LMFDB - Embedded newform 261.2.x.a.101.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.25
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.933128 - 2.13875i) q^{2} +(-0.534329 - 1.64757i) q^{3} +(-2.34319 - 2.52536i) q^{4} +(-2.32709 - 0.350752i) q^{5} +(-4.02235 - 0.394597i) q^{6} +(1.23383 + 1.14483i) q^{7} +(-3.18260 + 1.11364i) q^{8} +(-2.42898 + 1.76069i) q^{9} +(-2.92165 + 4.64977i) q^{10} +(0.990690 - 0.852557i) q^{11} +(-2.90867 + 5.20995i) q^{12} +(2.16395 - 3.17393i) q^{13} +(3.59982 - 1.57059i) q^{14} +(0.665543 + 4.02146i) q^{15} +(-0.0730851 + 0.975253i) q^{16} +(-1.97828 - 1.97828i) q^{17} +(1.49913 + 6.83795i) q^{18} +(2.81485 + 1.76869i) q^{19} +(4.56704 + 6.69862i) q^{20} +(1.22691 - 2.64454i) q^{21} +(-0.898969 - 2.91439i) q^{22} +(-2.59107 - 1.01692i) q^{23} +(3.53536 + 4.64852i) q^{24} +(0.514457 + 0.158689i) q^{25} +(-4.76902 - 7.58985i) q^{26} +(4.19874 + 3.06114i) q^{27} -5.79841i q^{28} +(-2.66387 - 4.68015i) q^{29} +(9.22196 + 2.32911i) q^{30} +(3.52698 - 2.60303i) q^{31} +(-3.94453 - 2.08474i) q^{32} +(-1.93400 - 1.17669i) q^{33} +(-6.07704 + 2.38506i) q^{34} +(-2.46968 - 3.09688i) q^{35} +(10.1379 + 2.00842i) q^{36} +(3.31464 + 9.47271i) q^{37} +(6.40940 - 4.36986i) q^{38} +(-6.38555 - 1.86934i) q^{39} +(7.79682 - 1.47524i) q^{40} +(10.9780 + 2.94155i) q^{41} +(-4.51114 - 5.09176i) q^{42} +(-2.28430 + 3.09512i) q^{43} +(-4.47439 - 0.504142i) q^{44} +(6.27003 - 3.24532i) q^{45} +(-4.59274 + 4.59274i) q^{46} +(-6.62027 - 7.69289i) q^{47} +(1.64585 - 0.400693i) q^{48} +(-0.311403 - 4.15538i) q^{49} +(0.819451 - 0.952220i) q^{50} +(-2.20230 + 4.31641i) q^{51} +(-13.0859 + 1.97238i) q^{52} +(8.87369 + 7.07653i) q^{53} +(10.4650 - 6.12364i) q^{54} +(-2.60446 + 1.63649i) q^{55} +(-5.20172 - 2.26949i) q^{56} +(1.40998 - 5.58273i) q^{57} +(-12.4954 + 1.33019i) q^{58} +(0.0424144 - 0.0244880i) q^{59} +(8.59615 - 11.1038i) q^{60} +(5.81477 - 0.217573i) q^{61} +(-2.27612 - 9.97231i) q^{62} +(-5.01264 - 0.608373i) q^{63} +(-9.66874 + 7.71056i) q^{64} +(-6.14898 + 6.62702i) q^{65} +(-4.32131 + 3.03836i) q^{66} +(6.26014 - 0.469133i) q^{67} +(-0.360380 + 9.63135i) q^{68} +(-0.290964 + 4.81235i) q^{69} +(-8.92800 + 2.39225i) q^{70} +(10.7697 - 5.18640i) q^{71} +(5.76972 - 8.30860i) q^{72} +(0.169595 - 1.50520i) q^{73} +(23.3528 + 1.75005i) q^{74} +(-0.0134380 - 0.932397i) q^{75} +(-2.12916 - 11.2529i) q^{76} +(2.19837 + 0.0822573i) q^{77} +(-9.95659 + 11.9128i) q^{78} +(-1.08284 + 5.72295i) q^{79} +(0.512148 - 2.24387i) q^{80} +(2.79993 - 8.55338i) q^{81} +(16.5352 - 20.7344i) q^{82} +(1.07916 - 3.49854i) q^{83} +(-9.55329 + 3.09826i) q^{84} +(3.90975 + 5.29752i) q^{85} +(4.48815 + 7.77370i) q^{86} +(-6.28749 + 6.88966i) q^{87} +(-2.20353 + 3.81662i) q^{88} +(1.07453 - 0.121070i) q^{89} +(-1.09018 - 16.4383i) q^{90} +(6.30355 - 1.43874i) q^{91} +(3.50328 + 8.92622i) q^{92} +(-6.17326 - 4.42008i) q^{93} +(-22.6308 + 6.98067i) q^{94} +(-5.93004 - 5.10321i) q^{95} +(-1.32709 + 7.61283i) q^{96} +(-5.95130 - 11.2604i) q^{97} +(-9.17792 - 3.21149i) q^{98} +(-0.905279 + 3.81515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.933128	−	2.13875i	0.659821	−	1.51233i	−0.188069	−	0.982156i	$-0.560223\pi$
$2$	0.933128	−	2.13875i	0.659821	−	1.51233i	0.847891	−	0.530171i	$-0.177872\pi$
$3$	−0.534329	−	1.64757i	−0.308495	−	0.951226i
$3$	−0.534329	−	1.64757i	−0.308495	−	0.951226i
$4$	−2.34319	−	2.52536i	−1.17159	−	1.26268i
$5$	−2.32709	−	0.350752i	−1.04071	−	0.156861i	−0.393616	−	0.919275i	$-0.628776\pi$
$5$	−2.32709	−	0.350752i	−1.04071	−	0.156861i	−0.647090	+	0.762414i	$0.724014\pi$
$6$	−4.02235	−	0.394597i	−1.64212	−	0.161094i
$7$	1.23383	+	1.14483i	0.466344	+	0.432704i	0.878018	−	0.478627i	$-0.158865\pi$
$7$	1.23383	+	1.14483i	0.466344	+	0.432704i	−0.411674	+	0.911331i	$0.635056\pi$
$8$	−3.18260	+	1.11364i	−1.12522	+	0.393732i
$9$	−2.42898	+	1.76069i	−0.809661	+	0.586897i
$10$	−2.92165	+	4.64977i	−0.923906	+	1.47039i
$11$	0.990690	−	0.852557i	0.298704	−	0.257056i	−0.490147	−	0.871640i	$-0.663057\pi$
$11$	0.990690	−	0.852557i	0.298704	−	0.257056i	0.788851	+	0.614584i	$0.210676\pi$
$12$	−2.90867	+	5.20995i	−0.839662	+	1.50398i
$13$	2.16395	−	3.17393i	0.600172	−	0.880291i	−0.399158	−	0.916882i	$-0.630698\pi$
$13$	2.16395	−	3.17393i	0.600172	−	0.880291i	0.999330	+	0.0365911i	$0.0116499\pi$
$14$	3.59982	−	1.57059i	0.962093	−	0.419757i
$15$	0.665543	+	4.02146i	0.171842	+	1.03834i
$16$	−0.0730851	+	0.975253i	−0.0182713	+	0.243813i
$17$	−1.97828	−	1.97828i	−0.479803	−	0.479803i	0.425265	−	0.905069i	$-0.360181\pi$
$17$	−1.97828	−	1.97828i	−0.479803	−	0.479803i	−0.905069	+	0.425265i	$0.860181\pi$
$18$	1.49913	+	6.83795i	0.353348	+	1.61172i
$19$	2.81485	+	1.76869i	0.645771	+	0.405765i	0.814716	−	0.579861i	$-0.196893\pi$
$19$	2.81485	+	1.76869i	0.645771	+	0.405765i	−0.168945	+	0.985626i	$0.554036\pi$
$20$	4.56704	+	6.69862i	1.02122	+	1.49786i
$21$	1.22691	−	2.64454i	0.267734	−	0.577085i
$22$	−0.898969	−	2.91439i	−0.191661	−	0.621349i
$23$	−2.59107	−	1.01692i	−0.540276	−	0.212043i	0.0794812	−	0.996836i	$-0.474674\pi$
$23$	−2.59107	−	1.01692i	−0.540276	−	0.212043i	−0.619757	+	0.784794i	$0.712769\pi$
$24$	3.53536	+	4.64852i	0.721653	+	0.948874i
$25$	0.514457	+	0.158689i	0.102891	+	0.0317378i
$26$	−4.76902	−	7.58985i	−0.935281	−	1.48849i
$27$	4.19874	+	3.06114i	0.808048	+	0.589116i
$28$		−	5.79841i		−	1.09580i
$29$	−2.66387	−	4.68015i	−0.494669	−	0.869082i
$29$	−2.66387	−	4.68015i	−0.494669	−	0.869082i
$30$	9.22196	+	2.32911i	1.68369	+	0.425236i
$31$	3.52698	−	2.60303i	0.633465	−	0.467519i	−0.229142	−	0.973393i	$-0.573592\pi$
$31$	3.52698	−	2.60303i	0.633465	−	0.467519i	0.862607	+	0.505874i	$0.168830\pi$
$32$	−3.94453	−	2.08474i	−0.697300	−	0.368534i
$33$	−1.93400	−	1.17669i	−0.336667	−	0.204835i
$34$	−6.07704	+	2.38506i	−1.04220	+	0.409035i
$35$	−2.46968	−	3.09688i	−0.417453	−	0.523469i
$36$	10.1379	+	2.00842i	1.68966	+	0.334737i
$37$	3.31464	+	9.47271i	0.544924	+	1.55730i	0.805957	+	0.591973i	$0.201651\pi$
$37$	3.31464	+	9.47271i	0.544924	+	1.55730i	−0.261033	+	0.965330i	$0.584063\pi$
$38$	6.40940	−	4.36986i	1.03974	−	0.708884i
$39$	−6.38555	−	1.86934i	−1.02251	−	0.299334i
$40$	7.79682	−	1.47524i	1.23279	−	0.233256i
$41$	10.9780	+	2.94155i	1.71448	+	0.459394i	0.976516	−	0.215446i	$-0.0691206\pi$
$41$	10.9780	+	2.94155i	1.71448	+	0.459394i	0.737964	+	0.674840i	$0.235787\pi$
$42$	−4.51114	−	5.09176i	−0.696085	−	0.785675i
$43$	−2.28430	+	3.09512i	−0.348353	+	0.472001i	−0.943385	−	0.331701i	$-0.892378\pi$
$43$	−2.28430	+	3.09512i	−0.348353	+	0.472001i	0.595032	+	0.803702i	$0.297139\pi$
$44$	−4.47439	−	0.504142i	−0.674539	−	0.0760023i
$45$	6.27003	−	3.24532i	0.934681	−	0.483783i
$46$	−4.59274	+	4.59274i	−0.677163	+	0.677163i
$47$	−6.62027	−	7.69289i	−0.965666	−	1.12212i	−0.992471	−	0.122483i	$-0.960914\pi$
$47$	−6.62027	−	7.69289i	−0.965666	−	1.12212i	0.0268049	−	0.999641i	$-0.491467\pi$
$48$	1.64585	−	0.400693i	0.237558	−	0.0578351i
$49$	−0.311403	−	4.15538i	−0.0444861	−	0.593626i
$50$	0.819451	−	0.952220i	0.115888	−	0.134664i
$51$	−2.20230	+	4.31641i	−0.308384	+	0.604418i
$52$	−13.0859	+	1.97238i	−1.81468	+	0.273520i
$53$	8.87369	+	7.07653i	1.21889	+	0.972036i	0.999993	−	0.00371068i	$-0.00118115\pi$
$53$	8.87369	+	7.07653i	1.21889	+	0.972036i	0.218902	+	0.975747i	$0.429753\pi$
$54$	10.4650	−	6.12364i	1.42410	−	0.833322i
$55$	−2.60446	+	1.63649i	−0.351185	+	0.220664i
$56$	−5.20172	−	2.26949i	−0.695109	−	0.303273i
$57$	1.40998	−	5.58273i	0.186757	−	0.739451i
$58$	−12.4954	+	1.33019i	−1.64073	+	0.174662i
$59$	0.0424144	−	0.0244880i	0.00552189	−	0.00318807i	−0.497237	−	0.867615i	$-0.665652\pi$
$59$	0.0424144	−	0.0244880i	0.00552189	−	0.00318807i	0.502758	+	0.864427i	$0.332319\pi$
$60$	8.59615	−	11.1038i	1.10976	−	1.43349i
$61$	5.81477	−	0.217573i	0.744505	−	0.0278574i	0.337553	−	0.941307i	$-0.390401\pi$
$61$	5.81477	−	0.217573i	0.744505	−	0.0278574i	0.406953	+	0.913449i	$0.366591\pi$
$62$	−2.27612	−	9.97231i	−0.289067	−	1.26649i
$63$	−5.01264	−	0.608373i	−0.631533	−	0.0766477i
$64$	−9.66874	+	7.71056i	−1.20859	+	0.963821i
$65$	−6.14898	+	6.62702i	−0.762687	+	0.821981i
$66$	−4.32131	+	3.03836i	−0.531917	+	0.373996i
$67$	6.26014	−	0.469133i	0.764798	−	0.0573137i	0.313382	−	0.949627i	$-0.398538\pi$
$67$	6.26014	−	0.469133i	0.764798	−	0.0573137i	0.451416	+	0.892314i	$0.350919\pi$
$68$	−0.360380	+	9.63135i	−0.0437025	+	1.16797i
$69$	−0.290964	+	4.81235i	−0.0350280	+	0.579338i
$70$	−8.92800	+	2.39225i	−1.06710	+	0.285929i
$71$	10.7697	−	5.18640i	1.27812	−	0.615512i	0.333217	−	0.942850i	$-0.391866\pi$
$71$	10.7697	−	5.18640i	1.27812	−	0.615512i	0.944907	+	0.327338i	$0.106152\pi$
$72$	5.76972	−	8.30860i	0.679967	−	0.979178i
$73$	0.169595	−	1.50520i	0.0198496	−	0.176170i	−0.979876	−	0.199609i	$-0.936033\pi$
$73$	0.169595	−	1.50520i	0.0198496	−	0.176170i	0.999725	+	0.0234387i	$0.00746145\pi$
$74$	23.3528	+	1.75005i	2.71470	+	0.203439i
$75$	−0.0134380	−	0.932397i	−0.00155169	−	0.107664i
$76$	−2.12916	−	11.2529i	−0.244231	−	1.29079i
$77$	2.19837	+	0.0822573i	0.250528	+	0.00937409i
$78$	−9.95659	+	11.9128i	−1.12736	+	1.34886i
$79$	−1.08284	+	5.72295i	−0.121829	+	0.643882i	0.867412	+	0.497590i	$0.165782\pi$
$79$	−1.08284	+	5.72295i	−0.121829	+	0.643882i	−0.989241	+	0.146292i	$0.953266\pi$
$80$	0.512148	−	2.24387i	0.0572599	−	0.250872i
$81$	2.79993	−	8.55338i	0.311103	−	0.950376i
$82$	16.5352	−	20.7344i	1.82600	−	2.28974i
$83$	1.07916	−	3.49854i	0.118453	−	0.384014i	−0.876857	−	0.480751i	$-0.840364\pi$
$83$	1.07916	−	3.49854i	0.118453	−	0.384014i	0.995310	+	0.0967365i	$0.0308404\pi$
$84$	−9.55329	+	3.09826i	−1.04235	+	0.338048i
$85$	3.90975	+	5.29752i	0.424072	+	0.574597i
$86$	4.48815	+	7.77370i	0.483969	+	0.838260i
$87$	−6.28749	+	6.88966i	−0.674090	+	0.738649i
$88$	−2.20353	+	3.81662i	−0.234897	+	0.406854i
$89$	1.07453	−	0.121070i	0.113900	−	0.0128334i	−0.0548307	−	0.998496i	$-0.517462\pi$
$89$	1.07453	−	0.121070i	0.113900	−	0.0128334i	0.168730	+	0.985662i	$0.446033\pi$
$90$	−1.09018	−	16.4383i	−0.114915	−	1.73275i
$91$	6.30355	−	1.43874i	0.660792	−	0.150821i
$92$	3.50328	+	8.92622i	0.365243	+	0.930623i
$93$	−6.17326	−	4.42008i	−0.640137	−	0.458341i
$94$	−22.6308	+	6.98067i	−2.33418	+	0.720001i
$95$	−5.93004	−	5.10321i	−0.608409	−	0.523578i
$96$	−1.32709	+	7.61283i	−0.135445	+	0.776981i
$97$	−5.95130	−	11.2604i	−0.604263	−	1.14332i	−0.976568	−	0.215211i	$-0.930956\pi$
$97$	−5.95130	−	11.2604i	−0.604263	−	1.14332i	0.372305	−	0.928111i	$-0.378568\pi$
$98$	−9.17792	−	3.21149i	−0.927110	−	0.324410i
$99$	−0.905279	+	3.81515i	−0.0909840	+	0.383437i
$100$	−0.804724	−	1.67103i	−0.0804724	−	0.167103i
$101$	10.3957	+	7.67240i	1.03441	+	0.763432i	0.972086	−	0.234623i	$-0.0753857\pi$
$101$	10.3957	+	7.67240i	1.03441	+	0.763432i	0.0623277	+	0.998056i	$0.480148\pi$
$102$	7.17670	+	8.73795i	0.710599	+	0.865186i
$103$	−3.41816	−	2.33046i	−0.336802	−	0.229627i	0.383095	−	0.923709i	$-0.374858\pi$
$103$	−3.41816	−	2.33046i	−0.336802	−	0.229627i	−0.719896	+	0.694082i	$0.755811\pi$
$104$	−3.35238	+	12.5112i	−0.328728	+	1.22683i
$105$	−3.78271	+	5.72373i	−0.369155	+	0.558579i
$106$	23.4152	−	12.3753i	2.27429	−	1.20200i
$107$	−4.39231	+	9.12072i	−0.424620	+	0.881733i	0.573426	+	0.819257i	$0.305614\pi$
$107$	−4.39231	+	9.12072i	−0.424620	+	0.881733i	−0.998046	+	0.0624758i	$0.980100\pi$
$108$	−2.10799	−	17.7762i	−0.202841	−	1.71051i
$109$	7.21361	+	1.64646i	0.690938	+	0.157702i	0.553551	−	0.832815i	$-0.313272\pi$
$109$	7.21361	+	1.64646i	0.690938	+	0.157702i	0.137387	+	0.990517i	$0.456130\pi$
$110$	1.06975	+	7.09735i	0.101997	+	0.676706i
$111$	13.8359	−	10.5227i	1.31324	−	0.998766i
$112$	−1.20667	+	1.11963i	−0.114020	+	0.105795i
$113$	−8.77725	+	16.6074i	−0.825695	+	1.56229i	0.00124486	+	0.999999i	$0.499604\pi$
$113$	−8.77725	+	16.6074i	−0.825695	+	1.56229i	−0.826939	+	0.562291i	$0.809920\pi$
$114$	−10.6244	−	8.22501i	−0.995065	−	0.770343i
$115$	5.67297	+	3.27529i	0.529007	+	0.305422i
$116$	−5.57709	+	17.6937i	−0.517820	+	1.64282i
$117$	0.332114	+	11.5195i	0.0307040	+	1.06498i
$118$	−0.0127956	−	0.113564i	−0.00117793	−	0.0104545i
$119$	−0.176073	−	4.70565i	−0.0161406	−	0.431366i
$120$	−6.59663	−	12.0576i	−0.602187	−	1.10070i
$121$	−1.38485	+	9.18790i	−0.125896	+	0.835264i
$122$	4.96059	−	12.6394i	0.449111	−	1.14432i
$123$	−1.01946	−	19.6588i	−0.0919218	−	1.77258i
$124$	−14.8380	−	2.80750i	−1.33249	−	0.252121i
$125$	9.46006	+	4.55573i	0.846134	+	0.407476i
$126$	−5.97860	+	10.1531i	−0.532616	+	0.904511i
$127$	0.860520	−	2.45923i	0.0763588	−	0.218221i	−0.899376	−	0.437175i	$-0.855979\pi$
$127$	0.860520	−	2.45923i	0.0763588	−	0.218221i	0.975735	+	0.218954i	$0.0702646\pi$
$128$	5.15935	+	19.2549i	0.456026	+	1.70191i
$129$	6.32000	+	2.10974i	0.556445	+	0.185752i
$130$	8.43577	+	19.3350i	0.739866	+	1.69579i
$131$	−3.90001	−	8.93891i	−0.340745	−	0.780996i	−0.999588	−	0.0287154i	$-0.990858\pi$
$131$	−3.90001	−	8.93891i	−0.340745	−	0.780996i	0.658842	−	0.752281i	$-0.271046\pi$
$132$	1.56019	+	7.64125i	0.135797	+	0.665085i
$133$	1.44821	+	5.40478i	0.125575	+	0.468654i
$134$	4.83815	−	13.8267i	0.417953	−	1.19444i
$135$	−8.69715	−	8.59626i	−0.748532	−	0.739848i
$136$	8.49917	+	4.09299i	0.728798	+	0.350971i
$137$	−10.4729	−	1.98158i	−0.894760	−	0.169298i	−0.281858	−	0.959456i	$-0.590951\pi$
$137$	−10.4729	−	1.98158i	−0.894760	−	0.169298i	−0.612903	+	0.790159i	$0.709998\pi$
$138$	10.0209	+	5.11284i	0.853037	+	0.435234i
$139$	−3.84974	+	9.80897i	−0.326531	+	0.831986i	0.669487	+	0.742824i	$0.266514\pi$
$139$	−3.84974	+	9.80897i	−0.326531	+	0.831986i	−0.996017	+	0.0891621i	$0.971581\pi$
$140$	−2.03381	+	13.4934i	−0.171888	+	1.14040i
$141$	−9.13719	+	15.0179i	−0.769490	+	1.26474i
$142$	−1.04294	−	27.8732i	−0.0875218	−	2.33907i
$143$	−0.562156	−	4.98928i	−0.0470099	−	0.417224i
$144$	−1.53960	−	2.49755i	−0.128300	−	0.208130i
$145$	4.55750	+	11.8255i	0.378480	+	0.982053i
$146$	−3.06099	−	1.76726i	−0.253329	−	0.146260i
$147$	−6.67990	+	2.73340i	−0.550949	+	0.225447i
$148$	16.1551	−	30.5670i	1.32794	−	2.51259i
$149$	−5.59928	+	5.19537i	−0.458711	+	0.425621i	−0.875379	−	0.483437i	$-0.839388\pi$
$149$	−5.59928	+	5.19537i	−0.458711	+	0.425621i	0.416668	+	0.909059i	$0.363198\pi$
$150$	−2.00671	−	0.841306i	−0.163847	−	0.0686923i
$151$	3.09817	+	20.5550i	0.252126	+	1.67274i	0.653573	+	0.756863i	$0.273269\pi$
$151$	3.09817	+	20.5550i	0.252126	+	1.67274i	−0.401448	+	0.915882i	$0.631493\pi$
$152$	−10.9282	−	2.49430i	−0.886397	−	0.202314i
$153$	8.28835	+	1.32207i	0.670074	+	0.106883i
$154$	2.22729	−	4.62502i	0.179480	−	0.372695i
$155$	−9.12063	+	4.82039i	−0.732587	+	0.387183i
$156$	10.2418	+	20.5060i	0.820000	+	1.64179i
$157$	−4.50960	+	16.8301i	−0.359905	+	1.34318i	0.514293	+	0.857615i	$0.328055\pi$
$157$	−4.50960	+	16.8301i	−0.359905	+	1.34318i	−0.874198	+	0.485570i	$0.838612\pi$
$158$	11.2295	+	7.65618i	0.893375	+	0.609093i
$159$	6.91762	−	18.4012i	0.548603	−	1.45931i
$160$	8.44804	+	6.23494i	0.667876	+	0.492915i
$161$	−2.03274	−	4.22104i	−0.160203	−	0.332664i
$162$	−15.6809	−	13.9698i	−1.23201	−	1.09757i
$163$	−18.4979	−	6.47271i	−1.44887	−	0.506982i	−0.512713	−	0.858560i	$-0.671359\pi$
$163$	−18.4979	−	6.47271i	−1.44887	−	0.506982i	−0.936158	+	0.351578i	$0.885645\pi$
$164$	−18.2951	−	34.6161i	−1.42861	−	2.70306i
$165$	4.08788	+	3.41661i	0.318241	+	0.265983i
$166$	−6.47551	−	5.57263i	−0.502597	−	0.432520i
$167$	3.09835	−	0.955716i	0.239758	−	0.0739555i	−0.172548	−	0.985001i	$-0.555200\pi$
$167$	3.09835	−	0.955716i	0.239758	−	0.0739555i	0.412305	+	0.911046i	$0.364724\pi$
$168$	−0.959711	+	9.78285i	−0.0740433	+	0.754764i
$169$	−0.641738	−	1.63512i	−0.0493645	−	0.125779i
$170$	14.9784	−	3.41872i	1.14879	−	0.262204i
$171$	−9.95134	+	0.659968i	−0.760998	+	0.0504691i
$172$	13.1688	−	1.48377i	1.00411	−	0.113137i
$173$	−0.375704	+	0.650739i	−0.0285643	+	0.0494747i	−0.879954	−	0.475059i	$-0.842427\pi$
$173$	−0.375704	+	0.650739i	−0.0285643	+	0.0494747i	0.851390	+	0.524533i	$0.175760\pi$
$174$	8.86825	+	19.8763i	0.672300	+	1.50682i
$175$	0.453081	+	0.784760i	0.0342497	+	0.0593223i
$176$	0.759055	+	1.02848i	0.0572159	+	0.0775248i
$177$	−0.0630090	−	0.0567962i	−0.00473605	−	0.00426906i
$178$	0.743732	−	2.41112i	0.0557451	−	0.180721i
$179$	−11.3740	+	14.2625i	−0.850131	+	1.06603i	0.146909	+	0.989150i	$0.453068\pi$
$179$	−11.3740	+	14.2625i	−0.850131	+	1.06603i	−0.997040	+	0.0768811i	$0.975504\pi$
$180$	−22.8875	−	8.22969i	−1.70593	−	0.613405i
$181$	1.49303	−	6.54140i	0.110976	−	0.486219i	−0.888642	−	0.458601i	$-0.848351\pi$
$181$	1.49303	−	6.54140i	0.110976	−	0.486219i	0.999619	−	0.0276176i	$-0.00879209\pi$
$182$	2.80490	−	14.8243i	0.207913	−	1.09885i
$183$	−3.46547	−	9.46400i	−0.256175	−	0.699599i
$184$	9.37884	+	0.350931i	0.691417	+	0.0258710i
$185$	−4.39090	−	23.2065i	−0.322825	−	1.70617i
$186$	−15.2139	+	9.07856i	−1.11554	+	0.665672i
$187$	−3.64646	−	0.273264i	−0.266655	−	0.0199831i
$188$	−3.91476	+	34.7445i	−0.285513	+	2.53400i
$189$	1.67606	+	8.58375i	0.121916	+	0.624376i
$190$	−16.4480	+	7.92094i	−1.19326	+	0.574645i
$191$	−22.7926	+	6.10725i	−1.64921	+	0.441905i	−0.959392	−	0.282075i	$-0.908977\pi$
$191$	−22.7926	+	6.10725i	−1.64921	+	0.441905i	−0.689821	+	0.723980i	$0.742311\pi$
$192$	17.8700	+	11.8100i	1.28966	+	0.852311i
$193$	0.218013	−	5.82653i	0.0156929	−	0.419403i	−0.969204	−	0.246260i	$-0.920798\pi$
$193$	0.218013	−	5.82653i	0.0156929	−	0.419403i	0.984897	−	0.173143i	$-0.0553922\pi$
$194$	−29.6366	+	2.22095i	−2.12778	+	0.159455i
$195$	14.2041	+	6.58987i	1.01717	+	0.471910i
$196$	−9.76416	+	10.5233i	−0.697440	+	0.751661i
$197$	16.0333	−	12.7861i	1.14232	−	0.910973i	0.145402	−	0.989373i	$-0.453552\pi$
$197$	16.0333	−	12.7861i	1.14232	−	0.910973i	0.996922	+	0.0783998i	$0.0249811\pi$
$198$	7.31492	+	5.49619i	0.519848	+	0.390597i
$199$	−3.99458	−	17.5014i	−0.283168	−	1.24064i	−0.893706	−	0.448653i	$-0.851904\pi$
$199$	−3.99458	−	17.5014i	−0.283168	−	1.24064i	0.610538	−	0.791987i	$-0.290953\pi$
$200$	−1.81404	+	0.0678764i	−0.128272	+	0.00479959i
$201$	−4.11791	−	10.0634i	−0.290455	−	0.709814i
$202$	26.1099	−	15.0746i	1.83709	−	1.06064i
$203$	2.07119	−	8.82418i	0.145369	−	0.619336i
$204$	16.0609	−	4.55256i	1.12449	−	0.318743i
$205$	−24.5151	−	10.6958i	−1.71221	−	0.747029i
$206$	−8.17387	+	5.13598i	−0.569501	+	0.357841i
$207$	8.08416	−	2.09199i	0.561888	−	0.145404i
$208$	2.93724	+	2.34237i	0.203661	+	0.162414i
$209$	4.29655	−	0.647601i	0.297199	−	0.0447955i
$210$	8.71190	+	13.4313i	0.601178	+	0.926846i
$211$	17.0068	−	19.7622i	1.17079	−	1.36049i	0.251049	−	0.967974i	$-0.419225\pi$
$211$	17.0068	−	19.7622i	1.17079	−	1.36049i	0.919746	−	0.392514i	$-0.128394\pi$
$212$	−2.92196	−	38.9909i	−0.200681	−	2.67791i
$213$	−14.2995	−	14.9726i	−0.979786	−	1.02590i
$214$	15.4084	+	17.9049i	1.05329	+	1.22395i
$215$	6.40140	−	6.40140i	0.436572	−	0.436572i
$216$	−16.7719	−	5.06649i	−1.14119	−	0.344731i
$217$	7.33172	+	0.826087i	0.497710	+	0.0560784i
$218$	10.2526	−	13.8918i	0.694393	−	0.940869i
$219$	−2.57054	+	0.524851i	−0.173701	+	0.0354662i
$220$	10.2355	+	2.74259i	0.690075	+	0.184905i
$221$	−10.5598	+	1.99803i	−0.710331	+	0.134402i
$222$	−9.59474	−	39.4105i	−0.643957	−	2.64506i
$223$	14.1085	−	9.61904i	0.944778	−	0.644139i	0.0102194	−	0.999948i	$-0.496747\pi$
$223$	14.1085	−	9.61904i	0.944778	−	0.644139i	0.934559	+	0.355809i	$0.115795\pi$
$224$	−2.48020	−	7.08802i	−0.165716	−	0.473588i
$225$	−1.52901	+	0.520347i	−0.101934	+	0.0346898i
$226$	27.3288	+	34.2692i	1.81788	+	2.27955i
$227$	−10.3235	+	4.05169i	−0.685197	+	0.268920i	−0.682296	−	0.731076i	$-0.739019\pi$
$227$	−10.3235	+	4.05169i	−0.685197	+	0.268920i	−0.00290071	+	0.999996i	$0.500923\pi$
$228$	−17.4022	+	9.52068i	−1.15249	+	0.630523i
$229$	4.97353	+	2.62859i	0.328660	+	0.173702i	0.623456	−	0.781858i	$-0.285728\pi$
$229$	4.97353	+	2.62859i	0.328660	+	0.173702i	−0.294796	+	0.955560i	$0.595252\pi$
$230$	12.2986	−	9.07681i	0.810949	−	0.598507i
$231$	−1.03913	−	3.66593i	−0.0683697	−	0.241200i
$232$	13.6901	+	11.9285i	0.898796	+	0.783141i
$233$			20.9159i			1.37025i	0.728427	+	0.685123i	$0.240252\pi$
$233$			20.9159i			1.37025i	−0.728427	+	0.685123i	$0.759748\pi$
$234$	24.9472	+	10.0389i	1.63085	+	0.656260i
$235$	12.7077	+	20.2241i	0.828957	+	1.31928i
$236$	−0.161226	−	0.0497317i	−0.0104949	−	0.00323725i
$237$	10.0076	−	1.27388i	0.650061	−	0.0827476i
$238$	−10.2285	−	4.01440i	−0.663016	−	0.260215i
$239$	−4.49596	−	14.5755i	−0.290819	−	0.942813i	−0.976611	−	0.215015i	$-0.931020\pi$
$239$	−4.49596	−	14.5755i	−0.290819	−	0.942813i	0.685791	−	0.727798i	$-0.259456\pi$
$240$	−3.97059	+	0.355163i	−0.256300	+	0.0229257i
$241$	8.87259	+	13.0137i	0.571534	+	0.838286i	0.997799	−	0.0663123i	$-0.0211234\pi$
$241$	8.87259	+	13.0137i	0.571534	+	0.838286i	−0.426265	+	0.904598i	$0.640171\pi$
$242$	18.3584	+	11.5353i	1.18012	+	0.741520i
$243$	−15.5884	−	0.0427620i	−0.999996	−	0.00274318i
$244$	−14.1746	−	14.1746i	−0.907434	−	0.907434i
$245$	−0.732848	+	9.77918i	−0.0468199	+	0.624769i
$246$	−42.9967	−	16.1639i	−2.74137	−	1.03057i
$247$	11.7049	−	5.10680i	0.744765	−	0.324938i
$248$	−8.32615	+	12.2122i	−0.528711	+	0.775477i
$249$	−6.34071	+	0.0913844i	−0.401826	+	0.00579125i
$250$	18.5710	−	15.9817i	1.17453	−	1.01077i
$251$	−4.32360	+	6.88097i	−0.272903	+	0.434323i	−0.954854	−	0.297075i	$-0.903989\pi$
$251$	−4.32360	+	6.88097i	−0.272903	+	0.434323i	0.681951	+	0.731398i	$0.261132\pi$
$252$	10.2092	+	14.0842i	0.643120	+	0.887224i
$253$	−3.43393	+	1.20158i	−0.215889	+	0.0755430i
$254$	−4.45670	−	4.13521i	−0.279638	−	0.259466i
$255$	6.63895	−	9.27221i	0.415747	−	0.580649i
$256$	21.5386	+	3.24642i	1.34616	+	0.202901i
$257$	9.53664	+	10.2781i	0.594879	+	0.641127i	0.956685	−	0.291126i	$-0.0940300\pi$
$257$	9.53664	+	10.2781i	0.594879	+	0.641127i	−0.361805	+	0.932254i	$0.617839\pi$
$258$	10.4096	−	11.5483i	0.648072	−	0.718963i
$259$	−6.75490	+	15.4824i	−0.419729	+	0.962029i
$260$	31.1438			1.93146
$261$	14.7108	+	6.67775i	0.910576	+	0.413342i
$262$	−22.7573			−1.40595
$263$	−2.39327	+	5.48543i	−0.147575	+	0.338246i	−0.974612	−	0.223903i	$-0.928120\pi$
$263$	−2.39327	+	5.48543i	−0.147575	+	0.338246i	0.827036	+	0.562148i	$0.190025\pi$
$264$	7.46557	+	1.59114i	0.459474	+	0.0979278i
$265$	−18.1678	−	19.5802i	−1.11604	−	1.20280i
$266$	12.9108	+	1.94600i	0.791615	+	0.119317i
$267$	−0.773623	−	1.70567i	−0.0473449	−	0.104385i
$268$	−15.8534	−	14.7098i	−0.968402	−	0.898546i
$269$	−3.24155	+	1.13427i	−0.197641	+	0.0691574i	−0.427284	−	0.904117i	$-0.640530\pi$
$269$	−3.24155	+	1.13427i	−0.197641	+	0.0691574i	0.229644	+	0.973275i	$0.426244\pi$
$270$	−26.5008	+	10.5796i	−1.61279	+	0.643857i
$271$	10.9634	−	17.4482i	0.665980	−	1.05990i	−0.327384	−	0.944891i	$-0.606167\pi$
$271$	10.9634	−	17.4482i	0.665980	−	1.05990i	0.993364	−	0.115010i	$-0.0366901\pi$
$272$	2.07391	−	1.78474i	0.125749	−	0.108216i
$273$	−5.73861	−	9.61679i	−0.347316	−	0.582035i
$274$	−14.0107	+	20.5499i	−0.846415	+	1.24146i
$275$	0.644959	−	0.281393i	0.0388925	−	0.0169686i
$276$	12.8347	−	10.5415i	0.772557	−	0.634521i
$277$	1.92637	−	25.7057i	0.115745	−	1.54450i	−0.573033	−	0.819532i	$-0.694233\pi$
$277$	1.92637	−	25.7057i	0.115745	−	1.54450i	0.688778	−	0.724972i	$-0.258148\pi$
$278$	17.3867	+	17.3867i	1.04278	+	1.04278i
$279$	−3.98385	+	12.5327i	−0.238507	+	0.750311i
$280$	11.3088	+	7.10581i	0.675832	+	0.424654i
$281$	5.21298	+	7.64604i	0.310980	+	0.456125i	0.949630	−	0.313373i	$-0.101459\pi$
$281$	5.21298	+	7.64604i	0.310980	+	0.456125i	−0.638650	+	0.769498i	$0.720507\pi$
$282$	23.5934	+	33.5558i	1.40497	+	1.99822i
$283$	−4.79568	−	15.5472i	−0.285074	−	0.924186i	−0.978951	−	0.204093i	$-0.934575\pi$
$283$	−4.79568	−	15.5472i	−0.285074	−	0.924186i	0.693878	−	0.720093i	$-0.255901\pi$
$284$	−38.3329	−	15.0445i	−2.27464	−	0.892730i
$285$	−5.23931	+	12.4970i	−0.310350	+	0.740256i
$286$	−11.1954	−	3.45332i	−0.661998	−	0.204199i
$287$	10.1774	+	16.1973i	0.600756	+	0.956097i
$288$	13.2518	−	1.88129i	0.780869	−	0.110856i
$289$		−	9.17282i		−	0.539577i
$290$	29.5445	+	1.28733i	1.73491	+	0.0755945i
$291$	−15.3724	+	15.8220i	−0.901145	+	0.927500i
$292$	−4.19856	+	3.09868i	−0.245702	+	0.181336i
$293$	22.0079	+	11.6315i	1.28572	+	0.679521i	0.963643	−	0.267194i	$-0.0860963\pi$
$293$	22.0079	+	11.6315i	1.28572	+	0.679521i	0.322074	+	0.946715i	$0.395620\pi$
$294$	−0.387133	+	16.8373i	−0.0225781	+	0.981970i
$295$	−0.107291	+	0.0421088i	−0.00624675	+	0.00245167i
$296$	−21.0984	−	26.4565i	−1.22632	−	1.53776i
$297$	6.76945	−	0.547033i	0.392803	−	0.0317421i
$298$	5.88677	+	16.8234i	0.341011	+	0.974554i
$299$	−8.83459	+	6.02332i	−0.510918	+	0.348338i
$300$	−2.32315	+	2.21872i	−0.134127	+	0.128098i
$301$	−6.36181	+	1.20372i	−0.366689	+	0.0693813i
$302$	46.8531	+	12.5543i	2.69609	+	0.722416i
$303$	7.08608	−	21.2273i	0.407085	−	1.21948i
$304$	−1.93064	+	2.61593i	−0.110730	+	0.150034i
$305$	−13.6078	−	1.53323i	−0.779181	−	0.0877926i
$306$	10.5617	−	16.4931i	0.603771	−	0.942846i
$307$	4.95541	−	4.95541i	0.282820	−	0.282820i	−0.551412	−	0.834233i	$-0.685911\pi$
$307$	4.95541	−	4.95541i	0.282820	−	0.282820i	0.834233	+	0.551412i	$0.185911\pi$
$308$	−4.94348	−	5.74442i	−0.281681	−	0.327319i
$309$	−2.01318	+	6.87690i	−0.114526	+	0.391213i
$310$	1.79891	+	24.0048i	0.102171	+	1.36338i
$311$	15.9413	−	18.5241i	0.903949	−	1.05041i	−0.0945440	−	0.995521i	$-0.530139\pi$
$311$	15.9413	−	18.5241i	0.903949	−	1.05041i	0.998493	−	0.0548866i	$-0.0174797\pi$
$312$	22.4044	−	1.16184i	1.26840	−	0.0657763i
$313$	−5.02775	+	0.757812i	−0.284185	+	0.0428341i	−0.289588	−	0.957151i	$-0.593518\pi$
$313$	−5.02775	+	0.757812i	−0.284185	+	0.0428341i	0.00540274	+	0.999985i	$0.498280\pi$
$314$	31.7873	+	25.3495i	1.79386	+	1.43056i
$315$	11.4515	+	3.17393i	0.645218	+	0.178831i
$316$	16.9898	−	10.6754i	0.955751	−	0.600538i
$317$	3.17041	+	1.38324i	0.178068	+	0.0776903i	0.487035	−	0.873383i	$-0.338078\pi$
$317$	3.17041	+	1.38324i	0.178068	+	0.0776903i	−0.308967	+	0.951073i	$0.599983\pi$
$318$	−32.9007	−	31.9658i	−1.84498	−	1.79255i
$319$	−6.62917	−	2.36547i	−0.371162	−	0.132441i
$320$	25.2045	−	14.5518i	1.40898	−	0.813473i
$321$	17.3740	+	2.36317i	0.969720	+	0.131899i
$322$	−10.9246	+	0.408768i	−0.608802	+	0.0227798i
$323$	−2.06960	−	9.06752i	−0.115156	−	0.504530i
$324$	−28.1611	+	12.9714i	−1.56451	+	0.720632i
$325$	1.61693	−	1.28946i	0.0896911	−	0.0715263i
$326$	−31.1045	+	33.5227i	−1.72272	+	1.85665i
$327$	−1.14178	−	12.7647i	−0.0631407	−	0.705889i
$328$	−38.2145	+	2.86378i	−2.11005	+	0.158126i
$329$	0.638744	−	17.0708i	0.0352151	−	0.941143i
$330$	11.1218	−	5.55482i	0.612235	−	0.305783i
$331$	−33.9227	+	9.08957i	−1.86456	+	0.499608i	−0.999996	−	0.00290946i	$-0.999074\pi$
$331$	−33.9227	+	9.08957i	−1.86456	+	0.499608i	−0.864567	+	0.502518i	$0.832407\pi$
$332$	−11.3637	+	5.47248i	−0.623665	+	0.300341i
$333$	−24.7297	−	17.1730i	−1.35518	−	0.941074i
$334$	0.847122	−	7.51842i	0.0463525	−	0.411390i
$335$	−14.7325	−	1.10405i	−0.804920	−	0.0603204i
$336$	2.48942	+	1.38983i	0.135809	+	0.0758213i
$337$	−1.24688	−	6.58990i	−0.0679217	−	0.358975i	0.932073	−	0.362271i	$-0.117998\pi$
$337$	−1.24688	−	6.58990i	−0.0679217	−	0.358975i	−0.999995	+	0.00329608i	$0.998951\pi$
$338$	−4.09595	−	0.153259i	−0.222790	−	0.00833622i
$339$	32.0518	+	5.58735i	1.74081	+	0.303463i
$340$	4.21686	−	22.2866i	0.228691	−	1.20866i
$341$	1.27491	−	5.58575i	0.0690404	−	0.302486i
$342$	−7.87437	+	21.8993i	−0.425797	+	1.18418i
$343$	11.7189	−	14.6951i	0.632763	−	0.793459i
$344$	3.82317	−	12.3944i	0.206132	−	0.668263i
$345$	2.36504	−	11.0967i	0.127330	−	0.597427i
$346$	1.04119	+	1.41076i	0.0559747	+	0.0758430i
$347$	−3.15915	−	5.47181i	−0.169592	−	0.293742i	0.768684	−	0.639628i	$-0.220912\pi$
$347$	−3.15915	−	5.47181i	−0.169592	−	0.293742i	−0.938276	+	0.345886i	$0.887578\pi$
$348$	32.1317	−	0.265616i	1.72244	−	0.0142385i
$349$	−4.78605	+	8.28968i	−0.256191	+	0.443736i	−0.965218	−	0.261445i	$-0.915801\pi$
$349$	−4.78605	+	8.28968i	−0.256191	+	0.443736i	0.709027	+	0.705181i	$0.249134\pi$
$350$	2.10119	−	0.236747i	0.112313	−	0.0126547i
$351$	18.8017	−	6.70238i	1.00356	−	0.357747i
$352$	−5.68516	+	1.29760i	−0.303020	+	0.0691624i
$353$	−1.36548	−	3.47919i	−0.0726773	−	0.185179i	0.889919	−	0.456119i	$-0.150761\pi$
$353$	−1.36548	−	3.47919i	−0.0726773	−	0.185179i	−0.962596	+	0.270940i	$0.912666\pi$
$354$	−0.180268	+	0.0817626i	−0.00958116	+	0.00434563i
$355$	−26.8811	+	8.29173i	−1.42670	+	0.440079i
$356$	−2.82357	−	2.42987i	−0.149649	−	0.128783i
$357$	−7.65881	+	2.80446i	−0.405347	+	0.148428i
$358$	19.8906	+	37.6349i	1.05125	+	1.98907i
$359$	−11.8233	−	4.13714i	−0.624009	−	0.218350i	−0.000291213	−	1.00000i	$-0.500093\pi$
$359$	−11.8233	−	4.13714i	−0.624009	−	0.218350i	−0.623717	+	0.781650i	$0.714378\pi$
$360$	−16.3409	+	17.3111i	−0.861242	+	0.912376i
$361$	−3.44866	−	7.16122i	−0.181509	−	0.376907i
$362$	−12.5973	−	9.29719i	−0.662097	−	0.488650i
$363$	15.8777	−	2.62772i	0.833363	−	0.137919i
$364$	−18.4038	−	12.5475i	−0.964619	−	0.657666i
$365$	−0.922615	+	3.44324i	−0.0482919	+	0.180228i
$366$	−23.4749	−	1.41934i	−1.22705	−	0.0741900i
$367$	−11.6192	+	6.14090i	−0.606515	+	0.320553i	−0.742178	−	0.670202i	$-0.766207\pi$
$367$	−11.6192	+	6.14090i	−0.606515	+	0.320553i	0.135663	+	0.990755i	$0.456683\pi$
$368$	1.18112	−	2.45263i	0.0615703	−	0.127852i
$369$	−31.8446	+	12.1839i	−1.65777	+	0.634270i
$370$	−53.7302	−	12.2636i	−2.79330	−	0.637552i
$371$	2.84722	+	18.8901i	0.147820	+	0.980724i
$372$	3.30282	+	25.9468i	0.171243	+	1.34528i
$373$	24.5858	−	22.8123i	1.27301	−	1.18118i	0.299101	−	0.954221i	$-0.403313\pi$
$373$	24.5858	−	22.8123i	1.27301	−	1.18118i	0.973905	−	0.226956i	$-0.0728773\pi$
$374$	−3.98706	+	7.54388i	−0.206166	+	0.390085i
$375$	2.45110	−	18.0204i	0.126574	−	0.930569i
$376$	29.6368	+	17.1108i	1.52840	+	0.882423i
$377$	−20.6190	−	1.67265i	−1.06193	−	0.0861461i
$378$	19.9225	+	4.42506i	1.02470	+	0.227601i
$379$	3.11951	+	27.6864i	0.160239	+	1.42216i	0.774260	+	0.632868i	$0.218122\pi$
$379$	3.11951	+	27.6864i	0.160239	+	1.42216i	−0.614021	+	0.789289i	$0.710449\pi$
$380$	1.00777	+	26.9333i	0.0516976	+	1.38165i
$381$	−4.51155	−	0.103732i	−0.231134	−	0.00531437i
$382$	−8.20650	+	54.4466i	−0.419881	+	2.78573i
$383$	−2.30161	+	5.86440i	−0.117607	+	0.299657i	−0.977540	−	0.210749i	$-0.932410\pi$
$383$	−2.30161	+	5.86440i	−0.117607	+	0.299657i	0.859934	+	0.510406i	$0.170505\pi$
$384$	28.9671	−	18.7889i	1.47822	−	0.958816i
$385$	−5.08696	−	0.962505i	−0.259255	−	0.0490538i
$386$	−12.2581	−	5.90318i	−0.623920	−	0.300464i
$387$	0.0989835	−	11.5399i	0.00503161	−	0.586608i
$388$	−14.4915	+	41.4144i	−0.735697	+	2.10250i
$389$	−1.20875	−	4.51113i	−0.0612863	−	0.228724i	0.928489	−	0.371360i	$-0.121109\pi$
$389$	−1.20875	−	4.51113i	−0.0612863	−	0.228724i	−0.989775	+	0.142637i	$0.954442\pi$
$390$	27.3483	−	24.2298i	1.38484	−	1.22692i
$391$	3.11411	+	7.13762i	0.157487	+	0.360965i
$392$	5.61868	+	12.8781i	0.283786	+	0.650445i
$393$	−12.6436	+	11.2019i	−0.637786	+	0.565059i
$394$	−12.3852	−	46.2223i	−0.623959	−	2.32865i
$395$	4.52721	−	12.9380i	0.227788	−	0.650982i
$396$	11.7559	−	6.65346i	0.590754	−	0.334349i
$397$	−26.3027	−	12.6667i	−1.32009	−	0.635723i	−0.364718	−	0.931118i	$-0.618834\pi$
$397$	−26.3027	−	12.6667i	−1.32009	−	0.635723i	−0.955375	+	0.295395i	$0.904549\pi$
$398$	−41.1586	−	7.78763i	−2.06309	−	0.390358i
$399$	8.13094	−	5.27395i	0.407056	−	0.264028i
$400$	−0.192361	+	0.490128i	−0.00961806	+	0.0245064i
$401$	−3.00846	+	19.9598i	−0.150235	+	0.996747i	0.778938	+	0.627101i	$0.215759\pi$
$401$	−3.00846	+	19.9598i	−0.150235	+	0.996747i	−0.929173	+	0.369645i	$0.879479\pi$
$402$	−25.3656	−	0.583221i	−1.26512	−	0.0290884i
$403$	−0.629632	−	16.8273i	−0.0313642	−	0.838225i
$404$	−4.98362	−	44.2308i	−0.247944	−	2.20057i
$405$	−9.51581	+	18.9224i	−0.472844	+	0.940262i
$406$	−16.9400	−	12.6639i	−0.840721	−	0.628497i
$407$	11.3598	+	6.55859i	0.563085	+	0.325097i
$408$	2.20213	−	16.1900i	0.109022	−	0.801524i
$409$	−5.75879	+	10.8962i	−0.284754	+	0.538781i	−0.984451	−	0.175659i	$-0.943794\pi$
$409$	−5.75879	+	10.8962i	−0.284754	+	0.538781i	0.699697	+	0.714440i	$0.253318\pi$
$410$	−45.7515	+	42.4512i	−2.25950	+	2.09651i
$411$	2.33118	+	18.3137i	0.114989	+	0.903346i
$412$	2.12415	+	14.0928i	0.104649	+	0.694303i
$413$	0.0803667	+	0.0183432i	0.00395459	+	0.000902609i
$414$	3.06930	−	19.2421i	0.150848	−	0.945698i
$415$	−3.73841	+	7.76289i	−0.183511	+	0.381065i
$416$	−15.1526	+	8.00838i	−0.742917	+	0.392643i
$417$	18.2180	+	1.10150i	0.892140	+	0.0539406i
$418$	2.62418	−	9.79356i	0.128353	−	0.479018i
$419$	29.1917	+	19.9026i	1.42611	+	0.972305i	0.997634	+	0.0687517i	$0.0219016\pi$
$419$	29.1917	+	19.9026i	1.42611	+	0.972305i	0.428476	+	0.903553i	$0.359051\pi$
$420$	23.3181	−	3.85909i	1.13781	−	0.188304i
$421$	0.0647744	+	0.0478057i	0.00315691	+	0.00232991i	0.595397	−	0.803431i	$-0.296995\pi$
$421$	0.0647744	+	0.0478057i	0.00315691	+	0.00232991i	−0.592241	+	0.805761i	$0.701756\pi$
$422$	−26.3970	−	54.8140i	−1.28499	−	2.66830i
$423$	29.6253	+	7.02966i	1.44043	+	0.341794i
$424$	−36.1221	−	12.6397i	−1.75425	−	0.613837i
$425$	−0.703809	−	1.33167i	−0.0341398	−	0.0645956i
$426$	−45.3659	+	16.6118i	−2.19798	+	0.804845i
$427$	7.42352	+	6.38846i	0.359249	+	0.309159i
$428$	33.3251	−	10.2794i	1.61083	−	0.496875i
$429$	−7.91981	+	3.59211i	−0.382372	+	0.173429i
$430$	−7.71768	−	19.6643i	−0.372180	−	0.948298i
$431$	0.724552	−	0.165374i	0.0349004	−	0.00796580i	−0.205035	−	0.978755i	$-0.565731\pi$
$431$	0.724552	−	0.165374i	0.0349004	−	0.00796580i	0.239936	+	0.970789i	$0.422874\pi$
$432$	−3.29225	+	3.87111i	−0.158398	+	0.186249i
$433$	−12.4102	+	1.39830i	−0.596398	+	0.0671980i	−0.405003	−	0.914315i	$-0.632730\pi$
$433$	−12.4102	+	1.39830i	−0.596398	+	0.0671980i	−0.191395	+	0.981513i	$0.561301\pi$
$434$	8.60823	−	14.9099i	0.413208	−	0.715698i
$435$	17.0481	−	13.8275i	0.817395	−	0.662978i
$436$	−12.7450	−	22.0749i	−0.610372	−	1.05720i
$437$	−5.49486	−	7.44528i	−0.262855	−	0.356156i
$438$	−1.27612	+	5.98750i	−0.0609752	+	0.286094i
$439$	−9.66861	+	31.3449i	−0.461458	+	1.49601i	0.363921	+	0.931430i	$0.381438\pi$
$439$	−9.66861	+	31.3449i	−0.461458	+	1.49601i	−0.825379	+	0.564579i	$0.809039\pi$
$440$	6.46650	−	8.10874i	0.308278	−	0.386569i
$441$	8.07274	+	9.54508i	0.384416	+	0.454528i
$442$	−5.58039	+	24.4493i	−0.265432	+	1.16293i
$443$	1.09583	−	5.79160i	0.0520644	−	0.275167i	−0.946854	−	0.321664i	$-0.895758\pi$
$443$	1.09583	−	5.79160i	0.0520644	−	0.275167i	0.998918	+	0.0464965i	$0.0148056\pi$
$444$	−58.9935	−	10.2839i	−2.79971	−	0.488052i
$445$	−2.54299	−	0.0951518i	−0.120549	−	0.00451063i
$446$	−7.40767	−	39.1505i	−0.350764	−	1.85383i
$447$	11.5516	+	6.44917i	0.546372	+	0.305035i
$448$	−20.7568	−	1.55551i	−0.980669	−	0.0734909i
$449$	1.91729	−	17.0164i	0.0904825	−	0.803055i	−0.863736	−	0.503944i	$-0.831882\pi$
$449$	1.91729	−	17.0164i	0.0904825	−	0.803055i	0.954219	−	0.299110i	$-0.0966898\pi$
$450$	−0.313869	+	3.75573i	−0.0147959	+	0.177047i
$451$	13.3837	−	6.44523i	0.630212	−	0.303494i
$452$	62.5063	−	16.7485i	2.94005	−	0.787784i
$453$	32.2104	−	16.0876i	1.51338	−	0.755862i
$454$	−0.967622	+	25.8602i	−0.0454127	+	1.21368i
$455$	−15.1736	+	1.13710i	−0.711348	+	0.0533082i
$456$	1.72974	+	19.3378i	0.0810026	+	0.905577i
$457$	−1.95940	+	2.11173i	−0.0916570	+	0.0987827i	−0.777215	−	0.629236i	$-0.783368\pi$
$457$	−1.95940	+	2.11173i	−0.0916570	+	0.0987827i	0.685558	+	0.728018i	$0.259558\pi$
$458$	10.2628	−	8.18434i	0.479551	−	0.382429i
$459$	−2.25050	−	14.3621i	−0.105045	−	0.670364i
$460$	−5.02156	−	22.0009i	−0.234132	−	1.02580i
$461$	22.2063	−	0.830902i	1.03425	−	0.0386990i	0.485131	−	0.874442i	$-0.338772\pi$
$461$	22.2063	−	0.830902i	1.03425	−	0.0386990i	0.549121	+	0.835743i	$0.314962\pi$
$462$	−8.81016	−	1.19834i	−0.409886	−	0.0557518i
$463$	−16.4210	+	9.48066i	−0.763148	+	0.440604i	−0.830425	−	0.557131i	$-0.811902\pi$
$463$	−16.4210	+	9.48066i	−0.763148	+	0.440604i	0.0672769	+	0.997734i	$0.478569\pi$
$464$	4.75902	−	2.25590i	0.220932	−	0.104728i
$465$	12.8154	+	12.4512i	0.594298	+	0.577411i
$466$	44.7339	+	19.5172i	2.07226	+	0.904118i
$467$	5.50558	−	3.45939i	0.254768	−	0.160081i	−0.398593	−	0.917128i	$-0.630501\pi$
$467$	5.50558	−	3.45939i	0.254768	−	0.160081i	0.653361	+	0.757047i	$0.273358\pi$
$468$	28.3126	−	27.8311i	1.30875	−	1.28649i
$469$	8.26102	+	6.58795i	0.381459	+	0.304203i
$470$	55.1123	−	8.30684i	2.54214	−	0.383166i
$471$	30.1383	−	1.56290i	1.38870	−	0.0720148i
$472$	−0.107718	+	0.125170i	−0.00495810	+	0.00576142i
$473$	0.375732	+	5.01380i	0.0172762	+	0.230535i
$474$	6.61382	−	22.5924i	0.303783	−	1.03770i
$475$	1.16745	+	1.35660i	0.0535662	+	0.0622451i
$476$	−11.4709	+	11.4709i	−0.525767	+	0.525767i
$477$	−34.0136	−	1.56495i	−1.55738	−	0.0716543i
$478$	−35.3688	−	3.98510i	−1.61773	−	0.182274i
$479$	−4.45413	+	6.03514i	−0.203515	+	0.275752i	−0.894454	−	0.447160i	$-0.852435\pi$
$479$	−4.45413	+	6.03514i	−0.203515	+	0.275752i	0.690939	+	0.722913i	$0.257197\pi$
$480$	5.75847	−	17.2503i	0.262837	−	0.787363i
$481$	37.2385	+	9.97802i	1.69793	+	0.454958i
$482$	36.1123	−	6.83282i	1.64487	−	0.311227i
$483$	−5.86830	+	5.60451i	−0.267017	+	0.255014i
$484$	26.4477	−	18.0317i	1.20217	−	0.819625i
$485$	9.89960	+	28.2914i	0.449518	+	1.28465i
$486$	−14.6374	+	33.2998i	−0.663967	+	1.51051i
$487$	17.3852	+	21.8003i	0.787797	+	0.987866i	0.999944	+	0.0106282i	$0.00338311\pi$
$487$	17.3852	+	21.8003i	0.787797	+	0.987866i	−0.212147	+	0.977238i	$0.568045\pi$
$488$	−18.2638	+	7.16802i	−0.826764	+	0.324481i
$489$	−0.780261	+	33.9353i	−0.0352846	+	1.53461i
$490$	20.2314	+	10.6926i	0.913962	+	0.483043i
$491$	−11.2284	+	8.28695i	−0.506731	+	0.373985i	−0.816976	−	0.576672i	$-0.804351\pi$
$491$	−11.2284	+	8.28695i	−0.506731	+	0.373985i	0.310244	+	0.950657i	$0.399589\pi$
$492$	−47.2568	+	48.6389i	−2.13050	+	2.19281i
$493$	−3.98875	+	14.5285i	−0.179644	+	0.654332i
$494$		−	29.7992i		−	1.34073i
$495$	3.44484	−	8.56066i	0.154834	−	0.384773i
$496$	2.28085	+	3.62995i	0.102413	+	0.162989i
$497$	19.2255	+	5.93027i	0.862380	+	0.266009i
$498$	−5.72125	+	13.6465i	−0.256375	+	0.611514i
$499$	−9.81995	−	3.85404i	−0.439601	−	0.172531i	0.135210	−	0.990817i	$-0.456829\pi$
$499$	−9.81995	−	3.85404i	−0.439601	−	0.172531i	−0.574811	+	0.818286i	$0.694924\pi$
$500$	−10.6619	−	34.5650i	−0.476814	−	1.54579i
$501$	−3.23015	−	4.59409i	−0.144313	−	0.205249i
$502$	10.6822	+	15.6679i	0.476771	+	0.699294i
$503$	1.03102	+	0.647834i	0.0459710	+	0.0288855i	0.554822	−	0.831969i	$-0.312787\pi$
$503$	1.03102	+	0.647834i	0.0459710	+	0.0288855i	−0.508851	+	0.860855i	$0.669929\pi$
$504$	16.6308	−	3.64607i	0.740793	−	0.162409i
$505$	−21.5007	−	21.5007i	−0.956768	−	0.956768i
$506$	−0.634406	+	8.46556i	−0.0282028	+	0.376340i
$507$	−2.35108	+	1.93100i	−0.104415	+	0.0857589i
$508$	−8.22679	+	3.58931i	−0.365005	+	0.159250i
$509$	−9.57125	+	14.0384i	−0.424238	+	0.622243i	−0.977543	−	0.210736i	$-0.932414\pi$
$509$	−9.57125	+	14.0384i	−0.424238	+	0.622243i	0.553305	+	0.832979i	$0.313366\pi$
$510$	−13.6360	−	22.8512i	−0.603811	−	1.01187i
$511$	1.93244	−	1.66300i	0.0854862	−	0.0735668i
$512$	5.83029	−	9.27886i	0.257665	−	0.410071i
$513$	6.40464	+	16.0429i	0.282772	+	0.708312i
$514$	30.8811	−	10.8058i	1.36211	−	0.476622i
$515$	7.13696	+	6.62213i	0.314492	+	0.291806i
$516$	−9.48111	−	20.9038i	−0.417383	−	0.920237i
$517$	−13.1173	−	1.97711i	−0.576897	−	0.0869532i
$518$	26.8098	+	28.8941i	1.17796	+	1.26954i
$519$	1.27289	+	0.271291i	0.0558736	+	0.0119083i
$520$	12.1896	−	27.9389i	0.534551	−	1.22520i
$521$	31.1681			1.36550			0.682749	−	0.730653i	$-0.260784\pi$
$521$	31.1681			1.36550			0.682749	+	0.730653i	$0.260784\pi$
$522$	28.0091	−	25.2316i	1.22593	−	1.10436i
$523$	−17.5458			−0.767226			−0.383613	−	0.923494i	$-0.625320\pi$
$523$	−17.5458			−0.767226			−0.383613	+	0.923494i	$0.625320\pi$
$524$	−13.4355	+	30.7945i	−0.586932	+	1.34526i
$525$	1.05085	−	1.16580i	0.0458630	−	0.0508799i
$526$	9.49874	+	10.2372i	0.414165	+	0.446364i
$527$	−12.1269	−	1.82783i	−0.528256	−	0.0796217i
$528$	1.28891	−	1.80014i	0.0560928	−	0.0783413i
$529$	−11.1807	−	10.3741i	−0.486116	−	0.451050i
$530$	−58.8300	+	20.5855i	−2.55541	+	0.894178i
$531$	−0.0599082	+	0.134160i	−0.00259980	+	0.00582204i
$532$	10.2556	−	16.3217i	0.444636	−	0.707633i
$533$	33.0922	−	28.4782i	1.43338	−	1.23353i
$534$	−4.36989	+	0.0629803i	−0.189104	+	0.00272542i
$535$	13.4204	−	19.6841i	0.580215	−	0.851019i
$536$	−19.4011	+	8.46461i	−0.838000	+	0.365616i
$537$	29.5760	+	11.1186i	1.27630	+	0.479802i
$538$	−0.598864	+	7.99128i	−0.0258189	+	0.344529i
$539$	−3.85121	−	3.85121i	−0.165883	−	0.165883i
$540$	−1.32956	+	42.1061i	−0.0572150	+	1.81196i
$541$	22.4738	+	14.1213i	0.966226	+	0.607120i	0.920045	−	0.391813i	$-0.128152\pi$
$541$	22.4738	+	14.1213i	0.966226	+	0.607120i	0.0461812	+	0.998933i	$0.485295\pi$
$542$	−27.0871	−	39.7294i	−1.16349	−	1.70653i
$543$	−11.5752	+	1.03538i	−0.496739	+	0.0444326i
$544$	3.67917	+	11.9276i	0.157743	+	0.511391i
$545$	−16.2092	−	6.36165i	−0.694326	−	0.272503i
$546$	−25.9228	+	3.29976i	−1.10939	+	0.141217i
$547$	15.2190	+	4.69443i	0.650716	+	0.200719i	0.602502	−	0.798118i	$-0.294171\pi$
$547$	15.2190	+	4.69443i	0.650716	+	0.200719i	0.0482146	+	0.998837i	$0.484647\pi$
$548$	19.5358	+	31.0910i	0.834528	+	1.32814i
$549$	−13.7409	+	10.7665i	−0.586448	+	0.459503i
$550$		−	1.64198i		−	0.0700144i
$551$	0.779314	−	17.8855i	0.0331999	−	0.761947i
$552$	−4.43320	−	15.6398i	−0.188690	−	0.665675i
$553$	−7.88783	+	5.82148i	−0.335425	+	0.247555i
$554$	−53.1805	−	28.1067i	−2.25942	−	1.19414i
$555$	−35.8881	+	19.6342i	−1.52337	+	0.833426i
$556$	33.7918	−	13.2623i	1.43309	−	0.562448i
$557$	16.0211	+	20.0899i	0.678837	+	0.851235i	0.995247	−	0.0973878i	$-0.0310487\pi$
$557$	16.0211	+	20.0899i	0.678837	+	0.851235i	−0.316409	+	0.948623i	$0.602477\pi$
$558$	23.0868	+	20.2151i	0.977343	+	0.855772i
$559$	4.88058	+	13.9479i	0.206427	+	0.589934i
$560$	3.20074	−	2.18223i	0.135256	−	0.0922160i
$561$	1.49819	+	6.15381i	0.0632535	+	0.259814i
$562$	21.2174	−	4.01454i	0.895001	−	0.169343i
$563$	3.92147	+	1.05075i	0.165270	+	0.0442840i	0.340505	−	0.940243i	$-0.389402\pi$
$563$	3.92147	+	1.05075i	0.165270	+	0.0442840i	−0.175235	+	0.984527i	$0.556069\pi$
$564$	59.3358	−	12.1151i	2.49849	−	0.510139i
$565$	26.2505	−	35.5682i	1.10437	−	1.49637i
$566$	−37.7266	−	4.25077i	−1.58577	−	0.178673i
$567$	13.2468	−	7.34799i	0.556313	−	0.308586i
$568$	−28.4998	+	28.4998i	−1.19582	+	1.19582i
$569$	29.5964	+	34.3917i	1.24075	+	1.44178i	0.854558	+	0.519356i	$0.173828\pi$
$569$	29.5964	+	34.3917i	1.24075	+	1.44178i	0.386189	+	0.922419i	$0.373791\pi$
$570$	21.8390	+	22.8669i	0.914733	+	0.957788i
$571$	1.69773	+	22.6546i	0.0710478	+	0.948067i	0.912854	+	0.408287i	$0.133874\pi$
$571$	1.69773	+	22.6546i	0.0710478	+	0.948067i	−0.841806	+	0.539780i	$0.818507\pi$
$572$	−11.2825	+	13.1105i	−0.471744	+	0.548176i
$573$	22.2409	+	34.2891i	0.929126	+	1.43245i
$574$	44.1389	−	6.65287i	1.84232	−	0.277686i
$575$	−1.17162	−	0.934337i	−0.0488600	−	0.0389645i
$576$	9.90930	−	35.7525i	0.412887	−	1.48969i
$577$	−18.1390	+	11.3975i	−0.755136	+	0.474484i	−0.853777	−	0.520640i	$-0.825694\pi$
$577$	−18.1390	+	11.3975i	−0.755136	+	0.474484i	0.0986403	+	0.995123i	$0.468551\pi$
$578$	−19.6184	−	8.55942i	−0.816017	−	0.356025i
$579$	−9.71612	+	2.75409i	−0.403788	+	0.114456i
$580$	19.1845	−	39.2187i	0.796593	−	1.62847i
$581$	5.33671	−	3.08115i	0.221404	−	0.127828i
$582$	19.4949	+	47.6416i	0.808088	+	1.97481i
$583$	14.8242	−	0.554683i	0.613956	−	0.0229726i
$584$	1.13650	+	4.97931i	0.0470285	+	0.206046i
$585$	3.26763	−	26.9234i	0.135100	−	1.11314i
$586$	45.4132	−	36.2158i	1.87600	−	1.49606i
$587$	−10.4100	+	11.2193i	−0.429667	+	0.463071i	−0.910360	−	0.413818i	$-0.864195\pi$
$587$	−10.4100	+	11.2193i	−0.429667	+	0.463071i	0.480692	+	0.876889i	$0.340385\pi$
$588$	22.5551	+	10.4643i	0.930156	+	0.431539i
$589$	14.5319	−	1.08901i	0.598776	−	0.0448721i
$590$	−0.0100564	+	0.268763i	−0.000414015	+	0.0110648i
$591$	−29.6331	−	19.5840i	−1.21894	−	0.805577i
$592$	−9.48054	+	2.54030i	−0.389648	+	0.104406i
$593$	−14.7013	+	7.07979i	−0.603712	+	0.290732i	−0.710664	−	0.703532i	$-0.751605\pi$
$593$	−14.7013	+	7.07979i	−0.603712	+	0.290732i	0.106952	+	0.994264i	$0.465891\pi$
$594$	5.14679	−	14.9886i	0.211175	−	0.614991i
$595$	−1.24078	+	11.0122i	−0.0508670	+	0.451457i
$596$	26.2403	+	1.96644i	1.07485	+	0.0805486i
$597$	−26.7004	+	15.9329i	−1.09277	+	0.652088i
$598$	4.63859	+	24.5155i	0.189686	+	1.00252i
$599$	9.13481	+	0.341801i	0.373238	+	0.0139656i	0.223353	−	0.974738i	$-0.428300\pi$
$599$	9.13481	+	0.341801i	0.373238	+	0.0139656i	0.149886	+	0.988703i	$0.452109\pi$
$600$	1.08112	+	2.95249i	0.0441367	+	0.120535i
$601$	5.40074	−	28.5436i	0.220301	−	1.16432i	−0.681385	−	0.731925i	$-0.738622\pi$
$601$	5.40074	−	28.5436i	0.220301	−	1.16432i	0.901686	−	0.432392i	$-0.142330\pi$
$602$	−3.36193	+	14.7296i	−0.137022	+	0.600333i
$603$	−14.3798	+	12.1617i	−0.585590	+	0.495262i
$604$	44.6492	−	55.9883i	1.81675	−	2.27813i
$605$	6.44536	−	20.8953i	0.262041	−	0.849516i
$606$	−38.7877	−	34.9632i	−1.57564	−	1.42028i
$607$	−5.58881	−	7.57257i	−0.226843	−	0.307361i	0.676363	−	0.736568i	$-0.263555\pi$
$607$	−5.58881	−	7.57257i	−0.226843	−	0.307361i	−0.903206	+	0.429207i	$0.858793\pi$
$608$	−7.41599	−	12.8449i	−0.300758	−	0.520928i
$609$	−15.6452	+	1.30258i	−0.633974	+	0.0527832i
$610$	−15.9770	+	27.6731i	−0.646892	+	1.12045i
$611$	−38.7427	+	4.36525i	−1.56736	+	0.176599i
$612$	−16.0825	−	24.0289i	−0.650096	−	0.971311i
$613$	29.2534	−	6.67690i	1.18153	−	0.269677i	0.413753	−	0.910389i	$-0.364218\pi$
$613$	29.2534	−	6.67690i	1.18153	−	0.269677i	0.767782	+	0.640712i	$0.221361\pi$
$614$	−5.97437	−	15.2224i	−0.241106	−	0.614328i
$615$	−4.52301	+	46.1055i	−0.182385	+	1.85915i
$616$	−7.08815	+	2.18641i	−0.285590	+	0.0880928i
$617$	−8.89727	−	7.65672i	−0.358191	−	0.308248i	0.454722	−	0.890633i	$-0.349739\pi$
$617$	−8.89727	−	7.65672i	−0.358191	−	0.308248i	−0.812913	+	0.582385i	$0.802120\pi$
$618$	12.8294	+	10.7227i	0.516076	+	0.431331i
$619$	6.48060	+	12.2619i	0.260477	+	0.492847i	0.979318	−	0.202328i	$-0.0648507\pi$
$619$	6.48060	+	12.2619i	0.260477	+	0.492847i	−0.718841	+	0.695175i	$0.755327\pi$
$620$	33.5446	+	11.7378i	1.34718	+	0.471400i
$621$	−7.76631	−	12.2014i	−0.311651	−	0.489626i
$622$	−24.7433	−	51.3799i	−0.992114	−	2.06015i
$623$	1.46439	+	1.08077i	0.0586694	+	0.0433000i
$624$	2.28977	−	6.09090i	0.0916641	−	0.243831i
$625$	−22.6406	−	15.4361i	−0.905625	−	0.617445i
$626$	−3.07077	+	11.4603i	−0.122733	+	0.458044i
$627$	−3.36274	−	6.73284i	−0.134295	−	0.268884i
$628$	53.0688	−	28.0477i	2.11767	−	1.11922i
$629$	12.1824	−	25.2970i	0.485743	−	1.00866i
$630$	17.4740	−	21.5302i	0.696179	−	0.857783i
$631$	−38.5453	−	8.79772i	−1.53447	−	0.350232i	−0.629937	−	0.776646i	$-0.716919\pi$
$631$	−38.5453	−	8.79772i	−1.53447	−	0.350232i	−0.904528	+	0.426414i	$0.859777\pi$
$632$	−2.92706	−	19.4198i	−0.116432	−	0.772477i
$633$	−41.6469	−	17.4603i	−1.65532	−	0.693986i
$634$	5.91680	−	5.48999i	0.234986	−	0.218035i
$635$	−2.86509	+	5.42101i	−0.113698	+	0.215126i
$636$	−62.6790	+	25.6481i	−2.48538	+	1.01701i
$637$	−13.8628	−	8.00368i	−0.549263	−	0.317117i
$638$	−11.2450	+	11.9709i	−0.445194	+	0.473931i
$639$	−17.0277	+	31.5597i	−0.673606	+	1.24848i
$640$	−5.25255	−	46.6176i	−0.207625	−	1.84272i
$641$	−1.32318	−	35.3628i	−0.0522626	−	1.39675i	−0.740888	−	0.671629i	$-0.765595\pi$
$641$	−1.32318	−	35.3628i	−0.0522626	−	1.39675i	0.688625	−	0.725117i	$-0.258215\pi$
$642$	21.2664	−	34.9535i	0.839317	−	1.37950i
$643$	4.10266	−	27.2194i	0.161793	−	1.07343i	−0.749600	−	0.661891i	$-0.769754\pi$
$643$	4.10266	−	27.2194i	0.161793	−	1.07343i	0.911393	−	0.411536i	$-0.135008\pi$
$644$	−5.89652	+	15.0241i	−0.232356	+	0.592032i
$645$	−13.9672	−	7.12630i	−0.549958	−	0.280598i
$646$	−21.3244	−	4.03479i	−0.838997	−	0.158747i
$647$	−5.32845	−	2.56604i	−0.209483	−	0.100882i	0.326200	−	0.945301i	$-0.394232\pi$
$647$	−5.32845	−	2.56604i	−0.209483	−	0.100882i	−0.535683	+	0.844419i	$0.679946\pi$
$648$	0.614332	+	30.3401i	0.0241333	+	1.19187i
$649$	0.0211421	−	0.0604207i	0.000829901	−	0.00237172i
$650$	−1.24903	−	4.66144i	−0.0489910	−	0.182837i
$651$	−2.55652	−	12.5209i	−0.100198	−	0.490734i
$652$	26.9983	+	61.8807i	1.05733	+	2.42344i
$653$	−9.74792	−	22.3425i	−0.381466	−	0.874328i	−0.996322	−	0.0856893i	$-0.972691\pi$
$653$	−9.74792	−	22.3425i	−0.381466	−	0.874328i	0.614856	−	0.788639i	$-0.289214\pi$
$654$	−28.3659	−	9.46910i	−1.10920	−	0.370271i
$655$	5.94032	+	22.1696i	0.232108	+	0.866238i
$656$	−3.67109	+	10.4914i	−0.143332	+	0.409619i
$657$	2.23825	+	3.95471i	0.0873223	+	0.154288i
$658$	−35.9142	−	17.2953i	−1.40008	−	0.674243i
$659$	3.61047	+	0.683137i	0.140644	+	0.0266113i	0.255757	−	0.966741i	$-0.417675\pi$
$659$	3.61047	+	0.683137i	0.140644	+	0.0266113i	−0.115113	+	0.993352i	$0.536723\pi$
$660$	−0.950505	−	18.3291i	−0.0369984	−	0.713460i
$661$	8.27249	−	21.0780i	0.321763	−	0.819838i	−0.674877	−	0.737930i	$-0.735803\pi$
$661$	8.27249	−	21.0780i	0.321763	−	0.819838i	0.996640	−	0.0819079i	$-0.0261013\pi$
$662$	−12.2139	+	81.0341i	−0.474708	+	3.14948i
$663$	8.93432	+	16.3305i	0.346980	+	0.634223i
$664$	0.461590	+	12.3362i	0.0179132	+	0.478739i
$665$	−1.47437	−	13.0854i	−0.0571735	−	0.507429i
$666$	−59.8048	+	36.8662i	−2.31739	+	1.42854i
$667$	2.14295	+	14.8355i	0.0829753	+	0.574435i
$668$	−9.67356	−	5.58503i	−0.374281	−	0.216091i
$669$	−23.3867	−	18.1051i	−0.904181	−	0.699984i
$670$	−16.1086	+	30.4789i	−0.622328	+	1.17750i
$671$	5.57514	−	5.17298i	0.215226	−	0.199700i
$672$	−10.3528	+	7.87365i	−0.399367	+	0.303733i
$673$	−0.584697	−	3.87921i	−0.0225384	−	0.149533i	0.974731	−	0.223382i	$-0.0717097\pi$
$673$	−0.584697	−	3.87921i	−0.0225384	−	0.149533i	−0.997269	+	0.0738493i	$0.976472\pi$
$674$	−15.2577	−	3.48246i	−0.587703	−	0.134139i
$675$	1.67431	+	2.24112i	0.0644440	+	0.0862607i
$676$	−2.62555	+	5.45202i	−0.100983	+	0.209693i
$677$	−0.0298463	+	0.0157742i	−0.00114709	+	0.000606253i	−0.467842	−	0.883812i	$-0.654968\pi$
$677$	−0.0298463	+	0.0157742i	−0.00114709	+	0.000606253i	0.466695	+	0.884418i	$0.345445\pi$
$678$	41.8584	−	63.3371i	1.60756	−	2.43245i
$679$	5.54833	−	20.7066i	0.212925	−	0.794648i
$680$	−18.3427	−	12.5059i	−0.703411	−	0.479578i
$681$	12.1916	+	14.8438i	0.467184	+	0.568817i
$682$	−10.7569	−	7.93895i	−0.411903	−	0.303998i
$683$	1.35821	+	2.82036i	0.0519706	+	0.107918i	0.925337	−	0.379146i	$-0.123782\pi$
$683$	1.35821	+	2.82036i	0.0519706	+	0.107918i	−0.873366	+	0.487064i	$0.838068\pi$
$684$	24.9845	+	23.5843i	0.955308	+	0.901767i
$685$	23.6763	+	8.28471i	0.904626	+	0.316542i
$686$	−20.4939	−	38.7763i	−0.782459	−	1.48048i
$687$	1.67328	−	9.59877i	0.0638397	−	0.366216i
$688$	−2.85158	−	2.45398i	−0.108715	−	0.0935571i
$689$	41.6627	−	12.8512i	1.58722	−	0.489593i
$690$	−21.5262	−	15.4129i	−0.819490	−	0.586759i
$691$	−6.44902	−	16.4318i	−0.245332	−	0.625097i	0.754169	−	0.656681i	$-0.228040\pi$
$691$	−6.44902	−	16.4318i	−0.245332	−	0.625097i	−0.999501	+	0.0315839i	$0.989945\pi$
$692$	2.52369	−	0.576017i	0.0959365	−	0.0218969i
$693$	−5.48464	+	3.67085i	−0.208344	+	0.139444i
$694$	−14.6507	+	1.65074i	−0.556134	+	0.0626613i
$695$	12.3992	−	21.4761i	0.470329	−	0.814633i
$696$	12.3380	−	28.9291i	0.467670	−	1.09655i
$697$	−15.8984	−	27.5368i	−0.602195	−	1.04303i
$698$	13.2636	+	17.9715i	0.502034	+	0.680232i
$699$	34.4604	−	11.1760i	1.30341	−	0.422714i
$700$	0.920144	−	2.98303i	0.0347782	−	0.112748i
$701$	−2.79354	+	3.50299i	−0.105510	+	0.132306i	−0.831783	−	0.555101i	$-0.812680\pi$
$701$	−2.79354	+	3.50299i	−0.105510	+	0.132306i	0.726273	+	0.687407i	$0.241251\pi$
$702$	3.20968	−	46.4664i	0.121142	−	1.75376i
$703$	−7.42403	+	32.5268i	−0.280003	+	1.22677i
$704$	−3.00502	+	15.8819i	−0.113256	+	0.598573i
$705$	26.5306	−	31.7431i	0.999201	−	1.19552i
$706$	−8.71530	−	0.326104i	−0.328005	−	0.0122731i
$707$	4.04300	+	21.3677i	0.152053	+	0.803617i
$708$	0.00421135	+	0.292205i	0.000158272	+	0.0109817i
$709$	49.3235	+	3.69629i	1.85238	+	0.138817i	0.953888	−	0.300163i	$-0.0970412\pi$
$709$	49.3235	+	3.69629i	1.85238	+	0.138817i	0.898497	+	0.438980i	$0.144660\pi$
$710$	−7.34958	+	65.2293i	−0.275825	+	2.44801i
$711$	−7.44615	−	15.8075i	−0.279252	−	0.592828i
$712$	−3.28496	+	1.58196i	−0.123109	+	0.0592863i
$713$	−11.7857	+	3.15798i	−0.441380	+	0.118267i
$714$	−1.14861	+	18.9972i	−0.0429857	+	0.710953i
$715$	−0.441812	+	11.8077i	−0.0165228	+	0.441582i
$716$	62.6694	−	4.69642i	2.34206	−	0.175514i
$717$	−21.6119	+	15.1956i	−0.807112	+	0.567488i
$718$	−19.8810	+	21.4266i	−0.741951	+	0.799633i
$719$	32.1313	−	25.6239i	1.19830	−	0.955610i	0.198596	−	0.980081i	$-0.436362\pi$
$719$	32.1313	−	25.6239i	1.19830	−	0.955610i	0.999701	+	0.0244717i	$0.00779037\pi$
$720$	2.70676	+	6.35205i	0.100875	+	0.236727i
$721$	−1.54945	−	6.78860i	−0.0577047	−	0.252821i
$722$	−18.5341	+	0.693498i	−0.689769	+	0.0258093i
$723$	16.7001	−	21.5718i	0.621084	−	0.802265i
$724$	−20.0178	+	11.5573i	−0.743957	+	0.429524i
$725$	−0.627761	−	2.83046i	−0.0233145	−	0.105121i
$726$	9.19588	−	36.4105i	0.341291	−	1.35132i
$727$	−23.3529	−	10.1888i	−0.866111	−	0.377881i	−0.0806139	−	0.996745i	$-0.525688\pi$
$727$	−23.3529	−	10.1888i	−0.866111	−	0.377881i	−0.785497	+	0.618865i	$0.787593\pi$
$728$	−18.4595	+	11.5988i	−0.684153	+	0.429882i
$729$	8.25888	+	25.7059i	0.305885	+	0.952069i
$730$	6.50333	+	5.18623i	0.240699	+	0.191951i
$731$	10.6420	−	1.60402i	0.393609	−	0.0593269i
$732$	−15.7797	+	30.9275i	−0.583236	+	1.14311i
$733$	−28.5604	+	33.1878i	−1.05490	+	1.22582i	−0.0815102	+	0.996673i	$0.525974\pi$
$733$	−28.5604	+	33.1878i	−1.05490	+	1.22582i	−0.973392	+	0.229146i	$0.926407\pi$
$734$	2.29171	+	30.5808i	0.0845886	+	1.12876i
$735$	16.5035	−	4.01788i	0.608740	−	0.148202i
$736$	8.10053	+	9.41299i	0.298590	+	0.346967i
$737$	5.80189	−	5.80189i	0.213715	−	0.213715i
$738$	−3.65670	+	79.4770i	−0.134605	+	2.92559i
$739$	7.63712	+	0.860496i	0.280936	+	0.0316539i	0.251308	−	0.967907i	$-0.419139\pi$
$739$	7.63712	+	0.860496i	0.280936	+	0.0316539i	0.0296277	+	0.999561i	$0.490568\pi$
$740$	−48.3159	+	65.4657i	−1.77613	+	2.40657i
$741$	−14.6681	−	16.5560i	−0.538845	−	0.608198i
$742$	43.0580	+	11.5374i	1.58071	+	0.423550i
$743$	−37.7344	+	7.13973i	−1.38434	+	0.261931i	−0.824122	−	0.566413i	$-0.808331\pi$
$743$	−37.7344	+	7.13973i	−1.38434	+	0.261931i	−0.560219	+	0.828344i	$0.689283\pi$
$744$	24.5694	+	7.19258i	0.900758	+	0.263693i
$745$	14.8523	−	10.1261i	0.544146	−	0.370993i
$746$	−25.8482	−	73.8698i	−0.946369	−	2.70457i
$747$	3.53859	+	10.3979i	0.129470	+	0.380441i
$748$	7.85425	+	9.84892i	0.287180	+	0.360112i
$749$	−15.8610	+	6.22498i	−0.579548	+	0.227456i
$750$	−36.2540	−	22.0576i	−1.32381	−	0.805431i
$751$	7.62080	+	4.02771i	0.278087	+	0.146973i	0.600497	−	0.799627i	$-0.294969\pi$
$751$	7.62080	+	4.02771i	0.278087	+	0.146973i	−0.322410	+	0.946600i	$0.604493\pi$
$752$	7.98636	−	5.89420i	0.291233	−	0.214939i
$753$	13.6471	+	3.44674i	0.497329	+	0.125606i
$754$	−22.8175	+	42.5381i	−0.830966	+	1.54915i
$755$		−	48.9201i		−	1.78039i
$756$	17.7497	−	24.3460i	0.645551	−	0.885456i
$757$	4.88050	+	7.76727i	0.177385	+	0.282306i	0.923568	−	0.383434i	$-0.125259\pi$
$757$	4.88050	+	7.76727i	0.177385	+	0.282306i	−0.746183	+	0.665740i	$0.768116\pi$
$758$	62.1254	+	19.1631i	2.25649	+	0.696036i
$759$	3.81455	+	5.01561i	0.138459	+	0.182055i
$760$	24.5561	+	9.63756i	0.890744	+	0.349591i
$761$	−5.81428	−	18.8494i	−0.210768	−	0.683292i	−0.997795	−	0.0663736i	$-0.978857\pi$
$761$	−5.81428	−	18.8494i	−0.210768	−	0.683292i	0.787027	−	0.616918i	$-0.211619\pi$
$762$	−4.43171	+	9.55230i	−0.160544	+	0.346043i
$763$	7.01545	+	10.2898i	0.253976	+	0.372515i
$764$	68.8304	+	43.2490i	2.49019	+	1.56469i
$765$	−18.8240	−	5.98374i	−0.680584	−	0.216342i
$766$	10.3948	+	10.3948i	0.375579	+	0.375579i
$767$	0.0140595	−	0.187612i	0.000507661	−	0.00677426i
$768$	−6.15999	−	37.2210i	−0.222279	−	1.34310i
$769$	−23.5200	+	10.2617i	−0.848152	+	0.370045i	−0.778590	−	0.627533i	$-0.784065\pi$
$769$	−23.5200	+	10.2617i	−0.848152	+	0.370045i	−0.0695616	+	0.997578i	$0.522160\pi$
$770$	−6.80535	+	9.98161i	−0.245248	+	0.359712i
$771$	11.8381	−	21.2042i	0.426340	−	0.763649i
$772$	−15.2249	+	13.1021i	−0.547957	+	0.471555i
$773$	−15.8305	+	25.1941i	−0.569383	+	0.906167i	0.430611	+	0.902538i	$0.358298\pi$
$773$	−15.8305	+	25.1941i	−0.569383	+	0.906167i	−0.999993	+	0.00362949i	$0.998845\pi$
$774$	−24.5887	−	10.9800i	−0.883824	−	0.394666i
$775$	2.22756	−	0.779456i	0.0800162	−	0.0279989i
$776$	31.4807	+	29.2098i	1.13009	+	1.04857i
$777$	29.1177	+	2.85648i	1.04459	+	0.102476i
$778$	−10.7761	−	1.62424i	−0.386343	−	0.0582318i
$779$	25.6988	+	27.6967i	0.920756	+	0.992339i
$780$	−16.6411	−	51.3117i	−0.595845	−	1.83725i
$781$	6.24769	−	14.3199i	0.223560	−	0.512405i
$782$	18.1715			0.649810
$783$	3.14165	−	27.8052i	0.112273	−	0.993677i
$784$	4.07531			0.145547
$785$	16.3974	−	37.5833i	0.585249	−	1.34141i
$786$	12.1599	+	37.4943i	0.433730	+	1.33738i
$787$	−9.04780	−	9.75121i	−0.322519	−	0.347593i	0.550892	−	0.834577i	$-0.314288\pi$
$787$	−9.04780	−	9.75121i	−0.322519	−	0.347593i	−0.873411	+	0.486983i	$0.838097\pi$
$788$	−69.8585	−	10.5295i	−2.48861	−	0.375097i
$789$	10.3164	+	1.01205i	0.367274	+	0.0360301i
$790$	−23.4467	−	21.7554i	−0.834198	−	0.774022i
$791$	−29.8422	+	10.4422i	−1.06107	+	0.371283i
$792$	−1.36756	−	13.1503i	−0.0485941	−	0.467274i
$793$	11.8923	−	18.9265i	0.422309	−	0.672101i
$794$	−51.6347	+	44.4352i	−1.83245	+	1.57695i
$795$	−22.5522	+	40.3950i	−0.799844	+	1.43266i
$796$	−34.8372	+	51.0968i	−1.23477	+	1.81108i
$797$	21.4375	−	9.35309i	0.759356	−	0.331304i	0.0157094	−	0.999877i	$-0.494999\pi$
$797$	21.4375	−	9.35309i	0.759356	−	0.331304i	0.743647	+	0.668573i	$0.233095\pi$
$798$	−3.69247	−	22.3113i	−0.130712	−	0.789813i
$799$	−2.12195	+	28.3154i	−0.0750692	+	1.00173i
$800$	−1.69846	−	1.69846i	−0.0600498	−	0.0600498i
$801$	−2.39684	+	2.18599i	−0.0846882	+	0.0772381i
$802$	39.8819	+	25.0594i	1.40828	+	0.884880i
$803$	−1.11525	−	1.63577i	−0.0393564	−	0.0577252i
$804$	−15.7645	+	33.9795i	−0.555973	+	1.19837i
$805$	3.24984	+	10.5357i	0.114542	+	0.371335i
$806$	−36.5769	−	14.3554i	−1.28837	−	0.505646i
$807$	3.60084	+	4.73461i	0.126755	+	0.166666i
$808$	−41.6298	−	12.8411i	−1.46453	−	0.451748i
$809$	7.24272	+	11.5267i	0.254640	+	0.405258i	0.949442	−	0.313944i	$-0.101650\pi$
$809$	7.24272	+	11.5267i	0.254640	+	0.405258i	−0.694801	+	0.719202i	$0.744508\pi$
$810$	31.5909	+	38.0090i	1.10999	+	1.33550i
$811$			28.8853i			1.01430i	0.861857	+	0.507151i	$0.169301\pi$
$811$			28.8853i			1.01430i	−0.861857	+	0.507151i	$0.830699\pi$
$812$	−27.1374	+	15.4462i	−0.952336	+	0.542056i
$813$	−34.6052	−	8.73995i	−1.21366	−	0.306523i
$814$	24.6274	−	18.1758i	0.863188	−	0.637062i
$815$	40.7761	+	21.5508i	1.42832	+	0.754891i
$816$	−4.04864	−	2.46327i	−0.141731	−	0.0862317i
$817$	−11.9043	+	4.67208i	−0.416478	+	0.163455i
$818$	17.9305	+	22.4842i	0.626926	+	0.786140i
$819$	−12.7780	+	14.5933i	−0.446501	+	0.509931i
$820$	30.4327	+	86.9718i	1.06276	+	3.03719i
$821$	1.60729	−	1.09583i	0.0560948	−	0.0382448i	−0.534948	−	0.844885i	$-0.679669\pi$
$821$	1.60729	−	1.09583i	0.0560948	−	0.0382448i	0.591043	+	0.806640i	$0.298716\pi$
$822$	41.3437	+	12.1032i	1.44203	+	0.422147i
$823$	−26.1818	+	4.95387i	−0.912641	+	0.172681i	−0.620967	−	0.783837i	$-0.713260\pi$
$823$	−26.1818	+	4.95387i	−0.912641	+	0.172681i	−0.291674	+	0.956518i	$0.594212\pi$
$824$	13.4740	+	3.61034i	0.469387	+	0.125772i
$825$	−0.808235	−	0.912260i	−0.0281391	−	0.0317608i
$826$	0.114224	−	0.154768i	0.00397436	−	0.00538507i
$827$	14.3371	+	1.61540i	0.498548	+	0.0561729i	0.357659	−	0.933852i	$-0.383575\pi$
$827$	14.3371	+	1.61540i	0.498548	+	0.0561729i	0.140890	+	0.990025i	$0.455004\pi$
$828$	−24.2257	−	15.5135i	−0.841903	−	0.539130i
$829$	6.48996	−	6.48996i	0.225406	−	0.225406i	−0.585365	−	0.810770i	$-0.699049\pi$
$829$	6.48996	−	6.48996i	0.225406	−	0.225406i	0.810770	+	0.585365i	$0.199049\pi$
$830$	13.1145	+	15.2393i	0.455211	+	0.528964i
$831$	−43.3813	+	10.5615i	−1.50488	+	0.366373i
$832$	3.55013	+	47.3732i	0.123079	+	1.64237i
$833$	−7.60447	+	8.83656i	−0.263479	+	0.306168i
$834$	19.3556	−	37.9360i	0.670229	−	1.31362i
$835$	−7.54537	+	1.13728i	−0.261118	+	0.0393572i
$836$	−11.7031	−	9.33288i	−0.404759	−	0.322784i
$837$	22.7771	−	0.132885i	0.787293	−	0.00459318i
$838$	69.8064	−	43.8622i	2.41142	−	1.51520i
$839$	−7.74985	−	3.38123i	−0.267555	−	0.116733i	0.261832	−	0.965113i	$-0.415673\pi$
$839$	−7.74985	−	3.38123i	−0.267555	−	0.116733i	−0.529387	+	0.848381i	$0.677578\pi$
$840$	5.66469	−	22.4290i	0.195450	−	0.773873i
$841$	−14.8076	+	24.9346i	−0.510605	+	0.859815i
$842$	0.162687	−	0.0939276i	0.00560658	−	0.00323696i
$843$	9.81195	−	12.6743i	0.337941	−	0.436525i
$844$	−89.7568	+	3.35846i	−3.08956	+	0.115603i
$845$	0.919860	+	4.03017i	0.0316441	+	0.138642i
$846$	42.6790	−	56.8017i	1.46733	−	1.95288i
$847$	−12.2272	+	9.75089i	−0.420132	+	0.335044i
$848$	−7.54994	+	8.13690i	−0.259266	+	0.279422i
$849$	−23.0527	+	16.2086i	−0.791166	+	0.556276i
$850$	−3.50486	+	0.262653i	−0.120216	+	0.00900893i
$851$	1.04451	−	27.9152i	0.0358054	−	0.956920i
$852$	−4.30459	+	71.1949i	−0.147473	+	2.43910i
$853$	−0.459519	+	0.123128i	−0.0157336	+	0.00421581i	−0.266677	−	0.963786i	$-0.585926\pi$
$853$	−0.459519	+	0.123128i	−0.0157336	+	0.00421581i	0.250944	+	0.968002i	$0.419259\pi$
$854$	20.5904	−	9.91583i	0.704590	−	0.339313i
$855$	23.3892	+	1.95465i	0.799892	+	0.0668477i
$856$	3.82176	−	33.9191i	0.130625	−	1.15933i
$857$	11.3936	+	0.853834i	0.389199	+	0.0291664i	0.267893	−	0.963449i	$-0.413673\pi$
$857$	11.3936	+	0.853834i	0.389199	+	0.0291664i	0.121306	+	0.992615i	$0.461292\pi$
$858$	0.292432	+	20.2904i	0.00998347	+	0.692704i
$859$	−2.87829	−	15.2121i	−0.0982060	−	0.519031i	−0.996778	−	0.0802059i	$-0.974442\pi$
$859$	−2.87829	−	15.2121i	−0.0982060	−	0.519031i	0.898572	−	0.438826i	$-0.144605\pi$
$860$	−31.1655	−	1.16613i	−1.06273	−	0.0397647i
$861$	21.2481	−	25.4228i	0.724134	−	0.866406i
$862$	0.322405	−	1.70395i	0.0109812	−	0.0580369i
$863$	4.86782	−	21.3273i	0.165702	−	0.725990i	−0.821980	−	0.569517i	$-0.807130\pi$
$863$	4.86782	−	21.3273i	0.165702	−	0.725990i	0.987682	−	0.156473i	$-0.0500125\pi$
$864$	−10.1804	−	20.8280i	−0.346343	−	0.708584i
$865$	1.10255	−	1.38255i	0.0374877	−	0.0470081i
$866$	−8.58974	+	27.8472i	−0.291891	+	0.946288i
$867$	−15.1129	+	4.90130i	−0.513260	+	0.166457i
$868$	−15.0935	−	20.4509i	−0.512305	−	0.694149i
$869$	3.80638	+	6.59285i	0.129123	+	0.223647i
$870$	−13.6655	−	49.3646i	−0.463305	−	1.67362i
$871$	12.0576	−	20.8845i	0.408558	−	0.707643i
$872$	−24.7916	+	2.79334i	−0.839550	+	0.0945946i
$873$	34.2817	+	16.8730i	1.16026	+	0.571063i
$874$	−21.0510	+	4.80476i	−0.712061	+	0.162523i
$875$	6.45659	+	16.4511i	0.218273	+	0.556149i
$876$	7.34870	+	5.26171i	0.248290	+	0.177777i
$877$	43.6188	−	13.4546i	1.47290	−	0.454330i	0.548631	−	0.836065i	$-0.315149\pi$
$877$	43.6188	−	13.4546i	1.47290	−	0.454330i	0.924272	+	0.381734i	$0.124673\pi$
$878$	58.0169	+	49.9275i	1.95797	+	1.68497i
$879$	7.40429	−	42.4747i	0.249741	−	1.43264i
$880$	−1.40565	−	2.65961i	−0.0473843	−	0.0896555i
$881$	−20.5310	−	7.18410i	−0.691707	−	0.242039i	−0.0385447	−	0.999257i	$-0.512272\pi$
$881$	−20.5310	−	7.18410i	−0.691707	−	0.242039i	−0.653162	+	0.757218i	$0.726558\pi$
$882$	27.9475	−	8.35882i	0.941040	−	0.281456i
$883$	0.902933	+	1.87496i	0.0303861	+	0.0630974i	0.915609	−	0.402069i	$-0.131709\pi$
$883$	0.902933	+	1.87496i	0.0303861	+	0.0630974i	−0.885223	+	0.465166i	$0.845995\pi$
$884$	29.7894	+	21.9856i	1.00193	+	0.739456i
$885$	0.126706	+	0.154270i	0.00425918	+	0.00518574i
$886$	−11.3642	−	7.74801i	−0.381789	−	0.260300i
$887$	−10.2661	+	38.3136i	−0.344702	+	1.28645i	0.548258	+	0.836309i	$0.315291\pi$
$887$	−10.2661	+	38.3136i	−0.344702	+	1.28645i	−0.892960	+	0.450136i	$0.851375\pi$
$888$	−32.3156	+	48.8976i	−1.08444	+	1.64090i
$889$	3.87712	−	2.04912i	0.130035	−	0.0687252i
$890$	−2.57644	+	5.35003i	−0.0863624	+	0.179333i
$891$	−4.51839	−	10.8609i	−0.151372	−	0.363852i
$892$	−57.3505	−	13.0899i	−1.92024	−	0.438282i
$893$	−5.02874	−	33.3635i	−0.168281	−	1.11647i
$894$	24.5723	−	18.6881i	0.821821	−	0.625024i
$895$	31.4709	−	29.2007i	1.05196	−	0.976073i
$896$	−15.6778	+	29.6639i	−0.523759	+	0.991001i
$897$	14.6444	+	11.3372i	0.488964	+	0.378538i
$898$	−34.6048	−	19.9791i	−1.15478	−	0.666712i
$899$	−21.5780	−	9.57266i	−0.719667	−	0.319266i
$900$	4.89683	+	2.64203i	0.163228	+	0.0880676i
$901$	−3.55528	−	31.5540i	−0.118444	−	1.05122i
$902$	−1.29608	−	34.6386i	−0.0431549	−	1.15334i
$903$	5.38252	+	9.83836i	0.179119	+	0.327400i
$904$	9.43986	−	62.6294i	0.313965	−	2.08302i
$905$	−5.76883	+	14.6987i	−0.191762	+	0.488603i
$906$	−4.35096	−	83.9020i	−0.144551	−	2.78746i
$907$	−41.1314	−	7.78248i	−1.36575	−	0.258413i	−0.549199	−	0.835692i	$-0.685067\pi$
$907$	−41.1314	−	7.78248i	−1.36575	−	0.258413i	−0.816547	+	0.577279i	$0.804115\pi$
$908$	34.4220	+	16.5767i	1.14233	+	0.550119i
$909$	−38.7598	−	0.332461i	−1.28558	−	0.0110270i
$910$	−11.7269	+	33.5136i	−0.388743	+	1.11096i
$911$	−10.9607	−	40.9059i	−0.363144	−	1.35527i	−0.869919	−	0.493194i	$-0.835829\pi$
$911$	−10.9607	−	40.9059i	−0.363144	−	1.35527i	0.506775	−	0.862078i	$-0.330837\pi$
$912$	5.34153	+	1.78310i	0.176876	+	0.0590445i
$913$	−1.91359	−	4.38601i	−0.0633307	−	0.145156i
$914$	2.68810	+	6.16119i	0.0889145	+	0.203794i
$915$	4.74494	+	23.2391i	0.156863	+	0.768261i
$916$	−5.01580	−	18.7192i	−0.165727	−	0.618500i
$917$	5.42156	−	15.4939i	0.179036	−	0.511655i
$918$	−32.8169	−	8.58839i	−1.08312	−	0.283459i
$919$	8.05077	+	3.87705i	0.265570	+	0.127892i	0.561931	−	0.827184i	$-0.310059\pi$
$919$	8.05077	+	3.87705i	0.265570	+	0.127892i	−0.296361	+	0.955076i	$0.595773\pi$
$920$	−21.7023	−	4.10630i	−0.715504	−	0.135381i
$921$	−10.8122	−	5.51658i	−0.356275	−	0.181777i
$922$	18.9443	−	48.2692i	0.623896	−	1.58966i
$923$	6.84375	−	45.4053i	0.225265	−	1.49453i
$924$	−6.82290	+	11.2141i	−0.224457	+	0.368918i
$925$	0.202028	+	5.39930i	0.00664263	+	0.177528i
$926$	4.95390	+	43.9671i	0.162795	+	1.44485i
$927$	12.4059	−	0.357670i	0.407463	−	0.0117474i
$928$	0.750814	+	24.0145i	0.0246467	+	0.788313i
$929$	21.7779	+	12.5735i	0.714510	+	0.412522i	0.812729	−	0.582642i	$-0.197981\pi$
$929$	21.7779	+	12.5735i	0.714510	+	0.412522i	−0.0982188	+	0.995165i	$0.531315\pi$
$930$	38.5885	−	15.7903i	1.26537	−	0.517785i
$931$	6.47302	−	12.2476i	0.212145	−	0.401398i
$932$	52.8201	−	49.0099i	1.73018	−	1.60537i
$933$	−39.0377	−	16.3665i	−1.27804	−	0.535814i
$934$	−2.26136	−	15.0031i	−0.0739939	−	0.490918i
$935$	8.38979	+	1.91491i	0.274375	+	0.0626244i
$936$	−13.8856	−	36.2921i	−0.453864	−	1.18624i
$937$	0.0247294	−	0.0513511i	0.000807873	−	0.00167757i	−0.900565	−	0.434722i	$-0.856847\pi$
$937$	0.0247294	−	0.0513511i	0.000807873	−	0.00167757i	0.901372	+	0.433045i	$0.142561\pi$
$938$	21.7986	−	11.5209i	0.711749	−	0.376170i
$939$	3.93503	+	7.87866i	0.128415	+	0.257110i
$940$	21.2967	−	79.4804i	0.694622	−	2.59236i
$941$	−32.9767	−	22.4831i	−1.07501	−	0.732929i	−0.109681	−	0.993967i	$-0.534983\pi$
$941$	−32.9767	−	22.4831i	−1.07501	−	0.732929i	−0.965329	+	0.261038i	$0.915935\pi$
$942$	24.7803	−	65.9168i	0.807385	−	2.14769i
$943$	−25.4535	−	18.7856i	−0.828881	−	0.611742i
$944$	0.0207821	+	0.0431545i	0.000676401	+	0.00140456i
$945$	−0.889577	−	20.5631i	−0.0289379	−	0.668916i
$946$	11.0739	+	3.87492i	0.360043	+	0.125985i
$947$	−6.80150	−	12.8691i	−0.221019	−	0.418188i	0.748525	−	0.663107i	$-0.230763\pi$
$947$	−6.80150	−	12.8691i	−0.221019	−	0.418188i	−0.969544	+	0.244919i	$0.921239\pi$
$948$	−26.6666	−	22.2877i	−0.866092	−	0.723872i
$949$	−4.41040	−	3.79546i	−0.143168	−	0.123206i
$950$	3.99081	−	1.23100i	0.129479	−	0.0399390i
$951$	0.584937	−	5.96258i	0.0189679	−	0.193350i
$952$	5.80077	+	14.7801i	0.188004	+	0.479027i
$953$	−26.3332	+	6.01039i	−0.853017	+	0.194696i	−0.626606	−	0.779336i	$-0.715556\pi$
$953$	−26.3332	+	6.01039i	−0.853017	+	0.194696i	−0.226411	+	0.974032i	$0.572699\pi$
$954$	−35.0861	+	71.2865i	−1.13596	+	2.30798i
$955$	55.1825	−	6.21758i	1.78566	−	0.201196i
$956$	−26.2736	+	45.5072i	−0.849748	+	1.47181i
$957$	−0.355121	+	12.1860i	−0.0114794	+	0.393916i
$958$	8.75139	+	15.1578i	0.282744	+	0.489728i
$959$	−10.6532	−	14.4346i	−0.344010	−	0.466117i
$960$	−37.4427	−	33.7508i	−1.20846	−	1.08930i
$961$	−3.47357	+	11.2610i	−0.112051	+	0.363259i
$962$	56.0888	−	70.3331i	1.80838	−	2.26763i
$963$	−5.38993	−	29.8876i	−0.173688	−	0.963114i
$964$	12.0741	−	52.9000i	0.388880	−	1.70380i
$965$	−2.55101	+	13.4824i	−0.0821198	+	0.434014i
$966$	6.51079	+	17.7806i	0.209481	+	0.572081i
$967$	−23.0122	−	0.861055i	−0.740022	−	0.0276897i	−0.335277	−	0.942119i	$-0.608830\pi$
$967$	−23.0122	−	0.861055i	−0.740022	−	0.0276897i	−0.404745	+	0.914430i	$0.632640\pi$
$968$	−5.82458	−	30.7837i	−0.187209	−	0.989425i
$969$	−13.8335	+	8.25486i	−0.444397	+	0.265184i
$970$	69.7460	+	5.22674i	2.23941	+	0.167820i
$971$	−2.74782	+	24.3876i	−0.0881818	+	0.782635i	0.869328	+	0.494235i	$0.164552\pi$
$971$	−2.74782	+	24.3876i	−0.0881818	+	0.782635i	−0.957510	+	0.288400i	$0.906877\pi$
$972$	36.4186	+	39.4665i	1.16813	+	1.26589i
$973$	−15.9795	+	7.69532i	−0.512279	+	0.246701i
$974$	62.8480	−	16.8401i	2.01378	−	0.539591i
$975$	−2.98845	−	1.97501i	−0.0957069	−	0.0632510i
$976$	−0.212784	+	5.68678i	−0.00681106	+	0.182029i
$977$	1.67379	−	0.125433i	0.0535493	−	0.00401297i	−0.0479285	−	0.998851i	$-0.515262\pi$
$977$	1.67379	−	0.125433i	0.0535493	−	0.00401297i	0.101478	+	0.994838i	$0.467643\pi$
$978$	71.8510	+	33.3347i	2.29754	+	1.06593i
$979$	0.961303	−	1.03604i	0.0307234	−	0.0331119i
$980$	26.4131	−	21.0638i	0.843736	−	0.672857i
$981$	−20.4206	+	8.70171i	−0.651981	+	0.277824i
$982$	7.24618	+	31.7476i	0.231235	+	1.01311i
$983$	−17.3530	+	0.649303i	−0.553475	+	0.0207096i	−0.312666	−	0.949863i	$-0.601222\pi$
$983$	−17.3530	+	0.649303i	−0.553475	+	0.0207096i	−0.240809	+	0.970573i	$0.577413\pi$
$984$	25.1374	+	61.4310i	0.801352	+	1.95835i
$985$	−41.7956	+	24.1307i	−1.33172	+	0.768869i
$986$	27.3509	+	22.0879i	0.871031	+	0.703423i
$987$	−28.4666	+	8.06904i	−0.906103	+	0.256840i
$988$	−40.3233	−	17.5929i	−1.28285	−	0.559704i
$989$	9.06628	−	5.69672i	0.288291	−	0.181145i
$990$	−15.0947	−	15.3559i	−0.479740	−	0.488041i
$991$	7.46784	+	5.95540i	0.237224	+	0.189180i	0.734885	−	0.678192i	$-0.237236\pi$
$991$	7.46784	+	5.95540i	0.237224	+	0.189180i	−0.497661	+	0.867372i	$0.665808\pi$
$992$	−19.3389	+	2.91488i	−0.614012	+	0.0925474i
$993$	33.1016	+	51.0333i	1.05045	+	1.61949i
$994$	30.6232	−	35.5848i	0.971309	−	1.12868i
$995$	3.15709	+	42.1284i	0.100086	+	1.33556i
$996$	15.0883	+	15.7984i	0.478090	+	0.500593i
$997$	−13.7699	−	16.0009i	−0.436096	−	0.506753i	0.496320	−	0.868140i	$-0.334684\pi$
$997$	−13.7699	−	16.0009i	−0.436096	−	0.506753i	−0.932416	+	0.361387i	$0.882303\pi$
$998$	−17.4061	+	17.4061i	−0.550981	+	0.550981i
$999$	−15.0799	+	49.9200i	−0.477107	+	1.57940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.25	yes	672
3.2	odd	2		783.2.be.a.710.4		672
9.4	even	3		783.2.be.a.449.25		672
9.5	odd	6	inner	261.2.x.a.14.4	✓	672
29.27	odd	28	inner	261.2.x.a.56.4	yes	672
87.56	even	28		783.2.be.a.143.25		672
261.85	odd	84		783.2.be.a.665.4		672
261.230	even	84	inner	261.2.x.a.230.25	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.4	✓	672	9.5	odd	6	inner
261.2.x.a.56.4	yes	672	29.27	odd	28	inner
261.2.x.a.101.25	yes	672	1.1	even	1	trivial
261.2.x.a.230.25	yes	672	261.230	even	84	inner
783.2.be.a.143.25		672	87.56	even	28
783.2.be.a.449.25		672	9.4	even	3
783.2.be.a.665.4		672	261.85	odd	84
783.2.be.a.710.4		672	3.2	odd	2

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.933128 - 2.13875i) q^{2} +(-0.534329 - 1.64757i) q^{3} +(-2.34319 - 2.52536i) q^{4} +(-2.32709 - 0.350752i) q^{5} +(-4.02235 - 0.394597i) q^{6} +(1.23383 + 1.14483i) q^{7} +(-3.18260 + 1.11364i) q^{8} +(-2.42898 + 1.76069i) q^{9} +(-2.92165 + 4.64977i) q^{10} +(0.990690 - 0.852557i) q^{11} +(-2.90867 + 5.20995i) q^{12} +(2.16395 - 3.17393i) q^{13} +(3.59982 - 1.57059i) q^{14} +(0.665543 + 4.02146i) q^{15} +(-0.0730851 + 0.975253i) q^{16} +(-1.97828 - 1.97828i) q^{17} +(1.49913 + 6.83795i) q^{18} +(2.81485 + 1.76869i) q^{19} +(4.56704 + 6.69862i) q^{20} +(1.22691 - 2.64454i) q^{21} +(-0.898969 - 2.91439i) q^{22} +(-2.59107 - 1.01692i) q^{23} +(3.53536 + 4.64852i) q^{24} +(0.514457 + 0.158689i) q^{25} +(-4.76902 - 7.58985i) q^{26} +(4.19874 + 3.06114i) q^{27} -5.79841i q^{28} +(-2.66387 - 4.68015i) q^{29} +(9.22196 + 2.32911i) q^{30} +(3.52698 - 2.60303i) q^{31} +(-3.94453 - 2.08474i) q^{32} +(-1.93400 - 1.17669i) q^{33} +(-6.07704 + 2.38506i) q^{34} +(-2.46968 - 3.09688i) q^{35} +(10.1379 + 2.00842i) q^{36} +(3.31464 + 9.47271i) q^{37} +(6.40940 - 4.36986i) q^{38} +(-6.38555 - 1.86934i) q^{39} +(7.79682 - 1.47524i) q^{40} +(10.9780 + 2.94155i) q^{41} +(-4.51114 - 5.09176i) q^{42} +(-2.28430 + 3.09512i) q^{43} +(-4.47439 - 0.504142i) q^{44} +(6.27003 - 3.24532i) q^{45} +(-4.59274 + 4.59274i) q^{46} +(-6.62027 - 7.69289i) q^{47} +(1.64585 - 0.400693i) q^{48} +(-0.311403 - 4.15538i) q^{49} +(0.819451 - 0.952220i) q^{50} +(-2.20230 + 4.31641i) q^{51} +(-13.0859 + 1.97238i) q^{52} +(8.87369 + 7.07653i) q^{53} +(10.4650 - 6.12364i) q^{54} +(-2.60446 + 1.63649i) q^{55} +(-5.20172 - 2.26949i) q^{56} +(1.40998 - 5.58273i) q^{57} +(-12.4954 + 1.33019i) q^{58} +(0.0424144 - 0.0244880i) q^{59} +(8.59615 - 11.1038i) q^{60} +(5.81477 - 0.217573i) q^{61} +(-2.27612 - 9.97231i) q^{62} +(-5.01264 - 0.608373i) q^{63} +(-9.66874 + 7.71056i) q^{64} +(-6.14898 + 6.62702i) q^{65} +(-4.32131 + 3.03836i) q^{66} +(6.26014 - 0.469133i) q^{67} +(-0.360380 + 9.63135i) q^{68} +(-0.290964 + 4.81235i) q^{69} +(-8.92800 + 2.39225i) q^{70} +(10.7697 - 5.18640i) q^{71} +(5.76972 - 8.30860i) q^{72} +(0.169595 - 1.50520i) q^{73} +(23.3528 + 1.75005i) q^{74} +(-0.0134380 - 0.932397i) q^{75} +(-2.12916 - 11.2529i) q^{76} +(2.19837 + 0.0822573i) q^{77} +(-9.95659 + 11.9128i) q^{78} +(-1.08284 + 5.72295i) q^{79} +(0.512148 - 2.24387i) q^{80} +(2.79993 - 8.55338i) q^{81} +(16.5352 - 20.7344i) q^{82} +(1.07916 - 3.49854i) q^{83} +(-9.55329 + 3.09826i) q^{84} +(3.90975 + 5.29752i) q^{85} +(4.48815 + 7.77370i) q^{86} +(-6.28749 + 6.88966i) q^{87} +(-2.20353 + 3.81662i) q^{88} +(1.07453 - 0.121070i) q^{89} +(-1.09018 - 16.4383i) q^{90} +(6.30355 - 1.43874i) q^{91} +(3.50328 + 8.92622i) q^{92} +(-6.17326 - 4.42008i) q^{93} +(-22.6308 + 6.98067i) q^{94} +(-5.93004 - 5.10321i) q^{95} +(-1.32709 + 7.61283i) q^{96} +(-5.95130 - 11.2604i) q^{97} +(-9.17792 - 3.21149i) q^{98} +(-0.905279 + 3.81515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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