LMFDB - Embedded newform 891.2.u.c.458.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(107,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("891.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.u (of order $30$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			458.2
Character	$\chi$	$=$	891.458
Dual form			891.2.u.c.107.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0265163 + 0.252286i) q^{2} +(1.89335 + 0.402444i) q^{4} +(2.90572 - 0.305404i) q^{5} +(-2.02056 - 1.81932i) q^{7} +(-0.308515 + 0.949513i) q^{8} +0.741170i q^{10} +(0.283644 - 3.30447i) q^{11} +(-1.16162 - 2.60905i) q^{13} +(0.512566 - 0.461517i) q^{14} +(3.30524 + 1.47159i) q^{16} +(3.60998 - 2.62280i) q^{17} +(-1.81761 - 0.590579i) q^{19} +(5.62446 + 0.591154i) q^{20} +(0.826150 + 0.159182i) q^{22} +(0.706997 + 0.408185i) q^{23} +(3.45921 - 0.735277i) q^{25} +(0.689029 - 0.223879i) q^{26} +(-3.09345 - 4.25777i) q^{28} +(6.38792 - 7.09451i) q^{29} +(-5.46853 + 2.43474i) q^{31} +(-1.45728 + 2.52408i) q^{32} +(0.565973 + 0.980294i) q^{34} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(0.197191 - 0.442898i) q^{38} +(-0.606475 + 2.85324i) q^{40} +(5.64300 + 6.26719i) q^{41} +(-10.2852 + 5.93817i) q^{43} +(1.86690 - 6.14238i) q^{44} +(-0.121726 + 0.167542i) q^{46} +(1.60470 + 7.54950i) q^{47} +(0.0410372 + 0.390443i) q^{49} +(0.0937745 + 0.892205i) q^{50} +(-1.14937 - 5.40734i) q^{52} +(-6.14564 + 8.45874i) q^{53} +(-0.185009 - 9.68851i) q^{55} +(2.35084 - 1.35726i) q^{56} +(1.62046 + 1.79970i) q^{58} +(-0.0193981 + 0.0912608i) q^{59} +(0.872063 - 1.95869i) q^{61} +(-0.469246 - 1.44419i) q^{62} +(5.25595 + 3.81867i) q^{64} +(-4.17217 - 7.22641i) q^{65} +(0.703892 - 1.21918i) q^{67} +(7.89049 - 3.51307i) q^{68} +(1.34843 - 1.49758i) q^{70} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(-1.47546 + 0.313619i) q^{74} +(-3.20371 - 1.84966i) q^{76} +(-6.58502 + 6.16085i) q^{77} +(7.09381 + 0.745590i) q^{79} +(10.0535 + 3.26659i) q^{80} +(-1.73075 + 1.25747i) q^{82} +(7.15699 + 3.18650i) q^{83} +(9.68858 - 8.72364i) q^{85} +(-1.22539 - 2.75227i) q^{86} +(3.05013 + 1.28880i) q^{88} +2.06830i q^{89} +(-2.39957 + 7.38512i) q^{91} +(1.17432 + 1.05736i) q^{92} +(-1.94718 + 0.204657i) q^{94} +(-5.46185 - 1.16095i) q^{95} +(-0.174608 + 1.66129i) q^{97} -0.0995913 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) $ 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0265163	+	0.252286i	−0.0187499	+	0.178393i	−0.999889	−	0.0149107i	$-0.995254\pi$
$2$	−0.0265163	+	0.252286i	−0.0187499	+	0.178393i	0.981139	+	0.193304i	$0.0619203\pi$
$3$		0			0
$3$		0			0
$4$	1.89335	+	0.402444i	0.946675	+	0.201222i
$5$	2.90572	−	0.305404i	1.29948	−	0.136581i	0.570602	−	0.821227i	$-0.306710\pi$
$5$	2.90572	−	0.305404i	1.29948	−	0.136581i	0.728876	+	0.684646i	$0.240043\pi$
$6$		0			0
$7$	−2.02056	−	1.81932i	−0.763700	−	0.687639i	0.192192	−	0.981357i	$-0.438440\pi$
$7$	−2.02056	−	1.81932i	−0.763700	−	0.687639i	−0.955892	+	0.293719i	$0.905107\pi$
$8$	−0.308515	+	0.949513i	−0.109077	+	0.335704i
$9$		0			0
$10$			0.741170i			0.234379i
$11$	0.283644	−	3.30447i	0.0855218	−	0.996336i
$11$	0.283644	−	3.30447i	0.0855218	−	0.996336i
$12$		0			0
$13$	−1.16162	−	2.60905i	−0.322177	−	0.723621i	0.677755	−	0.735288i	$-0.262953\pi$
$13$	−1.16162	−	2.60905i	−0.322177	−	0.723621i	−0.999932	+	0.0116668i	$0.996286\pi$
$14$	0.512566	−	0.461517i	0.136989	−	0.123346i
$15$		0			0
$16$	3.30524	+	1.47159i	0.826310	+	0.367897i
$17$	3.60998	−	2.62280i	0.875549	−	0.636124i	−0.0565211	−	0.998401i	$-0.518001\pi$
$17$	3.60998	−	2.62280i	0.875549	−	0.636124i	0.932070	+	0.362278i	$0.118001\pi$
$18$		0			0
$19$	−1.81761	−	0.590579i	−0.416989	−	0.135488i	0.0930053	−	0.995666i	$-0.470353\pi$
$19$	−1.81761	−	0.590579i	−0.416989	−	0.135488i	−0.509995	+	0.860178i	$0.670353\pi$
$20$	5.62446	+	0.591154i	1.25767	+	0.132186i
$21$		0			0
$22$	0.826150	+	0.159182i	0.176136	+	0.0339376i
$23$	0.706997	+	0.408185i	0.147419	+	0.0851124i	0.571895	−	0.820327i	$-0.306208\pi$
$23$	0.706997	+	0.408185i	0.147419	+	0.0851124i	−0.424476	+	0.905439i	$0.639542\pi$
$24$		0			0
$25$	3.45921	−	0.735277i	0.691841	−	0.147055i
$26$	0.689029	−	0.223879i	0.135130	−	0.0439063i
$27$		0			0
$28$	−3.09345	−	4.25777i	−0.584608	−	0.804644i
$29$	6.38792	−	7.09451i	1.18621	−	1.31742i	0.249058	−	0.968489i	$-0.419879\pi$
$29$	6.38792	−	7.09451i	1.18621	−	1.31742i	0.937149	−	0.348928i	$-0.113454\pi$
$30$		0			0
$31$	−5.46853	+	2.43474i	−0.982176	+	0.437293i	−0.834058	−	0.551677i	$-0.813988\pi$
$31$	−5.46853	+	2.43474i	−0.982176	+	0.437293i	−0.148118	+	0.988970i	$0.547322\pi$
$32$	−1.45728	+	2.52408i	−0.257613	+	0.446199i
$33$		0			0
$34$	0.565973	+	0.980294i	0.0970635	+	0.168119i
$35$	−6.42681	−	4.66935i	−1.08633	−	0.789265i
$36$		0			0
$37$	1.83750	+	5.65524i	0.302083	+	0.929717i	0.980750	+	0.195270i	$0.0625583\pi$
$37$	1.83750	+	5.65524i	0.302083	+	0.929717i	−0.678666	+	0.734447i	$0.737442\pi$
$38$	0.197191	−	0.442898i	0.0319886	−	0.0718476i
$39$		0			0
$40$	−0.606475	+	2.85324i	−0.0958922	+	0.451137i
$41$	5.64300	+	6.26719i	0.881289	+	0.978771i	0.999900	−	0.0141700i	$-0.00451061\pi$
$41$	5.64300	+	6.26719i	0.881289	+	0.978771i	−0.118610	+	0.992941i	$0.537844\pi$
$42$		0			0
$43$	−10.2852	+	5.93817i	−1.56848	+	0.905562i	−0.572133	+	0.820161i	$0.693884\pi$
$43$	−10.2852	+	5.93817i	−1.56848	+	0.905562i	−0.996347	+	0.0854008i	$0.972783\pi$
$44$	1.86690	−	6.14238i	0.281446	−	0.925998i
$45$		0			0
$46$	−0.121726	+	0.167542i	−0.0179475	+	0.0247027i
$47$	1.60470	+	7.54950i	0.234069	+	1.10121i	0.925495	+	0.378760i	$0.123650\pi$
$47$	1.60470	+	7.54950i	0.234069	+	1.10121i	−0.691426	+	0.722447i	$0.743017\pi$
$48$		0			0
$49$	0.0410372	+	0.390443i	0.00586246	+	0.0557776i
$50$	0.0937745	+	0.892205i	0.0132617	+	0.126177i
$51$		0			0
$52$	−1.14937	−	5.40734i	−0.159388	−	0.749863i
$53$	−6.14564	+	8.45874i	−0.844168	+	1.16190i	0.140950	+	0.990017i	$0.454984\pi$
$53$	−6.14564	+	8.45874i	−0.844168	+	1.16190i	−0.985118	+	0.171881i	$0.945016\pi$
$54$		0			0
$55$	−0.185009	−	9.68851i	−0.0249466	−	1.30640i
$56$	2.35084	−	1.35726i	0.314145	−	0.181371i
$57$		0			0
$58$	1.62046	+	1.79970i	0.212777	+	0.236312i
$59$	−0.0193981	+	0.0912608i	−0.00252541	+	0.0118811i	−0.979392	−	0.201967i	$-0.935267\pi$
$59$	−0.0193981	+	0.0912608i	−0.00252541	+	0.0118811i	0.976867	+	0.213848i	$0.0685999\pi$
$60$		0			0
$61$	0.872063	−	1.95869i	0.111656	−	0.250784i	−0.849071	−	0.528279i	$-0.822838\pi$
$61$	0.872063	−	1.95869i	0.111656	−	0.250784i	0.960727	+	0.277495i	$0.0895042\pi$
$62$	−0.469246	−	1.44419i	−0.0595943	−	0.183412i
$63$		0			0
$64$	5.25595	+	3.81867i	0.656994	+	0.477334i
$65$	−4.17217	−	7.22641i	−0.517494	−	0.896326i
$66$		0			0
$67$	0.703892	−	1.21918i	0.0859941	−	0.148946i	−0.819820	−	0.572621i	$-0.805927\pi$
$67$	0.703892	−	1.21918i	0.0859941	−	0.148946i	0.905814	+	0.423675i	$0.139260\pi$
$68$	7.89049	−	3.51307i	0.956863	−	0.426023i
$69$		0			0
$70$	1.34843	−	1.49758i	0.161168	−	0.178995i
$71$	−2.12141	−	2.91987i	−0.251765	−	0.346525i	0.664363	−	0.747410i	$-0.268703\pi$
$71$	−2.12141	−	2.91987i	−0.251765	−	0.346525i	−0.916128	+	0.400885i	$0.868703\pi$
$72$		0			0
$73$	−1.67338	+	0.543714i	−0.195854	+	0.0636369i	−0.405302	−	0.914183i	$-0.632833\pi$
$73$	−1.67338	+	0.543714i	−0.195854	+	0.0636369i	0.209447	+	0.977820i	$0.432833\pi$
$74$	−1.47546	+	0.313619i	−0.171519	+	0.0364575i
$75$		0			0
$76$	−3.20371	−	1.84966i	−0.367490	−	0.212171i
$77$	−6.58502	+	6.16085i	−0.750432	+	0.702094i
$78$		0			0
$79$	7.09381	+	0.745590i	0.798116	+	0.0838854i	0.494803	−	0.869005i	$-0.335240\pi$
$79$	7.09381	+	0.745590i	0.798116	+	0.0838854i	0.303314	+	0.952891i	$0.401907\pi$
$80$	10.0535	+	3.26659i	1.12402	+	0.365216i
$81$		0			0
$82$	−1.73075	+	1.25747i	−0.191130	+	0.138864i
$83$	7.15699	+	3.18650i	0.785581	+	0.349763i	0.760011	−	0.649910i	$-0.225193\pi$
$83$	7.15699	+	3.18650i	0.785581	+	0.349763i	0.0255699	+	0.999673i	$0.491860\pi$
$84$		0			0
$85$	9.68858	−	8.72364i	1.05087	−	0.946212i
$86$	−1.22539	−	2.75227i	−0.132137	−	0.296785i
$87$		0			0
$88$	3.05013	+	1.28880i	0.325145	+	0.137387i
$89$			2.06830i			0.219240i	0.993974	+	0.109620i	$0.0349633\pi$
$89$			2.06830i			0.219240i	−0.993974	+	0.109620i	$0.965037\pi$
$90$		0			0
$91$	−2.39957	+	7.38512i	−0.251543	+	0.774171i
$92$	1.17432	+	1.05736i	0.122431	+	0.110238i
$93$		0			0
$94$	−1.94718	+	0.204657i	−0.200836	+	0.0211088i
$95$	−5.46185	−	1.16095i	−0.560374	−	0.119111i
$96$		0			0
$97$	−0.174608	+	1.66129i	−0.0177288	+	0.168678i	−0.999804	−	0.0198129i	$-0.993693\pi$
$97$	−0.174608	+	1.66129i	−0.0177288	+	0.168678i	0.982075	+	0.188491i	$0.0603596\pi$
$98$	−0.0995913			−0.0100602
$99$		0			0
$100$	6.84540			0.684540
$101$	0.945739	−	8.99811i	0.0941046	−	0.895345i	−0.841015	−	0.541012i	$-0.818041\pi$
$101$	0.945739	−	8.99811i	0.0941046	−	0.895345i	0.935119	−	0.354333i	$-0.115292\pi$
$102$		0			0
$103$	16.2108	+	3.44571i	1.59730	+	0.339516i	0.918687	−	0.394985i	$-0.129250\pi$
$103$	16.2108	+	3.44571i	1.59730	+	0.339516i	0.678608	+	0.734501i	$0.262584\pi$
$104$	2.83571	−	0.298045i	0.278064	−	0.0292257i
$105$		0			0
$106$	−1.97106	−	1.77475i	−0.191446	−	0.172379i
$107$	−2.19803	+	6.76484i	−0.212492	+	0.653982i	0.786830	+	0.617169i	$0.211721\pi$
$107$	−2.19803	+	6.76484i	−0.212492	+	0.653982i	−0.999322	+	0.0368130i	$0.988279\pi$
$108$		0			0
$109$			8.62045i			0.825690i	0.910801	+	0.412845i	$0.135465\pi$
$109$			8.62045i			0.825690i	−0.910801	+	0.412845i	$0.864535\pi$
$110$	2.44918	+	0.210228i	0.233520	+	0.0200445i
$111$		0			0
$112$	−4.00115	−	8.98672i	−0.378073	−	0.849165i
$113$	8.47771	−	7.63336i	0.797516	−	0.718087i	−0.165887	−	0.986145i	$-0.553049\pi$
$113$	8.47771	−	7.63336i	0.797516	−	0.718087i	0.963403	+	0.268058i	$0.0863820\pi$
$114$		0			0
$115$	2.17900	+	0.970152i	0.203193	+	0.0904671i
$116$	14.9497	−	10.8616i	1.38805	−	1.00847i
$117$		0			0
$118$	−0.0225094	−	0.00731376i	−0.00207216	−	0.000673286i
$119$	−12.0659	−	1.26818i	−1.10608	−	0.116254i
$120$		0			0
$121$	−10.8391	−	1.87459i	−0.985372	−	0.170417i
$122$	0.471024	+	0.271946i	0.0426445	+	0.0246208i
$123$		0			0
$124$	−11.3337	+	2.40905i	−1.01779	+	0.216339i
$125$	−4.06670	+	1.32135i	−0.363737	+	0.118185i
$126$		0			0
$127$	−1.69463	−	2.33246i	−0.150374	−	0.206973i	0.727184	−	0.686443i	$-0.240829\pi$
$127$	−1.69463	−	2.33246i	−0.150374	−	0.206973i	−0.877558	+	0.479470i	$0.840829\pi$
$128$	−5.00321	+	5.55663i	−0.442225	+	0.491141i
$129$		0			0
$130$	1.93375	−	0.860962i	0.169601	−	0.0755113i
$131$	1.05078	−	1.82000i	0.0918067	−	0.159014i	−0.816465	−	0.577395i	$-0.804069\pi$
$131$	1.05078	−	1.82000i	0.0918067	−	0.159014i	0.908271	+	0.418382i	$0.137402\pi$
$132$		0			0
$133$	2.59815	+	4.50013i	0.225288	+	0.390210i
$134$	0.288916	+	0.209910i	0.0249586	+	0.0181335i
$135$		0			0
$136$	1.37665	+	4.23690i	0.118047	+	0.363311i
$137$	−2.06380	+	4.63537i	−0.176322	+	0.396026i	−0.979988	−	0.199054i	$-0.936213\pi$
$137$	−2.06380	+	4.63537i	−0.176322	+	0.396026i	0.803666	+	0.595080i	$0.202880\pi$
$138$		0			0
$139$	−3.63511	+	17.1019i	−0.308326	+	1.45056i	0.502145	+	0.864783i	$0.332544\pi$
$139$	−3.63511	+	17.1019i	−0.308326	+	1.45056i	−0.810471	+	0.585778i	$0.800789\pi$
$140$	−10.2891	−	11.4272i	−0.869584	−	0.965771i
$141$		0			0
$142$	0.792894	−	0.457777i	0.0665382	−	0.0384158i
$143$	−8.95103	+	3.09852i	−0.748523	+	0.259111i
$144$		0			0
$145$	16.3948	−	22.5656i	1.36152	−	1.87397i
$146$	−0.0927994	−	0.436587i	−0.00768013	−	0.0361322i
$147$		0			0
$148$	1.20311	+	11.4469i	0.0988952	+	0.940925i
$149$	−0.591269	−	5.62555i	−0.0484387	−	0.460863i	−0.991677	−	0.128748i	$-0.958904\pi$
$149$	−0.591269	−	5.62555i	−0.0484387	−	0.460863i	0.943239	−	0.332115i	$-0.107762\pi$
$150$		0			0
$151$	−1.90769	−	8.97498i	−0.155246	−	0.730373i	−0.985043	−	0.172308i	$-0.944877\pi$
$151$	−1.90769	−	8.97498i	−0.155246	−	0.730373i	0.829797	−	0.558065i	$-0.188456\pi$
$152$	1.12152	−	1.54365i	0.0909677	−	0.125206i
$153$		0			0
$154$	−1.37968	−	1.82467i	−0.111178	−	0.147036i
$155$	−15.1464	+	8.74480i	−1.21659	+	0.702399i
$156$		0			0
$157$	−2.04334	−	2.26936i	−0.163076	−	0.181115i	0.656069	−	0.754701i	$-0.272218\pi$
$157$	−2.04334	−	2.26936i	−0.163076	−	0.181115i	−0.819145	+	0.573587i	$0.805552\pi$
$158$	−0.376203	+	1.76990i	−0.0299291	+	0.140805i
$159$		0			0
$160$	−3.46359	+	7.77934i	−0.273820	+	0.615011i
$161$	−0.685911	−	2.11102i	−0.0540573	−	0.166371i
$162$		0			0
$163$	−6.39488	−	4.64615i	−0.500885	−	0.363914i	0.308470	−	0.951234i	$-0.400183\pi$
$163$	−6.39488	−	4.64615i	−0.500885	−	0.363914i	−0.809355	+	0.587320i	$0.800183\pi$
$164$	8.16199	+	14.1370i	0.637344	+	1.10391i
$165$		0			0
$166$	−0.993684	+	1.72111i	−0.0771248	+	0.133584i
$167$	−15.0258	+	6.68992i	−1.16273	+	0.517682i	−0.895111	−	0.445843i	$-0.852904\pi$
$167$	−15.0258	+	6.68992i	−1.16273	+	0.517682i	−0.267621	+	0.963524i	$0.586237\pi$
$168$		0			0
$169$	3.24092	−	3.59940i	0.249301	−	0.276877i
$170$	1.94394	+	2.67561i	0.149094	+	0.205210i
$171$		0			0
$172$	−21.8633	+	7.10381i	−1.66706	+	0.541660i
$173$	−15.1832	+	3.22729i	−1.15436	+	0.245366i	−0.745036	−	0.667024i	$-0.767568\pi$
$173$	−15.1832	+	3.22729i	−1.15436	+	0.245366i	−0.409322	+	0.912390i	$0.634235\pi$
$174$		0			0
$175$	−8.32724	−	4.80773i	−0.629480	−	0.363431i
$176$	5.80033	−	10.5047i	0.437216	−	0.791819i
$177$		0			0
$178$	−0.521803	−	0.0548437i	−0.0391108	−	0.00411071i
$179$	4.93538	+	1.60360i	0.368888	+	0.119859i	0.487594	−	0.873071i	$-0.337875\pi$
$179$	4.93538	+	1.60360i	0.368888	+	0.119859i	−0.118706	+	0.992929i	$0.537875\pi$
$180$		0			0
$181$	−4.29773	+	3.12248i	−0.319448	+	0.232092i	−0.735940	−	0.677047i	$-0.763259\pi$
$181$	−4.29773	+	3.12248i	−0.319448	+	0.232092i	0.416492	+	0.909139i	$0.363259\pi$
$182$	−1.79953	−	0.801203i	−0.133390	−	0.0593891i
$183$		0			0
$184$	−0.605696	+	0.545371i	−0.0446525	+	0.0402053i
$185$	7.06640	+	15.8714i	0.519532	+	1.16689i
$186$		0			0
$187$	−7.64304	−	12.6730i	−0.558915	−	0.926744i
$188$			14.9396i			1.08959i
$189$		0			0
$190$	0.437719	−	1.34716i	0.0317555	−	0.0977334i
$191$	−8.10000	−	7.29328i	−0.586096	−	0.527723i	0.321861	−	0.946787i	$-0.395692\pi$
$191$	−8.10000	−	7.29328i	−0.586096	−	0.527723i	−0.907957	+	0.419064i	$0.862358\pi$
$192$		0			0
$193$	−15.2822	+	1.60623i	−1.10004	+	0.115619i	−0.637108	−	0.770775i	$-0.719869\pi$
$193$	−15.2822	+	1.60623i	−1.10004	+	0.115619i	−0.462932	+	0.886394i	$0.653203\pi$
$194$	−0.414489	−	0.0881023i	−0.0297586	−	0.00632538i
$195$		0			0
$196$	−0.0794336	+	0.755760i	−0.00567383	+	0.0539829i
$197$	−7.24149			−0.515935			−0.257967	−	0.966154i	$-0.583053\pi$
$197$	−7.24149			−0.515935			−0.257967	+	0.966154i	$0.583053\pi$
$198$		0			0
$199$	−11.3726			−0.806181			−0.403090	−	0.915160i	$-0.632064\pi$
$199$	−11.3726			−0.806181			−0.403090	+	0.915160i	$0.632064\pi$
$200$	−0.369064	+	3.51141i	−0.0260967	+	0.248294i
$201$		0			0
$202$	2.24502	+	0.477193i	0.157959	+	0.0335752i
$203$	−25.8144	+	2.71320i	−1.81181	+	0.190429i
$204$		0			0
$205$	18.3110	+	16.4873i	1.27890	+	1.15152i
$206$	−1.29915	+	3.99838i	−0.0905162	+	0.278580i
$207$		0			0
$208$		−	10.3330i		−	0.716463i
$209$	−2.46711	+	5.83875i	−0.170653	+	0.403875i
$210$		0			0
$211$	−1.50420	−	3.37850i	−0.103554	−	0.232585i	0.854336	−	0.519720i	$-0.173964\pi$
$211$	−1.50420	−	3.37850i	−0.103554	−	0.232585i	−0.957890	+	0.287135i	$0.907297\pi$
$212$	−15.0400	+	13.5421i	−1.03295	+	0.930075i
$213$		0			0
$214$	−1.64839	−	0.733910i	−0.112682	−	0.0501691i
$215$	−28.0724	+	20.3958i	−1.91452	+	1.39098i
$216$		0			0
$217$	15.4791	+	5.02946i	1.05079	+	0.341422i
$218$	−2.17482	−	0.228582i	−0.147297	−	0.0154816i
$219$		0			0
$220$	3.54879	−	18.4182i	0.239260	−	1.24175i
$221$	−11.0365	−	6.37191i	−0.742394	−	0.428621i
$222$		0			0
$223$	0.277034	−	0.0588855i	0.0185516	−	0.00394326i	−0.198627	−	0.980075i	$-0.563648\pi$
$223$	0.277034	−	0.0588855i	0.0185516	−	0.00394326i	0.217178	+	0.976132i	$0.430315\pi$
$224$	7.53664	−	2.44880i	0.503563	−	0.163618i
$225$		0			0
$226$	1.70099	+	2.34121i	0.113148	+	0.155735i
$227$	−12.2156	+	13.5668i	−0.810780	+	0.900462i	−0.996623	−	0.0821175i	$-0.973832\pi$
$227$	−12.2156	+	13.5668i	−0.810780	+	0.900462i	0.185843	+	0.982579i	$0.440498\pi$
$228$		0			0
$229$	24.0955	−	10.7280i	1.59228	−	0.708927i	0.596663	−	0.802492i	$-0.296493\pi$
$229$	24.0955	−	10.7280i	1.59228	−	0.708927i	0.995613	+	0.0935649i	$0.0298263\pi$
$230$	−0.302534	+	0.524005i	−0.0199485	+	0.0345519i
$231$		0			0
$232$	4.76555	+	8.25418i	0.312874	+	0.541914i
$233$	8.73916	+	6.34937i	0.572521	+	0.415961i	0.836020	−	0.548699i	$-0.184877\pi$
$233$	8.73916	+	6.34937i	0.572521	+	0.415961i	−0.263499	+	0.964660i	$0.584877\pi$
$234$		0			0
$235$	6.96844	+	21.4467i	0.454571	+	1.39903i
$236$	−0.0734547	+	0.164982i	−0.00478150	+	0.0107394i
$237$		0			0
$238$	0.639886	−	3.01043i	0.0414777	−	0.195137i
$239$	4.96717	+	5.51660i	0.321300	+	0.356839i	0.882059	−	0.471140i	$-0.156157\pi$
$239$	4.96717	+	5.51660i	0.321300	+	0.356839i	−0.560759	+	0.827979i	$0.689491\pi$
$240$		0			0
$241$	2.31118	−	1.33436i	0.148876	−	0.0859539i	−0.423711	−	0.905797i	$-0.639273\pi$
$241$	2.31118	−	1.33436i	0.148876	−	0.0859539i	0.572588	+	0.819843i	$0.305940\pi$
$242$	0.760344	−	2.68484i	0.0488767	−	0.172588i
$243$		0			0
$244$	2.43938	−	3.35752i	0.156165	−	0.214943i
$245$	0.238485	+	1.12199i	0.0152363	+	0.0716810i
$246$		0			0
$247$	0.570536	+	5.42828i	0.0363023	+	0.345393i
$248$	−0.624697	−	5.94359i	−0.0396683	−	0.377419i
$249$		0			0
$250$	−0.225524	−	1.06101i	−0.0142634	−	0.0671041i
$251$	14.2630	−	19.6313i	0.900271	−	1.23912i	−0.0701107	−	0.997539i	$-0.522335\pi$
$251$	14.2630	−	19.6313i	0.900271	−	1.23912i	0.970382	−	0.241577i	$-0.0776647\pi$
$252$		0			0
$253$	1.54937	−	2.22047i	0.0974081	−	0.139600i
$254$	0.633383	−	0.365684i	0.0397420	−	0.0229450i
$255$		0			0
$256$	7.42511	+	8.24642i	0.464070	+	0.515401i
$257$	3.48379	−	16.3899i	0.217313	−	1.02238i	−0.725286	−	0.688448i	$-0.758293\pi$
$257$	3.48379	−	16.3899i	0.217313	−	1.02238i	0.942599	−	0.333928i	$-0.108374\pi$
$258$		0			0
$259$	6.57592	−	14.7698i	0.408608	−	0.917749i
$260$	−4.99116	−	15.3612i	−0.309538	−	0.952661i
$261$		0			0
$262$	0.431296	+	0.313355i	0.0266456	+	0.0193591i
$263$	−5.45728	−	9.45229i	−0.336511	−	0.582853i	0.647263	−	0.762267i	$-0.275913\pi$
$263$	−5.45728	−	9.45229i	−0.336511	−	0.582853i	−0.983774	+	0.179413i	$0.942580\pi$
$264$		0			0
$265$	−15.2742	+	26.4557i	−0.938285	+	1.62516i
$266$	−1.20421	+	0.536149i	−0.0738349	+	0.0328734i
$267$		0			0
$268$	1.82337	−	2.02505i	0.111380	−	0.123700i
$269$	9.22041	+	12.6908i	0.562178	+	0.773772i	0.991601	−	0.129331i	$-0.0412830\pi$
$269$	9.22041	+	12.6908i	0.562178	+	0.773772i	−0.429423	+	0.903103i	$0.641283\pi$
$270$		0			0
$271$	−2.76289	+	0.897717i	−0.167834	+	0.0545324i	−0.391728	−	0.920081i	$-0.628123\pi$
$271$	−2.76289	+	0.897717i	−0.167834	+	0.0545324i	0.223895	+	0.974613i	$0.428123\pi$
$272$	15.7915	−	3.35659i	0.957502	−	0.203523i
$273$		0			0
$274$	−1.11471	−	0.643579i	−0.0673422	−	0.0388801i
$275$	−1.44852	−	11.6394i	−0.0873492	−	0.701883i
$276$		0			0
$277$	−20.9993	−	2.20712i	−1.26173	−	0.132613i	−0.550057	−	0.835127i	$-0.685394\pi$
$277$	−20.9993	−	2.20712i	−1.26173	−	0.132613i	−0.711669	+	0.702515i	$0.752061\pi$
$278$	−4.21817	−	1.37057i	−0.252989	−	0.0822011i
$279$		0			0
$280$	6.41638	−	4.66177i	0.383452	−	0.278594i
$281$	2.82318	+	1.25696i	0.168417	+	0.0749841i	0.489214	−	0.872164i	$-0.337284\pi$
$281$	2.82318	+	1.25696i	0.168417	+	0.0749841i	−0.320796	+	0.947148i	$0.603951\pi$
$282$		0			0
$283$	16.6648	−	15.0051i	0.990620	−	0.891958i	−0.00352741	−	0.999994i	$-0.501123\pi$
$283$	16.6648	−	15.0051i	0.990620	−	0.891958i	0.994147	+	0.108036i	$0.0344561\pi$
$284$	−2.84149	−	6.38209i	−0.168611	−	0.378707i
$285$		0			0
$286$	−0.544364	−	2.34038i	−0.0321889	−	0.138389i
$287$		−	22.9297i		−	1.35350i
$288$		0			0
$289$	0.899570	−	2.76859i	0.0529159	−	0.162858i
$290$	5.25824	+	4.73454i	0.308774	+	0.278022i
$291$		0			0
$292$	−3.38711	+	0.355999i	−0.198215	+	0.0208333i
$293$	20.2877	+	4.31228i	1.18522	+	0.251926i	0.758020	−	0.652231i	$-0.226167\pi$
$293$	20.2877	+	4.31228i	1.18522	+	0.251926i	0.427200	+	0.904157i	$0.359500\pi$
$294$		0			0
$295$	−0.0284940	+	0.271103i	−0.00165899	+	0.0157842i
$296$	−5.93663			−0.345059
$297$		0			0
$298$	1.43492			0.0831229
$299$	0.243710	−	2.31875i	0.0140941	−	0.134097i
$300$		0			0
$301$	31.5853	+	6.71367i	1.82055	+	0.386969i
$302$	2.31484	−	0.243300i	0.133204	−	0.0140003i
$303$		0			0
$304$	−5.13856	−	4.62678i	−0.294717	−	0.265364i
$305$	1.93578	−	5.95772i	0.110843	−	0.341138i
$306$		0			0
$307$		−	15.0077i		−	0.856533i	−0.903652	−	0.428267i	$-0.859124\pi$
$307$		−	15.0077i		−	0.856533i	0.903652	−	0.428267i	$-0.140876\pi$
$308$	−14.9471	+	9.01455i	−0.851692	+	0.513651i
$309$		0			0
$310$	−1.80456	−	4.05311i	−0.102492	−	0.230201i
$311$	−1.53015	+	1.37775i	−0.0867666	+	0.0781250i	−0.711373	−	0.702815i	$-0.751926\pi$
$311$	−1.53015	+	1.37775i	−0.0867666	+	0.0781250i	0.624606	+	0.780940i	$0.285260\pi$
$312$		0			0
$313$	−22.7222	−	10.1166i	−1.28433	−	0.571822i	−0.352876	−	0.935670i	$-0.614796\pi$
$313$	−22.7222	−	10.1166i	−1.28433	−	0.571822i	−0.931458	+	0.363848i	$0.881463\pi$
$314$	0.626709	−	0.455330i	0.0353672	−	0.0256958i
$315$		0			0
$316$	13.1310	+	4.26652i	0.738677	+	0.240011i
$317$	0.430358	+	0.0452324i	0.0241713	+	0.00254051i	0.116606	−	0.993178i	$-0.462798\pi$
$317$	0.430358	+	0.0452324i	0.0241713	+	0.00254051i	−0.0924351	+	0.995719i	$0.529465\pi$
$318$		0			0
$319$	−21.6317	−	23.1210i	−1.21114	−	1.29453i
$320$	16.4386	+	9.49081i	0.918944	+	0.530553i
$321$		0			0
$322$	0.550767	−	0.117069i	0.0306930	−	0.00652401i
$323$	−8.11053	+	2.63527i	−0.451282	+	0.146630i
$324$		0			0
$325$	−5.93668	−	8.17113i	−0.329308	−	0.453253i
$326$	1.34173	−	1.49014i	0.0743113	−	0.0825310i
$327$		0			0
$328$	−7.69173	+	3.42458i	−0.424705	+	0.189091i
$329$	10.4926	−	18.1737i	0.578475	−	1.00195i
$330$		0			0
$331$	8.65452	+	14.9901i	0.475696	+	0.823929i	0.999612	−	0.0278406i	$-0.00886309\pi$
$331$	8.65452	+	14.9901i	0.475696	+	0.823929i	−0.523917	+	0.851769i	$0.675530\pi$
$332$	12.2683	+	8.91344i	0.673310	+	0.489189i
$333$		0			0
$334$	−1.28934	−	3.96819i	−0.0705497	−	0.217130i
$335$	1.67297	−	3.75756i	0.0914043	−	0.205297i
$336$		0			0
$337$	−5.21129	+	24.5172i	−0.283877	+	1.33554i	0.572805	+	0.819691i	$0.305855\pi$
$337$	−5.21129	+	24.5172i	−0.283877	+	1.33554i	−0.856682	+	0.515844i	$0.827478\pi$
$338$	0.822141	+	0.913080i	0.0447186	+	0.0496650i
$339$		0			0
$340$	21.8547	−	12.6178i	1.18524	−	0.684296i
$341$	6.49444	+	18.7612i	0.351694	+	1.01598i
$342$		0			0
$343$	−10.5596	+	14.5341i	−0.570166	+	0.784766i
$344$	−2.46522	−	11.5980i	−0.132916	−	0.625320i
$345$		0			0
$346$	−0.411597	−	3.91608i	−0.0221276	−	0.210530i
$347$	2.18182	+	20.7586i	0.117126	+	1.11438i	0.882342	+	0.470608i	$0.155965\pi$
$347$	2.18182	+	20.7586i	0.117126	+	1.11438i	−0.765216	+	0.643773i	$0.777368\pi$
$348$		0			0
$349$	3.74668	+	17.6267i	0.200555	+	0.943537i	0.957136	+	0.289638i	$0.0935348\pi$
$349$	3.74668	+	17.6267i	0.200555	+	0.943537i	−0.756581	+	0.653900i	$0.773132\pi$
$350$	1.43373	−	1.97336i	0.0766361	−	0.105481i
$351$		0			0
$352$	7.92742	+	5.53148i	0.422533	+	0.294829i
$353$	14.1122	−	8.14766i	0.751115	−	0.433656i	−0.0749818	−	0.997185i	$-0.523890\pi$
$353$	14.1122	−	8.14766i	0.751115	−	0.433656i	0.826097	+	0.563529i	$0.190557\pi$
$354$		0			0
$355$	−7.05597	−	7.83645i	−0.374492	−	0.415915i
$356$	−0.832376	+	3.91602i	−0.0441158	+	0.207549i
$357$		0			0
$358$	−0.535434	+	1.20260i	−0.0282986	+	0.0635596i
$359$	7.65875	+	23.5712i	0.404213	+	1.24404i	0.921550	+	0.388259i	$0.126923\pi$
$359$	7.65875	+	23.5712i	0.404213	+	1.24404i	−0.517337	+	0.855782i	$0.673077\pi$
$360$		0			0
$361$	−12.4164	−	9.02103i	−0.653494	−	0.474791i
$362$	−0.673798	−	1.16705i	−0.0354140	−	0.0613389i
$363$		0			0
$364$	−7.51532	+	13.0169i	−0.393910	+	0.682272i
$365$	−4.69632	+	2.09094i	−0.245817	+	0.109445i
$366$		0			0
$367$	5.99117	−	6.65387i	0.312736	−	0.347329i	−0.566200	−	0.824268i	$-0.691587\pi$
$367$	5.99117	−	6.65387i	0.312736	−	0.347329i	0.878936	+	0.476939i	$0.158254\pi$
$368$	1.73611	+	2.38956i	0.0905012	+	0.124564i
$369$		0			0
$370$	−4.19150	+	1.36190i	−0.217906	+	0.0708018i
$371$	27.8068	−	5.91052i	1.44366	−	0.306859i
$372$		0			0
$373$	−14.6365	−	8.45037i	−0.757848	−	0.437544i	0.0706745	−	0.997499i	$-0.477485\pi$
$373$	−14.6365	−	8.45037i	−0.757848	−	0.437544i	−0.828523	+	0.559956i	$0.810818\pi$
$374$	3.39989	−	1.59219i	0.175804	−	0.0823301i
$375$		0			0
$376$	−7.66342	−	0.805458i	−0.395211	−	0.0415383i
$377$	−25.9303	−	8.42527i	−1.33548	−	0.433923i
$378$		0			0
$379$	−15.9625	+	11.5975i	−0.819940	+	0.595722i	−0.916695	−	0.399587i	$-0.869154\pi$
$379$	−15.9625	+	11.5975i	−0.819940	+	0.595722i	0.0967550	+	0.995308i	$0.469154\pi$
$380$	−9.87397	−	4.39618i	−0.506524	−	0.225519i
$381$		0			0
$382$	2.05477	−	1.85012i	0.105131	−	0.0946606i
$383$	−2.03366	−	4.56766i	−0.103915	−	0.233397i	0.854104	−	0.520103i	$-0.174106\pi$
$383$	−2.03366	−	4.56766i	−0.103915	−	0.233397i	−0.958019	+	0.286706i	$0.907440\pi$
$384$		0			0
$385$	−17.2527	+	19.9128i	−0.879278	+	1.01485i
$386$		−	3.89808i		−	0.198407i
$387$		0			0
$388$	−0.999169	+	3.07513i	−0.0507251	+	0.156116i
$389$	−7.32251	−	6.59322i	−0.371266	−	0.334290i	0.462285	−	0.886731i	$-0.347030\pi$
$389$	−7.32251	−	6.59322i	−0.371266	−	0.334290i	−0.833552	+	0.552442i	$0.813696\pi$
$390$		0			0
$391$	3.62283	−	0.380775i	0.183215	−	0.0192566i
$392$	−0.383391	−	0.0814923i	−0.0193642	−	0.00411598i
$393$		0			0
$394$	0.192018	−	1.82692i	0.00967370	−	0.0920391i
$395$	20.8403			1.04859
$396$		0			0
$397$	−19.0245			−0.954812			−0.477406	−	0.878683i	$-0.658423\pi$
$397$	−19.0245			−0.954812			−0.477406	+	0.878683i	$0.658423\pi$
$398$	0.301559	−	2.86914i	0.0151158	−	0.143817i
$399$		0			0
$400$	12.5155	+	2.66026i	0.625776	+	0.133013i
$401$	30.5373	−	3.20960i	1.52496	−	0.160280i	0.695369	−	0.718652i	$-0.255241\pi$
$401$	30.5373	−	3.20960i	1.52496	−	0.160280i	0.829590	+	0.558373i	$0.188574\pi$
$402$		0			0
$403$	12.7048	+	11.4394i	0.632869	+	0.569838i
$404$	5.41185	−	16.6560i	0.269250	−	0.828665i
$405$		0			0
$406$		−	6.58454i		−	0.326785i
$407$	19.2088	−	4.46790i	0.952145	−	0.221465i
$408$		0			0
$409$	−4.82937	−	10.8469i	−0.238797	−	0.536347i	0.753899	−	0.656991i	$-0.228171\pi$
$409$	−4.82937	−	10.8469i	−0.238797	−	0.536347i	−0.992696	+	0.120644i	$0.961504\pi$
$410$	−4.64505	+	4.18243i	−0.229403	+	0.206555i
$411$		0			0
$412$	29.3060	+	13.0479i	1.44380	+	0.642822i
$413$	0.205228	−	0.149107i	0.0100986	−	0.00733706i
$414$		0			0
$415$	21.7694	+	7.07330i	1.06862	+	0.347215i
$416$	8.27828	+	0.870082i	0.405876	+	0.0426593i
$417$		0			0
$418$	−1.40761	−	0.777238i	−0.0688486	−	0.0380159i
$419$	−8.71474	−	5.03146i	−0.425743	−	0.245803i	0.271788	−	0.962357i	$-0.412385\pi$
$419$	−8.71474	−	5.03146i	−0.425743	−	0.245803i	−0.697531	+	0.716554i	$0.745718\pi$
$420$		0			0
$421$	6.11979	−	1.30080i	0.298260	−	0.0633972i	−0.0563510	−	0.998411i	$-0.517947\pi$
$421$	6.11979	−	1.30080i	0.298260	−	0.0633972i	0.354611	+	0.935014i	$0.384613\pi$
$422$	0.892232	−	0.289904i	0.0434332	−	0.0141123i
$423$		0			0
$424$	−6.13566	−	8.44502i	−0.297974	−	0.410126i
$425$	10.5592	−	11.7272i	0.512196	−	0.568851i
$426$		0			0
$427$	−5.32553	+	2.37108i	−0.257721	+	0.114745i
$428$	−6.88411	+	11.9236i	−0.332756	+	0.576351i
$429$		0			0
$430$	−4.40119	−	7.62309i	−0.212244	−	0.367618i
$431$	−15.8885	−	11.5436i	−0.765321	−	0.556038i	0.135217	−	0.990816i	$-0.456827\pi$
$431$	−15.8885	−	11.5436i	−0.765321	−	0.556038i	−0.900538	+	0.434778i	$0.856827\pi$
$432$		0			0
$433$	9.66882	+	29.7576i	0.464654	+	1.43006i	0.859418	+	0.511274i	$0.170826\pi$
$433$	9.66882	+	29.7576i	0.464654	+	1.43006i	−0.394764	+	0.918783i	$0.629174\pi$
$434$	−1.67931	+	3.77179i	−0.0806093	+	0.181052i
$435$		0			0
$436$	−3.46925	+	16.3215i	−0.166147	+	0.781660i
$437$	−1.04398	−	1.15946i	−0.0499405	−	0.0554645i
$438$		0			0
$439$	−17.4881	+	10.0967i	−0.834659	+	0.481891i	−0.855445	−	0.517893i	$-0.826717\pi$
$439$	−17.4881	+	10.0967i	−0.834659	+	0.481891i	0.0207859	+	0.999784i	$0.493383\pi$
$440$	9.25644	+	2.81339i	0.441283	+	0.134123i
$441$		0			0
$442$	1.90019	−	2.61539i	0.0903828	−	0.124401i
$443$	−5.06637	−	23.8354i	−0.240710	−	1.13245i	−0.917952	−	0.396692i	$-0.870158\pi$
$443$	−5.06637	−	23.8354i	−0.240710	−	1.13245i	0.677241	−	0.735761i	$-0.263175\pi$
$444$		0			0
$445$	0.631667	+	6.00991i	0.0299439	+	0.284897i
$446$	0.00751004	+	0.0714532i	0.000355611	+	0.00338341i
$447$		0			0
$448$	−3.67258	−	17.2781i	−0.173513	−	0.816315i
$449$	1.94082	−	2.67131i	0.0915930	−	0.126067i	−0.760761	−	0.649032i	$-0.775174\pi$
$449$	1.94082	−	2.67131i	0.0915930	−	0.126067i	0.852354	+	0.522965i	$0.175174\pi$
$450$		0			0
$451$	22.3104	−	16.8695i	1.05055	−	0.794354i
$452$	19.1233	−	11.0408i	0.899483	−	0.519317i
$453$		0			0
$454$	−3.09880	−	3.44157i	−0.145434	−	0.161521i
$455$	−4.71704	+	22.1919i	−0.221138	+	1.04037i
$456$		0			0
$457$	−6.35217	+	14.2672i	−0.297142	+	0.667392i	−0.998990	−	0.0449350i	$-0.985692\pi$
$457$	−6.35217	+	14.2672i	−0.297142	+	0.667392i	0.701848	+	0.712327i	$0.252359\pi$
$458$	2.06760	+	6.36342i	0.0966126	+	0.297343i
$459$		0			0
$460$	3.73517	+	2.71376i	0.174153	+	0.126530i
$461$	18.2842	+	31.6692i	0.851582	+	1.47498i	0.879780	+	0.475381i	$0.157690\pi$
$461$	18.2842	+	31.6692i	0.851582	+	1.47498i	−0.0281979	+	0.999602i	$0.508977\pi$
$462$		0			0
$463$	−2.22766	+	3.85841i	−0.103528	+	0.179316i	−0.913136	−	0.407655i	$-0.866346\pi$
$463$	−2.22766	+	3.85841i	−0.103528	+	0.179316i	0.809608	+	0.586971i	$0.199680\pi$
$464$	31.5538	−	14.0487i	1.46485	−	0.652192i
$465$		0			0
$466$	−1.83359	+	2.03640i	−0.0849392	+	0.0943345i
$467$	−24.4676	−	33.6768i	−1.13223	−	1.55838i	−0.783769	−	0.621052i	$-0.786706\pi$
$467$	−24.4676	−	33.6768i	−1.13223	−	1.55838i	−0.348458	−	0.937325i	$-0.613294\pi$
$468$		0			0
$469$	−3.64033	+	1.18282i	−0.168095	+	0.0546173i
$470$	−5.59546	+	1.18935i	−0.258100	+	0.0548607i
$471$		0			0
$472$	−0.0806687	−	0.0465741i	−0.00371308	−	0.00214375i
$473$	16.7052	+	35.6715i	0.768105	+	1.64018i
$474$		0			0
$475$	−6.72174	−	0.706484i	−0.308415	−	0.0324157i
$476$	−22.3346	−	7.25696i	−1.02371	−	0.332622i
$477$		0			0
$478$	−1.52347	+	1.10687i	−0.0696819	+	0.0506269i
$479$	−3.21705	−	1.43232i	−0.146991	−	0.0654446i	0.331923	−	0.943307i	$-0.392303\pi$
$479$	−3.21705	−	1.43232i	−0.146991	−	0.0654446i	−0.478914	+	0.877862i	$0.658969\pi$
$480$		0			0
$481$	12.6203	−	11.3634i	0.575438	−	0.518127i
$482$	0.275357	+	0.618461i	0.0125421	+	0.0281701i
$483$		0			0
$484$	−19.7678	−	7.91138i	−0.898536	−	0.359608i
$485$			4.88056i			0.221615i
$486$		0			0
$487$	9.85775	−	30.3390i	0.446697	−	1.37479i	−0.433914	−	0.900954i	$-0.642868\pi$
$487$	9.85775	−	30.3390i	0.446697	−	1.37479i	0.880611	−	0.473839i	$-0.157132\pi$
$488$	1.59075	+	1.43232i	0.0720100	+	0.0648381i
$489$		0			0
$490$	−0.289385	+	0.0304155i	−0.0130731	+	0.00137403i
$491$	−23.8856	−	5.07704i	−1.07794	−	0.229124i	−0.365469	−	0.930823i	$-0.619091\pi$
$491$	−23.8856	−	5.07704i	−1.07794	−	0.229124i	−0.712473	+	0.701700i	$0.752425\pi$
$492$		0			0
$493$	4.45277	−	42.3653i	0.200543	−	1.90804i
$494$	−1.38461			−0.0622964
$495$		0			0
$496$	−21.6577			−0.972460
$497$	−1.02574	+	9.75930i	−0.0460109	+	0.437765i
$498$		0			0
$499$	22.7607	+	4.83794i	1.01891	+	0.216576i	0.686940	−	0.726714i	$-0.258954\pi$
$499$	22.7607	+	4.83794i	1.01891	+	0.216576i	0.331969	+	0.943290i	$0.392287\pi$
$500$	−8.23146	+	0.865162i	−0.368122	+	0.0386912i
$501$		0			0
$502$	4.57449	+	4.11889i	0.204170	+	0.183835i
$503$	11.2856	−	34.7334i	0.503199	−	1.54869i	−0.300579	−	0.953757i	$-0.597180\pi$
$503$	11.2856	−	34.7334i	0.503199	−	1.54869i	0.803778	−	0.594930i	$-0.202820\pi$
$504$		0			0
$505$		−	26.4348i		−	1.17633i
$506$	0.519110	+	0.449763i	0.0230773	+	0.0199944i
$507$		0			0
$508$	−2.26985	−	5.09817i	−0.100708	−	0.226195i
$509$	18.4679	−	16.6286i	0.818575	−	0.737048i	−0.149216	−	0.988805i	$-0.547675\pi$
$509$	18.4679	−	16.6286i	0.818575	−	0.737048i	0.967791	+	0.251756i	$0.0810082\pi$
$510$		0			0
$511$	4.37035	+	1.94581i	0.193333	+	0.0860774i
$512$	−14.3757	+	10.4445i	−0.635321	+	0.461588i
$513$		0			0
$514$	4.04257	+	1.31351i	0.178310	+	0.0579364i
$515$	48.1563	+	5.06143i	2.12202	+	0.223033i
$516$		0			0
$517$	25.4023	−	3.16131i	1.11719	−	0.139034i
$518$	3.55183	+	2.05065i	0.156059	+	0.0901004i
$519$		0			0
$520$	8.14875	−	1.73207i	0.357346	−	0.0759563i
$521$	9.26334	−	3.00984i	0.405834	−	0.131864i	−0.0989844	−	0.995089i	$-0.531559\pi$
$521$	9.26334	−	3.00984i	0.405834	−	0.131864i	0.504819	+	0.863225i	$0.331559\pi$
$522$		0			0
$523$	19.5526	+	26.9118i	0.854975	+	1.17677i	0.982744	+	0.184968i	$0.0592182\pi$
$523$	19.5526	+	26.9118i	0.854975	+	1.17677i	−0.127769	+	0.991804i	$0.540782\pi$
$524$	2.72193	−	3.02301i	0.118908	−	0.132061i
$525$		0			0
$526$	2.52939	−	1.12615i	0.110286	−	0.0491027i
$527$	−13.3554	+	23.1323i	−0.581771	+	1.00766i
$528$		0			0
$529$	−11.1668	−	19.3414i	−0.485512	−	0.840931i
$530$	−6.26937	−	4.55496i	−0.272324	−	0.197855i
$531$		0			0
$532$	3.10816	+	9.56592i	0.134756	+	0.414735i
$533$	9.79637	−	22.0030i	0.424328	−	0.953057i
$534$		0			0
$535$	−4.32086	+	20.3280i	−0.186807	+	0.878858i
$536$	0.940463	+	1.04449i	0.0406218	+	0.0451151i
$537$		0			0
$538$	−3.44620	+	1.98966i	−0.148576	+	0.0857805i
$539$	1.30185	−	0.0248597i	0.0560746	−	0.00107078i
$540$		0			0
$541$	−6.85075	+	9.42925i	−0.294537	+	0.405395i	−0.930481	−	0.366340i	$-0.880611\pi$
$541$	−6.85075	+	9.42925i	−0.294537	+	0.405395i	0.635944	+	0.771735i	$0.280611\pi$
$542$	−0.153220	−	0.720841i	−0.00658134	−	0.0309628i
$543$		0			0
$544$	1.35942	+	12.9341i	0.0582848	+	0.554543i
$545$	2.63272	+	25.0486i	0.112773	+	1.07297i
$546$		0			0
$547$	−0.168987	−	0.795023i	−0.00722538	−	0.0339927i	0.974387	−	0.224877i	$-0.0721979\pi$
$547$	−0.168987	−	0.795023i	−0.00722538	−	0.0339927i	−0.981613	+	0.190884i	$0.938865\pi$
$548$	−5.77297	+	7.94581i	−0.246609	+	0.339428i
$549$		0			0
$550$	2.97487	−	0.0568072i	0.126849	−	0.00242227i
$551$	−15.8006	+	9.12251i	−0.673130	+	0.388632i
$552$		0			0
$553$	−12.9770	−	14.4124i	−0.551838	−	0.612879i
$554$	1.11365	−	5.23930i	0.0473143	−	0.222596i
$555$		0			0
$556$	−13.7651	+	30.9169i	−0.583770	+	1.31117i
$557$	2.14843	+	6.61219i	0.0910320	+	0.280168i	0.986199	−	0.165563i	$-0.0529440\pi$
$557$	2.14843	+	6.61219i	0.0910320	+	0.280168i	−0.895167	+	0.445730i	$0.852944\pi$
$558$		0			0
$559$	27.4405	+	19.9367i	1.16061	+	0.843233i
$560$	−14.3708	−	24.8909i	−0.607277	−	1.05183i
$561$		0			0
$562$	−0.391974	+	0.678919i	−0.0165344	+	0.0286385i
$563$	26.2714	−	11.6968i	1.10721	−	0.492960i	0.230056	−	0.973177i	$-0.426109\pi$
$563$	26.2714	−	11.6968i	1.10721	−	0.492960i	0.877149	+	0.480218i	$0.159442\pi$
$564$		0			0
$565$	22.3026	−	24.7696i	0.938278	−	1.04206i
$566$	3.34367	+	4.60217i	0.140545	+	0.193444i
$567$		0			0
$568$	3.42694	−	1.11348i	0.143791	−	0.0467207i
$569$	10.2206	−	2.17245i	0.428469	−	0.0910740i	0.0113711	−	0.999935i	$-0.496380\pi$
$569$	10.2206	−	2.17245i	0.428469	−	0.0910740i	0.417098	+	0.908861i	$0.363047\pi$
$570$		0			0
$571$	−18.4056	−	10.6265i	−0.770251	−	0.444704i	0.0627134	−	0.998032i	$-0.480025\pi$
$571$	−18.4056	−	10.6265i	−0.770251	−	0.444704i	−0.832964	+	0.553327i	$0.813358\pi$
$572$	−18.1944	+	2.26429i	−0.760747	+	0.0946747i
$573$		0			0
$574$	5.78483	+	0.608010i	0.241454	+	0.0253778i
$575$	2.74578	+	0.892157i	0.114507	+	0.0372055i
$576$		0			0
$577$	−12.6856	+	9.21665i	−0.528110	+	0.383694i	−0.819650	−	0.572864i	$-0.805832\pi$
$577$	−12.6856	+	9.21665i	−0.528110	+	0.383694i	0.291541	+	0.956558i	$0.405832\pi$
$578$	0.674623	+	0.300361i	0.0280606	+	0.0124934i
$579$		0			0
$580$	40.1225	−	36.1265i	1.66600	−	1.50007i
$581$	−8.66387	−	19.4594i	−0.359438	−	0.807310i
$582$		0			0
$583$	26.2085	+	22.7074i	1.08545	+	0.940443i
$584$		−	1.75664i		−	0.0726903i
$585$		0			0
$586$	−1.62588	+	5.00395i	−0.0671646	+	0.206711i
$587$	14.9785	+	13.4867i	0.618231	+	0.556658i	0.917613	−	0.397476i	$-0.130114\pi$
$587$	14.9785	+	13.4867i	0.618231	+	0.556658i	−0.299382	+	0.954133i	$0.596780\pi$
$588$		0			0
$589$	11.3776	−	1.19583i	0.468805	−	0.0492734i
$590$	−0.0676398	−	0.0143773i	−0.00278469	−	0.000591903i
$591$		0			0
$592$	−2.24881	+	21.3960i	−0.0924254	+	0.879369i
$593$	40.5694			1.66599			0.832993	−	0.553284i	$-0.186626\pi$
$593$	40.5694			1.66599			0.832993	+	0.553284i	$0.186626\pi$
$594$		0			0
$595$	−35.4475			−1.45320
$596$	1.14449	−	10.8891i	0.0468801	−	0.446034i
$597$		0			0
$598$	0.578525	+	0.122969i	0.0236576	+	0.00502859i
$599$	10.8776	−	1.14328i	0.444446	−	0.0467131i	0.120337	−	0.992733i	$-0.461602\pi$
$599$	10.8776	−	1.14328i	0.444446	−	0.0467131i	0.324108	+	0.946020i	$0.394936\pi$
$600$		0			0
$601$	−12.1550	−	10.9444i	−0.495813	−	0.446432i	0.382895	−	0.923792i	$-0.374927\pi$
$601$	−12.1550	−	10.9444i	−0.495813	−	0.446432i	−0.878708	+	0.477360i	$0.841594\pi$
$602$	−2.53129	+	7.79050i	−0.103168	+	0.317517i
$603$		0			0
$604$		−	17.7605i		−	0.722665i
$605$	−32.0679	−	2.13673i	−1.30374	−	0.0868702i
$606$		0			0
$607$	−9.70660	−	21.8014i	−0.393979	−	0.884890i	−0.996244	−	0.0865943i	$-0.972402\pi$
$607$	−9.70660	−	21.8014i	−0.393979	−	0.884890i	0.602265	−	0.798296i	$-0.294265\pi$
$608$	4.13944	−	3.72717i	0.167877	−	0.151157i
$609$		0			0
$610$	1.45172	+	0.646347i	0.0587784	+	0.0261698i
$611$	17.8330	−	12.9564i	0.721445	−	0.524161i
$612$		0			0
$613$	0.0461533	+	0.0149961i	0.00186411	+	0.000605687i	0.309949	−	0.950753i	$-0.399688\pi$
$613$	0.0461533	+	0.0149961i	0.00186411	+	0.000605687i	−0.308085	+	0.951359i	$0.599688\pi$
$614$	3.78622	+	0.397948i	0.152799	+	0.0160599i
$615$		0			0
$616$	−3.81823	−	8.15328i	−0.153841	−	0.328505i
$617$	−7.14090	−	4.12280i	−0.287482	−	0.165978i	0.349324	−	0.937002i	$-0.386411\pi$
$617$	−7.14090	−	4.12280i	−0.287482	−	0.165978i	−0.636806	+	0.771024i	$0.719745\pi$
$618$		0			0
$619$	1.70126	−	0.361615i	0.0683795	−	0.0145345i	−0.173595	−	0.984817i	$-0.555538\pi$
$619$	1.70126	−	0.361615i	0.0683795	−	0.0145345i	0.241974	+	0.970283i	$0.422205\pi$
$620$	−32.1968	+	10.4614i	−1.29305	+	0.420139i
$621$		0			0
$622$	−0.307013	−	0.422567i	−0.0123101	−	0.0169434i
$623$	3.76291	−	4.17913i	0.150758	−	0.167433i
$624$		0			0
$625$	−27.5669	+	12.2736i	−1.10267	+	0.490942i
$626$	3.15477	−	5.46423i	0.126090	−	0.218395i
$627$		0			0
$628$	−2.95547	−	5.11902i	−0.117936	−	0.204271i
$629$	21.4659	+	15.5959i	0.855903	+	0.621850i
$630$		0			0
$631$	−8.14182	−	25.0580i	−0.324121	−	0.997541i	−0.971836	−	0.235659i	$-0.924275\pi$
$631$	−8.14182	−	25.0580i	−0.324121	−	0.997541i	0.647715	−	0.761883i	$-0.275725\pi$
$632$	−2.89650	+	6.50564i	−0.115216	+	0.258780i
$633$		0			0
$634$	−0.0228230	+	0.107374i	−0.000906417	+	0.00426435i
$635$	−5.63648	−	6.25994i	−0.223677	−	0.248418i
$636$		0			0
$637$	0.971016	−	0.560616i	0.0384731	−	0.0222124i
$638$	6.40670	−	4.84429i	0.253644	−	0.191787i
$639$		0			0
$640$	−12.8409	+	17.6740i	−0.507582	+	0.698626i
$641$	1.80795	+	8.50575i	0.0714098	+	0.335957i	0.999321	−	0.0368445i	$-0.0117306\pi$
$641$	1.80795	+	8.50575i	0.0714098	+	0.335957i	−0.927911	+	0.372801i	$0.878397\pi$
$642$		0			0
$643$	2.25948	+	21.4975i	0.0891053	+	0.847780i	0.944214	+	0.329332i	$0.106823\pi$
$643$	2.25948	+	21.4975i	0.0891053	+	0.847780i	−0.855109	+	0.518448i	$0.826510\pi$
$644$	−0.449103	−	4.27293i	−0.0176972	−	0.168377i
$645$		0			0
$646$	−0.449780	−	2.11605i	−0.0176964	−	0.0832548i
$647$	−17.2616	+	23.7586i	−0.678625	+	0.934048i	−0.999916	−	0.0129330i	$-0.995883\pi$
$647$	−17.2616	+	23.7586i	−0.678625	+	0.934048i	0.321291	+	0.946980i	$0.395883\pi$
$648$		0			0
$649$	0.296067	+	0.0899860i	0.0116216	+	0.00353226i
$650$	2.21888	−	1.28107i	0.0870316	−	0.0502477i
$651$		0			0
$652$	−10.2379	−	11.3704i	−0.400948	−	0.445298i
$653$	4.92616	−	23.1758i	0.192775	−	0.906937i	−0.770295	−	0.637688i	$-0.779891\pi$
$653$	4.92616	−	23.1758i	0.192775	−	0.906937i	0.963070	−	0.269250i	$-0.0867756\pi$
$654$		0			0
$655$	2.49743	−	5.60931i	0.0975826	−	0.219174i
$656$	9.42876	+	29.0187i	0.368131	+	1.13299i
$657$		0			0
$658$	4.30674	+	3.12903i	0.167894	+	0.121982i
$659$	−17.2970	−	29.9594i	−0.673797	−	1.16705i	−0.976819	−	0.214067i	$-0.931329\pi$
$659$	−17.2970	−	29.9594i	−0.673797	−	1.16705i	0.303022	−	0.952984i	$-0.402004\pi$
$660$		0			0
$661$	−17.7456	+	30.7363i	−0.690225	+	1.19550i	0.281539	+	0.959550i	$0.409155\pi$
$661$	−17.7456	+	30.7363i	−0.690225	+	1.19550i	−0.971764	+	0.235955i	$0.924178\pi$
$662$	−4.01127	+	1.78593i	−0.155902	+	0.0694122i
$663$		0			0
$664$	−5.23366	+	5.81257i	−0.203105	+	0.225571i
$665$	8.92385	+	12.2826i	0.346052	+	0.476300i
$666$		0			0
$667$	7.41211	−	2.40834i	0.286998	−	0.0932513i
$668$	−31.1414	+	6.61932i	−1.20490	+	0.256109i
$669$		0			0
$670$	0.903618	+	0.521704i	0.0349098	+	0.0201552i
$671$	−6.22507	−	3.43728i	−0.240316	−	0.132695i
$672$		0			0
$673$	20.7868	+	2.18478i	0.801271	+	0.0842169i	0.496307	−	0.868147i	$-0.334689\pi$
$673$	20.7868	+	2.18478i	0.801271	+	0.0842169i	0.304964	+	0.952364i	$0.401356\pi$
$674$	−6.04715	−	1.96484i	−0.232928	−	0.0756827i
$675$		0			0
$676$	7.58475	−	5.51064i	0.291721	−	0.211948i
$677$	−22.1425	−	9.85849i	−0.851007	−	0.378893i	−0.0655801	−	0.997847i	$-0.520890\pi$
$677$	−22.1425	−	9.85849i	−0.851007	−	0.378893i	−0.785427	+	0.618955i	$0.787556\pi$
$678$		0			0
$679$	3.37522	−	3.03906i	0.129529	−	0.116628i
$680$	5.29413	+	11.8908i	0.203021	+	0.455992i
$681$		0			0
$682$	−4.90539	+	1.14098i	−0.187837	+	0.0436902i
$683$		−	17.6311i		−	0.674636i	−0.941391	−	0.337318i	$-0.890480\pi$
$683$		−	17.6311i		−	0.674636i	0.941391	−	0.337318i	$-0.109520\pi$
$684$		0			0
$685$	−4.58116	+	14.0994i	−0.175037	+	0.538709i
$686$	−3.38673	−	3.04943i	−0.129306	−	0.116428i
$687$		0			0
$688$	−42.7336	+	4.49148i	−1.62920	+	0.171236i
$689$	29.2082	+	6.20840i	1.11274	+	0.236521i
$690$		0			0
$691$	−3.04558	+	28.9767i	−0.115859	+	1.10233i	0.769894	+	0.638171i	$0.220309\pi$
$691$	−3.04558	+	28.9767i	−0.115859	+	1.10233i	−0.885754	+	0.464156i	$0.846358\pi$
$692$	−30.0459			−1.14218
$693$		0			0
$694$	−5.29496			−0.200994
$695$	−5.33966	+	50.8034i	−0.202545	+	1.92708i
$696$		0			0
$697$	36.8088	+	7.82394i	1.39423	+	0.296353i
$698$	−4.54632	+	0.477838i	−0.172081	+	0.0180864i
$699$		0			0
$700$	−13.8315	−	12.4540i	−0.522783	−	0.470716i
$701$	−4.54301	+	13.9820i	−0.171587	+	0.528091i	−0.999461	−	0.0328229i	$-0.989550\pi$
$701$	−4.54301	+	13.9820i	−0.171587	+	0.528091i	0.827874	+	0.560914i	$0.189550\pi$
$702$		0			0
$703$		−	11.3642i		−	0.428611i
$704$	14.1095	−	16.2850i	0.531773	−	0.613765i
$705$		0			0
$706$	1.68134	+	3.77634i	0.0632779	+	0.142125i
$707$	−18.2814	+	16.4606i	−0.687542	+	0.619065i
$708$		0			0
$709$	9.85018	+	4.38558i	0.369931	+	0.164704i	0.583278	−	0.812272i	$-0.301770\pi$
$709$	9.85018	+	4.38558i	0.369931	+	0.164704i	−0.213347	+	0.976977i	$0.568436\pi$
$710$	2.16412	−	1.57233i	0.0812180	−	0.0590083i
$711$		0			0
$712$	−1.96388	−	0.638103i	−0.0735995	−	0.0239139i
$713$	−4.86006	−	0.510813i	−0.182011	−	0.0191301i
$714$		0			0
$715$	−25.0629	+	11.7371i	−0.937299	+	0.438943i
$716$	8.69904	+	5.02239i	0.325098	+	0.187696i
$717$		0			0
$718$	−6.14976	+	1.30717i	−0.229507	+	0.0487832i
$719$	30.1960	−	9.81128i	1.12612	−	0.365899i	0.314020	−	0.949416i	$-0.398324\pi$
$719$	30.1960	−	9.81128i	1.12612	−	0.365899i	0.812101	+	0.583517i	$0.198324\pi$
$720$		0			0
$721$	−26.4860	−	36.4549i	−0.986390	−	1.35765i
$722$	2.60511	−	2.89327i	0.0969523	−	0.107676i
$723$		0			0
$724$	−9.39373	+	4.18236i	−0.349115	+	0.155436i
$725$	16.8807	−	29.2383i	0.626934	−	1.08588i
$726$		0			0
$727$	−11.8209	−	20.4744i	−0.438414	−	0.759355i	0.559154	−	0.829064i	$-0.311126\pi$
$727$	−11.8209	−	20.4744i	−0.438414	−	0.759355i	−0.997567	+	0.0697091i	$0.977793\pi$
$728$	−6.27196	−	4.55685i	−0.232454	−	0.168888i
$729$		0			0
$730$	−0.402984	−	1.24026i	−0.0149151	−	0.0459040i
$731$	−21.5547	+	48.4128i	−0.797231	+	1.79061i
$732$		0			0
$733$	−3.41483	+	16.0655i	−0.126130	+	0.593394i	0.868999	+	0.494813i	$0.164764\pi$
$733$	−3.41483	+	16.0655i	−0.126130	+	0.593394i	−0.995129	+	0.0985806i	$0.968570\pi$
$734$	1.51981	+	1.68792i	0.0560973	+	0.0623023i
$735$		0			0
$736$	−2.06059	+	1.18968i	−0.0759542	+	0.0438522i
$737$	−3.82908	−	2.67181i	−0.141046	−	0.0984172i
$738$		0			0
$739$	20.4813	−	28.1901i	0.753417	−	1.03699i	−0.244316	−	0.969696i	$-0.578563\pi$
$739$	20.4813	−	28.1901i	0.753417	−	1.03699i	0.997733	−	0.0672942i	$-0.0214366\pi$
$740$	6.99182	+	32.8939i	0.257024	+	1.20920i
$741$		0			0
$742$	0.753806	+	7.17198i	0.0276731	+	0.263292i
$743$	−5.51833	−	52.5034i	−0.202448	−	1.92616i	−0.349315	−	0.937005i	$-0.613586\pi$
$743$	−5.51833	−	52.5034i	−0.202448	−	1.92616i	0.146868	−	0.989156i	$-0.453081\pi$
$744$		0			0
$745$	−3.43613	−	16.1657i	−0.125890	−	0.592266i
$746$	2.52001	−	3.46850i	0.0922643	−	0.126991i
$747$		0			0
$748$	−9.37077	−	27.0704i	−0.342629	−	0.989791i
$749$	16.7487	−	9.66985i	0.611983	−	0.353329i
$750$		0			0
$751$	34.3784	+	38.1811i	1.25449	+	1.39325i	0.886047	+	0.463595i	$0.153441\pi$
$751$	34.3784	+	38.1811i	1.25449	+	1.39325i	0.368439	+	0.929652i	$0.379892\pi$
$752$	−5.80584	+	27.3144i	−0.211717	+	0.996052i
$753$		0			0
$754$	2.81315	−	6.31844i	0.102449	−	0.230104i
$755$	−8.28421	−	25.4962i	−0.301493	−	0.927900i
$756$		0			0
$757$	5.71877	+	4.15493i	0.207852	+	0.151013i	0.686841	−	0.726807i	$-0.258997\pi$
$757$	5.71877	+	4.15493i	0.207852	+	0.151013i	−0.478989	+	0.877821i	$0.658997\pi$
$758$	−2.50261	−	4.33464i	−0.0908987	−	0.157441i
$759$		0			0
$760$	2.78740	−	4.82792i	0.101110	−	0.175127i
$761$	−26.6140	+	11.8493i	−0.964758	+	0.429538i	−0.827790	−	0.561037i	$-0.810402\pi$
$761$	−26.6140	+	11.8493i	−0.964758	+	0.429538i	−0.136968	+	0.990576i	$0.543736\pi$
$762$		0			0
$763$	15.6834	−	17.4181i	0.567776	−	0.630579i
$764$	−12.4010	−	17.0685i	−0.448653	−	0.617517i
$765$		0			0
$766$	1.20628	−	0.391945i	0.0435847	−	0.0141615i
$767$	0.260637	−	0.0554002i	0.00941107	−	0.00200039i
$768$		0			0
$769$	−38.3136	−	22.1204i	−1.38162	−	0.797682i	−0.389273	−	0.921122i	$-0.627274\pi$
$769$	−38.3136	−	22.1204i	−1.38162	−	0.797682i	−0.992352	+	0.123441i	$0.960607\pi$
$770$	−4.56624	−	4.88062i	−0.164556	−	0.175885i
$771$		0			0
$772$	−29.5811	−	3.10910i	−1.06465	−	0.111899i
$773$	38.0786	+	12.3725i	1.36959	+	0.445007i	0.899234	−	0.437468i	$-0.144125\pi$
$773$	38.0786	+	12.3725i	1.36959	+	0.445007i	0.470358	+	0.882476i	$0.344125\pi$
$774$		0			0
$775$	−17.1266	+	12.4432i	−0.615204	+	0.446972i
$776$	−1.52354	−	0.678325i	−0.0546920	−	0.0243505i
$777$		0			0
$778$	1.85754	−	1.67254i	0.0665961	−	0.0599634i
$779$	−6.55554	−	14.7240i	−0.234877	−	0.527541i
$780$		0			0
$781$	−10.2504	+	6.18194i	−0.366787	+	0.221207i
$782$			0.924086i			0.0330453i
$783$		0			0
$784$	−0.438933	+	1.35090i	−0.0156762	+	0.0482463i
$785$	−6.63045	−	5.97008i	−0.236651	−	0.213081i
$786$		0			0
$787$	28.2087	−	2.96485i	1.00553	−	0.105686i	0.412578	−	0.910922i	$-0.364628\pi$
$787$	28.2087	−	2.96485i	1.00553	−	0.105686i	0.592954	+	0.805237i	$0.297962\pi$
$788$	−13.7107	−	2.91430i	−0.488423	−	0.103817i
$789$		0			0
$790$	−0.552609	+	5.25772i	−0.0196609	+	0.187061i
$791$	−31.0173			−1.10285
$792$		0			0
$793$	−6.12332			−0.217446
$794$	0.504459	−	4.79961i	0.0179026	−	0.170332i
$795$		0			0
$796$	−21.5323	−	4.57683i	−0.763191	−	0.162221i
$797$	−14.8619	+	1.56205i	−0.526435	+	0.0553305i	−0.364018	−	0.931392i	$-0.618595\pi$
$797$	−14.8619	+	1.56205i	−0.526435	+	0.0553305i	−0.162416	+	0.986722i	$0.551929\pi$
$798$		0			0
$799$	25.5938	+	23.0448i	0.905443	+	0.815265i
$800$	−3.18513	+	9.80283i	−0.112611	+	0.346582i
$801$		0			0
$802$			7.78923i			0.275047i
$803$	1.32204	+	5.68386i	0.0466540	+	0.200579i
$804$		0			0
$805$	−2.63778	−	5.92455i	−0.0929694	−	0.208813i
$806$	−3.22288	+	2.90190i	−0.113521	+	0.102215i
$807$		0			0
$808$	8.25205	+	3.67405i	0.290306	+	0.129253i
$809$	24.0892	−	17.5019i	0.846933	−	0.615333i	−0.0773660	−	0.997003i	$-0.524651\pi$
$809$	24.0892	−	17.5019i	0.846933	−	0.615333i	0.924299	+	0.381670i	$0.124651\pi$
$810$		0			0
$811$	41.9856	+	13.6420i	1.47432	+	0.479034i	0.932409	−	0.361405i	$-0.117703\pi$
$811$	41.9856	+	13.6420i	1.47432	+	0.479034i	0.541906	+	0.840439i	$0.317703\pi$
$812$	−49.9676	−	5.25180i	−1.75352	−	0.184302i
$813$		0			0
$814$	0.617840	+	4.96458i	0.0216553	+	0.174008i
$815$	−20.0007	−	11.5474i	−0.700593	−	0.404488i
$816$		0			0
$817$	22.2015	−	4.71907i	0.776732	−	0.165100i
$818$	2.86459	−	0.930761i	0.100158	−	0.0325433i
$819$		0			0
$820$	28.0340	+	38.5854i	0.978988	+	1.34746i
$821$	−2.67983	+	2.97626i	−0.0935269	+	0.103872i	−0.788091	−	0.615558i	$-0.788930\pi$
$821$	−2.67983	+	2.97626i	−0.0935269	+	0.103872i	0.694564	+	0.719431i	$0.255597\pi$
$822$		0			0
$823$	38.5354	−	17.1571i	1.34326	−	0.598058i	0.395919	−	0.918285i	$-0.370426\pi$
$823$	38.5354	−	17.1571i	1.34326	−	0.598058i	0.947341	+	0.320227i	$0.103759\pi$
$824$	−8.27302	+	14.3293i	−0.288204	+	0.499184i
$825$		0			0
$826$	0.0321756	+	0.0557298i	0.00111953	+	0.00193909i
$827$	−21.5183	−	15.6340i	−0.748266	−	0.543647i	0.147023	−	0.989133i	$-0.453031\pi$
$827$	−21.5183	−	15.6340i	−0.748266	−	0.543647i	−0.895289	+	0.445486i	$0.853031\pi$
$828$		0			0
$829$	3.77976	+	11.6329i	0.131276	+	0.404027i	0.994992	−	0.0999518i	$-0.0318689\pi$
$829$	3.77976	+	11.6329i	0.131276	+	0.404027i	−0.863716	+	0.503979i	$0.831869\pi$
$830$	−2.36174	+	5.30454i	−0.0819770	+	0.184123i
$831$		0			0
$832$	3.85767	−	18.1489i	0.133741	−	0.629201i
$833$	1.17220	+	1.30186i	0.0406143	+	0.0451067i
$834$		0			0
$835$	−41.6177	+	24.0280i	−1.44024	+	0.831523i
$836$	−7.02087	+	10.0619i	−0.242822	+	0.347999i
$837$		0			0
$838$	1.50045	−	2.06519i	0.0518321	−	0.0713408i
$839$	2.00561	+	9.43567i	0.0692415	+	0.325756i	0.999112	−	0.0421312i	$-0.0134147\pi$
$839$	2.00561	+	9.43567i	0.0692415	+	0.325756i	−0.929871	+	0.367887i	$0.880081\pi$
$840$		0			0
$841$	−6.49515	−	61.7972i	−0.223971	−	2.13094i
$842$	0.165899	+	1.57843i	0.00571727	+	0.0543962i
$843$		0			0
$844$	−1.48833	−	7.00204i	−0.0512304	−	0.241020i
$845$	8.31793	−	11.4486i	0.286146	−	0.393846i
$846$		0			0
$847$	18.4906	+	23.5075i	0.635344	+	0.807727i
$848$	−32.7606	+	18.9143i	−1.12500	+	0.649521i
$849$		0			0
$850$	2.67860	+	2.97489i	0.0918754	+	0.102038i
$851$	−1.00928	+	4.74828i	−0.0345976	+	0.162769i
$852$		0			0
$853$	−4.77450	+	10.7237i	−0.163476	+	0.367173i	−0.976647	−	0.214852i	$-0.931073\pi$
$853$	−4.77450	+	10.7237i	−0.163476	+	0.367173i	0.813171	+	0.582025i	$0.197740\pi$
$854$	−0.456976	−	1.40643i	−0.0156374	−	0.0481270i
$855$		0			0
$856$	−5.74518	−	4.17412i	−0.196366	−	0.142668i
$857$	24.3869	+	42.2393i	0.833041	+	1.44287i	0.895616	+	0.444828i	$0.146735\pi$
$857$	24.3869	+	42.2393i	0.833041	+	1.44287i	−0.0625753	+	0.998040i	$0.519931\pi$
$858$		0			0
$859$	15.5440	−	26.9230i	0.530355	−	0.918602i	−0.469018	−	0.883189i	$-0.655392\pi$
$859$	15.5440	−	26.9230i	0.530355	−	0.918602i	0.999373	−	0.0354131i	$-0.0112747\pi$
$860$	−61.3591	+	27.3188i	−2.09233	+	0.931564i
$861$		0			0
$862$	3.33360	−	3.70234i	0.113543	−	0.126102i
$863$	30.6459	+	42.1805i	1.04320	+	1.43584i	0.894559	+	0.446950i	$0.147490\pi$
$863$	30.6459	+	42.1805i	1.04320	+	1.43584i	0.148641	+	0.988891i	$0.452510\pi$
$864$		0			0
$865$	−43.1325	+	14.0146i	−1.46655	+	0.476511i
$866$	−7.76379	+	1.65024i	−0.263824	+	0.0560776i
$867$		0			0
$868$	27.2832	+	15.7520i	0.926053	+	0.534657i
$869$	4.47589	−	23.2298i	0.151834	−	0.788018i
$870$		0			0
$871$	−3.99856	−	0.420265i	−0.135486	−	0.0142401i
$872$	−8.18523	−	2.65954i	−0.277187	−	0.0900635i
$873$		0			0
$874$	0.320198	−	0.232637i	0.0108309	−	0.00786907i
$875$	10.6210	+	4.72877i	0.359055	+	0.159861i
$876$		0			0
$877$	−12.6244	+	11.3671i	−0.426295	+	0.383838i	−0.854165	−	0.520002i	$-0.825931\pi$
$877$	−12.6244	+	11.3671i	−0.426295	+	0.383838i	0.427869	+	0.903841i	$0.359264\pi$
$878$	−2.08354	−	4.67971i	−0.0703162	−	0.157933i
$879$		0			0
$880$	13.6460	−	32.2951i	0.460006	−	1.08867i
$881$			50.3115i			1.69504i	0.530765	+	0.847519i	$0.321905\pi$
$881$			50.3115i			1.69504i	−0.530765	+	0.847519i	$0.678095\pi$
$882$		0			0
$883$	4.44037	−	13.6660i	0.149430	−	0.459899i	−0.848124	−	0.529798i	$-0.822268\pi$
$883$	4.44037	−	13.6660i	0.149430	−	0.459899i	0.997554	+	0.0698990i	$0.0222677\pi$
$884$	−18.3316	−	16.5058i	−0.616558	−	0.555151i
$885$		0			0
$886$	6.14767	−	0.646146i	0.206535	−	0.0217077i
$887$	−40.3978	−	8.58682i	−1.35643	−	0.288317i	−0.528395	−	0.848999i	$-0.677206\pi$
$887$	−40.3978	−	8.58682i	−1.35643	−	0.288317i	−0.828032	+	0.560681i	$0.810539\pi$
$888$		0			0
$889$	−0.819389	+	7.79597i	−0.0274814	+	0.261468i
$890$	−1.53296			−0.0513851
$891$		0			0
$892$	0.548221			0.0183558
$893$	1.54186	−	14.6698i	0.0515963	−	0.490906i
$894$		0			0
$895$	14.8306	+	3.15234i	0.495732	+	0.105371i
$896$	20.2186	−	2.12506i	0.675455	−	0.0709932i
$897$		0			0
$898$	0.622470	+	0.560474i	0.0207721	+	0.0187033i
$899$	−17.6592	+	54.3495i	−0.588968	+	1.81266i
$900$		0			0
$901$			46.6547i			1.55429i
$902$	3.66435	+	6.07590i	0.122009	+	0.202305i
$903$		0			0
$904$	4.63247	+	10.4047i	0.154074	+	0.346055i
$905$	−11.5344	+	10.3856i	−0.383416	+	0.345229i
$906$		0			0
$907$	−23.8588	−	10.6226i	−0.792217	−	0.352718i	−0.0295951	−	0.999562i	$-0.509422\pi$
$907$	−23.8588	−	10.6226i	−0.792217	−	0.352718i	−0.762622	+	0.646844i	$0.776088\pi$
$908$	−28.5883	+	20.7706i	−0.948738	+	0.689298i
$909$		0			0
$910$	−5.47363	−	1.77849i	−0.181449	−	0.0589563i
$911$	−45.1640	−	4.74692i	−1.49635	−	0.157273i	−0.679309	−	0.733853i	$-0.737720\pi$
$911$	−45.1640	−	4.74692i	−1.49635	−	0.157273i	−0.817041	+	0.576580i	$0.804387\pi$
$912$		0			0
$913$	12.5597	−	22.7462i	0.415666	−	0.752791i
$914$	−3.43098	−	1.98088i	−0.113487	−	0.0655215i
$915$		0			0
$916$	49.9387	−	10.6148i	1.65002	−	0.350723i
$917$	−5.43431	+	1.76572i	−0.179457	+	0.0583091i
$918$		0			0
$919$	−16.3737	−	22.5365i	−0.540119	−	0.743410i	0.448511	−	0.893777i	$-0.351954\pi$
$919$	−16.3737	−	22.5365i	−0.540119	−	0.743410i	−0.988630	+	0.150367i	$0.951954\pi$
$920$	−1.59343	+	1.76968i	−0.0525337	+	0.0583446i
$921$		0			0
$922$	−8.47453	+	3.77310i	−0.279094	+	0.124260i
$923$	−5.15381	+	8.92667i	−0.169640	+	0.293825i
$924$		0			0
$925$	10.5145	+	18.2116i	0.345713	+	0.598793i
$926$	−0.914353	−	0.664317i	−0.0300475	−	0.0218308i
$927$		0			0
$928$	8.59813	+	26.4623i	0.282248	+	0.868669i
$929$	20.2370	−	45.4530i	0.663954	−	1.49127i	−0.195846	−	0.980635i	$-0.562745\pi$
$929$	20.2370	−	45.4530i	0.663954	−	1.49127i	0.859800	−	0.510631i	$-0.170588\pi$
$930$		0			0
$931$	0.155997	−	0.733910i	0.00511261	−	0.0240529i
$932$	13.9910	+	15.5386i	0.458291	+	0.508984i
$933$		0			0
$934$	9.14497	−	5.27985i	0.299232	−	0.172762i
$935$	−26.0789	−	34.4901i	−0.852872	−	1.12795i
$936$		0			0
$937$	11.9943	−	16.5087i	0.391837	−	0.539317i	−0.566835	−	0.823831i	$-0.691832\pi$
$937$	11.9943	−	16.5087i	0.391837	−	0.539317i	0.958672	+	0.284514i	$0.0918323\pi$
$938$	−0.201879	−	0.949768i	−0.00659159	−	0.0310110i
$939$		0			0
$940$	4.56262	+	43.4105i	0.148816	+	1.41589i
$941$	1.83378	+	17.4473i	0.0597796	+	0.568765i	0.982885	+	0.184219i	$0.0589755\pi$
$941$	1.83378	+	17.4473i	0.0597796	+	0.568765i	−0.923106	+	0.384547i	$0.874358\pi$
$942$		0			0
$943$	1.43141	+	6.73427i	0.0466133	+	0.219298i
$944$	−0.198413	+	0.273093i	−0.00645781	+	0.00888841i
$945$		0			0
$946$	−9.44237	+	3.26860i	−0.306998	+	0.106271i
$947$	−40.7614	+	23.5336i	−1.32457	+	0.764739i	−0.984453	−	0.175646i	$-0.943799\pi$
$947$	−40.7614	+	23.5336i	−1.32457	+	0.764739i	−0.340113	+	0.940385i	$0.610465\pi$
$948$		0			0
$949$	3.36242	+	3.73434i	0.109149	+	0.121222i
$950$	0.356471	−	1.67707i	0.0115655	−	0.0544112i
$951$		0			0
$952$	4.92667	−	11.0655i	0.159674	−	0.358634i
$953$	−15.9545	−	49.1029i	−0.516817	−	1.59060i	−0.779952	−	0.625839i	$-0.784757\pi$
$953$	−15.9545	−	49.1029i	−0.516817	−	1.59060i	0.263136	−	0.964759i	$-0.415243\pi$
$954$		0			0
$955$	−25.7637	−	18.7185i	−0.833695	−	0.605715i
$956$	7.18447	+	12.4439i	0.232362	+	0.402463i
$957$		0			0
$958$	0.446659	−	0.773636i	0.0144309	−	0.0249951i
$959$	12.6032	−	5.61133i	0.406980	−	0.181199i
$960$		0			0
$961$	3.23375	−	3.59144i	0.104315	−	0.115853i
$962$	2.53218	+	3.48525i	0.0816408	+	0.112369i
$963$		0			0
$964$	4.91289	−	1.59629i	0.158233	−	0.0514132i
$965$	−43.9154	+	9.33451i	−1.41369	+	0.300488i
$966$		0			0
$967$	−29.1820	−	16.8482i	−0.938429	−	0.541802i	−0.0489615	−	0.998801i	$-0.515591\pi$
$967$	−29.1820	−	16.8482i	−0.938429	−	0.541802i	−0.889467	+	0.456998i	$0.848924\pi$
$968$	5.12397	−	9.71352i	0.164691	−	0.312204i
$969$		0			0
$970$	−1.23130	−	0.129414i	−0.0395345	−	0.00415525i
$971$	53.1467	+	17.2684i	1.70556	+	0.554170i	0.989584	−	0.143955i	$-0.0459822\pi$
$971$	53.1467	+	17.2684i	1.70556	+	0.554170i	0.715976	+	0.698125i	$0.245982\pi$
$972$		0			0
$973$	38.4588	−	27.9419i	1.23293	−	0.895777i
$974$	7.39272	+	3.29145i	0.236878	+	0.105465i
$975$		0			0
$976$	5.76475	−	5.19061i	0.184525	−	0.166147i
$977$	8.40289	+	18.8732i	0.268832	+	0.603807i	0.996634	−	0.0819804i	$-0.0261245\pi$
$977$	8.40289	+	18.8732i	0.268832	+	0.603807i	−0.727802	+	0.685788i	$0.759458\pi$
$978$		0			0
$979$	6.83465	+	0.586661i	0.218436	+	0.0187498i
$980$			2.22029i			0.0709245i
$981$		0			0
$982$	1.91422	−	5.89137i	0.0610853	−	0.188001i
$983$	37.2519	+	33.5418i	1.18815	+	1.06982i	0.996082	+	0.0884351i	$0.0281866\pi$
$983$	37.2519	+	33.5418i	1.18815	+	1.06982i	0.192070	+	0.981381i	$0.438480\pi$
$984$		0			0
$985$	−21.0418	+	2.21158i	−0.670446	+	0.0704667i
$986$	10.5701	+	2.24674i	0.336620	+	0.0715508i
$987$		0			0
$988$	−1.10436	+	10.5072i	−0.0351343	+	0.334280i
$989$	−9.69548			−0.308298
$990$		0			0
$991$	45.3068			1.43922			0.719609	−	0.694379i	$-0.244321\pi$
$991$	45.3068			1.43922			0.719609	+	0.694379i	$0.244321\pi$
$992$	1.82368	−	17.3511i	0.0579018	−	0.550899i
$993$		0			0
$994$	−2.43493	−	0.517561i	−0.0772314	−	0.0164160i
$995$	−33.0455	+	3.47323i	−1.04761	+	0.110109i
$996$		0			0
$997$	−7.63945	−	6.87859i	−0.241944	−	0.217847i	0.539234	−	0.842156i	$-0.318714\pi$
$997$	−7.63945	−	6.87859i	−0.241944	−	0.217847i	−0.781177	+	0.624309i	$0.785381\pi$
$998$	−1.82407	+	5.61392i	−0.0577400	+	0.177705i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.458.2		32
3.2	odd	2	inner	891.2.u.c.458.3		32
9.2	odd	6	inner	891.2.u.c.755.2		32
9.4	even	3		99.2.j.a.62.2	yes	16
9.5	odd	6		99.2.j.a.62.3	yes	16
9.7	even	3	inner	891.2.u.c.755.3		32
11.8	odd	10	inner	891.2.u.c.701.2		32
33.8	even	10	inner	891.2.u.c.701.3		32
36.23	even	6		1584.2.cd.c.161.3		16
36.31	odd	6		1584.2.cd.c.161.2		16
99.5	odd	30		1089.2.d.g.1088.7		16
99.41	even	30		99.2.j.a.8.2	✓	16
99.49	even	15		1089.2.d.g.1088.10		16
99.50	even	30		1089.2.d.g.1088.9		16
99.52	odd	30	inner	891.2.u.c.107.3		32
99.74	even	30	inner	891.2.u.c.107.2		32
99.85	odd	30		99.2.j.a.8.3	yes	16
99.94	odd	30		1089.2.d.g.1088.8		16
396.239	odd	30		1584.2.cd.c.305.2		16
396.283	even	30		1584.2.cd.c.305.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.2	✓	16	99.41	even	30
99.2.j.a.8.3	yes	16	99.85	odd	30
99.2.j.a.62.2	yes	16	9.4	even	3
99.2.j.a.62.3	yes	16	9.5	odd	6
891.2.u.c.107.2		32	99.74	even	30	inner
891.2.u.c.107.3		32	99.52	odd	30	inner
891.2.u.c.458.2		32	1.1	even	1	trivial
891.2.u.c.458.3		32	3.2	odd	2	inner
891.2.u.c.701.2		32	11.8	odd	10	inner
891.2.u.c.701.3		32	33.8	even	10	inner
891.2.u.c.755.2		32	9.2	odd	6	inner
891.2.u.c.755.3		32	9.7	even	3	inner
1089.2.d.g.1088.7		16	99.5	odd	30
1089.2.d.g.1088.8		16	99.94	odd	30
1089.2.d.g.1088.9		16	99.50	even	30
1089.2.d.g.1088.10		16	99.49	even	15
1584.2.cd.c.161.2		16	36.31	odd	6
1584.2.cd.c.161.3		16	36.23	even	6
1584.2.cd.c.305.2		16	396.239	odd	30
1584.2.cd.c.305.3		16	396.283	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.u (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0265163 + 0.252286i) q^{2} +(1.89335 + 0.402444i) q^{4} +(2.90572 - 0.305404i) q^{5} +(-2.02056 - 1.81932i) q^{7} +(-0.308515 + 0.949513i) q^{8} +0.741170i q^{10} +(0.283644 - 3.30447i) q^{11} +(-1.16162 - 2.60905i) q^{13} +(0.512566 - 0.461517i) q^{14} +(3.30524 + 1.47159i) q^{16} +(3.60998 - 2.62280i) q^{17} +(-1.81761 - 0.590579i) q^{19} +(5.62446 + 0.591154i) q^{20} +(0.826150 + 0.159182i) q^{22} +(0.706997 + 0.408185i) q^{23} +(3.45921 - 0.735277i) q^{25} +(0.689029 - 0.223879i) q^{26} +(-3.09345 - 4.25777i) q^{28} +(6.38792 - 7.09451i) q^{29} +(-5.46853 + 2.43474i) q^{31} +(-1.45728 + 2.52408i) q^{32} +(0.565973 + 0.980294i) q^{34} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(0.197191 - 0.442898i) q^{38} +(-0.606475 + 2.85324i) q^{40} +(5.64300 + 6.26719i) q^{41} +(-10.2852 + 5.93817i) q^{43} +(1.86690 - 6.14238i) q^{44} +(-0.121726 + 0.167542i) q^{46} +(1.60470 + 7.54950i) q^{47} +(0.0410372 + 0.390443i) q^{49} +(0.0937745 + 0.892205i) q^{50} +(-1.14937 - 5.40734i) q^{52} +(-6.14564 + 8.45874i) q^{53} +(-0.185009 - 9.68851i) q^{55} +(2.35084 - 1.35726i) q^{56} +(1.62046 + 1.79970i) q^{58} +(-0.0193981 + 0.0912608i) q^{59} +(0.872063 - 1.95869i) q^{61} +(-0.469246 - 1.44419i) q^{62} +(5.25595 + 3.81867i) q^{64} +(-4.17217 - 7.22641i) q^{65} +(0.703892 - 1.21918i) q^{67} +(7.89049 - 3.51307i) q^{68} +(1.34843 - 1.49758i) q^{70} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(-1.47546 + 0.313619i) q^{74} +(-3.20371 - 1.84966i) q^{76} +(-6.58502 + 6.16085i) q^{77} +(7.09381 + 0.745590i) q^{79} +(10.0535 + 3.26659i) q^{80} +(-1.73075 + 1.25747i) q^{82} +(7.15699 + 3.18650i) q^{83} +(9.68858 - 8.72364i) q^{85} +(-1.22539 - 2.75227i) q^{86} +(3.05013 + 1.28880i) q^{88} +2.06830i q^{89} +(-2.39957 + 7.38512i) q^{91} +(1.17432 + 1.05736i) q^{92} +(-1.94718 + 0.204657i) q^{94} +(-5.46185 - 1.16095i) q^{95} +(-0.174608 + 1.66129i) q^{97} -0.0995913 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) \) 32 * q + 4 * q^4 + 20 * q^16 + 48 * q^22 + 32 * q^25 + 80 * q^28 - 16 * q^31 - 40 * q^34 - 24 * q^37 - 60 * q^40 - 80 * q^46 + 24 * q^49 + 40 * q^52 + 32 * q^55 - 12 * q^58 + 72 * q^64 - 96 * q^67 - 76 * q^70 - 40 * q^73 - 24 * q^82 + 100 * q^85 + 12 * q^88 - 144 * q^91 + 80 * q^94 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more