LMFDB - Embedded newform 783.2.be.a.710.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(8,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.8"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.be (of order $84$, degree $24$, not 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:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			710.25
Character	$\chi$	$=$	783.710
Dual form			783.2.be.a.665.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.915081 - 2.09739i) q^{2} +(-2.20132 - 2.37246i) q^{4} +(1.59462 + 0.240350i) q^{5} +(2.61989 + 2.43090i) q^{7} +(-2.67053 + 0.934460i) q^{8} +(1.96331 - 3.12459i) q^{10} +(2.89572 - 2.49197i) q^{11} +(-2.15055 + 3.15427i) q^{13} +(7.49596 - 3.27045i) q^{14} +(-0.000114643 + 0.00152981i) q^{16} +(2.40371 + 2.40371i) q^{17} +(3.94790 + 2.48063i) q^{19} +(-2.94004 - 4.31225i) q^{20} +(-2.57681 - 8.35381i) q^{22} +(-1.21407 - 0.476487i) q^{23} +(-2.29282 - 0.707243i) q^{25} +(4.64781 + 7.39694i) q^{26} -11.5668i q^{28} +(-5.35553 + 0.564198i) q^{29} +(5.64002 - 4.16253i) q^{31} +(-4.99976 - 2.64245i) q^{32} +(7.24111 - 2.84193i) q^{34} +(3.59346 + 4.50605i) q^{35} +(-3.43990 - 9.83068i) q^{37} +(8.81549 - 6.01030i) q^{38} +(-4.48308 + 0.848244i) q^{40} +(-3.98133 - 1.06680i) q^{41} +(-4.24116 + 5.74657i) q^{43} +(-12.2865 - 1.38436i) q^{44} +(-2.11035 + 2.11035i) q^{46} +(-1.51336 - 1.75856i) q^{47} +(0.431424 + 5.75696i) q^{49} +(-3.58148 + 4.16176i) q^{50} +(12.2174 - 1.84148i) q^{52} +(1.15186 + 0.918579i) q^{53} +(5.21652 - 3.27776i) q^{55} +(-9.26808 - 4.04362i) q^{56} +(-3.71740 + 11.7489i) q^{58} +(-10.0209 + 5.78554i) q^{59} +(1.11550 - 0.0417389i) q^{61} +(-3.56935 - 15.6384i) q^{62} +(-10.1198 + 8.07029i) q^{64} +(-4.18743 + 4.51298i) q^{65} +(1.39074 - 0.104222i) q^{67} +(0.411368 - 10.9940i) q^{68} +(12.7392 - 3.41347i) q^{70} +(-11.9049 + 5.73310i) q^{71} +(0.714449 - 6.34091i) q^{73} +(-23.7665 - 1.78106i) q^{74} +(-2.80540 - 14.8269i) q^{76} +(13.6442 + 0.510531i) q^{77} +(-1.64882 + 8.71422i) q^{79} +(-0.000550502 + 0.00241191i) q^{80} +(-5.88073 + 7.37420i) q^{82} +(2.03244 - 6.58902i) q^{83} +(3.25527 + 4.41074i) q^{85} +(8.17178 + 14.1539i) q^{86} +(-5.40448 + 9.36083i) q^{88} +(2.47228 - 0.278559i) q^{89} +(-13.3019 + 3.03608i) q^{91} +(1.54211 + 3.92923i) q^{92} +(-5.07324 + 1.56489i) q^{94} +(5.69917 + 4.90454i) q^{95} +(-2.31387 - 4.37806i) q^{97} +(12.4694 + 4.36322i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) $ 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.915081	−	2.09739i	0.647060	−	1.48308i	−0.215178	−	0.976575i	$-0.569033\pi$
$2$	0.915081	−	2.09739i	0.647060	−	1.48308i	0.862238	−	0.506503i	$-0.169062\pi$
$3$		0			0
$3$		0			0
$4$	−2.20132	−	2.37246i	−1.10066	−	1.18623i
$5$	1.59462	+	0.240350i	0.713135	+	0.107488i	0.495583	−	0.868561i	$-0.334955\pi$
$5$	1.59462	+	0.240350i	0.713135	+	0.107488i	0.217552	+	0.976049i	$0.430193\pi$
$6$		0			0
$7$	2.61989	+	2.43090i	0.990225	+	0.918794i	0.996699	−	0.0811846i	$-0.0258703\pi$
$7$	2.61989	+	2.43090i	0.990225	+	0.918794i	−0.00647413	+	0.999979i	$0.502061\pi$
$8$	−2.67053	+	0.934460i	−0.944176	+	0.330382i
$9$		0			0
$10$	1.96331	−	3.12459i	0.620854	−	0.988083i
$11$	2.89572	−	2.49197i	0.873094	−	0.751358i	−0.0966925	−	0.995314i	$-0.530826\pi$
$11$	2.89572	−	2.49197i	0.873094	−	0.751358i	0.969786	+	0.243956i	$0.0784454\pi$
$12$		0			0
$13$	−2.15055	+	3.15427i	−0.596454	+	0.874838i	−0.999180	−	0.0404830i	$-0.987110\pi$
$13$	−2.15055	+	3.15427i	−0.596454	+	0.874838i	0.402726	+	0.915321i	$0.368063\pi$
$14$	7.49596	−	3.27045i	2.00338	−	0.874065i
$15$		0			0
$16$	−0.000114643		0.00152981i	−2.86608e−5		0.000382452i
$17$	2.40371	+	2.40371i	0.582986	+	0.582986i	0.935723	−	0.352737i	$-0.114749\pi$
$17$	2.40371	+	2.40371i	0.582986	+	0.582986i	−0.352737	+	0.935723i	$0.614749\pi$
$18$		0			0
$19$	3.94790	+	2.48063i	0.905711	+	0.569096i	0.902400	−	0.430899i	$-0.141803\pi$
$19$	3.94790	+	2.48063i	0.905711	+	0.569096i	0.00331029	+	0.999995i	$0.498946\pi$
$20$	−2.94004	−	4.31225i	−0.657413	−	0.964248i
$21$		0			0
$22$	−2.57681	−	8.35381i	−0.549378	−	1.78104i
$23$	−1.21407	−	0.476487i	−0.253151	−	0.0993544i	0.235372	−	0.971905i	$-0.424369\pi$
$23$	−1.21407	−	0.476487i	−0.253151	−	0.0993544i	−0.488523	+	0.872551i	$0.662464\pi$
$24$		0			0
$25$	−2.29282	−	0.707243i	−0.458565	−	0.141449i
$26$	4.64781	+	7.39694i	0.911510	+	1.45066i
$27$		0			0
$28$		−	11.5668i		−	2.18591i
$29$	−5.35553	+	0.564198i	−0.994497	+	0.104769i
$29$	−5.35553	+	0.564198i	−0.994497	+	0.104769i
$30$		0			0
$31$	5.64002	−	4.16253i	1.01298	−	0.747612i	0.0450870	−	0.998983i	$-0.485643\pi$
$31$	5.64002	−	4.16253i	1.01298	−	0.747612i	0.967891	+	0.251371i	$0.0808816\pi$
$32$	−4.99976	−	2.64245i	−0.883841	−	0.467124i
$33$		0			0
$34$	7.24111	−	2.84193i	1.24184	−	0.487387i
$35$	3.59346	+	4.50605i	0.607405	+	0.761662i
$36$		0			0
$37$	−3.43990	−	9.83068i	−0.565517	−	1.61615i	−0.770537	−	0.637396i	$-0.780012\pi$
$37$	−3.43990	−	9.83068i	−0.565517	−	1.61615i	0.205020	−	0.978758i	$-0.434274\pi$
$38$	8.81549	−	6.01030i	1.43006	−	0.975000i
$39$		0			0
$40$	−4.48308	+	0.848244i	−0.708837	+	0.134119i
$41$	−3.98133	−	1.06680i	−0.621780	−	0.166605i	−0.0658431	−	0.997830i	$-0.520974\pi$
$41$	−3.98133	−	1.06680i	−0.621780	−	0.166605i	−0.555937	+	0.831225i	$0.687640\pi$
$42$		0			0
$43$	−4.24116	+	5.74657i	−0.646771	+	0.876343i	−0.998206	−	0.0598687i	$-0.980932\pi$
$43$	−4.24116	+	5.74657i	−0.646771	+	0.876343i	0.351435	+	0.936212i	$0.385694\pi$
$44$	−12.2865	−	1.38436i	−1.85226	−	0.208700i
$45$		0			0
$46$	−2.11035	+	2.11035i	−0.311154	+	0.311154i
$47$	−1.51336	−	1.75856i	−0.220747	−	0.256513i	0.636668	−	0.771138i	$-0.280312\pi$
$47$	−1.51336	−	1.75856i	−0.220747	−	0.256513i	−0.857415	+	0.514625i	$0.827931\pi$
$48$		0			0
$49$	0.431424	+	5.75696i	0.0616321	+	0.822423i
$50$	−3.58148	+	4.16176i	−0.506498	+	0.588562i
$51$		0			0
$52$	12.2174	−	1.84148i	1.69425	−	0.255367i
$53$	1.15186	+	0.918579i	0.158220	+	0.126177i	0.699400	−	0.714730i	$-0.253451\pi$
$53$	1.15186	+	0.918579i	0.158220	+	0.126177i	−0.541180	+	0.840907i	$0.682022\pi$
$54$		0			0
$55$	5.21652	−	3.27776i	0.703395	−	0.441973i
$56$	−9.26808	−	4.04362i	−1.23850	−	0.540352i
$57$		0			0
$58$	−3.71740	+	11.7489i	−0.488119	+	1.54271i
$59$	−10.0209	+	5.78554i	−1.30460	+	0.753214i	−0.981190	−	0.193044i	$-0.938164\pi$
$59$	−10.0209	+	5.78554i	−1.30460	+	0.753214i	−0.323414	+	0.946257i	$0.604831\pi$
$60$		0			0
$61$	1.11550	−	0.0417389i	0.142825	−	0.00534412i	0.0341167	−	0.999418i	$-0.489138\pi$
$61$	1.11550	−	0.0417389i	0.142825	−	0.00534412i	0.108708	+	0.994074i	$0.465329\pi$
$62$	−3.56935	−	15.6384i	−0.453308	−	1.98607i
$63$		0			0
$64$	−10.1198	+	8.07029i	−1.26498	+	1.00879i
$65$	−4.18743	+	4.51298i	−0.519387	+	0.559766i
$66$		0			0
$67$	1.39074	−	0.104222i	0.169907	−	0.0127327i	0.0104948	−	0.999945i	$-0.496659\pi$
$67$	1.39074	−	0.104222i	0.169907	−	0.0127327i	0.159412	+	0.987212i	$0.449040\pi$
$68$	0.411368	−	10.9940i	0.0498857	−	1.33322i
$69$		0			0
$70$	12.7392	−	3.41347i	1.52263	−	0.407988i
$71$	−11.9049	+	5.73310i	−1.41285	+	0.680394i	−0.975724	−	0.219005i	$-0.929719\pi$
$71$	−11.9049	+	5.73310i	−1.41285	+	0.680394i	−0.437129	+	0.899399i	$0.644005\pi$
$72$		0			0
$73$	0.714449	−	6.34091i	0.0836199	−	0.742147i	−0.880019	−	0.474939i	$-0.842470\pi$
$73$	0.714449	−	6.34091i	0.0836199	−	0.742147i	0.963639	−	0.267208i	$-0.0861012\pi$
$74$	−23.7665	−	1.78106i	−2.76280	−	0.207044i
$75$		0			0
$76$	−2.80540	−	14.8269i	−0.321801	−	1.70076i
$77$	13.6442	+	0.510531i	1.55490	+	0.0581804i
$78$		0			0
$79$	−1.64882	+	8.71422i	−0.185507	+	0.980426i	0.758791	+	0.651334i	$0.225790\pi$
$79$	−1.64882	+	8.71422i	−0.185507	+	0.980426i	−0.944298	+	0.329092i	$0.893257\pi$
$80$	−0.000550502		0.00241191i	−6.15480e−5		0.000269659i
$81$		0			0
$82$	−5.88073	+	7.37420i	−0.649418	+	0.814344i
$83$	2.03244	−	6.58902i	0.223090	−	0.723239i	−0.772961	−	0.634453i	$-0.781225\pi$
$83$	2.03244	−	6.58902i	0.223090	−	0.723239i	0.996051	−	0.0887853i	$-0.0282985\pi$
$84$		0			0
$85$	3.25527	+	4.41074i	0.353084	+	0.478412i
$86$	8.17178	+	14.1539i	0.881186	+	1.52626i
$87$		0			0
$88$	−5.40448	+	9.36083i	−0.576119	+	0.997868i
$89$	2.47228	−	0.278559i	0.262061	−	0.0295272i	0.0200435	−	0.999799i	$-0.493620\pi$
$89$	2.47228	−	0.278559i	0.262061	−	0.0295272i	0.242017	+	0.970272i	$0.422191\pi$
$90$		0			0
$91$	−13.3019	+	3.03608i	−1.39442	+	0.318267i
$92$	1.54211	+	3.92923i	0.160776	+	0.409650i
$93$		0			0
$94$	−5.07324	+	1.56489i	−0.523265	+	0.161406i
$95$	5.69917	+	4.90454i	0.584723	+	0.503195i
$96$		0			0
$97$	−2.31387	−	4.37806i	−0.234938	−	0.444525i	0.738252	−	0.674525i	$-0.235651\pi$
$97$	−2.31387	−	4.37806i	−0.234938	−	0.444525i	−0.973191	+	0.230000i	$0.926128\pi$
$98$	12.4694	+	4.36322i	1.25960	+	0.440752i
$99$		0			0
$100$	3.36933	+	6.99650i	0.336933	+	0.699650i
$101$	13.8186	+	10.1986i	1.37500	+	1.01479i	0.995996	+	0.0893988i	$0.0284946\pi$
$101$	13.8186	+	10.1986i	1.37500	+	1.01479i	0.379002	+	0.925396i	$0.376267\pi$
$102$		0			0
$103$	−1.09753	−	0.748281i	−0.108143	−	0.0737303i	0.508041	−	0.861333i	$-0.330370\pi$
$103$	−1.09753	−	0.748281i	−0.108143	−	0.0737303i	−0.616184	+	0.787602i	$0.711322\pi$
$104$	2.79556	−	10.4332i	0.274128	−	1.02306i
$105$		0			0
$106$	2.98066	−	1.57533i	0.289508	−	0.153009i
$107$	5.72054	−	11.8788i	0.553025	−	1.14837i	−0.417791	−	0.908543i	$-0.637196\pi$
$107$	5.72054	−	11.8788i	0.553025	−	1.14837i	0.970816	−	0.239825i	$-0.0770901\pi$
$108$		0			0
$109$	16.9223	+	3.86241i	1.62087	+	0.369952i	0.934124	−	0.356950i	$-0.116183\pi$
$109$	16.9223	+	3.86241i	1.62087	+	0.369952i	0.686742	+	0.726902i	$0.259040\pi$
$110$	−2.10119	−	13.9405i	−0.200341	−	1.32917i
$111$		0			0
$112$	−0.00401917	+	0.00372924i	−0.000379776	+	0.000352380i
$113$	−1.18842	+	2.24860i	−0.111797	+	0.211531i	−0.933665	−	0.358148i	$-0.883408\pi$
$113$	−1.18842	+	2.24860i	−0.111797	+	0.211531i	0.821868	+	0.569679i	$0.192932\pi$
$114$		0			0
$115$	−1.82145	−	1.05162i	−0.169851	−	0.0980637i
$116$	13.1278	+	11.4638i	1.21888	+	1.06439i
$117$		0			0
$118$	2.96464	+	26.3119i	0.272917	+	2.42220i
$119$	0.454271	+	12.1407i	0.0416430	+	1.11293i
$120$		0			0
$121$	0.535828	−	3.55499i	0.0487117	−	0.323181i
$122$	0.933226	−	2.37782i	0.0844903	−	0.215278i
$123$		0			0
$124$	−22.2909	−	4.21766i	−2.00178	−	0.378757i
$125$	−10.7508	−	5.17733i	−0.961584	−	0.463075i
$126$		0			0
$127$	5.05009	−	14.4323i	0.448123	−	1.28066i	−0.469403	−	0.882984i	$-0.655531\pi$
$127$	5.05009	−	14.4323i	0.448123	−	1.28066i	0.917525	−	0.397677i	$-0.130184\pi$
$128$	4.73878	+	17.6854i	0.418853	+	1.56318i
$129$		0			0
$130$	5.63362	+	12.9124i	0.494102	+	1.13249i
$131$	3.80156	+	8.71328i	0.332144	+	0.761282i	0.999858	+	0.0168642i	$0.00536831\pi$
$131$	3.80156	+	8.71328i	0.332144	+	0.761282i	−0.667714	+	0.744418i	$0.732727\pi$
$132$		0			0
$133$	4.31289	+	16.0959i	0.373975	+	1.39569i
$134$	1.05405	−	3.01230i	0.0910561	−	0.260223i
$135$		0			0
$136$	−8.66537	−	4.17302i	−0.743050	−	0.357834i
$137$	4.11753	+	0.779079i	0.351785	+	0.0665612i	0.358801	−	0.933414i	$-0.383186\pi$
$137$	4.11753	+	0.779079i	0.351785	+	0.0665612i	−0.00701627	+	0.999975i	$0.502233\pi$
$138$		0			0
$139$	0.236037	−	0.601414i	0.0200204	−	0.0510112i	−0.920514	−	0.390709i	$-0.872230\pi$
$139$	0.236037	−	0.601414i	0.0200204	−	0.0510112i	0.940534	+	0.339698i	$0.110325\pi$
$140$	2.78007	−	18.4446i	0.234959	−	1.55885i
$141$		0			0
$142$	1.13058	+	30.2155i	0.0948764	+	2.53563i
$143$	1.63297	+	14.4930i	0.136556	+	1.21197i
$144$		0			0
$145$	−8.67563	−	0.387520i	−0.720472	−	0.0321818i
$146$	−12.6456	−	7.30092i	−1.04655	−	0.604229i
$147$		0			0
$148$	−15.7505	+	29.8015i	−1.29469	+	2.44967i
$149$	1.90475	−	1.76735i	0.156043	−	0.144787i	−0.598288	−	0.801281i	$-0.704152\pi$
$149$	1.90475	−	1.76735i	0.156043	−	0.144787i	0.754331	+	0.656495i	$0.227962\pi$
$150$		0			0
$151$	−3.24963	−	21.5599i	−0.264451	−	1.75452i	−0.588516	−	0.808485i	$-0.700288\pi$
$151$	−3.24963	−	21.5599i	−0.264451	−	1.75452i	0.324065	−	0.946035i	$-0.394950\pi$
$152$	−12.8611	−	2.93545i	−1.04317	−	0.238097i
$153$		0			0
$154$	13.5563	−	28.1500i	1.09240	−	2.26839i
$155$	9.99414	−	5.28206i	0.802749	−	0.424265i
$156$		0			0
$157$	1.43522	−	5.35630i	0.114543	−	0.427479i	−0.884710	−	0.466143i	$-0.845643\pi$
$157$	1.43522	−	5.35630i	0.114543	−	0.427479i	0.999252	+	0.0386635i	$0.0123100\pi$
$158$	16.7683	+	11.4324i	1.33401	+	0.909515i
$159$		0			0
$160$	−7.33760	−	5.41539i	−0.580088	−	0.428124i
$161$	−2.02243	−	4.19962i	−0.159390	−	0.330977i
$162$		0			0
$163$	−22.9167	−	8.01891i	−1.79498	−	0.628090i	−0.999763	−	0.0217608i	$-0.993073\pi$
$163$	−22.9167	−	8.01891i	−1.79498	−	0.628090i	−0.795214	−	0.606329i	$-0.792642\pi$
$164$	6.23326	+	11.7939i	0.486736	+	0.920949i
$165$		0			0
$166$	−11.9599	−	10.2923i	−0.928267	−	0.798838i
$167$	−12.7167	+	3.92259i	−0.984051	+	0.303539i	−0.744704	−	0.667395i	$-0.767409\pi$
$167$	−12.7167	+	3.92259i	−0.984051	+	0.303539i	−0.239347	+	0.970934i	$0.576933\pi$
$168$		0			0
$169$	−0.575149	−	1.46546i	−0.0442422	−	0.112727i
$170$	12.2299	−	2.79139i	0.937988	−	0.214090i
$171$		0			0
$172$	22.9696	−	2.58806i	1.75142	−	0.197337i
$173$	−2.97576	+	5.15417i	−0.226243	+	0.391864i	−0.956692	−	0.291103i	$-0.905978\pi$
$173$	−2.97576	+	5.15417i	−0.226243	+	0.391864i	0.730449	+	0.682968i	$0.239311\pi$
$174$		0			0
$175$	−4.28771	−	7.42653i	−0.324120	−	0.561393i
$176$	0.00348027	+	0.00471559i	0.000262335	+	0.000355451i
$177$		0			0
$178$	1.67809	−	5.44023i	0.125778	−	0.407762i
$179$	−7.03123	+	8.81689i	−0.525539	+	0.659005i	−0.971775	−	0.235910i	$-0.924193\pi$
$179$	−7.03123	+	8.81689i	−0.525539	+	0.659005i	0.446236	+	0.894915i	$0.352764\pi$
$180$		0			0
$181$	−4.45707	+	19.5277i	−0.331292	+	1.45148i	0.485340	+	0.874325i	$0.338696\pi$
$181$	−4.45707	+	19.5277i	−0.331292	+	1.45148i	−0.816632	+	0.577159i	$0.804161\pi$
$182$	−5.80450	+	30.6775i	−0.430258	+	2.27397i
$183$		0			0
$184$	3.68747	+	0.137975i	0.271844	+	0.0101717i
$185$	−3.12253	−	16.5030i	−0.229573	−	1.21332i
$186$		0			0
$187$	12.9505	+	0.970504i	0.947033	+	0.0709703i
$188$	−0.840714	+	7.46155i	−0.0613154	+	0.544189i
$189$		0			0
$190$	15.5019	−	7.46533i	1.12463	−	0.541592i
$191$	10.6084	−	2.84252i	0.767599	−	0.205677i	0.146288	−	0.989242i	$-0.453267\pi$
$191$	10.6084	−	2.84252i	0.767599	−	0.205677i	0.621310	+	0.783565i	$0.286601\pi$
$192$		0			0
$193$	−0.756010	+	20.2048i	−0.0544188	+	1.45437i	0.658211	+	0.752833i	$0.271313\pi$
$193$	−0.756010	+	20.2048i	−0.0544188	+	1.45437i	−0.712630	+	0.701540i	$0.752496\pi$
$194$	−11.2999	+	0.846809i	−0.811284	+	0.0607973i
$195$		0			0
$196$	12.7084	−	13.6964i	0.907745	−	0.978317i
$197$	2.05623	−	1.63979i	0.146501	−	0.116830i	−0.547497	−	0.836808i	$-0.684419\pi$
$197$	2.05623	−	1.63979i	0.146501	−	0.116830i	0.693998	+	0.719977i	$0.255848\pi$
$198$		0			0
$199$	−3.59164	−	15.7360i	−0.254605	−	1.11550i	−0.926928	−	0.375239i	$-0.877561\pi$
$199$	−3.59164	−	15.7360i	−0.254605	−	1.11550i	0.672324	−	0.740257i	$-0.265296\pi$
$200$	6.78396	−	0.253838i	0.479698	−	0.0179490i
$201$		0			0
$202$	34.0354	−	19.6504i	2.39473	−	1.38260i
$203$	−15.4024	−	11.5406i	−1.08104	−	0.809993i
$204$		0			0
$205$	−6.09230	−	2.65805i	−0.425505	−	0.185646i
$206$	−2.57376	+	1.61720i	−0.179323	+	0.112676i
$207$		0			0
$208$	−0.00457889	−	0.00365154i	−0.000317489	−	0.000253189i
$209$	17.6137	−	2.65484i	1.21836	−	0.183639i
$210$		0			0
$211$	−9.07273	+	10.5427i	−0.624592	+	0.725789i	−0.977750	−	0.209775i	$-0.932727\pi$
$211$	−9.07273	+	10.5427i	−0.624592	+	0.725789i	0.353158	+	0.935564i	$0.385108\pi$
$212$	−0.356325	−	4.75483i	−0.0244725	−	0.326563i
$213$		0			0
$214$	−19.6797	−	22.8683i	−1.34528	−	1.56324i
$215$	−8.14422	+	8.14422i	−0.555431	+	0.555431i
$216$		0			0
$217$	24.8949	+	2.80498i	1.68998	+	0.190415i
$218$	23.5863	−	31.9583i	1.59746	−	2.16449i
$219$		0			0
$220$	−19.2596	−	5.16058i	−1.29848	−	0.347926i
$221$	−12.7513	+	2.41267i	−0.857743	+	0.162294i
$222$		0			0
$223$	−15.3217	+	10.4462i	−1.02602	+	0.699527i	−0.954591	−	0.297919i	$-0.903707\pi$
$223$	−15.3217	+	10.4462i	−1.02602	+	0.699527i	−0.0714264	+	0.997446i	$0.522755\pi$
$224$	−6.67528	−	19.0769i	−0.446011	−	1.27463i
$225$		0			0
$226$	3.62869	+	4.55024i	0.241377	+	0.302677i
$227$	9.52049	−	3.73652i	0.631897	−	0.248001i	−0.0277052	−	0.999616i	$-0.508820\pi$
$227$	9.52049	−	3.73652i	0.631897	−	0.248001i	0.659602	+	0.751615i	$0.270725\pi$
$228$		0			0
$229$	−6.98872	−	3.69364i	−0.461827	−	0.244083i	0.220136	−	0.975469i	$-0.429350\pi$
$229$	−6.98872	−	3.69364i	−0.461827	−	0.244083i	−0.681963	+	0.731386i	$0.738874\pi$
$230$	−3.87242	+	2.85798i	−0.255340	+	0.188450i
$231$		0			0
$232$	13.7749	−	6.51124i	0.904366	−	0.427484i
$233$		−	8.13511i		−	0.532949i	−0.963842	−	0.266474i	$-0.914141\pi$
$233$		−	8.13511i		−	0.532949i	0.963842	−	0.266474i	$-0.0858588\pi$
$234$		0			0
$235$	−1.99057	−	3.16797i	−0.129850	−	0.206656i
$236$	35.7851	+	11.0382i	2.32941	+	0.718527i
$237$		0			0
$238$	25.8794	+	10.1569i	1.67751	+	0.658374i
$239$	6.58210	+	21.3386i	0.425760	+	1.38028i	0.873808	+	0.486272i	$0.161643\pi$
$239$	6.58210	+	21.3386i	0.425760	+	1.38028i	−0.448047	+	0.894010i	$0.647880\pi$
$240$		0			0
$241$	11.8380	+	17.3632i	0.762554	+	1.11846i	0.989497	+	0.144554i	$0.0461746\pi$
$241$	11.8380	+	17.3632i	0.762554	+	1.11846i	−0.226943	+	0.973908i	$0.572873\pi$
$242$	−6.96586	−	4.37694i	−0.447783	−	0.281361i
$243$		0			0
$244$	−2.55458	−	2.55458i	−0.163541	−	0.163541i
$245$	−0.695728	+	9.28384i	−0.0444484	+	0.593123i
$246$		0			0
$247$	−16.3147	+	7.11804i	−1.03808	+	0.452910i
$248$	−11.1722	+	16.3865i	−0.709432	+	1.04055i
$249$		0			0
$250$	−20.6968	+	17.8110i	−1.30898	+	1.12647i
$251$	16.1458	−	25.6958i	1.01911	−	1.62191i	0.266046	−	0.963960i	$-0.414283\pi$
$251$	16.1458	−	25.6958i	1.01911	−	1.62191i	0.753066	−	0.657946i	$-0.228574\pi$
$252$		0			0
$253$	−4.70300	+	1.64565i	−0.295675	+	0.103461i
$254$	−25.6489	−	23.7987i	−1.60936	−	1.49327i
$255$		0			0
$256$	15.8311	+	2.38616i	0.989444	+	0.149135i
$257$	−1.98731	−	2.14181i	−0.123965	−	0.133602i	0.668019	−	0.744144i	$-0.267142\pi$
$257$	−1.98731	−	2.14181i	−0.123965	−	0.133602i	−0.791984	+	0.610542i	$0.790952\pi$
$258$		0			0
$259$	14.8852	−	34.1174i	0.924924	−	2.11995i
$260$	19.9247			1.23568
$261$		0			0
$262$	21.7539			1.34396
$263$	−12.9044	+	29.5773i	−0.795722	+	1.82381i	−0.305603	+	0.952159i	$0.598858\pi$
$263$	−12.9044	+	29.5773i	−0.795722	+	1.82381i	−0.490119	+	0.871655i	$0.663047\pi$
$264$		0			0
$265$	1.61600	+	1.74163i	0.0992701	+	0.106988i
$266$	37.7061	+	5.68328i	2.31191	+	0.348464i
$267$		0			0
$268$	−3.30873	−	3.07006i	−0.202113	−	0.187534i
$269$	21.1046	−	7.38481i	1.28677	−	0.450260i	0.401721	−	0.915762i	$-0.368412\pi$
$269$	21.1046	−	7.38481i	1.28677	−	0.450260i	0.885047	+	0.465503i	$0.154126\pi$
$270$		0			0
$271$	−13.1889	+	20.9901i	−0.801170	+	1.27505i	0.156641	+	0.987656i	$0.449934\pi$
$271$	−13.1889	+	20.9901i	−0.801170	+	1.27505i	−0.957811	+	0.287399i	$0.907209\pi$
$272$	−0.00395279	+	0.00340165i	−0.000239673	+	0.000206256i
$273$		0			0
$274$	5.40191	−	7.92314i	0.326341	−	0.478655i
$275$	−8.40182	+	3.66568i	−0.506649	+	0.221049i
$276$		0			0
$277$	−1.60047	+	21.3568i	−0.0961632	+	1.28321i	0.715305	+	0.698812i	$0.246288\pi$
$277$	−1.60047	+	21.3568i	−0.0961632	+	1.28321i	−0.811468	+	0.584396i	$0.801331\pi$
$278$	−1.04540	−	1.04540i	−0.0626992	−	0.0626992i
$279$		0			0
$280$	−13.8072	−	8.67562i	−0.825136	−	0.518467i
$281$	4.70631	+	6.90289i	0.280755	+	0.411792i	0.940551	−	0.339653i	$-0.110310\pi$
$281$	4.70631	+	6.90289i	0.280755	+	0.411792i	−0.659796	+	0.751445i	$0.729357\pi$
$282$		0			0
$283$	−0.880025	−	2.85297i	−0.0523121	−	0.169592i	0.925647	−	0.378388i	$-0.123522\pi$
$283$	−0.880025	−	2.85297i	−0.0523121	−	0.169592i	−0.977959	+	0.208797i	$0.933045\pi$
$284$	39.8080	+	15.6235i	2.36217	+	0.927084i
$285$		0			0
$286$	31.8918	+	9.83730i	1.88580	+	0.581692i
$287$	−7.83738	−	12.4731i	−0.462626	−	0.736265i
$288$		0			0
$289$		−	5.44432i		−	0.320254i
$290$	−8.75168	+	17.8415i	−0.513917	+	1.04769i
$291$		0			0
$292$	−16.6163	+	12.2634i	−0.972393	+	0.717659i
$293$	3.40982	+	1.80214i	0.199204	+	0.105282i	0.563896	−	0.825846i	$-0.309302\pi$
$293$	3.40982	+	1.80214i	0.199204	+	0.105282i	−0.364692	+	0.931128i	$0.618826\pi$
$294$		0			0
$295$	−17.3700	+	6.81722i	−1.01132	+	0.396914i
$296$	18.3728	+	23.0387i	1.06789	+	1.33910i
$297$		0			0
$298$	−1.96382	−	5.61226i	−0.113761	−	0.325110i
$299$	4.11388	−	2.80480i	0.237912	−	0.162206i
$300$		0			0
$301$	−25.0807	+	4.74553i	−1.44563	+	0.273528i
$302$	−48.1932	−	12.9133i	−2.77321	−	0.743078i
$303$		0			0
$304$	−0.00424749	+	0.00575515i	−0.000243610	+	0.000330080i
$305$	1.78882	+	0.201552i	0.102428	+	0.0115408i
$306$		0			0
$307$	−7.57437	+	7.57437i	−0.432292	+	0.432292i	−0.889407	−	0.457115i	$-0.848883\pi$
$307$	−7.57437	+	7.57437i	−0.432292	+	0.432292i	0.457115	+	0.889407i	$0.348883\pi$
$308$	−28.8241	−	33.4942i	−1.64240	−	1.90851i
$309$		0			0
$310$	−1.93308	−	25.7951i	−0.109791	−	1.46506i
$311$	−17.2932	+	20.0951i	−0.980609	+	1.13949i	0.00960794	+	0.999954i	$0.496942\pi$
$311$	−17.2932	+	20.0951i	−0.980609	+	1.13949i	−0.990217	+	0.139535i	$0.955439\pi$
$312$		0			0
$313$	4.70733	−	0.709516i	0.266074	−	0.0401042i	−0.0146501	−	0.999893i	$-0.504663\pi$
$313$	4.70733	−	0.709516i	0.266074	−	0.0401042i	0.280724	+	0.959788i	$0.409425\pi$
$314$	−9.92090	−	7.91165i	−0.559869	−	0.446480i
$315$		0			0
$316$	24.3037	−	15.2710i	1.36719	−	0.859062i
$317$	−5.82311	−	2.54060i	−0.327059	−	0.142694i	0.229946	−	0.973203i	$-0.426145\pi$
$317$	−5.82311	−	2.54060i	−0.327059	−	0.142694i	−0.557005	+	0.830509i	$0.688050\pi$
$318$		0			0
$319$	−14.1022	+	14.9796i	−0.789570	+	0.838696i
$320$	−18.0770	+	10.4367i	−1.01053	+	0.583431i
$321$		0			0
$322$	−10.6589	+	0.398829i	−0.593999	+	0.0222259i
$323$	3.52690	+	15.4523i	0.196242	+	0.859792i
$324$		0			0
$325$	7.16166	−	5.71123i	0.397258	−	0.316802i
$326$	−37.7894	+	40.7273i	−2.09296	+	2.25568i
$327$		0			0
$328$	11.6292	−	0.871485i	0.642113	−	0.0481197i
$329$	0.310043	−	8.28608i	0.0170932	−	0.456826i
$330$		0			0
$331$	12.1289	−	3.24993i	0.666666	−	0.178633i	0.0904133	−	0.995904i	$-0.471181\pi$
$331$	12.1289	−	3.24993i	0.666666	−	0.178633i	0.576252	+	0.817272i	$0.304515\pi$
$332$	−20.1062	+	9.68264i	−1.10347	+	0.531404i
$333$		0			0
$334$	−3.40964	+	30.2614i	−0.186567	+	1.65583i
$335$	2.24276	+	0.168071i	0.122535	+	0.00918272i
$336$		0			0
$337$	−3.80404	−	20.1048i	−0.207219	−	1.09518i	−0.919442	−	0.393226i	$-0.871359\pi$
$337$	−3.80404	−	20.1048i	−0.207219	−	1.09518i	0.712223	−	0.701953i	$-0.247688\pi$
$338$	−3.59994	−	0.134700i	−0.195811	−	0.00732672i
$339$		0			0
$340$	3.29839	−	17.4324i	0.178881	−	0.945407i
$341$	5.95905	−	26.1083i	0.322701	−	1.41384i
$342$		0			0
$343$	2.73392	−	3.42823i	0.147618	−	0.185107i
$344$	5.95622	−	19.3096i	0.321138	−	1.04110i
$345$		0			0
$346$	8.08724	+	10.9578i	0.434773	+	0.589096i
$347$	−8.09092	−	14.0139i	−0.434343	−	0.752305i	0.562899	−	0.826526i	$-0.309686\pi$
$347$	−8.09092	−	14.0139i	−0.434343	−	0.752305i	−0.997242	+	0.0742214i	$0.976353\pi$
$348$		0			0
$349$	3.65666	−	6.33352i	0.195736	−	0.339025i	−0.751405	−	0.659841i	$-0.770624\pi$
$349$	3.65666	−	6.33352i	0.195736	−	0.339025i	0.947142	+	0.320816i	$0.103957\pi$
$350$	−19.4999	+	2.19711i	−1.04231	+	0.117441i
$351$		0			0
$352$	−21.0628	+	4.80746i	−1.12265	+	0.256238i
$353$	−5.06632	−	12.9088i	−0.269653	−	0.687064i	−0.999992	−	0.00397948i	$-0.998733\pi$
$353$	−5.06632	−	12.9088i	−0.269653	−	0.687064i	0.730339	−	0.683085i	$-0.239362\pi$
$354$		0			0
$355$	−20.3617	+	6.28076i	−1.08069	+	0.333348i
$356$	−6.10313	−	5.25217i	−0.323465	−	0.278365i
$357$		0			0
$358$	12.0583	+	22.8154i	0.637300	+	1.20583i
$359$	−19.7861	−	6.92347i	−1.04427	−	0.365407i	−0.246993	−	0.969017i	$-0.579443\pi$
$359$	−19.7861	−	6.92347i	−1.04427	−	0.365407i	−0.797279	+	0.603610i	$0.793728\pi$
$360$		0			0
$361$	1.18860	+	2.46816i	0.0625579	+	0.129903i
$362$	36.8786	+	27.2177i	1.93830	+	1.43053i
$363$		0			0
$364$	36.4847	+	24.8749i	1.91232	+	1.30380i
$365$	2.66331	−	9.93961i	0.139404	−	0.520263i
$366$		0			0
$367$	−7.65862	+	4.04770i	−0.399777	+	0.211288i	−0.655058	−	0.755579i	$-0.727356\pi$
$367$	−7.65862	+	4.04770i	−0.399777	+	0.211288i	0.255281	+	0.966867i	$0.417832\pi$
$368$	0.000868119	−	0.00180267i	4.52538e−5	−	9.39705e-5i
$369$		0			0
$370$	−37.4705	−	8.55239i	−1.94800	−	0.444618i
$371$	0.784775	+	5.20664i	0.0407435	+	0.270315i
$372$		0			0
$373$	23.1266	−	21.4584i	1.19745	−	1.11107i	0.206278	−	0.978493i	$-0.433865\pi$
$373$	23.1266	−	21.4584i	1.19745	−	1.11107i	0.991173	−	0.132578i	$-0.0423255\pi$
$374$	13.8863	−	26.2741i	0.718042	−	1.35860i
$375$		0			0
$376$	5.68480	+	3.28212i	0.293171	+	0.169262i
$377$	9.73768	−	18.1061i	0.501516	−	0.932513i
$378$		0			0
$379$	−2.09845	−	18.6243i	−0.107790	−	0.956666i	−0.924907	−	0.380194i	$-0.875857\pi$
$379$	−2.09845	−	18.6243i	−0.107790	−	0.956666i	0.817117	−	0.576472i	$-0.195571\pi$
$380$	−0.909896	−	24.3175i	−0.0466767	−	1.24746i
$381$		0			0
$382$	3.74570	−	24.8511i	0.191647	−	1.27149i
$383$	8.76909	−	22.3433i	0.448080	−	1.14169i	−0.511258	−	0.859427i	$-0.670820\pi$
$383$	8.76909	−	22.3433i	0.448080	−	1.14169i	0.959338	−	0.282261i	$-0.0910845\pi$
$384$		0			0
$385$	21.6346	+	4.09349i	1.10260	+	0.208624i
$386$	41.6855	+	20.0747i	2.12174	+	1.02177i
$387$		0			0
$388$	−5.29319	+	15.1271i	−0.268721	+	0.767961i
$389$	5.77033	+	21.5352i	0.292567	+	1.09188i	0.943130	+	0.332424i	$0.107866\pi$
$389$	5.77033	+	21.5352i	0.292567	+	1.09188i	−0.650563	+	0.759452i	$0.725467\pi$
$390$		0			0
$391$	−1.77294	−	4.06361i	−0.0896612	−	0.205506i
$392$	−6.53178	−	14.9710i	−0.329905	−	0.756150i
$393$		0			0
$394$	−1.55766	−	5.81327i	−0.0784738	−	0.292868i
$395$	−4.72370	+	13.4996i	−0.237675	+	0.679236i
$396$		0			0
$397$	−2.98644	−	1.43819i	−0.149885	−	0.0721808i	0.357438	−	0.933937i	$-0.383650\pi$
$397$	−2.98644	−	1.43819i	−0.149885	−	0.0721808i	−0.507323	+	0.861756i	$0.669365\pi$
$398$	−36.2912	−	6.86666i	−1.81911	−	0.344194i
$399$		0			0
$400$	0.00134480	−	0.00342650i	6.72402e−5	−	0.000171325i
$401$	2.45064	−	16.2589i	0.122379	−	0.811931i	−0.840464	−	0.541868i	$-0.817717\pi$
$401$	2.45064	−	16.2589i	0.122379	−	0.811931i	0.962843	−	0.270063i	$-0.0870447\pi$
$402$		0			0
$403$	1.00061	+	26.7419i	0.0498439	+	1.33211i
$404$	−6.22340	−	55.2342i	−0.309626	−	2.74800i
$405$		0			0
$406$	−38.2996	+	21.7442i	−1.90078	+	1.07915i
$407$	−34.4588	−	19.8948i	−1.70806	−	0.986148i
$408$		0			0
$409$	−3.30015	+	6.24419i	−0.163182	+	0.308755i	−0.952124	−	0.305712i	$-0.901105\pi$
$409$	−3.30015	+	6.24419i	−0.163182	+	0.308755i	0.788942	+	0.614468i	$0.210629\pi$
$410$	−11.1499	+	10.3456i	−0.550655	+	0.510933i
$411$		0			0
$412$	0.640741	+	4.25104i	0.0315671	+	0.209434i
$413$	−40.3176	−	9.20223i	−1.98390	−	0.452812i
$414$		0			0
$415$	4.82464	−	10.0185i	0.236832	−	0.491787i
$416$	19.0872	−	10.0879i	0.935828	−	0.494600i
$417$		0			0
$418$	10.5497	−	39.3721i	0.516004	−	1.92575i
$419$	−6.38013	−	4.34990i	−0.311690	−	0.212506i	0.397364	−	0.917661i	$-0.369925\pi$
$419$	−6.38013	−	4.34990i	−0.311690	−	0.212506i	−0.709053	+	0.705155i	$0.750877\pi$
$420$		0			0
$421$	3.35566	+	2.47659i	0.163545	+	0.120702i	0.672518	−	0.740081i	$-0.265213\pi$
$421$	3.35566	+	2.47659i	0.163545	+	0.120702i	−0.508973	+	0.860783i	$0.669975\pi$
$422$	13.8099	+	28.6765i	0.672253	+	1.39595i
$423$		0			0
$424$	−3.93446	−	1.37673i	−0.191074	−	0.0668598i
$425$	−3.81129	−	7.21130i	−0.184874	−	0.349800i
$426$		0			0
$427$	3.02394	+	2.60231i	0.146339	+	0.125935i
$428$	−40.7747	+	12.5773i	−1.97092	+	0.607948i
$429$		0			0
$430$	9.62897	+	24.5342i	0.464350	+	1.18314i
$431$	4.50448	−	1.02812i	0.216973	−	0.0495227i	−0.112652	−	0.993634i	$-0.535935\pi$
$431$	4.50448	−	1.02812i	0.216973	−	0.0495227i	0.329626	+	0.944112i	$0.393078\pi$
$432$		0			0
$433$	−23.6255	+	2.66196i	−1.13537	+	0.127926i	−0.659581	−	0.751634i	$-0.729266\pi$
$433$	−23.6255	+	2.66196i	−1.13537	+	0.127926i	−0.475790	+	0.879559i	$0.657838\pi$
$434$	28.6640	−	49.6475i	1.37592	−	2.38316i
$435$		0			0
$436$	−28.0880	−	48.6499i	−1.34517	−	2.32991i
$437$	−3.61103	−	4.89278i	−0.172739	−	0.234053i
$438$		0			0
$439$	4.65426	−	15.0888i	0.222136	−	0.720147i	−0.774068	−	0.633102i	$-0.781781\pi$
$439$	4.65426	−	15.0888i	0.222136	−	0.720147i	0.996204	−	0.0870451i	$-0.0277424\pi$
$440$	−10.8680	+	13.6280i	−0.518110	+	0.649689i
$441$		0			0
$442$	−6.60814	+	28.9521i	−0.314317	+	1.37711i
$443$	−1.77046	+	9.35713i	−0.0841173	+	0.444571i	0.915034	+	0.403377i	$0.132164\pi$
$443$	−1.77046	+	9.35713i	−0.0841173	+	0.444571i	−0.999151	+	0.0411937i	$0.986884\pi$
$444$		0			0
$445$	4.00929	+	0.150017i	0.190058	+	0.00711149i
$446$	7.88906	+	41.6947i	0.373558	+	1.97430i
$447$		0			0
$448$	−46.1309	−	3.45703i	−2.17948	−	0.163330i
$449$	−0.582696	+	5.17157i	−0.0274991	+	0.244061i	0.972441	+	0.233148i	$0.0749026\pi$
$449$	−0.582696	+	5.17157i	−0.0274991	+	0.244061i	−0.999940	+	0.0109137i	$0.996526\pi$
$450$		0			0
$451$	−14.1873	+	6.83223i	−0.668052	+	0.321717i
$452$	7.95081	−	2.13041i	0.373975	−	0.100206i
$453$		0			0
$454$	0.875094	−	23.3874i	0.0410702	−	1.09762i
$455$	−21.9412	+	1.64427i	−1.02862	+	0.0770844i
$456$		0			0
$457$	−1.53515	+	1.65449i	−0.0718111	+	0.0773939i	−0.767935	−	0.640527i	$-0.778716\pi$
$457$	−1.53515	+	1.65449i	−0.0718111	+	0.0773939i	0.696124	+	0.717921i	$0.254906\pi$
$458$	−14.1422	+	11.2781i	−0.660824	+	0.526989i
$459$		0			0
$460$	1.51468	+	6.63626i	0.0706225	+	0.309417i
$461$	26.6785	−	0.998238i	1.24254	−	0.0464926i	0.591984	−	0.805950i	$-0.298345\pi$
$461$	26.6785	−	0.998238i	1.24254	−	0.0464926i	0.650557	+	0.759457i	$0.274535\pi$
$462$		0			0
$463$	−2.87207	+	1.65819i	−0.133476	+	0.0770625i	−0.565251	−	0.824919i	$-0.691221\pi$
$463$	−2.87207	+	1.65819i	−0.133476	+	0.0770625i	0.431775	+	0.901981i	$0.357887\pi$
$464$	−0.000249140	−	0.00825762i	−1.15660e−5	−	0.000383350i
$465$		0			0
$466$	−17.0625	−	7.44429i	−0.790404	−	0.344850i
$467$	−16.9709	+	10.6635i	−0.785318	+	0.493448i	−0.864024	−	0.503450i	$-0.832064\pi$
$467$	−16.9709	+	10.6635i	−0.785318	+	0.493448i	0.0787066	+	0.996898i	$0.474921\pi$
$468$		0			0
$469$	3.89695	+	3.10771i	0.179944	+	0.143501i
$470$	−8.46600	+	1.27604i	−0.390507	+	0.0588595i
$471$		0			0
$472$	21.3547	−	24.8146i	0.982928	−	1.14218i
$473$	2.03906	+	27.2093i	0.0937560	+	1.25109i
$474$		0			0
$475$	−7.29744	−	8.47978i	−0.334829	−	0.389079i
$476$	27.8032	−	27.8032i	1.27436	−	1.27436i
$477$		0			0
$478$	50.7786	+	5.72137i	2.32256	+	0.261689i
$479$	−15.0579	+	20.4027i	−0.688013	+	0.932224i	−0.999840	−	0.0179146i	$-0.994297\pi$
$479$	−15.0579	+	20.4027i	−0.688013	+	0.932224i	0.311827	+	0.950139i	$0.399059\pi$
$480$		0			0
$481$	38.4063	+	10.2909i	1.75118	+	0.469226i
$482$	47.2501	−	8.94020i	2.15218	−	0.407215i
$483$		0			0
$484$	−9.61359	+	6.55443i	−0.436981	+	0.297929i
$485$	−2.63748	−	7.53748i	−0.119762	−	0.342259i
$486$		0			0
$487$	−0.176535	−	0.221368i	−0.00799956	−	0.0100311i	0.777816	−	0.628493i	$-0.216328\pi$
$487$	−0.176535	−	0.221368i	−0.00799956	−	0.0100311i	−0.785815	+	0.618461i	$0.787756\pi$
$488$	−2.93997	+	1.15385i	−0.133086	+	0.0522324i
$489$		0			0
$490$	18.8352	+	9.95468i	0.850887	+	0.449707i
$491$	19.8916	−	14.6807i	0.897694	−	0.662529i	−0.0439880	−	0.999032i	$-0.514006\pi$
$491$	19.8916	−	14.6807i	0.897694	−	0.662529i	0.941682	+	0.336504i	$0.109244\pi$
$492$		0			0
$493$	−14.2293	−	11.5170i	−0.640857	−	0.518699i
$494$			40.7319i			1.83261i
$495$		0			0
$496$	0.00572128	+	0.00910536i	0.000256893	+	0.000408843i
$497$	−45.1261	−	13.9196i	−2.02418	−	0.624378i
$498$		0			0
$499$	27.9561	+	10.9720i	1.25149	+	0.491172i	0.896227	−	0.443595i	$-0.146297\pi$
$499$	27.9561	+	10.9720i	1.25149	+	0.491172i	0.355260	+	0.934768i	$0.384392\pi$
$500$	11.3830	+	36.9029i	0.509064	+	1.65035i
$501$		0			0
$502$	−39.1194	−	57.3777i	−1.74599	−	2.56089i
$503$	20.8110	+	13.0764i	0.927919	+	0.583050i	0.909011	−	0.416771i	$-0.136838\pi$
$503$	20.8110	+	13.0764i	0.927919	+	0.583050i	0.0189074	+	0.999821i	$0.493981\pi$
$504$		0			0
$505$	19.5841	+	19.5841i	0.871481	+	0.871481i
$506$	−0.852058	+	11.3699i	−0.0378786	+	0.505455i
$507$		0			0
$508$	−45.3569	+	19.7890i	−2.01239	+	0.877996i
$509$	−6.82933	+	10.0168i	−0.302705	+	0.443986i	−0.947210	−	0.320614i	$-0.896111\pi$
$509$	−6.82933	+	10.0168i	−0.302705	+	0.443986i	0.644505	+	0.764600i	$0.277063\pi$
$510$		0			0
$511$	17.2859	−	14.8757i	0.764683	−	0.658063i
$512$	0.00923413	−	0.0146960i	0.000408095	−	0.000649479i
$513$		0			0
$514$	−6.31074	+	2.20822i	−0.278355	+	0.0974006i
$515$	−1.57029	−	1.45701i	−0.0691951	−	0.0642037i
$516$		0			0
$517$	−8.76457	−	1.32105i	−0.385465	−	0.0580996i
$518$	−57.9361	−	62.4403i	−2.54557	−	2.74347i
$519$		0			0
$520$	6.96547	−	15.9650i	0.305456	−	0.700113i
$521$	−8.81512			−0.386197			−0.193099	−	0.981179i	$-0.561854\pi$
$521$	−8.81512			−0.386197			−0.193099	+	0.981179i	$0.561854\pi$
$522$		0			0
$523$	−21.5957			−0.944315			−0.472157	−	0.881514i	$-0.656525\pi$
$523$	−21.5957			−0.944315			−0.472157	+	0.881514i	$0.656525\pi$
$524$	12.3034	−	28.1997i	0.537477	−	1.23191i
$525$		0			0
$526$	50.2265	+	54.1313i	2.18998	+	2.36024i
$527$	23.5625	+	3.55148i	1.02640	+	0.154705i
$528$		0			0
$529$	−15.6133	−	14.4870i	−0.678838	−	0.629869i
$530$	5.13165	−	1.79564i	0.222905	−	0.0779977i
$531$		0			0
$532$	28.6929	−	45.6644i	1.24399	−	1.97980i
$533$	11.9270	−	10.2640i	0.516616	−	0.444584i
$534$		0			0
$535$	11.9771	−	17.5672i	0.517817	−	0.759498i
$536$	−3.61664	+	1.57792i	−0.156215	+	0.0681559i
$537$		0			0
$538$	3.82358	−	51.0222i	0.164846	−	2.19972i
$539$	15.5955	+	15.5955i	0.671744	+	0.671744i
$540$		0			0
$541$	11.6870	+	7.34345i	0.502465	+	0.315720i	0.759306	−	0.650734i	$-0.225539\pi$
$541$	11.6870	+	7.34345i	0.502465	+	0.315720i	−0.256841	+	0.966454i	$0.582682\pi$
$542$	31.9554	+	46.8699i	1.37260	+	2.01323i
$543$		0			0
$544$	−5.66630	−	18.3697i	−0.242940	−	0.787594i
$545$	26.0563	+	10.2264i	1.11613	+	0.438049i
$546$		0			0
$547$	28.8868	+	8.91040i	1.23511	+	0.380981i	0.842486	−	0.538717i	$-0.181091\pi$
$547$	28.8868	+	8.91040i	1.23511	+	0.380981i	0.392625	+	0.919699i	$0.371567\pi$
$548$	−7.21567	−	11.4837i	−0.308238	−	0.490558i
$549$		0			0
$550$			20.9763i			0.894431i
$551$	−22.5427	−	11.0577i	−0.960350	−	0.471073i
$552$		0			0
$553$	−25.5031	+	18.8222i	−1.08450	+	0.800400i
$554$	43.3290	+	22.9001i	1.84087	+	0.972930i
$555$		0			0
$556$	−1.94642	+	0.763914i	−0.0825467	+	0.0323972i
$557$	−6.23316	−	7.81614i	−0.264108	−	0.331181i	0.632041	−	0.774935i	$-0.282218\pi$
$557$	−6.23316	−	7.81614i	−0.264108	−	0.331181i	−0.896148	+	0.443755i	$0.853646\pi$
$558$		0			0
$559$	−9.00543	−	25.7360i	−0.380889	−	1.08852i
$560$	−0.00730536	+	0.00498071i	−0.000308708	+	0.000210474i
$561$		0			0
$562$	18.7847	−	3.55426i	0.792384	−	0.149927i
$563$	5.75271	+	1.54143i	0.242448	+	0.0649637i	0.377997	−	0.925807i	$-0.376613\pi$
$563$	5.75271	+	1.54143i	0.242448	+	0.0649637i	−0.135549	+	0.990771i	$0.543280\pi$
$564$		0			0
$565$	−2.43553	+	3.30003i	−0.102464	+	0.138833i
$566$	−6.78908	−	0.764946i	−0.285366	−	0.0321531i
$567$		0			0
$568$	26.4351	−	26.4351i	1.10919	−	1.10919i
$569$	−19.3194	−	22.4496i	−0.809913	−	0.941136i	0.189255	−	0.981928i	$-0.439393\pi$
$569$	−19.3194	−	22.4496i	−0.809913	−	0.941136i	−0.999168	+	0.0407920i	$0.987012\pi$
$570$		0			0
$571$	−2.21725	−	29.5871i	−0.0927889	−	1.23818i	−0.828150	−	0.560506i	$-0.810607\pi$
$571$	−2.21725	−	29.5871i	−0.0927889	−	1.23818i	0.735361	−	0.677675i	$-0.237012\pi$
$572$	30.7893	−	35.7779i	1.28737	−	1.49595i
$573$		0			0
$574$	−33.3328	+	5.02411i	−1.39128	+	0.209702i
$575$	2.44665	+	1.95114i	0.102033	+	0.0813683i
$576$		0			0
$577$	32.3269	−	20.3124i	1.34579	−	0.845615i	0.349951	−	0.936768i	$-0.386198\pi$
$577$	32.3269	−	20.3124i	1.34579	−	0.845615i	0.995837	+	0.0911529i	$0.0290552\pi$
$578$	−11.4189	−	4.98200i	−0.474962	−	0.207224i
$579$		0			0
$580$	18.1784	+	21.4356i	0.754819	+	0.890065i
$581$	21.3420	−	12.3218i	0.885417	−	0.511195i
$582$		0			0
$583$	5.62455	−	0.210456i	0.232945	−	0.00871619i
$584$	4.01737	+	17.6012i	0.166240	+	0.728344i
$585$		0			0
$586$	6.90006	−	5.50261i	0.285039	−	0.227311i
$587$	20.2300	−	21.8027i	0.834980	−	0.899895i	−0.161226	−	0.986918i	$-0.551545\pi$
$587$	20.2300	−	21.8027i	0.834980	−	0.899895i	0.996206	+	0.0870226i	$0.0277352\pi$
$588$		0			0
$589$	32.5919	−	2.44243i	1.34293	−	0.100638i
$590$	−1.59660	+	42.6699i	−0.0657308	+	1.75669i
$591$		0			0
$592$	0.0154334	−	0.00413537i	0.000634310	−	0.000169963i
$593$	29.0205	−	13.9755i	1.19173	−	0.573906i	0.270421	−	0.962742i	$-0.412837\pi$
$593$	29.0205	−	13.9755i	1.19173	−	0.573906i	0.921307	+	0.388837i	$0.127123\pi$
$594$		0			0
$595$	−2.19362	+	19.4689i	−0.0899295	+	0.798147i
$596$	−8.38592	−	0.628437i	−0.343500	−	0.0257418i
$597$		0			0
$598$	−2.11821	−	11.1950i	−0.0866201	−	0.457798i
$599$	3.56523	+	0.133401i	0.145671	+	0.00545063i	0.110127	−	0.993917i	$-0.464874\pi$
$599$	3.56523	+	0.133401i	0.145671	+	0.00545063i	0.0355438	+	0.999368i	$0.488684\pi$
$600$		0			0
$601$	5.75406	−	30.4109i	0.234713	−	1.24049i	−0.644703	−	0.764433i	$-0.723019\pi$
$601$	5.75406	−	30.4109i	0.234713	−	1.24049i	0.879416	−	0.476055i	$-0.157934\pi$
$602$	−12.9977	+	56.9465i	−0.529746	+	2.32097i
$603$		0			0
$604$	−43.9965	+	55.1698i	−1.79019	+	2.24483i
$605$	1.70888	−	5.54006i	0.0694760	−	0.225236i
$606$		0			0
$607$	−3.95105	−	5.35349i	−0.160368	−	0.217291i	0.717045	−	0.697027i	$-0.245494\pi$
$607$	−3.95105	−	5.35349i	−0.160368	−	0.217291i	−0.877413	+	0.479736i	$0.840732\pi$
$608$	−13.1836	−	22.8347i	−0.534666	−	0.926069i
$609$		0			0
$610$	2.05965	−	3.56742i	0.0833928	−	0.144440i
$611$	8.80154	−	0.991696i	0.356072	−	0.0401197i
$612$		0			0
$613$	46.5039	−	10.6142i	1.87827	−	0.428704i	0.879398	−	0.476087i	$-0.157945\pi$
$613$	46.5039	−	10.6142i	1.87827	−	0.428704i	0.998877	+	0.0473834i	$0.0150883\pi$
$614$	8.95523	+	22.8176i	0.361404	+	0.920842i
$615$		0			0
$616$	−36.9144	+	11.3866i	−1.48732	+	0.458779i
$617$	−3.97781	−	3.42318i	−0.160141	−	0.137812i	0.568567	−	0.822637i	$-0.307498\pi$
$617$	−3.97781	−	3.42318i	−0.160141	−	0.137812i	−0.728708	+	0.684825i	$0.759879\pi$
$618$		0			0
$619$	7.30593	+	13.8235i	0.293650	+	0.555613i	0.986160	−	0.165795i	$-0.0530190\pi$
$619$	7.30593	+	13.8235i	0.293650	+	0.555613i	−0.692510	+	0.721408i	$0.743495\pi$
$620$	−34.5318	−	12.0832i	−1.38683	−	0.485272i
$621$		0			0
$622$	26.3225	+	54.6593i	1.05544	+	2.19164i
$623$	7.15424	+	5.28007i	0.286628	+	0.211541i
$624$		0			0
$625$	−5.98663	−	4.08161i	−0.239465	−	0.163265i
$626$	2.81946	−	10.5224i	0.112688	−	0.420559i
$627$		0			0
$628$	−15.8670	+	8.38593i	−0.633160	+	0.334635i
$629$	15.3616	−	31.8987i	0.612507	−	1.27188i
$630$		0			0
$631$	21.6848	+	4.94942i	0.863260	+	0.197033i	0.631154	−	0.775657i	$-0.282581\pi$
$631$	21.6848	+	4.94942i	0.863260	+	0.197033i	0.232105	+	0.972691i	$0.425439\pi$
$632$	−3.73986	−	24.8124i	−0.148764	−	0.986983i
$633$		0			0
$634$	−10.6572	+	9.88848i	−0.423253	+	0.392722i
$635$	11.5218	−	21.8003i	0.457227	−	0.865117i
$636$		0			0
$637$	−19.0868	−	11.0198i	−0.756247	−	0.436619i
$638$	18.5134	+	43.2853i	0.732952	+	1.71368i
$639$		0			0
$640$	3.30587	+	29.3404i	0.130676	+	1.15978i
$641$	0.390253	+	10.4297i	0.0154141	+	0.411950i	0.985550	+	0.169387i	$0.0541787\pi$
$641$	0.390253	+	10.4297i	0.0154141	+	0.411950i	−0.970136	+	0.242563i	$0.922012\pi$
$642$		0			0
$643$	−1.90496	+	12.6386i	−0.0751244	+	0.498418i	0.919350	+	0.393440i	$0.128715\pi$
$643$	−1.90496	+	12.6386i	−0.0751244	+	0.498418i	−0.994475	+	0.104977i	$0.966523\pi$
$644$	−5.51141	+	14.0428i	−0.217180	+	0.553366i
$645$		0			0
$646$	35.6370	+	6.74288i	1.40212	+	0.265295i
$647$	21.4781	+	10.3433i	0.844390	+	0.406637i	0.805492	−	0.592606i	$-0.201901\pi$
$647$	21.4781	+	10.3433i	0.844390	+	0.406637i	0.0388978	+	0.999243i	$0.487615\pi$
$648$		0			0
$649$	−14.6002	+	41.7250i	−0.573109	+	1.63785i
$650$	−5.42517	−	20.2470i	−0.212793	−	0.794154i
$651$		0			0
$652$	31.4225	+	72.0212i	1.23060	+	2.82057i
$653$	−1.39197	−	3.19043i	−0.0544720	−	0.124851i	0.887198	−	0.461389i	$-0.152649\pi$
$653$	−1.39197	−	3.19043i	−0.0544720	−	0.124851i	−0.941670	+	0.336538i	$0.890744\pi$
$654$		0			0
$655$	3.96781	+	14.8081i	0.155035	+	0.578599i
$656$	0.00208843	−	0.00596838i	8.15394e−5	−	0.000233026i
$657$		0			0
$658$	−17.0954	−	8.23271i	−0.666448	−	0.320945i
$659$	30.7669	+	5.82142i	1.19851	+	0.226770i	0.746587	−	0.665287i	$-0.231691\pi$
$659$	30.7669	+	5.82142i	1.19851	+	0.226770i	0.451922	+	0.892058i	$0.350739\pi$
$660$		0			0
$661$	−0.0777038	+	0.197986i	−0.00302233	+	0.00770077i	−0.932377	−	0.361488i	$-0.882269\pi$
$661$	−0.0777038	+	0.197986i	−0.00302233	+	0.00770077i	0.929355	+	0.369188i	$0.120364\pi$
$662$	4.28257	−	28.4130i	0.166447	−	1.10430i
$663$		0			0
$664$	0.729467	+	19.4954i	0.0283088	+	0.756569i
$665$	3.00876	+	26.7035i	0.116675	+	1.03552i
$666$		0			0
$667$	6.77081	+	1.86686i	0.262167	+	0.0722852i
$668$	37.2998	+	21.5350i	1.44317	+	0.833216i
$669$		0			0
$670$	2.40482	−	4.55013i	0.0929061	−	0.175787i
$671$	3.12616	−	2.90065i	0.120684	−	0.111978i
$672$		0			0
$673$	−6.96874	−	46.2346i	−0.268625	−	1.78221i	−0.562934	−	0.826502i	$-0.690327\pi$
$673$	−6.96874	−	46.2346i	−0.268625	−	1.78221i	0.294309	−	0.955710i	$-0.404911\pi$
$674$	−45.6486	−	10.4190i	−1.75832	−	0.401325i
$675$		0			0
$676$	−2.21064	+	4.59045i	−0.0850248	+	0.176556i
$677$	−6.49580	+	3.43313i	−0.249654	+	0.131946i	−0.587415	−	0.809286i	$-0.699854\pi$
$677$	−6.49580	+	3.43313i	−0.249654	+	0.131946i	0.337761	+	0.941232i	$0.390330\pi$
$678$		0			0
$679$	4.58055	−	17.0948i	0.175785	−	0.656040i
$680$	−12.8150	−	8.73710i	−0.491432	−	0.335053i
$681$		0			0
$682$	−49.3062	−	36.3897i	−1.88803	−	1.39343i
$683$	9.39369	+	19.5062i	0.359440	+	0.746384i	0.999764	−	0.0217204i	$-0.00691435\pi$
$683$	9.39369	+	19.5062i	0.359440	+	0.746384i	−0.640324	+	0.768105i	$0.721200\pi$
$684$		0			0
$685$	6.37864	+	2.23198i	0.243715	+	0.0852797i
$686$	−4.68857	−	8.87121i	−0.179010	−	0.338704i
$687$		0			0
$688$	−0.00830493	−	0.00714697i	−0.000316623	−	0.000272476i
$689$	−5.37458	+	1.65784i	−0.204755	+	0.0631586i
$690$		0			0
$691$	4.15235	+	10.5800i	0.157963	+	0.402483i	0.987842	−	0.155460i	$-0.0496860\pi$
$691$	4.15235	+	10.5800i	0.157963	+	0.402483i	−0.829879	+	0.557943i	$0.811591\pi$
$692$	18.7787	−	4.28611i	0.713857	−	0.162933i
$693$		0			0
$694$	−36.7964	+	4.14596i	−1.39677	+	0.157378i
$695$	0.520940	−	0.902294i	0.0197604	−	0.0342260i
$696$		0			0
$697$	−7.00572	−	12.1343i	−0.265360	−	0.459618i
$698$	−9.93771	−	13.4651i	−0.376148	−	0.509662i
$699$		0			0
$700$	−8.18051	+	26.5206i	−0.309194	+	1.00238i
$701$	−30.6862	+	38.4793i	−1.15900	+	1.45334i	−0.291044	+	0.956710i	$0.594003\pi$
$701$	−30.6862	+	38.4793i	−1.15900	+	1.45334i	−0.867960	+	0.496635i	$0.834569\pi$
$702$		0			0
$703$	10.8059	−	47.3437i	0.407552	−	1.78560i
$704$	−9.19328	+	48.5877i	−0.346485	+	1.83122i
$705$		0			0
$706$	−31.7108	−	1.18653i	−1.19345	−	0.0446558i
$707$	11.4114	+	60.3107i	0.429170	+	2.26822i
$708$		0			0
$709$	21.0481	+	1.57734i	0.790477	+	0.0592381i	0.463848	−	0.885915i	$-0.346468\pi$
$709$	21.0481	+	1.57734i	0.790477	+	0.0592381i	0.326629	+	0.945153i	$0.394087\pi$
$710$	−5.45944	+	48.4539i	−0.204889	+	1.81844i
$711$		0			0
$712$	−6.34199	+	3.05414i	−0.237676	+	0.114459i
$713$	−8.83076	+	2.36620i	−0.330715	+	0.0886147i
$714$		0			0
$715$	−0.879431	+	23.5033i	−0.0328889	+	0.878973i
$716$	36.3957	−	2.72748i	1.36017	−	0.101931i
$717$		0			0
$718$	−32.6271	+	35.1637i	−1.21763	+	1.31230i
$719$	−24.1633	+	19.2696i	−0.901138	+	0.718634i	−0.960109	−	0.279626i	$-0.909790\pi$
$719$	−24.1633	+	19.2696i	−0.901138	+	0.718634i	0.0589707	+	0.998260i	$0.481218\pi$
$720$		0			0
$721$	−1.05640	−	4.62839i	−0.0393424	−	0.172370i
$722$	6.26435	−	0.234395i	0.233135	−	0.00872329i
$723$		0			0
$724$	56.1401	−	32.4125i	2.08643	−	1.20460i
$725$	12.6783	+	2.49405i	0.470861	+	0.0926267i
$726$		0			0
$727$	18.3310	+	7.99775i	0.679861	+	0.296620i	0.711303	−	0.702885i	$-0.248105\pi$
$727$	18.3310	+	7.99775i	0.679861	+	0.296620i	−0.0314425	+	0.999506i	$0.510010\pi$
$728$	32.6861	−	20.5381i	1.21143	−	0.761191i
$729$		0			0
$730$	−18.4101	−	14.6815i	−0.681387	−	0.543388i
$731$	−24.0076	+	3.61857i	−0.887955	+	0.133838i
$732$		0			0
$733$	−29.2263	+	33.9616i	−1.07950	+	1.25440i	−0.114142	+	0.993464i	$0.536412\pi$
$733$	−29.2263	+	33.9616i	−1.07950	+	1.25440i	−0.965356	+	0.260935i	$0.915969\pi$
$734$	1.48134	+	19.7671i	0.0546772	+	0.729616i
$735$		0			0
$736$	4.81096	+	5.59044i	0.177334	+	0.206066i
$737$	3.76749	−	3.76749i	0.138777	−	0.138777i
$738$		0			0
$739$	−16.9602	−	1.91095i	−0.623890	−	0.0702956i	−0.205641	−	0.978628i	$-0.565928\pi$
$739$	−16.9602	−	1.91095i	−0.623890	−	0.0702956i	−0.418250	+	0.908332i	$0.637356\pi$
$740$	−32.2789	+	43.7363i	−1.18660	+	1.60778i
$741$		0			0
$742$	11.6385	+	3.11852i	0.427262	+	0.114484i
$743$	−7.79992	+	1.47582i	−0.286151	+	0.0541427i	−0.327006	−	0.945022i	$-0.606040\pi$
$743$	−7.79992	+	1.47582i	−0.286151	+	0.0541427i	0.0408545	+	0.999165i	$0.486992\pi$
$744$		0			0
$745$	3.46213	−	2.36044i	0.126843	−	0.0864798i
$746$	−23.8438	−	68.1416i	−0.872983	−	2.49484i
$747$		0			0
$748$	−26.2056	−	32.8608i	−0.958173	−	1.20151i
$749$	43.8634	−	17.2151i	1.60273	−	0.629027i
$750$		0			0
$751$	−9.05811	−	4.78735i	−0.330535	−	0.174693i	0.293765	−	0.955878i	$-0.405092\pi$
$751$	−9.05811	−	4.78735i	−0.330535	−	0.174693i	−0.624300	+	0.781185i	$0.714616\pi$
$752$	0.00286376	−	0.00211355i	0.000104431	−	7.70733e-5i
$753$		0			0
$754$	−29.0648	−	36.9923i	−1.05848	−	1.34718i
$755$		−	35.1609i		−	1.27964i
$756$		0			0
$757$	0.486620	+	0.774451i	0.0176865	+	0.0281479i	0.855450	−	0.517885i	$-0.173280\pi$
$757$	0.486620	+	0.774451i	0.0176865	+	0.0281479i	−0.837764	+	0.546033i	$0.816137\pi$
$758$	−40.9826	−	12.6415i	−1.48856	−	0.459159i
$759$		0			0
$760$	−19.8029	−	7.77208i	−0.718328	−	0.281923i
$761$	8.70153	+	28.2097i	0.315430	+	1.02260i	0.964990	+	0.262288i	$0.0844772\pi$
$761$	8.70153	+	28.2097i	0.315430	+	1.02260i	−0.649559	+	0.760311i	$0.725047\pi$
$762$		0			0
$763$	34.9455	+	51.2556i	1.26511	+	1.85558i
$764$	−30.0963	−	18.9107i	−1.08884	−	0.684167i
$765$		0			0
$766$	−38.8381	−	38.8381i	−1.40328	−	1.40328i
$767$	3.30113	−	44.0506i	0.119197	−	1.59057i
$768$		0			0
$769$	20.8677	−	9.10450i	0.752510	−	0.328317i	0.0116102	−	0.999933i	$-0.496304\pi$
$769$	20.8677	−	9.10450i	0.752510	−	0.328317i	0.740899	+	0.671616i	$0.234400\pi$
$770$	28.3831	−	41.6303i	1.02285	−	1.50025i
$771$		0			0
$772$	49.5992	−	42.6836i	1.78512	−	1.53622i
$773$	24.0026	−	38.2000i	0.863315	−	1.37396i	−0.0633186	−	0.997993i	$-0.520168\pi$
$773$	24.0026	−	38.2000i	0.863315	−	1.37396i	0.926634	−	0.375965i	$-0.122689\pi$
$774$		0			0
$775$	−15.8755	+	5.55508i	−0.570265	+	0.199544i
$776$	10.2704	+	9.52954i	0.368686	+	0.342091i
$777$		0			0
$778$	50.4479	+	7.60380i	1.80864	+	0.272609i
$779$	−13.0716	−	14.0878i	−0.468338	−	0.504749i
$780$		0			0
$781$	−20.1866	+	46.2682i	−0.722333	+	1.65561i
$782$	−10.1454			−0.362797
$783$		0			0
$784$	−0.00885651			−0.000316304
$785$	3.57601	−	8.19630i	0.127633	−	0.292538i
$786$		0			0
$787$	−5.74106	−	6.18740i	−0.204647	−	0.220557i	0.622386	−	0.782710i	$-0.286163\pi$
$787$	−5.74106	−	6.18740i	−0.204647	−	0.220557i	−0.827033	+	0.562154i	$0.809973\pi$
$788$	−8.41676	−	1.26862i	−0.299835	−	0.0451928i
$789$		0			0
$790$	23.9912	+	22.2606i	0.853570	+	0.791997i
$791$	−8.57967	+	3.00216i	−0.305058	+	0.106744i
$792$		0			0
$793$	−2.26727	+	3.60834i	−0.0805131	+	0.128136i
$794$	−5.74928	+	4.94765i	−0.204034	+	0.175586i
$795$		0			0
$796$	−29.4267	+	43.1610i	−1.04300	+	1.52980i
$797$	15.6615	−	6.83305i	0.554760	−	0.242039i	−0.103760	−	0.994602i	$-0.533088\pi$
$797$	15.6615	−	6.83305i	0.554760	−	0.242039i	0.658520	+	0.752563i	$0.271183\pi$
$798$		0			0
$799$	0.589383	−	7.86477i	0.0208509	−	0.278236i
$800$	9.59472	+	9.59472i	0.339225	+	0.339225i
$801$		0			0
$802$	−31.8587	−	20.0182i	−1.12497	−	0.706866i
$803$	−13.7325	−	20.1419i	−0.484610	−	0.710792i
$804$		0			0
$805$	−2.21563	−	7.18289i	−0.0780906	−	0.253164i
$806$	57.0037	+	22.3723i	2.00787	+	0.788031i
$807$		0			0
$808$	−46.4331	−	14.3227i	−1.63351	−	0.503871i
$809$	8.84291	+	14.0734i	0.310900	+	0.494795i	0.965226	−	0.261418i	$-0.0841902\pi$
$809$	8.84291	+	14.0734i	0.310900	+	0.494795i	−0.654325	+	0.756213i	$0.727047\pi$
$810$		0			0
$811$		−	39.8566i		−	1.39955i	−0.714361	−	0.699777i	$-0.753283\pi$
$811$		−	39.8566i		−	1.39955i	0.714361	−	0.699777i	$-0.246717\pi$
$812$	6.52595	+	61.9461i	0.229016	+	2.17388i
$813$		0			0
$814$	−73.2597	+	54.0681i	−2.56775	+	1.89509i
$815$	−34.6161	−	18.2951i	−1.21255	−	0.640851i
$816$		0			0
$817$	−30.9988	+	12.1661i	−1.08451	+	0.425639i
$818$	10.0766	+	12.6356i	0.352319	+	0.441795i
$819$		0			0
$820$	7.10500	+	20.3049i	0.248118	+	0.709079i
$821$	−9.51431	+	6.48675i	−0.332052	+	0.226389i	−0.717856	−	0.696192i	$-0.754876\pi$
$821$	−9.51431	+	6.48675i	−0.332052	+	0.226389i	0.385804	+	0.922581i	$0.373924\pi$
$822$		0			0
$823$	−20.2227	+	3.82634i	−0.704919	+	0.133378i	−0.525998	−	0.850486i	$-0.676308\pi$
$823$	−20.2227	+	3.82634i	−0.704919	+	0.133378i	−0.178920	+	0.983864i	$0.557260\pi$
$824$	3.63022	+	0.972715i	0.126465	+	0.0338861i
$825$		0			0
$826$	−56.1946	+	76.1409i	−1.95526	+	2.64928i
$827$	−33.9079	−	3.82051i	−1.17909	−	0.132852i	−0.499416	−	0.866362i	$-0.666452\pi$
$827$	−33.9079	−	3.82051i	−1.17909	−	0.132852i	−0.679678	+	0.733510i	$0.737881\pi$
$828$		0			0
$829$	20.3339	−	20.3339i	0.706226	−	0.706226i	−0.259513	−	0.965740i	$-0.583562\pi$
$829$	20.3339	−	20.3339i	0.706226	−	0.706226i	0.965740	+	0.259513i	$0.0835622\pi$
$830$	−16.5977	−	19.2869i	−0.576114	−	0.669457i
$831$		0			0
$832$	−3.69274	−	49.2762i	−0.128023	−	1.70835i
$833$	−12.8011	+	14.8751i	−0.443530	+	0.515392i
$834$		0			0
$835$	−21.2211	+	3.19857i	−0.734388	+	0.110691i
$836$	−45.0718	−	35.9436i	−1.55884	−	1.24314i
$837$		0			0
$838$	−14.9618	+	9.40109i	−0.516845	+	0.324755i
$839$	8.03838	+	3.50711i	0.277516	+	0.121079i	0.534041	−	0.845459i	$-0.320673\pi$
$839$	8.03838	+	3.50711i	0.277516	+	0.121079i	−0.256525	+	0.966538i	$0.582578\pi$
$840$		0			0
$841$	28.3634	−	6.04316i	0.978047	−	0.208385i
$842$	8.26508	−	4.77185i	0.284833	−	0.164449i
$843$		0			0
$844$	44.9841	−	1.68318i	1.54842	−	0.0579376i
$845$	−0.564921	−	2.47508i	−0.0194339	−	0.0851453i
$846$		0			0
$847$	10.0456	−	8.01113i	0.345172	−	0.275266i
$848$	−0.00153730	+	0.00165682i	−5.27913e−5	+	5.68955e-5i
$849$		0			0
$850$	−18.6125	+	1.39482i	−0.638405	+	0.0478418i
$851$	−0.507910	+	13.5742i	−0.0174109	+	0.465317i
$852$		0			0
$853$	1.18186	−	0.316680i	0.0404663	−	0.0108429i	−0.238529	−	0.971135i	$-0.576665\pi$
$853$	1.18186	−	0.316680i	0.0404663	−	0.0108429i	0.278995	+	0.960292i	$0.409999\pi$
$854$	8.22520	−	3.96105i	0.281461	−	0.135544i
$855$		0			0
$856$	−4.17660	+	37.0684i	−0.142753	+	1.26697i
$857$	−6.71981	−	0.503580i	−0.229544	−	0.0172020i	−0.0405387	−	0.999178i	$-0.512907\pi$
$857$	−6.71981	−	0.503580i	−0.229544	−	0.0172020i	−0.189006	+	0.981976i	$0.560526\pi$
$858$		0			0
$859$	2.73205	+	14.4392i	0.0932164	+	0.492661i	0.997796	+	0.0663559i	$0.0211373\pi$
$859$	2.73205	+	14.4392i	0.0932164	+	0.492661i	−0.904580	+	0.426305i	$0.859815\pi$
$860$	37.2498	+	1.39379i	1.27021	+	0.0475279i
$861$		0			0
$862$	1.96560	−	10.3885i	0.0669487	−	0.353832i
$863$	−1.39105	+	6.09458i	−0.0473518	+	0.207462i	−0.993070	−	0.117527i	$-0.962503\pi$
$863$	−1.39105	+	6.09458i	−0.0473518	+	0.207462i	0.945718	+	0.324989i	$0.105361\pi$
$864$		0			0
$865$	−5.98401	+	7.50371i	−0.203462	+	0.255134i
$866$	−16.0361	+	51.9878i	−0.544929	+	1.76662i
$867$		0			0
$868$	−48.1469	−	65.2368i	−1.63421	−	2.21428i
$869$	16.9411	+	29.3428i	0.574686	+	0.995385i
$870$		0			0
$871$	−2.66212	+	4.61092i	−0.0902024	+	0.156235i
$872$	−48.8009	+	5.49854i	−1.65261	+	0.186204i
$873$		0			0
$874$	−13.5664	+	3.09645i	−0.458892	+	0.104739i
$875$	−15.5804	−	39.6983i	−0.526714	−	1.34205i
$876$		0			0
$877$	−46.5702	+	14.3650i	−1.57256	+	0.485071i	−0.953784	−	0.300494i	$-0.902849\pi$
$877$	−46.5702	+	14.3650i	−1.57256	+	0.485071i	−0.618779	+	0.785565i	$0.712372\pi$
$878$	−27.3879	−	23.5692i	−0.924299	−	0.795423i
$879$		0			0
$880$	0.00441630	+	0.00835605i	0.000148874	+	0.000281683i
$881$	43.3675	+	15.1749i	1.46109	+	0.511257i	0.939681	−	0.342051i	$-0.111122\pi$
$881$	43.3675	+	15.1749i	1.46109	+	0.511257i	0.521407	+	0.853308i	$0.325407\pi$
$882$		0			0
$883$	3.79987	+	7.89051i	0.127876	+	0.265537i	0.955071	−	0.296378i	$-0.0957790\pi$
$883$	3.79987	+	7.89051i	0.127876	+	0.265537i	−0.827195	+	0.561915i	$0.810065\pi$
$884$	33.7935	+	24.9408i	1.13660	+	0.838849i
$885$		0			0
$886$	18.0054	+	12.2759i	0.604904	+	0.412416i
$887$	0.709166	−	2.64664i	0.0238115	−	0.0888656i	−0.952998	−	0.302978i	$-0.902019\pi$
$887$	0.709166	−	2.64664i	0.0238115	−	0.0888656i	0.976809	+	0.214112i	$0.0686858\pi$
$888$		0			0
$889$	48.3142	−	25.5348i	1.62041	−	0.856410i
$890$	3.98347	−	8.27176i	0.133526	−	0.277270i
$891$		0			0
$892$	58.5110	+	13.3548i	1.95909	+	0.447151i
$893$	−1.61227	−	10.6967i	−0.0539526	−	0.357952i
$894$		0			0
$895$	−13.3313	+	12.3696i	−0.445615	+	0.413471i
$896$	−30.5763	+	57.8532i	−1.02148	+	1.93274i
$897$		0			0
$898$	10.3136	+	5.95455i	0.344168	+	0.198706i
$899$	−27.8568	+	25.4746i	−0.929076	+	0.849626i
$900$		0			0
$901$	0.560745	+	4.97675i	0.0186811	+	0.165800i
$902$	1.34733	+	36.0083i	0.0448613	+	1.19894i
$903$		0			0
$904$	1.07249	−	7.11551i	0.0356705	−	0.236658i
$905$	−11.8008	+	30.0680i	−0.392273	+	0.999494i
$906$		0			0
$907$	23.3442	+	4.41697i	0.775133	+	0.146663i	0.558404	−	0.829569i	$-0.311414\pi$
$907$	23.3442	+	4.41697i	0.775133	+	0.146663i	0.216729	+	0.976232i	$0.430461\pi$
$908$	−29.8224	−	14.3617i	−0.989690	−	0.476609i
$909$		0			0
$910$	−16.6293	+	47.5239i	−0.551256	+	1.57540i
$911$	−9.64349	−	35.9900i	−0.319503	−	1.19240i	−0.919723	−	0.392567i	$-0.871587\pi$
$911$	−9.64349	−	35.9900i	−0.319503	−	1.19240i	0.600220	−	0.799835i	$-0.295080\pi$
$912$		0			0
$913$	−10.5343	−	24.1448i	−0.348633	−	0.799075i
$914$	2.06533	+	4.73379i	0.0683151	+	0.156580i
$915$		0			0
$916$	6.62138	+	24.7113i	0.218776	+	0.816485i
$917$	−11.2214	+	32.0690i	−0.370565	+	1.05901i
$918$		0			0
$919$	20.6934	+	9.96540i	0.682611	+	0.328728i	0.742852	−	0.669456i	$-0.233473\pi$
$919$	20.6934	+	9.96540i	0.682611	+	0.328728i	−0.0602409	+	0.998184i	$0.519187\pi$
$920$	5.84694	+	1.10630i	0.192768	+	0.0364737i
$921$		0			0
$922$	22.3193	−	56.8686i	0.735046	−	1.87287i
$923$	7.51829	−	49.8806i	0.247468	−	1.64184i
$924$		0			0
$925$	0.934419	+	24.9729i	0.0307235	+	0.821103i
$926$	0.849691	+	7.54121i	0.0279226	+	0.247820i
$927$		0			0
$928$	28.2672	+	11.3309i	0.927917	+	0.371954i
$929$	−0.443013	−	0.255774i	−0.0145348	−	0.00839166i	0.492715	−	0.870191i	$-0.336005\pi$
$929$	−0.443013	−	0.255774i	−0.0145348	−	0.00839166i	−0.507250	+	0.861799i	$0.669338\pi$
$930$		0			0
$931$	−12.5777	+	23.7981i	−0.412216	+	0.779951i
$932$	−19.3002	+	17.9080i	−0.632199	+	0.586595i
$933$		0			0
$934$	6.83578	+	45.3525i	0.223674	+	1.48398i
$935$	20.4178	+	4.66023i	0.667734	+	0.152406i
$936$		0			0
$937$	−13.9108	+	28.8861i	−0.454446	+	0.943667i	0.540317	+	0.841462i	$0.318304\pi$
$937$	−13.9108	+	28.8861i	−0.454446	+	0.943667i	−0.994763	+	0.102206i	$0.967410\pi$
$938$	10.0841	−	5.32961i	0.329258	−	0.174018i
$939$		0			0
$940$	−3.13400	+	11.6963i	−0.102220	+	0.381490i
$941$	−3.19708	−	2.17973i	−0.104222	−	0.0710572i	0.510088	−	0.860122i	$-0.329613\pi$
$941$	−3.19708	−	2.17973i	−0.104222	−	0.0710572i	−0.614309	+	0.789065i	$0.710565\pi$
$942$		0			0
$943$	4.32530	+	3.19222i	0.140851	+	0.103953i
$944$	−0.00770196	−	0.0159933i	−0.000250677	−	0.000520537i
$945$		0			0
$946$	58.9344	+	20.6220i	1.91612	+	0.670481i
$947$	−2.89511	−	5.47782i	−0.0940785	−	0.178005i	0.832585	−	0.553898i	$-0.186860\pi$
$947$	−2.89511	−	5.47782i	−0.0940785	−	0.178005i	−0.926663	+	0.375892i	$0.877336\pi$
$948$		0			0
$949$	18.4645	+	15.8900i	0.599383	+	0.515811i
$950$	−24.4631	+	7.54588i	−0.793689	+	0.244821i
$951$		0			0
$952$	−12.5581	−	31.9975i	−0.407010	−	1.03705i
$953$	8.07682	−	1.84348i	0.261634	−	0.0597162i	−0.0896917	−	0.995970i	$-0.528588\pi$
$953$	8.07682	−	1.84348i	0.261634	−	0.0597162i	0.351326	+	0.936253i	$0.385731\pi$
$954$		0			0
$955$	17.5996	−	1.98300i	0.569509	−	0.0641683i
$956$	36.1357	−	62.5889i	1.16871	−	2.02427i
$957$		0			0
$958$	29.0132	+	50.2524i	0.937375	+	1.62358i
$959$	8.89361	+	12.0504i	0.287190	+	0.389128i
$960$		0			0
$961$	5.34581	−	17.3307i	0.172446	−	0.559055i
$962$	56.7290	−	71.1359i	1.82902	−	2.29351i
$963$		0			0
$964$	15.1342	−	66.3071i	0.487439	−	2.13561i
$965$	−6.06177	+	32.0372i	−0.195135	+	1.03132i
$966$		0			0
$967$	47.3679	+	1.77238i	1.52325	+	0.0569960i	0.785832	−	0.618440i	$-0.212235\pi$
$967$	47.3679	+	1.77238i	1.52325	+	0.0569960i	0.737419	+	0.675436i	$0.236045\pi$
$968$	1.89105	+	9.99443i	0.0607806	+	0.321233i
$969$		0			0
$970$	−18.2225	−	1.36559i	−0.585090	−	0.0438464i
$971$	5.56016	−	49.3478i	0.178434	−	1.58365i	−0.511183	−	0.859472i	$-0.670792\pi$
$971$	5.56016	−	49.3478i	0.178434	−	1.58365i	0.689617	−	0.724174i	$-0.257779\pi$
$972$		0			0
$973$	2.08037	−	1.00185i	0.0666936	−	0.0321179i
$974$	−0.625838	+	0.167693i	−0.0200531	+	0.00537322i
$975$		0			0
$976$	−6.40316e−5		0.00171128i	−2.04960e−6		5.47768e-5i
$977$	7.20845	−	0.540199i	0.230619	−	0.0172825i	0.0410806	−	0.999156i	$-0.486920\pi$
$977$	7.20845	−	0.540199i	0.230619	−	0.0172825i	0.189538	+	0.981873i	$0.439301\pi$
$978$		0			0
$979$	6.46487	−	6.96747i	0.206618	−	0.222681i
$980$	23.5570	−	18.7861i	0.752502	−	0.600100i
$981$		0			0
$982$	−12.5886	−	55.1543i	−0.401719	−	1.76005i
$983$	−12.2725	+	0.459204i	−0.391431	+	0.0146463i	−0.232383	−	0.972624i	$-0.574652\pi$
$983$	−12.2725	+	0.459204i	−0.391431	+	0.0146463i	−0.159048	+	0.987271i	$0.550843\pi$
$984$		0			0
$985$	3.67303	−	2.12063i	0.117033	−	0.0675688i
$986$	−37.1766	+	19.3054i	−1.18394	+	0.614811i
$987$		0			0
$988$	52.8012	+	23.0369i	1.67983	+	0.732902i
$989$	7.88722	−	4.95587i	0.250799	−	0.157588i
$990$		0			0
$991$	−7.07898	−	5.64530i	−0.224871	−	0.179329i	0.504573	−	0.863369i	$-0.331650\pi$
$991$	−7.07898	−	5.64530i	−0.224871	−	0.179329i	−0.729444	+	0.684040i	$0.760221\pi$
$992$	−39.1980	+	5.90815i	−1.24454	+	0.187584i
$993$		0			0
$994$	−70.4888	+	81.9095i	−2.23577	+	2.59801i
$995$	−1.94515	−	25.9562i	−0.0616653	−	0.822866i
$996$		0			0
$997$	18.3238	+	21.2926i	0.580320	+	0.674344i	0.969009	−	0.247025i	$-0.0794530\pi$
$997$	18.3238	+	21.2926i	0.580320	+	0.674344i	−0.388689	+	0.921369i	$0.627072\pi$
$998$	48.5946	−	48.5946i	1.53823	−	1.53823i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.be.a.710.25		672
3.2	odd	2		261.2.x.a.101.4	yes	672
9.4	even	3		261.2.x.a.14.25	✓	672
9.5	odd	6	inner	783.2.be.a.449.4		672
29.27	odd	28	inner	783.2.be.a.143.4		672
87.56	even	28		261.2.x.a.56.25	yes	672
261.85	odd	84		261.2.x.a.230.4	yes	672
261.230	even	84	inner	783.2.be.a.665.25		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.25	✓	672	9.4	even	3
261.2.x.a.56.25	yes	672	87.56	even	28
261.2.x.a.101.4	yes	672	3.2	odd	2
261.2.x.a.230.4	yes	672	261.85	odd	84
783.2.be.a.143.4		672	29.27	odd	28	inner
783.2.be.a.449.4		672	9.5	odd	6	inner
783.2.be.a.665.25		672	261.230	even	84	inner
783.2.be.a.710.25		672	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:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.be (of order \(84\), degree \(24\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.915081 - 2.09739i) q^{2} +(-2.20132 - 2.37246i) q^{4} +(1.59462 + 0.240350i) q^{5} +(2.61989 + 2.43090i) q^{7} +(-2.67053 + 0.934460i) q^{8} +(1.96331 - 3.12459i) q^{10} +(2.89572 - 2.49197i) q^{11} +(-2.15055 + 3.15427i) q^{13} +(7.49596 - 3.27045i) q^{14} +(-0.000114643 + 0.00152981i) q^{16} +(2.40371 + 2.40371i) q^{17} +(3.94790 + 2.48063i) q^{19} +(-2.94004 - 4.31225i) q^{20} +(-2.57681 - 8.35381i) q^{22} +(-1.21407 - 0.476487i) q^{23} +(-2.29282 - 0.707243i) q^{25} +(4.64781 + 7.39694i) q^{26} -11.5668i q^{28} +(-5.35553 + 0.564198i) q^{29} +(5.64002 - 4.16253i) q^{31} +(-4.99976 - 2.64245i) q^{32} +(7.24111 - 2.84193i) q^{34} +(3.59346 + 4.50605i) q^{35} +(-3.43990 - 9.83068i) q^{37} +(8.81549 - 6.01030i) q^{38} +(-4.48308 + 0.848244i) q^{40} +(-3.98133 - 1.06680i) q^{41} +(-4.24116 + 5.74657i) q^{43} +(-12.2865 - 1.38436i) q^{44} +(-2.11035 + 2.11035i) q^{46} +(-1.51336 - 1.75856i) q^{47} +(0.431424 + 5.75696i) q^{49} +(-3.58148 + 4.16176i) q^{50} +(12.2174 - 1.84148i) q^{52} +(1.15186 + 0.918579i) q^{53} +(5.21652 - 3.27776i) q^{55} +(-9.26808 - 4.04362i) q^{56} +(-3.71740 + 11.7489i) q^{58} +(-10.0209 + 5.78554i) q^{59} +(1.11550 - 0.0417389i) q^{61} +(-3.56935 - 15.6384i) q^{62} +(-10.1198 + 8.07029i) q^{64} +(-4.18743 + 4.51298i) q^{65} +(1.39074 - 0.104222i) q^{67} +(0.411368 - 10.9940i) q^{68} +(12.7392 - 3.41347i) q^{70} +(-11.9049 + 5.73310i) q^{71} +(0.714449 - 6.34091i) q^{73} +(-23.7665 - 1.78106i) q^{74} +(-2.80540 - 14.8269i) q^{76} +(13.6442 + 0.510531i) q^{77} +(-1.64882 + 8.71422i) q^{79} +(-0.000550502 + 0.00241191i) q^{80} +(-5.88073 + 7.37420i) q^{82} +(2.03244 - 6.58902i) q^{83} +(3.25527 + 4.41074i) q^{85} +(8.17178 + 14.1539i) q^{86} +(-5.40448 + 9.36083i) q^{88} +(2.47228 - 0.278559i) q^{89} +(-13.3019 + 3.03608i) q^{91} +(1.54211 + 3.92923i) q^{92} +(-5.07324 + 1.56489i) q^{94} +(5.69917 + 4.90454i) q^{95} +(-2.31387 - 4.37806i) q^{97} +(12.4694 + 4.36322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q + 36 q^{2} - 14 q^{4} + 42 q^{5} - 10 q^{7} - 56 q^{10} + 48 q^{11} - 14 q^{13} + 24 q^{14} - 54 q^{16} - 48 q^{19} + 30 q^{20} - 14 q^{22} + 30 q^{23} + 30 q^{25} - 12 q^{31} - 24 q^{32} - 14 q^{34}+ \cdots - 36 q^{97}+O(q^{100}) \) 672 * q + 36 * q^2 - 14 * q^4 + 42 * q^5 - 10 * q^7 - 56 * q^10 + 48 * q^11 - 14 * q^13 + 24 * q^14 - 54 * q^16 - 48 * q^19 + 30 * q^20 - 14 * q^22 + 30 * q^23 + 30 * q^25 - 12 * q^31 - 24 * q^32 - 14 * q^34 - 48 * q^37 + 42 * q^38 - 2 * q^40 + 24 * q^41 - 12 * q^43 - 64 * q^46 + 42 * q^47 + 22 * q^49 + 66 * q^50 + 22 * q^52 + 76 * q^55 + 42 * q^56 - 42 * q^58 + 132 * q^59 - 308 * q^64 + 66 * q^65 - 14 * q^67 - 60 * q^68 - 14 * q^70 - 48 * q^73 - 66 * q^74 - 28 * q^76 - 30 * q^77 - 12 * q^79 - 136 * q^82 - 246 * q^83 + 34 * q^85 + 8 * q^88 - 56 * q^91 - 462 * q^92 + 26 * q^94 + 246 * q^95 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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