LMFDB - Embedded newform 639.2.z.a.485.23

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			485.23
Character	$\chi$	$=$	639.485
Dual form			639.2.z.a.278.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88807 - 1.80518i) q^{2} +(0.216405 - 4.81862i) q^{4} +(1.07951 - 1.48582i) q^{5} +(-0.406367 - 0.0550462i) q^{7} +(-4.85259 - 5.55423i) q^{8} +O(q^{10})$	\(q+(1.88807 - 1.80518i) q^{2} +(0.216405 - 4.81862i) q^{4} +(1.07951 - 1.48582i) q^{5} +(-0.406367 - 0.0550462i) q^{7} +(-4.85259 - 5.55423i) q^{8} +(-0.643980 - 4.75405i) q^{10} +(-0.435059 + 0.259935i) q^{11} +(-1.18918 + 1.99036i) q^{13} +(-0.866618 + 0.629635i) q^{14} +(-9.58029 - 0.862242i) q^{16} +(0.630014 - 1.93898i) q^{17} +(-0.475736 + 0.720709i) q^{19} +(-6.92601 - 5.52331i) q^{20} +(-0.352191 + 1.27614i) q^{22} +(7.03857 + 3.38960i) q^{23} +(0.502765 + 1.54735i) q^{25} +(1.34769 + 5.90463i) q^{26} +(-0.353187 + 1.94622i) q^{28} +(0.0132957 + 0.0481760i) q^{29} +(-0.582259 - 6.46943i) q^{31} +(-8.11205 + 6.46915i) q^{32} +(-2.31070 - 4.79823i) q^{34} +(-0.520468 + 0.544366i) q^{35} +(2.28561 - 1.10069i) q^{37} +(0.402787 + 2.21954i) q^{38} +(-13.4910 + 1.21422i) q^{40} +(-1.57927 + 6.91923i) q^{41} +(-8.81340 - 1.59940i) q^{43} +(1.15838 + 2.15264i) q^{44} +(19.4081 - 6.30609i) q^{46} +(12.0068 - 4.50623i) q^{47} +(-6.58564 - 1.81752i) q^{49} +(3.74250 + 2.01393i) q^{50} +(9.33345 + 6.16096i) q^{52} +(0.477197 + 10.6256i) q^{53} +(-0.0834337 + 0.927024i) q^{55} +(1.66619 + 2.52417i) q^{56} +(0.112070 + 0.0669585i) q^{58} +(-3.11639 + 7.29115i) q^{59} +(8.56180 - 1.15977i) q^{61} +(-12.7778 - 11.1637i) q^{62} +(-1.05577 + 7.79400i) q^{64} +(1.67358 + 3.91554i) q^{65} +(-1.30847 - 0.0587635i) q^{67} +(-9.20690 - 3.45541i) q^{68} +1.96734i q^{70} +(-5.70241 - 6.20343i) q^{71} +(4.58808 + 4.79875i) q^{73} +(2.32844 - 6.20411i) q^{74} +(3.36987 + 2.44836i) q^{76} +(0.191102 - 0.0816809i) q^{77} +(4.30713 - 3.76303i) q^{79} +(-11.6232 + 13.3038i) q^{80} +(9.50868 + 15.9148i) q^{82} +(-8.67708 - 3.70876i) q^{83} +(-2.20088 - 3.02925i) q^{85} +(-19.5275 + 12.8900i) q^{86} +(3.55490 + 1.15506i) q^{88} +(10.9802 - 0.493120i) q^{89} +(0.592807 - 0.743357i) q^{91} +(17.8564 - 33.1827i) q^{92} +(14.5351 - 30.1825i) q^{94} +(0.557282 + 1.48487i) q^{95} +(8.45216 - 1.92915i) q^{97} +(-15.7151 + 8.45665i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/639\mathbb{Z}\right)^\times$.

$n$	$433$	$569$
$\chi(n)$	$e\left(\frac{3}{70}\right)$	$-1$

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 $

$2$	1.88807	−	1.80518i	1.33507	−	1.27645i	0.402518	−	0.915412i	$-0.368135\pi$
$2$	1.88807	−	1.80518i	1.33507	−	1.27645i	0.932549	−	0.361043i	$-0.117579\pi$
$3$		0			0
$3$		0			0
$4$	0.216405	−	4.81862i	0.108202	−	2.40931i
$5$	1.07951	−	1.48582i	0.482773	−	0.664480i	−0.496262	−	0.868173i	$-0.665294\pi$
$5$	1.07951	−	1.48582i	0.482773	−	0.664480i	0.979035	+	0.203693i	$0.0652944\pi$
$6$		0			0
$7$	−0.406367	−	0.0550462i	−0.153592	−	0.0208055i	0.0570334	−	0.998372i	$-0.481836\pi$
$7$	−0.406367	−	0.0550462i	−0.153592	−	0.0208055i	−0.210626	+	0.977567i	$0.567550\pi$
$8$	−4.85259	−	5.55423i	−1.71565	−	1.96372i
$9$		0			0
$10$	−0.643980	−	4.75405i	−0.203644	−	1.50336i
$11$	−0.435059	+	0.259935i	−0.131175	+	0.0783735i	−0.576988	−	0.816753i	$-0.695772\pi$
$11$	−0.435059	+	0.259935i	−0.131175	+	0.0783735i	0.445813	+	0.895126i	$0.352915\pi$
$12$		0			0
$13$	−1.18918	+	1.99036i	−0.329820	+	0.552026i	−0.977776	−	0.209652i	$-0.932767\pi$
$13$	−1.18918	+	1.99036i	−0.329820	+	0.552026i	0.647956	+	0.761678i	$0.275624\pi$
$14$	−0.866618	+	0.629635i	−0.231613	+	0.168277i
$15$		0			0
$16$	−9.58029	−	0.862242i	−2.39507	−	0.215560i
$17$	0.630014	−	1.93898i	0.152801	−	0.470273i	−0.845131	−	0.534560i	$-0.820477\pi$
$17$	0.630014	−	1.93898i	0.152801	−	0.470273i	0.997931	+	0.0642873i	$0.0204774\pi$
$18$		0			0
$19$	−0.475736	+	0.720709i	−0.109141	+	0.165342i	−0.885039	−	0.465517i	$-0.845869\pi$
$19$	−0.475736	+	0.720709i	−0.109141	+	0.165342i	0.775898	+	0.630858i	$0.217297\pi$
$20$	−6.92601	−	5.52331i	−1.54870	−	1.23505i
$21$		0			0
$22$	−0.352191	+	1.27614i	−0.0750874	+	0.272073i
$23$	7.03857	+	3.38960i	1.46764	+	0.706780i	0.985557	−	0.169344i	$-0.0541648\pi$
$23$	7.03857	+	3.38960i	1.46764	+	0.706780i	0.482087	+	0.876124i	$0.339879\pi$
$24$		0			0
$25$	0.502765	+	1.54735i	0.100553	+	0.309470i
$26$	1.34769	+	5.90463i	0.264304	+	1.15799i
$27$		0			0
$28$	−0.353187	+	1.94622i	−0.0667460	+	0.367801i
$29$	0.0132957	+	0.0481760i	0.00246896	+	0.00894607i	0.965187	−	0.261561i	$-0.0842372\pi$
$29$	0.0132957	+	0.0481760i	0.00246896	+	0.00894607i	−0.962718	+	0.270507i	$0.912809\pi$
$30$		0			0
$31$	−0.582259	−	6.46943i	−0.104577	−	1.16194i	−0.861261	−	0.508163i	$-0.830325\pi$
$31$	−0.582259	−	6.46943i	−0.104577	−	1.16194i	0.756684	−	0.653781i	$-0.226818\pi$
$32$	−8.11205	+	6.46915i	−1.43402	+	1.14359i
$33$		0			0
$34$	−2.31070	−	4.79823i	−0.396282	−	0.822889i
$35$	−0.520468	+	0.544366i	−0.0879751	+	0.0920147i
$36$		0			0
$37$	2.28561	−	1.10069i	0.375751	−	0.180952i	−0.236470	−	0.971639i	$-0.575990\pi$
$37$	2.28561	−	1.10069i	0.375751	−	0.180952i	0.612221	+	0.790686i	$0.290276\pi$
$38$	0.402787	+	2.21954i	0.0653406	+	0.360056i
$39$		0			0
$40$	−13.4910	+	1.21422i	−2.13312	+	0.191984i
$41$	−1.57927	+	6.91923i	−0.246640	+	1.08060i	0.688197	+	0.725524i	$0.258403\pi$
$41$	−1.57927	+	6.91923i	−0.246640	+	1.08060i	−0.934837	+	0.355077i	$0.884455\pi$
$42$		0			0
$43$	−8.81340	−	1.59940i	−1.34403	−	0.243906i	−0.541592	−	0.840641i	$-0.682178\pi$
$43$	−8.81340	−	1.59940i	−1.34403	−	0.243906i	−0.802438	+	0.596736i	$0.796464\pi$
$44$	1.15838	+	2.15264i	0.174633	+	0.324522i
$45$		0			0
$46$	19.4081	−	6.30609i	2.86158	−	0.929782i
$47$	12.0068	−	4.50623i	1.75137	−	0.657301i	0.751376	−	0.659874i	$-0.229391\pi$
$47$	12.0068	−	4.50623i	1.75137	−	0.657301i	0.999997	+	0.00257326i	$0.000819094\pi$
$48$		0			0
$49$	−6.58564	−	1.81752i	−0.940805	−	0.259646i
$50$	3.74250	+	2.01393i	0.529270	+	0.284812i
$51$		0			0
$52$	9.33345	+	6.16096i	1.29432	+	0.854371i
$53$	0.477197	+	10.6256i	0.0655481	+	1.45954i	0.714992	+	0.699132i	$0.246430\pi$
$53$	0.477197	+	10.6256i	0.0655481	+	1.45954i	−0.649444	+	0.760409i	$0.724998\pi$
$54$		0			0
$55$	−0.0834337	+	0.927024i	−0.0112502	+	0.125000i
$56$	1.66619	+	2.52417i	0.222654	+	0.337307i
$57$		0			0
$58$	0.112070	+	0.0669585i	0.0147155	+	0.00879209i
$59$	−3.11639	+	7.29115i	−0.405719	+	0.949228i	0.584715	+	0.811239i	$0.301207\pi$
$59$	−3.11639	+	7.29115i	−0.405719	+	0.949228i	−0.990434	+	0.137988i	$0.955936\pi$
$60$		0			0
$61$	8.56180	−	1.15977i	1.09623	−	0.148494i	0.436283	−	0.899810i	$-0.356295\pi$
$61$	8.56180	−	1.15977i	1.09623	−	0.148494i	0.659943	+	0.751316i	$0.270580\pi$
$62$	−12.7778	−	11.1637i	−1.62279	−	1.41779i
$63$		0			0
$64$	−1.05577	+	7.79400i	−0.131971	+	0.974250i
$65$	1.67358	+	3.91554i	0.207582	+	0.485663i
$66$		0			0
$67$	−1.30847	−	0.0587635i	−0.159855	−	0.00717911i	−0.0352066	−	0.999380i	$-0.511209\pi$
$67$	−1.30847	−	0.0587635i	−0.159855	−	0.00717911i	−0.124649	+	0.992201i	$0.539780\pi$
$68$	−9.20690	−	3.45541i	−1.11650	−	0.419030i
$69$		0			0
$70$			1.96734i			0.235142i
$71$	−5.70241	−	6.20343i	−0.676751	−	0.736212i
$71$	−5.70241	−	6.20343i	−0.676751	−	0.736212i
$72$		0			0
$73$	4.58808	+	4.79875i	0.536994	+	0.561652i	0.934507	−	0.355945i	$-0.115841\pi$
$73$	4.58808	+	4.79875i	0.536994	+	0.561652i	−0.397513	+	0.917597i	$0.630127\pi$
$74$	2.32844	−	6.20411i	0.270676	−	0.721213i
$75$		0			0
$76$	3.36987	+	2.44836i	0.386551	+	0.280846i
$77$	0.191102	−	0.0816809i	0.0217781	−	0.00930841i
$78$		0			0
$79$	4.30713	−	3.76303i	0.484590	−	0.423373i	−0.380659	−	0.924715i	$-0.624303\pi$
$79$	4.30713	−	3.76303i	0.484590	−	0.423373i	0.865249	+	0.501342i	$0.167160\pi$
$80$	−11.6232	+	13.3038i	−1.29951	+	1.48741i
$81$		0			0
$82$	9.50868	+	15.9148i	1.05006	+	1.75750i
$83$	−8.67708	−	3.70876i	−0.952433	−	0.407089i	−0.140005	−	0.990151i	$-0.544712\pi$
$83$	−8.67708	−	3.70876i	−0.952433	−	0.407089i	−0.812428	+	0.583061i	$0.801855\pi$
$84$		0			0
$85$	−2.20088	−	3.02925i	−0.238719	−	0.328568i
$86$	−19.5275	+	12.8900i	−2.10571	+	1.38996i
$87$		0			0
$88$	3.55490	+	1.15506i	0.378954	+	0.123130i
$89$	10.9802	−	0.493120i	1.16390	−	0.0522706i	0.545481	−	0.838123i	$-0.316347\pi$
$89$	10.9802	−	0.493120i	1.16390	−	0.0522706i	0.618414	+	0.785852i	$0.287775\pi$
$90$		0			0
$91$	0.592807	−	0.743357i	0.0621431	−	0.0779250i
$92$	17.8564	−	33.1827i	1.86166	−	3.45954i
$93$		0			0
$94$	14.5351	−	30.1825i	1.49918	−	3.11309i
$95$	0.557282	+	1.48487i	0.0571760	+	0.152345i
$96$		0			0
$97$	8.45216	−	1.92915i	0.858187	−	0.195876i	0.229284	−	0.973359i	$-0.426361\pi$
$97$	8.45216	−	1.92915i	0.858187	−	0.195876i	0.628903	+	0.777484i	$0.283504\pi$
$98$	−15.7151	+	8.45665i	−1.58746	+	0.854251i
$99$		0			0
$100$	7.56491	−	2.08778i	0.756491	−	0.208778i
$101$	8.86133	+	2.02254i	0.881735	+	0.201250i	0.639337	−	0.768926i	$-0.279209\pi$
$101$	8.86133	+	2.02254i	0.881735	+	0.201250i	0.242398	+	0.970177i	$0.422066\pi$
$102$		0			0
$103$	−5.69922	−	7.14660i	−0.561561	−	0.704175i	0.417285	−	0.908776i	$-0.362982\pi$
$103$	−5.69922	−	7.14660i	−0.561561	−	0.704175i	−0.978845	+	0.204601i	$0.934410\pi$
$104$	16.8255	−	3.05339i	1.64988	−	0.299409i
$105$		0			0
$106$	20.0821	+	19.2005i	1.95055	+	1.86492i
$107$	8.69959	+	8.31766i	0.841021	+	0.804099i	0.982582	−	0.185831i	$-0.0594977\pi$
$107$	8.69959	+	8.31766i	0.841021	+	0.804099i	−0.141561	+	0.989930i	$0.545212\pi$
$108$		0			0
$109$	−16.2551	+	2.94987i	−1.55696	+	0.282546i	−0.887677	−	0.460466i	$-0.847682\pi$
$109$	−16.2551	+	2.94987i	−1.55696	+	0.282546i	−0.669279	+	0.743012i	$0.733397\pi$
$110$	1.51592	+	1.90090i	0.144537	+	0.181244i
$111$		0			0
$112$	3.84565	+	0.877745i	0.363380	+	0.0829391i
$113$	4.85775	−	1.34065i	0.456979	−	0.126118i	−0.0299661	−	0.999551i	$-0.509540\pi$
$113$	4.85775	−	1.34065i	0.456979	−	0.126118i	0.486945	+	0.873433i	$0.338111\pi$
$114$		0			0
$115$	12.6346	−	6.79895i	1.17818	−	0.634006i
$116$	0.235020	−	0.0536417i	0.0218210	−	0.00498050i
$117$		0			0
$118$	7.27788	+	19.3919i	0.669984	+	1.78516i
$119$	−0.362751	+	0.753259i	−0.0332533	+	0.0690512i
$120$		0			0
$121$	−5.09085	+	9.46038i	−0.462804	+	0.860034i
$122$	14.0717	−	17.6453i	1.27399	−	1.59753i
$123$		0			0
$124$	−31.2998	+	1.40567i	−2.81080	+	0.126233i
$125$	11.5753	+	3.76104i	1.03532	+	0.336397i
$126$		0			0
$127$	−16.7868	+	11.0809i	−1.48959	+	0.983268i	−0.496232	+	0.868190i	$0.665283\pi$
$127$	−16.7868	+	11.0809i	−1.48959	+	0.983268i	−0.993356	+	0.115078i	$0.963288\pi$
$128$	−0.121172	−	0.166778i	−0.0107102	−	0.0147413i
$129$		0			0
$130$	10.2281	+	4.37169i	0.897062	+	0.383423i
$131$	7.77843	+	13.0189i	0.679605	+	1.13747i	0.982824	+	0.184546i	$0.0590815\pi$
$131$	7.77843	+	13.0189i	0.679605	+	1.13747i	−0.303219	+	0.952921i	$0.598061\pi$
$132$		0			0
$133$	0.232996	−	0.266685i	0.0202033	−	0.0231245i
$134$	−2.57656	+	2.25108i	−0.222581	+	0.194463i
$135$		0			0
$136$	−13.8268	+	5.90984i	−1.18564	+	0.506765i
$137$	−9.20474	−	6.68764i	−0.786414	−	0.571363i	0.120483	−	0.992715i	$-0.461556\pi$
$137$	−9.20474	−	6.68764i	−0.786414	−	0.571363i	−0.906897	+	0.421352i	$0.861556\pi$
$138$		0			0
$139$	−0.225097	+	0.599770i	−0.0190925	+	0.0508718i	−0.945436	−	0.325809i	$-0.894363\pi$
$139$	−0.225097	+	0.599770i	−0.0190925	+	0.0508718i	0.926343	+	0.376681i	$0.122935\pi$
$140$	2.51047	+	2.62574i	0.212173	+	0.221916i
$141$		0			0
$142$	−21.9649	−	1.41864i	−1.84325	−	0.119050i
$143$		−	1.17503i		−	0.0982613i
$144$		0			0
$145$	0.0859340	+	0.0322516i	0.00713643	+	0.00267835i
$146$	17.3252	+	0.778077i	1.43385	+	0.0643941i
$147$		0			0
$148$	−4.80920	−	11.2517i	−0.395313	−	0.924882i
$149$	−0.740162	+	5.46410i	−0.0606364	+	0.447636i	0.935025	+	0.354583i	$0.115377\pi$
$149$	−0.740162	+	5.46410i	−0.0606364	+	0.447636i	−0.995661	+	0.0930535i	$0.970337\pi$
$150$		0			0
$151$	−4.48332	−	3.91696i	−0.364847	−	0.318757i	0.455919	−	0.890021i	$-0.349311\pi$
$151$	−4.48332	−	3.91696i	−0.364847	−	0.318757i	−0.820767	+	0.571264i	$0.806453\pi$
$152$	6.31153	−	0.854955i	0.511933	−	0.0693460i
$153$		0			0
$154$	0.213365	−	0.499193i	0.0171935	−	0.0402261i
$155$	−10.2410	−	6.11870i	−0.822575	−	0.491466i
$156$		0			0
$157$	1.69692	+	2.57072i	0.135429	+	0.205166i	0.895959	−	0.444136i	$-0.146489\pi$
$157$	1.69692	+	2.57072i	0.135429	+	0.205166i	−0.760530	+	0.649303i	$0.775061\pi$
$158$	1.33922	−	14.8800i	0.106543	−	1.18379i
$159$		0			0
$160$	0.854935	+	19.0366i	0.0675885	+	1.50498i
$161$	−2.67366	−	1.76487i	−0.210714	−	0.139091i
$162$		0			0
$163$	−11.9535	−	6.43248i	−0.936274	−	0.503831i	−0.0667766	−	0.997768i	$-0.521271\pi$
$163$	−11.9535	−	6.43248i	−0.936274	−	0.503831i	−0.869497	+	0.493937i	$0.835557\pi$
$164$	32.9994	+	9.10725i	2.57682	+	0.711157i
$165$		0			0
$166$	−23.0779	+	8.66128i	−1.79119	+	0.672246i
$167$	−5.08173	+	1.65115i	−0.393236	+	0.127770i	−0.498959	−	0.866625i	$-0.666284\pi$
$167$	−5.08173	+	1.65115i	−0.393236	+	0.127770i	0.105723	+	0.994396i	$0.466284\pi$
$168$		0			0
$169$	3.61292	+	6.71393i	0.277917	+	0.516456i
$170$	−9.62375	−	1.74645i	−0.738108	−	0.133947i
$171$		0			0
$172$	−9.61415	+	42.1223i	−0.733072	+	3.21180i
$173$	−0.278673	+	0.0250810i	−0.0211871	+	0.00190688i	−0.100228	−	0.994965i	$-0.531957\pi$
$173$	−0.278673	+	0.0250810i	−0.0211871	+	0.00190688i	0.0790407	+	0.996871i	$0.474814\pi$
$174$		0			0
$175$	−0.119131	−	0.656468i	−0.00900549	−	0.0496244i
$176$	4.39212	−	2.11513i	0.331068	−	0.159434i
$177$		0			0
$178$	19.8412	−	20.7522i	1.48716	−	1.55544i
$179$	−8.41255	−	17.4688i	−0.628784	−	1.30568i	−0.935313	−	0.353822i	$-0.884882\pi$
$179$	−8.41255	−	17.4688i	−0.628784	−	1.30568i	0.306529	−	0.951861i	$-0.400832\pi$
$180$		0			0
$181$	−8.84480	+	7.05349i	−0.657429	+	0.524282i	−0.894419	−	0.447230i	$-0.852410\pi$
$181$	−8.84480	+	7.05349i	−0.657429	+	0.524282i	0.236990	+	0.971512i	$0.423839\pi$
$182$	−0.222631	−	2.47363i	−0.0165025	−	0.183358i
$183$		0			0
$184$	−15.3287	−	55.5422i	−1.13004	−	4.09463i
$185$	0.831912	−	4.58421i	0.0611634	−	0.337038i
$186$		0			0
$187$	0.229918	+	1.00733i	0.0168132	+	0.0736636i
$188$	−19.1155	−	58.8315i	−1.39414	−	4.29073i
$189$		0			0
$190$	3.73265	+	1.79755i	0.270795	+	0.130408i
$191$	−3.77353	+	13.6731i	−0.273043	+	0.989348i	0.690837	+	0.723011i	$0.257242\pi$
$191$	−3.77353	+	13.6731i	−0.273043	+	0.989348i	−0.963880	+	0.266338i	$0.914186\pi$
$192$		0			0
$193$	10.5161	+	8.38634i	0.756968	+	0.603662i	0.924046	−	0.382282i	$-0.124862\pi$
$193$	10.5161	+	8.38634i	0.756968	+	0.603662i	−0.167077	+	0.985944i	$0.553433\pi$
$194$	12.4758	−	18.9000i	0.895711	−	1.35694i
$195$		0			0
$196$	−10.1831	+	31.3404i	−0.727365	+	2.23860i
$197$	−4.92968	−	0.443679i	−0.351225	−	0.0316108i	−0.0873777	−	0.996175i	$-0.527849\pi$
$197$	−4.92968	−	0.443679i	−0.351225	−	0.0316108i	−0.263847	+	0.964564i	$0.584992\pi$
$198$		0			0
$199$	−8.62140	+	6.26382i	−0.611155	+	0.444030i	−0.849821	−	0.527072i	$-0.823290\pi$
$199$	−8.62140	+	6.26382i	−0.611155	+	0.444030i	0.238666	+	0.971102i	$0.423290\pi$
$200$	6.15464	−	10.3011i	0.435199	−	0.728401i
$201$		0			0
$202$	20.3819	−	12.1776i	1.43406	−	0.856813i
$203$	−0.00275105	−	0.0203090i	−0.000193086	−	0.00142542i
$204$		0			0
$205$	8.57590	+	9.81591i	0.598967	+	0.685573i
$206$	−23.6614	−	3.20516i	−1.64857	−	0.223314i
$207$		0			0
$208$	13.1089	−	18.0429i	0.908939	−	1.25105i
$209$	0.0196352	−	0.437211i	0.00135819	−	0.0302425i
$210$		0			0
$211$	−0.764809	+	0.731232i	−0.0526516	+	0.0503401i	−0.716930	−	0.697145i	$-0.754453\pi$
$211$	−0.764809	+	0.731232i	−0.0526516	+	0.0503401i	0.664278	+	0.747485i	$0.268739\pi$
$212$	51.3042			3.52358
$213$		0			0
$214$	31.4403			2.14922
$215$	−11.8906	+	11.3686i	−0.810932	+	0.775330i
$216$		0			0
$217$	−0.119506	+	2.66101i	−0.00811262	+	0.180641i
$218$	−25.3657	+	34.9129i	−1.71798	+	2.36460i
$219$		0			0
$220$	4.44892	+	0.602648i	0.299946	+	0.0406305i
$221$	3.11007	+	3.55976i	0.209206	+	0.239456i
$222$		0			0
$223$	−1.88288	−	13.9000i	−0.126087	−	0.930810i	−0.937903	−	0.346897i	$-0.887235\pi$
$223$	−1.88288	−	13.9000i	−0.126087	−	0.930810i	0.811816	−	0.583913i	$-0.198479\pi$
$224$	3.65257	−	2.18231i	0.244048	−	0.145812i
$225$		0			0
$226$	6.75165	−	11.3004i	0.449113	−	0.751689i
$227$	11.5624	−	8.40057i	0.767423	−	0.557565i	−0.133755	−	0.991014i	$-0.542704\pi$
$227$	11.5624	−	8.40057i	0.767423	−	0.557565i	0.901178	+	0.433449i	$0.142704\pi$
$228$		0			0
$229$	−25.9035	−	2.33136i	−1.71175	−	0.154061i	−0.810035	−	0.586382i	$-0.800552\pi$
$229$	−25.9035	−	2.33136i	−1.71175	−	0.154061i	−0.901720	+	0.432321i	$0.857695\pi$
$230$	11.5816	−	35.6446i	0.763670	−	2.35033i
$231$		0			0
$232$	0.203062	−	0.307626i	0.0133317	−	0.0201966i
$233$	−9.29333	−	7.41118i	−0.608826	−	0.485523i	0.269875	−	0.962895i	$-0.413018\pi$
$233$	−9.29333	−	7.41118i	−0.608826	−	0.485523i	−0.878701	+	0.477373i	$0.841589\pi$
$234$		0			0
$235$	6.26605	−	22.7045i	0.408752	−	1.48108i
$236$	34.4589	+	16.5946i	2.24309	+	1.08021i
$237$		0			0
$238$	0.674870	+	2.07704i	0.0437453	+	0.134634i
$239$	−1.02401	−	4.48646i	−0.0662374	−	0.290205i	0.930951	−	0.365145i	$-0.118981\pi$
$239$	−1.02401	−	4.48646i	−0.0662374	−	0.290205i	−0.997188	+	0.0749400i	$0.976123\pi$
$240$		0			0
$241$	1.53138	−	8.43858i	0.0986447	−	0.543577i	−0.896325	−	0.443398i	$-0.853773\pi$
$241$	1.53138	−	8.43858i	0.0986447	−	0.543577i	0.994969	−	0.100179i	$-0.0319415\pi$
$242$	7.46581	+	27.0517i	0.479920	+	1.73895i
$243$		0			0
$244$	−3.73570	−	41.5071i	−0.239154	−	2.65722i
$245$	−9.80979	+	7.82305i	−0.626725	+	0.499796i
$246$		0			0
$247$	−0.868732	−	1.80394i	−0.0552761	−	0.114782i
$248$	−33.1073	+	34.6275i	−2.10231	+	2.19885i
$249$		0			0
$250$	28.6443	−	13.7944i	1.81162	−	0.872432i
$251$	−0.264011	−	1.45482i	−0.0166642	−	0.0918274i	0.974526	−	0.224276i	$-0.0720017\pi$
$251$	−0.264011	−	1.45482i	−0.0166642	−	0.0918274i	−0.991190	+	0.132449i	$0.957716\pi$
$252$		0			0
$253$	−3.94327	+	0.354901i	−0.247911	+	0.0223124i
$254$	−11.6917	+	51.2247i	−0.733602	+	3.21412i
$255$		0			0
$256$	−16.0074	−	2.90492i	−1.00046	−	0.181557i
$257$	−13.2535	−	24.6291i	−0.826729	−	1.53632i	−0.843921	−	0.536467i	$-0.819759\pi$
$257$	−13.2535	−	24.6291i	−0.826729	−	1.53632i	0.0171926	−	0.999852i	$-0.494527\pi$
$258$		0			0
$259$	−0.989384	+	0.321470i	−0.0614773	+	0.0199752i
$260$	19.2297	−	7.21702i	1.19257	−	0.447580i
$261$		0			0
$262$	38.1877	+	10.5391i	2.35924	+	0.651110i
$263$	−20.2374	−	10.8902i	−1.24789	−	0.671518i	−0.289554	−	0.957162i	$-0.593507\pi$
$263$	−20.2374	−	10.8902i	−1.24789	−	0.671518i	−0.958336	+	0.285643i	$0.907793\pi$
$264$		0			0
$265$	16.3029	+	10.7615i	1.00148	+	0.661072i
$266$	−0.0415022	−	0.924119i	−0.00254466	−	0.0566614i
$267$		0			0
$268$	−0.566319	+	6.29232i	−0.0345934	+	0.384364i
$269$	−2.29402	−	3.47529i	−0.139869	−	0.211892i	0.757887	−	0.652386i	$-0.226232\pi$
$269$	−2.29402	−	3.47529i	−0.139869	−	0.211892i	−0.897756	+	0.440494i	$0.854803\pi$
$270$		0			0
$271$	8.86059	+	5.29396i	0.538243	+	0.321585i	0.756165	−	0.654381i	$-0.227071\pi$
$271$	8.86059	+	5.29396i	0.538243	+	0.321585i	−0.217922	+	0.975966i	$0.569928\pi$
$272$	−7.70759	+	18.0328i	−0.467341	+	1.09340i
$273$		0			0
$274$	−29.4516	+	3.98949i	−1.77924	+	0.241014i
$275$	−0.620944	−	0.542503i	−0.0374443	−	0.0327141i
$276$		0			0
$277$	−2.90113	+	21.4170i	−0.174312	+	1.28682i	0.666503	+	0.745502i	$0.267790\pi$
$277$	−2.90113	+	21.4170i	−0.174312	+	1.28682i	−0.840816	+	0.541322i	$0.817924\pi$
$278$	0.657693	+	1.53875i	0.0394458	+	0.0922881i
$279$		0			0
$280$	5.54915	+	0.249213i	0.331625	+	0.0148933i
$281$	−0.0495740	−	0.0186054i	−0.00295734	−	0.00110991i	0.349896	−	0.936789i	$-0.386217\pi$
$281$	−0.0495740	−	0.0186054i	−0.00295734	−	0.00110991i	−0.352853	+	0.935679i	$0.614788\pi$
$282$		0			0
$283$			13.8666i			0.824285i	0.911119	+	0.412143i	$0.135219\pi$
$283$			13.8666i			0.824285i	−0.911119	+	0.412143i	$0.864781\pi$
$284$	−31.1260	+	26.1353i	−1.84699	+	1.55085i
$285$		0			0
$286$	−2.12115	−	2.21855i	−0.125426	−	0.131185i
$287$	1.02264	−	2.72481i	0.0603645	−	0.160841i
$288$		0			0
$289$	10.3905	+	7.54918i	0.611209	+	0.444069i
$290$	0.220469	−	0.0942331i	0.0129464	−	0.00553356i
$291$		0			0
$292$	24.1163	−	21.0698i	1.41130	−	1.23301i
$293$	0.0751923	−	0.0860645i	0.00439278	−	0.00502794i	−0.750871	−	0.660449i	$-0.770366\pi$
$293$	0.0751923	−	0.0860645i	0.00439278	−	0.00502794i	0.755264	+	0.655421i	$0.227509\pi$
$294$		0			0
$295$	7.46918	+	12.5013i	0.434872	+	0.727854i
$296$	−17.2046	−	7.35360i	−0.999997	−	0.427419i
$297$		0			0
$298$	8.46620	+	11.6527i	0.490434	+	0.675024i
$299$	−15.1167	+	9.97843i	−0.874220	+	0.577068i
$300$		0			0
$301$	3.49343	+	1.13509i	0.201358	+	0.0654252i
$302$	−15.5356	+	0.697706i	−0.893975	+	0.0401484i
$303$		0			0
$304$	5.17911	−	6.49440i	0.297042	−	0.372479i
$305$	7.51936	−	13.9733i	0.430557	−	0.800109i
$306$		0			0
$307$	2.53579	−	5.26562i	0.144725	−	0.300525i	−0.815988	−	0.578069i	$-0.803806\pi$
$307$	2.53579	−	5.26562i	0.144725	−	0.300525i	0.960713	+	0.277545i	$0.0895206\pi$
$308$	−0.352234	−	0.938525i	−0.0200704	−	0.0534774i
$309$		0			0
$310$	−30.3810	+	6.93427i	−1.72553	+	0.393840i
$311$	−16.2375	+	8.73776i	−0.920743	+	0.495473i	−0.864325	−	0.502934i	$-0.832254\pi$
$311$	−16.2375	+	8.73776i	−0.920743	+	0.495473i	−0.0564184	+	0.998407i	$0.517968\pi$
$312$		0			0
$313$	−26.6297	+	7.34933i	−1.50520	+	0.415409i	−0.918836	−	0.394640i	$-0.870869\pi$
$313$	−26.6297	+	7.34933i	−1.50520	+	0.415409i	−0.586363	+	0.810048i	$0.699441\pi$
$314$	7.84452	+	1.79046i	0.442692	+	0.101042i
$315$		0			0
$316$	−17.2005	−	21.5688i	−0.967605	−	1.21334i
$317$	−1.93509	+	0.351167i	−0.108686	+	0.0197235i	−0.232627	−	0.972566i	$-0.574732\pi$
$317$	−1.93509	+	0.351167i	−0.108686	+	0.0197235i	0.123942	+	0.992290i	$0.460446\pi$
$318$		0			0
$319$	−0.0183071	−	0.0175034i	−0.00102500	−	0.000980001i
$320$	10.4408	+	9.98241i	0.583657	+	0.558034i
$321$		0			0
$322$	−8.23396	+	1.49424i	−0.458861	+	0.0832709i
$323$	1.09772	+	1.37650i	0.0610789	+	0.0765905i
$324$		0			0
$325$	−3.67767	−	0.839404i	−0.204000	−	0.0465617i
$326$	−34.1809	+	9.43333i	−1.89311	+	0.522464i
$327$		0			0
$328$	46.0945	−	24.8045i	2.54514	−	1.36960i
$329$	−5.12722	+	1.17026i	−0.282673	+	0.0645182i
$330$		0			0
$331$	4.47722	+	11.9295i	0.246091	+	0.655706i	0.999999	−	0.00127339i	$-0.000405334\pi$
$331$	4.47722	+	11.9295i	0.246091	+	0.655706i	−0.753909	+	0.656979i	$0.771834\pi$
$332$	−19.7489	+	41.0090i	−1.08386	+	2.25066i
$333$		0			0
$334$	−6.61403	+	12.2909i	−0.361904	+	0.672530i
$335$	−1.49982	+	1.88072i	−0.0819442	+	0.102755i
$336$		0			0
$337$	−25.2820	+	1.13542i	−1.37720	+	0.0618501i	−0.721104	−	0.692827i	$-0.756365\pi$
$337$	−25.2820	+	1.13542i	−1.37720	+	0.0618501i	−0.656096	+	0.754677i	$0.727793\pi$
$338$	18.9413	+	6.15440i	1.03027	+	0.334755i
$339$		0			0
$340$	−15.0731	+	9.94966i	−0.817453	+	0.539596i
$341$	1.93495	+	2.66323i	0.104783	+	0.144222i
$342$		0			0
$343$	5.21569	+	2.22929i	0.281621	+	0.120370i
$344$	33.8844	+	56.7129i	1.82692	+	3.05775i
$345$		0			0
$346$	−0.480879	+	0.550410i	−0.0258522	+	0.0295902i
$347$	−16.8111	+	14.6874i	−0.902468	+	0.788462i	−0.977983	−	0.208682i	$-0.933082\pi$
$347$	−16.8111	+	14.6874i	−0.902468	+	0.788462i	0.0755159	+	0.997145i	$0.475940\pi$
$348$		0			0
$349$	28.7235	−	12.2770i	1.53753	−	0.657174i	0.553130	−	0.833095i	$-0.313433\pi$
$349$	28.7235	−	12.2770i	1.53753	−	0.657174i	0.984404	+	0.175921i	$0.0562905\pi$
$350$	−1.40997	−	1.02440i	−0.0753662	−	0.0547567i
$351$		0			0
$352$	1.84766	−	4.92307i	0.0984805	−	0.262400i
$353$	20.3519	+	21.2864i	1.08322	+	1.13296i	0.990534	+	0.137265i	$0.0438311\pi$
$353$	20.3519	+	21.2864i	1.08322	+	1.13296i	0.0926863	+	0.995695i	$0.470455\pi$
$354$		0			0
$355$	−15.3730	+	1.77608i	−0.815915	+	0.0942646i
$356$		−	53.0160i		−	2.80984i
$357$		0			0
$358$	−47.4179	−	17.7962i	−2.50611	−	0.940560i
$359$	21.9406	+	0.985354i	1.15798	+	0.0520050i	0.615552	−	0.788097i	$-0.288933\pi$
$359$	21.9406	+	0.985354i	1.15798	+	0.0520050i	0.542429	+	0.840102i	$0.317505\pi$
$360$		0			0
$361$	7.17438	+	16.7853i	0.377599	+	0.883437i
$362$	−3.96678	+	29.2839i	−0.208489	+	1.53913i
$363$		0			0
$364$	−3.45367	−	3.01738i	−0.181022	−	0.158154i
$365$	12.0830	−	1.63675i	0.632452	−	0.0856715i
$366$		0			0
$367$	9.10848	−	21.3103i	0.475459	−	1.11239i	−0.494512	−	0.869171i	$-0.664653\pi$
$367$	9.10848	−	21.3103i	0.475459	−	1.11239i	0.969971	−	0.243220i	$-0.0782038\pi$
$368$	−64.5089	−	38.5423i	−3.36276	−	2.00915i
$369$		0			0
$370$	−6.70462	−	10.1571i	−0.348557	−	0.528041i
$371$	0.390983	−	4.34417i	0.0202988	−	0.225538i
$372$		0			0
$373$	1.22141	+	27.1968i	0.0632423	+	1.40820i	0.740304	+	0.672272i	$0.234682\pi$
$373$	1.22141	+	27.1968i	0.0632423	+	1.40820i	−0.677062	+	0.735926i	$0.736747\pi$
$374$	2.25252	+	1.48688i	0.116475	+	0.0768845i
$375$		0			0
$376$	−83.2927	−	44.8217i	−4.29550	−	2.31150i
$377$	−0.111699	−	0.0308269i	−0.00575278	−	0.00158767i
$378$		0			0
$379$	−19.4475	+	7.29876i	−0.998949	+	0.374912i	−0.796669	−	0.604416i	$-0.793407\pi$
$379$	−19.4475	+	7.29876i	−0.998949	+	0.374912i	−0.202280	+	0.979328i	$0.564835\pi$
$380$	7.27565	−	2.36400i	0.373233	−	0.121271i
$381$		0			0
$382$	17.5577	+	32.6276i	0.898328	+	1.66937i
$383$	−22.1569	−	4.02089i	−1.13217	−	0.205458i	−0.420038	−	0.907507i	$-0.637983\pi$
$383$	−22.1569	−	4.02089i	−1.13217	−	0.205458i	−0.712129	+	0.702049i	$0.752269\pi$
$384$		0			0
$385$	0.0849338	−	0.372119i	0.00432863	−	0.0189650i
$386$	34.9941	−	3.14952i	1.78115	−	0.160306i
$387$		0			0
$388$	−7.46677	−	41.1453i	−0.379068	−	2.08884i
$389$	29.7416	−	14.3228i	1.50796	−	0.726194i	0.516460	−	0.856312i	$-0.327250\pi$
$389$	29.7416	−	14.3228i	1.50796	−	0.726194i	0.991499	+	0.130117i	$0.0415353\pi$
$390$		0			0
$391$	11.0068	−	11.5122i	0.556636	−	0.582196i
$392$	21.8624	+	45.3978i	1.10422	+	2.29294i
$393$		0			0
$394$	−10.1085	+	8.06126i	−0.509259	+	0.406121i
$395$	−0.941585	−	10.4619i	−0.0473763	−	0.526394i
$396$		0			0
$397$	−2.30181	−	8.34043i	−0.115525	−	0.418594i	0.883205	−	0.468988i	$-0.155381\pi$
$397$	−2.30181	−	8.34043i	−0.115525	−	0.418594i	−0.998729	+	0.0503933i	$0.983953\pi$
$398$	−4.97050	+	27.3897i	−0.249149	+	1.37292i
$399$		0			0
$400$	−3.48244	−	15.2576i	−0.174122	−	0.762879i
$401$	−6.41669	−	19.7486i	−0.320434	−	0.986196i	−0.973459	−	0.228859i	$-0.926500\pi$
$401$	−6.41669	−	19.7486i	−0.320434	−	0.986196i	0.653025	−	0.757336i	$-0.273500\pi$
$402$		0			0
$403$	13.5689	+	6.53444i	0.675915	+	0.325504i
$404$	11.6635	−	42.2617i	0.580281	−	2.10260i
$405$		0			0
$406$	−0.0418556	−	0.0333788i	−0.00207726	−	0.00165656i
$407$	−0.708265	+	1.07297i	−0.0351074	+	0.0531854i
$408$		0			0
$409$	0.570704	−	1.75645i	0.0282195	−	0.0868507i	−0.935955	−	0.352120i	$-0.885461\pi$
$409$	0.570704	−	1.75645i	0.0282195	−	0.0868507i	0.964174	+	0.265269i	$0.0854609\pi$
$410$	33.9114	+	3.05208i	1.67476	+	0.150731i
$411$		0			0
$412$	−35.6701	+	25.9158i	−1.75734	+	1.27678i
$413$	1.66775	−	2.79134i	0.0820645	−	0.137353i
$414$		0			0
$415$	−14.8776	+	8.88894i	−0.730312	+	0.436341i
$416$	−3.22920	−	23.8389i	−0.158325	−	1.16880i
$417$		0			0
$418$	−0.752172	−	0.860930i	−0.0367899	−	0.0421095i
$419$	−1.00511	−	0.136151i	−0.0491027	−	0.00665141i	0.109641	−	0.993971i	$-0.465030\pi$
$419$	−1.00511	−	0.136151i	−0.0491027	−	0.00665141i	−0.158743	+	0.987320i	$0.550744\pi$
$420$		0			0
$421$	14.2532	−	19.6179i	0.694659	−	0.956116i	−0.305333	−	0.952246i	$-0.598768\pi$
$421$	14.2532	−	19.6179i	0.694659	−	0.956116i	0.999993	−	0.00387082i	$-0.00123212\pi$
$422$	−0.124007	+	2.76123i	−0.00603658	+	0.134415i
$423$		0			0
$424$	56.7016	−	54.2122i	2.75367	−	2.63278i
$425$	3.31704			0.160900
$426$		0			0
$427$	−3.54307			−0.171461
$428$	41.9623	−	40.1201i	2.02833	−	1.93928i
$429$		0			0
$430$	−1.92796	+	42.9293i	−0.0929744	+	2.07024i
$431$	−8.14061	+	11.2046i	−0.392119	+	0.539706i	−0.958744	−	0.284270i	$-0.908249\pi$
$431$	−8.14061	+	11.2046i	−0.392119	+	0.539706i	0.566625	+	0.823976i	$0.308249\pi$
$432$		0			0
$433$	34.1176	+	4.62154i	1.63959	+	0.222097i	0.895204	−	0.445656i	$-0.147030\pi$
$433$	34.1176	+	4.62154i	1.63959	+	0.222097i	0.744383	+	0.667753i	$0.232744\pi$
$434$	4.57797	+	5.23991i	0.219750	+	0.251524i
$435$		0			0
$436$	10.6966	+	78.9656i	0.512275	+	3.78177i
$437$	−5.79141	+	3.46021i	−0.277041	+	0.165524i
$438$		0			0
$439$	16.1740	−	27.0707i	0.771942	−	1.29201i	−0.179370	−	0.983782i	$-0.557406\pi$
$439$	16.1740	−	27.0707i	0.771942	−	1.29201i	0.951312	−	0.308231i	$-0.0997370\pi$
$440$	5.55378	−	4.03506i	0.264766	−	0.192364i
$441$		0			0
$442$	12.2980	+	1.10684i	0.584958	+	0.0526472i
$443$	5.64051	−	17.3597i	0.267989	−	0.824785i	−0.723001	−	0.690847i	$-0.757238\pi$
$443$	5.64051	−	17.3597i	0.267989	−	0.824785i	0.990990	−	0.133938i	$-0.0427623\pi$
$444$		0			0
$445$	11.1205	−	16.8469i	0.527165	−	0.798620i
$446$	−28.6469	−	22.8452i	−1.35647	−	1.08175i
$447$		0			0
$448$	0.858060	−	3.10911i	0.0405395	−	0.146892i
$449$	−4.63494	−	2.23207i	−0.218736	−	0.105338i	0.321307	−	0.946975i	$-0.395878\pi$
$449$	−4.63494	−	2.23207i	−0.218736	−	0.105338i	−0.540043	+	0.841637i	$0.681592\pi$
$450$		0			0
$451$	−1.11148	−	3.42078i	−0.0523374	−	0.161078i
$452$	−5.40887	−	23.6978i	−0.254412	−	1.11465i
$453$		0			0
$454$	6.66607	−	36.7331i	0.312854	−	1.72397i
$455$	−0.464553	−	1.68327i	−0.0217786	−	0.0789129i
$456$		0			0
$457$	−1.24100	−	13.7886i	−0.0580515	−	0.645004i	−0.971340	−	0.237692i	$-0.923609\pi$
$457$	−1.24100	−	13.7886i	−0.0580515	−	0.645004i	0.913289	−	0.407312i	$-0.133534\pi$
$458$	−53.1162	+	42.3588i	−2.48196	+	1.97930i
$459$		0			0
$460$	−30.0274	−	62.3526i	−1.40004	−	2.90720i
$461$	6.74478	−	7.05449i	0.314136	−	0.328560i	−0.546810	−	0.837257i	$-0.684158\pi$
$461$	6.74478	−	7.05449i	0.314136	−	0.328560i	0.860946	+	0.508696i	$0.169872\pi$
$462$		0			0
$463$	−11.7001	+	5.63446i	−0.543748	+	0.261855i	−0.685532	−	0.728042i	$-0.740430\pi$
$463$	−11.7001	+	5.63446i	−0.543748	+	0.261855i	0.141784	+	0.989898i	$0.454716\pi$
$464$	−0.0858377	−	0.473005i	−0.00398491	−	0.0219587i
$465$		0			0
$466$	−30.9250	+	2.78330i	−1.43257	+	0.128934i
$467$	4.53591	−	19.8731i	0.209897	−	0.919618i	−0.754738	−	0.656027i	$-0.772236\pi$
$467$	4.53591	−	19.8731i	0.209897	−	0.919618i	0.964634	−	0.263591i	$-0.0849070\pi$
$468$		0			0
$469$	0.528485	+	0.0959059i	0.0244032	+	0.00442852i
$470$	−29.1550	−	54.1791i	−1.34482	−	2.49909i
$471$		0			0
$472$	55.6193	−	18.0718i	2.56009	−	0.831823i
$473$	4.25008	−	1.59508i	0.195419	−	0.0733420i
$474$		0			0
$475$	−1.35437	−	0.373783i	−0.0621429	−	0.0171504i
$476$	3.55117	+	1.91097i	0.162768	+	0.0875891i
$477$		0			0
$478$	−10.0323	−	6.62224i	−0.458865	−	0.302894i
$479$	0.928695	+	20.6790i	0.0424332	+	0.944848i	0.901445	+	0.432893i	$0.142507\pi$
$479$	0.928695	+	20.6790i	0.0424332	+	0.944848i	−0.859012	+	0.511955i	$0.828921\pi$
$480$		0			0
$481$	−0.527239	+	5.85810i	−0.0240400	+	0.267106i
$482$	−12.3418	−	18.6970i	−0.562154	−	0.851627i
$483$		0			0
$484$	44.4843	+	26.5781i	2.02201	+	1.20810i
$485$	6.25785	−	14.6410i	0.284154	−	0.664812i
$486$		0			0
$487$	−13.4834	+	1.82645i	−0.610990	+	0.0827642i	−0.433190	−	0.901302i	$-0.642612\pi$
$487$	−13.4834	+	1.82645i	−0.610990	+	0.0827642i	−0.177800	+	0.984067i	$0.556898\pi$
$488$	−47.9885	−	41.9263i	−2.17234	−	1.89792i
$489$		0			0
$490$	−4.39957	+	32.4789i	−0.198752	+	1.46725i
$491$	−2.77243	−	6.48642i	−0.125118	−	0.292728i	0.845245	−	0.534378i	$-0.179454\pi$
$491$	−2.77243	−	6.48642i	−0.125118	−	0.292728i	−0.970363	+	0.241650i	$0.922311\pi$
$492$		0			0
$493$	0.101789	+	0.00457135i	0.00458435	+	0.000205883i
$494$	−4.89666	−	1.83775i	−0.220311	−	0.0826842i
$495$		0			0
$496$			62.4810i			2.80548i
$497$	1.97580	+	2.83477i	0.0886266	+	0.127157i
$498$		0			0
$499$	−26.1975	−	27.4004i	−1.17276	−	1.22661i	−0.968858	−	0.247618i	$-0.920352\pi$
$499$	−26.1975	−	27.4004i	−1.17276	−	1.22661i	−0.203901	−	0.978991i	$-0.565362\pi$
$500$	20.6280	−	54.9630i	0.922511	−	2.45802i
$501$		0			0
$502$	−3.12468	−	2.27021i	−0.139461	−	0.101325i
$503$	−1.89236	+	0.808832i	−0.0843760	+	0.0360640i	−0.434799	−	0.900527i	$-0.643181\pi$
$503$	−1.89236	+	0.808832i	−0.0843760	+	0.0360640i	0.350423	+	0.936591i	$0.386038\pi$
$504$		0			0
$505$	12.5711	−	10.9830i	0.559405	−	0.488737i
$506$	−6.80451	+	7.78839i	−0.302497	+	0.346236i
$507$		0			0
$508$	49.7618	+	83.2873i	2.20782	+	3.69527i
$509$	30.8827	+	13.1999i	1.36885	+	0.585075i	0.946895	−	0.321542i	$-0.104201\pi$
$509$	30.8827	+	13.1999i	1.36885	+	0.585075i	0.421955	+	0.906617i	$0.361344\pi$
$510$		0			0
$511$	−1.60029	−	2.20261i	−0.0707927	−	0.0974378i
$512$	−35.1229	+	23.1844i	−1.55223	+	1.02462i
$513$		0			0
$514$	−69.4834	−	22.5765i	−3.06478	−	0.995807i
$515$	−16.7710	+	0.753185i	−0.739017	+	0.0331893i
$516$		0			0
$517$	−4.05234	+	5.08147i	−0.178222	+	0.223483i
$518$	−1.28771	+	2.39297i	−0.0565789	+	0.105141i
$519$		0			0
$520$	13.6266	−	28.2960i	0.597566	−	1.24086i
$521$	−15.7032	−	41.8410i	−0.687969	−	1.83309i	−0.534992	−	0.844857i	$-0.679685\pi$
$521$	−15.7032	−	41.8410i	−0.687969	−	1.83309i	−0.152977	−	0.988230i	$-0.548886\pi$
$522$		0			0
$523$	11.5816	−	2.64342i	0.506427	−	0.115589i	0.0383287	−	0.999265i	$-0.487797\pi$
$523$	11.5816	−	2.64342i	0.506427	−	0.115589i	0.468098	+	0.883677i	$0.344939\pi$
$524$	64.4165	−	34.6640i	2.81405	−	1.51430i
$525$		0			0
$526$	−57.8684	+	15.9707i	−2.52318	+	0.696354i
$527$	−12.9109	−	2.94684i	−0.562410	−	0.128366i
$528$		0			0
$529$	23.7119	+	29.7337i	1.03095	+	1.29277i
$530$	50.2075	−	9.11131i	2.18087	−	0.395770i
$531$		0			0
$532$	−1.23463	−	1.18043i	−0.0535281	−	0.0511781i
$533$	−11.8937	−	11.3715i	−0.515174	−	0.492556i
$534$		0			0
$535$	21.7499	−	3.94702i	0.940330	−	0.170645i
$536$	6.02309	+	7.55271i	0.260158	+	0.326228i
$537$		0			0
$538$	−10.6048	−	2.42048i	−0.457205	−	0.104354i
$539$	3.33758	−	0.921113i	0.143760	−	0.0396751i
$540$		0			0
$541$	−7.13296	+	3.83841i	−0.306670	+	0.165026i	−0.619964	−	0.784630i	$-0.712853\pi$
$541$	−7.13296	+	3.83841i	−0.306670	+	0.165026i	0.313295	+	0.949656i	$0.398567\pi$
$542$	26.2860	−	5.99960i	1.12908	−	0.257705i
$543$		0			0
$544$	7.43286	+	19.8048i	0.318681	+	0.849123i
$545$	−13.1646	+	27.3366i	−0.563910	+	1.17097i
$546$		0			0
$547$	19.0194	−	35.3440i	0.813212	−	1.51120i	−0.0456279	−	0.998959i	$-0.514529\pi$
$547$	19.0194	−	35.3440i	0.813212	−	1.51120i	0.858840	−	0.512243i	$-0.171185\pi$
$548$	−34.2172	+	42.9070i	−1.46168	+	1.83289i
$549$		0			0
$550$	−2.15170	+	0.0966330i	−0.0917488	+	0.00412044i
$551$	−0.0410462	−	0.0133367i	−0.00174862	−	0.000568163i
$552$		0			0
$553$	−1.95742	+	1.29208i	−0.0832378	+	0.0549448i
$554$	33.1840	+	45.6739i	1.40985	+	1.94050i
$555$		0			0
$556$	2.84135	+	1.21445i	0.120500	+	0.0515043i
$557$	22.8051	+	38.1693i	0.966282	+	1.61728i	0.771296	+	0.636477i	$0.219609\pi$
$557$	22.8051	+	38.1693i	0.966282	+	1.61728i	0.194986	+	0.980806i	$0.437534\pi$
$558$		0			0
$559$	13.6641	−	15.6399i	0.577931	−	0.661495i
$560$	5.45561	−	4.76642i	0.230541	−	0.201418i
$561$		0			0
$562$	−0.127185	+	0.0543616i	−0.00536499	+	0.00229311i
$563$	6.33447	+	4.60226i	0.266966	+	0.193962i	0.713212	−	0.700948i	$-0.247239\pi$
$563$	6.33447	+	4.60226i	0.266966	+	0.193962i	−0.446246	+	0.894910i	$0.647239\pi$
$564$		0			0
$565$	3.25203	−	8.66501i	0.136814	−	0.364540i
$566$	25.0318	+	26.1812i	1.05216	+	1.10048i
$567$		0			0
$568$	−6.78387	+	61.7752i	−0.284645	+	2.59203i
$569$		−	22.2768i		−	0.933891i	−0.884286	−	0.466946i	$-0.845354\pi$
$569$		−	22.2768i		−	0.933891i	0.884286	−	0.466946i	$-0.154646\pi$
$570$		0			0
$571$	18.2131	+	6.83549i	0.762195	+	0.286056i	0.702045	−	0.712133i	$-0.252271\pi$
$571$	18.2131	+	6.83549i	0.762195	+	0.286056i	0.0601499	+	0.998189i	$0.480842\pi$
$572$	−5.66205	−	0.254283i	−0.236742	−	0.0106321i
$573$		0			0
$574$	−2.98796	−	6.99069i	−0.124715	−	0.291786i
$575$	−1.70615	+	12.5953i	−0.0711515	+	0.525261i
$576$		0			0
$577$	−16.3087	−	14.2485i	−0.678940	−	0.593172i	0.247829	−	0.968804i	$-0.420283\pi$
$577$	−16.3087	−	14.2485i	−0.678940	−	0.593172i	−0.926769	+	0.375632i	$0.877426\pi$
$578$	33.2457	−	4.50344i	1.38284	−	0.187318i
$579$		0			0
$580$	0.174005	−	0.407104i	0.00722515	−	0.0169041i
$581$	3.32193	+	1.98476i	0.137817	+	0.0823417i
$582$		0			0
$583$	−2.96959	−	4.49873i	−0.122988	−	0.186318i
$584$	4.38935	−	48.7696i	0.181632	−	2.01810i
$585$		0			0
$586$	−0.0133936	−	0.298231i	−0.000553284	−	0.0123198i
$587$	13.0380	+	8.60630i	0.538136	+	0.355220i	0.790548	−	0.612399i	$-0.209796\pi$
$587$	13.0380	+	8.60630i	0.538136	+	0.355220i	−0.252413	+	0.967620i	$0.581224\pi$
$588$		0			0
$589$	4.93958	+	2.65810i	0.203532	+	0.109525i
$590$	36.6694	+	10.1201i	1.50966	+	0.416639i
$591$		0			0
$592$	−22.8458	+	8.57418i	−0.938958	+	0.352397i
$593$	7.14857	−	2.32271i	0.293557	−	0.0953824i	−0.158536	−	0.987353i	$-0.550678\pi$
$593$	7.14857	−	2.32271i	0.293557	−	0.0953824i	0.452093	+	0.891971i	$0.350678\pi$
$594$		0			0
$595$	0.727616	+	1.35214i	0.0298293	+	0.0554322i
$596$	26.1692	+	4.74902i	1.07193	+	0.194527i
$597$		0			0
$598$	−10.5285	+	46.1283i	−0.430542	+	1.88633i
$599$	37.7031	−	3.39334i	1.54051	−	0.138648i	0.713425	−	0.700731i	$-0.247143\pi$
$599$	37.7031	−	3.39334i	1.54051	−	0.138648i	0.827081	+	0.562083i	$0.190000\pi$
$600$		0			0
$601$	−3.74363	−	20.6291i	−0.152706	−	0.841478i	−0.965789	−	0.259330i	$-0.916498\pi$
$601$	−3.74363	−	20.6291i	−0.152706	−	0.841478i	0.813083	−	0.582148i	$-0.197788\pi$
$602$	8.64488	−	4.16316i	0.352339	−	0.169678i
$603$		0			0
$604$	−19.8445	+	20.7558i	−0.807463	+	0.844540i
$605$	8.56081	+	17.7767i	0.348046	+	0.722725i
$606$		0			0
$607$	−15.9039	+	12.6830i	−0.645520	+	0.514785i	−0.890641	−	0.454707i	$-0.849744\pi$
$607$	−15.9039	+	12.6830i	−0.645520	+	0.514785i	0.245121	+	0.969493i	$0.421172\pi$
$608$	−0.803177	−	8.92403i	−0.0325731	−	0.361917i
$609$		0			0
$610$	−11.0273	−	39.9564i	−0.446481	−	1.61779i
$611$	−5.30929	+	29.2566i	−0.214791	+	1.18360i
$612$		0			0
$613$	−3.83461	−	16.8005i	−0.154879	−	0.678567i	−0.991426	−	0.130672i	$-0.958286\pi$
$613$	−3.83461	−	16.8005i	−0.154879	−	0.678567i	0.836547	−	0.547895i	$-0.184571\pi$
$614$	−4.71764	−	14.5194i	−0.190388	−	0.585955i
$615$		0			0
$616$	−1.38101	−	0.665062i	−0.0556427	−	0.0267961i
$617$	2.26620	−	8.21139i	0.0912338	−	0.330578i	−0.904069	−	0.427386i	$-0.859435\pi$
$617$	2.26620	−	8.21139i	0.0912338	−	0.330578i	0.995303	+	0.0968076i	$0.0308632\pi$
$618$		0			0
$619$	21.2291	+	16.9297i	0.853271	+	0.680461i	0.949113	−	0.314936i	$-0.101983\pi$
$619$	21.2291	+	16.9297i	0.853271	+	0.680461i	−0.0958419	+	0.995397i	$0.530554\pi$
$620$	−31.6999	+	48.0233i	−1.27310	+	1.92866i
$621$		0			0
$622$	−14.8843	+	45.8091i	−0.596805	+	1.83678i
$623$	−4.48912	−	0.404028i	−0.179853	−	0.0161871i
$624$		0			0
$625$	11.5026	−	8.35714i	0.460105	−	0.334286i
$626$	−37.0119	+	61.9474i	−1.47929	+	2.47592i
$627$		0			0
$628$	12.7546	−	7.62051i	0.508963	−	0.304091i
$629$	−0.694256	−	5.12520i	−0.0276818	−	0.204355i
$630$		0			0
$631$	−7.18627	−	8.22535i	−0.286081	−	0.327446i	0.592018	−	0.805924i	$-0.298331\pi$
$631$	−7.18627	−	8.22535i	−0.286081	−	0.327446i	−0.878099	+	0.478479i	$0.841188\pi$
$632$	−41.8015	−	5.66239i	−1.66277	−	0.225238i
$633$		0			0
$634$	−3.01967	+	4.15621i	−0.119926	+	0.165064i
$635$	−1.65737	+	36.9042i	−0.0657706	+	1.46450i
$636$		0			0
$637$	11.4491	−	10.9464i	0.453628	−	0.433713i
$638$	−0.0661618			−0.00261937
$639$		0			0
$640$	−0.378609			−0.0149658
$641$	27.6836	−	26.4682i	1.09344	−	1.04543i	0.0946825	−	0.995508i	$-0.469816\pi$
$641$	27.6836	−	26.4682i	1.09344	−	1.04543i	0.998753	−	0.0499239i	$-0.0158979\pi$
$642$		0			0
$643$	2.13471	−	47.5331i	0.0841848	−	1.87452i	−0.303639	−	0.952787i	$-0.598202\pi$
$643$	2.13471	−	47.5331i	0.0841848	−	1.87452i	0.387824	−	0.921734i	$-0.373227\pi$
$644$	−9.08283	+	12.5014i	−0.357914	+	0.492626i
$645$		0			0
$646$	4.55741	+	0.617343i	0.179309	+	0.0242890i
$647$	−12.2451	−	14.0157i	−0.481406	−	0.551014i	0.460162	−	0.887835i	$-0.347791\pi$
$647$	−12.2451	−	14.0157i	−0.481406	−	0.551014i	−0.941569	+	0.336821i	$0.890648\pi$
$648$		0			0
$649$	−0.539418	−	3.98214i	−0.0211740	−	0.156313i
$650$	−8.45897	+	5.05400i	−0.331788	+	0.198234i
$651$		0			0
$652$	−33.5825	+	56.2076i	−1.31519	+	2.20126i
$653$	−7.11052	+	5.16609i	−0.278256	+	0.202165i	−0.718156	−	0.695882i	$-0.755014\pi$
$653$	−7.11052	+	5.16609i	−0.278256	+	0.202165i	0.439900	+	0.898047i	$0.355014\pi$
$654$		0			0
$655$	27.7407	+	2.49671i	1.08392	+	0.0975545i
$656$	21.0959	−	64.9265i	0.823656	−	2.53495i
$657$		0			0
$658$	−7.56803	+	11.4651i	−0.295033	+	0.446955i
$659$	−15.2040	−	12.1248i	−0.592263	−	0.472314i	0.280903	−	0.959736i	$-0.409366\pi$
$659$	−15.2040	−	12.1248i	−0.592263	−	0.472314i	−0.873167	+	0.487422i	$0.837937\pi$
$660$		0			0
$661$	−9.25700	+	33.5420i	−0.360056	+	1.30463i	0.529696	+	0.848188i	$0.322306\pi$
$661$	−9.25700	+	33.5420i	−0.360056	+	1.30463i	−0.889752	+	0.456445i	$0.849123\pi$
$662$	29.9882	+	14.4416i	1.16553	+	0.561288i
$663$		0			0
$664$	21.5070	+	66.1916i	0.834632	+	2.56873i
$665$	−0.144725	−	0.634080i	−0.00561218	−	0.0245886i
$666$		0			0
$667$	−0.0697143	+	0.384158i	−0.00269935	+	0.0148746i
$668$	6.85658	+	24.8443i	0.265289	+	0.961253i
$669$		0			0
$670$	0.563265	+	6.25838i	0.0217608	+	0.241782i
$671$	−3.42342	+	2.73009i	−0.132160	+	0.105394i
$672$		0			0
$673$	−8.65204	−	17.9661i	−0.333512	−	0.692544i	0.665014	−	0.746831i	$-0.268426\pi$
$673$	−8.65204	−	17.9661i	−0.333512	−	0.692544i	−0.998525	+	0.0542871i	$0.982711\pi$
$674$	−45.6846	+	47.7824i	−1.75971	+	1.84051i
$675$		0			0
$676$	33.1338	−	15.9564i	1.27438	−	0.613707i
$677$	1.23938	+	6.82955i	0.0476333	+	0.262481i	0.998954	−	0.0457209i	$-0.0145585\pi$
$677$	1.23938	+	6.82955i	0.0476333	+	0.262481i	−0.951321	+	0.308202i	$0.900273\pi$
$678$		0			0
$679$	−3.54087	+	0.318684i	−0.135886	+	0.0122300i
$680$	−6.14520	+	26.9239i	−0.235658	+	1.03248i
$681$		0			0
$682$	8.46093	+	1.53543i	0.323986	+	0.0587948i
$683$	13.7454	+	25.5432i	0.525952	+	0.977383i	0.995526	+	0.0944900i	$0.0301220\pi$
$683$	13.7454	+	25.5432i	0.525952	+	0.977383i	−0.469573	+	0.882893i	$0.655592\pi$
$684$		0			0
$685$	−19.8733	+	6.45722i	−0.759319	+	0.246718i
$686$	13.8719	−	5.20620i	0.529630	−	0.198773i
$687$		0			0
$688$	83.0558	+	22.9220i	3.16647	+	0.873891i
$689$	−21.7163	−	11.6860i	−0.827325	−	0.445202i
$690$		0			0
$691$	−5.73536	−	3.78588i	−0.218183	−	0.144021i	0.437079	−	0.899423i	$-0.356013\pi$
$691$	−5.73536	−	3.78588i	−0.218183	−	0.144021i	−0.655262	+	0.755402i	$0.727442\pi$
$692$	0.0605499	+	1.34825i	0.00230176	+	0.0512527i
$693$		0			0
$694$	−5.22711	+	58.0780i	−0.198418	+	2.20461i
$695$	0.648156	+	0.981915i	0.0245860	+	0.0372461i
$696$		0			0
$697$	12.4213	+	7.42138i	0.470490	+	0.281105i
$698$	32.0698	−	75.0310i	1.21386	−	2.83996i
$699$		0			0
$700$	−3.18906	+	0.431987i	−0.120535	+	0.0163276i
$701$	21.4838	+	18.7698i	0.811432	+	0.708927i	0.960008	−	0.279974i	$-0.0903259\pi$
$701$	21.4838	+	18.7698i	0.811432	+	0.708927i	−0.148575	+	0.988901i	$0.547469\pi$
$702$		0			0
$703$	−0.294068	+	2.17089i	−0.0110910	+	0.0818768i
$704$	−1.56662	−	3.66528i	−0.0590440	−	0.138140i
$705$		0			0
$706$	76.8515	+	3.45141i	2.89234	+	0.129895i
$707$	−3.48962	−	1.30968i	−0.131241	−	0.0492555i
$708$		0			0
$709$			2.11647i			0.0794858i	0.999210	+	0.0397429i	$0.0126539\pi$
$709$			2.11647i			0.0794858i	−0.999210	+	0.0397429i	$0.987346\pi$
$710$	−25.8192	+	31.1044i	−0.968977	+	1.16733i
$711$		0			0
$712$	−56.0211	−	58.5935i	−2.09948	−	2.19588i
$713$	17.8305	−	47.5092i	0.667757	−	1.77923i
$714$		0			0
$715$	−1.74589	−	1.26847i	−0.0652927	−	0.0474379i
$716$	−85.9963	+	36.7566i	−3.21383	+	1.37366i
$717$		0			0
$718$	43.2041	−	37.7463i	1.61236	−	1.40868i
$719$	24.5658	−	28.1178i	0.916151	−	1.04862i	−0.0824950	−	0.996591i	$-0.526289\pi$
$719$	24.5658	−	28.1178i	0.916151	−	1.04862i	0.998646	−	0.0520274i	$-0.0165683\pi$
$720$		0			0
$721$	1.92258	+	3.21786i	0.0716007	+	0.119839i
$722$	43.8462	+	18.7408i	1.63179	+	0.697459i
$723$		0			0
$724$	32.0741	+	44.1462i	1.19202	+	1.64068i
$725$	−0.0678607	+	0.0447944i	−0.00252028	+	0.00166362i
$726$		0			0
$727$	−16.3970	−	5.32771i	−0.608131	−	0.197594i	−0.0112678	−	0.999937i	$-0.503587\pi$
$727$	−16.3970	−	5.32771i	−0.608131	−	0.197594i	−0.596864	+	0.802343i	$0.703587\pi$
$728$	−7.00543	+	0.314614i	−0.259638	+	0.0116604i
$729$		0			0
$730$	19.8589	−	24.9023i	0.735011	−	0.921674i
$731$	−8.65376	+	16.0814i	−0.320071	+	0.594792i
$732$		0			0
$733$	−21.2754	+	44.1787i	−0.785823	+	1.63178i	−0.0107219	+	0.999943i	$0.503413\pi$
$733$	−21.2754	+	44.1787i	−0.785823	+	1.63178i	−0.775102	+	0.631837i	$0.782301\pi$
$734$	−21.2716	−	56.6779i	−0.785148	−	2.09202i
$735$		0			0
$736$	−79.0251	+	18.0370i	−2.91290	+	0.664851i
$737$	0.584537	−	0.314553i	0.0215317	−	0.0115867i
$738$		0			0
$739$	17.8357	−	4.92233i	0.656096	−	0.181071i	0.0778899	−	0.996962i	$-0.475182\pi$
$739$	17.8357	−	4.92233i	0.656096	−	0.181071i	0.578206	+	0.815891i	$0.303753\pi$
$740$	−21.9096	−	5.00072i	−0.805412	−	0.183830i
$741$		0			0
$742$	−7.10381	−	8.90790i	−0.260789	−	0.327019i
$743$	2.79849	−	0.507851i	0.102667	−	0.0186313i	−0.126980	−	0.991905i	$-0.540529\pi$
$743$	2.79849	−	0.507851i	0.102667	−	0.0186313i	0.229647	+	0.973274i	$0.426243\pi$
$744$		0			0
$745$	7.31966	+	6.99831i	0.268172	+	0.256398i
$746$	51.4013	+	49.1447i	1.88193	+	1.79931i
$747$		0			0
$748$	4.90372	−	0.889895i	0.179298	−	0.0325378i
$749$	−3.07737	−	3.85890i	−0.112445	−	0.141001i
$750$		0			0
$751$	29.2364	+	6.67303i	1.06685	+	0.243502i	0.719685	−	0.694301i	$-0.244286\pi$
$751$	29.2364	+	6.67303i	1.06685	+	0.243502i	0.347168	+	0.937803i	$0.387143\pi$
$752$	−118.914	+	32.8182i	−4.33635	+	1.19676i
$753$		0			0
$754$	−0.266543	+	0.143433i	−0.00970693	+	0.00522352i
$755$	−10.6597	+	2.43301i	−0.387946	+	0.0885462i
$756$		0			0
$757$	9.56719	+	25.4917i	0.347726	+	0.926511i	0.987454	+	0.157910i	$0.0504756\pi$
$757$	9.56719	+	25.4917i	0.347726	+	0.926511i	−0.639728	+	0.768601i	$0.720953\pi$
$758$	−23.5426	+	48.8867i	−0.855106	+	1.77565i
$759$		0			0
$760$	5.54307	−	10.3008i	0.201068	−	0.373648i
$761$	−14.9375	+	18.7310i	−0.541484	+	0.679000i	−0.975015	−	0.222139i	$-0.928696\pi$
$761$	−14.9375	+	18.7310i	−0.541484	+	0.679000i	0.433531	+	0.901139i	$0.357268\pi$
$762$		0			0
$763$	6.76792	−	0.303947i	0.245015	−	0.0110036i
$764$	65.0688	+	21.1421i	2.35411	+	0.764895i
$765$		0			0
$766$	−49.0923	+	32.4055i	−1.77378	+	1.17086i
$767$	−10.8061	−	14.8733i	−0.390184	−	0.537042i
$768$		0			0
$769$	40.0441	+	17.1157i	1.44403	+	0.617207i	0.965391	−	0.260806i	$-0.0839883\pi$
$769$	40.0441	+	17.1157i	1.44403	+	0.617207i	0.478636	+	0.878013i	$0.341131\pi$
$770$	−0.511381	−	0.855908i	−0.0184289	−	0.0308448i
$771$		0			0
$772$	42.6864	−	48.8585i	1.53632	−	1.75846i
$773$	30.7915	−	26.9017i	1.10749	−	0.967588i	0.107847	−	0.994167i	$-0.465604\pi$
$773$	30.7915	−	26.9017i	1.10749	−	0.967588i	0.999647	+	0.0265791i	$0.00846138\pi$
$774$		0			0
$775$	9.71775	−	4.15356i	0.349072	−	0.149200i
$776$	−51.7298	−	37.5839i	−1.85699	−	1.34918i
$777$		0			0
$778$	30.2990	−	80.7313i	1.08627	−	2.89436i
$779$	−4.23543	−	4.42991i	−0.151750	−	0.158718i
$780$		0			0
$781$	4.09337	+	1.21660i	0.146472	+	0.0435333i
$782$		−	41.6050i		−	1.48779i
$783$		0			0
$784$	61.5252	+	23.0908i	2.19733	+	0.824671i
$785$	5.65149	+	0.253809i	0.201710	+	0.00905882i
$786$		0			0
$787$	−19.2334	−	44.9987i	−0.685596	−	1.60403i	−0.792578	−	0.609770i	$-0.791262\pi$
$787$	−19.2334	−	44.9987i	−0.685596	−	1.60403i	0.106982	−	0.994261i	$-0.465881\pi$
$788$	−3.20473	+	23.6583i	−0.114164	+	0.842791i
$789$		0			0
$790$	−20.6633	−	18.0530i	−0.735168	−	0.642297i
$791$	−2.04783	+	0.277397i	−0.0728124	+	0.00986310i
$792$		0			0
$793$	−7.87319	+	18.4202i	−0.279585	+	0.654122i
$794$	−19.4020	−	11.5921i	−0.688550	−	0.411389i
$795$		0			0
$796$	28.3173	+	42.8988i	1.00368	+	1.52051i
$797$	−2.01419	+	22.3794i	−0.0713461	+	0.792721i	0.878035	+	0.478596i	$0.158854\pi$
$797$	−2.01419	+	22.3794i	−0.0713461	+	0.792721i	−0.949382	+	0.314125i	$0.898289\pi$
$798$		0			0
$799$	−1.17305	−	26.1200i	−0.0414995	−	0.924059i
$800$	−14.0885	−	9.29974i	−0.498104	−	0.328796i
$801$		0			0
$802$	−47.7649	−	25.7034i	−1.68664	−	0.907617i
$803$	−3.24345	−	0.895135i	−0.114459	−	0.0315886i
$804$		0			0
$805$	−5.50853	+	2.06739i	−0.194150	+	0.0728658i
$806$	37.4149	−	12.1568i	1.31788	−	0.428206i
$807$		0			0
$808$	−31.7667	−	59.0325i	−1.11755	−	2.07675i
$809$	4.46287	+	0.809892i	0.156906	+	0.0284743i	0.256441	−	0.966560i	$-0.417450\pi$
$809$	4.46287	+	0.809892i	0.156906	+	0.0284743i	−0.0995353	+	0.995034i	$0.531736\pi$
$810$		0			0
$811$	2.18556	−	9.57557i	0.0767455	−	0.336244i	−0.921950	−	0.387309i	$-0.873405\pi$
$811$	2.18556	−	9.57557i	0.0767455	−	0.336244i	0.998695	+	0.0510654i	$0.0162617\pi$
$812$	−0.0984570	+	0.00886129i	−0.00345516	+	0.000310970i
$813$		0			0
$814$	0.599660	+	3.30440i	0.0210181	+	0.115819i
$815$	−22.4615	+	10.8169i	−0.786793	+	0.378900i
$816$		0			0
$817$	5.34555	−	5.59100i	0.187017	−	0.195604i
$818$	−2.09317	−	4.34652i	−0.0731860	−	0.151972i
$819$		0			0
$820$	49.1550	−	39.1998i	1.71657	−	1.36892i
$821$	3.07894	+	34.2098i	0.107456	+	1.19393i	0.850972	+	0.525212i	$0.176014\pi$
$821$	3.07894	+	34.2098i	0.107456	+	1.19393i	−0.743516	+	0.668718i	$0.766843\pi$
$822$		0			0
$823$	−2.36259	−	8.56064i	−0.0823546	−	0.298405i	0.911169	−	0.412033i	$-0.135181\pi$
$823$	−2.36259	−	8.56064i	−0.0823546	−	0.298405i	−0.993523	+	0.113628i	$0.963753\pi$
$824$	−12.0379	+	66.3343i	−0.419360	+	2.31086i
$825$		0			0
$826$	−1.89005	−	8.28083i	−0.0657631	−	0.288127i
$827$	−10.5169	−	32.3678i	−0.365709	−	1.12554i	−0.949536	−	0.313659i	$-0.898445\pi$
$827$	−10.5169	−	32.3678i	−0.365709	−	1.12554i	0.583826	−	0.811879i	$-0.301555\pi$
$828$		0			0
$829$	−37.6604	−	18.1363i	−1.30800	−	0.629899i	−0.355568	−	0.934651i	$-0.615712\pi$
$829$	−37.6604	−	18.1363i	−1.30800	−	0.629899i	−0.952432	+	0.304751i	$0.901427\pi$
$830$	−12.0438	+	43.6397i	−0.418046	+	1.51475i
$831$		0			0
$832$	−14.2574	−	11.3699i	−0.494285	−	0.394179i
$833$	−7.67318	+	11.6244i	−0.265860	+	0.402761i
$834$		0			0
$835$	−3.03247	+	9.33299i	−0.104943	+	0.322981i
$836$	−2.10251	−	0.189229i	−0.0727168	−	0.00654463i
$837$		0			0
$838$	−2.14349	+	1.55734i	−0.0740456	+	0.0537973i
$839$	24.4620	−	40.9425i	0.844523	−	1.41349i	−0.0650206	−	0.997884i	$-0.520711\pi$
$839$	24.4620	−	40.9425i	0.844523	−	1.41349i	0.909543	−	0.415609i	$-0.136432\pi$
$840$		0			0
$841$	24.8929	−	14.8728i	0.858375	−	0.512855i
$842$	−8.50271	−	62.7695i	−0.293023	−	2.16318i
$843$		0			0
$844$	3.35803	+	3.84357i	0.115588	+	0.132301i
$845$	13.8759	+	1.87962i	0.477346	+	0.0646609i
$846$		0			0
$847$	2.58951	−	3.56415i	0.0889766	−	0.122466i
$848$	4.59017	−	102.208i	0.157627	−	3.50984i
$849$		0			0
$850$	6.26280	−	5.98785i	0.214812	−	0.205382i
$851$	19.8183			0.679363
$852$		0			0
$853$	30.6955			1.05099			0.525497	−	0.850796i	$-0.323880\pi$
$853$	30.6955			1.05099			0.525497	+	0.850796i	$0.323880\pi$
$854$	−6.68957	+	6.39589i	−0.228912	+	0.218863i
$855$		0			0
$856$	3.98270	−	88.6817i	0.136126	−	3.03108i
$857$	−2.59105	+	3.56627i	−0.0885085	+	0.121821i	−0.850975	−	0.525206i	$-0.823988\pi$
$857$	−2.59105	+	3.56627i	−0.0885085	+	0.121821i	0.762467	+	0.647028i	$0.223988\pi$
$858$		0			0
$859$	−22.9616	−	3.11037i	−0.783441	−	0.106124i	−0.268420	−	0.963302i	$-0.586502\pi$
$859$	−22.9616	−	3.11037i	−0.783441	−	0.106124i	−0.515021	+	0.857178i	$0.672216\pi$
$860$	52.2077	+	59.7565i	1.78027	+	2.03768i
$861$		0			0
$862$	4.85625	+	35.8503i	0.165405	+	1.22107i
$863$	−6.74382	+	4.02924i	−0.229562	+	0.137157i	−0.623075	−	0.782162i	$-0.714117\pi$
$863$	−6.74382	+	4.02924i	−0.229562	+	0.137157i	0.393513	+	0.919319i	$0.371260\pi$
$864$		0			0
$865$	−0.263565	+	0.441134i	−0.00896149	+	0.0149990i
$866$	72.7591	−	52.8626i	2.47246	−	1.79634i
$867$		0			0
$868$	12.7966	+	1.15171i	0.434344	+	0.0390917i
$869$	−0.895710	+	2.75671i	−0.0303849	+	0.0935151i
$870$		0			0
$871$	1.67297	−	2.53445i	0.0566866	−	0.0858765i
$872$	95.2635	+	75.9701i	3.22603	+	2.57267i
$873$		0			0
$874$	−4.68829	+	16.9877i	−0.158584	+	0.574616i
$875$	−4.49678	−	2.16554i	−0.152019	−	0.0732085i
$876$		0			0
$877$	8.39200	+	25.8279i	0.283378	+	0.872147i	0.986880	+	0.161454i	$0.0516183\pi$
$877$	8.39200	+	25.8279i	0.283378	+	0.872147i	−0.703503	+	0.710693i	$0.748382\pi$
$878$	−18.3298	−	80.3083i	−0.618602	−	2.71027i
$879$		0			0
$880$	1.59864	−	8.80922i	0.0538900	−	0.296959i
$881$	9.19664	+	33.3233i	0.309843	+	1.12269i	0.938577	+	0.345069i	$0.112145\pi$
$881$	9.19664	+	33.3233i	0.309843	+	1.12269i	−0.628735	+	0.777620i	$0.716427\pi$
$882$		0			0
$883$	−0.236834	−	2.63144i	−0.00797011	−	0.0885552i	0.991005	−	0.133828i	$-0.0427271\pi$
$883$	−0.236834	−	2.63144i	−0.00797011	−	0.0885552i	−0.998975	+	0.0452731i	$0.985584\pi$
$884$	17.8262	−	14.2159i	0.599560	−	0.478133i
$885$		0			0
$886$	−20.6877	−	42.9585i	−0.695018	−	1.44322i
$887$	17.9989	−	18.8253i	0.604343	−	0.632093i	−0.347865	−	0.937545i	$-0.613093\pi$
$887$	17.9989	−	18.8253i	0.604343	−	0.632093i	0.952208	+	0.305452i	$0.0988075\pi$
$888$		0			0
$889$	7.43157	−	3.57885i	0.249247	−	0.120031i
$890$	−9.41533	−	51.8827i	−0.315602	−	1.73911i
$891$		0			0
$892$	−67.3862	+	6.06487i	−2.25626	+	0.203067i
$893$	−2.46439	+	10.7972i	−0.0824676	+	0.361314i
$894$		0			0
$895$	−35.0371	−	6.35829i	−1.17116	−	0.212534i
$896$	0.0400596	+	0.0744433i	0.00133830	+	0.00248697i
$897$		0			0
$898$	−12.7804	+	4.15260i	−0.426487	+	0.138574i
$899$	0.303930	−	0.114067i	0.0101366	−	0.00380434i
$900$		0			0
$901$	20.9036	+	5.76901i	0.696398	+	0.192194i
$902$	−8.27367	−	4.45225i	−0.275483	−	0.148244i
$903$		0			0
$904$	−31.0190	−	20.4754i	−1.03168	−	0.681003i
$905$	0.932159	+	20.7561i	0.0309860	+	0.689957i
$906$		0			0
$907$	−2.14605	+	23.8445i	−0.0712583	+	0.791745i	0.878291	+	0.478127i	$0.158684\pi$
$907$	−2.14605	+	23.8445i	−0.0712583	+	0.791745i	−0.949549	+	0.313618i	$0.898459\pi$
$908$	−37.9770	−	57.5327i	−1.26031	−	1.90929i
$909$		0			0
$910$	−3.91571	−	2.33953i	−0.129805	−	0.0775547i
$911$	−16.2267	+	37.9644i	−0.537616	+	1.25782i	0.402017	+	0.915632i	$0.368309\pi$
$911$	−16.2267	+	37.9644i	−0.537616	+	1.25782i	−0.939633	+	0.342183i	$0.888834\pi$
$912$		0			0
$913$	4.73908	−	0.641952i	0.156841	−	0.0212455i
$914$	−27.2340	−	23.7937i	−0.900822	−	0.787024i
$915$		0			0
$916$	−16.8396	+	124.315i	−0.556396	+	4.10748i
$917$	−2.44426	−	5.71863i	−0.0807166	−	0.188846i
$918$		0			0
$919$	9.51550	+	0.427342i	0.313887	+	0.0140967i	0.201251	−	0.979540i	$-0.435499\pi$
$919$	9.51550	+	0.427342i	0.313887	+	0.0140967i	0.112636	+	0.993636i	$0.464071\pi$
$920$	−99.0734	−	37.1829i	−3.26635	−	1.22588i
$921$		0			0
$922$		−	25.4949i		−	0.839630i
$923$	19.1283	−	3.97282i	0.629615	−	0.130767i
$924$		0			0
$925$	2.85228	+	2.98325i	0.0937823	+	0.0980886i
$926$	−11.9193	+	31.7590i	−0.391694	+	1.04366i
$927$		0			0
$928$	−0.419514	−	0.304795i	−0.0137712	−	0.0100054i
$929$	3.78050	−	1.61586i	0.124034	−	0.0530147i	−0.330113	−	0.943941i	$-0.607087\pi$
$929$	3.78050	−	1.61586i	0.124034	−	0.0530147i	0.454147	+	0.890927i	$0.349944\pi$
$930$		0			0
$931$	4.44292	−	3.88167i	0.145611	−	0.127216i
$932$	−37.7228	+	43.1773i	−1.23565	+	1.41432i
$933$		0			0
$934$	−27.3104	−	45.7099i	−0.893624	−	1.49568i
$935$	1.74492	+	0.745814i	0.0570650	+	0.0243907i
$936$		0			0
$937$	−25.9338	−	35.6948i	−0.847220	−	1.16610i	−0.984468	−	0.175562i	$-0.943826\pi$
$937$	−25.9338	−	35.6948i	−0.847220	−	1.16610i	0.137248	−	0.990537i	$-0.456174\pi$
$938$	1.17094	−	0.772934i	0.0382327	−	0.0252372i
$939$		0			0
$940$	−108.049	−	35.1071i	−3.52416	−	1.14507i
$941$	−31.6335	+	1.42066i	−1.03122	+	0.0463122i	−0.554038	−	0.832491i	$-0.686914\pi$
$941$	−31.6335	+	1.42066i	−1.03122	+	0.0463122i	−0.477184	+	0.878804i	$0.658342\pi$
$942$		0			0
$943$	−34.5692	+	43.3484i	−1.12573	+	1.41162i
$944$	36.1426	−	67.1643i	1.17634	−	2.18601i
$945$		0			0
$946$	5.14504	−	10.6838i	0.167280	−	0.347360i
$947$	−20.8029	−	55.4290i	−0.676002	−	1.80120i	−0.593841	−	0.804582i	$-0.702389\pi$
$947$	−20.8029	−	55.4290i	−0.676002	−	1.80120i	−0.0821609	−	0.996619i	$-0.526182\pi$
$948$		0			0
$949$	−15.0073	+	3.42532i	−0.487158	+	0.111191i
$950$	−3.23190	+	1.73916i	−0.104857	+	0.0564258i
$951$		0			0
$952$	5.94406	−	1.64046i	0.192648	−	0.0531675i
$953$	−25.3453	−	5.78489i	−0.821014	−	0.187391i	−0.208673	−	0.977985i	$-0.566915\pi$
$953$	−25.3453	−	5.78489i	−0.821014	−	0.187391i	−0.612340	+	0.790594i	$0.709772\pi$
$954$		0			0
$955$	16.2422	+	20.3670i	0.525584	+	0.659062i
$956$	−21.8402	+	3.96341i	−0.706362	+	0.128186i
$957$		0			0
$958$	39.0828	+	37.3670i	1.26271	+	1.20727i
$959$	3.37238	+	3.22432i	0.108900	+	0.104119i
$960$		0			0
$961$	−11.0127	+	1.99850i	−0.355247	+	0.0644679i
$962$	9.57946	+	12.0123i	0.308854	+	0.387291i
$963$		0			0
$964$	−40.3310	−	9.20528i	−1.29897	−	0.296482i
$965$	23.8129	−	6.57195i	0.766565	−	0.211559i
$966$		0			0
$967$	−53.3709	+	28.7201i	−1.71629	+	0.923577i	−0.751832	+	0.659355i	$0.770829\pi$
$967$	−53.3709	+	28.7201i	−1.71629	+	0.923577i	−0.964462	+	0.264222i	$0.914885\pi$
$968$	77.2489	−	17.6316i	2.48287	−	0.566700i
$969$		0			0
$970$	−14.6143	−	38.9397i	−0.469237	−	1.25028i
$971$	5.60300	−	11.6347i	0.179809	−	0.373377i	−0.791511	−	0.611155i	$-0.790705\pi$
$971$	5.60300	−	11.6347i	0.179809	−	0.373377i	0.971319	+	0.237779i	$0.0764193\pi$
$972$		0			0
$973$	0.124487	−	0.231336i	0.00399088	−	0.00741630i
$974$	−22.1605	+	27.7884i	−0.710068	+	0.890397i
$975$		0			0
$976$	−83.0245	+	3.72864i	−2.65755	+	0.119351i
$977$	−26.8382	−	8.72025i	−0.858629	−	0.278986i	−0.153573	−	0.988137i	$-0.549078\pi$
$977$	−26.8382	−	8.72025i	−0.858629	−	0.278986i	−0.705056	+	0.709152i	$0.749078\pi$
$978$		0			0
$979$	−4.64884	+	3.06867i	−0.148578	+	0.0980752i
$980$	35.5735	+	48.9627i	1.13635	+	1.56405i
$981$		0			0
$982$	−16.9437	−	7.24209i	−0.540695	−	0.231104i
$983$	0.602701	+	1.00875i	0.0192232	+	0.0321742i	0.867910	−	0.496722i	$-0.165463\pi$
$983$	0.602701	+	1.00875i	0.0192232	+	0.0321742i	−0.848686	+	0.528896i	$0.822606\pi$
$984$		0			0
$985$	−5.98088	+	6.84567i	−0.190567	+	0.218121i
$986$	0.200437	−	0.175117i	0.00638321	−	0.00557685i
$987$		0			0
$988$	−8.88051	+	3.79571i	−0.282527	+	0.120758i
$989$	−56.6124	−	41.1313i	−1.80017	−	1.30790i
$990$		0			0
$991$	−0.756235	+	2.01498i	−0.0240226	+	0.0640080i	−0.947699	−	0.319165i	$-0.896597\pi$
$991$	−0.756235	+	2.01498i	−0.0240226	+	0.0640080i	0.923676	+	0.383173i	$0.125169\pi$
$992$	46.5750	+	48.7136i	1.47876	+	1.54666i
$993$		0			0
$994$	8.84770	+	1.78557i	0.280632	+	0.0566348i
$995$			19.5718i			0.620466i
$996$		0			0
$997$	−52.3933	−	19.6635i	−1.65931	−	0.622750i	−0.666838	−	0.745203i	$-0.732353\pi$
$997$	−52.3933	−	19.6635i	−1.65931	−	0.622750i	−0.992474	+	0.122452i	$0.960924\pi$
$998$	−98.9252	−	4.44274i	−3.13142	−	0.140632i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	639.2.z.a.485.23	yes	576
3.2	odd	2	inner	639.2.z.a.485.2	yes	576
71.65	odd	70	inner	639.2.z.a.278.2	✓	576
213.65	even	70	inner	639.2.z.a.278.23	yes	576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
639.2.z.a.278.2	✓	576	71.65	odd	70	inner
639.2.z.a.278.23	yes	576	213.65	even	70	inner
639.2.z.a.485.2	yes	576	3.2	odd	2	inner
639.2.z.a.485.23	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)

\(f(q)\)	\(=\)	\(q+(1.88807 - 1.80518i) q^{2} +(0.216405 - 4.81862i) q^{4} +(1.07951 - 1.48582i) q^{5} +(-0.406367 - 0.0550462i) q^{7} +(-4.85259 - 5.55423i) q^{8} +O(q^{10})\)	\(q+(1.88807 - 1.80518i) q^{2} +(0.216405 - 4.81862i) q^{4} +(1.07951 - 1.48582i) q^{5} +(-0.406367 - 0.0550462i) q^{7} +(-4.85259 - 5.55423i) q^{8} +(-0.643980 - 4.75405i) q^{10} +(-0.435059 + 0.259935i) q^{11} +(-1.18918 + 1.99036i) q^{13} +(-0.866618 + 0.629635i) q^{14} +(-9.58029 - 0.862242i) q^{16} +(0.630014 - 1.93898i) q^{17} +(-0.475736 + 0.720709i) q^{19} +(-6.92601 - 5.52331i) q^{20} +(-0.352191 + 1.27614i) q^{22} +(7.03857 + 3.38960i) q^{23} +(0.502765 + 1.54735i) q^{25} +(1.34769 + 5.90463i) q^{26} +(-0.353187 + 1.94622i) q^{28} +(0.0132957 + 0.0481760i) q^{29} +(-0.582259 - 6.46943i) q^{31} +(-8.11205 + 6.46915i) q^{32} +(-2.31070 - 4.79823i) q^{34} +(-0.520468 + 0.544366i) q^{35} +(2.28561 - 1.10069i) q^{37} +(0.402787 + 2.21954i) q^{38} +(-13.4910 + 1.21422i) q^{40} +(-1.57927 + 6.91923i) q^{41} +(-8.81340 - 1.59940i) q^{43} +(1.15838 + 2.15264i) q^{44} +(19.4081 - 6.30609i) q^{46} +(12.0068 - 4.50623i) q^{47} +(-6.58564 - 1.81752i) q^{49} +(3.74250 + 2.01393i) q^{50} +(9.33345 + 6.16096i) q^{52} +(0.477197 + 10.6256i) q^{53} +(-0.0834337 + 0.927024i) q^{55} +(1.66619 + 2.52417i) q^{56} +(0.112070 + 0.0669585i) q^{58} +(-3.11639 + 7.29115i) q^{59} +(8.56180 - 1.15977i) q^{61} +(-12.7778 - 11.1637i) q^{62} +(-1.05577 + 7.79400i) q^{64} +(1.67358 + 3.91554i) q^{65} +(-1.30847 - 0.0587635i) q^{67} +(-9.20690 - 3.45541i) q^{68} +1.96734i q^{70} +(-5.70241 - 6.20343i) q^{71} +(4.58808 + 4.79875i) q^{73} +(2.32844 - 6.20411i) q^{74} +(3.36987 + 2.44836i) q^{76} +(0.191102 - 0.0816809i) q^{77} +(4.30713 - 3.76303i) q^{79} +(-11.6232 + 13.3038i) q^{80} +(9.50868 + 15.9148i) q^{82} +(-8.67708 - 3.70876i) q^{83} +(-2.20088 - 3.02925i) q^{85} +(-19.5275 + 12.8900i) q^{86} +(3.55490 + 1.15506i) q^{88} +(10.9802 - 0.493120i) q^{89} +(0.592807 - 0.743357i) q^{91} +(17.8564 - 33.1827i) q^{92} +(14.5351 - 30.1825i) q^{94} +(0.557282 + 1.48487i) q^{95} +(8.45216 - 1.92915i) q^{97} +(-15.7151 + 8.45665i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 576 q - 24 q^{4}+O(q^{10}) \) 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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