LMFDB - Embedded newform 158.2.e.a.97.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [158,2,Mod(21,158)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("158.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(158, base_ring=CyclotomicField(26)) chi = DirichletCharacter(H, H._module([18])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 158 = 2 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	158.e (of order $13$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.26163635194$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	158.97
Dual form			158.2.e.a.101.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.568065 + 0.822984i) q^{2} +(2.42930 + 0.598768i) q^{3} +(-0.354605 + 0.935016i) q^{4} +(0.846056 - 0.749541i) q^{5} +(0.887221 + 2.33941i) q^{6} +(-3.30267 - 0.814036i) q^{7} +(-0.970942 + 0.239316i) q^{8} +(2.88659 + 1.51500i) q^{9} +(1.09747 + 0.270503i) q^{10} +(-3.66300 - 3.24513i) q^{11} +(-1.42130 + 2.05911i) q^{12} +(0.892894 - 2.35437i) q^{13} +(-1.20619 - 3.18047i) q^{14} +(2.50412 - 1.31427i) q^{15} +(-0.748511 - 0.663123i) q^{16} +(-2.60867 + 6.87850i) q^{17} +(0.392950 + 3.23624i) q^{18} +(0.107321 + 0.883872i) q^{19} +(0.400817 + 1.05687i) q^{20} +(-7.53575 - 3.95507i) q^{21} +(0.589872 - 4.85803i) q^{22} +6.85549 q^{23} -2.50200 q^{24} +(-0.448683 + 3.69524i) q^{25} +(2.44483 - 0.602596i) q^{26} +(0.486930 + 0.431383i) q^{27} +(1.93228 - 2.79939i) q^{28} +(3.64272 - 1.91185i) q^{29} +(2.50412 + 1.31427i) q^{30} +(1.91329 + 2.77189i) q^{31} +(0.120537 - 0.992709i) q^{32} +(-6.95542 - 10.0767i) q^{33} +(-7.14279 + 1.76054i) q^{34} +(-3.40440 + 1.78677i) q^{35} +(-2.44015 + 2.16178i) q^{36} +(0.186804 + 1.53847i) q^{37} +(-0.666447 + 0.590420i) q^{38} +(3.57883 - 5.18482i) q^{39} +(-0.642095 + 0.930235i) q^{40} +(0.908281 - 0.804667i) q^{41} +(-1.02584 - 8.44854i) q^{42} +(-2.40308 + 2.12895i) q^{43} +(4.33317 - 2.27422i) q^{44} +(3.57777 - 0.881842i) q^{45} +(3.89436 + 5.64196i) q^{46} +(1.59157 - 13.1078i) q^{47} +(-1.42130 - 2.05911i) q^{48} +(4.04680 + 2.12393i) q^{49} +(-3.29600 + 1.72987i) q^{50} +(-10.4559 + 15.1479i) q^{51} +(1.88475 + 1.66974i) q^{52} +(0.277827 - 0.0684782i) q^{53} +(-0.0784130 + 0.645789i) q^{54} -5.53146 q^{55} +3.40152 q^{56} +(-0.268518 + 2.21145i) q^{57} +(3.64272 + 1.91185i) q^{58} +(-4.46876 - 11.7831i) q^{59} +(0.340885 + 2.80744i) q^{60} +(0.622369 + 5.12567i) q^{61} +(-1.19434 + 3.14922i) q^{62} +(-8.30020 - 7.35334i) q^{63} +(0.885456 - 0.464723i) q^{64} +(-1.00926 - 2.66119i) q^{65} +(4.34181 - 11.4484i) q^{66} +(0.320881 - 0.464876i) q^{67} +(-5.50646 - 4.87830i) q^{68} +(16.6540 + 4.10485i) q^{69} +(-3.40440 - 1.78677i) q^{70} +(-1.65139 + 0.407031i) q^{71} +(-3.16528 - 0.780170i) q^{72} +(5.40817 + 14.2602i) q^{73} +(-1.16002 + 1.02769i) q^{74} +(-3.30257 + 8.70817i) q^{75} +(-0.864491 - 0.213078i) q^{76} +(9.45603 + 13.6994i) q^{77} +6.30003 q^{78} +(2.64851 + 8.48442i) q^{79} -1.13032 q^{80} +(-4.63108 - 6.70928i) q^{81} +(1.17819 + 0.290398i) q^{82} +(-3.69908 + 9.75368i) q^{83} +(6.37027 - 5.64357i) q^{84} +(2.94863 + 7.77491i) q^{85} +(-3.11719 - 0.768319i) q^{86} +(9.99400 - 2.46330i) q^{87} +(4.33317 + 2.27422i) q^{88} +(13.0425 + 3.21470i) q^{89} +(2.75815 + 2.44351i) q^{90} +(-4.86548 + 7.04886i) q^{91} +(-2.43099 + 6.41000i) q^{92} +(2.98824 + 7.87935i) q^{93} +(11.6916 - 6.13623i) q^{94} +(0.753298 + 0.667364i) q^{95} +(0.887221 - 2.33941i) q^{96} +(-0.568822 - 4.68467i) q^{97} +(0.550889 + 4.53698i) q^{98} +(-5.65720 - 14.9168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 18 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 16 q^{13} + 5 q^{14} - 2 q^{15} - 4 q^{16} + 6 q^{17} - 18 q^{18} + 6 q^{19} - 2 q^{20}+ \cdots - 58 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 8 * q^7 - 4 * q^8 - 18 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 16 * q^13 + 5 * q^14 - 2 * q^15 - 4 * q^16 + 6 * q^17 - 18 * q^18 + 6 * q^19 - 2 * q^20 - 12 * q^21 + 5 * q^22 - 16 * q^23 + 24 * q^24 - 17 * q^25 + 3 * q^26 + 7 * q^27 - 8 * q^28 - 34 * q^29 - 2 * q^30 - 19 * q^31 - 4 * q^32 + 8 * q^33 - 20 * q^34 + 122 * q^35 - 18 * q^36 - 4 * q^37 - 20 * q^38 - 50 * q^39 - 2 * q^40 - 36 * q^41 + 14 * q^42 - 24 * q^43 + 18 * q^44 - 4 * q^45 + 10 * q^46 - 22 * q^47 - 2 * q^48 - 28 * q^49 - 4 * q^50 + 78 * q^51 - 10 * q^52 - 12 * q^53 + 7 * q^54 - 88 * q^55 + 18 * q^56 - 28 * q^57 - 34 * q^58 - 52 * q^59 + 11 * q^60 - 47 * q^61 + 20 * q^62 + 11 * q^63 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 67 * q^67 - 7 * q^68 - 4 * q^69 + 122 * q^70 - 12 * q^71 - 18 * q^72 + 101 * q^73 - 4 * q^74 - 62 * q^75 + 32 * q^76 + 113 * q^77 - 50 * q^78 - 2 * q^80 + 36 * q^81 + 29 * q^82 + 91 * q^83 + 53 * q^84 - q^85 - 24 * q^86 + 210 * q^87 + 18 * q^88 + 4 * q^89 + 126 * q^90 - 33 * q^91 - 3 * q^92 - 3 * q^93 + 17 * q^94 - 42 * q^95 - 2 * q^96 - 32 * q^97 + 24 * q^98 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/158\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{13}\right)$

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 $

$2$	0.568065	+	0.822984i	0.401682	+	0.581937i
$2$	0.568065	+	0.822984i	0.401682	+	0.581937i
$3$	2.42930	+	0.598768i	1.40256	+	0.345699i	0.866792	−	0.498670i	$-0.166178\pi$
$3$	2.42930	+	0.598768i	1.40256	+	0.345699i	0.535763	+	0.844368i	$0.320024\pi$
$4$	−0.354605	+	0.935016i	−0.177302	+	0.467508i
$5$	0.846056	−	0.749541i	0.378368	−	0.335205i	−0.452409	−	0.891811i	$-0.649435\pi$
$5$	0.846056	−	0.749541i	0.378368	−	0.335205i	0.830777	+	0.556606i	$0.187897\pi$
$6$	0.887221	+	2.33941i	0.362207	+	0.955060i
$7$	−3.30267	−	0.814036i	−1.24829	−	0.307677i	−0.440828	−	0.897592i	$-0.645315\pi$
$7$	−3.30267	−	0.814036i	−1.24829	−	0.307677i	−0.807465	+	0.589915i	$0.799161\pi$
$8$	−0.970942	+	0.239316i	−0.343280	+	0.0846109i
$9$	2.88659	+	1.51500i	0.962197	+	0.505000i
$10$	1.09747	+	0.270503i	0.347052	+	0.0855406i
$11$	−3.66300	−	3.24513i	−1.10444	−	0.978444i	−0.104564	−	0.994518i	$-0.533345\pi$
$11$	−3.66300	−	3.24513i	−1.10444	−	0.978444i	−0.999871	+	0.0160740i	$0.994883\pi$
$12$	−1.42130	+	2.05911i	−0.410293	+	0.594413i
$13$	0.892894	−	2.35437i	0.247644	−	0.652984i	−0.752339	−	0.658776i	$-0.771074\pi$
$13$	0.892894	−	2.35437i	0.247644	−	0.652984i	0.999983	+	0.00579183i	$0.00184361\pi$
$14$	−1.20619	−	3.18047i	−0.322369	−	0.850017i
$15$	2.50412	−	1.31427i	0.646562	−	0.339342i
$16$	−0.748511	−	0.663123i	−0.187128	−	0.165781i
$17$	−2.60867	+	6.87850i	−0.632696	+	1.66828i	0.106102	+	0.994355i	$0.466163\pi$
$17$	−2.60867	+	6.87850i	−0.632696	+	1.66828i	−0.738798	+	0.673927i	$0.764606\pi$
$18$	0.392950	+	3.23624i	0.0926192	+	0.762788i
$19$	0.107321	+	0.883872i	0.0246212	+	0.202774i	0.999829	−	0.0185193i	$-0.00589522\pi$
$19$	0.107321	+	0.883872i	0.0246212	+	0.202774i	−0.975207	+	0.221293i	$0.928972\pi$
$20$	0.400817	+	1.05687i	0.0896254	+	0.236323i
$21$	−7.53575	−	3.95507i	−1.64444	−	0.863067i
$22$	0.589872	−	4.85803i	0.125761	−	1.03574i
$23$	6.85549			1.42947			0.714735	−	0.699396i	$-0.246547\pi$
$23$	6.85549			1.42947			0.714735	+	0.699396i	$0.246547\pi$
$24$	−2.50200			−0.510719
$25$	−0.448683	+	3.69524i	−0.0897366	+	0.739047i
$26$	2.44483	−	0.602596i	0.479471	−	0.118179i
$27$	0.486930	+	0.431383i	0.0937098	+	0.0830196i
$28$	1.93228	−	2.79939i	0.365167	−	0.529035i
$29$	3.64272	−	1.91185i	0.676436	−	0.355021i	−0.0912674	−	0.995826i	$-0.529092\pi$
$29$	3.64272	−	1.91185i	0.676436	−	0.355021i	0.767703	+	0.640805i	$0.221399\pi$
$30$	2.50412	+	1.31427i	0.457188	+	0.239951i
$31$	1.91329	+	2.77189i	0.343638	+	0.497845i	0.956255	−	0.292534i	$-0.0944986\pi$
$31$	1.91329	+	2.77189i	0.343638	+	0.497845i	−0.612617	+	0.790380i	$0.709883\pi$
$32$	0.120537	−	0.992709i	0.0213081	−	0.175488i
$33$	−6.95542	−	10.0767i	−1.21078	−	1.75412i
$34$	−7.14279	+	1.76054i	−1.22498	+	0.301930i
$35$	−3.40440	+	1.78677i	−0.575449	+	0.302019i
$36$	−2.44015	+	2.16178i	−0.406691	+	0.360297i
$37$	0.186804	+	1.53847i	0.0307104	+	0.252923i	0.999976	+	0.00690688i	$0.00219854\pi$
$37$	0.186804	+	1.53847i	0.0307104	+	0.252923i	−0.969266	+	0.246016i	$0.920878\pi$
$38$	−0.666447	+	0.590420i	−0.108112	+	0.0957788i
$39$	3.57883	−	5.18482i	0.573071	−	0.830236i
$40$	−0.642095	+	0.930235i	−0.101524	+	0.147083i
$41$	0.908281	−	0.804667i	0.141850	−	0.125668i	−0.589214	−	0.807977i	$-0.700563\pi$
$41$	0.908281	−	0.804667i	0.141850	−	0.125668i	0.731064	+	0.682309i	$0.239024\pi$
$42$	−1.02584	−	8.44854i	−0.158290	−	1.30364i
$43$	−2.40308	+	2.12895i	−0.366467	+	0.324661i	−0.826180	−	0.563406i	$-0.809491\pi$
$43$	−2.40308	+	2.12895i	−0.366467	+	0.324661i	0.459713	+	0.888067i	$0.347952\pi$
$44$	4.33317	−	2.27422i	0.653250	−	0.342852i
$45$	3.57777	−	0.881842i	0.533343	−	0.131457i
$46$	3.89436	+	5.64196i	0.574193	+	0.831862i
$47$	1.59157	−	13.1078i	0.232155	−	1.91197i	−0.151445	−	0.988466i	$-0.548393\pi$
$47$	1.59157	−	13.1078i	0.232155	−	1.91197i	0.383600	−	0.923499i	$-0.374684\pi$
$48$	−1.42130	−	2.05911i	−0.205147	−	0.297206i
$49$	4.04680	+	2.12393i	0.578115	+	0.303418i
$50$	−3.29600	+	1.72987i	−0.466125	+	0.244641i
$51$	−10.4559	+	15.1479i	−1.46411	+	2.12114i
$52$	1.88475	+	1.66974i	0.261368	+	0.231551i
$53$	0.277827	−	0.0684782i	0.0381625	−	0.00940621i	−0.220188	−	0.975457i	$-0.570667\pi$
$53$	0.277827	−	0.0684782i	0.0381625	−	0.00940621i	0.258351	+	0.966051i	$0.416821\pi$
$54$	−0.0784130	+	0.645789i	−0.0106707	+	0.0878808i
$55$	−5.53146			−0.745862
$56$	3.40152			0.454547
$57$	−0.268518	+	2.21145i	−0.0355661	+	0.292913i
$58$	3.64272	+	1.91185i	0.478312	+	0.251038i
$59$	−4.46876	−	11.7831i	−0.581783	−	1.53404i	−0.825624	−	0.564220i	$-0.809177\pi$
$59$	−4.46876	−	11.7831i	−0.581783	−	1.53404i	0.243841	−	0.969815i	$-0.421592\pi$
$60$	0.340885	+	2.80744i	0.0440081	+	0.362439i
$61$	0.622369	+	5.12567i	0.0796862	+	0.656275i	0.976751	+	0.214376i	$0.0687719\pi$
$61$	0.622369	+	5.12567i	0.0796862	+	0.656275i	−0.897065	+	0.441899i	$0.854305\pi$
$62$	−1.19434	+	3.14922i	−0.151682	+	0.399952i
$63$	−8.30020	−	7.35334i	−1.04573	−	0.926433i
$64$	0.885456	−	0.464723i	0.110682	−	0.0580904i
$65$	−1.00926	−	2.66119i	−0.125183	−	0.330080i
$66$	4.34181	−	11.4484i	0.534440	−	1.40920i
$67$	0.320881	−	0.464876i	0.0392018	−	0.0567937i	−0.802893	−	0.596123i	$-0.796707\pi$
$67$	0.320881	−	0.464876i	0.0392018	−	0.0567937i	0.842095	+	0.539330i	$0.181322\pi$
$68$	−5.50646	−	4.87830i	−0.667757	−	0.591581i
$69$	16.6540	+	4.10485i	2.00491	+	0.494166i
$70$	−3.40440	−	1.78677i	−0.406904	−	0.213560i
$71$	−1.65139	+	0.407031i	−0.195984	+	0.0483057i	−0.336086	−	0.941831i	$-0.609103\pi$
$71$	−1.65139	+	0.407031i	−0.195984	+	0.0483057i	0.140102	+	0.990137i	$0.455257\pi$
$72$	−3.16528	−	0.780170i	−0.373031	−	0.0919439i
$73$	5.40817	+	14.2602i	0.632979	+	1.66903i	0.738203	+	0.674579i	$0.235675\pi$
$73$	5.40817	+	14.2602i	0.632979	+	1.66903i	−0.105224	+	0.994449i	$0.533556\pi$
$74$	−1.16002	+	1.02769i	−0.134850	+	0.119466i
$75$	−3.30257	+	8.70817i	−0.381348	+	1.00553i
$76$	−0.864491	−	0.213078i	−0.0991640	−	0.0244417i
$77$	9.45603	+	13.6994i	1.07761	+	1.56119i
$78$	6.30003			0.713338
$79$	2.64851	+	8.48442i	0.297981	+	0.954572i
$79$	2.64851	+	8.48442i	0.297981	+	0.954572i
$80$	−1.13032			−0.126374
$81$	−4.63108	−	6.70928i	−0.514565	−	0.745475i
$82$	1.17819	+	0.290398i	0.130109	+	0.0320691i
$83$	−3.69908	+	9.75368i	−0.406027	+	1.07060i	0.563607	+	0.826043i	$0.309413\pi$
$83$	−3.69908	+	9.75368i	−0.406027	+	1.07060i	−0.969634	+	0.244562i	$0.921356\pi$
$84$	6.37027	−	5.64357i	0.695053	−	0.615764i
$85$	2.94863	+	7.77491i	0.319824	+	0.843307i
$86$	−3.11719	−	0.768319i	−0.336136	−	0.0828500i
$87$	9.99400	−	2.46330i	1.07147	−	0.264093i
$88$	4.33317	+	2.27422i	0.461917	+	0.242433i
$89$	13.0425	+	3.21470i	1.38251	+	0.340757i	0.859310	−	0.511454i	$-0.170893\pi$
$89$	13.0425	+	3.21470i	1.38251	+	0.340757i	0.523197	+	0.852212i	$0.324739\pi$
$90$	2.75815	+	2.44351i	0.290734	+	0.257568i
$91$	−4.86548	+	7.04886i	−0.510041	+	0.738922i
$92$	−2.43099	+	6.41000i	−0.253448	+	0.668289i
$93$	2.98824	+	7.87935i	0.309866	+	0.817051i
$94$	11.6916	−	6.13623i	1.20590	−	0.632903i
$95$	0.753298	+	0.667364i	0.0772867	+	0.0684701i
$96$	0.887221	−	2.33941i	0.0905517	−	0.238765i
$97$	−0.568822	−	4.68467i	−0.0577551	−	0.475656i	−0.992677	−	0.120802i	$-0.961453\pi$
$97$	−0.568822	−	4.68467i	−0.0577551	−	0.475656i	0.934922	−	0.354855i	$-0.115470\pi$
$98$	0.550889	+	4.53698i	0.0556482	+	0.458304i
$99$	−5.65720	−	14.9168i	−0.568570	−	1.49920i
$100$	−3.29600	−	1.72987i	−0.329600	−	0.172987i
$101$	1.49565	−	12.3178i	0.148823	−	1.22566i	−0.706555	−	0.707658i	$-0.749752\pi$
$101$	1.49565	−	12.3178i	0.148823	−	1.22566i	0.855377	−	0.518005i	$-0.173325\pi$
$102$	−18.4061			−1.82248
$103$	−13.3209			−1.31255			−0.656273	−	0.754524i	$-0.727868\pi$
$103$	−13.3209			−1.31255			−0.656273	+	0.754524i	$0.727868\pi$
$104$	−0.303511	+	2.49964i	−0.0297617	+	0.245110i
$105$	−9.34016	+	2.30214i	−0.911506	+	0.224666i
$106$	0.214180	+	0.189747i	0.0208030	+	0.0184299i
$107$	−1.46102	+	2.11665i	−0.141242	+	0.204624i	−0.887220	−	0.461346i	$-0.847367\pi$
$107$	−1.46102	+	2.11665i	−0.141242	+	0.204624i	0.745979	+	0.665970i	$0.231982\pi$
$108$	−0.576018	+	0.302317i	−0.0554273	+	0.0290905i
$109$	−15.8450	−	8.31611i	−1.51768	−	0.796539i	−0.519363	−	0.854554i	$-0.673831\pi$
$109$	−15.8450	−	8.31611i	−1.51768	−	0.796539i	−0.998316	+	0.0580145i	$0.981523\pi$
$110$	−3.14223	−	4.55230i	−0.299600	−	0.434045i
$111$	−0.467384	+	3.84925i	−0.0443621	+	0.365355i
$112$	1.93228	+	2.79939i	0.182583	+	0.264518i
$113$	2.57849	−	0.635540i	0.242564	−	0.0597866i	−0.116159	−	0.993231i	$-0.537058\pi$
$113$	2.57849	−	0.635540i	0.242564	−	0.0597866i	0.358723	+	0.933444i	$0.383212\pi$
$114$	−1.97252	+	1.03526i	−0.184744	+	0.0969609i
$115$	5.80014	−	5.13847i	0.540865	−	0.479165i
$116$	0.495881	+	4.08395i	0.0460414	+	0.379185i
$117$	6.14429	−	5.44337i	0.568040	−	0.503239i
$118$	7.15880	−	10.3713i	0.659021	−	0.954756i
$119$	14.2149	−	20.5939i	1.30308	−	1.88784i
$120$	−2.11683	+	1.87535i	−0.193240	+	0.171195i
$121$	1.56076	+	12.8540i	0.141887	+	1.16855i
$122$	−3.86480	+	3.42391i	−0.349902	+	0.309986i
$123$	2.68829	−	1.41092i	0.242395	−	0.127219i
$124$	−3.27022	+	0.806037i	−0.293675	+	0.0723843i
$125$	5.60059	+	8.11386i	0.500932	+	0.725726i
$126$	1.33663	−	11.0081i	0.119076	−	0.980680i
$127$	−1.25536	−	1.81871i	−0.111396	−	0.161384i	0.763321	−	0.646020i	$-0.223568\pi$
$127$	−1.25536	−	1.81871i	−0.111396	−	0.161384i	−0.874716	+	0.484635i	$0.838952\pi$
$128$	0.885456	+	0.464723i	0.0782640	+	0.0410761i
$129$	−7.11254	+	3.73295i	−0.626225	+	0.328668i
$130$	1.61679	−	2.34233i	0.141802	−	0.205436i
$131$	−11.8164	−	10.4684i	−1.03241	−	0.914632i	−0.0360015	−	0.999352i	$-0.511462\pi$
$131$	−11.8164	−	10.4684i	−1.03241	−	0.914632i	−0.996405	+	0.0847196i	$0.973001\pi$
$132$	11.8883	−	2.93020i	1.03474	−	0.255041i
$133$	0.365056	−	3.00650i	0.0316543	−	0.260697i
$134$	0.564867			0.0487971
$135$	0.735310			0.0632854
$136$	0.886735	−	7.30292i	0.0760369	−	0.626220i
$137$	8.22920	+	4.31902i	0.703068	+	0.368998i	0.778064	−	0.628185i	$-0.216202\pi$
$137$	8.22920	+	4.31902i	0.703068	+	0.368998i	−0.0749959	+	0.997184i	$0.523894\pi$
$138$	6.08234	+	16.0378i	0.517763	+	1.36523i
$139$	1.02104	+	8.40902i	0.0866035	+	0.713244i	0.969742	+	0.244132i	$0.0785029\pi$
$139$	1.02104	+	8.40902i	0.0866035	+	0.713244i	−0.883139	+	0.469112i	$0.844574\pi$
$140$	−0.463439	−	3.81677i	−0.0391678	−	0.322576i
$141$	11.7149	−	30.8897i	0.986574	−	2.60138i
$142$	−1.27308	−	1.12785i	−0.106834	−	0.0946468i
$143$	−10.9109	+	5.72649i	−0.912416	+	0.478873i
$144$	−1.15601	−	3.04816i	−0.0963345	−	0.254013i
$145$	1.64894	−	4.34790i	0.136937	−	0.361073i
$146$	−8.66371	+	12.5515i	−0.717013	+	1.03877i
$147$	8.55915	+	7.58274i	0.705947	+	0.625414i
$148$	−1.50474	−	0.370884i	−0.123689	−	0.0304865i
$149$	−13.5483	−	7.11069i	−1.10992	−	0.582530i	−0.192837	−	0.981231i	$-0.561769\pi$
$149$	−13.5483	−	7.11069i	−1.10992	−	0.582530i	−0.917081	+	0.398700i	$0.869461\pi$
$150$	−9.04276	+	2.22884i	−0.738338	+	0.181984i
$151$	0.0943299	+	0.0232502i	0.00767646	+	0.00189208i	0.243152	−	0.969988i	$-0.421819\pi$
$151$	0.0943299	+	0.0232502i	0.00767646	+	0.00189208i	−0.235476	+	0.971880i	$0.575665\pi$
$152$	−0.315727	−	0.832505i	−0.0256089	−	0.0675250i
$153$	−17.9511	+	15.9033i	−1.45126	+	1.28570i
$154$	−5.90277	+	15.5643i	−0.475658	+	1.25421i
$155$	3.69640	+	0.911080i	0.296902	+	0.0731797i
$156$	3.57883	+	5.18482i	0.286535	+	0.415118i
$157$	3.76503			0.300482			0.150241	−	0.988649i	$-0.451995\pi$
$157$	3.76503			0.300482			0.150241	+	0.988649i	$0.451995\pi$
$158$	−5.47801	+	6.99938i	−0.435807	+	0.556841i
$159$	0.715927			0.0567767
$160$	−0.642095	−	0.930235i	−0.0507621	−	0.0735415i
$161$	−22.6415	−	5.58062i	−1.78440	−	0.439814i
$162$	2.89087	−	7.62261i	0.227129	−	0.598889i
$163$	17.7159	−	15.6949i	1.38762	−	1.22932i	0.444964	−	0.895548i	$-0.353216\pi$
$163$	17.7159	−	15.6949i	1.38762	−	1.22932i	0.942653	−	0.333773i	$-0.108322\pi$
$164$	0.430296	+	1.13460i	0.0336004	+	0.0885971i
$165$	−13.4376	−	3.31206i	−1.04611	−	0.257844i
$166$	−10.1284	+	2.49644i	−0.786119	+	0.193761i
$167$	−12.2442	−	6.42624i	−0.947482	−	0.497277i	−0.0811263	−	0.996704i	$-0.525852\pi$
$167$	−12.2442	−	6.42624i	−0.947482	−	0.497277i	−0.866356	+	0.499427i	$0.833544\pi$
$168$	8.26329	+	2.03672i	0.637527	+	0.157136i
$169$	4.98485	+	4.41619i	0.383450	+	0.339707i
$170$	−4.72361	+	6.84333i	−0.362284	+	0.524859i
$171$	−1.02927	+	2.71397i	−0.0787104	+	0.207542i
$172$	−1.13845	−	3.00186i	−0.0868063	−	0.228889i
$173$	13.3844	−	7.02470i	1.01760	−	0.534078i	0.128461	−	0.991715i	$-0.458996\pi$
$173$	13.3844	−	7.02470i	1.01760	−	0.534078i	0.889139	+	0.457636i	$0.151304\pi$
$174$	7.70449	+	6.82558i	0.584076	+	0.517446i
$175$	4.48991	−	11.8389i	0.339405	−	0.894938i
$176$	0.589872	+	4.85803i	0.0444633	+	0.366188i
$177$	−3.80057	−	31.3005i	−0.285668	−	2.35269i
$178$	4.76337	+	12.5600i	0.357029	+	0.941409i
$179$	5.14776	+	2.70175i	0.384761	+	0.201938i	0.646003	−	0.763335i	$-0.276440\pi$
$179$	5.14776	+	2.70175i	0.384761	+	0.201938i	−0.261241	+	0.965274i	$0.584132\pi$
$180$	−0.444159	+	3.65798i	−0.0331057	+	0.272650i
$181$	−9.19338			−0.683339			−0.341669	−	0.939820i	$-0.610992\pi$
$181$	−9.19338			−0.683339			−0.341669	+	0.939820i	$0.610992\pi$
$182$	−8.56501			−0.634881
$183$	−1.55717	+	12.8244i	−0.115109	+	0.948009i
$184$	−6.65629	+	1.64063i	−0.490708	+	0.120949i
$185$	1.31119	+	1.16162i	0.0964008	+	0.0854037i
$186$	−4.78706	+	6.93526i	−0.351005	+	0.508518i
$187$	31.8772	−	16.7304i	2.33109	−	1.22345i
$188$	11.6916	+	6.13623i	0.852698	+	0.447530i
$189$	−1.25701	−	1.82109i	−0.0914341	−	0.132465i
$190$	−0.121308	+	0.999058i	−0.00880058	+	0.0724793i
$191$	−2.66880	−	3.86643i	−0.193108	−	0.279765i	0.714455	−	0.699681i	$-0.246675\pi$
$191$	−2.66880	−	3.86643i	−0.193108	−	0.279765i	−0.907563	+	0.419917i	$0.862059\pi$
$192$	2.42930	−	0.598768i	0.175319	−	0.0432123i
$193$	−13.0765	+	6.86309i	−0.941269	+	0.494016i	−0.864277	−	0.503015i	$-0.832224\pi$
$193$	−13.0765	+	6.86309i	−0.941269	+	0.494016i	−0.0769920	+	0.997032i	$0.524532\pi$
$194$	3.53228	−	3.12933i	0.253603	−	0.224673i
$195$	−0.858348	−	7.06913i	−0.0614676	−	0.506231i
$196$	−3.42092	+	3.03067i	−0.244352	+	0.216477i
$197$	−2.98730	+	4.32785i	−0.212836	+	0.308347i	−0.914832	−	0.403834i	$-0.867677\pi$
$197$	−2.98730	+	4.32785i	−0.212836	+	0.308347i	0.701996	+	0.712181i	$0.252293\pi$
$198$	9.06264	−	13.1295i	0.644054	−	0.933073i
$199$	−9.84830	+	8.72483i	−0.698128	+	0.618487i	−0.935664	−	0.352891i	$-0.885198\pi$
$199$	−9.84830	+	8.72483i	−0.698128	+	0.618487i	0.237537	+	0.971379i	$0.423660\pi$
$200$	−0.448683	−	3.69524i	−0.0317267	−	0.261293i
$201$	1.05787	−	0.937189i	0.0746162	−	0.0661042i
$202$	10.9870	−	5.76640i	0.773039	−	0.405722i
$203$	−13.5870	+	3.34890i	−0.953622	+	0.235047i
$204$	−10.4559	−	15.1479i	−0.732057	−	1.06057i
$205$	0.165327	−	1.36159i	0.0115469	−	0.0950974i
$206$	−7.56712	−	10.9629i	−0.527226	−	0.763819i
$207$	19.7890	+	10.3861i	1.37543	+	0.721882i
$208$	−2.22958	+	1.17017i	−0.154593	+	0.0811368i
$209$	2.47516	−	3.58589i	0.171211	−	0.248041i
$210$	−7.20044	−	6.37903i	−0.496878	−	0.440195i
$211$	2.99255	−	0.737598i	0.206016	−	0.0507784i	−0.134957	−	0.990851i	$-0.543090\pi$
$211$	2.99255	−	0.737598i	0.206016	−	0.0507784i	0.340973	+	0.940073i	$0.389244\pi$
$212$	−0.0344906	+	0.284056i	−0.00236882	+	0.0195090i
$213$	−4.25543			−0.291577
$214$	−2.57192			−0.175813
$215$	−0.437412	+	3.60242i	−0.0298313	+	0.245683i
$216$	−0.576018	−	0.302317i	−0.0391930	−	0.0205701i
$217$	−4.06257	−	10.7121i	−0.275785	−	0.727186i
$218$	−2.15698	−	17.7643i	−0.146089	−	1.20315i
$219$	4.59952	+	37.8804i	0.310807	+	2.55972i
$220$	1.96148	−	5.17201i	0.132243	−	0.348697i
$221$	13.8653	+	12.2836i	0.932679	+	0.826281i
$222$	−3.43338	+	1.80198i	−0.230433	+	0.120941i
$223$	7.70003	+	20.3033i	0.515632	+	1.35961i	0.899782	+	0.436340i	$0.143726\pi$
$223$	7.70003	+	20.3033i	0.515632	+	1.35961i	−0.384149	+	0.923271i	$0.625505\pi$
$224$	−1.20619	+	3.18047i	−0.0805922	+	0.212504i
$225$	−6.89345	+	9.98688i	−0.459563	+	0.665792i
$226$	1.98779	+	1.76103i	0.132226	+	0.117142i
$227$	−4.16122	−	1.02565i	−0.276190	−	0.0680746i	0.0987880	−	0.995109i	$-0.468503\pi$
$227$	−4.16122	−	1.02565i	−0.276190	−	0.0680746i	−0.374978	+	0.927034i	$0.622350\pi$
$228$	−1.97252	−	1.03526i	−0.130633	−	0.0685617i
$229$	12.3892	−	3.05367i	0.818702	−	0.201792i	0.192344	−	0.981328i	$-0.438391\pi$
$229$	12.3892	−	3.05367i	0.818702	−	0.201792i	0.626358	+	0.779536i	$0.284545\pi$
$230$	7.52373	+	1.85443i	0.496100	+	0.122278i
$231$	14.7687	+	38.9419i	0.971711	+	2.56219i
$232$	−3.07933	+	2.72805i	−0.202168	+	0.179105i
$233$	7.67189	−	20.2291i	0.502602	−	1.32525i	−0.408381	−	0.912811i	$-0.633907\pi$
$233$	7.67189	−	20.2291i	0.502602	−	1.32525i	0.910984	−	0.412442i	$-0.135324\pi$
$234$	7.97016	+	1.96447i	0.521025	+	0.128421i
$235$	−8.47825	−	12.2829i	−0.553060	−	0.801246i
$236$	12.6021			0.820326
$237$	1.35383	+	22.1970i	0.0879406	+	1.44185i
$238$	25.0234			1.62203
$239$	−1.67312	−	2.42393i	−0.108225	−	0.156791i	0.765129	−	0.643877i	$-0.222675\pi$
$239$	−1.67312	−	2.42393i	−0.108225	−	0.156791i	−0.873354	+	0.487086i	$0.838060\pi$
$240$	−2.74588	−	0.676799i	−0.177246	−	0.0436872i
$241$	3.24865	−	8.56599i	0.209264	−	0.551784i	−0.788754	−	0.614709i	$-0.789274\pi$
$241$	3.24865	−	8.56599i	0.209264	−	0.551784i	0.998018	+	0.0629249i	$0.0200428\pi$
$242$	−9.69204	+	8.58640i	−0.623028	+	0.551954i
$243$	−7.92501	−	20.8965i	−0.508390	−	1.34051i
$244$	−5.01328	−	1.23566i	−0.320942	−	0.0791052i
$245$	5.01579	−	1.23628i	0.320447	−	0.0789832i
$246$	2.68829	+	1.41092i	0.171399	+	0.0899573i
$247$	2.17679	+	0.536530i	0.138506	+	0.0341386i
$248$	−2.52105	−	2.23346i	−0.160087	−	0.141825i
$249$	−14.8264	+	21.4797i	−0.939582	+	1.36122i
$250$	−3.49608	+	9.21840i	−0.221111	+	0.583023i
$251$	6.96234	+	18.3582i	0.439459	+	1.15876i	0.953606	+	0.301057i	$0.0973393\pi$
$251$	6.96234	+	18.3582i	0.439459	+	1.15876i	−0.514147	+	0.857702i	$0.671891\pi$
$252$	9.81878	−	5.15329i	0.618525	−	0.324627i
$253$	−25.1117	−	22.2470i	−1.57876	−	1.39866i
$254$	0.783640	−	2.06629i	0.0491700	−	0.129651i
$255$	2.50774	+	20.6531i	0.157041	+	1.29335i
$256$	0.120537	+	0.992709i	0.00753354	+	0.0620443i
$257$	4.71283	+	12.4267i	0.293978	+	0.775158i	0.997894	+	0.0648733i	$0.0206643\pi$
$257$	4.71283	+	12.4267i	0.293978	+	0.775158i	−0.703915	+	0.710284i	$0.748566\pi$
$258$	−7.11254	−	3.73295i	−0.442808	−	0.232403i
$259$	0.635417	−	5.23313i	0.0394829	−	0.325171i
$260$	2.84614			0.176510
$261$	13.4115			0.830150
$262$	1.90286	−	15.6715i	0.117559	−	0.968188i
$263$	30.9327	−	7.62422i	1.90739	−	0.470129i	0.908789	−	0.417256i	$-0.137008\pi$
$263$	30.9327	−	7.62422i	1.90739	−	0.470129i	0.998601	−	0.0528737i	$-0.0168381\pi$
$264$	9.16482	+	8.11932i	0.564056	+	0.499710i
$265$	0.183730	−	0.266179i	0.0112865	−	0.0163513i
$266$	2.68168	−	1.40745i	0.164424	−	0.0862965i
$267$	29.7594	+	15.6189i	1.82124	+	0.955862i
$268$	0.320881	+	0.464876i	0.0196009	+	0.0283968i
$269$	0.285585	−	2.35200i	0.0174124	−	0.143404i	−0.981410	−	0.191924i	$-0.938527\pi$
$269$	0.285585	−	2.35200i	0.0174124	−	0.143404i	0.998822	+	0.0485198i	$0.0154504\pi$
$270$	0.417703	+	0.605148i	0.0254206	+	0.0368281i
$271$	−7.38638	+	1.82058i	−0.448691	+	0.110592i	−0.457185	−	0.889372i	$-0.651142\pi$
$271$	−7.38638	+	1.82058i	−0.448691	+	0.110592i	0.00849423	+	0.999964i	$0.497296\pi$
$272$	6.51391	−	3.41876i	0.394964	−	0.207293i
$273$	−16.0403	+	14.2105i	−0.970805	+	0.860058i
$274$	1.12024	+	9.22598i	0.0676760	+	0.557362i
$275$	13.6351	−	12.0796i	0.822225	−	0.728428i
$276$	−9.74370	+	14.1162i	−0.586502	+	0.849695i
$277$	6.30772	−	9.13830i	0.378994	−	0.549068i	−0.586347	−	0.810060i	$-0.699434\pi$
$277$	6.30772	−	9.13830i	0.378994	−	0.549068i	0.965341	+	0.260993i	$0.0840498\pi$
$278$	−6.34047	+	5.61717i	−0.380276	+	0.336895i
$279$	1.32349	+	10.8999i	0.0792354	+	0.652562i
$280$	2.87787	−	2.54957i	0.171986	−	0.152366i
$281$	−25.7752	+	13.5279i	−1.53762	+	0.807005i	−0.999360	−	0.0357750i	$-0.988610\pi$
$281$	−25.7752	+	13.5279i	−1.53762	+	0.807005i	−0.538259	+	0.842780i	$0.680918\pi$
$282$	32.0765	−	7.90616i	1.91013	−	0.470805i
$283$	−6.60917	−	9.57503i	−0.392874	−	0.569177i	0.575775	−	0.817608i	$-0.304700\pi$
$283$	−6.60917	−	9.57503i	−0.392874	−	0.569177i	−0.968650	+	0.248431i	$0.920085\pi$
$284$	0.205010	−	1.68841i	0.0121651	−	0.100189i
$285$	1.43039	+	2.07228i	0.0847289	+	0.122751i
$286$	−10.9109	−	5.72649i	−0.645175	−	0.338614i
$287$	−3.65478	+	1.91818i	−0.215735	+	0.113226i
$288$	1.85189	−	2.68293i	0.109124	−	0.158093i
$289$	−27.7840	−	24.6144i	−1.63435	−	1.44791i
$290$	4.51495	−	1.11284i	0.265127	−	0.0653480i
$291$	1.42319	−	11.7210i	0.0834290	−	0.687100i
$292$	−15.2513			−0.892513
$293$	23.7086			1.38507			0.692535	−	0.721384i	$-0.256494\pi$
$293$	23.7086			1.38507			0.692535	+	0.721384i	$0.256494\pi$
$294$	−1.37833	+	11.3515i	−0.0803856	+	0.662035i
$295$	−12.6128	−	6.61969i	−0.734344	−	0.385413i
$296$	−0.549556	−	1.44906i	−0.0319423	−	0.0842249i
$297$	−0.383731	−	3.16031i	−0.0222663	−	0.183380i
$298$	−1.84432	−	15.1894i	−0.106839	−	0.879895i
$299$	6.12123	−	16.1404i	0.354000	−	0.933421i
$300$	−6.97117	−	6.17592i	−0.402481	−	0.356567i
$301$	9.66963	−	5.07501i	0.557348	−	0.292519i
$302$	0.0344509	+	0.0908396i	0.00198243	+	0.00522723i
$303$	11.0089	−	29.0280i	0.632442	−	1.66761i
$304$	0.505784	−	0.732755i	0.0290087	−	0.0420264i
$305$	4.36846	+	3.87012i	0.250137	+	0.221602i
$306$	−23.2855	−	5.73937i	−1.33115	−	0.328098i
$307$	27.6741	+	14.5245i	1.57945	+	0.828958i	0.999902	+	0.0140172i	$0.00446196\pi$
$307$	27.6741	+	14.5245i	1.57945	+	0.828958i	0.579545	+	0.814940i	$0.303230\pi$
$308$	−16.1623	+	3.98366i	−0.920934	+	0.226990i
$309$	−32.3604	−	7.97612i	−1.84092	−	0.453745i
$310$	1.34999	+	3.55963i	0.0766742	+	0.202173i
$311$	−25.0270	+	22.1720i	−1.41915	+	1.25726i	−0.498487	+	0.866897i	$0.666111\pi$
$311$	−25.0270	+	22.1720i	−1.41915	+	1.25726i	−0.920662	+	0.390360i	$0.872351\pi$
$312$	−2.23402	+	5.89063i	−0.126477	+	0.333491i
$313$	−11.5650	−	2.85051i	−0.653692	−	0.161121i	−0.101497	−	0.994836i	$-0.532363\pi$
$313$	−11.5650	−	2.85051i	−0.653692	−	0.161121i	−0.552195	+	0.833715i	$0.686209\pi$
$314$	2.13878	+	3.09856i	0.120698	+	0.174862i
$315$	−12.5341			−0.706215
$316$	−8.87225	−	0.532213i	−0.499103	−	0.0299393i
$317$	−11.1463			−0.626041			−0.313020	−	0.949746i	$-0.601341\pi$
$317$	−11.1463			−0.626041			−0.313020	+	0.949746i	$0.601341\pi$
$318$	0.406693	+	0.589196i	0.0228062	+	0.0330405i
$319$	−19.5475	−	4.81802i	−1.09445	−	0.269757i
$320$	0.400817	−	1.05687i	0.0224063	−	0.0590807i
$321$	−4.81663	+	4.26716i	−0.268838	+	0.238170i
$322$	−8.26906	−	21.8037i	−0.460816	−	1.21507i
$323$	−6.35968	−	1.56752i	−0.353862	−	0.0872192i
$324$	7.91549	−	1.95099i	0.439749	−	0.108388i
$325$	8.29932	+	4.35582i	0.460364	+	0.241618i
$326$	22.9805	+	5.66417i	1.27277	+	0.313710i
$327$	−33.5129	−	29.6898i	−1.85327	−	1.64185i
$328$	−0.689319	+	0.998650i	−0.0380613	+	0.0551412i
$329$	−15.9266	+	41.9951i	−0.878064	+	2.31526i
$330$	−4.90763	−	12.9404i	−0.270156	−	0.712343i
$331$	−26.3022	+	13.8045i	−1.44570	+	0.758763i	−0.991249	−	0.132008i	$-0.957858\pi$
$331$	−26.3022	+	13.8045i	−1.44570	+	0.758763i	−0.454453	+	0.890771i	$0.650165\pi$
$332$	−7.80813	−	6.91740i	−0.428527	−	0.379642i
$333$	−1.79156	+	4.72394i	−0.0981766	+	0.258871i
$334$	−1.66679	−	13.7273i	−0.0912028	−	0.751123i
$335$	−0.0769603	−	0.633825i	−0.00420479	−	0.0346295i
$336$	3.01790	+	7.95754i	0.164640	+	0.434119i
$337$	−1.99617	−	1.04767i	−0.108739	−	0.0570704i	0.409477	−	0.912320i	$-0.365711\pi$
$337$	−1.99617	−	1.04767i	−0.108739	−	0.0570704i	−0.518216	+	0.855250i	$0.673404\pi$
$338$	−0.802737	+	6.61113i	−0.0436631	+	0.359598i
$339$	6.64446			0.360877
$340$	−8.31526			−0.450959
$341$	1.98674	−	16.3623i	0.107588	−	0.886068i
$342$	−2.81825	+	0.694635i	−0.152393	+	0.0375616i
$343$	6.18618	+	5.48047i	0.334022	+	0.295918i
$344$	1.82376	−	2.64218i	0.0983307	−	0.142457i
$345$	17.1670	−	9.00994i	0.924240	−	0.485079i
$346$	13.3844	+	7.02470i	0.719552	+	0.377650i
$347$	−11.1597	−	16.1676i	−0.599085	−	0.867924i	0.399728	−	0.916634i	$-0.369105\pi$
$347$	−11.1597	−	16.1676i	−0.599085	−	0.867924i	−0.998813	+	0.0487095i	$0.984489\pi$
$348$	−1.24070	+	10.2180i	−0.0665083	+	0.547745i
$349$	−13.9308	−	20.1823i	−0.745701	−	1.08033i	−0.993755	−	0.111588i	$-0.964406\pi$
$349$	−13.9308	−	20.1823i	−0.745701	−	1.08033i	0.248054	−	0.968746i	$-0.420209\pi$
$350$	12.2938	−	3.03015i	0.657131	−	0.161968i
$351$	1.45041	−	0.761235i	0.0774172	−	0.0406317i
$352$	−3.66300	+	3.24513i	−0.195238	+	0.172966i
$353$	2.73539	+	22.5279i	0.145590	+	1.19904i	0.864026	+	0.503448i	$0.167935\pi$
$353$	2.73539	+	22.5279i	0.145590	+	1.19904i	−0.718435	+	0.695594i	$0.755141\pi$
$354$	23.6008	−	20.9085i	1.25437	−	1.11128i
$355$	−1.09208	+	1.58215i	−0.0579617	+	0.0839721i
$356$	−7.63075	+	11.0550i	−0.404429	+	0.585916i
$357$	46.8633	−	41.5172i	2.48027	−	2.19732i
$358$	0.700761	+	5.77129i	0.0370364	+	0.305022i
$359$	6.97080	−	6.17559i	0.367905	−	0.325935i	−0.458833	−	0.888523i	$-0.651732\pi$
$359$	6.97080	−	6.17559i	0.367905	−	0.325935i	0.826738	+	0.562587i	$0.190194\pi$
$360$	−3.26277	+	1.71243i	−0.171963	+	0.0902532i
$361$	17.6782	−	4.35728i	0.930431	−	0.229331i
$362$	−5.22244	−	7.56600i	−0.274485	−	0.397660i
$363$	−3.90502	+	32.1608i	−0.204961	+	1.68800i
$364$	−4.86548	−	7.04886i	−0.255020	−	0.369461i
$365$	15.2642	+	8.01127i	0.798965	+	0.419329i
$366$	−11.4389	+	6.00358i	−0.597919	+	0.313812i
$367$	4.92300	−	7.13220i	0.256979	−	0.372298i	−0.673166	−	0.739492i	$-0.735066\pi$
$367$	4.92300	−	7.13220i	0.256979	−	0.372298i	0.930144	+	0.367194i	$0.119681\pi$
$368$	−5.13141	−	4.54603i	−0.267493	−	0.236978i
$369$	3.84091	−	0.946698i	0.199950	−	0.0492831i
$370$	−0.211148	+	1.73896i	−0.0109771	+	0.0904044i
$371$	−0.973316			−0.0505320
$372$	−8.42697			−0.436918
$373$	0.592284	−	4.87790i	0.0306673	−	0.252568i	−0.969310	−	0.245841i	$-0.920936\pi$
$373$	0.592284	−	4.87790i	0.0306673	−	0.252568i	0.999977	−	0.00672656i	$-0.00214115\pi$
$374$	31.8772	+	16.7304i	1.64833	+	0.865111i
$375$	8.74718	+	23.0644i	0.451703	+	1.19104i
$376$	1.59157	+	13.1078i	0.0820790	+	0.675982i
$377$	−1.24863	−	10.2834i	−0.0643076	−	0.529621i
$378$	0.784668	−	2.06900i	0.0403590	−	0.106418i
$379$	−21.8140	−	19.3255i	−1.12051	−	0.992684i	−0.120508	−	0.992712i	$-0.538452\pi$
$379$	−21.8140	−	19.3255i	−1.12051	−	0.992684i	−1.00000		2.84201e-5i	$0.999991\pi$
$380$	−0.891119	+	0.467695i	−0.0457134	+	0.0239923i
$381$	−1.96067	−	5.16986i	−0.100448	−	0.264860i
$382$	1.66595	−	4.39276i	0.0852376	−	0.224753i
$383$	12.6459	−	18.3208i	0.646177	−	0.936149i	−0.353822	−	0.935313i	$-0.615118\pi$
$383$	12.6459	−	18.3208i	0.646177	−	0.936149i	1.00000		0.000836704i	$-0.000266331\pi$
$384$	1.87277	+	1.65913i	0.0955696	+	0.0846673i
$385$	18.2686	+	4.50281i	0.931054	+	0.229484i
$386$	−13.0765	−	6.86309i	−0.665578	−	0.349322i
$387$	−10.1621	+	2.50472i	−0.516567	+	0.127322i
$388$	4.58195	+	1.12935i	0.232613	+	0.0573340i
$389$	−0.966211	−	2.54769i	−0.0489889	−	0.129173i	0.908288	−	0.418344i	$-0.137389\pi$
$389$	−0.966211	−	2.54769i	−0.0489889	−	0.129173i	−0.957277	+	0.289171i	$0.906620\pi$
$390$	5.33018	−	4.72213i	0.269904	−	0.239114i
$391$	−17.8837	+	47.1555i	−0.904419	+	2.38476i
$392$	−4.43750	−	1.09375i	−0.224128	−	0.0552425i
$393$	−22.4374	−	32.5063i	−1.13182	−	1.63972i
$394$	−5.25873			−0.264931
$395$	8.60021	+	5.19313i	0.432723	+	0.261295i
$396$	15.9535			0.801695
$397$	15.7195	+	22.7736i	0.788937	+	1.14297i	0.986673	+	0.162717i	$0.0520257\pi$
$397$	15.7195	+	22.7736i	0.788937	+	1.14297i	−0.197736	+	0.980255i	$0.563359\pi$
$398$	−12.7749	−	3.14872i	−0.640346	−	0.157831i
$399$	2.68703	−	7.08511i	0.134520	−	0.354699i
$400$	2.78624	−	2.46839i	0.139312	−	0.123420i
$401$	−1.60093	−	4.22131i	−0.0799467	−	0.210802i	0.889083	−	0.457746i	$-0.151343\pi$
$401$	−1.60093	−	4.22131i	−0.0799467	−	0.210802i	−0.969030	+	0.246944i	$0.920574\pi$
$402$	1.37223	+	0.338224i	0.0684406	+	0.0168691i
$403$	8.23441	−	2.02960i	0.410185	−	0.101102i
$404$	10.9870	+	5.76640i	0.546621	+	0.286889i
$405$	−8.94703	−	2.20525i	−0.444582	−	0.109580i
$406$	−10.4744	−	9.27951i	−0.519836	−	0.460534i
$407$	4.30828	−	6.24162i	0.213553	−	0.309385i
$408$	6.52690	−	17.2100i	0.323130	−	0.852023i
$409$	7.47573	+	19.7119i	0.369651	+	0.974689i	0.982792	+	0.184716i	$0.0591365\pi$
$409$	7.47573	+	19.7119i	0.369651	+	0.974689i	−0.613141	+	0.789973i	$0.710094\pi$
$410$	1.21448	−	0.637408i	0.0599789	−	0.0314794i
$411$	17.4051	+	15.4195i	0.858529	+	0.760590i
$412$	4.72365	−	12.4552i	0.232718	−	0.613626i
$413$	5.16695	+	42.5536i	0.254249	+	2.09393i
$414$	2.69387	+	22.1860i	0.132396	+	1.09038i
$415$	4.18114	+	11.0248i	0.205244	+	0.541185i
$416$	−2.22958	−	1.17017i	−0.109314	−	0.0573724i
$417$	−2.55464	+	21.0394i	−0.125101	+	1.03030i
$418$	4.35718			0.213117
$419$	13.2197			0.645823			0.322911	−	0.946429i	$-0.395338\pi$
$419$	13.2197			0.645823			0.322911	+	0.946429i	$0.395338\pi$
$420$	1.15953	−	9.54955i	0.0565790	−	0.465970i
$421$	3.16934	−	0.781171i	0.154464	−	0.0380720i	−0.161325	−	0.986901i	$-0.551577\pi$
$421$	3.16934	−	0.781171i	0.154464	−	0.0380720i	0.315789	+	0.948829i	$0.397731\pi$
$422$	2.30700	+	2.04382i	0.112303	+	0.0994916i
$423$	24.4525	−	35.4255i	1.18892	−	1.72245i
$424$	−0.253366	+	0.132977i	−0.0123045	+	0.00645792i
$425$	−24.2472	−	12.7259i	−1.17616	−	0.617298i
$426$	−2.41736	−	3.50215i	−0.117122	−	0.169680i
$427$	2.11700	−	17.4350i	0.102449	−	0.843741i
$428$	−1.46102	−	2.11665i	−0.0706209	−	0.102312i
$429$	−29.9347	+	7.37823i	−1.44526	+	0.356224i
$430$	−3.21321	+	1.68642i	−0.154955	+	0.0813265i
$431$	−9.40345	+	8.33073i	−0.452948	+	0.401277i	−0.858515	−	0.512788i	$-0.828613\pi$
$431$	−9.40345	+	8.33073i	−0.452948	+	0.401277i	0.405567	+	0.914065i	$0.367074\pi$
$432$	−0.0784130	−	0.645789i	−0.00377265	−	0.0310705i
$433$	7.65890	−	6.78519i	0.368063	−	0.326075i	−0.458736	−	0.888573i	$-0.651698\pi$
$433$	7.65890	−	6.78519i	0.368063	−	0.326075i	0.826799	+	0.562497i	$0.190159\pi$
$434$	6.50810	−	9.42861i	0.312399	−	0.452588i
$435$	6.60914	−	9.57500i	0.316884	−	0.459086i
$436$	13.3944	−	11.8664i	0.641477	−	0.568299i
$437$	0.735742	+	6.05938i	0.0351953	+	0.289859i
$438$	−28.5622	+	25.3039i	−1.36475	+	1.20907i
$439$	9.12759	−	4.79053i	0.435636	−	0.228640i	−0.232625	−	0.972567i	$-0.574731\pi$
$439$	9.12759	−	4.79053i	0.435636	−	0.228640i	0.668261	+	0.743927i	$0.267039\pi$
$440$	5.37073	−	1.32377i	0.256039	−	0.0631080i
$441$	8.46372	+	12.2618i	0.403034	+	0.583896i
$442$	−2.23280	+	18.3887i	−0.106203	+	0.874663i
$443$	5.40615	+	7.83216i	0.256854	+	0.372117i	0.930103	−	0.367298i	$-0.119717\pi$
$443$	5.40615	+	7.83216i	0.256854	+	0.372117i	−0.673249	+	0.739416i	$0.735102\pi$
$444$	−3.43338	−	1.80198i	−0.162941	−	0.0855180i
$445$	13.4443	−	7.05610i	0.637320	−	0.334491i
$446$	−12.3352	+	17.8706i	−0.584088	+	0.846198i
$447$	−28.6551	−	25.3862i	−1.35534	−	1.20073i
$448$	−3.30267	+	0.814036i	−0.156037	+	0.0384596i
$449$	0.826227	−	6.80459i	0.0389921	−	0.321129i	−0.960142	−	0.279514i	$-0.909827\pi$
$449$	0.826227	−	6.80459i	0.0389921	−	0.321129i	0.999134	−	0.0416148i	$-0.0132502\pi$
$450$	−12.1350			−0.572048
$451$	−5.93828			−0.279623
$452$	−0.320104	+	2.63629i	−0.0150564	+	0.124001i
$453$	0.215234	+	0.112963i	0.0101126	+	0.00530748i
$454$	−1.51975	−	4.00725i	−0.0713253	−	0.188069i
$455$	1.16694	+	9.61061i	0.0547070	+	0.450552i
$456$	−0.268518	−	2.21145i	−0.0125745	−	0.103561i
$457$	0.157534	−	0.415384i	0.00736914	−	0.0194308i	−0.931281	−	0.364301i	$-0.881308\pi$
$457$	0.157534	−	0.415384i	0.00736914	−	0.0194308i	0.938650	+	0.344870i	$0.112077\pi$
$458$	9.55099	+	8.46144i	0.446288	+	0.395377i
$459$	−4.23751	+	2.22402i	−0.197790	+	0.103808i
$460$	2.74780	+	7.24535i	0.128117	+	0.337816i
$461$	−3.29788	+	8.69578i	−0.153597	+	0.405003i	−0.989623	−	0.143687i	$-0.954104\pi$
$461$	−3.29788	+	8.69578i	−0.153597	+	0.405003i	0.836026	+	0.548690i	$0.184873\pi$
$462$	−23.6590	+	34.2760i	−1.10072	+	1.59466i
$463$	−4.86977	−	4.31424i	−0.226317	−	0.200500i	0.542342	−	0.840158i	$-0.317538\pi$
$463$	−4.86977	−	4.31424i	−0.226317	−	0.200500i	−0.768660	+	0.639658i	$0.779076\pi$
$464$	−3.99440	−	0.984532i	−0.185435	−	0.0457057i
$465$	8.43412	+	4.42657i	0.391123	+	0.205277i
$466$	21.0064	−	5.17761i	0.973101	−	0.239848i
$467$	12.5635	+	3.09662i	0.581368	+	0.143294i	0.519023	−	0.854760i	$-0.326296\pi$
$467$	12.5635	+	3.09662i	0.581368	+	0.143294i	0.0623449	+	0.998055i	$0.480142\pi$
$468$	2.91084	+	7.67525i	0.134554	+	0.354789i
$469$	−1.43819	+	1.27413i	−0.0664095	+	0.0588337i
$470$	5.29240	−	13.9549i	0.244120	−	0.643693i
$471$	9.14637	+	2.25438i	0.421442	+	0.103876i
$472$	7.15880	+	10.3713i	0.329510	+	0.477378i
$473$	15.7112			0.722401
$474$	−17.4987	+	13.7235i	−0.803743	+	0.630342i
$475$	−3.31427			−0.152069
$476$	14.2149	+	20.5939i	0.651541	+	0.943920i
$477$	0.905718	+	0.223239i	0.0414700	+	0.0102214i
$478$	1.04442	−	2.75390i	0.0477706	−	0.125961i
$479$	3.95579	−	3.50452i	0.180745	−	0.160126i	−0.567899	−	0.823098i	$-0.692244\pi$
$479$	3.95579	−	3.50452i	0.180745	−	0.160126i	0.748644	+	0.662972i	$0.230705\pi$
$480$	−1.00284	−	2.64428i	−0.0457734	−	0.120694i
$481$	3.78892	+	0.933886i	0.172760	+	0.0425815i
$482$	8.89511	−	2.19245i	0.405161	−	0.0998633i
$483$	−51.6613	−	27.1140i	−2.35067	−	1.23373i
$484$	−12.5722	−	3.09876i	−0.571462	−	0.140853i
$485$	−3.99261	−	3.53714i	−0.181295	−	0.160613i
$486$	12.6956	−	18.3928i	0.575884	−	0.834312i
$487$	−6.72231	+	17.7253i	−0.304617	+	0.803209i	0.692066	+	0.721834i	$0.256700\pi$
$487$	−6.72231	+	17.7253i	−0.304617	+	0.803209i	−0.996684	+	0.0813754i	$0.974069\pi$
$488$	−1.83094	−	4.82779i	−0.0828827	−	0.218544i
$489$	52.4348	−	27.5199i	2.37118	−	1.24449i
$490$	3.86674	+	3.42563i	0.174681	+	0.154754i
$491$	−3.90214	+	10.2891i	−0.176101	+	0.464340i	−0.993784	−	0.111329i	$-0.964489\pi$
$491$	−3.90214	+	10.2891i	−0.176101	+	0.464340i	0.817683	+	0.575669i	$0.195258\pi$
$492$	0.365956	+	3.01392i	0.0164986	+	0.135878i
$493$	3.64798	+	30.0438i	0.164297	+	1.35311i
$494$	0.795001	+	2.09624i	0.0357688	+	0.0943145i
$495$	−15.9671	−	8.38016i	−0.717666	−	0.376660i
$496$	0.405979	−	3.34354i	0.0182290	−	0.150129i
$497$	5.78534			0.259508
$498$	−26.0998			−1.16956
$499$	1.38270	−	11.3875i	0.0618981	−	0.509777i	−0.928479	−	0.371384i	$-0.878883\pi$
$499$	1.38270	−	11.3875i	0.0618981	−	0.509777i	0.990377	−	0.138393i	$-0.0441936\pi$
$500$	−9.57259	+	2.35943i	−0.428099	+	0.105517i
$501$	−25.8969	−	22.9427i	−1.15699	−	1.02500i
$502$	−11.1534	+	16.1585i	−0.497802	+	0.721191i
$503$	−11.0316	+	5.78983i	−0.491875	+	0.258156i	−0.692375	−	0.721538i	$-0.743436\pi$
$503$	−11.0316	+	5.78983i	−0.491875	+	0.258156i	0.200500	+	0.979694i	$0.435743\pi$
$504$	9.81878	+	5.15329i	0.437363	+	0.229546i
$505$	−7.96727	−	11.5426i	−0.354539	−	0.513638i
$506$	4.04386	−	33.3042i	0.179772	−	1.48055i
$507$	9.46540	+	13.7130i	0.420373	+	0.609016i
$508$	2.14568	−	0.528863i	0.0951992	−	0.0234645i
$509$	2.36319	−	1.24030i	0.104747	−	0.0549753i	−0.411536	−	0.911393i	$-0.635008\pi$
$509$	2.36319	−	1.24030i	0.104747	−	0.0549753i	0.516283	+	0.856418i	$0.327315\pi$
$510$	−15.5726	+	13.7961i	−0.689567	+	0.610903i
$511$	−6.25313	−	51.4992i	−0.276622	−	2.27819i
$512$	−0.748511	+	0.663123i	−0.0330798	+	0.0293062i
$513$	−0.329029	+	0.476681i	−0.0145270	+	0.0210460i
$514$	−7.54980	+	10.9378i	−0.333007	+	0.482444i
$515$	−11.2702	+	9.98454i	−0.496625	+	0.439971i
$516$	−0.968227	−	7.97407i	−0.0426238	−	0.351039i
$517$	−48.3664	+	42.8489i	−2.12715	+	1.88449i
$518$	4.66774	−	2.44982i	0.205089	−	0.107639i
$519$	36.7210	−	9.05090i	1.61187	−	0.397291i
$520$	1.61679	+	2.34233i	0.0709011	+	0.102718i
$521$	−2.89575	+	23.8486i	−0.126865	+	1.04483i	0.780697	+	0.624909i	$0.214864\pi$
$521$	−2.89575	+	23.8486i	−0.126865	+	1.04483i	−0.907562	+	0.419918i	$0.862059\pi$
$522$	7.61859	+	11.0374i	0.333457	+	0.483095i
$523$	36.5381	+	19.1767i	1.59770	+	0.838538i	0.999303	+	0.0373399i	$0.0118884\pi$
$523$	36.5381	+	19.1767i	1.59770	+	0.838538i	0.598399	+	0.801198i	$0.295804\pi$
$524$	13.9783	−	7.33639i	0.610646	−	0.320492i
$525$	17.9961	−	26.0718i	0.785413	−	1.13787i
$526$	23.8464	+	21.1260i	1.03975	+	0.921139i
$527$	−24.0576	+	5.92966i	−1.04796	+	0.258300i
$528$	−1.47586	+	12.1548i	−0.0642285	+	0.528970i
$529$	23.9978			1.04338
$530$	0.323432			0.0140490
$531$	4.95199	−	40.7833i	0.214898	−	1.76984i
$532$	2.68168	+	1.40745i	0.116266	+	0.0610209i
$533$	−1.08348	−	2.85691i	−0.0469309	−	0.123747i
$534$	4.05113	+	33.3640i	0.175309	+	1.44380i
$535$	0.350411	+	2.88590i	0.0151496	+	0.124768i
$536$	−0.200305	+	0.528160i	−0.00865184	+	0.0228130i
$537$	10.8877	+	9.64566i	0.469839	+	0.416241i
$538$	2.09789	−	1.10106i	0.0904465	−	0.0474700i
$539$	−7.93101	−	20.9123i	−0.341613	−	0.900759i
$540$	−0.260744	+	0.687526i	−0.0112207	+	0.0295864i
$541$	21.1699	−	30.6699i	0.910165	−	1.31860i	−0.0374877	−	0.999297i	$-0.511936\pi$
$541$	21.1699	−	30.6699i	0.910165	−	1.31860i	0.947652	−	0.319304i	$-0.103449\pi$
$542$	−5.69425	−	5.04467i	−0.244589	−	0.216687i
$543$	−22.3334	−	5.50470i	−0.958420	−	0.236229i
$544$	6.51391	+	3.41876i	0.279282	+	0.146578i
$545$	−19.6391	+	4.84059i	−0.841245	+	0.207348i
$546$	−20.8069	−	5.12845i	−0.890455	−	0.219477i
$547$	8.06908	+	21.2764i	0.345009	+	0.909714i	0.989426	+	0.145039i	$0.0463309\pi$
$547$	8.06908	+	21.2764i	0.345009	+	0.909714i	−0.644417	+	0.764674i	$0.722900\pi$
$548$	−6.95646	+	6.16289i	−0.297165	+	0.263266i
$549$	−5.96887	+	15.7386i	−0.254745	+	0.671707i
$550$	17.6869	+	4.35943i	0.754173	+	0.185887i
$551$	2.08077	+	3.01451i	0.0886438	+	0.128423i
$552$	−17.1524			−0.730057
$553$	−1.84055	−	30.1773i	−0.0782683	−	1.28327i
$554$	11.1039			0.471758
$555$	2.48974	+	3.60701i	0.105684	+	0.153109i
$556$	−8.22463	−	2.02719i	−0.348802	−	0.0859720i
$557$	−10.0762	+	26.5687i	−0.426942	+	1.12575i	0.533139	+	0.846028i	$0.321012\pi$
$557$	−10.0762	+	26.5687i	−0.426942	+	1.12575i	−0.960080	+	0.279724i	$0.909757\pi$
$558$	−8.21865	+	7.28109i	−0.347923	+	0.308233i
$559$	2.86662	+	7.55867i	0.121245	+	0.319697i
$560$	3.73308	+	0.920121i	0.157751	+	0.0388822i
$561$	87.4568	−	21.5562i	3.69243	−	0.910102i
$562$	−25.7752	−	13.5279i	−1.08726	−	0.570638i
$563$	10.3603	+	2.55358i	0.436634	+	0.107621i	0.451505	−	0.892269i	$-0.350887\pi$
$563$	10.3603	+	2.55358i	0.436634	+	0.107621i	−0.0148704	+	0.999889i	$0.504734\pi$
$564$	24.7282	+	21.9073i	1.04124	+	0.922462i
$565$	1.70518	−	2.47039i	0.0717376	−	0.103930i
$566$	4.12566	−	10.8785i	0.173415	−	0.457257i
$567$	9.83335	+	25.9284i	0.412962	+	1.08889i
$568$	1.50599	−	0.790407i	0.0631901	−	0.0331647i
$569$	−8.58528	−	7.60589i	−0.359914	−	0.318856i	0.463716	−	0.885984i	$-0.346516\pi$
$569$	−8.58528	−	7.60589i	−0.359914	−	0.318856i	−0.823629	+	0.567128i	$0.808054\pi$
$570$	−0.892896	+	2.35437i	−0.0373993	+	0.0986138i
$571$	1.67924	+	13.8298i	0.0702740	+	0.578759i	0.984732	+	0.174078i	$0.0556944\pi$
$571$	1.67924	+	13.8298i	0.0702740	+	0.578759i	−0.914458	+	0.404681i	$0.867383\pi$
$572$	−1.48530	−	12.2325i	−0.0621034	−	0.511467i
$573$	−4.16822	−	10.9907i	−0.174130	−	0.459143i
$574$	−3.65478	−	1.91818i	−0.152548	−	0.0800632i
$575$	−3.07594	+	25.3327i	−0.128276	+	1.05645i
$576$	3.26000			0.135834
$577$	−10.5822			−0.440541			−0.220270	−	0.975439i	$-0.570694\pi$
$577$	−10.5822			−0.440541			−0.220270	+	0.975439i	$0.570694\pi$
$578$	4.47420	−	36.8483i	0.186102	−	1.53269i
$579$	−35.8762	+	8.84268i	−1.49096	+	0.367489i
$580$	3.48063	+	3.08357i	0.144525	+	0.128038i
$581$	20.1567	−	29.2020i	0.836241	−	1.21150i
$582$	10.4547	−	5.48705i	0.433361	−	0.227446i
$583$	−1.23990	−	0.650750i	−0.0513514	−	0.0269513i
$584$	−8.66371	−	12.5515i	−0.358507	−	0.519387i
$585$	1.11839	−	9.21079i	0.0462398	−	0.380819i
$586$	13.4680	+	19.5118i	0.556358	+	0.806024i
$587$	34.5648	−	8.51947i	1.42664	−	0.351636i	0.550964	−	0.834529i	$-0.314260\pi$
$587$	34.5648	−	8.51947i	1.42664	−	0.351636i	0.875679	+	0.482893i	$0.160414\pi$
$588$	−10.1251	+	5.31406i	−0.417552	+	0.219148i
$589$	−2.24465	+	1.98859i	−0.0924894	+	0.0819384i
$590$	−1.71697	−	14.1405i	−0.0706865	−	0.582156i
$591$	−9.84842	+	8.72494i	−0.405110	+	0.358896i
$592$	0.880370	−	1.27544i	0.0361830	−	0.0524201i
$593$	0.730332	−	1.05807i	0.0299912	−	0.0434497i	−0.807701	−	0.589592i	$-0.799289\pi$
$593$	0.730332	−	1.05807i	0.0299912	−	0.0434497i	0.837693	+	0.546142i	$0.183904\pi$
$594$	2.38290	−	2.11106i	0.0977715	−	0.0866180i
$595$	−3.40932	−	28.0783i	−0.139768	−	1.15110i
$596$	11.4529	−	10.1464i	0.469129	−	0.415612i
$597$	−29.1486	+	15.2984i	−1.19297	+	0.626120i
$598$	16.7605	−	4.13110i	0.685388	−	0.168933i
$599$	15.2345	+	22.0710i	0.622466	+	0.901797i	0.999704	−	0.0243189i	$-0.00774170\pi$
$599$	15.2345	+	22.0710i	0.622466	+	0.901797i	−0.377239	+	0.926116i	$0.623126\pi$
$600$	1.12260	−	9.24548i	0.0458302	−	0.377445i
$601$	−6.85698	−	9.93405i	−0.279702	−	0.405218i	0.657803	−	0.753190i	$-0.271486\pi$
$601$	−6.85698	−	9.93405i	−0.279702	−	0.405218i	−0.937505	+	0.347972i	$0.886871\pi$
$602$	9.66963	+	5.07501i	0.394105	+	0.206842i
$603$	1.63054	−	0.855773i	0.0664007	−	0.0348498i
$604$	−0.0551892	+	0.0799553i	−0.00224562	+	0.00325334i
$605$	10.9551	+	9.70537i	0.445388	+	0.394579i
$606$	30.1433	−	7.42965i	1.22449	−	0.301809i
$607$	1.87317	−	15.4269i	0.0760295	−	0.626160i	−0.904032	−	0.427465i	$-0.859407\pi$
$607$	1.87317	−	15.4269i	0.0760295	−	0.626160i	0.980061	−	0.198695i	$-0.0636702\pi$
$608$	0.890364			0.0361090
$609$	−35.0121			−1.41876
$610$	−0.703476	+	5.79365i	−0.0284829	+	0.234578i
$611$	−29.4394	−	15.4510i	−1.19099	−	0.625081i
$612$	−8.50428	−	22.4240i	−0.343765	−	0.906435i
$613$	−2.35733	−	19.4143i	−0.0952115	−	0.784137i	−0.959611	−	0.281331i	$-0.909224\pi$
$613$	−2.35733	−	19.4143i	−0.0952115	−	0.784137i	0.864399	−	0.502806i	$-0.167699\pi$
$614$	3.76727	+	31.0262i	0.152035	+	1.25212i
$615$	1.21690	−	3.20871i	0.0490702	−	0.129388i
$616$	−12.4597	−	11.0384i	−0.502017	−	0.444748i
$617$	−17.2728	+	9.06545i	−0.695376	+	0.364961i	−0.775085	−	0.631857i	$-0.782293\pi$
$617$	−17.2728	+	9.06545i	−0.695376	+	0.364961i	0.0797093	+	0.996818i	$0.474601\pi$
$618$	−11.8186	−	31.1630i	−0.475413	−	1.25356i
$619$	−9.24353	+	24.3732i	−0.371529	+	0.979641i	0.610685	+	0.791874i	$0.290894\pi$
$619$	−9.24353	+	24.3732i	−0.371529	+	0.979641i	−0.982214	+	0.187767i	$0.939875\pi$
$620$	−2.16263	+	3.13312i	−0.0868535	+	0.125829i
$621$	3.33815	+	2.95734i	0.133955	+	0.118674i
$622$	−32.4641	−	8.00168i	−1.30169	−	0.320838i
$623$	−40.4584	−	21.2342i	−1.62093	−	0.850730i
$624$	−6.11696	+	1.50770i	−0.244875	+	0.0603562i
$625$	−7.25097	−	1.78720i	−0.290039	−	0.0714882i
$626$	−4.22374	−	11.1371i	−0.168814	−	0.445127i
$627$	8.16002	−	7.22915i	0.325880	−	0.288704i
$628$	−1.33510	+	3.52036i	−0.0532762	+	0.140478i
$629$	−11.0697	−	2.72843i	−0.441377	−	0.108790i
$630$	−7.12016	−	10.3153i	−0.283674	−	0.410973i
$631$	4.00126			0.159288			0.0796438	−	0.996823i	$-0.474622\pi$
$631$	4.00126			0.159288			0.0796438	+	0.996823i	$0.474622\pi$
$632$	−4.60201	−	7.60405i	−0.183058	−	0.302473i
$633$	7.71145			0.306503
$634$	−6.33184	−	9.17325i	−0.251470	−	0.364316i
$635$	−2.42531	−	0.597784i	−0.0962454	−	0.0237224i
$636$	−0.253871	+	0.669403i	−0.0100666	+	0.0265436i
$637$	8.61388	−	7.63123i	0.341294	−	0.302360i
$638$	−7.13907	−	18.8242i	−0.282639	−	0.745257i
$639$	−5.38354	−	1.32692i	−0.212969	−	0.0524923i
$640$	1.09747	−	0.270503i	0.0433815	−	0.0106926i
$641$	−29.7080	−	15.5920i	−1.17340	−	0.615846i	−0.238631	−	0.971110i	$-0.576699\pi$
$641$	−29.7080	−	15.5920i	−1.17340	−	0.615846i	−0.934766	+	0.355264i	$0.884391\pi$
$642$	−6.24796	−	1.53998i	−0.246587	−	0.0607783i
$643$	16.9283	+	14.9971i	0.667585	+	0.591429i	0.927328	−	0.374249i	$-0.122099\pi$
$643$	16.9283	+	14.9971i	0.667585	+	0.591429i	−0.259743	+	0.965678i	$0.583638\pi$
$644$	13.2467	−	19.1912i	0.521995	−	0.756240i
$645$	−3.21962	+	8.48943i	−0.126772	+	0.334271i
$646$	−2.32267	−	6.12437i	−0.0913841	−	0.240960i
$647$	−13.9207	+	7.30617i	−0.547281	+	0.287235i	−0.715615	−	0.698495i	$-0.753854\pi$
$647$	−13.9207	+	7.30617i	−0.547281	+	0.287235i	0.168334	+	0.985730i	$0.446161\pi$
$648$	6.10215	+	5.40603i	0.239715	+	0.212369i
$649$	−21.8688	+	57.6634i	−0.858426	+	2.26348i
$650$	1.12978	+	9.30460i	0.0443137	+	0.364956i
$651$	−3.45512	−	28.4555i	−0.135417	−	1.11526i
$652$	8.39286	+	22.1302i	0.328690	+	0.866684i
$653$	−23.3719	−	12.2665i	−0.914614	−	0.480027i	−0.0593610	−	0.998237i	$-0.518906\pi$
$653$	−23.3719	−	12.2665i	−0.914614	−	0.480027i	−0.855253	+	0.518210i	$0.826599\pi$
$654$	5.39675	−	44.4463i	0.211030	−	1.73799i
$655$	−17.8439			−0.697219
$656$	−1.21345			−0.0473773
$657$	−5.99299	+	49.3567i	−0.233809	+	1.92559i
$658$	−43.6086	+	10.7486i	−1.70004	+	0.419023i
$659$	−33.2065	−	29.4184i	−1.29354	−	1.14598i	−0.980560	−	0.196221i	$-0.937133\pi$
$659$	−33.2065	−	29.4184i	−1.29354	−	1.14598i	−0.312984	−	0.949759i	$-0.601329\pi$
$660$	7.86185	−	11.3899i	0.306022	−	0.443350i
$661$	−10.0086	+	5.25292i	−0.389290	+	0.204315i	−0.648001	−	0.761640i	$-0.724395\pi$
$661$	−10.0086	+	5.25292i	−0.389290	+	0.204315i	0.258711	+	0.965955i	$0.416702\pi$
$662$	−26.3022	−	13.8045i	−1.02227	−	0.536526i
$663$	26.3278	+	38.1425i	1.02249	+	1.48133i
$664$	1.25739	−	10.3555i	0.0487960	−	0.401871i
$665$	−1.94464	−	2.81730i	−0.0754099	−	0.109250i
$666$	−4.90545	+	1.20908i	−0.190082	+	0.0468511i
$667$	24.9726	−	13.1067i	0.966944	−	0.507492i
$668$	10.3505	−	9.16972i	0.400472	−	0.354787i
$669$	6.54869	+	53.9333i	0.253187	+	2.08518i
$670$	0.477909	−	0.423391i	0.0184632	−	0.0163570i
$671$	14.3537	−	20.7950i	0.554120	−	0.802782i
$672$	−4.83457	+	7.00408i	−0.186497	+	0.270188i
$673$	17.8615	−	15.8239i	0.688510	−	0.609966i	−0.244572	−	0.969631i	$-0.578647\pi$
$673$	17.8615	−	15.8239i	0.688510	−	0.609966i	0.933082	+	0.359665i	$0.117109\pi$
$674$	−0.271738	−	2.23797i	−0.0104670	−	0.0862032i
$675$	−1.81254	+	1.60577i	−0.0697646	+	0.0618061i
$676$	−5.89686	+	3.09491i	−0.226802	+	0.119035i
$677$	16.3760	−	4.03631i	0.629380	−	0.155128i	0.0882924	−	0.996095i	$-0.471859\pi$
$677$	16.3760	−	4.03631i	0.629380	−	0.155128i	0.541087	+	0.840966i	$0.318013\pi$
$678$	3.77448	+	5.46828i	0.144958	+	0.210008i
$679$	−1.93486	+	15.9350i	−0.0742530	+	0.611528i
$680$	−4.72361	−	6.84333i	−0.181142	−	0.262430i
$681$	−9.49470	−	4.98320i	−0.363838	−	0.190957i
$682$	14.5945	−	7.65979i	0.558853	−	0.293309i
$683$	9.79089	−	14.1846i	0.374638	−	0.542757i	−0.589634	−	0.807671i	$-0.700728\pi$
$683$	9.79089	−	14.1846i	0.374638	−	0.542757i	0.964272	+	0.264913i	$0.0853434\pi$
$684$	−2.17262	−	1.92477i	−0.0830722	−	0.0735955i
$685$	10.1996	−	2.51399i	0.389708	−	0.0960545i
$686$	−0.996193	+	8.20439i	−0.0380348	+	0.313245i
$687$	31.9255			1.21803
$688$	3.21048			0.122399
$689$	0.0868472	−	0.715251i	0.00330862	−	0.0272489i
$690$	17.1670	+	9.00994i	0.653537	+	0.343002i
$691$	0.518482	+	1.36712i	0.0197240	+	0.0520078i	0.944517	−	0.328464i	$-0.106531\pi$
$691$	0.518482	+	1.36712i	0.0197240	+	0.0520078i	−0.924793	+	0.380472i	$0.875762\pi$
$692$	1.82202	+	15.0057i	0.0692627	+	0.570430i
$693$	6.54106	+	53.8705i	0.248474	+	2.04637i
$694$	6.96626	−	18.3685i	0.264436	−	0.697260i
$695$	7.16676	+	6.34919i	0.271851	+	0.240839i
$696$	−9.11408	+	4.78344i	−0.345468	+	0.181316i
$697$	3.16549	+	8.34672i	0.119902	+	0.316155i
$698$	8.69609	−	22.9297i	0.329152	−	0.867902i
$699$	30.7498	−	44.5488i	1.16307	−	1.68499i
$700$	9.47744	+	8.39628i	0.358213	+	0.317349i
$701$	3.76095	+	0.926991i	0.142049	+	0.0350120i	0.309699	−	0.950835i	$-0.399772\pi$
$701$	3.76095	+	0.926991i	0.142049	+	0.0350120i	−0.167650	+	0.985847i	$0.553618\pi$
$702$	1.45041	+	0.761235i	0.0547423	+	0.0287310i
$703$	−1.33976	+	0.330222i	−0.0505301	+	0.0124546i
$704$	−4.75151	−	1.17114i	−0.179079	−	0.0441391i
$705$	−13.2416	−	34.9152i	−0.498707	−	1.31498i
$706$	−16.9863	+	15.0485i	−0.639286	+	0.566358i
$707$	−14.9667	+	39.4641i	−0.562882	+	1.48420i
$708$	30.6142	+	7.54572i	1.15055	+	0.283586i
$709$	−20.7746	−	30.0972i	−0.780206	−	1.13032i	−0.988346	−	0.152224i	$-0.951356\pi$
$709$	−20.7746	−	30.0972i	−0.780206	−	1.13032i	0.208140	−	0.978099i	$-0.433259\pi$
$710$	−1.92246			−0.0721487
$711$	−5.20872	+	28.5035i	−0.195342	+	1.06897i
$712$	−13.4329			−0.503419
$713$	13.1166	+	19.0026i	0.491220	+	0.711655i
$714$	60.7894	+	14.9832i	2.27499	+	0.560734i
$715$	−4.93901	+	13.0231i	−0.184708	+	0.487036i
$716$	−4.35160	+	3.85518i	−0.162627	+	0.144075i
$717$	−2.61313	−	6.89027i	−0.0975893	−	0.257322i
$718$	9.04228	+	2.22872i	0.337455	+	0.0831752i
$719$	−37.7289	+	9.29935i	−1.40705	+	0.346807i	−0.868460	−	0.495760i	$-0.834890\pi$
$719$	−37.7289	+	9.29935i	−1.40705	+	0.346807i	−0.538592	+	0.842567i	$0.681044\pi$
$720$	−3.26277	−	1.71243i	−0.121596	−	0.0638187i
$721$	43.9945	+	10.8437i	1.63844	+	0.403840i
$722$	13.6283	+	12.0736i	0.507194	+	0.449334i
$723$	13.0210	−	18.8641i	0.484255	−	0.701565i
$724$	3.26002	−	8.59596i	0.121158	−	0.319466i
$725$	5.43030	+	14.3185i	0.201676	+	0.531777i
$726$	−28.6861	+	15.0556i	−1.06464	+	0.558767i
$727$	27.7223	+	24.5598i	1.02816	+	0.910873i	0.996066	−	0.0886115i	$-0.0282430\pi$
$727$	27.7223	+	24.5598i	1.02816	+	0.910873i	0.0320971	+	0.999485i	$0.489781\pi$
$728$	3.03719	−	8.00842i	0.112566	−	0.296812i
$729$	−3.79205	−	31.2303i	−0.140446	−	1.15668i
$730$	2.07791	+	17.1131i	0.0769068	+	0.633385i
$731$	−8.37510	−	22.0833i	−0.309764	−	0.816781i
$732$	−11.4389	−	6.00358i	−0.422793	−	0.221899i
$733$	1.60964	−	13.2566i	0.0594533	−	0.489642i	−0.932320	−	0.361635i	$-0.882219\pi$
$733$	1.60964	−	13.2566i	0.0594533	−	0.489642i	0.991773	−	0.128007i	$-0.0408581\pi$
$734$	8.66627			0.319878
$735$	12.9251			0.476749
$736$	0.826339	−	6.80551i	0.0304592	−	0.250854i
$737$	−2.68397	+	0.661539i	−0.0988653	+	0.0243681i
$738$	2.96100	+	2.62322i	0.108996	+	0.0965620i
$739$	−26.1912	+	37.9444i	−0.963457	+	1.39581i	−0.0455727	+	0.998961i	$0.514511\pi$
$739$	−26.1912	+	37.9444i	−0.963457	+	1.39581i	−0.917884	+	0.396848i	$0.870104\pi$
$740$	−1.55109	+	0.814072i	−0.0570190	+	0.0299259i
$741$	4.96681	+	2.60678i	0.182460	+	0.0957625i
$742$	−0.552906	−	0.801023i	−0.0202978	−	0.0294065i
$743$	3.67440	−	30.2614i	0.134801	−	1.11018i	−0.755609	−	0.655023i	$-0.772659\pi$
$743$	3.67440	−	30.2614i	0.134801	−	1.11018i	0.890410	−	0.455160i	$-0.150418\pi$
$744$	−4.78706	−	6.93526i	−0.175502	−	0.254259i
$745$	−16.7924	+	4.13895i	−0.615225	+	0.151639i
$746$	4.35089	−	2.28352i	0.159297	−	0.0836056i
$747$	−25.4546	+	22.5508i	−0.931333	+	0.825089i
$748$	4.33943	+	35.7384i	0.158665	+	1.30673i
$749$	6.54829	−	5.80128i	0.239269	−	0.211974i
$750$	−14.0127	+	20.3009i	−0.511671	+	0.741283i
$751$	6.67076	−	9.66427i	0.243420	−	0.352654i	−0.682163	−	0.731200i	$-0.738960\pi$
$751$	6.67076	−	9.66427i	0.243420	−	0.352654i	0.925582	+	0.378546i	$0.123576\pi$
$752$	−9.88337	+	8.75590i	−0.360409	+	0.319295i
$753$	5.92130	+	48.7663i	0.215784	+	1.77714i
$754$	7.75375	−	6.86923i	0.282375	−	0.250163i
$755$	0.0972354	−	0.0510331i	0.00353876	−	0.00185728i
$756$	2.14850	−	0.529557i	0.0781400	−	0.0192598i
$757$	−4.40922	−	6.38785i	−0.160256	−	0.232170i	0.734628	−	0.678470i	$-0.237357\pi$
$757$	−4.40922	−	6.38785i	−0.160256	−	0.232170i	−0.894883	+	0.446300i	$0.852741\pi$
$758$	3.51282	−	28.9307i	0.127591	−	1.05081i
$759$	−47.6829	−	69.0806i	−1.73078	−	2.50747i
$760$	−0.891119	−	0.467695i	−0.0323243	−	0.0169651i
$761$	16.4971	−	8.65834i	0.598019	−	0.313865i	−0.138415	−	0.990374i	$-0.544201\pi$
$761$	16.4971	−	8.65834i	0.598019	−	0.313865i	0.736434	+	0.676510i	$0.236508\pi$
$762$	3.14092	−	4.55041i	0.113784	−	0.164844i
$763$	45.5613	+	40.3638i	1.64943	+	1.46127i
$764$	4.56154	−	1.12432i	0.165031	−	0.0406764i
$765$	−3.26748	+	26.9102i	−0.118136	+	0.972939i
$766$	22.2614			0.804338
$767$	−31.7320			−1.14578
$768$	−0.301583	+	2.48376i	−0.0108824	+	0.0896249i
$769$	−25.1259	−	13.1871i	−0.906061	−	0.475538i	−0.0537393	−	0.998555i	$-0.517114\pi$
$769$	−25.1259	−	13.1871i	−0.906061	−	0.475538i	−0.852322	+	0.523017i	$0.824806\pi$
$770$	6.67201	+	17.5927i	0.240443	+	0.633995i
$771$	4.00815	+	33.0101i	0.144350	+	1.18883i
$772$	−1.78010	−	14.6605i	−0.0640673	−	0.527641i
$773$	1.75616	−	4.63061i	0.0631647	−	0.166552i	−0.899718	−	0.436471i	$-0.856228\pi$
$773$	1.75616	−	4.63061i	0.0631647	−	0.166552i	0.962883	+	0.269920i	$0.0869972\pi$
$774$	−7.83406	−	6.94037i	−0.281589	−	0.249466i
$775$	−11.1012	+	5.82638i	−0.398768	+	0.209290i
$776$	1.67341	+	4.41242i	0.0600719	+	0.158396i
$777$	4.67705	−	12.3324i	0.167788	−	0.442421i
$778$	1.54784	−	2.24243i	0.0554926	−	0.0803950i
$779$	0.808700	+	0.716446i	0.0289747	+	0.0256693i
$780$	6.91412	+	1.70418i	0.247565	+	0.0610194i
$781$	7.36990	+	3.86802i	0.263716	+	0.138409i
$782$	−48.9674	+	12.0694i	−1.75107	+	0.431600i
$783$	2.59849	+	0.640470i	0.0928624	+	0.0228885i
$784$	−1.62065	−	4.27331i	−0.0578804	−	0.152618i
$785$	3.18543	−	2.82204i	0.113693	−	0.100723i
$786$	14.0062	−	36.9313i	0.499585	−	1.31730i
$787$	−12.1971	−	3.00631i	−0.434779	−	0.107163i	0.0158508	−	0.999874i	$-0.494954\pi$
$787$	−12.1971	−	3.00631i	−0.434779	−	0.107163i	−0.450630	+	0.892711i	$0.648800\pi$
$788$	−2.98730	−	4.32785i	−0.106418	−	0.154173i
$789$	79.7098			2.83774
$790$	0.611614	+	10.0279i	0.0217602	+	0.356776i
$791$	−9.03326			−0.321186
$792$	9.06264	+	13.1295i	0.322027	+	0.466536i
$793$	12.6234	+	3.11140i	0.448271	+	0.110489i
$794$	−9.81260	+	25.8737i	−0.348236	+	0.918224i
$795$	0.605715	−	0.536616i	0.0214825	−	0.0190318i
$796$	−4.66561	−	12.3022i	−0.165368	−	0.436040i
$797$	11.0562	+	2.72510i	0.391630	+	0.0965281i	0.430213	−	0.902727i	$-0.358438\pi$
$797$	11.0562	+	2.72510i	0.391630	+	0.0965281i	−0.0385833	+	0.999255i	$0.512284\pi$
$798$	7.35733	−	1.81342i	0.260447	−	0.0641944i
$799$	86.0100	+	45.1415i	3.04281	+	1.59699i
$800$	3.61421	+	0.890823i	0.127782	+	0.0314954i
$801$	32.7782	+	29.0390i	1.15816	+	1.02604i
$802$	2.56464	−	3.71552i	0.0905605	−	0.131200i
$803$	26.4660	−	69.7852i	0.933966	−	2.46267i
$804$	0.501162	+	1.32146i	0.0176746	+	0.0466041i
$805$	−23.3389	+	12.2492i	−0.822586	+	0.431727i
$806$	6.34801	+	5.62384i	0.223599	+	0.198091i
$807$	2.10207	−	5.54271i	0.0739965	−	0.195113i
$808$	1.49565	+	12.3178i	0.0526167	+	0.433338i
$809$	1.52015	+	12.5195i	0.0534455	+	0.440163i	0.994728	+	0.102545i	$0.0326984\pi$
$809$	1.52015	+	12.5195i	0.0534455	+	0.440163i	−0.941283	+	0.337619i	$0.890379\pi$
$810$	−3.26761	−	8.61599i	−0.114812	−	0.302735i
$811$	11.6520	+	6.11546i	0.409158	+	0.214743i	0.656728	−	0.754127i	$-0.271940\pi$
$811$	11.6520	+	6.11546i	0.409158	+	0.214743i	−0.247570	+	0.968870i	$0.579632\pi$
$812$	1.68675	−	13.8916i	0.0591933	−	0.487500i
$813$	−19.0338			−0.667545
$814$	7.58413			0.265824
$815$	3.22468	−	26.5576i	0.112955	−	0.930272i
$816$	17.8713	−	4.40487i	0.625619	−	0.154201i
$817$	−2.13962	−	1.89554i	−0.0748557	−	0.0663164i
$818$	−11.9759	+	17.3500i	−0.418726	+	0.606629i
$819$	−24.7237	+	12.9760i	−0.863915	+	0.453418i
$820$	1.21448	+	0.637408i	0.0424115	+	0.0222593i
$821$	−0.216269	−	0.313320i	−0.00754784	−	0.0109349i	0.819192	−	0.573520i	$-0.194422\pi$
$821$	−0.216269	−	0.313320i	−0.00754784	−	0.0109349i	−0.826740	+	0.562585i	$0.809807\pi$
$822$	−2.80283	+	23.0834i	−0.0977600	+	0.805126i
$823$	−20.6191	−	29.8719i	−0.718735	−	1.04127i	−0.996739	−	0.0806882i	$-0.974288\pi$
$823$	−20.6191	−	29.8719i	−0.718735	−	1.04127i	0.278004	−	0.960580i	$-0.410327\pi$
$824$	12.9338	−	3.18790i	0.450570	−	0.111056i
$825$	40.3565	−	21.1807i	1.40503	−	0.737418i
$826$	−32.0858	+	28.4255i	−1.11641	+	0.989050i
$827$	4.44651	+	36.6203i	0.154620	+	1.27341i	0.838937	+	0.544228i	$0.183177\pi$
$827$	4.44651	+	36.6203i	0.154620	+	1.27341i	−0.684317	+	0.729184i	$0.739900\pi$
$828$	−16.7284	+	14.8201i	−0.581353	+	0.515034i
$829$	−12.9439	+	18.7525i	−0.449561	+	0.651302i	−0.980594	−	0.196050i	$-0.937189\pi$
$829$	−12.9439	+	18.7525i	−0.449561	+	0.651302i	0.531033	+	0.847351i	$0.321804\pi$
$830$	−6.69805	+	9.70380i	−0.232493	+	0.336824i
$831$	20.7950	−	18.4228i	0.721372	−	0.639080i
$832$	−0.303511	−	2.49964i	−0.0105224	−	0.0866594i
$833$	−25.1662	+	22.2953i	−0.871958	+	0.772487i
$834$	−18.7663	+	9.84929i	−0.649822	+	0.341053i
$835$	−15.1760	+	3.74054i	−0.525187	+	0.129447i
$836$	2.47516	+	3.58589i	0.0856053	+	0.124021i
$837$	−0.264102	+	2.17508i	−0.00912871	+	0.0751817i
$838$	7.50963	+	10.8796i	0.259416	+	0.375829i
$839$	−16.5145	−	8.66750i	−0.570145	−	0.299235i	0.154907	−	0.987929i	$-0.450492\pi$
$839$	−16.5145	−	8.66750i	−0.570145	−	0.299235i	−0.725052	+	0.688694i	$0.758184\pi$
$840$	8.51781	−	4.47049i	0.293892	−	0.154247i
$841$	−6.85963	+	9.93790i	−0.236539	+	0.342686i
$842$	2.44328	+	2.16456i	0.0842010	+	0.0745956i
$843$	−70.7156	+	17.4298i	−2.43558	+	0.600315i
$844$	−0.371508	+	3.05964i	−0.0127878	+	0.105317i
$845$	7.52758			0.258956
$846$	43.0452			1.47993
$847$	5.30895	−	43.7231i	0.182418	−	1.50234i
$848$	−0.253366	−	0.132977i	−0.00870063	−	0.00456644i
$849$	−10.3224	−	27.2180i	−0.354264	−	0.934118i
$850$	−3.30076	−	27.1842i	−0.113215	−	0.932411i
$851$	1.28063	+	10.5470i	0.0438996	+	0.361546i
$852$	1.50900	−	3.97890i	0.0516974	−	0.136315i
$853$	2.62353	+	2.32425i	0.0898280	+	0.0795807i	0.706842	−	0.707372i	$-0.250119\pi$
$853$	2.62353	+	2.32425i	0.0898280	+	0.0795807i	−0.617014	+	0.786952i	$0.711658\pi$
$854$	15.5514	−	8.16198i	0.532156	−	0.279297i
$855$	1.16341	+	3.06765i	0.0397877	+	0.104912i
$856$	0.912015	−	2.40479i	0.0311720	−	0.0821939i
$857$	17.1700	−	24.8750i	0.586515	−	0.849714i	−0.411582	−	0.911373i	$-0.635024\pi$
$857$	17.1700	−	24.8750i	0.586515	−	0.849714i	0.998097	+	0.0616585i	$0.0196390\pi$
$858$	−23.0770	−	20.4444i	−0.787836	−	0.697961i
$859$	−29.0773	−	7.16692i	−0.992106	−	0.244532i	−0.290328	−	0.956927i	$-0.593764\pi$
$859$	−29.0773	−	7.16692i	−0.992106	−	0.244532i	−0.701779	+	0.712395i	$0.747610\pi$
$860$	−3.21321	−	1.68642i	−0.109569	−	0.0575065i
$861$	−10.0271	+	2.47146i	−0.341722	+	0.0842270i
$862$	−12.1978	−	3.00649i	−0.415460	−	0.102402i
$863$	8.20339	+	21.6306i	0.279247	+	0.736313i	0.999109	+	0.0421963i	$0.0134355\pi$
$863$	8.20339	+	21.6306i	0.279247	+	0.736313i	−0.719863	+	0.694116i	$0.755795\pi$
$864$	0.486930	−	0.431383i	0.0165657	−	0.0146759i
$865$	6.05870	−	15.9755i	0.206002	−	0.543183i
$866$	9.93485	+	2.44872i	0.337600	+	0.0832109i
$867$	−52.7571	−	76.4319i	−1.79173	−	2.59576i
$868$	11.4566			0.388863
$869$	17.8316	−	39.6732i	0.604894	−	1.34582i
$870$	11.6345			0.394446
$871$	−0.807977	−	1.17056i	−0.0273773	−	0.0396628i
$872$	17.3748	+	4.28250i	0.588384	+	0.145024i
$873$	5.45532	−	14.3845i	0.184635	−	0.486841i
$874$	−4.56882	+	4.04762i	−0.154543	+	0.136913i
$875$	−11.8920	−	31.3565i	−0.402021	−	1.06004i
$876$	−37.0498	−	9.13197i	−1.25180	−	0.308541i
$877$	−49.3223	+	12.1568i	−1.66549	+	0.410508i	−0.955804	−	0.294006i	$-0.905012\pi$
$877$	−49.3223	+	12.1568i	−1.66549	+	0.410508i	−0.709691	+	0.704513i	$0.751165\pi$
$878$	9.12759	+	4.79053i	0.308041	+	0.161673i
$879$	57.5952	+	14.1959i	1.94264	+	0.478817i
$880$	4.14036	+	3.66804i	0.139571	+	0.123649i
$881$	7.64365	−	11.0737i	0.257521	−	0.373084i	−0.672803	−	0.739821i	$-0.734910\pi$
$881$	7.64365	−	11.0737i	0.257521	−	0.373084i	0.930324	+	0.366738i	$0.119525\pi$
$882$	−5.28333	+	13.9310i	−0.177899	+	0.469081i
$883$	13.7625	+	36.2887i	0.463145	+	1.22121i	0.939679	+	0.342056i	$0.111123\pi$
$883$	13.7625	+	36.2887i	0.463145	+	1.22121i	−0.476535	+	0.879156i	$0.658107\pi$
$884$	−16.4020	+	8.60844i	−0.551659	+	0.289533i
$885$	−26.6765	−	23.6333i	−0.896721	−	0.794425i
$886$	−3.37470	+	8.89835i	−0.113375	+	0.298946i
$887$	3.18233	+	26.2089i	0.106852	+	0.880007i	0.943296	+	0.331954i	$0.107708\pi$
$887$	3.18233	+	26.2089i	0.106852	+	0.880007i	−0.836443	+	0.548053i	$0.815369\pi$
$888$	−0.467384	−	3.84925i	−0.0156844	−	0.129172i
$889$	2.66556	+	7.02852i	0.0894002	+	0.235729i
$890$	13.4443	+	7.05610i	0.450653	+	0.236521i
$891$	−4.80886	+	39.6045i	−0.161103	+	1.32680i
$892$	−21.7144			−0.727052
$893$	11.7564			0.393413
$894$	4.61449	−	38.0038i	0.154332	−	1.27104i
$895$	6.38036	−	1.57262i	0.213272	−	0.0525668i
$896$	−2.54607	−	2.25562i	−0.0850582	−	0.0753550i
$897$	24.5346	−	35.5445i	0.819187	−	1.18680i
$898$	6.06942	−	3.18548i	0.202539	−	0.106301i
$899$	12.2690	+	6.43928i	0.409195	+	0.214762i
$900$	−6.89345	−	9.98688i	−0.229782	−	0.332896i
$901$	−0.253732	+	2.08967i	−0.00845304	+	0.0696171i
$902$	−3.37333	−	4.88711i	−0.112320	−	0.162723i
$903$	26.5292	−	6.53885i	0.882835	−	0.217599i
$904$	−2.35147	+	1.23415i	−0.0782087	+	0.0410471i
$905$	−7.77812	+	6.89081i	−0.258553	+	0.229058i
$906$	0.0292997	+	0.241304i	0.000973416	+	0.00801680i
$907$	−18.8943	+	16.7389i	−0.627376	+	0.555807i	−0.915769	−	0.401705i	$-0.868418\pi$
$907$	−18.8943	+	16.7389i	−0.627376	+	0.555807i	0.288393	+	0.957512i	$0.406879\pi$
$908$	2.43458	−	3.52710i	0.0807945	−	0.117051i
$909$	22.9787	−	33.2905i	0.762157	−	1.10417i
$910$	−7.24648	+	6.41982i	−0.240218	+	0.212815i
$911$	−4.16040	−	34.2640i	−0.137840	−	1.13522i	−0.883347	−	0.468719i	$-0.844716\pi$
$911$	−4.16040	−	34.2640i	−0.137840	−	1.13522i	0.745507	−	0.666498i	$-0.232207\pi$
$912$	1.66745	−	1.47723i	0.0552148	−	0.0489160i
$913$	45.2017	−	23.7237i	1.49596	−	0.785139i
$914$	0.431344	−	0.106317i	0.0142676	−	0.00351664i
$915$	8.29498	+	12.0174i	0.274224	+	0.397281i
$916$	−1.53805	+	12.6670i	−0.0508185	+	0.418528i
$917$	30.5041	+	44.1928i	1.00733	+	1.45938i
$918$	−4.23751	−	2.22402i	−0.139859	−	0.0734035i
$919$	−11.4764	+	6.02326i	−0.378570	+	0.198689i	−0.643266	−	0.765643i	$-0.722421\pi$
$919$	−11.4764	+	6.02326i	−0.378570	+	0.198689i	0.264695	+	0.964332i	$0.414729\pi$
$920$	−4.40188	+	6.37722i	−0.145126	+	0.210251i
$921$	58.5319	+	51.8547i	1.92869	+	1.70867i
$922$	−9.02990	+	2.22567i	−0.297384	+	0.0732985i
$923$	−0.516215	+	4.25142i	−0.0169914	+	0.139937i
$924$	−41.6484			−1.37013
$925$	−5.76883			−0.189678
$926$	0.784205	−	6.45851i	0.0257706	−	0.212240i
$927$	−38.4519	−	20.1811i	−1.26293	−	0.662835i
$928$	−1.45883	−	3.84661i	−0.0478883	−	0.126271i
$929$	1.96037	+	16.1451i	0.0643178	+	0.529705i	0.988885	+	0.148685i	$0.0475040\pi$
$929$	1.96037	+	16.1451i	0.0643178	+	0.529705i	−0.924567	+	0.381020i	$0.875573\pi$
$930$	1.14813	+	9.45572i	0.0376487	+	0.310065i
$931$	−1.44297	+	3.80480i	−0.0472914	+	0.124697i
$932$	16.1941	+	14.3467i	0.530454	+	0.469941i
$933$	−74.0738	+	38.8769i	−2.42507	+	1.27277i
$934$	4.58840	+	12.0986i	0.150137	+	0.395878i
$935$	14.4298	−	38.0482i	0.471904	−	1.24431i
$936$	−4.66306	+	6.75562i	−0.152417	+	0.220814i
$937$	0.798058	+	0.707018i	0.0260714	+	0.0230973i	0.676058	−	0.736849i	$-0.263687\pi$
$937$	0.798058	+	0.707018i	0.0260714	+	0.0230973i	−0.649986	+	0.759946i	$0.725225\pi$
$938$	−1.86557	−	0.459822i	−0.0609130	−	0.0150137i
$939$	−26.3880	−	13.8495i	−0.861140	−	0.451961i
$940$	14.4911	−	3.57174i	0.472648	−	0.116497i
$941$	45.4448	+	11.2011i	1.48146	+	0.365147i	0.895452	−	0.445159i	$-0.146853\pi$
$941$	45.4448	+	11.2011i	1.48146	+	0.365147i	0.586007	+	0.810306i	$0.300699\pi$
$942$	3.34041	+	8.80795i	0.108837	+	0.286978i
$943$	6.22671	−	5.51639i	0.202770	−	0.179638i
$944$	−4.46876	+	11.7831i	−0.145446	+	0.383509i
$945$	−2.42849	−	0.598568i	−0.0789987	−	0.0194714i
$946$	8.92497	+	12.9301i	0.290176	+	0.420392i
$947$	0.366690			0.0119158			0.00595791	−	0.999982i	$-0.498104\pi$
$947$	0.366690			0.0119158			0.00595791	+	0.999982i	$0.498104\pi$
$948$	−21.2346	−	6.60532i	−0.689669	−	0.214531i
$949$	38.4026			1.24660
$950$	−1.88272	−	2.72759i	−0.0610835	−	0.0884947i
$951$	−27.0778	−	6.67407i	−0.878056	−	0.216421i
$952$	−8.87344	+	23.3973i	−0.287590	+	0.758312i
$953$	−35.9739	+	31.8701i	−1.16531	+	1.03237i	−0.166381	+	0.986061i	$0.553208\pi$
$953$	−35.9739	+	31.8701i	−1.16531	+	1.03237i	−0.998927	+	0.0463117i	$0.985253\pi$
$954$	0.330784	+	0.872206i	0.0107095	+	0.0282387i
$955$	−5.15600	−	1.27084i	−0.166844	−	0.0411234i
$956$	2.85972	−	0.704856i	0.0924898	−	0.0227967i
$957$	−44.6017	−	23.4088i	−1.44177	−	0.756698i
$958$	5.13131	+	1.26475i	0.165785	+	0.0408624i
$959$	−23.6625	−	20.9632i	−0.764102	−	0.676936i
$960$	1.60652	−	2.32745i	0.0518503	−	0.0751181i
$961$	6.97010	−	18.3786i	0.224842	−	0.592859i
$962$	1.38378	+	3.64873i	0.0446149	+	0.117640i
$963$	−7.42408	+	3.89646i	−0.239238	+	0.125562i
$964$	6.85735	+	6.07508i	0.220860	+	0.195665i
$965$	−5.91932	+	15.6080i	−0.190550	+	0.502438i
$966$	−7.03263	−	57.9189i	−0.226271	−	1.86351i
$967$	−2.85253	−	23.4927i	−0.0917312	−	0.755474i	−0.963899	−	0.266268i	$-0.914209\pi$
$967$	−2.85253	−	23.4927i	−0.0917312	−	0.755474i	0.872168	−	0.489207i	$-0.162714\pi$
$968$	−4.59158	−	12.1070i	−0.147579	−	0.389133i
$969$	−14.5110	−	7.61595i	−0.466160	−	0.244659i
$970$	0.642951	−	5.29518i	0.0206439	−	0.170018i
$971$	16.8022			0.539209			0.269605	−	0.962971i	$-0.413107\pi$
$971$	16.8022			0.539209			0.269605	+	0.962971i	$0.413107\pi$
$972$	22.3489			0.716840
$973$	3.47308	−	28.6034i	0.111342	−	0.916983i
$974$	−18.4063	+	4.53675i	−0.589777	+	0.145367i
$975$	17.5534	+	15.5510i	0.562159	+	0.498029i
$976$	2.93310	−	4.24933i	0.0938862	−	0.136018i
$977$	10.4094	−	5.46328i	0.333026	−	0.174786i	−0.289919	−	0.957051i	$-0.593628\pi$
$977$	10.4094	−	5.46328i	0.333026	−	0.174786i	0.622945	+	0.782266i	$0.285936\pi$
$978$	52.4348	+	27.5199i	1.67668	+	0.879990i
$979$	−37.3427	−	54.1002i	−1.19348	−	1.72905i
$980$	−0.622681	+	5.12824i	−0.0198908	+	0.163816i
$981$	−33.1392	−	48.0104i	−1.05805	−	1.53286i
$982$	−10.6844	+	2.63347i	−0.340954	+	0.0840375i
$983$	−32.4907	+	17.0525i	−1.03629	+	0.543889i	−0.894994	−	0.446078i	$-0.852820\pi$
$983$	−32.4907	+	17.0525i	−1.03629	+	0.543889i	−0.141299	+	0.989967i	$0.545128\pi$
$984$	−2.27252	+	2.01328i	−0.0724453	+	0.0641809i
$985$	0.716476	+	5.90071i	0.0228288	+	0.188012i
$986$	−22.6533	+	20.0691i	−0.721428	+	0.639129i
$987$	−63.8358	+	92.4822i	−2.03192	+	2.94374i
$988$	−1.27356	+	1.84508i	−0.0405175	+	0.0586997i
$989$	−16.4743	+	14.5950i	−0.523853	+	0.464093i
$990$	−2.17359	−	17.9011i	−0.0690812	−	0.568935i
$991$	30.9488	−	27.4183i	0.983122	−	0.870970i	−0.00852323	−	0.999964i	$-0.502713\pi$
$991$	30.9488	−	27.4183i	0.983122	−	0.870970i	0.991645	+	0.128993i	$0.0411746\pi$
$992$	2.98230	−	1.56523i	0.0946881	−	0.0496961i
$993$	−72.1616	+	17.7862i	−2.28998	+	0.564429i
$994$	3.28645	+	4.76124i	0.104240	+	0.151017i
$995$	−1.79260	+	14.7634i	−0.0568293	+	0.468031i
$996$	−14.8264	−	21.4797i	−0.469791	−	0.680610i
$997$	6.07770	+	3.18982i	0.192483	+	0.101023i	0.558211	−	0.829699i	$-0.311488\pi$
$997$	6.07770	+	3.18982i	0.192483	+	0.101023i	−0.365729	+	0.930722i	$0.619180\pi$
$998$	10.1572	−	5.33093i	0.321522	−	0.168748i
$999$	−0.572709	+	0.829712i	−0.0181197	+	0.0262509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	158.2.e.a.97.4	✓	48
79.22	even	13	inner	158.2.e.a.101.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
158.2.e.a.97.4	✓	48	1.1	even	1	trivial
158.2.e.a.101.4	yes	48	79.22	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	158.e (of order \(13\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.568065 + 0.822984i) q^{2} +(2.42930 + 0.598768i) q^{3} +(-0.354605 + 0.935016i) q^{4} +(0.846056 - 0.749541i) q^{5} +(0.887221 + 2.33941i) q^{6} +(-3.30267 - 0.814036i) q^{7} +(-0.970942 + 0.239316i) q^{8} +(2.88659 + 1.51500i) q^{9} +(1.09747 + 0.270503i) q^{10} +(-3.66300 - 3.24513i) q^{11} +(-1.42130 + 2.05911i) q^{12} +(0.892894 - 2.35437i) q^{13} +(-1.20619 - 3.18047i) q^{14} +(2.50412 - 1.31427i) q^{15} +(-0.748511 - 0.663123i) q^{16} +(-2.60867 + 6.87850i) q^{17} +(0.392950 + 3.23624i) q^{18} +(0.107321 + 0.883872i) q^{19} +(0.400817 + 1.05687i) q^{20} +(-7.53575 - 3.95507i) q^{21} +(0.589872 - 4.85803i) q^{22} +6.85549 q^{23} -2.50200 q^{24} +(-0.448683 + 3.69524i) q^{25} +(2.44483 - 0.602596i) q^{26} +(0.486930 + 0.431383i) q^{27} +(1.93228 - 2.79939i) q^{28} +(3.64272 - 1.91185i) q^{29} +(2.50412 + 1.31427i) q^{30} +(1.91329 + 2.77189i) q^{31} +(0.120537 - 0.992709i) q^{32} +(-6.95542 - 10.0767i) q^{33} +(-7.14279 + 1.76054i) q^{34} +(-3.40440 + 1.78677i) q^{35} +(-2.44015 + 2.16178i) q^{36} +(0.186804 + 1.53847i) q^{37} +(-0.666447 + 0.590420i) q^{38} +(3.57883 - 5.18482i) q^{39} +(-0.642095 + 0.930235i) q^{40} +(0.908281 - 0.804667i) q^{41} +(-1.02584 - 8.44854i) q^{42} +(-2.40308 + 2.12895i) q^{43} +(4.33317 - 2.27422i) q^{44} +(3.57777 - 0.881842i) q^{45} +(3.89436 + 5.64196i) q^{46} +(1.59157 - 13.1078i) q^{47} +(-1.42130 - 2.05911i) q^{48} +(4.04680 + 2.12393i) q^{49} +(-3.29600 + 1.72987i) q^{50} +(-10.4559 + 15.1479i) q^{51} +(1.88475 + 1.66974i) q^{52} +(0.277827 - 0.0684782i) q^{53} +(-0.0784130 + 0.645789i) q^{54} -5.53146 q^{55} +3.40152 q^{56} +(-0.268518 + 2.21145i) q^{57} +(3.64272 + 1.91185i) q^{58} +(-4.46876 - 11.7831i) q^{59} +(0.340885 + 2.80744i) q^{60} +(0.622369 + 5.12567i) q^{61} +(-1.19434 + 3.14922i) q^{62} +(-8.30020 - 7.35334i) q^{63} +(0.885456 - 0.464723i) q^{64} +(-1.00926 - 2.66119i) q^{65} +(4.34181 - 11.4484i) q^{66} +(0.320881 - 0.464876i) q^{67} +(-5.50646 - 4.87830i) q^{68} +(16.6540 + 4.10485i) q^{69} +(-3.40440 - 1.78677i) q^{70} +(-1.65139 + 0.407031i) q^{71} +(-3.16528 - 0.780170i) q^{72} +(5.40817 + 14.2602i) q^{73} +(-1.16002 + 1.02769i) q^{74} +(-3.30257 + 8.70817i) q^{75} +(-0.864491 - 0.213078i) q^{76} +(9.45603 + 13.6994i) q^{77} +6.30003 q^{78} +(2.64851 + 8.48442i) q^{79} -1.13032 q^{80} +(-4.63108 - 6.70928i) q^{81} +(1.17819 + 0.290398i) q^{82} +(-3.69908 + 9.75368i) q^{83} +(6.37027 - 5.64357i) q^{84} +(2.94863 + 7.77491i) q^{85} +(-3.11719 - 0.768319i) q^{86} +(9.99400 - 2.46330i) q^{87} +(4.33317 + 2.27422i) q^{88} +(13.0425 + 3.21470i) q^{89} +(2.75815 + 2.44351i) q^{90} +(-4.86548 + 7.04886i) q^{91} +(-2.43099 + 6.41000i) q^{92} +(2.98824 + 7.87935i) q^{93} +(11.6916 - 6.13623i) q^{94} +(0.753298 + 0.667364i) q^{95} +(0.887221 - 2.33941i) q^{96} +(-0.568822 - 4.68467i) q^{97} +(0.550889 + 4.53698i) q^{98} +(-5.65720 - 14.9168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 11 q^{5} - 2 q^{6} - 8 q^{7} - 4 q^{8} - 18 q^{9} - 2 q^{10} - 8 q^{11} - 2 q^{12} + 16 q^{13} + 5 q^{14} - 2 q^{15} - 4 q^{16} + 6 q^{17} - 18 q^{18} + 6 q^{19} - 2 q^{20}+ \cdots - 58 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 + 11 * q^5 - 2 * q^6 - 8 * q^7 - 4 * q^8 - 18 * q^9 - 2 * q^10 - 8 * q^11 - 2 * q^12 + 16 * q^13 + 5 * q^14 - 2 * q^15 - 4 * q^16 + 6 * q^17 - 18 * q^18 + 6 * q^19 - 2 * q^20 - 12 * q^21 + 5 * q^22 - 16 * q^23 + 24 * q^24 - 17 * q^25 + 3 * q^26 + 7 * q^27 - 8 * q^28 - 34 * q^29 - 2 * q^30 - 19 * q^31 - 4 * q^32 + 8 * q^33 - 20 * q^34 + 122 * q^35 - 18 * q^36 - 4 * q^37 - 20 * q^38 - 50 * q^39 - 2 * q^40 - 36 * q^41 + 14 * q^42 - 24 * q^43 + 18 * q^44 - 4 * q^45 + 10 * q^46 - 22 * q^47 - 2 * q^48 - 28 * q^49 - 4 * q^50 + 78 * q^51 - 10 * q^52 - 12 * q^53 + 7 * q^54 - 88 * q^55 + 18 * q^56 - 28 * q^57 - 34 * q^58 - 52 * q^59 + 11 * q^60 - 47 * q^61 + 20 * q^62 + 11 * q^63 - 4 * q^64 - 16 * q^65 + 8 * q^66 + 67 * q^67 - 7 * q^68 - 4 * q^69 + 122 * q^70 - 12 * q^71 - 18 * q^72 + 101 * q^73 - 4 * q^74 - 62 * q^75 + 32 * q^76 + 113 * q^77 - 50 * q^78 - 2 * q^80 + 36 * q^81 + 29 * q^82 + 91 * q^83 + 53 * q^84 - q^85 - 24 * q^86 + 210 * q^87 + 18 * q^88 + 4 * q^89 + 126 * q^90 - 33 * q^91 - 3 * q^92 - 3 * q^93 + 17 * q^94 - 42 * q^95 - 2 * q^96 - 32 * q^97 + 24 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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