LMFDB - Embedded newform 297.2.t.a.233.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] 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("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			233.10
Character	$\chi$	$=$	297.233
Dual form			297.2.t.a.116.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.43736 - 0.518076i) q^{2} +(3.84522 - 1.71200i) q^{4} +(0.293969 - 1.38302i) q^{5} +(-3.11261 - 0.327148i) q^{7} +(4.45339 - 3.23558i) q^{8} -3.52320i q^{10} +(3.16251 + 0.999276i) q^{11} +(-4.00142 + 3.60290i) q^{13} +(-7.75603 + 0.815191i) q^{14} +(3.54533 - 3.93749i) q^{16} +(0.663043 + 2.04064i) q^{17} +(1.17531 + 1.61768i) q^{19} +(-1.23735 - 5.82127i) q^{20} +(8.22586 + 0.797174i) q^{22} +(1.15277 + 0.665550i) q^{23} +(2.74141 + 1.22055i) q^{25} +(-7.88632 + 10.8546i) q^{26} +(-12.5287 + 4.07083i) q^{28} +(0.107317 - 1.02105i) q^{29} +(-6.29538 - 6.99173i) q^{31} +(1.09663 - 1.89941i) q^{32} +(2.67328 + 4.63025i) q^{34} +(-1.36746 + 4.20862i) q^{35} +(-5.64362 - 4.10033i) q^{37} +(3.70273 + 3.33396i) q^{38} +(-3.16570 - 7.11027i) q^{40} +(0.334840 + 3.18579i) q^{41} +(4.42393 - 2.55416i) q^{43} +(13.8713 - 1.57178i) q^{44} +(3.15451 + 1.02496i) q^{46} +(1.89888 - 4.26495i) q^{47} +(2.73427 + 0.581187i) q^{49} +(7.31414 + 1.55467i) q^{50} +(-9.21818 + 20.7044i) q^{52} +(-4.78123 - 1.55352i) q^{53} +(2.31170 - 4.08004i) q^{55} +(-14.9202 + 8.61416i) q^{56} +(-0.267414 - 2.54427i) q^{58} +(-4.31758 - 9.69744i) q^{59} +(2.18293 + 1.96552i) q^{61} +(-18.9663 - 13.7799i) q^{62} +(-1.58577 + 4.88050i) q^{64} +(3.80657 + 6.59317i) q^{65} +(-0.745757 + 1.29169i) q^{67} +(6.04312 + 6.71156i) q^{68} +(-1.15261 + 10.9664i) q^{70} +(10.6126 - 3.44824i) q^{71} +(-5.45572 + 7.50916i) q^{73} +(-15.8798 - 7.07014i) q^{74} +(7.28879 + 4.20819i) q^{76} +(-9.51673 - 4.14496i) q^{77} +(-2.19814 - 10.3414i) q^{79} +(-4.40339 - 6.06075i) q^{80} +(2.46661 + 7.59144i) q^{82} +(-4.55756 + 5.06168i) q^{83} +(3.01715 - 0.317115i) q^{85} +(9.45944 - 8.51732i) q^{86} +(17.3171 - 5.78237i) q^{88} +8.06536i q^{89} +(13.6335 - 9.90535i) q^{91} +(5.57206 + 0.585647i) q^{92} +(2.41868 - 11.3790i) q^{94} +(2.58278 - 1.14993i) q^{95} +(2.31328 - 0.491702i) q^{97} +6.96550 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	2.43736	−	0.518076i	1.72347	−	0.366335i	0.763365	−	0.645968i	$-0.223546\pi$
$2$	2.43736	−	0.518076i	1.72347	−	0.366335i	0.960107	+	0.279632i	$0.0902126\pi$
$3$		0			0
$3$		0			0
$4$	3.84522	−	1.71200i	1.92261	−	0.856000i
$5$	0.293969	−	1.38302i	0.131467	−	0.618504i	−0.862241	−	0.506499i	$-0.830939\pi$
$5$	0.293969	−	1.38302i	0.131467	−	0.618504i	0.993708	−	0.112005i	$-0.0357272\pi$
$6$		0			0
$7$	−3.11261	−	0.327148i	−1.17646	−	0.123650i	−0.503943	−	0.863737i	$-0.668118\pi$
$7$	−3.11261	−	0.327148i	−1.17646	−	0.123650i	−0.672512	+	0.740086i	$0.734785\pi$
$8$	4.45339	−	3.23558i	1.57451	−	1.14395i
$9$		0			0
$10$		−	3.52320i		−	1.11413i
$11$	3.16251	+	0.999276i	0.953532	+	0.301293i
$11$	3.16251	+	0.999276i	0.953532	+	0.301293i
$12$		0			0
$13$	−4.00142	+	3.60290i	−1.10979	+	0.999264i	−0.109809	+	0.993953i	$0.535024\pi$
$13$	−4.00142	+	3.60290i	−1.10979	+	0.999264i	−0.999986	+	0.00531119i	$0.998309\pi$
$14$	−7.75603	+	0.815191i	−2.07289	+	0.217869i
$15$		0			0
$16$	3.54533	−	3.93749i	0.886332	−	0.984372i
$17$	0.663043	+	2.04064i	0.160812	+	0.494927i	0.998703	−	0.0509094i	$-0.0162120\pi$
$17$	0.663043	+	2.04064i	0.160812	+	0.494927i	−0.837892	+	0.545836i	$0.816212\pi$
$18$		0			0
$19$	1.17531	+	1.61768i	0.269635	+	0.371121i	0.922266	−	0.386555i	$-0.126335\pi$
$19$	1.17531	+	1.61768i	0.269635	+	0.371121i	−0.652632	+	0.757675i	$0.726335\pi$
$20$	−1.23735	−	5.82127i	−0.276680	−	1.30168i
$21$		0			0
$22$	8.22586	+	0.797174i	1.75376	+	0.169958i
$23$	1.15277	+	0.665550i	0.240369	+	0.138777i	0.615346	−	0.788257i	$-0.289016\pi$
$23$	1.15277	+	0.665550i	0.240369	+	0.138777i	−0.374978	+	0.927034i	$0.622350\pi$
$24$		0			0
$25$	2.74141	+	1.22055i	0.548282	+	0.244111i
$26$	−7.88632	+	10.8546i	−1.54663	+	2.12876i
$27$		0			0
$28$	−12.5287	+	4.07083i	−2.36771	+	0.769315i
$29$	0.107317	−	1.02105i	0.0199283	−	0.189605i	−0.980029	−	0.198855i	$-0.936278\pi$
$29$	0.107317	−	1.02105i	0.0199283	−	0.189605i	0.999957	+	0.00924995i	$0.00294439\pi$
$30$		0			0
$31$	−6.29538	−	6.99173i	−1.13068	−	1.25575i	−0.962880	−	0.269931i	$-0.912999\pi$
$31$	−6.29538	−	6.99173i	−1.13068	−	1.25575i	−0.167804	−	0.985820i	$-0.553668\pi$
$32$	1.09663	−	1.89941i	0.193858	−	0.335772i
$33$		0			0
$34$	2.67328	+	4.63025i	0.458463	+	0.794082i
$35$	−1.36746	+	4.20862i	−0.231143	+	0.711386i
$36$		0			0
$37$	−5.64362	−	4.10033i	−0.927805	−	0.674090i	0.0176490	−	0.999844i	$-0.494382\pi$
$37$	−5.64362	−	4.10033i	−0.927805	−	0.674090i	−0.945455	+	0.325754i	$0.894382\pi$
$38$	3.70273	+	3.33396i	0.600663	+	0.540839i
$39$		0			0
$40$	−3.16570	−	7.11027i	−0.500541	−	1.12423i
$41$	0.334840	+	3.18579i	0.0522932	+	0.497537i	0.989053	+	0.147563i	$0.0471429\pi$
$41$	0.334840	+	3.18579i	0.0522932	+	0.497537i	−0.936759	+	0.349974i	$0.886190\pi$
$42$		0			0
$43$	4.42393	−	2.55416i	0.674642	−	0.389505i	−0.123191	−	0.992383i	$-0.539313\pi$
$43$	4.42393	−	2.55416i	0.674642	−	0.389505i	0.797833	+	0.602878i	$0.205979\pi$
$44$	13.8713	−	1.57178i	2.09117	−	0.236955i
$45$		0			0
$46$	3.15451	+	1.02496i	0.465107	+	0.151122i
$47$	1.89888	−	4.26495i	0.276980	−	0.622107i	−0.720469	−	0.693487i	$-0.756074\pi$
$47$	1.89888	−	4.26495i	0.276980	−	0.622107i	0.997449	+	0.0713796i	$0.0227402\pi$
$48$		0			0
$49$	2.73427	+	0.581187i	0.390610	+	0.0830268i
$50$	7.31414	+	1.55467i	1.03438	+	0.219863i
$51$		0			0
$52$	−9.21818	+	20.7044i	−1.27833	+	2.87118i
$53$	−4.78123	−	1.55352i	−0.656752	−	0.213392i	−0.0383632	−	0.999264i	$-0.512214\pi$
$53$	−4.78123	−	1.55352i	−0.656752	−	0.213392i	−0.618389	+	0.785872i	$0.712214\pi$
$54$		0			0
$55$	2.31170	−	4.08004i	0.311709	−	0.550153i
$56$	−14.9202	+	8.61416i	−1.99379	+	1.15112i
$57$		0			0
$58$	−0.267414	−	2.54427i	−0.0351132	−	0.334079i
$59$	−4.31758	−	9.69744i	−0.562101	−	1.26250i	−0.941421	−	0.337233i	$-0.890509\pi$
$59$	−4.31758	−	9.69744i	−0.562101	−	1.26250i	0.379320	−	0.925265i	$-0.376158\pi$
$60$		0			0
$61$	2.18293	+	1.96552i	0.279496	+	0.251659i	0.796941	−	0.604057i	$-0.206450\pi$
$61$	2.18293	+	1.96552i	0.279496	+	0.251659i	−0.517445	+	0.855716i	$0.673117\pi$
$62$	−18.9663	−	13.7799i	−2.40873	−	1.75004i
$63$		0			0
$64$	−1.58577	+	4.88050i	−0.198221	+	0.610062i
$65$	3.80657	+	6.59317i	0.472147	+	0.817783i
$66$		0			0
$67$	−0.745757	+	1.29169i	−0.0911087	+	0.157805i	−0.907978	−	0.419018i	$-0.862374\pi$
$67$	−0.745757	+	1.29169i	−0.0911087	+	0.157805i	0.816869	+	0.576823i	$0.195708\pi$
$68$	6.04312	+	6.71156i	0.732835	+	0.813896i
$69$		0			0
$70$	−1.15261	+	10.9664i	−0.137763	+	1.31073i
$71$	10.6126	−	3.44824i	1.25948	−	0.409231i	0.398173	−	0.917310i	$-0.369644\pi$
$71$	10.6126	−	3.44824i	1.25948	−	0.409231i	0.861310	+	0.508080i	$0.169644\pi$
$72$		0			0
$73$	−5.45572	+	7.50916i	−0.638544	+	0.878880i	−0.998537	−	0.0540747i	$-0.982779\pi$
$73$	−5.45572	+	7.50916i	−0.638544	+	0.878880i	0.359993	+	0.932955i	$0.382779\pi$
$74$	−15.8798	−	7.07014i	−1.84599	−	0.821888i
$75$		0			0
$76$	7.28879	+	4.20819i	0.836082	+	0.482712i
$77$	−9.51673	−	4.14496i	−1.08453	−	0.472363i
$78$		0			0
$79$	−2.19814	−	10.3414i	−0.247310	−	1.16350i	−0.910000	−	0.414609i	$-0.863918\pi$
$79$	−2.19814	−	10.3414i	−0.247310	−	1.16350i	0.662689	−	0.748894i	$-0.269415\pi$
$80$	−4.40339	−	6.06075i	−0.492314	−	0.677612i
$81$		0			0
$82$	2.46661	+	7.59144i	0.272391	+	0.838334i
$83$	−4.55756	+	5.06168i	−0.500257	+	0.555591i	−0.939399	−	0.342826i	$-0.888616\pi$
$83$	−4.55756	+	5.06168i	−0.500257	+	0.555591i	0.439142	+	0.898418i	$0.355282\pi$
$84$		0			0
$85$	3.01715	−	0.317115i	0.327256	−	0.0343960i
$86$	9.45944	−	8.51732i	1.02004	−	0.918446i
$87$		0			0
$88$	17.3171	−	5.78237i	1.84601	−	0.616402i
$89$			8.06536i			0.854927i	0.904033	+	0.427463i	$0.140593\pi$
$89$			8.06536i			0.854927i	−0.904033	+	0.427463i	$0.859407\pi$
$90$		0			0
$91$	13.6335	−	9.90535i	1.42918	−	1.03836i
$92$	5.57206	+	0.585647i	0.580928	+	0.0610579i
$93$		0			0
$94$	2.41868	−	11.3790i	0.249467	−	1.17365i
$95$	2.58278	−	1.14993i	0.264988	−	0.117980i
$96$		0			0
$97$	2.31328	−	0.491702i	0.234878	−	0.0499248i	−0.0889689	−	0.996034i	$-0.528357\pi$
$97$	2.31328	−	0.491702i	0.234878	−	0.0499248i	0.323847	+	0.946110i	$0.395024\pi$
$98$	6.96550			0.703622
$99$		0			0
$100$	12.6309			1.26309
$101$	12.9788	−	2.75873i	1.29144	−	0.274503i	0.489548	−	0.871976i	$-0.337162\pi$
$101$	12.9788	−	2.75873i	1.29144	−	0.274503i	0.801889	+	0.597473i	$0.203828\pi$
$102$		0			0
$103$	−6.83033	+	3.04106i	−0.673013	+	0.299645i	−0.714644	−	0.699489i	$-0.753411\pi$
$103$	−6.83033	+	3.04106i	−0.673013	+	0.299645i	0.0416312	+	0.999133i	$0.486745\pi$
$104$	−6.16244	+	28.9920i	−0.604277	+	2.84290i
$105$		0			0
$106$	−12.4584	−	1.30943i	−1.21007	−	0.127183i
$107$	0.791122	−	0.574784i	0.0764807	−	0.0555664i	−0.548888	−	0.835896i	$-0.684949\pi$
$107$	0.791122	−	0.574784i	0.0764807	−	0.0555664i	0.625369	+	0.780329i	$0.284949\pi$
$108$		0			0
$109$			5.38041i			0.515350i	0.966232	+	0.257675i	$0.0829564\pi$
$109$			5.38041i			0.515350i	−0.966232	+	0.257675i	$0.917044\pi$
$110$	3.52065	−	11.1422i	0.335681	−	1.06236i
$111$		0			0
$112$	−12.3234	+	11.0960i	−1.16445	+	1.04847i
$113$	5.30003	−	0.557055i	0.498585	−	0.0524034i	0.148101	−	0.988972i	$-0.452684\pi$
$113$	5.30003	−	0.557055i	0.498585	−	0.0524034i	0.350484	+	0.936569i	$0.386017\pi$
$114$		0			0
$115$	1.25935	−	1.39864i	0.117435	−	0.130424i
$116$	−1.33539	−	4.10990i	−0.123988	−	0.381595i
$117$		0			0
$118$	−15.5475	−	21.3993i	−1.43126	−	1.96996i
$119$	−1.39620	−	6.56862i	−0.127990	−	0.602144i
$120$		0			0
$121$	9.00289	+	6.32043i	0.818445	+	0.574585i
$122$	6.33887	+	3.65975i	0.573895	+	0.331338i
$123$		0			0
$124$	−36.1769	−	16.1070i	−3.24879	−	1.44645i
$125$	6.64933	−	9.15201i	0.594734	−	0.818581i
$126$		0			0
$127$	10.2499	−	3.33040i	0.909534	−	0.295526i	0.183368	−	0.983044i	$-0.441300\pi$
$127$	10.2499	−	3.33040i	0.909534	−	0.295526i	0.726167	+	0.687519i	$0.241300\pi$
$128$	−1.79513	+	17.0795i	−0.158669	+	1.50963i
$129$		0			0
$130$	12.6937	+	14.0978i	1.11331	+	1.23646i
$131$	8.59739	−	14.8911i	0.751157	−	1.30104i	−0.196105	−	0.980583i	$-0.562829\pi$
$131$	8.59739	−	14.8911i	0.751157	−	1.30104i	0.947262	−	0.320460i	$-0.103837\pi$
$132$		0			0
$133$	−3.12906	−	5.41970i	−0.271324	−	0.469947i
$134$	−1.14848	+	3.53467i	−0.0992138	+	0.305349i
$135$		0			0
$136$	9.55542	+	6.94242i	0.819371	+	0.595308i
$137$	−7.32502	−	6.59548i	−0.625819	−	0.563490i	0.294014	−	0.955801i	$-0.405009\pi$
$137$	−7.32502	−	6.59548i	−0.625819	−	0.563490i	−0.919832	+	0.392311i	$0.871676\pi$
$138$		0			0
$139$	−0.898825	−	2.01879i	−0.0762374	−	0.171232i	0.871406	−	0.490562i	$-0.163209\pi$
$139$	−0.898825	−	2.01879i	−0.0762374	−	0.171232i	−0.947643	+	0.319331i	$0.896542\pi$
$140$	1.94697	+	18.5241i	0.164549	+	1.56558i
$141$		0			0
$142$	24.0802	−	13.9027i	2.02077	−	1.16669i
$143$	−16.2548	+	7.39566i	−1.35930	+	0.618456i
$144$		0			0
$145$	−1.38059	−	0.448580i	−0.114652	−	0.0372525i
$146$	−9.40723	+	21.1290i	−0.778548	+	1.74865i
$147$		0			0
$148$	−28.7207	−	6.10478i	−2.36083	−	0.501810i
$149$	−5.34203	−	1.13548i	−0.437636	−	0.0930224i	−0.0161755	−	0.999869i	$-0.505149\pi$
$149$	−5.34203	−	1.13548i	−0.437636	−	0.0930224i	−0.421461	+	0.906847i	$0.638482\pi$
$150$		0			0
$151$	−0.210462	+	0.472704i	−0.0171271	+	0.0384681i	−0.921907	−	0.387412i	$-0.873369\pi$
$151$	−0.210462	+	0.472704i	−0.0171271	+	0.0384681i	0.904779	+	0.425881i	$0.140036\pi$
$152$	10.4682	+	3.40134i	0.849086	+	0.275885i
$153$		0			0
$154$	−25.3431	−	5.17237i	−2.04220	−	0.416801i
$155$	−11.5203	+	6.65126i	−0.925335	+	0.534242i
$156$		0			0
$157$	1.40989	+	13.4142i	0.112522	+	1.07057i	0.894439	+	0.447189i	$0.147575\pi$
$157$	1.40989	+	13.4142i	0.112522	+	1.07057i	−0.781918	+	0.623382i	$0.785758\pi$
$158$	−10.7153	−	24.0670i	−0.852465	−	1.91467i
$159$		0			0
$160$	−2.30454	−	2.07502i	−0.182190	−	0.164045i
$161$	−3.37038	−	2.44872i	−0.265623	−	0.192986i
$162$		0			0
$163$	−5.94061	+	18.2833i	−0.465305	+	1.43206i	0.393295	+	0.919413i	$0.371335\pi$
$163$	−5.94061	+	18.2833i	−0.465305	+	1.43206i	−0.858599	+	0.512648i	$0.828665\pi$
$164$	6.74161	+	11.6768i	0.526431	+	0.911806i
$165$		0			0
$166$	−8.48606	+	14.6983i	−0.658646	+	1.14081i
$167$	0.394490	+	0.438126i	0.0305266	+	0.0339032i	0.758215	−	0.652005i	$-0.226072\pi$
$167$	0.394490	+	0.438126i	0.0305266	+	0.0339032i	−0.727688	+	0.685908i	$0.759405\pi$
$168$		0			0
$169$	1.67165	−	15.9046i	0.128588	−	1.22343i
$170$	7.18958	−	2.33604i	0.551416	−	0.179166i
$171$		0			0
$172$	12.6382	−	17.3950i	0.963657	−	1.32636i
$173$	3.32912	+	1.48222i	0.253109	+	0.112691i	0.529369	−	0.848392i	$-0.322429\pi$
$173$	3.32912	+	1.48222i	0.253109	+	0.112691i	−0.276261	+	0.961083i	$0.589095\pi$
$174$		0			0
$175$	−8.13363	−	4.69596i	−0.614845	−	0.354981i
$176$	15.1468	−	8.90957i	1.14173	−	0.671584i
$177$		0			0
$178$	4.17847	+	19.6582i	0.313190	+	1.47344i
$179$	3.36258	+	4.62819i	0.251331	+	0.345927i	0.915977	−	0.401231i	$-0.131418\pi$
$179$	3.36258	+	4.62819i	0.251331	+	0.345927i	−0.664646	+	0.747159i	$0.731418\pi$
$180$		0			0
$181$	−2.48530	−	7.64897i	−0.184731	−	0.568544i	0.815213	−	0.579162i	$-0.196620\pi$
$181$	−2.48530	−	7.64897i	−0.184731	−	0.568544i	−0.999944	+	0.0106182i	$0.996620\pi$
$182$	28.0981	−	31.2061i	2.08277	−	2.31315i
$183$		0			0
$184$	7.28716	−	0.765911i	0.537216	−	0.0564637i
$185$	−7.32988	+	6.59985i	−0.538903	+	0.485231i
$186$		0			0
$187$	0.0577182	+	7.11609i	0.00422077	+	0.520380i
$188$		−	19.6506i		−	1.43316i
$189$		0			0
$190$	5.69941	−	4.14086i	0.413478	−	0.300410i
$191$	12.1596	+	1.27802i	0.879835	+	0.0924743i	0.533663	−	0.845697i	$-0.320815\pi$
$191$	12.1596	+	1.27802i	0.879835	+	0.0924743i	0.346171	+	0.938171i	$0.387482\pi$
$192$		0			0
$193$	3.48411	−	16.3915i	0.250792	−	1.17988i	−0.654823	−	0.755782i	$-0.727257\pi$
$193$	3.48411	−	16.3915i	0.250792	−	1.17988i	0.905615	−	0.424101i	$-0.139410\pi$
$194$	5.38354	−	2.39691i	0.386516	−	0.172088i
$195$		0			0
$196$	11.5089	−	2.44628i	0.822062	−	0.174735i
$197$	6.63610			0.472803			0.236401	−	0.971656i	$-0.424032\pi$
$197$	6.63610			0.472803			0.236401	+	0.971656i	$0.424032\pi$
$198$		0			0
$199$	−3.24799			−0.230244			−0.115122	−	0.993351i	$-0.536726\pi$
$199$	−3.24799			−0.230244			−0.115122	+	0.993351i	$0.536726\pi$
$200$	16.1578	−	3.43444i	1.14253	−	0.242851i
$201$		0			0
$202$	30.2047	−	13.4480i	2.12520	−	0.946198i
$203$	−0.668072	+	3.14303i	−0.0468895	+	0.220598i
$204$		0			0
$205$	4.50444	+	0.473435i	0.314603	+	0.0330661i
$206$	−15.0725	+	10.9508i	−1.05015	+	0.762977i
$207$		0			0
$208$			28.5290i			1.97813i
$209$	2.10042	+	6.29037i	0.145289	+	0.435114i
$210$		0			0
$211$	5.93173	−	5.34095i	0.408357	−	0.367686i	−0.439201	−	0.898389i	$-0.644739\pi$
$211$	5.93173	−	5.34095i	0.408357	−	0.367686i	0.847558	+	0.530703i	$0.178072\pi$
$212$	−21.0445	+	2.21186i	−1.44534	+	0.151911i
$213$		0			0
$214$	1.63047	−	1.81082i	0.111456	−	0.123785i
$215$	−2.23194	−	6.86921i	−0.152217	−	0.468476i
$216$		0			0
$217$	17.3077	+	23.8220i	1.17492	+	1.61715i
$218$	2.78746	+	13.1140i	0.188791	+	0.888191i
$219$		0			0
$220$	1.90393	−	19.6463i	0.128363	−	1.32455i
$221$	−10.0053	−	5.77657i	−0.673031	−	0.388574i
$222$		0			0
$223$	−12.6995	−	5.65418i	−0.850421	−	0.378632i	−0.0652185	−	0.997871i	$-0.520774\pi$
$223$	−12.6995	−	5.65418i	−0.850421	−	0.378632i	−0.785202	+	0.619239i	$0.787441\pi$
$224$	−4.03476	+	5.55336i	−0.269583	+	0.371050i
$225$		0			0
$226$	12.6295	−	4.10356i	0.840099	−	0.272965i
$227$	2.17751	−	20.7176i	0.144526	−	1.37508i	−0.646322	−	0.763065i	$-0.723694\pi$
$227$	2.17751	−	20.7176i	0.144526	−	1.37508i	0.790848	−	0.612012i	$-0.209640\pi$
$228$		0			0
$229$	9.91278	+	11.0093i	0.655055	+	0.727512i	0.975560	−	0.219735i	$-0.0705192\pi$
$229$	9.91278	+	11.0093i	0.655055	+	0.727512i	−0.320505	+	0.947247i	$0.603853\pi$
$230$	2.34487	−	4.06143i	0.154616	−	0.267803i
$231$		0			0
$232$	−2.82577	−	4.89438i	−0.185521	−	0.321332i
$233$	−5.72371	+	17.6158i	−0.374972	+	1.15405i	0.568525	+	0.822666i	$0.307514\pi$
$233$	−5.72371	+	17.6158i	−0.374972	+	1.15405i	−0.943497	+	0.331380i	$0.892486\pi$
$234$		0			0
$235$	−5.34029	−	3.87995i	−0.348362	−	0.253100i
$236$	−33.2040	−	29.8971i	−2.16140	−	1.94613i
$237$		0			0
$238$	−6.80609	−	15.2867i	−0.441173	−	0.990891i
$239$	2.46907	+	23.4916i	0.159711	+	1.51955i	0.721587	+	0.692324i	$0.243413\pi$
$239$	2.46907	+	23.4916i	0.159711	+	1.51955i	−0.561876	+	0.827221i	$0.689920\pi$
$240$		0			0
$241$	−8.98897	+	5.18978i	−0.579030	+	0.334303i	−0.760748	−	0.649047i	$-0.775168\pi$
$241$	−8.98897	+	5.18978i	−0.579030	+	0.334303i	0.181718	+	0.983351i	$0.441834\pi$
$242$	25.2177	+	10.7410i	1.62106	+	0.690456i
$243$		0			0
$244$	11.7588	+	3.82067i	0.752781	+	0.244593i
$245$	1.60758	−	3.61069i	0.102705	−	0.230679i
$246$		0			0
$247$	−10.5312	−	2.23848i	−0.670087	−	0.142431i
$248$	−50.6580	−	10.7677i	−3.21679	−	0.683750i
$249$		0			0
$250$	11.4653	−	25.7516i	0.725132	−	1.62867i
$251$	6.21725	+	2.02011i	0.392429	+	0.127508i	0.498584	−	0.866842i	$-0.333854\pi$
$251$	6.21725	+	2.02011i	0.392429	+	0.127508i	−0.106154	+	0.994350i	$0.533854\pi$
$252$		0			0
$253$	2.98056	+	3.25674i	0.187386	+	0.204749i
$254$	23.2573	−	13.4276i	1.45930	−	0.842525i
$255$		0			0
$256$	3.40032	+	32.3519i	0.212520	+	2.02199i
$257$	4.33722	+	9.74155i	0.270548	+	0.607661i	0.996815	−	0.0797520i	$-0.0254128\pi$
$257$	4.33722	+	9.74155i	0.270548	+	0.607661i	−0.726267	+	0.687413i	$0.758746\pi$
$258$		0			0
$259$	16.2250	+	14.6090i	1.00817	+	0.907761i
$260$	25.9246	+	18.8353i	1.60778	+	1.16812i
$261$		0			0
$262$	13.2402	−	40.7491i	0.817981	−	2.51749i
$263$	−10.0693	−	17.4405i	−0.620897	−	1.07543i	−0.989319	−	0.145767i	$-0.953435\pi$
$263$	−10.0693	−	17.4405i	−0.620897	−	1.07543i	0.368422	−	0.929659i	$-0.379898\pi$
$264$		0			0
$265$	−3.55407	+	6.15583i	−0.218325	+	0.378150i
$266$	−10.4345	−	11.5886i	−0.639778	−	0.710545i
$267$		0			0
$268$	−0.656225	+	6.24356i	−0.0400853	+	0.381386i
$269$	−9.24045	+	3.00240i	−0.563400	+	0.183060i	−0.576850	−	0.816850i	$-0.695718\pi$
$269$	−9.24045	+	3.00240i	−0.563400	+	0.183060i	0.0134505	+	0.999910i	$0.495718\pi$
$270$		0			0
$271$	−13.7884	+	18.9781i	−0.837584	+	1.15284i	0.148880	+	0.988855i	$0.452433\pi$
$271$	−13.7884	+	18.9781i	−0.837584	+	1.15284i	−0.986464	+	0.163980i	$0.947567\pi$
$272$	10.3857	+	4.62401i	0.629725	+	0.280372i
$273$		0			0
$274$	−21.2707	−	12.2806i	−1.28501	−	0.741899i
$275$	7.45006	+	6.59944i	0.449255	+	0.397961i
$276$		0			0
$277$	3.62617	+	17.0598i	0.217875	+	1.02502i	0.942067	+	0.335425i	$0.108880\pi$
$277$	3.62617	+	17.0598i	0.217875	+	1.02502i	−0.724192	+	0.689599i	$0.757787\pi$
$278$	−3.23665	−	4.45486i	−0.194121	−	0.267185i
$279$		0			0
$280$	7.52746	+	23.1671i	0.449852	+	1.38450i
$281$	−15.3426	+	17.0397i	−0.915263	+	1.01650i	0.0845356	+	0.996420i	$0.473059\pi$
$281$	−15.3426	+	17.0397i	−0.915263	+	1.01650i	−0.999798	+	0.0200818i	$0.993607\pi$
$282$		0			0
$283$	−21.5196	+	2.26180i	−1.27921	+	0.134450i	−0.719647	−	0.694340i	$-0.755696\pi$
$283$	−21.5196	+	2.26180i	−1.27921	+	0.134450i	−0.559560	+	0.828790i	$0.689030\pi$
$284$	34.9043	−	31.4280i	2.07119	−	1.86491i
$285$		0			0
$286$	−35.7873	+	26.4471i	−2.11615	+	1.56385i
$287$		−	10.0257i		−	0.591796i
$288$		0			0
$289$	10.0287	−	7.28629i	0.589925	−	0.428605i
$290$	−3.59738	−	0.378100i	−0.211246	−	0.0222028i
$291$		0			0
$292$	−8.12275	+	38.2145i	−0.475348	+	2.23634i
$293$	−17.7719	+	7.91257i	−1.03825	+	0.462257i	−0.853809	−	0.520587i	$-0.825713\pi$
$293$	−17.7719	+	7.91257i	−1.03825	+	0.462257i	−0.184438	+	0.982844i	$0.559047\pi$
$294$		0			0
$295$	−14.6809	+	3.12053i	−0.854758	+	0.181684i
$296$	−38.4002			−2.23196
$297$		0			0
$298$	−13.6087			−0.788331
$299$	−7.01062	+	1.49015i	−0.405434	+	0.0861778i
$300$		0			0
$301$	−14.6055	+	6.50280i	−0.841849	+	0.374815i
$302$	−0.268073	+	1.26118i	−0.0154259	+	0.0725730i
$303$		0			0
$304$	10.5364	+	1.10743i	0.604307	+	0.0635152i
$305$	3.36006	−	2.44123i	0.192397	−	0.139784i
$306$		0			0
$307$			2.08212i			0.118833i	0.998233	+	0.0594164i	$0.0189240\pi$
$307$			2.08212i			0.118833i	−0.998233	+	0.0594164i	$0.981076\pi$
$308$	−43.6901	+	0.354368i	−2.48947	+	0.0201920i
$309$		0			0
$310$	−24.6333	+	22.1799i	−1.39908	+	1.25973i
$311$	13.0185	−	1.36830i	0.738212	−	0.0775892i	0.272043	−	0.962285i	$-0.412301\pi$
$311$	13.0185	−	1.36830i	0.738212	−	0.0775892i	0.466169	+	0.884696i	$0.345634\pi$
$312$		0			0
$313$	2.00518	−	2.22698i	0.113340	−	0.125876i	−0.683805	−	0.729665i	$-0.739676\pi$
$313$	2.00518	−	2.22698i	0.113340	−	0.125876i	0.797145	+	0.603788i	$0.206343\pi$
$314$	10.3860	+	31.9648i	0.586116	+	1.80388i
$315$		0			0
$316$	−26.1569	−	36.0019i	−1.47144	−	2.02526i
$317$	6.63939	+	31.2359i	0.372905	+	1.75438i	0.619245	+	0.785198i	$0.287439\pi$
$317$	6.63939	+	31.2359i	0.372905	+	1.75438i	−0.246340	+	0.969184i	$0.579228\pi$
$318$		0			0
$319$	1.35971	−	3.12185i	0.0761289	−	0.174790i
$320$	6.28364	+	3.62786i	0.351266	+	0.202804i
$321$		0			0
$322$	−9.48344	−	4.22230i	−0.528492	−	0.235300i
$323$	−2.52181	+	3.47097i	−0.140317	+	0.193130i
$324$		0			0
$325$	−15.3671	+	4.99306i	−0.852412	+	0.276965i
$326$	−5.00724	+	47.6407i	−0.277325	+	2.63857i
$327$		0			0
$328$	11.7990	+	13.1042i	0.651493	+	0.723557i
$329$	−7.30574	+	12.6539i	−0.402779	+	0.697633i
$330$		0			0
$331$	−13.1792	−	22.8271i	−0.724395	−	1.25469i	−0.959223	−	0.282652i	$-0.908786\pi$
$331$	−13.1792	−	22.8271i	−0.724395	−	1.25469i	0.234828	−	0.972037i	$-0.424547\pi$
$332$	−8.85919	+	27.2658i	−0.486211	+	1.49640i
$333$		0			0
$334$	1.18850	+	0.863494i	0.0650317	+	0.0472483i
$335$	1.56720	+	1.41111i	0.0856251	+	0.0770972i
$336$		0			0
$337$	−1.70543	−	3.83045i	−0.0929004	−	0.208658i	0.861118	−	0.508404i	$-0.169765\pi$
$337$	−1.70543	−	3.83045i	−0.0929004	−	0.208658i	−0.954019	+	0.299747i	$0.903098\pi$
$338$	−4.16542	−	39.6313i	−0.226569	−	2.15566i
$339$		0			0
$340$	11.0587	−	6.38474i	0.599742	−	0.346261i
$341$	−12.9225	−	28.4022i	−0.699793	−	1.53807i
$342$		0			0
$343$	12.5154	+	4.06651i	0.675769	+	0.219571i
$344$	11.4373	−	25.6886i	0.616658	−	1.38504i
$345$		0			0
$346$	8.88217	+	1.88796i	0.477508	+	0.101498i
$347$	33.6217	+	7.14651i	1.80491	+	0.383645i	0.982650	−	0.185470i	$-0.0593808\pi$
$347$	33.6217	+	7.14651i	1.80491	+	0.383645i	0.822258	+	0.569115i	$0.192714\pi$
$348$		0			0
$349$	−8.47152	+	19.0273i	−0.453470	+	1.01851i	0.531700	+	0.846932i	$0.321553\pi$
$349$	−8.47152	+	19.0273i	−0.453470	+	1.01851i	−0.985171	+	0.171578i	$0.945113\pi$
$350$	−22.2574	−	7.23188i	−1.18971	−	0.386560i
$351$		0			0
$352$	5.36612	−	4.91107i	0.286015	−	0.261761i
$353$	7.16833	−	4.13864i	0.381532	−	0.220278i	−0.296953	−	0.954892i	$-0.595970\pi$
$353$	7.16833	−	4.13864i	0.381532	−	0.220278i	0.678485	+	0.734615i	$0.262637\pi$
$354$		0			0
$355$	−1.64920	−	15.6911i	−0.0875303	−	0.832795i
$356$	13.8079	+	31.0131i	0.731818	+	1.64369i
$357$		0			0
$358$	10.5936	+	9.53849i	0.559887	+	0.504125i
$359$	−10.3031	−	7.48561i	−0.543774	−	0.395075i	0.281711	−	0.959499i	$-0.409098\pi$
$359$	−10.3031	−	7.48561i	−0.543774	−	0.395075i	−0.825485	+	0.564424i	$0.809098\pi$
$360$		0			0
$361$	4.63580	−	14.2675i	0.243989	−	0.750922i
$362$	−10.0203	−	17.3557i	−0.526656	−	0.912196i
$363$		0			0
$364$	35.4660	−	61.4289i	1.85892	−	3.21975i
$365$	8.78147	+	9.75281i	0.459643	+	0.510486i
$366$		0			0
$367$	2.19865	−	20.9188i	0.114769	−	1.09195i	−0.773870	−	0.633344i	$-0.781682\pi$
$367$	2.19865	−	20.9188i	0.114769	−	1.09195i	0.888639	−	0.458607i	$-0.151652\pi$
$368$	6.70753	−	2.17941i	0.349654	−	0.113610i
$369$		0			0
$370$	−14.4463	+	19.8836i	−0.751027	+	1.03370i
$371$	14.3739	+	6.39966i	0.746254	+	0.332254i
$372$		0			0
$373$	14.2942	+	8.25274i	0.740124	+	0.427311i	0.822114	−	0.569322i	$-0.192794\pi$
$373$	14.2942	+	8.25274i	0.740124	+	0.427311i	−0.0819904	+	0.996633i	$0.526128\pi$
$374$	3.82736	+	17.3146i	0.197908	+	0.895314i
$375$		0			0
$376$	−5.34313	−	25.1375i	−0.275551	−	1.29637i
$377$	3.24933	+	4.47232i	0.167349	+	0.230336i
$378$		0			0
$379$	−4.41092	−	13.5754i	−0.226574	−	0.697322i	−0.998128	−	0.0611588i	$-0.980520\pi$
$379$	−4.41092	−	13.5754i	−0.226574	−	0.697322i	0.771554	−	0.636163i	$-0.219480\pi$
$380$	7.96267	−	8.84344i	0.408476	−	0.453659i
$381$		0			0
$382$	30.2993	−	3.18458i	1.55025	−	0.162937i
$383$	−7.54769	+	6.79597i	−0.385669	+	0.347258i	−0.839046	−	0.544061i	$-0.816886\pi$
$383$	−7.54769	+	6.79597i	−0.385669	+	0.347258i	0.453377	+	0.891319i	$0.350219\pi$
$384$		0			0
$385$	−8.53018	+	11.9433i	−0.434738	+	0.608687i
$386$		−	41.7569i		−	2.12537i
$387$		0			0
$388$	8.05326	−	5.85103i	0.408842	−	0.297041i
$389$	−20.5653	−	2.16150i	−1.04270	−	0.109592i	−0.432336	−	0.901713i	$-0.642310\pi$
$389$	−20.5653	−	2.16150i	−1.04270	−	0.109592i	−0.610365	+	0.792120i	$0.708977\pi$
$390$		0			0
$391$	−0.593812	+	2.79367i	−0.0300304	+	0.141282i
$392$	14.0573	−	6.25869i	0.709998	−	0.316112i
$393$		0			0
$394$	16.1745	−	3.43801i	0.814862	−	0.173204i
$395$	−14.9486			−0.752144
$396$		0			0
$397$	33.6048			1.68658			0.843288	−	0.537463i	$-0.180617\pi$
$397$	33.6048			1.68658			0.843288	+	0.537463i	$0.180617\pi$
$398$	−7.91651	+	1.68271i	−0.396819	+	0.0843464i
$399$		0			0
$400$	14.5251	−	6.46700i	0.726256	−	0.323350i
$401$	−0.745837	+	3.50889i	−0.0372453	+	0.175225i	−0.992839	−	0.119463i	$-0.961883\pi$
$401$	−0.745837	+	3.50889i	−0.0372453	+	0.175225i	0.955593	+	0.294689i	$0.0952160\pi$
$402$		0			0
$403$	50.3810	+	5.29525i	2.50965	+	0.263775i
$404$	45.1833	−	32.8276i	2.24795	−	1.63323i
$405$		0			0
$406$			8.00681i			0.397371i
$407$	−13.7506	−	18.6069i	−0.681593	−	0.922308i
$408$		0			0
$409$	−2.82298	+	2.54182i	−0.139587	+	0.125685i	−0.735967	−	0.677018i	$-0.763272\pi$
$409$	−2.82298	+	2.54182i	−0.139587	+	0.125685i	0.596379	+	0.802703i	$0.296605\pi$
$410$	11.2242	−	1.17971i	0.554323	−	0.0582617i
$411$		0			0
$412$	−21.0578	+	23.3871i	−1.03744	+	1.15220i
$413$	10.2664	+	31.5968i	0.505178	+	1.55478i
$414$		0			0
$415$	5.66060	+	7.79115i	0.277868	+	0.382453i
$416$	2.45532	+	11.5514i	0.120382	+	0.566353i
$417$		0			0
$418$	8.37838	+	14.2437i	0.409800	+	0.696683i
$419$	−7.80619	−	4.50691i	−0.381357	−	0.220177i	0.297051	−	0.954862i	$-0.403997\pi$
$419$	−7.80619	−	4.50691i	−0.381357	−	0.220177i	−0.678409	+	0.734685i	$0.737330\pi$
$420$		0			0
$421$	8.08646	+	3.60032i	0.394110	+	0.175469i	0.594217	−	0.804305i	$-0.297462\pi$
$421$	8.08646	+	3.60032i	0.394110	+	0.175469i	−0.200107	+	0.979774i	$0.564129\pi$
$422$	11.6907	−	16.0909i	0.569095	−	0.783292i
$423$		0			0
$424$	−26.3192	+	8.55162i	−1.27817	+	0.415303i
$425$	−0.673035	+	6.40350i	−0.0326470	+	0.310616i
$426$		0			0
$427$	−6.15160	−	6.83204i	−0.297697	−	0.330626i
$428$	2.05801	−	3.56457i	0.0994775	−	0.172300i
$429$		0			0
$430$	−8.99881	−	15.5864i	−0.433961	−	0.751643i
$431$	11.5395	−	35.5149i	0.555837	−	1.71069i	−0.137886	−	0.990448i	$-0.544031\pi$
$431$	11.5395	−	35.5149i	0.555837	−	1.71069i	0.693723	−	0.720242i	$-0.255969\pi$
$432$		0			0
$433$	−32.3699	−	23.5181i	−1.55560	−	1.13021i	−0.939504	−	0.342537i	$-0.888714\pi$
$433$	−32.3699	−	23.5181i	−1.55560	−	1.13021i	−0.616095	−	0.787672i	$-0.711286\pi$
$434$	54.5267	+	49.0961i	2.61737	+	2.35669i
$435$		0			0
$436$	9.21127	+	20.6888i	0.441140	+	0.990816i
$437$	0.278214	+	2.64703i	0.0133088	+	0.126625i
$438$		0			0
$439$	−11.4812	+	6.62868i	−0.547968	+	0.316370i	−0.748302	−	0.663358i	$-0.769131\pi$
$439$	−11.4812	+	6.62868i	−0.547968	+	0.316370i	0.200334	+	0.979728i	$0.435797\pi$
$440$	−2.90641	−	25.6497i	−0.138558	−	1.22280i
$441$		0			0
$442$	−27.3792	−	8.89606i	−1.30230	−	0.423142i
$443$	−1.63044	+	3.66202i	−0.0774644	+	0.173988i	−0.948126	−	0.317894i	$-0.897024\pi$
$443$	−1.63044	+	3.66202i	−0.0774644	+	0.173988i	0.870662	+	0.491882i	$0.163691\pi$
$444$		0			0
$445$	11.1545	+	2.37097i	0.528775	+	0.112395i
$446$	−33.8825	−	7.20195i	−1.60438	−	0.341022i
$447$		0			0
$448$	6.53253	−	14.6723i	0.308633	−	0.693201i
$449$	−20.8754	−	6.78284i	−0.985172	−	0.320102i	−0.228247	−	0.973603i	$-0.573299\pi$
$449$	−20.8754	−	6.78284i	−0.985172	−	0.320102i	−0.756925	+	0.653501i	$0.773299\pi$
$450$		0			0
$451$	−2.12455	+	10.4097i	−0.100041	+	0.490173i
$452$	19.4261	−	11.2156i	0.913726	−	0.527540i
$453$		0			0
$454$	−5.42594	−	51.6244i	−0.254652	−	2.42285i
$455$	−9.69142	−	21.7673i	−0.454341	−	1.02047i
$456$		0			0
$457$	−13.2628	−	11.9418i	−0.620405	−	0.558616i	0.297846	−	0.954614i	$-0.403732\pi$
$457$	−13.2628	−	11.9418i	−0.620405	−	0.558616i	−0.918251	+	0.395998i	$0.870399\pi$
$458$	29.8646	+	21.6979i	1.39548	+	1.01388i
$459$		0			0
$460$	2.44797	−	7.53409i	0.114137	−	0.351279i
$461$	5.77269	+	9.99860i	0.268861	+	0.465681i	0.968568	−	0.248749i	$-0.0800194\pi$
$461$	5.77269	+	9.99860i	0.268861	+	0.465681i	−0.699707	+	0.714430i	$0.746686\pi$
$462$		0			0
$463$	−7.20503	+	12.4795i	−0.334846	+	0.579971i	−0.983455	−	0.181151i	$-0.942018\pi$
$463$	−7.20503	+	12.4795i	−0.334846	+	0.579971i	0.648609	+	0.761122i	$0.275351\pi$
$464$	−3.63991	−	4.04253i	−0.168979	−	0.187670i
$465$		0			0
$466$	−4.82441	+	45.9012i	−0.223487	+	2.12633i
$467$	22.0042	−	7.14959i	1.01823	−	0.330844i	0.248104	−	0.968733i	$-0.420192\pi$
$467$	22.0042	−	7.14959i	1.01823	−	0.330844i	0.770128	+	0.637890i	$0.220192\pi$
$468$		0			0
$469$	2.74382	−	3.77655i	0.126698	−	0.174385i
$470$	−15.0263	−	6.69014i	−0.693112	−	0.308593i
$471$		0			0
$472$	−50.6046	−	29.2166i	−2.32927	−	1.34480i
$473$	16.5430	−	3.65681i	0.760648	−	0.168140i
$474$		0			0
$475$	1.24755	+	5.86925i	0.0572414	+	0.269300i
$476$	−16.6142	−	22.8675i	−0.761510	−	1.04813i
$477$		0			0
$478$	18.1884	+	55.9783i	0.831920	+	2.56039i
$479$	−0.299837	+	0.333002i	−0.0136999	+	0.0152153i	−0.749956	−	0.661488i	$-0.769925\pi$
$479$	−0.299837	+	0.333002i	−0.0136999	+	0.0152153i	0.736256	+	0.676703i	$0.236592\pi$
$480$		0			0
$481$	37.3556	−	3.92623i	1.70327	−	0.179021i
$482$	−19.2206	+	17.3063i	−0.875476	+	0.788282i
$483$		0			0
$484$	45.4387	+	8.89048i	2.06539	+	0.404113i
$485$		−	3.34385i		−	0.151836i
$486$		0			0
$487$	3.32024	−	2.41230i	0.150455	−	0.109312i	−0.510011	−	0.860168i	$-0.670359\pi$
$487$	3.32024	−	2.41230i	0.150455	−	0.109312i	0.660466	+	0.750856i	$0.270359\pi$
$488$	16.0810	+	1.69018i	0.727954	+	0.0765111i
$489$		0			0
$490$	2.04764	−	9.63340i	0.0925030	−	0.435193i
$491$	−22.6072	+	10.0654i	−1.02025	+	0.454245i	−0.847542	−	0.530729i	$-0.821918\pi$
$491$	−22.6072	+	10.0654i	−1.02025	+	0.454245i	−0.172708	+	0.984973i	$0.555252\pi$
$492$		0			0
$493$	2.15476	−	0.458008i	0.0970454	−	0.0206276i
$494$	−26.8281			−1.20705
$495$		0			0
$496$	−49.8490			−2.23829
$497$	−34.1609	+	7.26113i	−1.53233	+	0.325706i
$498$		0			0
$499$	1.42258	−	0.633373i	0.0636834	−	0.0283537i	−0.374648	−	0.927167i	$-0.622236\pi$
$499$	1.42258	−	0.633373i	0.0636834	−	0.0283537i	0.438331	+	0.898814i	$0.355570\pi$
$500$	9.89985	−	46.5751i	0.442735	−	2.08290i
$501$		0			0
$502$	16.2002	+	1.70271i	0.723052	+	0.0759958i
$503$	3.60435	−	2.61872i	0.160710	−	0.116763i	−0.504524	−	0.863398i	$-0.668332\pi$
$503$	3.60435	−	2.61872i	0.160710	−	0.116763i	0.665234	+	0.746635i	$0.268332\pi$
$504$		0			0
$505$		−	18.7609i		−	0.834847i
$506$	8.95194	+	6.39368i	0.397962	+	0.284234i
$507$		0			0
$508$	33.7116	−	30.3540i	1.49571	−	1.34674i
$509$	28.7887	−	3.02581i	1.27604	−	0.134117i	0.557835	−	0.829952i	$-0.311632\pi$
$509$	28.7887	−	3.02581i	1.27604	−	0.134117i	0.718202	+	0.695835i	$0.244966\pi$
$510$		0			0
$511$	19.4381	−	21.5882i	0.859892	−	0.955007i
$512$	14.4346	+	44.4253i	0.637927	+	1.96334i
$513$		0			0
$514$	15.6182	+	21.4966i	0.688890	+	0.948176i
$515$	2.19793	+	10.3404i	0.0968523	+	0.455654i
$516$		0			0
$517$	10.2671	−	11.5904i	0.451546	−	0.509747i
$518$	47.1146	+	27.2016i	2.07010	+	1.19517i
$519$		0			0
$520$	38.2849	+	17.0455i	1.67890	+	0.747495i
$521$	24.7832	−	34.1112i	1.08577	−	1.49444i	0.232769	−	0.972532i	$-0.425221\pi$
$521$	24.7832	−	34.1112i	1.08577	−	1.49444i	0.853003	−	0.521905i	$-0.174779\pi$
$522$		0			0
$523$	−12.4929	+	4.05920i	−0.546277	+	0.177496i	−0.569137	−	0.822242i	$-0.692723\pi$
$523$	−12.4929	+	4.05920i	−0.546277	+	0.177496i	0.0228601	+	0.999739i	$0.492723\pi$
$524$	7.56523	−	71.9783i	0.330488	−	3.14439i
$525$		0			0
$526$	−33.5779	−	37.2920i	−1.46407	−	1.62601i
$527$	10.0935	−	17.4824i	0.439678	−	0.761545i
$528$		0			0
$529$	−10.6141	−	18.3841i	−0.461482	−	0.799310i
$530$	−5.47335	+	16.8452i	−0.237747	+	0.731711i
$531$		0			0
$532$	−21.3105	−	15.4829i	−0.923925	−	0.671271i
$533$	−12.8179	−	11.5413i	−0.555206	−	0.499909i
$534$		0			0
$535$	−0.562370	−	1.26310i	−0.0243134	−	0.0546087i
$536$	0.858212	+	8.16534i	0.0370691	+	0.352689i
$537$		0			0
$538$	−20.9668	+	12.1052i	−0.903943	+	0.521892i
$539$	8.06639	+	4.57030i	0.347444	+	0.196857i
$540$		0			0
$541$	−9.06438	−	2.94519i	−0.389708	−	0.126624i	0.107608	−	0.994193i	$-0.465681\pi$
$541$	−9.06438	−	2.94519i	−0.389708	−	0.126624i	−0.497316	+	0.867570i	$0.665681\pi$
$542$	−23.7751	+	53.3997i	−1.02123	+	2.29372i
$543$		0			0
$544$	4.60312	+	0.978423i	0.197357	+	0.0419495i
$545$	7.44120	+	1.58168i	0.318746	+	0.0677515i
$546$		0			0
$547$	−9.92567	+	22.2934i	−0.424391	+	0.953197i	0.567175	+	0.823597i	$0.308036\pi$
$547$	−9.92567	+	22.2934i	−0.424391	+	0.953197i	−0.991566	+	0.129600i	$0.958631\pi$
$548$	−39.4578	−	12.8206i	−1.68555	−	0.547669i
$549$		0			0
$550$	21.5775	+	12.2255i	0.920066	+	0.521297i
$551$	1.77787	−	1.02645i	0.0757397	−	0.0437283i
$552$		0			0
$553$	3.45877	+	32.9080i	0.147082	+	1.39939i
$554$	17.6765	+	39.7022i	0.751005	+	1.68678i
$555$		0			0
$556$	−6.91236	−	6.22391i	−0.293149	−	0.263953i
$557$	10.0179	+	7.27845i	0.424473	+	0.308398i	0.779435	−	0.626483i	$-0.215506\pi$
$557$	10.0179	+	7.27845i	0.424473	+	0.308398i	−0.354962	+	0.934881i	$0.615506\pi$
$558$		0			0
$559$	−8.49964	+	26.1592i	−0.359497	+	1.10642i
$560$	11.7233	+	20.3053i	0.495399	+	0.858056i
$561$		0			0
$562$	−28.5675	+	49.4804i	−1.20505	+	2.08721i
$563$	1.96151	+	2.17848i	0.0826679	+	0.0918120i	0.783060	−	0.621947i	$-0.213658\pi$
$563$	1.96151	+	2.17848i	0.0826679	+	0.0918120i	−0.700392	+	0.713759i	$0.746991\pi$
$564$		0			0
$565$	0.787628	−	7.49378i	0.0331358	−	0.315266i
$566$	−51.2792	+	16.6616i	−2.15542	+	0.700340i
$567$		0			0
$568$	36.1049	−	49.6942i	1.51493	−	2.08512i
$569$	−11.6758	−	5.19842i	−0.489476	−	0.217929i	0.147131	−	0.989117i	$-0.452996\pi$
$569$	−11.6758	−	5.19842i	−0.489476	−	0.217929i	−0.636607	+	0.771188i	$0.719663\pi$
$570$		0			0
$571$	0.582904	+	0.336539i	0.0243938	+	0.0140837i	0.512147	−	0.858898i	$-0.328850\pi$
$571$	0.582904	+	0.336539i	0.0243938	+	0.0140837i	−0.487754	+	0.872981i	$0.662184\pi$
$572$	−49.8419	+	56.2662i	−2.08400	+	2.35261i
$573$		0			0
$574$	−5.19406	−	24.4361i	−0.216796	−	1.01994i
$575$	2.34787	+	3.23156i	0.0979128	+	0.134765i
$576$		0			0
$577$	−7.29562	−	22.4536i	−0.303721	−	0.934756i	−0.980151	−	0.198250i	$-0.936474\pi$
$577$	−7.29562	−	22.4536i	−0.303721	−	0.934756i	0.676431	−	0.736506i	$-0.263526\pi$
$578$	20.6687	−	22.9549i	0.859705	−	0.954799i
$579$		0			0
$580$	−6.07663	+	0.638679i	−0.252318	+	0.0265197i
$581$	15.8418	−	14.2640i	0.657229	−	0.591772i
$582$		0			0
$583$	−13.5683	−	9.69077i	−0.561941	−	0.401351i
$584$			51.0936i			2.11427i
$585$		0			0
$586$	−39.2172	+	28.4930i	−1.62005	+	1.17703i
$587$	−12.9008	−	1.35593i	−0.532475	−	0.0559653i	−0.165524	−	0.986206i	$-0.552932\pi$
$587$	−12.9008	−	1.35593i	−0.532475	−	0.0559653i	−0.366951	+	0.930240i	$0.619598\pi$
$588$		0			0
$589$	3.91133	−	18.4013i	0.161163	−	0.758214i
$590$	−34.1660	+	15.2117i	−1.40659	+	0.626256i
$591$		0			0
$592$	−36.1535	+	7.68466i	−1.48590	+	0.315838i
$593$	35.3371			1.45112			0.725561	−	0.688158i	$-0.241581\pi$
$593$	35.3371			1.45112			0.725561	+	0.688158i	$0.241581\pi$
$594$		0			0
$595$	−9.49495			−0.389255
$596$	−22.4852	+	4.77938i	−0.921030	+	0.195771i
$597$		0			0
$598$	−16.3154	+	7.26407i	−0.667185	+	0.297050i
$599$	5.17750	−	24.3582i	0.211547	−	0.995250i	−0.736332	−	0.676620i	$-0.763444\pi$
$599$	5.17750	−	24.3582i	0.211547	−	0.995250i	0.947879	−	0.318630i	$-0.103223\pi$
$600$		0			0
$601$	−31.8867	−	3.35142i	−1.30068	−	0.136707i	−0.571260	−	0.820769i	$-0.693545\pi$
$601$	−31.8867	−	3.35142i	−1.30068	−	0.136707i	−0.729424	+	0.684062i	$0.760212\pi$
$602$	−32.2300	+	23.4164i	−1.31360	+	0.954383i
$603$		0			0
$604$			2.17796i			0.0886200i
$605$	11.3878	−	10.5931i	0.462982	−	0.430672i
$606$		0			0
$607$	17.8339	−	16.0577i	0.723857	−	0.651764i	−0.222483	−	0.974937i	$-0.571416\pi$
$607$	17.8339	−	16.0577i	0.723857	−	0.651764i	0.946340	+	0.323173i	$0.104750\pi$
$608$	4.36151	−	0.458413i	0.176883	−	0.0185911i
$609$		0			0
$610$	6.92493	−	7.69091i	0.280382	−	0.311396i
$611$	7.76797	+	23.9073i	0.314258	+	0.967188i
$612$		0			0
$613$	−21.1678	−	29.1350i	−0.854959	−	1.17675i	−0.982748	−	0.184949i	$-0.940788\pi$
$613$	−21.1678	−	29.1350i	−0.854959	−	1.17675i	0.127789	−	0.991801i	$-0.459212\pi$
$614$	1.07870	+	5.07487i	0.0435327	+	0.204805i
$615$		0			0
$616$	−55.7931	+	12.3330i	−2.24797	+	0.496910i
$617$	−39.9420	−	23.0605i	−1.60800	−	0.928381i	−0.989816	−	0.142350i	$-0.954534\pi$
$617$	−39.9420	−	23.0605i	−1.60800	−	0.928381i	−0.618187	−	0.786031i	$-0.712132\pi$
$618$		0			0
$619$	40.6867	+	18.1149i	1.63534	+	0.728100i	0.999060	−	0.0433597i	$-0.0138062\pi$
$619$	40.6867	+	18.1149i	1.63534	+	0.728100i	0.636279	+	0.771459i	$0.280473\pi$
$620$	−32.9112	+	45.2983i	−1.32174	+	1.81923i
$621$		0			0
$622$	31.0219	−	10.0796i	1.24386	−	0.404156i
$623$	2.63857	−	25.1043i	0.105712	−	1.00578i
$624$		0			0
$625$	−0.662894	−	0.736219i	−0.0265158	−	0.0294487i
$626$	3.73360	−	6.46678i	0.149225	−	0.258465i
$627$		0			0
$628$	28.3865	+	49.1668i	1.13274	+	1.96197i
$629$	4.62532	−	14.2353i	0.184424	−	0.567598i
$630$		0			0
$631$	29.7072	+	21.5835i	1.18262	+	0.859227i	0.992465	−	0.122527i	$-0.0390997\pi$
$631$	29.7072	+	21.5835i	1.18262	+	0.859227i	0.190159	+	0.981753i	$0.439100\pi$
$632$	−43.2497	−	38.9422i	−1.72038	−	1.54904i
$633$		0			0
$634$	32.3651	+	72.6933i	1.28538	+	2.88702i
$635$	−1.59284	−	15.1549i	−0.0632099	−	0.601402i
$636$		0			0
$637$	−13.0349	+	7.52572i	−0.516463	+	0.298180i
$638$	1.69673	−	8.31350i	0.0671743	−	0.329135i
$639$		0			0
$640$	23.0936	+	7.50356i	0.912854	+	0.296604i
$641$	14.2905	−	32.0971i	0.564442	−	1.26776i	−0.375626	−	0.926771i	$-0.622572\pi$
$641$	14.2905	−	32.0971i	0.564442	−	1.26776i	0.940068	−	0.340987i	$-0.110761\pi$
$642$		0			0
$643$	−4.78014	−	1.01605i	−0.188510	−	0.0400691i	0.112689	−	0.993630i	$-0.464054\pi$
$643$	−4.78014	−	1.01605i	−0.188510	−	0.0400691i	−0.301199	+	0.953561i	$0.597387\pi$
$644$	−17.1521	−	3.64578i	−0.675886	−	0.143664i
$645$		0			0
$646$	−4.34832	+	9.76649i	−0.171082	+	0.384257i
$647$	13.2744	+	4.31311i	0.521870	+	0.169566i	0.558094	−	0.829778i	$-0.311533\pi$
$647$	13.2744	+	4.31311i	0.521870	+	0.169566i	−0.0362237	+	0.999344i	$0.511533\pi$
$648$		0			0
$649$	−3.96395	−	34.9827i	−0.155599	−	1.37319i
$650$	−34.8683	+	20.1312i	−1.36765	+	0.789611i
$651$		0			0
$652$	8.45812	+	80.4737i	0.331246	+	3.15159i
$653$	−4.92843	−	11.0694i	−0.192865	−	0.433181i	0.791066	−	0.611730i	$-0.209526\pi$
$653$	−4.92843	−	11.0694i	−0.192865	−	0.433181i	−0.983931	+	0.178549i	$0.942860\pi$
$654$		0			0
$655$	−18.0673	−	16.2679i	−0.705948	−	0.635638i
$656$	13.7311	+	9.97625i	0.536111	+	0.389507i
$657$		0			0
$658$	−11.2510	+	34.6270i	−0.438610	+	1.34990i
$659$	24.0221	+	41.6074i	0.935767	+	1.62080i	0.773261	+	0.634088i	$0.218624\pi$
$659$	24.0221	+	41.6074i	0.935767	+	1.62080i	0.162506	+	0.986708i	$0.448042\pi$
$660$		0			0
$661$	0.589966	−	1.02185i	0.0229470	−	0.0397454i	−0.854324	−	0.519741i	$-0.826028\pi$
$661$	0.589966	−	1.02185i	0.0229470	−	0.0397454i	0.877271	+	0.479996i	$0.159362\pi$
$662$	−43.9486	−	48.8099i	−1.70811	−	1.89705i
$663$		0			0
$664$	−3.91912	+	37.2879i	−0.152091	+	1.44705i
$665$	−8.41538	+	2.73432i	−0.326334	+	0.106032i
$666$		0			0
$667$	0.803275	−	1.10561i	0.0311029	−	0.0428095i
$668$	2.26697	+	1.00932i	0.0877118	+	0.0390518i
$669$		0			0
$670$	4.55088	+	2.62745i	0.175816	+	0.101507i
$671$	4.93944	+	8.39732i	0.190685	+	0.324175i
$672$		0			0
$673$	5.10854	+	24.0338i	0.196920	+	0.926435i	0.959972	+	0.280097i	$0.0903668\pi$
$673$	5.10854	+	24.0338i	0.196920	+	0.926435i	−0.763052	+	0.646337i	$0.776300\pi$
$674$	−6.14120	−	8.45263i	−0.236550	−	0.325583i
$675$		0			0
$676$	−20.8009	−	64.0187i	−0.800036	−	2.46226i
$677$	28.0942	−	31.2017i	1.07975	−	1.19918i	0.100833	−	0.994903i	$-0.467849\pi$
$677$	28.0942	−	31.2017i	1.07975	−	1.19918i	0.978913	−	0.204276i	$-0.0654841\pi$
$678$		0			0
$679$	−7.36118	+	0.773692i	−0.282496	+	0.0296916i
$680$	12.4105	−	11.1745i	0.475920	−	0.428521i
$681$		0			0
$682$	−46.2113	−	62.5315i	−1.76952	−	2.39445i
$683$			45.5024i			1.74110i	0.492081	+	0.870550i	$0.336236\pi$
$683$			45.5024i			1.74110i	−0.492081	+	0.870550i	$0.663764\pi$
$684$		0			0
$685$	−11.2750	+	8.19176i	−0.430795	+	0.312991i
$686$	32.6113	+	3.42759i	1.24511	+	0.130866i
$687$		0			0
$688$	5.62732	−	26.4745i	0.214540	−	1.00933i
$689$	24.7289	−	11.0100i	0.942095	−	0.419448i
$690$		0			0
$691$	45.9376	−	9.76434i	1.74755	−	0.371453i	0.780324	−	0.625375i	$-0.215054\pi$
$691$	45.9376	−	9.76434i	1.74755	−	0.371453i	0.967225	+	0.253922i	$0.0817207\pi$
$692$	15.3388			0.583092
$693$		0			0
$694$	85.6506			3.25125
$695$	−3.05625	+	0.649627i	−0.115930	+	0.0246417i
$696$		0			0
$697$	−6.27903	+	2.79560i	−0.237835	+	0.105891i
$698$	−10.7905	+	50.7653i	−0.408427	+	1.92150i
$699$		0			0
$700$	−39.3151	−	4.13218i	−1.48597	−	0.156182i
$701$	−7.98290	+	5.79992i	−0.301510	+	0.219060i	−0.728245	−	0.685317i	$-0.759664\pi$
$701$	−7.98290	+	5.79992i	−0.301510	+	0.219060i	0.426735	+	0.904377i	$0.359664\pi$
$702$		0			0
$703$		−	13.9487i		−	0.526086i
$704$	−9.89197	+	13.8500i	−0.372818	+	0.521991i
$705$		0			0
$706$	15.3277	−	13.8011i	0.576864	−	0.519411i
$707$	−41.3004	+	4.34085i	−1.55326	+	0.163254i
$708$		0			0
$709$	−17.8763	+	19.8536i	−0.671357	+	0.745618i	−0.978545	−	0.206031i	$-0.933945\pi$
$709$	−17.8763	+	19.8536i	−0.671357	+	0.745618i	0.307188	+	0.951649i	$0.400612\pi$
$710$	−12.1489	−	37.3903i	−0.455938	−	1.40323i
$711$		0			0
$712$	26.0961	+	35.9182i	0.977992	+	1.34609i
$713$	−2.60376	−	12.2497i	−0.0975116	−	0.458756i
$714$		0			0
$715$	5.44990	+	24.6548i	0.203815	+	0.922036i
$716$	20.8533	+	12.0397i	0.779325	+	0.449944i
$717$		0			0
$718$	−28.9903	−	12.9073i	−1.08191	−	0.481697i
$719$	−16.7605	+	23.0689i	−0.625061	+	0.860323i	−0.997709	−	0.0676497i	$-0.978450\pi$
$719$	−16.7605	+	23.0689i	−0.625061	+	0.860323i	0.372648	+	0.927973i	$0.378450\pi$
$720$		0			0
$721$	22.2550	−	7.23110i	0.828821	−	0.269300i
$722$	3.90743	−	37.1768i	0.145420	−	1.38358i
$723$		0			0
$724$	−22.6516	−	25.1571i	−0.841839	−	0.934957i
$725$	1.54045	−	2.66814i	0.0572110	−	0.0990923i
$726$		0			0
$727$	−0.983296	−	1.70312i	−0.0364684	−	0.0631652i	0.847215	−	0.531250i	$-0.178278\pi$
$727$	−0.983296	−	1.70312i	−0.0364684	−	0.0631652i	−0.883684	+	0.468085i	$0.844944\pi$
$728$	28.6660	−	88.2247i	1.06243	−	3.26983i
$729$		0			0
$730$	26.4563	+	19.2216i	0.979191	+	0.711424i
$731$	8.14536	+	7.33411i	0.301267	+	0.271262i
$732$		0			0
$733$	−19.0092	−	42.6955i	−0.702122	−	1.57699i	−0.812406	−	0.583093i	$-0.801842\pi$
$733$	−19.0092	−	42.6955i	−0.702122	−	1.57699i	0.110283	−	0.993900i	$-0.464824\pi$
$734$	−5.47862	−	52.1256i	−0.202220	−	1.92399i
$735$		0			0
$736$	2.52831	−	1.45972i	0.0931947	−	0.0538060i
$737$	−3.64921	+	3.33976i	−0.134421	+	0.123022i
$738$		0			0
$739$	16.2275	+	5.27262i	0.596937	+	0.193957i	0.591874	−	0.806031i	$-0.298388\pi$
$739$	16.2275	+	5.27262i	0.596937	+	0.193957i	0.00506302	+	0.999987i	$0.498388\pi$
$740$	−16.8860	+	37.9266i	−0.620742	+	1.39421i
$741$		0			0
$742$	38.3497	+	8.15149i	1.40786	+	0.299251i
$743$	−40.4330	−	8.59430i	−1.48334	−	0.315294i	−0.606119	−	0.795374i	$-0.707274\pi$
$743$	−40.4330	−	8.59430i	−1.48334	−	0.315294i	−0.877225	+	0.480080i	$0.840608\pi$
$744$		0			0
$745$	−3.14078	+	7.05432i	−0.115069	+	0.258450i
$746$	39.1155	+	12.7094i	1.43212	+	0.465325i
$747$		0			0
$748$	12.4047	+	27.2641i	0.453560	+	0.996874i
$749$	−2.65049	+	1.53026i	−0.0968469	+	0.0559146i
$750$		0			0
$751$	−4.75912	−	45.2800i	−0.173663	−	1.65229i	−0.640508	−	0.767952i	$-0.721276\pi$
$751$	−4.75912	−	45.2800i	−0.173663	−	1.65229i	0.466845	−	0.884339i	$-0.345391\pi$
$752$	−10.0610	−	22.5975i	−0.366889	−	0.824045i
$753$		0			0
$754$	10.2368	+	9.21725i	0.372802	+	0.335672i
$755$	0.591889	+	0.430032i	0.0215410	+	0.0156505i
$756$		0			0
$757$	−13.3554	+	41.1036i	−0.485409	+	1.49393i	0.345979	+	0.938242i	$0.387547\pi$
$757$	−13.3554	+	41.1036i	−0.485409	+	1.49393i	−0.831388	+	0.555692i	$0.812453\pi$
$758$	−17.7841	−	30.8029i	−0.645947	−	1.11881i
$759$		0			0
$760$	7.78144	−	13.4779i	0.282263	−	0.488893i
$761$	13.3175	+	14.7906i	0.482761	+	0.536160i	0.934487	−	0.355996i	$-0.115858\pi$
$761$	13.3175	+	14.7906i	0.482761	+	0.536160i	−0.451727	+	0.892156i	$0.649192\pi$
$762$		0			0
$763$	1.76019	−	16.7471i	0.0637232	−	0.606286i
$764$	48.9441	−	15.9029i	1.77074	−	0.575347i
$765$		0			0
$766$	−14.8756	+	20.4745i	−0.537477	+	0.739774i
$767$	52.2153	+	23.2478i	1.88539	+	0.839428i
$768$		0			0
$769$	34.6081	+	19.9810i	1.24800	+	0.720534i	0.970711	−	0.240252i	$-0.0772300\pi$
$769$	34.6081	+	19.9810i	1.24800	+	0.720534i	0.277291	+	0.960786i	$0.410563\pi$
$770$	−14.6036	+	33.5294i	−0.526276	+	1.20832i
$771$		0			0
$772$	−14.6650	−	68.9936i	−0.527806	−	2.48313i
$773$	−0.983134	−	1.35317i	−0.0353609	−	0.0486701i	0.790970	−	0.611854i	$-0.209576\pi$
$773$	−0.983134	−	1.35317i	−0.0353609	−	0.0486701i	−0.826331	+	0.563184i	$0.809576\pi$
$774$		0			0
$775$	−8.72443	−	26.8510i	−0.313391	−	0.964518i
$776$	8.71098	−	9.67452i	0.312706	−	0.347295i
$777$		0			0
$778$	−51.2447	+	5.38604i	−1.83721	+	0.193099i
$779$	−4.76004	+	4.28596i	−0.170546	+	0.153560i
$780$		0			0
$781$	37.0081	−	0.300171i	1.32426	−	0.0107410i
$782$			7.11680i			0.254496i
$783$		0			0
$784$	11.9823	−	8.70566i	0.427940	−	0.310916i
$785$	18.9665	+	1.99346i	0.676945	+	0.0711498i
$786$		0			0
$787$	−1.95508	+	9.19792i	−0.0696910	+	0.327870i	−0.999158	−	0.0410357i	$-0.986934\pi$
$787$	−1.95508	+	9.19792i	−0.0696910	+	0.327870i	0.929467	+	0.368906i	$0.120268\pi$
$788$	25.5172	−	11.3610i	0.909014	−	0.404719i
$789$		0			0
$790$	−36.4350	+	7.74450i	−1.29630	+	0.275537i
$791$	−16.6791			−0.593042
$792$		0			0
$793$	−15.8164			−0.561657
$794$	81.9068	−	17.4098i	2.90676	−	0.617852i
$795$		0			0
$796$	−12.4892	+	5.56056i	−0.442669	+	0.197089i
$797$	−6.13517	+	28.8637i	−0.217319	+	1.02241i	0.725274	+	0.688461i	$0.241713\pi$
$797$	−6.13517	+	28.8637i	−0.217319	+	1.02241i	−0.942593	+	0.333945i	$0.891620\pi$
$798$		0			0
$799$	9.96226	+	1.04708i	0.352439	+	0.0370429i
$800$	5.32464	−	3.86857i	0.188254	−	0.136775i
$801$		0			0
$802$			8.93881i			0.315640i
$803$	−24.7575	+	18.2960i	−0.873672	+	0.645651i
$804$		0			0
$805$	−4.37741	+	3.94144i	−0.154284	+	0.138918i
$806$	125.540	−	13.1948i	4.42195	−	0.464766i
$807$		0			0
$808$	48.8735	−	54.2795i	1.71936	−	1.90955i
$809$	−16.3139	−	50.2091i	−0.573567	−	1.76526i	−0.641008	−	0.767534i	$-0.721484\pi$
$809$	−16.3139	−	50.2091i	−0.573567	−	1.76526i	0.0674416	−	0.997723i	$-0.478516\pi$
$810$		0			0
$811$	9.82048	+	13.5167i	0.344844	+	0.474636i	0.945848	−	0.324609i	$-0.105233\pi$
$811$	9.82048	+	13.5167i	0.344844	+	0.474636i	−0.601005	+	0.799245i	$0.705233\pi$
$812$	2.81199	+	13.2294i	0.0986816	+	0.464260i
$813$		0			0
$814$	−43.1550	−	38.2277i	−1.51258	−	1.33988i
$815$	23.5398	+	13.5907i	0.824562	+	0.476061i
$816$		0			0
$817$	9.33129	+	4.15456i	0.326460	+	0.145350i
$818$	−5.56375	+	7.65785i	−0.194532	+	0.267750i
$819$		0			0
$820$	18.1311	−	5.89114i	0.633164	−	0.205727i
$821$	−1.91377	+	18.2083i	−0.0667909	+	0.635473i	0.909004	+	0.416787i	$0.136844\pi$
$821$	−1.91377	+	18.2083i	−0.0667909	+	0.635473i	−0.975795	+	0.218686i	$0.929823\pi$
$822$		0			0
$823$	−7.62614	−	8.46969i	−0.265831	−	0.295235i	0.595421	−	0.803414i	$-0.296985\pi$
$823$	−7.62614	−	8.46969i	−0.265831	−	0.295235i	−0.861251	+	0.508179i	$0.830319\pi$
$824$	−20.5785	+	35.6431i	−0.716887	+	1.24169i
$825$		0			0
$826$	41.3925	+	71.6939i	1.44023	+	2.49455i
$827$	5.84858	−	18.0001i	0.203375	−	0.625924i	−0.796401	−	0.604769i	$-0.793266\pi$
$827$	5.84858	−	18.0001i	0.203375	−	0.625924i	0.999776	−	0.0211551i	$-0.00673439\pi$
$828$		0			0
$829$	13.0466	+	9.47891i	0.453127	+	0.329216i	0.790829	−	0.612037i	$-0.209650\pi$
$829$	13.0466	+	9.47891i	0.453127	+	0.329216i	−0.337702	+	0.941253i	$0.609650\pi$
$830$	17.8333	+	16.0572i	0.619004	+	0.557354i
$831$		0			0
$832$	−11.2386	−	25.2423i	−0.389628	−	0.875119i
$833$	0.626948	+	5.96501i	0.0217224	+	0.206675i
$834$		0			0
$835$	0.721904	−	0.416791i	0.0249825	−	0.0144237i
$836$	18.8457	+	20.5919i	0.651792	+	0.712187i
$837$		0			0
$838$	−21.3614	−	6.94074i	−0.737917	−	0.239764i
$839$	9.44446	−	21.2126i	0.326059	−	0.732341i	−0.673920	−	0.738804i	$-0.735391\pi$
$839$	9.44446	−	21.2126i	0.326059	−	0.732341i	0.999979	+	0.00646370i	$0.00205747\pi$
$840$		0			0
$841$	27.3352	+	5.81029i	0.942595	+	0.200355i
$842$	21.5748	+	4.58587i	0.743518	+	0.158040i
$843$		0			0
$844$	13.6651	−	30.6922i	0.470371	−	1.05647i
$845$	−21.5050	−	6.98739i	−0.739794	−	0.240374i
$846$		0			0
$847$	−25.9548	−	22.6183i	−0.891816	−	0.777175i
$848$	−23.0680	+	13.3183i	−0.792158	+	0.457352i
$849$		0			0
$850$	1.67708	+	15.9563i	0.0575232	+	0.547297i
$851$	−3.77680	−	8.48284i	−0.129467	−	0.290788i
$852$		0			0
$853$	18.3942	+	16.5622i	0.629805	+	0.567079i	0.920989	−	0.389588i	$-0.127383\pi$
$853$	18.3942	+	16.5622i	0.629805	+	0.567079i	−0.291184	+	0.956667i	$0.594049\pi$
$854$	−18.5332	−	13.4651i	−0.634191	−	0.460767i
$855$		0			0
$856$	1.66342	−	5.11947i	0.0568544	−	0.174980i
$857$	4.20876	+	7.28979i	0.143769	+	0.249014i	0.928913	−	0.370298i	$-0.120745\pi$
$857$	4.20876	+	7.28979i	0.143769	+	0.249014i	−0.785144	+	0.619313i	$0.787411\pi$
$858$		0			0
$859$	−26.3276	+	45.6007i	−0.898285	+	1.55587i	−0.0685984	+	0.997644i	$0.521853\pi$
$859$	−26.3276	+	45.6007i	−0.898285	+	1.55587i	−0.829686	+	0.558230i	$0.811481\pi$
$860$	−20.3424	−	22.5925i	−0.693670	−	0.770398i
$861$		0			0
$862$	9.72642	−	92.5407i	0.331283	−	3.15195i
$863$	−37.6211	+	12.2238i	−1.28064	+	0.416104i	−0.868804	−	0.495156i	$-0.835111\pi$
$863$	−37.6211	+	12.2238i	−1.28064	+	0.416104i	−0.411832	+	0.911260i	$0.635111\pi$
$864$		0			0
$865$	3.02860	−	4.16851i	0.102975	−	0.141733i
$866$	−91.0812	−	40.5520i	−3.09507	−	1.37801i
$867$		0			0
$868$	107.335	+	61.9701i	3.64320	+	2.10340i
$869$	3.38232	−	34.9014i	0.114737	−	1.18395i
$870$		0			0
$871$	−1.66973	−	7.85548i	−0.0565768	−	0.266173i
$872$	17.4087	+	23.9611i	0.589534	+	0.811424i
$873$		0			0
$874$	2.04947	+	6.30763i	0.0693245	+	0.213359i
$875$	−23.6908	+	26.3113i	−0.800896	+	0.889485i
$876$		0			0
$877$	−38.1756	+	4.01242i	−1.28910	+	0.135490i	−0.724154	−	0.689639i	$-0.757769\pi$
$877$	−38.1756	+	4.01242i	−1.28910	+	0.135490i	−0.564945	+	0.825129i	$0.691103\pi$
$878$	−24.5496	+	22.1046i	−0.828510	+	0.745994i
$879$		0			0
$880$	−7.86939	−	23.5674i	−0.265277	−	0.794456i
$881$			25.4083i			0.856026i	0.903772	+	0.428013i	$0.140786\pi$
$881$			25.4083i			0.856026i	−0.903772	+	0.428013i	$0.859214\pi$
$882$		0			0
$883$	4.42613	−	3.21577i	0.148951	−	0.108219i	−0.510814	−	0.859691i	$-0.670656\pi$
$883$	4.42613	−	3.21577i	0.148951	−	0.108219i	0.659765	+	0.751472i	$0.270656\pi$
$884$	−48.3621	−	5.08306i	−1.62659	−	0.170962i
$885$		0			0
$886$	−2.07675	+	9.77034i	−0.0697698	+	0.328241i
$887$	−3.83963	+	1.70951i	−0.128922	+	0.0573998i	−0.470184	−	0.882568i	$-0.655812\pi$
$887$	−3.83963	+	1.70951i	−0.128922	+	0.0573998i	0.341262	+	0.939968i	$0.389146\pi$
$888$		0			0
$889$	−32.9936	+	7.01300i	−1.10657	+	0.235208i
$890$	28.4159			0.952504
$891$		0			0
$892$	−58.5123			−1.95914
$893$	9.13109	−	1.94087i	0.305560	−	0.0649489i
$894$		0			0
$895$	7.38936	−	3.28996i	0.246999	−	0.109971i
$896$	11.1751	−	52.5747i	0.373333	−	1.75640i
$897$		0			0
$898$	−54.3949	−	5.71713i	−1.81518	−	0.190783i
$899$	−7.81454	+	5.67759i	−0.260629	+	0.189358i
$900$		0			0
$901$		−	10.7868i		−	0.359360i
$902$	0.214719	+	26.4728i	0.00714938	+	0.881448i
$903$		0			0
$904$	21.8007	−	19.6294i	0.725080	−	0.652865i
$905$	−11.3093	+	1.18865i	−0.375932	+	0.0395121i
$906$		0			0
$907$	−26.3613	+	29.2772i	−0.875312	+	0.972133i	−0.999798	−	0.0200885i	$-0.993605\pi$
$907$	−26.3613	+	29.2772i	−0.875312	+	0.972133i	0.124486	+	0.992221i	$0.460272\pi$
$908$	−27.0956	−	83.3917i	−0.899199	−	2.76745i
$909$		0			0
$910$	−34.8986	−	48.0338i	−1.15688	−	1.59230i
$911$	1.63359	+	7.68544i	0.0541233	+	0.254630i	0.996888	−	0.0788280i	$-0.0251178\pi$
$911$	1.63359	+	7.68544i	0.0541233	+	0.254630i	−0.942765	+	0.333458i	$0.891784\pi$
$912$		0			0
$913$	−19.4713	+	11.4533i	−0.644407	+	0.379050i
$914$	−38.5129	−	22.2354i	−1.27389	−	0.735482i
$915$		0			0
$916$	56.9646	+	25.3623i	1.88216	+	0.837994i
$917$	−31.6319	+	43.5376i	−1.04458	+	1.43774i
$918$		0			0
$919$	−39.9674	+	12.9862i	−1.31840	+	0.428376i	−0.881947	−	0.471349i	$-0.843767\pi$
$919$	−39.9674	+	12.9862i	−1.31840	+	0.428376i	−0.436458	+	0.899725i	$0.643767\pi$
$920$	1.08293	−	10.3034i	0.0357032	−	0.339693i
$921$		0			0
$922$	19.2502	+	21.3795i	0.633970	+	0.704095i
$923$	−30.0418	+	52.0339i	−0.988838	+	1.71272i
$924$		0			0
$925$	−10.4668	−	18.1290i	−0.344146	−	0.596079i
$926$	−11.0959	+	34.1497i	−0.364635	+	1.12223i
$927$		0			0
$928$	−1.82172	−	1.32355i	−0.0598007	−	0.0434478i
$929$	−14.8715	−	13.3904i	−0.487919	−	0.439324i	0.388088	−	0.921622i	$-0.373136\pi$
$929$	−14.8715	−	13.3904i	−0.487919	−	0.439324i	−0.876007	+	0.482298i	$0.839802\pi$
$930$		0			0
$931$	2.27345	+	5.10625i	0.0745092	+	0.167350i
$932$	8.14930	+	77.5354i	0.266939	+	2.53976i
$933$		0			0
$934$	49.9280	−	28.8260i	1.63369	−	0.943214i
$935$	9.85864	+	2.01209i	0.322412	+	0.0658023i
$936$		0			0
$937$	−39.0020	−	12.6725i	−1.27414	−	0.413993i	−0.407627	−	0.913149i	$-0.633643\pi$
$937$	−39.0020	−	12.6725i	−1.27414	−	0.413993i	−0.866512	+	0.499156i	$0.833643\pi$
$938$	4.73114	−	10.6263i	0.154477	−	0.346961i
$939$		0			0
$940$	−27.1770	−	5.77666i	−0.886417	−	0.188414i
$941$	−14.9704	−	3.18207i	−0.488023	−	0.103732i	−0.0426729	−	0.999089i	$-0.513587\pi$
$941$	−14.9704	−	3.18207i	−0.488023	−	0.103732i	−0.445350	+	0.895357i	$0.646921\pi$
$942$		0			0
$943$	−1.73431	+	3.89533i	−0.0564770	+	0.126849i
$944$	−53.4908	−	17.3802i	−1.74098	−	0.565677i
$945$		0			0
$946$	38.4267	−	17.4835i	1.24936	−	0.568437i
$947$	−30.7631	+	17.7611i	−0.999667	+	0.577158i	−0.908150	−	0.418645i	$-0.862505\pi$
$947$	−30.7631	+	17.7611i	−0.999667	+	0.577158i	−0.0915174	+	0.995803i	$0.529172\pi$
$948$		0			0
$949$	−5.22407	−	49.7037i	−0.169581	−	1.61345i
$950$	6.08144	+	13.6591i	0.197308	+	0.443161i
$951$		0			0
$952$	−27.4711	−	24.7351i	−0.890343	−	0.801669i
$953$	24.4990	+	17.7996i	0.793602	+	0.576585i	0.909030	−	0.416730i	$-0.136824\pi$
$953$	24.4990	+	17.7996i	0.793602	+	0.576585i	−0.115428	+	0.993316i	$0.536824\pi$
$954$		0			0
$955$	5.34206	−	16.4412i	0.172865	−	0.532024i
$956$	49.7117	+	86.1033i	1.60779	+	2.78478i
$957$		0			0
$958$	−0.558288	+	0.966984i	−0.0180375	+	0.0312418i
$959$	20.6422	+	22.9255i	0.666572	+	0.740304i
$960$		0			0
$961$	−6.01207	+	57.2010i	−0.193938	+	1.84519i
$962$	89.0148	−	28.9227i	2.86995	−	0.932504i
$963$		0			0
$964$	−25.6796	+	35.3450i	−0.827085	+	1.13838i
$965$	−21.6455	−	9.63718i	−0.696792	−	0.310232i
$966$		0			0
$967$	−17.1890	−	9.92405i	−0.552760	−	0.319136i	0.197474	−	0.980308i	$-0.436726\pi$
$967$	−17.1890	−	9.92405i	−0.552760	−	0.319136i	−0.750234	+	0.661172i	$0.770059\pi$
$968$	60.5436	−	0.982197i	1.94595	−	0.0315690i
$969$		0			0
$970$	−1.73237	−	8.15015i	−0.0556230	−	0.261685i
$971$	2.26406	+	3.11621i	0.0726570	+	0.100004i	0.843799	−	0.536660i	$-0.180314\pi$
$971$	2.26406	+	3.11621i	0.0726570	+	0.100004i	−0.771142	+	0.636663i	$0.780314\pi$
$972$		0			0
$973$	2.13725	+	6.57777i	0.0685170	+	0.210874i
$974$	6.84286	−	7.59977i	0.219260	−	0.243512i
$975$		0			0
$976$	15.4784	−	1.62685i	0.495452	−	0.0520741i
$977$	4.61642	−	4.15665i	0.147693	−	0.132983i	−0.591973	−	0.805958i	$-0.701651\pi$
$977$	4.61642	−	4.15665i	0.147693	−	0.132983i	0.739665	+	0.672975i	$0.234984\pi$
$978$		0			0
$979$	−8.05953	+	25.5068i	−0.257584	+	0.815200i
$980$		−	16.6361i		−	0.531420i
$981$		0			0
$982$	−49.8873	+	36.2452i	−1.59197	+	1.15663i
$983$	28.8816	+	3.03558i	0.921179	+	0.0968198i	0.553232	−	0.833027i	$-0.313394\pi$
$983$	28.8816	+	3.03558i	0.921179	+	0.0968198i	0.367947	+	0.929847i	$0.380061\pi$
$984$		0			0
$985$	1.95081	−	9.17784i	0.0621580	−	0.292430i
$986$	5.01463	−	2.23266i	0.159698	−	0.0711023i
$987$		0			0
$988$	−44.3272	+	9.42204i	−1.41024	+	0.299755i
$989$	6.79967			0.216217
$990$		0			0
$991$	−0.476493			−0.0151363			−0.00756816	−	0.999971i	$-0.502409\pi$
$991$	−0.476493			−0.0151363			−0.00756816	+	0.999971i	$0.502409\pi$
$992$	−20.1838	+	4.29021i	−0.640838	+	0.136214i
$993$		0			0
$994$	−79.5006	+	35.3959i	−2.52160	+	1.12269i
$995$	−0.954809	+	4.49202i	−0.0302695	+	0.142407i
$996$		0			0
$997$	25.7030	+	2.70150i	0.814024	+	0.0855573i	0.502386	−	0.864644i	$-0.332456\pi$
$997$	25.7030	+	2.70150i	0.814024	+	0.0855573i	0.311638	+	0.950201i	$0.399122\pi$
$998$	3.13920	−	2.28076i	0.0993696	−	0.0721963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.233.10		80
3.2	odd	2		99.2.p.a.68.1	yes	80
9.2	odd	6	inner	297.2.t.a.35.10		80
9.4	even	3		891.2.k.a.728.1		80
9.5	odd	6		891.2.k.a.728.20		80
9.7	even	3		99.2.p.a.2.1	✓	80
11.6	odd	10	inner	297.2.t.a.17.10		80
33.17	even	10		99.2.p.a.50.1	yes	80
99.50	even	30		891.2.k.a.809.1		80
99.61	odd	30		99.2.p.a.83.1	yes	80
99.83	even	30	inner	297.2.t.a.116.10		80
99.94	odd	30		891.2.k.a.809.20		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.2.1	✓	80	9.7	even	3
99.2.p.a.50.1	yes	80	33.17	even	10
99.2.p.a.68.1	yes	80	3.2	odd	2
99.2.p.a.83.1	yes	80	99.61	odd	30
297.2.t.a.17.10		80	11.6	odd	10	inner
297.2.t.a.35.10		80	9.2	odd	6	inner
297.2.t.a.116.10		80	99.83	even	30	inner
297.2.t.a.233.10		80	1.1	even	1	trivial
891.2.k.a.728.1		80	9.4	even	3
891.2.k.a.728.20		80	9.5	odd	6
891.2.k.a.809.1		80	99.50	even	30
891.2.k.a.809.20		80	99.94	odd	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.43736 - 0.518076i) q^{2} +(3.84522 - 1.71200i) q^{4} +(0.293969 - 1.38302i) q^{5} +(-3.11261 - 0.327148i) q^{7} +(4.45339 - 3.23558i) q^{8} -3.52320i q^{10} +(3.16251 + 0.999276i) q^{11} +(-4.00142 + 3.60290i) q^{13} +(-7.75603 + 0.815191i) q^{14} +(3.54533 - 3.93749i) q^{16} +(0.663043 + 2.04064i) q^{17} +(1.17531 + 1.61768i) q^{19} +(-1.23735 - 5.82127i) q^{20} +(8.22586 + 0.797174i) q^{22} +(1.15277 + 0.665550i) q^{23} +(2.74141 + 1.22055i) q^{25} +(-7.88632 + 10.8546i) q^{26} +(-12.5287 + 4.07083i) q^{28} +(0.107317 - 1.02105i) q^{29} +(-6.29538 - 6.99173i) q^{31} +(1.09663 - 1.89941i) q^{32} +(2.67328 + 4.63025i) q^{34} +(-1.36746 + 4.20862i) q^{35} +(-5.64362 - 4.10033i) q^{37} +(3.70273 + 3.33396i) q^{38} +(-3.16570 - 7.11027i) q^{40} +(0.334840 + 3.18579i) q^{41} +(4.42393 - 2.55416i) q^{43} +(13.8713 - 1.57178i) q^{44} +(3.15451 + 1.02496i) q^{46} +(1.89888 - 4.26495i) q^{47} +(2.73427 + 0.581187i) q^{49} +(7.31414 + 1.55467i) q^{50} +(-9.21818 + 20.7044i) q^{52} +(-4.78123 - 1.55352i) q^{53} +(2.31170 - 4.08004i) q^{55} +(-14.9202 + 8.61416i) q^{56} +(-0.267414 - 2.54427i) q^{58} +(-4.31758 - 9.69744i) q^{59} +(2.18293 + 1.96552i) q^{61} +(-18.9663 - 13.7799i) q^{62} +(-1.58577 + 4.88050i) q^{64} +(3.80657 + 6.59317i) q^{65} +(-0.745757 + 1.29169i) q^{67} +(6.04312 + 6.71156i) q^{68} +(-1.15261 + 10.9664i) q^{70} +(10.6126 - 3.44824i) q^{71} +(-5.45572 + 7.50916i) q^{73} +(-15.8798 - 7.07014i) q^{74} +(7.28879 + 4.20819i) q^{76} +(-9.51673 - 4.14496i) q^{77} +(-2.19814 - 10.3414i) q^{79} +(-4.40339 - 6.06075i) q^{80} +(2.46661 + 7.59144i) q^{82} +(-4.55756 + 5.06168i) q^{83} +(3.01715 - 0.317115i) q^{85} +(9.45944 - 8.51732i) q^{86} +(17.3171 - 5.78237i) q^{88} +8.06536i q^{89} +(13.6335 - 9.90535i) q^{91} +(5.57206 + 0.585647i) q^{92} +(2.41868 - 11.3790i) q^{94} +(2.58278 - 1.14993i) q^{95} +(2.31328 - 0.491702i) q^{97} +6.96550 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more