LMFDB - Embedded newform 483.2.bb.a.215.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [483,2,Mod(26,483)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([33, 55, 48])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("483.26"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$483 = 3 \cdot 7 \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	483.bb (of order $66$ , degree $20$ , 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$60$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			215.19
Character	$\chi$	$=$	483.215
Dual form			483.2.bb.a.164.19

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.661740 + 0.841471i) q^{2} +(0.427135 + 1.67856i) q^{3} +(0.201344 + 0.829953i) q^{4} +(4.29751 - 0.828278i) q^{5} +(-1.69511 - 0.751347i) q^{6} +(-0.329969 + 2.62509i) q^{7} +(-2.77914 - 1.26919i) q^{8} +(-2.63511 + 1.43394i) q^{9} +(-2.14687 + 4.16434i) q^{10} +(-1.52616 - 1.94068i) q^{11} +(-1.30712 + 0.692470i) q^{12} +(0.665313 + 1.03525i) q^{13} +(-1.99059 - 2.01479i) q^{14} +(3.22593 + 6.85984i) q^{15} +(1.38888 - 0.716018i) q^{16} +(2.42001 + 2.30748i) q^{17} +(0.537137 - 3.16627i) q^{18} +(0.348273 + 0.365258i) q^{19} +(1.55271 + 3.39996i) q^{20} +(-4.54731 + 0.567400i) q^{21} +2.64295 q^{22} +(-1.97124 - 4.37198i) q^{23} +(0.943342 - 5.20707i) q^{24} +(13.1407 - 5.26076i) q^{25} +(-1.31140 - 0.125223i) q^{26} +(-3.53250 - 3.81070i) q^{27} +(-2.24514 + 0.254690i) q^{28} +(0.514705 + 1.75292i) q^{29} +(-7.90708 - 1.82490i) q^{30} +(0.373007 + 3.90630i) q^{31} +(0.839846 - 4.35753i) q^{32} +(2.60566 - 3.39069i) q^{33} +(-3.54309 + 0.509420i) q^{34} +(0.756263 + 11.5547i) q^{35} +(-1.72067 - 1.89830i) q^{36} +(-1.92784 - 5.57012i) q^{37} +(-0.537821 + 0.0513557i) q^{38} +(-1.45354 + 1.55896i) q^{39} +(-12.9946 - 3.15247i) q^{40} +(7.44760 + 8.59499i) q^{41} +(2.53169 - 4.20190i) q^{42} +(-2.14338 - 4.69335i) q^{43} +(1.30338 - 1.65739i) q^{44} +(-10.1367 + 8.34499i) q^{45} +(4.98334 + 1.23437i) q^{46} +(0.499932 - 0.865907i) q^{47} +(1.79512 + 2.02548i) q^{48} +(-6.78224 - 1.73240i) q^{49} +(-4.26898 + 14.5388i) q^{50} +(-2.83956 + 5.04774i) q^{51} +(-0.725250 + 0.760620i) q^{52} +(-11.0425 - 0.526021i) q^{53} +(5.54419 - 0.450809i) q^{54} +(-8.16613 - 7.07599i) q^{55} +(4.24878 - 6.87672i) q^{56} +(-0.464347 + 0.740611i) q^{57} +(-1.81564 - 0.726871i) q^{58} +(-5.82765 - 3.00436i) q^{59} +(-5.04382 + 4.05856i) q^{60} +(8.89647 - 6.33515i) q^{61} +(-3.53388 - 2.27108i) q^{62} +(-2.89473 - 7.39057i) q^{63} +(5.15753 + 5.95211i) q^{64} +(3.71666 + 3.89793i) q^{65} +(1.12890 + 4.43634i) q^{66} +(-8.31798 + 3.33002i) q^{67} +(-1.42784 + 2.47309i) q^{68} +(6.49663 - 5.17627i) q^{69} +(-10.2234 - 7.00982i) q^{70} +(14.2424 + 2.04775i) q^{71} +(9.14330 - 0.640671i) q^{72} +(8.11105 - 1.96772i) q^{73} +(5.96282 + 2.06375i) q^{74} +(14.4434 + 19.8104i) q^{75} +(-0.233024 + 0.362593i) q^{76} +(5.59804 - 3.36596i) q^{77} +(-0.349949 - 2.25474i) q^{78} +(-0.328821 - 6.90281i) q^{79} +(5.37568 - 4.22748i) q^{80} +(4.88762 - 7.55720i) q^{81} +(-12.1608 + 0.579291i) q^{82} +(1.44316 - 1.66549i) q^{83} +(-1.38649 - 3.65981i) q^{84} +(12.3113 + 7.91197i) q^{85} +(5.36768 + 1.30219i) q^{86} +(-2.72254 + 1.61270i) q^{87} +(1.77834 + 7.33041i) q^{88} +(-5.70420 - 0.544685i) q^{89} +(-0.314195 - 14.0520i) q^{90} +(-2.93716 + 1.40491i) q^{91} +(3.23164 - 2.51631i) q^{92} +(-6.39763 + 2.29463i) q^{93} +(0.397811 + 0.993684i) q^{94} +(1.79924 + 1.28124i) q^{95} +(7.67310 - 0.451528i) q^{96} +(9.31283 - 8.06961i) q^{97} +(5.94584 - 4.56066i) q^{98} +(6.80443 + 2.92546i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$1200 q - 27 q^{3} - 74 q^{4} - 36 q^{7} - 13 q^{9} - 54 q^{10} - 15 q^{12} - 64 q^{15} + 38 q^{16} + 43 q^{18} - 54 q^{19} - 70 q^{21} - 160 q^{22} - 66 q^{24} + 34 q^{25} - 76 q^{28} - 23 q^{30} - 54 q^{31}+ \cdots + 196 q^{99}+O(q^{100})$ 1200 * q - 27 * q^3 - 74 * q^4 - 36 * q^7 - 13 * q^9 - 54 * q^10 - 15 * q^12 - 64 * q^15 + 38 * q^16 + 43 * q^18 - 54 * q^19 - 70 * q^21 - 160 * q^22 - 66 * q^24 + 34 * q^25 - 76 * q^28 - 23 * q^30 - 54 * q^31 - 3 * q^33 - 28 * q^36 + 26 * q^37 + 5 * q^39 - 30 * q^40 - 68 * q^42 - 176 * q^43 - 96 * q^45 - 22 * q^46 - 128 * q^49 - 23 * q^51 - 102 * q^52 + 21 * q^54 - 36 * q^57 + 58 * q^58 - 43 * q^60 - 126 * q^61 + 41 * q^63 + 40 * q^64 - 132 * q^66 - 10 * q^67 + 20 * q^70 + 59 * q^72 - 30 * q^73 - 81 * q^75 + 164 * q^78 - 14 * q^79 - 97 * q^81 - 66 * q^82 + 24 * q^84 - 56 * q^85 - 399 * q^87 - 74 * q^88 - 156 * q^91 + 8 * q^93 - 126 * q^94 - 117 * q^96 + 196 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$ .

$n$	$323$	$346$	$442$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{11}\right)$

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

)

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

$2$	−0.661740	+	0.841471i	−0.467921	+	0.595010i	−0.961539	−	0.274669i	$-0.911432\pi$
$2$	−0.661740	+	0.841471i	−0.467921	+	0.595010i	0.493618	+	0.869679i	$0.335674\pi$
$3$	0.427135	+	1.67856i	0.246607	+	0.969116i
$3$	0.427135	+	1.67856i	0.246607	+	0.969116i
$4$	0.201344	+	0.829953i	0.100672	+	0.414976i
$5$	4.29751	−	0.828278i	1.92191	−	0.370417i	0.922045	−	0.387083i	$-0.126517\pi$
$5$	4.29751	−	0.828278i	1.92191	−	0.370417i	0.999861	+	0.0166657i	$0.00530510\pi$
$6$	−1.69511	−	0.751347i	−0.692026	−	0.306736i
$7$	−0.329969	+	2.62509i	−0.124716	+	0.992192i
$7$	−0.329969	+	2.62509i	−0.124716	+	0.992192i
$8$	−2.77914	−	1.26919i	−0.982576	−	0.448727i
$9$	−2.63511	+	1.43394i	−0.878370	+	0.477981i
$10$	−2.14687	+	4.16434i	−0.678898	+	1.31688i
$11$	−1.52616	−	1.94068i	−0.460156	−	0.585136i	0.499500	−	0.866314i	$-0.333517\pi$
$11$	−1.52616	−	1.94068i	−0.460156	−	0.585136i	−0.959656	+	0.281178i	$0.909275\pi$
$12$	−1.30712	+	0.692470i	−0.377334	+	0.199899i
$13$	0.665313	+	1.03525i	0.184525	+	0.287126i	0.921176	−	0.389147i	$-0.127230\pi$
$13$	0.665313	+	1.03525i	0.184525	+	0.287126i	−0.736651	+	0.676273i	$0.763594\pi$
$14$	−1.99059	−	2.01479i	−0.532007	−	0.538475i
$15$	3.22593	+	6.85984i	0.832932	+	1.77120i
$16$	1.38888	−	0.716018i	0.347220	−	0.179005i
$17$	2.42001	+	2.30748i	0.586939	+	0.559645i	0.924269	−	0.381741i	$-0.124675\pi$
$17$	2.42001	+	2.30748i	0.586939	+	0.559645i	−0.337330	+	0.941386i	$0.609524\pi$
$18$	0.537137	−	3.16627i	0.126604	−	0.746296i
$19$	0.348273	+	0.365258i	0.0798993	+	0.0837960i	0.762470	−	0.647024i	$-0.223987\pi$
$19$	0.348273	+	0.365258i	0.0798993	+	0.0837960i	−0.682571	+	0.730820i	$0.739138\pi$
$20$	1.55271	+	3.39996i	0.347197	+	0.760255i
$21$	−4.54731	+	0.567400i	−0.992305	+	0.123817i
$22$	2.64295			0.563478
$23$	−1.97124	−	4.37198i	−0.411033	−	0.911621i
$23$	−1.97124	−	4.37198i	−0.411033	−	0.911621i
$24$	0.943342	−	5.20707i	0.192559	−	1.06289i
$25$	13.1407	−	5.26076i	2.62815	−	1.05215i
$26$	−1.31140	−	0.125223i	−0.257186	−	0.0245583i
$27$	−3.53250	−	3.81070i	−0.679831	−	0.733369i
$28$	−2.24514	+	0.254690i	−0.424292	+	0.0481318i
$29$	0.514705	+	1.75292i	0.0955783	+	0.325510i	0.993378	−	0.114895i	$-0.0366531\pi$
$29$	0.514705	+	1.75292i	0.0955783	+	0.325510i	−0.897799	+	0.440405i	$0.854835\pi$
$30$	−7.90708	−	1.82490i	−1.44363	−	0.333180i
$31$	0.373007	+	3.90630i	0.0669940	+	0.701593i	0.965112	+	0.261838i	$0.0843286\pi$
$31$	0.373007	+	3.90630i	0.0669940	+	0.701593i	−0.898118	+	0.439755i	$0.855065\pi$
$32$	0.839846	−	4.35753i	0.148465	−	0.770310i
$33$	2.60566	−	3.39069i	0.453587	−	0.590243i
$34$	−3.54309	+	0.509420i	−0.607636	+	0.0873648i
$35$	0.756263	+	11.5547i	0.127832	+	1.95310i
$36$	−1.72067	−	1.89830i	−0.286778	−	0.316383i
$37$	−1.92784	−	5.57012i	−0.316934	−	0.915721i	−0.985141	−	0.171746i	$-0.945059\pi$
$37$	−1.92784	−	5.57012i	−0.316934	−	0.915721i	0.668207	−	0.743975i	$-0.267062\pi$
$38$	−0.537821	+	0.0513557i	−0.0872460	+	0.00833099i
$39$	−1.45354	+	1.55896i	−0.232753	+	0.249633i
$40$	−12.9946	−	3.15247i	−2.05463	−	0.498449i
$41$	7.44760	+	8.59499i	1.16312	+	1.34231i	0.928989	+	0.370107i	$0.120679\pi$
$41$	7.44760	+	8.59499i	1.16312	+	1.34231i	0.234131	+	0.972205i	$0.424776\pi$
$42$	2.53169	−	4.20190i	0.390648	−	0.648368i
$43$	−2.14338	−	4.69335i	−0.326863	−	0.715729i	0.672848	−	0.739781i	$-0.265071\pi$
$43$	−2.14338	−	4.69335i	−0.326863	−	0.715729i	−0.999711	+	0.0240513i	$0.992343\pi$
$44$	1.30338	−	1.65739i	0.196493	−	0.249861i
$45$	−10.1367	+	8.34499i	−1.51109	+	1.24400i
$46$	4.98334	+	1.23437i	0.734754	+	0.181998i
$47$	0.499932	−	0.865907i	0.0729226	−	0.126306i	−0.827258	−	0.561822i	$-0.810101\pi$
$47$	0.499932	−	0.865907i	0.0729226	−	0.126306i	0.900181	+	0.435516i	$0.143434\pi$
$48$	1.79512	+	2.02548i	0.259103	+	0.292353i
$49$	−6.78224	−	1.73240i	−0.968892	−	0.247485i
$50$	−4.26898	+	14.5388i	−0.603724	+	2.05610i
$51$	−2.83956	+	5.04774i	−0.397618	+	0.706824i
$52$	−0.725250	+	0.760620i	−0.100574	+	0.105479i
$53$	−11.0425	−	0.526021i	−1.51681	−	0.0722545i	−0.727439	−	0.686172i	$-0.759290\pi$
$53$	−11.0425	−	0.526021i	−1.51681	−	0.0722545i	−0.789370	+	0.613918i	$0.789593\pi$
$54$	5.54419	−	0.450809i	0.754469	−	0.0613474i
$55$	−8.16613	−	7.07599i	−1.10112	−	0.954126i
$56$	4.24878	−	6.87672i	0.567767	−	0.918941i
$57$	−0.464347	+	0.740611i	−0.0615043	+	0.0980964i
$58$	−1.81564	−	0.726871i	−0.238405	−	0.0954429i
$59$	−5.82765	−	3.00436i	−0.758695	−	0.391134i	0.0350496	−	0.999386i	$-0.488841\pi$
$59$	−5.82765	−	3.00436i	−0.758695	−	0.391134i	−0.793745	+	0.608251i	$0.791871\pi$
$60$	−5.04382	+	4.05856i	−0.651154	+	0.523958i
$61$	8.89647	−	6.33515i	1.13908	−	0.811133i	0.154831	−	0.987941i	$-0.450517\pi$
$61$	8.89647	−	6.33515i	1.13908	−	0.811133i	0.984245	+	0.176808i	$0.0565773\pi$
$62$	−3.53388	−	2.27108i	−0.448803	−	0.288428i
$63$	−2.89473	−	7.39057i	−0.364702	−	0.931124i
$64$	5.15753	+	5.95211i	0.644691	+	0.744014i
$65$	3.71666	+	3.89793i	0.460996	+	0.483478i
$66$	1.12890	+	4.43634i	0.138957	+	0.546075i
$67$	−8.31798	+	3.33002i	−1.01620	+	0.406826i	−0.819158	−	0.573568i	$-0.805559\pi$
$67$	−8.31798	+	3.33002i	−1.01620	+	0.406826i	−0.197045	+	0.980394i	$0.563135\pi$
$68$	−1.42784	+	2.47309i	−0.173151	+	0.299907i
$69$	6.49663	−	5.17627i	0.782102	−	0.623150i
$70$	−10.2234	−	7.00982i	−1.22193	−	0.837834i
$71$	14.2424	+	2.04775i	1.69027	+	0.243024i	0.919217	−	0.393751i	$-0.128823\pi$
$71$	14.2424	+	2.04775i	1.69027	+	0.243024i	0.771050	+	0.636775i	$0.219732\pi$
$72$	9.14330	−	0.640671i	1.07755	−	0.0755038i
$73$	8.11105	−	1.96772i	0.949326	−	0.230304i	0.268939	−	0.963157i	$-0.413327\pi$
$73$	8.11105	−	1.96772i	0.949326	−	0.230304i	0.680387	+	0.732853i	$0.261812\pi$
$74$	5.96282	+	2.06375i	0.693163	+	0.239906i
$75$	14.4434	+	19.8104i	1.66777	+	2.28751i
$76$	−0.233024	+	0.362593i	−0.0267297	+	0.0415923i
$77$	5.59804	−	3.36596i	0.637956	−	0.383587i
$78$	−0.349949	−	2.25474i	−0.0396240	−	0.255299i
$79$	−0.328821	−	6.90281i	−0.0369953	−	0.776627i	−0.938796	−	0.344474i	$-0.888057\pi$
$79$	−0.328821	−	6.90281i	−0.0369953	−	0.776627i	0.901800	−	0.432153i	$-0.142246\pi$
$80$	5.37568	−	4.22748i	0.601019	−	0.472646i
$81$	4.88762	−	7.55720i	0.543068	−	0.839688i
$82$	−12.1608	+	0.579291i	−1.34294	+	0.0639720i
$83$	1.44316	−	1.66549i	0.158407	−	0.182812i	−0.670998	−	0.741459i	$-0.734134\pi$
$83$	1.44316	−	1.66549i	0.158407	−	0.182812i	0.829405	+	0.558647i	$0.188680\pi$
$84$	−1.38649	−	3.65981i	−0.151279	−	0.399318i
$85$	12.3113	+	7.91197i	1.33534	+	0.858174i
$86$	5.36768	+	1.30219i	0.578812	+	0.140418i
$87$	−2.72254	+	1.61270i	−0.291886	+	0.172899i
$88$	1.77834	+	7.33041i	0.189572	+	0.781424i
$89$	−5.70420	−	0.544685i	−0.604644	−	0.0577365i	−0.211756	−	0.977323i	$-0.567918\pi$
$89$	−5.70420	−	0.544685i	−0.604644	−	0.0577365i	−0.392888	+	0.919586i	$0.628524\pi$
$90$	−0.314195	−	14.0520i	−0.0331190	−	1.48121i
$91$	−2.93716	+	1.40491i	−0.307898	+	0.147275i
$92$	3.23164	−	2.51631i	0.336921	−	0.262344i
$93$	−6.39763	+	2.29463i	−0.663403	+	0.237942i
$94$	0.397811	+	0.993684i	0.0410311	+	0.102491i
$95$	1.79924	+	1.28124i	0.184599	+	0.131452i
$96$	7.67310	−	0.451528i	0.783132	−	0.0460838i
$97$	9.31283	−	8.06961i	0.945575	−	0.819345i	−0.0381051	−	0.999274i	$-0.512132\pi$
$97$	9.31283	−	8.06961i	0.945575	−	0.819345i	0.983680	+	0.179929i	$0.0575867\pi$
$98$	5.94584	−	4.56066i	0.600621	−	0.460697i
$99$	6.80443	+	2.92546i	0.683871	+	0.294020i
$100$	7.01199	+	9.84696i	0.701199	+	0.984696i
$101$	−1.58463	−	0.305413i	−0.157677	−	0.0303897i	0.109802	−	0.993953i	$-0.464978\pi$
$101$	−1.58463	−	0.305413i	−0.157677	−	0.0303897i	−0.267479	+	0.963564i	$0.586190\pi$
$102$	−2.36847	−	5.72970i	−0.234514	−	0.567325i
$103$	−0.309468	+	0.773014i	−0.0304928	+	0.0761674i	−0.942833	−	0.333266i	$-0.891849\pi$
$103$	−0.309468	+	0.773014i	−0.0304928	+	0.0761674i	0.912340	+	0.409433i	$0.134274\pi$
$104$	−0.535073	−	3.72151i	−0.0524682	−	0.364924i
$105$	−19.0722	+	6.20485i	−1.86125	+	0.605531i
$106$	7.74992	−	8.94388i	0.752739	−	0.868707i
$107$	−4.30743	+	3.06731i	−0.416415	+	0.296528i	−0.768996	−	0.639253i	$-0.779244\pi$
$107$	−4.30743	+	3.06731i	−0.416415	+	0.296528i	0.352581	+	0.935781i	$0.385304\pi$
$108$	2.45145	−	3.69907i	0.235891	−	0.355944i
$109$	9.99911	+	9.53413i	0.957741	+	0.913204i	0.996291	−	0.0860522i	$-0.0274252\pi$
$109$	9.99911	+	9.53413i	0.957741	+	0.913204i	−0.0385493	+	0.999257i	$0.512274\pi$
$110$	11.3581	−	2.18909i	1.08295	−	0.208722i
$111$	8.52631	−	5.61518i	0.809282	−	0.532969i
$112$	1.42133	+	3.88221i	0.134303	+	0.366834i
$113$	−2.37686	−	0.341742i	−0.223597	−	0.0321483i	0.0296058	−	0.999562i	$-0.490575\pi$
$113$	−2.37686	−	0.341742i	−0.223597	−	0.0321483i	−0.253202	+	0.967413i	$0.581484\pi$
$114$	−0.315926	−	0.880827i	−0.0295892	−	0.0824970i
$115$	−12.0927	−	17.1559i	−1.12765	−	1.59980i
$116$	−1.35121	+	0.780122i	−0.125457	+	0.0724325i
$117$	−3.23766	−	1.77397i	−0.299322	−	0.164004i
$118$	6.38447	−	2.91569i	0.587738	−	0.268411i
$119$	−6.85587	+	5.59137i	−0.628477	+	0.512560i
$120$	−0.258877	−	23.1588i	−0.0236321	−	2.11410i
$121$	1.15630	−	4.76635i	0.105119	−	0.433305i
$122$	−0.556308	+	11.6783i	−0.0503658	+	1.05731i
$123$	−11.2461	+	16.1725i	−1.01402	+	1.45822i
$124$	−3.16694	+	1.09609i	−0.284400	+	0.0984318i
$125$	33.7059	−	21.6615i	3.01475	−	1.93746i
$126$	8.13451	+	2.45480i	0.724680	+	0.218691i
$127$	1.22317	+	8.50734i	0.108539	+	0.754904i	0.969298	+	0.245891i	$0.0790805\pi$
$127$	1.22317	+	8.50734i	0.108539	+	0.754904i	−0.860759	+	0.509013i	$0.830010\pi$
$128$	0.443932	−	0.0211471i	0.0392384	−	0.00186916i
$129$	6.96255	−	5.60249i	0.613018	−	0.493271i
$130$	−5.73946	+	0.548052i	−0.503384	+	0.0480673i
$131$	−1.34224	+	0.691975i	−0.117272	+	0.0604581i	−0.515865	−	0.856670i	$-0.672529\pi$
$131$	−1.34224	+	0.691975i	−0.117272	+	0.0604581i	0.398592	+	0.917128i	$0.369499\pi$
$132$	3.33874	+	1.47988i	0.290600	+	0.128807i
$133$	−1.07376	+	0.793726i	−0.0931065	+	0.0688248i
$134$	2.70223	−	9.20295i	0.233437	−	0.795014i
$135$	−18.3373	−	13.4506i	−1.57822	−	1.15765i
$136$	−3.79693	−	9.48427i	−0.325584	−	0.813270i
$137$	−5.54370	+	3.20066i	−0.473631	+	0.273451i	−0.717758	−	0.696292i	$-0.754832\pi$
$137$	−5.54370	+	3.20066i	−0.473631	+	0.273451i	0.244128	+	0.969743i	$0.421498\pi$
$138$	0.0566042	+	8.89207i	0.00481847	+	0.756944i
$139$			15.9683i			1.35442i	0.735791	+	0.677208i	$0.236810\pi$
$139$			15.9683i			1.35442i	−0.735791	+	0.677208i	$0.763190\pi$
$140$	−9.43757	+	2.95413i	−0.797620	+	0.249670i
$141$	1.66701	+	0.469305i	0.140388	+	0.0395226i
$142$	−11.1479	+	10.6295i	−0.935513	+	0.892010i
$143$	0.993702	−	2.87111i	0.0830976	−	0.240095i
$144$	−2.63313	+	3.87836i	−0.219427	+	0.323197i
$145$	3.66386	+	7.10690i	0.304267	+	0.590196i
$146$	−3.71163	+	8.12733i	−0.307176	+	0.672623i
$147$	0.0109921	−	12.1244i	0.000906617	−	1.00000i
$148$	4.23477	−	2.72152i	0.348096	−	0.223708i
$149$	−0.895564	+	2.23701i	−0.0733675	+	0.183263i	−0.960519	−	0.278216i	$-0.910257\pi$
$149$	−0.895564	+	2.23701i	−0.0733675	+	0.183263i	0.887151	+	0.461479i	$0.152681\pi$
$150$	−26.2276	−	0.955686i	−2.14148	−	0.0780314i
$151$	−3.32685	−	1.71511i	−0.270735	−	0.139574i	0.317513	−	0.948254i	$-0.397152\pi$
$151$	−3.32685	−	1.71511i	−0.270735	−	0.139574i	−0.588249	+	0.808680i	$0.700182\pi$
$152$	−0.504318	−	1.45713i	−0.0409056	−	0.118189i
$153$	−9.68579	−	2.61030i	−0.783050	−	0.211030i
$154$	−0.872089	+	6.93798i	−0.0702749	+	0.559079i
$155$	4.83851	+	16.4784i	0.388638	+	1.32358i
$156$	−1.58652	−	0.892485i	−0.127024	−	0.0714560i
$157$	1.54849	−	0.375661i	0.123583	−	0.0299810i	−0.173490	−	0.984836i	$-0.555505\pi$
$157$	1.54849	−	0.375661i	0.123583	−	0.0299810i	0.297074	+	0.954855i	$0.403989\pi$
$158$	6.02611	+	4.29117i	0.479412	+	0.341388i
$159$	−3.83370	−	18.7602i	−0.304032	−	1.48778i
$160$		−	19.4222i		−	1.53546i
$161$	12.1273	−	3.73209i	0.955766	−	0.294130i
$162$	3.12483	+	9.11369i	0.245510	+	0.716039i
$163$	4.16881	+	3.27839i	0.326527	+	0.256783i	0.767942	−	0.640520i	$-0.221281\pi$
$163$	4.16881	+	3.27839i	0.326527	+	0.256783i	−0.441415	+	0.897303i	$0.645523\pi$
$164$	−5.63390	+	7.91171i	−0.439934	+	0.617801i
$165$	8.38941	−	16.7297i	0.653115	−	1.30241i
$166$	0.446469	+	2.31650i	0.0346527	+	0.179795i
$167$	−3.14653	+	0.923904i	−0.243486	+	0.0714939i	−0.401198	−	0.915991i	$-0.631406\pi$
$167$	−3.14653	+	0.923904i	−0.243486	+	0.0714939i	0.157713	+	0.987485i	$0.449588\pi$
$168$	13.3578	+	4.19453i	1.03057	+	0.323615i
$169$	4.77130	−	10.4477i	0.367023	−	0.803668i
$170$	−14.8046	+	5.12391i	−1.13546	+	0.392986i
$171$	−1.44150	−	0.463092i	−0.110234	−	0.0354136i
$172$	3.46370	−	2.72389i	0.264105	−	0.207694i
$173$	21.1656	+	8.47343i	1.60919	+	0.644223i	0.990006	−	0.141023i	$-0.0450390\pi$
$173$	21.1656	+	8.47343i	1.60919	+	0.644223i	0.619185	+	0.785245i	$0.287463\pi$
$174$	0.444572	−	3.35812i	0.0337029	−	0.254579i
$175$	9.47395	+	36.2315i	0.716163	+	2.73885i
$176$	−3.50922	−	1.60261i	−0.264517	−	0.120801i
$177$	2.55380	−	11.0653i	0.191955	−	0.831720i
$178$	4.23303	−	4.43948i	0.317279	−	0.332753i
$179$	1.65904	+	0.574198i	0.124002	+	0.0429176i	0.388364	−	0.921506i	$-0.373040\pi$
$179$	1.65904	+	0.574198i	0.124002	+	0.0429176i	−0.264362	+	0.964423i	$0.585161\pi$
$180$	−8.96692	−	6.73278i	−0.668355	−	0.501832i
$181$	−5.98419	+	2.73289i	−0.444801	+	0.203134i	−0.625208	−	0.780458i	$-0.714986\pi$
$181$	−5.98419	+	2.73289i	−0.444801	+	0.203134i	0.180407	+	0.983592i	$0.442259\pi$
$182$	0.761442	−	3.40122i	0.0564418	−	0.252115i
$183$	14.4339	+	12.2273i	1.06699	+	0.903866i
$184$	−0.0705111	+	14.6522i	−0.00519815	+	1.08018i
$185$	−12.8985	−	22.3409i	−0.948317	−	1.64253i
$186$	2.30270	−	6.90187i	0.168842	−	0.506070i
$187$	0.784728	−	8.21805i	0.0573850	−	0.600963i
$188$	0.819321	+	0.240574i	0.0597551	+	0.0175457i
$189$	11.1691	−	8.01575i	0.812429	−	0.583060i
$190$	−2.26875	+	0.666166i	−0.164593	+	0.0483288i
$191$	−5.46893	−	10.6083i	−0.395718	−	0.767586i	0.603846	−	0.797101i	$-0.293634\pi$
$191$	−5.46893	−	10.6083i	−0.395718	−	0.767586i	−0.999564	+	0.0295146i	$0.990604\pi$
$192$	−7.78799	+	11.1996i	−0.562050	+	0.808259i
$193$	−21.6292	−	4.16869i	−1.55690	−	0.300069i	−0.663102	−	0.748529i	$-0.730761\pi$
$193$	−21.6292	−	4.16869i	−1.55690	−	0.300069i	−0.893803	+	0.448460i	$0.851973\pi$
$194$	0.627672	+	13.1765i	0.0450642	+	0.946015i
$195$	−4.95537	+	7.90358i	−0.354862	+	0.565987i
$196$	0.0722416	−	5.97775i	0.00516011	−	0.426982i
$197$	−3.42562	−	5.33036i	−0.244065	−	0.379773i	0.697510	−	0.716575i	$-0.254291\pi$
$197$	−3.42562	−	5.33036i	−0.244065	−	0.379773i	−0.941576	+	0.336802i	$0.890655\pi$
$198$	−6.96446	+	3.78983i	−0.494942	+	0.269332i
$199$	0.480606	+	5.03313i	0.0340692	+	0.356789i	0.996391	+	0.0848774i	$0.0270499\pi$
$199$	0.480606	+	5.03313i	0.0340692	+	0.356789i	−0.962322	+	0.271912i	$0.912344\pi$
$200$	−43.1969	−	2.05772i	−3.05448	−	0.145503i
$201$	−9.14253	−	12.5398i	−0.644864	−	0.884492i
$202$	1.30561	−	1.13132i	0.0918624	−	0.0795992i
$203$	−4.77143	+	0.772740i	−0.334889	+	0.0542357i
$204$	−4.76111	−	1.34037i	−0.333344	−	0.0938445i
$205$	39.1252	+	30.7684i	2.73262	+	2.14896i
$206$	−0.445682	−	0.771943i	−0.0310521	−	0.0537838i
$207$	11.4636	+	8.69400i	0.796776	+	0.604274i
$208$	1.66530	+	0.961460i	0.115468	+	0.0666653i
$209$	0.177326	−	1.23333i	0.0122659	−	0.0853112i
$210$	7.39962	−	20.1547i	0.510623	−	1.39080i
$211$	−3.74748	−	1.10036i	−0.257987	−	0.0757519i	0.150181	−	0.988658i	$-0.452014\pi$
$211$	−3.74748	−	1.10036i	−0.257987	−	0.0757519i	−0.408169	+	0.912907i	$0.633832\pi$
$212$	−1.78678	−	9.27069i	−0.122717	−	0.636714i
$213$	2.64618	+	24.7814i	0.181313	+	1.69800i
$214$	0.269349	−	5.65434i	0.0184124	−	0.386523i
$215$	−13.0986	−	18.3944i	−0.893318	−	1.25449i
$216$	4.98083	+	15.0739i	0.338903	+	1.02565i
$217$	−10.3775	−	0.309779i	−0.704470	−	0.0210292i
$218$	−14.6395	+	2.10484i	−0.991513	+	0.142558i
$219$	6.76744	+	12.7744i	0.457301	+	0.863212i
$220$	4.22853	−	8.20221i	0.285088	−	0.552993i
$221$	−0.778744	+	4.04051i	−0.0523840	+	0.271794i
$222$	−0.917194	+	10.8904i	−0.0615581	+	0.730918i
$223$	8.31422	−	12.9372i	0.556762	−	0.866338i	−0.442780	−	0.896631i	$-0.646008\pi$
$223$	8.31422	−	12.9372i	0.556762	−	0.866338i	0.999541	+	0.0302926i	$0.00964392\pi$
$224$	11.1618	+	3.64252i	0.745780	+	0.243376i
$225$	−27.0837	+	32.7057i	−1.80558	+	2.18038i
$226$	1.86043	−	1.77392i	0.123754	−	0.117999i
$227$	9.73022	−	13.6642i	0.645817	−	0.906923i	−0.353779	−	0.935329i	$-0.615104\pi$
$227$	9.73022	−	13.6642i	0.645817	−	0.906923i	0.999596	+	0.0284057i	$0.00904302\pi$
$228$	−0.708166	−	0.236268i	−0.0468994	−	0.0156473i
$229$	−13.8186	−	7.97815i	−0.913156	−	0.527211i	−0.0317106	−	0.999497i	$-0.510095\pi$
$229$	−13.8186	−	7.97815i	−0.913156	−	0.527211i	−0.881445	+	0.472286i	$0.843429\pi$
$230$	22.4384	+	1.17712i	1.47954	+	0.0776172i
$231$	8.04108	+	7.95891i	0.529064	+	0.523658i
$232$	0.794359	−	5.52489i	0.0521522	−	0.362727i
$233$	−1.03895	+	10.8804i	−0.0680639	+	0.712797i	0.895454	+	0.445154i	$0.146851\pi$
$233$	−1.03895	+	10.8804i	−0.0680639	+	0.712797i	−0.963518	+	0.267644i	$0.913755\pi$
$234$	3.63523	−	1.55049i	0.237643	−	0.101359i
$235$	1.43125	−	4.13533i	0.0933646	−	0.269759i
$236$	1.32011	−	5.44158i	0.0859321	−	0.354217i
$237$	11.4463	−	3.50038i	0.743518	−	0.227374i
$238$	−0.168166	−	9.46905i	−0.0109006	−	0.613787i
$239$	7.95032	+	6.88899i	0.514264	+	0.445612i	0.872924	−	0.487856i	$-0.162221\pi$
$239$	7.95032	+	6.88899i	0.514264	+	0.445612i	−0.358660	+	0.933468i	$0.616766\pi$
$240$	9.39221	+	7.21767i	0.606264	+	0.465899i
$241$	2.77975	+	3.53474i	0.179059	+	0.227693i	0.867295	−	0.497795i	$-0.165857\pi$
$241$	2.77975	+	3.53474i	0.179059	+	0.227693i	−0.688235	+	0.725488i	$0.741614\pi$
$242$	3.24557	+	4.12708i	0.208633	+	0.265299i
$243$	14.7729	+	4.97620i	0.947680	+	0.319223i
$244$	7.04913	+	6.10810i	0.451274	+	0.391031i
$245$	−30.5817	−	1.82742i	−1.95379	−	0.116749i
$246$	−6.16669	−	20.1652i	−0.393174	−	1.28569i
$247$	−0.146422	+	0.603560i	−0.00931662	+	0.0384036i
$248$	3.92121	−	11.3296i	0.248997	−	0.719430i
$249$	3.41205	+	1.71103i	0.216230	+	0.108432i
$250$	−4.07705	+	42.6968i	−0.257856	+	2.70039i
$251$	0.833280	−	5.79559i	0.0525962	−	0.365814i	−0.946477	−	0.322771i	$-0.895386\pi$
$251$	0.833280	−	5.79559i	0.0525962	−	0.365814i	0.999073	−	0.0430432i	$-0.0137053\pi$
$252$	5.55099	−	3.89054i	0.349679	−	0.245081i
$253$	−5.47615	+	10.4979i	−0.344283	+	0.659997i
$254$	−7.96810	−	4.60038i	−0.499963	−	0.288654i
$255$	−8.02212	+	24.0447i	−0.502365	+	1.50573i
$256$	−9.41276	+	13.2184i	−0.588297	+	0.826148i
$257$	−14.8170	+	14.1280i	−0.924259	+	0.881279i	−0.993209	−	0.116341i	$-0.962884\pi$
$257$	−14.8170	+	14.1280i	−0.924259	+	0.881279i	0.0689501	+	0.997620i	$0.478035\pi$
$258$	0.106934	+	9.56617i	0.00665741	+	0.595564i
$259$	15.2582	−	3.22279i	0.948099	−	0.200254i
$260$	−2.48676	+	3.86948i	−0.154223	+	0.239975i
$261$	−3.86990	−	3.88109i	−0.239541	−	0.240234i
$262$	0.305940	−	1.58737i	0.0189010	−	0.0980678i
$263$	−6.59293	+	12.7885i	−0.406538	+	0.788573i	−0.999866	−	0.0163878i	$-0.994783\pi$
$263$	−6.59293	+	12.7885i	−0.406538	+	0.788573i	0.593328	+	0.804961i	$0.297814\pi$
$264$	−11.5449	+	6.11612i	−0.710541	+	0.376421i
$265$	−47.8911	+	6.88570i	−2.94193	+	0.422985i
$266$	0.0426505	−	1.42878i	0.00261507	−	0.0876039i
$267$	−1.52218	−	9.80748i	−0.0931559	−	0.600208i
$268$	−4.43854	−	6.23305i	−0.271127	−	0.380744i
$269$	0.745955	−	15.6595i	0.0454817	−	0.954778i	−0.854662	−	0.519185i	$-0.826236\pi$
$269$	0.745955	−	15.6595i	0.0454817	−	0.954778i	0.900144	−	0.435593i	$-0.143461\pi$
$270$	23.4528	−	6.52949i	1.42729	−	0.397372i
$271$	−2.82730	−	14.6694i	−0.171746	−	0.891103i	−0.960898	−	0.276904i	$-0.910692\pi$
$271$	−2.82730	−	14.6694i	−0.171746	−	0.891103i	0.789152	−	0.614198i	$-0.210521\pi$
$272$	5.01331	+	1.47204i	0.303976	+	0.0892555i
$273$	−3.61279	−	4.33010i	−0.218656	−	0.262069i
$274$	0.975230	−	6.78287i	0.0589158	−	0.409768i
$275$	−30.2643	−	17.4731i	−1.82501	−	1.05367i
$276$	5.60412	+	4.34968i	0.337329	+	0.261820i
$277$	2.05187	+	3.55394i	0.123285	+	0.213536i	0.921061	−	0.389418i	$-0.127324\pi$
$277$	2.05187	+	3.55394i	0.123285	+	0.213536i	−0.797776	+	0.602953i	$0.793990\pi$
$278$	−13.4369	−	10.5669i	−0.805891	−	0.633760i
$279$	−6.58433	−	9.75867i	−0.394194	−	0.584236i
$280$	12.5634	−	33.0720i	0.750804	−	1.97643i
$281$	4.72206	−	4.09169i	0.281695	−	0.244090i	−0.502540	−	0.864554i	$-0.667601\pi$
$281$	4.72206	−	4.09169i	0.281695	−	0.244090i	0.784235	+	0.620464i	$0.213056\pi$
$282$	−1.49804	+	1.09219i	−0.0892068	+	0.0650387i
$283$	−25.1566	−	1.19835i	−1.49540	−	0.0712348i	−0.716151	−	0.697946i	$-0.754098\pi$
$283$	−25.1566	−	1.19835i	−1.49540	−	0.0712348i	−0.779252	+	0.626711i	$0.784401\pi$
$284$	1.16810	+	12.2329i	0.0693138	+	0.725886i
$285$	−1.38211	+	3.56740i	−0.0818690	+	0.211314i
$286$	1.75839	+	2.73610i	0.103976	+	0.161789i
$287$	−25.0201	+	16.7146i	−1.47689	+	0.986631i
$288$	4.03537	+	12.6869i	0.237786	+	0.747581i
$289$	−0.276883	−	5.81250i	−0.0162873	−	0.341912i
$290$	−8.40477	−	1.61989i	−0.493545	−	0.0951230i
$291$	17.5231	+	12.1853i	1.02723	+	0.714315i
$292$	3.26623	+	6.33560i	0.191141	+	0.370763i
$293$	−25.6736	+	7.53846i	−1.49987	+	0.440402i	−0.925676	−	0.378317i	$-0.876503\pi$
$293$	−25.6736	+	7.53846i	−1.49987	+	0.440402i	−0.574194	+	0.818719i	$0.694685\pi$
$294$	10.1950	+	8.03242i	0.594585	+	0.468460i
$295$	−27.5328	−	8.08437i	−1.60302	−	0.470690i
$296$	−1.71182	+	17.9269i	−0.0994973	+	1.04198i
$297$	−2.00414	+	12.6712i	−0.116292	+	0.735257i
$298$	−1.28975	−	2.23391i	−0.0747132	−	0.129407i
$299$	3.21459	−	4.94946i	0.185904	−	0.286235i
$300$	−13.5336	+	15.9760i	−0.781364	+	0.922376i
$301$	13.0277	−	4.07792i	0.750906	−	0.235047i
$302$	3.64473	−	1.66449i	0.209731	−	0.0957808i
$303$	−0.164199	−	2.79035i	−0.00943301	−	0.160301i
$304$	0.745242	+	0.257931i	0.0427426	+	0.0147933i
$305$	32.9854	−	34.5941i	1.88874	−	1.98085i
$306$	8.60597	−	6.42297i	0.491970	−	0.367177i
$307$	−11.1240	−	5.08017i	−0.634881	−	0.289940i	0.0718580	−	0.997415i	$-0.477107\pi$
$307$	−11.1240	−	5.08017i	−0.634881	−	0.289940i	−0.706739	+	0.707474i	$0.749834\pi$
$308$	3.92072	+	3.96839i	0.223404	+	0.226120i
$309$	−1.42973	−	0.189278i	−0.0813347	−	0.0107677i
$310$	−17.0680	−	6.83298i	−0.969395	−	0.388087i
$311$	22.1624	−	17.4287i	1.25672	−	0.988292i	0.256954	−	0.966424i	$-0.417281\pi$
$311$	22.1624	−	17.4287i	1.25672	−	0.988292i	0.999761	−	0.0218682i	$-0.00696142\pi$
$312$	6.01822	−	2.48774i	0.340715	−	0.140841i
$313$	−10.4115	+	3.60347i	−0.588496	+	0.203680i	−0.605056	−	0.796183i	$-0.706849\pi$
$313$	−10.4115	+	3.60347i	−0.588496	+	0.203680i	0.0165609	+	0.999863i	$0.494728\pi$
$314$	−0.708593	+	1.55160i	−0.0399882	+	0.0875620i
$315$	−18.5616	−	29.3634i	−1.04583	−	1.65444i
$316$	5.66280	−	1.66275i	0.318557	−	0.0935369i
$317$	4.59788	+	23.8561i	0.258243	+	1.33989i	0.847006	+	0.531584i	$0.178403\pi$
$317$	4.59788	+	23.8561i	0.258243	+	1.33989i	−0.588763	+	0.808306i	$0.700385\pi$
$318$	18.3231	+	9.18844i	1.02751	+	0.515262i
$319$	2.61633	−	3.67413i	0.146487	−	0.205712i
$320$	27.0946	+	21.3074i	1.51463	+	1.19112i
$321$	−6.98851	−	5.92012i	−0.390061	−	0.330429i
$322$	−4.88468	+	12.6744i	−0.272213	+	0.706319i
$323$			1.68756i			0.0938985i
$324$	7.25621	+	2.53489i	0.403123	+	0.140827i
$325$	14.1889	+	10.1039i	0.787058	+	0.560461i
$326$	−5.51734	+	1.33849i	−0.305577	+	0.0741323i
$327$	−11.7326	+	20.8565i	−0.648815	+	1.15336i
$328$	−9.78926	−	33.3392i	−0.540521	−	1.84085i
$329$	2.10813	+	1.59809i	0.116225	+	0.0881056i
$330$	8.52596	+	18.1302i	0.469339	+	0.998033i
$331$	8.09105	+	23.3776i	0.444724	+	1.28495i	0.915366	+	0.402622i	$0.131901\pi$
$331$	8.09105	+	23.3776i	0.444724	+	1.28495i	−0.470642	+	0.882324i	$0.655978\pi$
$332$	1.67285	+	0.862416i	0.0918098	+	0.0473312i
$333$	13.0673	+	11.9135i	0.716083	+	0.652854i
$334$	1.30475	−	3.25910i	0.0713925	−	0.178330i
$335$	−32.9885	+	21.2004i	−1.80235	+	1.15830i
$336$	−5.90941	+	4.04401i	−0.322385	+	0.220619i
$337$	10.3201	−	22.5979i	0.562172	−	1.23098i	−0.388690	−	0.921368i	$-0.627072\pi$
$337$	10.3201	−	22.5979i	0.562172	−	1.23098i	0.950862	−	0.309615i	$-0.100200\pi$
$338$	5.63407	+	10.9286i	0.306453	+	0.594436i
$339$	−0.441610	−	4.13567i	−0.0239850	−	0.224619i
$340$	−4.08776	+	11.8108i	−0.221690	+	0.640531i
$341$	7.01160	−	6.68554i	0.379699	−	0.362043i
$342$	1.34358	−	0.906532i	0.0726523	−	0.0490196i
$343$	6.78563	−	17.2324i	0.366390	−	0.930462i
$344$			15.7639i			0.849930i
$345$	23.6320	−	27.6261i	1.27230	−	1.48734i
$346$	−21.1363	+	12.2030i	−1.13629	+	0.656039i
$347$	−9.44417	−	23.5904i	−0.506990	−	1.26640i	−0.932410	−	0.361403i	$-0.882298\pi$
$347$	−9.44417	−	23.5904i	−0.506990	−	1.26640i	0.425420	−	0.904996i	$-0.360126\pi$
$348$	−1.88663	−	1.93487i	−0.101134	−	0.103720i
$349$	−6.10642	+	20.7965i	−0.326869	+	1.11321i	0.618112	+	0.786090i	$0.287898\pi$
$349$	−6.10642	+	20.7965i	−0.326869	+	1.11321i	−0.944981	+	0.327124i	$0.893921\pi$
$350$	−36.7571	−	16.0038i	−1.96475	−	0.855440i
$351$	1.59479	−	6.19232i	0.0851237	−	0.330522i
$352$	−9.73830	+	5.02044i	−0.519053	+	0.267590i
$353$	0.133960	−	0.0127917i	0.00712999	−	0.000680832i	−0.0914904	−	0.995806i	$-0.529163\pi$
$353$	0.133960	−	0.0127917i	0.00712999	−	0.000680832i	0.0986204	+	0.995125i	$0.468557\pi$
$354$	7.62119	+	9.47131i	0.405062	+	0.503394i
$355$	62.9032	−	2.99645i	3.33855	−	0.159035i
$356$	−0.696446	−	4.84389i	−0.0369115	−	0.256725i
$357$	−12.3138	−	9.11971i	−0.651716	−	0.482666i
$358$	−1.58102	+	1.01606i	−0.0835596	+	0.0537005i
$359$	4.15051	−	1.43651i	0.219056	−	0.0758159i	−0.215336	−	0.976540i	$-0.569085\pi$
$359$	4.15051	−	1.43651i	0.219056	−	0.0758159i	0.434392	+	0.900724i	$0.356963\pi$
$360$	38.7628	−	10.3265i	2.04298	−	0.544253i
$361$	0.891937	−	18.7241i	0.0469440	−	0.985477i
$362$	1.66033	−	6.84398i	0.0872652	−	0.359712i
$363$	8.49449	−	0.0949543i	0.445845	−	0.00498381i
$364$	−1.75739	−	2.15483i	−0.0921122	−	0.112944i
$365$	33.2275	−	15.1745i	1.73921	−	0.794269i
$366$	−19.8404	+	4.05444i	−1.03707	+	0.211929i
$367$	17.0425	−	9.83949i	0.889611	−	0.513617i	0.0157960	−	0.999875i	$-0.494972\pi$
$367$	17.0425	−	9.83949i	0.889611	−	0.513617i	0.873815	+	0.486258i	$0.161638\pi$
$368$	−5.86824	−	4.66071i	−0.305903	−	0.242957i
$369$	−31.9500	−	11.9693i	−1.66325	−	0.623098i
$370$	27.3346	+	3.93013i	1.42106	+	0.204318i
$371$	5.02454	−	28.8141i	0.260861	−	1.49595i
$372$	−3.19256	−	4.84772i	−0.165527	−	0.251343i
$373$	−9.83260	+	1.89508i	−0.509113	+	0.0981234i	−0.437338	−	0.899297i	$-0.644079\pi$
$373$	−9.83260	+	1.89508i	−0.509113	+	0.0981234i	−0.0717752	+	0.997421i	$0.522866\pi$
$374$	6.39596	+	6.09854i	0.330727	+	0.315348i
$375$	50.7570	+	47.3250i	2.62108	+	2.44385i
$376$	−2.48839	+	1.77197i	−0.128329	+	0.0913825i
$377$	−1.47227	+	1.69909i	−0.0758258	+	0.0875077i
$378$	−0.645992	+	14.7028i	−0.0332262	+	0.756229i
$379$	3.91744	+	27.2464i	0.201225	+	1.39955i	0.800656	+	0.599125i	$0.204485\pi$
$379$	3.91744	+	27.2464i	0.201225	+	1.39955i	−0.599431	+	0.800427i	$0.704606\pi$
$380$	−0.701097	+	1.75126i	−0.0359655	+	0.0898376i
$381$	−13.7576	+	5.68695i	−0.704823	+	0.291351i
$382$	12.5456	+	2.41796i	0.641886	+	0.123713i
$383$	−15.4388	−	21.6808i	−0.788886	−	1.10784i	−0.991694	−	0.128617i	$-0.958946\pi$
$383$	−15.4388	−	21.6808i	−0.788886	−	1.10784i	0.202808	−	0.979219i	$-0.434993\pi$
$384$	0.225116	+	0.736133i	0.0114879	+	0.0375656i
$385$	21.2697	−	19.1020i	1.08400	−	0.973528i
$386$	17.8208	−	15.4418i	0.907052	−	0.785965i
$387$	12.3780	+	9.29401i	0.629211	+	0.472441i
$388$	8.57248	+	6.10444i	0.435202	+	0.309906i
$389$	−1.00641	−	2.51389i	−0.0510270	−	0.127459i	0.900664	−	0.434515i	$-0.143080\pi$
$389$	−1.00641	−	2.51389i	−0.0510270	−	0.127459i	−0.951691	+	0.307056i	$0.900656\pi$
$390$	−3.37146	−	9.39992i	−0.170721	−	0.475983i
$391$	5.31781	−	15.1288i	0.268933	−	0.765099i
$392$	16.6501	+	13.4226i	0.840956	+	0.677941i
$393$	−1.73484	−	1.95747i	−0.0875111	−	0.0987411i
$394$	6.75221	+	0.644758i	0.340172	+	0.0324825i
$395$	−7.13056	−	29.3926i	−0.358777	−	1.47890i
$396$	−1.05796	+	6.23638i	−0.0531646	+	0.313390i
$397$	−29.7937	−	7.22787i	−1.49530	−	0.362757i	−0.597039	−	0.802212i	$-0.703656\pi$
$397$	−29.7937	−	7.22787i	−1.49530	−	0.362757i	−0.898264	+	0.439456i	$0.855171\pi$
$398$	−4.55327	−	2.92621i	−0.228235	−	0.146678i
$399$	−1.79095	−	1.46333i	−0.0896599	−	0.0732583i
$400$	14.4841	−	16.7156i	0.724206	−	0.835779i
$401$	16.1341	−	0.768560i	0.805696	−	0.0383800i	0.359308	−	0.933219i	$-0.383013\pi$
$401$	16.1341	−	0.768560i	0.805696	−	0.0383800i	0.446389	+	0.894839i	$0.352710\pi$
$402$	16.6019	+	0.604942i	0.828027	+	0.0301718i
$403$	−3.79583	+	2.98507i	−0.189084	+	0.148697i
$404$	−0.0655785	−	1.37666i	−0.00326265	−	0.0684915i
$405$	14.7451	−	36.5254i	0.732692	−	1.81496i
$406$	2.50721	−	4.52637i	0.124431	−	0.224640i
$407$	−7.86759	+	12.2422i	−0.389982	+	0.606824i
$408$	14.2981	−	10.4244i	0.707861	−	0.516086i
$409$	2.56194	+	0.886696i	0.126680	+	0.0438443i	0.389672	−	0.920954i	$-0.372588\pi$
$409$	2.56194	+	0.886696i	0.126680	+	0.0438443i	−0.262993	+	0.964798i	$0.584709\pi$
$410$	−51.7814	+	12.5620i	−2.55730	+	0.620395i
$411$	−7.74040	−	7.93831i	−0.381806	−	0.391568i
$412$	−0.703875	−	0.101202i	−0.0346774	−	0.00498586i
$413$	9.80967	−	14.3068i	0.482702	−	0.703991i
$414$	−14.9017	+	3.89313i	−0.732378	+	0.191337i
$415$	4.82250	−	8.35282i	0.236727	−	0.410024i
$416$	5.06989	−	2.02968i	0.248572	−	0.0995131i
$417$	−26.8038	+	6.82064i	−1.31259	+	0.334008i
$418$	0.920467	+	0.965358i	0.0450215	+	0.0472172i
$419$	1.45621	+	1.68056i	0.0711406	+	0.0821006i	0.790204	−	0.612844i	$-0.209974\pi$
$419$	1.45621	+	1.68056i	0.0711406	+	0.0821006i	−0.719064	+	0.694944i	$0.755429\pi$
$420$	−8.98980	−	14.5797i	−0.438657	−	0.711416i
$421$	−18.0828	−	11.6211i	−0.881302	−	0.566378i	0.0198881	−	0.999802i	$-0.493669\pi$
$421$	−18.0828	−	11.6211i	−0.881302	−	0.566378i	−0.901190	+	0.433424i	$0.857305\pi$
$422$	3.40578	−	2.42524i	0.165791	−	0.118059i
$423$	−0.0757141	+	2.99864i	−0.00368134	+	0.145799i
$424$	30.0212	+	15.4770i	1.45796	+	0.751629i
$425$	43.9398	+	17.5908i	2.13139	+	0.853281i
$426$	−22.6039	−	14.1722i	−1.09516	−	0.686644i
$427$	13.6948	+	25.4445i	0.662738	+	1.23134i
$428$	−3.41300	−	2.95738i	−0.164974	−	0.142950i
$429$	5.24378	+	0.441632i	0.253172	+	0.0213222i
$430$	24.1462	+	1.15023i	1.16444	+	0.0554689i
$431$	11.1955	−	11.7415i	0.539270	−	0.565570i	−0.396566	−	0.918006i	$-0.629798\pi$
$431$	11.1955	−	11.7415i	0.539270	−	0.565570i	0.935836	+	0.352436i	$0.114647\pi$
$432$	−7.63476	−	2.76327i	−0.367328	−	0.132948i
$433$	1.19062	−	4.05488i	0.0572176	−	0.194865i	−0.925924	−	0.377709i	$-0.876712\pi$
$433$	1.19062	−	4.05488i	0.0572176	−	0.194865i	0.983142	+	0.182844i	$0.0585302\pi$
$434$	7.12788	−	8.52737i	0.342149	−	0.409327i
$435$	−10.3644	+	9.18561i	−0.496934	+	0.440416i
$436$	−5.89962	+	10.2184i	−0.282540	+	0.489374i
$437$	0.910370	−	2.24266i	0.0435489	−	0.107281i
$438$	−15.2276	−	2.75871i	−0.727601	−	0.131816i
$439$	−18.5074	+	23.5341i	−0.883310	+	1.12322i	0.108321	+	0.994116i	$0.465452\pi$
$439$	−18.5074	+	23.5341i	−0.883310	+	1.12322i	−0.991631	+	0.129104i	$0.958790\pi$
$440$	13.7140	+	30.0296i	0.653792	+	1.43160i
$441$	20.3561	−	5.16029i	0.969339	−	0.245728i
$442$	−2.88464	−	3.32906i	−0.137209	−	0.158347i
$443$	5.02738	+	1.21963i	0.238858	+	0.0579463i	0.353401	−	0.935472i	$-0.385025\pi$
$443$	5.02738	+	1.21963i	0.238858	+	0.0579463i	−0.114543	+	0.993418i	$0.536540\pi$
$444$	6.37706	+	5.94585i	0.302642	+	0.282178i
$445$	−24.9650	+	2.38387i	−1.18346	+	0.113006i
$446$	5.38441	+	15.5572i	0.254959	+	0.736656i
$447$	−4.13748	−	0.547749i	−0.195696	−	0.0259077i
$448$	−17.3267	+	11.5750i	−0.818608	+	0.546867i
$449$	−29.6934	+	4.26927i	−1.40132	+	0.201479i	−0.801184	−	0.598418i	$-0.795796\pi$
$449$	−29.6934	+	4.26927i	−1.40132	+	0.201479i	−0.600136	+	0.799898i	$0.704887\pi$
$450$	−9.59858	−	44.4328i	−0.452481	−	2.09458i
$451$	5.31382	−	27.5707i	0.250218	−	1.29826i
$452$	−0.194939	−	2.04149i	−0.00916916	−	0.0960238i
$453$	1.45790	−	6.31690i	0.0684980	−	0.296794i
$454$	5.05913	+	17.2298i	0.237437	+	0.808636i
$455$	−11.4588	+	8.47040i	−0.537197	+	0.397099i
$456$	2.23047	−	1.46892i	0.104451	−	0.0687884i
$457$	−36.6294	−	3.49768i	−1.71345	−	0.163615i	−0.808318	−	0.588747i	$-0.799622\pi$
$457$	−36.6294	−	3.49768i	−1.71345	−	0.163615i	−0.905131	+	0.425132i	$0.860228\pi$
$458$	15.8577	−	6.34845i	0.740980	−	0.296644i
$459$	0.244391	−	17.3731i	0.0114072	−	0.810907i
$460$	11.8038	−	13.4906i	0.550355	−	0.629001i
$461$	3.45975			0.161137			0.0805684	−	0.996749i	$-0.474326\pi$
$461$	3.45975			0.161137			0.0805684	+	0.996749i	$0.474326\pi$
$462$	−12.0183	+	1.49961i	−0.559142	+	0.0697680i
$463$	−0.486598	−	1.06550i	−0.0226141	−	0.0495180i	0.897988	−	0.440020i	$-0.145029\pi$
$463$	−0.486598	−	1.06550i	−0.0226141	−	0.0495180i	−0.920602	+	0.390502i	$0.872301\pi$
$464$	1.96999	+	2.06607i	0.0914545	+	0.0959148i
$465$	−25.5933	+	15.1602i	−1.18686	+	0.703039i
$466$	−8.46801	−	8.07423i	−0.392273	−	0.374031i
$467$	−12.4310	+	6.40863i	−0.575239	+	0.296556i	−0.721192	−	0.692735i	$-0.756405\pi$
$467$	−12.4310	+	6.40863i	−0.575239	+	0.296556i	0.145953	+	0.989292i	$0.453375\pi$
$468$	0.820427	−	3.04428i	0.0379243	−	0.140722i
$469$	−5.99694	−	22.9343i	−0.276913	−	1.05901i
$470$	2.53264	+	3.94087i	0.116822	+	0.181779i
$471$	1.29198	+	2.43878i	0.0595315	+	0.112373i
$472$	12.3828	+	15.7460i	0.569963	+	0.724766i
$473$	−5.83712	+	11.3224i	−0.268391	+	0.520606i
$474$	−4.62902	+	11.9481i	−0.212618	+	0.548794i
$475$	6.49810	+	2.96758i	0.298153	+	0.136162i
$476$	−6.02096	−	4.56426i	−0.275970	−	0.209203i
$477$	29.8526	−	14.4482i	1.36686	−	0.661540i
$478$	−11.0579	+	2.13124i	−0.505778	+	0.0974808i
$479$	1.87241	+	7.71818i	0.0855526	+	0.352652i	0.998458	−	0.0555196i	$-0.0176815\pi$
$479$	1.87241	+	7.71818i	0.0855526	+	0.352652i	−0.912905	+	0.408172i	$0.866166\pi$
$480$	32.6012	−	8.29590i	1.48804	−	0.378654i
$481$	4.48383	−	5.70166i	0.204445	−	0.259973i
$482$	−4.81385			−0.219265
$483$	11.4445	+	18.7623i	0.520744	+	0.853713i
$484$	4.18866			0.190394
$485$	33.3381	−	42.3929i	1.51381	−	1.92496i
$486$	−13.9631	+	9.13799i	−0.633380	+	0.414507i
$487$	−7.25110	−	29.8894i	−0.328579	−	1.35442i	−0.861286	−	0.508120i	$-0.830340\pi$
$487$	−7.25110	−	29.8894i	−0.328579	−	1.35442i	0.532707	−	0.846300i	$-0.321175\pi$
$488$	−32.7651	+	6.31495i	−1.48321	+	0.285865i
$489$	−3.72232	+	8.39791i	−0.168329	+	0.379767i
$490$	21.7748	−	24.5243i	0.983687	−	1.10790i
$491$	−2.76633	−	1.26334i	−0.124843	−	0.0570137i	0.352014	−	0.935995i	$-0.385497\pi$
$491$	−2.76633	−	1.26334i	−0.124843	−	0.0570137i	−0.476857	+	0.878981i	$0.658224\pi$
$492$	−15.6867	−	6.07746i	−0.707211	−	0.273993i
$493$	−2.79924	+	5.42977i	−0.126071	+	0.244545i
$494$	−0.410985	−	0.522610i	−0.0184911	−	0.0235133i
$495$	31.6652	+	6.93625i	1.42325	+	0.311761i
$496$	3.31505	+	5.15831i	0.148850	+	0.231615i
$497$	−10.0751	+	36.7121i	−0.451930	+	1.64676i
$498$	−3.69768	+	1.73888i	−0.165697	+	0.0779213i
$499$	−23.5974	+	12.1653i	−1.05637	+	0.544595i	−0.896728	−	0.442581i	$-0.854063\pi$
$499$	−23.5974	+	12.1653i	−1.05637	+	0.544595i	−0.159638	+	0.987176i	$0.551033\pi$
$500$	24.7645	+	23.6129i	1.10750	+	1.05600i
$501$	−2.89482	−	4.88700i	−0.129331	−	0.218335i
$502$	4.32541	+	4.53635i	0.193052	+	0.202467i
$503$	13.9535	+	30.5539i	0.622155	+	1.36233i	0.913941	+	0.405846i	$0.133023\pi$
$503$	13.9535	+	30.5539i	0.622155	+	1.36233i	−0.291786	+	0.956484i	$0.594250\pi$
$504$	−1.33518	+	24.2134i	−0.0594736	+	1.07855i
$505$	−7.06294			−0.314297
$506$	−5.20989	−	11.5549i	−0.231608	−	0.513678i
$507$	19.5750	+	3.54632i	0.869358	+	0.157498i
$508$	−6.81441	+	2.72808i	−0.302341	+	0.121039i
$509$	−37.8874	−	3.61780i	−1.67933	−	0.160356i	−0.788604	−	0.614901i	$-0.789196\pi$
$509$	−37.8874	−	3.61780i	−1.67933	−	0.160356i	−0.890724	+	0.454545i	$0.849802\pi$
$510$	−14.9243	−	22.6617i	−0.660860	−	1.00348i
$511$	2.48906	+	21.9415i	0.110109	+	0.970637i
$512$	−4.64365	−	15.8148i	−0.205222	−	0.698923i
$513$	0.161612	−	2.61744i	0.00713536	−	0.115563i
$514$	−2.08328	−	21.8171i	−0.0918897	−	0.962313i
$515$	−0.689673	+	3.57836i	−0.0303906	+	0.157682i
$516$	6.05167	+	4.65055i	0.266410	+	0.204729i
$517$	−2.44342	+	0.351311i	−0.107462	+	0.0154506i
$518$	−7.38508	+	14.9720i	−0.324482	+	0.657831i
$519$	−5.18256	+	39.1470i	−0.227489	+	1.71836i
$520$	−5.38193	−	15.5501i	−0.236013	−	0.681915i
$521$	12.2445	−	1.16921i	0.536442	−	0.0512240i	0.176681	−	0.984268i	$-0.443464\pi$
$521$	12.2445	−	1.16921i	0.536442	−	0.0512240i	0.359762	+	0.933044i	$0.382858\pi$
$522$	5.82669	−	0.688133i	0.255027	−	0.0301188i
$523$	4.09922	+	0.994460i	0.179246	+	0.0434847i	0.324377	−	0.945928i	$-0.394845\pi$
$523$	4.09922	+	0.994460i	0.179246	+	0.0434847i	−0.145131	+	0.989412i	$0.546360\pi$
$524$	−0.844560	−	0.974674i	−0.0368948	−	0.0425788i
$525$	−56.7701	+	31.3784i	−2.47765	+	1.36946i
$526$	−6.39835	−	14.0104i	−0.278981	−	0.610884i
$527$	−8.11103	+	10.3140i	−0.353322	+	0.449285i
$528$	1.19116	−	6.57496i	0.0518384	−	0.286138i
$529$	−15.2284	+	17.2365i	−0.662104	+	0.749412i
$530$	25.8974	−	44.8555i	1.12491	−	1.94840i
$531$	19.6646	−	0.439690i	0.853370	−	0.0190809i
$532$	−0.874950	−	0.731355i	−0.0379339	−	0.0317083i
$533$	−3.94296	+	13.4285i	−0.170788	+	0.581652i
$534$	9.26000	+	5.20913i	0.400719	+	0.225421i
$535$	−15.9707	+	16.7495i	−0.690472	+	0.724146i
$536$	27.3433	+	1.30252i	1.18105	+	0.0562604i
$537$	−0.255191	+	3.03005i	−0.0110123	+	0.130756i
$538$	12.6834	+	10.9902i	0.546820	+	0.473823i
$539$	6.98879	+	15.8061i	0.301029	+	0.680815i
$540$	7.47127	−	17.9273i	0.321512	−	0.771468i
$541$	−28.0411	−	11.2260i	−1.20558	−	0.482642i	−0.320129	−	0.947374i	$-0.603726\pi$
$541$	−28.0411	−	11.2260i	−1.20558	−	0.482642i	−0.885451	+	0.464732i	$0.846151\pi$
$542$	14.2148	+	7.32824i	0.610578	+	0.314775i
$543$	−7.14337	−	8.87749i	−0.306551	−	0.380970i
$544$	12.0873	−	8.60736i	0.518241	−	0.369038i
$545$	50.8682	+	32.6910i	2.17896	+	1.40033i
$546$	6.03438	−	0.174657i	0.258248	−	0.00747463i
$547$	23.7450	+	27.4032i	1.01526	+	1.17168i	0.985074	+	0.172132i	$0.0550656\pi$
$547$	23.7450	+	27.4032i	1.01526	+	1.17168i	0.0301893	+	0.999544i	$0.490389\pi$
$548$	−3.77259	−	3.95658i	−0.161157	−	0.169017i
$549$	−14.3589	+	29.4508i	−0.612825	+	1.25693i
$550$	34.7302	−	13.9039i	1.48090	−	0.592864i
$551$	−0.461012	+	0.798497i	−0.0196398	+	0.0340171i
$552$	−24.6248	+	6.14014i	−1.04810	+	0.261342i
$553$	18.2290	+	1.41452i	0.775177	+	0.0601516i
$554$	−4.34834	−	0.625197i	−0.184743	−	0.0265621i
$555$	31.9910	−	31.1934i	1.35794	−	1.32409i
$556$	−13.2530	+	3.21513i	−0.562051	+	0.136352i
$557$	−27.1535	−	9.39790i	−1.15053	−	0.398202i	−0.315780	−	0.948832i	$-0.602266\pi$
$557$	−27.1535	−	9.39790i	−1.15053	−	0.398202i	−0.834749	+	0.550631i	$0.814387\pi$
$558$	12.5688	+	0.917182i	0.532078	+	0.0388274i
$559$	3.43276	−	5.34148i	0.145190	−	0.225921i
$560$	9.32373	+	15.5066i	0.393999	+	0.655273i
$561$	14.1296	−	2.19301i	0.596554	−	0.0925889i
$562$	0.318261	+	6.68111i	0.0134250	+	0.281826i
$563$	−20.0496	+	15.7672i	−0.844992	+	0.664509i	−0.943771	−	0.330600i	$-0.892749\pi$
$563$	−20.0496	+	15.7672i	−0.844992	+	0.664509i	0.0987789	+	0.995109i	$0.468506\pi$
$564$	−0.0538568	+	1.47803i	−0.00226778	+	0.0622365i
$565$	−10.4977	+	0.500065i	−0.441640	+	0.0210379i
$566$	17.6555	−	20.3755i	0.742115	−	0.856447i
$567$	18.2256	+	15.3241i	0.765403	+	0.643551i
$568$	−36.9828	−	23.7674i	−1.55176	−	0.997258i
$569$	15.1923	+	3.68562i	0.636896	+	0.154509i	0.541190	−	0.840900i	$-0.317974\pi$
$569$	15.1923	+	3.68562i	0.636896	+	0.154509i	0.0957058	+	0.995410i	$0.469489\pi$
$570$	−2.08726	−	3.52369i	−0.0874259	−	0.147591i
$571$	−7.39555	−	30.4849i	−0.309494	−	1.27575i	−0.887913	−	0.460012i	$-0.847845\pi$
$571$	−7.39555	−	30.4849i	−0.309494	−	1.27575i	0.578418	−	0.815740i	$-0.303670\pi$
$572$	2.58297	+	0.246643i	0.107999	+	0.0103127i
$573$	15.4706	−	13.7111i	0.646293	−	0.572789i
$574$	2.49199	−	32.1144i	0.104014	−	1.34043i
$575$	−48.9035	−	47.0808i	−2.03942	−	1.96340i
$576$	−22.1256	−	8.28886i	−0.921902	−	0.345369i
$577$	5.00497	+	12.5018i	0.208359	+	0.520457i	0.995330	−	0.0965342i	$-0.0307757\pi$
$577$	5.00497	+	12.5018i	0.208359	+	0.520457i	−0.786970	+	0.616991i	$0.788351\pi$
$578$	5.07427	+	3.61337i	0.211062	+	0.150297i
$579$	−2.24122	−	38.0865i	−0.0931419	−	1.58282i
$580$	−5.16069	+	4.47176i	−0.214286	+	0.185680i
$581$	3.89588	+	4.33799i	0.161628	+	0.179970i
$582$	−21.8493	+	6.68172i	−0.905685	+	0.276966i
$583$	15.8319	+	22.2328i	0.655690	+	0.920787i
$584$	−25.0392	−	4.82591i	−1.03613	−	0.199697i
$585$	−15.3832	−	4.94198i	−0.636018	−	0.204326i
$586$	10.6459	−	26.5921i	0.439777	−	1.09851i
$587$	−2.68991	−	18.7087i	−0.111024	−	0.772192i	−0.966927	−	0.255054i	$-0.917907\pi$
$587$	−2.68991	−	18.7087i	−0.111024	−	0.772192i	0.855902	−	0.517138i	$-0.173002\pi$
$588$	10.0649	−	2.43205i	0.415067	−	0.100296i
$589$	−1.29690	+	1.49670i	−0.0534379	+	0.0616706i
$590$	25.0223	−	17.8183i	1.03015	−	0.733569i
$591$	7.48412	−	8.02688i	0.307856	−	0.330182i
$592$	−6.66584	−	6.35587i	−0.273964	−	0.261225i
$593$	2.30652	−	0.444545i	0.0947174	−	0.0182553i	−0.141672	−	0.989914i	$-0.545248\pi$
$593$	2.30652	−	0.444545i	0.0947174	−	0.0182553i	0.236390	+	0.971658i	$0.424036\pi$
$594$	−9.33622	−	10.0715i	−0.383070	−	0.413237i
$595$	−24.8320	+	29.7075i	−1.01801	+	1.21789i
$596$	−2.03693	−	0.292866i	−0.0834359	−	0.0119963i
$597$	−8.24312	+	2.95655i	−0.337368	+	0.121004i
$598$	2.03761	+	5.98024i	0.0833240	+	0.244550i
$599$	4.92402	−	2.84288i	0.201190	−	0.116157i	−0.396020	−	0.918242i	$-0.629609\pi$
$599$	4.92402	−	2.84288i	0.201190	−	0.116157i	0.597210	+	0.802085i	$0.296276\pi$
$600$	−14.9969	−	73.3874i	−0.612247	−	2.99603i
$601$	31.5048	−	14.3878i	1.28511	−	0.586890i	0.348514	−	0.937303i	$-0.386686\pi$
$601$	31.5048	−	14.3878i	1.28511	−	0.586890i	0.936595	+	0.350414i	$0.113959\pi$
$602$	−5.18953	+	13.6610i	−0.211509	+	0.556780i
$603$	17.1437	−	20.7025i	0.698147	−	0.843070i
$604$	0.753619	−	3.10646i	0.0306643	−	0.126400i
$605$	1.02137	−	21.4412i	0.0415246	−	0.871708i
$606$	2.45665	+	1.70832i	0.0997947	+	0.0693956i
$607$	−6.23389	+	2.15757i	−0.253026	+	0.0875730i	−0.450637	−	0.892707i	$-0.648803\pi$
$607$	−6.23389	+	2.15757i	−0.253026	+	0.0875730i	0.197611	+	0.980281i	$0.436682\pi$
$608$	1.88412	−	1.21085i	0.0764112	−	0.0491065i
$609$	−3.33513	−	7.67905i	−0.135146	−	0.311171i
$610$	7.28217	+	50.6486i	0.294846	+	2.05070i
$611$	1.22904	−	0.0585464i	0.0497216	−	0.00236853i
$612$	0.216245	−	8.56432i	0.00874118	−	0.346192i
$613$	−16.8325	+	1.60731i	−0.679859	+	0.0649187i	−0.429272	−	0.903175i	$-0.641230\pi$
$613$	−16.8325	+	1.60731i	−0.679859	+	0.0649187i	−0.250587	+	0.968094i	$0.580624\pi$
$614$	11.6360	−	5.99878i	0.469591	−	0.242091i
$615$	−34.9348	+	78.8162i	−1.40871	+	3.17817i
$616$	−19.8298	+	2.24950i	−0.798966	+	0.0906350i
$617$	11.0678	−	37.6935i	0.445573	−	1.51748i	−0.364529	−	0.931192i	$-0.618770\pi$
$617$	11.0678	−	37.6935i	0.445573	−	1.51748i	0.810101	−	0.586290i	$-0.199412\pi$
$618$	1.10538	−	1.07783i	0.0444651	−	0.0433565i
$619$	−9.04741	−	22.5993i	−0.363646	−	0.908344i	−0.991511	−	0.130022i	$-0.958495\pi$
$619$	−9.04741	−	22.5993i	−0.363646	−	0.908344i	0.627865	−	0.778322i	$-0.283929\pi$
$620$	−12.7021	+	7.33357i	−0.510129	+	0.294523i
$621$	−9.69686	+	22.9558i	−0.389121	+	0.921186i
$622$			30.1823i			1.21020i
$623$	3.31206	−	14.7943i	0.132695	−	0.592722i
$624$	−0.902558	+	3.20597i	−0.0361313	+	0.128342i
$625$	75.6889	−	72.1692i	3.02756	−	2.88677i
$626$	3.85752	−	11.1456i	0.154178	−	0.445467i
$627$	2.14596	−	0.229147i	0.0857012	−	0.00915124i
$628$	0.623561	+	1.20954i	0.0248828	+	0.0482659i
$629$	8.18753	−	17.9282i	0.326458	−	0.714844i
$630$	36.9914	+	3.81192i	1.47377	+	0.151870i
$631$	−29.6036	+	19.0251i	−1.17850	+	0.757377i	−0.975110	−	0.221721i	$-0.928833\pi$
$631$	−29.6036	+	19.0251i	−1.17850	+	0.757377i	−0.203391	+	0.979098i	$0.565196\pi$
$632$	−7.84716	+	19.6012i	−0.312143	+	0.779696i
$633$	0.246335	−	6.76036i	0.00979094	−	0.268700i
$634$	−23.1168	−	11.9175i	−0.918085	−	0.473306i
$635$	12.3030	+	35.5473i	0.488231	+	1.41065i
$636$	14.7982	−	6.95905i	0.586787	−	0.275944i
$637$	−2.71886	−	8.17389i	−0.107725	−	0.323861i
$638$	1.36034	+	4.63289i	0.0538563	+	0.183418i
$639$	−40.4668	+	15.0268i	−1.60084	+	0.594451i
$640$	1.89029	−	0.458579i	0.0747202	−	0.0181269i
$641$	16.0644	+	11.4394i	0.634507	+	0.451830i	0.851508	−	0.524341i	$-0.175688\pi$
$641$	16.0644	+	11.4394i	0.634507	+	0.451830i	−0.217001	+	0.976171i	$0.569628\pi$
$642$	9.60619	−	1.96305i	0.379126	−	0.0774754i
$643$			4.49062i			0.177093i	0.996072	+	0.0885463i	$0.0282221\pi$
$643$			4.49062i			0.177093i	−0.996072	+	0.0885463i	$0.971778\pi$
$644$	5.53922	+	9.31366i	0.218276	+	0.367009i
$645$	25.2812	−	29.8437i	0.995447	−	1.17509i
$646$	−1.42003	−	1.11673i	−0.0558705	−	0.0439371i
$647$	−1.61382	+	2.26629i	−0.0634458	+	0.0890971i	−0.845080	−	0.534640i	$-0.820447\pi$
$647$	−1.61382	+	2.26629i	−0.0634458	+	0.0890971i	0.781634	+	0.623737i	$0.214387\pi$
$648$	−23.1749	+	14.7992i	−0.910397	+	0.581368i
$649$	3.06346	+	15.8947i	0.120251	+	0.623922i
$650$	−17.8915	+	5.25341i	−0.701761	+	0.206056i
$651$	−3.91261	−	17.5515i	−0.153347	−	0.687899i
$652$	−1.88154	+	4.12000i	−0.0736869	+	0.161352i
$653$	10.3469	−	3.58108i	0.404904	−	0.140139i	−0.117022	−	0.993129i	$-0.537335\pi$
$653$	10.3469	−	3.58108i	0.404904	−	0.140139i	0.521926	+	0.852991i	$0.325214\pi$
$654$	−9.78616	−	23.6742i	−0.382669	−	0.925735i
$655$	−5.19516	+	4.08552i	−0.202992	+	0.159635i
$656$	16.4980	+	6.60481i	0.644139	+	0.257874i
$657$	−18.5519	+	16.8159i	−0.723779	+	0.656052i
$658$	−2.73978	+	0.716407i	−0.106808	+	0.0279285i
$659$	4.22091	+	1.92763i	0.164423	+	0.0750897i	0.495927	−	0.868364i	$-0.334828\pi$
$659$	4.22091	+	1.92763i	0.164423	+	0.0750897i	−0.331503	+	0.943454i	$0.607556\pi$
$660$	15.5740	+	3.59438i	0.606219	+	0.139911i
$661$	−24.4781	+	25.6719i	−0.952089	+	0.998522i	−1.00000		0.000329321i	$-0.999895\pi$
$661$	−24.4781	+	25.6719i	−0.952089	+	0.998522i	0.0479109	+	0.998852i	$0.484744\pi$
$662$	−25.0257	−	8.66148i	−0.972652	−	0.336638i
$663$	−7.11485	+	0.418677i	−0.276318	+	0.0162601i
$664$	−6.12458	+	2.79700i	−0.237680	+	0.108545i
$665$	−3.95706	+	4.30042i	−0.153448	+	0.166763i
$666$	−18.6720	+	3.11213i	−0.723525	+	0.120592i
$667$	6.64914	−	5.70572i	0.257456	−	0.220926i
$668$	−1.40033	−	2.42545i	−0.0541805	−	0.0938434i
$669$	25.2671	+	8.42997i	0.976883	+	0.325922i
$670$	3.99027	−	41.7880i	0.154158	−	1.61441i
$671$	−25.8719	−	7.59669i	−0.998775	−	0.293267i
$672$	−1.34658	+	20.2916i	−0.0519454	+	0.782765i
$673$	−32.2006	+	9.45494i	−1.24124	+	0.364461i	−0.835481	−	0.549519i	$-0.814811\pi$
$673$	−32.2006	+	9.45494i	−1.24124	+	0.364461i	−0.405759	+	0.913980i	$0.632993\pi$
$674$	12.1862	+	23.6380i	0.469396	+	0.910501i
$675$	−66.4668	−	31.4917i	−2.55831	−	1.21212i
$676$	9.63176	+	1.85637i	0.370452	+	0.0713988i
$677$	−0.656058	−	13.7723i	−0.0252143	−	0.529314i	−0.975775	−	0.218776i	$-0.929794\pi$
$677$	−0.656058	−	13.7723i	−0.0252143	−	0.529314i	0.950561	−	0.310538i	$-0.100509\pi$
$678$	3.77228	+	2.36514i	0.144874	+	0.0908326i
$679$	18.1106	+	27.1098i	0.695019	+	1.04038i
$680$	−24.1730	−	37.6139i	−0.926991	−	1.44243i
$681$	27.0922	+	10.4963i	1.03818	+	0.402218i
$682$	0.985837	+	10.3241i	0.0377496	+	0.395332i
$683$	0.582807	+	0.0277625i	0.0223005	+	0.00106230i	0.0587292	−	0.998274i	$-0.481295\pi$
$683$	0.582807	+	0.0277625i	0.0223005	+	0.00106230i	−0.0364287	+	0.999336i	$0.511598\pi$
$684$	0.0941074	−	1.28962i	0.00359828	−	0.0493097i
$685$	−21.1731	+	18.3466i	−0.808983	+	0.700988i
$686$	10.0102	+	17.1133i	0.382192	+	0.653388i
$687$	7.48938	−	26.6030i	0.285738	−	1.01497i
$688$	−6.33743	−	4.98381i	−0.241612	−	0.190006i
$689$	−6.80218	−	11.7817i	−0.259143	−	0.448848i
$690$	7.60836	+	38.1669i	0.289645	+	1.45299i
$691$	17.8038	+	10.2790i	0.677287	+	0.391032i	0.798832	−	0.601554i	$-0.205452\pi$
$691$	17.8038	+	10.2790i	0.677287	+	0.391032i	−0.121545	+	0.992586i	$0.538785\pi$
$692$	−2.77097	+	19.2725i	−0.105337	+	0.732632i
$693$	−9.92486	+	16.8970i	−0.377014	+	0.641862i
$694$	26.1002	+	7.66372i	0.990751	+	0.290911i
$695$	13.2262	+	68.6241i	0.501699	+	2.60306i
$696$	9.61314	−	1.02650i	0.364385	−	0.0389093i
$697$	−1.80946	+	37.9852i	−0.0685380	+	1.43879i
$698$	−13.4588	−	18.9003i	−0.509424	−	0.715386i
$699$	−18.7071	+	2.90346i	−0.707568	+	0.109819i
$700$	−28.1629	+	15.1579i	−1.06446	+	0.572917i
$701$	14.5838	−	2.09683i	0.550821	−	0.0791962i	0.138716	−	0.990332i	$-0.455703\pi$
$701$	14.5838	−	2.09683i	0.550821	−	0.0791962i	0.412106	+	0.911136i	$0.364793\pi$
$702$	4.15532	+	5.43968i	0.156833	+	0.205308i
$703$	1.36312	−	2.64408i	0.0514110	−	0.0997234i
$704$	3.67987	−	19.0930i	0.138690	−	0.719594i
$705$	7.55273	+	0.636092i	0.284452	+	0.0239566i
$706$	−0.0778832	+	0.121189i	−0.00293117	+	0.00456099i
$707$	1.32462	−	4.05903i	0.0498173	−	0.152655i
$708$	9.69788	−	0.108406i	0.364469	−	0.00407415i
$709$	15.3630	−	14.6486i	0.576969	−	0.550138i	−0.344403	−	0.938822i	$-0.611919\pi$
$709$	15.3630	−	14.6486i	0.576969	−	0.550138i	0.921371	+	0.388684i	$0.127070\pi$
$710$	−39.1041	+	54.9141i	−1.46755	+	2.06089i
$711$	10.7647	+	17.7182i	0.403709	+	0.664483i
$712$	15.1615	+	8.75348i	0.568201	+	0.328051i
$713$	16.3430	−	9.33106i	0.612050	−	0.349451i
$714$	15.8225	−	4.32684i	0.592143	−	0.161928i
$715$	1.89237	−	13.1617i	0.0707706	−	0.492220i
$716$	−0.142520	+	1.49253i	−0.00532621	+	0.0557786i
$717$	−8.16771	+	16.2876i	−0.305029	+	0.608272i
$718$	−1.53778	+	4.44313i	−0.0573895	+	0.165816i
$719$	−10.2360	+	42.1934i	−0.381739	+	1.57355i	0.379572	+	0.925162i	$0.376071\pi$
$719$	−10.2360	+	42.1934i	−0.381739	+	1.57355i	−0.761311	+	0.648387i	$0.775444\pi$
$720$	−8.10354	+	18.8483i	−0.302001	+	0.702434i
$721$	−1.92712	−	1.06745i	−0.0717697	−	0.0397541i
$722$	15.1655	+	13.1410i	0.564402	+	0.489057i
$723$	−4.74593	+	6.17578i	−0.176503	+	0.229680i
$724$	−3.47305	−	4.41634i	−0.129075	−	0.164132i
$725$	15.9853	+	20.3270i	0.593679	+	0.754925i
$726$	−5.54124	+	7.21070i	−0.205655	+	0.267614i
$727$	−14.6617	−	12.7045i	−0.543773	−	0.471182i	0.339129	−	0.940740i	$-0.389868\pi$
$727$	−14.6617	−	12.7045i	−0.543773	−	0.471182i	−0.882902	+	0.469558i	$0.844413\pi$
$728$	9.94588	−	0.176635i	0.368619	−	0.00654651i
$729$	−2.04282	+	26.9226i	−0.0756601	+	0.997134i
$730$	−9.21908	+	38.0016i	−0.341213	+	1.40650i
$731$	5.64279	−	16.3038i	0.208706	−	0.603017i
$732$	−7.24187	+	14.4414i	−0.267667	+	0.533768i
$733$	−0.0204923	+	0.214605i	−0.000756901	+	0.00792662i	−0.995842	−	0.0910920i	$-0.970964\pi$
$733$	−0.0204923	+	0.214605i	−0.000756901	+	0.00792662i	0.995086	+	0.0990186i	$0.0315703\pi$
$734$	−2.99806	+	20.8520i	−0.110660	+	0.769660i
$735$	−9.99509	−	52.1137i	−0.368674	−	1.92224i
$736$	−20.7066	+	4.91797i	−0.763255	+	0.181279i
$737$	19.1571	+	11.0603i	0.705660	+	0.407413i
$738$	31.2144	−	18.9644i	1.14902	−	0.698089i
$739$	11.4720	−	16.1101i	0.422003	−	0.592620i	−0.547770	−	0.836629i	$-0.684523\pi$
$739$	11.4720	−	16.1101i	0.422003	−	0.592620i	0.969773	+	0.244009i	$0.0784627\pi$
$740$	15.9448	−	15.2034i	0.586143	−	0.558886i
$741$	−1.07565	+	0.0120240i	−0.0395151	+	0.000441713i
$742$	20.9213	+	23.2955i	0.768046	+	0.855204i
$743$	10.8810	−	16.9312i	0.399185	−	0.621144i	−0.582234	−	0.813021i	$-0.697821\pi$
$743$	10.8810	−	16.9312i	0.399185	−	0.621144i	0.981419	+	0.191878i	$0.0614576\pi$
$744$	20.6923	+	1.74271i	0.758615	+	0.0638907i
$745$	−1.99583	+	10.3554i	−0.0731216	+	0.379391i
$746$	4.91197	−	9.52790i	0.179840	−	0.348841i
$747$	−1.41466	+	6.45817i	−0.0517597	+	0.236292i
$748$	6.97859	−	1.00337i	0.255163	−	0.0366868i
$749$	−6.63066	−	12.3195i	−0.242279	−	0.450146i
$750$	−73.4106	+	11.3938i	−2.68057	+	0.416041i
$751$	−4.49029	−	6.30573i	−0.163853	−	0.230099i	0.724484	−	0.689292i	$-0.242078\pi$
$751$	−4.49029	−	6.30573i	−0.163853	−	0.230099i	−0.888337	+	0.459193i	$0.848139\pi$
$752$	0.0743407	−	1.56060i	0.00271093	−	0.0569094i
$753$	10.0842	−	1.07679i	0.367487	−	0.0392405i
$754$	−0.455475	−	2.36323i	−0.0165874	−	0.0860638i
$755$	−15.7178	−	4.61516i	−0.572029	−	0.167963i
$756$	8.90152	+	7.65586i	0.323745	+	0.278441i
$757$	−1.15190	+	8.01161i	−0.0418663	+	0.291187i	0.958122	+	0.286360i	$0.0924454\pi$
$757$	−1.15190	+	8.01161i	−0.0418663	+	0.291187i	−0.999988	+	0.00482654i	$0.998464\pi$
$758$	−25.5193	−	14.7336i	−0.926904	−	0.535149i
$759$	−19.9604	−	4.70801i	−0.724516	−	0.170890i
$760$	−3.37422	−	5.84432i	−0.122396	−	0.211996i
$761$	−16.5795	−	13.0383i	−0.601008	−	0.472638i	0.270700	−	0.962664i	$-0.412745\pi$
$761$	−16.5795	−	13.0383i	−0.601008	−	0.472638i	−0.871708	+	0.490026i	$0.836987\pi$
$762$	4.31855	−	15.3399i	0.156445	−	0.555706i
$763$	−28.3274	+	23.1027i	−1.02552	+	0.836372i
$764$	7.70321	−	6.67487i	0.278692	−	0.241488i
$765$	−43.7869	−	3.19527i	−1.58312	−	0.115525i
$766$	28.4602	+	1.35573i	1.02831	+	0.0489844i
$767$	−0.766953	−	8.03190i	−0.0276931	−	0.290015i
$768$	−26.2083	−	10.1538i	−0.945711	−	0.366395i
$769$	14.3878	+	22.3878i	0.518837	+	0.807326i	0.997500	−	0.0706732i	$-0.0225147\pi$
$769$	14.3878	+	22.3878i	0.518837	+	0.807326i	−0.478663	+	0.877999i	$0.658878\pi$
$770$	1.99876	+	30.5384i	0.0720304	+	1.10053i
$771$	−30.0435	−	18.8366i	−1.08199	−	0.678385i
$772$	−0.895105	−	18.7906i	−0.0322155	−	0.676287i
$773$	−34.4614	−	6.64188i	−1.23949	−	0.238892i	−0.472950	−	0.881089i	$-0.656811\pi$
$773$	−34.4614	−	6.64188i	−1.23949	−	0.238892i	−0.766539	+	0.642198i	$0.778023\pi$
$774$	−16.0117	+	4.26555i	−0.575528	+	0.153322i
$775$	25.4517	+	49.3694i	0.914252	+	1.77340i
$776$	−36.1236	+	10.6068i	−1.29676	+	0.380763i
$777$	11.9270	+	24.2352i	0.427877	+	0.869433i
$778$	2.78135	+	0.816677i	0.0997161	+	0.0292793i
$779$	−0.545593	+	5.71370i	−0.0195479	+	0.204715i
$780$	−7.55733	−	2.52138i	−0.270596	−	0.0902801i
$781$	−17.7623	−	30.7652i	−0.635584	−	1.10086i
$782$	9.21148	+	14.4861i	0.329402	+	0.518023i
$783$	4.86167	−	8.15360i	0.173742	−	0.291386i
$784$	−10.6602	+	2.45011i	−0.380720	+	0.0875041i
$785$	6.34352	−	2.89699i	0.226410	−	0.103398i
$786$	2.79516	−	0.164483i	0.0997002	−	0.00586691i
$787$	39.8274	+	13.7844i	1.41969	+	0.491360i	0.925751	−	0.378134i	$-0.123434\pi$
$787$	39.8274	+	13.7844i	1.41969	+	0.491360i	0.493942	+	0.869495i	$0.335555\pi$
$788$	3.73422	−	3.91634i	0.133026	−	0.139514i
$789$	−24.2823	−	5.60419i	−0.864473	−	0.199515i
$790$	29.4516	+	13.4501i	1.04784	+	0.478532i
$791$	1.68139	−	6.12673i	0.0597835	−	0.217841i
$792$	−15.1975	−	16.7664i	−0.540020	−	0.595768i
$793$	12.4774	+	4.99519i	0.443085	+	0.177384i
$794$	25.7977	−	20.2876i	0.915527	−	0.719979i
$795$	−32.0140	−	77.4469i	−1.13542	−	2.74676i
$796$	−4.08049	+	1.41227i	−0.144629	+	0.0500567i
$797$	−10.4785	+	22.9447i	−0.371168	+	0.812744i	0.628229	+	0.778028i	$0.283780\pi$
$797$	−10.4785	+	22.9447i	−0.371168	+	0.812744i	−0.999397	+	0.0347159i	$0.988947\pi$
$798$	2.41650	−	0.538690i	0.0855432	−	0.0190694i
$799$	3.20790	−	0.941925i	0.113487	−	0.0333229i
$800$	−11.8877	−	61.6794i	−0.420295	−	2.18070i
$801$	15.8122	−	6.74419i	0.558698	−	0.238294i
$802$	−10.0298	+	14.0849i	−0.354166	+	0.497356i
$803$	−16.1975	−	12.7378i	−0.571597	−	0.449509i
$804$	8.56668	−	10.1127i	0.302124	−	0.356647i
$805$	49.0260	−	26.0835i	1.72794	−	0.919321i
$806$		−	5.16942i		−	0.182085i
$807$	26.6040	−	5.43661i	0.936506	−	0.191378i
$808$	4.01629	+	2.85999i	0.141293	+	0.100614i
$809$	8.51588	−	2.06593i	0.299403	−	0.0726343i	−0.0832437	−	0.996529i	$-0.526528\pi$
$809$	8.51588	−	2.06593i	0.299403	−	0.0726343i	0.382646	+	0.923895i	$0.375013\pi$
$810$	20.9777	+	36.5780i	0.737080	+	1.28522i
$811$	2.74811	+	9.35920i	0.0964992	+	0.328646i	0.993567	−	0.113247i	$-0.0361252\pi$
$811$	2.74811	+	9.35920i	0.0964992	+	0.328646i	−0.897068	+	0.441893i	$0.854307\pi$
$812$	−1.60204	−	3.80447i	−0.0562205	−	0.133511i
$813$	23.4158	−	11.0116i	0.821228	−	0.386194i
$814$	−5.09517	−	14.7215i	−0.178585	−	0.515989i
$815$	20.6309	+	10.6360i	0.722671	+	0.372563i
$816$	−0.329542	+	9.04389i	−0.0115363	+	0.316599i
$817$	0.967804	−	2.41746i	0.0338592	−	0.0845761i
$818$	−2.44147	+	1.56904i	−0.0853639	+	0.0548601i
$819$	5.72517	−	7.91381i	0.200054	−	0.276531i
$820$	−17.6587	+	38.6671i	−0.616668	+	1.35031i
$821$	23.9577	+	46.4714i	0.836129	+	1.62186i	0.781956	+	0.623333i	$0.214222\pi$
$821$	23.9577	+	46.4714i	0.836129	+	1.62186i	0.0541729	+	0.998532i	$0.482748\pi$
$822$	11.8020	−	1.26023i	0.411642	−	0.0439554i
$823$	8.08315	−	23.3547i	0.281761	−	0.814095i	−0.711961	−	0.702219i	$-0.752193\pi$
$823$	8.08315	−	23.3547i	0.281761	−	0.814095i	0.993722	−	0.111876i	$-0.0356860\pi$
$824$	1.84116	−	1.75554i	0.0641399	−	0.0611572i
$825$	16.4027	−	58.2638i	0.571068	−	2.02849i
$826$	5.54729	+	17.7219i	0.193015	+	0.616625i
$827$			54.8718i			1.90808i	0.299679	+	0.954040i	$0.403120\pi$
$827$			54.8718i			1.90808i	−0.299679	+	0.954040i	$0.596880\pi$
$828$	−4.90747	+	11.2647i	−0.170546	+	0.391477i
$829$	−2.38067	+	1.37448i	−0.0826841	+	0.0477377i	−0.540772	−	0.841169i	$-0.681868\pi$
$829$	−2.38067	+	1.37448i	−0.0826841	+	0.0477377i	0.458088	+	0.888907i	$0.348534\pi$
$830$	3.83741	+	9.58539i	0.133199	+	0.332714i
$831$	−5.08907	+	4.96219i	−0.176538	+	0.172137i
$832$	−2.73053	+	9.29934i	−0.0946642	+	0.322397i
$833$	−12.4156	−	19.8423i	−0.430177	−	0.687495i
$834$	11.9978	−	27.0681i	0.415448	−	0.937291i
$835$	−12.7570	+	6.57669i	−0.441474	+	0.227596i
$836$	1.05931	−	0.101152i	0.0366370	−	0.00349840i
$837$	13.5681	−	15.2205i	0.468982	−	0.526096i
$838$	−2.37777	+	0.113267i	−0.0821389	+	0.00391276i
$839$	−1.59913	−	11.1222i	−0.0552080	−	0.383980i	−0.998627	−	0.0523780i	$-0.983320\pi$
$839$	−1.59913	−	11.1222i	−0.0552080	−	0.383980i	0.943419	−	0.331602i	$-0.107589\pi$
$840$	60.8795	+	6.96210i	2.10054	+	0.240215i
$841$	21.5885	−	13.8741i	0.744432	−	0.478417i
$842$	21.7450	−	7.52600i	0.749381	−	0.259363i
$843$	8.88509	+	6.17855i	0.306019	+	0.212800i
$844$	0.158712	−	3.33178i	0.00546311	−	0.114685i
$845$	11.8511	−	48.8510i	0.407691	−	1.68053i
$846$	−2.47316	−	2.04803i	−0.0850291	−	0.0704127i
$847$	12.1306	+	4.60815i	0.416812	+	0.158338i
$848$	−15.7134	+	7.17608i	−0.539601	+	0.246428i
$849$	−8.73375	−	42.7386i	−0.299742	−	1.46678i
$850$	−43.8789	+	25.3335i	−1.50503	+	0.868932i
$851$	−20.5522	+	19.4085i	−0.704520	+	0.665315i
$852$	−20.0346	+	7.18580i	−0.686375	+	0.246182i
$853$	15.2645	+	2.19470i	0.522645	+	0.0751450i	0.398588	−	0.917130i	$-0.369500\pi$
$853$	15.2645	+	2.19470i	0.522645	+	0.0751450i	0.124057	+	0.992275i	$0.460409\pi$
$854$	−30.4732	−	5.31385i	−1.04277	−	0.181836i
$855$	−6.57842	−	0.796185i	−0.224977	−	0.0272290i
$856$	15.8640	−	3.05753i	0.542220	−	0.104504i
$857$	0.242665	+	0.231380i	0.00828927	+	0.00790381i	0.694212	−	0.719770i	$-0.255753\pi$
$857$	0.242665	+	0.231380i	0.00828927	+	0.00790381i	−0.685923	+	0.727674i	$0.740601\pi$
$858$	−3.84164	+	4.12024i	−0.131151	+	0.140663i
$859$	−34.8875	+	24.8432i	−1.19034	+	0.847640i	−0.991206	−	0.132331i	$-0.957754\pi$
$859$	−34.8875	+	24.8432i	−1.19034	+	0.847640i	−0.199139	+	0.979971i	$0.563814\pi$
$860$	12.6292	−	14.5748i	0.430651	−	0.496998i
$861$	−38.7434	−	34.8583i	−1.32037	−	1.18797i
$862$	2.47163	+	17.1906i	0.0841841	+	0.585513i
$863$	0.903820	−	2.25763i	0.0307664	−	0.0768507i	−0.912189	−	0.409769i	$-0.865609\pi$
$863$	0.903820	−	2.25763i	0.0307664	−	0.0768507i	0.942956	+	0.332919i	$0.108033\pi$
$864$	−19.5720	+	12.1926i	−0.665853	+	0.414801i
$865$	97.9778	+	18.8837i	3.33135	+	0.642064i
$866$	2.62418	+	3.68515i	0.0891734	+	0.125227i
$867$	9.63834	−	2.94749i	0.327335	−	0.100102i
$868$	−1.83235	−	8.67520i	−0.0621940	−	0.294456i
$869$	−12.8943	+	11.1730i	−0.437409	+	0.379017i
$870$	−0.870903	−	14.7998i	−0.0295264	−	0.501760i
$871$	−8.98146	−	6.39567i	−0.304325	−	0.216709i
$872$	−15.6883	−	39.1875i	−0.531274	−	1.32706i
$873$	−12.9690	+	34.6184i	−0.438933	+	1.17165i
$874$	1.28470	+	2.25011i	0.0434557	+	0.0761110i
$875$	45.7416	+	95.6289i	1.54635	+	3.23285i
$876$	−9.23954	+	8.18871i	−0.312175	+	0.276671i
$877$	−15.9197	−	1.52015i	−0.537571	−	0.0513318i	−0.177260	−	0.984164i	$-0.556723\pi$
$877$	−15.9197	−	1.52015i	−0.537571	−	0.0513318i	−0.360311	+	0.932832i	$0.617329\pi$
$878$	−7.55615	−	31.1469i	−0.255008	−	1.05116i
$879$	−23.6199	−	39.8747i	−0.796678	−	1.34494i
$880$	−16.4083	−	3.98062i	−0.553124	−	0.134187i
$881$	23.7269	+	15.2484i	0.799381	+	0.513731i	0.875414	−	0.483374i	$-0.160589\pi$
$881$	23.7269	+	15.2484i	0.799381	+	0.513731i	−0.0760329	+	0.997105i	$0.524225\pi$
$882$	−9.12822	+	20.5439i	−0.307363	+	0.691747i
$883$	1.67043	−	1.92778i	0.0562146	−	0.0648751i	−0.726946	−	0.686695i	$-0.759061\pi$
$883$	1.67043	−	1.92778i	0.0562146	−	0.0648751i	0.783160	+	0.621820i	$0.213606\pi$
$884$	−3.51023	+	0.167213i	−0.118062	+	0.00562397i
$885$	1.80983	−	49.6686i	0.0608368	−	1.66959i
$886$	−4.35310	+	3.42331i	−0.146245	+	0.115008i
$887$	1.98225	+	41.6126i	0.0665576	+	1.39722i	0.747200	+	0.664599i	$0.231398\pi$
$887$	1.98225	+	41.6126i	0.0665576	+	1.39722i	−0.680642	+	0.732616i	$0.738299\pi$
$888$	−30.8226	+	4.78385i	−1.03434	+	0.160536i
$889$	−22.7362	+	0.403785i	−0.762547	+	0.0135425i
$890$	14.5144	−	22.5848i	0.486524	−	0.757046i
$891$	−22.1254	+	2.04824i	−0.741228	+	0.0686188i
$892$	12.4113	+	4.29558i	0.415560	+	0.143827i
$893$	0.490393	−	0.118968i	0.0164104	−	0.00398111i
$894$	3.19885	−	3.11910i	0.106986	−	0.104318i
$895$	7.60532	+	1.09348i	0.254218	+	0.0365510i
$896$	−0.0909705	+	1.17234i	−0.00303911	+	0.0391652i
$897$	9.68102	+	3.28178i	0.323240	+	0.109575i
$898$	16.0569	−	27.8113i	0.535825	−	0.928076i
$899$	−6.65547	+	2.66445i	−0.221972	+	0.0888643i
$900$	−32.5974	−	15.8930i	−1.08658	−	0.529768i
$901$	−25.5093	−	26.7534i	−0.849838	−	0.891284i
$902$	19.6836	+	22.7161i	0.655392	+	0.756363i
$903$	12.4096	+	20.1260i	0.412967	+	0.669751i
$904$	6.17191	+	3.96645i	0.205275	+	0.131922i
$905$	−23.4535	+	16.7012i	−0.779622	+	0.555166i
$906$	4.35074	+	5.40692i	0.144544	+	0.179633i
$907$	20.8682	+	10.7583i	0.692918	+	0.357224i	0.768442	−	0.639920i	$-0.221032\pi$
$907$	20.8682	+	10.7583i	0.692918	+	0.357224i	−0.0755234	+	0.997144i	$0.524063\pi$
$908$	13.2997	+	5.32441i	0.441368	+	0.176697i
$909$	4.61362	−	1.46747i	0.153024	−	0.0486730i
$910$	0.455153	−	15.2475i	0.0150882	−	0.505448i
$911$	41.2642	+	35.7557i	1.36715	+	1.18464i	0.962859	+	0.270006i	$0.0870256\pi$
$911$	41.2642	+	35.7557i	1.36715	+	1.18464i	0.404286	+	0.914632i	$0.367520\pi$
$912$	−0.114632	+	1.36110i	−0.00379586	+	0.0450706i
$913$	−5.43468	−	0.258886i	−0.179862	−	0.00856787i
$914$	27.1823	−	28.5080i	0.899111	−	0.942960i
$915$	72.1575	+	40.5916i	2.38545	+	1.34192i
$916$	3.83920	−	13.0751i	0.126851	−	0.432014i
$917$	−1.37360	−	3.75185i	−0.0453603	−	0.123897i
$918$	14.4572	+	11.7021i	0.477160	+	0.386228i
$919$	−1.35508	+	2.34707i	−0.0447000	+	0.0774227i	−0.887510	−	0.460789i	$-0.847567\pi$
$919$	−1.35508	+	2.34707i	−0.0447000	+	0.0774227i	0.842810	+	0.538212i	$0.180900\pi$
$920$	11.8331	+	63.0266i	0.390126	+	2.07793i
$921$	3.77589	−	20.8422i	0.124420	−	0.686774i
$922$	−2.28946	+	2.91128i	−0.0753993	+	0.0958780i
$923$	7.35575	+	16.1069i	0.242118	+	0.530163i
$924$	−4.98649	+	8.27620i	−0.164044	+	0.272267i
$925$	−54.6362	−	63.0535i	−1.79643	−	2.07319i
$926$	1.21859	+	0.295626i	0.0400453	+	0.00971489i
$927$	−0.292975	−	2.48074i	−0.00962257	−	0.0814781i
$928$	8.07070	−	0.770658i	0.264934	−	0.0252981i
$929$	−11.2755	−	32.5783i	−0.369936	−	1.06886i	−0.964334	−	0.264688i	$-0.914731\pi$
$929$	−11.2755	−	32.5783i	−0.369936	−	1.06886i	0.594398	−	0.804171i	$-0.297390\pi$
$930$	4.17922	−	31.5682i	0.137042	−	1.03516i
$931$	−1.72930	−	3.08062i	−0.0566755	−	0.100963i
$932$	−9.23939	+	1.32842i	−0.302646	+	0.0435140i
$933$	38.7215	+	29.7565i	1.26768	+	0.974183i
$934$	2.83342	−	14.7012i	0.0927124	−	0.481038i
$935$	−3.43444	−	35.9671i	−0.112318	−	1.17625i
$936$	6.74641	+	9.03933i	0.220513	+	0.295460i
$937$	−6.13164	−	20.8824i	−0.200312	−	0.682199i	−0.996971	−	0.0777710i	$-0.975220\pi$
$937$	−6.13164	−	20.8824i	−0.200312	−	0.682199i	0.796659	−	0.604428i	$-0.206598\pi$
$938$	23.2670	+	10.1303i	0.759693	+	0.330766i
$939$	−10.4958	−	15.9372i	−0.342517	−	0.520091i
$940$	3.72030	+	0.355246i	0.121343	+	0.0115868i
$941$	−17.9222	+	7.17496i	−0.584246	+	0.233897i	−0.644906	−	0.764262i	$-0.723104\pi$
$941$	−17.9222	+	7.17496i	−0.584246	+	0.233897i	0.0606601	+	0.998158i	$0.480679\pi$
$942$	−2.90712	−	0.526670i	−0.0947191	−	0.0171598i
$943$	22.8961	−	49.5036i	0.745599	−	1.61206i
$944$	−10.2451			−0.333449
$945$	41.3599	−	43.6989i	1.34544	−	1.42152i
$946$	−5.66484	−	12.4043i	−0.184180	−	0.403298i
$947$	−15.6437	−	16.4067i	−0.508353	−	0.533146i	0.418675	−	0.908136i	$-0.362495\pi$
$947$	−15.6437	−	16.4067i	−0.508353	−	0.533146i	−0.927029	+	0.374990i	$0.877646\pi$
$948$	5.20980	+	8.79512i	0.169207	+	0.285652i
$949$	7.43346	+	7.08779i	0.241300	+	0.230079i
$950$	−6.79719	+	3.50419i	−0.220530	+	0.113691i
$951$	−38.0798	+	17.9076i	−1.23482	+	0.580693i
$952$	26.1500	−	6.83779i	0.847526	−	0.221614i
$953$	−23.4817	−	36.5382i	−0.760646	−	1.18359i	−0.978225	−	0.207545i	$-0.933453\pi$
$953$	−23.4817	−	36.5382i	−0.760646	−	1.18359i	0.217580	−	0.976043i	$-0.430184\pi$
$954$	−7.59688	+	34.6811i	−0.245958	+	1.12284i
$955$	−32.2894	−	41.0593i	−1.04486	−	1.32865i
$956$	−4.11679	+	7.98545i	−0.133146	+	0.258268i
$957$	7.28476	+	2.82232i	0.235483	+	0.0912325i
$958$	−7.73367	−	3.53185i	−0.249864	−	0.114109i
$959$	−6.57278	−	15.6089i	−0.212246	−	0.504036i
$960$	−24.1926	+	54.5809i	−0.780814	+	1.76159i
$961$	15.3197	−	2.95263i	0.494184	−	0.0952462i
$962$	1.83065	+	7.54603i	0.0590225	+	0.243294i
$963$	6.95222	−	14.2593i	0.224032	−	0.459500i
$964$	−2.37398	+	3.01876i	−0.0764608	+	0.0972278i
$965$	−96.4047			−3.10338
$966$	−23.3612	−	2.78551i	−0.751635	−	0.0896224i
$967$	29.6986			0.955041			0.477521	−	0.878621i	$-0.341536\pi$
$967$	29.6986			0.955041			0.477521	+	0.878621i	$0.341536\pi$
$968$	−9.26295	+	11.7788i	−0.297723	+	0.378585i
$969$	−2.83267	+	0.720818i	−0.0909985	+	0.0231560i
$970$	13.6112	+	56.1061i	0.437029	+	1.80146i
$971$	52.3084	−	10.0816i	1.67866	−	0.323535i	0.741108	−	0.671386i	$-0.234301\pi$
$971$	52.3084	−	10.0816i	1.67866	−	0.323535i	0.937550	+	0.347852i	$0.113089\pi$
$972$	−1.15558	+	13.2627i	−0.0370651	+	0.425402i
$973$	−41.9184	−	5.26905i	−1.34384	−	0.168918i
$974$	29.9494	+	13.6775i	0.959642	+	0.438254i
$975$	−10.8993	+	28.1326i	−0.349058	+	0.900964i
$976$	7.82006	−	15.1688i	0.250314	−	0.485542i
$977$	−1.98794	−	2.52788i	−0.0635999	−	0.0808739i	0.753212	−	0.657777i	$-0.228503\pi$
$977$	−1.98794	−	2.52788i	−0.0635999	−	0.0808739i	−0.816812	+	0.576904i	$0.804261\pi$
$978$	−4.60339	−	8.68946i	−0.147200	−	0.277858i
$979$	7.64849	+	11.9013i	0.244447	+	0.380366i
$980$	−4.64078	−	25.7493i	−0.148244	−	0.822531i
$981$	−40.0202	−	10.7853i	−1.27775	−	0.344350i
$982$	2.89365	−	1.49178i	0.0923402	−	0.0476047i
$983$	−7.90313	−	7.53562i	−0.252071	−	0.240349i	0.553499	−	0.832850i	$-0.313292\pi$
$983$	−7.90313	−	7.53562i	−0.252071	−	0.240349i	−0.805570	+	0.592501i	$0.798141\pi$
$984$	51.7803	−	30.6722i	1.65070	−	0.977793i
$985$	−19.1367	−	20.0699i	−0.609744	−	0.639482i
$986$	−2.71662	−	5.94858i	−0.0865149	−	0.189441i
$987$	−1.78203	+	4.22121i	−0.0567227	+	0.134363i
$988$	−0.530408			−0.0168745
$989$	−16.2941	+	18.6226i	−0.518122	+	0.592163i
$990$	−26.7908	+	22.0554i	−0.851468	+	0.700965i
$991$	−21.4077	+	8.57035i	−0.680038	+	0.272246i	−0.685856	−	0.727737i	$-0.740572\pi$
$991$	−21.4077	+	8.57035i	−0.680038	+	0.272246i	0.00581827	+	0.999983i	$0.498148\pi$
$992$	17.3351	+	1.65530i	0.550390	+	0.0525559i
$993$	−35.7846	+	23.5667i	−1.13559	+	0.747866i
$994$	−24.2250	−	32.7718i	−0.768371	−	1.03946i
$995$	6.23424	+	21.2319i	0.197639	+	0.673096i
$996$	−0.733080	+	3.17635i	−0.0232285	+	0.100646i
$997$	−1.42940	−	14.9694i	−0.0452696	−	0.474084i	−0.989473	−	0.144720i	$-0.953772\pi$
$997$	−1.42940	−	14.9694i	−0.0452696	−	0.474084i	0.944203	−	0.329364i	$-0.106834\pi$
$998$	5.37860	−	27.9068i	0.170257	−	0.883375i
$999$	−14.4159	+	27.0229i	−0.456100	+	0.854965i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.bb.a.215.19	yes	1200
3.2	odd	2	inner	483.2.bb.a.215.42	yes	1200
7.3	odd	6	inner	483.2.bb.a.353.19	yes	1200
21.17	even	6	inner	483.2.bb.a.353.42	yes	1200
23.3	even	11	inner	483.2.bb.a.26.42	yes	1200
69.26	odd	22	inner	483.2.bb.a.26.19	✓	1200
161.3	odd	66	inner	483.2.bb.a.164.42	yes	1200
483.164	even	66	inner	483.2.bb.a.164.19	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.bb.a.26.19	✓	1200	69.26	odd	22	inner
483.2.bb.a.26.42	yes	1200	23.3	even	11	inner
483.2.bb.a.164.19	yes	1200	483.164	even	66	inner
483.2.bb.a.164.42	yes	1200	161.3	odd	66	inner
483.2.bb.a.215.19	yes	1200	1.1	even	1	trivial
483.2.bb.a.215.42	yes	1200	3.2	odd	2	inner
483.2.bb.a.353.19	yes	1200	7.3	odd	6	inner
483.2.bb.a.353.42	yes	1200	21.17	even	6	inner

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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

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	483.2.bb.a.215.19

Level	$483$
Weight	$2$
Character	483.215
Analytic conductor	$3.857$
Analytic rank	$0$
Dimension	$1200$
Inner twists	$8$