LMFDB - Embedded newform 891.2.u.c.512.3

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 = [32,0,0,4,0] 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:	$32$
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			512.3
Character	$\chi$	$=$	891.512
Dual form			891.2.u.c.134.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.673250 + 0.143104i) q^{2} +(-1.39430 - 0.620784i) q^{4} +(-0.00833908 - 0.0392323i) q^{5} +(-0.245496 + 0.0258027i) q^{7} +(-1.96356 - 1.42661i) q^{8} -0.0276065i q^{10} +(-0.586694 + 3.26432i) q^{11} +(1.71036 + 1.54002i) q^{13} +(-0.168973 - 0.0177597i) q^{14} +(0.924716 + 1.02700i) q^{16} +(-1.32142 + 4.06692i) q^{17} +(-3.64429 + 5.01593i) q^{19} +(-0.0127276 + 0.0598785i) q^{20} +(-0.862129 + 2.11375i) q^{22} +(5.88883 - 3.39992i) q^{23} +(4.56626 - 2.03303i) q^{25} +(0.931121 + 1.28158i) q^{26} +(0.358314 + 0.116423i) q^{28} +(0.584914 + 5.56509i) q^{29} +(3.21007 - 3.56515i) q^{31} +(2.90269 + 5.02760i) q^{32} +(-1.47164 + 2.54895i) q^{34} +(0.00305951 + 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(-3.17132 + 2.85547i) q^{38} +(-0.0395948 + 0.0889314i) q^{40} +(-1.00378 + 9.55032i) q^{41} +(-0.893447 - 0.515832i) q^{43} +(2.84447 - 4.18724i) q^{44} +(4.45120 - 1.44628i) q^{46} +(4.52544 + 10.1643i) q^{47} +(-6.78743 + 1.44271i) q^{49} +(3.36517 - 0.715289i) q^{50} +(-1.42875 - 3.20902i) q^{52} +(-8.52885 + 2.77119i) q^{53} +(0.132959 - 0.00420408i) q^{55} +(0.518855 + 0.299561i) q^{56} +(-0.402591 + 3.83040i) q^{58} +(-1.13411 + 2.54726i) q^{59} +(-6.30521 + 5.67724i) q^{61} +(2.67137 - 1.94086i) q^{62} +(0.380665 + 1.17156i) q^{64} +(0.0461556 - 0.0799438i) q^{65} +(-3.97294 - 6.88133i) q^{67} +(4.36714 - 4.85020i) q^{68} +(0.000712321 + 0.00677728i) q^{70} +(3.16559 + 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(2.53454 - 1.12845i) q^{74} +(8.19506 - 4.73142i) q^{76} +(0.0598028 - 0.816515i) q^{77} +(0.626023 - 2.94520i) q^{79} +(0.0325803 - 0.0448429i) q^{80} +(-2.04248 + 6.28611i) q^{82} +(-3.54224 - 3.93406i) q^{83} +(0.170574 + 0.0179280i) q^{85} +(-0.527696 - 0.475140i) q^{86} +(5.80891 - 5.57270i) q^{88} +8.54422i q^{89} +(-0.459624 - 0.333936i) q^{91} +(-10.3214 + 1.08483i) q^{92} +(1.59220 + 7.49072i) q^{94} +(0.227176 + 0.101145i) q^{95} +(2.96207 + 0.629607i) q^{97} -4.77610 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.673250	+	0.143104i	0.476060	+	0.101190i	0.439692	−	0.898149i	$-0.355088\pi$
$2$	0.673250	+	0.143104i	0.476060	+	0.101190i	0.0363682	+	0.999338i	$0.488421\pi$
$3$		0			0
$3$		0			0
$4$	−1.39430	−	0.620784i	−0.697152	−	0.310392i
$5$	−0.00833908	−	0.0392323i	−0.00372935	−	0.0175452i	0.976244	−	0.216676i	$-0.0695215\pi$
$5$	−0.00833908	−	0.0392323i	−0.00372935	−	0.0175452i	−0.979973	+	0.199131i	$0.936188\pi$
$6$		0			0
$7$	−0.245496	+	0.0258027i	−0.0927887	+	0.00975249i	−0.150809	−	0.988563i	$-0.548188\pi$
$7$	−0.245496	+	0.0258027i	−0.0927887	+	0.00975249i	0.0580203	+	0.998315i	$0.481521\pi$
$8$	−1.96356	−	1.42661i	−0.694222	−	0.504382i
$9$		0			0
$10$		−	0.0276065i		−	0.00872994i
$11$	−0.586694	+	3.26432i	−0.176895	+	0.984230i
$11$	−0.586694	+	3.26432i	−0.176895	+	0.984230i
$12$		0			0
$13$	1.71036	+	1.54002i	0.474370	+	0.427124i	0.871320	−	0.490716i	$-0.163265\pi$
$13$	1.71036	+	1.54002i	0.474370	+	0.427124i	−0.396950	+	0.917840i	$0.629931\pi$
$14$	−0.168973	−	0.0177597i	−0.0451598	−	0.00474649i
$15$		0			0
$16$	0.924716	+	1.02700i	0.231179	+	0.256750i
$17$	−1.32142	+	4.06692i	−0.320492	+	0.986372i	0.652943	+	0.757407i	$0.273534\pi$
$17$	−1.32142	+	4.06692i	−0.320492	+	0.986372i	−0.973435	+	0.228965i	$0.926466\pi$
$18$		0			0
$19$	−3.64429	+	5.01593i	−0.836057	+	1.15073i	0.150708	+	0.988578i	$0.451845\pi$
$19$	−3.64429	+	5.01593i	−0.836057	+	1.15073i	−0.986765	+	0.162156i	$0.948155\pi$
$20$	−0.0127276	+	0.0598785i	−0.00284597	+	0.0133892i
$21$		0			0
$22$	−0.862129	+	2.11375i	−0.183806	+	0.450652i
$23$	5.88883	−	3.39992i	1.22791	−	0.708932i	0.261315	−	0.965254i	$-0.415844\pi$
$23$	5.88883	−	3.39992i	1.22791	−	0.708932i	0.966592	+	0.256321i	$0.0825105\pi$
$24$		0			0
$25$	4.56626	−	2.03303i	0.913252	−	0.406606i
$26$	0.931121	+	1.28158i	0.182608	+	0.251338i
$27$		0			0
$28$	0.358314	+	0.116423i	0.0677149	+	0.0220019i
$29$	0.584914	+	5.56509i	0.108616	+	1.03341i	0.904066	+	0.427392i	$0.140568\pi$
$29$	0.584914	+	5.56509i	0.108616	+	1.03341i	−0.795450	+	0.606019i	$0.792766\pi$
$30$		0			0
$31$	3.21007	−	3.56515i	0.576546	−	0.640319i	−0.382370	−	0.924009i	$-0.624892\pi$
$31$	3.21007	−	3.56515i	0.576546	−	0.640319i	0.958916	+	0.283690i	$0.0915586\pi$
$32$	2.90269	+	5.02760i	0.513128	+	0.888763i
$33$		0			0
$34$	−1.47164	+	2.54895i	−0.252384	+	0.437142i
$35$	0.00305951	+	0.00941619i	0.000517151	+	0.00159163i
$36$		0			0
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	−0.286529	−	0.958072i	$-0.592502\pi$
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	0.822638	+	0.568566i	$0.192502\pi$
$38$	−3.17132	+	2.85547i	−0.514456	+	0.463218i
$39$		0			0
$40$	−0.0395948	+	0.0889314i	−0.00626049	+	0.0140613i
$41$	−1.00378	+	9.55032i	−0.156764	+	1.49151i	0.579587	+	0.814910i	$0.303214\pi$
$41$	−1.00378	+	9.55032i	−0.156764	+	1.49151i	−0.736351	+	0.676600i	$0.763453\pi$
$42$		0			0
$43$	−0.893447	−	0.515832i	−0.136249	−	0.0786636i	0.430326	−	0.902674i	$-0.358399\pi$
$43$	−0.893447	−	0.515832i	−0.136249	−	0.0786636i	−0.566575	+	0.824010i	$0.691732\pi$
$44$	2.84447	−	4.18724i	0.428820	−	0.631251i
$45$		0			0
$46$	4.45120	−	1.44628i	0.656294	−	0.213243i
$47$	4.52544	+	10.1643i	0.660103	+	1.48262i	0.863932	+	0.503609i	$0.167995\pi$
$47$	4.52544	+	10.1643i	0.660103	+	1.48262i	−0.203829	+	0.979007i	$0.565339\pi$
$48$		0			0
$49$	−6.78743	+	1.44271i	−0.969633	+	0.206102i
$50$	3.36517	−	0.715289i	0.475907	−	0.101157i
$51$		0			0
$52$	−1.42875	−	3.20902i	−0.198132	−	0.445011i
$53$	−8.52885	+	2.77119i	−1.17153	+	0.380652i	−0.829213	−	0.558933i	$-0.811211\pi$
$53$	−8.52885	+	2.77119i	−1.17153	+	0.380652i	−0.342314	+	0.939585i	$0.611211\pi$
$54$		0			0
$55$	0.132959	−	0.00420408i	0.0179282	−	0.000566878i
$56$	0.518855	+	0.299561i	0.0693350	+	0.0400306i
$57$		0			0
$58$	−0.402591	+	3.83040i	−0.0528628	+	0.502956i
$59$	−1.13411	+	2.54726i	−0.147649	+	0.331624i	−0.972196	−	0.234169i	$-0.924763\pi$
$59$	−1.13411	+	2.54726i	−0.147649	+	0.331624i	0.824547	+	0.565793i	$0.191430\pi$
$60$		0			0
$61$	−6.30521	+	5.67724i	−0.807299	+	0.726896i	−0.965469	−	0.260516i	$-0.916107\pi$
$61$	−6.30521	+	5.67724i	−0.807299	+	0.726896i	0.158170	+	0.987412i	$0.449441\pi$
$62$	2.67137	−	1.94086i	0.339264	−	0.246490i
$63$		0			0
$64$	0.380665	+	1.17156i	0.0475831	+	0.146446i
$65$	0.0461556	−	0.0799438i	0.00572489	−	0.00991581i
$66$		0			0
$67$	−3.97294	−	6.88133i	−0.485372	−	0.840689i	0.514487	−	0.857498i	$-0.327982\pi$
$67$	−3.97294	−	6.88133i	−0.485372	−	0.840689i	−0.999859	+	0.0168095i	$0.994649\pi$
$68$	4.36714	−	4.85020i	0.529594	−	0.588173i
$69$		0			0
$70$	0.000712321		0.00677728i	8.51386e−5		0.000810040i
$71$	3.16559	+	1.02856i	0.375687	+	0.122068i	0.490773	−	0.871288i	$-0.336714\pi$
$71$	3.16559	+	1.02856i	0.375687	+	0.122068i	−0.115086	+	0.993355i	$0.536714\pi$
$72$		0			0
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	−0.990455	−	0.137834i	$-0.955986\pi$
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	0.174980	−	0.984572i	$-0.444014\pi$
$74$	2.53454	−	1.12845i	0.294634	−	0.131179i
$75$		0			0
$76$	8.19506	−	4.73142i	0.940038	−	0.542731i
$77$	0.0598028	−	0.816515i	0.00681516	−	0.0930506i
$78$		0			0
$79$	0.626023	−	2.94520i	0.0704330	−	0.331361i	−0.928797	−	0.370588i	$-0.879156\pi$
$79$	0.626023	−	2.94520i	0.0704330	−	0.331361i	0.999230	+	0.0392267i	$0.0124895\pi$
$80$	0.0325803	−	0.0448429i	0.00364259	−	0.00501359i
$81$		0			0
$82$	−2.04248	+	6.28611i	−0.225554	+	0.694185i
$83$	−3.54224	−	3.93406i	−0.388811	−	0.431819i	0.516683	−	0.856177i	$-0.327167\pi$
$83$	−3.54224	−	3.93406i	−0.388811	−	0.431819i	−0.905495	+	0.424358i	$0.860500\pi$
$84$		0			0
$85$	0.170574	+	0.0179280i	0.0185013	+	0.00194457i
$86$	−0.527696	−	0.475140i	−0.0569029	−	0.0512356i
$87$		0			0
$88$	5.80891	−	5.57270i	0.619232	−	0.594052i
$89$			8.54422i			0.905686i	0.891590	+	0.452843i	$0.149590\pi$
$89$			8.54422i			0.905686i	−0.891590	+	0.452843i	$0.850410\pi$
$90$		0			0
$91$	−0.459624	−	0.333936i	−0.0481817	−	0.0350060i
$92$	−10.3214	+	1.08483i	−1.07608	+	0.113101i
$93$		0			0
$94$	1.59220	+	7.49072i	0.164223	+	0.772609i
$95$	0.227176	+	0.101145i	0.0233078	+	0.0103773i
$96$		0			0
$97$	2.96207	+	0.629607i	0.300752	+	0.0639269i	0.355816	−	0.934556i	$-0.384203\pi$
$97$	2.96207	+	0.629607i	0.300752	+	0.0639269i	−0.0550639	+	0.998483i	$0.517536\pi$
$98$	−4.77610			−0.482459
$99$		0			0
$100$	−7.62882			−0.762882
$101$	6.80006	+	1.44540i	0.676631	+	0.143822i	0.533395	−	0.845866i	$-0.320916\pi$
$101$	6.80006	+	1.44540i	0.676631	+	0.143822i	0.143236	+	0.989689i	$0.454249\pi$
$102$		0			0
$103$	11.9852	+	5.33614i	1.18093	+	0.525786i	0.900825	−	0.434182i	$-0.142963\pi$
$103$	11.9852	+	5.33614i	1.18093	+	0.525786i	0.280109	+	0.959968i	$0.409629\pi$
$104$	−1.16139	−	5.46393i	−0.113884	−	0.535783i
$105$		0			0
$106$	−6.13862	+	0.645194i	−0.596235	+	0.0626668i
$107$	−1.10712	−	0.804368i	−0.107029	−	0.0777612i	0.532983	−	0.846126i	$-0.321071\pi$
$107$	−1.10712	−	0.804368i	−0.107029	−	0.0777612i	−0.640012	+	0.768365i	$0.721071\pi$
$108$		0			0
$109$		−	7.34454i		−	0.703480i	−0.936098	−	0.351740i	$-0.885590\pi$
$109$		−	7.34454i		−	0.703480i	0.936098	−	0.351740i	$-0.114410\pi$
$110$	0.0901164	+	0.0161966i	0.00859227	+	0.00154428i
$111$		0			0
$112$	−0.253513	−	0.228264i	−0.0239547	−	0.0215690i
$113$	−0.525647	−	0.0552477i	−0.0494487	−	0.00519727i	0.0797718	−	0.996813i	$-0.474581\pi$
$113$	−0.525647	−	0.0552477i	−0.0494487	−	0.00519727i	−0.129221	+	0.991616i	$0.541248\pi$
$114$		0			0
$115$	−0.182494	−	0.202680i	−0.0170177	−	0.0189000i
$116$	2.63917	−	8.12253i	0.245041	−	0.754158i
$117$		0			0
$118$	−1.12806	+	1.55265i	−0.103847	+	0.142933i
$119$	0.219466	−	1.03251i	0.0201184	−	0.0946498i
$120$		0			0
$121$	−10.3116	−	3.83032i	−0.937416	−	0.348210i
$122$	−5.05742	+	2.91990i	−0.457877	+	0.264355i
$123$		0			0
$124$	−6.68900	+	2.97814i	−0.600690	+	0.267445i
$125$	−0.235715	−	0.324434i	−0.0210830	−	0.0290183i
$126$		0			0
$127$	12.1468	+	3.94673i	1.07785	+	0.350215i	0.793541	−	0.608517i	$-0.208235\pi$
$127$	12.1468	+	3.94673i	1.07785	+	0.350215i	0.284311	+	0.958732i	$0.408235\pi$
$128$	−1.12503	−	10.7039i	−0.0994393	−	0.946101i
$129$		0			0
$130$	0.0425145	−	0.0472171i	0.00372877	−	0.00414122i
$131$	−9.07668	−	15.7213i	−0.793033	−	1.37357i	−0.924081	−	0.382198i	$-0.875167\pi$
$131$	−9.07668	−	15.7213i	−0.793033	−	1.37357i	0.131047	−	0.991376i	$-0.458166\pi$
$132$		0			0
$133$	0.765233	−	1.32542i	0.0663542	−	0.114929i
$134$	−1.69004	−	5.20140i	−0.145997	−	0.449333i
$135$		0			0
$136$	8.39658	−	6.10048i	0.720001	−	0.523111i
$137$	11.9446	−	10.7549i	1.02049	−	0.918855i	0.0237666	−	0.999718i	$-0.492434\pi$
$137$	11.9446	−	10.7549i	1.02049	−	0.918855i	0.996725	+	0.0808625i	$0.0257675\pi$
$138$		0			0
$139$	1.56891	−	3.52382i	0.133073	−	0.298887i	−0.834703	−	0.550701i	$-0.814361\pi$
$139$	1.56891	−	3.52382i	0.133073	−	0.298887i	0.967776	+	0.251814i	$0.0810272\pi$
$140$	0.00157954	−	0.0150283i	0.000133495	−	0.00127012i
$141$		0			0
$142$	1.98404	+	1.14549i	0.166497	+	0.0961273i
$143$	−6.03057	+	4.67966i	−0.504302	+	0.391333i
$144$		0			0
$145$	0.213453	−	0.0693552i	0.0177263	−	0.00575964i
$146$	−3.31848	−	7.45343i	−0.274639	−	0.616850i
$147$		0			0
$148$	−6.01766	+	1.27909i	−0.494649	+	0.105141i
$149$	−10.0456	+	2.13525i	−0.822965	+	0.174927i	−0.600102	−	0.799923i	$-0.704873\pi$
$149$	−10.0456	+	2.13525i	−0.822965	+	0.174927i	−0.222863	+	0.974850i	$0.571540\pi$
$150$		0			0
$151$	3.56725	+	8.01218i	0.290299	+	0.652022i	0.998544	−	0.0539449i	$-0.0171795\pi$
$151$	3.56725	+	8.01218i	0.290299	+	0.652022i	−0.708245	+	0.705967i	$0.750513\pi$
$152$	14.3115	−	4.65010i	1.16082	−	0.377173i
$153$		0			0
$154$	0.157109	−	0.541161i	0.0126602	−	0.0436080i
$155$	−0.166638	−	0.0962084i	−0.0133847	−	0.00772765i
$156$		0			0
$157$	1.36209	−	12.9595i	0.108707	−	1.03428i	−0.795141	−	0.606424i	$-0.792603\pi$
$157$	1.36209	−	12.9595i	0.108707	−	1.03428i	0.903848	−	0.427853i	$-0.140730\pi$
$158$	0.842940	−	1.89327i	0.0670607	−	0.150621i
$159$		0			0
$160$	0.173039	−	0.155805i	0.0136799	−	0.0123174i
$161$	−1.35796	+	0.986614i	−0.107022	+	0.0777561i
$162$		0			0
$163$	−2.83608	−	8.72855i	−0.222139	−	0.683673i	−0.998569	−	0.0534700i	$-0.982972\pi$
$163$	−2.83608	−	8.72855i	−0.222139	−	0.683673i	0.776431	−	0.630203i	$-0.217028\pi$
$164$	7.32826	−	12.6929i	0.572241	−	0.991151i
$165$		0			0
$166$	−1.82184	−	3.15551i	−0.141402	−	0.244915i
$167$	−5.09164	+	5.65484i	−0.394003	+	0.437585i	−0.907209	−	0.420681i	$-0.861791\pi$
$167$	−5.09164	+	5.65484i	−0.394003	+	0.437585i	0.513206	+	0.858266i	$0.328458\pi$
$168$		0			0
$169$	−0.805183	−	7.66080i	−0.0619371	−	0.589292i
$170$	0.112273	+	0.0364798i	0.00861097	+	0.00279787i
$171$		0			0
$172$	0.925516	+	1.27386i	0.0705699	+	0.0971312i
$173$	−15.1835	+	6.76013i	−1.15438	+	0.513963i	−0.892460	−	0.451126i	$-0.851022\pi$
$173$	−15.1835	+	6.76013i	−1.15438	+	0.513963i	−0.261920	+	0.965090i	$0.584356\pi$
$174$		0			0
$175$	−1.06854	+	0.616922i	−0.0807740	+	0.0466349i
$176$	−3.89499	+	2.41603i	−0.293596	+	0.182115i
$177$		0			0
$178$	−1.22271	+	5.75240i	−0.0916460	+	0.431161i
$179$	−4.14376	+	5.70340i	−0.309719	+	0.426292i	−0.935294	−	0.353872i	$-0.884865\pi$
$179$	−4.14376	+	5.70340i	−0.309719	+	0.426292i	0.625574	+	0.780165i	$0.284865\pi$
$180$		0			0
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	0.346517	+	0.938044i	$0.387364\pi$
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	−0.831706	+	0.555216i	$0.812636\pi$
$182$	−0.261654	−	0.290597i	−0.0193951	−	0.0215405i
$183$		0			0
$184$	−16.4134	−	1.72512i	−1.21001	−	0.127177i
$185$	−0.120146	−	0.108180i	−0.00883329	−	0.00795353i
$186$		0			0
$187$	−12.5005	−	6.69958i	−0.914124	−	0.489922i
$188$		−	16.9814i		−	1.23850i
$189$		0			0
$190$	0.138472	+	0.100606i	0.0100458	+	0.00729873i
$191$	13.5934	−	1.42872i	0.983583	−	0.103379i	0.400937	−	0.916105i	$-0.368684\pi$
$191$	13.5934	−	1.42872i	0.983583	−	0.103379i	0.582645	+	0.812727i	$0.302018\pi$
$192$		0			0
$193$	5.20504	+	24.4878i	0.374667	+	1.76267i	0.611622	+	0.791150i	$0.290517\pi$
$193$	5.20504	+	24.4878i	0.374667	+	1.76267i	−0.236955	+	0.971521i	$0.576149\pi$
$194$	1.90411	+	0.847766i	0.136707	+	0.0608661i
$195$		0			0
$196$	10.3594	+	2.20195i	0.739954	+	0.157282i
$197$	21.0442			1.49934			0.749668	−	0.661814i	$-0.230213\pi$
$197$	21.0442			1.49934			0.749668	+	0.661814i	$0.230213\pi$
$198$		0			0
$199$	−10.3709			−0.735176			−0.367588	−	0.929989i	$-0.619816\pi$
$199$	−10.3709			−0.735176			−0.367588	+	0.929989i	$0.619816\pi$
$200$	−11.8664	−	2.52229i	−0.839084	−	0.178353i
$201$		0			0
$202$	4.37130	+	1.94623i	0.307564	+	0.136936i
$203$	−0.287188	−	1.35111i	−0.0201566	−	0.0948296i
$204$		0			0
$205$	0.383051	−	0.0402603i	0.0267535	−	0.00281190i
$206$	7.30540	+	5.30768i	0.508991	+	0.369804i
$207$		0			0
$208$			3.18062i			0.220537i
$209$	−14.2355	−	14.8389i	−0.984693	−	1.02643i
$210$		0			0
$211$	13.9292	+	12.5419i	0.958927	+	0.863422i	0.990699	−	0.136073i	$-0.0434483\pi$
$211$	13.9292	+	12.5419i	0.958927	+	0.863422i	−0.0317716	+	0.999495i	$0.510115\pi$
$212$	13.6121	+	1.43069i	0.934884	+	0.0982602i
$213$		0			0
$214$	−0.630259	−	0.699974i	−0.0430836	−	0.0478492i
$215$	−0.0127867	+	0.0393535i	−0.000872048	+	0.00268389i
$216$		0			0
$217$	−0.696069	+	0.958057i	−0.0472523	+	0.0650372i
$218$	1.05103	−	4.94472i	0.0711848	−	0.334898i
$219$		0			0
$220$	−0.187995	−	0.0766772i	−0.0126746	−	0.00516957i
$221$	−8.52324	+	4.92090i	−0.573335	+	0.331015i
$222$		0			0
$223$	8.83301	−	3.93271i	0.591502	−	0.263354i	−0.0890812	−	0.996024i	$-0.528393\pi$
$223$	8.83301	−	3.93271i	0.591502	−	0.263354i	0.680583	+	0.732671i	$0.261726\pi$
$224$	−0.842323	−	1.15936i	−0.0562801	−	0.0774629i
$225$		0			0
$226$	−0.345986	−	0.112418i	−0.0230146	−	0.00747791i
$227$	−1.22467	−	11.6520i	−0.0812845	−	0.773370i	−0.956911	−	0.290381i	$-0.906218\pi$
$227$	−1.22467	−	11.6520i	−0.0812845	−	0.773370i	0.875626	−	0.482989i	$-0.160449\pi$
$228$		0			0
$229$	13.7039	−	15.2197i	0.905580	−	1.00575i	−0.0943680	−	0.995537i	$-0.530083\pi$
$229$	13.7039	−	15.2197i	0.905580	−	1.00575i	0.999948	−	0.0102110i	$-0.00325031\pi$
$230$	−0.0938599	−	0.162570i	−0.00618894	−	0.0107196i
$231$		0			0
$232$	6.79068	−	11.7618i	0.445830	−	0.772201i
$233$	4.98842	+	15.3528i	0.326802	+	1.00579i	0.970621	+	0.240615i	$0.0773492\pi$
$233$	4.98842	+	15.3528i	0.326802	+	1.00579i	−0.643818	+	0.765178i	$0.722651\pi$
$234$		0			0
$235$	0.361031	−	0.262304i	0.0235510	−	0.0171108i
$236$	3.16259	−	2.84761i	0.205867	−	0.185364i
$237$		0			0
$238$	0.295511	−	0.663730i	0.0191552	−	0.0430232i
$239$	2.96730	−	28.2320i	0.191939	−	1.82618i	−0.298166	−	0.954514i	$-0.596375\pi$
$239$	2.96730	−	28.2320i	0.191939	−	1.82618i	0.490105	−	0.871663i	$-0.336958\pi$
$240$		0			0
$241$	12.4408	+	7.18270i	0.801383	+	0.462679i	0.843954	−	0.536415i	$-0.180222\pi$
$241$	12.4408	+	7.18270i	0.801383	+	0.462679i	−0.0425716	+	0.999093i	$0.513555\pi$
$242$	−6.39414	−	4.05439i	−0.411031	−	0.260626i
$243$		0			0
$244$	12.3157	−	4.00162i	0.788433	−	0.256177i
$245$	0.113202	+	0.254255i	0.00723220	+	0.0162438i
$246$		0			0
$247$	−13.9577	+	2.96680i	−0.888107	+	0.188773i
$248$	−11.3892	+	2.42086i	−0.723217	+	0.153724i
$249$		0			0
$250$	−0.112268	−	0.252157i	−0.00710043	−	0.0159478i
$251$	6.60298	−	2.14544i	0.416776	−	0.135419i	−0.0931196	−	0.995655i	$-0.529684\pi$
$251$	6.60298	−	2.14544i	0.416776	−	0.135419i	0.509896	+	0.860236i	$0.329684\pi$
$252$		0			0
$253$	7.64348	+	21.2178i	0.480542	+	1.33395i
$254$	7.61303	+	4.39538i	0.477684	+	0.275791i
$255$		0			0
$256$	1.03187	−	9.81763i	0.0644921	−	0.613602i
$257$	−4.23750	+	9.51759i	−0.264328	+	0.593691i	−0.996136	−	0.0878199i	$-0.972010\pi$
$257$	−4.23750	+	9.51759i	−0.264328	+	0.593691i	0.731808	+	0.681511i	$0.238677\pi$
$258$		0			0
$259$	−0.739434	+	0.665789i	−0.0459462	+	0.0413701i
$260$	−0.113983	+	0.0828133i	−0.00706891	+	0.00513586i
$261$		0			0
$262$	−3.86110	−	11.8833i	−0.238540	−	0.734150i
$263$	2.13055	−	3.69022i	0.131375	−	0.227549i	−0.792832	−	0.609441i	$-0.791394\pi$
$263$	2.13055	−	3.69022i	0.131375	−	0.227549i	0.924207	+	0.381892i	$0.124727\pi$
$264$		0			0
$265$	0.179843	+	0.311497i	0.0110477	+	0.0191351i
$266$	0.704867	−	0.782834i	0.0432182	−	0.0479986i
$267$		0			0
$268$	1.26766	+	12.0610i	0.0774348	+	0.736743i
$269$	−10.5223	−	3.41889i	−0.641553	−	0.208453i	−0.0298672	−	0.999554i	$-0.509508\pi$
$269$	−10.5223	−	3.41889i	−0.641553	−	0.208453i	−0.611686	+	0.791101i	$0.709508\pi$
$270$		0			0
$271$	9.34327	+	12.8599i	0.567563	+	0.781184i	0.992263	−	0.124150i	$-0.0396205\pi$
$271$	9.34327	+	12.8599i	0.567563	+	0.781184i	−0.424700	+	0.905334i	$0.639621\pi$
$272$	−5.39867	+	2.40364i	−0.327342	+	0.145742i
$273$		0			0
$274$	9.58074	−	5.53144i	0.578794	−	0.334167i
$275$	3.95746	+	16.0985i	0.238644	+	0.970776i
$276$		0			0
$277$	−2.35794	+	11.0932i	−0.141675	+	0.666527i	0.848787	+	0.528736i	$0.177334\pi$
$277$	−2.35794	+	11.0932i	−0.141675	+	0.666527i	−0.990461	+	0.137791i	$0.956000\pi$
$278$	1.56054	−	2.14790i	0.0935949	−	0.128822i
$279$		0			0
$280$	0.00742570	−	0.0228539i	0.000443770	−	0.00136578i
$281$	1.04404	+	1.15953i	0.0622823	+	0.0691715i	0.773481	−	0.633820i	$-0.218514\pi$
$281$	1.04404	+	1.15953i	0.0622823	+	0.0691715i	−0.711198	+	0.702991i	$0.751847\pi$
$282$		0			0
$283$	−26.4199	−	2.77684i	−1.57050	−	0.165066i	−0.721106	−	0.692825i	$-0.756366\pi$
$283$	−26.4199	−	2.77684i	−1.57050	−	0.165066i	−0.849394	+	0.527759i	$0.823033\pi$
$284$	−3.77528	−	3.39928i	−0.224022	−	0.201710i
$285$		0			0
$286$	−4.72976	+	2.28758i	−0.279677	+	0.135268i
$287$		−	2.37046i		−	0.139924i
$288$		0			0
$289$	−1.04038	−	0.755878i	−0.0611986	−	0.0444634i
$290$	0.153633	−	0.0161474i	0.00902161	−	0.000948210i
$291$		0			0
$292$	3.76149	+	17.6964i	0.220125	+	1.03560i
$293$	−24.0578	−	10.7112i	−1.40547	−	0.625756i	−0.442848	−	0.896597i	$-0.646032\pi$
$293$	−24.0578	−	10.7112i	−1.40547	−	0.625756i	−0.962624	+	0.270840i	$0.912698\pi$
$294$		0			0
$295$	0.109392	+	0.0232520i	0.00636905	+	0.00135378i
$296$	−9.78322			−0.568638
$297$		0			0
$298$	−7.06874			−0.409481
$299$	15.3080	+	3.25381i	0.885284	+	0.188173i
$300$		0			0
$301$	0.232647	+	0.103581i	0.0134096	+	0.00597032i
$302$	1.25508	+	5.90469i	0.0722217	+	0.339777i
$303$		0			0
$304$	−8.52130	+	0.895625i	−0.488730	+	0.0513676i
$305$	0.275310	+	0.200025i	0.0157642	+	0.0114534i
$306$		0			0
$307$		−	26.0083i		−	1.48437i	−0.670195	−	0.742185i	$-0.733789\pi$
$307$		−	26.0083i		−	1.48437i	0.670195	−	0.742185i	$-0.266211\pi$
$308$	−0.590263	+	1.10135i	−0.0336334	+	0.0627550i
$309$		0			0
$310$	−0.0984212	−	0.0886189i	−0.00558995	−	0.00503321i
$311$	13.2518	+	1.39282i	0.751439	+	0.0789794i	0.472502	−	0.881330i	$-0.343351\pi$
$311$	13.2518	+	1.39282i	0.751439	+	0.0789794i	0.278938	+	0.960309i	$0.410018\pi$
$312$		0			0
$313$	−7.52659	−	8.35913i	−0.425428	−	0.472486i	0.491880	−	0.870663i	$-0.336310\pi$
$313$	−7.52659	−	8.35913i	−0.425428	−	0.472486i	−0.917309	+	0.398177i	$0.869643\pi$
$314$	2.77158	−	8.53004i	0.156409	−	0.481378i
$315$		0			0
$316$	−2.70120	+	3.71788i	−0.151954	+	0.209147i
$317$	−2.27718	+	10.7133i	−0.127899	+	0.601718i	0.866780	+	0.498692i	$0.166186\pi$
$317$	−2.27718	+	10.7133i	−0.127899	+	0.601718i	−0.994679	+	0.103026i	$0.967147\pi$
$318$		0			0
$319$	−18.5094	−	1.35566i	−1.03633	−	0.0759022i
$320$	0.0427888	−	0.0247041i	0.00239196	−	0.00138100i
$321$		0			0
$322$	−1.05543	+	0.469909i	−0.0588170	+	0.0261870i
$323$	−15.5837	−	21.4492i	−0.867103	−	1.19346i
$324$		0			0
$325$	10.9409	+	3.55490i	0.606890	+	0.197191i
$326$	−0.660302	−	6.28235i	−0.0365707	−	0.347947i
$327$		0			0
$328$	15.5955	−	17.3206i	0.861120	−	0.956370i
$329$	−1.37324	−	2.37852i	−0.0757093	−	0.131132i
$330$		0			0
$331$	−2.11643	+	3.66576i	−0.116329	+	0.201488i	−0.918310	−	0.395861i	$-0.870446\pi$
$331$	−2.11643	+	3.66576i	−0.116329	+	0.201488i	0.801981	+	0.597349i	$0.203779\pi$
$332$	2.49676	+	7.68424i	0.137027	+	0.421727i
$333$		0			0
$334$	−4.23718	+	3.07849i	−0.231848	+	0.168447i
$335$	−0.236840	+	0.213251i	−0.0129399	+	0.0116512i
$336$		0			0
$337$	−1.08289	+	2.43221i	−0.0589887	+	0.132491i	−0.940635	−	0.339420i	$-0.889769\pi$
$337$	−1.08289	+	2.43221i	−0.0589887	+	0.132491i	0.881646	+	0.471911i	$0.156436\pi$
$338$	0.554200	−	5.27286i	0.0301445	−	0.286806i
$339$		0			0
$340$	−0.226702	−	0.130887i	−0.0122947	−	0.00709832i
$341$	9.75446	+	12.5704i	0.528233	+	0.680723i
$342$		0			0
$343$	3.27243	−	1.06328i	0.176694	−	0.0574115i
$344$	1.01844	+	2.28746i	0.0549108	+	0.123332i
$345$		0			0
$346$	−11.1897	+	2.37844i	−0.601562	+	0.127866i
$347$	16.2403	−	3.45199i	0.871827	−	0.185313i	0.249790	−	0.968300i	$-0.419638\pi$
$347$	16.2403	−	3.45199i	0.871827	−	0.185313i	0.622038	+	0.782987i	$0.286305\pi$
$348$		0			0
$349$	−5.60270	−	12.5839i	−0.299906	−	0.673599i	0.699242	−	0.714885i	$-0.253521\pi$
$349$	−5.60270	−	12.5839i	−0.299906	−	0.673599i	−0.999147	+	0.0412862i	$0.986854\pi$
$350$	−0.807679	+	0.262431i	−0.0431722	+	0.0140275i
$351$		0			0
$352$	−18.1147	+	6.52564i	−0.965517	+	0.347818i
$353$	9.54783	+	5.51244i	0.508180	+	0.293398i	0.732085	−	0.681213i	$-0.238547\pi$
$353$	9.54783	+	5.51244i	0.508180	+	0.293398i	−0.223905	+	0.974611i	$0.571881\pi$
$354$		0			0
$355$	0.0139548	−	0.132771i	0.000740641	−	0.00704673i
$356$	5.30412	−	11.9132i	0.281118	−	0.631400i
$357$		0			0
$358$	−3.60597	+	3.24683i	−0.190581	+	0.171600i
$359$	−15.3828	+	11.1763i	−0.811875	+	0.589862i	−0.914374	−	0.404871i	$-0.867316\pi$
$359$	−15.3828	+	11.1763i	−0.811875	+	0.589862i	0.102499	+	0.994733i	$0.467316\pi$
$360$		0			0
$361$	−6.00743	−	18.4890i	−0.316180	−	0.973103i
$362$	−7.26960	+	12.5913i	−0.382082	+	0.661785i
$363$		0			0
$364$	0.433553	+	0.750936i	0.0227243	+	0.0393597i
$365$	−0.318129	+	0.353318i	−0.0166516	+	0.0184935i
$366$		0			0
$367$	0.595517	+	5.66597i	0.0310857	+	0.295761i	0.999009	+	0.0445141i	$0.0141740\pi$
$367$	0.595517	+	5.66597i	0.0310857	+	0.295761i	−0.967923	+	0.251247i	$0.919159\pi$
$368$	8.93722	+	2.90388i	0.465885	+	0.151375i
$369$		0			0
$370$	−0.0654073	−	0.0900254i	−0.00340036	−	0.00468020i
$371$	2.02229	−	0.900382i	0.104992	−	0.0467455i
$372$		0			0
$373$	19.1906	−	11.0797i	0.993651	−	0.573684i	0.0872871	−	0.996183i	$-0.472180\pi$
$373$	19.1906	−	11.0797i	0.993651	−	0.573684i	0.906364	+	0.422499i	$0.138847\pi$
$374$	−7.45720	−	6.29936i	−0.385603	−	0.325732i
$375$		0			0
$376$	5.61451	−	26.4142i	0.289546	−	1.36221i
$377$	−7.56992	+	10.4191i	−0.389871	+	0.536611i
$378$		0			0
$379$	−0.117844	+	0.362687i	−0.00605325	+	0.0186300i	−0.954038	−	0.299687i	$-0.903118\pi$
$379$	−0.117844	+	0.362687i	−0.00605325	+	0.0186300i	0.947984	+	0.318317i	$0.103118\pi$
$380$	−0.253964	−	0.282055i	−0.0130281	−	0.0144691i
$381$		0			0
$382$	9.35620	+	0.983377i	0.478705	+	0.0503139i
$383$	9.41151	+	8.47416i	0.480906	+	0.433009i	0.873589	−	0.486664i	$-0.161787\pi$
$383$	9.41151	+	8.47416i	0.480906	+	0.433009i	−0.392684	+	0.919674i	$0.628453\pi$
$384$		0			0
$385$	−0.0325325	+	0.00446278i	−0.00165801	+	0.000227445i
$386$			17.2313i			0.877049i
$387$		0			0
$388$	−3.73917	−	2.71667i	−0.189828	−	0.137918i
$389$	−23.6682	+	2.48763i	−1.20003	+	0.126128i	−0.683375	−	0.730068i	$-0.739489\pi$
$389$	−23.6682	+	2.48763i	−1.20003	+	0.126128i	−0.516652	+	0.856196i	$0.672822\pi$
$390$		0			0
$391$	6.04556	+	28.4421i	0.305737	+	1.43838i
$392$	15.3857	+	6.85015i	0.777095	+	0.345985i
$393$		0			0
$394$	14.1680	+	3.01150i	0.713774	+	0.151717i
$395$	−0.120768			−0.00607647
$396$		0			0
$397$	5.00497			0.251192			0.125596	−	0.992081i	$-0.459916\pi$
$397$	5.00497			0.251192			0.125596	+	0.992081i	$0.459916\pi$
$398$	−6.98224	−	1.48412i	−0.349988	−	0.0743922i
$399$		0			0
$400$	6.31041	+	2.80958i	0.315521	+	0.140479i
$401$	0.882409	+	4.15141i	0.0440654	+	0.207311i	0.994673	−	0.103085i	$-0.0328715\pi$
$401$	0.882409	+	4.15141i	0.0440654	+	0.207311i	−0.950607	+	0.310397i	$0.899538\pi$
$402$		0			0
$403$	10.9808	−	1.15413i	0.546992	−	0.0574912i
$404$	−8.58407	−	6.23669i	−0.427073	−	0.310287i
$405$		0			0
$406$		−	0.950735i		−	0.0471842i
$407$	5.82084	+	12.0351i	0.288528	+	0.596556i
$408$		0			0
$409$	8.77325	+	7.89947i	0.433809	+	0.390604i	0.856899	−	0.515484i	$-0.172388\pi$
$409$	8.77325	+	7.89947i	0.433809	+	0.390604i	−0.423090	+	0.906088i	$0.639055\pi$
$410$	0.263651	+	0.0277108i	0.0130208	+	0.00136854i
$411$		0			0
$412$	−13.3984	−	14.8804i	−0.660091	−	0.733105i
$413$	0.212694	−	0.654604i	0.0104660	−	0.0322109i
$414$		0			0
$415$	−0.124803	+	0.171777i	−0.00612634	+	0.00843218i
$416$	−2.77795	+	13.0692i	−0.136200	+	0.640771i
$417$		0			0
$418$	−7.46057	−	12.0275i	−0.364908	−	0.588284i
$419$	18.1688	−	10.4898i	0.887604	−	0.512459i	0.0144463	−	0.999896i	$-0.495401\pi$
$419$	18.1688	−	10.4898i	0.887604	−	0.512459i	0.873158	+	0.487437i	$0.162068\pi$
$420$		0			0
$421$	−2.53945	+	1.13064i	−0.123765	+	0.0551039i	−0.467685	−	0.883895i	$-0.654912\pi$
$421$	−2.53945	+	1.13064i	−0.123765	+	0.0551039i	0.343920	+	0.938999i	$0.388245\pi$
$422$	7.58306	+	10.4372i	0.369137	+	0.508074i
$423$		0			0
$424$	20.7003	+	6.72593i	1.00529	+	0.326640i
$425$	2.23421	+	21.2571i	0.108375	+	1.03112i
$426$		0			0
$427$	1.40141	−	1.55643i	0.0678192	−	0.0753209i
$428$	1.04432	+	1.80881i	0.0504791	+	0.0874324i
$429$		0			0
$430$	−0.0142403	+	0.0246649i	−0.000686729	+	0.00118945i
$431$	−8.63060	−	26.5623i	−0.415722	−	1.27946i	−0.911604	−	0.411070i	$-0.865155\pi$
$431$	−8.63060	−	26.5623i	−0.415722	−	1.27946i	0.495882	−	0.868390i	$-0.334845\pi$
$432$		0			0
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	−0.395123	−	0.918628i	$-0.629298\pi$
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	0.751568	+	0.659656i	$0.229298\pi$
$434$	−0.605731	+	0.545402i	−0.0290760	+	0.0261801i
$435$		0			0
$436$	−4.55937	+	10.2405i	−0.218354	+	0.490432i
$437$	−4.40684	+	41.9283i	−0.210808	+	2.00570i
$438$		0			0
$439$	2.53842	+	1.46556i	0.121152	+	0.0699472i	0.559351	−	0.828931i	$-0.311050\pi$
$439$	2.53842	+	1.46556i	0.121152	+	0.0699472i	−0.438199	+	0.898878i	$0.644384\pi$
$440$	−0.267071	−	0.181426i	−0.0127321	−	0.00864913i
$441$		0			0
$442$	−6.44247	+	2.09329i	−0.306437	+	0.0995675i
$443$	14.5780	+	32.7427i	0.692622	+	1.55565i	0.825425	+	0.564512i	$0.190936\pi$
$443$	14.5780	+	32.7427i	0.692622	+	1.55565i	−0.132803	+	0.991142i	$0.542398\pi$
$444$		0			0
$445$	0.335209	−	0.0712509i	0.0158904	−	0.00337762i
$446$	6.50961	−	1.38366i	0.308239	−	0.0655183i
$447$		0			0
$448$	−0.123681	−	0.277792i	−0.00584338	−	0.0131244i
$449$	−13.5184	+	4.39241i	−0.637974	+	0.207290i	−0.610104	−	0.792321i	$-0.708872\pi$
$449$	−13.5184	+	4.39241i	−0.637974	+	0.207290i	−0.0278700	+	0.999612i	$0.508872\pi$
$450$		0			0
$451$	−30.5864	−	8.87978i	−1.44026	−	0.418132i
$452$	0.698615	+	0.403345i	0.0328601	+	0.0189718i
$453$		0			0
$454$	0.842933	−	8.01997i	0.0395608	−	0.376396i
$455$	−0.00926824	+	0.0208168i	−0.000434502	+	0.000975907i
$456$		0			0
$457$	−15.1596	+	13.6498i	−0.709137	+	0.638510i	−0.942626	−	0.333850i	$-0.891652\pi$
$457$	−15.1596	+	13.6498i	−0.709137	+	0.638510i	0.233489	+	0.972359i	$0.424986\pi$
$458$	11.4042	−	8.28561i	0.532882	−	0.387161i
$459$		0			0
$460$	0.128631	+	0.395887i	0.00599747	+	0.0184583i
$461$	0.385177	−	0.667146i	0.0179395	−	0.0310721i	−0.856916	−	0.515456i	$-0.827623\pi$
$461$	0.385177	−	0.667146i	0.0179395	−	0.0310721i	0.874856	+	0.484383i	$0.160956\pi$
$462$		0			0
$463$	−18.8974	−	32.7312i	−0.878236	−	1.52115i	−0.853275	−	0.521461i	$-0.825387\pi$
$463$	−18.8974	−	32.7312i	−0.878236	−	1.52115i	−0.0249608	−	0.999688i	$-0.507946\pi$
$464$	−5.17447	+	5.74683i	−0.240219	+	0.266790i
$465$		0			0
$466$	1.16141	+	11.0501i	0.0538015	+	0.511887i
$467$	16.7411	+	5.43950i	0.774684	+	0.251710i	0.669569	−	0.742750i	$-0.266479\pi$
$467$	16.7411	+	5.43950i	0.774684	+	0.251710i	0.105115	+	0.994460i	$0.466479\pi$
$468$		0			0
$469$	1.15290	+	1.58683i	0.0532358	+	0.0732728i
$470$	0.280601	−	0.124931i	0.0129431	−	0.00576266i
$471$		0			0
$472$	5.86083	−	3.38375i	0.269766	−	0.155750i
$473$	2.20802	−	2.61386i	0.101525	−	0.120185i
$474$		0			0
$475$	−6.44323	+	30.3130i	−0.295635	+	1.39086i
$476$	−0.946967	+	1.30339i	−0.0434042	+	0.0597407i
$477$		0			0
$478$	6.03785	−	18.5826i	0.276165	−	0.849948i
$479$	1.60983	+	1.78790i	0.0735552	+	0.0816914i	0.778799	−	0.627273i	$-0.215829\pi$
$479$	1.60983	+	1.78790i	0.0735552	+	0.0816914i	−0.705244	+	0.708965i	$0.749162\pi$
$480$		0			0
$481$	9.22626	+	0.969719i	0.420681	+	0.0442154i
$482$	7.34791	+	6.61608i	0.334688	+	0.301354i
$483$		0			0
$484$	11.9997	+	11.7419i	0.545440	+	0.533722i
$485$		−	0.121459i		−	0.00551517i
$486$		0			0
$487$	−11.8099	−	8.58039i	−0.535157	−	0.388815i	0.287126	−	0.957893i	$-0.407300\pi$
$487$	−11.8099	−	8.58039i	−0.535157	−	0.388815i	−0.822283	+	0.569078i	$0.807300\pi$
$488$	20.4798	−	2.15252i	0.927078	−	0.0974398i
$489$		0			0
$490$	0.0398282	+	0.187377i	0.00179926	+	0.00846484i
$491$	22.8773	+	10.1856i	1.03244	+	0.459672i	0.851794	−	0.523876i	$-0.175515\pi$
$491$	22.8773	+	10.1856i	1.03244	+	0.459672i	0.180646	+	0.983548i	$0.442181\pi$
$492$		0			0
$493$	−23.4057	−	4.97503i	−1.05414	−	0.224064i
$494$	−9.82158			−0.441894
$495$		0			0
$496$	6.62982			0.297688
$497$	−0.803679	−	0.170827i	−0.0360499	−	0.00766265i
$498$		0			0
$499$	20.7480	+	9.23762i	0.928810	+	0.413533i	0.814665	−	0.579931i	$-0.196921\pi$
$499$	20.7480	+	9.23762i	0.928810	+	0.413533i	0.114145	+	0.993464i	$0.463587\pi$
$500$	0.127255	+	0.598688i	0.00569102	+	0.0267742i
$501$		0			0
$502$	4.75248	−	0.499506i	0.212113	−	0.0222940i
$503$	−8.41953	−	6.11715i	−0.375408	−	0.272750i	0.384042	−	0.923316i	$-0.374532\pi$
$503$	−8.41953	−	6.11715i	−0.375408	−	0.272750i	−0.759450	+	0.650566i	$0.774532\pi$
$504$		0			0
$505$		−	0.278835i		−	0.0124080i
$506$	2.10964	+	15.3787i	0.0937848	+	0.683665i
$507$		0			0
$508$	−14.4862	−	13.0435i	−0.642722	−	0.578710i
$509$	−8.04120	−	0.845164i	−0.356420	−	0.0374613i	−0.0753734	−	0.997155i	$-0.524015\pi$
$509$	−8.04120	−	0.845164i	−0.356420	−	0.0374613i	−0.281047	+	0.959694i	$0.590682\pi$
$510$		0			0
$511$	1.95792	+	2.17449i	0.0866132	+	0.0961937i
$512$	−4.55217	+	14.0102i	−0.201180	+	0.619167i
$513$		0			0
$514$	−4.21490	+	5.80132i	−0.185911	+	0.255885i
$515$	0.109404	−	0.514704i	0.00482090	−	0.0226806i
$516$		0			0
$517$	−35.8346	+	8.80915i	−1.57600	+	0.387426i
$518$	−0.593101	+	0.342427i	−0.0260594	+	0.0150454i
$519$		0			0
$520$	−0.204678	+	0.0911283i	−0.00897570	+	0.00399624i
$521$	20.5846	+	28.3323i	0.901828	+	1.24126i	0.969881	+	0.243578i	$0.0783211\pi$
$521$	20.5846	+	28.3323i	0.901828	+	1.24126i	−0.0680535	+	0.997682i	$0.521679\pi$
$522$		0			0
$523$	41.1766	+	13.3791i	1.80052	+	0.585026i	0.999900	−	0.0141400i	$-0.00450104\pi$
$523$	41.1766	+	13.3791i	1.80052	+	0.585026i	0.800625	+	0.599166i	$0.204501\pi$
$524$	2.89613	+	27.5549i	0.126518	+	1.20374i
$525$		0			0
$526$	1.96248	−	2.17955i	0.0855681	−	0.0950330i
$527$	10.2573	+	17.7662i	0.446815	+	0.773906i
$528$		0			0
$529$	11.6189	−	20.1245i	0.505170	−	0.874980i
$530$	0.0765028	+	0.235452i	0.00332307	+	0.0102274i
$531$		0			0
$532$	−1.88977	+	1.37300i	−0.0819319	+	0.0595270i
$533$	−16.4245	+	14.7887i	−0.711424	+	0.640569i
$534$		0			0
$535$	−0.0223249	+	0.0501424i	−0.000965188	+	0.00216785i
$536$	−2.01587	+	19.1797i	−0.0870723	+	0.828438i
$537$		0			0
$538$	−6.59486	−	3.80754i	−0.284324	−	0.164155i
$539$	−0.727333	−	23.0028i	−0.0313284	−	0.990800i
$540$		0			0
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	−0.313641	−	0.949542i	$-0.601549\pi$
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	0.304386	+	0.952549i	$0.401549\pi$
$542$	4.45006	+	9.99499i	0.191146	+	0.429322i
$543$		0			0
$544$	−24.2825	+	5.16141i	−1.04110	+	0.221294i
$545$	−0.288143	+	0.0612467i	−0.0123427	+	0.00262352i
$546$		0			0
$547$	−6.69621	−	15.0399i	−0.286309	−	0.643061i	0.711938	−	0.702242i	$-0.247818\pi$
$547$	−6.69621	−	15.0399i	−0.286309	−	0.643061i	−0.998247	+	0.0591812i	$0.981151\pi$
$548$	−23.3308	+	7.58064i	−0.996643	+	0.323829i
$549$		0			0
$550$	0.360607	+	11.4046i	0.0153763	+	0.486296i
$551$	−30.0457	−	17.3469i	−1.27999	−	0.739003i
$552$		0			0
$553$	−0.0776919	+	0.739189i	−0.00330379	+	0.0314335i
$554$	−3.17496	+	7.13108i	−0.134891	+	0.302971i
$555$		0			0
$556$	−4.37506	+	3.93932i	−0.185544	+	0.167065i
$557$	21.2624	−	15.4481i	0.900919	−	0.654556i	−0.0377832	−	0.999286i	$-0.512030\pi$
$557$	21.2624	−	15.4481i	0.900919	−	0.654556i	0.938702	+	0.344730i	$0.112030\pi$
$558$		0			0
$559$	−0.733729	−	2.25818i	−0.0310334	−	0.0955110i
$560$	−0.00684126	+	0.0118494i	−0.000289096	+	0.000500729i
$561$		0			0
$562$	0.536969	+	0.930057i	0.0226507	+	0.0392321i
$563$	24.3334	−	27.0250i	1.02553	−	1.13897i	0.0353234	−	0.999376i	$-0.488754\pi$
$563$	24.3334	−	27.0250i	1.02553	−	1.13897i	0.990209	−	0.139593i	$-0.0445795\pi$
$564$		0			0
$565$	0.00221592	+	0.0210830i	9.32243e−5	+	0.000886970i
$566$	−17.3898	−	5.65030i	−0.730949	−	0.237500i
$567$		0			0
$568$	−4.74846	−	6.53570i	−0.199241	−	0.274232i
$569$	18.4816	−	8.22855i	0.774790	−	0.344959i	0.0190401	−	0.999819i	$-0.493939\pi$
$569$	18.4816	−	8.22855i	0.774790	−	0.344959i	0.755750	+	0.654860i	$0.227272\pi$
$570$		0			0
$571$	21.1312	−	12.2001i	0.884313	−	0.510558i	0.0122350	−	0.999925i	$-0.496105\pi$
$571$	21.1312	−	12.2001i	0.884313	−	0.510558i	0.872078	+	0.489367i	$0.162772\pi$
$572$	11.3135	−	2.78118i	0.473042	−	0.116287i
$573$		0			0
$574$	0.339222	−	1.59592i	0.0141589	−	0.0666123i
$575$	19.9778	−	27.4971i	0.833132	−	1.14671i
$576$		0			0
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	0.746748	+	0.665107i	$0.231614\pi$
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	−0.995072	+	0.0991553i	$0.968386\pi$
$578$	−0.592265	−	0.657777i	−0.0246350	−	0.0273599i
$579$		0			0
$580$	−0.340673	−	0.0358062i	−0.0141457	−	0.00148677i
$581$	0.971115	+	0.874395i	0.0402886	+	0.0362760i
$582$		0			0
$583$	−4.04223	−	29.4667i	−0.167412	−	1.22039i
$584$			28.7700i			1.19051i
$585$		0			0
$586$	−14.6641	−	10.6541i	−0.605769	−	0.440117i
$587$	−19.0315	+	2.00029i	−0.785513	+	0.0825608i	−0.488789	−	0.872402i	$-0.662561\pi$
$587$	−19.0315	+	2.00029i	−0.785513	+	0.0825608i	−0.296725	+	0.954963i	$0.595894\pi$
$588$		0			0
$589$	6.18411	+	29.0939i	0.254812	+	1.19880i
$590$	0.0703208	+	0.0313088i	0.00289506	+	0.00128896i
$591$		0			0
$592$	5.44876	+	1.15817i	0.223943	+	0.0476005i
$593$	−14.9885			−0.615503			−0.307751	−	0.951467i	$-0.599577\pi$
$593$	−14.9885			−0.615503			−0.307751	+	0.951467i	$0.599577\pi$
$594$		0			0
$595$	−0.0423378			−0.00173568
$596$	15.3321	+	3.25894i	0.628027	+	0.133491i
$597$		0			0
$598$	9.84047	+	4.38126i	0.402407	+	0.179163i
$599$	−6.93195	−	32.6123i	−0.283232	−	1.33250i	−0.857774	−	0.514027i	$-0.828153\pi$
$599$	−6.93195	−	32.6123i	−0.283232	−	1.33250i	0.574542	−	0.818475i	$-0.305180\pi$
$600$		0			0
$601$	42.0414	−	4.41873i	1.71490	−	0.180244i	0.804497	−	0.593957i	$-0.202435\pi$
$601$	42.0414	−	4.41873i	1.71490	−	0.180244i	0.910407	+	0.413713i	$0.135768\pi$
$602$	0.141807	+	0.103029i	0.00577962	+	0.00419914i
$603$		0			0
$604$		−	13.3859i		−	0.544664i
$605$	−0.0642829	+	0.436488i	−0.00261347	+	0.0177458i
$606$		0			0
$607$	22.9527	+	20.6667i	0.931621	+	0.838835i	0.987179	−	0.159620i	$-0.0510269\pi$
$607$	22.9527	+	20.6667i	0.931621	+	0.838835i	−0.0555574	+	0.998455i	$0.517694\pi$
$608$	−35.7964	−	3.76235i	−1.45173	−	0.152583i
$609$		0			0
$610$	0.156729	+	0.174065i	0.00634575	+	0.00704767i
$611$	−7.91306	+	24.3539i	−0.320128	+	0.985254i
$612$		0			0
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	−0.955383	−	0.295368i	$-0.904558\pi$
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	0.576142	+	0.817350i	$0.304558\pi$
$614$	3.72188	−	17.5101i	0.150203	−	0.706649i
$615$		0			0
$616$	−1.28227	+	1.51796i	−0.0516643	+	0.0611603i
$617$	2.28088	−	1.31687i	0.0918248	−	0.0530151i	−0.453384	−	0.891315i	$-0.649784\pi$
$617$	2.28088	−	1.31687i	0.0918248	−	0.0530151i	0.545209	+	0.838300i	$0.316450\pi$
$618$		0			0
$619$	18.4988	−	8.23620i	0.743530	−	0.331041i	0.000230521	−	1.00000i	$-0.499927\pi$
$619$	18.4988	−	8.23620i	0.743530	−	0.331041i	0.743299	+	0.668959i	$0.233260\pi$
$620$	0.172619	+	0.237590i	0.00693255	+	0.00954184i
$621$		0			0
$622$	8.72244	+	2.83409i	0.349738	+	0.113637i
$623$	−0.220464	−	2.09757i	−0.00883269	−	0.0840374i
$624$		0			0
$625$	16.7121	−	18.5607i	0.668485	−	0.742428i
$626$	−3.87106	−	6.70487i	−0.154719	−	0.267980i
$627$		0			0
$628$	−9.94420	+	17.2239i	−0.396817	+	0.687307i
$629$	5.32645	+	16.3931i	0.212379	+	0.653636i
$630$		0			0
$631$	−6.82846	+	4.96116i	−0.271837	+	0.197501i	−0.715349	−	0.698767i	$-0.753732\pi$
$631$	−6.82846	+	4.96116i	−0.271837	+	0.197501i	0.443512	+	0.896268i	$0.353732\pi$
$632$	−5.43088	+	4.88999i	−0.216029	+	0.194513i
$633$		0			0
$634$	−3.06622	+	6.88685i	−0.121775	+	0.273512i
$635$	0.0535461	−	0.509458i	0.00212491	−	0.0202172i
$636$		0			0
$637$	−13.8308	−	7.98521i	−0.547996	−	0.316385i
$638$	−12.2675	−	3.56146i	−0.485673	−	0.141000i
$639$		0			0
$640$	−0.410557	+	0.133398i	−0.0162287	+	0.00527302i
$641$	−13.1435	−	29.5207i	−0.519136	−	1.16600i	−0.962901	−	0.269855i	$-0.913024\pi$
$641$	−13.1435	−	29.5207i	−0.519136	−	1.16600i	0.443765	−	0.896143i	$-0.353643\pi$
$642$		0			0
$643$	−13.4757	+	2.86434i	−0.531428	+	0.112958i	−0.465807	−	0.884886i	$-0.654236\pi$
$643$	−13.4757	+	2.86434i	−0.531428	+	0.112958i	−0.0656206	+	0.997845i	$0.520903\pi$
$644$	2.50588	−	0.532641i	0.0987455	−	0.0209890i
$645$		0			0
$646$	−7.42230	−	16.6708i	−0.292027	−	0.655903i
$647$	8.11003	−	2.63511i	0.318838	−	0.103597i	−0.145226	−	0.989399i	$-0.546391\pi$
$647$	8.11003	−	2.63511i	0.318838	−	0.103597i	0.464064	+	0.885802i	$0.346391\pi$
$648$		0			0
$649$	−7.64968	−	5.19656i	−0.300276	−	0.203983i
$650$	6.85722	+	3.95902i	0.268962	+	0.155285i
$651$		0			0
$652$	−1.46419	+	13.9308i	−0.0573421	+	0.545574i
$653$	0.491333	−	1.10355i	0.0192273	−	0.0431853i	−0.903677	−	0.428216i	$-0.859142\pi$
$653$	0.491333	−	1.10355i	0.0192273	−	0.0431853i	0.922904	+	0.385030i	$0.125809\pi$
$654$		0			0
$655$	−0.541090	+	0.487200i	−0.0211421	+	0.0190365i
$656$	−10.7364	+	7.80045i	−0.419186	+	0.304556i
$657$		0			0
$658$	−0.584160	−	1.79786i	−0.0227729	−	0.0700878i
$659$	4.70527	−	8.14977i	0.183291	−	0.317470i	−0.759708	−	0.650264i	$-0.774658\pi$
$659$	4.70527	−	8.14977i	0.183291	−	0.317470i	0.942999	+	0.332794i	$0.107991\pi$
$660$		0			0
$661$	−7.55133	−	13.0793i	−0.293713	−	0.508725i	0.680972	−	0.732309i	$-0.261558\pi$
$661$	−7.55133	−	13.0793i	−0.293713	−	0.508725i	−0.974685	+	0.223584i	$0.928224\pi$
$662$	−1.94947	+	2.16510i	−0.0757682	+	0.0841491i
$663$		0			0
$664$	1.34304	+	12.7781i	0.0521199	+	0.495888i
$665$	−0.0583807	−	0.0189690i	−0.00226391	−	0.000735588i
$666$		0			0
$667$	22.3653	+	30.7832i	0.865988	+	1.19193i
$668$	10.6097	−	4.72375i	0.410503	−	0.182768i
$669$		0			0
$670$	−0.189970	+	0.109679i	−0.00733916	+	0.00423727i
$671$	−14.8331	−	23.9130i	−0.572625	−	0.923152i
$672$		0			0
$673$	−8.64889	+	40.6898i	−0.333390	+	1.56848i	0.417892	+	0.908497i	$0.362769\pi$
$673$	−8.64889	+	40.6898i	−0.333390	+	1.56848i	−0.751282	+	0.659981i	$0.770564\pi$
$674$	−1.07711	+	1.48252i	−0.0414888	+	0.0571045i
$675$		0			0
$676$	−3.63303	+	11.1813i	−0.139732	+	0.430051i
$677$	−3.02484	−	3.35943i	−0.116254	−	0.129113i	0.682208	−	0.731158i	$-0.261020\pi$
$677$	−3.02484	−	3.35943i	−0.116254	−	0.129113i	−0.798463	+	0.602044i	$0.794353\pi$
$678$		0			0
$679$	−0.743421	−	0.0781367i	−0.0285299	−	0.00299861i
$680$	−0.309355	−	0.278545i	−0.0118632	−	0.0106817i
$681$		0			0
$682$	4.76832	+	9.85890i	0.182589	+	0.377517i
$683$		−	34.7783i		−	1.33075i	−0.746507	−	0.665377i	$-0.768271\pi$
$683$		−	34.7783i		−	1.33075i	0.746507	−	0.665377i	$-0.231729\pi$
$684$		0			0
$685$	−0.521547	−	0.378926i	−0.0199273	−	0.0144780i
$686$	2.35532	−	0.247554i	0.0899266	−	0.00945166i
$687$		0			0
$688$	−0.296425	−	1.39457i	−0.0113011	−	0.0531674i
$689$	−18.8551	−	8.39484i	−0.718323	−	0.319818i
$690$		0			0
$691$	17.4927	+	3.71819i	0.665453	+	0.141446i	0.528240	−	0.849095i	$-0.322852\pi$
$691$	17.4927	+	3.71819i	0.665453	+	0.141446i	0.137213	+	0.990542i	$0.456185\pi$
$692$	25.3670			0.964308
$693$		0			0
$694$	11.4278			0.433794
$695$	−0.151331	−	0.0321663i	−0.00574030	−	0.00122014i
$696$		0			0
$697$	−37.5140	−	16.7023i	−1.42094	−	0.632644i
$698$	−1.97122	−	9.27386i	−0.0746118	−	0.351021i
$699$		0			0
$700$	1.87284	−	0.196844i	0.0707868	−	0.00744000i
$701$	−14.1345	−	10.2693i	−0.533852	−	0.387866i	0.287945	−	0.957647i	$-0.407028\pi$
$701$	−14.1345	−	10.2693i	−0.533852	−	0.387866i	−0.821797	+	0.569781i	$0.807028\pi$
$702$		0			0
$703$			24.9914i			0.942568i
$704$	−4.04770	+	0.555261i	−0.152553	+	0.0209272i
$705$		0			0
$706$	5.63923	+	5.07758i	0.212235	+	0.191097i
$707$	−1.70668	−	0.179379i	−0.0641864	−	0.00674626i
$708$		0			0
$709$	5.57954	+	6.19670i	0.209544	+	0.232722i	0.838750	−	0.544516i	$-0.183287\pi$
$709$	5.57954	+	6.19670i	0.209544	+	0.232722i	−0.629206	+	0.777238i	$0.716620\pi$
$710$	0.0283950	−	0.0873909i	0.00106565	−	0.00327972i
$711$		0			0
$712$	12.1893	−	16.7771i	0.456812	−	0.628747i
$713$	6.78237	−	31.9086i	0.254002	−	1.19498i
$714$		0			0
$715$	0.233883	+	0.197569i	0.00874673	+	0.00738867i
$716$	9.31824	−	5.37989i	0.348239	−	0.201056i
$717$		0			0
$718$	−11.9559	+	5.32310i	−0.446189	+	0.198656i
$719$	−13.8736	−	19.0953i	−0.517397	−	0.712136i	0.467748	−	0.883862i	$-0.345066\pi$
$719$	−13.8736	−	19.0953i	−0.517397	−	0.712136i	−0.985145	+	0.171726i	$0.945066\pi$
$720$		0			0
$721$	−3.08000	−	1.00075i	−0.114705	−	0.0372699i
$722$	−1.39866	−	13.3074i	−0.0520528	−	0.495249i
$723$		0			0
$724$	21.5728	−	23.9590i	0.801747	−	0.890430i
$725$	13.9849	+	24.2225i	0.519384	+	0.899600i
$726$		0			0
$727$	−0.952312	+	1.64945i	−0.0353193	+	0.0611748i	−0.883145	−	0.469101i	$-0.844578\pi$
$727$	−0.952312	+	1.64945i	−0.0353193	+	0.0611748i	0.847825	+	0.530275i	$0.177911\pi$
$728$	0.426102	+	1.31141i	0.0157924	+	0.0486039i
$729$		0			0
$730$	−0.264742	+	0.192346i	−0.00979854	+	0.00711905i
$731$	3.27847	−	2.95194i	0.121258	−	0.109182i
$732$		0			0
$733$	−7.16336	+	16.0892i	−0.264585	+	0.594267i	−0.996166	−	0.0874876i	$-0.972116\pi$
$733$	−7.16336	+	16.0892i	−0.264585	+	0.594267i	0.731581	+	0.681755i	$0.238783\pi$
$734$	−0.409889	+	3.89984i	−0.0151293	+	0.143946i
$735$		0			0
$736$	34.1869	+	19.7378i	1.26015	+	0.727545i
$737$	24.7938	−	8.93171i	0.913291	−	0.329004i
$738$		0			0
$739$	−4.54355	+	1.47629i	−0.167137	+	0.0543062i	−0.391390	−	0.920225i	$-0.628006\pi$
$739$	−4.54355	+	1.47629i	−0.167137	+	0.0543062i	0.224253	+	0.974531i	$0.428006\pi$
$740$	0.100363	+	0.225420i	0.00368943	+	0.00828660i
$741$		0			0
$742$	1.49036	−	0.316785i	0.0547127	−	0.0116295i
$743$	−1.79761	+	0.382093i	−0.0659478	+	0.0140176i	−0.240767	−	0.970583i	$-0.577399\pi$
$743$	−1.79761	+	0.382093i	−0.0659478	+	0.0140176i	0.174820	+	0.984600i	$0.444066\pi$
$744$		0			0
$745$	0.167541	+	0.376304i	0.00613825	+	0.0137867i
$746$	14.5056	−	4.71316i	0.531088	−	0.172561i
$747$		0			0
$748$	13.2704	+	17.1013i	0.485215	+	0.625287i
$749$	0.292548	+	0.168902i	0.0106895	+	0.00617156i
$750$		0			0
$751$	3.96629	−	37.7367i	0.144732	−	1.37703i	−0.645283	−	0.763944i	$-0.723260\pi$
$751$	3.96629	−	37.7367i	0.144732	−	1.37703i	0.790015	−	0.613088i	$-0.210073\pi$
$752$	−6.25400	+	14.0467i	−0.228060	+	0.512231i
$753$		0			0
$754$	−6.58746	+	5.93138i	−0.239901	+	0.216008i
$755$	0.284588	−	0.206765i	0.0103572	−	0.00752497i
$756$		0			0
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	−0.962128	−	0.272596i	$-0.912118\pi$
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	0.618150	−	0.786060i	$-0.287882\pi$
$758$	−0.131240	+	0.227315i	−0.00476687	+	0.00825646i
$759$		0			0
$760$	−0.301779	−	0.522697i	−0.0109467	−	0.0189602i
$761$	−20.6529	+	22.9373i	−0.748666	+	0.831478i	−0.990308	−	0.138888i	$-0.955647\pi$
$761$	−20.6529	+	22.9373i	−0.748666	+	0.831478i	0.241642	+	0.970365i	$0.422314\pi$
$762$		0			0
$763$	0.189509	+	1.80305i	0.00686067	+	0.0652750i
$764$	−19.8402	−	6.44648i	−0.717794	−	0.233225i
$765$		0			0
$766$	5.12362	+	7.05205i	0.185124	+	0.254801i
$767$	−5.86256	+	2.61018i	−0.211685	+	0.0942482i
$768$		0			0
$769$	−16.7276	+	9.65771i	−0.603214	+	0.348266i	−0.770305	−	0.637676i	$-0.779896\pi$
$769$	−16.7276	+	9.65771i	−0.603214	+	0.348266i	0.167091	+	0.985942i	$0.446563\pi$
$770$	−0.0225411	−	0.00165095i	−0.000812326	−	5.94960e-5i
$771$		0			0
$772$	7.94423	−	37.3746i	0.285919	−	1.34514i
$773$	−1.72928	+	2.38015i	−0.0621980	+	0.0856082i	−0.838983	−	0.544158i	$-0.816849\pi$
$773$	−1.72928	+	2.38015i	−0.0621980	+	0.0856082i	0.776785	+	0.629766i	$0.216849\pi$
$774$		0			0
$775$	7.40997	−	22.8056i	0.266174	−	0.819200i
$776$	−4.91799	−	5.46198i	−0.176545	−	0.196074i
$777$		0			0
$778$	−16.2906	−	1.71221i	−0.584047	−	0.0613859i
$779$	−44.2457	−	39.8390i	−1.58527	−	1.42738i
$780$		0			0
$781$	−5.21479	+	9.73005i	−0.186600	+	0.348169i
$782$			20.0138i			0.715693i
$783$		0			0
$784$	−7.75811	−	5.63660i	−0.277075	−	0.201307i
$785$	−0.519788	+	0.0546319i	−0.0185520	+	0.00194990i
$786$		0			0
$787$	1.67279	+	7.86987i	0.0596286	+	0.280531i	0.997853	−	0.0654976i	$-0.0208635\pi$
$787$	1.67279	+	7.86987i	0.0596286	+	0.280531i	−0.938224	+	0.346028i	$0.887530\pi$
$788$	−29.3420	−	13.0639i	−1.04527	−	0.465382i
$789$		0			0
$790$	−0.0813068	−	0.0172823i	−0.00289277	−	0.000614876i
$791$	0.130470			0.00463897
$792$		0			0
$793$	−19.5272			−0.693433
$794$	3.36960	+	0.716230i	0.119582	+	0.0254180i
$795$		0			0
$796$	14.4602	+	6.43811i	0.512530	+	0.228193i
$797$	11.4189	+	53.7217i	0.404478	+	1.90292i	0.429166	+	0.903226i	$0.358808\pi$
$797$	11.4189	+	53.7217i	0.404478	+	1.90292i	−0.0246872	+	0.999695i	$0.507859\pi$
$798$		0			0
$799$	−47.3174	+	4.97326i	−1.67397	+	0.175941i
$800$	23.4757	+	17.0561i	0.829991	+	0.603024i
$801$		0			0
$802$			2.92121i			0.103152i
$803$	35.3921	−	17.1176i	1.24896	−	0.604068i
$804$		0			0
$805$	0.0500312	+	0.0450483i	0.00176337	+	0.00158774i
$806$	7.55798	+	0.794376i	0.266218	+	0.0279807i
$807$		0			0
$808$	−11.2903	−	12.5391i	−0.397191	−	0.441125i
$809$	7.52538	−	23.1607i	0.264578	−	0.814288i	−0.727212	−	0.686413i	$-0.759184\pi$
$809$	7.52538	−	23.1607i	0.264578	−	0.814288i	0.991790	−	0.127875i	$-0.0408156\pi$
$810$		0			0
$811$	−12.2026	+	16.7955i	−0.428493	+	0.589770i	−0.967607	−	0.252463i	$-0.918759\pi$
$811$	−12.2026	+	16.7955i	−0.428493	+	0.589770i	0.539114	+	0.842233i	$0.318759\pi$
$812$	−0.438322	+	2.06214i	−0.0153821	+	0.0723671i
$813$		0			0
$814$	2.19662	+	8.93559i	0.0769915	+	0.313192i
$815$	−0.318790	+	0.184054i	−0.0111667	+	0.00644712i
$816$		0			0
$817$	5.84336	−	2.60163i	0.204433	−	0.0910195i
$818$	4.77615	+	6.57380i	0.166994	+	0.229848i
$819$		0			0
$820$	−0.559083	−	0.181657i	−0.0195240	−	0.00634374i
$821$	−2.99341	−	28.4804i	−0.104471	−	0.993974i	−0.913675	−	0.406446i	$-0.866768\pi$
$821$	−2.99341	−	28.4804i	−0.104471	−	0.993974i	0.809204	−	0.587528i	$-0.199899\pi$
$822$		0			0
$823$	1.66469	−	1.84883i	0.0580275	−	0.0644460i	−0.713432	−	0.700724i	$-0.752860\pi$
$823$	1.66469	−	1.84883i	0.0580275	−	0.0644460i	0.771460	+	0.636278i	$0.219527\pi$
$824$	−15.9210	−	27.5760i	−0.554634	−	0.960654i
$825$		0			0
$826$	0.236872	−	0.410275i	0.00824184	−	0.0142753i
$827$	−7.36490	−	22.6668i	−0.256103	−	0.788202i	−0.993610	−	0.112864i	$-0.963998\pi$
$827$	−7.36490	−	22.6668i	−0.256103	−	0.788202i	0.737508	−	0.675338i	$-0.236002\pi$
$828$		0			0
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.154386	−	0.988011i	$-0.450660\pi$
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.987362	+	0.158482i	$0.0506601\pi$
$830$	−0.108606	+	0.0977888i	−0.00376975	+	0.00339430i
$831$		0			0
$832$	−1.15316	+	2.59003i	−0.0399785	+	0.0897932i
$833$	3.10166	−	29.5104i	0.107466	−	1.02247i
$834$		0			0
$835$	0.264312	+	0.152600i	0.00914688	+	0.00528096i
$836$	10.6369	+	29.5272i	0.367884	+	1.02122i
$837$		0			0
$838$	13.7333	−	4.46221i	0.474408	−	0.154145i
$839$	−23.2748	−	52.2760i	−0.803534	−	1.80477i	−0.544136	−	0.838997i	$-0.683143\pi$
$839$	−23.2748	−	52.2760i	−0.803534	−	1.80477i	−0.259398	−	0.965771i	$-0.583524\pi$
$840$		0			0
$841$	−2.26179	+	0.480758i	−0.0779928	+	0.0165779i
$842$	−1.87149	+	0.397797i	−0.0644957	+	0.0137090i
$843$		0			0
$844$	−11.6357	−	26.1343i	−0.400519	−	0.899579i
$845$	−0.293836	+	0.0954731i	−0.0101083	+	0.00328438i
$846$		0			0
$847$	2.63028	+	0.674260i	0.0903776	+	0.0231679i
$848$	−10.7328	−	6.19657i	−0.368565	−	0.212791i
$849$		0			0
$850$	−1.53779	+	14.6311i	−0.0527456	+	0.501841i
$851$	11.1483	−	25.0395i	0.382158	−	0.858341i
$852$		0			0
$853$	22.6965	−	20.4360i	0.777114	−	0.699716i	−0.181824	−	0.983331i	$-0.558200\pi$
$853$	22.6965	−	20.4360i	0.777114	−	0.699716i	0.958938	+	0.283615i	$0.0915336\pi$
$854$	1.16623	−	0.847318i	0.0399077	−	0.0289946i
$855$		0			0
$856$	1.02637	+	3.15885i	0.0350807	+	0.107967i
$857$	3.07390	−	5.32416i	0.105003	−	0.181870i	−0.808737	−	0.588171i	$-0.799848\pi$
$857$	3.07390	−	5.32416i	0.105003	−	0.181870i	0.913739	+	0.406301i	$0.133182\pi$
$858$		0			0
$859$	13.7994	+	23.9013i	0.470830	+	0.815501i	0.999443	−	0.0333614i	$-0.0106212\pi$
$859$	13.7994	+	23.9013i	0.470830	+	0.815501i	−0.528614	+	0.848863i	$0.677288\pi$
$860$	0.0422586	−	0.0469329i	0.00144101	−	0.00160040i
$861$		0			0
$862$	−2.00940	−	19.1181i	−0.0684403	−	0.651166i
$863$	40.7061	+	13.2262i	1.38565	+	0.450226i	0.904523	−	0.426424i	$-0.140227\pi$
$863$	40.7061	+	13.2262i	1.38565	+	0.450226i	0.481129	+	0.876650i	$0.340227\pi$
$864$		0			0
$865$	0.391832	+	0.539310i	0.0133227	+	0.0183371i
$866$	5.76476	−	2.56664i	0.195895	−	0.0872179i
$867$		0			0
$868$	1.56528	−	0.903714i	0.0531290	−	0.0306741i
$869$	9.24681	+	3.77147i	0.313677	+	0.127938i
$870$		0			0
$871$	3.80221	−	17.8880i	0.128833	−	0.606111i
$872$	−10.4778	+	14.4214i	−0.354822	+	0.488371i
$873$		0			0
$874$	−8.96700	+	27.5976i	−0.303313	+	0.933503i
$875$	0.0662384	+	0.0735652i	0.00223927	+	0.00248696i
$876$		0			0
$877$	−11.1690	−	1.17391i	−0.377149	−	0.0396400i	−0.0859424	−	0.996300i	$-0.527390\pi$
$877$	−11.1690	−	1.17391i	−0.377149	−	0.0396400i	−0.291207	+	0.956660i	$0.594057\pi$
$878$	1.49926	+	1.34994i	0.0505977	+	0.0455584i
$879$		0			0
$880$	0.127267	+	0.132662i	0.00429017	+	0.00447202i
$881$		−	47.3136i		−	1.59403i	−0.603957	−	0.797017i	$-0.706410\pi$
$881$		−	47.3136i		−	1.59403i	0.603957	−	0.797017i	$-0.293590\pi$
$882$		0			0
$883$	−14.7740	−	10.7340i	−0.497186	−	0.361227i	0.310755	−	0.950490i	$-0.399418\pi$
$883$	−14.7740	−	10.7340i	−0.497186	−	0.361227i	−0.807941	+	0.589263i	$0.799418\pi$
$884$	14.9388	−	1.57013i	0.502446	−	0.0528092i
$885$		0			0
$886$	5.12904	+	24.1302i	0.172313	+	0.810671i
$887$	37.1908	+	16.5584i	1.24874	+	0.555976i	0.921285	−	0.388889i	$-0.127141\pi$
$887$	37.1908	+	16.5584i	1.24874	+	0.555976i	0.327459	+	0.944865i	$0.393808\pi$
$888$		0			0
$889$	−3.08382	−	0.655486i	−0.103428	−	0.0219843i
$890$	0.235876			0.00790658
$891$		0			0
$892$	−14.7573			−0.494110
$893$	−67.4755	−	14.3424i	−2.25798	−	0.479948i
$894$		0			0
$895$	0.258313	+	0.115008i	0.00863444	+	0.00384430i
$896$	0.552379	+	2.59874i	0.0184537	+	0.0868177i
$897$		0			0
$898$	−9.72986	+	1.02265i	−0.324690	+	0.0341263i
$899$	21.7180	+	15.7790i	0.724335	+	0.526260i
$900$		0			0
$901$		−	38.3480i		−	1.27756i
$902$	−19.3216	−	10.3553i	−0.643338	−	0.344795i
$903$		0			0
$904$	0.953321	+	0.858374i	0.0317070	+	0.0285491i
$905$	0.842600	+	0.0885609i	0.0280090	+	0.00294386i
$906$		0			0
$907$	0.790718	+	0.878181i	0.0262554	+	0.0291595i	0.756129	−	0.654422i	$-0.227088\pi$
$907$	0.790718	+	0.878181i	0.0262554	+	0.0291595i	−0.729874	+	0.683582i	$0.760421\pi$
$908$	−5.52581	+	17.0067i	−0.183380	+	0.564387i
$909$		0			0
$910$	−0.00921881	+	0.0126886i	−0.000305601	+	0.000420623i
$911$	−4.40026	+	20.7016i	−0.145787	+	0.685875i	0.843167	+	0.537652i	$0.180689\pi$
$911$	−4.40026	+	20.7016i	−0.145787	+	0.685875i	−0.988954	+	0.148223i	$0.952645\pi$
$912$		0			0
$913$	14.9202	−	9.25492i	0.493788	−	0.306293i
$914$	−12.1596	+	7.02032i	−0.402202	+	0.232212i
$915$		0			0
$916$	−28.5556	+	12.7138i	−0.943503	+	0.420075i
$917$	2.63394	+	3.62530i	0.0869803	+	0.119718i
$918$		0			0
$919$	−13.4009	−	4.35422i	−0.442055	−	0.143633i	0.0795283	−	0.996833i	$-0.474659\pi$
$919$	−13.4009	−	4.35422i	−0.442055	−	0.143633i	−0.521584	+	0.853200i	$0.674659\pi$
$920$	0.0691924	+	0.658321i	0.00228120	+	0.0217042i
$921$		0			0
$922$	0.354792	−	0.394036i	0.0116844	−	0.0129769i
$923$	3.83031	+	6.63429i	0.126076	+	0.218370i
$924$		0			0
$925$	10.0739	−	17.4485i	0.331227	−	0.573702i
$926$	−8.03871	−	24.7406i	−0.264168	−	0.813027i
$927$		0			0
$928$	−26.2812	+	19.0944i	−0.862723	+	0.626805i
$929$	25.3306	−	22.8078i	0.831070	−	0.748299i	−0.139215	−	0.990262i	$-0.544458\pi$
$929$	25.3306	−	22.8078i	0.831070	−	0.748299i	0.970285	+	0.241963i	$0.0777913\pi$
$930$		0			0
$931$	17.4988	−	39.3030i	0.573500	−	1.28810i
$932$	2.57539	−	24.5032i	0.0843596	−	0.802628i
$933$		0			0
$934$	10.4925	+	6.05786i	0.343326	+	0.198219i
$935$	−0.158598	+	0.546290i	−0.00518669	+	0.0178656i
$936$		0			0
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	−0.202271	−	0.979330i	$-0.564832\pi$
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	0.411995	+	0.911186i	$0.364832\pi$
$938$	0.549107	+	1.23332i	0.0179290	+	0.0402692i
$939$		0			0
$940$	−0.666220	+	0.141610i	−0.0217297	+	0.00461879i
$941$	−32.5702	+	6.92302i	−1.06176	+	0.225684i	−0.705505	−	0.708705i	$-0.749280\pi$
$941$	−32.5702	+	6.92302i	−1.06176	+	0.225684i	−0.356255	+	0.934389i	$0.615946\pi$
$942$		0			0
$943$	26.5592	+	59.6530i	0.864888	+	1.94257i
$944$	−3.66476	+	1.19075i	−0.119278	+	0.0387557i
$945$		0			0
$946$	1.86060	−	1.44381i	0.0604934	−	0.0469422i
$947$	0.650586	+	0.375616i	0.0211412	+	0.0122059i	0.510533	−	0.859858i	$-0.329448\pi$
$947$	0.650586	+	0.375616i	0.0211412	+	0.0122059i	−0.489392	+	0.872064i	$0.662781\pi$
$948$		0			0
$949$	2.85170	−	27.1321i	0.0925700	−	0.880745i
$950$	−8.67581	+	19.4862i	−0.281480	+	0.632215i
$951$		0			0
$952$	−1.90392	+	1.71430i	−0.0617063	+	0.0555606i
$953$	−3.76491	+	2.73537i	−0.121957	+	0.0886073i	−0.647092	−	0.762412i	$-0.724015\pi$
$953$	−3.76491	+	2.73537i	−0.121957	+	0.0886073i	0.525134	+	0.851019i	$0.324015\pi$
$954$		0			0
$955$	−0.169408	−	0.521385i	−0.00548192	−	0.0168716i
$956$	−21.6633	+	37.5220i	−0.700641	+	1.21355i
$957$		0			0
$958$	0.827966	+	1.43408i	0.0267504	+	0.0463330i
$959$	−2.65483	+	2.94849i	−0.0857290	+	0.0952117i
$960$		0			0
$961$	0.834675	+	7.94141i	0.0269250	+	0.256174i
$962$	6.07281	+	1.97318i	0.195795	+	0.0636177i
$963$		0			0
$964$	−12.8874	−	17.7379i	−0.415074	−	0.571300i
$965$	0.917307	−	0.408411i	0.0295292	−	0.0131472i
$966$		0			0
$967$	18.8385	−	10.8764i	0.605807	−	0.349763i	−0.165516	−	0.986207i	$-0.552929\pi$
$967$	18.8385	−	10.8764i	0.605807	−	0.349763i	0.771323	+	0.636444i	$0.219596\pi$
$968$	14.7830	+	22.2316i	0.475144	+	0.714551i
$969$		0			0
$970$	0.0173812	−	0.0817723i	0.000558078	−	0.00262555i
$971$	3.45215	−	4.75147i	0.110785	−	0.152482i	−0.750024	−	0.661410i	$-0.769958\pi$
$971$	3.45215	−	4.75147i	0.110785	−	0.152482i	0.860809	+	0.508928i	$0.169958\pi$
$972$		0			0
$973$	−0.294236	+	0.905565i	−0.00943277	+	0.0290311i
$974$	−6.72313	−	7.46679i	−0.215423	−	0.239251i
$975$		0			0
$976$	−11.6611	−	1.22563i	−0.373261	−	0.0392313i
$977$	0.683688	+	0.615595i	0.0218731	+	0.0196946i	0.679995	−	0.733217i	$-0.261982\pi$
$977$	0.683688	+	0.615595i	0.0218731	+	0.0196946i	−0.658122	+	0.752912i	$0.728649\pi$
$978$		0			0
$979$	−27.8911	−	5.01284i	−0.891403	−	0.160211i
$980$		−	0.424783i		−	0.0135692i
$981$		0			0
$982$	13.9446	+	10.1313i	0.444989	+	0.323304i
$983$	46.3804	−	4.87478i	1.47931	−	0.155481i	0.669778	−	0.742562i	$-0.266389\pi$
$983$	46.3804	−	4.87478i	1.47931	−	0.155481i	0.809529	+	0.587080i	$0.199723\pi$
$984$		0			0
$985$	−0.175489	−	0.825612i	−0.00559155	−	0.0263062i
$986$	−15.0459	−	6.69888i	−0.479160	−	0.213336i
$987$		0			0
$988$	21.3030	+	4.52809i	0.677739	+	0.144058i
$989$	−7.01515			−0.223069
$990$		0			0
$991$	6.21090			0.197296			0.0986478	−	0.995122i	$-0.468548\pi$
$991$	6.21090			0.197296			0.0986478	+	0.995122i	$0.468548\pi$
$992$	27.2420	+	5.79046i	0.864934	+	0.183847i
$993$		0			0
$994$	−0.516631	−	0.230019i	−0.0163865	−	0.00729576i
$995$	0.0864841	+	0.406876i	0.00274173	+	0.0128988i
$996$		0			0
$997$	28.4103	−	2.98604i	0.899763	−	0.0945689i	0.356659	−	0.934235i	$-0.383916\pi$
$997$	28.4103	−	2.98604i	0.899763	−	0.0945689i	0.543104	+	0.839666i	$0.317249\pi$
$998$	12.6467	+	9.18836i	0.400324	+	0.290852i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.u.c.512.3		32
3.2	odd	2	inner	891.2.u.c.512.2		32
9.2	odd	6		99.2.j.a.17.3	yes	16
9.4	even	3	inner	891.2.u.c.215.2		32
9.5	odd	6	inner	891.2.u.c.215.3		32
9.7	even	3		99.2.j.a.17.2	✓	16
11.2	odd	10	inner	891.2.u.c.431.3		32
33.2	even	10	inner	891.2.u.c.431.2		32
36.7	odd	6		1584.2.cd.c.17.3		16
36.11	even	6		1584.2.cd.c.17.2		16
99.2	even	30		99.2.j.a.35.2	yes	16
99.13	odd	30	inner	891.2.u.c.134.2		32
99.25	even	15		1089.2.d.g.1088.6		16
99.47	odd	30		1089.2.d.g.1088.11		16
99.52	odd	30		1089.2.d.g.1088.12		16
99.68	even	30	inner	891.2.u.c.134.3		32
99.74	even	30		1089.2.d.g.1088.5		16
99.79	odd	30		99.2.j.a.35.3	yes	16
396.79	even	30		1584.2.cd.c.1025.2		16
396.299	odd	30		1584.2.cd.c.1025.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.2	✓	16	9.7	even	3
99.2.j.a.17.3	yes	16	9.2	odd	6
99.2.j.a.35.2	yes	16	99.2	even	30
99.2.j.a.35.3	yes	16	99.79	odd	30
891.2.u.c.134.2		32	99.13	odd	30	inner
891.2.u.c.134.3		32	99.68	even	30	inner
891.2.u.c.215.2		32	9.4	even	3	inner
891.2.u.c.215.3		32	9.5	odd	6	inner
891.2.u.c.431.2		32	33.2	even	10	inner
891.2.u.c.431.3		32	11.2	odd	10	inner
891.2.u.c.512.2		32	3.2	odd	2	inner
891.2.u.c.512.3		32	1.1	even	1	trivial
1089.2.d.g.1088.5		16	99.74	even	30
1089.2.d.g.1088.6		16	99.25	even	15
1089.2.d.g.1088.11		16	99.47	odd	30
1089.2.d.g.1088.12		16	99.52	odd	30
1584.2.cd.c.17.2		16	36.11	even	6
1584.2.cd.c.17.3		16	36.7	odd	6
1584.2.cd.c.1025.2		16	396.79	even	30
1584.2.cd.c.1025.3		16	396.299	odd	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.673250 + 0.143104i) q^{2} +(-1.39430 - 0.620784i) q^{4} +(-0.00833908 - 0.0392323i) q^{5} +(-0.245496 + 0.0258027i) q^{7} +(-1.96356 - 1.42661i) q^{8} -0.0276065i q^{10} +(-0.586694 + 3.26432i) q^{11} +(1.71036 + 1.54002i) q^{13} +(-0.168973 - 0.0177597i) q^{14} +(0.924716 + 1.02700i) q^{16} +(-1.32142 + 4.06692i) q^{17} +(-3.64429 + 5.01593i) q^{19} +(-0.0127276 + 0.0598785i) q^{20} +(-0.862129 + 2.11375i) q^{22} +(5.88883 - 3.39992i) q^{23} +(4.56626 - 2.03303i) q^{25} +(0.931121 + 1.28158i) q^{26} +(0.358314 + 0.116423i) q^{28} +(0.584914 + 5.56509i) q^{29} +(3.21007 - 3.56515i) q^{31} +(2.90269 + 5.02760i) q^{32} +(-1.47164 + 2.54895i) q^{34} +(0.00305951 + 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(-3.17132 + 2.85547i) q^{38} +(-0.0395948 + 0.0889314i) q^{40} +(-1.00378 + 9.55032i) q^{41} +(-0.893447 - 0.515832i) q^{43} +(2.84447 - 4.18724i) q^{44} +(4.45120 - 1.44628i) q^{46} +(4.52544 + 10.1643i) q^{47} +(-6.78743 + 1.44271i) q^{49} +(3.36517 - 0.715289i) q^{50} +(-1.42875 - 3.20902i) q^{52} +(-8.52885 + 2.77119i) q^{53} +(0.132959 - 0.00420408i) q^{55} +(0.518855 + 0.299561i) q^{56} +(-0.402591 + 3.83040i) q^{58} +(-1.13411 + 2.54726i) q^{59} +(-6.30521 + 5.67724i) q^{61} +(2.67137 - 1.94086i) q^{62} +(0.380665 + 1.17156i) q^{64} +(0.0461556 - 0.0799438i) q^{65} +(-3.97294 - 6.88133i) q^{67} +(4.36714 - 4.85020i) q^{68} +(0.000712321 + 0.00677728i) q^{70} +(3.16559 + 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(2.53454 - 1.12845i) q^{74} +(8.19506 - 4.73142i) q^{76} +(0.0598028 - 0.816515i) q^{77} +(0.626023 - 2.94520i) q^{79} +(0.0325803 - 0.0448429i) q^{80} +(-2.04248 + 6.28611i) q^{82} +(-3.54224 - 3.93406i) q^{83} +(0.170574 + 0.0179280i) q^{85} +(-0.527696 - 0.475140i) q^{86} +(5.80891 - 5.57270i) q^{88} +8.54422i q^{89} +(-0.459624 - 0.333936i) q^{91} +(-10.3214 + 1.08483i) q^{92} +(1.59220 + 7.49072i) q^{94} +(0.227176 + 0.101145i) q^{95} +(2.96207 + 0.629607i) q^{97} -4.77610 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) \) 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

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Database

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