LMFDB - Embedded newform 669.2.i.a.4.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(4,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(74)) chi = DirichletCharacter(H, H._module([0, 46])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.i (of order $37$, degree $36$, minimal)

Newform invariants

comment:select newform

sage:traces = [648] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.34199189522$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$18$ over $\Q(\zeta_{37})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{37}]$

Embedding invariants

Embedding label			4.11
Character	$\chi$	$=$	669.4
Dual form			669.2.i.a.502.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173139 - 0.0611740i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(-1.52984 + 1.23526i) q^{4} +(-0.169781 - 0.275742i) q^{5} +(-0.00779341 + 0.183463i) q^{6} +(-0.312492 + 2.44030i) q^{7} +(-0.381865 + 0.620188i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-0.0462641 - 0.0373556i) q^{10} +(0.00825142 - 0.194245i) q^{11} +(-0.575772 - 1.88009i) q^{12} +(-0.986794 - 2.45573i) q^{13} +(0.0951780 + 0.441628i) q^{14} +(0.319162 - 0.0547259i) q^{15} +(0.800333 - 3.71356i) q^{16} +(-0.315208 + 7.42025i) q^{17} +(-0.167328 - 0.0756368i) q^{18} +(-4.50434 + 1.17284i) q^{19} +(0.600350 + 0.212117i) q^{20} +(-2.14781 - 1.19984i) q^{21} +(-0.0104541 - 0.0341361i) q^{22} +(-2.68035 - 4.35316i) q^{23} +(-0.433085 - 0.585569i) q^{24} +(2.20381 - 4.37100i) q^{25} +(-0.321079 - 0.364817i) q^{26} +(0.911228 - 0.411901i) q^{27} +(-2.53633 - 4.11927i) q^{28} +(0.488607 - 2.26714i) q^{29} +(0.0519117 - 0.0289996i) q^{30} +(-8.84951 + 0.753204i) q^{31} +(-0.273624 - 2.13677i) q^{32} +(0.177161 + 0.0800818i) q^{33} +(0.399351 + 1.30402i) q^{34} +(0.725949 - 0.328150i) q^{35} +(1.95920 + 0.166752i) q^{36} +(-0.245415 - 5.77727i) q^{37} +(-0.708131 + 0.478613i) q^{38} +2.64658 q^{39} +0.235846 q^{40} +(0.435642 - 0.294443i) q^{41} +(-0.445269 - 0.0763491i) q^{42} +(-1.76926 - 3.50911i) q^{43} +(0.227319 + 0.307355i) q^{44} +(-0.0682222 + 0.316552i) q^{45} +(-0.730373 - 0.589735i) q^{46} +(-6.67117 - 1.73704i) q^{47} +(3.14736 + 2.12724i) q^{48} +(0.916727 + 0.238697i) q^{49} +(0.114175 - 0.891607i) q^{50} +(-6.76764 - 3.05917i) q^{51} +(4.54309 + 2.53792i) q^{52} +(-9.36069 + 10.6358i) q^{53} +(0.132572 - 0.127060i) q^{54} +(-0.0549625 + 0.0307039i) q^{55} +(-1.39411 - 1.12567i) q^{56} +(0.591208 - 4.61683i) q^{57} +(-0.0540932 - 0.422421i) q^{58} +(-3.11055 + 10.1570i) q^{59} +(-0.420666 + 0.477969i) q^{60} +(5.60214 + 13.9415i) q^{61} +(-1.48612 + 0.671769i) q^{62} +(1.91414 - 1.54556i) q^{63} +(3.24240 + 6.43091i) q^{64} +(-0.509610 + 0.689038i) q^{65} +(0.0355724 + 0.00302766i) q^{66} +(6.26328 - 5.05724i) q^{67} +(-8.68370 - 11.7411i) q^{68} +(5.03863 - 0.863960i) q^{69} +(0.105616 - 0.101225i) q^{70} +(4.05106 - 13.2281i) q^{71} +(0.704821 - 0.183521i) q^{72} +(-2.71973 - 1.51933i) q^{73} +(-0.395910 - 0.985259i) q^{74} +(3.23410 + 3.67465i) q^{75} +(5.44215 - 7.35827i) q^{76} +(0.471437 + 0.0808359i) q^{77} +(0.458226 - 0.161902i) q^{78} +(-3.72101 + 2.51496i) q^{79} +(-1.15987 + 0.409807i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(0.0574145 - 0.0776295i) q^{82} +(-1.81176 + 3.59341i) q^{83} +(4.76791 - 0.817540i) q^{84} +(2.09959 - 1.17290i) q^{85} +(-0.520994 - 0.499332i) q^{86} +(1.92148 + 1.29869i) q^{87} +(0.117317 + 0.0792926i) q^{88} +(-6.65162 + 10.8029i) q^{89} +(0.00755282 + 0.0589810i) q^{90} +(6.30108 - 1.64067i) q^{91} +(9.47776 + 3.34871i) q^{92} +(2.60071 - 8.49220i) q^{93} +(-1.26130 + 0.107353i) q^{94} +(1.08815 + 1.04291i) q^{95} +(2.08471 + 0.542815i) q^{96} +(8.34304 - 13.5500i) q^{97} +(0.173323 - 0.0147520i) q^{98} +(-0.140363 + 0.134527i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/669\mathbb{Z}\right)^\times$.

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{23}{37}\right)$

Coefficient data

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

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

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

$2$	0.173139	−	0.0611740i	0.122428	−	0.0432565i	−0.271223	−	0.962517i	$-0.587428\pi$
$2$	0.173139	−	0.0611740i	0.122428	−	0.0432565i	0.393651	+	0.919260i	$0.371212\pi$
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$3$	−0.372856	+	0.927889i	−0.215269	+	0.535717i
$4$	−1.52984	+	1.23526i	−0.764918	+	0.617628i
$5$	−0.169781	−	0.275742i	−0.0759285	−	0.123316i	0.811330	−	0.584589i	$-0.198744\pi$
$5$	−0.169781	−	0.275742i	−0.0759285	−	0.123316i	−0.887258	+	0.461273i	$0.847393\pi$
$6$	−0.00779341	+	0.183463i	−0.00318165	+	0.0748985i
$7$	−0.312492	+	2.44030i	−0.118111	+	0.922346i	0.819116	+	0.573627i	$0.194464\pi$
$7$	−0.312492	+	2.44030i	−0.118111	+	0.922346i	−0.937227	+	0.348719i	$0.886617\pi$
$8$	−0.381865	+	0.620188i	−0.135010	+	0.219269i
$9$	−0.721956	−	0.691939i	−0.240652	−	0.230646i
$10$	−0.0462641	−	0.0373556i	−0.0146300	−	0.0118129i
$11$	0.00825142	−	0.194245i	0.00248790	−	0.0585670i	−0.997426	−	0.0717065i	$-0.977156\pi$
$11$	0.00825142	−	0.194245i	0.00248790	−	0.0585670i	0.999914	+	0.0131395i	$0.00418254\pi$
$12$	−0.575772	−	1.88009i	−0.166211	−	0.542736i
$13$	−0.986794	−	2.45573i	−0.273687	−	0.681097i	0.726293	−	0.687385i	$-0.241242\pi$
$13$	−0.986794	−	2.45573i	−0.273687	−	0.681097i	−0.999980	+	0.00628820i	$0.997998\pi$
$14$	0.0951780	+	0.441628i	0.0254374	+	0.118030i
$15$	0.319162	−	0.0547259i	0.0824074	−	0.0141302i
$16$	0.800333	−	3.71356i	0.200083	−	0.928389i
$17$	−0.315208	+	7.42025i	−0.0764493	+	1.79968i	0.395931	+	0.918280i	$0.370422\pi$
$17$	−0.315208	+	7.42025i	−0.0764493	+	1.79968i	−0.472380	+	0.881395i	$0.656605\pi$
$18$	−0.167328	−	0.0756368i	−0.0394395	−	0.0178278i
$19$	−4.50434	+	1.17284i	−1.03337	+	0.269068i	−0.729741	−	0.683724i	$-0.760359\pi$
$19$	−4.50434	+	1.17284i	−1.03337	+	0.269068i	−0.303626	+	0.952791i	$0.598197\pi$
$20$	0.600350	+	0.212117i	0.134242	+	0.0474309i
$21$	−2.14781	−	1.19984i	−0.468691	−	0.261826i
$22$	−0.0104541	−	0.0341361i	−0.00222882	−	0.00727785i
$23$	−2.68035	−	4.35316i	−0.558891	−	0.907696i	−0.999948	−	0.0102172i	$-0.996748\pi$
$23$	−2.68035	−	4.35316i	−0.558891	−	0.907696i	0.441057	−	0.897479i	$-0.354604\pi$
$24$	−0.433085	−	0.585569i	−0.0884030	−	0.119529i
$25$	2.20381	−	4.37100i	0.440762	−	0.874199i
$26$	−0.321079	−	0.364817i	−0.0629689	−	0.0715465i
$27$	0.911228	−	0.411901i	0.175366	−	0.0792704i
$28$	−2.53633	−	4.11927i	−0.479322	−	0.778468i
$29$	0.488607	−	2.26714i	0.0907320	−	0.420998i	−0.909257	−	0.416236i	$-0.863349\pi$
$29$	0.488607	−	2.26714i	0.0907320	−	0.420998i	0.999989	−	0.00476212i	$-0.00151584\pi$
$30$	0.0519117	−	0.0289996i	0.00947774	−	0.00529458i
$31$	−8.84951	+	0.753204i	−1.58942	+	0.135279i	−0.845865	−	0.533397i	$-0.820915\pi$
$31$	−8.84951	+	0.753204i	−1.58942	+	0.135279i	−0.743553	+	0.668677i	$0.766861\pi$
$32$	−0.273624	−	2.13677i	−0.0483703	−	0.377731i
$33$	0.177161	+	0.0800818i	0.0308398	+	0.0139405i
$34$	0.399351	+	1.30402i	0.0684882	+	0.223637i
$35$	0.725949	−	0.328150i	0.122708	−	0.0554674i
$36$	1.95920	+	0.166752i	0.326533	+	0.0277920i
$37$	−0.245415	−	5.77727i	−0.0403461	−	0.949777i	−0.899195	−	0.437548i	$-0.855847\pi$
$37$	−0.245415	−	5.77727i	−0.0403461	−	0.949777i	0.858849	−	0.512229i	$-0.171180\pi$
$38$	−0.708131	+	0.478613i	−0.114874	+	0.0776413i
$39$	2.64658			0.423792
$40$	0.235846			0.0372905
$41$	0.435642	−	0.294443i	0.0680359	−	0.0459842i	−0.525485	−	0.850803i	$-0.676116\pi$
$41$	0.435642	−	0.294443i	0.0680359	−	0.0459842i	0.593520	+	0.804819i	$0.297738\pi$
$42$	−0.445269	−	0.0763491i	−0.0687065	−	0.0117809i
$43$	−1.76926	−	3.50911i	−0.269809	−	0.535134i	0.716990	−	0.697083i	$-0.245519\pi$
$43$	−1.76926	−	3.50911i	−0.269809	−	0.535134i	−0.986799	+	0.161949i	$0.948222\pi$
$44$	0.227319	+	0.307355i	0.0342696	+	0.0463356i
$45$	−0.0682222	+	0.316552i	−0.0101700	+	0.0471888i
$46$	−0.730373	−	0.589735i	−0.107688	−	0.0869517i
$47$	−6.67117	−	1.73704i	−0.973090	−	0.253373i	−0.268730	−	0.963216i	$-0.586604\pi$
$47$	−6.67117	−	1.73704i	−0.973090	−	0.253373i	−0.704360	+	0.709843i	$0.748766\pi$
$48$	3.14736	+	2.12724i	0.454282	+	0.307041i
$49$	0.916727	+	0.238697i	0.130961	+	0.0340996i
$50$	0.114175	−	0.891607i	0.0161467	−	0.126092i
$51$	−6.76764	−	3.05917i	−0.947659	−	0.428369i
$52$	4.54309	+	2.53792i	0.630013	+	0.351947i
$53$	−9.36069	+	10.6358i	−1.28579	+	1.46094i	−0.469913	+	0.882712i	$0.655715\pi$
$53$	−9.36069	+	10.6358i	−1.28579	+	1.46094i	−0.815876	+	0.578228i	$0.803745\pi$
$54$	0.132572	−	0.127060i	0.0180407	−	0.0172906i
$55$	−0.0549625	+	0.0307039i	−0.00741114	+	0.00414011i
$56$	−1.39411	−	1.12567i	−0.186296	−	0.150424i
$57$	0.591208	−	4.61683i	0.0783074	−	0.611514i
$58$	−0.0540932	−	0.422421i	−0.00710278	−	0.0554667i
$59$	−3.11055	+	10.1570i	−0.404959	+	1.32233i	0.488256	+	0.872701i	$0.337633\pi$
$59$	−3.11055	+	10.1570i	−0.404959	+	1.32233i	−0.893215	+	0.449630i	$0.851556\pi$
$60$	−0.420666	+	0.477969i	−0.0543077	+	0.0617056i
$61$	5.60214	+	13.9415i	0.717280	+	1.78502i	0.612418	+	0.790534i	$0.290197\pi$
$61$	5.60214	+	13.9415i	0.717280	+	1.78502i	0.104862	+	0.994487i	$0.466560\pi$
$62$	−1.48612	+	0.671769i	−0.188737	+	0.0853147i
$63$	1.91414	−	1.54556i	0.241159	−	0.194723i
$64$	3.24240	+	6.43091i	0.405300	+	0.803864i
$65$	−0.509610	+	0.689038i	−0.0632093	+	0.0854647i
$66$	0.0355724	+	0.00302766i	0.00437866	+	0.000372679i
$67$	6.26328	−	5.05724i	0.765181	−	0.617841i	−0.164427	−	0.986389i	$-0.552578\pi$
$67$	6.26328	−	5.05724i	0.765181	−	0.617841i	0.929608	+	0.368549i	$0.120145\pi$
$68$	−8.68370	−	11.7411i	−1.05305	−	1.42382i
$69$	5.03863	−	0.863960i	0.606580	−	0.104009i
$70$	0.105616	−	0.101225i	0.0126235	−	0.0120987i
$71$	4.05106	−	13.2281i	0.480772	−	1.56989i	−0.305618	−	0.952154i	$-0.598863\pi$
$71$	4.05106	−	13.2281i	0.480772	−	1.56989i	0.786390	−	0.617731i	$-0.211948\pi$
$72$	0.704821	−	0.183521i	0.0830640	−	0.0216282i
$73$	−2.71973	−	1.51933i	−0.318321	−	0.177825i	0.320361	−	0.947295i	$-0.396196\pi$
$73$	−2.71973	−	1.51933i	−0.318321	−	0.177825i	−0.638682	+	0.769471i	$0.720520\pi$
$74$	−0.395910	−	0.985259i	−0.0460236	−	0.114534i
$75$	3.23410	+	3.67465i	0.373441	+	0.424312i
$76$	5.44215	−	7.35827i	0.624257	−	0.844052i
$77$	0.471437	+	0.0808359i	0.0537252	+	0.00921211i
$78$	0.458226	−	0.161902i	0.0518839	−	0.0183318i
$79$	−3.72101	+	2.51496i	−0.418646	+	0.282955i	−0.751131	−	0.660153i	$-0.770491\pi$
$79$	−3.72101	+	2.51496i	−0.418646	+	0.282955i	0.332485	+	0.943109i	$0.392113\pi$
$80$	−1.15987	+	0.409807i	−0.129677	+	0.0458178i
$81$	0.0424412	+	0.999099i	0.00471569	+	0.111011i
$82$	0.0574145	−	0.0776295i	0.00634037	−	0.00857274i
$83$	−1.81176	+	3.59341i	−0.198867	+	0.394428i	−0.970308	−	0.241872i	$-0.922239\pi$
$83$	−1.81176	+	3.59341i	−0.198867	+	0.394428i	0.771442	+	0.636300i	$0.219536\pi$
$84$	4.76791	−	0.817540i	0.520222	−	0.0892009i
$85$	2.09959	−	1.17290i	0.227733	−	0.127219i
$86$	−0.520994	−	0.499332i	−0.0561802	−	0.0538444i
$87$	1.92148	+	1.29869i	0.206004	+	0.139234i
$88$	0.117317	+	0.0792926i	0.0125061	+	0.00845262i
$89$	−6.65162	+	10.8029i	−0.705071	+	1.14511i	0.277769	+	0.960648i	$0.410405\pi$
$89$	−6.65162	+	10.8029i	−0.705071	+	1.14511i	−0.982840	+	0.184460i	$0.940946\pi$
$90$	0.00755282	+	0.0589810i	0.000796137	+	0.00621715i
$91$	6.30108	−	1.64067i	0.660533	−	0.171989i
$92$	9.47776	+	3.34871i	0.988125	+	0.349127i
$93$	2.60071	−	8.49220i	0.269681	−	0.880600i
$94$	−1.26130	+	0.107353i	−0.130093	+	0.0110726i
$95$	1.08815	+	1.04291i	0.111642	+	0.107001i
$96$	2.08471	+	0.542815i	0.212769	+	0.0554008i
$97$	8.34304	−	13.5500i	0.847107	−	1.37579i	−0.0783456	−	0.996926i	$-0.524964\pi$
$97$	8.34304	−	13.5500i	0.847107	−	1.37579i	0.925453	−	0.378863i	$-0.123685\pi$
$98$	0.173323	−	0.0147520i	0.0175083	−	0.00149018i
$99$	−0.140363	+	0.134527i	−0.0141070	+	0.0135204i
$100$	2.02783	+	9.40918i	0.202783	+	0.940918i
$101$	4.63094	+	5.26178i	0.460796	+	0.523566i	0.933945	−	0.357416i	$-0.116342\pi$
$101$	4.63094	+	5.26178i	0.460796	+	0.523566i	−0.473149	+	0.880982i	$0.656883\pi$
$102$	−1.35889	−	0.115658i	−0.134550	−	0.0114519i
$103$	−4.92331	+	12.2521i	−0.485108	+	1.20724i	0.462160	+	0.886796i	$0.347075\pi$
$103$	−4.92331	+	12.2521i	−0.485108	+	1.20724i	−0.947268	+	0.320442i	$0.896169\pi$
$104$	1.89984	+	0.325759i	0.186294	+	0.0319433i
$105$	0.0338117	+	0.795953i	0.00329968	+	0.0776771i
$106$	−0.970067	+	2.41410i	−0.0942212	+	0.234479i
$107$	4.78730	+	9.49504i	0.462805	+	0.917920i	0.997348	+	0.0727783i	$0.0231866\pi$
$107$	4.78730	+	9.49504i	0.462805	+	0.917920i	−0.534543	+	0.845141i	$0.679516\pi$
$108$	−0.885227	+	1.75574i	−0.0851810	+	0.168946i
$109$	0.101982	+	0.473198i	0.00976811	+	0.0453242i	0.982177	−	0.187961i	$-0.0601877\pi$
$109$	0.101982	+	0.473198i	0.00976811	+	0.0453242i	−0.972408	+	0.233285i	$0.925053\pi$
$110$	−0.00763788	+	0.00867831i	−0.000728243	+	0.000827445i
$111$	5.45217	+	1.92637i	0.517497	+	0.182843i
$112$	8.81209	+	3.11351i	0.832664	+	0.294199i
$113$	−12.2743	+	13.9463i	−1.15466	+	1.31195i	−0.212362	+	0.977191i	$0.568116\pi$
$113$	−12.2743	+	13.9463i	−1.15466	+	1.31195i	−0.942302	+	0.334763i	$0.891344\pi$
$114$	−0.180068	−	0.835521i	−0.0168650	−	0.0782537i
$115$	−0.745278	+	1.47817i	−0.0694975	+	0.137840i
$116$	2.05302	+	4.07191i	0.190618	+	0.378068i
$117$	−0.986794	+	2.45573i	−0.0912291	+	0.227032i
$118$	0.0827866	+	1.94886i	0.00762113	+	0.179407i
$119$	−18.0091	−	3.08797i	−1.65089	−	0.283074i
$120$	−0.0879365	+	0.218838i	−0.00802747	+	0.0199771i
$121$	10.9227	+	0.929660i	0.992974	+	0.0845145i
$122$	1.82280	+	2.07111i	0.165029	+	0.187509i
$123$	0.110778	+	0.514012i	0.00998853	+	0.0463469i
$124$	12.6079	−	12.0837i	1.13222	−	1.08515i
$125$	−3.19270	+	0.271739i	−0.285564	+	0.0243051i
$126$	0.236865	−	0.384693i	0.0211016	−	0.0342712i
$127$	−20.7229	−	5.39582i	−1.83886	−	0.478802i	−0.840815	−	0.541323i	$-0.817924\pi$
$127$	−20.7229	−	5.39582i	−1.83886	−	0.478802i	−0.998044	+	0.0625210i	$0.980086\pi$
$128$	4.06529	+	3.89626i	0.359324	+	0.344384i
$129$	3.91574	−	0.333279i	0.344762	−	0.0293436i
$130$	−0.0460823	+	0.150474i	−0.00404168	+	0.0131975i
$131$	5.17742	+	1.82930i	0.452353	+	0.159827i	0.549590	−	0.835435i	$-0.314784\pi$
$131$	5.17742	+	1.82930i	0.452353	+	0.159827i	−0.0972363	+	0.995261i	$0.531000\pi$
$132$	−0.369949	+	0.0963272i	−0.0321999	+	0.00838421i
$133$	−1.45451	−	11.3584i	−0.126122	−	0.984902i
$134$	0.775047	−	1.25876i	0.0669539	−	0.108740i
$135$	−0.268288	−	0.181331i	−0.0230906	−	0.0156065i
$136$	−4.48158	−	3.02902i	−0.384292	−	0.259736i
$137$	4.80295	+	4.60326i	0.410344	+	0.393283i	0.868581	−	0.495547i	$-0.165032\pi$
$137$	4.80295	+	4.60326i	0.410344	+	0.393283i	−0.458237	+	0.888830i	$0.651519\pi$
$138$	0.819533	−	0.457818i	0.0697633	−	0.0389721i
$139$	−0.957195	+	0.164128i	−0.0811882	+	0.0139211i	−0.209452	−	0.977819i	$-0.567168\pi$
$139$	−0.957195	+	0.164128i	−0.0811882	+	0.0139211i	0.128263	+	0.991740i	$0.459060\pi$
$140$	−0.705234	+	1.39875i	−0.0596032	+	0.118216i
$141$	4.09917	−	5.54244i	0.345212	−	0.466758i
$142$	−0.107818	−	2.53812i	−0.00904789	−	0.212994i
$143$	−0.485155	+	0.171416i	−0.0405707	+	0.0143345i
$144$	−3.14736	+	2.12724i	−0.262280	+	0.177270i
$145$	−0.708104	+	0.250189i	−0.0588049	+	0.0207771i
$146$	−0.563836	−	0.0966794i	−0.0466634	−	0.00800125i
$147$	−0.563292	+	0.761621i	−0.0464595	+	0.0628174i
$148$	7.51186	+	8.53513i	0.617471	+	0.701583i
$149$	3.33836	+	8.30783i	0.273489	+	0.680604i	0.999978	−	0.00657408i	$-0.00209261\pi$
$149$	3.33836	+	8.30783i	0.273489	+	0.680604i	−0.726489	+	0.687178i	$0.758849\pi$
$150$	0.784741	+	0.438383i	0.0640739	+	0.0357938i
$151$	−6.99864	+	1.82230i	−0.569541	+	0.148297i	−0.525592	−	0.850737i	$-0.676156\pi$
$151$	−6.99864	+	1.82230i	−0.569541	+	0.148297i	−0.0439491	+	0.999034i	$0.513994\pi$
$152$	0.992668	−	3.24140i	0.0805160	−	0.262912i
$153$	5.36193	−	5.13899i	0.433486	−	0.415463i
$154$	0.0865692	−	0.0148438i	0.00697594	−	0.00119615i
$155$	1.71017	+	2.31230i	0.137364	+	0.185729i
$156$	−4.04883	+	3.26920i	−0.324166	+	0.261746i
$157$	15.2868	+	1.30110i	1.22002	+	0.103839i	0.677067	−	0.735922i	$-0.263251\pi$
$157$	15.2868	+	1.30110i	1.22002	+	0.103839i	0.542957	+	0.839761i	$0.317305\pi$
$158$	−0.490402	+	0.663067i	−0.0390143	+	0.0527508i
$159$	−6.37865	−	12.6513i	−0.505860	−	1.00331i
$160$	−0.542741	+	0.438233i	−0.0429075	+	0.0346454i
$161$	11.4606	−	5.18051i	0.903221	−	0.408282i
$162$	0.0684671	+	0.170387i	0.00537928	+	0.0133869i
$163$	0.915327	−	1.04001i	0.0716940	−	0.0814602i	−0.713720	−	0.700432i	$-0.752991\pi$
$163$	0.915327	−	1.04001i	0.0716940	−	0.0814602i	0.785414	+	0.618971i	$0.212450\pi$
$164$	−0.302749	+	0.988579i	−0.0236407	+	0.0771950i
$165$	−0.00799668	−	0.0624472i	−0.000622540	−	0.00486151i
$166$	−0.0938634	+	0.732993i	−0.00728522	+	0.0568913i
$167$	−0.305092	−	0.246344i	−0.0236087	−	0.0190627i	0.616343	−	0.787478i	$-0.288613\pi$
$167$	−0.305092	−	0.246344i	−0.0236087	−	0.0190627i	−0.639952	+	0.768415i	$0.721046\pi$
$168$	1.56430	−	0.873870i	0.120688	−	0.0674205i
$169$	4.32858	−	4.14861i	0.332967	−	0.319123i
$170$	0.291771	−	0.331516i	0.0223778	−	0.0254261i
$171$	4.06347	+	2.26999i	0.310741	+	0.173591i
$172$	7.04133	+	3.18288i	0.536896	+	0.242692i
$173$	−0.297229	+	2.32110i	−0.0225979	+	0.176470i	−0.999267	−	0.0382792i	$-0.987812\pi$
$173$	−0.297229	+	2.32110i	−0.0225979	+	0.176470i	0.976669	+	0.214749i	$0.0688935\pi$
$174$	0.412129	+	0.107310i	0.0312434	+	0.00813516i
$175$	9.97786	+	6.74386i	0.754256	+	0.509788i
$176$	−0.714735	−	0.186103i	−0.0538752	−	0.0140280i
$177$	−8.26479	−	6.67336i	−0.621220	−	0.501600i
$178$	−0.490799	+	2.27732i	−0.0367869	+	0.170692i
$179$	−8.26058	−	11.1690i	−0.617425	−	0.834813i	0.378443	−	0.925624i	$-0.376459\pi$
$179$	−8.26058	−	11.1690i	−0.617425	−	0.834813i	−0.995868	+	0.0908111i	$0.971054\pi$
$180$	−0.286654	−	0.568545i	−0.0213660	−	0.0423769i
$181$	2.22634	+	0.381744i	0.165482	+	0.0283748i	0.251145	−	0.967949i	$-0.419193\pi$
$181$	2.22634	+	0.381744i	0.165482	+	0.0283748i	−0.0856631	+	0.996324i	$0.527301\pi$
$182$	0.990597	−	0.669527i	0.0734280	−	0.0496286i
$183$	−15.0249			−1.11067
$184$	3.72330			0.274486
$185$	−1.55137	+	1.04854i	−0.114059	+	0.0770905i
$186$	−0.0692172	−	1.62943i	−0.00507525	−	0.119475i
$187$	1.43874	+	0.122455i	0.105211	+	0.00895481i
$188$	12.3515	−	5.58322i	0.900825	−	0.407199i
$189$	0.720410	+	2.35239i	0.0524021	+	0.171111i
$190$	0.252201	+	0.114002i	0.0182966	+	0.00827059i
$191$	0.540669	+	4.22216i	0.0391214	+	0.305505i	0.999629	+	0.0272499i	$0.00867498\pi$
$191$	0.540669	+	4.22216i	0.0391214	+	0.305505i	−0.960507	+	0.278255i	$0.910244\pi$
$192$	−7.17612	+	0.610778i	−0.517892	+	0.0440791i
$193$	−12.1764	+	6.80216i	−0.876479	+	0.489630i	−0.860035	−	0.510234i	$-0.829559\pi$
$193$	−12.1764	+	6.80216i	−0.876479	+	0.489630i	−0.0164433	+	0.999865i	$0.505234\pi$
$194$	0.615602	−	2.85640i	0.0441977	−	0.205078i
$195$	−0.449340	−	0.729774i	−0.0321779	−	0.0522602i
$196$	−1.69729	+	0.767225i	−0.121235	+	0.0548018i
$197$	−11.7509	−	13.3516i	−0.837214	−	0.951260i	0.162155	−	0.986765i	$-0.448156\pi$
$197$	−11.7509	−	13.3516i	−0.837214	−	0.951260i	−0.999369	+	0.0355050i	$0.988696\pi$
$198$	−0.0160727	+	0.0318784i	−0.00114224	+	0.00226550i
$199$	−11.8666	−	16.0448i	−0.841204	−	1.13738i	−0.988934	−	0.148355i	$-0.952602\pi$
$199$	−11.8666	−	16.0448i	−0.841204	−	1.13738i	0.147730	−	0.989028i	$-0.452803\pi$
$200$	1.86928	+	3.03591i	0.132178	+	0.214671i
$201$	2.35726	+	7.69725i	0.166268	+	0.542922i
$202$	1.12368	+	0.627726i	0.0790620	+	0.0441667i
$203$	5.37982	+	1.90081i	0.377589	+	0.133411i
$204$	14.1322	−	3.67975i	0.989455	−	0.257634i
$205$	−0.155154	−	0.0701341i	−0.0108364	−	0.00489838i
$206$	−0.102907	+	2.42250i	−0.00716984	+	0.168784i
$207$	−1.07703	+	4.99742i	−0.0748586	+	0.347345i
$208$	−9.90926	+	1.69911i	−0.687084	+	0.117812i
$209$	0.190651	+	0.884622i	0.0131876	+	0.0611906i
$210$	0.0545457	+	0.135742i	0.00376401	+	0.00936711i
$211$	2.13911	+	6.98493i	0.147262	+	0.480862i	0.999076	−	0.0429830i	$-0.0136861\pi$
$211$	2.13911	+	6.98493i	0.147262	+	0.480862i	−0.851813	+	0.523845i	$0.824497\pi$
$212$	1.18237	−	27.8339i	0.0812055	−	1.91164i
$213$	10.7637	+	8.69111i	0.737519	+	0.595505i
$214$	1.40972	+	1.35110i	0.0963663	+	0.0923596i
$215$	−0.667224	+	1.08364i	−0.0455043	+	0.0739037i
$216$	−0.0925099	+	0.722423i	−0.00629450	+	0.0491547i
$217$	0.927361	−	21.8308i	0.0629534	−	1.48197i
$218$	0.0466045	+	0.0756905i	0.00315645	+	0.00512641i
$219$	2.42384	−	1.95712i	0.163788	−	0.132250i
$220$	0.0461564	−	0.114865i	0.00311186	−	0.00774417i
$221$	18.5332	−	6.54819i	1.24668	−	0.440479i
$222$	1.06183			0.0712653
$223$	12.9550	+	7.42745i	0.867533	+	0.497379i
$223$	12.9550	+	7.42745i	0.867533	+	0.497379i
$224$	5.29986			0.354112
$225$	−4.61552	+	1.63077i	−0.307701	+	0.108718i
$226$	−1.27201	+	3.16551i	−0.0846126	+	0.210567i
$227$	−17.1267	+	13.8288i	−1.13674	+	0.917852i	−0.997376	−	0.0723896i	$-0.976938\pi$
$227$	−17.1267	+	13.8288i	−1.13674	+	0.917852i	−0.139362	+	0.990242i	$0.544505\pi$
$228$	4.79852	+	7.79329i	0.317790	+	0.516123i
$229$	0.681185	−	16.0356i	0.0450140	−	1.05966i	−0.824533	−	0.565814i	$-0.808562\pi$
$229$	0.681185	−	16.0356i	0.0450140	−	1.05966i	0.869547	−	0.493850i	$-0.164411\pi$
$230$	−0.0386112	+	0.301521i	−0.00254595	+	0.0198817i
$231$	−0.250785	+	0.407301i	−0.0165004	+	0.0267984i
$232$	1.21947	+	1.16877i	0.0800623	+	0.0767335i
$233$	4.77428	+	3.85496i	0.312773	+	0.252547i	0.771785	−	0.635883i	$-0.219364\pi$
$233$	4.77428	+	3.85496i	0.312773	+	0.252547i	−0.459012	+	0.888430i	$0.651796\pi$
$234$	−0.0206259	+	0.485549i	−0.00134836	+	0.0317413i
$235$	0.653665	+	2.13444i	0.0426404	+	0.139236i
$236$	−7.78789	−	19.3809i	−0.506948	−	1.26159i
$237$	−0.946204	−	4.39040i	−0.0614626	−	0.285187i
$238$	−3.30699	+	0.567040i	−0.214360	+	0.0367558i
$239$	−5.94020	+	27.5626i	−0.384240	+	1.78288i	0.209066	+	0.977901i	$0.432957\pi$
$239$	−5.94020	+	27.5626i	−0.384240	+	1.78288i	−0.593306	+	0.804977i	$0.702178\pi$
$240$	0.0522084	−	1.22903i	0.00337004	−	0.0793333i
$241$	19.6721	+	8.89235i	1.26719	+	0.572806i	0.929629	−	0.368497i	$-0.120127\pi$
$241$	19.6721	+	8.89235i	1.26719	+	0.572806i	0.337562	+	0.941303i	$0.390398\pi$
$242$	1.94802	−	0.507225i	0.125223	−	0.0326057i
$243$	−0.942877	−	0.333140i	−0.0604856	−	0.0213709i
$244$	−25.7916	−	14.4081i	−1.65114	−	0.922382i
$245$	−0.0898242	−	0.293307i	−0.00573866	−	0.0187387i
$246$	0.0506242	+	0.0822189i	0.00322768	+	0.00524209i
$247$	7.32503	+	9.90410i	0.466081	+	0.630183i
$248$	2.91219	−	5.77598i	0.184924	−	0.366775i
$249$	−2.65876	−	3.02094i	−0.168492	−	0.191444i
$250$	−0.536159	+	0.242359i	−0.0339097	+	0.0153281i
$251$	10.0502	+	16.3226i	0.634366	+	1.03028i	0.995220	+	0.0976535i	$0.0311337\pi$
$251$	10.0502	+	16.3226i	0.634366	+	1.03028i	−0.360855	+	0.932622i	$0.617515\pi$
$252$	−1.01916	+	4.72892i	−0.0642010	+	0.297894i
$253$	−0.867695	+	0.484723i	−0.0545515	+	0.0304743i
$254$	−3.91803	+	0.333473i	−0.245839	+	0.0209240i
$255$	0.305477	+	2.38552i	0.0191297	+	0.149387i
$256$	−12.1832	−	5.50717i	−0.761453	−	0.344198i
$257$	−2.32661	−	7.59717i	−0.145130	−	0.473898i	0.853777	−	0.520638i	$-0.174306\pi$
$257$	−2.32661	−	7.59717i	−0.145130	−	0.473898i	−0.998907	+	0.0467399i	$0.985117\pi$
$258$	0.657581	−	0.297245i	0.0409392	−	0.0185057i
$259$	14.1750	+	1.20647i	0.880789	+	0.0749662i
$260$	−0.0715191	−	1.68362i	−0.00443543	−	0.104413i
$261$	−1.92148	+	1.29869i	−0.118936	+	0.0803870i
$262$	1.00832			0.0622942
$263$	7.65428			0.471983			0.235992	−	0.971755i	$-0.424166\pi$
$263$	7.65428			0.471983			0.235992	+	0.971755i	$0.424166\pi$
$264$	−0.117317	+	0.0792926i	−0.00722038	+	0.00488012i
$265$	4.52201	+	0.775377i	0.277785	+	0.0476310i
$266$	−0.946673	−	1.87761i	−0.0580442	−	0.115124i
$267$	−7.54381	−	10.1999i	−0.461674	−	0.624224i
$268$	−3.33480	+	15.4735i	−0.203705	+	0.945195i
$269$	−14.0555	−	11.3490i	−0.856977	−	0.691960i	0.0958760	−	0.995393i	$-0.469435\pi$
$269$	−14.0555	−	11.3490i	−0.856977	−	0.691960i	−0.952853	+	0.303433i	$0.901867\pi$
$270$	−0.0575440	−	0.0149833i	−0.00350201	−	0.000911854i
$271$	−13.2591	−	8.96158i	−0.805432	−	0.544377i	0.0866562	−	0.996238i	$-0.472382\pi$
$271$	−13.2591	−	8.96158i	−0.805432	−	0.544377i	−0.892088	+	0.451861i	$0.850760\pi$
$272$	27.3033	+	7.10921i	1.65550	+	0.431059i
$273$	−0.827036	+	6.45844i	−0.0500545	+	0.390883i
$274$	1.11318	+	0.503189i	0.0672496	+	0.0303987i
$275$	−0.830859	−	0.464146i	−0.0501027	−	0.0279890i
$276$	−6.64107	+	7.54572i	−0.399746	+	0.454199i
$277$	−22.9155	+	21.9628i	−1.37686	+	1.31961i	−0.480023	+	0.877256i	$0.659372\pi$
$277$	−22.9155	+	21.9628i	−1.37686	+	1.31961i	−0.896838	+	0.442359i	$0.854142\pi$
$278$	−0.155688	+	0.0869723i	−0.00933752	+	0.00521625i
$279$	6.91013	+	5.57954i	0.413698	+	0.334038i
$280$	−0.0736999	+	0.575533i	−0.00440441	+	0.0343947i
$281$	−3.70087	−	28.9006i	−0.220775	−	1.72407i	−0.601067	−	0.799199i	$-0.705257\pi$
$281$	−3.70087	−	28.9006i	−0.220775	−	1.72407i	0.380292	−	0.924867i	$-0.375824\pi$
$282$	0.370673	−	1.21038i	0.0220733	−	0.0720768i
$283$	1.55802	−	1.77026i	0.0926150	−	0.105231i	−0.702519	−	0.711665i	$-0.747941\pi$
$283$	1.55802	−	1.77026i	0.0926150	−	0.105231i	0.795134	+	0.606434i	$0.207401\pi$
$284$	10.1426	+	25.2409i	0.601854	+	1.49777i
$285$	−1.37343	+	0.620830i	−0.0813551	+	0.0367748i
$286$	−0.0735132	+	0.0593577i	−0.00434692	+	0.00350990i
$287$	0.582393	+	1.15511i	0.0343776	+	0.0681838i
$288$	−1.28097	+	1.73198i	−0.0754818	+	0.102058i
$289$	−38.0220	−	3.23615i	−2.23659	−	0.190362i
$290$	−0.107296	+	0.0866351i	−0.00630061	+	0.00508739i
$291$	9.46210	+	12.7936i	0.554678	+	0.749974i
$292$	6.03752	−	1.03524i	0.353319	−	0.0605826i
$293$	−16.3476	+	15.6679i	−0.955036	+	0.915328i	−0.996482	−	0.0838125i	$-0.973290\pi$
$293$	−16.3476	+	15.6679i	−0.955036	+	0.915328i	0.0414451	+	0.999141i	$0.486804\pi$
$294$	−0.0509365	+	0.166325i	−0.00297068	+	0.00970028i
$295$	3.32883	−	0.866761i	0.193812	−	0.0504648i
$296$	3.67671	+	2.05393i	0.213704	+	0.119382i
$297$	−0.0724907	−	0.180400i	−0.00420634	−	0.0104679i
$298$	1.08622	+	1.23419i	0.0629232	+	0.0714947i
$299$	−8.04524	+	10.8779i	−0.465268	+	0.629084i
$300$	−9.48677	−	1.62667i	−0.547719	−	0.0939158i
$301$	9.11616	−	3.22094i	0.525447	−	0.185652i
$302$	−1.10026	+	0.743647i	−0.0633129	+	0.0427920i
$303$	−6.60902	+	2.33512i	−0.379678	+	0.134149i
$304$	0.750434	+	17.6658i	0.0430403	+	1.01320i
$305$	2.89311	−	3.91175i	0.165659	−	0.223986i
$306$	0.613987	−	1.21777i	0.0350993	−	0.0696153i
$307$	−14.2728	+	2.44732i	−0.814591	+	0.139676i	−0.561191	−	0.827686i	$-0.689657\pi$
$307$	−14.2728	+	2.44732i	−0.814591	+	0.139676i	−0.253400	+	0.967362i	$0.581549\pi$
$308$	−0.821074	+	0.458679i	−0.0467850	+	0.0261357i
$309$	−9.53293	−	9.13657i	−0.542309	−	0.519761i
$310$	0.437551	+	0.295733i	0.0248512	+	0.0167965i
$311$	−3.93611	−	2.66035i	−0.223197	−	0.150855i	0.443273	−	0.896387i	$-0.353817\pi$
$311$	−3.93611	−	2.66035i	−0.223197	−	0.150855i	−0.666470	+	0.745532i	$0.732196\pi$
$312$	−1.01063	+	1.64137i	−0.0572159	+	0.0929245i
$313$	−4.28076	−	33.4291i	−0.241963	−	1.88952i	−0.423128	−	0.906070i	$-0.639068\pi$
$313$	−4.28076	−	33.4291i	−0.241963	−	1.88952i	0.181165	−	0.983453i	$-0.442013\pi$
$314$	2.72635	−	0.709885i	0.153857	−	0.0400611i
$315$	−0.751163	−	0.265403i	−0.0423232	−	0.0149538i
$316$	2.58591	−	8.44388i	0.145469	−	0.475005i
$317$	34.4258	−	2.93006i	1.93354	−	0.164569i	0.946246	−	0.323449i	$-0.104842\pi$
$317$	34.4258	−	2.93006i	1.93354	−	0.164569i	0.987298	+	0.158880i	$0.0507883\pi$
$318$	−1.87833	−	1.80023i	−0.105331	−	0.100952i
$319$	−0.436349	−	0.113616i	−0.0244309	−	0.00636130i
$320$	1.22278	−	1.98592i	0.0683553	−	0.111016i
$321$	−10.5953	+	0.901794i	−0.591373	+	0.0503332i
$322$	1.66736	−	1.59804i	0.0929186	−	0.0890553i
$323$	−7.28296	−	33.7930i	−0.405234	−	1.88029i
$324$	−1.29907	−	1.47603i	−0.0721707	−	0.0820018i
$325$	−12.9087	−	1.09869i	−0.716046	−	0.0609445i
$326$	0.0948572	−	0.236061i	0.00525366	−	0.0130742i
$327$	−0.477100	−	0.0818070i	−0.0263837	−	0.00452394i
$328$	0.0162534	+	0.382617i	0.000897442	+	0.0211265i
$329$	6.32358	−	15.7368i	0.348630	−	0.867600i
$330$	−0.00520468	−	0.0103229i	−0.000286508	−	0.000568255i
$331$	−8.20431	+	16.2723i	−0.450950	+	0.894406i	0.547394	+	0.836875i	$0.315620\pi$
$331$	−8.20431	+	16.2723i	−0.450950	+	0.894406i	−0.998344	+	0.0575305i	$0.981677\pi$
$332$	−1.66709	−	7.73532i	−0.0914934	−	0.424531i
$333$	−3.82034	+	4.34075i	−0.209353	+	0.237872i
$334$	−0.0678932	−	0.0239882i	−0.00371495	−	0.00131257i
$335$	−2.45788	−	0.868426i	−0.134289	−	0.0474472i
$336$	−6.17463	+	7.01575i	−0.336854	+	0.382740i
$337$	1.91194	+	8.87144i	0.104150	+	0.483258i	0.999297	+	0.0374870i	$0.0119353\pi$
$337$	1.91194	+	8.87144i	0.104150	+	0.483258i	−0.895147	+	0.445771i	$0.852930\pi$
$338$	0.495660	−	0.983082i	0.0269603	−	0.0534726i
$339$	−8.36405	−	16.5891i	−0.454273	−	0.900996i
$340$	−1.76320	+	4.38789i	−0.0956229	+	0.237967i
$341$	0.0732850	+	1.72519i	0.00396860	+	0.0934240i
$342$	0.842410	+	0.144446i	0.0455523	+	0.00781073i
$343$	−7.29014	+	18.1422i	−0.393630	+	0.979587i
$344$	2.85192	+	0.242734i	0.153765	+	0.0130874i
$345$	−1.09370	−	1.24268i	−0.0588826	−	0.0669037i
$346$	0.0905291	+	0.420056i	0.00486687	+	0.0225824i
$347$	−15.5066	+	14.8619i	−0.832437	+	0.797826i	−0.981592	−	0.190988i	$-0.938831\pi$
$347$	−15.5066	+	14.8619i	−0.832437	+	0.797826i	0.149156	+	0.988814i	$0.452344\pi$
$348$	−4.54377	+	0.386731i	−0.243571	+	0.0207310i
$349$	−5.54524	+	9.00604i	−0.296830	+	0.482082i	−0.965116	−	0.261822i	$-0.915677\pi$
$349$	−5.54524	+	9.00604i	−0.296830	+	0.482082i	0.668286	+	0.743904i	$0.267028\pi$
$350$	2.14011	+	0.557241i	0.114394	+	0.0297858i
$351$	−1.91071	−	1.83127i	−0.101986	−	0.0977460i
$352$	−0.417314	+	0.0355186i	−0.0222429	+	0.00189315i
$353$	7.49306	−	24.4674i	0.398815	−	1.30227i	−0.500791	−	0.865568i	$-0.666958\pi$
$353$	7.49306	−	24.4674i	0.398815	−	1.30227i	0.899607	−	0.436701i	$-0.143853\pi$
$354$	−1.83920	−	0.649829i	−0.0977521	−	0.0345380i
$355$	−4.33534	+	1.12883i	−0.230096	+	0.0599123i
$356$	−3.16849	−	24.7432i	−0.167929	−	1.31139i
$357$	9.58012	−	15.5591i	0.507034	−	0.823475i
$358$	−2.11348	−	1.42847i	−0.111701	−	0.0754968i
$359$	6.60267	+	4.46263i	0.348476	+	0.235528i	0.721690	−	0.692217i	$-0.243366\pi$
$359$	6.60267	+	4.46263i	0.348476	+	0.235528i	−0.373214	+	0.927745i	$0.621744\pi$
$360$	−0.170270	−	0.163191i	−0.00897402	−	0.00860090i
$361$	2.32627	−	1.29953i	0.122435	−	0.0683965i
$362$	0.408819	−	0.0700990i	0.0214870	−	0.00368432i
$363$	−4.93522	+	9.78843i	−0.259032	+	0.513759i
$364$	−7.61297	+	10.2934i	−0.399028	+	0.539522i
$365$	0.0428151	+	1.00790i	0.00224104	+	0.0527559i
$366$	−2.60140	+	0.919134i	−0.135977	+	0.0480439i
$367$	18.6783	−	12.6243i	0.975001	−	0.658985i	0.0347241	−	0.999397i	$-0.488945\pi$
$367$	18.6783	−	12.6243i	0.975001	−	0.658985i	0.940277	+	0.340412i	$0.110566\pi$
$368$	−18.3109	+	6.46964i	−0.954520	+	0.337253i
$369$	−0.518251	−	0.0888630i	−0.0269791	−	0.00462602i
$370$	−0.204460	+	0.276448i	−0.0106294	+	0.0143718i
$371$	−23.0294	−	26.1665i	−1.19563	−	1.35850i
$372$	6.51139	+	16.2042i	0.337600	+	0.840149i
$373$	−7.27200	−	4.06238i	−0.376530	−	0.210342i	0.287955	−	0.957644i	$-0.407025\pi$
$373$	−7.27200	−	4.06238i	−0.376530	−	0.210342i	−0.664485	+	0.747302i	$0.731349\pi$
$374$	0.256594	−	0.0668119i	0.0132682	−	0.00345476i
$375$	0.938277	−	3.06380i	0.0484524	−	0.158214i
$376$	3.62477	−	3.47406i	0.186933	−	0.179161i
$377$	−6.04965	+	1.03732i	−0.311573	+	0.0534245i
$378$	0.268636	+	0.363220i	0.0138171	+	0.0186820i
$379$	19.2865	−	15.5727i	0.990680	−	0.799918i	0.0108885	−	0.999941i	$-0.496534\pi$
$379$	19.2865	−	15.5727i	0.990680	−	0.799918i	0.979791	+	0.200023i	$0.0641016\pi$
$380$	−2.95296	−	0.251334i	−0.151484	−	0.0128932i
$381$	12.7334	−	17.2167i	0.652351	−	0.882037i
$382$	0.351897	+	0.697947i	0.0180046	+	0.0357101i
$383$	8.28812	−	6.69219i	0.423503	−	0.341955i	−0.392754	−	0.919643i	$-0.628478\pi$
$383$	8.28812	−	6.69219i	0.423503	−	0.341955i	0.816257	+	0.577689i	$0.196045\pi$
$384$	−5.13107	+	2.31939i	−0.261844	+	0.118361i
$385$	−0.0577513	−	0.143720i	−0.00294328	−	0.00732462i
$386$	−1.69210	+	1.92260i	−0.0861257	+	0.0978578i
$387$	−1.15076	+	3.75764i	−0.0584967	+	0.191012i
$388$	3.97419	+	31.0350i	0.201759	+	1.57556i
$389$	0.146228	−	1.14191i	0.00741405	−	0.0578974i	−0.987771	−	0.155912i	$-0.950168\pi$
$389$	0.146228	−	1.14191i	0.00741405	−	0.0578974i	0.995185	+	0.0980150i	$0.0312493\pi$
$390$	−0.122441	−	0.0988646i	−0.00620006	−	0.00500620i
$391$	33.1464	−	18.5167i	1.67629	−	0.936429i
$392$	−0.498103	+	0.477393i	−0.0251580	+	0.0241120i
$393$	−3.62782	+	4.12201i	−0.182999	+	0.207928i
$394$	−2.85130	−	1.59283i	−0.143647	−	0.0802458i
$395$	1.32524	+	0.599046i	0.0666800	+	0.0301413i
$396$	0.0485569	−	0.379188i	0.00244008	−	0.0190549i
$397$	−7.14710	−	1.86096i	−0.358703	−	0.0933989i	0.0682614	−	0.997667i	$-0.478255\pi$
$397$	−7.14710	−	1.86096i	−0.358703	−	0.0933989i	−0.426964	+	0.904269i	$0.640417\pi$
$398$	−3.03610	−	2.05205i	−0.152186	−	0.102860i
$399$	11.0817	+	2.88545i	0.554779	+	0.144453i
$400$	−14.4682	−	11.6822i	−0.723408	−	0.584111i
$401$	−1.00459	+	4.66131i	−0.0501667	+	0.232775i	−0.995685	−	0.0927935i	$-0.970420\pi$
$401$	−1.00459	+	4.66131i	−0.0501667	+	0.232775i	0.945519	+	0.325568i	$0.105555\pi$
$402$	0.879005	+	1.18849i	0.0438408	+	0.0592767i
$403$	10.5823	+	20.9887i	0.527142	+	1.04552i
$404$	−13.5842	−	2.32925i	−0.675841	−	0.115885i
$405$	0.268288	−	0.181331i	0.0133314	−	0.00901042i
$406$	1.04774			0.0519984
$407$	−1.12423			−0.0557260
$408$	4.48158	−	3.02902i	0.221871	−	0.149959i
$409$	−0.352823	−	8.30573i	−0.0174460	−	0.410692i	−0.986492	−	0.163811i	$-0.947621\pi$
$409$	−0.352823	−	8.30573i	−0.0174460	−	0.410692i	0.969046	−	0.246881i	$-0.0794057\pi$
$410$	−0.0311537	−	0.00265157i	−0.00153857	−	0.000130952i
$411$	−6.06213	+	2.74025i	−0.299023	+	0.135167i
$412$	−7.60266	−	24.8253i	−0.374556	−	1.22306i
$413$	−23.8141	−	10.7647i	−1.17182	−	0.529694i
$414$	0.119237	+	0.931136i	0.00586016	+	0.0457628i
$415$	1.29846	−	0.110515i	0.0637389	−	0.00542498i
$416$	−4.97732	+	2.78050i	−0.244033	+	0.136325i
$417$	0.204604	−	0.949367i	0.0100195	−	0.0464907i
$418$	0.0871250	+	0.141500i	0.00426142	+	0.00692099i
$419$	2.63480	−	1.19101i	0.128719	−	0.0581845i	−0.346513	−	0.938045i	$-0.612634\pi$
$419$	2.63480	−	1.19101i	0.128719	−	0.0581845i	0.475232	+	0.879861i	$0.342364\pi$
$420$	−1.03493	−	1.17591i	−0.0504995	−	0.0573786i
$421$	−3.45131	+	6.84527i	−0.168207	+	0.333618i	−0.961310	−	0.275469i	$-0.911167\pi$
$421$	−3.45131	+	6.84527i	−0.168207	+	0.333618i	0.793103	+	0.609087i	$0.208464\pi$
$422$	0.797660	+	1.07851i	0.0388295	+	0.0525009i
$423$	3.61437	+	5.87011i	0.175737	+	0.285414i
$424$	−3.02168	−	9.86682i	−0.146746	−	0.479175i
$425$	31.7392	+	17.7306i	1.53958	+	0.860060i
$426$	2.39529	+	0.846311i	0.116052	+	0.0410039i
$427$	−35.7719	+	9.31429i	−1.73113	+	0.450750i
$428$	−19.0526	−	8.61231i	−0.920942	−	0.416292i
$429$	0.0218380	−	0.514084i	0.00105435	−	0.0248202i
$430$	−0.0492320	+	0.228437i	−0.00237418	+	0.0110162i
$431$	33.4103	−	5.72878i	1.60932	−	0.275946i	0.707065	−	0.707149i	$-0.250019\pi$
$431$	33.4103	−	5.72878i	1.60932	−	0.275946i	0.902255	+	0.431203i	$0.141911\pi$
$432$	−0.800333	−	3.71356i	−0.0385060	−	0.178669i
$433$	−5.86503	−	14.5957i	−0.281856	−	0.701424i	−0.999985	−	0.00551474i	$-0.998245\pi$
$433$	−5.86503	−	14.5957i	−0.281856	−	0.701424i	0.718129	−	0.695910i	$-0.244999\pi$
$434$	−1.17491	−	3.83650i	−0.0563977	−	0.184158i
$435$	0.0318735	−	0.750327i	0.00152822	−	0.0359754i
$436$	−0.740537	−	0.597942i	−0.0354653	−	0.0286362i
$437$	17.1787	+	16.4645i	0.821771	+	0.787604i
$438$	0.299938	−	0.487130i	0.0143316	−	0.0232760i
$439$	0.689458	−	5.38408i	0.0329060	−	0.256968i	−0.967091	−	0.254432i	$-0.918112\pi$
$439$	0.689458	−	5.38408i	0.0329060	−	0.256968i	0.999997	−	0.00253624i	$-0.000807313\pi$
$440$	0.00194606	−	0.0458118i	9.27747e−5	−	0.00218399i
$441$	−0.496673	−	0.806648i	−0.0236511	−	0.0384118i
$442$	2.80824	−	2.26750i	0.133574	−	0.107854i
$443$	−11.8616	+	29.5187i	−0.563562	+	1.40248i	0.325872	+	0.945414i	$0.394342\pi$
$443$	−11.8616	+	29.5187i	−0.563562	+	1.40248i	−0.889434	+	0.457064i	$0.848901\pi$
$444$	−10.7205	+	3.78779i	−0.508772	+	0.179761i
$445$	4.10815			0.194745
$446$	2.69739	+	0.493473i	0.127725	+	0.0233666i
$447$	−8.95347			−0.423485
$448$	−16.7066	+	5.90280i	−0.789311	+	0.278881i
$449$	−10.7906	+	26.8535i	−0.509240	+	1.26729i	0.423222	+	0.906026i	$0.360899\pi$
$449$	−10.7906	+	26.8535i	−0.509240	+	1.26729i	−0.932462	+	0.361267i	$0.882344\pi$
$450$	−0.699366	+	0.564699i	−0.0329685	+	0.0266202i
$451$	−0.0535993	−	0.0870507i	−0.00252389	−	0.00409906i
$452$	1.55039	−	36.4974i	0.0729241	−	1.71669i
$453$	0.918592	−	7.17342i	0.0431592	−	0.337037i
$454$	−2.11934	+	3.44202i	−0.0994654	+	0.161542i
$455$	−1.52221	−	1.45892i	−0.0713623	−	0.0683952i
$456$	2.63754	+	2.12966i	0.123514	+	0.0997307i
$457$	0.413274	−	9.72879i	0.0193321	−	0.455094i	−0.963176	−	0.268873i	$-0.913349\pi$
$457$	0.413274	−	9.72879i	0.0193321	−	0.455094i	0.982508	−	0.186221i	$-0.0596240\pi$
$458$	−0.863023	−	2.81807i	−0.0403264	−	0.131680i
$459$	2.76918	+	6.89138i	0.129254	+	0.321662i
$460$	−0.685767	−	3.18197i	−0.0319740	−	0.148360i
$461$	6.52795	−	1.11933i	0.304037	−	0.0521324i	−0.0149601	−	0.999888i	$-0.504762\pi$
$461$	6.52795	−	1.11933i	0.304037	−	0.0521324i	0.318997	+	0.947756i	$0.396654\pi$
$462$	−0.0185045	+	0.0858612i	−0.000860908	+	0.00399462i
$463$	1.23224	−	29.0080i	0.0572672	−	1.34812i	−0.708825	−	0.705384i	$-0.750774\pi$
$463$	1.23224	−	29.0080i	0.0572672	−	1.34812i	0.766092	−	0.642731i	$-0.222199\pi$
$464$	−8.02812	−	3.62894i	−0.372696	−	0.168469i
$465$	−2.78321	+	0.724692i	−0.129068	+	0.0336068i
$466$	1.06244	+	0.375383i	0.0492165	+	0.0173893i
$467$	13.7653	+	7.68975i	0.636981	+	0.355839i	0.772573	−	0.634926i	$-0.218969\pi$
$467$	13.7653	+	7.68975i	0.636981	+	0.355839i	−0.135592	+	0.990765i	$0.543294\pi$
$468$	−1.52382	−	4.97581i	−0.0704388	−	0.230007i
$469$	10.3840	+	16.8646i	0.479486	+	0.778736i
$470$	0.243747	+	0.329568i	0.0112432	+	0.0152018i
$471$	−6.90708	+	13.6994i	−0.318261	+	0.631234i
$472$	−5.11145	−	5.80773i	−0.235273	−	0.267322i
$473$	−0.696225	+	0.314714i	−0.0320125	+	0.0144705i
$474$	−0.432403	−	0.702268i	−0.0198609	−	0.0322562i
$475$	−4.80024	+	22.2732i	−0.220250	+	1.02196i
$476$	31.3655	−	17.5218i	1.43763	−	0.803110i
$477$	14.1173	−	1.20156i	0.646388	−	0.0550157i
$478$	0.657634	+	5.13556i	0.0300795	+	0.234895i
$479$	15.0496	+	6.80284i	0.687633	+	0.310830i	0.725273	−	0.688462i	$-0.241714\pi$
$479$	15.0496	+	6.80284i	0.687633	+	0.310830i	−0.0376398	+	0.999291i	$0.511984\pi$
$480$	−0.204267	−	0.667002i	−0.00932347	−	0.0304443i
$481$	−13.9452	+	6.30365i	−0.635849	+	0.287422i
$482$	3.94999	+	0.336194i	0.179917	+	0.0153132i
$483$	0.533786	+	12.5657i	0.0242881	+	0.571761i
$484$	−17.8583	+	12.0701i	−0.811742	+	0.548642i
$485$	−5.15279			−0.233976
$486$	−0.183629			−0.00832956
$487$	−22.7216	+	15.3571i	−1.02962	+	0.695899i	−0.953560	−	0.301205i	$-0.902611\pi$
$487$	−22.7216	+	15.3571i	−1.02962	+	0.695899i	−0.0760563	+	0.997104i	$0.524233\pi$
$488$	−10.7856	−	1.84937i	−0.488240	−	0.0837172i
$489$	0.623732	+	1.23710i	0.0282061	+	0.0559435i
$490$	−0.0334948	−	0.0452880i	−0.00151314	−	0.00204590i
$491$	5.97091	−	27.7051i	0.269463	−	1.25031i	−0.616795	−	0.787124i	$-0.711569\pi$
$491$	5.97091	−	27.7051i	0.269463	−	1.25031i	0.886259	−	0.463191i	$-0.153296\pi$
$492$	−0.804410	−	0.649515i	−0.0362656	−	0.0292824i
$493$	16.6688	+	4.34021i	0.750723	+	0.195473i
$494$	1.87412	+	1.26669i	0.0843208	+	0.0569909i
$495$	0.0609257	+	0.0158638i	0.00273841	+	0.000713025i
$496$	−4.28548	+	33.4660i	−0.192424	+	1.50267i
$497$	31.0146	+	14.0195i	1.39119	+	0.628859i
$498$	−0.645139	−	0.360396i	−0.0289094	−	0.0161497i
$499$	−1.65477	+	1.88019i	−0.0740778	+	0.0841687i	−0.786531	−	0.617551i	$-0.788125\pi$
$499$	−1.65477	+	1.88019i	−0.0740778	+	0.0841687i	0.712453	+	0.701720i	$0.247584\pi$
$500$	4.54865	−	4.35953i	0.203422	−	0.194964i
$501$	0.342336	−	0.191240i	0.0152944	−	0.00854398i
$502$	2.73861	+	2.21127i	0.122230	+	0.0986940i
$503$	−2.67113	+	20.8592i	−0.119100	+	0.930066i	0.816584	+	0.577226i	$0.195865\pi$
$503$	−2.67113	+	20.8592i	−0.119100	+	0.930066i	−0.935684	+	0.352840i	$0.885216\pi$
$504$	0.227595	+	1.77732i	0.0101379	+	0.0791683i
$505$	0.664647	−	2.17030i	0.0295764	−	0.0965771i
$506$	−0.120580	+	0.137005i	−0.00536041	+	0.00609061i
$507$	2.23551	+	5.56327i	0.0992824	+	0.247074i
$508$	38.3678	−	17.3434i	1.70230	−	0.769487i
$509$	12.9118	−	10.4256i	0.572306	−	0.462105i	−0.298035	−	0.954555i	$-0.596331\pi$
$509$	12.9118	−	10.4256i	0.572306	−	0.462105i	0.870341	+	0.492450i	$0.163899\pi$
$510$	0.198822	+	0.394339i	0.00880396	+	0.0174616i
$511$	4.55753	−	6.16218i	0.201613	−	0.272599i
$512$	−13.6676	−	1.16328i	−0.604028	−	0.0514104i
$513$	−3.62139	+	2.92407i	−0.159888	+	0.129101i
$514$	−0.867576	−	1.17304i	−0.0382671	−	0.0517406i
$515$	4.21432	−	0.722617i	0.185705	−	0.0318423i
$516$	−5.57876	+	5.34681i	−0.245591	+	0.235380i
$517$	−0.392457	+	1.28151i	−0.0172602	+	0.0563606i
$518$	2.52804	−	0.658252i	0.111076	−	0.0289219i
$519$	−2.04290	−	1.14123i	−0.0896734	−	0.0500946i
$520$	−0.232731	−	0.579173i	−0.0102059	−	0.0253984i
$521$	19.0458	+	21.6403i	0.834413	+	0.948078i	0.999269	−	0.0382402i	$-0.0121752\pi$
$521$	19.0458	+	21.6403i	0.834413	+	0.948078i	−0.164855	+	0.986318i	$0.552716\pi$
$522$	−0.253237	+	0.342399i	−0.0110839	+	0.0149864i
$523$	−26.5878	−	4.55893i	−1.16260	−	0.199348i	−0.444823	−	0.895619i	$-0.646733\pi$
$523$	−26.5878	−	4.55893i	−1.16260	−	0.199348i	−0.717779	+	0.696271i	$0.754841\pi$
$524$	−10.1803	+	3.59692i	−0.444727	+	0.157132i
$525$	−9.97786	+	6.74386i	−0.435470	+	0.294326i
$526$	1.32526	−	0.468243i	0.0577839	−	0.0204164i
$527$	−2.79952	−	65.9030i	−0.121949	−	2.87078i
$528$	0.439176	−	0.593805i	0.0191127	−	0.0258421i
$529$	−1.41105	+	2.79865i	−0.0613499	+	0.121680i
$530$	0.830370	−	0.142381i	0.0360690	−	0.00618465i
$531$	9.27372	−	5.18061i	0.402445	−	0.224819i
$532$	16.2557	+	15.5799i	0.704776	+	0.675473i
$533$	−1.15296	−	0.779265i	−0.0499403	−	0.0337537i
$534$	−1.93010	−	1.30452i	−0.0835235	−	0.0564521i
$535$	1.80539	−	2.93214i	0.0780538	−	0.126768i
$536$	0.744715	+	5.81559i	0.0321668	+	0.251195i
$537$	13.4436	−	3.50045i	0.580136	−	0.151056i
$538$	−3.12781	−	1.10513i	−0.134850	−	0.0476454i
$539$	0.0539300	−	0.176100i	0.00232293	−	0.00758515i
$540$	0.634428	−	0.0539978i	0.0273014	−	0.00232369i
$541$	−14.4775	−	13.8756i	−0.622438	−	0.596559i	0.313128	−	0.949711i	$-0.398623\pi$
$541$	−14.4775	−	13.8756i	−0.622438	−	0.596559i	−0.935566	+	0.353152i	$0.885110\pi$
$542$	−2.84388	−	0.740489i	−0.122155	−	0.0318067i
$543$	−1.18432	+	1.92346i	−0.0508240	+	0.0825434i
$544$	15.9416	−	1.35683i	0.683491	−	0.0581736i
$545$	0.113166	−	0.108461i	0.00484751	−	0.00464596i
$546$	0.251896	+	1.16880i	0.0107802	+	0.0500201i
$547$	28.0307	+	31.8491i	1.19851	+	1.36177i	0.915331	+	0.402701i	$0.131929\pi$
$547$	28.0307	+	31.8491i	1.19851	+	1.36177i	0.283176	+	0.959068i	$0.408612\pi$
$548$	−13.0339	−	1.10935i	−0.556782	−	0.0473892i
$549$	5.60214	−	13.9415i	0.239093	−	0.595007i
$550$	−0.172248	−	0.0295349i	−0.00734467	−	0.00125937i
$551$	0.458143	+	10.7850i	0.0195176	+	0.459459i
$552$	−1.38826	+	3.45481i	−0.0590882	+	0.147047i
$553$	−4.97447	−	9.86628i	−0.211536	−	0.419557i
$554$	−2.62403	+	5.20445i	−0.111484	+	0.221116i
$555$	−0.394494	−	1.83046i	−0.0167453	−	0.0776986i
$556$	1.26161	−	1.43347i	0.0535043	−	0.0607927i
$557$	23.3841	+	8.26212i	0.990815	+	0.350077i	0.778857	−	0.627202i	$-0.215800\pi$
$557$	23.3841	+	8.26212i	0.990815	+	0.350077i	0.211958	+	0.977279i	$0.432016\pi$
$558$	1.53774	+	0.543317i	0.0650976	+	0.0230004i
$559$	−6.87154	+	7.80759i	−0.290635	+	0.330226i
$560$	−0.637602	−	2.95848i	−0.0269436	−	0.125019i
$561$	−0.650070	+	1.28934i	−0.0274460	+	0.0544358i
$562$	−2.40873	−	4.77743i	−0.101606	−	0.201524i
$563$	−12.1035	+	30.1207i	−0.510102	+	1.26944i	0.421787	+	0.906695i	$0.361403\pi$
$563$	−12.1035	+	30.1207i	−0.510102	+	1.26944i	−0.931889	+	0.362743i	$0.881840\pi$
$564$	0.575281	+	13.5426i	0.0242237	+	0.570244i
$565$	5.92952	+	1.01672i	0.249457	+	0.0427736i
$566$	0.161461	−	0.401812i	0.00678672	−	0.0168894i
$567$	−2.45136	−	0.208642i	−0.102948	−	0.00876213i
$568$	6.65694	+	7.56375i	0.279319	+	0.317368i
$569$	−2.10529	−	9.76857i	−0.0882582	−	0.409520i	0.911741	−	0.410766i	$-0.134739\pi$
$569$	−2.10529	−	9.76857i	−0.0882582	−	0.409520i	−0.999999	+	0.00124593i	$0.999603\pi$
$570$	−0.199816	+	0.191508i	−0.00836938	+	0.00802140i
$571$	30.0519	−	2.55779i	1.25763	−	0.107040i	0.563031	−	0.826435i	$-0.309635\pi$
$571$	30.0519	−	2.55779i	1.25763	−	0.107040i	0.694601	+	0.719395i	$0.255581\pi$
$572$	0.530465	−	0.861530i	0.0221799	−	0.0360224i
$573$	−4.11929	−	1.07258i	−0.172086	−	0.0448077i
$574$	0.171498	+	0.164367i	0.00715817	+	0.00686055i
$575$	−24.9346	+	2.12225i	−1.03985	+	0.0885039i
$576$	2.10893	−	6.88638i	0.0878720	−	0.286932i
$577$	5.95780	+	2.10502i	0.248026	+	0.0876333i	0.454259	−	0.890870i	$-0.349904\pi$
$577$	5.95780	+	2.10502i	0.248026	+	0.0876333i	−0.206233	+	0.978503i	$0.566120\pi$
$578$	−6.78107	+	1.76565i	−0.282055	+	0.0734415i
$579$	−1.77159	−	13.8346i	−0.0736248	−	0.574947i
$580$	0.774236	−	1.25744i	0.0321484	−	0.0522123i
$581$	−8.20284	−	5.54415i	−0.340311	−	0.230010i
$582$	2.42090	+	1.63624i	0.100349	+	0.0678243i
$583$	1.98871	+	1.90602i	0.0823640	+	0.0789395i
$584$	1.98084	−	1.10657i	0.0819678	−	0.0457900i
$585$	0.844688	−	0.144836i	0.0349236	−	0.00598825i
$586$	−1.87194	+	3.71277i	−0.0773292	+	0.153373i
$587$	8.46554	−	11.4462i	0.349410	−	0.472434i	−0.593808	−	0.804607i	$-0.702376\pi$
$587$	8.46554	−	11.4462i	0.349410	−	0.472434i	0.943219	+	0.332173i	$0.107782\pi$
$588$	−0.0790529	−	1.86097i	−0.00326009	−	0.0767449i
$589$	38.9778	−	13.7717i	1.60605	−	0.567455i
$590$	0.523328	−	0.353708i	0.0215451	−	0.0145619i
$591$	16.7702	−	5.92528i	0.689832	−	0.243733i
$592$	−21.6506	−	3.71237i	−0.889836	−	0.152578i
$593$	17.2395	−	23.3093i	0.707941	−	0.957199i	−0.292059	−	0.956400i	$-0.594340\pi$
$593$	17.2395	−	23.3093i	0.707941	−	0.957199i	1.00000		0.000798873i	$-0.000254289\pi$
$594$	−0.0235868	−	0.0267998i	−0.000967777	−	0.00109961i
$595$	2.20613	+	5.49016i	0.0904424	+	0.225075i
$596$	−15.3694	−	8.58589i	−0.629557	−	0.351692i
$597$	19.3123	−	5.02853i	0.790400	−	0.205804i
$598$	−0.727503	+	2.37555i	−0.0297498	+	0.0971433i
$599$	25.5383	−	24.4764i	1.04346	−	1.00008i	0.0434652	−	0.999055i	$-0.486160\pi$
$599$	25.5383	−	24.4764i	1.04346	−	1.00008i	0.999999	−	0.00102496i	$-0.000326254\pi$
$600$	−3.51396	+	0.602528i	−0.143457	+	0.0245981i
$601$	19.6662	+	26.5905i	0.802203	+	1.08465i	0.994646	+	0.103341i	$0.0329534\pi$
$601$	19.6662	+	26.5905i	0.802203	+	1.08465i	−0.192443	+	0.981308i	$0.561641\pi$
$602$	1.38133	−	1.11534i	0.0562986	−	0.0454580i
$603$	−8.02111	−	0.682697i	−0.326645	−	0.0278016i
$604$	8.45576	−	11.4329i	0.344060	−	0.465200i
$605$	−1.59813	−	3.16969i	−0.0649731	−	0.128866i
$606$	−1.00143	+	0.808600i	−0.0406804	+	0.0328471i
$607$	−2.52913	+	1.14324i	−0.102654	+	0.0464027i	−0.462574	−	0.886580i	$-0.653074\pi$
$607$	−2.52913	+	1.14324i	−0.102654	+	0.0464027i	0.359920	+	0.932983i	$0.382804\pi$
$608$	3.73858	+	9.30382i	0.151619	+	0.377320i
$609$	−3.76964	+	4.28315i	−0.152754	+	0.173562i
$610$	0.261614	−	0.854260i	0.0105924	−	0.0345880i
$611$	2.31737	+	18.0967i	0.0937509	+	0.732114i
$612$	−1.85490	+	14.4852i	−0.0749798	+	0.585528i
$613$	10.3096	+	8.32439i	0.416399	+	0.336219i	0.813509	−	0.581552i	$-0.197554\pi$
$613$	10.3096	+	8.32439i	0.416399	+	0.336219i	−0.397110	+	0.917771i	$0.629987\pi$
$614$	−2.32147	+	1.29685i	−0.0936868	+	0.0523366i
$615$	0.122927	−	0.117816i	0.00495689	−	0.00475080i
$616$	−0.230158	+	0.261511i	−0.00927335	+	0.0105366i
$617$	−9.08624	−	5.07588i	−0.365798	−	0.204347i	0.293973	−	0.955814i	$-0.405022\pi$
$617$	−9.08624	−	5.07588i	−0.365798	−	0.204347i	−0.659771	+	0.751467i	$0.729347\pi$
$618$	−2.20944	−	0.998731i	−0.0888768	−	0.0401749i
$619$	4.01526	−	31.3557i	0.161387	−	1.26029i	−0.685323	−	0.728239i	$-0.740339\pi$
$619$	4.01526	−	31.3557i	0.161387	−	1.26029i	0.846710	−	0.532054i	$-0.178580\pi$
$620$	−5.47257	−	1.42495i	−0.219784	−	0.0572273i
$621$	−4.23548	−	2.86268i	−0.169964	−	0.114876i
$622$	−0.844240	−	0.219823i	−0.0338509	−	0.00881410i
$623$	−24.2838	−	19.6078i	−0.972909	−	0.785569i
$624$	2.11814	−	9.82822i	0.0847936	−	0.393444i
$625$	−13.9371	−	18.8442i	−0.557483	−	0.753767i
$626$	−2.78616	−	5.52601i	−0.111357	−	0.220864i
$627$	−0.891917	−	0.152934i	−0.0356197	−	0.00610761i
$628$	−24.9936	+	16.8927i	−0.997352	+	0.674093i
$629$	42.9462			1.71238
$630$	−0.146291			−0.00582839
$631$	−9.99688	+	6.75671i	−0.397969	+	0.268980i	−0.742569	−	0.669769i	$-0.766393\pi$
$631$	−9.99688	+	6.75671i	−0.397969	+	0.268980i	0.344600	+	0.938750i	$0.388015\pi$
$632$	−0.138827	−	3.26810i	−0.00552225	−	0.129998i
$633$	−7.27882	−	0.619519i	−0.289307	−	0.0246237i
$634$	5.78120	−	2.61327i	0.229601	−	0.103786i
$635$	2.03050	+	6.63029i	0.0805781	+	0.263115i
$636$	25.3859	+	11.4752i	1.00662	+	0.455019i
$637$	−0.318445	−	2.48678i	−0.0126172	−	0.0985298i
$638$	−0.0824995	+	0.00702174i	−0.00326619	+	0.000277993i
$639$	−12.0777	+	6.74702i	−0.477787	+	0.266908i
$640$	0.384155	−	1.78249i	0.0151851	−	0.0704589i
$641$	12.1335	+	19.7060i	0.479244	+	0.778342i	0.997017	−	0.0771759i	$-0.0245903\pi$
$641$	12.1335	+	19.7060i	0.479244	+	0.778342i	−0.517773	+	0.855518i	$0.673239\pi$
$642$	−1.77930	+	0.804293i	−0.0702233	+	0.0317429i
$643$	13.5307	+	15.3739i	0.533599	+	0.606287i	0.953541	−	0.301265i	$-0.0974088\pi$
$643$	13.5307	+	15.3739i	0.533599	+	0.606287i	−0.419941	+	0.907551i	$0.637949\pi$
$644$	−11.1336	+	22.0821i	−0.438724	+	0.870157i
$645$	−0.756720	−	1.02315i	−0.0297958	−	0.0402866i
$646$	−3.32822	−	5.40537i	−0.130947	−	0.212671i
$647$	8.68633	+	28.3638i	0.341495	+	1.11510i	0.947532	+	0.319661i	$0.103569\pi$
$647$	8.68633	+	28.3638i	0.341495	+	1.11510i	−0.606037	+	0.795436i	$0.707242\pi$
$648$	−0.635836	−	0.355199i	−0.0249780	−	0.0139535i
$649$	1.94728	+	0.688018i	0.0764374	+	0.0270071i
$650$	−2.30221	+	0.599450i	−0.0903002	+	0.0235123i
$651$	19.9108	+	9.00025i	0.780365	+	0.352747i
$652$	−0.115617	+	2.72172i	−0.00452791	+	0.106591i
$653$	0.154848	−	0.718496i	0.00605966	−	0.0281169i	−0.974424	−	0.224716i	$-0.927855\pi$
$653$	0.154848	−	0.718496i	0.00605966	−	0.0281169i	0.980484	+	0.196599i	$0.0629897\pi$
$654$	−0.0876092	+	0.0150221i	−0.00342579	+	0.000587411i
$655$	−0.374614	−	1.73822i	−0.0146374	−	0.0679177i
$656$	−0.744771	−	1.85343i	−0.0290784	−	0.0723644i
$657$	0.912242	+	2.97878i	0.0355899	+	0.116213i
$658$	0.132175	−	3.11150i	0.00515272	−	0.121299i
$659$	−3.32353	−	2.68357i	−0.129467	−	0.104537i	0.561309	−	0.827607i	$-0.310298\pi$
$659$	−3.32353	−	2.68357i	−0.129467	−	0.104537i	−0.690775	+	0.723070i	$0.742731\pi$
$660$	0.0893719	+	0.0856561i	0.00347880	+	0.00333416i
$661$	12.1586	−	19.7468i	0.472915	−	0.768062i	−0.523557	−	0.851991i	$-0.675395\pi$
$661$	12.1586	−	19.7468i	0.472915	−	0.768062i	0.996472	+	0.0839283i	$0.0267467\pi$
$662$	−0.425048	+	3.31926i	−0.0165200	+	0.129007i
$663$	−0.834224	+	19.6383i	−0.0323986	+	0.762687i
$664$	−1.53674	−	2.49583i	−0.0596372	−	0.0968569i
$665$	−2.88506	+	2.32952i	−0.111878	+	0.0903349i
$666$	−0.395910	+	0.985259i	−0.0153412	+	0.0381780i
$667$	−11.1789	+	3.94975i	−0.432848	+	0.152935i
$668$	0.771039			0.0298324
$669$	−11.7222	+	9.25146i	−0.453207	+	0.357682i
$670$	−0.478681			−0.0184931
$671$	2.75428	−	0.973149i	0.106328	−	0.0375680i
$672$	−1.97609	+	4.91768i	−0.0762292	+	0.189704i
$673$	−10.0319	+	8.10019i	−0.386701	+	0.312239i	−0.801863	−	0.597508i	$-0.796158\pi$
$673$	−10.0319	+	8.10019i	−0.386701	+	0.312239i	0.415161	+	0.909748i	$0.363725\pi$
$674$	0.873733	+	1.41903i	0.0336549	+	0.0546591i
$675$	0.207756	−	4.89073i	0.00799652	−	0.188244i
$676$	−1.49742	+	11.6936i	−0.0575932	+	0.449754i
$677$	−9.16182	+	14.8797i	−0.352117	+	0.571875i	−0.978144	−	0.207926i	$-0.933329\pi$
$677$	−9.16182	+	14.8797i	−0.352117	+	0.571875i	0.626027	+	0.779801i	$0.284680\pi$
$678$	−2.46297	−	2.36056i	−0.0945896	−	0.0906568i
$679$	30.4588	+	24.5938i	1.16890	+	0.943822i
$680$	−0.0743405	+	1.75003i	−0.00285083	+	0.0671107i
$681$	−6.44583	−	21.0478i	−0.247005	−	0.806555i
$682$	0.118225	+	0.294214i	0.00452707	+	0.0112660i
$683$	1.67582	+	7.77582i	0.0641234	+	0.297534i	0.998231	−	0.0594585i	$-0.0189374\pi$
$683$	1.67582	+	7.77582i	0.0641234	+	0.297534i	−0.934107	+	0.356992i	$0.883802\pi$
$684$	−9.02047	+	1.54671i	−0.344906	+	0.0591401i
$685$	0.453862	−	2.10593i	0.0173412	−	0.0804633i
$686$	−0.152378	+	3.58709i	−0.00581781	+	0.136956i
$687$	14.6253	+	6.61105i	0.557990	+	0.252227i
$688$	−14.4473	+	3.76178i	−0.550797	+	0.143416i
$689$	35.3557	+	12.4920i	1.34695	+	0.475906i
$690$	−0.265381	−	0.148251i	−0.0101029	−	0.00564382i
$691$	−5.95082	−	19.4315i	−0.226380	−	0.739208i	−0.995033	−	0.0995422i	$-0.968262\pi$
$691$	−5.95082	−	19.4315i	−0.226380	−	0.739208i	0.768654	−	0.639665i	$-0.220927\pi$
$692$	−2.41245	−	3.91806i	−0.0917074	−	0.148942i
$693$	−0.284423	−	0.384565i	−0.0108043	−	0.0146084i
$694$	−1.77564	+	3.52177i	−0.0674023	+	0.133684i
$695$	0.207771	+	0.236073i	0.00788119	+	0.00895478i
$696$	−1.53918	+	0.695752i	−0.0583424	+	0.0263724i
$697$	2.04752	+	3.32538i	0.0775553	+	0.125958i
$698$	−0.409163	+	1.89852i	−0.0154871	+	0.0718602i
$699$	−5.35710	+	2.99265i	−0.202624	+	0.113193i
$700$	−23.5949	+	2.00822i	−0.891803	+	0.0759036i
$701$	−5.48639	−	42.8440i	−0.207218	−	1.61820i	−0.677392	−	0.735623i	$-0.736890\pi$
$701$	−5.48639	−	42.8440i	−0.207218	−	1.61820i	0.470173	−	0.882574i	$-0.344191\pi$
$702$	−0.442845	−	0.200179i	−0.0167141	−	0.00755526i
$703$	7.88125	+	25.7350i	0.297247	+	0.970613i
$704$	1.27592	−	0.576754i	0.0480882	−	0.0217373i
$705$	−2.22425	−	0.189311i	−0.0837700	−	0.00712988i
$706$	−0.199426	−	4.69465i	−0.00750551	−	0.176685i
$707$	−14.2874	+	9.65662i	−0.537334	+	0.363175i
$708$	20.8871			0.784985
$709$	20.0344			0.752408			0.376204	−	0.926537i	$-0.377229\pi$
$709$	20.0344			0.752408			0.376204	+	0.926537i	$0.377229\pi$
$710$	−0.681562	+	0.460655i	−0.0255786	+	0.0172881i
$711$	4.42660	+	0.759018i	0.166011	+	0.0284654i
$712$	−4.15982	−	8.25051i	−0.155896	−	0.309201i
$713$	26.9986	+	36.5045i	1.01110	+	1.36710i
$714$	0.706882	−	3.27994i	0.0264544	−	0.122749i
$715$	0.129637	+	0.104675i	0.00484815	+	0.00391461i
$716$	26.4340	+	6.88287i	0.987884	+	0.257225i
$717$	−23.3602	−	15.7888i	−0.872403	−	0.589642i
$718$	1.41618	+	0.368744i	0.0528513	+	0.0137614i
$719$	1.37134	−	10.7090i	0.0511423	−	0.399378i	−0.946021	−	0.324106i	$-0.894937\pi$
$719$	1.37134	−	10.7090i	0.0511423	−	0.399378i	0.997163	−	0.0752716i	$-0.0239824\pi$
$720$	1.12093	+	0.506694i	0.0417748	+	0.0188834i
$721$	−28.3603	−	15.8430i	−1.05619	−	0.590026i
$722$	0.323271	−	0.367308i	0.0120309	−	0.0136698i
$723$	−15.5860	+	14.9380i	−0.579649	+	0.555548i
$724$	−3.87748	+	2.16609i	−0.144105	+	0.0805021i
$725$	−8.83288	−	7.13206i	−0.328045	−	0.264878i
$726$	−0.255683	+	1.99667i	−0.00948930	+	0.0741033i
$727$	−0.688970	−	5.38027i	−0.0255525	−	0.199543i	0.974094	−	0.226145i	$-0.0726124\pi$
$727$	−0.688970	−	5.38027i	−0.0255525	−	0.199543i	−0.999646	+	0.0266021i	$0.991531\pi$
$728$	−1.38863	+	4.53437i	−0.0514662	+	0.168055i
$729$	0.660675	−	0.750672i	0.0244694	−	0.0278027i
$730$	0.0690703	+	0.171888i	0.00255641	+	0.00636186i
$731$	26.5962	−	12.0222i	0.983695	−	0.444658i
$732$	22.9857	−	18.5596i	0.849575	−	0.685984i
$733$	19.5572	+	38.7894i	0.722361	+	1.43272i	0.894234	+	0.447599i	$0.147721\pi$
$733$	19.5572	+	38.7894i	0.722361	+	1.43272i	−0.171873	+	0.985119i	$0.554982\pi$
$734$	2.46167	−	3.32840i	0.0908618	−	0.122853i
$735$	0.305648	+	0.0260145i	0.0112740	+	0.000959558i
$736$	−8.56828	+	6.91840i	−0.315831	+	0.255016i
$737$	−0.930662	−	1.25834i	−0.0342814	−	0.0463515i
$738$	−0.0951656	+	0.0163178i	−0.00350309	+	0.000600666i
$739$	2.33149	−	2.23456i	0.0857654	−	0.0821995i	−0.647834	−	0.761781i	$-0.724325\pi$
$739$	2.33149	−	2.23456i	0.0857654	−	0.0821995i	0.733600	+	0.679582i	$0.237839\pi$
$740$	1.07812	−	3.52044i	0.0396326	−	0.129414i
$741$	−11.9211	+	3.10401i	−0.437932	+	0.114029i
$742$	−5.58800	−	3.12164i	−0.205142	−	0.114599i
$743$	−5.53266	−	13.7685i	−0.202974	−	0.505119i	0.791369	−	0.611339i	$-0.209369\pi$
$743$	−5.53266	−	13.7685i	−0.202974	−	0.505119i	−0.994343	+	0.106220i	$0.966125\pi$
$744$	4.27364	+	4.85580i	0.156679	+	0.178022i
$745$	1.72403	−	2.33104i	0.0631635	−	0.0854027i
$746$	−1.50758	−	0.258501i	−0.0551964	−	0.00946438i
$747$	3.79443	−	1.34066i	0.138831	−	0.0490521i
$748$	−2.35231	+	1.58988i	−0.0860088	+	0.0581318i
$749$	−24.6667	+	8.71530i	−0.901302	+	0.318450i
$750$	−0.0249720	−	0.587861i	−0.000911850	−	0.0214657i
$751$	11.4781	−	15.5194i	0.418842	−	0.566312i	−0.543064	−	0.839691i	$-0.682736\pi$
$751$	11.4781	−	15.5194i	0.418842	−	0.566312i	0.961906	+	0.273379i	$0.0881414\pi$
$752$	−11.7897	+	23.3836i	−0.429928	+	0.852711i
$753$	−18.8929	+	3.23951i	−0.688495	+	0.118054i
$754$	−0.983975	+	0.549681i	−0.0358342	+	0.0200182i
$755$	1.69072	+	1.62043i	0.0615318	+	0.0589734i
$756$	−4.00791	−	2.70887i	−0.145766	−	0.0985208i
$757$	−16.8360	−	11.3792i	−0.611916	−	0.413583i	0.214435	−	0.976738i	$-0.431209\pi$
$757$	−16.8360	−	11.3792i	−0.611916	−	0.413583i	−0.826351	+	0.563155i	$0.809587\pi$
$758$	2.38660	−	3.87608i	0.0866852	−	0.140786i
$759$	−0.126244	−	0.985857i	−0.00458236	−	0.0357843i
$760$	−1.06233	+	0.276609i	−0.0385347	+	0.0100337i
$761$	44.8157	+	15.8344i	1.62457	+	0.573997i	0.981441	−	0.191763i	$-0.0614204\pi$
$761$	44.8157	+	15.8344i	1.62457	+	0.573997i	0.643127	+	0.765759i	$0.277637\pi$
$762$	1.15144	−	3.75983i	0.0417121	−	0.136204i
$763$	−1.18661	+	0.100996i	−0.0429583	+	0.00365629i
$764$	−6.04259	−	5.79135i	−0.218613	−	0.209524i
$765$	−2.32739	−	0.606006i	−0.0841471	−	0.0219102i
$766$	1.02561	−	1.66570i	0.0370568	−	0.0601841i
$767$	28.0124	−	2.38420i	1.01147	−	0.0860886i
$768$	9.65265	−	9.25131i	0.348310	−	0.333828i
$769$	−5.59236	−	25.9486i	−0.201666	−	0.935732i	−0.959154	−	0.282884i	$-0.908709\pi$
$769$	−5.59236	−	25.9486i	−0.201666	−	0.935732i	0.757489	−	0.652848i	$-0.226426\pi$
$770$	−0.0187909	−	0.0213506i	−0.000677177	−	0.000769422i
$771$	7.91682	+	0.673821i	0.285117	+	0.0242671i
$772$	10.2255	−	25.4472i	0.368025	−	0.915865i
$773$	−3.21544	−	0.551343i	−0.115651	−	0.0198304i	0.110884	−	0.993833i	$-0.464632\pi$
$773$	−3.21544	−	0.551343i	−0.115651	−	0.0198304i	−0.226535	+	0.974003i	$0.572740\pi$
$774$	0.0306274	+	0.720992i	0.00110088	+	0.0259155i
$775$	−16.2104	+	40.3411i	−0.582294	+	1.44909i
$776$	5.21760	+	10.3485i	0.187301	+	0.371489i
$777$	−6.40469	+	12.7029i	−0.229767	+	0.455716i
$778$	−0.0445377	−	0.206655i	−0.00159675	−	0.00740896i
$779$	−1.61695	+	1.83721i	−0.0579331	+	0.0658248i
$780$	1.58887	+	0.561385i	0.0568908	+	0.0201008i
$781$	−2.53606	−	0.896047i	−0.0907474	−	0.0320631i
$782$	4.60620	−	5.23366i	0.164717	−	0.187155i
$783$	−0.488607	−	2.26714i	−0.0174614	−	0.0810211i
$784$	1.62010	−	3.21328i	0.0578608	−	0.114760i
$785$	−2.23665	−	4.43614i	−0.0798296	−	0.158332i
$786$	−0.375959	+	0.935609i	−0.0134100	+	0.0333721i
$787$	1.34408	+	31.6407i	0.0479113	+	1.12787i	0.848683	+	0.528901i	$0.177396\pi$
$787$	1.34408	+	31.6407i	0.0479113	+	1.12787i	−0.800772	+	0.598969i	$0.795577\pi$
$788$	34.4695	+	5.91039i	1.22793	+	0.210549i
$789$	−2.85395	+	7.10233i	−0.101603	+	0.252850i
$790$	0.266097	+	0.0226482i	0.00946730	+	0.000805786i
$791$	−30.1974	−	34.3109i	−1.07370	−	1.21996i
$792$	−0.0298323	−	0.138422i	−0.00106004	−	0.00491862i
$793$	28.7083	−	27.5147i	1.01946	−	0.977075i
$794$	−1.35129	+	0.115011i	−0.0479553	+	0.00408160i
$795$	−2.40553	+	3.90682i	−0.0853152	+	0.138561i
$796$	37.9734	+	9.88751i	1.34593	+	0.350453i
$797$	2.42570	+	2.32484i	0.0859225	+	0.0823501i	0.733674	−	0.679502i	$-0.237804\pi$
$797$	2.42570	+	2.32484i	0.0859225	+	0.0823501i	−0.647751	+	0.761852i	$0.724290\pi$
$798$	2.09519	−	0.178327i	0.0741689	−	0.00631270i
$799$	14.9921	−	48.9542i	0.530381	−	1.73188i
$800$	−9.94282	−	3.51302i	−0.351532	−	0.124204i
$801$	12.2771	−	3.19672i	0.433792	−	0.112951i
$802$	0.111217	+	0.868509i	0.00392721	+	0.0306681i
$803$	−0.317564	+	0.515757i	−0.0112066	+	0.0182007i
$804$	−13.1143	−	8.86372i	−0.462506	−	0.312599i
$805$	−3.37428	−	2.28062i	−0.118928	−	0.0803812i
$806$	3.11618	+	2.98661i	0.109763	+	0.105199i
$807$	15.7713	−	8.81036i	0.555175	−	0.310140i
$808$	−5.03168	+	0.862768i	−0.177014	+	0.0303521i
$809$	5.79401	−	11.4917i	0.203707	−	0.404028i	−0.767921	−	0.640545i	$-0.778709\pi$
$809$	5.79401	−	11.4917i	0.203707	−	0.404028i	0.971627	+	0.236517i	$0.0760058\pi$
$810$	0.0353585	−	0.0478078i	0.00124237	−	0.00167979i
$811$	0.283534	+	6.67461i	0.00995623	+	0.234377i	0.997180	+	0.0750405i	$0.0239086\pi$
$811$	0.283534	+	6.67461i	0.00995623	+	0.234377i	−0.987224	+	0.159337i	$0.949064\pi$
$812$	−10.5782	+	3.73753i	−0.371223	+	0.131162i
$813$	13.2591	−	8.96158i	0.465016	−	0.314296i
$814$	−0.194648	+	0.0687736i	−0.00682241	+	0.00241051i
$815$	−0.442181	−	0.0758196i	−0.0154889	−	0.00265585i
$816$	−16.7768	+	22.6837i	−0.587304	+	0.794087i
$817$	12.0850	+	13.7312i	0.422799	+	0.480393i
$818$	−0.569182	−	1.41646i	−0.0199010	−	0.0495255i
$819$	−5.68435	−	3.17547i	−0.198627	−	0.110960i
$820$	0.323994	−	0.0843616i	0.0113144	−	0.00294603i
$821$	6.27327	−	20.4844i	0.218939	−	0.714910i	−0.777368	−	0.629046i	$-0.783446\pi$
$821$	6.27327	−	20.4844i	0.218939	−	0.714910i	0.996307	−	0.0858639i	$-0.0273650\pi$
$822$	−0.881959	+	0.845289i	−0.0307619	+	0.0294829i
$823$	−13.7356	+	2.35521i	−0.478794	+	0.0820974i	−0.403337	−	0.915052i	$-0.632150\pi$
$823$	−13.7356	+	2.35521i	−0.478794	+	0.0820974i	−0.0754570	+	0.997149i	$0.524042\pi$
$824$	−5.71858	−	7.73203i	−0.199216	−	0.269358i
$825$	0.740467	−	0.597885i	0.0257797	−	0.0208157i
$826$	−4.78167	−	0.406981i	−0.166376	−	0.0141607i
$827$	−12.2933	+	16.6217i	−0.427481	+	0.577992i	−0.964002	−	0.265894i	$-0.914333\pi$
$827$	−12.2933	+	16.6217i	−0.427481	+	0.577992i	0.536521	+	0.843887i	$0.319738\pi$
$828$	−4.52543	−	8.97565i	−0.157269	−	0.311925i
$829$	−36.4697	+	29.4472i	−1.26664	+	1.02274i	−0.268412	+	0.963304i	$0.586499\pi$
$829$	−36.4697	+	29.4472i	−1.26664	+	1.02274i	−0.998232	+	0.0594389i	$0.981069\pi$
$830$	0.218054	−	0.0985664i	0.00756875	−	0.00342129i
$831$	−11.8348	−	29.4520i	−0.410545	−	1.02168i
$832$	12.5930	−	14.3084i	0.436584	−	0.496056i
$833$	−2.06015	+	6.72710i	−0.0713800	+	0.233080i
$834$	−0.0226515	−	0.176889i	−0.000784358	−	0.00612516i
$835$	−0.0161287	+	0.125951i	−0.000558157	+	0.00435873i
$836$	−1.38440	−	1.11782i	−0.0478805	−	0.0386608i
$837$	−7.75368	+	4.33146i	−0.268006	+	0.149717i
$838$	0.383329	−	0.367391i	0.0132419	−	0.0126913i
$839$	−13.7992	+	15.6789i	−0.476400	+	0.541296i	−0.938385	−	0.345592i	$-0.887678\pi$
$839$	−13.7992	+	15.6789i	−0.476400	+	0.541296i	0.461984	+	0.886888i	$0.347138\pi$
$840$	−0.506552	−	0.282977i	−0.0174777	−	0.00976362i
$841$	21.5244	+	9.72965i	0.742221	+	0.335505i
$842$	−0.178805	+	1.39631i	−0.00616203	+	0.0481202i
$843$	28.1964	+	7.34178i	0.971137	+	0.252864i
$844$	−11.9007	−	8.04345i	−0.409638	−	0.276867i
$845$	−1.87886	−	0.489217i	−0.0646347	−	0.0168296i
$846$	0.984886	+	0.795240i	0.0338611	+	0.0273409i
$847$	−5.68191	+	26.3642i	−0.195233	+	0.905883i
$848$	32.0050	+	43.2736i	1.09906	+	1.48602i
$849$	1.06169	+	2.10573i	0.0364369	+	0.0722684i
$850$	6.57996	+	1.12825i	0.225691	+	0.0386985i
$851$	−24.4916	+	16.5534i	−0.839560	+	0.567444i
$852$	−27.2025			−0.931943
$853$	10.6269			0.363857			0.181928	−	0.983312i	$-0.441766\pi$
$853$	10.6269			0.363857			0.181928	+	0.983312i	$0.441766\pi$
$854$	−5.62373	+	3.80098i	−0.192440	+	0.130067i
$855$	−0.0639687	−	1.50587i	−0.00218768	−	0.0514998i
$856$	−7.71680	−	0.656797i	−0.263755	−	0.0224488i
$857$	−48.6070	+	21.9717i	−1.66038	+	0.750540i	−1.00000		0.000388639i	$-0.999876\pi$
$857$	−48.6070	+	21.9717i	−1.66038	+	0.750540i	−0.660383	+	0.750929i	$0.729606\pi$
$858$	−0.0276675	−	0.0903440i	−0.000944554	−	0.00308429i
$859$	−3.16698	−	1.43156i	−0.108056	−	0.0488443i	0.357149	−	0.934048i	$-0.383749\pi$
$859$	−3.16698	−	1.43156i	−0.108056	−	0.0488443i	−0.465205	+	0.885203i	$0.654019\pi$
$860$	−0.317831	−	2.48199i	−0.0108379	−	0.0846350i
$861$	−1.28896	+	0.109707i	−0.0439277	+	0.00373879i
$862$	5.43419	−	3.03572i	0.185089	−	0.103397i
$863$	−3.00132	+	13.9262i	−0.102166	+	0.474053i	0.897301	+	0.441419i	$0.145525\pi$
$863$	−3.00132	+	13.9262i	−0.102166	+	0.474053i	−0.999467	+	0.0326341i	$0.989610\pi$
$864$	−1.12947	−	1.83438i	−0.0384254	−	0.0624068i
$865$	0.690490	−	0.312121i	0.0234774	−	0.0106124i
$866$	−1.90834	−	2.16830i	−0.0648482	−	0.0736818i
$867$	17.1795	−	34.0736i	0.583448	−	1.15720i
$868$	25.5479	+	34.5431i	0.867154	+	1.17247i
$869$	0.457815	+	0.743538i	0.0155303	+	0.0252228i
$870$	−0.0403819	−	0.131861i	−0.00136908	−	0.00447050i
$871$	−18.5998	−	10.3905i	−0.630230	−	0.352068i
$872$	−0.332415	−	0.117450i	−0.0112570	−	0.00397735i
$873$	−15.3990	+	4.00960i	−0.521179	+	0.135704i
$874$	3.98151	+	1.79976i	0.134677	+	0.0608777i
$875$	0.334571	−	7.87607i	0.0113106	−	0.266260i
$876$	−1.29054	+	5.98814i	−0.0436034	+	0.202321i
$877$	−0.192787	+	0.0330566i	−0.00650995	+	0.00111624i	−0.172255	−	0.985052i	$-0.555105\pi$
$877$	−0.192787	+	0.0330566i	−0.00650995	+	0.00111624i	0.165745	+	0.986169i	$0.446997\pi$
$878$	−0.209993	−	0.974371i	−0.00708692	−	0.0328834i
$879$	−8.44276	−	21.0106i	−0.284767	−	0.708671i
$880$	0.0700323	+	0.228680i	0.00236079	+	0.00770879i
$881$	−0.236098	+	5.55794i	−0.00795436	+	0.187252i	0.990725	+	0.135880i	$0.0433863\pi$
$881$	−0.236098	+	5.55794i	−0.00795436	+	0.187252i	−0.998680	+	0.0513714i	$0.983641\pi$
$882$	−0.135339	−	0.109279i	−0.00455711	−	0.00367961i
$883$	−13.2781	−	12.7260i	−0.446843	−	0.428264i	0.434550	−	0.900647i	$-0.356907\pi$
$883$	−13.2781	−	12.7260i	−0.446843	−	0.428264i	−0.881393	+	0.472383i	$0.843394\pi$
$884$	−20.2640	+	32.9109i	−0.681554	+	1.10691i
$885$	−0.436919	+	3.41197i	−0.0146869	+	0.114692i
$886$	−0.247930	+	5.83647i	−0.00832938	+	0.196080i
$887$	−16.7582	−	27.2170i	−0.562684	−	0.913856i	−0.999895	−	0.0144976i	$-0.995385\pi$
$887$	−16.7582	−	27.2170i	−0.562684	−	0.913856i	0.437211	−	0.899359i	$-0.355966\pi$
$888$	−3.27670	+	2.64575i	−0.109959	+	0.0887857i
$889$	19.6432	−	48.8839i	0.658810	−	1.63951i
$890$	0.711281	−	0.251312i	0.0238422	−	0.00842399i
$891$	0.194420			0.00651331
$892$	−28.9939	+	4.64000i	−0.970788	+	0.155359i
$893$	32.0865			1.07373
$894$	−1.55020	+	0.547719i	−0.0518463	+	0.0183185i
$895$	−1.67729	+	4.17409i	−0.0560655	+	0.139524i
$896$	−10.7784	+	8.70296i	−0.360082	+	0.290746i
$897$	−7.09374	−	11.5210i	−0.236853	−	0.384674i
$898$	−0.225544	+	5.30949i	−0.00752652	+	0.177180i
$899$	−2.61631	+	20.4311i	−0.0872588	+	0.681416i
$900$	5.04657	−	8.19615i	0.168219	−	0.273205i
$901$	−75.9698	−	72.8111i	−2.53092	−	2.42569i
$902$	−0.0146054	−	0.0117930i	−0.000486306	−	0.000392664i
$903$	−0.410340	+	9.65973i	−0.0136553	+	0.321456i
$904$	−3.96219	−	12.9379i	−0.131781	−	0.430309i
$905$	−0.272727	−	0.678708i	−0.00906577	−	0.0225610i
$906$	−0.279782	−	1.29819i	−0.00929514	−	0.0431296i
$907$	17.6556	−	3.02736i	0.586246	−	0.100522i	0.131769	−	0.991280i	$-0.457934\pi$
$907$	17.6556	−	3.02736i	0.586246	−	0.100522i	0.454477	+	0.890759i	$0.349826\pi$
$908$	9.11887	−	42.3117i	0.302620	−	1.40416i
$909$	0.297488	−	7.00310i	0.00986706	−	0.232278i
$910$	−0.352802	−	0.159477i	−0.0116953	−	0.00528660i
$911$	−4.73653	+	1.23330i	−0.156928	+	0.0408609i	−0.329613	−	0.944116i	$-0.606918\pi$
$911$	−4.73653	+	1.23330i	−0.156928	+	0.0408609i	0.172684	+	0.984977i	$0.444756\pi$
$912$	−16.6717	−	5.89049i	−0.552055	−	0.195053i
$913$	0.683052	+	0.381576i	0.0226057	+	0.0126283i
$914$	−0.523595	−	1.70972i	−0.0173190	−	0.0565524i
$915$	2.55095	+	4.14301i	0.0843319	+	0.136964i
$916$	18.7660	+	25.3733i	0.620046	+	0.838358i
$917$	−6.08194	+	12.0628i	−0.200843	+	0.398349i
$918$	0.901027	+	1.02377i	0.0297383	+	0.0337893i
$919$	43.9024	−	19.8451i	1.44821	−	0.654631i	0.474049	−	0.880499i	$-0.342792\pi$
$919$	43.9024	−	19.8451i	1.44821	−	0.654631i	0.974158	+	0.225868i	$0.0725218\pi$
$920$	−0.632148	−	1.02667i	−0.0208413	−	0.0338484i
$921$	3.05086	−	14.1561i	0.100529	−	0.466458i
$922$	1.06177	−	0.593140i	0.0349675	−	0.0195340i
$923$	−36.4822	+	3.10509i	−1.20083	+	0.102205i
$924$	−0.119461	−	0.932887i	−0.00392997	−	0.0306897i
$925$	−25.7933	−	11.6593i	−0.848078	−	0.383355i
$926$	−1.56118	−	5.09780i	−0.0513037	−	0.167524i
$927$	12.0321	−	5.43887i	0.395187	−	0.178636i
$928$	−4.97805	−	0.423695i	−0.163413	−	0.0139085i
$929$	−1.21406	−	28.5799i	−0.0398320	−	0.937676i	−0.902180	−	0.431360i	$-0.858034\pi$
$929$	−1.21406	−	28.5799i	−0.0398320	−	0.937676i	0.862348	−	0.506316i	$-0.168993\pi$
$930$	−0.437551	+	0.295733i	−0.0143478	+	0.00969745i
$931$	−4.40920			−0.144506
$932$	−12.0657			−0.395226
$933$	3.93611	−	2.66035i	0.128863	−	0.0870959i
$934$	2.85372	+	0.489320i	0.0933767	+	0.0160110i
$935$	−0.210506	−	0.417513i	−0.00688428	−	0.0136541i
$936$	−1.14619	−	1.54975i	−0.0374645	−	0.0506553i
$937$	4.29547	−	19.9310i	0.140327	−	0.651119i	−0.851588	−	0.524212i	$-0.824360\pi$
$937$	4.29547	−	19.9310i	0.140327	−	0.651119i	0.991915	−	0.126907i	$-0.0405049\pi$
$938$	2.82954	+	2.28470i	0.0923879	+	0.0745980i
$939$	32.6146	+	8.49217i	1.06434	+	0.277132i
$940$	−3.63658	−	2.45790i	−0.118612	−	0.0801679i
$941$	−28.7519	−	7.48642i	−0.937286	−	0.244050i	−0.248183	−	0.968713i	$-0.579833\pi$
$941$	−28.7519	−	7.48642i	−0.937286	−	0.244050i	−0.689104	+	0.724663i	$0.741995\pi$
$942$	−0.357841	+	2.79443i	−0.0116591	+	0.0910475i
$943$	−2.44943	−	1.10721i	−0.0797643	−	0.0360557i
$944$	35.2292	+	19.6802i	1.14661	+	0.640536i
$945$	0.526340	−	0.598039i	0.0171219	−	0.0194542i
$946$	−0.101292	+	0.0970801i	−0.00329327	+	0.00315635i
$947$	12.5492	−	7.01039i	0.407793	−	0.227807i	−0.270310	−	0.962773i	$-0.587126\pi$
$947$	12.5492	−	7.01039i	0.407793	−	0.227807i	0.678104	+	0.734966i	$0.262802\pi$
$948$	6.87081	+	5.54779i	0.223154	+	0.180184i
$949$	−1.04726	+	8.17820i	−0.0339955	+	0.265476i
$950$	0.531430	+	4.15001i	0.0172419	+	0.134644i
$951$	−10.1171	+	33.0358i	−0.328069	+	1.07126i
$952$	8.79217	−	9.98985i	0.284956	−	0.323773i
$953$	−1.09995	−	2.73733i	−0.0356308	−	0.0886707i	0.909014	−	0.416766i	$-0.136837\pi$
$953$	−1.09995	−	2.73733i	−0.0356308	−	0.0886707i	−0.944645	+	0.328095i	$0.893593\pi$
$954$	2.37076	−	1.07165i	0.0767561	−	0.0346960i
$955$	1.07243	−	0.865930i	0.0347032	−	0.0280208i
$956$	−24.9594	−	49.5040i	−0.807244	−	1.60107i
$957$	0.268119	−	0.362521i	0.00866706	−	0.0117186i
$958$	3.02183	+	0.257196i	0.0976309	+	0.00830961i
$959$	−12.7342	+	10.2822i	−0.411209	+	0.332028i
$960$	1.38679	+	1.87506i	0.0447584	+	0.0605174i
$961$	47.1924	−	8.09194i	1.52233	−	0.261030i
$962$	−2.02885	+	1.94449i	−0.0654127	+	0.0626930i
$963$	3.11377	−	10.1675i	0.100340	−	0.327644i
$964$	−41.0794	+	10.6962i	−1.32308	+	0.344503i
$965$	3.94298	+	2.20268i	0.126929	+	0.0709067i
$966$	0.861116	+	2.14297i	0.0277059	+	0.0689489i
$967$	−10.1126	−	11.4901i	−0.325198	−	0.369496i	0.564984	−	0.825102i	$-0.308882\pi$
$967$	−10.1126	−	11.4901i	−0.325198	−	0.369496i	−0.890182	+	0.455605i	$0.849423\pi$
$968$	−4.74756	+	6.41912i	−0.152592	+	0.206318i
$969$	34.0717	+	5.84218i	1.09454	+	0.187678i
$970$	−0.892150	+	0.315217i	−0.0286452	+	0.0101210i
$971$	−17.0853	+	11.5476i	−0.548293	+	0.370582i	−0.802577	−	0.596548i	$-0.796539\pi$
$971$	−17.0853	+	11.5476i	−0.548293	+	0.370582i	0.254284	+	0.967130i	$0.418160\pi$
$972$	1.85396	−	0.655046i	0.0594658	−	0.0210106i
$973$	−0.101404	−	2.38713i	−0.00325086	−	0.0765279i
$974$	−2.99455	+	4.04890i	−0.0959515	+	0.129735i
$975$	5.83256	−	11.5682i	0.186791	−	0.370478i
$976$	56.2560	−	9.64606i	1.80071	−	0.308763i
$977$	−35.1412	+	19.6310i	−1.12427	+	0.628052i	−0.935273	−	0.353926i	$-0.884846\pi$
$977$	−35.1412	+	19.6310i	−1.12427	+	0.628052i	−0.188992	+	0.981979i	$0.560522\pi$
$978$	0.183671	+	0.176034i	0.00587314	+	0.00562895i
$979$	2.04353	+	1.38118i	0.0653114	+	0.0441428i
$980$	0.499726	+	0.337756i	0.0159631	+	0.0107892i
$981$	0.253798	−	0.412194i	0.00810314	−	0.0131603i
$982$	−0.661033	−	5.16211i	−0.0210944	−	0.164729i
$983$	−14.6821	+	3.82293i	−0.468288	+	0.121933i	−0.478635	−	0.878014i	$-0.658868\pi$
$983$	−14.6821	+	3.82293i	−0.468288	+	0.121933i	0.0103476	+	0.999946i	$0.496706\pi$
$984$	−0.361086	−	0.127580i	−0.0115110	−	0.00406710i
$985$	−1.68652	+	5.50706i	−0.0537369	+	0.175470i
$986$	3.15152	−	0.268234i	0.100365	−	0.00854232i
$987$	12.2442	+	11.7352i	0.389739	+	0.373534i
$988$	−23.4402	−	6.10336i	−0.745732	−	0.194174i
$989$	−10.5335	+	17.1075i	−0.334946	+	0.543986i
$990$	0.0115191		0.000980418i	0.000366100		3.11597e-5i
$991$	3.56237	−	3.41426i	0.113162	−	0.108457i	−0.633229	−	0.773964i	$-0.718271\pi$
$991$	3.56237	−	3.41426i	0.113162	−	0.108457i	0.746392	+	0.665507i	$0.231785\pi$
$992$	4.03086	+	18.7032i	0.127980	+	0.593829i
$993$	−12.0398	−	13.6799i	−0.382073	−	0.434119i
$994$	6.22746	+	0.530035i	0.197523	+	0.0168117i
$995$	−2.40949	+	5.99624i	−0.0763858	+	0.190093i
$996$	7.79911	+	1.33729i	0.247124	+	0.0423737i
$997$	−1.21773	−	28.6663i	−0.0385658	−	0.907870i	−0.909306	−	0.416127i	$-0.863387\pi$
$997$	−1.21773	−	28.6663i	−0.0385658	−	0.907870i	0.870741	−	0.491743i	$-0.163640\pi$
$998$	−0.171487	+	0.426763i	−0.00542834	+	0.0135089i
$999$	−2.60329	−	5.16333i	−0.0823646	−	0.163360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.i.a.4.11	✓	648
223.56	even	37	inner	669.2.i.a.502.11	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.i.a.4.11	✓	648	1.1	even	1	trivial
669.2.i.a.502.11	yes	648	223.56	even	37	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:	\( N \)	\(=\)	\( 669 = 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	669.i (of order \(37\), degree \(36\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173139 - 0.0611740i) q^{2} +(-0.372856 + 0.927889i) q^{3} +(-1.52984 + 1.23526i) q^{4} +(-0.169781 - 0.275742i) q^{5} +(-0.00779341 + 0.183463i) q^{6} +(-0.312492 + 2.44030i) q^{7} +(-0.381865 + 0.620188i) q^{8} +(-0.721956 - 0.691939i) q^{9} +(-0.0462641 - 0.0373556i) q^{10} +(0.00825142 - 0.194245i) q^{11} +(-0.575772 - 1.88009i) q^{12} +(-0.986794 - 2.45573i) q^{13} +(0.0951780 + 0.441628i) q^{14} +(0.319162 - 0.0547259i) q^{15} +(0.800333 - 3.71356i) q^{16} +(-0.315208 + 7.42025i) q^{17} +(-0.167328 - 0.0756368i) q^{18} +(-4.50434 + 1.17284i) q^{19} +(0.600350 + 0.212117i) q^{20} +(-2.14781 - 1.19984i) q^{21} +(-0.0104541 - 0.0341361i) q^{22} +(-2.68035 - 4.35316i) q^{23} +(-0.433085 - 0.585569i) q^{24} +(2.20381 - 4.37100i) q^{25} +(-0.321079 - 0.364817i) q^{26} +(0.911228 - 0.411901i) q^{27} +(-2.53633 - 4.11927i) q^{28} +(0.488607 - 2.26714i) q^{29} +(0.0519117 - 0.0289996i) q^{30} +(-8.84951 + 0.753204i) q^{31} +(-0.273624 - 2.13677i) q^{32} +(0.177161 + 0.0800818i) q^{33} +(0.399351 + 1.30402i) q^{34} +(0.725949 - 0.328150i) q^{35} +(1.95920 + 0.166752i) q^{36} +(-0.245415 - 5.77727i) q^{37} +(-0.708131 + 0.478613i) q^{38} +2.64658 q^{39} +0.235846 q^{40} +(0.435642 - 0.294443i) q^{41} +(-0.445269 - 0.0763491i) q^{42} +(-1.76926 - 3.50911i) q^{43} +(0.227319 + 0.307355i) q^{44} +(-0.0682222 + 0.316552i) q^{45} +(-0.730373 - 0.589735i) q^{46} +(-6.67117 - 1.73704i) q^{47} +(3.14736 + 2.12724i) q^{48} +(0.916727 + 0.238697i) q^{49} +(0.114175 - 0.891607i) q^{50} +(-6.76764 - 3.05917i) q^{51} +(4.54309 + 2.53792i) q^{52} +(-9.36069 + 10.6358i) q^{53} +(0.132572 - 0.127060i) q^{54} +(-0.0549625 + 0.0307039i) q^{55} +(-1.39411 - 1.12567i) q^{56} +(0.591208 - 4.61683i) q^{57} +(-0.0540932 - 0.422421i) q^{58} +(-3.11055 + 10.1570i) q^{59} +(-0.420666 + 0.477969i) q^{60} +(5.60214 + 13.9415i) q^{61} +(-1.48612 + 0.671769i) q^{62} +(1.91414 - 1.54556i) q^{63} +(3.24240 + 6.43091i) q^{64} +(-0.509610 + 0.689038i) q^{65} +(0.0355724 + 0.00302766i) q^{66} +(6.26328 - 5.05724i) q^{67} +(-8.68370 - 11.7411i) q^{68} +(5.03863 - 0.863960i) q^{69} +(0.105616 - 0.101225i) q^{70} +(4.05106 - 13.2281i) q^{71} +(0.704821 - 0.183521i) q^{72} +(-2.71973 - 1.51933i) q^{73} +(-0.395910 - 0.985259i) q^{74} +(3.23410 + 3.67465i) q^{75} +(5.44215 - 7.35827i) q^{76} +(0.471437 + 0.0808359i) q^{77} +(0.458226 - 0.161902i) q^{78} +(-3.72101 + 2.51496i) q^{79} +(-1.15987 + 0.409807i) q^{80} +(0.0424412 + 0.999099i) q^{81} +(0.0574145 - 0.0776295i) q^{82} +(-1.81176 + 3.59341i) q^{83} +(4.76791 - 0.817540i) q^{84} +(2.09959 - 1.17290i) q^{85} +(-0.520994 - 0.499332i) q^{86} +(1.92148 + 1.29869i) q^{87} +(0.117317 + 0.0792926i) q^{88} +(-6.65162 + 10.8029i) q^{89} +(0.00755282 + 0.0589810i) q^{90} +(6.30108 - 1.64067i) q^{91} +(9.47776 + 3.34871i) q^{92} +(2.60071 - 8.49220i) q^{93} +(-1.26130 + 0.107353i) q^{94} +(1.08815 + 1.04291i) q^{95} +(2.08471 + 0.542815i) q^{96} +(8.34304 - 13.5500i) q^{97} +(0.173323 - 0.0147520i) q^{98} +(-0.140363 + 0.134527i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + q^{2} + 18 q^{3} - 17 q^{4} + 4 q^{5} - q^{6} + 4 q^{7} + 9 q^{8} - 18 q^{9} + 8 q^{10} + 6 q^{11} + 17 q^{12} - 2 q^{13} + 12 q^{14} - 4 q^{15} - 7 q^{16} + 8 q^{17} + q^{18} - 66 q^{19} + 14 q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 648 * q + q^2 + 18 * q^3 - 17 * q^4 + 4 * q^5 - q^6 + 4 * q^7 + 9 * q^8 - 18 * q^9 + 8 * q^10 + 6 * q^11 + 17 * q^12 - 2 * q^13 + 12 * q^14 - 4 * q^15 - 7 * q^16 + 8 * q^17 + q^18 - 66 * q^19 + 14 * q^20 - 4 * q^21 - 24 * q^22 - 2 * q^23 - 9 * q^24 - 26 * q^25 - 8 * q^26 + 18 * q^27 + 8 * q^28 - 27 * q^29 - 8 * q^30 + 16 * q^31 + 19 * q^32 - 6 * q^33 - 50 * q^34 + 16 * q^35 - 17 * q^36 + 16 * q^37 - 28 * q^38 - 72 * q^39 + 212 * q^40 + 240 * q^41 - 86 * q^42 + 6 * q^43 - 128 * q^44 + 4 * q^45 + 16 * q^46 - 14 * q^47 + 7 * q^48 - 28 * q^49 + 23 * q^50 + 66 * q^51 - 286 * q^52 + 10 * q^53 - q^54 + 14 * q^55 + 25 * q^56 - 8 * q^57 + 49 * q^58 + 22 * q^59 - 14 * q^60 - 2 * q^61 - 23 * q^62 + 4 * q^63 + 257 * q^64 - 116 * q^65 - 50 * q^66 + 8 * q^67 + 211 * q^68 + 2 * q^69 + 82 * q^70 + 9 * q^72 + 10 * q^73 - 10 * q^74 + 26 * q^75 + 7 * q^76 - 116 * q^77 - 66 * q^78 - 14 * q^79 - 477 * q^80 - 18 * q^81 - 234 * q^82 - 142 * q^83 - 8 * q^84 + 98 * q^85 + 35 * q^86 - 10 * q^87 - 72 * q^88 + 2 * q^89 + 8 * q^90 + 6 * q^91 - 46 * q^92 - 16 * q^93 - 206 * q^94 - 6 * q^95 - 19 * q^96 - 34 * q^97 + 4 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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