LMFDB - Embedded newform 882.2.bl.a.395.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(17,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 25])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			395.15
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-0.924397 - 0.630244i) q^{5} +(1.36229 - 2.26807i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-0.630244 - 0.924397i) q^{10} +(-0.924207 - 6.13171i) q^{11} +(2.15845 - 1.72131i) q^{13} +(2.09674 - 1.61359i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-4.51289 - 1.39204i) q^{17} +(-4.88179 + 2.81850i) q^{19} +(-0.248957 - 1.09075i) q^{20} +(1.37985 - 6.04550i) q^{22} +(0.299773 + 0.971839i) q^{23} +(-1.36940 - 3.48918i) q^{25} +(2.63811 - 0.813750i) q^{26} +(2.54131 - 0.736021i) q^{28} +(1.14103 - 0.260434i) q^{29} +(5.75165 + 3.32072i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-3.69236 - 2.94456i) q^{34} +(-2.68874 + 1.23802i) q^{35} +(4.50654 - 4.18146i) q^{37} +(-5.57405 + 0.840152i) q^{38} +(0.166749 - 1.10631i) q^{40} +(7.52027 - 3.62157i) q^{41} +(8.54429 + 4.11471i) q^{43} +(3.49313 - 5.12348i) q^{44} +(-0.0760022 + 1.01418i) q^{46} +(0.589901 - 1.50304i) q^{47} +(-3.28831 - 6.17956i) q^{49} -3.74828i q^{50} +(2.75305 + 0.206312i) q^{52} +(0.592437 - 0.638495i) q^{53} +(-3.01014 + 6.25061i) q^{55} +(2.63454 + 0.243303i) q^{56} +(1.15731 + 0.174436i) q^{58} +(-1.05910 + 0.722085i) q^{59} +(8.96313 + 9.65996i) q^{61} +(4.14086 + 5.19248i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-3.08011 + 0.230823i) q^{65} +(2.32005 - 4.01844i) q^{67} +(-2.36135 - 4.08998i) q^{68} +(-2.95518 + 0.170138i) q^{70} +(-13.0590 - 2.98064i) q^{71} +(-7.08624 + 2.78115i) q^{73} +(5.72268 - 2.24598i) q^{74} +(-5.49568 - 1.25435i) q^{76} +(-15.1662 - 6.25702i) q^{77} +(1.51603 + 2.62584i) q^{79} +(0.559401 - 0.968911i) q^{80} +(8.32353 - 0.623762i) q^{82} +(-11.3221 + 14.1974i) q^{83} +(3.29438 + 4.13102i) q^{85} +(6.45038 + 6.95186i) q^{86} +(5.12348 - 3.49313i) q^{88} +(1.88234 + 0.283717i) q^{89} +(-0.963610 - 7.24046i) q^{91} +(-0.441270 + 0.916306i) q^{92} +(1.09825 - 1.18363i) q^{94} +(6.28906 + 0.471300i) q^{95} -0.768508i q^{97} +(-0.803359 - 6.95375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{42}\right)$	$-1$

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 $

$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$2$	0.930874	+	0.365341i	0.658227	+	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−0.924397	−	0.630244i	−0.413403	−	0.281853i	0.338706	−	0.940892i	$-0.390011\pi$
$5$	−0.924397	−	0.630244i	−0.413403	−	0.281853i	−0.752109	+	0.659039i	$0.770963\pi$
$6$		0			0
$7$	1.36229	−	2.26807i	0.514898	−	0.857251i
$7$	1.36229	−	2.26807i	0.514898	−	0.857251i
$8$	0.433884	+	0.900969i	0.153401	+	0.318541i
$9$		0			0
$10$	−0.630244	−	0.924397i	−0.199300	−	0.292320i
$11$	−0.924207	−	6.13171i	−0.278659	−	1.84878i	−0.490455	−	0.871467i	$-0.663169\pi$
$11$	−0.924207	−	6.13171i	−0.278659	−	1.84878i	0.211796	−	0.977314i	$-0.432069\pi$
$12$		0			0
$13$	2.15845	−	1.72131i	0.598647	−	0.477405i	−0.276663	−	0.960967i	$-0.589229\pi$
$13$	2.15845	−	1.72131i	0.598647	−	0.477405i	0.875310	+	0.483562i	$0.160657\pi$
$14$	2.09674	−	1.61359i	0.560378	−	0.431250i
$15$		0			0
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−4.51289	−	1.39204i	−1.09454	−	0.337620i	−0.305640	−	0.952147i	$-0.598871\pi$
$17$	−4.51289	−	1.39204i	−1.09454	−	0.337620i	−0.788896	+	0.614527i	$0.789347\pi$
$18$		0			0
$19$	−4.88179	+	2.81850i	−1.11996	+	0.646609i	−0.941391	−	0.337318i	$-0.890480\pi$
$19$	−4.88179	+	2.81850i	−1.11996	+	0.646609i	−0.178569	+	0.983927i	$0.557147\pi$
$20$	−0.248957	−	1.09075i	−0.0556684	−	0.243899i
$21$		0			0
$22$	1.37985	−	6.04550i	0.294184	−	1.28891i
$23$	0.299773	+	0.971839i	0.0625069	+	0.202642i	0.981439	−	0.191772i	$-0.0614235\pi$
$23$	0.299773	+	0.971839i	0.0625069	+	0.202642i	−0.918933	+	0.394415i	$0.870947\pi$
$24$		0			0
$25$	−1.36940	−	3.48918i	−0.273880	−	0.697836i
$26$	2.63811	−	0.813750i	0.517376	−	0.159590i
$27$		0			0
$28$	2.54131	−	0.736021i	0.480263	−	0.139095i
$29$	1.14103	−	0.260434i	0.211885	−	0.0483613i	−0.115261	−	0.993335i	$-0.536770\pi$
$29$	1.14103	−	0.260434i	0.211885	−	0.0483613i	0.327146	+	0.944974i	$0.393913\pi$
$30$		0			0
$31$	5.75165	+	3.32072i	1.03303	+	0.596418i	0.917850	−	0.396927i	$-0.129923\pi$
$31$	5.75165	+	3.32072i	1.03303	+	0.596418i	0.115176	+	0.993345i	$0.463257\pi$
$32$	−0.294755	+	0.955573i	−0.0521058	+	0.168923i
$33$		0			0
$34$	−3.69236	−	2.94456i	−0.633234	−	0.504988i
$35$	−2.68874	+	1.23802i	−0.454480	+	0.209264i
$36$		0			0
$37$	4.50654	−	4.18146i	0.740870	−	0.687427i	−0.216503	−	0.976282i	$-0.569465\pi$
$37$	4.50654	−	4.18146i	0.740870	−	0.687427i	0.957373	+	0.288855i	$0.0932745\pi$
$38$	−5.57405	+	0.840152i	−0.904230	+	0.136291i
$39$		0			0
$40$	0.166749	−	1.10631i	0.0263653	−	0.174922i
$41$	7.52027	−	3.62157i	1.17447	−	0.565594i	0.258174	−	0.966099i	$-0.416879\pi$
$41$	7.52027	−	3.62157i	1.17447	−	0.565594i	0.916295	+	0.400504i	$0.131165\pi$
$42$		0			0
$43$	8.54429	+	4.11471i	1.30299	+	0.627488i	0.951196	−	0.308589i	$-0.0998567\pi$
$43$	8.54429	+	4.11471i	1.30299	+	0.627488i	0.351796	+	0.936077i	$0.385571\pi$
$44$	3.49313	−	5.12348i	0.526609	−	0.772394i
$45$		0			0
$46$	−0.0760022	+	1.01418i	−0.0112059	+	0.149533i
$47$	0.589901	−	1.50304i	0.0860459	−	0.219241i	−0.881374	−	0.472420i	$-0.843381\pi$
$47$	0.589901	−	1.50304i	0.0860459	−	0.219241i	0.967420	+	0.253178i	$0.0814759\pi$
$48$		0			0
$49$	−3.28831	−	6.17956i	−0.469759	−	0.882795i
$50$		−	3.74828i		−	0.530087i
$51$		0			0
$52$	2.75305	+	0.206312i	0.381779	+	0.0286104i
$53$	0.592437	−	0.638495i	0.0813774	−	0.0877040i	−0.691050	−	0.722807i	$-0.742852\pi$
$53$	0.592437	−	0.638495i	0.0813774	−	0.0877040i	0.772428	+	0.635103i	$0.219042\pi$
$54$		0			0
$55$	−3.01014	+	6.25061i	−0.405887	+	0.842833i
$56$	2.63454	+	0.243303i	0.352055	+	0.0325128i
$57$		0			0
$58$	1.15731	+	0.174436i	0.151962	+	0.0229046i
$59$	−1.05910	+	0.722085i	−0.137884	+	0.0940075i	−0.630297	−	0.776354i	$-0.717067\pi$
$59$	−1.05910	+	0.722085i	−0.137884	+	0.0940075i	0.492414	+	0.870361i	$0.336115\pi$
$60$		0			0
$61$	8.96313	+	9.65996i	1.14761	+	1.23683i	0.967414	+	0.253200i	$0.0814831\pi$
$61$	8.96313	+	9.65996i	1.14761	+	1.23683i	0.180197	+	0.983630i	$0.442326\pi$
$62$	4.14086	+	5.19248i	0.525890	+	0.659446i
$63$		0			0
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−3.08011	+	0.230823i	−0.382041	+	0.0286300i
$66$		0			0
$67$	2.32005	−	4.01844i	0.283439	−	0.490930i	−0.688791	−	0.724960i	$-0.741858\pi$
$67$	2.32005	−	4.01844i	0.283439	−	0.490930i	0.972229	+	0.234030i	$0.0751914\pi$
$68$	−2.36135	−	4.08998i	−0.286356	−	0.495983i
$69$		0			0
$70$	−2.95518	+	0.170138i	−0.353211	+	0.0203354i
$71$	−13.0590	−	2.98064i	−1.54982	−	0.353737i	−0.639881	−	0.768474i	$-0.721016\pi$
$71$	−13.0590	−	2.98064i	−1.54982	−	0.353737i	−0.909941	+	0.414737i	$0.863874\pi$
$72$		0			0
$73$	−7.08624	+	2.78115i	−0.829382	+	0.325508i	−0.741777	−	0.670647i	$-0.766017\pi$
$73$	−7.08624	+	2.78115i	−0.829382	+	0.325508i	−0.0876052	+	0.996155i	$0.527921\pi$
$74$	5.72268	−	2.24598i	0.665248	−	0.261090i
$75$		0			0
$76$	−5.49568	−	1.25435i	−0.630397	−	0.143884i
$77$	−15.1662	−	6.25702i	−1.72835	−	0.713054i
$78$		0			0
$79$	1.51603	+	2.62584i	0.170567	+	0.295430i	0.938618	−	0.344958i	$-0.112107\pi$
$79$	1.51603	+	2.62584i	0.170567	+	0.295430i	−0.768051	+	0.640388i	$0.778773\pi$
$80$	0.559401	−	0.968911i	0.0625429	−	0.108328i
$81$		0			0
$82$	8.32353	−	0.623762i	0.919180	−	0.0688830i
$83$	−11.3221	+	14.1974i	−1.24276	+	1.55837i	−0.557117	+	0.830434i	$0.688093\pi$
$83$	−11.3221	+	14.1974i	−1.24276	+	1.55837i	−0.685643	+	0.727938i	$0.740479\pi$
$84$		0			0
$85$	3.29438	+	4.13102i	0.357325	+	0.448072i
$86$	6.45038	+	6.95186i	0.695562	+	0.749638i
$87$		0			0
$88$	5.12348	−	3.49313i	0.546165	−	0.372369i
$89$	1.88234	+	0.283717i	0.199527	+	0.0300739i	0.248045	−	0.968748i	$-0.420212\pi$
$89$	1.88234	+	0.283717i	0.199527	+	0.0300739i	−0.0485181	+	0.998822i	$0.515450\pi$
$90$		0			0
$91$	−0.963610	−	7.24046i	−0.101014	−	0.759006i
$92$	−0.441270	+	0.916306i	−0.0460055	+	0.0955315i
$93$		0			0
$94$	1.09825	−	1.18363i	0.113275	−	0.122082i
$95$	6.28906	+	0.471300i	0.645244	+	0.0483543i
$96$		0			0
$97$		−	0.768508i		−	0.0780301i	−0.999239	−	0.0390151i	$-0.987578\pi$
$97$		−	0.768508i		−	0.0780301i	0.999239	−	0.0390151i	$-0.0124220\pi$
$98$	−0.803359	−	6.95375i	−0.0811515	−	0.702435i
$99$		0			0
$100$	1.36940	−	3.48918i	0.136940	−	0.348918i
$101$	−0.847999	+	11.3158i	−0.0843790	+	1.12596i	0.780895	+	0.624662i	$0.214763\pi$
$101$	−0.847999	+	11.3158i	−0.0843790	+	1.12596i	−0.865275	+	0.501298i	$0.832856\pi$
$102$		0			0
$103$	−0.534269	+	0.783629i	−0.0526431	+	0.0772132i	−0.851658	−	0.524098i	$-0.824402\pi$
$103$	−0.534269	+	0.783629i	−0.0526431	+	0.0772132i	0.799015	+	0.601311i	$0.205355\pi$
$104$	2.48736	+	1.19785i	0.243906	+	0.117459i
$105$		0			0
$106$	0.784752	−	0.377917i	0.0762218	−	0.0367065i
$107$	2.33479	−	15.4903i	0.225713	−	1.49751i	−0.533018	−	0.846104i	$-0.678942\pi$
$107$	2.33479	−	15.4903i	0.225713	−	1.49751i	0.758731	−	0.651404i	$-0.225820\pi$
$108$		0			0
$109$	15.8297	−	2.38594i	1.51621	−	0.228532i	0.662413	−	0.749139i	$-0.269532\pi$
$109$	15.8297	−	2.38594i	1.51621	−	0.228532i	0.853797	+	0.520607i	$0.174294\pi$
$110$	−5.08566	+	4.71881i	−0.484899	+	0.449921i
$111$		0			0
$112$	2.36354	+	1.18899i	0.223333	+	0.112349i
$113$	5.56859	+	4.44081i	0.523849	+	0.417756i	0.849385	−	0.527774i	$-0.176973\pi$
$113$	5.56859	+	4.44081i	0.523849	+	0.417756i	−0.325536	+	0.945530i	$0.605545\pi$
$114$		0			0
$115$	0.335386	−	1.08730i	0.0312749	−	0.101391i
$116$	1.01358	+	0.585189i	0.0941083	+	0.0543335i
$117$		0			0
$118$	−1.24970	+	0.285236i	−0.115044	+	0.0262581i
$119$	−9.30513	+	8.33919i	−0.853000	+	0.764453i
$120$		0			0
$121$	−26.2324	+	8.09163i	−2.38477	+	0.735603i
$122$	4.81436	+	12.2668i	0.435872	+	1.11058i
$123$		0			0
$124$	1.95760	+	6.34637i	0.175797	+	0.569921i
$125$	−2.17794	+	9.54220i	−0.194801	+	0.853480i
$126$		0			0
$127$	1.77537	+	7.77839i	0.157538	+	0.690221i	0.990571	+	0.136998i	$0.0437452\pi$
$127$	1.77537	+	7.77839i	0.157538	+	0.690221i	−0.833033	+	0.553223i	$0.813398\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.95153	−	0.910425i	−0.258866	−	0.0798496i
$131$	0.955823	+	12.7546i	0.0835106	+	1.11437i	0.868774	+	0.495210i	$0.164909\pi$
$131$	0.955823	+	12.7546i	0.0835106	+	1.11437i	−0.785263	+	0.619162i	$0.787472\pi$
$132$		0			0
$133$	−0.257858	+	14.9119i	−0.0223591	+	1.29302i
$134$	3.62777	−	2.89305i	0.313392	−	0.249921i
$135$		0			0
$136$	−0.703883	−	4.66996i	−0.0603574	−	0.400445i
$137$	3.86517	+	5.66916i	0.330223	+	0.484349i	0.955062	−	0.296405i	$-0.0957878\pi$
$137$	3.86517	+	5.66916i	0.330223	+	0.484349i	−0.624839	+	0.780754i	$0.714835\pi$
$138$		0			0
$139$	−5.54916	−	11.5230i	−0.470674	−	0.977364i	−0.992261	−	0.124166i	$-0.960374\pi$
$139$	−5.54916	−	11.5230i	−0.470674	−	0.977364i	0.521588	−	0.853198i	$-0.325340\pi$
$140$	−2.81306	−	0.921270i	−0.237747	−	0.0778616i
$141$		0			0
$142$	−11.0674	−	7.54560i	−0.928752	−	0.633213i
$143$	−12.5494	−	11.6442i	−1.04944	−	0.973734i
$144$		0			0
$145$	−1.21891	−	0.478385i	−0.101225	−	0.0397277i
$146$	−7.61246			−0.630012
$147$		0			0
$148$	6.14764			0.505333
$149$	10.4131	+	4.08686i	0.853078	+	0.334808i	0.751270	−	0.659996i	$-0.229442\pi$
$149$	10.4131	+	4.08686i	0.853078	+	0.334808i	0.101809	+	0.994804i	$0.467537\pi$
$150$		0			0
$151$	−1.85718	−	1.72321i	−0.151135	−	0.140233i	0.600982	−	0.799263i	$-0.294776\pi$
$151$	−1.85718	−	1.72321i	−0.151135	−	0.140233i	−0.752117	+	0.659030i	$0.770967\pi$
$152$	−4.65751	−	3.17544i	−0.377774	−	0.257562i
$153$		0			0
$154$	−11.8319	−	11.3653i	−0.953440	−	0.915845i
$155$	−3.22395	−	6.69460i	−0.258954	−	0.537723i
$156$		0			0
$157$	−10.9897	−	16.1190i	−0.877077	−	1.28644i	−0.957134	−	0.289645i	$-0.906463\pi$
$157$	−10.9897	−	16.1190i	−0.877077	−	1.28644i	0.0800576	−	0.996790i	$-0.474490\pi$
$158$	0.451905	+	2.99820i	0.0359516	+	0.238524i
$159$		0			0
$160$	0.874714	−	0.697562i	0.0691523	−	0.0551471i
$161$	2.61258	+	0.644023i	0.205900	+	0.0507561i
$162$		0			0
$163$	1.51869	+	20.2654i	0.118953	+	1.58731i	0.663236	+	0.748411i	$0.269183\pi$
$163$	1.51869	+	20.2654i	0.118953	+	1.58731i	−0.544283	+	0.838902i	$0.683198\pi$
$164$	7.97604	+	2.46028i	0.622824	+	0.192116i
$165$		0			0
$166$	−15.7263	+	9.07961i	−1.22060	+	0.704714i
$167$	−0.516575	−	2.26326i	−0.0399738	−	0.175137i	0.951000	−	0.309190i	$-0.100058\pi$
$167$	−0.516575	−	2.26326i	−0.0399738	−	0.175137i	−0.990974	+	0.134053i	$0.957201\pi$
$168$		0			0
$169$	−1.19676	+	5.24333i	−0.0920581	+	0.403333i
$170$	1.55742	+	5.04903i	0.119449	+	0.387243i
$171$		0			0
$172$	3.46469	+	8.82789i	0.264180	+	0.673120i
$173$	16.0441	−	4.94895i	1.21981	−	0.376262i	0.382997	−	0.923750i	$-0.374892\pi$
$173$	16.0441	−	4.94895i	1.21981	−	0.376262i	0.836813	+	0.547488i	$0.184416\pi$
$174$		0			0
$175$	−9.77924	−	1.64738i	−0.739241	−	0.124530i
$176$	6.04550	−	1.37985i	0.455697	−	0.104010i
$177$		0			0
$178$	1.64856	+	0.951799i	0.123565	+	0.0713404i
$179$	6.09437	−	19.7575i	0.455514	−	1.47674i	−0.378814	−	0.925473i	$-0.623668\pi$
$179$	6.09437	−	19.7575i	0.455514	−	1.47674i	0.834328	−	0.551268i	$-0.185856\pi$
$180$		0			0
$181$	6.97049	+	5.55878i	0.518112	+	0.413181i	0.847325	−	0.531075i	$-0.178212\pi$
$181$	6.97049	+	5.55878i	0.518112	+	0.413181i	−0.329213	+	0.944256i	$0.606783\pi$
$182$	1.74824	−	7.09200i	0.129588	−	0.525694i
$183$		0			0
$184$	−0.745530	+	0.691751i	−0.0549612	+	0.0509966i
$185$	−6.80117	+	1.02511i	−0.500032	+	0.0753677i
$186$		0			0
$187$	−4.36476	+	28.9583i	−0.319183	+	2.11764i
$188$	1.45476	−	0.700574i	0.106099	−	0.0510946i
$189$		0			0
$190$	5.68214	+	2.73637i	0.412225	+	0.198517i
$191$	11.7684	−	17.2611i	0.851535	−	1.24897i	−0.115238	−	0.993338i	$-0.536763\pi$
$191$	11.7684	−	17.2611i	0.851535	−	1.24897i	0.966773	−	0.255635i	$-0.0822844\pi$
$192$		0			0
$193$	1.01184	−	13.5021i	0.0728340	−	0.971903i	−0.834368	−	0.551208i	$-0.814167\pi$
$193$	1.01184	−	13.5021i	0.0728340	−	0.971903i	0.907202	−	0.420695i	$-0.138214\pi$
$194$	0.280767	−	0.715384i	0.0201579	−	0.0513616i
$195$		0			0
$196$	1.79266	−	6.76656i	0.128047	−	0.483326i
$197$			4.67784i			0.333282i	0.986018	+	0.166641i	$0.0532921\pi$
$197$			4.67784i			0.333282i	−0.986018	+	0.166641i	$0.946708\pi$
$198$		0			0
$199$	−20.7359	−	1.55394i	−1.46993	−	0.110156i	−0.684456	−	0.729054i	$-0.739960\pi$
$199$	−20.7359	−	1.55394i	−1.46993	−	0.110156i	−0.785471	+	0.618899i	$0.787579\pi$
$200$	2.54948	−	2.74769i	0.180275	−	0.194291i
$201$		0			0
$202$	−4.92349	+	10.2237i	−0.346416	+	0.719339i
$203$	0.963741	−	2.94274i	0.0676413	−	0.206540i
$204$		0			0
$205$	−9.23419	−	1.39183i	−0.644944	−	0.0972096i
$206$	−0.783629	+	0.534269i	−0.0545980	+	0.0372243i
$207$		0			0
$208$	1.87780	+	2.02378i	0.130202	+	0.140324i
$209$	21.7940	+	27.3289i	1.50753	+	1.89038i
$210$		0			0
$211$	9.28004	−	11.6368i	0.638865	−	0.801111i	−0.351996	−	0.936002i	$-0.614497\pi$
$211$	9.28004	−	11.6368i	0.638865	−	0.801111i	0.990860	+	0.134891i	$0.0430683\pi$
$212$	0.868573	−	0.0650906i	0.0596539	−	0.00447044i
$213$		0			0
$214$	7.83266	−	13.5666i	0.535429	−	0.927391i
$215$	−5.30505	−	9.18861i	−0.361801	−	0.626658i
$216$		0			0
$217$	15.3671	−	8.52137i	1.04318	−	0.578468i
$218$	15.6071	+	3.56223i	1.05705	+	0.241264i
$219$		0			0
$220$	−6.45808	+	2.53461i	−0.435404	+	0.170883i
$221$	−12.1370	+	4.76342i	−0.816422	+	0.320422i
$222$		0			0
$223$	−20.8453	−	4.75781i	−1.39591	−	0.318606i	−0.542588	−	0.839999i	$-0.682556\pi$
$223$	−20.8453	−	4.75781i	−1.39591	−	0.318606i	−0.853317	+	0.521393i	$0.825413\pi$
$224$	1.76577	+	1.97030i	0.117980	+	0.131646i
$225$		0			0
$226$	3.56125	+	6.16826i	0.236891	+	0.410307i
$227$	−3.18721	+	5.52041i	−0.211542	+	0.366402i	−0.952197	−	0.305483i	$-0.901182\pi$
$227$	−3.18721	+	5.52041i	−0.211542	+	0.366402i	0.740655	+	0.671886i	$0.234515\pi$
$228$		0			0
$229$	−0.465808	+	0.0349075i	−0.0307815	+	0.00230675i	−0.0901119	−	0.995932i	$-0.528722\pi$
$229$	−0.465808	+	0.0349075i	−0.0307815	+	0.00230675i	0.0593305	+	0.998238i	$0.481103\pi$
$230$	0.709436	−	0.889604i	0.0467788	−	0.0586588i
$231$		0			0
$232$	0.729719	+	0.915039i	0.0479084	+	0.0600752i
$233$	16.8250	+	18.1330i	1.10224	+	1.18793i	0.980735	+	0.195342i	$0.0625816\pi$
$233$	16.8250	+	18.1330i	1.10224	+	1.18793i	0.121505	+	0.992591i	$0.461228\pi$
$234$		0			0
$235$	−1.49259	+	1.01763i	−0.0973656	+	0.0663827i
$236$	−1.26752	−	0.191048i	−0.0825086	−	0.0124362i
$237$		0			0
$238$	−11.7085	+	4.36319i	−0.758952	+	0.282824i
$239$	−6.23665	+	12.9505i	−0.403416	+	0.837701i	0.595982	+	0.802998i	$0.296763\pi$
$239$	−6.23665	+	12.9505i	−0.403416	+	0.837701i	−0.999398	+	0.0347034i	$0.988951\pi$
$240$		0			0
$241$	4.53582	−	4.88846i	0.292178	−	0.314893i	−0.569855	−	0.821745i	$-0.693001\pi$
$241$	4.53582	−	4.88846i	0.292178	−	0.314893i	0.862033	+	0.506852i	$0.169191\pi$
$242$	−27.3753	−	2.05149i	−1.75975	−	0.131875i
$243$		0			0
$244$			13.1777i			0.843617i
$245$	−0.854919	+	7.78481i	−0.0546188	+	0.497353i
$246$		0			0
$247$	−5.68560	+	14.4867i	−0.361766	+	0.921766i
$248$	−0.496315	+	6.62286i	−0.0315160	+	0.420552i
$249$		0			0
$250$	−5.51355	+	8.08689i	−0.348707	+	0.511460i
$251$	13.6293	+	6.56351i	0.860272	+	0.414285i	0.811380	−	0.584519i	$-0.198717\pi$
$251$	13.6293	+	6.56351i	0.860272	+	0.414285i	0.0488921	+	0.998804i	$0.484431\pi$
$252$		0			0
$253$	5.68199	−	2.73630i	0.357223	−	0.172030i
$254$	−1.18912	+	7.88932i	−0.0746122	+	0.495020i
$255$		0			0
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	7.15741	−	6.64111i	0.446467	−	0.414261i	−0.424634	−	0.905365i	$-0.639597\pi$
$257$	7.15741	−	6.64111i	0.446467	−	0.414261i	0.871101	+	0.491104i	$0.163407\pi$
$258$		0			0
$259$	−3.34462	−	15.9175i	−0.207825	−	0.989067i
$260$	−2.41488	−	1.92580i	−0.149765	−	0.119433i
$261$		0			0
$262$	−3.77002	+	12.2221i	−0.232912	+	0.755084i
$263$	8.70607	+	5.02645i	0.536839	+	0.309944i	0.743797	−	0.668406i	$-0.233023\pi$
$263$	8.70607	+	5.02645i	0.536839	+	0.309944i	−0.206958	+	0.978350i	$0.566356\pi$
$264$		0			0
$265$	−0.950054	+	0.216844i	−0.0583614	+	0.0133206i
$266$	−5.68796	+	13.7869i	−0.348751	+	0.845328i
$267$		0			0
$268$	4.43394	−	1.36769i	0.270846	−	0.0835450i
$269$	1.42151	+	3.62195i	0.0866711	+	0.220834i	0.967637	−	0.252345i	$-0.0812016\pi$
$269$	1.42151	+	3.62195i	0.0866711	+	0.220834i	−0.880966	+	0.473179i	$0.843106\pi$
$270$		0			0
$271$	−3.68025	−	11.9311i	−0.223559	−	0.724762i	−0.995974	−	0.0896430i	$-0.971427\pi$
$271$	−3.68025	−	11.9311i	−0.223559	−	0.724762i	0.772415	−	0.635119i	$-0.219049\pi$
$272$	1.05090	−	4.60430i	0.0637202	−	0.279176i
$273$		0			0
$274$	1.52681	+	6.68937i	0.0922377	+	0.404120i
$275$	−20.1290	+	11.6215i	−1.21383	+	0.700803i
$276$		0			0
$277$	−13.7508	−	4.24156i	−0.826206	−	0.254851i	−0.147315	−	0.989090i	$-0.547063\pi$
$277$	−13.7508	−	4.24156i	−0.826206	−	0.254851i	−0.678891	+	0.734239i	$0.737539\pi$
$278$	−0.955761	−	12.7537i	−0.0573228	−	0.764919i
$279$		0			0
$280$	−2.28202	−	1.88531i	−0.136377	−	0.112669i
$281$	−0.450935	+	0.359608i	−0.0269005	+	0.0214524i	−0.636848	−	0.770990i	$-0.719762\pi$
$281$	−0.450935	+	0.359608i	−0.0269005	+	0.0214524i	0.609947	+	0.792442i	$0.291191\pi$
$282$		0			0
$283$	0.190057	+	1.26095i	0.0112977	+	0.0749556i	0.993769	−	0.111457i	$-0.0355519\pi$
$283$	0.190057	+	1.26095i	0.0112977	+	0.0749556i	−0.982471	+	0.186413i	$0.940314\pi$
$284$	−7.54560	−	11.0674i	−0.447749	−	0.656727i
$285$		0			0
$286$	−7.42784	−	15.4241i	−0.439218	−	0.912045i
$287$	2.03082	−	21.9902i	0.119876	−	1.29804i
$288$		0			0
$289$	4.38232	+	2.98781i	0.257783	+	0.175754i
$290$	−0.959874	−	0.890633i	−0.0563657	−	0.0522998i
$291$		0			0
$292$	−7.08624	−	2.78115i	−0.414691	−	0.162754i
$293$	11.4137			0.666797			0.333399	−	0.942786i	$-0.391805\pi$
$293$	11.4137			0.666797			0.333399	+	0.942786i	$0.391805\pi$
$294$		0			0
$295$	1.43412			0.0834979
$296$	5.72268	+	2.24598i	0.332624	+	0.130545i
$297$		0			0
$298$	8.20023	+	7.60870i	0.475026	+	0.440760i
$299$	2.31988	+	1.58167i	0.134162	+	0.0914702i
$300$		0			0
$301$	20.9723	−	13.7736i	1.20882	−	0.793899i
$302$	−1.09924	−	2.28259i	−0.0632540	−	0.131348i
$303$		0			0
$304$	−3.17544	−	4.65751i	−0.182124	−	0.267127i
$305$	−2.19737	−	14.5786i	−0.125821	−	0.834768i
$306$		0			0
$307$	−9.66634	+	7.70865i	−0.551687	+	0.439956i	−0.859238	−	0.511576i	$-0.829062\pi$
$307$	−9.66634	+	7.70865i	−0.551687	+	0.439956i	0.307551	+	0.951532i	$0.400490\pi$
$308$	−6.86177	−	14.9024i	−0.390985	−	0.849141i
$309$		0			0
$310$	−0.555278	−	7.40967i	−0.0315377	−	0.420841i
$311$	−6.06500	−	1.87080i	−0.343914	−	0.106084i	0.117986	−	0.993015i	$-0.462356\pi$
$311$	−6.06500	−	1.87080i	−0.343914	−	0.106084i	−0.461901	+	0.886932i	$0.652832\pi$
$312$		0			0
$313$	26.3626	−	15.2204i	1.49010	−	0.860310i	0.490165	−	0.871630i	$-0.336936\pi$
$313$	26.3626	−	15.2204i	1.49010	−	0.860310i	0.999936	+	0.0113192i	$0.00360310\pi$
$314$	−4.34113	−	19.0197i	−0.244984	−	1.07335i
$315$		0			0
$316$	−0.674697	+	2.95604i	−0.0379547	+	0.166290i
$317$	−0.562789	−	1.82452i	−0.0316094	−	0.102475i	0.938393	−	0.345569i	$-0.112314\pi$
$317$	−0.562789	−	1.82452i	−0.0316094	−	0.102475i	−0.970003	+	0.243094i	$0.921838\pi$
$318$		0			0
$319$	−2.65146	−	6.75580i	−0.148453	−	0.378252i
$320$	1.06910	−	0.329773i	0.0597643	−	0.0184349i
$321$		0			0
$322$	2.19669	+	1.55399i	0.122417	+	0.0866003i
$323$	25.9545	−	5.92393i	1.44414	−	0.329617i
$324$		0			0
$325$	−8.96174	−	5.17407i	−0.497108	−	0.287005i
$326$	−5.99009	+	19.4194i	−0.331761	+	1.07554i
$327$		0			0
$328$	6.52584	+	5.20419i	0.360329	+	0.287353i
$329$	−2.60539	−	3.38552i	−0.143640	−	0.186650i
$330$		0			0
$331$	−25.4192	+	23.5855i	−1.39716	+	1.29638i	−0.492461	+	0.870335i	$0.663902\pi$
$331$	−25.4192	+	23.5855i	−1.39716	+	1.29638i	−0.904703	+	0.426043i	$0.859907\pi$
$332$	−17.9564	+	2.70649i	−0.985485	+	0.148538i
$333$		0			0
$334$	0.345997	−	2.29554i	0.0189321	−	0.125606i
$335$	−4.67724	+	2.25244i	−0.255545	+	0.123064i
$336$		0			0
$337$	9.31415	+	4.48546i	0.507374	+	0.244338i	0.670016	−	0.742347i	$-0.266287\pi$
$337$	9.31415	+	4.48546i	0.507374	+	0.244338i	−0.162642	+	0.986685i	$0.552002\pi$
$338$	−3.02963	+	4.44365i	−0.164790	+	0.241703i
$339$		0			0
$340$	−0.394857	+	5.26900i	−0.0214141	+	0.285751i
$341$	15.0460	−	38.3365i	0.814784	−	2.07604i
$342$		0			0
$343$	−18.4953	−	0.960235i	−0.998655	−	0.0518478i
$344$			9.48344i			0.511313i
$345$		0			0
$346$	16.7431	+	1.25472i	0.900114	+	0.0674542i
$347$	1.08346	−	1.16769i	0.0581630	−	0.0626848i	−0.703300	−	0.710893i	$-0.748291\pi$
$347$	1.08346	−	1.16769i	0.0581630	−	0.0626848i	0.761463	+	0.648208i	$0.224481\pi$
$348$		0			0
$349$	8.54305	−	17.7398i	0.457299	−	0.949591i	−0.537062	−	0.843543i	$-0.680466\pi$
$349$	8.54305	−	17.7398i	0.457299	−	0.949591i	0.994361	−	0.106048i	$-0.0338198\pi$
$350$	−8.50138	−	5.10626i	−0.454418	−	0.272941i
$351$		0			0
$352$	6.13171	+	0.924207i	0.326821	+	0.0492604i
$353$	−2.41313	+	1.64525i	−0.128438	+	0.0875676i	−0.625835	−	0.779955i	$-0.715242\pi$
$353$	−2.41313	+	1.64525i	−0.128438	+	0.0875676i	0.497397	+	0.867523i	$0.334289\pi$
$354$		0			0
$355$	10.1932	+	10.9857i	0.540999	+	0.583059i
$356$	1.18687	+	1.48829i	0.0629042	+	0.0788794i
$357$		0			0
$358$	12.8913	−	16.1652i	0.681326	−	0.854356i
$359$	−28.4978	+	2.13561i	−1.50406	+	0.112713i	−0.801105	−	0.598524i	$-0.795754\pi$
$359$	−28.4978	+	2.13561i	−1.50406	+	0.112713i	−0.702951	+	0.711238i	$0.748135\pi$
$360$		0			0
$361$	6.38793	−	11.0642i	0.336207	−	0.582327i
$362$	4.45779	+	7.72112i	0.234296	+	0.405813i
$363$		0			0
$364$	4.21839	−	5.96305i	0.221104	−	0.312549i
$365$	8.30330	+	1.89517i	0.434615	+	0.0991980i
$366$		0			0
$367$	−2.37627	+	0.932615i	−0.124040	+	0.0486821i	−0.426549	−	0.904464i	$-0.640271\pi$
$367$	−2.37627	+	0.932615i	−0.124040	+	0.0486821i	0.302509	+	0.953146i	$0.402176\pi$
$368$	−0.946720	+	0.371560i	−0.0493512	+	0.0193689i
$369$		0			0
$370$	−6.70554	−	1.53050i	−0.348605	−	0.0795667i
$371$	−0.641081	−	2.21351i	−0.0332833	−	0.114920i
$372$		0			0
$373$	1.73721	+	3.00893i	0.0899492	+	0.155797i	0.907489	−	0.420075i	$-0.137996\pi$
$373$	1.73721	+	3.00893i	0.0899492	+	0.155797i	−0.817540	+	0.575872i	$0.804663\pi$
$374$	−14.6427	+	25.3619i	−0.757155	+	1.31143i
$375$		0			0
$376$	1.61014	−	0.120664i	0.0830368	−	0.00622275i
$377$	2.01458	−	2.52621i	0.103756	−	0.130106i
$378$		0			0
$379$	17.3272	+	21.7276i	0.890037	+	1.11607i	0.992610	+	0.121345i	$0.0387208\pi$
$379$	17.3272	+	21.7276i	0.890037	+	1.11607i	−0.102574	+	0.994725i	$0.532708\pi$
$380$	4.28964	+	4.62313i	0.220054	+	0.237162i
$381$		0			0
$382$	17.2611	−	11.7684i	0.883157	−	0.602126i
$383$	28.7750	+	4.33713i	1.47033	+	0.221617i	0.834842	−	0.550490i	$-0.185559\pi$
$383$	28.7750	+	4.33713i	1.47033	+	0.221617i	0.635492	+	0.772107i	$0.280797\pi$
$384$		0			0
$385$	10.0762	+	15.3424i	0.513529	+	0.781920i
$386$	5.87477	−	12.1991i	0.299018	−	0.620917i
$387$		0			0
$388$	0.522718	−	0.563356i	0.0265370	−	0.0286001i
$389$	−14.1571	−	1.06093i	−0.717793	−	0.0537911i	−0.289174	−	0.957277i	$-0.593381\pi$
$389$	−14.1571	−	1.06093i	−0.717793	−	0.0537911i	−0.428619	+	0.903485i	$0.641000\pi$
$390$		0			0
$391$		−	4.80310i		−	0.242903i
$392$	4.14085	−	5.64388i	0.209144	−	0.285059i
$393$		0			0
$394$	−1.70901	+	4.35447i	−0.0860984	+	0.219375i
$395$	0.253505	−	3.38279i	0.0127552	−	0.170207i
$396$		0			0
$397$	3.37261	−	4.94671i	0.169266	−	0.248268i	−0.732227	−	0.681060i	$-0.761519\pi$
$397$	3.37261	−	4.94671i	0.169266	−	0.248268i	0.901494	+	0.432792i	$0.142472\pi$
$398$	−18.7348	−	9.02218i	−0.939088	−	0.452241i
$399$		0			0
$400$	3.37709	−	1.62632i	0.168854	−	0.0813159i
$401$	−0.465492	+	3.08833i	−0.0232455	+	0.154224i	−0.997442	−	0.0714763i	$-0.977229\pi$
$401$	−0.465492	+	3.08833i	−0.0232455	+	0.154224i	0.974197	+	0.225700i	$0.0724671\pi$
$402$		0			0
$403$	18.1306	−	2.73275i	0.903152	−	0.136128i
$404$	−8.31830	+	7.71825i	−0.413851	+	0.383997i
$405$		0			0
$406$	1.97222	−	2.38722i	0.0978798	−	0.118476i
$407$	−29.8045	−	23.7683i	−1.47735	−	1.17815i
$408$		0			0
$409$	5.63929	−	18.2821i	0.278845	−	0.903993i	−0.702491	−	0.711693i	$-0.747929\pi$
$409$	5.63929	−	18.2821i	0.278845	−	0.903993i	0.981336	−	0.192301i	$-0.0615949\pi$
$410$	−8.08737	−	4.66925i	−0.399407	−	0.230598i
$411$		0			0
$412$	−0.924650	+	0.211045i	−0.0455542	+	0.0103975i
$413$	0.194932	+	3.38582i	0.00959196	+	0.166605i
$414$		0			0
$415$	19.4140	−	5.98841i	0.952993	−	0.293960i
$416$	1.00862	+	2.56992i	0.0494517	+	0.126001i
$417$		0			0
$418$	10.3031	+	33.4020i	0.503943	+	1.63374i
$419$	−7.06400	+	30.9494i	−0.345099	+	1.51198i	0.443052	+	0.896496i	$0.353896\pi$
$419$	−7.06400	+	30.9494i	−0.345099	+	1.51198i	−0.788151	+	0.615482i	$0.788961\pi$
$420$		0			0
$421$	8.41495	+	36.8683i	0.410120	+	1.79685i	0.583630	+	0.812020i	$0.301632\pi$
$421$	8.41495	+	36.8683i	0.410120	+	1.79685i	−0.173510	+	0.984832i	$0.555511\pi$
$422$	12.8900	−	7.44202i	0.627473	−	0.362272i
$423$		0			0
$424$	0.832312	+	0.256734i	0.0404207	+	0.0124681i
$425$	1.32287	+	17.6525i	0.0641688	+	0.856274i
$426$		0			0
$427$	34.1199	−	7.16935i	1.65118	−	0.346949i
$428$	12.2476	−	9.76716i	0.592012	−	0.472114i
$429$		0			0
$430$	−1.58135	−	10.4916i	−0.0762596	−	0.505949i
$431$	−0.703991	−	1.03257i	−0.0339101	−	0.0497369i	0.808909	−	0.587933i	$-0.200058\pi$
$431$	−0.703991	−	1.03257i	−0.0339101	−	0.0497369i	−0.842819	+	0.538196i	$0.819106\pi$
$432$		0			0
$433$	1.45210	+	3.01531i	0.0697834	+	0.144907i	0.932943	−	0.360025i	$-0.117232\pi$
$433$	1.45210	+	3.01531i	0.0697834	+	0.144907i	−0.863159	+	0.504932i	$0.831518\pi$
$434$	17.4180	−	2.31811i	0.836091	−	0.111273i
$435$		0			0
$436$	13.2268	+	9.01791i	0.633451	+	0.431879i
$437$	−4.20256	−	3.89941i	−0.201036	−	0.186534i
$438$		0			0
$439$	−18.1308	−	7.11581i	−0.865336	−	0.339619i	−0.109189	−	0.994021i	$-0.534825\pi$
$439$	−18.1308	−	7.11581i	−0.865336	−	0.339619i	−0.756147	+	0.654402i	$0.772921\pi$
$440$	−6.93766			−0.330740
$441$		0			0
$442$	−13.0383			−0.620168
$443$	26.9305	+	10.5694i	1.27951	+	0.502170i	0.905141	−	0.425111i	$-0.139765\pi$
$443$	26.9305	+	10.5694i	1.27951	+	0.502170i	0.374366	+	0.927281i	$0.377860\pi$
$444$		0			0
$445$	−1.56122	−	1.44860i	−0.0740088	−	0.0686701i
$446$	−17.6661	−	12.0446i	−0.836515	−	0.570327i
$447$		0			0
$448$	0.923875	+	2.47920i	0.0436490	+	0.117131i
$449$	−9.22677	−	19.1596i	−0.435438	−	0.904197i	−0.997047	−	0.0767940i	$-0.975532\pi$
$449$	−9.22677	−	19.1596i	−0.435438	−	0.904197i	0.561609	−	0.827403i	$-0.310183\pi$
$450$		0			0
$451$	−29.1567	−	42.7650i	−1.37294	−	2.01373i
$452$	1.06155	+	7.04295i	0.0499313	+	0.331272i
$453$		0			0
$454$	−4.98372	+	3.97438i	−0.233898	+	0.186527i
$455$	−3.67249	+	7.30037i	−0.172169	+	0.342247i
$456$		0			0
$457$	−0.905504	−	12.0831i	−0.0423577	−	0.565224i	−0.977498	−	0.210946i	$-0.932346\pi$
$457$	−0.905504	−	12.0831i	−0.0423577	−	0.565224i	0.935140	−	0.354278i	$-0.115273\pi$
$458$	−0.446362	−	0.137684i	−0.0208571	−	0.00643357i
$459$		0			0
$460$	0.985404	−	0.568923i	0.0459447	−	0.0265262i
$461$	5.24407	+	22.9758i	0.244241	+	1.07009i	0.937112	+	0.349028i	$0.113488\pi$
$461$	5.24407	+	22.9758i	0.244241	+	1.07009i	−0.692871	+	0.721061i	$0.743655\pi$
$462$		0			0
$463$	3.40613	−	14.9232i	0.158296	−	0.693541i	−0.832024	−	0.554740i	$-0.812818\pi$
$463$	3.40613	−	14.9232i	0.158296	−	0.693541i	0.990320	−	0.138801i	$-0.0443250\pi$
$464$	0.344975	+	1.11838i	0.0160151	+	0.0519196i
$465$		0			0
$466$	9.03719	+	23.0264i	0.418640	+	1.06668i
$467$	−11.5332	+	3.55753i	−0.533694	+	0.164623i	−0.549876	−	0.835246i	$-0.685325\pi$
$467$	−11.5332	+	3.55753i	−0.533694	+	0.164623i	0.0161821	+	0.999869i	$0.494849\pi$
$468$		0			0
$469$	−5.95353	−	10.7363i	−0.274908	−	0.495757i
$470$	−1.76119	+	0.401980i	−0.0812377	+	0.0185420i
$471$		0			0
$472$	−1.11010	−	0.640919i	−0.0510967	−	0.0295007i
$473$	17.3335	−	56.1940i	0.796997	−	2.58380i
$474$		0			0
$475$	16.5194	+	13.1738i	0.757962	+	0.604454i
$476$	−12.4932	−	0.216034i	−0.572626	−	0.00990190i
$477$		0			0
$478$	−10.5369	+	9.77682i	−0.481947	+	0.447181i
$479$	27.6836	−	4.17263i	1.26489	−	0.190652i	0.517876	−	0.855456i	$-0.326723\pi$
$479$	27.6836	−	4.17263i	1.26489	−	0.190652i	0.747018	+	0.664804i	$0.231485\pi$
$480$		0			0
$481$	2.52957	−	16.7826i	0.115339	−	0.765222i
$482$	6.00823	−	2.89341i	0.273667	−	0.131791i
$483$		0			0
$484$	−24.7334	−	11.9110i	−1.12425	−	0.541409i
$485$	−0.484347	+	0.710407i	−0.0219931	+	0.0322579i
$486$		0			0
$487$	0.231033	−	3.08293i	0.0104691	−	0.139701i	−0.989520	−	0.144397i	$-0.953876\pi$
$487$	0.231033	−	3.08293i	0.0104691	−	0.139701i	0.999989	+	0.00469620i	$0.00149485\pi$
$488$	−4.81436	+	12.2668i	−0.217936	+	0.555292i
$489$		0			0
$490$	−3.63993	+	6.93434i	−0.164435	+	0.313261i
$491$		−	5.31784i		−	0.239991i	−0.992774	−	0.119995i	$-0.961712\pi$
$491$		−	5.31784i		−	0.239991i	0.992774	−	0.119995i	$-0.0382880\pi$
$492$		0			0
$493$	−5.51190	−	0.413059i	−0.248243	−	0.0186033i
$494$	−10.5852	+	11.4081i	−0.476249	+	0.513274i
$495$		0			0
$496$	−2.88161	+	5.98372i	−0.129388	+	0.268677i
$497$	−24.5505	+	25.5583i	−1.10124	+	1.14645i
$498$		0			0
$499$	−7.35271	−	1.10824i	−0.329152	−	0.0496117i	−0.0176127	−	0.999845i	$-0.505607\pi$
$499$	−7.35271	−	1.10824i	−0.329152	−	0.0496117i	−0.311540	+	0.950233i	$0.600845\pi$
$500$	−8.08689	+	5.51355i	−0.361657	+	0.246573i
$501$		0			0
$502$	10.2892	+	11.0891i	0.459230	+	0.494932i
$503$	−27.5828	−	34.5877i	−1.22985	−	1.54219i	−0.744054	−	0.668120i	$-0.767099\pi$
$503$	−27.5828	−	34.5877i	−1.22985	−	1.54219i	−0.485801	−	0.874069i	$-0.661472\pi$
$504$		0			0
$505$	7.91557	−	9.92581i	0.352238	−	0.441693i
$506$	6.28889	−	0.471287i	0.279575	−	0.0209513i
$507$		0			0
$508$	−3.98922	+	6.90952i	−0.176993	+	0.306561i
$509$	13.4763	+	23.3416i	0.597325	+	1.03460i	0.993214	+	0.116299i	$0.0371031\pi$
$509$	13.4763	+	23.3416i	0.597325	+	1.03460i	−0.395889	+	0.918298i	$0.629564\pi$
$510$		0			0
$511$	−3.34570	+	19.8609i	−0.148005	+	0.878593i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$		0			0
$514$	9.08892	−	3.56714i	0.400895	−	0.157340i
$515$	0.987754	−	0.387665i	0.0435256	−	0.0170826i
$516$		0			0
$517$	−9.76142	−	2.22798i	−0.429307	−	0.0979864i
$518$	2.70190	−	16.0391i	0.118715	−	0.704719i
$519$		0			0
$520$	−1.54437	−	2.67494i	−0.0677253	−	0.117304i
$521$	10.2929	−	17.8279i	0.450941	−	0.781053i	−0.547504	−	0.836803i	$-0.684422\pi$
$521$	10.2929	−	17.8279i	0.450941	−	0.781053i	0.998445	+	0.0557505i	$0.0177551\pi$
$522$		0			0
$523$	35.9621	−	2.69498i	1.57251	−	0.117843i	0.740290	−	0.672288i	$-0.234688\pi$
$523$	35.9621	−	2.69498i	1.57251	−	0.117843i	0.832221	+	0.554444i	$0.187069\pi$
$524$	−7.97464	+	9.99989i	−0.348374	+	0.436847i
$525$		0			0
$526$	6.26788	+	7.85968i	0.273293	+	0.342698i
$527$	−21.3340	−	22.9925i	−0.929322	−	1.00157i
$528$		0			0
$529$	18.1489	−	12.3737i	0.789082	−	0.537987i
$530$	−0.963602	−	0.145240i	−0.0418562	−	0.00630881i
$531$		0			0
$532$	−10.3317	+	10.7558i	−0.447935	+	0.466323i
$533$	9.99831	−	20.7617i	0.433075	−	0.899289i
$534$		0			0
$535$	−11.9210	+	12.8477i	−0.515388	+	0.555456i
$536$	4.62712	+	0.346754i	0.199861	+	0.0149775i
$537$		0			0
$538$			3.89092i			0.167749i
$539$	−34.8522	+	25.8742i	−1.50119	+	1.11448i
$540$		0			0
$541$	7.10015	−	18.0909i	0.305259	−	0.777788i	−0.693117	−	0.720825i	$-0.743763\pi$
$541$	7.10015	−	18.0909i	0.305259	−	0.777788i	0.998376	−	0.0569631i	$-0.0181417\pi$
$542$	0.933064	−	12.4509i	0.0400785	−	0.534811i
$543$		0			0
$544$	2.66039	−	3.90208i	0.114063	−	0.167300i
$545$	−16.1367	−	7.77100i	−0.691218	−	0.332873i
$546$		0			0
$547$	13.0575	−	6.28814i	0.558297	−	0.268862i	−0.133385	−	0.991064i	$-0.542585\pi$
$547$	13.0575	−	6.28814i	0.558297	−	0.268862i	0.691681	+	0.722203i	$0.256870\pi$
$548$	−1.02264	+	6.78477i	−0.0436850	+	0.289831i
$549$		0			0
$550$	−22.9834	+	3.46419i	−0.980015	+	0.147713i
$551$	−4.83626	+	4.48739i	−0.206032	+	0.191169i
$552$		0			0
$553$	8.02088	+	0.138698i	0.341082	+	0.00589802i
$554$	−11.2507	−	8.97210i	−0.477995	−	0.381188i
$555$		0			0
$556$	3.76977	−	12.2213i	0.159874	−	0.518299i
$557$	17.3953	+	10.0432i	0.737064	+	0.425544i	0.821001	−	0.570927i	$-0.193416\pi$
$557$	17.3953	+	10.0432i	0.737064	+	0.425544i	−0.0839368	+	0.996471i	$0.526749\pi$
$558$		0			0
$559$	25.5251	−	5.82595i	1.07960	−	0.246411i
$560$	−1.43549	−	2.58870i	−0.0606606	−	0.109393i
$561$		0			0
$562$	−0.551143	+	0.170005i	−0.0232486	+	0.00717123i
$563$	−3.05588	−	7.78626i	−0.128790	−	0.328152i	0.851905	−	0.523697i	$-0.175448\pi$
$563$	−3.05588	−	7.78626i	−0.128790	−	0.328152i	−0.980695	+	0.195545i	$0.937352\pi$
$564$		0			0
$565$	−2.34880	−	7.61464i	−0.0988150	−	0.320350i
$566$	−0.283757	+	1.24322i	−0.0119272	+	0.0522564i
$567$		0			0
$568$	−2.98064	−	13.0590i	−0.125065	−	0.547945i
$569$	25.4923	−	14.7180i	1.06869	−	0.617011i	0.140870	−	0.990028i	$-0.455010\pi$
$569$	25.4923	−	14.7180i	1.06869	−	0.617011i	0.927825	+	0.373017i	$0.121677\pi$
$570$		0			0
$571$	39.2458	+	12.1057i	1.64239	+	0.506609i	0.971916	−	0.235326i	$-0.0756158\pi$
$571$	39.2458	+	12.1057i	1.64239	+	0.506609i	0.670471	+	0.741936i	$0.266092\pi$
$572$	−1.27934	−	17.0716i	−0.0534918	−	0.713798i
$573$		0			0
$574$	9.92435	−	19.7281i	0.414234	−	0.823436i
$575$	2.98041	−	2.37680i	0.124292	−	0.0991193i
$576$		0			0
$577$	6.21797	+	41.2535i	0.258857	+	1.71741i	0.619750	+	0.784799i	$0.287234\pi$
$577$	6.21797	+	41.2535i	0.258857	+	1.71741i	−0.360893	+	0.932607i	$0.617528\pi$
$578$	2.98781	+	4.38232i	0.124277	+	0.182280i
$579$		0			0
$580$	−0.568137	−	1.17975i	−0.0235906	−	0.0489864i
$581$	16.7769	+	45.0204i	0.696021	+	1.86776i
$582$		0			0
$583$	−4.46260	−	3.04255i	−0.184822	−	0.126009i
$584$	−5.58033	−	5.17779i	−0.230916	−	0.214259i
$585$		0			0
$586$	10.6247	+	4.16990i	0.438904	+	0.172257i
$587$	0.379130			0.0156484			0.00782419	−	0.999969i	$-0.497509\pi$
$587$	0.379130			0.0156484			0.00782419	+	0.999969i	$0.497509\pi$
$588$		0			0
$589$	−37.4378			−1.54260
$590$	1.33499	+	0.523944i	0.0549606	+	0.0215704i
$591$		0			0
$592$	4.50654	+	4.18146i	0.185218	+	0.171857i
$593$	18.9595	+	12.9263i	0.778571	+	0.530821i	0.886163	−	0.463374i	$-0.153361\pi$
$593$	18.9595	+	12.9263i	0.778571	+	0.530821i	−0.107591	+	0.994195i	$0.534314\pi$
$594$		0			0
$595$	13.8574	−	1.84423i	0.568096	−	0.0756061i
$596$	4.85361	+	10.0786i	0.198811	+	0.412836i
$597$		0			0
$598$	1.58167	+	2.31988i	0.0646792	+	0.0948670i
$599$	0.144436	+	0.958267i	0.00590148	+	0.0391537i	0.991588	−	0.129436i	$-0.0413167\pi$
$599$	0.144436	+	0.958267i	0.00590148	+	0.0391537i	−0.985686	+	0.168590i	$0.946079\pi$
$600$		0			0
$601$	−26.4395	+	21.0848i	−1.07849	+	0.860066i	−0.990699	−	0.136074i	$-0.956552\pi$
$601$	−26.4395	+	21.0848i	−1.07849	+	0.860066i	−0.0877893	+	0.996139i	$0.527980\pi$
$602$	24.5546	−	5.15947i	1.00077	−	0.210284i
$603$		0			0
$604$	−0.189328	−	2.52640i	−0.00770363	−	0.102798i
$605$	29.3489	+	9.05293i	1.19320	+	0.368054i
$606$		0			0
$607$	−3.05951	+	1.76641i	−0.124182	+	0.0716964i	−0.560804	−	0.827948i	$-0.689508\pi$
$607$	−3.05951	+	1.76641i	−0.124182	+	0.0716964i	0.436622	+	0.899645i	$0.356175\pi$
$608$	−1.25435	−	5.49568i	−0.0508707	−	0.222879i
$609$		0			0
$610$	3.28068	−	14.3736i	0.132831	−	0.581971i
$611$	−1.31393	−	4.25965i	−0.0531559	−	0.172327i
$612$		0			0
$613$	−8.07521	−	20.5753i	−0.326155	−	0.831029i	−0.996068	−	0.0885895i	$-0.971764\pi$
$613$	−8.07521	−	20.5753i	−0.326155	−	0.831029i	0.669914	−	0.742439i	$-0.266331\pi$
$614$	−11.8144	+	3.64427i	−0.476791	+	0.147071i
$615$		0			0
$616$	−0.942994	−	16.3791i	−0.0379943	−	0.659933i
$617$	−5.33113	+	1.21679i	−0.214623	+	0.0489863i	−0.328480	−	0.944511i	$-0.606536\pi$
$617$	−5.33113	+	1.21679i	−0.214623	+	0.0489863i	0.113857	+	0.993497i	$0.463679\pi$
$618$		0			0
$619$	−9.10119	−	5.25457i	−0.365808	−	0.211199i	0.305818	−	0.952090i	$-0.401070\pi$
$619$	−9.10119	−	5.25457i	−0.365808	−	0.211199i	−0.671625	+	0.740891i	$0.734404\pi$
$620$	2.19016	−	7.10033i	0.0879590	−	0.285156i
$621$		0			0
$622$	−4.96227	−	3.95727i	−0.198969	−	0.158672i
$623$	3.20778	−	3.88277i	0.128517	−	0.155560i
$624$		0			0
$625$	−5.71123	+	5.29925i	−0.228449	+	0.211970i
$626$	30.1009	−	4.53698i	1.20307	−	0.181334i
$627$		0			0
$628$	2.90765	−	19.2910i	0.116028	−	0.769794i
$629$	−26.1583	+	12.5972i	−1.04300	+	0.502281i
$630$		0			0
$631$	−28.5738	−	13.7604i	−1.13751	−	0.547794i	−0.232248	−	0.972657i	$-0.574608\pi$
$631$	−28.5738	−	13.7604i	−1.13751	−	0.547794i	−0.905258	+	0.424863i	$0.860322\pi$
$632$	−1.70802	+	2.50521i	−0.0679414	+	0.0996517i
$633$		0			0
$634$	0.142685	−	1.90401i	0.00566676	−	0.0756177i
$635$	3.26114	−	8.30924i	0.129414	−	0.329742i
$636$		0			0
$637$	−17.7346	−	7.67809i	−0.702671	−	0.304217i
$638$		−	7.25748i		−	0.287327i
$639$		0			0
$640$	1.11567	+	0.0836082i	0.0441009	+	0.00330490i
$641$	−6.93796	+	7.47734i	−0.274033	+	0.295337i	−0.855041	−	0.518561i	$-0.826468\pi$
$641$	−6.93796	+	7.47734i	−0.274033	+	0.295337i	0.581008	+	0.813898i	$0.302658\pi$
$642$		0			0
$643$	0.108664	−	0.225643i	0.00428529	−	0.00889850i	−0.898815	−	0.438328i	$-0.855571\pi$
$643$	0.108664	−	0.225643i	0.00428529	−	0.00889850i	0.903101	+	0.429429i	$0.141285\pi$
$644$	1.47711	+	2.24911i	0.0582063	+	0.0886273i
$645$		0			0
$646$	26.3246	+	3.96779i	1.03573	+	0.156111i
$647$	15.4916	−	10.5620i	0.609039	−	0.415236i	−0.219145	−	0.975692i	$-0.570327\pi$
$647$	15.4916	−	10.5620i	0.609039	−	0.415236i	0.828184	+	0.560457i	$0.189374\pi$
$648$		0			0
$649$	5.40645	+	5.82677i	0.212222	+	0.228721i
$650$	−6.45195	−	8.09049i	−0.253066	−	0.317335i
$651$		0			0
$652$	−12.6707	+	15.8886i	−0.496224	+	0.622245i
$653$	−8.89481	+	0.666574i	−0.348081	+	0.0260850i	−0.247624	−	0.968856i	$-0.579650\pi$
$653$	−8.89481	+	0.666574i	−0.348081	+	0.0260850i	−0.100457	+	0.994941i	$0.532031\pi$
$654$		0			0
$655$	7.15493	−	12.3927i	0.279566	−	0.484223i
$656$	4.17343	+	7.22860i	0.162945	+	0.282229i
$657$		0			0
$658$	−1.18842	−	4.10335i	−0.0463295	−	0.159965i
$659$	−18.5140	−	4.22570i	−0.721204	−	0.164610i	−0.153862	−	0.988092i	$-0.549171\pi$
$659$	−18.5140	−	4.22570i	−0.721204	−	0.164610i	−0.567342	+	0.823482i	$0.692028\pi$
$660$		0			0
$661$	6.47521	−	2.54133i	0.251857	−	0.0988464i	−0.236054	−	0.971740i	$-0.575854\pi$
$661$	6.47521	−	2.54133i	0.251857	−	0.0988464i	0.487911	+	0.872893i	$0.337759\pi$
$662$	−32.2788	+	12.6685i	−1.25455	+	0.492375i
$663$		0			0
$664$	−17.7039	−	4.04080i	−0.687045	−	0.156814i
$665$	9.63649	−	13.6220i	0.373687	−	0.528239i
$666$		0			0
$667$	0.595151	+	1.03083i	0.0230443	+	0.0399139i
$668$	1.16073	−	2.01045i	0.0449101	−	0.0777866i
$669$		0			0
$670$	−5.17683	+	0.387949i	−0.199998	+	0.0149878i
$671$	50.9483	−	63.8871i	1.96684	−	2.46634i
$672$		0			0
$673$	15.7901	+	19.8001i	0.608662	+	0.763238i	0.986700	−	0.162552i	$-0.0519726\pi$
$673$	15.7901	+	19.8001i	0.608662	+	0.763238i	−0.378038	+	0.925790i	$0.623401\pi$
$674$	7.03158	+	7.57824i	0.270846	+	0.291903i
$675$		0			0
$676$	−4.44365	+	3.02963i	−0.170910	+	0.116524i
$677$	31.7511	+	4.78571i	1.22029	+	0.183930i	0.727434	−	0.686178i	$-0.240713\pi$
$677$	31.7511	+	4.78571i	1.22029	+	0.183930i	0.492861	+	0.870108i	$0.335951\pi$
$678$		0			0
$679$	−1.74303	−	1.04693i	−0.0668914	−	0.0401776i
$680$	−2.29254	+	4.76051i	−0.0879150	+	0.182557i
$681$		0			0
$682$	28.0118	−	30.1895i	1.07263	−	1.15602i
$683$	−11.1878	−	0.838407i	−0.428088	−	0.0320808i	−0.141056	−	0.990002i	$-0.545050\pi$
$683$	−11.1878	−	0.838407i	−0.428088	−	0.0320808i	−0.287032	+	0.957921i	$0.592669\pi$
$684$		0			0
$685$		−	7.67655i		−	0.293306i
$686$	−16.8660	−	7.65097i	−0.643948	−	0.292115i
$687$		0			0
$688$	−3.46469	+	8.82789i	−0.132090	+	0.336560i
$689$	0.179700	−	2.39793i	0.00684602	−	0.0913538i
$690$		0			0
$691$	−11.0978	+	16.2775i	−0.422181	+	0.619225i	−0.977126	−	0.212662i	$-0.931787\pi$
$691$	−11.0978	+	16.2775i	−0.422181	+	0.619225i	0.554945	+	0.831887i	$0.312739\pi$
$692$	15.1273	+	7.28492i	0.575054	+	0.276931i
$693$		0			0
$694$	1.43516	−	0.691139i	0.0544781	−	0.0262353i
$695$	−2.13263	+	14.1491i	−0.0808955	+	0.536706i
$696$		0			0
$697$	−38.9795	+	5.87521i	−1.47645	+	0.222540i
$698$	14.4336	−	13.3924i	0.546319	−	0.506910i
$699$		0			0
$700$	−6.04819	−	7.85919i	−0.228600	−	0.297049i
$701$	−26.4633	−	21.1038i	−0.999506	−	0.797079i	−0.0202681	−	0.999795i	$-0.506452\pi$
$701$	−26.4633	−	21.1038i	−0.999506	−	0.797079i	−0.979238	+	0.202715i	$0.935023\pi$
$702$		0			0
$703$	−10.2145	+	33.1147i	−0.385248	+	1.24894i
$704$	5.37020	+	3.10049i	0.202397	+	0.116854i
$705$		0			0
$706$	−2.84740	+	0.649900i	−0.107163	+	0.0244593i
$707$	24.5097	+	17.3387i	0.921784	+	0.652089i
$708$		0			0
$709$	−25.2108	+	7.77651i	−0.946813	+	0.292053i	−0.729447	−	0.684037i	$-0.760223\pi$
$709$	−25.2108	+	7.77651i	−0.946813	+	0.292053i	−0.217366	+	0.976090i	$0.569746\pi$
$710$	5.47508	+	13.9503i	0.205476	+	0.523544i
$711$		0			0
$712$	0.561095	+	1.81903i	0.0210279	+	0.0681709i
$713$	−1.50301	+	6.58514i	−0.0562883	+	0.246615i
$714$		0			0
$715$	4.26200	+	18.6730i	0.159390	+	0.698332i
$716$	17.9060	−	10.3380i	0.669177	−	0.386350i
$717$		0			0
$718$	−27.3081	−	8.42343i	−1.01913	−	0.314359i
$719$	0.0835564	+	1.11498i	0.00311613	+	0.0415818i	0.998545	−	0.0539229i	$-0.0171725\pi$
$719$	0.0835564	+	1.11498i	0.00311613	+	0.0415818i	−0.995429	+	0.0955048i	$0.969553\pi$
$720$		0			0
$721$	1.04950	+	2.27929i	0.0390853	+	0.0848853i
$722$	9.98857	−	7.96562i	0.371736	−	0.296450i
$723$		0			0
$724$	1.32880	+	8.81601i	0.0493844	+	0.327644i
$725$	−2.47123	−	3.62463i	−0.0917793	−	0.134616i
$726$		0			0
$727$	10.8231	+	22.4743i	0.401405	+	0.833526i	0.999485	+	0.0320894i	$0.0102161\pi$
$727$	10.8231	+	22.4743i	0.401405	+	0.833526i	−0.598080	+	0.801436i	$0.704070\pi$
$728$	6.10533	−	4.00970i	0.226279	−	0.148609i
$729$		0			0
$730$	7.03694	+	4.79771i	0.260449	+	0.177571i
$731$	−32.8316	−	30.4632i	−1.21432	−	1.12672i
$732$		0			0
$733$	−16.9226	−	6.64161i	−0.625049	−	0.245314i	0.0316113	−	0.999500i	$-0.489936\pi$
$733$	−16.9226	−	6.64161i	−0.625049	−	0.245314i	−0.656660	+	0.754187i	$0.728031\pi$
$734$	−2.55273			−0.0942228
$735$		0			0
$736$	−1.01702			−0.0374880
$737$	−26.7841	−	10.5120i	−0.986605	−	0.387214i
$738$		0			0
$739$	−26.7446	−	24.8154i	−0.983816	−	0.912848i	0.0123858	−	0.999923i	$-0.496057\pi$
$739$	−26.7446	−	24.8154i	−0.983816	−	0.912848i	−0.996202	+	0.0870755i	$0.972248\pi$
$740$	−5.68286	−	3.87451i	−0.208906	−	0.142430i
$741$		0			0
$742$	0.211919	−	2.29471i	0.00777981	−	0.0842414i
$743$	14.7106	+	30.5469i	0.539681	+	1.12066i	0.975373	+	0.220562i	$0.0707893\pi$
$743$	14.7106	+	30.5469i	0.539681	+	1.12066i	−0.435692	+	0.900096i	$0.643496\pi$
$744$		0			0
$745$	−7.05017	−	10.3407i	−0.258298	−	0.378854i
$746$	0.517835	+	3.43561i	0.0189593	+	0.125787i
$747$		0			0
$748$	−22.8962	+	18.2591i	−0.837168	+	0.667620i
$749$	−31.9526	−	26.3979i	−1.16752	−	0.964557i
$750$		0			0
$751$	0.164133	+	2.19020i	0.00598930	+	0.0799217i	0.999397	−	0.0347092i	$-0.0110505\pi$
$751$	0.164133	+	2.19020i	0.00598930	+	0.0799217i	−0.993408	+	0.114631i	$0.963431\pi$
$752$	1.54292	+	0.475929i	0.0562646	+	0.0173553i
$753$		0			0
$754$	2.79825	−	1.61557i	0.101906	−	0.0588356i
$755$	0.630729	+	2.76340i	0.0229546	+	0.100571i
$756$		0			0
$757$	2.06873	−	9.06369i	0.0751892	−	0.329426i	−0.923319	−	0.384035i	$-0.874534\pi$
$757$	2.06873	−	9.06369i	0.0751892	−	0.329426i	0.998508	+	0.0546094i	$0.0173914\pi$
$758$	8.19143	+	26.5560i	0.297526	+	0.964556i
$759$		0			0
$760$	2.30409	+	5.87074i	0.0835783	+	0.212954i
$761$	−22.1878	+	6.84402i	−0.804305	+	0.248095i	−0.669534	−	0.742781i	$-0.733506\pi$
$761$	−22.1878	+	6.84402i	−0.804305	+	0.248095i	−0.134771	+	0.990877i	$0.543030\pi$
$762$		0			0
$763$	16.1532	−	39.1533i	0.584785	−	1.41744i
$764$	20.3674	−	4.64874i	0.736868	−	0.168185i
$765$		0			0
$766$	25.2014	+	14.5500i	0.910562	+	0.525713i
$767$	−1.04310	+	3.38163i	−0.0376640	+	0.122104i
$768$		0			0
$769$	−25.1878	−	20.0866i	−0.908295	−	0.724341i	0.0533682	−	0.998575i	$-0.483004\pi$
$769$	−25.1878	−	20.0866i	−0.908295	−	0.724341i	−0.961663	+	0.274234i	$0.911576\pi$
$770$	3.77443	+	17.9631i	0.136021	+	0.647344i
$771$		0			0
$772$	9.92550	−	9.20951i	0.357226	−	0.331458i
$773$	−25.4127	+	3.83035i	−0.914032	+	0.137768i	−0.589185	−	0.807998i	$-0.700551\pi$
$773$	−25.4127	+	3.83035i	−0.914032	+	0.137768i	−0.324847	+	0.945767i	$0.605313\pi$
$774$		0			0
$775$	3.71025	−	24.6159i	0.133276	−	0.884230i
$776$	0.692402	−	0.333443i	0.0248558	−	0.0119699i
$777$		0			0
$778$	−12.7909	−	6.15975i	−0.458574	−	0.220838i
$779$	−26.5050	+	38.8757i	−0.949639	+	1.39287i
$780$		0			0
$781$	−6.20717	+	82.8290i	−0.222110	+	2.96385i
$782$	1.75477	−	4.47108i	0.0627504	−	0.159885i
$783$		0			0
$784$	5.91655	−	3.74092i	0.211305	−	0.133604i
$785$			21.8266i			0.779023i
$786$		0			0
$787$	−22.9010	−	1.71620i	−0.816334	−	0.0611758i	−0.339984	−	0.940431i	$-0.610422\pi$
$787$	−22.9010	−	1.71620i	−0.816334	−	0.0611758i	−0.476350	+	0.879256i	$0.658041\pi$
$788$	−3.18174	+	3.42910i	−0.113345	+	0.122156i
$789$		0			0
$790$	1.47185	−	3.05633i	0.0523662	−	0.108739i
$791$	17.6581	−	6.58030i	0.627851	−	0.233969i
$792$		0			0
$793$	35.9743	+	5.42225i	1.27748	+	0.192550i
$794$	4.94671	−	3.37261i	0.175552	−	0.119689i
$795$		0			0
$796$	−14.1435	−	15.2431i	−0.501304	−	0.540277i
$797$	19.6475	+	24.6372i	0.695950	+	0.872694i	0.996714	−	0.0810051i	$-0.0258130\pi$
$797$	19.6475	+	24.6372i	0.695950	+	0.872694i	−0.300764	+	0.953699i	$0.597242\pi$
$798$		0			0
$799$	−4.75446	+	5.96190i	−0.168201	+	0.210917i
$800$	3.73780	−	0.280110i	0.132151	−	0.00990337i
$801$		0			0
$802$	−1.56161	+	2.70479i	−0.0551423	+	0.0955093i
$803$	23.6023	+	40.8804i	0.832908	+	1.44264i
$804$		0			0
$805$	−2.00917	−	2.24190i	−0.0708140	−	0.0790164i
$806$	17.8757	+	4.08002i	0.629646	+	0.143713i
$807$		0			0
$808$	−10.5631	+	4.14570i	−0.371608	+	0.145845i
$809$	−8.55126	+	3.35612i	−0.300646	+	0.117995i	−0.510869	−	0.859658i	$-0.670676\pi$
$809$	−8.55126	+	3.35612i	−0.300646	+	0.117995i	0.210223	+	0.977654i	$0.432581\pi$
$810$		0			0
$811$	−37.5695	−	8.57499i	−1.31924	−	0.301108i	−0.495765	−	0.868457i	$-0.665112\pi$
$811$	−37.5695	−	8.57499i	−1.31924	−	0.301108i	−0.823478	+	0.567348i	$0.807969\pi$
$812$	2.70804	−	1.50167i	0.0950336	−	0.0526983i
$813$		0			0
$814$	−19.0607	−	33.0140i	−0.668076	−	1.15714i
$815$	11.3683	−	19.6905i	0.398214	−	0.689727i
$816$		0			0
$817$	−53.3088	+	3.99494i	−1.86504	+	0.139765i
$818$	11.9287	−	14.9581i	0.417077	−	0.522997i
$819$		0			0
$820$	−5.82245	−	7.30113i	−0.203329	−	0.254966i
$821$	−24.2309	−	26.1147i	−0.845663	−	0.911408i	0.151363	−	0.988478i	$-0.451634\pi$
$821$	−24.2309	−	26.1147i	−0.845663	−	0.911408i	−0.997026	+	0.0770706i	$0.975443\pi$
$822$		0			0
$823$	−8.64165	+	5.89178i	−0.301229	+	0.205374i	−0.704496	−	0.709708i	$-0.748827\pi$
$823$	−8.64165	+	5.89178i	−0.301229	+	0.205374i	0.403267	+	0.915082i	$0.367875\pi$
$824$	−0.937836	−	0.141356i	−0.0326711	−	0.00492437i
$825$		0			0
$826$	−1.05552	+	3.22299i	−0.0367263	+	0.112142i
$827$	−20.9530	+	43.5094i	−0.728608	+	1.51297i	0.125058	+	0.992149i	$0.460088\pi$
$827$	−20.9530	+	43.5094i	−0.728608	+	1.51297i	−0.853666	+	0.520821i	$0.825626\pi$
$828$		0			0
$829$	16.1253	−	17.3790i	0.560056	−	0.603597i	−0.388016	−	0.921653i	$-0.626840\pi$
$829$	16.1253	−	17.3790i	0.560056	−	0.603597i	0.948072	+	0.318056i	$0.103030\pi$
$830$	20.2598	+	1.51826i	0.703226	+	0.0526995i
$831$		0			0
$832$			2.76077i			0.0957123i
$833$	6.23759	+	32.4651i	0.216120	+	1.12485i
$834$		0			0
$835$	−0.948886	+	2.41772i	−0.0328376	+	0.0836687i
$836$	−2.61218	+	34.8572i	−0.0903443	+	1.20556i
$837$		0			0
$838$	−17.8828	+	26.2292i	−0.617751	+	0.906074i
$839$	−5.82225	−	2.80385i	−0.201006	−	0.0967995i	0.330673	−	0.943746i	$-0.392724\pi$
$839$	−5.82225	−	2.80385i	−0.201006	−	0.0967995i	−0.531679	+	0.846946i	$0.678439\pi$
$840$		0			0
$841$	−24.8940	+	11.9883i	−0.858413	+	0.413390i
$842$	−5.63625	+	37.3941i	−0.194238	+	1.28869i
$843$		0			0
$844$	14.7178	−	2.21835i	0.506607	−	0.0763588i
$845$	4.41085	−	4.09267i	0.151738	−	0.140792i
$846$		0			0
$847$	−17.3838	+	70.5203i	−0.597316	+	2.42310i
$848$	0.680982	+	0.543065i	0.0233850	+	0.0186489i
$849$		0			0
$850$	−5.21776	+	16.9156i	−0.178968	+	0.580200i
$851$	5.41464	+	3.12614i	0.185611	+	0.107163i
$852$		0			0
$853$	26.9338	−	6.14746i	0.922195	−	0.210485i	0.265037	−	0.964238i	$-0.414616\pi$
$853$	26.9338	−	6.14746i	0.922195	−	0.210485i	0.657158	+	0.753753i	$0.271759\pi$
$854$	34.3806	+	5.79164i	1.17648	+	0.198186i
$855$		0			0
$856$	14.9693	−	4.61743i	0.511642	−	0.157821i
$857$	17.4852	+	44.5514i	0.597282	+	1.52185i	0.834850	+	0.550478i	$0.185554\pi$
$857$	17.4852	+	44.5514i	0.597282	+	1.52185i	−0.237568	+	0.971371i	$0.576350\pi$
$858$		0			0
$859$	−5.37190	−	17.4153i	−0.183287	−	0.594202i	−0.999856	−	0.0169543i	$-0.994603\pi$
$859$	−5.37190	−	17.4153i	−0.183287	−	0.594202i	0.816569	−	0.577247i	$-0.195873\pi$
$860$	2.36097	−	10.3441i	0.0805083	−	0.352730i
$861$		0			0
$862$	−0.278088	−	1.21838i	−0.00947173	−	0.0414984i
$863$	−27.9042	+	16.1105i	−0.949870	+	0.548407i	−0.893040	−	0.449976i	$-0.851432\pi$
$863$	−27.9042	+	16.1105i	−0.949870	+	0.548407i	−0.0568292	+	0.998384i	$0.518099\pi$
$864$		0			0
$865$	−17.9502	−	5.53689i	−0.610324	−	0.188260i
$866$	0.250103	+	3.33739i	0.00849883	+	0.113409i
$867$		0			0
$868$	17.0609	+	4.20564i	0.579083	+	0.142749i
$869$	14.6998	−	11.7227i	0.498656	−	0.397665i
$870$		0			0
$871$	−1.90926	−	12.6671i	−0.0646929	−	0.429209i
$872$	9.01791	+	13.2268i	0.305385	+	0.447917i
$873$		0			0
$874$	−2.48744	−	5.16522i	−0.0841389	−	0.174716i
$875$	18.6754	+	17.9390i	0.631344	+	0.606449i
$876$		0			0
$877$	40.6156	+	27.6912i	1.37149	+	0.935067i	0.999978	+	0.00663917i	$0.00211333\pi$
$877$	40.6156	+	27.6912i	1.37149	+	0.935067i	0.371513	+	0.928428i	$0.378839\pi$
$878$	−14.2778	−	13.2478i	−0.481852	−	0.447093i
$879$		0			0
$880$	−6.45808	−	2.53461i	−0.217702	−	0.0854417i
$881$	20.1106			0.677542			0.338771	−	0.940869i	$-0.389989\pi$
$881$	20.1106			0.677542			0.338771	+	0.940869i	$0.389989\pi$
$882$		0			0
$883$	0.823811			0.0277234			0.0138617	−	0.999904i	$-0.495588\pi$
$883$	0.823811			0.0277234			0.0138617	+	0.999904i	$0.495588\pi$
$884$	−12.1370	−	4.76342i	−0.408211	−	0.160211i
$885$		0			0
$886$	21.2075	+	19.6776i	0.712478	+	0.661083i
$887$	−34.1998	−	23.3170i	−1.14832	−	0.782910i	−0.169076	−	0.985603i	$-0.554078\pi$
$887$	−34.1998	−	23.3170i	−1.14832	−	0.782910i	−0.979242	+	0.202693i	$0.935031\pi$
$888$		0			0
$889$	20.0605	+	6.56979i	0.672809	+	0.220344i
$890$	−0.924064	−	1.91884i	−0.0309747	−	0.0643196i
$891$		0			0
$892$	−12.0446	−	17.6661i	−0.403282	−	0.591506i
$893$	1.35656	+	9.00018i	0.0453955	+	0.301180i
$894$		0			0
$895$	−18.0856	+	14.4228i	−0.604536	+	0.482101i
$896$	−0.0457437	+	2.64536i	−0.00152819	+	0.0883751i
$897$		0			0
$898$	−1.58918	−	21.2061i	−0.0530315	−	0.707656i
$899$	7.42766	+	2.29113i	0.247726	+	0.0764134i
$900$		0			0
$901$	−3.56241	+	2.05676i	−0.118681	+	0.0685206i
$902$	−11.5174	−	50.4610i	−0.383487	−	1.68017i
$903$		0			0
$904$	−1.58490	+	6.94392i	−0.0527132	+	0.230951i
$905$	−2.94012	−	9.53162i	−0.0977328	−	0.316842i
$906$		0			0
$907$	19.1515	+	48.7973i	0.635916	+	1.62029i	0.776426	+	0.630209i	$0.217031\pi$
$907$	19.1515	+	48.7973i	0.635916	+	1.62029i	−0.140509	+	0.990079i	$0.544874\pi$
$908$	−6.09122	+	1.87889i	−0.202144	+	0.0623532i
$909$		0			0
$910$	−6.08575	+	5.45401i	−0.201741	+	0.180799i
$911$	−17.3284	+	3.95510i	−0.574116	+	0.131038i	−0.499715	−	0.866190i	$-0.666562\pi$
$911$	−17.3284	+	3.95510i	−0.574116	+	0.131038i	−0.0744015	+	0.997228i	$0.523705\pi$
$912$		0			0
$913$	97.5186	+	56.3024i	3.22739	+	1.86334i
$914$	3.57155	−	11.5787i	0.118136	−	0.382988i
$915$		0			0
$916$	−0.365205	−	0.291241i	−0.0120667	−	0.00962287i
$917$	30.2304	+	15.2076i	0.998296	+	0.502199i
$918$		0			0
$919$	−23.2650	+	21.5868i	−0.767442	+	0.712082i	−0.963264	−	0.268558i	$-0.913453\pi$
$919$	−23.2650	+	21.5868i	−0.767442	+	0.712082i	0.195822	+	0.980639i	$0.437263\pi$
$920$	1.12514	−	0.169587i	0.0370947	−	0.00559113i
$921$		0			0
$922$	−3.51243	+	23.3034i	−0.115676	+	0.767458i
$923$	−33.3179	+	16.0451i	−1.09667	+	0.528130i
$924$		0			0
$925$	−20.7611	−	9.99802i	−0.682621	−	0.328733i
$926$	8.62274	−	12.6472i	0.283361	−	0.415614i
$927$		0			0
$928$	−0.0874625	+	1.16711i	−0.00287110	+	0.0383121i
$929$	−1.23989	+	3.15918i	−0.0406794	+	0.103649i	−0.949770	−	0.312950i	$-0.898683\pi$
$929$	−1.23989	+	3.15918i	−0.0406794	+	0.103649i	0.909090	+	0.416599i	$0.136778\pi$
$930$		0			0
$931$	33.4700	+	20.8992i	1.09693	+	0.684944i
$932$			24.7363i			0.810265i
$933$		0			0
$934$	−12.0357	−	0.901950i	−0.393820	−	0.0295127i
$935$	22.2855	−	24.0181i	0.728815	−	0.785475i
$936$		0			0
$937$	20.2195	−	41.9862i	0.660542	−	1.37163i	−0.254026	−	0.967197i	$-0.581755\pi$
$937$	20.2195	−	41.9862i	0.660542	−	1.37163i	0.914568	−	0.404432i	$-0.132531\pi$
$938$	−1.61956	−	12.1692i	−0.0528806	−	0.397339i
$939$		0			0
$940$	−1.78631	−	0.269242i	−0.0582629	−	0.00878172i
$941$	−20.6729	+	14.0946i	−0.673918	+	0.459470i	−0.851305	−	0.524672i	$-0.824188\pi$
$941$	−20.6729	+	14.0946i	−0.673918	+	0.459470i	0.177387	+	0.984141i	$0.443236\pi$
$942$		0			0
$943$	5.77395	+	6.22284i	0.188026	+	0.202644i
$944$	−0.799213	−	1.00218i	−0.0260122	−	0.0326182i
$945$		0			0
$946$	36.6653	−	45.9768i	1.19209	−	1.49484i
$947$	16.3579	−	1.22585i	0.531560	−	0.0398349i	0.193753	−	0.981050i	$-0.437934\pi$
$947$	16.3579	−	1.22585i	0.531560	−	0.0398349i	0.337807	+	0.941215i	$0.390315\pi$
$948$		0			0
$949$	−10.5081	+	18.2006i	−0.341108	+	0.590816i
$950$	10.5645	+	18.2983i	0.342759	+	0.593676i
$951$		0			0
$952$	−11.5507	−	4.76539i	−0.374360	−	0.154447i
$953$	−30.0796	−	6.86547i	−0.974373	−	0.222394i	−0.294441	−	0.955670i	$-0.595133\pi$
$953$	−30.0796	−	6.86547i	−0.974373	−	0.222394i	−0.679932	+	0.733275i	$0.737991\pi$
$954$		0			0
$955$	−21.7574	+	8.53917i	−0.704054	+	0.276321i
$956$	−13.3804	+	5.25142i	−0.432753	+	0.169843i
$957$		0			0
$958$	27.2943	+	6.22975i	0.881840	+	0.201274i
$959$	18.1235	−	1.04343i	0.585240	−	0.0336940i
$960$		0			0
$961$	6.55430	+	11.3524i	0.211429	+	0.366206i
$962$	8.48610	−	14.6984i	0.273603	−	0.473894i
$963$		0			0
$964$	6.64999	−	0.498348i	0.214182	−	0.0160507i
$965$	−9.44496	+	11.8436i	−0.304044	+	0.381259i
$966$		0			0
$967$	−8.20129	−	10.2841i	−0.263736	−	0.330714i	0.632277	−	0.774742i	$-0.282120\pi$
$967$	−8.20129	−	10.2841i	−0.263736	−	0.330714i	−0.896013	+	0.444028i	$0.853549\pi$
$968$	−18.6721	−	20.1238i	−0.600145	−	0.646803i
$969$		0			0
$970$	−0.710407	+	0.484347i	−0.0228098	+	0.0155514i
$971$	17.1731	+	2.58843i	0.551112	+	0.0830668i	0.418695	−	0.908127i	$-0.362488\pi$
$971$	17.1731	+	2.58843i	0.551112	+	0.0830668i	0.132418	+	0.991194i	$0.457726\pi$
$972$		0			0
$973$	−33.6945	−	3.11173i	−1.08020	−	0.0997576i
$974$	1.34138	−	2.78541i	0.0429806	−	0.0892502i
$975$		0			0
$976$	−8.96313	+	9.65996i	−0.286903	+	0.309208i
$977$	−22.1489	−	1.65983i	−0.708607	−	0.0531027i	−0.284449	−	0.958691i	$-0.591811\pi$
$977$	−22.1489	−	1.65983i	−0.708607	−	0.0531027i	−0.424158	+	0.905588i	$0.639430\pi$
$978$		0			0
$979$		−	11.8042i		−	0.377263i
$980$	−5.92172	+	5.12518i	−0.189162	+	0.163718i
$981$		0			0
$982$	1.94282	−	4.95024i	0.0619980	−	0.157968i
$983$	3.82918	−	51.0969i	0.122132	−	1.62974i	−0.513742	−	0.857945i	$-0.671741\pi$
$983$	3.82918	−	51.0969i	0.122132	−	1.62974i	0.635874	−	0.771793i	$-0.280640\pi$
$984$		0			0
$985$	2.94818	−	4.32418i	0.0939367	−	0.137780i
$986$	−4.97997	−	2.39823i	−0.158595	−	0.0763751i
$987$		0			0
$988$	−14.0213	+	6.75230i	−0.446077	+	0.214819i
$989$	−1.43749	+	9.53715i	−0.0457097	+	0.303264i
$990$		0			0
$991$	−34.8901	+	5.25883i	−1.10832	+	0.167052i	−0.677598	−	0.735433i	$-0.736979\pi$
$991$	−34.8901	+	5.25883i	−1.10832	+	0.167052i	−0.430721	+	0.902485i	$0.641741\pi$
$992$	−4.86851	+	4.51732i	−0.154575	+	0.143425i
$993$		0			0
$994$	−32.1910	+	14.8223i	−1.02104	+	0.470134i
$995$	18.1888	+	14.5051i	0.576624	+	0.459843i
$996$		0			0
$997$	−12.6944	+	41.1544i	−0.402037	+	1.30337i	0.497855	+	0.867260i	$0.334121\pi$
$997$	−12.6944	+	41.1544i	−0.402037	+	1.30337i	−0.899892	+	0.436112i	$0.856355\pi$
$998$	−6.43956	−	3.71788i	−0.203841	−	0.117687i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.395.15	yes	240
3.2	odd	2	inner	882.2.bl.a.395.6	✓	240
49.33	odd	42	inner	882.2.bl.a.719.6	yes	240
147.131	even	42	inner	882.2.bl.a.719.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.6	✓	240	3.2	odd	2	inner
882.2.bl.a.395.15	yes	240	1.1	even	1	trivial
882.2.bl.a.719.6	yes	240	49.33	odd	42	inner
882.2.bl.a.719.15	yes	240	147.131	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(0.733052 + 0.680173i) q^{4} +(-0.924397 - 0.630244i) q^{5} +(1.36229 - 2.26807i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-0.630244 - 0.924397i) q^{10} +(-0.924207 - 6.13171i) q^{11} +(2.15845 - 1.72131i) q^{13} +(2.09674 - 1.61359i) q^{14} +(0.0747301 + 0.997204i) q^{16} +(-4.51289 - 1.39204i) q^{17} +(-4.88179 + 2.81850i) q^{19} +(-0.248957 - 1.09075i) q^{20} +(1.37985 - 6.04550i) q^{22} +(0.299773 + 0.971839i) q^{23} +(-1.36940 - 3.48918i) q^{25} +(2.63811 - 0.813750i) q^{26} +(2.54131 - 0.736021i) q^{28} +(1.14103 - 0.260434i) q^{29} +(5.75165 + 3.32072i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-3.69236 - 2.94456i) q^{34} +(-2.68874 + 1.23802i) q^{35} +(4.50654 - 4.18146i) q^{37} +(-5.57405 + 0.840152i) q^{38} +(0.166749 - 1.10631i) q^{40} +(7.52027 - 3.62157i) q^{41} +(8.54429 + 4.11471i) q^{43} +(3.49313 - 5.12348i) q^{44} +(-0.0760022 + 1.01418i) q^{46} +(0.589901 - 1.50304i) q^{47} +(-3.28831 - 6.17956i) q^{49} -3.74828i q^{50} +(2.75305 + 0.206312i) q^{52} +(0.592437 - 0.638495i) q^{53} +(-3.01014 + 6.25061i) q^{55} +(2.63454 + 0.243303i) q^{56} +(1.15731 + 0.174436i) q^{58} +(-1.05910 + 0.722085i) q^{59} +(8.96313 + 9.65996i) q^{61} +(4.14086 + 5.19248i) q^{62} +(-0.623490 + 0.781831i) q^{64} +(-3.08011 + 0.230823i) q^{65} +(2.32005 - 4.01844i) q^{67} +(-2.36135 - 4.08998i) q^{68} +(-2.95518 + 0.170138i) q^{70} +(-13.0590 - 2.98064i) q^{71} +(-7.08624 + 2.78115i) q^{73} +(5.72268 - 2.24598i) q^{74} +(-5.49568 - 1.25435i) q^{76} +(-15.1662 - 6.25702i) q^{77} +(1.51603 + 2.62584i) q^{79} +(0.559401 - 0.968911i) q^{80} +(8.32353 - 0.623762i) q^{82} +(-11.3221 + 14.1974i) q^{83} +(3.29438 + 4.13102i) q^{85} +(6.45038 + 6.95186i) q^{86} +(5.12348 - 3.49313i) q^{88} +(1.88234 + 0.283717i) q^{89} +(-0.963610 - 7.24046i) q^{91} +(-0.441270 + 0.916306i) q^{92} +(1.09825 - 1.18363i) q^{94} +(6.28906 + 0.471300i) q^{95} -0.768508i q^{97} +(-0.803359 - 6.95375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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