LMFDB - Embedded newform 465.2.bt.a.38.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(38,465)] 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("465.38"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([30, 45, 56])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.bt (of order $60$, 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:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$960$
Relative dimension:	$60$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			38.12
Character	$\chi$	$=$	465.38
Dual form			465.2.bt.a.257.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.895320 + 1.75716i) q^{2} +(-1.08132 - 1.35305i) q^{3} +(-1.11046 - 1.52841i) q^{4} +(-2.17633 + 0.513419i) q^{5} +(3.34566 - 0.688650i) q^{6} +(1.94619 - 0.747072i) q^{7} +(-0.215773 + 0.0341750i) q^{8} +(-0.661483 + 2.92616i) q^{9} +(1.04635 - 4.28384i) q^{10} +(-3.37137 + 0.354345i) q^{11} +(-0.867256 + 3.15521i) q^{12} +(0.0136843 - 0.261112i) q^{13} +(-0.429733 + 4.08864i) q^{14} +(3.04799 + 2.38951i) q^{15} +(1.30074 - 4.00326i) q^{16} +(6.18335 - 5.00718i) q^{17} +(-4.54951 - 3.78219i) q^{18} +(0.00134415 + 0.00121028i) q^{19} +(3.20144 + 2.75620i) q^{20} +(-3.11528 - 1.82546i) q^{21} +(2.39581 - 6.24130i) q^{22} +(4.50454 - 0.713448i) q^{23} +(0.279560 + 0.254997i) q^{24} +(4.47280 - 2.23474i) q^{25} +(0.446565 + 0.257824i) q^{26} +(4.67452 - 2.26911i) q^{27} +(-3.30300 - 2.14499i) q^{28} +(2.45437 + 7.55377i) q^{29} +(-6.92768 + 3.21645i) q^{30} +(4.74566 + 2.91183i) q^{31} +(5.56086 + 5.56086i) q^{32} +(4.12498 + 4.17847i) q^{33} +(3.26236 + 15.3482i) q^{34} +(-3.85198 + 2.62508i) q^{35} +(5.20694 - 2.23836i) q^{36} +(-10.1680 - 2.72452i) q^{37} +(-0.00333011 + 0.00127831i) q^{38} +(-0.368095 + 0.263831i) q^{39} +(0.452046 - 0.185158i) q^{40} +(2.29095 - 10.7781i) q^{41} +(5.99681 - 3.83969i) q^{42} +(10.9223 - 0.572412i) q^{43} +(4.28535 + 4.75936i) q^{44} +(-0.0627455 - 6.70791i) q^{45} +(-2.77935 + 8.55397i) q^{46} +(2.86850 - 1.46158i) q^{47} +(-6.82313 + 2.56886i) q^{48} +(-1.97248 + 1.77603i) q^{49} +(-0.0777893 + 9.86025i) q^{50} +(-13.4611 - 2.95200i) q^{51} +(-0.414283 + 0.269039i) q^{52} +(2.64186 - 6.88229i) q^{53} +(-0.197994 + 10.2455i) q^{54} +(7.15527 - 2.50210i) q^{55} +(-0.394403 + 0.227709i) q^{56} +(0.000184106 - 0.00312741i) q^{57} +(-15.4707 - 2.45031i) q^{58} +(-5.06862 + 1.07737i) q^{59} +(0.267486 - 7.31204i) q^{60} +5.27011 q^{61} +(-9.36544 + 5.73188i) q^{62} +(0.898684 + 6.18904i) q^{63} +(-6.74357 + 2.19112i) q^{64} +(0.104278 + 0.575291i) q^{65} +(-11.0354 + 3.50721i) q^{66} +(0.468619 + 1.74891i) q^{67} +(-14.5194 - 3.89046i) q^{68} +(-5.83619 - 5.32339i) q^{69} +(-1.16395 - 9.11885i) q^{70} +(2.51395 + 5.64641i) q^{71} +(0.0427282 - 0.653993i) q^{72} +(4.01102 - 4.95320i) q^{73} +(13.8911 - 15.4276i) q^{74} +(-7.86025 - 3.63545i) q^{75} +(0.000357185 - 0.00339839i) q^{76} +(-6.29660 + 3.20828i) q^{77} +(-0.134032 - 0.883016i) q^{78} +(-4.06155 - 0.426886i) q^{79} +(-0.775482 + 9.38024i) q^{80} +(-8.12488 - 3.87122i) q^{81} +(16.8877 + 13.6754i) q^{82} +(-2.74714 + 1.78401i) q^{83} +(0.669327 + 6.78854i) q^{84} +(-10.8862 + 14.0719i) q^{85} +(-8.77311 + 19.7047i) q^{86} +(7.56666 - 11.4889i) q^{87} +(0.715339 - 0.191675i) q^{88} +(0.717788 - 0.521504i) q^{89} +(11.8431 + 5.89547i) q^{90} +(-0.168437 - 0.518396i) q^{91} +(-6.09254 - 6.09254i) q^{92} +(-1.19174 - 9.56973i) q^{93} +6.34901i q^{94} +(-0.00354670 - 0.00194385i) q^{95} +(1.51103 - 13.5372i) q^{96} +(0.713443 - 4.50450i) q^{97} +(-1.35478 - 5.05609i) q^{98} +(1.19323 - 10.0996i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 960 q - 14 q^{3} - 16 q^{6} - 60 q^{7} - 44 q^{10} - 64 q^{12} - 36 q^{13} + 4 q^{15} + 176 q^{16} - 14 q^{18} - 36 q^{21} - 88 q^{22} - 20 q^{25} - 8 q^{27} - 56 q^{28} - 200 q^{30} - 56 q^{31} + 44 q^{33}+ \cdots + 44 q^{97}+O(q^{100}) $ 960 * q - 14 * q^3 - 16 * q^6 - 60 * q^7 - 44 * q^10 - 64 * q^12 - 36 * q^13 + 4 * q^15 + 176 * q^16 - 14 * q^18 - 36 * q^21 - 88 * q^22 - 20 * q^25 - 8 * q^27 - 56 * q^28 - 200 * q^30 - 56 * q^31 + 44 * q^33 - 32 * q^36 - 80 * q^37 - 52 * q^40 - 30 * q^42 - 36 * q^43 - 8 * q^45 - 164 * q^46 - 28 * q^48 - 44 * q^51 - 100 * q^52 - 88 * q^55 + 24 * q^57 + 64 * q^58 - 124 * q^60 - 176 * q^61 - 116 * q^63 + 48 * q^66 - 28 * q^67 - 36 * q^70 - 154 * q^72 - 12 * q^73 - 178 * q^75 + 112 * q^76 + 54 * q^78 - 52 * q^81 - 92 * q^82 - 24 * q^85 - 32 * q^87 + 52 * q^88 - 20 * q^90 + 40 * q^91 + 134 * q^93 + 8 * q^96 + 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{14}{15}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.895320	+	1.75716i	−0.633087	+	1.24250i	0.322158	+	0.946686i	$0.395592\pi$
$2$	−0.895320	+	1.75716i	−0.633087	+	1.24250i	−0.955245	+	0.295817i	$0.904408\pi$
$3$	−1.08132	−	1.35305i	−0.624302	−	0.781183i
$3$	−1.08132	−	1.35305i	−0.624302	−	0.781183i
$4$	−1.11046	−	1.52841i	−0.555229	−	0.764207i
$5$	−2.17633	+	0.513419i	−0.973283	+	0.229608i
$5$	−2.17633	+	0.513419i	−0.973283	+	0.229608i
$6$	3.34566	−	0.688650i	1.36586	−	0.281140i
$7$	1.94619	−	0.747072i	0.735590	−	0.282367i	0.0384094	−	0.999262i	$-0.487771\pi$
$7$	1.94619	−	0.747072i	0.735590	−	0.282367i	0.697181	+	0.716896i	$0.254438\pi$
$8$	−0.215773	+	0.0341750i	−0.0762872	+	0.0120827i
$9$	−0.661483	+	2.92616i	−0.220494	+	0.975388i
$10$	1.04635	−	4.28384i	0.330884	−	1.35467i
$11$	−3.37137	+	0.354345i	−1.01651	+	0.106839i	−0.598100	−	0.801421i	$-0.704078\pi$
$11$	−3.37137	+	0.354345i	−1.01651	+	0.106839i	−0.418406	+	0.908260i	$0.637411\pi$
$12$	−0.867256	+	3.15521i	−0.250355	+	0.910832i
$13$	0.0136843	−	0.261112i	0.00379534	−	0.0724195i	−0.996075	−	0.0885113i	$-0.971789\pi$
$13$	0.0136843	−	0.261112i	0.00379534	−	0.0724195i	0.999871	+	0.0160918i	$0.00512240\pi$
$14$	−0.429733	+	4.08864i	−0.114851	+	1.09274i
$15$	3.04799	+	2.38951i	0.786988	+	0.616968i
$16$	1.30074	−	4.00326i	0.325185	−	1.00082i
$17$	6.18335	−	5.00718i	1.49968	−	1.21442i	0.584490	−	0.811401i	$-0.301295\pi$
$17$	6.18335	−	5.00718i	1.49968	−	1.21442i	0.915192	−	0.403018i	$-0.132039\pi$
$18$	−4.54951	−	3.78219i	−1.07233	−	0.891470i
$19$	0.00134415	+	0.00121028i	0.000308370	+	0.000277658i	0.669285	−	0.743006i	$-0.266601\pi$
$19$	0.00134415	+	0.00121028i	0.000308370	+	0.000277658i	−0.668976	+	0.743284i	$0.733267\pi$
$20$	3.20144	+	2.75620i	0.715863	+	0.616305i
$21$	−3.11528	−	1.82546i	−0.679810	−	0.398349i
$22$	2.39581	−	6.24130i	0.510789	−	1.33065i
$23$	4.50454	−	0.713448i	0.939261	−	0.148764i	0.332011	−	0.943275i	$-0.392273\pi$
$23$	4.50454	−	0.713448i	0.939261	−	0.148764i	0.607249	+	0.794511i	$0.292273\pi$
$24$	0.279560	+	0.254997i	0.0570650	+	0.0520510i
$25$	4.47280	−	2.23474i	0.894560	−	0.446947i
$26$	0.446565	+	0.257824i	0.0875786	+	0.0505635i
$27$	4.67452	−	2.26911i	0.899612	−	0.436690i
$28$	−3.30300	−	2.14499i	−0.624207	−	0.405365i
$29$	2.45437	+	7.55377i	0.455765	+	1.40270i	0.870235	+	0.492637i	$0.163967\pi$
$29$	2.45437	+	7.55377i	0.455765	+	1.40270i	−0.414470	+	0.910063i	$0.636033\pi$
$30$	−6.92768	+	3.21645i	−1.26482	+	0.587241i
$31$	4.74566	+	2.91183i	0.852345	+	0.522980i
$31$	4.74566	+	2.91183i	0.852345	+	0.522980i
$32$	5.56086	+	5.56086i	0.983031	+	0.983031i
$33$	4.12498	+	4.17847i	0.718067	+	0.727378i
$34$	3.26236	+	15.3482i	0.559490	+	2.63219i
$35$	−3.85198	+	2.62508i	−0.651104	+	0.443720i
$36$	5.20694	−	2.23836i	0.867824	−	0.373061i
$37$	−10.1680	−	2.72452i	−1.67161	−	0.447908i	−0.706070	−	0.708142i	$-0.749533\pi$
$37$	−10.1680	−	2.72452i	−1.67161	−	0.447908i	−0.965545	+	0.260235i	$0.916200\pi$
$38$	−0.00333011	+	0.00127831i	−0.000540215	+	0.000207369i
$39$	−0.368095	+	0.263831i	−0.0589423	+	0.0422467i
$40$	0.452046	−	0.185158i	0.0714747	−	0.0292760i
$41$	2.29095	−	10.7781i	0.357786	−	1.68325i	−0.319542	−	0.947572i	$-0.603529\pi$
$41$	2.29095	−	10.7781i	0.357786	−	1.68325i	0.677329	−	0.735681i	$-0.263138\pi$
$42$	5.99681	−	3.83969i	0.925328	−	0.592477i
$43$	10.9223	−	0.572412i	1.66563	−	0.0872921i	0.803936	−	0.594716i	$-0.202736\pi$
$43$	10.9223	−	0.572412i	1.66563	−	0.0872921i	0.861696	+	0.507424i	$0.169402\pi$
$44$	4.28535	+	4.75936i	0.646041	+	0.717501i
$45$	−0.0627455	−	6.70791i	−0.00935355	−	0.999956i
$46$	−2.77935	+	8.55397i	−0.409793	+	1.26121i
$47$	2.86850	−	1.46158i	0.418414	−	0.213193i	−0.232092	−	0.972694i	$-0.574557\pi$
$47$	2.86850	−	1.46158i	0.418414	−	0.213193i	0.650506	+	0.759501i	$0.274557\pi$
$48$	−6.82313	+	2.56886i	−0.984834	+	0.370782i
$49$	−1.97248	+	1.77603i	−0.281783	+	0.253719i
$50$	−0.0777893	+	9.86025i	−0.0110011	+	1.39445i
$51$	−13.4611	−	2.95200i	−1.88494	−	0.413363i
$52$	−0.414283	+	0.269039i	−0.0574508	+	0.0373090i
$53$	2.64186	−	6.88229i	0.362888	−	0.945356i	−0.623632	−	0.781718i	$-0.714344\pi$
$53$	2.64186	−	6.88229i	0.362888	−	0.945356i	0.986520	−	0.163638i	$-0.0523229\pi$
$54$	−0.197994	+	10.2455i	−0.0269436	+	1.39423i
$55$	7.15527	−	2.50210i	0.964817	−	0.337383i
$56$	−0.394403	+	0.227709i	−0.0527043	+	0.0304289i
$57$	0.000184106	−	0.00312741i	2.43855e−5	−	0.000414236i
$58$	−15.4707	−	2.45031i	−2.03140	−	0.321742i
$59$	−5.06862	+	1.07737i	−0.659878	+	0.140261i	−0.525666	−	0.850691i	$-0.676184\pi$
$59$	−5.06862	+	1.07737i	−0.659878	+	0.140261i	−0.134212	+	0.990953i	$0.542850\pi$
$60$	0.267486	−	7.31204i	0.0345323	−	0.943981i
$61$	5.27011			0.674769			0.337384	−	0.941367i	$-0.390458\pi$
$61$	5.27011			0.674769			0.337384	+	0.941367i	$0.390458\pi$
$62$	−9.36544	+	5.73188i	−1.18941	+	0.727949i
$63$	0.898684	+	6.18904i	0.113224	+	0.779746i
$64$	−6.74357	+	2.19112i	−0.842946	+	0.273890i
$65$	0.104278	+	0.575291i	0.0129341	+	0.0713561i
$66$	−11.0354	+	3.50721i	−1.35837	+	0.431708i
$67$	0.468619	+	1.74891i	0.0572509	+	0.213663i	0.988625	−	0.150400i	$-0.0480560\pi$
$67$	0.468619	+	1.74891i	0.0572509	+	0.213663i	−0.931374	+	0.364063i	$0.881389\pi$
$68$	−14.5194	−	3.89046i	−1.76073	−	0.471787i
$69$	−5.83619	−	5.32339i	−0.702594	−	0.640861i
$70$	−1.16395	−	9.11885i	−0.139118	−	1.08991i
$71$	2.51395	+	5.64641i	0.298350	+	0.670106i	0.999060	−	0.0433402i	$-0.0137999\pi$
$71$	2.51395	+	5.64641i	0.298350	+	0.670106i	−0.700710	+	0.713446i	$0.747133\pi$
$72$	0.0427282	−	0.653993i	0.00503556	−	0.0770738i
$73$	4.01102	−	4.95320i	0.469455	−	0.579728i	−0.486338	−	0.873771i	$-0.661667\pi$
$73$	4.01102	−	4.95320i	0.469455	−	0.579728i	0.955792	+	0.294043i	$0.0950008\pi$
$74$	13.8911	−	15.4276i	1.61480	−	1.79342i
$75$	−7.86025	−	3.63545i	−0.907623	−	0.419785i
$76$	0.000357185	−	0.00339839i	4.09720e−5	−	0.000389822i
$77$	−6.29660	+	3.20828i	−0.717564	+	0.365617i
$78$	−0.134032	−	0.883016i	−0.0151761	−	0.0999818i
$79$	−4.06155	−	0.426886i	−0.456960	−	0.0480284i	−0.126747	−	0.991935i	$-0.540454\pi$
$79$	−4.06155	−	0.426886i	−0.456960	−	0.0480284i	−0.330213	+	0.943907i	$0.607120\pi$
$80$	−0.775482	+	9.38024i	−0.0867015	+	1.04874i
$81$	−8.12488	−	3.87122i	−0.902764	−	0.430135i
$82$	16.8877	+	13.6754i	1.86494	+	1.51020i
$83$	−2.74714	+	1.78401i	−0.301537	+	0.195821i	−0.686535	−	0.727097i	$-0.740869\pi$
$83$	−2.74714	+	1.78401i	−0.301537	+	0.195821i	0.384997	+	0.922918i	$0.374202\pi$
$84$	0.669327	+	6.78854i	0.0730295	+	0.740691i
$85$	−10.8862	+	14.0719i	−1.18078	+	1.52631i
$86$	−8.77311	+	19.7047i	−0.946029	+	2.12482i
$87$	7.56666	−	11.4889i	0.811231	−	1.23174i
$88$	0.715339	−	0.191675i	0.0762554	−	0.0204326i
$89$	0.717788	−	0.521504i	0.0760854	−	0.0552793i	−0.549092	−	0.835762i	$-0.685026\pi$
$89$	0.717788	−	0.521504i	0.0760854	−	0.0552793i	0.625178	+	0.780482i	$0.285026\pi$
$90$	11.8431	+	5.89547i	1.24837	+	0.621437i
$91$	−0.168437	−	0.518396i	−0.0176570	−	0.0543427i
$92$	−6.09254	−	6.09254i	−0.635191	−	0.635191i
$93$	−1.19174	−	9.56973i	−0.123577	−	0.992335i
$94$			6.34901i			0.654851i
$95$	−0.00354670	−	0.00194385i	−0.000363884	−	0.000199435i
$96$	1.51103	−	13.5372i	0.154219	−	1.38164i
$97$	0.713443	−	4.50450i	0.0724391	−	0.457363i	−0.924631	−	0.380865i	$-0.875626\pi$
$97$	0.713443	−	4.50450i	0.0724391	−	0.457363i	0.997070	−	0.0764976i	$-0.0243737\pi$
$98$	−1.35478	−	5.05609i	−0.136853	−	0.510742i
$99$	1.19323	−	10.0996i	0.119924	−	1.01505i
$100$	−8.38246	−	4.35471i	−0.838246	−	0.435471i
$101$	10.2467	−	14.1033i	1.01958	−	1.40333i	0.107082	−	0.994250i	$-0.465849\pi$
$101$	10.2467	−	14.1033i	1.01958	−	1.40333i	0.912498	−	0.409081i	$-0.134151\pi$
$102$	17.2392	−	21.0105i	1.70693	−	2.08035i
$103$	−1.60996	−	2.47911i	−0.158634	−	0.244274i	0.750413	−	0.660970i	$-0.229855\pi$
$103$	−1.60996	−	2.47911i	−0.158634	−	0.244274i	−0.909046	+	0.416695i	$0.863188\pi$
$104$	0.00597081	+	0.0568085i	0.000585487	+	0.00557053i
$105$	7.71710	+	2.37336i	0.753112	+	0.231616i
$106$	9.72801	+	10.8040i	0.944867	+	1.04938i
$107$	7.57437	−	6.13360i	0.732242	−	0.592958i	−0.188987	−	0.981980i	$-0.560520\pi$
$107$	7.57437	−	6.13360i	0.732242	−	0.592958i	0.921229	+	0.389022i	$0.127187\pi$
$108$	−8.65900	−	4.62485i	−0.833213	−	0.445027i
$109$	−9.67439	−	3.14340i	−0.926639	−	0.301083i	−0.193451	−	0.981110i	$-0.561968\pi$
$109$	−9.67439	−	3.14340i	−0.926639	−	0.301083i	−0.733187	+	0.680027i	$0.761968\pi$
$110$	−2.00967	+	14.8132i	−0.191614	+	1.41238i
$111$	7.30852	+	16.7039i	0.693694	+	1.58547i
$112$	−0.459241	−	8.76285i	−0.0433942	−	0.828011i
$113$	−5.32160	−	4.30934i	−0.500614	−	0.405389i	0.345478	−	0.938427i	$-0.387717\pi$
$113$	−5.32160	−	4.30934i	−0.500614	−	0.405389i	−0.846091	+	0.533038i	$0.821050\pi$
$114$	0.00533054	+	0.00312354i	0.000499251	+	0.000292546i
$115$	−9.43705	+	3.86541i	−0.880009	+	0.360452i
$116$	8.81982	−	12.1394i	0.818900	−	1.12712i
$117$	0.755005	+	0.212764i	0.0698002	+	0.0196700i
$118$	2.64492	−	9.87098i	0.243485	−	0.908697i
$119$	8.29324	−	14.3643i	0.760240	−	1.31677i
$120$	−0.739335	−	0.411425i	−0.0674917	−	0.0375578i
$121$	0.480944	−	0.102228i	0.0437222	−	0.00929344i
$122$	−4.71844	+	9.26045i	−0.427187	+	0.838402i
$123$	−17.0605	+	8.55481i	−1.53830	+	0.771361i
$124$	−0.819370	−	10.4868i	−0.0735816	−	0.941742i
$125$	−8.58692	+	7.15994i	−0.768038	+	0.640405i
$126$	−11.6798	−	3.96204i	−1.04052	−	0.352966i
$127$	−5.15318	+	7.93520i	−0.457271	+	0.704135i	−0.989830	−	0.142258i	$-0.954564\pi$
$127$	−5.15318	+	7.93520i	−0.457271	+	0.704135i	0.532559	+	0.846393i	$0.321230\pi$
$128$	−0.272981	+	1.72353i	−0.0241283	+	0.152340i
$129$	−12.5850	−	14.1594i	−1.10805	−	1.24667i
$130$	−1.10424	−	0.331835i	−0.0968486	−	0.0291039i
$131$	1.06430	−	2.39045i	0.0929881	−	0.208855i	−0.861063	−	0.508498i	$-0.830201\pi$
$131$	1.06430	−	2.39045i	0.0929881	−	0.208855i	0.954051	+	0.299643i	$0.0968676\pi$
$132$	1.80581	−	10.9447i	0.157175	−	0.952614i
$133$	0.00352014	+	0.00135126i	0.000305235	+	0.000117169i
$134$	−3.49269	−	0.742393i	−0.301722	−	0.0641330i
$135$	−9.00828	+	7.33831i	−0.775310	+	0.631581i
$136$	−1.16308	+	1.29173i	−0.0997330	+	0.110765i
$137$	−0.0184376	+	0.351810i	−0.00157523	+	0.0300571i	−0.999304	−	0.0373015i	$-0.988124\pi$
$137$	−0.0184376	+	0.351810i	−0.00157523	+	0.0300571i	0.997729	+	0.0673586i	$0.0214572\pi$
$138$	14.5793	−	5.48900i	1.24107	−	0.467255i
$139$	16.2463	+	5.27875i	1.37799	+	0.447737i	0.902009	−	0.431716i	$-0.142092\pi$
$139$	16.2463	+	5.27875i	1.37799	+	0.447737i	0.475985	+	0.879454i	$0.342092\pi$
$140$	8.28968	+	2.97238i	0.700606	+	0.251212i
$141$	−5.07936	−	2.30079i	−0.427759	−	0.193762i
$142$	−12.1725	−	0.637932i	−1.02149	−	0.0535340i
$143$	0.0463890	+	0.885154i	0.00387924	+	0.0740203i
$144$	10.8538	+	6.45427i	0.904483	+	0.537856i
$145$	−9.21976	−	15.1794i	−0.765660	−	1.26058i
$146$	5.11244	+	11.4827i	0.423108	+	0.950317i
$147$	4.53595	+	0.748402i	0.374118	+	0.0617272i
$148$	7.12699	+	18.5664i	0.585835	+	1.52615i
$149$	−1.88367	−	3.26262i	−0.154316	−	0.267284i	0.778493	−	0.627653i	$-0.215984\pi$
$149$	−1.88367	−	3.26262i	−0.154316	−	0.267284i	−0.932810	+	0.360369i	$0.882651\pi$
$150$	13.4255	−	10.5569i	1.09619	−	0.861964i
$151$	13.3356	−	9.68889i	1.08524	−	0.788471i	0.106648	−	0.994297i	$-0.465988\pi$
$151$	13.3356	−	9.68889i	1.08524	−	0.788471i	0.978589	+	0.205826i	$0.0659882\pi$
$152$	−0.000331393	0	0.000215209i	−2.68795e−5	0	1.74558e-5i
$153$	10.5616	+	21.4057i	0.853858	+	1.73054i
$154$		−	13.9366i		−	1.12304i
$155$	−11.8231	−	3.90058i	−0.949653	−	0.313302i
$156$	0.811996	+	0.269628i	0.0650117	+	0.0215875i
$157$	−2.99055	−	1.52376i	−0.238672	−	0.121609i	0.330564	−	0.943784i	$-0.392761\pi$
$157$	−2.99055	−	1.52376i	−0.238672	−	0.121609i	−0.569236	+	0.822174i	$0.692761\pi$
$158$	4.38649	−	6.75461i	0.348971	−	0.537368i
$159$	−12.1688	+	3.86741i	−0.965048	+	0.306705i
$160$	−14.9573	−	9.24720i	−1.18248	−	0.731056i
$161$	8.23368	−	4.75371i	0.648905	−	0.374645i
$162$	14.0767	−	10.8108i	1.10597	−	0.849375i
$163$	0.873782	+	5.51684i	0.0684399	+	0.432112i	0.997988	+	0.0634103i	$0.0201977\pi$
$163$	0.873782	+	5.51684i	0.0684399	+	0.432112i	−0.929548	+	0.368702i	$0.879802\pi$
$164$	−19.0174	+	8.46708i	−1.48501	+	0.661168i
$165$	−11.1226	−	6.97586i	−0.865895	−	0.543070i
$166$	−0.675235	−	6.42443i	−0.0524084	−	0.498633i
$167$	−15.5397	+	0.814402i	−1.20250	+	0.0630203i	−0.643037	−	0.765835i	$-0.722326\pi$
$167$	−15.5397	+	0.814402i	−1.20250	+	0.0630203i	−0.559463	+	0.828856i	$0.688992\pi$
$168$	0.734578	+	0.287420i	0.0566739	+	0.0221749i
$169$	12.8608	+	1.35172i	0.989292	+	0.103979i
$170$	−14.9800	−	31.7277i	−1.14891	−	2.43340i
$171$	−0.00443062	+	0.00313263i	−0.000338818	+	0.000239559i
$172$	−13.0036	−	16.0581i	−0.991516	−	1.22442i
$173$	7.02552	+	0.368192i	0.534141	+	0.0279931i	0.317500	−	0.948258i	$-0.397157\pi$
$173$	7.02552	+	0.368192i	0.534141	+	0.0279931i	0.216641	+	0.976251i	$0.430490\pi$
$174$	13.4134	+	23.5822i	1.01687	+	1.78776i
$175$	7.03540	−	7.69072i	0.531827	−	0.581364i
$176$	−2.96673	+	13.9574i	−0.223626	+	1.05208i
$177$	6.93854	+	5.69310i	0.521533	+	0.427920i
$178$	0.273718	+	1.72819i	0.0205160	+	0.129533i
$179$	−11.1075	−	4.94539i	−0.830215	−	0.369635i	−0.0527856	−	0.998606i	$-0.516810\pi$
$179$	−11.1075	−	4.94539i	−0.830215	−	0.369635i	−0.777429	+	0.628970i	$0.783477\pi$
$180$	−10.1828	+	7.54475i	−0.758980	+	0.562353i
$181$	−5.32140	+	9.21694i	−0.395537	+	0.685090i	−0.993170	−	0.116680i	$-0.962775\pi$
$181$	−5.32140	+	9.21694i	−0.395537	+	0.685090i	0.597633	+	0.801770i	$0.296108\pi$
$182$	1.06171	+	0.168159i	0.0786994	+	0.0124648i
$183$	−5.69869	−	7.13072i	−0.421259	−	0.527118i
$184$	−0.947573	+	0.307885i	−0.0698560	+	0.0226976i
$185$	23.5278	+	0.708976i	1.72980	+	0.0521250i
$186$	17.8826	+	6.47389i	1.31121	+	0.474689i
$187$	−19.0721	+	19.0721i	−1.39469	+	1.39469i
$188$	−5.41925	−	2.76124i	−0.395239	−	0.201384i
$189$	7.40231	−	7.90831i	0.538439	−	0.575245i
$190$	0.00659110	−	0.00449176i	0.000478169	−	0.000325867i
$191$	7.93102	+	4.57898i	0.573868	+	0.331323i	0.758693	−	0.651448i	$-0.225838\pi$
$191$	7.93102	+	4.57898i	0.573868	+	0.331323i	−0.184824	+	0.982772i	$0.559172\pi$
$192$	10.2567	+	6.75508i	0.740211	+	0.487506i
$193$	−5.68744	−	14.8163i	−0.409391	−	1.06650i	−0.970996	−	0.239094i	$-0.923150\pi$
$193$	−5.68744	−	14.8163i	−0.409391	−	1.06650i	0.561606	−	0.827405i	$-0.310184\pi$
$194$	7.27639	+	5.28660i	0.522414	+	0.379556i
$195$	0.665638	−	0.763169i	0.0476674	−	0.0546517i
$196$	4.90487	+	1.04256i	0.350348	+	0.0744687i
$197$	3.09852	−	3.82635i	0.220760	−	0.272616i	−0.654718	−	0.755873i	$-0.727213\pi$
$197$	3.09852	−	3.82635i	0.220760	−	0.272616i	0.875479	+	0.483257i	$0.160546\pi$
$198$	16.6783	+	11.1391i	1.18527	+	0.791618i
$199$	−15.7296	+	14.1630i	−1.11504	+	1.00398i	−0.115095	+	0.993355i	$0.536717\pi$
$199$	−15.7296	+	14.1630i	−1.11504	+	1.00398i	−0.999943	+	0.0106305i	$0.996616\pi$
$200$	−0.888736	+	0.635053i	−0.0628431	+	0.0449050i
$201$	1.85963	−	2.52520i	0.131168	−	0.178114i
$202$	15.6078	+	30.6320i	1.09816	+	2.15526i
$203$	10.4199	+	12.8675i	0.731332	+	0.903120i
$204$	10.4362	+	23.8523i	0.730678	+	1.66999i
$205$	0.547812	+	24.6328i	0.0382608	+	1.72043i
$206$	5.79764	−	0.609356i	0.403940	−	0.0424558i
$207$	−0.892006	+	13.6529i	−0.0619987	+	0.948945i
$208$	−1.02750	−	0.394421i	−0.0712444	−	0.0273481i
$209$	−0.00496050	−	0.00360401i	−0.000343125	−	0.000249295i
$210$	−11.0797	+	11.4353i	−0.764569	+	0.789110i
$211$	−0.513015	−	0.888568i	−0.0353174	−	0.0611716i	0.847826	−	0.530274i	$-0.177911\pi$
$211$	−0.513015	−	0.888568i	−0.0353174	−	0.0611716i	−0.883144	+	0.469102i	$0.844578\pi$
$212$	−13.4527	+	3.60463i	−0.923934	+	0.247567i
$213$	4.92149	−	9.50709i	0.337215	−	0.651415i
$214$	3.99627	+	18.8010i	0.273179	+	1.28521i
$215$	−23.4766	+	6.85346i	−1.60109	+	0.467402i
$216$	−0.931087	+	0.649364i	−0.0633524	+	0.0441836i
$217$	11.4113	+	2.12162i	0.774648	+	0.144025i
$218$	14.1851	−	14.1851i	0.960739	−	0.960739i
$219$	−11.0391	−	0.0711026i	−0.745955	−	0.00480467i
$220$	−11.7699	−	8.15775i	−0.793525	−	0.549996i
$221$	−1.22282	−	1.68307i	−0.0822557	−	0.113215i
$222$	−35.8950	−	2.11309i	−2.40912	−	0.141821i
$223$	−0.231163	+	0.862713i	−0.0154798	+	0.0577715i	−0.973234	−	0.229818i	$-0.926187\pi$
$223$	−0.231163	+	0.862713i	−0.0154798	+	0.0577715i	0.957754	+	0.287589i	$0.0928537\pi$
$224$	14.9768	+	6.66812i	1.00068	+	0.445533i
$225$	3.58052	+	14.5664i	0.238702	+	0.971093i
$226$	12.3368	−	5.49268i	0.820629	−	0.365367i
$227$	1.86158	+	2.86658i	0.123557	+	0.190262i	0.895036	−	0.445993i	$-0.147149\pi$
$227$	1.86158	+	2.86658i	0.123557	+	0.190262i	−0.771479	+	0.636255i	$0.780483\pi$
$228$	−0.00498442	+	0.00319147i	−0.000330101	+	0.000211360i
$229$	15.9468	+	14.3585i	1.05379	+	0.948839i	0.998767	−	0.0496464i	$-0.0158094\pi$
$229$	15.9468	+	14.3585i	1.05379	+	0.948839i	0.0550252	+	0.998485i	$0.482476\pi$
$230$	1.65701	−	20.0432i	0.109260	−	1.32161i
$231$	11.1496	+	5.05042i	0.733590	+	0.332293i
$232$	−0.787736	−	1.54602i	−0.0517174	−	0.101501i
$233$	3.29928	+	6.47520i	0.216143	+	0.424204i	0.973465	−	0.228838i	$-0.0734925\pi$
$233$	3.29928	+	6.47520i	0.216143	+	0.424204i	−0.757322	+	0.653042i	$0.773492\pi$
$234$	−1.04983	+	1.13618i	−0.0686297	+	0.0742742i
$235$	−5.49240	+	4.65361i	−0.358285	+	0.303568i
$236$	7.27515	+	6.55058i	0.473572	+	0.426406i
$237$	3.81425	+	5.95708i	0.247762	+	0.386954i
$238$	17.8154	+	27.4332i	1.15480	+	1.77823i
$239$	3.16567	−	1.40945i	0.204770	−	0.0911695i	−0.301789	−	0.953375i	$-0.597584\pi$
$239$	3.16567	−	1.40945i	0.204770	−	0.0911695i	0.506559	+	0.862205i	$0.330917\pi$
$240$	13.5305	−	9.09380i	0.873388	−	0.587002i
$241$	14.8382	+	6.60641i	0.955814	+	0.425556i	0.824549	−	0.565791i	$-0.191429\pi$
$241$	14.8382	+	6.60641i	0.955814	+	0.425556i	0.131266	+	0.991347i	$0.458096\pi$
$242$	−0.250968	+	0.936625i	−0.0161328	+	0.0602085i
$243$	3.54767	+	15.1794i	0.227583	+	0.973759i
$244$	−5.85224	−	8.05491i	−0.374651	−	0.515663i
$245$	3.38092	−	4.87793i	0.215999	−	0.311640i
$246$	0.242421	−	37.6374i	0.0154562	−	2.39967i
$247$	0.000334413	0	0.000334413i	2.12782e−5	0	2.12782e-5i
$248$	−1.12349	−	0.466110i	−0.0713420	−	0.0295980i
$249$	5.38440	+	1.78792i	0.341222	+	0.113305i
$250$	−4.89315	−	21.4991i	−0.309470	−	1.35972i
$251$	4.05026	+	19.0550i	0.255650	+	1.20274i	0.899270	+	0.437394i	$0.144099\pi$
$251$	4.05026	+	19.0550i	0.255650	+	1.20274i	−0.643620	+	0.765345i	$0.722568\pi$
$252$	8.46147	−	8.24623i	0.533023	−	0.519464i
$253$	−14.9336	+	4.00146i	−0.938870	+	0.251569i
$254$	−9.32971	−	16.1595i	−0.585398	−	1.01394i
$255$	30.8115	−	0.486694i	1.92949	−	0.0304780i
$256$	−14.2570	−	10.3583i	−0.891061	−	0.647394i
$257$	4.78860	+	1.83817i	0.298705	+	0.114662i	0.503105	−	0.864225i	$-0.332191\pi$
$257$	4.78860	+	1.83817i	0.298705	+	0.114662i	−0.204400	+	0.978887i	$0.565524\pi$
$258$	36.1480	−	9.43672i	2.25048	−	0.587505i
$259$	−21.8243	+	2.29383i	−1.35610	+	0.142532i
$260$	0.763486	−	0.798217i	0.0473494	−	0.0495033i
$261$	−23.7271	+	2.18520i	−1.46867	+	0.135260i
$262$	3.24753	+	4.01036i	0.200633	+	0.247761i
$263$	−2.29932	−	4.51267i	−0.141782	−	0.278263i	0.809186	−	0.587553i	$-0.199909\pi$
$263$	−2.29932	−	4.51267i	−0.141782	−	0.278263i	−0.950968	+	0.309290i	$0.899909\pi$
$264$	−1.03286	−	0.760627i	−0.0635680	−	0.0468134i
$265$	−2.21606	+	16.3345i	−0.136132	+	1.00342i
$266$	−0.00552603	+	0.00497566i	−0.000338823	+	0.000305077i
$267$	−1.48178	−	0.407289i	−0.0906835	−	0.0249257i
$268$	2.15268	−	2.65834i	0.131496	−	0.162384i
$269$	16.9513	+	3.60310i	1.03354	+	0.219685i	0.693296	−	0.720653i	$-0.256158\pi$
$269$	16.9513	+	3.60310i	1.03354	+	0.219685i	0.340241	+	0.940338i	$0.389491\pi$
$270$	−4.82933	−	22.3992i	−0.293903	−	1.36317i
$271$	−19.2417	−	13.9799i	−1.16885	−	0.849221i	−0.177982	−	0.984034i	$-0.556957\pi$
$271$	−19.2417	−	13.9799i	−1.16885	−	0.849221i	−0.990871	+	0.134813i	$0.956957\pi$
$272$	−12.0021	−	31.2666i	−0.727736	−	1.89582i
$273$	−0.519281	+	0.788457i	−0.0314283	+	0.0477196i
$274$	−0.601680	−	0.347380i	−0.0363488	−	0.0209860i
$275$	−14.2876	+	9.11904i	−0.861574	+	0.549899i
$276$	−1.65550	+	14.8315i	−0.0996497	+	0.892752i
$277$	8.42683	+	4.29368i	0.506319	+	0.257983i	0.688440	−	0.725294i	$-0.258296\pi$
$277$	8.42683	+	4.29368i	0.506319	+	0.257983i	−0.182120	+	0.983276i	$0.558296\pi$
$278$	−23.8213	+	23.8213i	−1.42870	+	1.42870i
$279$	−11.6597	+	11.9604i	−0.698046	+	0.716053i
$280$	0.741440	−	0.698063i	0.0443095	−	0.0417172i
$281$	13.1947	−	4.28721i	0.787128	−	0.255753i	0.112247	−	0.993680i	$-0.464195\pi$
$281$	13.1947	−	4.28721i	0.787128	−	0.255753i	0.674881	+	0.737927i	$0.264195\pi$
$282$	8.59052	−	6.86533i	0.511558	−	0.408824i
$283$	1.42908	+	0.226344i	0.0849500	+	0.0134548i	0.198765	−	0.980047i	$-0.436307\pi$
$283$	1.42908	+	0.226344i	0.0849500	+	0.0134548i	−0.113815	+	0.993502i	$0.536307\pi$
$284$	5.83843	−	10.1125i	0.346447	−	0.600064i
$285$	0.00120500	+	0.00690079i	7.13779e−5	+	0.000408768i
$286$	−1.59689	−	0.710983i	−0.0944263	−	0.0420413i
$287$	−3.59337	−	22.6877i	−0.212110	−	1.33921i
$288$	−19.9504	+	12.5936i	−1.17559	+	0.742084i
$289$	9.62748	−	45.2937i	0.566322	−	2.66434i
$290$	34.9273	−	2.61025i	2.05100	−	0.153279i
$291$	−6.86627	+	3.90549i	−0.402508	+	0.228944i
$292$	−12.0246	−	0.630183i	−0.703687	−	0.0368787i
$293$	8.44546	+	10.4293i	0.493389	+	0.609285i	0.961641	−	0.274310i	$-0.0884495\pi$
$293$	8.44546	+	10.4293i	0.493389	+	0.609285i	−0.468252	+	0.883595i	$0.655116\pi$
$294$	−5.37619	+	7.30034i	−0.313546	+	0.425765i
$295$	10.4778	−	4.94703i	0.610043	−	0.288027i
$296$	2.28709	+	0.240383i	0.132935	+	0.0139720i
$297$	−14.9555	+	9.30640i	−0.867805	+	0.540012i
$298$	7.41944	−	0.388836i	0.429797	−	0.0225247i
$299$	−0.124649	−	1.18595i	−0.00720861	−	0.0685853i
$300$	3.17200	+	16.0507i	0.183136	+	0.926689i
$301$	20.8292	−	9.27375i	1.20057	−	0.534530i
$302$	5.08533	+	32.1075i	0.292628	+	1.84758i
$303$	−30.1624	+	1.38600i	−1.73278	+	0.0796237i
$304$	0.00659347	−	0.00380674i	0.000378161	−	0.000218332i
$305$	−11.4695	+	2.70578i	−0.656741	+	0.154932i
$306$	−47.0693	−	0.606368i	−2.69077	−	0.0346638i
$307$	9.86021	−	15.1834i	0.562752	−	0.866562i	−0.436702	−	0.899606i	$-0.643854\pi$
$307$	9.86021	−	15.1834i	0.562752	−	0.866562i	0.999454	+	0.0330442i	$0.0105202\pi$
$308$	11.8957	+	6.06115i	0.677819	+	0.345366i
$309$	−1.61348	+	4.85907i	−0.0917878	+	0.276423i
$310$	17.4394	−	17.2828i	0.990492	−	0.981599i
$311$			3.65174i			0.207071i	0.994626	+	0.103535i	$0.0330155\pi$
$311$			3.65174i			0.207071i	−0.994626	+	0.103535i	$0.966984\pi$
$312$	0.0704083	−	0.0695071i	0.00398609	−	0.00393507i
$313$	10.4091	+	6.75977i	0.588359	+	0.382085i	0.804213	−	0.594341i	$-0.202587\pi$
$313$	10.4091	+	6.75977i	0.588359	+	0.382085i	−0.215854	+	0.976426i	$0.569254\pi$
$314$	5.35500	−	3.89064i	0.302200	−	0.219561i
$315$	−5.13340	−	13.0080i	−0.289235	−	0.732917i
$316$	3.85772	+	6.68177i	0.217014	+	0.375879i
$317$	−8.89246	−	23.1656i	−0.499450	−	1.30111i	−0.919314	−	0.393525i	$-0.871256\pi$
$317$	−8.89246	−	23.1656i	−0.499450	−	1.30111i	0.419864	−	0.907587i	$-0.362078\pi$
$318$	4.09929	−	24.8451i	0.229877	−	1.39325i
$319$	−10.9512	−	24.5969i	−0.613151	−	1.37716i
$320$	13.5513	−	8.23087i	0.757538	−	0.460120i
$321$	−16.4894	−	3.61609i	−0.920349	−	0.201830i
$322$	0.981284	+	18.7240i	0.0546848	+	1.04345i
$323$	0.0143715		0.000753176i	0.000799650		4.19079e-5i
$324$	3.10552	+	16.7170i	0.172529	+	0.928723i
$325$	−0.522309	−	1.19848i	−0.0289725	−	0.0664799i
$326$	−10.4763	−	3.40396i	−0.580229	−	0.188528i
$327$	6.20796	+	16.4890i	0.343301	+	0.911841i
$328$	−0.125983	+	2.40391i	−0.00695627	+	0.132734i
$329$	4.49075	−	4.98748i	0.247583	−	0.274969i
$330$	22.2160	−	13.2986i	1.22295	−	0.732066i
$331$	13.6962	+	2.91122i	0.752812	+	0.160015i	0.568307	−	0.822817i	$-0.307599\pi$
$331$	13.6962	+	2.91122i	0.752812	+	0.160015i	0.184505	+	0.982832i	$0.440932\pi$
$332$	5.77729	+	2.21769i	0.317070	+	0.121712i
$333$	14.6984	−	27.9511i	0.805466	−	1.53171i
$334$	12.4820	−	28.0350i	0.682984	−	1.53401i
$335$	−1.91779	−	3.56560i	−0.104780	−	0.194810i
$336$	−11.3600	+	10.0968i	−0.619737	+	0.550828i
$337$	3.06170	−	19.3308i	0.166782	−	1.05302i	−0.752262	−	0.658864i	$-0.771037\pi$
$337$	3.06170	−	19.3308i	0.166782	−	1.05302i	0.919044	−	0.394155i	$-0.128963\pi$
$338$	−13.8897	+	21.3883i	−0.755501	+	1.16337i
$339$	−0.0763909	+	11.8602i	−0.00414898	+	0.644156i
$340$	33.5964	+	1.01238i	1.82202	+	0.0549039i
$341$	−17.0311	−	8.13525i	−0.922288	−	0.440549i
$342$	−0.00153773	−	0.0105900i	−8.31511e−5	−	0.000572643i
$343$	−9.13688	+	17.9321i	−0.493345	+	0.968244i
$344$	−2.33717	+	0.496780i	−0.126012	+	0.0267846i
$345$	15.4346	+	8.58903i	0.830970	+	0.462418i
$346$	−6.93707	+	12.0154i	−0.372939	+	0.645949i
$347$	−7.13196	+	26.6168i	−0.382864	+	1.42887i	0.458643	+	0.888621i	$0.348336\pi$
$347$	−7.13196	+	26.6168i	−0.382864	+	1.42887i	−0.841507	+	0.540246i	$0.818331\pi$
$348$	−25.9623	+	1.19300i	−1.39173	+	0.0639517i
$349$	20.2823	−	27.9162i	1.08569	−	1.49432i	0.232583	−	0.972577i	$-0.425282\pi$
$349$	20.2823	−	27.9162i	1.08569	−	1.49432i	0.853103	−	0.521742i	$-0.174718\pi$
$350$	7.21492	+	19.2480i	0.385654	+	1.02885i
$351$	−0.528524	−	1.25162i	−0.0282105	−	0.0668068i
$352$	−20.7182	−	16.7773i	−1.10428	−	0.894231i
$353$	−0.282955	−	5.39910i	−0.0150602	−	0.287365i	−0.995769	−	0.0918911i	$-0.970709\pi$
$353$	−0.282955	−	5.39910i	−0.0150602	−	0.287365i	0.980709	−	0.195474i	$-0.0626245\pi$
$354$	−16.2159	+	7.09501i	−0.861867	+	0.377095i
$355$	−8.37015	−	10.9977i	−0.444241	−	0.583699i
$356$	−1.59415	−	0.517970i	−0.0844897	−	0.0274524i
$357$	−28.4033	+	4.31130i	−1.50326	+	0.228178i
$358$	18.6346	−	15.0900i	0.984871	−	0.797533i
$359$	0.0865540	+	0.0961279i	0.00456814	+	0.00507344i	0.745425	−	0.666590i	$-0.232247\pi$
$359$	0.0865540	+	0.0961279i	0.00456814	+	0.00507344i	−0.740856	+	0.671663i	$0.765580\pi$
$360$	0.242782	+	1.44524i	0.0127957	+	0.0761708i
$361$	−1.98604	−	18.8959i	−0.104528	−	0.994522i
$362$	−11.4313	−	17.6027i	−0.600817	−	0.925177i
$363$	−0.658375	−	0.540200i	−0.0345557	−	0.0283531i
$364$	−0.605282	+	0.833099i	−0.0317254	+	0.0436663i
$365$	−6.18623	+	12.8391i	−0.323802	+	0.672030i
$366$	17.6320	−	3.62926i	0.921639	−	0.189704i
$367$	6.87197	+	25.6465i	0.358714	+	1.33874i	0.875746	+	0.482772i	$0.160370\pi$
$367$	6.87197	+	25.6465i	0.358714	+	1.33874i	−0.517032	+	0.855966i	$0.672963\pi$
$368$	3.00310	−	18.9609i	0.156548	−	0.988403i
$369$	30.0230	+	13.8332i	1.56293	+	0.720128i
$370$	−22.3107	+	40.7074i	−1.15988	+	2.11628i
$371$		−	15.3679i		−	0.797862i
$372$	−13.3031	+	12.4483i	−0.689736	+	0.645412i
$373$	8.42080	+	8.42080i	0.436012	+	0.436012i	0.890668	−	0.454655i	$-0.150237\pi$
$373$	8.42080	+	8.42080i	0.436012	+	0.436012i	−0.454655	+	0.890668i	$0.650237\pi$
$374$	−16.4372	−	50.5884i	−0.849945	−	2.61586i
$375$	18.9730	+	3.87632i	0.979761	+	0.200172i
$376$	−0.568995	+	0.413399i	−0.0293437	+	0.0213194i
$377$	2.00597	−	0.537497i	0.103313	−	0.0276825i
$378$	7.26877	+	20.0875i	0.373865	+	1.03319i
$379$	1.90954	−	4.28891i	0.0980867	−	0.220306i	−0.857837	−	0.513922i	$-0.828192\pi$
$379$	1.90954	−	4.28891i	0.0980867	−	0.220306i	0.955923	+	0.293616i	$0.0948587\pi$
$380$	0.000967447		0.00757940i	4.96290e−5		0.000388815i
$381$	16.3090	−	1.60801i	0.835533	−	0.0823807i
$382$	−15.1468	+	9.83645i	−0.774978	+	0.503277i
$383$	2.81102	+	2.27632i	0.143636	+	0.116314i	0.698446	−	0.715663i	$-0.253875\pi$
$383$	2.81102	+	2.27632i	0.143636	+	0.116314i	−0.554809	+	0.831978i	$0.687209\pi$
$384$	2.62721	−	1.49434i	0.134069	−	0.0762577i
$385$	12.0563	−	10.2151i	0.614444	−	0.520607i
$386$	31.1267	+	3.27155i	1.58431	+	0.166517i
$387$	−5.54993	+	32.3390i	−0.282119	+	1.64389i
$388$	−7.67699	+	3.91162i	−0.389740	+	0.198582i
$389$	0.107237	−	1.02029i	0.00543714	−	0.0517309i	−0.991467	−	0.130359i	$-0.958387\pi$
$389$	0.107237	−	1.02029i	0.00543714	−	0.0517309i	0.996904	+	0.0786276i	$0.0250538\pi$
$390$	0.745054	+	1.85292i	0.0377273	+	0.0938261i
$391$	24.2807	−	26.9665i	1.22793	−	1.36375i
$392$	0.364912	−	0.450628i	0.0184308	−	0.0227602i
$393$	−4.38525	+	1.14480i	−0.221206	+	0.0577476i
$394$	3.94936	+	8.87041i	0.198966	+	0.446885i
$395$	9.05843	−	1.15623i	0.455779	−	0.0581764i
$396$	−16.7614	+	9.39140i	−0.842290	+	0.471936i
$397$	−1.67440	−	0.448654i	−0.0840356	−	0.0225173i	0.216556	−	0.976270i	$-0.430518\pi$
$397$	−1.67440	−	0.448654i	−0.0840356	−	0.0225173i	−0.300592	+	0.953753i	$0.597184\pi$
$398$	−10.8037	−	40.3198i	−0.541538	−	2.02105i
$399$	−0.00197809	−	0.00622407i	−9.90286e−5	−	0.000311593i
$400$	−3.12829	−	20.8126i	−0.156415	−	1.04063i
$401$	2.54269	−	0.826171i	0.126976	−	0.0412570i	−0.244840	−	0.969564i	$-0.578735\pi$
$401$	2.54269	−	0.826171i	0.126976	−	0.0412570i	0.371816	+	0.928307i	$0.378735\pi$
$402$	2.77223	+	5.52854i	0.138266	+	0.275739i
$403$	0.825255	−	1.19930i	0.0411089	−	0.0597415i
$404$	−32.9342			−1.63854
$405$	19.6700	+	4.25357i	0.977408	+	0.211361i
$406$	−31.9394	+	6.78893i	−1.58513	+	0.336929i
$407$	35.2456	+	5.58236i	1.74706	+	0.276707i
$408$	3.00543	+	0.176926i	0.148791	+	0.00875912i
$409$	−27.9656	+	16.1460i	−1.38281	+	0.798366i	−0.992491	−	0.122314i	$-0.960969\pi$
$409$	−27.9656	+	16.1460i	−1.38281	+	0.798366i	−0.390319	+	0.920680i	$0.627635\pi$
$410$	−43.7744	−	21.0917i	−2.16186	−	1.04164i
$411$	0.495953	−	0.355473i	0.0244635	−	0.0175342i
$412$	−2.00133	+	5.21363i	−0.0985982	+	0.256857i
$413$	−9.05961	+	5.88338i	−0.445794	+	0.289502i
$414$	−23.1918	−	13.7912i	−1.13982	−	0.677798i
$415$	5.06272	−	5.29303i	0.248519	−	0.259824i
$416$	1.52810	−	1.37591i	0.0749215	−	0.0674596i
$417$	−10.4251	−	27.6901i	−0.510519	−	1.35599i
$418$	0.0107741	−	0.00548966i	0.000526977	−	0.000268508i
$419$	3.68434	−	11.3392i	0.179992	−	0.553958i	−0.819834	−	0.572601i	$-0.805934\pi$
$419$	3.68434	−	11.3392i	0.179992	−	0.553958i	0.999826	+	0.0186427i	$0.00593449\pi$
$420$	−4.94204	−	14.4304i	−0.241147	−	0.704133i
$421$	3.99336	+	4.43508i	0.194625	+	0.216153i	0.832556	−	0.553940i	$-0.186876\pi$
$421$	3.99336	+	4.43508i	0.194625	+	0.216153i	−0.637932	+	0.770093i	$0.720210\pi$
$422$	2.02067	−	0.105899i	0.0983648	−	0.00515508i
$423$	2.37935	+	9.36052i	0.115688	+	0.455124i
$424$	−0.334840	+	1.57530i	−0.0162612	+	0.0765032i
$425$	16.4672	−	36.2143i	0.798775	−	1.75665i
$426$	12.2992	+	17.1597i	0.595898	+	0.831393i
$427$	10.2566	−	3.93715i	0.496353	−	0.190532i
$428$	−17.7857	−	4.76567i	−0.859705	−	0.230357i
$429$	1.14750	−	1.01990i	0.0554016	−	0.0492414i
$430$	8.97638	−	47.3882i	0.432879	−	2.28526i
$431$	3.14633	+	14.8023i	0.151553	+	0.713002i	0.986644	+	0.162890i	$0.0520817\pi$
$431$	3.14633	+	14.8023i	0.151553	+	0.713002i	−0.835091	+	0.550112i	$0.814585\pi$
$432$	−3.00351	−	21.6649i	−0.144506	−	1.04235i
$433$	−13.7797	−	13.7797i	−0.662209	−	0.662209i	0.293692	−	0.955900i	$-0.405116\pi$
$433$	−13.7797	−	13.7797i	−0.662209	−	0.662209i	−0.955900	+	0.293692i	$0.905116\pi$
$434$	−13.9448	+	18.1520i	−0.669371	+	0.871322i
$435$	−10.5689	+	28.8886i	−0.506739	+	1.38510i
$436$	5.93859	+	18.2771i	0.284407	+	0.875314i
$437$	0.00691826	+	0.00449277i	0.000330945	+	0.000214918i
$438$	10.0085	−	19.3339i	0.478224	−	0.923810i
$439$	−10.7589	−	6.21167i	−0.513496	−	0.296467i	0.220774	−	0.975325i	$-0.429142\pi$
$439$	−10.7589	−	6.21167i	−0.513496	−	0.296467i	−0.734270	+	0.678858i	$0.762475\pi$
$440$	−1.45840	+	0.784416i	−0.0695267	+	0.0373956i
$441$	−3.89219	−	6.94662i	−0.185343	−	0.330791i
$442$	4.05224	−	0.641812i	0.192745	−	0.0305279i
$443$	2.65294	−	6.91114i	0.126045	−	0.328358i	−0.856008	−	0.516962i	$-0.827063\pi$
$443$	2.65294	−	6.91114i	0.126045	−	0.328358i	0.982053	+	0.188604i	$0.0603962\pi$
$444$	17.4147	−	29.7195i	0.826466	−	1.41042i
$445$	−1.29439	+	1.50349i	−0.0613601	+	0.0712722i
$446$	−1.30896	−	1.17860i	−0.0619812	−	0.0558081i
$447$	−2.37762	+	6.07664i	−0.112458	+	0.287415i
$448$	−11.4873	+	9.30226i	−0.542726	+	0.439490i
$449$	−1.68728	+	5.19292i	−0.0796277	+	0.245069i	−0.982944	−	0.183907i	$-0.941125\pi$
$449$	−1.68728	+	5.19292i	−0.0796277	+	0.245069i	0.903316	+	0.428976i	$0.141125\pi$
$450$	−28.8013	−	6.75001i	−1.35770	−	0.318199i
$451$	−3.90448	+	37.1487i	−0.183855	+	1.74926i
$452$	−0.677053	+	12.9189i	−0.0318459	+	0.607656i
$453$	−27.5296	−	7.56692i	−1.29346	−	0.355525i
$454$	−6.70377	+	0.704594i	−0.314623	+	0.0330682i
$455$	0.632729	+	1.04172i	0.0296628	+	0.0488366i
$456$	6.71542e−5	0	0.000681102i	3.14479e−6	0	3.18955e-5i
$457$	−19.6383	+	3.11040i	−0.918642	+	0.145499i	−0.597810	−	0.801638i	$-0.703962\pi$
$457$	−19.6383	+	3.11040i	−0.918642	+	0.145499i	−0.320832	+	0.947136i	$0.603962\pi$
$458$	−39.5078	+	15.1656i	−1.84608	+	0.708642i
$459$	17.5424	−	37.4368i	0.818807	−	1.74740i
$460$	16.3874	+	10.1313i	0.764066	+	0.472376i
$461$	−3.57678	−	4.92302i	−0.166587	−	0.229288i	0.717559	−	0.696498i	$-0.245259\pi$
$461$	−3.57678	−	4.92302i	−0.166587	−	0.229288i	−0.884147	+	0.467210i	$0.845259\pi$
$462$	−18.8569	+	15.0699i	−0.877302	+	0.701117i
$463$	6.99665	−	13.7317i	0.325162	−	0.638166i	−0.669332	−	0.742964i	$-0.733419\pi$
$463$	6.99665	−	13.7317i	0.325162	−	0.638166i	0.994494	+	0.104797i	$0.0334194\pi$
$464$	33.4322			1.55205
$465$	7.50689	+	20.2150i	0.348124	+	0.937449i
$466$	−14.3319			−0.663912
$467$	−6.01386	+	11.8029i	−0.278288	+	0.546172i	−0.987270	−	0.159056i	$-0.949155\pi$
$467$	−6.01386	+	11.8029i	−0.278288	+	0.546172i	0.708981	+	0.705227i	$0.249155\pi$
$468$	−0.513210	−	1.39023i	−0.0237232	−	0.0642632i
$469$	2.21858	+	3.05362i	0.102445	+	0.141003i
$470$	−3.25970	−	13.8175i	−0.150359	−	0.637355i
$471$	1.17203	+	5.69404i	0.0540041	+	0.262368i
$472$	1.05685	−	0.405687i	0.0486455	−	0.0186732i
$473$	−36.6202	+	5.80007i	−1.68380	+	0.266687i
$474$	−13.8825	+	1.36877i	−0.637646	+	0.0628697i
$475$	0.00871679	+	0.00240952i	0.000399954	+	0.000110556i
$476$	−31.1639	+	3.27546i	−1.42840	+	0.150130i
$477$	18.3912	+	12.2831i	0.842074	+	0.562402i
$478$	−0.357657	+	6.82450i	−0.0163589	+	0.312146i
$479$	−4.35629	+	41.4473i	−0.199044	+	1.89378i	0.204579	+	0.978850i	$0.434417\pi$
$479$	−4.35629	+	41.4473i	−0.199044	+	1.89378i	−0.403623	+	0.914925i	$0.632249\pi$
$480$	3.66176	+	30.2372i	0.167136	+	1.38013i
$481$	−0.850547	+	2.61771i	−0.0387816	+	0.119357i
$482$	−24.8935	+	20.1584i	−1.13387	+	0.918188i
$483$	−15.3353	−	6.00027i	−0.697779	−	0.273022i
$484$	−0.690315	−	0.621562i	−0.0313780	−	0.0282528i
$485$	0.760012	+	10.1696i	0.0345103	+	0.461776i
$486$	−29.8490	−	7.35657i	−1.35398	−	0.333701i
$487$	−2.33415	+	6.08068i	−0.105771	+	0.275542i	−0.976244	−	0.216673i	$-0.930479\pi$
$487$	−2.33415	+	6.08068i	−0.105771	+	0.275542i	0.870474	+	0.492215i	$0.163813\pi$
$488$	−1.13715	+	0.180106i	−0.0514762	+	0.00815303i
$489$	6.51971	−	7.14775i	0.294832	−	0.323233i
$490$	5.54433	+	10.3081i	0.250467	+	0.465674i
$491$	−25.1630	−	14.5279i	−1.13559	−	0.655633i	−0.190255	−	0.981735i	$-0.560931\pi$
$491$	−25.1630	−	14.5279i	−1.13559	−	0.655633i	−0.945335	+	0.326102i	$0.894265\pi$
$492$	32.0203	+	16.5758i	1.44359	+	0.747294i
$493$	52.9993	+	34.4181i	2.38697	+	1.55012i
$494$	0.000288212	0	0.000887025i	1.29673e−5	0	3.99091e-5i
$495$	2.58845	+	22.5926i	0.116342	+	1.01546i
$496$	17.8297	−	15.2106i	0.800576	−	0.682975i
$497$	9.11089	+	9.11089i	0.408679	+	0.408679i
$498$	−7.96242	+	7.86051i	−0.356805	+	0.352238i
$499$	−1.51605	−	7.13246i	−0.0678678	−	0.319293i	0.931098	−	0.364770i	$-0.118852\pi$
$499$	−1.51605	−	7.13246i	−0.0678678	−	0.319293i	−0.998965	+	0.0454774i	$0.985519\pi$
$500$	20.4788	+	5.17357i	0.915839	+	0.231369i
$501$	17.9054	+	20.1454i	0.799953	+	0.900029i
$502$	−37.1090	−	9.94333i	−1.65626	−	0.443792i
$503$	23.7387	−	9.11244i	1.05846	−	0.406304i	0.234005	−	0.972235i	$-0.424817\pi$
$503$	23.7387	−	9.11244i	1.05846	−	0.406304i	0.824452	+	0.565932i	$0.191483\pi$
$504$	−0.405422	−	1.30471i	−0.0180589	−	0.0581166i
$505$	−15.0592	+	35.9542i	−0.670124	+	1.59994i
$506$	6.33917	−	29.8234i	0.281810	−	1.32581i
$507$	−12.0777	−	18.8629i	−0.536390	−	0.837732i
$508$	17.8507	−	0.935514i	0.791995	−	0.0415067i
$509$	−14.1278	−	15.6905i	−0.626203	−	0.695469i	0.343667	−	0.939091i	$-0.388331\pi$
$509$	−14.1278	−	15.6905i	−0.626203	−	0.695469i	−0.969870	+	0.243623i	$0.921664\pi$
$510$	−26.7309	+	54.5766i	−1.18367	+	2.41669i
$511$	4.10581	−	12.6364i	0.181630	−	0.559000i
$512$	27.8561	−	14.1934i	1.23108	−	0.627266i
$513$	0.00902954	+	0.00260745i	0.000398664	+	0.000115122i
$514$	−7.51730	+	6.76861i	−0.331574	+	0.298550i
$515$	4.77661	+	4.56878i	0.210483	+	0.201325i
$516$	−7.66633	+	34.9585i	−0.337491	+	1.53896i
$517$	−9.15288	+	5.94395i	−0.402543	+	0.261415i
$518$	15.5091	−	40.4026i	0.681431	−	1.77519i
$519$	−7.09868	−	9.90401i	−0.311597	−	0.434738i
$520$	−0.0421610	−	0.120568i	−0.00184888	−	0.00528727i
$521$	−25.4811	+	14.7115i	−1.11635	+	0.644522i	−0.940465	−	0.339889i	$-0.889610\pi$
$521$	−25.4811	+	14.7115i	−1.11635	+	0.644522i	−0.175880	+	0.984412i	$0.556277\pi$
$522$	17.4036	−	43.6489i	0.761735	−	1.91046i
$523$	−7.55787	−	1.19705i	−0.330483	−	0.0523433i	−0.0110117	−	0.999939i	$-0.503505\pi$
$523$	−7.55787	−	1.19705i	−0.330483	−	0.0523433i	−0.319471	+	0.947596i	$0.603505\pi$
$524$	−4.83546	+	1.02781i	−0.211238	+	0.0449000i
$525$	−18.0135	−	1.20310i	−0.786172	−	0.0525075i
$526$	9.98812			0.435503
$527$	43.9241	−	5.75748i	1.91336	−	0.250800i
$528$	22.0930	−	11.0783i	0.961476	−	0.482121i
$529$	−2.09247	+	0.679885i	−0.0909770	+	0.0295602i
$530$	−26.7183	−	18.5186i	−1.16057	−	0.804396i
$531$	0.200248	−	15.5443i	0.00869004	−	0.674564i
$532$	−0.00184369	−	0.00688075i	−7.99342e−5	−	0.000298318i
$533$	−2.78294	−	0.745685i	−0.120542	−	0.0322992i
$534$	2.04234	−	2.23908i	0.0883808	−	0.0968944i
$535$	−13.3352	+	17.2376i	−0.576531	+	0.745245i
$536$	−0.160884	−	0.361352i	−0.00694914	−	0.0156080i
$537$	5.31946	+	20.3766i	0.229552	+	0.879314i
$538$	−21.5080	+	26.5602i	−0.927278	+	1.14509i
$539$	6.02064	−	6.68659i	0.259327	−	0.288012i
$540$	21.2193	+	5.61950i	0.913133	+	0.241825i
$541$	−2.24035	+	21.3155i	−0.0963202	+	0.916425i	0.834515	+	0.550986i	$0.185748\pi$
$541$	−2.24035	+	21.3155i	−0.0963202	+	0.916425i	−0.930835	+	0.365440i	$0.880919\pi$
$542$	41.7926	−	21.2944i	1.79515	−	0.914672i
$543$	18.2251	−	2.76637i	0.782115	−	0.118716i
$544$	62.2290	+	6.54053i	2.66804	+	0.280423i
$545$	22.6685	+	1.87405i	0.971013	+	0.0802755i
$546$	−0.920527	−	1.61838i	−0.0393949	−	0.0692604i
$547$	−8.63297	−	6.99084i	−0.369119	−	0.298907i	0.426757	−	0.904366i	$-0.359656\pi$
$547$	−8.63297	−	6.99084i	−0.369119	−	0.298907i	−0.795876	+	0.605460i	$0.792989\pi$
$548$	0.558185	−	0.362490i	0.0238445	−	0.0154848i
$549$	−3.48609	+	15.4212i	−0.148783	+	0.658161i
$550$	−3.23168	−	33.2701i	−0.137799	−	1.41864i
$551$	−0.00584314	+	0.0131239i	−0.000248926	+	0.000559097i
$552$	1.44122	+	0.949190i	0.0613422	+	0.0404002i
$553$	−8.22345	+	2.20347i	−0.349697	+	0.0937010i
$554$	−15.0894	+	10.9631i	−0.641088	+	0.465778i
$555$	−24.4819	−	32.6009i	−1.03920	−	1.38383i
$556$	−9.97274	−	30.6929i	−0.422938	−	1.30167i
$557$	−13.3470	−	13.3470i	−0.565529	−	0.565529i	0.365344	−	0.930873i	$-0.380951\pi$
$557$	−13.3470	−	13.3470i	−0.565529	−	0.565529i	−0.930873	+	0.365344i	$0.880951\pi$
$558$	−10.5773	−	31.1964i	−0.447774	−	1.32065i
$559$		−	2.85977i		−	0.120955i
$560$	5.49847	+	18.8350i	0.232353	+	0.795926i
$561$	46.4285	+	5.18239i	1.96021	+	0.218801i
$562$	−4.28012	+	27.0236i	−0.180546	+	1.13992i
$563$	−4.99345	−	18.6358i	−0.210449	−	0.785406i	−0.987719	−	0.156239i	$-0.950063\pi$
$563$	−4.99345	−	18.6358i	−0.210449	−	0.785406i	0.777270	−	0.629167i	$-0.216604\pi$
$564$	2.12386	+	10.3183i	0.0894305	+	0.434479i
$565$	13.7940	+	6.64633i	0.580319	+	0.279613i
$566$	−1.67721	+	2.30848i	−0.0704983	+	0.0970326i
$567$	−18.7046	−	1.46425i	−0.785520	−	0.0614926i
$568$	−0.735407	−	1.13243i	−0.0308570	−	0.0475156i
$569$	4.35483	+	41.4335i	0.182564	+	1.73698i	0.575841	+	0.817562i	$0.304675\pi$
$569$	4.35483	+	41.4335i	0.182564	+	1.73698i	−0.393277	+	0.919420i	$0.628659\pi$
$570$	−0.0132047	−	0.00406104i	−0.000553083	−	0.000170098i
$571$	−26.9093	−	29.8858i	−1.12612	−	1.25068i	−0.964573	−	0.263816i	$-0.915019\pi$
$571$	−26.9093	−	29.8858i	−1.12612	−	1.25068i	−0.161546	−	0.986865i	$-0.551648\pi$
$572$	1.30137	−	1.05383i	0.0544130	−	0.0440628i
$573$	−2.38041	−	15.6824i	−0.0994431	−	0.655142i
$574$	43.0832	+	13.9986i	1.79826	+	0.584289i
$575$	18.5535	−	13.2576i	0.773735	−	0.552879i
$576$	−1.95082	−	21.1822i	−0.0812841	−	0.882591i
$577$	−0.935455	−	17.8495i	−0.0389435	−	0.743086i	−0.946411	−	0.322964i	$-0.895321\pi$
$577$	−0.935455	−	17.8495i	−0.0389435	−	0.743086i	0.907468	−	0.420122i	$-0.138013\pi$
$578$	70.9688	+	57.4694i	2.95191	+	2.39041i
$579$	−13.8972	+	23.7166i	−0.577548	+	0.985626i
$580$	−12.9622	+	30.9477i	−0.538226	+	1.28503i
$581$	−4.01366	+	5.52433i	−0.166515	+	0.229188i
$582$	−0.715086	−	15.5618i	−0.0296413	−	0.645059i
$583$	−6.46799	+	24.1389i	−0.267877	+	0.999730i
$584$	−0.696193	+	1.20584i	−0.0288087	+	0.0498981i
$585$	−1.75237	−	0.0754095i	−0.0724518	−	0.00311780i
$586$	−25.8873	+	5.50252i	−1.06940	+	0.227307i
$587$	−4.52974	+	8.89011i	−0.186962	+	0.366934i	−0.965394	−	0.260795i	$-0.916015\pi$
$587$	−4.52974	+	8.89011i	−0.186962	+	0.366934i	0.778432	+	0.627729i	$0.216015\pi$
$588$	−3.89311	−	7.76387i	−0.160549	−	0.320177i
$589$	0.00285476	+	0.00965753i	0.000117628	+	0.000397931i
$590$	−0.688264	+	22.8404i	−0.0283354	+	0.940326i
$591$	−8.52774	−	0.0549268i	−0.350784	−	0.00225939i
$592$	−24.1329	+	37.1614i	−0.991857	+	1.52733i
$593$	5.92192	−	37.3896i	0.243184	−	1.53541i	−0.499827	−	0.866126i	$-0.666603\pi$
$593$	5.92192	−	37.3896i	0.243184	−	1.53541i	0.743011	−	0.669279i	$-0.233397\pi$
$594$	−2.96292	−	34.6114i	−0.121570	−	1.42012i
$595$	−10.6739	+	35.5193i	−0.437587	+	1.45615i
$596$	−2.89489	+	6.50203i	−0.118579	+	0.266334i
$597$	36.1719	+	5.96813i	1.48042	+	0.244259i
$598$	2.19551	+	0.842778i	0.0897812	+	0.0344638i
$599$	1.54968	+	0.329394i	0.0633181	+	0.0134587i	0.239462	−	0.970906i	$-0.423029\pi$
$599$	1.54968	+	0.329394i	0.0633181	+	0.0134587i	−0.176144	+	0.984364i	$0.556362\pi$
$600$	1.82027	+	0.515806i	0.0743121	+	0.0210577i
$601$	−30.5115	+	33.8864i	−1.24459	+	1.38226i	−0.349151	+	0.937066i	$0.613530\pi$
$601$	−30.5115	+	33.8864i	−1.24459	+	1.38226i	−0.895437	+	0.445189i	$0.853137\pi$
$602$	−2.35328	+	44.9033i	−0.0959125	+	1.83012i
$603$	−5.42758	+	0.214382i	−0.221028	+	0.00873032i
$604$	−29.6173	−	9.62324i	−1.20511	−	0.391564i
$605$	−0.994206	+	0.469407i	−0.0404202	+	0.0190841i
$606$	24.5696	−	54.2412i	0.998070	−	2.20340i
$607$	0.237811	+	0.0124632i	0.00965246	+	0.000505864i	0.0571616	−	0.998365i	$-0.481795\pi$
$607$	0.237811	+	0.0124632i	0.00965246	+	0.000505864i	−0.0475091	+	0.998871i	$0.515128\pi$
$608$	0.000744445		0.0142049i	3.01912e−5		0.000576083i
$609$	6.14308	−	28.0125i	0.248930	−	1.13512i
$610$	5.51437	−	22.5763i	0.223270	−	0.914088i
$611$	−0.342382	−	0.769002i	−0.0138513	−	0.0311105i
$612$	20.9885	−	39.9127i	0.848408	−	1.61337i
$613$	−2.08376	−	5.42837i	−0.0841622	−	0.219250i	0.885041	−	0.465514i	$-0.154130\pi$
$613$	−2.08376	−	5.42837i	−0.0841622	−	0.219250i	−0.969203	+	0.246264i	$0.920797\pi$
$614$	17.8517	+	30.9200i	0.720435	+	1.24783i
$615$	32.7371	−	27.3773i	1.32009	−	1.10396i
$616$	1.24899	−	0.907445i	0.0503233	−	0.0365620i
$617$	−32.1575	−	20.8833i	−1.29461	−	0.840731i	−0.301004	−	0.953623i	$-0.597322\pi$
$617$	−32.1575	−	20.8833i	−1.29461	−	0.840731i	−0.993607	+	0.112892i	$0.963989\pi$
$618$	−7.09360	−	7.18557i	−0.285347	−	0.289046i
$619$		−	28.7223i		−	1.15445i	−0.816586	−	0.577223i	$-0.804136\pi$
$619$		−	28.7223i		−	1.15445i	0.816586	−	0.577223i	$-0.195864\pi$
$620$	7.16734	+	22.4020i	0.287847	+	0.899687i
$621$	19.4377	−	13.5563i	0.780006	−	0.543996i
$622$	−6.41670	−	3.26947i	−0.257286	−	0.131094i
$623$	1.00735	−	1.55118i	0.0403587	−	0.0621469i
$624$	0.577389	+	1.81675i	0.0231141	+	0.0727284i
$625$	15.0119	−	19.9911i	0.600476	−	0.799643i
$626$	−21.1975	+	12.2384i	−0.847223	+	0.489145i
$627$	0.000487492		0.0106089i	1.94686e−5		0.000423678i
$628$	0.991942	+	6.26288i	0.0395828	+	0.249916i
$629$	−76.5146	+	34.0665i	−3.05084	+	1.35832i
$630$	27.4532	+	2.62607i	1.09376	+	0.104625i
$631$	3.69896	+	35.1932i	0.147253	+	1.40102i	0.779572	+	0.626312i	$0.215437\pi$
$631$	3.69896	+	35.1932i	0.147253	+	1.40102i	−0.632319	+	0.774708i	$0.717897\pi$
$632$	0.890960	−	0.0466932i	0.0354405	−	0.00185736i
$633$	−0.647542	+	1.65496i	−0.0257375	+	0.0657789i
$634$	48.6674	+	5.11515i	1.93283	+	0.203149i
$635$	7.14092	−	19.9153i	0.283379	−	0.790316i
$636$	19.4239	+	14.3044i	0.770209	+	0.567205i
$637$	0.436751	+	0.539342i	0.0173047	+	0.0213695i
$638$	53.0256	+	2.77895i	2.09930	+	0.110020i
$639$	−18.1853	+	3.62121i	−0.719398	+	0.143253i
$640$	−0.290799	−	3.89113i	−0.0114949	−	0.153810i
$641$	−3.56120	+	16.7541i	−0.140659	+	0.661748i	0.850157	+	0.526529i	$0.176507\pi$
$641$	−3.56120	+	16.7541i	−0.140659	+	0.661748i	−0.990816	+	0.135219i	$0.956826\pi$
$642$	21.1174	−	25.7370i	0.833436	−	1.01576i
$643$	−5.95535	−	37.6006i	−0.234856	−	1.48282i	−0.769990	−	0.638056i	$-0.779739\pi$
$643$	−5.95535	−	37.6006i	−0.234856	−	1.48282i	0.535134	−	0.844767i	$-0.320261\pi$
$644$	−16.4088	−	7.30567i	−0.646597	−	0.287884i
$645$	34.6588	+	24.3541i	1.36469	+	0.958943i
$646$	−0.0141905	+	0.0245787i	−0.000558318	+	0.000967036i
$647$	34.0357	+	5.39073i	1.33808	+	0.211931i	0.784119	−	0.620610i	$-0.213115\pi$
$647$	34.0357	+	5.39073i	1.33808	+	0.211931i	0.553963	+	0.832542i	$0.313115\pi$
$648$	1.88543	+	0.557635i	0.0740665	+	0.0219060i
$649$	16.7064	−	5.42824i	0.655784	−	0.213077i
$650$	2.57357	+	0.155242i	0.100944	+	0.00608911i
$651$	−9.46862	−	17.7342i	−0.371104	−	0.695057i
$652$	7.46172	−	7.46172i	0.292223	−	0.292223i
$653$	−7.30705	−	3.72313i	−0.285947	−	0.145697i	0.305134	−	0.952309i	$-0.401299\pi$
$653$	−7.30705	−	3.72313i	−0.285947	−	0.145697i	−0.591081	+	0.806612i	$0.701299\pi$
$654$	−34.5319	−	3.85448i	−1.35030	−	0.150722i
$655$	−1.08896	+	5.74883i	−0.0425490	+	0.224626i
$656$	−40.1675	−	23.1907i	−1.56828	−	0.905446i
$657$	11.8407	+	15.0134i	0.461948	+	0.585727i
$658$	4.74317	+	12.3564i	0.184908	+	0.481701i
$659$	26.0737	+	18.9436i	1.01569	+	0.737940i	0.965394	−	0.260795i	$-0.0839846\pi$
$659$	26.0737	+	18.9436i	1.01569	+	0.737940i	0.0502926	+	0.998735i	$0.483985\pi$
$660$	1.68919	+	24.7464i	0.0657517	+	0.963251i
$661$	3.30833	+	0.703208i	0.128679	+	0.0273516i	0.271801	−	0.962353i	$-0.412381\pi$
$661$	3.30833	+	0.703208i	0.128679	+	0.0273516i	−0.143122	+	0.989705i	$0.545714\pi$
$662$	−17.3780	+	21.4600i	−0.675414	+	0.834067i
$663$	−0.955009	+	3.47447i	−0.0370895	+	0.134937i
$664$	0.531788	−	0.478824i	0.0206374	−	0.0185820i
$665$	−0.00835474	−	0.00113347i	−0.000323983	−	4.39540e-5i
$666$	35.9550	+	50.8527i	1.39323	+	1.97050i
$667$	16.4450	+	32.2752i	0.636754	+	1.24970i
$668$	18.5009	+	22.8468i	0.715823	+	0.883968i
$669$	1.41725	−	0.620096i	0.0547942	−	0.0239743i
$670$	7.98239	−	0.177521i	0.308386	−	0.00685824i
$671$	−17.7675	+	1.86744i	−0.685906	+	0.0720917i
$672$	−7.17251	−	27.4748i	−0.276685	−	1.05986i
$673$	−31.3440	−	12.0318i	−1.20822	−	0.463792i	−0.330886	−	0.943671i	$-0.607347\pi$
$673$	−31.3440	−	12.0318i	−1.20822	−	0.463792i	−0.877335	+	0.479878i	$0.840681\pi$
$674$	31.2263	+	22.6872i	1.20279	+	0.873879i
$675$	15.8373	−	20.5956i	0.609580	−	0.792725i
$676$	−12.2154	−	21.1577i	−0.469822	−	0.813756i
$677$	1.19619	−	0.320518i	0.0459733	−	0.0123185i	−0.235759	−	0.971812i	$-0.575758\pi$
$677$	1.19619	−	0.320518i	0.0459733	−	0.0123185i	0.281732	+	0.959493i	$0.409091\pi$
$678$	−20.7719	−	10.7529i	−0.797739	−	0.412962i
$679$	−1.97669	−	9.29959i	−0.0758584	−	0.356886i
$680$	1.86804	−	3.40837i	0.0716360	−	0.130705i
$681$	1.86566	−	5.61851i	0.0714921	−	0.215302i
$682$	29.5433	−	22.6429i	1.13127	−	0.867041i
$683$	−33.9887	+	33.9887i	−1.30054	+	1.30054i	−0.372515	+	0.928026i	$0.621504\pi$
$683$	−33.9887	+	33.9887i	−1.30054	+	1.30054i	−0.928026	+	0.372515i	$0.878496\pi$
$684$	0.00970798	+	0.00329316i	0.000371194	+	0.000125917i
$685$	−0.140500	−	0.775119i	−0.00536822	−	0.0296158i
$686$	−23.3293	−	32.1100i	−0.890716	−	1.22596i
$687$	2.18420	−	37.1030i	0.0833324	−	1.41557i
$688$	11.9155	−	44.4693i	0.454275	−	1.69538i
$689$	−1.76090	−	0.784002i	−0.0670849	−	0.0298681i
$690$	−28.9112	+	19.4312i	−1.10063	+	0.739732i
$691$	−0.864762	+	0.385017i	−0.0328971	+	0.0146467i	−0.423119	−	0.906074i	$-0.639065\pi$
$691$	−0.864762	+	0.385017i	−0.0328971	+	0.0146467i	0.390222	+	0.920721i	$0.372398\pi$
$692$	−7.23880	−	11.1468i	−0.275178	−	0.423737i
$693$	−5.22285	−	20.5471i	−0.198400	−	0.780520i
$694$	−40.3848	−	36.3626i	−1.53299	−	1.38031i
$695$	−38.0675	−	3.14711i	−1.44398	−	0.119377i
$696$	−1.24004	+	2.73759i	−0.0470037	+	0.103768i
$697$	−39.8020	−	78.1158i	−1.50761	−	2.95885i
$698$	30.8942	+	60.6332i	1.16936	+	2.29500i
$699$	5.19368	−	11.4659i	0.196443	−	0.433679i
$700$	−19.5671	−	2.21279i	−0.739568	−	0.0836357i
$701$	15.6764	+	14.1151i	0.592089	+	0.533120i	0.909789	−	0.415072i	$-0.136244\pi$
$701$	15.6764	+	14.1151i	0.592089	+	0.533120i	−0.317699	+	0.948192i	$0.602910\pi$
$702$	2.67251	+	0.191901i	0.100867	+	0.00724283i
$703$	−0.0103700	−	0.0159684i	−0.000391111	−	0.000602258i
$704$	21.9587	−	9.77662i	0.827598	−	0.368470i
$705$	12.2356	+	2.39943i	0.460820	+	0.0903679i
$706$	9.74044	+	4.33672i	0.366586	+	0.163215i
$707$	9.40573	−	35.1027i	0.353739	−	1.32017i
$708$	0.996464	−	16.9269i	0.0374494	−	0.636153i
$709$	−17.4915	−	24.0749i	−0.656906	−	0.904153i	0.342469	−	0.939529i	$-0.388737\pi$
$709$	−17.4915	−	24.0749i	−0.656906	−	0.904153i	−0.999374	+	0.0353764i	$0.988737\pi$
$710$	26.8188	−	4.86123i	1.00649	−	0.182439i
$711$	3.93578	−	11.6024i	0.147603	−	0.435123i
$712$	−0.137057	+	0.137057i	−0.00513642	+	0.00513642i
$713$	23.4544	+	9.73066i	0.878375	+	0.364416i
$714$	17.8544	−	53.7692i	0.668183	−	2.01226i
$715$	−0.555413	−	1.90257i	−0.0207713	−	0.0711520i
$716$	4.77583	+	22.4685i	0.178481	+	0.839688i
$717$	−5.33016	−	2.75924i	−0.199058	−	0.103046i
$718$	−0.246406	+	0.0660243i	−0.00919579	+	0.00246401i
$719$	9.20472	+	15.9430i	0.343278	+	0.594575i	0.985039	−	0.172329i	$-0.0551293\pi$
$719$	9.20472	+	15.9430i	0.343278	+	0.594575i	−0.641761	+	0.766905i	$0.721796\pi$
$720$	−26.9351	−	8.47406i	−1.00381	−	0.315809i
$721$	−4.98535	−	3.62207i	−0.185664	−	0.134893i
$722$	34.9814	+	13.4281i	1.30187	+	0.499742i
$723$	−7.10612	−	27.2205i	−0.264280	−	1.01234i
$724$	19.9965	−	2.10172i	0.743164	−	0.0781097i
$725$	27.8586	+	28.3017i	1.03464	+	1.05110i
$726$	1.53868	−	0.673222i	0.0571056	−	0.0249856i
$727$	1.97610	+	2.44028i	0.0732894	+	0.0905049i	0.812472	−	0.583000i	$-0.198121\pi$
$727$	1.97610	+	2.44028i	0.0732894	+	0.0905049i	−0.739183	+	0.673505i	$0.764788\pi$
$728$	0.0540603	+	0.106099i	0.00200361	+	0.00393231i
$729$	16.7023	−	21.2140i	0.618603	−	0.785704i
$730$	−17.0218	−	22.3653i	−0.630005	−	0.827778i
$731$	64.6701	−	58.2292i	2.39191	−	2.15368i
$732$	−4.57054	+	16.6283i	−0.168932	+	0.614601i
$733$	−4.33676	+	5.35545i	−0.160182	+	0.197808i	−0.850918	−	0.525299i	$-0.823953\pi$
$733$	−4.33676	+	5.35545i	−0.160182	+	0.197808i	0.690736	+	0.723107i	$0.257287\pi$
$734$	−51.2178	−	10.8867i	−1.89048	−	0.401835i
$735$	−10.2559	+	0.700072i	−0.378296	+	0.0258226i
$736$	29.0165	+	21.0817i	1.06956	+	0.777082i
$737$	−2.19961	−	5.73017i	−0.0810235	−	0.211073i
$738$	−51.1874	+	40.3702i	−1.88423	+	1.48605i
$739$	10.6943	+	6.17434i	0.393395	+	0.227127i	0.683630	−	0.729829i	$-0.260400\pi$
$739$	10.6943	+	6.17434i	0.393395	+	0.227127i	−0.290235	+	0.956955i	$0.593733\pi$
$740$	−25.0430	−	36.7475i	−0.920600	−	1.35087i
$741$	−0.000814085	0	9.08688e-5i	−2.99062e−5	0	3.33815e-6i
$742$	27.0039	+	13.7592i	0.991345	+	0.505116i
$743$	1.28225	−	1.28225i	0.0470413	−	0.0470413i	−0.683195	−	0.730236i	$-0.739410\pi$
$743$	1.28225	−	1.28225i	0.0470413	−	0.0470413i	0.730236	+	0.683195i	$0.239410\pi$
$744$	0.584190	+	2.02416i	0.0214175	+	0.0742093i
$745$	5.77458	+	6.13341i	0.211564	+	0.224711i
$746$	−22.3360	+	7.25742i	−0.817780	+	0.265713i
$747$	−3.40313	−	9.21867i	−0.124514	−	0.337293i
$748$	50.3288	+	7.97130i	1.84020	+	0.291459i
$749$	10.1589	−	17.5957i	0.371198	−	0.642934i
$750$	−23.7982	+	29.8681i	−0.868988	+	1.09063i
$751$	−15.8426	−	7.05357i	−0.578104	−	0.257388i	0.0967881	−	0.995305i	$-0.469143\pi$
$751$	−15.8426	−	7.05357i	−0.578104	−	0.257388i	−0.674892	+	0.737917i	$0.735810\pi$
$752$	−2.11990	−	13.3845i	−0.0773047	−	0.488083i
$753$	21.4027	−	26.0848i	0.779957	−	0.950582i
$754$	−0.851512	+	4.00605i	−0.0310102	+	0.145892i
$755$	−24.0482	+	27.9330i	−0.875203	+	1.01658i
$756$	−20.3071	−	2.53194i	−0.738563	−	0.0920859i
$757$	9.62462	+	0.504405i	0.349813	+	0.0183329i	0.226433	−	0.974027i	$-0.427293\pi$
$757$	9.62462	+	0.504405i	0.349813	+	0.0183329i	0.123379	+	0.992360i	$0.460627\pi$
$758$	5.82666	+	7.19533i	0.211634	+	0.261346i
$759$	21.5623	+	15.8791i	0.782660	+	0.576374i
$760$	0.000831712	0	0.000298222i	3.01694e−5	0	1.08176e-5i
$761$	9.45552	+	0.993816i	0.342762	+	0.0360258i	0.274346	−	0.961631i	$-0.411539\pi$
$761$	9.45552	+	0.993816i	0.342762	+	0.0360258i	0.0684165	+	0.997657i	$0.478205\pi$
$762$	−11.7762	+	30.0972i	−0.426607	+	1.09031i
$763$	−21.1765	+	1.10982i	−0.766642	+	0.0401780i
$764$	−1.80849	−	17.2066i	−0.0654289	−	0.622515i
$765$	−33.9757	−	41.1632i	−1.22839	−	1.48826i
$766$	−6.51663	+	2.90139i	−0.235455	+	0.104831i
$767$	0.211953	+	1.33822i	0.00765319	+	0.0483203i
$768$	1.40110	+	30.4910i	0.0505580	+	1.10025i
$769$	−19.6286	+	11.3326i	−0.707825	+	0.408663i	−0.810255	−	0.586077i	$-0.800672\pi$
$769$	−19.6286	+	11.3326i	−0.707825	+	0.408663i	0.102430	+	0.994740i	$0.467338\pi$
$770$	7.15531	+	30.3306i	0.257860	+	1.09304i
$771$	−2.69089	−	8.46687i	−0.0969099	−	0.304927i
$772$	−16.3298	+	25.1456i	−0.587721	+	0.905011i
$773$	35.4479	+	18.0616i	1.27497	+	0.649631i	0.954665	−	0.297683i	$-0.0962138\pi$
$773$	35.4479	+	18.0616i	1.27497	+	0.649631i	0.320307	+	0.947314i	$0.396214\pi$
$774$	−51.8560	−	38.7059i	−1.86393	−	1.39126i
$775$	27.7335	+	2.41874i	0.996218	+	0.0868839i
$776$			0.996330i			0.0357661i
$777$	26.7028	+	27.0490i	0.957957	+	0.970378i
$778$	1.69681	+	1.10192i	0.0608336	+	0.0395058i
$779$	0.0161239	−	0.0117147i	0.000577698	−	0.000419723i
$780$	−1.90560	−	0.169904i	−0.0682315	−	0.00608354i
$781$	−10.4762	−	18.1453i	−0.374869	−	0.649291i
$782$	25.6455	+	66.8089i	0.917082	+	2.38908i
$783$	28.6133	+	29.7410i	1.02256	+	1.06286i
$784$	4.54423	+	10.2065i	0.162294	+	0.364518i
$785$	7.29075	+	1.78080i	0.260218	+	0.0635594i
$786$	1.91459	−	8.73056i	0.0682913	−	0.311409i
$787$	0.987312	+	18.8390i	0.0351939	+	0.671539i	0.958086	+	0.286481i	$0.0924854\pi$
$787$	0.987312	+	18.8390i	0.0351939	+	0.671539i	−0.922892	+	0.385058i	$0.874181\pi$
$788$	−9.28903	−	0.486817i	−0.330908	−	0.0173421i
$789$	−3.61955	+	7.99074i	−0.128860	+	0.284478i
$790$	−6.07850	+	16.9524i	−0.216263	+	0.603138i
$791$	−13.5762	−	4.41118i	−0.482715	−	0.156843i
$792$	0.0876866	+	2.21999i	0.00311581	+	0.0788839i
$793$	0.0721178	−	1.37609i	0.00256098	−	0.0488664i
$794$	2.28748	−	2.54050i	0.0811796	−	0.0901591i
$795$	24.4977	−	14.6644i	0.868843	−	0.520094i
$796$	39.1139	+	8.31391i	1.38635	+	0.294679i
$797$	−9.18247	−	3.52482i	−0.325260	−	0.124856i	0.190259	−	0.981734i	$-0.439067\pi$
$797$	−9.18247	−	3.52482i	−0.325260	−	0.124856i	−0.515519	+	0.856878i	$0.672401\pi$
$798$	0.0127077	+	0.00209670i	0.000449849	+	7.42223e-5i
$799$	10.4186	−	23.4005i	0.368583	−	0.827852i
$800$	37.2997	+	12.4456i	1.31874	+	0.440017i
$801$	1.05120	+	2.44533i	0.0371424	+	0.0864016i
$802$	−0.824806	+	5.20762i	−0.0291249	+	0.183887i
$803$	−11.7675	+	18.1203i	−0.415266	+	0.639453i
$804$	−5.92460	−	0.0381601i	−0.208944	−	0.00134580i
$805$	−15.4785	+	14.5730i	−0.545546	+	0.513630i
$806$	1.36850	+	2.52387i	0.0482035	+	0.0888994i
$807$	−13.4546	−	26.8320i	−0.473625	−	0.944531i
$808$	−1.72897	+	3.39329i	−0.0608248	+	0.119375i
$809$	26.9982	−	5.73864i	0.949205	−	0.201760i	0.292804	−	0.956172i	$-0.405412\pi$
$809$	26.9982	−	5.73864i	0.949205	−	0.201760i	0.656400	+	0.754413i	$0.272078\pi$
$810$	−25.0851	+	30.7550i	−0.881401	+	1.08062i
$811$	−16.8648	+	29.2107i	−0.592202	+	1.02572i	0.401733	+	0.915757i	$0.368408\pi$
$811$	−16.8648	+	29.2107i	−0.592202	+	1.02572i	−0.993935	+	0.109968i	$0.964925\pi$
$812$	8.09600	−	30.2147i	0.284114	−	1.06033i
$813$	1.89098	+	41.1519i	0.0663196	+	1.44326i
$814$	−41.3652	+	56.9344i	−1.44985	+	1.99555i
$815$	−4.73409	−	11.5578i	−0.165828	−	0.404853i
$816$	−29.3271	+	50.0487i	−1.02665	+	1.75206i
$817$	0.0153740	+	0.0124496i	0.000537868	+	0.000435557i
$818$	−3.33292	−	63.5960i	−0.116533	−	2.22358i
$819$	1.62833	−	0.149965i	0.0568985	−	0.00524019i
$820$	37.0409	−	28.1910i	1.29352	−	0.984473i
$821$	−33.5491	−	10.9008i	−1.17087	−	0.380439i	−0.341903	−	0.939735i	$-0.611072\pi$
$821$	−33.5491	−	10.9008i	−1.17087	−	0.380439i	−0.828968	+	0.559296i	$0.811072\pi$
$822$	0.180588	+	1.18973i	0.00629872	+	0.0414967i
$823$	−21.3733	+	17.3077i	−0.745025	+	0.603309i	−0.924825	−	0.380394i	$-0.875788\pi$
$823$	−21.3733	+	17.3077i	−0.745025	+	0.603309i	0.179799	+	0.983703i	$0.442455\pi$
$824$	0.432108	+	0.479905i	0.0150532	+	0.0167183i
$825$	27.7880	+	9.47120i	0.967454	+	0.329745i
$826$	−2.22682	−	21.1867i	−0.0774808	−	0.737181i
$827$	−19.7563	−	30.4220i	−0.686992	−	1.05788i	−0.994337	−	0.106277i	$-0.966107\pi$
$827$	−19.7563	−	30.4220i	−0.686992	−	1.05788i	0.307344	−	0.951598i	$-0.400560\pi$
$828$	21.8579	−	13.7977i	0.759614	−	0.479502i
$829$	−19.3271	+	26.6015i	−0.671258	+	0.923907i	−0.999788	−	0.0205863i	$-0.993447\pi$
$829$	−19.3271	+	26.6015i	−0.671258	+	0.923907i	0.328530	+	0.944493i	$0.393447\pi$
$830$	4.76796	+	13.6350i	0.165498	+	0.473277i
$831$	−3.30256	−	16.0448i	−0.114564	−	0.556587i
$832$	0.479847	+	1.79081i	0.0166357	+	0.0620852i
$833$	−3.30364	+	20.8584i	−0.114464	+	0.722700i
$834$	57.9898	+	6.47287i	2.00802	+	0.224137i
$835$	33.4014	−	9.75079i	1.15590	−	0.337440i
$836$			0.0115838i			0.000400634i
$837$	28.7909	+	2.84300i	0.995160	+	0.0982683i
$838$	16.6262	+	16.6262i	0.574344	+	0.574344i
$839$	4.69504	+	14.4498i	0.162091	+	0.498864i	0.998810	−	0.0487681i	$-0.0155295\pi$
$839$	4.69504	+	14.4498i	0.162091	+	0.498864i	−0.836720	+	0.547632i	$0.815530\pi$
$840$	−1.74625	−	0.248374i	−0.0602513	−	0.00856971i
$841$	−27.5741	+	20.0337i	−0.950830	+	0.690819i
$842$	−11.3685	+	3.04618i	−0.391785	+	0.104978i
$843$	−20.0685	−	13.2172i	−0.691196	−	0.455224i
$844$	−0.788419	+	1.77082i	−0.0271385	+	0.0609541i
$845$	−28.6833	+	3.66118i	−0.986735	+	0.125949i
$846$	−18.5783	−	4.19976i	−0.638733	−	0.144391i
$847$	0.859636	−	0.558254i	0.0295375	−	0.0191819i
$848$	−24.1153	−	19.5281i	−0.828121	−	0.670599i
$849$	−1.23904	−	2.17837i	−0.0425238	−	0.0747613i
$850$	48.8910	+	61.3589i	1.67695	+	2.10459i
$851$	−47.7461	−	5.01832i	−1.63671	−	0.172026i
$852$	−19.9959	+	3.03515i	−0.685047	+	0.103982i
$853$	−21.8943	+	11.1557i	−0.749647	+	0.381964i	−0.786689	−	0.617350i	$-0.788206\pi$
$853$	−21.8943	+	11.1557i	−0.749647	+	0.381964i	0.0370421	+	0.999314i	$0.488206\pi$
$854$	−2.26474	+	21.5476i	−0.0774979	+	0.737343i
$855$	0.00803412	−	0.00909240i	0.000274761	−	0.000310954i
$856$	−1.42473	+	1.58232i	−0.0486961	+	0.0540825i
$857$	−20.9745	+	25.9013i	−0.716474	+	0.884772i	−0.997182	−	0.0750211i	$-0.976098\pi$
$857$	−20.9745	+	25.9013i	−0.716474	+	0.884772i	0.280707	+	0.959793i	$0.409431\pi$
$858$	0.764763	+	2.92948i	0.0261086	+	0.100011i
$859$	10.5394	+	23.6720i	0.359601	+	0.807677i	0.999239	+	0.0390010i	$0.0124175\pi$
$859$	10.5394	+	23.6720i	0.359601	+	0.807677i	−0.639638	+	0.768676i	$0.720916\pi$
$860$	36.5447	+	28.2714i	1.24616	+	0.964048i
$861$	−26.8119	+	29.3947i	−0.913748	+	1.00177i
$862$	−28.8271	−	7.72419i	−0.981854	−	0.263087i
$863$	−1.64690	−	6.14631i	−0.0560611	−	0.209223i	0.932214	−	0.361908i	$-0.117875\pi$
$863$	−1.64690	−	6.14631i	−0.0560611	−	0.209223i	−0.988275	+	0.152685i	$0.951208\pi$
$864$	38.6126	+	13.3762i	1.31363	+	0.455066i
$865$	−15.4789	+	2.80573i	−0.526298	+	0.0953978i
$866$	36.5504	−	11.8759i	1.24203	−	0.403561i
$867$	−71.6950	+	35.9507i	−2.43489	+	1.22095i
$868$	−9.42903	−	19.7971i	−0.320042	−	0.671959i
$869$	13.8442			0.469634
$870$	−41.2995	−	44.4358i	−1.40018	−	1.50651i
$871$	0.463074	−	0.0984294i	0.0156907	−	0.00333515i
$872$	2.19490	+	0.347637i	0.0743285	+	0.0117725i
$873$	12.7090	+	5.06730i	0.430134	+	0.171502i
$874$	−0.0140886	+	0.00813405i	−0.000476554	+	0.000275138i
$875$	−11.3628	+	20.3496i	−0.384132	+	0.687943i
$876$	12.1498	+	16.9513i	0.410504	+	0.572732i
$877$	4.77869	−	12.4489i	0.161365	−	0.420370i	−0.828930	−	0.559352i	$-0.811050\pi$
$877$	4.77869	−	12.4489i	0.161365	−	0.420370i	0.990295	+	0.138983i	$0.0443832\pi$
$878$	20.5476	−	13.3438i	0.693449	−	0.450331i
$879$	4.97905	−	22.7045i	0.167939	−	0.765805i
$880$	−0.709405	−	31.8990i	−0.0239141	−	1.07532i
$881$	13.7646	−	12.3937i	0.463741	−	0.417554i	−0.403856	−	0.914823i	$-0.632330\pi$
$881$	13.7646	−	12.3937i	0.463741	−	0.417554i	0.867597	+	0.497269i	$0.165664\pi$
$882$	15.6911	−	0.619778i	0.528347	−	0.0208690i
$883$	38.2626	−	19.4958i	1.28764	−	0.656086i	0.329981	−	0.943988i	$-0.392958\pi$
$883$	38.2626	−	19.4958i	1.28764	−	0.656086i	0.957660	+	0.287902i	$0.0929577\pi$
$884$	−1.21453	+	3.73795i	−0.0408492	+	0.125721i
$885$	−18.0235	−	8.82768i	−0.605853	−	0.296739i
$886$	9.76877	+	10.8493i	0.328188	+	0.364490i
$887$	51.4016	−	2.69384i	1.72590	−	0.0904504i	0.836609	−	0.547800i	$-0.184534\pi$
$887$	51.4016	−	2.69384i	1.72590	−	0.0904504i	0.889287	+	0.457349i	$0.151201\pi$
$888$	−2.14784	−	3.35448i	−0.0720767	−	0.112569i
$889$	−4.10089	+	19.2932i	−0.137540	+	0.647073i
$890$	−1.48298	−	3.62056i	−0.0497097	−	0.121362i
$891$	28.7637	+	10.1723i	0.963621	+	0.340784i
$892$	1.57528	−	0.604693i	0.0527443	−	0.0202466i
$893$	0.00562463	+	0.00150711i	0.000188221	+	5.04337e-5i
$894$	−8.54893	−	9.61841i	−0.285919	−	0.321688i
$895$	26.7126	+	5.05996i	0.892905	+	0.169136i
$896$	0.756331	+	3.55826i	0.0252672	+	0.118873i
$897$	−1.46987	+	1.45105i	−0.0490774	+	0.0484492i
$898$	−7.61415	−	7.61415i	−0.254088	−	0.254088i
$899$	−10.3477	+	42.9943i	−0.345115	+	1.43394i
$900$	18.2875	−	21.6479i	0.609582	−	0.721597i
$901$	−18.1253	−	55.7839i	−0.603841	−	1.85843i
$902$	−61.7805	−	40.1207i	−2.05707	−	1.33587i
$903$	−35.0709	−	18.1550i	−1.16709	−	0.604160i
$904$	1.29553	+	0.747973i	0.0430886	+	0.0248772i
$905$	6.84896	−	22.7912i	0.227667	−	0.757605i
$906$	37.9442	−	41.5993i	1.26061	−	1.38204i
$907$	−25.6710	+	4.06589i	−0.852393	+	0.135006i	−0.567317	−	0.823499i	$-0.692019\pi$
$907$	−25.6710	+	4.06589i	−0.852393	+	0.135006i	−0.285076	+	0.958505i	$0.592019\pi$
$908$	2.31412	−	6.02849i	0.0767967	−	0.200062i
$909$	34.4906	+	39.3125i	1.14398	+	1.30391i
$910$	−2.39697	+	0.179135i	−0.0794588	+	0.00593827i
$911$	28.7989	+	25.9306i	0.954150	+	0.859121i	0.990119	−	0.140232i	$-0.0447850\pi$
$911$	28.7989	+	25.9306i	0.954150	+	0.859121i	−0.0359686	+	0.999353i	$0.511452\pi$
$912$	−0.0122804	−	0.00480497i	−0.000406644	−	0.000159109i
$913$	8.62946	−	6.98800i	0.285593	−	0.231269i
$914$	12.1171	−	37.2926i	0.400798	−	1.23353i
$915$	16.0633	+	12.5930i	0.531035	+	0.416310i
$916$	4.23757	−	40.3178i	0.140013	−	1.33214i
$917$	0.285485	−	5.44737i	0.00942754	−	0.179888i
$918$	50.0767	+	64.3428i	1.65278	+	2.12363i
$919$	−16.0784	+	1.68991i	−0.530379	+	0.0557451i	−0.365933	−	0.930641i	$-0.619250\pi$
$919$	−16.0784	+	1.68991i	−0.530379	+	0.0557451i	−0.164446	+	0.986386i	$0.552583\pi$
$920$	1.90416	−	1.15656i	0.0627782	−	0.0381307i
$921$	−31.2059	+	3.07680i	−1.02827	+	0.101384i
$922$	11.8529	−	1.87732i	0.390355	−	0.0618261i
$923$	1.50875	−	0.579154i	0.0496611	−	0.0190631i
$924$	−4.66203	−	22.6495i	−0.153370	−	0.745114i
$925$	−51.5682	+	10.5367i	−1.69555	+	0.346443i
$926$	17.8646	+	24.5885i	0.587068	+	0.808029i
$927$	8.31925	−	3.07110i	0.273240	−	0.100868i
$928$	−28.3571	+	55.6539i	−0.930867	+	1.82693i
$929$	−55.7907			−1.83043			−0.915216	−	0.402963i	$-0.867980\pi$
$929$	−55.7907			−1.83043			−0.915216	+	0.402963i	$0.867980\pi$
$930$	−42.2422	−	4.90805i	−1.38518	−	0.160941i
$931$	−0.00480082			−0.000157340
$932$	6.23308	−	12.2331i	0.204171	−	0.400709i
$933$	4.94098	−	3.94870i	0.161760	−	0.129275i
$934$	−15.3553	−	21.1347i	−0.502439	−	0.691548i
$935$	31.7151	−	51.2991i	1.03720	−	1.67766i
$936$	−0.170181	−	0.0201063i	−0.00556253	−	0.000657194i
$937$	14.1983	−	5.45021i	0.463838	−	0.178051i	−0.115215	−	0.993341i	$-0.536756\pi$
$937$	14.1983	−	5.45021i	0.463838	−	0.178051i	0.579053	+	0.815290i	$0.303422\pi$
$938$	−7.35204	+	1.16445i	−0.240053	+	0.0380206i
$939$	−2.10933	−	21.3935i	−0.0688354	−	0.698152i
$940$	13.2117	+	3.22703i	0.430919	+	0.105254i
$941$	17.2671	−	1.81485i	0.562892	−	0.0591623i	0.181191	−	0.983448i	$-0.442005\pi$
$941$	17.2671	−	1.81485i	0.562892	−	0.0591623i	0.381701	+	0.924286i	$0.375338\pi$
$942$	−11.0547	−	3.03855i	−0.360182	−	0.0990012i
$943$	2.63007	−	50.1847i	0.0856468	−	1.63424i
$944$	−2.27996	+	21.6924i	−0.0742064	+	0.706027i
$945$	−12.0496	+	21.0116i	−0.391972	+	0.683506i
$946$	22.5951	−	69.5406i	0.734631	−	2.26096i
$947$	−22.2330	+	18.0039i	−0.722476	+	0.585049i	−0.918439	−	0.395562i	$-0.870550\pi$
$947$	−22.2330	+	18.0039i	−0.722476	+	0.585049i	0.195964	+	0.980611i	$0.437217\pi$
$948$	4.86932	−	12.4448i	0.158148	−	0.404189i
$949$	−1.23845	−	1.11511i	−0.0402019	−	0.0361979i
$950$	−0.0120382	+	0.0131595i	−0.000390572	+	0.000426952i
$951$	−21.7286	+	37.0815i	−0.704599	+	1.20245i
$952$	−1.29855	+	3.38285i	−0.0420864	+	0.109639i
$953$	−42.3219	+	6.70313i	−1.37094	+	0.217136i	−0.798097	−	0.602529i	$-0.794160\pi$
$953$	−42.3219	+	6.70313i	−1.37094	+	0.217136i	−0.572844	+	0.819664i	$0.694160\pi$
$954$	−38.0493	+	21.3191i	−1.23189	+	0.690230i
$955$	−19.6114	−	5.89341i	−0.634611	−	0.190706i
$956$	−5.66956	−	3.27332i	−0.183367	−	0.105867i
$957$	−21.4390	+	41.4147i	−0.693023	+	1.33875i
$958$	−68.9294	−	44.7633i	−2.22701	−	1.44624i
$959$	0.226944	+	0.698462i	0.00732840	+	0.0225545i
$960$	−25.7900	−	9.43529i	−0.832370	−	0.304523i
$961$	14.0425	+	27.6371i	0.452984	+	0.891519i
$962$	−3.83824	−	3.83824i	−0.123750	−	0.123750i
$963$	12.9376	+	26.2211i	0.416909	+	0.844964i
$964$	−6.37991	−	30.0151i	−0.205483	−	0.966721i
$965$	19.9847	+	29.3250i	0.643330	+	0.944006i
$966$	24.2734	−	21.5744i	0.780985	−	0.694146i
$967$	50.2977	+	13.4772i	1.61746	+	0.433398i	0.950255	−	0.311473i	$-0.100822\pi$
$967$	50.2977	+	13.4772i	1.61746	+	0.433398i	0.667209	+	0.744871i	$0.267489\pi$
$968$	−0.100281	+	0.0384943i	−0.00322315	+	0.00123725i
$969$	−0.0145211	−	0.0202597i	−0.000466485	−	0.000650836i
$970$	−18.5500	−	7.76954i	−0.595606	−	0.249465i
$971$	3.47839	−	16.3646i	0.111627	−	0.525164i	−0.886430	−	0.462862i	$-0.846823\pi$
$971$	3.47839	−	16.3646i	0.111627	−	0.525164i	0.998057	−	0.0623017i	$-0.0198441\pi$
$972$	19.2609	−	22.2784i	0.617793	−	0.714580i
$973$	35.5620	−	1.86372i	1.14006	−	0.0597483i
$974$	−8.59493	−	9.54564i	−0.275399	−	0.305862i
$975$	−1.05682	+	2.00266i	−0.0338454	+	0.0641364i
$976$	6.85504	−	21.0976i	0.219424	−	0.675319i
$977$	−30.0935	+	15.3334i	−0.962775	+	0.490558i	−0.863416	−	0.504493i	$-0.831679\pi$
$977$	−30.0935	+	15.3334i	−0.962775	+	0.490558i	−0.0993592	+	0.995052i	$0.531679\pi$
$978$	6.72255	+	17.8557i	0.214963	+	0.570963i
$979$	−2.23514	+	2.01253i	−0.0714353	+	0.0643206i
$980$	−11.2099	+	0.249297i	−0.358086	+	0.00796351i
$981$	15.5976	−	26.2296i	0.497992	−	0.837445i
$982$	48.0567	−	31.2084i	1.53355	−	0.995901i
$983$	−12.5874	+	32.7913i	−0.401475	+	1.04588i	0.572636	+	0.819810i	$0.305921\pi$
$983$	−12.5874	+	32.7913i	−0.401475	+	1.04588i	−0.974111	+	0.226069i	$0.927413\pi$
$984$	3.38883	−	2.42894i	0.108032	−	0.0774317i
$985$	−4.77887	+	9.91823i	−0.152267	+	0.316021i
$986$	−107.930	+	62.3132i	−3.43718	+	1.98446i
$987$	−11.6043	−	0.683126i	−0.369367	−	0.0217441i
$988$	−0.000882473	0	0.000139770i	−2.80752e−5	0	4.44668e-6i
$989$	48.7914	−	10.3709i	1.55148	−	0.329776i
$990$	−42.0164	−	15.6793i	−1.33537	−	0.498320i
$991$	30.0286			0.953890			0.476945	−	0.878933i	$-0.341744\pi$
$991$	30.0286			0.953890			0.476945	+	0.878933i	$0.341744\pi$
$992$	10.1977	+	42.5822i	0.323776	+	1.35199i
$993$	−10.8710	−	21.6796i	−0.344981	−	0.687981i
$994$	−24.1665	+	7.85217i	−0.766514	+	0.249056i
$995$	26.9611	−	38.8991i	0.854725	−	1.23318i
$996$	−3.24647	−	10.2150i	−0.102868	−	0.323675i
$997$	6.95445	+	25.9544i	0.220250	+	0.821983i	0.984252	+	0.176770i	$0.0565648\pi$
$997$	6.95445	+	25.9544i	0.220250	+	0.821983i	−0.764003	+	0.645213i	$0.776769\pi$
$998$	13.8903	+	3.72188i	0.439688	+	0.117814i
$999$	−53.7129	+	10.3366i	−1.69940	+	0.327035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.bt.a.38.12	✓	960
3.2	odd	2	inner	465.2.bt.a.38.49	yes	960
5.2	odd	4	inner	465.2.bt.a.317.12	yes	960
15.2	even	4	inner	465.2.bt.a.317.49	yes	960
31.9	even	15	inner	465.2.bt.a.443.49	yes	960
93.71	odd	30	inner	465.2.bt.a.443.12	yes	960
155.102	odd	60	inner	465.2.bt.a.257.49	yes	960
465.257	even	60	inner	465.2.bt.a.257.12	yes	960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.bt.a.38.12	✓	960	1.1	even	1	trivial
465.2.bt.a.38.49	yes	960	3.2	odd	2	inner
465.2.bt.a.257.12	yes	960	465.257	even	60	inner
465.2.bt.a.257.49	yes	960	155.102	odd	60	inner
465.2.bt.a.317.12	yes	960	5.2	odd	4	inner
465.2.bt.a.317.49	yes	960	15.2	even	4	inner
465.2.bt.a.443.12	yes	960	93.71	odd	30	inner
465.2.bt.a.443.49	yes	960	31.9	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.bt (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.895320 + 1.75716i) q^{2} +(-1.08132 - 1.35305i) q^{3} +(-1.11046 - 1.52841i) q^{4} +(-2.17633 + 0.513419i) q^{5} +(3.34566 - 0.688650i) q^{6} +(1.94619 - 0.747072i) q^{7} +(-0.215773 + 0.0341750i) q^{8} +(-0.661483 + 2.92616i) q^{9} +(1.04635 - 4.28384i) q^{10} +(-3.37137 + 0.354345i) q^{11} +(-0.867256 + 3.15521i) q^{12} +(0.0136843 - 0.261112i) q^{13} +(-0.429733 + 4.08864i) q^{14} +(3.04799 + 2.38951i) q^{15} +(1.30074 - 4.00326i) q^{16} +(6.18335 - 5.00718i) q^{17} +(-4.54951 - 3.78219i) q^{18} +(0.00134415 + 0.00121028i) q^{19} +(3.20144 + 2.75620i) q^{20} +(-3.11528 - 1.82546i) q^{21} +(2.39581 - 6.24130i) q^{22} +(4.50454 - 0.713448i) q^{23} +(0.279560 + 0.254997i) q^{24} +(4.47280 - 2.23474i) q^{25} +(0.446565 + 0.257824i) q^{26} +(4.67452 - 2.26911i) q^{27} +(-3.30300 - 2.14499i) q^{28} +(2.45437 + 7.55377i) q^{29} +(-6.92768 + 3.21645i) q^{30} +(4.74566 + 2.91183i) q^{31} +(5.56086 + 5.56086i) q^{32} +(4.12498 + 4.17847i) q^{33} +(3.26236 + 15.3482i) q^{34} +(-3.85198 + 2.62508i) q^{35} +(5.20694 - 2.23836i) q^{36} +(-10.1680 - 2.72452i) q^{37} +(-0.00333011 + 0.00127831i) q^{38} +(-0.368095 + 0.263831i) q^{39} +(0.452046 - 0.185158i) q^{40} +(2.29095 - 10.7781i) q^{41} +(5.99681 - 3.83969i) q^{42} +(10.9223 - 0.572412i) q^{43} +(4.28535 + 4.75936i) q^{44} +(-0.0627455 - 6.70791i) q^{45} +(-2.77935 + 8.55397i) q^{46} +(2.86850 - 1.46158i) q^{47} +(-6.82313 + 2.56886i) q^{48} +(-1.97248 + 1.77603i) q^{49} +(-0.0777893 + 9.86025i) q^{50} +(-13.4611 - 2.95200i) q^{51} +(-0.414283 + 0.269039i) q^{52} +(2.64186 - 6.88229i) q^{53} +(-0.197994 + 10.2455i) q^{54} +(7.15527 - 2.50210i) q^{55} +(-0.394403 + 0.227709i) q^{56} +(0.000184106 - 0.00312741i) q^{57} +(-15.4707 - 2.45031i) q^{58} +(-5.06862 + 1.07737i) q^{59} +(0.267486 - 7.31204i) q^{60} +5.27011 q^{61} +(-9.36544 + 5.73188i) q^{62} +(0.898684 + 6.18904i) q^{63} +(-6.74357 + 2.19112i) q^{64} +(0.104278 + 0.575291i) q^{65} +(-11.0354 + 3.50721i) q^{66} +(0.468619 + 1.74891i) q^{67} +(-14.5194 - 3.89046i) q^{68} +(-5.83619 - 5.32339i) q^{69} +(-1.16395 - 9.11885i) q^{70} +(2.51395 + 5.64641i) q^{71} +(0.0427282 - 0.653993i) q^{72} +(4.01102 - 4.95320i) q^{73} +(13.8911 - 15.4276i) q^{74} +(-7.86025 - 3.63545i) q^{75} +(0.000357185 - 0.00339839i) q^{76} +(-6.29660 + 3.20828i) q^{77} +(-0.134032 - 0.883016i) q^{78} +(-4.06155 - 0.426886i) q^{79} +(-0.775482 + 9.38024i) q^{80} +(-8.12488 - 3.87122i) q^{81} +(16.8877 + 13.6754i) q^{82} +(-2.74714 + 1.78401i) q^{83} +(0.669327 + 6.78854i) q^{84} +(-10.8862 + 14.0719i) q^{85} +(-8.77311 + 19.7047i) q^{86} +(7.56666 - 11.4889i) q^{87} +(0.715339 - 0.191675i) q^{88} +(0.717788 - 0.521504i) q^{89} +(11.8431 + 5.89547i) q^{90} +(-0.168437 - 0.518396i) q^{91} +(-6.09254 - 6.09254i) q^{92} +(-1.19174 - 9.56973i) q^{93} +6.34901i q^{94} +(-0.00354670 - 0.00194385i) q^{95} +(1.51103 - 13.5372i) q^{96} +(0.713443 - 4.50450i) q^{97} +(-1.35478 - 5.05609i) q^{98} +(1.19323 - 10.0996i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 960 q - 14 q^{3} - 16 q^{6} - 60 q^{7} - 44 q^{10} - 64 q^{12} - 36 q^{13} + 4 q^{15} + 176 q^{16} - 14 q^{18} - 36 q^{21} - 88 q^{22} - 20 q^{25} - 8 q^{27} - 56 q^{28} - 200 q^{30} - 56 q^{31} + 44 q^{33}+ \cdots + 44 q^{97}+O(q^{100}) \) 960 * q - 14 * q^3 - 16 * q^6 - 60 * q^7 - 44 * q^10 - 64 * q^12 - 36 * q^13 + 4 * q^15 + 176 * q^16 - 14 * q^18 - 36 * q^21 - 88 * q^22 - 20 * q^25 - 8 * q^27 - 56 * q^28 - 200 * q^30 - 56 * q^31 + 44 * q^33 - 32 * q^36 - 80 * q^37 - 52 * q^40 - 30 * q^42 - 36 * q^43 - 8 * q^45 - 164 * q^46 - 28 * q^48 - 44 * q^51 - 100 * q^52 - 88 * q^55 + 24 * q^57 + 64 * q^58 - 124 * q^60 - 176 * q^61 - 116 * q^63 + 48 * q^66 - 28 * q^67 - 36 * q^70 - 154 * q^72 - 12 * q^73 - 178 * q^75 + 112 * q^76 + 54 * q^78 - 52 * q^81 - 92 * q^82 - 24 * q^85 - 32 * q^87 + 52 * q^88 - 20 * q^90 + 40 * q^91 + 134 * q^93 + 8 * q^96 + 44 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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