LMFDB - Embedded newform 639.2.z.a.494.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [639,2,Mod(35,639)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(639, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([35, 29]))

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

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

chi := DirichletCharacter("639.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 639 = 3^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	639.z (of order $70$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.10244068916$
Analytic rank:	$0$
Dimension:	$576$
Relative dimension:	$24$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			494.21
Character	$\chi$	$=$	639.494
Dual form			639.2.z.a.260.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29363 - 1.48068i) q^{2} +(-0.250462 - 1.84898i) q^{4} +(3.26680 - 1.06145i) q^{5} +(-2.14637 + 0.917402i) q^{7} +(0.220095 + 0.145283i) q^{8} +O(q^{10})$	\(q+(1.29363 - 1.48068i) q^{2} +(-0.250462 - 1.84898i) q^{4} +(3.26680 - 1.06145i) q^{5} +(-2.14637 + 0.917402i) q^{7} +(0.220095 + 0.145283i) q^{8} +(2.65436 - 6.21020i) q^{10} +(0.197285 - 4.39289i) q^{11} +(-2.83205 + 0.127187i) q^{13} +(-1.41823 + 4.36485i) q^{14} +(4.09710 - 1.13073i) q^{16} +(1.71469 + 1.24579i) q^{17} +(3.24472 - 0.588831i) q^{19} +(-2.78081 - 5.77442i) q^{20} +(-6.24923 - 5.97487i) q^{22} +(0.415918 - 1.82226i) q^{23} +(5.50025 - 3.99616i) q^{25} +(-3.47529 + 4.35788i) q^{26} +(2.23385 + 3.73883i) q^{28} +(-6.35391 + 6.07496i) q^{29} +(0.326285 - 1.18227i) q^{31} +(3.39703 - 7.05401i) q^{32} +(4.06278 - 0.927303i) q^{34} +(-6.03799 + 5.27524i) q^{35} +(0.00289836 + 0.0126986i) q^{37} +(3.32560 - 5.56611i) q^{38} +(0.873218 + 0.240993i) q^{40} +(2.50706 + 3.14376i) q^{41} +(-0.686909 + 0.410409i) q^{43} +(-8.17179 + 0.735475i) q^{44} +(-2.16013 - 2.97316i) q^{46} +(3.97443 + 7.38572i) q^{47} +(-1.07216 + 1.12139i) q^{49} +(1.19825 - 13.3136i) q^{50} +(0.944488 + 5.20456i) q^{52} +(-1.13823 + 8.40276i) q^{53} +(-4.01833 - 14.5601i) q^{55} +(-0.605688 - 0.109916i) q^{56} +(0.775454 + 17.2668i) q^{58} +(-11.0718 - 4.15531i) q^{59} +(-12.9690 - 5.54323i) q^{61} +(-1.32846 - 2.01254i) q^{62} +(-2.70928 - 6.33867i) q^{64} +(-9.11675 + 3.42157i) q^{65} +(-0.645269 + 0.0874077i) q^{67} +(1.87399 - 3.48245i) q^{68} +15.7645i q^{70} +(-6.76371 - 5.02515i) q^{71} +(11.9005 + 10.3972i) q^{73} +(0.0225518 + 0.0121357i) q^{74} +(-1.90142 - 5.85197i) q^{76} +(3.60660 + 9.60975i) q^{77} +(-5.49761 + 8.32853i) q^{79} +(12.1842 - 8.04273i) q^{80} +(7.89809 + 0.354703i) q^{82} +(1.08637 - 2.89463i) q^{83} +(6.92389 + 2.24971i) q^{85} +(-0.280921 + 1.54800i) q^{86} +(0.681635 - 0.938190i) q^{88} +(15.2244 + 2.06228i) q^{89} +(5.96194 - 2.87112i) q^{91} +(-3.47350 - 0.312620i) q^{92} +(16.0773 + 3.66953i) q^{94} +(9.97486 - 5.36770i) q^{95} +(1.66165 + 1.32512i) q^{97} +(0.273442 + 3.03819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 576 q - 24 q^{4}+O(q^{10}) $ 576 * q - 24 * q^4	$ 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) $ 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{61}{70}\right)$	$-1$

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 $

$2$	1.29363	−	1.48068i	0.914733	−	1.04700i	−0.0839900	−	0.996467i	$-0.526766\pi$
$2$	1.29363	−	1.48068i	0.914733	−	1.04700i	0.998723	−	0.0505291i	$-0.0160908\pi$
$3$		0			0
$3$		0			0
$4$	−0.250462	−	1.84898i	−0.125231	−	0.924492i
$5$	3.26680	−	1.06145i	1.46096	−	0.474694i	0.532596	−	0.846369i	$-0.321216\pi$
$5$	3.26680	−	1.06145i	1.46096	−	0.474694i	0.928363	+	0.371675i	$0.121216\pi$
$6$		0			0
$7$	−2.14637	+	0.917402i	−0.811252	+	0.346746i	−0.758345	−	0.651854i	$-0.773992\pi$
$7$	−2.14637	+	0.917402i	−0.811252	+	0.346746i	−0.0529070	+	0.998599i	$0.516849\pi$
$8$	0.220095	+	0.145283i	0.0778153	+	0.0513654i
$9$		0			0
$10$	2.65436	−	6.21020i	0.839384	−	1.96384i
$11$	0.197285	−	4.39289i	0.0594836	−	1.32451i	−0.718194	−	0.695842i	$-0.755031\pi$
$11$	0.197285	−	4.39289i	0.0594836	−	1.32451i	0.777678	−	0.628663i	$-0.216397\pi$
$12$		0			0
$13$	−2.83205	+	0.127187i	−0.785469	+	0.0352755i	−0.433987	−	0.900919i	$-0.642894\pi$
$13$	−2.83205	+	0.127187i	−0.785469	+	0.0352755i	−0.351482	+	0.936195i	$0.614322\pi$
$14$	−1.41823	+	4.36485i	−0.379037	+	1.16656i
$15$		0			0
$16$	4.09710	−	1.13073i	1.02427	−	0.282682i
$17$	1.71469	+	1.24579i	0.415873	+	0.302149i	0.775975	−	0.630764i	$-0.217258\pi$
$17$	1.71469	+	1.24579i	0.415873	+	0.302149i	−0.360102	+	0.932913i	$0.617258\pi$
$18$		0			0
$19$	3.24472	−	0.588831i	0.744391	−	0.135087i	0.206906	−	0.978361i	$-0.433660\pi$
$19$	3.24472	−	0.588831i	0.744391	−	0.135087i	0.537484	+	0.843274i	$0.319375\pi$
$20$	−2.78081	−	5.77442i	−0.621809	−	1.29120i
$21$		0			0
$22$	−6.24923	−	5.97487i	−1.33234	−	1.27385i
$23$	0.415918	−	1.82226i	0.0867249	−	0.379967i	−0.912875	−	0.408238i	$-0.866143\pi$
$23$	0.415918	−	1.82226i	0.0867249	−	0.379967i	0.999600	+	0.0282717i	$0.00900037\pi$
$24$		0			0
$25$	5.50025	−	3.99616i	1.10005	−	0.799233i
$26$	−3.47529	+	4.35788i	−0.681561	+	0.854650i
$27$		0			0
$28$	2.23385	+	3.73883i	0.422157	+	0.706573i
$29$	−6.35391	+	6.07496i	−1.17989	+	1.12809i	−0.190673	+	0.981654i	$0.561067\pi$
$29$	−6.35391	+	6.07496i	−1.17989	+	1.12809i	−0.989220	+	0.146439i	$0.953219\pi$
$30$		0			0
$31$	0.326285	−	1.18227i	0.0586026	−	0.212342i	−0.928797	−	0.370589i	$-0.879156\pi$
$31$	0.326285	−	1.18227i	0.0586026	−	0.212342i	0.987399	+	0.158247i	$0.0505844\pi$
$32$	3.39703	−	7.05401i	0.600516	−	1.24698i
$33$		0			0
$34$	4.06278	−	0.927303i	0.696761	−	0.159031i
$35$	−6.03799	+	5.27524i	−1.02061	+	0.891678i
$36$		0			0
$37$	0.00289836	+	0.0126986i	0.000476488	+	0.00208763i	0.975166	−	0.221477i	$-0.0710878\pi$
$37$	0.00289836	+	0.0126986i	0.000476488	+	0.00208763i	−0.974689	+	0.223565i	$0.928231\pi$
$38$	3.32560	−	5.56611i	0.539483	−	0.902942i
$39$		0			0
$40$	0.873218	+	0.240993i	0.138068	+	0.0381043i
$41$	2.50706	+	3.14376i	0.391537	+	0.490972i	0.938060	−	0.346472i	$-0.112620\pi$
$41$	2.50706	+	3.14376i	0.391537	+	0.490972i	−0.546523	+	0.837444i	$0.684049\pi$
$42$		0			0
$43$	−0.686909	+	0.410409i	−0.104753	+	0.0625868i	−0.564320	−	0.825556i	$-0.690862\pi$
$43$	−0.686909	+	0.410409i	−0.104753	+	0.0625868i	0.459567	+	0.888143i	$0.348004\pi$
$44$	−8.17179	+	0.735475i	−1.23194	+	0.110877i
$45$		0			0
$46$	−2.16013	−	2.97316i	−0.318493	−	0.438368i
$47$	3.97443	+	7.38572i	0.579730	+	1.07732i	0.986496	+	0.163786i	$0.0523706\pi$
$47$	3.97443	+	7.38572i	0.579730	+	1.07732i	−0.406766	+	0.913532i	$0.633344\pi$
$48$		0			0
$49$	−1.07216	+	1.12139i	−0.153166	+	0.160199i
$50$	1.19825	−	13.3136i	0.169458	−	1.88283i
$51$		0			0
$52$	0.944488	+	5.20456i	0.130977	+	0.721743i
$53$	−1.13823	+	8.40276i	−0.156348	+	1.15421i	0.727389	+	0.686225i	$0.240733\pi$
$53$	−1.13823	+	8.40276i	−0.156348	+	1.15421i	−0.883737	+	0.467983i	$0.844981\pi$
$54$		0			0
$55$	−4.01833	−	14.5601i	−0.541832	−	1.96328i
$56$	−0.605688	−	0.109916i	−0.0809385	−	0.0146882i
$57$		0			0
$58$	0.775454	+	17.2668i	0.101822	+	2.26725i
$59$	−11.0718	−	4.15531i	−1.44142	−	0.540976i	−0.496435	−	0.868074i	$-0.665358\pi$
$59$	−11.0718	−	4.15531i	−1.44142	−	0.540976i	−0.944990	+	0.327098i	$0.893929\pi$
$60$		0			0
$61$	−12.9690	−	5.54323i	−1.66051	−	0.709738i	−0.661329	−	0.750096i	$-0.730007\pi$
$61$	−12.9690	−	5.54323i	−1.66051	−	0.709738i	−0.999185	+	0.0403579i	$0.987150\pi$
$62$	−1.32846	−	2.01254i	−0.168715	−	0.255593i
$63$		0			0
$64$	−2.70928	−	6.33867i	−0.338660	−	0.792334i
$65$	−9.11675	+	3.42157i	−1.13079	+	0.424394i
$66$		0			0
$67$	−0.645269	+	0.0874077i	−0.0788322	+	0.0106785i	−0.173543	−	0.984826i	$-0.555522\pi$
$67$	−0.645269	+	0.0874077i	−0.0788322	+	0.0106785i	0.0947109	+	0.995505i	$0.469807\pi$
$68$	1.87399	−	3.48245i	0.227254	−	0.422309i
$69$		0			0
$70$			15.7645i			1.88422i
$71$	−6.76371	−	5.02515i	−0.802705	−	0.596376i
$71$	−6.76371	−	5.02515i	−0.802705	−	0.596376i
$72$		0			0
$73$	11.9005	+	10.3972i	1.39285	+	1.21690i	0.946771	+	0.321908i	$0.104324\pi$
$73$	11.9005	+	10.3972i	1.39285	+	1.21690i	0.446083	+	0.894992i	$0.352819\pi$
$74$	0.0225518	+	0.0121357i	0.00262160	+	0.00141074i
$75$		0			0
$76$	−1.90142	−	5.85197i	−0.218108	−	0.671266i
$77$	3.60660	+	9.60975i	0.411010	+	1.09513i
$78$		0			0
$79$	−5.49761	+	8.32853i	−0.618530	+	0.937033i	0.381391	+	0.924414i	$0.375445\pi$
$79$	−5.49761	+	8.32853i	−0.618530	+	0.937033i	−0.999920	+	0.0126186i	$0.995983\pi$
$80$	12.1842	−	8.04273i	1.36224	−	0.899204i
$81$		0			0
$82$	7.89809	+	0.354703i	0.872198	+	0.0391704i
$83$	1.08637	−	2.89463i	0.119245	−	0.317727i	−0.863036	−	0.505143i	$-0.831440\pi$
$83$	1.08637	−	2.89463i	0.119245	−	0.317727i	0.982281	+	0.187416i	$0.0600112\pi$
$84$		0			0
$85$	6.92389	+	2.24971i	0.751001	+	0.244015i
$86$	−0.280921	+	1.54800i	−0.0302925	+	0.166926i
$87$		0			0
$88$	0.681635	−	0.938190i	0.0726625	−	0.100011i
$89$	15.2244	+	2.06228i	1.61378	+	0.218602i	0.884813	−	0.465946i	$-0.154286\pi$
$89$	15.2244	+	2.06228i	1.61378	+	0.218602i	0.728969	+	0.684547i	$0.240000\pi$
$90$		0			0
$91$	5.96194	−	2.87112i	0.624981	−	0.300975i
$92$	−3.47350	−	0.312620i	−0.362137	−	0.0325929i
$93$		0			0
$94$	16.0773	+	3.66953i	1.65825	+	0.378484i
$95$	9.97486	−	5.36770i	1.02340	−	0.550715i
$96$		0			0
$97$	1.66165	+	1.32512i	0.168715	+	0.134545i	0.704207	−	0.709995i	$-0.251303\pi$
$97$	1.66165	+	1.32512i	0.168715	+	0.134545i	−0.535493	+	0.844540i	$0.679874\pi$
$98$	0.273442	+	3.03819i	0.0276218	+	0.306904i
$99$		0			0
$100$	−8.76645	−	9.16899i	−0.876645	−	0.916899i
$101$	−6.51880	+	5.19857i	−0.648645	+	0.517277i	−0.891637	−	0.452751i	$-0.850443\pi$
$101$	−6.51880	+	5.19857i	−0.648645	+	0.517277i	0.242992	+	0.970028i	$0.421871\pi$
$102$		0			0
$103$	−6.53389	−	3.14656i	−0.643803	−	0.310039i	0.0833440	−	0.996521i	$-0.473440\pi$
$103$	−6.53389	−	3.14656i	−0.643803	−	0.310039i	−0.727147	+	0.686482i	$0.759154\pi$
$104$	−0.641798	−	0.383456i	−0.0629335	−	0.0376010i
$105$		0			0
$106$	10.9693	+	12.5554i	1.06543	+	1.21949i
$107$	11.5849	+	13.2600i	1.11995	+	1.28189i	0.955333	+	0.295532i	$0.0954969\pi$
$107$	11.5849	+	13.2600i	1.11995	+	1.28189i	0.164620	+	0.986357i	$0.447360\pi$
$108$		0			0
$109$	10.6223	+	6.34654i	1.01743	+	0.607888i	0.921855	−	0.387534i	$-0.126673\pi$
$109$	10.6223	+	6.34654i	1.01743	+	0.607888i	0.0955778	+	0.995422i	$0.469530\pi$
$110$	−26.7570	−	12.8855i	−2.55118	−	1.22858i
$111$		0			0
$112$	−7.75656	+	6.18565i	−0.732926	+	0.584489i
$113$	−6.71959	−	7.02814i	−0.632125	−	0.661151i	0.326706	−	0.945126i	$-0.394061\pi$
$113$	−6.71959	−	7.02814i	−0.632125	−	0.661151i	−0.958832	+	0.283974i	$0.908347\pi$
$114$		0			0
$115$	−0.575509	−	6.39443i	−0.0536665	−	0.596284i
$116$	12.8239	+	10.2267i	1.19067	+	0.949529i
$117$		0			0
$118$	−20.4754	+	11.0183i	−1.88492	+	1.01432i
$119$	−4.82324	−	1.10087i	−0.442146	−	0.100917i
$120$		0			0
$121$	−8.30281	−	0.747267i	−0.754801	−	0.0679333i
$122$	−24.9848	+	12.0321i	−2.26202	+	1.08933i
$123$		0			0
$124$	−2.26772	−	0.307183i	−0.203647	−	0.0275859i
$125$	3.63153	−	4.99837i	0.324814	−	0.447068i
$126$		0			0
$127$	2.65100	−	14.6082i	0.235239	−	1.29627i	−0.622677	−	0.782479i	$-0.713955\pi$
$127$	2.65100	−	14.6082i	0.235239	−	1.29627i	0.857915	−	0.513792i	$-0.171760\pi$
$128$	2.00200	+	0.650489i	0.176953	+	0.0574957i
$129$		0			0
$130$	−6.72743	+	17.9252i	−0.590035	+	1.57214i
$131$	15.9733	+	0.717363i	1.39560	+	0.0626763i	0.729903	−	0.683550i	$-0.239565\pi$
$131$	15.9733	+	0.717363i	1.39560	+	0.0626763i	0.665692	+	0.746227i	$0.268136\pi$
$132$		0			0
$133$	−6.42418	+	4.24057i	−0.557047	+	0.367704i
$134$	−0.705316	+	1.06851i	−0.0609300	+	0.0923050i
$135$		0			0
$136$	0.196401	+	0.523308i	0.0168412	+	0.0448733i
$137$	1.09354	+	3.36557i	0.0934276	+	0.287540i	0.986841	−	0.161696i	$-0.0516962\pi$
$137$	1.09354	+	3.36557i	0.0934276	+	0.287540i	−0.893413	+	0.449236i	$0.851696\pi$
$138$		0			0
$139$	−0.335966	−	0.180791i	−0.0284962	−	0.0153345i	0.459559	−	0.888147i	$-0.348008\pi$
$139$	−0.335966	−	0.180791i	−0.0284962	−	0.0153345i	−0.488055	+	0.872813i	$0.662293\pi$
$140$	11.2661	+	9.84291i	0.952161	+	0.831878i
$141$		0			0
$142$	−16.1903	+	3.51419i	−1.35866	+	0.294904i
$143$			12.4660i			1.04246i
$144$		0			0
$145$	−14.3087	+	26.5901i	−1.18828	+	2.20819i
$146$	30.7897	−	4.17076i	2.54818	−	0.345174i
$147$		0			0
$148$	0.0227535	−	0.00853953i	0.00187033	−	0.000701945i
$149$	5.65744	+	13.2362i	0.463475	+	1.08435i	0.974419	+	0.224740i	$0.0721533\pi$
$149$	5.65744	+	13.2362i	0.463475	+	1.08435i	−0.510943	+	0.859614i	$0.670704\pi$
$150$		0			0
$151$	−8.43879	−	12.7842i	−0.686739	−	1.04037i	−0.995997	−	0.0893868i	$-0.971509\pi$
$151$	−8.43879	−	12.7842i	−0.686739	−	1.04037i	0.309258	−	0.950978i	$-0.399919\pi$
$152$	0.799695	+	0.341806i	0.0648638	+	0.0277241i
$153$		0			0
$154$	18.8945	+	7.09123i	1.52256	+	0.571428i
$155$	−0.189007	−	4.20857i	−0.0151814	−	0.338041i
$156$		0			0
$157$	−21.3260	−	3.87010i	−1.70200	−	0.308867i	−0.761374	−	0.648313i	$-0.775475\pi$
$157$	−21.3260	−	3.87010i	−1.70200	−	0.308867i	−0.940626	+	0.339445i	$0.889761\pi$
$158$	5.21998	+	18.9142i	0.415280	+	1.50473i
$159$		0			0
$160$	3.60996	−	26.6498i	0.285393	−	2.10685i
$161$	0.779028	+	4.29280i	0.0613960	+	0.338320i
$162$		0			0
$163$	1.33690	−	14.8542i	0.104714	−	1.16347i	−0.756066	−	0.654495i	$-0.772881\pi$
$163$	1.33690	−	14.8542i	0.104714	−	1.16347i	0.860780	−	0.508976i	$-0.169976\pi$
$164$	5.18483	−	5.42291i	0.404867	−	0.423458i
$165$		0			0
$166$	−2.88065	−	5.35314i	−0.223582	−	0.415484i
$167$	−3.81702	−	5.25368i	−0.295370	−	0.406542i	0.635379	−	0.772200i	$-0.280844\pi$
$167$	−3.81702	−	5.25368i	−0.295370	−	0.406542i	−0.930749	+	0.365658i	$0.880844\pi$
$168$		0			0
$169$	−4.94334	+	0.444909i	−0.380257	+	0.0342237i
$170$	12.2880	−	7.34175i	0.942448	−	0.563086i
$171$		0			0
$172$	0.930884	+	1.16729i	0.0709792	+	0.0890052i
$173$	21.8265	+	6.02372i	1.65943	+	0.457975i	0.965144	−	0.261720i	$-0.0842896\pi$
$173$	21.8265	+	6.02372i	1.65943	+	0.457975i	0.694291	+	0.719695i	$0.255718\pi$
$174$		0			0
$175$	−8.13948	+	13.6232i	−0.615286	+	1.02982i
$176$	−4.15886	−	18.2212i	−0.313486	−	1.37347i
$177$		0			0
$178$	22.7483	−	19.8746i	1.70505	−	1.48966i
$179$	1.61899	−	0.369524i	0.121009	−	0.0276195i	−0.161588	−	0.986858i	$-0.551661\pi$
$179$	1.61899	−	0.369524i	0.121009	−	0.0276195i	0.282596	+	0.959239i	$0.408804\pi$
$180$		0			0
$181$	3.17997	−	6.60327i	0.236365	−	0.490817i	−0.748720	−	0.662887i	$-0.769331\pi$
$181$	3.17997	−	6.60327i	0.236365	−	0.490817i	0.985085	+	0.172069i	$0.0550453\pi$
$182$	3.46133	−	12.5419i	0.256571	−	0.929665i
$183$		0			0
$184$	0.356285	−	0.340643i	0.0262657	−	0.0251126i
$185$	0.0229472	+	0.0384072i	0.00168711	+	0.00282375i
$186$		0			0
$187$	5.81091	−	7.28665i	0.424936	−	0.532852i
$188$	12.6606	−	9.19850i	0.923372	−	0.670869i
$189$		0			0
$190$	4.95593	−	21.7133i	0.359541	−	1.57525i
$191$	−16.7741	−	16.0377i	−1.21373	−	1.16044i	−0.982245	−	0.187605i	$-0.939927\pi$
$191$	−16.7741	−	16.0377i	−1.21373	−	1.16044i	−0.231485	−	0.972839i	$-0.574358\pi$
$192$		0			0
$193$	1.29294	+	2.68482i	0.0930681	+	0.193258i	0.942306	−	0.334752i	$-0.108653\pi$
$193$	1.29294	+	2.68482i	0.0930681	+	0.193258i	−0.849238	+	0.528010i	$0.822938\pi$
$194$	4.11162	−	0.746149i	0.295197	−	0.0535704i
$195$		0			0
$196$	2.34198	+	1.70155i	0.167284	+	0.121539i
$197$	−0.507285	+	0.140002i	−0.0361426	+	0.00997471i	−0.284061	−	0.958806i	$-0.591682\pi$
$197$	−0.507285	+	0.140002i	−0.0361426	+	0.00997471i	0.247919	+	0.968781i	$0.420253\pi$
$198$		0			0
$199$	4.11274	−	12.6577i	0.291545	−	0.897282i	−0.692816	−	0.721115i	$-0.743630\pi$
$199$	4.11274	−	12.6577i	0.291545	−	0.897282i	0.984360	−	0.176167i	$-0.0563699\pi$
$200$	1.79115	−	0.0804408i	0.126654	−	0.00568802i
$201$		0			0
$202$	−0.735503	+	16.3772i	−0.0517498	+	1.15230i
$203$	8.06466	−	18.8682i	0.566028	−	1.32429i
$204$		0			0
$205$	11.5270	+	7.60892i	0.805082	+	0.531430i
$206$	−13.1114	+	5.60410i	−0.913518	+	0.390456i
$207$		0			0
$208$	−11.4594	+	3.72338i	−0.794565	+	0.258170i
$209$	−1.94653	−	14.3699i	−0.134644	−	0.993985i
$210$		0			0
$211$	−7.06598	+	8.08766i	−0.486442	+	0.556778i	−0.942947	−	0.332943i	$-0.891958\pi$
$211$	−7.06598	+	8.08766i	−0.486442	+	0.556778i	0.456505	+	0.889721i	$0.349101\pi$
$212$	15.8217			1.08664
$213$		0			0
$214$	34.6202			2.36659
$215$	−1.80837	+	2.06984i	−0.123330	+	0.141162i
$216$		0			0
$217$	0.384287	+	2.83692i	0.0260871	+	0.192583i
$218$	23.1385	−	7.51815i	1.56714	−	0.509193i
$219$		0			0
$220$	−25.9150	+	11.0766i	−1.74719	+	0.746784i
$221$	−5.01453	−	3.31006i	−0.337313	−	0.222659i
$222$		0			0
$223$	4.25947	−	9.96552i	0.285235	−	0.667341i	−0.714234	−	0.699907i	$-0.753225\pi$
$223$	4.25947	−	9.96552i	0.285235	−	0.667341i	0.999470	+	0.0325657i	$0.0103678\pi$
$224$	−0.819920	+	18.2569i	−0.0547832	+	1.21984i
$225$		0			0
$226$	−19.0990	+	0.857738i	−1.27045	+	0.0570559i
$227$	−0.873042	+	2.68695i	−0.0579459	+	0.178339i	−0.975840	−	0.218486i	$-0.929888\pi$
$227$	−0.873042	+	2.68695i	−0.0579459	+	0.178339i	0.917894	+	0.396825i	$0.129888\pi$
$228$		0			0
$229$	−0.848595	+	0.234197i	−0.0560767	+	0.0154762i	−0.293963	−	0.955817i	$-0.594974\pi$
$229$	−0.848595	+	0.234197i	−0.0560767	+	0.0154762i	0.237886	+	0.971293i	$0.423546\pi$
$230$	−10.2126	−	7.41986i	−0.673397	−	0.489251i
$231$		0			0
$232$	−2.28106	+	0.413951i	−0.149759	+	0.0271772i
$233$	−6.30553	−	13.0936i	−0.413089	−	0.857789i	−0.998880	−	0.0473259i	$-0.984930\pi$
$233$	−6.30553	−	13.0936i	−0.413089	−	0.857789i	0.585790	−	0.810463i	$-0.300784\pi$
$234$		0			0
$235$	20.8232	+	19.9091i	1.35836	+	1.29872i
$236$	−4.91005	+	21.5123i	−0.319617	+	1.40033i
$237$		0			0
$238$	−7.86952	+	5.71754i	−0.510105	+	0.370613i
$239$	−17.8292	+	22.3571i	−1.15327	+	1.44616i	−0.279288	+	0.960207i	$0.590098\pi$
$239$	−17.8292	+	22.3571i	−1.15327	+	1.44616i	−0.873986	+	0.485952i	$0.838473\pi$
$240$		0			0
$241$	−2.91324	−	4.87595i	−0.187658	−	0.314087i	0.750133	−	0.661287i	$-0.229990\pi$
$241$	−2.91324	−	4.87595i	−0.187658	−	0.314087i	−0.937791	+	0.347200i	$0.887132\pi$
$242$	−11.8472	+	11.3271i	−0.761567	+	0.728133i
$243$		0			0
$244$	−7.00110	+	25.3679i	−0.448199	+	1.62401i
$245$	−2.31224	+	4.80142i	−0.147724	+	0.306752i
$246$		0			0
$247$	−9.11433	+	2.08029i	−0.579931	+	0.132365i
$248$	0.243578	−	0.212807i	0.0154672	−	0.0135133i
$249$		0			0
$250$	−2.70312	−	11.8431i	−0.170960	−	0.749026i
$251$	−13.3524	+	22.3481i	−0.842794	+	1.41060i	0.0679761	+	0.997687i	$0.478346\pi$
$251$	−13.3524	+	22.3481i	−0.842794	+	1.41060i	−0.910770	+	0.412913i	$0.864511\pi$
$252$		0			0
$253$	−7.92291	−	2.18658i	−0.498109	−	0.137469i
$254$	−18.2006	−	22.8229i	−1.14201	−	1.43203i
$255$		0			0
$256$	15.3883	−	9.19406i	0.961767	−	0.574629i
$257$	−13.3142	+	1.19830i	−0.830516	+	0.0747478i	−0.496734	−	0.867903i	$-0.665468\pi$
$257$	−13.3142	+	1.19830i	−0.830516	+	0.0747478i	−0.333781	+	0.942650i	$0.608325\pi$
$258$		0			0
$259$	−0.0178706	−	0.0245968i	−0.00111043	−	0.00152837i
$260$	8.60983	+	15.9997i	0.533959	+	0.992262i
$261$		0			0
$262$	21.7257	−	22.7233i	1.34222	−	1.40385i
$263$	1.73439	−	19.2707i	0.106947	−	1.18828i	−0.745878	−	0.666083i	$-0.767970\pi$
$263$	1.73439	−	19.2707i	0.106947	−	1.18828i	0.852825	−	0.522197i	$-0.174887\pi$
$264$		0			0
$265$	5.20072	+	28.6583i	0.319478	+	1.76047i
$266$	−2.03160	+	14.9978i	−0.124565	+	0.919577i
$267$		0			0
$268$	0.323231	+	1.17120i	0.0197445	+	0.0715425i
$269$	−13.8743	−	2.51782i	−0.845933	−	0.153514i	−0.261750	−	0.965136i	$-0.584299\pi$
$269$	−13.8743	−	2.51782i	−0.845933	−	0.153514i	−0.584184	+	0.811622i	$0.698585\pi$
$270$		0			0
$271$	0.227889	+	5.07434i	0.0138433	+	0.308244i	0.993954	+	0.109794i	$0.0350193\pi$
$271$	0.227889	+	5.07434i	0.0138433	+	0.308244i	−0.980111	+	0.198450i	$0.936409\pi$
$272$	8.43389	+	3.16529i	0.511380	+	0.191924i
$273$		0			0
$274$	6.39796	+	2.73462i	0.386515	+	0.165204i
$275$	−16.4696	−	24.9503i	−0.993153	−	1.50456i
$276$		0			0
$277$	−1.01032	−	2.36376i	−0.0607043	−	0.142025i	0.886429	−	0.462864i	$-0.153178\pi$
$277$	−1.01032	−	2.36376i	−0.0607043	−	0.142025i	−0.947134	+	0.320839i	$0.896035\pi$
$278$	−0.702307	+	0.263580i	−0.0421216	+	0.0158085i
$279$		0			0
$280$	−2.09534	+	0.283833i	−0.125220	+	0.0169622i
$281$	12.1042	−	22.4934i	0.722078	−	1.34185i	−0.209321	−	0.977847i	$-0.567125\pi$
$281$	12.1042	−	22.4934i	0.722078	−	1.34185i	0.931399	−	0.363999i	$-0.118589\pi$
$282$		0			0
$283$		−	13.2401i		−	0.787039i	−0.919316	−	0.393520i	$-0.871257\pi$
$283$		−	13.2401i		−	0.787039i	0.919316	−	0.393520i	$-0.128743\pi$
$284$	−7.59738	+	13.7646i	−0.450822	+	0.816780i
$285$		0			0
$286$	18.4580	+	16.1263i	1.09145	+	0.953569i
$287$	−8.26517	−	4.44768i	−0.487878	−	0.262538i
$288$		0			0
$289$	−3.86514	−	11.8957i	−0.227361	−	0.699745i
$290$	20.8611	+	55.5842i	1.22501	+	3.26402i
$291$		0			0
$292$	16.2436	−	24.6080i	0.950586	−	1.44008i
$293$	27.7442	−	18.3138i	1.62083	−	1.06990i	0.678835	−	0.734291i	$-0.262485\pi$
$293$	27.7442	−	18.3138i	1.62083	−	1.06990i	0.942000	−	0.335613i	$-0.108943\pi$
$294$		0			0
$295$	−40.5800	−	1.82245i	−2.36266	−	0.106107i
$296$	−0.00120697	+	0.00321597i	−7.01539e−5	+	0.000186925i
$297$		0			0
$298$	26.9172	+	8.74592i	1.55927	+	0.506638i
$299$	−0.946132	+	5.21362i	−0.0547162	+	0.301511i
$300$		0			0
$301$	1.09785	−	1.51106i	0.0632790	−	0.0870961i
$302$	−29.8459	−	4.04291i	−1.71744	−	0.232643i
$303$		0			0
$304$	12.6281	−	6.08140i	0.724274	−	0.348792i
$305$	−48.2511	−	4.34268i	−2.76285	−	0.248661i
$306$		0			0
$307$	12.8030	+	2.92219i	0.730704	+	0.166778i	0.571657	−	0.820493i	$-0.306301\pi$
$307$	12.8030	+	2.92219i	0.730704	+	0.166778i	0.159047	+	0.987271i	$0.449158\pi$
$308$	16.8650	−	9.07542i	0.960970	−	0.517120i
$309$		0			0
$310$	−6.47604	−	5.16447i	−0.367814	−	0.293322i
$311$	−0.905573	−	10.0617i	−0.0513503	−	0.570549i	−0.979920	−	0.199391i	$-0.936104\pi$
$311$	−0.905573	−	10.0617i	−0.0513503	−	0.570549i	0.928570	−	0.371158i	$-0.121039\pi$
$312$		0			0
$313$	−3.50423	−	3.66513i	−0.198071	−	0.207166i	0.616299	−	0.787512i	$-0.288631\pi$
$313$	−3.50423	−	3.66513i	−0.198071	−	0.207166i	−0.814370	+	0.580347i	$0.802917\pi$
$314$	−33.3183	+	26.5704i	−1.88026	+	1.49946i
$315$		0			0
$316$	16.7763	+	8.07902i	0.943738	+	0.454481i
$317$	3.11822	+	1.86305i	0.175137	+	0.104639i	0.597792	−	0.801651i	$-0.296045\pi$
$317$	3.11822	+	1.86305i	0.175137	+	0.104639i	−0.422655	+	0.906290i	$0.638902\pi$
$318$		0			0
$319$	25.4331	+	29.1105i	1.42398	+	1.62988i
$320$	−15.5789	−	17.8314i	−0.870885	−	0.996808i
$321$		0			0
$322$	7.36402	+	4.39979i	0.410381	+	0.245191i
$323$	6.29724	+	3.03259i	0.350388	+	0.168738i
$324$		0			0
$325$	−15.0687	+	12.0169i	−0.835862	+	0.666577i
$326$	−20.2648	−	21.1953i	−1.12236	−	1.17390i
$327$		0			0
$328$	0.0950560	+	1.05616i	0.00524859	+	0.0583166i
$329$	−15.3063	−	12.2063i	−0.843862	−	0.672957i
$330$		0			0
$331$	−1.97497	+	1.06278i	−0.108554	+	0.0584155i	−0.527245	−	0.849713i	$-0.676775\pi$
$331$	−1.97497	+	1.06278i	−0.108554	+	0.0584155i	0.418691	+	0.908129i	$0.362489\pi$
$332$	−5.62422	−	1.28369i	−0.308669	−	0.0704517i
$333$		0			0
$334$	−12.7168	−	1.14453i	−0.695833	−	0.0626261i
$335$	−2.01519	+	0.970464i	−0.110102	+	0.0530221i
$336$		0			0
$337$	21.8916	+	2.96542i	1.19251	+	0.161537i	0.703471	−	0.710724i	$-0.251633\pi$
$337$	21.8916	+	2.96542i	1.19251	+	0.161537i	0.489041	+	0.872261i	$0.337347\pi$
$338$	−5.73607	+	7.89503i	−0.312001	+	0.429433i
$339$		0			0
$340$	2.42550	−	13.3656i	0.131541	−	0.724853i
$341$	−5.12920	−	1.66658i	−0.277762	−	0.0902503i
$342$		0			0
$343$	7.01376	−	18.6881i	0.378708	−	1.00906i
$344$	−0.210811	−	0.00946752i	−0.0113662	−	0.000510454i
$345$		0			0
$346$	37.1545	−	24.5254i	1.99744	−	1.31850i
$347$	−12.6868	+	19.2197i	−0.681063	+	1.03177i	0.315500	+	0.948926i	$0.397828\pi$
$347$	−12.6868	+	19.2197i	−0.681063	+	1.03177i	−0.996563	+	0.0828405i	$0.973601\pi$
$348$		0			0
$349$	−10.9831	−	29.2645i	−0.587914	−	1.56649i	−0.806852	−	0.590753i	$-0.798831\pi$
$349$	−10.9831	−	29.2645i	−0.587914	−	1.56649i	0.218938	−	0.975739i	$-0.429741\pi$
$350$	9.64207	+	29.6752i	0.515390	+	1.58621i
$351$		0			0
$352$	−30.3173	−	16.3144i	−1.61592	−	0.869561i
$353$	−15.0430	−	13.1427i	−0.800657	−	0.699513i	0.156945	−	0.987607i	$-0.449835\pi$
$353$	−15.0430	−	13.1427i	−0.800657	−	0.699513i	−0.957602	+	0.288094i	$0.906978\pi$
$354$		0			0
$355$	−27.4297	−	9.23686i	−1.45582	−	0.490241i
$356$		−	28.6662i		−	1.51930i
$357$		0			0
$358$	1.54722	−	2.87522i	0.0817733	−	0.151960i
$359$	−0.611269	+	0.0828020i	−0.0322615	+	0.00437012i	−0.150346	−	0.988633i	$-0.548039\pi$
$359$	−0.611269	+	0.0828020i	−0.0322615	+	0.00437012i	0.118085	+	0.993004i	$0.462325\pi$
$360$		0			0
$361$	−7.60695	+	2.85494i	−0.400366	+	0.150260i
$362$	−5.66361	−	13.2507i	−0.297673	−	0.696440i
$363$		0			0
$364$	−6.80190	−	10.3044i	−0.356516	−	0.540099i
$365$	49.9129	+	21.3338i	2.61256	+	1.11666i
$366$		0			0
$367$	−27.4678	−	10.3088i	−1.43381	−	0.538117i	−0.490913	−	0.871208i	$-0.663337\pi$
$367$	−27.4678	−	10.3088i	−1.43381	−	0.538117i	−0.942895	+	0.333091i	$0.891908\pi$
$368$	−0.356418	−	7.93625i	−0.0185796	−	0.413706i
$369$		0			0
$370$	0.0865538	+	0.0157072i	0.00449972	+	0.000816578i
$371$	−5.26565	−	19.0796i	−0.273379	−	0.990566i
$372$		0			0
$373$	−0.933042	+	6.88799i	−0.0483111	+	0.356647i	0.950617	+	0.310365i	$0.100451\pi$
$373$	−0.933042	+	6.88799i	−0.0483111	+	0.356647i	−0.998928	+	0.0462815i	$0.985263\pi$
$374$	−3.27201	−	18.0303i	−0.169192	−	0.932323i
$375$		0			0
$376$	−0.198272	+	2.20298i	−0.0102251	+	0.113610i
$377$	17.2219	−	18.0127i	0.886975	−	0.927703i
$378$		0			0
$379$	11.3372	+	21.0680i	0.582352	+	1.08219i	0.985916	+	0.167240i	$0.0534855\pi$
$379$	11.3372	+	21.0680i	0.582352	+	1.08219i	−0.403564	+	0.914951i	$0.632229\pi$
$380$	−12.4231	−	17.0990i	−0.637293	−	0.877158i
$381$		0			0
$382$	−45.4459	+	4.09021i	−2.32522	+	0.209273i
$383$	12.0232	−	7.18353i	0.614357	−	0.367061i	−0.171760	−	0.985139i	$-0.554945\pi$
$383$	12.0232	−	7.18353i	0.614357	−	0.367061i	0.786117	+	0.618077i	$0.212088\pi$
$384$		0			0
$385$	21.9823	+	27.5649i	1.12032	+	1.40484i
$386$	5.64794	+	1.55873i	0.287473	+	0.0793374i
$387$		0			0
$388$	2.03394	−	3.40425i	0.103258	−	0.172825i
$389$	6.24278	+	27.3514i	0.316522	+	1.38677i	0.843608	+	0.536960i	$0.180427\pi$
$389$	6.24278	+	27.3514i	0.316522	+	1.38677i	−0.527086	+	0.849812i	$0.676716\pi$
$390$		0			0
$391$	2.98332	−	2.60645i	0.150873	−	0.131814i
$392$	−0.398897	+	0.0910457i	−0.0201474	+	0.00459850i
$393$		0			0
$394$	−0.448940	+	0.932234i	−0.0226173	+	0.0469653i
$395$	−9.11932	+	33.0431i	−0.458843	+	1.66258i
$396$		0			0
$397$	3.16952	−	3.03037i	0.159073	−	0.152090i	−0.607329	−	0.794450i	$-0.707759\pi$
$397$	3.16952	−	3.03037i	0.159073	−	0.152090i	0.766403	+	0.642361i	$0.222045\pi$
$398$	−13.4216	−	22.4640i	−0.672765	−	1.12602i
$399$		0			0
$400$	18.0165	−	22.5920i	0.900825	−	1.12960i
$401$	−20.3323	+	14.7723i	−1.01535	+	0.737692i	−0.965324	−	0.261056i	$-0.915929\pi$
$401$	−20.3323	+	14.7723i	−1.01535	+	0.737692i	−0.0500224	+	0.998748i	$0.515929\pi$
$402$		0			0
$403$	−0.773687	+	3.38974i	−0.0385401	+	0.168855i
$404$	11.2448	+	10.7511i	0.559449	+	0.534888i
$405$		0			0
$406$	−17.5050	−	36.3496i	−0.868761	−	1.80400i
$407$	0.0563551	−	0.0102269i	0.00279342	−	0.000506931i
$408$		0			0
$409$	−22.3919	−	16.2687i	−1.10721	−	0.804435i	−0.124988	−	0.992158i	$-0.539889\pi$
$409$	−22.3919	−	16.2687i	−1.10721	−	0.804435i	−0.982222	+	0.187723i	$0.939889\pi$
$410$	26.1780	−	7.22467i	1.29284	−	0.356801i
$411$		0			0
$412$	−4.18144	+	12.8692i	−0.206005	+	0.634018i
$413$	27.5763	−	1.23845i	1.35694	−	0.0609402i
$414$		0			0
$415$	0.476465	−	10.6093i	0.0233887	−	0.520791i
$416$	−8.72337	+	20.4093i	−0.427699	+	1.00065i
$417$		0			0
$418$	−23.7952	−	15.7071i	−1.16386	−	0.768258i
$419$	12.6322	−	5.39928i	0.617125	−	0.263772i	−0.0616735	−	0.998096i	$-0.519644\pi$
$419$	12.6322	−	5.39928i	0.617125	−	0.263772i	0.678799	+	0.734324i	$0.262501\pi$
$420$		0			0
$421$	−17.1920	+	5.58601i	−0.837885	+	0.272245i	−0.696363	−	0.717690i	$-0.745200\pi$
$421$	−17.1920	+	5.58601i	−0.837885	+	0.272245i	−0.141522	+	0.989935i	$0.545200\pi$
$422$	2.83446	+	20.9248i	0.137979	+	1.01861i
$423$		0			0
$424$	−1.47130	+	1.68404i	−0.0714527	+	0.0817842i
$425$	14.4096			0.698968
$426$		0			0
$427$	32.9217			1.59319
$428$	21.6159	−	24.7414i	1.04484	−	1.19592i
$429$		0			0
$430$	0.725413	+	5.35521i	0.0349825	+	0.258251i
$431$	7.18059	−	2.33311i	0.345877	−	0.112382i	−0.130927	−	0.991392i	$-0.541795\pi$
$431$	7.18059	−	2.33311i	0.345877	−	0.112382i	0.476804	+	0.879010i	$0.341795\pi$
$432$		0			0
$433$	2.79733	−	1.19564i	0.134431	−	0.0574586i	−0.324758	−	0.945797i	$-0.605283\pi$
$433$	2.79733	−	1.19564i	0.134431	−	0.0574586i	0.459189	+	0.888339i	$0.348140\pi$
$434$	4.69768	+	3.10091i	0.225496	+	0.148849i
$435$		0			0
$436$	9.07416	−	21.2301i	0.434574	−	1.01674i
$437$	0.276539	−	6.15762i	0.0132287	−	0.294559i
$438$		0			0
$439$	25.4954	−	1.14500i	1.21683	−	0.0546478i	0.572829	−	0.819675i	$-0.305846\pi$
$439$	25.4954	−	1.14500i	1.21683	−	0.0546478i	0.643998	+	0.765027i	$0.277274\pi$
$440$	1.23093	−	3.78840i	0.0586821	−	0.180605i
$441$		0			0
$442$	−11.3881	+	3.14290i	−0.541674	+	0.149493i
$443$	13.9317	+	10.1220i	0.661917	+	0.480911i	0.867310	−	0.497769i	$-0.165847\pi$
$443$	13.9317	+	10.1220i	0.661917	+	0.480911i	−0.205393	+	0.978680i	$0.565847\pi$
$444$		0			0
$445$	51.9241	−	9.42283i	2.46144	−	0.446685i
$446$	−9.24554	−	19.1986i	−0.437789	−	0.909078i
$447$		0			0
$448$	11.6302	+	11.1196i	0.549477	+	0.525354i
$449$	4.75075	−	20.8144i	0.224202	−	0.982292i	−0.730075	−	0.683367i	$-0.760515\pi$
$449$	4.75075	−	20.8144i	0.224202	−	0.982292i	0.954277	−	0.298925i	$-0.0966279\pi$
$450$		0			0
$451$	14.3048	−	10.3930i	0.673585	−	0.489388i
$452$	−11.3119	+	14.1847i	−0.532068	+	0.667192i
$453$		0			0
$454$	2.84911	+	4.76860i	0.133715	+	0.223802i
$455$	16.4289	−	15.7077i	0.770201	−	0.736388i
$456$		0			0
$457$	3.07062	−	11.1261i	0.143638	−	0.520459i	−0.856354	−	0.516389i	$-0.827276\pi$
$457$	3.07062	−	11.1261i	0.143638	−	0.520459i	0.999992	−	0.00406995i	$-0.00129551\pi$
$458$	−0.750995	+	1.55946i	−0.0350917	+	0.0728687i
$459$		0			0
$460$	−11.6791	+	2.66567i	−0.544539	+	0.124287i
$461$	19.2616	−	16.8283i	0.897100	−	0.783773i	−0.0799463	−	0.996799i	$-0.525475\pi$
$461$	19.2616	−	16.8283i	0.897100	−	0.783773i	0.977046	+	0.213026i	$0.0683320\pi$
$462$		0			0
$463$	5.44357	+	23.8498i	0.252984	+	1.10840i	0.928583	+	0.371126i	$0.121028\pi$
$463$	5.44357	+	23.8498i	0.252984	+	1.10840i	−0.675598	+	0.737270i	$0.736115\pi$
$464$	−19.1635	+	32.0743i	−0.889643	+	1.48901i
$465$		0			0
$466$	−27.5443	−	7.60176i	−1.27597	−	0.352145i
$467$	−20.2562	−	25.4004i	−0.937343	−	1.17539i	−0.984302	−	0.176494i	$-0.943524\pi$
$467$	−20.2562	−	25.4004i	−0.937343	−	1.17539i	0.0469588	−	0.998897i	$-0.485047\pi$
$468$		0			0
$469$	1.30480	−	0.779581i	0.0602500	−	0.0359977i
$470$	56.4163	−	5.07756i	2.60229	−	0.234211i
$471$		0			0
$472$	−1.83315	−	2.52311i	−0.0843775	−	0.116136i
$473$	1.66736	+	3.09848i	0.0766654	+	0.142468i
$474$		0			0
$475$	15.4937	−	16.2052i	0.710901	−	0.743544i
$476$	−0.827460	+	9.19383i	−0.0379266	+	0.421399i
$477$		0			0
$478$	10.0393	+	55.3210i	0.459186	+	2.53032i
$479$	−4.03183	+	29.7642i	−0.184219	+	1.35996i	0.628730	+	0.777624i	$0.283575\pi$
$479$	−4.03183	+	29.7642i	−0.184219	+	1.35996i	−0.812949	+	0.582336i	$0.802139\pi$
$480$		0			0
$481$	−0.00982340	−	0.0355943i	−0.000447908	−	0.00162296i
$482$	−10.9883	−	1.99409i	−0.500505	−	0.0908283i
$483$		0			0
$484$	0.697855	+	15.5389i	0.0317207	+	0.706315i
$485$	6.83482	+	2.56515i	0.310353	+	0.116477i
$486$		0			0
$487$	25.4587	+	10.8816i	1.15365	+	0.493092i	0.882901	−	0.469559i	$-0.155587\pi$
$487$	25.4587	+	10.8816i	1.15365	+	0.493092i	0.270745	+	0.962651i	$0.412730\pi$
$488$	−2.04908	−	3.10422i	−0.0927574	−	0.140522i
$489$		0			0
$490$	4.11817	+	9.63493i	0.186040	+	0.435262i
$491$	−24.9119	+	9.34961i	−1.12426	+	0.421942i	−0.843120	−	0.537725i	$-0.819284\pi$
$491$	−24.9119	+	9.34961i	−1.12426	+	0.421942i	−0.281140	+	0.959667i	$0.590713\pi$
$492$		0			0
$493$	−18.4631	+	2.50100i	−0.831537	+	0.112639i
$494$	−8.71031	+	16.1865i	−0.391895	+	0.728264i
$495$		0			0
$496$		−	5.21281i		−	0.234062i
$497$	19.1275	+	4.58079i	0.857987	+	0.205477i
$498$		0			0
$499$	−11.4044	−	9.96371i	−0.510531	−	0.446037i	0.363723	−	0.931507i	$-0.381506\pi$
$499$	−11.4044	−	9.96371i	−0.510531	−	0.446037i	−0.874253	+	0.485470i	$0.838648\pi$
$500$	−10.1515	−	5.46274i	−0.453987	−	0.244301i
$501$		0			0
$502$	15.8173	+	48.6807i	0.705961	+	2.17272i
$503$	3.29575	+	8.78150i	0.146950	+	0.391548i	0.989012	−	0.147833i	$-0.0472298\pi$
$503$	3.29575	+	8.78150i	0.146950	+	0.391548i	−0.842062	+	0.539381i	$0.818658\pi$
$504$		0			0
$505$	−15.7776	+	23.9021i	−0.702095	+	1.06363i
$506$	−13.4869	+	8.90263i	−0.599566	+	0.395770i
$507$		0			0
$508$	−27.6744	−	1.24286i	−1.22785	−	0.0551429i
$509$	7.08512	−	18.8782i	0.314043	−	0.836763i	−0.680530	−	0.732720i	$-0.738251\pi$
$509$	7.08512	−	18.8782i	0.314043	−	0.836763i	0.994573	−	0.104043i	$-0.0331781\pi$
$510$		0			0
$511$	−35.0814	−	11.3986i	−1.55191	−	0.504246i
$512$	5.54153	−	30.5363i	0.244903	−	1.34953i
$513$		0			0
$514$	−15.4493	+	21.2641i	−0.681439	+	0.937920i
$515$	−24.6848	−	3.34379i	−1.08774	−	0.147345i
$516$		0			0
$517$	33.2287	−	16.0021i	1.46140	−	0.703772i
$518$	−0.0595379	−	0.00535850i	−0.00261594	−	0.000235439i
$519$		0			0
$520$	−2.50365	−	0.571441i	−0.109792	−	0.0250593i
$521$	20.4265	−	10.9920i	0.894901	−	0.481567i	0.0393149	−	0.999227i	$-0.487482\pi$
$521$	20.4265	−	10.9920i	0.894901	−	0.481567i	0.855586	+	0.517660i	$0.173197\pi$
$522$		0			0
$523$	0.856048	+	0.682676i	0.0374324	+	0.0298513i	0.642027	−	0.766682i	$-0.278094\pi$
$523$	0.856048	+	0.682676i	0.0374324	+	0.0298513i	−0.604595	+	0.796533i	$0.706665\pi$
$524$	−2.67432	−	29.7141i	−0.116828	−	1.29807i
$525$		0			0
$526$	−26.2899	−	27.4971i	−1.14630	−	1.19893i
$527$	2.03234	−	1.62074i	0.0885301	−	0.0706004i
$528$		0			0
$529$	17.5747	+	8.46351i	0.764115	+	0.367979i
$530$	49.1615	+	29.3726i	2.13544	+	1.27587i
$531$		0			0
$532$	9.44976	+	10.8161i	0.409699	+	0.468938i
$533$	−7.49997	−	8.58440i	−0.324860	−	0.371832i
$534$		0			0
$535$	51.9203	+	31.0209i	2.24471	+	1.34115i
$536$	−0.154719	−	0.0745089i	−0.00668286	−	0.00321830i
$537$		0			0
$538$	−21.6763	+	17.2863i	−0.934531	+	0.745264i
$539$	4.71464	+	4.93112i	0.203074	+	0.212398i
$540$		0			0
$541$	1.06174	+	11.7969i	0.0456480	+	0.507190i	0.985972	+	0.166910i	$0.0533790\pi$
$541$	1.06174	+	11.7969i	0.0456480	+	0.507190i	−0.940324	+	0.340280i	$0.889478\pi$
$542$	7.80826	+	6.22688i	0.335393	+	0.267467i
$543$		0			0
$544$	14.6127	−	7.86341i	0.626513	−	0.337141i
$545$	41.4375	+	9.45785i	1.77499	+	0.405130i
$546$		0			0
$547$	−18.0366	−	1.62332i	−0.771188	−	0.0694082i	−0.302945	−	0.953008i	$-0.597970\pi$
$547$	−18.0366	−	1.62332i	−0.771188	−	0.0694082i	−0.468243	+	0.883600i	$0.655113\pi$
$548$	5.94901	−	2.86489i	0.254129	−	0.122382i
$549$		0			0
$550$	−58.2489	−	7.89035i	−2.48374	−	0.336445i
$551$	−17.0396	+	23.4530i	−0.725910	+	0.999130i
$552$		0			0
$553$	4.15930	−	22.9196i	0.176871	−	0.974641i
$554$	−4.80695	−	1.56187i	−0.204228	−	0.0663576i
$555$		0			0
$556$	−0.250133	+	0.666476i	−0.0106080	+	0.0282649i
$557$	29.1987	+	1.31131i	1.23719	+	0.0555622i	0.653823	−	0.756648i	$-0.273164\pi$
$557$	29.1987	+	1.31131i	1.23719	+	0.0555622i	0.583365	+	0.812210i	$0.301736\pi$
$558$		0			0
$559$	1.89316	−	1.24966i	0.0800721	−	0.0528552i
$560$	−18.7734	+	28.4405i	−0.793321	+	1.20183i
$561$		0			0
$562$	−17.6471	−	47.0206i	−0.744399	−	1.98344i
$563$	11.4935	+	35.3733i	0.484392	+	1.49081i	0.832859	+	0.553485i	$0.186702\pi$
$563$	11.4935	+	35.3733i	0.484392	+	1.49081i	−0.348467	+	0.937321i	$0.613298\pi$
$564$		0			0
$565$	−29.4116	−	15.8270i	−1.23735	−	0.665849i
$566$	−19.6042	−	17.1277i	−0.824027	−	0.719931i
$567$		0			0
$568$	−0.758588	−	2.08867i	−0.0318296	−	0.0876385i
$569$			16.2812i			0.682545i	0.939964	+	0.341273i	$0.110858\pi$
$569$			16.2812i			0.682545i	−0.939964	+	0.341273i	$0.889142\pi$
$570$		0			0
$571$	8.78593	−	16.3270i	0.367680	−	0.683263i	−0.627786	−	0.778386i	$-0.716039\pi$
$571$	8.78593	−	16.3270i	0.367680	−	0.683263i	0.995466	+	0.0951227i	$0.0303243\pi$
$572$	23.0494	−	3.12225i	0.963743	−	0.130548i
$573$		0			0
$574$	−17.2776	+	6.48440i	−0.721154	+	0.270654i
$575$	−4.99438	−	11.6849i	−0.208280	−	0.487296i
$576$		0			0
$577$	−3.29379	−	4.98988i	−0.137122	−	0.207731i	0.759524	−	0.650480i	$-0.225432\pi$
$577$	−3.29379	−	4.98988i	−0.137122	−	0.207731i	−0.896646	+	0.442748i	$0.854003\pi$
$578$	−22.6137	−	9.66555i	−0.940605	−	0.402034i
$579$		0			0
$580$	52.7484	+	19.7968i	2.19026	+	0.822018i
$581$	0.323783	+	7.20959i	0.0134328	+	0.299104i
$582$		0			0
$583$	36.6878	+	6.65786i	1.51945	+	0.275740i
$584$	1.10871	+	4.01732i	0.0458788	+	0.166238i
$585$		0			0
$586$	8.77389	−	64.7714i	0.362446	−	2.67568i
$587$	−3.11301	−	17.1541i	−0.128488	−	0.708026i	−0.982281	−	0.187414i	$-0.939989\pi$
$587$	−3.11301	−	17.1541i	−0.128488	−	0.708026i	0.853793	−	0.520612i	$-0.174296\pi$
$588$		0			0
$589$	0.362550	−	4.02826i	0.0149386	−	0.165982i
$590$	−55.1939	+	57.7283i	−2.27230	+	2.37664i
$591$		0			0
$592$	0.0262335	+	0.0487500i	0.00107819	+	0.00200361i
$593$	2.89244	+	3.98111i	0.118778	+	0.163484i	0.864266	−	0.503035i	$-0.167783\pi$
$593$	2.89244	+	3.98111i	0.118778	+	0.163484i	−0.745488	+	0.666519i	$0.767783\pi$
$594$		0			0
$595$	−16.9251	+	1.52329i	−0.693862	+	0.0624487i
$596$	23.0566	−	13.7757i	0.944436	−	0.564274i
$597$		0			0
$598$	6.49573	+	8.14539i	0.265630	+	0.333090i
$599$	26.0886	+	7.20000i	1.06595	+	0.294184i	0.754650	−	0.656127i	$-0.227806\pi$
$599$	26.0886	+	7.20000i	1.06595	+	0.294184i	0.311302	+	0.950311i	$0.399235\pi$
$600$		0			0
$601$	−14.9405	+	25.0062i	−0.609435	+	1.02002i	0.385806	+	0.922580i	$0.373924\pi$
$601$	−14.9405	+	25.0062i	−0.609435	+	1.02002i	−0.995241	+	0.0974430i	$0.968934\pi$
$602$	−0.817182	−	3.58031i	−0.0333059	−	0.145922i
$603$		0			0
$604$	−21.5242	+	18.8052i	−0.875808	+	0.765171i
$605$	−27.9169	+	6.37184i	−1.13498	+	0.259052i
$606$		0			0
$607$	20.6265	−	42.8313i	0.837202	−	1.73847i	0.181583	−	0.983376i	$-0.441878\pi$
$607$	20.6265	−	42.8313i	0.837202	−	1.73847i	0.655619	−	0.755092i	$-0.272408\pi$
$608$	6.86881	−	24.8886i	0.278567	−	1.00936i
$609$		0			0
$610$	−68.8491	+	65.8265i	−2.78762	+	2.66524i
$611$	−12.1951	−	20.4112i	−0.493363	−	0.825750i
$612$		0			0
$613$	−14.7394	+	18.4826i	−0.595317	+	0.746504i	−0.984640	−	0.174597i	$-0.944138\pi$
$613$	−14.7394	+	18.4826i	−0.595317	+	0.746504i	0.389323	+	0.921101i	$0.372709\pi$
$614$	20.8891	−	15.1768i	0.843014	−	0.612486i
$615$		0			0
$616$	−0.602343	+	2.63904i	−0.0242691	+	0.106330i
$617$	23.1162	+	22.1014i	0.930625	+	0.889768i	0.994128	−	0.108213i	$-0.0345130\pi$
$617$	23.1162	+	22.1014i	0.930625	+	0.889768i	−0.0635030	+	0.997982i	$0.520227\pi$
$618$		0			0
$619$	4.12106	+	8.55748i	0.165640	+	0.343954i	0.967223	−	0.253929i	$-0.0817230\pi$
$619$	4.12106	+	8.55748i	0.165640	+	0.343954i	−0.801583	+	0.597883i	$0.796009\pi$
$620$	−7.73425	+	1.40356i	−0.310615	+	0.0563683i
$621$		0			0
$622$	−16.0696	−	11.6753i	−0.644334	−	0.468136i
$623$	−34.5691	+	9.54047i	−1.38498	+	0.382231i
$624$		0			0
$625$	−3.94656	+	12.1463i	−0.157863	+	0.485851i
$626$	−9.96004	+	0.447306i	−0.398083	+	0.0178779i
$627$		0			0
$628$	−1.81440	+	40.4008i	−0.0724024	+	1.61217i
$629$	−0.0108500	+	0.0253848i	−0.000432617	+	0.00101216i
$630$		0			0
$631$	−36.1217	−	23.8437i	−1.43798	−	0.949203i	−0.998706	−	0.0508510i	$-0.983807\pi$
$631$	−36.1217	−	23.8437i	−1.43798	−	0.949203i	−0.439275	−	0.898352i	$-0.644765\pi$
$632$	−2.41999	+	1.03435i	−0.0962622	+	0.0411444i
$633$		0			0
$634$	6.79239	−	2.20698i	0.269760	−	0.0876505i
$635$	−6.84558	−	50.5361i	−0.271659	−	2.00547i
$636$		0			0
$637$	2.89379	−	3.31221i	0.114656	−	0.131234i
$638$	76.0042			3.00903
$639$		0			0
$640$	7.23060			0.285815
$641$	13.3520	−	15.2826i	0.527373	−	0.603627i	−0.426259	−	0.904601i	$-0.640169\pi$
$641$	13.3520	−	15.2826i	0.527373	−	0.603627i	0.953632	+	0.300974i	$0.0973117\pi$
$642$		0			0
$643$	0.0137668	+	0.101630i	0.000542908	+	0.00400791i	0.991219	−	0.132229i	$-0.0422134\pi$
$643$	0.0137668	+	0.101630i	0.000542908	+	0.00400791i	−0.990676	+	0.136237i	$0.956499\pi$
$644$	7.74220	−	2.51559i	0.305086	−	0.0991283i
$645$		0			0
$646$	12.6366	−	5.40113i	0.497179	−	0.212505i
$647$	−33.7103	−	22.2520i	−1.32529	−	0.874816i	−0.327739	−	0.944768i	$-0.606287\pi$
$647$	−33.7103	−	22.2520i	−1.32529	−	0.874816i	−0.997550	+	0.0699525i	$0.977715\pi$
$648$		0			0
$649$	−20.4381	+	47.8174i	−0.802266	+	1.87700i
$650$	−1.70017	+	37.8573i	−0.0666862	+	1.48488i
$651$		0			0
$652$	−27.8001	+	1.24850i	−1.08873	+	0.0488951i
$653$	−2.49146	+	7.66793i	−0.0974984	+	0.300069i	−0.987897	−	0.155113i	$-0.950426\pi$
$653$	−2.49146	+	7.66793i	−0.0974984	+	0.300069i	0.890398	+	0.455182i	$0.150426\pi$
$654$		0			0
$655$	52.9431	−	14.6114i	2.06866	−	0.570914i
$656$	13.8264	+	10.0455i	0.539831	+	0.392210i
$657$		0			0
$658$	−37.8742	+	6.87316i	−1.47649	+	0.267944i
$659$	14.3990	+	29.8999i	0.560907	+	1.16473i	0.967907	+	0.251307i	$0.0808603\pi$
$659$	14.3990	+	29.8999i	0.560907	+	1.16473i	−0.407001	+	0.913428i	$0.633425\pi$
$660$		0			0
$661$	20.3084	+	19.4169i	0.789907	+	0.755229i	0.973724	−	0.227732i	$-0.0731310\pi$
$661$	20.3084	+	19.4169i	0.789907	+	0.755229i	−0.183817	+	0.982961i	$0.558845\pi$
$662$	−0.981248	+	4.29913i	−0.0381373	+	0.167090i
$663$		0			0
$664$	0.659647	−	0.479261i	0.0255993	−	0.0185990i
$665$	−16.4854	+	20.6720i	−0.639276	+	0.801627i
$666$		0			0
$667$	8.42743	+	14.1051i	0.326312	+	0.546153i
$668$	−8.75796	+	8.37347i	−0.338856	+	0.323979i
$669$		0			0
$670$	−1.16996	+	4.23926i	−0.0451996	+	0.163777i
$671$	−26.9094	+	55.8779i	−1.03882	+	2.15714i
$672$		0			0
$673$	−0.743582	+	0.169718i	−0.0286630	+	0.00654214i	−0.236828	−	0.971552i	$-0.576108\pi$
$673$	−0.743582	+	0.169718i	−0.0286630	+	0.00654214i	0.208165	+	0.978094i	$0.433251\pi$
$674$	32.7104	−	28.5782i	1.25996	−	1.10079i
$675$		0			0
$676$	2.06075	+	9.02873i	0.0792595	+	0.347259i
$677$	18.8310	−	31.5178i	0.723734	−	1.21133i	−0.246496	−	0.969144i	$-0.579279\pi$
$677$	18.8310	−	31.5178i	0.723734	−	1.21133i	0.970231	−	0.242183i	$-0.0778635\pi$
$678$		0			0
$679$	−4.78217	−	1.31980i	−0.183523	−	0.0506491i
$680$	1.19707	+	1.50108i	0.0459054	+	0.0575636i
$681$		0			0
$682$	−9.10294	+	5.43875i	−0.348569	+	0.208261i
$683$	18.5211	−	1.66693i	0.708691	−	0.0637834i	0.270571	−	0.962700i	$-0.412787\pi$
$683$	18.5211	−	1.66693i	0.708691	−	0.0637834i	0.438120	+	0.898917i	$0.355644\pi$
$684$		0			0
$685$	7.14477	+	9.83393i	0.272988	+	0.375735i
$686$	−18.5978	−	34.5605i	−0.710068	−	1.31953i
$687$		0			0
$688$	−2.35027	+	2.45819i	−0.0896033	+	0.0937177i
$689$	2.15480	−	23.9418i	0.0820914	−	0.912110i
$690$		0			0
$691$	−2.47920	−	13.6615i	−0.0943132	−	0.519709i	−0.996152	−	0.0876371i	$-0.972068\pi$
$691$	−2.47920	−	13.6615i	−0.0943132	−	0.519709i	0.901839	−	0.432072i	$-0.142217\pi$
$692$	5.67107	−	41.8655i	0.215582	−	1.59149i
$693$		0			0
$694$	12.0461	+	43.6481i	0.457264	+	1.65686i
$695$	−1.28943	−	0.233998i	−0.0489110	−	0.00887604i
$696$		0			0
$697$	0.382357	+	8.51383i	0.0144828	+	0.322484i
$698$	−57.5393	−	21.5949i	−2.17789	−	0.817377i
$699$		0			0
$700$	27.2277	+	11.6377i	1.02911	+	0.439863i
$701$	4.04886	+	6.13376i	0.152923	+	0.231669i	0.902957	−	0.429730i	$-0.141391\pi$
$701$	4.04886	+	6.13376i	0.152923	+	0.231669i	−0.750034	+	0.661399i	$0.769963\pi$
$702$		0			0
$703$	0.0168817	+	0.0394967i	0.000636705	+	0.00148964i
$704$	−28.3796	+	10.6510i	−1.06960	+	0.401426i
$705$		0			0
$706$	−38.9200	+	5.27207i	−1.46477	+	0.198417i
$707$	9.22258	−	17.1384i	0.346851	−	0.644557i
$708$		0			0
$709$			27.4619i			1.03135i	0.856783	+	0.515676i	$0.172459\pi$
$709$			27.4619i			1.03135i	−0.856783	+	0.515676i	$0.827541\pi$
$710$	−49.1606	+	28.6654i	−1.84496	+	1.07579i
$711$		0			0
$712$	3.05119	+	2.66575i	0.114348	+	0.0999032i
$713$	−2.01869	−	1.08630i	−0.0756005	−	0.0406823i
$714$		0			0
$715$	13.2320	+	40.7239i	0.494848	+	1.52299i
$716$	−1.08874	−	2.90093i	−0.0406881	−	0.108413i
$717$		0			0
$718$	−0.668151	+	1.01221i	−0.0249352	+	0.0377752i
$719$	−17.2380	+	11.3787i	−0.642868	+	0.424353i	−0.829832	−	0.558013i	$-0.811564\pi$
$719$	−17.2380	+	11.3787i	−0.642868	+	0.424353i	0.186964	+	0.982367i	$0.440135\pi$
$720$		0			0
$721$	16.9108	+	0.759465i	0.629791	+	0.0282840i
$722$	−5.61332	+	14.9566i	−0.208906	+	0.556629i
$723$		0			0
$724$	−13.0058	−	4.22584i	−0.483357	−	0.157052i
$725$	−10.6716	+	58.8051i	−0.396331	+	2.18397i
$726$		0			0
$727$	19.4038	−	26.7071i	0.719648	−	0.990511i	−0.279887	−	0.960033i	$-0.590297\pi$
$727$	19.4038	−	26.7071i	0.719648	−	0.990511i	0.999535	−	0.0304777i	$-0.00970285\pi$
$728$	1.72932	+	0.234252i	0.0640928	+	0.00868196i
$729$		0			0
$730$	96.1570	−	46.3068i	3.55893	−	1.71389i
$731$	−1.68912	−	0.152023i	−0.0624743	−	0.00562278i
$732$		0			0
$733$	−39.1845	−	8.94362i	−1.44731	−	0.330340i	−0.574545	−	0.818473i	$-0.694821\pi$
$733$	−39.1845	−	8.94362i	−1.44731	−	0.330340i	−0.872769	+	0.488133i	$0.837678\pi$
$734$	−50.7972	+	27.3351i	−1.87496	+	1.00896i
$735$		0			0
$736$	−11.4413	−	9.12415i	−0.421733	−	0.336320i
$737$	0.256670	+	2.85184i	0.00945457	+	0.105049i
$738$		0			0
$739$	1.98221	+	2.07323i	0.0729169	+	0.0762651i	0.758247	−	0.651968i	$-0.226056\pi$
$739$	1.98221	+	2.07323i	0.0729169	+	0.0762651i	−0.685330	+	0.728233i	$0.740342\pi$
$740$	0.0652669	−	0.0520486i	0.00239926	−	0.00191335i
$741$		0			0
$742$	−35.0626	−	16.8852i	−1.28719	−	0.619877i
$743$	1.65100	+	0.986424i	0.0605691	+	0.0361884i	0.542865	−	0.839820i	$-0.317340\pi$
$743$	1.65100	+	0.986424i	0.0605691	+	0.0361884i	−0.482295	+	0.876009i	$0.660197\pi$
$744$		0			0
$745$	32.5313	+	37.2351i	1.19186	+	1.36419i
$746$	8.99188	+	10.2920i	0.329216	+	0.376818i
$747$		0			0
$748$	−14.9283	−	8.91925i	−0.545833	−	0.326120i
$749$	−37.0302	−	17.8328i	−1.35305	−	0.651596i
$750$		0			0
$751$	12.7742	−	10.1870i	0.466135	−	0.371731i	−0.362074	−	0.932149i	$-0.617931\pi$
$751$	12.7742	−	10.1870i	0.466135	−	0.371731i	0.828209	+	0.560419i	$0.189360\pi$
$752$	24.6349	+	25.7660i	0.898341	+	0.939591i
$753$		0			0
$754$	−4.39225	−	48.8019i	−0.159956	−	1.77726i
$755$	−41.1377	−	32.8062i	−1.49715	−	1.19394i
$756$		0			0
$757$	−35.6794	+	19.1999i	−1.29679	+	0.697833i	−0.969034	−	0.246929i	$-0.920579\pi$
$757$	−35.6794	+	19.1999i	−1.29679	+	0.697833i	−0.327758	+	0.944762i	$0.606293\pi$
$758$	45.8610	+	10.4675i	1.66575	+	0.380196i
$759$		0			0
$760$	2.97525	+	0.267778i	0.107924	+	0.00971332i
$761$	43.6929	−	21.0414i	1.58387	−	0.762750i	0.585032	−	0.811010i	$-0.301082\pi$
$761$	43.6929	−	21.0414i	1.58387	−	0.762750i	0.998835	+	0.0482604i	$0.0153677\pi$
$762$		0			0
$763$	−28.6217	−	3.87708i	−1.03618	−	0.140360i
$764$	−25.4521	+	35.0318i	−0.920825	+	1.26741i
$765$		0			0
$766$	4.91707	−	27.0953i	0.177661	−	0.978992i
$767$	31.8844	+	10.3599i	1.15128	+	0.374073i
$768$		0			0
$769$	11.2502	−	29.9759i	0.405691	−	1.08096i	−0.561627	−	0.827391i	$-0.689824\pi$
$769$	11.2502	−	29.9759i	0.405691	−	1.08096i	0.967317	−	0.253568i	$-0.0816043\pi$
$770$	69.2516	+	3.11010i	2.49566	+	0.112080i
$771$		0			0
$772$	4.64037	−	3.06308i	0.167010	−	0.110243i
$773$	−14.8868	+	22.5526i	−0.535442	+	0.811160i	−0.997116	−	0.0758898i	$-0.975820\pi$
$773$	−14.8868	+	22.5526i	−0.535442	+	0.811160i	0.461674	+	0.887049i	$0.347249\pi$
$774$		0			0
$775$	−2.92989	−	7.80666i	−0.105245	−	0.280424i
$776$	0.173202	+	0.533061i	0.00621760	+	0.0191358i
$777$		0			0
$778$	48.5744	+	26.1390i	1.74148	+	0.937128i
$779$	9.98586	+	8.72439i	0.357781	+	0.312584i
$780$		0			0
$781$	−23.4093	+	28.7208i	−0.837651	+	1.02771i
$782$		−	7.78911i		−	0.278538i
$783$		0			0
$784$	−3.12477	+	5.80679i	−0.111599	+	0.207385i
$785$	−73.7758	+	9.99361i	−2.63317	+	0.356687i
$786$		0			0
$787$	0.705357	−	0.264725i	0.0251433	−	0.00943643i	−0.338772	−	0.940869i	$-0.610011\pi$
$787$	0.705357	−	0.264725i	0.0251433	−	0.00943643i	0.363915	+	0.931432i	$0.381440\pi$
$788$	0.385917	+	0.902897i	0.0137477	+	0.0321644i
$789$		0			0
$790$	37.1291	+	56.2482i	1.32099	+	2.00122i
$791$	20.8703	+	8.92041i	0.742064	+	0.317173i
$792$		0			0
$793$	37.4340	+	14.0492i	1.32932	+	0.498902i
$794$	−0.386819	−	8.61319i	−0.0137277	−	0.305671i
$795$		0			0
$796$	−24.4340	−	4.43412i	−0.866041	−	0.157163i
$797$	3.57500	+	12.9537i	0.126633	+	0.458844i	0.999580	−	0.0289704i	$-0.00922284\pi$
$797$	3.57500	+	12.9537i	0.126633	+	0.458844i	−0.872947	+	0.487814i	$0.837794\pi$
$798$		0			0
$799$	−2.38618	+	17.6155i	−0.0844171	+	0.623192i
$800$	−9.50446	−	52.3739i	−0.336033	−	1.85170i
$801$		0			0
$802$	−4.42946	+	49.2153i	−0.156410	+	1.73785i
$803$	48.0215	−	50.2266i	1.69464	−	1.77246i
$804$		0			0
$805$	7.10152	+	13.1968i	0.250296	+	0.465127i
$806$	4.01825	+	5.53064i	0.141537	+	0.194809i
$807$		0			0
$808$	−2.19002	+	0.197106i	−0.0770447	+	0.00693415i
$809$	−23.8186	+	14.2309i	−0.837416	+	0.500333i	−0.866461	−	0.499245i	$-0.833611\pi$
$809$	−23.8186	+	14.2309i	−0.837416	+	0.500333i	0.0290447	+	0.999578i	$0.490753\pi$
$810$		0			0
$811$	−3.12124	−	3.91391i	−0.109601	−	0.137436i	0.724005	−	0.689795i	$-0.242299\pi$
$811$	−3.12124	−	3.91391i	−0.109601	−	0.137436i	−0.833606	+	0.552359i	$0.813728\pi$
$812$	−36.9069	−	10.1857i	−1.29518	−	0.357447i
$813$		0			0
$814$	0.0577597	−	0.0966735i	0.00202448	−	0.00338840i
$815$	−11.3996	−	49.9449i	−0.399310	−	1.74949i
$816$		0			0
$817$	−1.98717	+	1.73614i	−0.0695222	+	0.0607397i
$818$	−53.0555	+	12.1096i	−1.85504	+	0.423401i
$819$		0			0
$820$	11.1817	−	23.2190i	0.390482	−	0.810843i
$821$	3.19140	−	11.5638i	0.111380	−	0.403578i	−0.886915	−	0.461932i	$-0.847157\pi$
$821$	3.19140	−	11.5638i	0.111380	−	0.403578i	0.998296	+	0.0583536i	$0.0185851\pi$
$822$		0			0
$823$	−30.2828	+	28.9533i	−1.05559	+	1.00925i	−0.0556508	+	0.998450i	$0.517723\pi$
$823$	−30.2828	+	28.9533i	−1.05559	+	1.00925i	−0.999942	+	0.0107994i	$0.996562\pi$
$824$	−0.980934	−	1.64181i	−0.0341724	−	0.0571950i
$825$		0			0
$826$	33.8397	−	42.4336i	1.17743	−	1.47645i
$827$	−1.87794	+	1.36440i	−0.0653023	+	0.0474449i	−0.619958	−	0.784635i	$-0.712850\pi$
$827$	−1.87794	+	1.36440i	−0.0653023	+	0.0474449i	0.554655	+	0.832080i	$0.312850\pi$
$828$		0			0
$829$	2.10840	−	9.23748i	0.0732276	−	0.320831i	−0.925026	−	0.379904i	$-0.875957\pi$
$829$	2.10840	−	9.23748i	0.0732276	−	0.320831i	0.998254	+	0.0590725i	$0.0188143\pi$
$830$	−15.0926	−	14.4300i	−0.523871	−	0.500872i
$831$		0			0
$832$	8.47901	+	17.6069i	0.293957	+	0.610408i
$833$	−3.23545	+	0.587147i	−0.112102	+	0.0203434i
$834$		0			0
$835$	−18.0460	−	13.1112i	−0.624507	−	0.453731i
$836$	−26.0821	+	7.19821i	−0.902070	+	0.248955i
$837$		0			0
$838$	8.34683	−	25.6889i	0.288336	−	0.887408i
$839$	9.69909	−	0.435586i	0.334850	−	0.0150381i	0.123195	−	0.992383i	$-0.460686\pi$
$839$	9.69909	−	0.435586i	0.334850	−	0.0150381i	0.211655	+	0.977344i	$0.432115\pi$
$840$		0			0
$841$	2.16596	−	48.2288i	0.0746882	−	1.66306i
$842$	−13.9689	+	32.6819i	−0.481401	+	1.12629i
$843$		0			0
$844$	16.7237	+	11.0392i	0.575654	+	0.379986i
$845$	−15.6767	+	6.70053i	−0.539294	+	0.230505i
$846$		0			0
$847$	18.5065	−	6.01311i	0.635889	−	0.206613i
$848$	4.83779	+	35.7140i	0.166130	+	1.22642i
$849$		0			0
$850$	18.6406	−	21.3359i	0.639369	−	0.731816i
$851$	0.0243455			0.000834553
$852$		0			0
$853$	−34.6380			−1.18598			−0.592992	−	0.805209i	$-0.702053\pi$
$853$	−34.6380			−1.18598			−0.592992	+	0.805209i	$0.702053\pi$
$854$	42.5884	−	48.7464i	1.45735	−	1.66807i
$855$		0			0
$856$	0.623321	+	4.60154i	0.0213047	+	0.157277i
$857$	−17.5658	+	5.70749i	−0.600037	+	0.194964i	−0.593257	−	0.805013i	$-0.702158\pi$
$857$	−17.5658	+	5.70749i	−0.600037	+	0.194964i	−0.00678030	+	0.999977i	$0.502158\pi$
$858$		0			0
$859$	−1.13991	+	0.487219i	−0.0388931	+	0.0166237i	−0.412384	−	0.911010i	$-0.635304\pi$
$859$	−1.13991	+	0.487219i	−0.0388931	+	0.0166237i	0.373491	+	0.927634i	$0.378161\pi$
$860$	4.28004	+	2.82523i	0.145948	+	0.0963394i
$861$		0			0
$862$	5.83442	−	13.6503i	0.198721	−	0.464931i
$863$	−0.602148	+	13.4079i	−0.0204973	+	0.456409i	0.962330	+	0.271883i	$0.0876464\pi$
$863$	−0.602148	+	13.4079i	−0.0204973	+	0.456409i	−0.982828	+	0.184526i	$0.940925\pi$
$864$		0			0
$865$	77.6966	−	3.48936i	2.64176	−	0.118642i
$866$	1.84835	−	5.68865i	0.0628096	−	0.193308i
$867$		0			0
$868$	5.14917	−	1.42108i	0.174774	−	0.0482347i
$869$	35.5017	+	25.7935i	1.20431	+	0.874984i
$870$		0			0
$871$	1.81632	−	0.329613i	0.0615436	−	0.0111685i
$872$	1.41587	+	2.94009i	0.0479474	+	0.0995639i
$873$		0			0
$874$	−8.75970	−	8.37513i	−0.296301	−	0.283293i
$875$	−3.20909	+	14.0599i	−0.108487	+	0.475312i
$876$		0			0
$877$	45.2613	−	32.8842i	1.52836	−	1.11042i	0.571225	−	0.820794i	$-0.306468\pi$
$877$	45.2613	−	32.8842i	1.52836	−	1.11042i	0.957139	−	0.289628i	$-0.0935315\pi$
$878$	31.2861	−	39.2316i	1.05586	−	1.32400i
$879$		0			0
$880$	−32.9270	−	55.1106i	−1.10997	−	1.85778i
$881$	20.7177	−	19.8081i	0.697996	−	0.667352i	−0.256170	−	0.966632i	$-0.582461\pi$
$881$	20.7177	−	19.8081i	0.697996	−	0.667352i	0.954165	+	0.299280i	$0.0967464\pi$
$882$		0			0
$883$	7.30929	−	26.4846i	0.245977	−	0.891279i	−0.731780	−	0.681541i	$-0.761310\pi$
$883$	7.30929	−	26.4846i	0.245977	−	0.891279i	0.977758	−	0.209738i	$-0.0672612\pi$
$884$	−4.86430	+	10.1008i	−0.163604	+	0.339728i
$885$		0			0
$886$	33.0099	−	7.53429i	1.10899	−	0.253119i
$887$	32.5989	−	28.4808i	1.09456	−	0.956291i	0.0953305	−	0.995446i	$-0.469609\pi$
$887$	32.5989	−	28.4808i	1.09456	−	0.956291i	0.999233	+	0.0391542i	$0.0124664\pi$
$888$		0			0
$889$	7.71159	+	33.7867i	0.258639	+	1.13317i
$890$	53.2183	−	89.0724i	1.78388	−	2.98571i
$891$		0			0
$892$	−19.4929	−	5.37971i	−0.652672	−	0.180126i
$893$	17.2449	+	21.6244i	0.577077	+	0.723632i
$894$		0			0
$895$	4.89669	−	2.92563i	0.163678	−	0.0977932i
$896$	−4.89379	+	0.440449i	−0.163490	+	0.0147144i
$897$		0			0
$898$	−24.6737	−	33.9604i	−0.823371	−	1.13327i
$899$	5.10905	+	9.49421i	0.170396	+	0.316650i
$900$		0			0
$901$	−12.4198	+	12.9901i	−0.413764	+	0.432763i
$902$	3.11634	−	34.6254i	0.103763	−	1.15290i
$903$		0			0
$904$	−0.457875	−	2.52310i	−0.0152287	−	0.0839171i
$905$	3.37930	−	24.9470i	0.112332	−	0.829265i
$906$		0			0
$907$	−10.2411	−	37.1079i	−0.340051	−	1.23215i	−0.911428	−	0.411459i	$-0.865019\pi$
$907$	−10.2411	−	37.1079i	−0.340051	−	1.23215i	0.571378	−	0.820687i	$-0.306409\pi$
$908$	5.18679	+	0.941264i	0.172130	+	0.0312369i
$909$		0			0
$910$	−2.00505	−	44.6458i	−0.0664666	−	1.47999i
$911$	1.51331	+	0.567954i	0.0501381	+	0.0188172i	0.376318	−	0.926491i	$-0.377190\pi$
$911$	1.51331	+	0.567954i	0.0501381	+	0.0188172i	−0.326180	+	0.945308i	$0.605761\pi$
$912$		0			0
$913$	−12.5015	−	5.34338i	−0.413738	−	0.176840i
$914$	−12.5020	−	18.9397i	−0.413528	−	0.626468i
$915$		0			0
$916$	0.645568	+	1.51038i	0.0213302	+	0.0499044i
$917$	−34.9428	+	13.1142i	−1.15391	+	0.433070i
$918$		0			0
$919$	−49.6020	+	6.71905i	−1.63622	+	0.221641i	−0.893855	−	0.448356i	$-0.852010\pi$
$919$	−49.6020	+	6.71905i	−1.63622	+	0.221641i	−0.742364	+	0.669997i	$0.766295\pi$
$920$	0.802338	−	1.49099i	0.0264523	−	0.0491566i
$921$		0			0
$922$		−	50.2897i		−	1.65620i
$923$	19.7943	+	13.3712i	0.651538	+	0.440119i
$924$		0			0
$925$	0.0666872	+	0.0582629i	0.00219266	+	0.00191567i
$926$	42.3558	+	22.7926i	1.39190	+	0.749012i
$927$		0			0
$928$	21.2684	+	65.4574i	0.698169	+	2.14874i
$929$	5.21118	+	13.8851i	0.170973	+	0.455557i	0.993591	−	0.113039i	$-0.0360584\pi$
$929$	5.21118	+	13.8851i	0.170973	+	0.455557i	−0.822617	+	0.568596i	$0.807487\pi$
$930$		0			0
$931$	−2.81856	+	4.26994i	−0.0923746	+	0.139942i
$932$	−22.6305	+	14.9383i	−0.741287	+	0.489320i
$933$		0			0
$934$	−63.8137	−	2.86588i	−2.08805	−	0.0937743i
$935$	11.2487	−	29.9720i	0.367872	−	0.980190i
$936$		0			0
$937$	17.8824	+	5.81035i	0.584193	+	0.189816i	0.586178	−	0.810182i	$-0.300632\pi$
$937$	17.8824	+	5.81035i	0.584193	+	0.189816i	−0.00198521	+	0.999998i	$0.500632\pi$
$938$	0.533617	−	2.94047i	0.0174232	−	0.0960098i
$939$		0			0
$940$	31.5961	−	43.4883i	1.03055	−	1.41843i
$941$	−15.8754	−	2.15047i	−0.517524	−	0.0701034i	−0.129186	−	0.991620i	$-0.541236\pi$
$941$	−15.8754	−	2.15047i	−0.517524	−	0.0701034i	−0.388338	+	0.921517i	$0.626951\pi$
$942$		0			0
$943$	6.77146	−	3.26096i	0.220509	−	0.106192i
$944$	−50.0608	−	4.50555i	−1.62934	−	0.146643i
$945$		0			0
$946$	6.74479	+	1.53945i	0.219292	+	0.0500520i
$947$	−2.85560	+	1.53666i	−0.0927945	+	0.0499348i	−0.519608	−	0.854405i	$-0.673922\pi$
$947$	−2.85560	+	1.53666i	−0.0927945	+	0.0499348i	0.426813	+	0.904340i	$0.359636\pi$
$948$		0			0
$949$	−35.0253	−	27.9318i	−1.13697	−	0.906704i
$950$	−3.95149	−	43.9046i	−0.128203	−	1.42445i
$951$		0			0
$952$	−0.901633	−	0.943034i	−0.0292221	−	0.0305639i
$953$	−28.8574	+	23.0130i	−0.934784	+	0.745465i	−0.967202	−	0.254009i	$-0.918251\pi$
$953$	−28.8574	+	23.0130i	−0.934784	+	0.745465i	0.0324178	+	0.999474i	$0.489679\pi$
$954$		0			0
$955$	−71.8207	−	34.5870i	−2.32406	−	1.11921i
$956$	45.8034	+	27.3663i	1.48139	+	0.885089i
$957$		0			0
$958$	38.8554	+	44.4736i	1.25536	+	1.43688i
$959$	−5.43473	−	6.22055i	−0.175497	−	0.200872i
$960$		0			0
$961$	25.3206	+	15.1284i	0.816794	+	0.488012i
$962$	−0.0654114	−	0.0315005i	−0.00210895	−	0.00101562i
$963$		0			0
$964$	−8.28589	+	6.60778i	−0.266871	+	0.212822i
$965$	7.07360	+	7.39840i	0.227707	+	0.238163i
$966$		0			0
$967$	0.464962	+	5.16615i	0.0149522	+	0.166132i	0.999980	−	0.00626087i	$-0.00199291\pi$
$967$	0.464962	+	5.16615i	0.0149522	+	0.166132i	−0.985028	+	0.172393i	$0.944850\pi$
$968$	−1.71884	−	1.37073i	−0.0552457	−	0.0440570i
$969$		0			0
$970$	12.6399	−	6.80180i	0.405841	−	0.218393i
$971$	−13.2024	−	3.01336i	−0.423685	−	0.0967033i	0.00536181	−	0.999986i	$-0.498293\pi$
$971$	−13.2024	−	3.01336i	−0.423685	−	0.0967033i	−0.429047	+	0.903282i	$0.641150\pi$
$972$		0			0
$973$	0.886964	+	0.0798282i	0.0284348	+	0.00255918i
$974$	49.0462	−	23.6194i	1.57154	−	0.756815i
$975$		0			0
$976$	−59.4033	−	8.04672i	−1.90145	−	0.257569i
$977$	25.4041	−	34.9657i	0.812748	−	1.11865i	−0.178146	−	0.984004i	$-0.557010\pi$
$977$	25.4041	−	34.9657i	0.812748	−	1.11865i	0.990894	−	0.134647i	$-0.0429902\pi$
$978$		0			0
$979$	12.0629	−	66.4722i	0.385533	−	2.12446i
$980$	9.45688	+	3.07273i	0.302089	+	0.0981547i
$981$		0			0
$982$	−18.3830	+	48.9814i	−0.586626	+	1.56306i
$983$	8.98693	+	0.403603i	0.286638	+	0.0128729i	0.187720	−	0.982223i	$-0.439890\pi$
$983$	8.98693	+	0.403603i	0.286638	+	0.0128729i	0.0989185	+	0.995096i	$0.468462\pi$
$984$		0			0
$985$	−1.50860	+	0.995815i	−0.0480679	+	0.0317293i
$986$	−20.1812	+	30.5732i	−0.642701	+	0.973651i
$987$		0			0
$988$	6.12921	+	16.3312i	0.194996	+	0.519565i
$989$	0.462172	+	1.42242i	0.0146962	+	0.0452303i
$990$		0			0
$991$	9.63504	+	5.18484i	0.306067	+	0.164702i	0.619692	−	0.784845i	$-0.287258\pi$
$991$	9.63504	+	5.18484i	0.306067	+	0.164702i	−0.313625	+	0.949547i	$0.601543\pi$
$992$	−7.23133	−	6.31782i	−0.229595	−	0.200591i
$993$		0			0
$994$	31.5265	−	22.3958i	0.999961	−	0.710352i
$995$		−	45.7157i		−	1.44929i
$996$		0			0
$997$	14.7904	−	27.4853i	0.468418	−	0.870467i	−0.531311	−	0.847177i	$-0.678300\pi$
$997$	14.7904	−	27.4853i	0.468418	−	0.870467i	0.999729	−	0.0232896i	$-0.00741398\pi$
$998$	−29.5061	+	3.99687i	−0.933998	+	0.126519i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.494.21	yes	576
3.2	odd	2	inner	639.2.z.a.494.4	yes	576
71.47	odd	70	inner	639.2.z.a.260.4	✓	576
213.47	even	70	inner	639.2.z.a.260.21	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.260.4	✓	576	71.47	odd	70	inner
639.2.z.a.260.21	yes	576	213.47	even	70	inner
639.2.z.a.494.4	yes	576	3.2	odd	2	inner
639.2.z.a.494.21	yes	576	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 639 = 3^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	639.z (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29363 - 1.48068i) q^{2} +(-0.250462 - 1.84898i) q^{4} +(3.26680 - 1.06145i) q^{5} +(-2.14637 + 0.917402i) q^{7} +(0.220095 + 0.145283i) q^{8} +O(q^{10})\)	\(q+(1.29363 - 1.48068i) q^{2} +(-0.250462 - 1.84898i) q^{4} +(3.26680 - 1.06145i) q^{5} +(-2.14637 + 0.917402i) q^{7} +(0.220095 + 0.145283i) q^{8} +(2.65436 - 6.21020i) q^{10} +(0.197285 - 4.39289i) q^{11} +(-2.83205 + 0.127187i) q^{13} +(-1.41823 + 4.36485i) q^{14} +(4.09710 - 1.13073i) q^{16} +(1.71469 + 1.24579i) q^{17} +(3.24472 - 0.588831i) q^{19} +(-2.78081 - 5.77442i) q^{20} +(-6.24923 - 5.97487i) q^{22} +(0.415918 - 1.82226i) q^{23} +(5.50025 - 3.99616i) q^{25} +(-3.47529 + 4.35788i) q^{26} +(2.23385 + 3.73883i) q^{28} +(-6.35391 + 6.07496i) q^{29} +(0.326285 - 1.18227i) q^{31} +(3.39703 - 7.05401i) q^{32} +(4.06278 - 0.927303i) q^{34} +(-6.03799 + 5.27524i) q^{35} +(0.00289836 + 0.0126986i) q^{37} +(3.32560 - 5.56611i) q^{38} +(0.873218 + 0.240993i) q^{40} +(2.50706 + 3.14376i) q^{41} +(-0.686909 + 0.410409i) q^{43} +(-8.17179 + 0.735475i) q^{44} +(-2.16013 - 2.97316i) q^{46} +(3.97443 + 7.38572i) q^{47} +(-1.07216 + 1.12139i) q^{49} +(1.19825 - 13.3136i) q^{50} +(0.944488 + 5.20456i) q^{52} +(-1.13823 + 8.40276i) q^{53} +(-4.01833 - 14.5601i) q^{55} +(-0.605688 - 0.109916i) q^{56} +(0.775454 + 17.2668i) q^{58} +(-11.0718 - 4.15531i) q^{59} +(-12.9690 - 5.54323i) q^{61} +(-1.32846 - 2.01254i) q^{62} +(-2.70928 - 6.33867i) q^{64} +(-9.11675 + 3.42157i) q^{65} +(-0.645269 + 0.0874077i) q^{67} +(1.87399 - 3.48245i) q^{68} +15.7645i q^{70} +(-6.76371 - 5.02515i) q^{71} +(11.9005 + 10.3972i) q^{73} +(0.0225518 + 0.0121357i) q^{74} +(-1.90142 - 5.85197i) q^{76} +(3.60660 + 9.60975i) q^{77} +(-5.49761 + 8.32853i) q^{79} +(12.1842 - 8.04273i) q^{80} +(7.89809 + 0.354703i) q^{82} +(1.08637 - 2.89463i) q^{83} +(6.92389 + 2.24971i) q^{85} +(-0.280921 + 1.54800i) q^{86} +(0.681635 - 0.938190i) q^{88} +(15.2244 + 2.06228i) q^{89} +(5.96194 - 2.87112i) q^{91} +(-3.47350 - 0.312620i) q^{92} +(16.0773 + 3.66953i) q^{94} +(9.97486 - 5.36770i) q^{95} +(1.66165 + 1.32512i) q^{97} +(0.273442 + 3.03819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 576 * q - 24 * q^4	\( 576 q - 24 q^{4} - 16 q^{10} + 76 q^{16} - 8 q^{19} + 20 q^{22} + 168 q^{25} - 20 q^{28} - 28 q^{31} + 40 q^{37} + 32 q^{40} + 52 q^{43} - 20 q^{46} - 208 q^{52} - 92 q^{55} + 56 q^{58} + 56 q^{61} - 144 q^{64} - 16 q^{67} - 44 q^{73} - 336 q^{76} + 88 q^{79} - 124 q^{82} + 60 q^{85} - 260 q^{88} + 80 q^{91} + 56 q^{94} - 56 q^{97}+O(q^{100}) \) 576 * q - 24 * q^4 - 16 * q^10 + 76 * q^16 - 8 * q^19 + 20 * q^22 + 168 * q^25 - 20 * q^28 - 28 * q^31 + 40 * q^37 + 32 * q^40 + 52 * q^43 - 20 * q^46 - 208 * q^52 - 92 * q^55 + 56 * q^58 + 56 * q^61 - 144 * q^64 - 16 * q^67 - 44 * q^73 - 336 * q^76 + 88 * q^79 - 124 * q^82 + 60 * q^85 - 260 * q^88 + 80 * q^91 + 56 * q^94 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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