520	−	3.64429i	−0.604758	−	0.282003i	−0.700782	+	0.713376i	$0.747165\pi$
$168$	−1.28442	−	0.112373i	−0.0990955	−	0.00866973i
$169$	−6.76389	+	1.19266i	−0.520299	+	0.0917428i
$170$		0			0
$171$	−3.18117	−	13.2473i	−0.243270	−	1.01305i
$172$	−0.133652	+	0.133652i	−0.0101908	+	0.0101908i
$173$	7.73878	+	5.41875i	0.588369	+	0.411980i	0.829495	−	0.558514i	$-0.188628\pi$
$173$	7.73878	+	5.41875i	0.588369	+	0.411980i	−0.241127	+	0.970494i	$0.577517\pi$
$174$	−0.00949044	+	0.00796343i	−0.000719469	+	0.000603706i
$175$		0			0
$176$	−21.5514	−	7.84408i	−1.62450	−	0.591270i
$177$	5.25244	−	0.459529i	0.394797	−	0.0345403i
$178$	−26.1969	+	7.01944i	−1.96354	+	0.526130i
$179$	3.58941	+	6.21705i	0.268285	+	0.464684i	0.968419	−	0.249328i	$-0.0802096\pi$
$179$	3.58941	+	6.21705i	0.268285	+	0.464684i	−0.700134	+	0.714012i	$0.746876\pi$
$180$		0			0
$181$	−1.58706	−	0.279841i	−0.117965	−	0.0208004i	0.114354	−	0.993440i	$-0.463520\pi$
$181$	−1.58706	−	0.279841i	−0.117965	−	0.0208004i	−0.232319	+	0.972640i	$0.574631\pi$
$182$	1.17782	+	0.315595i	0.0873056	+	0.0233935i
$183$	2.56736	+	9.58153i	0.189785	+	0.708287i
$184$	10.5609	+	8.86161i	0.778557	+	0.653287i
$185$		0			0
$186$	−4.81913	−	13.2404i	−0.353356	−	0.970837i
$187$	−1.92784	+	22.0354i	−0.140978	+	1.61139i
$188$	2.72375	−	3.88992i	0.198650	−	0.283702i
$189$	0.0892037			0.00648861
$190$		0			0
$191$	4.58246			0.331575			0.165787	−	0.986162i	$-0.446983\pi$
$191$	4.58246			0.331575			0.165787	+	0.986162i	$0.446983\pi$
$192$	2.15449	−	3.07693i	0.155487	−	0.222058i
$193$	−1.06893	+	12.2179i	−0.0769431	+	0.879464i	0.855419	+	0.517937i	$0.173300\pi$
$193$	−1.06893	+	12.2179i	−0.0769431	+	0.879464i	−0.932362	+	0.361526i	$0.882256\pi$
$194$	−3.49955	−	9.61494i	−0.251253	−	0.690312i
$195$		0			0
$196$	−4.99228	−	4.18902i	−0.356591	−	0.299216i
$197$	−0.0436698	−	0.162978i	−0.00311135	−	0.0116117i	0.964353	−	0.264620i	$-0.0852466\pi$
$197$	−0.0436698	−	0.162978i	−0.00311135	−	0.0116117i	−0.967464	+	0.253009i	$0.918580\pi$
$198$	23.7689	+	6.36886i	1.68918	+	0.452615i
$199$	−4.92176	−	0.867839i	−0.348894	−	0.0615195i	−0.00354503	−	0.999994i	$-0.501128\pi$
$199$	−4.92176	−	0.867839i	−0.348894	−	0.0615195i	−0.345349	+	0.938474i	$0.612240\pi$
$200$		0			0
$201$	11.2221	+	19.4372i	0.791543	+	1.37099i
$202$	18.4535	−	4.94459i	1.29838	−	0.347900i
$203$	−0.000834624	0	7.30201e-5i	−5.85791e−5	0	5.12501e-6i
$204$	10.5588	+	3.84307i	0.739260	+	0.269069i
$205$		0			0
$206$	1.08417	−	0.909729i	0.0755379	−	0.0633838i
$207$	−19.4517	−	13.6202i	−1.35199	−	0.946671i
$208$	−8.74896	+	8.74896i	−0.606631	+	0.606631i
$209$	11.8999	−	16.0837i	0.823135	−	1.11253i
$210$		0			0
$211$	−0.0936993	+	0.0165217i	−0.00645053	+	0.00113740i	−0.176873	−	0.984234i	$-0.556598\pi$
$211$	−0.0936993	+	0.0165217i	−0.00645053	+	0.00113740i	0.170422	+	0.985371i	$0.445487\pi$
$212$	−2.47836	−	0.216828i	−0.170214	−	0.0148918i
$213$	−28.4152	−	13.2502i	−1.94698	−	0.907890i
$214$	9.14671	−	25.1304i	0.625257	−	1.71788i
$215$		0			0
$216$	−0.281914	+	0.488290i	−0.0191818	+	0.0332239i
$217$	0.246619	−	0.920396i	0.0167416	−	0.0624805i
$218$	−13.2795	+	9.29842i	−0.899402	+	0.629768i
$219$	4.64118	−	26.3214i	0.313622	−	1.77864i
$220$		0			0
$221$	10.3344	+	5.96660i	0.695170	+	0.401357i
$222$	−2.85778	−	32.6646i	−0.191802	−	2.19231i
$223$	−0.622900	+	0.290463i	−0.0417125	+	0.0194508i	−0.443363	−	0.896342i	$-0.646215\pi$
$223$	−0.622900	+	0.290463i	−0.0417125	+	0.0194508i	0.401650	+	0.915793i	$0.368437\pi$
$224$	−1.33304	+	0.485187i	−0.0890675	+	0.0324179i
$225$		0			0
$226$	0.549375	+	3.11566i	0.0365439	+	0.207250i
$227$	−3.13234	−	3.13234i	−0.207901	−	0.207901i	0.595474	−	0.803375i	$-0.296964\pi$
$227$	−3.13234	−	3.13234i	−0.207901	−	0.207901i	−0.803375	+	0.595474i	$0.796964\pi$
$228$	−6.32731	−	7.95362i	−0.419036	−	0.526742i
$229$		−	1.64132i		−	0.108462i	−0.998528	−	0.0542308i	$-0.982729\pi$
$229$		−	1.64132i		−	0.108462i	0.998528	−	0.0542308i	$-0.0172707\pi$
$230$		0			0
$231$	2.09636	+	2.49834i	0.137930	+	0.164379i
$232$	0.00223799	−	0.00479939i	0.000146932	−	0.000315096i
$233$	−4.08407	−	8.75832i	−0.267556	−	0.573776i	0.725925	−	0.687774i	$-0.241412\pi$
$233$	−4.08407	−	8.75832i	−0.267556	−	0.573776i	−0.993481	+	0.113998i	$0.963634\pi$
$234$	8.53323	−	10.1695i	0.557835	−	0.664802i
$235$		0			0
$236$	1.73806	−	1.00347i	0.113138	−	0.0653204i
$237$	7.78492	+	11.1180i	0.505685	+	0.722193i
$238$	1.36112	+	1.94388i	0.0882284	+	0.126003i
$239$	−5.41584	+	3.12684i	−0.350321	+	0.202258i	−0.664827	−	0.746998i	$-0.731495\pi$
$239$	−5.41584	+	3.12684i	−0.350321	+	0.202258i	0.314505	+	0.949256i	$0.398161\pi$
$240$		0			0
$241$	−8.06290	+	9.60899i	−0.519377	+	0.618970i	−0.960433	−	0.278510i	$-0.910159\pi$
$241$	−8.06290	+	9.60899i	−0.519377	+	0.618970i	0.441056	+	0.897479i	$0.354604\pi$
$242$	7.29827	+	15.6512i	0.469151	+	1.00610i
$243$	−9.39727	+	20.1525i	−0.602835	+	1.29278i
$244$	2.42704	+	2.89243i	0.155375	+	0.185169i
$245$		0			0
$246$		−	0.877254i		−	0.0559316i
$247$	−5.15081	−	9.48539i	−0.327739	−	0.603541i
$248$	4.25873	+	4.25873i	0.270430	+	0.270430i
$249$	6.87066	+	38.9654i	0.435410	+	2.46934i
$250$		0			0
$251$	−8.58890	+	3.12610i	−0.542127	+	0.197318i	−0.598545	−	0.801089i	$-0.704254\pi$
$251$	−8.58890	+	3.12610i	−0.542127	+	0.197318i	0.0564182	+	0.998407i	$0.482032\pi$
$252$	0.766136	−	0.357255i	0.0482620	−	0.0225049i
$253$	−3.03931	−	34.7395i	−0.191080	−	2.18405i
$254$	14.9679	+	8.64170i	0.939167	+	0.542228i
$255$		0			0
$256$	3.19183	−	18.1018i	0.199489	−	1.13136i
$257$	24.3625	−	17.0588i	1.51969	−	1.06410i	0.545576	−	0.838062i	$-0.316311\pi$
$257$	24.3625	−	17.0588i	1.51969	−	1.06410i	0.974118	−	0.226040i	$-0.0725779\pi$
$258$	−0.220442	+	0.822702i	−0.0137241	+	0.0512192i
$259$	1.10871	−	1.92034i	0.0688918	−	0.119324i
$260$		0			0
$261$	−0.00311968	+	0.00857125i	−0.000193103	+	0.000530547i
$262$	30.4105	+	14.1807i	1.87877	+	0.876084i
$263$	15.7124	+	1.37466i	0.968867	+	0.0847649i	0.560590	−	0.828093i	$-0.310574\pi$
$263$	15.7124	+	1.37466i	0.968867	+	0.0847649i	0.408277	+	0.912858i	$0.366130\pi$
$264$	−20.3008	+	3.57958i	−1.24943	+	0.220308i
$265$		0			0
$266$	−0.131154	−	2.14243i	−0.00804154	−	0.131361i
$267$	−27.6717	+	27.6717i	−1.69348	+	1.69348i
$268$	6.99818	+	4.90018i	0.427482	+	0.299326i
$269$	−8.63004	+	7.24147i	−0.526183	+	0.441520i	−0.866781	−	0.498689i	$-0.833815\pi$
$269$	−8.63004	+	7.24147i	−0.526183	+	0.441520i	0.340598	+	0.940209i	$0.389371\pi$
$270$		0			0
$271$	−19.5383	−	7.11134i	−1.18686	−	0.431983i	−0.328243	−	0.944593i	$-0.606456\pi$
$271$	−19.5383	−	7.11134i	−1.18686	−	0.431983i	−0.858621	+	0.512610i	$0.828679\pi$
$272$	−23.9876	+	2.09864i	−1.45446	+	0.127249i
$273$	1.69951	−	0.455381i	0.102859	−	0.0275609i
$274$	−9.14041	−	15.8317i	−0.552192	−	0.956425i
$275$		0			0
$276$	−17.4454	−	3.07610i	−1.05009	−	0.185159i
$277$	−7.37493	−	1.97611i	−0.443116	−	0.118733i	0.0303603	−	0.999539i	$-0.490335\pi$
$277$	−7.37493	−	1.97611i	−0.443116	−	0.118733i	−0.473477	+	0.880806i	$0.657001\pi$
$278$	6.81861	+	25.4474i	0.408953	+	1.52623i
$279$	−7.94688	−	6.66822i	−0.475767	−	0.399216i
$280$		0			0
$281$	−1.88216	−	5.17119i	−0.112280	−	0.308488i	0.870807	−	0.491625i	$-0.163597\pi$
$281$	−1.88216	−	5.17119i	−0.112280	−	0.308488i	−0.983087	+	0.183137i	$0.941375\pi$
$282$	1.86501	−	21.3172i	0.111060	−	1.26942i
$283$	−6.62055	+	9.45513i	−0.393551	+	0.562049i	−0.966214	−	0.257742i	$-0.917022\pi$
$283$	−6.62055	+	9.45513i	−0.393551	+	0.562049i	0.572663	+	0.819791i	$0.305910\pi$
$284$	−11.9342			−0.708164
$285$		0			0
$286$	19.4954			1.15279
$287$	0.0340275	−	0.0485963i	0.00200858	−	0.00286855i
$288$	−1.34606	+	15.3856i	−0.0793175	+	0.906603i
$289$	2.12857	+	5.84820i	0.125210	+	0.344012i
$290$		0			0
$291$	−11.3099	−	9.49014i	−0.662999	−	0.556322i
$292$	−2.63313	−	9.82698i	−0.154092	−	0.575080i
$293$	−23.4584	−	6.28567i	−1.37046	−	0.367213i	−0.502811	−	0.864397i	$-0.667701\pi$
$293$	−23.4584	−	6.28567i	−1.37046	−	0.367213i	−0.867645	+	0.497184i	$0.834367\pi$
$294$	−28.9205	−	5.09946i	−1.68668	−	0.297407i
$295$		0			0
$296$	7.00780	+	12.1379i	0.407320	+	0.705499i
$297$	1.37760	−	0.369128i	0.0799367	−	0.0214190i
$298$	16.5374	−	1.44683i	0.957983	−	0.0838127i
$299$	−17.6785	−	6.43445i	−1.02237	−	0.372114i
$300$		0			0
$301$	−0.0441232	+	0.0370237i	−0.00254322	+	0.00213401i
$302$	4.36211	+	3.05438i	0.251011	+	0.175760i
$303$	19.4923	−	19.4923i	1.11981	−	1.11981i
$304$	19.4921	+	9.71707i	1.11795	+	0.557312i
$305$		0			0
$306$	25.4430	−	4.48629i	1.45448	−	0.256464i
$307$	−4.54580	−	0.397706i	−0.259442	−	0.0226983i	−0.0433075	−	0.999062i	$-0.513790\pi$
$307$	−4.54580	−	0.397706i	−0.259442	−	0.0226983i	−0.216135	+	0.976364i	$0.569345\pi$
$308$	1.12510	+	0.524644i	0.0641086	+	0.0298943i
$309$	0.698459	−	1.91900i	0.0397339	−	0.109168i
$310$		0			0
$311$	−2.78134	+	4.81742i	−0.157715	+	0.273171i	−0.934044	−	0.357157i	$-0.883746\pi$
$311$	−2.78134	+	4.81742i	−0.157715	+	0.273171i	0.776329	+	0.630328i	$0.217079\pi$
$312$	−2.87832	+	10.7420i	−0.162953	+	0.608149i
$313$	−8.29578	+	5.80877i	−0.468905	+	0.328331i	−0.784034	−	0.620718i	$-0.786841\pi$
$313$	−8.29578	+	5.80877i	−0.468905	+	0.328331i	0.315129	+	0.949049i	$0.397952\pi$
$314$	−4.80922	+	27.2744i	−0.271400	+	1.53919i
$315$		0			0
$316$	4.47416	+	2.58316i	0.251691	+	0.145314i
$317$	−2.24516	−	25.6623i	−0.126101	−	1.44134i	−0.750829	−	0.660497i	$-0.770346\pi$
$317$	−2.24516	−	25.6623i	−0.126101	−	1.44134i	0.624728	−	0.780843i	$-0.285210\pi$
$318$	−10.1603	+	4.73781i	−0.569759	+	0.265683i
$319$	−0.0125872	+	0.00458138i	−0.000704750	+	0.000256508i
$320$		0			0
$321$	−6.70083	−	38.0023i	−0.374004	−	2.12108i
$322$	−2.64541	−	2.64541i	−0.147423	−	0.147423i
$323$	4.18678	−	20.5844i	0.232959	−	1.14535i
$324$			8.10910i			0.450506i
$325$		0			0
$326$	0.0911679	+	0.108650i	0.00504933	+	0.00601755i
$327$	−9.88578	+	21.2001i	−0.546685	+	1.17237i
$328$	0.158472	+	0.339844i	0.00875013	+	0.0187647i
$329$	0.930180	−	1.10855i	0.0512825	−	0.0611161i
$330$		0			0
$331$	−11.0824	+	6.39845i	−0.609146	+	0.351690i	−0.772631	−	0.634855i	$-0.781060\pi$
$331$	−11.0824	+	6.39845i	−0.609146	+	0.351690i	0.163485	+	0.986546i	$0.447726\pi$
$332$	8.63849	+	12.3370i	0.474098	+	0.677083i
$333$	−13.8468	−	19.7753i	−0.758801	−	1.08368i
$334$	−12.8092	+	7.39540i	−0.700889	+	0.404658i
$335$		0			0
$336$	−2.28209	+	2.71969i	−0.124498	+	0.148371i
$337$	−8.64171	−	18.5322i	−0.470744	−	1.00951i	−0.988110	−	0.153749i	$-0.950865\pi$
$337$	−8.64171	−	18.5322i	−0.470744	−	1.00951i	0.517366	−	0.855764i	$-0.326913\pi$
$338$	−4.97876	+	10.6770i	−0.270809	+	0.580751i
$339$	2.93434	+	3.49701i	0.159371	+	0.189932i
$340$		0			0
$341$		−	15.2345i		−	0.824996i
$342$	−21.7429	−	8.56338i	−1.17572	−	0.463055i
$343$	−2.82529	−	2.82529i	−0.152551	−	0.152551i
$344$	−0.0632189	−	0.358532i	−0.00340854	−	0.0193308i
$345$		0			0
$346$	15.2272	−	5.54227i	0.818622	−	0.297954i
$347$	−16.0127	+	7.46684i	−0.859606	+	0.400841i	−0.801875	−	0.597491i	$-0.796164\pi$
$347$	−16.0127	+	7.46684i	−0.859606	+	0.400841i	−0.0577308	+	0.998332i	$0.518386\pi$
$348$	0.000593050		0.00677859i	3.17908e−5		0.000363371i
$349$	−10.6670	−	6.15858i	−0.570990	−	0.329661i	0.186555	−	0.982445i	$-0.440268\pi$
$349$	−10.6670	−	6.15858i	−0.570990	−	0.329661i	−0.757545	+	0.652783i	$0.773601\pi$
$350$		0			0
$351$	0.133608	−	0.757727i	0.00713145	−	0.0404445i
$352$	−18.5789	+	13.0091i	−0.990258	+	0.693386i
$353$	1.47805	−	5.51616i	0.0786687	−	0.293596i	−0.915371	−	0.402610i	$-0.868103\pi$
$353$	1.47805	−	5.51616i	0.0786687	−	0.293596i	0.994040	+	0.109015i	$0.0347696\pi$
$354$	4.52183	−	7.83204i	0.240333	−	0.416268i
$355$		0			0
$356$	−5.09473	+	13.9976i	−0.270020	+	0.741874i
$357$	3.10332	+	1.44710i	0.164245	+	0.0765886i
$358$	12.2666	+	1.07319i	0.648312	+	0.0567199i
$359$	25.5870	−	4.51167i	1.35043	−	0.238117i	0.548807	−	0.835949i	$-0.315082\pi$
$359$	25.5870	−	4.51167i	1.35043	−	0.238117i	0.801621	+	0.597832i	$0.203971\pi$
$360$		0			0
$361$	−12.9565	+	13.8971i	−0.681919	+	0.731428i
$362$	−1.95458	+	1.95458i	−0.102731	+	0.102731i
$363$	20.4118	+	14.2925i	1.07134	+	0.750161i
$364$	0.513040	−	0.430491i	0.0268906	−	0.0225639i
$365$		0			0
$366$	15.9884	+	5.81929i	0.835726	+	0.304179i
$367$	0.0825751	−	0.00722438i	0.00431038	−	0.000377110i	−0.0850003	−	0.996381i	$-0.527089\pi$
$367$	0.0825751	−	0.00722438i	0.00431038	−	0.000377110i	0.0893107	+	0.996004i	$0.471534\pi$
$368$	36.6682	−	9.82521i	1.91146	−	0.512175i
$369$	−0.322939	−	0.559347i	−0.0168115	−	0.0291184i
$370$		0			0
$371$	−0.746612	−	0.131648i	−0.0387621	−	0.00683481i
$372$	−7.47521	−	2.00298i	−0.387572	−	0.103850i
$373$	−0.678465	−	2.53207i	−0.0351296	−	0.131105i	0.946134	−	0.323775i	$-0.104952\pi$
$373$	−0.678465	−	2.53207i	−0.0351296	−	0.131105i	−0.981264	+	0.192670i	$0.938285\pi$
$374$	29.0641	+	24.3877i	1.50287	+	1.26106i
$375$		0			0
$376$	3.12835	+	8.59507i	0.161332	+	0.443257i
$377$	−0.000629827		0.00719896i	−3.24377e−5		0.000370765i
$378$	0.0877610	−	0.125336i	0.00451394	−	0.00644657i
$379$	29.0243			1.49088			0.745440	−	0.666573i	$-0.232239\pi$
$379$	29.0243			1.49088			0.745440	+	0.666573i	$0.232239\pi$
$380$		0			0
$381$	24.9387			1.27765
$382$	4.50835	−	6.43858i	0.230667	−	0.329427i
$383$	−1.84015	+	21.0330i	−0.0940271	+	1.07473i	0.791819	+	0.610756i	$0.209134\pi$
$383$	−1.84015	+	21.0330i	−0.0940271	+	1.07473i	−0.885846	+	0.463979i	$0.846421\pi$
$384$	−10.5692	−	29.0386i	−0.539357	−	1.48187i
$385$		0			0
$386$	16.1151	+	13.5222i	0.820239	+	0.688262i
$387$	0.162301	+	0.605715i	0.00825021	+	0.0307902i
$388$	−5.42834	−	1.45452i	−0.275582	−	0.0738420i
$389$	−4.17947	−	0.736954i	−0.211908	−	0.0373650i	0.0666864	−	0.997774i	$-0.478757\pi$
$389$	−4.17947	−	0.736954i	−0.211908	−	0.0373650i	−0.278594	+	0.960409i	$0.589868\pi$
$390$		0			0
$391$	−18.3063	−	31.7075i	−0.925791	−	1.60352i
$392$	12.1248	−	3.24884i	0.612397	−	0.164091i
$393$	48.2322	−	4.21977i	2.43299	−	0.212859i
$394$	−0.271956	−	0.0989839i	−0.0137009	−	0.00498674i
$395$		0			0
$396$	10.3534	−	8.68751i	0.520277	−	0.436564i
$397$	16.9218	+	11.8488i	0.849282	+	0.594674i	0.915131	−	0.403156i	$-0.132087\pi$
$397$	16.9218	+	11.8488i	0.849282	+	0.594674i	−0.0658493	+	0.997830i	$0.520976\pi$
$398$	−6.06152	+	6.06152i	−0.303837	+	0.303837i
$399$	−1.70958	−	2.58258i	−0.0855858	−	0.129291i
$400$		0			0
$401$	17.8894	−	3.15438i	0.893354	−	0.157522i	0.291918	−	0.956443i	$-0.405707\pi$
$401$	17.8894	−	3.15438i	0.893354	−	0.157522i	0.601436	+	0.798921i	$0.294596\pi$
$402$	38.3508	+	3.35526i	1.91276	+	0.167345i
$403$	−7.44878	−	3.47342i	−0.371050	−	0.173024i
$404$	3.58880	−	9.86014i	0.178549	−	0.490560i
$405$		0			0
$406$	−0.000718529		0.00124453i	−3.56600e−5		6.17649e-5i
$407$	9.17575	−	34.2444i	0.454825	−	1.69743i
$408$	−17.7288	+	12.4138i	−0.877706	+	0.614576i
$409$	2.14098	−	12.1421i	0.105865	−	0.600388i	−0.885007	−	0.465578i	$-0.845846\pi$
$409$	2.14098	−	12.1421i	0.105865	−	0.600388i	0.990871	−	0.134810i	$-0.0430425\pi$
$410$		0			0
$411$	−22.8439	−	13.1890i	−1.12681	−	0.650563i
$412$	−0.0677491	−	0.774375i	−0.00333776	−	0.0381507i
$413$	0.554286	−	0.258468i	0.0272746	−	0.0127184i
$414$	−38.2742	+	13.9307i	−1.88107	+	0.684655i
$415$		0			0
$416$	2.12474	+	12.0500i	0.104174	+	0.590800i
$417$	26.8800	+	26.8800i	1.31632	+	1.31632i
$418$	−10.8909	−	32.5436i	−0.532691	−	1.59176i
$419$			30.7781i			1.50361i	0.659386	+	0.751805i	$0.270816\pi$
$419$			30.7781i			1.50361i	−0.659386	+	0.751805i	$0.729184\pi$
$420$		0			0
$421$	10.7205	+	12.7761i	0.522483	+	0.622671i	0.961166	−	0.275971i	$-0.0889994\pi$
$421$	10.7205	+	12.7761i	0.522483	+	0.622671i	−0.438683	+	0.898642i	$0.644555\pi$
$422$	−0.0689701	+	0.147907i	−0.00335741	+	0.00720000i
$423$	−6.65824	−	14.2786i	−0.323735	−	0.694252i
$424$	3.08017	−	3.67081i	0.149586	−	0.178270i
$425$		0			0
$426$	−46.5729	+	26.8889i	−2.25646	+	1.30277i
$427$	0.659969	+	0.942534i	0.0319382	+	0.0456124i
$428$	−8.42495	−	12.0321i	−0.407235	−	0.581593i
$429$	24.3617	−	14.0652i	1.17619	−	0.679076i
$430$		0			0
$431$	9.97761	−	11.8908i	0.480604	−	0.572762i	−0.470198	−	0.882561i	$-0.655817\pi$
$431$	9.97761	−	11.8908i	0.480604	−	0.572762i	0.950802	+	0.309799i	$0.100262\pi$
$432$	0.656139	+	1.40709i	0.0315685	+	0.0676988i
$433$	5.44902	−	11.6855i	0.261863	−	0.561568i	−0.730784	−	0.682608i	$-0.760845\pi$
$433$	5.44902	−	11.6855i	0.261863	−	0.561568i	0.992648	+	0.121041i	$0.0386232\pi$
$434$	−1.05057	−	1.25202i	−0.0504291	−	0.0600990i
$435$		0			0
$436$			8.90391i			0.426420i
$437$	−0.865085	+	33.1052i	−0.0413826	+	1.58363i
$438$	−32.4169	−	32.4169i	−1.54894	−	1.54894i
$439$	−5.84172	−	33.1300i	−0.278810	−	1.58121i	−0.726593	−	0.687068i	$-0.758898\pi$
$439$	−5.84172	−	33.1300i	−0.278810	−	1.58121i	0.447783	−	0.894142i	$-0.352214\pi$
$440$		0			0
$441$	−20.3173	+	7.39489i	−0.967490	+	0.352137i
$442$	18.5507	−	8.65033i	0.882366	−	0.411454i
$443$	1.46104	+	16.6998i	0.0694162	+	0.793431i	0.948503	+	0.316769i	$0.102598\pi$
$443$	1.46104	+	16.6998i	0.0694162	+	0.793431i	−0.879087	+	0.476662i	$0.841846\pi$
$444$	−15.5965	−	9.00463i	−0.740176	−	0.427341i
$445$		0			0
$446$	−0.204711	+	1.16097i	−0.00969333	+	0.0549736i
$447$	19.6214	−	13.7391i	0.928062	−	0.649836i
$448$	0.112769	−	0.420860i	0.00532784	−	0.0198838i
$449$	−8.68158	+	15.0369i	−0.409709	+	0.709637i	−0.994857	−	0.101290i	$-0.967703\pi$
$449$	−8.68158	+	15.0369i	−0.409709	+	0.709637i	0.585148	+	0.810927i	$0.301036\pi$
$450$		0			0
$451$	0.324406	−	0.891298i	0.0152757	−	0.0419696i
$452$	1.57484	+	0.734361i	0.0740743	+	0.0345414i
$453$	7.65457	+	0.669688i	0.359643	+	0.0314647i
$454$	−7.48278	+	1.31942i	−0.351184	+	0.0619233i
$455$		0			0
$456$	19.5396	−	1.19616i	0.915024	−	0.0560153i
$457$	4.18473	−	4.18473i	0.195753	−	0.195753i	−0.602423	−	0.798177i	$-0.705798\pi$
$457$	4.18473	−	4.18473i	0.195753	−	0.195753i	0.798177	+	0.602423i	$0.205798\pi$
$458$	−2.30614	−	1.61478i	−0.107759	−	0.0754535i
$459$	1.14706	−	0.962499i	0.0535403	−	0.0449256i
$460$		0			0
$461$	13.1750	+	4.79530i	0.613620	+	0.223339i	0.630086	−	0.776525i	$-0.283019\pi$
$461$	13.1750	+	4.79530i	0.613620	+	0.223339i	−0.0164665	+	0.999864i	$0.505242\pi$
$462$	5.57276	−	0.487553i	0.259268	−	0.0226830i
$463$	−13.9101	+	3.72721i	−0.646459	+	0.173218i	−0.567127	−	0.823630i	$-0.691945\pi$
$463$	−13.9101	+	3.72721i	−0.646459	+	0.173218i	−0.0793316	+	0.996848i	$0.525279\pi$
$464$	−0.00729090	−	0.0126282i	−0.000338472	−	0.000586250i
$465$		0			0
$466$	−16.3239	−	2.87835i	−0.756190	−	0.133337i
$467$	8.43685	+	2.26065i	0.390411	+	0.104610i	0.448684	−	0.893690i	$-0.351893\pi$
$467$	8.43685	+	2.26065i	0.390411	+	0.104610i	−0.0582734	+	0.998301i	$0.518560\pi$
$468$	−1.88714	−	7.04292i	−0.0872332	−	0.325559i
$469$	1.99433	+	1.67345i	0.0920898	+	0.0772725i
$470$		0			0
$471$	13.6679	+	37.5522i	0.629782	+	1.73031i
$472$	−0.336914	+	3.85094i	−0.0155077	+	0.177254i
$473$	−0.528204	+	0.754354i	−0.0242869	+	0.0346852i
$474$	23.2804			1.06930
$475$		0			0
$476$	1.30337			0.0597399
$477$	−4.73420	+	6.76113i	−0.216764	+	0.309571i
$478$	−0.934886	+	10.6858i	−0.0427607	+	0.488757i
$479$	6.83164	+	18.7698i	0.312145	+	0.857613i	0.992223	+	0.124473i	$0.0397239\pi$
$479$	6.83164	+	18.7698i	0.312145	+	0.857613i	−0.680078	+	0.733140i	$0.738054\pi$
$480$		0			0
$481$	−14.6514	−	12.2940i	−0.668048	−	0.560558i
$482$	5.56862	+	20.7824i	0.253644	+	0.946611i
$483$	−5.21431	−	1.39717i	−0.237259	−	0.0635735i
$484$	9.34084	+	1.64704i	0.424584	+	0.0748656i
$485$		0			0
$486$	19.0700	+	33.0303i	0.865034	+	1.49828i
$487$	−12.8690	+	3.44824i	−0.583150	+	0.156254i	−0.538320	−	0.842740i	$-0.680941\pi$
$487$	−12.8690	+	3.44824i	−0.583150	+	0.156254i	−0.0448291	+	0.998995i	$0.514274\pi$
$488$	−7.24504	+	0.633859i	−0.327968	+	0.0286935i
$489$	0.192311	+	0.0699956i	0.00869662	+	0.00316531i
$490$		0			0
$491$	−18.9123	+	15.8693i	−0.853501	+	0.716172i	−0.960558	−	0.278081i	$-0.910302\pi$
$491$	−18.9123	+	15.8693i	−0.853501	+	0.716172i	0.107057	+	0.994253i	$0.465857\pi$
$492$	−0.394687	−	0.276363i	−0.0177938	−	0.0124594i
$493$	−0.00994447	+	0.00994447i	−0.000447876	+	0.000447876i
$494$	−18.3950	−	2.09483i	−0.827629	−	0.0942507i
$495$		0			0
$496$	16.3323	−	2.87982i	0.733341	−	0.129308i
$497$	−3.62294	−	0.316966i	−0.162511	−	0.0142179i
$498$	61.5080	+	28.6817i	2.75624	+	1.28526i
$499$	6.45641	−	17.7388i	0.289028	−	0.794099i	−0.707175	−	0.707039i	$-0.750031\pi$
$499$	6.45641	−	17.7388i	0.289028	−	0.794099i	0.996203	−	0.0870601i	$-0.0277472\pi$
$500$		0			0
$501$	−10.6710	+	18.4828i	−0.476747	+	0.825749i
$502$	−4.05766	+	15.1434i	−0.181102	+	0.675883i
$503$	11.7261	−	8.21072i	0.522842	−	0.366098i	−0.282162	−	0.959367i	$-0.591052\pi$
$503$	11.7261	−	8.21072i	0.522842	−	0.366098i	0.805005	+	0.593269i	$0.202163\pi$
$504$	−0.282740	+	1.60350i	−0.0125943	+	0.0714256i
$505$		0			0
$506$	−51.8009	−	29.9073i	−2.30283	−	1.32954i
$507$	1.48154	+	16.9341i	0.0657975	+	0.752069i
$508$	8.60335	−	4.01181i	0.381712	−	0.177995i
$509$	32.7191	−	11.9088i	1.45025	−	0.527847i	0.507588	−	0.861600i	$-0.330537\pi$
$509$	32.7191	−	11.9088i	1.45025	−	0.527847i	0.942661	+	0.333752i	$0.108315\pi$
$510$		0			0
$511$	−0.538357	−	3.05317i	−0.0238155	−	0.135064i
$512$	−4.63603	−	4.63603i	−0.204886	−	0.204886i
$513$	−1.33951	+	0.200265i	−0.0591407	+	0.00884193i
$514$		−	51.0136i		−	2.25011i
$515$		0			0
$516$	0.300697	+	0.358357i	0.0132374	+	0.0157758i
$517$	9.77791	−	20.9688i	0.430032	−	0.922206i
$518$	−1.60740	−	3.44707i	−0.0706250	−	0.151456i
$519$	15.0296	−	17.9116i	0.659727	−	0.786232i
$520$		0			0
$521$	3.47559	−	2.00663i	0.152268	−	0.0879121i	−0.421930	−	0.906628i	$-0.638647\pi$
$521$	3.47559	−	2.00663i	0.152268	−	0.0879121i	0.574198	+	0.818716i	$0.305314\pi$
$522$	0.00897382	+	0.0128159i	0.000392773	+	0.000560938i
$523$	−18.5171	−	26.4451i	−0.809695	−	1.15636i	−0.985119	−	0.171872i	$-0.945019\pi$
$523$	−18.5171	−	26.4451i	−0.809695	−	1.15636i	0.175424	−	0.984493i	$-0.443870\pi$
$524$	15.9603	−	9.21469i	0.697230	−	0.402546i
$525$		0			0
$526$	17.3897	−	20.7243i	0.758228	−	0.903621i
$527$	−6.75973	−	14.4963i	−0.294458	−	0.631468i
$528$	−23.9889	+	51.4444i	−1.04398	+	2.23883i
$529$	22.3183	+	26.5979i	0.970360	+	1.15643i
$530$		0			0
$531$		−	6.65840i		−	0.288950i
$532$	−1.00522	−	0.615925i	−0.0435818	−	0.0267037i
$533$	−0.361829	−	0.361829i	−0.0156725	−	0.0156725i
$534$	11.6560	+	66.1044i	0.504404	+	2.86062i
$535$		0			0
$536$	−15.4630	+	5.62808i	−0.667900	+	0.243096i
$537$	16.1028	−	7.50886i	0.694888	−	0.324031i
$538$	1.68416	+	19.2500i	0.0726092	+	0.829927i
$539$	−27.4977	−	15.8758i	−1.18441	−	0.683820i
$540$		0			0
$541$	−2.75071	+	15.6000i	−0.118262	+	0.670698i	0.866821	+	0.498620i	$0.166160\pi$
$541$	−2.75071	+	15.6000i	−0.118262	+	0.670698i	−0.985083	+	0.172079i	$0.944952\pi$
$542$	−29.2141	+	20.4559i	−1.25485	+	0.878657i
$543$	−1.03231	+	3.85263i	−0.0443007	+	0.165332i
$544$	−11.9063	+	20.6223i	−0.510479	+	0.884176i
$545$		0			0
$546$	1.03219	−	2.83591i	0.0441735	−	0.121366i
$547$	38.1131	+	17.7724i	1.62960	+	0.759893i	0.999857	−	0.0169130i	$-0.00538383\pi$
$547$	38.1131	+	17.7724i	1.62960	+	0.759893i	0.629740	+	0.776806i	$0.283162\pi$
$548$	−10.0024	−	0.875093i	−0.427280	−	0.0373821i
$549$	12.3366	−	2.17528i	0.526514	−	0.0928386i
$550$		0			0
$551$	0.0123690	−	0.00297025i	0.000526938	−	0.000126537i
$552$	24.1270	−	24.1270i	1.02691	−	1.02691i
$553$	1.28964	+	0.903017i	0.0548411	+	0.0384002i
$554$	−10.0322	+	8.41800i	−0.426227	+	0.357647i
$555$		0			0
$556$	13.5972	+	4.94896i	0.576648	+	0.209883i
$557$	−19.2126	+	1.68089i	−0.814066	+	0.0712215i	−0.486582	−	0.873635i	$-0.661756\pi$
$557$	−19.2126	+	1.68089i	−0.814066	+	0.0712215i	−0.327484	+	0.944857i	$0.606201\pi$
$558$	−17.1876	+	4.60539i	−0.727607	+	0.194962i
$559$	0.248406	+	0.430251i	0.0105064	+	0.0181977i
$560$		0			0
$561$	53.9138	+	9.50645i	2.27624	+	0.401363i
$562$	−9.11752	−	2.44303i	−0.384599	−	0.103053i
$563$	−4.96746	−	18.5388i	−0.209354	−	0.781318i	−0.988078	−	0.153952i	$-0.950800\pi$
$563$	−4.96746	−	18.5388i	−0.209354	−	0.781318i	0.778725	−	0.627366i	$-0.215867\pi$
$564$	−9.00331	−	7.55468i	−0.379108	−	0.318109i
$565$		0			0
$566$	6.77146	+	18.6044i	0.284626	+	0.782002i
$567$	−0.215374	+	2.46173i	−0.00904484	+	0.103383i
$568$	13.1848	−	18.8298i	0.553220	−	0.790080i
$569$	−32.0305			−1.34279			−0.671393	−	0.741101i	$-0.734304\pi$
$569$	−32.0305			−1.34279			−0.671393	+	0.741101i	$0.734304\pi$
$570$		0			0
$571$	24.9840			1.04555			0.522774	−	0.852471i	$-0.324897\pi$
$571$	24.9840			1.04555			0.522774	+	0.852471i	$0.324897\pi$
$572$	6.14167	−	8.77121i	0.256796	−	0.366743i
$573$	0.988477	−	11.2983i	0.0412942	−	0.471995i
$574$	−0.0348031	−	0.0956208i	−0.00145265	−	0.00399114i
$575$		0			0
$576$	−3.63379	−	3.04911i	−0.151408	−	0.127046i
$577$	0.896843	+	3.34706i	0.0373361	+	0.139340i	0.982078	−	0.188475i	$-0.0603544\pi$
$577$	0.896843	+	3.34706i	0.0373361	+	0.139340i	−0.944742	+	0.327815i	$0.893688\pi$
$578$	10.3112	+	2.76287i	0.428888	+	0.114920i
$579$	29.8935	+	5.27102i	1.24233	+	0.219056i
$580$		0			0
$581$	2.29477	+	3.97466i	0.0952032	+	0.164897i
$582$	−24.4611	+	6.55434i	−1.01395	+	0.271686i
$583$	−12.0750	+	1.05642i	−0.500094	+	0.0437525i
$584$	18.4141	+	6.70217i	0.761980	+	0.277338i
$585$		0			0
$586$	−31.9107	+	26.7763i	−1.31822	+	1.10612i
$587$	−25.8643	−	18.1103i	−1.06753	−	0.747494i	−0.0986764	−	0.995120i	$-0.531461\pi$
$587$	−25.8643	−	18.1103i	−1.06753	−	0.747494i	−0.968856	+	0.247625i	$0.920350\pi$
$588$	−11.4052	+	11.4052i	−0.470342	+	0.470342i
$589$	−1.63699	+	14.3746i	−0.0674508	+	0.592295i
$590$		0			0
$591$	−0.411253	+	0.0725150i	−0.0169167	+	0.00298287i
$592$	38.4464	+	3.36363i	1.58014	+	0.138244i
$593$	8.33375	+	3.88609i	0.342226	+	0.159583i	0.586131	−	0.810217i	$-0.300651\pi$
$593$	8.33375	+	3.88609i	0.342226	+	0.159583i	−0.243904	+	0.969799i	$0.578428\pi$
$594$	0.836681	−	2.29876i	0.0343294	−	0.0943194i
$595$		0			0
$596$	4.55884	−	7.89615i	0.186737	−	0.323439i
$597$	−3.20138	+	11.9477i	−0.131024	+	0.488988i
$598$	−26.4333	+	18.5088i	−1.08094	+	0.756882i
$599$	7.60255	−	43.1162i	0.310632	−	1.76168i	−0.285102	−	0.958497i	$-0.592027\pi$
$599$	7.60255	−	43.1162i	0.310632	−	1.76168i	0.595734	−	0.803182i	$-0.296861\pi$
$600$		0			0
$601$	26.5782	+	15.3449i	1.08415	+	0.625932i	0.932012	−	0.362428i	$-0.118052\pi$
$601$	26.5782	+	15.3449i	1.08415	+	0.625932i	0.152134	+	0.988360i	$0.451385\pi$
$602$	0.00861066	+	0.0984203i	0.000350944	+	0.00401131i
$603$	25.6881	−	11.9785i	1.04610	−	0.487804i
$604$	2.74840	−	1.00034i	0.111831	−	0.0407031i
$605$		0			0
$606$	−8.21064	−	46.5648i	−0.333534	−	1.89157i
$607$	−7.95200	−	7.95200i	−0.322762	−	0.322762i	0.527064	−	0.849826i	$-0.323293\pi$
$607$	−7.95200	−	7.95200i	−0.322762	−	0.322762i	−0.849826	+	0.527064i	$0.823293\pi$
$608$	18.9280	−	10.2784i	0.767634	−	0.416845i
$609$			0.00207357i			8.40253e-5i
$610$		0			0
$611$	−8.02317	−	9.56164i	−0.324583	−	0.386822i
$612$	5.99692	−	12.8604i	0.242411	−	0.519852i
$613$	16.8269	+	36.0854i	0.679632	+	1.45748i	0.878644	+	0.477478i	$0.158449\pi$
$613$	16.8269	+	36.0854i	0.679632	+	1.45748i	−0.199012	+	0.979997i	$0.563773\pi$
$614$	−5.03108	+	5.99580i	−0.203038	+	0.241971i
$615$		0			0
$616$	−2.07078	+	1.19557i	−0.0834342	+	0.0481708i
$617$	14.9718	+	21.3819i	0.602740	+	0.860803i	0.998339	−	0.0576212i	$-0.0183516\pi$
$617$	14.9718	+	21.3819i	0.602740	+	0.860803i	−0.395598	+	0.918424i	$0.629463\pi$
$618$	−2.00913	−	2.86934i	−0.0808191	−	0.115422i
$619$	−14.8409	+	8.56837i	−0.596504	+	0.344392i	−0.767665	−	0.640851i	$-0.778582\pi$
$619$	−14.8409	+	8.56837i	−0.596504	+	0.344392i	0.171161	+	0.985243i	$0.445248\pi$
$620$		0			0
$621$	−1.51741	+	1.80838i	−0.0608916	+	0.0725678i
$622$	4.03237	+	8.64743i	0.161683	+	0.346731i
$623$	−1.91841	+	4.11404i	−0.0768594	+	0.164825i
$624$	19.6839	+	23.4584i	0.787987	+	0.939086i
$625$		0			0
$626$			17.3708i			0.694277i
$627$	−37.0884	−	32.8094i	−1.48117	−	1.31028i
$628$	10.7560	+	10.7560i	0.429213	+	0.429213i
$629$	−6.46350	−	36.6563i	−0.257716	−	1.46158i
$630$		0			0
$631$	20.1799	−	7.34487i	0.803348	−	0.292395i	0.0924747	−	0.995715i	$-0.470522\pi$
$631$	20.1799	−	7.34487i	0.803348	−	0.292395i	0.710873	+	0.703320i	$0.248300\pi$
$632$	−9.01871	+	4.20549i	−0.358745	+	0.167286i
$633$	0.0205236	+	0.234586i	0.000815740	+	0.00932395i
$634$	−38.2657	−	22.0927i	−1.51973	−	0.877415i
$635$		0			0
$636$	−1.06921	+	6.06378i	−0.0423969	+	0.240445i
$637$	−14.0317	+	9.82513i	−0.555958	+	0.389286i
$638$	−0.00594660	+	0.0221930i	−0.000235428	+	0.000878629i
$639$	−19.7969	+	34.2893i	−0.783155	+	1.35646i
$640$		0			0
$641$	12.0700	−	33.1619i	0.476735	−	1.30982i	−0.435515	−	0.900182i	$-0.643434\pi$
$641$	12.0700	−	33.1619i	0.476735	−	1.30982i	0.912249	−	0.409636i	$-0.134344\pi$
$642$	−59.9876	−	27.9727i	−2.36752	−	1.10399i
$643$	−18.7728	−	1.64241i	−0.740327	−	0.0647702i	−0.289248	−	0.957254i	$-0.593405\pi$
$643$	−18.7728	−	1.64241i	−0.740327	−	0.0647702i	−0.451079	+	0.892484i	$0.648961\pi$
$644$	−2.02359	+	0.356814i	−0.0797407	+	0.0140604i
$645$		0			0
$646$	−24.8031	−	26.1341i	−0.975864	−	1.02823i
$647$	17.6606	−	17.6606i	0.694309	−	0.694309i	−0.268868	−	0.963177i	$-0.586650\pi$
$647$	17.6606	−	17.6606i	0.694309	−	0.694309i	0.963177	+	0.268868i	$0.0866496\pi$
$648$	−12.7946	−	8.95884i	−0.502617	−	0.351937i
$649$	7.49049	−	6.28527i	0.294027	−	0.246718i
$650$		0			0
$651$	−2.21610	−	0.806594i	−0.0868557	−	0.0316129i
$652$	0.0776036	−	0.00678943i	0.00303919	−	0.000265895i
$653$	−5.40330	+	1.44781i	−0.211447	+	0.0566572i	−0.362988	−	0.931794i	$-0.618243\pi$
$653$	−5.40330	+	1.44781i	−0.211447	+	0.0566572i	0.151540	+	0.988451i	$0.451577\pi$
$654$	20.0613	+	34.7473i	0.784461	+	1.35873i
$655$		0			0
$656$	1.01685	+	0.179297i	0.0397012	+	0.00700039i
$657$	−32.6028	−	8.73590i	−1.27196	−	0.340820i
$658$	−0.642427	−	2.39757i	−0.0250444	−	0.0934669i
$659$	−5.03828	−	4.22762i	−0.196264	−	0.164685i	0.539360	−	0.842075i	$-0.318666\pi$
$659$	−5.03828	−	4.22762i	−0.196264	−	0.164685i	−0.735623	+	0.677391i	$0.763111\pi$
$660$		0			0
$661$	−13.4502	−	36.9540i	−0.523150	−	1.43734i	−0.866995	−	0.498317i	$-0.833951\pi$
$661$	−13.4502	−	36.9540i	−0.523150	−	1.43734i	0.343844	−	0.939027i	$-0.388271\pi$
$662$	−1.91306	+	21.8664i	−0.0743531	+	0.849860i
$663$	16.9403	−	24.1932i	0.657906	−	0.939587i
$664$	−29.0091			−1.12577
$665$		0			0
$666$	−41.4082			−1.60454
$667$	0.0127172	−	0.0181620i	0.000492411	−	0.000703236i
$668$	−0.708028	+	8.09280i	−0.0273944	+	0.313120i
$669$	0.581791	+	1.59846i	0.0224933	+	0.0617999i
$670$		0			0
$671$	14.0924	+	11.8249i	0.544031	+	0.456496i
$672$	0.908711	+	3.39136i	0.0350543	+	0.130824i
$673$	−9.39609	−	2.51767i	−0.362193	−	0.0970492i	0.0731333	−	0.997322i	$-0.476700\pi$
$673$	−9.39609	−	2.51767i	−0.362193	−	0.0970492i	−0.435326	+	0.900273i	$0.643367\pi$
$674$	−34.5406	−	6.09045i	−1.33046	−	0.234595i
$675$		0			0
$676$	3.23523	+	5.60359i	0.124432	+	0.215523i
$677$	−39.3476	+	10.5432i	−1.51225	+	0.405207i	−0.917182	−	0.398468i	$-0.869542\pi$
$677$	−39.3476	+	10.5432i	−1.51225	+	0.405207i	−0.595069	+	0.803675i	$0.702875\pi$
$678$	7.80036	−	0.682443i	0.299571	−	0.0262091i
$679$	−1.60928	−	0.585731i	−0.0617586	−	0.0224783i
$680$		0			0
$681$	−8.39866	+	7.04731i	−0.321837	+	0.270054i
$682$	−21.4053	−	14.9881i	−0.819651	−	0.573926i
$683$	−11.3169	+	11.3169i	−0.433030	+	0.433030i	−0.889658	−	0.456628i	$-0.849057\pi$
$683$	−11.3169	+	11.3169i	−0.433030	+	0.433030i	0.456628	+	0.889658i	$0.349057\pi$
$684$	−10.7025	+	7.08464i	−0.409219	+	0.270888i
$685$		0			0
$686$	−6.74927	+	1.19008i	−0.257688	+	0.0454374i
$687$	−4.04678	−	0.354048i	−0.154394	−	0.0135078i
$688$	−0.908559	−	0.423668i	−0.0346385	−	0.0161522i
$689$	−2.23652	+	6.14480i	−0.0852048	+	0.234098i
$690$		0			0
$691$	1.45852	−	2.52622i	0.0554846	−	0.0961021i	−0.836949	−	0.547281i	$-0.815663\pi$
$691$	1.45852	−	2.52622i	0.0554846	−	0.0961021i	0.892434	+	0.451179i	$0.148996\pi$
$692$	2.30353	−	8.59691i	0.0875672	−	0.326805i
$693$	3.37377	−	2.36234i	0.128159	−	0.0897379i
$694$	−5.26243	+	29.8447i	−0.199759	+	1.13289i
$695$		0			0
$696$	−0.0113505	−	0.00655319i	−0.000430238	−	0.000248398i
$697$	−0.0867931	−	0.992050i	−0.00328752	−	0.0375766i
$698$	−19.1476	+	8.92866i	−0.724747	+	0.337955i
$699$	−22.4752	+	8.18030i	−0.850089	+	0.309407i
$700$		0			0
$701$	−7.75792	−	43.9973i	−0.293012	−	1.66176i	−0.675173	−	0.737660i	$-0.735931\pi$
$701$	−7.75792	−	43.9973i	−0.293012	−	1.66176i	0.382160	−	0.924096i	$-0.375180\pi$
$702$	−0.933199	−	0.933199i	−0.0352213	−	0.0352213i
$703$	−12.3375	+	31.3254i	−0.465316	+	1.18146i
$704$		−	6.96614i		−	0.262546i
$705$		0			0
$706$	−6.29634	−	7.50369i	−0.236966	−	0.282405i
$707$	1.35135	−	2.89799i	0.0508229	−	0.108990i
$708$	−2.09921	−	4.50177i	−0.0788931	−	0.169187i
$709$	−27.4318	+	32.6919i	−1.03022	+	1.22777i	−0.0568877	+	0.998381i	$0.518118\pi$
$709$	−27.4318	+	32.6919i	−1.03022	+	1.22777i	−0.973334	+	0.229390i	$0.926327\pi$
$710$		0			0
$711$	14.8439	−	8.57011i	0.556688	−	0.321404i
$712$	−16.4569	−	23.5029i	−0.616749	−	0.880808i
$713$	14.4636	+	20.6561i	0.541665	+	0.773577i
$714$	5.08638	−	2.93662i	0.190353	−	0.109900i
$715$		0			0
$716$	4.34722	−	5.18081i	0.162463	−	0.193616i
$717$	6.54117	+	14.0276i	0.244285	+	0.523870i
$718$	18.8340	−	40.3897i	0.702880	−	1.50733i
$719$	−11.9438	−	14.2341i	−0.445429	−	0.530841i	0.495879	−	0.868392i	$-0.334846\pi$
$719$	−11.9438	−	14.2341i	−0.445429	−	0.530841i	−0.941307	+	0.337550i	$0.890402\pi$
$720$		0			0
$721$		−	0.236881i		−	0.00882192i
$722$	6.77927	+	31.8769i	0.252298	+	1.18633i
$723$	21.9524	+	21.9524i	0.816417	+	0.816417i
$724$	0.263635	+	1.49515i	0.00979790	+	0.0555667i
$725$		0			0
$726$	40.1634	−	14.6183i	1.49060	−	0.542535i
$727$	−16.0098	+	7.46550i	−0.593771	+	0.276880i	−0.696186	−	0.717862i	$-0.745121\pi$
$727$	−16.0098	+	7.46550i	−0.593771	+	0.276880i	0.102414	+	0.994742i	$0.467343\pi$
$728$	0.112430	+	1.28508i	0.00416692	+	0.0476281i
$729$	25.2971	+	14.6053i	0.936928	+	0.540936i
$730$		0			0
$731$	−0.167893	+	0.952169i	−0.00620975	+	0.0352173i
$732$	7.65501	−	5.36010i	0.282937	−	0.198115i
$733$	10.6117	−	39.6034i	0.391952	−	1.46279i	−0.434957	−	0.900451i	$-0.643236\pi$
$733$	10.6117	−	39.6034i	0.391952	−	1.46279i	0.826909	−	0.562335i	$-0.190097\pi$
$734$	0.0710890	−	0.123130i	0.00262394	−	0.00454480i
$735$		0			0
$736$	12.8399	−	35.2774i	0.473286	−	1.30034i
$737$	37.7240	+	17.5910i	1.38958	+	0.647973i
$738$	−1.10363	−	0.0965549i	−0.0406251	−	0.00355424i
$739$	13.0374	−	2.29884i	0.479587	−	0.0845642i	0.0713718	−	0.997450i	$-0.477262\pi$
$739$	13.0374	−	2.29884i	0.479587	−	0.0845642i	0.408215	+	0.912886i	$0.366151\pi$
$740$		0			0
$741$	−24.4979	+	10.6536i	−0.899954	+	0.391369i
$742$	−0.919509	+	0.919509i	−0.0337562	+	0.0337562i
$743$	−0.404372	−	0.283145i	−0.0148350	−	0.0103876i	0.566135	−	0.824312i	$-0.308438\pi$
$743$	−0.404372	−	0.283145i	−0.0148350	−	0.0103876i	−0.580970	+	0.813925i	$0.697327\pi$
$744$	11.4188	−	9.58153i	0.418634	−	0.351276i
$745$		0			0
$746$	−4.22518	−	1.53784i	−0.154695	−	0.0563043i
$747$	49.7767	−	4.35489i	1.82123	−	0.159337i
$748$	20.1284	−	5.39340i	0.735969	−	0.197202i
$749$	−2.23805	−	3.87642i	−0.0817765	−	0.141641i
$750$		0			0
$751$	−41.0072	−	7.23068i	−1.49637	−	0.263851i	−0.635275	−	0.772286i	$-0.719113\pi$
$751$	−41.0072	−	7.23068i	−1.49637	−	0.263851i	−0.861100	+	0.508435i	$0.830224\pi$
$752$	24.3281	+	6.51869i	0.887154	+	0.237712i
$753$	5.85491	+	21.8508i	0.213365	+	0.796289i
$754$	0.00949526	+	0.00796747i	0.000345797	+	0.000290158i
$755$		0			0
$756$	−0.0287425	−	0.0789694i	−0.00104536	−	0.00287209i
$757$	3.70042	−	42.2960i	0.134494	−	1.53728i	−0.566472	−	0.824081i	$-0.691692\pi$
$757$	3.70042	−	42.2960i	0.134494	−	1.53728i	0.700966	−	0.713195i	$-0.252752\pi$
$758$	28.5549	−	40.7807i	1.03716	−	1.48122i
$759$	−86.3081			−3.13278
$760$		0			0
$761$	−24.7086			−0.895686			−0.447843	−	0.894112i	$-0.647808\pi$
$761$	−24.7086			−0.895686			−0.447843	+	0.894112i	$0.647808\pi$
$762$	24.5354	−	35.0401i	0.888823	−	1.26937i
$763$	−0.236483	+	2.70301i	−0.00856126	+	0.0978557i
$764$	−1.47652	−	4.05671i	−0.0534187	−	0.146767i
$765$		0			0
$766$	27.7420	+	23.2783i	1.00236	+	0.841080i
$767$	−1.36532	−	5.09543i	−0.0492987	−	0.183985i
$768$	−43.9426	−	11.7744i	−1.58564	−	0.424871i
$769$	28.5485	+	5.03387i	1.02948	+	0.181526i	0.662782	−	0.748812i	$-0.269376\pi$
$769$	28.5485	+	5.03387i	1.02948	+	0.181526i	0.366703	+	0.930338i	$0.380487\pi$
$770$		0			0
$771$	−36.8045	−	63.7472i	−1.32548	−	2.29580i
$772$	11.1606	−	2.99047i	0.401678	−	0.107629i
$773$	−32.1932	+	2.81654i	−1.15791	+	0.101304i	−0.649880	−	0.760037i	$-0.725181\pi$
$773$	−32.1932	+	2.81654i	−1.15791	+	0.101304i	−0.508028	+	0.861341i	$0.669625\pi$
$774$	1.01074	+	0.367878i	0.0363302	+	0.0132231i
$775$		0			0
$776$	8.29211	−	6.95791i	0.297669	−	0.249774i
$777$	−4.49556	−	3.14783i	−0.161277	−	0.112928i
$778$	−5.14734	+	5.14734i	−0.184541	+	0.184541i
$779$	−0.401867	+	0.806130i	−0.0143984	+	0.0288826i
$780$		0			0
$781$	−57.2619	+	10.0968i	−2.04899	+	0.361293i
$782$	−62.5609	−	5.47337i	−2.23717	−	0.195727i
$783$	0.000821821	0	0.000383221i	2.93695e−5	0	1.36952e-5i
$784$	11.8218	−	32.4802i	0.422208	−	1.16001i
$785$		0			0
$786$	41.5232	−	71.9202i	1.48108	−	2.56531i
$787$	4.81711	−	17.9777i	0.171711	−	0.640836i	−0.825377	−	0.564582i	$-0.809037\pi$
$787$	4.81711	−	17.9777i	0.171711	−	0.640836i	0.997088	−	0.0762539i	$-0.0242960\pi$
$788$	−0.130209	+	0.0911732i	−0.00463850	+	0.00324791i
$789$	6.77860	−	38.4434i	0.241325	−	1.36862i
$790$		0			0
$791$	0.458580	+	0.264761i	0.0163052	+	0.00941383i
$792$	2.26888	+	25.9334i	0.0806212	+	0.921504i
$793$	8.99471	−	4.19430i	0.319411	−	0.148944i
$794$	33.2963	−	12.1189i	1.18164	−	0.430082i
$795$		0			0
$796$	0.817579	+	4.63672i	0.0289783	+	0.164344i
$797$	−17.8040	−	17.8040i	−0.630650	−	0.630650i	0.317581	−	0.948231i	$-0.397129\pi$
$797$	−17.8040	−	17.8040i	−0.630650	−	0.630650i	−0.948231	+	0.317581i	$0.897129\pi$
$798$	−5.31059	−	0.138773i	−0.187993	−	0.00491252i
$799$		−	24.2912i		−	0.859362i
$800$		0			0
$801$	31.7667	+	37.8581i	1.12242	+	1.33765i
$802$	13.1680	−	28.2389i	0.464979	−	0.997150i
$803$	−20.9482	−	44.9235i	−0.739245	−	1.58532i
$804$	13.5913	−	16.1975i	0.479328	−	0.571240i
$805$		0			0
$806$	−12.2087	+	7.04867i	−0.430032	+	0.248279i
$807$	15.9927	+	22.8400i	0.562971	+	0.804006i
$808$	11.5925	+	16.5558i	0.407822	+	0.582430i
$809$	−9.34965	+	5.39802i	−0.328716	+	0.189784i	−0.655271	−	0.755394i	$-0.727446\pi$
$809$	−9.34965	+	5.39802i	−0.328716	+	0.189784i	0.326555	+	0.945178i	$0.394112\pi$
$810$		0			0
$811$	−29.9351	+	35.6753i	−1.05116	+	1.25273i	−0.0845686	+	0.996418i	$0.526951\pi$
$811$	−29.9351	+	35.6753i	−1.05116	+	1.25273i	−0.966595	+	0.256310i	$0.917493\pi$
$812$	0.000333569	0	0.000715340i	1.17060e−5	0	2.51035e-5i
$813$	−21.7481	+	46.6389i	−0.762738	+	1.63570i
$814$	−39.0877	−	46.5829i	−1.37002	−	1.63273i
$815$		0			0
$816$			59.5957i			2.08627i
$817$	0.579447	−	0.655017i	0.0202723	−	0.0229161i
$818$	−14.9539	−	14.9539i	−0.522852	−	0.522852i
$819$	−0.385836	−	2.18818i	−0.0134822	−	0.0764613i
$820$		0			0
$821$	42.5776	−	15.4970i	1.48597	−	0.540848i	0.533583	−	0.845748i	$-0.320845\pi$
$821$	42.5776	−	15.4970i	1.48597	−	0.540848i	0.952384	+	0.304900i	$0.0986232\pi$
$822$	−41.0056	+	19.1212i	−1.43024	+	0.666930i
$823$	4.79043	+	54.7548i	0.166984	+	1.90863i	0.369296	+	0.929312i	$0.379599\pi$
$823$	4.79043	+	54.7548i	0.166984	+	1.90863i	−0.202312	+	0.979321i	$0.564846\pi$
$824$	1.29666	+	0.748626i	0.0451712	+	0.0260796i
$825$		0			0
$826$	0.182161	−	1.03309i	0.00633820	−	0.0359457i
$827$	5.78980	−	4.05406i	0.201331	−	0.140973i	−0.468563	−	0.883430i	$-0.655228\pi$
$827$	5.78980	−	4.05406i	0.201331	−	0.140973i	0.669894	+	0.742456i	$0.266339\pi$
$828$	−5.79001	+	21.6086i	−0.201217	+	0.750951i
$829$	3.92941	−	6.80594i	0.136474	−	0.236380i	−0.789685	−	0.613512i	$-0.789756\pi$
$829$	3.92941	−	6.80594i	0.136474	−	0.236380i	0.926160	+	0.377132i	$0.123090\pi$
$830$		0			0
$831$	−6.46306	+	17.7571i	−0.224201	+	0.615987i
$832$	−3.40603	−	1.58826i	−0.118083	−	0.0550630i
$833$	−33.2095	−	2.90546i	−1.15064	−	0.100668i
$834$	64.2131	−	11.3225i	2.22352	−	0.392066i
$835$		0			0
$836$	−18.0727	−	5.35231i	−0.625057	−	0.185113i
$837$	−0.729240	+	0.729240i	−0.0252062	+	0.0252062i
$838$	43.2448	+	30.2804i	1.49387	+	1.04602i
$839$	13.3579	−	11.2087i	0.461168	−	0.386966i	−0.382393	−	0.924000i	$-0.624900\pi$
$839$	13.3579	−	11.2087i	0.461168	−	0.386966i	0.843560	+	0.537034i	$0.180455\pi$
$840$		0			0
$841$	27.2511	+	9.91858i	0.939692	+	0.342020i
$842$	28.4982	−	2.49327i	0.982113	−	0.0859238i
$843$	−13.1559	+	3.52512i	−0.453114	+	0.121412i
$844$	0.0448173	+	0.0776258i	0.00154267	+	0.00267199i
$845$		0			0
$846$	−26.6128	−	4.69255i	−0.914967	−	0.161333i
$847$	2.79191	+	0.748091i	0.0959313	+	0.0257047i
$848$	−3.41511	−	12.7453i	−0.117275	−	0.437677i
$849$	21.8841	+	18.3630i	0.751061	+	0.630215i
$850$		0			0
$851$	20.0702	+	55.1425i	0.687998	+	1.89026i
$852$	−2.57431	+	29.4245i	−0.0881945	+	1.00807i
$853$	28.1590	−	40.2152i	0.964146	−	1.37694i	0.0382064	−	0.999270i	$-0.487836\pi$
$853$	28.1590	−	40.2152i	0.964146	−	1.37694i	0.925939	−	0.377673i	$-0.123276\pi$
$854$	1.97360			0.0675354
$855$		0			0
$856$	28.2920			0.967001
$857$	−0.0631803	+	0.0902309i	−0.00215820	+	0.00308223i	−0.820230	−	0.572034i	$-0.806154\pi$
$857$	−0.0631803	+	0.0902309i	−0.00215820	+	0.00308223i	0.818071	+	0.575117i	$0.195043\pi$
$858$	4.20533	−	48.0672i	0.143568	−	1.64099i
$859$	13.8823	+	38.1414i	0.473659	+	1.30137i	0.914792	+	0.403926i	$0.132355\pi$
$859$	13.8823	+	38.1414i	0.473659	+	1.30137i	−0.441132	+	0.897442i	$0.645423\pi$
$860$		0			0
$861$	−0.112477	−	0.0943798i	−0.00383322	−	0.00321645i
$862$	−6.89101	−	25.7176i	−0.234709	−	0.875945i
$863$	−17.8927	−	4.79433i	−0.609074	−	0.163201i	−0.0589178	−	0.998263i	$-0.518765\pi$
$863$	−17.8927	−	4.79433i	−0.609074	−	0.163201i	−0.550156	+	0.835062i	$0.685432\pi$
$864$	1.51204	+	0.266614i	0.0514407	+	0.00907038i
$865$		0			0
$866$	−11.0578	−	19.1526i	−0.375759	−	0.650833i
$867$	14.8783	−	3.98662i	0.505292	−	0.135393i
$868$	−0.894263	+	0.0782379i	−0.0303533	+	0.00265557i
$869$	23.6531	+	8.60903i	0.802377	+	0.292041i
$870$		0			0
$871$	17.2019	−	14.4341i	0.582865	−	0.489082i
$872$	−14.0486	−	9.83693i	−0.475745	−	0.333121i
$873$	−13.1839	+	13.1839i	−0.446207	+	0.446207i
$874$	45.6634	+	33.7853i	1.54459	+	1.14280i
$875$		0			0
$876$	−24.7971	+	4.37239i	−0.837815	+	0.147729i
$877$	−30.8351	−	2.69772i	−1.04123	−	0.0910956i	−0.446307	−	0.894880i	$-0.647261\pi$
$877$	−30.8351	−	2.69772i	−1.04123	−	0.0910956i	−0.594921	+	0.803784i	$0.702817\pi$
$878$	−52.2966	−	24.3863i	−1.76493	−	0.822998i
$879$	−20.5579	+	56.4824i	−0.693401	+	1.90510i
$880$		0			0
$881$	0.542908	−	0.940344i	0.0182910	−	0.0316810i	−0.856735	−	0.515757i	$-0.827511\pi$
$881$	0.542908	−	0.940344i	0.0182910	−	0.0316810i	0.875026	+	0.484076i	$0.160844\pi$
$882$	−9.59851	+	35.8221i	−0.323199	+	1.20619i
$883$	22.0280	−	15.4242i	0.741302	−	0.519065i	−0.140850	−	0.990031i	$-0.544983\pi$
$883$	22.0280	−	15.4242i	0.741302	−	0.519065i	0.882151	+	0.470966i	$0.156095\pi$
$884$	1.95217	−	11.0713i	0.0656585	−	0.372368i
$885$		0			0
$886$	24.9015	+	14.3769i	0.836582	+	0.483001i
$887$	2.05570	+	23.4968i	0.0690238	+	0.788946i	0.949277	+	0.314441i	$0.101817\pi$
$887$	2.05570	+	23.4968i	0.0690238	+	0.788946i	−0.880253	+	0.474504i	$0.842627\pi$
$888$	31.4383	−	14.6599i	1.05500	−	0.491955i
$889$	2.71832	−	0.989389i	0.0911696	−	0.0331830i
$890$		0			0
$891$	6.86064	+	38.9086i	0.229840	+	1.30349i
$892$	0.457845	+	0.457845i	0.0153298	+	0.0153298i
$893$	−11.4791	+	18.7345i	−0.384134	+	0.626927i
$894$		−	41.0860i		−	1.37412i
$895$		0			0
$896$	−2.30409	−	2.74591i	−0.0769743	−	0.0917344i
$897$	−19.6780	+	42.1996i	−0.657029	+	1.40900i
$898$	12.5865	+	26.9918i	0.420017	+	0.900729i
$899$	0.00622611	−	0.00741999i	0.000207652	−	0.000247471i
$900$		0			0
$901$	−11.0211	+	6.36302i	−0.367165	+	0.211983i
$902$	−0.933160	−	1.33269i	−0.0310708	−	0.0443737i
$903$	0.0817667	+	0.116775i	0.00272102	+	0.00388602i
$904$	−2.89854	+	1.67347i	−0.0964040	+	0.0556589i
$905$		0			0
$906$	8.47172	−	10.0962i	0.281454	−	0.335424i
$907$	2.75446	+	5.90696i	0.0914603	+	0.196137i	0.946716	−	0.322068i	$-0.104378\pi$
$907$	2.75446	+	5.90696i	0.0914603	+	0.196137i	−0.855256	+	0.518205i	$0.826600\pi$
$908$	−1.76369	+	3.78225i	−0.0585301	+	0.125518i
$909$	−22.3769	−	26.6677i	−0.742195	−	0.884513i
$910$		0			0
$911$		−	27.6418i		−	0.915812i	−0.889001	−	0.457906i	$-0.848600\pi$
$911$		−	27.6418i		−	0.915812i	0.889001	−	0.457906i	$-0.151400\pi$
$912$	28.1627	−	45.9630i	0.932560	−	1.52199i
$913$	51.8863	+	51.8863i	1.71719	+	1.71719i
$914$	−1.76271	−	9.99681i	−0.0583052	−	0.330665i
$915$		0			0
$916$	−1.45301	+	0.528854i	−0.0480089	+	0.0174738i
$917$	5.08991	−	2.37346i	0.168084	−	0.0783787i
$918$	−0.223850	−	2.55861i	−0.00738814	−	0.0844468i
$919$	23.3008	+	13.4527i	0.768623	+	0.443764i	0.832383	−	0.554201i	$-0.186976\pi$
$919$	23.3008	+	13.4527i	0.768623	+	0.443764i	−0.0637605	+	0.997965i	$0.520309\pi$
$920$		0			0
$921$	−1.96114	+	11.1222i	−0.0646217	+	0.366488i
$922$	19.6995	−	13.7938i	0.648770	−	0.454274i
$923$	−8.11879	+	30.2997i	−0.267233	+	0.997328i
$924$	1.53624	−	2.66084i	0.0505385	−	0.0875353i
$925$		0			0
$926$	−8.44826	+	23.2114i	−0.277627	+	0.762774i
$927$	−2.33732	−	1.08991i	−0.0767677	−	0.0357973i
$928$	−0.0143655	−	0.00125682i	−0.000471570	−	4.12570e-5i
$929$	−49.9574	+	8.80883i	−1.63905	+	0.289008i	−0.915817	−	0.401597i	$-0.868455\pi$
$929$	−49.9574	+	8.80883i	−1.63905	+	0.289008i	−0.723232	+	0.690605i	$0.757344\pi$
$930$		0			0
$931$	24.2397	+	17.9344i	0.794424	+	0.587776i
$932$	−6.43755	+	6.43755i	−0.210869	+	0.210869i
$933$	11.2777	+	7.89674i	0.369216	+	0.258527i
$934$	11.4767	−	9.63011i	0.375530	−	0.315107i
$935$		0			0
$936$	13.1972	+	4.80339i	0.431364	+	0.157004i
$937$	−8.98755	+	0.786309i	−0.293610	+	0.0256876i	−0.233009	−	0.972474i	$-0.574857\pi$
$937$	−8.98755	+	0.786309i	−0.293610	+	0.0256876i	−0.0606010	+	0.998162i	$0.519302\pi$
$938$	4.31336	−	1.15576i	0.140836	−	0.0377369i
$939$	12.5324	+	21.7068i	0.408980	+	0.708374i
$940$		0			0
$941$	−1.15162	−	0.203063i	−0.0375419	−	0.00661965i	0.154846	−	0.987939i	$-0.450512\pi$
$941$	−1.15162	−	0.203063i	−0.0375419	−	0.00661965i	−0.192388	+	0.981319i	$0.561623\pi$
$942$	66.2095	+	17.7408i	2.15722	+	0.578026i
$943$	0.406339	+	1.51648i	0.0132322	+	0.0493833i
$944$	8.15412	+	6.84212i	0.265394	+	0.222692i
$945$		0			0
$946$	0.540244	+	1.48431i	0.0175648	+	0.0482590i
$947$	−0.504745	+	5.76927i	−0.0164020	+	0.187476i	0.983574	+	0.180507i	$0.0577739\pi$
$947$	−0.504745	+	5.76927i	−0.0164020	+	0.187476i	−0.999976	+	0.00696893i	$0.997782\pi$
$948$	7.33406	−	10.4741i	0.238199	−	0.340184i
$949$	−26.7411			−0.868051
$950$		0			0
$951$	−63.7565			−2.06744
$952$	−1.43995	+	2.05646i	−0.0466690	+	0.0666503i
$953$	0.183503	−	2.09745i	0.00594425	−	0.0679431i	−0.992643	−	0.121077i	$-0.961365\pi$
$953$	0.183503	−	2.09745i	0.00594425	−	0.0679431i	0.998587	+	0.0531335i	$0.0169209\pi$
$954$	4.84211	+	13.3036i	0.156769	+	0.430719i
$955$		0			0
$956$	4.51315	+	3.78698i	0.145966	+	0.122480i
$957$	0.00858051	+	0.0320229i	0.000277368	+	0.00103515i
$958$	33.0936	+	8.86741i	1.06921	+	0.286493i
$959$	−3.01324	−	0.531315i	−0.0973025	−	0.0171571i
$960$		0			0
$961$	−9.99187	−	17.3064i	−0.322319	−	0.558272i
$962$	−31.6882	+	8.49082i	−1.02167	+	0.273755i
$963$	−48.5462	+	4.24725i	−1.56438	+	0.136866i
$964$	11.1045	+	4.04172i	0.357653	+	0.130175i
$965$		0			0
$966$	−7.09308	+	5.95180i	−0.228216	+	0.191496i
$967$	35.0900	+	24.5703i	1.12842	+	0.790127i	0.980039	−	0.198804i	$-0.0637056\pi$
$967$	35.0900	+	24.5703i	1.12842	+	0.790127i	0.148379	+	0.988931i	$0.452595\pi$
$968$	−12.9184	+	12.9184i	−0.415212	+	0.415212i
$969$	−49.8491	−	14.7630i	−1.60138	−	0.474256i
$970$		0			0
$971$	29.4711	−	5.19655i	0.945772	−	0.166765i	0.320567	−	0.947226i	$-0.396126\pi$
$971$	29.4711	−	5.19655i	0.945772	−	0.166765i	0.625205	+	0.780461i	$0.285015\pi$
$972$	20.8684	+	1.82574i	0.669353	+	0.0585608i
$973$	3.99633	+	1.86352i	0.128117	+	0.0597417i
$974$	−7.81592	+	21.4741i	−0.250438	+	0.688073i
$975$		0			0
$976$	−10.0131	+	17.3431i	−0.320511	+	0.555141i
$977$	4.89371	−	18.2636i	0.156564	−	0.584303i	−0.842403	−	0.538848i	$-0.818860\pi$
$977$	4.89371	−	18.2636i	0.156564	−	0.584303i	0.998966	−	0.0454549i	$-0.0144737\pi$
$978$	0.287549	−	0.201344i	0.00919480	−	0.00643827i
$979$	−12.6026	+	71.4730i	−0.402782	+	2.28429i
$980$		0			0
$981$	25.5827	+	14.7702i	0.816793	+	0.471576i
$982$	3.69075	+	42.1854i	0.117777	+	1.34619i
$983$	46.3328	−	21.6053i	1.47779	−	0.689103i	0.494168	−	0.869367i	$-0.335473\pi$
$983$	46.3328	−	21.6053i	1.47779	−	0.689103i	0.983618	+	0.180264i	$0.0576951\pi$
$984$	0.872090	−	0.317415i	0.0278012	−	0.0101188i
$985$		0			0
$986$	0.00418885	+	0.0237561i	0.000133400	+	0.000756549i
$987$	−2.53254	−	2.53254i	−0.0806117	−	0.0806117i
$988$	−6.73748	+	7.61618i	−0.214348	+	0.242303i
$989$		−	1.52428i		−	0.0484694i
$990$		0			0
$991$	35.3727	+	42.1556i	1.12365	+	1.33912i	0.934003	+	0.357264i	$0.116290\pi$
$991$	35.3727	+	42.1556i	1.12365	+	1.33912i	0.189648	+	0.981852i	$0.439265\pi$
$992$	6.93120	−	14.8640i	0.220066	−	0.471933i
$993$	13.3852	+	28.7047i	0.424767	+	0.910915i
$994$	−4.00970	+	4.77857i	−0.127180	+	0.151567i
$995$		0			0
$996$	32.2812	−	18.6375i	1.02287	−	0.590553i
$997$	8.15440	+	11.6457i	0.258252	+	0.368823i	0.927251	−	0.374441i	$-0.122166\pi$
$997$	8.15440	+	11.6457i	0.258252	+	0.368823i	−0.668998	+	0.743264i	$0.733277\pi$
$998$	−18.5720	−	26.5235i	−0.587886	−	0.839588i
$999$	−2.07842	+	1.19997i	−0.0657582	+	0.0379655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.bb.b.143.6		96
5.2	odd	4	inner	475.2.bb.b.257.6		96
5.3	odd	4		95.2.r.a.67.3	yes	96
5.4	even	2		95.2.r.a.48.3	yes	96
15.8	even	4		855.2.dl.a.352.6		96
15.14	odd	2		855.2.dl.a.523.6		96
19.2	odd	18	inner	475.2.bb.b.268.6		96
95.2	even	36	inner	475.2.bb.b.382.6		96
95.59	odd	18		95.2.r.a.78.3	yes	96
95.78	even	36		95.2.r.a.2.3	✓	96
285.59	even	18		855.2.dl.a.838.6		96
285.173	odd	36		855.2.dl.a.667.6		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.3	✓	96	95.78	even	36
95.2.r.a.48.3	yes	96	5.4	even	2
95.2.r.a.67.3	yes	96	5.3	odd	4
95.2.r.a.78.3	yes	96	95.59	odd	18
475.2.bb.b.143.6		96	1.1	even	1	trivial
475.2.bb.b.257.6		96	5.2	odd	4	inner
475.2.bb.b.268.6		96	19.2	odd	18	inner
475.2.bb.b.382.6		96	95.2	even	36	inner
855.2.dl.a.352.6		96	15.8	even	4
855.2.dl.a.523.6		96	15.14	odd	2
855.2.dl.a.667.6		96	285.173	odd	36
855.2.dl.a.838.6		96	285.59	even	18

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bb (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.983828 - 1.40505i) q^{2} +(0.215709 - 2.46557i) q^{3} +(-0.322212 - 0.885271i) q^{4} +(-3.25203 - 2.72877i) q^{6} +(-0.0743036 - 0.277305i) q^{7} +(1.75276 + 0.469650i) q^{8} +(-3.07806 - 0.542745i) q^{9} +(-2.29500 - 3.97505i) q^{11} +(-2.25220 + 0.603475i) q^{12} +(-2.46682 + 0.215819i) q^{13} +(-0.462730 - 0.168420i) q^{14} +(3.82765 - 3.21178i) q^{16} +(-3.94756 - 2.76411i) q^{17} +(-3.79086 + 3.79086i) q^{18} +(1.73832 + 3.99728i) q^{19} +(-0.699742 + 0.123383i) q^{21} +(-7.84303 - 0.686176i) q^{22} +(6.88562 + 3.21082i) q^{23} +(1.53604 - 4.22023i) q^{24} +(-2.12369 + 3.67833i) q^{26} +(-0.0804202 + 0.300132i) q^{27} +(-0.221548 + 0.155130i) q^{28} +(0.000506761 - 0.00287398i) q^{29} +(2.87440 + 1.65954i) q^{31} +(-0.430665 - 4.92252i) q^{32} +(-10.2958 + 4.80101i) q^{33} +(-7.76743 + 2.82711i) q^{34} +(0.511312 + 2.89980i) q^{36} +(5.46158 + 5.46158i) q^{37} +(7.32659 + 1.49020i) q^{38} +6.12865i q^{39} +(0.132829 + 0.158299i) q^{41} +(-0.515065 + 1.10456i) q^{42} +(-0.0847905 - 0.181834i) q^{43} +(-2.77952 + 3.31250i) q^{44} +(11.2856 - 6.51576i) q^{46} +(2.89119 + 4.12905i) q^{47} +(-7.09320 - 10.1301i) q^{48} +(5.99080 - 3.45879i) q^{49} +(-7.66662 + 9.13672i) q^{51} +(0.985897 + 2.11426i) q^{52} +(1.11603 - 2.39334i) q^{53} +(0.342582 + 0.408273i) q^{54} -0.520945i q^{56} +(10.2305 - 3.42370i) q^{57} +(-0.00353953 - 0.00353953i) q^{58} +(0.369926 + 2.09795i) q^{59} +(-3.76621 + 1.37079i) q^{61} +(5.15965 - 2.40598i) q^{62} +(0.0782052 + 0.893889i) q^{63} +(1.31435 + 0.758840i) q^{64} +(-3.38362 + 19.1895i) q^{66} +(-7.42839 + 5.20141i) q^{67} +(-1.17503 + 4.38529i) q^{68} +(9.40177 - 16.2843i) q^{69} +(4.33266 - 11.9039i) q^{71} +(-5.14019 - 2.39691i) q^{72} +(10.7580 + 0.941200i) q^{73} +(13.0471 - 2.30055i) q^{74} +(2.97856 - 2.82686i) q^{76} +(-0.931774 + 0.931774i) q^{77} +(8.61107 + 6.02954i) q^{78} +(-4.20092 + 3.52499i) q^{79} +(-8.08850 - 2.94397i) q^{81} +(0.353099 - 0.0308922i) q^{82} +(-15.4419 + 4.13763i) q^{83} +(0.334693 + 0.579705i) q^{84} +(-0.338905 - 0.0597581i) q^{86} +(-0.00697668 - 0.00186940i) q^{87} +(-2.15569 - 8.04514i) q^{88} +(-12.1125 - 10.1636i) q^{89} +(0.243141 + 0.668024i) q^{91} +(0.623812 - 7.13020i) q^{92} +(4.71173 - 6.72905i) q^{93} +8.64596 q^{94} -12.2297 q^{96} +(3.42156 - 4.88649i) q^{97} +(1.03414 - 11.8202i) q^{98} +(4.90670 + 13.4810i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{2} + 12 q^{3} - 12 q^{6} + 18 q^{8} - 12 q^{11} + 18 q^{12} + 12 q^{13} + 12 q^{16} + 30 q^{17} + 24 q^{21} + 24 q^{22} - 48 q^{26} + 18 q^{27} - 36 q^{31} - 18 q^{32} - 90 q^{33} + 24 q^{36}+ \cdots + 90 q^{98}+O(q^{100}) \) 96 * q + 12 * q^2 + 12 * q^3 - 12 * q^6 + 18 * q^8 - 12 * q^11 + 18 * q^12 + 12 * q^13 + 12 * q^16 + 30 * q^17 + 24 * q^21 + 24 * q^22 - 48 * q^26 + 18 * q^27 - 36 * q^31 - 18 * q^32 - 90 * q^33 + 24 * q^36 - 54 * q^38 + 12 * q^41 - 24 * q^42 - 48 * q^43 - 36 * q^46 + 24 * q^47 - 60 * q^48 - 96 * q^51 + 30 * q^53 + 66 * q^57 - 120 * q^58 - 48 * q^61 - 60 * q^62 + 126 * q^63 + 72 * q^66 - 108 * q^67 - 18 * q^68 - 24 * q^71 - 48 * q^72 - 6 * q^73 + 60 * q^76 - 168 * q^77 + 138 * q^78 - 120 * q^81 - 60 * q^82 - 180 * q^86 + 6 * q^87 + 198 * q^88 - 24 * q^91 + 72 * q^92 + 90 * q^93 - 192 * q^96 + 72 * q^97 + 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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