LMFDB - Embedded newform 729.2.i.a.10.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [729,2,Mod(10,729)] 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("729.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(729, base_ring=CyclotomicField(162)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, 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:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.4
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.82656 - 0.285668i) q^{2} +(1.35020 + 0.432926i) q^{4} +(0.984150 + 0.447351i) q^{5} +(0.0949117 + 0.694877i) q^{7} +(0.961673 + 0.482970i) q^{8} +(-1.66981 - 1.09825i) q^{10} +(0.605270 - 0.0470453i) q^{11} +(1.37185 + 4.00939i) q^{13} +(0.0251426 - 1.29634i) q^{14} +(-3.92567 - 2.80590i) q^{16} +(0.887557 - 2.05759i) q^{17} +(-2.74277 + 3.68418i) q^{19} +(1.13513 + 1.03008i) q^{20} +(-1.11900 - 0.0869755i) q^{22} +(2.68957 + 2.08457i) q^{23} +(-2.51918 - 2.88666i) q^{25} +(-1.36041 - 7.71526i) q^{26} +(-0.172680 + 0.979315i) q^{28} +(-1.70050 + 1.02626i) q^{29} +(2.00236 - 0.0777008i) q^{31} +(4.83233 + 4.73951i) q^{32} +(-2.20896 + 3.50475i) q^{34} +(-0.217446 + 0.726322i) q^{35} +(-3.62850 + 3.84598i) q^{37} +(6.06227 - 5.94584i) q^{38} +(0.730373 + 0.905521i) q^{40} +(-1.82290 + 4.72142i) q^{41} +(0.202757 + 0.787149i) q^{43} +(0.837605 + 0.198516i) q^{44} +(-4.31715 - 4.57592i) q^{46} +(-7.76222 - 0.301210i) q^{47} +(6.26975 - 1.74530i) q^{49} +(3.77679 + 5.99229i) q^{50} +(0.116513 + 6.00740i) q^{52} +(2.73818 - 0.996617i) q^{53} +(0.616722 + 0.224469i) q^{55} +(-0.244331 + 0.714084i) q^{56} +(3.39922 - 1.38874i) q^{58} +(4.04047 + 8.44992i) q^{59} +(7.31088 - 2.34414i) q^{61} +(-3.67962 - 0.430086i) q^{62} +(-1.70959 - 2.29638i) q^{64} +(-0.443496 + 4.55954i) q^{65} +(12.6369 + 7.62639i) q^{67} +(2.08917 - 2.39392i) q^{68} +(0.604665 - 1.26455i) q^{70} +(-0.252560 + 4.33629i) q^{71} +(-6.65114 + 4.37452i) q^{73} +(7.72632 - 5.98835i) q^{74} +(-5.29827 + 3.78698i) q^{76} +(0.0901379 + 0.416123i) q^{77} +(-9.22948 + 11.4428i) q^{79} +(-2.60823 - 4.51758i) q^{80} +(4.67838 - 8.10320i) q^{82} +(4.63725 + 12.0108i) q^{83} +(1.79395 - 1.62792i) q^{85} +(-0.145483 - 1.49569i) q^{86} +(0.604794 + 0.247085i) q^{88} +(0.360012 + 6.18117i) q^{89} +(-2.65582 + 1.33381i) q^{91} +(2.72900 + 3.97898i) q^{92} +(14.0921 + 2.76760i) q^{94} +(-4.34742 + 2.39880i) q^{95} +(10.2460 - 4.65740i) q^{97} +(-11.9506 + 1.39683i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

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 $

$2$	−1.82656	−	0.285668i	−1.29157	−	0.201998i	−0.528844	−	0.848719i	$-0.677374\pi$
$2$	−1.82656	−	0.285668i	−1.29157	−	0.201998i	−0.762726	+	0.646721i	$0.776140\pi$
$3$		0			0
$3$		0			0
$4$	1.35020	+	0.432926i	0.675102	+	0.216463i
$5$	0.984150	+	0.447351i	0.440125	+	0.200061i	0.621601	−	0.783334i	$-0.286483\pi$
$5$	0.984150	+	0.447351i	0.440125	+	0.200061i	−0.181476	+	0.983395i	$0.558087\pi$
$6$		0			0
$7$	0.0949117	+	0.694877i	0.0358733	+	0.262639i	0.999996	−	0.00281803i	$-0.000897009\pi$
$7$	0.0949117	+	0.694877i	0.0358733	+	0.262639i	−0.964123	+	0.265457i	$0.914477\pi$
$8$	0.961673	+	0.482970i	0.340003	+	0.170756i
$9$		0			0
$10$	−1.66981	−	1.09825i	−0.528041	−	0.347298i
$11$	0.605270	−	0.0470453i	0.182496	−	0.0141847i	0.0140807	−	0.999901i	$-0.495518\pi$
$11$	0.605270	−	0.0470453i	0.182496	−	0.0141847i	0.168415	+	0.985716i	$0.446135\pi$
$12$		0			0
$13$	1.37185	+	4.00939i	0.380483	+	1.11200i	0.955786	+	0.294063i	$0.0950076\pi$
$13$	1.37185	+	4.00939i	0.380483	+	1.11200i	−0.575303	+	0.817940i	$0.695116\pi$
$14$	0.0251426	−	1.29634i	0.00671963	−	0.346463i
$15$		0			0
$16$	−3.92567	−	2.80590i	−0.981418	−	0.701476i
$17$	0.887557	−	2.05759i	0.215264	−	0.499038i	−0.776031	−	0.630694i	$-0.782770\pi$
$17$	0.887557	−	2.05759i	0.215264	−	0.499038i	0.991295	+	0.131656i	$0.0420295\pi$
$18$		0			0
$19$	−2.74277	+	3.68418i	−0.629234	+	0.845208i	−0.996385	−	0.0849531i	$-0.972926\pi$
$19$	−2.74277	+	3.68418i	−0.629234	+	0.845208i	0.367151	+	0.930161i	$0.380333\pi$
$20$	1.13513	+	1.03008i	0.253824	+	0.230333i
$21$		0			0
$22$	−1.11900	−	0.0869755i	−0.238571	−	0.0185432i
$23$	2.68957	+	2.08457i	0.560814	+	0.434664i	0.853160	−	0.521649i	$-0.174683\pi$
$23$	2.68957	+	2.08457i	0.560814	+	0.434664i	−0.292346	+	0.956313i	$0.594436\pi$
$24$		0			0
$25$	−2.51918	−	2.88666i	−0.503836	−	0.577332i
$26$	−1.36041	−	7.71526i	−0.266798	−	1.51309i
$27$		0			0
$28$	−0.172680	+	0.979315i	−0.0326334	+	0.185073i
$29$	−1.70050	+	1.02626i	−0.315774	+	0.190571i	−0.665725	−	0.746197i	$-0.731877\pi$
$29$	−1.70050	+	1.02626i	−0.315774	+	0.190571i	0.349950	+	0.936768i	$0.386198\pi$
$30$		0			0
$31$	2.00236	−	0.0777008i	0.359635	−	0.0139555i	0.141675	−	0.989913i	$-0.454751\pi$
$31$	2.00236	−	0.0777008i	0.359635	−	0.0139555i	0.217960	+	0.975958i	$0.430060\pi$
$32$	4.83233	+	4.73951i	0.854243	+	0.837836i
$33$		0			0
$34$	−2.20896	+	3.50475i	−0.378833	+	0.601060i
$35$	−0.217446	+	0.726322i	−0.0367552	+	0.122771i
$36$		0			0
$37$	−3.62850	+	3.84598i	−0.596521	+	0.632275i	−0.953340	−	0.301898i	$-0.902380\pi$
$37$	−3.62850	+	3.84598i	−0.596521	+	0.632275i	0.356819	+	0.934173i	$0.383861\pi$
$38$	6.06227	−	5.94584i	0.983431	−	0.964542i
$39$		0			0
$40$	0.730373	+	0.905521i	0.115482	+	0.143175i
$41$	−1.82290	+	4.72142i	−0.284689	+	0.737362i	0.714596	+	0.699538i	$0.246611\pi$
$41$	−1.82290	+	4.72142i	−0.284689	+	0.737362i	−0.999284	+	0.0378245i	$0.987957\pi$
$42$		0			0
$43$	0.202757	+	0.787149i	0.0309201	+	0.120039i	0.981988	−	0.188942i	$-0.0605058\pi$
$43$	0.202757	+	0.787149i	0.0309201	+	0.120039i	−0.951068	+	0.308981i	$0.900012\pi$
$44$	0.837605	+	0.198516i	0.126274	+	0.0299274i
$45$		0			0
$46$	−4.31715	−	4.57592i	−0.636530	−	0.674682i
$47$	−7.76222	−	0.301210i	−1.13224	−	0.0439359i	−0.534166	−	0.845380i	$-0.679374\pi$
$47$	−7.76222	−	0.301210i	−1.13224	−	0.0439359i	−0.598070	+	0.801444i	$0.704066\pi$
$48$		0			0
$49$	6.26975	−	1.74530i	0.895679	−	0.249329i
$50$	3.77679	+	5.99229i	0.534119	+	0.847438i
$51$		0			0
$52$	0.116513	+	6.00740i	0.0161575	+	0.833077i
$53$	2.73818	−	0.996617i	0.376118	−	0.136896i	−0.147042	−	0.989130i	$-0.546975\pi$
$53$	2.73818	−	0.996617i	0.376118	−	0.136896i	0.523160	+	0.852234i	$0.324753\pi$
$54$		0			0
$55$	0.616722	+	0.224469i	0.0831588	+	0.0302673i
$56$	−0.244331	+	0.714084i	−0.0326501	+	0.0954235i
$57$		0			0
$58$	3.39922	−	1.38874i	0.446340	−	0.182350i
$59$	4.04047	+	8.44992i	0.526024	+	1.10009i	0.978105	+	0.208110i	$0.0667311\pi$
$59$	4.04047	+	8.44992i	0.526024	+	1.10009i	−0.452081	+	0.891977i	$0.649318\pi$
$60$		0			0
$61$	7.31088	−	2.34414i	0.936063	−	0.300136i	0.202130	−	0.979359i	$-0.435214\pi$
$61$	7.31088	−	2.34414i	0.936063	−	0.300136i	0.733933	+	0.679222i	$0.237683\pi$
$62$	−3.67962	−	0.430086i	−0.467313	−	0.0546210i
$63$		0			0
$64$	−1.70959	−	2.29638i	−0.213699	−	0.287048i
$65$	−0.443496	+	4.55954i	−0.0550089	+	0.565541i
$66$		0			0
$67$	12.6369	+	7.62639i	1.54384	+	0.931712i	0.995429	+	0.0955023i	$0.0304457\pi$
$67$	12.6369	+	7.62639i	1.54384	+	0.931712i	0.548410	+	0.836210i	$0.315233\pi$
$68$	2.08917	−	2.39392i	0.253348	−	0.290305i
$69$		0			0
$70$	0.604665	−	1.26455i	0.0722713	−	0.151143i
$71$	−0.252560	+	4.33629i	−0.0299734	+	0.514623i	0.949591	+	0.313492i	$0.101499\pi$
$71$	−0.252560	+	4.33629i	−0.0299734	+	0.514623i	−0.979564	+	0.201131i	$0.935538\pi$
$72$		0			0
$73$	−6.65114	+	4.37452i	−0.778457	+	0.511999i	−0.875463	−	0.483285i	$-0.839444\pi$
$73$	−6.65114	+	4.37452i	−0.778457	+	0.511999i	0.0970064	+	0.995284i	$0.469073\pi$
$74$	7.72632	−	5.98835i	0.898167	−	0.696132i
$75$		0			0
$76$	−5.29827	+	3.78698i	−0.607754	+	0.434396i
$77$	0.0901379	+	0.416123i	0.0102722	+	0.0474216i
$78$		0			0
$79$	−9.22948	+	11.4428i	−1.03840	+	1.28741i	−0.0815978	+	0.996665i	$0.526002\pi$
$79$	−9.22948	+	11.4428i	−1.03840	+	1.28741i	−0.956800	+	0.290746i	$0.906096\pi$
$80$	−2.60823	−	4.51758i	−0.291609	−	0.505081i
$81$		0			0
$82$	4.67838	−	8.10320i	0.516641	−	0.894848i
$83$	4.63725	+	12.0108i	0.509004	+	1.31835i	0.914622	+	0.404310i	$0.132488\pi$
$83$	4.63725	+	12.0108i	0.509004	+	1.31835i	−0.405618	+	0.914043i	$0.632944\pi$
$84$		0			0
$85$	1.79395	−	1.62792i	0.194581	−	0.176573i
$86$	−0.145483	−	1.49569i	−0.0156878	−	0.161285i
$87$		0			0
$88$	0.604794	+	0.247085i	0.0644712	+	0.0263394i
$89$	0.360012	+	6.18117i	0.0381612	+	0.655203i	0.962106	+	0.272676i	$0.0879088\pi$
$89$	0.360012	+	6.18117i	0.0381612	+	0.655203i	−0.923945	+	0.382526i	$0.875054\pi$
$90$		0			0
$91$	−2.65582	+	1.33381i	−0.278406	+	0.139821i
$92$	2.72900	+	3.97898i	0.284518	+	0.414838i
$93$		0			0
$94$	14.0921	+	2.76760i	1.45349	+	0.285456i
$95$	−4.34742	+	2.39880i	−0.446035	+	0.246112i
$96$		0			0
$97$	10.2460	−	4.65740i	1.04033	−	0.472887i	0.180555	−	0.983565i	$-0.442211\pi$
$97$	10.2460	−	4.65740i	1.04033	−	0.472887i	0.859772	+	0.510678i	$0.170606\pi$
$98$	−11.9506	+	1.39683i	−1.20720	+	0.141101i
$99$		0			0
$100$	−2.15170	−	4.98820i	−0.215170	−	0.498820i
$101$	0.945162	−	4.36335i	0.0940472	−	0.434170i	−0.905896	−	0.423500i	$-0.860801\pi$
$101$	0.945162	−	4.36335i	0.0940472	−	0.434170i	0.999943	−	0.0106696i	$-0.00339631\pi$
$102$		0			0
$103$	3.19996	−	4.66566i	0.315301	−	0.459721i	−0.634342	−	0.773052i	$-0.718729\pi$
$103$	3.19996	−	4.66566i	0.315301	−	0.459721i	0.949644	+	0.313332i	$0.101445\pi$
$104$	−0.617143	+	4.51828i	−0.0605158	+	0.443054i
$105$		0			0
$106$	−5.28614	+	1.03816i	−0.513436	+	0.100835i
$107$	11.9571	−	10.0332i	1.15594	−	0.969948i	0.156098	−	0.987742i	$-0.450109\pi$
$107$	11.9571	−	10.0332i	1.15594	−	0.969948i	0.999842	+	0.0177934i	$0.00566412\pi$
$108$		0			0
$109$	10.1987	+	8.55772i	0.976858	+	0.819681i	0.983612	−	0.180296i	$-0.0577056\pi$
$109$	10.1987	+	8.55772i	0.976858	+	0.819681i	−0.00675459	+	0.999977i	$0.502150\pi$
$110$	−1.06235	−	0.586182i	−0.101291	−	0.0558903i
$111$		0			0
$112$	1.57716	−	2.99417i	0.149028	−	0.282923i
$113$	0.278597	−	1.08158i	0.0262082	−	0.101746i	−0.953949	−	0.299970i	$-0.903023\pi$
$113$	0.278597	−	1.08158i	0.0262082	−	0.101746i	0.980157	+	0.198224i	$0.0635172\pi$
$114$		0			0
$115$	1.71440	+	3.25471i	0.159869	+	0.303504i
$116$	−2.74031	+	0.649466i	−0.254432	+	0.0603014i
$117$		0			0
$118$	−4.96627	−	16.5885i	−0.457182	−	1.52709i
$119$	1.51401	+	0.421453i	0.138789	+	0.0386346i
$120$		0			0
$121$	−10.5037	+	1.64276i	−0.954886	+	0.149341i
$122$	−14.0234	+	2.19322i	−1.26962	+	0.198565i
$123$		0			0
$124$	2.73724	+	0.761962i	0.245811	+	0.0684262i
$125$	−2.73815	−	9.14605i	−0.244907	−	0.818047i
$126$		0			0
$127$	−7.01217	+	1.66191i	−0.622229	+	0.147471i	−0.529625	−	0.848232i	$-0.677667\pi$
$127$	−7.01217	+	1.66191i	−0.622229	+	0.147471i	−0.0926042	+	0.995703i	$0.529519\pi$
$128$	−3.84229	−	7.29441i	−0.339614	−	0.644741i
$129$		0			0
$130$	2.11258	−	8.20155i	0.185286	−	0.719324i
$131$	−5.21826	+	9.90663i	−0.455922	+	0.865546i	0.543733	+	0.839258i	$0.317011\pi$
$131$	−5.21826	+	9.90663i	−0.455922	+	0.865546i	−0.999654	+	0.0262875i	$0.991631\pi$
$132$		0			0
$133$	−2.82037	−	1.55621i	−0.244557	−	0.134941i
$134$	−20.9033	−	17.5400i	−1.80577	−	1.51522i
$135$		0			0
$136$	1.84729	−	1.55006i	0.158404	−	0.132917i
$137$	−3.80498	+	0.747274i	−0.325082	+	0.0638439i	−0.352591	−	0.935778i	$-0.614699\pi$
$137$	−3.80498	+	0.747274i	−0.325082	+	0.0638439i	0.0275092	+	0.999622i	$0.491242\pi$
$138$		0			0
$139$	−0.340338	+	2.49172i	−0.0288671	+	0.211345i	−0.999583	−	0.0288870i	$-0.990804\pi$
$139$	−0.340338	+	2.49172i	−0.0288671	+	0.211345i	0.970716	+	0.240232i	$0.0772234\pi$
$140$	−0.608040	+	0.886545i	−0.0513888	+	0.0749267i
$141$		0			0
$142$	1.70006	−	7.84834i	0.142666	−	0.658618i
$143$	1.01896	+	2.36222i	0.0852100	+	0.197539i
$144$		0			0
$145$	−2.13264	+	0.249270i	−0.177106	+	0.0207007i
$146$	13.3983	−	6.09029i	1.10885	−	0.504036i
$147$		0			0
$148$	−6.56423	+	3.62199i	−0.539577	+	0.297726i
$149$	−21.6436	−	4.25066i	−1.77311	−	0.348228i	−0.803959	−	0.594685i	$-0.797277\pi$
$149$	−21.6436	−	4.25066i	−1.77311	−	0.348228i	−0.969154	+	0.246457i	$0.920734\pi$
$150$		0			0
$151$	3.52460	+	5.13899i	0.286828	+	0.418205i	0.941139	−	0.338020i	$-0.109757\pi$
$151$	3.52460	+	5.13899i	0.286828	+	0.418205i	−0.654311	+	0.756226i	$0.727041\pi$
$152$	−4.41700	+	2.21830i	−0.358266	+	0.179928i
$153$		0			0
$154$	−0.0457689	−	0.785821i	−0.00368816	−	0.0633233i
$155$	2.00538	+	0.819290i	0.161076	+	0.0658069i
$156$		0			0
$157$	−1.46124	−	15.0228i	−0.116620	−	1.19895i	−0.852825	−	0.522196i	$-0.825113\pi$
$157$	−1.46124	−	15.0228i	−0.116620	−	1.19895i	0.736206	−	0.676758i	$-0.236616\pi$
$158$	20.1270	−	18.2643i	1.60122	−	1.45303i
$159$		0			0
$160$	2.63551	+	6.82614i	0.208355	+	0.539654i
$161$	−1.19325	+	2.06677i	−0.0940413	+	0.162884i
$162$		0			0
$163$	−5.92506	−	10.2625i	−0.464087	−	0.803822i	0.535073	−	0.844806i	$-0.320284\pi$
$163$	−5.92506	−	10.2625i	−0.464087	−	0.803822i	−0.999160	+	0.0409842i	$0.986951\pi$
$164$	−4.50531	+	5.58571i	−0.351805	+	0.436170i
$165$		0			0
$166$	−5.03910	−	23.2631i	−0.391110	−	1.80556i
$167$	6.80706	−	4.86539i	0.526746	−	0.376495i	−0.286805	−	0.957989i	$-0.592593\pi$
$167$	6.80706	−	4.86539i	0.526746	−	0.376495i	0.813551	+	0.581494i	$0.197531\pi$
$168$		0			0
$169$	−3.91810	+	3.03675i	−0.301392	+	0.233597i
$170$	−3.74180	+	2.46102i	−0.286983	+	0.188752i
$171$		0			0
$172$	−0.0670143	+	1.15059i	−0.00510979	+	0.0877317i
$173$	8.29561	−	17.3488i	0.630703	−	1.31900i	−0.300248	−	0.953861i	$-0.597070\pi$
$173$	8.29561	−	17.3488i	0.630703	−	1.31900i	0.930952	−	0.365143i	$-0.118980\pi$
$174$		0			0
$175$	1.76677	−	2.02450i	0.133555	−	0.153038i
$176$	−2.50810	−	1.51364i	−0.189055	−	0.114095i
$177$		0			0
$178$	1.10818	−	11.3931i	0.0830617	−	0.853948i
$179$	6.60031	+	8.86575i	0.493330	+	0.662658i	0.977160	−	0.212505i	$-0.0681620\pi$
$179$	6.60031	+	8.86575i	0.493330	+	0.662658i	−0.483830	+	0.875162i	$0.660755\pi$
$180$		0			0
$181$	14.8463	+	1.73529i	1.10352	+	0.128983i	0.648292	−	0.761392i	$-0.275484\pi$
$181$	14.8463	+	1.73529i	1.10352	+	0.128983i	0.455228	+	0.890375i	$0.349558\pi$
$182$	5.23204	−	1.67759i	0.387824	−	0.124351i
$183$		0			0
$184$	1.57970	+	3.30366i	0.116457	+	0.243549i
$185$	−5.29149	+	2.16181i	−0.389038	+	0.158939i
$186$		0			0
$187$	0.440412	−	1.28715i	0.0322061	−	0.0941258i
$188$	−10.3502	−	3.76716i	−0.754865	−	0.274748i
$189$		0			0
$190$	8.62606	−	3.13963i	0.625800	−	0.227773i
$191$	−0.172369	−	8.88730i	−0.0124722	−	0.643063i	−0.952936	−	0.303170i	$-0.901955\pi$
$191$	−0.172369	−	8.88730i	−0.0124722	−	0.643063i	0.940464	−	0.339893i	$-0.110391\pi$
$192$		0			0
$193$	−2.88053	−	4.57027i	−0.207345	−	0.328976i	0.726169	−	0.687516i	$-0.241299\pi$
$193$	−2.88053	−	4.57027i	−0.207345	−	0.328976i	−0.933514	+	0.358541i	$0.883274\pi$
$194$	−20.0454	+	5.58003i	−1.43918	+	0.400623i
$195$		0			0
$196$	9.22103	+	0.357818i	0.658645	+	0.0255584i
$197$	−14.7949	−	15.6817i	−1.05410	−	1.11728i	−0.992876	−	0.119151i	$-0.961983\pi$
$197$	−14.7949	−	15.6817i	−1.05410	−	1.11728i	−0.0612189	−	0.998124i	$-0.519499\pi$
$198$		0			0
$199$	−22.2192	−	5.26604i	−1.57508	−	0.373300i	−0.652092	−	0.758140i	$-0.726108\pi$
$199$	−22.2192	−	5.26604i	−1.57508	−	0.373300i	−0.922983	+	0.384840i	$0.874257\pi$
$200$	−1.02846	−	3.99271i	−0.0727228	−	0.282327i
$201$		0			0
$202$	−2.97286	+	7.69991i	−0.209170	+	0.541764i
$203$	−0.874518	−	1.08423i	−0.0613791	−	0.0760982i
$204$		0			0
$205$	−3.90614	+	3.83111i	−0.272816	+	0.267576i
$206$	−7.17773	+	7.60795i	−0.500096	+	0.530071i
$207$		0			0
$208$	5.86451	−	19.5888i	0.406630	−	1.35824i
$209$	−1.48679	+	2.35896i	−0.102844	+	0.163172i
$210$		0			0
$211$	−6.87941	−	6.74728i	−0.473598	−	0.464502i	0.423779	−	0.905765i	$-0.360703\pi$
$211$	−6.87941	−	6.74728i	−0.473598	−	0.464502i	−0.897377	+	0.441264i	$0.854530\pi$
$212$	4.12857	−	0.160207i	0.283551	−	0.0110031i
$213$		0			0
$214$	−24.7065	+	14.9105i	−1.68890	+	1.01926i
$215$	−0.152589	+	0.865376i	−0.0104065	+	0.0590182i
$216$		0			0
$217$	0.244040	+	1.38402i	0.0165665	+	0.0939534i
$218$	−16.1838	−	18.5446i	−1.09611	−	1.25600i
$219$		0			0
$220$	0.735523	+	0.570073i	0.0495889	+	0.0384343i
$221$	9.46726	+	0.735853i	0.636837	+	0.0494989i
$222$		0			0
$223$	−15.6352	−	14.1882i	−1.04701	−	0.950109i	−0.0481961	−	0.998838i	$-0.515347\pi$
$223$	−15.6352	−	14.1882i	−1.04701	−	0.950109i	−0.998812	+	0.0487286i	$0.984483\pi$
$224$	−2.83473	+	3.80771i	−0.189404	+	0.254413i
$225$		0			0
$226$	−0.817845	+	1.89598i	−0.0544023	+	0.126119i
$227$	−1.89613	−	1.35528i	−0.125851	−	0.0899528i	0.516825	−	0.856091i	$-0.327114\pi$
$227$	−1.89613	−	1.35528i	−0.125851	−	0.0899528i	−0.642676	+	0.766138i	$0.722176\pi$
$228$		0			0
$229$	−0.200651	+	10.3455i	−0.0132594	+	0.683651i	0.932934	+	0.360048i	$0.117240\pi$
$229$	−0.200651	+	10.3455i	−0.0132594	+	0.683651i	−0.946193	+	0.323603i	$0.895106\pi$
$230$	−2.20169	−	6.43467i	−0.145175	−	0.424290i
$231$		0			0
$232$	−2.13097	+	0.165632i	−0.139905	+	0.0108743i
$233$	23.2797	+	15.3113i	1.52511	+	1.00308i	0.987094	+	0.160140i	$0.0511946\pi$
$233$	23.2797	+	15.3113i	1.52511	+	1.00308i	0.538011	+	0.842938i	$0.319176\pi$
$234$		0			0
$235$	−7.50444	−	3.76887i	−0.489536	−	0.245854i
$236$	1.79727	+	13.1583i	0.116992	+	0.856536i
$237$		0			0
$238$	−2.64503	−	1.20231i	−0.171452	−	0.0779343i
$239$	1.01322	+	0.324877i	0.0655400	+	0.0210146i	0.337915	−	0.941177i	$-0.390278\pi$
$239$	1.01322	+	0.324877i	0.0655400	+	0.0210146i	−0.272375	+	0.962191i	$0.587809\pi$
$240$		0			0
$241$	−2.66464	−	0.416743i	−0.171645	−	0.0268448i	0.0681123	−	0.997678i	$-0.478302\pi$
$241$	−2.66464	−	0.416743i	−0.171645	−	0.0268448i	−0.239757	+	0.970833i	$0.577068\pi$
$242$	19.6550			1.26347
$243$		0			0
$244$	10.8860			0.696906
$245$	6.95114	+	1.08714i	0.444092	+	0.0694547i
$246$		0			0
$247$	−18.5340	−	5.94268i	−1.17929	−	0.378123i
$248$	1.96315	+	0.892359i	0.124660	+	0.0566649i
$249$		0			0
$250$	2.38864	+	17.4880i	0.151071	+	1.10604i
$251$	23.0894	+	11.5959i	1.45739	+	0.731928i	0.988485	−	0.151321i	$-0.0483528\pi$
$251$	23.0894	+	11.5959i	1.45739	+	0.731928i	0.468904	+	0.883249i	$0.344649\pi$
$252$		0			0
$253$	1.72599	+	1.13520i	0.108512	+	0.0713693i
$254$	13.2829	−	1.03243i	0.833441	−	0.0647802i
$255$		0			0
$256$	6.78800	+	19.8387i	0.424250	+	1.23992i
$257$	0.589920	−	30.4161i	0.0367982	−	1.89731i	−0.297326	−	0.954776i	$-0.596095\pi$
$257$	0.589920	−	30.4161i	0.0367982	−	1.89731i	0.334124	−	0.942529i	$-0.391560\pi$
$258$		0			0
$259$	−3.01687	−	2.15633i	−0.187459	−	0.133988i
$260$	−2.57275	+	5.96430i	−0.159555	+	0.369890i
$261$		0			0
$262$	12.3615	−	16.6043i	0.763693	−	1.02582i
$263$	8.07031	+	7.32342i	0.497637	+	0.451581i	0.881758	−	0.471701i	$-0.156360\pi$
$263$	8.07031	+	7.32342i	0.497637	+	0.451581i	−0.384122	+	0.923282i	$0.625496\pi$
$264$		0			0
$265$	3.14062	+	0.244108i	0.192927	+	0.0149954i
$266$	4.70700	+	3.64820i	0.288605	+	0.223686i
$267$		0			0
$268$	13.7607	+	15.7680i	0.840568	+	0.963185i
$269$	0.719840	+	4.08241i	0.0438894	+	0.248909i	0.998857	−	0.0478014i	$-0.0152215\pi$
$269$	0.719840	+	4.08241i	0.0438894	+	0.248909i	−0.954967	+	0.296711i	$0.904110\pi$
$270$		0			0
$271$	−2.07529	+	11.7696i	−0.126065	+	0.714951i	0.854604	+	0.519280i	$0.173800\pi$
$271$	−2.07529	+	11.7696i	−0.126065	+	0.714951i	−0.980670	+	0.195671i	$0.937311\pi$
$272$	−9.25764	+	5.58702i	−0.561327	+	0.338763i
$273$		0			0
$274$	7.16348	−	0.277976i	0.432762	−	0.0167931i
$275$	−1.66059	−	1.62869i	−0.100137	−	0.0982139i
$276$		0			0
$277$	−12.8893	+	20.4503i	−0.774444	+	1.22874i	0.194364	+	0.980929i	$0.437736\pi$
$277$	−12.8893	+	20.4503i	−0.774444	+	1.22874i	−0.968809	+	0.247810i	$0.920289\pi$
$278$	1.33345	−	4.45404i	0.0799751	−	0.267135i
$279$		0			0
$280$	−0.559904	+	0.593464i	−0.0334607	+	0.0354663i
$281$	17.5228	−	17.1862i	1.04532	−	1.02525i	0.0456684	−	0.998957i	$-0.485458\pi$
$281$	17.5228	−	17.1862i	1.04532	−	1.02525i	0.999654	−	0.0262887i	$-0.00836892\pi$
$282$		0			0
$283$	−8.32461	−	10.3209i	−0.494847	−	0.613514i	0.467945	−	0.883757i	$-0.344994\pi$
$283$	−8.32461	−	10.3209i	−0.494847	−	0.613514i	−0.962792	+	0.270244i	$0.912896\pi$
$284$	−2.21830	+	5.74554i	−0.131632	+	0.340935i
$285$		0			0
$286$	−1.18638	−	4.60582i	−0.0701522	−	0.272348i
$287$	−3.45382	−	0.818570i	−0.203873	−	0.0483187i
$288$		0			0
$289$	8.22020	+	8.71290i	0.483541	+	0.512524i
$290$	3.96660	+	0.153922i	0.232927	+	0.00903861i
$291$		0			0
$292$	−10.8742	+	3.02705i	−0.636367	+	0.177145i
$293$	1.94392	+	3.08424i	0.113565	+	0.180183i	0.897958	−	0.440081i	$-0.145050\pi$
$293$	1.94392	+	3.08424i	0.113565	+	0.180183i	−0.784393	+	0.620264i	$0.787025\pi$
$294$		0			0
$295$	0.196345	+	10.1235i	0.0114317	+	0.589413i
$296$	−5.34692	+	1.94612i	−0.310784	+	0.113116i
$297$		0			0
$298$	38.3190	+	13.9470i	2.21976	+	0.807926i
$299$	−4.66817	+	13.6432i	−0.269967	+	0.789009i
$300$		0			0
$301$	−0.527728	+	0.215600i	−0.0304177	+	0.0124270i
$302$	−4.96983	−	10.3935i	−0.285982	−	0.598080i
$303$		0			0
$304$	21.1047	−	6.76694i	1.21043	−	0.388110i
$305$	8.24366	+	0.963545i	0.472030	+	0.0551724i
$306$		0			0
$307$	15.3437	+	20.6102i	0.875714	+	1.17629i	0.983282	+	0.182090i	$0.0582863\pi$
$307$	15.3437	+	20.6102i	0.875714	+	1.17629i	−0.107568	+	0.994198i	$0.534306\pi$
$308$	−0.0584457	+	0.600874i	−0.00333025	+	0.0342380i
$309$		0			0
$310$	−3.42890	−	2.06935i	−0.194749	−	0.117531i
$311$	3.09105	−	3.54195i	0.175277	−	0.200846i	−0.659075	−	0.752077i	$-0.729052\pi$
$311$	3.09105	−	3.54195i	0.175277	−	0.200846i	0.834352	+	0.551232i	$0.185842\pi$
$312$		0			0
$313$	9.95657	−	20.8224i	0.562779	−	1.17695i	−0.402425	−	0.915453i	$-0.631833\pi$
$313$	9.95657	−	20.8224i	0.562779	−	1.17695i	0.965204	−	0.261499i	$-0.0842168\pi$
$314$	−1.62251	+	27.8575i	−0.0915638	+	1.57209i
$315$		0			0
$316$	−17.4156	+	11.4544i	−0.979702	+	0.644360i
$317$	−14.5285	+	11.2604i	−0.816000	+	0.632448i	−0.932673	−	0.360722i	$-0.882530\pi$
$317$	−14.5285	+	11.2604i	−0.816000	+	0.632448i	0.116673	+	0.993170i	$0.462777\pi$
$318$		0			0
$319$	−0.980980	+	0.701162i	−0.0549243	+	0.0392575i
$320$	−0.655207	−	3.02477i	−0.0366272	−	0.169090i
$321$		0			0
$322$	2.76995	−	3.43420i	0.154363	−	0.191380i
$323$	5.14616	+	8.91340i	0.286340	+	0.495955i
$324$		0			0
$325$	8.11779	−	14.0604i	0.450294	−	0.779932i
$326$	7.89078	+	20.4376i	0.437030	+	1.13194i
$327$		0			0
$328$	−4.03334	+	3.66006i	−0.222704	+	0.202093i
$329$	−0.527422	−	5.42237i	−0.0290777	−	0.298945i
$330$		0			0
$331$	−25.0146	−	10.2196i	−1.37493	−	0.561719i	−0.434179	−	0.900827i	$-0.642961\pi$
$331$	−25.0146	−	10.2196i	−1.37493	−	0.561719i	−0.940748	+	0.339108i	$0.889875\pi$
$332$	1.06146	+	18.2246i	0.0582552	+	1.00020i
$333$		0			0
$334$	−13.8234	+	6.94235i	−0.756381	+	0.379869i
$335$	9.02490	+	13.1586i	0.493083	+	0.718933i
$336$		0			0
$337$	12.0377	+	2.36413i	0.655736	+	0.128782i	0.509504	−	0.860468i	$-0.329829\pi$
$337$	12.0377	+	2.36413i	0.655736	+	0.128782i	0.146231	+	0.989250i	$0.453286\pi$
$338$	8.02413	−	4.42753i	0.436455	−	0.240826i
$339$		0			0
$340$	3.12697	−	1.42138i	0.169584	−	0.0770853i
$341$	1.20831	−	0.141232i	0.0654339	−	0.00764813i
$342$		0			0
$343$	3.75232	+	8.69885i	0.202606	+	0.469694i
$344$	−0.185184	+	0.854906i	−0.00998447	+	0.0460934i
$345$		0			0
$346$	−20.1084	+	29.3187i	−1.08103	+	1.57619i
$347$	−2.20588	+	16.1499i	−0.118418	+	0.866974i	0.831731	+	0.555179i	$0.187350\pi$
$347$	−2.20588	+	16.1499i	−0.118418	+	0.866974i	−0.950149	+	0.311795i	$0.899070\pi$
$348$		0			0
$349$	29.0779	−	5.71072i	1.55650	−	0.305688i	0.660878	−	0.750493i	$-0.270184\pi$
$349$	29.0779	−	5.71072i	1.55650	−	0.305688i	0.895627	+	0.444806i	$0.146727\pi$
$350$	−3.80544	+	3.19315i	−0.203409	+	0.170681i
$351$		0			0
$352$	3.14784	+	2.64135i	0.167780	+	0.140784i
$353$	−27.2196	−	15.0191i	−1.44875	−	0.799388i	−0.453005	−	0.891508i	$-0.649648\pi$
$353$	−27.2196	−	15.0191i	−1.44875	−	0.799388i	−0.995748	+	0.0921198i	$0.970636\pi$
$354$		0			0
$355$	−2.18840	+	4.15458i	−0.116148	+	0.220502i
$356$	−2.18990	+	8.50170i	−0.116064	+	0.450589i
$357$		0			0
$358$	−9.52317	−	18.0793i	−0.503315	−	0.955520i
$359$	9.56876	−	2.26784i	0.505020	−	0.119692i	0.0297944	−	0.999556i	$-0.490515\pi$
$359$	9.56876	−	2.26784i	0.505020	−	0.119692i	0.475225	+	0.879864i	$0.342367\pi$
$360$		0			0
$361$	−0.601124	−	2.00790i	−0.0316381	−	0.105679i
$362$	−26.6219	−	7.41073i	−1.39922	−	0.389499i
$363$		0			0
$364$	−4.16334	+	0.651135i	−0.218219	+	0.0341288i
$365$	−8.50266	+	1.32979i	−0.445050	+	0.0696045i
$366$		0			0
$367$	34.2962	+	9.54701i	1.79025	+	0.498350i	0.994263	−	0.106965i	$-0.0341133\pi$
$367$	34.2962	+	9.54701i	1.79025	+	0.498350i	0.795986	+	0.605315i	$0.206953\pi$
$368$	−4.70926	−	15.7300i	−0.245487	−	0.819984i
$369$		0			0
$370$	10.2828	−	2.43706i	0.534575	−	0.126697i
$371$	0.952411	+	1.80811i	0.0494467	+	0.0938723i
$372$		0			0
$373$	6.06302	−	23.5381i	0.313931	−	1.21876i	−0.595655	−	0.803241i	$-0.703107\pi$
$373$	6.06302	−	23.5381i	0.313931	−	1.21876i	0.909586	−	0.415516i	$-0.136399\pi$
$374$	−1.17213	+	2.22524i	−0.0606096	+	0.115065i
$375$		0			0
$376$	−7.31925	−	4.03859i	−0.377461	−	0.208274i
$377$	−6.44748	−	5.41008i	−0.332062	−	0.278633i
$378$		0			0
$379$	−5.98166	+	5.01921i	−0.307257	+	0.257819i	−0.783357	−	0.621572i	$-0.786494\pi$
$379$	−5.98166	+	5.01921i	−0.307257	+	0.257819i	0.476100	+	0.879391i	$0.342050\pi$
$380$	−6.90840	+	1.35677i	−0.354394	+	0.0696006i
$381$		0			0
$382$	−2.22398	+	16.2824i	−0.113789	+	0.833080i
$383$	−5.57304	+	8.12570i	−0.284769	+	0.415204i	−0.940501	−	0.339790i	$-0.889644\pi$
$383$	−5.57304	+	8.12570i	−0.284769	+	0.415204i	0.655732	+	0.754994i	$0.272360\pi$
$384$		0			0
$385$	−0.0974438	+	0.449851i	−0.00496619	+	0.0229265i
$386$	3.95587	+	9.17074i	0.201349	+	0.466778i
$387$		0			0
$388$	15.8506	−	1.85266i	0.804690	−	0.0940547i
$389$	−7.97327	+	3.62430i	−0.404261	+	0.183759i	−0.605612	−	0.795760i	$-0.707072\pi$
$389$	−7.97327	+	3.62430i	−0.404261	+	0.183759i	0.201351	+	0.979519i	$0.435467\pi$
$390$		0			0
$391$	6.67634	−	3.68385i	0.337637	−	0.186300i
$392$	6.87238	+	1.34969i	0.347108	+	0.0681697i
$393$		0			0
$394$	22.5440	+	32.8700i	1.13575	+	1.65596i
$395$	−14.2021	+	7.13258i	−0.714587	+	0.358879i
$396$		0			0
$397$	−0.163823	−	2.81274i	−0.00822207	−	0.141167i	−0.999921	−	0.0125844i	$-0.995994\pi$
$397$	−0.163823	−	2.81274i	−0.00822207	−	0.141167i	0.991699	−	0.128583i	$-0.0410429\pi$
$398$	39.0802	+	15.9660i	1.95891	+	0.800305i
$399$		0			0
$400$	1.78979	+	18.4006i	0.0894895	+	0.920032i
$401$	22.2240	−	20.1672i	1.10982	−	1.00710i	0.109902	−	0.993942i	$-0.464946\pi$
$401$	22.2240	−	20.1672i	1.10982	−	1.00710i	0.999913	−	0.0131614i	$-0.00418953\pi$
$402$		0			0
$403$	3.05848	+	7.92165i	0.152354	+	0.394606i
$404$	3.16517	−	5.48224i	0.157473	−	0.272751i
$405$		0			0
$406$	1.28763	+	2.23023i	0.0639038	+	0.110685i
$407$	−2.01528	+	2.49856i	−0.0998939	+	0.123849i
$408$		0			0
$409$	−3.60890	−	16.6605i	−0.178448	−	0.823810i	−0.975518	−	0.219922i	$-0.929420\pi$
$409$	−3.60890	−	16.6605i	−0.178448	−	0.823810i	0.797069	−	0.603888i	$-0.206383\pi$
$410$	8.22920	−	5.88188i	0.406411	−	0.290485i
$411$		0			0
$412$	6.34048	−	4.91424i	0.312373	−	0.242107i
$413$	−5.48817	+	3.60962i	−0.270055	+	0.177618i
$414$		0			0
$415$	−0.809284	+	13.8949i	−0.0397262	+	0.682072i
$416$	−12.3733	+	25.8766i	−0.606651	+	1.26870i
$417$		0			0
$418$	3.38959	−	3.88404i	0.165790	−	0.189974i
$419$	−16.0887	−	9.70959i	−0.785985	−	0.474344i	0.0660583	−	0.997816i	$-0.478958\pi$
$419$	−16.0887	−	9.70959i	−0.785985	−	0.474344i	−0.852043	+	0.523471i	$0.824637\pi$
$420$		0			0
$421$	1.23667	−	12.7141i	0.0602718	−	0.619649i	−0.915716	−	0.401825i	$-0.868376\pi$
$421$	1.23667	−	12.7141i	0.0602718	−	0.619649i	0.975988	−	0.217823i	$-0.0698957\pi$
$422$	10.6381	+	14.2895i	0.517857	+	0.695602i
$423$		0			0
$424$	3.11457	+	0.364041i	0.151257	+	0.0176794i
$425$	−8.17547	+	2.62136i	−0.396568	+	0.127155i
$426$		0			0
$427$	2.32278	+	4.85768i	0.112407	+	0.235079i
$428$	20.4882	−	8.37035i	0.990335	−	0.404596i
$429$		0			0
$430$	0.525923	−	1.53707i	0.0253623	−	0.0741240i
$431$	7.23781	+	2.63435i	0.348633	+	0.126892i	0.510400	−	0.859937i	$-0.329497\pi$
$431$	7.23781	+	2.63435i	0.348633	+	0.126892i	−0.161767	+	0.986829i	$0.551719\pi$
$432$		0			0
$433$	−4.03661	+	1.46921i	−0.193987	+	0.0706055i	−0.437187	−	0.899371i	$-0.644025\pi$
$433$	−4.03661	+	1.46921i	−0.193987	+	0.0706055i	0.243200	+	0.969976i	$0.421803\pi$
$434$	−0.0503824	−	2.59771i	−0.00241843	−	0.124694i
$435$		0			0
$436$	10.0655	+	15.9699i	0.482048	+	0.764822i
$437$	−15.0568	+	4.19135i	−0.720265	+	0.200499i
$438$		0			0
$439$	−4.81881	−	0.186992i	−0.229989	−	0.00892463i	−0.0764769	−	0.997071i	$-0.524367\pi$
$439$	−4.81881	−	0.186992i	−0.229989	−	0.00892463i	−0.153512	+	0.988147i	$0.549059\pi$
$440$	0.484674	+	0.513724i	0.0231059	+	0.0244908i
$441$		0			0
$442$	−17.0823	−	4.04857i	−0.812520	−	0.192571i
$443$	−9.63846	−	37.4188i	−0.457937	−	1.77782i	−0.613178	−	0.789945i	$-0.710109\pi$
$443$	−9.63846	−	37.4188i	−0.457937	−	1.77782i	0.155241	−	0.987877i	$-0.450385\pi$
$444$		0			0
$445$	−2.41085	+	6.24425i	−0.114285	+	0.296006i
$446$	24.5054	+	30.3819i	1.16036	+	1.43863i
$447$		0			0
$448$	1.43344	−	1.40591i	0.0677237	−	0.0664230i
$449$	−9.44876	+	10.0151i	−0.445915	+	0.472642i	−0.910871	−	0.412692i	$-0.864589\pi$
$449$	−9.44876	+	10.0151i	−0.445915	+	0.472642i	0.464956	+	0.885334i	$0.346070\pi$
$450$		0			0
$451$	−0.881224	+	2.94349i	−0.0414952	+	0.138604i
$452$	0.844406	−	1.33974i	0.0397175	−	0.0630161i
$453$		0			0
$454$	3.07624	+	3.01715i	0.144375	+	0.141602i
$455$	−3.21041	+	0.124578i	−0.150506	+	0.00584033i
$456$		0			0
$457$	2.90939	−	1.75582i	0.136095	−	0.0821340i	−0.447017	−	0.894525i	$-0.647514\pi$
$457$	2.90939	−	1.75582i	0.136095	−	0.0821340i	0.583113	+	0.812391i	$0.301835\pi$
$458$	3.32188	−	18.8393i	0.155221	−	0.880305i
$459$		0			0
$460$	0.905746	+	5.13674i	0.0422306	+	0.239502i
$461$	−1.86063	−	2.13204i	−0.0866581	−	0.0992992i	0.708469	−	0.705742i	$-0.249386\pi$
$461$	−1.86063	−	2.13204i	−0.0866581	−	0.0992992i	−0.795127	+	0.606443i	$0.792596\pi$
$462$		0			0
$463$	8.02280	+	6.21814i	0.372851	+	0.288981i	0.781742	−	0.623602i	$-0.214331\pi$
$463$	8.02280	+	6.21814i	0.372851	+	0.288981i	−0.408891	+	0.912583i	$0.634084\pi$
$464$	9.55517	+	0.742686i	0.443588	+	0.0344784i
$465$		0			0
$466$	−38.1478	−	34.6173i	−1.76716	−	1.60361i
$467$	22.2017	−	29.8220i	1.02737	−	1.38000i	0.104660	−	0.994508i	$-0.466625\pi$
$467$	22.2017	−	29.8220i	1.02737	−	1.38000i	0.922712	−	0.385491i	$-0.125968\pi$
$468$		0			0
$469$	−4.10001	+	9.50490i	−0.189321	+	0.438895i
$470$	12.6306	+	9.02784i	0.582608	+	0.416423i
$471$		0			0
$472$	−0.195453	+	10.0775i	−0.00899644	+	0.463854i
$473$	0.159754	+	0.466899i	0.00734550	+	0.0214680i
$474$		0			0
$475$	17.5445	−	1.36367i	0.804996	−	0.0625693i
$476$	1.86176	+	1.22450i	0.0853338	+	0.0561249i
$477$		0			0
$478$	−1.75790	−	0.882853i	−0.0804047	−	0.0403807i
$479$	4.72405	+	34.5862i	0.215848	+	1.58028i	0.705721	+	0.708490i	$0.250623\pi$
$479$	4.72405	+	34.5862i	0.215848	+	1.58028i	−0.489873	+	0.871794i	$0.662957\pi$
$480$		0			0
$481$	−20.3978	−	9.27193i	−0.930059	−	0.422763i
$482$	4.74807	+	1.52241i	0.216269	+	0.0693438i
$483$		0			0
$484$	−14.8934	−	2.32929i	−0.676973	−	0.105877i
$485$	12.1671			0.552481
$486$		0			0
$487$	−33.6675			−1.52562			−0.762809	−	0.646623i	$-0.776181\pi$
$487$	−33.6675			−1.52562			−0.762809	+	0.646623i	$0.776181\pi$
$488$	8.16283	+	1.27664i	0.369514	+	0.0577909i
$489$		0			0
$490$	−12.3861	−	3.97144i	−0.559546	−	0.179411i
$491$	−4.69980	−	2.13632i	−0.212099	−	0.0964107i	0.304944	−	0.952370i	$-0.401362\pi$
$491$	−4.69980	−	2.13632i	−0.212099	−	0.0964107i	−0.517043	+	0.855960i	$0.672967\pi$
$492$		0			0
$493$	0.602323	+	4.40978i	0.0271272	+	0.198607i
$494$	32.1557	+	16.1492i	1.44675	+	0.726587i
$495$		0			0
$496$	−8.07864	−	5.31341i	−0.362742	−	0.238579i
$497$	−3.03716	+	0.236067i	−0.136235	+	0.0105890i
$498$		0			0
$499$	−0.242251	−	0.708004i	−0.0108446	−	0.0316946i	0.940593	−	0.339536i	$-0.110270\pi$
$499$	−0.242251	−	0.708004i	−0.0108446	−	0.0316946i	−0.951438	+	0.307841i	$0.900393\pi$
$500$	0.262500	−	13.5344i	0.0117394	−	0.605279i
$501$		0			0
$502$	−38.8615	−	27.7765i	−1.73447	−	1.23973i
$503$	13.0092	−	30.1587i	0.580052	−	1.34471i	−0.335322	−	0.942104i	$-0.608845\pi$
$503$	13.0092	−	30.1587i	0.580052	−	1.34471i	0.915373	−	0.402607i	$-0.131896\pi$
$504$		0			0
$505$	2.88213	−	3.87138i	0.128253	−	0.172274i
$506$	−2.82832	−	2.56656i	−0.125734	−	0.114098i
$507$		0			0
$508$	−10.1873	−	0.791823i	−0.451990	−	0.0351315i
$509$	−24.3070	−	18.8393i	−1.07739	−	0.835039i	−0.0904122	−	0.995904i	$-0.528818\pi$
$509$	−24.3070	−	18.8393i	−1.07739	−	0.835039i	−0.986976	+	0.160865i	$0.948572\pi$
$510$		0			0
$511$	−3.67103	−	4.20653i	−0.162397	−	0.186086i
$512$	−3.86810	−	21.9371i	−0.170948	−	0.969492i
$513$		0			0
$514$	−9.76644	+	55.3882i	−0.430779	+	2.44307i
$515$	5.23643	−	3.16020i	0.230744	−	0.139255i
$516$		0			0
$517$	−4.71241	+	0.182863i	−0.207252	+	0.00804230i
$518$	4.89449	+	4.80048i	0.215051	+	0.210921i
$519$		0			0
$520$	−2.62862	+	4.17059i	−0.115273	+	0.182892i
$521$	1.18940	−	3.97287i	0.0521086	−	0.174055i	−0.927974	−	0.372645i	$-0.878451\pi$
$521$	1.18940	−	3.97287i	0.0521086	−	0.174055i	0.980083	+	0.198590i	$0.0636362\pi$
$522$		0			0
$523$	−13.8337	+	14.6628i	−0.604904	+	0.641161i	−0.955369	−	0.295415i	$-0.904542\pi$
$523$	−13.8337	+	14.6628i	−0.604904	+	0.641161i	0.350465	+	0.936576i	$0.386024\pi$
$524$	−11.3346	+	11.1169i	−0.495152	+	0.485642i
$525$		0			0
$526$	−12.6488	−	15.6821i	−0.551514	−	0.683770i
$527$	1.61733	−	4.18900i	0.0704522	−	0.182476i
$528$		0			0
$529$	−2.84881	−	11.0598i	−0.123861	−	0.480859i
$530$	−5.66678	−	1.34305i	−0.246149	−	0.0583384i
$531$		0			0
$532$	−3.13435	−	3.32222i	−0.135891	−	0.144036i
$533$	−21.4307	−	0.831610i	−0.928269	−	0.0360210i
$534$		0			0
$535$	16.2560	−	4.52516i	0.702807	−	0.195640i
$536$	8.46922	+	13.4373i	0.365815	+	0.580404i
$537$		0			0
$538$	−0.148612	−	7.66239i	−0.00640712	−	0.330349i
$539$	3.71278	−	1.35134i	0.159921	−	0.0582065i
$540$		0			0
$541$	−17.6496	−	6.42393i	−0.758816	−	0.276186i	−0.0665051	−	0.997786i	$-0.521185\pi$
$541$	−17.6496	−	6.42393i	−0.758816	−	0.276186i	−0.692310	+	0.721600i	$0.743407\pi$
$542$	7.15284	−	20.9050i	0.307241	−	0.897945i
$543$		0			0
$544$	14.0409	−	5.73635i	0.602000	−	0.245944i
$545$	6.20874	+	12.9845i	0.265953	+	0.556194i
$546$		0			0
$547$	43.4618	−	13.9355i	1.85829	−	0.595838i	0.862301	−	0.506396i	$-0.169023\pi$
$547$	43.4618	−	13.9355i	1.85829	−	0.595838i	0.995992	−	0.0894417i	$-0.0285083\pi$
$548$	−5.46102	−	0.638301i	−0.233283	−	0.0272669i
$549$		0			0
$550$	2.56789	+	3.44927i	0.109495	+	0.147078i
$551$	0.883164	−	9.07972i	0.0376240	−	0.386809i
$552$		0			0
$553$	−8.82730	−	5.32730i	−0.375375	−	0.226540i
$554$	29.3851	−	33.6716i	1.24845	−	1.43057i
$555$		0			0
$556$	−1.53825	+	3.21699i	−0.0652365	+	0.136431i
$557$	1.74125	−	29.8961i	0.0737790	−	1.26674i	−0.734773	−	0.678313i	$-0.762711\pi$
$557$	1.74125	−	29.8961i	0.0737790	−	1.26674i	0.808552	−	0.588424i	$-0.200252\pi$
$558$		0			0
$559$	−2.87783	+	1.89278i	−0.121719	+	0.0800561i
$560$	2.89161	−	2.24117i	0.122193	−	0.0947066i
$561$		0			0
$562$	−36.9159	+	26.3859i	−1.55721	+	1.11302i
$563$	−7.99190	−	36.8947i	−0.336818	−	1.55493i	−0.760636	−	0.649179i	$-0.775113\pi$
$563$	−7.99190	−	36.8947i	−0.336818	−	1.55493i	0.423817	−	0.905748i	$-0.360690\pi$
$564$		0			0
$565$	0.758026	−	0.939805i	0.0318904	−	0.0395379i
$566$	12.2570	+	21.2298i	0.515201	+	0.892354i
$567$		0			0
$568$	−2.33718	+	4.04812i	−0.0980660	+	0.169855i
$569$	3.01252	+	7.80263i	0.126292	+	0.327103i	0.981581	−	0.191048i	$-0.0611885\pi$
$569$	3.01252	+	7.80263i	0.126292	+	0.327103i	−0.855289	+	0.518151i	$0.826621\pi$
$570$		0			0
$571$	22.1842	−	20.1311i	0.928381	−	0.842461i	−0.0594115	−	0.998234i	$-0.518922\pi$
$571$	22.1842	−	20.1311i	0.928381	−	0.842461i	0.987793	+	0.155772i	$0.0497866\pi$
$572$	0.353142	+	3.63062i	0.0147656	+	0.151804i
$573$		0			0
$574$	6.07476	+	2.48181i	0.253555	+	0.103589i
$575$	−0.758054	−	13.0153i	−0.0316130	−	0.542775i
$576$		0			0
$577$	24.3331	−	12.2205i	1.01300	−	0.508748i	0.136750	−	0.990606i	$-0.456334\pi$
$577$	24.3331	−	12.2205i	1.01300	−	0.508748i	0.876249	+	0.481858i	$0.160038\pi$
$578$	−12.5257	−	18.2629i	−0.520999	−	0.759634i
$579$		0			0
$580$	−2.98742	−	0.586709i	−0.124046	−	0.0243618i
$581$	−7.90587	+	4.36228i	−0.327991	+	0.180978i
$582$		0			0
$583$	1.61045	−	0.732041i	0.0666982	−	0.0303180i
$584$	−8.50899	+	0.994558i	−0.352104	+	0.0411551i
$585$		0			0
$586$	−2.66961	−	6.18885i	−0.110281	−	0.255659i
$587$	−8.61095	+	39.7526i	−0.355412	+	1.64076i	0.353477	+	0.935443i	$0.384999\pi$
$587$	−8.61095	+	39.7526i	−0.355412	+	1.64076i	−0.708889	+	0.705320i	$0.750803\pi$
$588$		0			0
$589$	−5.20575	+	7.59018i	−0.214499	+	0.312748i
$590$	2.53333	−	18.5472i	0.104295	−	0.763577i
$591$		0			0
$592$	25.0357	−	4.91686i	1.02896	−	0.202082i
$593$	−4.80649	+	4.03313i	−0.197379	+	0.165621i	−0.736121	−	0.676850i	$-0.763344\pi$
$593$	−4.80649	+	4.03313i	−0.197379	+	0.165621i	0.538742	+	0.842471i	$0.318900\pi$
$594$		0			0
$595$	1.30147	+	1.09207i	0.0533552	+	0.0447704i
$596$	−27.3831	−	15.1093i	−1.12165	−	0.618903i
$597$		0			0
$598$	12.4241	−	23.5866i	0.508060	−	0.964528i
$599$	−6.47874	+	25.1520i	−0.264714	+	1.02768i	0.688463	+	0.725271i	$0.258286\pi$
$599$	−6.47874	+	25.1520i	−0.264714	+	1.02768i	−0.953177	+	0.302412i	$0.902208\pi$
$600$		0			0
$601$	−6.96845	−	13.2293i	−0.284249	−	0.539633i	0.700492	−	0.713660i	$-0.252964\pi$
$601$	−6.96845	−	13.2293i	−0.284249	−	0.539633i	−0.984741	+	0.174027i	$0.944322\pi$
$602$	1.02551	−	0.243051i	0.0417968	−	0.00990603i
$603$		0			0
$604$	2.53413	+	8.46458i	0.103112	+	0.344419i
$605$	−11.0722	−	3.08214i	−0.450147	−	0.125307i
$606$		0			0
$607$	−28.1141	+	4.39696i	−1.14111	+	0.178467i	−0.696706	−	0.717357i	$-0.745352\pi$
$607$	−28.1141	+	4.39696i	−1.14111	+	0.178467i	−0.444409	+	0.895824i	$0.646586\pi$
$608$	−30.7152	+	4.80376i	−1.24566	+	0.194818i
$609$		0			0
$610$	−14.7822	−	4.11492i	−0.598516	−	0.166608i
$611$	−9.44095	−	31.5350i	−0.381940	−	1.27577i
$612$		0			0
$613$	20.2538	−	4.80024i	0.818043	−	0.193880i	0.199770	−	0.979843i	$-0.435981\pi$
$613$	20.2538	−	4.80024i	0.818043	−	0.193880i	0.618274	+	0.785963i	$0.287832\pi$
$614$	−22.1385	−	42.0290i	−0.893438	−	1.69615i
$615$		0			0
$616$	−0.114292	+	0.443708i	−0.00460495	+	0.0178775i
$617$	0.764375	−	1.45113i	0.0307726	−	0.0584203i	−0.868893	−	0.495000i	$-0.835168\pi$
$617$	0.764375	−	1.45113i	0.0307726	−	0.0584203i	0.899666	+	0.436579i	$0.143810\pi$
$618$		0			0
$619$	−14.3250	−	7.90421i	−0.575771	−	0.317697i	0.168366	−	0.985725i	$-0.446151\pi$
$619$	−14.3250	−	7.90421i	−0.575771	−	0.317697i	−0.744136	+	0.668028i	$0.767139\pi$
$620$	2.35299	+	1.97439i	0.0944983	+	0.0792934i
$621$		0			0
$622$	−6.65780	+	5.58655i	−0.266953	+	0.224000i
$623$	−4.26098	+	0.836829i	−0.170713	+	0.0335269i
$624$		0			0
$625$	−1.19575	+	8.75441i	−0.0478298	+	0.350176i
$626$	−24.1345	+	35.1890i	−0.964610	+	1.40644i
$627$		0			0
$628$	4.53081	−	20.9165i	0.180799	−	0.834660i
$629$	4.69295	+	10.8795i	0.187120	+	0.433793i
$630$		0			0
$631$	5.50988	−	0.644012i	0.219345	−	0.0256377i	−0.00571067	−	0.999984i	$-0.501818\pi$
$631$	5.50988	−	0.644012i	0.219345	−	0.0256377i	0.225055	+	0.974346i	$0.427744\pi$
$632$	−14.4023	+	6.54663i	−0.572891	+	0.260411i
$633$		0			0
$634$	29.7538	−	16.4175i	1.18167	−	0.652021i
$635$	−7.64448	−	1.50133i	−0.303362	−	0.0595783i
$636$		0			0
$637$	15.5988	+	22.7436i	0.618046	+	0.901132i
$638$	1.99211	−	1.00048i	0.0788685	−	0.0396093i
$639$		0			0
$640$	−0.518229	−	8.89765i	−0.0204848	−	0.351710i
$641$	−16.9593	−	6.92862i	−0.669851	−	0.273664i	0.0176538	−	0.999844i	$-0.494380\pi$
$641$	−16.9593	−	6.92862i	−0.669851	−	0.273664i	−0.687505	+	0.726180i	$0.741294\pi$
$642$		0			0
$643$	0.595554	+	6.12283i	0.0234863	+	0.241461i	0.999697	+	0.0246343i	$0.00784215\pi$
$643$	0.595554	+	6.12283i	0.0234863	+	0.241461i	−0.976210	+	0.216826i	$0.930429\pi$
$644$	−2.50589	+	2.27397i	−0.0987459	+	0.0896071i
$645$		0			0
$646$	−6.85347	−	17.7509i	−0.269646	−	0.698401i
$647$	−19.5199	+	33.8095i	−0.767408	+	1.32919i	0.171557	+	0.985174i	$0.445120\pi$
$647$	−19.5199	+	33.8095i	−0.767408	+	1.32919i	−0.938964	+	0.344015i	$0.888213\pi$
$648$		0			0
$649$	2.84310	+	4.92440i	0.111602	+	0.193300i
$650$	−18.8442	+	23.3632i	−0.739131	+	0.916379i
$651$		0			0
$652$	−3.55714	−	16.4216i	−0.139308	−	0.643119i
$653$	39.4245	−	28.1789i	1.54280	−	1.10273i	0.586654	−	0.809838i	$-0.300445\pi$
$653$	39.4245	−	28.1789i	1.54280	−	1.10273i	0.956146	−	0.292889i	$-0.0946168\pi$
$654$		0			0
$655$	−9.56729	+	7.41521i	−0.373825	+	0.289736i
$656$	20.4039	−	13.4199i	0.796640	−	0.523958i
$657$		0			0
$658$	−0.585633	+	10.0549i	−0.0228304	+	0.391982i
$659$	−8.84896	+	18.5060i	−0.344707	+	0.720893i	−0.999387	−	0.0350131i	$-0.988853\pi$
$659$	−8.84896	+	18.5060i	−0.344707	+	0.720893i	0.654680	+	0.755906i	$0.272803\pi$
$660$		0			0
$661$	11.7688	−	13.4855i	0.457752	−	0.524526i	−0.477441	−	0.878664i	$-0.658436\pi$
$661$	11.7688	−	13.4855i	0.457752	−	0.524526i	0.935193	+	0.354138i	$0.115226\pi$
$662$	42.7711	+	25.8125i	1.66235	+	1.00323i
$663$		0			0
$664$	−1.34133	+	13.7901i	−0.0520537	+	0.535159i
$665$	−2.07949	−	2.79324i	−0.0806393	−	0.108317i
$666$		0			0
$667$	−6.71291	−	0.784627i	−0.259925	−	0.0303809i
$668$	11.2973	−	3.62233i	0.437105	−	0.140152i
$669$		0			0
$670$	−12.7255	−	26.6131i	−0.491628	−	1.02815i
$671$	4.31478	−	1.76278i	0.166570	−	0.0680514i
$672$		0			0
$673$	13.5326	−	39.5507i	0.521645	−	1.52457i	−0.299642	−	0.954052i	$-0.596867\pi$
$673$	13.5326	−	39.5507i	0.521645	−	1.52457i	0.821288	−	0.570514i	$-0.193256\pi$
$674$	−21.3122	−	7.75700i	−0.820915	−	0.298789i
$675$		0			0
$676$	−6.60492	+	2.40399i	−0.254035	+	0.0924613i
$677$	−0.229944	−	11.8558i	−0.00883746	−	0.455657i	−0.977927	−	0.208947i	$-0.932996\pi$
$677$	−0.229944	−	11.8558i	−0.00883746	−	0.455657i	0.969089	−	0.246710i	$-0.0793494\pi$
$678$		0			0
$679$	4.20878	+	6.67769i	0.161518	+	0.256266i
$680$	2.51144	−	0.699106i	0.0963092	−	0.0268095i
$681$		0			0
$682$	−2.24740	−	0.0872093i	−0.0860574	−	0.00333942i
$683$	−20.6159	−	21.8515i	−0.788844	−	0.836126i	0.200805	−	0.979631i	$-0.435644\pi$
$683$	−20.6159	−	21.8515i	−0.788844	−	0.836126i	−0.989650	+	0.143505i	$0.954163\pi$
$684$		0			0
$685$	−4.07897	−	0.966733i	−0.155849	−	0.0369370i
$686$	−4.36883	−	16.9609i	−0.166803	−	0.647569i
$687$		0			0
$688$	1.41271	−	3.65901i	0.0538590	−	0.139498i
$689$	7.75220	+	9.61122i	0.295335	+	0.366158i
$690$		0			0
$691$	1.23755	−	1.21378i	0.0470785	−	0.0461743i	−0.676297	−	0.736629i	$-0.736417\pi$
$691$	1.23755	−	1.21378i	0.0470785	−	0.0461743i	0.723376	+	0.690454i	$0.242589\pi$
$692$	18.7115	−	19.8330i	0.711304	−	0.753939i
$693$		0			0
$694$	8.64269	−	28.8686i	0.328072	−	1.09584i
$695$	−1.44962	+	2.29997i	−0.0549871	+	0.0872429i
$696$		0			0
$697$	8.09681	+	7.94130i	0.306689	+	0.300798i
$698$	−54.7438	+	2.12431i	−2.07208	+	0.0804063i
$699$		0			0
$700$	3.26196	−	1.96860i	0.123291	−	0.0744062i
$701$	−1.88777	+	10.7061i	−0.0713000	+	0.404363i	0.928180	+	0.372131i	$0.121373\pi$
$701$	−1.88777	+	10.7061i	−0.0713000	+	0.404363i	−0.999480	+	0.0322320i	$0.989738\pi$
$702$		0			0
$703$	−4.21715	−	23.9167i	−0.159053	−	0.902034i
$704$	−1.14280	−	1.30950i	−0.0430708	−	0.0493537i
$705$		0			0
$706$	45.4276	+	35.2091i	1.70969	+	1.32511i
$707$	3.12170	+	0.242638i	0.117404	+	0.00912533i
$708$		0			0
$709$	−34.9482	−	31.7138i	−1.31251	−	1.19104i	−0.967625	−	0.252392i	$-0.918783\pi$
$709$	−34.9482	−	31.7138i	−1.31251	−	1.19104i	−0.344883	−	0.938646i	$-0.612081\pi$
$710$	5.18407	−	6.96342i	0.194555	−	0.261332i
$711$		0			0
$712$	−2.63911	+	6.11814i	−0.0989047	+	0.229287i
$713$	5.54747	+	3.96509i	0.207754	+	0.148494i
$714$		0			0
$715$	−0.0539300	+	2.78061i	−0.00201687	+	0.103989i
$716$	5.07356	+	14.8280i	0.189608	+	0.554149i
$717$		0			0
$718$	−18.1257	+	1.40884i	−0.676446	+	0.0525775i
$719$	18.4532	+	12.1368i	0.688186	+	0.452627i	0.844835	−	0.535027i	$-0.179699\pi$
$719$	18.4532	+	12.1368i	0.688186	+	0.452627i	−0.156648	+	0.987654i	$0.550069\pi$
$720$		0			0
$721$	3.54577	+	1.78075i	0.132051	+	0.0663187i
$722$	0.524396	+	3.83926i	0.0195160	+	0.142882i
$723$		0			0
$724$	19.2943	+	8.77035i	0.717068	+	0.325948i
$725$	7.24631	+	2.32343i	0.269121	+	0.0862902i
$726$		0			0
$727$	32.8130	+	5.13187i	1.21697	+	0.190330i	0.730220	−	0.683212i	$-0.239418\pi$
$727$	32.8130	+	5.13187i	1.21697	+	0.190330i	0.486748	+	0.873542i	$0.338183\pi$
$728$	−3.19822			−0.118534
$729$		0			0
$730$	15.9105			0.588873
$731$	1.79959	+	0.281450i	0.0665601	+	0.0104098i
$732$		0			0
$733$	26.4264	+	8.47328i	0.976081	+	0.312968i	0.750218	−	0.661191i	$-0.229949\pi$
$733$	26.4264	+	8.47328i	0.976081	+	0.312968i	0.225864	+	0.974159i	$0.427480\pi$
$734$	−59.9167	−	27.2355i	−2.21157	−	1.00528i
$735$		0			0
$736$	3.11702	+	22.8206i	0.114895	+	0.841178i
$737$	8.00750	+	4.02152i	0.294960	+	0.148135i
$738$		0			0
$739$	30.7497	+	20.2244i	1.13115	+	0.743968i	0.970034	−	0.242968i	$-0.0781211\pi$
$739$	30.7497	+	20.2244i	1.13115	+	0.743968i	0.161114	+	0.986936i	$0.448491\pi$
$740$	−8.08049	+	0.628066i	−0.297045	+	0.0230881i
$741$		0			0
$742$	−1.22311	−	3.57468i	−0.0449019	−	0.131231i
$743$	−0.0535603	+	2.76155i	−0.00196494	+	0.101312i	0.997545	+	0.0700222i	$0.0223070\pi$
$743$	−0.0535603	+	2.76155i	−0.00196494	+	0.101312i	−0.999510	+	0.0312894i	$0.990039\pi$
$744$		0			0
$745$	−19.3990	−	13.8656i	−0.710725	−	0.507995i
$746$	−17.7985	+	41.2616i	−0.651651	+	1.51070i
$747$		0			0
$748$	1.15189	−	1.54725i	0.0421171	−	0.0565731i
$749$	8.10672	+	7.35646i	0.296213	+	0.268799i
$750$		0			0
$751$	−30.2557	−	2.35166i	−1.10405	−	0.0858133i	−0.487494	−	0.873127i	$-0.662089\pi$
$751$	−30.2557	−	2.35166i	−1.10405	−	0.0858133i	−0.616553	+	0.787313i	$0.711471\pi$
$752$	29.6268	+	22.9625i	1.08038	+	0.837356i
$753$		0			0
$754$	10.2312	+	11.7237i	0.372598	+	0.426950i
$755$	1.16980	+	6.63427i	0.0425734	+	0.241446i
$756$		0			0
$757$	0.857698	−	4.86425i	0.0311736	−	0.176794i	−0.965246	−	0.261344i	$-0.915834\pi$
$757$	0.857698	−	4.86425i	0.0311736	−	0.176794i	0.996419	+	0.0845502i	$0.0269453\pi$
$758$	12.3597	−	7.45909i	0.448923	−	0.270927i
$759$		0			0
$760$	−5.33934	+	0.207191i	−0.193678	+	0.00751560i
$761$	24.4153	+	23.9463i	0.885053	+	0.868054i	0.992003	−	0.126210i	$-0.0402815\pi$
$761$	24.4153	+	23.9463i	0.885053	+	0.868054i	−0.106950	+	0.994264i	$0.534109\pi$
$762$		0			0
$763$	−4.97859	+	7.89906i	−0.180237	+	0.285965i
$764$	3.61481	−	12.0743i	0.130779	−	0.436833i
$765$		0			0
$766$	12.5007	−	13.2500i	0.451670	−	0.478742i
$767$	−28.3361	+	27.7918i	−1.02316	+	1.00351i
$768$		0			0
$769$	2.33974	+	2.90083i	0.0843733	+	0.104606i	0.818792	−	0.574090i	$-0.194644\pi$
$769$	2.33974	+	2.90083i	0.0843733	+	0.104606i	−0.734419	+	0.678696i	$0.762545\pi$
$770$	0.306494	−	0.793841i	0.0110453	−	0.0286080i
$771$		0			0
$772$	−1.91072	−	7.41786i	−0.0687682	−	0.266975i
$773$	−51.0391	−	12.0965i	−1.83575	−	0.435080i	−0.841323	−	0.540532i	$-0.818223\pi$
$773$	−51.0391	−	12.0965i	−1.83575	−	0.435080i	−0.994424	+	0.105452i	$0.966371\pi$
$774$		0			0
$775$	−5.26861	−	5.58440i	−0.189254	−	0.200597i
$776$	12.1027	+	0.469641i	0.434462	+	0.0168591i
$777$		0			0
$778$	15.5990	−	4.34227i	0.559250	−	0.155678i
$779$	−12.3948	−	19.6656i	−0.444089	−	0.704595i
$780$		0			0
$781$	0.0511351	+	2.63651i	0.00182976	+	0.0943418i
$782$	−13.2471	+	4.82154i	−0.473714	+	0.172418i
$783$		0			0
$784$	−29.5101	−	10.7408i	−1.05393	−	0.383600i
$785$	5.28241	−	15.4384i	0.188537	−	0.551021i
$786$		0			0
$787$	1.45708	−	0.595283i	0.0519393	−	0.0212196i	−0.352081	−	0.935969i	$-0.614526\pi$
$787$	1.45708	−	0.595283i	0.0519393	−	0.0212196i	0.404021	+	0.914750i	$0.367612\pi$
$788$	−13.1872	−	27.5786i	−0.469773	−	0.982448i
$789$		0			0
$790$	27.9785	−	8.97095i	0.995431	−	0.319172i
$791$	0.778006	+	0.0909359i	0.0276627	+	0.00323331i
$792$		0			0
$793$	19.4280	+	26.0963i	0.689909	+	0.926708i
$794$	−0.504278	+	5.18443i	−0.0178961	+	0.183988i
$795$		0			0
$796$	−27.7206	−	16.7295i	−0.982531	−	0.592961i
$797$	11.7771	−	13.4950i	0.417165	−	0.478018i	−0.505938	−	0.862570i	$-0.668854\pi$
$797$	11.7771	−	13.4950i	0.417165	−	0.478018i	0.923104	+	0.384551i	$0.125644\pi$
$798$		0			0
$799$	−7.50917	+	15.7041i	−0.265656	+	0.555571i
$800$	1.50786	−	25.8890i	0.0533109	−	0.915313i
$801$		0			0
$802$	−46.3546	+	30.4879i	−1.63684	+	1.07656i
$803$	−3.81993	+	2.96067i	−0.134803	+	0.104480i
$804$		0			0
$805$	−2.09891	+	1.50021i	−0.0739768	+	0.0528754i
$806$	−3.32351	−	15.3430i	−0.117066	−	0.540436i
$807$		0			0
$808$	3.01631	−	3.73964i	0.106113	−	0.131560i
$809$	22.5895	+	39.1261i	0.794204	+	1.37560i	0.923343	+	0.383975i	$0.125445\pi$
$809$	22.5895	+	39.1261i	0.794204	+	1.37560i	−0.129139	+	0.991626i	$0.541221\pi$
$810$		0			0
$811$	21.7211	−	37.6220i	0.762731	−	1.32109i	−0.178707	−	0.983902i	$-0.557191\pi$
$811$	21.7211	−	37.6220i	0.762731	−	1.32109i	0.941438	−	0.337186i	$-0.109475\pi$
$812$	−0.711386	−	1.84254i	−0.0249648	−	0.0646604i
$813$		0			0
$814$	4.39479	−	3.98806i	0.154037	−	0.139781i
$815$	−1.24021	−	12.7504i	−0.0434425	−	0.446628i
$816$		0			0
$817$	−3.45611	−	1.41198i	−0.120914	−	0.0493988i
$818$	1.83247	+	31.4623i	0.0640709	+	1.10005i
$819$		0			0
$820$	−6.93267	+	3.48172i	−0.242099	+	0.121587i
$821$	22.0785	+	32.1912i	0.770545	+	1.12348i	0.989041	+	0.147644i	$0.0471689\pi$
$821$	22.0785	+	32.1912i	0.770545	+	1.12348i	−0.218496	+	0.975838i	$0.570115\pi$
$822$		0			0
$823$	16.3716	+	3.21528i	0.570678	+	0.112078i	0.469724	−	0.882813i	$-0.344354\pi$
$823$	16.3716	+	3.21528i	0.570678	+	0.112078i	0.100955	+	0.994891i	$0.467810\pi$
$824$	5.33069	−	2.94135i	0.185703	−	0.102467i
$825$		0			0
$826$	11.0556	−	5.02539i	0.384674	−	0.174856i
$827$	8.97669	−	1.04923i	0.312150	−	0.0364851i	0.0414245	−	0.999142i	$-0.486810\pi$
$827$	8.97669	−	1.04923i	0.312150	−	0.0364851i	0.270726	+	0.962657i	$0.412736\pi$
$828$		0			0
$829$	−8.19570	−	18.9998i	−0.284649	−	0.659890i	0.714564	−	0.699570i	$-0.246625\pi$
$829$	−8.19570	−	18.9998i	−0.284649	−	0.659890i	−0.999212	+	0.0396807i	$0.987366\pi$
$830$	5.44752	−	25.1486i	0.189086	−	0.872920i
$831$		0			0
$832$	6.86177	−	10.0047i	0.237889	−	0.346851i
$833$	1.97364	−	14.4496i	0.0683826	−	0.500650i
$834$		0			0
$835$	8.87570	−	1.74313i	0.307156	−	0.0603235i
$836$	−3.02873	+	2.54140i	−0.104751	+	0.0878963i
$837$		0			0
$838$	26.6132	+	22.3311i	0.919338	+	0.771416i
$839$	9.03175	+	4.98351i	0.311811	+	0.172050i	0.631297	−	0.775541i	$-0.282523\pi$
$839$	9.03175	+	4.98351i	0.311811	+	0.172050i	−0.319487	+	0.947591i	$0.603510\pi$
$840$		0			0
$841$	−11.6768	+	22.1678i	−0.402647	+	0.764407i
$842$	−5.89088	+	22.8698i	−0.203013	+	0.788145i
$843$		0			0
$844$	−6.36754	−	12.0885i	−0.219180	−	0.416103i
$845$	−5.21449	+	1.23586i	−0.179384	+	0.0425148i
$846$		0			0
$847$	−2.13844	−	7.14289i	−0.0734777	−	0.245433i
$848$	−13.5456	−	3.77068i	−0.465158	−	0.129486i
$849$		0			0
$850$	15.6818	−	2.45259i	0.537881	−	0.0841230i
$851$	−17.7763	+	2.78017i	−0.609365	+	0.0953029i
$852$		0			0
$853$	51.8694	+	14.4388i	1.77597	+	0.494376i	0.991980	−	0.126394i	$-0.0403403\pi$
$853$	51.8694	+	14.4388i	1.77597	+	0.494376i	0.783993	+	0.620770i	$0.213180\pi$
$854$	−2.85500	−	9.53636i	−0.0976960	−	0.326327i
$855$		0			0
$856$	16.3446	−	3.87374i	0.558647	−	0.132402i
$857$	0.398712	+	0.756936i	0.0136197	+	0.0258564i	0.891477	−	0.453066i	$-0.149670\pi$
$857$	0.398712	+	0.756936i	0.0136197	+	0.0258564i	−0.877857	+	0.478922i	$0.841028\pi$
$858$		0			0
$859$	9.04347	−	35.1089i	0.308559	−	1.19790i	−0.606666	−	0.794957i	$-0.707493\pi$
$859$	9.04347	−	35.1089i	0.308559	−	1.19790i	0.915225	−	0.402943i	$-0.132013\pi$
$860$	−0.580670	+	1.10237i	−0.0198007	+	0.0375907i
$861$		0			0
$862$	−12.4677	−	6.87939i	−0.424652	−	0.234313i
$863$	25.8582	+	21.6976i	0.880224	+	0.738596i	0.966225	−	0.257699i	$-0.0829644\pi$
$863$	25.8582	+	21.6976i	0.880224	+	0.738596i	−0.0860011	+	0.996295i	$0.527409\pi$
$864$		0			0
$865$	15.9251	−	13.3628i	0.541470	−	0.454347i
$866$	7.79280	−	1.53046i	0.264810	−	0.0520070i
$867$		0			0
$868$	−0.269674	+	1.97436i	−0.00915333	+	0.0670142i
$869$	−5.04800	+	7.36017i	−0.171242	+	0.249677i
$870$		0			0
$871$	−13.2412	+	61.1284i	−0.448662	+	2.07126i
$872$	5.67469	+	13.1554i	0.192169	+	0.445498i
$873$		0			0
$874$	28.6994	−	3.35448i	0.970773	−	0.113467i
$875$	6.09549	−	2.77074i	0.206065	−	0.0936681i
$876$		0			0
$877$	−33.7022	+	18.5961i	−1.13804	+	0.627945i	−0.936198	−	0.351472i	$-0.885681\pi$
$877$	−33.7022	+	18.5961i	−1.13804	+	0.627945i	−0.201844	+	0.979418i	$0.564693\pi$
$878$	8.74841	+	1.71813i	0.295245	+	0.0579841i
$879$		0			0
$880$	−1.79121	−	2.61165i	−0.0603818	−	0.0880388i
$881$	−47.7632	+	23.9876i	−1.60918	+	0.808162i	−0.609299	+	0.792941i	$0.708549\pi$
$881$	−47.7632	+	23.9876i	−1.60918	+	0.808162i	−0.999884	+	0.0152213i	$0.995155\pi$
$882$		0			0
$883$	−1.20820	−	20.7440i	−0.0406592	−	0.698091i	−0.955630	−	0.294571i	$-0.904823\pi$
$883$	−1.20820	−	20.7440i	−0.0406592	−	0.698091i	0.914971	−	0.403521i	$-0.132214\pi$
$884$	12.4642	+	5.09217i	0.419215	+	0.171268i
$885$		0			0
$886$	6.91583	+	71.1010i	0.232342	+	2.38868i
$887$	−15.0247	+	13.6342i	−0.504479	+	0.457790i	−0.884063	−	0.467367i	$-0.845203\pi$
$887$	−15.0247	+	13.6342i	−0.504479	+	0.457790i	0.379585	+	0.925157i	$0.376067\pi$
$888$		0			0
$889$	−1.82036	−	4.71486i	−0.0610530	−	0.158131i
$890$	6.18733	−	10.7168i	0.207400	−	0.359227i
$891$		0			0
$892$	−14.9683	−	25.9258i	−0.501174	−	0.868059i
$893$	22.3997	−	27.7713i	0.749577	−	0.929330i
$894$		0			0
$895$	2.52959	+	11.6779i	0.0845549	+	0.390349i
$896$	4.70404	−	3.36224i	0.157151	−	0.112325i
$897$		0			0
$898$	20.1197	−	15.5939i	0.671403	−	0.520376i
$899$	−3.32527	+	2.18707i	−0.110904	+	0.0729427i
$900$		0			0
$901$	0.379665	−	6.51860i	0.0126485	−	0.217166i
$902$	2.45047	−	5.12472i	0.0815916	−	0.170634i
$903$		0			0
$904$	0.790290	−	0.905572i	0.0262846	−	0.0301189i
$905$	13.8347	+	8.34931i	0.459882	+	0.277540i
$906$		0			0
$907$	−5.61145	+	57.6907i	−0.186325	+	1.91559i	0.177498	+	0.984121i	$0.443200\pi$
$907$	−5.61145	+	57.6907i	−0.186325	+	1.91559i	−0.363823	+	0.931468i	$0.618529\pi$
$908$	−1.97344	−	2.65078i	−0.0654908	−	0.0879694i
$909$		0			0
$910$	5.89958	+	0.689562i	0.195569	+	0.0228587i
$911$	−7.07949	+	2.26995i	−0.234554	+	0.0752067i	−0.420279	−	0.907395i	$-0.638068\pi$
$911$	−7.07949	+	2.26995i	−0.234554	+	0.0752067i	0.185725	+	0.982602i	$0.440537\pi$
$912$		0			0
$913$	3.37184	+	7.05160i	0.111591	+	0.233374i
$914$	−5.81574	+	2.37599i	−0.192368	+	0.0785909i
$915$		0			0
$916$	−4.74976	+	13.8817i	−0.156936	+	0.458664i
$917$	−7.37916	−	2.68579i	−0.243681	−	0.0886927i
$918$		0			0
$919$	−18.7154	+	6.81184i	−0.617364	+	0.224702i	−0.631722	−	0.775195i	$-0.717652\pi$
$919$	−18.7154	+	6.81184i	−0.617364	+	0.224702i	0.0143585	+	0.999897i	$0.495429\pi$
$920$	0.0767649	+	3.95798i	0.00253086	+	0.130491i
$921$		0			0
$922$	2.78948	+	4.42582i	0.0918668	+	0.145757i
$923$	−17.7324	+	4.93614i	−0.583668	+	0.162475i
$924$		0			0
$925$	20.2429	+	0.785515i	0.665581	+	0.0258276i
$926$	−12.8778	−	13.6496i	−0.423190	−	0.448555i
$927$		0			0
$928$	−13.0813	−	3.10033i	−0.429415	−	0.101773i
$929$	−2.62074	−	10.1743i	−0.0859838	−	0.333809i	0.910906	−	0.412613i	$-0.135384\pi$
$929$	−2.62074	−	10.1743i	−0.0859838	−	0.333809i	−0.996890	+	0.0788036i	$0.974890\pi$
$930$		0			0
$931$	−10.7665	+	27.8858i	−0.352857	+	0.913922i
$932$	24.8037	+	30.7518i	0.812473	+	1.00731i
$933$		0			0
$934$	−49.0718	+	48.1293i	−1.60568	+	1.57484i
$935$	1.00924	−	1.06973i	0.0330057	−	0.0349840i
$936$		0			0
$937$	1.63789	−	5.47092i	0.0535074	−	0.178727i	−0.927059	−	0.374916i	$-0.877671\pi$
$937$	1.63789	−	5.47092i	0.0535074	−	0.178727i	0.980566	+	0.196189i	$0.0628567\pi$
$938$	10.2042	−	16.1900i	0.333177	−	0.528622i
$939$		0			0
$940$	−8.50089	−	8.33761i	−0.277268	−	0.271943i
$941$	42.3718	−	1.64422i	1.38128	−	0.0536000i	0.662617	−	0.748958i	$-0.269446\pi$
$941$	42.3718	−	1.64422i	1.38128	−	0.0536000i	0.718663	+	0.695358i	$0.244754\pi$
$942$		0			0
$943$	−14.7450	+	8.89863i	−0.480162	+	0.289779i
$944$	7.84810	−	44.5088i	0.255434	−	1.44864i
$945$		0			0
$946$	−0.158422	−	0.898454i	−0.00515073	−	0.0292113i
$947$	21.0407	+	24.1099i	0.683730	+	0.783468i	0.985457	−	0.169927i	$-0.0543531\pi$
$947$	21.0407	+	24.1099i	0.683730	+	0.783468i	−0.301726	+	0.953395i	$0.597563\pi$
$948$		0			0
$949$	−26.6635	−	20.6658i	−0.865535	−	0.670840i
$950$	−32.4355	−	2.52109i	−1.05235	−	0.0817950i
$951$		0			0
$952$	1.25243	+	1.13652i	0.0405916	+	0.0368349i
$953$	−10.1014	+	13.5686i	−0.327217	+	0.439529i	−0.935039	−	0.354545i	$-0.884636\pi$
$953$	−10.1014	+	13.5686i	−0.327217	+	0.439529i	0.607822	+	0.794073i	$0.292043\pi$
$954$		0			0
$955$	3.80611	−	8.82355i	0.123163	−	0.285523i
$956$	1.22741	+	0.877302i	0.0396974	+	0.0283740i
$957$		0			0
$958$	1.25142	−	64.5231i	0.0404317	−	2.08465i
$959$	−0.880401	−	2.57307i	−0.0284296	−	0.0830887i
$960$		0			0
$961$	−26.9034	+	2.09109i	−0.867850	+	0.0674547i
$962$	34.6090	+	22.7627i	1.11584	+	0.733899i
$963$		0			0
$964$	−3.41740	−	1.71628i	−0.110067	−	0.0552777i
$965$	−0.790358	−	5.78644i	−0.0254425	−	0.186272i
$966$		0			0
$967$	0.271535	+	0.123428i	0.00873199	+	0.00396918i	0.418172	−	0.908368i	$-0.362671\pi$
$967$	0.271535	+	0.123428i	0.00873199	+	0.00396918i	−0.409440	+	0.912337i	$0.634276\pi$
$968$	−10.8946	−	3.49321i	−0.350165	−	0.112276i
$969$		0			0
$970$	−22.2239	−	3.47576i	−0.713568	−	0.111600i
$971$	−36.8154			−1.18146			−0.590731	−	0.806868i	$-0.701161\pi$
$971$	−36.8154			−1.18146			−0.590731	+	0.806868i	$0.701161\pi$
$972$		0			0
$973$	−1.76374			−0.0565429
$974$	61.4955	+	9.61772i	1.97044	+	0.308172i
$975$		0			0
$976$	−35.2776	−	11.3113i	−1.12921	−	0.362066i
$977$	36.4183	+	16.5541i	1.16512	+	0.529614i	0.900551	−	0.434751i	$-0.143164\pi$
$977$	36.4183	+	16.5541i	1.16512	+	0.529614i	0.264574	+	0.964365i	$0.414769\pi$
$978$		0			0
$979$	0.508699	+	3.72434i	0.0162581	+	0.119030i
$980$	8.91481	+	4.47718i	0.284773	+	0.143018i
$981$		0			0
$982$	7.97416	+	5.24469i	0.254466	+	0.167365i
$983$	44.9596	−	3.49453i	1.43399	−	0.111458i	0.663148	−	0.748488i	$-0.269220\pi$
$983$	44.9596	−	3.49453i	1.43399	−	0.111458i	0.770839	+	0.637030i	$0.219837\pi$
$984$		0			0
$985$	−7.54520	−	22.0517i	−0.240410	−	0.702625i
$986$	0.159558	−	8.22678i	0.00508137	−	0.261994i
$987$		0			0
$988$	−22.4519	−	16.0477i	−0.714290	−	0.510544i
$989$	−1.09554	+	2.53975i	−0.0348362	+	0.0807595i
$990$		0			0
$991$	−0.903804	+	1.21402i	−0.0287103	+	0.0385646i	−0.816247	−	0.577704i	$-0.803949\pi$
$991$	−0.903804	+	1.21402i	−0.0287103	+	0.0385646i	0.787536	+	0.616268i	$0.211356\pi$
$992$	10.0443	+	9.11475i	0.318908	+	0.289394i
$993$		0			0
$994$	5.61498	+	0.436431i	0.178096	+	0.0138427i
$995$	−19.5112	−	15.1223i	−0.618547	−	0.479410i
$996$		0			0
$997$	19.9004	+	22.8033i	0.630252	+	0.722189i	0.976395	−	0.215993i	$-0.0692989\pi$
$997$	19.9004	+	22.8033i	0.630252	+	0.722189i	−0.346143	+	0.938182i	$0.612509\pi$
$998$	0.240230	+	1.36241i	0.00760435	+	0.0431264i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.4		1404
3.2	odd	2		243.2.i.a.13.23	✓	1404
243.56	odd	162		243.2.i.a.187.23	yes	1404
243.187	even	81	inner	729.2.i.a.73.4		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.23	✓	1404	3.2	odd	2
243.2.i.a.187.23	yes	1404	243.56	odd	162
729.2.i.a.10.4		1404	1.1	even	1	trivial
729.2.i.a.73.4		1404	243.187	even	81	inner

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.82656 - 0.285668i) q^{2} +(1.35020 + 0.432926i) q^{4} +(0.984150 + 0.447351i) q^{5} +(0.0949117 + 0.694877i) q^{7} +(0.961673 + 0.482970i) q^{8} +(-1.66981 - 1.09825i) q^{10} +(0.605270 - 0.0470453i) q^{11} +(1.37185 + 4.00939i) q^{13} +(0.0251426 - 1.29634i) q^{14} +(-3.92567 - 2.80590i) q^{16} +(0.887557 - 2.05759i) q^{17} +(-2.74277 + 3.68418i) q^{19} +(1.13513 + 1.03008i) q^{20} +(-1.11900 - 0.0869755i) q^{22} +(2.68957 + 2.08457i) q^{23} +(-2.51918 - 2.88666i) q^{25} +(-1.36041 - 7.71526i) q^{26} +(-0.172680 + 0.979315i) q^{28} +(-1.70050 + 1.02626i) q^{29} +(2.00236 - 0.0777008i) q^{31} +(4.83233 + 4.73951i) q^{32} +(-2.20896 + 3.50475i) q^{34} +(-0.217446 + 0.726322i) q^{35} +(-3.62850 + 3.84598i) q^{37} +(6.06227 - 5.94584i) q^{38} +(0.730373 + 0.905521i) q^{40} +(-1.82290 + 4.72142i) q^{41} +(0.202757 + 0.787149i) q^{43} +(0.837605 + 0.198516i) q^{44} +(-4.31715 - 4.57592i) q^{46} +(-7.76222 - 0.301210i) q^{47} +(6.26975 - 1.74530i) q^{49} +(3.77679 + 5.99229i) q^{50} +(0.116513 + 6.00740i) q^{52} +(2.73818 - 0.996617i) q^{53} +(0.616722 + 0.224469i) q^{55} +(-0.244331 + 0.714084i) q^{56} +(3.39922 - 1.38874i) q^{58} +(4.04047 + 8.44992i) q^{59} +(7.31088 - 2.34414i) q^{61} +(-3.67962 - 0.430086i) q^{62} +(-1.70959 - 2.29638i) q^{64} +(-0.443496 + 4.55954i) q^{65} +(12.6369 + 7.62639i) q^{67} +(2.08917 - 2.39392i) q^{68} +(0.604665 - 1.26455i) q^{70} +(-0.252560 + 4.33629i) q^{71} +(-6.65114 + 4.37452i) q^{73} +(7.72632 - 5.98835i) q^{74} +(-5.29827 + 3.78698i) q^{76} +(0.0901379 + 0.416123i) q^{77} +(-9.22948 + 11.4428i) q^{79} +(-2.60823 - 4.51758i) q^{80} +(4.67838 - 8.10320i) q^{82} +(4.63725 + 12.0108i) q^{83} +(1.79395 - 1.62792i) q^{85} +(-0.145483 - 1.49569i) q^{86} +(0.604794 + 0.247085i) q^{88} +(0.360012 + 6.18117i) q^{89} +(-2.65582 + 1.33381i) q^{91} +(2.72900 + 3.97898i) q^{92} +(14.0921 + 2.76760i) q^{94} +(-4.34742 + 2.39880i) q^{95} +(10.2460 - 4.65740i) q^{97} +(-11.9506 + 1.39683i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26}+ \cdots - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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