LMFDB - Embedded newform 270.2.m.a.197.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(17,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("270.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.m (of order $12$, degree $4$, not 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	270.197
Dual form			270.2.m.a.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(-4.40508 + 1.18034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.224745 - 2.22474i) q^{10} +(0.550510 + 0.317837i) q^{11} +(-3.34607 - 0.896575i) q^{13} +(-2.28024 - 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.317837 + 0.317837i) q^{17} +6.44949i q^{19} +(2.09077 - 0.792893i) q^{20} +(-0.164525 + 0.614014i) q^{22} +(0.258819 - 0.965926i) q^{23} +(4.74264 + 1.58346i) q^{25} -3.46410i q^{26} +(3.22474 - 3.22474i) q^{28} +(0.158919 - 0.275255i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.389270 - 0.224745i) q^{34} +(10.1459 - 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-6.22973 + 1.66925i) q^{38} +(1.30701 + 1.81431i) q^{40} +(-6.39898 + 3.69445i) q^{41} +(-0.896575 - 3.34607i) q^{43} -0.635674 q^{44} +1.00000 q^{46} +(2.32937 + 8.69333i) q^{47} +(11.9494 - 6.89898i) q^{49} +(-0.302023 + 4.99087i) q^{50} +(3.34607 - 0.896575i) q^{52} +(-3.78194 - 3.78194i) q^{53} +(-1.10102 - 0.898979i) q^{55} +(3.94949 + 2.28024i) q^{56} +(0.307007 + 0.0822623i) q^{58} +(4.48905 + 7.77526i) q^{59} +(0.275255 - 0.476756i) q^{61} +(0.317837 - 0.317837i) q^{62} +1.00000i q^{64} +(7.06350 + 3.17914i) q^{65} +(-1.71089 + 6.38512i) q^{67} +(0.116337 - 0.434174i) q^{68} +(3.61597 + 9.53491i) q^{70} -6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(-3.22474 - 5.58542i) q^{76} +(-2.80020 - 0.750311i) q^{77} +(-2.12132 - 1.22474i) q^{79} +(-1.41421 + 1.73205i) q^{80} +(-5.22474 - 5.22474i) q^{82} +(-5.26380 + 1.41043i) q^{83} +(0.815515 - 0.587486i) q^{85} +(3.00000 - 1.73205i) q^{86} +(-0.164525 - 0.614014i) q^{88} +8.02458 q^{89} +15.7980 q^{91} +(0.258819 + 0.965926i) q^{92} +(-7.79423 + 4.50000i) q^{94} +(2.31356 - 14.2347i) q^{95} +(-2.59405 + 0.695075i) q^{97} +(9.75663 + 9.75663i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100}) $ 8 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 + 24 * q^11 + 4 * q^16 - 8 * q^22 + 4 * q^25 + 16 * q^28 + 8 * q^31 - 24 * q^37 - 12 * q^38 + 4 * q^40 - 12 * q^41 + 8 * q^46 - 24 * q^50 - 48 * q^55 + 12 * q^56 - 4 * q^58 + 12 * q^61 + 24 * q^65 + 4 * q^67 + 12 * q^68 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 24 * q^77 - 32 * q^82 - 12 * q^83 - 20 * q^85 + 24 * q^86 - 8 * q^88 + 48 * q^91 + 24 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$6$		0			0
$7$	−4.40508	+	1.18034i	−1.66497	+	0.446126i	−0.963746	−	0.266820i	$-0.914027\pi$
$7$	−4.40508	+	1.18034i	−1.66497	+	0.446126i	−0.701219	+	0.712946i	$0.747360\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.224745	−	2.22474i	−0.0710706	−	0.703526i
$11$	0.550510	+	0.317837i	0.165985	+	0.0958315i	0.580691	−	0.814124i	$-0.302782\pi$
$11$	0.550510	+	0.317837i	0.165985	+	0.0958315i	−0.414706	+	0.909955i	$0.636116\pi$
$12$		0			0
$13$	−3.34607	−	0.896575i	−0.928032	−	0.248665i	−0.237016	−	0.971506i	$-0.576170\pi$
$13$	−3.34607	−	0.896575i	−0.928032	−	0.248665i	−0.691015	+	0.722840i	$0.742836\pi$
$14$	−2.28024	−	3.94949i	−0.609419	−	1.05555i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.317837	+	0.317837i	−0.0770869	+	0.0770869i	−0.744599	−	0.667512i	$-0.767359\pi$
$17$	−0.317837	+	0.317837i	−0.0770869	+	0.0770869i	0.667512	+	0.744599i	$0.267359\pi$
$18$		0			0
$19$			6.44949i			1.47961i	0.672819	+	0.739807i	$0.265083\pi$
$19$			6.44949i			1.47961i	−0.672819	+	0.739807i	$0.734917\pi$
$20$	2.09077	−	0.792893i	0.467510	−	0.177296i
$21$		0			0
$22$	−0.164525	+	0.614014i	−0.0350768	+	0.130908i
$23$	0.258819	−	0.965926i	0.0539675	−	0.201409i	−0.933678	−	0.358113i	$-0.883420\pi$
$23$	0.258819	−	0.965926i	0.0539675	−	0.201409i	0.987646	+	0.156704i	$0.0500868\pi$
$24$		0			0
$25$	4.74264	+	1.58346i	0.948528	+	0.316693i
$26$		−	3.46410i		−	0.679366i
$27$		0			0
$28$	3.22474	−	3.22474i	0.609419	−	0.609419i
$29$	0.158919	−	0.275255i	0.0295104	−	0.0511136i	−0.850893	−	0.525339i	$-0.823939\pi$
$29$	0.158919	−	0.275255i	0.0295104	−	0.0511136i	0.880403	+	0.474225i	$0.157272\pi$
$30$		0			0
$31$	−0.224745	−	0.389270i	−0.0403654	−	0.0699149i	0.845137	−	0.534550i	$-0.179519\pi$
$31$	−0.224745	−	0.389270i	−0.0403654	−	0.0699149i	−0.885502	+	0.464635i	$0.846186\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$		0			0
$34$	−0.389270	−	0.224745i	−0.0667592	−	0.0385434i
$35$	10.1459	−	1.02494i	1.71497	−	0.173247i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−6.22973	+	1.66925i	−1.01060	+	0.270788i
$39$		0			0
$40$	1.30701	+	1.81431i	0.206656	+	0.286868i
$41$	−6.39898	+	3.69445i	−0.999353	+	0.576977i	−0.908057	−	0.418847i	$-0.862434\pi$
$41$	−6.39898	+	3.69445i	−0.999353	+	0.576977i	−0.0912960	+	0.995824i	$0.529101\pi$
$42$		0			0
$43$	−0.896575	−	3.34607i	−0.136726	−	0.510270i	−0.999985	−	0.00550783i	$-0.998247\pi$
$43$	−0.896575	−	3.34607i	−0.136726	−	0.510270i	0.863258	−	0.504762i	$-0.168420\pi$
$44$	−0.635674			−0.0958315
$45$		0			0
$46$	1.00000			0.147442
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	0.898600	+	0.438768i	$0.144585\pi$
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	−0.558827	+	0.829285i	$0.688748\pi$
$48$		0			0
$49$	11.9494	−	6.89898i	1.70705	−	0.985568i
$50$	−0.302023	+	4.99087i	−0.0427126	+	0.705816i
$51$		0			0
$52$	3.34607	−	0.896575i	0.464016	−	0.124333i
$53$	−3.78194	−	3.78194i	−0.519489	−	0.519489i	0.397928	−	0.917417i	$-0.369730\pi$
$53$	−3.78194	−	3.78194i	−0.519489	−	0.519489i	−0.917417	+	0.397928i	$0.869730\pi$
$54$		0			0
$55$	−1.10102	−	0.898979i	−0.148462	−	0.121218i
$56$	3.94949	+	2.28024i	0.527773	+	0.304710i
$57$		0			0
$58$	0.307007	+	0.0822623i	0.0403120	+	0.0108016i
$59$	4.48905	+	7.77526i	0.584424	+	1.01225i	0.994947	+	0.100402i	$0.0320128\pi$
$59$	4.48905	+	7.77526i	0.584424	+	1.01225i	−0.410523	+	0.911850i	$0.634654\pi$
$60$		0			0
$61$	0.275255	−	0.476756i	0.0352428	−	0.0610423i	−0.847866	−	0.530211i	$-0.822113\pi$
$61$	0.275255	−	0.476756i	0.0352428	−	0.0610423i	0.883109	+	0.469168i	$0.155446\pi$
$62$	0.317837	−	0.317837i	0.0403654	−	0.0403654i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	7.06350	+	3.17914i	0.876120	+	0.394323i
$66$		0			0
$67$	−1.71089	+	6.38512i	−0.209018	+	0.780067i	0.779169	+	0.626814i	$0.215642\pi$
$67$	−1.71089	+	6.38512i	−0.209018	+	0.780067i	−0.988187	+	0.153253i	$0.951025\pi$
$68$	0.116337	−	0.434174i	0.0141079	−	0.0526513i
$69$		0			0
$70$	3.61597	+	9.53491i	0.432191	+	1.13964i
$71$		−	6.29253i		−	0.746786i	−0.927673	−	0.373393i	$-0.878194\pi$
$71$		−	6.29253i		−	0.746786i	0.927673	−	0.373393i	$-0.121806\pi$
$72$		0			0
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	−0.984249	−	0.176785i	$-0.943430\pi$
$73$	−6.89898	+	6.89898i	−0.807464	+	0.807464i	0.176785	+	0.984249i	$0.443430\pi$
$74$	2.12132	−	3.67423i	0.246598	−	0.427121i
$75$		0			0
$76$	−3.22474	−	5.58542i	−0.369904	−	0.640692i
$77$	−2.80020	−	0.750311i	−0.319112	−	0.0855059i
$78$		0			0
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	0.375897	−	0.926662i	$-0.377335\pi$
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	−0.614564	+	0.788867i	$0.710668\pi$
$80$	−1.41421	+	1.73205i	−0.158114	+	0.193649i
$81$		0			0
$82$	−5.22474	−	5.22474i	−0.576977	−	0.576977i
$83$	−5.26380	+	1.41043i	−0.577777	+	0.154815i	−0.535861	−	0.844306i	$-0.680013\pi$
$83$	−5.26380	+	1.41043i	−0.577777	+	0.154815i	−0.0419163	+	0.999121i	$0.513346\pi$
$84$		0			0
$85$	0.815515	−	0.587486i	0.0884550	−	0.0637218i
$86$	3.00000	−	1.73205i	0.323498	−	0.186772i
$87$		0			0
$88$	−0.164525	−	0.614014i	−0.0175384	−	0.0654542i
$89$	8.02458			0.850604			0.425302	−	0.905052i	$-0.360168\pi$
$89$	8.02458			0.850604			0.425302	+	0.905052i	$0.360168\pi$
$90$		0			0
$91$	15.7980			1.65608
$92$	0.258819	+	0.965926i	0.0269838	+	0.100705i
$93$		0			0
$94$	−7.79423	+	4.50000i	−0.803913	+	0.464140i
$95$	2.31356	−	14.2347i	0.237366	−	1.46045i
$96$		0			0
$97$	−2.59405	+	0.695075i	−0.263386	+	0.0705741i	−0.388095	−	0.921619i	$-0.626867\pi$
$97$	−2.59405	+	0.695075i	−0.263386	+	0.0705741i	0.124709	+	0.992193i	$0.460200\pi$
$98$	9.75663	+	9.75663i	0.985568	+	0.985568i
$99$		0			0
$100$	−4.89898	+	1.00000i	−0.489898	+	0.100000i
$101$	−10.8990	−	6.29253i	−1.08449	−	0.626130i	−0.152385	−	0.988321i	$-0.548695\pi$
$101$	−10.8990	−	6.29253i	−1.08449	−	0.626130i	−0.932104	+	0.362191i	$0.882029\pi$
$102$		0			0
$103$	9.42418	+	2.52520i	0.928592	+	0.248816i	0.691254	−	0.722612i	$-0.257058\pi$
$103$	9.42418	+	2.52520i	0.928592	+	0.248816i	0.237338	+	0.971427i	$0.423725\pi$
$104$	1.73205	+	3.00000i	0.169842	+	0.294174i
$105$		0			0
$106$	2.67423	−	4.63191i	0.259745	−	0.449891i
$107$	−13.6100	+	13.6100i	−1.31573	+	1.31573i	−0.398606	+	0.917122i	$0.630506\pi$
$107$	−13.6100	+	13.6100i	−1.31573	+	1.31573i	−0.917122	+	0.398606i	$0.869494\pi$
$108$		0			0
$109$		−	5.65153i		−	0.541318i	−0.962675	−	0.270659i	$-0.912758\pi$
$109$		−	5.65153i		−	0.541318i	0.962675	−	0.270659i	$-0.0872417\pi$
$110$	0.583382	−	1.29618i	0.0556233	−	0.123586i
$111$		0			0
$112$	−1.18034	+	4.40508i	−0.111532	+	0.416241i
$113$	1.50062	−	5.60040i	0.141167	−	0.526841i	−0.858729	−	0.512429i	$-0.828746\pi$
$113$	1.50062	−	5.60040i	0.141167	−	0.526841i	0.999896	−	0.0144120i	$-0.00458763\pi$
$114$		0			0
$115$	−0.917738	+	2.03906i	−0.0855795	+	0.190143i
$116$			0.317837i			0.0295104i
$117$		0			0
$118$	−6.34847	+	6.34847i	−0.584424	+	0.584424i
$119$	1.02494	−	1.77526i	0.0939565	−	0.162737i
$120$		0			0
$121$	−5.29796	−	9.17633i	−0.481633	−	0.834212i
$122$	0.531752	+	0.142483i	0.0481426	+	0.0128998i
$123$		0			0
$124$	0.389270	+	0.224745i	0.0349574	+	0.0201827i
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$		0			0
$127$	1.87628	+	1.87628i	0.166493	+	0.166493i	0.785436	−	0.618943i	$-0.212439\pi$
$127$	1.87628	+	1.87628i	0.166493	+	0.166493i	−0.618943	+	0.785436i	$0.712439\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$		0			0
$130$	−1.24264	+	7.64564i	−0.108987	+	0.670567i
$131$	3.12372	−	1.80348i	0.272921	−	0.157571i	−0.357293	−	0.933992i	$-0.616300\pi$
$131$	3.12372	−	1.80348i	0.272921	−	0.157571i	0.630214	+	0.776421i	$0.282967\pi$
$132$		0			0
$133$	−7.61258	−	28.4105i	−0.660095	−	2.46351i
$134$	−6.61037			−0.571049
$135$		0			0
$136$	0.449490			0.0385434
$137$	−5.64173	−	21.0552i	−0.482005	−	1.79887i	−0.593183	−	0.805068i	$-0.702129\pi$
$137$	−5.64173	−	21.0552i	−0.482005	−	1.79887i	0.111178	−	0.993801i	$-0.464538\pi$
$138$		0			0
$139$	2.68556	−	1.55051i	0.227786	−	0.131513i	−0.381764	−	0.924260i	$-0.624683\pi$
$139$	2.68556	−	1.55051i	0.227786	−	0.131513i	0.609550	+	0.792747i	$0.291350\pi$
$140$	−8.27414	+	5.96058i	−0.699292	+	0.503761i
$141$		0			0
$142$	6.07812	−	1.62863i	0.510064	−	0.136671i
$143$	−1.55708	−	1.55708i	−0.130209	−	0.130209i
$144$		0			0
$145$	−0.449490	+	0.550510i	−0.0373281	+	0.0457174i
$146$	−8.44949	−	4.87832i	−0.699285	−	0.403732i
$147$		0			0
$148$	4.09808	+	1.09808i	0.336860	+	0.0902613i
$149$	−2.20881	−	3.82577i	−0.180952	−	0.313419i	0.761253	−	0.648455i	$-0.224585\pi$
$149$	−2.20881	−	3.82577i	−0.180952	−	0.313419i	−0.942205	+	0.335036i	$0.891251\pi$
$150$		0			0
$151$	−8.79796	+	15.2385i	−0.715968	+	1.24009i	0.246617	+	0.969113i	$0.420681\pi$
$151$	−8.79796	+	15.2385i	−0.715968	+	1.24009i	−0.962585	+	0.270980i	$0.912652\pi$
$152$	4.56048	−	4.56048i	0.369904	−	0.369904i
$153$		0			0
$154$		−	2.89898i		−	0.233606i
$155$	0.356397	+	0.939780i	0.0286265	+	0.0754849i
$156$		0			0
$157$	−3.78780	+	14.1363i	−0.302300	+	1.12820i	0.632945	+	0.774196i	$0.281846\pi$
$157$	−3.78780	+	14.1363i	−0.302300	+	1.12820i	−0.935245	+	0.354001i	$0.884821\pi$
$158$	0.633975	−	2.36603i	0.0504363	−	0.188231i
$159$		0			0
$160$	−2.03906	−	0.917738i	−0.161202	−	0.0725535i
$161$			4.56048i			0.359416i
$162$		0			0
$163$	4.44949	−	4.44949i	0.348511	−	0.348511i	−0.511044	−	0.859555i	$-0.670741\pi$
$163$	4.44949	−	4.44949i	0.348511	−	0.348511i	0.859555	+	0.511044i	$0.170741\pi$
$164$	3.69445	−	6.39898i	0.288488	−	0.499676i
$165$		0			0
$166$	−2.72474	−	4.71940i	−0.211481	−	0.366296i
$167$	8.49818	+	2.27708i	0.657609	+	0.176206i	0.572167	−	0.820137i	$-0.306103\pi$
$167$	8.49818	+	2.27708i	0.657609	+	0.176206i	0.0854420	+	0.996343i	$0.472770\pi$
$168$		0			0
$169$	−0.866025	−	0.500000i	−0.0666173	−	0.0384615i
$170$	0.778539	+	0.635674i	0.0597112	+	0.0487540i
$171$		0			0
$172$	2.44949	+	2.44949i	0.186772	+	0.186772i
$173$	12.4595	−	3.33850i	0.947275	−	0.253822i	0.248069	−	0.968742i	$-0.420204\pi$
$173$	12.4595	−	3.33850i	0.947275	−	0.253822i	0.699206	+	0.714921i	$0.253537\pi$
$174$		0			0
$175$	−22.7608	−	1.37737i	−1.72055	−	0.104119i
$176$	0.550510	−	0.317837i	0.0414963	−	0.0239579i
$177$		0			0
$178$	2.07691	+	7.75115i	0.155671	+	0.580973i
$179$	−10.6780			−0.798114			−0.399057	−	0.916926i	$-0.630662\pi$
$179$	−10.6780			−0.798114			−0.399057	+	0.916926i	$0.630662\pi$
$180$		0			0
$181$	−15.4495			−1.14835			−0.574176	−	0.818732i	$-0.694677\pi$
$181$	−15.4495			−1.14835			−0.574176	+	0.818732i	$0.694677\pi$
$182$	4.08881	+	15.2597i	0.303083	+	1.13112i
$183$		0			0
$184$	−0.866025	+	0.500000i	−0.0638442	+	0.0368605i
$185$	5.54516	+	7.69748i	0.407688	+	0.565930i
$186$		0			0
$187$	−0.275993	+	0.0739521i	−0.0201826	+	0.00540792i
$188$	−6.36396	−	6.36396i	−0.464140	−	0.464140i
$189$		0			0
$190$	14.3485	−	1.44949i	1.04095	−	0.105157i
$191$	15.1237	+	8.73169i	1.09431	+	0.631803i	0.934722	−	0.355380i	$-0.115649\pi$
$191$	15.1237	+	8.73169i	1.09431	+	0.631803i	0.159593	+	0.987183i	$0.448982\pi$
$192$		0			0
$193$	16.7303	+	4.48288i	1.20428	+	0.322685i	0.804513	−	0.593934i	$-0.202426\pi$
$193$	16.7303	+	4.48288i	1.20428	+	0.322685i	0.399762	+	0.916619i	$0.369093\pi$
$194$	−1.34278	−	2.32577i	−0.0964061	−	0.166980i
$195$		0			0
$196$	−6.89898	+	11.9494i	−0.492784	+	0.853527i
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	−0.909443	−	0.415829i	$-0.863492\pi$
$197$	−6.92820	+	6.92820i	−0.493614	+	0.493614i	0.415829	+	0.909443i	$0.363492\pi$
$198$		0			0
$199$			8.44949i			0.598968i	0.954101	+	0.299484i	$0.0968146\pi$
$199$			8.44949i			0.598968i	−0.954101	+	0.299484i	$0.903185\pi$
$200$	−2.23388	−	4.47323i	−0.157959	−	0.316305i
$201$		0			0
$202$	3.25725	−	12.1562i	0.229179	−	0.855310i
$203$	−0.375156	+	1.40010i	−0.0263308	+	0.0982677i
$204$		0			0
$205$	15.4485	−	5.85861i	1.07897	−	0.409183i
$206$			9.75663i			0.679777i
$207$		0			0
$208$	−2.44949	+	2.44949i	−0.169842	+	0.169842i
$209$	−2.04989	+	3.55051i	−0.141794	+	0.245594i
$210$		0			0
$211$	−4.55051	−	7.88171i	−0.313270	−	0.542600i	0.665798	−	0.746132i	$-0.268091\pi$
$211$	−4.55051	−	7.88171i	−0.313270	−	0.542600i	−0.979068	+	0.203532i	$0.934758\pi$
$212$	5.16622	+	1.38429i	0.354818	+	0.0950731i
$213$		0			0
$214$	−16.6688	−	9.62372i	−1.13945	−	0.657864i
$215$	0.778539	+	7.70674i	0.0530959	+	0.525595i
$216$		0			0
$217$	1.44949	+	1.44949i	0.0983978	+	0.0983978i
$218$	5.45896	−	1.46272i	0.369727	−	0.0990682i
$219$		0			0
$220$	1.40300	+	0.228029i	0.0945903	+	0.0153737i
$221$	1.34847	−	0.778539i	0.0907079	−	0.0523702i
$222$		0			0
$223$	6.63374	+	24.7575i	0.444228	+	1.65788i	0.717966	+	0.696078i	$0.245073\pi$
$223$	6.63374	+	24.7575i	0.444228	+	1.65788i	−0.273738	+	0.961804i	$0.588260\pi$
$224$	−4.56048			−0.304710
$225$		0			0
$226$	5.79796			0.385674
$227$	−6.44433	−	24.0506i	−0.427725	−	1.59629i	−0.757899	−	0.652372i	$-0.773774\pi$
$227$	−6.44433	−	24.0506i	−0.427725	−	1.59629i	0.330174	−	0.943920i	$-0.392893\pi$
$228$		0			0
$229$	−1.43027	+	0.825765i	−0.0945147	+	0.0545681i	−0.546512	−	0.837451i	$-0.684045\pi$
$229$	−1.43027	+	0.825765i	−0.0945147	+	0.0545681i	0.451998	+	0.892019i	$0.350712\pi$
$230$	−2.20711	−	0.358719i	−0.145532	−	0.0236533i
$231$		0			0
$232$	−0.307007	+	0.0822623i	−0.0201560	+	0.00540079i
$233$	14.4600	+	14.4600i	0.947304	+	0.947304i	0.998679	−	0.0513751i	$-0.0163604\pi$
$233$	14.4600	+	14.4600i	0.947304	+	0.947304i	−0.0513751	+	0.998679i	$0.516360\pi$
$234$		0			0
$235$	−2.02270	−	20.0227i	−0.131947	−	1.30614i
$236$	−7.77526	−	4.48905i	−0.506126	−	0.292212i
$237$		0			0
$238$	1.98004	+	0.530550i	0.128347	+	0.0343905i
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	0.998353	+	0.0573782i	$0.0182741\pi$
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	−0.449485	+	0.893288i	$0.648393\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$	7.49245	−	7.49245i	0.481633	−	0.481633i
$243$		0			0
$244$			0.550510i			0.0352428i
$245$	−28.8484	+	10.9403i	−1.84305	+	0.698951i
$246$		0			0
$247$	5.78245	−	21.5804i	0.367929	−	1.37313i
$248$	−0.116337	+	0.434174i	−0.00738738	+	0.0275701i
$249$		0			0
$250$	2.45692	−	10.9070i	0.155389	−	0.689822i
$251$		−	2.68556i		−	0.169511i	−0.996402	−	0.0847556i	$-0.972989\pi$
$251$		−	2.68556i		−	0.169511i	0.996402	−	0.0847556i	$-0.0270110\pi$
$252$		0			0
$253$	0.449490	−	0.449490i	0.0282592	−	0.0282592i
$254$	−1.32673	+	2.29796i	−0.0832463	+	0.144187i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	17.4305	+	4.67050i	1.08729	+	0.291337i	0.757578	−	0.652745i	$-0.226383\pi$
$257$	17.4305	+	4.67050i	1.08729	+	0.291337i	0.329709	+	0.944083i	$0.393049\pi$
$258$		0			0
$259$	16.7563	+	9.67423i	1.04118	+	0.601128i
$260$	−7.70674	+	0.778539i	−0.477952	+	0.0482829i
$261$		0			0
$262$	2.55051	+	2.55051i	0.157571	+	0.157571i
$263$	−16.1280	+	4.32149i	−0.994495	+	0.266474i	−0.719138	−	0.694868i	$-0.755463\pi$
$263$	−16.1280	+	4.32149i	−0.994495	+	0.266474i	−0.275358	+	0.961342i	$0.588796\pi$
$264$		0			0
$265$	6.99049	+	9.70380i	0.429422	+	0.596100i
$266$	25.4722	−	14.7064i	1.56180	−	0.901706i
$267$		0			0
$268$	−1.71089	−	6.38512i	−0.104509	−	0.390033i
$269$	15.0956			0.920398			0.460199	−	0.887816i	$-0.347778\pi$
$269$	15.0956			0.920398			0.460199	+	0.887816i	$0.347778\pi$
$270$		0			0
$271$	28.0454			1.70364			0.851819	−	0.523837i	$-0.175500\pi$
$271$	28.0454			1.70364			0.851819	+	0.523837i	$0.175500\pi$
$272$	0.116337	+	0.434174i	0.00705394	+	0.0263257i
$273$		0			0
$274$	18.8776	−	10.8990i	1.14044	−	0.658431i
$275$	2.10759	+	2.37910i	0.127092	+	0.143465i
$276$		0			0
$277$	27.1825	−	7.28353i	1.63324	−	0.437625i	0.678386	−	0.734705i	$-0.262680\pi$
$277$	27.1825	−	7.28353i	1.63324	−	0.437625i	0.954852	+	0.297080i	$0.0960129\pi$
$278$	2.19275	+	2.19275i	0.131513	+	0.131513i
$279$		0			0
$280$	−7.89898	−	6.44949i	−0.472054	−	0.385431i
$281$	14.8485	+	8.57277i	0.885785	+	0.511408i	0.872562	−	0.488504i	$-0.162457\pi$
$281$	14.8485	+	8.57277i	0.885785	+	0.511408i	0.0132238	+	0.999913i	$0.495791\pi$
$282$		0			0
$283$	−23.3914	−	6.26772i	−1.39048	−	0.372577i	−0.515561	−	0.856853i	$-0.672417\pi$
$283$	−23.3914	−	6.26772i	−1.39048	−	0.372577i	−0.874916	+	0.484275i	$0.839083\pi$
$284$	3.14626	+	5.44949i	0.186696	+	0.323368i
$285$		0			0
$286$	1.10102	−	1.90702i	0.0651047	−	0.112765i
$287$	23.8273	−	23.8273i	1.40648	−	1.40648i
$288$		0			0
$289$			16.7980i			0.988115i
$290$	−0.648089	−	0.291691i	−0.0380571	−	0.0171287i
$291$		0			0
$292$	2.52520	−	9.42418i	0.147776	−	0.551508i
$293$	−5.70577	+	21.2942i	−0.333335	+	1.24402i	0.572329	+	0.820024i	$0.306040\pi$
$293$	−5.70577	+	21.2942i	−0.333335	+	1.24402i	−0.905663	+	0.423998i	$0.860626\pi$
$294$		0			0
$295$	−7.11867	−	18.7711i	−0.414465	−	1.09290i
$296$			4.24264i			0.246598i
$297$		0			0
$298$	3.12372	−	3.12372i	0.180952	−	0.180952i
$299$	−1.73205	+	3.00000i	−0.100167	+	0.173494i
$300$		0			0
$301$	7.89898	+	13.6814i	0.455290	+	0.788585i
$302$	−16.9964	−	4.55416i	−0.978030	−	0.262062i
$303$		0			0
$304$	5.58542	+	3.22474i	0.320346	+	0.184952i
$305$	−0.778539	+	0.953512i	−0.0445790	+	0.0545979i
$306$		0			0
$307$	−6.67423	−	6.67423i	−0.380919	−	0.380919i	0.490514	−	0.871433i	$-0.336809\pi$
$307$	−6.67423	−	6.67423i	−0.380919	−	0.380919i	−0.871433	+	0.490514i	$0.836809\pi$
$308$	2.80020	−	0.750311i	0.159556	−	0.0427529i
$309$		0			0
$310$	−0.815515	+	0.587486i	−0.0463181	+	0.0333670i
$311$	−23.8207	+	13.7529i	−1.35075	+	0.779853i	−0.988354	−	0.152172i	$-0.951373\pi$
$311$	−23.8207	+	13.7529i	−1.35075	+	0.779853i	−0.362392	+	0.932026i	$0.618040\pi$
$312$		0			0
$313$	3.09273	+	11.5422i	0.174811	+	0.652405i	0.996584	+	0.0825888i	$0.0263188\pi$
$313$	3.09273	+	11.5422i	0.174811	+	0.652405i	−0.821772	+	0.569816i	$0.807015\pi$
$314$	−14.6349			−0.825898
$315$		0			0
$316$	2.44949			0.137795
$317$	2.82086	+	10.5276i	0.158435	+	0.591289i	0.998787	+	0.0492469i	$0.0156821\pi$
$317$	2.82086	+	10.5276i	0.158435	+	0.591289i	−0.840351	+	0.542042i	$0.817651\pi$
$318$		0			0
$319$	0.174973	−	0.101021i	0.00979659	−	0.00565606i
$320$	0.358719	−	2.20711i	0.0200530	−	0.123381i
$321$		0			0
$322$	−4.40508	+	1.18034i	−0.245486	+	0.0657777i
$323$	−2.04989	−	2.04989i	−0.114059	−	0.114059i
$324$		0			0
$325$	−14.4495	−	9.55051i	−0.801513	−	0.529767i
$326$	5.44949	+	3.14626i	0.301819	+	0.174255i
$327$		0			0
$328$	7.13713	+	1.91239i	0.394082	+	0.105594i
$329$	−20.5222	−	35.5454i	−1.13142	−	1.95968i
$330$		0			0
$331$	−0.224745	+	0.389270i	−0.0123531	+	0.0213962i	−0.872136	−	0.489264i	$-0.837266\pi$
$331$	−0.224745	+	0.389270i	−0.0123531	+	0.0213962i	0.859783	+	0.510660i	$0.170599\pi$
$332$	3.85337	−	3.85337i	0.211481	−	0.211481i
$333$		0			0
$334$			8.79796i			0.481403i
$335$	6.06658	−	13.4789i	0.331453	−	0.736432i
$336$		0			0
$337$	−0.806003	+	3.00804i	−0.0439058	+	0.163859i	−0.984398	−	0.175957i	$-0.943698\pi$
$337$	−0.806003	+	3.00804i	−0.0439058	+	0.163859i	0.940492	+	0.339816i	$0.110365\pi$
$338$	0.258819	−	0.965926i	0.0140779	−	0.0525394i
$339$		0			0
$340$	−0.412514	+	0.916536i	−0.0223717	+	0.0497061i
$341$		−	0.285729i		−	0.0154731i
$342$		0			0
$343$	−21.9217	+	21.9217i	−1.18366	+	1.18366i
$344$	−1.73205	+	3.00000i	−0.0933859	+	0.161749i
$345$		0			0
$346$	6.44949	+	11.1708i	0.346727	+	0.600548i
$347$	−22.9871	−	6.15937i	−1.23401	−	0.330652i	−0.417870	−	0.908507i	$-0.637223\pi$
$347$	−22.9871	−	6.15937i	−1.23401	−	0.330652i	−0.816140	+	0.577855i	$0.803890\pi$
$348$		0			0
$349$	−25.1541	−	14.5227i	−1.34647	−	0.777383i	−0.358719	−	0.933446i	$-0.616786\pi$
$349$	−25.1541	−	14.5227i	−1.34647	−	0.777383i	−0.987747	+	0.156063i	$0.950120\pi$
$350$	−4.56048	−	22.3417i	−0.243768	−	1.19421i
$351$		0			0
$352$	0.449490	+	0.449490i	0.0239579	+	0.0239579i
$353$	33.1244	−	8.87564i	1.76303	−	0.472403i	0.775704	−	0.631097i	$-0.217395\pi$
$353$	33.1244	−	8.87564i	1.76303	−	0.472403i	0.987328	+	0.158694i	$0.0507284\pi$
$354$		0			0
$355$	−2.25725	+	13.8883i	−0.119803	+	0.737114i
$356$	−6.94949	+	4.01229i	−0.368322	+	0.212651i
$357$		0			0
$358$	−2.76368	−	10.3142i	−0.146065	−	0.545122i
$359$	−3.32124			−0.175288			−0.0876441	−	0.996152i	$-0.527934\pi$
$359$	−3.32124			−0.175288			−0.0876441	+	0.996152i	$0.527934\pi$
$360$		0			0
$361$	−22.5959			−1.18926
$362$	−3.99862	−	14.9231i	−0.210163	−	0.784339i
$363$		0			0
$364$	−13.6814	+	7.89898i	−0.717102	+	0.414019i
$365$	17.7016	−	12.7520i	0.926543	−	0.667469i
$366$		0			0
$367$	3.96008	−	1.06110i	0.206714	−	0.0553890i	−0.153976	−	0.988075i	$-0.549208\pi$
$367$	3.96008	−	1.06110i	0.206714	−	0.0553890i	0.360690	+	0.932686i	$0.382541\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$		0			0
$370$	−6.00000	+	7.34847i	−0.311925	+	0.382029i
$371$	21.1237	+	12.1958i	1.09669	+	0.633174i
$372$		0			0
$373$	0.476018	+	0.127549i	0.0246473	+	0.00660422i	0.271122	−	0.962545i	$-0.412605\pi$
$373$	0.476018	+	0.127549i	0.0246473	+	0.00660422i	−0.246474	+	0.969149i	$0.579272\pi$
$374$	−0.142865	−	0.247449i	−0.00738735	−	0.0127953i
$375$		0			0
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$	−0.778539	+	0.778539i	−0.0400968	+	0.0400968i
$378$		0			0
$379$		−	21.3485i		−	1.09660i	−0.836283	−	0.548299i	$-0.815276\pi$
$379$		−	21.3485i		−	1.09660i	0.836283	−	0.548299i	$-0.184724\pi$
$380$	5.11376	+	13.4844i	0.262330	+	0.691735i
$381$		0			0
$382$	−4.51985	+	16.8683i	−0.231256	+	0.863058i
$383$	2.12284	−	7.92256i	0.108472	−	0.404824i	−0.890244	−	0.455485i	$-0.849466\pi$
$383$	2.12284	−	7.92256i	0.108472	−	0.404824i	0.998716	+	0.0506606i	$0.0161327\pi$
$384$		0			0
$385$	5.91119	+	2.66050i	0.301262	+	0.135592i
$386$			17.3205i			0.881591i
$387$		0			0
$388$	1.89898	−	1.89898i	0.0964061	−	0.0964061i
$389$	−18.4008	+	31.8712i	−0.932959	+	1.61593i	−0.154726	+	0.987957i	$0.549449\pi$
$389$	−18.4008	+	31.8712i	−0.932959	+	1.61593i	−0.778233	+	0.627975i	$0.783884\pi$
$390$		0			0
$391$	0.224745	+	0.389270i	0.0113658	+	0.0196862i
$392$	−13.3278	−	3.57117i	−0.673156	−	0.180372i
$393$		0			0
$394$	−8.48528	−	4.89898i	−0.427482	−	0.246807i
$395$	4.24264	+	3.46410i	0.213470	+	0.174298i
$396$		0			0
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	0.920428	−	0.390913i	$-0.127841\pi$
$397$	10.5505	+	10.5505i	0.529515	+	0.529515i	−0.390913	+	0.920428i	$0.627841\pi$
$398$	−8.16158	+	2.18689i	−0.409103	+	0.109619i
$399$		0			0
$400$	3.74264	−	3.31552i	0.187132	−	0.165776i
$401$	−7.65153	+	4.41761i	−0.382099	+	0.220605i	−0.678731	−	0.734387i	$-0.737470\pi$
$401$	−7.65153	+	4.41761i	−0.382099	+	0.220605i	0.296632	+	0.954992i	$0.404137\pi$
$402$		0			0
$403$	0.403001	+	1.50402i	0.0200749	+	0.0749207i
$404$	12.5851			0.626130
$405$		0			0
$406$	−1.44949			−0.0719370
$407$	−0.698019	−	2.60504i	−0.0345995	−	0.129127i
$408$		0			0
$409$	−25.0273	+	14.4495i	−1.23752	+	0.714481i	−0.968586	−	0.248678i	$-0.920004\pi$
$409$	−25.0273	+	14.4495i	−1.23752	+	0.714481i	−0.268932	+	0.963159i	$0.586671\pi$
$410$	9.65735	+	13.4058i	0.476943	+	0.662065i
$411$		0			0
$412$	−9.42418	+	2.52520i	−0.464296	+	0.124408i
$413$	−28.9521	−	28.9521i	−1.42464	−	1.42464i
$414$		0			0
$415$	12.1237	−	1.22474i	0.595130	−	0.0601204i
$416$	−3.00000	−	1.73205i	−0.147087	−	0.0849208i
$417$		0			0
$418$	−3.96008	−	1.06110i	−0.193694	−	0.0519001i
$419$	−2.51059	−	4.34847i	−0.122650	−	0.212437i	0.798162	−	0.602443i	$-0.205806\pi$
$419$	−2.51059	−	4.34847i	−0.122650	−	0.212437i	−0.920812	+	0.390007i	$0.872473\pi$
$420$		0			0
$421$	2.55051	−	4.41761i	0.124304	−	0.215301i	−0.797157	−	0.603773i	$-0.793663\pi$
$421$	2.55051	−	4.41761i	0.124304	−	0.215301i	0.921461	+	0.388471i	$0.126997\pi$
$422$	6.43539	−	6.43539i	0.313270	−	0.313270i
$423$		0			0
$424$			5.34847i			0.259745i
$425$	−2.01067	+	1.00410i	−0.0975319	+	0.0487062i
$426$		0			0
$427$	−0.649788	+	2.42504i	−0.0314455	+	0.117356i
$428$	4.98161	−	18.5916i	0.240795	−	0.898659i
$429$		0			0
$430$	−7.24264	+	2.74666i	−0.349271	+	0.132456i
$431$			15.5563i			0.749323i	0.927162	+	0.374661i	$0.122241\pi$
$431$			15.5563i			0.749323i	−0.927162	+	0.374661i	$0.877759\pi$
$432$		0			0
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	−0.305766	−	0.952107i	$-0.598912\pi$
$433$	13.4495	−	13.4495i	0.646341	−	0.646341i	0.952107	+	0.305766i	$0.0989124\pi$
$434$	−1.02494	+	1.77526i	−0.0491989	+	0.0852150i
$435$		0			0
$436$	2.82577	+	4.89437i	0.135330	+	0.234398i
$437$	6.22973	+	1.66925i	0.298008	+	0.0798511i
$438$		0			0
$439$	−25.8058	−	14.8990i	−1.23164	−	0.711089i	−0.264271	−	0.964449i	$-0.585131\pi$
$439$	−25.8058	−	14.8990i	−1.23164	−	0.711089i	−0.967372	+	0.253359i	$0.918465\pi$
$440$	0.142865	+	1.41421i	0.00681080	+	0.0674200i
$441$		0			0
$442$	1.10102	+	1.10102i	0.0523702	+	0.0523702i
$443$	5.26380	−	1.41043i	0.250091	−	0.0670116i	−0.131596	−	0.991303i	$-0.542010\pi$
$443$	5.26380	−	1.41043i	0.250091	−	0.0670116i	0.381687	+	0.924292i	$0.375343\pi$
$444$		0			0
$445$	−17.7111	−	2.87857i	−0.839587	−	0.136457i
$446$	−22.1969	+	12.8154i	−1.05106	+	0.606827i
$447$		0			0
$448$	−1.18034	−	4.40508i	−0.0557658	−	0.208121i
$449$	−0.921404			−0.0434837			−0.0217419	−	0.999764i	$-0.506921\pi$
$449$	−0.921404			−0.0434837			−0.0217419	+	0.999764i	$0.506921\pi$
$450$		0			0
$451$	−4.69694			−0.221170
$452$	1.50062	+	5.60040i	0.0705833	+	0.263421i
$453$		0			0
$454$	21.5631	−	12.4495i	1.01201	−	0.584284i
$455$	−34.8678	−	5.66704i	−1.63463	−	0.265675i
$456$		0			0
$457$	14.1363	−	3.78780i	0.661267	−	0.177186i	0.0874492	−	0.996169i	$-0.472128\pi$
$457$	14.1363	−	3.78780i	0.661267	−	0.177186i	0.573818	+	0.818983i	$0.305462\pi$
$458$	−1.16781	−	1.16781i	−0.0545681	−	0.0545681i
$459$		0			0
$460$	−0.224745	−	2.22474i	−0.0104788	−	0.103729i
$461$	−28.6237	−	16.5259i	−1.33314	−	0.769689i	−0.347360	−	0.937732i	$-0.612922\pi$
$461$	−28.6237	−	16.5259i	−1.33314	−	0.769689i	−0.985780	+	0.168043i	$0.946255\pi$
$462$		0			0
$463$	11.8182	+	3.16668i	0.549239	+	0.147168i	0.522758	−	0.852481i	$-0.324903\pi$
$463$	11.8182	+	3.16668i	0.549239	+	0.147168i	0.0264810	+	0.999649i	$0.491570\pi$
$464$	−0.158919	−	0.275255i	−0.00737761	−	0.0127784i
$465$		0			0
$466$	−10.2247	+	17.7098i	−0.473652	+	0.820390i
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	−0.769514	−	0.638630i	$-0.779501\pi$
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	0.638630	+	0.769514i	$0.279501\pi$
$468$		0			0
$469$		−	30.1464i		−	1.39203i
$470$	18.8169	−	7.13604i	0.867960	−	0.329161i
$471$		0			0
$472$	2.32370	−	8.67217i	0.106957	−	0.399169i
$473$	0.569930	−	2.12701i	0.0262054	−	0.0977999i
$474$		0			0
$475$	−10.2125	+	30.5876i	−0.468583	+	1.40346i
$476$			2.04989i			0.0939565i
$477$		0			0
$478$	−12.0000	+	12.0000i	−0.548867	+	0.548867i
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	−0.773879	−	0.633333i	$-0.781686\pi$
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	0.935422	+	0.353533i	$0.115020\pi$
$480$		0			0
$481$	7.34847	+	12.7279i	0.335061	+	0.580343i
$482$	−18.3526	−	4.91756i	−0.835938	−	0.223989i
$483$		0			0
$484$	9.17633	+	5.29796i	0.417106	+	0.240816i
$485$	5.97469	−	0.603566i	0.271297	−	0.0274065i
$486$		0			0
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	0.380861	−	0.924632i	$-0.375628\pi$
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	−0.924632	+	0.380861i	$0.875628\pi$
$488$	−0.531752	+	0.142483i	−0.0240713	+	0.00644988i
$489$		0			0
$490$	−18.0340	−	25.0338i	−0.814695	−	1.13091i
$491$	24.2474	−	13.9993i	1.09427	−	0.631778i	0.159561	−	0.987188i	$-0.448992\pi$
$491$	24.2474	−	13.9993i	1.09427	−	0.631778i	0.934711	+	0.355410i	$0.115659\pi$
$492$		0			0
$493$	0.0369761	+	0.137997i	0.00166532	+	0.00621505i
$494$	22.3417			1.00520
$495$		0			0
$496$	−0.449490			−0.0201827
$497$	7.42731	+	27.7191i	0.333161	+	1.24337i
$498$		0			0
$499$	0.778539	−	0.449490i	0.0348522	−	0.0201219i	−0.482473	−	0.875911i	$-0.660261\pi$
$499$	0.778539	−	0.449490i	0.0348522	−	0.0201219i	0.517325	+	0.855789i	$0.326928\pi$
$500$	11.1713	−	0.449747i	0.499595	−	0.0201133i
$501$		0			0
$502$	2.59405	−	0.695075i	0.115778	−	0.0310227i
$503$	−4.02834	−	4.02834i	−0.179615	−	0.179615i	0.611573	−	0.791188i	$-0.290537\pi$
$503$	−4.02834	−	4.02834i	−0.179615	−	0.179615i	−0.791188	+	0.611573i	$0.790537\pi$
$504$		0			0
$505$	21.7980	+	17.7980i	0.969996	+	0.791999i
$506$	0.550510	+	0.317837i	0.0244732	+	0.0141296i
$507$		0			0
$508$	−2.56304	−	0.686765i	−0.113717	−	0.0304702i
$509$	4.22659	+	7.32066i	0.187340	+	0.324483i	0.944363	−	0.328906i	$-0.106680\pi$
$509$	4.22659	+	7.32066i	0.187340	+	0.324483i	−0.757022	+	0.653389i	$0.773347\pi$
$510$		0			0
$511$	22.2474	−	38.5337i	0.984169	−	1.70463i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			18.0454i			0.795949i
$515$	−19.8943	−	8.95403i	−0.876649	−	0.394562i
$516$		0			0
$517$	−1.48072	+	5.52613i	−0.0651221	+	0.243039i
$518$	−5.00775	+	18.6892i	−0.220028	+	0.821156i
$519$		0			0
$520$	−2.74666	−	7.24264i	−0.120449	−	0.317611i
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$		0			0
$523$	4.22474	−	4.22474i	0.184735	−	0.184735i	−0.608680	−	0.793416i	$-0.708301\pi$
$523$	4.22474	−	4.22474i	0.184735	−	0.184735i	0.793416	+	0.608680i	$0.208301\pi$
$524$	−1.80348	+	3.12372i	−0.0787855	+	0.136461i
$525$		0			0
$526$	−8.34847	−	14.4600i	−0.364011	−	0.630485i
$527$	0.195157	+	0.0522921i	0.00850116	+	0.00227788i
$528$		0			0
$529$	19.0526	+	11.0000i	0.828372	+	0.478261i
$530$	−7.56388	+	9.26382i	−0.328554	+	0.402395i
$531$		0			0
$532$	20.7980	+	20.7980i	0.901706	+	0.901706i
$533$	24.7238	−	6.62471i	1.07090	−	0.286948i
$534$		0			0
$535$	34.9209	−	25.1566i	1.50976	−	1.08761i
$536$	5.72474	−	3.30518i	0.247271	−	0.142762i
$537$		0			0
$538$	3.90704	+	14.5813i	0.168444	+	0.628643i
$539$	8.77101			0.377794
$540$		0			0
$541$	27.9444			1.20142			0.600712	−	0.799466i	$-0.294884\pi$
$541$	27.9444			1.20142			0.600712	+	0.799466i	$0.294884\pi$
$542$	7.25869	+	27.0898i	0.311787	+	1.16361i
$543$		0			0
$544$	−0.389270	+	0.224745i	−0.0166898	+	0.00963586i
$545$	−2.02731	+	12.4735i	−0.0868406	+	0.534307i
$546$		0			0
$547$	3.92907	−	1.05279i	0.167995	−	0.0450140i	−0.173841	−	0.984774i	$-0.555618\pi$
$547$	3.92907	−	1.05279i	0.167995	−	0.0450140i	0.341836	+	0.939760i	$0.388951\pi$
$548$	15.4135	+	15.4135i	0.658431	+	0.658431i
$549$		0			0
$550$	−1.75255	+	2.65153i	−0.0747290	+	0.113062i
$551$	1.77526	+	1.02494i	0.0756284	+	0.0436641i
$552$		0			0
$553$	10.7902	+	2.89123i	0.458846	+	0.122947i
$554$	14.0707	+	24.3712i	0.597807	+	1.03543i
$555$		0			0
$556$	−1.55051	+	2.68556i	−0.0657563	+	0.113893i
$557$	7.88171	−	7.88171i	0.333959	−	0.333959i	−0.520129	−	0.854088i	$-0.674116\pi$
$557$	7.88171	−	7.88171i	0.333959	−	0.333959i	0.854088	+	0.520129i	$0.174116\pi$
$558$		0			0
$559$			12.0000i			0.507546i
$560$	4.18532	−	9.29908i	0.176862	−	0.392958i
$561$		0			0
$562$	−4.43759	+	16.5613i	−0.187188	+	0.698597i
$563$	−5.08619	+	18.9819i	−0.214357	+	0.799993i	0.772034	+	0.635581i	$0.219239\pi$
$563$	−5.08619	+	18.9819i	−0.214357	+	0.799993i	−0.986392	+	0.164412i	$0.947427\pi$
$564$		0			0
$565$	−5.32101	+	11.8224i	−0.223856	+	0.497371i
$566$		−	24.2166i		−	1.01790i
$567$		0			0
$568$	−4.44949	+	4.44949i	−0.186696	+	0.186696i
$569$	9.58166	−	16.5959i	0.401684	−	0.695737i	−0.592245	−	0.805758i	$-0.701758\pi$
$569$	9.58166	−	16.5959i	0.401684	−	0.695737i	0.993929	+	0.110021i	$0.0350917\pi$
$570$		0			0
$571$	−18.4495	−	31.9555i	−0.772087	−	1.33729i	−0.936417	−	0.350889i	$-0.885880\pi$
$571$	−18.4495	−	31.9555i	−0.772087	−	1.33729i	0.164330	−	0.986405i	$-0.447454\pi$
$572$	2.12701	+	0.569930i	0.0889347	+	0.0238300i
$573$		0			0
$574$	29.1824	+	16.8485i	1.21805	+	0.703242i
$575$	2.75699	−	4.17121i	0.114975	−	0.173951i
$576$		0			0
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$	−16.2256	+	4.34763i	−0.674895	+	0.180838i
$579$		0			0
$580$	0.114014	−	0.701501i	0.00473419	−	0.0291282i
$581$	21.5227	−	12.4261i	0.892912	−	0.515523i
$582$		0			0
$583$	−0.879955	−	3.28404i	−0.0364440	−	0.136011i
$584$	9.75663			0.403732
$585$		0			0
$586$	−22.0454			−0.910687
$587$	−3.37640	−	12.6009i	−0.139359	−	0.520095i	−0.999942	−	0.0107843i	$-0.996567\pi$
$587$	−3.37640	−	12.6009i	−0.139359	−	0.520095i	0.860583	−	0.509310i	$-0.170099\pi$
$588$		0			0
$589$	2.51059	−	1.44949i	0.103447	−	0.0597252i
$590$	16.2891	−	11.7344i	0.670610	−	0.483099i
$591$		0			0
$592$	−4.09808	+	1.09808i	−0.168430	+	0.0451307i
$593$	7.24604	+	7.24604i	0.297559	+	0.297559i	0.840057	−	0.542498i	$-0.182521\pi$
$593$	7.24604	+	7.24604i	0.297559	+	0.297559i	−0.542498	+	0.840057i	$0.682521\pi$
$594$		0			0
$595$	−2.89898	+	3.55051i	−0.118847	+	0.145557i
$596$	3.82577	+	2.20881i	0.156709	+	0.0904762i
$597$		0			0
$598$	−3.34607	−	0.896575i	−0.136831	−	0.0366637i
$599$	−9.97093	−	17.2702i	−0.407401	−	0.705639i	0.587197	−	0.809444i	$-0.300232\pi$
$599$	−9.97093	−	17.2702i	−0.407401	−	0.705639i	−0.994598	+	0.103805i	$0.966898\pi$
$600$		0			0
$601$	−2.65153	+	4.59259i	−0.108158	+	0.187335i	−0.915024	−	0.403399i	$-0.867829\pi$
$601$	−2.65153	+	4.59259i	−0.108158	+	0.187335i	0.806866	+	0.590735i	$0.201162\pi$
$602$	−11.1708	+	11.1708i	−0.455290	+	0.455290i
$603$		0			0
$604$		−	17.5959i		−	0.715968i
$605$	8.40143	+	22.1536i	0.341567	+	0.900673i
$606$		0			0
$607$	3.04744	−	11.3732i	0.123692	−	0.461624i	−0.876098	−	0.482133i	$-0.839862\pi$
$607$	3.04744	−	11.3732i	0.123692	−	0.461624i	0.999790	+	0.0205092i	$0.00652872\pi$
$608$	−1.66925	+	6.22973i	−0.0676971	+	0.252649i
$609$		0			0
$610$	−1.12252	−	0.505224i	−0.0454496	−	0.0204559i
$611$		−	31.1769i		−	1.26128i
$612$		0			0
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	−0.556369	−	0.830936i	$-0.687806\pi$
$613$	6.79796	−	6.79796i	0.274567	−	0.274567i	0.830936	+	0.556369i	$0.187806\pi$
$614$	4.71940	−	8.17423i	0.190459	−	0.329885i
$615$		0			0
$616$	1.44949	+	2.51059i	0.0584016	+	0.101155i
$617$	16.3232	+	4.37378i	0.657146	+	0.176082i	0.571958	−	0.820283i	$-0.306184\pi$
$617$	16.3232	+	4.37378i	0.657146	+	0.176082i	0.0851882	+	0.996365i	$0.472851\pi$
$618$		0			0
$619$	42.2121	+	24.3712i	1.69665	+	0.979560i	0.948900	+	0.315578i	$0.102198\pi$
$619$	42.2121	+	24.3712i	1.69665	+	0.979560i	0.747748	+	0.663982i	$0.231135\pi$
$620$	−0.778539	−	0.635674i	−0.0312669	−	0.0255293i
$621$		0			0
$622$	−19.4495	−	19.4495i	−0.779853	−	0.779853i
$623$	−35.3489	+	9.47172i	−1.41623	+	0.379476i
$624$		0			0
$625$	19.9853	+	15.0196i	0.799411	+	0.600784i
$626$	−10.3485	+	5.97469i	−0.413608	+	0.238797i
$627$		0			0
$628$	−3.78780	−	14.1363i	−0.151150	−	0.564099i
$629$	1.90702			0.0760380
$630$		0			0
$631$	−3.10102			−0.123450			−0.0617248	−	0.998093i	$-0.519660\pi$
$631$	−3.10102			−0.123450			−0.0617248	+	0.998093i	$0.519660\pi$
$632$	0.633975	+	2.36603i	0.0252182	+	0.0941154i
$633$		0			0
$634$	−9.43879	+	5.44949i	−0.374862	+	0.216427i
$635$	−3.46808	−	4.81420i	−0.137627	−	0.191046i
$636$		0			0
$637$	−46.1689	+	12.3709i	−1.82928	+	0.490153i
$638$	0.142865	+	0.142865i	0.00565606	+	0.00565606i
$639$		0			0
$640$	2.22474	−	0.224745i	0.0879408	−	0.00888382i
$641$	−16.7474	−	9.66914i	−0.661484	−	0.381908i	0.131358	−	0.991335i	$-0.458066\pi$
$641$	−16.7474	−	9.66914i	−0.661484	−	0.381908i	−0.792842	+	0.609427i	$0.791400\pi$
$642$		0			0
$643$	−6.10913	−	1.63694i	−0.240921	−	0.0645545i	0.136338	−	0.990662i	$-0.456467\pi$
$643$	−6.10913	−	1.63694i	−0.240921	−	0.0645545i	−0.377259	+	0.926108i	$0.623133\pi$
$644$	−2.28024	−	3.94949i	−0.0898540	−	0.155632i
$645$		0			0
$646$	1.44949	−	2.51059i	0.0570294	−	0.0987778i
$647$	−23.5416	+	23.5416i	−0.925516	+	0.925516i	−0.997412	−	0.0718961i	$-0.977095\pi$
$647$	−23.5416	+	23.5416i	−0.925516	+	0.925516i	0.0718961	+	0.997412i	$0.477095\pi$
$648$		0			0
$649$			5.70714i			0.224025i
$650$	5.48528	−	16.4290i	0.215150	−	0.644398i
$651$		0			0
$652$	−1.62863	+	6.07812i	−0.0637819	+	0.238037i
$653$	−6.84563	+	25.5482i	−0.267890	+	0.999780i	0.692567	+	0.721353i	$0.256480\pi$
$653$	−6.84563	+	25.5482i	−0.267890	+	0.999780i	−0.960457	+	0.278427i	$0.910187\pi$
$654$		0			0
$655$	−7.54134	+	2.85994i	−0.294664	+	0.111747i
$656$			7.38891i			0.288488i
$657$		0			0
$658$	29.0227	−	29.0227i	1.13142	−	1.13142i
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	−0.954917	−	0.296872i	$-0.904056\pi$
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	0.734557	+	0.678546i	$0.237390\pi$
$660$		0			0
$661$	0.651531	+	1.12848i	0.0253416	+	0.0438930i	0.878418	−	0.477893i	$-0.158599\pi$
$661$	0.651531	+	1.12848i	0.0253416	+	0.0438930i	−0.853076	+	0.521786i	$0.825266\pi$
$662$	−0.434174	−	0.116337i	−0.0168746	−	0.00452155i
$663$		0			0
$664$	4.71940	+	2.72474i	0.183148	+	0.105741i
$665$	6.61037	+	65.4359i	0.256339	+	2.53749i
$666$		0			0
$667$	−0.224745	−	0.224745i	−0.00870216	−	0.00870216i
$668$	−8.49818	+	2.27708i	−0.328804	+	0.0881028i
$669$		0			0
$670$	14.5898	+	2.37127i	0.563653	+	0.0916100i
$671$	0.303062	−	0.174973i	0.0116996	−	0.00675474i
$672$		0			0
$673$	−6.02093	−	22.4704i	−0.232090	−	0.866171i	−0.979439	−	0.201740i	$-0.935340\pi$
$673$	−6.02093	−	22.4704i	−0.232090	−	0.866171i	0.747349	−	0.664431i	$-0.231326\pi$
$674$	−3.11416			−0.119953
$675$		0			0
$676$	1.00000			0.0384615
$677$	11.8011	+	44.0423i	0.453553	+	1.69268i	0.692308	+	0.721602i	$0.256594\pi$
$677$	11.8011	+	44.0423i	0.453553	+	1.69268i	−0.238755	+	0.971080i	$0.576739\pi$
$678$		0			0
$679$	10.6066	−	6.12372i	0.407044	−	0.235007i
$680$	−0.992072	−	0.161241i	−0.0380442	−	0.00618330i
$681$		0			0
$682$	0.275993	−	0.0739521i	0.0105683	−	0.00283177i
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	0.920632	−	0.390431i	$-0.127674\pi$
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	−0.390431	+	0.920632i	$0.627674\pi$
$684$		0			0
$685$	4.89898	+	48.4949i	0.187180	+	1.85289i
$686$	−26.8485	−	15.5010i	−1.02508	−	0.591830i
$687$		0			0
$688$	−3.34607	−	0.896575i	−0.127568	−	0.0341816i
$689$	9.26382	+	16.0454i	0.352923	+	0.611281i
$690$		0			0
$691$	10.4722	−	18.1384i	0.398381	−	0.690016i	−0.595145	−	0.803618i	$-0.702906\pi$
$691$	10.4722	−	18.1384i	0.398381	−	0.690016i	0.993526	+	0.113602i	$0.0362388\pi$
$692$	−9.12096	+	9.12096i	−0.346727	+	0.346727i
$693$		0			0
$694$		−	23.7980i		−	0.903358i
$695$	−6.48352	+	2.45878i	−0.245934	+	0.0932668i
$696$		0			0
$697$	0.859599	−	3.20807i	0.0325596	−	0.121514i
$698$	7.51750	−	28.0557i	0.284542	−	1.06192i
$699$		0			0
$700$	20.4001	−	10.1875i	0.771050	−	0.385053i
$701$			21.1024i			0.797028i	0.917162	+	0.398514i	$0.130474\pi$
$701$			21.1024i			0.797028i	−0.917162	+	0.398514i	$0.869526\pi$
$702$		0			0
$703$	19.3485	−	19.3485i	0.729741	−	0.729741i
$704$	−0.317837	+	0.550510i	−0.0119789	+	0.0207481i
$705$		0			0
$706$	17.1464	+	29.6985i	0.645314	+	1.11772i
$707$	55.4382	+	14.8546i	2.08497	+	0.558666i
$708$		0			0
$709$	−25.6790	−	14.8258i	−0.964394	−	0.556793i	−0.0668716	−	0.997762i	$-0.521302\pi$
$709$	−25.6790	−	14.8258i	−0.964394	−	0.556793i	−0.897523	+	0.440968i	$0.854635\pi$
$710$	−13.9993	+	1.41421i	−0.525383	+	0.0530745i
$711$		0			0
$712$	−5.67423	−	5.67423i	−0.212651	−	0.212651i
$713$	−0.434174	+	0.116337i	−0.0162599	+	0.00435684i
$714$		0			0
$715$	2.87808	+	3.99519i	0.107634	+	0.149412i
$716$	9.24745	−	5.33902i	0.345593	−	0.199528i
$717$		0			0
$718$	−0.859599	−	3.20807i	−0.0320800	−	0.119724i
$719$	−32.5269			−1.21305			−0.606525	−	0.795065i	$-0.707437\pi$
$719$	−32.5269			−1.21305			−0.606525	+	0.795065i	$0.707437\pi$
$720$		0			0
$721$	−44.4949			−1.65708
$722$	−5.84825	−	21.8260i	−0.217649	−	0.812279i
$723$		0			0
$724$	13.3797	−	7.72474i	0.497251	−	0.287088i
$725$	1.18955	−	1.05379i	0.0441788	−	0.0391369i
$726$		0			0
$727$	−46.6759	+	12.5068i	−1.73111	+	0.463850i	−0.980439	−	0.196822i	$-0.936938\pi$
$727$	−46.6759	+	12.5068i	−1.73111	+	0.463850i	−0.750674	+	0.660673i	$0.770271\pi$
$728$	−11.1708	−	11.1708i	−0.414019	−	0.414019i
$729$		0			0
$730$	16.8990	+	13.7980i	0.625459	+	0.510685i
$731$	1.34847	+	0.778539i	0.0498749	+	0.0287953i
$732$		0			0
$733$	−32.9846	−	8.83821i	−1.21832	−	0.326447i	−0.408296	−	0.912850i	$-0.633877\pi$
$733$	−32.9846	−	8.83821i	−1.21832	−	0.326447i	−0.810019	+	0.586403i	$0.800543\pi$
$734$	2.04989	+	3.55051i	0.0756627	+	0.131052i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	−2.97129	+	2.97129i	−0.109449	+	0.109449i
$738$		0			0
$739$			28.9444i			1.06474i	0.846513	+	0.532368i	$0.178698\pi$
$739$			28.9444i			1.06474i	−0.846513	+	0.532368i	$0.821302\pi$
$740$	−8.65099	−	3.89363i	−0.318017	−	0.143133i
$741$		0			0
$742$	−6.31300	+	23.5605i	−0.231758	+	0.864931i
$743$	2.56204	−	9.56168i	0.0939923	−	0.350784i	−0.902872	−	0.429909i	$-0.858546\pi$
$743$	2.56204	−	9.56168i	0.0939923	−	0.350784i	0.996865	+	0.0791245i	$0.0252125\pi$
$744$		0			0
$745$	3.50270	+	9.23621i	0.128329	+	0.338389i
$746$			0.492810i			0.0180431i
$747$		0			0
$748$	0.202041	−	0.202041i	0.00738735	−	0.00738735i
$749$	43.8888	−	76.0176i	1.60366	−	2.77762i
$750$		0			0
$751$	−10.3485	−	17.9241i	−0.377621	−	0.654059i	0.613095	−	0.790010i	$-0.289924\pi$
$751$	−10.3485	−	17.9241i	−0.377621	−	0.654059i	−0.990716	+	0.135951i	$0.956591\pi$
$752$	8.69333	+	2.32937i	0.317013	+	0.0849434i
$753$		0			0
$754$	−0.953512	−	0.550510i	−0.0347248	−	0.0200484i
$755$	24.8844	−	30.4770i	0.905636	−	1.10917i
$756$		0			0
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	0.983292	−	0.182038i	$-0.0582693\pi$
$757$	22.0454	+	22.0454i	0.801254	+	0.801254i	−0.182038	+	0.983292i	$0.558269\pi$
$758$	20.6210	−	5.52539i	0.748990	−	0.200691i
$759$		0			0
$760$	−11.7014	+	8.42953i	−0.424454	+	0.305771i
$761$	5.60102	−	3.23375i	0.203037	−	0.117223i	−0.395034	−	0.918666i	$-0.629267\pi$
$761$	5.60102	−	3.23375i	0.203037	−	0.117223i	0.598071	+	0.801443i	$0.295934\pi$
$762$		0			0
$763$	6.67072	+	24.8955i	0.241496	+	0.901276i
$764$	−17.4634			−0.631803
$765$		0			0
$766$	8.20204			0.296352
$767$	−8.04954	−	30.0413i	−0.290652	−	1.08473i
$768$		0			0
$769$	−8.39780	+	4.84847i	−0.302832	+	0.174840i	−0.643715	−	0.765266i	$-0.722608\pi$
$769$	−8.39780	+	4.84847i	−0.302832	+	0.174840i	0.340882	+	0.940106i	$0.389274\pi$
$770$	−1.03992	+	6.39836i	−0.0374761	+	0.230581i
$771$		0			0
$772$	−16.7303	+	4.48288i	−0.602138	+	0.161342i
$773$	−30.8270	−	30.8270i	−1.10877	−	1.10877i	−0.993313	−	0.115456i	$-0.963167\pi$
$773$	−30.8270	−	30.8270i	−1.10877	−	1.10877i	−0.115456	−	0.993313i	$-0.536833\pi$
$774$		0			0
$775$	−0.449490	−	2.20204i	−0.0161461	−	0.0790996i
$776$	2.32577	+	1.34278i	0.0834901	+	0.0482030i
$777$		0			0
$778$	−35.5477	−	9.52497i	−1.27445	−	0.341487i
$779$	−23.8273	−	41.2702i	−0.853703	−	1.47866i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	−0.317837	+	0.317837i	−0.0113658	+	0.0113658i
$783$		0			0
$784$		−	13.7980i		−	0.492784i
$785$	13.4310	−	29.8415i	0.479374	−	1.06509i
$786$		0			0
$787$	−2.52520	+	9.42418i	−0.0900137	+	0.335936i	−0.996216	−	0.0869079i	$-0.972301\pi$
$787$	−2.52520	+	9.42418i	−0.0900137	+	0.335936i	0.906203	+	0.422844i	$0.138968\pi$
$788$	2.53590	−	9.46410i	0.0903376	−	0.337145i
$789$		0			0
$790$	−2.24799	+	4.99465i	−0.0799799	+	0.177702i
$791$			26.4415i			0.940150i
$792$		0			0
$793$	−1.34847	+	1.34847i	−0.0478855	+	0.0478855i
$794$	−7.46034	+	12.9217i	−0.264757	+	0.458573i
$795$		0			0
$796$	−4.22474	−	7.31747i	−0.149742	−	0.259361i
$797$	−38.4419	−	10.3005i	−1.36168	−	0.364861i	−0.497248	−	0.867609i	$-0.665656\pi$
$797$	−38.4419	−	10.3005i	−1.36168	−	0.364861i	−0.864433	+	0.502747i	$0.832323\pi$
$798$		0			0
$799$	−3.50343	−	2.02270i	−0.123942	−	0.0715581i
$800$	4.17121	+	2.75699i	0.147474	+	0.0974745i
$801$		0			0
$802$	−6.24745	−	6.24745i	−0.220605	−	0.220605i
$803$	−5.99071	+	1.60521i	−0.211408	+	0.0566465i
$804$		0			0
$805$	1.63593	−	10.0655i	0.0576590	−	0.354761i
$806$	−1.34847	+	0.778539i	−0.0474978	+	0.0274229i
$807$		0			0
$808$	3.25725	+	12.1562i	0.114590	+	0.427655i
$809$	19.4490			0.683792			0.341896	−	0.939738i	$-0.388931\pi$
$809$	19.4490			0.683792			0.341896	+	0.939738i	$0.388931\pi$
$810$		0			0
$811$	−39.6413			−1.39200			−0.695998	−	0.718044i	$-0.745038\pi$
$811$	−39.6413			−1.39200			−0.695998	+	0.718044i	$0.745038\pi$
$812$	−0.375156	−	1.40010i	−0.0131654	−	0.0491339i
$813$		0			0
$814$	2.33562	−	1.34847i	0.0818633	−	0.0472638i
$815$	−11.4166	+	8.22438i	−0.399907	+	0.288087i
$816$		0			0
$817$	21.5804	−	5.78245i	0.755003	−	0.202302i
$818$	−20.4347	−	20.4347i	−0.714481	−	0.714481i
$819$		0			0
$820$	−10.4495	+	12.7980i	−0.364912	+	0.446924i
$821$	−19.3207	−	11.1548i	−0.674296	−	0.389305i	0.123407	−	0.992356i	$-0.460618\pi$
$821$	−19.3207	−	11.1548i	−0.674296	−	0.389305i	−0.797702	+	0.603051i	$0.793951\pi$
$822$		0			0
$823$	−3.23908	−	0.867910i	−0.112907	−	0.0302534i	0.201923	−	0.979401i	$-0.435281\pi$
$823$	−3.23908	−	0.867910i	−0.112907	−	0.0302534i	−0.314830	+	0.949148i	$0.601948\pi$
$824$	−4.87832	−	8.44949i	−0.169944	−	0.294352i
$825$		0			0
$826$	20.4722	−	35.4589i	0.712319	−	1.23377i
$827$	−31.5662	+	31.5662i	−1.09766	+	1.09766i	−0.102980	+	0.994683i	$0.532838\pi$
$827$	−31.5662	+	31.5662i	−1.09766	+	1.09766i	−0.994683	+	0.102980i	$0.967162\pi$
$828$		0			0
$829$		−	10.5505i		−	0.366434i	−0.983072	−	0.183217i	$-0.941349\pi$
$829$		−	10.5505i		−	0.366434i	0.983072	−	0.183217i	$-0.0586512\pi$
$830$	4.32086	+	11.3936i	0.149979	+	0.395479i
$831$		0			0
$832$	0.896575	−	3.34607i	0.0310832	−	0.116004i
$833$	−1.60521	+	5.99071i	−0.0556171	+	0.207566i
$834$		0			0
$835$	−17.9395	−	8.07422i	−0.620824	−	0.279420i
$836$		−	4.09978i		−	0.141794i
$837$		0			0
$838$	3.55051	−	3.55051i	0.122650	−	0.122650i
$839$	−0.246405	+	0.426786i	−0.00850684	+	0.0147343i	−0.870247	−	0.492615i	$-0.836041\pi$
$839$	−0.246405	+	0.426786i	−0.00850684	+	0.0147343i	0.861741	+	0.507349i	$0.169375\pi$
$840$		0			0
$841$	14.4495	+	25.0273i	0.498258	+	0.863009i
$842$	4.92721	+	1.32024i	0.169803	+	0.0454985i
$843$		0			0
$844$	7.88171	+	4.55051i	0.271300	+	0.156635i
$845$	1.73205	+	1.41421i	0.0595844	+	0.0486504i
$846$		0			0
$847$	34.1691	+	34.1691i	1.17407	+	1.17407i
$848$	−5.16622	+	1.38429i	−0.177409	+	0.0475366i
$849$		0			0
$850$	−1.49029	−	1.68228i	−0.0511165	−	0.0577017i
$851$	−3.67423	+	2.12132i	−0.125951	+	0.0727179i
$852$		0			0
$853$	−0.641478	−	2.39403i	−0.0219638	−	0.0819700i	0.954074	−	0.299571i	$-0.0968435\pi$
$853$	−0.641478	−	2.39403i	−0.0219638	−	0.0819700i	−0.976038	+	0.217601i	$0.930177\pi$
$854$	−2.51059			−0.0859106
$855$		0			0
$856$	19.2474			0.657864
$857$	−4.08881	−	15.2597i	−0.139671	−	0.521260i	−0.999935	−	0.0114106i	$-0.996368\pi$
$857$	−4.08881	−	15.2597i	−0.139671	−	0.521260i	0.860264	−	0.509849i	$-0.170299\pi$
$858$		0			0
$859$	−40.2658	+	23.2474i	−1.37385	+	0.793193i	−0.991410	−	0.130788i	$-0.958249\pi$
$859$	−40.2658	+	23.2474i	−1.37385	+	0.793193i	−0.382440	+	0.923980i	$0.624916\pi$
$860$	−4.52761	−	6.28497i	−0.154390	−	0.214316i
$861$		0			0
$862$	−15.0263	+	4.02628i	−0.511797	+	0.137136i
$863$	20.7132	+	20.7132i	0.705085	+	0.705085i	0.965497	−	0.260413i	$-0.0838586\pi$
$863$	20.7132	+	20.7132i	0.705085	+	0.705085i	−0.260413	+	0.965497i	$0.583859\pi$
$864$		0			0
$865$	−28.6969	+	2.89898i	−0.975725	+	0.0985683i
$866$	16.4722	+	9.51023i	0.559748	+	0.323171i
$867$		0			0
$868$	−1.98004	−	0.530550i	−0.0672069	−	0.0180080i
$869$	−0.778539	−	1.34847i	−0.0264101	−	0.0457437i
$870$		0			0
$871$	11.4495	−	19.8311i	0.387951	−	0.671951i
$872$	−3.99624	+	3.99624i	−0.135330	+	0.135330i
$873$		0			0
$874$			6.44949i			0.218157i
$875$	49.7413	+	11.2047i	1.68156	+	0.378789i
$876$		0			0
$877$	11.0713	−	41.3188i	0.373852	−	1.39524i	−0.481162	−	0.876632i	$-0.659785\pi$
$877$	11.0713	−	41.3188i	0.373852	−	1.39524i	0.855014	−	0.518604i	$-0.173548\pi$
$878$	7.71228	−	28.7826i	0.260277	−	0.971366i
$879$		0			0
$880$	−1.32905	+	0.504022i	−0.0448022	+	0.0169906i
$881$		−	54.8365i		−	1.84749i	−0.383010	−	0.923744i	$-0.625113\pi$
$881$		−	54.8365i		−	1.84749i	0.383010	−	0.923744i	$-0.374887\pi$
$882$		0			0
$883$	6.27015	−	6.27015i	0.211007	−	0.211007i	−0.593688	−	0.804695i	$-0.702329\pi$
$883$	6.27015	−	6.27015i	0.211007	−	0.211007i	0.804695	+	0.593688i	$0.202329\pi$
$884$	−0.778539	+	1.34847i	−0.0261851	+	0.0453539i
$885$		0			0
$886$	2.72474	+	4.71940i	0.0915396	+	0.158551i
$887$	7.92256	+	2.12284i	0.266014	+	0.0712781i	0.389360	−	0.921085i	$-0.372696\pi$
$887$	7.92256	+	2.12284i	0.266014	+	0.0712781i	−0.123347	+	0.992364i	$0.539363\pi$
$888$		0			0
$889$	−10.4798	−	6.05051i	−0.351481	−	0.202928i
$890$	−1.80348	−	17.8526i	−0.0604529	−	0.598422i
$891$		0			0
$892$	−18.1237	−	18.1237i	−0.606827	−	0.606827i
$893$	−56.0676	+	15.0233i	−1.87623	+	0.502734i
$894$		0			0
$895$	23.5676	+	3.83042i	0.787777	+	0.128037i
$896$	3.94949	−	2.28024i	0.131943	−	0.0761774i
$897$		0			0
$898$	−0.238477	−	0.890008i	−0.00795807	−	0.0296999i
$899$	−0.142865			−0.00476480
$900$		0			0
$901$	2.40408			0.0800916
$902$	−1.21566	−	4.53689i	−0.0404770	−	0.151062i
$903$		0			0
$904$	−5.02118	+	2.89898i	−0.167002	+	0.0964186i
$905$	34.0987	+	5.54203i	1.13348	+	0.184223i
$906$		0			0
$907$	3.65307	−	0.978838i	0.121298	−	0.0325018i	−0.197659	−	0.980271i	$-0.563334\pi$
$907$	3.65307	−	0.978838i	0.121298	−	0.0325018i	0.318957	+	0.947769i	$0.396667\pi$
$908$	17.6062	+	17.6062i	0.584284	+	0.584284i
$909$		0			0
$910$	−3.55051	−	35.1464i	−0.117698	−	1.16509i
$911$	6.12372	+	3.53553i	0.202888	+	0.117137i	0.598002	−	0.801495i	$-0.295962\pi$
$911$	6.12372	+	3.53553i	0.202888	+	0.117137i	−0.395114	+	0.918632i	$0.629295\pi$
$912$		0			0
$913$	−3.34607	−	0.896575i	−0.110739	−	0.0296723i
$914$	7.31747	+	12.6742i	0.242040	+	0.419226i
$915$		0			0
$916$	0.825765	−	1.43027i	0.0272841	−	0.0472574i
$917$	−11.6315	+	11.6315i	−0.384107	+	0.384107i
$918$		0			0
$919$			12.6515i			0.417335i	0.977987	+	0.208668i	$0.0669127\pi$
$919$			12.6515i			0.417335i	−0.977987	+	0.208668i	$0.933087\pi$
$920$	2.09077	−	0.792893i	0.0689307	−	0.0261409i
$921$		0			0
$922$	8.55444	−	31.9256i	0.281726	−	1.05141i
$923$	−5.64173	+	21.0552i	−0.185700	+	0.693041i
$924$		0			0
$925$	−9.47753	−	18.9783i	−0.311619	−	0.624003i
$926$			12.2351i			0.402071i
$927$		0			0
$928$	0.224745	−	0.224745i	0.00737761	−	0.00737761i
$929$	−21.1024	+	36.5505i	−0.692349	+	1.19918i	0.278717	+	0.960373i	$0.410091\pi$
$929$	−21.1024	+	36.5505i	−0.692349	+	1.19918i	−0.971066	+	0.238810i	$0.923243\pi$
$930$		0			0
$931$	44.4949	+	77.0674i	1.45826	+	2.52578i
$932$	−19.7527	−	5.29272i	−0.647021	−	0.173369i
$933$		0			0
$934$	−3.46410	−	2.00000i	−0.113349	−	0.0654420i
$935$	0.635674	−	0.0642162i	0.0207888	−	0.00210009i
$936$		0			0
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	0.654637	−	0.755943i	$-0.272821\pi$
$937$	−3.10102	−	3.10102i	−0.101306	−	0.101306i	−0.755943	+	0.654637i	$0.772821\pi$
$938$	29.1192	−	7.80247i	0.950776	−	0.254760i
$939$		0			0
$940$	11.7631	+	16.3288i	0.383669	+	0.532587i
$941$	−27.5227	+	15.8902i	−0.897215	+	0.518007i	−0.876295	−	0.481774i	$-0.839993\pi$
$941$	−27.5227	+	15.8902i	−0.897215	+	0.518007i	−0.0209191	+	0.999781i	$0.506659\pi$
$942$		0			0
$943$	1.91239	+	7.13713i	0.0622760	+	0.232417i
$944$	8.97809			0.292212
$945$		0			0
$946$	2.20204			0.0715945
$947$	−0.788210	−	2.94164i	−0.0256134	−	0.0955904i	0.951936	−	0.306297i	$-0.0990901\pi$
$947$	−0.788210	−	2.94164i	−0.0256134	−	0.0955904i	−0.977549	+	0.210707i	$0.932423\pi$
$948$		0			0
$949$	29.2699	−	16.8990i	0.950141	−	0.548564i
$950$	−32.1886	−	1.94790i	−1.04433	−	0.0631981i
$951$		0			0
$952$	−1.98004	+	0.530550i	−0.0641735	+	0.0171952i
$953$	5.79972	+	5.79972i	0.187871	+	0.187871i	0.794775	−	0.606904i	$-0.207589\pi$
$953$	5.79972	+	5.79972i	0.187871	+	0.187871i	−0.606904	+	0.794775i	$0.707589\pi$
$954$		0			0
$955$	−30.2474	−	24.6969i	−0.978784	−	0.799174i
$956$	−14.6969	−	8.48528i	−0.475333	−	0.274434i
$957$		0			0
$958$	6.83013	+	1.83013i	0.220671	+	0.0591287i
$959$	49.7046	+	86.0908i	1.60504	+	2.78002i
$960$		0			0
$961$	15.3990	−	26.6718i	0.496741	−	0.860381i
$962$	−10.3923	+	10.3923i	−0.335061	+	0.335061i
$963$		0			0
$964$		−	19.0000i		−	0.611949i
$965$	−35.3175	−	15.8957i	−1.13691	−	0.511700i
$966$		0			0
$967$	−10.3679	+	38.6937i	−0.333411	+	1.24431i	0.572171	+	0.820134i	$0.306101\pi$
$967$	−10.3679	+	38.6937i	−0.333411	+	1.24431i	−0.905582	+	0.424172i	$0.860565\pi$
$968$	−2.74243	+	10.2349i	−0.0881449	+	0.328961i
$969$		0			0
$970$	2.12936	+	5.61489i	0.0683698	+	0.180283i
$971$			21.4989i			0.689934i	0.938615	+	0.344967i	$0.112110\pi$
$971$			21.4989i			0.689934i	−0.938615	+	0.344967i	$0.887890\pi$
$972$		0			0
$973$	−10.0000	+	10.0000i	−0.320585	+	0.320585i
$974$	8.48528	−	14.6969i	0.271886	−	0.470920i
$975$		0			0
$976$	−0.275255	−	0.476756i	−0.00881070	−	0.0152606i
$977$	−6.27359	−	1.68100i	−0.200710	−	0.0537801i	0.157063	−	0.987589i	$-0.449797\pi$
$977$	−6.27359	−	1.68100i	−0.200710	−	0.0537801i	−0.357773	+	0.933808i	$0.616464\pi$
$978$		0			0
$979$	4.41761	+	2.55051i	0.141188	+	0.0815147i
$980$	19.5133	−	23.8988i	0.623328	−	0.763418i
$981$		0			0
$982$	19.7980	+	19.7980i	0.631778	+	0.631778i
$983$	26.2752	−	7.04041i	0.838047	−	0.224554i	0.185826	−	0.982583i	$-0.440504\pi$
$983$	26.2752	−	7.04041i	0.838047	−	0.224554i	0.652221	+	0.758029i	$0.273837\pi$
$984$		0			0
$985$	17.7766	−	12.8060i	0.566408	−	0.408033i
$986$	−0.123724	+	0.0714323i	−0.00394019	+	0.00227487i
$987$		0			0
$988$	5.78245	+	21.5804i	0.183964	+	0.686564i
$989$	−3.46410			−0.110152
$990$		0			0
$991$	16.7423			0.531838			0.265919	−	0.963995i	$-0.414325\pi$
$991$	16.7423			0.531838			0.265919	+	0.963995i	$0.414325\pi$
$992$	−0.116337	−	0.434174i	−0.00369369	−	0.0137850i
$993$		0			0
$994$	−24.8523	+	14.3485i	−0.788266	+	0.455106i
$995$	3.03100	−	18.6489i	0.0960890	−	0.591211i
$996$		0			0
$997$	6.49211	−	1.73955i	0.205607	−	0.0550922i	−0.154545	−	0.987986i	$-0.549391\pi$
$997$	6.49211	−	1.73955i	0.205607	−	0.0550922i	0.360153	+	0.932893i	$0.382725\pi$
$998$	0.635674	+	0.635674i	0.0201219	+	0.0201219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.m.a.197.2		8
3.2	odd	2		90.2.l.a.47.1	yes	8
5.2	odd	4		1350.2.q.g.143.1		8
5.3	odd	4	inner	270.2.m.a.143.2		8
5.4	even	2		1350.2.q.g.1007.1		8
9.2	odd	6		810.2.f.b.647.2		8
9.4	even	3		90.2.l.a.77.1	yes	8
9.5	odd	6	inner	270.2.m.a.17.2		8
9.7	even	3		810.2.f.b.647.3		8
12.11	even	2		720.2.cu.a.497.1		8
15.2	even	4		450.2.p.a.443.2		8
15.8	even	4		90.2.l.a.83.1	yes	8
15.14	odd	2		450.2.p.a.407.2		8
36.31	odd	6		720.2.cu.a.257.1		8
45.4	even	6		450.2.p.a.257.2		8
45.13	odd	12		90.2.l.a.23.1	✓	8
45.14	odd	6		1350.2.q.g.557.1		8
45.22	odd	12		450.2.p.a.293.2		8
45.23	even	12	inner	270.2.m.a.233.2		8
45.32	even	12		1350.2.q.g.1043.1		8
45.38	even	12		810.2.f.b.323.4		8
45.43	odd	12		810.2.f.b.323.1		8
60.23	odd	4		720.2.cu.a.353.1		8
180.103	even	12		720.2.cu.a.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.1	✓	8	45.13	odd	12
90.2.l.a.47.1	yes	8	3.2	odd	2
90.2.l.a.77.1	yes	8	9.4	even	3
90.2.l.a.83.1	yes	8	15.8	even	4
270.2.m.a.17.2		8	9.5	odd	6	inner
270.2.m.a.143.2		8	5.3	odd	4	inner
270.2.m.a.197.2		8	1.1	even	1	trivial
270.2.m.a.233.2		8	45.23	even	12	inner
450.2.p.a.257.2		8	45.4	even	6
450.2.p.a.293.2		8	45.22	odd	12
450.2.p.a.407.2		8	15.14	odd	2
450.2.p.a.443.2		8	15.2	even	4
720.2.cu.a.113.1		8	180.103	even	12
720.2.cu.a.257.1		8	36.31	odd	6
720.2.cu.a.353.1		8	60.23	odd	4
720.2.cu.a.497.1		8	12.11	even	2
810.2.f.b.323.1		8	45.43	odd	12
810.2.f.b.323.4		8	45.38	even	12
810.2.f.b.647.2		8	9.2	odd	6
810.2.f.b.647.3		8	9.7	even	3
1350.2.q.g.143.1		8	5.2	odd	4
1350.2.q.g.557.1		8	45.14	odd	6
1350.2.q.g.1007.1		8	5.4	even	2
1350.2.q.g.1043.1		8	45.32	even	12

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(-4.40508 + 1.18034i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.224745 - 2.22474i) q^{10} +(0.550510 + 0.317837i) q^{11} +(-3.34607 - 0.896575i) q^{13} +(-2.28024 - 3.94949i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.317837 + 0.317837i) q^{17} +6.44949i q^{19} +(2.09077 - 0.792893i) q^{20} +(-0.164525 + 0.614014i) q^{22} +(0.258819 - 0.965926i) q^{23} +(4.74264 + 1.58346i) q^{25} -3.46410i q^{26} +(3.22474 - 3.22474i) q^{28} +(0.158919 - 0.275255i) q^{29} +(-0.224745 - 0.389270i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-0.389270 - 0.224745i) q^{34} +(10.1459 - 1.02494i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-6.22973 + 1.66925i) q^{38} +(1.30701 + 1.81431i) q^{40} +(-6.39898 + 3.69445i) q^{41} +(-0.896575 - 3.34607i) q^{43} -0.635674 q^{44} +1.00000 q^{46} +(2.32937 + 8.69333i) q^{47} +(11.9494 - 6.89898i) q^{49} +(-0.302023 + 4.99087i) q^{50} +(3.34607 - 0.896575i) q^{52} +(-3.78194 - 3.78194i) q^{53} +(-1.10102 - 0.898979i) q^{55} +(3.94949 + 2.28024i) q^{56} +(0.307007 + 0.0822623i) q^{58} +(4.48905 + 7.77526i) q^{59} +(0.275255 - 0.476756i) q^{61} +(0.317837 - 0.317837i) q^{62} +1.00000i q^{64} +(7.06350 + 3.17914i) q^{65} +(-1.71089 + 6.38512i) q^{67} +(0.116337 - 0.434174i) q^{68} +(3.61597 + 9.53491i) q^{70} -6.29253i q^{71} +(-6.89898 + 6.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(-3.22474 - 5.58542i) q^{76} +(-2.80020 - 0.750311i) q^{77} +(-2.12132 - 1.22474i) q^{79} +(-1.41421 + 1.73205i) q^{80} +(-5.22474 - 5.22474i) q^{82} +(-5.26380 + 1.41043i) q^{83} +(0.815515 - 0.587486i) q^{85} +(3.00000 - 1.73205i) q^{86} +(-0.164525 - 0.614014i) q^{88} +8.02458 q^{89} +15.7980 q^{91} +(0.258819 + 0.965926i) q^{92} +(-7.79423 + 4.50000i) q^{94} +(2.31356 - 14.2347i) q^{95} +(-2.59405 + 0.695075i) q^{97} +(9.75663 + 9.75663i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100}) \) 8 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 + 24 * q^11 + 4 * q^16 - 8 * q^22 + 4 * q^25 + 16 * q^28 + 8 * q^31 - 24 * q^37 - 12 * q^38 + 4 * q^40 - 12 * q^41 + 8 * q^46 - 24 * q^50 - 48 * q^55 + 12 * q^56 - 4 * q^58 + 12 * q^61 + 24 * q^65 + 4 * q^67 + 12 * q^68 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 24 * q^77 - 32 * q^82 - 12 * q^83 - 20 * q^85 + 24 * q^86 - 8 * q^88 + 48 * q^91 + 24 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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