LMFDB - Embedded newform 471.2.l.b.50.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(50,471)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 11]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("471.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.l (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$50$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.10
Character	$\chi$	$=$	471.50
Dual form			471.2.l.b.179.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43787 + 1.43787i) q^{2} +(1.07451 - 1.35846i) q^{3} -2.13496i q^{4} +(-0.618816 - 2.30945i) q^{5} +(0.408280 + 3.49831i) q^{6} +(-2.17897 + 2.17897i) q^{7} +(0.194052 + 0.194052i) q^{8} +(-0.690836 - 2.91937i) q^{9} +O(q^{10})$	\(q+(-1.43787 + 1.43787i) q^{2} +(1.07451 - 1.35846i) q^{3} -2.13496i q^{4} +(-0.618816 - 2.30945i) q^{5} +(0.408280 + 3.49831i) q^{6} +(-2.17897 + 2.17897i) q^{7} +(0.194052 + 0.194052i) q^{8} +(-0.690836 - 2.91937i) q^{9} +(4.21048 + 2.43092i) q^{10} +(0.738989 + 0.426656i) q^{11} +(-2.90026 - 2.29404i) q^{12} +(-3.16923 + 1.82976i) q^{13} -6.26616i q^{14} +(-3.80223 - 1.64090i) q^{15} +3.71187 q^{16} +(0.00698006 + 0.00402994i) q^{17} +(5.19102 + 3.20435i) q^{18} +(-1.12009 + 1.94006i) q^{19} +(-4.93058 + 1.32115i) q^{20} +(0.618712 + 5.30138i) q^{21} +(-1.67605 + 0.449096i) q^{22} +(-6.45630 - 6.45630i) q^{23} +(0.472124 - 0.0551005i) q^{24} +(-0.620511 + 0.358252i) q^{25} +(1.92600 - 7.18792i) q^{26} +(-4.70817 - 2.19844i) q^{27} +(4.65201 + 4.65201i) q^{28} +(-7.28745 + 7.28745i) q^{29} +(7.82653 - 3.10771i) q^{30} +(-4.75642 + 2.74612i) q^{31} +(-5.72530 + 5.72530i) q^{32} +(1.37365 - 0.545441i) q^{33} +(-0.0158310 + 0.00424190i) q^{34} +(6.38061 + 3.68385i) q^{35} +(-6.23274 + 1.47491i) q^{36} +(-1.16690 - 2.02112i) q^{37} +(-1.17901 - 4.40011i) q^{38} +(-0.919733 + 6.27139i) q^{39} +(0.328072 - 0.568237i) q^{40} +(-4.69736 + 4.69736i) q^{41} +(-8.51235 - 6.73309i) q^{42} +(2.59393 - 9.68069i) q^{43} +(0.910892 - 1.57771i) q^{44} +(-6.31466 + 3.40201i) q^{45} +18.5667 q^{46} +(-4.29874 + 2.48188i) q^{47} +(3.98846 - 5.04243i) q^{48} -2.49582i q^{49} +(0.377095 - 1.40734i) q^{50} +(0.0129747 - 0.00515191i) q^{51} +(3.90646 + 6.76618i) q^{52} +(3.07157 - 11.4633i) q^{53} +(9.93082 - 3.60868i) q^{54} +(0.528043 - 1.97068i) q^{55} -0.845668 q^{56} +(1.43194 + 3.60623i) q^{57} -20.9569i q^{58} +(7.64222 - 7.64222i) q^{59} +(-3.50326 + 8.11760i) q^{60} +(4.45192 - 1.19289i) q^{61} +(2.89056 - 10.7877i) q^{62} +(7.86654 + 4.85592i) q^{63} -9.04078i q^{64} +(6.18691 + 6.18691i) q^{65} +(-1.19086 + 2.75941i) q^{66} +3.50711 q^{67} +(0.00860375 - 0.0149021i) q^{68} +(-15.7080 + 1.83325i) q^{69} +(-14.4714 + 3.87760i) q^{70} +(-3.58698 + 2.07095i) q^{71} +(0.432453 - 0.700569i) q^{72} +(-6.41830 + 1.71978i) q^{73} +(4.58397 + 1.22827i) q^{74} +(-0.180076 + 1.22789i) q^{75} +(4.14194 + 2.39135i) q^{76} +(-2.53991 + 0.680566i) q^{77} +(-7.69500 - 10.3399i) q^{78} +(1.02641 - 1.02641i) q^{79} +(-2.29696 - 8.57239i) q^{80} +(-8.04549 + 4.03362i) q^{81} -13.5084i q^{82} +(3.01737 - 11.2610i) q^{83} +(11.3182 - 1.32092i) q^{84} +(0.00498758 - 0.0186139i) q^{85} +(10.1899 + 17.6493i) q^{86} +(2.06925 + 17.7302i) q^{87} +(0.0606090 + 0.226196i) q^{88} +(8.81131 + 5.08721i) q^{89} +(4.18802 - 13.9713i) q^{90} +(2.91868 - 10.8927i) q^{91} +(-13.7839 + 13.7839i) q^{92} +(-1.38034 + 9.41216i) q^{93} +(2.61241 - 9.74966i) q^{94} +(5.17361 + 1.38626i) q^{95} +(1.62568 + 13.9295i) q^{96} +(2.09510 + 0.561382i) q^{97} +(3.58868 + 3.58868i) q^{98} +(0.735047 - 2.45214i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 6 q^{3} - 10 q^{9}+O(q^{10}) $ 200 * q - 6 * q^3 - 10 * q^9	$ 200 q - 6 q^{3} - 10 q^{9} - 36 q^{10} - 16 q^{12} - 24 q^{13} + 8 q^{15} - 208 q^{16} + 8 q^{18} - 12 q^{19} - 24 q^{22} - 20 q^{24} - 24 q^{25} + 64 q^{28} - 14 q^{30} - 48 q^{31} + 18 q^{33} + 32 q^{34} + 78 q^{36} + 44 q^{37} - 72 q^{39} + 60 q^{40} + 42 q^{42} - 24 q^{43} - 32 q^{45} - 32 q^{46} - 102 q^{48} - 54 q^{51} + 36 q^{52} + 48 q^{54} - 20 q^{55} - 6 q^{57} - 8 q^{61} - 8 q^{63} - 32 q^{66} - 16 q^{67} - 52 q^{69} + 60 q^{70} - 42 q^{72} - 64 q^{73} - 32 q^{75} + 132 q^{76} + 106 q^{78} + 40 q^{79} + 14 q^{81} + 172 q^{84} - 160 q^{85} - 88 q^{87} + 8 q^{88} + 84 q^{91} + 220 q^{93} + 128 q^{94} - 108 q^{96} - 36 q^{97} - 104 q^{99}+O(q^{100}) $ 200 * q - 6 * q^3 - 10 * q^9 - 36 * q^10 - 16 * q^12 - 24 * q^13 + 8 * q^15 - 208 * q^16 + 8 * q^18 - 12 * q^19 - 24 * q^22 - 20 * q^24 - 24 * q^25 + 64 * q^28 - 14 * q^30 - 48 * q^31 + 18 * q^33 + 32 * q^34 + 78 * q^36 + 44 * q^37 - 72 * q^39 + 60 * q^40 + 42 * q^42 - 24 * q^43 - 32 * q^45 - 32 * q^46 - 102 * q^48 - 54 * q^51 + 36 * q^52 + 48 * q^54 - 20 * q^55 - 6 * q^57 - 8 * q^61 - 8 * q^63 - 32 * q^66 - 16 * q^67 - 52 * q^69 + 60 * q^70 - 42 * q^72 - 64 * q^73 - 32 * q^75 + 132 * q^76 + 106 * q^78 + 40 * q^79 + 14 * q^81 + 172 * q^84 - 160 * q^85 - 88 * q^87 + 8 * q^88 + 84 * q^91 + 220 * q^93 + 128 * q^94 - 108 * q^96 - 36 * q^97 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−1.43787	+	1.43787i	−1.01673	+	1.01673i	−0.0168721	+	0.999858i	$0.505371\pi$
$2$	−1.43787	+	1.43787i	−1.01673	+	1.01673i	−0.999858	+	0.0168721i	$0.994629\pi$
$3$	1.07451	−	1.35846i	0.620371	−	0.784308i
$3$	1.07451	−	1.35846i	0.620371	−	0.784308i
$4$		−	2.13496i		−	1.06748i
$5$	−0.618816	−	2.30945i	−0.276743	−	1.03282i	−0.954664	−	0.297684i	$-0.903786\pi$
$5$	−0.618816	−	2.30945i	−0.276743	−	1.03282i	0.677921	−	0.735134i	$-0.262881\pi$
$6$	0.408280	+	3.49831i	0.166679	+	1.42818i
$7$	−2.17897	+	2.17897i	−0.823573	+	0.823573i	−0.986619	−	0.163045i	$-0.947868\pi$
$7$	−2.17897	+	2.17897i	−0.823573	+	0.823573i	0.163045	+	0.986619i	$0.447868\pi$
$8$	0.194052	+	0.194052i	0.0686078	+	0.0686078i
$9$	−0.690836	−	2.91937i	−0.230279	−	0.973125i
$10$	4.21048	+	2.43092i	1.33147	+	0.768725i
$11$	0.738989	+	0.426656i	0.222814	+	0.128642i	0.607252	−	0.794509i	$-0.292272\pi$
$11$	0.738989	+	0.426656i	0.222814	+	0.128642i	−0.384439	+	0.923151i	$0.625605\pi$
$12$	−2.90026	−	2.29404i	−0.837232	−	0.662233i
$13$	−3.16923	+	1.82976i	−0.878988	+	0.507484i	−0.870324	−	0.492479i	$-0.836091\pi$
$13$	−3.16923	+	1.82976i	−0.878988	+	0.507484i	−0.00866309	+	0.999962i	$0.502758\pi$
$14$		−	6.26616i		−	1.67470i
$15$	−3.80223	−	1.64090i	−0.981732	−	0.423679i
$16$	3.71187			0.927968
$17$	0.00698006	+	0.00402994i	0.00169291	+	0.000977404i	0.500846	−	0.865536i	$-0.333022\pi$
$17$	0.00698006	+	0.00402994i	0.00169291	+	0.000977404i	−0.499153	+	0.866514i	$0.666356\pi$
$18$	5.19102	+	3.20435i	1.22354	+	0.755274i
$19$	−1.12009	+	1.94006i	−0.256967	+	0.445080i	−0.965428	−	0.260670i	$-0.916057\pi$
$19$	−1.12009	+	1.94006i	−0.256967	+	0.445080i	0.708461	+	0.705750i	$0.249390\pi$
$20$	−4.93058	+	1.32115i	−1.10251	+	0.295417i
$21$	0.618712	+	5.30138i	0.135014	+	1.15686i
$22$	−1.67605	+	0.449096i	−0.357335	+	0.0957476i
$23$	−6.45630	−	6.45630i	−1.34623	−	1.34623i	−0.889716	−	0.456515i	$-0.849097\pi$
$23$	−6.45630	−	6.45630i	−1.34623	−	1.34623i	−0.456515	−	0.889716i	$-0.650903\pi$
$24$	0.472124	−	0.0551005i	0.0963720	−	0.0112473i
$25$	−0.620511	+	0.358252i	−0.124102	+	0.0716505i
$26$	1.92600	−	7.18792i	0.377719	−	1.40967i
$27$	−4.70817	−	2.19844i	−0.906088	−	0.423089i
$28$	4.65201	+	4.65201i	0.879147	+	0.879147i
$29$	−7.28745	+	7.28745i	−1.35325	+	1.35325i	−0.471241	+	0.882004i	$0.656194\pi$
$29$	−7.28745	+	7.28745i	−1.35325	+	1.35325i	−0.882004	+	0.471241i	$0.843806\pi$
$30$	7.82653	−	3.10771i	1.42892	−	0.567388i
$31$	−4.75642	+	2.74612i	−0.854279	+	0.493218i	−0.862092	−	0.506752i	$-0.830846\pi$
$31$	−4.75642	+	2.74612i	−0.854279	+	0.493218i	0.00781362	+	0.999969i	$0.497513\pi$
$32$	−5.72530	+	5.72530i	−1.01210	+	1.01210i
$33$	1.37365	−	0.545441i	0.239122	−	0.0949491i
$34$	−0.0158310	+	0.00424190i	−0.00271499	+	0.000727480i
$35$	6.38061	+	3.68385i	1.07852	+	0.622684i
$36$	−6.23274	+	1.47491i	−1.03879	+	0.245818i
$37$	−1.16690	−	2.02112i	−0.191837	−	0.332271i	0.754022	−	0.656849i	$-0.228111\pi$
$37$	−1.16690	−	2.02112i	−0.191837	−	0.332271i	−0.945859	+	0.324578i	$0.894778\pi$
$38$	−1.17901	−	4.40011i	−0.191260	−	0.713792i
$39$	−0.919733	+	6.27139i	−0.147275	+	1.00423i
$40$	0.328072	−	0.568237i	0.0518727	−	0.0898461i
$41$	−4.69736	+	4.69736i	−0.733605	+	0.733605i	−0.971332	−	0.237727i	$-0.923598\pi$
$41$	−4.69736	+	4.69736i	−0.733605	+	0.733605i	0.237727	+	0.971332i	$0.423598\pi$
$42$	−8.51235	−	6.73309i	−1.31348	−	1.03894i
$43$	2.59393	−	9.68069i	0.395571	−	1.47629i	−0.425234	−	0.905083i	$-0.639808\pi$
$43$	2.59393	−	9.68069i	0.395571	−	1.47629i	0.820805	−	0.571208i	$-0.193525\pi$
$44$	0.910892	−	1.57771i	0.137322	−	0.237849i
$45$	−6.31466	+	3.40201i	−0.941333	+	0.507142i
$46$	18.5667			2.73751
$47$	−4.29874	+	2.48188i	−0.627035	+	0.362019i	−0.779603	−	0.626274i	$-0.784579\pi$
$47$	−4.29874	+	2.48188i	−0.627035	+	0.362019i	0.152568	+	0.988293i	$0.451246\pi$
$48$	3.98846	−	5.04243i	0.575685	−	0.727813i
$49$		−	2.49582i		−	0.356546i
$50$	0.377095	−	1.40734i	0.0533293	−	0.199028i
$51$	0.0129747	−	0.00515191i	0.00181682	−	0.000721412i
$52$	3.90646	+	6.76618i	0.541728	+	0.938301i
$53$	3.07157	−	11.4633i	0.421913	−	1.57460i	−0.348661	−	0.937249i	$-0.613363\pi$
$53$	3.07157	−	11.4633i	0.421913	−	1.57460i	0.770574	−	0.637351i	$-0.219970\pi$
$54$	9.93082	−	3.60868i	1.35141	−	0.491079i
$55$	0.528043	−	1.97068i	0.0712013	−	0.265727i
$56$	−0.845668			−0.113007
$57$	1.43194	+	3.60623i	0.189665	+	0.477656i
$58$		−	20.9569i		−	2.75177i
$59$	7.64222	−	7.64222i	0.994933	−	0.994933i	−0.00505460	−	0.999987i	$-0.501609\pi$
$59$	7.64222	−	7.64222i	0.994933	−	0.994933i	0.999987	+	0.00505460i	$0.00160894\pi$
$60$	−3.50326	+	8.11760i	−0.452269	+	1.04798i
$61$	4.45192	−	1.19289i	0.570010	−	0.152734i	0.0377087	−	0.999289i	$-0.487994\pi$
$61$	4.45192	−	1.19289i	0.570010	−	0.152734i	0.532301	+	0.846555i	$0.321327\pi$
$62$	2.89056	−	10.7877i	0.367101	−	1.37004i
$63$	7.86654	+	4.85592i	0.991091	+	0.611788i
$64$		−	9.04078i		−	1.13010i
$65$	6.18691	+	6.18691i	0.767392	+	0.767392i
$66$	−1.19086	+	2.75941i	−0.146585	+	0.339660i
$67$	3.50711			0.428462			0.214231	−	0.976783i	$-0.431276\pi$
$67$	3.50711			0.428462			0.214231	+	0.976783i	$0.431276\pi$
$68$	0.00860375	−	0.0149021i	0.00104336	−	0.00180715i
$69$	−15.7080	+	1.83325i	−1.89102	+	0.220697i
$70$	−14.4714	+	3.87760i	−1.72966	+	0.463462i
$71$	−3.58698	+	2.07095i	−0.425697	+	0.245776i	−0.697512	−	0.716573i	$-0.745709\pi$
$71$	−3.58698	+	2.07095i	−0.425697	+	0.245776i	0.271815	+	0.962350i	$0.412376\pi$
$72$	0.432453	−	0.700569i	0.0509650	−	0.0825629i
$73$	−6.41830	+	1.71978i	−0.751206	+	0.201285i	−0.614053	−	0.789265i	$-0.710462\pi$
$73$	−6.41830	+	1.71978i	−0.751206	+	0.201285i	−0.137153	+	0.990550i	$0.543795\pi$
$74$	4.58397	+	1.22827i	0.532875	+	0.142784i
$75$	−0.180076	+	1.22789i	−0.0207934	+	0.141784i
$76$	4.14194	+	2.39135i	0.475114	+	0.274307i
$77$	−2.53991	+	0.680566i	−0.289449	+	0.0775577i
$78$	−7.69500	−	10.3399i	−0.871287	−	1.17076i
$79$	1.02641	−	1.02641i	0.115480	−	0.115480i	−0.647005	−	0.762485i	$-0.723979\pi$
$79$	1.02641	−	1.02641i	0.115480	−	0.115480i	0.762485	+	0.647005i	$0.223979\pi$
$80$	−2.29696	−	8.57239i	−0.256808	−	0.958422i
$81$	−8.04549	+	4.03362i	−0.893943	+	0.448180i
$82$		−	13.5084i		−	1.49176i
$83$	3.01737	−	11.2610i	0.331199	−	1.23605i	−0.576732	−	0.816933i	$-0.695672\pi$
$83$	3.01737	−	11.2610i	0.331199	−	1.23605i	0.907931	−	0.419119i	$-0.137661\pi$
$84$	11.3182	−	1.32092i	1.23492	−	0.144125i
$85$	0.00498758	−	0.0186139i	0.000540979	−	0.00201896i
$86$	10.1899	+	17.6493i	1.09880	+	1.90318i
$87$	2.06925	+	17.7302i	0.221847	+	1.90088i
$88$	0.0606090	+	0.226196i	0.00646094	+	0.0241126i
$89$	8.81131	+	5.08721i	0.933997	+	0.539243i	0.888073	−	0.459702i	$-0.152044\pi$
$89$	8.81131	+	5.08721i	0.933997	+	0.539243i	0.0459234	+	0.998945i	$0.485377\pi$
$90$	4.18802	−	13.9713i	0.441456	−	1.47271i
$91$	2.91868	−	10.8927i	0.305961	−	1.14186i
$92$	−13.7839	+	13.7839i	−1.43707	+	1.43707i
$93$	−1.38034	+	9.41216i	−0.143135	+	0.975996i
$94$	2.61241	−	9.74966i	0.269450	−	1.00560i
$95$	5.17361	+	1.38626i	0.530801	+	0.142228i
$96$	1.62568	+	13.9295i	0.165921	+	1.42168i
$97$	2.09510	+	0.561382i	0.212726	+	0.0569997i	0.363608	−	0.931552i	$-0.381545\pi$
$97$	2.09510	+	0.561382i	0.212726	+	0.0569997i	−0.150882	+	0.988552i	$0.548211\pi$
$98$	3.58868	+	3.58868i	0.362511	+	0.362511i
$99$	0.735047	−	2.45214i	0.0738750	−	0.246449i
$100$	0.764854	+	1.32477i	0.0764854	+	0.132477i
$101$			12.8649i			1.28010i	0.768332	+	0.640051i	$0.221087\pi$
$101$			12.8649i			1.28010i	−0.768332	+	0.640051i	$0.778913\pi$
$102$	−0.0112482	+	0.0260638i	−0.00111373	+	0.00258070i
$103$	4.80582	+	4.80582i	0.473532	+	0.473532i	0.903055	−	0.429524i	$-0.141319\pi$
$103$	4.80582	+	4.80582i	0.473532	+	0.473532i	−0.429524	+	0.903055i	$0.641319\pi$
$104$	−0.970065	−	0.259928i	−0.0951227	−	0.0254881i
$105$	11.8604	−	4.70947i	1.15746	−	0.459597i
$106$	12.0662	+	20.8992i	1.17197	+	2.02991i
$107$	−9.99403	−	2.67789i	−0.966159	−	0.258882i	−0.258954	−	0.965890i	$-0.583378\pi$
$107$	−9.99403	−	2.67789i	−0.966159	−	0.258882i	−0.707205	+	0.707008i	$0.750044\pi$
$108$	−4.69357	+	10.0517i	−0.451639	+	0.967230i
$109$	1.68133	−	2.91215i	0.161043	−	0.278934i	−0.774200	−	0.632941i	$-0.781848\pi$
$109$	1.68133	−	2.91215i	0.161043	−	0.278934i	0.935243	+	0.354007i	$0.115181\pi$
$110$	2.07433	+	3.59285i	0.197780	+	0.342565i
$111$	−3.99947	−	0.586543i	−0.379613	−	0.0556722i
$112$	−8.08806	+	8.08806i	−0.764249	+	0.764249i
$113$	7.84738	+	4.53068i	0.738219	+	0.426211i	0.821421	−	0.570322i	$-0.193181\pi$
$113$	7.84738	+	4.53068i	0.738219	+	0.426211i	−0.0832024	+	0.996533i	$0.526515\pi$
$114$	−7.24424	−	3.12635i	−0.678485	−	0.292809i
$115$	−10.9153	+	18.9058i	−1.01785	+	1.76297i
$116$	15.5584	+	15.5584i	1.44456	+	1.44456i
$117$	7.53117	+	7.98812i	0.696257	+	0.738502i
$118$			21.9771i			2.02316i
$119$	−0.0239905	+	0.00642822i	−0.00219920	+	0.000589274i
$120$	−0.419410	−	1.05625i	−0.0382867	−	0.0964222i
$121$	−5.13593	−	8.89569i	−0.466903	−	0.808699i
$122$	−4.68607	+	8.11651i	−0.424257	+	0.734835i
$123$	1.33380	+	11.4286i	0.120265	+	1.03048i
$124$	5.86285	+	10.1548i	0.526500	+	0.911924i
$125$	−7.24183	−	7.24183i	−0.647729	−	0.647729i
$126$	−18.2933	+	4.32889i	−1.62969	+	0.385649i
$127$	12.4791	−	7.20483i	1.10734	−	0.639325i	0.169204	−	0.985581i	$-0.445880\pi$
$127$	12.4791	−	7.20483i	1.10734	−	0.639325i	0.938140	+	0.346256i	$0.112547\pi$
$128$	1.54888	+	1.54888i	0.136903	+	0.136903i
$129$	−10.3636	−	13.9258i	−0.912466	−	1.22610i
$130$	−17.7920			−1.56046
$131$	−5.23401	−	1.40245i	−0.457298	−	0.122533i	0.0228142	−	0.999740i	$-0.492737\pi$
$131$	−5.23401	−	1.40245i	−0.457298	−	0.122533i	−0.480112	+	0.877207i	$0.659404\pi$
$132$	−1.16449	−	2.93269i	−0.101356	−	0.255258i
$133$	−1.78668	−	6.66798i	−0.154925	−	0.578187i
$134$	−5.04278	+	5.04278i	−0.435630	+	0.435630i
$135$	−2.16369	+	12.2337i	−0.186221	+	1.05291i
$136$	0.000572477		0.00213651i	4.90895e−5		0.000183205i
$137$	1.93543	+	7.22311i	0.165355	+	0.617112i	0.997995	+	0.0632972i	$0.0201616\pi$
$137$	1.93543	+	7.22311i	0.165355	+	0.617112i	−0.832640	+	0.553814i	$0.813172\pi$
$138$	19.9502	−	25.2221i	1.69827	−	2.14705i
$139$	−8.54746	−	2.29028i	−0.724986	−	0.194259i	−0.122591	−	0.992457i	$-0.539120\pi$
$139$	−8.54746	−	2.29028i	−0.724986	−	0.194259i	−0.602395	+	0.798198i	$0.705787\pi$
$140$	7.86486	−	13.6223i	0.664702	−	1.15130i
$141$	−1.24752	+	8.50648i	−0.105060	+	0.716375i
$142$	2.17987	−	8.13538i	0.182931	−	0.682706i
$143$	−3.12271			−0.261134
$144$	−2.56429	−	10.8363i	−0.213691	−	0.903028i
$145$	21.3396	+	12.3204i	1.77216	+	1.02316i
$146$	6.75588	−	11.7015i	0.559121	−	0.968425i
$147$	−3.39048	−	2.68180i	−0.279642	−	0.221191i
$148$	−4.31501	+	2.49127i	−0.354692	+	0.204782i
$149$	4.76250	−	4.76250i	0.390159	−	0.390159i	−0.484585	−	0.874744i	$-0.661029\pi$
$149$	4.76250	−	4.76250i	0.390159	−	0.390159i	0.874744	+	0.484585i	$0.161029\pi$
$150$	−1.50662	−	2.02447i	−0.123015	−	0.165298i
$151$	−13.9750	+	3.74459i	−1.13727	+	0.304731i	−0.777853	−	0.628446i	$-0.783691\pi$
$151$	−13.9750	+	3.74459i	−1.13727	+	0.304731i	−0.359417	+	0.933177i	$0.617025\pi$
$152$	−0.593829	+	0.159116i	−0.0481659	+	0.0129060i
$153$	0.00694282	−	0.0231614i	0.000561294	−	0.00187249i
$154$	2.67350	−	4.63063i	0.215436	−	0.373147i
$155$	9.28539	+	9.28539i	0.745820	+	0.745820i
$156$	13.3891	+	1.96359i	1.07199	+	0.157213i
$157$	−4.26902	−	11.7803i	−0.340705	−	0.940170i
$157$	−4.26902	−	11.7803i	−0.340705	−	0.940170i
$158$			2.95169i			0.234824i
$159$	−12.2720	−	16.4901i	−0.973229	−	1.30775i
$160$	16.7652	+	9.67941i	1.32541	+	0.765224i
$161$	28.1362			2.21744
$162$	5.76856	−	17.3682i	0.453221	−	1.36458i
$163$	2.86777	+	10.7027i	0.224621	+	0.838298i	0.982556	+	0.185967i	$0.0595419\pi$
$163$	2.86777	+	10.7027i	0.224621	+	0.838298i	−0.757935	+	0.652330i	$0.773791\pi$
$164$	10.0287	+	10.0287i	0.783108	+	0.783108i
$165$	−2.10971	−	2.83485i	−0.164240	−	0.220693i
$166$	11.8533	+	20.5304i	0.919991	+	1.59347i
$167$	3.55993	−	6.16599i	0.275476	−	0.477138i	−0.694779	−	0.719223i	$-0.744498\pi$
$167$	3.55993	−	6.16599i	0.275476	−	0.477138i	0.970255	+	0.242085i	$0.0778312\pi$
$168$	−0.908682	+	1.14881i	−0.0701064	+	0.0886324i
$169$	0.196032	−	0.339538i	0.0150794	−	0.0261183i
$170$	0.0195929	+	0.0339359i	0.00150271	+	0.00260277i
$171$	6.43756	+	1.92971i	0.492292	+	0.147569i
$172$	−20.6679	−	5.53794i	−1.57591	−	0.422264i
$173$			0.410944i			0.0312435i	0.999878	+	0.0156217i	$0.00497276\pi$
$173$			0.410944i			0.0312435i	−0.999878	+	0.0156217i	$0.995027\pi$
$174$	−28.4691	−	22.5185i	−2.15824	−	1.70712i
$175$	0.571454	−	2.13270i	0.0431979	−	0.161217i
$176$	2.74303	+	1.58369i	0.206764	+	0.119375i
$177$	−2.16999	−	18.5933i	−0.163106	−	1.39756i
$178$	−19.9843	+	5.35478i	−1.49789	+	0.401358i
$179$	2.42365	+	9.04517i	0.181152	+	0.676068i	0.995422	+	0.0955812i	$0.0304709\pi$
$179$	2.42365	+	9.04517i	0.181152	+	0.676068i	−0.814270	+	0.580487i	$0.802862\pi$
$180$	7.26315	+	13.4815i	0.541363	+	1.00485i
$181$	24.4670	−	6.55590i	1.81861	−	0.487296i	0.821998	−	0.569490i	$-0.192859\pi$
$181$	24.4670	−	6.55590i	1.81861	−	0.487296i	0.996616	+	0.0821942i	$0.0261928\pi$
$182$	11.4656	+	19.8589i	0.849884	+	1.47204i
$183$	3.16316	−	7.32954i	0.233827	−	0.541815i
$184$		−	2.50572i		−	0.184724i
$185$	−3.94560	+	3.94560i	−0.290086	+	0.290086i
$186$	−11.5487	−	15.5183i	−0.846794	−	1.13785i
$187$	0.00343879	+	0.00595617i	0.000251470	+	0.000435558i
$188$	5.29870	+	9.17762i	0.386448	+	0.669347i
$189$	15.0493	−	5.46864i	1.09467	−	0.397785i
$190$	−9.43226	+	5.44572i	−0.684288	+	0.395074i
$191$	−3.84999	−	14.3684i	−0.278575	−	1.03966i	−0.953407	−	0.301686i	$-0.902451\pi$
$191$	−3.84999	−	14.3684i	−0.278575	−	1.03966i	0.674832	−	0.737971i	$-0.264216\pi$
$192$	−12.2815	−	9.71445i	−0.886344	−	0.701080i
$193$	5.02788	−	2.90285i	0.361915	−	0.208951i	−0.308006	−	0.951385i	$-0.599662\pi$
$193$	5.02788	−	2.90285i	0.361915	−	0.208951i	0.669920	+	0.742433i	$0.266328\pi$
$194$	−3.81969	+	2.20530i	−0.274238	+	0.158331i
$195$	15.0526	−	1.75676i	1.07794	−	0.125804i
$196$	−5.32847			−0.380605
$197$	−4.74826	−	2.74141i	−0.338299	−	0.195317i	0.321220	−	0.947004i	$-0.395907\pi$
$197$	−4.74826	−	2.74141i	−0.338299	−	0.195317i	−0.659520	+	0.751687i	$0.729240\pi$
$198$	2.46896	+	4.58276i	0.175461	+	0.325683i
$199$	−14.0783	−	8.12810i	−0.997983	−	0.576186i	−0.0903323	−	0.995912i	$-0.528793\pi$
$199$	−14.0783	−	8.12810i	−0.997983	−	0.576186i	−0.907651	+	0.419726i	$0.862126\pi$
$200$	−0.189931	−	0.0508919i	−0.0134302	−	0.00359860i
$201$	3.76844	−	4.76427i	0.265805	−	0.336046i
$202$	−18.4980	−	18.4980i	−1.30152	−	1.30152i
$203$		−	31.7583i		−	2.22899i
$204$	−0.0109991	−	0.0277004i	−0.000770092	−	0.00193942i
$205$	13.7551	+	7.94154i	0.960701	+	0.554661i
$206$	−13.8203			−0.962907
$207$	−14.3881	+	23.3086i	−1.00004	+	1.62006i
$208$	−11.7638	+	6.79183i	−0.815672	+	0.470928i
$209$	−1.65547	+	0.955789i	−0.114512	+	0.0661133i
$210$	−10.2822	+	23.8254i	−0.709537	+	1.64411i
$211$	1.49121	−	1.49121i	0.102659	−	0.102659i	−0.653912	−	0.756571i	$-0.726873\pi$
$211$	1.49121	−	1.49121i	0.102659	−	0.102659i	0.756571	+	0.653912i	$0.226873\pi$
$212$	−24.4736	−	6.55768i	−1.68085	−	0.450383i
$213$	−1.04097	+	7.09804i	−0.0713258	+	0.486350i
$214$	18.2206	−	10.5197i	1.24554	−	0.719110i
$215$	−23.9623			−1.63421
$216$	−0.487020	−	1.34024i	−0.0331375	−	0.0911919i
$217$	4.38038	−	16.3478i	0.297360	−	1.10976i
$218$	1.76976	+	6.60485i	0.119864	+	0.447337i
$219$	−4.56031	+	10.5669i	−0.308157	+	0.714048i
$220$	−4.20732	−	1.12735i	−0.283658	−	0.0760059i
$221$	−0.0294953			−0.00198407
$222$	6.59410	−	4.90735i	0.442567	−	0.329360i
$223$	−4.39653	−	1.17805i	−0.294413	−	0.0788878i	0.108589	−	0.994087i	$-0.465367\pi$
$223$	−4.39653	−	1.17805i	−0.294413	−	0.0788878i	−0.403002	+	0.915199i	$0.632033\pi$
$224$		−	24.9505i		−	1.66708i
$225$	1.47454	+	1.56401i	0.0983030	+	0.104267i
$226$	−17.7981	+	4.76898i	−1.18391	+	0.317228i
$227$	−0.874412	−	3.26335i	−0.0580368	−	0.216596i	0.930817	−	0.365485i	$-0.119097\pi$
$227$	−0.874412	−	3.26335i	−0.0580368	−	0.216596i	−0.988854	+	0.148889i	$0.952430\pi$
$228$	7.69914	−	3.05713i	0.509888	−	0.202463i
$229$	24.1999	+	6.48436i	1.59918	+	0.428498i	0.944794	−	0.327665i	$-0.106262\pi$
$229$	24.1999	+	6.48436i	1.59918	+	0.428498i	0.654383	+	0.756163i	$0.272928\pi$
$230$	−11.4894	−	42.8788i	−0.757585	−	2.82735i
$231$	−1.80464	+	4.18164i	−0.118737	+	0.275132i
$232$	−2.82829			−0.185686
$233$	−12.9015	+	22.3460i	−0.845204	+	1.46394i	0.0402402	+	0.999190i	$0.487188\pi$
$233$	−12.9015	+	22.3460i	−0.845204	+	1.46394i	−0.885444	+	0.464746i	$0.846146\pi$
$234$	−22.3148	−	0.657031i	−1.45876	−	0.0429515i
$235$	8.39190	+	8.39190i	0.547427	+	0.547427i
$236$	−16.3158	−	16.3158i	−1.06207	−	1.06207i
$237$	−0.291446	−	2.49723i	−0.0189314	−	0.162212i
$238$	0.0252523	−	0.0437382i	0.00163686	−	0.00283513i
$239$	−8.13613			−0.526282			−0.263141	−	0.964757i	$-0.584758\pi$
$239$	−8.13613			−0.526282			−0.263141	+	0.964757i	$0.584758\pi$
$240$	−14.1134	−	6.09082i	−0.911015	−	0.393161i
$241$	−4.57425	−	17.0713i	−0.294653	−	1.09966i	−0.941492	−	0.337035i	$-0.890576\pi$
$241$	−4.57425	−	17.0713i	−0.294653	−	1.09966i	0.646839	−	0.762627i	$-0.276091\pi$
$242$	20.1757	+	5.40606i	1.29694	+	0.347515i
$243$	−3.16548	+	15.2637i	−0.203066	+	0.979165i
$244$	−2.54677	−	9.50466i	−0.163040	−	0.608473i
$245$	−5.76398	+	1.54445i	−0.368247	+	0.0986716i
$246$	−18.3507	−	14.5150i	−1.17000	−	0.925443i
$247$		−	8.19800i		−	0.521626i
$248$	−1.45588	−	0.390103i	−0.0924488	−	0.0247716i
$249$	−12.0554	−	16.1991i	−0.763980	−	1.02657i
$250$	20.8257			1.31713
$251$	−27.2686	−	7.30660i	−1.72118	−	0.461188i	−0.743058	−	0.669227i	$-0.766625\pi$
$251$	−27.2686	−	7.30660i	−1.72118	−	0.461188i	−0.978121	+	0.208038i	$0.933292\pi$
$252$	10.3672	−	16.7947i	0.653071	−	1.05797i
$253$	−2.01652	−	7.52575i	−0.126777	−	0.473140i
$254$	−7.58377	+	28.3030i	−0.475848	+	1.77589i
$255$	−0.0199271	−	0.0267764i	−0.00124788	−	0.00167680i
$256$	13.6274			0.851710
$257$	14.8737	−	8.58733i	0.927796	−	0.535663i	0.0416818	−	0.999131i	$-0.486728\pi$
$257$	14.8737	−	8.58733i	0.927796	−	0.535663i	0.886114	+	0.463468i	$0.153395\pi$
$258$	34.9251	+	5.12196i	2.17434	+	0.318879i
$259$	6.94660	+	1.86134i	0.431641	+	0.115658i
$260$	13.2088	−	13.2088i	0.819175	−	0.819175i
$261$	26.3092	+	16.2404i	1.62850	+	1.00525i
$262$	9.54239	−	5.50930i	0.589531	−	0.340366i
$263$	−12.3709	+	7.14235i	−0.762824	+	0.440416i	−0.830309	−	0.557304i	$-0.811836\pi$
$263$	−12.3709	+	7.14235i	−0.762824	+	0.440416i	0.0674851	+	0.997720i	$0.478503\pi$
$264$	0.372404	+	0.160716i	0.0229199	+	0.00989138i
$265$	−28.3746			−1.74304
$266$	12.1567	+	7.01869i	0.745377	+	0.430344i
$267$	16.3787	−	6.50354i	1.00236	−	0.398010i
$268$		−	7.48753i		−	0.457374i
$269$	−0.203137	−	0.203137i	−0.0123855	−	0.0123855i	0.700887	−	0.713272i	$-0.252788\pi$
$269$	−0.203137	−	0.203137i	−0.0123855	−	0.0123855i	−0.713272	+	0.700887i	$0.752788\pi$
$270$	−14.4794	−	20.7017i	−0.881190	−	1.25986i
$271$	−8.55850	−	2.29324i	−0.519892	−	0.139305i	−0.0106752	−	0.999943i	$-0.503398\pi$
$271$	−8.55850	−	2.29324i	−0.519892	−	0.139305i	−0.509216	+	0.860638i	$0.670065\pi$
$272$	0.0259091	+	0.0149586i	0.00157097	+	0.000906999i
$273$	−11.6611	−	15.6692i	−0.705762	−	0.948345i
$274$	−13.1688	−	7.60301i	−0.795557	−	0.459315i
$275$	−0.611402			−0.0368689
$276$	3.91390	+	33.5360i	0.235589	+	2.01863i
$277$	−23.4482	+	13.5378i	−1.40887	+	0.813410i	−0.995279	−	0.0970536i	$-0.969058\pi$
$277$	−23.4482	+	13.5378i	−1.40887	+	0.813410i	−0.413589	+	0.910464i	$0.635725\pi$
$278$	15.5833	−	8.99702i	0.934624	−	0.539605i
$279$	11.3029	+	11.9887i	0.676685	+	0.717742i
$280$	0.523313	+	1.95303i	0.0312739	+	0.116716i
$281$	16.5801	−	9.57254i	0.989087	−	0.571050i	0.0840861	−	0.996458i	$-0.473203\pi$
$281$	16.5801	−	9.57254i	0.989087	−	0.571050i	0.905001	+	0.425409i	$0.139870\pi$
$282$	−10.4375	−	14.0250i	−0.621542	−	0.835178i
$283$	−3.49052	−	6.04576i	−0.207490	−	0.359383i	0.743433	−	0.668810i	$-0.233196\pi$
$283$	−3.49052	−	6.04576i	−0.207490	−	0.359383i	−0.950923	+	0.309427i	$0.899863\pi$
$284$	4.42138	+	7.65806i	0.262361	+	0.454422i
$285$	7.44230	−	5.53858i	0.440844	−	0.328077i
$286$	4.49006	−	4.49006i	0.265503	−	0.265503i
$287$		−	20.4708i		−	1.20836i
$288$	20.6695	+	12.7591i	1.21796	+	0.751835i
$289$	−8.49997	−	14.7224i	−0.499998	−	0.866022i
$290$	−48.3989	+	12.9684i	−2.84208	+	0.761533i
$291$	3.01384	−	2.24291i	0.176674	−	0.131482i
$292$	3.67166	+	13.7028i	0.214867	+	0.801896i
$293$	−12.3746	+	3.31576i	−0.722932	+	0.193709i	−0.601479	−	0.798888i	$-0.705422\pi$
$293$	−12.3746	+	3.31576i	−0.722932	+	0.193709i	−0.121452	+	0.992597i	$0.538755\pi$
$294$	8.73116	−	1.01899i	0.509212	−	0.0594289i
$295$	−22.3785	−	12.9202i	−1.30293	−	0.752244i
$296$	0.165765	−	0.618642i	0.00963488	−	0.0359579i
$297$	−2.54131	−	3.63339i	−0.147462	−	0.210831i
$298$			13.6957i			0.793373i
$299$	32.2750	+	8.64806i	1.86651	+	0.500130i
$300$	2.62149	+	0.384456i	0.151352	+	0.0221966i
$301$	15.4418	+	26.7460i	0.890052	+	1.54162i
$302$	14.7100	−	25.4785i	0.846468	−	1.46613i
$303$	17.4764	+	13.8235i	1.00399	+	0.794139i
$304$	−4.15764	+	7.20125i	−0.238457	+	0.413020i
$305$	−5.50984	−	9.54332i	−0.315492	−	0.546449i
$306$	0.0233203	+	0.0432861i	0.00133313	+	0.00247450i
$307$	18.4958	+	18.4958i	1.05561	+	1.05561i	0.998360	+	0.0572520i	$0.0182339\pi$
$307$	18.4958	+	18.4958i	1.05561	+	1.05561i	0.0572520	+	0.998360i	$0.481766\pi$
$308$	1.45298	+	5.42259i	0.0827912	+	0.308981i
$309$	11.6924	−	1.36460i	0.665160	−	0.0776293i
$310$	−26.7024			−1.51660
$311$	21.2194	+	12.2510i	1.20324	+	0.694692i	0.961275	−	0.275592i	$-0.0888738\pi$
$311$	21.2194	+	12.2510i	1.20324	+	0.694692i	0.241968	+	0.970284i	$0.422207\pi$
$312$	−1.39545	+	1.03850i	−0.0790019	+	0.0587935i
$313$		−	12.5626i		−	0.710083i	−0.934851	−	0.355041i	$-0.884467\pi$
$313$		−	12.5626i		−	0.710083i	0.934851	−	0.355041i	$-0.115533\pi$
$314$	23.0769	+	10.8003i	1.30230	+	0.609494i
$315$	6.34657	−	21.1723i	0.357589	−	1.19293i
$316$	−2.19134	−	2.19134i	−0.123272	−	0.123272i
$317$	−3.20842	+	5.55715i	−0.180203	+	0.312121i	−0.941950	−	0.335754i	$-0.891009\pi$
$317$	−3.20842	+	5.55715i	−0.180203	+	0.312121i	0.761747	+	0.647875i	$0.224342\pi$
$318$	41.3561	+	6.06510i	2.31914	+	0.340114i
$319$	−8.49458	+	2.27612i	−0.475605	+	0.127438i
$320$	−20.8792	+	5.59458i	−1.16719	+	0.312746i
$321$	−14.3765	+	10.6991i	−0.802420	+	0.597164i
$322$	−40.4562	+	40.4562i	−2.25454	+	2.25454i
$323$	−0.0156366	+	0.00902782i	−0.000870046	+	0.000502321i
$324$	8.61161	+	17.1768i	0.478423	+	0.954266i
$325$	1.31103	−	2.27077i	0.0727229	−	0.125960i
$326$	−19.5126	−	11.2656i	−1.08070	−	0.623943i
$327$	−2.14943	−	5.41318i	−0.118864	−	0.299350i
$328$	−1.82307			−0.100662
$329$	3.95888	−	14.7748i	0.218260	−	0.814559i
$330$	7.10965	+	1.04267i	0.391373	+	0.0573970i
$331$	−5.10640	+	8.84455i	−0.280673	+	0.486141i	−0.971551	−	0.236831i	$-0.923891\pi$
$331$	−5.10640	+	8.84455i	−0.280673	+	0.486141i	0.690877	+	0.722972i	$0.257224\pi$
$332$	−24.0417	−	6.44195i	−1.31946	−	0.353548i
$333$	−5.09428	+	4.80287i	−0.279165	+	0.263196i
$334$	3.74717	+	13.9846i	0.205036	+	0.765205i
$335$	−2.17026	−	8.09950i	−0.118574	−	0.442523i
$336$	2.29658	+	19.6780i	0.125289	+	1.07353i
$337$	−1.41725	+	1.41725i	−0.0772025	+	0.0772025i	−0.744654	−	0.667451i	$-0.767385\pi$
$337$	−1.41725	+	1.41725i	−0.0772025	+	0.0772025i	0.667451	+	0.744654i	$0.267385\pi$
$338$	0.206343	+	0.770081i	0.0112236	+	0.0418869i
$339$	14.5869	−	5.79207i	0.792251	−	0.314582i
$340$	−0.0397399	−	0.0106483i	−0.00215520	−	0.000577484i
$341$	−4.68659			−0.253793
$342$	−12.0311	+	6.48172i	−0.650566	+	0.350491i
$343$	−9.81447	−	9.81447i	−0.529932	−	0.529932i
$344$	2.38192	−	1.37520i	0.128424	−	0.0741458i
$345$	13.9542	+	35.1425i	0.751267	+	1.89201i
$346$	−0.590885	−	0.590885i	−0.0317662	−	0.0317662i
$347$	−17.1179	−	29.6491i	−0.918938	−	1.59165i	−0.801031	−	0.598623i	$-0.795715\pi$
$347$	−17.1179	−	29.6491i	−0.918938	−	1.59165i	−0.117907	−	0.993025i	$-0.537618\pi$
$348$	37.8532	−	4.41776i	2.02915	−	0.236817i
$349$	2.30797	−	3.99752i	0.123543	−	0.213982i	−0.797620	−	0.603161i	$-0.793908\pi$
$349$	2.30797	−	3.99752i	0.123543	−	0.213982i	0.921162	+	0.389178i	$0.127241\pi$
$350$	2.24487	+	3.88823i	0.119993	+	0.207834i
$351$	18.9439	−	1.64746i	1.01115	−	0.0879348i
$352$	−6.67367	+	1.78821i	−0.355708	+	0.0953117i
$353$			31.6483i			1.68447i	0.539113	+	0.842234i	$0.318760\pi$
$353$			31.6483i			1.68447i	−0.539113	+	0.842234i	$0.681240\pi$
$354$	29.8550	+	23.6147i	1.58678	+	1.25511i
$355$	7.00243	+	7.00243i	0.371651	+	0.371651i
$356$	10.8610	−	18.8118i	0.575631	−	0.997022i
$357$	−0.0170456	+	0.0394973i	−0.000902149	+	0.00209042i
$358$	−16.4907	−	9.52091i	−0.871561	−	0.503196i
$359$	3.72778	−	3.72778i	0.196745	−	0.196745i	−0.601858	−	0.798603i	$-0.705573\pi$
$359$	3.72778	−	3.72778i	0.196745	−	0.196745i	0.798603	+	0.601858i	$0.205573\pi$
$360$	−1.88554	−	0.565205i	−0.0993767	−	0.0297889i
$361$	6.99078	+	12.1084i	0.367936	+	0.637284i
$362$	−25.7538	+	44.6069i	−1.35359	+	2.34449i
$363$	−17.6031	−	2.58159i	−0.923922	−	0.135498i
$364$	−23.2554	−	6.23126i	−1.21891	−	0.326607i
$365$	7.94350	+	13.7585i	0.415782	+	0.720155i
$366$	5.99072	+	15.0872i	0.313140	+	0.788619i
$367$	−12.0223	−	3.22138i	−0.627561	−	0.168155i	−0.0689985	−	0.997617i	$-0.521980\pi$
$367$	−12.0223	−	3.22138i	−0.627561	−	0.168155i	−0.558563	+	0.829462i	$0.688647\pi$
$368$	−23.9649	−	23.9649i	−1.24926	−	1.24926i
$369$	16.9585	+	10.4683i	0.882823	+	0.544956i
$370$		−	11.3465i		−	0.589878i
$371$	18.2852	+	31.6710i	0.949322	+	1.64427i
$372$	20.0946	+	2.94698i	1.04186	+	0.152794i
$373$	−2.96818	−	2.96818i	−0.153687	−	0.153687i	0.626076	−	0.779762i	$-0.284660\pi$
$373$	−2.96818	−	2.96818i	−0.153687	−	0.153687i	−0.779762	+	0.626076i	$0.784660\pi$
$374$	−0.0135088	−	0.00361966i	−0.000698521	−	0.000187168i
$375$	−17.6192	+	2.05630i	−0.909852	+	0.106187i
$376$	−1.31579	−	0.352566i	−0.0678568	−	0.0181822i
$377$	9.76137	−	36.4299i	0.502736	−	1.87624i
$378$	−13.7758	+	29.5022i	−0.708549	+	1.51743i
$379$	−20.4813	+	20.4813i	−1.05205	+	1.05205i	−0.0534851	+	0.998569i	$0.517033\pi$
$379$	−20.4813	+	20.4813i	−1.05205	+	1.05205i	−0.998569	+	0.0534851i	$0.982967\pi$
$380$	2.95961	−	11.0454i	0.151825	−	0.566619i
$381$	3.62152	−	24.6941i	0.185536	−	1.26512i
$382$	26.1957	+	15.1241i	1.34029	+	0.773815i
$383$	−1.83227	−	6.83812i	−0.0936246	−	0.349412i	0.903183	−	0.429256i	$-0.141224\pi$
$383$	−1.83227	−	6.83812i	−0.0936246	−	0.349412i	−0.996807	+	0.0798446i	$0.974558\pi$
$384$	3.76840	−	0.439801i	0.192305	−	0.0224435i
$385$	3.14347	+	5.44465i	0.160206	+	0.277485i
$386$	−3.05553	+	11.4034i	−0.155522	+	0.580417i
$387$	−30.0535	−	0.884889i	−1.52771	−	0.0449815i
$388$	1.19853	−	4.47296i	0.0608459	−	0.227080i
$389$			2.55791i			0.129691i	0.997895	+	0.0648457i	$0.0206555\pi$
$389$			2.55791i			0.129691i	−0.997895	+	0.0648457i	$0.979344\pi$
$390$	−19.1178	+	24.1697i	−0.968065	+	1.22388i
$391$	−0.0190469	−	0.0710838i	−0.000963241	−	0.00359486i
$392$	0.484320	−	0.484320i	0.0244618	−	0.0244618i
$393$	−7.52920	+	5.60325i	−0.379798	+	0.282647i
$394$	10.7692	−	2.88559i	0.542544	−	0.145374i
$395$	−3.00560	−	1.73528i	−0.151228	−	0.0873116i
$396$	−5.23521	−	1.56929i	−0.263079	−	0.0788600i
$397$	9.55660	+	2.56068i	0.479632	+	0.128517i	0.490531	−	0.871424i	$-0.336803\pi$
$397$	9.55660	+	2.56068i	0.479632	+	0.128517i	−0.0108991	+	0.999941i	$0.503469\pi$
$398$	31.9300	−	8.55561i	1.60050	−	0.428854i
$399$	−10.9780	−	4.73771i	−0.549588	−	0.237182i
$400$	−2.30326	+	1.32979i	−0.115163	+	0.0664893i
$401$	0.984228	−	0.263723i	0.0491500	−	0.0131697i	−0.234160	−	0.972198i	$-0.575234\pi$
$401$	0.984228	−	0.263723i	0.0491500	−	0.0131697i	0.283310	+	0.959028i	$0.408567\pi$
$402$	1.43188	+	12.2690i	0.0714158	+	0.611920i
$403$	10.0495	−	17.4062i	0.500600	−	0.867065i
$404$	27.4659			1.36648
$405$	14.2941	+	16.0846i	0.710281	+	0.799251i
$406$	45.6644	+	45.6644i	2.26628	+	2.26628i
$407$		−	1.99145i		−	0.0987126i
$408$	0.00351751	+	0.00151803i	0.000174143	+	7.51536e-5i
$409$	4.58150	−	17.0984i	0.226541	−	0.845461i	−0.755241	−	0.655448i	$-0.772480\pi$
$409$	4.58150	−	17.0984i	0.226541	−	0.845461i	0.981781	−	0.190014i	$-0.0608533\pi$
$410$	−31.1971	+	8.35923i	−1.54071	+	0.412833i
$411$	11.8920	+	5.13213i	0.586587	+	0.253149i
$412$	10.2602	−	10.2602i	0.505485	−	0.505485i
$413$			33.3043i			1.63880i
$414$	−12.8265	−	54.2031i	−0.630389	−	2.66393i
$415$	−27.8739			−1.36827
$416$	7.66891	−	28.6208i	0.375999	−	1.40325i
$417$	−12.2956	+	9.15045i	−0.602120	+	0.448099i
$418$	1.00606	−	3.75467i	0.0492080	−	0.183647i
$419$	13.9078	+	24.0891i	0.679442	+	1.17683i	0.975149	+	0.221549i	$0.0711112\pi$
$419$	13.9078	+	24.0891i	0.679442	+	1.17683i	−0.295708	+	0.955278i	$0.595555\pi$
$420$	−10.0545	−	25.3215i	−0.490610	−	1.23556i
$421$	−4.72912	+	17.6493i	−0.230483	+	0.860175i	0.749650	+	0.661834i	$0.230222\pi$
$421$	−4.72912	+	17.6493i	−0.230483	+	0.860175i	−0.980133	+	0.198340i	$0.936445\pi$
$422$			4.28834i			0.208753i
$423$	10.2152	+	10.8350i	0.496682	+	0.526818i
$424$	2.82052	−	1.62843i	0.136976	−	0.0790833i
$425$	−0.00577494			−0.000280126
$426$	−8.70930	−	11.7029i	−0.421967	−	0.567005i
$427$	−7.10133	+	12.2999i	−0.343657	+	0.595232i
$428$	−5.71719	+	21.3368i	−0.276351	+	1.03135i
$429$	−3.35540	+	4.24208i	−0.162000	+	0.204810i
$430$	34.4547	−	34.4547i	1.66155	−	1.66155i
$431$	11.5667	−	20.0341i	0.557149	−	0.965011i	−0.440584	−	0.897712i	$-0.645228\pi$
$431$	11.5667	−	20.0341i	0.557149	−	0.965011i	0.997733	−	0.0672993i	$-0.0214382\pi$
$432$	−17.4761	−	8.16031i	−0.840820	−	0.392613i
$433$	3.02399	+	11.2857i	0.145324	+	0.542356i	0.999741	+	0.0227679i	$0.00724786\pi$
$433$	3.02399	+	11.2857i	0.145324	+	0.542356i	−0.854417	+	0.519588i	$0.826085\pi$
$434$	17.2076	+	29.8045i	0.825994	+	1.43066i
$435$	39.6666	−	15.7506i	1.90187	−	0.755182i
$436$	−6.21733	−	3.58958i	−0.297756	−	0.171909i
$437$	19.7573	−	5.29394i	0.945118	−	0.253243i
$438$	−8.63678	−	21.7511i	−0.412682	−	1.03931i
$439$	25.9035	−	25.9035i	1.23631	−	1.23631i	0.274808	−	0.961499i	$-0.411386\pi$
$439$	25.9035	−	25.9035i	1.23631	−	1.23631i	0.961499	−	0.274808i	$-0.0886142\pi$
$440$	0.484883	−	0.279947i	0.0231159	−	0.0133460i
$441$	−7.28624	+	1.72420i	−0.346964	+	0.0821050i
$442$	0.0424104	−	0.0424104i	0.00201726	−	0.00201726i
$443$	−2.54427	−	2.54427i	−0.120882	−	0.120882i	0.644078	−	0.764960i	$-0.277241\pi$
$443$	−2.54427	−	2.54427i	−0.120882	−	0.120882i	−0.764960	+	0.644078i	$0.777241\pi$
$444$	−1.25225	+	8.53869i	−0.0594289	+	0.405228i
$445$	6.29610	−	23.4973i	0.298464	−	1.11388i
$446$	8.01553	−	4.62777i	0.379546	−	0.219131i
$447$	−1.35230	−	11.5871i	−0.0639615	−	0.548049i
$448$	19.6996	+	19.6996i	0.930718	+	0.930718i
$449$	−18.5140	+	4.96082i	−0.873730	+	0.234115i	−0.667700	−	0.744430i	$-0.732721\pi$
$449$	−18.5140	+	4.96082i	−0.873730	+	0.234115i	−0.206030	+	0.978546i	$0.566055\pi$
$450$	−4.36906	−	0.128642i	−0.205959	−	0.00606422i
$451$	−5.47546	+	1.46715i	−0.257829	+	0.0690852i
$452$	9.67282	−	16.7538i	0.454971	−	0.788033i
$453$	−9.92947	+	23.0081i	−0.466527	+	1.08102i
$454$	5.94958	+	3.43499i	0.279227	+	0.161212i
$455$	−26.9622			−1.26401
$456$	−0.421925	+	0.977667i	−0.0197585	+	0.0457834i
$457$		−	15.9449i		−	0.745872i	−0.927857	−	0.372936i	$-0.878351\pi$
$457$		−	15.9449i		−	0.745872i	0.927857	−	0.372936i	$-0.121649\pi$
$458$	−44.1201	+	25.4728i	−2.06160	+	1.19026i
$459$	−0.0240038	−	0.0343189i	−0.00112040	−	0.00160187i
$460$	40.3630	+	23.3036i	1.88194	+	1.08654i
$461$	−0.0438817	−	0.0253351i	−0.00204377	−	0.00117997i	0.498978	−	0.866615i	$-0.333709\pi$
$461$	−0.0438817	−	0.0253351i	−0.00204377	−	0.00117997i	−0.501022	+	0.865435i	$0.667042\pi$
$462$	−3.41782	−	8.60752i	−0.159012	−	0.400458i
$463$	−17.3542	−	17.3542i	−0.806517	−	0.806517i	0.177588	−	0.984105i	$-0.443171\pi$
$463$	−17.3542	−	17.3542i	−0.806517	−	0.806517i	−0.984105	+	0.177588i	$0.943171\pi$
$464$	−27.0501	+	27.0501i	−1.25577	+	1.25577i
$465$	22.5911	−	2.63656i	1.04764	−	0.122267i
$466$	−13.5800	−	50.6814i	−0.629083	−	2.34777i
$467$			0.312455i			0.0144587i	0.999974	+	0.00722936i	$0.00230120\pi$
$467$			0.312455i			0.0144587i	−0.999974	+	0.00722936i	$0.997699\pi$
$468$	17.0543	−	16.0787i	0.788335	−	0.743240i
$469$	−7.64189	+	7.64189i	−0.352870	+	0.352870i
$470$	−24.1330			−1.11317
$471$	−20.5902	−	6.85881i	−0.948747	−	0.316037i
$472$	2.96598			0.136520
$473$	6.04721	−	6.04721i	0.278051	−	0.278051i
$474$	4.00976	+	3.17164i	0.184174	+	0.145678i
$475$		−	1.60510i		−	0.0736473i
$476$	0.0137240	+	0.0512186i	0.000629038	+	0.00234760i
$477$	−35.5875	−	1.04783i	−1.62944	−	0.0479768i
$478$	11.6987	−	11.6987i	0.535087	−	0.535087i
$479$	2.64912	+	2.64912i	0.121041	+	0.121041i	0.765033	−	0.643991i	$-0.222723\pi$
$479$	2.64912	+	2.64912i	0.121041	+	0.121041i	−0.643991	+	0.765033i	$0.722723\pi$
$480$	31.1636	−	12.3743i	1.42242	−	0.564805i
$481$	7.39634	+	4.27028i	0.337244	+	0.194708i
$482$	31.1236	+	17.9692i	1.41764	+	0.818476i
$483$	30.2327	−	38.2219i	1.37564	−	1.73916i
$484$	−18.9919	+	10.9650i	−0.863269	+	0.498409i
$485$		−	5.18594i		−	0.235481i
$486$	−17.3957	−	26.4988i	−0.789083	−	1.20201i
$487$	−32.5772			−1.47621			−0.738106	−	0.674685i	$-0.764280\pi$
$487$	−32.5772			−1.47621			−0.738106	+	0.674685i	$0.764280\pi$
$488$	1.09539	+	0.632422i	0.0495858	+	0.0286284i
$489$	17.6206	+	7.60442i	0.796832	+	0.343884i
$490$	6.06715	−	10.5086i	0.274086	−	0.474730i
$491$	7.10319	−	1.90329i	0.320562	−	0.0858944i	−0.0949498	−	0.995482i	$-0.530269\pi$
$491$	7.10319	−	1.90329i	0.320562	−	0.0858944i	0.415512	+	0.909588i	$0.363602\pi$
$492$	24.3995	−	2.84761i	1.10002	−	0.128380i
$493$	−0.0802348	+	0.0214989i	−0.00361359	+	0.000968260i
$494$	11.7877	+	11.7877i	0.530353	+	0.530353i
$495$	−6.11795	−	0.180136i	−0.274981	−	0.00809649i
$496$	−17.6552	+	10.1932i	−0.792743	+	0.457690i
$497$	3.30340	−	12.3285i	0.148178	−	0.553007i
$498$	40.6263	+	5.95807i	1.82051	+	0.266987i
$499$	−23.3836	−	23.3836i	−1.04679	−	1.04679i	−0.998850	−	0.0479415i	$-0.984734\pi$
$499$	−23.3836	−	23.3836i	−1.04679	−	1.04679i	−0.0479415	−	0.998850i	$-0.515266\pi$
$500$	−15.4610	+	15.4610i	−0.691437	+	0.691437i
$501$	−4.55106	−	11.4615i	−0.203326	−	0.512061i
$502$	49.7148	−	28.7028i	2.21888	−	1.28107i
$503$	−21.8295	+	21.8295i	−0.973330	+	0.973330i	−0.999653	−	0.0263235i	$-0.991620\pi$
$503$	−21.8295	+	21.8295i	−0.973330	+	0.973330i	0.0263235	+	0.999653i	$0.491620\pi$
$504$	0.584218	+	2.46882i	0.0260231	+	0.109970i
$505$	29.7108	−	7.96098i	1.32211	−	0.354259i
$506$	13.7206	+	7.92158i	0.609954	+	0.352157i
$507$	−0.250609	−	0.631140i	−0.0111300	−	0.0280299i
$508$	−15.3820	−	26.6424i	−0.682466	−	1.18207i
$509$	3.16909	+	11.8272i	0.140468	+	0.524232i	0.999915	+	0.0130088i	$0.00414094\pi$
$509$	3.16909	+	11.8272i	0.140468	+	0.524232i	−0.859448	+	0.511224i	$0.829192\pi$
$510$	0.0671536	+	0.00984843i	0.00297361	+	0.000436096i
$511$	10.2379	−	17.7326i	0.452900	−	0.784446i
$512$	−22.6922	+	22.6922i	−1.00286	+	1.00286i
$513$	9.53869	−	6.67168i	0.421143	−	0.294562i
$514$	−9.03899	+	33.7340i	−0.398693	+	1.48794i
$515$	8.12490	−	14.0727i	0.358026	−	0.620119i
$516$	−29.7310	+	22.1259i	−1.30883	+	0.974039i
$517$	−4.23563			−0.186283
$518$	−12.6647	+	7.31197i	−0.556455	+	0.321269i
$519$	0.558252	+	0.441565i	0.0245045	+	0.0193826i
$520$			2.40117i			0.105298i
$521$	0.950810	−	3.54847i	0.0416557	−	0.155461i	−0.941965	−	0.335710i	$-0.891024\pi$
$521$	0.950810	−	3.54847i	0.0416557	−	0.155461i	0.983621	+	0.180249i	$0.0576904\pi$
$522$	−61.1809	+	14.4778i	−2.67782	+	0.633674i
$523$	−4.50702	−	7.80639i	−0.197078	−	0.341350i	0.750501	−	0.660869i	$-0.229812\pi$
$523$	−4.50702	−	7.80639i	−0.197078	−	0.341350i	−0.947580	+	0.319519i	$0.896479\pi$
$524$	−2.99417	+	11.1744i	−0.130801	+	0.488156i
$525$	−2.28315	−	3.06791i	−0.0996449	−	0.133895i
$526$	7.51801	−	28.0576i	0.327801	−	1.22337i
$527$	−0.0442668			−0.00192829
$528$	5.09881	−	2.02461i	0.221897	−	0.0881097i
$529$			60.3675i			2.62468i
$530$	40.7991	−	40.7991i	1.77220	−	1.77220i
$531$	−27.5900	−	17.0310i	−1.19731	−	0.739082i
$532$	−14.2359	+	3.81449i	−0.617203	+	0.165379i
$533$	6.29201	−	23.4821i	0.272537	−	1.01712i
$534$	−14.1992	+	32.9017i	−0.614458	+	1.42380i
$535$			24.7379i			1.06951i
$536$	0.680562	+	0.680562i	0.0293958	+	0.0293958i
$537$	14.8918	+	6.42674i	0.642627	+	0.277334i
$538$	0.584172			0.0251854
$539$	1.06486	−	1.84439i	0.0458666	−	0.0794433i
$540$	26.1185	+	4.61939i	1.12396	+	0.198787i
$541$	−9.59959	+	2.57220i	−0.412719	+	0.110588i	−0.459203	−	0.888331i	$-0.651865\pi$
$541$	−9.59959	+	2.57220i	−0.412719	+	0.110588i	0.0464842	+	0.998919i	$0.485198\pi$
$542$	15.6034	−	9.00864i	0.670224	−	0.386954i
$543$	17.3842	−	40.2818i	0.746026	−	1.72866i
$544$	−0.0630356	+	0.0168903i	−0.00270263	+	0.000724167i
$545$	−7.76592	−	2.08087i	−0.332655	−	0.0891347i
$546$	39.2975	+	5.76320i	1.68178	+	0.246642i
$547$	−30.9186	−	17.8509i	−1.32198	−	0.763248i	−0.337940	−	0.941168i	$-0.609730\pi$
$547$	−30.9186	−	17.8509i	−1.32198	−	0.763248i	−0.984045	+	0.177920i	$0.943063\pi$
$548$	15.4210	−	4.13205i	0.658754	−	0.176512i
$549$	−6.55803	−	12.1727i	−0.279890	−	0.519519i
$550$	0.879118	−	0.879118i	0.0374857	−	0.0374857i
$551$	−5.97546	−	22.3007i	−0.254563	−	0.950042i
$552$	−3.40392	−	2.69243i	−0.144880	−	0.114597i
$553$			4.47303i			0.190213i
$554$	14.2499	−	53.1813i	0.605419	−	2.25946i
$555$	1.12034	+	9.59954i	0.0475558	+	0.407478i
$556$	−4.88966	+	18.2485i	−0.207368	+	0.773907i
$557$	20.9476	+	36.2822i	0.887577	+	1.53733i	0.842732	+	0.538334i	$0.180946\pi$
$557$	20.9476	+	36.2822i	0.887577	+	1.53733i	0.0448449	+	0.998994i	$0.485721\pi$
$558$	−33.4902	−	0.986079i	−1.41776	−	0.0417441i
$559$	9.49254	+	35.4266i	0.401492	+	1.49839i
$560$	23.6840	+	13.6740i	1.00083	+	0.577830i
$561$	0.0117863	+	0.00172852i	0.000497616	+	7.29781e-5i
$562$	−10.0760	+	37.6042i	−0.425031	+	1.58624i
$563$	−8.06626	+	8.06626i	−0.339952	+	0.339952i	−0.856349	−	0.516397i	$-0.827273\pi$
$563$	−8.06626	+	8.06626i	−0.339952	+	0.339952i	0.516397	+	0.856349i	$0.327273\pi$
$564$	18.1610	+	2.66341i	0.764715	+	0.112150i
$565$	5.60732	−	20.9268i	0.235902	−	0.880397i
$566$	13.7120	+	3.67411i	0.576357	+	0.154434i
$567$	8.74175	−	26.3200i	0.367119	−	1.10534i
$568$	−1.09793	−	0.294190i	−0.0460683	−	0.0123440i
$569$	−25.1660	−	25.1660i	−1.05501	−	1.05501i	−0.998396	−	0.0566157i	$-0.981969\pi$
$569$	−25.1660	−	25.1660i	−1.05501	−	1.05501i	−0.0566157	−	0.998396i	$-0.518031\pi$
$570$	−2.73730	+	18.6649i	−0.114653	+	0.781785i
$571$	1.21155	+	2.09846i	0.0507017	+	0.0878178i	0.890262	−	0.455448i	$-0.150521\pi$
$571$	1.21155	+	2.09846i	0.0507017	+	0.0878178i	−0.839561	+	0.543266i	$0.817188\pi$
$572$			6.66685i			0.278755i
$573$	−23.6557	−	10.2089i	−0.988232	−	0.426485i
$574$	29.4345	+	29.4345i	1.22857	+	1.22857i
$575$	6.31919	+	1.69322i	0.263528	+	0.0706122i
$576$	−26.3934	+	6.24570i	−1.09973	+	0.260237i
$577$	−21.9140	−	37.9561i	−0.912290	−	1.58013i	−0.810822	−	0.585293i	$-0.800979\pi$
$577$	−21.9140	−	37.9561i	−0.912290	−	1.58013i	−0.101468	−	0.994839i	$-0.532354\pi$
$578$	33.3908	+	8.94703i	1.38887	+	0.372148i
$579$	1.45912	−	9.94933i	0.0606391	−	0.413480i
$580$	26.3036	−	45.5592i	1.09220	−	1.89174i
$581$	17.9626	+	31.1121i	0.745213	+	1.29075i
$582$	−1.10850	+	7.55853i	−0.0459488	+	0.313311i
$583$	7.16073	−	7.16073i	0.296567	−	0.296567i
$584$	−1.57921	−	0.911759i	−0.0653483	−	0.0377288i
$585$	13.7878	−	22.3361i	0.570054	−	0.923482i
$586$	13.0255	−	22.5608i	0.538077	−	0.931976i
$587$	15.8525	+	15.8525i	0.654302	+	0.654302i	0.954026	−	0.299724i	$-0.0968946\pi$
$587$	15.8525	+	15.8525i	0.654302	+	0.654302i	−0.299724	+	0.954026i	$0.596895\pi$
$588$	−5.72552	+	7.23853i	−0.236117	+	0.298512i
$589$		−	12.3037i		−	0.506963i
$590$	50.7551	−	13.5998i	2.08955	−	0.559894i
$591$	−8.82617	+	3.50464i	−0.363060	+	0.144162i
$592$	−4.33137	−	7.50215i	−0.178018	−	0.308336i
$593$	1.23539	−	2.13976i	0.0507315	−	0.0878695i	−0.839545	−	0.543291i	$-0.817178\pi$
$593$	1.23539	−	2.13976i	0.0507315	−	0.0878695i	0.890276	+	0.455421i	$0.150511\pi$
$594$	8.87844	+	1.57027i	0.364287	+	0.0644288i
$595$	0.0296914	+	0.0514269i	0.00121723	+	0.00210830i
$596$	−10.1677	−	10.1677i	−0.416487	−	0.416487i
$597$	−26.1690	+	10.3910i	−1.07103	+	0.425277i
$598$	−58.8421	+	33.9725i	−2.40623	+	1.38924i
$599$	−10.2551	−	10.2551i	−0.419011	−	0.419011i	0.465852	−	0.884863i	$-0.345748\pi$
$599$	−10.2551	−	10.2551i	−0.419011	−	0.419011i	−0.884863	+	0.465852i	$0.845748\pi$
$600$	−0.273219	+	0.203330i	−0.0111541	+	0.00830092i
$601$	−7.94731			−0.324177			−0.162089	−	0.986776i	$-0.551823\pi$
$601$	−7.94731			−0.324177			−0.162089	+	0.986776i	$0.551823\pi$
$602$	−60.6608	−	16.2540i	−2.47235	−	0.662464i
$603$	−2.42284	−	10.2386i	−0.0986656	−	0.416947i
$604$	7.99455	+	29.8361i	0.325294	+	1.21401i
$605$	−17.3660	+	17.3660i	−0.706028	+	0.706028i
$606$	−45.0053	+	5.25246i	−1.82822	+	0.213367i
$607$	−11.6366	−	43.4285i	−0.472316	−	1.76271i	−0.631416	−	0.775444i	$-0.717526\pi$
$607$	−11.6366	−	43.4285i	−0.472316	−	1.76271i	0.159100	−	0.987262i	$-0.449141\pi$
$608$	−4.69455	−	17.5203i	−0.190389	−	0.710542i
$609$	−43.1424	−	34.1247i	−1.74822	−	1.38280i
$610$	21.6445	+	5.79963i	0.876361	+	0.234820i
$611$	9.08247	−	15.7313i	0.367437	−	0.636420i
$612$	−0.0494487	−	0.0148226i	−0.00199884	−	0.000599169i
$613$	−6.45740	+	24.0993i	−0.260812	+	0.973363i	0.703952	+	0.710247i	$0.251417\pi$
$613$	−6.45740	+	24.0993i	−0.260812	+	0.973363i	−0.964764	+	0.263116i	$0.915250\pi$
$614$	−53.1893			−2.14654
$615$	25.5684	−	10.1525i	1.03102	−	0.409390i
$616$	−0.624940	−	0.360809i	−0.0251795	−	0.0145374i
$617$	11.9776	−	20.7458i	0.482200	−	0.835195i	−0.517591	−	0.855628i	$-0.673171\pi$
$617$	11.9776	−	20.7458i	0.482200	−	0.835195i	0.999791	+	0.0204328i	$0.00650440\pi$
$618$	−14.8501	+	18.7744i	−0.597360	+	0.755216i
$619$	−20.5608	+	11.8708i	−0.826408	+	0.477127i	−0.852621	−	0.522529i	$-0.824988\pi$
$619$	−20.5608	+	11.8708i	−0.826408	+	0.477127i	0.0262132	+	0.999656i	$0.491655\pi$
$620$	19.8239	−	19.8239i	0.796147	−	0.796147i
$621$	16.2036	+	44.5911i	0.650228	+	1.78938i
$622$	−48.1263	+	12.8954i	−1.92969	+	0.517058i
$623$	−30.2845	+	8.11470i	−1.21332	+	0.325108i
$624$	−3.41393	+	23.2786i	−0.136667	+	0.931889i
$625$	−14.0346	+	24.3086i	−0.561383	+	0.972344i
$626$	18.0635	+	18.0635i	0.721962	+	0.721962i
$627$	−0.480429	+	3.27591i	−0.0191865	+	0.130827i
$628$	−25.1504	+	9.11418i	−1.00361	+	0.363695i
$629$		−	0.0188101i		−	0.000750007i
$630$	21.3175	+	39.5687i	0.849311	+	1.57645i
$631$	32.6583	+	18.8553i	1.30011	+	0.750617i	0.980422	−	0.196908i	$-0.0630899\pi$
$631$	32.6583	+	18.8553i	1.30011	+	0.750617i	0.319684	+	0.947524i	$0.396423\pi$
$632$	0.398354			0.0158457
$633$	−0.423424	−	3.62808i	−0.0168296	−	0.144203i
$634$	−3.37717	−	12.6038i	−0.134125	−	0.500560i
$635$	−24.3615	−	24.3615i	−0.966756	−	0.966756i
$636$	−35.2056	+	26.2001i	−1.39599	+	1.03890i
$637$	4.56675	+	7.90985i	0.180941	+	0.313400i
$638$	8.94136	−	15.4869i	0.353992	−	0.613132i
$639$	8.52388	+	9.04106i	0.337200	+	0.357659i
$640$	2.61860	−	4.53555i	0.103509	−	0.179283i
$641$	10.7316	+	18.5877i	0.423874	+	0.734171i	0.996315	−	0.0857753i	$-0.0273367\pi$
$641$	10.7316	+	18.5877i	0.423874	+	0.734171i	−0.572441	+	0.819946i	$0.694003\pi$
$642$	5.28774	−	36.0556i	0.208690	−	1.42300i
$643$	23.9977	+	6.43017i	0.946378	+	0.253581i	0.698825	−	0.715293i	$-0.253707\pi$
$643$	23.9977	+	6.43017i	0.946378	+	0.253581i	0.247554	+	0.968874i	$0.420373\pi$
$644$		−	60.0695i		−	2.36707i
$645$	−25.7478	+	32.5518i	−1.01382	+	1.28173i
$646$	0.00950265	−	0.0354644i	0.000373877	−	0.00139533i
$647$	−1.72140	−	0.993852i	−0.0676753	−	0.0390723i	0.465781	−	0.884900i	$-0.345774\pi$
$647$	−1.72140	−	0.993852i	−0.0676753	−	0.0390723i	−0.533456	+	0.845828i	$0.679107\pi$
$648$	−2.34398	−	0.778512i	−0.0920801	−	0.0305829i
$649$	8.90812	−	2.38692i	0.349674	−	0.0936949i
$650$	1.37999	+	5.15018i	0.0541275	+	0.202007i
$651$	−17.5011	−	23.5166i	−0.685922	−	0.921686i
$652$	22.8497	−	6.12257i	0.894865	−	0.239778i
$653$	15.1930	+	26.3151i	0.594548	+	1.02979i	0.993610	+	0.112864i	$0.0360024\pi$
$653$	15.1930	+	26.3151i	0.594548	+	1.02979i	−0.399062	+	0.916924i	$0.630664\pi$
$654$	10.8741	+	4.69285i	0.425210	+	0.183505i
$655$			12.9556i			0.506216i
$656$	−17.4360	+	17.4360i	−0.680762	+	0.680762i
$657$	9.45467	+	17.5493i	0.368862	+	0.684665i
$658$	15.5518	+	26.9366i	0.606274	+	1.05010i
$659$	1.56553	+	2.71157i	0.0609843	+	0.105628i	0.894906	−	0.446255i	$-0.147243\pi$
$659$	1.56553	+	2.71157i	0.0609843	+	0.105628i	−0.833921	+	0.551883i	$0.813909\pi$
$660$	−6.05229	+	4.50414i	−0.235585	+	0.175323i
$661$	−21.9388	+	12.6664i	−0.853321	+	0.492665i	−0.861770	−	0.507299i	$-0.830644\pi$
$661$	−21.9388	+	12.6664i	−0.853321	+	0.492665i	0.00844893	+	0.999964i	$0.497311\pi$
$662$	−5.37498	−	20.0597i	−0.208905	−	0.779643i
$663$	−0.0316931	+	0.0400682i	−0.00123086	+	0.00155612i
$664$	2.77074	−	1.59969i	0.107526	−	0.0620800i
$665$	−14.2938	+	8.25251i	−0.554288	+	0.320018i
$666$	0.419010	−	14.2309i	0.0162363	−	0.551434i
$667$	94.0999			3.64356
$668$	−13.1641	−	7.60031i	−0.509335	−	0.294065i
$669$	−6.32446	+	4.70669i	−0.244518	+	0.181971i
$670$	14.7666	+	8.52551i	0.570484	+	0.329369i
$671$	3.79887	+	1.01790i	0.146654	+	0.0392958i
$672$	−33.8943	−	26.8097i	−1.30750	−	1.03421i
$673$	25.9063	+	25.9063i	0.998615	+	0.998615i	0.999999	−	0.00138452i	$-0.000440707\pi$
$673$	25.9063	+	25.9063i	0.998615	+	0.998615i	−0.00138452	+	0.999999i	$0.500441\pi$
$674$		−	4.07565i		−	0.156988i
$675$	3.70907	−	0.322559i	0.142762	−	0.0124153i
$676$	−0.724899	−	0.418520i	−0.0278807	−	0.0160969i
$677$	18.5474			0.712834			0.356417	−	0.934327i	$-0.383998\pi$
$677$	18.5474			0.712834			0.356417	+	0.934327i	$0.383998\pi$
$678$	−12.6458	+	29.3023i	−0.485660	+	1.12535i
$679$	−5.78841	+	3.34194i	−0.222139	+	0.128252i
$680$	0.00457992	−	0.00264422i	0.000175632	−	0.000101401i
$681$	−5.37270	−	2.31866i	−0.205882	−	0.0888513i
$682$	6.73873	−	6.73873i	0.258039	−	0.258039i
$683$	−44.6048	−	11.9518i	−1.70676	−	0.457324i	−0.732130	−	0.681165i	$-0.761474\pi$
$683$	−44.6048	−	11.9518i	−1.70676	−	0.457324i	−0.974626	+	0.223841i	$0.928140\pi$
$684$	4.11985	−	13.7439i	0.157526	−	0.525512i
$685$	15.4837	−	8.93955i	0.591604	−	0.341563i
$686$	28.2239			1.07759
$687$	34.8120	−	25.9072i	1.32816	−	0.988420i
$688$	9.62834	−	35.9335i	0.367077	−	1.36995i
$689$	11.2405	+	41.9500i	0.428228	+	1.59817i
$690$	−70.5947	−	30.4661i	−2.68750	−	1.15982i
$691$	−9.05578	−	2.42649i	−0.344498	−	0.0923080i	0.0824216	−	0.996598i	$-0.473735\pi$
$691$	−9.05578	−	2.42649i	−0.344498	−	0.0923080i	−0.426920	+	0.904290i	$0.640401\pi$
$692$	0.877348			0.0333518
$693$	3.74149	+	6.94478i	0.142127	+	0.263810i
$694$	67.2450	+	18.0183i	2.55259	+	0.683964i
$695$			21.1572i			0.802539i
$696$	−3.03904	+	3.84213i	−0.115195	+	0.145635i
$697$	−0.0517180	+	0.0138578i	−0.00195896	+	0.000524901i
$698$	2.42936	+	9.06649i	0.0919526	+	0.343172i
$699$	16.4934	+	41.5373i	0.623837	+	1.57108i
$700$	−4.55322	−	1.22003i	−0.172095	−	0.0461128i
$701$	4.83399	+	18.0407i	0.182577	+	0.681388i	0.995136	+	0.0985088i	$0.0314073\pi$
$701$	4.83399	+	18.0407i	0.182577	+	0.681388i	−0.812559	+	0.582879i	$0.801926\pi$
$702$	−24.8701	+	29.6078i	−0.938661	+	1.11747i
$703$	5.22813			0.197183
$704$	3.85730	−	6.68104i	0.145377	−	0.251801i
$705$	20.4173	−	2.38286i	0.768960	−	0.0897435i
$706$	−45.5062	−	45.5062i	−1.71265	−	1.71265i
$707$	−28.0322	−	28.0322i	−1.05426	−	1.05426i
$708$	−39.6960	+	4.63283i	−1.49187	+	0.174112i
$709$	16.9008	−	29.2731i	0.634723	−	1.09937i	−0.351850	−	0.936056i	$-0.614447\pi$
$709$	16.9008	−	29.2731i	0.634723	−	1.09937i	0.986574	−	0.163317i	$-0.0522192\pi$
$710$	−20.1372			−0.755736
$711$	−3.70555	−	2.28739i	−0.138969	−	0.0857839i
$712$	0.722669	+	2.69704i	0.0270832	+	0.101076i
$713$	48.4386	+	12.9791i	1.81404	+	0.486071i
$714$	−0.0322827	−	0.0813016i	−0.00120815	−	0.00304264i
$715$	1.93238	+	7.21175i	0.0722670	+	0.269704i
$716$	19.3111	−	5.17438i	0.721688	−	0.193376i
$717$	−8.74239	+	11.0526i	−0.326490	+	0.412768i
$718$			10.7201i			0.400072i
$719$	38.5963	+	10.3419i	1.43940	+	0.385686i	0.892324	−	0.451396i	$-0.149074\pi$
$719$	38.5963	+	10.3419i	1.43940	+	0.385686i	0.547077	+	0.837082i	$0.315741\pi$
$720$	−23.4392	+	12.6278i	−0.873527	+	0.470611i
$721$	−20.9435			−0.779976
$722$	−27.4622	−	7.35847i	−1.02204	−	0.273854i
$723$	−28.1059	−	12.1295i	−1.04527	−	0.451099i
$724$	−13.9966	−	52.2359i	−0.520178	−	1.94133i
$725$	1.91120	−	7.13269i	0.0709802	−	0.264902i
$726$	29.0230	−	21.5990i	1.07714	−	0.801614i
$727$	21.1515			0.784467			0.392233	−	0.919866i	$-0.371703\pi$
$727$	21.1515			0.784467			0.392233	+	0.919866i	$0.371703\pi$
$728$	2.68012	−	1.54737i	0.0993318	−	0.0573493i
$729$	17.3338	+	20.7012i	0.641991	+	0.766712i
$730$	−31.2048	−	8.36129i	−1.15494	−	0.309465i
$731$	0.0571184	−	0.0571184i	0.00211260	−	0.00211260i
$732$	−15.6482	−	6.75321i	−0.578376	−	0.249606i
$733$	43.7043	−	25.2327i	1.61426	−	0.931991i	0.625887	−	0.779914i	$-0.284737\pi$
$733$	43.7043	−	25.2327i	1.61426	−	0.931991i	0.988369	−	0.152077i	$-0.0485963\pi$
$734$	21.9185	−	12.6547i	0.809028	−	0.467093i
$735$	−4.09540	+	9.48969i	−0.151061	+	0.350032i
$736$	73.9285			2.72504
$737$	2.59172	+	1.49633i	0.0954671	+	0.0551180i
$738$	−39.4362	+	9.33211i	−1.45166	+	0.343520i
$739$		−	17.8705i		−	0.657379i	−0.944438	−	0.328689i	$-0.893393\pi$
$739$		−	17.8705i		−	0.657379i	0.944438	−	0.328689i	$-0.106607\pi$
$740$	8.42368	+	8.42368i	0.309661	+	0.309661i
$741$	−11.1367	−	8.80887i	−0.409116	−	0.323602i
$742$	−71.8307	−	19.2470i	−2.63699	−	0.706579i
$743$	14.6660	+	8.46739i	0.538042	+	0.310639i	0.744285	−	0.667862i	$-0.232790\pi$
$743$	14.6660	+	8.46739i	0.538042	+	0.310639i	−0.206243	+	0.978501i	$0.566124\pi$
$744$	−2.09431	+	1.55859i	−0.0767811	+	0.0571408i
$745$	−13.9459	−	8.05166i	−0.510938	−	0.294990i
$746$	8.53574			0.312516
$747$	−34.9595	−	1.02934i	−1.27910	−	0.0376616i
$748$	0.0127162	−	0.00734168i	0.000464949	−	0.000268438i
$749$	27.6117	−	15.9416i	1.00891	−	0.582495i
$750$	22.3775	−	28.2909i	0.817111	−	1.03304i
$751$	0.934841	+	3.48887i	0.0341128	+	0.127311i	0.980882	−	0.194601i	$-0.0623412\pi$
$751$	0.934841	+	3.48887i	0.0341128	+	0.127311i	−0.946770	+	0.321912i	$0.895675\pi$
$752$	−15.9564	+	9.21241i	−0.581868	+	0.335942i
$753$	−39.2263	+	29.1923i	−1.42948	+	1.06383i
$754$	38.3460	+	66.4172i	1.39648	+	2.41877i
$755$	17.2959	+	29.9574i	0.629463	+	1.09026i
$756$	−11.6753	−	32.1296i	−0.424627	−	1.16854i
$757$	−29.2604	+	29.2604i	−1.06349	+	1.06349i	−0.0656432	+	0.997843i	$0.520910\pi$
$757$	−29.2604	+	29.2604i	−1.06349	+	1.06349i	−0.997843	+	0.0656432i	$0.979090\pi$
$758$		−	58.8990i		−	2.13931i
$759$	−12.3902	−	5.34717i	−0.449737	−	0.194090i
$760$	0.734942	+	1.27296i	0.0266591	+	0.0461750i
$761$	18.2751	−	4.89679i	0.662470	−	0.177508i	0.0881097	−	0.996111i	$-0.471917\pi$
$761$	18.2751	−	4.89679i	0.662470	−	0.177508i	0.574361	+	0.818602i	$0.305251\pi$
$762$	30.2997	+	40.7143i	1.09764	+	1.47492i
$763$	2.68192	+	10.0091i	0.0970921	+	0.362353i
$764$	−30.6758	+	8.21956i	−1.10981	+	0.297373i
$765$	−0.0577866	−	0.00170145i	−0.00208928	−	6.15162e-5i
$766$	12.4669	+	7.19778i	0.450448	+	0.260066i
$767$	−10.2366	+	38.2034i	−0.369621	+	1.37945i
$768$	14.6428	−	18.5122i	0.528376	−	0.668003i
$769$			4.97354i			0.179350i	0.995971	+	0.0896752i	$0.0285829\pi$
$769$			4.97354i			0.179350i	−0.995971	+	0.0896752i	$0.971417\pi$
$770$	−12.3486	−	3.30880i	−0.445013	−	0.119241i
$771$	4.31644	−	29.4326i	0.155453	−	1.05999i
$772$	−6.19746	−	10.7343i	−0.223051	−	0.386336i
$773$	−21.8797	+	37.8968i	−0.786959	+	1.36305i	0.140863	+	0.990029i	$0.455012\pi$
$773$	−21.8797	+	37.8968i	−0.786959	+	1.36305i	−0.927822	+	0.373024i	$0.878321\pi$
$774$	44.4855	−	41.9408i	1.59900	−	1.50753i
$775$	1.96761	−	3.40800i	0.0706786	−	0.122419i
$776$	0.297622	+	0.515497i	0.0106840	+	0.0185053i
$777$	9.99278	−	7.43666i	0.358489	−	0.266789i
$778$	−3.67796	−	3.67796i	−0.131861	−	0.131861i
$779$	−3.85168	−	14.3747i	−0.138001	−	0.515025i
$780$	−3.75060	−	32.1367i	−0.134293	−	1.15068i
$781$	−3.53432			−0.126468
$782$	0.129596	+	0.0748226i	0.00463436	+	0.00267565i
$783$	50.3316	−	18.2896i	1.79870	−	0.653616i
$784$		−	9.26417i		−	0.330863i
$785$	−24.5643	+	17.1489i	−0.876738	+	0.612072i
$786$	2.76926	−	18.8828i	0.0987764	−	0.673527i
$787$	25.8189	+	25.8189i	0.920344	+	0.920344i	0.997054	−	0.0767092i	$-0.0244413\pi$
$787$	25.8189	+	25.8189i	0.920344	+	0.920344i	−0.0767092	+	0.997054i	$0.524441\pi$
$788$	−5.85279	+	10.1373i	−0.208497	+	0.361127i
$789$	−3.59012	+	24.4800i	−0.127812	+	0.871510i
$790$	6.81679	−	1.82655i	0.242531	−	0.0649859i
$791$	−26.9714	+	7.22697i	−0.958993	+	0.256962i
$792$	0.618480	−	0.333205i	0.0219767	−	0.0118399i
$793$	−11.9265	+	11.9265i	−0.423522	+	0.423522i
$794$	−17.4231	+	10.0592i	−0.618324	+	0.356989i
$795$	−30.4889	+	38.5458i	−1.08133	+	1.36708i
$796$	−17.3532	+	30.0565i	−0.615066	+	1.06533i
$797$	−41.7686	−	24.1151i	−1.47952	−	0.854201i	−0.479789	−	0.877384i	$-0.659287\pi$
$797$	−41.7686	−	24.1151i	−1.47952	−	0.854201i	−0.999731	+	0.0231826i	$0.992620\pi$
$798$	22.5972	−	8.97276i	0.799932	−	0.317632i
$799$	−0.0400072			−0.00141535
$800$	1.50151	−	5.60372i	0.0530865	−	0.198121i
$801$	8.76430	−	29.2379i	0.309671	−	1.03307i
$802$	−1.03600	+	1.79440i	−0.0365823	+	0.0633623i
$803$	−5.47681	−	1.46751i	−0.193272	−	0.0517872i
$804$	−10.1715	−	8.04546i	−0.358722	−	0.283742i
$805$	−17.4111	−	64.9791i	−0.613661	−	2.29021i
$806$	10.5780	+	39.4778i	0.372596	+	1.39055i
$807$	−0.494229	+	0.0576803i	−0.0173977	+	0.00203044i
$808$	−2.49646	+	2.49646i	−0.0878250	+	0.0878250i
$809$	−7.94303	−	29.6438i	−0.279262	−	1.04222i	−0.952931	−	0.303187i	$-0.901949\pi$
$809$	−7.94303	−	29.6438i	−0.279262	−	1.04222i	0.673669	−	0.739033i	$-0.264717\pi$
$810$	−43.6808	−	2.57449i	−1.53479	−	0.0904582i
$811$	5.91720	+	1.58551i	0.207781	+	0.0556748i	0.361208	−	0.932485i	$-0.382364\pi$
$811$	5.91720	+	1.58551i	0.207781	+	0.0556748i	−0.153427	+	0.988160i	$0.549031\pi$
$812$	−67.8026			−2.37940
$813$	−12.3115	+	9.16227i	−0.431784	+	0.321335i
$814$	2.86346	+	2.86346i	0.100364	+	0.100364i
$815$	22.9427	−	13.2460i	0.803647	−	0.463986i
$816$	0.0481604	−	0.0191232i	0.00168595	−	0.000669447i
$817$	15.8757	+	15.8757i	0.555419	+	0.555419i
$818$	17.9977	+	31.1729i	0.629275	+	1.08994i
$819$	−33.8161	−	0.995673i	−1.18163	−	0.0347916i
$820$	16.9548	−	29.3667i	0.592089	−	1.02553i
$821$	−13.5854	−	23.5307i	−0.474135	−	0.821226i	0.525426	−	0.850839i	$-0.323906\pi$
$821$	−13.5854	−	23.5307i	−0.474135	−	0.821226i	−0.999561	+	0.0296130i	$0.990573\pi$
$822$	−24.4785	+	9.71977i	−0.853785	+	0.339016i
$823$	−15.4549	+	4.14112i	−0.538723	+	0.144350i	−0.517913	−	0.855433i	$-0.673291\pi$
$823$	−15.4549	+	4.14112i	−0.538723	+	0.144350i	−0.0208096	+	0.999783i	$0.506624\pi$
$824$			1.86516i			0.0649759i
$825$	−0.656960	+	0.830566i	−0.0228724	+	0.0289166i
$826$	−47.8874	−	47.8874i	−1.66622	−	1.66622i
$827$	−17.9477	+	31.0863i	−0.624103	+	1.08098i	0.364611	+	0.931160i	$0.381202\pi$
$827$	−17.9477	+	31.0863i	−0.624103	+	1.08098i	−0.988714	+	0.149818i	$0.952131\pi$
$828$	49.7629	+	30.7180i	1.72938	+	1.06752i
$829$	−3.83392	−	2.21352i	−0.133158	−	0.0768786i	0.431941	−	0.901902i	$-0.357829\pi$
$829$	−3.83392	−	2.21352i	−0.133158	−	0.0768786i	−0.565099	+	0.825023i	$0.691162\pi$
$830$	40.0791	−	40.0791i	1.39117	−	1.39117i
$831$	−6.80483	+	46.4001i	−0.236057	+	1.60960i
$832$	16.5424	+	28.6523i	0.573506	+	0.993341i
$833$	0.0100580	−	0.0174210i	0.000348489	−	0.000603601i
$834$	4.52237	−	30.8367i	0.156597	−	1.06779i
$835$	−16.4430	−	4.40589i	−0.569033	−	0.152472i
$836$	2.04057	+	3.53437i	0.0705745	+	0.122239i
$837$	28.4312	−	2.47252i	0.982727	−	0.0854629i
$838$	−54.6347	−	14.6393i	−1.88732	−	0.505707i
$839$	14.8694	+	14.8694i	0.513349	+	0.513349i	0.915551	−	0.402202i	$-0.131755\pi$
$839$	14.8694	+	14.8694i	0.513349	+	0.513349i	−0.402202	+	0.915551i	$0.631755\pi$
$840$	3.21542	+	1.38766i	0.110943	+	0.0478788i
$841$		−	77.2139i		−	2.66255i
$842$	−18.5776	−	32.1773i	−0.640226	−	1.10890i
$843$	4.81166	−	32.8093i	0.165722	−	1.13001i
$844$	−3.18367	−	3.18367i	−0.109586	−	0.109586i
$845$	−0.905454	−	0.242616i	−0.0311486	−	0.00834623i
$846$	−30.2677	−	0.891194i	−1.04062	−	0.0306399i
$847$	30.5745	+	8.19241i	1.05055	+	0.281494i
$848$	11.4013	−	42.5501i	0.391521	−	1.46118i
$849$	−11.9635	−	1.75452i	−0.410588	−	0.0602149i
$850$	0.00830363	−	0.00830363i	0.000284812	−	0.000284812i
$851$	−5.51515	+	20.5828i	−0.189057	+	0.705569i
$852$	15.1540	+	2.22242i	0.519168	+	0.0761388i
$853$	38.2682	+	22.0941i	1.31028	+	0.756489i	0.982142	−	0.188142i	$-0.0602465\pi$
$853$	38.2682	+	22.0941i	1.31028	+	0.756489i	0.328135	+	0.944631i	$0.393580\pi$
$854$	−7.47483	−	27.8965i	−0.255783	−	0.954597i
$855$	0.472907	−	16.0614i	0.0161731	−	0.549287i
$856$	−1.41971	−	2.45901i	−0.0485248	−	0.0840474i
$857$	8.18852	−	30.5600i	0.279714	−	1.04391i	−0.672901	−	0.739732i	$-0.734952\pi$
$857$	8.18852	−	30.5600i	0.279714	−	1.04391i	0.952616	−	0.304176i	$-0.0983812\pi$
$858$	−1.27494	−	10.9242i	−0.0435257	−	0.372946i
$859$	−4.77455	+	17.8188i	−0.162905	+	0.607971i	0.835393	+	0.549654i	$0.185240\pi$
$859$	−4.77455	+	17.8188i	−0.162905	+	0.607971i	−0.998298	+	0.0583176i	$0.981426\pi$
$860$			51.1584i			1.74449i
$861$	−27.8088	−	21.9962i	−0.947723	−	0.749629i
$862$	12.1751	+	45.4380i	0.414685	+	1.54763i
$863$	−13.4073	+	13.4073i	−0.456390	+	0.456390i	−0.897468	−	0.441079i	$-0.854596\pi$
$863$	−13.4073	+	13.4073i	−0.456390	+	0.456390i	0.441079	+	0.897468i	$0.354596\pi$
$864$	39.5424	−	14.3690i	1.34526	−	0.488843i
$865$	0.949056	−	0.254299i	0.0322689	−	0.00864641i
$866$	−20.5755	−	11.8793i	−0.699184	−	0.403674i
$867$	−29.1331	−	4.27253i	−0.989413	−	0.145103i
$868$	−34.9019	−	9.35194i	−1.18465	−	0.317425i
$869$	1.19643	−	0.320582i	0.0405861	−	0.0108750i
$870$	−34.3882	+	79.6828i	−1.16587	+	2.70150i
$871$	−11.1149	+	6.41716i	−0.376612	+	0.217437i
$872$	0.891376	−	0.238844i	0.0301858	−	0.00808826i
$873$	0.191509	−	6.50422i	0.00648159	−	0.220134i
$874$	−20.7964	+	36.0204i	−0.703449	+	1.21841i
$875$	31.5595			1.06691
$876$	22.5600	+	9.73606i	0.762231	+	0.328951i
$877$	−1.52950	−	1.52950i	−0.0516477	−	0.0516477i	0.680811	−	0.732459i	$-0.261627\pi$
$877$	−1.52950	−	1.52950i	−0.0516477	−	0.0516477i	−0.732459	+	0.680811i	$0.761627\pi$
$878$			74.4919i			2.51398i
$879$	−8.79235	+	20.3733i	−0.296559	+	0.687173i
$880$	1.96003	−	7.31492i	0.0660725	−	0.246586i
$881$	28.9606	−	7.75997i	0.975707	−	0.261440i	0.264471	−	0.964394i	$-0.414803\pi$
$881$	28.9606	−	7.75997i	0.975707	−	0.261440i	0.711236	+	0.702954i	$0.248136\pi$
$882$	7.99750	−	12.9559i	0.269290	−	0.436247i
$883$	4.40037	−	4.40037i	0.148084	−	0.148084i	−0.629177	−	0.777262i	$-0.716608\pi$
$883$	4.40037	−	4.40037i	0.148084	−	0.148084i	0.777262	+	0.629177i	$0.216608\pi$
$884$			0.0629711i			0.00211795i
$885$	−41.5976	+	16.5173i	−1.39829	+	0.555224i
$886$	7.31669			0.245809
$887$	0.781636	−	2.91710i	0.0262448	−	0.0979468i	−0.951561	−	0.307460i	$-0.900521\pi$
$887$	0.781636	−	2.91710i	0.0262448	−	0.0979468i	0.977806	+	0.209513i	$0.0671878\pi$
$888$	−0.662285	−	0.889925i	−0.0222248	−	0.0298639i
$889$	−11.4925	+	42.8908i	−0.385448	+	1.43851i
$890$	24.7332	+	42.8392i	0.829059	+	1.43597i
$891$	−7.66650	−	0.451853i	−0.256837	−	0.0151376i
$892$	−2.51508	+	9.38640i	−0.0842110	+	0.314280i
$893$		−	11.1197i		−	0.372108i
$894$	18.6051	+	14.7163i	0.622249	+	0.492186i
$895$	19.3896	−	11.1946i	0.648123	−	0.374194i
$896$	−6.74994			−0.225500
$897$	46.4280	−	34.5519i	1.55019	−	1.15365i
$898$	19.4878	−	33.7538i	0.650316	−	1.12638i
$899$	14.6500	−	54.6744i	0.488604	−	1.82349i
$900$	3.33910	−	3.14809i	0.111303	−	0.104936i
$901$	0.0676360	−	0.0676360i	0.00225328	−	0.00225328i
$902$	5.76345	−	9.98259i	0.191902	−	0.332384i
$903$	52.9259	+	7.76187i	1.76126	+	0.258299i
$904$	0.643611	+	2.40199i	0.0214062	+	0.0798890i
$905$	−30.2811	−	52.4484i	−1.00658	−	1.74344i
$906$	−18.8055	−	47.3601i	−0.624770	−	1.57343i
$907$	34.7272	+	20.0498i	1.15310	+	0.665742i	0.949640	−	0.313342i	$-0.101449\pi$
$907$	34.7272	+	20.0498i	1.15310	+	0.665742i	0.203458	+	0.979084i	$0.434782\pi$
$908$	−6.96711	+	1.86683i	−0.231212	+	0.0619530i
$909$	37.5574	−	8.88752i	1.24570	−	0.294780i
$910$	38.7682	−	38.7682i	1.28515	−	1.28515i
$911$	−19.2779	+	11.1301i	−0.638706	+	0.368757i	−0.784116	−	0.620614i	$-0.786883\pi$
$911$	−19.2779	+	11.1301i	−0.638706	+	0.368757i	0.145410	+	0.989372i	$0.453550\pi$
$912$	5.31517	+	13.3858i	0.176003	+	0.443250i
$913$	7.03436	−	7.03436i	0.232803	−	0.232803i
$914$	22.9268	+	22.9268i	0.758351	+	0.758351i
$915$	−18.8846	−	2.76953i	−0.624307	−	0.0915579i
$916$	13.8438	−	51.6659i	0.457413	−	1.70709i
$917$	14.4607	−	8.34886i	0.477533	−	0.275704i
$918$	0.0838605	+	0.0148318i	0.00276781	+	0.000489523i
$919$	−34.8850	−	34.8850i	−1.15075	−	1.15075i	−0.986403	−	0.164346i	$-0.947449\pi$
$919$	−34.8850	−	34.8850i	−1.15075	−	1.15075i	−0.164346	−	0.986403i	$-0.552551\pi$
$920$	−5.78683	+	1.55058i	−0.190786	+	0.0511210i
$921$	44.9999	−	5.25183i	1.48280	−	0.173054i
$922$	0.0995250	−	0.0266676i	0.00327768	−	0.000878252i
$923$	7.57866	−	13.1266i	0.249455	−	0.432068i
$924$	8.92763	+	3.85284i	0.293698	+	0.126749i
$925$	1.44814	+	0.836087i	0.0476147	+	0.0274904i
$926$	49.9062			1.64002
$927$	10.7100	−	17.3500i	0.351761	−	0.569850i
$928$		−	83.4457i		−	2.73924i
$929$	9.66246	−	5.57863i	0.317015	−	0.183029i	−0.333046	−	0.942911i	$-0.608077\pi$
$929$	9.66246	−	5.57863i	0.317015	−	0.183029i	0.650061	+	0.759882i	$0.274743\pi$
$930$	−28.6921	+	36.2742i	−0.940852	+	1.18948i
$931$	4.84204	+	2.79555i	0.158692	+	0.0916206i
$932$	47.7078	+	27.5441i	1.56272	+	0.902237i
$933$	39.4431	−	15.6618i	1.29131	−	0.512746i
$934$	−0.449271	−	0.449271i	−0.0147006	−	0.0147006i
$935$	0.0116275	−	0.0116275i	0.000380260	−	0.000380260i
$936$	−0.0886714	+	3.01155i	−0.00289832	+	0.0984357i
$937$	11.6046	+	43.3088i	0.379104	+	1.41484i	0.847254	+	0.531188i	$0.178254\pi$
$937$	11.6046	+	43.3088i	0.379104	+	1.41484i	−0.468150	+	0.883649i	$0.655079\pi$
$938$		−	21.9761i		−	0.717546i
$939$	−17.0659	−	13.4988i	−0.556924	−	0.440515i
$940$	17.9164	−	17.9164i	0.584367	−	0.584367i
$941$	4.65260			0.151670			0.0758352	−	0.997120i	$-0.475838\pi$
$941$	4.65260			0.151670			0.0758352	+	0.997120i	$0.475838\pi$
$942$	39.4682	−	19.7440i	1.28594	−	0.643295i
$943$	60.6552			1.97520
$944$	28.3669	−	28.3669i	0.923265	−	0.923265i
$945$	−21.9423	−	31.3715i	−0.713783	−	1.02052i
$946$			17.3902i			0.565406i
$947$	9.26797	+	34.5885i	0.301169	+	1.12398i	0.936194	+	0.351485i	$0.114323\pi$
$947$	9.26797	+	34.5885i	0.301169	+	1.12398i	−0.635025	+	0.772491i	$0.719010\pi$
$948$	−5.33148	+	0.622224i	−0.173158	+	0.0202089i
$949$	17.1943	−	17.1943i	0.558151	−	0.558151i
$950$	2.30794	+	2.30794i	0.0748794	+	0.0748794i
$951$	4.10168	+	10.3298i	0.133006	+	0.334965i
$952$	−0.00590281	−	0.00340799i	−0.000191311	−	0.000110454i
$953$	−35.3521	−	20.4105i	−1.14517	−	0.661162i	−0.197462	−	0.980311i	$-0.563270\pi$
$953$	−35.3521	−	20.4105i	−1.14517	−	0.661162i	−0.947705	+	0.319148i	$0.896603\pi$
$954$	52.6770	−	49.6637i	1.70548	−	1.60792i
$955$	−30.8006	+	17.7827i	−0.996684	+	0.575436i
$956$			17.3703i			0.561795i
$957$	−6.03554	+	13.9853i	−0.195101	+	0.452080i
$958$	−7.61820			−0.246133
$959$	−19.9562	−	11.5217i	−0.644418	−	0.372055i
$960$	−14.8350	+	34.3751i	−0.478799	+	1.10945i
$961$	−0.417636	+	0.723367i	−0.0134721	+	0.0233344i
$962$	−16.7751	+	4.49488i	−0.540851	+	0.144921i
$963$	−0.913531	+	31.0263i	−0.0294381	+	0.999808i
$964$	−36.4466	+	9.76583i	−1.17387	+	0.314536i
$965$	−9.81532	−	9.81532i	−0.315966	−	0.315966i
$966$	11.4874	+	98.4290i	0.369602	+	3.16690i
$967$	−35.9522	+	20.7570i	−1.15614	+	0.667500i	−0.950377	−	0.311100i	$-0.899302\pi$
$967$	−35.9522	+	20.7570i	−1.15614	+	0.667500i	−0.205768	+	0.978601i	$0.565969\pi$
$968$	0.729590	−	2.72287i	0.0234499	−	0.0875162i
$969$	−0.00453785	+	0.0309423i	−0.000145777	+	0.000994010i
$970$	7.45672	+	7.45672i	0.239421	+	0.239421i
$971$	12.7142	−	12.7142i	0.408019	−	0.408019i	−0.473028	−	0.881047i	$-0.656839\pi$
$971$	12.7142	−	12.7142i	0.408019	−	0.408019i	0.881047	+	0.473028i	$0.156839\pi$
$972$	32.5873	+	6.75817i	1.04524	+	0.216768i
$973$	23.6151	−	13.6342i	0.757066	−	0.437092i
$974$	46.8418	−	46.8418i	1.50091	−	1.50091i
$975$	−1.67603	−	4.22096i	−0.0536761	−	0.135179i
$976$	16.5249	−	4.42785i	0.528951	−	0.141732i
$977$	−6.64997	−	3.83936i	−0.212751	−	0.122832i	0.389838	−	0.920883i	$-0.372531\pi$
$977$	−6.64997	−	3.83936i	−0.212751	−	0.122832i	−0.602589	+	0.798051i	$0.705864\pi$
$978$	−36.2704	+	14.4020i	−1.15980	+	0.460526i
$979$	4.34098	+	7.51879i	0.138738	+	0.240302i
$980$	3.29735	+	12.3059i	0.105330	+	0.393096i
$981$	−9.66319	−	2.89662i	−0.308522	−	0.0924819i
$982$	−7.47679	+	12.9502i	−0.238594	+	0.413257i
$983$	−34.9479	+	34.9479i	−1.11467	+	1.11467i	−0.122155	+	0.992511i	$0.538981\pi$
$983$	−34.9479	+	34.9479i	−1.11467	+	1.11467i	−0.992511	+	0.122155i	$0.961019\pi$
$984$	−1.95891	+	2.47657i	−0.0624479	+	0.0789501i
$985$	−3.39285	+	12.6623i	−0.108105	+	0.403454i
$986$	0.0844549	−	0.146280i	0.00268959	−	0.00465851i
$987$	−15.8171	−	21.2537i	−0.503462	−	0.676512i
$988$	−17.5024			−0.556825
$989$	−79.2486	+	45.7542i	−2.51996	+	1.45490i
$990$	9.05585	−	8.53782i	0.287814	−	0.271350i
$991$		−	24.6094i		−	0.781744i	−0.920445	−	0.390872i	$-0.872174\pi$
$991$		−	24.6094i		−	0.781744i	0.920445	−	0.390872i	$-0.127826\pi$
$992$	11.5096	−	42.9543i	0.365429	−	1.36380i
$993$	6.52808	+	16.4405i	0.207162	+	0.521722i
$994$	12.9769	+	22.4766i	0.411602	+	0.712915i
$995$	−10.0596	+	37.5429i	−0.318911	+	1.19019i
$996$	−34.5843	+	25.7378i	−1.09585	+	0.815532i
$997$	−11.4425	+	42.7038i	−0.362386	+	1.35244i	0.508543	+	0.861036i	$0.330184\pi$
$997$	−11.4425	+	42.7038i	−0.362386	+	1.35244i	−0.870930	+	0.491408i	$0.836482\pi$
$998$	67.2452			2.12861
$999$	1.05064	+	12.0811i	0.0332407	+	0.382231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.l.b.50.10	✓	200
3.2	odd	2	inner	471.2.l.b.50.41	yes	200
157.22	odd	12	inner	471.2.l.b.179.41	yes	200
471.179	even	12	inner	471.2.l.b.179.10	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.l.b.50.10	✓	200	1.1	even	1	trivial
471.2.l.b.50.41	yes	200	3.2	odd	2	inner
471.2.l.b.179.10	yes	200	471.179	even	12	inner
471.2.l.b.179.41	yes	200	157.22	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43787 + 1.43787i) q^{2} +(1.07451 - 1.35846i) q^{3} -2.13496i q^{4} +(-0.618816 - 2.30945i) q^{5} +(0.408280 + 3.49831i) q^{6} +(-2.17897 + 2.17897i) q^{7} +(0.194052 + 0.194052i) q^{8} +(-0.690836 - 2.91937i) q^{9} +O(q^{10})\)	\(q+(-1.43787 + 1.43787i) q^{2} +(1.07451 - 1.35846i) q^{3} -2.13496i q^{4} +(-0.618816 - 2.30945i) q^{5} +(0.408280 + 3.49831i) q^{6} +(-2.17897 + 2.17897i) q^{7} +(0.194052 + 0.194052i) q^{8} +(-0.690836 - 2.91937i) q^{9} +(4.21048 + 2.43092i) q^{10} +(0.738989 + 0.426656i) q^{11} +(-2.90026 - 2.29404i) q^{12} +(-3.16923 + 1.82976i) q^{13} -6.26616i q^{14} +(-3.80223 - 1.64090i) q^{15} +3.71187 q^{16} +(0.00698006 + 0.00402994i) q^{17} +(5.19102 + 3.20435i) q^{18} +(-1.12009 + 1.94006i) q^{19} +(-4.93058 + 1.32115i) q^{20} +(0.618712 + 5.30138i) q^{21} +(-1.67605 + 0.449096i) q^{22} +(-6.45630 - 6.45630i) q^{23} +(0.472124 - 0.0551005i) q^{24} +(-0.620511 + 0.358252i) q^{25} +(1.92600 - 7.18792i) q^{26} +(-4.70817 - 2.19844i) q^{27} +(4.65201 + 4.65201i) q^{28} +(-7.28745 + 7.28745i) q^{29} +(7.82653 - 3.10771i) q^{30} +(-4.75642 + 2.74612i) q^{31} +(-5.72530 + 5.72530i) q^{32} +(1.37365 - 0.545441i) q^{33} +(-0.0158310 + 0.00424190i) q^{34} +(6.38061 + 3.68385i) q^{35} +(-6.23274 + 1.47491i) q^{36} +(-1.16690 - 2.02112i) q^{37} +(-1.17901 - 4.40011i) q^{38} +(-0.919733 + 6.27139i) q^{39} +(0.328072 - 0.568237i) q^{40} +(-4.69736 + 4.69736i) q^{41} +(-8.51235 - 6.73309i) q^{42} +(2.59393 - 9.68069i) q^{43} +(0.910892 - 1.57771i) q^{44} +(-6.31466 + 3.40201i) q^{45} +18.5667 q^{46} +(-4.29874 + 2.48188i) q^{47} +(3.98846 - 5.04243i) q^{48} -2.49582i q^{49} +(0.377095 - 1.40734i) q^{50} +(0.0129747 - 0.00515191i) q^{51} +(3.90646 + 6.76618i) q^{52} +(3.07157 - 11.4633i) q^{53} +(9.93082 - 3.60868i) q^{54} +(0.528043 - 1.97068i) q^{55} -0.845668 q^{56} +(1.43194 + 3.60623i) q^{57} -20.9569i q^{58} +(7.64222 - 7.64222i) q^{59} +(-3.50326 + 8.11760i) q^{60} +(4.45192 - 1.19289i) q^{61} +(2.89056 - 10.7877i) q^{62} +(7.86654 + 4.85592i) q^{63} -9.04078i q^{64} +(6.18691 + 6.18691i) q^{65} +(-1.19086 + 2.75941i) q^{66} +3.50711 q^{67} +(0.00860375 - 0.0149021i) q^{68} +(-15.7080 + 1.83325i) q^{69} +(-14.4714 + 3.87760i) q^{70} +(-3.58698 + 2.07095i) q^{71} +(0.432453 - 0.700569i) q^{72} +(-6.41830 + 1.71978i) q^{73} +(4.58397 + 1.22827i) q^{74} +(-0.180076 + 1.22789i) q^{75} +(4.14194 + 2.39135i) q^{76} +(-2.53991 + 0.680566i) q^{77} +(-7.69500 - 10.3399i) q^{78} +(1.02641 - 1.02641i) q^{79} +(-2.29696 - 8.57239i) q^{80} +(-8.04549 + 4.03362i) q^{81} -13.5084i q^{82} +(3.01737 - 11.2610i) q^{83} +(11.3182 - 1.32092i) q^{84} +(0.00498758 - 0.0186139i) q^{85} +(10.1899 + 17.6493i) q^{86} +(2.06925 + 17.7302i) q^{87} +(0.0606090 + 0.226196i) q^{88} +(8.81131 + 5.08721i) q^{89} +(4.18802 - 13.9713i) q^{90} +(2.91868 - 10.8927i) q^{91} +(-13.7839 + 13.7839i) q^{92} +(-1.38034 + 9.41216i) q^{93} +(2.61241 - 9.74966i) q^{94} +(5.17361 + 1.38626i) q^{95} +(1.62568 + 13.9295i) q^{96} +(2.09510 + 0.561382i) q^{97} +(3.58868 + 3.58868i) q^{98} +(0.735047 - 2.45214i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 6 q^{3} - 10 q^{9}+O(q^{10}) \) 200 * q - 6 * q^3 - 10 * q^9	\( 200 q - 6 q^{3} - 10 q^{9} - 36 q^{10} - 16 q^{12} - 24 q^{13} + 8 q^{15} - 208 q^{16} + 8 q^{18} - 12 q^{19} - 24 q^{22} - 20 q^{24} - 24 q^{25} + 64 q^{28} - 14 q^{30} - 48 q^{31} + 18 q^{33} + 32 q^{34} + 78 q^{36} + 44 q^{37} - 72 q^{39} + 60 q^{40} + 42 q^{42} - 24 q^{43} - 32 q^{45} - 32 q^{46} - 102 q^{48} - 54 q^{51} + 36 q^{52} + 48 q^{54} - 20 q^{55} - 6 q^{57} - 8 q^{61} - 8 q^{63} - 32 q^{66} - 16 q^{67} - 52 q^{69} + 60 q^{70} - 42 q^{72} - 64 q^{73} - 32 q^{75} + 132 q^{76} + 106 q^{78} + 40 q^{79} + 14 q^{81} + 172 q^{84} - 160 q^{85} - 88 q^{87} + 8 q^{88} + 84 q^{91} + 220 q^{93} + 128 q^{94} - 108 q^{96} - 36 q^{97} - 104 q^{99}+O(q^{100}) \) 200 * q - 6 * q^3 - 10 * q^9 - 36 * q^10 - 16 * q^12 - 24 * q^13 + 8 * q^15 - 208 * q^16 + 8 * q^18 - 12 * q^19 - 24 * q^22 - 20 * q^24 - 24 * q^25 + 64 * q^28 - 14 * q^30 - 48 * q^31 + 18 * q^33 + 32 * q^34 + 78 * q^36 + 44 * q^37 - 72 * q^39 + 60 * q^40 + 42 * q^42 - 24 * q^43 - 32 * q^45 - 32 * q^46 - 102 * q^48 - 54 * q^51 + 36 * q^52 + 48 * q^54 - 20 * q^55 - 6 * q^57 - 8 * q^61 - 8 * q^63 - 32 * q^66 - 16 * q^67 - 52 * q^69 + 60 * q^70 - 42 * q^72 - 64 * q^73 - 32 * q^75 + 132 * q^76 + 106 * q^78 + 40 * q^79 + 14 * q^81 + 172 * q^84 - 160 * q^85 - 88 * q^87 + 8 * q^88 + 84 * q^91 + 220 * q^93 + 128 * q^94 - 108 * q^96 - 36 * q^97 - 104 * q^99

Introduction

L-functions

Modular forms

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