LMFDB - Embedded newform 891.2.u.e.458.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(107,891)] 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("891.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [64,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			458.3
Character	$\chi$	$=$	891.458
Dual form			891.2.u.e.107.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.106570 + 1.01395i) q^{2} +(0.939559 + 0.199709i) q^{4} +(-3.08748 + 0.324507i) q^{5} +(3.11115 + 2.80129i) q^{7} +(-0.932731 + 2.87065i) q^{8} -3.16513i q^{10} +(3.27533 - 0.521762i) q^{11} +(-0.145286 - 0.326318i) q^{13} +(-3.17193 + 2.85602i) q^{14} +(-1.05628 - 0.470288i) q^{16} +(-2.52248 + 1.83269i) q^{17} +(-0.384024 - 0.124777i) q^{19} +(-2.96567 - 0.311705i) q^{20} +(0.179988 + 3.37662i) q^{22} +(2.44458 + 1.41138i) q^{23} +(4.53649 - 0.964260i) q^{25} +(0.346353 - 0.112537i) q^{26} +(2.36367 + 3.25331i) q^{28} +(4.15306 - 4.61244i) q^{29} +(-7.39141 + 3.29087i) q^{31} +(-2.42897 + 4.20709i) q^{32} +(-1.58943 - 2.75298i) q^{34} +(-10.5147 - 7.63935i) q^{35} +(1.01570 + 3.12601i) q^{37} +(0.167443 - 0.376083i) q^{38} +(1.94824 - 9.16576i) q^{40} +(-5.08934 - 5.65229i) q^{41} +(-8.02668 + 4.63421i) q^{43} +(3.18156 + 0.163887i) q^{44} +(-1.69159 + 2.32827i) q^{46} +(2.63310 + 12.3878i) q^{47} +(1.10032 + 10.4689i) q^{49} +(0.494256 + 4.70253i) q^{50} +(-0.0713360 - 0.335610i) q^{52} +(2.07104 - 2.85055i) q^{53} +(-9.94319 + 2.67380i) q^{55} +(-10.9434 + 6.31818i) q^{56} +(4.23419 + 4.70255i) q^{58} +(-2.42122 + 11.3909i) q^{59} +(-0.483540 + 1.08605i) q^{61} +(-2.54907 - 7.84522i) q^{62} +(-5.87777 - 4.27045i) q^{64} +(0.554460 + 0.960353i) q^{65} +(7.66446 - 13.2752i) q^{67} +(-2.73603 + 1.21816i) q^{68} +(8.86647 - 9.84721i) q^{70} +(-0.357651 - 0.492264i) q^{71} +(10.8303 - 3.51899i) q^{73} +(-3.27786 + 0.696732i) q^{74} +(-0.335894 - 0.193928i) q^{76} +(11.6517 + 7.55187i) q^{77} +(-4.81384 - 0.505955i) q^{79} +(3.41387 + 1.10923i) q^{80} +(6.27351 - 4.55797i) q^{82} +(6.05341 + 2.69515i) q^{83} +(7.19339 - 6.47696i) q^{85} +(-3.84345 - 8.63252i) q^{86} +(-1.55720 + 9.88899i) q^{88} +7.29922i q^{89} +(0.462105 - 1.42221i) q^{91} +(2.01496 + 1.81428i) q^{92} +(-12.8412 + 1.34966i) q^{94} +(1.22616 + 0.260628i) q^{95} +(0.543471 - 5.17078i) q^{97} -10.7322 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70}+ \cdots + 24 q^{97}+O(q^{100}) $ 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * 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 $

$2$	−0.106570	+	1.01395i	−0.0753567	+	0.716971i	0.889987	+	0.455987i	$0.150714\pi$
$2$	−0.106570	+	1.01395i	−0.0753567	+	0.716971i	−0.965343	+	0.260984i	$0.915953\pi$
$3$		0			0
$3$		0			0
$4$	0.939559	+	0.199709i	0.469779	+	0.0998547i
$5$	−3.08748	+	0.324507i	−1.38076	+	0.145124i	−0.765621	−	0.643292i	$-0.777568\pi$
$5$	−3.08748	+	0.324507i	−1.38076	+	0.145124i	−0.615142	+	0.788416i	$0.710901\pi$
$6$		0			0
$7$	3.11115	+	2.80129i	1.17591	+	1.05879i	0.997192	+	0.0748887i	$0.0238601\pi$
$7$	3.11115	+	2.80129i	1.17591	+	1.05879i	0.178713	+	0.983901i	$0.442807\pi$
$8$	−0.932731	+	2.87065i	−0.329770	+	1.01493i
$9$		0			0
$10$		−	3.16513i		−	1.00090i
$11$	3.27533	−	0.521762i	0.987548	−	0.157317i
$11$	3.27533	−	0.521762i	0.987548	−	0.157317i
$12$		0			0
$13$	−0.145286	−	0.326318i	−0.0402951	−	0.0905043i	0.892276	−	0.451489i	$-0.149107\pi$
$13$	−0.145286	−	0.326318i	−0.0402951	−	0.0905043i	−0.932572	+	0.360985i	$0.882440\pi$
$14$	−3.17193	+	2.85602i	−0.847734	+	0.763303i
$15$		0			0
$16$	−1.05628	−	0.470288i	−0.264071	−	0.117572i
$17$	−2.52248	+	1.83269i	−0.611792	+	0.444493i	−0.850045	−	0.526710i	$-0.823425\pi$
$17$	−2.52248	+	1.83269i	−0.611792	+	0.444493i	0.238253	+	0.971203i	$0.423425\pi$
$18$		0			0
$19$	−0.384024	−	0.124777i	−0.0881011	−	0.0286258i	0.264635	−	0.964349i	$-0.414749\pi$
$19$	−0.384024	−	0.124777i	−0.0881011	−	0.0286258i	−0.352736	+	0.935723i	$0.614749\pi$
$20$	−2.96567	−	0.311705i	−0.663145	−	0.0696994i
$21$		0			0
$22$	0.179988	+	3.37662i	0.0383735	+	0.719898i
$23$	2.44458	+	1.41138i	0.509731	+	0.294293i	0.732723	−	0.680527i	$-0.238249\pi$
$23$	2.44458	+	1.41138i	0.509731	+	0.294293i	−0.222992	+	0.974820i	$0.571582\pi$
$24$		0			0
$25$	4.53649	−	0.964260i	0.907297	−	0.192852i
$26$	0.346353	−	0.112537i	0.0679254	−	0.0220703i
$27$		0			0
$28$	2.36367	+	3.25331i	0.446691	+	0.614817i
$29$	4.15306	−	4.61244i	0.771204	−	0.856509i	−0.221738	−	0.975106i	$-0.571173\pi$
$29$	4.15306	−	4.61244i	0.771204	−	0.856509i	0.992942	+	0.118597i	$0.0378397\pi$
$30$		0			0
$31$	−7.39141	+	3.29087i	−1.32754	+	0.591057i	−0.943227	−	0.332147i	$-0.892227\pi$
$31$	−7.39141	+	3.29087i	−1.32754	+	0.591057i	−0.384309	+	0.923205i	$0.625560\pi$
$32$	−2.42897	+	4.20709i	−0.429384	+	0.743716i
$33$		0			0
$34$	−1.58943	−	2.75298i	−0.272586	−	0.472132i
$35$	−10.5147	−	7.63935i	−1.77730	−	1.29129i
$36$		0			0
$37$	1.01570	+	3.12601i	0.166981	+	0.513914i	0.999177	−	0.0405678i	$-0.0129167\pi$
$37$	1.01570	+	3.12601i	0.166981	+	0.513914i	−0.832196	+	0.554481i	$0.812917\pi$
$38$	0.167443	−	0.376083i	0.0271628	−	0.0610087i
$39$		0			0
$40$	1.94824	−	9.16576i	0.308044	−	1.44923i
$41$	−5.08934	−	5.65229i	−0.794822	−	0.882739i	0.200467	−	0.979701i	$-0.435754\pi$
$41$	−5.08934	−	5.65229i	−0.794822	−	0.882739i	−0.995288	+	0.0969618i	$0.969088\pi$
$42$		0			0
$43$	−8.02668	+	4.63421i	−1.22406	+	0.706710i	−0.965781	−	0.259361i	$-0.916488\pi$
$43$	−8.02668	+	4.63421i	−1.22406	+	0.706710i	−0.258277	+	0.966071i	$0.583155\pi$
$44$	3.18156	+	0.163887i	0.479639	+	0.0247069i
$45$		0			0
$46$	−1.69159	+	2.32827i	−0.249411	+	0.343285i
$47$	2.63310	+	12.3878i	0.384077	+	1.80694i	0.566891	+	0.823793i	$0.308146\pi$
$47$	2.63310	+	12.3878i	0.384077	+	1.80694i	−0.182814	+	0.983147i	$0.558521\pi$
$48$		0			0
$49$	1.10032	+	10.4689i	0.157189	+	1.49555i
$50$	0.494256	+	4.70253i	0.0698983	+	0.665038i
$51$		0			0
$52$	−0.0713360	−	0.335610i	−0.00989253	−	0.0465407i
$53$	2.07104	−	2.85055i	0.284480	−	0.391553i	−0.642731	−	0.766092i	$-0.722199\pi$
$53$	2.07104	−	2.85055i	0.284480	−	0.391553i	0.927211	+	0.374539i	$0.122199\pi$
$54$		0			0
$55$	−9.94319	+	2.67380i	−1.34074	+	0.360535i
$56$	−10.9434	+	6.31818i	−1.46238	+	0.844303i
$57$		0			0
$58$	4.23419	+	4.70255i	0.555977	+	0.617475i
$59$	−2.42122	+	11.3909i	−0.315216	+	1.48297i	0.480333	+	0.877086i	$0.340516\pi$
$59$	−2.42122	+	11.3909i	−0.315216	+	1.48297i	−0.795549	+	0.605889i	$0.792818\pi$
$60$		0			0
$61$	−0.483540	+	1.08605i	−0.0619110	+	0.139054i	−0.941851	−	0.336030i	$-0.890916\pi$
$61$	−0.483540	+	1.08605i	−0.0619110	+	0.139054i	0.879940	+	0.475084i	$0.157582\pi$
$62$	−2.54907	−	7.84522i	−0.323732	−	0.996345i
$63$		0			0
$64$	−5.87777	−	4.27045i	−0.734721	−	0.533806i
$65$	0.554460	+	0.960353i	0.0687723	+	0.119117i
$66$		0			0
$67$	7.66446	−	13.2752i	0.936362	−	1.62183i	0.164176	−	0.986431i	$-0.447504\pi$
$67$	7.66446	−	13.2752i	0.936362	−	1.62183i	0.772187	−	0.635396i	$-0.219163\pi$
$68$	−2.73603	+	1.21816i	−0.331792	+	0.147723i
$69$		0			0
$70$	8.86647	−	9.84721i	1.05975	−	1.17697i
$71$	−0.357651	−	0.492264i	−0.0424453	−	0.0584210i	0.787267	−	0.616612i	$-0.211495\pi$
$71$	−0.357651	−	0.492264i	−0.0424453	−	0.0584210i	−0.829712	+	0.558192i	$0.811495\pi$
$72$		0			0
$73$	10.8303	−	3.51899i	1.26760	−	0.411867i	0.403401	−	0.915023i	$-0.367828\pi$
$73$	10.8303	−	3.51899i	1.26760	−	0.411867i	0.864195	+	0.503157i	$0.167828\pi$
$74$	−3.27786	+	0.696732i	−0.381044	+	0.0809934i
$75$		0			0
$76$	−0.335894	−	0.193928i	−0.0385296	−	0.0222451i
$77$	11.6517	+	7.55187i	1.32783	+	0.860616i
$78$		0			0
$79$	−4.81384	−	0.505955i	−0.541600	−	0.0569244i	−0.170221	−	0.985406i	$-0.554448\pi$
$79$	−4.81384	−	0.505955i	−0.541600	−	0.0569244i	−0.371379	+	0.928482i	$0.621115\pi$
$80$	3.41387	+	1.10923i	0.381682	+	0.124016i
$81$		0			0
$82$	6.27351	−	4.55797i	0.692793	−	0.503343i
$83$	6.05341	+	2.69515i	0.664448	+	0.295831i	0.711111	−	0.703079i	$-0.248192\pi$
$83$	6.05341	+	2.69515i	0.664448	+	0.295831i	−0.0466635	+	0.998911i	$0.514859\pi$
$84$		0			0
$85$	7.19339	−	6.47696i	0.780233	−	0.702525i
$86$	−3.84345	−	8.63252i	−0.414450	−	0.930869i
$87$		0			0
$88$	−1.55720	+	9.88899i	−0.165998	+	1.05417i
$89$			7.29922i			0.773716i	0.922139	+	0.386858i	$0.126440\pi$
$89$			7.29922i			0.773716i	−0.922139	+	0.386858i	$0.873560\pi$
$90$		0			0
$91$	0.462105	−	1.42221i	0.0484418	−	0.149088i
$92$	2.01496	+	1.81428i	0.210075	+	0.189152i
$93$		0			0
$94$	−12.8412	+	1.34966i	−1.32447	+	0.139207i
$95$	1.22616	+	0.260628i	0.125801	+	0.0267398i
$96$		0			0
$97$	0.543471	−	5.17078i	0.0551811	−	0.525013i	−0.931661	−	0.363328i	$-0.881640\pi$
$97$	0.543471	−	5.17078i	0.0551811	−	0.525013i	0.986842	−	0.161685i	$-0.0516929\pi$
$98$	−10.7322			−1.08411
$99$		0			0
$100$	4.45487			0.445487
$101$	0.850579	−	8.09272i	0.0846357	−	0.805255i	−0.867058	−	0.498207i	$-0.833992\pi$
$101$	0.850579	−	8.09272i	0.0846357	−	0.805255i	0.951694	−	0.307048i	$-0.0993413\pi$
$102$		0			0
$103$	−13.5007	−	2.86966i	−1.33026	−	0.282756i	−0.512685	−	0.858577i	$-0.671349\pi$
$103$	−13.5007	−	2.86966i	−1.33026	−	0.282756i	−0.817576	+	0.575821i	$0.804683\pi$
$104$	1.07226	−	0.112699i	0.105144	−	0.0110510i
$105$		0			0
$106$	2.66960	+	2.40372i	0.259295	+	0.233470i
$107$	−1.25282	+	3.85579i	−0.121115	+	0.372753i	−0.993173	−	0.116649i	$-0.962785\pi$
$107$	−1.25282	+	3.85579i	−0.121115	+	0.372753i	0.872058	+	0.489402i	$0.162785\pi$
$108$		0			0
$109$		−	5.57814i		−	0.534289i	−0.963656	−	0.267145i	$-0.913920\pi$
$109$		−	5.57814i		−	0.534289i	0.963656	−	0.267145i	$-0.0860801\pi$
$110$	−1.65145	−	10.3668i	−0.157459	−	0.988439i
$111$		0			0
$112$	−1.96885	−	4.42210i	−0.186039	−	0.417850i
$113$	5.41414	−	4.87492i	0.509320	−	0.458594i	−0.373957	−	0.927446i	$-0.621999\pi$
$113$	5.41414	−	4.87492i	0.509320	−	0.458594i	0.883276	+	0.468853i	$0.155332\pi$
$114$		0			0
$115$	−8.00561	−	3.56433i	−0.746527	−	0.332375i
$116$	4.82319	−	3.50426i	0.447822	−	0.325362i
$117$		0			0
$118$	−11.2918	−	3.66893i	−1.03950	−	0.337753i
$119$	−12.9817	−	1.36444i	−1.19003	−	0.125078i
$120$		0			0
$121$	10.4555	−	3.41788i	0.950503	−	0.310717i
$122$	−1.04967	−	0.606026i	−0.0950324	−	0.0548670i
$123$		0			0
$124$	−7.60188	+	1.61583i	−0.682669	+	0.145106i
$125$	1.06931	−	0.347441i	0.0956422	−	0.0310760i
$126$		0			0
$127$	8.05590	+	11.0880i	0.714846	+	0.983901i	0.999679	+	0.0253237i	$0.00806165\pi$
$127$	8.05590	+	11.0880i	0.714846	+	0.983901i	−0.284834	+	0.958577i	$0.591938\pi$
$128$	−1.54476	+	1.71563i	−0.136539	+	0.151642i
$129$		0			0
$130$	−1.03284	+	0.459849i	−0.0905859	+	0.0403315i
$131$	9.26411	−	16.0459i	0.809409	−	1.40194i	−0.103865	−	0.994591i	$-0.533121\pi$
$131$	9.26411	−	16.0459i	0.809409	−	1.40194i	0.913274	−	0.407346i	$-0.133546\pi$
$132$		0			0
$133$	−0.845220	−	1.46396i	−0.0732898	−	0.126942i
$134$	12.6436	+	9.18612i	1.09224	+	0.793560i
$135$		0			0
$136$	−2.90822	−	8.95058i	−0.249378	−	0.767506i
$137$	7.90337	−	17.7513i	0.675231	−	1.51659i	−0.171847	−	0.985124i	$-0.554973\pi$
$137$	7.90337	−	17.7513i	0.675231	−	1.51659i	0.847078	−	0.531469i	$-0.178360\pi$
$138$		0			0
$139$	−0.731452	+	3.44121i	−0.0620409	+	0.291880i	−0.998220	−	0.0596447i	$-0.981003\pi$
$139$	−0.731452	+	3.44121i	−0.0620409	+	0.291880i	0.936179	+	0.351524i	$0.114337\pi$
$140$	−8.35349	−	9.27749i	−0.705999	−	0.784091i
$141$		0			0
$142$	0.537246	−	0.310179i	0.0450847	−	0.0260296i
$143$	−0.646120	−	0.992993i	−0.0540312	−	0.0830382i
$144$		0			0
$145$	−11.3257	+	15.5885i	−0.940550	+	1.29456i
$146$	2.41389	+	11.3564i	0.199775	+	0.939866i
$147$		0			0
$148$	0.330019	+	3.13992i	0.0271274	+	0.258100i
$149$	−0.000998745	−	0.00950242i	−8.18203e−5	−	0.000778469i	0.994481	−	0.104918i	$-0.0334579\pi$
$149$	−0.000998745	−	0.00950242i	−8.18203e−5	−	0.000778469i	−0.994563	+	0.104139i	$0.966791\pi$
$150$		0			0
$151$	0.0802079	+	0.377348i	0.00652722	+	0.0307082i	0.981291	−	0.192532i	$-0.0616699\pi$
$151$	0.0802079	+	0.377348i	0.00652722	+	0.0307082i	−0.974763	+	0.223240i	$0.928337\pi$
$152$	0.716382	−	0.986015i	0.0581062	−	0.0799764i
$153$		0			0
$154$	−8.89894	+	11.0094i	−0.717097	+	0.887161i
$155$	21.7529	−	12.5590i	1.74724	−	1.00877i
$156$		0			0
$157$	1.95997	+	2.17676i	0.156422	+	0.173725i	0.816262	−	0.577682i	$-0.196043\pi$
$157$	1.95997	+	2.17676i	0.156422	+	0.173725i	−0.659840	+	0.751406i	$0.729376\pi$
$158$	1.02603	−	4.82707i	0.0816263	−	0.384021i
$159$		0			0
$160$	6.13415	−	13.7775i	0.484947	−	1.08921i
$161$	3.65178	+	11.2390i	0.287801	+	0.885759i
$162$		0			0
$163$	10.8005	+	7.84704i	0.845962	+	0.614627i	0.924030	−	0.382321i	$-0.124875\pi$
$163$	10.8005	+	7.84704i	0.845962	+	0.614627i	−0.0780678	+	0.996948i	$0.524875\pi$
$164$	−3.65292	−	6.32704i	−0.285245	−	0.494059i
$165$		0			0
$166$	−3.37786	+	5.85063i	−0.262173	+	0.454097i
$167$	−7.01598	+	3.12372i	−0.542913	+	0.241720i	−0.659822	−	0.751422i	$-0.729368\pi$
$167$	−7.01598	+	3.12372i	−0.542913	+	0.241720i	0.116909	+	0.993143i	$0.462701\pi$
$168$		0			0
$169$	8.61332	−	9.56606i	0.662563	−	0.735851i
$170$	5.80071	+	7.98399i	0.444894	+	0.612344i
$171$		0			0
$172$	−8.46704	+	2.75111i	−0.645605	+	0.209770i
$173$	−12.1464	+	2.58179i	−0.923471	+	0.196290i	−0.645025	−	0.764162i	$-0.723153\pi$
$173$	−12.1464	+	2.58179i	−0.923471	+	0.196290i	−0.278447	+	0.960452i	$0.589820\pi$
$174$		0			0
$175$	16.8149	+	9.70807i	1.27109	+	0.733861i
$176$	−3.70506	−	0.989219i	−0.279279	−	0.0745652i
$177$		0			0
$178$	−7.40104	−	0.777881i	−0.554731	−	0.0583046i
$179$	5.04243	+	1.63838i	0.376889	+	0.122459i	0.491335	−	0.870971i	$-0.336509\pi$
$179$	5.04243	+	1.63838i	0.376889	+	0.122459i	−0.114446	+	0.993429i	$0.536509\pi$
$180$		0			0
$181$	13.8366	−	10.0529i	1.02846	−	0.747224i	0.0604641	−	0.998170i	$-0.480742\pi$
$181$	13.8366	−	10.0529i	1.02846	−	0.747224i	0.968001	+	0.250947i	$0.0807419\pi$
$182$	1.39281	+	0.620117i	0.103242	+	0.0459662i
$183$		0			0
$184$	−6.33173	+	5.70111i	−0.466781	+	0.420292i
$185$	−4.15038	−	9.32190i	−0.305142	−	0.685360i
$186$		0			0
$187$	−7.30572	+	7.31880i	−0.534247	+	0.535203i
$188$			12.1649i			0.887215i
$189$		0			0
$190$	−0.394935	+	1.21549i	−0.0286516	+	0.0881806i
$191$	6.59701	+	5.93997i	0.477343	+	0.429801i	0.872354	−	0.488875i	$-0.162593\pi$
$191$	6.59701	+	5.93997i	0.477343	+	0.429801i	−0.395011	+	0.918676i	$0.629259\pi$
$192$		0			0
$193$	−1.43531	+	0.150857i	−0.103316	+	0.0108590i	−0.156045	−	0.987750i	$-0.549875\pi$
$193$	−1.43531	+	0.150857i	−0.103316	+	0.0108590i	0.0527293	+	0.998609i	$0.483208\pi$
$194$	5.18500	+	1.10210i	0.372261	+	0.0791265i
$195$		0			0
$196$	−1.05691	+	10.0559i	−0.0754938	+	0.718275i
$197$	18.4552			1.31488			0.657441	−	0.753506i	$-0.271639\pi$
$197$	18.4552			1.31488			0.657441	+	0.753506i	$0.271639\pi$
$198$		0			0
$199$	18.3392			1.30003			0.650016	−	0.759921i	$-0.274762\pi$
$199$	18.3392			1.30003			0.650016	+	0.759921i	$0.274762\pi$
$200$	−1.46327	+	13.9221i	−0.103469	+	0.984439i
$201$		0			0
$202$	8.11496	+	1.72489i	0.570967	+	0.121363i
$203$	25.8416	−	2.71606i	1.81373	−	0.190630i
$204$		0			0
$205$	17.5474	+	15.7998i	1.22557	+	1.10351i
$206$	4.34846	−	13.3832i	0.302972	−	0.932451i
$207$		0			0
$208$			0.413011i			0.0286372i
$209$	−1.32291	−	0.208316i	−0.0915074	−	0.0144095i
$210$		0			0
$211$	−1.86211	−	4.18237i	−0.128193	−	0.287926i	0.838034	−	0.545618i	$-0.183705\pi$
$211$	−1.86211	−	4.18237i	−0.128193	−	0.287926i	−0.966227	+	0.257691i	$0.917038\pi$
$212$	2.51515	−	2.26465i	0.172741	−	0.155537i
$213$		0			0
$214$	−3.77606	−	1.68121i	−0.258126	−	0.114925i
$215$	23.2784	−	16.9127i	1.58757	−	1.15344i
$216$		0			0
$217$	−32.2145	−	10.4671i	−2.18686	−	0.710555i
$218$	5.65596	+	0.594465i	0.383070	+	0.0402622i
$219$		0			0
$220$	−9.87619	+	0.526441i	−0.665853	+	0.0354926i
$221$	0.964521	+	0.556866i	0.0648807	+	0.0374589i
$222$		0			0
$223$	10.6764	−	2.26935i	0.714947	−	0.151967i	0.163943	−	0.986470i	$-0.447579\pi$
$223$	10.6764	−	2.26935i	0.714947	−	0.151967i	0.551003	+	0.834503i	$0.314245\pi$
$224$	−19.3422	+	6.28466i	−1.29235	+	0.419911i
$225$		0			0
$226$	4.36593	+	6.00919i	0.290418	+	0.399725i
$227$	1.88722	−	2.09597i	0.125259	−	0.139114i	−0.677253	−	0.735750i	$-0.736830\pi$
$227$	1.88722	−	2.09597i	0.125259	−	0.139114i	0.802512	+	0.596636i	$0.203496\pi$
$228$		0			0
$229$	1.81905	−	0.809892i	0.120206	−	0.0535192i	−0.345752	−	0.938326i	$-0.612376\pi$
$229$	1.81905	−	0.809892i	0.120206	−	0.0535192i	0.465958	+	0.884807i	$0.345710\pi$
$230$	4.46721	−	7.73743i	0.294559	−	0.510191i
$231$		0			0
$232$	9.36703	+	16.2242i	0.614976	+	1.06517i
$233$	−19.6843	−	14.3015i	−1.28956	−	0.936923i	−0.289768	−	0.957097i	$-0.593578\pi$
$233$	−19.6843	−	14.3015i	−1.28956	−	0.936923i	−0.999796	+	0.0201739i	$0.993578\pi$
$234$		0			0
$235$	−12.1496	−	37.3925i	−0.792550	−	2.43922i
$236$	−4.54976	+	10.2189i	−0.296164	+	0.665195i
$237$		0			0
$238$	2.76694	−	13.0174i	0.179354	−	0.843794i
$239$	6.71150	+	7.45388i	0.434131	+	0.482151i	0.920021	−	0.391868i	$-0.128171\pi$
$239$	6.71150	+	7.45388i	0.434131	+	0.482151i	−0.485890	+	0.874020i	$0.661505\pi$
$240$		0			0
$241$	−14.9974	+	8.65877i	−0.966069	+	0.557760i	−0.898036	−	0.439923i	$-0.855006\pi$
$241$	−14.9974	+	8.65877i	−0.966069	+	0.557760i	−0.0680336	+	0.997683i	$0.521673\pi$
$242$	2.35131	+	10.9656i	0.151148	+	0.704897i
$243$		0			0
$244$	−0.671208	+	0.923839i	−0.0429697	+	0.0591427i
$245$	−6.79444	−	31.9653i	−0.434081	−	2.04219i
$246$		0			0
$247$	0.0150764	+	0.143442i	0.000959287	+	0.00912700i
$248$	−2.55274	−	24.2877i	−0.162099	−	1.54227i
$249$		0			0
$250$	0.238330	+	1.12126i	0.0150733	+	0.0709144i
$251$	9.57729	−	13.1820i	0.604513	−	0.832041i	−0.391599	−	0.920136i	$-0.628078\pi$
$251$	9.57729	−	13.1820i	0.604513	−	0.832041i	0.996112	+	0.0880949i	$0.0280779\pi$
$252$		0			0
$253$	8.74322	+	3.34724i	0.549681	+	0.210439i
$254$	−12.1012	+	6.98663i	−0.759296	+	0.438380i
$255$		0			0
$256$	−11.2978	−	12.5475i	−0.706115	−	0.784220i
$257$	−1.54480	+	7.26770i	−0.0963618	+	0.453346i	0.903340	+	0.428925i	$0.141108\pi$
$257$	−1.54480	+	7.26770i	−0.0963618	+	0.453346i	−0.999702	+	0.0244212i	$0.992226\pi$
$258$		0			0
$259$	−5.59688	+	12.5708i	−0.347773	+	0.781111i
$260$	0.329156	+	1.01304i	0.0204134	+	0.0628260i
$261$		0			0
$262$	15.2825	+	11.1034i	0.944153	+	0.685968i
$263$	−0.812112	−	1.40662i	−0.0500769	−	0.0867358i	0.839900	−	0.542741i	$-0.182613\pi$
$263$	−0.812112	−	1.40662i	−0.0500769	−	0.0867358i	−0.889977	+	0.456005i	$0.849280\pi$
$264$		0			0
$265$	−5.46928	+	9.47308i	−0.335975	+	0.581927i
$266$	1.57446	−	0.700995i	0.0965364	−	0.0429808i
$267$		0			0
$268$	9.85239	−	10.9422i	0.601831	−	0.668401i
$269$	7.63802	+	10.5128i	0.465699	+	0.640979i	0.975678	−	0.219207i	$-0.0703471\pi$
$269$	7.63802	+	10.5128i	0.465699	+	0.640979i	−0.509980	+	0.860186i	$0.670347\pi$
$270$		0			0
$271$	7.28021	−	2.36548i	0.442241	−	0.143693i	−0.0794282	−	0.996841i	$-0.525309\pi$
$271$	7.28021	−	2.36548i	0.442241	−	0.143693i	0.521669	+	0.853148i	$0.325309\pi$
$272$	3.52635	−	0.749549i	0.213817	−	0.0454481i
$273$		0			0
$274$	17.1566	+	9.90538i	1.03647	+	0.598406i
$275$	14.3554	−	5.52523i	0.865661	−	0.333184i
$276$		0			0
$277$	16.7960	+	1.76533i	1.00917	+	0.106068i	0.594662	−	0.803976i	$-0.297286\pi$
$277$	16.7960	+	1.76533i	1.00917	+	0.106068i	0.414511	+	0.910044i	$0.363953\pi$
$278$	−3.41126	−	1.10839i	−0.204594	−	0.0664766i
$279$		0			0
$280$	31.7373	−	23.0585i	1.89666	−	1.37801i
$281$	−9.91362	−	4.41383i	−0.591397	−	0.263307i	0.0891419	−	0.996019i	$-0.471588\pi$
$281$	−9.91362	−	4.41383i	−0.591397	−	0.263307i	−0.680539	+	0.732712i	$0.738254\pi$
$282$		0			0
$283$	−13.0133	+	11.7172i	−0.773558	+	0.696514i	−0.958139	−	0.286303i	$-0.907574\pi$
$283$	−13.0133	+	11.7172i	−0.773558	+	0.696514i	0.184582	+	0.982817i	$0.440907\pi$
$284$	−0.237724	−	0.533937i	−0.0141063	−	0.0316833i
$285$		0			0
$286$	1.07570	−	0.549309i	0.0636076	−	0.0324813i
$287$		−	31.8419i		−	1.87957i
$288$		0			0
$289$	−2.24913	+	6.92210i	−0.132302	+	0.407182i
$290$	−14.5990	−	13.1450i	−0.857282	−	0.771900i
$291$		0			0
$292$	10.8785	−	1.14338i	0.636617	−	0.0669112i
$293$	12.7634	+	2.71294i	0.745645	+	0.158492i	0.565040	−	0.825064i	$-0.308861\pi$
$293$	12.7634	+	2.71294i	0.745645	+	0.158492i	0.180606	+	0.983556i	$0.442194\pi$
$294$		0			0
$295$	3.77902	−	35.9550i	0.220023	−	2.09338i
$296$	−9.92108			−0.576651
$297$		0			0
$298$	0.00974141			0.000564305
$299$	0.105395	−	1.00277i	0.00609514	−	0.0579914i
$300$		0			0
$301$	−37.9540	−	8.06738i	−2.18763	−	0.464996i
$302$	−0.391160	+	0.0411126i	−0.0225087	+	0.00236576i
$303$		0			0
$304$	0.346957	+	0.312402i	0.0198994	+	0.0179175i
$305$	1.14049	−	3.51007i	0.0653042	−	0.200986i
$306$		0			0
$307$			27.5790i			1.57402i	0.616941	+	0.787009i	$0.288372\pi$
$307$			27.5790i			1.57402i	−0.616941	+	0.787009i	$0.711628\pi$
$308$	9.43923	+	9.42237i	0.537850	+	0.536889i
$309$		0			0
$310$	10.4160	+	23.3948i	0.591591	+	1.32873i
$311$	5.66217	−	5.09824i	0.321072	−	0.289095i	−0.492795	−	0.870145i	$-0.664025\pi$
$311$	5.66217	−	5.09824i	0.321072	−	0.289095i	0.813867	+	0.581051i	$0.197358\pi$
$312$		0			0
$313$	12.1953	+	5.42971i	0.689320	+	0.306905i	0.721339	−	0.692582i	$-0.243527\pi$
$313$	12.1953	+	5.42971i	0.689320	+	0.306905i	−0.0320187	+	0.999487i	$0.510194\pi$
$314$	−2.41600	+	1.75533i	−0.136343	+	0.0990589i
$315$		0			0
$316$	−4.42184	−	1.43674i	−0.248748	−	0.0808232i
$317$	7.62489	+	0.801408i	0.428256	+	0.0450116i	0.316205	−	0.948691i	$-0.397591\pi$
$317$	7.62489	+	0.801408i	0.428256	+	0.0450116i	0.112051	+	0.993702i	$0.464258\pi$
$318$		0			0
$319$	11.1960	−	17.2742i	0.626858	−	0.967168i
$320$	19.5333	+	11.2775i	1.09194	+	0.630434i
$321$		0			0
$322$	−11.7850	+	2.50497i	−0.656751	+	0.139597i
$323$	1.19737	−	0.389049i	0.0666235	−	0.0216473i
$324$		0			0
$325$	−0.973743	−	1.34024i	−0.0540136	−	0.0743433i
$326$	−9.10752	+	10.1149i	−0.504419	+	0.560214i
$327$		0			0
$328$	20.9727	−	9.33766i	1.15803	−	0.515586i
$329$	−26.5098	+	45.9163i	−1.46153	+	2.53145i
$330$		0			0
$331$	3.66294	+	6.34439i	0.201333	+	0.348719i	0.948958	−	0.315402i	$-0.102139\pi$
$331$	3.66294	+	6.34439i	0.201333	+	0.348719i	−0.747625	+	0.664121i	$0.768806\pi$
$332$	5.14928	+	3.74117i	0.282604	+	0.205324i
$333$		0			0
$334$	−2.41959	−	7.44675i	−0.132394	−	0.407468i
$335$	−19.3559	+	43.4742i	−1.05753	+	2.37525i
$336$		0			0
$337$	−1.50372	+	7.07443i	−0.0819126	+	0.385369i	−0.999938	−	0.0111535i	$-0.996450\pi$
$337$	−1.50372	+	7.07443i	−0.0819126	+	0.385369i	0.918025	+	0.396522i	$0.129783\pi$
$338$	8.78158	+	9.75293i	0.477655	+	0.530490i
$339$		0			0
$340$	8.05212	−	4.64889i	0.436688	−	0.252122i
$341$	−22.4922	+	14.6352i	−1.21802	+	0.792542i
$342$		0			0
$343$	−8.67788	+	11.9441i	−0.468561	+	0.644919i
$344$	−5.81646	−	27.3643i	−0.313602	−	1.47538i
$345$		0			0
$346$	−1.32336	−	12.5909i	−0.0711444	−	0.676893i
$347$	−2.58144	−	24.5608i	−0.138579	−	1.31849i	−0.813916	−	0.580983i	$-0.802668\pi$
$347$	−2.58144	−	24.5608i	−0.138579	−	1.31849i	0.675337	−	0.737509i	$-0.263998\pi$
$348$		0			0
$349$	−2.93663	−	13.8158i	−0.157194	−	0.739541i	−0.984159	−	0.177287i	$-0.943268\pi$
$349$	−2.93663	−	13.8158i	−0.157194	−	0.739541i	0.826965	−	0.562254i	$-0.190065\pi$
$350$	−11.6355	+	16.0148i	−0.621942	+	0.856029i
$351$		0			0
$352$	−5.76055	+	15.0469i	−0.307039	+	0.802005i
$353$	13.0466	−	7.53244i	0.694399	−	0.400911i	−0.110859	−	0.993836i	$-0.535360\pi$
$353$	13.0466	−	7.53244i	0.694399	−	0.400911i	0.805258	+	0.592925i	$0.202027\pi$
$354$		0			0
$355$	1.26398	+	1.40379i	0.0670852	+	0.0745057i
$356$	−1.45772	+	6.85804i	−0.0772591	+	0.363476i
$357$		0			0
$358$	−2.19861	+	4.93816i	−0.116200	+	0.260990i
$359$	2.21156	+	6.80649i	0.116722	+	0.359233i	0.992302	−	0.123840i	$-0.0395208\pi$
$359$	2.21156	+	6.80649i	0.116722	+	0.359233i	−0.875580	+	0.483072i	$0.839521\pi$
$360$		0			0
$361$	−15.2394	−	11.0721i	−0.802075	−	0.582741i
$362$	8.71853	+	15.1009i	0.458236	+	0.793687i
$363$		0			0
$364$	0.718204	−	1.24397i	0.0376441	−	0.0652016i
$365$	−32.2965	+	14.3793i	−1.69048	+	0.752649i
$366$		0			0
$367$	2.84048	−	3.15467i	0.148272	−	0.164673i	−0.664434	−	0.747347i	$-0.731327\pi$
$367$	2.84048	−	3.15467i	0.148272	−	0.164673i	0.812705	+	0.582675i	$0.197994\pi$
$368$	−1.91842	−	2.64048i	−0.100005	−	0.137645i
$369$		0			0
$370$	9.89424	−	3.21483i	0.514377	−	0.167131i
$371$	14.4286	−	3.06689i	0.749094	−	0.159225i
$372$		0			0
$373$	17.6199	+	10.1729i	0.912324	+	0.526730i	0.881178	−	0.472785i	$-0.156751\pi$
$373$	17.6199	+	10.1729i	0.912324	+	0.526730i	0.0311456	+	0.999515i	$0.490084\pi$
$374$	−6.64232	−	8.18760i	−0.343466	−	0.423371i
$375$		0			0
$376$	−38.0169	−	3.99574i	−1.96057	−	0.206065i
$377$	−2.10850	−	0.685095i	−0.108593	−	0.0352842i
$378$		0			0
$379$	−23.6596	+	17.1897i	−1.21531	+	0.882977i	−0.995702	−	0.0926103i	$-0.970479\pi$
$379$	−23.6596	+	17.1897i	−1.21531	+	0.882977i	−0.219611	+	0.975587i	$0.570479\pi$
$380$	1.10000	+	0.489750i	0.0564286	+	0.0251236i
$381$		0			0
$382$	−6.72588	+	6.05601i	−0.344126	+	0.309852i
$383$	1.99738	+	4.48620i	0.102062	+	0.229234i	0.957358	−	0.288906i	$-0.0932914\pi$
$383$	1.99738	+	4.48620i	0.102062	+	0.229234i	−0.855296	+	0.518140i	$0.826625\pi$
$384$		0			0
$385$	−38.4249	−	19.5352i	−1.95831	−	0.995606i
$386$		−	1.47141i		−	0.0748929i
$387$		0			0
$388$	1.54328	−	4.74972i	0.0783480	−	0.241130i
$389$	12.7394	+	11.4706i	0.645915	+	0.581585i	0.925598	−	0.378508i	$-0.123563\pi$
$389$	12.7394	+	11.4706i	0.645915	+	0.581585i	−0.279683	+	0.960092i	$0.590229\pi$
$390$		0			0
$391$	−8.75305	+	0.919982i	−0.442661	+	0.0465255i
$392$	−31.0788	−	6.60599i	−1.56971	−	0.333653i
$393$		0			0
$394$	−1.96678	+	18.7127i	−0.0990850	+	0.942731i
$395$	15.0268			0.756082
$396$		0			0
$397$	−7.94416			−0.398706			−0.199353	−	0.979928i	$-0.563884\pi$
$397$	−7.94416			−0.398706			−0.199353	+	0.979928i	$0.563884\pi$
$398$	−1.95442	+	18.5950i	−0.0979661	+	0.932085i
$399$		0			0
$400$	−5.24530	−	1.11492i	−0.262265	−	0.0557462i
$401$	−6.40831	+	0.673540i	−0.320016	+	0.0336350i	−0.263175	−	0.964748i	$-0.584770\pi$
$401$	−6.40831	+	0.673540i	−0.320016	+	0.0336350i	−0.0568411	+	0.998383i	$0.518103\pi$
$402$		0			0
$403$	2.14774	+	1.93383i	0.106986	+	0.0963310i
$404$	2.41536	−	7.43371i	0.120169	−	0.369841i
$405$		0			0
$406$			26.4916i			1.31475i
$407$	4.95780	+	9.70876i	0.245749	+	0.481245i
$408$		0			0
$409$	−6.49403	−	14.5858i	−0.321109	−	0.721223i	0.678805	−	0.734319i	$-0.262498\pi$
$409$	−6.49403	−	14.5858i	−0.321109	−	0.721223i	−0.999914	+	0.0130954i	$0.995831\pi$
$410$	−17.8902	+	16.1084i	−0.883535	+	0.795539i
$411$		0			0
$412$	−12.1116	−	5.39242i	−0.596695	−	0.265666i
$413$	−39.4422	+	28.6564i	−1.94082	+	1.41009i
$414$		0			0
$415$	−19.5644	−	6.35685i	−0.960377	−	0.312045i
$416$	1.72574	+	0.181383i	0.0846115	+	0.00889303i
$417$		0			0
$418$	0.352205	−	1.31916i	0.0172269	−	0.0645222i
$419$	−3.15494	−	1.82151i	−0.154129	−	0.0889865i	0.420952	−	0.907083i	$-0.361696\pi$
$419$	−3.15494	−	1.82151i	−0.154129	−	0.0889865i	−0.575081	+	0.818096i	$0.695029\pi$
$420$		0			0
$421$	−12.9155	+	2.74527i	−0.629463	+	0.133797i	−0.511587	−	0.859232i	$-0.670942\pi$
$421$	−12.9155	+	2.74527i	−0.629463	+	0.133797i	−0.117877	+	0.993028i	$0.537609\pi$
$422$	4.43916	−	1.44237i	0.216095	−	0.0702135i
$423$		0			0
$424$	6.25120	+	8.60405i	0.303585	+	0.417849i
$425$	−9.67601	+	10.7463i	−0.469356	+	0.521272i
$426$		0			0
$427$	−4.54671	+	2.02433i	−0.220031	+	0.0979640i
$428$	−1.94714	+	3.37254i	−0.0941184	+	0.163018i
$429$		0			0
$430$	14.6679	+	25.4055i	0.707348	+	1.22516i
$431$	12.5748	+	9.13610i	0.605705	+	0.440071i	0.847899	−	0.530157i	$-0.177867\pi$
$431$	12.5748	+	9.13610i	0.605705	+	0.440071i	−0.242194	+	0.970228i	$0.577867\pi$
$432$		0			0
$433$	−3.84495	−	11.8336i	−0.184777	−	0.568684i	0.815168	−	0.579225i	$-0.196645\pi$
$433$	−3.84495	−	11.8336i	−0.184777	−	0.568684i	−0.999944	+	0.0105407i	$0.996645\pi$
$434$	14.0462	−	31.5484i	0.674241	−	1.51437i
$435$		0			0
$436$	1.11401	−	5.24099i	0.0533513	−	0.250998i
$437$	−0.762671	−	0.847031i	−0.0364835	−	0.0405190i
$438$		0			0
$439$	−9.93333	+	5.73501i	−0.474092	+	0.273717i	−0.717951	−	0.696094i	$-0.754920\pi$
$439$	−9.93333	+	5.73501i	−0.474092	+	0.273717i	0.243859	+	0.969811i	$0.421587\pi$
$440$	1.59878	−	31.0374i	0.0762190	−	1.47965i
$441$		0			0
$442$	−0.667424	+	0.918630i	−0.0317461	+	0.0436948i
$443$	−1.52848	−	7.19093i	−0.0726202	−	0.341651i	0.926805	−	0.375542i	$-0.122543\pi$
$443$	−1.52848	−	7.19093i	−0.0726202	−	0.341651i	−0.999426	+	0.0338909i	$0.989210\pi$
$444$		0			0
$445$	−2.36865	−	22.5362i	−0.112285	−	1.06832i
$446$	1.16321	+	11.0672i	0.0550796	+	0.524047i
$447$		0			0
$448$	−6.32385	−	29.7514i	−0.298774	−	1.40562i
$449$	−2.58876	+	3.56312i	−0.122171	+	0.168154i	−0.865722	−	0.500525i	$-0.833140\pi$
$449$	−2.58876	+	3.56312i	−0.122171	+	0.168154i	0.743551	+	0.668680i	$0.233140\pi$
$450$		0			0
$451$	−19.6184	−	15.8577i	−0.923794	−	0.746708i
$452$	6.06047	−	3.49902i	0.285061	−	0.164580i
$453$		0			0
$454$	1.92408	+	2.13691i	0.0903017	+	0.100290i
$455$	−0.965222	+	4.54101i	−0.0452503	+	0.212886i
$456$		0			0
$457$	2.56291	−	5.75638i	0.119888	−	0.269272i	−0.843626	−	0.536931i	$-0.819583\pi$
$457$	2.56291	−	5.75638i	0.119888	−	0.269272i	0.963514	+	0.267659i	$0.0862501\pi$
$458$	0.627333	+	1.93073i	0.0293133	+	0.0902172i
$459$		0			0
$460$	−6.80991	−	4.94769i	−0.317514	−	0.230687i
$461$	−5.15950	−	8.93652i	−0.240302	−	0.416215i	0.720498	−	0.693457i	$-0.243913\pi$
$461$	−5.15950	−	8.93652i	−0.240302	−	0.416215i	−0.960800	+	0.277241i	$0.910580\pi$
$462$		0			0
$463$	−0.846612	+	1.46637i	−0.0393454	+	0.0681482i	−0.885028	−	0.465539i	$-0.845861\pi$
$463$	−0.846612	+	1.46637i	−0.0393454	+	0.0681482i	0.845682	+	0.533687i	$0.179194\pi$
$464$	−6.55600	+	2.91892i	−0.304354	+	0.135507i
$465$		0			0
$466$	16.5988	−	18.4348i	0.768924	−	0.853976i
$467$	−14.1753	−	19.5106i	−0.655953	−	0.902842i	0.343386	−	0.939194i	$-0.388426\pi$
$467$	−14.1753	−	19.5106i	−0.655953	−	0.902842i	−0.999339	+	0.0363528i	$0.988426\pi$
$468$		0			0
$469$	61.0331	−	19.8309i	2.81825	−	0.915704i
$470$	39.2089	−	8.33410i	1.80857	−	0.384424i
$471$		0			0
$472$	−30.4411	−	17.5752i	−1.40117	−	0.808963i
$473$	−23.8721	+	19.3666i	−1.09764	+	0.890476i
$474$		0			0
$475$	−1.86244	−	0.195750i	−0.0854544	−	0.00898162i
$476$	−11.9246	−	3.87454i	−0.546564	−	0.177589i
$477$		0			0
$478$	−8.27311	+	6.01076i	−0.378403	+	0.274926i
$479$	−34.0664	−	15.1673i	−1.55653	−	0.693014i	−0.565270	−	0.824906i	$-0.691228\pi$
$479$	−34.0664	−	15.1673i	−1.55653	−	0.693014i	−0.991264	+	0.131892i	$0.957895\pi$
$480$		0			0
$481$	0.872506	−	0.785608i	0.0397829	−	0.0358207i
$482$	−7.18127	−	16.1294i	−0.327098	−	0.734674i
$483$		0			0
$484$	10.5062	−	1.12323i	0.477553	−	0.0510561i
$485$			16.1410i			0.732927i
$486$		0			0
$487$	11.7540	−	36.1751i	0.532624	−	1.63925i	−0.216102	−	0.976371i	$-0.569335\pi$
$487$	11.7540	−	36.1751i	0.532624	−	1.63925i	0.748727	−	0.662879i	$-0.230665\pi$
$488$	−2.66666	−	2.40107i	−0.120714	−	0.108691i
$489$		0			0
$490$	33.1353	−	3.48266i	1.49690	−	0.157331i
$491$	−28.0112	−	5.95397i	−1.26413	−	0.268699i	−0.473390	−	0.880853i	$-0.656970\pi$
$491$	−28.0112	−	5.95397i	−1.26413	−	0.268699i	−0.790739	+	0.612154i	$0.790303\pi$
$492$		0			0
$493$	−2.02284	+	19.2461i	−0.0911044	+	0.866800i
$494$	−0.147050			−0.00661608
$495$		0			0
$496$	9.35509			0.420056
$497$	0.266270	−	2.53339i	0.0119439	−	0.113638i
$498$		0			0
$499$	15.0551	+	3.20005i	0.673958	+	0.143254i	0.532163	−	0.846642i	$-0.321379\pi$
$499$	15.0551	+	3.20005i	0.673958	+	0.143254i	0.141795	+	0.989896i	$0.454713\pi$
$500$	1.07407	−	0.112889i	0.0480338	−	0.00504856i
$501$		0			0
$502$	12.3452	+	11.1157i	0.550995	+	0.496118i
$503$	−1.24129	+	3.82031i	−0.0553466	+	0.170339i	−0.974909	−	0.222606i	$-0.928544\pi$
$503$	−1.24129	+	3.82031i	−0.0553466	+	0.170339i	0.919562	+	0.392945i	$0.128544\pi$
$504$		0			0
$505$			25.2621i			1.12415i
$506$	−4.32570	+	8.50847i	−0.192301	+	0.378247i
$507$		0			0
$508$	5.35462	+	12.0267i	0.237573	+	0.533597i
$509$	15.5560	−	14.0067i	0.689507	−	0.620835i	−0.248017	−	0.968756i	$-0.579779\pi$
$509$	15.5560	−	14.0067i	0.689507	−	0.620835i	0.937524	+	0.347921i	$0.113112\pi$
$510$		0			0
$511$	43.5526	+	19.3909i	1.92665	+	0.857801i
$512$	10.1912	−	7.40431i	0.450390	−	0.327227i
$513$		0			0
$514$	−7.20445	−	2.34087i	−0.317775	−	0.103251i
$515$	42.6143	+	4.47894i	1.87781	+	0.197366i
$516$		0			0
$517$	15.0877	+	39.2001i	0.663557	+	1.72402i
$518$	−12.1497	−	7.01463i	−0.533827	−	0.308205i
$519$		0			0
$520$	−3.27400	+	0.695911i	−0.143575	+	0.0305177i
$521$	−34.9601	+	11.3592i	−1.53163	+	0.497656i	−0.949052	−	0.315120i	$-0.897955\pi$
$521$	−34.9601	+	11.3592i	−1.53163	+	0.497656i	−0.582576	+	0.812776i	$0.697955\pi$
$522$		0			0
$523$	−3.90101	−	5.36927i	−0.170579	−	0.234782i	0.715165	−	0.698955i	$-0.246351\pi$
$523$	−3.90101	−	5.36927i	−0.170579	−	0.234782i	−0.885744	+	0.464173i	$0.846351\pi$
$524$	11.9087	−	13.2259i	0.520233	−	0.577778i
$525$		0			0
$526$	1.51279	−	0.673536i	0.0659607	−	0.0293676i
$527$	12.6136	−	21.8473i	0.549455	−	0.951684i
$528$		0			0
$529$	−7.51600	−	13.0181i	−0.326783	−	0.566004i
$530$	−9.02236	−	6.55513i	−0.391906	−	0.284737i
$531$		0			0
$532$	−0.501766	−	1.54428i	−0.0217543	−	0.0669529i
$533$	−1.10503	+	2.48194i	−0.0478642	+	0.107505i
$534$		0			0
$535$	2.61683	−	12.3112i	0.113135	−	0.532261i
$536$	30.9597	+	34.3842i	1.33725	+	1.48517i
$537$		0			0
$538$	−11.4735	+	6.62421i	−0.494657	+	0.285590i
$539$	9.06616	+	33.7148i	0.390507	+	1.45220i
$540$		0			0
$541$	−0.307811	+	0.423665i	−0.0132338	+	0.0182148i	−0.815583	−	0.578641i	$-0.803583\pi$
$541$	−0.307811	+	0.423665i	−0.0132338	+	0.0182148i	0.802349	+	0.596855i	$0.203583\pi$
$542$	1.62263	+	7.63386i	0.0696978	+	0.327902i
$543$		0			0
$544$	−1.58327	−	15.0639i	−0.0678823	−	0.645857i
$545$	1.81015	+	17.2224i	0.0775382	+	0.737726i
$546$		0			0
$547$	−7.06474	−	33.2370i	−0.302067	−	1.42111i	−0.823256	−	0.567670i	$-0.807845\pi$
$547$	−7.06474	−	33.2370i	−0.302067	−	1.42111i	0.521189	−	0.853441i	$-0.325489\pi$
$548$	10.9708	−	15.1000i	0.468648	−	0.645039i
$549$		0			0
$550$	4.07245	+	15.1444i	0.173650	+	0.645761i
$551$	−2.17040	+	1.25308i	−0.0924622	+	0.0533831i
$552$		0			0
$553$	−13.5593	−	15.0591i	−0.576599	−	0.640378i
$554$	−3.57991	+	16.8422i	−0.152096	+	0.715555i
$555$		0			0
$556$	−1.37448	+	3.08714i	−0.0582911	+	0.130924i
$557$	−9.71173	−	29.8896i	−0.411499	−	1.26646i	−0.915345	−	0.402671i	$-0.868082\pi$
$557$	−9.71173	−	29.8896i	−0.411499	−	1.26646i	0.503846	−	0.863794i	$-0.331918\pi$
$558$		0			0
$559$	2.67839	+	1.94596i	0.113284	+	0.0823055i
$560$	7.51378	+	13.0143i	0.317515	+	0.549952i
$561$		0			0
$562$	5.53190	−	9.58153i	0.233349	−	0.404172i
$563$	2.73909	−	1.21952i	0.115439	−	0.0513966i	−0.348205	−	0.937419i	$-0.613209\pi$
$563$	2.73909	−	1.21952i	0.115439	−	0.0513966i	0.463643	+	0.886022i	$0.346542\pi$
$564$		0			0
$565$	−15.1341	+	16.8081i	−0.636697	+	0.707124i
$566$	−10.4938	−	14.4435i	−0.441088	−	0.607105i
$567$		0			0
$568$	1.74671	−	0.567541i	0.0732903	−	0.0238135i
$569$	−40.2013	+	8.54505i	−1.68533	+	0.358227i	−0.948236	−	0.317567i	$-0.897134\pi$
$569$	−40.2013	+	8.54505i	−1.68533	+	0.358227i	−0.737090	+	0.675794i	$0.763801\pi$
$570$		0			0
$571$	−11.6392	−	6.71989i	−0.487085	−	0.281219i	0.236279	−	0.971685i	$-0.424072\pi$
$571$	−11.6392	−	6.71989i	−0.487085	−	0.281219i	−0.723364	+	0.690466i	$0.757405\pi$
$572$	−0.408757	−	1.06201i	−0.0170910	−	0.0444049i
$573$		0			0
$574$	32.2861	+	3.39340i	1.34759	+	0.141638i
$575$	12.4508	+	4.04550i	0.519233	+	0.168709i
$576$		0			0
$577$	−6.44828	+	4.68495i	−0.268445	+	0.195037i	−0.713862	−	0.700287i	$-0.753056\pi$
$577$	−6.44828	+	4.68495i	−0.268445	+	0.195037i	0.445417	+	0.895323i	$0.353056\pi$
$578$	−6.77897	−	3.01819i	−0.281968	−	0.125540i
$579$		0			0
$580$	−13.7544	+	12.3845i	−0.571118	+	0.514237i
$581$	11.2832	+	25.3424i	0.468105	+	1.05138i
$582$		0			0
$583$	5.29604	−	10.4171i	0.219340	−	0.431431i
$584$			34.3724i			1.42234i
$585$		0			0
$586$	−4.11099	+	12.6523i	−0.169823	+	0.522662i
$587$	17.6354	+	15.8790i	0.727890	+	0.655396i	0.947340	−	0.320228i	$-0.103760\pi$
$587$	17.6354	+	15.8790i	0.727890	+	0.655396i	−0.219450	+	0.975624i	$0.570426\pi$
$588$		0			0
$589$	3.24910	−	0.341494i	0.133877	−	0.0140710i
$590$	36.0538	+	7.66348i	1.48431	+	0.315500i
$591$		0			0
$592$	0.397256	−	3.77963i	0.0163271	−	0.155342i
$593$	−29.4804			−1.21062			−0.605308	−	0.795991i	$-0.706950\pi$
$593$	−29.4804			−1.21062			−0.605308	+	0.795991i	$0.706950\pi$
$594$		0			0
$595$	40.5236			1.66131
$596$	0.000959343	−	0.00912754i	3.92962e−5	−	0.000373879i
$597$		0			0
$598$	1.00552	+	0.213730i	0.0411188	+	0.00874008i
$599$	−29.7194	+	3.12364i	−1.21430	+	0.127628i	−0.689940	−	0.723866i	$-0.742363\pi$
$599$	−29.7194	+	3.12364i	−1.21430	+	0.127628i	−0.524363	+	0.851495i	$0.675697\pi$
$600$		0			0
$601$	−4.94680	−	4.45412i	−0.201784	−	0.181687i	0.562043	−	0.827108i	$-0.310015\pi$
$601$	−4.94680	−	4.45412i	−0.201784	−	0.181687i	−0.763827	+	0.645421i	$0.776682\pi$
$602$	12.2247	−	37.6237i	0.498241	−	1.53343i
$603$		0			0
$604$			0.370559i			0.0150778i
$605$	−31.1721	+	13.9455i	−1.26733	+	0.566967i
$606$		0			0
$607$	13.0541	+	29.3201i	0.529852	+	1.19007i	0.958108	+	0.286409i	$0.0924615\pi$
$607$	13.0541	+	29.3201i	0.529852	+	1.19007i	−0.428256	+	0.903657i	$0.640872\pi$
$608$	1.45773	−	1.31254i	0.0591187	−	0.0532307i
$609$		0			0
$610$	3.43749	+	1.53047i	0.139180	+	0.0619668i
$611$	3.65979	−	2.65900i	0.148059	−	0.107571i
$612$		0			0
$613$	10.3905	+	3.37608i	0.419668	+	0.136358i	0.511236	−	0.859440i	$-0.329188\pi$
$613$	10.3905	+	3.37608i	0.419668	+	0.136358i	−0.0915678	+	0.995799i	$0.529188\pi$
$614$	−27.9638	−	2.93911i	−1.12853	−	0.118613i
$615$		0			0
$616$	−32.5467	+	26.4040i	−1.31134	+	1.06385i
$617$	6.10692	+	3.52583i	0.245855	+	0.141945i	0.617865	−	0.786284i	$-0.287998\pi$
$617$	6.10692	+	3.52583i	0.245855	+	0.141945i	−0.372010	+	0.928229i	$0.621331\pi$
$618$		0			0
$619$	37.9792	−	8.07273i	1.52651	−	0.324470i	0.633229	−	0.773964i	$-0.281729\pi$
$619$	37.9792	−	8.07273i	1.52651	−	0.324470i	0.893283	+	0.449494i	$0.148396\pi$
$620$	22.9463	−	7.45570i	0.921545	−	0.299428i
$621$		0			0
$622$	4.56594	+	6.28448i	0.183077	+	0.251985i
$623$	−20.4473	+	22.7090i	−0.819202	+	0.909816i
$624$		0			0
$625$	−24.3731	+	10.8516i	−0.974924	+	0.434064i
$626$	−6.80511	+	11.7868i	−0.271987	+	0.471095i
$627$		0			0
$628$	1.40678	+	2.43662i	0.0561368	+	0.0972317i
$629$	−8.29111	−	6.02384i	−0.330588	−	0.240186i
$630$		0			0
$631$	−9.93575	−	30.5791i	−0.395536	−	1.21733i	−0.928543	−	0.371224i	$-0.878938\pi$
$631$	−9.93575	−	30.5791i	−0.395536	−	1.21733i	0.533007	−	0.846111i	$-0.321062\pi$
$632$	5.94244	−	13.3469i	0.236378	−	0.530913i
$633$		0			0
$634$	−1.62518	+	7.64585i	−0.0645439	+	0.303655i
$635$	−28.4706	−	31.6198i	−1.12982	−	1.25479i
$636$		0			0
$637$	3.25631	−	1.88003i	0.129020	−	0.0744896i
$638$	16.3220	+	13.1931i	0.646193	+	0.522321i
$639$		0			0
$640$	4.21268	−	5.79826i	0.166521	−	0.229196i
$641$	6.51391	+	30.6456i	0.257284	+	1.21043i	0.897075	+	0.441878i	$0.145688\pi$
$641$	6.51391	+	30.6456i	0.257284	+	1.21043i	−0.639791	+	0.768549i	$0.720979\pi$
$642$		0			0
$643$	1.11732	+	10.6306i	0.0440630	+	0.419231i	0.994212	+	0.107435i	$0.0342638\pi$
$643$	1.11732	+	10.6306i	0.0440630	+	0.419231i	−0.950149	+	0.311796i	$0.899070\pi$
$644$	1.18652	+	11.2890i	0.0467556	+	0.444850i
$645$		0			0
$646$	0.266872	+	1.25553i	0.0104999	+	0.0493983i
$647$	14.2861	−	19.6631i	0.561644	−	0.773037i	−0.429890	−	0.902881i	$-0.641448\pi$
$647$	14.2861	−	19.6631i	0.561644	−	0.773037i	0.991534	+	0.129844i	$0.0414477\pi$
$648$		0			0
$649$	−1.98692	+	38.5724i	−0.0779936	+	1.51410i
$650$	1.46271	−	0.844496i	0.0573722	−	0.0331239i
$651$		0			0
$652$	8.58059	+	9.52972i	0.336042	+	0.373212i
$653$	9.89638	−	46.5588i	0.387275	−	1.82199i	−0.162542	−	0.986702i	$-0.551969\pi$
$653$	9.89638	−	46.5588i	0.387275	−	1.82199i	0.549817	−	0.835285i	$-0.314697\pi$
$654$		0			0
$655$	−23.3957	+	52.5477i	−0.914147	+	2.05321i
$656$	2.71759	+	8.36388i	0.106104	+	0.326555i
$657$		0			0
$658$	−43.7316	−	31.7729i	−1.70484	−	1.23864i
$659$	11.5685	+	20.0373i	0.450646	+	0.780542i	0.998426	−	0.0560804i	$-0.0178603\pi$
$659$	11.5685	+	20.0373i	0.450646	+	0.780542i	−0.547780	+	0.836622i	$0.684527\pi$
$660$		0			0
$661$	9.44397	−	16.3574i	0.367328	−	0.636231i	−0.621819	−	0.783161i	$-0.713606\pi$
$661$	9.44397	−	16.3574i	0.367328	−	0.636231i	0.989147	+	0.146930i	$0.0469393\pi$
$662$	−6.82325	+	3.03791i	−0.265193	+	0.118072i
$663$		0			0
$664$	−13.3830	+	14.8634i	−0.519363	+	0.576811i
$665$	3.08466	+	4.24568i	0.119618	+	0.164640i
$666$		0			0
$667$	16.6624	−	5.41395i	0.645172	−	0.209629i
$668$	−7.21576	+	1.53376i	−0.279186	+	0.0593428i
$669$		0			0
$670$	−42.0178	−	24.2590i	−1.62329	−	0.937207i
$671$	−1.01709	+	3.80946i	−0.0392644	+	0.147062i
$672$		0			0
$673$	−29.0179	−	3.04990i	−1.11856	−	0.117565i	−0.472845	−	0.881146i	$-0.656773\pi$
$673$	−29.0179	−	3.04990i	−1.11856	−	0.117565i	−0.645712	+	0.763581i	$0.723440\pi$
$674$	−7.01286	−	2.27862i	−0.270125	−	0.0877691i
$675$		0			0
$676$	10.0032	−	7.26772i	0.384737	−	0.279528i
$677$	14.5818	+	6.49222i	0.560423	+	0.249516i	0.667342	−	0.744751i	$-0.267432\pi$
$677$	14.5818	+	6.49222i	0.560423	+	0.249516i	−0.106919	+	0.994268i	$0.534099\pi$
$678$		0			0
$679$	16.1757	−	14.5647i	0.620767	−	0.558941i
$680$	11.8836	+	26.6910i	0.455715	+	1.02355i
$681$		0			0
$682$	−12.4424	−	24.3657i	−0.476443	−	0.933010i
$683$		−	4.33022i		−	0.165691i	−0.996562	−	0.0828457i	$-0.973599\pi$
$683$		−	4.33022i		−	0.165691i	0.996562	−	0.0828457i	$-0.0264009\pi$
$684$		0			0
$685$	−18.6411	+	57.3714i	−0.712239	+	2.19205i
$686$	−11.1859	−	10.0718i	−0.427079	−	0.384544i
$687$		0			0
$688$	10.6579	−	1.12019i	0.406328	−	0.0427068i
$689$	−1.23108	−	0.261674i	−0.0469004	−	0.00996898i
$690$		0			0
$691$	2.38448	−	22.6868i	0.0907098	−	0.863047i	−0.850670	−	0.525699i	$-0.823804\pi$
$691$	2.38448	−	22.6868i	0.0907098	−	0.863047i	0.941380	−	0.337347i	$-0.109530\pi$
$692$	−11.9278			−0.453428
$693$		0			0
$694$	25.1785			0.955763
$695$	1.14165	−	10.8620i	0.0433051	−	0.412020i
$696$		0			0
$697$	23.1967	+	4.93060i	0.878636	+	0.186760i
$698$	14.3214	−	1.50524i	0.542075	−	0.0569743i
$699$		0			0
$700$	13.8598	+	12.4794i	0.523850	+	0.471677i
$701$	−11.9110	+	36.6583i	−0.449872	+	1.38456i	0.427180	+	0.904167i	$0.359507\pi$
$701$	−11.9110	+	36.6583i	−0.449872	+	1.38456i	−0.877052	+	0.480396i	$0.840493\pi$
$702$		0			0
$703$		−	1.32720i		−	0.0500563i
$704$	−21.4798	−	10.9203i	−0.809550	−	0.411575i
$705$		0			0
$706$	6.24714	+	14.0313i	0.235114	+	0.528075i
$707$	25.3164	−	22.7950i	0.952120	−	0.857292i
$708$		0			0
$709$	23.5945	+	10.5049i	0.886108	+	0.394521i	0.798755	−	0.601657i	$-0.205492\pi$
$709$	23.5945	+	10.5049i	0.886108	+	0.394521i	0.0873535	+	0.996177i	$0.472159\pi$
$710$	−1.55808	+	1.13201i	−0.0584737	+	0.0424836i
$711$		0			0
$712$	−20.9535	−	6.80821i	−0.785266	−	0.255148i
$713$	−22.7136	−	2.38729i	−0.850631	−	0.0894049i
$714$		0			0
$715$	2.31711	+	2.85617i	0.0866551	+	0.106815i
$716$	4.41046	+	2.54638i	0.164826	+	0.0951626i
$717$		0			0
$718$	−7.13713	+	1.51704i	−0.266355	+	0.0566155i
$719$	28.7908	−	9.35469i	1.07371	−	0.348871i	0.281781	−	0.959479i	$-0.409075\pi$
$719$	28.7908	−	9.35469i	1.07371	−	0.348871i	0.791933	+	0.610608i	$0.209075\pi$
$720$		0			0
$721$	−33.9639	−	46.7473i	−1.26488	−	1.74096i
$722$	12.8506	−	14.2720i	0.478250	−	0.531151i
$723$		0			0
$724$	15.0079	−	6.68196i	0.557765	−	0.248333i
$725$	14.3927	−	24.9289i	0.534532	−	0.925837i
$726$		0			0
$727$	20.5282	+	35.5559i	0.761349	+	1.31870i	0.942155	+	0.335177i	$0.108796\pi$
$727$	20.5282	+	35.5559i	0.761349	+	1.31870i	−0.180806	+	0.983519i	$0.557871\pi$
$728$	3.65166	+	2.65309i	0.135340	+	0.0983299i
$729$		0			0
$730$	−11.1381	−	34.2795i	−0.412239	−	1.26874i
$731$	11.7541	−	26.4001i	0.434741	−	0.976444i
$732$		0			0
$733$	2.06574	−	9.71852i	0.0762997	−	0.358962i	−0.923390	−	0.383863i	$-0.874594\pi$
$733$	2.06574	−	9.71852i	0.0762997	−	0.358962i	0.999690	+	0.0249008i	$0.00792698\pi$
$734$	2.89597	+	3.21630i	0.106892	+	0.118716i
$735$		0			0
$736$	−11.8756	+	6.85639i	−0.437741	+	0.252730i
$737$	18.1771	−	47.4797i	0.669562	−	1.74894i
$738$		0			0
$739$	−16.1574	+	22.2387i	−0.594359	+	0.818065i	−0.995177	−	0.0980925i	$-0.968726\pi$
$739$	−16.1574	+	22.2387i	−0.594359	+	0.818065i	0.400818	+	0.916158i	$0.368726\pi$
$740$	−2.03785	−	9.58734i	−0.0749129	−	0.352438i
$741$		0			0
$742$	1.57201	+	14.9567i	0.0577103	+	0.549077i
$743$	3.00160	+	28.5583i	0.110118	+	1.04770i	0.900431	+	0.434999i	$0.143251\pi$
$743$	3.00160	+	28.5583i	0.110118	+	1.04770i	−0.790313	+	0.612703i	$0.790082\pi$
$744$		0			0
$745$	0.00616721	+	0.0290144i	0.000225949	+	0.00106301i
$746$	−12.1925	+	16.7816i	−0.446400	+	0.614417i
$747$		0			0
$748$	−8.32579	+	5.41742i	−0.304421	+	0.198080i
$749$	−14.6989	+	8.48643i	−0.537087	+	0.310087i
$750$		0			0
$751$	19.1906	+	21.3133i	0.700275	+	0.777734i	0.983420	−	0.181343i	$-0.0580445\pi$
$751$	19.1906	+	21.3133i	0.700275	+	0.777734i	−0.283145	+	0.959077i	$0.591378\pi$
$752$	3.04452	−	14.3233i	0.111022	−	0.522318i
$753$		0			0
$754$	0.919356	−	2.06491i	0.0334810	−	0.0751995i
$755$	−0.370092	−	1.13903i	−0.0134690	−	0.0414534i
$756$		0			0
$757$	23.4351	+	17.0266i	0.851763	+	0.618842i	0.925632	−	0.378426i	$-0.123534\pi$
$757$	23.4351	+	17.0266i	0.851763	+	0.618842i	−0.0738684	+	0.997268i	$0.523534\pi$
$758$	−14.9081	−	25.8216i	−0.541487	−	0.937883i
$759$		0			0
$760$	−1.89185	+	3.27677i	−0.0686244	+	0.118861i
$761$	41.0676	−	18.2845i	1.48870	−	0.662812i	0.508543	−	0.861037i	$-0.330184\pi$
$761$	41.0676	−	18.2845i	1.48870	−	0.662812i	0.980157	+	0.198225i	$0.0635176\pi$
$762$		0			0
$763$	15.6260	−	17.3545i	0.565700	−	0.628273i
$764$	5.01201	+	6.89844i	0.181328	+	0.249577i
$765$		0			0
$766$	−4.76164	+	1.54715i	−0.172045	+	0.0559008i
$767$	4.06884	−	0.864858i	0.146917	−	0.0312282i
$768$		0			0
$769$	0.942343	+	0.544062i	0.0339818	+	0.0196194i	0.516895	−	0.856049i	$-0.327088\pi$
$769$	0.942343	+	0.544062i	0.0339818	+	0.0196194i	−0.482913	+	0.875668i	$0.660421\pi$
$770$	23.9027	−	36.8790i	0.861392	−	1.32903i
$771$		0			0
$772$	−1.37869	−	0.144906i	−0.0496201	−	0.00521528i
$773$	−5.28257	−	1.71641i	−0.190001	−	0.0617350i	0.212471	−	0.977167i	$-0.431849\pi$
$773$	−5.28257	−	1.71641i	−0.190001	−	0.0617350i	−0.402472	+	0.915432i	$0.631849\pi$
$774$		0			0
$775$	−30.3578	+	22.0562i	−1.09048	+	0.792282i
$776$	14.3366	+	6.38307i	0.514654	+	0.229139i
$777$		0			0
$778$	−12.9883	+	11.6947i	−0.465653	+	0.419276i
$779$	1.24915	+	2.80564i	0.0447555	+	0.100523i
$780$		0			0
$781$	−1.42827	−	1.42572i	−0.0511074	−	0.0510161i
$782$		−	8.97319i		−	0.320881i
$783$		0			0
$784$	3.76113	−	11.5756i	0.134326	−	0.413413i
$785$	−6.75773	−	6.08469i	−0.241194	−	0.217172i
$786$		0			0
$787$	24.0925	−	2.53222i	0.858805	−	0.0902640i	0.335119	−	0.942176i	$-0.391223\pi$
$787$	24.0925	−	2.53222i	0.858805	−	0.0902640i	0.523685	+	0.851912i	$0.324557\pi$
$788$	17.3398	+	3.68568i	0.617704	+	0.131297i
$789$		0			0
$790$	−1.60141	+	15.2364i	−0.0569758	+	0.542088i
$791$	30.5003			1.08447
$792$		0			0
$793$	0.424649			0.0150797
$794$	0.846612	−	8.05498i	0.0300451	−	0.285860i
$795$		0			0
$796$	17.2308	+	3.66251i	0.610728	+	0.129814i
$797$	10.6926	−	1.12384i	0.378751	−	0.0398083i	0.0867595	−	0.996229i	$-0.472349\pi$
$797$	10.6926	−	1.12384i	0.378751	−	0.0398083i	0.291991	+	0.956421i	$0.405682\pi$
$798$		0			0
$799$	−29.3449	−	26.4222i	−1.03815	−	0.934752i
$800$	−6.96224	+	21.4276i	−0.246152	+	0.757579i
$801$		0			0
$802$		−	6.56948i		−	0.231976i
$803$	33.6368	−	17.1767i	1.18702	−	0.606153i
$804$		0			0
$805$	−14.9219	−	33.5152i	−0.525929	−	1.18126i
$806$	−2.18969	+	1.97161i	−0.0771286	+	0.0694469i
$807$		0			0
$808$	22.4380	+	9.99005i	0.789366	+	0.351449i
$809$	−12.6347	+	9.17967i	−0.444213	+	0.322740i	−0.787307	−	0.616561i	$-0.788525\pi$
$809$	−12.6347	+	9.17967i	−0.444213	+	0.322740i	0.343093	+	0.939301i	$0.388525\pi$
$810$		0			0
$811$	51.9356	+	16.8749i	1.82370	+	0.592557i	0.999661	+	0.0260296i	$0.00828640\pi$
$811$	51.9356	+	16.8749i	1.82370	+	0.592557i	0.824043	+	0.566528i	$0.191714\pi$
$812$	24.8221	+	2.60891i	0.871086	+	0.0915549i
$813$		0			0
$814$	−10.3725	+	3.99229i	−0.363558	+	0.139930i
$815$	−35.8928	−	20.7227i	−1.25727	−	0.725885i
$816$		0			0
$817$	3.66068	−	0.778101i	0.128071	−	0.0272223i
$818$	15.4814	−	5.03020i	0.541294	−	0.175877i
$819$		0			0
$820$	13.3315	+	18.3492i	0.465556	+	0.640782i
$821$	13.4524	−	14.9405i	0.469494	−	0.521425i	−0.461165	−	0.887314i	$-0.652568\pi$
$821$	13.4524	−	14.9405i	0.469494	−	0.521425i	0.930659	+	0.365889i	$0.119235\pi$
$822$		0			0
$823$	−36.5599	+	16.2775i	−1.27440	+	0.567398i	−0.928660	−	0.370933i	$-0.879038\pi$
$823$	−36.5599	+	16.2775i	−1.27440	+	0.567398i	−0.345738	+	0.938331i	$0.612371\pi$
$824$	20.8303	−	36.0791i	0.725658	−	1.25688i
$825$		0			0
$826$	−24.8528	−	43.0463i	−0.864740	−	1.49777i
$827$	36.6966	+	26.6617i	1.27607	+	0.927117i	0.999427	−	0.0338566i	$-0.0107789\pi$
$827$	36.6966	+	26.6617i	1.27607	+	0.927117i	0.276640	+	0.960974i	$0.410779\pi$
$828$		0			0
$829$	−11.8926	−	36.6018i	−0.413049	−	1.27123i	−0.913985	−	0.405749i	$-0.867011\pi$
$829$	−11.8926	−	36.6018i	−0.413049	−	1.27123i	0.500936	−	0.865484i	$-0.332989\pi$
$830$	8.53051	−	19.1598i	0.296098	−	0.665047i
$831$		0			0
$832$	−0.539566	+	2.53846i	−0.0187061	+	0.0880052i
$833$	−21.9617	−	24.3910i	−0.760928	−	0.845097i
$834$		0			0
$835$	20.6480	−	11.9211i	0.714554	−	0.412548i
$836$	−1.20135	−	0.459922i	−0.0415494	−	0.0159067i
$837$		0			0
$838$	2.18314	−	3.00484i	0.0754154	−	0.103800i
$839$	1.23360	+	5.80364i	0.0425886	+	0.200364i	0.994298	−	0.106636i	$-0.0340081\pi$
$839$	1.23360	+	5.80364i	0.0425886	+	0.200364i	−0.951709	+	0.307000i	$0.900675\pi$
$840$		0			0
$841$	−0.995378	−	9.47039i	−0.0343234	−	0.326565i
$842$	−1.40716	−	13.3882i	−0.0484939	−	0.461389i
$843$		0			0
$844$	−0.914304	−	4.30146i	−0.0314716	−	0.148062i
$845$	−23.4892	+	32.3301i	−0.808053	+	1.11219i
$846$		0			0
$847$	42.1032	+	18.6555i	1.44668	+	0.641009i
$848$	−3.52819	+	2.03700i	−0.121159	+	0.0699510i
$849$		0			0
$850$	−9.86503	−	10.9562i	−0.338368	−	0.375796i
$851$	−1.92903	+	9.07535i	−0.0661261	+	0.311099i
$852$		0			0
$853$	1.27493	−	2.86355i	0.0436529	−	0.0980460i	−0.890403	−	0.455174i	$-0.849577\pi$
$853$	1.27493	−	2.86355i	0.0436529	−	0.0980460i	0.934056	+	0.357128i	$0.116244\pi$
$854$	−1.56802	−	4.82587i	−0.0536565	−	0.165138i
$855$		0			0
$856$	−9.90009	−	7.19283i	−0.338378	−	0.245846i
$857$	−21.2277	−	36.7674i	−0.725124	−	1.25595i	−0.958923	−	0.283666i	$-0.908449\pi$
$857$	−21.2277	−	36.7674i	−0.725124	−	1.25595i	0.233800	−	0.972285i	$-0.424884\pi$
$858$		0			0
$859$	−0.508100	+	0.880055i	−0.0173361	+	0.0300271i	−0.874563	−	0.484911i	$-0.838852\pi$
$859$	−0.508100	+	0.880055i	−0.0173361	+	0.0300271i	0.857227	+	0.514938i	$0.172185\pi$
$860$	25.2490	−	11.2416i	0.860985	−	0.383335i
$861$		0			0
$862$	−10.6036	+	11.7765i	−0.361162	+	0.401111i
$863$	6.08271	+	8.37213i	0.207058	+	0.284991i	0.899898	−	0.436101i	$-0.143641\pi$
$863$	6.08271	+	8.37213i	0.207058	+	0.284991i	−0.692840	+	0.721091i	$0.743641\pi$
$864$		0			0
$865$	36.6638	−	11.9128i	1.24661	−	0.405048i
$866$	12.4084	−	2.63748i	0.421654	−	0.0896253i
$867$		0			0
$868$	−28.1770	−	16.2680i	−0.956390	−	0.552172i
$869$	−16.0309	+	0.854512i	−0.543811	+	0.0289873i
$870$		0			0
$871$	−5.44548	−	0.572343i	−0.184513	−	0.0193931i
$872$	16.0129	+	5.20291i	0.542265	+	0.176193i
$873$		0			0
$874$	0.940125	−	0.683041i	0.0318002	−	0.0231042i
$875$	4.30008	+	1.91452i	0.145369	+	0.0647225i
$876$		0			0
$877$	21.8143	−	19.6417i	0.736616	−	0.663252i	−0.212863	−	0.977082i	$-0.568279\pi$
$877$	21.8143	−	19.6417i	0.736616	−	0.663252i	0.949479	+	0.313830i	$0.101612\pi$
$878$	−4.75641	−	10.6831i	−0.160521	−	0.360536i
$879$		0			0
$880$	11.7603	+	1.85187i	0.396439	+	0.0624267i
$881$		−	28.0964i		−	0.946592i	−0.880903	−	0.473296i	$-0.843064\pi$
$881$		−	28.0964i		−	0.946592i	0.880903	−	0.473296i	$-0.156936\pi$
$882$		0			0
$883$	−3.44111	+	10.5906i	−0.115802	+	0.356403i	−0.992114	−	0.125342i	$-0.959997\pi$
$883$	−3.44111	+	10.5906i	−0.115802	+	0.356403i	0.876311	+	0.481746i	$0.159997\pi$
$884$	0.795013	+	0.715833i	0.0267392	+	0.0240761i
$885$		0			0
$886$	7.45413	−	0.783460i	0.250426	−	0.0263209i
$887$	−23.2787	−	4.94803i	−0.781621	−	0.166139i	−0.200215	−	0.979752i	$-0.564164\pi$
$887$	−23.2787	−	4.94803i	−0.781621	−	0.166139i	−0.581406	+	0.813613i	$0.697497\pi$
$888$		0			0
$889$	−5.99761	+	57.0634i	−0.201153	+	1.91385i
$890$	23.1030			0.774414
$891$		0			0
$892$	10.4843			0.351042
$893$	0.534533	−	5.08574i	0.0178875	−	0.170188i
$894$		0			0
$895$	−16.1001	−	3.42217i	−0.538166	−	0.114391i
$896$	−9.61198	+	1.01026i	−0.321114	+	0.0337504i
$897$		0			0
$898$	−3.33694	−	3.00460i	−0.111355	−	0.100265i
$899$	−15.5180	+	47.7596i	−0.517556	+	1.59287i
$900$		0			0
$901$			10.9860i			0.365998i
$902$	18.1696	−	18.2021i	0.604982	−	0.606064i
$903$		0			0
$904$	8.94425	+	20.0891i	0.297481	+	0.668154i
$905$	−39.4579	+	35.5281i	−1.31163	+	1.18099i
$906$		0			0
$907$	−1.06814	−	0.475566i	−0.0354670	−	0.0157909i	0.388927	−	0.921269i	$-0.372846\pi$
$907$	−1.06814	−	0.475566i	−0.0354670	−	0.0157909i	−0.424393	+	0.905478i	$0.639513\pi$
$908$	2.19174	−	1.59239i	0.0727353	−	0.0528453i
$909$		0			0
$910$	−4.50149	−	1.46262i	−0.149223	−	0.0484855i
$911$	1.42271	+	0.149533i	0.0471365	+	0.00495425i	0.128067	−	0.991765i	$-0.459123\pi$
$911$	1.42271	+	0.149533i	0.0471365	+	0.00495425i	−0.0809308	+	0.996720i	$0.525789\pi$
$912$		0			0
$913$	21.2331	+	5.66906i	0.702713	+	0.187619i
$914$	5.56355	+	3.21212i	0.184026	+	0.106247i
$915$		0			0
$916$	1.87084	−	0.397660i	0.0618144	−	0.0131391i
$917$	73.7713	−	23.9698i	2.43614	−	0.791551i
$918$		0			0
$919$	−7.86498	−	10.8252i	−0.259442	−	0.357091i	0.659348	−	0.751838i	$-0.270832\pi$
$919$	−7.86498	−	10.8252i	−0.259442	−	0.357091i	−0.918790	+	0.394747i	$0.870832\pi$
$920$	17.6990	−	19.6568i	0.583519	−	0.648064i
$921$		0			0
$922$	9.61103	−	4.27911i	0.316522	−	0.140925i
$923$	−0.108673	+	0.188227i	−0.00357701	+	0.00619556i
$924$		0			0
$925$	7.62201	+	13.2017i	0.250610	+	0.434070i
$926$	−1.39661	−	1.01469i	−0.0458953	−	0.0333449i
$927$		0			0
$928$	9.31732	+	28.6758i	0.305856	+	0.941328i
$929$	−22.4295	+	50.3774i	−0.735887	+	1.65283i	0.0214206	+	0.999771i	$0.493181\pi$
$929$	−22.4295	+	50.3774i	−0.735887	+	1.65283i	−0.757307	+	0.653058i	$0.773486\pi$
$930$		0			0
$931$	0.883722	−	4.15758i	0.0289628	−	0.136259i
$932$	−15.6384	−	17.3683i	−0.512254	−	0.568916i
$933$		0			0
$934$	21.2934	−	12.2937i	0.696741	−	0.402264i
$935$	20.1813	−	24.9674i	0.659998	−	0.816521i
$936$		0			0
$937$	14.4585	−	19.9004i	0.472339	−	0.650118i	−0.504671	−	0.863312i	$-0.668386\pi$
$937$	14.4585	−	19.9004i	0.472339	−	0.650118i	0.977010	+	0.213193i	$0.0683863\pi$
$938$	13.6032	+	63.9979i	0.444159	+	2.08960i
$939$		0			0
$940$	−3.94759	−	37.5588i	−0.128756	−	1.22503i
$941$	−2.27892	−	21.6825i	−0.0742908	−	0.706829i	−0.966754	−	0.255709i	$-0.917691\pi$
$941$	−2.27892	−	21.6825i	−0.0742908	−	0.706829i	0.892463	−	0.451121i	$-0.148976\pi$
$942$		0			0
$943$	−4.46379	−	21.0005i	−0.145361	−	0.683870i
$944$	7.91453	−	10.8934i	0.257596	−	0.354550i
$945$		0			0
$946$	−17.0927	−	26.2690i	−0.555731	−	0.854078i
$947$	−41.1841	+	23.7776i	−1.33830	+	0.772669i	−0.986556	−	0.163426i	$-0.947745\pi$
$947$	−41.1841	+	23.7776i	−1.33830	+	0.772669i	−0.351747	+	0.936095i	$0.614412\pi$
$948$		0			0
$949$	−2.72181	−	3.02287i	−0.0883536	−	0.0981266i
$950$	0.396961	−	1.86755i	0.0128791	−	0.0605915i
$951$		0			0
$952$	16.0253	−	35.9934i	0.519383	−	1.16655i
$953$	13.1907	+	40.5969i	0.427290	+	1.31506i	0.900785	+	0.434266i	$0.142992\pi$
$953$	13.1907	+	40.5969i	0.427290	+	1.31506i	−0.473495	+	0.880797i	$0.657008\pi$
$954$		0			0
$955$	−22.2957	−	16.1988i	−0.721472	−	0.524180i
$956$	4.81724	+	8.34371i	0.155801	+	0.269855i
$957$		0			0
$958$	19.0094	−	32.9252i	0.614166	−	1.06377i
$959$	74.3151	−	33.0872i	2.39976	−	1.06844i
$960$		0			0
$961$	23.0601	−	25.6108i	0.743873	−	0.826155i
$962$	0.703584	+	0.968400i	0.0226845	+	0.0312225i
$963$		0			0
$964$	−15.8202	+	5.14029i	−0.509534	+	0.165558i
$965$	4.38254	−	0.931538i	0.141079	−	0.0299873i
$966$		0			0
$967$	−1.29188	−	0.745867i	−0.0415440	−	0.0239855i	0.479084	−	0.877769i	$-0.340969\pi$
$967$	−1.29188	−	0.745867i	−0.0415440	−	0.0239855i	−0.520628	+	0.853784i	$0.674302\pi$
$968$	0.0593507	+	33.2022i	0.00190760	+	1.06716i
$969$		0			0
$970$	−16.3662	−	1.72016i	−0.525487	−	0.0552309i
$971$	−2.12249	−	0.689639i	−0.0681140	−	0.0221316i	0.274762	−	0.961512i	$-0.411401\pi$
$971$	−2.12249	−	0.689639i	−0.0681140	−	0.0221316i	−0.342876	+	0.939381i	$0.611401\pi$
$972$		0			0
$973$	−11.9155	+	8.65712i	−0.381994	+	0.277535i
$974$	35.4271	+	15.7732i	1.13516	+	0.505404i
$975$		0			0
$976$	1.02151	−	0.919774i	0.0326978	−	0.0294412i
$977$	−17.9877	−	40.4009i	−0.575476	−	1.29254i	−0.933416	−	0.358796i	$-0.883187\pi$
$977$	−17.9877	−	40.4009i	−0.575476	−	1.29254i	0.357940	−	0.933745i	$-0.383479\pi$
$978$		0			0
$979$	3.80846	+	23.9073i	0.121719	+	0.764081i
$980$		−	31.3902i		−	1.00272i
$981$		0			0
$982$	9.02219	−	27.7674i	0.287910	−	0.886095i
$983$	−31.6826	−	28.5271i	−1.01052	−	0.909874i	−0.0145772	−	0.999894i	$-0.504640\pi$
$983$	−31.6826	−	28.5271i	−1.01052	−	0.909874i	−0.995940	+	0.0900200i	$0.971307\pi$
$984$		0			0
$985$	−56.9802	+	5.98886i	−1.81554	+	0.190821i
$986$	−19.2990	−	4.10213i	−0.614605	−	0.130638i
$987$		0			0
$988$	−0.0144816	+	0.137783i	−0.000460721	+	0.00438347i
$989$	−26.1625			−0.831920
$990$		0			0
$991$	−1.45490			−0.0462164			−0.0231082	−	0.999733i	$-0.507356\pi$
$991$	−1.45490			−0.0462164			−0.0231082	+	0.999733i	$0.507356\pi$
$992$	4.10850	−	39.0897i	0.130445	−	1.24110i
$993$		0			0
$994$	2.54036	+	0.539969i	0.0805752	+	0.0171268i
$995$	−56.6219	+	5.95120i	−1.79504	+	0.188666i
$996$		0			0
$997$	−39.0040	−	35.1194i	−1.23527	−	1.11224i	−0.989744	−	0.142851i	$-0.954373\pi$
$997$	−39.0040	−	35.1194i	−1.23527	−	1.11224i	−0.245525	−	0.969390i	$-0.578960\pi$
$998$	−4.84912	+	14.9241i	−0.153496	+	0.472413i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.e.458.3		64
3.2	odd	2	inner	891.2.u.e.458.6		64
9.2	odd	6	inner	891.2.u.e.755.3		64
9.4	even	3		297.2.k.a.161.3	yes	32
9.5	odd	6		297.2.k.a.161.6	yes	32
9.7	even	3	inner	891.2.u.e.755.6		64
11.8	odd	10	inner	891.2.u.e.701.3		64
33.8	even	10	inner	891.2.u.e.701.6		64
99.41	even	30		297.2.k.a.107.3	✓	32
99.52	odd	30	inner	891.2.u.e.107.6		64
99.74	even	30	inner	891.2.u.e.107.3		64
99.85	odd	30		297.2.k.a.107.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.k.a.107.3	✓	32	99.41	even	30
297.2.k.a.107.6	yes	32	99.85	odd	30
297.2.k.a.161.3	yes	32	9.4	even	3
297.2.k.a.161.6	yes	32	9.5	odd	6
891.2.u.e.107.3		64	99.74	even	30	inner
891.2.u.e.107.6		64	99.52	odd	30	inner
891.2.u.e.458.3		64	1.1	even	1	trivial
891.2.u.e.458.6		64	3.2	odd	2	inner
891.2.u.e.701.3		64	11.8	odd	10	inner
891.2.u.e.701.6		64	33.8	even	10	inner
891.2.u.e.755.3		64	9.2	odd	6	inner
891.2.u.e.755.6		64	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.106570 + 1.01395i) q^{2} +(0.939559 + 0.199709i) q^{4} +(-3.08748 + 0.324507i) q^{5} +(3.11115 + 2.80129i) q^{7} +(-0.932731 + 2.87065i) q^{8} -3.16513i q^{10} +(3.27533 - 0.521762i) q^{11} +(-0.145286 - 0.326318i) q^{13} +(-3.17193 + 2.85602i) q^{14} +(-1.05628 - 0.470288i) q^{16} +(-2.52248 + 1.83269i) q^{17} +(-0.384024 - 0.124777i) q^{19} +(-2.96567 - 0.311705i) q^{20} +(0.179988 + 3.37662i) q^{22} +(2.44458 + 1.41138i) q^{23} +(4.53649 - 0.964260i) q^{25} +(0.346353 - 0.112537i) q^{26} +(2.36367 + 3.25331i) q^{28} +(4.15306 - 4.61244i) q^{29} +(-7.39141 + 3.29087i) q^{31} +(-2.42897 + 4.20709i) q^{32} +(-1.58943 - 2.75298i) q^{34} +(-10.5147 - 7.63935i) q^{35} +(1.01570 + 3.12601i) q^{37} +(0.167443 - 0.376083i) q^{38} +(1.94824 - 9.16576i) q^{40} +(-5.08934 - 5.65229i) q^{41} +(-8.02668 + 4.63421i) q^{43} +(3.18156 + 0.163887i) q^{44} +(-1.69159 + 2.32827i) q^{46} +(2.63310 + 12.3878i) q^{47} +(1.10032 + 10.4689i) q^{49} +(0.494256 + 4.70253i) q^{50} +(-0.0713360 - 0.335610i) q^{52} +(2.07104 - 2.85055i) q^{53} +(-9.94319 + 2.67380i) q^{55} +(-10.9434 + 6.31818i) q^{56} +(4.23419 + 4.70255i) q^{58} +(-2.42122 + 11.3909i) q^{59} +(-0.483540 + 1.08605i) q^{61} +(-2.54907 - 7.84522i) q^{62} +(-5.87777 - 4.27045i) q^{64} +(0.554460 + 0.960353i) q^{65} +(7.66446 - 13.2752i) q^{67} +(-2.73603 + 1.21816i) q^{68} +(8.86647 - 9.84721i) q^{70} +(-0.357651 - 0.492264i) q^{71} +(10.8303 - 3.51899i) q^{73} +(-3.27786 + 0.696732i) q^{74} +(-0.335894 - 0.193928i) q^{76} +(11.6517 + 7.55187i) q^{77} +(-4.81384 - 0.505955i) q^{79} +(3.41387 + 1.10923i) q^{80} +(6.27351 - 4.55797i) q^{82} +(6.05341 + 2.69515i) q^{83} +(7.19339 - 6.47696i) q^{85} +(-3.84345 - 8.63252i) q^{86} +(-1.55720 + 9.88899i) q^{88} +7.29922i q^{89} +(0.462105 - 1.42221i) q^{91} +(2.01496 + 1.81428i) q^{92} +(-12.8412 + 1.34966i) q^{94} +(1.22616 + 0.260628i) q^{95} +(0.543471 - 5.17078i) q^{97} -10.7322 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 8 q^{4} + 4 q^{16} - 36 q^{22} - 8 q^{25} - 200 q^{28} - 8 q^{31} + 64 q^{34} - 24 q^{37} + 60 q^{40} - 40 q^{46} - 100 q^{52} + 16 q^{55} - 24 q^{58} - 60 q^{61} + 72 q^{64} + 24 q^{67} - 8 q^{70}+ \cdots + 24 q^{97}+O(q^{100}) \) 64 * q + 8 * q^4 + 4 * q^16 - 36 * q^22 - 8 * q^25 - 200 * q^28 - 8 * q^31 + 64 * q^34 - 24 * q^37 + 60 * q^40 - 40 * q^46 - 100 * q^52 + 16 * q^55 - 24 * q^58 - 60 * q^61 + 72 * q^64 + 24 * q^67 - 8 * q^70 + 160 * q^73 + 60 * q^79 + 144 * q^82 + 20 * q^85 + 24 * q^88 + 48 * q^91 - 20 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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