LMFDB - Embedded newform 475.2.bb.b.143.8

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			143.8
Character	$\chi$	$=$	475.143
Dual form			475.2.bb.b.382.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34445 - 1.92007i) q^{2} +(-0.165797 + 1.89507i) q^{3} +(-1.19510 - 3.28350i) q^{4} +(3.41577 + 2.86617i) q^{6} +(0.719307 + 2.68449i) q^{7} +(-3.38309 - 0.906496i) q^{8} +(-0.609382 - 0.107451i) q^{9} +(1.57593 + 2.72958i) q^{11} +(6.42061 - 1.72040i) q^{12} +(3.82311 - 0.334479i) q^{13} +(6.12149 + 2.22804i) q^{14} +(-0.935465 + 0.784949i) q^{16} +(-4.24326 - 2.97116i) q^{17} +(-1.02560 + 1.02560i) q^{18} +(1.72391 - 4.00352i) q^{19} +(-5.20656 + 0.918057i) q^{21} +(7.35975 + 0.643895i) q^{22} +(0.380240 + 0.177309i) q^{23} +(2.27878 - 6.26090i) q^{24} +(4.49776 - 7.79034i) q^{26} +(-1.17240 + 4.37546i) q^{27} +(7.95488 - 5.57007i) q^{28} +(-1.19676 + 6.78718i) q^{29} +(0.180067 + 0.103962i) q^{31} +(-0.361041 - 4.12672i) q^{32} +(-5.43404 + 2.53393i) q^{33} +(-11.4097 + 4.15279i) q^{34} +(0.375456 + 2.12932i) q^{36} +(-7.00958 - 7.00958i) q^{37} +(-5.36933 - 8.69256i) q^{38} +7.30052i q^{39} +(1.39301 + 1.66012i) q^{41} +(-5.23722 + 11.2313i) q^{42} +(-3.30995 - 7.09822i) q^{43} +(7.07920 - 8.43666i) q^{44} +(0.851660 - 0.491706i) q^{46} +(4.91842 + 7.02423i) q^{47} +(-1.33244 - 1.90292i) q^{48} +(-0.626908 + 0.361945i) q^{49} +(6.33409 - 7.54867i) q^{51} +(-5.66724 - 12.1534i) q^{52} +(1.58924 - 3.40813i) q^{53} +(6.82497 + 8.13369i) q^{54} -9.73392i q^{56} +(7.30113 + 3.93070i) q^{57} +(11.4229 + 11.4229i) q^{58} +(-0.351612 - 1.99409i) q^{59} +(-9.55401 + 3.47738i) q^{61} +(0.441706 - 0.205971i) q^{62} +(-0.149883 - 1.71317i) q^{63} +(-10.5241 - 6.07611i) q^{64} +(-2.44045 + 13.8405i) q^{66} +(-1.34021 + 0.938425i) q^{67} +(-4.68471 + 17.4836i) q^{68} +(-0.399056 + 0.691185i) q^{69} +(1.12813 - 3.09950i) q^{71} +(1.96419 + 0.915917i) q^{72} +(-12.4408 - 1.08843i) q^{73} +(-22.8829 + 4.03488i) q^{74} +(-15.2058 - 0.875867i) q^{76} +(-6.19397 + 6.19397i) q^{77} +(14.0175 + 9.81518i) q^{78} +(3.75275 - 3.14893i) q^{79} +(-9.84183 - 3.58213i) q^{81} +(5.06038 - 0.442726i) q^{82} +(-1.17716 + 0.315418i) q^{83} +(9.23677 + 15.9986i) q^{84} +(-18.0792 - 3.18784i) q^{86} +(-12.6638 - 3.39324i) q^{87} +(-2.85714 - 10.6630i) q^{88} +(-2.74193 - 2.30075i) q^{89} +(3.64790 + 10.0225i) q^{91} +(0.127770 - 1.46042i) q^{92} +(-0.226870 + 0.324004i) q^{93} +20.0996 q^{94} +7.88029 q^{96} +(-4.27760 + 6.10904i) q^{97} +(-0.147884 + 1.69033i) q^{98} +(-0.667046 - 1.83269i) 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 $

$2$	1.34445	−	1.92007i	0.950670	−	1.35770i	0.0168863	−	0.999857i	$-0.494625\pi$
$2$	1.34445	−	1.92007i	0.950670	−	1.35770i	0.933783	−	0.357839i	$-0.116486\pi$
$3$	−0.165797	+	1.89507i	−0.0957231	+	1.09412i	0.784682	+	0.619898i	$0.212826\pi$
$3$	−0.165797	+	1.89507i	−0.0957231	+	1.09412i	−0.880405	+	0.474222i	$0.842730\pi$
$4$	−1.19510	−	3.28350i	−0.597548	−	1.64175i
$5$		0			0
$5$		0			0
$6$	3.41577	+	2.86617i	1.39448	+	1.17011i
$7$	0.719307	+	2.68449i	0.271872	+	1.01464i	0.957908	+	0.287074i	$0.0926826\pi$
$7$	0.719307	+	2.68449i	0.271872	+	1.01464i	−0.686036	+	0.727568i	$0.740651\pi$
$8$	−3.38309	−	0.906496i	−1.19610	−	0.320495i
$9$	−0.609382	−	0.107451i	−0.203127	−	0.0358168i
$10$		0			0
$11$	1.57593	+	2.72958i	0.475159	+	0.823000i	0.999595	−	0.0284497i	$-0.00905704\pi$
$11$	1.57593	+	2.72958i	0.475159	+	0.823000i	−0.524436	+	0.851450i	$0.675724\pi$
$12$	6.42061	−	1.72040i	1.85347	−	0.496636i
$13$	3.82311	−	0.334479i	1.06034	−	0.0927677i	0.456382	−	0.889784i	$-0.349145\pi$
$13$	3.82311	−	0.334479i	1.06034	−	0.0927677i	0.603958	+	0.797016i	$0.293589\pi$
$14$	6.12149	+	2.22804i	1.63604	+	0.595469i
$15$		0			0
$16$	−0.935465	+	0.784949i	−0.233866	+	0.196237i
$17$	−4.24326	−	2.97116i	−1.02914	−	0.720613i	−0.0682872	−	0.997666i	$-0.521753\pi$
$17$	−4.24326	−	2.97116i	−1.02914	−	0.720613i	−0.960855	+	0.277053i	$0.910642\pi$
$18$	−1.02560	+	1.02560i	−0.241735	+	0.241735i
$19$	1.72391	−	4.00352i	0.395492	−	0.918470i
$19$	1.72391	−	4.00352i	0.395492	−	0.918470i
$20$		0			0
$21$	−5.20656	+	0.918057i	−1.13616	+	0.200336i
$22$	7.35975	+	0.643895i	1.56910	+	0.137279i
$23$	0.380240	+	0.177309i	0.0792855	+	0.0369715i	0.461857	−	0.886955i	$-0.347183\pi$
$23$	0.380240	+	0.177309i	0.0792855	+	0.0369715i	−0.382571	+	0.923926i	$0.624961\pi$
$24$	2.27878	−	6.26090i	0.465154	−	1.27800i
$25$		0			0
$26$	4.49776	−	7.79034i	0.882083	−	1.52781i
$27$	−1.17240	+	4.37546i	−0.225629	+	0.842058i
$28$	7.95488	−	5.57007i	1.50333	−	1.05264i
$29$	−1.19676	+	6.78718i	−0.222233	+	1.26035i	0.645671	+	0.763616i	$0.276578\pi$
$29$	−1.19676	+	6.78718i	−0.222233	+	1.26035i	−0.867904	+	0.496731i	$0.834533\pi$
$30$		0			0
$31$	0.180067	+	0.103962i	0.0323411	+	0.0186721i	0.516083	−	0.856538i	$-0.327389\pi$
$31$	0.180067	+	0.103962i	0.0323411	+	0.0186721i	−0.483742	+	0.875210i	$0.660723\pi$
$32$	−0.361041	−	4.12672i	−0.0638237	−	0.729508i
$33$	−5.43404	+	2.53393i	−0.945945	+	0.441101i
$34$	−11.4097	+	4.15279i	−1.95675	+	0.712198i
$35$		0			0
$36$	0.375456	+	2.12932i	0.0625761	+	0.354887i
$37$	−7.00958	−	7.00958i	−1.15237	−	1.15237i	−0.986077	−	0.166291i	$-0.946821\pi$
$37$	−7.00958	−	7.00958i	−1.15237	−	1.15237i	−0.166291	−	0.986077i	$-0.553179\pi$
$38$	−5.36933	−	8.69256i	−0.871021	−	1.41012i
$39$			7.30052i			1.16902i
$40$		0			0
$41$	1.39301	+	1.66012i	0.217551	+	0.259267i	0.863772	−	0.503883i	$-0.168096\pi$
$41$	1.39301	+	1.66012i	0.217551	+	0.259267i	−0.646221	+	0.763151i	$0.723651\pi$
$42$	−5.23722	+	11.2313i	−0.808121	+	1.73302i
$43$	−3.30995	−	7.09822i	−0.504763	−	1.08247i	−0.979334	−	0.202251i	$-0.935174\pi$
$43$	−3.30995	−	7.09822i	−0.504763	−	1.08247i	0.474571	−	0.880217i	$-0.342603\pi$
$44$	7.07920	−	8.43666i	1.06723	−	1.27187i
$45$		0			0
$46$	0.851660	−	0.491706i	0.125570	−	0.0724981i
$47$	4.91842	+	7.02423i	0.717425	+	1.02459i	0.997903	+	0.0647288i	$0.0206182\pi$
$47$	4.91842	+	7.02423i	0.717425	+	1.02459i	−0.280478	+	0.959861i	$0.590493\pi$
$48$	−1.33244	−	1.90292i	−0.192321	−	0.274662i
$49$	−0.626908	+	0.361945i	−0.0895582	+	0.0517065i
$50$		0			0
$51$	6.33409	−	7.54867i	0.886949	−	1.05703i
$52$	−5.66724	−	12.1534i	−0.785905	−	1.68538i
$53$	1.58924	−	3.40813i	0.218298	−	0.468142i	−0.766410	−	0.642351i	$-0.777959\pi$
$53$	1.58924	−	3.40813i	0.218298	−	0.468142i	0.984709	+	0.174209i	$0.0557368\pi$
$54$	6.82497	+	8.13369i	0.928761	+	1.10685i
$55$		0			0
$56$		−	9.73392i		−	1.30075i
$57$	7.30113	+	3.93070i	0.967058	+	0.520634i
$58$	11.4229	+	11.4229i	1.49990	+	1.49990i
$59$	−0.351612	−	1.99409i	−0.0457760	−	0.259609i	0.953328	−	0.301938i	$-0.0976334\pi$
$59$	−0.351612	−	1.99409i	−0.0457760	−	0.259609i	−0.999104	+	0.0423288i	$0.986522\pi$
$60$		0			0
$61$	−9.55401	+	3.47738i	−1.22327	+	0.445232i	−0.871286	−	0.490775i	$-0.836714\pi$
$61$	−9.55401	+	3.47738i	−1.22327	+	0.445232i	−0.351980	+	0.936008i	$0.614491\pi$
$62$	0.441706	−	0.205971i	0.0560967	−	0.0261583i
$63$	−0.149883	−	1.71317i	−0.0188835	−	0.215839i
$64$	−10.5241	−	6.07611i	−1.31552	−	0.759513i
$65$		0			0
$66$	−2.44045	+	13.8405i	−0.300399	+	1.70365i
$67$	−1.34021	+	0.938425i	−0.163733	+	0.114647i	−0.652571	−	0.757727i	$-0.726310\pi$
$67$	−1.34021	+	0.938425i	−0.163733	+	0.114647i	0.488838	+	0.872374i	$0.337421\pi$
$68$	−4.68471	+	17.4836i	−0.568104	+	2.12019i
$69$	−0.399056	+	0.691185i	−0.0480407	+	0.0832088i
$70$		0			0
$71$	1.12813	−	3.09950i	0.133884	−	0.367843i	−0.854576	−	0.519327i	$-0.826183\pi$
$71$	1.12813	−	3.09950i	0.133884	−	0.367843i	0.988460	+	0.151483i	$0.0484050\pi$
$72$	1.96419	+	0.915917i	0.231482	+	0.107942i
$73$	−12.4408	−	1.08843i	−1.45608	−	0.127391i	−0.668552	−	0.743666i	$-0.733085\pi$
$73$	−12.4408	−	1.08843i	−1.45608	−	0.127391i	−0.787531	+	0.616275i	$0.788641\pi$
$74$	−22.8829	+	4.03488i	−2.66009	+	0.469045i
$75$		0			0
$76$	−15.2058	−	0.875867i	−1.74422	−	0.100469i
$77$	−6.19397	+	6.19397i	−0.705868	+	0.705868i
$78$	14.0175	+	9.81518i	1.58717	+	1.11135i
$79$	3.75275	−	3.14893i	0.422217	−	0.354282i	−0.406788	−	0.913522i	$-0.633351\pi$
$79$	3.75275	−	3.14893i	0.422217	−	0.354282i	0.829006	+	0.559240i	$0.188907\pi$
$80$		0			0
$81$	−9.84183	−	3.58213i	−1.09354	−	0.398015i
$82$	5.06038	−	0.442726i	0.558826	−	0.0488909i
$83$	−1.17716	+	0.315418i	−0.129210	+	0.0346216i	−0.322844	−	0.946452i	$-0.604639\pi$
$83$	−1.17716	+	0.315418i	−0.129210	+	0.0346216i	0.193635	+	0.981074i	$0.437972\pi$
$84$	9.23677	+	15.9986i	1.00781	+	1.74559i
$85$		0			0
$86$	−18.0792	−	3.18784i	−1.94953	−	0.343754i
$87$	−12.6638	−	3.39324i	−1.35770	−	0.363794i
$88$	−2.85714	−	10.6630i	−0.304572	−	1.13668i
$89$	−2.74193	−	2.30075i	−0.290644	−	0.243879i	0.485794	−	0.874074i	$-0.338531\pi$
$89$	−2.74193	−	2.30075i	−0.290644	−	0.243879i	−0.776437	+	0.630195i	$0.782975\pi$
$90$		0			0
$91$	3.64790	+	10.0225i	0.382403	+	1.05064i
$92$	0.127770	−	1.46042i	0.0133210	−	0.152259i
$93$	−0.226870	+	0.324004i	−0.0235253	+	0.0335976i
$94$	20.0996			2.07312
$95$		0			0
$96$	7.88029			0.804278
$97$	−4.27760	+	6.10904i	−0.434324	+	0.620279i	−0.975333	−	0.220737i	$-0.929154\pi$
$97$	−4.27760	+	6.10904i	−0.434324	+	0.620279i	0.541009	+	0.841017i	$0.318043\pi$
$98$	−0.147884	+	1.69033i	−0.0149386	+	0.170749i
$99$	−0.667046	−	1.83269i	−0.0670406	−	0.184193i
$100$		0			0
$101$	6.90331	+	5.79257i	0.686905	+	0.576382i	0.918015	−	0.396546i	$-0.129791\pi$
$101$	6.90331	+	5.79257i	0.686905	+	0.576382i	−0.231110	+	0.972928i	$0.574236\pi$
$102$	−5.97814	−	22.3107i	−0.591924	−	2.20909i
$103$	−5.35479	−	1.43481i	−0.527623	−	0.141376i	−0.0148324	−	0.999890i	$-0.504721\pi$
$103$	−5.35479	−	1.43481i	−0.527623	−	0.141376i	−0.512790	+	0.858514i	$0.671388\pi$
$104$	−13.2371	−	2.33406i	−1.29801	−	0.228874i
$105$		0			0
$106$	−4.40721	−	7.63350i	−0.428066	−	0.741431i
$107$	8.55488	−	2.29227i	0.827031	−	0.221602i	0.179613	−	0.983737i	$-0.442515\pi$
$107$	8.55488	−	2.29227i	0.827031	−	0.221602i	0.647418	+	0.762135i	$0.275849\pi$
$108$	15.7680	−	1.37952i	1.51727	−	0.132744i
$109$	−12.5747	−	4.57682i	−1.20444	−	0.438380i	−0.339667	−	0.940546i	$-0.610314\pi$
$109$	−12.5747	−	4.57682i	−1.20444	−	0.438380i	−0.864771	+	0.502166i	$0.832537\pi$
$110$		0			0
$111$	14.4458	−	12.1215i	1.37114	−	1.15052i
$112$	−2.78007	−	1.94663i	−0.262692	−	0.183939i
$113$	7.92213	−	7.92213i	0.745252	−	0.745252i	−0.228332	−	0.973583i	$-0.573327\pi$
$113$	7.92213	−	7.92213i	0.745252	−	0.745252i	0.973583	+	0.228332i	$0.0733271\pi$
$114$	17.3632	−	8.73407i	1.62622	−	0.818021i
$115$		0			0
$116$	23.7159	−	4.18176i	2.20197	−	0.388266i
$117$	−2.36568	−	0.206970i	−0.218707	−	0.0191344i
$118$	−4.30153	−	2.00584i	−0.395988	−	0.184652i
$119$	4.92385	−	13.5282i	0.451369	−	1.24013i
$120$		0			0
$121$	0.532917	−	0.923039i	0.0484470	−	0.0839126i
$122$	−6.16807	+	23.0196i	−0.558431	+	2.08409i
$123$	−3.37700	+	2.36460i	−0.304494	+	0.213209i
$124$	0.126161	−	0.715496i	0.0113296	−	0.0642534i
$125$		0			0
$126$	−3.49092	−	2.01549i	−0.310996	−	0.179554i
$127$	−0.537991	−	6.14927i	−0.0477390	−	0.545659i	−0.981976	−	0.189006i	$-0.939473\pi$
$127$	−0.537991	−	6.14927i	−0.0477390	−	0.545659i	0.934237	−	0.356653i	$-0.116082\pi$
$128$	−18.3070	+	8.53669i	−1.61812	+	0.754544i
$129$	14.0004	−	5.09573i	1.23267	−	0.448654i
$130$		0			0
$131$	0.921493	+	5.22605i	0.0805113	+	0.456602i	0.998235	+	0.0593834i	$0.0189134\pi$
$131$	0.921493	+	5.22605i	0.0805113	+	0.456602i	−0.917724	+	0.397219i	$0.869975\pi$
$132$	14.8144	+	14.8144i	1.28942	+	1.28942i
$133$	11.9874	+	1.74806i	1.03944	+	0.151576i
$134$			3.83497i			0.331291i
$135$		0			0
$136$	11.6620	+	13.8982i	1.00001	+	1.19176i
$137$	3.69172	−	7.91691i	0.315405	−	0.676387i	−0.683142	−	0.730286i	$-0.739387\pi$
$137$	3.69172	−	7.91691i	0.315405	−	0.676387i	0.998546	+	0.0538984i	$0.0171647\pi$
$138$	0.790615	+	1.69548i	0.0673016	+	0.144329i
$139$	−4.01532	+	4.78527i	−0.340575	+	0.405882i	−0.908961	−	0.416880i	$-0.863123\pi$
$139$	−4.01532	+	4.78527i	−0.340575	+	0.405882i	0.568386	+	0.822762i	$0.307568\pi$
$140$		0			0
$141$	−14.1269	+	8.15616i	−1.18970	+	0.686872i
$142$	−4.43456	−	6.33321i	−0.372140	−	0.531471i
$143$	6.93793	+	9.90839i	0.580179	+	0.828581i
$144$	0.654399	−	0.377817i	0.0545332	−	0.0314848i
$145$		0			0
$146$	−18.8159	+	22.4239i	−1.55721	+	1.85581i
$147$	−0.581973	−	1.24804i	−0.0480003	−	0.102937i
$148$	−14.6388	+	31.3931i	−1.20330	+	2.58049i
$149$	−3.35260	−	3.99547i	−0.274656	−	0.327322i	0.611030	−	0.791608i	$-0.290756\pi$
$149$	−3.35260	−	3.99547i	−0.274656	−	0.327322i	−0.885686	+	0.464286i	$0.846311\pi$
$150$		0			0
$151$		−	20.4770i		−	1.66639i	−0.552976	−	0.833197i	$-0.686508\pi$
$151$		−	20.4770i		−	1.66639i	0.552976	−	0.833197i	$-0.313492\pi$
$152$	−9.46130	+	11.9815i	−0.767413	+	0.971831i
$153$	2.26651	+	2.26651i	0.183237	+	0.183237i
$154$	3.56539	+	20.2203i	0.287307	+	1.62940i
$155$		0			0
$156$	23.9713	−	8.72482i	1.91924	−	0.698545i
$157$	10.5695	−	4.92866i	0.843542	−	0.393350i	0.0477051	−	0.998861i	$-0.484809\pi$
$157$	10.5695	−	4.92866i	0.843542	−	0.393350i	0.795837	+	0.605512i	$0.207031\pi$
$158$	−1.00079	−	11.4391i	−0.0796189	−	0.910049i
$159$	6.19515	+	3.57677i	0.491307	+	0.283656i
$160$		0			0
$161$	−0.202475	+	1.14829i	−0.0159572	+	0.0904979i
$162$	−20.1098	+	14.0810i	−1.57998	+	1.10631i
$163$	1.22020	−	4.55384i	0.0955732	−	0.356684i	−0.901533	−	0.432711i	$-0.857557\pi$
$163$	1.22020	−	4.55384i	0.0955732	−	0.356684i	0.997106	+	0.0760273i	$0.0242236\pi$
$164$	3.78623	−	6.55794i	0.295655	−	0.512089i
$165$		0			0
$166$	−0.977002	+	2.68429i	−0.0758300	+	0.208341i
$167$	−0.290604	−	0.135511i	−0.0224876	−	0.0104862i	0.411342	−	0.911481i	$-0.365060\pi$
$167$	−0.290604	−	0.135511i	−0.0224876	−	0.0104862i	−0.433830	+	0.900995i	$0.642838\pi$
$168$	18.4465	+	1.61386i	1.42318	+	0.124512i
$169$	1.70180	−	0.300073i	0.130908	−	0.0230825i
$170$		0			0
$171$	−1.48070	+	2.25444i	−0.113232	+	0.172401i
$172$	−19.3513	+	19.3513i	−1.47552	+	1.47552i
$173$	6.22183	+	4.35657i	0.473037	+	0.331224i	0.785666	−	0.618651i	$-0.212321\pi$
$173$	6.22183	+	4.35657i	0.473037	+	0.331224i	−0.312628	+	0.949875i	$0.601209\pi$
$174$	−23.5411	+	19.7533i	−1.78464	+	1.49749i
$175$		0			0
$176$	−3.61681	−	1.31641i	−0.272627	−	0.0992281i
$177$	3.83724	−	0.335715i	0.288425	−	0.0252339i
$178$	−8.10399	+	2.17146i	−0.607420	+	0.162758i
$179$	7.76584	+	13.4508i	0.580446	+	1.00536i	0.995426	+	0.0955314i	$0.0304550\pi$
$179$	7.76584	+	13.4508i	0.580446	+	1.00536i	−0.414981	+	0.909830i	$0.636212\pi$
$180$		0			0
$181$	10.1081	+	1.78233i	0.751330	+	0.132480i	0.536183	−	0.844102i	$-0.319866\pi$
$181$	10.1081	+	1.78233i	0.751330	+	0.132480i	0.215147	+	0.976582i	$0.430977\pi$
$182$	24.1484	+	6.47053i	1.79000	+	0.479628i
$183$	−5.00585	−	18.6821i	−0.370043	−	1.38102i
$184$	−1.12566	−	0.944537i	−0.0829845	−	0.0696322i
$185$		0			0
$186$	0.317096	+	0.871214i	0.0232506	+	0.0638805i
$187$	1.42297	−	16.2647i	0.104058	−	1.18939i
$188$	17.1861	−	24.5442i	1.25342	−	1.79007i
$189$	−12.5892			−0.915730
$190$		0			0
$191$	−0.338908			−0.0245225			−0.0122613	−	0.999925i	$-0.503903\pi$
$191$	−0.338908			−0.0245225			−0.0122613	+	0.999925i	$0.503903\pi$
$192$	13.2595	−	18.9366i	0.956924	−	1.36663i
$193$	−1.29709	+	14.8258i	−0.0933662	+	1.06718i	0.794557	+	0.607190i	$0.207703\pi$
$193$	−1.29709	+	14.8258i	−0.0933662	+	1.06718i	−0.887923	+	0.459992i	$0.847852\pi$
$194$	5.97880	+	16.4266i	0.429252	+	1.17936i
$195$		0			0
$196$	1.93766	+	1.62589i	0.138404	+	0.116135i
$197$	1.93347	+	7.21580i	0.137754	+	0.514105i	0.999971	+	0.00756626i	$0.00240844\pi$
$197$	1.93347	+	7.21580i	0.137754	+	0.514105i	−0.862217	+	0.506538i	$0.830925\pi$
$198$	−4.41572	−	1.18319i	−0.313811	−	0.0840855i
$199$	−13.1293	−	2.31506i	−0.930714	−	0.164110i	−0.312319	−	0.949977i	$-0.601106\pi$
$199$	−13.1293	−	2.31506i	−0.930714	−	0.164110i	−0.618395	+	0.785867i	$0.712217\pi$
$200$		0			0
$201$	−1.55618	−	2.69538i	−0.109764	−	0.190118i
$202$	20.4033	−	5.46705i	1.43557	−	0.384660i
$203$	−19.0809	+	1.66937i	−1.33922	+	0.117167i
$204$	−32.3559	−	11.7766i	−2.26536	−	0.824525i
$205$		0			0
$206$	−9.95418	+	8.35255i	−0.693541	+	0.581950i
$207$	−0.212660	−	0.148906i	−0.0147809	−	0.0103497i
$208$	−3.31384	+	3.31384i	−0.229773	+	0.229773i
$209$	13.6447	−	1.60369i	0.943822	−	0.110930i
$210$		0			0
$211$	−10.4614	+	1.84463i	−0.720195	+	0.126990i	−0.521721	−	0.853116i	$-0.674710\pi$
$211$	−10.4614	+	1.84463i	−0.720195	+	0.126990i	−0.198474	+	0.980106i	$0.563599\pi$
$212$	−13.0899	−	1.14521i	−0.899016	−	0.0786537i
$213$	5.68674	+	2.65177i	0.389649	+	0.181696i
$214$	7.10027	−	19.5078i	0.485365	−	1.33353i
$215$		0			0
$216$	7.93268	−	13.7398i	0.539750	−	0.934875i
$217$	−0.149561	+	0.558170i	−0.0101529	+	0.0378910i
$218$	−25.6939	+	17.9910i	−1.74021	+	1.21851i
$219$	4.12529	−	23.3957i	0.278761	−	1.58093i
$220$		0			0
$221$	−17.2162	−	9.93980i	−1.15809	−	0.668624i
$222$	−3.85245	−	44.0338i	−0.258560	−	2.95535i
$223$	23.9770	−	11.1806i	1.60562	−	0.748712i	0.606687	−	0.794941i	$-0.292498\pi$
$223$	23.9770	−	11.1806i	1.60562	−	0.748712i	0.998931	+	0.0462295i	$0.0147206\pi$
$224$	10.8184	−	3.93759i	0.722837	−	0.263091i
$225$		0			0
$226$	−4.56017	−	25.8620i	−0.303338	−	1.72031i
$227$	16.0488	+	16.0488i	1.06520	+	1.06520i	0.997721	+	0.0674780i	$0.0214953\pi$
$227$	16.0488	+	16.0488i	1.06520	+	1.06520i	0.0674780	+	0.997721i	$0.478505\pi$
$228$	4.18090	−	28.6708i	0.276887	−	1.89877i
$229$		−	4.46621i		−	0.295135i	−0.989052	−	0.147568i	$-0.952856\pi$
$229$		−	4.46621i		−	0.295135i	0.989052	−	0.147568i	$-0.0471444\pi$
$230$		0			0
$231$	−10.7111	−	12.7649i	−0.704736	−	0.839872i
$232$	10.2013	−	21.8768i	0.669748	−	1.43628i
$233$	−7.77862	−	16.6813i	−0.509594	−	1.09283i	−0.977864	−	0.209243i	$-0.932900\pi$
$233$	−7.77862	−	16.6813i	−0.509594	−	1.09283i	0.468270	−	0.883586i	$-0.344878\pi$
$234$	−3.57793	+	4.26401i	−0.233897	+	0.278747i
$235$		0			0
$236$	−6.12739	+	3.53765i	−0.398859	+	0.230281i
$237$	5.34525	+	7.63381i	0.347211	+	0.495869i
$238$	−19.3552	−	27.6421i	−1.25461	−	1.79177i
$239$	−11.9733	+	6.91280i	−0.774490	+	0.447152i	−0.834474	−	0.551047i	$-0.814228\pi$
$239$	−11.9733	+	6.91280i	−0.774490	+	0.447152i	0.0599839	+	0.998199i	$0.480895\pi$
$240$		0			0
$241$	−1.42682	+	1.70042i	−0.0919095	+	0.109534i	−0.810039	−	0.586376i	$-0.800554\pi$
$241$	−1.42682	+	1.70042i	−0.0919095	+	0.109534i	0.718129	+	0.695910i	$0.244999\pi$
$242$	−1.05582	−	2.26422i	−0.0678708	−	0.145549i
$243$	2.67700	−	5.74084i	0.171730	−	0.368275i
$244$	22.8359	+	27.2148i	1.46192	+	1.74225i
$245$		0			0
$246$			9.66318i			0.616102i
$247$	5.25160	−	15.8825i	0.334151	−	1.01058i
$248$	−0.514943	−	0.514943i	−0.0326989	−	0.0326989i
$249$	−0.402570	−	2.28309i	−0.0255119	−	0.144685i
$250$		0			0
$251$	−21.5140	+	7.83045i	−1.35795	+	0.494254i	−0.915420	−	0.402499i	$-0.868142\pi$
$251$	−21.5140	+	7.83045i	−1.35795	+	0.494254i	−0.442531	+	0.896753i	$0.645919\pi$
$252$	−5.44607	+	2.53954i	−0.343070	+	0.159976i
$253$	0.115251	+	1.31732i	0.00724575	+	0.0828194i
$254$	−12.5303	−	7.23440i	−0.786224	−	0.453926i
$255$		0			0
$256$	−4.00134	+	22.6927i	−0.250084	+	1.41830i
$257$	−14.0349	+	9.82734i	−0.875473	+	0.613013i	−0.922550	−	0.385879i	$-0.873898\pi$
$257$	−14.0349	+	9.82734i	−0.875473	+	0.613013i	0.0470768	+	0.998891i	$0.485009\pi$
$258$	9.03867	−	33.7328i	0.562723	−	2.10011i
$259$	13.7751	−	23.8592i	0.855944	−	1.48254i
$260$		0			0
$261$	1.45857	−	4.00739i	0.0902833	−	0.248051i
$262$	11.2733	+	5.25683i	0.696467	+	0.324768i
$263$	−5.42848	−	0.474931i	−0.334735	−	0.0292855i	−0.0814505	−	0.996677i	$-0.525955\pi$
$263$	−5.42848	−	0.474931i	−0.334735	−	0.0292855i	−0.253284	+	0.967392i	$0.581511\pi$
$264$	20.6808	−	3.64659i	1.27282	−	0.224432i
$265$		0			0
$266$	19.4729	−	20.6665i	1.19396	−	1.26715i
$267$	4.81469	−	4.81469i	0.294654	−	0.294654i
$268$	4.68300	+	3.27907i	0.286060	+	0.200301i
$269$	5.61407	−	4.71077i	0.342296	−	0.287220i	−0.455392	−	0.890291i	$-0.650501\pi$
$269$	5.61407	−	4.71077i	0.342296	−	0.287220i	0.797688	+	0.603071i	$0.206056\pi$
$270$		0			0
$271$	28.3871	+	10.3321i	1.72439	+	0.627628i	0.998206	−	0.0598702i	$-0.0190687\pi$
$271$	28.3871	+	10.3321i	1.72439	+	0.627628i	0.726186	+	0.687498i	$0.241291\pi$
$272$	6.30163	−	0.551321i	0.382093	−	0.0334288i
$273$	−19.5982	+	5.25132i	−1.18614	+	0.317824i
$274$	−10.2377	−	17.7323i	−0.618483	−	1.07124i
$275$		0			0
$276$	2.74641	+	0.484267i	0.165315	+	0.0291494i
$277$	−25.9124	−	6.94321i	−1.55693	−	0.417177i	−0.625238	−	0.780434i	$-0.714998\pi$
$277$	−25.9124	−	6.94321i	−1.55693	−	0.417177i	−0.931689	+	0.363257i	$0.881665\pi$
$278$	3.78968	+	14.1433i	0.227290	+	0.848257i
$279$	−0.0985591	−	0.0827009i	−0.00590058	−	0.00495117i
$280$		0			0
$281$	5.24613	+	14.4136i	0.312958	+	0.859845i	0.992056	+	0.125797i	$0.0401489\pi$
$281$	5.24613	+	14.4136i	0.312958	+	0.859845i	−0.679098	+	0.734048i	$0.737629\pi$
$282$	−3.33246	+	38.0902i	−0.198445	+	2.26824i
$283$	6.11947	−	8.73951i	0.363765	−	0.519510i	−0.594994	−	0.803730i	$-0.702846\pi$
$283$	6.11947	−	8.73951i	0.363765	−	0.519510i	0.958759	+	0.284220i	$0.0917346\pi$
$284$	−11.5254			−0.683908
$285$		0			0
$286$	28.3525			1.67652
$287$	−3.45458	+	4.93365i	−0.203917	+	0.291224i
$288$	−0.223406	+	2.55354i	−0.0131643	+	0.150469i
$289$	3.36311	+	9.24007i	0.197830	+	0.543533i
$290$		0			0
$291$	−10.8679	−	9.11922i	−0.637085	−	0.534578i
$292$	11.2941	+	42.1500i	0.660935	+	2.46664i
$293$	10.8601	+	2.90994i	0.634451	+	0.170001i	0.561689	−	0.827349i	$-0.310152\pi$
$293$	10.8601	+	2.90994i	0.634451	+	0.170001i	0.0727625	+	0.997349i	$0.476819\pi$
$294$	−3.17877	−	0.560503i	−0.185390	−	0.0326892i
$295$		0			0
$296$	17.3599	+	30.0682i	1.00902	+	1.74768i
$297$	−13.7908	+	3.69524i	−0.800224	+	0.214419i
$298$	−12.1790	+	1.06553i	−0.705511	+	0.0617242i
$299$	1.51301	+	0.550689i	0.0874994	+	0.0318472i
$300$		0			0
$301$	16.6742	−	13.9913i	0.961086	−	0.806447i
$302$	−39.3173	−	27.5303i	−2.26246	−	1.58419i
$303$	−12.1219	+	12.1219i	−0.696384	+	0.696384i
$304$	1.52990	+	5.09833i	0.0877456	+	0.292409i
$305$		0			0
$306$	7.39909	−	1.30466i	0.422978	−	0.0745824i
$307$	16.7187	+	1.46270i	0.954188	+	0.0834807i	0.553605	−	0.832780i	$-0.313252\pi$
$307$	16.7187	+	1.46270i	0.954188	+	0.0834807i	0.400584	+	0.916260i	$0.368807\pi$
$308$	27.7403	+	12.9355i	1.58065	+	0.737068i
$309$	3.60688	−	9.90981i	0.205188	−	0.563749i
$310$		0			0
$311$	−11.7668	+	20.3806i	−0.667231	+	1.15568i	0.311444	+	0.950265i	$0.399187\pi$
$311$	−11.7668	+	20.3806i	−0.667231	+	1.15568i	−0.978675	+	0.205414i	$0.934146\pi$
$312$	6.61789	−	24.6983i	0.374664	−	1.39827i
$313$	−4.57185	+	3.20124i	−0.258416	+	0.180945i	−0.695604	−	0.718425i	$-0.744863\pi$
$313$	−4.57185	+	3.20124i	−0.258416	+	0.180945i	0.437188	+	0.899370i	$0.355974\pi$
$314$	4.74684	−	26.9206i	0.267879	−	1.51922i
$315$		0			0
$316$	−14.8244	−	8.55887i	−0.833938	−	0.481474i
$317$	2.04113	+	23.3302i	0.114641	+	1.31035i	0.807751	+	0.589523i	$0.200684\pi$
$317$	2.04113	+	23.3302i	0.114641	+	1.31035i	−0.693110	+	0.720832i	$0.743760\pi$
$318$	15.1967	−	7.08635i	0.852190	−	0.397383i
$319$	−20.4122	+	7.42942i	−1.14286	+	0.415968i
$320$		0			0
$321$	2.92564	+	16.5922i	0.163294	+	0.926084i
$322$	1.93258	+	1.93258i	0.107699	+	0.107699i
$323$	−19.2101	+	11.8659i	−1.06888	+	0.660239i
$324$			36.5966i			2.03315i
$325$		0			0
$326$	−7.10320	−	8.46527i	−0.393410	−	0.468848i
$327$	10.7582	−	23.0711i	0.594932	−	1.27584i
$328$	−3.20777	−	6.87909i	−0.177120	−	0.379834i
$329$	−15.3186	+	18.2560i	−0.844543	+	1.00649i
$330$		0			0
$331$	13.3073	−	7.68298i	0.731436	−	0.422295i	−0.0875111	−	0.996164i	$-0.527891\pi$
$331$	13.3073	−	7.68298i	0.731436	−	0.422295i	0.818947	+	0.573869i	$0.194558\pi$
$332$	2.44249	+	3.48824i	0.134049	+	0.191442i
$333$	3.51833	+	5.02470i	0.192803	+	0.275352i
$334$	−0.650894	+	0.375794i	−0.0356153	+	0.0205625i
$335$		0			0
$336$	4.14993	−	4.94569i	0.226397	−	0.269810i
$337$	−0.842678	−	1.80713i	−0.0459036	−	0.0984406i	0.882018	−	0.471215i	$-0.156184\pi$
$337$	−0.842678	−	1.80713i	−0.0459036	−	0.0984406i	−0.927922	+	0.372774i	$0.878407\pi$
$338$	1.71182	−	3.67101i	0.0931107	−	0.199677i
$339$	13.6995	+	16.3265i	0.744057	+	0.886732i
$340$		0			0
$341$			0.655345i			0.0354889i
$342$	2.33796	+	5.87403i	0.126422	+	0.317631i
$343$	12.3337	+	12.3337i	0.665957	+	0.665957i
$344$	4.76336	+	27.0144i	0.256823	+	1.45652i
$345$		0			0
$346$	16.7299	−	6.08918i	0.899404	−	0.327356i
$347$	23.7149	−	11.0584i	1.27308	−	0.593647i	0.335705	−	0.941967i	$-0.391025\pi$
$347$	23.7149	−	11.0584i	1.27308	−	0.593647i	0.937376	+	0.348320i	$0.113248\pi$
$348$	3.99269	+	45.6367i	0.214031	+	2.44638i
$349$	18.8907	+	10.9065i	1.01119	+	0.583813i	0.911541	−	0.411209i	$-0.134893\pi$
$349$	18.8907	+	10.9065i	1.01119	+	0.583813i	0.0996533	+	0.995022i	$0.468227\pi$
$350$		0			0
$351$	−3.01872	+	17.1200i	−0.161127	+	0.913799i
$352$	10.6953	−	7.48890i	0.570059	−	0.399159i
$353$	−4.46820	+	16.6755i	−0.237818	+	0.887549i	0.739040	+	0.673661i	$0.235279\pi$
$353$	−4.46820	+	16.6755i	−0.237818	+	0.887549i	−0.976858	+	0.213888i	$0.931387\pi$
$354$	4.51438	−	7.81914i	0.239937	−	0.415583i
$355$		0			0
$356$	−4.27764	+	11.7527i	−0.226715	+	0.622893i
$357$	24.8205	+	11.5740i	1.31364	+	0.612560i
$358$	36.2673	+	3.17298i	1.91679	+	0.167697i
$359$	2.68655	−	0.473710i	0.141790	−	0.0250015i	−0.102302	−	0.994753i	$-0.532621\pi$
$359$	2.68655	−	0.473710i	0.141790	−	0.0250015i	0.244093	+	0.969752i	$0.421510\pi$
$360$		0			0
$361$	−13.0563	−	13.8034i	−0.687173	−	0.726494i
$362$	17.0121	−	17.0121i	0.894134	−	0.894134i
$363$	1.66087	+	1.16295i	0.0871730	+	0.0610392i
$364$	28.5493	−	23.9557i	1.49639	−	1.25562i
$365$		0			0
$366$	−42.6011	−	15.5055i	−2.22679	−	0.810486i
$367$	−16.4071	+	1.43543i	−0.856443	+	0.0749290i	−0.506914	−	0.861997i	$-0.669214\pi$
$367$	−16.4071	+	1.43543i	−0.856443	+	0.0749290i	−0.349529	+	0.936926i	$0.613658\pi$
$368$	−0.494880	+	0.132603i	−0.0257974	+	0.00691239i
$369$	−0.670493	−	1.16133i	−0.0349045	−	0.0604563i
$370$		0			0
$371$	10.2922	+	1.81480i	0.534346	+	0.0942196i
$372$	1.33500	+	0.357712i	0.0692164	+	0.0185465i
$373$	1.13949	+	4.25262i	0.0590003	+	0.220192i	0.989131	−	0.147036i	$-0.0469734\pi$
$373$	1.13949	+	4.25262i	0.0590003	+	0.220192i	−0.930131	+	0.367228i	$0.880307\pi$
$374$	−29.3162	−	24.5992i	−1.51591	−	1.27200i
$375$		0			0
$376$	−10.2720	−	28.2221i	−0.529739	−	1.45544i
$377$	−2.30519	+	26.3484i	−0.118723	+	1.35701i
$378$	−16.9256	+	24.1722i	−0.870557	+	1.24328i
$379$	−6.71745			−0.345052			−0.172526	−	0.985005i	$-0.555193\pi$
$379$	−6.71745			−0.345052			−0.172526	+	0.985005i	$0.555193\pi$
$380$		0			0
$381$	11.7425			0.601586
$382$	−0.455644	+	0.650728i	−0.0233128	+	0.0332941i
$383$	2.20643	−	25.2196i	0.112743	−	1.28866i	−0.703394	−	0.710800i	$-0.748333\pi$
$383$	2.20643	−	25.2196i	0.112743	−	1.28866i	0.816137	−	0.577859i	$-0.196112\pi$
$384$	−13.1424	−	36.1084i	−0.670670	−	1.84265i
$385$		0			0
$386$	26.7227	+	22.4230i	1.36015	+	1.14130i
$387$	1.25432	+	4.68118i	0.0637606	+	0.237958i
$388$	25.1712	+	6.74460i	1.27787	+	0.342405i
$389$	10.5707	+	1.86390i	0.535957	+	0.0945036i	0.435074	−	0.900395i	$-0.356722\pi$
$389$	10.5707	+	1.86390i	0.535957	+	0.0945036i	0.100883	+	0.994898i	$0.467833\pi$
$390$		0			0
$391$	−1.08664	−	1.88212i	−0.0549540	−	0.0951830i
$392$	2.44899	−	0.656204i	0.123692	−	0.0331433i
$393$	−10.0565	+	0.879831i	−0.507284	+	0.0443816i
$394$	16.4543	+	5.98888i	0.828956	+	0.301715i
$395$		0			0
$396$	−5.22046	+	4.38049i	−0.262338	+	0.220128i
$397$	−1.15577	−	0.809277i	−0.0580063	−	0.0406164i	0.544214	−	0.838947i	$-0.316828\pi$
$397$	−1.15577	−	0.809277i	−0.0580063	−	0.0406164i	−0.602220	+	0.798330i	$0.705717\pi$
$398$	−22.0968	+	22.0968i	−1.10761	+	1.10761i
$399$	−5.30018	+	22.4272i	−0.265341	+	1.12276i
$400$		0			0
$401$	15.3650	−	2.70927i	0.767292	−	0.135294i	0.223716	−	0.974654i	$-0.428181\pi$
$401$	15.3650	−	2.70927i	0.767292	−	0.135294i	0.543576	+	0.839360i	$0.317070\pi$
$402$	−7.26754	−	0.635827i	−0.362472	−	0.0317122i
$403$	0.723191	+	0.337229i	0.0360247	+	0.0167986i
$404$	10.7698	−	29.5897i	0.535816	−	1.47214i
$405$		0			0
$406$	−22.4481	+	38.8812i	−1.11408	+	1.92964i
$407$	8.08666	−	30.1798i	0.400841	−	1.49596i
$408$	−28.2716	+	19.7960i	−1.39965	+	0.980048i
$409$	−6.55532	+	37.1771i	−0.324140	+	1.83829i	0.191514	+	0.981490i	$0.438660\pi$
$409$	−6.55532	+	37.1771i	−0.324140	+	1.83829i	−0.515653	+	0.856797i	$0.672451\pi$
$410$		0			0
$411$	14.3910	+	8.30867i	0.709857	+	0.409836i
$412$	1.68828	+	19.2972i	0.0831757	+	0.950703i
$413$	5.10021	−	2.37827i	0.250965	−	0.117027i
$414$	−0.571820	+	0.208126i	−0.0281034	+	0.0102288i
$415$		0			0
$416$	−2.76060	−	15.6561i	−0.135350	−	0.767606i
$417$	−8.40270	−	8.40270i	−0.411482	−	0.411482i
$418$	15.2654	−	28.3549i	0.746654	−	1.38688i
$419$			5.57741i			0.272474i	0.990676	+	0.136237i	$0.0435009\pi$
$419$			5.57741i			0.272474i	−0.990676	+	0.136237i	$0.956499\pi$
$420$		0			0
$421$	18.7653	+	22.3636i	0.914565	+	1.08994i	0.995645	+	0.0932288i	$0.0297188\pi$
$421$	18.7653	+	22.3636i	0.914565	+	1.08994i	−0.0810795	+	0.996708i	$0.525837\pi$
$422$	−10.5230	+	22.5667i	−0.512254	+	1.09853i
$423$	−2.24244	−	4.80893i	−0.109031	−	0.233818i
$424$	−8.46598	+	10.0894i	−0.411144	+	0.489983i
$425$		0			0
$426$	12.7371	−	7.35378i	0.617115	−	0.356292i
$427$	−16.2073	−	23.1464i	−0.784324	−	1.12013i
$428$	−17.7506	−	25.3504i	−0.858006	−	1.22536i
$429$	−19.9274	+	11.5051i	−0.962103	+	0.555470i
$430$		0			0
$431$	16.0481	−	19.1254i	0.773012	−	0.921240i	−0.225583	−	0.974224i	$-0.572429\pi$
$431$	16.0481	−	19.1254i	0.773012	−	0.921240i	0.998595	+	0.0529840i	$0.0168732\pi$
$432$	−2.33777	−	5.01337i	−0.112476	−	0.241206i
$433$	−8.63426	+	18.5162i	−0.414936	+	0.889833i	0.582116	+	0.813106i	$0.302225\pi$
$433$	−8.63426	+	18.5162i	−0.414936	+	0.889833i	−0.997052	+	0.0767272i	$0.975553\pi$
$434$	0.870649	+	1.03760i	0.0417925	+	0.0498064i
$435$		0			0
$436$			46.7587i			2.23934i
$437$	1.36536	−	1.21663i	0.0653139	−	0.0581994i
$438$	−39.3752	−	39.3752i	−1.88142	−	1.88142i
$439$	2.43092	+	13.7864i	0.116022	+	0.657991i	0.986239	+	0.165324i	$0.0528668\pi$
$439$	2.43092	+	13.7864i	0.116022	+	0.657991i	−0.870218	+	0.492667i	$0.836022\pi$
$440$		0			0
$441$	0.420918	−	0.153201i	0.0200437	−	0.00729531i
$442$	−42.2315	+	19.6929i	−2.00875	+	0.936695i
$443$	2.03038	+	23.2073i	0.0964662	+	1.10261i	0.877971	+	0.478715i	$0.158897\pi$
$443$	2.03038	+	23.2073i	0.0964662	+	1.10261i	−0.781504	+	0.623900i	$0.785547\pi$
$444$	−57.0650	−	32.9465i	−2.70819	−	1.56357i
$445$		0			0
$446$	10.7682	−	61.0694i	0.509888	−	2.89172i
$447$	8.12756	−	5.69098i	0.384420	−	0.269174i
$448$	8.74117	−	32.6225i	0.412981	−	1.54127i
$449$	−7.01160	+	12.1444i	−0.330898	+	0.573132i	−0.982688	−	0.185267i	$-0.940685\pi$
$449$	−7.01160	+	12.1444i	−0.330898	+	0.573132i	0.651790	+	0.758399i	$0.274018\pi$
$450$		0			0
$451$	−2.33616	+	6.41856i	−0.110006	+	0.302238i
$452$	−35.4800	−	16.5446i	−1.66884	−	0.778193i
$453$	38.8054	+	3.39503i	1.82324	+	0.159512i
$454$	52.3918	−	9.23809i	2.45887	−	0.433565i
$455$		0			0
$456$	−21.1372	−	19.9163i	−0.989840	−	0.932669i
$457$	1.92188	−	1.92188i	0.0899016	−	0.0899016i	−0.660726	−	0.750627i	$-0.729751\pi$
$457$	1.92188	−	1.92188i	0.0899016	−	0.0899016i	0.750627	+	0.660726i	$0.229751\pi$
$458$	−8.57545	−	6.00459i	−0.400704	−	0.280576i
$459$	17.9750	−	15.0828i	0.839002	−	0.704006i
$460$		0			0
$461$	−33.1987	−	12.0833i	−1.54622	−	0.562777i	−0.578690	−	0.815547i	$-0.696436\pi$
$461$	−33.1987	−	12.0833i	−1.54622	−	0.562777i	−0.967526	+	0.252771i	$0.918658\pi$
$462$	−38.9101	+	3.40419i	−1.81026	+	0.158377i
$463$	4.92635	−	1.32001i	0.228947	−	0.0613462i	−0.142522	−	0.989792i	$-0.545521\pi$
$463$	4.92635	−	1.32001i	0.228947	−	0.0613462i	0.371469	+	0.928446i	$0.378854\pi$
$464$	−4.20805	−	7.28856i	−0.195354	−	0.338363i
$465$		0			0
$466$	−42.4873	−	7.49165i	−1.96818	−	0.347044i
$467$	−26.1210	−	6.99909i	−1.20873	−	0.323879i	−0.402469	−	0.915434i	$-0.631848\pi$
$467$	−26.1210	−	6.99909i	−1.20873	−	0.323879i	−0.806265	+	0.591554i	$0.798515\pi$
$468$	2.14762	+	8.01504i	0.0992739	+	0.370495i
$469$	−3.48322	−	2.92277i	−0.160840	−	0.134961i
$470$		0			0
$471$	7.58776	+	20.8472i	0.349626	+	0.960588i
$472$	−0.618101	+	7.06493i	−0.0284504	+	0.325190i
$473$	14.1589	−	20.2211i	0.651029	−	0.929765i
$474$	21.8439			1.00332
$475$		0			0
$476$	−50.3042			−2.30569
$477$	−1.33466	+	1.90609i	−0.0611097	+	0.0872737i
$478$	−2.82445	+	32.2836i	−0.129187	+	1.47662i
$479$	−4.36649	−	11.9968i	−0.199510	−	0.548149i	0.799081	−	0.601224i	$-0.205320\pi$
$479$	−4.36649	−	11.9968i	−0.199510	−	0.548149i	−0.998591	+	0.0530748i	$0.983098\pi$
$480$		0			0
$481$	−29.1430	−	24.4538i	−1.32880	−	1.11500i
$482$	1.34664	+	5.02572i	0.0613377	+	0.228915i
$483$	−2.14252	−	0.574087i	−0.0974881	−	0.0261219i
$484$	−3.66768	−	0.646711i	−0.166713	−	0.0293960i
$485$		0			0
$486$	−7.42375	−	12.8583i	−0.336748	−	0.583265i
$487$	−20.1547	+	5.40044i	−0.913298	+	0.244717i	−0.684718	−	0.728808i	$-0.740075\pi$
$487$	−20.1547	+	5.40044i	−0.913298	+	0.244717i	−0.228580	+	0.973525i	$0.573408\pi$
$488$	35.4743	−	3.10360i	1.60585	−	0.140493i
$489$	8.42754	+	3.06737i	0.381106	+	0.138711i
$490$		0			0
$491$	−13.9474	+	11.7033i	−0.629438	+	0.528161i	−0.900754	−	0.434329i	$-0.856985\pi$
$491$	−13.9474	+	11.7033i	−0.629438	+	0.528161i	0.271316	+	0.962490i	$0.412541\pi$
$492$	11.8000	+	8.26246i	0.531986	+	0.372500i
$493$	25.2440	−	25.2440i	1.13693	−	1.13693i
$494$	−23.4350	−	31.4367i	−1.05439	−	1.41440i
$495$		0			0
$496$	−0.250052	+	0.0440908i	−0.0112276	+	0.00197974i
$497$	9.13205	+	0.798951i	0.409628	+	0.0358378i
$498$	−4.92494	−	2.29654i	−0.220692	−	0.102910i
$499$	−10.1881	+	27.9915i	−0.456081	+	1.25307i	0.472299	+	0.881438i	$0.343424\pi$
$499$	−10.1881	+	27.9915i	−0.456081	+	1.25307i	−0.928380	+	0.371633i	$0.878798\pi$
$500$		0			0
$501$	0.304985	−	0.528249i	0.0136257	−	0.0236004i
$502$	−13.8894	+	51.8361i	−0.619916	+	2.31356i
$503$	−12.5766	+	8.80620i	−0.560761	+	0.392649i	−0.819311	−	0.573349i	$-0.805644\pi$
$503$	−12.5766	+	8.80620i	−0.560761	+	0.392649i	0.258551	+	0.965998i	$0.416755\pi$
$504$	−1.04591	+	5.93168i	−0.0465887	+	0.264218i
$505$		0			0
$506$	2.68430	+	1.54978i	0.119332	+	0.0688963i
$507$	0.286506	+	3.27478i	0.0127242	+	0.145438i
$508$	−19.5482	+	9.11546i	−0.867309	+	0.404433i
$509$	2.72263	−	0.990955i	0.120678	−	0.0439233i	−0.280975	−	0.959715i	$-0.590658\pi$
$509$	2.72263	−	0.990955i	0.120678	−	0.0439233i	0.401653	+	0.915792i	$0.368436\pi$
$510$		0			0
$511$	−6.02687	−	34.1801i	−0.266613	−	1.51204i
$512$	9.62565	+	9.62565i	0.425398	+	0.425398i
$513$	15.4961	+	12.2366i	0.684171	+	0.540260i
$514$			40.1604i			1.77140i
$515$		0			0
$516$	−33.4637	−	39.8804i	−1.47316	−	1.75564i
$517$	−11.4222	+	24.4949i	−0.502346	+	1.07728i
$518$	−27.2914	−	58.5267i	−1.19912	−	2.57152i
$519$	−9.28758	+	11.0685i	−0.407680	+	0.485854i
$520$		0			0
$521$	9.37387	−	5.41201i	0.410677	−	0.237104i	−0.280404	−	0.959882i	$-0.590468\pi$
$521$	9.37387	−	5.41201i	0.410677	−	0.237104i	0.691080	+	0.722778i	$0.257135\pi$
$522$	−5.73351	−	8.18830i	−0.250949	−	0.358392i
$523$	−1.55246	−	2.21715i	−0.0678845	−	0.0969491i	0.783774	−	0.621046i	$-0.213292\pi$
$523$	−1.55246	−	2.21715i	−0.0678845	−	0.0969491i	−0.851659	+	0.524097i	$0.824403\pi$
$524$	16.0585	−	9.27135i	0.701517	−	0.405021i
$525$		0			0
$526$	−8.21023	+	9.78457i	−0.357983	+	0.426627i
$527$	−0.455185	−	0.976147i	−0.0198282	−	0.0425217i
$528$	3.09435	−	6.63585i	0.134664	−	0.288788i
$529$	−14.6710	−	17.4842i	−0.637868	−	0.760182i
$530$		0			0
$531$			1.25295i			0.0543732i
$532$	−8.58636	−	41.4498i	−0.372266	−	1.79708i
$533$	5.88089	+	5.88089i	0.254730	+	0.254730i
$534$	−2.77145	−	15.7177i	−0.119932	−	0.680170i
$535$		0			0
$536$	5.38473	−	1.95988i	0.232585	−	0.0846540i
$537$	−26.7778	+	12.4867i	−1.15555	+	0.538841i
$538$	−1.49718	−	17.1128i	−0.0645479	−	0.737786i
$539$	−1.97592	−	1.14080i	−0.0851089	−	0.0491376i
$540$		0			0
$541$	2.66157	−	15.0945i	0.114430	−	0.648964i	−0.872601	−	0.488434i	$-0.837568\pi$
$541$	2.66157	−	15.0945i	0.114430	−	0.648964i	0.987031	−	0.160530i	$-0.0513205\pi$
$542$	58.0033	−	40.6144i	2.49146	−	1.74454i
$543$	−5.05354	+	18.8601i	−0.216868	+	0.809363i
$544$	−10.7292	+	18.5835i	−0.460009	+	0.796759i
$545$		0			0
$546$	−16.2659	+	44.6901i	−0.696114	+	1.91256i
$547$	18.9948	+	8.85743i	0.812160	+	0.378717i	0.783902	−	0.620884i	$-0.213226\pi$
$547$	18.9948	+	8.85743i	0.812160	+	0.378717i	0.0282579	+	0.999601i	$0.491004\pi$
$548$	−30.4071	−	2.66028i	−1.29893	−	0.113641i
$549$	6.19569	−	1.09247i	0.264426	−	0.0466254i
$550$		0			0
$551$	25.1095	+	16.4917i	1.06970	+	0.702571i
$552$	1.97660	−	1.97660i	0.0841295	−	0.0841295i
$553$	11.1527	+	7.80917i	0.474259	+	0.332080i
$554$	−48.1694	+	40.4189i	−2.04652	+	1.71724i
$555$		0			0
$556$	20.5111	+	7.46544i	0.869866	+	0.316605i
$557$	3.18999	−	0.279088i	0.135164	−	0.0118253i	−0.0193729	−	0.999812i	$-0.506167\pi$
$557$	3.18999	−	0.279088i	0.135164	−	0.0118253i	0.154537	+	0.987987i	$0.450611\pi$
$558$	−0.291300	+	0.0780535i	−0.0123317	+	0.00330427i
$559$	−15.0285	−	26.0302i	−0.635639	−	1.10096i
$560$		0			0
$561$	30.5868	+	5.39327i	1.29137	+	0.227704i
$562$	34.7284	+	9.30544i	1.46493	+	0.392526i
$563$	11.3121	+	42.2175i	0.476750	+	1.77925i	0.614641	+	0.788807i	$0.289301\pi$
$563$	11.3121	+	42.2175i	0.476750	+	1.77925i	−0.137891	+	0.990447i	$0.544033\pi$
$564$	43.6637	+	36.6382i	1.83857	+	1.54275i
$565$		0			0
$566$	−8.55318	−	23.4997i	−0.359517	−	0.987765i
$567$	2.53690	−	28.9969i	0.106540	−	1.21776i
$568$	−6.62624	+	9.46325i	−0.278031	+	0.397069i
$569$	13.7435			0.576156			0.288078	−	0.957607i	$-0.406984\pi$
$569$	13.7435			0.576156			0.288078	+	0.957607i	$0.406984\pi$
$570$		0			0
$571$	30.4258			1.27328			0.636640	−	0.771161i	$-0.280324\pi$
$571$	30.4258			1.27328			0.636640	+	0.771161i	$0.280324\pi$
$572$	24.2427	−	34.6221i	1.01364	−	1.44762i
$573$	0.0561900	−	0.642254i	0.00234737	−	0.0268306i
$574$	4.82846	+	13.2661i	0.201536	+	0.553716i
$575$		0			0
$576$	5.76033	+	4.83349i	0.240014	+	0.201396i
$577$	7.35372	+	27.4445i	0.306140	+	1.14253i	0.931960	+	0.362561i	$0.118098\pi$
$577$	7.35372	+	27.4445i	0.306140	+	1.14253i	−0.625820	+	0.779967i	$0.715236\pi$
$578$	22.2631	+	5.96539i	0.926024	+	0.248127i
$579$	−27.8808	−	4.91614i	−1.15869	−	0.204308i
$580$		0			0
$581$	−1.69347	−	2.93318i	−0.0702571	−	0.121689i
$582$	−32.1209	+	8.60676i	−1.33145	+	0.356762i
$583$	11.8073	−	1.03300i	0.489008	−	0.0427826i
$584$	41.1016	+	14.9598i	1.70080	+	0.619039i
$585$		0			0
$586$	20.1881	−	16.9398i	0.833963	−	0.699778i
$587$	−20.2475	−	14.1774i	−0.835702	−	0.585165i	0.0754898	−	0.997147i	$-0.475948\pi$
$587$	−20.2475	−	14.1774i	−0.835702	−	0.585165i	−0.911192	+	0.411981i	$0.864837\pi$
$588$	−3.40244	+	3.40244i	−0.140314	+	0.140314i
$589$	0.726633	−	0.541682i	0.0299404	−	0.0223196i
$590$		0			0
$591$	−13.9950	+	2.46770i	−0.575678	+	0.101508i
$592$	12.0594	+	1.05506i	0.495637	+	0.0433627i
$593$	−36.1551	−	16.8594i	−1.48471	−	0.692332i	−0.499919	−	0.866072i	$-0.666637\pi$
$593$	−36.1551	−	16.8594i	−1.48471	−	0.692332i	−0.984791	+	0.173741i	$0.944415\pi$
$594$	−11.4459	+	31.4474i	−0.469632	+	1.29030i
$595$		0			0
$596$	−9.11245	+	15.7832i	−0.373261	+	0.646506i
$597$	6.56400	−	24.4972i	0.268647	−	1.00260i
$598$	3.09152	−	2.16471i	0.126422	−	0.0885215i
$599$	6.31827	−	35.8327i	0.258158	−	1.46408i	−0.529678	−	0.848199i	$-0.677687\pi$
$599$	6.31827	−	35.8327i	0.258158	−	1.46408i	0.787835	−	0.615886i	$-0.211202\pi$
$600$		0			0
$601$	−12.9169	−	7.45756i	−0.526890	−	0.304200i	0.212859	−	0.977083i	$-0.431723\pi$
$601$	−12.9169	−	7.45756i	−0.526890	−	0.304200i	−0.739749	+	0.672883i	$0.765056\pi$
$602$	−4.44673	−	50.8264i	−0.181235	−	2.07153i
$603$	0.917535	−	0.427853i	0.0373649	−	0.0174235i
$604$	−67.2362	+	24.4720i	−2.73580	+	0.995750i
$605$		0			0
$606$	6.97764	+	39.5721i	0.283447	+	1.60751i
$607$	22.5020	+	22.5020i	0.913328	+	0.913328i	0.996532	−	0.0832045i	$-0.0265155\pi$
$607$	22.5020	+	22.5020i	0.913328	+	0.913328i	−0.0832045	+	0.996532i	$0.526515\pi$
$608$	−17.1438	−	5.66865i	−0.695273	−	0.229894i
$609$		−	36.4365i		−	1.47648i
$610$		0			0
$611$	21.1531	+	25.2093i	0.855764	+	1.01986i
$612$	4.73339	−	10.1508i	0.191336	−	0.410322i
$613$	18.1486	+	38.9199i	0.733016	+	1.57196i	0.817763	+	0.575556i	$0.195214\pi$
$613$	18.1486	+	38.9199i	0.733016	+	1.57196i	−0.0847463	+	0.996403i	$0.527008\pi$
$614$	25.2860	−	30.1347i	1.02046	−	1.21614i
$615$		0			0
$616$	26.5695	−	15.3399i	1.07052	−	0.618063i
$617$	0.699375	+	0.998810i	0.0281558	+	0.0402106i	0.832983	−	0.553298i	$-0.186631\pi$
$617$	0.699375	+	0.998810i	0.0281558	+	0.0402106i	−0.804827	+	0.593509i	$0.797742\pi$
$618$	−14.1783	−	20.2487i	−0.570335	−	0.814522i
$619$	3.27678	−	1.89185i	0.131705	−	0.0760398i	−0.432700	−	0.901538i	$-0.642439\pi$
$619$	3.27678	−	1.89185i	0.131705	−	0.0760398i	0.564405	+	0.825498i	$0.309106\pi$
$620$		0			0
$621$	−1.22160	+	1.45585i	−0.0490212	+	0.0584212i
$622$	23.3125	+	49.9937i	0.934745	+	2.00457i
$623$	4.20405	−	9.01562i	0.168432	−	0.361203i
$624$	−5.73053	−	6.82938i	−0.229405	−	0.273394i
$625$		0			0
$626$			13.0822i			0.522869i
$627$	0.776858	+	26.1235i	0.0310247	+	1.04327i
$628$	−28.8149	−	28.8149i	−1.14984	−	1.14984i
$629$	8.91687	+	50.5701i	0.355539	+	2.01636i
$630$		0			0
$631$	−3.78252	+	1.37673i	−0.150580	+	0.0548066i	−0.416210	−	0.909268i	$-0.636642\pi$
$631$	−3.78252	+	1.37673i	−0.150580	+	0.0548066i	0.265631	+	0.964075i	$0.414420\pi$
$632$	−15.5504	+	7.25126i	−0.618561	+	0.288440i
$633$	−1.76123	−	20.1310i	−0.0700028	−	0.800136i
$634$	47.5399	+	27.4472i	1.88805	+	1.09007i
$635$		0			0
$636$	4.34053	−	24.6164i	0.172113	−	0.976102i
$637$	−2.27567	+	1.59344i	−0.0901655	+	0.0631346i
$638$	−13.1781	+	49.1813i	−0.521726	+	1.94711i
$639$	−1.02050	+	1.76756i	−0.0403705	+	0.0699237i
$640$		0			0
$641$	6.61703	−	18.1801i	0.261357	−	0.718072i	−0.737720	−	0.675107i	$-0.764097\pi$
$641$	6.61703	−	18.1801i	0.261357	−	0.718072i	0.999077	−	0.0429652i	$-0.0136805\pi$
$642$	35.7915	+	16.6899i	1.41258	+	0.658696i
$643$	−10.6357	−	0.930507i	−0.419433	−	0.0366956i	−0.124514	−	0.992218i	$-0.539737\pi$
$643$	−10.6357	−	0.930507i	−0.419433	−	0.0366956i	−0.294919	+	0.955522i	$0.595293\pi$
$644$	4.01239	−	0.707492i	0.158110	−	0.0278791i
$645$		0			0
$646$	−3.04352	+	52.8380i	−0.119746	+	2.07888i
$647$	−2.55151	+	2.55151i	−0.100310	+	0.100310i	−0.755481	−	0.655171i	$-0.772597\pi$
$647$	−2.55151	+	2.55151i	−0.100310	+	0.100310i	0.655171	+	0.755481i	$0.272597\pi$
$648$	30.0486	+	21.0402i	1.18042	+	0.826539i
$649$	4.88893	−	4.10230i	0.191907	−	0.161029i
$650$		0			0
$651$	−1.03297	−	0.375972i	−0.0404855	−	0.0147355i
$652$	−16.4108	+	1.43576i	−0.642695	+	0.0562285i
$653$	18.8262	−	5.04447i	0.736727	−	0.197405i	0.129104	−	0.991631i	$-0.458790\pi$
$653$	18.8262	−	5.04447i	0.736727	−	0.197405i	0.607623	+	0.794226i	$0.292123\pi$
$654$	−29.8343	−	51.6746i	−1.16661	−	2.02064i
$655$		0			0
$656$	−2.60622	−	0.459547i	−0.101756	−	0.0179423i
$657$	7.46424	+	2.00004i	0.291208	+	0.0780288i
$658$	14.4578	+	53.9572i	0.563623	+	2.10347i
$659$	11.3356	+	9.51168i	0.441571	+	0.370522i	0.836297	−	0.548277i	$-0.184716\pi$
$659$	11.3356	+	9.51168i	0.441571	+	0.370522i	−0.394726	+	0.918799i	$0.629160\pi$
$660$		0			0
$661$	−1.66485	−	4.57414i	−0.0647551	−	0.177913i	0.903095	−	0.429441i	$-0.141289\pi$
$661$	−1.66485	−	4.57414i	−0.0647551	−	0.177913i	−0.967850	+	0.251528i	$0.919067\pi$
$662$	3.13913	−	35.8804i	0.122006	−	1.39453i
$663$	21.6910	−	30.9780i	0.842410	−	1.20309i
$664$	4.26835			0.165644
$665$		0			0
$666$	14.3780			0.557136
$667$	−1.65848	+	2.36856i	−0.0642167	+	0.0917110i
$668$	−0.0976503	+	1.11615i	−0.00377820	+	0.0431851i
$669$	17.2128	+	47.2918i	0.665486	+	1.82841i
$670$		0			0
$671$	−24.5482	−	20.5984i	−0.947673	−	0.795192i
$672$	5.66835	+	21.1546i	0.218661	+	0.816055i
$673$	−17.5750	−	4.70920i	−0.677465	−	0.181526i	−0.0963501	−	0.995348i	$-0.530717\pi$
$673$	−17.5750	−	4.70920i	−0.677465	−	0.181526i	−0.581115	+	0.813821i	$0.697384\pi$
$674$	−4.60276	−	0.811590i	−0.177292	−	0.0312613i
$675$		0			0
$676$	−3.01910	−	5.22923i	−0.116119	−	0.201124i
$677$	21.5062	−	5.76257i	0.826551	−	0.221474i	0.179342	−	0.983787i	$-0.442603\pi$
$677$	21.5062	−	5.76257i	0.826551	−	0.221474i	0.647208	+	0.762313i	$0.275936\pi$
$678$	49.7664	−	4.35399i	1.91127	−	0.167214i
$679$	−19.4766	−	7.08889i	−0.747442	−	0.272047i
$680$		0			0
$681$	−33.0745	+	27.7528i	−1.26742	+	1.06349i
$682$	1.25831	+	0.881079i	0.0481832	+	0.0337383i
$683$	−19.0369	+	19.0369i	−0.728429	+	0.728429i	−0.970307	−	0.241878i	$-0.922237\pi$
$683$	−19.0369	+	19.0369i	−0.728429	+	0.728429i	0.241878	+	0.970307i	$0.422237\pi$
$684$	9.17202	+	2.16761i	0.350701	+	0.0828805i
$685$		0			0
$686$	40.2637	−	7.09957i	1.53727	−	0.271063i
$687$	8.46379	+	0.740485i	0.322914	+	0.0282513i
$688$	8.66808	+	4.04199i	0.330468	+	0.154100i
$689$	4.93588	−	13.5612i	0.188042	−	0.516641i
$690$		0			0
$691$	17.0521	−	29.5351i	0.648693	−	1.12357i	−0.334742	−	0.942310i	$-0.608649\pi$
$691$	17.0521	−	29.5351i	0.648693	−	1.12357i	0.983435	−	0.181260i	$-0.0580174\pi$
$692$	6.86912	−	25.6359i	0.261125	−	0.974531i
$693$	4.44004	−	3.10895i	0.168663	−	0.118099i
$694$	10.6505	−	60.4018i	0.404286	−	2.29282i
$695$		0			0
$696$	39.7667	+	22.9593i	1.50735	+	0.870270i
$697$	−0.978401	−	11.1832i	−0.0370596	−	0.423593i
$698$	46.3389	−	21.6082i	1.75395	−	0.817882i
$699$	32.9019	−	11.9753i	1.24446	−	0.452948i
$700$		0			0
$701$	4.51519	+	25.6069i	0.170536	+	0.967160i	0.943171	+	0.332309i	$0.107828\pi$
$701$	4.51519	+	25.6069i	0.170536	+	0.967160i	−0.772634	+	0.634851i	$0.781061\pi$
$702$	28.8132	+	28.8132i	1.08748	+	1.08748i
$703$	−40.1468	+	15.9791i	−1.51417	+	0.602663i
$704$		−	38.3020i		−	1.44356i
$705$		0			0
$706$	26.0110	+	30.9987i	0.978936	+	1.16665i
$707$	−10.5845	+	22.6985i	−0.398071	+	0.853665i
$708$	−5.68819	−	12.1984i	−0.213775	−	0.458443i
$709$	26.4386	−	31.5083i	0.992922	−	1.18332i	0.00987689	−	0.999951i	$-0.496856\pi$
$709$	26.4386	−	31.5083i	0.992922	−	1.18332i	0.983045	−	0.183367i	$-0.0586995\pi$
$710$		0			0
$711$	−2.62521	+	1.51567i	−0.0984532	+	0.0568420i
$712$	7.19056	+	10.2692i	0.269478	+	0.384854i
$713$	0.0500355	+	0.0714581i	0.00187384	+	0.00267613i
$714$	55.5928	−	32.0965i	2.08051	−	1.20118i
$715$		0			0
$716$	34.8848	−	41.5741i	1.30371	−	1.55370i
$717$	−11.1151	−	23.8364i	−0.415101	−	0.890188i
$718$	2.70237	−	5.79524i	0.100851	−	0.216277i
$719$	−22.6318	−	26.9715i	−0.844022	−	1.00587i	−0.999837	−	0.0180804i	$-0.994245\pi$
$719$	−22.6318	−	26.9715i	−0.844022	−	1.00587i	0.155814	−	0.987786i	$-0.450200\pi$
$720$		0			0
$721$		−	15.4069i		−	0.573784i
$722$	−44.0570	+	6.51104i	−1.63963	+	0.242316i
$723$	−2.98585	−	2.98585i	−0.111045	−	0.111045i
$724$	−6.22787	−	35.3200i	−0.231457	−	1.31266i
$725$		0			0
$726$	4.46591	−	1.62546i	0.165745	−	0.0603264i
$727$	−5.02377	+	2.34262i	−0.186321	+	0.0868831i	−0.513540	−	0.858065i	$-0.671666\pi$
$727$	−5.02377	+	2.34262i	−0.186321	+	0.0868831i	0.327219	+	0.944949i	$0.393889\pi$
$728$	−3.25579	−	37.2138i	−0.120668	−	1.37924i
$729$	−16.7754	−	9.68526i	−0.621310	−	0.358713i
$730$		0			0
$731$	−7.04497	+	39.9540i	−0.260568	+	1.47775i
$732$	−55.3601	+	38.7636i	−2.04617	+	1.43274i
$733$	7.22490	−	26.9637i	0.266858	−	0.995927i	−0.694246	−	0.719738i	$-0.744262\pi$
$733$	7.22490	−	26.9637i	0.266858	−	0.995927i	0.961103	−	0.276189i	$-0.0890715\pi$
$734$	−19.3024	+	33.4327i	−0.712463	+	1.23402i
$735$		0			0
$736$	0.594422	−	1.63316i	0.0219107	−	0.0601991i
$737$	−4.67358	−	2.17933i	−0.172154	−	0.0802766i
$738$	−3.13128	−	0.273951i	−0.115264	−	0.0100843i
$739$	−40.2963	+	7.10532i	−1.48232	+	0.261373i	−0.855506	−	0.517794i	$-0.826753\pi$
$739$	−40.2963	+	7.10532i	−1.48232	+	0.261373i	−0.626816	+	0.779167i	$0.715642\pi$
$740$		0			0
$741$	29.2278	+	12.5854i	1.07371	+	0.462337i
$742$	17.3219	−	17.3219i	0.635908	−	0.635908i
$743$	8.82484	+	6.17922i	0.323752	+	0.226694i	0.724141	−	0.689651i	$-0.242236\pi$
$743$	8.82484	+	6.17922i	0.323752	+	0.226694i	−0.400389	+	0.916345i	$0.631125\pi$
$744$	1.06123	−	0.890477i	0.0389066	−	0.0326465i
$745$		0			0
$746$	9.69732	+	3.52954i	0.355044	+	0.129225i
$747$	0.751230	−	0.0657241i	0.0274861	−	0.00240472i
$748$	−55.1056	+	14.7655i	−2.01486	+	0.539880i
$749$	12.3072	+	21.3166i	0.449694	+	0.778893i
$750$		0			0
$751$	17.7962	+	3.13795i	0.649392	+	0.114505i	0.488634	−	0.872489i	$-0.337495\pi$
$751$	17.7962	+	3.13795i	0.649392	+	0.114505i	0.160757	+	0.986994i	$0.448606\pi$
$752$	−10.1147	−	2.71022i	−0.368844	−	0.0988315i
$753$	−11.2723	−	42.0688i	−0.410786	−	1.53307i
$754$	47.4917	+	39.8502i	1.72954	+	1.45126i
$755$		0			0
$756$	15.0453	+	41.3366i	0.547192	+	1.50340i
$757$	4.14061	−	47.3274i	0.150493	−	1.72014i	−0.427427	−	0.904050i	$-0.640580\pi$
$757$	4.14061	−	47.3274i	0.150493	−	1.72014i	0.577920	−	0.816093i	$-0.303865\pi$
$758$	−9.03128	+	12.8980i	−0.328031	+	0.468476i
$759$	−2.51553			−0.0913079
$760$		0			0
$761$	−45.4640			−1.64807			−0.824034	−	0.566540i	$-0.808282\pi$
$761$	−45.4640			−1.64807			−0.824034	+	0.566540i	$0.808282\pi$
$762$	15.7872	−	22.5464i	0.571910	−	0.816772i
$763$	3.24135	−	37.0488i	0.117345	−	1.34126i
$764$	0.405027	+	1.11280i	0.0146534	+	0.0402598i
$765$		0			0
$766$	−45.4570	−	38.1429i	−1.64243	−	1.37816i
$767$	−2.01124	−	7.50603i	−0.0726215	−	0.271027i
$768$	−42.3409	−	11.3452i	−1.52785	−	0.409385i
$769$	2.43552	+	0.429448i	0.0878271	+	0.0154863i	0.217389	−	0.976085i	$-0.430246\pi$
$769$	2.43552	+	0.429448i	0.0878271	+	0.0154863i	−0.129562	+	0.991571i	$0.541357\pi$
$770$		0			0
$771$	−16.2966	−	28.2265i	−0.586906	−	1.01655i
$772$	50.2305	−	13.4592i	1.80783	−	0.484408i
$773$	30.2133	−	2.64332i	1.08670	−	0.0950737i	0.470298	−	0.882508i	$-0.344146\pi$
$773$	30.2133	−	2.64332i	1.08670	−	0.0950737i	0.616399	+	0.787434i	$0.288591\pi$
$774$	10.6746	+	3.88523i	0.383690	+	0.139652i
$775$		0			0
$776$	20.0093	−	16.7898i	0.718293	−	0.602719i
$777$	42.9310	+	30.0606i	1.54014	+	1.07842i
$778$	17.7906	−	17.7906i	0.637825	−	0.637825i
$779$	9.04774	−	2.71503i	0.324169	−	0.0972760i
$780$		0			0
$781$	10.2382	−	1.80527i	0.366351	−	0.0645976i
$782$	−5.07475	−	0.443983i	−0.181473	−	0.0158768i
$783$	−28.2940	−	13.1937i	−1.01114	−	0.471504i
$784$	0.302342	−	0.830678i	0.0107979	−	0.0296671i
$785$		0			0
$786$	−11.8311	+	20.4921i	−0.422003	+	0.730930i
$787$	4.39533	−	16.4036i	0.156677	−	0.584725i	−0.842279	−	0.539041i	$-0.818787\pi$
$787$	4.39533	−	16.4036i	0.156677	−	0.584725i	0.998956	−	0.0456838i	$-0.0145467\pi$
$788$	21.3824	−	14.9721i	0.761716	−	0.533359i
$789$	1.80006	−	10.2086i	0.0640837	−	0.363437i
$790$		0			0
$791$	26.9653	+	15.5684i	0.958777	+	0.553550i
$792$	0.595346	+	6.80484i	0.0211547	+	0.241799i
$793$	−35.3629	+	16.4900i	−1.25577	+	0.585577i
$794$	−3.10774	+	1.13113i	−0.110290	+	0.0401421i
$795$		0			0
$796$	8.08933	+	45.8769i	0.286719	+	1.62606i
$797$	−24.9487	−	24.9487i	−0.883730	−	0.883730i	0.110182	−	0.993911i	$-0.464857\pi$
$797$	−24.9487	−	24.9487i	−0.883730	−	0.883730i	−0.993911	+	0.110182i	$0.964857\pi$
$798$	35.9360	+	40.3290i	1.27212	+	1.42763i
$799$		−	44.4191i		−	1.57143i
$800$		0			0
$801$	1.42366	+	1.69666i	0.0503027	+	0.0599484i
$802$	15.4555	−	33.1444i	0.545753	−	1.17037i
$803$	−16.6348	−	35.6734i	−0.587029	−	1.25889i
$804$	−6.99050	+	8.33095i	−0.246536	+	0.293810i
$805$		0			0
$806$	1.61980	−	0.935191i	0.0570550	−	0.0329407i
$807$	7.99644	+	11.4201i	0.281488	+	0.402006i
$808$	−18.1036	−	25.8546i	−0.636882	−	0.909561i
$809$	−36.4322	+	21.0341i	−1.28089	+	0.739521i	−0.977011	−	0.213190i	$-0.931615\pi$
$809$	−36.4322	+	21.0341i	−1.28089	+	0.739521i	−0.303877	+	0.952711i	$0.598281\pi$
$810$		0			0
$811$	−15.4261	+	18.3841i	−0.541682	+	0.645551i	−0.965564	−	0.260166i	$-0.916223\pi$
$811$	−15.4261	+	18.3841i	−0.541682	+	0.645551i	0.423882	+	0.905717i	$0.360667\pi$
$812$	28.2849	+	60.6572i	0.992606	+	2.12865i
$813$	−24.2865	+	52.0825i	−0.851764	+	1.82661i
$814$	−47.0753	−	56.1022i	−1.64999	−	1.96638i
$815$		0			0
$816$			12.0335i			0.421255i
$817$	−34.1239	+	1.01477i	−1.19384	+	0.0355024i
$818$	62.5694	+	62.5694i	2.18769	+	2.18769i
$819$	−1.14604	−	6.49951i	−0.0400458	−	0.227111i
$820$		0			0
$821$	−27.5761	+	10.0369i	−0.962411	+	0.350289i	−0.774978	−	0.631988i	$-0.782239\pi$
$821$	−27.5761	+	10.0369i	−0.962411	+	0.350289i	−0.187433	+	0.982277i	$0.560017\pi$
$822$	35.3013	−	16.4612i	1.23127	−	0.574152i
$823$	−2.19630	−	25.1038i	−0.0765582	−	0.875064i	−0.933248	−	0.359233i	$-0.883038\pi$
$823$	−2.19630	−	25.1038i	−0.0765582	−	0.875064i	0.856690	−	0.515832i	$-0.172517\pi$
$824$	16.8151	+	9.70818i	0.585780	+	0.338200i
$825$		0			0
$826$	2.29053	−	12.9902i	0.0796976	−	0.451988i
$827$	30.9809	−	21.6931i	1.07731	−	0.754342i	0.106532	−	0.994309i	$-0.466025\pi$
$827$	30.9809	−	21.6931i	1.07731	−	0.754342i	0.970781	+	0.239967i	$0.0771366\pi$
$828$	−0.234784	+	0.876224i	−0.00815929	+	0.0304509i
$829$	2.51575	−	4.35740i	0.0873755	−	0.151339i	−0.819025	−	0.573757i	$-0.805485\pi$
$829$	2.51575	−	4.35740i	0.0873755	−	0.151339i	0.906401	+	0.422418i	$0.138819\pi$
$830$		0			0
$831$	17.4541	−	47.9547i	0.605476	−	1.66353i
$832$	−42.2672	−	19.7095i	−1.46535	−	0.683305i
$833$	3.73553	+	0.326817i	0.129428	+	0.0113235i
$834$	−27.4308	+	4.83679i	−0.949851	+	0.167484i
$835$		0			0
$836$	−21.5724	−	42.8857i	−0.746098	−	1.48323i
$837$	−0.665993	+	0.665993i	−0.0230201	+	0.0230201i
$838$	10.7090	+	7.49854i	0.369937	+	0.259033i
$839$	2.80005	−	2.34952i	0.0966686	−	0.0811146i	−0.593173	−	0.805075i	$-0.702125\pi$
$839$	2.80005	−	2.34952i	0.0966686	−	0.0811146i	0.689841	+	0.723961i	$0.257680\pi$
$840$		0			0
$841$	−17.3824	−	6.32669i	−0.599394	−	0.218162i
$842$	68.1688	−	5.96400i	2.34925	−	0.205533i
$843$	−28.1846	+	7.55205i	−0.970731	+	0.260107i
$844$	18.5593	+	32.1456i	0.638836	+	1.10650i
$845$		0			0
$846$	−12.2483	−	2.15971i	−0.421107	−	0.0742525i
$847$	2.86122	+	0.766661i	0.0983127	+	0.0263428i
$848$	1.18853	+	4.43565i	0.0408143	+	0.152321i
$849$	15.5474	+	13.0458i	0.533585	+	0.447731i
$850$		0			0
$851$	−1.42246	−	3.90818i	−0.0487614	−	0.133971i
$852$	1.91088	−	21.8415i	0.0654658	−	0.748278i
$853$	−29.2009	+	41.7032i	−0.999820	+	1.42789i	−0.0982982	+	0.995157i	$0.531340\pi$
$853$	−29.2009	+	41.7032i	−0.999820	+	1.42789i	−0.901522	+	0.432734i	$0.857549\pi$
$854$	−66.2325			−2.26643
$855$		0			0
$856$	−31.0198			−1.06024
$857$	−9.40002	+	13.4246i	−0.321099	+	0.458576i	−0.946957	−	0.321360i	$-0.895860\pi$
$857$	−9.40002	+	13.4246i	−0.321099	+	0.458576i	0.625858	+	0.779937i	$0.284749\pi$
$858$	−4.70077	+	53.7300i	−0.160482	+	1.83431i
$859$	6.29056	+	17.2832i	0.214631	+	0.589694i	0.999553	−	0.0299006i	$-0.00951909\pi$
$859$	6.29056	+	17.2832i	0.214631	+	0.589694i	−0.784922	+	0.619595i	$0.787297\pi$
$860$		0			0
$861$	−8.77686	−	7.36466i	−0.299114	−	0.250987i
$862$	−15.1463	−	56.5268i	−0.515885	−	1.92531i
$863$	−17.8481	−	4.78239i	−0.607558	−	0.162795i	−0.0580925	−	0.998311i	$-0.518502\pi$
$863$	−17.8481	−	4.78239i	−0.607558	−	0.162795i	−0.549465	+	0.835517i	$0.685169\pi$
$864$	18.4796	+	3.25845i	0.628689	+	0.110855i
$865$		0			0
$866$	23.9442	+	41.4725i	0.813656	+	1.40929i
$867$	−18.0682	+	4.84135i	−0.613627	+	0.164421i
$868$	2.01149	−	0.175983i	0.0682744	−	0.00597324i
$869$	14.5093	+	5.28096i	0.492195	+	0.179144i
$870$		0			0
$871$	−4.80989	+	4.03598i	−0.162977	+	0.136754i
$872$	38.3925	+	26.8827i	1.30013	+	0.910363i
$873$	3.26311	−	3.26311i	0.110440	−	0.110440i
$874$	−0.500369	−	4.25729i	−0.0169252	−	0.144005i
$875$		0			0
$876$	−81.7499	+	14.4147i	−2.76207	+	0.487028i
$877$	23.6389	+	2.06814i	0.798230	+	0.0698361i	0.478970	−	0.877831i	$-0.341010\pi$
$877$	23.6389	+	2.06814i	0.798230	+	0.0698361i	0.319260	+	0.947667i	$0.396566\pi$
$878$	29.7392	+	13.8676i	1.00365	+	0.468010i
$879$	−7.31512	+	20.0981i	−0.246733	+	0.677893i
$880$		0			0
$881$	−10.5557	+	18.2830i	−0.355630	+	0.615969i	−0.987226	−	0.159329i	$-0.949067\pi$
$881$	−10.5557	+	18.2830i	−0.355630	+	0.615969i	0.631595	+	0.775298i	$0.282400\pi$
$882$	0.271745	−	1.01416i	0.00915011	−	0.0341487i
$883$	29.7779	−	20.8507i	1.00211	−	0.701682i	0.0472899	−	0.998881i	$-0.484942\pi$
$883$	29.7779	−	20.8507i	1.00211	−	0.701682i	0.954815	+	0.297200i	$0.0960527\pi$
$884$	−12.0623	+	68.4085i	−0.405698	+	2.30083i
$885$		0			0
$886$	47.2895	+	27.3026i	1.58872	+	0.917250i
$887$	3.77343	+	43.1305i	0.126699	+	1.44818i	0.747527	+	0.664232i	$0.231241\pi$
$887$	3.77343	+	43.1305i	0.126699	+	1.44818i	−0.620827	+	0.783947i	$0.713203\pi$
$888$	−59.8596	+	27.9130i	−2.00876	+	0.936698i
$889$	16.1207	−	5.86744i	0.540670	−	0.196788i
$890$		0			0
$891$	−5.73226	−	32.5093i	−0.192038	−	1.08910i
$892$	−65.3664	−	65.3664i	−2.18863	−	2.18863i
$893$	36.6005	−	7.58184i	1.22479	−	0.253717i
$894$		−	23.2567i		−	0.777822i
$895$		0			0
$896$	−36.0850	−	43.0044i	−1.20552	−	1.43668i
$897$	−1.29445	+	2.77595i	−0.0432203	+	0.0926863i
$898$	13.8915	+	29.7904i	0.463565	+	0.994118i
$899$	−0.921106	+	1.09773i	−0.0307206	+	0.0366114i
$900$		0			0
$901$	−16.8696	+	9.73969i	−0.562009	+	0.324476i
$902$	9.18324	+	13.1150i	0.305769	+	0.436683i
$903$	23.7500	+	33.9186i	0.790352	+	1.12874i
$904$	−33.9827	+	19.6199i	−1.13025	+	0.652548i
$905$		0			0
$906$	58.6906	−	69.9447i	1.94986	−	2.32376i
$907$	−5.33479	−	11.4405i	−0.177139	−	0.379875i	0.797612	−	0.603171i	$-0.206096\pi$
$907$	−5.33479	−	11.4405i	−0.177139	−	0.379875i	−0.974751	+	0.223295i	$0.928319\pi$
$908$	33.5164	−	71.8762i	1.11228	−	2.38530i
$909$	−3.58434	−	4.27165i	−0.118885	−	0.141682i
$910$		0			0
$911$		−	14.5784i		−	0.483003i	−0.970400	−	0.241502i	$-0.922360\pi$
$911$		−	14.5784i		−	0.483003i	0.970400	−	0.241502i	$-0.0776399\pi$
$912$	−9.91535	+	2.05398i	−0.328330	+	0.0680139i
$913$	−2.71607	−	2.71607i	−0.0898888	−	0.0898888i
$914$	−1.10628	−	6.27401i	−0.0365924	−	0.207526i
$915$		0			0
$916$	−14.6648	+	5.33755i	−0.484538	+	0.176358i
$917$	−13.3664	+	6.23287i	−0.441399	+	0.205828i
$918$	−4.79363	−	54.7915i	−0.158213	−	1.80839i
$919$	33.2115	+	19.1746i	1.09554	+	0.632513i	0.935047	−	0.354523i	$-0.115357\pi$
$919$	33.2115	+	19.1746i	1.09554	+	0.632513i	0.160497	+	0.987036i	$0.448690\pi$
$920$		0			0
$921$	−5.54384	+	31.4407i	−0.182676	+	1.03601i
$922$	−67.8348	+	47.4985i	−2.23402	+	1.56428i
$923$	3.27623	−	12.2271i	0.107839	−	0.402459i
$924$	−29.1129	+	50.4251i	−0.957745	+	1.65886i
$925$		0			0
$926$	4.08871	−	11.2336i	0.134363	−	0.369161i
$927$	3.10894	+	1.44972i	0.102111	+	0.0476151i
$928$	28.4409	+	2.48825i	0.933617	+	0.0816809i
$929$	41.0625	−	7.24042i	1.34722	−	0.237550i	0.546934	−	0.837175i	$-0.315795\pi$
$929$	41.0625	−	7.24042i	1.34722	−	0.237550i	0.800281	+	0.599625i	$0.204684\pi$
$930$		0			0
$931$	0.368322	+	3.13380i	0.0120713	+	0.102706i
$932$	−45.4768	+	45.4768i	−1.48964	+	1.48964i
$933$	−36.6718	−	25.6779i	−1.20058	−	0.840656i
$934$	−48.5571	+	40.7442i	−1.58884	+	1.33319i
$935$		0			0
$936$	7.81567	+	2.84467i	0.255463	+	0.0929810i
$937$	14.5913	−	1.27657i	0.476676	−	0.0417037i	0.153713	−	0.988116i	$-0.450877\pi$
$937$	14.5913	−	1.27657i	0.476676	−	0.0417037i	0.322962	+	0.946412i	$0.395321\pi$
$938$	−10.2949	+	2.75852i	−0.336142	+	0.0900689i
$939$	−5.30858	−	9.19473i	−0.173239	−	0.300059i
$940$		0			0
$941$	53.1484	+	9.37150i	1.73259	+	0.305502i	0.948883	−	0.315629i	$-0.102215\pi$
$941$	53.1484	+	9.37150i	1.73259	+	0.305502i	0.783707	+	0.621131i	$0.213326\pi$
$942$	50.2295	+	13.4590i	1.63657	+	0.438517i
$943$	0.235323	+	0.878237i	0.00766317	+	0.0285993i
$944$	1.89418	+	1.58941i	0.0616504	+	0.0517308i
$945$		0			0
$946$	−19.7899	−	54.3724i	−0.643426	−	1.76780i
$947$	−4.83820	+	55.3009i	−0.157220	+	1.79704i	0.351585	+	0.936156i	$0.385643\pi$
$947$	−4.83820	+	55.3009i	−0.157220	+	1.79704i	−0.508805	+	0.860882i	$0.669913\pi$
$948$	18.6775	−	26.6743i	0.606618	−	0.866340i
$949$	−47.9265			−1.55576
$950$		0			0
$951$	−44.5508			−1.44466
$952$	−28.9211	+	41.3035i	−0.937337	+	1.33866i
$953$	2.37795	−	27.1801i	0.0770295	−	0.880451i	−0.855132	−	0.518410i	$-0.826524\pi$
$953$	2.37795	−	27.1801i	0.0770295	−	0.880451i	0.932162	−	0.362042i	$-0.117920\pi$
$954$	1.86545	+	5.12528i	0.0603961	+	0.165937i
$955$		0			0
$956$	37.0075	+	31.0529i	1.19691	+	1.00432i
$957$	−10.6950	−	39.9143i	−0.345720	−	1.29025i
$958$	−28.9053	−	7.74516i	−0.933888	−	0.250235i
$959$	23.9083	+	4.21569i	0.772041	+	0.136132i
$960$		0			0
$961$	−15.4784	−	26.8093i	−0.499303	−	0.864818i
$962$	−86.1344	+	23.0796i	−2.77708	+	0.744118i
$963$	−5.45950	+	0.477644i	−0.175930	+	0.0153919i
$964$	7.28850	+	2.65280i	0.234747	+	0.0854409i
$965$		0			0
$966$	−3.98280	+	3.34197i	−0.128145	+	0.107526i
$967$	14.8205	+	10.3774i	0.476596	+	0.333716i	0.787068	−	0.616866i	$-0.211598\pi$
$967$	14.8205	+	10.3774i	0.476596	+	0.333716i	−0.310472	+	0.950583i	$0.600487\pi$
$968$	−2.63963	+	2.63963i	−0.0848411	+	0.0848411i
$969$	−19.3018	−	38.3718i	−0.620064	−	1.23268i
$970$		0			0
$971$	−1.40453	+	0.247657i	−0.0450736	+	0.00794770i	−0.196140	−	0.980576i	$-0.562841\pi$
$971$	−1.40453	+	0.247657i	−0.0450736	+	0.00794770i	0.151066	+	0.988524i	$0.451729\pi$
$972$	−22.0493	−	1.92907i	−0.707232	−	0.0618748i
$973$	−15.7343	−	7.33701i	−0.504417	−	0.235214i
$974$	−16.7278	+	45.9592i	−0.535992	+	1.47263i
$975$		0			0
$976$	6.20789	−	10.7524i	0.198710	−	0.344175i
$977$	−9.25123	+	34.5261i	−0.295973	+	1.10459i	0.644468	+	0.764631i	$0.277079\pi$
$977$	−9.25123	+	34.5261i	−0.295973	+	1.10459i	−0.940441	+	0.339956i	$0.889588\pi$
$978$	17.2200	−	12.0576i	0.550634	−	0.385558i
$979$	1.95902	−	11.1101i	0.0626104	−	0.355081i
$980$		0			0
$981$	7.17102	+	4.14019i	0.228953	+	0.132186i
$982$	3.71954	+	42.5145i	0.118695	+	1.35669i
$983$	43.7984	−	20.4235i	1.39695	−	0.651410i	0.429176	−	0.903221i	$-0.358804\pi$
$983$	43.7984	−	20.4235i	1.39695	−	0.651410i	0.967776	+	0.251811i	$0.0810261\pi$
$984$	13.5682	−	4.93842i	0.432539	−	0.157431i
$985$		0			0
$986$	−14.5310	−	82.4095i	−0.462762	−	2.62445i
$987$	−32.0567	−	32.0567i	−1.02038	−	1.02038i
$988$	−58.4263	+	1.73747i	−1.85879	+	0.0552764i
$989$		−	3.28591i		−	0.104486i
$990$		0			0
$991$	−19.0947	−	22.7562i	−0.606564	−	0.722875i	0.372134	−	0.928179i	$-0.378626\pi$
$991$	−19.0947	−	22.7562i	−0.606564	−	0.722875i	−0.978698	+	0.205304i	$0.934182\pi$
$992$	0.364010	−	0.780622i	0.0115573	−	0.0247848i
$993$	12.3535	+	26.4921i	0.392026	+	0.840702i
$994$	13.8116	−	16.4601i	0.438078	−	0.522081i
$995$		0			0
$996$	−7.01541	+	4.05035i	−0.222292	+	0.128340i
$997$	−6.96664	−	9.94939i	−0.220636	−	0.315100i	0.693540	−	0.720418i	$-0.256050\pi$
$997$	−6.96664	−	9.94939i	−0.220636	−	0.315100i	−0.914176	+	0.405317i	$0.867161\pi$
$998$	40.0484	+	57.1950i	1.26771	+	1.81048i
$999$	38.8882	−	22.4521i	1.23037	−	0.710353i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.bb.b.143.8		96
5.2	odd	4	inner	475.2.bb.b.257.8		96
5.3	odd	4		95.2.r.a.67.1	yes	96
5.4	even	2		95.2.r.a.48.1	yes	96
15.8	even	4		855.2.dl.a.352.8		96
15.14	odd	2		855.2.dl.a.523.8		96
19.2	odd	18	inner	475.2.bb.b.268.8		96
95.2	even	36	inner	475.2.bb.b.382.8		96
95.59	odd	18		95.2.r.a.78.1	yes	96
95.78	even	36		95.2.r.a.2.1	✓	96
285.59	even	18		855.2.dl.a.838.8		96
285.173	odd	36		855.2.dl.a.667.8		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.r.a.2.1	✓	96	95.78	even	36
95.2.r.a.48.1	yes	96	5.4	even	2
95.2.r.a.67.1	yes	96	5.3	odd	4
95.2.r.a.78.1	yes	96	95.59	odd	18
475.2.bb.b.143.8		96	1.1	even	1	trivial
475.2.bb.b.257.8		96	5.2	odd	4	inner
475.2.bb.b.268.8		96	19.2	odd	18	inner
475.2.bb.b.382.8		96	95.2	even	36	inner
855.2.dl.a.352.8		96	15.8	even	4
855.2.dl.a.523.8		96	15.14	odd	2
855.2.dl.a.667.8		96	285.173	odd	36
855.2.dl.a.838.8		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+(1.34445 - 1.92007i) q^{2} +(-0.165797 + 1.89507i) q^{3} +(-1.19510 - 3.28350i) q^{4} +(3.41577 + 2.86617i) q^{6} +(0.719307 + 2.68449i) q^{7} +(-3.38309 - 0.906496i) q^{8} +(-0.609382 - 0.107451i) q^{9} +(1.57593 + 2.72958i) q^{11} +(6.42061 - 1.72040i) q^{12} +(3.82311 - 0.334479i) q^{13} +(6.12149 + 2.22804i) q^{14} +(-0.935465 + 0.784949i) q^{16} +(-4.24326 - 2.97116i) q^{17} +(-1.02560 + 1.02560i) q^{18} +(1.72391 - 4.00352i) q^{19} +(-5.20656 + 0.918057i) q^{21} +(7.35975 + 0.643895i) q^{22} +(0.380240 + 0.177309i) q^{23} +(2.27878 - 6.26090i) q^{24} +(4.49776 - 7.79034i) q^{26} +(-1.17240 + 4.37546i) q^{27} +(7.95488 - 5.57007i) q^{28} +(-1.19676 + 6.78718i) q^{29} +(0.180067 + 0.103962i) q^{31} +(-0.361041 - 4.12672i) q^{32} +(-5.43404 + 2.53393i) q^{33} +(-11.4097 + 4.15279i) q^{34} +(0.375456 + 2.12932i) q^{36} +(-7.00958 - 7.00958i) q^{37} +(-5.36933 - 8.69256i) q^{38} +7.30052i q^{39} +(1.39301 + 1.66012i) q^{41} +(-5.23722 + 11.2313i) q^{42} +(-3.30995 - 7.09822i) q^{43} +(7.07920 - 8.43666i) q^{44} +(0.851660 - 0.491706i) q^{46} +(4.91842 + 7.02423i) q^{47} +(-1.33244 - 1.90292i) q^{48} +(-0.626908 + 0.361945i) q^{49} +(6.33409 - 7.54867i) q^{51} +(-5.66724 - 12.1534i) q^{52} +(1.58924 - 3.40813i) q^{53} +(6.82497 + 8.13369i) q^{54} -9.73392i q^{56} +(7.30113 + 3.93070i) q^{57} +(11.4229 + 11.4229i) q^{58} +(-0.351612 - 1.99409i) q^{59} +(-9.55401 + 3.47738i) q^{61} +(0.441706 - 0.205971i) q^{62} +(-0.149883 - 1.71317i) q^{63} +(-10.5241 - 6.07611i) q^{64} +(-2.44045 + 13.8405i) q^{66} +(-1.34021 + 0.938425i) q^{67} +(-4.68471 + 17.4836i) q^{68} +(-0.399056 + 0.691185i) q^{69} +(1.12813 - 3.09950i) q^{71} +(1.96419 + 0.915917i) q^{72} +(-12.4408 - 1.08843i) q^{73} +(-22.8829 + 4.03488i) q^{74} +(-15.2058 - 0.875867i) q^{76} +(-6.19397 + 6.19397i) q^{77} +(14.0175 + 9.81518i) q^{78} +(3.75275 - 3.14893i) q^{79} +(-9.84183 - 3.58213i) q^{81} +(5.06038 - 0.442726i) q^{82} +(-1.17716 + 0.315418i) q^{83} +(9.23677 + 15.9986i) q^{84} +(-18.0792 - 3.18784i) q^{86} +(-12.6638 - 3.39324i) q^{87} +(-2.85714 - 10.6630i) q^{88} +(-2.74193 - 2.30075i) q^{89} +(3.64790 + 10.0225i) q^{91} +(0.127770 - 1.46042i) q^{92} +(-0.226870 + 0.324004i) q^{93} +20.0996 q^{94} +7.88029 q^{96} +(-4.27760 + 6.10904i) q^{97} +(-0.147884 + 1.69033i) q^{98} +(-0.667046 - 1.83269i) 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

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Database

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