LMFDB - Embedded newform 324.2.l.a.179.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [324,2,Mod(35,324)] 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("324.35"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(324, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			179.7
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.438668 - 1.34446i) q^{2} +(-1.61514 + 1.17954i) q^{4} +(-3.32285 - 0.585909i) q^{5} +(1.72640 + 2.05745i) q^{7} +(2.29436 + 1.65406i) q^{8} +(0.669899 + 4.72446i) q^{10} +(0.506730 + 2.87381i) q^{11} +(0.552703 - 0.201167i) q^{13} +(2.00883 - 3.22361i) q^{14} +(1.21736 - 3.81025i) q^{16} +(6.36286 + 3.67360i) q^{17} +(-2.82795 + 1.63272i) q^{19} +(6.05798 - 2.97312i) q^{20} +(3.64143 - 1.94193i) q^{22} +(0.365077 + 0.306336i) q^{23} +(5.99961 + 2.18368i) q^{25} +(-0.512914 - 0.654840i) q^{26} +(-5.21523 - 1.28670i) q^{28} +(-1.49502 + 4.10753i) q^{29} +(-3.73778 + 4.45451i) q^{31} +(-5.65675 + 0.0347450i) q^{32} +(2.14782 - 10.1661i) q^{34} +(-4.53111 - 7.84811i) q^{35} +(-1.59532 + 2.76318i) q^{37} +(3.43565 + 3.08584i) q^{38} +(-6.65468 - 6.84050i) q^{40} +(1.09875 + 3.01880i) q^{41} +(1.79304 - 0.316161i) q^{43} +(-4.20822 - 4.04390i) q^{44} +(0.251708 - 0.625211i) q^{46} +(-0.940800 + 0.789425i) q^{47} +(-0.0370819 + 0.210302i) q^{49} +(0.304032 - 9.02414i) q^{50} +(-0.655407 + 0.976849i) q^{52} -7.37157i q^{53} -9.84615i q^{55} +(0.557836 + 7.57609i) q^{56} +(6.17822 + 0.208150i) q^{58} +(-0.718733 + 4.07614i) q^{59} +(0.421725 - 0.353869i) q^{61} +(7.62855 + 3.07124i) q^{62} +(2.52815 + 7.59002i) q^{64} +(-1.95442 + 0.344616i) q^{65} +(3.46492 + 9.51978i) q^{67} +(-14.6101 + 1.57188i) q^{68} +(-8.56381 + 9.53460i) q^{70} +(-0.616505 + 1.06782i) q^{71} +(1.18077 + 2.04515i) q^{73} +(4.41480 + 0.932727i) q^{74} +(2.64168 - 5.97275i) q^{76} +(-5.03789 + 6.00392i) q^{77} +(3.33584 - 9.16514i) q^{79} +(-6.27757 + 11.9477i) q^{80} +(3.57666 - 2.80148i) q^{82} +(-16.8988 - 6.15067i) q^{83} +(-18.9905 - 15.9349i) q^{85} +(-1.21161 - 2.27198i) q^{86} +(-3.59084 + 7.43171i) q^{88} +(4.81205 - 2.77824i) q^{89} +(1.36808 + 0.789860i) q^{91} +(-0.950986 - 0.0641520i) q^{92} +(1.47405 + 0.918571i) q^{94} +(10.3535 - 3.76836i) q^{95} +(1.83865 + 10.4275i) q^{97} +(0.299009 - 0.0423976i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.438668	−	1.34446i	−0.310185	−	0.950676i
$2$	−0.438668	−	1.34446i	−0.310185	−	0.950676i
$3$		0			0
$3$		0			0
$4$	−1.61514	+	1.17954i	−0.807570	+	0.589771i
$5$	−3.32285	−	0.585909i	−1.48603	−	0.262026i	−0.629043	−	0.777371i	$-0.716553\pi$
$5$	−3.32285	−	0.585909i	−1.48603	−	0.262026i	−0.856983	+	0.515344i	$0.827664\pi$
$6$		0			0
$7$	1.72640	+	2.05745i	0.652519	+	0.777641i	0.986292	−	0.165012i	$-0.0527663\pi$
$7$	1.72640	+	2.05745i	0.652519	+	0.777641i	−0.333773	+	0.942653i	$0.608322\pi$
$8$	2.29436	+	1.65406i	0.811178	+	0.584800i
$9$		0			0
$10$	0.669899	+	4.72446i	0.211841	+	1.49401i
$11$	0.506730	+	2.87381i	0.152785	+	0.866486i	0.960783	+	0.277301i	$0.0894400\pi$
$11$	0.506730	+	2.87381i	0.152785	+	0.866486i	−0.807998	+	0.589185i	$0.799449\pi$
$12$		0			0
$13$	0.552703	−	0.201167i	0.153292	−	0.0557938i	−0.264234	−	0.964458i	$-0.585119\pi$
$13$	0.552703	−	0.201167i	0.153292	−	0.0557938i	0.417527	+	0.908665i	$0.362897\pi$
$14$	2.00883	−	3.22361i	0.536884	−	0.861547i
$15$		0			0
$16$	1.21736	−	3.81025i	0.304340	−	0.952563i
$17$	6.36286	+	3.67360i	1.54322	+	0.890979i	0.998633	+	0.0522747i	$0.0166472\pi$
$17$	6.36286	+	3.67360i	1.54322	+	0.890979i	0.544588	+	0.838704i	$0.316686\pi$
$18$		0			0
$19$	−2.82795	+	1.63272i	−0.648776	+	0.374571i	−0.787987	−	0.615692i	$-0.788877\pi$
$19$	−2.82795	+	1.63272i	−0.648776	+	0.374571i	0.139211	+	0.990263i	$0.455543\pi$
$20$	6.05798	−	2.97312i	1.35461	−	0.664810i
$21$		0			0
$22$	3.64143	−	1.94193i	0.776356	−	0.414020i
$23$	0.365077	+	0.306336i	0.0761238	+	0.0638754i	0.680056	−	0.733161i	$-0.261956\pi$
$23$	0.365077	+	0.306336i	0.0761238	+	0.0638754i	−0.603932	+	0.797036i	$0.706400\pi$
$24$		0			0
$25$	5.99961	+	2.18368i	1.19992	+	0.436736i
$26$	−0.512914	−	0.654840i	−0.100591	−	0.128425i
$27$		0			0
$28$	−5.21523	−	1.28670i	−0.985585	−	0.243164i
$29$	−1.49502	+	4.10753i	−0.277618	+	0.762749i	0.720013	+	0.693960i	$0.244136\pi$
$29$	−1.49502	+	4.10753i	−0.277618	+	0.762749i	−0.997631	+	0.0687888i	$0.978087\pi$
$30$		0			0
$31$	−3.73778	+	4.45451i	−0.671325	+	0.800054i	−0.988964	−	0.148158i	$-0.952666\pi$
$31$	−3.73778	+	4.45451i	−0.671325	+	0.800054i	0.317639	+	0.948212i	$0.397110\pi$
$32$	−5.65675	+	0.0347450i	−0.999981	+	0.00614210i
$33$		0			0
$34$	2.14782	−	10.1661i	0.368348	−	1.74347i
$35$	−4.53111	−	7.84811i	−0.765897	−	1.32657i
$36$		0			0
$37$	−1.59532	+	2.76318i	−0.262269	+	0.454264i	−0.966845	−	0.255365i	$-0.917804\pi$
$37$	−1.59532	+	2.76318i	−0.262269	+	0.454264i	0.704575	+	0.709629i	$0.251138\pi$
$38$	3.43565	+	3.08584i	0.557336	+	0.500589i
$39$		0			0
$40$	−6.65468	−	6.84050i	−1.05220	−	1.08158i
$41$	1.09875	+	3.01880i	0.171596	+	0.471457i	0.995443	−	0.0953554i	$-0.0303987\pi$
$41$	1.09875	+	3.01880i	0.171596	+	0.471457i	−0.823847	+	0.566812i	$0.808177\pi$
$42$		0			0
$43$	1.79304	−	0.316161i	0.273436	−	0.0482141i	−0.0352488	−	0.999379i	$-0.511222\pi$
$43$	1.79304	−	0.316161i	0.273436	−	0.0482141i	0.308685	+	0.951164i	$0.400111\pi$
$44$	−4.20822	−	4.04390i	−0.634413	−	0.609641i
$45$		0			0
$46$	0.251708	−	0.625211i	0.0371124	−	0.0921823i
$47$	−0.940800	+	0.789425i	−0.137230	+	0.115149i	−0.708819	−	0.705391i	$-0.750772\pi$
$47$	−0.940800	+	0.789425i	−0.137230	+	0.115149i	0.571589	+	0.820540i	$0.306327\pi$
$48$		0			0
$49$	−0.0370819	+	0.210302i	−0.00529741	+	0.0300431i
$50$	0.304032	−	9.02414i	0.0429965	−	1.27621i
$51$		0			0
$52$	−0.655407	+	0.976849i	−0.0908886	+	0.135465i
$53$		−	7.37157i		−	1.01256i	−0.862368	−	0.506282i	$-0.831020\pi$
$53$		−	7.37157i		−	1.01256i	0.862368	−	0.506282i	$-0.168980\pi$
$54$		0			0
$55$		−	9.84615i		−	1.32765i
$56$	0.557836	+	7.57609i	0.0745440	+	1.01240i
$57$		0			0
$58$	6.17822	+	0.208150i	0.811240	+	0.0273314i
$59$	−0.718733	+	4.07614i	−0.0935710	+	0.530668i	0.901605	+	0.432561i	$0.142390\pi$
$59$	−0.718733	+	4.07614i	−0.0935710	+	0.530668i	−0.995176	+	0.0981070i	$0.968721\pi$
$60$		0			0
$61$	0.421725	−	0.353869i	0.0539963	−	0.0453083i	−0.615390	−	0.788223i	$-0.711002\pi$
$61$	0.421725	−	0.353869i	0.0539963	−	0.0453083i	0.669386	+	0.742914i	$0.266557\pi$
$62$	7.62855	+	3.07124i	0.968827	+	0.390048i
$63$		0			0
$64$	2.52815	+	7.59002i	0.316018	+	0.948753i
$65$	−1.95442	+	0.344616i	−0.242415	+	0.0427444i
$66$		0			0
$67$	3.46492	+	9.51978i	0.423307	+	1.16303i	0.949803	+	0.312849i	$0.101283\pi$
$67$	3.46492	+	9.51978i	0.423307	+	1.16303i	−0.526496	+	0.850178i	$0.676495\pi$
$68$	−14.6101	+	1.57188i	−1.77173	+	0.190619i
$69$		0			0
$70$	−8.56381	+	9.53460i	−1.02357	+	1.13960i
$71$	−0.616505	+	1.06782i	−0.0731657	+	0.126727i	−0.900287	−	0.435297i	$-0.856644\pi$
$71$	−0.616505	+	1.06782i	−0.0731657	+	0.126727i	0.827121	+	0.562023i	$0.189977\pi$
$72$		0			0
$73$	1.18077	+	2.04515i	0.138198	+	0.239366i	0.926815	−	0.375519i	$-0.122536\pi$
$73$	1.18077	+	2.04515i	0.138198	+	0.239366i	−0.788616	+	0.614885i	$0.789202\pi$
$74$	4.41480	+	0.932727i	0.513210	+	0.108427i
$75$		0			0
$76$	2.64168	−	5.97275i	0.303021	−	0.685121i
$77$	−5.03789	+	6.00392i	−0.574121	+	0.684210i
$78$		0			0
$79$	3.33584	−	9.16514i	0.375311	−	1.03116i	−0.597965	−	0.801522i	$-0.704024\pi$
$79$	3.33584	−	9.16514i	0.375311	−	1.03116i	0.973276	−	0.229637i	$-0.0737538\pi$
$80$	−6.27757	+	11.9477i	−0.701854	+	1.33579i
$81$		0			0
$82$	3.57666	−	2.80148i	0.394976	−	0.309371i
$83$	−16.8988	−	6.15067i	−1.85489	−	0.675124i	−0.982487	−	0.186333i	$-0.940340\pi$
$83$	−16.8988	−	6.15067i	−1.85489	−	0.675124i	−0.872401	−	0.488790i	$-0.837438\pi$
$84$		0			0
$85$	−18.9905	−	15.9349i	−2.05981	−	1.72838i
$86$	−1.21161	−	2.27198i	−0.130652	−	0.244994i
$87$		0			0
$88$	−3.59084	+	7.43171i	−0.382785	+	0.792223i
$89$	4.81205	−	2.77824i	0.510076	−	0.294493i	−0.222789	−	0.974867i	$-0.571516\pi$
$89$	4.81205	−	2.77824i	0.510076	−	0.294493i	0.732865	+	0.680374i	$0.238183\pi$
$90$		0			0
$91$	1.36808	+	0.789860i	0.143413	+	0.0827998i
$92$	−0.950986	−	0.0641520i	−0.0991472	−	0.00668831i
$93$		0			0
$94$	1.47405	+	0.918571i	0.152036	+	0.0947434i
$95$	10.3535	−	3.76836i	1.06224	−	0.386626i
$96$		0			0
$97$	1.83865	+	10.4275i	0.186687	+	1.05875i	0.923769	+	0.382951i	$0.125092\pi$
$97$	1.83865	+	10.4275i	0.186687	+	1.05875i	−0.737082	+	0.675803i	$0.763797\pi$
$98$	0.299009	−	0.0423976i	0.0302045	−	0.00428280i
$99$		0			0
$100$	−12.2660	+	3.54984i	−1.22660	+	0.354984i
$101$	−5.49760	−	6.55178i	−0.547032	−	0.651927i	0.419717	−	0.907655i	$-0.362129\pi$
$101$	−5.49760	−	6.55178i	−0.547032	−	0.651927i	−0.966749	+	0.255728i	$0.917685\pi$
$102$		0			0
$103$	−16.7001	−	2.94469i	−1.64551	−	0.290149i	−0.727326	−	0.686292i	$-0.759237\pi$
$103$	−16.7001	−	2.94469i	−1.64551	−	0.290149i	−0.918189	+	0.396144i	$0.870348\pi$
$104$	1.60084	+	0.452656i	0.156975	+	0.0443865i
$105$		0			0
$106$	−9.91078	+	3.23367i	−0.962620	+	0.314082i
$107$	3.73466			0.361043			0.180522	−	0.983571i	$-0.442221\pi$
$107$	3.73466			0.361043			0.180522	+	0.983571i	$0.442221\pi$
$108$		0			0
$109$	10.6061			1.01588			0.507940	−	0.861393i	$-0.330407\pi$
$109$	10.6061			1.01588			0.507940	+	0.861393i	$0.330407\pi$
$110$	−13.2377	+	4.31919i	−1.26217	+	0.411819i
$111$		0			0
$112$	9.94104	−	4.07338i	0.939340	−	0.384898i
$113$	5.75136	+	1.01412i	0.541042	+	0.0954004i	0.437489	−	0.899224i	$-0.355868\pi$
$113$	5.75136	+	1.01412i	0.541042	+	0.0954004i	0.103553	+	0.994624i	$0.466979\pi$
$114$		0			0
$115$	−1.03361	−	1.23181i	−0.0963848	−	0.114867i
$116$	−2.43034	−	8.39768i	−0.225651	−	0.779705i
$117$		0			0
$118$	5.79548	−	0.821763i	0.533517	−	0.0756494i
$119$	3.42662	+	19.4333i	0.314118	+	1.78145i
$120$		0			0
$121$	2.33461	−	0.849729i	0.212237	−	0.0772481i
$122$	−0.660760	−	0.411761i	−0.0598224	−	0.0372791i
$123$		0			0
$124$	0.782755	−	11.6035i	0.0702935	−	1.04203i
$125$	−4.04606	−	2.33599i	−0.361890	−	0.208937i
$126$		0			0
$127$	−1.06513	+	0.614951i	−0.0945147	+	0.0545681i	−0.546512	−	0.837451i	$-0.684045\pi$
$127$	−1.06513	+	0.614951i	−0.0945147	+	0.0545681i	0.451998	+	0.892019i	$0.350712\pi$
$128$	9.09546	−	6.72849i	0.803933	−	0.594720i
$129$		0			0
$130$	1.32066	+	2.47646i	0.115830	+	0.217200i
$131$	13.5213	+	11.3457i	1.18136	+	0.991278i	0.999969	+	0.00786658i	$0.00250404\pi$
$131$	13.5213	+	11.3457i	1.18136	+	0.991278i	0.181390	+	0.983411i	$0.441940\pi$
$132$		0			0
$133$	−8.24140	−	2.99962i	−0.714620	−	0.260100i
$134$	11.2790	−	8.83446i	0.974358	−	0.763181i
$135$		0			0
$136$	8.52231	+	18.9531i	0.730782	+	1.62522i
$137$	3.54986	−	9.75317i	0.303285	−	0.833269i	−0.690639	−	0.723200i	$-0.742671\pi$
$137$	3.54986	−	9.75317i	0.303285	−	0.833269i	0.993924	−	0.110069i	$-0.0351073\pi$
$138$		0			0
$139$	14.0279	−	16.7178i	1.18983	−	1.41798i	0.304820	−	0.952410i	$-0.401404\pi$
$139$	14.0279	−	16.7178i	1.18983	−	1.41798i	0.885009	−	0.465573i	$-0.154152\pi$
$140$	16.5756	+	7.33117i	1.40089	+	0.619597i
$141$		0			0
$142$	1.70608	+	0.360448i	0.143171	+	0.0302482i
$143$	0.858188	+	1.48642i	0.0717653	+	0.124301i
$144$		0			0
$145$	7.37437	−	12.7728i	0.612408	−	1.06072i
$146$	2.23165	−	2.48463i	0.184693	−	0.205630i
$147$		0			0
$148$	−0.682616	−	6.34467i	−0.0561107	−	0.521529i
$149$	−1.27723	−	3.50915i	−0.104635	−	0.287481i	0.876317	−	0.481736i	$-0.159993\pi$
$149$	−1.27723	−	3.50915i	−0.104635	−	0.287481i	−0.980951	+	0.194255i	$0.937771\pi$
$150$		0			0
$151$	14.3762	−	2.53492i	1.16992	−	0.206289i	0.445265	−	0.895399i	$-0.353109\pi$
$151$	14.3762	−	2.53492i	1.16992	−	0.206289i	0.724657	+	0.689110i	$0.241998\pi$
$152$	−9.18894	−	0.931571i	−0.745321	−	0.0755604i
$153$		0			0
$154$	10.2820	+	4.13951i	0.828546	+	0.333571i
$155$	15.0300	−	12.6117i	1.20724	−	1.01300i
$156$		0			0
$157$	−2.89506	+	16.4187i	−0.231051	+	1.31036i	0.619722	+	0.784822i	$0.287245\pi$
$157$	−2.89506	+	16.4187i	−0.231051	+	1.31036i	−0.850773	+	0.525534i	$0.823866\pi$
$158$	−13.7855	−	0.464445i	−1.09671	−	0.0369493i
$159$		0			0
$160$	18.8169	+	3.19889i	1.48761	+	0.252894i
$161$			1.27998i			0.100877i
$162$		0			0
$163$		−	2.78256i		−	0.217947i	−0.994045	−	0.108973i	$-0.965244\pi$
$163$		−	2.78256i		−	0.217947i	0.994045	−	0.108973i	$-0.0347563\pi$
$164$	−5.33544	−	3.57976i	−0.416628	−	0.279532i
$165$		0			0
$166$	−0.856352	+	25.4179i	−0.0664658	+	1.97281i
$167$	2.46126	−	13.9585i	0.190458	−	1.08014i	−0.728282	−	0.685278i	$-0.759681\pi$
$167$	2.46126	−	13.9585i	0.190458	−	1.08014i	0.918740	−	0.394863i	$-0.129208\pi$
$168$		0			0
$169$	−9.69357	+	8.13387i	−0.745659	+	0.625682i
$170$	−13.0933	+	32.5220i	−1.00421	+	2.49433i
$171$		0			0
$172$	−2.52308	+	2.62561i	−0.192383	+	0.200201i
$173$	−1.21493	+	0.214226i	−0.0923698	+	0.0162873i	−0.219642	−	0.975581i	$-0.570489\pi$
$173$	−1.21493	+	0.214226i	−0.0923698	+	0.0162873i	0.127272	+	0.991868i	$0.459378\pi$
$174$		0			0
$175$	5.86494	+	16.1138i	0.443348	+	1.21809i
$176$	11.5668	+	1.56769i	0.871882	+	0.118169i
$177$		0			0
$178$	−5.84612	−	5.25088i	−0.438185	−	0.393570i
$179$	8.60015	−	14.8959i	0.642805	−	1.11337i	−0.341998	−	0.939701i	$-0.611104\pi$
$179$	8.60015	−	14.8959i	0.642805	−	1.11337i	0.984804	−	0.173671i	$-0.0555630\pi$
$180$		0			0
$181$	−10.8176	−	18.7366i	−0.804065	−	1.39268i	−0.916920	−	0.399071i	$-0.869333\pi$
$181$	−10.8176	−	18.7366i	−0.804065	−	1.39268i	0.112855	−	0.993611i	$-0.464000\pi$
$182$	0.461803	−	2.18581i	0.0342311	−	0.162023i
$183$		0			0
$184$	0.330918	+	1.30670i	0.0243956	+	0.0963315i
$185$	6.91999	−	8.24693i	0.508768	−	0.606326i
$186$		0			0
$187$	−7.33297	+	20.1472i	−0.536240	+	1.47331i
$188$	0.588364	−	2.38474i	0.0429109	−	0.173925i
$189$		0			0
$190$	−9.60815	−	12.2668i	−0.697048	−	0.889925i
$191$	4.48414	+	1.63210i	0.324461	+	0.118094i	0.499115	−	0.866536i	$-0.333658\pi$
$191$	4.48414	+	1.63210i	0.324461	+	0.118094i	−0.174654	+	0.984630i	$0.555881\pi$
$192$		0			0
$193$	6.94036	+	5.82365i	0.499578	+	0.419196i	0.857444	−	0.514577i	$-0.172051\pi$
$193$	6.94036	+	5.82365i	0.499578	+	0.419196i	−0.357866	+	0.933773i	$0.616496\pi$
$194$	13.2128	−	7.04621i	0.948625	−	0.505888i
$195$		0			0
$196$	−0.188167	−	0.383407i	−0.0134405	−	0.0273862i
$197$	−1.80241	+	1.04062i	−0.128416	+	0.0741411i	−0.562832	−	0.826571i	$-0.690288\pi$
$197$	−1.80241	+	1.04062i	−0.128416	+	0.0741411i	0.434416	+	0.900712i	$0.356955\pi$
$198$		0			0
$199$	−9.74989	−	5.62910i	−0.691151	−	0.399036i	0.112892	−	0.993607i	$-0.463989\pi$
$199$	−9.74989	−	5.62910i	−0.691151	−	0.399036i	−0.804043	+	0.594571i	$0.797322\pi$
$200$	10.1533	+	14.9339i	0.717947	+	1.05598i
$201$		0			0
$202$	−6.39699	+	10.2654i	−0.450090	+	0.722268i
$203$	−11.0320	+	4.01533i	−0.774296	+	0.281821i
$204$		0			0
$205$	−1.88225	−	10.6748i	−0.131462	−	0.745560i
$206$	3.36681	+	23.7444i	0.234577	+	1.65435i
$207$		0			0
$208$	−0.0936603	−	2.35083i	−0.00649417	−	0.163001i
$209$	−6.12512	−	7.29964i	−0.423684	−	0.504926i
$210$		0			0
$211$	5.42064	+	0.955805i	0.373172	+	0.0658003i	0.357089	−	0.934070i	$-0.383769\pi$
$211$	5.42064	+	0.955805i	0.373172	+	0.0658003i	0.0160832	+	0.999871i	$0.494880\pi$
$212$	8.69508	+	11.9061i	0.597181	+	0.817716i
$213$		0			0
$214$	−1.63828	−	5.02110i	−0.111990	−	0.343235i
$215$	−6.14325			−0.418966
$216$		0			0
$217$	−15.6178			−1.06021
$218$	−4.65255	−	14.2595i	−0.315111	−	0.965773i
$219$		0			0
$220$	11.6140	+	15.9029i	0.783012	+	1.07217i
$221$	4.25578	+	0.750408i	0.286275	+	0.0504779i
$222$		0			0
$223$	3.51114	+	4.18441i	0.235123	+	0.280209i	0.870685	−	0.491841i	$-0.163676\pi$
$223$	3.51114	+	4.18441i	0.235123	+	0.280209i	−0.635562	+	0.772050i	$0.719231\pi$
$224$	−9.83731	−	11.5785i	−0.657283	−	0.773619i
$225$		0			0
$226$	−1.15949	−	8.17733i	−0.0771284	−	0.543948i
$227$	0.257802	+	1.46207i	0.0171109	+	0.0970410i	0.992167	−	0.124917i	$-0.0398664\pi$
$227$	0.257802	+	1.46207i	0.0171109	+	0.0970410i	−0.975056	+	0.221958i	$0.928755\pi$
$228$		0			0
$229$	24.4836	−	8.91131i	1.61792	−	0.588876i	0.634938	−	0.772563i	$-0.281026\pi$
$229$	24.4836	−	8.91131i	1.61792	−	0.588876i	0.982985	+	0.183688i	$0.0588035\pi$
$230$	−1.20271	+	1.93001i	−0.0793042	+	0.127261i
$231$		0			0
$232$	−10.2242	+	6.95128i	−0.671253	+	0.456374i
$233$	−5.81401	−	3.35672i	−0.380889	−	0.219906i	0.297316	−	0.954779i	$-0.403908\pi$
$233$	−5.81401	−	3.35672i	−0.380889	−	0.219906i	−0.678205	+	0.734873i	$0.737242\pi$
$234$		0			0
$235$	3.58867	−	2.07192i	0.234099	−	0.135157i
$236$	−3.64712	−	7.43131i	−0.237407	−	0.483737i
$237$		0			0
$238$	24.6242	−	13.1317i	1.59615	−	0.851204i
$239$	−15.7014	−	13.1750i	−1.01564	−	0.852223i	−0.0265665	−	0.999647i	$-0.508457\pi$
$239$	−15.7014	−	13.1750i	−1.01564	−	0.852223i	−0.989073	+	0.147424i	$0.952902\pi$
$240$		0			0
$241$	−11.8674	−	4.31940i	−0.764449	−	0.278237i	−0.0697765	−	0.997563i	$-0.522229\pi$
$241$	−11.8674	−	4.31940i	−0.764449	−	0.278237i	−0.694673	+	0.719326i	$0.744451\pi$
$242$	−2.16654	−	2.76604i	−0.139271	−	0.177808i
$243$		0			0
$244$	−0.263741	+	1.06899i	−0.0168843	+	0.0684351i
$245$	0.246436	−	0.677076i	0.0157442	−	0.0432568i
$246$		0			0
$247$	−1.23456	+	1.47130i	−0.0785535	+	0.0936164i
$248$	−15.9438	+	4.03771i	−1.01243	+	0.256395i
$249$		0			0
$250$	−1.36577	+	6.46448i	−0.0863789	+	0.408850i
$251$	6.38939	+	11.0668i	0.403295	+	0.698527i	0.994121	−	0.108272i	$-0.0345316\pi$
$251$	6.38939	+	11.0668i	0.403295	+	0.698527i	−0.590827	+	0.806799i	$0.701198\pi$
$252$		0			0
$253$	−0.695355	+	1.20439i	−0.0437166	+	0.0757194i
$254$	1.29401	+	1.16226i	0.0811936	+	0.0729266i
$255$		0			0
$256$	−13.0361	−	9.27690i	−0.814754	−	0.579806i
$257$	3.40030	+	9.34225i	0.212105	+	0.582754i	0.999429	−	0.0337856i	$-0.0107563\pi$
$257$	3.40030	+	9.34225i	0.212105	+	0.582754i	−0.787324	+	0.616539i	$0.788534\pi$
$258$		0			0
$259$	−8.43926	+	1.48807i	−0.524390	+	0.0924641i
$260$	2.75017	−	2.86192i	0.170558	−	0.177489i
$261$		0			0
$262$	9.32247	−	23.1558i	0.575944	−	1.43057i
$263$	−14.9780	+	12.5681i	−0.923586	+	0.774981i	−0.974655	−	0.223715i	$-0.928182\pi$
$263$	−14.9780	+	12.5681i	−0.923586	+	0.774981i	0.0510689	+	0.998695i	$0.483737\pi$
$264$		0			0
$265$	−4.31907	+	24.4947i	−0.265318	+	1.50470i
$266$	−0.417634	+	12.3961i	−0.0256068	+	0.760051i
$267$		0			0
$268$	−16.8253	−	11.2888i	−1.02777	−	0.689571i
$269$			30.3293i			1.84921i	0.380930	+	0.924604i	$0.375604\pi$
$269$			30.3293i			1.84921i	−0.380930	+	0.924604i	$0.624396\pi$
$270$		0			0
$271$			19.1257i			1.16181i	0.813973	+	0.580903i	$0.197301\pi$
$271$			19.1257i			1.16181i	−0.813973	+	0.580903i	$0.802699\pi$
$272$	21.7432	−	19.7720i	1.31838	−	1.19885i
$273$		0			0
$274$	−14.6699	−	0.494244i	−0.886244	−	0.0298583i
$275$	−3.23530	+	18.3483i	−0.195096	+	1.10644i
$276$		0			0
$277$	7.54011	−	6.32690i	0.453041	−	0.380147i	−0.387522	−	0.921861i	$-0.626669\pi$
$277$	7.54011	−	6.32690i	0.453041	−	0.380147i	0.840563	+	0.541714i	$0.182224\pi$
$278$	−28.6299	−	11.5264i	−1.71711	−	0.691305i
$279$		0			0
$280$	2.58529	−	25.5011i	0.154501	−	1.52398i
$281$	22.8259	−	4.02483i	1.36168	−	0.240101i	0.555375	−	0.831600i	$-0.312575\pi$
$281$	22.8259	−	4.02483i	1.36168	−	0.240101i	0.806306	+	0.591499i	$0.201463\pi$
$282$		0			0
$283$	−5.96637	−	16.3925i	−0.354664	−	0.974432i	−0.980851	−	0.194759i	$-0.937608\pi$
$283$	−5.96637	−	16.3925i	−0.354664	−	0.974432i	0.626187	−	0.779673i	$-0.284615\pi$
$284$	−0.263794	−	2.45187i	−0.0156533	−	0.145492i
$285$		0			0
$286$	1.62198	−	1.80584i	0.0959096	−	0.106782i
$287$	−4.31412	+	7.47228i	−0.254655	+	0.441075i
$288$		0			0
$289$	18.4907	+	32.0268i	1.08769	+	1.88393i
$290$	−20.4074	−	4.31153i	−1.19836	−	0.253182i
$291$		0			0
$292$	−4.31944	−	1.91044i	−0.252776	−	0.111800i
$293$	−12.2291	+	14.5741i	−0.714431	+	0.851426i	−0.994077	−	0.108678i	$-0.965338\pi$
$293$	−12.2291	+	14.5741i	−0.714431	+	0.851426i	0.279646	+	0.960103i	$0.409783\pi$
$294$		0			0
$295$	4.77649	−	13.1233i	0.278098	−	0.764068i
$296$	−8.23071	+	3.70095i	−0.478400	+	0.215114i
$297$		0			0
$298$	−4.15763	+	3.25653i	−0.240845	+	0.188646i
$299$	0.263404	+	0.0958711i	0.0152330	+	0.00554437i
$300$		0			0
$301$	3.74599	+	3.14326i	0.215915	+	0.181174i
$302$	−9.71449	−	18.2163i	−0.559006	−	1.04823i
$303$		0			0
$304$	2.77843	+	12.7628i	0.159354	+	0.731997i
$305$	−1.60867	+	0.928763i	−0.0921119	+	0.0531808i
$306$		0			0
$307$	−14.3110	−	8.26248i	−0.816773	−	0.471564i	0.0325291	−	0.999471i	$-0.489644\pi$
$307$	−14.3110	−	8.26248i	−0.816773	−	0.471564i	−0.849303	+	0.527906i	$0.822977\pi$
$308$	1.05502	−	15.6396i	0.0601154	−	0.891148i
$309$		0			0
$310$	−23.5491	−	14.6749i	−1.33750	−	0.833479i
$311$	−1.95536	+	0.711694i	−0.110879	+	0.0403565i	−0.396864	−	0.917878i	$-0.629901\pi$
$311$	−1.95536	+	0.711694i	−0.110879	+	0.0403565i	0.285985	+	0.958234i	$0.407679\pi$
$312$		0			0
$313$	−0.0264293	−	0.149888i	−0.00149387	−	0.00847218i	0.984052	−	0.177883i	$-0.0569248\pi$
$313$	−0.0264293	−	0.149888i	−0.00149387	−	0.00847218i	−0.985546	+	0.169410i	$0.945814\pi$
$314$	23.3442	−	3.31007i	1.31739	−	0.186798i
$315$		0			0
$316$	5.42282	+	18.7377i	0.305057	+	1.05408i
$317$	4.31448	+	5.14180i	0.242325	+	0.288792i	0.873475	−	0.486869i	$-0.161861\pi$
$317$	4.31448	+	5.14180i	0.242325	+	0.288792i	−0.631150	+	0.775661i	$0.717417\pi$
$318$		0			0
$319$	−12.5618	−	2.21499i	−0.703327	−	0.124016i
$320$	−3.95360	−	26.7018i	−0.221013	−	1.49268i
$321$		0			0
$322$	1.72089	−	0.561488i	0.0959013	−	0.0312905i
$323$	−23.9918			−1.33494
$324$		0			0
$325$	3.75529			0.208306
$326$	−3.74103	+	1.22062i	−0.207197	+	0.0676038i
$327$		0			0
$328$	−2.47235	+	8.74360i	−0.136513	+	0.482785i
$329$	−3.24840	−	0.572780i	−0.179090	−	0.0315784i
$330$		0			0
$331$	−8.49106	−	10.1192i	−0.466711	−	0.556204i	0.480426	−	0.877035i	$-0.340482\pi$
$331$	−8.49106	−	10.1192i	−0.466711	−	0.556204i	−0.947136	+	0.320831i	$0.896038\pi$
$332$	34.5490	−	9.99868i	1.89612	−	0.548749i
$333$		0			0
$334$	−19.8463	+	2.81408i	−1.08594	+	0.153980i
$335$	−5.93569	−	33.6630i	−0.324301	−	1.83920i
$336$		0			0
$337$	18.1807	−	6.61722i	0.990364	−	0.360463i	0.204503	−	0.978866i	$-0.434442\pi$
$337$	18.1807	−	6.61722i	0.990364	−	0.360463i	0.785861	+	0.618403i	$0.212220\pi$
$338$	15.1879	+	9.46454i	0.826113	+	0.514803i
$339$		0			0
$340$	49.4682	+	3.33704i	2.68279	+	0.180976i
$341$	−14.6955	−	8.48443i	−0.795804	−	0.459458i
$342$		0			0
$343$	15.7851	−	9.11354i	0.852316	−	0.492085i
$344$	4.63682	+	2.24041i	0.250001	+	0.120795i
$345$		0			0
$346$	0.820971	+	1.53946i	0.0441357	+	0.0827617i
$347$	−9.79587	−	8.21971i	−0.525870	−	0.441257i	0.340803	−	0.940135i	$-0.389301\pi$
$347$	−9.79587	−	8.21971i	−0.525870	−	0.441257i	−0.866672	+	0.498878i	$0.833746\pi$
$348$		0			0
$349$	11.3836	+	4.14328i	0.609348	+	0.221785i	0.628218	−	0.778037i	$-0.283785\pi$
$349$	11.3836	+	4.14328i	0.609348	+	0.221785i	−0.0188700	+	0.999822i	$0.506007\pi$
$350$	19.0916	−	14.9538i	1.02049	−	0.799313i
$351$		0			0
$352$	−2.96630	−	16.2388i	−0.158104	−	0.865532i
$353$	−6.82994	+	18.7651i	−0.363521	+	0.998766i	0.614254	+	0.789108i	$0.289457\pi$
$353$	−6.82994	+	18.7651i	−0.363521	+	0.998766i	−0.977775	+	0.209657i	$0.932765\pi$
$354$		0			0
$355$	2.67420	−	3.18699i	0.141932	−	0.169148i
$356$	−4.49509	+	10.1633i	−0.238239	+	0.538652i
$357$		0			0
$358$	−23.7995	−	5.02820i	−1.25784	−	0.265749i
$359$	10.5259	+	18.2314i	0.555535	+	0.962214i	0.997862	+	0.0653605i	$0.0208197\pi$
$359$	10.5259	+	18.2314i	0.555535	+	0.962214i	−0.442327	+	0.896854i	$0.645847\pi$
$360$		0			0
$361$	−4.16848	+	7.22001i	−0.219393	+	0.380001i
$362$	−20.4453	+	22.7630i	−1.07458	+	1.19639i
$363$		0			0
$364$	−3.14131	+	0.337970i	−0.164649	+	0.0177144i
$365$	−2.72524	−	7.48755i	−0.142646	−	0.391916i
$366$		0			0
$367$	−27.4150	+	4.83400i	−1.43105	+	0.252333i	−0.834838	−	0.550495i	$-0.814439\pi$
$367$	−27.4150	+	4.83400i	−1.43105	+	0.252333i	−0.596211	+	0.802828i	$0.703328\pi$
$368$	1.61165	−	1.01811i	0.0840129	−	0.0530729i
$369$		0			0
$370$	−14.1232	−	5.68599i	−0.734232	−	0.295600i
$371$	15.1666	−	12.7263i	0.787411	−	0.660717i
$372$		0			0
$373$	1.03662	−	5.87895i	0.0536740	−	0.304400i	−0.946139	−	0.323762i	$-0.895052\pi$
$373$	1.03662	−	5.87895i	0.0536740	−	0.304400i	0.999813	+	0.0193617i	$0.00616340\pi$
$374$	30.3038	+	1.02096i	1.56697	+	0.0527927i
$375$		0			0
$376$	−3.46429	+	0.255079i	−0.178657	+	0.0131547i
$377$			2.57099i			0.132413i
$378$		0			0
$379$			14.2394i			0.731429i	0.930727	+	0.365715i	$0.119175\pi$
$379$			14.2394i			0.731429i	−0.930727	+	0.365715i	$0.880825\pi$
$380$	−12.2774	+	18.2988i	−0.629817	+	0.938709i
$381$		0			0
$382$	0.227235	−	6.74470i	0.0116263	−	0.345089i
$383$	2.77843	−	15.7573i	0.141971	−	0.805159i	−0.827778	−	0.561056i	$-0.810395\pi$
$383$	2.77843	−	15.7573i	0.141971	−	0.805159i	0.969749	−	0.244103i	$-0.0784935\pi$
$384$		0			0
$385$	20.2579	−	16.9984i	1.03244	−	0.866319i
$386$	4.78515	−	11.8857i	0.243558	−	0.604965i
$387$		0			0
$388$	−15.2694	−	14.6731i	−0.775185	−	0.744916i
$389$	−17.5295	+	3.09093i	−0.888782	+	0.156716i	−0.599355	−	0.800484i	$-0.704576\pi$
$389$	−17.5295	+	3.09093i	−0.888782	+	0.156716i	−0.289427	+	0.957200i	$0.593465\pi$
$390$		0			0
$391$	1.19758	+	3.29032i	0.0605641	+	0.166399i
$392$	−0.432932	+	0.421172i	−0.0218664	+	0.0212724i
$393$		0			0
$394$	2.18973	+	1.96678i	0.110317	+	0.0990847i
$395$	−16.4544	+	28.4999i	−0.827913	+	1.43399i
$396$		0			0
$397$	−9.34449	−	16.1851i	−0.468987	−	0.812309i	0.530385	−	0.847757i	$-0.322047\pi$
$397$	−9.34449	−	16.1851i	−0.468987	−	0.812309i	−0.999372	+	0.0354484i	$0.988714\pi$
$398$	−3.29113	+	15.5776i	−0.164970	+	0.780836i
$399$		0			0
$400$	15.6241	−	20.2017i	0.781203	−	1.01009i
$401$	19.8603	−	23.6686i	0.991778	−	1.18195i	0.00847759	−	0.999964i	$-0.497301\pi$
$401$	19.8603	−	23.6686i	0.991778	−	1.18195i	0.983300	−	0.181991i	$-0.0582541\pi$
$402$		0			0
$403$	−1.16978	+	3.21394i	−0.0582708	+	0.160098i
$404$	16.6075	+	4.09740i	0.826254	+	0.203853i
$405$		0			0
$406$	10.2378	+	13.0707i	0.508095	+	0.648688i
$407$	−8.74925	−	3.18447i	−0.433684	−	0.157848i
$408$		0			0
$409$	−18.8560	−	15.8220i	−0.932368	−	0.782349i	0.0438734	−	0.999037i	$-0.486030\pi$
$409$	−18.8560	−	15.8220i	−0.932368	−	0.782349i	−0.976241	+	0.216688i	$0.930475\pi$
$410$	−13.5261	+	7.21330i	−0.668008	+	0.356240i
$411$		0			0
$412$	30.4465	−	14.9424i	1.49999	−	0.736161i
$413$	−9.62725	+	5.55829i	−0.473726	+	0.273506i
$414$		0			0
$415$	52.5486	+	30.3390i	2.57951	+	1.48928i
$416$	−3.11951	+	1.15716i	−0.152947	+	0.0567342i
$417$		0			0
$418$	−7.12717	+	11.4371i	−0.348601	+	0.559407i
$419$	7.48245	−	2.72339i	0.365542	−	0.133046i	−0.152718	−	0.988270i	$-0.548802\pi$
$419$	7.48245	−	2.72339i	0.365542	−	0.133046i	0.518259	+	0.855224i	$0.326580\pi$
$420$		0			0
$421$	−0.713817	−	4.04826i	−0.0347893	−	0.197300i	0.962460	−	0.271425i	$-0.0874948\pi$
$421$	−0.713817	−	4.04826i	−0.0347893	−	0.197300i	−0.997249	+	0.0741247i	$0.976384\pi$
$422$	−1.09282	−	7.70711i	−0.0531977	−	0.375176i
$423$		0			0
$424$	12.1931	−	16.9130i	0.592147	−	0.821369i
$425$	30.1527	+	35.9346i	1.46262	+	1.74309i
$426$		0			0
$427$	1.45613	+	0.256755i	0.0704672	+	0.0124253i
$428$	−6.03201	+	4.40519i	−0.291568	+	0.212933i
$429$		0			0
$430$	2.69485	+	8.25935i	0.129957	+	0.398301i
$431$	34.6402			1.66856			0.834281	−	0.551340i	$-0.185883\pi$
$431$	34.6402			1.66856			0.834281	+	0.551340i	$0.185883\pi$
$432$		0			0
$433$	−8.55521			−0.411137			−0.205569	−	0.978643i	$-0.565904\pi$
$433$	−8.55521			−0.411137			−0.205569	+	0.978643i	$0.565904\pi$
$434$	6.85104	+	20.9975i	0.328860	+	1.00791i
$435$		0			0
$436$	−17.1303	+	12.5103i	−0.820394	+	0.599137i
$437$	−1.53258	−	0.270235i	−0.0733131	−	0.0129271i
$438$		0			0
$439$	−5.14956	−	6.13700i	−0.245775	−	0.292903i	0.629027	−	0.777383i	$-0.283453\pi$
$439$	−5.14956	−	6.13700i	−0.245775	−	0.292903i	−0.874802	+	0.484480i	$0.839009\pi$
$440$	16.2862	−	22.5906i	0.776412	−	1.07696i
$441$		0			0
$442$	−0.857980	−	6.05090i	−0.0408099	−	0.287812i
$443$	1.37913	+	7.82143i	0.0655244	+	0.371607i	0.999883	+	0.0152741i	$0.00486210\pi$
$443$	1.37913	+	7.82143i	0.0655244	+	0.371607i	−0.934359	+	0.356333i	$0.884027\pi$
$444$		0			0
$445$	−17.6175	+	6.41226i	−0.835151	+	0.303970i
$446$	4.08555	−	6.55615i	0.193456	−	0.310443i
$447$		0			0
$448$	−11.2515	+	18.3050i	−0.531582	+	0.864828i
$449$	−0.748371	−	0.432072i	−0.0353178	−	0.0203907i	0.482237	−	0.876041i	$-0.339824\pi$
$449$	−0.748371	−	0.432072i	−0.0353178	−	0.0203907i	−0.517555	+	0.855650i	$0.673158\pi$
$450$		0			0
$451$	−8.11868	+	4.68732i	−0.382294	+	0.220717i
$452$	−10.4855	+	5.14603i	−0.493194	+	0.242049i
$453$		0			0
$454$	1.85260	−	0.987968i	0.0869470	−	0.0463676i
$455$	−4.08314	−	3.42616i	−0.191420	−	0.160621i
$456$		0			0
$457$	27.5979	+	10.0448i	1.29098	+	0.469877i	0.894048	−	0.447972i	$-0.147853\pi$
$457$	27.5979	+	10.0448i	1.29098	+	0.469877i	0.396930	+	0.917849i	$0.370076\pi$
$458$	−22.7211	−	29.0081i	−1.06169	−	1.35546i
$459$		0			0
$460$	3.12240	+	0.770359i	0.145583	+	0.0359182i
$461$	1.96584	−	5.40111i	0.0915585	−	0.251555i	−0.885458	−	0.464720i	$-0.846155\pi$
$461$	1.96584	−	5.40111i	0.0915585	−	0.251555i	0.977016	+	0.213165i	$0.0683772\pi$
$462$		0			0
$463$	17.6836	−	21.0745i	0.821825	−	0.979413i	−0.178164	−	0.984001i	$-0.557016\pi$
$463$	17.6836	−	21.0745i	0.821825	−	0.979413i	0.999989	+	0.00458769i	$0.00146031\pi$
$464$	13.8308	+	10.6967i	0.642077	+	0.496584i
$465$		0			0
$466$	−1.96255	+	9.28919i	−0.0909136	+	0.430313i
$467$	−8.41790	−	14.5802i	−0.389534	−	0.674692i	0.602853	−	0.797852i	$-0.294031\pi$
$467$	−8.41790	−	14.5802i	−0.389534	−	0.674692i	−0.992387	+	0.123160i	$0.960697\pi$
$468$		0			0
$469$	−13.6046	+	23.5638i	−0.628202	+	1.08808i
$470$	−4.35985	−	3.91594i	−0.201105	−	0.180629i
$471$		0			0
$472$	−8.39122	+	8.16328i	−0.386237	+	0.375745i
$473$	1.81717	+	4.99264i	0.0835537	+	0.229562i
$474$		0			0
$475$	−20.5319	+	3.62033i	−0.942069	+	0.166112i
$476$	−28.4569	−	27.3457i	−1.30432	−	1.25339i
$477$		0			0
$478$	−10.8256	+	26.8894i	−0.495152	+	1.22989i
$479$	−1.69205	+	1.41980i	−0.0773119	+	0.0648724i	−0.680625	−	0.732632i	$-0.738292\pi$
$479$	−1.69205	+	1.41980i	−0.0773119	+	0.0648724i	0.603313	+	0.797505i	$0.293847\pi$
$480$		0			0
$481$	−0.325877	+	1.84814i	−0.0148587	+	0.0842680i
$482$	−0.601385	+	17.8501i	−0.0273923	+	0.813049i
$483$		0			0
$484$	−2.76843	+	4.12620i	−0.125838	+	0.187555i
$485$		−	35.7264i		−	1.62225i
$486$		0			0
$487$			40.4859i			1.83459i	0.398206	+	0.917296i	$0.369633\pi$
$487$			40.4859i			1.83459i	−0.398206	+	0.917296i	$0.630367\pi$
$488$	1.55291	−	0.114342i	0.0702969	−	0.00517604i
$489$		0			0
$490$	−1.01840	−	0.0343110i	−0.0460068	−	0.00155001i
$491$	−2.74760	+	15.5824i	−0.123998	+	0.703225i	0.857901	+	0.513816i	$0.171768\pi$
$491$	−2.74760	+	15.5824i	−0.123998	+	0.703225i	−0.981898	+	0.189409i	$0.939343\pi$
$492$		0			0
$493$	−24.6020	+	20.6435i	−1.10802	+	0.929738i
$494$	2.51966	+	1.01441i	0.113365	+	0.0456405i
$495$		0			0
$496$	12.4226	+	19.6646i	0.557791	+	0.882968i
$497$	−3.26131	+	0.575058i	−0.146290	+	0.0257949i
$498$		0			0
$499$	11.4425	+	31.4380i	0.512236	+	1.40736i	0.878901	+	0.477004i	$0.158277\pi$
$499$	11.4425	+	31.4380i	0.512236	+	1.40736i	−0.366665	+	0.930353i	$0.619501\pi$
$500$	9.29035	−	0.999538i	0.415477	−	0.0447007i
$501$		0			0
$502$	12.0760	−	13.4449i	0.538977	−	0.600075i
$503$	12.0161	−	20.8125i	0.535772	−	0.927984i	−0.463354	−	0.886173i	$-0.653354\pi$
$503$	12.0161	−	20.8125i	0.535772	−	0.927984i	0.999126	−	0.0418106i	$-0.0133126\pi$
$504$		0			0
$505$	14.4290	+	24.9917i	0.642081	+	1.11212i
$506$	1.92428	+	0.406549i	0.0855449	+	0.0180733i
$507$		0			0
$508$	0.994968	−	2.24959i	0.0441446	−	0.0998096i
$509$	15.9558	−	19.0154i	0.707228	−	0.842841i	−0.286096	−	0.958201i	$-0.592358\pi$
$509$	15.9558	−	19.0154i	0.707228	−	0.842841i	0.993324	+	0.115360i	$0.0368022\pi$
$510$		0			0
$511$	−2.16930	+	5.96011i	−0.0959643	+	0.263660i
$512$	−6.75391	+	21.5959i	−0.298484	+	0.954415i
$513$		0			0
$514$	11.0687	−	8.66972i	0.488218	−	0.382405i
$515$	53.7669	+	19.5695i	2.36925	+	0.862337i
$516$		0			0
$517$	−2.74539	−	2.30365i	−0.120742	−	0.101315i
$518$	5.70268	+	10.6935i	0.250561	+	0.469844i
$519$		0			0
$520$	−5.05415	−	2.44206i	−0.221639	−	0.107091i
$521$	13.6964	−	7.90761i	0.600049	−	0.346439i	−0.169012	−	0.985614i	$-0.554058\pi$
$521$	13.6964	−	7.90761i	0.600049	−	0.346439i	0.769061	+	0.639175i	$0.220724\pi$
$522$		0			0
$523$	−27.0410	−	15.6122i	−1.18242	−	0.682672i	−0.225849	−	0.974162i	$-0.572515\pi$
$523$	−27.0410	−	15.6122i	−1.18242	−	0.682672i	−0.956574	+	0.291491i	$0.905849\pi$
$524$	−35.2215	−	2.37598i	−1.53866	−	0.103795i
$525$		0			0
$526$	23.4676	+	14.6242i	1.02324	+	0.637644i
$527$	−40.1470	+	14.6123i	−1.74883	+	0.636523i
$528$		0			0
$529$	−3.95447	−	22.4269i	−0.171933	−	0.975083i
$530$	34.8267	−	4.93821i	1.51278	−	0.214502i
$531$		0			0
$532$	16.8492	−	4.87626i	0.730506	−	0.211413i
$533$	1.21457	+	1.44746i	0.0526087	+	0.0626966i
$534$		0			0
$535$	−12.4097	−	2.18817i	−0.536520	−	0.0946029i
$536$	−7.79657	+	27.5730i	−0.336760	+	1.19097i
$537$		0			0
$538$	40.7765	−	13.3045i	1.75800	−	0.573597i
$539$	−0.623158			−0.0268413
$540$		0			0
$541$	−14.4554			−0.621486			−0.310743	−	0.950494i	$-0.600578\pi$
$541$	−14.4554			−0.621486			−0.310743	+	0.950494i	$0.600578\pi$
$542$	25.7138	−	8.38985i	1.10450	−	0.360375i
$543$		0			0
$544$	−36.1207	−	20.5595i	−1.54866	−	0.881483i
$545$	−35.2425	−	6.21421i	−1.50962	−	0.266187i
$546$		0			0
$547$	23.0006	+	27.4110i	0.983434	+	1.17201i	0.985095	+	0.172012i	$0.0550267\pi$
$547$	23.0006	+	27.4110i	0.983434	+	1.17201i	−0.00166132	+	0.999999i	$0.500529\pi$
$548$	5.77074	+	19.9400i	0.246514	+	0.851792i
$549$		0			0
$550$	26.0877	−	3.69908i	1.11238	−	0.157729i
$551$	−2.47860	−	14.0568i	−0.105592	−	0.598841i
$552$		0			0
$553$	24.6158	−	8.95941i	1.04677	−	0.380993i
$554$	−11.8139	−	7.36196i	−0.501923	−	0.312780i
$555$		0			0
$556$	−2.93768	+	43.5480i	−0.124585	+	1.84685i
$557$	25.5879	+	14.7732i	1.08419	+	0.625960i	0.932025	−	0.362394i	$-0.118041\pi$
$557$	25.5879	+	14.7732i	1.08419	+	0.625960i	0.152170	+	0.988354i	$0.451374\pi$
$558$		0			0
$559$	0.927416	−	0.535444i	0.0392255	−	0.0226469i
$560$	−35.4193	+	7.71069i	−1.49674	+	0.325836i
$561$		0			0
$562$	−15.4242	−	28.9230i	−0.650632	−	1.22004i
$563$	8.84941	+	7.42554i	0.372958	+	0.312949i	0.809930	−	0.586526i	$-0.199505\pi$
$563$	8.84941	+	7.42554i	0.372958	+	0.312949i	−0.436972	+	0.899475i	$0.643949\pi$
$564$		0			0
$565$	−18.5168	−	6.73955i	−0.779006	−	0.283535i
$566$	−19.4218	+	15.2124i	−0.816358	+	0.639425i
$567$		0			0
$568$	−3.18072	+	1.43022i	−0.133460	+	0.0600106i
$569$	−4.36916	+	12.0042i	−0.183165	+	0.503241i	−0.996960	−	0.0779103i	$-0.975175\pi$
$569$	−4.36916	+	12.0042i	−0.183165	+	0.503241i	0.813796	+	0.581151i	$0.197397\pi$
$570$		0			0
$571$	24.8893	−	29.6619i	1.04158	−	1.24131i	0.0717799	−	0.997420i	$-0.477132\pi$
$571$	24.8893	−	29.6619i	1.04158	−	1.24131i	0.969803	−	0.243890i	$-0.0784235\pi$
$572$	−3.13939	−	1.38852i	−0.131265	−	0.0580568i
$573$		0			0
$574$	11.9386	+	2.52231i	0.498309	+	0.105279i
$575$	1.52138	+	2.63511i	0.0634459	+	0.109892i
$576$		0			0
$577$	10.5964	−	18.3535i	0.441134	−	0.764067i	−0.556640	−	0.830754i	$-0.687910\pi$
$577$	10.5964	−	18.3535i	0.441134	−	0.764067i	0.997774	+	0.0666873i	$0.0212430\pi$
$578$	34.9474	−	38.9091i	1.45362	−	1.61840i
$579$		0			0
$580$	3.15539	+	29.3282i	0.131020	+	1.21779i
$581$	−16.5195	−	45.3870i	−0.685344	−	1.88297i
$582$		0			0
$583$	21.1845	−	3.73540i	0.877372	−	0.154704i
$584$	−0.673704	+	6.64536i	−0.0278781	+	0.274987i
$585$		0			0
$586$	24.9587	+	10.0483i	1.03104	+	0.415093i
$587$	11.6298	−	9.75855i	0.480013	−	0.402778i	−0.370418	−	0.928865i	$-0.620786\pi$
$587$	11.6298	−	9.75855i	0.480013	−	0.402778i	0.850431	+	0.526087i	$0.176341\pi$
$588$		0			0
$589$	3.29729	−	18.6999i	0.135862	−	0.770514i
$590$	−19.7390	−	0.665025i	−0.812643	−	0.0273787i
$591$		0			0
$592$	8.58633	+	9.44236i	0.352896	+	0.388079i
$593$		−	25.8789i		−	1.06272i	−0.847147	−	0.531359i	$-0.821681\pi$
$593$		−	25.8789i		−	1.06272i	0.847147	−	0.531359i	$-0.178319\pi$
$594$		0			0
$595$		−	66.5819i		−	2.72959i
$596$	6.20209	+	4.16123i	0.254048	+	0.170451i
$597$		0			0
$598$	0.0133480	−	0.396191i	0.000545841	−	0.0162015i
$599$	0.0271904	−	0.154204i	0.00111097	−	0.00630062i	−0.984247	−	0.176798i	$-0.943426\pi$
$599$	0.0271904	−	0.154204i	0.00111097	−	0.00630062i	0.985358	+	0.170497i	$0.0545373\pi$
$600$		0			0
$601$	3.42031	−	2.86998i	0.139517	−	0.117069i	−0.570358	−	0.821396i	$-0.693196\pi$
$601$	3.42031	−	2.86998i	0.139517	−	0.117069i	0.709875	+	0.704327i	$0.248751\pi$
$602$	2.58274	−	6.41517i	0.105264	−	0.261463i
$603$		0			0
$604$	−20.2296	+	21.0516i	−0.823131	+	0.856579i
$605$	−8.25544	+	1.45566i	−0.335631	+	0.0591808i
$606$		0			0
$607$	−12.8586	−	35.3287i	−0.521914	−	1.43395i	−0.868387	−	0.495886i	$-0.834843\pi$
$607$	−12.8586	−	35.3287i	−0.521914	−	1.43395i	0.346474	−	0.938060i	$-0.387379\pi$
$608$	15.9403	−	9.33412i	0.646463	−	0.378549i
$609$		0			0
$610$	1.95435	+	1.75537i	0.0791295	+	0.0710727i
$611$	−0.361176	+	0.625575i	−0.0146116	+	0.0253081i
$612$		0			0
$613$	−9.84356	−	17.0495i	−0.397577	−	0.688624i	0.595849	−	0.803096i	$-0.296816\pi$
$613$	−9.84356	−	17.0495i	−0.397577	−	0.688624i	−0.993426	+	0.114472i	$0.963482\pi$
$614$	−4.83077	+	22.8651i	−0.194954	+	0.922759i
$615$		0			0
$616$	−21.4896	+	5.44215i	−0.865840	+	0.219270i
$617$	−14.8351	+	17.6798i	−0.597241	+	0.711764i	−0.976980	−	0.213330i	$-0.931569\pi$
$617$	−14.8351	+	17.6798i	−0.597241	+	0.711764i	0.379740	+	0.925093i	$0.376014\pi$
$618$		0			0
$619$	0.717110	−	1.97024i	0.0288231	−	0.0791908i	−0.924447	−	0.381312i	$-0.875472\pi$
$619$	0.717110	−	1.97024i	0.0288231	−	0.0791908i	0.953270	+	0.302121i	$0.0976947\pi$
$620$	−9.39959	+	38.0982i	−0.377497	+	1.53006i
$621$		0			0
$622$	1.81460	+	2.31671i	0.0727588	+	0.0928916i
$623$	14.0236	+	5.10417i	0.561844	+	0.204494i
$624$		0			0
$625$	−12.3789	−	10.3871i	−0.495155	−	0.415484i
$626$	−0.189925	+	0.101284i	−0.00759092	+	0.00404813i
$627$		0			0
$628$	−14.6906	−	29.9334i	−0.586220	−	1.19447i
$629$	−20.3016	+	11.7211i	−0.809479	+	0.467353i
$630$		0			0
$631$	4.15935	+	2.40140i	0.165581	+	0.0955982i	0.580500	−	0.814260i	$-0.302857\pi$
$631$	4.15935	+	2.40140i	0.165581	+	0.0955982i	−0.414920	+	0.909858i	$0.636190\pi$
$632$	22.8133	−	15.5104i	0.907465	−	0.616971i
$633$		0			0
$634$	5.02031	−	8.05618i	0.199382	−	0.319952i
$635$	3.89957	−	1.41933i	0.154750	−	0.0563242i
$636$		0			0
$637$	0.0218106	+	0.123694i	0.000864167	+	0.00490094i
$638$	2.53251	+	17.8605i	0.100263	+	0.707104i
$639$		0			0
$640$	−34.1652	+	17.0287i	−1.35050	+	0.673118i
$641$	−18.2093	−	21.7010i	−0.719223	−	0.857136i	0.275332	−	0.961349i	$-0.411212\pi$
$641$	−18.2093	−	21.7010i	−0.719223	−	0.857136i	−0.994555	+	0.104213i	$0.966768\pi$
$642$		0			0
$643$	3.69392	+	0.651338i	0.145674	+	0.0256863i	0.246010	−	0.969267i	$-0.420881\pi$
$643$	3.69392	+	0.651338i	0.145674	+	0.0256863i	−0.100336	+	0.994954i	$0.531992\pi$
$644$	−1.50980	−	2.06736i	−0.0594943	−	0.0814652i
$645$		0			0
$646$	10.5244	+	32.2560i	0.414078	+	1.26909i
$647$	44.7799			1.76048			0.880239	−	0.474530i	$-0.157382\pi$
$647$	44.7799			1.76048			0.880239	+	0.474530i	$0.157382\pi$
$648$		0			0
$649$	−12.0782			−0.474112
$650$	−1.64732	−	5.04883i	−0.0646133	−	0.198031i
$651$		0			0
$652$	3.28214	+	4.49422i	0.128539	+	0.176007i
$653$	33.2582	+	5.86432i	1.30149	+	0.229489i	0.781083	−	0.624427i	$-0.214667\pi$
$653$	33.2582	+	5.86432i	1.30149	+	0.229489i	0.520411	+	0.853916i	$0.325779\pi$
$654$		0			0
$655$	−38.2817	−	45.6223i	−1.49579	−	1.78261i
$656$	12.8400	−	0.511561i	0.501316	−	0.0199731i
$657$		0			0
$658$	0.654888	+	4.61860i	0.0255302	+	0.180052i
$659$	−5.48543	−	31.1094i	−0.213682	−	1.21185i	−0.883179	−	0.469036i	$-0.844601\pi$
$659$	−5.48543	−	31.1094i	−0.213682	−	1.21185i	0.669497	−	0.742815i	$-0.266510\pi$
$660$		0			0
$661$	4.54548	−	1.65442i	0.176799	−	0.0643495i	−0.252104	−	0.967700i	$-0.581123\pi$
$661$	4.54548	−	1.65442i	0.176799	−	0.0643495i	0.428903	+	0.903351i	$0.358900\pi$
$662$	−9.88016	+	15.8549i	−0.384003	+	0.616217i
$663$		0			0
$664$	−28.5983	−	42.0636i	−1.10983	−	1.63238i
$665$	25.6275	+	14.7960i	0.993791	+	0.573765i
$666$		0			0
$667$	−1.80408	+	1.04159i	−0.0698542	+	0.0403304i
$668$	12.4894	+	25.4481i	0.483228	+	0.984616i
$669$		0			0
$670$	−42.6547	+	22.7472i	−1.64789	+	0.878799i
$671$	1.23065	+	1.03264i	0.0475088	+	0.0398646i
$672$		0			0
$673$	−20.9411	−	7.62193i	−0.807220	−	0.293804i	−0.0947448	−	0.995502i	$-0.530204\pi$
$673$	−20.9411	−	7.62193i	−0.807220	−	0.293804i	−0.712475	+	0.701698i	$0.752426\pi$
$674$	−16.8719	−	21.5404i	−0.649880	−	0.829705i
$675$		0			0
$676$	6.06223	−	24.5713i	0.233163	−	0.945050i
$677$	0.302359	−	0.830725i	0.0116206	−	0.0319274i	−0.933747	−	0.357934i	$-0.883481\pi$
$677$	0.302359	−	0.830725i	0.0116206	−	0.0319274i	0.945367	+	0.326007i	$0.105703\pi$
$678$		0			0
$679$	−18.2798	+	21.7850i	−0.701514	+	0.836032i
$680$	−17.2136	−	67.9718i	−0.660111	−	2.60660i
$681$		0			0
$682$	−4.96054	+	23.4793i	−0.189949	+	0.899069i
$683$	−13.1484	−	22.7737i	−0.503110	−	0.871412i	−0.999994	−	0.00359510i	$-0.998856\pi$
$683$	−13.1484	−	22.7737i	−0.503110	−	0.871412i	0.496883	−	0.867817i	$-0.334478\pi$
$684$		0			0
$685$	−17.5101	+	30.3285i	−0.669028	+	1.15879i
$686$	−19.1772	−	17.2246i	−0.732189	−	0.657640i
$687$		0			0
$688$	0.978120	−	7.21681i	0.0372905	−	0.275138i
$689$	−1.48292	−	4.07429i	−0.0564947	−	0.155218i
$690$		0			0
$691$	26.8477	−	4.73397i	1.02133	−	0.180089i	0.362189	−	0.932105i	$-0.382029\pi$
$691$	26.8477	−	4.73397i	1.02133	−	0.180089i	0.659145	+	0.752016i	$0.270918\pi$
$692$	1.70960	−	1.77907i	0.0649893	−	0.0676302i
$693$		0			0
$694$	−6.75393	+	16.7759i	−0.256376	+	0.636803i
$695$	−56.4077	+	47.3317i	−2.13967	+	1.79539i
$696$		0			0
$697$	−4.09864	+	23.2446i	−0.155247	+	0.880450i
$698$	0.576864	−	17.1223i	0.0218346	−	0.648087i
$699$		0			0
$700$	−28.4796	−	19.1081i	−1.07643	−	0.722218i
$701$		−	0.940626i		−	0.0355270i	−0.999842	−	0.0177635i	$-0.994345\pi$
$701$		−	0.940626i		−	0.0355270i	0.999842	−	0.0177635i	$-0.00565459\pi$
$702$		0			0
$703$		−	10.4188i		−	0.392954i
$704$	−20.5312	+	11.1115i	−0.773799	+	0.418781i
$705$		0			0
$706$	28.2250	+	0.950925i	1.06226	+	0.0357885i
$707$	3.98887	−	22.6220i	0.150017	−	0.850789i
$708$		0			0
$709$	27.4140	−	23.0031i	1.02956	−	0.863899i	0.0387572	−	0.999249i	$-0.487660\pi$
$709$	27.4140	−	23.0031i	1.02956	−	0.863899i	0.990798	+	0.135349i	$0.0432157\pi$
$710$	−5.45786	−	2.19733i	−0.204830	−	0.0824641i
$711$		0			0
$712$	15.6359	+	1.58517i	0.585981	+	0.0594066i
$713$	−2.72915	+	0.481223i	−0.102208	+	0.0180219i
$714$		0			0
$715$	−1.98072	−	5.44199i	−0.0740749	−	0.203519i
$716$	3.67989	+	34.2032i	0.137524	+	1.27823i
$717$		0			0
$718$	19.8940	−	22.1491i	0.742436	−	0.826598i
$719$	−16.5947	+	28.7429i	−0.618879	+	1.07193i	0.370812	+	0.928708i	$0.379079\pi$
$719$	−16.5947	+	28.7429i	−0.618879	+	1.07193i	−0.989691	+	0.143221i	$0.954254\pi$
$720$		0			0
$721$	−22.7726	−	39.4434i	−0.848097	−	1.46895i
$722$	11.5356	+	2.43716i	0.429310	+	0.0907016i
$723$		0			0
$724$	39.5726	+	17.5025i	1.47070	+	0.650474i
$725$	−17.9391	+	21.3789i	−0.666240	+	0.793994i
$726$		0			0
$727$	11.0347	−	30.3175i	0.409253	−	1.12441i	−0.548331	−	0.836261i	$-0.684737\pi$
$727$	11.0347	−	30.3175i	0.409253	−	1.12441i	0.957585	−	0.288153i	$-0.0930410\pi$
$728$	1.83238	+	4.07511i	0.0679125	+	0.151034i
$729$		0			0
$730$	−8.87122	+	6.94853i	−0.328339	+	0.257177i
$731$	12.5703	+	4.57522i	0.464929	+	0.169220i
$732$		0			0
$733$	33.6290	+	28.2180i	1.24211	+	1.04226i	0.997356	+	0.0726730i	$0.0231530\pi$
$733$	33.6290	+	28.2180i	1.24211	+	1.04226i	0.244758	+	0.969584i	$0.421291\pi$
$734$	18.5252	+	34.7378i	0.683777	+	1.28219i
$735$		0			0
$736$	−2.07579	−	1.72018i	−0.0765147	−	0.0634067i
$737$	−25.6023	+	14.7815i	−0.943071	+	0.544482i
$738$		0			0
$739$	14.8213	+	8.55709i	0.545211	+	0.314778i	0.747188	−	0.664613i	$-0.231403\pi$
$739$	14.8213	+	8.55709i	0.545211	+	0.314778i	−0.201977	+	0.979390i	$0.564737\pi$
$740$	−1.44917	+	21.4824i	−0.0532724	+	0.789708i
$741$		0			0
$742$	−23.7631	−	14.8083i	−0.872371	−	0.543629i
$743$	41.1116	−	14.9634i	1.50824	−	0.548954i	0.550061	−	0.835124i	$-0.314604\pi$
$743$	41.1116	−	14.9634i	1.50824	−	0.548954i	0.958179	+	0.286170i	$0.0923822\pi$
$744$		0			0
$745$	2.18800	+	12.4087i	0.0801620	+	0.454621i
$746$	−8.35873	+	1.18522i	−0.306035	+	0.0433938i
$747$		0			0
$748$	−11.9207	−	41.1901i	−0.435863	−	1.50606i
$749$	6.44753	+	7.68387i	0.235588	+	0.280762i
$750$		0			0
$751$	5.87467	+	1.03586i	0.214370	+	0.0377992i	0.279801	−	0.960058i	$-0.409731\pi$
$751$	5.87467	+	1.03586i	0.214370	+	0.0377992i	−0.0654317	+	0.997857i	$0.520842\pi$
$752$	1.86262	+	4.54570i	0.0679226	+	0.165765i
$753$		0			0
$754$	3.45659	−	1.12781i	0.125882	−	0.0410725i
$755$	−49.2554			−1.79259
$756$		0			0
$757$	33.2521			1.20857			0.604284	−	0.796769i	$-0.293459\pi$
$757$	33.2521			1.20857			0.604284	+	0.796769i	$0.293459\pi$
$758$	19.1443	−	6.24637i	0.695353	−	0.226879i
$759$		0			0
$760$	29.9877	+	8.47936i	1.08777	+	0.307579i
$761$	4.94688	+	0.872268i	0.179324	+	0.0316197i	0.262589	−	0.964908i	$-0.415424\pi$
$761$	4.94688	+	0.872268i	0.179324	+	0.0316197i	−0.0832649	+	0.996527i	$0.526535\pi$
$762$		0			0
$763$	18.3104	+	21.8215i	0.662880	+	0.789990i
$764$	−9.16765	+	2.65317i	−0.331674	+	0.0959885i
$765$		0			0
$766$	−22.4038	+	3.17672i	−0.809482	+	0.114780i
$767$	0.422740	+	2.39748i	0.0152642	+	0.0865678i
$768$		0			0
$769$	−48.6273	+	17.6989i	−1.75355	+	0.638239i	−0.999820	−	0.0189509i	$-0.993967\pi$
$769$	−48.6273	+	17.6989i	−1.75355	+	0.638239i	−0.753725	+	0.657189i	$0.771745\pi$
$770$	−31.7402	−	19.7793i	−1.14384	−	0.712796i
$771$		0			0
$772$	−18.0789	−	1.21957i	−0.650674	−	0.0438934i
$773$	−8.36174	−	4.82765i	−0.300751	−	0.173639i	0.342029	−	0.939689i	$-0.388886\pi$
$773$	−8.36174	−	4.82765i	−0.300751	−	0.173639i	−0.642780	+	0.766051i	$0.722219\pi$
$774$		0			0
$775$	−32.1524	+	18.5632i	−1.15495	+	0.666811i
$776$	−13.0293	+	26.9657i	−0.467723	+	0.968012i
$777$		0			0
$778$	11.8453	+	22.2118i	0.424673	+	0.796333i
$779$	−8.03605	−	6.74305i	−0.287921	−	0.241595i
$780$		0			0
$781$	−3.38111	−	1.23062i	−0.120986	−	0.0440352i
$782$	3.89836	−	3.05345i	0.139405	−	0.109191i
$783$		0			0
$784$	0.756161	+	0.397305i	0.0270058	+	0.0141894i
$785$	19.2397	−	52.8607i	0.686695	−	1.88668i
$786$		0			0
$787$	−25.8465	+	30.8027i	−0.921329	+	1.09800i	0.0735865	+	0.997289i	$0.476555\pi$
$787$	−25.8465	+	30.8027i	−0.921329	+	1.09800i	−0.994916	+	0.100709i	$0.967889\pi$
$788$	1.68369	−	3.80676i	0.0599788	−	0.135610i
$789$		0			0
$790$	45.5350	+	9.62032i	1.62006	+	0.342276i
$791$	7.84266	+	13.5839i	0.278853	+	0.482987i
$792$		0			0
$793$	0.161901	−	0.280422i	0.00574929	−	0.00995806i
$794$	−17.6611	+	19.6632i	−0.626770	+	0.697820i
$795$		0			0
$796$	22.3872	−	2.40861i	0.793494	−	0.0853711i
$797$	1.57213	+	4.31940i	0.0556878	+	0.153001i	0.964417	−	0.264384i	$-0.0851687\pi$
$797$	1.57213	+	4.31940i	0.0556878	+	0.153001i	−0.908730	+	0.417385i	$0.862947\pi$
$798$		0			0
$799$	−8.88621	+	1.56688i	−0.314371	+	0.0554322i
$800$	−34.0142	−	12.1441i	−1.20258	−	0.429358i
$801$		0			0
$802$	−40.5336	−	16.3187i	−1.43129	−	0.576235i
$803$	−5.27903	+	4.42963i	−0.186293	+	0.156318i
$804$		0			0
$805$	0.749954	−	4.25320i	0.0264324	−	0.149906i
$806$	4.83415	+	0.162867i	0.170276	+	0.00573674i
$807$		0			0
$808$	−1.77639	−	24.1255i	−0.0624931	−	0.848732i
$809$			17.3051i			0.608415i	0.952606	+	0.304208i	$0.0983917\pi$
$809$			17.3051i			0.608415i	−0.952606	+	0.304208i	$0.901608\pi$
$810$		0			0
$811$		−	4.64157i		−	0.162987i	−0.996674	−	0.0814937i	$-0.974031\pi$
$811$		−	4.64157i		−	0.162987i	0.996674	−	0.0814937i	$-0.0259691\pi$
$812$	13.0820	−	19.4981i	0.459089	−	0.684248i
$813$		0			0
$814$	−0.443370	+	13.1599i	−0.0155401	+	0.461255i
$815$	−1.63032	+	9.24603i	−0.0571078	+	0.323874i
$816$		0			0
$817$	−4.55442	+	3.82161i	−0.159339	+	0.133701i
$818$	−13.0006	+	32.2917i	−0.454554	+	1.12905i
$819$		0			0
$820$	15.6315	+	15.0211i	0.545875	+	0.524559i
$821$	34.5874	−	6.09870i	1.20711	−	0.212846i	0.466340	−	0.884605i	$-0.345572\pi$
$821$	34.5874	−	6.09870i	1.20711	−	0.212846i	0.740769	+	0.671759i	$0.234461\pi$
$822$		0			0
$823$	−0.0707205	−	0.194303i	−0.00246516	−	0.00677298i	0.938454	−	0.345404i	$-0.112258\pi$
$823$	−0.0707205	−	0.194303i	−0.00246516	−	0.00677298i	−0.940919	+	0.338631i	$0.890036\pi$
$824$	−33.4454	−	34.3793i	−1.16513	−	1.19766i
$825$		0			0
$826$	11.6961	+	10.5052i	0.406958	+	0.365523i
$827$	−6.40289	+	11.0901i	−0.222650	+	0.385642i	−0.955612	−	0.294628i	$-0.904804\pi$
$827$	−6.40289	+	11.0901i	−0.222650	+	0.385642i	0.732962	+	0.680270i	$0.238137\pi$
$828$		0			0
$829$	14.0149	+	24.2745i	0.486757	+	0.843088i	0.999884	−	0.0152250i	$-0.00484646\pi$
$829$	14.0149	+	24.2745i	0.486757	+	0.843088i	−0.513127	+	0.858313i	$0.671513\pi$
$830$	17.7381	−	83.9582i	0.615699	−	2.91423i
$831$		0			0
$832$	2.92418	+	3.68645i	0.101378	+	0.127805i
$833$	−1.00851	+	1.20190i	−0.0349429	+	0.0416433i
$834$		0			0
$835$	−16.3568	+	44.9400i	−0.566051	+	1.55521i
$836$	18.5032	+	4.56510i	0.639945	+	0.157887i
$837$		0			0
$838$	−6.94380	−	8.86519i	−0.239869	−	0.306243i
$839$	−31.3898	−	11.4250i	−1.08370	−	0.394434i	−0.262415	−	0.964955i	$-0.584519\pi$
$839$	−31.3898	−	11.4250i	−1.08370	−	0.394434i	−0.821283	+	0.570521i	$0.806741\pi$
$840$		0			0
$841$	7.57857	+	6.35918i	0.261330	+	0.219282i
$842$	−5.12959	+	2.73554i	−0.176777	+	0.0942729i
$843$		0			0
$844$	−9.88251	+	4.85011i	−0.340170	+	0.166948i
$845$	36.9760	−	21.3481i	1.27201	−	0.734397i
$846$		0			0
$847$	5.77875	+	3.33636i	0.198560	+	0.114639i
$848$	−28.0876	−	8.97386i	−0.964531	−	0.308164i
$849$		0			0
$850$	35.0856	−	56.3025i	1.20343	−	1.93116i
$851$	−1.42888	+	0.520068i	−0.0489812	+	0.0178277i
$852$		0			0
$853$	7.02953	+	39.8664i	0.240686	+	1.36500i	0.830301	+	0.557315i	$0.188169\pi$
$853$	7.02953	+	39.8664i	0.240686	+	1.36500i	−0.589615	+	0.807685i	$0.700720\pi$
$854$	−0.293561	−	2.07034i	−0.0100455	−	0.0708456i
$855$		0			0
$856$	8.56865	+	6.17737i	0.292870	+	0.211138i
$857$	−9.81314	−	11.6948i	−0.335210	−	0.399488i	0.571940	−	0.820296i	$-0.306191\pi$
$857$	−9.81314	−	11.6948i	−0.335210	−	0.399488i	−0.907150	+	0.420808i	$0.861747\pi$
$858$		0			0
$859$	24.9446	+	4.39840i	0.851098	+	0.150071i	0.582148	−	0.813083i	$-0.302212\pi$
$859$	24.9446	+	4.39840i	0.851098	+	0.150071i	0.268950	+	0.963154i	$0.413323\pi$
$860$	9.92221	−	7.24622i	0.338345	−	0.247094i
$861$		0			0
$862$	−15.1956	−	46.5724i	−0.517563	−	1.58626i
$863$	−25.0571			−0.852954			−0.426477	−	0.904498i	$-0.640245\pi$
$863$	−25.0571			−0.852954			−0.426477	+	0.904498i	$0.640245\pi$
$864$		0			0
$865$	4.16257			0.141532
$866$	3.75290	+	11.5021i	0.127529	+	0.390858i
$867$		0			0
$868$	25.2250	−	18.4219i	0.856192	−	0.625279i
$869$	28.0292	+	4.94231i	0.950827	+	0.167656i
$870$		0			0
$871$	3.83014	+	4.56458i	0.129779	+	0.154665i
$872$	24.3342	+	17.5432i	0.824059	+	0.594086i
$873$		0			0
$874$	0.308973	+	2.17903i	0.0104512	+	0.0737068i
$875$	−2.17894	−	12.3574i	−0.0736617	−	0.417756i
$876$		0			0
$877$	−28.3388	+	10.3145i	−0.956932	+	0.348295i	−0.772830	−	0.634613i	$-0.781160\pi$
$877$	−28.3388	+	10.3145i	−0.956932	+	0.348295i	−0.184101	+	0.982907i	$0.558937\pi$
$878$	−5.99200	+	9.61547i	−0.202220	+	0.324507i
$879$		0			0
$880$	−37.5163	−	11.9863i	−1.26468	−	0.404059i
$881$	−33.7727	−	19.4987i	−1.13783	−	0.656927i	−0.191938	−	0.981407i	$-0.561477\pi$
$881$	−33.7727	−	19.4987i	−1.13783	−	0.656927i	−0.945892	+	0.324480i	$0.894811\pi$
$882$		0			0
$883$	7.27427	−	4.19980i	0.244799	−	0.141335i	−0.372582	−	0.927999i	$-0.621527\pi$
$883$	7.27427	−	4.19980i	0.244799	−	0.141335i	0.617380	+	0.786665i	$0.288194\pi$
$884$	−7.75882	+	3.80785i	−0.260957	+	0.128072i
$885$		0			0
$886$	9.91061	−	5.28519i	0.332954	−	0.177560i
$887$	18.2466	+	15.3107i	0.612661	+	0.514083i	0.895487	−	0.445088i	$-0.146828\pi$
$887$	18.2466	+	15.3107i	0.612661	+	0.514083i	−0.282826	+	0.959171i	$0.591272\pi$
$888$		0			0
$889$	−3.10406	−	1.12979i	−0.104107	−	0.0378918i
$890$	16.3493	+	20.8732i	0.548029	+	0.699671i
$891$		0			0
$892$	−10.6067	−	2.61688i	−0.355138	−	0.0876195i
$893$	1.37163	−	3.76851i	0.0458997	−	0.126108i
$894$		0			0
$895$	−37.3047	+	44.4580i	−1.24696	+	1.48607i
$896$	29.5459	+	7.09734i	0.987060	+	0.237105i
$897$		0			0
$898$	−0.252617	+	1.19569i	−0.00842994	+	0.0399007i
$899$	−12.7090	−	22.0126i	−0.423868	−	0.734162i
$900$		0			0
$901$	27.0802	−	46.9043i	0.902173	−	1.56261i
$902$	9.86331	+	8.85905i	0.328412	+	0.294974i
$903$		0			0
$904$	11.5183	+	11.8399i	0.383091	+	0.393788i
$905$	24.9673	+	68.5972i	0.829942	+	2.28025i
$906$		0			0
$907$	13.3699	−	2.35747i	0.443940	−	0.0782785i	0.0527900	−	0.998606i	$-0.483189\pi$
$907$	13.3699	−	2.35747i	0.443940	−	0.0782785i	0.391150	+	0.920327i	$0.372077\pi$
$908$	−2.14096	−	2.05736i	−0.0710503	−	0.0682759i
$909$		0			0
$910$	−2.81519	+	6.99256i	−0.0933226	+	0.231801i
$911$	2.94930	−	2.47476i	0.0977147	−	0.0819924i	−0.592622	−	0.805481i	$-0.701907\pi$
$911$	2.94930	−	2.47476i	0.0977147	−	0.0819924i	0.690336	+	0.723489i	$0.257463\pi$
$912$		0			0
$913$	9.11271	−	51.6808i	0.301587	−	1.71038i
$914$	1.39853	−	41.5107i	0.0462593	−	1.37305i
$915$		0			0
$916$	−29.0332	+	43.2725i	−0.959285	+	1.42976i
$917$			47.4065i			1.56550i
$918$		0			0
$919$		−	7.14983i		−	0.235851i	−0.993022	−	0.117926i	$-0.962376\pi$
$919$		−	7.14983i		−	0.235851i	0.993022	−	0.117926i	$-0.0376244\pi$
$920$	−0.333981	−	4.53587i	−0.0110110	−	0.149543i
$921$		0			0
$922$	−8.12393	−	0.273703i	−0.267547	−	0.00901391i
$923$	−0.125934	+	0.714207i	−0.00414516	+	0.0235084i
$924$		0			0
$925$	−15.6052	+	13.0943i	−0.513096	+	0.430539i
$926$	−36.0910	−	14.5301i	−1.18602	−	0.477490i
$927$		0			0
$928$	8.31423	−	23.2872i	0.272928	−	0.764440i
$929$	−24.6142	+	4.34015i	−0.807566	+	0.142396i	−0.562164	−	0.827026i	$-0.690031\pi$
$929$	−24.6142	+	4.34015i	−0.807566	+	0.142396i	−0.245402	+	0.969421i	$0.578920\pi$
$930$		0			0
$931$	−0.238498	−	0.655267i	−0.00781644	−	0.0214755i
$932$	13.3498	−	1.43630i	0.437289	−	0.0470474i
$933$		0			0
$934$	−15.9099	+	17.7134i	−0.520586	+	0.579600i
$935$	36.1708	−	62.6497i	1.18291	−	2.04886i
$936$		0			0
$937$	−1.71158	−	2.96455i	−0.0559150	−	0.0968475i	0.836713	−	0.547642i	$-0.184474\pi$
$937$	−1.71158	−	2.96455i	−0.0559150	−	0.0968475i	−0.892628	+	0.450794i	$0.851141\pi$
$938$	37.6485	+	7.95411i	1.22927	+	0.259711i
$939$		0			0
$940$	−3.35229	+	7.57943i	−0.109340	+	0.247214i
$941$	−23.4217	+	27.9129i	−0.763525	+	0.909934i	−0.998065	−	0.0621723i	$-0.980197\pi$
$941$	−23.4217	+	27.9129i	−0.763525	+	0.909934i	0.234540	+	0.972106i	$0.424642\pi$
$942$		0			0
$943$	−0.523637	+	1.43868i	−0.0170520	+	0.0468499i
$944$	14.6562	+	7.70068i	0.477017	+	0.250636i
$945$		0			0
$946$	5.91527	−	4.63323i	0.192322	−	0.150639i
$947$	−6.56612	−	2.38987i	−0.213370	−	0.0776605i	0.233124	−	0.972447i	$-0.425105\pi$
$947$	−6.56612	−	2.38987i	−0.213370	−	0.0776605i	−0.446494	+	0.894787i	$0.647328\pi$
$948$		0			0
$949$	1.06403	+	0.892826i	0.0345398	+	0.0289824i
$950$	13.8741	+	26.0162i	0.450135	+	0.844077i
$951$		0			0
$952$	−24.2821	+	50.2549i	−0.786987	+	1.62877i
$953$	−6.10328	+	3.52373i	−0.197705	+	0.114145i	−0.595584	−	0.803293i	$-0.703079\pi$
$953$	−6.10328	+	3.52373i	−0.197705	+	0.114145i	0.397880	+	0.917438i	$0.369746\pi$
$954$		0			0
$955$	−13.9439	−	8.05052i	−0.451214	−	0.260509i
$956$	40.9005	+	2.75908i	1.32282	+	0.0892351i
$957$		0			0
$958$	2.65112	+	1.65208i	0.0856536	+	0.0533761i
$959$	26.1951	−	9.53424i	0.845884	−	0.307877i
$960$		0			0
$961$	−0.488585	−	2.77090i	−0.0157608	−	0.0893840i
$962$	2.62770	−	0.372592i	0.0847206	−	0.0120128i
$963$		0			0
$964$	24.2625	−	7.02172i	0.781443	−	0.226154i
$965$	−19.6497	−	23.4176i	−0.632545	−	0.753838i
$966$		0			0
$967$	26.0009	+	4.58465i	0.836131	+	0.147433i	0.575290	−	0.817949i	$-0.304889\pi$
$967$	26.0009	+	4.58465i	0.836131	+	0.147433i	0.260841	+	0.965382i	$0.416000\pi$
$968$	6.76194	+	1.91201i	0.217337	+	0.0614544i
$969$		0			0
$970$	−48.0327	+	15.6720i	−1.54224	+	0.503199i
$971$	34.6797			1.11292			0.556462	−	0.830873i	$-0.312159\pi$
$971$	34.6797			1.11292			0.556462	+	0.830873i	$0.312159\pi$
$972$		0			0
$973$	58.6137			1.87907
$974$	54.4317	−	17.7599i	1.74410	−	0.569063i
$975$		0			0
$976$	−0.834940	−	2.03766i	−0.0267258	−	0.0652240i
$977$	−44.4064	−	7.83005i	−1.42069	−	0.250505i	−0.590071	−	0.807351i	$-0.700900\pi$
$977$	−44.4064	−	7.83005i	−1.42069	−	0.250505i	−0.830616	+	0.556846i	$0.812011\pi$
$978$		0			0
$979$	10.4225	+	12.4211i	0.333106	+	0.396980i
$980$	0.400612	+	1.38425i	0.0127971	+	0.0442184i
$981$		0			0
$982$	22.1552	−	3.14147i	0.707002	−	0.100248i
$983$	6.89149	+	39.0836i	0.219804	+	1.24657i	0.872372	+	0.488843i	$0.162581\pi$
$983$	6.89149	+	39.0836i	0.219804	+	1.24657i	−0.652568	+	0.757731i	$0.726308\pi$
$984$		0			0
$985$	6.59884	−	2.40178i	0.210257	−	0.0765272i
$986$	38.5465	+	24.0207i	1.22757	+	0.764976i
$987$		0			0
$988$	0.258539	−	3.83257i	0.00822522	−	0.121930i
$989$	0.751448	+	0.433849i	0.0238947	+	0.0137956i
$990$		0			0
$991$	16.9550	−	9.78895i	0.538592	−	0.310956i	−0.205916	−	0.978570i	$-0.566017\pi$
$991$	16.9550	−	9.78895i	0.538592	−	0.310956i	0.744508	+	0.667613i	$0.232684\pi$
$992$	20.9889	−	25.3279i	0.666398	−	0.804162i
$993$		0			0
$994$	2.20378	+	4.13244i	0.0698995	+	0.131073i
$995$	29.0993	+	24.4172i	0.922511	+	0.774078i
$996$		0			0
$997$	35.2892	+	12.8442i	1.11762	+	0.406780i	0.833783	−	0.552092i	$-0.186170\pi$
$997$	35.2892	+	12.8442i	1.11762	+	0.406780i	0.283837	+	0.958873i	$0.408393\pi$
$998$	37.2476	−	29.1748i	1.17905	−	0.923512i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.179.7		96
3.2	odd	2		108.2.l.a.23.10	yes	96
4.3	odd	2	inner	324.2.l.a.179.13		96
9.2	odd	6		972.2.l.c.215.12		96
9.4	even	3		972.2.l.a.863.15		96
9.5	odd	6		972.2.l.d.863.2		96
9.7	even	3		972.2.l.b.215.5		96
12.11	even	2		108.2.l.a.23.4	✓	96
27.2	odd	18		972.2.l.a.107.9		96
27.7	even	9		108.2.l.a.47.4	yes	96
27.11	odd	18		972.2.l.b.755.3		96
27.16	even	9		972.2.l.c.755.14		96
27.20	odd	18	inner	324.2.l.a.143.13		96
27.25	even	9		972.2.l.d.107.8		96
36.7	odd	6		972.2.l.b.215.3		96
36.11	even	6		972.2.l.c.215.14		96
36.23	even	6		972.2.l.d.863.8		96
36.31	odd	6		972.2.l.a.863.9		96
108.7	odd	18		108.2.l.a.47.10	yes	96
108.11	even	18		972.2.l.b.755.5		96
108.43	odd	18		972.2.l.c.755.12		96
108.47	even	18	inner	324.2.l.a.143.7		96
108.79	odd	18		972.2.l.d.107.2		96
108.83	even	18		972.2.l.a.107.15		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.4	✓	96	12.11	even	2
108.2.l.a.23.10	yes	96	3.2	odd	2
108.2.l.a.47.4	yes	96	27.7	even	9
108.2.l.a.47.10	yes	96	108.7	odd	18
324.2.l.a.143.7		96	108.47	even	18	inner
324.2.l.a.143.13		96	27.20	odd	18	inner
324.2.l.a.179.7		96	1.1	even	1	trivial
324.2.l.a.179.13		96	4.3	odd	2	inner
972.2.l.a.107.9		96	27.2	odd	18
972.2.l.a.107.15		96	108.83	even	18
972.2.l.a.863.9		96	36.31	odd	6
972.2.l.a.863.15		96	9.4	even	3
972.2.l.b.215.3		96	36.7	odd	6
972.2.l.b.215.5		96	9.7	even	3
972.2.l.b.755.3		96	27.11	odd	18
972.2.l.b.755.5		96	108.11	even	18
972.2.l.c.215.12		96	9.2	odd	6
972.2.l.c.215.14		96	36.11	even	6
972.2.l.c.755.12		96	108.43	odd	18
972.2.l.c.755.14		96	27.16	even	9
972.2.l.d.107.2		96	108.79	odd	18
972.2.l.d.107.8		96	27.25	even	9
972.2.l.d.863.2		96	9.5	odd	6
972.2.l.d.863.8		96	36.23	even	6

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.438668 - 1.34446i) q^{2} +(-1.61514 + 1.17954i) q^{4} +(-3.32285 - 0.585909i) q^{5} +(1.72640 + 2.05745i) q^{7} +(2.29436 + 1.65406i) q^{8} +(0.669899 + 4.72446i) q^{10} +(0.506730 + 2.87381i) q^{11} +(0.552703 - 0.201167i) q^{13} +(2.00883 - 3.22361i) q^{14} +(1.21736 - 3.81025i) q^{16} +(6.36286 + 3.67360i) q^{17} +(-2.82795 + 1.63272i) q^{19} +(6.05798 - 2.97312i) q^{20} +(3.64143 - 1.94193i) q^{22} +(0.365077 + 0.306336i) q^{23} +(5.99961 + 2.18368i) q^{25} +(-0.512914 - 0.654840i) q^{26} +(-5.21523 - 1.28670i) q^{28} +(-1.49502 + 4.10753i) q^{29} +(-3.73778 + 4.45451i) q^{31} +(-5.65675 + 0.0347450i) q^{32} +(2.14782 - 10.1661i) q^{34} +(-4.53111 - 7.84811i) q^{35} +(-1.59532 + 2.76318i) q^{37} +(3.43565 + 3.08584i) q^{38} +(-6.65468 - 6.84050i) q^{40} +(1.09875 + 3.01880i) q^{41} +(1.79304 - 0.316161i) q^{43} +(-4.20822 - 4.04390i) q^{44} +(0.251708 - 0.625211i) q^{46} +(-0.940800 + 0.789425i) q^{47} +(-0.0370819 + 0.210302i) q^{49} +(0.304032 - 9.02414i) q^{50} +(-0.655407 + 0.976849i) q^{52} -7.37157i q^{53} -9.84615i q^{55} +(0.557836 + 7.57609i) q^{56} +(6.17822 + 0.208150i) q^{58} +(-0.718733 + 4.07614i) q^{59} +(0.421725 - 0.353869i) q^{61} +(7.62855 + 3.07124i) q^{62} +(2.52815 + 7.59002i) q^{64} +(-1.95442 + 0.344616i) q^{65} +(3.46492 + 9.51978i) q^{67} +(-14.6101 + 1.57188i) q^{68} +(-8.56381 + 9.53460i) q^{70} +(-0.616505 + 1.06782i) q^{71} +(1.18077 + 2.04515i) q^{73} +(4.41480 + 0.932727i) q^{74} +(2.64168 - 5.97275i) q^{76} +(-5.03789 + 6.00392i) q^{77} +(3.33584 - 9.16514i) q^{79} +(-6.27757 + 11.9477i) q^{80} +(3.57666 - 2.80148i) q^{82} +(-16.8988 - 6.15067i) q^{83} +(-18.9905 - 15.9349i) q^{85} +(-1.21161 - 2.27198i) q^{86} +(-3.59084 + 7.43171i) q^{88} +(4.81205 - 2.77824i) q^{89} +(1.36808 + 0.789860i) q^{91} +(-0.950986 - 0.0641520i) q^{92} +(1.47405 + 0.918571i) q^{94} +(10.3535 - 3.76836i) q^{95} +(1.83865 + 10.4275i) q^{97} +(0.299009 - 0.0423976i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38}+ \cdots + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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