LMFDB - Embedded newform 205.2.y.a.112.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [205,2,Mod(7,205)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("205.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(205, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([10, 39])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 205 = 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	205.y (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.63693324144$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$19$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			112.4
Character	$\chi$	$=$	205.112
Dual form			205.2.y.a.108.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60835 - 1.16853i) q^{2} +(-1.01747 - 2.45639i) q^{3} +(0.603281 + 1.85671i) q^{4} +(-2.09264 + 0.787934i) q^{5} +(-1.23393 + 5.13969i) q^{6} +(-0.133098 + 0.217196i) q^{7} +(-0.0293286 + 0.0902643i) q^{8} +(-2.87730 + 2.87730i) q^{9} +(4.28643 + 1.17805i) q^{10} +(-1.26260 + 1.47832i) q^{11} +(3.94699 - 3.37105i) q^{12} +(0.933385 - 3.88783i) q^{13} +(0.467869 - 0.193798i) q^{14} +(4.06468 + 4.33866i) q^{15} +(3.31147 - 2.40592i) q^{16} +(-1.18644 - 1.01332i) q^{17} +(7.98994 - 1.26548i) q^{18} +(-2.12351 + 3.46525i) q^{19} +(-2.72542 - 3.41009i) q^{20} +(0.668942 + 0.105950i) q^{21} +(3.75817 - 0.902256i) q^{22} +(0.705636 + 4.45521i) q^{23} +(0.251566 - 0.0197986i) q^{24} +(3.75832 - 3.29773i) q^{25} +(-6.04427 + 5.16230i) q^{26} +(2.62618 + 1.08780i) q^{27} +(-0.483565 - 0.116094i) q^{28} +(-0.523941 + 6.65730i) q^{29} +(-1.46756 - 11.7278i) q^{30} +(-5.20942 - 1.69264i) q^{31} -7.94759 q^{32} +(4.91599 + 1.59730i) q^{33} +(0.724118 + 3.01617i) q^{34} +(0.107390 - 0.559386i) q^{35} +(-7.07814 - 3.60649i) q^{36} +(-1.97309 + 3.87240i) q^{37} +(7.46461 - 3.09194i) q^{38} +(-10.4997 + 1.66299i) q^{39} +(-0.00974785 - 0.212000i) q^{40} +(0.336449 - 6.39428i) q^{41} +(-0.952086 - 0.952086i) q^{42} +(-4.94576 + 6.80726i) q^{43} +(-3.50651 - 1.45244i) q^{44} +(3.75405 - 8.28830i) q^{45} +(4.07116 - 7.99009i) q^{46} +(-8.02287 + 4.91642i) q^{47} +(-9.27922 - 5.68632i) q^{48} +(3.14847 + 6.17923i) q^{49} +(-9.89820 + 0.912175i) q^{50} +(-1.28194 + 3.94540i) q^{51} +(7.78166 - 0.612430i) q^{52} +(-8.63012 - 10.1046i) q^{53} +(-2.95269 - 4.81835i) q^{54} +(1.47736 - 4.08844i) q^{55} +(-0.0157015 - 0.0183840i) q^{56} +(10.6726 + 1.69038i) q^{57} +(8.62196 - 10.0950i) q^{58} +(4.08316 - 5.61998i) q^{59} +(-5.60348 + 10.1644i) q^{60} +(1.84041 - 11.6199i) q^{61} +(6.40066 + 8.80975i) q^{62} +(-0.241976 - 1.00790i) q^{63} +(6.15955 + 4.47518i) q^{64} +(1.11011 + 8.87129i) q^{65} +(-6.04013 - 8.31352i) q^{66} +(-6.73932 - 0.530396i) q^{67} +(1.16568 - 2.81420i) q^{68} +(10.2258 - 6.26637i) q^{69} +(-0.826383 + 0.774199i) q^{70} +(1.08472 + 0.926438i) q^{71} +(-0.175330 - 0.344105i) q^{72} +8.42805i q^{73} +(7.69844 - 3.92255i) q^{74} +(-11.9245 - 5.87657i) q^{75} +(-7.71504 - 1.85222i) q^{76} +(-0.153035 - 0.470993i) q^{77} +(18.8305 + 9.59462i) q^{78} +(-1.98066 + 4.78173i) q^{79} +(-5.03402 + 7.64396i) q^{80} +4.64962i q^{81} +(-8.01306 + 9.89108i) q^{82} +(-7.57937 + 7.57937i) q^{83} +(0.206842 + 1.30595i) q^{84} +(3.28123 + 1.18568i) q^{85} +(15.9090 - 5.16916i) q^{86} +(16.8860 - 5.48661i) q^{87} +(-0.0964088 - 0.157325i) q^{88} +(-3.97340 + 0.953929i) q^{89} +(-15.7230 + 8.94374i) q^{90} +(0.720189 + 0.720189i) q^{91} +(-7.84633 + 3.99791i) q^{92} +(1.14264 + 14.5186i) q^{93} +(18.6486 + 1.46767i) q^{94} +(1.71336 - 8.92472i) q^{95} +(8.08644 + 19.5224i) q^{96} +(-0.541427 + 6.87949i) q^{97} +(2.15679 - 13.6175i) q^{98} +(-0.620677 - 7.88645i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) $ 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/205\mathbb{Z}\right)^\times$.

$n$	$6$	$42$
$\chi(n)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.60835	−	1.16853i	−1.13727	−	0.826278i	−0.150537	−	0.988604i	$-0.548100\pi$
$2$	−1.60835	−	1.16853i	−1.13727	−	0.826278i	−0.986737	+	0.162326i	$0.948100\pi$
$3$	−1.01747	−	2.45639i	−0.587438	−	1.41820i	−0.885944	−	0.463792i	$-0.846488\pi$
$3$	−1.01747	−	2.45639i	−0.587438	−	1.41820i	0.298506	−	0.954408i	$-0.403512\pi$
$4$	0.603281	+	1.85671i	0.301641	+	0.928355i
$5$	−2.09264	+	0.787934i	−0.935859	+	0.352375i
$5$	−2.09264	+	0.787934i	−0.935859	+	0.352375i
$6$	−1.23393	+	5.13969i	−0.503750	+	2.09827i
$7$	−0.133098	+	0.217196i	−0.0503062	+	0.0820923i	−0.876805	−	0.480847i	$-0.840329\pi$
$7$	−0.133098	+	0.217196i	−0.0503062	+	0.0820923i	0.826498	+	0.562939i	$0.190329\pi$
$8$	−0.0293286	+	0.0902643i	−0.0103692	+	0.0319132i
$9$	−2.87730	+	2.87730i	−0.959101	+	0.959101i
$10$	4.28643	+	1.17805i	1.35549	+	0.372533i
$11$	−1.26260	+	1.47832i	−0.380689	+	0.445729i	−0.917358	−	0.398064i	$-0.869682\pi$
$11$	−1.26260	+	1.47832i	−0.380689	+	0.445729i	0.536669	+	0.843793i	$0.319682\pi$
$12$	3.94699	−	3.37105i	1.13940	−	0.973137i
$13$	0.933385	−	3.88783i	0.258875	−	1.07829i	−0.679776	−	0.733420i	$-0.737923\pi$
$13$	0.933385	−	3.88783i	0.258875	−	1.07829i	0.938650	−	0.344870i	$-0.112077\pi$
$14$	0.467869	−	0.193798i	0.125043	−	0.0517946i
$15$	4.06468	+	4.33866i	1.04950	+	1.12024i
$16$	3.31147	−	2.40592i	0.827867	−	0.601481i
$17$	−1.18644	−	1.01332i	−0.287755	−	0.245766i	0.493839	−	0.869553i	$-0.335593\pi$
$17$	−1.18644	−	1.01332i	−0.287755	−	0.245766i	−0.781594	+	0.623787i	$0.785593\pi$
$18$	7.98994	−	1.26548i	1.88325	−	0.298277i
$19$	−2.12351	+	3.46525i	−0.487166	+	0.794983i	−0.997901	−	0.0647551i	$-0.979373\pi$
$19$	−2.12351	+	3.46525i	−0.487166	+	0.794983i	0.510735	+	0.859738i	$0.329373\pi$
$20$	−2.72542	−	3.41009i	−0.609422	−	0.762518i
$21$	0.668942	+	0.105950i	0.145975	+	0.0231202i
$22$	3.75817	−	0.902256i	0.801244	−	0.192362i
$23$	0.705636	+	4.45521i	0.147135	+	0.928975i	0.945221	+	0.326431i	$0.105846\pi$
$23$	0.705636	+	4.45521i	0.147135	+	0.928975i	−0.798086	+	0.602544i	$0.794154\pi$
$24$	0.251566	−	0.0197986i	0.0513506	−	0.00404138i
$25$	3.75832	−	3.29773i	0.751664	−	0.659546i
$26$	−6.04427	+	5.16230i	−1.18538	+	1.01241i
$27$	2.62618	+	1.08780i	0.505409	+	0.209347i
$28$	−0.483565	−	0.116094i	−0.0913852	−	0.0219396i
$29$	−0.523941	+	6.65730i	−0.0972933	+	1.23623i	0.733516	+	0.679672i	$0.237878\pi$
$29$	−0.523941	+	6.65730i	−0.0972933	+	1.23623i	−0.830810	+	0.556557i	$0.812122\pi$
$30$	−1.46756	−	11.7278i	−0.267938	−	2.14119i
$31$	−5.20942	−	1.69264i	−0.935639	−	0.304008i	−0.198773	−	0.980046i	$-0.563696\pi$
$31$	−5.20942	−	1.69264i	−0.935639	−	0.304008i	−0.736867	+	0.676038i	$0.763696\pi$
$32$	−7.94759			−1.40495
$33$	4.91599	+	1.59730i	0.855764	+	0.278055i
$34$	0.724118	+	3.01617i	0.124185	+	0.517269i
$35$	0.107390	−	0.559386i	0.0181523	−	0.0945535i
$36$	−7.07814	−	3.60649i	−1.17969	−	0.601082i
$37$	−1.97309	+	3.87240i	−0.324373	+	0.636618i	−0.994396	−	0.105723i	$-0.966284\pi$
$37$	−1.97309	+	3.87240i	−0.324373	+	0.636618i	0.670022	+	0.742341i	$0.266284\pi$
$38$	7.46461	−	3.09194i	1.21092	−	0.501579i
$39$	−10.4997	+	1.66299i	−1.68130	+	0.266292i
$40$	−0.00974785	−	0.212000i	−0.00154127	−	0.0335202i
$41$	0.336449	−	6.39428i	0.0525445	−	0.998619i
$41$	0.336449	−	6.39428i	0.0525445	−	0.998619i
$42$	−0.952086	−	0.952086i	−0.146910	−	0.146910i
$43$	−4.94576	+	6.80726i	−0.754222	+	1.03810i	0.243451	+	0.969913i	$0.421721\pi$
$43$	−4.94576	+	6.80726i	−0.754222	+	1.03810i	−0.997673	+	0.0681843i	$0.978279\pi$
$44$	−3.50651	−	1.45244i	−0.528626	−	0.218964i
$45$	3.75405	−	8.28830i	0.559620	−	1.23555i
$46$	4.07116	−	7.99009i	0.600259	−	1.17807i
$47$	−8.02287	+	4.91642i	−1.17026	+	0.717133i	−0.965173	−	0.261611i	$-0.915746\pi$
$47$	−8.02287	+	4.91642i	−1.17026	+	0.717133i	−0.205082	+	0.978745i	$0.565746\pi$
$48$	−9.27922	−	5.68632i	−1.33934	−	0.820749i
$49$	3.14847	+	6.17923i	0.449782	+	0.882747i
$50$	−9.89820	+	0.912175i	−1.39982	+	0.129001i
$51$	−1.28194	+	3.94540i	−0.179507	+	0.552466i
$52$	7.78166	−	0.612430i	1.07912	−	0.0849288i
$53$	−8.63012	−	10.1046i	−1.18544	−	1.38797i	−0.903529	−	0.428528i	$-0.859032\pi$
$53$	−8.63012	−	10.1046i	−1.18544	−	1.38797i	−0.281909	−	0.959441i	$-0.590968\pi$
$54$	−2.95269	−	4.81835i	−0.401810	−	0.655694i
$55$	1.47736	−	4.08844i	0.199207	−	0.551285i
$56$	−0.0157015	−	0.0183840i	−0.00209819	−	0.00245667i
$57$	10.6726	+	1.69038i	1.41362	+	0.223896i
$58$	8.62196	−	10.0950i	1.13212	−	1.32554i
$59$	4.08316	−	5.61998i	0.531582	−	0.731659i	−0.455789	−	0.890088i	$-0.650643\pi$
$59$	4.08316	−	5.61998i	0.531582	−	0.731659i	0.987370	+	0.158429i	$0.0506428\pi$
$60$	−5.60348	+	10.1644i	−0.723406	+	1.31221i
$61$	1.84041	−	11.6199i	0.235640	−	1.48777i	−0.531920	−	0.846795i	$-0.678529\pi$
$61$	1.84041	−	11.6199i	0.235640	−	1.48777i	0.767560	−	0.640977i	$-0.221471\pi$
$62$	6.40066	+	8.80975i	0.812884	+	1.11884i
$63$	−0.241976	−	1.00790i	−0.0304861	−	0.126984i
$64$	6.15955	+	4.47518i	0.769944	+	0.559397i
$65$	1.11011	+	8.87129i	0.137692	+	1.10035i
$66$	−6.04013	−	8.31352i	−0.743488	−	1.02332i
$67$	−6.73932	−	0.530396i	−0.823339	−	0.0647982i	−0.340212	−	0.940349i	$-0.610499\pi$
$67$	−6.73932	−	0.530396i	−0.823339	−	0.0647982i	−0.483127	+	0.875550i	$0.660499\pi$
$68$	1.16568	−	2.81420i	0.141359	−	0.341272i
$69$	10.2258	−	6.26637i	1.23104	−	0.754382i
$70$	−0.826383	+	0.774199i	−0.0987717	+	0.0925344i
$71$	1.08472	+	0.926438i	0.128733	+	0.109948i	0.711483	−	0.702703i	$-0.248024\pi$
$71$	1.08472	+	0.926438i	0.128733	+	0.109948i	−0.582751	+	0.812651i	$0.698024\pi$
$72$	−0.175330	−	0.344105i	−0.0206629	−	0.0405532i
$73$			8.42805i			0.986429i	0.869908	+	0.493214i	$0.164178\pi$
$73$			8.42805i			0.986429i	−0.869908	+	0.493214i	$0.835822\pi$
$74$	7.69844	−	3.92255i	0.894925	−	0.455987i
$75$	−11.9245	−	5.87657i	−1.37692	−	0.678568i
$76$	−7.71504	−	1.85222i	−0.884975	−	0.212464i
$77$	−0.153035	−	0.470993i	−0.0174399	−	0.0536746i
$78$	18.8305	+	9.59462i	2.13214	+	1.08638i
$79$	−1.98066	+	4.78173i	−0.222841	+	0.537987i	−0.995274	−	0.0971105i	$-0.969040\pi$
$79$	−1.98066	+	4.78173i	−0.222841	+	0.537987i	0.772432	+	0.635097i	$0.219040\pi$
$80$	−5.03402	+	7.64396i	−0.562821	+	0.854621i
$81$			4.64962i			0.516624i
$82$	−8.01306	+	9.89108i	−0.884895	+	1.09229i
$83$	−7.57937	+	7.57937i	−0.831944	+	0.831944i	−0.987783	−	0.155838i	$-0.950192\pi$
$83$	−7.57937	+	7.57937i	−0.831944	+	0.831944i	0.155838	+	0.987783i	$0.450192\pi$
$84$	0.206842	+	1.30595i	0.0225683	+	0.142491i
$85$	3.28123	+	1.18568i	0.355900	+	0.128605i
$86$	15.9090	−	5.16916i	1.71552	−	0.557405i
$87$	16.8860	−	5.48661i	1.81037	−	0.588226i
$88$	−0.0964088	−	0.157325i	−0.0102772	−	0.0167709i
$89$	−3.97340	+	0.953929i	−0.421180	+	0.101116i	−0.438495	−	0.898734i	$-0.644488\pi$
$89$	−3.97340	+	0.953929i	−0.421180	+	0.101116i	0.0173150	+	0.999850i	$0.494488\pi$
$90$	−15.7230	+	8.94374i	−1.65735	+	0.942753i
$91$	0.720189	+	0.720189i	0.0754963	+	0.0754963i
$92$	−7.84633	+	3.99791i	−0.818036	+	0.416810i
$93$	1.14264	+	14.5186i	0.118486	+	1.50551i
$94$	18.6486	+	1.46767i	1.92345	+	0.151379i
$95$	1.71336	−	8.92472i	0.175787	−	0.915657i
$96$	8.08644	+	19.5224i	0.825319	+	1.99250i
$97$	−0.541427	+	6.87949i	−0.0549736	+	0.698506i	0.906251	+	0.422740i	$0.138932\pi$
$97$	−0.541427	+	6.87949i	−0.0549736	+	0.698506i	−0.961225	+	0.275766i	$0.911068\pi$
$98$	2.15679	−	13.6175i	0.217869	−	1.37557i
$99$	−0.620677	−	7.88645i	−0.0623804	−	0.792618i
$100$	8.39025	+	4.98865i	0.839025	+	0.498865i
$101$	−9.89938	−	6.06635i	−0.985026	−	0.603624i	−0.0659989	−	0.997820i	$-0.521023\pi$
$101$	−9.89938	−	6.06635i	−0.985026	−	0.603624i	−0.919027	+	0.394195i	$0.871023\pi$
$102$	6.67213	−	4.84759i	0.660640	−	0.479983i
$103$	5.83812	−	4.24164i	0.575247	−	0.417942i	−0.261760	−	0.965133i	$-0.584303\pi$
$103$	5.83812	−	4.24164i	0.575247	−	0.417942i	0.837008	+	0.547191i	$0.184303\pi$
$104$	0.323557	+	0.198276i	0.0317274	+	0.0194426i
$105$	−1.48334	+	0.305366i	−0.144759	+	0.0298007i
$106$	2.07271	+	26.3363i	0.201319	+	2.55800i
$107$	2.79191	−	17.6274i	0.269904	−	1.70411i	−0.364581	−	0.931172i	$-0.618788\pi$
$107$	2.79191	−	17.6274i	0.269904	−	1.70411i	0.634485	−	0.772935i	$-0.281212\pi$
$108$	−0.435402	+	5.53231i	−0.0418966	+	0.532347i
$109$	−4.18121	−	10.0943i	−0.400487	−	0.966862i	−0.987548	−	0.157319i	$-0.949715\pi$
$109$	−4.18121	−	10.0943i	−0.400487	−	0.966862i	0.587061	−	0.809543i	$-0.300285\pi$
$110$	−7.15359	+	4.84929i	−0.682068	+	0.462362i
$111$	11.5197	+	0.906620i	1.09340	+	0.0860525i
$112$	0.0818073	+	1.03946i	0.00773007	+	0.0982198i
$113$	16.8484	−	8.58467i	1.58496	−	0.807578i	0.584968	−	0.811057i	$-0.301107\pi$
$113$	16.8484	−	8.58467i	1.58496	−	0.807578i	0.999994	+	0.00347838i	$0.00110721\pi$
$114$	−15.1901	−	15.1901i	−1.42268	−	1.42268i
$115$	−4.98705	−	8.76717i	−0.465045	−	0.817543i
$116$	−12.6767	+	3.04342i	−1.17701	+	0.282574i
$117$	8.50083	+	13.8721i	0.785902	+	1.28248i
$118$	−13.1343	+	4.26759i	−1.20911	+	0.392863i
$119$	0.378002	−	0.122820i	0.0346514	−	0.0112589i
$120$	−0.510838	+	0.239649i	−0.0466329	+	0.0218768i
$121$	1.12952	+	7.13152i	0.102684	+	0.648320i
$122$	−16.5382	+	16.5382i	−1.49730	+	1.49730i
$123$	−16.0492	+	5.67955i	−1.44711	+	0.512107i
$124$		−	10.6935i		−	0.960306i
$125$	−5.26644	+	9.86228i	−0.471044	+	0.882109i
$126$	−0.788586	+	1.90381i	−0.0702528	+	0.169605i
$127$	−8.71700	−	4.44153i	−0.773508	−	0.394122i	0.0222377	−	0.999753i	$-0.492921\pi$
$127$	−8.71700	−	4.44153i	−0.773508	−	0.394122i	−0.795746	+	0.605631i	$0.792921\pi$
$128$	0.234562	+	0.721908i	0.0207326	+	0.0638083i
$129$	21.7535	+	5.22255i	1.91529	+	0.459820i
$130$	8.58096	−	15.5653i	0.752600	−	1.36517i
$131$	6.65841	−	3.39263i	0.581748	−	0.296415i	−0.138244	−	0.990398i	$-0.544146\pi$
$131$	6.65841	−	3.39263i	0.581748	−	0.296415i	0.719991	+	0.693983i	$0.244146\pi$
$132$			10.0912i			0.878325i
$133$	−0.470004	−	0.922435i	−0.0407545	−	0.0799852i
$134$	10.2194	+	8.72819i	0.882821	+	0.754001i
$135$	−6.35278	−	0.207122i	−0.546760	−	0.0178262i
$136$	0.126263	−	0.0773742i	0.0108270	−	0.00663478i
$137$	3.78581	−	9.13976i	0.323444	−	0.780862i	−0.675605	−	0.737263i	$-0.736118\pi$
$137$	3.78581	−	9.13976i	0.323444	−	0.780862i	0.999049	−	0.0435989i	$-0.0138824\pi$
$138$	−23.7691	−	1.87067i	−2.02336	−	0.159242i
$139$	−8.46455	−	11.6505i	−0.717954	−	0.988179i	−0.999589	−	0.0286573i	$-0.990877\pi$
$139$	−8.46455	−	11.6505i	−0.717954	−	0.988179i	0.281635	−	0.959522i	$-0.409123\pi$
$140$	1.10340	−	0.138074i	0.0932546	−	0.0116694i
$141$	20.2397	+	14.7050i	1.70449	+	1.23838i
$142$	−0.662034	−	2.75757i	−0.0555566	−	0.231410i
$143$	4.56895	+	6.28862i	0.382075	+	0.525881i
$144$	−2.60553	+	16.4507i	−0.217128	+	1.37089i
$145$	−4.14909	−	14.3442i	−0.344563	−	1.19122i
$146$	9.84846	−	13.5552i	0.815065	−	1.12184i
$147$	11.9751	−	14.0211i	0.987693	−	1.15644i
$148$	−8.38024	−	1.32730i	−0.688852	−	0.109103i
$149$	−14.7857	−	17.3119i	−1.21130	−	1.41824i	−0.880171	−	0.474657i	$-0.842572\pi$
$149$	−14.7857	−	17.3119i	−1.21130	−	1.41824i	−0.331124	−	0.943587i	$-0.607428\pi$
$150$	12.3118	+	23.3858i	1.00525	+	1.90944i
$151$	0.632569	+	1.03226i	0.0514778	+	0.0840041i	0.877344	−	0.479862i	$-0.159313\pi$
$151$	0.632569	+	1.03226i	0.0514778	+	0.0840041i	−0.825866	+	0.563866i	$0.809313\pi$
$152$	−0.250509	−	0.293308i	−0.0203189	−	0.0237904i
$153$	6.32938	−	0.498133i	0.511700	−	0.0402717i
$154$	−0.304238	+	0.936347i	−0.0245162	+	0.0754530i
$155$	12.2352	−	0.562577i	0.982751	−	0.0451873i
$156$	−9.42199	−	18.4917i	−0.754363	−	1.48052i
$157$	−2.01429	−	1.23436i	−0.160758	−	0.0985128i	0.439793	−	0.898099i	$-0.355052\pi$
$157$	−2.01429	−	1.23436i	−0.160758	−	0.0985128i	−0.600551	+	0.799587i	$0.705052\pi$
$158$	8.77321	−	5.37623i	0.697959	−	0.427710i
$159$	−16.0399	+	31.4801i	−1.27205	+	2.49653i
$160$	16.6315	−	6.26217i	1.31483	−	0.495068i
$161$	−1.06157	−	0.439717i	−0.0836636	−	0.0346546i
$162$	5.43324	−	7.47821i	0.426875	−	0.587543i
$163$	−0.358877	−	0.358877i	−0.0281094	−	0.0281094i	0.692912	−	0.721022i	$-0.256327\pi$
$163$	−0.358877	−	0.358877i	−0.0281094	−	0.0281094i	−0.721022	+	0.692912i	$0.756327\pi$
$164$	12.0753	−	3.23286i	0.942922	−	0.252444i
$165$	−11.5460	+	0.530889i	−0.898854	+	0.0413297i
$166$	21.0470	−	3.33352i	1.63357	−	0.258732i
$167$	−0.969494	+	0.401577i	−0.0750217	+	0.0310750i	−0.419879	−	0.907580i	$-0.637927\pi$
$167$	−0.969494	+	0.401577i	−0.0750217	+	0.0310750i	0.344857	+	0.938655i	$0.387927\pi$
$168$	−0.0291827	+	0.0572742i	−0.00225149	+	0.00441880i
$169$	−2.66093	−	1.35581i	−0.204687	−	0.104293i
$170$	−3.89186	−	5.74121i	−0.298492	−	0.440331i
$171$	−3.86060	−	16.0806i	−0.295227	−	1.22971i
$172$	−15.6228	−	5.07615i	−1.19123	−	0.387053i
$173$	11.1048			0.844284			0.422142	−	0.906530i	$-0.361278\pi$
$173$	11.1048			0.844284			0.422142	+	0.906530i	$0.361278\pi$
$174$	−33.5699	−	10.9075i	−2.54493	−	0.826898i
$175$	0.216029	+	1.25521i	0.0163303	+	0.0948851i
$176$	−0.624350	+	7.93312i	−0.0470622	+	0.597982i
$177$	−17.9594	−	4.31167i	−1.34991	−	0.324085i
$178$	7.50531	+	3.10880i	0.562547	+	0.233015i
$179$	−2.27220	+	1.94064i	−0.169832	+	0.145050i	−0.730302	−	0.683125i	$-0.760621\pi$
$179$	−2.27220	+	1.94064i	−0.169832	+	0.145050i	0.560470	+	0.828175i	$0.310621\pi$
$180$	17.6537	+	1.97000i	1.31583	+	0.146835i
$181$	−9.18830	+	0.723135i	−0.682961	+	0.0537502i	−0.415193	−	0.909733i	$-0.636286\pi$
$181$	−9.18830	+	0.723135i	−0.682961	+	0.0537502i	−0.267768	+	0.963483i	$0.586286\pi$
$182$	−0.316750	−	1.99988i	−0.0234791	−	0.148241i
$183$	−30.4155	+	7.30213i	−2.24838	+	0.539789i
$184$	−0.422842	−	0.0669715i	−0.0311723	−	0.00493721i
$185$	1.07777	−	9.65821i	0.0792394	−	0.710086i
$186$	15.1277	−	24.6862i	1.10922	−	1.81008i
$187$	2.99601	−	0.474522i	0.219090	−	0.0347005i
$188$	−13.9684	−	11.9301i	−1.01875	−	0.870095i
$189$	−0.585805	+	0.425612i	−0.0426110	+	0.0309587i
$190$	−13.1845	+	12.3520i	−0.956506	+	0.896105i
$191$	−7.30199	+	3.02458i	−0.528353	+	0.218851i	−0.630882	−	0.775879i	$-0.717307\pi$
$191$	−7.30199	+	3.02458i	−0.528353	+	0.218851i	0.102528	+	0.994730i	$0.467307\pi$
$192$	4.72563	−	19.6837i	0.341043	−	1.42055i
$193$	3.76311	−	3.21400i	0.270875	−	0.231349i	−0.503626	−	0.863922i	$-0.668001\pi$
$193$	3.76311	−	3.21400i	0.270875	−	0.231349i	0.774501	+	0.632573i	$0.218001\pi$
$194$	8.90972	−	10.4319i	0.639681	−	0.748970i
$195$	20.6619	−	11.7532i	1.47963	−	0.841661i
$196$	−9.57362	+	9.57362i	−0.683830	+	0.683830i
$197$	−6.45474	+	19.8657i	−0.459882	+	1.41537i	0.405426	+	0.914128i	$0.367123\pi$
$197$	−6.45474	+	19.8657i	−0.459882	+	1.41537i	−0.865307	+	0.501242i	$0.832877\pi$
$198$	−8.21732	+	13.4095i	−0.583980	+	0.952968i
$199$	1.73192	−	7.21397i	0.122773	−	0.511385i	−0.876763	−	0.480922i	$-0.840302\pi$
$199$	1.73192	−	7.21397i	0.122773	−	0.511385i	0.999536	−	0.0304626i	$-0.00969806\pi$
$200$	0.187441	+	0.435960i	0.0132541	+	0.0308270i
$201$	5.55421	+	17.0941i	0.391764	+	1.20572i
$202$	8.83293	+	21.3246i	0.621483	+	1.50039i
$203$	−1.37620	−	0.999869i	−0.0965904	−	0.0701771i
$204$	−8.09882			−0.567031
$205$	4.33420	+	13.6461i	0.302714	+	0.953082i
$206$	−14.3462			−0.999550
$207$	−14.8493	−	10.7887i	−1.03210	−	0.749864i
$208$	−6.26294	−	15.1201i	−0.434257	−	1.04839i
$209$	−2.44159	−	7.51445i	−0.168889	−	0.519785i
$210$	2.74256	+	1.24220i	0.189255	+	0.0857197i
$211$	−5.15926	+	21.4899i	−0.355178	+	1.47942i	0.453544	+	0.891234i	$0.350160\pi$
$211$	−5.15926	+	21.4899i	−0.355178	+	1.47942i	−0.808722	+	0.588191i	$0.799840\pi$
$212$	13.5549	−	22.1195i	0.930951	−	1.51917i
$213$	1.17203	−	3.60712i	0.0803059	−	0.247156i
$214$	−25.0886	+	25.0886i	−1.71502	+	1.71502i
$215$	4.98606	−	18.1421i	0.340046	−	1.23728i
$216$	−0.175212	+	0.205147i	−0.0119217	+	0.0139585i
$217$	1.06100	−	0.906177i	0.0720252	−	0.0615153i
$218$	−5.07073	+	21.1211i	−0.343433	+	1.43050i
$219$	20.7026	−	8.57530i	1.39895	−	0.579465i
$220$	8.48230	+	0.276551i	0.571877	+	0.0186451i
$221$	−5.04702	+	3.66687i	−0.339499	+	0.246661i
$222$	−17.4683	−	14.9193i	−1.17239	−	1.00132i
$223$	−15.2394	+	2.41368i	−1.02050	+	0.161632i	−0.644194	−	0.764862i	$-0.722807\pi$
$223$	−15.2394	+	2.41368i	−1.02050	+	0.161632i	−0.376310	+	0.926494i	$0.622807\pi$
$224$	1.05781	−	1.72618i	0.0706776	−	0.115335i
$225$	−1.32526	+	20.3024i	−0.0883506	+	1.35349i
$226$	−37.1296	−	5.88074i	−2.46982	−	0.391181i
$227$	12.0053	−	2.88221i	0.796817	−	0.191299i	0.185458	−	0.982652i	$-0.440623\pi$
$227$	12.0053	−	2.88221i	0.796817	−	0.191299i	0.611359	+	0.791353i	$0.290623\pi$
$228$	3.30006	+	20.8357i	0.218552	+	1.37988i
$229$	4.14206	−	0.325987i	0.273715	−	0.0215419i	0.0591413	−	0.998250i	$-0.481164\pi$
$229$	4.14206	−	0.325987i	0.273715	−	0.0215419i	0.214574	+	0.976708i	$0.431164\pi$
$230$	−2.22382	+	19.9282i	−0.146634	+	1.31403i
$231$	−1.00123	+	0.855135i	−0.0658764	+	0.0562638i
$232$	−0.585549	−	0.242543i	−0.0384432	−	0.0159237i
$233$	12.6735	+	3.04265i	0.830271	+	0.199330i	0.626236	−	0.779633i	$-0.284595\pi$
$233$	12.6735	+	3.04265i	0.830271	+	0.199330i	0.204034	+	0.978964i	$0.434595\pi$
$234$	2.53771	−	32.2447i	0.165895	−	2.10790i
$235$	12.9152	−	16.6098i	0.842494	−	1.08350i
$236$	12.8980	+	4.19080i	0.839586	+	0.272798i
$237$	13.7611			0.893878
$238$	−0.751478	−	0.244170i	−0.0487111	−	0.0158272i
$239$	3.09462	+	12.8900i	0.200174	+	0.833786i	0.978554	+	0.205992i	$0.0660421\pi$
$239$	3.09462	+	12.8900i	0.200174	+	0.833786i	−0.778379	+	0.627794i	$0.783958\pi$
$240$	23.8986	+	4.58802i	1.54265	+	0.296156i
$241$	−5.08956	−	2.59326i	−0.327847	−	0.167047i	0.282317	−	0.959321i	$-0.408897\pi$
$241$	−5.08956	−	2.59326i	−0.327847	−	0.167047i	−0.610165	+	0.792274i	$0.708897\pi$
$242$	6.51676	−	12.7899i	0.418913	−	0.822163i
$243$	19.2998	−	7.99426i	1.23809	−	0.512832i
$244$	22.6850	−	3.59295i	1.45226	−	0.230015i
$245$	−11.4575	−	10.4501i	−0.731990	−	0.667635i
$246$	32.4495	+	9.61934i	2.06890	+	0.613307i
$247$	11.4903	+	11.4903i	0.731107	+	0.731107i
$248$	0.305570	−	0.420582i	0.0194037	−	0.0267070i
$249$	26.3297	+	10.9061i	1.66858	+	0.691148i
$250$	19.9947	−	9.70799i	1.26457	−	0.613987i
$251$	−1.89961	+	3.72820i	−0.119903	+	0.235322i	−0.943155	−	0.332354i	$-0.892157\pi$
$251$	−1.89961	+	3.72820i	−0.119903	+	0.235322i	0.823252	+	0.567676i	$0.192157\pi$
$252$	1.72540	−	1.05733i	0.108690	−	0.0666053i
$253$	−7.47715	−	4.58200i	−0.470084	−	0.288068i
$254$	8.82989	+	17.3296i	0.554037	+	1.08736i
$255$	−0.426073	−	9.26639i	−0.0266817	−	0.580284i
$256$	5.17180	−	15.9172i	0.323237	−	0.994822i
$257$	6.39370	−	0.503195i	0.398828	−	0.0313884i	0.122540	−	0.992464i	$-0.460896\pi$
$257$	6.39370	−	0.503195i	0.398828	−	0.0313884i	0.276287	+	0.961075i	$0.410896\pi$
$258$	−28.8845	−	33.8194i	−1.79827	−	2.10550i
$259$	−0.578456	−	0.943954i	−0.0359435	−	0.0586544i
$260$	−15.8017	+	7.41303i	−0.979980	+	0.459737i
$261$	−17.6475	−	20.6626i	−1.09235	−	1.27898i
$262$	−14.6734	−	2.32405i	−0.906529	−	0.143580i
$263$	−12.8701	+	15.0689i	−0.793604	+	0.929190i	−0.998772	−	0.0495362i	$-0.984226\pi$
$263$	−12.8701	+	15.0689i	−0.793604	+	0.929190i	0.205169	+	0.978727i	$0.434226\pi$
$264$	−0.288359	+	0.396892i	−0.0177472	+	0.0244270i
$265$	26.0215	+	14.3453i	1.59849	+	0.881225i
$266$	−0.321966	+	2.03281i	−0.0197410	+	0.124640i
$267$	6.38605	+	8.78964i	0.390820	+	0.537917i
$268$	−3.08092	−	12.8329i	−0.188197	−	0.783896i
$269$	16.2088	+	11.7764i	0.988268	+	0.718018i	0.959541	−	0.281569i	$-0.0908548\pi$
$269$	16.2088	+	11.7764i	0.988268	+	0.718018i	0.0287266	+	0.999587i	$0.490855\pi$
$270$	9.97546	+	7.75657i	0.607087	+	0.472050i
$271$	15.1956	+	20.9149i	0.923065	+	1.27049i	0.962504	+	0.271268i	$0.0874430\pi$
$271$	15.1956	+	20.9149i	0.923065	+	1.27049i	−0.0394389	+	0.999222i	$0.512557\pi$
$272$	−6.36684	−	0.501081i	−0.386046	−	0.0303825i
$273$	1.03630	−	2.50184i	0.0627195	−	0.151418i
$274$	−16.7690	+	10.2761i	−1.01305	+	0.620800i
$275$	0.129827	+	9.71971i	0.00782885	+	0.586120i
$276$	17.8039	+	15.2059i	1.07167	+	0.915289i
$277$	8.84880	+	17.3667i	0.531673	+	1.04347i	0.988115	+	0.153714i	$0.0491234\pi$
$277$	8.84880	+	17.3667i	0.531673	+	1.04347i	−0.456443	+	0.889753i	$0.650877\pi$
$278$			28.6291i			1.71706i
$279$	19.8593	−	10.1188i	1.18895	−	0.605799i
$280$	0.0473430	+	0.0260995i	0.00282928	+	0.00155975i
$281$	−18.0650	−	4.33702i	−1.07767	−	0.258725i	−0.344508	−	0.938783i	$-0.611954\pi$
$281$	−18.0650	−	4.33702i	−1.07767	−	0.258725i	−0.733158	+	0.680058i	$0.761954\pi$
$282$	−15.3692	−	47.3016i	−0.915223	−	2.81677i
$283$	−20.7098	−	10.5522i	−1.23107	−	0.627260i	−0.287291	−	0.957843i	$-0.592755\pi$
$283$	−20.7098	−	10.5522i	−1.23107	−	0.627260i	−0.943777	+	0.330583i	$0.892755\pi$
$284$	−1.06573	+	2.57291i	−0.0632397	+	0.152674i
$285$	−23.6659	+	4.87196i	−1.40185	+	0.288590i
$286$		−	15.4533i		−	0.913771i
$287$	1.34403	+	0.924140i	0.0793356	+	0.0545503i
$288$	22.8676	−	22.8676i	1.34749	−	1.34749i
$289$	−2.27855	−	14.3862i	−0.134032	−	0.846248i
$290$	−10.0885	+	27.9188i	−0.592416	+	1.63945i
$291$	17.4496	−	5.66972i	1.02291	−	0.332365i
$292$	−15.6484	+	5.08449i	−0.915755	+	0.297547i
$293$	−1.34192	−	2.18982i	−0.0783959	−	0.127931i	0.811039	−	0.584991i	$-0.198902\pi$
$293$	−1.34192	−	2.18982i	−0.0783959	−	0.127931i	−0.889435	+	0.457061i	$0.848902\pi$
$294$	−35.6443	+	8.55744i	−2.07882	+	0.499080i
$295$	−4.11642	+	14.9779i	−0.239667	+	0.872046i
$296$	−0.291671	−	0.291671i	−0.0169530	−	0.0169530i
$297$	−4.92394	+	2.50887i	−0.285716	+	0.145579i
$298$	3.55111	+	45.1212i	0.205711	+	2.61380i
$299$	17.9797	+	1.41503i	1.03979	+	0.0818336i
$300$	3.71725	−	25.6856i	0.214615	−	1.48296i
$301$	−0.820239	−	1.98023i	−0.0472778	−	0.114139i
$302$	0.188838	−	2.39941i	0.0108664	−	0.138071i
$303$	−4.82900	+	30.4891i	−0.277419	+	1.75155i
$304$	1.30519	+	16.5841i	0.0748581	+	0.951162i
$305$	5.30437	+	25.7664i	0.303727	+	1.47538i
$306$	−10.7619	−	6.59493i	−0.615219	−	0.377007i
$307$	−14.2763	+	10.3724i	−0.814793	+	0.591982i	−0.915216	−	0.402963i	$-0.867980\pi$
$307$	−14.2763	+	10.3724i	−0.814793	+	0.591982i	0.100423	+	0.994945i	$0.467980\pi$
$308$	0.782173	−	0.568282i	0.0445685	−	0.0323809i
$309$	−16.3593	−	10.0250i	−0.930647	−	0.570301i
$310$	−20.3358	−	13.3924i	−1.15500	−	0.760636i
$311$	−2.23563	−	28.4063i	−0.126771	−	1.61078i	−0.650918	−	0.759148i	$-0.725616\pi$
$311$	−2.23563	−	28.4063i	−0.126771	−	1.61078i	0.524147	−	0.851628i	$-0.324384\pi$
$312$	0.157834	−	0.996524i	0.00893559	−	0.0564171i
$313$	0.532426	−	6.76511i	0.0300945	−	0.382387i	−0.963364	−	0.268196i	$-0.913573\pi$
$313$	0.532426	−	6.76511i	0.0300945	−	0.382387i	0.993459	−	0.114191i	$-0.0364275\pi$
$314$	1.79730	+	4.33906i	0.101427	+	0.244867i
$315$	1.30053	+	1.91852i	0.0732765	+	0.108096i
$316$	−10.0732	−	0.792776i	−0.566661	−	0.0445972i
$317$	1.79471	+	22.8040i	0.100801	+	1.28080i	0.814425	+	0.580269i	$0.197053\pi$
$317$	1.79471	+	22.8040i	0.100801	+	1.28080i	−0.713624	+	0.700529i	$0.752947\pi$
$318$	62.5833	−	31.8878i	3.50950	−	1.78818i
$319$	−9.18006	−	9.18006i	−0.513985	−	0.513985i
$320$	−16.4159	−	4.51164i	−0.917677	−	0.252208i
$321$	−46.1406	+	11.0774i	−2.57532	+	0.618279i
$322$	1.19355	+	1.94770i	0.0665141	+	0.108541i
$323$	6.03083	−	1.95953i	0.335564	−	0.109031i
$324$	−8.63299	+	2.80503i	−0.479610	+	0.155835i
$325$	−9.31305	−	17.6898i	−0.516595	−	0.981252i
$326$	0.157839	+	0.996559i	0.00874192	+	0.0551943i
$327$	−20.5414	+	20.5414i	−1.13594	+	1.13594i
$328$	0.567307	+	0.217905i	0.0313243	+	0.0120318i
$329$		−	2.39690i		−	0.132145i
$330$	19.1903	+	12.6380i	1.05639	+	0.695700i
$331$	2.78533	−	6.72438i	0.153095	−	0.369605i	−0.828660	−	0.559752i	$-0.810896\pi$
$331$	2.78533	−	6.72438i	0.153095	−	0.369605i	0.981756	+	0.190147i	$0.0608964\pi$
$332$	−18.6452	−	9.50020i	−1.02329	−	0.521391i
$333$	−5.46490	−	16.8192i	−0.299475	−	0.921688i
$334$	2.02854	+	0.487010i	0.110997	+	0.0266480i
$335$	14.5209	−	4.20021i	0.793363	−	0.229482i
$336$	2.47009	−	1.25857i	0.134754	−	0.0686608i
$337$		−	20.6416i		−	1.12442i	−0.826995	−	0.562209i	$-0.809952\pi$
$337$		−	20.6416i		−	1.12442i	0.826995	−	0.562209i	$-0.190048\pi$
$338$	2.69539	+	5.29000i	0.146610	+	0.287738i
$339$	−38.2301	−	32.6516i	−2.07637	−	1.77339i
$340$	−0.221950	+	6.80759i	−0.0120369	+	0.369193i
$341$	9.07969	−	5.56404i	0.491693	−	0.301310i
$342$	−12.5815	+	30.3744i	−0.680329	+	1.64246i
$343$	−3.53879	−	0.278509i	−0.191077	−	0.0150381i
$344$	−0.469400	−	0.646074i	−0.0253083	−	0.0348340i
$345$	−16.4614	+	21.1705i	−0.886255	+	1.13978i
$346$	−17.8604	−	12.9764i	−0.960183	−	0.697614i
$347$	−3.25584	−	13.5616i	−0.174783	−	0.728023i	−0.989056	−	0.147541i	$-0.952864\pi$
$347$	−3.25584	−	13.5616i	−0.174783	−	0.728023i	0.814273	−	0.580482i	$-0.197136\pi$
$348$	20.3741	+	28.0425i	1.09216	+	1.50324i
$349$	1.40033	−	8.84132i	0.0749578	−	0.473265i	−0.921444	−	0.388511i	$-0.872990\pi$
$349$	1.40033	−	8.84132i	0.0749578	−	0.473265i	0.996402	−	0.0847541i	$-0.0270105\pi$
$350$	1.11931	−	2.27126i	0.0598296	−	0.121404i
$351$	6.68042	−	9.19482i	0.356575	−	0.490783i
$352$	10.0346	−	11.7490i	0.534848	−	0.626226i
$353$	18.4671	+	2.92490i	0.982904	+	0.155677i	0.627146	−	0.778901i	$-0.284223\pi$
$353$	18.4671	+	2.92490i	0.982904	+	0.155677i	0.355758	+	0.934578i	$0.384223\pi$
$354$	23.8466	+	27.9208i	1.26743	+	1.48397i
$355$	−2.99990	−	1.08402i	−0.159218	−	0.0575337i
$356$	−4.16825	−	6.80196i	−0.220917	−	0.360503i
$357$	−0.686301	−	0.803555i	−0.0363229	−	0.0425286i
$358$	5.92219	−	0.466086i	0.312997	−	0.0246334i
$359$	−6.06879	+	18.6778i	−0.320298	+	0.985777i	0.653220	+	0.757168i	$0.273418\pi$
$359$	−6.06879	+	18.6778i	−0.320298	+	0.985777i	−0.973518	+	0.228609i	$0.926582\pi$
$360$	0.638036	+	0.581941i	0.0336274	+	0.0306710i
$361$	1.12714	+	2.21214i	0.0593233	+	0.116429i
$362$	15.6230	+	9.57379i	0.821127	+	0.503187i
$363$	16.3686	−	10.0307i	0.859127	−	0.526474i
$364$	−0.902705	+	1.77166i	−0.0473146	+	0.0928601i
$365$	−6.64074	−	17.6369i	−0.347592	−	0.923158i
$366$	57.4516	+	23.7972i	3.00304	+	1.24390i
$367$	−7.01050	+	9.64912i	−0.365945	+	0.503680i	−0.951793	−	0.306741i	$-0.900761\pi$
$367$	−7.01050	+	9.64912i	−0.365945	+	0.503680i	0.585848	+	0.810421i	$0.300761\pi$
$368$	13.0556	+	13.0556i	0.680569	+	0.680569i
$369$	17.4302	+	19.3663i	0.907381	+	1.00817i
$370$	−13.0194	+	14.2744i	−0.676846	+	0.742089i
$371$	3.34332	−	0.529530i	0.173577	−	0.0274918i
$372$	−26.2675	+	10.8804i	−1.36191	+	0.564120i
$373$	−4.26056	+	8.36182i	−0.220603	+	0.432958i	−0.974610	−	0.223908i	$-0.928118\pi$
$373$	−4.26056	+	8.36182i	−0.220603	+	0.432958i	0.754007	+	0.656866i	$0.228118\pi$
$374$	−5.37313	−	2.73775i	−0.277838	−	0.141565i
$375$	29.5841	+	2.90185i	1.52772	+	0.149851i
$376$	−0.208477	−	0.868370i	−0.0107514	−	0.0447828i
$377$	25.3934	+	8.25081i	1.30783	+	0.424939i
$378$	1.43952			0.0740410
$379$	14.4294	+	4.68840i	0.741189	+	0.240827i	0.655185	−	0.755468i	$-0.272590\pi$
$379$	14.4294	+	4.68840i	0.741189	+	0.240827i	0.0860032	+	0.996295i	$0.472590\pi$
$380$	17.6043	−	2.20291i	0.903079	−	0.113007i
$381$	−2.04085	+	25.9315i	−0.104556	+	1.32851i
$382$	15.2785	+	3.66804i	0.781715	+	0.187673i
$383$	20.3283	+	8.42025i	1.03873	+	0.430255i	0.835855	−	0.548951i	$-0.184972\pi$
$383$	20.3283	+	8.42025i	1.03873	+	0.430255i	0.202872	+	0.979205i	$0.434972\pi$
$384$	1.53463	−	1.31070i	0.0783138	−	0.0668863i
$385$	0.691358	+	0.865039i	0.0352349	+	0.0440865i
$386$	−9.80807	+	0.771912i	−0.499217	+	0.0392893i
$387$	−5.35609	−	33.8170i	−0.272265	−	1.71902i
$388$	−13.0998	+	3.14499i	−0.665044	+	0.159663i
$389$	−24.7255	−	3.91613i	−1.25363	−	0.198556i	−0.505920	−	0.862580i	$-0.668847\pi$
$389$	−24.7255	−	3.91613i	−1.25363	−	0.198556i	−0.747711	+	0.664025i	$0.768847\pi$
$390$	−46.9655	−	5.24094i	−2.37819	−	0.265385i
$391$	3.67735	−	6.00089i	0.185972	−	0.303478i
$392$	−0.650104	+	0.102966i	−0.0328352	+	0.00520059i
$393$	−15.1084	−	12.9038i	−0.762117	−	0.650909i
$394$	33.5952	−	24.4083i	1.69250	−	1.22967i
$395$	0.377125	−	11.5671i	0.0189752	−	0.582003i
$396$	14.2684	−	5.91017i	0.717014	−	0.296997i
$397$	−1.08181	+	4.50604i	−0.0542942	+	0.226152i	−0.992920	−	0.118786i	$-0.962100\pi$
$397$	−1.08181	+	4.50604i	−0.0542942	+	0.226152i	0.938626	+	0.344937i	$0.112100\pi$
$398$	−11.2153	+	9.57878i	−0.562172	+	0.480141i
$399$	−1.78765	+	2.09307i	−0.0894943	+	0.104784i
$400$	4.51148	−	19.9626i	0.225574	−	0.998128i
$401$	22.3924	−	22.3924i	1.11823	−	1.11823i	0.126224	−	0.992002i	$-0.459714\pi$
$401$	22.3924	−	22.3924i	1.11823	−	1.11823i	0.992002	−	0.126224i	$-0.0402857\pi$
$402$	11.0419	−	33.9836i	0.550721	−	1.69495i
$403$	−11.4431	+	18.6734i	−0.570022	+	0.930191i
$404$	5.29133	−	22.0400i	0.263254	−	1.09653i
$405$	−3.66359	−	9.72999i	−0.182045	−	0.483487i
$406$	1.04503	+	3.21628i	0.0518641	+	0.159621i
$407$	−3.23341	−	7.80614i	−0.160274	−	0.386936i
$408$	−0.318531	−	0.231426i	−0.0157696	−	0.0114573i
$409$	−14.1123			−0.697806			−0.348903	−	0.937159i	$-0.613446\pi$
$409$	−14.1123			−0.697806			−0.348903	+	0.937159i	$0.613446\pi$
$410$	8.97497	−	27.0123i	0.443242	−	1.33404i
$411$	−26.3028			−1.29742
$412$	11.3975	+	8.28079i	0.561516	+	0.407965i
$413$	0.677178	+	1.63485i	0.0333217	+	0.0804458i
$414$	11.2760	+	34.7039i	0.554184	+	1.70560i
$415$	9.88889	−	21.8330i	0.485426	−	1.07174i
$416$	−7.41816	+	30.8989i	−0.363705	+	1.51494i
$417$	−20.0057	+	32.6463i	−0.979682	+	1.59870i
$418$	−4.85396	+	14.9389i	−0.237415	+	0.730688i
$419$	4.80702	−	4.80702i	0.234838	−	0.234838i	−0.579871	−	0.814709i	$-0.696897\pi$
$419$	4.80702	−	4.80702i	0.234838	−	0.234838i	0.814709	+	0.579871i	$0.196897\pi$
$420$	−1.46185	−	2.56991i	−0.0713308	−	0.125399i
$421$	9.44412	−	11.0576i	0.460278	−	0.538917i	−0.480923	−	0.876763i	$-0.659698\pi$
$421$	9.44412	−	11.0576i	0.460278	−	0.538917i	0.941201	+	0.337846i	$0.109698\pi$
$422$	33.4096	−	28.5345i	1.62635	−	1.38904i
$423$	8.93819	−	37.2302i	0.434590	−	1.81020i
$424$	1.16519	−	0.482638i	0.0565867	−	0.0234390i
$425$	−7.80069	+	0.104194i	−0.378389	+	0.00505417i
$426$	−6.10007	+	4.43196i	−0.295550	+	0.214729i
$427$	2.27883	+	1.94631i	0.110281	+	0.0941885i
$428$	34.4133	−	5.45053i	1.66343	−	0.263461i
$429$	10.7986	−	17.6216i	0.521359	−	0.850781i
$430$	−29.2190	+	23.3525i	−1.40907	+	1.12616i
$431$	−1.11591	−	0.176743i	−0.0537516	−	0.00851342i	0.129501	−	0.991579i	$-0.458663\pi$
$431$	−1.11591	−	0.176743i	−0.0537516	−	0.00851342i	−0.183252	+	0.983066i	$0.558663\pi$
$432$	11.3137	−	2.71618i	0.544330	−	0.130682i
$433$	−1.10104	−	6.95170i	−0.0529126	−	0.334077i	−0.999917	−	0.0128575i	$-0.995907\pi$
$433$	−1.10104	−	6.95170i	−0.0529126	−	0.334077i	0.947005	−	0.321220i	$-0.104093\pi$
$434$	−2.76535	+	0.217638i	−0.132741	+	0.0104470i
$435$	−31.0134	+	24.7866i	−1.48698	+	1.18843i
$436$	16.2198	−	13.8530i	0.776787	−	0.663439i
$437$	−16.9368	−	7.01547i	−0.810199	−	0.335595i
$438$	−43.3176	−	10.3996i	−2.06979	−	0.496913i
$439$	0.317206	−	4.03049i	0.0151394	−	0.192365i	−0.984697	−	0.174275i	$-0.944242\pi$
$439$	0.317206	−	4.03049i	0.0151394	−	0.192365i	0.999836	−	0.0180893i	$-0.00575831\pi$
$440$	0.325711	+	0.253261i	0.0155277	+	0.0120738i
$441$	−26.8386	−	8.72040i	−1.27803	−	0.415257i
$442$	12.4022			0.589914
$443$	−7.32337	−	2.37951i	−0.347944	−	0.113054i	0.129831	−	0.991536i	$-0.458557\pi$
$443$	−7.32337	−	2.37951i	−0.347944	−	0.113054i	−0.477775	+	0.878482i	$0.658557\pi$
$444$	5.26629	+	21.9357i	0.249927	+	1.04102i
$445$	7.56328	−	5.12701i	0.358534	−	0.243044i
$446$	27.3307	+	13.9257i	1.29415	+	0.659401i
$447$	−27.4807	+	53.9340i	−1.29979	+	2.55099i
$448$	−1.79181	+	0.742193i	−0.0846552	+	0.0350653i
$449$	−2.01649	+	0.319380i	−0.0951639	+	0.0150725i	−0.203835	−	0.979005i	$-0.565341\pi$
$449$	−2.01649	+	0.319380i	−0.0951639	+	0.0150725i	0.108671	+	0.994078i	$0.465341\pi$
$450$	25.8555	−	31.1047i	1.21884	−	1.46629i
$451$	9.02797	+	8.57081i	0.425110	+	0.403583i
$452$	26.1036	+	26.1036i	1.22781	+	1.22781i
$453$	1.89201	−	2.60413i	0.0888946	−	0.122353i
$454$	−22.6766	−	9.39296i	−1.06427	−	0.440833i
$455$	−2.07456	−	0.939638i	−0.0972569	−	0.0440509i
$456$	−0.465595	+	0.913781i	−0.0218035	+	0.0427917i
$457$	18.0537	−	11.0633i	0.844515	−	0.517519i	−0.0316680	−	0.999498i	$-0.510082\pi$
$457$	18.0537	−	11.0633i	0.844515	−	0.517519i	0.876183	+	0.481979i	$0.160082\pi$
$458$	−7.04281	−	4.31584i	−0.329089	−	0.201666i
$459$	−2.01353	−	3.95177i	−0.0939835	−	0.184453i
$460$	13.2695	−	14.5486i	0.618693	−	0.678331i
$461$	−0.0406541	+	0.125120i	−0.00189345	+	0.00582744i	−0.951999	−	0.306102i	$-0.900975\pi$
$461$	−0.0406541	+	0.125120i	−0.00189345	+	0.00582744i	0.950105	+	0.311929i	$0.100975\pi$
$462$	2.60959	−	0.205379i	0.121409	−	0.00955511i
$463$	−17.3668	−	20.3340i	−0.807106	−	0.944999i	0.192233	−	0.981349i	$-0.438427\pi$
$463$	−17.3668	−	20.3340i	−0.807106	−	0.944999i	−0.999339	+	0.0363498i	$0.988427\pi$
$464$	14.2819	+	23.3060i	0.663022	+	1.08195i
$465$	−13.8308	−	29.4820i	−0.641390	−	1.36719i
$466$	−16.8280	−	19.7031i	−0.779544	−	0.912728i
$467$	16.3814	+	2.59455i	0.758039	+	0.120062i	0.523477	−	0.852040i	$-0.324635\pi$
$467$	16.3814	+	2.59455i	0.758039	+	0.120062i	0.234562	+	0.972101i	$0.424635\pi$
$468$	−20.6281	+	24.1524i	−0.953532	+	1.11644i
$469$	1.01219	−	1.39316i	0.0467385	−	0.0643301i
$470$	−40.1813	+	11.6225i	−1.85342	+	0.536107i
$471$	−0.982590	+	6.20383i	−0.0452754	+	0.285857i
$472$	0.387530	+	0.533389i	0.0178375	+	0.0245512i
$473$	−3.81876	−	15.9063i	−0.175587	−	0.731371i
$474$	−22.1326	−	16.0803i	−1.01659	−	0.738592i
$475$	3.44664	+	20.0263i	0.158142	+	0.918869i
$476$	0.456083	+	0.627744i	0.0209045	+	0.0287726i
$477$	53.9054	+	4.24244i	2.46816	+	0.194248i
$478$	10.0852	−	24.3478i	0.461286	−	1.11364i
$479$	−13.4486	+	8.24130i	−0.614481	+	0.376554i	−0.794638	−	0.607083i	$-0.792339\pi$
$479$	−13.4486	+	8.24130i	−0.614481	+	0.376554i	0.180157	+	0.983638i	$0.442339\pi$
$480$	−32.3044	−	34.4819i	−1.47449	−	1.57387i
$481$	13.2136	+	11.2855i	0.602487	+	0.514573i
$482$	5.15548	+	10.1182i	0.234826	+	0.460871i
$483$			3.05504i			0.139009i
$484$	−12.5597	+	6.39951i	−0.570897	+	0.290887i
$485$	−4.28756	−	14.8229i	−0.194688	−	0.673074i
$486$	−40.3824	−	9.69497i	−1.83178	−	0.439773i
$487$	−5.28838	−	16.2760i	−0.239639	−	0.737534i	−0.996472	−	0.0839254i	$-0.973254\pi$
$487$	−5.28838	−	16.2760i	−0.239639	−	0.737534i	0.756833	−	0.653609i	$-0.226746\pi$
$488$	0.994883	+	0.506918i	0.0450362	+	0.0229471i
$489$	−0.516396	+	1.24669i	−0.0233522	+	0.0563773i
$490$	6.21625	+	30.1959i	0.280822	+	1.36411i
$491$		−	5.58324i		−	0.251968i	−0.992032	−	0.125984i	$-0.959791\pi$
$491$		−	5.58324i		−	0.251968i	0.992032	−	0.125984i	$-0.0402088\pi$
$492$	−20.2274	−	26.3723i	−0.911924	−	1.18896i
$493$	7.36759	−	7.36759i	0.331819	−	0.331819i
$494$	−5.05359	−	31.9071i	−0.227372	−	1.43557i
$495$	7.51286	+	16.0145i	0.337678	+	0.719798i
$496$	−21.3232	+	6.92833i	−0.957440	+	0.311091i
$497$	−0.345592	+	0.112290i	−0.0155019	+	0.00503688i
$498$	−29.6032	−	48.3080i	−1.32655	−	2.16474i
$499$	14.5141	−	3.48453i	0.649741	−	0.155989i	0.104839	−	0.994489i	$-0.466567\pi$
$499$	14.5141	−	3.48453i	0.649741	−	0.155989i	0.544901	+	0.838500i	$0.316567\pi$
$500$	−21.4885	−	3.82851i	−0.960997	−	0.171216i
$501$	1.97287	+	1.97287i	0.0881411	+	0.0881411i
$502$	7.41177	−	3.77649i	0.330803	−	0.168553i
$503$	0.941611	+	11.9643i	0.0419844	+	0.533462i	0.981564	+	0.191132i	$0.0612159\pi$
$503$	0.941611	+	11.9643i	0.0419844	+	0.533462i	−0.939580	+	0.342330i	$0.888784\pi$
$504$	0.0980743	+	0.00771861i	0.00436858	+	0.000343814i
$505$	25.4958	+	4.89466i	1.13455	+	0.217809i
$506$	6.67164	+	16.1068i	0.296591	+	0.716033i
$507$	−0.622986	+	7.91578i	−0.0276678	+	0.351552i
$508$	2.98783	−	18.8644i	0.132564	−	0.836973i
$509$	−1.50538	−	19.1276i	−0.0667246	−	0.847817i	−0.935663	−	0.352896i	$-0.885197\pi$
$509$	−1.50538	−	19.1276i	−0.0667246	−	0.847817i	0.868938	−	0.494921i	$-0.164803\pi$
$510$	−10.1428	+	15.4015i	−0.449132	+	0.681989i
$511$	−1.83054	−	1.12175i	−0.0809782	−	0.0496235i
$512$	−25.6896	+	18.6646i	−1.13533	+	0.824866i
$513$	−9.34622	+	6.79043i	−0.412646	+	0.299805i
$514$	−10.8713	−	6.66194i	−0.479512	−	0.293846i
$515$	−8.87498	+	13.4763i	−0.391078	+	0.593837i
$516$	3.42672	+	43.5406i	0.150853	+	1.91677i
$517$	2.86166	−	18.0678i	0.125856	−	0.794622i
$518$	−0.172684	+	2.19415i	−0.00758728	+	0.0964055i
$519$	−11.2988	−	27.2778i	−0.495964	−	1.19736i
$520$	−0.833319	−	0.159980i	−0.0365434	−	0.00701558i
$521$	−25.0247	−	1.96949i	−1.09635	−	0.0862848i	−0.482644	−	0.875817i	$-0.660323\pi$
$521$	−25.0247	−	1.96949i	−1.09635	−	0.0862848i	−0.613709	+	0.789532i	$0.710323\pi$
$522$	4.23843	+	53.8544i	0.185511	+	2.35714i
$523$	−25.8058	+	13.1487i	−1.12841	+	0.574953i	−0.915580	−	0.402137i	$-0.868268\pi$
$523$	−25.8058	+	13.1487i	−1.12841	+	0.574953i	−0.212828	+	0.977090i	$0.568268\pi$
$524$	10.3160	+	10.3160i	0.450657	+	0.450657i
$525$	2.86349	−	1.80780i	0.124973	−	0.0788987i
$526$	38.3082	−	9.19698i	1.67032	−	0.401007i
$527$	4.46550	+	7.28703i	0.194520	+	0.317428i
$528$	20.1221	−	6.53808i	0.875704	−	0.284533i
$529$	2.52333	−	0.819881i	0.109710	−	0.0356470i
$530$	−25.0887	−	53.4793i	−1.08978	−	2.32299i
$531$	4.42191	+	27.9189i	0.191895	+	1.21158i
$532$	1.42915	−	1.42915i	0.0619614	−	0.0619614i
$533$	−24.5458	−	7.27638i	−1.06320	−	0.315175i
$534$		−	21.5991i		−	0.934686i
$535$	8.04677	+	39.0878i	0.347892	+	1.68991i
$536$	0.245531	−	0.592764i	0.0106053	−	0.0256035i
$537$	7.07887	+	3.60686i	0.305476	+	0.155648i
$538$	−12.3083	−	37.8811i	−0.530649	−	1.63317i
$539$	−13.1101	−	3.14746i	−0.564693	−	0.135571i
$540$	−3.44795	−	11.9202i	−0.148376	−	0.512965i
$541$	−25.8245	+	13.1583i	−1.11028	+	0.565718i	−0.910245	−	0.414070i	$-0.864107\pi$
$541$	−25.8245	+	13.1583i	−1.11028	+	0.565718i	−0.200039	+	0.979788i	$0.564107\pi$
$542$		−	51.3950i		−	2.20760i
$543$	11.1251	+	21.8343i	0.477426	+	0.937000i
$544$	9.42936	+	8.05344i	0.404281	+	0.345288i
$545$	16.7035	+	17.8293i	0.715497	+	0.763725i
$546$	−4.59021	+	2.81289i	−0.196443	+	0.120380i
$547$	−6.70272	+	16.1818i	−0.286588	+	0.691884i	−0.999960	−	0.00890082i	$-0.997167\pi$
$547$	−6.70272	+	16.1818i	−0.286588	+	0.691884i	0.713373	+	0.700785i	$0.247167\pi$
$548$	19.2538	+	1.51531i	0.822481	+	0.0647307i
$549$	28.1385	+	38.7293i	1.20092	+	1.65293i
$550$	11.1490	−	15.7844i	0.475395	−	0.673049i
$551$	−21.9566	−	15.9524i	−0.935383	−	0.679596i
$552$	0.265721	+	1.10681i	0.0113098	+	0.0471088i
$553$	−0.774951	−	1.06663i	−0.0329543	−	0.0453577i
$554$	6.06168	−	38.2719i	0.257536	−	1.62602i
$555$	−24.8210	+	7.17952i	−1.05359	+	0.304754i
$556$	16.5250	−	22.7447i	0.700816	−	0.964591i
$557$	15.3351	−	17.9551i	0.649767	−	0.760780i	−0.333539	−	0.942736i	$-0.608243\pi$
$557$	15.3351	−	17.9551i	0.649767	−	0.760780i	0.983307	+	0.181956i	$0.0582429\pi$
$558$	−43.7649	−	6.93168i	−1.85272	−	0.293442i
$559$	21.8492	+	25.5821i	0.924121	+	1.08201i
$560$	−0.990220	−	2.11076i	−0.0418444	−	0.0891960i
$561$	−4.21397	−	6.87657i	−0.177914	−	0.290329i
$562$	23.9868	+	28.0850i	1.01182	+	1.18469i
$563$	7.27853	−	0.572833i	0.306753	−	0.0241420i	0.0758517	−	0.997119i	$-0.475832\pi$
$563$	7.27853	−	0.572833i	0.306753	−	0.0241420i	0.230902	+	0.972977i	$0.425832\pi$
$564$	−15.0927	+	46.4505i	−0.635517	+	1.95592i
$565$	−28.4935	+	31.2401i	−1.19873	+	1.31428i
$566$	20.9780	+	41.1716i	0.881770	+	1.73057i
$567$	−1.00988	−	0.618854i	−0.0424109	−	0.0259894i
$568$	−0.115438	+	0.0707403i	−0.00484365	+	0.00296820i
$569$	−20.6925	+	40.6112i	−0.867473	+	1.70251i	−0.170571	+	0.985345i	$0.554561\pi$
$569$	−20.6925	+	40.6112i	−0.867473	+	1.70251i	−0.696902	+	0.717166i	$0.745439\pi$
$570$	43.7561	+	19.8186i	1.83274	+	0.830111i
$571$	19.9990	+	8.28385i	0.836931	+	0.346668i	0.759643	−	0.650340i	$-0.225374\pi$
$571$	19.9990	+	8.28385i	0.836931	+	0.346668i	0.0772885	+	0.997009i	$0.475374\pi$
$572$	−8.91978	+	12.2770i	−0.372955	+	0.513328i
$573$	14.8591	+	14.8591i	0.620749	+	0.620749i
$574$	−1.08178	−	3.05689i	−0.0451527	−	0.127592i
$575$	17.3441	+	14.4171i	0.723298	+	0.601235i
$576$	−30.5993	+	4.84646i	−1.27497	+	0.201936i
$577$	38.5593	−	15.9718i	1.60524	−	0.664914i	0.613100	−	0.790006i	$-0.289922\pi$
$577$	38.5593	−	15.9718i	1.60524	−	0.664914i	0.992145	+	0.125092i	$0.0399224\pi$
$578$	−13.1461	+	25.8006i	−0.546804	+	1.07316i
$579$	−11.7237	−	5.97353i	−0.487221	−	0.248251i
$580$	24.1299	−	16.3572i	1.00194	−	0.679197i
$581$	−0.637411	−	2.65501i	−0.0264442	−	0.110148i
$582$	−34.6903	−	11.2716i	−1.43796	−	0.467222i
$583$	25.8342			1.06994
$584$	−0.760752	−	0.247183i	−0.0314801	−	0.0102285i
$585$	−28.7195	−	22.3313i	−1.18741	−	0.923285i
$586$	−0.400598	+	5.09007i	−0.0165485	+	0.210269i
$587$	−9.73929	−	2.33820i	−0.401984	−	0.0965078i	0.0274119	−	0.999624i	$-0.491273\pi$
$587$	−9.73929	−	2.33820i	−0.401984	−	0.0965078i	−0.429396	+	0.903116i	$0.641273\pi$
$588$	33.2575	+	13.7757i	1.37151	+	0.568100i
$589$	16.9277	−	14.4576i	0.697493	−	0.595715i
$590$	24.1228	−	19.2795i	0.993120	−	0.793724i
$591$	55.3654	−	4.35735i	2.27743	−	0.179238i
$592$	2.78288	+	17.5704i	0.114376	+	0.722140i
$593$	4.34281	−	1.04262i	0.178338	−	0.0428151i	−0.143293	−	0.989680i	$-0.545769\pi$
$593$	4.34281	−	1.04262i	0.178338	−	0.0428151i	0.321631	+	0.946865i	$0.395769\pi$
$594$	10.8511	+	1.71865i	0.445227	+	0.0705170i
$595$	−0.694249	+	0.554859i	−0.0284614	+	0.0227470i
$596$	23.2232	−	37.8968i	0.951258	−	1.55231i
$597$	−19.4825	+	3.08573i	−0.797367	+	0.126291i
$598$	−27.2642	−	23.2858i	−1.11491	−	0.952227i
$599$	−19.8880	+	14.4495i	−0.812603	+	0.590391i	−0.914584	−	0.404396i	$-0.867482\pi$
$599$	−19.8880	+	14.4495i	−0.812603	+	0.590391i	0.101981	+	0.994786i	$0.467482\pi$
$600$	0.880174	−	0.904005i	0.0359330	−	0.0369059i
$601$	35.0530	−	14.5194i	1.42984	−	0.592260i	0.472530	−	0.881314i	$-0.343341\pi$
$601$	35.0530	−	14.5194i	1.42984	−	0.592260i	0.957313	+	0.289054i	$0.0933407\pi$
$602$	−0.994738	+	4.14338i	−0.0405425	+	0.168872i
$603$	20.9172	−	17.8650i	0.851813	−	0.727517i
$604$	−1.53499	+	1.79724i	−0.0624578	+	0.0731287i
$605$	−7.98285	−	14.0337i	−0.324549	−	0.570553i
$606$	43.3943	−	43.3943i	1.76277	−	1.76277i
$607$	−9.11557	+	28.0548i	−0.369990	+	1.13871i	0.576808	+	0.816880i	$0.304298\pi$
$607$	−9.11557	+	28.0548i	−0.369990	+	1.13871i	−0.946797	+	0.321831i	$0.895702\pi$
$608$	16.8768	−	27.5404i	0.684443	−	1.11691i
$609$	−1.05583	+	4.39783i	−0.0427842	+	0.178209i
$610$	21.5776	−	47.6397i	0.873652	−	1.92887i
$611$	11.6258	+	35.7805i	0.470328	+	1.44752i
$612$	4.74329	+	11.4513i	0.191736	+	0.462892i
$613$	15.1960	+	11.0406i	0.613762	+	0.445925i	0.850737	−	0.525591i	$-0.176156\pi$
$613$	15.1960	+	11.0406i	0.613762	+	0.445925i	−0.236975	+	0.971516i	$0.576156\pi$
$614$	35.0818			1.41579
$615$	29.1102	−	24.5310i	1.17383	−	0.989184i
$616$	0.0470021			0.00189377
$617$	−33.2361	−	24.1475i	−1.33804	−	0.972140i	−0.999514	−	0.0311818i	$-0.990073\pi$
$617$	−33.2361	−	24.1475i	−1.33804	−	0.972140i	−0.338522	−	0.940958i	$-0.609927\pi$
$618$	14.5969	+	35.2400i	0.587173	+	1.41756i
$619$	−6.73731	−	20.7353i	−0.270795	−	0.833422i	−0.990301	−	0.138936i	$-0.955632\pi$
$619$	−6.73731	−	20.7353i	−0.270795	−	0.833422i	0.719506	−	0.694486i	$-0.244368\pi$
$620$	8.42578	+	22.3777i	0.338388	+	0.898711i
$621$	−2.99325	+	12.4678i	−0.120115	+	0.500315i
$622$	−29.5981	+	48.2997i	−1.18678	+	1.93664i
$623$	0.321661	−	0.989972i	0.0128871	−	0.0396624i
$624$	−30.7685	+	30.7685i	−1.23173	+	1.23173i
$625$	3.24995	−	24.7879i	0.129998	−	0.991514i
$626$	−8.76159	+	10.2585i	−0.350183	+	0.410012i
$627$	−15.9742	+	13.6433i	−0.637948	+	0.544859i
$628$	1.07666	−	4.48463i	0.0429636	−	0.178956i
$629$	6.26493	−	2.59502i	0.249799	−	0.103470i
$630$	0.150150	−	4.60536i	0.00598212	−	0.183482i
$631$	−36.7927	+	26.7314i	−1.46469	+	1.06416i	−0.482584	+	0.875850i	$0.660302\pi$
$631$	−36.7927	+	26.7314i	−1.46469	+	1.06416i	−0.982109	+	0.188312i	$0.939698\pi$
$632$	−0.373529	−	0.319024i	−0.0148582	−	0.0126901i
$633$	58.0370	−	9.19216i	2.30677	−	0.365356i
$634$	23.7607	−	38.7739i	0.943658	−	1.53991i
$635$	21.7412	+	2.42613i	0.862773	+	0.0962780i
$636$	−68.1259	−	10.7901i	−2.70137	−	0.427855i
$637$	26.9625	−	6.47313i	1.06829	−	0.256475i
$638$	4.03753	+	25.4920i	0.159847	+	1.00924i
$639$	−5.78671	+	0.455424i	−0.228919	+	0.0180163i
$640$	−1.05967	−	1.32588i	−0.0418872	−	0.0524099i
$641$	−19.9209	+	17.0141i	−0.786829	+	0.672015i	−0.949186	−	0.314717i	$-0.898091\pi$
$641$	−19.9209	+	17.0141i	−0.786829	+	0.672015i	0.162357	+	0.986732i	$0.448091\pi$
$642$	87.1545	+	36.1006i	3.43971	+	1.42478i
$643$	31.9140	+	7.66187i	1.25856	+	0.302154i	0.807249	−	0.590210i	$-0.200955\pi$
$643$	31.9140	+	7.66187i	1.25856	+	0.302154i	0.451315	+	0.892365i	$0.350955\pi$
$644$	0.176001	−	2.23630i	0.00693541	−	0.0881227i
$645$	−49.6373	+	6.21137i	−1.95447	+	0.244572i
$646$	−11.9895	−	3.89561i	−0.471719	−	0.153271i
$647$	27.5116			1.08159			0.540795	−	0.841154i	$-0.318123\pi$
$647$	27.5116			1.08159			0.540795	+	0.841154i	$0.318123\pi$
$648$	−0.419694	−	0.136367i	−0.0164871	−	0.00535700i
$649$	3.15271	+	13.1320i	0.123755	+	0.515476i
$650$	−5.69245	+	39.3339i	−0.223276	+	1.54280i
$651$	−3.30546	−	1.68422i	−0.129551	−	0.0660097i
$652$	0.449826	−	0.882834i	0.0176166	−	0.0345744i
$653$	12.8616	−	5.32745i	0.503313	−	0.208479i	−0.116556	−	0.993184i	$-0.537185\pi$
$653$	12.8616	−	5.32745i	0.503313	−	0.208479i	0.619870	+	0.784705i	$0.287185\pi$
$654$	57.0411	−	9.03442i	2.23048	−	0.353274i
$655$	−11.2605	+	12.3460i	−0.439985	+	0.482396i
$656$	−14.2700	−	21.9839i	−0.557150	−	0.858328i
$657$	−24.2501	−	24.2501i	−0.946085	−	0.946085i
$658$	−2.80086	+	3.85505i	−0.109189	+	0.150285i
$659$	−10.2662	−	4.25242i	−0.399916	−	0.165651i	0.173655	−	0.984807i	$-0.444442\pi$
$659$	−10.2662	−	4.25242i	−0.399916	−	0.165651i	−0.573571	+	0.819156i	$0.694442\pi$
$660$	−7.95119	−	21.1173i	−0.309499	−	0.821988i
$661$	−5.47204	+	10.7395i	−0.212838	+	0.417717i	−0.972600	−	0.232483i	$-0.925315\pi$
$661$	−5.47204	+	10.7395i	−0.212838	+	0.417717i	0.759763	+	0.650200i	$0.225315\pi$
$662$	−12.3374	+	7.56039i	−0.479508	+	0.293843i
$663$	14.1425	+	8.66653i	0.549249	+	0.336580i
$664$	−0.461854	−	0.906439i	−0.0179234	−	0.0351767i
$665$	1.71037	+	1.56000i	0.0663252	+	0.0604940i
$666$	−10.8644	+	33.4371i	−0.420986	+	1.29566i
$667$	−30.0294	+	2.36336i	−1.16274	+	0.0915097i
$668$	−1.33049	−	1.55780i	−0.0514782	−	0.0602732i
$669$	21.4346	+	34.9781i	0.828709	+	1.35233i
$670$	−28.2628	−	10.2128i	−1.09189	−	0.394554i
$671$	14.8542	+	17.3920i	0.573438	+	0.671410i
$672$	−5.31647	−	0.842047i	−0.205087	−	0.0324827i
$673$	−19.9638	+	23.3746i	−0.769548	+	0.901024i	−0.997355	−	0.0726817i	$-0.976844\pi$
$673$	−19.9638	+	23.3746i	−0.769548	+	0.901024i	0.227808	+	0.973706i	$0.426844\pi$
$674$	−24.1204	+	33.1989i	−0.929083	+	1.27877i
$675$	13.4573	−	4.57214i	0.517972	−	0.175982i
$676$	0.912057	−	5.75850i	0.0350791	−	0.221481i
$677$	−9.90429	−	13.6321i	−0.380653	−	0.523924i	0.575105	−	0.818080i	$-0.304961\pi$
$677$	−9.90429	−	13.6321i	−0.380653	−	0.523924i	−0.955757	+	0.294156i	$0.904961\pi$
$678$	23.3328	+	97.1883i	0.896093	+	3.73249i
$679$	−1.42213	−	1.03324i	−0.0545765	−	0.0396521i
$680$	−0.203258	+	0.261404i	−0.00779460	+	0.0100244i
$681$	−19.2949	−	26.5571i	−0.739380	−	1.01767i
$682$	−21.1051	−	1.66101i	−0.808155	−	0.0636032i
$683$	15.9397	−	38.4817i	0.609914	−	1.47246i	−0.253180	−	0.967419i	$-0.581476\pi$
$683$	15.9397	−	38.4817i	0.609914	−	1.47246i	0.863094	−	0.505044i	$-0.168524\pi$
$684$	27.5279	−	16.8691i	1.05256	−	0.645007i
$685$	−0.720834	+	22.1092i	−0.0275417	+	0.844750i
$686$	5.36617	+	4.58314i	0.204881	+	0.174985i
$687$	−5.01519	−	9.84286i	−0.191341	−	0.375528i
$688$			34.4412i			1.31306i
$689$	−47.3401	+	24.1210i	−1.80351	+	0.918936i
$690$	51.2142	−	14.8138i	1.94969	−	0.563953i
$691$	−19.9744	−	4.79542i	−0.759860	−	0.182426i	−0.165042	−	0.986287i	$-0.552776\pi$
$691$	−19.9744	−	4.79542i	−0.759860	−	0.182426i	−0.594818	+	0.803860i	$0.702776\pi$
$692$	6.69934	+	20.6184i	0.254671	+	0.783795i
$693$	1.79552	+	0.914861i	0.0682060	+	0.0347527i
$694$	−10.6106	+	25.6163i	−0.402774	+	0.972382i
$695$	26.8931	+	17.7108i	1.02011	+	0.671807i
$696$			1.68512i			0.0638743i
$697$	−6.87862	+	7.24552i	−0.260546	+	0.274444i
$698$	−12.5836	+	12.5836i	−0.476296	+	0.476296i
$699$	−5.42102	−	34.2270i	−0.205042	−	1.29458i
$700$	−2.20024	+	1.15835i	−0.0831612	+	0.0437815i
$701$	−2.66291	+	0.865233i	−0.100577	+	0.0326794i	−0.358873	−	0.933386i	$-0.616839\pi$
$701$	−2.66291	+	0.865233i	−0.100577	+	0.0326794i	0.258296	+	0.966066i	$0.416839\pi$
$702$	−21.4889	+	6.98217i	−0.811047	+	0.263525i
$703$	−9.22897	−	15.0603i	−0.348077	−	0.568010i
$704$	−14.3928	+	3.45540i	−0.542449	+	0.130230i
$705$	−53.9411	−	14.8248i	−2.03154	−	0.558334i
$706$	−26.2837	−	26.2837i	−0.989200	−	0.989200i
$707$	2.63517	−	1.34269i	0.0991059	−	0.0504970i
$708$	−2.82905	−	35.9465i	−0.106322	−	1.35095i
$709$	−5.87181	−	0.462122i	−0.220520	−	0.0173553i	−0.0322825	−	0.999479i	$-0.510278\pi$
$709$	−5.87181	−	0.462122i	−0.220520	−	0.0173553i	−0.188238	+	0.982123i	$0.560278\pi$
$710$	3.55818	+	5.24897i	0.133536	+	0.196990i
$711$	−8.05954	−	19.4574i	−0.302256	−	0.729711i
$712$	0.0304287	−	0.386634i	0.00114036	−	0.0144897i
$713$	3.86513	−	24.4034i	0.144750	−	0.913916i
$714$	0.164830	+	2.09436i	0.00616861	+	0.0783796i
$715$	−14.5162	−	9.55982i	−0.542875	−	0.357517i
$716$	−4.97397	−	3.04806i	−0.185886	−	0.113911i
$717$	28.5143	−	20.7168i	1.06489	−	0.773685i
$718$	31.5864	−	22.9488i	1.17879	−	0.856443i
$719$	−29.7988	−	18.2608i	−1.11131	−	0.681011i	−0.159346	−	0.987223i	$-0.550938\pi$
$719$	−29.7988	−	18.2608i	−1.11131	−	0.681011i	−0.951963	+	0.306212i	$0.900938\pi$
$720$	−7.50959	−	36.4784i	−0.279866	−	1.35947i
$721$	0.144226	+	1.83257i	0.00537127	+	0.0682485i
$722$	0.772125	−	4.87500i	0.0287355	−	0.181429i
$723$	−1.19159	+	15.1405i	−0.0443156	+	0.563083i
$724$	−6.88578	−	16.6237i	−0.255908	−	0.617817i
$725$	19.9848	+	26.7481i	0.742218	+	0.993398i
$726$	−38.0476	−	2.99441i	−1.41208	−	0.111133i
$727$	−3.26258	−	41.4550i	−0.121002	−	1.53748i	−0.695230	−	0.718787i	$-0.744698\pi$
$727$	−3.26258	−	41.4550i	−0.121002	−	1.53748i	0.574228	−	0.818696i	$-0.305302\pi$
$728$	−0.0861295	+	0.0438852i	−0.00319217	+	0.00162649i
$729$	−29.4108	−	29.4108i	−1.08929	−	1.08929i
$730$	−9.92870	+	36.1262i	−0.367478	+	1.33709i
$731$	12.7658	−	3.06480i	0.472160	−	0.113356i
$732$	−31.9071	−	52.0676i	−1.17932	−	1.92447i
$733$	3.31573	−	1.07735i	0.122469	−	0.0397927i	−0.247141	−	0.968979i	$-0.579491\pi$
$733$	3.31573	−	1.07735i	0.122469	−	0.0397927i	0.369610	+	0.929187i	$0.379491\pi$
$734$	22.5507	−	7.32715i	0.832360	−	0.270450i
$735$	−14.0120	+	38.7768i	−0.516841	+	1.43030i
$736$	−5.60810	−	35.4082i	−0.206717	−	1.30516i
$737$	9.29317	−	9.29317i	0.342318	−	0.342318i
$738$	−5.40364	−	51.5156i	−0.198911	−	1.89632i
$739$			29.7205i			1.09329i	0.837366	+	0.546643i	$0.184094\pi$
$739$			29.7205i			1.09329i	−0.837366	+	0.546643i	$0.815906\pi$
$740$	18.5827	−	3.82551i	0.683113	−	0.140628i
$741$	16.5336	−	39.9156i	0.607376	−	1.46634i
$742$	−5.99600	−	3.05511i	−0.220120	−	0.112157i
$743$	3.03536	+	9.34186i	0.111356	+	0.342720i	0.991170	−	0.132600i	$-0.0423325\pi$
$743$	3.03536	+	9.34186i	0.111356	+	0.342720i	−0.879813	+	0.475319i	$0.842332\pi$
$744$	−1.34402	−	0.322671i	−0.0492743	−	0.0118297i
$745$	44.5819	+	24.5774i	1.63335	+	0.900447i
$746$	16.6235	−	8.47011i	0.608631	−	0.310113i
$747$		−	43.6163i		−	1.59584i
$748$	2.68849	+	5.27645i	0.0983008	+	0.192926i
$749$	3.45701	+	2.95256i	0.126316	+	0.107884i
$750$	−44.1907	−	39.2372i	−1.61362	−	1.43274i
$751$	42.5382	−	26.0674i	1.55224	−	0.951214i	0.559781	−	0.828641i	$-0.310885\pi$
$751$	42.5382	−	26.0674i	1.55224	−	0.951214i	0.992459	−	0.122573i	$-0.0391146\pi$
$752$	−14.7390	+	35.5830i	−0.537474	+	1.29758i
$753$	11.0907	+	0.872860i	0.404169	+	0.0318088i
$754$	−31.2001	−	42.9432i	−1.13624	−	1.56390i
$755$	−2.13709	−	1.66173i	−0.0777768	−	0.0604765i
$756$	−1.14364	−	0.830906i	−0.0415939	−	0.0302197i
$757$	8.46924	+	35.2769i	0.307820	+	1.28216i	0.885018	+	0.465557i	$0.154146\pi$
$757$	8.46924	+	35.2769i	0.307820	+	1.28216i	−0.577198	+	0.816604i	$0.695854\pi$
$758$	−17.7290	−	24.4018i	−0.643945	−	0.886314i
$759$	−3.64742	+	23.0289i	−0.132393	+	0.835895i
$760$	0.755333	+	0.416405i	0.0273988	+	0.0151046i
$761$	18.4146	−	25.3455i	0.667527	−	0.918772i	−0.332174	−	0.943218i	$-0.607782\pi$
$761$	18.4146	−	25.3455i	0.667527	−	0.918772i	0.999701	+	0.0244457i	$0.00778208\pi$
$762$	33.5843	−	39.3221i	1.21663	−	1.42449i
$763$	2.74896	+	0.435392i	0.0995190	+	0.0157623i
$764$	−10.0209	−	11.7330i	−0.362544	−	0.424485i
$765$	−12.8527	+	6.02955i	−0.464689	+	0.217999i
$766$	−22.8556	−	37.2970i	−0.825808	−	1.34760i
$767$	−18.0384	−	21.1202i	−0.651328	−	0.762607i
$768$	−44.3610	+	3.49128i	−1.60074	+	0.125981i
$769$	−1.46433	+	4.50675i	−0.0528051	+	0.162517i	−0.973981	−	0.226628i	$-0.927230\pi$
$769$	−1.46433	+	4.50675i	−0.0528051	+	0.162517i	0.921176	+	0.389146i	$0.127230\pi$
$770$	−0.101118	−	2.19916i	−0.00364405	−	0.0792522i
$771$	−7.74145	−	15.1934i	−0.278801	−	0.547179i
$772$	8.23768	+	5.04806i	0.296481	+	0.181684i
$773$	−24.8638	+	15.2366i	−0.894290	+	0.548022i	−0.892030	−	0.451976i	$-0.850719\pi$
$773$	−24.8638	+	15.2366i	−0.894290	+	0.548022i	−0.00225999	+	0.999997i	$0.500719\pi$
$774$	−30.9019	+	60.6484i	−1.11075	+	2.17996i
$775$	−25.1606	+	10.8178i	−0.903794	+	0.388586i
$776$	−0.605093	−	0.250638i	−0.0217216	−	0.00899736i
$777$	−1.73016	+	2.38136i	−0.0620691	+	0.0854309i
$778$	35.1911	+	35.1911i	1.26166	+	1.26166i
$779$	21.4433	+	14.7442i	0.768287	+	0.528265i
$780$	34.2871	+	31.2726i	1.22768	+	1.11974i
$781$	−2.73914	+	0.433837i	−0.0980141	+	0.0155239i
$782$	−12.9267	+	5.35442i	−0.462258	+	0.191474i
$783$	−8.61777	+	16.9133i	−0.307974	+	0.604433i
$784$	25.2928	+	12.8873i	0.903315	+	0.460262i
$785$	5.18780	+	0.995949i	0.185160	+	0.0355469i
$786$	9.22105	+	38.4084i	0.328904	+	1.36998i
$787$	12.4759	+	4.05366i	0.444717	+	0.144497i	0.522811	−	0.852449i	$-0.324883\pi$
$787$	12.4759	+	4.05366i	0.444717	+	0.144497i	−0.0780936	+	0.996946i	$0.524883\pi$
$788$	−40.7788			−1.45268
$789$	50.1102	+	16.2818i	1.78397	+	0.579647i
$790$	−14.1231	+	18.1632i	−0.502477	+	0.646219i
$791$	−0.377925	+	4.80200i	−0.0134375	+	0.170739i
$792$	0.730069	+	0.175274i	0.0259419	+	0.00622809i
$793$	−43.4583	−	18.0010i	−1.54325	−	0.639235i
$794$	7.00539	−	5.98316i	0.248612	−	0.212335i
$795$	8.76159	−	78.5150i	0.310742	−	2.78464i
$796$	14.4391	−	1.13638i	0.511780	−	0.0402779i
$797$	0.0116354	+	0.0734630i	0.000412147	+	0.00260219i	0.987894	−	0.155133i	$-0.0495807\pi$
$797$	0.0116354	+	0.0734630i	0.000412147	+	0.00260219i	−0.987481	+	0.157735i	$0.949581\pi$
$798$	5.32098	−	1.27745i	0.188361	−	0.0452214i
$799$	14.5006	+	2.29667i	0.512994	+	0.0812502i
$800$	−29.8696	+	26.2090i	−1.05605	+	0.926628i
$801$	8.68793	−	14.1774i	0.306973	−	0.500935i
$802$	−62.1812	+	9.84854i	−2.19570	+	0.347764i
$803$	−12.4593	−	10.6413i	−0.439680	−	0.375522i
$804$	−28.3880	+	20.6251i	−1.00117	+	0.727391i
$805$	2.56796	+	0.0837240i	0.0905087	+	0.00295088i
$806$	40.2251	−	16.6618i	1.41687	−	0.586886i
$807$	12.4354	−	51.7973i	0.437748	−	1.82335i
$808$	0.837910	−	0.715643i	0.0294776	−	0.0251762i
$809$	−21.7821	+	25.5036i	−0.765819	+	0.896658i	−0.997090	−	0.0762308i	$-0.975711\pi$
$809$	−21.7821	+	25.5036i	−0.765819	+	0.896658i	0.231272	+	0.972889i	$0.425711\pi$
$810$	−5.47750	+	19.9303i	−0.192460	+	0.700278i
$811$	−18.6543	+	18.6543i	−0.655040	+	0.655040i	−0.954202	−	0.299162i	$-0.903293\pi$
$811$	−18.6543	+	18.6543i	−0.655040	+	0.655040i	0.299162	+	0.954202i	$0.403293\pi$
$812$	1.02623	−	3.15841i	0.0360136	−	0.110838i
$813$	35.9142	−	58.6066i	1.25957	−	2.05542i
$814$	−3.92129	+	16.3334i	−0.137441	+	0.572484i
$815$	1.03377	+	0.468230i	0.0362115	+	0.0164014i
$816$	5.24723	+	16.1493i	0.183690	+	0.565339i
$817$	−13.0865	−	31.5936i	−0.457839	−	1.10532i
$818$	22.6974	+	16.4906i	0.793597	+	0.576582i
$819$	−4.14440			−0.144817
$820$	−22.7220	+	16.2798i	−0.793487	+	0.568514i
$821$	−6.88229			−0.240194			−0.120097	−	0.992762i	$-0.538320\pi$
$821$	−6.88229			−0.240194			−0.120097	+	0.992762i	$0.538320\pi$
$822$	42.3041	+	30.7357i	1.47553	+	1.07203i
$823$	−2.61201	−	6.30595i	−0.0910489	−	0.219812i	0.871795	−	0.489872i	$-0.162956\pi$
$823$	−2.61201	−	6.30595i	−0.0910489	−	0.219812i	−0.962843	+	0.270060i	$0.912956\pi$
$824$	0.211645	+	0.651375i	0.00737299	+	0.0226917i
$825$	23.7433	−	10.2084i	0.826637	−	0.355412i
$826$	0.821242	−	3.42072i	0.0285747	−	0.119022i
$827$	21.3007	−	34.7595i	0.740697	−	1.20871i	−0.231110	−	0.972928i	$-0.574236\pi$
$827$	21.3007	−	34.7595i	0.740697	−	1.20871i	0.971807	−	0.235779i	$-0.0757643\pi$
$828$	11.0731	−	34.0795i	0.384816	−	1.18434i
$829$	2.43289	−	2.43289i	0.0844977	−	0.0844977i	−0.663595	−	0.748092i	$-0.730970\pi$
$829$	2.43289	−	2.43289i	0.0844977	−	0.0844977i	0.748092	+	0.663595i	$0.230970\pi$
$830$	−41.4174	+	23.5595i	−1.43762	+	0.817764i
$831$	33.6562	−	39.4063i	1.16752	−	1.36699i
$832$	23.1480	−	19.7702i	0.802511	−	0.685409i
$833$	2.52604	−	10.5217i	0.0875221	−	0.364556i
$834$	70.3244	−	29.1293i	2.43514	−	1.00867i
$835$	1.71239	−	1.60426i	0.0592597	−	0.0555176i
$836$	12.4792	−	9.06666i	0.431602	−	0.313577i
$837$	−11.8396	−	10.1120i	−0.409238	−	0.349522i
$838$	−13.3485	+	2.11420i	−0.461117	+	0.0730338i
$839$	23.4499	−	38.2667i	0.809580	−	1.32111i	−0.134339	−	0.990935i	$-0.542891\pi$
$839$	23.4499	−	38.2667i	0.809580	−	1.32111i	0.943918	−	0.330179i	$-0.107109\pi$
$840$	0.0159407	−	0.142849i	0.000550005	−	0.00492874i
$841$	−15.4021	−	2.43945i	−0.531107	−	0.0841191i
$842$	−28.1107	+	6.74878i	−0.968758	+	0.232578i
$843$	7.72718	+	48.7875i	0.266138	+	1.68033i
$844$	−43.0130	+	3.38519i	−1.48057	+	0.116523i
$845$	6.63666	+	0.740594i	0.228308	+	0.0254772i
$846$	−57.8805	+	49.4347i	−1.98997	+	1.69960i
$847$	−1.69927	−	0.703862i	−0.0583877	−	0.0241850i
$848$	−52.8892	−	12.6976i	−1.81622	−	0.436036i
$849$	−4.84864	+	61.6079i	−0.166405	+	2.11438i
$850$	12.6680	+	8.94779i	0.434508	+	0.306907i
$851$	−18.6446	−	6.05800i	−0.639129	−	0.207666i
$852$	7.40444			0.253672
$853$	−10.1250	−	3.28983i	−0.346675	−	0.112641i	0.130504	−	0.991448i	$-0.458341\pi$
$853$	−10.1250	−	3.28983i	−0.346675	−	0.112641i	−0.477179	+	0.878806i	$0.658341\pi$
$854$	−1.39083	−	5.79324i	−0.0475934	−	0.198241i
$855$	20.7493	+	30.6090i	0.709610	+	1.04681i
$856$	1.50924	+	0.768998i	0.0515849	+	0.0262838i
$857$	−5.05814	+	9.92716i	−0.172783	+	0.339105i	−0.961117	−	0.276142i	$-0.910944\pi$
$857$	−5.05814	+	9.92716i	−0.172783	+	0.339105i	0.788334	+	0.615248i	$0.210944\pi$
$858$	−37.9593	+	15.7233i	−1.29591	+	0.536783i
$859$	30.6981	−	4.86210i	1.04741	−	0.165893i	0.391069	−	0.920361i	$-0.372105\pi$
$859$	30.6981	−	4.86210i	1.04741	−	0.165893i	0.656336	+	0.754468i	$0.272105\pi$
$860$	36.6926	−	1.68714i	1.25121	−	0.0575311i
$861$	0.902539	−	4.24175i	0.0307584	−	0.144559i
$862$	1.58825	+	1.58825i	0.0540959	+	0.0540959i
$863$	1.93316	−	2.66077i	0.0658056	−	0.0905737i	−0.774846	−	0.632150i	$-0.782172\pi$
$863$	1.93316	−	2.66077i	0.0658056	−	0.0905737i	0.840651	+	0.541577i	$0.182172\pi$
$864$	−20.8718	−	8.64539i	−0.710073	−	0.294122i
$865$	−23.2385	+	8.74987i	−0.790131	+	0.297504i
$866$	−6.35244	+	12.4674i	−0.215865	+	0.423658i
$867$	−33.0198	+	20.2346i	−1.12141	+	0.687203i
$868$	2.32259	+	1.42328i	0.0788338	+	0.0483094i
$869$	−4.56813	−	8.96546i	−0.154963	−	0.304132i
$870$	78.8443	−	3.62530i	2.67307	−	0.122909i
$871$	−8.35247	+	25.7063i	−0.283013	+	0.871024i
$872$	1.03379	−	0.0813608i	0.0350084	−	0.00275522i
$873$	−18.2365	−	21.3522i	−0.617213	−	0.722663i
$874$	19.0425	+	31.0746i	0.644124	+	1.05111i
$875$	−1.44110	−	2.45650i	−0.0487179	−	0.0830447i
$876$	28.4113	+	33.2654i	0.959930	+	1.12393i
$877$	−54.3894	−	8.61443i	−1.83660	−	0.290889i	−0.860700	−	0.509113i	$-0.829974\pi$
$877$	−54.3894	−	8.61443i	−1.83660	−	0.290889i	−0.975899	+	0.218224i	$0.929974\pi$
$878$	−5.21994	+	6.11177i	−0.176165	+	0.206262i
$879$	−4.01369	+	5.52437i	−0.135378	+	0.186332i
$880$	−4.94423	−	17.0932i	−0.166670	−	0.576210i
$881$	5.16219	−	32.5928i	0.173918	−	1.09808i	−0.734067	−	0.679077i	$-0.762380\pi$
$881$	5.16219	−	32.5928i	0.173918	−	1.09808i	0.907986	−	0.419001i	$-0.137620\pi$
$882$	32.9758	+	45.3873i	1.11035	+	1.52827i
$883$	11.6603	+	48.5688i	0.392402	+	1.63447i	0.723107	+	0.690736i	$0.242713\pi$
$883$	11.6603	+	48.5688i	0.392402	+	1.63447i	−0.330705	+	0.943734i	$0.607287\pi$
$884$	−9.85309	−	7.15869i	−0.331395	−	0.240773i
$885$	40.9799	−	5.12802i	1.37752	−	0.172376i
$886$	8.99801	+	12.3847i	0.302294	+	0.416072i
$887$	21.3932	+	1.68369i	0.718315	+	0.0565326i	0.432348	−	0.901707i	$-0.357685\pi$
$887$	21.3932	+	1.68369i	0.718315	+	0.0565326i	0.285967	+	0.958239i	$0.407685\pi$
$888$	−0.419692	+	1.01323i	−0.0140840	+	0.0340017i
$889$	2.12490	−	1.30214i	0.0712667	−	0.0436723i
$890$	−18.1555	−	0.591929i	−0.608573	−	0.0198415i
$891$	−6.87361	−	5.87061i	−0.230274	−	0.196673i
$892$	−13.6751	−	26.8390i	−0.457877	−	0.898635i
$893$		−	38.2413i		−	1.27970i
$894$	107.222	−	54.6325i	3.58605	−	1.82718i
$895$	3.22580	−	5.85140i	0.107827	−	0.195591i
$896$	−0.188015	−	0.0451385i	−0.00628115	−	0.00150797i
$897$	−14.8180	−	45.6050i	−0.494758	−	1.52271i
$898$	3.61642	+	1.84266i	0.120682	+	0.0614903i
$899$	13.9979	−	33.7938i	0.466854	−	1.12709i
$900$	−38.4952	+	9.78744i	−1.28317	+	0.326248i
$901$			20.7336i			0.690735i
$902$	−4.50485	−	24.3343i	−0.149995	−	0.810245i
$903$	−4.02966	+	4.02966i	−0.134099	+	0.134099i
$904$	0.280750	+	1.77258i	0.00933759	+	0.0589552i
$905$	18.6581	−	8.75304i	0.620215	−	0.290961i
$906$	−6.08604	+	1.97747i	−0.202195	+	0.0656972i
$907$	35.7559	−	11.6178i	1.18726	−	0.385763i	0.352198	−	0.935926i	$-0.385434\pi$
$907$	35.7559	−	11.6178i	1.18726	−	0.385763i	0.835057	+	0.550163i	$0.185434\pi$
$908$	12.5940	+	20.5515i	0.417946	+	0.682025i
$909$	45.9383	−	11.0288i	1.52368	−	0.365802i
$910$	2.23862	+	3.93546i	0.0742095	+	0.130459i
$911$	−8.00097	−	8.00097i	−0.265084	−	0.265084i	0.562032	−	0.827116i	$-0.310020\pi$
$911$	−8.00097	−	8.00097i	−0.265084	−	0.265084i	−0.827116	+	0.562032i	$0.810020\pi$
$912$	39.4090	−	20.0799i	1.30496	−	0.664912i
$913$	−1.63498	−	20.7744i	−0.0541101	−	0.687534i
$914$	−41.9644	−	3.30267i	−1.38806	−	0.109243i
$915$	57.8953	−	39.2462i	1.91396	−	1.29744i
$916$	3.10409	+	7.49394i	0.102562	+	0.247607i
$917$	−0.149355	+	1.89773i	−0.00493212	+	0.0626686i
$918$	−1.37932	+	8.70871i	−0.0455245	+	0.287430i
$919$	−2.53525	−	32.2134i	−0.0836302	−	1.06262i	−0.885351	−	0.464923i	$-0.846082\pi$
$919$	−2.53525	−	32.2134i	−0.0836302	−	1.06262i	0.801721	−	0.597699i	$-0.203918\pi$
$920$	0.937626	−	0.193024i	0.0309126	−	0.00636380i
$921$	40.0044	+	24.5147i	1.31819	+	0.807787i
$922$	0.211593	−	0.153732i	0.00696846	−	0.00506288i
$923$	4.61430	−	3.35248i	0.151881	−	0.110348i
$924$	−2.19176	−	1.34311i	−0.0721037	−	0.0441852i
$925$	5.35464	+	21.0604i	0.176059	+	0.692462i
$926$	4.17102	+	52.9979i	0.137068	+	1.74162i
$927$	−4.59355	+	29.0025i	−0.150872	+	0.952568i
$928$	4.16406	−	52.9094i	0.136692	−	1.73684i
$929$	13.1005	+	31.6274i	0.429814	+	1.03766i	0.979346	+	0.202190i	$0.0648059\pi$
$929$	13.1005	+	31.6274i	0.429814	+	1.03766i	−0.549532	+	0.835473i	$0.685194\pi$
$930$	−12.2059	+	63.5791i	−0.400246	+	2.08484i
$931$	−28.0984	−	2.21139i	−0.920888	−	0.0724754i
$932$	1.99640	+	25.3666i	0.0653942	+	0.830912i
$933$	−67.5025	+	34.3942i	−2.20993	+	1.12602i
$934$	−23.3151	−	23.3151i	−0.762894	−	0.762894i
$935$	−5.89570	+	3.35366i	−0.192810	+	0.109677i
$936$	−1.50147	+	0.360472i	−0.0490772	+	0.0117824i
$937$	4.37594	+	7.14089i	0.142956	+	0.233283i	0.916102	−	0.400945i	$-0.131318\pi$
$937$	4.37594	+	7.14089i	0.142956	+	0.233283i	−0.773146	+	0.634228i	$0.781318\pi$
$938$	−3.25591	+	1.05791i	−0.106309	+	0.0345419i
$939$	−17.1595	+	5.57546i	−0.559979	+	0.181948i
$940$	38.6311	+	13.9594i	1.26001	+	0.455305i
$941$	1.93229	+	12.2000i	0.0629908	+	0.397708i	0.998959	+	0.0456230i	$0.0145273\pi$
$941$	1.93229	+	12.2000i	0.0629908	+	0.397708i	−0.935968	+	0.352085i	$0.885473\pi$
$942$	8.82974	−	8.82974i	0.287688	−	0.287688i
$943$	28.7253	−	3.01308i	0.935423	−	0.0981194i
$944$		−	28.4342i		−	0.925453i
$945$	0.890527	−	1.35223i	0.0289689	−	0.0439881i
$946$	−12.4451	+	30.0452i	−0.404626	+	0.976853i
$947$	−17.5490	−	8.94165i	−0.570265	−	0.290565i	0.144984	−	0.989434i	$-0.453687\pi$
$947$	−17.5490	−	8.94165i	−0.570265	−	0.290565i	−0.715249	+	0.698869i	$0.753687\pi$
$948$	8.30180	+	25.5503i	0.269630	+	0.829836i
$949$	32.7668	+	7.86662i	1.06366	+	0.255361i
$950$	17.8580	−	36.2368i	0.579390	−	1.17568i
$951$	54.1895	−	27.6109i	1.75721	−	0.895345i
$952$			0.0377222i			0.00122258i
$953$	−7.45276	−	14.6269i	−0.241419	−	0.473811i	0.738225	−	0.674554i	$-0.235664\pi$
$953$	−7.45276	−	14.6269i	−0.241419	−	0.473811i	−0.979644	+	0.200744i	$0.935664\pi$
$954$	−81.7412	−	69.8136i	−2.64647	−	2.26030i
$955$	12.8973	−	12.0829i	0.417347	−	0.390992i
$956$	−22.0661	+	13.5221i	−0.713669	+	0.437337i
$957$	−13.2094	+	31.8903i	−0.426999	+	1.03087i
$958$	31.2602	+	2.46023i	1.00997	+	0.0794866i
$959$	1.48123	+	2.03874i	0.0478316	+	0.0658345i
$960$	5.62036	+	44.9144i	0.181396	+	1.44961i
$961$	−0.806513	−	0.585966i	−0.0260166	−	0.0189021i
$962$	−8.06460	−	33.5915i	−0.260013	−	1.08303i
$963$	42.6863	+	58.7526i	1.37555	+	1.89328i
$964$	1.74449	−	11.0143i	0.0561864	−	0.354747i
$965$	−5.34243	+	9.69084i	−0.171979	+	0.311959i
$966$	3.56992	−	4.91357i	0.114860	−	0.158091i
$967$	−34.1868	+	40.0276i	−1.09937	+	1.28720i	−0.144724	+	0.989472i	$0.546229\pi$
$967$	−34.1868	+	40.0276i	−1.09937	+	1.28720i	−0.954650	+	0.297730i	$0.903771\pi$
$968$	−0.676849	−	0.107202i	−0.0217547	−	0.00344561i
$969$	−10.9496	−	12.8203i	−0.351751	−	0.411848i
$970$	−10.4252	+	28.8506i	−0.334733	+	0.926337i
$971$	17.5575	+	28.6513i	0.563448	+	0.919464i	0.999806	+	0.0196910i	$0.00626824\pi$
$971$	17.5575	+	28.6513i	0.563448	+	0.919464i	−0.436358	+	0.899773i	$0.643732\pi$
$972$	26.4862	+	31.0114i	0.849547	+	0.994691i
$973$	3.65704	−	0.287816i	0.117239	−	0.00922695i
$974$	−10.5135	+	32.3571i	−0.336873	+	1.03679i
$975$	−33.9773	+	40.8754i	−1.08814	+	1.30906i
$976$	−21.8621	−	42.9067i	−0.699788	−	1.37341i
$977$	−31.7585	−	19.4616i	−1.01604	−	0.622632i	−0.0883942	−	0.996086i	$-0.528174\pi$
$977$	−31.7585	−	19.4616i	−1.01604	−	0.622632i	−0.927649	+	0.373454i	$0.878174\pi$
$978$	2.28734	−	1.40169i	0.0731412	−	0.0448210i
$979$	3.60661	−	7.07838i	0.115268	−	0.226226i
$980$	12.4908	−	27.5775i	0.399004	−	0.880932i
$981$	41.0751	+	17.0139i	1.31143	+	0.543211i
$982$	−6.52420	+	8.97979i	−0.208196	+	0.286557i
$983$	7.71006	+	7.71006i	0.245913	+	0.245913i	0.819291	−	0.573378i	$-0.194367\pi$
$983$	7.71006	+	7.71006i	0.245913	+	0.245913i	−0.573378	+	0.819291i	$0.694367\pi$
$984$	−0.0419590	−	1.61524i	−0.00133761	−	0.0514920i
$985$	−2.14534	−	46.6577i	−0.0683562	−	1.48664i
$986$	−20.4589	+	3.24038i	−0.651545	+	0.103195i
$987$	−5.88773	+	2.43878i	−0.187408	+	0.0776271i
$988$	−14.4022	+	28.2659i	−0.458195	+	0.899259i
$989$	−33.8177	−	17.2310i	−1.07534	−	0.547913i
$990$	6.63018	−	34.5359i	0.210721	−	1.09762i
$991$	1.75164	+	7.29609i	0.0556426	+	0.231768i	0.993261	−	0.115898i	$-0.0369744\pi$
$991$	1.75164	+	7.29609i	0.0556426	+	0.231768i	−0.937619	+	0.347666i	$0.886974\pi$
$992$	41.4023	+	13.4524i	1.31452	+	0.427115i
$993$	−19.3517			−0.614108
$994$	0.687048	+	0.223235i	0.0217918	+	0.00708059i
$995$	2.05984	+	16.4609i	0.0653012	+	0.521846i
$996$	−4.36528	+	55.4661i	−0.138319	+	1.75751i
$997$	−56.8531	−	13.6492i	−1.80056	−	0.432275i	−0.812066	−	0.583566i	$-0.801657\pi$
$997$	−56.8531	−	13.6492i	−1.80056	−	0.432275i	−0.988489	+	0.151291i	$0.951657\pi$
$998$	−27.4155	−	11.3559i	−0.867824	−	0.359464i
$999$	−9.39408	+	8.02330i	−0.297216	+	0.253846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	205.2.y.a.112.4	yes	304
5.3	odd	4		205.2.bb.a.153.4	yes	304
41.26	odd	40		205.2.bb.a.67.4	yes	304
205.108	even	40	inner	205.2.y.a.108.4	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
205.2.y.a.108.4	✓	304	205.108	even	40	inner
205.2.y.a.112.4	yes	304	1.1	even	1	trivial
205.2.bb.a.67.4	yes	304	41.26	odd	40
205.2.bb.a.153.4	yes	304	5.3	odd	4

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:	\( N \)	\(=\)	\( 205 = 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	205.y (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60835 - 1.16853i) q^{2} +(-1.01747 - 2.45639i) q^{3} +(0.603281 + 1.85671i) q^{4} +(-2.09264 + 0.787934i) q^{5} +(-1.23393 + 5.13969i) q^{6} +(-0.133098 + 0.217196i) q^{7} +(-0.0293286 + 0.0902643i) q^{8} +(-2.87730 + 2.87730i) q^{9} +(4.28643 + 1.17805i) q^{10} +(-1.26260 + 1.47832i) q^{11} +(3.94699 - 3.37105i) q^{12} +(0.933385 - 3.88783i) q^{13} +(0.467869 - 0.193798i) q^{14} +(4.06468 + 4.33866i) q^{15} +(3.31147 - 2.40592i) q^{16} +(-1.18644 - 1.01332i) q^{17} +(7.98994 - 1.26548i) q^{18} +(-2.12351 + 3.46525i) q^{19} +(-2.72542 - 3.41009i) q^{20} +(0.668942 + 0.105950i) q^{21} +(3.75817 - 0.902256i) q^{22} +(0.705636 + 4.45521i) q^{23} +(0.251566 - 0.0197986i) q^{24} +(3.75832 - 3.29773i) q^{25} +(-6.04427 + 5.16230i) q^{26} +(2.62618 + 1.08780i) q^{27} +(-0.483565 - 0.116094i) q^{28} +(-0.523941 + 6.65730i) q^{29} +(-1.46756 - 11.7278i) q^{30} +(-5.20942 - 1.69264i) q^{31} -7.94759 q^{32} +(4.91599 + 1.59730i) q^{33} +(0.724118 + 3.01617i) q^{34} +(0.107390 - 0.559386i) q^{35} +(-7.07814 - 3.60649i) q^{36} +(-1.97309 + 3.87240i) q^{37} +(7.46461 - 3.09194i) q^{38} +(-10.4997 + 1.66299i) q^{39} +(-0.00974785 - 0.212000i) q^{40} +(0.336449 - 6.39428i) q^{41} +(-0.952086 - 0.952086i) q^{42} +(-4.94576 + 6.80726i) q^{43} +(-3.50651 - 1.45244i) q^{44} +(3.75405 - 8.28830i) q^{45} +(4.07116 - 7.99009i) q^{46} +(-8.02287 + 4.91642i) q^{47} +(-9.27922 - 5.68632i) q^{48} +(3.14847 + 6.17923i) q^{49} +(-9.89820 + 0.912175i) q^{50} +(-1.28194 + 3.94540i) q^{51} +(7.78166 - 0.612430i) q^{52} +(-8.63012 - 10.1046i) q^{53} +(-2.95269 - 4.81835i) q^{54} +(1.47736 - 4.08844i) q^{55} +(-0.0157015 - 0.0183840i) q^{56} +(10.6726 + 1.69038i) q^{57} +(8.62196 - 10.0950i) q^{58} +(4.08316 - 5.61998i) q^{59} +(-5.60348 + 10.1644i) q^{60} +(1.84041 - 11.6199i) q^{61} +(6.40066 + 8.80975i) q^{62} +(-0.241976 - 1.00790i) q^{63} +(6.15955 + 4.47518i) q^{64} +(1.11011 + 8.87129i) q^{65} +(-6.04013 - 8.31352i) q^{66} +(-6.73932 - 0.530396i) q^{67} +(1.16568 - 2.81420i) q^{68} +(10.2258 - 6.26637i) q^{69} +(-0.826383 + 0.774199i) q^{70} +(1.08472 + 0.926438i) q^{71} +(-0.175330 - 0.344105i) q^{72} +8.42805i q^{73} +(7.69844 - 3.92255i) q^{74} +(-11.9245 - 5.87657i) q^{75} +(-7.71504 - 1.85222i) q^{76} +(-0.153035 - 0.470993i) q^{77} +(18.8305 + 9.59462i) q^{78} +(-1.98066 + 4.78173i) q^{79} +(-5.03402 + 7.64396i) q^{80} +4.64962i q^{81} +(-8.01306 + 9.89108i) q^{82} +(-7.57937 + 7.57937i) q^{83} +(0.206842 + 1.30595i) q^{84} +(3.28123 + 1.18568i) q^{85} +(15.9090 - 5.16916i) q^{86} +(16.8860 - 5.48661i) q^{87} +(-0.0964088 - 0.157325i) q^{88} +(-3.97340 + 0.953929i) q^{89} +(-15.7230 + 8.94374i) q^{90} +(0.720189 + 0.720189i) q^{91} +(-7.84633 + 3.99791i) q^{92} +(1.14264 + 14.5186i) q^{93} +(18.6486 + 1.46767i) q^{94} +(1.71336 - 8.92472i) q^{95} +(8.08644 + 19.5224i) q^{96} +(-0.541427 + 6.87949i) q^{97} +(2.15679 - 13.6175i) q^{98} +(-0.620677 - 7.88645i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 16 q^{2} - 16 q^{3} - 68 q^{4} - 16 q^{5} - 32 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{9} - 12 q^{10} - 32 q^{11} + 20 q^{12} - 4 q^{13} - 16 q^{14} + 16 q^{15} - 76 q^{16} - 16 q^{17} + 28 q^{18} - 40 q^{20}+ \cdots - 72 q^{99}+O(q^{100}) \) 304 * q - 16 * q^2 - 16 * q^3 - 68 * q^4 - 16 * q^5 - 32 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^9 - 12 * q^10 - 32 * q^11 + 20 * q^12 - 4 * q^13 - 16 * q^14 + 16 * q^15 - 76 * q^16 - 16 * q^17 + 28 * q^18 - 40 * q^20 - 40 * q^21 - 40 * q^22 - 20 * q^23 + 40 * q^24 - 20 * q^25 - 24 * q^26 - 76 * q^27 - 4 * q^28 + 76 * q^29 - 8 * q^30 - 40 * q^31 + 48 * q^32 - 120 * q^33 + 16 * q^34 - 80 * q^35 - 24 * q^36 + 24 * q^37 - 20 * q^38 - 16 * q^39 + 56 * q^40 - 32 * q^41 + 176 * q^42 + 20 * q^43 + 16 * q^44 - 32 * q^46 + 40 * q^47 + 76 * q^48 - 8 * q^49 - 8 * q^50 - 24 * q^51 - 80 * q^52 - 16 * q^53 + 40 * q^54 + 48 * q^55 + 24 * q^56 + 12 * q^57 + 20 * q^58 - 40 * q^59 + 120 * q^60 + 4 * q^61 - 20 * q^62 + 108 * q^63 - 68 * q^64 - 92 * q^65 - 40 * q^66 + 8 * q^67 + 76 * q^68 + 32 * q^69 + 48 * q^70 - 40 * q^71 - 220 * q^72 + 144 * q^74 + 44 * q^75 - 48 * q^76 + 72 * q^77 - 212 * q^78 + 232 * q^80 - 72 * q^82 - 112 * q^83 - 256 * q^84 + 116 * q^85 - 40 * q^86 - 20 * q^87 + 92 * q^88 - 80 * q^89 + 212 * q^90 - 72 * q^91 + 20 * q^92 + 96 * q^93 - 40 * q^94 - 36 * q^95 - 8 * q^96 - 136 * q^97 - 12 * q^98 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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