LMFDB - Embedded newform 369.2.ba.b.341.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [369,2,Mod(17,369)] 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("369.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(369, base_ring=CyclotomicField(40)) chi = DirichletCharacter(H, H._module([20, 33])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 369 = 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	369.ba (of order $40$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [112,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.94647983459$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$7$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			341.6
Character	$\chi$	$=$	369.341
Dual form			369.2.ba.b.224.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.814144 - 1.59785i) q^{2} +(-0.714715 - 0.983721i) q^{4} +(0.595885 - 3.76227i) q^{5} +(2.85103 + 2.43501i) q^{7} +(1.38874 - 0.219955i) q^{8} +(-5.52639 - 4.01516i) q^{10} +(-2.20898 + 1.35366i) q^{11} +(1.45014 + 0.114128i) q^{13} +(6.21192 - 2.57306i) q^{14} +(1.53067 - 4.71093i) q^{16} +(-3.62559 - 0.870427i) q^{17} +(-5.01227 + 0.394474i) q^{19} +(-4.12691 + 2.10276i) q^{20} +(0.364522 + 4.63169i) q^{22} +(1.36058 + 4.18744i) q^{23} +(-9.04429 - 2.93867i) q^{25} +(1.36298 - 2.22418i) q^{26} +(0.357695 - 4.54495i) q^{28} +(2.50409 - 0.601179i) q^{29} +(-4.04600 + 5.56884i) q^{31} +(-4.29271 - 4.29271i) q^{32} +(-4.34256 + 5.08448i) q^{34} +(10.8600 - 9.27534i) q^{35} +(8.62255 - 6.26465i) q^{37} +(-3.45040 + 8.33000i) q^{38} -5.35587i q^{40} +(-6.04317 - 2.11661i) q^{41} +(-0.560875 - 0.285780i) q^{43} +(2.91042 + 1.20554i) q^{44} +(7.79861 + 1.23518i) q^{46} +(7.81834 + 9.15410i) q^{47} +(1.10406 + 6.97073i) q^{49} +(-12.0589 + 12.0589i) q^{50} +(-0.924164 - 1.50810i) q^{52} +(1.07245 + 4.46708i) q^{53} +(3.77655 + 9.11740i) q^{55} +(4.49492 + 2.75449i) q^{56} +(1.07810 - 4.49060i) q^{58} +(-11.4924 + 3.73410i) q^{59} +(2.85704 + 5.60726i) q^{61} +(5.60413 + 10.9987i) q^{62} +(-0.932106 + 0.302860i) q^{64} +(1.29350 - 5.38780i) q^{65} +(10.1124 + 6.19691i) q^{67} +(1.73501 + 4.18867i) q^{68} +(-5.97895 - 24.9041i) q^{70} +(-0.295608 - 0.482388i) q^{71} +(-1.50300 + 1.50300i) q^{73} +(-2.98996 - 18.8778i) q^{74} +(3.97040 + 4.64874i) q^{76} +(-9.59405 - 1.51955i) q^{77} +(-4.52212 - 1.87312i) q^{79} +(-16.8117 - 8.56598i) q^{80} +(-8.30204 + 7.93284i) q^{82} -7.97207i q^{83} +(-5.43521 + 13.1218i) q^{85} +(-0.913266 + 0.663527i) q^{86} +(-2.76995 + 2.36576i) q^{88} +(9.86205 - 11.5470i) q^{89} +(3.85648 + 3.85648i) q^{91} +(3.14685 - 4.33126i) q^{92} +(20.9921 - 5.03976i) q^{94} +(-1.50262 + 19.0926i) q^{95} +(-1.77371 + 2.89443i) q^{97} +(12.0370 + 3.91107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 4 q^{5} - 24 q^{8} + 12 q^{11} - 4 q^{13} + 4 q^{14} + 28 q^{16} + 4 q^{17} - 88 q^{20} + 8 q^{22} - 24 q^{23} + 60 q^{26} - 8 q^{29} - 48 q^{32} + 152 q^{35} + 8 q^{37} + 56 q^{38} - 12 q^{41}+ \cdots - 60 q^{98}+O(q^{100}) $ 112 * q + 4 * q^5 - 24 * q^8 + 12 * q^11 - 4 * q^13 + 4 * q^14 + 28 * q^16 + 4 * q^17 - 88 * q^20 + 8 * q^22 - 24 * q^23 + 60 * q^26 - 8 * q^29 - 48 * q^32 + 152 * q^35 + 8 * q^37 + 56 * q^38 - 12 * q^41 - 24 * q^43 + 60 * q^44 - 56 * q^46 + 28 * q^47 + 64 * q^52 - 16 * q^53 - 8 * q^55 - 72 * q^56 - 16 * q^58 - 40 * q^59 + 28 * q^61 - 68 * q^62 - 172 * q^65 + 48 * q^67 + 36 * q^68 - 232 * q^70 + 32 * q^71 - 72 * q^73 + 4 * q^74 - 176 * q^76 + 60 * q^77 - 72 * q^79 + 128 * q^80 - 192 * q^82 + 16 * q^85 + 40 * q^86 - 112 * q^88 - 48 * q^89 - 80 * q^91 - 64 * q^94 - 20 * q^95 - 72 * q^97 - 60 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/369\mathbb{Z}\right)^\times$.

$n$	$83$	$334$
$\chi(n)$	$-1$	$e\left(\frac{31}{40}\right)$

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 $

$2$	0.814144	−	1.59785i	0.575687	−	1.12985i	−0.401180	−	0.915999i	$-0.631400\pi$
$2$	0.814144	−	1.59785i	0.575687	−	1.12985i	0.976867	−	0.213849i	$-0.0686002\pi$
$3$		0			0
$3$		0			0
$4$	−0.714715	−	0.983721i	−0.357358	−	0.491860i
$5$	0.595885	−	3.76227i	0.266488	−	1.68254i	−0.384246	−	0.923231i	$-0.625538\pi$
$5$	0.595885	−	3.76227i	0.266488	−	1.68254i	0.650733	−	0.759306i	$-0.274462\pi$
$6$		0			0
$7$	2.85103	+	2.43501i	1.07759	+	0.920346i	0.997077	−	0.0764074i	$-0.0243450\pi$
$7$	2.85103	+	2.43501i	1.07759	+	0.920346i	0.0805105	+	0.996754i	$0.474345\pi$
$8$	1.38874	−	0.219955i	0.490993	−	0.0777657i
$9$		0			0
$10$	−5.52639	−	4.01516i	−1.74760	−	1.26970i
$11$	−2.20898	+	1.35366i	−0.666033	+	0.408145i	−0.814014	−	0.580845i	$-0.802722\pi$
$11$	−2.20898	+	1.35366i	−0.666033	+	0.408145i	0.147982	+	0.988990i	$0.452722\pi$
$12$		0			0
$13$	1.45014	+	0.114128i	0.402196	+	0.0316535i	0.277944	−	0.960597i	$-0.410347\pi$
$13$	1.45014	+	0.114128i	0.402196	+	0.0316535i	0.124252	+	0.992251i	$0.460347\pi$
$14$	6.21192	−	2.57306i	1.66020	−	0.687679i
$15$		0			0
$16$	1.53067	−	4.71093i	0.382669	−	1.17773i
$17$	−3.62559	−	0.870427i	−0.879334	−	0.211109i	−0.231449	−	0.972847i	$-0.574347\pi$
$17$	−3.62559	−	0.870427i	−0.879334	−	0.211109i	−0.647886	+	0.761738i	$0.724347\pi$
$18$		0			0
$19$	−5.01227	+	0.394474i	−1.14989	+	0.0904986i	−0.639043	−	0.769171i	$-0.720669\pi$
$19$	−5.01227	+	0.394474i	−1.14989	+	0.0904986i	−0.510851	+	0.859670i	$0.670669\pi$
$20$	−4.12691	+	2.10276i	−0.922805	+	0.470193i
$21$		0			0
$22$	0.364522	+	4.63169i	0.0777163	+	0.987480i
$23$	1.36058	+	4.18744i	0.283701	+	0.873143i	0.986785	+	0.162036i	$0.0518059\pi$
$23$	1.36058	+	4.18744i	0.283701	+	0.873143i	−0.703084	+	0.711107i	$0.748194\pi$
$24$		0			0
$25$	−9.04429	−	2.93867i	−1.80886	−	0.587734i
$26$	1.36298	−	2.22418i	0.267302	−	0.436198i
$27$		0			0
$28$	0.357695	−	4.54495i	0.0675981	−	0.858915i
$29$	2.50409	−	0.601179i	0.464998	−	0.111636i	0.00582502	−	0.999983i	$-0.498146\pi$
$29$	2.50409	−	0.601179i	0.464998	−	0.111636i	0.459173	+	0.888347i	$0.348146\pi$
$30$		0			0
$31$	−4.04600	+	5.56884i	−0.726683	+	1.00019i	0.272592	+	0.962130i	$0.412119\pi$
$31$	−4.04600	+	5.56884i	−0.726683	+	1.00019i	−0.999275	+	0.0380639i	$0.987881\pi$
$32$	−4.29271	−	4.29271i	−0.758851	−	0.758851i
$33$		0			0
$34$	−4.34256	+	5.08448i	−0.744743	+	0.871982i
$35$	10.8600	−	9.27534i	1.83568	−	1.56782i
$36$		0			0
$37$	8.62255	−	6.26465i	1.41754	−	1.02990i	0.425366	−	0.905021i	$-0.360145\pi$
$37$	8.62255	−	6.26465i	1.41754	−	1.02990i	0.992172	−	0.124880i	$-0.0398547\pi$
$38$	−3.45040	+	8.33000i	−0.559729	+	1.35130i
$39$		0			0
$40$		−	5.35587i		−	0.846838i
$41$	−6.04317	−	2.11661i	−0.943785	−	0.330560i
$41$	−6.04317	−	2.11661i	−0.943785	−	0.330560i
$42$		0			0
$43$	−0.560875	−	0.285780i	−0.0855326	−	0.0435811i	0.410701	−	0.911770i	$-0.365284\pi$
$43$	−0.560875	−	0.285780i	−0.0855326	−	0.0435811i	−0.496234	+	0.868189i	$0.665284\pi$
$44$	2.91042	+	1.20554i	0.438762	+	0.181741i
$45$		0			0
$46$	7.79861	+	1.23518i	1.14984	+	0.182117i
$47$	7.81834	+	9.15410i	1.14042	+	1.33526i	0.934197	+	0.356758i	$0.116118\pi$
$47$	7.81834	+	9.15410i	1.14042	+	1.33526i	0.206225	+	0.978505i	$0.433882\pi$
$48$		0			0
$49$	1.10406	+	6.97073i	0.157722	+	0.995819i
$50$	−12.0589	+	12.0589i	−1.70539	+	1.70539i
$51$		0			0
$52$	−0.924164	−	1.50810i	−0.128159	−	0.209136i
$53$	1.07245	+	4.46708i	0.147312	+	0.613600i	0.996357	+	0.0852791i	$0.0271782\pi$
$53$	1.07245	+	4.46708i	0.147312	+	0.613600i	−0.849045	+	0.528321i	$0.822822\pi$
$54$		0			0
$55$	3.77655	+	9.11740i	0.509230	+	1.22939i
$56$	4.49492	+	2.75449i	0.600659	+	0.368084i
$57$		0			0
$58$	1.07810	−	4.49060i	0.141561	−	0.589645i
$59$	−11.4924	+	3.73410i	−1.49618	+	0.486139i	−0.938901	−	0.344186i	$-0.888155\pi$
$59$	−11.4924	+	3.73410i	−1.49618	+	0.486139i	−0.557280	+	0.830325i	$0.688155\pi$
$60$		0			0
$61$	2.85704	+	5.60726i	0.365807	+	0.717936i	0.998400	−	0.0565480i	$-0.0180094\pi$
$61$	2.85704	+	5.60726i	0.365807	+	0.717936i	−0.632593	+	0.774484i	$0.718009\pi$
$62$	5.60413	+	10.9987i	0.711726	+	1.39684i
$63$		0			0
$64$	−0.932106	+	0.302860i	−0.116513	+	0.0378575i
$65$	1.29350	−	5.38780i	0.160438	−	0.668274i
$66$		0			0
$67$	10.1124	+	6.19691i	1.23543	+	0.757073i	0.977875	−	0.209191i	$-0.0670830\pi$
$67$	10.1124	+	6.19691i	1.23543	+	0.757073i	0.257555	+	0.966264i	$0.417083\pi$
$68$	1.73501	+	4.18867i	0.210400	+	0.507951i
$69$		0			0
$70$	−5.97895	−	24.9041i	−0.714622	−	2.97661i
$71$	−0.295608	−	0.482388i	−0.0350822	−	0.0572490i	0.834618	−	0.550829i	$-0.185688\pi$
$71$	−0.295608	−	0.482388i	−0.0350822	−	0.0572490i	−0.869701	+	0.493580i	$0.835688\pi$
$72$		0			0
$73$	−1.50300	+	1.50300i	−0.175913	+	0.175913i	−0.789572	−	0.613659i	$-0.789697\pi$
$73$	−1.50300	+	1.50300i	−0.175913	+	0.175913i	0.613659	+	0.789572i	$0.289697\pi$
$74$	−2.98996	−	18.8778i	−0.347575	−	2.19450i
$75$		0			0
$76$	3.97040	+	4.64874i	0.455436	+	0.533247i
$77$	−9.59405	−	1.51955i	−1.09334	−	0.173169i
$78$		0			0
$79$	−4.52212	−	1.87312i	−0.508778	−	0.210743i	0.113501	−	0.993538i	$-0.463793\pi$
$79$	−4.52212	−	1.87312i	−0.508778	−	0.210743i	−0.622280	+	0.782795i	$0.713793\pi$
$80$	−16.8117	−	8.56598i	−1.87960	−	0.957706i
$81$		0			0
$82$	−8.30204	+	7.93284i	−0.916807	+	0.876035i
$83$		−	7.97207i		−	0.875049i	−0.899207	−	0.437524i	$-0.855855\pi$
$83$		−	7.97207i		−	0.875049i	0.899207	−	0.437524i	$-0.144145\pi$
$84$		0			0
$85$	−5.43521	+	13.1218i	−0.589531	+	1.42325i
$86$	−0.913266	+	0.663527i	−0.0984800	+	0.0715499i
$87$		0			0
$88$	−2.76995	+	2.36576i	−0.295278	+	0.252191i
$89$	9.86205	−	11.5470i	1.04538	−	1.22398i	0.0713708	−	0.997450i	$-0.477263\pi$
$89$	9.86205	−	11.5470i	1.04538	−	1.22398i	0.974005	−	0.226528i	$-0.0727374\pi$
$90$		0			0
$91$	3.85648	+	3.85648i	0.404269	+	0.404269i
$92$	3.14685	−	4.33126i	0.328082	−	0.451565i
$93$		0			0
$94$	20.9921	−	5.03976i	2.16517	−	0.519811i
$95$	−1.50262	+	19.0926i	−0.154165	+	1.95886i
$96$		0			0
$97$	−1.77371	+	2.89443i	−0.180093	+	0.293885i	−0.929929	−	0.367738i	$-0.880132\pi$
$97$	−1.77371	+	2.89443i	−0.180093	+	0.293885i	0.749836	+	0.661623i	$0.230132\pi$
$98$	12.0370	+	3.91107i	1.21592	+	0.395077i
$99$		0			0
$100$	3.57326	+	10.9974i	0.357326	+	1.09974i
$101$	0.374953	+	4.76423i	0.0373092	+	0.474058i	0.986984	+	0.160820i	$0.0514138\pi$
$101$	0.374953	+	4.76423i	0.0373092	+	0.474058i	−0.949675	+	0.313238i	$0.898586\pi$
$102$		0			0
$103$	1.54257	−	0.785977i	0.151994	−	0.0774447i	−0.376339	−	0.926482i	$-0.622817\pi$
$103$	1.54257	−	0.785977i	0.151994	−	0.0774447i	0.528333	+	0.849037i	$0.322817\pi$
$104$	2.03896	−	0.160470i	0.199937	−	0.0157354i
$105$		0			0
$106$	8.01083	+	1.92323i	0.778081	+	0.186801i
$107$	−0.196837	+	0.605801i	−0.0190289	+	0.0585650i	−0.960120	−	0.279588i	$-0.909802\pi$
$107$	−0.196837	+	0.605801i	−0.0190289	+	0.0585650i	0.941091	+	0.338153i	$0.109802\pi$
$108$		0			0
$109$	15.5379	−	6.43602i	1.48826	−	0.616459i	0.517326	−	0.855788i	$-0.326928\pi$
$109$	15.5379	−	6.43602i	1.48826	−	0.616459i	0.970938	+	0.239329i	$0.0769275\pi$
$110$	17.6429	+	1.38852i	1.68218	+	0.132391i
$111$		0			0
$112$	15.8352	−	9.70379i	1.49628	−	0.916922i
$113$	−11.4875	−	8.34617i	−1.08065	−	0.785142i	−0.102858	−	0.994696i	$-0.532799\pi$
$113$	−11.4875	−	8.34617i	−1.08065	−	0.785142i	−0.977797	+	0.209554i	$0.932799\pi$
$114$		0			0
$115$	16.5650	−	2.62364i	1.54470	−	0.244656i
$116$	−2.38110	−	2.03365i	−0.221080	−	0.188820i
$117$		0			0
$118$	−3.38993	+	21.4032i	−0.312068	+	1.97032i
$119$	−8.21716	−	11.3099i	−0.753265	−	1.03678i
$120$		0			0
$121$	−1.94671	+	3.82063i	−0.176974	+	0.347330i
$122$	11.2856			1.02175
$123$		0			0
$124$	8.36992			0.751641
$125$	−7.79879	+	15.3060i	−0.697545	+	1.36901i
$126$		0			0
$127$	−9.65653	−	13.2911i	−0.856878	−	1.17939i	−0.982305	−	0.187289i	$-0.940030\pi$
$127$	−9.65653	−	13.2911i	−0.856878	−	1.17939i	0.125427	−	0.992103i	$-0.459970\pi$
$128$	1.62442	−	10.2562i	0.143580	−	0.906528i
$129$		0			0
$130$	−7.55578	−	6.45325i	−0.662686	−	0.565987i
$131$	−6.29848	+	0.997581i	−0.550300	+	0.0871590i	−0.425392	−	0.905009i	$-0.639864\pi$
$131$	−6.29848	+	0.997581i	−0.550300	+	0.0871590i	−0.124909	+	0.992168i	$0.539864\pi$
$132$		0			0
$133$	−15.2507	−	11.0803i	−1.32240	−	0.960780i
$134$	18.1347	−	11.1129i	1.56660	−	0.960013i
$135$		0			0
$136$	−5.22645	−	0.411330i	−0.448164	−	0.0352713i
$137$	−9.59319	+	3.97363i	−0.819602	+	0.339490i	−0.752778	−	0.658275i	$-0.771287\pi$
$137$	−9.59319	+	3.97363i	−0.819602	+	0.339490i	−0.0668239	+	0.997765i	$0.521287\pi$
$138$		0			0
$139$	−1.29054	+	3.97187i	−0.109462	+	0.336889i	−0.990752	−	0.135687i	$-0.956676\pi$
$139$	−1.29054	+	3.97187i	−0.109462	+	0.336889i	0.881290	+	0.472576i	$0.156676\pi$
$140$	−16.8862	−	4.05401i	−1.42714	−	0.342627i
$141$		0			0
$142$	−1.01145	+	0.0796029i	−0.0848790	+	0.00668012i
$143$	−3.35781	+	1.71089i	−0.280795	+	0.143072i
$144$		0			0
$145$	−0.769647	−	9.77929i	−0.0639157	−	0.812126i
$146$	1.17791	+	3.62523i	0.0974843	+	0.300026i
$147$		0			0
$148$	−12.3253	−	4.00474i	−1.01314	−	0.329188i
$149$	8.57378	−	13.9911i	0.702391	−	1.14620i	−0.280115	−	0.959967i	$-0.590373\pi$
$149$	8.57378	−	13.9911i	0.702391	−	1.14620i	0.982506	−	0.186232i	$-0.0596275\pi$
$150$		0			0
$151$	0.934876	−	11.8787i	0.0760791	−	0.966677i	−0.833871	−	0.551959i	$-0.813880\pi$
$151$	0.934876	−	11.8787i	0.0760791	−	0.966677i	0.909950	−	0.414718i	$-0.136120\pi$
$152$	−6.87396	+	1.65029i	−0.557552	+	0.133856i
$153$		0			0
$154$	−10.2389	+	14.0927i	−0.825077	+	1.13562i
$155$	18.5405	+	18.5405i	1.48921	+	1.48921i
$156$		0			0
$157$	−13.1721	+	15.4226i	−1.05125	+	1.23085i	−0.0790070	+	0.996874i	$0.525175\pi$
$157$	−13.1721	+	15.4226i	−1.05125	+	1.23085i	−0.972241	+	0.233980i	$0.924825\pi$
$158$	−6.67462	+	5.70066i	−0.531004	+	0.453520i
$159$		0			0
$160$	−18.7083	+	13.5924i	−1.47902	+	1.07457i
$161$	−6.31740	+	15.2516i	−0.497881	+	1.20199i
$162$		0			0
$163$		−	8.87430i		−	0.695088i	−0.937664	−	0.347544i	$-0.887016\pi$
$163$		−	8.87430i		−	0.695088i	0.937664	−	0.347544i	$-0.112984\pi$
$164$	2.23699	+	7.45757i	0.174679	+	0.582339i
$165$		0			0
$166$	−12.7382	−	6.49041i	−0.988672	−	0.503754i
$167$	5.04841	+	2.09112i	0.390658	+	0.161816i	0.569362	−	0.822087i	$-0.307190\pi$
$167$	5.04841	+	2.09112i	0.390658	+	0.161816i	−0.178704	+	0.983903i	$0.557190\pi$
$168$		0			0
$169$	−10.7501	−	1.70264i	−0.826929	−	0.130973i
$170$	16.5415	+	19.3676i	1.26868	+	1.48543i
$171$		0			0
$172$	0.119738	+	0.755996i	0.00912994	+	0.0576441i
$173$	−5.93837	+	5.93837i	−0.451486	+	0.451486i	−0.895848	−	0.444361i	$-0.853431\pi$
$173$	−5.93837	+	5.93837i	−0.451486	+	0.451486i	0.444361	+	0.895848i	$0.353431\pi$
$174$		0			0
$175$	−18.6299	−	30.4012i	−1.40828	−	2.29811i
$176$	2.99579	+	12.4784i	0.225816	+	0.940593i
$177$		0			0
$178$	−10.4212	−	25.1590i	−0.781101	−	1.88574i
$179$	−7.01720	−	4.30015i	−0.524490	−	0.321408i	0.234926	−	0.972013i	$-0.424515\pi$
$179$	−7.01720	−	4.30015i	−0.524490	−	0.321408i	−0.759416	+	0.650605i	$0.774515\pi$
$180$		0			0
$181$	−0.601878	+	2.50700i	−0.0447372	+	0.186344i	−0.990264	−	0.139199i	$-0.955547\pi$
$181$	−0.601878	+	2.50700i	−0.0447372	+	0.186344i	0.945527	+	0.325543i	$0.105547\pi$
$182$	9.30179	−	3.02233i	0.689494	−	0.224030i
$183$		0			0
$184$	2.81054	+	5.51600i	0.207196	+	0.406645i
$185$	−18.4312	−	36.1733i	−1.35509	−	2.65952i
$186$		0			0
$187$	9.18712	−	2.98508i	0.671829	−	0.218290i
$188$	3.41719	−	14.2336i	0.249224	−	1.03809i
$189$		0			0
$190$	29.2836	+	17.9450i	2.12446	+	1.30187i
$191$	1.89847	+	4.58332i	0.137369	+	0.331638i	0.977561	−	0.210650i	$-0.0675582\pi$
$191$	1.89847	+	4.58332i	0.137369	+	0.331638i	−0.840193	+	0.542288i	$0.817558\pi$
$192$		0			0
$193$	1.35485	+	5.64336i	0.0975242	+	0.406218i	0.999683	−	0.0251870i	$-0.00801812\pi$
$193$	1.35485	+	5.64336i	0.0975242	+	0.406218i	−0.902159	+	0.431405i	$0.858018\pi$
$194$	3.18080	+	5.19060i	0.228368	+	0.372663i
$195$		0			0
$196$	6.06817	−	6.06817i	0.433441	−	0.433441i
$197$	2.65760	+	16.7794i	0.189346	+	1.19548i	0.880951	+	0.473208i	$0.156904\pi$
$197$	2.65760	+	16.7794i	0.189346	+	1.19548i	−0.691605	+	0.722276i	$0.743096\pi$
$198$		0			0
$199$	−1.50315	−	1.75997i	−0.106556	−	0.124761i	0.704565	−	0.709639i	$-0.251142\pi$
$199$	−1.50315	−	1.75997i	−0.106556	−	0.124761i	−0.811121	+	0.584879i	$0.801142\pi$
$200$	−13.2065	−	2.09171i	−0.933843	−	0.147906i
$201$		0			0
$202$	7.91777	+	3.27965i	0.557092	+	0.230755i
$203$	8.60311	+	4.38350i	0.603820	+	0.307662i
$204$		0			0
$205$	−11.5643	+	21.4748i	−0.807686	+	1.49986i
$206$		−	3.10469i		−	0.216314i
$207$		0			0
$208$	2.75734	−	6.65680i	0.191187	−	0.461566i
$209$	10.5380	−	7.65632i	0.728930	−	0.529599i
$210$		0			0
$211$	5.39797	−	4.61030i	0.371612	−	0.317386i	−0.443955	−	0.896049i	$-0.646425\pi$
$211$	5.39797	−	4.61030i	0.371612	−	0.317386i	0.815567	+	0.578663i	$0.196425\pi$
$212$	3.62786	−	4.24768i	0.249162	−	0.291732i
$213$		0			0
$214$	0.807724	+	0.807724i	0.0552148	+	0.0552148i
$215$	−1.40940	+	1.93987i	−0.0961201	+	0.132298i
$216$		0			0
$217$	−25.0954	+	6.02488i	−1.70359	+	0.408996i
$218$	2.36633	−	30.0671i	0.160268	−	2.03640i
$219$		0			0
$220$	6.26982	−	10.2314i	0.422711	−	0.689802i
$221$	−5.15826	−	1.67602i	−0.346982	−	0.112741i
$222$		0			0
$223$	−7.64852	−	23.5397i	−0.512183	−	1.57634i	−0.788350	−	0.615228i	$-0.789064\pi$
$223$	−7.64852	−	23.5397i	−0.512183	−	1.57634i	0.276167	−	0.961110i	$-0.410936\pi$
$224$	−1.78585	−	22.6914i	−0.119322	−	1.51613i
$225$		0			0
$226$	−22.6884	+	11.5603i	−1.50921	+	0.768981i
$227$	−15.6230	+	1.22956i	−1.03693	+	0.0816085i	−0.585481	−	0.810686i	$-0.699094\pi$
$227$	−15.6230	+	1.22956i	−1.03693	+	0.0816085i	−0.451453	+	0.892295i	$0.649094\pi$
$228$		0			0
$229$	−4.81442	−	1.15584i	−0.318146	−	0.0763800i	0.0712275	−	0.997460i	$-0.477308\pi$
$229$	−4.81442	−	1.15584i	−0.318146	−	0.0763800i	−0.389373	+	0.921080i	$0.627308\pi$
$230$	9.29414	−	28.6044i	0.612837	−	1.88612i
$231$		0			0
$232$	3.34529	−	1.38567i	0.219629	−	0.0909734i
$233$	15.1583	+	1.19298i	0.993053	+	0.0781549i	0.564562	−	0.825391i	$-0.309045\pi$
$233$	15.1583	+	1.19298i	0.993053	+	0.0781549i	0.428491	+	0.903546i	$0.359045\pi$
$234$		0			0
$235$	39.0990	−	23.9599i	2.55054	−	1.56297i
$236$	11.8871	+	8.63648i	0.773784	+	0.562187i
$237$		0			0
$238$	−24.7615	+	3.92184i	−1.60505	+	0.254215i
$239$	3.33907	+	2.85184i	0.215987	+	0.184470i	0.750858	−	0.660463i	$-0.229640\pi$
$239$	3.33907	+	2.85184i	0.215987	+	0.184470i	−0.534872	+	0.844933i	$0.679640\pi$
$240$		0			0
$241$	−4.72653	+	29.8421i	−0.304462	+	1.92230i	0.0751877	+	0.997169i	$0.476044\pi$
$241$	−4.72653	+	29.8421i	−0.304462	+	1.92230i	−0.379650	+	0.925130i	$0.623956\pi$
$242$	4.51989	+	6.22109i	0.290549	+	0.399907i
$243$		0			0
$244$	3.47401	−	6.81813i	0.222401	−	0.436486i
$245$	26.8836			1.71753
$246$		0			0
$247$	−7.31350			−0.465347
$248$	−4.39394	+	8.62360i	−0.279016	+	0.547599i
$249$		0			0
$250$	18.1073	+	24.9226i	1.14521	+	1.57624i
$251$	3.43804	−	21.7069i	0.217007	−	1.37013i	−0.602983	−	0.797754i	$-0.706022\pi$
$251$	3.43804	−	21.7069i	0.217007	−	1.37013i	0.819991	−	0.572377i	$-0.193978\pi$
$252$		0			0
$253$	−8.67390	−	7.40821i	−0.545323	−	0.465750i
$254$	−29.0989	+	4.60881i	−1.82583	+	0.289183i
$255$		0			0
$256$	−16.6511	−	12.0977i	−1.04069	−	0.756109i
$257$	2.63925	−	1.61733i	0.164632	−	0.100886i	−0.437742	−	0.899101i	$-0.644222\pi$
$257$	2.63925	−	1.61733i	0.164632	−	0.100886i	0.602374	+	0.798214i	$0.294222\pi$
$258$		0			0
$259$	39.8376	+	3.13529i	2.47539	+	0.194817i
$260$	−6.22457	+	2.57830i	−0.386031	+	0.159899i
$261$		0			0
$262$	−3.53388	+	10.8762i	−0.218324	+	0.671932i
$263$	7.65951	+	1.83889i	0.472306	+	0.113391i	0.462609	−	0.886562i	$-0.346913\pi$
$263$	7.65951	+	1.83889i	0.472306	+	0.113391i	0.00969678	+	0.999953i	$0.496913\pi$
$264$		0			0
$265$	17.4454	−	1.37298i	1.07166	−	0.0843416i
$266$	−30.1208	+	15.3473i	−1.84682	+	0.941004i
$267$		0			0
$268$	−1.13148	−	14.3768i	−0.0691162	−	0.878205i
$269$	−2.00338	−	6.16578i	−0.122148	−	0.375934i	0.871222	−	0.490889i	$-0.163328\pi$
$269$	−2.00338	−	6.16578i	−0.122148	−	0.375934i	−0.993371	+	0.114954i	$0.963328\pi$
$270$		0			0
$271$	10.4978	+	3.41095i	0.637698	+	0.207201i	0.609982	−	0.792415i	$-0.291177\pi$
$271$	10.4978	+	3.41095i	0.637698	+	0.207201i	0.0277158	+	0.999616i	$0.491177\pi$
$272$	−9.65012	+	15.7476i	−0.585124	+	0.954836i
$273$		0			0
$274$	−1.46098	+	18.5636i	−0.0882613	+	1.12147i
$275$	23.9566	−	5.75148i	1.44464	−	0.346827i
$276$		0			0
$277$	9.66773	−	13.3065i	0.580878	−	0.799510i	−0.412914	−	0.910770i	$-0.635489\pi$
$277$	9.66773	−	13.3065i	0.580878	−	0.799510i	0.993791	+	0.111261i	$0.0354888\pi$
$278$	5.29575	+	5.29575i	0.317618	+	0.317618i
$279$		0			0
$280$	13.0416	−	15.2697i	0.779384	−	0.912541i
$281$	−17.3210	+	14.7936i	−1.03329	+	0.882510i	−0.993169	−	0.116685i	$-0.962773\pi$
$281$	−17.3210	+	14.7936i	−1.03329	+	0.882510i	−0.0401170	+	0.999195i	$0.512773\pi$
$282$		0			0
$283$	9.76502	−	7.09471i	0.580470	−	0.421736i	−0.258423	−	0.966032i	$-0.583203\pi$
$283$	9.76502	−	7.09471i	0.580470	−	0.421736i	0.838894	+	0.544295i	$0.183203\pi$
$284$	−0.263260	+	0.635566i	−0.0156216	+	0.0377139i
$285$		0			0
$286$			6.75819i			0.399620i
$287$	−12.0753	−	20.7497i	−0.712781	−	1.22482i
$288$		0			0
$289$	−2.75987	−	1.40622i	−0.162345	−	0.0827190i
$290$	−16.2524	−	6.73197i	−0.954375	−	0.395315i
$291$		0			0
$292$	2.55275	+	0.404316i	0.149388	+	0.0236608i
$293$	3.02866	+	3.54611i	0.176936	+	0.207166i	0.841786	−	0.539811i	$-0.181504\pi$
$293$	3.02866	+	3.54611i	0.176936	+	0.207166i	−0.664850	+	0.746977i	$0.731504\pi$
$294$		0			0
$295$	7.20056	+	45.4625i	0.419233	+	2.64693i
$296$	10.5965	−	10.5965i	0.615910	−	0.615910i
$297$		0			0
$298$	−15.3754	−	25.0904i	−0.890673	−	1.45345i
$299$	1.49513	+	6.22765i	0.0864654	+	0.360154i
$300$		0			0
$301$	−0.903194	−	2.18050i	−0.0520592	−	0.125682i
$302$	−18.2193	−	11.1648i	−1.04840	−	0.642461i
$303$		0			0
$304$	−5.81381	+	24.2163i	−0.333445	+	1.38890i
$305$	22.7985	−	7.40768i	1.30544	−	0.424162i
$306$		0			0
$307$	−6.12485	−	12.0207i	−0.349564	−	0.686057i	0.647546	−	0.762026i	$-0.275795\pi$
$307$	−6.12485	−	12.0207i	−0.349564	−	0.686057i	−0.997110	+	0.0759685i	$0.975795\pi$
$308$	5.36220	+	10.5239i	0.305540	+	0.599655i
$309$		0			0
$310$	44.7196	−	14.5303i	2.53990	−	0.825264i
$311$	−4.51613	+	18.8111i	−0.256086	+	1.06668i	0.685009	+	0.728535i	$0.259798\pi$
$311$	−4.51613	+	18.8111i	−0.256086	+	1.06668i	−0.941095	+	0.338142i	$0.890202\pi$
$312$		0			0
$313$	−27.6177	−	16.9241i	−1.56104	−	0.956609i	−0.990830	−	0.135112i	$-0.956860\pi$
$313$	−27.6177	−	16.9241i	−1.56104	−	0.956609i	−0.570214	−	0.821496i	$-0.693140\pi$
$314$	13.9189	+	33.6032i	0.785489	+	1.89634i
$315$		0			0
$316$	1.38940	+	5.78725i	0.0781597	+	0.325558i
$317$	−7.79221	−	12.7157i	−0.437654	−	0.714187i	0.555433	−	0.831561i	$-0.312552\pi$
$317$	−7.79221	−	12.7157i	−0.437654	−	0.714187i	−0.993088	+	0.117374i	$0.962552\pi$
$318$		0			0
$319$	−4.71769	+	4.71769i	−0.264140	+	0.264140i
$320$	0.584011	+	3.68730i	0.0326472	+	0.206127i
$321$		0			0
$322$	19.2264	+	22.5112i	1.07144	+	1.25450i
$323$	18.5158	+	2.93261i	1.03025	+	0.163175i
$324$		0			0
$325$	−12.7801	−	5.29368i	−0.708911	−	0.293641i
$326$	−14.1798	−	7.22495i	−0.785345	−	0.400153i
$327$		0			0
$328$	−8.85794	−	1.61020i	−0.489098	−	0.0889085i
$329$			45.1363i			2.48844i
$330$		0			0
$331$	−9.80631	+	23.6745i	−0.539004	+	1.30127i	0.386415	+	0.922325i	$0.373713\pi$
$331$	−9.80631	+	23.6745i	−0.539004	+	1.30127i	−0.925419	+	0.378945i	$0.876287\pi$
$332$	−7.84229	+	5.69776i	−0.430402	+	0.312705i
$333$		0			0
$334$	7.45143	−	6.36412i	0.407724	−	0.348229i
$335$	29.3403	−	34.3530i	1.60303	−	1.87691i
$336$		0			0
$337$	15.6907	+	15.6907i	0.854727	+	0.854727i	0.990711	−	0.135984i	$-0.0434197\pi$
$337$	15.6907	+	15.6907i	0.854727	+	0.854727i	−0.135984	+	0.990711i	$0.543420\pi$
$338$	−11.4727	+	15.7908i	−0.624031	+	0.858905i
$339$		0			0
$340$	16.7928	−	4.03159i	0.910716	−	0.218644i
$341$	1.39919	−	17.7784i	0.0757704	−	0.962754i
$342$		0			0
$343$	−0.112881	+	0.184206i	−0.00609502	+	0.00994616i
$344$	−0.841767	−	0.273507i	−0.0453850	−	0.0147465i
$345$		0			0
$346$	4.65392	+	14.3233i	0.250196	+	0.770026i
$347$	−2.08262	−	26.4622i	−0.111801	−	1.42057i	−0.755430	−	0.655229i	$-0.772572\pi$
$347$	−2.08262	−	26.4622i	−0.111801	−	1.42057i	0.643629	−	0.765338i	$-0.277428\pi$
$348$		0			0
$349$	31.3931	−	15.9956i	1.68043	−	0.856224i	0.689130	−	0.724638i	$-0.257993\pi$
$349$	31.3931	−	15.9956i	1.68043	−	0.856224i	0.991305	−	0.131587i	$-0.0420071\pi$
$350$	−63.7438	+	5.01674i	−3.40725	+	0.268156i
$351$		0			0
$352$	15.2934	+	3.67162i	0.815141	+	0.195698i
$353$	−0.243118	+	0.748242i	−0.0129399	+	0.0398249i	−0.957318	−	0.289037i	$-0.906665\pi$
$353$	−0.243118	+	0.748242i	−0.0129399	+	0.0398249i	0.944378	+	0.328862i	$0.106665\pi$
$354$		0			0
$355$	−1.99102	+	0.824708i	−0.105672	+	0.0437710i
$356$	−18.4076	−	1.44871i	−0.975599	−	0.0767813i
$357$		0			0
$358$	−12.5840	+	7.71148i	−0.665084	+	0.407564i
$359$	4.26181	+	3.09639i	0.224930	+	0.163421i	0.694543	−	0.719451i	$-0.255607\pi$
$359$	4.26181	+	3.09639i	0.224930	+	0.163421i	−0.469613	+	0.882872i	$0.655607\pi$
$360$		0			0
$361$	6.20116	−	0.982168i	0.326377	−	0.0516930i
$362$	3.51579	+	3.00277i	0.184786	+	0.157822i
$363$		0			0
$364$	1.03741	−	6.54998i	0.0543753	−	0.343312i
$365$	4.75908	+	6.55031i	0.249102	+	0.342859i
$366$		0			0
$367$	5.31483	−	10.4309i	0.277432	−	0.544491i	−0.709679	−	0.704525i	$-0.751160\pi$
$367$	5.31483	−	10.4309i	0.277432	−	0.544491i	0.987112	+	0.160034i	$0.0511602\pi$
$368$	21.8094			1.13689
$369$		0			0
$370$	−72.8051			−3.78496
$371$	−7.81978	+	15.3472i	−0.405983	+	0.796786i
$372$		0			0
$373$	13.2081	+	18.1795i	0.683892	+	0.941297i	0.999972	−	0.00743589i	$-0.00236694\pi$
$373$	13.2081	+	18.1795i	0.683892	+	0.941297i	−0.316080	+	0.948732i	$0.602367\pi$
$374$	2.70994	−	17.1099i	0.140128	−	0.884731i
$375$		0			0
$376$	12.8711	+	10.9930i	0.663777	+	0.566919i
$377$	3.69989	−	0.586004i	0.190554	−	0.0301808i
$378$		0			0
$379$	−1.56091	−	1.13407i	−0.0801788	−	0.0582533i	0.546974	−	0.837150i	$-0.315780\pi$
$379$	−1.56091	−	1.13407i	−0.0801788	−	0.0582533i	−0.627153	+	0.778896i	$0.715780\pi$
$380$	19.8557	−	12.1676i	1.01858	−	0.624184i
$381$		0			0
$382$	8.86908	+	0.698012i	0.453782	+	0.0357134i
$383$	−24.8402	+	10.2892i	−1.26928	+	0.525752i	−0.912744	−	0.408531i	$-0.866041\pi$
$383$	−24.8402	+	10.2892i	−1.26928	+	0.525752i	−0.356533	+	0.934283i	$0.616041\pi$
$384$		0			0
$385$	−11.4339	+	35.1899i	−0.582725	+	1.79344i
$386$	10.1203	+	2.42966i	0.515108	+	0.123666i
$387$		0			0
$388$	4.11501	−	0.323858i	0.208908	−	0.0164414i
$389$	15.3243	−	7.80814i	0.776975	−	0.395888i	−0.0200776	−	0.999798i	$-0.506391\pi$
$389$	15.3243	−	7.80814i	0.776975	−	0.395888i	0.797053	+	0.603910i	$0.206391\pi$
$390$		0			0
$391$	−1.28805	−	16.3662i	−0.0651395	−	0.827676i
$392$	3.06649	+	9.43768i	0.154881	+	0.476675i
$393$		0			0
$394$	28.9746	+	9.41442i	1.45972	+	0.474292i
$395$	−9.74185	+	15.8973i	−0.490166	+	0.799878i
$396$		0			0
$397$	2.28376	−	29.0180i	0.114619	−	1.45637i	−0.623566	−	0.781771i	$-0.714317\pi$
$397$	2.28376	−	29.0180i	0.114619	−	1.45637i	0.738185	−	0.674599i	$-0.235683\pi$
$398$	−4.03594	+	0.968944i	−0.202303	+	0.0485688i
$399$		0			0
$400$	−27.6877	+	38.1089i	−1.38439	+	1.90545i
$401$	8.86378	+	8.86378i	0.442636	+	0.442636i	0.892897	−	0.450261i	$-0.148669\pi$
$401$	8.86378	+	8.86378i	0.442636	+	0.442636i	−0.450261	+	0.892897i	$0.648669\pi$
$402$		0			0
$403$	−6.50282	+	7.61382i	−0.323928	+	0.379271i
$404$	4.41868	−	3.77391i	0.219838	−	0.187759i
$405$		0			0
$406$	14.0083	−	10.1776i	0.695222	−	0.505108i
$407$	−10.5668	+	25.5105i	−0.523777	+	1.26451i
$408$		0			0
$409$		−	37.9577i		−	1.87689i	−0.345430	−	0.938444i	$-0.612267\pi$
$409$		−	37.9577i		−	1.87689i	0.345430	−	0.938444i	$-0.387733\pi$
$410$	24.8984	+	35.9615i	1.22964	+	1.77601i
$411$		0			0
$412$	−1.87568	−	0.955706i	−0.0924081	−	0.0470843i
$413$	−41.8577	−	17.3380i	−2.05968	−	0.853148i
$414$		0			0
$415$	−29.9931	−	4.75044i	−1.47230	−	0.233190i
$416$	−5.73509	−	6.71493i	−0.281186	−	0.329227i
$417$		0			0
$418$	−3.65417	−	23.0715i	−0.178731	−	1.12846i
$419$	3.04580	−	3.04580i	0.148797	−	0.148797i	−0.628783	−	0.777580i	$-0.716447\pi$
$419$	3.04580	−	3.04580i	0.148797	−	0.148797i	0.777580	+	0.628783i	$0.216447\pi$
$420$		0			0
$421$	7.49500	+	12.2307i	0.365284	+	0.596089i	0.981494	−	0.191493i	$-0.0613328\pi$
$421$	7.49500	+	12.2307i	0.365284	+	0.596089i	−0.616210	+	0.787582i	$0.711333\pi$
$422$	−2.97183	−	12.3786i	−0.144667	−	0.602580i
$423$		0			0
$424$	2.47191	+	5.96771i	0.120046	+	0.289817i
$425$	30.2330	+	18.5268i	1.46652	+	0.898682i
$426$		0			0
$427$	−5.50822	+	22.9434i	−0.266561	+	1.11031i
$428$	0.736621	−	0.239343i	0.0356059	−	0.0115691i
$429$		0			0
$430$	1.95216	+	3.83134i	0.0941417	+	0.184763i
$431$	14.7207	+	28.8910i	0.709072	+	1.39163i	0.911072	+	0.412247i	$0.135256\pi$
$431$	14.7207	+	28.8910i	0.709072	+	1.39163i	−0.202000	+	0.979385i	$0.564744\pi$
$432$		0			0
$433$	−3.29649	+	1.07109i	−0.158419	+	0.0514735i	−0.387153	−	0.922016i	$-0.626541\pi$
$433$	−3.29649	+	1.07109i	−0.158419	+	0.0514735i	0.228734	+	0.973489i	$0.426541\pi$
$434$	−10.8045	+	45.0038i	−0.518630	+	2.16025i
$435$		0			0
$436$	−17.4364	−	10.6851i	−0.835054	−	0.511722i
$437$	−8.47145	−	20.4519i	−0.405244	−	0.978347i
$438$		0			0
$439$	−3.82078	−	15.9147i	−0.182356	−	0.759568i	−0.986313	−	0.164881i	$-0.947276\pi$
$439$	−3.82078	−	15.9147i	−0.182356	−	0.759568i	0.803957	−	0.594687i	$-0.202724\pi$
$440$	7.25006	+	11.8310i	0.345633	+	0.564022i
$441$		0			0
$442$	−6.87759	+	6.87759i	−0.327133	+	0.327133i
$443$	3.43181	+	21.6676i	0.163050	+	1.02946i	0.924485	+	0.381218i	$0.124495\pi$
$443$	3.43181	+	21.6676i	0.163050	+	1.02946i	−0.761435	+	0.648241i	$0.775505\pi$
$444$		0			0
$445$	−37.5662	−	43.9843i	−1.78081	−	2.08506i
$446$	−43.8399	−	6.94356i	−2.07588	−	0.328787i
$447$		0			0
$448$	−3.39493	−	1.40622i	−0.160395	−	0.0664379i
$449$	−13.6106	−	6.93494i	−0.642324	−	0.327280i	0.102311	−	0.994752i	$-0.467376\pi$
$449$	−13.6106	−	6.93494i	−0.642324	−	0.327280i	−0.744635	+	0.667472i	$0.767376\pi$
$450$		0			0
$451$	16.2144	−	3.50487i	0.763508	−	0.165038i
$452$			17.2656i			0.812108i
$453$		0			0
$454$	−10.7547	+	25.9642i	−0.504744	+	1.21856i
$455$	16.8071	−	12.2111i	0.787930	−	0.572464i
$456$		0			0
$457$	−7.82018	+	6.67907i	−0.365813	+	0.312434i	−0.813287	−	0.581863i	$-0.802324\pi$
$457$	−7.82018	+	6.67907i	−0.365813	+	0.312434i	0.447474	+	0.894297i	$0.352324\pi$
$458$	−5.76648	+	6.75169i	−0.269450	+	0.315486i
$459$		0			0
$460$	−14.4202	−	14.4202i	−0.672346	−	0.672346i
$461$	10.5415	−	14.5091i	0.490965	−	0.675755i	−0.489601	−	0.871947i	$-0.662857\pi$
$461$	10.5415	−	14.5091i	0.490965	−	0.675755i	0.980566	+	0.196192i	$0.0628574\pi$
$462$		0			0
$463$	0.447778	−	0.107502i	0.0208100	−	0.00499604i	−0.223027	−	0.974812i	$-0.571594\pi$
$463$	0.447778	−	0.107502i	0.0208100	−	0.00499604i	0.243837	+	0.969816i	$0.421594\pi$
$464$	1.00083	−	12.7168i	0.0464626	−	0.590363i
$465$		0			0
$466$	14.2472	−	23.2494i	0.659990	−	1.07701i
$467$	−31.8139	−	10.3370i	−1.47217	−	0.478338i	−0.540408	−	0.841403i	$-0.681730\pi$
$467$	−31.8139	−	10.3370i	−1.47217	−	0.478338i	−0.931764	+	0.363066i	$0.881730\pi$
$468$		0			0
$469$	13.7413	+	42.2914i	0.634515	+	1.95284i
$470$	−6.45205	−	81.9810i	−0.297611	−	3.78150i
$471$		0			0
$472$	−15.1386	+	7.71349i	−0.696810	+	0.355042i
$473$	1.62581	−	0.127954i	0.0747549	−	0.00588334i
$474$		0			0
$475$	46.4917	+	11.1617i	2.13318	+	0.512132i
$476$	−5.25290	+	16.1668i	−0.240766	+	0.741003i
$477$		0			0
$478$	7.27528	−	3.01352i	0.332764	−	0.137835i
$479$	−17.0772	−	1.34400i	−0.780276	−	0.0614091i	−0.317937	−	0.948112i	$-0.602990\pi$
$479$	−17.0772	−	1.34400i	−0.780276	−	0.0614091i	−0.462340	+	0.886703i	$0.652990\pi$
$480$		0			0
$481$	13.2188	−	8.10052i	0.602728	−	0.369352i
$482$	43.8351	+	31.8480i	1.99663	+	1.45064i
$483$		0			0
$484$	5.14978	−	0.815645i	0.234081	−	0.0370748i
$485$	9.83269	+	8.39791i	0.446479	+	0.381330i
$486$		0			0
$487$	4.44151	−	28.0426i	0.201264	−	1.27073i	−0.655568	−	0.755136i	$-0.727571\pi$
$487$	4.44151	−	28.0426i	0.201264	−	1.27073i	0.856832	−	0.515595i	$-0.172429\pi$
$488$	5.20103	+	7.15860i	0.235439	+	0.324055i
$489$		0			0
$490$	21.8871	−	42.9559i	0.988761	−	1.94055i
$491$	28.7843			1.29902			0.649509	−	0.760354i	$-0.274974\pi$
$491$	28.7843			1.29902			0.649509	+	0.760354i	$0.274974\pi$
$492$		0			0
$493$	−9.60208			−0.432456
$494$	−5.95424	+	11.6859i	−0.267894	+	0.525771i
$495$		0			0
$496$	20.0413	+	27.5845i	0.899882	+	1.23858i
$497$	0.331833	−	2.09511i	0.0148847	−	0.0939785i
$498$		0			0
$499$	−6.13776	−	5.24214i	−0.274764	−	0.234670i	0.501379	−	0.865228i	$-0.332826\pi$
$499$	−6.13776	−	5.24214i	−0.274764	−	0.234670i	−0.776143	+	0.630557i	$0.782826\pi$
$500$	20.6307	−	3.26759i	0.922635	−	0.146131i
$501$		0			0
$502$	−31.8853	−	23.1660i	−1.42311	−	1.03395i
$503$	−3.54654	+	2.17332i	−0.158132	+	0.0969036i	−0.599313	−	0.800514i	$-0.704560\pi$
$503$	−3.54654	+	2.17332i	−0.158132	+	0.0969036i	0.441181	+	0.897418i	$0.354560\pi$
$504$		0			0
$505$	18.1477	+	1.42826i	0.807563	+	0.0635566i
$506$	−18.8990	+	7.82822i	−0.840162	+	0.348007i
$507$		0			0
$508$	−6.17304	+	18.9987i	−0.273884	+	0.842929i
$509$	−4.62243	−	1.10975i	−0.204886	−	0.0491887i	0.129703	−	0.991553i	$-0.458598\pi$
$509$	−4.62243	−	1.10975i	−0.204886	−	0.0491887i	−0.334589	+	0.942364i	$0.608598\pi$
$510$		0			0
$511$	−7.94492	+	0.625279i	−0.351463	+	0.0276607i
$512$	−14.3822	+	7.32812i	−0.635611	+	0.323860i
$513$		0			0
$514$	−0.435524	−	5.53385i	−0.0192101	−	0.244088i
$515$	−2.03787	−	6.27190i	−0.0897991	−	0.276373i
$516$		0			0
$517$	−29.6621	−	9.63781i	−1.30454	−	0.423870i
$518$	37.4432	−	61.1018i	1.64516	−	2.68466i
$519$		0			0
$520$	0.611256	−	7.76675i	0.0268054	−	0.340594i
$521$	20.5008	−	4.92180i	0.898156	−	0.215628i	0.242020	−	0.970271i	$-0.422190\pi$
$521$	20.5008	−	4.92180i	0.898156	−	0.215628i	0.656135	+	0.754643i	$0.272190\pi$
$522$		0			0
$523$	2.19950	−	3.02735i	0.0961773	−	0.132377i	−0.758216	−	0.652003i	$-0.773929\pi$
$523$	2.19950	−	3.02735i	0.0961773	−	0.132377i	0.854394	+	0.519626i	$0.173929\pi$
$524$	5.48296	+	5.48296i	0.239524	+	0.239524i
$525$		0			0
$526$	9.17420	−	10.7416i	0.400014	−	0.468357i
$527$	19.5164	−	16.6686i	0.850148	−	0.726095i
$528$		0			0
$529$	2.92388	−	2.12433i	0.127125	−	0.0923620i
$530$	12.0092	−	28.9929i	0.521648	−	1.25937i
$531$		0			0
$532$			22.9216i			0.993779i
$533$	−8.52186	−	3.75908i	−0.369123	−	0.162824i
$534$		0			0
$535$	2.16189	+	1.10154i	0.0934667	+	0.0476237i
$536$	15.4066	+	6.38161i	0.665462	+	0.275643i
$537$		0			0
$538$	−11.4830	−	1.81873i	−0.495068	−	0.0784111i
$539$	−11.8749	−	13.9037i	−0.511487	−	0.598874i
$540$		0			0
$541$	3.36710	+	21.2590i	0.144763	+	0.913997i	0.947985	+	0.318316i	$0.103117\pi$
$541$	3.36710	+	21.2590i	0.144763	+	0.913997i	−0.803222	+	0.595680i	$0.796883\pi$
$542$	13.9969	−	13.9969i	0.601219	−	0.601219i
$543$		0			0
$544$	11.8271	+	19.3001i	0.507083	+	0.827484i
$545$	−14.9552	−	62.2930i	−0.640611	−	2.66834i
$546$		0			0
$547$	1.81461	+	4.38085i	0.0775871	+	0.187312i	0.957914	−	0.287056i	$-0.0926766\pi$
$547$	1.81461	+	4.38085i	0.0775871	+	0.187312i	−0.880327	+	0.474368i	$0.842677\pi$
$548$	10.7653	+	6.59701i	0.459873	+	0.281810i
$549$		0			0
$550$	10.3142	−	42.9616i	0.439797	−	1.83189i
$551$	−12.3140	+	4.00107i	−0.524595	+	0.170451i
$552$		0			0
$553$	−8.33162	−	16.3517i	−0.354296	−	0.695346i
$554$	−13.3908	−	26.2810i	−0.568921	−	1.11657i
$555$		0			0
$556$	4.82957	−	1.56922i	0.204820	−	0.0665499i
$557$	−0.306985	+	1.27868i	−0.0130074	+	0.0541796i	−0.978496	−	0.206265i	$-0.933869\pi$
$557$	−0.306985	+	1.27868i	−0.0130074	+	0.0541796i	0.965489	+	0.260445i	$0.0838691\pi$
$558$		0			0
$559$	−0.780730	−	0.478432i	−0.0330214	−	0.0202355i
$560$	−27.0723	−	65.3584i	−1.14402	−	2.76190i
$561$		0			0
$562$	9.53603	+	39.7204i	0.402253	+	1.67551i
$563$	4.90670	+	8.00701i	0.206793	+	0.337455i	0.939175	−	0.343438i	$-0.111592\pi$
$563$	4.90670	+	8.00701i	0.206793	+	0.337455i	−0.732382	+	0.680893i	$0.761592\pi$
$564$		0			0
$565$	−38.2458	+	38.2458i	−1.60901	+	1.60901i
$566$	−3.38612	−	21.3791i	−0.142329	−	0.898632i
$567$		0			0
$568$	−0.516626	−	0.604891i	−0.0216771	−	0.0253807i
$569$	−7.46138	−	1.18177i	−0.312797	−	0.0495422i	−0.00193778	−	0.999998i	$-0.500617\pi$
$569$	−7.46138	−	1.18177i	−0.312797	−	0.0495422i	−0.310859	+	0.950456i	$0.600617\pi$
$570$		0			0
$571$	3.94854	+	1.63554i	0.165241	+	0.0684452i	0.463771	−	0.885955i	$-0.346496\pi$
$571$	3.94854	+	1.63554i	0.165241	+	0.0684452i	−0.298529	+	0.954400i	$0.596496\pi$
$572$	4.08292	+	2.08035i	0.170716	+	0.0869839i
$573$		0			0
$574$	−42.9859	+	2.40121i	−1.79420	+	0.100225i
$575$		−	41.8708i		−	1.74613i
$576$		0			0
$577$	−1.70907	+	4.12605i	−0.0711493	+	0.171770i	−0.955454	−	0.295141i	$-0.904633\pi$
$577$	−1.70907	+	4.12605i	−0.0711493	+	0.171770i	0.884304	+	0.466911i	$0.154633\pi$
$578$	−4.49386	+	3.26498i	−0.186920	+	0.135805i
$579$		0			0
$580$	−9.07001	+	7.74652i	−0.376612	+	0.321657i
$581$	19.4121	−	22.7286i	0.805348	−	0.942941i
$582$		0			0
$583$	−8.41594	−	8.41594i	−0.348553	−	0.348553i
$584$	−1.75668	+	2.41787i	−0.0726921	+	0.100052i
$585$		0			0
$586$	8.13191	−	1.95230i	0.335926	−	0.0806487i
$587$	−2.98714	+	37.9552i	−0.123292	+	1.56658i	0.555041	+	0.831823i	$0.312703\pi$
$587$	−2.98714	+	37.9552i	−0.123292	+	1.56658i	−0.678333	+	0.734755i	$0.737297\pi$
$588$		0			0
$589$	18.0829	−	29.5086i	0.745092	−	1.21588i
$590$	78.5044	+	25.5076i	3.23198	+	1.05013i
$591$		0			0
$592$	−16.3140	−	50.2094i	−0.670502	−	2.06359i
$593$	−1.71798	−	21.8290i	−0.0705488	−	0.896408i	−0.925756	−	0.378122i	$-0.876570\pi$
$593$	−1.71798	−	21.8290i	−0.0705488	−	0.896408i	0.855207	−	0.518286i	$-0.173430\pi$
$594$		0			0
$595$	−47.4475	+	24.1757i	−1.94516	+	0.991108i
$596$	−19.8912	+	1.56547i	−0.814774	+	0.0641241i
$597$		0			0
$598$	11.1681	+	2.68122i	0.456697	+	0.109643i
$599$	2.59956	−	8.00062i	0.106215	−	0.326896i	−0.883799	−	0.467867i	$-0.845022\pi$
$599$	2.59956	−	8.00062i	0.106215	−	0.326896i	0.990014	+	0.140971i	$0.0450225\pi$
$600$		0			0
$601$	4.90444	−	2.03149i	0.200056	−	0.0828661i	−0.280406	−	0.959882i	$-0.590469\pi$
$601$	4.90444	−	2.03149i	0.200056	−	0.0828661i	0.480462	+	0.877016i	$0.340469\pi$
$602$	−4.21944	−	0.332077i	−0.171971	−	0.0135344i
$603$		0			0
$604$	−12.3535	+	7.57025i	−0.502658	+	0.308029i
$605$	13.2142	+	9.60070i	0.537235	+	0.390324i
$606$		0			0
$607$	17.5450	−	2.77885i	0.712130	−	0.112790i	0.210149	−	0.977669i	$-0.432605\pi$
$607$	17.5450	−	2.77885i	0.712130	−	0.112790i	0.501980	+	0.864879i	$0.332605\pi$
$608$	23.2096	+	19.8228i	0.941272	+	0.803923i
$609$		0			0
$610$	6.72491	−	42.4594i	0.272284	−	1.71913i
$611$	10.2929	+	14.1670i	0.416407	+	0.573135i
$612$		0			0
$613$	12.3738	−	24.2849i	0.499772	−	0.980857i	−0.494004	−	0.869460i	$-0.664467\pi$
$613$	12.3738	−	24.2849i	0.499772	−	0.980857i	0.993776	−	0.111398i	$-0.0355327\pi$
$614$	−24.1937			−0.976380
$615$		0			0
$616$	−13.6579			−0.550291
$617$	−3.46177	+	6.79411i	−0.139366	+	0.273520i	−0.950131	−	0.311851i	$-0.899051\pi$
$617$	−3.46177	+	6.79411i	−0.139366	+	0.273520i	0.810766	+	0.585371i	$0.199051\pi$
$618$		0			0
$619$	−15.8070	−	21.7564i	−0.635335	−	0.874464i	0.363021	−	0.931781i	$-0.381745\pi$
$619$	−15.8070	−	21.7564i	−0.635335	−	0.874464i	−0.998356	+	0.0573171i	$0.981745\pi$
$620$	4.98751	−	31.4899i	0.200303	−	1.26466i
$621$		0			0
$622$	26.3804	+	22.5310i	1.05776	+	0.903411i
$623$	56.2340	−	8.90659i	2.25297	−	0.356835i
$624$		0			0
$625$	14.4704	+	10.5133i	0.578815	+	0.420534i
$626$	−49.5270	+	30.3502i	−1.97950	+	1.21304i
$627$		0			0
$628$	24.5858	+	1.93494i	0.981080	+	0.0772127i
$629$	−36.7147	+	15.2077i	−1.46391	+	0.606372i
$630$		0			0
$631$	−13.7926	+	42.4493i	−0.549076	+	1.68988i	0.162022	+	0.986787i	$0.448199\pi$
$631$	−13.7926	+	42.4493i	−0.549076	+	1.68988i	−0.711097	+	0.703094i	$0.751801\pi$
$632$	−6.69204	−	1.60662i	−0.266195	−	0.0639078i
$633$		0			0
$634$	−26.6618	+	2.09833i	−1.05887	+	0.0833353i
$635$	−55.7587	+	28.4105i	−2.21272	+	1.12744i
$636$		0			0
$637$	0.805474	+	10.2345i	0.0319140	+	0.405506i
$638$	3.69727	+	11.3790i	0.146376	+	0.450500i
$639$		0			0
$640$	−37.6186	−	12.2230i	−1.48700	−	0.483157i
$641$	−2.31911	+	3.78444i	−0.0915994	+	0.149477i	−0.895158	−	0.445749i	$-0.852937\pi$
$641$	−2.31911	+	3.78444i	−0.0915994	+	0.149477i	0.803559	+	0.595226i	$0.202937\pi$
$642$		0			0
$643$	0.633086	−	8.04412i	0.0249665	−	0.317229i	−0.971735	−	0.236074i	$-0.924139\pi$
$643$	0.633086	−	8.04412i	0.0249665	−	0.317229i	0.996702	−	0.0811549i	$-0.0258608\pi$
$644$	19.5184	−	4.68596i	0.769133	−	0.184653i
$645$		0			0
$646$	19.7604	−	27.1978i	0.777462	−	1.07008i
$647$	6.24364	+	6.24364i	0.245463	+	0.245463i	0.819106	−	0.573643i	$-0.194470\pi$
$647$	6.24364	+	6.24364i	0.245463	+	0.245463i	−0.573643	+	0.819106i	$0.694470\pi$
$648$		0			0
$649$	20.3317	−	23.8054i	0.798090	−	0.934443i
$650$	−18.8633	+	16.1108i	−0.739880	+	0.631917i
$651$		0			0
$652$	−8.72983	+	6.34259i	−0.341887	+	0.248395i
$653$	−9.97746	+	24.0877i	−0.390448	+	0.942625i	0.599394	+	0.800454i	$0.295408\pi$
$653$	−9.97746	+	24.0877i	−0.390448	+	0.942625i	−0.989842	+	0.142171i	$0.954592\pi$
$654$		0			0
$655$			24.2910i			0.949128i
$656$	−19.2214	+	25.2291i	−0.750468	+	0.985032i
$657$		0			0
$658$	72.1209	+	36.7474i	2.81157	+	1.43256i
$659$	22.9239	+	9.49540i	0.892989	+	0.369888i	0.781520	−	0.623880i	$-0.214444\pi$
$659$	22.9239	+	9.49540i	0.892989	+	0.369888i	0.111469	+	0.993768i	$0.464444\pi$
$660$		0			0
$661$	37.4753	+	5.93550i	1.45762	+	0.230864i	0.834390	−	0.551175i	$-0.185820\pi$
$661$	37.4753	+	5.93550i	1.45762	+	0.230864i	0.623229	+	0.782039i	$0.285820\pi$
$662$	29.8445	+	34.9435i	1.15994	+	1.35812i
$663$		0			0
$664$	−1.75349	−	11.0711i	−0.0680487	−	0.429643i
$665$	−50.7745	+	50.7745i	−1.96895	+	1.96895i
$666$		0			0
$667$	5.92443	+	9.66779i	0.229395	+	0.374338i
$668$	−1.55110	−	6.46078i	−0.0600137	−	0.249975i
$669$		0			0
$670$	−31.0037	−	74.8496i	−1.19778	−	2.89169i
$671$	−13.9015	−	8.51885i	−0.536662	−	0.328867i
$672$		0			0
$673$	10.3421	−	43.0779i	0.398658	−	1.66053i	−0.306796	−	0.951775i	$-0.599257\pi$
$673$	10.3421	−	43.0779i	0.398658	−	1.66053i	0.705454	−	0.708755i	$-0.250743\pi$
$674$	37.8458	−	12.2969i	1.45777	−	0.473657i
$675$		0			0
$676$	6.00831	+	11.7920i	0.231089	+	0.453538i
$677$	1.96144	+	3.84954i	0.0753842	+	0.147950i	0.925622	−	0.378448i	$-0.123542\pi$
$677$	1.96144	+	3.84954i	0.0753842	+	0.147950i	−0.850238	+	0.526398i	$0.823542\pi$
$678$		0			0
$679$	−12.1048	+	3.93310i	−0.464541	+	0.150939i
$680$	−4.66189	+	19.4182i	−0.178775	+	0.744653i
$681$		0			0
$682$	−27.2680	−	16.7099i	−1.04415	−	0.639854i
$683$	11.9074	+	28.7470i	0.455623	+	1.09997i	0.970152	+	0.242499i	$0.0779671\pi$
$683$	11.9074	+	28.7470i	0.455623	+	1.09997i	−0.514528	+	0.857473i	$0.672033\pi$
$684$		0			0
$685$	9.23343	+	38.4600i	0.352791	+	1.46948i
$686$	0.202431	+	0.330337i	0.00772884	+	0.0126123i
$687$		0			0
$688$	−2.20481	+	2.20481i	−0.0840575	+	0.0840575i
$689$	1.04538	+	6.60027i	0.0398258	+	0.251450i
$690$		0			0
$691$	3.03144	+	3.54936i	0.115321	+	0.135024i	0.815064	−	0.579371i	$-0.196702\pi$
$691$	3.03144	+	3.54936i	0.115321	+	0.135024i	−0.699742	+	0.714395i	$0.746702\pi$
$692$	10.0859	+	1.59746i	0.383410	+	0.0607262i
$693$		0			0
$694$	−43.9782	−	18.2164i	−1.66939	−	0.691483i
$695$	14.1742	+	7.22212i	0.537659	+	0.273951i
$696$		0			0
$697$	20.0677	+	12.9341i	0.760118	+	0.489914i
$698$		−	63.1841i		−	2.39155i
$699$		0			0
$700$	−16.5912	+	40.0547i	−0.627089	+	1.51393i
$701$	−6.84714	+	4.97474i	−0.258613	+	0.187893i	−0.709535	−	0.704670i	$-0.751095\pi$
$701$	−6.84714	+	4.97474i	−0.258613	+	0.187893i	0.450922	+	0.892563i	$0.351095\pi$
$702$		0			0
$703$	−40.7473	+	34.8015i	−1.53681	+	1.31256i
$704$	1.64903	−	1.93077i	0.0621503	−	0.0727687i
$705$		0			0
$706$	0.997642	+	0.997642i	0.0375468	+	0.0375468i
$707$	−10.5319	+	14.4960i	−0.396094	+	0.545176i
$708$		0			0
$709$	0.282312	−	0.0677772i	0.0106025	−	0.00254543i	−0.228141	−	0.973628i	$-0.573265\pi$
$709$	0.282312	−	0.0677772i	0.0106025	−	0.00254543i	0.238743	+	0.971083i	$0.423265\pi$
$710$	−0.303220	+	3.85278i	−0.0113797	+	0.144592i
$711$		0			0
$712$	11.1560	−	18.2049i	0.418089	−	0.682259i
$713$	−28.8241	−	9.36553i	−1.07947	−	0.350742i
$714$		0			0
$715$	4.43596	+	13.6525i	0.165896	+	0.510574i
$716$	0.785155	+	9.97634i	0.0293426	+	0.372833i
$717$		0			0
$718$	8.41728	−	4.28882i	0.314130	−	0.160057i
$719$	11.8294	−	0.930995i	0.441163	−	0.0347203i	0.144067	−	0.989568i	$-0.453982\pi$
$719$	11.8294	−	0.930995i	0.441163	−	0.0347203i	0.297096	+	0.954848i	$0.403982\pi$
$720$		0			0
$721$	6.31176	+	1.51532i	0.235062	+	0.0564335i
$722$	3.47928	−	10.7081i	0.129486	−	0.398516i
$723$		0			0
$724$	2.89636	−	1.19971i	0.107642	−	0.0445869i
$725$	−24.4144	−	1.92145i	−0.906728	−	0.0713610i
$726$		0			0
$727$	−23.7547	+	14.5569i	−0.881012	+	0.539885i	−0.887871	−	0.460092i	$-0.847816\pi$
$727$	−23.7547	+	14.5569i	−0.881012	+	0.539885i	0.00685962	+	0.999976i	$0.497816\pi$
$728$	6.20389	+	4.50739i	0.229931	+	0.167055i
$729$		0			0
$730$	14.3410	−	2.27139i	0.530783	−	0.0840678i
$731$	1.78475	+	1.52432i	0.0660114	+	0.0563791i
$732$		0			0
$733$	−2.88665	+	18.2256i	−0.106621	+	0.673178i	0.875256	+	0.483659i	$0.160693\pi$
$733$	−2.88665	+	18.2256i	−0.106621	+	0.673178i	−0.981877	+	0.189518i	$0.939307\pi$
$734$	−12.3400	−	16.9846i	−0.455479	−	0.626912i
$735$		0			0
$736$	12.1349	−	23.8161i	0.447298	−	0.877872i
$737$	−30.7267			−1.13183
$738$		0			0
$739$	−23.8465			−0.877207			−0.438603	−	0.898681i	$-0.644527\pi$
$739$	−23.8465			−0.877207			−0.438603	+	0.898681i	$0.644527\pi$
$740$	−22.4114	+	43.9848i	−0.823859	+	1.61691i
$741$		0			0
$742$	18.1560	+	24.9896i	0.666529	+	0.917398i
$743$	−0.364544	+	2.30164i	−0.0133738	+	0.0844390i	−0.993472	−	0.114072i	$-0.963611\pi$
$743$	−0.364544	+	2.30164i	−0.0133738	+	0.0844390i	0.980099	+	0.198511i	$0.0636105\pi$
$744$		0			0
$745$	−47.5294	−	40.5939i	−1.74134	−	1.48725i
$746$	39.8013	−	6.30391i	1.45723	−	0.230803i
$747$		0			0
$748$	−9.50265	−	6.90408i	−0.347451	−	0.252438i
$749$	−2.03632	+	1.24786i	−0.0744054	+	0.0455957i
$750$		0			0
$751$	−24.7566	−	1.94839i	−0.903381	−	0.0710977i	−0.381747	−	0.924267i	$-0.624677\pi$
$751$	−24.7566	−	1.94839i	−0.903381	−	0.0710977i	−0.521634	+	0.853169i	$0.674677\pi$
$752$	55.0917	−	22.8197i	2.00899	−	0.832149i
$753$		0			0
$754$	2.07589	−	6.38894i	0.0755996	−	0.232672i
$755$	−44.1339	−	10.5956i	−1.60620	−	0.385614i
$756$		0			0
$757$	−34.7576	+	2.73548i	−1.26329	+	0.0994228i	−0.692344	−	0.721567i	$-0.743422\pi$
$757$	−34.7576	+	2.73548i	−1.26329	+	0.0994228i	−0.570942	+	0.820990i	$0.693422\pi$
$758$	−3.08288	+	1.57081i	−0.111975	+	0.0570542i
$759$		0			0
$760$	2.11275	+	26.8451i	0.0766376	+	0.973773i
$761$	−9.99870	−	30.7728i	−0.362453	−	1.11551i	−0.951561	−	0.307460i	$-0.900521\pi$
$761$	−9.99870	−	30.7728i	−0.362453	−	1.11551i	0.589108	−	0.808054i	$-0.299479\pi$
$762$		0			0
$763$	59.9709	+	19.4857i	2.17109	+	0.705430i
$764$	3.15184	−	5.14334i	0.114030	−	0.186079i
$765$		0			0
$766$	−3.78302	+	48.0678i	−0.136686	+	1.73676i
$767$	−17.0917	+	4.10335i	−0.617145	+	0.148164i
$768$		0			0
$769$	−19.2954	+	26.5578i	−0.695810	+	0.957700i	0.304177	+	0.952615i	$0.401618\pi$
$769$	−19.2954	+	26.5578i	−0.695810	+	0.957700i	−0.999987	+	0.00508457i	$0.998382\pi$
$770$	46.9192	+	46.9192i	1.69085	+	1.69085i
$771$		0			0
$772$	4.58316	−	5.36619i	0.164951	−	0.193133i
$773$	10.0608	−	8.59271i	0.361861	−	0.309058i	−0.449866	−	0.893096i	$-0.648528\pi$
$773$	10.0608	−	8.59271i	0.361861	−	0.309058i	0.811726	+	0.584038i	$0.198528\pi$
$774$		0			0
$775$	52.9582	−	38.4764i	1.90232	−	1.38211i
$776$	−1.82657	+	4.40974i	−0.0655702	+	0.158300i
$777$		0			0
$778$		−	30.8429i		−	1.10577i
$779$	31.1250	+	8.22517i	1.11517	+	0.294697i
$780$		0			0
$781$	1.30598	+	0.665432i	0.0467318	+	0.0238110i
$782$	−27.1994	−	11.2664i	−0.972649	−	0.402884i
$783$		0			0
$784$	34.5286	+	5.46879i	1.23316	+	0.195314i
$785$	50.1747	+	58.7470i	1.79081	+	2.09677i
$786$		0			0
$787$	4.46841	+	28.2125i	0.159282	+	1.00567i	0.929751	+	0.368189i	$0.120022\pi$
$787$	4.46841	+	28.2125i	0.159282	+	1.00567i	−0.770469	+	0.637477i	$0.779978\pi$
$788$	14.6068	−	14.6068i	0.520347	−	0.520347i
$789$		0			0
$790$	17.4701	+	28.5086i	0.621559	+	1.01429i
$791$	−12.4282	−	51.7674i	−0.441897	−	1.84064i
$792$		0			0
$793$	3.50316	+	8.45737i	0.124401	+	0.300330i
$794$	−44.5070	−	27.2739i	−1.57949	−	0.967914i
$795$		0			0
$796$	−0.656990	+	2.73656i	−0.0232864	+	0.0969947i
$797$	−24.4797	+	7.95394i	−0.867116	+	0.281743i	−0.708597	−	0.705613i	$-0.750672\pi$
$797$	−24.4797	+	7.95394i	−0.867116	+	0.281743i	−0.158518	+	0.987356i	$0.550672\pi$
$798$		0			0
$799$	−20.3781	−	39.9943i	−0.720925	−	1.41490i
$800$	26.2097	+	51.4394i	0.926651	+	1.81866i
$801$		0			0
$802$	21.3793	−	6.94657i	0.754931	−	0.245292i
$803$	1.28554	−	5.35466i	0.0453657	−	0.188962i
$804$		0			0
$805$	53.6160	+	32.8559i	1.88971	+	1.15802i
$806$	6.87149	+	16.5893i	0.242038	+	0.584331i
$807$		0			0
$808$	1.56862	+	6.53379i	0.0551840	+	0.229858i
$809$	16.1305	+	26.3226i	0.567119	+	0.925454i	0.999715	+	0.0238659i	$0.00759747\pi$
$809$	16.1305	+	26.3226i	0.567119	+	0.925454i	−0.432597	+	0.901588i	$0.642403\pi$
$810$		0			0
$811$	21.4227	−	21.4227i	0.752253	−	0.752253i	−0.222646	−	0.974899i	$-0.571469\pi$
$811$	21.4227	−	21.4227i	0.752253	−	0.752253i	0.974899	+	0.222646i	$0.0714694\pi$
$812$	−1.83663	−	11.5960i	−0.0644530	−	0.406940i
$813$		0			0
$814$	32.1590	+	37.6534i	1.12717	+	1.31975i
$815$	−33.3875	−	5.28806i	−1.16951	−	0.185233i
$816$		0			0
$817$	2.92399	+	1.21116i	0.102297	+	0.0423730i
$818$	−60.6506	−	30.9030i	−2.12060	−	1.08050i
$819$		0			0
$820$	29.3904	−	3.97230i	1.02636	−	0.138719i
$821$		−	30.5245i		−	1.06531i	−0.846331	−	0.532657i	$-0.821194\pi$
$821$		−	30.5245i		−	1.06531i	0.846331	−	0.532657i	$-0.178806\pi$
$822$		0			0
$823$	9.95339	−	24.0296i	0.346953	−	0.837619i	−0.650023	−	0.759914i	$-0.725241\pi$
$823$	9.95339	−	24.0296i	0.346953	−	0.837619i	0.996976	−	0.0777048i	$-0.0247592\pi$
$824$	1.96934	−	1.43081i	0.0686053	−	0.0498447i
$825$		0			0
$826$	−61.7817	+	52.7665i	−2.14966	+	1.83598i
$827$	−26.7239	+	31.2897i	−0.929282	+	1.08805i	0.0666347	+	0.997777i	$0.478774\pi$
$827$	−26.7239	+	31.2897i	−0.929282	+	1.08805i	−0.995917	+	0.0902724i	$0.971226\pi$
$828$		0			0
$829$	−19.7700	−	19.7700i	−0.686642	−	0.686642i	0.274846	−	0.961488i	$-0.411373\pi$
$829$	−19.7700	−	19.7700i	−0.686642	−	0.686642i	−0.961488	+	0.274846i	$0.911373\pi$
$830$	−32.0091	+	44.0568i	−1.11105	+	1.52923i
$831$		0			0
$832$	−1.38625	+	0.332808i	−0.0480595	+	0.0115381i
$833$	2.06466	−	26.2340i	0.0715362	−	0.908954i
$834$		0			0
$835$	10.8756	−	17.7474i	0.376367	−	0.614175i
$836$	−15.0634	−	4.89438i	−0.520977	−	0.169276i
$837$		0			0
$838$	−2.38700	−	7.34644i	−0.0824577	−	0.253779i
$839$	0.388483	+	4.93614i	0.0134119	+	0.170415i	0.999975	+	0.00703531i	$0.00223943\pi$
$839$	0.388483	+	4.93614i	0.0134119	+	0.170415i	−0.986563	+	0.163379i	$0.947761\pi$
$840$		0			0
$841$	−19.9301	+	10.1549i	−0.687246	+	0.350169i
$842$	25.6448	−	2.01829i	0.883779	−	0.0695549i
$843$		0			0
$844$	−8.39326	−	2.01504i	−0.288908	−	0.0693607i
$845$	−12.8116	+	39.4301i	−0.440733	+	1.35644i
$846$		0			0
$847$	−14.8534	+	6.15248i	−0.510369	+	0.211402i
$848$	22.6857	+	1.78540i	0.779029	+	0.0613109i
$849$		0			0
$850$	54.2170	−	33.2242i	1.85963	−	1.13958i
$851$	37.9646	+	27.5829i	1.30141	+	0.945528i
$852$		0			0
$853$	15.0018	−	2.37604i	0.513650	−	0.0813542i	0.105772	−	0.994390i	$-0.466269\pi$
$853$	15.0018	−	2.37604i	0.513650	−	0.0813542i	0.407878	+	0.913036i	$0.366269\pi$
$854$	32.1755	+	27.4805i	1.10102	+	0.940363i
$855$		0			0
$856$	−0.140106	+	0.884594i	−0.00478872	+	0.0302348i
$857$	−20.1093	−	27.6781i	−0.686922	−	0.945467i	0.313069	−	0.949730i	$-0.398643\pi$
$857$	−20.1093	−	27.6781i	−0.686922	−	0.945467i	−0.999991	+	0.00426317i	$0.998643\pi$
$858$		0			0
$859$	−12.5277	+	24.5869i	−0.427439	+	0.838896i	0.572382	+	0.819987i	$0.306019\pi$
$859$	−12.5277	+	24.5869i	−0.427439	+	0.838896i	−0.999821	+	0.0189090i	$0.993981\pi$
$860$	2.91561			0.0994214
$861$		0			0
$862$	58.1482			1.98054
$863$	25.0530	−	49.1693i	0.852814	−	1.67374i	0.120565	−	0.992705i	$-0.461529\pi$
$863$	25.0530	−	49.1693i	0.852814	−	1.67374i	0.732249	−	0.681037i	$-0.238471\pi$
$864$		0			0
$865$	18.8032	+	25.8803i	0.639327	+	0.879958i
$866$	−0.972371	+	6.13931i	−0.0330425	+	0.208622i
$867$		0			0
$868$	23.8629	+	20.3808i	0.809959	+	0.691770i
$869$	12.5249	−	1.98374i	0.424877	−	0.0672938i
$870$		0			0
$871$	13.9572	+	10.1405i	0.472921	+	0.343597i
$872$	20.1625	−	12.3556i	0.682788	−	0.418413i
$873$		0			0
$874$	−39.5760	−	3.11470i	−1.33868	−	0.105356i
$875$	−59.5048	+	24.6477i	−2.01163	+	0.833244i
$876$		0			0
$877$	1.57215	−	4.83859i	0.0530878	−	0.163387i	−0.920997	−	0.389569i	$-0.872624\pi$
$877$	1.57215	−	4.83859i	0.0530878	−	0.163387i	0.974085	+	0.226181i	$0.0726241\pi$
$878$	−28.5399	−	6.85184i	−0.963177	−	0.231238i
$879$		0			0
$880$	48.7321	−	3.83530i	1.64276	−	0.129288i
$881$	12.2787	−	6.25633i	0.413681	−	0.210781i	−0.234748	−	0.972056i	$-0.575426\pi$
$881$	12.2787	−	6.25633i	0.413681	−	0.210781i	0.648429	+	0.761275i	$0.275426\pi$
$882$		0			0
$883$	−3.75557	−	47.7191i	−0.126385	−	1.60587i	−0.654070	−	0.756434i	$-0.726940\pi$
$883$	−3.75557	−	47.7191i	−0.126385	−	1.60587i	0.527685	−	0.849440i	$-0.323060\pi$
$884$	2.03795	+	6.27216i	0.0685436	+	0.210956i
$885$		0			0
$886$	37.4155	+	12.1570i	1.25700	+	0.408423i
$887$	15.6778	−	25.5839i	0.526410	−	0.859023i	−0.473351	−	0.880874i	$-0.656956\pi$
$887$	15.6778	−	25.5839i	0.526410	−	0.859023i	0.999761	+	0.0218506i	$0.00695583\pi$
$888$		0			0
$889$	4.83283	−	61.4069i	0.162088	−	2.05952i
$890$	−100.865	+	24.2154i	−3.38099	+	0.811703i
$891$		0			0
$892$	−17.6900	+	24.3482i	−0.592305	+	0.815239i
$893$	−42.7987	−	42.7987i	−1.43220	−	1.43220i
$894$		0			0
$895$	−20.3597	+	23.8382i	−0.680551	+	0.796823i
$896$	29.6052	−	25.2852i	0.989039	−	0.844719i
$897$		0			0
$898$	−22.1620	+	16.1016i	−0.739554	+	0.537317i
$899$	−6.78368	+	16.3773i	−0.226248	+	0.546212i
$900$		0			0
$901$		−	17.1293i		−	0.570658i
$902$	7.60064	−	28.7617i	0.253073	−	0.957659i
$903$		0			0
$904$	−17.7889	−	9.06391i	−0.591651	−	0.301461i
$905$	9.07336	+	3.75831i	0.301609	+	0.124930i
$906$		0			0
$907$	−10.6037	−	1.67946i	−0.352089	−	0.0557654i	−0.0221149	−	0.999755i	$-0.507040\pi$
$907$	−10.6037	−	1.67946i	−0.352089	−	0.0557654i	−0.329974	+	0.943990i	$0.607040\pi$
$908$	12.3755	+	14.4899i	0.410696	+	0.480864i
$909$		0			0
$910$	−5.82804	−	36.7968i	−0.193198	−	1.21980i
$911$	21.9898	−	21.9898i	0.728554	−	0.728554i	−0.241778	−	0.970332i	$-0.577731\pi$
$911$	21.9898	−	21.9898i	0.728554	−	0.728554i	0.970332	+	0.241778i	$0.0777306\pi$
$912$		0			0
$913$	10.7915	+	17.6102i	0.357147	+	0.582811i
$914$	4.30538	+	17.9332i	0.142409	+	0.593177i
$915$		0			0
$916$	2.30391	+	5.56214i	0.0761235	+	0.183778i
$917$	−20.3862	−	12.4927i	−0.673213	−	0.412546i
$918$		0			0
$919$	−8.98543	+	37.4270i	−0.296402	+	1.23460i	0.603092	+	0.797671i	$0.293935\pi$
$919$	−8.98543	+	37.4270i	−0.296402	+	1.23460i	−0.899494	+	0.436932i	$0.856065\pi$
$920$	22.4274	−	7.28711i	0.739410	−	0.240249i
$921$		0			0
$922$	−14.6010	−	28.6561i	−0.480859	−	0.943739i
$923$	−0.373618	−	0.733266i	−0.0122978	−	0.0241358i
$924$		0			0
$925$	−96.3946	+	31.3205i	−3.16943	+	1.02981i
$926$	0.192784	−	0.803002i	0.00633527	−	0.0263883i
$927$		0			0
$928$	−13.3300	−	8.16864i	−0.437579	−	0.268149i
$929$	22.2144	+	53.6303i	0.728830	+	1.75955i	0.646458	+	0.762950i	$0.276250\pi$
$929$	22.2144	+	53.6303i	0.728830	+	1.75955i	0.0823724	+	0.996602i	$0.473750\pi$
$930$		0			0
$931$	−8.28360	−	34.5037i	−0.271484	−	1.13081i
$932$	−9.66030	−	15.7642i	−0.316434	−	0.516373i
$933$		0			0
$934$	−42.4180	+	42.4180i	−1.38796	+	1.38796i
$935$	−5.75619	−	36.3432i	−0.188248	−	1.18855i
$936$		0			0
$937$	29.8702	+	34.9735i	0.975817	+	1.14254i	0.989776	+	0.142633i	$0.0455568\pi$
$937$	29.8702	+	34.9735i	0.975817	+	1.14254i	−0.0139582	+	0.999903i	$0.504443\pi$
$938$	78.7626	+	12.4748i	2.57169	+	0.407316i
$939$		0			0
$940$	−51.5145	−	21.3380i	−1.68022	−	0.695969i
$941$	−1.68174	−	0.856888i	−0.0548231	−	0.0279338i	0.426364	−	0.904552i	$-0.359794\pi$
$941$	−1.68174	−	0.856888i	−0.0548231	−	0.0279338i	−0.481187	+	0.876618i	$0.659794\pi$
$942$		0			0
$943$	0.640967	−	28.1853i	0.0208728	−	0.917839i
$944$			59.8555i			1.94813i
$945$		0			0
$946$	1.11919	−	2.70197i	0.0363881	−	0.0878487i
$947$	−5.71910	+	4.15517i	−0.185846	+	0.135025i	−0.676818	−	0.736150i	$-0.736642\pi$
$947$	−5.71910	+	4.15517i	−0.185846	+	0.135025i	0.490972	+	0.871175i	$0.336642\pi$
$948$		0			0
$949$	−2.35109	+	2.00802i	−0.0763197	+	0.0651832i
$950$	55.6855	−	65.1994i	1.80668	−	2.11535i
$951$		0			0
$952$	−13.8991	−	13.8991i	−0.450474	−	0.450474i
$953$	−3.98479	+	5.48459i	−0.129080	+	0.177663i	−0.868665	−	0.495400i	$-0.835022\pi$
$953$	−3.98479	+	5.48459i	−0.129080	+	0.177663i	0.739585	+	0.673063i	$0.235022\pi$
$954$		0			0
$955$	18.3750	−	4.41144i	0.594600	−	0.142751i
$956$	0.418926	−	5.32296i	0.0135490	−	0.172157i
$957$		0			0
$958$	−16.0508	+	26.1925i	−0.518578	+	0.846242i
$959$	−37.0263	−	12.0306i	−1.19564	−	0.388487i
$960$		0			0
$961$	−5.06235	−	15.5803i	−0.163302	−	0.502591i
$962$	−2.18135	−	27.7167i	−0.0703296	−	0.893622i
$963$		0			0
$964$	32.7344	−	16.6790i	1.05430	−	0.537195i
$965$	22.0392	−	1.73452i	0.709465	−	0.0558361i
$966$		0			0
$967$	−18.4416	−	4.42742i	−0.593040	−	0.142376i	−0.0741938	−	0.997244i	$-0.523638\pi$
$967$	−18.4416	−	4.42742i	−0.593040	−	0.142376i	−0.518846	+	0.854867i	$0.673638\pi$
$968$	−1.86311	+	5.73405i	−0.0598825	+	0.184299i
$969$		0			0
$970$	21.4238	−	8.87403i	0.687877	−	0.284928i
$971$	21.4588	+	1.68885i	0.688647	+	0.0541977i	0.417954	−	0.908468i	$-0.362747\pi$
$971$	21.4588	+	1.68885i	0.688647	+	0.0541977i	0.270693	+	0.962666i	$0.412747\pi$
$972$		0			0
$973$	−13.3509	+	8.18143i	−0.428010	+	0.262285i
$974$	−41.1917	−	29.9275i	−1.31987	−	0.958941i
$975$		0			0
$976$	30.7886	−	4.87644i	0.985520	−	0.156091i
$977$	0.377440	+	0.322364i	0.0120754	+	0.0103133i	0.655465	−	0.755225i	$-0.272473\pi$
$977$	0.377440	+	0.322364i	0.0120754	+	0.0103133i	−0.643390	+	0.765539i	$0.722473\pi$
$978$		0			0
$979$	−6.15434	+	38.8570i	−0.196694	+	1.24187i
$980$	−19.2141	−	26.4460i	−0.613773	−	0.844786i
$981$		0			0
$982$	23.4346	−	45.9930i	0.747828	−	1.46769i
$983$	10.1572			0.323964			0.161982	−	0.986794i	$-0.448211\pi$
$983$	10.1572			0.323964			0.161982	+	0.986794i	$0.448211\pi$
$984$		0			0
$985$	64.7123			2.06190
$986$	−7.81748	+	15.3427i	−0.248959	+	0.488610i
$987$		0			0
$988$	5.22707	+	7.19444i	0.166295	+	0.228886i
$989$	0.433571	−	2.73746i	0.0137868	−	0.0870462i
$990$		0			0
$991$	30.2662	+	25.8498i	0.961437	+	0.821145i	0.983921	−	0.178602i	$-0.0571575\pi$
$991$	30.2662	+	25.8498i	0.961437	+	0.821145i	−0.0224839	+	0.999747i	$0.507157\pi$
$992$	41.2737	−	6.53711i	1.31044	−	0.207554i
$993$		0			0
$994$	−3.07751	−	2.23594i	−0.0976126	−	0.0709197i
$995$	−7.51717	+	4.60653i	−0.238310	+	0.146037i
$996$		0			0
$997$	43.0384	+	3.38719i	1.36304	+	0.107273i	0.738781	−	0.673945i	$-0.235402\pi$
$997$	43.0384	+	3.38719i	1.36304	+	0.107273i	0.624257	+	0.781219i	$0.285402\pi$
$998$	−13.3732	+	5.53934i	−0.423320	+	0.175345i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	369.2.ba.b.341.6	yes	112
3.2	odd	2		369.2.ba.a.341.2	yes	112
41.19	odd	40		369.2.ba.a.224.2	✓	112
123.101	even	40	inner	369.2.ba.b.224.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
369.2.ba.a.224.2	✓	112	41.19	odd	40
369.2.ba.a.341.2	yes	112	3.2	odd	2
369.2.ba.b.224.6	yes	112	123.101	even	40	inner
369.2.ba.b.341.6	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 369 = 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	369.ba (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.814144 - 1.59785i) q^{2} +(-0.714715 - 0.983721i) q^{4} +(0.595885 - 3.76227i) q^{5} +(2.85103 + 2.43501i) q^{7} +(1.38874 - 0.219955i) q^{8} +(-5.52639 - 4.01516i) q^{10} +(-2.20898 + 1.35366i) q^{11} +(1.45014 + 0.114128i) q^{13} +(6.21192 - 2.57306i) q^{14} +(1.53067 - 4.71093i) q^{16} +(-3.62559 - 0.870427i) q^{17} +(-5.01227 + 0.394474i) q^{19} +(-4.12691 + 2.10276i) q^{20} +(0.364522 + 4.63169i) q^{22} +(1.36058 + 4.18744i) q^{23} +(-9.04429 - 2.93867i) q^{25} +(1.36298 - 2.22418i) q^{26} +(0.357695 - 4.54495i) q^{28} +(2.50409 - 0.601179i) q^{29} +(-4.04600 + 5.56884i) q^{31} +(-4.29271 - 4.29271i) q^{32} +(-4.34256 + 5.08448i) q^{34} +(10.8600 - 9.27534i) q^{35} +(8.62255 - 6.26465i) q^{37} +(-3.45040 + 8.33000i) q^{38} -5.35587i q^{40} +(-6.04317 - 2.11661i) q^{41} +(-0.560875 - 0.285780i) q^{43} +(2.91042 + 1.20554i) q^{44} +(7.79861 + 1.23518i) q^{46} +(7.81834 + 9.15410i) q^{47} +(1.10406 + 6.97073i) q^{49} +(-12.0589 + 12.0589i) q^{50} +(-0.924164 - 1.50810i) q^{52} +(1.07245 + 4.46708i) q^{53} +(3.77655 + 9.11740i) q^{55} +(4.49492 + 2.75449i) q^{56} +(1.07810 - 4.49060i) q^{58} +(-11.4924 + 3.73410i) q^{59} +(2.85704 + 5.60726i) q^{61} +(5.60413 + 10.9987i) q^{62} +(-0.932106 + 0.302860i) q^{64} +(1.29350 - 5.38780i) q^{65} +(10.1124 + 6.19691i) q^{67} +(1.73501 + 4.18867i) q^{68} +(-5.97895 - 24.9041i) q^{70} +(-0.295608 - 0.482388i) q^{71} +(-1.50300 + 1.50300i) q^{73} +(-2.98996 - 18.8778i) q^{74} +(3.97040 + 4.64874i) q^{76} +(-9.59405 - 1.51955i) q^{77} +(-4.52212 - 1.87312i) q^{79} +(-16.8117 - 8.56598i) q^{80} +(-8.30204 + 7.93284i) q^{82} -7.97207i q^{83} +(-5.43521 + 13.1218i) q^{85} +(-0.913266 + 0.663527i) q^{86} +(-2.76995 + 2.36576i) q^{88} +(9.86205 - 11.5470i) q^{89} +(3.85648 + 3.85648i) q^{91} +(3.14685 - 4.33126i) q^{92} +(20.9921 - 5.03976i) q^{94} +(-1.50262 + 19.0926i) q^{95} +(-1.77371 + 2.89443i) q^{97} +(12.0370 + 3.91107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 4 q^{5} - 24 q^{8} + 12 q^{11} - 4 q^{13} + 4 q^{14} + 28 q^{16} + 4 q^{17} - 88 q^{20} + 8 q^{22} - 24 q^{23} + 60 q^{26} - 8 q^{29} - 48 q^{32} + 152 q^{35} + 8 q^{37} + 56 q^{38} - 12 q^{41}+ \cdots - 60 q^{98}+O(q^{100}) \) 112 * q + 4 * q^5 - 24 * q^8 + 12 * q^11 - 4 * q^13 + 4 * q^14 + 28 * q^16 + 4 * q^17 - 88 * q^20 + 8 * q^22 - 24 * q^23 + 60 * q^26 - 8 * q^29 - 48 * q^32 + 152 * q^35 + 8 * q^37 + 56 * q^38 - 12 * q^41 - 24 * q^43 + 60 * q^44 - 56 * q^46 + 28 * q^47 + 64 * q^52 - 16 * q^53 - 8 * q^55 - 72 * q^56 - 16 * q^58 - 40 * q^59 + 28 * q^61 - 68 * q^62 - 172 * q^65 + 48 * q^67 + 36 * q^68 - 232 * q^70 + 32 * q^71 - 72 * q^73 + 4 * q^74 - 176 * q^76 + 60 * q^77 - 72 * q^79 + 128 * q^80 - 192 * q^82 + 16 * q^85 + 40 * q^86 - 112 * q^88 - 48 * q^89 - 80 * q^91 - 64 * q^94 - 20 * q^95 - 72 * q^97 - 60 * q^98

Introduction

L-functions

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