LMFDB - Embedded newform 460.2.x.a.33.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	460.33
Dual form			460.2.x.a.237.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.632093 - 2.90569i) q^{3} +(-1.58894 - 1.57330i) q^{5} +(0.867718 + 1.58911i) q^{7} +(-5.31457 + 2.42708i) q^{9} +O(q^{10})$	\(q+(-0.632093 - 2.90569i) q^{3} +(-1.58894 - 1.57330i) q^{5} +(0.867718 + 1.58911i) q^{7} +(-5.31457 + 2.42708i) q^{9} +(-2.69466 - 2.33494i) q^{11} +(-2.27783 - 1.24379i) q^{13} +(-3.56717 + 5.61143i) q^{15} +(2.96152 - 3.95612i) q^{17} +(-0.433218 + 3.01310i) q^{19} +(4.06896 - 3.52578i) q^{21} +(2.37095 + 4.16876i) q^{23} +(0.0494416 + 4.99976i) q^{25} +(5.06554 + 6.76676i) q^{27} +(-7.93043 + 1.14022i) q^{29} +(-2.32054 + 1.49132i) q^{31} +(-5.08131 + 9.30573i) q^{33} +(1.12140 - 3.89017i) q^{35} +(0.266884 - 0.715545i) q^{37} +(-2.17426 + 7.40484i) q^{39} +(4.20705 - 9.21215i) q^{41} +(-4.98299 + 1.08398i) q^{43} +(12.2631 + 4.50494i) q^{45} +(-3.62564 + 3.62564i) q^{47} +(2.01216 - 3.13098i) q^{49} +(-13.3672 - 6.10460i) q^{51} +(9.35307 - 5.10716i) q^{53} +(0.608085 + 7.94958i) q^{55} +(9.02896 - 0.645764i) q^{57} +(-4.20109 - 14.3076i) q^{59} +(-5.27788 - 8.21254i) q^{61} +(-8.46844 - 6.33940i) q^{63} +(1.66247 + 5.56001i) q^{65} +(0.154258 - 2.15681i) q^{67} +(10.6144 - 9.52429i) q^{69} +(-0.739818 - 0.853796i) q^{71} +(1.98368 - 1.48496i) q^{73} +(14.4965 - 3.30397i) q^{75} +(1.37226 - 6.30816i) q^{77} +(-8.36811 + 2.45710i) q^{79} +(4.98203 - 5.74957i) q^{81} +(7.90684 + 2.94910i) q^{83} +(-10.9298 + 1.62667i) q^{85} +(8.32590 + 22.3226i) q^{87} +(-12.6126 - 8.10560i) q^{89} -4.69897i q^{91} +(5.80011 + 5.80011i) q^{93} +(5.42887 - 4.10604i) q^{95} +(1.24008 - 0.462527i) q^{97} +(19.9880 + 5.86902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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			0
$2$		0			0
$3$	−0.632093	−	2.90569i	−0.364939	−	1.67760i	−0.683700	−	0.729763i	$-0.739630\pi$
$3$	−0.632093	−	2.90569i	−0.364939	−	1.67760i	0.318761	−	0.947835i	$-0.396733\pi$
$4$		0			0
$5$	−1.58894	−	1.57330i	−0.710594	−	0.703602i
$5$	−1.58894	−	1.57330i	−0.710594	−	0.703602i
$6$		0			0
$7$	0.867718	+	1.58911i	0.327966	+	0.600626i	0.988685	−	0.150008i	$-0.0479300\pi$
$7$	0.867718	+	1.58911i	0.327966	+	0.600626i	−0.660718	+	0.750634i	$0.729748\pi$
$8$		0			0
$9$	−5.31457	+	2.42708i	−1.77152	+	0.809028i
$10$		0			0
$11$	−2.69466	−	2.33494i	−0.812470	−	0.704009i	0.145974	−	0.989288i	$-0.453368\pi$
$11$	−2.69466	−	2.33494i	−0.812470	−	0.704009i	−0.958445	+	0.285279i	$0.907914\pi$
$12$		0			0
$13$	−2.27783	−	1.24379i	−0.631756	−	0.344965i	0.131257	−	0.991348i	$-0.458099\pi$
$13$	−2.27783	−	1.24379i	−0.631756	−	0.344965i	−0.763013	+	0.646384i	$0.776281\pi$
$14$		0			0
$15$	−3.56717	+	5.61143i	−0.921038	+	1.44886i
$16$		0			0
$17$	2.96152	−	3.95612i	0.718273	−	0.959500i	−0.281727	−	0.959495i	$-0.590907\pi$
$17$	2.96152	−	3.95612i	0.718273	−	0.959500i	1.00000		5.71570e-6i	$-1.81936e-6\pi$
$18$		0			0
$19$	−0.433218	+	3.01310i	−0.0993871	+	0.691253i	0.877824	+	0.478983i	$0.158995\pi$
$19$	−0.433218	+	3.01310i	−0.0993871	+	0.691253i	−0.977211	+	0.212269i	$0.931915\pi$
$20$		0			0
$21$	4.06896	−	3.52578i	0.887921	−	0.769388i
$22$		0			0
$23$	2.37095	+	4.16876i	0.494378	+	0.869247i
$23$	2.37095	+	4.16876i	0.494378	+	0.869247i
$24$		0			0
$25$	0.0494416	+	4.99976i	0.00988832	+	0.999951i
$26$		0			0
$27$	5.06554	+	6.76676i	0.974863	+	1.30226i
$28$		0			0
$29$	−7.93043	+	1.14022i	−1.47264	+	0.211734i	−0.831430	−	0.555629i	$-0.812478\pi$
$29$	−7.93043	+	1.14022i	−1.47264	+	0.211734i	−0.641213	+	0.767363i	$0.721568\pi$
$30$		0			0
$31$	−2.32054	+	1.49132i	−0.416782	+	0.267849i	−0.732181	−	0.681110i	$-0.761498\pi$
$31$	−2.32054	+	1.49132i	−0.416782	+	0.267849i	0.315400	+	0.948959i	$0.397861\pi$
$32$		0			0
$33$	−5.08131	+	9.30573i	−0.884543	+	1.61992i
$34$		0			0
$35$	1.12140	−	3.89017i	0.189550	−	0.657559i
$36$		0			0
$37$	0.266884	−	0.715545i	0.0438755	−	0.117635i	−0.913164	−	0.407592i	$-0.866368\pi$
$37$	0.266884	−	0.715545i	0.0438755	−	0.117635i	0.957040	+	0.289958i	$0.0936412\pi$
$38$		0			0
$39$	−2.17426	+	7.40484i	−0.348160	+	1.18572i
$40$		0			0
$41$	4.20705	−	9.21215i	0.657031	−	1.43870i	−0.228233	−	0.973607i	$-0.573295\pi$
$41$	4.20705	−	9.21215i	0.657031	−	1.43870i	0.885263	−	0.465090i	$-0.153978\pi$
$42$		0			0
$43$	−4.98299	+	1.08398i	−0.759899	+	0.165306i	−0.575787	−	0.817600i	$-0.695304\pi$
$43$	−4.98299	+	1.08398i	−0.759899	+	0.165306i	−0.184111	+	0.982905i	$0.558941\pi$
$44$		0			0
$45$	12.2631	+	4.50494i	1.82807	+	0.671557i
$46$		0			0
$47$	−3.62564	+	3.62564i	−0.528854	+	0.528854i	−0.920231	−	0.391376i	$-0.871999\pi$
$47$	−3.62564	+	3.62564i	−0.528854	+	0.528854i	0.391376	+	0.920231i	$0.371999\pi$
$48$		0			0
$49$	2.01216	−	3.13098i	0.287452	−	0.447283i
$50$		0			0
$51$	−13.3672	−	6.10460i	−1.87178	−	0.854814i
$52$		0			0
$53$	9.35307	−	5.10716i	1.28474	−	0.701523i	0.315805	−	0.948824i	$-0.397726\pi$
$53$	9.35307	−	5.10716i	1.28474	−	0.701523i	0.968939	+	0.247301i	$0.0795437\pi$
$54$		0			0
$55$	0.608085	+	7.94958i	0.0819942	+	1.07192i
$56$		0			0
$57$	9.02896	−	0.645764i	1.19591	−	0.0855335i
$58$		0			0
$59$	−4.20109	−	14.3076i	−0.546935	−	1.86269i	−0.504167	−	0.863606i	$-0.668200\pi$
$59$	−4.20109	−	14.3076i	−0.546935	−	1.86269i	−0.0427682	−	0.999085i	$-0.513618\pi$
$60$		0			0
$61$	−5.27788	−	8.21254i	−0.675763	−	1.05151i	−0.994608	−	0.103701i	$-0.966931\pi$
$61$	−5.27788	−	8.21254i	−0.675763	−	1.05151i	0.318845	−	0.947807i	$-0.396705\pi$
$62$		0			0
$63$	−8.46844	−	6.33940i	−1.06692	−	0.798689i
$64$		0			0
$65$	1.66247	+	5.56001i	0.206204	+	0.689635i
$66$		0			0
$67$	0.154258	−	2.15681i	0.0188456	−	0.263496i	−0.979290	−	0.202462i	$-0.935106\pi$
$67$	0.154258	−	2.15681i	0.0188456	−	0.263496i	0.998136	−	0.0610338i	$-0.0194397\pi$
$68$		0			0
$69$	10.6144	−	9.52429i	1.27783	−	1.14659i
$70$		0			0
$71$	−0.739818	−	0.853796i	−0.0878003	−	0.101327i	0.710149	−	0.704051i	$-0.248627\pi$
$71$	−0.739818	−	0.853796i	−0.0878003	−	0.101327i	−0.797950	+	0.602724i	$0.794082\pi$
$72$		0			0
$73$	1.98368	−	1.48496i	0.232172	−	0.173802i	−0.476857	−	0.878981i	$-0.658224\pi$
$73$	1.98368	−	1.48496i	0.232172	−	0.173802i	0.709030	+	0.705179i	$0.249133\pi$
$74$		0			0
$75$	14.4965	−	3.30397i	1.67391	−	0.381510i
$76$		0			0
$77$	1.37226	−	6.30816i	0.156383	−	0.718882i
$78$		0			0
$79$	−8.36811	+	2.45710i	−0.941485	+	0.276445i	−0.716238	−	0.697856i	$-0.754137\pi$
$79$	−8.36811	+	2.45710i	−0.941485	+	0.276445i	−0.225248	+	0.974302i	$0.572319\pi$
$80$		0			0
$81$	4.98203	−	5.74957i	0.553559	−	0.638841i
$82$		0			0
$83$	7.90684	+	2.94910i	0.867888	+	0.323706i	0.743668	−	0.668549i	$-0.233084\pi$
$83$	7.90684	+	2.94910i	0.867888	+	0.323706i	0.124220	+	0.992255i	$0.460357\pi$
$84$		0			0
$85$	−10.9298	+	1.62667i	−1.18551	+	0.176437i
$86$		0			0
$87$	8.32590	+	22.3226i	0.892630	+	2.39323i
$88$		0			0
$89$	−12.6126	−	8.10560i	−1.33693	−	0.859192i	−0.340227	−	0.940343i	$-0.610504\pi$
$89$	−12.6126	−	8.10560i	−1.33693	−	0.859192i	−0.996702	+	0.0811515i	$0.974140\pi$
$90$		0			0
$91$		−	4.69897i		−	0.492585i
$92$		0			0
$93$	5.80011	+	5.80011i	0.601443	+	0.601443i
$94$		0			0
$95$	5.42887	−	4.10604i	0.556991	−	0.421271i
$96$		0			0
$97$	1.24008	−	0.462527i	0.125911	−	0.0469625i	−0.285719	−	0.958314i	$-0.592232\pi$
$97$	1.24008	−	0.462527i	0.125911	−	0.0469625i	0.411630	+	0.911351i	$0.364960\pi$
$98$		0			0
$99$	19.9880	+	5.86902i	2.00887	+	0.589859i
$100$		0			0
$101$	2.10807	+	4.61602i	0.209760	+	0.459311i	0.985044	−	0.172302i	$-0.0551204\pi$
$101$	2.10807	+	4.61602i	0.209760	+	0.459311i	−0.775284	+	0.631613i	$0.782393\pi$
$102$		0			0
$103$	−0.781186	−	10.9224i	−0.0769725	−	1.07622i	−0.878338	−	0.478041i	$-0.841347\pi$
$103$	−0.781186	−	10.9224i	−0.0769725	−	1.07622i	0.801365	−	0.598175i	$-0.204107\pi$
$104$		0			0
$105$	−12.0124	−	0.799471i	−1.17229	−	0.0780204i
$106$		0			0
$107$	−18.0306	−	3.92231i	−1.74308	−	0.379184i	−0.775422	−	0.631443i	$-0.782463\pi$
$107$	−18.0306	−	3.92231i	−1.74308	−	0.379184i	−0.967660	+	0.252259i	$0.918827\pi$
$108$		0			0
$109$	0.291534	+	2.02766i	0.0279239	+	0.194215i	0.999008	−	0.0445208i	$-0.0141761\pi$
$109$	0.291534	+	2.02766i	0.0279239	+	0.194215i	−0.971085	+	0.238736i	$0.923267\pi$
$110$		0			0
$111$	−2.24784	−	0.323191i	−0.213356	−	0.0306759i
$112$		0			0
$113$	1.89257	+	0.135359i	0.178038	+	0.0127335i	0.160073	−	0.987105i	$-0.448827\pi$
$113$	1.89257	+	0.135359i	0.178038	+	0.0127335i	0.0179644	+	0.999839i	$0.494281\pi$
$114$		0			0
$115$	2.79143	−	10.3541i	0.260302	−	0.965527i
$116$		0			0
$117$	15.1245	+	1.08172i	1.39826	+	0.100005i
$118$		0			0
$119$	8.85645	+	1.27337i	0.811870	+	0.116729i
$120$		0			0
$121$	0.243801	+	1.69567i	0.0221637	+	0.154152i
$122$		0			0
$123$	−29.4269	−	6.40142i	−2.65333	−	0.577197i
$124$		0			0
$125$	7.78757	−	8.02208i	0.696541	−	0.717517i
$126$		0			0
$127$	−0.232395	−	3.24931i	−0.0206217	−	0.288329i	−0.997290	−	0.0735746i	$-0.976559\pi$
$127$	−0.232395	−	3.24931i	−0.0206217	−	0.288329i	0.976668	−	0.214755i	$-0.0688953\pi$
$128$		0			0
$129$	6.29943	+	13.7938i	0.554634	+	1.21448i
$130$		0			0
$131$	17.3096	+	5.08256i	1.51235	+	0.444065i	0.929594	−	0.368584i	$-0.120157\pi$
$131$	17.3096	+	5.08256i	1.51235	+	0.444065i	0.582753	+	0.812649i	$0.301976\pi$
$132$		0			0
$133$	−5.16405	+	1.92609i	−0.447780	+	0.167013i
$134$		0			0
$135$	2.59735	−	18.7216i	0.223544	−	1.61130i
$136$		0			0
$137$	−4.67253	−	4.67253i	−0.399201	−	0.399201i	0.478750	−	0.877951i	$-0.341090\pi$
$137$	−4.67253	−	4.67253i	−0.399201	−	0.399201i	−0.877951	+	0.478750i	$0.841090\pi$
$138$		0			0
$139$			10.7485i			0.911673i	0.890064	+	0.455836i	$0.150660\pi$
$139$			10.7485i			0.911673i	−0.890064	+	0.455836i	$0.849340\pi$
$140$		0			0
$141$	12.8267	+	8.24323i	1.08020	+	0.694206i
$142$		0			0
$143$	3.23380	+	8.67016i	0.270424	+	0.725035i
$144$		0			0
$145$	14.3949	+	10.6652i	1.19543	+	0.885698i
$146$		0			0
$147$	−10.3695	−	3.86764i	−0.855264	−	0.318997i
$148$		0			0
$149$	−5.02662	+	5.80103i	−0.411797	+	0.475239i	−0.923320	−	0.384030i	$-0.874536\pi$
$149$	−5.02662	+	5.80103i	−0.411797	+	0.475239i	0.511524	+	0.859269i	$0.329081\pi$
$150$		0			0
$151$	21.0842	−	6.19087i	1.71580	−	0.503806i	0.731735	−	0.681589i	$-0.238711\pi$
$151$	21.0842	−	6.19087i	1.71580	−	0.503806i	0.984070	+	0.177783i	$0.0568925\pi$
$152$		0			0
$153$	−6.13735	+	28.2129i	−0.496175	+	2.28088i
$154$		0			0
$155$	6.03349	+	1.28130i	0.484622	+	0.102916i
$156$		0			0
$157$	16.6473	−	12.4620i	1.32860	−	0.994578i	0.329880	−	0.944023i	$-0.392992\pi$
$157$	16.6473	−	12.4620i	1.32860	−	0.994578i	0.998721	−	0.0505551i	$-0.0160991\pi$
$158$		0			0
$159$	−20.7518	−	23.9489i	−1.64573	−	1.89927i
$160$		0			0
$161$	−4.56729	+	7.38501i	−0.359953	+	0.582020i
$162$		0			0
$163$	−0.750259	+	10.4900i	−0.0587648	+	0.821639i	0.879539	+	0.475827i	$0.157851\pi$
$163$	−0.750259	+	10.4900i	−0.0587648	+	0.821639i	−0.938304	+	0.345812i	$0.887603\pi$
$164$		0			0
$165$	22.7146	−	6.79178i	1.76833	−	0.528739i
$166$		0			0
$167$	13.2402	+	9.91150i	1.02456	+	0.766975i	0.972791	−	0.231684i	$-0.0744235\pi$
$167$	13.2402	+	9.91150i	1.02456	+	0.766975i	0.0517677	+	0.998659i	$0.483514\pi$
$168$		0			0
$169$	−3.38684	−	5.27003i	−0.260526	−	0.405387i
$170$		0			0
$171$	−5.01068	−	17.0648i	−0.383176	−	1.30498i
$172$		0			0
$173$	14.0521	−	1.00503i	1.06836	−	0.0764108i	0.473935	−	0.880560i	$-0.342833\pi$
$173$	14.0521	−	1.00503i	1.06836	−	0.0764108i	0.594427	+	0.804149i	$0.297379\pi$
$174$		0			0
$175$	−7.90224	+	4.41694i	−0.597353	+	0.333890i
$176$		0			0
$177$	−38.9179	+	21.2508i	−2.92525	+	1.59731i
$178$		0			0
$179$	2.47453	+	1.13008i	0.184955	+	0.0844663i	0.505740	−	0.862686i	$-0.331219\pi$
$179$	2.47453	+	1.13008i	0.184955	+	0.0844663i	−0.320785	+	0.947152i	$0.603947\pi$
$180$		0			0
$181$	−11.5046	+	17.9015i	−0.855131	+	1.33061i	0.0872913	+	0.996183i	$0.472179\pi$
$181$	−11.5046	+	17.9015i	−0.855131	+	1.33061i	−0.942422	+	0.334426i	$0.891457\pi$
$182$		0			0
$183$	−20.5270	+	20.5270i	−1.51740	+	1.51740i
$184$		0			0
$185$	−1.54983	+	0.717066i	−0.113946	+	0.0527197i
$186$		0			0
$187$	−17.2176	+	3.74545i	−1.25907	+	0.273894i
$188$		0			0
$189$	−6.35765	+	13.9213i	−0.462451	+	1.01263i
$190$		0			0
$191$	3.55542	−	12.1086i	0.257261	−	0.876150i	−0.725019	−	0.688729i	$-0.758169\pi$
$191$	3.55542	−	12.1086i	0.257261	−	0.876150i	0.982280	−	0.187421i	$-0.0600128\pi$
$192$		0			0
$193$	6.49444	−	17.4123i	0.467480	−	1.25336i	−0.462784	−	0.886471i	$-0.653150\pi$
$193$	6.49444	−	17.4123i	0.467480	−	1.25336i	0.930264	−	0.366891i	$-0.119578\pi$
$194$		0			0
$195$	15.1048	−	8.34506i	1.08168	−	0.597602i
$196$		0			0
$197$	5.73321	−	10.4996i	0.408474	−	0.748065i	−0.589753	−	0.807584i	$-0.700775\pi$
$197$	5.73321	−	10.4996i	0.408474	−	0.748065i	0.998227	+	0.0595188i	$0.0189566\pi$
$198$		0			0
$199$	−9.34340	+	6.00464i	−0.662336	+	0.425658i	−0.828155	−	0.560499i	$-0.810610\pi$
$199$	−9.34340	+	6.00464i	−0.662336	+	0.425658i	0.165819	+	0.986156i	$0.446973\pi$
$200$		0			0
$201$	−6.36451	+	0.915078i	−0.448918	+	0.0645446i
$202$		0			0
$203$	−8.69331	−	11.6129i	−0.610151	−	0.815066i
$204$		0			0
$205$	−21.1782	+	8.01857i	−1.47915	+	0.560041i
$206$		0			0
$207$	−22.7185	−	16.4007i	−1.57905	−	1.13993i
$208$		0			0
$209$	8.20277	−	7.10774i	0.567398	−	0.491653i
$210$		0			0
$211$	−1.52199	+	10.5857i	−0.104778	+	0.728748i	0.867925	+	0.496695i	$0.165453\pi$
$211$	−1.52199	+	10.5857i	−0.104778	+	0.728748i	−0.972703	+	0.232053i	$0.925456\pi$
$212$		0			0
$213$	−2.01323	+	2.68936i	−0.137944	+	0.184272i
$214$		0			0
$215$	9.62309	+	6.11737i	0.656289	+	0.417201i
$216$		0			0
$217$	−4.38344	−	2.39354i	−0.297567	−	0.162484i
$218$		0			0
$219$	−5.56871	−	4.82532i	−0.376299	−	0.326065i
$220$		0			0
$221$	−11.6664	+	5.32786i	−0.784767	+	0.358391i
$222$		0			0
$223$	10.1104	+	18.5158i	0.677040	+	1.23991i	0.959792	+	0.280713i	$0.0905711\pi$
$223$	10.1104	+	18.5158i	0.677040	+	1.23991i	−0.282751	+	0.959193i	$0.591247\pi$
$224$		0			0
$225$	−12.3976	−	26.4516i	−0.826506	−	1.76344i
$226$		0			0
$227$	−2.60728	−	11.9855i	−0.173051	−	0.795502i	−0.979056	−	0.203593i	$-0.934738\pi$
$227$	−2.60728	−	11.9855i	−0.173051	−	0.795502i	0.806005	−	0.591909i	$-0.201626\pi$
$228$		0			0
$229$	4.97690			0.328883			0.164441	−	0.986387i	$-0.447418\pi$
$229$	4.97690			0.328883			0.164441	+	0.986387i	$0.447418\pi$
$230$		0			0
$231$	−19.1969			−1.26307
$232$		0			0
$233$	3.01811	+	13.8740i	0.197723	+	0.908917i	0.963895	+	0.266282i	$0.0857952\pi$
$233$	3.01811	+	13.8740i	0.197723	+	0.908917i	−0.766173	+	0.642635i	$0.777841\pi$
$234$		0			0
$235$	11.4651	−	0.0566869i	0.747904	−	0.00369785i
$236$		0			0
$237$	12.4290	+	22.7620i	0.807349	+	1.47855i
$238$		0			0
$239$	8.26011	−	3.77227i	0.534302	−	0.244008i	−0.129944	−	0.991521i	$-0.541480\pi$
$239$	8.26011	−	3.77227i	0.534302	−	0.244008i	0.664247	+	0.747514i	$0.268753\pi$
$240$		0			0
$241$	−12.6163	−	10.9321i	−0.812685	−	0.704196i	0.145807	−	0.989313i	$-0.453422\pi$
$241$	−12.6163	−	10.9321i	−0.812685	−	0.704196i	−0.958493	+	0.285117i	$0.907967\pi$
$242$		0			0
$243$	2.40083	+	1.31095i	0.154014	+	0.0840977i
$244$		0			0
$245$	−8.12318	+	1.80920i	−0.518971	+	0.115585i
$246$		0			0
$247$	4.73446	−	6.32449i	0.301246	−	0.402418i
$248$		0			0
$249$	3.57129	−	24.8389i	0.226322	−	1.57410i
$250$		0			0
$251$	6.77030	−	5.86650i	0.427337	−	0.370290i	−0.414475	−	0.910061i	$-0.636035\pi$
$251$	6.77030	−	5.86650i	0.427337	−	0.370290i	0.841812	+	0.539771i	$0.181489\pi$
$252$		0			0
$253$	3.34488	−	16.7694i	0.210291	−	1.05428i
$254$		0			0
$255$	11.6353	+	30.7305i	0.728629	+	1.92442i
$256$		0			0
$257$	−17.5195	−	23.4033i	−1.09284	−	1.45986i	−0.875159	−	0.483836i	$-0.839243\pi$
$257$	−17.5195	−	23.4033i	−1.09284	−	1.45986i	−0.217677	−	0.976021i	$-0.569848\pi$
$258$		0			0
$259$	1.36866	−	0.196783i	0.0850442	−	0.0122275i
$260$		0			0
$261$	39.3794	−	25.3076i	2.43752	−	1.56650i
$262$		0			0
$263$	6.72958	−	12.3243i	0.414964	−	0.759950i	−0.583681	−	0.811983i	$-0.698388\pi$
$263$	6.72958	−	12.3243i	0.414964	−	0.759950i	0.998645	+	0.0520331i	$0.0165701\pi$
$264$		0			0
$265$	−22.8966	−	6.60025i	−1.40652	−	0.405450i
$266$		0			0
$267$	−15.5800	+	41.7716i	−0.953481	+	2.55638i
$268$		0			0
$269$	−8.04743	+	27.4070i	−0.490660	+	1.67104i	0.226408	+	0.974032i	$0.427302\pi$
$269$	−8.04743	+	27.4070i	−0.490660	+	1.67104i	−0.717069	+	0.697003i	$0.754517\pi$
$270$		0			0
$271$	−6.56253	+	14.3699i	−0.398645	+	0.872911i	0.598761	+	0.800928i	$0.295660\pi$
$271$	−6.56253	+	14.3699i	−0.398645	+	0.872911i	−0.997406	+	0.0719830i	$0.977067\pi$
$272$		0			0
$273$	−13.6537	+	2.97018i	−0.826361	+	0.179764i
$274$		0			0
$275$	11.5409	−	13.5881i	0.695941	−	0.819392i
$276$		0			0
$277$	4.71575	−	4.71575i	0.283342	−	0.283342i	−0.551098	−	0.834440i	$-0.685791\pi$
$277$	4.71575	−	4.71575i	0.283342	−	0.283342i	0.834440	+	0.551098i	$0.185791\pi$
$278$		0			0
$279$	8.71312	−	13.5579i	0.521641	−	0.811689i
$280$		0			0
$281$	−6.22715	−	2.84384i	−0.371481	−	0.169650i	0.220922	−	0.975291i	$-0.429093\pi$
$281$	−6.22715	−	2.84384i	−0.371481	−	0.169650i	−0.592403	+	0.805642i	$0.701821\pi$
$282$		0			0
$283$	−16.5979	+	9.06314i	−0.986643	+	0.538748i	−0.889702	−	0.456542i	$-0.849088\pi$
$283$	−16.5979	+	9.06314i	−0.986643	+	0.538748i	−0.0969415	+	0.995290i	$0.530906\pi$
$284$		0			0
$285$	−15.3624	−	13.1792i	−0.909992	−	0.780669i
$286$		0			0
$287$	18.2896	−	1.30810i	1.07960	−	0.0772147i
$288$		0			0
$289$	−2.09087	−	7.12084i	−0.122992	−	0.418873i
$290$		0			0
$291$	−2.12781	−	3.31093i	−0.124734	−	0.194090i
$292$		0			0
$293$	−14.2204	−	10.6453i	−0.830765	−	0.621903i	0.0969094	−	0.995293i	$-0.469104\pi$
$293$	−14.2204	−	10.6453i	−0.830765	−	0.621903i	−0.927674	+	0.373390i	$0.878195\pi$
$294$		0			0
$295$	−15.8349	+	29.3435i	−0.921944	+	1.70844i
$296$		0			0
$297$	2.15006	−	30.0618i	0.124759	−	1.74436i
$298$		0			0
$299$	−0.215568	−	12.4447i	−0.0124666	−	0.719695i
$300$		0			0
$301$	−6.04639	−	6.97791i	−0.348508	−	0.402200i
$302$		0			0
$303$	12.0802	−	9.04313i	0.693990	−	0.519514i
$304$		0			0
$305$	−4.53459	+	21.3529i	−0.259650	+	1.22266i
$306$		0			0
$307$	−1.83467	+	8.43385i	−0.104710	+	0.481345i	0.894689	+	0.446689i	$0.147397\pi$
$307$	−1.83467	+	8.43385i	−0.104710	+	0.481345i	−0.999399	+	0.0346558i	$0.988967\pi$
$308$		0			0
$309$	−31.2433	+	9.17386i	−1.77737	+	0.521882i
$310$		0			0
$311$	−7.69611	+	8.88178i	−0.436406	+	0.503639i	−0.930765	−	0.365619i	$-0.880857\pi$
$311$	−7.69611	+	8.88178i	−0.436406	+	0.503639i	0.494359	+	0.869258i	$0.335403\pi$
$312$		0			0
$313$	26.5225	+	9.89239i	1.49914	+	0.559151i	0.959244	−	0.282580i	$-0.0911902\pi$
$313$	26.5225	+	9.89239i	1.49914	+	0.559151i	0.539898	+	0.841731i	$0.318463\pi$
$314$		0			0
$315$	3.48204	+	23.3963i	0.196191	+	1.31823i
$316$		0			0
$317$	7.31356	+	19.6084i	0.410770	+	1.10132i	0.963442	+	0.267919i	$0.0863358\pi$
$317$	7.31356	+	19.6084i	0.410770	+	1.10132i	−0.552671	+	0.833399i	$0.686391\pi$
$318$		0			0
$319$	24.0321	+	15.4445i	1.34554	+	0.864727i
$320$		0			0
$321$			54.8705i			3.06257i
$322$		0			0
$323$	10.6372	+	10.6372i	0.591870	+	0.591870i
$324$		0			0
$325$	6.10602	−	11.4501i	0.338701	−	0.635136i
$326$		0			0
$327$	5.70748	−	2.12878i	0.315624	−	0.117722i
$328$		0			0
$329$	−8.90756	−	2.61550i	−0.491090	−	0.144197i
$330$		0			0
$331$	5.84713	+	12.8034i	0.321387	+	0.703740i	0.999513	−	0.0312062i	$-0.00993486\pi$
$331$	5.84713	+	12.8034i	0.321387	+	0.703740i	−0.678126	+	0.734946i	$0.737208\pi$
$332$		0			0
$333$	0.318311	+	4.45056i	0.0174433	+	0.243889i
$334$		0			0
$335$	−3.63841	+	3.18434i	−0.198788	+	0.173979i
$336$		0			0
$337$	12.0011	+	2.61068i	0.653741	+	0.142213i	0.527190	−	0.849747i	$-0.323246\pi$
$337$	12.0011	+	2.61068i	0.653741	+	0.142213i	0.126551	+	0.991960i	$0.459609\pi$
$338$		0			0
$339$	−0.802969	−	5.58477i	−0.0436113	−	0.303323i
$340$		0			0
$341$	9.73521	+	1.39971i	0.527191	+	0.0757986i
$342$		0			0
$343$	19.3632	+	1.38488i	1.04551	+	0.0747767i
$344$		0			0
$345$	−31.8503	−	1.56623i	−1.71476	−	0.0843230i
$346$		0			0
$347$	4.66679	+	0.333775i	0.250526	+	0.0179180i	0.196038	−	0.980596i	$-0.437193\pi$
$347$	4.66679	+	0.333775i	0.250526	+	0.0179180i	0.0544888	+	0.998514i	$0.482647\pi$
$348$		0			0
$349$	24.5633	+	3.53166i	1.31484	+	0.189046i	0.763811	−	0.645440i	$-0.223326\pi$
$349$	24.5633	+	3.53166i	1.31484	+	0.189046i	0.551030	+	0.834486i	$0.314235\pi$
$350$		0			0
$351$	−3.12200	−	21.7140i	−0.166640	−	1.15901i
$352$		0			0
$353$	1.49398	+	0.324996i	0.0795166	+	0.0172978i	0.252148	−	0.967689i	$-0.418863\pi$
$353$	1.49398	+	0.324996i	0.0795166	+	0.0172978i	−0.172631	+	0.984987i	$0.555227\pi$
$354$		0			0
$355$	−0.167754	+	2.52059i	−0.00890346	+	0.133779i
$356$		0			0
$357$	−1.89810	−	26.5390i	−0.100458	−	1.40459i
$358$		0			0
$359$	−6.13595	−	13.4359i	−0.323843	−	0.709118i	0.675765	−	0.737117i	$-0.263814\pi$
$359$	−6.13595	−	13.4359i	−0.323843	−	0.709118i	−0.999608	+	0.0279997i	$0.991086\pi$
$360$		0			0
$361$	9.33927	+	2.74226i	0.491540	+	0.144329i
$362$		0			0
$363$	4.77298	−	1.78023i	0.250517	−	0.0934379i
$364$		0			0
$365$	−5.48824	−	0.761413i	−0.287268	−	0.0398542i
$366$		0			0
$367$	4.69644	+	4.69644i	0.245152	+	0.245152i	0.818978	−	0.573826i	$-0.194541\pi$
$367$	4.69644	+	4.69644i	0.245152	+	0.245152i	−0.573826	+	0.818978i	$0.694541\pi$
$368$		0			0
$369$			59.1695i			3.08024i
$370$		0			0
$371$	16.2317	+	10.4314i	0.842705	+	0.541574i
$372$		0			0
$373$	−3.50729	−	9.40340i	−0.181600	−	0.486889i	0.813970	−	0.580907i	$-0.197302\pi$
$373$	−3.50729	−	9.40340i	−0.181600	−	0.486889i	−0.995571	+	0.0940172i	$0.970029\pi$
$374$		0			0
$375$	−28.2321	−	17.5575i	−1.45790	−	0.906666i
$376$		0			0
$377$	19.4823	+	7.26654i	1.00339	+	0.374246i
$378$		0			0
$379$	−13.3480	+	15.4045i	−0.685643	+	0.791274i	−0.986738	−	0.162320i	$-0.948102\pi$
$379$	−13.3480	+	15.4045i	−0.685643	+	0.791274i	0.301095	+	0.953594i	$0.402648\pi$
$380$		0			0
$381$	−9.29457	+	2.72913i	−0.476175	+	0.139818i
$382$		0			0
$383$	2.29557	−	10.5526i	0.117298	−	0.539211i	−0.880568	−	0.473920i	$-0.842839\pi$
$383$	2.29557	−	10.5526i	0.117298	−	0.539211i	0.997866	−	0.0652912i	$-0.0207976\pi$
$384$		0			0
$385$	−12.1051	+	7.86430i	−0.616932	+	0.400802i
$386$		0			0
$387$	23.8515	−	17.8550i	1.21244	−	0.907623i
$388$		0			0
$389$	−9.79190	−	11.3005i	−0.496469	−	0.572956i	0.451114	−	0.892466i	$-0.351027\pi$
$389$	−9.79190	−	11.3005i	−0.496469	−	0.572956i	−0.947583	+	0.319511i	$0.896481\pi$
$390$		0			0
$391$	23.5137	+	2.96607i	1.18914	+	0.150001i
$392$		0			0
$393$	3.82703	−	53.5089i	0.193048	−	2.69917i
$394$		0			0
$395$	17.1621	+	9.26138i	0.863521	+	0.465991i
$396$		0			0
$397$	21.4760	+	16.0767i	1.07785	+	0.806867i	0.982066	−	0.188536i	$-0.0603742\pi$
$397$	21.4760	+	16.0767i	1.07785	+	0.806867i	0.0957813	+	0.995402i	$0.469465\pi$
$398$		0			0
$399$	8.86077	+	13.7876i	0.443594	+	0.690245i
$400$		0			0
$401$	−11.1922	−	38.1170i	−0.558910	−	1.90347i	−0.401209	−	0.915987i	$-0.631410\pi$
$401$	−11.1922	−	38.1170i	−0.558910	−	1.90347i	−0.157701	−	0.987487i	$-0.550408\pi$
$402$		0			0
$403$	7.14068	−	0.510712i	0.355703	−	0.0254404i
$404$		0			0
$405$	−16.9619	+	1.29746i	−0.842845	+	0.0644715i
$406$		0			0
$407$	−2.38991	+	1.30499i	−0.118464	+	0.0646860i
$408$		0			0
$409$	−17.2592	−	7.88199i	−0.853410	−	0.389739i	−0.0598327	−	0.998208i	$-0.519057\pi$
$409$	−17.2592	−	7.88199i	−0.853410	−	0.389739i	−0.793578	+	0.608469i	$0.791784\pi$
$410$		0			0
$411$	−10.6234	+	16.5304i	−0.524015	+	0.815383i
$412$		0			0
$413$	19.0909	−	19.0909i	0.939404	−	0.939404i
$414$		0			0
$415$	−7.92364	−	17.1258i	−0.388956	−	0.840671i
$416$		0			0
$417$	31.2317	−	6.79403i	1.52942	−	0.332705i
$418$		0			0
$419$	2.37845	−	5.20808i	0.116195	−	0.254431i	−0.842595	−	0.538548i	$-0.818973\pi$
$419$	2.37845	−	5.20808i	0.116195	−	0.254431i	0.958790	+	0.284117i	$0.0917003\pi$
$420$		0			0
$421$	2.27591	−	7.75105i	0.110921	−	0.377763i	−0.885257	−	0.465101i	$-0.846018\pi$
$421$	2.27591	−	7.75105i	0.110921	−	0.377763i	0.996179	+	0.0873382i	$0.0278361\pi$
$422$		0			0
$423$	10.4690	−	28.0685i	0.509020	−	1.36474i
$424$		0			0
$425$	19.9261	+	14.6113i	0.966556	+	0.708750i
$426$		0			0
$427$	8.47089	−	15.5133i	0.409935	−	0.750740i
$428$		0			0
$429$	23.1487	−	14.8768i	1.11763	−	0.718257i
$430$		0			0
$431$	−13.2504	+	1.90512i	−0.638249	+	0.0917664i	−0.453840	−	0.891083i	$-0.649946\pi$
$431$	−13.2504	+	1.90512i	−0.638249	+	0.0917664i	−0.184409	+	0.982850i	$0.559037\pi$
$432$		0			0
$433$	−17.8211	−	23.8063i	−0.856429	−	1.14406i	−0.988260	−	0.152783i	$-0.951176\pi$
$433$	−17.8211	−	23.8063i	−0.856429	−	1.14406i	0.131830	−	0.991272i	$-0.457915\pi$
$434$		0			0
$435$	21.8909	−	48.5684i	1.04959	−	2.32868i
$436$		0			0
$437$	−13.5880	+	5.33794i	−0.650004	+	0.255348i
$438$		0			0
$439$	−0.570357	+	0.494217i	−0.0272216	+	0.0235877i	−0.668365	−	0.743833i	$-0.733006\pi$
$439$	−0.570357	+	0.494217i	−0.0272216	+	0.0235877i	0.641144	+	0.767421i	$0.278460\pi$
$440$		0			0
$441$	−3.09462	+	21.5235i	−0.147363	+	1.02493i
$442$		0			0
$443$	1.28112	−	1.71138i	0.0608679	−	0.0813099i	−0.769074	−	0.639159i	$-0.779282\pi$
$443$	1.28112	−	1.71138i	0.0608679	−	0.0813099i	0.829942	+	0.557849i	$0.188373\pi$
$444$		0			0
$445$	7.28801	+	32.7227i	0.345485	+	1.55120i
$446$		0			0
$447$	20.0333	+	10.9390i	0.947540	+	0.517396i
$448$		0			0
$449$	22.6962	+	19.6664i	1.07110	+	0.928113i	0.997604	−	0.0691827i	$-0.0220392\pi$
$449$	22.6962	+	19.6664i	1.07110	+	0.928113i	0.0734953	+	0.997296i	$0.476585\pi$
$450$		0			0
$451$	−32.8463	+	15.0004i	−1.54667	+	0.706342i
$452$		0			0
$453$	−31.3159	−	57.3508i	−1.47135	−	2.69457i
$454$		0			0
$455$	−7.39289	+	7.46636i	−0.346584	+	0.350028i
$456$		0			0
$457$	−1.22155	−	5.61537i	−0.0571416	−	0.262676i	0.939709	−	0.341974i	$-0.111096\pi$
$457$	−1.22155	−	5.61537i	−0.0571416	−	0.262676i	−0.996851	+	0.0792985i	$0.974732\pi$
$458$		0			0
$459$	41.7718			1.94974
$460$		0			0
$461$	−14.8552			−0.691875			−0.345937	−	0.938258i	$-0.612439\pi$
$461$	−14.8552			−0.691875			−0.345937	+	0.938258i	$0.612439\pi$
$462$		0			0
$463$	−5.92712	−	27.2465i	−0.275456	−	1.26625i	−0.882018	−	0.471216i	$-0.843815\pi$
$463$	−5.92712	−	27.2465i	−0.275456	−	1.26625i	0.606561	−	0.795037i	$-0.292548\pi$
$464$		0			0
$465$	−0.0906847	−	18.3413i	−0.00420540	−	0.850559i
$466$		0			0
$467$	−9.68082	−	17.7291i	−0.447975	−	0.820405i	0.551934	−	0.833888i	$-0.313890\pi$
$467$	−9.68082	−	17.7291i	−0.447975	−	0.820405i	−0.999909	+	0.0134828i	$0.995708\pi$
$468$		0			0
$469$	3.56125	−	1.62637i	0.164443	−	0.0750987i
$470$		0			0
$471$	−46.7334	−	40.4947i	−2.15336	−	1.86590i
$472$		0			0
$473$	15.9585	+	8.71399i	0.733772	+	0.400670i
$474$		0			0
$475$	−15.0862	−	2.01701i	−0.692202	−	0.0925469i
$476$		0			0
$477$	−37.3121	+	49.8431i	−1.70840	+	2.28216i
$478$		0			0
$479$	2.87792	−	20.0164i	0.131495	−	0.914571i	−0.812111	−	0.583503i	$-0.801682\pi$
$479$	2.87792	−	20.0164i	0.131495	−	0.914571i	0.943607	−	0.331068i	$-0.107409\pi$
$480$		0			0
$481$	−1.49790	+	1.29794i	−0.0682985	+	0.0591809i
$482$		0			0
$483$	24.3455	+	8.60309i	1.10776	+	0.391454i
$484$		0			0
$485$	−2.69811	−	1.21610i	−0.122515	−	0.0552202i
$486$		0			0
$487$	−3.48889	−	4.66061i	−0.158097	−	0.211192i	0.714498	−	0.699638i	$-0.246655\pi$
$487$	−3.48889	−	4.66061i	−0.158097	−	0.211192i	−0.872595	+	0.488445i	$0.837564\pi$
$488$		0			0
$489$	30.9548	−	4.45063i	1.39983	−	0.201265i
$490$		0			0
$491$	−17.8403	+	11.4652i	−0.805120	+	0.517419i	−0.877283	−	0.479974i	$-0.840646\pi$
$491$	−17.8403	+	11.4652i	−0.805120	+	0.517419i	0.0721629	+	0.997393i	$0.477010\pi$
$492$		0			0
$493$	−18.9752	+	34.7505i	−0.854601	+	1.56508i
$494$		0			0
$495$	−22.5260	−	40.7727i	−1.01247	−	1.83260i
$496$		0			0
$497$	0.714819	−	1.91650i	0.0320640	−	0.0859669i
$498$		0			0
$499$	9.46591	−	32.2379i	0.423752	−	1.44317i	−0.420535	−	0.907276i	$-0.638158\pi$
$499$	9.46591	−	32.2379i	0.423752	−	1.44317i	0.844287	−	0.535891i	$-0.180024\pi$
$500$		0			0
$501$	20.4307	−	44.7369i	0.912775	−	1.99870i
$502$		0			0
$503$	32.0298	−	6.96765i	1.42814	−	0.310672i	0.568967	−	0.822361i	$-0.307343\pi$
$503$	32.0298	−	6.96765i	1.42814	−	0.310672i	0.859171	+	0.511688i	$0.170980\pi$
$504$		0			0
$505$	3.91281	−	10.6512i	0.174118	−	0.473972i
$506$		0			0
$507$	−13.1722	+	13.1722i	−0.585000	+	0.585000i
$508$		0			0
$509$	1.72269	−	2.68055i	0.0763567	−	0.118813i	−0.800975	−	0.598698i	$-0.795685\pi$
$509$	1.72269	−	2.68055i	0.0763567	−	0.118813i	0.877332	+	0.479884i	$0.159321\pi$
$510$		0			0
$511$	4.08104	+	1.86375i	0.180535	+	0.0824474i
$512$		0			0
$513$	−22.5834	+	12.3315i	−0.997083	+	0.544448i
$514$		0			0
$515$	−15.9430	+	18.5840i	−0.702532	+	0.818911i
$516$		0			0
$517$	18.2355	−	1.30423i	0.801997	−	0.0573599i
$518$		0			0
$519$	−11.8025	−	40.1957i	−0.518074	−	1.76440i
$520$		0			0
$521$	3.39650	+	5.28506i	0.148803	+	0.231543i	0.907651	−	0.419726i	$-0.137874\pi$
$521$	3.39650	+	5.28506i	0.148803	+	0.231543i	−0.758848	+	0.651268i	$0.774237\pi$
$522$		0			0
$523$	29.8788	+	22.3670i	1.30651	+	0.978040i	0.999655	+	0.0262829i	$0.00836708\pi$
$523$	29.8788	+	22.3670i	1.30651	+	0.978040i	0.306854	+	0.951757i	$0.400724\pi$
$524$		0			0
$525$	17.8292	+	20.1695i	0.778130	+	0.880270i
$526$		0			0
$527$	−0.972470	+	13.5969i	−0.0423615	+	0.592291i
$528$		0			0
$529$	−11.7572	+	19.7679i	−0.511181	+	0.859473i
$530$		0			0
$531$	57.0528	+	65.8424i	2.47588	+	2.85732i
$532$		0			0
$533$	−21.0409	+	15.7510i	−0.911382	+	0.682252i
$534$		0			0
$535$	22.4785	+	34.5999i	0.971829	+	1.49588i
$536$		0			0
$537$	1.71953	−	7.90453i	0.0742030	−	0.341106i
$538$		0			0
$539$	−12.7327	+	3.73867i	−0.548438	+	0.161036i
$540$		0			0
$541$	13.1815	−	15.2122i	0.566715	−	0.654024i	−0.397980	−	0.917394i	$-0.630289\pi$
$541$	13.1815	−	15.2122i	0.566715	−	0.654024i	0.964695	+	0.263370i	$0.0848340\pi$
$542$		0			0
$543$	59.2882	+	22.1133i	2.54430	+	0.948974i
$544$		0			0
$545$	2.72690	−	3.68050i	0.116807	−	0.157655i
$546$		0			0
$547$	−9.37097	−	25.1245i	−0.400674	−	1.07425i	−0.968043	−	0.250784i	$-0.919311\pi$
$547$	−9.37097	−	25.1245i	−0.400674	−	1.07425i	0.567369	−	0.823464i	$-0.307961\pi$
$548$		0			0
$549$	47.9822	+	30.8363i	2.04783	+	1.31606i
$550$		0			0
$551$		−	24.3891i		−	1.03901i
$552$		0			0
$553$	−11.1657	−	11.1657i	−0.474816	−	0.474816i
$554$		0			0
$555$	3.06320	+	4.05007i	0.130026	+	0.171916i
$556$		0			0
$557$	−36.5110	+	13.6179i	−1.54702	+	0.577008i	−0.970717	−	0.240228i	$-0.922778\pi$
$557$	−36.5110	+	13.6179i	−1.54702	+	0.577008i	−0.576303	+	0.817236i	$0.695505\pi$
$558$		0			0
$559$	12.6986	+	3.72866i	0.537095	+	0.157705i
$560$		0			0
$561$	21.7662	+	47.6613i	0.918970	+	2.01226i
$562$		0			0
$563$	2.90656	+	40.6391i	0.122497	+	1.71273i	0.572665	+	0.819789i	$0.305909\pi$
$563$	2.90656	+	40.6391i	0.122497	+	1.71273i	−0.450168	+	0.892944i	$0.648636\pi$
$564$		0			0
$565$	−2.79421	−	3.19266i	−0.117553	−	0.134316i
$566$		0			0
$567$	13.4597	+	2.92797i	0.565253	+	0.122963i
$568$		0			0
$569$	0.824056	+	5.73143i	0.0345462	+	0.240274i	0.999777	−	0.0211256i	$-0.00672499\pi$
$569$	0.824056	+	5.73143i	0.0345462	+	0.240274i	−0.965231	+	0.261400i	$0.915816\pi$
$570$		0			0
$571$	10.6339	+	1.52892i	0.445014	+	0.0639833i	0.361179	−	0.932496i	$-0.382374\pi$
$571$	10.6339	+	1.52892i	0.445014	+	0.0639833i	0.0838344	+	0.996480i	$0.473283\pi$
$572$		0			0
$573$	−37.4312	−	2.67714i	−1.56371	−	0.111839i
$574$		0			0
$575$	−20.7256	+	12.0603i	−0.864316	+	0.502949i
$576$		0			0
$577$	−20.2714	−	1.44984i	−0.843908	−	0.0603575i	−0.357312	−	0.933985i	$-0.616307\pi$
$577$	−20.2714	−	1.44984i	−0.843908	−	0.0603575i	−0.486595	+	0.873628i	$0.661761\pi$
$578$		0			0
$579$	−54.6996	−	7.86462i	−2.27324	−	0.326843i
$580$		0			0
$581$	2.17447	+	15.1238i	0.0902123	+	0.627440i
$582$		0			0
$583$	−37.1282	−	8.07675i	−1.53769	−	0.334505i
$584$		0			0
$585$	−22.3299	−	25.5141i	−0.923229	−	1.05488i
$586$		0			0
$587$	−2.67825	−	37.4468i	−0.110543	−	1.54560i	−0.685902	−	0.727694i	$-0.740592\pi$
$587$	−2.67825	−	37.4468i	−0.110543	−	1.54560i	0.575359	−	0.817901i	$-0.304862\pi$
$588$		0			0
$589$	−3.48820	−	7.63809i	−0.143729	−	0.314722i
$590$		0			0
$591$	−34.1324	−	10.0222i	−1.40402	−	0.412258i
$592$		0			0
$593$	3.25063	−	1.21242i	0.133487	−	0.0497881i	−0.281833	−	0.959464i	$-0.590942\pi$
$593$	3.25063	−	1.21242i	0.133487	−	0.0497881i	0.415320	+	0.909675i	$0.363670\pi$
$594$		0			0
$595$	−12.0690	−	15.9572i	−0.494779	−	0.654180i
$596$		0			0
$597$	23.3535	+	23.3535i	0.955795	+	0.955795i
$598$		0			0
$599$		−	28.3255i		−	1.15735i	−0.815559	−	0.578674i	$-0.803570\pi$
$599$		−	28.3255i		−	1.15735i	0.815559	−	0.578674i	$-0.196430\pi$
$600$		0			0
$601$	6.78254	+	4.35887i	0.276666	+	0.177802i	0.671614	−	0.740901i	$-0.265601\pi$
$601$	6.78254	+	4.35887i	0.276666	+	0.177802i	−0.394949	+	0.918703i	$0.629238\pi$
$602$		0			0
$603$	4.41494	+	11.8369i	0.179790	+	0.482036i
$604$		0			0
$605$	2.28042	−	3.07789i	0.0927122	−	0.125134i
$606$		0			0
$607$	−27.7004	−	10.3317i	−1.12432	−	0.419352i	−0.282589	−	0.959241i	$-0.591193\pi$
$607$	−27.7004	−	10.3317i	−1.12432	−	0.419352i	−0.841736	+	0.539890i	$0.818466\pi$
$608$		0			0
$609$	−28.2485	+	32.6005i	−1.14469	+	1.32104i
$610$		0			0
$611$	12.7681	−	3.74906i	0.516543	−	0.151671i
$612$		0			0
$613$	3.57967	−	16.4555i	0.144582	−	0.664631i	−0.846612	−	0.532210i	$-0.821362\pi$
$613$	3.57967	−	16.4555i	0.144582	−	0.664631i	0.991194	−	0.132420i	$-0.0422748\pi$
$614$		0			0
$615$	36.6861	+	56.4688i	1.47932	+	2.27704i
$616$		0			0
$617$	−7.65339	+	5.72926i	−0.308114	+	0.230651i	−0.742133	−	0.670252i	$-0.766186\pi$
$617$	−7.65339	+	5.72926i	−0.308114	+	0.230651i	0.434019	+	0.900904i	$0.357095\pi$
$618$		0			0
$619$	5.61749	+	6.48293i	0.225786	+	0.260571i	0.857328	−	0.514771i	$-0.172123\pi$
$619$	5.61749	+	6.48293i	0.225786	+	0.260571i	−0.631542	+	0.775342i	$0.717578\pi$
$620$		0			0
$621$	−16.1989	+	37.1607i	−0.650039	+	1.49121i
$622$		0			0
$623$	1.93652	−	27.0761i	0.0775850	−	1.08478i
$624$		0			0
$625$	−24.9951	+	0.494392i	−0.999804	+	0.0197757i
$626$		0			0
$627$	−25.8378	−	19.3419i	−1.03186	−	0.772442i
$628$		0			0
$629$	−2.04040	−	3.17492i	−0.0813560	−	0.126592i
$630$		0			0
$631$	4.77422	+	16.2595i	0.190059	+	0.647280i	0.998292	+	0.0584182i	$0.0186057\pi$
$631$	4.77422	+	16.2595i	0.190059	+	0.647280i	−0.808234	+	0.588862i	$0.799576\pi$
$632$		0			0
$633$	31.7207	−	2.26871i	1.26078	−	0.0901731i
$634$		0			0
$635$	−4.74288	+	5.52857i	−0.188216	+	0.219395i
$636$		0			0
$637$	−8.47764	+	4.62914i	−0.335896	+	0.183413i
$638$		0			0
$639$	6.00405	+	2.74196i	0.237517	+	0.108470i
$640$		0			0
$641$	−24.3407	+	37.8748i	−0.961399	+	1.49597i	−0.0956944	+	0.995411i	$0.530507\pi$
$641$	−24.3407	+	37.8748i	−0.961399	+	1.49597i	−0.865705	+	0.500555i	$0.833129\pi$
$642$		0			0
$643$	10.7461	−	10.7461i	0.423786	−	0.423786i	−0.462719	−	0.886505i	$-0.653126\pi$
$643$	10.7461	−	10.7461i	0.423786	−	0.423786i	0.886505	+	0.462719i	$0.153126\pi$
$644$		0			0
$645$	11.6925	−	31.8284i	0.460390	−	1.25324i
$646$		0			0
$647$	−8.77419	+	1.90871i	−0.344949	+	0.0750391i	−0.381702	−	0.924285i	$-0.624662\pi$
$647$	−8.77419	+	1.90871i	−0.344949	+	0.0750391i	0.0367533	+	0.999324i	$0.488298\pi$
$648$		0			0
$649$	−22.0868	+	48.3634i	−0.866983	+	1.89843i
$650$		0			0
$651$	−4.18413	+	14.2498i	−0.163989	+	0.558496i
$652$		0			0
$653$	−10.7592	+	28.8465i	−0.421040	+	1.12885i	0.537343	+	0.843364i	$0.319428\pi$
$653$	−10.7592	+	28.8465i	−0.421040	+	1.12885i	−0.958383	+	0.285487i	$0.907845\pi$
$654$		0			0
$655$	−19.5075	−	35.3091i	−0.762220	−	1.37964i
$656$		0			0
$657$	−6.93828	+	12.7065i	−0.270688	+	0.495728i
$658$		0			0
$659$	9.23178	−	5.93290i	0.359619	−	0.231113i	−0.348337	−	0.937369i	$-0.613254\pi$
$659$	9.23178	−	5.93290i	0.359619	−	0.231113i	0.707956	+	0.706256i	$0.249617\pi$
$660$		0			0
$661$	44.6395	−	6.41819i	1.73628	−	0.249639i	0.799774	−	0.600301i	$-0.204953\pi$
$661$	44.6395	−	6.41819i	1.73628	−	0.249639i	0.936502	+	0.350663i	$0.114044\pi$
$662$		0			0
$663$	22.8554	+	30.5312i	0.887628	+	1.18573i
$664$		0			0
$665$	11.2357	+	5.06417i	0.435701	+	0.196380i
$666$		0			0
$667$	−23.5560	−	30.3566i	−0.912092	−	1.17541i
$668$		0			0
$669$	47.4103	−	41.0812i	1.83299	−	1.58829i
$670$		0			0
$671$	−4.95367	+	34.4535i	−0.191234	+	1.33006i
$672$		0			0
$673$	−7.91235	+	10.5697i	−0.304999	+	0.407431i	−0.926687	−	0.375834i	$-0.877356\pi$
$673$	−7.91235	+	10.5697i	−0.304999	+	0.407431i	0.621688	+	0.783265i	$0.286447\pi$
$674$		0			0
$675$	−33.5817	+	25.6610i	−1.29256	+	0.987693i
$676$		0			0
$677$	7.16859	+	3.91434i	0.275511	+	0.150440i	0.611065	−	0.791581i	$-0.290742\pi$
$677$	7.16859	+	3.91434i	0.275511	+	0.150440i	−0.335554	+	0.942021i	$0.608923\pi$
$678$		0			0
$679$	1.81105	+	1.56928i	0.0695015	+	0.0602234i
$680$		0			0
$681$	−33.1779	+	15.1518i	−1.27138	+	0.580620i
$682$		0			0
$683$	−7.11113	−	13.0231i	−0.272100	−	0.498313i	0.705521	−	0.708689i	$-0.250713\pi$
$683$	−7.11113	−	13.0231i	−0.272100	−	0.498313i	−0.977621	+	0.210376i	$0.932531\pi$
$684$		0			0
$685$	0.0730549	+	14.7756i	0.00279129	+	0.564548i
$686$		0			0
$687$	−3.14586	−	14.4613i	−0.120022	−	0.551733i
$688$		0			0
$689$	−27.6569			−1.05364
$690$		0			0
$691$	25.8521			0.983458			0.491729	−	0.870748i	$-0.336365\pi$
$691$	25.8521			0.983458			0.491729	+	0.870748i	$0.336365\pi$
$692$		0			0
$693$	8.01748	+	36.8558i	0.304559	+	1.40004i
$694$		0			0
$695$	16.9106	−	17.0786i	0.641455	−	0.647829i
$696$		0			0
$697$	−23.9851	−	43.9255i	−0.908502	−	1.66380i
$698$		0			0
$699$	38.4058	−	17.5393i	1.45264	−	0.663399i
$700$		0			0
$701$	8.43887	+	7.31232i	0.318732	+	0.276183i	0.799501	−	0.600664i	$-0.205097\pi$
$701$	8.43887	+	7.31232i	0.318732	+	0.276183i	−0.480770	+	0.876847i	$0.659643\pi$
$702$		0			0
$703$	2.04039	+	1.11414i	0.0769547	+	0.0420205i
$704$		0			0
$705$	−7.41176	−	33.2783i	−0.279143	−	1.25333i
$706$		0			0
$707$	−5.50614	+	7.35534i	−0.207080	+	0.276626i
$708$		0			0
$709$	−6.08406	+	42.3155i	−0.228492	+	1.58919i	0.475977	+	0.879458i	$0.342095\pi$
$709$	−6.08406	+	42.3155i	−0.228492	+	1.58919i	−0.704468	+	0.709735i	$0.748814\pi$
$710$		0			0
$711$	38.5093	−	33.3685i	1.44421	−	1.25142i
$712$		0			0
$713$	−11.7189	−	6.13793i	−0.438875	−	0.229867i
$714$		0			0
$715$	8.50248	−	18.8641i	0.317975	−	0.705477i
$716$		0			0
$717$	−16.1822	−	21.6169i	−0.604335	−	0.807297i
$718$		0			0
$719$	−9.17866	+	1.31969i	−0.342306	+	0.0492162i	−0.311324	−	0.950304i	$-0.600773\pi$
$719$	−9.17866	+	1.31969i	−0.342306	+	0.0492162i	−0.0309820	+	0.999520i	$0.509863\pi$
$720$		0			0
$721$	16.6790	−	10.7189i	0.621159	−	0.399194i
$722$		0			0
$723$	−23.7905	+	43.5690i	−0.884777	+	1.62035i
$724$		0			0
$725$	−6.09293	−	39.5938i	−0.226286	−	1.47048i
$726$		0			0
$727$	6.65641	−	17.8465i	0.246872	−	0.661891i	−0.753119	−	0.657884i	$-0.771452\pi$
$727$	6.65641	−	17.8465i	0.246872	−	0.661891i	0.999992	−	0.00400700i	$-0.00127547\pi$
$728$		0			0
$729$	8.72174	−	29.7035i	0.323027	−	1.10013i
$730$		0			0
$731$	−10.4688	+	22.9235i	−0.387204	+	0.847858i
$732$		0			0
$733$	28.5682	−	6.21462i	1.05519	−	0.229542i	0.348677	−	0.937243i	$-0.386631\pi$
$733$	28.5682	−	6.21462i	1.05519	−	0.229542i	0.706512	+	0.707701i	$0.250267\pi$
$734$		0			0
$735$	10.3916	+	22.4598i	0.383299	+	0.828443i
$736$		0			0
$737$	−5.45168	+	5.45168i	−0.200815	+	0.200815i
$738$		0			0
$739$	4.01599	−	6.24900i	0.147731	−	0.229873i	−0.759500	−	0.650508i	$-0.774556\pi$
$739$	4.01599	−	6.24900i	0.147731	−	0.229873i	0.907230	+	0.420634i	$0.138193\pi$
$740$		0			0
$741$	−21.3696	−	9.75917i	−0.785032	−	0.358512i
$742$		0			0
$743$	4.21392	−	2.30097i	0.154594	−	0.0844145i	−0.400090	−	0.916476i	$-0.631021\pi$
$743$	4.21392	−	2.30097i	0.154594	−	0.0844145i	0.554684	+	0.832061i	$0.312839\pi$
$744$		0			0
$745$	17.1137	−	1.30908i	0.626999	−	0.0479609i
$746$		0			0
$747$	−49.1792	+	3.51736i	−1.79937	+	0.128694i
$748$		0			0
$749$	−9.41248	−	32.0560i	−0.343925	−	1.17130i
$750$		0			0
$751$	−24.2330	−	37.7073i	−0.884276	−	1.37596i	−0.926277	−	0.376843i	$-0.877010\pi$
$751$	−24.2330	−	37.7073i	−0.884276	−	1.37596i	0.0420013	−	0.999118i	$-0.486627\pi$
$752$		0			0
$753$	−21.3257	−	15.9642i	−0.777150	−	0.581767i
$754$		0			0
$755$	−43.2415	−	23.3349i	−1.57372	−	0.849242i
$756$		0			0
$757$	2.06393	−	28.8575i	0.0750148	−	1.04884i	−0.810957	−	0.585105i	$-0.801053\pi$
$757$	2.06393	−	28.8575i	0.0750148	−	1.04884i	0.885972	−	0.463738i	$-0.153492\pi$
$758$		0			0
$759$	−50.8409	+	0.880673i	−1.84541	+	0.0319664i
$760$		0			0
$761$	−11.6888	−	13.4896i	−0.423719	−	0.488998i	0.503247	−	0.864142i	$-0.332138\pi$
$761$	−11.6888	−	13.4896i	−0.423719	−	0.488998i	−0.926966	+	0.375145i	$0.877593\pi$
$762$		0			0
$763$	−2.96920	+	2.22272i	−0.107492	+	0.0804678i
$764$		0			0
$765$	54.1393	−	35.1727i	1.95741	−	1.27167i
$766$		0			0
$767$	−8.22626	+	37.8155i	−0.297033	+	1.36544i
$768$		0			0
$769$	36.3748	−	10.6806i	1.31171	−	0.385152i	0.450215	−	0.892920i	$-0.351347\pi$
$769$	36.3748	−	10.6806i	1.31171	−	0.385152i	0.861494	+	0.507768i	$0.169529\pi$
$770$		0			0
$771$	−56.9287	+	65.6992i	−2.05024	+	2.36610i
$772$		0			0
$773$	4.41386	+	1.64628i	0.158756	+	0.0592127i	0.427586	−	0.903975i	$-0.359364\pi$
$773$	4.41386	+	1.64628i	0.158756	+	0.0592127i	−0.268830	+	0.963188i	$0.586637\pi$
$774$		0			0
$775$	−7.57097	−	11.5284i	−0.271957	−	0.414113i
$776$		0			0
$777$	−1.43691	−	3.85250i	−0.0515488	−	0.138208i
$778$		0			0
$779$	25.9346	+	16.6671i	0.929202	+	0.597162i
$780$		0			0
$781$			4.02812i			0.144137i
$782$		0			0
$783$	−47.8875	−	47.8875i	−1.71136	−	1.71136i
$784$		0			0
$785$	−46.0581	−	6.38989i	−1.64388	−	0.228065i
$786$		0			0
$787$	−0.868501	+	0.323934i	−0.0309587	+	0.0115470i	−0.364896	−	0.931048i	$-0.618895\pi$
$787$	−0.868501	+	0.323934i	−0.0309587	+	0.0115470i	0.333937	+	0.942595i	$0.391623\pi$
$788$		0			0
$789$	−40.0643	−	11.7639i	−1.42633	−	0.418807i
$790$		0			0
$791$	1.42711	+	3.12495i	0.0507424	+	0.111110i
$792$		0			0
$793$	1.80744	+	25.2713i	0.0641841	+	0.897411i
$794$		0			0
$795$	−4.70548	+	70.7022i	−0.166886	+	2.50755i
$796$		0			0
$797$	0.915441	+	0.199142i	0.0324266	+	0.00705397i	0.228749	−	0.973485i	$-0.426536\pi$
$797$	0.915441	+	0.199142i	0.0324266	+	0.00705397i	−0.196323	+	0.980539i	$0.562900\pi$
$798$		0			0
$799$	3.60609	+	25.0809i	0.127574	+	0.887298i
$800$		0			0
$801$	86.7033	+	12.4661i	3.06351	+	0.440467i
$802$		0			0
$803$	−8.81264	−	0.630292i	−0.310991	−	0.0222425i
$804$		0			0
$805$	18.8760	−	4.54859i	0.665291	−	0.160317i
$806$		0			0
$807$	84.7229	+	6.05950i	2.98239	+	0.213305i
$808$		0			0
$809$	−50.2756	−	7.22854i	−1.76760	−	0.254142i	−0.819716	−	0.572770i	$-0.805869\pi$
$809$	−50.2756	−	7.22854i	−1.76760	−	0.254142i	−0.947880	+	0.318628i	$0.896778\pi$
$810$		0			0
$811$	−7.16387	−	49.8258i	−0.251557	−	1.74962i	−0.588870	−	0.808228i	$-0.700427\pi$
$811$	−7.16387	−	49.8258i	−0.251557	−	1.74962i	0.337312	−	0.941393i	$-0.390482\pi$
$812$		0			0
$813$	45.9026	+	9.98550i	1.60988	+	0.350207i
$814$		0			0
$815$	17.6960	−	15.4875i	0.619865	−	0.542505i
$816$		0			0
$817$	−1.10743	−	15.4838i	−0.0387440	−	0.541711i
$818$		0			0
$819$	11.4048	+	24.9730i	0.398515	+	0.872627i
$820$		0			0
$821$	25.2708	+	7.42017i	0.881956	+	0.258966i	0.691193	−	0.722671i	$-0.257086\pi$
$821$	25.2708	+	7.42017i	0.881956	+	0.258966i	0.190763	+	0.981636i	$0.438904\pi$
$822$		0			0
$823$	−36.9824	+	13.7937i	−1.28913	+	0.480819i	−0.898194	−	0.439600i	$-0.855120\pi$
$823$	−36.9824	+	13.7937i	−1.28913	+	0.480819i	−0.390933	+	0.920419i	$0.627848\pi$
$824$		0			0
$825$	−46.7776	−	24.9452i	−1.62859	−	0.868481i
$826$		0			0
$827$	19.9623	+	19.9623i	0.694156	+	0.694156i	0.963144	−	0.268988i	$-0.0866892\pi$
$827$	19.9623	+	19.9623i	0.694156	+	0.694156i	−0.268988	+	0.963144i	$0.586689\pi$
$828$		0			0
$829$			12.3100i			0.427546i	0.976883	+	0.213773i	$0.0685752\pi$
$829$			12.3100i			0.427546i	−0.976883	+	0.213773i	$0.931425\pi$
$830$		0			0
$831$	−16.6833	−	10.7217i	−0.578737	−	0.371931i
$832$		0			0
$833$	−6.42751	−	17.2328i	−0.222700	−	0.597082i
$834$		0			0
$835$	−5.44408	−	36.5796i	−0.188400	−	1.26589i
$836$		0			0
$837$	−21.8462	−	8.14821i	−0.755115	−	0.281643i
$838$		0			0
$839$	−19.5625	+	22.5763i	−0.675372	+	0.779421i	−0.985207	−	0.171370i	$-0.945181\pi$
$839$	−19.5625	+	22.5763i	−0.675372	+	0.779421i	0.309835	+	0.950790i	$0.399726\pi$
$840$		0			0
$841$	33.7663	−	9.91467i	1.16435	−	0.341885i
$842$		0			0
$843$	−4.32718	+	19.8917i	−0.149036	+	0.685107i
$844$		0			0
$845$	−2.90987	+	13.7023i	−0.100102	+	0.471372i
$846$		0			0
$847$	−2.48305	+	1.85879i	−0.0853186	+	0.0638687i
$848$		0			0
$849$	36.8261	+	42.4996i	1.26387	+	1.45858i
$850$		0			0
$851$	3.61571	−	0.583946i	0.123945	−	0.0200174i
$852$		0			0
$853$	−0.839477	+	11.7374i	−0.0287431	+	0.401882i	0.962631	+	0.270817i	$0.0872940\pi$
$853$	−0.839477	+	11.7374i	−0.0287431	+	0.401882i	−0.991374	+	0.131064i	$0.958161\pi$
$854$		0			0
$855$	−18.8864	+	34.9982i	−0.645902	+	1.19691i
$856$		0			0
$857$	34.0512	+	25.4904i	1.16317	+	0.870736i	0.993395	−	0.114748i	$-0.0366059\pi$
$857$	34.0512	+	25.4904i	1.16317	+	0.870736i	0.169772	+	0.985483i	$0.445697\pi$
$858$		0			0
$859$	−22.9598	−	35.7262i	−0.783379	−	1.21896i	−0.971552	−	0.236825i	$-0.923893\pi$
$859$	−22.9598	−	35.7262i	−0.783379	−	1.21896i	0.188174	−	0.982136i	$-0.439743\pi$
$860$		0			0
$861$	−15.3617	−	52.3170i	−0.523524	−	1.78296i
$862$		0			0
$863$	−6.84475	+	0.489546i	−0.232998	+	0.0166644i	−0.187350	−	0.982293i	$-0.559990\pi$
$863$	−6.84475	+	0.489546i	−0.232998	+	0.0166644i	−0.0456481	+	0.998958i	$0.514535\pi$
$864$		0			0
$865$	−23.9091	−	20.5113i	−0.812935	−	0.697405i
$866$		0			0
$867$	−19.3693	+	10.5764i	−0.657816	+	0.359195i
$868$		0			0
$869$	28.2864	+	12.9179i	0.959549	+	0.438211i
$870$		0			0
$871$	−3.03398	+	4.72097i	−0.102803	+	0.159964i
$872$		0			0
$873$	−5.46792	+	5.46792i	−0.185061	+	0.185061i
$874$		0			0
$875$	19.5053	+	5.41437i	0.659401	+	0.183039i
$876$		0			0
$877$	31.4508	−	6.84170i	1.06202	−	0.231028i	0.352570	−	0.935786i	$-0.385308\pi$
$877$	31.4508	−	6.84170i	1.06202	−	0.231028i	0.709448	+	0.704758i	$0.248944\pi$
$878$		0			0
$879$	−21.9432	+	48.0488i	−0.740125	+	1.62065i
$880$		0			0
$881$	−5.28568	+	18.0014i	−0.178079	+	0.606482i	0.821274	+	0.570533i	$0.193263\pi$
$881$	−5.28568	+	18.0014i	−0.178079	+	0.606482i	−0.999354	+	0.0359487i	$0.988555\pi$
$882$		0			0
$883$	−0.918158	+	2.46168i	−0.0308985	+	0.0828421i	−0.951483	−	0.307701i	$-0.900440\pi$
$883$	−0.918158	+	2.46168i	−0.0308985	+	0.0828421i	0.920584	+	0.390544i	$0.127713\pi$
$884$		0			0
$885$	95.2720	+	27.4635i	3.20253	+	0.923174i
$886$		0			0
$887$	−13.0719	+	23.9393i	−0.438911	+	0.803805i	−0.999708	−	0.0241481i	$-0.992313\pi$
$887$	−13.0719	+	23.9393i	−0.438911	+	0.803805i	0.560798	+	0.827953i	$0.310494\pi$
$888$		0			0
$889$	4.96184	−	3.18878i	0.166415	−	0.106948i
$890$		0			0
$891$	−26.8497	+	3.86041i	−0.899500	+	0.129329i
$892$		0			0
$893$	−9.35373	−	12.4951i	−0.313011	−	0.418133i
$894$		0			0
$895$	−2.15392	−	5.68882i	−0.0719976	−	0.190156i
$896$		0			0
$897$	−36.0241	+	8.49258i	−1.20281	+	0.283559i
$898$		0			0
$899$	16.7024	−	14.4728i	0.557058	−	0.482693i
$900$		0			0
$901$	7.49471	−	52.1268i	0.249685	−	1.73660i
$902$		0			0
$903$	−16.4537	+	21.9796i	−0.547546	+	0.731435i
$904$		0			0
$905$	46.4446	−	10.3442i	1.54387	−	0.343852i
$906$		0			0
$907$	−8.45157	−	4.61490i	−0.280630	−	0.153235i	0.332770	−	0.943008i	$-0.392017\pi$
$907$	−8.45157	−	4.61490i	−0.280630	−	0.153235i	−0.613400	+	0.789773i	$0.710199\pi$
$908$		0			0
$909$	−22.4069	−	19.4157i	−0.743191	−	0.643979i
$910$		0			0
$911$	−14.7162	+	6.72067i	−0.487570	+	0.222666i	−0.644003	−	0.765023i	$-0.722728\pi$
$911$	−14.7162	+	6.72067i	−0.487570	+	0.222666i	0.156433	+	0.987689i	$0.450000\pi$
$912$		0			0
$913$	−14.4203	−	26.4088i	−0.477241	−	0.874002i
$914$		0			0
$915$	64.9111	−	0.320939i	2.14590	−	0.0106099i
$916$		0			0
$917$	6.94312	+	31.9170i	0.229282	+	1.05399i
$918$		0			0
$919$	10.2513			0.338160			0.169080	−	0.985602i	$-0.445920\pi$
$919$	10.2513			0.338160			0.169080	+	0.985602i	$0.445920\pi$
$920$		0			0
$921$	25.6658			0.845717
$922$		0			0
$923$	0.623238	+	2.86498i	0.0205141	+	0.0943019i
$924$		0			0
$925$	3.59074	+	1.29898i	0.118063	+	0.0427102i
$926$		0			0
$927$	30.6613	+	56.1519i	1.00705	+	1.84427i
$928$		0			0
$929$	12.8273	−	5.85802i	0.420849	−	0.192195i	−0.193722	−	0.981056i	$-0.562056\pi$
$929$	12.8273	−	5.85802i	0.420849	−	0.192195i	0.614572	+	0.788861i	$0.289329\pi$
$930$		0			0
$931$	8.56227	+	7.41925i	0.280617	+	0.243156i
$932$		0			0
$933$	30.6723	+	16.7484i	1.00417	+	0.548316i
$934$		0			0
$935$	33.2503	+	21.1371i	1.08740	+	0.691258i
$936$		0			0
$937$	22.6861	−	30.3051i	0.741123	−	0.990024i	−0.258588	−	0.965988i	$-0.583257\pi$
$937$	22.6861	−	30.3051i	0.741123	−	0.990024i	0.999711	−	0.0240364i	$-0.00765177\pi$
$938$		0			0
$939$	11.9795	−	83.3190i	0.390935	−	2.71901i
$940$		0			0
$941$	−18.5057	+	16.0353i	−0.603268	+	0.522735i	−0.902075	−	0.431579i	$-0.857957\pi$
$941$	−18.5057	+	16.0353i	−0.603268	+	0.522735i	0.298807	+	0.954314i	$0.403411\pi$
$942$		0			0
$943$	48.3780	−	4.30340i	1.57540	−	0.140138i
$944$		0			0
$945$	32.0043	−	12.1176i	1.04110	−	0.394185i
$946$		0			0
$947$	13.9680	+	18.6590i	0.453897	+	0.606336i	0.967864	−	0.251474i	$-0.0809154\pi$
$947$	13.9680	+	18.6590i	0.453897	+	0.606336i	−0.513967	+	0.857810i	$0.671824\pi$
$948$		0			0
$949$	−6.36546	+	0.915216i	−0.206632	+	0.0297092i
$950$		0			0
$951$	52.3530	−	33.6453i	1.69766	−	1.09102i
$952$		0			0
$953$	−19.8575	+	36.3664i	−0.643249	+	1.17802i	0.329057	+	0.944310i	$0.393269\pi$
$953$	−19.8575	+	36.3664i	−0.643249	+	1.17802i	−0.972306	+	0.233712i	$0.924913\pi$
$954$		0			0
$955$	−24.6999	+	13.6461i	−0.799269	+	0.441578i
$956$		0			0
$957$	29.6864	−	79.5922i	0.959624	−	2.57285i
$958$		0			0
$959$	3.37071	−	11.4796i	0.108846	−	0.370695i
$960$		0			0
$961$	−9.71699	+	21.2772i	−0.313451	+	0.686363i
$962$		0			0
$963$	105.345	−	22.9163i	3.39468	−	0.738468i
$964$		0			0
$965$	−37.7140	+	17.4493i	−1.21406	+	0.561712i
$966$		0			0
$967$	−21.2351	+	21.2351i	−0.682876	+	0.682876i	−0.960647	−	0.277771i	$-0.910404\pi$
$967$	−21.2351	+	21.2351i	−0.682876	+	0.682876i	0.277771	+	0.960647i	$0.410404\pi$
$968$		0			0
$969$	24.1847	−	37.6321i	0.776924	−	1.20892i
$970$		0			0
$971$	−48.4369	−	22.1204i	−1.55442	−	0.709878i	−0.561365	−	0.827569i	$-0.689724\pi$
$971$	−48.4369	−	22.1204i	−1.55442	−	0.709878i	−0.993050	+	0.117691i	$0.962451\pi$
$972$		0			0
$973$	−17.0804	+	9.32663i	−0.547574	+	0.298998i
$974$		0			0
$975$	−37.1299	−	10.5046i	−1.18911	−	0.336418i
$976$		0			0
$977$	−11.4741	+	0.820646i	−0.367090	+	0.0262548i	−0.253666	−	0.967292i	$-0.581636\pi$
$977$	−11.4741	+	0.820646i	−0.367090	+	0.0262548i	−0.113424	+	0.993547i	$0.536182\pi$
$978$		0			0
$979$	15.0605	+	51.2913i	0.481336	+	1.63928i
$980$		0			0
$981$	−6.47069	−	10.0686i	−0.206593	−	0.321465i
$982$		0			0
$983$	−19.4625	−	14.5694i	−0.620756	−	0.464692i	0.242025	−	0.970270i	$-0.422188\pi$
$983$	−19.4625	−	14.5694i	−0.620756	−	0.464692i	−0.862781	+	0.505578i	$0.831279\pi$
$984$		0			0
$985$	−25.6287	+	7.66312i	−0.816600	+	0.244167i
$986$		0			0
$987$	−1.96940	+	27.5358i	−0.0626867	+	0.876475i
$988$		0			0
$989$	−16.3333	−	18.2028i	−0.519369	−	0.578816i
$990$		0			0
$991$	30.2714	+	34.9350i	0.961601	+	1.10975i	0.993902	+	0.110269i	$0.0351712\pi$
$991$	30.2714	+	34.9350i	0.961601	+	1.10975i	−0.0323004	+	0.999478i	$0.510283\pi$
$992$		0			0
$993$	33.5068	−	25.0829i	1.06331	−	0.795981i
$994$		0			0
$995$	24.2932	+	5.15900i	0.770146	+	0.163551i
$996$		0			0
$997$	−3.90311	+	17.9423i	−0.123613	+	0.568239i	0.873123	+	0.487501i	$0.162091\pi$
$997$	−3.90311	+	17.9423i	−0.123613	+	0.568239i	−0.996735	+	0.0807379i	$0.974272\pi$
$998$		0			0
$999$	6.19383	−	1.81867i	0.195964	−	0.0575403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.33.1	✓	240
5.2	odd	4	inner	460.2.x.a.217.1	yes	240
23.7	odd	22	inner	460.2.x.a.53.1	yes	240
115.7	even	44	inner	460.2.x.a.237.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.1	✓	240	1.1	even	1	trivial
460.2.x.a.53.1	yes	240	23.7	odd	22	inner
460.2.x.a.217.1	yes	240	5.2	odd	4	inner
460.2.x.a.237.1	yes	240	115.7	even	44	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.632093 - 2.90569i) q^{3} +(-1.58894 - 1.57330i) q^{5} +(0.867718 + 1.58911i) q^{7} +(-5.31457 + 2.42708i) q^{9} +O(q^{10})\)	\(q+(-0.632093 - 2.90569i) q^{3} +(-1.58894 - 1.57330i) q^{5} +(0.867718 + 1.58911i) q^{7} +(-5.31457 + 2.42708i) q^{9} +(-2.69466 - 2.33494i) q^{11} +(-2.27783 - 1.24379i) q^{13} +(-3.56717 + 5.61143i) q^{15} +(2.96152 - 3.95612i) q^{17} +(-0.433218 + 3.01310i) q^{19} +(4.06896 - 3.52578i) q^{21} +(2.37095 + 4.16876i) q^{23} +(0.0494416 + 4.99976i) q^{25} +(5.06554 + 6.76676i) q^{27} +(-7.93043 + 1.14022i) q^{29} +(-2.32054 + 1.49132i) q^{31} +(-5.08131 + 9.30573i) q^{33} +(1.12140 - 3.89017i) q^{35} +(0.266884 - 0.715545i) q^{37} +(-2.17426 + 7.40484i) q^{39} +(4.20705 - 9.21215i) q^{41} +(-4.98299 + 1.08398i) q^{43} +(12.2631 + 4.50494i) q^{45} +(-3.62564 + 3.62564i) q^{47} +(2.01216 - 3.13098i) q^{49} +(-13.3672 - 6.10460i) q^{51} +(9.35307 - 5.10716i) q^{53} +(0.608085 + 7.94958i) q^{55} +(9.02896 - 0.645764i) q^{57} +(-4.20109 - 14.3076i) q^{59} +(-5.27788 - 8.21254i) q^{61} +(-8.46844 - 6.33940i) q^{63} +(1.66247 + 5.56001i) q^{65} +(0.154258 - 2.15681i) q^{67} +(10.6144 - 9.52429i) q^{69} +(-0.739818 - 0.853796i) q^{71} +(1.98368 - 1.48496i) q^{73} +(14.4965 - 3.30397i) q^{75} +(1.37226 - 6.30816i) q^{77} +(-8.36811 + 2.45710i) q^{79} +(4.98203 - 5.74957i) q^{81} +(7.90684 + 2.94910i) q^{83} +(-10.9298 + 1.62667i) q^{85} +(8.32590 + 22.3226i) q^{87} +(-12.6126 - 8.10560i) q^{89} -4.69897i q^{91} +(5.80011 + 5.80011i) q^{93} +(5.42887 - 4.10604i) q^{95} +(1.24008 - 0.462527i) q^{97} +(19.9880 + 5.86902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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