LMFDB - Embedded newform 666.2.bs.b.557.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(17,666)] 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("666.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([18, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.6
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.b.611.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-0.700099 - 0.326462i) q^{5} +(4.53856 - 1.65190i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.386237 + 0.668982i) q^{10} +(2.42393 + 4.19837i) q^{11} +(-2.50551 - 3.57824i) q^{13} +(-1.25005 - 4.66526i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-1.37892 + 1.96930i) q^{17} +(5.73695 - 0.501918i) q^{19} +(0.632774 + 0.443073i) q^{20} +(4.39365 - 2.04879i) q^{22} +(5.80632 - 1.55580i) q^{23} +(-2.83038 - 3.37311i) q^{25} +(-3.78299 + 2.18411i) q^{26} +(-4.75646 + 0.838692i) q^{28} +(-1.94369 - 0.520811i) q^{29} +(-2.21486 - 2.21486i) q^{31} +(0.422618 - 0.906308i) q^{32} +(1.84162 + 1.54530i) q^{34} +(-3.71672 - 0.325171i) q^{35} +(2.35421 + 5.60872i) q^{37} -5.75886i q^{38} +(0.496537 - 0.591749i) q^{40} +(1.55885 - 8.84070i) q^{41} +(5.76488 - 5.76488i) q^{43} +(-1.65806 - 4.55550i) q^{44} +(-1.04383 - 5.91983i) q^{46} +(-8.09588 - 4.67416i) q^{47} +(12.5074 - 10.4950i) q^{49} +(-3.60696 + 2.52562i) q^{50} +(1.84609 + 3.95896i) q^{52} +(-0.878899 + 2.41476i) q^{53} +(-0.326385 - 3.73059i) q^{55} +(0.420948 + 4.81146i) q^{56} +(-0.688233 + 1.89090i) q^{58} +(-3.50297 - 7.51215i) q^{59} +(-3.07615 + 2.15394i) q^{61} +(-2.39947 + 2.01339i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.585948 + 3.32308i) q^{65} +(4.27780 + 11.7532i) q^{67} +(1.69993 - 1.69993i) q^{68} +(-0.647868 + 3.67424i) q^{70} +(-6.82252 + 8.13076i) q^{71} +5.96741i q^{73} +(5.79256 - 1.85642i) q^{74} +(-5.73695 - 0.501918i) q^{76} +(17.9364 + 15.0505i) q^{77} +(-5.34136 + 11.4546i) q^{79} +(-0.546222 - 0.546222i) q^{80} +(-8.67120 - 2.32344i) q^{82} +(7.54117 - 1.32971i) q^{83} +(1.60828 - 0.928540i) q^{85} +(-5.24050 - 6.24539i) q^{86} +(-4.68267 + 1.25472i) q^{88} +(8.54762 - 3.98582i) q^{89} +(-17.2823 - 12.1012i) q^{91} +(-5.98827 + 0.523906i) q^{92} +(-5.36197 + 7.65769i) q^{94} +(-4.18029 - 1.52150i) q^{95} +(-0.616938 - 2.30244i) q^{97} +(-9.36496 - 13.3745i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82}+ \cdots + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{1}{36}\right)$

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 $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$		0			0
$3$		0			0
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	−0.700099	−	0.326462i	−0.313094	−	0.145998i	0.259719	−	0.965684i	$-0.416370\pi$
$5$	−0.700099	−	0.326462i	−0.313094	−	0.145998i	−0.572813	+	0.819686i	$0.694148\pi$
$6$		0			0
$7$	4.53856	−	1.65190i	1.71541	−	0.624360i	0.717988	−	0.696055i	$-0.245063\pi$
$7$	4.53856	−	1.65190i	1.71541	−	0.624360i	0.997427	+	0.0716957i	$0.0228410\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−0.386237	+	0.668982i	−0.122139	+	0.211551i
$11$	2.42393	+	4.19837i	0.730842	+	1.26586i	0.956524	+	0.291654i	$0.0942057\pi$
$11$	2.42393	+	4.19837i	0.730842	+	1.26586i	−0.225682	+	0.974201i	$0.572461\pi$
$12$		0			0
$13$	−2.50551	−	3.57824i	−0.694904	−	0.992425i	−0.999206	−	0.0398497i	$-0.987312\pi$
$13$	−2.50551	−	3.57824i	−0.694904	−	0.992425i	0.304302	−	0.952576i	$-0.401577\pi$
$14$	−1.25005	−	4.66526i	−0.334091	−	1.24684i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−1.37892	+	1.96930i	−0.334436	+	0.477624i	−0.950786	−	0.309848i	$-0.899722\pi$
$17$	−1.37892	+	1.96930i	−0.334436	+	0.477624i	0.616350	+	0.787472i	$0.288611\pi$
$18$		0			0
$19$	5.73695	−	0.501918i	1.31615	−	0.115148i	0.592641	−	0.805467i	$-0.298085\pi$
$19$	5.73695	−	0.501918i	1.31615	−	0.115148i	0.723505	+	0.690319i	$0.242530\pi$
$20$	0.632774	+	0.443073i	0.141493	+	0.0990741i
$21$		0			0
$22$	4.39365	−	2.04879i	0.936729	−	0.436804i
$23$	5.80632	−	1.55580i	1.21070	−	0.324407i	0.403665	−	0.914907i	$-0.367736\pi$
$23$	5.80632	−	1.55580i	1.21070	−	0.324407i	0.807037	+	0.590500i	$0.201070\pi$
$24$		0			0
$25$	−2.83038	−	3.37311i	−0.566075	−	0.674622i
$26$	−3.78299	+	2.18411i	−0.741906	+	0.428340i
$27$		0			0
$28$	−4.75646	+	0.838692i	−0.898886	+	0.158498i
$29$	−1.94369	−	0.520811i	−0.360934	−	0.0967121i	0.0737944	−	0.997273i	$-0.476489\pi$
$29$	−1.94369	−	0.520811i	−0.360934	−	0.0967121i	−0.434729	+	0.900561i	$0.643156\pi$
$30$		0			0
$31$	−2.21486	−	2.21486i	−0.397800	−	0.397800i	0.479656	−	0.877456i	$-0.340761\pi$
$31$	−2.21486	−	2.21486i	−0.397800	−	0.397800i	−0.877456	+	0.479656i	$0.840761\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$		0			0
$34$	1.84162	+	1.54530i	0.315836	+	0.265017i
$35$	−3.71672	−	0.325171i	−0.628241	−	0.0549640i
$36$		0			0
$37$	2.35421	+	5.60872i	0.387029	+	0.922067i
$37$	2.35421	+	5.60872i	0.387029	+	0.922067i
$38$		−	5.75886i		−	0.934211i
$39$		0			0
$40$	0.496537	−	0.591749i	0.0785094	−	0.0935638i
$41$	1.55885	−	8.84070i	0.243452	−	1.38069i	−0.580608	−	0.814183i	$-0.697185\pi$
$41$	1.55885	−	8.84070i	0.243452	−	1.38069i	0.824060	−	0.566502i	$-0.191704\pi$
$42$		0			0
$43$	5.76488	−	5.76488i	0.879136	−	0.879136i	−0.114309	−	0.993445i	$-0.536465\pi$
$43$	5.76488	−	5.76488i	0.879136	−	0.879136i	0.993445	+	0.114309i	$0.0364654\pi$
$44$	−1.65806	−	4.55550i	−0.249963	−	0.686767i
$45$		0			0
$46$	−1.04383	−	5.91983i	−0.153904	−	0.872831i
$47$	−8.09588	−	4.67416i	−1.18091	−	0.681796i	−0.224681	−	0.974432i	$-0.572134\pi$
$47$	−8.09588	−	4.67416i	−1.18091	−	0.681796i	−0.956224	+	0.292636i	$0.905467\pi$
$48$		0			0
$49$	12.5074	−	10.4950i	1.78678	−	1.49928i
$50$	−3.60696	+	2.52562i	−0.510101	+	0.357177i
$51$		0			0
$52$	1.84609	+	3.95896i	0.256007	+	0.549008i
$53$	−0.878899	+	2.41476i	−0.120726	+	0.331692i	−0.985305	−	0.170805i	$-0.945363\pi$
$53$	−0.878899	+	2.41476i	−0.120726	+	0.331692i	0.864579	+	0.502497i	$0.167585\pi$
$54$		0			0
$55$	−0.326385	−	3.73059i	−0.0440097	−	0.503033i
$56$	0.420948	+	4.81146i	0.0562515	+	0.642958i
$57$		0			0
$58$	−0.688233	+	1.89090i	−0.0903694	+	0.248288i
$59$	−3.50297	−	7.51215i	−0.456048	−	0.977999i	−0.991093	−	0.133175i	$-0.957483\pi$
$59$	−3.50297	−	7.51215i	−0.456048	−	0.977999i	0.535044	−	0.844824i	$-0.320295\pi$
$60$		0			0
$61$	−3.07615	+	2.15394i	−0.393861	+	0.275784i	−0.753685	−	0.657236i	$-0.771726\pi$
$61$	−3.07615	+	2.15394i	−0.393861	+	0.275784i	0.359824	+	0.933020i	$0.382837\pi$
$62$	−2.39947	+	2.01339i	−0.304733	+	0.255701i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.585948	+	3.32308i	0.0726779	+	0.412177i
$66$		0			0
$67$	4.27780	+	11.7532i	0.522616	+	1.43588i	0.867598	+	0.497267i	$0.165663\pi$
$67$	4.27780	+	11.7532i	0.522616	+	1.43588i	−0.344981	+	0.938610i	$0.612115\pi$
$68$	1.69993	−	1.69993i	0.206147	−	0.206147i
$69$		0			0
$70$	−0.647868	+	3.67424i	−0.0774350	+	0.439156i
$71$	−6.82252	+	8.13076i	−0.809684	+	0.964944i	−0.999859	−	0.0168061i	$-0.994650\pi$
$71$	−6.82252	+	8.13076i	−0.809684	+	0.964944i	0.190174	+	0.981750i	$0.439095\pi$
$72$		0			0
$73$			5.96741i			0.698433i	0.937042	+	0.349217i	$0.113552\pi$
$73$			5.96741i			0.698433i	−0.937042	+	0.349217i	$0.886448\pi$
$74$	5.79256	−	1.85642i	0.673371	−	0.215804i
$75$		0			0
$76$	−5.73695	−	0.501918i	−0.658073	−	0.0575739i
$77$	17.9364	+	15.0505i	2.04405	+	1.71516i
$78$		0			0
$79$	−5.34136	+	11.4546i	−0.600950	+	1.28874i	0.336847	+	0.941559i	$0.390639\pi$
$79$	−5.34136	+	11.4546i	−0.600950	+	1.28874i	−0.937798	+	0.347183i	$0.887138\pi$
$80$	−0.546222	−	0.546222i	−0.0610694	−	0.0610694i
$81$		0			0
$82$	−8.67120	−	2.32344i	−0.957574	−	0.256581i
$83$	7.54117	−	1.32971i	0.827751	−	0.145955i	0.256307	−	0.966595i	$-0.417494\pi$
$83$	7.54117	−	1.32971i	0.827751	−	0.145955i	0.571445	+	0.820641i	$0.306383\pi$
$84$		0			0
$85$	1.60828	−	0.928540i	0.174442	−	0.100714i
$86$	−5.24050	−	6.24539i	−0.565098	−	0.673457i
$87$		0			0
$88$	−4.68267	+	1.25472i	−0.499174	+	0.133753i
$89$	8.54762	−	3.98582i	0.906046	−	0.422496i	0.0869894	−	0.996209i	$-0.472275\pi$
$89$	8.54762	−	3.98582i	0.906046	−	0.422496i	0.819056	+	0.573713i	$0.194498\pi$
$90$		0			0
$91$	−17.2823	−	12.1012i	−1.81168	−	1.26855i
$92$	−5.98827	+	0.523906i	−0.624321	+	0.0546210i
$93$		0			0
$94$	−5.36197	+	7.65769i	−0.553045	+	0.789831i
$95$	−4.18029	−	1.52150i	−0.428889	−	0.156103i
$96$		0			0
$97$	−0.616938	−	2.30244i	−0.0626406	−	0.233778i	0.927507	−	0.373806i	$-0.121947\pi$
$97$	−0.616938	−	2.30244i	−0.0626406	−	0.233778i	−0.990148	+	0.140028i	$0.955281\pi$
$98$	−9.36496	−	13.3745i	−0.946004	−	1.35103i
$99$		0			0
$100$	2.20164	+	3.81336i	0.220164	+	0.381336i
$101$	−7.59134	+	13.1486i	−0.755367	+	1.30833i	0.189825	+	0.981818i	$0.439208\pi$
$101$	−7.59134	+	13.1486i	−0.755367	+	1.30833i	−0.945192	+	0.326516i	$0.894125\pi$
$102$		0			0
$103$	−3.73836	+	13.9517i	−0.368351	+	1.37471i	0.494470	+	0.869195i	$0.335362\pi$
$103$	−3.73836	+	13.9517i	−0.368351	+	1.37471i	−0.862821	+	0.505510i	$0.831304\pi$
$104$	4.10479	−	1.49402i	0.402508	−	0.146501i
$105$		0			0
$106$	2.32897	+	1.08601i	0.226209	+	0.105483i
$107$	10.0900	+	1.77915i	0.975442	+	0.171997i	0.638578	−	0.769557i	$-0.279523\pi$
$107$	10.0900	+	1.77915i	0.975442	+	0.171997i	0.336863	+	0.941554i	$0.390634\pi$
$108$		0			0
$109$	0.847015	−	9.68143i	0.0811293	−	0.927312i	−0.841153	−	0.540797i	$-0.818123\pi$
$109$	0.847015	−	9.68143i	0.0811293	−	0.927312i	0.922283	−	0.386516i	$-0.126322\pi$
$110$	−3.74484			−0.357057
$111$		0			0
$112$	4.82983			0.456377
$113$	0.235893	−	2.69626i	0.0221909	−	0.253643i	−0.976994	−	0.213268i	$-0.931589\pi$
$113$	0.235893	−	2.69626i	0.0221909	−	0.253643i	0.999185	−	0.0403750i	$-0.0128553\pi$
$114$		0			0
$115$	−4.57291	−	0.806328i	−0.426426	−	0.0751905i
$116$	1.82372	+	0.850417i	0.169329	+	0.0789592i
$117$		0			0
$118$	−7.78887	+	2.83492i	−0.717024	+	0.260975i
$119$	−3.00521	+	11.2156i	−0.275487	+	1.02813i
$120$		0			0
$121$	−6.25086	+	10.8268i	−0.568260	+	0.984255i
$122$	1.87764	+	3.25217i	0.169994	+	0.294438i
$123$		0			0
$124$	1.79660	+	2.56582i	0.161340	+	0.230417i
$125$	1.88001	+	7.01629i	0.168153	+	0.627556i
$126$		0			0
$127$	−9.30258	−	3.38586i	−0.825470	−	0.300447i	−0.105472	−	0.994422i	$-0.533635\pi$
$127$	−9.30258	−	3.38586i	−0.825470	−	0.300447i	−0.719998	+	0.693976i	$0.755857\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$		0			0
$130$	3.36150	−	0.294093i	0.294823	−	0.0257937i
$131$	3.57335	+	2.50209i	0.312205	+	0.218609i	0.719168	−	0.694836i	$-0.244523\pi$
$131$	3.57335	+	2.50209i	0.312205	+	0.218609i	−0.406963	+	0.913445i	$0.633412\pi$
$132$		0			0
$133$	25.2084	−	11.7549i	2.18584	−	1.01928i
$134$	12.0813	−	3.23717i	1.04366	−	0.279648i
$135$		0			0
$136$	−1.54530	−	1.84162i	−0.132509	−	0.157918i
$137$	−12.5405	+	7.24028i	−1.07141	+	0.618579i	−0.928567	−	0.371166i	$-0.878958\pi$
$137$	−12.5405	+	7.24028i	−1.07141	+	0.618579i	−0.142844	+	0.989745i	$0.545625\pi$
$138$		0			0
$139$	5.42951	−	0.957370i	0.460525	−	0.0812030i	0.0614278	−	0.998112i	$-0.480435\pi$
$139$	5.42951	−	0.957370i	0.460525	−	0.0812030i	0.399098	+	0.916908i	$0.369323\pi$
$140$	3.60379	+	0.965634i	0.304576	+	0.0816109i
$141$		0			0
$142$	7.50520	+	7.50520i	0.629823	+	0.629823i
$143$	8.94959	−	19.1925i	0.748402	−	1.60495i
$144$		0			0
$145$	1.19075	+	0.999160i	0.0988866	+	0.0829757i
$146$	5.94471	+	0.520094i	0.491987	+	0.0430433i
$147$		0			0
$148$	−1.34450	−	5.93231i	−0.110517	−	0.487633i
$149$			10.9793i			0.899458i	0.893165	+	0.449729i	$0.148479\pi$
$149$			10.9793i			0.899458i	−0.893165	+	0.449729i	$0.851521\pi$
$150$		0			0
$151$	−10.0789	+	12.0115i	−0.820207	+	0.977484i	−0.999981	−	0.00622350i	$-0.998019\pi$
$151$	−10.0789	+	12.0115i	−0.820207	+	0.977484i	0.179774	+	0.983708i	$0.442463\pi$
$152$	−1.00002	+	5.67137i	−0.0811120	+	0.460009i
$153$		0			0
$154$	16.5564	−	16.5564i	1.33416	−	1.33416i
$155$	0.827554	+	2.27369i	0.0664708	+	0.182627i
$156$		0			0
$157$	0.747096	+	4.23699i	0.0596247	+	0.338149i	0.999998	−	0.00199559i	$-0.000635218\pi$
$157$	0.747096	+	4.23699i	0.0596247	+	0.338149i	−0.940373	+	0.340144i	$0.889524\pi$
$158$	10.9455	+	6.31937i	0.870775	+	0.502742i
$159$		0			0
$160$	−0.591749	+	0.496537i	−0.0467819	+	0.0392547i
$161$	23.7823	−	16.6526i	1.87431	−	1.31241i
$162$		0			0
$163$	4.95999	+	10.6367i	0.388496	+	0.833133i	0.999149	+	0.0412349i	$0.0131292\pi$
$163$	4.95999	+	10.6367i	0.388496	+	0.833133i	−0.610653	+	0.791898i	$0.709093\pi$
$164$	−3.07034	+	8.43570i	−0.239754	+	0.658717i
$165$		0			0
$166$	−0.667396	−	7.62837i	−0.0518000	−	0.592076i
$167$	−1.73092	−	19.7845i	−0.133942	−	1.53097i	−0.704495	−	0.709709i	$-0.748827\pi$
$167$	−1.73092	−	19.7845i	−0.133942	−	1.53097i	0.570553	−	0.821261i	$-0.306729\pi$
$168$		0			0
$169$	−2.07996	+	5.71463i	−0.159997	+	0.439587i
$170$	−0.784836	−	1.68309i	−0.0601941	−	0.129087i
$171$		0			0
$172$	−6.67836	+	4.67624i	−0.509220	+	0.356560i
$173$	−15.4542	+	12.9676i	−1.17496	+	0.985909i	−0.174961	+	0.984575i	$0.555980\pi$
$173$	−15.4542	+	12.9676i	−1.17496	+	0.985909i	−0.999999	+	0.00133371i	$0.999575\pi$
$174$		0			0
$175$	−18.4179	−	10.6336i	−1.39226	−	0.803822i
$176$	0.841822	+	4.77421i	0.0634547	+	0.359869i
$177$		0			0
$178$	−3.22568	−	8.86248i	−0.241775	−	0.664271i
$179$	−0.932166	+	0.932166i	−0.0696733	+	0.0696733i	−0.741085	−	0.671411i	$-0.765688\pi$
$179$	−0.932166	+	0.932166i	−0.0696733	+	0.0696733i	0.671411	+	0.741085i	$0.265688\pi$
$180$		0			0
$181$	−0.426058	+	2.41629i	−0.0316686	+	0.179602i	−0.996539	−	0.0831239i	$-0.973510\pi$
$181$	−0.426058	+	2.41629i	−0.0316686	+	0.179602i	0.964871	+	0.262726i	$0.0846214\pi$
$182$	−13.5614	+	16.1619i	−1.00524	+	1.19800i
$183$		0			0
$184$			6.01115i			0.443148i
$185$	0.182853	−	4.69522i	0.0134436	−	0.345199i
$186$		0			0
$187$	−11.6102	−	1.01576i	−0.849024	−	0.0742799i
$188$	7.16122	+	6.00898i	0.522286	+	0.438250i
$189$		0			0
$190$	−1.88005	+	4.03178i	−0.136393	+	0.292496i
$191$	−14.1268	−	14.1268i	−1.02218	−	1.02218i	−0.999748	−	0.0224327i	$-0.992859\pi$
$191$	−14.1268	−	14.1268i	−1.02218	−	1.02218i	−0.0224327	−	0.999748i	$-0.507141\pi$
$192$		0			0
$193$	7.67390	+	2.05621i	0.552379	+	0.148010i	0.524203	−	0.851593i	$-0.324363\pi$
$193$	7.67390	+	2.05621i	0.552379	+	0.148010i	0.0281763	+	0.999603i	$0.491030\pi$
$194$	−2.34745	+	0.413919i	−0.168537	+	0.0297177i
$195$		0			0
$196$	−14.1399	+	8.16365i	−1.00999	+	0.583118i
$197$	10.0495	+	11.9765i	0.715997	+	0.853292i	0.994235	−	0.107220i	$-0.0341950\pi$
$197$	10.0495	+	11.9765i	0.715997	+	0.853292i	−0.278239	+	0.960512i	$0.589751\pi$
$198$		0			0
$199$	−9.50441	+	2.54670i	−0.673750	+	0.180531i	−0.579443	−	0.815012i	$-0.696730\pi$
$199$	−9.50441	+	2.54670i	−0.673750	+	0.180531i	−0.0943064	+	0.995543i	$0.530063\pi$
$200$	3.99073	−	1.86091i	0.282187	−	0.131586i
$201$		0			0
$202$	12.4369	+	8.70843i	0.875059	+	0.612723i
$203$	−9.68189	+	0.847056i	−0.679535	+	0.0594516i
$204$		0			0
$205$	−3.97750	+	5.68046i	−0.277801	+	0.396741i
$206$	13.5728	+	4.94010i	0.945663	+	0.344193i
$207$		0			0
$208$	−1.13058	−	4.21938i	−0.0783916	−	0.292561i
$209$	16.0132	+	22.8692i	1.10766	+	1.58190i
$210$		0			0
$211$	−5.69398	−	9.86226i	−0.391990	−	0.678946i	0.600722	−	0.799458i	$-0.294880\pi$
$211$	−5.69398	−	9.86226i	−0.391990	−	0.678946i	−0.992712	+	0.120512i	$0.961546\pi$
$212$	1.28486	−	2.22545i	0.0882449	−	0.152845i
$213$		0			0
$214$	2.65178	−	9.89659i	0.181272	−	0.676517i
$215$	−5.91800	+	2.15398i	−0.403604	+	0.146900i
$216$		0			0
$217$	−13.7110	−	6.39354i	−0.930763	−	0.434022i
$218$	−9.57076	−	1.68758i	−0.648214	−	0.114298i
$219$		0			0
$220$	−0.326385	+	3.73059i	−0.0220048	+	0.251517i
$221$	10.5015			0.706408
$222$		0			0
$223$	22.7165			1.52121			0.760604	−	0.649216i	$-0.224903\pi$
$223$	22.7165			1.52121			0.760604	+	0.649216i	$0.224903\pi$
$224$	0.420948	−	4.81146i	0.0281258	−	0.321479i
$225$		0			0
$226$	−2.66544	−	0.469990i	−0.177303	−	0.0312633i
$227$	12.4715	+	5.81557i	0.827765	+	0.385993i	0.789859	−	0.613288i	$-0.210154\pi$
$227$	12.4715	+	5.81557i	0.827765	+	0.385993i	0.0379059	+	0.999281i	$0.487931\pi$
$228$		0			0
$229$	−4.84646	+	1.76397i	−0.320263	+	0.116566i	−0.497149	−	0.867665i	$-0.665620\pi$
$229$	−4.84646	+	1.76397i	−0.320263	+	0.116566i	0.176886	+	0.984231i	$0.443398\pi$
$230$	−1.20181	+	4.48523i	−0.0792453	+	0.295748i
$231$		0			0
$232$	1.00613	−	1.74267i	0.0660556	−	0.114412i
$233$	2.78253	+	4.81949i	0.182290	+	0.315735i	0.942660	−	0.333755i	$-0.108316\pi$
$233$	2.78253	+	4.81949i	0.182290	+	0.315735i	−0.760370	+	0.649490i	$0.774982\pi$
$234$		0			0
$235$	4.14199	+	5.91537i	0.270193	+	0.385876i
$236$	2.14528	+	8.00631i	0.139646	+	0.521166i
$237$		0			0
$238$	10.9110	+	3.97128i	0.707255	+	0.257420i
$239$	10.6846	−	15.2592i	0.691132	−	0.987038i	−0.308230	−	0.951312i	$-0.599737\pi$
$239$	10.6846	−	15.2592i	0.691132	−	0.987038i	0.999362	−	0.0357263i	$-0.0113745\pi$
$240$		0			0
$241$	−2.27697	+	0.199209i	−0.146673	+	0.0128322i	−0.160256	−	0.987076i	$-0.551232\pi$
$241$	−2.27697	+	0.199209i	−0.146673	+	0.0128322i	0.0135829	+	0.999908i	$0.495676\pi$
$242$	10.2408	+	7.17069i	0.658304	+	0.460950i
$243$		0			0
$244$	3.40345	−	1.58705i	0.217883	−	0.101601i
$245$	−12.1827	+	3.26433i	−0.778322	+	0.208551i
$246$		0			0
$247$	−16.1700	−	19.2706i	−1.02887	−	1.22616i
$248$	2.71264	−	1.56614i	0.172253	−	0.0994501i
$249$		0			0
$250$	7.15344	−	1.26134i	0.452423	−	0.0797744i
$251$	−21.7854	−	5.83737i	−1.37508	−	0.368452i	−0.505749	−	0.862681i	$-0.668784\pi$
$251$	−21.7854	−	5.83737i	−1.37508	−	0.368452i	−0.869332	+	0.494229i	$0.835450\pi$
$252$		0			0
$253$	20.6059	+	20.6059i	1.29548	+	1.29548i
$254$	−4.18375	+	8.97208i	−0.262512	+	0.562958i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−13.5323	−	1.18392i	−0.844120	−	0.0738510i	−0.343113	−	0.939294i	$-0.611481\pi$
$257$	−13.5323	−	1.18392i	−0.844120	−	0.0738510i	−0.501007	+	0.865443i	$0.667037\pi$
$258$		0			0
$259$	19.9498	+	21.5666i	1.23962	+	1.34008i
$260$		−	3.37434i		−	0.209268i
$261$		0			0
$262$	2.80401	−	3.34168i	0.173232	−	0.206450i
$263$	−1.43378	+	8.13140i	−0.0884110	+	0.501403i	0.908157	+	0.418629i	$0.137489\pi$
$263$	−1.43378	+	8.13140i	−0.0884110	+	0.501403i	−0.996568	+	0.0827745i	$0.973622\pi$
$264$		0			0
$265$	1.40364	−	1.40364i	0.0862250	−	0.0862250i
$266$	−9.51307	−	26.1369i	−0.583284	−	1.60256i
$267$		0			0
$268$	−2.17190	−	12.3174i	−0.132670	−	0.752407i
$269$	−4.64654	−	2.68268i	−0.283304	−	0.163566i	0.351614	−	0.936145i	$-0.385633\pi$
$269$	−4.64654	−	2.68268i	−0.283304	−	0.163566i	−0.634918	+	0.772579i	$0.718966\pi$
$270$		0			0
$271$	−7.74885	+	6.50205i	−0.470709	+	0.394972i	−0.847053	−	0.531508i	$-0.821625\pi$
$271$	−7.74885	+	6.50205i	−0.470709	+	0.394972i	0.376344	+	0.926480i	$0.377181\pi$
$272$	−1.96930	+	1.37892i	−0.119406	+	0.0836091i
$273$		0			0
$274$	6.11975	+	13.1239i	0.369708	+	0.792841i
$275$	7.30093	−	20.0591i	0.440263	−	1.20961i
$276$		0			0
$277$	−2.00383	−	22.9039i	−0.120398	−	1.37616i	−0.780581	−	0.625055i	$-0.785077\pi$
$277$	−2.00383	−	22.9039i	−0.120398	−	1.37616i	0.660182	−	0.751105i	$-0.270479\pi$
$278$	−0.480513	−	5.49229i	−0.0288193	−	0.329406i
$279$		0			0
$280$	1.27605	−	3.50592i	0.0762586	−	0.209519i
$281$	−9.14766	−	19.6172i	−0.545703	−	1.17026i	−0.964960	−	0.262397i	$-0.915487\pi$
$281$	−9.14766	−	19.6172i	−0.545703	−	1.17026i	0.419257	−	0.907868i	$-0.362291\pi$
$282$		0			0
$283$	−10.9550	+	7.67077i	−0.651206	+	0.455980i	−0.851921	−	0.523670i	$-0.824562\pi$
$283$	−10.9550	+	7.67077i	−0.651206	+	0.455980i	0.200715	+	0.979650i	$0.435674\pi$
$284$	8.13076	−	6.82252i	0.482472	−	0.404842i
$285$		0			0
$286$	−18.3394	−	10.5883i	−1.08443	−	0.626097i
$287$	−7.52901	−	42.6991i	−0.444423	−	2.52045i
$288$		0			0
$289$	3.83762	+	10.5438i	0.225743	+	0.620223i
$290$	1.09914	−	1.09914i	0.0645436	−	0.0645436i
$291$		0			0
$292$	1.03623	−	5.87676i	0.0606408	−	0.343911i
$293$	−0.512469	+	0.610737i	−0.0299388	+	0.0356796i	−0.780806	−	0.624773i	$-0.785191\pi$
$293$	−0.512469	+	0.610737i	−0.0299388	+	0.0356796i	0.750867	+	0.660453i	$0.229636\pi$
$294$		0			0
$295$			6.40284i			0.372788i
$296$	−6.02692	+	0.822346i	−0.350308	+	0.0477979i
$297$		0			0
$298$	10.9375	+	0.956908i	0.633593	+	0.0554322i
$299$	−20.1148	−	16.8783i	−1.16327	−	0.976100i
$300$		0			0
$301$	16.6412	−	35.6873i	0.959186	−	2.05698i
$302$	11.0874	+	11.0874i	0.638008	+	0.638008i
$303$		0			0
$304$	5.56263	+	1.49050i	0.319039	+	0.0854862i
$305$	2.85679	−	0.503729i	0.163579	−	0.0288435i
$306$		0			0
$307$	2.15411	−	1.24367i	0.122941	−	0.0709802i	−0.437268	−	0.899331i	$-0.644054\pi$
$307$	2.15411	−	1.24367i	0.122941	−	0.0709802i	0.560210	+	0.828351i	$0.310721\pi$
$308$	−15.0505	−	17.9364i	−0.857579	−	1.02202i
$309$		0			0
$310$	2.33716	−	0.626240i	0.132742	−	0.0355681i
$311$	−11.9333	+	5.56461i	−0.676678	+	0.315540i	−0.730404	−	0.683016i	$-0.760668\pi$
$311$	−11.9333	+	5.56461i	−0.676678	+	0.315540i	0.0537257	+	0.998556i	$0.482890\pi$
$312$		0			0
$313$	−0.847475	−	0.593409i	−0.0479021	−	0.0335414i	0.549380	−	0.835573i	$-0.314864\pi$
$313$	−0.847475	−	0.593409i	−0.0479021	−	0.0335414i	−0.597282	+	0.802031i	$0.703753\pi$
$314$	4.28598	−	0.374975i	0.241872	−	0.0211610i
$315$		0			0
$316$	7.24928	−	10.3530i	0.407804	−	0.582404i
$317$	13.9900	+	5.09193i	0.785755	+	0.285991i	0.703570	−	0.710626i	$-0.251588\pi$
$317$	13.9900	+	5.09193i	0.785755	+	0.285991i	0.0821847	+	0.996617i	$0.473810\pi$
$318$		0			0
$319$	−2.52482	−	9.42274i	−0.141363	−	0.527572i
$320$	0.443073	+	0.632774i	0.0247685	+	0.0353731i
$321$		0			0
$322$	−14.5164	−	25.1432i	−0.808969	−	1.40118i
$323$	−6.92234	+	11.9899i	−0.385170	+	0.667133i
$324$		0			0
$325$	−4.97826	+	18.5791i	−0.276144	+	1.03058i
$326$	11.0285	−	4.01406i	0.610815	−	0.222318i
$327$		0			0
$328$	8.13600	+	3.79388i	0.449235	+	0.209482i
$329$	−44.4649	−	7.84036i	−2.45143	−	0.432253i
$330$		0			0
$331$	−0.839060	+	9.59050i	−0.0461189	+	0.527142i	0.937635	+	0.347621i	$0.113010\pi$
$331$	−0.839060	+	9.59050i	−0.0461189	+	0.527142i	−0.983754	+	0.179521i	$0.942545\pi$
$332$	−7.65751			−0.420260
$333$		0			0
$334$	−19.8601			−1.08669
$335$	0.842071	−	9.62491i	0.0460072	−	0.525865i
$336$		0			0
$337$	−15.0598	−	2.65545i	−0.820361	−	0.144652i	−0.252311	−	0.967646i	$-0.581191\pi$
$337$	−15.0598	−	2.65545i	−0.820361	−	0.144652i	−0.568049	+	0.822994i	$0.692302\pi$
$338$	5.51161	+	2.57011i	0.299792	+	0.139795i
$339$		0			0
$340$	−1.74508	+	0.635158i	−0.0946404	+	0.0344463i
$341$	3.93013	−	14.6674i	0.212828	−	0.794287i
$342$		0			0
$343$	22.5247	−	39.0139i	1.21622	−	2.10655i
$344$	4.07639	+	7.06051i	0.219784	+	0.380677i
$345$		0			0
$346$	11.5713	+	16.5256i	0.622079	+	0.888421i
$347$	4.90451	+	18.3039i	0.263288	+	0.982604i	0.963290	+	0.268463i	$0.0865158\pi$
$347$	4.90451	+	18.3039i	0.263288	+	0.982604i	−0.700002	+	0.714141i	$0.746817\pi$
$348$		0			0
$349$	7.67936	+	2.79506i	0.411067	+	0.149616i	0.539272	−	0.842132i	$-0.318699\pi$
$349$	7.67936	+	2.79506i	0.411067	+	0.149616i	−0.128205	+	0.991748i	$0.540922\pi$
$350$	−12.1983	+	17.4210i	−0.652028	+	0.931192i
$351$		0			0
$352$	4.82941	−	0.422519i	0.257408	−	0.0225203i
$353$	6.62053	+	4.63574i	0.352375	+	0.246736i	0.736340	−	0.676612i	$-0.236553\pi$
$353$	6.62053	+	4.63574i	0.352375	+	0.246736i	−0.383964	+	0.923348i	$0.625441\pi$
$354$		0			0
$355$	7.43083	−	3.46505i	0.394387	−	0.183906i
$356$	−9.10989	+	2.44099i	−0.482823	+	0.129372i
$357$		0			0
$358$	0.847375	+	1.00986i	0.0447852	+	0.0533729i
$359$	−1.93796	+	1.11888i	−0.102282	+	0.0590523i	−0.550268	−	0.834988i	$-0.685475\pi$
$359$	−1.93796	+	1.11888i	−0.102282	+	0.0590523i	0.447987	+	0.894040i	$0.352141\pi$
$360$		0			0
$361$	13.9493	−	2.45964i	0.734174	−	0.129455i
$362$	2.36996	+	0.635030i	0.124563	+	0.0333764i
$363$		0			0
$364$	14.9184	+	14.9184i	0.781937	+	0.781937i
$365$	1.94813	−	4.17778i	0.101970	−	0.218675i
$366$		0			0
$367$	9.56558	+	8.02648i	0.499319	+	0.418979i	0.857352	−	0.514730i	$-0.172108\pi$
$367$	9.56558	+	8.02648i	0.499319	+	0.418979i	−0.358033	+	0.933709i	$0.616552\pi$
$368$	5.98827	+	0.523906i	0.312160	+	0.0273105i
$369$		0			0
$370$	−4.66141	−	0.591372i	−0.242335	−	0.0307440i
$371$			12.4114i			0.644366i
$372$		0			0
$373$	−4.81976	+	5.74396i	−0.249557	+	0.297411i	−0.876251	−	0.481855i	$-0.839963\pi$
$373$	−4.81976	+	5.74396i	−0.249557	+	0.297411i	0.626694	+	0.779266i	$0.284408\pi$
$374$	−2.02380	+	11.4775i	−0.104648	+	0.593488i
$375$		0			0
$376$	6.61026	−	6.61026i	0.340898	−	0.340898i
$377$	3.00635	+	8.25989i	0.154835	+	0.425406i
$378$		0			0
$379$	−1.34229	−	7.61251i	−0.0689489	−	0.391029i	−0.999679	−	0.0253226i	$-0.991939\pi$
$379$	−1.34229	−	7.61251i	−0.0689489	−	0.391029i	0.930730	−	0.365706i	$-0.119172\pi$
$380$	3.85258	+	2.22429i	0.197633	+	0.114103i
$381$		0			0
$382$	−15.3043	+	12.8418i	−0.783036	+	0.657045i
$383$	4.87023	−	3.41017i	0.248857	−	0.174252i	−0.442492	−	0.896772i	$-0.645906\pi$
$383$	4.87023	−	3.41017i	0.248857	−	0.174252i	0.691349	+	0.722521i	$0.257017\pi$
$384$		0			0
$385$	−7.64389	−	16.3924i	−0.389569	−	0.835432i
$386$	2.71721	−	7.46548i	0.138303	−	0.379983i
$387$		0			0
$388$	0.207750	+	2.37460i	0.0105469	+	0.120552i
$389$	−2.91280	−	33.2934i	−0.147685	−	1.68804i	−0.603022	−	0.797725i	$-0.706037\pi$
$389$	−2.91280	−	33.2934i	−0.147685	−	1.68804i	0.455337	−	0.890319i	$-0.349519\pi$
$390$		0			0
$391$	−4.94260	+	13.5797i	−0.249958	+	0.686754i
$392$	6.90022	+	14.7976i	0.348514	+	0.747390i
$393$		0			0
$394$	12.8068	−	8.96743i	0.645198	−	0.451773i
$395$	7.47897	−	6.27560i	0.376308	−	0.315760i
$396$		0			0
$397$	−6.33061	−	3.65498i	−0.317724	−	0.183438i	0.332654	−	0.943049i	$-0.392056\pi$
$397$	−6.33061	−	3.65498i	−0.317724	−	0.183438i	−0.650378	+	0.759611i	$0.725389\pi$
$398$	1.70864	+	9.69020i	0.0856466	+	0.485726i
$399$		0			0
$400$	−1.50601	−	4.13773i	−0.0753006	−	0.206887i
$401$	2.85652	−	2.85652i	0.142648	−	0.142648i	−0.632177	−	0.774824i	$-0.717838\pi$
$401$	2.85652	−	2.85652i	0.142648	−	0.142648i	0.774824	+	0.632177i	$0.217838\pi$
$402$		0			0
$403$	−2.37594	+	13.4746i	−0.118354	+	0.671220i
$404$	9.75924	−	11.6306i	0.485541	−	0.578645i
$405$		0			0
$406$			9.71887i			0.482340i
$407$	−17.8410	+	23.4790i	−0.884347	+	1.16381i
$408$		0			0
$409$	1.09538	+	0.0958335i	0.0541632	+	0.00473866i	0.114205	−	0.993457i	$-0.463568\pi$
$409$	1.09538	+	0.0958335i	0.0541632	+	0.00473866i	−0.0600420	+	0.998196i	$0.519123\pi$
$410$	5.31218	+	4.45745i	0.262350	+	0.220138i
$411$		0			0
$412$	6.10425	−	13.0906i	0.300735	−	0.644928i
$413$	−28.3078	−	28.3078i	−1.39293	−	1.39293i
$414$		0			0
$415$	−5.71367	−	1.53097i	−0.280473	−	0.0751525i
$416$	−4.30186	+	0.758534i	−0.210916	+	0.0371902i
$417$		0			0
$418$	24.1778	−	13.9591i	1.18258	−	0.682761i
$419$	−7.77299	−	9.26348i	−0.379735	−	0.452551i	0.541995	−	0.840381i	$-0.317669\pi$
$419$	−7.77299	−	9.26348i	−0.379735	−	0.452551i	−0.921731	+	0.387831i	$0.873225\pi$
$420$		0			0
$421$	−9.46844	+	2.53706i	−0.461463	+	0.123649i	−0.482058	−	0.876139i	$-0.660111\pi$
$421$	−9.46844	+	2.53706i	−0.461463	+	0.123649i	0.0205949	+	0.999788i	$0.493444\pi$
$422$	−10.3210	+	4.81276i	−0.502418	+	0.234281i
$423$		0			0
$424$	−2.10500	−	1.47394i	−0.102228	−	0.0715807i
$425$	10.5455	−	0.922612i	0.511532	−	0.0447533i
$426$		0			0
$427$	−10.4032	+	14.8573i	−0.503446	+	0.718995i
$428$	−9.62781	−	3.50424i	−0.465378	−	0.169384i
$429$		0			0
$430$	1.62999	+	6.08321i	0.0786052	+	0.293359i
$431$	−6.26981	−	8.95421i	−0.302006	−	0.431309i	0.639252	−	0.768997i	$-0.279244\pi$
$431$	−6.26981	−	8.95421i	−0.302006	−	0.431309i	−0.941258	+	0.337688i	$0.890355\pi$
$432$		0			0
$433$	−19.2059	−	33.2656i	−0.922978	−	1.59864i	−0.794782	−	0.606895i	$-0.792415\pi$
$433$	−19.2059	−	33.2656i	−0.922978	−	1.59864i	−0.128196	−	0.991749i	$-0.540919\pi$
$434$	−7.56420	+	13.1016i	−0.363093	+	0.628896i
$435$		0			0
$436$	−2.51531	+	9.38726i	−0.120461	+	0.449568i
$437$	32.5297	−	11.8398i	1.55611	−	0.566376i
$438$		0			0
$439$	15.4648	+	7.21136i	0.738095	+	0.344179i	0.755041	−	0.655677i	$-0.227617\pi$
$439$	15.4648	+	7.21136i	0.738095	+	0.344179i	−0.0169465	+	0.999856i	$0.505395\pi$
$440$	3.68795	+	0.650285i	0.175816	+	0.0310011i
$441$		0			0
$442$	0.915266	−	10.4615i	0.0435348	−	0.497605i
$443$	−24.2781			−1.15349			−0.576744	−	0.816925i	$-0.695677\pi$
$443$	−24.2781			−1.15349			−0.576744	+	0.816925i	$0.695677\pi$
$444$		0			0
$445$	−7.28540			−0.345361
$446$	1.97987	−	22.6300i	0.0937497	−	1.07156i
$447$		0			0
$448$	−4.75646	−	0.838692i	−0.224722	−	0.0396245i
$449$	−16.2885	−	7.59547i	−0.768704	−	0.358452i	−0.00161930	−	0.999999i	$-0.500515\pi$
$449$	−16.2885	−	7.59547i	−0.768704	−	0.358452i	−0.767084	+	0.641546i	$0.778293\pi$
$450$		0			0
$451$	40.8951	−	14.8846i	1.92567	−	0.700888i
$452$	−0.700510	+	2.61434i	−0.0329492	+	0.122968i
$453$		0			0
$454$	6.88041	−	11.9172i	0.322914	−	0.559303i
$455$	8.14875	+	14.1141i	0.382019	+	0.661677i
$456$		0			0
$457$	−0.280815	−	0.401046i	−0.0131360	−	0.0187601i	0.812530	−	0.582919i	$-0.198089\pi$
$457$	−0.280815	−	0.401046i	−0.0131360	−	0.0187601i	−0.825666	+	0.564159i	$0.809201\pi$
$458$	1.33486	+	4.98176i	0.0623739	+	0.232782i
$459$		0			0
$460$	4.36342	+	1.58816i	0.203446	+	0.0740481i
$461$	14.1082	−	20.1486i	0.657084	−	0.938413i	−0.342916	−	0.939366i	$-0.611415\pi$
$461$	14.1082	−	20.1486i	0.657084	−	0.938413i	1.00000		0.000953260i	$0.000303432\pi$
$462$		0			0
$463$	−27.4934	+	2.40536i	−1.27773	+	0.111787i	−0.705737	−	0.708474i	$-0.749384\pi$
$463$	−27.4934	+	2.40536i	−1.27773	+	0.111787i	−0.571990	+	0.820261i	$0.693828\pi$
$464$	−1.64835	−	1.15418i	−0.0765225	−	0.0535816i
$465$		0			0
$466$	5.04367	−	2.35190i	0.233643	−	0.108950i
$467$	−35.7621	+	9.58242i	−1.65487	+	0.443422i	−0.960971	−	0.276649i	$-0.910776\pi$
$467$	−35.7621	+	9.58242i	−1.65487	+	0.443422i	−0.693901	+	0.720071i	$0.744109\pi$
$468$		0			0
$469$	38.8301	+	46.2759i	1.79301	+	2.13682i
$470$	6.25386	−	3.61067i	0.288469	−	0.166548i
$471$		0			0
$472$	8.16282	−	1.43932i	0.375724	−	0.0662503i
$473$	38.1767	+	10.2294i	1.75537	+	0.470350i
$474$		0			0
$475$	−17.9307	−	17.9307i	−0.822719	−	0.822719i
$476$	4.90712	−	10.5234i	0.224918	−	0.482337i
$477$		0			0
$478$	−14.2699	−	11.9739i	−0.652692	−	0.547674i
$479$	33.1595	+	2.90108i	1.51510	+	0.132554i	0.814148	−	0.580658i	$-0.197205\pi$
$479$	33.1595	+	2.90108i	1.51510	+	0.132554i	0.700949	+	0.713212i	$0.252760\pi$
$480$		0			0
$481$	14.1708	−	22.4766i	0.646135	−	1.02485i
$482$			2.28567i			0.104109i
$483$		0			0
$484$	8.03595	−	9.57687i	0.365270	−	0.435312i
$485$	−0.319742	+	1.81335i	−0.0145187	+	0.0823398i
$486$		0			0
$487$	−23.4650	+	23.4650i	−1.06330	+	1.06330i	−0.0654434	+	0.997856i	$0.520846\pi$
$487$	−23.4650	+	23.4650i	−1.06330	+	1.06330i	−0.997856	+	0.0654434i	$0.979154\pi$
$488$	−1.28438	−	3.52881i	−0.0581413	−	0.159742i
$489$		0			0
$490$	2.19012	+	12.4208i	0.0989397	+	0.561115i
$491$	19.3042	+	11.1453i	0.871186	+	0.502979i	0.867742	−	0.497015i	$-0.165571\pi$
$491$	19.3042	+	11.1453i	0.871186	+	0.502979i	0.00344362	+	0.999994i	$0.498904\pi$
$492$		0			0
$493$	3.70582	−	3.10955i	0.166902	−	0.140047i
$494$	−20.6066	+	14.4289i	−0.927134	+	0.649187i
$495$		0			0
$496$	−1.32376	−	2.83881i	−0.0594386	−	0.127466i
$497$	−17.5332	+	48.1721i	−0.786472	+	2.16081i
$498$		0			0
$499$	−2.93219	−	33.5151i	−0.131263	−	1.50034i	−0.721106	−	0.692825i	$-0.756366\pi$
$499$	−2.93219	−	33.5151i	−0.131263	−	1.50034i	0.589843	−	0.807518i	$-0.299190\pi$
$500$	−0.633081	−	7.23615i	−0.0283123	−	0.323611i
$501$		0			0
$502$	−7.71388	+	21.1937i	−0.344287	+	0.945922i
$503$	10.6967	+	22.9391i	0.476941	+	1.02280i	0.986710	+	0.162492i	$0.0519530\pi$
$503$	10.6967	+	22.9391i	0.476941	+	1.02280i	−0.509769	+	0.860311i	$0.670269\pi$
$504$		0			0
$505$	9.60721	−	6.72704i	0.427515	−	0.299349i
$506$	22.3234	−	18.7316i	0.992398	−	0.832721i
$507$		0			0
$508$	8.57330	+	4.94980i	0.380379	+	0.219612i
$509$	−0.447421	−	2.53745i	−0.0198316	−	0.112470i	0.973285	−	0.229600i	$-0.0737418\pi$
$509$	−0.447421	−	2.53745i	−0.0198316	−	0.112470i	−0.993117	+	0.117130i	$0.962631\pi$
$510$		0			0
$511$	9.85758	+	27.0835i	0.436074	+	1.19810i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−2.35883	+	13.3776i	−0.104044	+	0.590061i
$515$	7.17193	−	8.54717i	0.316033	−	0.376633i
$516$		0			0
$517$		−	45.3193i		−	1.99314i
$518$	23.2233	−	17.9942i	1.02037	−	0.790619i
$519$		0			0
$520$	−3.36150	−	0.294093i	−0.147412	−	0.0128968i
$521$	26.2417	+	22.0194i	1.14967	+	0.964687i	0.999712	−	0.0240057i	$-0.00764199\pi$
$521$	26.2417	+	22.0194i	1.14967	+	0.964687i	0.149957	+	0.988692i	$0.452086\pi$
$522$		0			0
$523$	9.22759	−	19.7886i	0.403494	−	0.865296i	−0.594626	−	0.804003i	$-0.702700\pi$
$523$	9.22759	−	19.7886i	0.403494	−	0.865296i	0.998120	−	0.0612933i	$-0.0195225\pi$
$524$	−3.08458	−	3.08458i	−0.134751	−	0.134751i
$525$		0			0
$526$	7.97549	+	2.13703i	0.347748	+	0.0931788i
$527$	7.41581	−	1.30761i	0.323038	−	0.0569603i
$528$		0			0
$529$	11.3743	−	6.56696i	0.494535	−	0.285520i
$530$	−1.27597	−	1.52064i	−0.0554244	−	0.0660522i
$531$		0			0
$532$	−26.8666	+	7.19889i	−1.16482	+	0.312111i
$533$	−35.5399	+	16.5725i	−1.53940	+	0.717835i
$534$		0			0
$535$	−6.48321	−	4.53959i	−0.280294	−	0.196264i
$536$	−12.4599	+	1.09010i	−0.538184	+	0.0470850i
$537$		0			0
$538$	−3.07744	+	4.39505i	−0.132678	+	0.189484i
$539$	74.3790	+	27.0717i	3.20373	+	1.16606i
$540$		0			0
$541$	10.9911	+	41.0192i	0.472543	+	1.76355i	0.630584	+	0.776121i	$0.282815\pi$
$541$	10.9911	+	41.0192i	0.472543	+	1.76355i	−0.158042	+	0.987432i	$0.550518\pi$
$542$	5.80195	+	8.28605i	0.249215	+	0.355916i
$543$		0			0
$544$	1.20203	+	2.08198i	0.0515368	+	0.0892643i
$545$	−3.75361	+	6.50144i	−0.160787	+	0.278491i
$546$		0			0
$547$	−7.71351	+	28.7872i	−0.329806	+	1.23085i	0.579586	+	0.814911i	$0.303214\pi$
$547$	−7.71351	+	28.7872i	−0.329806	+	1.23085i	−0.909392	+	0.415941i	$0.863452\pi$
$548$	13.6073	−	4.95265i	0.581274	−	0.211567i
$549$		0			0
$550$	−19.3465	−	9.02142i	−0.824937	−	0.384675i
$551$	−11.4123	−	2.01229i	−0.486179	−	0.0857264i
$552$		0			0
$553$	−5.32025	+	60.8107i	−0.226240	+	2.58594i
$554$	−22.9914			−0.976809
$555$		0			0
$556$	−5.51327			−0.233815
$557$	−1.09335	+	12.4971i	−0.0463269	+	0.529519i	0.937204	+	0.348781i	$0.113404\pi$
$557$	−1.09335	+	12.4971i	−0.0463269	+	0.529519i	−0.983531	+	0.180738i	$0.942151\pi$
$558$		0			0
$559$	−35.0721	−	6.18416i	−1.48339	−	0.261562i
$560$	−3.38136	−	1.57676i	−0.142889	−	0.0666301i
$561$		0			0
$562$	−20.3398	+	7.40309i	−0.857984	+	0.312281i
$563$	−1.11046	+	4.14429i	−0.0468003	+	0.174661i	−0.985370	−	0.170428i	$-0.945485\pi$
$563$	−1.11046	+	4.14429i	−0.0468003	+	0.174661i	0.938570	+	0.345090i	$0.112151\pi$
$564$		0			0
$565$	−1.04537	+	1.81064i	−0.0439793	+	0.0761743i
$566$	6.68679	+	11.5819i	0.281067	+	0.486822i
$567$		0			0
$568$	−6.08792	−	8.69445i	−0.255443	−	0.364811i
$569$	6.35699	+	23.7246i	0.266499	+	0.994588i	0.961326	+	0.275411i	$0.0888141\pi$
$569$	6.35699	+	23.7246i	0.266499	+	0.994588i	−0.694827	+	0.719176i	$0.744519\pi$
$570$		0			0
$571$	30.7894	+	11.2064i	1.28850	+	0.468974i	0.893233	−	0.449594i	$-0.148431\pi$
$571$	30.7894	+	11.2064i	1.28850	+	0.468974i	0.395263	+	0.918568i	$0.370654\pi$
$572$	−12.1464	+	17.3468i	−0.507865	+	0.725306i
$573$		0			0
$574$	−43.1928	+	3.77888i	−1.80283	+	0.157728i
$575$	−21.6820	−	15.1819i	−0.904201	−	0.633128i
$576$		0			0
$577$	0.500001	−	0.233154i	0.0208153	−	0.00970633i	−0.412183	−	0.911101i	$-0.635233\pi$
$577$	0.500001	−	0.233154i	0.0208153	−	0.00970633i	0.432998	+	0.901395i	$0.357456\pi$
$578$	10.8381	−	2.90407i	0.450807	−	0.120793i
$579$		0			0
$580$	−0.999160	−	1.19075i	−0.0414879	−	0.0494433i
$581$	32.0295	−	18.4923i	1.32881	−	0.767188i
$582$		0			0
$583$	−12.2684	+	2.16325i	−0.508106	+	0.0895928i
$584$	−5.76408	−	1.54448i	−0.238519	−	0.0639111i
$585$		0			0
$586$	0.563748	+	0.563748i	0.0232882	+	0.0232882i
$587$	−4.63066	+	9.93049i	−0.191128	+	0.409875i	−0.978397	−	0.206734i	$-0.933716\pi$
$587$	−4.63066	+	9.93049i	−0.191128	+	0.409875i	0.787269	+	0.616609i	$0.211494\pi$
$588$		0			0
$589$	−13.8182	−	11.5948i	−0.569369	−	0.477757i
$590$	6.37847	+	0.558044i	0.262598	+	0.0229743i
$591$		0			0
$592$	0.293936	+	6.07566i	0.0120807	+	0.249708i
$593$			33.2747i			1.36643i	0.730219	+	0.683213i	$0.239418\pi$
$593$			33.2747i			1.36643i	−0.730219	+	0.683213i	$0.760582\pi$
$594$		0			0
$595$	5.76541	−	6.87095i	0.236359	−	0.281681i
$596$	1.90653	−	10.8125i	0.0780946	−	0.442897i
$597$		0			0
$598$	−18.5672	+	18.5672i	−0.759271	+	0.759271i
$599$	−12.2743	−	33.7235i	−0.501516	−	1.37790i	−0.889795	−	0.456361i	$-0.849153\pi$
$599$	−12.2743	−	33.7235i	−0.501516	−	1.37790i	0.388279	−	0.921542i	$-0.373070\pi$
$600$		0			0
$601$	−1.99181	−	11.2961i	−0.0812475	−	0.460777i	−0.998103	−	0.0615592i	$-0.980393\pi$
$601$	−1.99181	−	11.2961i	−0.0812475	−	0.460777i	0.916856	−	0.399218i	$-0.130718\pi$
$602$	−34.1011	−	19.6883i	−1.38986	−	0.802434i
$603$		0			0
$604$	12.0115	−	10.0789i	0.488742	−	0.410103i
$605$	7.91076	−	5.53917i	0.321618	−	0.225199i
$606$		0			0
$607$	−15.2512	−	32.7063i	−0.619027	−	1.32751i	−0.926623	−	0.375991i	$-0.877302\pi$
$607$	−15.2512	−	32.7063i	−0.619027	−	1.32751i	0.307596	−	0.951517i	$-0.400475\pi$
$608$	1.96965	−	5.41156i	0.0798797	−	0.219468i
$609$		0			0
$610$	−0.252827	−	2.88982i	−0.0102367	−	0.117005i
$611$	3.55905	+	40.6801i	0.143984	+	1.64574i
$612$		0			0
$613$	−12.6318	+	34.7056i	−0.510194	+	1.40175i	0.370841	+	0.928696i	$0.379070\pi$
$613$	−12.6318	+	34.7056i	−0.510194	+	1.40175i	−0.881035	+	0.473051i	$0.843153\pi$
$614$	−1.05120	−	2.25430i	−0.0424229	−	0.0909763i
$615$		0			0
$616$	−19.1799	+	13.4299i	−0.772781	+	0.541107i
$617$	−6.66131	+	5.58951i	−0.268174	+	0.225025i	−0.766951	−	0.641705i	$-0.778227\pi$
$617$	−6.66131	+	5.58951i	−0.268174	+	0.225025i	0.498777	+	0.866730i	$0.333783\pi$
$618$		0			0
$619$	18.9610	+	10.9471i	0.762105	+	0.440002i	0.830051	−	0.557687i	$-0.188311\pi$
$619$	18.9610	+	10.9471i	0.762105	+	0.440002i	−0.0679458	+	0.997689i	$0.521644\pi$
$620$	−0.420160	−	2.38285i	−0.0168740	−	0.0956975i
$621$		0			0
$622$	4.50338	+	12.3729i	0.180569	+	0.496109i
$623$	32.2097	−	32.2097i	1.29045	−	1.29045i
$624$		0			0
$625$	−2.84876	+	16.1561i	−0.113950	+	0.646244i
$626$	−0.665013	+	0.792531i	−0.0265793	+	0.0316759i
$627$		0			0
$628$		−	4.30235i		−	0.171683i
$629$	−14.2915	−	3.09782i	−0.569839	−	0.123518i
$630$		0			0
$631$	28.1732	+	2.46483i	1.12156	+	0.0981235i	0.632813	−	0.774304i	$-0.281900\pi$
$631$	28.1732	+	2.46483i	1.12156	+	0.0981235i	0.488743	+	0.872428i	$0.337456\pi$
$632$	−9.68184	−	8.12402i	−0.385123	−	0.323156i
$633$		0			0
$634$	6.29186	−	13.4929i	0.249882	−	0.535873i
$635$	5.40737	+	5.40737i	0.214585	+	0.214585i
$636$		0			0
$637$	−68.8911	−	18.4593i	−2.72957	−	0.731385i
$638$	−9.60694	+	1.69396i	−0.380342	+	0.0670646i
$639$		0			0
$640$	0.668982	−	0.386237i	0.0264438	−	0.0152674i
$641$	−0.265891	−	0.316877i	−0.0105021	−	0.0125159i	0.760768	−	0.649024i	$-0.224823\pi$
$641$	−0.265891	−	0.316877i	−0.0105021	−	0.0125159i	−0.771270	+	0.636508i	$0.780378\pi$
$642$		0			0
$643$	18.6696	−	5.00251i	0.736258	−	0.197280i	0.128844	−	0.991665i	$-0.458873\pi$
$643$	18.6696	−	5.00251i	0.736258	−	0.197280i	0.607414	+	0.794385i	$0.292207\pi$
$644$	−26.3127	+	12.2698i	−1.03687	+	0.483498i
$645$		0			0
$646$	11.3409	+	7.94099i	0.446202	+	0.312434i
$647$	23.9628	−	2.09647i	0.942075	−	0.0824209i	0.394240	−	0.919007i	$-0.371008\pi$
$647$	23.9628	−	2.09647i	0.942075	−	0.0824209i	0.547835	+	0.836587i	$0.315452\pi$
$648$		0			0
$649$	23.0478	−	32.9157i	0.904706	−	1.29205i
$650$	18.0745	+	6.57860i	0.708942	+	0.258034i
$651$		0			0
$652$	−3.03759	−	11.3364i	−0.118961	−	0.443969i
$653$	5.00399	+	7.14644i	0.195821	+	0.279662i	0.905040	−	0.425327i	$-0.139841\pi$
$653$	5.00399	+	7.14644i	0.195821	+	0.279662i	−0.709218	+	0.704989i	$0.750952\pi$
$654$		0			0
$655$	−1.68487	−	2.91827i	−0.0658332	−	0.114026i
$656$	4.48854	−	7.77438i	0.175248	−	0.303539i
$657$		0			0
$658$	−11.6859	+	43.6123i	−0.455563	+	1.70019i
$659$	0.814198	−	0.296344i	0.0317167	−	0.0115439i	−0.326113	−	0.945331i	$-0.605739\pi$
$659$	0.814198	−	0.296344i	0.0317167	−	0.0115439i	0.357830	+	0.933787i	$0.383517\pi$
$660$		0			0
$661$	−22.2246	−	10.3635i	−0.864435	−	0.403093i	−0.0607539	−	0.998153i	$-0.519350\pi$
$661$	−22.2246	−	10.3635i	−0.864435	−	0.403093i	−0.803681	+	0.595060i	$0.797128\pi$
$662$	9.48088	+	1.67173i	0.368485	+	0.0649738i
$663$		0			0
$664$	−0.667396	+	7.62837i	−0.0259000	+	0.296038i
$665$	−21.4859			−0.833186
$666$		0			0
$667$	−12.0960			−0.468358
$668$	−1.73092	+	19.7845i	−0.0669712	+	0.765485i
$669$		0			0
$670$	−9.51489	−	1.67773i	−0.367592	−	0.0648165i
$671$	−16.4994	−	7.69380i	−0.636953	−	0.297016i
$672$		0			0
$673$	14.6601	−	5.33583i	0.565104	−	0.205681i	−0.0436404	−	0.999047i	$-0.513896\pi$
$673$	14.6601	−	5.33583i	0.565104	−	0.205681i	0.608745	+	0.793366i	$0.291673\pi$
$674$	−3.95790	+	14.7711i	−0.152453	+	0.568961i
$675$		0			0
$676$	3.04069	−	5.26664i	0.116950	−	0.202563i
$677$	10.6755	+	18.4905i	0.410293	+	0.710648i	0.994922	−	0.100653i	$-0.0320931\pi$
$677$	10.6755	+	18.4905i	0.410293	+	0.710648i	−0.584629	+	0.811301i	$0.698760\pi$
$678$		0			0
$679$	−6.60342	−	9.43066i	−0.253416	−	0.361916i
$680$	0.480647	+	1.79380i	0.0184320	+	0.0687891i
$681$		0			0
$682$	−14.2691	−	5.19353i	−0.546392	−	0.198870i
$683$	25.2240	−	36.0237i	0.965171	−	1.37841i	0.0398570	−	0.999205i	$-0.487310\pi$
$683$	25.2240	−	36.0237i	0.965171	−	1.37841i	0.925314	−	0.379202i	$-0.123801\pi$
$684$		0			0
$685$	11.1433	−	0.974912i	0.425764	−	0.0372495i
$686$	−36.9023	−	25.8392i	−1.40894	−	0.986547i
$687$		0			0
$688$	7.38892	−	3.44551i	0.281700	−	0.131359i
$689$	10.8427	−	2.90528i	0.413073	−	0.110683i
$690$		0			0
$691$	19.2621	+	22.9556i	0.732763	+	0.873273i	0.995804	−	0.0915114i	$-0.0291698\pi$
$691$	19.2621	+	22.9556i	0.732763	+	0.873273i	−0.263041	+	0.964785i	$0.584725\pi$
$692$	17.4712	−	10.0870i	0.664156	−	0.383451i
$693$		0			0
$694$	18.6617	−	3.29056i	0.708388	−	0.124908i
$695$	−4.11374	−	1.10227i	−0.156043	−	0.0418116i
$696$		0			0
$697$	15.2604	+	15.2604i	0.578030	+	0.578030i
$698$	3.45372	−	7.40653i	0.130725	−	0.280341i
$699$		0			0
$700$	16.2916	+	13.6703i	0.615763	+	0.516687i
$701$	−30.5339	−	2.67137i	−1.15325	−	0.100896i	−0.505554	−	0.862795i	$-0.668712\pi$
$701$	−30.5339	−	2.67137i	−1.15325	−	0.100896i	−0.647697	+	0.761898i	$0.724268\pi$
$702$		0			0
$703$	16.3211	+	30.9953i	0.615561	+	1.16901i
$704$		−	4.84786i		−	0.182710i
$705$		0			0
$706$	5.19512	−	6.19130i	0.195521	−	0.233013i
$707$	−12.7336	+	72.2158i	−0.478896	+	2.71596i
$708$		0			0
$709$	5.44016	−	5.44016i	0.204309	−	0.204309i	−0.597534	−	0.801843i	$-0.703853\pi$
$709$	5.44016	−	5.44016i	0.204309	−	0.204309i	0.801843	+	0.597534i	$0.203853\pi$
$710$	−2.80423	−	7.70455i	−0.105241	−	0.289147i
$711$		0			0
$712$	1.63772	+	9.28797i	0.0613761	+	0.348081i
$713$	−16.3061	−	9.41431i	−0.610667	−	0.352569i
$714$		0			0
$715$	−12.5312	+	10.5149i	−0.468640	+	0.393236i
$716$	1.07987	−	0.756135i	0.0403567	−	0.0282581i
$717$		0			0
$718$	0.945719	+	2.02810i	0.0352939	+	0.0756881i
$719$	15.7141	−	43.1743i	0.586039	−	1.61013i	−0.191640	−	0.981465i	$-0.561380\pi$
$719$	15.7141	−	43.1743i	0.586039	−	1.61013i	0.777678	−	0.628663i	$-0.216397\pi$
$720$		0			0
$721$	6.08013	+	69.4962i	0.226436	+	2.58817i
$722$	−1.23452	−	14.1106i	−0.0459440	−	0.525142i
$723$		0			0
$724$	0.839170	−	2.30560i	0.0311875	−	0.0856869i
$725$	3.74463	+	8.03038i	0.139072	+	0.298241i
$726$		0			0
$727$	−25.5264	+	17.8738i	−0.946724	+	0.662903i	−0.941475	−	0.337083i	$-0.890560\pi$
$727$	−25.5264	+	17.8738i	−0.946724	+	0.662903i	−0.00524871	+	0.999986i	$0.501671\pi$
$728$	16.1619	−	13.5614i	0.598998	−	0.502619i
$729$		0			0
$730$	−3.99209	−	2.30484i	−0.147754	−	0.0853058i
$731$	3.40347	+	19.3020i	0.125882	+	0.713912i
$732$		0			0
$733$	−16.8426	−	46.2746i	−0.622094	−	1.70919i	−0.701802	−	0.712372i	$-0.747621\pi$
$733$	−16.8426	−	46.2746i	−0.622094	−	1.70919i	0.0797078	−	0.996818i	$-0.474601\pi$
$734$	8.82963	−	8.82963i	0.325908	−	0.325908i
$735$		0			0
$736$	1.04383	−	5.91983i	0.0384759	−	0.218208i
$737$	−38.9750	+	46.4486i	−1.43566	+	1.71096i
$738$		0			0
$739$		−	10.8537i		−	0.399261i	−0.979871	−	0.199630i	$-0.936026\pi$
$739$		−	10.8537i		−	0.399261i	0.979871	−	0.199630i	$-0.0639741\pi$
$740$	−0.995391	+	4.59213i	−0.0365913	+	0.168810i
$741$		0			0
$742$	12.3641	+	1.08172i	0.453902	+	0.0397113i
$743$	−30.9949	−	26.0078i	−1.13709	−	0.954134i	−0.137753	−	0.990467i	$-0.543988\pi$
$743$	−30.9949	−	26.0078i	−1.13709	−	0.954134i	−0.999340	+	0.0363330i	$0.988432\pi$
$744$		0			0
$745$	3.58432	−	7.68659i	0.131319	−	0.281615i
$746$	5.30203	+	5.30203i	0.194121	+	0.194121i
$747$		0			0
$748$	11.2575	+	3.01643i	0.411613	+	0.110291i
$749$	48.7333	−	8.59299i	1.78067	−	0.313981i
$750$		0			0
$751$	−22.2775	+	12.8619i	−0.812918	+	0.469338i	−0.847968	−	0.530047i	$-0.822174\pi$
$751$	−22.2775	+	12.8619i	−0.812918	+	0.469338i	0.0350504	+	0.999386i	$0.488841\pi$
$752$	−6.00898	−	7.16122i	−0.219125	−	0.261143i
$753$		0			0
$754$	8.49048	−	2.27502i	0.309205	−	0.0828513i
$755$	10.9775	−	5.11890i	0.399513	−	0.186296i
$756$		0			0
$757$	9.37743	+	6.56615i	0.340828	+	0.238651i	0.731441	−	0.681904i	$-0.238848\pi$
$757$	9.37743	+	6.56615i	0.340828	+	0.238651i	−0.390613	+	0.920555i	$0.627737\pi$
$758$	−7.70053	+	0.673709i	−0.279696	+	0.0244702i
$759$		0			0
$760$	2.55160	−	3.64406i	0.0925561	−	0.132184i
$761$	4.34813	+	1.58259i	0.157620	+	0.0573689i	0.419625	−	0.907698i	$-0.362162\pi$
$761$	4.34813	+	1.58259i	0.157620	+	0.0573689i	−0.262005	+	0.965066i	$0.584384\pi$
$762$		0			0
$763$	−12.1485	−	45.3389i	−0.439806	−	1.64138i
$764$	11.4591	+	16.3653i	0.414576	+	0.592076i
$765$		0			0
$766$	−2.97273	−	5.14891i	−0.107409	−	0.186038i
$767$	−18.1035	+	31.3563i	−0.653681	+	1.13221i
$768$		0			0
$769$	−10.0271	+	37.4216i	−0.361586	+	1.34946i	0.510405	+	0.859934i	$0.329495\pi$
$769$	−10.0271	+	37.4216i	−0.361586	+	1.34946i	−0.871991	+	0.489522i	$0.837171\pi$
$770$	−16.9962	+	6.18611i	−0.612501	+	0.222932i
$771$		0			0
$772$	−7.20025	−	3.35753i	−0.259143	−	0.120840i
$773$	34.1798	+	6.02682i	1.22936	+	0.216770i	0.750351	−	0.661039i	$-0.229884\pi$
$773$	34.1798	+	6.02682i	1.22936	+	0.216770i	0.479011	+	0.877809i	$0.340995\pi$
$774$		0			0
$775$	−1.20208	+	13.7398i	−0.0431800	+	0.493550i
$776$	2.38367			0.0855686
$777$		0			0
$778$	−33.4206			−1.19819
$779$	4.50576	−	51.5011i	0.161436	−	1.84522i
$780$		0			0
$781$	−50.6732	−	8.93506i	−1.81323	−	0.319722i
$782$	13.0972	+	6.10734i	0.468356	+	0.218398i
$783$		0			0
$784$	15.3426	−	5.58427i	0.547952	−	0.199438i
$785$	0.860174	−	3.21021i	0.0307009	−	0.114577i
$786$		0			0
$787$	21.0515	−	36.4622i	0.750403	−	1.29974i	−0.197224	−	0.980358i	$-0.563193\pi$
$787$	21.0515	−	36.4622i	0.750403	−	1.29974i	0.947627	−	0.319378i	$-0.103474\pi$
$788$	−7.81712	−	13.5396i	−0.278473	−	0.482330i
$789$		0			0
$790$	−5.59988	−	7.99746i	−0.199235	−	0.284537i
$791$	−3.38335	−	12.6268i	−0.120298	−	0.448958i
$792$		0			0
$793$	15.4147	+	5.61048i	0.547390	+	0.199234i
$794$	−4.19282	+	5.98797i	−0.148798	+	0.212505i
$795$		0			0
$796$	9.80225	−	0.857586i	0.347431	−	0.0303963i
$797$	−23.3259	−	16.3329i	−0.826245	−	0.578543i	0.0821676	−	0.996619i	$-0.473816\pi$
$797$	−23.3259	−	16.3329i	−0.826245	−	0.578543i	−0.908412	+	0.418076i	$0.862705\pi$
$798$		0			0
$799$	20.3683	−	9.49791i	0.720580	−	0.336012i
$800$	−4.25325	+	1.13965i	−0.150375	+	0.0402928i
$801$		0			0
$802$	−2.59668	−	3.09461i	−0.0916921	−	0.109274i
$803$	−25.0534	+	14.4646i	−0.884115	+	0.510444i
$804$		0			0
$805$	−22.0864	+	3.89443i	−0.778444	+	0.137261i
$806$	13.2163	+	3.54129i	0.465524	+	0.124737i
$807$		0			0
$808$	−10.7358	−	10.7358i	−0.377683	−	0.377683i
$809$	20.6278	−	44.2364i	0.725234	−	1.55527i	−0.102869	−	0.994695i	$-0.532802\pi$
$809$	20.6278	−	44.2364i	0.725234	−	1.55527i	0.828103	−	0.560575i	$-0.189420\pi$
$810$		0			0
$811$	−25.8419	−	21.6839i	−0.907432	−	0.761426i	0.0641963	−	0.997937i	$-0.479552\pi$
$811$	−25.8419	−	21.6839i	−0.907432	−	0.761426i	−0.971629	+	0.236511i	$0.923996\pi$
$812$	9.68189	+	0.847056i	0.339768	+	0.0297258i
$813$		0			0
$814$	21.8347	+	19.8195i	0.765305	+	0.694672i
$815$		−	9.06601i		−	0.317569i
$816$		0			0
$817$	30.1793	−	35.9663i	1.05584	−	1.25830i
$818$	0.190938	−	1.08286i	0.00667598	−	0.0378614i
$819$		0			0
$820$	4.90348	−	4.90348i	0.171237	−	0.171237i
$821$	−7.11745	−	19.5550i	−0.248401	−	0.682475i	−0.999745	−	0.0225653i	$-0.992817\pi$
$821$	−7.11745	−	19.5550i	−0.248401	−	0.682475i	0.751345	−	0.659910i	$-0.229406\pi$
$822$		0			0
$823$	4.18380	+	23.7275i	0.145838	+	0.827090i	0.966690	+	0.255949i	$0.0823879\pi$
$823$	4.18380	+	23.7275i	0.145838	+	0.827090i	−0.820852	+	0.571141i	$0.806501\pi$
$824$	−12.5088	−	7.22195i	−0.435764	−	0.251588i
$825$		0			0
$826$	−30.6673	+	25.7329i	−1.06705	+	0.895361i
$827$	−19.5528	+	13.6910i	−0.679916	+	0.476083i	−0.861807	−	0.507236i	$-0.830667\pi$
$827$	−19.5528	+	13.6910i	−0.679916	+	0.476083i	0.181891	+	0.983319i	$0.441778\pi$
$828$		0			0
$829$	−5.89904	−	12.6505i	−0.204882	−	0.439371i	0.776838	−	0.629700i	$-0.216822\pi$
$829$	−5.89904	−	12.6505i	−0.204882	−	0.439371i	−0.981720	+	0.190329i	$0.939045\pi$
$830$	−2.02313	+	5.55850i	−0.0702238	+	0.192938i
$831$		0			0
$832$	0.380716	+	4.35160i	0.0131989	+	0.150865i
$833$	3.42103	+	39.1026i	0.118532	+	1.35482i
$834$		0			0
$835$	−5.24706	+	14.4162i	−0.181582	+	0.498893i
$836$	−11.7987	−	25.3024i	−0.408067	−	0.875103i
$837$		0			0
$838$	−9.90569	+	6.93604i	−0.342187	+	0.239602i
$839$	12.3861	−	10.3932i	0.427616	−	0.358813i	−0.403435	−	0.915008i	$-0.632184\pi$
$839$	12.3861	−	10.3932i	0.427616	−	0.358813i	0.831051	+	0.556196i	$0.187739\pi$
$840$		0			0
$841$	−21.6080	−	12.4754i	−0.745105	−	0.430187i
$842$	1.70218	+	9.65353i	0.0586609	+	0.332682i
$843$		0			0
$844$	3.89491	+	10.7012i	0.134068	+	0.368350i
$845$	3.32178	−	3.32178i	0.114273	−	0.114273i
$846$		0			0
$847$	−10.4851	+	59.4639i	−0.360272	+	2.04320i
$848$	−1.65179	+	1.96853i	−0.0567227	+	0.0675995i
$849$		0			0
$850$		−	10.5858i		−	0.363090i
$851$	22.3953	+	28.9034i	0.767702	+	0.990794i
$852$		0			0
$853$	5.37273	+	0.470053i	0.183959	+	0.0160943i	0.178763	−	0.983892i	$-0.442791\pi$
$853$	5.37273	+	0.470053i	0.183959	+	0.0160943i	0.00519595	+	0.999987i	$0.498346\pi$
$854$	13.8941	+	11.6585i	0.475445	+	0.398946i
$855$		0			0
$856$	−4.33002	+	9.28576i	−0.147997	+	0.317381i
$857$	25.0440	+	25.0440i	0.855486	+	0.855486i	0.990802	−	0.135317i	$-0.0432051\pi$
$857$	25.0440	+	25.0440i	0.855486	+	0.855486i	−0.135317	+	0.990802i	$0.543205\pi$
$858$		0			0
$859$	−6.97412	−	1.86871i	−0.237954	−	0.0637596i	0.137871	−	0.990450i	$-0.455974\pi$
$859$	−6.97412	−	1.86871i	−0.237954	−	0.0637596i	−0.375825	+	0.926691i	$0.622641\pi$
$860$	6.20213	−	1.09360i	0.211491	−	0.0372915i
$861$		0			0
$862$	−9.46659	+	5.46554i	−0.322433	+	0.186157i
$863$	9.61826	+	11.4626i	0.327409	+	0.390191i	0.904489	−	0.426496i	$-0.140252\pi$
$863$	9.61826	+	11.4626i	0.327409	+	0.390191i	−0.577080	+	0.816688i	$0.695808\pi$
$864$		0			0
$865$	15.0529	−	4.03341i	0.511814	−	0.137140i
$866$	−34.8130	+	16.2335i	−1.18299	+	0.551638i
$867$		0			0
$868$	12.3925	+	8.67730i	0.420628	+	0.294527i
$869$	−61.0376	+	5.34010i	−2.07056	+	0.181151i
$870$		0			0
$871$	31.3375	−	44.7546i	1.06183	−	1.51645i
$872$	9.13232	+	3.32389i	0.309259	+	0.112561i
$873$		0			0
$874$	−8.95964	−	33.4378i	−0.303064	−	1.13105i
$875$	20.1227	+	28.7382i	0.680273	+	0.971530i
$876$		0			0
$877$	27.2652	+	47.2246i	0.920679	+	1.59466i	0.798367	+	0.602171i	$0.205697\pi$
$877$	27.2652	+	47.2246i	0.920679	+	1.59466i	0.122311	+	0.992492i	$0.460969\pi$
$878$	8.53176	−	14.7774i	0.287933	−	0.498715i
$879$		0			0
$880$	0.969237	−	3.61724i	0.0326730	−	0.121937i
$881$	40.1846	−	14.6260i	1.35385	−	0.492763i	0.439706	−	0.898142i	$-0.355083\pi$
$881$	40.1846	−	14.6260i	1.35385	−	0.492763i	0.914149	+	0.405379i	$0.132860\pi$
$882$		0			0
$883$	−23.2956	−	10.8629i	−0.783958	−	0.365566i	−0.0109323	−	0.999940i	$-0.503480\pi$
$883$	−23.2956	−	10.8629i	−0.783958	−	0.365566i	−0.773026	+	0.634375i	$0.781258\pi$
$884$	−10.3420	−	1.82357i	−0.347838	−	0.0613332i
$885$		0			0
$886$	−2.11598	+	24.1857i	−0.0710877	+	0.812536i
$887$	−16.5964			−0.557251			−0.278626	−	0.960400i	$-0.589879\pi$
$887$	−16.5964			−0.557251			−0.278626	+	0.960400i	$0.589879\pi$
$888$		0			0
$889$	−47.8134			−1.60361
$890$	−0.634964	+	7.25767i	−0.0212840	+	0.243278i
$891$		0			0
$892$	−22.3714	−	3.94468i	−0.749049	−	0.132078i
$893$	−48.7917	−	22.7519i	−1.63275	−	0.761364i
$894$		0			0
$895$	0.956925	−	0.348292i	0.0319865	−	0.0116421i
$896$	−1.25005	+	4.66526i	−0.0417613	+	0.155855i
$897$		0			0
$898$	−8.98621	+	15.5646i	−0.299874	+	0.519396i
$899$	3.15148	+	5.45852i	0.105108	+	0.182052i
$900$		0			0
$901$	−3.54344	−	5.06056i	−0.118049	−	0.168592i
$902$	−11.2637	−	42.0367i	−0.375040	−	1.39967i
$903$		0			0
$904$	2.54334	+	0.925699i	0.0845901	+	0.0307883i
$905$	1.08711	−	1.55255i	0.0361367	−	0.0516086i
$906$		0			0
$907$	19.6568	−	1.71975i	0.652693	−	0.0571032i	0.244000	−	0.969775i	$-0.421540\pi$
$907$	19.6568	−	1.71975i	0.652693	−	0.0571032i	0.408693	+	0.912672i	$0.365985\pi$
$908$	−11.2722	−	7.89288i	−0.374081	−	0.261935i
$909$		0			0
$910$	14.7706	−	6.88762i	0.489639	−	0.228323i
$911$	−0.192021	+	0.0514519i	−0.00636194	+	0.00170468i	−0.261999	−	0.965068i	$-0.584382\pi$
$911$	−0.192021	+	0.0514519i	−0.00636194	+	0.00170468i	0.255637	+	0.966773i	$0.417715\pi$
$912$		0			0
$913$	23.8619	+	28.4375i	0.789713	+	0.941144i
$914$	−0.423994	+	0.244793i	−0.0140245	+	0.00809704i
$915$		0			0
$916$	5.07914	−	0.895590i	0.167820	−	0.0295911i
$917$	20.3511	+	5.45306i	0.672052	+	0.180076i
$918$		0			0
$919$	26.8943	+	26.8943i	0.887163	+	0.887163i	0.994250	−	0.107087i	$-0.0341524\pi$
$919$	26.8943	+	26.8943i	0.887163	+	0.887163i	−0.107087	+	0.994250i	$0.534152\pi$
$920$	1.96241	−	4.20840i	0.0646987	−	0.138747i
$921$		0			0
$922$	−18.8423	−	15.8106i	−0.620538	−	0.520693i
$923$	46.1877	+	4.04090i	1.52029	+	0.133008i
$924$		0			0
$925$	12.2555	−	23.8158i	0.402960	−	0.783058i
$926$			27.5984i			0.906941i
$927$		0			0
$928$	−1.29345	+	1.54148i	−0.0424597	+	0.0506015i
$929$	9.15549	−	51.9234i	0.300382	−	1.70355i	−0.344101	−	0.938933i	$-0.611816\pi$
$929$	9.15549	−	51.9234i	0.300382	−	1.70355i	0.644483	−	0.764619i	$-0.277073\pi$
$930$		0			0
$931$	66.4869	−	66.4869i	2.17902	−	2.17902i
$932$	−1.90337	−	5.22945i	−0.0623468	−	0.171296i
$933$		0			0
$934$	6.42909	+	36.4612i	0.210366	+	1.19305i
$935$	7.79670	+	4.50143i	0.254979	+	0.147212i
$936$		0			0
$937$	38.8883	−	32.6312i	1.27043	−	1.06601i	0.275937	−	0.961176i	$-0.411012\pi$
$937$	38.8883	−	32.6312i	1.27043	−	1.06601i	0.994489	−	0.104838i	$-0.0334325\pi$
$938$	49.4841	−	34.6491i	1.61571	−	1.13133i
$939$		0			0
$940$	−3.05187	−	6.54475i	−0.0995409	−	0.213466i
$941$	4.76293	−	13.0861i	0.155267	−	0.426593i	−0.837531	−	0.546389i	$-0.816002\pi$
$941$	4.76293	−	13.0861i	0.155267	−	0.426593i	0.992799	+	0.119796i	$0.0382241\pi$
$942$		0			0
$943$	−4.70315	−	53.7572i	−0.153156	−	1.75058i
$944$	−0.722411	−	8.25720i	−0.0235125	−	0.268749i
$945$		0			0
$946$	13.5178	−	37.1399i	0.439502	−	1.20752i
$947$	15.2185	+	32.6362i	0.494536	+	1.06053i	0.982258	+	0.187536i	$0.0600501\pi$
$947$	15.2185	+	32.6362i	0.494536	+	1.06053i	−0.487722	+	0.872999i	$0.662172\pi$
$948$		0			0
$949$	21.3528	−	14.9514i	0.693143	−	0.485344i
$950$	−19.4253	+	16.2997i	−0.630239	+	0.528834i
$951$		0			0
$952$	−10.0556	−	5.80562i	−0.325905	−	0.188161i
$953$	−2.27881	−	12.9238i	−0.0738181	−	0.418643i	−0.999214	−	0.0396412i	$-0.987379\pi$
$953$	−2.27881	−	12.9238i	−0.0738181	−	0.418643i	0.925396	−	0.379002i	$-0.123733\pi$
$954$		0			0
$955$	5.27831	+	14.5020i	0.170802	+	0.469275i
$956$	−13.1721	+	13.1721i	−0.426015	+	0.426015i
$957$		0			0
$958$	5.78008	−	32.7805i	0.186746	−	1.05909i
$959$	−44.9558	+	53.5762i	−1.45170	+	1.73007i
$960$		0			0
$961$		−	21.1888i		−	0.683510i
$962$	−21.1560	−	16.0759i	−0.682097	−	0.518307i
$963$		0			0
$964$	2.27697	+	0.199209i	0.0733363	+	0.00641610i
$965$	−4.70121	−	3.94479i	−0.151337	−	0.126987i
$966$		0			0
$967$	13.0979	−	28.0886i	0.421201	−	0.903269i	−0.575160	−	0.818041i	$-0.695060\pi$
$967$	13.0979	−	28.0886i	0.421201	−	0.903269i	0.996361	−	0.0852283i	$-0.0271620\pi$
$968$	−8.84005	−	8.84005i	−0.284130	−	0.284130i
$969$		0			0
$970$	1.77858	+	0.476569i	0.0571067	+	0.0153017i
$971$	−39.1543	+	6.90396i	−1.25652	+	0.221558i	−0.761983	−	0.647598i	$-0.775774\pi$
$971$	−39.1543	+	6.90396i	−1.25652	+	0.221558i	−0.494538	+	0.869156i	$0.664663\pi$
$972$		0			0
$973$	23.0607	−	13.3141i	0.739292	−	0.426830i
$974$	21.3306	+	25.4208i	0.683476	+	0.814535i
$975$		0			0
$976$	−3.62733	+	0.971940i	−0.116108	+	0.0311110i
$977$	−14.5955	+	6.80601i	−0.466952	+	0.217743i	−0.641830	−	0.766847i	$-0.721825\pi$
$977$	−14.5955	+	6.80601i	−0.466952	+	0.217743i	0.174878	+	0.984590i	$0.444047\pi$
$978$		0			0
$979$	37.4527	+	26.2247i	1.19700	+	0.838145i
$980$	12.5644	−	1.09924i	0.401356	−	0.0351141i
$981$		0			0
$982$	12.7853	−	18.2594i	0.407996	−	0.582679i
$983$	−37.0776	−	13.4951i	−1.18259	−	0.430428i	−0.325475	−	0.945551i	$-0.605524\pi$
$983$	−37.0776	−	13.4951i	−1.18259	−	0.430428i	−0.857116	+	0.515123i	$0.827746\pi$
$984$		0			0
$985$	−3.12577	−	11.6655i	−0.0995952	−	0.371695i
$986$	−2.77473	−	3.96273i	−0.0883655	−	0.126199i
$987$		0			0
$988$	12.5780	+	21.7857i	0.400160	+	0.693097i
$989$	24.5038	−	42.4418i	0.779174	−	1.34957i
$990$		0			0
$991$	−3.83494	+	14.3122i	−0.121821	+	0.454641i	−0.999706	−	0.0242291i	$-0.992287\pi$
$991$	−3.83494	+	14.3122i	−0.121821	+	0.454641i	0.877886	+	0.478870i	$0.158954\pi$
$992$	−2.94338	+	1.07130i	−0.0934525	+	0.0340139i
$993$		0			0
$994$	46.4607	+	21.6650i	1.47364	+	0.687171i
$995$	7.48543	+	1.31988i	0.237304	+	0.0418431i
$996$		0			0
$997$	−1.31057	+	14.9799i	−0.0415061	+	0.474417i	0.946788	+	0.321857i	$0.104307\pi$
$997$	−1.31057	+	14.9799i	−0.0415061	+	0.474417i	−0.988294	+	0.152559i	$0.951248\pi$
$998$	−33.6431			−1.06496
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.557.6	yes	96
3.2	odd	2	inner	666.2.bs.b.557.3	✓	96
37.19	odd	36	inner	666.2.bs.b.611.3	yes	96
111.56	even	36	inner	666.2.bs.b.611.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.557.3	✓	96	3.2	odd	2	inner
666.2.bs.b.557.6	yes	96	1.1	even	1	trivial
666.2.bs.b.611.3	yes	96	37.19	odd	36	inner
666.2.bs.b.611.6	yes	96	111.56	even	36	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(-0.700099 - 0.326462i) q^{5} +(4.53856 - 1.65190i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-0.386237 + 0.668982i) q^{10} +(2.42393 + 4.19837i) q^{11} +(-2.50551 - 3.57824i) q^{13} +(-1.25005 - 4.66526i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-1.37892 + 1.96930i) q^{17} +(5.73695 - 0.501918i) q^{19} +(0.632774 + 0.443073i) q^{20} +(4.39365 - 2.04879i) q^{22} +(5.80632 - 1.55580i) q^{23} +(-2.83038 - 3.37311i) q^{25} +(-3.78299 + 2.18411i) q^{26} +(-4.75646 + 0.838692i) q^{28} +(-1.94369 - 0.520811i) q^{29} +(-2.21486 - 2.21486i) q^{31} +(0.422618 - 0.906308i) q^{32} +(1.84162 + 1.54530i) q^{34} +(-3.71672 - 0.325171i) q^{35} +(2.35421 + 5.60872i) q^{37} -5.75886i q^{38} +(0.496537 - 0.591749i) q^{40} +(1.55885 - 8.84070i) q^{41} +(5.76488 - 5.76488i) q^{43} +(-1.65806 - 4.55550i) q^{44} +(-1.04383 - 5.91983i) q^{46} +(-8.09588 - 4.67416i) q^{47} +(12.5074 - 10.4950i) q^{49} +(-3.60696 + 2.52562i) q^{50} +(1.84609 + 3.95896i) q^{52} +(-0.878899 + 2.41476i) q^{53} +(-0.326385 - 3.73059i) q^{55} +(0.420948 + 4.81146i) q^{56} +(-0.688233 + 1.89090i) q^{58} +(-3.50297 - 7.51215i) q^{59} +(-3.07615 + 2.15394i) q^{61} +(-2.39947 + 2.01339i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.585948 + 3.32308i) q^{65} +(4.27780 + 11.7532i) q^{67} +(1.69993 - 1.69993i) q^{68} +(-0.647868 + 3.67424i) q^{70} +(-6.82252 + 8.13076i) q^{71} +5.96741i q^{73} +(5.79256 - 1.85642i) q^{74} +(-5.73695 - 0.501918i) q^{76} +(17.9364 + 15.0505i) q^{77} +(-5.34136 + 11.4546i) q^{79} +(-0.546222 - 0.546222i) q^{80} +(-8.67120 - 2.32344i) q^{82} +(7.54117 - 1.32971i) q^{83} +(1.60828 - 0.928540i) q^{85} +(-5.24050 - 6.24539i) q^{86} +(-4.68267 + 1.25472i) q^{88} +(8.54762 - 3.98582i) q^{89} +(-17.2823 - 12.1012i) q^{91} +(-5.98827 + 0.523906i) q^{92} +(-5.36197 + 7.65769i) q^{94} +(-4.18029 - 1.52150i) q^{95} +(-0.616938 - 2.30244i) q^{97} +(-9.36496 - 13.3745i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82}+ \cdots + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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