LMFDB - Embedded newform 189.2.v.b.22.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(22,189)] 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("189.22"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.v (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [54,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			22.1
Character	$\chi$	$=$	189.22
Dual form			189.2.v.b.43.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.12375 + 1.78204i) q^{2} +(1.53024 + 0.811393i) q^{3} +(0.987362 - 5.59961i) q^{4} +(0.371253 - 0.135125i) q^{5} +(-4.69579 + 1.00376i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(5.10945 + 8.84983i) q^{8} +(1.68328 + 2.48326i) q^{9} +(-0.547652 + 0.948561i) q^{10} +(0.858023 + 0.312295i) q^{11} +(6.05439 - 7.76762i) q^{12} +(4.66167 + 3.91160i) q^{13} +(2.12375 + 1.78204i) q^{14} +(0.677747 + 0.0944580i) q^{15} +(-15.9358 - 5.80016i) q^{16} +(-0.721703 + 1.25003i) q^{17} +(-8.00014 - 2.27414i) q^{18} +(-0.261925 - 0.453668i) q^{19} +(-0.390087 - 2.21229i) q^{20} +(0.533342 - 1.64789i) q^{21} +(-2.37875 + 0.865794i) q^{22} +(0.618922 - 3.51008i) q^{23} +(0.638011 + 17.6882i) q^{24} +(-3.71065 + 3.11361i) q^{25} -16.8709 q^{26} +(0.560936 + 5.16579i) q^{27} -5.68599 q^{28} +(-1.38378 + 1.16113i) q^{29} +(-1.60770 + 1.00717i) q^{30} +(0.551369 - 3.12697i) q^{31} +(24.9745 - 9.08999i) q^{32} +(1.05959 + 1.17408i) q^{33} +(-0.694878 - 3.94085i) q^{34} +(-0.197540 - 0.342149i) q^{35} +(15.5673 - 6.97386i) q^{36} +(4.47389 - 7.74901i) q^{37} +(1.36472 + 0.496717i) q^{38} +(3.95963 + 9.76815i) q^{39} +(3.09274 + 2.59511i) q^{40} +(-6.98574 - 5.86173i) q^{41} +(1.80392 + 4.45015i) q^{42} +(6.60241 + 2.40308i) q^{43} +(2.59591 - 4.49625i) q^{44} +(0.960475 + 0.694463i) q^{45} +(4.94067 + 8.55749i) q^{46} +(0.203260 + 1.15275i) q^{47} +(-19.6794 - 21.8058i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(2.33194 - 13.2251i) q^{50} +(-2.11864 + 1.32726i) q^{51} +(26.5062 - 22.2414i) q^{52} -6.97045 q^{53} +(-10.3969 - 9.97124i) q^{54} +0.360743 q^{55} +(7.82814 - 6.56859i) q^{56} +(-0.0327063 - 0.906746i) q^{57} +(0.869630 - 4.93192i) q^{58} +(0.928507 - 0.337949i) q^{59} +(1.19811 - 3.70186i) q^{60} +(1.66474 + 9.44121i) q^{61} +(4.40142 + 7.62348i) q^{62} +(2.15323 - 2.08892i) q^{63} +(-19.8825 + 34.4375i) q^{64} +(2.25922 + 0.822287i) q^{65} +(-4.34256 - 0.605226i) q^{66} +(-7.65690 - 6.42490i) q^{67} +(6.28708 + 5.27549i) q^{68} +(3.79515 - 4.86908i) q^{69} +(1.02925 + 0.374616i) q^{70} +(1.91230 - 3.31221i) q^{71} +(-13.3757 + 27.5849i) q^{72} +(-1.88018 - 3.25656i) q^{73} +(4.30760 + 24.4296i) q^{74} +(-8.20455 + 1.75378i) q^{75} +(-2.79898 + 1.01874i) q^{76} +(0.158556 - 0.899217i) q^{77} +(-25.8165 - 13.6889i) q^{78} +(-3.44060 + 2.88701i) q^{79} -6.69997 q^{80} +(-3.33311 + 8.36004i) q^{81} +25.2818 q^{82} +(10.7479 - 9.01854i) q^{83} +(-8.70095 - 4.61357i) q^{84} +(-0.0990247 + 0.561597i) q^{85} +(-18.3043 + 6.66221i) q^{86} +(-3.05966 + 0.654022i) q^{87} +(1.62027 + 9.18901i) q^{88} +(-6.47537 - 11.2157i) q^{89} +(-3.27737 + 0.236737i) q^{90} +(3.04269 - 5.27009i) q^{91} +(-19.0440 - 6.93144i) q^{92} +(3.38093 - 4.33765i) q^{93} +(-2.48591 - 2.08593i) q^{94} +(-0.158542 - 0.133033i) q^{95} +(45.5927 + 6.35428i) q^{96} +(-6.24118 - 2.27161i) q^{97} +(1.38618 - 2.40094i) q^{98} +(0.668788 + 2.65637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{3} - 3 q^{5} + 9 q^{8} + 3 q^{9} - 6 q^{11} - 60 q^{12} + 9 q^{13} - 9 q^{15} + 30 q^{17} - 3 q^{18} + 18 q^{20} + 3 q^{21} - 9 q^{22} + 36 q^{24} - 45 q^{25} - 54 q^{26} - 57 q^{27} - 54 q^{28}+ \cdots + 51 q^{99}+O(q^{100}) $ 54 * q + 3 * q^3 - 3 * q^5 + 9 * q^8 + 3 * q^9 - 6 * q^11 - 60 * q^12 + 9 * q^13 - 9 * q^15 + 30 * q^17 - 3 * q^18 + 18 * q^20 + 3 * q^21 - 9 * q^22 + 36 * q^24 - 45 * q^25 - 54 * q^26 - 57 * q^27 - 54 * q^28 + 30 * q^29 + 24 * q^30 - 9 * q^31 + 51 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 48 * q^36 - 78 * q^38 - 36 * q^39 + 45 * q^40 - 51 * q^41 - 12 * q^42 - 9 * q^43 + 30 * q^44 + 51 * q^45 - 9 * q^47 + 15 * q^48 + 126 * q^50 - 12 * q^51 + 9 * q^52 - 60 * q^53 - 90 * q^54 + 9 * q^56 + 39 * q^57 - 27 * q^58 + 42 * q^59 + 135 * q^60 + 36 * q^62 + 9 * q^63 - 27 * q^64 - 18 * q^65 - 147 * q^66 - 27 * q^67 - 81 * q^68 + 48 * q^69 + 75 * q^72 + 84 * q^74 + 15 * q^75 + 54 * q^76 - 3 * q^77 - 66 * q^78 + 72 * q^79 - 222 * q^80 - 69 * q^81 - 54 * q^83 - 12 * q^84 + 18 * q^85 + 66 * q^86 + 3 * q^87 + 54 * q^88 + 90 * q^89 + 15 * q^90 - 129 * q^92 + 21 * q^93 + 36 * q^94 - 48 * q^95 + 36 * q^96 + 3 * q^98 + 51 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.12375	+	1.78204i	−1.50172	+	1.26009i	−0.623512	+	0.781814i	$0.714295\pi$
$2$	−2.12375	+	1.78204i	−1.50172	+	1.26009i	−0.878208	+	0.478279i	$0.841261\pi$
$3$	1.53024	+	0.811393i	0.883486	+	0.468458i
$3$	1.53024	+	0.811393i	0.883486	+	0.468458i
$4$	0.987362	−	5.59961i	0.493681	−	2.79980i
$5$	0.371253	−	0.135125i	0.166030	−	0.0604298i	−0.257668	−	0.966233i	$-0.582954\pi$
$5$	0.371253	−	0.135125i	0.166030	−	0.0604298i	0.423698	+	0.905804i	$0.360732\pi$
$6$	−4.69579	+	1.00376i	−1.91705	+	0.409781i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$7$	−0.173648	−	0.984808i	−0.0656328	−	0.372222i
$8$	5.10945	+	8.84983i	1.80646	+	3.12889i
$9$	1.68328	+	2.48326i	0.561094	+	0.827752i
$10$	−0.547652	+	0.948561i	−0.173183	+	0.299961i
$11$	0.858023	+	0.312295i	0.258704	+	0.0941604i	0.468116	−	0.883667i	$-0.344933\pi$
$11$	0.858023	+	0.312295i	0.258704	+	0.0941604i	−0.209412	+	0.977827i	$0.567155\pi$
$12$	6.05439	−	7.76762i	1.74775	−	2.24232i
$13$	4.66167	+	3.91160i	1.29291	+	1.08488i	0.991323	+	0.131446i	$0.0419621\pi$
$13$	4.66167	+	3.91160i	1.29291	+	1.08488i	0.301591	+	0.953437i	$0.402482\pi$
$14$	2.12375	+	1.78204i	0.567597	+	0.476270i
$15$	0.677747	+	0.0944580i	0.174994	+	0.0243890i
$16$	−15.9358	−	5.80016i	−3.98395	−	1.45004i
$17$	−0.721703	+	1.25003i	−0.175039	+	0.303176i	−0.940175	−	0.340693i	$-0.889338\pi$
$17$	−0.721703	+	1.25003i	−0.175039	+	0.303176i	0.765136	+	0.643869i	$0.222672\pi$
$18$	−8.00014	−	2.27414i	−1.88565	−	0.536020i
$19$	−0.261925	−	0.453668i	−0.0600897	−	0.104078i	0.834416	−	0.551136i	$-0.185805\pi$
$19$	−0.261925	−	0.453668i	−0.0600897	−	0.104078i	−0.894505	+	0.447057i	$0.852472\pi$
$20$	−0.390087	−	2.21229i	−0.0872260	−	0.494683i
$21$	0.533342	−	1.64789i	0.116385	−	0.359599i
$22$	−2.37875	+	0.865794i	−0.507151	+	0.184588i
$23$	0.618922	−	3.51008i	0.129054	−	0.731902i	−0.849763	−	0.527165i	$-0.823255\pi$
$23$	0.618922	−	3.51008i	0.129054	−	0.731902i	0.978817	−	0.204737i	$-0.0656340\pi$
$24$	0.638011	+	17.6882i	0.130233	+	3.61058i
$25$	−3.71065	+	3.11361i	−0.742130	+	0.622721i
$26$	−16.8709			−3.30865
$27$	0.560936	+	5.16579i	0.107952	+	0.994156i
$28$	−5.68599			−1.07455
$29$	−1.38378	+	1.16113i	−0.256962	+	0.215617i	−0.762163	−	0.647385i	$-0.775863\pi$
$29$	−1.38378	+	1.16113i	−0.256962	+	0.215617i	0.505201	+	0.863002i	$0.331418\pi$
$30$	−1.60770	+	1.00717i	−0.293524	+	0.183883i
$31$	0.551369	−	3.12697i	0.0990289	−	0.561621i	−0.894409	−	0.447250i	$-0.852404\pi$
$31$	0.551369	−	3.12697i	0.0990289	−	0.561621i	0.993438	−	0.114371i	$-0.0364853\pi$
$32$	24.9745	−	9.08999i	4.41492	−	1.60690i
$33$	1.05959	+	1.17408i	0.184451	+	0.204381i
$34$	−0.694878	−	3.94085i	−0.119171	−	0.675850i
$35$	−0.197540	−	0.342149i	−0.0333903	−	0.0578337i
$36$	15.5673	−	6.97386i	2.59454	−	1.16231i
$37$	4.47389	−	7.74901i	0.735504	−	1.27393i	−0.218999	−	0.975725i	$-0.570279\pi$
$37$	4.47389	−	7.74901i	0.735504	−	1.27393i	0.954502	−	0.298204i	$-0.0963877\pi$
$38$	1.36472	+	0.496717i	0.221386	+	0.0805781i
$39$	3.95963	+	9.76815i	0.634049	+	1.56416i
$40$	3.09274	+	2.59511i	0.489005	+	0.410324i
$41$	−6.98574	−	5.86173i	−1.09099	−	0.915449i	−0.0942030	−	0.995553i	$-0.530030\pi$
$41$	−6.98574	−	5.86173i	−1.09099	−	0.915449i	−0.996787	+	0.0801041i	$0.974475\pi$
$42$	1.80392	+	4.45015i	0.278351	+	0.686673i
$43$	6.60241	+	2.40308i	1.00686	+	0.366466i	0.792225	−	0.610229i	$-0.208923\pi$
$43$	6.60241	+	2.40308i	1.00686	+	0.366466i	0.214632	+	0.976695i	$0.431145\pi$
$44$	2.59591	−	4.49625i	0.391348	−	0.677834i
$45$	0.960475	+	0.694463i	0.143179	+	0.103524i
$46$	4.94067	+	8.55749i	0.728462	+	1.26173i
$47$	0.203260	+	1.15275i	0.0296486	+	0.168145i	0.996037	−	0.0889416i	$-0.0283484\pi$
$47$	0.203260	+	1.15275i	0.0296486	+	0.168145i	−0.966388	+	0.257087i	$0.917237\pi$
$48$	−19.6794	−	21.8058i	−2.84048	−	3.14740i
$49$	−0.939693	+	0.342020i	−0.134242	+	0.0488600i
$50$	2.33194	−	13.2251i	0.329785	−	1.87031i
$51$	−2.11864	+	1.32726i	−0.296669	+	0.185853i
$52$	26.5062	−	22.2414i	3.67575	−	3.08432i
$53$	−6.97045			−0.957465			−0.478733	−	0.877961i	$-0.658904\pi$
$53$	−6.97045			−0.957465			−0.478733	+	0.877961i	$0.658904\pi$
$54$	−10.3969	−	9.97124i	−1.41484	−	1.35691i
$55$	0.360743			0.0486425
$56$	7.82814	−	6.56859i	1.04608	−	0.877764i
$57$	−0.0327063	−	0.906746i	−0.00433205	−	0.120101i
$58$	0.869630	−	4.93192i	0.114188	−	0.647592i
$59$	0.928507	−	0.337949i	0.120881	−	0.0439972i	−0.280871	−	0.959745i	$-0.590623\pi$
$59$	0.928507	−	0.337949i	0.120881	−	0.0439972i	0.401753	+	0.915748i	$0.368401\pi$
$60$	1.19811	−	3.70186i	0.154675	−	0.477907i
$61$	1.66474	+	9.44121i	0.213148	+	1.20882i	0.884091	+	0.467314i	$0.154778\pi$
$61$	1.66474	+	9.44121i	0.213148	+	1.20882i	−0.670943	+	0.741509i	$0.734111\pi$
$62$	4.40142	+	7.62348i	0.558980	+	0.968183i
$63$	2.15323	−	2.08892i	0.271281	−	0.263180i
$64$	−19.8825	+	34.4375i	−2.48531	+	4.30469i
$65$	2.25922	+	0.822287i	0.280221	+	0.101992i
$66$	−4.34256	−	0.605226i	−0.534533	−	0.0744982i
$67$	−7.65690	−	6.42490i	−0.935439	−	0.784927i	0.0413467	−	0.999145i	$-0.486835\pi$
$67$	−7.65690	−	6.42490i	−0.935439	−	0.784927i	−0.976786	+	0.214218i	$0.931280\pi$
$68$	6.28708	+	5.27549i	0.762420	+	0.639747i
$69$	3.79515	−	4.86908i	0.456883	−	0.586169i
$70$	1.02925	+	0.374616i	0.123019	+	0.0447752i
$71$	1.91230	−	3.31221i	0.226949	−	0.393087i	−0.729954	−	0.683497i	$-0.760458\pi$
$71$	1.91230	−	3.31221i	0.226949	−	0.393087i	0.956902	+	0.290410i	$0.0937916\pi$
$72$	−13.3757	+	27.5849i	−1.57635	+	3.25091i
$73$	−1.88018	−	3.25656i	−0.220058	−	0.381152i	0.734767	−	0.678319i	$-0.237291\pi$
$73$	−1.88018	−	3.25656i	−0.220058	−	0.381152i	−0.954825	+	0.297168i	$0.903958\pi$
$74$	4.30760	+	24.4296i	0.500749	+	2.83989i
$75$	−8.20455	+	1.75378i	−0.947380	+	0.202509i
$76$	−2.79898	+	1.01874i	−0.321065	+	0.116858i
$77$	0.158556	−	0.899217i	0.0180692	−	0.102475i
$78$	−25.8165	−	13.6889i	−2.92314	−	1.54996i
$79$	−3.44060	+	2.88701i	−0.387098	+	0.324814i	−0.815481	−	0.578783i	$-0.803528\pi$
$79$	−3.44060	+	2.88701i	−0.387098	+	0.324814i	0.428383	+	0.903597i	$0.359083\pi$
$80$	−6.69997			−0.749079
$81$	−3.33311	+	8.36004i	−0.370346	+	0.928894i
$82$	25.2818			2.79191
$83$	10.7479	−	9.01854i	1.17973	−	0.989913i	0.179752	−	0.983712i	$-0.442470\pi$
$83$	10.7479	−	9.01854i	1.17973	−	0.989913i	0.999981	−	0.00620155i	$-0.00197403\pi$
$84$	−8.70095	−	4.61357i	−0.949351	−	0.503382i
$85$	−0.0990247	+	0.561597i	−0.0107407	+	0.0609137i
$86$	−18.3043	+	6.66221i	−1.97380	+	0.718404i
$87$	−3.05966	+	0.654022i	−0.328030	+	0.0701185i
$88$	1.62027	+	9.18901i	0.172721	+	0.979552i
$89$	−6.47537	−	11.2157i	−0.686388	−	1.18886i	−0.972998	−	0.230812i	$-0.925862\pi$
$89$	−6.47537	−	11.2157i	−0.686388	−	1.18886i	0.286610	−	0.958047i	$-0.407472\pi$
$90$	−3.27737	+	0.236737i	−0.345465	+	0.0249543i
$91$	3.04269	−	5.27009i	0.318960	−	0.552456i
$92$	−19.0440	−	6.93144i	−1.98547	−	0.722653i
$93$	3.38093	−	4.33765i	0.350586	−	0.449793i
$94$	−2.48591	−	2.08593i	−0.256403	−	0.215147i
$95$	−0.158542	−	0.133033i	−0.0162661	−	0.0136489i
$96$	45.5927	+	6.35428i	4.65328	+	0.648531i
$97$	−6.24118	−	2.27161i	−0.633696	−	0.230647i	0.00514304	−	0.999987i	$-0.498363\pi$
$97$	−6.24118	−	2.27161i	−0.633696	−	0.230647i	−0.638839	+	0.769340i	$0.720585\pi$
$98$	1.38618	−	2.40094i	0.140025	−	0.242531i
$99$	0.668788	+	2.65637i	0.0672157	+	0.266975i
$100$	13.7712	+	23.8525i	1.37712	+	2.38525i
$101$	−1.16755	−	6.62152i	−0.116176	−	0.658866i	−0.986161	−	0.165788i	$-0.946983\pi$
$101$	−1.16755	−	6.62152i	−0.116176	−	0.658866i	0.869986	−	0.493077i	$-0.164128\pi$
$102$	2.13425	−	6.59428i	0.211322	−	0.652931i
$103$	3.94539	−	1.43601i	0.388751	−	0.141494i	−0.140248	−	0.990116i	$-0.544790\pi$
$103$	3.94539	−	1.43601i	0.388751	−	0.141494i	0.528999	+	0.848623i	$0.322568\pi$
$104$	−10.7985	+	61.2411i	−1.05888	+	6.00519i
$105$	−0.0246665	−	0.683853i	−0.00240721	−	0.0667372i
$106$	14.8035	−	12.4216i	1.43784	−	1.20650i
$107$	−8.81185			−0.851874			−0.425937	−	0.904753i	$-0.640055\pi$
$107$	−8.81185			−0.851874			−0.425937	+	0.904753i	$0.640055\pi$
$108$	29.4802	+	1.95948i	2.83674	+	0.188551i
$109$	−7.54273			−0.722462			−0.361231	−	0.932476i	$-0.617643\pi$
$109$	−7.54273			−0.722462			−0.361231	+	0.932476i	$0.617643\pi$
$110$	−0.766128	+	0.642858i	−0.0730475	+	0.0612941i
$111$	13.1336	−	8.22778i	1.24659	−	0.780946i
$112$	−2.94482	+	16.7009i	−0.278259	+	1.57809i
$113$	0.688523	−	0.250602i	0.0647708	−	0.0235746i	−0.309432	−	0.950922i	$-0.600139\pi$
$113$	0.688523	−	0.250602i	0.0647708	−	0.0235746i	0.374202	+	0.927347i	$0.377917\pi$
$114$	1.68532	+	1.86742i	0.157844	+	0.174900i
$115$	−0.244523	−	1.38676i	−0.0228019	−	0.129316i
$116$	5.13559	+	8.89511i	0.476828	+	0.825890i
$117$	−1.86660	+	18.1605i	−0.172568	+	1.67893i
$118$	−1.36968	+	2.37236i	−0.126089	+	0.218393i
$119$	1.35636	+	0.493674i	0.124337	+	0.0452550i
$120$	2.62698	+	6.48058i	0.239809	+	0.591593i
$121$	−7.78781	−	6.53475i	−0.707983	−	0.594068i
$122$	−20.3601	−	17.0842i	−1.84332	−	1.54673i
$123$	−5.93371	−	14.6381i	−0.535025	−	1.31987i
$124$	−16.9654	−	6.17491i	−1.52354	−	0.554523i
$125$	−1.94456	+	3.36808i	−0.173927	+	0.301251i
$126$	−0.850383	+	8.27350i	−0.0757581	+	0.737062i
$127$	−0.200688	−	0.347602i	−0.0178082	−	0.0308447i	0.856984	−	0.515343i	$-0.172335\pi$
$127$	−0.200688	−	0.347602i	−0.0178082	−	0.0308447i	−0.874792	+	0.484498i	$0.839002\pi$
$128$	−9.91328	−	56.2210i	−0.876219	−	4.96928i
$129$	8.15344	+	9.03444i	0.717870	+	0.795438i
$130$	−6.26337	+	2.27968i	−0.549334	+	0.199941i
$131$	1.71298	−	9.71477i	0.149663	−	0.848784i	−0.813840	−	0.581089i	$-0.802627\pi$
$131$	1.71298	−	9.71477i	0.149663	−	0.848784i	0.963504	−	0.267695i	$-0.0862620\pi$
$132$	7.62059	−	4.77404i	0.663287	−	0.415527i
$133$	−0.401293	+	0.336724i	−0.0347965	+	0.0291977i
$134$	27.7108			2.39385
$135$	0.906277	+	1.84202i	0.0779999	+	0.158536i
$136$	−14.7500			−1.26480
$137$	−4.57208	+	3.83643i	−0.390619	+	0.327768i	−0.816854	−	0.576844i	$-0.804284\pi$
$137$	−4.57208	+	3.83643i	−0.390619	+	0.327768i	0.426235	+	0.904612i	$0.359840\pi$
$138$	0.616935	+	17.1038i	0.0525170	+	1.45598i
$139$	1.77451	−	10.0637i	0.150512	−	0.853596i	−0.812263	−	0.583291i	$-0.801765\pi$
$139$	1.77451	−	10.0637i	0.150512	−	0.853596i	0.962775	−	0.270304i	$-0.0871243\pi$
$140$	−2.11094	+	0.768321i	−0.178407	+	0.0649349i
$141$	−0.624293	+	1.92891i	−0.0525749	+	0.162443i
$142$	1.84123	+	10.4421i	0.154512	+	0.876283i
$143$	2.77824	+	4.81206i	0.232329	+	0.402405i
$144$	−12.4212	−	49.3360i	−1.03510	−	4.11133i
$145$	−0.356836	+	0.618058i	−0.0296336	+	0.0513269i
$146$	9.79635	+	3.56558i	0.810752	+	0.295090i
$147$	−1.71547	−	0.239086i	−0.141490	−	0.0197195i
$148$	−38.9741	−	32.7031i	−3.20365	−	2.68818i
$149$	12.4877	+	10.4784i	1.02303	+	0.858423i	0.990005	−	0.141032i	$-0.0450420\pi$
$149$	12.4877	+	10.4784i	1.02303	+	0.858423i	0.0330234	+	0.999455i	$0.489486\pi$
$150$	14.2991	−	18.3454i	1.16752	−	1.49790i
$151$	−3.95308	−	1.43880i	−0.321697	−	0.117088i	0.176124	−	0.984368i	$-0.443644\pi$
$151$	−3.95308	−	1.43880i	−0.321697	−	0.117088i	−0.497821	+	0.867280i	$0.665866\pi$
$152$	2.67659	−	4.63599i	0.217100	−	0.376028i
$153$	−4.31897	+	0.311976i	−0.349168	+	0.0252217i
$154$	1.26571	+	2.19227i	0.101994	+	0.176658i
$155$	−0.217835	−	1.23540i	−0.0174969	−	0.0992299i
$156$	58.6074	−	12.5277i	4.69235	−	1.00302i
$157$	−8.97798	+	3.26772i	−0.716521	+	0.260792i	−0.674448	−	0.738322i	$-0.735618\pi$
$157$	−8.97798	+	3.26772i	−0.716521	+	0.260792i	−0.0420728	+	0.999115i	$0.513396\pi$
$158$	2.16222	−	12.2626i	0.172017	−	0.975559i
$159$	−10.6665	−	5.65578i	−0.845907	−	0.448532i
$160$	8.04360	−	6.74938i	0.635902	−	0.533585i
$161$	−3.56423			−0.280901
$162$	−7.81922	−	23.6944i	−0.614336	−	1.86161i
$163$	−10.6526			−0.834376			−0.417188	−	0.908820i	$-0.636984\pi$
$163$	−10.6526			−0.834376			−0.417188	+	0.908820i	$0.636984\pi$
$164$	−39.7209	+	33.3298i	−3.10168	+	2.60262i
$165$	0.552024	+	0.292704i	0.0429750	+	0.0227870i
$166$	−6.75443	+	38.3063i	−0.524246	+	2.97315i
$167$	14.5109	−	5.28153i	1.12289	−	0.408697i	0.287182	−	0.957876i	$-0.407282\pi$
$167$	14.5109	−	5.28153i	1.12289	−	0.408697i	0.835705	+	0.549179i	$0.185059\pi$
$168$	17.3086	−	3.69984i	1.33539	−	0.285448i
$169$	4.17308	+	23.6667i	0.321006	+	1.82052i
$170$	−0.790484	−	1.36916i	−0.0606274	−	0.105010i
$171$	0.685678	−	1.41408i	0.0524351	−	0.108137i
$172$	19.9753	−	34.5982i	1.52310	−	2.63809i
$173$	15.1196	+	5.50307i	1.14952	+	0.418391i	0.845342	−	0.534225i	$-0.179396\pi$
$173$	15.1196	+	5.50307i	1.14952	+	0.418391i	0.304177	+	0.952616i	$0.401619\pi$
$174$	5.33247	−	6.84142i	0.404253	−	0.518646i
$175$	3.71065	+	3.11361i	0.280499	+	0.235367i
$176$	−11.8619	−	9.95334i	−0.894126	−	0.750261i
$177$	1.69505	+	0.236240i	0.127408	+	0.0177569i
$178$	33.7389	+	12.2799i	2.52884	+	0.920421i
$179$	−6.03715	+	10.4567i	−0.451238	+	0.781567i	−0.998463	−	0.0554181i	$-0.982351\pi$
$179$	−6.03715	+	10.4567i	−0.451238	+	0.781567i	0.547225	+	0.836985i	$0.315684\pi$
$180$	4.83706	−	4.69260i	0.360533	−	0.349766i
$181$	0.622309	+	1.07787i	0.0462559	+	0.0801175i	0.888226	−	0.459406i	$-0.151938\pi$
$181$	0.622309	+	1.07787i	0.0462559	+	0.0801175i	−0.841971	+	0.539524i	$0.818604\pi$
$182$	2.92960	+	16.6146i	0.217156	+	1.23155i
$183$	−5.11307	+	15.7981i	−0.377969	+	1.16783i
$184$	34.2260	−	12.4572i	2.52317	−	0.918360i
$185$	0.613862	−	3.48138i	0.0451320	−	0.255956i
$186$	0.549599	+	15.2370i	0.0402986	+	1.11723i
$187$	−1.00961	+	0.847167i	−0.0738303	+	0.0619510i
$188$	6.65562			0.485411
$189$	4.98990	−	1.44944i	0.362962	−	0.105431i
$190$	0.573775			0.0416260
$191$	−2.25413	+	1.89144i	−0.163103	+	0.136860i	−0.720686	−	0.693261i	$-0.756173\pi$
$191$	−2.25413	+	1.89144i	−0.163103	+	0.136860i	0.557583	+	0.830121i	$0.311729\pi$
$192$	−58.3674	+	36.5652i	−4.21230	+	2.63887i
$193$	−3.50463	+	19.8757i	−0.252268	+	1.43069i	0.550720	+	0.834690i	$0.314353\pi$
$193$	−3.50463	+	19.8757i	−0.252268	+	1.43069i	−0.802988	+	0.595995i	$0.796758\pi$
$194$	17.3028	−	6.29771i	1.24227	−	0.452149i
$195$	2.78995	+	3.09141i	0.199792	+	0.221381i
$196$	0.987362	+	5.59961i	0.0705259	+	0.399972i
$197$	7.13202	+	12.3530i	0.508135	+	0.880116i	0.999956	+	0.00941947i	$0.00299836\pi$
$197$	7.13202	+	12.3530i	0.508135	+	0.880116i	−0.491820	+	0.870697i	$0.663668\pi$
$198$	−6.15410	−	4.44967i	−0.437353	−	0.316224i
$199$	12.4639	−	21.5881i	0.883540	−	1.53034i	0.0361630	−	0.999346i	$-0.488486\pi$
$199$	12.4639	−	21.5881i	0.883540	−	1.53034i	0.847377	−	0.530991i	$-0.178180\pi$
$200$	−46.5143	−	16.9298i	−3.28906	−	1.19712i
$201$	−6.50379	−	16.0444i	−0.458742	−	1.13169i
$202$	14.2794	+	11.9818i	1.00470	+	0.843040i
$203$	1.38378	+	1.16113i	0.0971226	+	0.0814955i
$204$	5.34026	+	13.1741i	0.373893	+	0.922369i
$205$	−3.38555	−	1.23224i	−0.236457	−	0.0860633i
$206$	−5.82002	+	10.0806i	−0.405500	+	0.702347i
$207$	9.75825	−	4.37152i	0.678245	−	0.303842i
$208$	−51.5995	−	89.3729i	−3.57778	−	6.19690i
$209$	−0.0830597	−	0.471055i	−0.00574536	−	0.0325836i
$210$	1.27104	+	1.40838i	0.0877100	+	0.0971873i
$211$	−11.6775	+	4.25025i	−0.803910	+	0.292599i	−0.711106	−	0.703085i	$-0.751805\pi$
$211$	−11.6775	+	4.25025i	−0.803910	+	0.292599i	−0.0928043	+	0.995684i	$0.529583\pi$
$212$	−6.88236	+	39.0318i	−0.472683	+	2.68072i
$213$	5.61379	−	3.51685i	0.384651	−	0.240971i
$214$	18.7142	−	15.7031i	1.27928	−	1.07344i
$215$	2.77588			0.189314
$216$	−42.8503	+	31.3585i	−2.91559	+	2.13368i
$217$	−3.17521			−0.215547
$218$	16.0189	−	13.4414i	1.08494	−	0.910370i
$219$	−0.234775	−	6.50889i	−0.0158646	−	0.439830i
$220$	0.356184	−	2.02002i	0.0240139	−	0.136190i
$221$	−8.25395	+	3.00419i	−0.555221	+	0.202084i
$222$	−13.2304	+	40.8784i	−0.887963	+	2.74358i
$223$	2.07374	+	11.7607i	0.138868	+	0.787558i	0.972088	+	0.234617i	$0.0753835\pi$
$223$	2.07374	+	11.7607i	0.138868	+	0.787558i	−0.833220	+	0.552941i	$0.813505\pi$
$224$	−13.2887	−	23.0167i	−0.887887	−	1.53787i
$225$	−13.9780	−	3.97341i	−0.931864	−	0.264894i
$226$	−1.01567	+	1.75919i	−0.0675614	+	0.117020i
$227$	18.5329	+	6.74541i	1.23007	+	0.447709i	0.873621	−	0.486607i	$-0.161766\pi$
$227$	18.5329	+	6.74541i	1.23007	+	0.447709i	0.356448	+	0.934315i	$0.383988\pi$
$228$	−5.10971	−	0.712144i	−0.338399	−	0.0471629i
$229$	2.75982	+	2.31577i	0.182374	+	0.153030i	0.729404	−	0.684083i	$-0.239797\pi$
$229$	2.75982	+	2.31577i	0.182374	+	0.153030i	−0.547030	+	0.837113i	$0.684242\pi$
$230$	2.99057	+	2.50939i	0.197192	+	0.165464i
$231$	0.972248	−	1.24737i	0.0639692	−	0.0820708i
$232$	−17.3462	−	6.31350i	−1.13883	−	0.414502i
$233$	−8.94471	+	15.4927i	−0.585987	+	1.01496i	0.408764	+	0.912640i	$0.365960\pi$
$233$	−8.94471	+	15.4927i	−0.585987	+	1.01496i	−0.994752	+	0.102320i	$0.967374\pi$
$234$	−28.3984	−	41.8947i	−1.85646	−	2.73874i
$235$	0.231226	+	0.400495i	0.0150835	+	0.0261254i
$236$	−0.975609	−	5.53295i	−0.0635068	−	0.360165i
$237$	−7.60746	+	1.62614i	−0.494157	+	0.105629i
$238$	−3.76032	+	1.36864i	−0.243745	+	0.0887160i
$239$	0.374518	−	2.12400i	0.0242256	−	0.137390i	−0.970296	−	0.241920i	$-0.922223\pi$
$239$	0.374518	−	2.12400i	0.0242256	−	0.137390i	0.994522	+	0.104530i	$0.0333339\pi$
$240$	−10.2526	−	5.43630i	−0.661801	−	0.350912i
$241$	−13.0022	+	10.9101i	−0.837545	+	0.702783i	−0.957010	−	0.290055i	$-0.906326\pi$
$241$	−13.0022	+	10.9101i	−0.837545	+	0.702783i	0.119465	+	0.992838i	$0.461882\pi$
$242$	28.1846			1.81177
$243$	−11.8838	+	10.0884i	−0.762343	+	0.647173i
$244$	54.5108			3.48969
$245$	−0.302648	+	0.253952i	−0.0193355	+	0.0162244i
$246$	38.6873	+	20.5135i	2.46661	+	1.30789i
$247$	0.553560	−	3.13940i	0.0352222	−	0.199755i
$248$	30.4904	−	11.0976i	1.93614	−	0.704697i
$249$	23.7644	−	5.07980i	1.50601	−	0.321919i
$250$	−1.87229	−	10.6183i	−0.118414	−	0.671558i
$251$	−10.7261	−	18.5781i	−0.677024	−	1.17264i	−0.975873	−	0.218339i	$-0.929936\pi$
$251$	−10.7261	−	18.5781i	−0.677024	−	1.17264i	0.298850	−	0.954300i	$-0.403397\pi$
$252$	−9.57114	−	14.1198i	−0.602925	−	0.889462i
$253$	1.62723	−	2.81844i	0.102303	−	0.177194i
$254$	1.04565	+	0.380586i	0.0656101	+	0.0238801i
$255$	−0.607207	+	0.779031i	−0.0380248	+	0.0487848i
$256$	60.3179	+	50.6127i	3.76987	+	3.16330i
$257$	−7.08978	−	5.94903i	−0.442248	−	0.371090i	0.394302	−	0.918981i	$-0.370986\pi$
$257$	−7.08978	−	5.94903i	−0.442248	−	0.371090i	−0.836550	+	0.547891i	$0.815431\pi$
$258$	−33.4156	−	4.65716i	−2.08037	−	0.289942i
$259$	−8.40817	−	3.06032i	−0.522458	−	0.190159i
$260$	6.83515	−	11.8388i	0.423898	−	0.734213i
$261$	−5.21269	−	1.48177i	−0.322657	−	0.0917195i
$262$	13.6742	+	23.6844i	0.844793	+	1.46323i
$263$	0.00646882	+	0.0366865i	0.000398884	+	0.00226219i	0.985007	−	0.172517i	$-0.0551900\pi$
$263$	0.00646882	+	0.0366865i	0.000398884	+	0.00226219i	−0.984608	+	0.174779i	$0.944079\pi$
$264$	−4.97649	+	15.3761i	−0.306282	+	0.946333i
$265$	−2.58780	+	0.941884i	−0.158968	+	0.0578595i
$266$	0.252190	−	1.43024i	0.0154627	−	0.0876936i
$267$	−0.808572	−	22.4168i	−0.0494838	−	1.37188i
$268$	−43.5371	+	36.5319i	−2.65945	+	2.23154i
$269$	0.463911			0.0282851			0.0141426	−	0.999900i	$-0.495498\pi$
$269$	0.463911			0.0282851			0.0141426	+	0.999900i	$0.495498\pi$
$270$	−5.20726	−	2.29697i	−0.316904	−	0.139789i
$271$	−2.12136			−0.128863			−0.0644317	−	0.997922i	$-0.520523\pi$
$271$	−2.12136			−0.128863			−0.0644317	+	0.997922i	$0.520523\pi$
$272$	18.7513	−	15.7342i	1.13696	−	0.954025i
$273$	8.93216	−	5.59570i	0.540599	−	0.338667i
$274$	2.87329	−	16.2953i	0.173582	−	0.984432i
$275$	−4.15619	+	1.51273i	−0.250628	+	0.0912210i
$276$	−23.5178	−	26.0589i	−1.41560	−	1.56856i
$277$	2.17193	+	12.3176i	0.130499	+	0.740095i	0.977889	+	0.209125i	$0.0670614\pi$
$277$	2.17193	+	12.3176i	0.130499	+	0.740095i	−0.847390	+	0.530970i	$0.821827\pi$
$278$	14.1654	+	24.5352i	0.849583	+	1.47152i
$279$	8.69318	−	3.89439i	0.520447	−	0.233151i
$280$	2.01864	−	3.49639i	0.120637	−	0.208949i
$281$	−14.6878	−	5.34593i	−0.876202	−	0.318911i	−0.135526	−	0.990774i	$-0.543272\pi$
$281$	−14.6878	−	5.34593i	−0.876202	−	0.318911i	−0.740676	+	0.671862i	$0.765495\pi$
$282$	−2.11154	−	5.20903i	−0.125741	−	0.310193i
$283$	−2.52290	−	2.11696i	−0.149971	−	0.125840i	0.564715	−	0.825286i	$-0.308986\pi$
$283$	−2.52290	−	2.11696i	−0.149971	−	0.125840i	−0.714686	+	0.699445i	$0.753430\pi$
$284$	−16.6589	−	13.9785i	−0.988526	−	0.829472i
$285$	−0.134666	−	0.332213i	−0.00797695	−	0.0196786i
$286$	−14.4756	−	5.26868i	−0.855960	−	0.311544i
$287$	−4.55962	+	7.89749i	−0.269146	+	0.466174i
$288$	64.6120	+	46.7171i	3.80730	+	2.75283i
$289$	7.45829	+	12.9181i	0.438723	+	0.759890i
$290$	−0.343573	−	1.94850i	−0.0201753	−	0.114420i
$291$	−7.70736	−	8.54016i	−0.451813	−	0.500633i
$292$	−20.0919	+	7.31285i	−1.17579	+	0.427952i
$293$	4.61099	−	26.1502i	0.269377	−	1.52771i	−0.486898	−	0.873459i	$-0.661872\pi$
$293$	4.61099	−	26.1502i	0.269377	−	1.52771i	0.756275	−	0.654254i	$-0.227017\pi$
$294$	4.06930	−	2.54928i	0.237326	−	0.148677i
$295$	0.299046	−	0.250929i	0.0174111	−	0.0146097i
$296$	91.4366			5.31464
$297$	−1.13195	+	4.60754i	−0.0656825	+	0.267357i
$298$	−45.1936			−2.61799
$299$	16.6153	−	13.9419i	0.960885	−	0.806278i
$300$	1.71960	+	47.6739i	0.0992809	+	2.75245i
$301$	1.22008	−	6.91939i	0.0703240	−	0.398827i
$302$	10.9594	−	3.98888i	0.630640	−	0.229534i
$303$	3.58601	−	11.0799i	0.206011	−	0.636522i
$304$	1.54264	+	8.74876i	0.0884766	+	0.501776i
$305$	1.89378	+	3.28013i	0.108438	+	0.187820i
$306$	8.61646	−	8.35913i	0.492570	−	0.477860i
$307$	2.33682	−	4.04748i	0.133369	−	0.231002i	−0.791604	−	0.611034i	$-0.790754\pi$
$307$	2.33682	−	4.04748i	0.133369	−	0.231002i	0.924973	+	0.380032i	$0.124087\pi$
$308$	−4.87871	−	1.77571i	−0.277990	−	0.101180i
$309$	7.20257	+	1.00383i	0.409740	+	0.0571057i
$310$	2.66416	+	2.23550i	0.151314	+	0.126968i
$311$	24.4340	+	20.5026i	1.38553	+	1.16260i	0.967116	+	0.254337i	$0.0818574\pi$
$311$	24.4340	+	20.5026i	1.38553	+	1.16260i	0.418411	+	0.908258i	$0.362587\pi$
$312$	−66.2149	+	84.9520i	−3.74868	+	4.80946i
$313$	16.0819	+	5.85333i	0.909002	+	0.330850i	0.753854	−	0.657042i	$-0.228193\pi$
$313$	16.0819	+	5.85333i	0.909002	+	0.330850i	0.155147	+	0.987891i	$0.450415\pi$
$314$	13.2438	−	22.9389i	0.747391	−	1.29452i
$315$	0.517128	−	1.06648i	0.0291368	−	0.0600891i
$316$	12.7690	+	22.1166i	0.718312	+	1.24415i
$317$	−2.62165	−	14.8681i	−0.147246	−	0.835076i	−0.965536	−	0.260270i	$-0.916189\pi$
$317$	−2.62165	−	14.8681i	−0.147246	−	0.835076i	0.818290	−	0.574806i	$-0.194923\pi$
$318$	32.7318	−	6.99663i	1.83551	−	0.392352i
$319$	−1.54993	+	0.564130i	−0.0867796	+	0.0315852i
$320$	−2.72807	+	15.4717i	−0.152504	+	0.864893i
$321$	−13.4843	−	7.14987i	−0.752619	−	0.399067i
$322$	7.56954	−	6.35160i	0.421834	−	0.353961i
$323$	0.756129			0.0420721
$324$	43.5220	+	26.9185i	2.41789	+	1.49547i
$325$	−29.4770			−1.63509
$326$	22.6235	−	18.9834i	1.25300	−	1.05139i
$327$	−11.5422	−	6.12012i	−0.638285	−	0.338443i
$328$	16.1820	−	91.7729i	0.893503	−	5.06731i
$329$	1.09994	−	0.400345i	0.0606415	−	0.0220717i
$330$	−1.69397	+	0.362098i	−0.0932501	+	0.0199328i
$331$	−4.97474	−	28.2131i	−0.273436	−	1.55073i	−0.743885	−	0.668307i	$-0.767019\pi$
$331$	−4.97474	−	28.2131i	−0.273436	−	1.55073i	0.470449	−	0.882427i	$-0.344092\pi$
$332$	−39.8883	−	69.0885i	−2.18915	−	3.79172i
$333$	26.7736	−	1.93396i	1.46718	−	0.105980i
$334$	−21.4056	+	37.0757i	−1.17126	+	2.02869i
$335$	−3.71082	−	1.35063i	−0.202744	−	0.0737926i
$336$	−18.0573	+	23.1670i	−0.985104	+	1.26386i
$337$	11.5983	+	9.73215i	0.631801	+	0.530144i	0.901488	−	0.432804i	$-0.142476\pi$
$337$	11.5983	+	9.73215i	0.631801	+	0.530144i	−0.269687	+	0.962948i	$0.586920\pi$
$338$	−51.0376	−	42.8256i	−2.77608	−	2.32941i
$339$	1.25694	+	0.175181i	0.0682678	+	0.00951453i
$340$	3.04695	+	1.10900i	0.165244	+	0.0601439i
$341$	1.44962	−	2.51082i	0.0785016	−	0.135969i
$342$	1.06373	+	4.22506i	0.0575201	+	0.228465i
$343$	0.500000	+	0.866025i	0.0269975	+	0.0467610i
$344$	12.4678	+	70.7086i	0.672220	+	3.81235i
$345$	0.751028	−	2.32048i	0.0404340	−	0.124931i
$346$	−41.9169	+	15.2565i	−2.25347	+	0.820195i
$347$	−5.45626	+	30.9440i	−0.292908	+	1.66116i	0.382680	+	0.923881i	$0.375001\pi$
$347$	−5.45626	+	30.9440i	−0.292908	+	1.66116i	−0.675587	+	0.737280i	$0.736110\pi$
$348$	0.641275	+	17.7787i	0.0343760	+	0.953036i
$349$	−12.0640	+	10.1229i	−0.645772	+	0.541867i	−0.905785	−	0.423738i	$-0.860718\pi$
$349$	−12.0640	+	10.1229i	−0.645772	+	0.541867i	0.260013	+	0.965605i	$0.416273\pi$
$350$	−13.4291			−0.717814
$351$	−17.5916	+	26.2753i	−0.938971	+	1.40247i
$352$	24.2675			1.29346
$353$	−14.6548	+	12.2969i	−0.779998	+	0.654496i	−0.943248	−	0.332089i	$-0.892247\pi$
$353$	−14.6548	+	12.2969i	−0.779998	+	0.654496i	0.163251	+	0.986585i	$0.447802\pi$
$354$	−4.02086	+	2.51893i	−0.213706	+	0.133880i
$355$	0.262387	−	1.48807i	0.0139260	−	0.0789785i
$356$	−69.1969	+	25.1856i	−3.66743	+	1.33484i
$357$	1.67499	+	1.85598i	0.0886501	+	0.0982289i
$358$	−5.81276	−	32.9658i	−0.307214	−	1.74230i
$359$	8.47118	+	14.6725i	0.447092	+	0.774386i	0.998195	−	0.0600513i	$-0.0191264\pi$
$359$	8.47118	+	14.6725i	0.447092	+	0.774386i	−0.551104	+	0.834437i	$0.685793\pi$
$360$	−1.23838	+	12.0484i	−0.0652683	+	0.635005i
$361$	9.36279	−	16.2168i	0.492778	−	0.853517i
$362$	−3.24244	−	1.18015i	−0.170419	−	0.0620274i
$363$	−6.61499	−	16.3187i	−0.347197	−	0.856511i
$364$	−26.5062	−	22.2414i	−1.38930	−	1.16576i
$365$	−1.13807	−	0.954950i	−0.0595691	−	0.0499844i
$366$	−17.2939	−	42.6629i	−0.903968	−	2.23003i
$367$	6.60354	+	2.40349i	0.344702	+	0.125461i	0.508569	−	0.861021i	$-0.330175\pi$
$367$	6.60354	+	2.40349i	0.344702	+	0.125461i	−0.163867	+	0.986482i	$0.552397\pi$
$368$	−30.2220	+	52.3461i	−1.57543	+	2.72873i
$369$	2.79720	−	27.2143i	0.145616	−	1.41672i
$370$	4.90027	+	8.48752i	0.254753	+	0.441245i
$371$	1.21041	+	6.86456i	0.0628412	+	0.356390i
$372$	−20.9509	−	23.2147i	−1.08625	−	1.20363i
$373$	13.1854	−	4.79908i	0.682712	−	0.248487i	0.0227007	−	0.999742i	$-0.492774\pi$
$373$	13.1854	−	4.79908i	0.682712	−	0.248487i	0.660012	+	0.751255i	$0.270551\pi$
$374$	0.634486	−	3.59835i	0.0328085	−	0.186066i
$375$	−5.70849	+	3.57618i	−0.294785	+	0.184673i
$376$	−9.16306	+	7.68872i	−0.472549	+	0.396516i
$377$	−10.9926			−0.566149
$378$	−8.01435	+	11.9705i	−0.412214	+	0.615694i
$379$	8.59341			0.441414			0.220707	−	0.975340i	$-0.429164\pi$
$379$	8.59341			0.441414			0.220707	+	0.975340i	$0.429164\pi$
$380$	−0.901471	+	0.756424i	−0.0462445	+	0.0388037i
$381$	−0.0250597	−	0.694752i	−0.00128385	−	0.0355932i
$382$	1.41660	−	8.03391i	0.0724793	−	0.411051i
$383$	15.4975	−	5.64062i	0.791883	−	0.288222i	0.0857646	−	0.996315i	$-0.472667\pi$
$383$	15.4975	−	5.64062i	0.791883	−	0.288222i	0.706119	+	0.708093i	$0.250444\pi$
$384$	30.4476	−	94.0753i	1.55377	−	4.80076i
$385$	−0.0626423	−	0.355262i	−0.00319255	−	0.0181058i
$386$	−27.9764	−	48.4565i	−1.42396	−	2.46637i
$387$	5.14626	+	20.4405i	0.261599	+	1.03905i
$388$	−18.8824	+	32.7053i	−0.958609	+	1.66036i
$389$	1.22676	+	0.446504i	0.0621992	+	0.0226387i	0.372932	−	0.927859i	$-0.378352\pi$
$389$	1.22676	+	0.446504i	0.0621992	+	0.0226387i	−0.310733	+	0.950497i	$0.600575\pi$
$390$	−11.4342	−	1.59359i	−0.578992	−	0.0806945i
$391$	3.94102	+	3.30691i	0.199306	+	0.167237i
$392$	−7.82814	−	6.56859i	−0.395381	−	0.331764i
$393$	10.5038	−	13.4761i	0.529845	−	0.679777i
$394$	−37.1602	−	13.5252i	−1.87210	−	0.681390i
$395$	−0.887228	+	1.53672i	−0.0446413	+	0.0773210i
$396$	15.5350	−	1.12215i	0.780662	−	0.0563902i
$397$	11.1967	+	19.3932i	0.561946	+	0.973319i	0.997327	+	0.0730724i	$0.0232804\pi$
$397$	11.1967	+	19.3932i	0.561946	+	0.973319i	−0.435381	+	0.900246i	$0.643386\pi$
$398$	12.0006	+	68.0588i	0.601536	+	3.41148i
$399$	−0.887291	+	0.189664i	−0.0444201	+	0.00949508i
$400$	77.1916	−	28.0954i	3.85958	−	1.40477i
$401$	−0.323376	+	1.83396i	−0.0161487	+	0.0915836i	−0.991817	−	0.127669i	$-0.959251\pi$
$401$	−0.323376	+	1.83396i	−0.0161487	+	0.0915836i	0.975668	+	0.219252i	$0.0703617\pi$
$402$	42.4042	+	22.4843i	2.11493	+	1.12142i
$403$	14.8018	−	12.4202i	0.737329	−	0.618693i
$404$	−38.2307			−1.90205
$405$	−0.107777	+	3.55408i	−0.00535550	+	0.176604i
$406$	−5.00800			−0.248543
$407$	6.25868	−	5.25166i	0.310231	−	0.260315i
$408$	−22.5711	−	11.9681i	−1.11744	−	0.592508i
$409$	2.50306	−	14.1955i	0.123768	−	0.701924i	−0.858264	−	0.513209i	$-0.828457\pi$
$409$	2.50306	−	14.1955i	0.123768	−	0.701924i	0.982032	−	0.188715i	$-0.0604323\pi$
$410$	9.38596	−	3.41621i	0.463540	−	0.168715i
$411$	−10.1092	+	2.16091i	−0.498652	+	0.106590i
$412$	−4.14554	−	23.5105i	−0.204236	−	1.15828i
$413$	−0.494048	−	0.855717i	−0.0243105	−	0.0421071i
$414$	−12.9339	+	26.6736i	−0.635666	+	1.31094i
$415$	2.77155	−	4.80047i	0.136050	−	0.235646i
$416$	151.980	+	55.3160i	7.45141	+	2.71209i
$417$	10.8811	−	13.9601i	0.532849	−	0.683631i
$418$	1.01584	+	0.852389i	0.0496862	+	0.0416917i
$419$	24.2352	+	20.3357i	1.18397	+	0.993465i	0.999944	+	0.0105430i	$0.00335600\pi$
$419$	24.2352	+	20.3357i	1.18397	+	0.993465i	0.184021	+	0.982922i	$0.441088\pi$
$420$	−3.85367	−	0.537088i	−0.188040	−	0.0262072i
$421$	16.7963	+	6.11337i	0.818603	+	0.297947i	0.717173	−	0.696895i	$-0.245436\pi$
$421$	16.7963	+	6.11337i	0.818603	+	0.297947i	0.101431	+	0.994843i	$0.467658\pi$
$422$	17.2259	−	29.8362i	0.838546	−	1.45240i
$423$	−2.52042	+	2.44515i	−0.122547	+	0.118887i
$424$	−35.6152	−	61.6873i	−1.72963	−	2.99580i
$425$	−1.21410	−	6.88551i	−0.0588926	−	0.333996i
$426$	−5.65514	+	17.4729i	−0.273992	+	0.846566i
$427$	9.00870	−	3.27890i	0.435961	−	0.158677i
$428$	−8.70049	+	49.3429i	−0.420554	+	2.38508i
$429$	0.346916	+	9.61787i	0.0167493	+	0.464355i
$430$	−5.89529	+	4.94673i	−0.284296	+	0.238553i
$431$	−8.62602			−0.415501			−0.207750	−	0.978182i	$-0.566614\pi$
$431$	−8.62602			−0.415501			−0.207750	+	0.978182i	$0.566614\pi$
$432$	21.0234	−	85.5745i	1.01149	−	4.11720i
$433$	−0.763374			−0.0366854			−0.0183427	−	0.999832i	$-0.505839\pi$
$433$	−0.763374			−0.0366854			−0.0183427	+	0.999832i	$0.505839\pi$
$434$	6.74336	−	5.65835i	0.323692	−	0.271610i
$435$	−1.04753	+	0.656245i	−0.0502254	+	0.0314645i
$436$	−7.44741	+	42.2363i	−0.356666	+	2.02275i
$437$	−1.75452	+	0.638593i	−0.0839301	+	0.0305481i
$438$	12.0977	+	13.4049i	0.578051	+	0.640511i
$439$	−3.42610	−	19.4304i	−0.163519	−	0.927361i	−0.950579	−	0.310484i	$-0.899509\pi$
$439$	−3.42610	−	19.4304i	−0.163519	−	0.927361i	0.787060	−	0.616877i	$-0.211602\pi$
$440$	1.84320	+	3.19251i	0.0878710	+	0.152197i
$441$	−2.43109	−	1.75778i	−0.115766	−	0.0837038i
$442$	12.1758	−	21.0890i	0.579142	−	1.00310i
$443$	23.0193	+	8.37833i	1.09368	+	0.398066i	0.824982	−	0.565159i	$-0.191185\pi$
$443$	23.0193	+	8.37833i	1.09368	+	0.398066i	0.268696	+	0.963225i	$0.413407\pi$
$444$	−33.1047	−	81.6670i	−1.57108	−	3.87574i
$445$	−3.91952	−	3.28887i	−0.185803	−	0.155907i
$446$	−25.3622	−	21.2814i	−1.20094	−	1.00771i
$447$	10.6070	+	26.1669i	0.501696	+	1.23765i
$448$	37.3669	+	13.6004i	1.76542	+	0.642560i
$449$	3.33278	−	5.77255i	0.157284	−	0.272423i	−0.776605	−	0.629988i	$-0.783060\pi$
$449$	3.33278	−	5.77255i	0.157284	−	0.272423i	0.933888	+	0.357565i	$0.116393\pi$
$450$	36.7665	−	16.4707i	1.73319	−	0.776438i
$451$	−4.16334	−	7.21111i	−0.196044	−	0.339558i
$452$	−0.723451	−	4.10289i	−0.0340283	−	0.192984i
$453$	−4.88173	−	5.40921i	−0.229364	−	0.254147i
$454$	−51.3798	+	18.7007i	−2.41137	+	0.877668i
$455$	0.417486	−	2.36768i	0.0195721	−	0.110999i
$456$	7.85743	−	4.92242i	0.367958	−	0.230513i
$457$	10.0910	−	8.46733i	0.472036	−	0.396085i	−0.375501	−	0.926822i	$-0.622529\pi$
$457$	10.0910	−	8.46733i	0.472036	−	0.396085i	0.847537	+	0.530737i	$0.178085\pi$
$458$	−9.98797			−0.466707
$459$	−6.86220	−	3.02698i	−0.320300	−	0.141287i
$460$	−8.00675			−0.373317
$461$	−31.9610	+	26.8185i	−1.48857	+	1.24906i	−0.592176	+	0.805809i	$0.701731\pi$
$461$	−31.9610	+	26.8185i	−1.48857	+	1.24906i	−0.896397	+	0.443252i	$0.853825\pi$
$462$	0.158047	+	4.38169i	0.00735302	+	0.203855i
$463$	−5.03876	+	28.5762i	−0.234171	+	1.32805i	0.610181	+	0.792262i	$0.291097\pi$
$463$	−5.03876	+	28.5762i	−0.234171	+	1.32805i	−0.844352	+	0.535788i	$0.820015\pi$
$464$	28.7864	−	10.4774i	1.33638	−	0.486402i
$465$	0.669057	−	2.06721i	0.0310268	−	0.0958648i
$466$	−8.61224	−	48.8425i	−0.398955	−	2.26258i
$467$	−15.8784	−	27.5022i	−0.734765	−	1.27265i	−0.954826	−	0.297164i	$-0.903959\pi$
$467$	−15.8784	−	27.5022i	−0.734765	−	1.27265i	0.220062	−	0.975486i	$-0.429374\pi$
$468$	99.8484	+	28.3832i	4.61549	+	1.31201i
$469$	−4.99769	+	8.65625i	−0.230772	+	0.399708i
$470$	−1.20477	−	0.438499i	−0.0555717	−	0.0202264i
$471$	−16.3899	−	2.28427i	−0.755206	−	0.105254i
$472$	7.73495	+	6.49040i	0.356030	+	0.298745i
$473$	4.91455	+	4.12379i	0.225971	+	0.189612i
$474$	13.2585	−	17.0103i	0.608983	−	0.781310i
$475$	2.38446	+	0.867871i	0.109406	+	0.0398206i
$476$	4.10360	−	7.10764i	0.188088	−	0.325778i
$477$	−11.7332	−	17.3094i	−0.537229	−	0.792544i
$478$	2.98966	+	5.17825i	0.136744	+	0.236848i
$479$	−2.37278	−	13.4567i	−0.108415	−	0.614853i	−0.989801	−	0.142456i	$-0.954500\pi$
$479$	−2.37278	−	13.4567i	−0.108415	−	0.614853i	0.881386	−	0.472397i	$-0.156611\pi$
$480$	17.7851	−	3.80167i	0.811773	−	0.173522i
$481$	51.1669	−	18.6232i	2.33301	−	0.849146i
$482$	8.17114	−	46.3409i	0.372185	−	2.11077i
$483$	−5.45413	−	2.89199i	−0.248172	−	0.131590i
$484$	−44.2814	+	37.1565i	−2.01279	+	1.68893i
$485$	−2.62401			−0.119150
$486$	7.26017	−	42.6027i	0.329328	−	1.93250i
$487$	−8.80332			−0.398917			−0.199458	−	0.979906i	$-0.563918\pi$
$487$	−8.80332			−0.398917			−0.199458	+	0.979906i	$0.563918\pi$
$488$	−75.0472	+	62.9721i	−3.39723	+	2.85061i
$489$	−16.3011	−	8.64344i	−0.737160	−	0.390870i
$490$	0.190197	−	1.07866i	0.00859225	−	0.0487290i
$491$	−33.0422	+	12.0264i	−1.49117	+	0.542742i	−0.953758	−	0.300576i	$-0.902821\pi$
$491$	−33.0422	+	12.0264i	−1.49117	+	0.542742i	−0.537414	+	0.843318i	$0.680599\pi$
$492$	−87.8261	+	18.7734i	−3.95951	+	0.846370i
$493$	−0.452765	−	2.56776i	−0.0203915	−	0.115646i
$494$	4.41890	+	7.65377i	0.198816	+	0.344359i
$495$	0.607232	+	0.895816i	0.0272931	+	0.0402640i
$496$	−26.9234	+	46.6328i	−1.20890	+	2.09387i
$497$	−3.59396	−	1.30809i	−0.161211	−	0.0586760i
$498$	−41.4174	+	53.1374i	−1.85596	+	2.38114i
$499$	−11.8468	−	9.94063i	−0.530335	−	0.445004i	0.337882	−	0.941188i	$-0.390289\pi$
$499$	−11.8468	−	9.94063i	−0.530335	−	0.445004i	−0.868217	+	0.496185i	$0.834734\pi$
$500$	16.9400	+	14.2143i	0.757578	+	0.635684i
$501$	26.4906	+	3.69201i	1.18351	+	0.164947i
$502$	55.8864	+	20.3410i	2.49433	+	0.907863i
$503$	−17.0832	+	29.5890i	−0.761704	+	1.31931i	0.180268	+	0.983618i	$0.442304\pi$
$503$	−17.0832	+	29.5890i	−0.761704	+	1.31931i	−0.941972	+	0.335692i	$0.891030\pi$
$504$	29.4884	+	8.38247i	1.31352	+	0.373385i
$505$	−1.32819	−	2.30050i	−0.0591037	−	0.102371i
$506$	1.56675	+	8.88546i	0.0696504	+	0.395007i
$507$	−12.8172	+	39.6018i	−0.569231	+	1.75878i
$508$	−2.14459	+	0.780566i	−0.0951506	+	0.0346320i
$509$	3.98530	−	22.6018i	0.176645	−	1.00181i	−0.759582	−	0.650412i	$-0.774596\pi$
$509$	3.98530	−	22.6018i	0.176645	−	1.00181i	0.936227	−	0.351395i	$-0.114292\pi$
$510$	−0.0987068	−	2.73654i	−0.00437081	−	0.121176i
$511$	−2.88060	+	2.41711i	−0.127430	+	0.106927i
$512$	−104.118			−4.60139
$513$	2.19663	−	1.60753i	0.0969834	−	0.0709741i
$514$	25.6583			1.13174
$515$	1.27070	−	1.06624i	0.0559937	−	0.0469843i
$516$	58.6397	−	36.7358i	2.58147	−	1.61720i
$517$	−0.185595	+	1.05256i	−0.00816245	+	0.0462915i
$518$	23.3105	−	8.48432i	1.02420	−	0.372780i
$519$	18.6714	+	20.6889i	0.819586	+	0.908144i
$520$	4.26625	+	24.1951i	0.187088	+	1.06103i
$521$	15.1217	+	26.1915i	0.662492	+	1.14747i	0.979959	+	0.199200i	$0.0638344\pi$
$521$	15.1217	+	26.1915i	0.662492	+	1.14747i	−0.317467	+	0.948269i	$0.602832\pi$
$522$	13.7110	−	6.14230i	0.600116	−	0.268841i
$523$	−4.98167	+	8.62850i	−0.217833	+	0.377298i	−0.954145	−	0.299344i	$-0.903232\pi$
$523$	−4.98167	+	8.62850i	−0.217833	+	0.377298i	0.736312	+	0.676642i	$0.236566\pi$
$524$	−52.7076	−	19.1840i	−2.30254	−	0.838057i
$525$	3.15184	+	7.77537i	0.137558	+	0.339345i
$526$	−0.0791149	−	0.0663853i	−0.00344958	−	0.00289454i
$527$	3.51087	+	2.94597i	0.152936	+	0.128329i
$528$	−10.0756	−	24.8557i	−0.438482	−	1.08171i
$529$	9.67533	+	3.52153i	0.420667	+	0.153110i
$530$	3.81738	−	6.61190i	0.165816	−	0.287203i
$531$	2.40215	+	1.73686i	0.104245	+	0.0753731i
$532$	1.48930	+	2.57955i	0.0645695	+	0.111838i
$533$	−9.63643	−	54.6509i	−0.417400	−	2.36719i
$534$	41.6648	+	46.1668i	1.80301	+	1.99783i
$535$	−3.27143	+	1.19070i	−0.141436	+	0.0514786i
$536$	17.7367	−	100.590i	0.766110	−	4.34483i
$537$	−17.7228	+	11.1027i	−0.764794	+	0.479118i
$538$	−0.985232	+	0.826708i	−0.0424764	+	0.0356419i
$539$	−0.913089			−0.0393295
$540$	11.2094	−	3.25606i	0.482376	−	0.140118i
$541$	−22.4103			−0.963493			−0.481747	−	0.876311i	$-0.659997\pi$
$541$	−22.4103			−0.963493			−0.481747	+	0.876311i	$0.659997\pi$
$542$	4.50524	−	3.78035i	0.193517	−	0.162380i
$543$	0.0777069	+	2.15434i	0.00333472	+	0.0924516i
$544$	−6.66148	+	37.7791i	−0.285609	+	1.61977i
$545$	−2.80026	+	1.01921i	−0.119950	+	0.0436583i
$546$	−8.99794	+	27.8014i	−0.385076	+	1.18979i
$547$	2.70938	+	15.3657i	0.115845	+	0.656989i	0.986328	+	0.164792i	$0.0526951\pi$
$547$	2.70938	+	15.3657i	0.115845	+	0.656989i	−0.870483	+	0.492198i	$0.836194\pi$
$548$	16.9682	+	29.3898i	0.724846	+	1.25547i
$549$	−20.6427	+	20.0262i	−0.881009	+	0.854697i
$550$	6.13097	−	10.6192i	0.261426	−	0.452802i
$551$	0.889216	+	0.323648i	0.0378819	+	0.0137879i
$552$	62.4817	+	8.70812i	2.65940	+	0.370642i
$553$	3.44060	+	2.88701i	0.146309	+	0.122768i
$554$	−26.5632	−	22.2891i	−1.12856	−	0.946975i
$555$	3.76412	−	4.82927i	0.159778	−	0.204991i
$556$	−54.6010	−	19.8731i	−2.31560	−	0.842808i
$557$	21.5322	−	37.2948i	0.912348	−	1.58023i	0.101609	−	0.994824i	$-0.467601\pi$
$557$	21.5322	−	37.2948i	0.912348	−	1.58023i	0.810739	−	0.585408i	$-0.199066\pi$
$558$	−11.5222	+	23.7623i	−0.487774	+	1.00594i
$559$	21.3783	+	37.0284i	0.904207	+	1.56613i
$560$	1.16344	+	6.59818i	0.0491642	+	0.278824i
$561$	−2.23234	+	0.477177i	−0.0942495	+	0.0201464i
$562$	40.7200	−	14.8209i	1.71767	−	0.625180i
$563$	−5.16743	+	29.3060i	−0.217781	+	1.23510i	0.658233	+	0.752814i	$0.271304\pi$
$563$	−5.16743	+	29.3060i	−0.217781	+	1.23510i	−0.876014	+	0.482285i	$0.839807\pi$
$564$	10.1847	+	5.40032i	0.428854	+	0.227395i
$565$	0.221754	−	0.186074i	0.00932926	−	0.00782817i
$566$	9.13053			0.383785
$567$	8.81183	+	1.83077i	0.370062	+	0.0768851i
$568$	39.0833			1.63990
$569$	−4.46659	+	3.74791i	−0.187249	+	0.157121i	−0.731593	−	0.681741i	$-0.761223\pi$
$569$	−4.46659	+	3.74791i	−0.187249	+	0.157121i	0.544344	+	0.838862i	$0.316779\pi$
$570$	0.878015	+	0.465557i	0.0367760	+	0.0195000i
$571$	4.98452	−	28.2686i	0.208596	−	1.18301i	−0.683084	−	0.730340i	$-0.739362\pi$
$571$	4.98452	−	28.2686i	0.208596	−	1.18301i	0.891680	−	0.452666i	$-0.149527\pi$
$572$	29.6888	−	10.8058i	1.24135	−	0.451815i
$573$	−4.98407	+	1.06538i	−0.208213	+	0.0445068i
$574$	−4.39014	−	24.8977i	−0.183241	−	1.03921i
$575$	8.63241	+	14.9518i	0.359996	+	0.623532i
$576$	−118.985	+	8.59475i	−4.95771	+	0.358115i
$577$	14.7665	−	25.5763i	0.614737	−	1.06476i	−0.375694	−	0.926744i	$-0.622595\pi$
$577$	14.7665	−	25.5763i	0.614737	−	1.06476i	0.990431	−	0.138012i	$-0.0440712\pi$
$578$	−38.8602	−	14.1440i	−1.61637	−	0.588311i
$579$	−21.4899	+	27.5710i	−0.893091	+	1.14581i
$580$	3.10856	+	2.60839i	0.129076	+	0.108308i
$581$	−10.7479	−	9.01854i	−0.445897	−	0.374152i
$582$	31.5874	+	4.40236i	1.30934	+	0.182484i
$583$	−5.98081	−	2.17684i	−0.247700	−	0.0901554i
$584$	19.2133	−	33.2785i	0.795054	−	1.37707i
$585$	1.76095	+	6.99435i	0.0728064	+	0.289181i
$586$	36.8082	+	63.7536i	1.52053	+	2.63364i
$587$	−2.55577	−	14.4945i	−0.105488	−	0.598251i	−0.991024	−	0.133682i	$-0.957320\pi$
$587$	−2.55577	−	14.4945i	−0.105488	−	0.598251i	0.885536	−	0.464570i	$-0.153791\pi$
$588$	−3.03258	+	9.36990i	−0.125061	+	0.386408i
$589$	−1.56302	+	0.568894i	−0.0644033	+	0.0234409i
$590$	−0.187933	+	1.06582i	−0.00773710	+	0.0438793i
$591$	0.890566	+	24.6900i	0.0366330	+	1.01561i
$592$	−116.241	+	97.5374i	−4.77746	+	4.00876i
$593$	11.4808			0.471462			0.235731	−	0.971818i	$-0.424252\pi$
$593$	11.4808			0.471462			0.235731	+	0.971818i	$0.424252\pi$
$594$	−5.80684	−	11.8025i	−0.238257	−	0.484261i
$595$	0.570260			0.0233784
$596$	71.0047	−	59.5800i	2.90847	−	2.44049i
$597$	36.5891	−	22.9219i	1.49749	−	0.938130i
$598$	−10.4417	+	59.2181i	−0.426995	+	2.42161i
$599$	−12.9672	+	4.71966i	−0.529824	+	0.192840i	−0.593060	−	0.805158i	$-0.702080\pi$
$599$	−12.9672	+	4.71966i	−0.529824	+	0.192840i	0.0632358	+	0.997999i	$0.479858\pi$
$600$	−57.4414	−	63.6481i	−2.34504	−	2.59842i
$601$	−1.84613	−	10.4699i	−0.0753053	−	0.427078i	−0.999031	−	0.0440220i	$-0.985983\pi$
$601$	−1.84613	−	10.4699i	−0.0753053	−	0.427078i	0.923725	−	0.383056i	$-0.125128\pi$
$602$	9.73949	+	16.8693i	0.396952	+	0.687541i
$603$	3.06594	−	29.8290i	0.124855	−	1.21473i
$604$	−11.9598	+	20.7151i	−0.486639	+	0.842884i
$605$	−3.77426	−	1.37372i	−0.153446	−	0.0558496i
$606$	12.1290	+	29.9213i	0.492706	+	1.21547i
$607$	19.9790	+	16.7643i	0.810921	+	0.680443i	0.950827	−	0.309721i	$-0.100236\pi$
$607$	19.9790	+	16.7643i	0.810921	+	0.680443i	−0.139906	+	0.990165i	$0.544680\pi$
$608$	−10.6653	−	8.94925i	−0.432535	−	0.362940i
$609$	1.17539	+	2.89961i	0.0476292	+	0.117498i
$610$	−9.86726	−	3.59139i	−0.399514	−	0.145411i
$611$	−3.56156	+	6.16880i	−0.144085	+	0.249563i
$612$	−2.51744	+	24.4926i	−0.101762	+	0.990053i
$613$	0.0265367	+	0.0459628i	0.00107181	+	0.00185642i	0.866561	−	0.499072i	$-0.166326\pi$
$613$	0.0265367	+	0.0459628i	0.00107181	+	0.00185642i	−0.865489	+	0.500928i	$0.832992\pi$
$614$	2.24996	+	12.7602i	0.0908010	+	0.514958i
$615$	−4.18088	−	4.63263i	−0.168589	−	0.186806i
$616$	8.76806	−	3.19131i	0.353275	−	0.128582i
$617$	−7.97116	+	45.2067i	−0.320907	+	1.81995i	0.216095	+	0.976372i	$0.430668\pi$
$617$	−7.97116	+	45.2067i	−0.320907	+	1.81995i	−0.537002	+	0.843581i	$0.680443\pi$
$618$	−17.0853	+	10.7034i	−0.687273	+	0.430554i
$619$	−6.40579	+	5.37510i	−0.257471	+	0.216043i	−0.762381	−	0.647128i	$-0.775970\pi$
$619$	−6.40579	+	5.37510i	−0.257471	+	0.216043i	0.504911	+	0.863172i	$0.331525\pi$
$620$	−7.13285			−0.286462
$621$	18.4795	+	1.22829i	0.741557	+	0.0492895i
$622$	−88.4283			−3.54565
$623$	−9.92085	+	8.32458i	−0.397470	+	0.333517i
$624$	−6.44317	−	178.630i	−0.257933	−	7.15091i
$625$	3.93887	−	22.3384i	0.157555	−	0.893538i
$626$	−44.5848	+	16.2275i	−1.78197	+	0.648583i
$627$	0.255109	−	0.788223i	0.0101881	−	0.0314786i
$628$	9.43342	+	53.4996i	0.376435	+	2.13487i
$629$	6.45765	+	11.1850i	0.257483	+	0.445974i
$630$	0.802250	+	3.18647i	0.0319624	+	0.126952i
$631$	19.3630	−	33.5378i	0.770830	−	1.33512i	−0.166278	−	0.986079i	$-0.553175\pi$
$631$	19.3630	−	33.5378i	0.770830	−	1.33512i	0.937108	−	0.349038i	$-0.113492\pi$
$632$	−43.1291	−	15.6977i	−1.71559	−	0.624422i
$633$	−21.3180	−	2.97110i	−0.847314	−	0.118091i
$634$	32.0633	+	26.9043i	1.27340	+	1.06851i
$635$	−0.121476	−	0.101930i	−0.00482062	−	0.00404498i
$636$	−42.2018	+	54.1438i	−1.67341	+	2.14694i
$637$	−5.71838	−	2.08132i	−0.226571	−	0.0824649i
$638$	2.28637	−	3.96012i	0.0905184	−	0.156783i
$639$	11.4440	−	0.826645i	0.452718	−	0.0327016i
$640$	−11.2772	−	19.5327i	−0.445771	−	0.772098i
$641$	2.84951	+	16.1604i	0.112549	+	0.638296i	0.987935	+	0.154871i	$0.0494963\pi$
$641$	2.84951	+	16.1604i	0.112549	+	0.638296i	−0.875386	+	0.483425i	$0.839393\pi$
$642$	41.3786	−	8.84495i	1.63308	−	0.349082i
$643$	22.5155	−	8.19497i	0.887924	−	0.323178i	0.142521	−	0.989792i	$-0.454479\pi$
$643$	22.5155	−	8.19497i	0.887924	−	0.323178i	0.745403	+	0.666614i	$0.232257\pi$
$644$	−3.51918	+	19.9583i	−0.138675	+	0.786467i
$645$	4.24777	+	2.25233i	0.167256	+	0.0886854i
$646$	−1.60583	+	1.34745i	−0.0631806	+	0.0530148i
$647$	11.7421			0.461629			0.230815	−	0.972998i	$-0.425861\pi$
$647$	11.7421			0.461629			0.230815	+	0.972998i	$0.425861\pi$
$648$	−91.0154	+	13.2178i	−3.57542	+	0.519242i
$649$	0.902220			0.0354152
$650$	62.6019	−	52.5292i	2.45545	−	2.06037i
$651$	−4.85884	−	2.57634i	−0.190433	−	0.100975i
$652$	−10.5180	+	59.6504i	−0.411916	+	2.33609i
$653$	28.4626	−	10.3595i	1.11383	−	0.405399i	0.281430	−	0.959582i	$-0.409191\pi$
$653$	28.4626	−	10.3595i	1.11383	−	0.405399i	0.832395	+	0.554182i	$0.186969\pi$
$654$	35.4191	−	7.57106i	1.38500	−	0.296052i
$655$	−0.676762	−	3.83811i	−0.0264433	−	0.149967i
$656$	77.3244	+	133.930i	3.01901	+	5.22908i
$657$	4.92200	−	10.1507i	0.192026	−	0.396016i
$658$	−1.62257	+	2.81037i	−0.0632542	+	0.109559i
$659$	−37.8348	−	13.7708i	−1.47384	−	0.536432i	−0.524697	−	0.851289i	$-0.675821\pi$
$659$	−37.8348	−	13.7708i	−1.47384	−	0.536432i	−0.949139	+	0.314857i	$0.898043\pi$
$660$	2.18408	−	2.80211i	0.0850151	−	0.109072i
$661$	16.2318	+	13.6201i	0.631343	+	0.529759i	0.901346	−	0.433100i	$-0.142580\pi$
$661$	16.2318	+	13.6201i	0.631343	+	0.529759i	−0.270003	+	0.962859i	$0.587025\pi$
$662$	60.8421	+	51.0526i	2.36469	+	1.98421i
$663$	−15.0681	−	2.10005i	−0.585198	−	0.0815593i
$664$	134.728	+	49.0371i	5.22847	+	1.90301i
$665$	−0.103481	+	0.179235i	−0.00401283	+	0.00695043i
$666$	−53.4141	+	51.8189i	−2.06975	+	2.00794i
$667$	3.21921	+	5.57584i	0.124648	+	0.215897i
$668$	−15.2470	−	86.4701i	−0.589925	−	3.34563i
$669$	−6.36927	+	19.6794i	−0.246250	+	0.760850i
$670$	10.2877	−	3.74443i	0.397449	−	0.144660i
$671$	−1.52006	+	8.62066i	−0.0586811	+	0.332797i
$672$	−1.65934	−	46.0034i	−0.0640105	−	1.77462i
$673$	8.96380	−	7.52152i	0.345529	−	0.289933i	−0.453463	−	0.891275i	$-0.649811\pi$
$673$	8.96380	−	7.52152i	0.345529	−	0.289933i	0.798992	+	0.601342i	$0.205367\pi$
$674$	−41.9751			−1.61682
$675$	−18.1657	−	17.4219i	−0.699197	−	0.670569i
$676$	136.645			5.25556
$677$	−15.3809	+	12.9061i	−0.591135	+	0.496021i	−0.888582	−	0.458717i	$-0.848309\pi$
$677$	−15.3809	+	12.9061i	−0.591135	+	0.496021i	0.297447	+	0.954738i	$0.403865\pi$
$678$	−2.98162	+	1.86788i	−0.114508	+	0.0717356i
$679$	−1.15332	+	6.54083i	−0.0442605	+	0.251014i
$680$	−5.47600	+	1.99310i	−0.209995	+	0.0764319i
$681$	22.8866	+	25.3595i	0.877016	+	0.971780i
$682$	1.39574	+	7.91566i	0.0534458	+	0.303106i
$683$	−11.5584	−	20.0197i	−0.442270	−	0.766034i	0.555588	−	0.831458i	$-0.312493\pi$
$683$	−11.5584	−	20.0197i	−0.442270	−	0.766034i	−0.997858	+	0.0654240i	$0.979160\pi$
$684$	−7.24127	−	5.23574i	−0.276877	−	0.200193i
$685$	−1.17900	+	2.04209i	−0.0450473	+	0.0780242i
$686$	−2.60517	−	0.948204i	−0.0994658	−	0.0362026i
$687$	2.34420	+	5.78298i	0.0894369	+	0.220635i
$688$	−91.2764	−	76.5900i	−3.47988	−	2.91997i
$689$	−32.4939	−	27.2657i	−1.23792	−	1.03874i
$690$	2.54020	+	6.26650i	0.0967037	+	0.238561i
$691$	−39.0571	−	14.2156i	−1.48580	−	0.540788i	−0.533461	−	0.845824i	$-0.679109\pi$
$691$	−39.0571	−	14.2156i	−1.48580	−	0.540788i	−0.952341	+	0.305037i	$0.901331\pi$
$692$	45.7435	−	79.2301i	1.73891	−	3.01188i
$693$	2.49988	−	1.11990i	0.0949626	−	0.0425415i
$694$	−43.5557	−	75.4407i	−1.65335	−	2.86369i
$695$	−0.701073	−	3.97598i	−0.0265932	−	0.150818i
$696$	−21.4212	−	23.7358i	−0.811967	−	0.899702i
$697$	12.3690	−	4.50193i	0.468508	−	0.170523i
$698$	7.58156	−	42.9971i	0.286966	−	1.62747i
$699$	−26.2582	+	16.4499i	−0.993177	+	0.622192i
$700$	21.0987	−	17.7039i	0.797457	−	0.669146i
$701$	−12.4735			−0.471116			−0.235558	−	0.971860i	$-0.575692\pi$
$701$	−12.4735			−0.471116			−0.235558	+	0.971860i	$0.575692\pi$
$702$	−9.46348	−	87.1513i	−0.357176	−	3.28931i
$703$	−4.68730			−0.176785
$704$	−27.8143	+	23.3390i	−1.04829	+	0.879621i
$705$	0.0288729	+	0.800470i	0.00108742	+	0.0301475i
$706$	9.20973	−	52.2310i	0.346613	−	1.96574i
$707$	−6.31818	+	2.29963i	−0.237620	+	0.0864865i
$708$	2.99648	−	9.25836i	0.112615	−	0.347951i
$709$	−2.93337	−	16.6360i	−0.110165	−	0.624777i	−0.989031	−	0.147708i	$-0.952810\pi$
$709$	−2.93337	−	16.6360i	−0.110165	−	0.624777i	0.878866	−	0.477069i	$-0.158301\pi$
$710$	2.09455	+	3.62787i	0.0786072	+	0.136152i
$711$	−12.9607	−	3.68424i	−0.486064	−	0.138170i
$712$	66.1712	−	114.612i	2.47987	−	4.29526i
$713$	−10.6347	−	3.87070i	−0.398271	−	0.144959i
$714$	−6.86470	−	0.956738i	−0.256905	−	0.0358050i
$715$	1.68166	+	1.41108i	0.0628906	+	0.0527715i
$716$	52.5923	+	44.1302i	1.96547	+	1.64922i
$717$	2.29650	−	2.94635i	0.0857643	−	0.110033i
$718$	−44.1377	−	16.0648i	−1.64720	−	0.599533i
$719$	−0.835127	+	1.44648i	−0.0311450	+	0.0539447i	−0.881178	−	0.472785i	$-0.843249\pi$
$719$	−0.835127	+	1.44648i	−0.0311450	+	0.0539447i	0.850033	+	0.526730i	$0.176582\pi$
$720$	−11.2779	−	16.6377i	−0.420304	−	0.620051i
$721$	−2.09930	−	3.63609i	−0.0781820	−	0.135415i
$722$	9.01479	+	51.1254i	0.335496	+	1.90269i
$723$	−28.7489	+	6.14526i	−1.06918	+	0.228545i
$724$	6.65010	−	2.42044i	0.247149	−	0.0899549i
$725$	1.51943	−	8.61712i	0.0564302	−	0.320032i
$726$	43.1292	+	22.8688i	1.60068	+	0.848739i
$727$	29.4838	−	24.7399i	1.09350	−	0.917551i	0.0965245	−	0.995331i	$-0.469227\pi$
$727$	29.4838	−	24.7399i	1.09350	−	0.917551i	0.996971	+	0.0777792i	$0.0247829\pi$
$728$	62.1859			2.30476
$729$	−26.3707	+	5.79535i	−0.976693	+	0.214643i
$730$	4.11873			0.152441
$731$	−7.76889	+	6.51887i	−0.287343	+	0.241109i
$732$	83.4147	+	44.2296i	3.08310	+	1.63477i
$733$	−0.114541	+	0.649596i	−0.00423068	+	0.0239934i	−0.986850	−	0.161639i	$-0.948322\pi$
$733$	−0.114541	+	0.649596i	−0.00423068	+	0.0239934i	0.982619	+	0.185632i	$0.0594332\pi$
$734$	−18.3074	+	6.66335i	−0.675739	+	0.245949i
$735$	−0.669181	+	0.143042i	−0.0246831	+	0.00527617i
$736$	−16.4493	−	93.2887i	−0.606330	−	3.43867i
$737$	−4.56333	−	7.90392i	−0.168093	−	0.291145i
$738$	42.5565	+	62.7812i	1.56653	+	2.31101i
$739$	−0.452272	+	0.783357i	−0.0166371	+	0.0288163i	−0.874224	−	0.485523i	$-0.838629\pi$
$739$	−0.452272	+	0.783357i	−0.0166371	+	0.0288163i	0.857587	+	0.514339i	$0.171963\pi$
$740$	−18.8883	−	6.87477i	−0.694347	−	0.252722i
$741$	3.39436	−	4.35488i	0.124695	−	0.159981i
$742$	−14.8035	−	12.4216i	−0.543454	−	0.456012i
$743$	29.6264	+	24.8595i	1.08689	+	0.912008i	0.996474	−	0.0838967i	$-0.0267366\pi$
$743$	29.6264	+	24.8595i	1.08689	+	0.912008i	0.0904138	+	0.995904i	$0.471181\pi$
$744$	55.6622	+	7.75767i	2.04067	+	0.284410i
$745$	6.05198	+	2.20274i	0.221727	+	0.0807021i
$746$	−19.4503	+	33.6889i	−0.712126	+	1.23344i
$747$	40.4871	+	11.5090i	1.48134	+	0.421091i
$748$	3.74695	+	6.48991i	0.137002	+	0.237295i
$749$	1.53016	+	8.67798i	0.0559109	+	0.317087i
$750$	5.75053	−	17.7677i	0.209980	−	0.648784i
$751$	−4.90427	+	1.78501i	−0.178959	+	0.0651359i	−0.429946	−	0.902855i	$-0.641467\pi$
$751$	−4.90427	+	1.78501i	−0.178959	+	0.0651359i	0.250986	+	0.967991i	$0.419245\pi$
$752$	3.44699	−	19.5489i	0.125699	−	0.712874i
$753$	−1.33935	−	37.1320i	−0.0488087	−	1.35317i
$754$	23.3456	−	19.5893i	0.850198	−	0.713401i
$755$	−1.66201			−0.0604868
$756$	−3.18948	−	29.3726i	−0.116000	−	1.06827i
$757$	−31.7625			−1.15443			−0.577215	−	0.816592i	$-0.695860\pi$
$757$	−31.7625			−1.15443			−0.577215	+	0.816592i	$0.695860\pi$
$758$	−18.2503	+	15.3138i	−0.662880	+	0.556222i
$759$	4.77692	−	2.99258i	0.173391	−	0.108624i
$760$	0.367254	−	2.08280i	0.0133217	−	0.0755511i
$761$	−1.96342	+	0.714626i	−0.0711739	+	0.0259052i	−0.377362	−	0.926066i	$-0.623169\pi$
$761$	−1.96342	+	0.714626i	−0.0711739	+	0.0259052i	0.306188	+	0.951971i	$0.400946\pi$
$762$	1.29130	+	1.43082i	0.0467787	+	0.0518333i
$763$	1.30978	+	7.42814i	0.0474173	+	0.268917i
$764$	8.36569	+	14.4898i	0.302660	+	0.524223i
$765$	−1.56127	+	0.699423i	−0.0564480	+	0.0252877i
$766$	−22.8610	+	39.5964i	−0.826001	+	1.43068i
$767$	5.65031	+	2.05655i	0.204021	+	0.0742576i
$768$	51.2342	+	126.391i	1.84876	+	4.56075i
$769$	25.1394	+	21.0945i	0.906550	+	0.760685i	0.971459	−	0.237206i	$-0.0762316\pi$
$769$	25.1394	+	21.0945i	0.906550	+	0.760685i	−0.0649099	+	0.997891i	$0.520676\pi$
$770$	0.766128	+	0.642858i	0.0276094	+	0.0231670i
$771$	−6.02208	−	14.8560i	−0.216880	−	0.535027i
$772$	107.836	+	39.2491i	3.88110	+	1.41260i
$773$	24.9200	−	43.1628i	0.896311	−	1.55246i	0.0641385	−	0.997941i	$-0.479570\pi$
$773$	24.9200	−	43.1628i	0.896311	−	1.55246i	0.832173	−	0.554516i	$-0.187097\pi$
$774$	−47.3552	−	34.2398i	−1.70215	−	1.23072i
$775$	7.69022	+	13.3199i	0.276241	+	0.478463i
$776$	−11.7857	−	66.8401i	−0.423082	−	2.39942i
$777$	−10.3834	−	11.5054i	−0.372503	−	0.412753i
$778$	−3.40102	+	1.23787i	−0.121933	+	0.0443798i
$779$	−0.829537	+	4.70454i	−0.0297213	+	0.168558i
$780$	20.0654	−	12.5703i	0.718456	−	0.450089i
$781$	2.67519	−	2.24475i	0.0957257	−	0.0803234i
$782$	−14.2628			−0.510036
$783$	−6.77438	−	6.49701i	−0.242096	−	0.232184i
$784$	16.9585			0.605662
$785$	−2.89155	+	2.42630i	−0.103204	+	0.0865984i
$786$	1.70748	+	47.3380i	0.0609037	+	1.68849i
$787$	−2.93375	+	16.6381i	−0.104577	+	0.593085i	0.886811	+	0.462131i	$0.152915\pi$
$787$	−2.93375	+	16.6381i	−0.104577	+	0.593085i	−0.991388	+	0.130954i	$0.958196\pi$
$788$	76.2140	−	27.7396i	2.71501	−	0.988183i
$789$	−0.0198683	+	0.0613880i	−0.000707330	+	0.00218547i
$790$	−0.854251	−	4.84470i	−0.0303929	−	0.172367i
$791$	−0.366355	−	0.634546i	−0.0130261	−	0.0225619i
$792$	−20.0913	+	19.4913i	−0.713913	+	0.692592i
$793$	−29.1698	+	50.5236i	−1.03585	+	1.79414i
$794$	−58.3385	−	21.2335i	−2.07036	−	0.753548i
$795$	−4.72421	−	0.658415i	−0.167550	−	0.0233516i
$796$	−108.578	−	91.1080i	−3.84846	−	3.22924i
$797$	−35.8794	−	30.1064i	−1.27091	−	1.06642i	−0.994429	−	0.105405i	$-0.966386\pi$
$797$	−35.8794	−	30.1064i	−1.27091	−	1.06642i	−0.276485	−	0.961018i	$-0.589170\pi$
$798$	1.54640	−	1.98399i	0.0547419	−	0.0702324i
$799$	−1.58766	−	0.577860i	−0.0561673	−	0.0204432i
$800$	−64.3692	+	111.491i	−2.27579	+	3.94179i
$801$	16.9515	−	34.9592i	0.598952	−	1.23522i
$802$	−2.58142	−	4.47115i	−0.0911530	−	0.157882i
$803$	−0.596228	−	3.38137i	−0.0210404	−	0.119326i
$804$	−96.2640	+	20.5771i	−3.39497	+	0.725697i
$805$	−1.32323	+	0.481617i	−0.0466378	+	0.0169748i
$806$	−9.30208	+	52.7547i	−0.327652	+	1.85821i
$807$	0.709896	+	0.376414i	0.0249895	+	0.0132504i
$808$	52.6338	−	44.1650i	1.85165	−	1.55372i
$809$	15.6033			0.548582			0.274291	−	0.961647i	$-0.411557\pi$
$809$	15.6033			0.548582			0.274291	+	0.961647i	$0.411557\pi$
$810$	−6.10462	−	7.74006i	−0.214495	−	0.271958i
$811$	−31.7541			−1.11504			−0.557518	−	0.830165i	$-0.688246\pi$
$811$	−31.7541			−1.11504			−0.557518	+	0.830165i	$0.688246\pi$
$812$	7.86818	−	6.60219i	0.276119	−	0.231691i
$813$	−3.24620	−	1.72126i	−0.113849	−	0.0603671i
$814$	−3.93323	+	22.3064i	−0.137860	+	0.781840i
$815$	−3.95481	+	1.43943i	−0.138531	+	0.0504212i
$816$	41.4606	−	8.86247i	1.45141	−	0.310248i
$817$	−0.639137	−	3.62472i	−0.0223606	−	0.126813i
$818$	19.9811	+	34.6083i	0.698624	+	1.21005i
$819$	18.2087	−	1.31528i	0.636263	−	0.0459597i
$820$	−10.2428	+	17.7411i	−0.357695	+	0.619545i
$821$	−9.39408	−	3.41916i	−0.327856	−	0.119330i	0.172848	−	0.984949i	$-0.444703\pi$
$821$	−9.39408	−	3.41916i	−0.327856	−	0.119330i	−0.500703	+	0.865619i	$0.666925\pi$
$822$	17.6187	−	22.6043i	0.614522	−	0.788416i
$823$	5.71566	+	4.79600i	0.199235	+	0.167178i	0.736947	−	0.675950i	$-0.236267\pi$
$823$	5.71566	+	4.79600i	0.199235	+	0.167178i	−0.537712	+	0.843129i	$0.680711\pi$
$824$	32.8672	+	27.5789i	1.14498	+	0.960755i
$825$	−7.58739	−	1.05746i	−0.264159	−	0.0368160i
$826$	2.57416	+	0.936917i	0.0895664	+	0.0325995i
$827$	17.6755	−	30.6149i	0.614638	−	1.06458i	−0.375809	−	0.926697i	$-0.622635\pi$
$827$	17.6755	−	30.6149i	0.614638	−	1.06458i	0.990448	−	0.137888i	$-0.0440314\pi$
$828$	−14.8439	−	58.9586i	−0.515860	−	2.04895i
$829$	−27.7877	−	48.1297i	−0.965107	−	1.67161i	−0.709327	−	0.704879i	$-0.751001\pi$
$829$	−27.7877	−	48.1297i	−0.965107	−	1.67161i	−0.255780	−	0.966735i	$-0.582332\pi$
$830$	2.66854	+	15.1340i	0.0926263	+	0.525310i
$831$	−6.67086	+	20.6113i	−0.231410	+	0.714997i
$832$	−227.392	+	82.7638i	−7.88338	+	2.86932i
$833$	0.250645	−	1.42148i	0.00868433	−	0.0492513i
$834$	1.76881	+	49.0384i	0.0612490	+	1.69806i
$835$	4.67355	−	3.92157i	0.161735	−	0.135712i
$836$	−2.71973			−0.0940640
$837$	16.4626	+	1.09423i	0.569029	+	0.0378220i
$838$	−87.7086			−3.02984
$839$	10.6253	−	8.91571i	0.366827	−	0.307805i	−0.440678	−	0.897665i	$-0.645262\pi$
$839$	10.6253	−	8.91571i	0.366827	−	0.307805i	0.807505	+	0.589861i	$0.200817\pi$
$840$	5.92595	−	3.71241i	0.204465	−	0.128090i
$841$	−4.46917	+	25.3459i	−0.154109	+	0.873997i
$842$	−46.5655	+	16.9485i	−1.60475	+	0.584083i
$843$	−18.1383	−	20.0982i	−0.624715	−	0.692217i
$844$	12.2699	+	69.5858i	0.422346	+	2.39524i
$845$	4.74724	+	8.22246i	0.163310	+	0.282861i
$846$	0.995398	−	9.68437i	0.0342225	−	0.332956i
$847$	−5.08313	+	8.80425i	−0.174659	+	0.302517i
$848$	111.080	+	40.4297i	3.81449	+	1.38836i
$849$	−2.14296	−	5.28653i	−0.0735461	−	0.181433i
$850$	14.8487	+	12.4596i	0.509307	+	0.427359i
$851$	−24.4307	−	20.4998i	−0.837472	−	0.702723i
$852$	−14.1502	−	34.9075i	−0.484776	−	1.19591i
$853$	−44.4408	−	16.1751i	−1.52162	−	0.553826i	−0.560070	−	0.828445i	$-0.689226\pi$
$853$	−44.4408	−	16.1751i	−1.52162	−	0.553826i	−0.961553	+	0.274620i	$0.911448\pi$
$854$	−13.2891	+	23.0174i	−0.454744	+	0.787640i
$855$	0.0634828	−	0.617634i	0.00217107	−	0.0211226i
$856$	−45.0237	−	77.9834i	−1.53888	−	2.66542i
$857$	−0.557766	−	3.16325i	−0.0190529	−	0.108054i	0.973798	−	0.227414i	$-0.0730270\pi$
$857$	−0.557766	−	3.16325i	−0.0190529	−	0.108054i	−0.992851	+	0.119359i	$0.961916\pi$
$858$	−17.8762	−	19.8078i	−0.610283	−	0.676226i
$859$	−33.8907	+	12.3352i	−1.15633	+	0.420871i	−0.847787	−	0.530337i	$-0.822065\pi$
$859$	−33.8907	+	12.3352i	−1.15633	+	0.420871i	−0.308548	+	0.951209i	$0.599843\pi$
$860$	2.74080	−	15.5439i	0.0934605	−	0.530041i
$861$	−13.3853	+	8.38543i	−0.456169	+	0.285775i
$862$	18.3195	−	15.3719i	0.623966	−	0.523570i
$863$	−3.36407			−0.114514			−0.0572571	−	0.998359i	$-0.518235\pi$
$863$	−3.36407			−0.114514			−0.0572571	+	0.998359i	$0.518235\pi$
$864$	60.9661	+	123.914i	2.07411	+	4.21565i
$865$	6.35679			0.216137
$866$	1.62122	−	1.36036i	0.0550912	−	0.0462270i
$867$	0.931307	+	25.8195i	0.0316289	+	0.876876i
$868$	−3.13508	+	17.7799i	−0.106412	+	0.603490i
$869$	−3.85371	+	1.40264i	−0.130728	+	0.0475812i
$870$	1.05525	−	3.26045i	0.0357763	−	0.110540i
$871$	−10.5623	−	59.9015i	−0.357888	−	2.02969i
$872$	−38.5392	−	66.7519i	−1.30510	−	2.26050i
$873$	−4.86471	−	19.3222i	−0.164645	−	0.653958i
$874$	2.58817	−	4.48284i	0.0875461	−	0.151634i
$875$	3.65459	+	1.33016i	0.123548	+	0.0449676i
$876$	−36.6791	−	5.11198i	−1.23927	−	0.172718i
$877$	−4.34919	−	3.64940i	−0.146862	−	0.123231i	0.566397	−	0.824133i	$-0.308337\pi$
$877$	−4.34919	−	3.64940i	−0.146862	−	0.123231i	−0.713258	+	0.700901i	$0.752781\pi$
$878$	41.9019	+	35.1599i	1.41412	+	1.18659i
$879$	28.2740	−	36.2749i	0.953660	−	1.22352i
$880$	−5.74872	−	2.09236i	−0.193789	−	0.0705336i
$881$	0.343162	−	0.594375i	0.0115614	−	0.0200250i	−0.860187	−	0.509979i	$-0.829653\pi$
$881$	0.343162	−	0.594375i	0.0115614	−	0.0200250i	0.871748	+	0.489954i	$0.162986\pi$
$882$	8.29547	−	0.599214i	0.279323	−	0.0201766i
$883$	6.39841	+	11.0824i	0.215323	+	0.372951i	0.953373	−	0.301796i	$-0.0975861\pi$
$883$	6.39841	+	11.0824i	0.215323	+	0.372951i	−0.738049	+	0.674747i	$0.764253\pi$
$884$	8.67266	+	49.1851i	0.291693	+	1.65427i
$885$	0.661215	−	0.141339i	0.0222265	−	0.00475106i
$886$	−63.8178	+	23.2278i	−2.14400	+	0.780352i
$887$	−0.831018	+	4.71294i	−0.0279028	+	0.158245i	−0.995576	−	0.0939644i	$-0.970046\pi$
$887$	−0.831018	+	4.71294i	−0.0279028	+	0.158245i	0.967673	+	0.252209i	$0.0811571\pi$
$888$	139.920	+	74.1910i	4.69541	+	2.48969i
$889$	−0.307472	+	0.258000i	−0.0103123	+	0.00865303i
$890$	14.1850			0.475482
$891$	−5.47069	+	6.13220i	−0.183275	+	0.205436i
$892$	67.9031			2.27356
$893$	0.469725	−	0.394146i	0.0157187	−	0.0131896i
$894$	−69.1571	−	36.6698i	−2.31296	−	1.22642i
$895$	−0.828356	+	4.69784i	−0.0276889	+	0.157031i
$896$	−53.6455	+	19.5254i	−1.79217	+	0.652296i
$897$	36.7377	−	7.85292i	1.22664	−	0.262201i
$898$	3.20891	+	18.1986i	0.107083	+	0.607296i
$899$	2.86785	+	4.96727i	0.0956482	+	0.165668i
$900$	−36.0509	+	74.3479i	−1.20170	+	2.47826i
$901$	5.03060	−	8.71325i	0.167594	−	0.290281i
$902$	21.6924	+	7.89538i	0.722278	+	0.262888i
$903$	7.48135	−	9.59838i	0.248964	−	0.319414i
$904$	5.73576	+	4.81287i	0.190769	+	0.160074i
$905$	0.376682	+	0.316073i	0.0125213	+	0.0105066i
$906$	20.0070	+	2.78839i	0.664689	+	0.0926381i
$907$	−5.16966	−	1.88160i	−0.171656	−	0.0624776i	0.254763	−	0.967004i	$-0.418003\pi$
$907$	−5.16966	−	1.88160i	−0.171656	−	0.0624776i	−0.426418	+	0.904526i	$0.640225\pi$
$908$	56.0703	−	97.1166i	1.86076	−	3.22293i
$909$	14.4776	−	14.0452i	0.480192	−	0.465851i
$910$	3.33267	+	5.77235i	0.110477	+	0.191352i
$911$	−4.36843	−	24.7746i	−0.144733	−	0.820819i	−0.967582	−	0.252559i	$-0.918728\pi$
$911$	−4.36843	−	24.7746i	−0.144733	−	0.820819i	0.822849	−	0.568260i	$-0.192383\pi$
$912$	−4.73807	+	14.6394i	−0.156893	+	0.484759i
$913$	12.0384	−	4.38161i	0.398412	−	0.145010i
$914$	−6.34161	+	35.9650i	−0.209762	+	1.18962i
$915$	0.236475	+	6.55600i	0.00781761	+	0.216735i
$916$	15.6923	−	13.1674i	0.518489	−	0.435064i
$917$	−9.86464			−0.325759
$918$	19.9678	−	5.80016i	0.659036	−	0.191434i
$919$	39.3115			1.29677			0.648383	−	0.761315i	$-0.275446\pi$
$919$	39.3115			1.29677			0.648383	+	0.761315i	$0.275446\pi$
$920$	11.0232	−	9.24958i	0.363425	−	0.304950i
$921$	6.86000	−	4.29756i	0.226045	−	0.141609i
$922$	20.0857	−	113.912i	0.661487	−	3.75148i
$923$	21.8706	−	7.96024i	0.719879	−	0.262015i
$924$	−6.02482	−	6.67581i	−0.198202	−	0.219618i
$925$	7.52631	+	42.6838i	0.247464	+	1.40344i
$926$	−40.2229	−	69.6681i	−1.32181	−	2.28944i
$927$	10.2072	+	7.38022i	0.335248	+	0.242398i
$928$	−24.0047	+	41.5773i	−0.787992	+	1.36484i
$929$	40.0078	+	14.5617i	1.31261	+	0.477753i	0.901084	−	0.433644i	$-0.142772\pi$
$929$	40.0078	+	14.5617i	1.31261	+	0.477753i	0.411530	+	0.911396i	$0.364995\pi$
$930$	2.26295	+	5.58254i	0.0742050	+	0.183059i
$931$	0.401293	+	0.336724i	0.0131518	+	0.0110357i
$932$	77.9213	+	65.3838i	2.55240	+	2.14172i
$933$	20.7543	+	51.1995i	0.679467	+	1.67620i
$934$	82.7318	+	30.1119i	2.70707	+	0.985292i
$935$	−0.260349	+	0.450938i	−0.00851433	+	0.0147473i
$936$	−170.254	+	76.2708i	−5.56493	+	2.49299i
$937$	11.7036	+	20.2711i	0.382338	+	0.662229i	0.991396	−	0.130896i	$-0.0417856\pi$
$937$	11.7036	+	20.2711i	0.382338	+	0.662229i	−0.609058	+	0.793126i	$0.708452\pi$
$938$	−4.81193	−	27.2898i	−0.157115	−	0.891044i
$939$	19.8598	+	22.0057i	0.648101	+	0.718130i
$940$	2.47092	−	0.899342i	0.0805926	−	0.0293333i
$941$	−9.60371	+	54.4653i	−0.313072	+	1.77552i	0.269761	+	0.962927i	$0.413055\pi$
$941$	−9.60371	+	54.4653i	−0.313072	+	1.77552i	−0.582833	+	0.812592i	$0.698056\pi$
$942$	38.8787	−	24.3562i	1.26674	−	0.793568i
$943$	−24.8988	+	20.8926i	−0.810816	+	0.680355i
$944$	−16.7567			−0.545383
$945$	1.65666	−	1.21237i	0.0538912	−	0.0394385i
$946$	−17.7860			−0.578274
$947$	−23.5202	+	19.7358i	−0.764305	+	0.641328i	−0.939244	−	0.343251i	$-0.888472\pi$
$947$	−23.5202	+	19.7358i	−0.764305	+	0.641328i	0.174939	+	0.984579i	$0.444027\pi$
$948$	1.59445	+	44.2044i	0.0517853	+	1.43569i
$949$	3.97362	−	22.5355i	0.128989	−	0.731534i
$950$	−6.61057	+	2.40605i	−0.214475	+	0.0780626i
$951$	8.05212	−	24.8790i	0.261108	−	0.806757i
$952$	2.56132	+	14.5259i	0.0830127	+	0.470789i
$953$	−9.01526	−	15.6149i	−0.292033	−	0.505816i	0.682257	−	0.731112i	$-0.260998\pi$
$953$	−9.01526	−	15.6149i	−0.292033	−	0.505816i	−0.974290	+	0.225296i	$0.927665\pi$
$954$	55.7646	+	15.8518i	1.80545	+	0.513221i
$955$	−0.581273	+	1.00679i	−0.0188096	+	0.0325791i
$956$	−11.5238	−	4.19431i	−0.372705	−	0.135654i
$957$	−2.82951	−	0.394350i	−0.0914649	−	0.0127475i
$958$	29.0196	+	24.3503i	0.937581	+	0.786724i
$959$	4.57208	+	3.83643i	0.147640	+	0.123885i
$960$	−16.7282	+	21.4619i	−0.539901	+	0.692679i
$961$	19.6565	+	7.15439i	0.634082	+	0.230787i
$962$	−75.4785	+	130.733i	−2.43352	+	4.21499i
$963$	−14.8328	−	21.8821i	−0.477982	−	0.705140i
$964$	48.2546	+	83.5794i	1.55418	+	2.69191i
$965$	1.38461	+	7.85249i	0.0445720	+	0.252781i
$966$	16.7369	−	3.57761i	0.538500	−	0.115108i
$967$	−42.1673	+	15.3477i	−1.35601	+	0.493547i	−0.914818	−	0.403865i	$-0.867666\pi$
$967$	−42.1673	+	15.3477i	−1.35601	+	0.493547i	−0.441192	+	0.897413i	$0.645444\pi$
$968$	18.0400	−	102.310i	0.579827	−	3.28836i
$969$	1.15706	+	0.613517i	0.0371701	+	0.0197090i
$970$	5.57275	−	4.67609i	0.178930	−	0.150140i
$971$	−1.47459			−0.0473220			−0.0236610	−	0.999720i	$-0.507532\pi$
$971$	−1.47459			−0.0473220			−0.0236610	+	0.999720i	$0.507532\pi$
$972$	44.7577	+	76.5053i	1.43560	+	2.45391i
$973$	−10.2190			−0.327606
$974$	18.6961	−	15.6879i	0.599061	−	0.502672i
$975$	−45.1070	−	23.9174i	−1.44458	−	0.765971i
$976$	28.2315	−	160.109i	0.903669	−	5.12496i
$977$	−20.3422	+	7.40394i	−0.650804	+	0.236873i	−0.646261	−	0.763117i	$-0.723668\pi$
$977$	−20.3422	+	7.40394i	−0.650804	+	0.236873i	−0.00454265	+	0.999990i	$0.501446\pi$
$978$	50.0224	−	10.6926i	1.59954	−	0.341912i
$979$	−2.05342	−	11.6455i	−0.0656276	−	0.372193i
$980$	1.12321	+	1.94546i	0.0358796	+	0.0621453i
$981$	−12.6966	−	18.7305i	−0.405370	−	0.598020i
$982$	48.7419	−	84.4235i	1.55542	−	2.69406i
$983$	22.1135	+	8.04867i	0.705313	+	0.256713i	0.669677	−	0.742652i	$-0.266432\pi$
$983$	22.1135	+	8.04867i	0.705313	+	0.256713i	0.0356351	+	0.999365i	$0.488655\pi$
$984$	99.2263	−	127.305i	3.16322	−	4.05833i
$985$	4.31699	+	3.62238i	0.137551	+	0.115419i
$986$	5.53741	+	4.64644i	0.176347	+	0.147973i
$987$	2.00801	+	0.279857i	0.0639156	+	0.00890796i
$988$	−17.0328	−	6.19944i	−0.541886	−	0.197230i
$989$	12.5214	−	21.6877i	0.398157	−	0.689627i
$990$	−2.88599	−	0.820380i	−0.0917229	−	0.0260734i
$991$	10.4745	+	18.1424i	0.332734	+	0.576312i	0.983047	−	0.183354i	$-0.0586955\pi$
$991$	10.4745	+	18.1424i	0.332734	+	0.576312i	−0.650313	+	0.759667i	$0.725362\pi$
$992$	−14.6539	−	83.1066i	−0.465263	−	2.63864i
$993$	15.2794	−	47.2094i	0.484877	−	1.49815i
$994$	9.96375	−	3.62651i	0.316031	−	0.115026i
$995$	1.71016	−	9.69882i	0.0542158	−	0.307473i
$996$	−4.98080	−	138.087i	−0.157823	−	4.37546i
$997$	−37.7655	+	31.6890i	−1.19604	+	1.00360i	−0.196310	+	0.980542i	$0.562896\pi$
$997$	−37.7655	+	31.6890i	−1.19604	+	1.00360i	−0.999734	+	0.0230587i	$0.992660\pi$
$998$	42.8742			1.35716
$999$	42.5393	+	18.7645i	1.34588	+	0.593682i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.v.b.22.1	✓	54
3.2	odd	2		567.2.v.a.442.9		54
27.4	even	9		5103.2.a.g.1.1		27
27.11	odd	18		567.2.v.a.127.9		54
27.16	even	9	inner	189.2.v.b.43.1	yes	54
27.23	odd	18		5103.2.a.h.1.27		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.v.b.22.1	✓	54	1.1	even	1	trivial
189.2.v.b.43.1	yes	54	27.16	even	9	inner
567.2.v.a.127.9		54	27.11	odd	18
567.2.v.a.442.9		54	3.2	odd	2
5103.2.a.g.1.1		27	27.4	even	9
5103.2.a.h.1.27		27	27.23	odd	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.v (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.12375 + 1.78204i) q^{2} +(1.53024 + 0.811393i) q^{3} +(0.987362 - 5.59961i) q^{4} +(0.371253 - 0.135125i) q^{5} +(-4.69579 + 1.00376i) q^{6} +(-0.173648 - 0.984808i) q^{7} +(5.10945 + 8.84983i) q^{8} +(1.68328 + 2.48326i) q^{9} +(-0.547652 + 0.948561i) q^{10} +(0.858023 + 0.312295i) q^{11} +(6.05439 - 7.76762i) q^{12} +(4.66167 + 3.91160i) q^{13} +(2.12375 + 1.78204i) q^{14} +(0.677747 + 0.0944580i) q^{15} +(-15.9358 - 5.80016i) q^{16} +(-0.721703 + 1.25003i) q^{17} +(-8.00014 - 2.27414i) q^{18} +(-0.261925 - 0.453668i) q^{19} +(-0.390087 - 2.21229i) q^{20} +(0.533342 - 1.64789i) q^{21} +(-2.37875 + 0.865794i) q^{22} +(0.618922 - 3.51008i) q^{23} +(0.638011 + 17.6882i) q^{24} +(-3.71065 + 3.11361i) q^{25} -16.8709 q^{26} +(0.560936 + 5.16579i) q^{27} -5.68599 q^{28} +(-1.38378 + 1.16113i) q^{29} +(-1.60770 + 1.00717i) q^{30} +(0.551369 - 3.12697i) q^{31} +(24.9745 - 9.08999i) q^{32} +(1.05959 + 1.17408i) q^{33} +(-0.694878 - 3.94085i) q^{34} +(-0.197540 - 0.342149i) q^{35} +(15.5673 - 6.97386i) q^{36} +(4.47389 - 7.74901i) q^{37} +(1.36472 + 0.496717i) q^{38} +(3.95963 + 9.76815i) q^{39} +(3.09274 + 2.59511i) q^{40} +(-6.98574 - 5.86173i) q^{41} +(1.80392 + 4.45015i) q^{42} +(6.60241 + 2.40308i) q^{43} +(2.59591 - 4.49625i) q^{44} +(0.960475 + 0.694463i) q^{45} +(4.94067 + 8.55749i) q^{46} +(0.203260 + 1.15275i) q^{47} +(-19.6794 - 21.8058i) q^{48} +(-0.939693 + 0.342020i) q^{49} +(2.33194 - 13.2251i) q^{50} +(-2.11864 + 1.32726i) q^{51} +(26.5062 - 22.2414i) q^{52} -6.97045 q^{53} +(-10.3969 - 9.97124i) q^{54} +0.360743 q^{55} +(7.82814 - 6.56859i) q^{56} +(-0.0327063 - 0.906746i) q^{57} +(0.869630 - 4.93192i) q^{58} +(0.928507 - 0.337949i) q^{59} +(1.19811 - 3.70186i) q^{60} +(1.66474 + 9.44121i) q^{61} +(4.40142 + 7.62348i) q^{62} +(2.15323 - 2.08892i) q^{63} +(-19.8825 + 34.4375i) q^{64} +(2.25922 + 0.822287i) q^{65} +(-4.34256 - 0.605226i) q^{66} +(-7.65690 - 6.42490i) q^{67} +(6.28708 + 5.27549i) q^{68} +(3.79515 - 4.86908i) q^{69} +(1.02925 + 0.374616i) q^{70} +(1.91230 - 3.31221i) q^{71} +(-13.3757 + 27.5849i) q^{72} +(-1.88018 - 3.25656i) q^{73} +(4.30760 + 24.4296i) q^{74} +(-8.20455 + 1.75378i) q^{75} +(-2.79898 + 1.01874i) q^{76} +(0.158556 - 0.899217i) q^{77} +(-25.8165 - 13.6889i) q^{78} +(-3.44060 + 2.88701i) q^{79} -6.69997 q^{80} +(-3.33311 + 8.36004i) q^{81} +25.2818 q^{82} +(10.7479 - 9.01854i) q^{83} +(-8.70095 - 4.61357i) q^{84} +(-0.0990247 + 0.561597i) q^{85} +(-18.3043 + 6.66221i) q^{86} +(-3.05966 + 0.654022i) q^{87} +(1.62027 + 9.18901i) q^{88} +(-6.47537 - 11.2157i) q^{89} +(-3.27737 + 0.236737i) q^{90} +(3.04269 - 5.27009i) q^{91} +(-19.0440 - 6.93144i) q^{92} +(3.38093 - 4.33765i) q^{93} +(-2.48591 - 2.08593i) q^{94} +(-0.158542 - 0.133033i) q^{95} +(45.5927 + 6.35428i) q^{96} +(-6.24118 - 2.27161i) q^{97} +(1.38618 - 2.40094i) q^{98} +(0.668788 + 2.65637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{3} - 3 q^{5} + 9 q^{8} + 3 q^{9} - 6 q^{11} - 60 q^{12} + 9 q^{13} - 9 q^{15} + 30 q^{17} - 3 q^{18} + 18 q^{20} + 3 q^{21} - 9 q^{22} + 36 q^{24} - 45 q^{25} - 54 q^{26} - 57 q^{27} - 54 q^{28}+ \cdots + 51 q^{99}+O(q^{100}) \) 54 * q + 3 * q^3 - 3 * q^5 + 9 * q^8 + 3 * q^9 - 6 * q^11 - 60 * q^12 + 9 * q^13 - 9 * q^15 + 30 * q^17 - 3 * q^18 + 18 * q^20 + 3 * q^21 - 9 * q^22 + 36 * q^24 - 45 * q^25 - 54 * q^26 - 57 * q^27 - 54 * q^28 + 30 * q^29 + 24 * q^30 - 9 * q^31 + 51 * q^32 - 12 * q^33 - 9 * q^34 - 12 * q^35 + 48 * q^36 - 78 * q^38 - 36 * q^39 + 45 * q^40 - 51 * q^41 - 12 * q^42 - 9 * q^43 + 30 * q^44 + 51 * q^45 - 9 * q^47 + 15 * q^48 + 126 * q^50 - 12 * q^51 + 9 * q^52 - 60 * q^53 - 90 * q^54 + 9 * q^56 + 39 * q^57 - 27 * q^58 + 42 * q^59 + 135 * q^60 + 36 * q^62 + 9 * q^63 - 27 * q^64 - 18 * q^65 - 147 * q^66 - 27 * q^67 - 81 * q^68 + 48 * q^69 + 75 * q^72 + 84 * q^74 + 15 * q^75 + 54 * q^76 - 3 * q^77 - 66 * q^78 + 72 * q^79 - 222 * q^80 - 69 * q^81 - 54 * q^83 - 12 * q^84 + 18 * q^85 + 66 * q^86 + 3 * q^87 + 54 * q^88 + 90 * q^89 + 15 * q^90 - 129 * q^92 + 21 * q^93 + 36 * q^94 - 48 * q^95 + 36 * q^96 + 3 * q^98 + 51 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more