LMFDB - Embedded newform 648.2.t.a.253.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			253.15
Character	$\chi$	$=$	648.253
Dual form			648.2.t.a.397.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.289471 - 1.38427i) q^{2} +(-1.83241 + 0.801412i) q^{4} +(1.55785 - 1.85658i) q^{5} +(0.763942 + 0.278052i) q^{7} +(1.63980 + 2.30457i) q^{8} +(-3.02096 - 1.61907i) q^{10} +(2.23007 + 2.65769i) q^{11} +(2.83964 + 0.500705i) q^{13} +(0.163761 - 1.13799i) q^{14} +(2.71548 - 2.93704i) q^{16} +(3.55127 - 6.15099i) q^{17} +(-5.16371 + 2.98127i) q^{19} +(-1.36675 + 4.65050i) q^{20} +(3.03343 - 3.85634i) q^{22} +(6.58997 - 2.39855i) q^{23} +(-0.151733 - 0.860521i) q^{25} +(-0.128881 - 4.07577i) q^{26} +(-1.62269 + 0.102726i) q^{28} +(-6.59552 + 1.16297i) q^{29} +(2.55724 - 0.930757i) q^{31} +(-4.85171 - 2.90877i) q^{32} +(-9.54262 - 3.13539i) q^{34} +(1.70634 - 0.985154i) q^{35} +(3.59434 + 2.07519i) q^{37} +(5.62163 + 6.28499i) q^{38} +(6.83319 + 0.545766i) q^{40} +(0.742124 - 4.20880i) q^{41} +(-1.77034 - 2.10981i) q^{43} +(-6.21631 - 3.08279i) q^{44} +(-5.22785 - 8.42800i) q^{46} +(-2.80028 - 1.01922i) q^{47} +(-4.85602 - 4.07468i) q^{49} +(-1.14727 + 0.459136i) q^{50} +(-5.60467 + 1.35822i) q^{52} -7.38929i q^{53} +8.40834 q^{55} +(0.611922 + 2.21651i) q^{56} +(3.51907 + 8.79334i) q^{58} +(4.72368 - 5.62947i) q^{59} +(0.0900385 - 0.247379i) q^{61} +(-2.02867 - 3.27048i) q^{62} +(-2.62210 + 7.55808i) q^{64} +(5.35335 - 4.49199i) q^{65} +(2.20513 + 0.388825i) q^{67} +(-1.57793 + 14.1172i) q^{68} +(-1.85765 - 2.07686i) q^{70} +(-2.69918 + 4.67512i) q^{71} +(-1.97245 - 3.41639i) q^{73} +(1.83217 - 5.57624i) q^{74} +(7.07283 - 9.60118i) q^{76} +(0.964666 + 2.65040i) q^{77} +(1.76846 + 10.0295i) q^{79} +(-1.22252 - 9.61697i) q^{80} +(-6.04094 + 0.191022i) q^{82} +(-7.86515 + 1.38684i) q^{83} +(-5.88742 - 16.1756i) q^{85} +(-2.40809 + 3.06136i) q^{86} +(-2.46797 + 9.49744i) q^{88} +(-2.14833 - 3.72101i) q^{89} +(2.03010 + 1.17208i) q^{91} +(-10.1533 + 9.67643i) q^{92} +(-0.600276 + 4.17138i) q^{94} +(-2.50935 + 14.2312i) q^{95} +(4.28345 - 3.59424i) q^{97} +(-4.23479 + 7.90155i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.289471	−	1.38427i	−0.204687	−	0.978828i
$2$	−0.289471	−	1.38427i	−0.204687	−	0.978828i
$3$		0			0
$3$		0			0
$4$	−1.83241	+	0.801412i	−0.916207	+	0.400706i
$5$	1.55785	−	1.85658i	0.696694	−	0.830287i	−0.295454	−	0.955357i	$-0.595471\pi$
$5$	1.55785	−	1.85658i	0.696694	−	0.830287i	0.992148	+	0.125070i	$0.0399154\pi$
$6$		0			0
$7$	0.763942	+	0.278052i	0.288743	+	0.105094i	0.482331	−	0.875989i	$-0.339790\pi$
$7$	0.763942	+	0.278052i	0.288743	+	0.105094i	−0.193588	+	0.981083i	$0.562012\pi$
$8$	1.63980	+	2.30457i	0.579758	+	0.814789i
$9$		0			0
$10$	−3.02096	−	1.61907i	−0.955312	−	0.511994i
$11$	2.23007	+	2.65769i	0.672391	+	0.801324i	0.989107	−	0.147196i	$-0.0470248\pi$
$11$	2.23007	+	2.65769i	0.672391	+	0.801324i	−0.316716	+	0.948520i	$0.602580\pi$
$12$		0			0
$13$	2.83964	+	0.500705i	0.787574	+	0.138871i	0.552949	−	0.833215i	$-0.313502\pi$
$13$	2.83964	+	0.500705i	0.787574	+	0.138871i	0.234626	+	0.972086i	$0.424614\pi$
$14$	0.163761	−	1.13799i	0.0437669	−	0.304141i
$15$		0			0
$16$	2.71548	−	2.93704i	0.678869	−	0.734259i
$17$	3.55127	−	6.15099i	0.861310	−	1.49183i	−0.00935441	−	0.999956i	$-0.502978\pi$
$17$	3.55127	−	6.15099i	0.861310	−	1.49183i	0.870665	−	0.491877i	$-0.163689\pi$
$18$		0			0
$19$	−5.16371	+	2.98127i	−1.18464	+	0.683950i	−0.957083	−	0.289815i	$-0.906406\pi$
$19$	−5.16371	+	2.98127i	−1.18464	+	0.683950i	−0.227554	+	0.973765i	$0.573073\pi$
$20$	−1.36675	+	4.65050i	−0.305614	+	1.03988i
$21$		0			0
$22$	3.03343	−	3.85634i	0.646729	−	0.822175i
$23$	6.58997	−	2.39855i	1.37410	−	0.500133i	0.453719	−	0.891145i	$-0.350097\pi$
$23$	6.58997	−	2.39855i	1.37410	−	0.500133i	0.920386	+	0.391012i	$0.127875\pi$
$24$		0			0
$25$	−0.151733	−	0.860521i	−0.0303466	−	0.172104i
$26$	−0.128881	−	4.07577i	−0.0252757	−	0.799325i
$27$		0			0
$28$	−1.62269	+	0.102726i	−0.306660	+	0.0194134i
$29$	−6.59552	+	1.16297i	−1.22476	+	0.215958i	−0.748372	−	0.663279i	$-0.769164\pi$
$29$	−6.59552	+	1.16297i	−1.22476	+	0.215958i	−0.476385	+	0.879237i	$0.658053\pi$
$30$		0			0
$31$	2.55724	−	0.930757i	0.459293	−	0.167169i	−0.102003	−	0.994784i	$-0.532525\pi$
$31$	2.55724	−	0.930757i	0.459293	−	0.167169i	0.561296	+	0.827615i	$0.310303\pi$
$32$	−4.85171	−	2.90877i	−0.857669	−	0.514203i
$33$		0			0
$34$	−9.54262	−	3.13539i	−1.63655	−	0.537716i
$35$	1.70634	−	0.985154i	0.288423	−	0.166521i
$36$		0			0
$37$	3.59434	+	2.07519i	0.590905	+	0.341159i	0.765455	−	0.643489i	$-0.222514\pi$
$37$	3.59434	+	2.07519i	0.590905	+	0.341159i	−0.174550	+	0.984648i	$0.555847\pi$
$38$	5.62163	+	6.28499i	0.911949	+	1.01956i
$39$		0			0
$40$	6.83319	+	0.545766i	1.08042	+	0.0862932i
$41$	0.742124	−	4.20880i	0.115900	−	0.657304i	−0.870400	−	0.492345i	$-0.836140\pi$
$41$	0.742124	−	4.20880i	0.115900	−	0.657304i	0.986301	−	0.164959i	$-0.0527490\pi$
$42$		0			0
$43$	−1.77034	−	2.10981i	−0.269975	−	0.321743i	0.613975	−	0.789326i	$-0.289570\pi$
$43$	−1.77034	−	2.10981i	−0.269975	−	0.321743i	−0.883950	+	0.467582i	$0.845125\pi$
$44$	−6.21631	−	3.08279i	−0.937145	−	0.464748i
$45$		0			0
$46$	−5.22785	−	8.42800i	−0.770805	−	1.24264i
$47$	−2.80028	−	1.01922i	−0.408463	−	0.148668i	0.129613	−	0.991565i	$-0.458626\pi$
$47$	−2.80028	−	1.01922i	−0.408463	−	0.148668i	−0.538076	+	0.842896i	$0.680849\pi$
$48$		0			0
$49$	−4.85602	−	4.07468i	−0.693717	−	0.582097i
$50$	−1.14727	+	0.459136i	−0.162249	+	0.0649316i
$51$		0			0
$52$	−5.60467	+	1.35822i	−0.777227	+	0.188352i
$53$		−	7.38929i		−	1.01500i	−0.861653	−	0.507498i	$-0.830570\pi$
$53$		−	7.38929i		−	1.01500i	0.861653	−	0.507498i	$-0.169430\pi$
$54$		0			0
$55$	8.40834			1.13378
$56$	0.611922	+	2.21651i	0.0817716	+	0.296194i
$57$		0			0
$58$	3.51907	+	8.79334i	0.462077	+	1.15462i
$59$	4.72368	−	5.62947i	0.614971	−	0.732894i	−0.365226	−	0.930919i	$-0.619008\pi$
$59$	4.72368	−	5.62947i	0.614971	−	0.732894i	0.980197	+	0.198025i	$0.0634526\pi$
$60$		0			0
$61$	0.0900385	−	0.247379i	0.0115283	−	0.0316736i	−0.933795	−	0.357808i	$-0.883524\pi$
$61$	0.0900385	−	0.247379i	0.0115283	−	0.0316736i	0.945323	+	0.326135i	$0.105746\pi$
$62$	−2.02867	−	3.27048i	−0.257641	−	0.415351i
$63$		0			0
$64$	−2.62210	+	7.55808i	−0.327762	+	0.944760i
$65$	5.35335	−	4.49199i	0.664001	−	0.557163i
$66$		0			0
$67$	2.20513	+	0.388825i	0.269400	+	0.0475025i	0.306716	−	0.951801i	$-0.400770\pi$
$67$	2.20513	+	0.388825i	0.269400	+	0.0475025i	−0.0373162	+	0.999304i	$0.511881\pi$
$68$	−1.57793	+	14.1172i	−0.191352	+	1.71196i
$69$		0			0
$70$	−1.85765	−	2.07686i	−0.222032	−	0.248232i
$71$	−2.69918	+	4.67512i	−0.320334	+	0.554835i	−0.980557	−	0.196235i	$-0.937129\pi$
$71$	−2.69918	+	4.67512i	−0.320334	+	0.554835i	0.660223	+	0.751070i	$0.270462\pi$
$72$		0			0
$73$	−1.97245	−	3.41639i	−0.230858	−	0.399858i	0.727203	−	0.686423i	$-0.240820\pi$
$73$	−1.97245	−	3.41639i	−0.230858	−	0.399858i	−0.958061	+	0.286565i	$0.907487\pi$
$74$	1.83217	−	5.57624i	0.212986	−	0.648225i
$75$		0			0
$76$	7.07283	−	9.60118i	0.811309	−	1.10133i
$77$	0.964666	+	2.65040i	0.109934	+	0.302041i
$78$		0			0
$79$	1.76846	+	10.0295i	0.198968	+	1.12840i	0.906654	+	0.421875i	$0.138628\pi$
$79$	1.76846	+	10.0295i	0.198968	+	1.12840i	−0.707686	+	0.706527i	$0.750261\pi$
$80$	−1.22252	−	9.61697i	−0.136682	−	1.07521i
$81$		0			0
$82$	−6.04094	+	0.191022i	−0.667110	+	0.0210949i
$83$	−7.86515	+	1.38684i	−0.863312	+	0.152225i	−0.587735	−	0.809054i	$-0.699980\pi$
$83$	−7.86515	+	1.38684i	−0.863312	+	0.152225i	−0.275577	+	0.961279i	$0.588869\pi$
$84$		0			0
$85$	−5.88742	−	16.1756i	−0.638581	−	1.75449i
$86$	−2.40809	+	3.06136i	−0.259671	+	0.330115i
$87$		0			0
$88$	−2.46797	+	9.49744i	−0.263087	+	1.01243i
$89$	−2.14833	−	3.72101i	−0.227722	−	0.394426i	0.729410	−	0.684076i	$-0.239794\pi$
$89$	−2.14833	−	3.72101i	−0.227722	−	0.394426i	−0.957133	+	0.289650i	$0.906461\pi$
$90$		0			0
$91$	2.03010	+	1.17208i	0.212812	+	0.122867i
$92$	−10.1533	+	9.67643i	−1.05856	+	1.00884i
$93$		0			0
$94$	−0.600276	+	4.17138i	−0.0619137	+	0.430245i
$95$	−2.50935	+	14.2312i	−0.257454	+	1.46009i
$96$		0			0
$97$	4.28345	−	3.59424i	0.434918	−	0.364940i	−0.398886	−	0.917001i	$-0.630603\pi$
$97$	4.28345	−	3.59424i	0.434918	−	0.364940i	0.833804	+	0.552061i	$0.186159\pi$
$98$	−4.23479	+	7.90155i	−0.427778	+	0.798177i
$99$		0			0
$100$	0.967670	+	1.45523i	0.0967670	+	0.145523i
$101$	−5.64914	+	15.5209i	−0.562110	+	1.54438i	0.254427	+	0.967092i	$0.418113\pi$
$101$	−5.64914	+	15.5209i	−0.562110	+	1.54438i	−0.816537	+	0.577293i	$0.804109\pi$
$102$		0			0
$103$	14.0312	+	11.7736i	1.38254	+	1.16009i	0.968262	+	0.249938i	$0.0804101\pi$
$103$	14.0312	+	11.7736i	1.38254	+	1.16009i	0.414278	+	0.910151i	$0.364034\pi$
$104$	3.50254	+	7.36521i	0.343452	+	0.722218i
$105$		0			0
$106$	−10.2288	+	2.13898i	−0.993506	+	0.207756i
$107$			17.0660i			1.64983i	0.565254	+	0.824917i	$0.308778\pi$
$107$			17.0660i			1.64983i	−0.565254	+	0.824917i	$0.691222\pi$
$108$		0			0
$109$			18.3759i			1.76009i	0.474890	+	0.880045i	$0.342488\pi$
$109$			18.3759i			1.76009i	−0.474890	+	0.880045i	$0.657512\pi$
$110$	−2.43397	−	11.6394i	−0.232070	−	1.10978i
$111$		0			0
$112$	2.89112	−	1.48868i	0.273185	−	0.140667i
$113$	−6.55711	−	5.50207i	−0.616841	−	0.517591i	0.279968	−	0.960009i	$-0.409676\pi$
$113$	−6.55711	−	5.50207i	−0.616841	−	0.517591i	−0.896809	+	0.442418i	$0.854121\pi$
$114$		0			0
$115$	5.81311	−	15.9714i	0.542076	−	1.48934i
$116$	11.1537	−	7.41677i	1.03560	−	0.688630i
$117$		0			0
$118$	−9.16008	−	4.90929i	−0.843254	−	0.451937i
$119$	4.42326	−	3.71156i	0.405480	−	0.340238i
$120$		0			0
$121$	−0.179992	+	1.02079i	−0.0163629	+	0.0927987i
$122$	−0.368503	−	0.0530288i	−0.0333627	−	0.00480100i
$123$		0			0
$124$	−3.93999	+	3.75493i	−0.353822	+	0.337203i
$125$	8.66046	+	5.00012i	0.774615	+	0.447224i
$126$		0			0
$127$	−2.28240	−	3.95324i	−0.202530	−	0.350793i	0.746813	−	0.665034i	$-0.231583\pi$
$127$	−2.28240	−	3.95324i	−0.202530	−	0.350793i	−0.949343	+	0.314242i	$0.898250\pi$
$128$	11.2215	+	1.44185i	0.991846	+	0.127443i
$129$		0			0
$130$	−7.76777	−	6.11018i	−0.681278	−	0.535898i
$131$	−4.55139	−	12.5048i	−0.397657	−	1.09255i	−0.963422	−	0.267987i	$-0.913641\pi$
$131$	−4.55139	−	12.5048i	−0.397657	−	1.09255i	0.565766	−	0.824566i	$-0.308581\pi$
$132$		0			0
$133$	−4.77372	+	0.841736i	−0.413934	+	0.0729878i
$134$	−0.100083	−	3.16506i	−0.00864587	−	0.273419i
$135$		0			0
$136$	19.9988	−	1.90223i	1.71488	−	0.163115i
$137$	0.374428	+	2.12348i	0.0319895	+	0.181422i	0.996616	−	0.0821992i	$-0.0261944\pi$
$137$	0.374428	+	2.12348i	0.0319895	+	0.181422i	−0.964626	+	0.263621i	$0.915083\pi$
$138$		0			0
$139$	−0.200125	−	0.549839i	−0.0169744	−	0.0466367i	0.930916	−	0.365233i	$-0.119011\pi$
$139$	−0.200125	−	0.549839i	−0.0169744	−	0.0466367i	−0.947890	+	0.318596i	$0.896789\pi$
$140$	−2.33720	+	3.17269i	−0.197529	+	0.268141i
$141$		0			0
$142$	7.25297	+	2.38309i	0.608656	+	0.199985i
$143$	5.00187	+	8.66350i	0.418278	+	0.724478i
$144$		0			0
$145$	−8.11572	+	14.0568i	−0.673974	+	1.16736i
$146$	−4.15824	+	3.71936i	−0.344139	+	0.307816i
$147$		0			0
$148$	−8.24940	−	0.922063i	−0.678096	−	0.0757931i
$149$	21.5708	+	3.80351i	1.76715	+	0.311596i	0.960259	−	0.279109i	$-0.0900390\pi$
$149$	21.5708	+	3.80351i	1.76715	+	0.311596i	0.806888	+	0.590705i	$0.201150\pi$
$150$		0			0
$151$	5.91767	−	4.96552i	0.481573	−	0.404088i	−0.369422	−	0.929262i	$-0.620444\pi$
$151$	5.91767	−	4.96552i	0.481573	−	0.404088i	0.850995	+	0.525174i	$0.176000\pi$
$152$	−15.3380	−	7.01145i	−1.24408	−	0.568704i
$153$		0			0
$154$	3.38963	−	2.10257i	0.273144	−	0.169430i
$155$	2.25578	−	6.19769i	0.181188	−	0.497811i
$156$		0			0
$157$	−0.882254	+	1.05143i	−0.0704116	+	0.0839132i	−0.800100	−	0.599866i	$-0.795220\pi$
$157$	−0.882254	+	1.05143i	−0.0704116	+	0.0839132i	0.729689	+	0.683779i	$0.239665\pi$
$158$	13.3716	−	5.35127i	1.06378	−	0.425724i
$159$		0			0
$160$	−12.9586	+	4.47613i	−1.02447	+	0.353869i
$161$	5.70128			0.449324
$162$		0			0
$163$			13.5989i			1.06515i	0.846383	+	0.532574i	$0.178775\pi$
$163$			13.5989i			1.06515i	−0.846383	+	0.532574i	$0.821225\pi$
$164$	2.01310	+	8.30700i	0.157197	+	0.648668i
$165$		0			0
$166$	4.19649	+	10.4861i	0.325711	+	0.813875i
$167$	−3.38292	−	2.83861i	−0.261778	−	0.219658i	0.502446	−	0.864609i	$-0.332434\pi$
$167$	−3.38292	−	2.83861i	−0.261778	−	0.219658i	−0.764224	+	0.644950i	$0.776878\pi$
$168$		0			0
$169$	−4.40315	−	1.60262i	−0.338704	−	0.123278i
$170$	−20.6871	+	12.8321i	−1.58663	+	0.984180i
$171$		0			0
$172$	4.93483	+	2.44727i	0.376277	+	0.186603i
$173$	−12.4793	−	14.8722i	−0.948781	−	1.13071i	−0.991301	−	0.131617i	$-0.957983\pi$
$173$	−12.4793	−	14.8722i	−0.948781	−	1.13071i	0.0425201	−	0.999096i	$-0.486461\pi$
$174$		0			0
$175$	0.123355	−	0.699578i	0.00932472	−	0.0528831i
$176$	13.8614	+	0.667109i	1.04485	+	0.0502853i
$177$		0			0
$178$	−4.52901	+	4.05099i	−0.339464	+	0.303635i
$179$	−4.00038	−	2.30962i	−0.299002	−	0.172629i	0.342992	−	0.939338i	$-0.388559\pi$
$179$	−4.00038	−	2.30962i	−0.299002	−	0.172629i	−0.641995	+	0.766709i	$0.721893\pi$
$180$		0			0
$181$	5.55052	−	3.20459i	0.412567	−	0.238195i	−0.279325	−	0.960197i	$-0.590111\pi$
$181$	5.55052	−	3.20459i	0.412567	−	0.238195i	0.691892	+	0.722001i	$0.256777\pi$
$182$	1.03482	−	3.14949i	0.0767059	−	0.233456i
$183$		0			0
$184$	16.3339	+	11.2539i	1.20415	+	0.829649i
$185$	9.45221	−	3.44032i	0.694940	−	0.252938i
$186$		0			0
$187$	24.2670	−	4.27893i	1.77458	−	0.312906i
$188$	5.94809	−	0.376549i	0.433809	−	0.0274626i
$189$		0			0
$190$	20.4263	−	0.645905i	1.48188	−	0.0468588i
$191$	3.51460	+	19.9323i	0.254307	+	1.44225i	0.797844	+	0.602864i	$0.205974\pi$
$191$	3.51460	+	19.9323i	0.254307	+	1.44225i	−0.543537	+	0.839385i	$0.682915\pi$
$192$		0			0
$193$	5.28857	−	1.92488i	0.380680	−	0.138556i	−0.144590	−	0.989492i	$-0.546186\pi$
$193$	5.28857	−	1.92488i	0.380680	−	0.138556i	0.525270	+	0.850935i	$0.323964\pi$
$194$	−6.21533	−	4.88902i	−0.446235	−	0.351011i
$195$		0			0
$196$	12.1637	+	3.57483i	0.868838	+	0.255345i
$197$	−3.79439	+	2.19069i	−0.270339	+	0.156080i	−0.629042	−	0.777371i	$-0.716553\pi$
$197$	−3.79439	+	2.19069i	−0.270339	+	0.156080i	0.358703	+	0.933452i	$0.383219\pi$
$198$		0			0
$199$	−6.64564	+	11.5106i	−0.471097	+	0.815963i	−0.999453	−	0.0330592i	$-0.989475\pi$
$199$	−6.64564	+	11.5106i	−0.471097	+	0.815963i	0.528357	+	0.849022i	$0.322808\pi$
$200$	1.73432	−	1.76076i	0.122635	−	0.124505i
$201$		0			0
$202$	23.1204	+	3.32710i	1.62674	+	0.234094i
$203$	−5.36196	−	0.945458i	−0.376336	−	0.0663582i
$204$		0			0
$205$	−6.65784	−	7.93450i	−0.465004	−	0.554170i
$206$	12.2362	−	22.8312i	0.852539	−	1.59072i
$207$		0			0
$208$	9.18157	−	6.98047i	0.636627	−	0.484009i
$209$	−19.4387	−	7.07512i	−1.34460	−	0.489396i
$210$		0			0
$211$	−16.0858	+	19.1703i	−1.10739	+	1.31974i	−0.164597	+	0.986361i	$0.552632\pi$
$211$	−16.0858	+	19.1703i	−1.10739	+	1.31974i	−0.942794	+	0.333376i	$0.891812\pi$
$212$	5.92186	+	13.5402i	0.406715	+	0.929946i
$213$		0			0
$214$	23.6240	−	4.94011i	1.61490	−	0.337699i
$215$	−6.67497			−0.455229
$216$		0			0
$217$	2.21238			0.150186
$218$	25.4372	−	5.31928i	1.72283	−	0.360267i
$219$		0			0
$220$	−15.4076	+	6.73854i	−1.03878	+	0.454313i
$221$	13.1642	−	15.6884i	0.885518	−	1.05532i
$222$		0			0
$223$	1.52221	+	0.554040i	0.101935	+	0.0371013i	0.392484	−	0.919759i	$-0.371616\pi$
$223$	1.52221	+	0.554040i	0.101935	+	0.0371013i	−0.290549	+	0.956860i	$0.593838\pi$
$224$	−2.89763	−	3.57116i	−0.193606	−	0.238608i
$225$		0			0
$226$	−5.71827	+	10.6695i	−0.380373	+	0.709725i
$227$	−4.47903	−	5.33790i	−0.297284	−	0.354289i	0.596639	−	0.802510i	$-0.296502\pi$
$227$	−4.47903	−	5.33790i	−0.297284	−	0.354289i	−0.893923	+	0.448221i	$0.852058\pi$
$228$		0			0
$229$	−24.7618	−	4.36618i	−1.63631	−	0.288525i	−0.721500	−	0.692415i	$-0.756547\pi$
$229$	−24.7618	−	4.36618i	−1.63631	−	0.288525i	−0.914808	+	0.403890i	$0.867658\pi$
$230$	−23.7915	−	3.42367i	−1.56876	−	0.225750i
$231$		0			0
$232$	−13.4955	−	13.2928i	−0.886022	−	0.872716i
$233$	−7.86096	+	13.6156i	−0.514989	+	0.891987i	0.484860	+	0.874592i	$0.338871\pi$
$233$	−7.86096	+	13.6156i	−0.514989	+	0.891987i	−0.999849	+	0.0173948i	$0.994463\pi$
$234$		0			0
$235$	−6.25469	+	3.61115i	−0.408011	+	0.235565i
$236$	−4.14422	+	14.1011i	−0.269766	+	0.917905i
$237$		0			0
$238$	−6.41821	−	5.04861i	−0.416031	−	0.327253i
$239$	−14.6050	+	5.31579i	−0.944720	+	0.343850i	−0.768028	−	0.640416i	$-0.778762\pi$
$239$	−14.6050	+	5.31579i	−0.944720	+	0.343850i	−0.176692	+	0.984266i	$0.556540\pi$
$240$		0			0
$241$	−2.19088	−	12.4251i	−0.141127	−	0.800370i	−0.970396	−	0.241520i	$-0.922354\pi$
$241$	−2.19088	−	12.4251i	−0.141127	−	0.800370i	0.829269	−	0.558850i	$-0.188757\pi$
$242$	1.46515	−	0.0463299i	0.0941832	−	0.00297820i
$243$		0			0
$244$	0.0332646	+	0.525458i	0.00212955	+	0.0336390i
$245$	−15.1299	+	2.66782i	−0.966616	+	0.170441i
$246$		0			0
$247$	−16.1558	+	5.88024i	−1.02797	+	0.374151i
$248$	6.33836	+	4.36707i	0.402486	+	0.277309i
$249$		0			0
$250$	4.41457	−	13.4358i	0.279202	−	0.849755i
$251$	−4.86765	+	2.81034i	−0.307244	+	0.177387i	−0.645692	−	0.763598i	$-0.723431\pi$
$251$	−4.86765	+	2.81034i	−0.307244	+	0.177387i	0.338449	+	0.940985i	$0.390098\pi$
$252$		0			0
$253$	21.0707	+	12.1652i	1.32470	+	0.764818i
$254$	−4.81166	+	4.30381i	−0.301910	+	0.270045i
$255$		0			0
$256$	−1.25237	−	15.9509i	−0.0782730	−	0.996932i
$257$	−3.35726	+	19.0399i	−0.209420	+	1.18768i	0.680911	+	0.732366i	$0.261584\pi$
$257$	−3.35726	+	19.0399i	−0.209420	+	1.18768i	−0.890331	+	0.455313i	$0.849527\pi$
$258$		0			0
$259$	2.16885	+	2.58474i	0.134766	+	0.160608i
$260$	−6.20961	+	12.5214i	−0.385103	+	0.776545i
$261$		0			0
$262$	−15.9926	+	9.92015i	−0.988026	+	0.612869i
$263$	−10.8424	−	3.94631i	−0.668571	−	0.243340i	−0.0146383	−	0.999893i	$-0.504660\pi$
$263$	−10.8424	−	3.94631i	−0.668571	−	0.243340i	−0.653932	+	0.756553i	$0.726882\pi$
$264$		0			0
$265$	−13.7188	−	11.5114i	−0.842739	−	0.707142i
$266$	2.54705	+	6.36447i	0.156169	+	0.390231i
$267$		0			0
$268$	−4.35233	+	1.05473i	−0.265861	+	0.0644281i
$269$		−	13.3630i		−	0.814758i	−0.913259	−	0.407379i	$-0.866443\pi$
$269$		−	13.3630i		−	0.814758i	0.913259	−	0.407379i	$-0.133557\pi$
$270$		0			0
$271$	3.26667			0.198436			0.0992182	−	0.995066i	$-0.468366\pi$
$271$	3.26667			0.198436			0.0992182	+	0.995066i	$0.468366\pi$
$272$	−8.42227	−	27.1331i	−0.510675	−	1.64518i
$273$		0			0
$274$	2.83109	−	1.13300i	0.171033	−	0.0684468i
$275$	1.94863	−	2.32228i	0.117507	−	0.140039i
$276$		0			0
$277$	0.102104	−	0.280528i	0.00613482	−	0.0168553i	−0.936587	−	0.350434i	$-0.886034\pi$
$277$	0.102104	−	0.280528i	0.00613482	−	0.0168553i	0.942722	+	0.333579i	$0.108256\pi$
$278$	−0.703196	+	0.436190i	−0.0421749	+	0.0261609i
$279$		0			0
$280$	5.06841	+	2.31692i	0.302895	+	0.138462i
$281$	13.3262	−	11.1820i	0.794976	−	0.667064i	−0.151996	−	0.988381i	$-0.548570\pi$
$281$	13.3262	−	11.1820i	0.794976	−	0.667064i	0.946972	+	0.321317i	$0.104126\pi$
$282$		0			0
$283$	−1.31422	−	0.231732i	−0.0781220	−	0.0137750i	0.134451	−	0.990920i	$-0.457073\pi$
$283$	−1.31422	−	0.231732i	−0.0781220	−	0.0137750i	−0.212573	+	0.977145i	$0.568184\pi$
$284$	1.19932	−	10.7299i	0.0711665	−	0.636704i
$285$		0			0
$286$	10.5447	−	9.43178i	0.623523	−	0.557713i
$287$	1.73720	−	3.00893i	0.102544	−	0.177611i
$288$		0			0
$289$	−16.7231	−	28.9652i	−0.983711	−	1.70384i
$290$	21.8077	+	7.16531i	1.28059	+	0.420762i
$291$		0			0
$292$	6.35229	+	4.67949i	0.371739	+	0.273846i
$293$	2.77744	+	7.63095i	0.162260	+	0.445805i	0.994003	−	0.109356i	$-0.0348789\pi$
$293$	2.77744	+	7.63095i	0.162260	+	0.445805i	−0.831743	+	0.555161i	$0.812657\pi$
$294$		0			0
$295$	−3.09274	−	17.5398i	−0.180066	−	1.02121i
$296$	1.11157	+	11.6863i	0.0646089	+	0.679253i
$297$		0			0
$298$	−0.979021	−	30.9608i	−0.0567132	−	1.79351i
$299$	19.9141	−	3.51140i	1.15166	−	0.203069i
$300$		0			0
$301$	−0.765801	−	2.10402i	−0.0441400	−	0.121274i
$302$	−8.58661	−	6.75429i	−0.494104	−	0.388666i
$303$		0			0
$304$	−5.26584	+	23.2616i	−0.302017	+	1.33414i
$305$	−0.319011	−	0.552544i	−0.0182665	−	0.0316386i
$306$		0			0
$307$	−22.1985	−	12.8163i	−1.26693	−	0.731464i	−0.292527	−	0.956257i	$-0.594496\pi$
$307$	−22.1985	−	12.8163i	−1.26693	−	0.731464i	−0.974406	+	0.224793i	$0.927829\pi$
$308$	−3.89173	−	4.08353i	−0.221752	−	0.232681i
$309$		0			0
$310$	−9.23227	−	1.32855i	−0.524358	−	0.0754568i
$311$	3.08781	−	17.5119i	0.175094	−	0.993007i	−0.762942	−	0.646467i	$-0.776246\pi$
$311$	3.08781	−	17.5119i	0.175094	−	0.993007i	0.938035	−	0.346539i	$-0.112643\pi$
$312$		0			0
$313$	−25.2201	+	21.1622i	−1.42553	+	1.19616i	−0.477226	+	0.878781i	$0.658358\pi$
$313$	−25.2201	+	21.1622i	−1.42553	+	1.19616i	−0.948299	+	0.317377i	$0.897198\pi$
$314$	1.71085	+	0.916921i	0.0965489	+	0.0517448i
$315$		0			0
$316$	−11.2783	−	16.9608i	−0.634453	−	0.954122i
$317$	2.41535	−	6.63611i	0.135659	−	0.372721i	−0.853198	−	0.521587i	$-0.825340\pi$
$317$	2.41535	−	6.63611i	0.135659	−	0.372721i	0.988857	+	0.148866i	$0.0475624\pi$
$318$		0			0
$319$	−17.7993	−	14.9354i	−0.996568	−	0.836220i
$320$	9.94732	+	16.6425i	0.556072	+	0.930346i
$321$		0			0
$322$	−1.65035	−	7.89212i	−0.0919706	−	0.439810i
$323$			42.3492i			2.35637i
$324$		0			0
$325$		−	2.51954i		−	0.139759i
$326$	18.8246	−	3.93649i	1.04260	−	0.218022i
$327$		0			0
$328$	10.9164	−	5.19131i	0.602758	−	0.286642i
$329$	−1.85586	−	1.55725i	−0.102317	−	0.0858539i
$330$		0			0
$331$	4.15163	−	11.4065i	0.228194	−	0.626958i	−0.771766	−	0.635907i	$-0.780626\pi$
$331$	4.15163	−	11.4065i	0.228194	−	0.626958i	0.999960	+	0.00894876i	$0.00284852\pi$
$332$	13.3008	−	8.84449i	0.729975	−	0.485404i
$333$		0			0
$334$	−2.95015	+	5.50457i	−0.161425	+	0.301197i
$335$	4.15716	−	3.48827i	0.227130	−	0.190585i
$336$		0			0
$337$	−4.48506	+	25.4361i	−0.244317	+	1.38559i	0.577757	+	0.816209i	$0.303928\pi$
$337$	−4.48506	+	25.4361i	−0.244317	+	1.38559i	−0.822074	+	0.569381i	$0.807183\pi$
$338$	−0.943872	+	6.55907i	−0.0513399	+	0.356766i
$339$		0			0
$340$	23.7515	+	24.9221i	1.28811	+	1.35159i
$341$	8.17648	+	4.72069i	0.442781	+	0.255640i
$342$		0			0
$343$	−5.42214	−	9.39142i	−0.292768	−	0.507089i
$344$	1.95920	−	7.53955i	0.105633	−	0.406506i
$345$		0			0
$346$	−16.9748	+	21.5797i	−0.912570	+	1.16013i
$347$	−4.43311	−	12.1799i	−0.237982	−	0.653849i	−0.999980	−	0.00627055i	$-0.998004\pi$
$347$	−4.43311	−	12.1799i	−0.237982	−	0.653849i	0.761999	−	0.647578i	$-0.224218\pi$
$348$		0			0
$349$	1.00479	−	0.177171i	0.0537849	−	0.00948374i	−0.146691	−	0.989182i	$-0.546862\pi$
$349$	1.00479	−	0.177171i	0.0537849	−	0.00948374i	0.200476	+	0.979699i	$0.435751\pi$
$350$	−1.00411	+	0.0317514i	−0.0536721	+	0.00169718i
$351$		0			0
$352$	−3.08902	−	19.3811i	−0.164645	−	1.03302i
$353$	2.87234	+	16.2899i	0.152879	+	0.867022i	0.960699	+	0.277592i	$0.0895364\pi$
$353$	2.87234	+	16.2899i	0.152879	+	0.867022i	−0.807820	+	0.589430i	$0.799352\pi$
$354$		0			0
$355$	4.47480	+	12.2944i	0.237498	+	0.652520i
$356$	6.91869	+	5.09673i	0.366690	+	0.270126i
$357$		0			0
$358$	−2.03915	+	6.20617i	−0.107772	+	0.328006i
$359$	−9.03871	−	15.6555i	−0.477045	−	0.826266i	0.522609	−	0.852573i	$-0.324959\pi$
$359$	−9.03871	−	15.6555i	−0.477045	−	0.826266i	−0.999654	+	0.0263063i	$0.991625\pi$
$360$		0			0
$361$	8.27594	−	14.3343i	0.435576	−	0.754439i
$362$	−6.04274	−	6.75579i	−0.317599	−	0.355076i
$363$		0			0
$364$	−4.65930	−	0.520786i	−0.244213	−	0.0272966i
$365$	−9.41559	−	1.66022i	−0.492835	−	0.0869000i
$366$		0			0
$367$	−15.6345	+	13.1189i	−0.816112	+	0.684799i	−0.952058	−	0.305917i	$-0.901037\pi$
$367$	−15.6345	+	13.1189i	−0.816112	+	0.684799i	0.135946	+	0.990716i	$0.456593\pi$
$368$	10.8503	−	25.8682i	0.565610	−	1.34847i
$369$		0			0
$370$	−7.49848	−	12.0886i	−0.389827	−	0.628454i
$371$	2.05461	−	5.64499i	0.106670	−	0.293073i
$372$		0			0
$373$	18.6443	−	22.2194i	0.965366	−	1.15048i	−0.0232061	−	0.999731i	$-0.507387\pi$
$373$	18.6443	−	22.2194i	0.965366	−	1.15048i	0.988572	−	0.150748i	$-0.0481681\pi$
$374$	−12.9478	−	32.3535i	−0.669514	−	1.67296i
$375$		0			0
$376$	−2.24304	−	8.12476i	−0.115676	−	0.419003i
$377$	−19.3112			−0.994578
$378$		0			0
$379$		−	18.7878i		−	0.965062i	−0.875879	−	0.482531i	$-0.839718\pi$
$379$		−	18.7878i		−	0.965062i	0.875879	−	0.482531i	$-0.160282\pi$
$380$	−6.80691	−	28.0885i	−0.349187	−	1.44091i
$381$		0			0
$382$	26.5743	−	10.6350i	1.35966	−	0.544132i
$383$	11.4097	+	9.57391i	0.583010	+	0.489204i	0.885934	−	0.463811i	$-0.153518\pi$
$383$	11.4097	+	9.57391i	0.583010	+	0.489204i	−0.302924	+	0.953015i	$0.597963\pi$
$384$		0			0
$385$	6.42348	+	2.33796i	0.327371	+	0.119153i
$386$	−4.19545	−	6.76362i	−0.213543	−	0.344259i
$387$		0			0
$388$	−4.96858	+	10.0189i	−0.252241	+	0.508634i
$389$	11.3184	+	13.4888i	0.573866	+	0.683907i	0.972420	−	0.233238i	$-0.0749321\pi$
$389$	11.3184	+	13.4888i	0.573866	+	0.683907i	−0.398553	+	0.917145i	$0.630488\pi$
$390$		0			0
$391$	8.64932	−	49.0527i	0.437415	−	2.48070i
$392$	1.42749	−	17.8727i	0.0720992	−	0.902708i
$393$		0			0
$394$	4.13088	+	4.61833i	0.208111	+	0.232668i
$395$	21.3755	+	12.3411i	1.07552	+	0.620950i
$396$		0			0
$397$	13.1290	−	7.58002i	0.658924	−	0.380430i	−0.132943	−	0.991124i	$-0.542443\pi$
$397$	13.1290	−	7.58002i	0.658924	−	0.380430i	0.791867	+	0.610694i	$0.209109\pi$
$398$	17.8575	+	5.86739i	0.895115	+	0.294105i
$399$		0			0
$400$	−2.93941	−	1.89108i	−0.146971	−	0.0945540i
$401$	−0.563391	+	0.205057i	−0.0281344	+	0.0102401i	−0.356049	−	0.934467i	$-0.615876\pi$
$401$	−0.563391	+	0.205057i	−0.0281344	+	0.0102401i	0.327915	+	0.944707i	$0.393654\pi$
$402$		0			0
$403$	7.72766	−	1.36260i	0.384942	−	0.0678757i
$404$	−2.08706	−	32.9679i	−0.103835	−	1.64022i
$405$		0			0
$406$	0.243360	+	7.69609i	0.0120778	+	0.381951i
$407$	2.50040	+	14.1805i	0.123940	+	0.702899i
$408$		0			0
$409$	26.7235	−	9.72655i	1.32139	−	0.480947i	0.417487	−	0.908683i	$-0.362911\pi$
$409$	26.7235	−	9.72655i	1.32139	−	0.480947i	0.903904	+	0.427736i	$0.140689\pi$
$410$	−9.05626	+	11.5131i	−0.447257	+	0.568590i
$411$		0			0
$412$	−35.1466	−	10.3293i	−1.73155	−	0.508889i
$413$	5.17391	−	2.98716i	0.254591	−	0.146988i
$414$		0			0
$415$	−9.67799	+	16.7628i	−0.475074	+	0.822852i
$416$	−12.3207	−	10.6891i	−0.604070	−	0.524078i
$417$		0			0
$418$	−4.16694	+	28.9565i	−0.203812	+	1.41631i
$419$	−27.5479	−	4.85743i	−1.34580	−	0.237301i	−0.546110	−	0.837713i	$-0.683892\pi$
$419$	−27.5479	−	4.85743i	−1.34580	−	0.237301i	−0.799691	+	0.600412i	$0.795003\pi$
$420$		0			0
$421$	21.0378	+	25.0719i	1.02532	+	1.22193i	0.974771	+	0.223208i	$0.0716530\pi$
$421$	21.0378	+	25.0719i	1.02532	+	1.22193i	0.0505502	+	0.998722i	$0.483903\pi$
$422$	31.1932	+	16.7178i	1.51846	+	0.813812i
$423$		0			0
$424$	17.0291	−	12.1170i	0.827008	−	0.588452i
$425$	−5.83190	−	2.12264i	−0.282889	−	0.102963i
$426$		0			0
$427$	0.137568	−	0.163948i	0.00665740	−	0.00793398i
$428$	−13.6769	−	31.2720i	−0.661098	−	1.51159i
$429$		0			0
$430$	1.93221	+	9.23997i	0.0931794	+	0.445591i
$431$	9.98011			0.480725			0.240363	−	0.970683i	$-0.422734\pi$
$431$	9.98011			0.480725			0.240363	+	0.970683i	$0.422734\pi$
$432$		0			0
$433$	17.4899			0.840513			0.420257	−	0.907405i	$-0.361940\pi$
$433$	17.4899			0.840513			0.420257	+	0.907405i	$0.361940\pi$
$434$	−0.640419	−	3.06253i	−0.0307411	−	0.147006i
$435$		0			0
$436$	−14.7267	−	33.6722i	−0.705279	−	1.61261i
$437$	−26.8780	+	32.0319i	−1.28575	+	1.53229i
$438$		0			0
$439$	7.21777	+	2.62705i	0.344485	+	0.125382i	0.508468	−	0.861081i	$-0.330212\pi$
$439$	7.21777	+	2.62705i	0.344485	+	0.125382i	−0.163983	+	0.986463i	$0.552434\pi$
$440$	13.7880	+	19.3776i	0.657317	+	0.923792i
$441$		0			0
$442$	−25.5277	−	13.6814i	−1.21423	−	0.650759i
$443$	−3.13735	−	3.73895i	−0.149060	−	0.177643i	0.686348	−	0.727274i	$-0.259213\pi$
$443$	−3.13735	−	3.73895i	−0.149060	−	0.177643i	−0.835408	+	0.549631i	$0.814768\pi$
$444$		0			0
$445$	−10.2551	−	1.80826i	−0.486140	−	0.0857196i
$446$	0.326306	−	2.26753i	0.0154510	−	0.107371i
$447$		0			0
$448$	−4.10467	+	5.04486i	−0.193928	+	0.238347i
$449$	2.49179	−	4.31590i	0.117595	−	0.203680i	−0.801219	−	0.598371i	$-0.795815\pi$
$449$	2.49179	−	4.31590i	0.117595	−	0.203680i	0.918814	+	0.394691i	$0.129148\pi$
$450$		0			0
$451$	12.8407	−	7.41357i	0.604644	−	0.349091i
$452$	16.4248	+	4.82712i	0.772556	+	0.227049i
$453$		0			0
$454$	−6.09255	+	7.74536i	−0.285938	+	0.363508i
$455$	5.33865	−	1.94311i	0.250280	−	0.0910944i
$456$		0			0
$457$	3.50014	+	19.8503i	0.163729	+	0.928556i	0.950365	+	0.311138i	$0.100710\pi$
$457$	3.50014	+	19.8503i	0.163729	+	0.928556i	−0.786635	+	0.617418i	$0.788179\pi$
$458$	1.12385	+	35.5410i	0.0525141	+	1.66072i
$459$		0			0
$460$	2.14765	+	33.9249i	0.100135	+	1.58176i
$461$	−33.4428	+	5.89687i	−1.55759	+	0.274645i	−0.885077	−	0.465444i	$-0.845895\pi$
$461$	−33.4428	+	5.89687i	−1.55759	+	0.274645i	−0.672510	+	0.740088i	$0.734784\pi$
$462$		0			0
$463$	−35.9891	+	13.0990i	−1.67256	+	0.608760i	−0.992260	−	0.124178i	$-0.960371\pi$
$463$	−35.9891	+	13.0990i	−1.67256	+	0.608760i	−0.680295	+	0.732938i	$0.738148\pi$
$464$	−14.4943	+	22.5293i	−0.672881	+	1.04590i
$465$		0			0
$466$	21.1232	+	6.94039i	0.978512	+	0.321507i
$467$	9.53283	−	5.50378i	0.441127	−	0.254685i	−0.262949	−	0.964810i	$-0.584695\pi$
$467$	9.53283	−	5.50378i	0.441127	−	0.254685i	0.704075	+	0.710125i	$0.251362\pi$
$468$		0			0
$469$	1.57648	+	0.910182i	0.0727951	+	0.0420283i
$470$	6.80936	+	7.61287i	0.314092	+	0.351155i
$471$		0			0
$472$	20.7194	+	1.65486i	0.953689	+	0.0761710i
$473$	1.65925	−	9.41005i	0.0762922	−	0.432675i
$474$		0			0
$475$	3.34895	+	3.99113i	0.153660	+	0.183125i
$476$	−5.13076	+	10.3460i	−0.235168	+	0.474206i
$477$		0			0
$478$	11.5862	+	18.6785i	0.529942	+	0.854337i
$479$	−21.5794	−	7.85427i	−0.985989	−	0.358871i	−0.201823	−	0.979422i	$-0.564687\pi$
$479$	−21.5794	−	7.85427i	−0.985989	−	0.358871i	−0.784166	+	0.620551i	$0.786909\pi$
$480$		0			0
$481$	9.16757	+	7.69250i	0.418005	+	0.350748i
$482$	−16.5655	+	6.62947i	−0.754537	+	0.301964i
$483$		0			0
$484$	−0.488250	−	2.01475i	−0.0221932	−	0.0915795i
$485$		−	13.5519i		−	0.615358i
$486$		0			0
$487$	8.81274			0.399343			0.199672	−	0.979863i	$-0.436012\pi$
$487$	8.81274			0.399343			0.199672	+	0.979863i	$0.436012\pi$
$488$	0.717747	−	0.198152i	0.0324909	−	0.00896992i
$489$		0			0
$490$	8.07266	+	20.1717i	0.364685	+	0.911264i
$491$	−7.55920	+	9.00870i	−0.341142	+	0.406557i	−0.909152	−	0.416465i	$-0.863269\pi$
$491$	−7.55920	+	9.00870i	−0.341142	+	0.406557i	0.568010	+	0.823022i	$0.307713\pi$
$492$		0			0
$493$	−16.2691	+	44.6990i	−0.732723	+	2.01314i
$494$	12.8165	+	20.6619i	0.576641	+	0.929622i
$495$		0			0
$496$	4.21044	−	10.0381i	0.189055	−	0.450726i
$497$	−3.36195	+	2.82101i	−0.150804	+	0.126540i
$498$		0			0
$499$	−17.3768	−	3.06399i	−0.777891	−	0.137163i	−0.229414	−	0.973329i	$-0.573681\pi$
$499$	−17.3768	−	3.06399i	−0.777891	−	0.137163i	−0.548477	+	0.836166i	$0.684792\pi$
$500$	−19.8767	−	2.22169i	−0.888913	−	0.0993568i
$501$		0			0
$502$	5.29932	+	5.92464i	0.236520	+	0.264430i
$503$	10.0037	−	17.3268i	0.446041	−	0.772565i	−0.552083	−	0.833789i	$-0.686167\pi$
$503$	10.0037	−	17.3268i	0.446041	−	0.772565i	0.998124	+	0.0612236i	$0.0195003\pi$
$504$		0			0
$505$	20.0152	+	34.6673i	0.890664	+	1.54268i
$506$	10.7406	−	32.6890i	0.477476	−	1.45320i
$507$		0			0
$508$	7.35047	+	5.41482i	0.326125	+	0.240244i
$509$	3.57485	+	9.82182i	0.158452	+	0.435345i	0.993360	−	0.115045i	$-0.0367013\pi$
$509$	3.57485	+	9.82182i	0.158452	+	0.435345i	−0.834908	+	0.550390i	$0.814479\pi$
$510$		0			0
$511$	−0.556906	−	3.15837i	−0.0246361	−	0.139718i
$512$	−21.7179	+	6.35094i	−0.959803	+	0.280675i
$513$		0			0
$514$	27.3283	−	0.864155i	1.20540	−	0.0381163i
$515$	43.7173	−	7.70853i	1.92641	−	0.339679i
$516$		0			0
$517$	−3.53605	−	9.71521i	−0.155515	−	0.427274i
$518$	2.95016	−	3.75049i	0.129623	−	0.164787i
$519$		0			0
$520$	19.1305	+	4.97119i	0.838930	+	0.218001i
$521$	10.0111	+	17.3397i	0.438593	+	0.759665i	0.997581	−	0.0695105i	$-0.0221437\pi$
$521$	10.0111	+	17.3397i	0.438593	+	0.759665i	−0.558988	+	0.829175i	$0.688810\pi$
$522$		0			0
$523$	−17.8863	−	10.3267i	−0.782114	−	0.451554i	0.0550649	−	0.998483i	$-0.482463\pi$
$523$	−17.8863	−	10.3267i	−0.782114	−	0.451554i	−0.837179	+	0.546929i	$0.815797\pi$
$524$	18.3616	+	19.2665i	0.802129	+	0.841661i
$525$		0			0
$526$	−2.32421	+	16.1512i	−0.101340	+	0.704224i
$527$	3.35636	−	19.0349i	0.146206	−	0.829173i
$528$		0			0
$529$	20.0556	−	16.8287i	0.871985	−	0.731682i
$530$	−11.9638	+	22.3228i	−0.519672	+	0.969638i
$531$		0			0
$532$	8.07286	−	5.36813i	0.350003	−	0.232738i
$533$	4.21473	−	11.5799i	0.182560	−	0.501580i
$534$		0			0
$535$	31.6844	+	26.5864i	1.36984	+	1.14943i
$536$	2.71991	+	5.71949i	0.117482	+	0.247044i
$537$		0			0
$538$	−18.4981	+	3.86821i	−0.797508	+	0.166770i
$539$		−	21.9926i		−	0.947289i
$540$		0			0
$541$		−	31.7185i		−	1.36368i	−0.731499	−	0.681842i	$-0.761179\pi$
$541$		−	31.7185i		−	1.36368i	0.731499	−	0.681842i	$-0.238821\pi$
$542$	−0.945607	−	4.52196i	−0.0406173	−	0.194235i
$543$		0			0
$544$	−35.1215	+	19.5129i	−1.50582	+	0.836610i
$545$	34.1163	+	28.6270i	1.46138	+	1.22624i
$546$		0			0
$547$	−2.69951	+	7.41685i	−0.115423	+	0.317122i	−0.983930	−	0.178555i	$-0.942858\pi$
$547$	−2.69951	+	7.41685i	−0.115423	+	0.317122i	0.868507	+	0.495677i	$0.165080\pi$
$548$	−2.38789	−	3.59103i	−0.102006	−	0.153401i
$549$		0			0
$550$	−3.77874	−	2.02519i	−0.161126	−	0.0863545i
$551$	30.5902	−	25.6683i	1.30319	−	1.09350i
$552$		0			0
$553$	−1.43771	+	8.15365i	−0.0611376	+	0.346728i
$554$	−0.417883	−	0.0601347i	−0.0177541	−	0.00255488i
$555$		0			0
$556$	0.807359	+	0.847150i	0.0342397	+	0.0359271i
$557$	−11.9380	−	6.89241i	−0.505829	−	0.292041i	0.225288	−	0.974292i	$-0.427668\pi$
$557$	−11.9380	−	6.89241i	−0.505829	−	0.292041i	−0.731118	+	0.682251i	$0.761001\pi$
$558$		0			0
$559$	−3.97074	−	6.87753i	−0.167944	−	0.290888i
$560$	1.74008	−	7.68673i	0.0735320	−	0.324824i
$561$		0			0
$562$	−19.3365	−	15.2102i	−0.815662	−	0.641605i
$563$	−4.49431	−	12.3480i	−0.189413	−	0.520407i	0.808242	−	0.588850i	$-0.200419\pi$
$563$	−4.49431	−	12.3480i	−0.189413	−	0.520407i	−0.997655	+	0.0684431i	$0.978197\pi$
$564$		0			0
$565$	−20.4301	+	3.60237i	−0.859499	+	0.151553i
$566$	0.0596476	+	1.88631i	0.00250718	+	0.0792876i
$567$		0			0
$568$	−15.2003	+	1.44581i	−0.637790	+	0.0606650i
$569$	6.12718	+	34.7490i	0.256865	+	1.45675i	0.791241	+	0.611505i	$0.209436\pi$
$569$	6.12718	+	34.7490i	0.256865	+	1.45675i	−0.534376	+	0.845247i	$0.679453\pi$
$570$		0			0
$571$	13.0508	+	35.8568i	0.546159	+	1.50056i	0.838856	+	0.544354i	$0.183225\pi$
$571$	13.0508	+	35.8568i	0.546159	+	1.50056i	−0.292697	+	0.956205i	$0.594553\pi$
$572$	−16.1085	−	11.8665i	−0.673531	−	0.496165i
$573$		0			0
$574$	−4.66804	−	1.53377i	−0.194840	−	0.0640182i
$575$	−3.06392	−	5.30687i	−0.127774	−	0.221312i
$576$		0			0
$577$	−13.9536	+	24.1683i	−0.580895	+	1.00614i	0.414478	+	0.910059i	$0.363964\pi$
$577$	−13.9536	+	24.1683i	−0.580895	+	1.00614i	−0.995374	+	0.0960807i	$0.969369\pi$
$578$	−35.2549	+	31.5339i	−1.46641	+	1.31164i
$579$		0			0
$580$	3.60603	−	32.2620i	0.149732	−	1.33961i
$581$	−6.39413	−	1.12746i	−0.265273	−	0.0467748i
$582$		0			0
$583$	19.6384	−	16.4786i	0.813341	−	0.682474i
$584$	4.63888	−	10.1479i	0.191958	−	0.419921i
$585$		0			0
$586$	9.75931	−	6.05366i	0.403153	−	0.250074i
$587$	3.04495	−	8.36592i	0.125678	−	0.345299i	−0.860857	−	0.508847i	$-0.830072\pi$
$587$	3.04495	−	8.36592i	0.125678	−	0.345299i	0.986535	+	0.163549i	$0.0522941\pi$
$588$		0			0
$589$	−10.4300	+	12.4300i	−0.429760	+	0.512168i
$590$	−23.3846	+	9.35844i	−0.962727	+	0.385281i
$591$		0			0
$592$	15.8553	−	4.92156i	0.651647	−	0.202275i
$593$	13.6477			0.560446			0.280223	−	0.959935i	$-0.409592\pi$
$593$	13.6477			0.560446			0.280223	+	0.959935i	$0.409592\pi$
$594$		0			0
$595$		−	13.9942i		−	0.573706i
$596$	−42.5748	+	10.3175i	−1.74393	+	0.422621i
$597$		0			0
$598$	−10.6253	−	26.5501i	−0.434500	−	1.08571i
$599$	−23.2233	−	19.4867i	−0.948878	−	0.796203i	0.0302302	−	0.999543i	$-0.490376\pi$
$599$	−23.2233	−	19.4867i	−0.948878	−	0.796203i	−0.979108	+	0.203340i	$0.934820\pi$
$600$		0			0
$601$	2.85426	+	1.03887i	0.116428	+	0.0423762i	0.399577	−	0.916700i	$-0.369157\pi$
$601$	2.85426	+	1.03887i	0.116428	+	0.0423762i	−0.283149	+	0.959076i	$0.591379\pi$
$602$	−2.69086	+	1.66913i	−0.109671	+	0.0680286i
$603$		0			0
$604$	−6.86419	+	13.8414i	−0.279300	+	0.563197i
$605$	1.61477	+	1.92441i	0.0656497	+	0.0782382i
$606$		0			0
$607$	−4.34423	+	24.6374i	−0.176327	+	0.999999i	0.760274	+	0.649602i	$0.225065\pi$
$607$	−4.34423	+	24.6374i	−0.176327	+	0.999999i	−0.936601	+	0.350397i	$0.886047\pi$
$608$	33.7246	+	0.555803i	1.36771	+	0.0225408i
$609$		0			0
$610$	−0.672526	+	0.601543i	−0.0272298	+	0.0243558i
$611$	−7.44146	−	4.29633i	−0.301049	−	0.173811i
$612$		0			0
$613$	−11.1629	+	6.44490i	−0.450865	+	0.260307i	−0.708195	−	0.706017i	$-0.750490\pi$
$613$	−11.1629	+	6.44490i	−0.450865	+	0.260307i	0.257331	+	0.966323i	$0.417157\pi$
$614$	−11.3154	+	34.4386i	−0.456653	+	1.38983i
$615$		0			0
$616$	−4.52617	+	6.56927i	−0.182365	+	0.264683i
$617$	−23.2620	+	8.46669i	−0.936495	+	0.340856i	−0.764781	−	0.644291i	$-0.777153\pi$
$617$	−23.2620	+	8.46669i	−0.936495	+	0.340856i	−0.171714	+	0.985147i	$0.554930\pi$
$618$		0			0
$619$	−7.07392	+	1.24732i	−0.284325	+	0.0501341i	−0.313992	−	0.949426i	$-0.601666\pi$
$619$	−7.07392	+	1.24732i	−0.284325	+	0.0501341i	0.0296670	+	0.999560i	$0.490555\pi$
$620$	0.833393	+	13.1645i	0.0334699	+	0.528701i
$621$		0			0
$622$	−25.1350	+	0.794801i	−1.00782	+	0.0318686i
$623$	−0.606562	−	3.43998i	−0.0243014	−	0.137820i
$624$		0			0
$625$	26.8803	−	9.78364i	1.07521	−	0.391346i
$626$	36.5947	+	28.7856i	1.46262	+	1.15051i
$627$		0			0
$628$	0.774026	−	2.63370i	0.0308870	−	0.105096i
$629$	25.5289	−	14.7391i	1.01791	−	0.587688i
$630$		0			0
$631$	19.7806	−	34.2610i	0.787453	−	1.36391i	−0.140070	−	0.990142i	$-0.544733\pi$
$631$	19.7806	−	34.2610i	0.787453	−	1.36391i	0.927523	−	0.373767i	$-0.121934\pi$
$632$	−20.2137	+	20.5219i	−0.804057	+	0.816316i
$633$		0			0
$634$	−9.88534	−	1.42253i	−0.392597	−	0.0564960i
$635$	−10.8951	−	1.92111i	−0.432361	−	0.0762368i
$636$		0			0
$637$	−11.7491	−	14.0021i	−0.465517	−	0.554782i
$638$	−15.5222	+	28.9624i	−0.614531	+	1.14663i
$639$		0			0
$640$	20.1583	−	18.5873i	0.796827	−	0.734728i
$641$	−20.4795	−	7.45392i	−0.808891	−	0.294412i	−0.0957255	−	0.995408i	$-0.530517\pi$
$641$	−20.4795	−	7.45392i	−0.808891	−	0.294412i	−0.713166	+	0.700995i	$0.752739\pi$
$642$		0			0
$643$	24.0829	−	28.7008i	0.949735	−	1.13185i	−0.0414197	−	0.999142i	$-0.513188\pi$
$643$	24.0829	−	28.7008i	0.949735	−	1.13185i	0.991155	−	0.132709i	$-0.0423675\pi$
$644$	−10.4471	+	4.56907i	−0.411673	+	0.180047i
$645$		0			0
$646$	58.6228	−	12.2589i	2.30648	−	0.482318i
$647$	13.9531			0.548554			0.274277	−	0.961651i	$-0.411561\pi$
$647$	13.9531			0.548554			0.274277	+	0.961651i	$0.411561\pi$
$648$		0			0
$649$	25.4955			1.00079
$650$	−3.48773	+	0.729335i	−0.136800	+	0.0286069i
$651$		0			0
$652$	−10.8983	−	24.9188i	−0.426812	−	0.975896i
$653$	16.3129	−	19.4409i	0.638372	−	0.760782i	−0.345740	−	0.938330i	$-0.612372\pi$
$653$	16.3129	−	19.4409i	0.638372	−	0.760782i	0.984112	+	0.177548i	$0.0568166\pi$
$654$		0			0
$655$	−30.3066	−	11.0307i	−1.18418	−	0.431006i
$656$	−10.3462	−	13.6085i	−0.403950	−	0.531324i
$657$		0			0
$658$	−1.61844	+	3.01979i	−0.0630933	+	0.117724i
$659$	23.0007	+	27.4112i	0.895981	+	1.06779i	0.997336	+	0.0729384i	$0.0232376\pi$
$659$	23.0007	+	27.4112i	0.895981	+	1.06779i	−0.101355	+	0.994850i	$0.532318\pi$
$660$		0			0
$661$	29.1329	+	5.13692i	1.13314	+	0.199803i	0.708603	−	0.705608i	$-0.249326\pi$
$661$	29.1329	+	5.13692i	1.13314	+	0.199803i	0.424536	+	0.905411i	$0.360437\pi$
$662$	−16.9915	−	2.44513i	−0.660392	−	0.0950326i
$663$		0			0
$664$	−16.0934	−	15.8517i	−0.624543	−	0.615164i
$665$	−5.87402	+	10.1741i	−0.227785	+	0.394535i
$666$		0			0
$667$	−40.6749	+	23.4836i	−1.57494	+	0.909290i
$668$	8.47380	+	2.49039i	0.327861	+	0.0963560i
$669$		0			0
$670$	−6.03209	−	4.74489i	−0.233040	−	0.183311i
$671$	0.858249	−	0.312377i	0.0331323	−	0.0120592i
$672$		0			0
$673$	3.21781	+	18.2491i	0.124038	+	0.703452i	0.981875	+	0.189531i	$0.0606967\pi$
$673$	3.21781	+	18.2491i	0.124038	+	0.703452i	−0.857837	+	0.513922i	$0.828192\pi$
$674$	36.5087	−	1.15445i	1.40626	−	0.0444678i
$675$		0			0
$676$	9.35275	−	0.592084i	0.359721	−	0.0227725i
$677$	31.1495	−	5.49250i	1.19717	−	0.211094i	0.460698	−	0.887557i	$-0.347599\pi$
$677$	31.1495	−	5.49250i	1.19717	−	0.211094i	0.736477	+	0.676463i	$0.236488\pi$
$678$		0			0
$679$	4.27169	−	1.55477i	0.163932	−	0.0596665i
$680$	27.6235	−	40.0927i	1.05931	−	1.53748i
$681$		0			0
$682$	4.16787	−	12.6850i	0.159596	−	0.485732i
$683$	−29.5187	+	17.0426i	−1.12950	+	0.652117i	−0.943809	−	0.330491i	$-0.892786\pi$
$683$	−29.5187	+	17.0426i	−1.12950	+	0.652117i	−0.185691	+	0.982608i	$0.559452\pi$
$684$		0			0
$685$	4.52572	+	2.61293i	0.172919	+	0.0998348i
$686$	−11.4307	+	10.2242i	−0.436427	+	0.390364i
$687$		0			0
$688$	−11.0039	−	0.529586i	−0.419520	−	0.0201903i
$689$	3.69985	−	20.9829i	0.140953	−	0.799385i
$690$		0			0
$691$	5.27112	+	6.28188i	0.200523	+	0.238974i	0.856930	−	0.515433i	$-0.172369\pi$
$691$	5.27112	+	6.28188i	0.200523	+	0.238974i	−0.656407	+	0.754407i	$0.727925\pi$
$692$	34.7859	+	17.2510i	1.32236	+	0.655784i
$693$		0			0
$694$	−15.5770	+	9.66233i	−0.591294	+	0.366777i
$695$	−1.33259	−	0.485021i	−0.0505478	−	0.0183979i
$696$		0			0
$697$	−23.2528	−	19.5114i	−0.880761	−	0.739046i
$698$	−0.536109	−	1.33961i	−0.0202920	−	0.0507050i
$699$		0			0
$700$	0.334614	+	1.38077i	0.0126472	+	0.0521884i
$701$			1.97965i			0.0747704i	0.999301	+	0.0373852i	$0.0119029\pi$
$701$			1.97965i			0.0747704i	−0.999301	+	0.0373852i	$0.988097\pi$
$702$		0			0
$703$	−24.7468			−0.933344
$704$	−25.9345	+	9.88631i	−0.977444	+	0.372604i
$705$		0			0
$706$	21.7181	−	8.69154i	0.817373	−	0.327110i
$707$	−8.63122	+	10.2863i	−0.324611	+	0.386856i
$708$		0			0
$709$	5.97488	−	16.4158i	0.224391	−	0.616510i	−0.775499	−	0.631349i	$-0.782501\pi$
$709$	5.97488	−	16.4158i	0.224391	−	0.616510i	0.999890	+	0.0148394i	$0.00472370\pi$
$710$	15.7235	−	9.75321i	0.590092	−	0.366031i
$711$		0			0
$712$	5.05251	−	11.0527i	0.189351	−	0.414217i
$713$	14.6196	−	12.2673i	0.547510	−	0.459415i
$714$		0			0
$715$	23.8767	+	4.21010i	0.892936	+	0.157449i
$716$	9.18130	+	1.02622i	0.343121	+	0.0383518i
$717$		0			0
$718$	−19.0550	+	17.0438i	−0.711127	+	0.636071i
$719$	−17.2073	+	29.8038i	−0.641722	+	1.11150i	0.343326	+	0.939216i	$0.388446\pi$
$719$	−17.2073	+	29.8038i	−0.641722	+	1.11150i	−0.985048	+	0.172279i	$0.944887\pi$
$720$		0			0
$721$	7.44538	+	12.8958i	0.277280	+	0.480264i
$722$	−22.2383	−	7.30677i	−0.827623	−	0.271930i
$723$		0			0
$724$	−7.60264	+	10.3204i	−0.282550	+	0.383554i
$725$	2.00152	+	5.49913i	0.0743345	+	0.204232i
$726$		0			0
$727$	4.21802	+	23.9216i	0.156438	+	0.887203i	0.957460	+	0.288567i	$0.0931789\pi$
$727$	4.21802	+	23.9216i	0.156438	+	0.887203i	−0.801022	+	0.598635i	$0.795710\pi$
$728$	0.627822	+	6.60048i	0.0232686	+	0.244630i
$729$		0			0
$730$	0.427340	+	13.5143i	0.0158166	+	0.500187i
$731$	−19.2644	+	3.39683i	−0.712519	+	0.125636i
$732$		0			0
$733$	7.76866	+	21.3442i	0.286942	+	0.788366i	0.996490	+	0.0837095i	$0.0266768\pi$
$733$	7.76866	+	21.3442i	0.286942	+	0.788366i	−0.709548	+	0.704657i	$0.751101\pi$
$734$	22.6858	+	17.8448i	0.837348	+	0.658663i
$735$		0			0
$736$	−38.9494	−	7.53164i	−1.43570	−	0.277620i
$737$	3.88422	+	6.72767i	0.143077	+	0.247817i
$738$		0			0
$739$	0.214406	+	0.123787i	0.00788706	+	0.00455360i	0.503938	−	0.863740i	$-0.331884\pi$
$739$	0.214406	+	0.123787i	0.00788706	+	0.00455360i	−0.496051	+	0.868293i	$0.665217\pi$
$740$	−14.5632	+	13.8792i	−0.535355	+	0.510210i
$741$		0			0
$742$	−8.40894	−	1.21007i	−0.308702	−	0.0444232i
$743$	−0.843956	+	4.78631i	−0.0309618	+	0.175593i	−0.996367	−	0.0851603i	$-0.972860\pi$
$743$	−0.843956	+	4.78631i	−0.0309618	+	0.175593i	0.965406	+	0.260753i	$0.0839709\pi$
$744$		0			0
$745$	40.6657	−	34.1225i	1.48987	−	1.25015i
$746$	−36.1547	−	19.3769i	−1.32372	−	0.709439i
$747$		0			0
$748$	−41.0380	+	27.2886i	−1.50050	+	0.997772i
$749$	−4.74524	+	13.0374i	−0.173387	+	0.476378i
$750$		0			0
$751$	23.6852	+	19.8743i	0.864287	+	0.725223i	0.962887	−	0.269905i	$-0.0869921\pi$
$751$	23.6852	+	19.8743i	0.864287	+	0.725223i	−0.0986005	+	0.995127i	$0.531437\pi$
$752$	−10.5976	+	5.45686i	−0.386454	+	0.198991i
$753$		0			0
$754$	5.59003	+	26.7320i	0.203577	+	0.973520i
$755$		−	18.7222i		−	0.681370i
$756$		0			0
$757$			15.9221i			0.578697i	0.957224	+	0.289349i	$0.0934387\pi$
$757$			15.9221i			0.578697i	−0.957224	+	0.289349i	$0.906561\pi$
$758$	−26.0074	+	5.43851i	−0.944630	+	0.197535i
$759$		0			0
$760$	−36.9117	+	17.5534i	−1.33893	+	0.636729i
$761$	−12.1040	−	10.1564i	−0.438768	−	0.368170i	0.396480	−	0.918043i	$-0.370232\pi$
$761$	−12.1040	−	10.1564i	−0.438768	−	0.368170i	−0.835248	+	0.549873i	$0.814676\pi$
$762$		0			0
$763$	−5.10946	+	14.0381i	−0.184975	+	0.508214i
$764$	−22.4142	−	33.7075i	−0.810916	−	1.21950i
$765$		0			0
$766$	9.95010	−	18.5655i	0.359512	−	0.670800i
$767$	16.2323	−	13.6205i	0.586113	−	0.491807i
$768$		0			0
$769$	−7.98567	+	45.2890i	−0.287970	+	1.63316i	0.406507	+	0.913648i	$0.366747\pi$
$769$	−7.98567	+	45.2890i	−0.287970	+	1.63316i	−0.694478	+	0.719514i	$0.744365\pi$
$770$	1.37696	−	9.56861i	0.0496220	−	0.344829i
$771$		0			0
$772$	−8.14823	+	7.76551i	−0.293261	+	0.279487i
$773$	−35.6666	−	20.5921i	−1.28284	−	0.740647i	−0.305472	−	0.952201i	$-0.598814\pi$
$773$	−35.6666	−	20.5921i	−1.28284	−	0.740647i	−0.977366	+	0.211554i	$0.932147\pi$
$774$		0			0
$775$	−1.18895	−	2.05933i	−0.0427085	−	0.0739733i
$776$	15.3072	+	3.97767i	0.549496	+	0.142790i
$777$		0			0
$778$	15.3957	−	19.5724i	0.551964	−	0.701703i
$779$	8.71544	+	23.9455i	0.312263	+	0.857936i
$780$		0			0
$781$	−18.4444	+	3.25225i	−0.659993	+	0.116375i
$782$	−70.4060	+	2.22633i	−2.51771	+	0.0796134i
$783$		0			0
$784$	−25.1539	+	3.19759i	−0.898353	+	0.114200i
$785$	0.577638	+	3.27595i	0.0206168	+	0.116924i
$786$		0			0
$787$	6.23669	+	17.1352i	0.222314	+	0.610803i	0.999837	−	0.0180518i	$-0.00574638\pi$
$787$	6.23669	+	17.1352i	0.222314	+	0.610803i	−0.777523	+	0.628854i	$0.783524\pi$
$788$	5.19725	−	7.05513i	0.185144	−	0.251329i
$789$		0			0
$790$	10.8959	−	33.1619i	0.387659	−	1.17985i
$791$	−3.47939	−	6.02648i	−0.123713	−	0.214277i
$792$		0			0
$793$	0.379541	−	0.657384i	0.0134779	−	0.0233444i
$794$	−14.2933	−	15.9799i	−0.507249	−	0.567104i
$795$		0			0
$796$	2.95283	−	26.4180i	0.104660	−	0.936362i
$797$	40.7976	+	7.19372i	1.44512	+	0.254814i	0.840550	−	0.541734i	$-0.182232\pi$
$797$	40.7976	+	7.19372i	1.44512	+	0.254814i	0.604575	+	0.796548i	$0.293343\pi$
$798$		0			0
$799$	−16.2138	+	13.6050i	−0.573602	+	0.481309i
$800$	−1.76689	+	4.61635i	−0.0624692	+	0.163213i
$801$		0			0
$802$	0.446940	+	0.720527i	0.0157820	+	0.0254427i
$803$	4.68101	−	12.8610i	0.165189	−	0.453853i
$804$		0			0
$805$	8.88176	−	10.5849i	0.313041	−	0.373068i
$806$	−4.12313	−	10.3027i	−0.145231	−	0.362899i
$807$		0			0
$808$	−45.0324	+	12.4323i	−1.58424	+	0.437367i
$809$	19.2719			0.677564			0.338782	−	0.940865i	$-0.389985\pi$
$809$	19.2719			0.677564			0.338782	+	0.940865i	$0.389985\pi$
$810$		0			0
$811$		−	15.7750i		−	0.553935i	−0.960879	−	0.276968i	$-0.910671\pi$
$811$		−	15.7750i		−	0.553935i	0.960879	−	0.276968i	$-0.0893295\pi$
$812$	10.5830	−	2.56467i	0.371392	−	0.0900023i
$813$		0			0
$814$	18.9058	−	7.56606i	0.662648	−	0.265190i
$815$	25.2474	+	21.1851i	0.884380	+	0.742083i
$816$		0			0
$817$	15.4315	+	5.61659i	0.539878	+	0.196500i
$818$	−21.1999	−	34.1770i	−0.741236	−	1.19497i
$819$		0			0
$820$	18.5587	+	9.20362i	0.648099	+	0.321404i
$821$	6.66717	+	7.94562i	0.232686	+	0.277304i	0.869735	−	0.493519i	$-0.164290\pi$
$821$	6.66717	+	7.94562i	0.232686	+	0.277304i	−0.637049	+	0.770823i	$0.719845\pi$
$822$		0			0
$823$	9.20557	−	52.2074i	0.320886	−	1.81983i	−0.216249	−	0.976338i	$-0.569382\pi$
$823$	9.20557	−	52.2074i	0.320886	−	1.81983i	0.537135	−	0.843496i	$-0.319507\pi$
$824$	−4.12467	+	51.6424i	−0.143690	+	1.79905i
$825$		0			0
$826$	−5.63273	−	6.29740i	−0.195988	−	0.219114i
$827$	−23.9359	−	13.8194i	−0.832332	−	0.480547i	0.0223184	−	0.999751i	$-0.492895\pi$
$827$	−23.9359	−	13.8194i	−0.832332	−	0.480547i	−0.854650	+	0.519204i	$0.826229\pi$
$828$		0			0
$829$	34.2649	−	19.7829i	1.19007	−	0.687088i	0.231748	−	0.972776i	$-0.425555\pi$
$829$	34.2649	−	19.7829i	1.19007	−	0.687088i	0.958323	+	0.285688i	$0.0922221\pi$
$830$	26.0057	+	8.54463i	0.902671	+	0.296588i
$831$		0			0
$832$	−11.2302	+	20.1493i	−0.389337	+	0.698552i
$833$	−42.3084	+	15.3990i	−1.46590	+	0.533543i
$834$		0			0
$835$	−10.5402	+	1.85852i	−0.364759	+	0.0643168i
$836$	41.2899	−	2.61389i	1.42804	−	0.0904033i
$837$		0			0
$838$	1.25030	+	39.5398i	0.0431909	+	1.36588i
$839$	−4.95699	−	28.1125i	−0.171134	−	0.970551i	−0.942512	−	0.334173i	$-0.891543\pi$
$839$	−4.95699	−	28.1125i	−0.171134	−	0.970551i	0.771378	−	0.636378i	$-0.219568\pi$
$840$		0			0
$841$	14.8973	−	5.42218i	0.513700	−	0.186972i
$842$	28.6165	−	36.3796i	0.986189	−	1.25373i
$843$		0			0
$844$	14.1125	−	48.0192i	0.485772	−	1.65289i
$845$	−9.83486	+	5.67816i	−0.338329	+	0.195335i
$846$		0			0
$847$	−0.421335	+	0.729774i	−0.0144773	+	0.0250753i
$848$	−21.7026	−	20.0654i	−0.745270	−	0.689050i
$849$		0			0
$850$	−1.25014	+	8.68737i	−0.0428795	+	0.297974i
$851$	28.6640	+	5.05424i	0.982591	+	0.173257i
$852$		0			0
$853$	−4.41611	−	5.26292i	−0.151205	−	0.180199i	0.685125	−	0.728425i	$-0.259748\pi$
$853$	−4.41611	−	5.26292i	−0.151205	−	0.180199i	−0.836330	+	0.548227i	$0.815303\pi$
$854$	−0.266770	−	0.142974i	−0.00912868	−	0.00489247i
$855$		0			0
$856$	−39.3298	+	27.9849i	−1.34427	+	0.956503i
$857$	26.6254	+	9.69084i	0.909505	+	0.331033i	0.754055	−	0.656811i	$-0.228095\pi$
$857$	26.6254	+	9.69084i	0.909505	+	0.331033i	0.155450	+	0.987844i	$0.450317\pi$
$858$		0			0
$859$	−14.7282	+	17.5524i	−0.502520	+	0.598879i	−0.956355	−	0.292206i	$-0.905611\pi$
$859$	−14.7282	+	17.5524i	−0.502520	+	0.598879i	0.453836	+	0.891085i	$0.350055\pi$
$860$	12.2313	−	5.34940i	0.417084	−	0.182413i
$861$		0			0
$862$	−2.88895	−	13.8152i	−0.0983981	−	0.470547i
$863$	−24.0297			−0.817980			−0.408990	−	0.912539i	$-0.634119\pi$
$863$	−24.0297			−0.817980			−0.408990	+	0.912539i	$0.634119\pi$
$864$		0			0
$865$	−47.0523			−1.59983
$866$	−5.06283	−	24.2108i	−0.172042	−	0.822717i
$867$		0			0
$868$	−4.05399	+	1.77303i	−0.137601	+	0.0601805i
$869$	−22.7114	+	27.0664i	−0.770432	+	0.918165i
$870$		0			0
$871$	6.06710	+	2.20824i	0.205576	+	0.0748235i
$872$	−42.3485	+	30.1328i	−1.43410	+	1.02043i
$873$		0			0
$874$	52.1213	+	27.9341i	1.76303	+	0.944885i
$875$	5.22579	+	6.22786i	0.176664	+	0.210540i
$876$		0			0
$877$	0.500115	+	0.0881838i	0.0168877	+	0.00297776i	0.182086	−	0.983283i	$-0.441715\pi$
$877$	0.500115	+	0.0881838i	0.0168877	+	0.00297776i	−0.165198	+	0.986260i	$0.552826\pi$
$878$	1.54722	−	10.7518i	0.0522162	−	0.362856i
$879$		0			0
$880$	22.8326	−	24.6956i	0.769688	−	0.832488i
$881$	11.2219	−	19.4369i	0.378076	−	0.654847i	−0.612706	−	0.790311i	$-0.709919\pi$
$881$	11.2219	−	19.4369i	0.378076	−	0.654847i	0.990782	+	0.135464i	$0.0432525\pi$
$882$		0			0
$883$	45.9402	−	26.5236i	1.54601	−	0.892589i	0.547570	−	0.836760i	$-0.315553\pi$
$883$	45.9402	−	26.5236i	1.54601	−	0.892589i	0.998440	−	0.0558294i	$-0.0177803\pi$
$884$	−11.5493	+	39.2976i	−0.388445	+	1.32172i
$885$		0			0
$886$	−4.26755	+	5.42526i	−0.143371	+	0.182265i
$887$	26.2975	−	9.57151i	0.882984	−	0.321380i	0.139571	−	0.990212i	$-0.455428\pi$
$887$	26.2975	−	9.57151i	0.882984	−	0.321380i	0.743413	+	0.668832i	$0.233206\pi$
$888$		0			0
$889$	−0.644417	−	3.65467i	−0.0216130	−	0.122574i
$890$	0.465444	+	14.7193i	0.0156017	+	0.493393i
$891$		0			0
$892$	−3.23334	+	0.204689i	−0.108260	+	0.00685351i
$893$	17.4984	−	3.08544i	0.585562	−	0.103250i
$894$		0			0
$895$	−10.5200	+	3.82896i	−0.351644	+	0.127988i
$896$	8.17163	+	4.22164i	0.272995	+	0.141035i
$897$		0			0
$898$	−6.69567	−	2.19998i	−0.223438	−	0.0734143i
$899$	−15.7839	+	9.11281i	−0.526421	+	0.303929i
$900$		0			0
$901$	−45.4514	−	26.2414i	−1.51421	−	0.874227i
$902$	−13.9794	−	15.6290i	−0.465463	−	0.520387i
$903$		0			0
$904$	1.92755	−	24.1336i	0.0641094	−	0.802673i
$905$	2.69732	−	15.2973i	0.0896620	−	0.508498i
$906$		0			0
$907$	−17.3874	−	20.7215i	−0.577338	−	0.688045i	0.395781	−	0.918345i	$-0.370474\pi$
$907$	−17.3874	−	20.7215i	−0.577338	−	0.688045i	−0.973120	+	0.230300i	$0.926029\pi$
$908$	12.4853	+	6.19169i	0.414339	+	0.205478i
$909$		0			0
$910$	−4.23518	−	6.82767i	−0.140395	−	0.226335i
$911$	−9.03367	−	3.28799i	−0.299299	−	0.108936i	0.188006	−	0.982168i	$-0.439798\pi$
$911$	−9.03367	−	3.28799i	−0.299299	−	0.108936i	−0.487305	+	0.873232i	$0.662020\pi$
$912$		0			0
$913$	−21.2256	−	17.8104i	−0.702465	−	0.589438i
$914$	26.4649	−	10.5912i	0.875383	−	0.350326i
$915$		0			0
$916$	48.8730	−	11.8438i	1.61481	−	0.391330i
$917$		−	10.8185i		−	0.357258i
$918$		0			0
$919$	0.257674			0.00849989			0.00424994	−	0.999991i	$-0.498647\pi$
$919$	0.257674			0.00849989			0.00424994	+	0.999991i	$0.498647\pi$
$920$	46.3396	−	12.7932i	1.52777	−	0.421779i
$921$		0			0
$922$	17.8436	+	44.5870i	0.587647	+	1.46839i
$923$	−10.0056	+	11.9242i	−0.329337	+	0.392489i
$924$		0			0
$925$	1.24037	−	3.40788i	0.0407830	−	0.112050i
$926$	28.5503	+	46.0269i	0.938221	+	1.51254i
$927$		0			0
$928$	35.3823	+	13.5425i	1.16148	+	0.444554i
$929$	27.9758	−	23.4745i	0.917856	−	0.770173i	−0.0557411	−	0.998445i	$-0.517752\pi$
$929$	27.9758	−	23.4745i	0.917856	−	0.770173i	0.973597	+	0.228273i	$0.0733077\pi$
$930$		0			0
$931$	37.2228	+	6.56338i	1.21993	+	0.215106i
$932$	3.49284	−	31.2492i	0.114412	−	1.02360i
$933$		0			0
$934$	−10.3782	−	11.6028i	−0.339585	−	0.379656i
$935$	29.8603	−	51.7196i	0.976536	−	1.69141i
$936$		0			0
$937$	−4.21635	−	7.30293i	−0.137742	−	0.238576i	0.788899	−	0.614522i	$-0.210651\pi$
$937$	−4.21635	−	7.30293i	−0.137742	−	0.238576i	−0.926642	+	0.375946i	$0.877318\pi$
$938$	0.803593	−	2.44575i	0.0262382	−	0.0798565i
$939$		0			0
$940$	8.56716	−	11.6297i	0.279430	−	0.379319i
$941$	6.23285	+	17.1246i	0.203185	+	0.558246i	0.998873	−	0.0474602i	$-0.0151127\pi$
$941$	6.23285	+	17.1246i	0.203185	+	0.558246i	−0.795688	+	0.605707i	$0.792891\pi$
$942$		0			0
$943$	−5.20444	−	29.5159i	−0.169480	−	0.961169i
$944$	−3.70690	−	29.1603i	−0.120649	−	0.949088i
$945$		0			0
$946$	−13.5064	+	0.427089i	−0.439130	+	0.0138859i
$947$	−30.4479	+	5.36879i	−0.989424	+	0.174462i	−0.644860	−	0.764301i	$-0.723084\pi$
$947$	−30.4479	+	5.36879i	−0.989424	+	0.174462i	−0.344564	+	0.938763i	$0.611973\pi$
$948$		0			0
$949$	−3.89045	−	10.6889i	−0.126289	−	0.346977i
$950$	4.55538	−	5.79117i	0.147796	−	0.187890i
$951$		0			0
$952$	15.8068	+	4.10750i	0.512302	+	0.133125i
$953$	−17.3439	−	30.0406i	−0.561825	−	0.973109i	−0.997337	−	0.0729266i	$-0.976766\pi$
$953$	−17.3439	−	30.0406i	−0.561825	−	0.973109i	0.435512	−	0.900183i	$-0.356567\pi$
$954$		0			0
$955$	42.4811	+	24.5265i	1.37466	+	0.793658i
$956$	22.5023	−	21.4454i	0.727776	−	0.693593i
$957$		0			0
$958$	−4.62583	+	32.1454i	−0.149454	+	1.03857i
$959$	−0.304398	+	1.72633i	−0.00982954	+	0.0557461i
$960$		0			0
$961$	−18.0742	+	15.1661i	−0.583040	+	0.489229i
$962$	7.99476	−	14.9172i	0.257762	−	0.480948i
$963$		0			0
$964$	13.9722	+	21.0121i	0.450015	+	0.676754i
$965$	4.66513	−	12.8173i	0.150176	−	0.412605i
$966$		0			0
$967$	23.6086	+	19.8100i	0.759202	+	0.637046i	0.937919	−	0.346854i	$-0.112750\pi$
$967$	23.6086	+	19.8100i	0.759202	+	0.637046i	−0.178717	+	0.983901i	$0.557195\pi$
$968$	−2.64763	+	1.25908i	−0.0850979	+	0.0404684i
$969$		0			0
$970$	−18.7594	+	3.92287i	−0.602329	+	0.125956i
$971$		−	43.2999i		−	1.38956i	−0.719223	−	0.694779i	$-0.755502\pi$
$971$		−	43.2999i		−	1.38956i	0.719223	−	0.694779i	$-0.244498\pi$
$972$		0			0
$973$		−	0.475690i		−	0.0152499i
$974$	−2.55103	−	12.1992i	−0.0817403	−	0.390888i
$975$		0			0
$976$	−0.482063	−	0.936198i	−0.0154305	−	0.0299670i
$977$	−4.11710	−	3.45466i	−0.131718	−	0.110524i	0.574549	−	0.818470i	$-0.305178\pi$
$977$	−4.11710	−	3.45466i	−0.131718	−	0.110524i	−0.706267	+	0.707946i	$0.749622\pi$
$978$		0			0
$979$	5.09839	−	14.0077i	0.162945	−	0.447688i
$980$	25.5863	−	17.0139i	0.817324	−	0.543488i
$981$		0			0
$982$	14.6587	+	7.85622i	0.467776	+	0.250702i
$983$	−0.806129	+	0.676422i	−0.0257115	+	0.0215745i	−0.655553	−	0.755149i	$-0.727564\pi$
$983$	−0.806129	+	0.676422i	−0.0257115	+	0.0215745i	0.629841	+	0.776724i	$0.283120\pi$
$984$		0			0
$985$	−1.84392	+	10.4574i	−0.0587521	+	0.333200i
$986$	66.5849	+	9.58179i	2.12050	+	0.305146i
$987$		0			0
$988$	24.8916	−	23.7225i	0.791909	−	0.754713i
$989$	−16.7270	−	9.65734i	−0.531888	−	0.307086i
$990$		0			0
$991$	10.7235	+	18.5737i	0.340644	+	0.590013i	0.984553	−	0.175090i	$-0.0560215\pi$
$991$	10.7235	+	18.5737i	0.340644	+	0.590013i	−0.643908	+	0.765103i	$0.722688\pi$
$992$	−15.1143	−	2.92265i	−0.479880	−	0.0927942i
$993$		0			0
$994$	4.87823	+	3.83725i	0.154728	+	0.121710i
$995$	11.0174	+	30.2700i	0.349274	+	0.959622i
$996$		0			0
$997$	−9.02724	+	1.59175i	−0.285896	+	0.0504111i	−0.314757	−	0.949172i	$-0.601923\pi$
$997$	−9.02724	+	1.59175i	−0.285896	+	0.0504111i	0.0288614	+	0.999583i	$0.490812\pi$
$998$	0.788669	+	24.9411i	0.0249649	+	0.789496i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.253.15		204
3.2	odd	2		216.2.t.a.13.20	yes	204
8.5	even	2	inner	648.2.t.a.253.16		204
12.11	even	2		864.2.bf.a.337.29		204
24.5	odd	2		216.2.t.a.13.19	✓	204
24.11	even	2		864.2.bf.a.337.6		204
27.2	odd	18		216.2.t.a.133.19	yes	204
27.25	even	9	inner	648.2.t.a.397.16		204
108.83	even	18		864.2.bf.a.241.6		204
216.29	odd	18		216.2.t.a.133.20	yes	204
216.83	even	18		864.2.bf.a.241.29		204
216.133	even	18	inner	648.2.t.a.397.15		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.19	✓	204	24.5	odd	2
216.2.t.a.13.20	yes	204	3.2	odd	2
216.2.t.a.133.19	yes	204	27.2	odd	18
216.2.t.a.133.20	yes	204	216.29	odd	18
648.2.t.a.253.15		204	1.1	even	1	trivial
648.2.t.a.253.16		204	8.5	even	2	inner
648.2.t.a.397.15		204	216.133	even	18	inner
648.2.t.a.397.16		204	27.25	even	9	inner
864.2.bf.a.241.6		204	108.83	even	18
864.2.bf.a.241.29		204	216.83	even	18
864.2.bf.a.337.6		204	24.11	even	2
864.2.bf.a.337.29		204	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.289471 - 1.38427i) q^{2} +(-1.83241 + 0.801412i) q^{4} +(1.55785 - 1.85658i) q^{5} +(0.763942 + 0.278052i) q^{7} +(1.63980 + 2.30457i) q^{8} +(-3.02096 - 1.61907i) q^{10} +(2.23007 + 2.65769i) q^{11} +(2.83964 + 0.500705i) q^{13} +(0.163761 - 1.13799i) q^{14} +(2.71548 - 2.93704i) q^{16} +(3.55127 - 6.15099i) q^{17} +(-5.16371 + 2.98127i) q^{19} +(-1.36675 + 4.65050i) q^{20} +(3.03343 - 3.85634i) q^{22} +(6.58997 - 2.39855i) q^{23} +(-0.151733 - 0.860521i) q^{25} +(-0.128881 - 4.07577i) q^{26} +(-1.62269 + 0.102726i) q^{28} +(-6.59552 + 1.16297i) q^{29} +(2.55724 - 0.930757i) q^{31} +(-4.85171 - 2.90877i) q^{32} +(-9.54262 - 3.13539i) q^{34} +(1.70634 - 0.985154i) q^{35} +(3.59434 + 2.07519i) q^{37} +(5.62163 + 6.28499i) q^{38} +(6.83319 + 0.545766i) q^{40} +(0.742124 - 4.20880i) q^{41} +(-1.77034 - 2.10981i) q^{43} +(-6.21631 - 3.08279i) q^{44} +(-5.22785 - 8.42800i) q^{46} +(-2.80028 - 1.01922i) q^{47} +(-4.85602 - 4.07468i) q^{49} +(-1.14727 + 0.459136i) q^{50} +(-5.60467 + 1.35822i) q^{52} -7.38929i q^{53} +8.40834 q^{55} +(0.611922 + 2.21651i) q^{56} +(3.51907 + 8.79334i) q^{58} +(4.72368 - 5.62947i) q^{59} +(0.0900385 - 0.247379i) q^{61} +(-2.02867 - 3.27048i) q^{62} +(-2.62210 + 7.55808i) q^{64} +(5.35335 - 4.49199i) q^{65} +(2.20513 + 0.388825i) q^{67} +(-1.57793 + 14.1172i) q^{68} +(-1.85765 - 2.07686i) q^{70} +(-2.69918 + 4.67512i) q^{71} +(-1.97245 - 3.41639i) q^{73} +(1.83217 - 5.57624i) q^{74} +(7.07283 - 9.60118i) q^{76} +(0.964666 + 2.65040i) q^{77} +(1.76846 + 10.0295i) q^{79} +(-1.22252 - 9.61697i) q^{80} +(-6.04094 + 0.191022i) q^{82} +(-7.86515 + 1.38684i) q^{83} +(-5.88742 - 16.1756i) q^{85} +(-2.40809 + 3.06136i) q^{86} +(-2.46797 + 9.49744i) q^{88} +(-2.14833 - 3.72101i) q^{89} +(2.03010 + 1.17208i) q^{91} +(-10.1533 + 9.67643i) q^{92} +(-0.600276 + 4.17138i) q^{94} +(-2.50935 + 14.2312i) q^{95} +(4.28345 - 3.59424i) q^{97} +(-4.23479 + 7.90155i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more