LMFDB - Embedded newform 669.2.m.b.19.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [669,2,Mod(19,669)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(669, base_ring=CyclotomicField(222)) chi = DirichletCharacter(H, H._module([0, 172])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("669.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 669 = 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	669.m (of order $111$, degree $72$, minimal)

Newform invariants

comment:select newform

sage:traces = [1368] 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:	$1368$
Relative dimension:	$19$ over $\Q(\zeta_{111})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{111}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	669.19
Dual form			669.2.m.b.493.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.164723 + 1.28634i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(0.307920 - 0.0801761i) q^{4} +(-2.05355 + 0.292560i) q^{5} +(-0.961286 - 0.870484i) q^{6} +(1.65357 - 2.23577i) q^{7} +(1.12093 + 2.78954i) q^{8} +(0.155037 - 0.987909i) q^{9} +(-0.714600 - 2.59338i) q^{10} +(1.52659 - 0.491246i) q^{11} +(-0.181889 + 0.261073i) q^{12} +(5.40433 - 1.90947i) q^{13} +(3.14835 + 1.75877i) q^{14} +(1.37043 - 1.55711i) q^{15} +(-2.84811 + 1.59105i) q^{16} +(-1.38766 + 6.43877i) q^{17} +(1.29633 + 0.0366993i) q^{18} +(4.46941 + 4.79739i) q^{19} +(-0.608874 + 0.254731i) q^{20} +(0.196597 + 2.77386i) q^{21} +(0.883375 + 1.88280i) q^{22} +(-2.36526 - 3.01565i) q^{23} +(-2.66501 - 1.39131i) q^{24} +(-0.669584 + 0.194738i) q^{25} +(3.34645 + 6.63729i) q^{26} +(0.524307 + 0.851529i) q^{27} +(0.329911 - 0.821015i) q^{28} +(0.641450 + 0.382545i) q^{29} +(2.22872 + 1.50635i) q^{30} +(0.203467 - 2.04727i) q^{31} +(1.05955 + 1.43261i) q^{32} +(-0.840822 + 1.36558i) q^{33} +(-8.51105 - 0.724397i) q^{34} +(-2.74159 + 5.07504i) q^{35} +(-0.0314678 - 0.316627i) q^{36} +(-3.53660 + 3.20254i) q^{37} +(-5.43487 + 6.53943i) q^{38} +(-2.86587 + 4.96383i) q^{39} +(-3.11800 - 5.40054i) q^{40} +(-3.15501 - 0.540981i) q^{41} +(-3.53575 + 0.709809i) q^{42} +(1.96351 + 8.00376i) q^{43} +(0.430681 - 0.273660i) q^{44} +(-0.0293529 + 2.07408i) q^{45} +(3.48955 - 3.53928i) q^{46} +(8.73533 - 9.37636i) q^{47} +(1.13025 - 3.06034i) q^{48} +(-0.214624 - 0.700821i) q^{49} +(-0.360795 - 0.829238i) q^{50} +(-3.13056 - 5.79508i) q^{51} +(1.51101 - 1.02126i) q^{52} +(7.22946 - 0.409663i) q^{53} +(-1.00899 + 0.814705i) q^{54} +(-2.99121 + 1.45542i) q^{55} +(8.09031 + 2.10655i) q^{56} +(-6.51474 - 0.740705i) q^{57} +(-0.386423 + 0.888139i) q^{58} +(1.44305 - 0.122822i) q^{59} +(0.297140 - 0.589341i) q^{60} +(1.35299 - 7.27136i) q^{61} +(2.66701 - 0.0755035i) q^{62} +(-1.95237 - 1.98020i) q^{63} +(-6.37889 + 6.11367i) q^{64} +(-10.5394 + 5.50229i) q^{65} +(-1.89511 - 0.856643i) q^{66} +(-0.782414 + 2.83949i) q^{67} +(0.0889471 + 2.09388i) q^{68} +(3.75760 + 0.754345i) q^{69} +(-6.97985 - 2.69065i) q^{70} +(-4.05943 + 8.65213i) q^{71} +(2.92960 - 0.674896i) q^{72} +(1.27674 + 0.621215i) q^{73} +(-4.70212 - 4.02175i) q^{74} +(0.382271 - 0.583211i) q^{75} +(1.76086 + 1.11887i) q^{76} +(1.42600 - 4.22541i) q^{77} +(-6.85726 - 2.86884i) q^{78} +(0.0483102 + 0.130808i) q^{79} +(5.38326 - 4.10054i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(0.176185 - 4.14754i) q^{82} +(1.00104 - 4.08049i) q^{83} +(0.282934 + 0.838365i) q^{84} +(0.965907 - 13.6283i) q^{85} +(-9.97215 + 3.84415i) q^{86} +(-0.736117 + 0.126220i) q^{87} +(3.08155 + 3.70783i) q^{88} +(-5.60648 - 0.798730i) q^{89} +(-2.67282 + 0.303890i) q^{90} +(4.66728 - 15.2403i) q^{91} +(-0.970094 - 0.738941i) q^{92} +(1.17607 + 1.68807i) q^{93} +(13.5001 + 9.69213i) q^{94} +(-10.5817 - 8.54412i) q^{95} +(-1.73638 - 0.400011i) q^{96} +(-1.05441 + 1.34434i) q^{97} +(0.866143 - 0.391521i) q^{98} +(-0.248629 - 1.58429i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) $ 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Character values

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

$n$	$224$	$226$
$\chi(n)$	$1$	$e\left(\frac{86}{111}\right)$

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 $

$2$	0.164723	+	1.28634i	0.116477	+	0.909582i	0.939732	+	0.341911i	$0.111074\pi$
$2$	0.164723	+	1.28634i	0.116477	+	0.909582i	−0.823256	+	0.567671i	$0.807845\pi$
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$3$	−0.759946	+	0.649986i	−0.438755	+	0.375270i
$4$	0.307920	−	0.0801761i	0.153960	−	0.0400881i
$5$	−2.05355	+	0.292560i	−0.918377	+	0.130837i	−0.584141	−	0.811652i	$-0.698568\pi$
$5$	−2.05355	+	0.292560i	−0.918377	+	0.130837i	−0.334236	+	0.942489i	$0.608478\pi$
$6$	−0.961286	−	0.870484i	−0.392443	−	0.355374i
$7$	1.65357	−	2.23577i	0.624989	−	0.845042i	−0.371528	−	0.928422i	$-0.621166\pi$
$7$	1.65357	−	2.23577i	0.624989	−	0.845042i	0.996518	+	0.0833801i	$0.0265716\pi$
$8$	1.12093	+	2.78954i	0.396309	+	0.986253i
$9$	0.155037	−	0.987909i	0.0516789	−	0.329303i
$10$	−0.714600	−	2.59338i	−0.225976	−	0.820100i
$11$	1.52659	−	0.491246i	0.460284	−	0.148116i	−0.0670952	−	0.997747i	$-0.521373\pi$
$11$	1.52659	−	0.491246i	0.460284	−	0.148116i	0.527379	+	0.849630i	$0.323175\pi$
$12$	−0.181889	+	0.261073i	−0.0525069	+	0.0753653i
$13$	5.40433	−	1.90947i	1.49889	−	0.529592i	0.547293	−	0.836941i	$-0.315658\pi$
$13$	5.40433	−	1.90947i	1.49889	−	0.529592i	0.951597	+	0.307349i	$0.0994419\pi$
$14$	3.14835	+	1.75877i	0.841431	+	0.470052i
$15$	1.37043	−	1.55711i	0.353843	−	0.402044i
$16$	−2.84811	+	1.59105i	−0.712027	+	0.397762i
$17$	−1.38766	+	6.43877i	−0.336557	+	1.56163i	0.419888	+	0.907576i	$0.362069\pi$
$17$	−1.38766	+	6.43877i	−0.336557	+	1.56163i	−0.756446	+	0.654056i	$0.773066\pi$
$18$	1.29633	+	0.0366993i	0.305547	+	0.00865011i
$19$	4.46941	+	4.79739i	1.02535	+	1.10060i	0.994880	+	0.101060i	$0.0322235\pi$
$19$	4.46941	+	4.79739i	1.02535	+	1.10060i	0.0304719	+	0.999536i	$0.490299\pi$
$20$	−0.608874	+	0.254731i	−0.136148	+	0.0569596i
$21$	0.196597	+	2.77386i	0.0429010	+	0.605306i
$22$	0.883375	+	1.88280i	0.188336	+	0.401414i
$23$	−2.36526	−	3.01565i	−0.493191	−	0.628806i	0.474709	−	0.880143i	$-0.342553\pi$
$23$	−2.36526	−	3.01565i	−0.493191	−	0.628806i	−0.967900	+	0.251337i	$0.919130\pi$
$24$	−2.66501	−	1.39131i	−0.543993	−	0.284001i
$25$	−0.669584	+	0.194738i	−0.133917	+	0.0389476i
$26$	3.34645	+	6.63729i	0.656293	+	1.30168i
$27$	0.524307	+	0.851529i	0.100903	+	0.163877i
$28$	0.329911	−	0.821015i	0.0623473	−	0.155157i
$29$	0.641450	+	0.382545i	0.119114	+	0.0710368i	0.570529	−	0.821277i	$-0.306738\pi$
$29$	0.641450	+	0.382545i	0.119114	+	0.0710368i	−0.451415	+	0.892314i	$0.649081\pi$
$30$	2.22872	+	1.50635i	0.406907	+	0.275021i
$31$	0.203467	−	2.04727i	0.0365437	−	0.367700i	−0.959695	−	0.281045i	$-0.909319\pi$
$31$	0.203467	−	2.04727i	0.0365437	−	0.367700i	0.996238	−	0.0866555i	$-0.0276179\pi$
$32$	1.05955	+	1.43261i	0.187304	+	0.253252i
$33$	−0.840822	+	1.36558i	−0.146368	+	0.237717i
$34$	−8.51105	−	0.724397i	−1.45963	−	0.124233i
$35$	−2.74159	+	5.07504i	−0.463413	+	0.857838i
$36$	−0.0314678	−	0.316627i	−0.00524464	−	0.0527712i
$37$	−3.53660	+	3.20254i	−0.581413	+	0.526494i	−0.908163	−	0.418617i	$-0.862515\pi$
$37$	−3.53660	+	3.20254i	−0.581413	+	0.526494i	0.326750	+	0.945111i	$0.394046\pi$
$38$	−5.43487	+	6.53943i	−0.881653	+	1.06084i
$39$	−2.86587	+	4.96383i	−0.458906	+	0.794849i
$40$	−3.11800	−	5.40054i	−0.492999	−	0.853900i
$41$	−3.15501	−	0.540981i	−0.492730	−	0.0844871i	−0.0827291	−	0.996572i	$-0.526364\pi$
$41$	−3.15501	−	0.540981i	−0.492730	−	0.0844871i	−0.410001	+	0.912085i	$0.634472\pi$
$42$	−3.53575	+	0.709809i	−0.545578	+	0.109526i
$43$	1.96351	+	8.00376i	0.299433	+	1.22056i	0.905223	+	0.424938i	$0.139704\pi$
$43$	1.96351	+	8.00376i	0.299433	+	1.22056i	−0.605790	+	0.795624i	$0.707143\pi$
$44$	0.430681	−	0.273660i	0.0649276	−	0.0412559i
$45$	−0.0293529	+	2.07408i	−0.00437568	+	0.309186i
$46$	3.48955	−	3.53928i	0.514506	−	0.521839i
$47$	8.73533	−	9.37636i	1.27418	−	1.36768i	0.376878	−	0.926263i	$-0.376998\pi$
$47$	8.73533	−	9.37636i	1.27418	−	1.36768i	0.897301	−	0.441419i	$-0.145525\pi$
$48$	1.13025	−	3.06034i	0.163137	−	0.441722i
$49$	−0.214624	−	0.700821i	−0.0306606	−	0.100117i
$50$	−0.360795	−	0.829238i	−0.0510242	−	0.117272i
$51$	−3.13056	−	5.79508i	−0.438367	−	0.811474i
$52$	1.51101	−	1.02126i	0.209539	−	0.141624i
$53$	7.22946	−	0.409663i	0.993042	−	0.0562715i	0.447438	−	0.894315i	$-0.352336\pi$
$53$	7.22946	−	0.409663i	0.993042	−	0.0562715i	0.545604	+	0.838043i	$0.316300\pi$
$54$	−1.00899	+	0.814705i	−0.137307	+	0.110867i
$55$	−2.99121	+	1.45542i	−0.403335	+	0.196249i
$56$	8.09031	+	2.10655i	1.08111	+	0.281500i
$57$	−6.51474	−	0.740705i	−0.862899	−	0.0981087i
$58$	−0.386423	+	0.888139i	−0.0507398	+	0.116618i
$59$	1.44305	−	0.122822i	0.187869	−	0.0159900i	0.00950637	−	0.999955i	$-0.496974\pi$
$59$	1.44305	−	0.122822i	0.187869	−	0.0159900i	0.178363	+	0.983965i	$0.442920\pi$
$60$	0.297140	−	0.589341i	0.0383606	−	0.0760836i
$61$	1.35299	−	7.27136i	0.173232	−	0.931002i	−0.779320	−	0.626626i	$-0.784435\pi$
$61$	1.35299	−	7.27136i	0.173232	−	0.931002i	0.952552	−	0.304375i	$-0.0984477\pi$
$62$	2.66701	−	0.0755035i	0.338710	−	0.00958895i
$63$	−1.95237	−	1.98020i	−0.245976	−	0.249482i
$64$	−6.37889	+	6.11367i	−0.797361	+	0.764209i
$65$	−10.5394	+	5.50229i	−1.30726	+	0.682475i
$66$	−1.89511	−	0.856643i	−0.233272	−	0.105445i
$67$	−0.782414	+	2.83949i	−0.0955871	+	0.346899i	−0.996133	−	0.0878629i	$-0.971996\pi$
$67$	−0.782414	+	2.83949i	−0.0955871	+	0.346899i	0.900546	+	0.434762i	$0.143167\pi$
$68$	0.0889471	+	2.09388i	0.0107864	+	0.253921i
$69$	3.75760	+	0.754345i	0.452362	+	0.0908125i
$70$	−6.97985	−	2.69065i	−0.834251	−	0.321594i
$71$	−4.05943	+	8.65213i	−0.481765	+	1.02682i	0.504767	+	0.863255i	$0.331578\pi$
$71$	−4.05943	+	8.65213i	−0.481765	+	1.02682i	−0.986533	+	0.163564i	$0.947701\pi$
$72$	2.92960	−	0.674896i	0.345257	−	0.0795373i
$73$	1.27674	+	0.621215i	0.149431	+	0.0727077i	0.510725	−	0.859744i	$-0.329377\pi$
$73$	1.27674	+	0.621215i	0.149431	+	0.0727077i	−0.361295	+	0.932452i	$0.617665\pi$
$74$	−4.70212	−	4.02175i	−0.546610	−	0.467518i
$75$	0.382271	−	0.583211i	0.0441409	−	0.0673434i
$76$	1.76086	+	1.11887i	0.201984	+	0.128343i
$77$	1.42600	−	4.22541i	0.162508	−	0.481530i
$78$	−6.85726	−	2.86884i	−0.776432	−	0.324832i
$79$	0.0483102	+	0.130808i	0.00543533	+	0.0147171i	0.940758	−	0.339080i	$-0.110116\pi$
$79$	0.0483102	+	0.130808i	0.00543533	+	0.0147171i	−0.935322	+	0.353797i	$0.884890\pi$
$80$	5.38326	−	4.10054i	0.601867	−	0.458455i
$81$	−0.951927	−	0.306324i	−0.105770	−	0.0340360i
$82$	0.176185	−	4.14754i	0.0194564	−	0.458019i
$83$	1.00104	−	4.08049i	0.109878	−	0.447892i	−0.890091	−	0.455784i	$-0.849359\pi$
$83$	1.00104	−	4.08049i	0.109878	−	0.447892i	0.999969	+	0.00789222i	$0.00251220\pi$
$84$	0.282934	+	0.838365i	0.0308706	+	0.0914731i
$85$	0.965907	−	13.6283i	0.104767	−	1.47820i
$86$	−9.97215	+	3.84415i	−1.07532	+	0.414525i
$87$	−0.736117	+	0.126220i	−0.0789200	+	0.0135322i
$88$	3.08155	+	3.70783i	0.328495	+	0.395256i
$89$	−5.60648	−	0.798730i	−0.594286	−	0.0846652i	−0.162604	−	0.986691i	$-0.551989\pi$
$89$	−5.60648	−	0.798730i	−0.594286	−	0.0846652i	−0.431681	+	0.902026i	$0.642080\pi$
$90$	−2.67282	+	0.303890i	−0.281739	+	0.0320328i
$91$	4.66728	−	15.2403i	0.489264	−	1.59761i
$92$	−0.970094	−	0.738941i	−0.101139	−	0.0770399i
$93$	1.17607	+	1.68807i	0.121953	+	0.175044i
$94$	13.5001	+	9.69213i	1.39243	+	0.999667i
$95$	−10.5817	−	8.54412i	−1.08566	−	0.876608i
$96$	−1.73638	−	0.400011i	−0.177218	−	0.0408260i
$97$	−1.05441	+	1.34434i	−0.107059	+	0.136497i	−0.837412	−	0.546573i	$-0.815932\pi$
$97$	−1.05441	+	1.34434i	−0.107059	+	0.136497i	0.730353	+	0.683070i	$0.239356\pi$
$98$	0.866143	−	0.391521i	0.0874937	−	0.0395496i
$99$	−0.248629	−	1.58429i	−0.0249882	−	0.159227i
$100$	−0.190565	+	0.113648i	−0.0190565	+	0.0113648i
$101$	7.84667	+	0.444638i	0.780773	+	0.0442431i	0.442457	−	0.896790i	$-0.354107\pi$
$101$	7.84667	+	0.444638i	0.780773	+	0.0442431i	0.338315	+	0.941033i	$0.390143\pi$
$102$	6.93879	−	4.98156i	0.687043	−	0.493248i
$103$	−1.14255	−	0.403687i	−0.112578	−	0.0397765i	0.276256	−	0.961084i	$-0.410906\pi$
$103$	−1.14255	−	0.403687i	−0.112578	−	0.0397765i	−0.388835	+	0.921308i	$0.627122\pi$
$104$	11.3844	+	12.9352i	1.11634	+	1.26840i
$105$	−1.21524	−	5.63875i	−0.118596	−	0.550286i
$106$	1.71782	+	9.23208i	0.166850	+	0.896699i
$107$	−16.5351	−	4.80897i	−1.59851	−	0.464901i	−0.644482	−	0.764619i	$-0.722927\pi$
$107$	−16.5351	−	4.80897i	−1.59851	−	0.464901i	−0.954028	+	0.299719i	$0.903107\pi$
$108$	0.229717	+	0.220166i	0.0221045	+	0.0211855i
$109$	−0.212448	−	15.0116i	−0.0203488	−	1.43785i	−0.705118	−	0.709090i	$-0.749106\pi$
$109$	−0.212448	−	15.0116i	−0.0203488	−	1.43785i	0.684769	−	0.728760i	$-0.259903\pi$
$110$	−2.36489	−	3.60798i	−0.225483	−	0.344008i
$111$	0.606019	−	4.73249i	0.0575208	−	0.449188i
$112$	−1.15232	+	8.99861i	−0.108884	+	0.850289i
$113$	2.76847	+	4.22370i	0.260435	+	0.397332i	0.942630	−	0.333838i	$-0.108344\pi$
$113$	2.76847	+	4.22370i	0.260435	+	0.397332i	−0.682195	+	0.731170i	$0.738974\pi$
$114$	−0.120325	−	8.50221i	−0.0112695	−	0.796305i
$115$	5.73945	+	5.50081i	0.535206	+	0.512954i
$116$	0.228186	+	0.0663643i	0.0211866	+	0.00616177i
$117$	−1.04851	−	5.63502i	−0.0969351	−	0.520958i
$118$	0.395694	+	1.83603i	0.0364266	+	0.169020i
$119$	12.1010	+	13.7494i	1.10930	+	1.26041i
$120$	5.87979	+	2.07746i	0.536749	+	0.189645i
$121$	−6.84650	+	4.91530i	−0.622409	+	0.446845i
$122$	9.57633	+	0.542650i	0.867000	+	0.0491293i
$123$	2.74927	−	1.63960i	0.247893	−	0.147838i
$124$	−0.101491	−	0.646708i	−0.00911413	−	0.0580761i
$125$	10.7688	−	4.86781i	0.963191	−	0.435390i
$126$	2.22562	−	2.83761i	0.198274	−	0.252794i
$127$	16.7934	+	3.86871i	1.49017	+	0.343293i	0.889771	−	0.456407i	$-0.150864\pi$
$127$	16.7934	+	3.86871i	1.49017	+	0.343293i	0.600400	+	0.799700i	$0.295008\pi$
$128$	−6.14233	−	4.95958i	−0.542910	−	0.438370i
$129$	−6.69449	−	4.80617i	−0.589417	−	0.423160i
$130$	−8.81392	−	12.6510i	−0.773032	−	1.10956i
$131$	0.515765	+	0.392869i	0.0450626	+	0.0343252i	0.628239	−	0.778020i	$-0.283776\pi$
$131$	0.515765	+	0.392869i	0.0450626	+	0.0343252i	−0.583176	+	0.812346i	$0.698190\pi$
$132$	−0.149419	+	0.487904i	−0.0130052	+	0.0424666i
$133$	18.1163	−	2.05976i	1.57088	−	0.178604i
$134$	−3.78144	−	0.538725i	−0.326667	−	0.0465387i
$135$	−1.32582	−	1.59527i	−0.114108	−	0.137299i
$136$	−19.5167	+	3.34648i	−1.67355	+	0.286958i
$137$	16.8478	−	6.49462i	1.43940	−	0.554873i	0.490780	−	0.871284i	$-0.336712\pi$
$137$	16.8478	−	6.49462i	1.43940	−	0.554873i	0.948622	+	0.316411i	$0.102478\pi$
$138$	−0.351385	+	4.95782i	−0.0299119	+	0.422038i
$139$	−6.75913	−	20.0281i	−0.573302	−	1.69876i	−0.706537	−	0.707676i	$-0.749744\pi$
$139$	−6.75913	−	20.0281i	−0.573302	−	1.69876i	0.133235	−	0.991085i	$-0.457464\pi$
$140$	−0.437293	+	1.78252i	−0.0369580	+	0.150650i
$141$	−0.543880	+	12.8034i	−0.0458030	+	1.07824i
$142$	−11.7983	−	3.79661i	−0.990091	−	0.318605i
$143$	7.31216	−	5.56983i	0.611473	−	0.465772i
$144$	1.13025	+	3.06034i	0.0941874	+	0.255028i
$145$	−1.42917	−	0.597914i	−0.118686	−	0.0496540i
$146$	−0.588789	+	1.74465i	−0.0487285	+	0.144388i
$147$	0.618627	+	0.393084i	0.0510235	+	0.0324210i
$148$	−0.832221	+	1.26968i	−0.0684082	+	0.104367i
$149$	−2.21155	−	1.89155i	−0.181177	−	0.154962i	0.554763	−	0.832009i	$-0.312809\pi$
$149$	−2.21155	−	1.89155i	−0.181177	−	0.154962i	−0.735940	+	0.677047i	$0.763260\pi$
$150$	0.813178	+	0.395664i	0.0663957	+	0.0323058i
$151$	−7.33060	+	1.68876i	−0.596556	+	0.137429i	−0.511994	−	0.858989i	$-0.671093\pi$
$151$	−7.33060	+	1.68876i	−0.596556	+	0.137429i	−0.0845614	+	0.996418i	$0.526949\pi$
$152$	−8.37263	+	17.8452i	−0.679110	+	1.44743i
$153$	6.14578	+	2.36913i	0.496857	+	0.191533i
$154$	5.67022	+	1.13831i	0.456919	+	0.0917274i
$155$	0.181120	+	4.26370i	0.0145479	+	0.342469i
$156$	−0.484478	+	1.75824i	−0.0387892	+	0.140772i
$157$	−8.80508	−	3.98015i	−0.702722	−	0.317650i	0.0286880	−	0.999588i	$-0.490867\pi$
$157$	−8.80508	−	3.98015i	−0.702722	−	0.317650i	−0.731410	+	0.681938i	$0.761137\pi$
$158$	−0.160306	+	0.0836906i	−0.0127533	+	0.00665807i
$159$	−5.22772	+	5.01037i	−0.414585	+	0.397348i
$160$	−2.59497	−	2.63195i	−0.205150	−	0.208074i
$161$	−10.6534	+	0.301600i	−0.839606	+	0.0237694i
$162$	0.237234	−	1.27496i	0.0186389	−	0.100171i
$163$	0.820319	−	1.62701i	0.0642524	−	0.127437i	−0.858523	−	0.512775i	$-0.828618\pi$
$163$	0.820319	−	1.62701i	0.0642524	−	0.127437i	0.922776	+	0.385338i	$0.125915\pi$
$164$	−1.01487	+	0.0863778i	−0.0792477	+	0.00674497i
$165$	1.32716	−	3.05028i	0.103319	−	0.237464i
$166$	5.41380	+	0.615531i	0.420192	+	0.0477745i
$167$	16.9286	+	4.40788i	1.30998	+	0.341092i	0.840480	−	0.541842i	$-0.182273\pi$
$167$	16.9286	+	4.40788i	1.30998	+	0.341092i	0.469497	+	0.882934i	$0.344435\pi$
$168$	−7.51743	+	3.65772i	−0.579983	+	0.282199i
$169$	15.4462	−	12.4719i	1.18817	−	0.959379i
$170$	17.6898	−	1.00241i	1.35675	−	0.0768812i
$171$	5.43230	−	3.67160i	0.415418	−	0.280774i
$172$	1.24631	+	2.30709i	0.0950306	+	0.175914i
$173$	−7.91912	−	18.2010i	−0.602079	−	1.38379i	−0.902791	−	0.430080i	$-0.858485\pi$
$173$	−7.91912	−	18.2010i	−0.602079	−	1.38379i	0.300712	−	0.953715i	$-0.402776\pi$
$174$	−0.283617	−	0.926108i	−0.0215010	−	0.0702080i
$175$	−0.671814	+	1.81905i	−0.0507843	+	0.137507i
$176$	−3.56629	+	3.82800i	−0.268819	+	0.288546i
$177$	−1.01681	+	1.03130i	−0.0764280	+	0.0775173i
$178$	0.103926	−	7.34343i	0.00778959	−	0.550413i
$179$	−9.81270	+	6.23512i	−0.733435	+	0.466035i	−0.849755	−	0.527177i	$-0.823250\pi$
$179$	−9.81270	+	6.23512i	−0.733435	+	0.466035i	0.116320	+	0.993212i	$0.462890\pi$
$180$	0.157253	+	0.641004i	0.0117210	+	0.0477776i
$181$	−9.95796	+	1.99908i	−0.740169	+	0.148590i	−0.552349	−	0.833613i	$-0.686268\pi$
$181$	−9.95796	+	1.99908i	−0.740169	+	0.148590i	−0.187820	+	0.982203i	$0.560142\pi$
$182$	20.3730	+	3.49331i	1.51015	+	0.258941i
$183$	3.69808	+	6.40526i	0.273370	+	0.473491i
$184$	5.76099	−	9.97833i	0.424706	−	0.735613i
$185$	6.32565	−	7.61124i	0.465071	−	0.559590i
$186$	−1.97771	+	1.79090i	−0.145012	+	0.131315i
$187$	1.04463	+	10.5110i	0.0763912	+	0.768643i
$188$	1.93802	−	3.58753i	0.141345	−	0.261648i
$189$	2.77080	+	0.235830i	0.201546	+	0.0171541i
$190$	9.24762	−	15.0191i	0.670893	−	1.08960i
$191$	−11.9268	−	16.1261i	−0.862994	−	1.16684i	−0.984696	−	0.174278i	$-0.944241\pi$
$191$	−11.9268	−	16.1261i	−0.862994	−	1.16684i	0.121702	−	0.992567i	$-0.461165\pi$
$192$	0.873813	−	8.79225i	0.0630620	−	0.634526i
$193$	−3.46185	−	2.33980i	−0.249190	−	0.168423i	0.429012	−	0.903299i	$-0.358862\pi$
$193$	−3.46185	−	2.33980i	−0.249190	−	0.168423i	−0.678201	+	0.734876i	$0.737240\pi$
$194$	−1.90297	−	1.13488i	−0.136625	−	0.0814799i
$195$	4.43299	−	11.0319i	0.317453	−	0.790013i
$196$	−0.122276	−	0.198589i	−0.00873401	−	0.0141849i
$197$	−7.18771	−	14.2560i	−0.512103	−	1.01570i	−0.990495	−	0.137550i	$-0.956077\pi$
$197$	−7.18771	−	14.2560i	−0.512103	−	1.01570i	0.478391	−	0.878147i	$-0.341220\pi$
$198$	1.99699	−	0.580791i	0.141920	−	0.0412750i
$199$	−4.12361	−	2.15280i	−0.292315	−	0.152608i	0.310303	−	0.950638i	$-0.399569\pi$
$199$	−4.12361	−	2.15280i	−0.292315	−	0.152608i	−0.602618	+	0.798030i	$0.705876\pi$
$200$	−1.29379	−	1.64955i	−0.0914846	−	0.116641i
$201$	−1.25104	−	2.66642i	−0.0882412	−	0.188075i
$202$	0.720568	+	10.1668i	0.0506990	+	0.715330i
$203$	1.91596	−	0.801571i	0.134474	−	0.0562593i
$204$	−1.42859	−	1.53343i	−0.100021	−	0.107361i
$205$	6.63726	+	0.187902i	0.463566	+	0.0131236i
$206$	0.331077	−	1.53620i	0.0230672	−	0.107032i
$207$	−3.34589	+	1.86912i	−0.232555	+	0.129913i
$208$	−12.3540	+	14.0369i	−0.856598	+	0.973285i
$209$	9.17964	+	5.12805i	0.634969	+	0.354715i
$210$	7.05319	−	2.49205i	0.486717	−	0.171968i
$211$	−5.95279	+	8.54428i	−0.409807	+	0.588213i	−0.970884	−	0.239551i	$-0.923000\pi$
$211$	−5.95279	+	8.54428i	−0.409807	+	0.588213i	0.561077	+	0.827764i	$0.310387\pi$
$212$	2.19325	−	0.705773i	0.150633	−	0.0484727i
$213$	−2.53882	−	9.21373i	−0.173957	−	0.631314i
$214$	3.46228	−	22.0620i	0.236676	−	1.50813i
$215$	−6.37376	−	15.8617i	−0.434687	−	1.08176i
$216$	−1.78767	+	2.41708i	−0.121635	+	0.164462i
$217$	−4.24078	−	3.84020i	−0.287883	−	0.260690i
$218$	19.2751	−	2.74603i	1.30547	−	0.185985i
$219$	−1.37403	+	0.357770i	−0.0928484	+	0.0241758i
$220$	−0.804364	+	0.687976i	−0.0542302	+	0.0463834i
$221$	4.79527	+	37.4469i	0.322565	+	2.51895i
$222$	6.18744			0.415273
$223$	7.73167	−	12.7758i	0.517751	−	0.855532i
$223$	7.73167	−	12.7758i	0.517751	−	0.855532i
$224$	4.95502			0.331071
$225$	0.0885731	+	0.691680i	0.00590487	+	0.0461120i
$226$	−4.97710	+	4.25694i	−0.331072	+	0.283167i
$227$	7.54830	−	1.96543i	0.500999	−	0.130450i	0.00710937	−	0.999975i	$-0.497737\pi$
$227$	7.54830	−	1.96543i	0.500999	−	0.130450i	0.493889	+	0.869525i	$0.335575\pi$
$228$	−2.06541	+	0.294249i	−0.136785	+	0.0194871i
$229$	−19.6141	−	17.7614i	−1.29613	−	1.17370i	−0.973883	−	0.227051i	$-0.927092\pi$
$229$	−19.6141	−	17.7614i	−1.29613	−	1.17370i	−0.322252	−	0.946654i	$-0.604440\pi$
$230$	−6.13052	+	8.28901i	−0.404234	+	0.546561i
$231$	1.66277	+	4.13796i	0.109402	+	0.272258i
$232$	−0.348105	+	2.21816i	−0.0228542	+	0.145629i
$233$	−1.87027	−	6.78747i	−0.122525	−	0.444662i	0.876821	−	0.480817i	$-0.159660\pi$
$233$	−1.87027	−	6.78747i	−0.122525	−	0.444662i	−0.999346	+	0.0361555i	$0.988489\pi$
$234$	7.07585	−	2.27696i	0.462563	−	0.148850i
$235$	−15.1953	+	21.8105i	−0.991233	+	1.42276i
$236$	0.434497	−	0.153517i	0.0282833	−	0.00999314i
$237$	−0.121737	−	0.0680061i	−0.00790764	−	0.00441747i
$238$	−15.6932	+	17.8309i	−1.01724	+	1.15581i
$239$	−10.1363	+	5.66249i	−0.655664	+	0.366276i	−0.779835	−	0.625985i	$-0.784697\pi$
$239$	−10.1363	+	5.66249i	−0.655664	+	0.366276i	0.124171	+	0.992261i	$0.460373\pi$
$240$	−1.42569	+	6.61524i	−0.0920281	+	0.427012i
$241$	−7.03164	−	0.199067i	−0.452948	−	0.0128230i	−0.198911	−	0.980018i	$-0.563740\pi$
$241$	−7.03164	−	0.199067i	−0.452948	−	0.0128230i	−0.254037	+	0.967195i	$0.581758\pi$
$242$	−7.45054	−	7.99728i	−0.478939	−	0.514085i
$243$	0.922520	−	0.385950i	0.0591797	−	0.0247587i
$244$	−0.166377	−	2.34747i	−0.0106512	−	0.150282i
$245$	0.645774	+	1.37638i	0.0412570	+	0.0879339i
$246$	2.56195	+	3.26643i	0.163344	+	0.208260i
$247$	33.3146	+	17.3924i	2.11976	+	1.10665i
$248$	5.93902	−	1.72727i	0.377128	−	0.109682i
$249$	1.89152	+	3.75161i	0.119870	+	0.237749i
$250$	8.03554	+	13.0505i	0.508212	+	0.825389i
$251$	−8.60570	+	21.4161i	−0.543187	+	1.35177i	0.364139	+	0.931345i	$0.381363\pi$
$251$	−8.60570	+	21.4161i	−0.543187	+	1.35177i	−0.907326	+	0.420428i	$0.861880\pi$
$252$	−0.759939	−	0.453209i	−0.0478717	−	0.0285495i
$253$	−5.09220	−	3.44173i	−0.320144	−	0.216380i
$254$	−2.21024	+	22.2393i	−0.138683	+	1.39542i
$255$	8.12419	+	10.9846i	0.508757	+	0.687884i
$256$	−3.89715	+	6.32937i	−0.243572	+	0.395586i
$257$	8.10946	+	0.690217i	0.505854	+	0.0430545i	0.334955	−	0.942234i	$-0.391279\pi$
$257$	8.10946	+	0.690217i	0.505854	+	0.0430545i	0.170899	+	0.985289i	$0.445333\pi$
$258$	5.07965	−	9.40310i	0.316246	−	0.585412i
$259$	1.31214	+	13.2026i	0.0815322	+	0.820371i
$260$	−2.80415	+	2.53928i	−0.173906	+	0.157479i
$261$	0.477368	−	0.574386i	0.0295483	−	0.0355536i
$262$	−0.420407	+	0.728166i	−0.0259728	+	0.0449862i
$263$	−3.48577	−	6.03753i	−0.214942	−	0.372290i	0.738313	−	0.674458i	$-0.235623\pi$
$263$	−3.48577	−	6.03753i	−0.214942	−	0.372290i	−0.953255	+	0.302168i	$0.902289\pi$
$264$	−4.75185	−	0.814787i	−0.292456	−	0.0501467i
$265$	−14.7262	+	2.95632i	−0.904625	+	0.181605i
$266$	5.63373	+	22.9645i	0.345426	+	1.40804i
$267$	4.77979	−	3.03714i	0.292518	−	0.185870i
$268$	−0.0132616	+	0.937066i	−0.000810082	+	0.0572404i
$269$	6.72816	−	6.82405i	0.410223	−	0.416070i	−0.475915	−	0.879491i	$-0.657883\pi$
$269$	6.72816	−	6.82405i	0.410223	−	0.416070i	0.886138	+	0.463422i	$0.153378\pi$
$270$	1.83367	−	1.96823i	0.111594	−	0.119783i
$271$	−5.22679	+	14.1524i	−0.317505	+	0.859698i	0.675036	+	0.737785i	$0.264128\pi$
$271$	−5.22679	+	14.1524i	−0.317505	+	0.859698i	−0.992541	+	0.121913i	$0.961097\pi$
$272$	−6.29219	−	20.5461i	−0.381520	−	1.24579i
$273$	6.35908	+	14.6154i	0.384869	+	0.884567i
$274$	11.1295	+	20.6022i	0.672359	+	1.24462i
$275$	−0.926515	+	0.626215i	−0.0558710	+	0.0377622i
$276$	1.21752	−	0.0689918i	0.0732861	−	0.00415282i
$277$	−14.7767	+	11.9313i	−0.887845	+	0.716885i	−0.959848	−	0.280519i	$-0.909493\pi$
$277$	−14.7767	+	11.9313i	−0.887845	+	0.716885i	0.0720030	+	0.997404i	$0.477061\pi$
$278$	24.6496	−	11.9936i	1.47839	−	0.719331i
$279$	−1.99097	−	0.518408i	−0.119196	−	0.0310363i
$280$	−17.2302	−	1.95902i	−1.02970	−	0.117074i
$281$	5.97655	−	13.7363i	0.356531	−	0.819437i	−0.642074	−	0.766642i	$-0.721926\pi$
$281$	5.97655	−	13.7363i	0.356531	−	0.819437i	0.998605	−	0.0527943i	$-0.0168128\pi$
$282$	−16.5591	+	1.40939i	−0.986081	+	0.0839279i
$283$	11.9523	−	23.7061i	0.710493	−	1.40918i	−0.193270	−	0.981146i	$-0.561909\pi$
$283$	11.9523	−	23.7061i	0.710493	−	1.40918i	0.903763	−	0.428033i	$-0.140793\pi$
$284$	−0.556284	+	2.98963i	−0.0330094	+	0.177402i
$285$	13.5951	−	0.384879i	0.805302	−	0.0227983i
$286$	8.36919	+	8.48847i	0.494881	+	0.501934i
$287$	−6.42653	+	6.15933i	−0.379346	+	0.363574i
$288$	1.57955	−	0.824633i	0.0930761	−	0.0485920i
$289$	−24.0413	−	10.8674i	−1.41419	−	0.639256i
$290$	0.533706	−	1.93689i	0.0313403	−	0.113738i
$291$	−0.0725114	−	1.70698i	−0.00425070	−	0.100065i
$292$	0.442939	+	0.0889208i	0.0259210	+	0.00520370i
$293$	−19.5282	−	7.52788i	−1.14085	−	0.439784i	−0.285777	−	0.958296i	$-0.592252\pi$
$293$	−19.5282	−	7.52788i	−1.14085	−	0.439784i	−0.855070	+	0.518513i	$0.826486\pi$
$294$	−0.403739	+	0.860516i	−0.0235465	+	0.0501863i
$295$	−2.92745	+	0.674400i	−0.170443	+	0.0392651i
$296$	−12.8979	−	6.27567i	−0.749675	−	0.364766i
$297$	1.21871	+	1.04237i	0.0707168	+	0.0604845i
$298$	2.06889	−	3.15640i	0.119848	−	0.182845i
$299$	−18.5409	−	11.7812i	−1.07225	−	0.681322i
$300$	0.0709494	−	0.210231i	0.00409627	−	0.0121377i
$301$	21.1414	+	8.84479i	1.21857	+	0.509805i
$302$	−3.37984	−	9.15149i	−0.194488	−	0.526609i
$303$	−6.25205	+	4.76232i	−0.359171	+	0.273588i
$304$	−20.3622	−	6.55243i	−1.16785	−	0.375808i
$305$	−0.651123	+	15.3279i	−0.0372832	+	0.877676i
$306$	−2.03516	+	8.29584i	−0.116343	+	0.474241i
$307$	−1.66753	−	4.94109i	−0.0951712	−	0.282003i	0.889361	−	0.457205i	$-0.151149\pi$
$307$	−1.66753	−	4.94109i	−0.0951712	−	0.282003i	−0.984533	+	0.175202i	$0.943942\pi$
$308$	0.100318	−	1.41542i	0.00571613	−	0.0806510i
$309$	1.13066	−	0.435858i	0.0643212	−	0.0247951i
$310$	−5.45475	+	0.935311i	−0.309809	+	0.0531221i
$311$	4.95592	+	5.96314i	0.281024	+	0.338138i	0.890766	−	0.454462i	$-0.150168\pi$
$311$	4.95592	+	5.96314i	0.281024	+	0.338138i	−0.609742	+	0.792600i	$0.708727\pi$
$312$	−17.0593	−	2.43036i	−0.965791	−	0.137592i
$313$	−23.1813	+	2.63564i	−1.31028	+	0.148975i	−0.740075	−	0.672525i	$-0.765210\pi$
$313$	−23.1813	+	2.63564i	−1.31028	+	0.148975i	−0.570209	+	0.821500i	$0.693138\pi$
$314$	3.66944	−	11.9820i	0.207078	−	0.676182i
$315$	4.58863	+	3.49526i	0.258540	+	0.196935i
$316$	0.0253634	+	0.0364051i	0.00142680	+	0.00204795i
$317$	−7.01486	−	5.03617i	−0.393994	−	0.282860i	0.368791	−	0.929512i	$-0.379772\pi$
$317$	−7.01486	−	5.03617i	−0.393994	−	0.282860i	−0.762784	+	0.646653i	$0.776168\pi$
$318$	−7.30618	−	5.89933i	−0.409710	−	0.330818i
$319$	1.16715	+	0.268879i	0.0653481	+	0.0150543i
$320$	11.3108	−	14.4210i	0.632291	−	0.806156i
$321$	15.6916	−	7.09303i	0.875817	−	0.395894i
$322$	−2.14282	−	13.6543i	−0.119415	−	0.760922i
$323$	−37.0913	+	22.1203i	−2.06382	+	1.23081i
$324$	−0.317677	−	0.0180014i	−0.0176487	−	0.00100008i
$325$	−3.24681	+	2.33098i	−0.180100	+	0.129299i
$326$	2.22801	+	0.787207i	0.123398	+	0.0435994i
$327$	9.91877	+	11.2699i	0.548509	+	0.623228i
$328$	−2.02746	−	9.40745i	−0.111948	−	0.519440i
$329$	−6.51893	−	35.0346i	−0.359400	−	1.93152i
$330$	4.14233	+	1.20473i	0.228028	+	0.0663181i
$331$	18.1139	+	17.3608i	0.995631	+	0.954235i	0.998952	−	0.0457594i	$-0.0145708\pi$
$331$	18.1139	+	17.3608i	0.995631	+	0.954235i	−0.00332146	+	0.999994i	$0.501057\pi$
$332$	−0.0189177	−	1.33672i	−0.00103824	−	0.0733622i
$333$	2.61551	+	3.99034i	0.143329	+	0.218669i
$334$	−2.88151	+	22.5021i	−0.157669	+	1.23126i
$335$	0.776006	−	6.05995i	0.0423978	−	0.331090i
$336$	−4.97327	−	7.58745i	−0.271314	−	0.413929i
$337$	0.310617	+	21.9482i	0.0169204	+	1.19560i	0.809982	+	0.586454i	$0.199477\pi$
$337$	0.310617	+	21.9482i	0.0169204	+	1.19560i	−0.793062	+	0.609141i	$0.791514\pi$
$338$	18.5875	+	17.8147i	1.01103	+	0.968992i
$339$	−4.84923	−	1.41032i	−0.263374	−	0.0765981i
$340$	−0.795245	−	4.27388i	−0.0431282	−	0.231784i
$341$	−0.695103	−	3.22529i	−0.0376419	−	0.174659i
$342$	5.61776	+	6.38301i	0.303773	+	0.345154i
$343$	16.4320	+	5.80580i	0.887246	+	0.313484i
$344$	−20.1259	+	14.4490i	−1.08512	+	0.779036i
$345$	−7.93712	−	0.449763i	−0.427320	−	0.0242145i
$346$	22.1083	−	13.1848i	1.18855	−	0.708820i
$347$	1.01973	+	6.49784i	0.0547422	+	0.348822i	0.999762	+	0.0218099i	$0.00694285\pi$
$347$	1.01973	+	6.49784i	0.0547422	+	0.348822i	−0.945020	+	0.327013i	$0.893958\pi$
$348$	−0.216545	+	0.0978846i	−0.0116080	+	0.00524717i
$349$	9.29410	−	11.8498i	0.497502	−	0.634303i	−0.471349	−	0.881947i	$-0.656233\pi$
$349$	9.29410	−	11.8498i	0.497502	−	0.634303i	0.968851	+	0.247644i	$0.0796563\pi$
$350$	−2.45058	−	0.564544i	−0.130989	−	0.0301762i
$351$	4.45950	+	3.60079i	0.238030	+	0.192196i
$352$	2.32126	+	1.66650i	0.123724	+	0.0888248i
$353$	−8.61592	−	12.3668i	−0.458579	−	0.658217i	0.522317	−	0.852752i	$-0.325068\pi$
$353$	−8.61592	−	12.3668i	−0.458579	−	0.658217i	−0.980896	+	0.194534i	$0.937680\pi$
$354$	−1.49410	−	1.13809i	−0.0794104	−	0.0604886i
$355$	5.80498	−	18.9552i	0.308096	−	1.00604i
$356$	−1.79039	+	0.203561i	−0.0948903	+	0.0107887i
$357$	−18.1331	−	2.58334i	−0.959704	−	0.136725i
$358$	−9.63688	−	11.5954i	−0.509325	−	0.612838i
$359$	−21.4363	+	3.67561i	−1.13136	+	0.193992i	−0.704076	−	0.710125i	$-0.748638\pi$
$359$	−21.4363	+	3.67561i	−1.13136	+	0.193992i	−0.427286	+	0.904116i	$0.640530\pi$
$360$	−5.81864	+	2.24302i	−0.306669	+	0.118218i
$361$	−1.69607	+	23.9305i	−0.0892669	+	1.25950i
$362$	−4.21180	−	12.4801i	−0.221368	−	0.655937i
$363$	2.00809	−	8.18549i	0.105398	−	0.429627i
$364$	0.215243	−	5.06699i	0.0112818	−	0.265582i
$365$	−2.80359	−	0.902176i	−0.146746	−	0.0472220i
$366$	−7.63021	+	5.81209i	−0.398838	+	0.303803i
$367$	10.0658	+	27.2549i	0.525431	+	1.42269i	0.874237	+	0.485499i	$0.161362\pi$
$367$	10.0658	+	27.2549i	0.525431	+	1.42269i	−0.348806	+	0.937195i	$0.613413\pi$
$368$	11.5346	+	4.82565i	0.601280	+	0.251554i
$369$	−1.02358	+	3.03299i	−0.0532856	+	0.157891i
$370$	10.8327	+	6.88322i	0.563163	+	0.357841i
$371$	11.0385	−	16.8408i	0.573089	−	0.874331i
$372$	0.497479	+	0.425496i	0.0257931	+	0.0220609i
$373$	−16.7756	−	8.16243i	−0.868609	−	0.422635i	−0.0511968	−	0.998689i	$-0.516304\pi$
$373$	−16.7756	−	8.16243i	−0.868609	−	0.422635i	−0.817412	+	0.576054i	$0.804592\pi$
$374$	−13.3487	+	3.07517i	−0.690246	+	0.159013i
$375$	−5.01971	+	10.6988i	−0.259217	+	0.552486i
$376$	35.9475	+	13.8573i	1.85385	+	0.714638i
$377$	4.19706	+	0.842569i	0.216160	+	0.0433945i
$378$	0.153056	+	3.60305i	0.00787233	+	0.185321i
$379$	−8.82398	+	32.0235i	−0.453257	+	1.64493i	0.276342	+	0.961059i	$0.410878\pi$
$379$	−8.82398	+	32.0235i	−0.453257	+	1.64493i	−0.729599	+	0.683875i	$0.760293\pi$
$380$	−3.94335	−	1.78251i	−0.202289	−	0.0914406i
$381$	−15.2767	+	7.97545i	−0.782648	+	0.408594i
$382$	18.7791	−	17.9983i	0.960823	−	0.920874i
$383$	5.79666	+	5.87928i	0.296196	+	0.300417i	0.844167	−	0.536080i	$-0.180095\pi$
$383$	5.79666	+	5.87928i	0.296196	+	0.300417i	−0.547972	+	0.836497i	$0.684600\pi$
$384$	7.89150	−	0.223410i	0.402711	−	0.0114008i
$385$	−1.69218	+	9.09429i	−0.0862417	+	0.463488i
$386$	2.43955	−	4.83855i	0.124170	−	0.246276i
$387$	8.21140	−	0.698893i	0.417409	−	0.0355267i
$388$	−0.216888	+	0.498488i	−0.0110108	+	0.0253069i
$389$	−36.2383	−	4.12018i	−1.83736	−	0.208901i	−0.875643	−	0.482960i	$-0.839562\pi$
$389$	−36.2383	−	4.12018i	−1.83736	−	0.208901i	−0.961713	+	0.274058i	$0.911634\pi$
$390$	14.9211	+	3.88514i	0.755557	+	0.196732i
$391$	22.6993	−	11.0447i	1.14795	−	0.558553i
$392$	1.71439	−	1.38428i	0.0865899	−	0.0699165i
$393$	−0.647314	+	0.0366805i	−0.0326526	+	0.00185029i
$394$	17.1541	−	11.5942i	0.864211	−	0.584105i
$395$	−0.137477	−	0.254488i	−0.00691721	−	0.0128047i
$396$	−0.203580	−	0.467901i	−0.0102303	−	0.0235129i
$397$	−2.40219	−	7.84398i	−0.120563	−	0.393678i	0.875405	−	0.483390i	$-0.160595\pi$
$397$	−2.40219	−	7.84398i	−0.120563	−	0.393678i	−0.995968	+	0.0897118i	$0.971405\pi$
$398$	2.08999	−	5.65900i	0.104762	−	0.283660i
$399$	−12.4286	+	13.3407i	−0.622209	+	0.667868i
$400$	1.59721	−	1.61997i	0.0798605	−	0.0809987i
$401$	−0.199537	+	14.0993i	−0.00996439	+	0.704084i	0.930895	+	0.365287i	$0.119029\pi$
$401$	−0.199537	+	14.0993i	−0.00996439	+	0.704084i	−0.940859	+	0.338797i	$0.889980\pi$
$402$	3.22385	−	2.04848i	0.160791	−	0.102169i
$403$	−2.80960	−	11.4526i	−0.139956	−	0.570496i
$404$	2.45180	−	0.492203i	0.121981	−	0.0244880i
$405$	2.04445	+	0.350556i	0.101590	+	0.0174193i
$406$	1.34670	+	2.33255i	0.0668355	+	0.115763i
$407$	−3.82569	+	6.62629i	−0.189632	+	0.328453i
$408$	12.6565	−	15.2287i	0.626590	−	0.753935i
$409$	23.9916	−	21.7254i	1.18631	−	1.07425i	0.190601	−	0.981667i	$-0.438956\pi$
$409$	23.9916	−	21.7254i	1.18631	−	1.07425i	0.995705	−	0.0925828i	$-0.0295123\pi$
$410$	0.851601	+	8.56874i	0.0420576	+	0.423180i
$411$	−8.58198	+	15.8864i	−0.423318	+	0.783617i
$412$	−0.384179	−	0.0326984i	−0.0189271	−	0.00161094i
$413$	2.11158	−	3.42942i	0.103904	−	0.168751i
$414$	−2.95548	−	3.99607i	−0.145254	−	0.196396i
$415$	−0.861898	+	8.67236i	−0.0423089	+	0.425709i
$416$	8.46168	+	5.71910i	0.414868	+	0.280402i
$417$	18.1546	+	10.8269i	0.889032	+	0.530197i
$418$	−5.08434	+	12.6529i	−0.248683	+	0.618872i
$419$	2.99685	+	4.86719i	0.146406	+	0.237778i	0.916392	−	0.400283i	$-0.131088\pi$
$419$	2.99685	+	4.86719i	0.146406	+	0.237778i	−0.769986	+	0.638061i	$0.779737\pi$
$420$	−0.826291	−	1.63885i	−0.0403189	−	0.0799677i
$421$	32.5696	−	9.47235i	1.58735	−	0.461654i	0.636490	−	0.771285i	$-0.280385\pi$
$421$	32.5696	−	9.47235i	1.58735	−	0.461654i	0.950857	+	0.309630i	$0.100205\pi$
$422$	−11.9714	−	6.24989i	−0.582761	−	0.304240i
$423$	−7.90869	−	10.0834i	−0.384534	−	0.490271i
$424$	9.24650	+	19.7077i	0.449050	+	0.957090i
$425$	−0.324716	−	4.58153i	−0.0157510	−	0.222237i
$426$	11.4338	−	4.78350i	0.553970	−	0.231761i
$427$	−14.0198	−	15.0486i	−0.678467	−	0.728255i
$428$	−5.47706	−	0.155057i	−0.264743	−	0.00749494i
$429$	−1.93654	+	8.98557i	−0.0934970	+	0.433827i
$430$	19.3537	−	10.8116i	0.933318	−	0.521383i
$431$	−4.63464	+	5.26597i	−0.223243	+	0.253653i	−0.851502	−	0.524351i	$-0.824308\pi$
$431$	−4.63464	+	5.26597i	−0.223243	+	0.253653i	0.628260	+	0.778004i	$0.283768\pi$
$432$	−2.84811	−	1.59105i	−0.137030	−	0.0765493i
$433$	30.2813	−	10.6991i	1.45523	−	0.514165i	0.515739	−	0.856745i	$-0.327517\pi$
$433$	30.2813	−	10.6991i	1.45523	−	0.514165i	0.939488	+	0.342581i	$0.111301\pi$
$434$	4.24127	−	6.08766i	0.203587	−	0.292217i
$435$	1.47473	−	0.474558i	0.0707078	−	0.0227533i
$436$	−1.26899	−	4.60534i	−0.0607735	−	0.220556i
$437$	3.89593	−	24.8252i	0.186367	−	1.18755i
$438$	−0.686549	−	1.70854i	−0.0328046	−	0.0816373i
$439$	−22.7736	+	30.7920i	−1.08693	+	1.46962i	−0.217173	+	0.976133i	$0.569684\pi$
$439$	−22.7736	+	30.7920i	−1.08693	+	1.46962i	−0.869753	+	0.493487i	$0.835722\pi$
$440$	−7.41290	−	6.71269i	−0.353396	−	0.320015i
$441$	−0.725622	+	0.103376i	−0.0345534	+	0.00492267i
$442$	−47.3797	+	12.3367i	−2.25362	+	0.586798i
$443$	3.34446	−	2.86053i	0.158900	−	0.135908i	−0.566974	−	0.823736i	$-0.691886\pi$
$443$	3.34446	−	2.86053i	0.158900	−	0.135908i	0.725874	+	0.687828i	$0.241436\pi$
$444$	−0.192827	−	1.50582i	−0.00915119	−	0.0714629i
$445$	11.7469			0.556856
$446$	17.7077	+	7.84111i	0.838482	+	0.371287i
$447$	2.91014			0.137645
$448$	3.12084	+	24.3711i	0.147446	+	1.15143i
$449$	11.6292	−	9.94650i	0.548815	−	0.469404i	−0.331725	−	0.943376i	$-0.607631\pi$
$449$	11.6292	−	9.94650i	0.548815	−	0.469404i	0.880540	+	0.473972i	$0.157180\pi$
$450$	−0.875148	+	0.227871i	−0.0412549	+	0.0107419i
$451$	−5.08216	+	0.724032i	−0.239310	+	0.0340933i
$452$	1.19111	+	1.07860i	0.0560249	+	0.0507329i
$453$	4.47319	−	6.04815i	0.210169	−	0.284167i
$454$	3.77159	+	9.38596i	0.177009	+	0.440505i
$455$	−5.12581	+	32.6622i	−0.240302	+	1.53123i
$456$	−5.23635	−	19.0034i	−0.245215	−	0.889918i
$457$	−10.7380	+	3.45542i	−0.502302	+	0.161638i	−0.546622	−	0.837380i	$-0.684086\pi$
$457$	−10.7380	+	3.45542i	−0.502302	+	0.161638i	0.0443191	+	0.999017i	$0.485888\pi$
$458$	19.6163	−	28.1561i	0.916611	−	1.31565i
$459$	−6.21036	+	2.19426i	−0.289875	+	0.102419i
$460$	2.20832	+	1.23364i	0.102964	+	0.0575189i
$461$	1.36211	−	1.54766i	0.0634399	−	0.0720818i	−0.718087	−	0.695954i	$-0.754982\pi$
$461$	1.36211	−	1.54766i	0.0634399	−	0.0720818i	0.781527	+	0.623872i	$0.214441\pi$
$462$	−5.04895	+	2.82051i	−0.234898	+	0.131222i
$463$	−1.92895	+	8.95036i	−0.0896459	+	0.415958i	0.910352	+	0.413835i	$0.135811\pi$
$463$	−1.92895	+	8.95036i	−0.0896459	+	0.415958i	−0.999998	+	0.00212329i	$0.999324\pi$
$464$	−2.43557	−	0.0689514i	−0.113068	−	0.00320099i
$465$	−2.90899	−	3.12246i	−0.134901	−	0.144801i
$466$	8.42294	−	3.52386i	0.390185	−	0.163240i
$467$	1.24676	+	17.5910i	0.0576931	+	0.814013i	0.939532	+	0.342462i	$0.111261\pi$
$467$	1.24676	+	17.5910i	0.0576931	+	0.814013i	−0.881839	+	0.471551i	$0.843694\pi$
$468$	−0.774652	−	1.65107i	−0.0358083	−	0.0763207i
$469$	5.05467	+	6.44458i	0.233403	+	0.297583i
$470$	−30.5588	−	15.9537i	−1.40957	−	0.735890i
$471$	9.27843	−	2.69848i	0.427527	−	0.124339i
$472$	1.96018	+	3.88778i	0.0902245	+	0.178950i
$473$	6.92929	+	11.2539i	0.318609	+	0.517454i
$474$	0.0674265	−	0.167797i	0.00309700	−	0.00770718i
$475$	−3.92688	−	2.34189i	−0.180177	−	0.107453i
$476$	4.82852	+	3.26351i	0.221315	+	0.149583i
$477$	0.716121	−	7.20556i	0.0327889	−	0.329920i
$478$	−8.95359	−	12.1061i	−0.409528	−	0.553718i
$479$	−22.0606	+	35.8288i	−1.00798	+	1.63706i	−0.269228	+	0.963077i	$0.586768\pi$
$479$	−22.0606	+	35.8288i	−1.00798	+	1.63706i	−0.738749	+	0.673981i	$0.764583\pi$
$480$	3.68277	+	0.313450i	0.168095	+	0.0143070i
$481$	−12.9978	+	24.0606i	−0.592647	+	1.09707i
$482$	−0.902203	−	9.07790i	−0.0410942	−	0.413487i
$483$	7.89998	−	7.15377i	0.359462	−	0.325508i
$484$	−1.71408	+	2.06244i	−0.0779129	+	0.0937475i
$485$	1.77198	−	3.06915i	0.0804613	−	0.139363i
$486$	0.648424	+	1.12310i	0.0294131	+	0.0509450i
$487$	−35.7573	−	6.13120i	−1.62032	−	0.277831i	−0.713910	−	0.700238i	$-0.753077\pi$
$487$	−35.7573	−	6.13120i	−1.62032	−	0.277831i	−0.906406	+	0.422407i	$0.861185\pi$
$488$	21.8004	−	4.37647i	0.986857	−	0.198113i
$489$	0.434133	+	1.76963i	0.0196322	+	0.0800256i
$490$	−1.66413	+	1.05741i	−0.0751776	+	0.0477689i
$491$	−0.299214	+	21.1425i	−0.0135033	+	0.954147i	0.871998	+	0.489510i	$0.162824\pi$
$491$	−0.299214	+	21.1425i	−0.0135033	+	0.954147i	−0.885501	+	0.464637i	$0.846185\pi$
$492$	0.715099	−	0.725291i	0.0322391	−	0.0326986i
$493$	−3.35324	+	3.59931i	−0.151022	+	0.162105i
$494$	−16.8850	+	45.7189i	−0.759691	+	2.05699i
$495$	0.974074	+	3.18069i	0.0437814	+	0.142961i
$496$	2.67781	+	6.15457i	0.120237	+	0.276348i
$497$	12.6316	+	23.3828i	0.566607	+	1.04886i
$498$	−4.51428	+	3.05112i	−0.202290	+	0.136724i
$499$	23.9089	−	1.35482i	1.07031	−	0.0606500i	0.487394	−	0.873182i	$-0.337948\pi$
$499$	23.9089	−	1.35482i	1.07031	−	0.0606500i	0.582916	+	0.812532i	$0.301912\pi$
$500$	2.92565	−	2.36230i	0.130839	−	0.105645i
$501$	−15.7299	+	7.65363i	−0.702761	+	0.341939i
$502$	−28.9660	−	7.54217i	−1.29282	−	0.336623i
$503$	21.1938	+	2.40967i	0.944985	+	0.107442i	0.571871	−	0.820344i	$-0.306218\pi$
$503$	21.1938	+	2.40967i	0.944985	+	0.107442i	0.373114	+	0.927785i	$0.378290\pi$
$504$	3.33538	−	7.66590i	0.148570	−	0.341466i
$505$	−16.2436	+	1.38254i	−0.722832	+	0.0615221i
$506$	3.58844	−	7.11725i	0.159526	−	0.316400i
$507$	−3.63170	+	19.5178i	−0.161289	+	0.866816i
$508$	5.48120	−	0.155174i	0.243189	−	0.00688472i
$509$	−24.1197	−	24.4635i	−1.06909	−	1.08432i	−0.996210	−	0.0869841i	$-0.972277\pi$
$509$	−24.1197	−	24.4635i	−1.06909	−	1.08432i	−0.0728781	−	0.997341i	$-0.523218\pi$
$510$	−12.7918	+	12.2599i	−0.566429	+	0.542878i
$511$	3.50006	−	1.82727i	0.154834	−	0.0808335i
$512$	−23.1714	−	10.4741i	−1.02404	−	0.462895i
$513$	−1.74177	+	6.32113i	−0.0769011	+	0.279085i
$514$	0.447956	+	10.5452i	0.0197585	+	0.465131i
$515$	2.46438	+	0.494729i	0.108594	+	0.0218004i
$516$	−2.44671	−	0.943178i	−0.107710	−	0.0415211i
$517$	8.72915	−	18.6050i	0.383908	−	0.818248i
$518$	−16.7670	+	3.86263i	−0.736698	+	0.169714i
$519$	17.8485	+	8.68445i	0.783461	+	0.381205i
$520$	−27.1629	−	23.2325i	−1.19117	−	1.01881i
$521$	16.3154	−	24.8915i	0.714789	−	1.09051i	−0.276780	−	0.960933i	$-0.589267\pi$
$521$	16.3154	−	24.8915i	0.714789	−	1.09051i	0.991569	−	0.129582i	$-0.0413634\pi$
$522$	0.817491	+	0.519445i	0.0357806	+	0.0227355i
$523$	13.4764	−	39.9323i	0.589284	−	1.74612i	−0.0734892	−	0.997296i	$-0.523413\pi$
$523$	13.4764	−	39.9323i	0.589284	−	1.74612i	0.662773	−	0.748820i	$-0.269379\pi$
$524$	0.190313	+	0.0796203i	0.00831387	+	0.00347823i
$525$	−0.671814	−	1.81905i	−0.0293203	−	0.0793898i
$526$	7.19215	−	5.47841i	0.313593	−	0.238870i
$527$	12.8996	+	4.15099i	0.561914	+	0.180820i
$528$	0.222045	−	5.22711i	0.00966326	−	0.227481i
$529$	1.98026	−	8.07205i	0.0860984	−	0.350959i
$530$	−6.22858	−	18.4560i	−0.270552	−	0.801678i
$531$	0.102389	−	1.44464i	0.00444331	−	0.0626922i
$532$	5.41323	−	2.08674i	0.234693	−	0.0904716i
$533$	−18.0837	+	3.10076i	−0.783292	+	0.134309i
$534$	4.69415	+	5.64816i	0.203136	+	0.244420i
$535$	35.3626	+	5.03796i	1.52886	+	0.217810i
$536$	−8.79791	+	1.00029i	−0.380012	+	0.0432061i
$537$	3.40438	−	11.1165i	0.146910	−	0.479711i
$538$	9.88635	+	7.53065i	0.426231	+	0.324669i
$539$	−0.671918	−	0.964432i	−0.0289416	−	0.0415410i
$540$	−0.536148	−	0.384916i	−0.0230721	−	0.0165642i
$541$	−17.7488	−	14.3311i	−0.763080	−	0.616144i	0.165956	−	0.986133i	$-0.446929\pi$
$541$	−17.7488	−	14.3311i	−0.763080	−	0.616144i	−0.929036	+	0.369989i	$0.879361\pi$
$542$	−19.0658	−	4.39222i	−0.818948	−	0.188662i
$543$	6.26814	−	7.99173i	0.268992	−	0.342958i
$544$	−10.6945	+	4.83423i	−0.458524	+	0.207266i
$545$	4.82807	+	30.7649i	0.206812	+	1.31783i
$546$	−17.7530	+	10.5875i	−0.759758	+	0.453101i
$547$	37.4557	+	2.12246i	1.60149	+	0.0907497i	0.834536	−	0.550954i	$-0.185736\pi$
$547$	37.4557	+	2.12246i	1.60149	+	0.0907497i	0.766953	+	0.641703i	$0.221772\pi$
$548$	4.66705	−	3.35061i	0.199367	−	0.143131i
$549$	−6.97367	−	2.46396i	−0.297629	−	0.105159i
$550$	−0.958146	−	1.08866i	−0.0408555	−	0.0464208i
$551$	1.03168	+	4.78703i	0.0439513	+	0.203935i
$552$	2.10773	+	11.3276i	0.0897110	+	0.482133i
$553$	0.372341	+	0.108289i	0.0158335	+	0.00460493i
$554$	−17.7819	−	17.0425i	−0.755479	−	0.724068i
$555$	0.140047	+	9.89572i	0.00594466	+	0.420050i
$556$	−3.68705	−	5.62513i	−0.156366	−	0.238559i
$557$	5.33620	−	41.6711i	0.226102	−	1.76566i	−0.339138	−	0.940737i	$-0.610135\pi$
$557$	5.33620	−	41.6711i	0.226102	−	1.76566i	0.565240	−	0.824926i	$-0.308784\pi$
$558$	0.338893	−	2.64647i	0.0143465	−	0.112034i
$559$	25.8944	+	39.5057i	1.09522	+	1.67091i
$560$	−0.266293	−	18.8163i	−0.0112529	−	0.795132i
$561$	−7.62589	−	7.30883i	−0.321965	−	0.308579i
$562$	18.6540	+	5.42522i	0.786872	+	0.228849i
$563$	−2.48962	−	13.3800i	−0.104925	−	0.563898i	−0.994291	−	0.106702i	$-0.965971\pi$
$563$	−2.48962	−	13.3800i	−0.104925	−	0.563898i	0.889366	−	0.457196i	$-0.151146\pi$
$564$	0.859053	+	3.98602i	0.0361727	+	0.167842i
$565$	−6.92088	−	7.86365i	−0.291164	−	0.330826i
$566$	32.4630	+	11.4699i	1.36452	+	0.482115i
$567$	−2.25895	+	1.62176i	−0.0948668	+	0.0681076i
$568$	−28.6858	−	1.62551i	−1.20363	−	0.0682048i
$569$	18.1466	−	10.8222i	0.760743	−	0.453689i	−0.0788620	−	0.996886i	$-0.525129\pi$
$569$	18.1466	−	10.8222i	0.760743	−	0.453689i	0.839605	+	0.543197i	$0.182786\pi$
$570$	2.73450	+	17.4245i	0.114536	+	0.729833i
$571$	13.4427	−	6.07647i	0.562558	−	0.254292i	−0.110507	−	0.993875i	$-0.535248\pi$
$571$	13.4427	−	6.07647i	0.562558	−	0.254292i	0.673065	+	0.739583i	$0.264977\pi$
$572$	1.80499	−	2.30132i	0.0754705	−	0.0962231i
$573$	19.5455	+	4.50272i	0.816524	+	0.188104i
$574$	−8.98162	−	7.25215i	−0.374885	−	0.302699i
$575$	2.17100	+	1.55863i	0.0905370	+	0.0649992i
$576$	5.05079	+	7.24960i	0.210449	+	0.302067i
$577$	10.0704	+	7.67086i	0.419237	+	0.319342i	0.794154	−	0.607716i	$-0.207914\pi$
$577$	10.0704	+	7.67086i	0.419237	+	0.319342i	−0.374917	+	0.927058i	$0.622329\pi$
$578$	10.0190	−	32.7155i	0.416736	−	1.36078i
$579$	4.15166	−	0.472030i	0.172537	−	0.0196169i
$580$	−0.488008	−	0.0695243i	−0.0202634	−	0.00288684i
$581$	−7.46774	−	8.98545i	−0.309814	−	0.372779i
$582$	2.18381	−	0.374452i	0.0905220	−	0.0155215i
$583$	10.8352	−	4.17683i	0.448746	−	0.172987i
$584$	−0.301775	+	4.25785i	−0.0124875	+	0.176191i
$585$	3.80176	+	11.2651i	0.157183	+	0.465753i
$586$	6.46671	−	26.3599i	0.267137	−	1.08892i
$587$	−0.0722107	+	1.69990i	−0.00298045	+	0.0701622i	−0.999973	−	0.00733393i	$-0.997666\pi$
$587$	−0.0722107	+	1.69990i	−0.00298045	+	0.0701622i	0.996993	+	0.0774961i	$0.0246925\pi$
$588$	0.222003	+	0.0714393i	0.00915527	+	0.00294611i
$589$	10.7309	−	8.17397i	0.442160	−	0.336803i
$590$	−1.34973	−	3.65461i	−0.0555674	−	0.150458i
$591$	14.7285	+	6.16187i	0.605848	+	0.253465i
$592$	4.97721	−	14.7481i	0.204562	−	0.606141i
$593$	−3.72517	−	2.36702i	−0.152974	−	0.0972020i	0.457611	−	0.889153i	$-0.348705\pi$
$593$	−3.72517	−	2.36702i	−0.152974	−	0.0972020i	−0.610585	+	0.791951i	$0.709066\pi$
$594$	−1.14010	+	1.73938i	−0.0467787	+	0.0713678i
$595$	−28.8726	−	24.6949i	−1.18366	−	1.01239i
$596$	−0.832638	−	0.405133i	−0.0341062	−	0.0165949i
$597$	4.53301	−	1.04428i	0.185524	−	0.0427394i
$598$	12.1005	−	25.7906i	0.494826	−	1.05466i
$599$	15.3334	+	5.91086i	0.626507	+	0.241511i	0.652066	−	0.758162i	$-0.273902\pi$
$599$	15.3334	+	5.91086i	0.626507	+	0.241511i	−0.0255593	+	0.999673i	$0.508137\pi$
$600$	2.05539	+	0.412624i	0.0839110	+	0.0168453i
$601$	−0.290219	−	6.83198i	−0.0118383	−	0.278682i	−0.995254	−	0.0973146i	$-0.968975\pi$
$601$	−0.290219	−	6.83198i	−0.0118383	−	0.278682i	0.983415	−	0.181367i	$-0.0580523\pi$
$602$	−7.89498	+	28.6520i	−0.321775	+	1.16777i
$603$	2.68385	+	1.21318i	0.109295	+	0.0494044i
$604$	−2.12184	+	1.10774i	−0.0863364	+	0.0450734i
$605$	12.6216	−	12.0968i	0.513142	−	0.491807i
$606$	−7.15584	−	7.25783i	−0.290686	−	0.294829i
$607$	46.8771	−	1.32710i	1.90268	−	0.0538653i	0.942655	−	0.333769i	$-0.108320\pi$
$607$	46.8771	−	1.32710i	1.90268	−	0.0538653i	0.960028	+	0.279903i	$0.0903024\pi$
$608$	−2.13721	+	11.4860i	−0.0866752	+	0.465818i
$609$	−0.935019	+	1.85450i	−0.0378889	+	0.0751481i
$610$	−19.8243	+	1.68729i	−0.802661	+	0.0683165i
$611$	29.3047	−	67.3527i	1.18554	−	2.72480i
$612$	2.08236	+	0.236757i	0.0841743	+	0.00957034i
$613$	38.7184	+	10.0815i	1.56382	+	0.407187i	0.930378	−	0.366603i	$-0.119479\pi$
$613$	38.7184	+	10.0815i	1.56382	+	0.407187i	0.633443	+	0.773790i	$0.281641\pi$
$614$	6.08126	−	2.95893i	0.245420	−	0.119413i
$615$	−5.16609	+	4.17133i	−0.208317	+	0.168204i
$616$	13.3854	−	0.758495i	0.539314	−	0.0305606i
$617$	−15.5072	+	10.4811i	−0.624298	+	0.421952i	−0.830860	−	0.556482i	$-0.812151\pi$
$617$	−15.5072	+	10.4811i	−0.624298	+	0.421952i	0.206562	+	0.978434i	$0.433773\pi$
$618$	0.746909	+	1.38263i	0.0300451	+	0.0556174i
$619$	−8.89977	−	20.4549i	−0.357712	−	0.822151i	−0.998517	−	0.0544470i	$-0.982660\pi$
$619$	−8.89977	−	20.4549i	−0.357712	−	0.822151i	0.640805	−	0.767704i	$-0.278601\pi$
$620$	0.397618	+	1.29836i	0.0159687	+	0.0521433i
$621$	1.32779	−	3.59521i	0.0532824	−	0.144271i
$622$	−6.85429	+	7.35728i	−0.274832	+	0.295000i
$623$	−11.0565	+	11.2140i	−0.442968	+	0.449281i
$624$	0.264608	−	18.6973i	0.0105928	−	0.748489i
$625$	−17.7474	+	11.2769i	−0.709895	+	0.451077i
$626$	−7.20882	−	29.3850i	−0.288122	−	1.17446i
$627$	−10.3092	+	2.06959i	−0.411710	+	0.0826515i
$628$	−3.03037	−	0.519610i	−0.120925	−	0.0207347i
$629$	−15.7128	−	27.2154i	−0.626510	−	1.08515i
$630$	−3.74025	+	6.47830i	−0.149015	+	0.258102i
$631$	−28.3687	+	34.1342i	−1.12934	+	1.35886i	−0.204338	+	0.978900i	$0.565504\pi$
$631$	−28.3687	+	34.1342i	−1.12934	+	1.35886i	−0.925003	+	0.379961i	$0.875937\pi$
$632$	−0.310743	+	0.281390i	−0.0123607	+	0.0111931i
$633$	−1.02986	−	10.3624i	−0.0409334	−	0.411869i
$634$	5.32274	−	9.85309i	0.211393	−	0.391316i
$635$	−35.6179	−	3.03153i	−1.41345	−	0.120303i
$636$	−1.20801	+	1.96193i	−0.0479007	+	0.0777956i
$637$	−2.49809	−	3.37765i	−0.0989781	−	0.133827i
$638$	−0.153614	+	1.54565i	−0.00608163	+	0.0611929i
$639$	7.91816	+	5.35174i	0.313237	+	0.211712i
$640$	14.0646	+	8.38777i	0.555951	+	0.331556i
$641$	0.997270	−	2.48180i	0.0393898	−	0.0980253i	−0.906899	−	0.421349i	$-0.861557\pi$
$641$	0.997270	−	2.48180i	0.0393898	−	0.0980253i	0.946289	+	0.323323i	$0.104800\pi$
$642$	11.7088	+	19.0163i	0.462111	+	0.750515i
$643$	3.57840	+	7.09733i	0.141118	+	0.279892i	0.952450	−	0.304694i	$-0.0985543\pi$
$643$	3.57840	+	7.09733i	0.141118	+	0.279892i	−0.811332	+	0.584586i	$0.801257\pi$
$644$	−3.25622	+	0.947018i	−0.128313	+	0.0373177i
$645$	15.1536	+	7.91119i	0.596672	+	0.311503i
$646$	−34.5641	−	44.0684i	−1.35991	−	1.73385i
$647$	−14.1793	−	30.2213i	−0.557446	−	1.18812i	−0.961859	−	0.273546i	$-0.911803\pi$
$647$	−14.1793	−	30.2213i	−0.557446	−	1.18812i	0.404413	−	0.914576i	$-0.367476\pi$
$648$	−0.212541	−	2.99881i	−0.00834938	−	0.117804i
$649$	2.14261	−	0.896391i	0.0841047	−	0.0351864i
$650$	−3.53326	−	3.79254i	−0.138586	−	0.148756i
$651$	5.71884	+	0.161901i	0.224139	+	0.00634542i
$652$	0.122146	−	0.566758i	0.00478359	−	0.0221959i
$653$	23.6864	−	13.2320i	0.926921	−	0.517809i	0.0501632	−	0.998741i	$-0.484026\pi$
$653$	23.6864	−	13.2320i	0.926921	−	0.517809i	0.876758	+	0.480932i	$0.159702\pi$
$654$	−12.8631	+	14.6154i	−0.502988	+	0.571506i
$655$	−1.17409	−	0.655886i	−0.0458755	−	0.0256276i
$656$	9.84654	−	3.47900i	0.384443	−	0.135832i
$657$	0.811644	−	1.16499i	0.0316653	−	0.0454505i
$658$	43.9927	−	14.1566i	1.71502	−	0.551881i
$659$	−8.27264	−	30.0226i	−0.322256	−	1.16951i	−0.927608	−	0.373555i	$-0.878139\pi$
$659$	−8.27264	−	30.0226i	−0.322256	−	1.16951i	0.605351	−	0.795958i	$-0.293033\pi$
$660$	0.164098	−	1.04565i	0.00638751	−	0.0407019i
$661$	17.5983	+	43.7950i	0.684493	+	1.70343i	0.710435	+	0.703763i	$0.248498\pi$
$661$	17.5983	+	43.7950i	0.684493	+	1.70343i	−0.0259419	+	0.999663i	$0.508258\pi$
$662$	−19.3482	+	26.1604i	−0.751988	+	1.01675i
$663$	−27.9841	−	25.3408i	−1.08681	−	0.984155i
$664$	12.5048	−	1.78150i	0.485280	−	0.0691357i
$665$	−36.6002	+	9.52995i	−1.41930	+	0.369556i
$666$	−4.70212	+	4.02175i	−0.182203	+	0.155839i
$667$	−0.363575	−	2.83921i	−0.0140777	−	0.109935i
$668$	5.56607			0.215358
$669$	2.42845	+	14.7344i	0.0938892	+	0.569665i
$670$	7.92300			0.306092
$671$	−1.50657	−	11.7650i	−0.0581605	−	0.454183i
$672$	−3.76555	+	3.22069i	−0.145259	+	0.124241i
$673$	−28.7769	+	7.49293i	−1.10927	+	0.288831i	−0.761122	−	0.648609i	$-0.775351\pi$
$673$	−28.7769	+	7.49293i	−1.10927	+	0.288831i	−0.348147	+	0.937440i	$0.613189\pi$
$674$	−28.1818	+	4.01493i	−1.08552	+	0.154649i
$675$	−0.516893	−	0.468068i	−0.0198952	−	0.0180160i
$676$	3.75624	−	5.07877i	0.144471	−	0.195337i
$677$	−4.45297	−	11.0816i	−0.171141	−	0.425902i	0.817552	−	0.575855i	$-0.195331\pi$
$677$	−4.45297	−	11.0816i	−0.171141	−	0.425902i	−0.988693	+	0.149954i	$0.952088\pi$
$678$	1.01538	−	6.47009i	0.0389953	−	0.248482i
$679$	1.26211	+	4.58037i	0.0484352	+	0.175778i
$680$	39.0996	−	12.5820i	1.49940	−	0.482497i
$681$	−4.45881	+	6.39991i	−0.170862	+	0.245245i
$682$	4.03433	−	1.42542i	0.154482	−	0.0545821i
$683$	26.0828	+	14.5707i	0.998031	+	0.557533i	0.899185	−	0.437569i	$-0.144161\pi$
$683$	26.0828	+	14.5707i	0.998031	+	0.557533i	0.0988459	+	0.995103i	$0.468485\pi$
$684$	1.37834	−	1.56610i	0.0527021	−	0.0598813i
$685$	−32.6977	+	18.2660i	−1.24932	+	0.697909i
$686$	−4.76153	+	22.0936i	−0.181796	+	0.843537i
$687$	26.4503	+	0.748813i	1.00914	+	0.0285690i
$688$	−18.3267	−	19.6715i	−0.698697	−	0.749970i
$689$	38.2881	−	16.0184i	1.45866	−	0.610252i
$690$	−0.728874	−	10.2840i	−0.0277478	−	0.391503i
$691$	−4.60188	−	9.80831i	−0.175064	−	0.373126i	0.798345	−	0.602200i	$-0.205709\pi$
$691$	−4.60188	−	9.80831i	−0.175064	−	0.373126i	−0.973409	+	0.229075i	$0.926430\pi$
$692$	−3.89774	−	4.96952i	−0.148170	−	0.188913i
$693$	−3.95323	−	2.06385i	−0.150171	−	0.0783993i
$694$	−8.19048	+	2.38207i	−0.310907	+	0.0904221i
$695$	19.7397	+	39.1513i	0.748768	+	1.48509i
$696$	−1.17723	−	1.91195i	−0.0446229	−	0.0724721i
$697$	7.86135	−	19.5637i	0.297770	−	0.741029i
$698$	16.7738	+	10.0035i	0.634898	+	0.378637i
$699$	5.83306	+	3.94246i	0.220627	+	0.149118i
$700$	−0.0610206	+	0.613985i	−0.00230636	+	0.0232064i
$701$	27.9160	+	37.7449i	1.05437	+	1.42561i	0.899104	+	0.437734i	$0.144219\pi$
$701$	27.9160	+	37.7449i	1.05437	+	1.42561i	0.155269	+	0.987872i	$0.450376\pi$
$702$	−3.89727	+	6.32958i	−0.147093	+	0.238894i
$703$	−31.1703	−	2.65298i	−1.17561	−	0.100059i
$704$	−6.73462	+	12.4667i	−0.253820	+	0.469855i
$705$	−2.62887	−	26.4515i	−0.0990090	−	0.996222i
$706$	14.4887	−	13.1201i	0.545289	−	0.493782i
$707$	13.9691	−	16.8081i	0.525362	−	0.632134i
$708$	−0.230410	+	0.399082i	−0.00865934	+	0.0149984i
$709$	−14.8211	−	25.6708i	−0.556617	−	0.964089i	−0.997776	−	0.0666596i	$-0.978766\pi$
$709$	−14.8211	−	25.6708i	−0.556617	−	0.964089i	0.441159	−	0.897429i	$-0.354567\pi$
$710$	25.3392	+	4.34484i	0.950962	+	0.163059i
$711$	0.136716	−	0.0274461i	0.00512726	−	0.00102931i
$712$	−4.05639	−	16.5349i	−0.152020	−	0.619670i
$713$	−6.65510	+	4.22874i	−0.249235	+	0.158368i
$714$	0.336129	−	23.7509i	0.0125793	−	0.888854i
$715$	−13.3864	+	13.5772i	−0.500623	+	0.507758i
$716$	−2.52162	+	2.70666i	−0.0942373	+	0.101153i
$717$	4.02252	−	10.8917i	0.150224	−	0.406756i
$718$	−8.25914	−	26.9689i	−0.308228	−	1.00647i
$719$	−14.6050	−	33.5676i	−0.544675	−	1.25186i	−0.942441	−	0.334372i	$-0.891476\pi$
$719$	−14.6050	−	33.5676i	−0.544675	−	1.25186i	0.397766	−	0.917487i	$-0.369786\pi$
$720$	−3.21636	−	5.95390i	−0.119867	−	0.221889i
$721$	−2.79183	+	1.88695i	−0.103973	+	0.0702735i
$722$	−31.0622	+	1.76016i	−1.15602	+	0.0655065i
$723$	5.47306	−	4.41919i	0.203545	−	0.164351i
$724$	−2.90598	+	1.41395i	−0.108000	+	0.0525489i
$725$	−0.504001	−	0.131232i	−0.0187181	−	0.00487382i
$726$	10.8601	+	1.23476i	0.403057	+	0.0458263i
$727$	−3.14277	+	7.22323i	−0.116559	+	0.267895i	−0.965409	−	0.260738i	$-0.916034\pi$
$727$	−3.14277	+	7.22323i	−0.116559	+	0.267895i	0.848850	+	0.528633i	$0.177295\pi$
$728$	47.7451	−	4.06371i	1.76955	−	0.150611i
$729$	−0.450204	+	0.892926i	−0.0166742	+	0.0330713i
$730$	0.698694	−	3.75498i	0.0258598	−	0.138978i
$731$	−54.2591	+	1.53609i	−2.00685	+	0.0568142i
$732$	1.65226	+	1.67581i	0.0610694	+	0.0619398i
$733$	−10.5018	+	10.0651i	−0.387892	+	0.371764i	−0.860450	−	0.509535i	$-0.829817\pi$
$733$	−10.5018	+	10.0651i	−0.387892	+	0.371764i	0.472558	+	0.881300i	$0.343331\pi$
$734$	−33.4011	+	17.4376i	−1.23286	+	0.643633i
$735$	−1.38538	−	0.626233i	−0.0511006	−	0.0230989i
$736$	1.81413	−	6.58372i	0.0668696	−	0.242679i
$737$	0.200464	+	4.71909i	0.00738420	+	0.173830i
$738$	−4.07008	−	0.817076i	−0.149822	−	0.0300770i
$739$	−16.8754	−	6.50526i	−0.620770	−	0.239300i	0.0288196	−	0.999585i	$-0.490825\pi$
$739$	−16.8754	−	6.50526i	−0.620770	−	0.239300i	−0.649590	+	0.760285i	$0.725059\pi$
$740$	1.33755	−	2.85082i	0.0491695	−	0.104798i
$741$	−36.6221	+	8.43669i	−1.34535	+	0.309930i
$742$	23.4813	+	11.4252i	0.862027	+	0.419433i
$743$	−0.0673551	−	0.0576092i	−0.00247102	−	0.00211348i	0.648750	−	0.761002i	$-0.275292\pi$
$743$	−0.0673551	−	0.0576092i	−0.00247102	−	0.00211348i	−0.651221	+	0.758889i	$0.725743\pi$
$744$	−3.39064	+	5.17291i	−0.124307	+	0.189648i
$745$	5.09493	+	3.23739i	0.186664	+	0.118609i
$746$	7.73637	−	22.9237i	0.283249	−	0.839298i
$747$	−3.87595	−	1.62156i	−0.141814	−	0.0593298i
$748$	1.16440	+	3.15280i	0.0425746	+	0.115278i
$749$	−38.0937	+	29.0167i	−1.39191	+	1.06025i
$750$	−14.5893	−	4.69473i	−0.532724	−	0.171427i
$751$	−1.35598	+	31.9209i	−0.0494806	+	1.16481i	0.787049	+	0.616890i	$0.211608\pi$
$751$	−1.35598	+	31.9209i	−0.0494806	+	1.16481i	−0.836530	+	0.547921i	$0.815419\pi$
$752$	−9.96092	+	40.6032i	−0.363237	+	1.48065i
$753$	−7.38030	−	21.8687i	−0.268953	−	0.796939i
$754$	−0.392481	+	5.53766i	−0.0142933	+	0.201670i
$755$	14.5597	−	5.61260i	0.529882	−	0.204263i
$756$	0.872093	−	0.149535i	0.0317177	−	0.00543855i
$757$	6.14035	+	7.38828i	0.223175	+	0.268532i	0.868844	−	0.495085i	$-0.164863\pi$
$757$	6.14035	+	7.38828i	0.223175	+	0.268532i	−0.645670	+	0.763617i	$0.723422\pi$
$758$	−42.6467	−	6.07568i	−1.54900	−	0.220679i
$759$	6.10688	−	0.694332i	0.221666	−	0.0252026i
$760$	11.9729	−	39.0955i	0.434301	−	1.41814i
$761$	16.6182	+	12.6584i	0.602409	+	0.458868i	0.862040	−	0.506840i	$-0.169187\pi$
$761$	16.6182	+	12.6584i	0.602409	+	0.458868i	−0.259631	+	0.965708i	$0.583601\pi$
$762$	−12.7756	−	18.3373i	−0.462810	−	0.664291i
$763$	−33.9138	−	24.3477i	−1.22776	−	0.881445i
$764$	−4.96543	−	4.00931i	−0.179643	−	0.145052i
$765$	−13.3138	−	3.06712i	−0.481362	−	0.110892i
$766$	−6.60793	+	8.42495i	−0.238754	+	0.304406i
$767$	7.56419	−	3.41923i	0.273127	−	0.123461i
$768$	−1.15238	−	7.34308i	−0.0415829	−	0.264970i
$769$	−4.72874	+	2.82011i	−0.170523	+	0.101696i	−0.594936	−	0.803773i	$-0.702823\pi$
$769$	−4.72874	+	2.82011i	−0.170523	+	0.101696i	0.424413	+	0.905469i	$0.360480\pi$
$770$	−11.9771	−	0.678693i	−0.431625	−	0.0244584i
$771$	−6.61138	+	4.74651i	−0.238103	+	0.170941i
$772$	−1.25357	−	0.442914i	−0.0451170	−	0.0159408i
$773$	−26.5250	−	30.1382i	−0.954037	−	1.08400i	−0.996390	−	0.0848940i	$-0.972945\pi$
$773$	−26.5250	−	30.1382i	−0.954037	−	1.08400i	0.0423528	−	0.999103i	$-0.486515\pi$
$774$	2.25162	+	10.4476i	0.0809328	+	0.375530i
$775$	0.262442	+	1.41044i	0.00942721	+	0.0506646i
$776$	−4.93202	−	1.43440i	−0.177049	−	0.0514919i
$777$	−9.57867	−	9.18041i	−0.343633	−	0.329345i
$778$	−0.669312	−	47.2936i	−0.0239960	−	1.69556i
$779$	−11.5057	−	17.5537i	−0.412236	−	0.628926i
$780$	0.480510	−	3.75237i	0.0172050	−	0.134356i
$781$	−1.94675	+	15.2024i	−0.0696600	+	0.543985i
$782$	17.9463	+	27.3797i	0.641759	+	0.979097i
$783$	0.0105687	+	0.746785i	0.000377694	+	0.0266879i
$784$	1.72631	+	1.65454i	0.0616540	+	0.0590906i
$785$	19.2461	+	5.59743i	0.686924	+	0.199781i
$786$	−0.153811	−	0.826625i	−0.00548626	−	0.0294848i
$787$	−6.09244	−	28.2690i	−0.217172	−	1.00768i	−0.946296	−	0.323300i	$-0.895208\pi$
$787$	−6.09244	−	28.2690i	−0.217172	−	1.00768i	0.729124	−	0.684381i	$-0.239928\pi$
$788$	−3.35623	−	3.81342i	−0.119561	−	0.135847i
$789$	6.57331	+	2.32250i	0.234016	+	0.0826831i
$790$	0.304713	−	0.218762i	0.0108412	−	0.00778322i
$791$	14.0211	+	0.794515i	0.498532	+	0.0282497i
$792$	4.14075	−	2.46944i	0.147135	−	0.0877479i
$793$	−6.57244	−	41.8803i	−0.233394	−	1.48721i
$794$	9.69435	−	4.38212i	0.344040	−	0.155516i
$795$	9.26957	−	11.8185i	0.328758	−	0.419158i
$796$	−1.44235	−	0.332275i	−0.0511226	−	0.0117772i
$797$	42.2594	+	34.1221i	1.49690	+	1.20867i	0.920040	+	0.391824i	$0.128156\pi$
$797$	42.2594	+	34.1221i	1.49690	+	1.20867i	0.576863	+	0.816841i	$0.304277\pi$
$798$	−19.2079	−	13.7899i	−0.679954	−	0.488159i
$799$	48.2506	+	69.2560i	1.70698	+	2.45010i
$800$	−0.988441	−	0.752917i	−0.0349467	−	0.0266196i
$801$	−1.65828	+	5.41486i	−0.0585925	+	0.191325i
$802$	−18.1694	+	2.06580i	−0.641583	+	0.0729459i
$803$	2.25422	+	0.321148i	0.0795496	+	0.0113331i
$804$	−0.599002	−	0.720740i	−0.0211252	−	0.0254185i
$805$	21.7891	−	3.73612i	0.767965	−	0.131681i
$806$	14.2692	−	5.50062i	0.502611	−	0.193751i
$807$	−0.677502	+	9.55912i	−0.0238492	+	0.336497i
$808$	7.55524	+	22.3870i	0.265792	+	0.787573i
$809$	−4.51148	+	18.3899i	−0.158615	+	0.646556i	0.836511	+	0.547950i	$0.184591\pi$
$809$	−4.51148	+	18.3899i	−0.158615	+	0.646556i	−0.995127	+	0.0986059i	$0.968562\pi$
$810$	−0.114168	+	2.68761i	−0.00401147	+	0.0944330i
$811$	−4.27322	−	1.37509i	−0.150053	−	0.0482861i	0.230345	−	0.973109i	$-0.426015\pi$
$811$	−4.27322	−	1.37509i	−0.150053	−	0.0482861i	−0.380398	+	0.924823i	$0.624213\pi$
$812$	0.525697	−	0.400434i	0.0184483	−	0.0140525i
$813$	−5.22679	−	14.1524i	−0.183312	−	0.496347i
$814$	−9.15386	−	3.82965i	−0.320843	−	0.134229i
$815$	−1.20857	+	3.58114i	−0.0423344	+	0.125442i
$816$	18.1364	+	11.5241i	0.634902	+	0.403425i
$817$	−29.6214	+	45.1918i	−1.03632	+	1.58106i
$818$	31.8982	+	27.2827i	1.11530	+	0.953918i
$819$	−14.3324	−	6.97364i	−0.500814	−	0.243679i
$820$	2.05881	−	0.474291i	0.0718968	−	0.0165630i
$821$	−13.2751	+	28.2942i	−0.463305	+	0.987474i	0.527167	+	0.849762i	$0.323254\pi$
$821$	−13.2751	+	28.2942i	−0.463305	+	0.987474i	−0.990472	+	0.137712i	$0.956025\pi$
$822$	−21.8490	−	8.42253i	−0.762071	−	0.293770i
$823$	31.5770	+	6.33913i	1.10070	+	0.220968i	0.713242	−	0.700918i	$-0.247226\pi$
$823$	31.5770	+	6.33913i	1.10070	+	0.220968i	0.387461	+	0.921886i	$0.373352\pi$
$824$	−0.154612	−	3.63969i	−0.00538616	−	0.126795i
$825$	0.297071	−	1.07811i	0.0103427	−	0.0375350i
$826$	4.75924	+	2.15131i	0.165595	+	0.0748537i
$827$	31.3299	−	16.3563i	1.08945	−	0.568765i	0.179614	−	0.983737i	$-0.442515\pi$
$827$	31.3299	−	16.3563i	1.08945	−	0.568765i	0.909834	+	0.414973i	$0.136209\pi$
$828$	−0.880407	+	0.843801i	−0.0305962	+	0.0293241i
$829$	20.1625	+	20.4499i	0.700274	+	0.710254i	0.967357	−	0.253419i	$-0.0815552\pi$
$829$	20.1625	+	20.4499i	0.700274	+	0.710254i	−0.267083	+	0.963674i	$0.586060\pi$
$830$	−11.2976	+	0.319837i	−0.392146	+	0.0111017i
$831$	3.47429	−	18.6718i	0.120522	−	0.647718i
$832$	−22.7997	+	45.2206i	−0.790438	+	1.56774i
$833$	4.81025	−	0.409413i	0.166665	−	0.0141853i
$834$	−10.9367	+	25.1364i	−0.378706	+	0.870404i
$835$	−36.0534	−	4.09916i	−1.24768	−	0.141857i
$836$	3.23774	+	0.843042i	0.111980	+	0.0291572i
$837$	1.84999	−	0.900140i	0.0639450	−	0.0311134i
$838$	−5.76723	+	4.65671i	−0.199226	+	0.160863i
$839$	8.30294	−	0.470493i	0.286649	−	0.0162432i	0.0873356	−	0.996179i	$-0.472165\pi$
$839$	8.30294	−	0.470493i	0.286649	−	0.0162432i	0.199314	+	0.979936i	$0.436129\pi$
$840$	14.3673	−	9.71063i	0.495721	−	0.335049i
$841$	−13.5184	−	25.0242i	−0.466150	−	0.862905i
$842$	17.5497	+	40.3354i	0.604801	+	1.39005i
$843$	4.38652	+	14.3235i	0.151080	+	0.493327i
$844$	−1.14793	+	3.10823i	−0.0395135	+	0.106990i
$845$	−28.0708	+	30.1307i	−0.965665	+	1.03653i
$846$	11.6680	−	11.8343i	0.401153	−	0.406870i
$847$	−0.331658	+	23.4350i	−0.0113959	+	0.805235i
$848$	−19.9385	+	12.6692i	−0.684690	+	0.435061i
$849$	6.32546	+	25.7842i	0.217089	+	0.884911i
$850$	5.83994	−	1.17238i	0.200308	−	0.0402122i
$851$	18.0227	+	3.09030i	0.617810	+	0.105934i
$852$	−1.52047	−	2.63354i	−0.0520906	−	0.0902235i
$853$	2.83346	−	4.90771i	0.0970160	−	0.168037i	−0.813432	−	0.581660i	$-0.802404\pi$
$853$	2.83346	−	4.90771i	0.0970160	−	0.168037i	0.910448	+	0.413623i	$0.135737\pi$
$854$	17.0483	−	20.5132i	0.583382	−	0.701946i
$855$	−10.0814	+	9.12909i	−0.344775	+	0.312208i
$856$	−5.11989	−	51.5160i	−0.174994	−	1.76078i
$857$	−21.7569	+	40.2749i	−0.743202	+	1.37576i	0.176957	+	0.984218i	$0.443374\pi$
$857$	−21.7569	+	40.2749i	−0.743202	+	1.37576i	−0.920159	+	0.391545i	$0.871941\pi$
$858$	−11.8775	−	1.01093i	−0.405492	−	0.0345124i
$859$	−23.7782	+	38.6183i	−0.811302	+	1.31764i	0.133848	+	0.991002i	$0.457266\pi$
$859$	−23.7782	+	38.6183i	−0.811302	+	1.31764i	−0.945150	+	0.326636i	$0.894085\pi$
$860$	−3.23434	−	4.37311i	−0.110290	−	0.149122i
$861$	0.880340	−	8.85792i	0.0300019	−	0.301877i
$862$	−7.53728	−	5.09431i	−0.256721	−	0.173513i
$863$	−11.4980	−	6.85712i	−0.391396	−	0.233419i	0.303033	−	0.952980i	$-0.402001\pi$
$863$	−11.4980	−	6.85712i	−0.391396	−	0.233419i	−0.694429	+	0.719561i	$0.744343\pi$
$864$	−0.664377	+	1.65336i	−0.0226026	+	0.0562486i
$865$	21.5872	+	35.0599i	0.733987	+	1.19207i
$866$	18.7507	+	37.1898i	0.637175	+	1.26376i
$867$	25.3337	−	7.36791i	0.860379	−	0.250227i
$868$	−1.61371	−	0.842466i	−0.0547730	−	0.0285952i
$869$	0.138009	+	0.175958i	0.00468163	+	0.00596896i
$870$	0.853365	+	1.81884i	0.0289318	+	0.0616643i
$871$	1.19350	+	16.8395i	0.0404402	+	0.570585i
$872$	41.6374	−	17.4196i	1.41002	−	0.589902i
$873$	1.16461	+	1.25008i	0.0394162	+	0.0423087i
$874$	32.5755	+	0.922219i	1.10188	+	0.0311945i
$875$	6.92364	−	32.1258i	0.234062	−	1.08605i
$876$	−0.394407	+	0.220329i	−0.0133258	+	0.00744423i
$877$	−7.99718	+	9.08656i	−0.270046	+	0.306831i	−0.869851	−	0.493315i	$-0.835785\pi$
$877$	−7.99718	+	9.08656i	−0.270046	+	0.306831i	0.599805	+	0.800146i	$0.295245\pi$
$878$	−43.3604	−	24.2226i	−1.46334	−	0.817472i
$879$	19.7334	−	6.97224i	0.665590	−	0.235168i
$880$	6.20364	−	8.90435i	0.209125	−	0.300165i
$881$	−41.7723	+	13.4421i	−1.40734	+	0.452874i	−0.909975	−	0.414664i	$-0.863899\pi$
$881$	−41.7723	+	13.4421i	−1.40734	+	0.452874i	−0.497370	+	0.867538i	$0.665701\pi$
$882$	−0.252503	−	0.916370i	−0.00850223	−	0.0308558i
$883$	7.62382	−	48.5798i	0.256562	−	1.63484i	−0.426506	−	0.904485i	$-0.640256\pi$
$883$	7.62382	−	48.5798i	0.256562	−	1.63484i	0.683068	−	0.730355i	$-0.260645\pi$
$884$	4.47891	+	11.1462i	0.150642	+	0.374887i
$885$	1.78635	−	2.41531i	0.0600476	−	0.0811897i
$886$	4.23053	+	3.83092i	0.142127	+	0.128702i
$887$	14.7654	−	2.10356i	0.495774	−	0.0706307i	0.111339	−	0.993783i	$-0.464486\pi$
$887$	14.7654	−	2.10356i	0.495774	−	0.0706307i	0.384435	+	0.923152i	$0.374396\pi$
$888$	13.8808	−	3.61428i	0.465809	−	0.121287i
$889$	36.4185	−	31.1490i	1.22144	−	1.04470i
$890$	1.93498	+	15.1105i	0.0648606	+	0.506506i
$891$	−1.60368			−0.0537253
$892$	1.35642	−	4.55382i	0.0454163	−	0.152473i
$893$	84.0238			2.81175
$894$	0.479367	+	3.74344i	0.0160324	+	0.125199i
$895$	18.3267	−	15.6750i	0.612595	−	0.523956i
$896$	−21.2452	+	5.53183i	−0.709754	+	0.184805i
$897$	21.7477	−	3.09829i	0.726134	−	0.103449i
$898$	14.7102	+	13.3207i	0.490886	+	0.444518i
$899$	0.913687	−	1.23539i	0.0304732	−	0.0412024i
$900$	0.0827296	+	0.205881i	0.00275765	+	0.00686269i
$901$	−7.39431	+	47.1173i	−0.246340	+	1.56970i
$902$	−1.76850	−	6.41814i	−0.0588847	−	0.213701i
$903$	−21.8153	+	7.02002i	−0.725967	+	0.233612i
$904$	−8.67894	+	12.4572i	−0.288657	+	0.414322i
$905$	19.8643	−	7.01852i	0.660313	−	0.233304i
$906$	8.51684	+	4.75779i	0.282953	+	0.158067i
$907$	−32.8491	+	37.3239i	−1.09074	+	1.23932i	−0.121658	+	0.992572i	$0.538821\pi$
$907$	−32.8491	+	37.3239i	−1.09074	+	1.23932i	−0.969080	+	0.246747i	$0.920638\pi$
$908$	2.16669	−	1.21039i	0.0719043	−	0.0401681i
$909$	1.65578	−	7.68286i	0.0549188	−	0.254824i
$910$	−42.8591	−	1.21335i	−1.42076	−	0.0402221i
$911$	−21.5261	−	23.1058i	−0.713193	−	0.765530i	0.266974	−	0.963704i	$-0.413976\pi$
$911$	−21.5261	−	23.1058i	−0.713193	−	0.765530i	−0.980167	+	0.198174i	$0.936499\pi$
$912$	19.7332	−	8.25566i	0.653431	−	0.273372i
$913$	−0.476349	−	6.72098i	−0.0157648	−	0.222432i
$914$	−6.21365	−	13.2436i	−0.205529	−	0.438058i
$915$	−9.46813	−	12.0716i	−0.313007	−	0.399076i
$916$	−7.46361	−	3.89650i	−0.246604	−	0.128744i
$917$	1.73122	−	0.503497i	0.0571699	−	0.0166269i
$918$	−3.84556	−	7.62722i	−0.126922	−	0.251736i
$919$	−27.3926	−	44.4883i	−0.903597	−	1.46754i	−0.883872	−	0.467730i	$-0.845072\pi$
$919$	−27.3926	−	44.4883i	−0.903597	−	1.46754i	−0.0197257	−	0.999805i	$-0.506279\pi$
$920$	−8.91124	+	22.1765i	−0.293795	+	0.731137i
$921$	4.47888	+	2.67109i	0.147584	+	0.0880155i
$922$	2.21519	+	1.49721i	0.0729536	+	0.0493080i
$923$	−5.41748	+	54.5103i	−0.178319	+	1.79423i
$924$	0.843766	+	1.14085i	0.0277579	+	0.0375311i
$925$	1.74439	−	2.83308i	0.0573553	−	0.0931510i
$926$	−11.8310	−	1.00696i	−0.388790	−	0.0330909i
$927$	−0.575942	+	1.06614i	−0.0189164	+	0.0350168i
$928$	0.131612	+	1.32427i	0.00432038	+	0.0434714i
$929$	−2.67214	+	2.41973i	−0.0876700	+	0.0793888i	−0.713891	−	0.700256i	$-0.753069\pi$
$929$	−2.67214	+	2.41973i	−0.0876700	+	0.0793888i	0.626222	+	0.779645i	$0.284601\pi$
$930$	3.53738	−	4.25630i	0.115995	−	0.139570i
$931$	2.40287	−	4.16189i	0.0787508	−	0.136400i
$932$	−1.12009	−	1.94005i	−0.0366896	−	0.0635483i
$933$	−7.64219	−	1.31038i	−0.250194	−	0.0429001i
$934$	−22.4226	+	4.50139i	−0.733691	+	0.147290i
$935$	−5.22033	−	21.2794i	−0.170723	−	0.695909i
$936$	14.5438	−	9.24134i	0.475380	−	0.302063i
$937$	−0.0115903	+	0.818970i	−0.000378638	+	0.0267546i	−1.00000		0.000772282i	$-0.999754\pi$
$937$	−0.0115903	+	0.818970i	−0.000378638	+	0.0267546i	0.999621	+	0.0275269i	$0.00876318\pi$
$938$	−7.45733	+	7.56361i	−0.243490	+	0.246961i
$939$	15.9034	−	17.0705i	0.518988	−	0.557073i
$940$	−2.93026	+	7.93418i	−0.0955746	+	0.258784i
$941$	16.3512	+	53.3924i	0.533035	+	1.74054i	0.662601	+	0.748973i	$0.269453\pi$
$941$	16.3512	+	53.3924i	0.533035	+	1.74054i	−0.129566	+	0.991571i	$0.541358\pi$
$942$	4.99954	+	11.4907i	0.162894	+	0.374389i
$943$	5.83102	+	10.7940i	0.189884	+	0.351500i
$944$	−3.91455	+	2.64577i	−0.127408	+	0.0861125i
$945$	−5.75898	+	0.326337i	−0.187340	+	0.0106158i
$946$	−13.3349	+	10.7672i	−0.433556	+	0.350072i
$947$	31.2824	−	15.2209i	1.01654	−	0.494614i	0.147347	−	0.989085i	$-0.452926\pi$
$947$	31.2824	−	15.2209i	1.01654	−	0.494614i	0.869194	+	0.494471i	$0.164638\pi$
$948$	−0.0429376	−	0.0111801i	−0.00139455	−	0.000363112i
$949$	8.08608	+	0.919361i	0.262485	+	0.0298437i
$950$	2.36563	−	5.43708i	0.0767513	−	0.176402i
$951$	8.60435	−	0.732339i	0.279015	−	0.0237477i
$952$	−24.7902	+	49.1685i	−0.803456	+	1.59356i
$953$	−10.7110	+	57.5642i	−0.346964	+	1.86469i	0.138403	+	0.990376i	$0.455803\pi$
$953$	−10.7110	+	57.5642i	−0.346964	+	1.86469i	−0.485367	+	0.874310i	$0.661314\pi$
$954$	9.38678	−	0.265742i	0.303908	−	0.00860370i
$955$	29.2102	+	29.6265i	0.945220	+	0.958692i
$956$	−2.66718	+	2.55629i	−0.0862628	+	0.0826762i
$957$	−1.06174	+	0.554300i	−0.0343212	+	0.0179180i
$958$	−49.7220	−	22.4757i	−1.60644	−	0.726158i
$959$	13.3384	−	48.4070i	0.430720	−	1.56314i
$960$	0.777841	+	18.3110i	0.0251047	+	0.590985i
$961$	26.2437	+	5.26847i	0.846570	+	0.169951i
$962$	−33.0912	−	12.7563i	−1.06690	−	0.411279i
$963$	−7.31437	+	15.5896i	−0.235702	+	0.502368i
$964$	−2.18114	+	0.502473i	−0.0702499	+	0.0161836i
$965$	7.79363	+	3.79211i	0.250886	+	0.122072i
$966$	10.5035	+	8.98370i	0.337945	+	0.289046i
$967$	−8.80618	+	13.4351i	−0.283188	+	0.432044i	−0.949565	−	0.313571i	$-0.898475\pi$
$967$	−8.80618	+	13.4351i	−0.283188	+	0.432044i	0.666377	+	0.745615i	$0.267844\pi$
$968$	−21.3859	−	13.5889i	−0.687369	−	0.436764i
$969$	13.8095	−	40.9191i	0.443625	−	1.31451i
$970$	4.23987	+	1.77381i	0.136134	+	0.0569536i
$971$	−2.20843	−	5.97970i	−0.0708720	−	0.191898i	0.897713	−	0.440581i	$-0.145227\pi$
$971$	−2.20843	−	5.97970i	−0.0708720	−	0.191898i	−0.968585	+	0.248683i	$0.920002\pi$
$972$	0.253118	−	0.192806i	0.00811878	−	0.00618424i
$973$	−55.9549	−	18.0059i	−1.79383	−	0.577243i
$974$	1.99679	−	47.0061i	0.0639814	−	1.50617i
$975$	0.952296	−	3.88180i	0.0304979	−	0.124317i
$976$	7.71562	+	22.8623i	0.246971	+	0.731803i
$977$	−1.56430	+	22.0713i	−0.0500465	+	0.706125i	0.907902	+	0.419183i	$0.137684\pi$
$977$	−1.56430	+	22.0713i	−0.0500465	+	0.706125i	−0.957948	+	0.286942i	$0.907361\pi$
$978$	−2.20484	+	0.849942i	−0.0705031	+	0.0271782i
$979$	−8.95116	+	1.53483i	−0.286080	+	0.0490534i
$980$	0.309200	+	0.372040i	0.00987703	+	0.0118844i
$981$	−14.8630	−	2.11747i	−0.474540	−	0.0676055i
$982$	−27.2458	+	3.09776i	−0.869448	+	0.0988534i
$983$	0.611739	−	1.99754i	0.0195114	−	0.0637115i	−0.945880	−	0.324516i	$-0.894799\pi$
$983$	0.611739	−	1.99754i	0.0195114	−	0.0637115i	0.965392	+	0.260804i	$0.0839878\pi$
$984$	7.65548	+	5.83134i	0.244048	+	0.185896i
$985$	18.9311	+	27.1726i	0.603195	+	0.865790i
$986$	−5.18230	−	3.72053i	−0.165038	−	0.118486i
$987$	27.7260	+	22.3872i	0.882530	+	0.712593i
$988$	11.6527	+	2.68445i	0.370721	+	0.0854036i
$989$	19.4923	−	24.8522i	0.619820	−	0.790255i
$990$	−3.93100	+	1.77693i	−0.124935	+	0.0564744i
$991$	3.63769	+	23.1797i	0.115555	+	0.736328i	0.974521	+	0.224296i	$0.0720081\pi$
$991$	3.63769	+	23.1797i	0.115555	+	0.736328i	−0.858966	+	0.512032i	$0.828893\pi$
$992$	3.14852	−	1.87770i	0.0999655	−	0.0596170i
$993$	−25.0499	−	1.41947i	−0.794934	−	0.0450456i
$994$	−27.9976	+	20.1003i	−0.888031	+	0.637543i
$995$	9.09788	+	3.21449i	0.288422	+	0.101906i
$996$	0.883227	+	1.00354i	0.0279861	+	0.0317984i
$997$	−9.50662	−	44.1109i	−0.301078	−	1.39701i	−0.834431	−	0.551113i	$-0.814203\pi$
$997$	−9.50662	−	44.1109i	−0.301078	−	1.39701i	0.533353	−	0.845893i	$-0.320932\pi$
$998$	5.68110	+	30.5319i	0.179832	+	0.966470i
$999$	−4.58131	−	1.33240i	−0.144946	−	0.0421553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	669.2.m.b.19.14	✓	1368
223.47	even	111	inner	669.2.m.b.493.14	yes	1368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
669.2.m.b.19.14	✓	1368	1.1	even	1	trivial
669.2.m.b.493.14	yes	1368	223.47	even	111	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.m (of order \(111\), degree \(72\), minimal)

\(f(q)\)	\(=\)	\(q+(0.164723 + 1.28634i) q^{2} +(-0.759946 + 0.649986i) q^{3} +(0.307920 - 0.0801761i) q^{4} +(-2.05355 + 0.292560i) q^{5} +(-0.961286 - 0.870484i) q^{6} +(1.65357 - 2.23577i) q^{7} +(1.12093 + 2.78954i) q^{8} +(0.155037 - 0.987909i) q^{9} +(-0.714600 - 2.59338i) q^{10} +(1.52659 - 0.491246i) q^{11} +(-0.181889 + 0.261073i) q^{12} +(5.40433 - 1.90947i) q^{13} +(3.14835 + 1.75877i) q^{14} +(1.37043 - 1.55711i) q^{15} +(-2.84811 + 1.59105i) q^{16} +(-1.38766 + 6.43877i) q^{17} +(1.29633 + 0.0366993i) q^{18} +(4.46941 + 4.79739i) q^{19} +(-0.608874 + 0.254731i) q^{20} +(0.196597 + 2.77386i) q^{21} +(0.883375 + 1.88280i) q^{22} +(-2.36526 - 3.01565i) q^{23} +(-2.66501 - 1.39131i) q^{24} +(-0.669584 + 0.194738i) q^{25} +(3.34645 + 6.63729i) q^{26} +(0.524307 + 0.851529i) q^{27} +(0.329911 - 0.821015i) q^{28} +(0.641450 + 0.382545i) q^{29} +(2.22872 + 1.50635i) q^{30} +(0.203467 - 2.04727i) q^{31} +(1.05955 + 1.43261i) q^{32} +(-0.840822 + 1.36558i) q^{33} +(-8.51105 - 0.724397i) q^{34} +(-2.74159 + 5.07504i) q^{35} +(-0.0314678 - 0.316627i) q^{36} +(-3.53660 + 3.20254i) q^{37} +(-5.43487 + 6.53943i) q^{38} +(-2.86587 + 4.96383i) q^{39} +(-3.11800 - 5.40054i) q^{40} +(-3.15501 - 0.540981i) q^{41} +(-3.53575 + 0.709809i) q^{42} +(1.96351 + 8.00376i) q^{43} +(0.430681 - 0.273660i) q^{44} +(-0.0293529 + 2.07408i) q^{45} +(3.48955 - 3.53928i) q^{46} +(8.73533 - 9.37636i) q^{47} +(1.13025 - 3.06034i) q^{48} +(-0.214624 - 0.700821i) q^{49} +(-0.360795 - 0.829238i) q^{50} +(-3.13056 - 5.79508i) q^{51} +(1.51101 - 1.02126i) q^{52} +(7.22946 - 0.409663i) q^{53} +(-1.00899 + 0.814705i) q^{54} +(-2.99121 + 1.45542i) q^{55} +(8.09031 + 2.10655i) q^{56} +(-6.51474 - 0.740705i) q^{57} +(-0.386423 + 0.888139i) q^{58} +(1.44305 - 0.122822i) q^{59} +(0.297140 - 0.589341i) q^{60} +(1.35299 - 7.27136i) q^{61} +(2.66701 - 0.0755035i) q^{62} +(-1.95237 - 1.98020i) q^{63} +(-6.37889 + 6.11367i) q^{64} +(-10.5394 + 5.50229i) q^{65} +(-1.89511 - 0.856643i) q^{66} +(-0.782414 + 2.83949i) q^{67} +(0.0889471 + 2.09388i) q^{68} +(3.75760 + 0.754345i) q^{69} +(-6.97985 - 2.69065i) q^{70} +(-4.05943 + 8.65213i) q^{71} +(2.92960 - 0.674896i) q^{72} +(1.27674 + 0.621215i) q^{73} +(-4.70212 - 4.02175i) q^{74} +(0.382271 - 0.583211i) q^{75} +(1.76086 + 1.11887i) q^{76} +(1.42600 - 4.22541i) q^{77} +(-6.85726 - 2.86884i) q^{78} +(0.0483102 + 0.130808i) q^{79} +(5.38326 - 4.10054i) q^{80} +(-0.951927 - 0.306324i) q^{81} +(0.176185 - 4.14754i) q^{82} +(1.00104 - 4.08049i) q^{83} +(0.282934 + 0.838365i) q^{84} +(0.965907 - 13.6283i) q^{85} +(-9.97215 + 3.84415i) q^{86} +(-0.736117 + 0.126220i) q^{87} +(3.08155 + 3.70783i) q^{88} +(-5.60648 - 0.798730i) q^{89} +(-2.67282 + 0.303890i) q^{90} +(4.66728 - 15.2403i) q^{91} +(-0.970094 - 0.738941i) q^{92} +(1.17607 + 1.68807i) q^{93} +(13.5001 + 9.69213i) q^{94} +(-10.5817 - 8.54412i) q^{95} +(-1.73638 - 0.400011i) q^{96} +(-1.05441 + 1.34434i) q^{97} +(0.866143 - 0.391521i) q^{98} +(-0.248629 - 1.58429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1368 q - 2 q^{2} + 19 q^{3} - 38 q^{4} + q^{5} + q^{6} + 4 q^{7} + 19 q^{9} - 5 q^{10} - 4 q^{11} + 19 q^{12} - 12 q^{13} - 8 q^{14} - 2 q^{15} - 30 q^{16} + 8 q^{17} + q^{18} - 71 q^{19} + 10 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) \) 1368 * q - 2 * q^2 + 19 * q^3 - 38 * q^4 + q^5 + q^6 + 4 * q^7 + 19 * q^9 - 5 * q^10 - 4 * q^11 + 19 * q^12 - 12 * q^13 - 8 * q^14 - 2 * q^15 - 30 * q^16 + 8 * q^17 + q^18 - 71 * q^19 + 10 * q^20 - 2 * q^21 + 5 * q^22 + 6 * q^23 + 20 * q^25 - 38 * q^27 - 24 * q^28 + 71 * q^29 + 10 * q^30 + 2 * q^31 + 8 * q^32 + 8 * q^33 - 130 * q^34 + 11 * q^35 + 19 * q^36 + 18 * q^37 - 6 * q^38 - 68 * q^39 - 223 * q^40 - 236 * q^41 - 70 * q^42 + 10 * q^43 - 172 * q^44 + q^45 + 4 * q^46 + 11 * q^47 + 15 * q^48 + 10 * q^49 + 9 * q^50 - 78 * q^51 + 530 * q^52 + 24 * q^53 - 2 * q^54 - 4 * q^55 - 22 * q^56 + 3 * q^57 - 52 * q^58 - 34 * q^59 - 20 * q^60 - 12 * q^61 + 5 * q^62 - 2 * q^63 - 214 * q^64 - 106 * q^65 + 138 * q^66 - 12 * q^67 - 144 * q^68 + 6 * q^69 - 67 * q^70 + 8 * q^71 + 17 * q^73 - 8 * q^74 + 20 * q^75 + 26 * q^76 - 142 * q^77 - 74 * q^78 - 14 * q^79 + 977 * q^80 + 19 * q^81 - 194 * q^82 - 130 * q^83 + 12 * q^84 - 52 * q^85 + 15 * q^86 + 6 * q^87 + 62 * q^88 - 22 * q^89 - 5 * q^90 - 4 * q^91 + 32 * q^92 + 2 * q^93 + 417 * q^94 - 74 * q^95 - 4 * q^96 - 15 * q^97 - 80 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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