LMFDB - Embedded newform 187.2.j.a.135.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [187,2,Mod(16,187)] 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("187.16"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(187, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 187 = 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	187.j (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.49320251780$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			135.2
Character	$\chi$	$=$	187.135
Dual form			187.2.j.a.169.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.20158 + 1.59954i) q^{2} +(2.67663 - 0.869690i) q^{3} +(1.67040 - 5.14095i) q^{4} +(-0.525344 + 0.723074i) q^{5} +(-4.50172 + 6.19609i) q^{6} +(-1.60348 - 0.521001i) q^{7} +(2.86380 + 8.81387i) q^{8} +(3.98094 - 2.89232i) q^{9} -2.43222i q^{10} +(3.01526 + 1.38139i) q^{11} -15.2132i q^{12} +(3.39946 - 2.46985i) q^{13} +(4.36356 - 1.41781i) q^{14} +(-0.777302 + 2.39229i) q^{15} +(-11.6568 - 8.46914i) q^{16} +(3.77203 - 1.66487i) q^{17} +(-4.13798 + 12.7354i) q^{18} +(0.621965 + 1.91421i) q^{19} +(2.83976 + 3.90859i) q^{20} -4.74503 q^{21} +(-8.84793 + 1.78180i) q^{22} -0.224129i q^{23} +(15.3307 + 21.1009i) q^{24} +(1.29824 + 3.99556i) q^{25} +(-3.53356 + 10.8752i) q^{26} +(3.17734 - 4.37323i) q^{27} +(-5.35688 + 7.37312i) q^{28} +(-7.72540 - 2.51014i) q^{29} +(-2.11528 - 6.51015i) q^{30} +(-2.95114 - 4.06190i) q^{31} +20.6752 q^{32} +(9.27211 + 1.07512i) q^{33} +(-5.64142 + 9.69887i) q^{34} +(1.21910 - 0.885728i) q^{35} +(-8.21954 - 25.2971i) q^{36} +(0.147419 + 0.0478995i) q^{37} +(-4.43117 - 3.21943i) q^{38} +(6.95109 - 9.56736i) q^{39} +(-7.87756 - 2.55958i) q^{40} +(-10.1359 + 3.29336i) q^{41} +(10.4466 - 7.58988i) q^{42} -2.05890 q^{43} +(12.1383 - 13.1938i) q^{44} +4.39798i q^{45} +(0.358504 + 0.493439i) q^{46} +(2.14137 + 6.59047i) q^{47} +(-38.5664 - 12.5310i) q^{48} +(-3.36342 - 2.44367i) q^{49} +(-9.24925 - 6.71997i) q^{50} +(8.64842 - 7.73673i) q^{51} +(-7.01894 - 21.6021i) q^{52} +(-2.80455 + 2.03762i) q^{53} +14.7103i q^{54} +(-2.58289 + 1.45455i) q^{55} -15.6249i q^{56} +(3.32954 + 4.58272i) q^{57} +(21.0232 - 6.83085i) q^{58} +(0.0485272 - 0.149351i) q^{59} +(11.0002 + 7.99214i) q^{60} +(-3.26617 + 4.49549i) q^{61} +(12.9944 + 4.22213i) q^{62} +(-7.89025 + 2.56370i) q^{63} +(-22.2047 + 16.1327i) q^{64} +3.75558i q^{65} +(-22.1330 + 12.4642i) q^{66} +8.35113 q^{67} +(-2.25821 - 22.1728i) q^{68} +(-0.194923 - 0.599910i) q^{69} +(-1.26719 + 3.90001i) q^{70} +(-4.33739 + 5.96990i) q^{71} +(36.8932 + 26.8045i) q^{72} +(2.25371 + 0.732274i) q^{73} +(-0.401173 + 0.130349i) q^{74} +(6.94979 + 9.56557i) q^{75} +10.8798 q^{76} +(-4.11519 - 3.78597i) q^{77} +32.1819i q^{78} +(-8.70134 - 11.9764i) q^{79} +(12.2476 - 3.97950i) q^{80} +(0.139453 - 0.429193i) q^{81} +(17.0472 - 23.4635i) q^{82} +(-2.26611 - 1.64643i) q^{83} +(-7.92607 + 24.3939i) q^{84} +(-0.777793 + 3.60209i) q^{85} +(4.53283 - 3.29330i) q^{86} -22.8611 q^{87} +(-3.54026 + 30.5321i) q^{88} -7.97444 q^{89} +(-7.03476 - 9.68252i) q^{90} +(-6.73775 + 2.18923i) q^{91} +(-1.15224 - 0.374384i) q^{92} +(-11.4317 - 8.30563i) q^{93} +(-15.2562 - 11.0842i) q^{94} +(-1.71086 - 0.555892i) q^{95} +(55.3400 - 17.9810i) q^{96} +(0.770351 + 1.06030i) q^{97} +11.3136 q^{98} +(15.9990 - 3.22188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) $ 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/187\mathbb{Z}\right)^\times$.

$n$	$35$	$122$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$

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 $

$2$	−2.20158	+	1.59954i	−1.55676	+	1.13105i	−0.618148	+	0.786062i	$0.712117\pi$
$2$	−2.20158	+	1.59954i	−1.55676	+	1.13105i	−0.938608	+	0.344987i	$0.887883\pi$
$3$	2.67663	−	0.869690i	1.54535	−	0.502116i	0.592506	−	0.805566i	$-0.298139\pi$
$3$	2.67663	−	0.869690i	1.54535	−	0.502116i	0.952847	+	0.303450i	$0.0981386\pi$
$4$	1.67040	−	5.14095i	0.835198	−	2.57048i
$5$	−0.525344	+	0.723074i	−0.234941	+	0.323369i	−0.910166	−	0.414243i	$-0.864046\pi$
$5$	−0.525344	+	0.723074i	−0.234941	+	0.323369i	0.675225	+	0.737612i	$0.264046\pi$
$6$	−4.50172	+	6.19609i	−1.83782	+	2.52954i
$7$	−1.60348	−	0.521001i	−0.606057	−	0.196920i	−0.0101173	−	0.999949i	$-0.503220\pi$
$7$	−1.60348	−	0.521001i	−0.606057	−	0.196920i	−0.595940	+	0.803029i	$0.703220\pi$
$8$	2.86380	+	8.81387i	1.01251	+	3.11618i
$9$	3.98094	−	2.89232i	1.32698	−	0.964108i
$10$		−	2.43222i		−	0.769135i
$11$	3.01526	+	1.38139i	0.909134	+	0.416503i
$11$	3.01526	+	1.38139i	0.909134	+	0.416503i
$12$		−	15.2132i		−	4.39166i
$13$	3.39946	−	2.46985i	0.942840	−	0.685014i	−0.00626239	−	0.999980i	$-0.501993\pi$
$13$	3.39946	−	2.46985i	0.942840	−	0.685014i	0.949103	+	0.314967i	$0.101993\pi$
$14$	4.36356	−	1.41781i	1.16621	−	0.378924i
$15$	−0.777302	+	2.39229i	−0.200698	+	0.617686i
$16$	−11.6568	−	8.46914i	−2.91419	−	2.11729i
$17$	3.77203	−	1.66487i	0.914852	−	0.403789i
$17$	3.77203	−	1.66487i	0.914852	−	0.403789i
$18$	−4.13798	+	12.7354i	−0.975331	+	3.00176i
$19$	0.621965	+	1.91421i	0.142688	+	0.439150i	0.996707	−	0.0810935i	$-0.0258412\pi$
$19$	0.621965	+	1.91421i	0.142688	+	0.439150i	−0.854018	+	0.520243i	$0.825841\pi$
$20$	2.83976	+	3.90859i	0.634989	+	0.873987i
$21$	−4.74503			−1.03545
$22$	−8.84793	+	1.78180i	−1.88638	+	0.379881i
$23$		−	0.224129i		−	0.0467341i	−0.999727	−	0.0233670i	$-0.992561\pi$
$23$		−	0.224129i		−	0.0467341i	0.999727	−	0.0233670i	$-0.00743864\pi$
$24$	15.3307	+	21.1009i	3.12936	+	4.30720i
$25$	1.29824	+	3.99556i	0.259647	+	0.799111i
$26$	−3.53356	+	10.8752i	−0.692988	+	2.13280i
$27$	3.17734	−	4.37323i	0.611479	−	0.841629i
$28$	−5.35688	+	7.37312i	−1.01236	+	1.39339i
$29$	−7.72540	−	2.51014i	−1.43457	−	0.466120i	−0.514371	−	0.857568i	$-0.671974\pi$
$29$	−7.72540	−	2.51014i	−1.43457	−	0.466120i	−0.920200	+	0.391447i	$0.871974\pi$
$30$	−2.11528	−	6.51015i	−0.386195	−	1.18859i
$31$	−2.95114	−	4.06190i	−0.530041	−	0.729539i	0.457096	−	0.889418i	$-0.348890\pi$
$31$	−2.95114	−	4.06190i	−0.530041	−	0.729539i	−0.987137	+	0.159879i	$0.948890\pi$
$32$	20.6752			3.65490
$33$	9.27211	+	1.07512i	1.61407	+	0.187154i
$34$	−5.64142	+	9.69887i	−0.967495	+	1.66334i
$35$	1.21910	−	0.885728i	0.206065	−	0.149715i
$36$	−8.21954	−	25.2971i	−1.36992	−	4.21619i
$37$	0.147419	+	0.0478995i	0.0242356	+	0.00787462i	0.321110	−	0.947042i	$-0.395944\pi$
$37$	0.147419	+	0.0478995i	0.0242356	+	0.00787462i	−0.296874	+	0.954917i	$0.595944\pi$
$38$	−4.43117	−	3.21943i	−0.718831	−	0.522261i
$39$	6.95109	−	9.56736i	1.11307	−	1.53200i
$40$	−7.87756	−	2.55958i	−1.24555	−	0.404704i
$41$	−10.1359	+	3.29336i	−1.58297	+	0.514337i	−0.962819	−	0.270148i	$-0.912927\pi$
$41$	−10.1359	+	3.29336i	−1.58297	+	0.514337i	−0.620148	+	0.784485i	$0.712927\pi$
$42$	10.4466	−	7.58988i	1.61194	−	1.17114i
$43$	−2.05890			−0.313979			−0.156989	−	0.987600i	$-0.550179\pi$
$43$	−2.05890			−0.313979			−0.156989	+	0.987600i	$0.550179\pi$
$44$	12.1383	−	13.1938i	1.82992	−	1.98904i
$45$			4.39798i			0.655612i
$46$	0.358504	+	0.493439i	0.0528585	+	0.0727535i
$47$	2.14137	+	6.59047i	0.312351	+	0.961318i	0.976831	+	0.214012i	$0.0686532\pi$
$47$	2.14137	+	6.59047i	0.312351	+	0.961318i	−0.664480	+	0.747306i	$0.731347\pi$
$48$	−38.5664	−	12.5310i	−5.56658	−	1.80869i
$49$	−3.36342	−	2.44367i	−0.480489	−	0.349096i
$50$	−9.24925	−	6.71997i	−1.30804	−	0.950347i
$51$	8.64842	−	7.73673i	1.21102	−	1.08336i
$52$	−7.01894	−	21.6021i	−0.973352	−	2.99567i
$53$	−2.80455	+	2.03762i	−0.385234	+	0.279889i	−0.763500	−	0.645808i	$-0.776521\pi$
$53$	−2.80455	+	2.03762i	−0.385234	+	0.279889i	0.378265	+	0.925697i	$0.376521\pi$
$54$			14.7103i			2.00182i
$55$	−2.58289	+	1.45455i	−0.348277	+	0.196132i
$56$		−	15.6249i		−	2.08796i
$57$	3.32954	+	4.58272i	0.441008	+	0.606996i
$58$	21.0232	−	6.83085i	2.76048	−	0.896935i
$59$	0.0485272	−	0.149351i	0.00631771	−	0.0194439i	−0.947848	−	0.318723i	$-0.896746\pi$
$59$	0.0485272	−	0.149351i	0.00631771	−	0.0194439i	0.954166	+	0.299279i	$0.0967461\pi$
$60$	11.0002	+	7.99214i	1.42012	+	1.03178i
$61$	−3.26617	+	4.49549i	−0.418190	+	0.575589i	−0.965192	−	0.261542i	$-0.915769\pi$
$61$	−3.26617	+	4.49549i	−0.418190	+	0.575589i	0.547002	+	0.837131i	$0.315769\pi$
$62$	12.9944	+	4.22213i	1.65029	+	0.536211i
$63$	−7.89025	+	2.56370i	−0.994078	+	0.322996i
$64$	−22.2047	+	16.1327i	−2.77559	+	2.01658i
$65$			3.75558i			0.465823i
$66$	−22.1330	+	12.4642i	−2.72439	+	1.53423i
$67$	8.35113			1.02025			0.510127	−	0.860099i	$-0.329599\pi$
$67$	8.35113			1.02025			0.510127	+	0.860099i	$0.329599\pi$
$68$	−2.25821	−	22.1728i	−0.273848	−	2.68885i
$69$	−0.194923	−	0.599910i	−0.0234659	−	0.0722207i
$70$	−1.26719	+	3.90001i	−0.151458	+	0.466140i
$71$	−4.33739	+	5.96990i	−0.514753	+	0.708497i	−0.984712	−	0.174191i	$-0.944269\pi$
$71$	−4.33739	+	5.96990i	−0.514753	+	0.708497i	0.469958	+	0.882689i	$0.344269\pi$
$72$	36.8932	+	26.8045i	4.34790	+	3.15894i
$73$	2.25371	+	0.732274i	0.263777	+	0.0857062i	0.437920	−	0.899014i	$-0.355715\pi$
$73$	2.25371	+	0.732274i	0.263777	+	0.0857062i	−0.174143	+	0.984720i	$0.555715\pi$
$74$	−0.401173	+	0.130349i	−0.0466355	+	0.0151528i
$75$	6.94979	+	9.56557i	0.802493	+	1.10454i
$76$	10.8798			1.24800
$77$	−4.11519	−	3.78597i	−0.468970	−	0.431452i
$78$			32.1819i			3.64389i
$79$	−8.70134	−	11.9764i	−0.978977	−	1.34745i	−0.937378	−	0.348313i	$-0.886755\pi$
$79$	−8.70134	−	11.9764i	−0.978977	−	1.34745i	−0.0415990	−	0.999134i	$-0.513245\pi$
$80$	12.2476	−	3.97950i	1.36933	−	0.444921i
$81$	0.139453	−	0.429193i	0.0154948	−	0.0476881i
$82$	17.0472	−	23.4635i	1.88255	−	2.59111i
$83$	−2.26611	−	1.64643i	−0.248738	−	0.180719i	0.456429	−	0.889760i	$-0.349128\pi$
$83$	−2.26611	−	1.64643i	−0.248738	−	0.180719i	−0.705168	+	0.709041i	$0.749128\pi$
$84$	−7.92607	+	24.3939i	−0.864806	+	2.66160i
$85$	−0.777793	+	3.60209i	−0.0843635	+	0.390701i
$86$	4.53283	−	3.29330i	0.488788	−	0.355125i
$87$	−22.8611			−2.45097
$88$	−3.54026	+	30.5321i	−0.377393	+	3.25473i
$89$	−7.97444			−0.845288			−0.422644	−	0.906296i	$-0.638898\pi$
$89$	−7.97444			−0.845288			−0.422644	+	0.906296i	$0.638898\pi$
$90$	−7.03476	−	9.68252i	−0.741529	−	1.02063i
$91$	−6.73775	+	2.18923i	−0.706308	+	0.229493i
$92$	−1.15224	−	0.374384i	−0.120129	−	0.0390322i
$93$	−11.4317	−	8.30563i	−1.18541	−	0.861254i
$94$	−15.2562	−	11.0842i	−1.57355	−	1.14325i
$95$	−1.71086	−	0.555892i	−0.175531	−	0.0570334i
$96$	55.3400	−	17.9810i	5.64811	−	1.83518i
$97$	0.770351	+	1.06030i	0.0782173	+	0.107657i	0.846333	−	0.532654i	$-0.178805\pi$
$97$	0.770351	+	1.06030i	0.0782173	+	0.107657i	−0.768116	+	0.640311i	$0.778805\pi$
$98$	11.3136			1.14285
$99$	15.9990	−	3.22188i	1.60796	−	0.323811i
$100$	22.7095			2.27095
$101$	11.4206	−	8.29752i	1.13639	−	0.825634i	0.149776	−	0.988720i	$-0.452145\pi$
$101$	11.4206	−	8.29752i	1.13639	−	0.825634i	0.986612	+	0.163086i	$0.0521448\pi$
$102$	−6.66498	+	30.8666i	−0.659931	+	3.05625i
$103$	0.159849	−	0.491964i	0.0157504	−	0.0484746i	−0.942872	−	0.333154i	$-0.891887\pi$
$103$	0.159849	−	0.491964i	0.0157504	−	0.0484746i	0.958623	+	0.284679i	$0.0918871\pi$
$104$	31.5043	+	22.8892i	3.08925	+	2.24447i
$105$	2.49277	−	3.43101i	0.243270	−	0.334832i
$106$	2.91518	−	8.97200i	0.283147	−	0.871438i
$107$	2.47018	−	0.802609i	0.238801	−	0.0775911i	−0.187172	−	0.982327i	$-0.559932\pi$
$107$	2.47018	−	0.802609i	0.238801	−	0.0775911i	0.425973	+	0.904736i	$0.359932\pi$
$108$	−17.1752	−	23.6396i	−1.65268	−	2.27472i
$109$		−	8.48233i		−	0.812459i	−0.913771	−	0.406230i	$-0.866843\pi$
$109$		−	8.48233i		−	0.812459i	0.913771	−	0.406230i	$-0.133157\pi$
$110$	3.35983	−	7.33377i	0.320348	−	0.699247i
$111$	0.436245			0.0414065
$112$	14.2789	+	19.6533i	1.34923	+	1.85706i
$113$	−1.35014	+	0.438686i	−0.127010	+	0.0412681i	−0.371832	−	0.928300i	$-0.621270\pi$
$113$	−1.35014	+	0.438686i	−0.127010	+	0.0412681i	0.244822	+	0.969568i	$0.421270\pi$
$114$	−14.6605	−	4.76349i	−1.37308	−	0.446142i
$115$	0.162062	+	0.117745i	0.0151123	+	0.0109798i
$116$	−25.8090	+	35.5230i	−2.39630	+	3.29823i
$117$	6.38944	−	19.6647i	0.590704	−	1.81800i
$118$	0.132058	+	0.406431i	0.0121569	+	0.0374150i
$119$	−6.91576	+	0.704341i	−0.633967	+	0.0645668i
$120$	−23.3114			−2.12803
$121$	7.18355	+	8.33047i	0.653050	+	0.757315i
$122$		−	15.1216i		−	1.36904i
$123$	−24.2659	+	17.6302i	−2.18799	+	1.58966i
$124$	−25.8116	+	8.38670i	−2.31795	+	0.753148i
$125$	−7.82123	−	2.54127i	−0.699552	−	0.227298i
$126$	13.2703	−	18.2650i	1.18221	−	1.62718i
$127$	13.3585	+	9.70554i	1.18538	+	0.861227i	0.992768	−	0.120049i	$-0.0383050\pi$
$127$	13.3585	+	9.70554i	1.18538	+	0.861227i	0.192609	+	0.981276i	$0.438305\pi$
$128$	10.3026	−	31.7082i	0.910633	−	2.80264i
$129$	−5.51090	+	1.79060i	−0.485208	+	0.157654i
$130$	−6.00722	−	8.26823i	−0.526868	−	0.725172i
$131$			15.4990i			1.35416i	0.735911	+	0.677078i	$0.236754\pi$
$131$			15.4990i			1.35416i	−0.735911	+	0.677078i	$0.763246\pi$
$132$	21.0152	−	45.8716i	1.82914	−	3.99261i
$133$		−	3.39344i		−	0.294248i
$134$	−18.3857	+	13.3580i	−1.58828	+	1.15396i
$135$	1.49297	+	4.59490i	0.128495	+	0.395466i
$136$	25.4763	+	28.4784i	2.18457	+	2.44200i
$137$	−12.1176	−	8.80395i	−1.03528	−	0.752173i	−0.0659187	−	0.997825i	$-0.520998\pi$
$137$	−12.1176	−	8.80395i	−1.03528	−	0.752173i	−0.969358	+	0.245652i	$0.920998\pi$
$138$	1.38872	+	1.00897i	0.118216	+	0.0858888i
$139$	13.3471	+	4.33673i	1.13208	+	0.367836i	0.814368	−	0.580349i	$-0.197084\pi$
$139$	13.3471	+	4.33673i	1.13208	+	0.367836i	0.317716	+	0.948186i	$0.397084\pi$
$140$	−2.51710	−	7.74685i	−0.212734	−	0.654728i
$141$	11.4633	+	15.7779i	0.965386	+	1.32874i
$142$		−	20.0811i		−	1.68517i
$143$	13.6621	−	2.75127i	1.14248	−	0.230073i
$144$	−70.9004			−5.90837
$145$	5.87351	−	4.26735i	0.487768	−	0.354384i
$146$	−6.13303	+	1.99274i	−0.507573	+	0.164921i
$147$	−11.1279	−	3.61567i	−0.917812	−	0.298215i
$148$	0.492498	−	0.677865i	0.0404830	−	0.0557201i
$149$	−5.67493	−	4.12308i	−0.464908	−	0.337776i	0.330545	−	0.943790i	$-0.392767\pi$
$149$	−5.67493	−	4.12308i	−0.464908	−	0.337776i	−0.795454	+	0.606014i	$0.792767\pi$
$150$	−30.6011	−	9.94290i	−2.49857	−	0.811835i
$151$	2.52211	+	7.76226i	0.205246	+	0.631683i	0.999703	+	0.0243627i	$0.00775566\pi$
$151$	2.52211	+	7.76226i	0.205246	+	0.631683i	−0.794457	+	0.607321i	$0.792244\pi$
$152$	−15.0904	+	10.9638i	−1.22400	+	0.889285i
$153$	10.2009	−	17.5377i	0.824694	−	1.41784i
$154$	15.1158	+	1.75271i	1.21806	+	0.141237i
$155$	4.48742			0.360438
$156$	−37.5742	−	51.7165i	−3.00835	−	4.14063i
$157$	−1.18767	−	3.65529i	−0.0947868	−	0.291724i	0.892411	−	0.451223i	$-0.149012\pi$
$157$	−1.18767	−	3.65529i	−0.0947868	−	0.291724i	−0.987198	+	0.159499i	$0.949012\pi$
$158$	38.3135	+	12.4488i	3.04806	+	0.990374i
$159$	−5.73464	+	7.89306i	−0.454787	+	0.625960i
$160$	−10.8616	+	14.9497i	−0.858686	+	1.18188i
$161$	−0.116771	+	0.359386i	−0.00920288	+	0.0283235i
$162$	0.379495	+	1.16797i	0.0298160	+	0.0917641i
$163$	4.97874	+	6.85265i	0.389965	+	0.536741i	0.958190	−	0.286132i	$-0.0923696\pi$
$163$	4.97874	+	6.85265i	0.389965	+	0.536741i	−0.568225	+	0.822873i	$0.692370\pi$
$164$			57.6095i			4.49855i
$165$	−5.64844	+	6.13961i	−0.439730	+	0.477968i
$166$	7.62258			0.591627
$167$	2.21762	+	3.05230i	0.171605	+	0.236194i	0.886153	−	0.463392i	$-0.153368\pi$
$167$	2.21762	+	3.05230i	0.171605	+	0.236194i	−0.714548	+	0.699586i	$0.753368\pi$
$168$	−13.5888	−	41.8221i	−1.04840	−	3.22664i
$169$	1.43893	−	4.42858i	0.110687	−	0.340660i
$170$	−4.04932	−	9.17441i	−0.310569	−	0.703645i
$171$	8.01252	+	5.82144i	0.612733	+	0.445176i
$172$	−3.43917	+	10.5847i	−0.262234	+	0.807075i
$173$	4.40426	−	1.43103i	0.334850	−	0.108799i	−0.136766	−	0.990603i	$-0.543671\pi$
$173$	4.40426	−	1.43103i	0.334850	−	0.108799i	0.471616	+	0.881804i	$0.343671\pi$
$174$	50.3306	−	36.5673i	3.81555	−	2.77216i
$175$		−	7.08317i		−	0.535437i
$176$	−23.4490	−	41.6392i	−1.76754	−	3.13867i
$177$		−	0.441962i		−	0.0332199i
$178$	17.5564	−	12.7555i	1.31591	−	0.956062i
$179$	−4.22135	−	12.9920i	−0.315519	−	0.971066i	−0.975540	−	0.219820i	$-0.929453\pi$
$179$	−4.22135	−	12.9920i	−0.315519	−	0.971066i	0.660022	−	0.751246i	$-0.270547\pi$
$180$	22.6098	+	7.34637i	1.68523	+	0.547566i
$181$	−2.68301	+	3.69284i	−0.199426	+	0.274487i	−0.897004	−	0.442022i	$-0.854261\pi$
$181$	−2.68301	+	3.69284i	−0.199426	+	0.274487i	0.697578	+	0.716509i	$0.254261\pi$
$182$	11.3320	−	15.5971i	0.839981	−	1.15613i
$183$	−4.83264	+	14.8733i	−0.357239	+	1.09947i
$184$	1.97544	−	0.641861i	0.145632	−	0.0473186i
$185$	−0.112081	+	0.0814314i	−0.00824034	+	0.00598696i
$186$	38.4531			2.81952
$187$	13.6735	+	0.190632i	0.999903	+	0.0139404i
$188$	37.4582			2.73192
$189$	−7.37325	+	5.35698i	−0.536325	+	0.389663i
$190$	4.65578	−	1.51275i	0.337766	−	0.109747i
$191$	−0.737579	+	2.27003i	−0.0533693	+	0.164254i	−0.974189	−	0.225736i	$-0.927521\pi$
$191$	−0.737579	+	2.27003i	−0.0533693	+	0.164254i	0.920819	+	0.389990i	$0.127521\pi$
$192$	−45.4034	+	62.4924i	−3.27671	+	4.51000i
$193$	5.24892	−	7.22451i	0.377825	−	0.520032i	−0.577181	−	0.816616i	$-0.695847\pi$
$193$	5.24892	−	7.22451i	0.377825	−	0.520032i	0.955007	+	0.296584i	$0.0958475\pi$
$194$	−3.39199	−	1.10212i	−0.243530	−	0.0791278i
$195$	3.26619	+	10.0523i	0.233897	+	0.719861i
$196$	−18.1810	+	13.2093i	−1.29864	+	0.943521i
$197$		−	6.75748i		−	0.481450i	−0.970593	−	0.240725i	$-0.922615\pi$
$197$		−	6.75748i		−	0.481450i	0.970593	−	0.240725i	$-0.0773852\pi$
$198$	−30.0695	+	32.6843i	−2.13695	+	2.32277i
$199$			15.0195i			1.06470i	0.846523	+	0.532352i	$0.178692\pi$
$199$			15.0195i			1.06470i	−0.846523	+	0.532352i	$0.821308\pi$
$200$	−31.4985	+	22.8850i	−2.22728	+	1.61821i
$201$	22.3529	−	7.26290i	1.57665	−	0.512285i
$202$	−11.8711	+	36.5354i	−0.835245	+	2.57062i
$203$	11.0797	+	8.04989i	0.777644	+	0.564992i
$204$	−25.3279	−	57.3845i	−1.77331	−	4.01772i
$205$	2.94350	−	9.05918i	0.205583	−	0.632720i
$206$	0.434997	+	1.33878i	0.0303077	+	0.0932775i
$207$	−0.648253	−	0.892244i	−0.0450567	−	0.0620152i
$208$	−60.5443			−4.19799
$209$	−0.768880	+	6.63101i	−0.0531845	+	0.458676i
$210$			11.5409i			0.796401i
$211$	1.37734	+	1.89574i	0.0948198	+	0.130508i	0.853791	−	0.520616i	$-0.174298\pi$
$211$	1.37734	+	1.89574i	0.0948198	+	0.130508i	−0.758971	+	0.651124i	$0.774298\pi$
$212$	5.79062	+	17.8217i	0.397701	+	1.22400i
$213$	−6.41762	+	19.7514i	−0.439728	+	1.35334i
$214$	−4.15449	+	5.71817i	−0.283995	+	0.390886i
$215$	1.08163	−	1.48873i	0.0737665	−	0.101531i
$216$	47.6444	+	15.4806i	3.24179	+	1.05332i
$217$	2.61584	+	8.05072i	0.177575	+	0.546518i
$218$	13.5679	+	18.6746i	0.918931	+	1.26480i
$219$	6.66920			0.450663
$220$	3.16332	+	15.7082i	0.213271	+	1.05905i
$221$	8.71089	−	14.9760i	0.585958	−	1.00739i
$222$	−0.960430	+	0.697793i	−0.0644598	+	0.0468328i
$223$	−7.53054	−	23.1766i	−0.504282	−	1.55202i	−0.801974	−	0.597359i	$-0.796217\pi$
$223$	−7.53054	−	23.1766i	−0.504282	−	1.55202i	0.297692	−	0.954662i	$-0.403783\pi$
$224$	−33.1523	−	10.7718i	−2.21508	−	0.719723i
$225$	16.7246	+	12.1512i	1.11498	+	0.810077i
$226$	2.27074	−	3.12541i	0.151048	−	0.207899i
$227$	2.28161	+	0.741340i	0.151436	+	0.0492045i	0.383754	−	0.923435i	$-0.374631\pi$
$227$	2.28161	+	0.741340i	0.151436	+	0.0492045i	−0.232318	+	0.972640i	$0.574631\pi$
$228$	29.1212	−	9.46204i	1.92860	−	0.626639i
$229$	−16.3661	+	11.8906i	−1.08150	+	0.785755i	−0.977944	−	0.208868i	$-0.933022\pi$
$229$	−16.3661	+	11.8906i	−1.08150	+	0.785755i	−0.103556	+	0.994624i	$0.533022\pi$
$230$	−0.545131			−0.0359448
$231$	−14.3075	−	6.55471i	−0.941363	−	0.431268i
$232$		−	75.2793i		−	4.94233i
$233$	−10.4997	−	14.4517i	−0.687861	−	0.946760i	0.312133	−	0.950038i	$-0.398956\pi$
$233$	−10.4997	−	14.4517i	−0.687861	−	0.946760i	−0.999995	+	0.00327854i	$0.998956\pi$
$234$	17.3876	+	53.5136i	1.13666	+	3.49829i
$235$	−5.89035	−	1.91389i	−0.384244	−	0.124849i
$236$	−0.686749	−	0.498952i	−0.0447036	−	0.0324790i
$237$	−33.7060	−	24.4889i	−2.18944	−	1.59072i
$238$	14.0990	−	12.6127i	0.913903	−	0.817562i
$239$	8.60731	+	26.4906i	0.556760	+	1.71353i	0.691249	+	0.722617i	$0.257061\pi$
$239$	8.60731	+	26.4906i	0.556760	+	1.71353i	−0.134488	+	0.990915i	$0.542939\pi$
$240$	29.3215	−	21.3033i	1.89269	−	1.37512i
$241$		−	16.5848i		−	1.06832i	−0.845384	−	0.534160i	$-0.820628\pi$
$241$		−	16.5848i		−	1.06832i	0.845384	−	0.534160i	$-0.179372\pi$
$242$	−29.1401	−	6.84982i	−1.87320	−	0.440323i
$243$			14.9468i			0.958835i
$244$	17.6553	+	24.3005i	1.13027	+	1.55568i
$245$	3.53391	−	1.14824i	0.225773	−	0.0733581i
$246$	25.2232	−	77.6289i	1.60817	−	4.94944i
$247$	6.84216	+	4.97112i	0.435356	+	0.316305i
$248$	27.3496	−	37.6435i	1.73670	−	2.39036i
$249$	−7.49744	−	2.43606i	−0.475131	−	0.154379i
$250$	21.2840	−	6.91558i	1.34612	−	0.437380i
$251$	12.6696	−	9.20498i	0.799696	−	0.581013i	−0.111129	−	0.993806i	$-0.535447\pi$
$251$	12.6696	−	9.20498i	0.799696	−	0.581013i	0.910825	+	0.412793i	$0.135447\pi$
$252$			44.8458i			2.82502i
$253$	0.309608	−	0.675806i	0.0194649	−	0.0424876i
$254$	−44.9344			−2.81943
$255$	1.05083	+	10.3179i	0.0658057	+	0.646131i
$256$	11.0737	+	34.0815i	0.692109	+	2.13009i
$257$	7.56478	−	23.2820i	0.471878	−	1.45229i	−0.378244	−	0.925706i	$-0.623472\pi$
$257$	7.56478	−	23.2820i	0.471878	−	1.45229i	0.850122	−	0.526586i	$-0.176528\pi$
$258$	9.26857	−	12.7571i	0.577036	−	0.794222i
$259$	−0.211428	−	0.153611i	−0.0131375	−	0.00954495i
$260$	19.3073	+	6.27331i	1.19739	+	0.389054i
$261$	−38.0145	+	12.3517i	−2.35304	+	0.764548i
$262$	−24.7914	−	34.1224i	−1.53162	−	2.10809i
$263$	−13.8006			−0.850983			−0.425491	−	0.904962i	$-0.639899\pi$
$263$	−13.8006			−0.850983			−0.425491	+	0.904962i	$0.639899\pi$
$264$	17.0775	+	84.8021i	1.05105	+	5.21921i
$265$		−	3.09835i		−	0.190330i
$266$	5.42795	+	7.47094i	0.332809	+	0.458073i
$267$	−21.3446	+	6.93529i	−1.30627	+	0.424433i
$268$	13.9497	−	42.9328i	0.852114	−	2.62254i
$269$	10.4693	−	14.4097i	0.638324	−	0.878578i	−0.360201	−	0.932875i	$-0.617292\pi$
$269$	10.4693	−	14.4097i	0.638324	−	0.878578i	0.998525	+	0.0542969i	$0.0172918\pi$
$270$	−10.6367	−	7.72798i	−0.647326	−	0.470310i
$271$	−3.63210	+	11.1785i	−0.220634	+	0.679043i	0.778071	+	0.628176i	$0.216198\pi$
$271$	−3.63210	+	11.1785i	−0.220634	+	0.679043i	−0.998705	+	0.0508664i	$0.983802\pi$
$272$	−58.0697	−	12.5389i	−3.52099	−	0.760283i
$273$	−16.1305	+	11.7195i	−0.976264	+	0.709297i
$274$	40.7602			2.46242
$275$	−1.60489	+	13.8410i	−0.0967787	+	0.834643i
$276$	−3.40971			−0.205240
$277$	−6.75039	−	9.29111i	−0.405592	−	0.558249i	0.556545	−	0.830818i	$-0.312127\pi$
$277$	−6.75039	−	9.29111i	−0.405592	−	0.558249i	−0.962136	+	0.272569i	$0.912127\pi$
$278$	−36.3215	+	11.8016i	−2.17842	+	0.707811i
$279$	−23.4967	−	7.63453i	−1.40671	−	0.457067i
$280$	11.2980	+	8.20844i	0.675182	+	0.490548i
$281$	−1.72666	−	1.25449i	−0.103004	−	0.0748368i	0.535091	−	0.844794i	$-0.320277\pi$
$281$	−1.72666	−	1.25449i	−0.103004	−	0.0748368i	−0.638095	+	0.769958i	$0.720277\pi$
$282$	−50.4750	−	16.4003i	−3.00574	−	0.976624i
$283$	−3.78094	+	1.22850i	−0.224753	+	0.0730268i	−0.419229	−	0.907881i	$-0.637700\pi$
$283$	−3.78094	+	1.22850i	−0.224753	+	0.0730268i	0.194476	+	0.980907i	$0.437700\pi$
$284$	23.4458	+	32.2704i	1.39125	+	1.91490i
$285$	−5.06280			−0.299894
$286$	−25.6774	+	27.9102i	−1.51834	+	1.65037i
$287$	17.9686			1.06065
$288$	82.3069	−	59.7995i	4.84998	−	3.52372i
$289$	11.4564	−	12.5599i	0.673908	−	0.738815i
$290$	−6.10520	+	18.7899i	−0.358510	+	1.10338i
$291$	2.98408	+	2.16806i	0.174930	+	0.127094i
$292$	7.52917	−	10.3630i	0.440611	−	0.606450i
$293$	−6.02676	+	18.5485i	−0.352087	+	1.08361i	0.605592	+	0.795775i	$0.292936\pi$
$293$	−6.02676	+	18.5485i	−0.352087	+	1.08361i	−0.957679	+	0.287838i	$0.907064\pi$
$294$	30.2824	−	9.83934i	1.76610	−	0.573842i
$295$	0.0824987	+	0.113550i	0.00480326	+	0.00661112i
$296$			1.43651i			0.0834955i
$297$	15.6216	−	8.79728i	0.906458	−	0.510470i
$298$	19.0889			1.10579
$299$	−0.553565	−	0.761917i	−0.0320135	−	0.0440628i
$300$	60.7850	−	19.7503i	3.50943	−	1.14028i
$301$	3.30139	+	1.07269i	0.190289	+	0.0618287i
$302$	−17.9687	−	13.0550i	−1.03398	−	0.751233i
$303$	23.3523	−	32.1417i	1.34156	−	1.84649i
$304$	8.96162	−	27.5810i	0.513984	−	1.58188i
$305$	−1.53471	−	4.72336i	−0.0878774	−	0.270459i
$306$	5.59413	+	54.9274i	0.319795	+	3.13999i
$307$	11.2038			0.639435			0.319718	−	0.947513i	$-0.396412\pi$
$307$	11.2038			0.639435			0.319718	+	0.947513i	$0.396412\pi$
$308$	−26.3375	+	14.8319i	−1.50072	+	0.845127i
$309$		−	1.45582i		−	0.0828189i
$310$	−9.87943	+	7.17783i	−0.561114	+	0.407673i
$311$	−4.54421	+	1.47650i	−0.257678	+	0.0837247i	−0.435007	−	0.900427i	$-0.643254\pi$
$311$	−4.54421	+	1.47650i	−0.257678	+	0.0837247i	0.177329	+	0.984152i	$0.443254\pi$
$312$	104.232	+	33.8670i	5.90098	+	1.91734i
$313$	−13.4234	+	18.4758i	−0.758738	+	1.04431i	0.238580	+	0.971123i	$0.423318\pi$
$313$	−13.4234	+	18.4758i	−0.758738	+	1.04431i	−0.997318	+	0.0731902i	$0.976682\pi$
$314$	8.46156	+	6.14768i	0.477513	+	0.346934i
$315$	2.29135	−	7.05206i	0.129103	−	0.397339i
$316$	−76.1046	+	24.7279i	−4.28122	+	1.39105i
$317$	15.5125	+	21.3512i	0.871272	+	1.19920i	0.978763	+	0.204996i	$0.0657183\pi$
$317$	15.5125	+	21.3512i	0.871272	+	1.19920i	−0.107491	+	0.994206i	$0.534282\pi$
$318$		−	26.5500i		−	1.48885i
$319$	−19.8266	−	18.2405i	−1.11008	−	1.02127i
$320$		−	24.5309i		−	1.37132i
$321$	5.91373	−	4.29658i	0.330072	−	0.239811i
$322$	−0.317771	−	0.977999i	−0.0177087	−	0.0545017i
$323$	5.53297	+	6.18497i	0.307863	+	0.344141i
$324$	−1.97352	−	1.43384i	−0.109640	−	0.0796580i
$325$	14.2817	+	10.3763i	0.792208	+	0.575573i
$326$	−21.9222	−	7.12297i	−1.21416	−	0.394505i
$327$	−7.37699	−	22.7041i	−0.407949	−	1.25554i
$328$	−58.0546	−	79.9053i	−3.20553	−	4.41203i
$329$		−	11.6833i		−	0.644122i
$330$	2.61493	−	22.5518i	0.143947	−	1.24144i
$331$	−18.7494			−1.03056			−0.515279	−	0.857022i	$-0.672312\pi$
$331$	−18.7494			−1.03056			−0.515279	+	0.857022i	$0.672312\pi$
$332$	−12.2495	+	8.89980i	−0.672280	+	0.488440i
$333$	0.725408	−	0.235700i	0.0397521	−	0.0129163i
$334$	−9.76457	−	3.17270i	−0.534294	−	0.173603i
$335$	−4.38722	+	6.03849i	−0.239699	+	0.329918i
$336$	55.3117	+	40.1863i	3.01750	+	2.19234i
$337$	25.5683	+	8.30764i	1.39279	+	0.452546i	0.906853	−	0.421446i	$-0.138477\pi$
$337$	25.5683	+	8.30764i	1.39279	+	0.452546i	0.485940	+	0.873992i	$0.338477\pi$
$338$	3.91578	+	12.0515i	0.212990	+	0.655517i
$339$	−3.23230	+	2.34840i	−0.175554	+	0.127548i
$340$	17.2189	+	10.0155i	0.933827	+	0.543167i
$341$	−3.28740	−	16.3243i	−0.178023	−	0.884013i
$342$	−26.9519			−1.45739
$343$	11.0570	+	15.2187i	0.597024	+	0.821733i
$344$	−5.89627	−	18.1469i	−0.317906	−	0.978413i
$345$	0.536181	+	0.174216i	0.0288670	+	0.00937946i
$346$	−7.40735	+	10.1953i	−0.398222	+	0.548105i
$347$	−5.79937	+	7.98215i	−0.311326	+	0.428504i	−0.935794	−	0.352546i	$-0.885316\pi$
$347$	−5.79937	+	7.98215i	−0.311326	+	0.428504i	0.624468	+	0.781050i	$0.285316\pi$
$348$	−38.1871	+	117.528i	−2.04704	+	6.30015i
$349$	0.209712	+	0.645429i	0.0112257	+	0.0345490i	0.956512	−	0.291692i	$-0.0942181\pi$
$349$	0.209712	+	0.645429i	0.0112257	+	0.0345490i	−0.945287	+	0.326241i	$0.894218\pi$
$350$	11.3298	+	15.5942i	0.605606	+	0.833545i
$351$		−	22.7142i		−	1.21239i
$352$	62.3412	+	28.5605i	3.32279	+	1.52228i
$353$	−13.6534			−0.726700			−0.363350	−	0.931653i	$-0.618367\pi$
$353$	−13.6534			−0.726700			−0.363350	+	0.931653i	$0.618367\pi$
$354$	0.706939	+	0.973018i	0.0375734	+	0.0517153i
$355$	−2.03806	−	6.27251i	−0.108169	−	0.332910i
$356$	−13.3205	+	40.9962i	−0.705983	+	2.17279i
$357$	−17.8984	+	7.89983i	−0.947283	+	0.418103i
$358$	30.0749	+	21.8507i	1.58951	+	1.15485i
$359$	8.22116	−	25.3021i	0.433896	−	1.33540i	−0.460317	−	0.887754i	$-0.652264\pi$
$359$	8.22116	−	25.3021i	0.433896	−	1.33540i	0.894214	−	0.447641i	$-0.147736\pi$
$360$	−38.7632	+	12.5949i	−2.04300	+	0.663812i
$361$	12.0940	−	8.78678i	0.636524	−	0.462462i
$362$		−	12.4217i		−	0.652870i
$363$	26.4726	+	16.0501i	1.38945	+	0.842413i
$364$			38.2953i			2.00722i
$365$	−1.71346	+	1.24490i	−0.0896866	+	0.0651611i
$366$	−13.1511	−	40.4749i	−0.687419	−	2.11566i
$367$	20.9892	+	6.81981i	1.09563	+	0.355991i	0.800419	−	0.599441i	$-0.204611\pi$
$367$	20.9892	+	6.81981i	1.09563	+	0.355991i	0.295209	+	0.955433i	$0.404611\pi$
$368$	−1.89818	+	2.61262i	−0.0989495	+	0.136192i
$369$	−30.8251	+	42.4271i	−1.60469	+	2.20866i
$370$	0.116502	−	0.358556i	0.00605665	−	0.0186405i
$371$	5.55864	−	1.80611i	0.288590	−	0.0937686i
$372$	−61.7943	+	44.8962i	−3.20389	+	2.32776i
$373$	−2.80930			−0.145460			−0.0727300	−	0.997352i	$-0.523171\pi$
$373$	−2.80930			−0.145460			−0.0727300	+	0.997352i	$0.523171\pi$
$374$	−30.4082	+	21.4516i	−1.57237	+	1.10924i
$375$	−23.1447			−1.19518
$376$	−51.9551	+	37.7476i	−2.67938	+	1.94668i
$377$	−32.4619	+	10.5475i	−1.67187	+	0.543224i
$378$	7.66410	−	23.5877i	0.394199	−	1.21322i
$379$	21.4707	−	29.5519i	1.10288	−	1.51798i	0.271362	−	0.962477i	$-0.412526\pi$
$379$	21.4707	−	29.5519i	1.10288	−	1.51798i	0.831515	−	0.555503i	$-0.187474\pi$
$380$	−5.71563	+	7.86689i	−0.293206	+	0.403563i
$381$	44.1966	+	14.3604i	2.26426	+	0.735704i
$382$	−2.00718	−	6.17746i	−0.102696	−	0.316066i
$383$	25.6415	−	18.6296i	1.31022	−	0.951929i	0.310219	−	0.950665i	$-0.399598\pi$
$383$	25.6415	−	18.6296i	1.31022	−	0.951929i	0.999999	−	0.00126426i	$-0.000402428\pi$
$384$		−	93.8314i		−	4.78831i
$385$	4.89943	−	0.986650i	0.249698	−	0.0502843i
$386$			24.3013i			1.23690i
$387$	−8.19634	+	5.95499i	−0.416644	+	0.302709i
$388$	6.73773	−	2.18922i	0.342056	−	0.111141i
$389$	2.18001	−	6.70938i	0.110531	−	0.340179i	−0.880458	−	0.474125i	$-0.842765\pi$
$389$	2.18001	−	6.70938i	0.110531	−	0.340179i	0.990989	+	0.133945i	$0.0427646\pi$
$390$	−23.2699	−	16.9066i	−1.17832	−	0.856098i
$391$	−0.373144	−	0.845421i	−0.0188707	−	0.0427548i
$392$	11.9060	−	36.6430i	0.601345	−	1.85075i
$393$	13.4794	+	41.4852i	0.679943	+	2.09265i
$394$	10.8089	+	14.8772i	0.544544	+	0.749500i
$395$	13.2310			0.665724
$396$	10.1611	−	87.6317i	0.510614	−	4.40366i
$397$			3.35047i			0.168155i	0.996459	+	0.0840776i	$0.0267944\pi$
$397$			3.35047i			0.168155i	−0.996459	+	0.0840776i	$0.973206\pi$
$398$	−24.0244	−	33.0667i	−1.20423	−	1.65748i
$399$	−2.95124	−	9.08298i	−0.147747	−	0.454718i
$400$	18.7057	−	57.5703i	0.935286	−	2.87851i
$401$	18.6347	−	25.6485i	0.930573	−	1.28082i	−0.0290622	−	0.999578i	$-0.509252\pi$
$401$	18.6347	−	25.6485i	0.930573	−	1.28082i	0.959636	−	0.281247i	$-0.0907479\pi$
$402$	−37.5945	+	51.7443i	−1.87504	+	2.58077i
$403$	−20.0646	−	6.51938i	−0.999488	−	0.324753i
$404$	−23.5803	−	72.5727i	−1.17316	−	3.61062i
$405$	0.237077	+	0.326309i	0.0117805	+	0.0162144i
$406$	−37.2691			−1.84963
$407$	0.378340	+	0.348072i	0.0187536	+	0.0172533i
$408$	92.9579	+	54.0696i	4.60210	+	2.67684i
$409$	4.24732	−	3.08586i	0.210016	−	0.152586i	−0.477805	−	0.878466i	$-0.658567\pi$
$409$	4.24732	−	3.08586i	0.210016	−	0.152586i	0.687821	+	0.725880i	$0.258567\pi$
$410$	8.01018	+	24.6528i	0.395595	+	1.21752i
$411$	−40.0911	−	13.0264i	−1.97755	−	0.642544i
$412$	−2.26215	−	1.64355i	−0.111448	−	0.0809718i
$413$	−0.155625	+	0.214199i	−0.00765779	+	0.0105400i
$414$	2.85437	+	0.927440i	0.140284	+	0.0455812i
$415$	2.38098	−	0.773627i	0.116878	−	0.0379759i
$416$	70.2846	−	51.0648i	3.44599	−	2.50366i
$417$	39.4968			1.93417
$418$	−8.91384	−	15.8286i	−0.435990	−	0.774201i
$419$		−	32.3660i		−	1.58118i	−0.612346	−	0.790590i	$-0.709774\pi$
$419$		−	32.3660i		−	1.58118i	0.612346	−	0.790590i	$-0.290226\pi$
$420$	−13.4747	−	18.5464i	−0.657499	−	0.904969i
$421$	4.03670	+	12.4237i	0.196737	+	0.605493i	0.999952	+	0.00980408i	$0.00312079\pi$
$421$	4.03670	+	12.4237i	0.196737	+	0.605493i	−0.803215	+	0.595689i	$0.796879\pi$
$422$	−6.06465	−	1.97052i	−0.295223	−	0.0959236i
$423$	27.5864	+	20.0427i	1.34130	+	0.974510i
$424$	−25.9910	−	18.8836i	−1.26224	−	0.917068i
$425$	11.5491	+	12.9100i	0.560211	+	0.626226i
$426$	−17.4643	−	53.7497i	−0.846150	−	2.60418i
$427$	7.57938	−	5.50674i	0.366792	−	0.266490i
$428$		−	14.0397i		−	0.678636i
$429$	34.1755	−	19.2459i	1.65001	−	0.929201i
$430$			5.00769i			0.241492i
$431$	0.349839	+	0.481512i	0.0168512	+	0.0231936i	0.817359	−	0.576128i	$-0.195437\pi$
$431$	0.349839	+	0.481512i	0.0168512	+	0.0231936i	−0.800508	+	0.599322i	$0.795437\pi$
$432$	−74.0750	+	24.0684i	−3.56394	+	1.15799i
$433$	−5.74057	+	17.6676i	−0.275874	+	0.849053i	0.713113	+	0.701049i	$0.247285\pi$
$433$	−5.74057	+	17.6676i	−0.275874	+	0.849053i	−0.988987	+	0.148004i	$0.952715\pi$
$434$	−18.6365	−	13.5402i	−0.894579	−	0.649950i
$435$	12.0099	−	16.5303i	0.575832	−	0.792565i
$436$	−43.6072	−	14.1688i	−2.08841	−	0.678565i
$437$	0.429030	−	0.139400i	0.0205233	−	0.00666842i
$438$	−14.6828	+	10.6677i	−0.701571	+	0.509721i
$439$			17.1573i			0.818875i	0.912338	+	0.409437i	$0.134275\pi$
$439$			17.1573i			0.818875i	−0.912338	+	0.409437i	$0.865725\pi$
$440$	−20.2171	−	18.5997i	−0.963813	−	0.886707i
$441$	−20.4575			−0.974165
$442$	4.77701	+	46.9044i	0.227219	+	2.23101i
$443$	5.76745	+	17.7504i	0.274020	+	0.843346i	0.989477	+	0.144690i	$0.0462183\pi$
$443$	5.76745	+	17.7504i	0.274020	+	0.843346i	−0.715457	+	0.698656i	$0.753782\pi$
$444$	0.728702	−	2.24271i	0.0345827	−	0.106434i
$445$	4.18932	−	5.76611i	0.198593	−	0.273340i
$446$	53.6511	+	38.9798i	2.54045	+	1.84575i
$447$	−18.7755	−	6.10053i	−0.888050	−	0.288545i
$448$	44.0099	−	14.2997i	2.07927	−	0.675597i
$449$	−16.2517	−	22.3686i	−0.766967	−	1.05564i	−0.996602	−	0.0823629i	$-0.973753\pi$
$449$	−16.2517	−	22.3686i	−0.766967	−	1.05564i	0.229635	−	0.973277i	$-0.426247\pi$
$450$	−56.2570			−2.65198
$451$	−35.1118	−	4.07129i	−1.65335	−	0.191710i
$452$			7.67377i			0.360944i
$453$	13.5015	+	18.5832i	0.634356	+	0.873117i
$454$	−6.20896	+	2.01741i	−0.291401	+	0.0946819i
$455$	1.95666	−	6.02199i	0.0917298	−	0.282315i
$456$	−30.8564	+	42.4701i	−1.44498	+	1.98885i
$457$	−16.2175	−	11.7827i	−0.758624	−	0.551172i	0.139864	−	0.990171i	$-0.455333\pi$
$457$	−16.2175	−	11.7827i	−0.758624	−	0.551172i	−0.898488	+	0.438998i	$0.855333\pi$
$458$	17.0116	−	52.3565i	0.794902	−	2.44646i
$459$	4.70418	−	21.7858i	0.219572	−	1.01687i
$460$	0.876027	−	0.636471i	0.0408450	−	0.0296756i
$461$	1.42911			0.0665605			0.0332803	−	0.999446i	$-0.489405\pi$
$461$	1.42911			0.0665605			0.0332803	+	0.999446i	$0.489405\pi$
$462$	41.9837	−	8.45469i	1.95326	−	0.393348i
$463$	7.60345			0.353362			0.176681	−	0.984268i	$-0.443464\pi$
$463$	7.60345			0.353362			0.176681	+	0.984268i	$0.443464\pi$
$464$	68.7946	+	94.6876i	3.19371	+	4.39576i
$465$	12.0112	−	3.90266i	0.557005	−	0.180982i
$466$	46.2321	+	15.0217i	2.14166	+	0.695868i
$467$	−16.3230	−	11.8594i	−0.755340	−	0.548787i	0.142137	−	0.989847i	$-0.454603\pi$
$467$	−16.3230	−	11.8594i	−0.755340	−	0.548787i	−0.897478	+	0.441060i	$0.854603\pi$
$468$	−90.4222	−	65.6956i	−4.17977	−	3.03678i
$469$	−13.3909	−	4.35095i	−0.618332	−	0.200908i
$470$	16.0295	−	5.20829i	0.739384	−	0.240240i
$471$	−6.35793	−	8.75094i	−0.292958	−	0.403222i
$472$	1.45534			0.0669874
$473$	−6.20810	−	2.84413i	−0.285449	−	0.130773i
$474$	113.378			5.20761
$475$	−6.84088	+	4.97019i	−0.313881	+	0.228048i
$476$	−7.93108	+	36.7301i	−0.363521	+	1.68352i
$477$	−5.27128	+	16.2233i	−0.241355	+	0.742815i
$478$	−61.3225	−	44.5534i	−2.80483	−	2.03783i
$479$	−7.51634	+	10.3453i	−0.343430	+	0.472691i	−0.945439	−	0.325798i	$-0.894367\pi$
$479$	−7.51634	+	10.3453i	−0.343430	+	0.472691i	0.602009	+	0.798489i	$0.294367\pi$
$480$	−16.0709	+	49.4611i	−0.733533	+	2.25758i
$481$	0.619451	−	0.201272i	0.0282445	−	0.00917720i
$482$	26.5281	+	36.5128i	1.20832	+	1.66311i
$483$			1.06350i			0.0483908i
$484$	54.8259	−	23.0151i	2.49209	−	1.04614i
$485$	−1.17137			−0.0531893
$486$	−23.9080	−	32.9065i	−1.08449	−	1.49267i
$487$	−12.9765	+	4.21633i	−0.588023	+	0.191060i	−0.587891	−	0.808940i	$-0.700042\pi$
$487$	−12.9765	+	4.21633i	−0.588023	+	0.191060i	−0.000131189		1.00000i	$0.500042\pi$
$488$	−48.9764	−	15.9134i	−2.21706	−	0.720365i
$489$	19.2859	+	14.0121i	0.872140	+	0.633647i
$490$	−5.94354	+	8.18058i	−0.268502	+	0.369561i
$491$	−2.01228	+	6.19315i	−0.0908128	+	0.279493i	−0.986140	−	0.165916i	$-0.946942\pi$
$491$	−2.01228	+	6.19315i	−0.0908128	+	0.279493i	0.895327	+	0.445409i	$0.146942\pi$
$492$	50.1024	+	154.199i	2.25879	+	6.95185i
$493$	−33.3195	+	3.39345i	−1.50063	+	0.152833i
$494$	−23.0151			−1.03550
$495$	−6.07531	+	13.2610i	−0.273065	+	0.596039i
$496$			72.3423i			3.24827i
$497$	10.0652	−	7.31282i	0.451487	−	0.328025i
$498$	20.4028	−	6.62928i	0.914273	−	0.297065i
$499$	−24.5197	−	7.96693i	−1.09765	−	0.356649i	−0.296454	−	0.955047i	$-0.595804\pi$
$499$	−24.5197	−	7.96693i	−1.09765	−	0.356649i	−0.801199	+	0.598398i	$0.795804\pi$
$500$	−26.1291	+	35.9636i	−1.16853	+	1.60834i
$501$	8.59032	+	6.24123i	0.383787	+	0.278838i
$502$	−13.1693	+	40.5311i	−0.587777	+	1.80899i
$503$	18.5667	−	6.03267i	0.827847	−	0.268984i	0.135709	−	0.990749i	$-0.456669\pi$
$503$	18.5667	−	6.03267i	0.827847	−	0.268984i	0.692138	+	0.721765i	$0.256669\pi$
$504$	−45.1922	−	62.2018i	−2.01302	−	2.77069i
$505$			12.6170i			0.561447i
$506$	0.399353	+	1.98308i	0.0177534	+	0.0881585i
$507$		−	13.1051i		−	0.582018i
$508$	72.2097	−	52.4634i	3.20379	−	2.32769i
$509$	−0.654046	−	2.01295i	−0.0289901	−	0.0892222i	0.935515	−	0.353288i	$-0.114936\pi$
$509$	−0.654046	−	2.01295i	−0.0289901	−	0.0892222i	−0.964505	+	0.264066i	$0.914936\pi$
$510$	−18.8174	−	21.0349i	−0.833250	−	0.931439i
$511$	−3.23225	−	2.34837i	−0.142986	−	0.103886i
$512$	−24.9493	−	18.1267i	−1.10261	−	0.801095i
$513$	10.3475	+	3.36210i	0.456852	+	0.148440i
$514$	20.5861	+	63.3575i	0.908014	+	2.79458i
$515$	0.271751	+	0.374032i	0.0119748	+	0.0164818i
$516$			31.3223i			1.37889i
$517$	−2.64719	+	22.8300i	−0.116423	+	1.00406i
$518$	0.711185			0.0312477
$519$	10.5440	−	7.66068i	0.462831	−	0.336267i
$520$	−33.1012	+	10.7552i	−1.45158	+	0.471649i
$521$	−24.1849	−	7.85816i	−1.05956	−	0.344272i	−0.273147	−	0.961972i	$-0.588065\pi$
$521$	−24.1849	−	7.85816i	−1.05956	−	0.344272i	−0.786414	+	0.617700i	$0.788065\pi$
$522$	63.9351	−	87.9991i	2.79836	−	3.85162i
$523$	−3.41536	−	2.48141i	−0.149343	−	0.108504i	0.510605	−	0.859816i	$-0.329422\pi$
$523$	−3.41536	−	2.48141i	−0.149343	−	0.108504i	−0.659948	+	0.751311i	$0.729422\pi$
$524$	79.6798	+	25.8895i	3.48083	+	1.13099i
$525$	−6.16016	−	18.9590i	−0.268851	−	0.827440i
$526$	30.3832	−	22.0747i	1.32477	−	0.962503i
$527$	−17.8943	−	10.4084i	−0.779489	−	0.453395i
$528$	−98.9775	−	91.0593i	−4.30744	−	3.96285i
$529$	22.9498			0.997816
$530$	4.95595	+	6.82128i	0.215273	+	0.296297i
$531$	−0.238789	−	0.734916i	−0.0103625	−	0.0318926i
$532$	−17.4455	−	5.66838i	−0.756358	−	0.245756i
$533$	−26.3226	+	36.2299i	−1.14016	+	1.56929i
$534$	35.8987	−	49.4103i	1.55349	−	2.13819i
$535$	−0.717347	+	2.20777i	−0.0310136	+	0.0954501i
$536$	23.9160	+	73.6058i	1.03301	+	3.17929i
$537$	−22.5980	−	31.1035i	−0.975176	−	1.34221i
$538$			48.4704i			2.08971i
$539$	−6.76593	−	12.0145i	−0.291429	−	0.517500i
$540$	26.1160			1.12385
$541$	−19.2994	−	26.5633i	−0.829745	−	1.14205i	−0.987970	−	0.154643i	$-0.950577\pi$
$541$	−19.2994	−	26.5633i	−0.829745	−	1.14205i	0.158226	−	0.987403i	$-0.449423\pi$
$542$	−9.88406	−	30.4200i	−0.424557	−	1.30665i
$543$	−3.96979	+	12.2178i	−0.170360	+	0.524314i
$544$	77.9876	−	34.4215i	3.34369	−	1.47581i
$545$	6.13335	+	4.45614i	0.262724	+	0.190880i
$546$	16.7668	−	51.6030i	0.717554	−	2.20840i
$547$	14.4146	−	4.68359i	0.616324	−	0.200256i	0.0158166	−	0.999875i	$-0.494965\pi$
$547$	14.4146	−	4.68359i	0.616324	−	0.200256i	0.600508	+	0.799619i	$0.294965\pi$
$548$	−65.5019	+	47.5899i	−2.79810	+	2.03294i
$549$			27.3431i			1.16698i
$550$	−18.6060	−	33.0392i	−0.793362	−	1.40880i
$551$		−	16.3493i		−	0.696502i
$552$	4.72931	−	3.43605i	0.201293	−	0.146248i
$553$	7.71270	+	23.7372i	0.327977	+	1.00941i
$554$	29.7231	+	9.65762i	1.26281	+	0.410313i
$555$	−0.229179	+	0.315437i	−0.00972809	+	0.0133896i
$556$	44.5898	−	61.3726i	1.89103	−	2.60278i
$557$	−4.57094	+	14.0679i	−0.193677	+	0.596076i	0.806313	+	0.591490i	$0.201460\pi$
$557$	−4.57094	+	14.0679i	−0.193677	+	0.596076i	−0.999989	+	0.00458637i	$0.998540\pi$
$558$	63.9416	−	20.7759i	2.70687	−	0.879514i
$559$	−6.99913	+	5.08517i	−0.296032	+	0.215080i
$560$	−21.7121			−0.917505
$561$	36.7646	−	11.3814i	1.55220	−	0.480524i
$562$	5.80801			0.244996
$563$	25.4361	−	18.4804i	1.07200	−	0.778855i	0.0957312	−	0.995407i	$-0.469481\pi$
$563$	25.4361	−	18.4804i	1.07200	−	0.778855i	0.976271	+	0.216552i	$0.0694811\pi$
$564$	100.262	−	32.5770i	4.22178	−	1.37174i
$565$	0.392084	−	1.20671i	0.0164951	−	0.0507667i
$566$	6.35901	−	8.75243i	0.267289	−	0.367892i
$567$	−0.447220	+	0.615546i	−0.0187815	+	0.0258505i
$568$	−65.0394	−	21.1326i	−2.72899	−	0.886704i
$569$	4.68646	+	14.4234i	0.196467	+	0.604662i	0.999956	+	0.00934349i	$0.00297417\pi$
$569$	4.68646	+	14.4234i	0.196467	+	0.604662i	−0.803490	+	0.595319i	$0.797026\pi$
$570$	11.1462	−	8.09817i	0.466862	−	0.339195i
$571$			25.6527i			1.07353i	0.843731	+	0.536766i	$0.180354\pi$
$571$			25.6527i			1.07353i	−0.843731	+	0.536766i	$0.819646\pi$
$572$	8.67689	−	74.8317i	0.362799	−	3.12887i
$573$			6.71751i			0.280628i
$574$	−39.5593	+	28.7415i	−1.65118	+	1.19965i
$575$	0.895520	−	0.290972i	0.0373458	−	0.0121344i
$576$	−41.7348	+	128.446i	−1.73895	+	5.35194i
$577$	−15.0252	−	10.9165i	−0.625508	−	0.454458i	0.229333	−	0.973348i	$-0.426346\pi$
$577$	−15.0252	−	10.9165i	−0.625508	−	0.454458i	−0.854841	+	0.518890i	$0.826346\pi$
$578$	−5.13228	+	45.9767i	−0.213475	+	1.91238i
$579$	7.76632	−	23.9023i	0.322757	−	0.993345i
$580$	−12.1272	−	37.3236i	−0.503553	−	1.54978i
$581$	2.77587	+	3.82066i	0.115163	+	0.158508i
$582$	−10.0376			−0.416072
$583$	−11.2712	+	2.26980i	−0.466805	+	0.0940053i
$584$			21.9610i			0.908752i
$585$	10.8624	+	14.9507i	0.449103	+	0.618137i
$586$	−16.4007	−	50.4761i	−0.677506	−	2.08515i
$587$	−10.3235	+	31.7726i	−0.426098	+	1.31139i	0.475841	+	0.879531i	$0.342144\pi$
$587$	−10.3235	+	31.7726i	−0.426098	+	1.31139i	−0.901939	+	0.431863i	$0.857856\pi$
$588$	−37.1759	+	51.1683i	−1.53311	+	2.11014i
$589$	5.93983	−	8.17547i	0.244746	−	0.336864i
$590$	−0.363256	−	0.118029i	−0.0149550	−	0.00485917i
$591$	−5.87691	−	18.0873i	−0.241744	−	0.744011i
$592$	−1.31277	−	1.80687i	−0.0539544	−	0.0742619i
$593$	6.45698			0.265156			0.132578	−	0.991173i	$-0.457674\pi$
$593$	6.45698			0.265156			0.132578	+	0.991173i	$0.457674\pi$
$594$	−20.3206	+	44.3554i	−0.833766	+	1.81992i
$595$	3.12386	−	5.37063i	0.128066	−	0.220174i
$596$	−30.6759	+	22.2874i	−1.25653	+	0.912926i
$597$	13.0623	+	40.2017i	0.534605	+	1.64534i
$598$	2.43744	+	0.791972i	0.0996743	+	0.0323862i
$599$	22.7829	+	16.5528i	0.930885	+	0.676327i	0.946209	−	0.323555i	$-0.104878\pi$
$599$	22.7829	+	16.5528i	0.930885	+	0.676327i	−0.0153246	+	0.999883i	$0.504878\pi$
$600$	−64.4069	+	88.6485i	−2.62940	+	3.61906i
$601$	25.0097	+	8.12615i	1.02017	+	0.331473i	0.770896	−	0.636961i	$-0.219809\pi$
$601$	25.0097	+	8.12615i	1.02017	+	0.331473i	0.249272	+	0.968434i	$0.419809\pi$
$602$	−8.98411	+	2.91911i	−0.366165	+	0.118974i
$603$	33.2454	−	24.1542i	1.35386	−	0.983634i
$604$	44.1183			1.79515
$605$	−9.79738	+	0.817876i	−0.398320	+	0.0332514i
$606$			108.116i			4.39191i
$607$	12.5361	+	17.2545i	0.508825	+	0.700337i	0.983721	−	0.179705i	$-0.0575142\pi$
$607$	12.5361	+	17.2545i	0.508825	+	0.700337i	−0.474896	+	0.880042i	$0.657514\pi$
$608$	12.8593	+	39.5768i	0.521512	+	1.60505i
$609$	36.6572	+	11.9107i	1.48543	+	0.482644i
$610$	10.9340	+	7.94404i	0.442706	+	0.321645i
$611$	23.5570	+	17.1151i	0.953013	+	0.692405i
$612$	−73.1207	−	81.7372i	−2.95573	−	3.30403i
$613$	−8.88013	−	27.3302i	−0.358665	−	1.10386i	−0.953854	−	0.300271i	$-0.902923\pi$
$613$	−8.88013	−	27.3302i	−0.358665	−	1.10386i	0.595189	−	0.803586i	$-0.297077\pi$
$614$	−24.6661	+	17.9210i	−0.995444	+	0.723232i
$615$		−	26.8080i		−	1.08100i
$616$	21.5840	−	47.1131i	0.869644	−	1.89824i
$617$			18.3316i			0.738003i	0.929429	+	0.369002i	$0.120300\pi$
$617$			18.3316i			0.738003i	−0.929429	+	0.369002i	$0.879700\pi$
$618$	2.32865	+	3.20512i	0.0936722	+	0.128929i
$619$	13.0924	−	4.25398i	0.526229	−	0.170982i	−0.0338416	−	0.999427i	$-0.510774\pi$
$619$	13.0924	−	4.25398i	0.526229	−	0.170982i	0.560070	+	0.828445i	$0.310774\pi$
$620$	7.49577	−	23.0696i	0.301037	−	0.926498i
$621$	−0.980167	−	0.712133i	−0.0393328	−	0.0285769i
$622$	7.64272	−	10.5193i	0.306445	−	0.421786i
$623$	12.7868	+	4.15469i	0.512293	+	0.166454i
$624$	−162.055	+	52.6547i	−6.48738	+	2.10788i
$625$	−11.0478	+	8.02667i	−0.441910	+	0.321067i
$626$		−	62.1474i		−	2.48391i
$627$	3.70892	+	18.4174i	0.148120	+	0.735522i
$628$	−20.7755			−0.829034
$629$	0.635817	−	0.0647552i	0.0253517	−	0.00258196i
$630$	6.23548	+	19.1908i	0.248427	+	0.764581i
$631$	5.51405	−	16.9705i	0.219511	−	0.675584i	−0.779292	−	0.626661i	$-0.784421\pi$
$631$	5.51405	−	16.9705i	0.219511	−	0.675584i	0.998803	−	0.0489232i	$-0.0155790\pi$
$632$	80.6393	−	110.990i	3.20766	−	4.41496i
$633$	5.33533	+	3.87635i	0.212060	+	0.154071i
$634$	−68.3044	−	22.1934i	−2.71271	−	0.881414i
$635$	−14.0356	+	4.56046i	−0.556987	+	0.180976i
$636$	30.9987	+	42.6660i	1.22918	+	1.69182i
$637$	−17.4693			−0.692159
$638$	72.8264	+	8.44437i	2.88322	+	0.334316i
$639$			36.3110i			1.43644i
$640$	17.5150	+	24.1073i	0.692340	+	0.952925i
$641$	46.1065	−	14.9809i	1.82110	−	0.591710i	0.821322	−	0.570465i	$-0.193237\pi$
$641$	46.1065	−	14.9809i	1.82110	−	0.591710i	0.999774	−	0.0212453i	$-0.00676311\pi$
$642$	−6.14701	+	18.9185i	−0.242603	+	0.746655i
$643$	−13.6965	+	18.8516i	−0.540136	+	0.743434i	−0.988633	−	0.150351i	$-0.951960\pi$
$643$	−13.6965	+	18.8516i	−0.540136	+	0.743434i	0.448496	+	0.893785i	$0.351960\pi$
$644$	1.65253	+	1.20063i	0.0651188	+	0.0473115i
$645$	1.60038	−	4.92547i	0.0630150	−	0.193940i
$646$	−22.0744	−	4.76650i	−0.868508	−	0.187536i
$647$	30.3922	−	22.0812i	1.19484	−	0.868103i	0.201074	−	0.979576i	$-0.435557\pi$
$647$	30.3922	−	22.0812i	1.19484	−	0.868103i	0.993767	+	0.111473i	$0.0355568\pi$
$648$	4.18222			0.164293
$649$	0.352634	−	0.383298i	0.0138421	−	0.0150458i
$650$	−48.0398			−1.88427
$651$	14.0033	+	19.2738i	0.548831	+	0.755401i
$652$	43.5456	−	14.1488i	1.70538	−	0.554111i
$653$	23.7396	+	7.71345i	0.929001	+	0.301851i	0.734154	−	0.678983i	$-0.237579\pi$
$653$	23.7396	+	7.71345i	0.929001	+	0.301851i	0.194847	+	0.980834i	$0.437579\pi$
$654$	52.5572	+	38.1851i	2.05515	+	1.49315i
$655$	−11.2069	−	8.14232i	−0.437892	−	0.318147i
$656$	146.044	+	47.4527i	5.70207	+	1.85271i
$657$	11.0899	−	3.60331i	0.432656	−	0.140579i
$658$	18.6880	+	25.7218i	0.728534	+	1.00274i
$659$	−36.5532			−1.42391			−0.711956	−	0.702224i	$-0.752190\pi$
$659$	−36.5532			−1.42391			−0.711956	+	0.702224i	$0.752190\pi$
$660$	22.1283	+	39.2939i	0.861343	+	1.52951i
$661$	−17.6207			−0.685367			−0.342683	−	0.939451i	$-0.611336\pi$
$661$	−17.6207			−0.685367			−0.342683	+	0.939451i	$0.611336\pi$
$662$	41.2783	−	29.9905i	1.60433	−	1.16561i
$663$	10.2914	−	47.6610i	0.399684	−	1.85100i
$664$	8.02171	−	24.6883i	0.311303	−	0.958092i
$665$	2.45371	+	1.78272i	0.0951506	+	0.0691310i
$666$	−1.22004	+	1.67924i	−0.0472754	+	0.0650691i
$667$	−0.562594	+	1.73149i	−0.0217837	+	0.0670434i
$668$	19.3960	−	6.30215i	0.750455	−	0.243838i
$669$	−40.3129	−	55.4860i	−1.55859	−	2.14521i
$670$		−	20.3118i		−	0.784713i
$671$	−16.0583	+	9.04323i	−0.619925	+	0.349110i
$672$	−98.1046			−3.78447
$673$	−21.3307	−	29.3592i	−0.822238	−	1.13171i	−0.989318	−	0.145771i	$-0.953434\pi$
$673$	−21.3307	−	29.3592i	−0.822238	−	1.13171i	0.167080	−	0.985943i	$-0.446566\pi$
$674$	−69.5792	+	22.6076i	−2.68009	+	0.870814i
$675$	21.5984	+	7.01775i	0.831324	+	0.270113i
$676$	−20.3635	−	14.7950i	−0.783213	−	0.569038i
$677$	−18.2631	+	25.1369i	−0.701906	+	0.966091i	0.298027	+	0.954557i	$0.403671\pi$
$677$	−18.2631	+	25.1369i	−0.701906	+	0.966091i	−0.999933	+	0.0115339i	$0.996329\pi$
$678$	3.35980	−	10.3404i	0.129032	−	0.397121i
$679$	−0.682824	−	2.10152i	−0.0262044	−	0.0806488i
$680$	−33.9758	+	3.46029i	−1.30291	+	0.132696i
$681$	6.75176			0.258728
$682$	33.3490	+	30.6811i	1.27700	+	1.17484i
$683$		−	31.8355i		−	1.21815i	−0.793112	−	0.609076i	$-0.791540\pi$
$683$		−	31.8355i		−	1.21815i	0.793112	−	0.609076i	$-0.208460\pi$
$684$	43.3118	−	31.4679i	1.65607	−	1.20320i
$685$	12.7318	−	4.13682i	0.486458	−	0.158060i
$686$	−48.6860	−	15.8190i	−1.85884	−	0.603974i
$687$	−33.4647	+	46.0602i	−1.27676	+	1.75731i
$688$	24.0001	+	17.4371i	0.914995	+	0.664783i
$689$	−4.50132	+	13.8536i	−0.171487	+	0.527782i
$690$	−1.45911	+	0.474095i	−0.0555475	+	0.0180485i
$691$	4.30046	+	5.91907i	0.163597	+	0.225172i	0.882943	−	0.469480i	$-0.155558\pi$
$691$	4.30046	+	5.91907i	0.163597	+	0.225172i	−0.719346	+	0.694652i	$0.755558\pi$
$692$		−	25.0325i		−	0.951592i
$693$	−27.3326	−	3.16927i	−1.03828	−	0.120391i
$694$		−	26.8497i		−	1.01920i
$695$	−10.1476	+	7.37265i	−0.384920	+	0.279660i
$696$	−65.4696	−	201.495i	−2.48162	−	7.63764i
$697$	−32.7500	+	29.2976i	−1.24050	+	1.10973i
$698$	−1.49409	−	1.08552i	−0.0565522	−	0.0410876i
$699$	−40.6724	−	29.5502i	−1.53837	−	1.11769i
$700$	−36.4142	−	11.8317i	−1.37633	−	0.447196i
$701$	−15.4193	−	47.4556i	−0.582377	−	1.79237i	−0.609556	−	0.792743i	$-0.708652\pi$
$701$	−15.4193	−	47.4556i	−0.582377	−	1.79237i	0.0271788	−	0.999631i	$-0.491348\pi$
$702$	36.3323	+	50.0072i	1.37128	+	1.88740i
$703$			0.311983i			0.0117667i
$704$	−89.2384	+	17.9709i	−3.36330	+	0.677303i
$705$	−17.4308			−0.656482
$706$	30.0592	−	21.8393i	1.13129	−	0.821933i
$707$	−22.6356	+	7.35476i	−0.851300	+	0.276604i
$708$	−2.27211	−	0.738252i	−0.0853910	−	0.0277452i
$709$	−21.2227	+	29.2105i	−0.797035	+	1.09702i	0.196162	+	0.980572i	$0.437152\pi$
$709$	−21.2227	+	29.2105i	−0.797035	+	1.09702i	−0.993196	+	0.116452i	$0.962848\pi$
$710$	14.5201	+	10.5495i	0.544930	+	0.395915i
$711$	−69.2791	−	22.5101i	−2.59817	−	0.844196i
$712$	−22.8372	−	70.2857i	−0.855860	−	2.63407i
$713$	−0.910389	+	0.661436i	−0.0340943	+	0.0247710i
$714$	26.7687	−	46.0214i	1.00179	−	1.72231i
$715$	−5.18791	+	11.3240i	−0.194017	+	0.423495i
$716$	−73.8425			−2.75962
$717$	46.0772	+	63.4198i	1.72078	+	2.36845i
$718$	22.3723	+	68.8549i	0.834927	+	2.56964i
$719$	40.1065	+	13.0314i	1.49572	+	0.485989i	0.938766	−	0.344554i	$-0.111970\pi$
$719$	40.1065	+	13.0314i	1.49572	+	0.485989i	0.556954	+	0.830543i	$0.311970\pi$
$720$	37.2471	−	51.2663i	1.38812	−	1.91058i
$721$	−0.512627	+	0.705571i	−0.0190912	+	0.0262768i
$722$	−12.5710	+	38.6897i	−0.467845	+	1.43988i
$723$	−14.4236	−	44.3913i	−0.536420	−	1.65093i
$724$	14.5030	+	19.9617i	0.539001	+	0.741872i
$725$		−	34.1260i		−	1.26741i
$726$	−83.9546	+	7.00846i	−3.11585	+	0.260108i
$727$	41.6927			1.54630			0.773148	−	0.634226i	$-0.218681\pi$
$727$	41.6927			1.54630			0.773148	+	0.634226i	$0.218681\pi$
$728$	−38.5912	−	53.1162i	−1.43028	−	1.96862i
$729$	13.4174	+	41.2945i	0.496941	+	1.52943i
$730$	1.78105	−	5.48151i	0.0659197	−	0.202880i
$731$	−7.76622	+	3.42779i	−0.287244	+	0.126781i
$732$	68.3906	+	49.6887i	2.52779	+	1.83655i
$733$	−7.67557	+	23.6230i	−0.283504	+	0.872535i	0.703339	+	0.710854i	$0.251691\pi$
$733$	−7.67557	+	23.6230i	−0.283504	+	0.872535i	−0.986843	+	0.161680i	$0.948309\pi$
$734$	−57.1181	+	18.5588i	−2.10827	+	0.685018i
$735$	8.46036	−	6.14681i	0.312065	−	0.226728i
$736$		−	4.63392i		−	0.170808i
$737$	25.1808	+	11.5361i	0.927547	+	0.424939i
$738$		−	142.713i		−	5.25333i
$739$	11.4997	−	8.35501i	0.423023	−	0.307344i	−0.355830	−	0.934551i	$-0.615802\pi$
$739$	11.4997	−	8.35501i	0.423023	−	0.307344i	0.778853	+	0.627207i	$0.215802\pi$
$740$	0.231416	+	0.712224i	0.00850701	+	0.0261819i
$741$	22.6373	+	7.35529i	0.831601	+	0.270203i
$742$	−9.34885	+	12.8676i	−0.343207	+	0.472384i
$743$	10.1893	−	14.0244i	0.373810	−	0.514505i	−0.580122	−	0.814530i	$-0.696995\pi$
$743$	10.1893	−	14.0244i	0.373810	−	0.514505i	0.953931	+	0.300025i	$0.0969950\pi$
$744$	40.4666	−	124.543i	1.48358	−	4.56598i
$745$	5.96258	−	1.93736i	0.218452	−	0.0709794i
$746$	6.18491	−	4.49360i	0.226446	−	0.164522i
$747$	−13.7833			−0.504304
$748$	23.8201	−	69.9762i	0.870950	−	2.55858i
$749$	−4.37903			−0.160006
$750$	50.9549	−	37.0209i	1.86061	−	1.35181i
$751$	−5.46879	+	1.77692i	−0.199559	+	0.0648406i	−0.407091	−	0.913388i	$-0.633457\pi$
$751$	−5.46879	+	1.77692i	−0.199559	+	0.0648406i	0.207532	+	0.978228i	$0.433457\pi$
$752$	30.8541	−	94.9592i	1.12513	−	3.46281i
$753$	25.9063	−	35.6569i	0.944078	−	1.29941i
$754$	54.5963	−	75.1454i	1.98828	−	2.73663i
$755$	−6.93766	−	2.25418i	−0.252487	−	0.0820381i
$756$	15.2237	+	46.8538i	0.553681	+	1.70406i
$757$	−3.41796	+	2.48329i	−0.124228	+	0.0902568i	−0.648164	−	0.761501i	$-0.724463\pi$
$757$	−3.41796	+	2.48329i	−0.124228	+	0.0902568i	0.523936	+	0.851757i	$0.324463\pi$
$758$			99.4044i			3.61053i
$759$	0.240966	−	2.07815i	0.00874649	−	0.0754319i
$760$		−	16.6713i		−	0.604731i
$761$	37.5437	−	27.2771i	1.36096	−	0.988794i	0.362575	−	0.931955i	$-0.381898\pi$
$761$	37.5437	−	27.2771i	1.36096	−	0.988794i	0.998383	−	0.0568391i	$-0.0181022\pi$
$762$	−120.273	+	39.0790i	−4.35702	+	1.41568i
$763$	−4.41930	+	13.6012i	−0.159990	+	0.492397i
$764$	10.4381	+	7.58371i	0.377637	+	0.274369i
$765$	7.32205	+	16.5893i	0.264729	+	0.599788i
$766$	−26.6530	+	82.0294i	−0.963011	+	2.96384i
$767$	−0.203910	−	0.627569i	−0.00736275	−	0.0226602i
$768$	59.2806	+	81.5928i	2.13910	+	2.94423i
$769$	−32.2973			−1.16467			−0.582336	−	0.812948i	$-0.697861\pi$
$769$	−32.2973			−1.16467			−0.582336	+	0.812948i	$0.697861\pi$
$770$	−9.20832	+	10.0091i	−0.331845	+	0.360701i
$771$		−	68.8964i		−	2.48124i
$772$	−28.3731	−	39.0522i	−1.02117	−	1.40552i
$773$	3.59766	+	11.0725i	0.129399	+	0.398249i	0.994677	−	0.103044i	$-0.0328581\pi$
$773$	3.59766	+	11.0725i	0.129399	+	0.398249i	−0.865278	+	0.501292i	$0.832858\pi$
$774$	8.51966	−	26.2208i	0.306233	−	0.942488i
$775$	12.3983	−	17.0648i	0.445359	−	0.612985i
$776$	−7.13920	+	9.82626i	−0.256282	+	0.352742i
$777$	−0.699509	−	0.227284i	−0.0250947	−	0.00815378i
$778$	5.93248	+	18.2583i	0.212690	+	0.654592i
$779$	−12.6084	−	17.3539i	−0.451742	−	0.621770i
$780$	57.1343			2.04573
$781$	−21.3251	+	12.0092i	−0.763071	+	0.429723i
$782$	2.17380	+	1.26440i	0.0777348	+	0.0452150i
$783$	−35.5236	+	25.8094i	−1.26951	+	0.922353i
$784$	18.5109	+	56.9706i	0.661103	+	2.03466i
$785$	3.26698	+	1.06151i	0.116604	+	0.0378868i
$786$	−96.0333	−	69.7723i	−3.42540	−	2.48870i
$787$	−18.4784	+	25.4333i	−0.658683	+	0.906600i	−0.999437	−	0.0335527i	$-0.989318\pi$
$787$	−18.4784	+	25.4333i	−0.658683	+	0.906600i	0.340753	+	0.940153i	$0.389318\pi$
$788$	−34.7399	−	11.2877i	−1.23756	−	0.402106i
$789$	−36.9392	+	12.0023i	−1.31507	+	0.427292i
$790$	−29.1292	+	21.1636i	−1.03637	+	0.752966i
$791$	2.39347			0.0851020
$792$	74.2151	+	131.786i	2.63712	+	4.68282i
$793$			23.3492i			0.829154i
$794$	−5.35923	−	7.37634i	−0.190192	−	0.261777i
$795$	−2.69460	−	8.29314i	−0.0955678	−	0.294127i
$796$	77.2145	+	25.0885i	2.73680	+	0.889239i
$797$	−40.7061	−	29.5747i	−1.44189	−	1.04759i	−0.987644	−	0.156712i	$-0.949911\pi$
$797$	−40.7061	−	29.5747i	−1.44189	−	1.04759i	−0.454241	−	0.890879i	$-0.650089\pi$
$798$	21.0260	+	15.2763i	0.744313	+	0.540775i
$799$	19.0496	+	21.2943i	0.673925	+	0.753340i
$800$	26.8413	+	82.6091i	0.948984	+	2.92067i
$801$	−31.7458	+	23.0646i	−1.12168	+	0.814949i
$802$			86.2744i			3.04645i
$803$	5.78396	+	5.32123i	0.204111	+	0.187782i
$804$		−	127.047i		−	4.48060i
$805$	−0.198517	−	0.273235i	−0.00699681	−	0.00963028i
$806$	54.6019	−	17.7412i	1.92327	−	0.624908i
$807$	15.4904	−	47.6746i	0.545289	−	1.67823i
$808$	105.839	+	76.8969i	3.72342	+	2.70522i
$809$	−25.7994	+	35.5098i	−0.907059	+	1.24846i	0.0611021	+	0.998132i	$0.480538\pi$
$809$	−25.7994	+	35.5098i	−0.907059	+	1.24846i	−0.968161	+	0.250328i	$0.919462\pi$
$810$	−1.04389	−	0.339181i	−0.0366786	−	0.0119176i
$811$	−14.1586	+	4.60040i	−0.497175	+	0.161542i	−0.546862	−	0.837223i	$-0.684178\pi$
$811$	−14.1586	+	4.60040i	−0.497175	+	0.161542i	0.0496869	+	0.998765i	$0.484178\pi$
$812$	59.8916	−	43.5138i	2.10178	−	1.52704i
$813$			33.0794i			1.16014i
$814$	−1.38970	−	0.161139i	−0.0487091	−	0.00564792i
$815$	−7.57053			−0.265184
$816$	−166.336	+	16.9406i	−5.82293	+	0.593041i
$817$	−1.28056	−	3.94116i	−0.0448011	−	0.137884i
$818$	−4.41487	+	13.5876i	−0.154362	+	0.475078i
$819$	−20.4906	+	28.2029i	−0.716001	+	0.985490i
$820$	−41.6560	−	30.2648i	−1.45469	−	1.05689i
$821$	−6.06420	−	1.97038i	−0.211642	−	0.0687666i	0.201277	−	0.979534i	$-0.435491\pi$
$821$	−6.06420	−	1.97038i	−0.211642	−	0.0687666i	−0.412919	+	0.910768i	$0.635491\pi$
$822$	109.100	−	35.4488i	3.80530	−	1.23642i
$823$	22.2282	+	30.5945i	0.774825	+	1.06646i	0.995834	+	0.0911837i	$0.0290650\pi$
$823$	22.2282	+	30.5945i	0.774825	+	1.06646i	−0.221009	+	0.975272i	$0.570935\pi$
$824$	4.79388			0.167003
$825$	7.74167	+	38.4430i	0.269530	+	1.33841i
$826$		−	0.720506i		−	0.0250696i
$827$	−13.4197	−	18.4707i	−0.466649	−	0.642288i	0.509222	−	0.860635i	$-0.329933\pi$
$827$	−13.4197	−	18.4707i	−0.466649	−	0.642288i	−0.975871	+	0.218348i	$0.929933\pi$
$828$	−5.66982	+	1.84224i	−0.197040	+	0.0640221i
$829$	4.71413	−	14.5086i	0.163728	−	0.503904i	−0.835212	−	0.549928i	$-0.814655\pi$
$829$	4.71413	−	14.5086i	0.163728	−	0.503904i	0.998940	+	0.0460239i	$0.0146550\pi$
$830$	−4.00448	+	5.51169i	−0.138997	+	0.191314i
$831$	−26.1487	−	18.9981i	−0.907088	−	0.659038i
$832$	−35.6387	+	109.685i	−1.23555	+	3.80263i
$833$	−16.7553	−	3.61795i	−0.580537	−	0.125355i
$834$	−86.9555	+	63.1769i	−3.01102	+	2.18764i
$835$	−3.37205			−0.116695
$836$	32.8054	+	15.0292i	1.13460	+	0.519795i
$837$	−27.1404			−0.938110
$838$	51.7708	+	71.2564i	1.78839	+	2.46151i
$839$	−11.0511	+	3.59071i	−0.381526	+	0.123965i	−0.493500	−	0.869746i	$-0.664283\pi$
$839$	−11.0511	+	3.59071i	−0.381526	+	0.123965i	0.111974	+	0.993711i	$0.464283\pi$
$840$	37.3793	+	12.1453i	1.28971	+	0.419051i
$841$	29.9196	+	21.7378i	1.03171	+	0.749581i
$842$	−28.7593	−	20.8949i	−0.991112	−	0.720085i
$843$	−5.71266	−	1.85615i	−0.196754	−	0.0639293i
$844$	12.0466	−	3.91418i	0.414662	−	0.134732i
$845$	2.44626	+	3.36699i	0.0841538	+	0.115828i
$846$	−92.7931			−3.19029
$847$	−7.17847	−	17.1003i	−0.246655	−	0.587575i
$848$	49.9489			1.71525
$849$	−9.05176	+	6.57649i	−0.310656	+	0.225704i
$850$	−46.0763	−	9.94919i	−1.58040	−	0.341254i
$851$	0.0107357	−	0.0330409i	0.000368013	−	0.00113263i
$852$	90.8211	+	65.9854i	3.11148	+	2.26062i
$853$	4.19768	−	5.77761i	0.143726	−	0.197822i	−0.731085	−	0.682287i	$-0.760986\pi$
$853$	4.19768	−	5.77761i	0.143726	−	0.197822i	0.874811	+	0.484465i	$0.160986\pi$
$854$	−7.87837	+	24.2471i	−0.269592	+	0.829719i
$855$	−8.41866	+	2.73539i	−0.287912	+	0.0935483i
$856$	14.1482	+	19.4733i	0.483575	+	0.665584i
$857$		−	38.1033i		−	1.30158i	−0.759256	−	0.650792i	$-0.774437\pi$
$857$		−	38.1033i		−	1.30158i	0.759256	−	0.650792i	$-0.225563\pi$
$858$	−44.4556	+	97.0368i	−1.51769	+	3.31278i
$859$	−44.1377			−1.50596			−0.752980	−	0.658043i	$-0.771384\pi$
$859$	−44.1377			−1.50596			−0.752980	+	0.658043i	$0.771384\pi$
$860$	−5.84676	−	8.04738i	−0.199373	−	0.274413i
$861$	48.0953	−	15.6271i	1.63908	−	0.532570i
$862$	−1.54040	−	0.500506i	−0.0524662	−	0.0170473i
$863$	22.2207	+	16.1443i	0.756402	+	0.549558i	0.897805	−	0.440394i	$-0.145161\pi$
$863$	22.2207	+	16.1443i	0.756402	+	0.549558i	−0.141403	+	0.989952i	$0.545161\pi$
$864$	65.6922	−	90.4176i	2.23489	−	3.07607i
$865$	−1.27901	+	3.93639i	−0.0434877	+	0.133841i
$866$	−15.6219	−	48.0791i	−0.530852	−	1.63379i
$867$	19.7415	−	43.5816i	0.670456	−	1.48011i
$868$	45.7578			1.55312
$869$	−9.69280	−	48.1317i	−0.328806	−	1.63276i
$870$			55.6032i			1.88512i
$871$	28.3893	−	20.6261i	0.961936	−	0.698887i
$872$	74.7622	−	24.2917i	2.53177	−	0.822621i
$873$	6.13345	+	1.99288i	0.207586	+	0.0674487i
$874$	−0.721568	+	0.993153i	−0.0244074	+	0.0335939i
$875$	11.2172	+	8.14974i	0.379209	+	0.275511i
$876$	11.1402	−	34.2860i	0.376392	−	1.15842i
$877$	51.9938	−	16.8938i	1.75571	−	0.570464i	0.758966	−	0.651131i	$-0.225705\pi$
$877$	51.9938	−	16.8938i	1.75571	−	0.570464i	0.996741	+	0.0806668i	$0.0257050\pi$
$878$	−27.4439	−	37.7733i	−0.926187	−	1.27479i
$879$			54.8888i			1.85135i
$880$	42.4270	+	4.91950i	1.43021	+	0.165836i
$881$			12.6420i			0.425920i	0.977061	+	0.212960i	$0.0683104\pi$
$881$			12.6420i			0.425920i	−0.977061	+	0.212960i	$0.931690\pi$
$882$	45.0388	−	32.7226i	1.51654	−	1.10183i
$883$	−0.801950	−	2.46815i	−0.0269878	−	0.0830598i	0.936655	−	0.350252i	$-0.113904\pi$
$883$	−0.801950	−	2.46815i	−0.0269878	−	0.0830598i	−0.963643	+	0.267192i	$0.913904\pi$
$884$	−62.4402	−	69.7981i	−2.10009	−	2.34757i
$885$	0.319572	+	0.232182i	0.0107423	+	0.00780472i
$886$	−41.0900	−	29.8537i	−1.38045	−	1.00295i
$887$	−10.4303	−	3.38899i	−0.350214	−	0.113791i	0.128627	−	0.991693i	$-0.458943\pi$
$887$	−10.4303	−	3.38899i	−0.350214	−	0.113791i	−0.478841	+	0.877902i	$0.658943\pi$
$888$	1.24932	+	3.84501i	0.0419244	+	0.129030i
$889$	−16.3635	−	22.5224i	−0.548814	−	0.755378i
$890$			19.3956i			0.650141i
$891$	1.01337	−	1.10149i	0.0339491	−	0.0369013i
$892$	−131.729			−4.41061
$893$	−11.2837	+	8.19807i	−0.377594	+	0.274338i
$894$	51.0939	−	16.6014i	1.70884	−	0.555234i
$895$	11.6118	+	3.77291i	0.388141	+	0.126115i
$896$	−33.0401	+	45.4758i	−1.10379	+	1.51924i
$897$	−2.14432	−	1.55794i	−0.0715968	−	0.0520181i
$898$	71.5592	+	23.2510i	2.38796	+	0.775895i
$899$	12.6029	+	38.7876i	0.420329	+	1.29364i
$900$	90.4053	−	65.6833i	3.01351	−	2.18944i
$901$	−7.18648	+	12.3552i	−0.239416	+	0.411611i
$902$	83.8139	−	47.1997i	2.79070	−	1.57158i
$903$	9.76952			0.325109
$904$	−7.73305	−	10.6436i	−0.257197	−	0.354002i
$905$	−1.26070	−	3.88003i	−0.0419070	−	0.128976i
$906$	−59.4494	−	19.3163i	−1.97508	−	0.641741i
$907$	−23.8888	+	32.8802i	−0.793216	+	1.09177i	0.200484	+	0.979697i	$0.435748\pi$
$907$	−23.8888	+	32.8802i	−0.793216	+	1.09177i	−0.993700	+	0.112071i	$0.964252\pi$
$908$	7.62238	−	10.4913i	0.252958	−	0.348166i
$909$	21.4654	−	66.0639i	0.711964	−	2.19120i
$910$	5.32468	+	16.3877i	0.176512	+	0.543247i
$911$	28.9832	+	39.8920i	0.960257	+	1.32168i	0.946817	+	0.321771i	$0.104278\pi$
$911$	28.9832	+	39.8920i	0.960257	+	1.32168i	0.0134398	+	0.999910i	$0.495722\pi$
$912$		−	81.6181i		−	2.70264i
$913$	−4.55857	−	8.09478i	−0.150866	−	0.267898i
$914$	54.5512			1.80439
$915$	−8.21572	−	11.3080i	−0.271603	−	0.373830i
$916$	33.7914	+	103.999i	1.11650	+	3.43623i
$917$	8.07502	−	24.8523i	0.266661	−	0.820697i
$918$	24.4907	+	55.4878i	0.808314	+	1.83137i
$919$	8.93581	+	6.49225i	0.294765	+	0.214159i	0.725332	−	0.688399i	$-0.241686\pi$
$919$	8.93581	+	6.49225i	0.294765	+	0.214159i	−0.430567	+	0.902559i	$0.641686\pi$
$920$	−0.573675	+	1.76559i	−0.0189135	+	0.0582098i
$921$	29.9885	−	9.74384i	0.988153	−	0.321070i
$922$	−3.14632	+	2.28593i	−0.103618	+	0.0752832i
$923$			31.0072i			1.02061i
$924$	−57.5966	+	62.6051i	−1.89479	+	2.05956i
$925$			0.651207i			0.0214116i
$926$	−16.7396	+	12.1621i	−0.550099	+	0.399670i
$927$	−0.786569	−	2.42081i	−0.0258343	−	0.0795099i
$928$	−159.725	−	51.8976i	−5.24321	−	1.70362i
$929$	19.3552	−	26.6401i	0.635023	−	0.874034i	−0.363315	−	0.931666i	$-0.618355\pi$
$929$	19.3552	−	26.6401i	0.635023	−	0.874034i	0.998338	+	0.0576323i	$0.0183551\pi$
$930$	−20.2011	+	27.8044i	−0.662421	+	0.911744i
$931$	2.58577	−	7.95817i	0.0847451	−	0.260819i
$932$	−91.8340	+	29.8387i	−3.00812	+	0.977398i
$933$	−10.8791	+	7.90410i	−0.356164	+	0.258769i
$934$	54.9062			1.79659
$935$	−7.32111	+	9.78678i	−0.239426	+	0.320062i
$936$	191.620			6.26329
$937$	9.07504	−	6.59340i	0.296469	−	0.215397i	−0.429600	−	0.903019i	$-0.641345\pi$
$937$	9.07504	−	6.59340i	0.296469	−	0.215397i	0.726069	+	0.687622i	$0.241345\pi$
$938$	36.4406	−	11.8403i	1.18983	−	0.386599i
$939$	−19.8614	+	61.1271i	−0.648152	+	1.99481i
$940$	−19.6784	+	27.0851i	−0.641840	+	0.883417i
$941$	−22.1771	+	30.5242i	−0.722953	+	0.995059i	0.276468	+	0.961023i	$0.410836\pi$
$941$	−22.1771	+	30.5242i	−0.722953	+	0.995059i	−0.999421	+	0.0340357i	$0.989164\pi$
$942$	27.9951	+	9.09614i	0.912128	+	0.296368i
$943$	0.738138	+	2.27175i	0.0240371	+	0.0739785i
$944$	−1.83055	+	1.32997i	−0.0595793	+	0.0432869i
$945$		−	8.14566i		−	0.264978i
$946$	18.2170	−	3.66854i	0.592285	−	0.119275i
$947$		−	37.9318i		−	1.23262i	−0.787505	−	0.616309i	$-0.788627\pi$
$947$		−	37.9318i		−	1.23262i	0.787505	−	0.616309i	$-0.211373\pi$
$948$	−182.198	+	132.375i	−5.91753	+	4.29934i
$949$	9.47000	−	3.07699i	0.307409	−	0.0998833i
$950$	7.11073	−	21.8846i	0.230703	−	0.710030i
$951$	60.0903	+	43.6581i	1.94856	+	1.41571i
$952$	−26.0134	−	58.9376i	−0.843098	−	1.91018i
$953$	8.35267	−	25.7069i	0.270570	−	0.832728i	−0.719788	−	0.694194i	$-0.755761\pi$
$953$	8.35267	−	25.7069i	0.270570	−	0.832728i	0.990358	−	0.138534i	$-0.0442390\pi$
$954$	−14.3448	−	44.1486i	−0.464429	−	1.42937i
$955$	−1.25392	−	1.72587i	−0.0405759	−	0.0558479i
$956$	150.564			4.86960
$957$	−68.9321	−	31.5800i	−2.22826	−	1.02084i
$958$		−	34.7989i		−	1.12430i
$959$	14.8434	+	20.4302i	0.479319	+	0.659726i
$960$	−21.3342	−	65.6601i	−0.688560	−	2.11917i
$961$	1.78974	−	5.50825i	0.0577335	−	0.177685i
$962$	−1.04183	+	1.43396i	−0.0335899	+	0.0462326i
$963$	7.51222	−	10.3397i	0.242078	−	0.333192i
$964$	−85.2615	−	27.7031i	−2.74609	−	0.892258i
$965$	2.46637	+	7.59071i	0.0793953	+	0.244354i
$966$	−1.70111	−	2.34138i	−0.0547324	−	0.0753326i
$967$	−31.3526			−1.00823			−0.504117	−	0.863636i	$-0.668182\pi$
$967$	−31.3526			−1.00823			−0.504117	+	0.863636i	$0.668182\pi$
$968$	−52.8514	+	87.1717i	−1.69871	+	2.80180i
$969$	20.1887	+	11.7429i	0.648556	+	0.377237i
$970$	2.57888	−	1.87366i	0.0828027	−	0.0601597i
$971$	−5.06696	−	15.5945i	−0.162607	−	0.500451i	0.836245	−	0.548355i	$-0.184746\pi$
$971$	−5.06696	−	15.5945i	−0.162607	−	0.500451i	−0.998852	+	0.0479039i	$0.984746\pi$
$972$	76.8405	+	24.9670i	2.46466	+	0.800817i
$973$	−19.1423	−	13.9077i	−0.613674	−	0.445860i
$974$	21.8247	−	30.0391i	0.699309	−	0.962516i
$975$	47.2511	+	15.3528i	1.51325	+	0.491683i
$976$	76.1460	−	24.7413i	2.43737	−	0.791950i
$977$	30.0488	−	21.8317i	0.961346	−	0.698459i	0.00788288	−	0.999969i	$-0.497491\pi$
$977$	30.0488	−	21.8317i	0.961346	−	0.698459i	0.953463	+	0.301510i	$0.0974908\pi$
$978$	−64.8725			−2.07439
$979$	−24.0450	−	11.0158i	−0.768481	−	0.352066i
$980$		−	20.0857i		−	0.641613i
$981$	−24.5336	−	33.7676i	−0.783298	−	1.07812i
$982$	−5.47603	−	16.8535i	−0.174747	−	0.537816i
$983$	14.0049	+	4.55048i	0.446688	+	0.145138i	0.523719	−	0.851891i	$-0.324544\pi$
$983$	14.0049	+	4.55048i	0.446688	+	0.145138i	−0.0770313	+	0.997029i	$0.524544\pi$
$984$	−224.884	−	163.387i	−7.16903	−	5.20860i
$985$	4.88616	+	3.55000i	0.155686	+	0.113112i
$986$	67.9277	−	60.7670i	2.16326	−	1.93522i
$987$	−10.1609	−	31.2719i	−0.323424	−	0.995397i
$988$	36.9854	−	26.8715i	1.17666	−	0.854895i
$989$			0.461458i			0.0146735i
$990$	−7.83632	−	38.9130i	−0.249055	−	1.23674i
$991$			48.8323i			1.55121i	0.631219	+	0.775605i	$0.282555\pi$
$991$			48.8323i			1.55121i	−0.631219	+	0.775605i	$0.717445\pi$
$992$	−61.0156	−	83.9808i	−1.93725	−	2.66639i
$993$	−50.1852	+	16.3061i	−1.59258	+	0.517460i
$994$	−10.4623	+	32.1996i	−0.331843	+	1.02131i
$995$	−10.8602	−	7.89040i	−0.344292	−	0.250143i
$996$	−25.0474	+	34.4748i	−0.793656	+	1.09237i
$997$	39.1455	+	12.7191i	1.23975	+	0.402819i	0.854237	−	0.519883i	$-0.174025\pi$
$997$	39.1455	+	12.7191i	1.23975	+	0.402819i	0.385513	+	0.922703i	$0.374025\pi$
$998$	66.7256	−	21.6805i	2.11216	−	0.686283i
$999$	0.677877	−	0.492506i	0.0214471	−	0.0155822i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	187.2.j.a.135.2	yes	64
11.4	even	5	inner	187.2.j.a.169.1	yes	64
17.16	even	2	inner	187.2.j.a.135.1	✓	64
187.169	even	10	inner	187.2.j.a.169.2	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.j.a.135.1	✓	64	17.16	even	2	inner
187.2.j.a.135.2	yes	64	1.1	even	1	trivial
187.2.j.a.169.1	yes	64	11.4	even	5	inner
187.2.j.a.169.2	yes	64	187.169	even	10	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:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.20158 + 1.59954i) q^{2} +(2.67663 - 0.869690i) q^{3} +(1.67040 - 5.14095i) q^{4} +(-0.525344 + 0.723074i) q^{5} +(-4.50172 + 6.19609i) q^{6} +(-1.60348 - 0.521001i) q^{7} +(2.86380 + 8.81387i) q^{8} +(3.98094 - 2.89232i) q^{9} -2.43222i q^{10} +(3.01526 + 1.38139i) q^{11} -15.2132i q^{12} +(3.39946 - 2.46985i) q^{13} +(4.36356 - 1.41781i) q^{14} +(-0.777302 + 2.39229i) q^{15} +(-11.6568 - 8.46914i) q^{16} +(3.77203 - 1.66487i) q^{17} +(-4.13798 + 12.7354i) q^{18} +(0.621965 + 1.91421i) q^{19} +(2.83976 + 3.90859i) q^{20} -4.74503 q^{21} +(-8.84793 + 1.78180i) q^{22} -0.224129i q^{23} +(15.3307 + 21.1009i) q^{24} +(1.29824 + 3.99556i) q^{25} +(-3.53356 + 10.8752i) q^{26} +(3.17734 - 4.37323i) q^{27} +(-5.35688 + 7.37312i) q^{28} +(-7.72540 - 2.51014i) q^{29} +(-2.11528 - 6.51015i) q^{30} +(-2.95114 - 4.06190i) q^{31} +20.6752 q^{32} +(9.27211 + 1.07512i) q^{33} +(-5.64142 + 9.69887i) q^{34} +(1.21910 - 0.885728i) q^{35} +(-8.21954 - 25.2971i) q^{36} +(0.147419 + 0.0478995i) q^{37} +(-4.43117 - 3.21943i) q^{38} +(6.95109 - 9.56736i) q^{39} +(-7.87756 - 2.55958i) q^{40} +(-10.1359 + 3.29336i) q^{41} +(10.4466 - 7.58988i) q^{42} -2.05890 q^{43} +(12.1383 - 13.1938i) q^{44} +4.39798i q^{45} +(0.358504 + 0.493439i) q^{46} +(2.14137 + 6.59047i) q^{47} +(-38.5664 - 12.5310i) q^{48} +(-3.36342 - 2.44367i) q^{49} +(-9.24925 - 6.71997i) q^{50} +(8.64842 - 7.73673i) q^{51} +(-7.01894 - 21.6021i) q^{52} +(-2.80455 + 2.03762i) q^{53} +14.7103i q^{54} +(-2.58289 + 1.45455i) q^{55} -15.6249i q^{56} +(3.32954 + 4.58272i) q^{57} +(21.0232 - 6.83085i) q^{58} +(0.0485272 - 0.149351i) q^{59} +(11.0002 + 7.99214i) q^{60} +(-3.26617 + 4.49549i) q^{61} +(12.9944 + 4.22213i) q^{62} +(-7.89025 + 2.56370i) q^{63} +(-22.2047 + 16.1327i) q^{64} +3.75558i q^{65} +(-22.1330 + 12.4642i) q^{66} +8.35113 q^{67} +(-2.25821 - 22.1728i) q^{68} +(-0.194923 - 0.599910i) q^{69} +(-1.26719 + 3.90001i) q^{70} +(-4.33739 + 5.96990i) q^{71} +(36.8932 + 26.8045i) q^{72} +(2.25371 + 0.732274i) q^{73} +(-0.401173 + 0.130349i) q^{74} +(6.94979 + 9.56557i) q^{75} +10.8798 q^{76} +(-4.11519 - 3.78597i) q^{77} +32.1819i q^{78} +(-8.70134 - 11.9764i) q^{79} +(12.2476 - 3.97950i) q^{80} +(0.139453 - 0.429193i) q^{81} +(17.0472 - 23.4635i) q^{82} +(-2.26611 - 1.64643i) q^{83} +(-7.92607 + 24.3939i) q^{84} +(-0.777793 + 3.60209i) q^{85} +(4.53283 - 3.29330i) q^{86} -22.8611 q^{87} +(-3.54026 + 30.5321i) q^{88} -7.97444 q^{89} +(-7.03476 - 9.68252i) q^{90} +(-6.73775 + 2.18923i) q^{91} +(-1.15224 - 0.374384i) q^{92} +(-11.4317 - 8.30563i) q^{93} +(-15.2562 - 11.0842i) q^{94} +(-1.71086 - 0.555892i) q^{95} +(55.3400 - 17.9810i) q^{96} +(0.770351 + 1.06030i) q^{97} +11.3136 q^{98} +(15.9990 - 3.22188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{2} - 20 q^{4} - 4 q^{8} + 30 q^{9} - 4 q^{13} - 34 q^{15} - 16 q^{16} - 14 q^{17} + 10 q^{18} - 72 q^{21} + 36 q^{25} + 22 q^{26} - 8 q^{30} + 84 q^{32} - 44 q^{33} - 44 q^{34} + 18 q^{35} - 32 q^{36}+ \cdots + 72 q^{98}+O(q^{100}) \) 64 * q - 8 * q^2 - 20 * q^4 - 4 * q^8 + 30 * q^9 - 4 * q^13 - 34 * q^15 - 16 * q^16 - 14 * q^17 + 10 * q^18 - 72 * q^21 + 36 * q^25 + 22 * q^26 - 8 * q^30 + 84 * q^32 - 44 * q^33 - 44 * q^34 + 18 * q^35 - 32 * q^36 - 60 * q^38 - 10 * q^42 + 32 * q^43 + 16 * q^47 - 18 * q^49 + 4 * q^50 - 2 * q^51 + 44 * q^52 - 16 * q^53 + 22 * q^55 - 50 * q^59 + 68 * q^60 - 80 * q^64 - 172 * q^66 + 40 * q^67 + 18 * q^68 + 6 * q^69 + 128 * q^70 + 186 * q^72 - 116 * q^76 - 30 * q^77 + 48 * q^81 - 12 * q^83 + 68 * q^84 - 108 * q^85 - 16 * q^86 + 92 * q^87 - 40 * q^89 - 80 * q^93 - 188 * q^94 + 72 * q^98

Introduction

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