LMFDB - Embedded newform 891.2.u.c.215.3

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			215.3
Character	$\chi$	$=$	891.215
Dual form			891.2.u.c.431.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.460557 - 0.511500i) q^{2} +(0.159537 + 1.51789i) q^{4} +(0.0298066 - 0.0268380i) q^{5} +(0.100402 - 0.225507i) q^{7} +(1.96356 + 1.42661i) q^{8} -0.0276065i q^{10} +(2.53364 + 2.14025i) q^{11} +(0.478513 - 2.25123i) q^{13} +(-0.0691059 - 0.155214i) q^{14} +(-1.35177 + 0.287327i) q^{16} +(1.32142 - 4.06692i) q^{17} +(-3.64429 + 5.01593i) q^{19} +(0.0454925 + 0.0409616i) q^{20} +(2.26162 - 0.310248i) q^{22} +(5.88883 + 3.39992i) q^{23} +(-0.522474 + 4.97101i) q^{25} +(-0.931121 - 1.28158i) q^{26} +(0.358314 + 0.116423i) q^{28} +(5.11196 + 2.27599i) q^{29} +(-4.69255 - 0.997431i) q^{31} +(-2.90269 + 5.02760i) q^{32} +(-1.47164 - 2.54895i) q^{34} +(-0.00305951 - 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(0.887248 + 4.17418i) q^{38} +(0.0968143 - 0.0101756i) q^{40} +(-8.77271 + 3.90586i) q^{41} +(0.893447 - 0.515832i) q^{43} +(-2.84447 + 4.18724i) q^{44} +(4.45120 - 1.44628i) q^{46} +(11.0653 + 1.16301i) q^{47} +(4.64314 + 5.15673i) q^{49} +(2.30204 + 2.55668i) q^{50} +(3.49347 + 0.367178i) q^{52} +(8.52885 - 2.77119i) q^{53} +(0.132959 - 0.00420408i) q^{55} +(0.518855 - 0.299561i) q^{56} +(3.51852 - 1.56655i) q^{58} +(-2.77304 + 0.291459i) q^{59} +(-1.76403 - 8.29909i) q^{61} +(-2.67137 + 1.94086i) q^{62} +(0.380665 + 1.17156i) q^{64} +(-0.0461556 - 0.0799438i) q^{65} +(-3.97294 + 6.88133i) q^{67} +(6.38397 + 1.35695i) q^{68} +(-0.00622546 - 0.00277175i) q^{70} +(-3.16559 - 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(0.290003 - 2.75920i) q^{74} +(-8.19506 - 4.73142i) q^{76} +(0.737025 - 0.356467i) q^{77} +(2.23761 + 2.01475i) q^{79} +(-0.0325803 + 0.0448429i) q^{80} +(-2.04248 + 6.28611i) q^{82} +(-5.17811 + 1.10064i) q^{83} +(-0.0697608 - 0.156685i) q^{85} +(0.147635 - 0.694568i) q^{86} +(1.92164 + 7.81702i) q^{88} -8.54422i q^{89} +(-0.459624 - 0.333936i) q^{91} +(-4.22123 + 9.48104i) q^{92} +(5.69106 - 5.12425i) q^{94} +(0.0259937 + 0.247313i) q^{95} +(-2.02629 + 2.25042i) q^{97} +4.77610 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.460557	−	0.511500i	0.325663	−	0.361685i	−0.557974	−	0.829859i	$-0.688421\pi$
$2$	0.460557	−	0.511500i	0.325663	−	0.361685i	0.883637	+	0.468173i	$0.155088\pi$
$3$		0			0
$3$		0			0
$4$	0.159537	+	1.51789i	0.0797686	+	0.758947i
$5$	0.0298066	−	0.0268380i	0.0133299	−	0.0120023i	−0.662439	−	0.749116i	$-0.730479\pi$
$5$	0.0298066	−	0.0268380i	0.0133299	−	0.0120023i	0.675769	+	0.737114i	$0.263812\pi$
$6$		0			0
$7$	0.100402	−	0.225507i	0.0379485	−	0.0852336i	−0.893577	−	0.448911i	$-0.851812\pi$
$7$	0.100402	−	0.225507i	0.0379485	−	0.0852336i	0.931525	+	0.363677i	$0.118479\pi$
$8$	1.96356	+	1.42661i	0.694222	+	0.504382i
$9$		0			0
$10$		−	0.0276065i		−	0.00872994i
$11$	2.53364	+	2.14025i	0.763921	+	0.645310i
$11$	2.53364	+	2.14025i	0.763921	+	0.645310i
$12$		0			0
$13$	0.478513	−	2.25123i	0.132716	−	0.624378i	−0.860632	−	0.509227i	$-0.829931\pi$
$13$	0.478513	−	2.25123i	0.132716	−	0.624378i	0.993348	−	0.115151i	$-0.0367353\pi$
$14$	−0.0691059	−	0.155214i	−0.0184693	−	0.0414828i
$15$		0			0
$16$	−1.35177	+	0.287327i	−0.337942	+	0.0718317i
$17$	1.32142	−	4.06692i	0.320492	−	0.986372i	−0.652943	−	0.757407i	$-0.726466\pi$
$17$	1.32142	−	4.06692i	0.320492	−	0.986372i	0.973435	−	0.228965i	$-0.0735342\pi$
$18$		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	$0.948155\pi$
$20$	0.0454925	+	0.0409616i	0.0101724	+	0.00915930i
$21$		0			0
$22$	2.26162	−	0.310248i	0.482180	−	0.0661451i
$23$	5.88883	+	3.39992i	1.22791	+	0.708932i	0.966592	−	0.256321i	$-0.0825105\pi$
$23$	5.88883	+	3.39992i	1.22791	+	0.708932i	0.261315	+	0.965254i	$0.415844\pi$
$24$		0			0
$25$	−0.522474	+	4.97101i	−0.104495	+	0.994202i
$26$	−0.931121	−	1.28158i	−0.182608	−	0.251338i
$27$		0			0
$28$	0.358314	+	0.116423i	0.0677149	+	0.0220019i
$29$	5.11196	+	2.27599i	0.949268	+	0.422641i	0.822166	−	0.569248i	$-0.192766\pi$
$29$	5.11196	+	2.27599i	0.949268	+	0.422641i	0.127102	+	0.991890i	$0.459432\pi$
$30$		0			0
$31$	−4.69255	−	0.997431i	−0.842806	−	0.179144i	−0.233775	−	0.972291i	$-0.575108\pi$
$31$	−4.69255	−	0.997431i	−0.842806	−	0.179144i	−0.609031	+	0.793147i	$0.708441\pi$
$32$	−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	$0.192502\pi$
$38$	0.887248	+	4.17418i	0.143931	+	0.677141i
$39$		0			0
$40$	0.0968143	−	0.0101756i	0.0153077	−	0.00160890i
$41$	−8.77271	+	3.90586i	−1.37007	+	0.609993i	−0.954128	−	0.299399i	$-0.903214\pi$
$41$	−8.77271	+	3.90586i	−1.37007	+	0.609993i	−0.415939	+	0.909392i	$0.636547\pi$
$42$		0			0
$43$	0.893447	−	0.515832i	0.136249	−	0.0786636i	−0.430326	−	0.902674i	$-0.641601\pi$
$43$	0.893447	−	0.515832i	0.136249	−	0.0786636i	0.566575	+	0.824010i	$0.308268\pi$
$44$	−2.84447	+	4.18724i	−0.428820	+	0.631251i
$45$		0			0
$46$	4.45120	−	1.44628i	0.656294	−	0.213243i
$47$	11.0653	+	1.16301i	1.61403	+	0.169642i	0.868104	−	0.496382i	$-0.165339\pi$
$47$	11.0653	+	1.16301i	1.61403	+	0.169642i	0.745930	+	0.666024i	$0.232005\pi$
$48$		0			0
$49$	4.64314	+	5.15673i	0.663306	+	0.736676i
$50$	2.30204	+	2.55668i	0.325558	+	0.361569i
$51$		0			0
$52$	3.49347	+	0.367178i	0.484457	+	0.0509184i
$53$	8.52885	−	2.77119i	1.17153	−	0.380652i	0.342314	−	0.939585i	$-0.388789\pi$
$53$	8.52885	−	2.77119i	1.17153	−	0.380652i	0.829213	+	0.558933i	$0.188789\pi$
$54$		0			0
$55$	0.132959	−	0.00420408i	0.0179282	−	0.000566878i
$56$	0.518855	−	0.299561i	0.0693350	−	0.0400306i
$57$		0			0
$58$	3.51852	−	1.56655i	0.462004	−	0.205698i
$59$	−2.77304	+	0.291459i	−0.361020	+	0.0379447i	−0.283302	−	0.959031i	$-0.591430\pi$
$59$	−2.77304	+	0.291459i	−0.361020	+	0.0379447i	−0.0777175	+	0.996975i	$0.524763\pi$
$60$		0			0
$61$	−1.76403	−	8.29909i	−0.225860	−	1.06259i	−0.934209	−	0.356727i	$-0.883893\pi$
$61$	−1.76403	−	8.29909i	−0.225860	−	1.06259i	0.708348	−	0.705863i	$-0.249441\pi$
$62$	−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	−0.999859	−	0.0168095i	$-0.994649\pi$
$67$	−3.97294	+	6.88133i	−0.485372	+	0.840689i	0.514487	+	0.857498i	$0.327982\pi$
$68$	6.38397	+	1.35695i	0.774170	+	0.164555i
$69$		0			0
$70$	−0.00622546	−	0.00277175i	−0.000744084	−	0.000331288i
$71$	−3.16559	−	1.02856i	−0.375687	−	0.122068i	0.115086	−	0.993355i	$-0.463286\pi$
$71$	−3.16559	−	1.02856i	−0.375687	−	0.122068i	−0.490773	+	0.871288i	$0.663286\pi$
$72$		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	$-0.444014\pi$
$74$	0.290003	−	2.75920i	0.0337122	−	0.320750i
$75$		0			0
$76$	−8.19506	−	4.73142i	−0.940038	−	0.542731i
$77$	0.737025	−	0.356467i	0.0839917	−	0.0406232i
$78$		0			0
$79$	2.23761	+	2.01475i	0.251751	+	0.226678i	0.785337	−	0.619068i	$-0.212489\pi$
$79$	2.23761	+	2.01475i	0.251751	+	0.226678i	−0.533587	+	0.845745i	$0.679156\pi$
$80$	−0.0325803	+	0.0448429i	−0.00364259	+	0.00501359i
$81$		0			0
$82$	−2.04248	+	6.28611i	−0.225554	+	0.694185i
$83$	−5.17811	+	1.10064i	−0.568372	+	0.120811i	−0.483129	−	0.875549i	$-0.660500\pi$
$83$	−5.17811	+	1.10064i	−0.568372	+	0.120811i	−0.0852426	+	0.996360i	$0.527167\pi$
$84$		0			0
$85$	−0.0697608	−	0.156685i	−0.00756662	−	0.0169949i
$86$	0.147635	−	0.694568i	0.0159199	−	0.0748972i
$87$		0			0
$88$	1.92164	+	7.81702i	0.204848	+	0.833297i
$89$		−	8.54422i		−	0.905686i	−0.891590	−	0.452843i	$-0.850410\pi$
$89$		−	8.54422i		−	0.905686i	0.891590	−	0.452843i	$-0.149590\pi$
$90$		0			0
$91$	−0.459624	−	0.333936i	−0.0481817	−	0.0350060i
$92$	−4.22123	+	9.48104i	−0.440094	+	0.988467i
$93$		0			0
$94$	5.69106	−	5.12425i	0.586988	−	0.528526i
$95$	0.0259937	+	0.247313i	0.00266690	+	0.0253738i
$96$		0			0
$97$	−2.02629	+	2.25042i	−0.205738	+	0.228496i	−0.837180	−	0.546928i	$-0.815797\pi$
$97$	−2.02629	+	2.25042i	−0.205738	+	0.228496i	0.631441	+	0.775424i	$0.282464\pi$
$98$	4.77610			0.482459
$99$		0			0
$100$	−7.62882			−0.762882
$101$	4.65178	−	5.16633i	0.462869	−	0.514069i	−0.465844	−	0.884867i	$-0.654249\pi$
$101$	4.65178	−	5.16633i	0.462869	−	0.514069i	0.928713	+	0.370798i	$0.120916\pi$
$102$		0			0
$103$	−1.37135	−	13.0475i	−0.135123	−	1.28561i	−0.826425	−	0.563046i	$-0.809629\pi$
$103$	−1.37135	−	13.0475i	−0.135123	−	1.28561i	0.691302	−	0.722566i	$-0.257037\pi$
$104$	4.15121	−	3.73776i	0.407059	−	0.366518i
$105$		0			0
$106$	2.51055	−	5.63879i	0.243846	−	0.547688i
$107$	1.10712	+	0.804368i	0.107029	+	0.0777612i	0.640012	−	0.768365i	$-0.278929\pi$
$107$	1.10712	+	0.804368i	0.107029	+	0.0777612i	−0.532983	+	0.846126i	$0.678929\pi$
$108$		0			0
$109$		−	7.34454i		−	0.703480i	−0.936098	−	0.351740i	$-0.885590\pi$
$109$		−	7.34454i		−	0.703480i	0.936098	−	0.351740i	$-0.114410\pi$
$110$	0.0590849	−	0.0699448i	0.00563352	−	0.00666898i
$111$		0			0
$112$	−0.0709261	+	0.333681i	−0.00670189	+	0.0315299i
$113$	−0.214978	−	0.482848i	−0.0202234	−	0.0454225i	0.903151	−	0.429322i	$-0.141248\pi$
$113$	−0.214978	−	0.482848i	−0.0202234	−	0.0454225i	−0.923375	+	0.383900i	$0.874581\pi$
$114$		0			0
$115$	0.266773	−	0.0567044i	0.0248767	−	0.00528771i
$116$	−2.63917	+	8.12253i	−0.245041	+	0.754158i
$117$		0			0
$118$	−1.12806	+	1.55265i	−0.103847	+	0.142933i
$119$	−0.784445	−	0.706317i	−0.0719099	−	0.0647480i
$120$		0			0
$121$	1.83864	+	10.8452i	0.167149	+	0.985932i
$122$	−5.05742	−	2.91990i	−0.457877	−	0.264355i
$123$		0			0
$124$	0.765360	−	7.28192i	0.0687314	−	0.653935i
$125$	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	$0.408235\pi$
$128$	−9.83238	−	4.37766i	−0.869067	−	0.386934i
$129$		0			0
$130$	−0.0621485	−	0.0132101i	−0.00545078	−	0.00115860i
$131$	9.07668	−	15.7213i	0.793033	−	1.37357i	−0.131047	−	0.991376i	$-0.541834\pi$
$131$	9.07668	−	15.7213i	0.793033	−	1.37357i	0.924081	−	0.382198i	$-0.124833\pi$
$132$		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
$137$	−3.34176	−	15.7217i	−0.285506	−	1.34320i	−0.853897	−	0.520441i	$-0.825767\pi$
$137$	−3.34176	−	15.7217i	−0.285506	−	1.34320i	0.568392	−	0.822758i	$-0.307566\pi$
$138$		0			0
$139$	−3.83617	+	0.403198i	−0.325380	+	0.0341988i	−0.265810	−	0.964025i	$-0.585639\pi$
$139$	−3.83617	+	0.403198i	−0.325380	+	0.0341988i	−0.0595696	+	0.998224i	$0.518973\pi$
$140$	0.0138047	−	0.00614624i	0.00116671	−	0.000519452i
$141$		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
$146$	−8.11410	−	0.852826i	−0.671528	−	0.0705804i
$147$		0			0
$148$	4.11656	+	4.57190i	0.338379	+	0.375808i
$149$	−6.87196	−	7.63209i	−0.562973	−	0.625245i	0.392703	−	0.919665i	$-0.371540\pi$
$149$	−6.87196	−	7.63209i	−0.562973	−	0.625245i	−0.955676	+	0.294420i	$0.904873\pi$
$150$		0			0
$151$	−8.72237	−	0.916758i	−0.709817	−	0.0746047i	−0.257262	−	0.966342i	$-0.582820\pi$
$151$	−8.72237	−	0.916758i	−0.709817	−	0.0746047i	−0.452554	+	0.891737i	$0.649487\pi$
$152$	−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
$157$	−11.9043	+	5.30012i	−0.950064	+	0.422996i	−0.822456	−	0.568829i	$-0.807397\pi$
$157$	−11.9043	+	5.30012i	−0.950064	+	0.422996i	−0.127608	+	0.991825i	$0.540730\pi$
$158$	2.06109	−	0.216630i	0.163972	−	0.0172341i
$159$		0			0
$160$	0.0484115	+	0.227758i	0.00382726	+	0.0180059i
$161$	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
$167$	−7.44305	−	1.58207i	−0.575961	−	0.122424i	−0.0892837	−	0.996006i	$-0.528458\pi$
$167$	−7.44305	−	1.58207i	−0.575961	−	0.122424i	−0.486677	+	0.873582i	$0.661791\pi$
$168$		0			0
$169$	7.03704	+	3.13309i	0.541311	+	0.241007i
$170$	−0.112273	−	0.0364798i	−0.00861097	−	0.00279787i
$171$		0			0
$172$	0.925516	+	1.27386i	0.0705699	+	0.0971312i
$173$	−1.73731	+	16.5294i	−0.132085	+	1.25670i	0.704832	+	0.709374i	$0.251022\pi$
$173$	−1.73731	+	16.5294i	−0.132085	+	1.25670i	−0.836917	+	0.547330i	$0.815644\pi$
$174$		0			0
$175$	1.06854	+	0.616922i	0.0807740	+	0.0466349i
$176$	−4.03984	−	2.16514i	−0.304514	−	0.163204i
$177$		0			0
$178$	−4.37037	−	3.93510i	−0.327573	−	0.294948i
$179$	4.14376	−	5.70340i	0.309719	−	0.426292i	−0.625574	−	0.780165i	$-0.715135\pi$
$179$	4.14376	−	5.70340i	0.309719	−	0.426292i	0.935294	+	0.353872i	$0.115135\pi$
$180$		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	$0.812636\pi$
$182$	−0.382491	+	0.0813010i	−0.0283521	+	0.00602643i
$183$		0			0
$184$	6.71271	+	15.0770i	0.494868	+	1.11149i
$185$	0.0336135	−	0.158139i	0.00247132	−	0.0116266i
$186$		0			0
$187$	12.0522	−	7.47592i	0.881347	−	0.546693i
$188$			16.9814i			1.23850i
$189$		0			0
$190$	0.138472	+	0.100606i	0.0100458	+	0.00729873i
$191$	5.55938	−	12.4866i	0.402263	−	0.903497i	−0.592902	−	0.805275i	$-0.702018\pi$
$191$	5.55938	−	12.4866i	0.402263	−	0.903497i	0.995165	−	0.0982221i	$-0.0313155\pi$
$192$		0			0
$193$	18.6045	−	16.7516i	1.33918	−	1.20581i	0.379345	−	0.925255i	$-0.376149\pi$
$193$	18.6045	−	16.7516i	1.33918	−	1.20581i	0.959839	−	0.280552i	$-0.0905174\pi$
$194$	0.217870	+	2.07289i	0.0156421	+	0.148825i
$195$		0			0
$196$	−7.08662	+	7.87049i	−0.506187	+	0.562178i
$197$	−21.0442			−1.49934			−0.749668	−	0.661814i	$-0.769787\pi$
$197$	−21.0442			−1.49934			−0.749668	+	0.661814i	$0.769787\pi$
$198$		0			0
$199$	−10.3709			−0.735176			−0.367588	−	0.929989i	$-0.619816\pi$
$199$	−10.3709			−0.735176			−0.367588	+	0.929989i	$0.619816\pi$
$200$	−8.11759	+	9.01550i	−0.574000	+	0.637492i
$201$		0			0
$202$	−0.500167	−	4.75877i	−0.0351916	−	0.334826i
$203$	1.02650	−	0.924269i	0.0720465	−	0.0648710i
$204$		0			0
$205$	−0.156659	+	0.351862i	−0.0109416	+	0.0245751i
$206$	−7.30540	−	5.30768i	−0.508991	−	0.369804i
$207$		0			0
$208$			3.18062i			0.220537i
$209$	−19.9687	+	4.90886i	−1.38126	+	0.339553i
$210$		0			0
$211$	3.89702	−	18.3340i	0.268282	−	1.26217i	−0.613192	−	0.789934i	$-0.710115\pi$
$211$	3.89702	−	18.3340i	0.268282	−	1.26217i	0.881474	−	0.472233i	$-0.156552\pi$
$212$	5.56704	+	12.5038i	0.382346	+	0.858763i
$213$		0			0
$214$	0.921325	−	0.195834i	0.0629805	−	0.0133869i
$215$	0.0127867	−	0.0393535i	0.000872048	−	0.00268389i
$216$		0			0
$217$	−0.696069	+	0.958057i	−0.0472523	+	0.0650372i
$218$	−3.75673	−	3.38258i	−0.254438	−	0.229097i
$219$		0			0
$220$	0.0275933	+	0.201147i	0.00186034	+	0.0135613i
$221$	−8.52324	−	4.92090i	−0.573335	−	0.331015i
$222$		0			0
$223$	−1.01068	+	9.61597i	−0.0676801	+	0.643933i	0.907123	+	0.420866i	$0.138274\pi$
$223$	−1.01068	+	9.61597i	−0.0676801	+	0.643933i	−0.974803	+	0.223067i	$0.928393\pi$
$224$	0.842323	+	1.15936i	0.0562801	+	0.0774629i
$225$		0			0
$226$	−0.345986	−	0.112418i	−0.0230146	−	0.00747791i
$227$	−10.7033	−	4.76540i	−0.710401	−	0.316291i	0.0195325	−	0.999809i	$-0.493782\pi$
$227$	−10.7033	−	4.76540i	−0.710401	−	0.316291i	−0.729933	+	0.683518i	$0.760449\pi$
$228$		0			0
$229$	−20.0326	−	4.25807i	−1.32379	−	0.281381i	−0.508817	−	0.860875i	$-0.669917\pi$
$229$	−20.0326	−	4.25807i	−1.32379	−	0.281381i	−0.814977	+	0.579494i	$0.803250\pi$
$230$	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	$-0.922651\pi$
$233$	−4.98842	−	15.3528i	−0.326802	−	1.00579i	0.643818	−	0.765178i	$-0.277349\pi$
$234$		0			0
$235$	0.361031	−	0.262304i	0.0235510	−	0.0171108i
$236$	−0.884807	−	4.16269i	−0.0575960	−	0.270968i
$237$		0			0
$238$	−0.722562	+	0.0759444i	−0.0468368	+	0.00492274i
$239$	25.9333	−	11.5462i	1.67749	−	0.746865i	0.677550	−	0.735476i	$-0.263042\pi$
$239$	25.9333	−	11.5462i	1.67749	−	0.746865i	0.999935	−	0.0113883i	$-0.00362510\pi$
$240$		0			0
$241$	−12.4408	+	7.18270i	−0.801383	+	0.462679i	−0.843954	−	0.536415i	$-0.819778\pi$
$241$	−12.4408	+	7.18270i	−0.801383	+	0.462679i	0.0425716	+	0.999093i	$0.486445\pi$
$242$	6.39414	+	4.05439i	0.411031	+	0.260626i
$243$		0			0
$244$	12.3157	−	4.00162i	0.788433	−	0.256177i
$245$	0.276793	+	0.0290921i	0.0176836	+	0.00185862i
$246$		0			0
$247$	9.54817	+	10.6043i	0.607535	+	0.674737i
$248$	−7.79114	−	8.65294i	−0.494738	−	0.549462i
$249$		0			0
$250$	0.274508	+	0.0288520i	0.0173614	+	0.00182476i
$251$	−6.60298	+	2.14544i	−0.416776	+	0.135419i	−0.509896	−	0.860236i	$-0.670316\pi$
$251$	−6.60298	+	2.14544i	−0.416776	+	0.135419i	0.0931196	+	0.995655i	$0.470316\pi$
$252$		0			0
$253$	7.64348	+	21.2178i	0.480542	+	1.33395i
$254$	7.61303	−	4.39538i	0.477684	−	0.275791i
$255$		0			0
$256$	−9.01825	+	4.01518i	−0.563641	+	0.250949i
$257$	−10.3612	+	1.08901i	−0.646315	+	0.0679305i	−0.422014	−	0.906589i	$-0.638677\pi$
$257$	−10.3612	+	1.08901i	−0.646315	+	0.0679305i	−0.224301	+	0.974520i	$0.572010\pi$
$258$		0			0
$259$	−0.206873	−	0.973263i	−0.0128545	−	0.0604756i
$260$	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	$-0.208606\pi$
$263$	−2.13055	−	3.69022i	−0.131375	−	0.227549i	−0.924207	+	0.381892i	$0.875273\pi$
$264$		0			0
$265$	0.179843	−	0.311497i	0.0110477	−	0.0191351i
$266$	1.03039	+	0.219016i	0.0631771	+	0.0134287i
$267$		0			0
$268$	−11.0790	−	4.93268i	−0.676756	−	0.301311i
$269$	10.5223	+	3.41889i	0.641553	+	0.208453i	0.611686	−	0.791101i	$-0.290492\pi$
$269$	10.5223	+	3.41889i	0.641553	+	0.208453i	0.0298672	+	0.999554i	$0.490492\pi$
$270$		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	$0.639621\pi$
$272$	−0.617719	+	5.87720i	−0.0374547	+	0.356358i
$273$		0			0
$274$	−9.58074	−	5.53144i	−0.578794	−	0.334167i
$275$	−11.9630	+	11.4765i	−0.721395	+	0.692060i
$276$		0			0
$277$	−8.42804	−	7.58864i	−0.506392	−	0.455957i	0.375900	−	0.926660i	$-0.377334\pi$
$277$	−8.42804	−	7.58864i	−0.506392	−	0.455957i	−0.882292	+	0.470703i	$0.844000\pi$
$278$	−1.56054	+	2.14790i	−0.0935949	+	0.128822i
$279$		0			0
$280$	0.00742570	−	0.0228539i	0.000443770	−	0.00136578i
$281$	1.52620	−	0.324404i	0.0910454	−	0.0193523i	−0.162164	−	0.986764i	$-0.551847\pi$
$281$	1.52620	−	0.324404i	0.0910454	−	0.0193523i	0.253209	+	0.967412i	$0.418514\pi$
$282$		0			0
$283$	10.8051	+	24.2687i	0.642299	+	1.44263i	0.881750	+	0.471718i	$0.156366\pi$
$283$	10.8051	+	24.2687i	0.642299	+	1.44263i	−0.239451	+	0.970908i	$0.576967\pi$
$284$	1.05622	−	4.96913i	0.0626752	−	0.294863i
$285$		0			0
$286$	0.383777	−	5.23989i	0.0226932	−	0.309841i
$287$			2.37046i			0.139924i
$288$		0			0
$289$	−1.04038	−	0.755878i	−0.0611986	−	0.0444634i
$290$	0.0628322	−	0.141123i	0.00368963	−	0.00828705i
$291$		0			0
$292$	13.4448	−	12.1058i	0.786798	−	0.708436i
$293$	−2.75271	−	26.1903i	−0.160815	−	1.53005i	−0.715867	−	0.698237i	$-0.753968\pi$
$293$	−2.75271	−	26.1903i	−0.160815	−	1.53005i	0.555052	−	0.831816i	$-0.312698\pi$
$294$		0			0
$295$	−0.0748329	+	0.0831103i	−0.00435694	+	0.00483887i
$296$	9.78322			0.568638
$297$		0			0
$298$	−7.06874			−0.409481
$299$	10.4719	−	11.6302i	0.605604	−	0.672592i
$300$		0			0
$301$	−0.0266197	−	0.253269i	−0.00153433	−	0.0145982i
$302$	−4.48607	+	4.03927i	−0.258144	+	0.232434i
$303$		0			0
$304$	3.48502	−	7.82747i	0.199879	−	0.448936i
$305$	−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	$-0.266211\pi$
$308$	0.658662	+	1.06186i	0.0375307	+	0.0605048i
$309$		0			0
$310$	−0.0275356	+	0.129545i	−0.00156392	+	0.00735765i
$311$	5.41967	+	12.1728i	0.307321	+	0.690255i	0.999505	−	0.0314665i	$-0.0100177\pi$
$311$	5.41967	+	12.1728i	0.307321	+	0.690255i	−0.692183	+	0.721722i	$0.743351\pi$
$312$		0			0
$313$	11.0025	−	2.33866i	0.621899	−	0.132189i	0.113823	−	0.993501i	$-0.463690\pi$
$313$	11.0025	−	2.33866i	0.621899	−	0.132189i	0.508076	+	0.861312i	$0.330357\pi$
$314$	−2.77158	+	8.53004i	−0.156409	+	0.481378i
$315$		0			0
$316$	−2.70120	+	3.71788i	−0.151954	+	0.209147i
$317$	8.13939	+	7.32874i	0.457154	+	0.411623i	0.865269	−	0.501307i	$-0.167147\pi$
$317$	8.13939	+	7.32874i	0.457154	+	0.411623i	−0.408116	+	0.912930i	$0.633814\pi$
$318$		0			0
$319$	8.08067	+	16.7074i	0.452430	+	0.935437i
$320$	0.0427888	+	0.0247041i	0.00239196	+	0.00138100i
$321$		0			0
$322$	0.120763	−	1.14899i	0.00672988	−	0.0640305i
$323$	15.5837	+	21.4492i	0.867103	+	1.19346i
$324$		0			0
$325$	10.9409	+	3.55490i	0.606890	+	0.197191i
$326$	−5.77083	−	2.56934i	−0.319616	−	0.142302i
$327$		0			0
$328$	−22.7979	−	4.84583i	−1.25880	−	0.267566i
$329$	1.37324	−	2.37852i	0.0757093	−	0.131132i
$330$		0			0
$331$	−2.11643	−	3.66576i	−0.116329	−	0.201488i	0.801981	−	0.597349i	$-0.203779\pi$
$331$	−2.11643	−	3.66576i	−0.116329	−	0.201488i	−0.918310	+	0.395861i	$0.870446\pi$
$332$	−2.49676	−	7.68424i	−0.137027	−	0.421727i
$333$		0			0
$334$	−4.23718	+	3.07849i	−0.231848	+	0.168447i
$335$	0.0662613	+	0.311735i	0.00362024	+	0.0170319i
$336$		0			0
$337$	2.64780	−	0.278295i	0.144235	−	0.0151597i	−0.0321359	−	0.999484i	$-0.510231\pi$
$337$	2.64780	−	0.278295i	0.144235	−	0.0151597i	0.176371	+	0.984324i	$0.443564\pi$
$338$	4.84353	−	2.15648i	0.263453	−	0.117297i
$339$		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
$344$	2.49022	+	0.261733i	0.134264	+	0.0141117i
$345$		0			0
$346$	7.65464	+	8.50134i	0.411516	+	0.457035i
$347$	11.1097	+	12.3386i	0.596399	+	0.662368i	0.963467	−	0.267826i	$-0.0863051\pi$
$347$	11.1097	+	12.3386i	0.596399	+	0.662368i	−0.367068	+	0.930194i	$0.619638\pi$
$348$		0			0
$349$	13.6993	+	1.43985i	0.733307	+	0.0770736i	0.463819	−	0.885930i	$-0.346479\pi$
$349$	13.6993	+	1.43985i	0.733307	+	0.0770736i	0.269488	+	0.963004i	$0.413146\pi$
$350$	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	−0.223905	−	0.974611i	$-0.571881\pi$
$353$	9.54783	−	5.51244i	0.508180	−	0.293398i	0.732085	+	0.681213i	$0.238547\pi$
$354$		0			0
$355$	−0.121960	+	0.0543001i	−0.00647297	+	0.00288195i
$356$	12.9692	−	1.36312i	0.687368	−	0.0722453i
$357$		0			0
$358$	−1.00885	−	4.74627i	−0.0533195	−	0.250848i
$359$	15.3828	−	11.1763i	0.811875	−	0.589862i	−0.102499	−	0.994733i	$-0.532684\pi$
$359$	15.3828	−	11.1763i	0.811875	−	0.589862i	0.914374	+	0.404871i	$0.132684\pi$
$360$		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
$365$	−0.465047	−	0.0988489i	−0.0243417	−	0.00517399i
$366$		0			0
$367$	−5.20463	−	2.31725i	−0.271680	−	0.120960i	0.266375	−	0.963869i	$-0.414174\pi$
$367$	−5.20463	−	2.31725i	−0.271680	−	0.120960i	−0.538055	+	0.842910i	$0.680841\pi$
$368$	−8.93722	−	2.90388i	−0.465885	−	0.151375i
$369$		0			0
$370$	−0.0654073	−	0.0900254i	−0.00340036	−	0.00468020i
$371$	0.231392	−	2.20155i	0.0120133	−	0.114299i
$372$		0			0
$373$	−19.1906	−	11.0797i	−0.993651	−	0.573684i	−0.0872871	−	0.996183i	$-0.527820\pi$
$373$	−19.1906	−	11.0797i	−0.993651	−	0.573684i	−0.906364	+	0.422499i	$0.861153\pi$
$374$	1.72680	−	9.60780i	0.0892909	−	0.496808i
$375$		0			0
$376$	20.0681	+	18.0694i	1.03493	+	0.931859i
$377$	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	$0.103118\pi$
$380$	−0.371249	+	0.0789113i	−0.0190447	+	0.00404807i
$381$		0			0
$382$	−3.82647	−	8.59440i	−0.195779	−	0.439728i
$383$	−2.63308	+	12.3877i	−0.134544	+	0.632981i	0.858258	+	0.513218i	$0.171547\pi$
$383$	−2.63308	+	12.3877i	−0.134544	+	0.632981i	−0.992803	+	0.119763i	$0.961787\pi$
$384$		0			0
$385$	0.0124013	−	0.0304053i	0.000632031	−	0.00154960i
$386$		−	17.2313i		−	0.877049i
$387$		0			0
$388$	−3.73917	−	2.71667i	−0.189828	−	0.137918i
$389$	−9.67976	+	21.7411i	−0.490783	+	1.10232i	0.483161	+	0.875531i	$0.339489\pi$
$389$	−9.67976	+	21.7411i	−0.490783	+	1.10232i	−0.973945	+	0.226786i	$0.927178\pi$
$390$		0			0
$391$	21.6088	−	19.4567i	1.09281	−	0.983966i
$392$	1.76044	+	16.7495i	0.0889157	+	0.845976i
$393$		0			0
$394$	−9.69204	+	10.7641i	−0.488278	+	0.542288i
$395$	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	$0.459916\pi$
$398$	−4.77641	+	5.30474i	−0.239420	+	0.265902i
$399$		0			0
$400$	−0.722042	−	6.86977i	−0.0361021	−	0.343488i
$401$	−3.15402	+	2.83989i	−0.157504	+	0.141817i	−0.744115	−	0.668052i	$-0.767129\pi$
$401$	−3.15402	+	2.83989i	−0.157504	+	0.141817i	0.586611	+	0.809869i	$0.300462\pi$
$402$		0			0
$403$	−4.49089	+	10.0867i	−0.223707	+	0.502455i
$404$	8.58407	+	6.23669i	0.427073	+	0.310287i
$405$		0			0
$406$		−	0.950735i		−	0.0471842i
$407$	13.3331	+	0.976535i	0.660897	+	0.0484051i
$408$		0			0
$409$	2.45452	−	11.5476i	0.121368	−	0.570992i	−0.874872	−	0.484354i	$-0.839055\pi$
$409$	2.45452	−	11.5476i	0.121368	−	0.570992i	0.996240	−	0.0866372i	$-0.0276121\pi$
$410$	0.107827	+	0.242184i	0.00532520	+	0.0119606i
$411$		0			0
$412$	19.5860	−	4.16313i	0.964933	−	0.205103i
$413$	−0.212694	+	0.654604i	−0.0104660	+	0.0322109i
$414$		0			0
$415$	−0.124803	+	0.171777i	−0.00612634	+	0.00843218i
$416$	9.92930	+	8.94039i	0.486824	+	0.438338i
$417$		0			0
$418$	−6.68582	+	12.4748i	−0.327014	+	0.610162i
$419$	18.1688	+	10.4898i	0.887604	+	0.512459i	0.873158	−	0.487437i	$-0.162068\pi$
$419$	18.1688	+	10.4898i	0.887604	+	0.512459i	0.0144463	+	0.999896i	$0.495401\pi$
$420$		0			0
$421$	0.290566	−	2.76455i	0.0141613	−	0.134736i	−0.985157	−	0.171656i	$-0.945088\pi$
$421$	0.290566	−	2.76455i	0.0141613	−	0.134736i	0.999318	+	0.0369204i	$0.0117548\pi$
$422$	−7.58306	−	10.4372i	−0.369137	−	0.508074i
$423$		0			0
$424$	20.7003	+	6.72593i	1.00529	+	0.326640i
$425$	19.5263	+	8.69366i	0.947164	+	0.421704i
$426$		0			0
$427$	−2.04861	−	0.435446i	−0.0991394	−	0.0210727i
$428$	−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	$0.134845\pi$
$431$	8.63060	+	26.5623i	0.415722	+	1.27946i	−0.495882	+	0.868390i	$0.665155\pi$
$432$		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	$0.229298\pi$
$434$	0.169467	+	0.797279i	0.00813467	+	0.0382706i
$435$		0			0
$436$	11.1482	−	1.17173i	0.533904	−	0.0561156i
$437$	−38.5144	+	17.1477i	−1.84239	+	0.820286i
$438$		0			0
$439$	−2.53842	+	1.46556i	−0.121152	+	0.0699472i	−0.559351	−	0.828931i	$-0.688950\pi$
$439$	−2.53842	+	1.46556i	−0.121152	+	0.0699472i	0.438199	+	0.898878i	$0.355616\pi$
$440$	0.267071	+	0.181426i	0.0127321	+	0.00864913i
$441$		0			0
$442$	−6.44247	+	2.09329i	−0.306437	+	0.0995675i
$443$	35.6451	+	3.74645i	1.69355	+	0.177999i	0.901594	−	0.432583i	$-0.142398\pi$
$443$	35.6451	+	3.74645i	1.69355	+	0.177999i	0.791953	+	0.610582i	$0.209064\pi$
$444$		0			0
$445$	−0.229310	−	0.254674i	−0.0108703	−	0.0120727i
$446$	4.45309	+	4.94566i	0.210860	+	0.234184i
$447$		0			0
$448$	0.302416	+	0.0317852i	0.0142878	+	0.00150171i
$449$	13.5184	−	4.39241i	0.637974	−	0.207290i	0.0278700	−	0.999612i	$-0.491128\pi$
$449$	13.5184	−	4.39241i	0.637974	−	0.207290i	0.610104	+	0.792321i	$0.291128\pi$
$450$		0			0
$451$	−30.5864	−	8.87978i	−1.44026	−	0.418132i
$452$	0.698615	−	0.403345i	0.0328601	−	0.0189718i
$453$		0			0
$454$	−7.36696	+	3.27998i	−0.345749	+	0.153937i
$455$	−0.0226620	+	0.00238187i	−0.00106241	+	0.000111664i
$456$		0			0
$457$	−4.24125	−	19.9535i	−0.198397	−	0.933386i	−0.958833	−	0.283972i	$-0.908348\pi$
$457$	−4.24125	−	19.9535i	−0.198397	−	0.933386i	0.760435	−	0.649414i	$-0.224986\pi$
$458$	−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	$-0.172377\pi$
$461$	−0.385177	−	0.667146i	−0.0179395	−	0.0310721i	−0.874856	+	0.484383i	$0.839044\pi$
$462$		0			0
$463$	−18.8974	+	32.7312i	−0.878236	+	1.52115i	−0.0249608	+	0.999688i	$0.507946\pi$
$463$	−18.8974	+	32.7312i	−0.878236	+	1.52115i	−0.853275	+	0.521461i	$0.825387\pi$
$464$	−7.56414	−	1.60781i	−0.351156	−	0.0746406i
$465$		0			0
$466$	−10.1504	−	4.51925i	−0.470208	−	0.209350i
$467$	−16.7411	−	5.43950i	−0.774684	−	0.251710i	−0.105115	−	0.994460i	$-0.533521\pi$
$467$	−16.7411	−	5.43950i	−0.774684	−	0.251710i	−0.669569	+	0.742750i	$0.733521\pi$
$468$		0			0
$469$	1.15290	+	1.58683i	0.0532358	+	0.0732728i
$470$	0.0321065	−	0.305473i	0.00148096	−	0.0140904i
$471$		0			0
$472$	−5.86083	−	3.38375i	−0.269766	−	0.155750i
$473$	3.36768	+	0.605271i	0.154846	+	0.0278304i
$474$		0			0
$475$	−23.0302	−	20.7365i	−1.05670	−	0.951456i
$476$	0.946967	−	1.30339i	0.0434042	−	0.0597407i
$477$		0			0
$478$	6.03785	−	18.5826i	0.276165	−	0.849948i
$479$	2.35329	−	0.500206i	0.107524	−	0.0228550i	−0.153835	−	0.988097i	$-0.549162\pi$
$479$	2.35329	−	0.500206i	0.107524	−	0.0228550i	0.261360	+	0.965242i	$0.415829\pi$
$480$		0			0
$481$	−3.77333	−	8.47503i	−0.172049	−	0.386428i
$482$	−2.05574	+	9.67152i	−0.0936366	+	0.440525i
$483$		0			0
$484$	−16.1686	+	4.52108i	−0.734937	+	0.205504i
$485$			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	$0.807300\pi$
$488$	8.37578	−	18.8123i	0.379154	−	0.851593i
$489$		0			0
$490$	0.142359	−	0.128181i	0.00643114	−	0.00579062i
$491$	2.61764	+	24.9052i	0.118132	+	1.12396i	0.879587	+	0.475737i	$0.157819\pi$
$491$	2.61764	+	24.9052i	0.118132	+	1.12396i	−0.761455	+	0.648218i	$0.775515\pi$
$492$		0			0
$493$	16.0113	−	17.7824i	0.721114	−	0.800879i
$494$	9.82158			0.441894
$495$		0			0
$496$	6.62982			0.297688
$497$	−0.549780	+	0.610593i	−0.0246610	+	0.0273888i
$498$		0			0
$499$	−2.37400	−	22.5871i	−0.106275	−	1.01114i	−0.909568	−	0.415555i	$-0.863587\pi$
$499$	−2.37400	−	22.5871i	−0.106275	−	1.01114i	0.803293	−	0.595584i	$-0.203079\pi$
$500$	−0.454852	+	0.409550i	−0.0203416	+	0.0183156i
$501$		0			0
$502$	−1.94365	+	4.36552i	−0.0867496	+	0.194843i
$503$	8.41953	+	6.11715i	0.375408	+	0.272750i	0.759450	−	0.650566i	$-0.225468\pi$
$503$	8.41953	+	6.11715i	0.375408	+	0.272750i	−0.384042	+	0.923316i	$0.625468\pi$
$504$		0			0
$505$		−	0.278835i		−	0.0124080i
$506$	14.3731	+	5.86234i	0.638964	+	0.260613i
$507$		0			0
$508$	−4.05285	+	19.0672i	−0.179816	+	0.845969i
$509$	−3.28867	−	7.38647i	−0.145768	−	0.327399i	0.825875	−	0.563853i	$-0.190682\pi$
$509$	−3.28867	−	7.38647i	−0.145768	−	0.327399i	−0.971643	+	0.236454i	$0.924015\pi$
$510$		0			0
$511$	−2.86212	+	0.608363i	−0.126613	+	0.0269124i
$512$	4.55217	−	14.0102i	0.201180	−	0.619167i
$513$		0			0
$514$	−4.21490	+	5.80132i	−0.185911	+	0.255885i
$515$	−0.391045	−	0.352098i	−0.0172315	−	0.0155153i
$516$		0			0
$517$	25.5462	+	26.6291i	1.12352	+	1.17115i
$518$	−0.593101	−	0.342427i	−0.0260594	−	0.0150454i
$519$		0			0
$520$	0.0234193	−	0.222820i	0.00102701	−	0.00977131i
$521$	−20.5846	−	28.3323i	−0.901828	−	1.24126i	−0.969881	−	0.243578i	$-0.921679\pi$
$521$	−20.5846	−	28.3323i	−0.901828	−	1.24126i	0.0680535	−	0.997682i	$-0.478321\pi$
$522$		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	$0.204501\pi$
$524$	25.3113	+	11.2693i	1.10573	+	0.492302i
$525$		0			0
$526$	−2.86879	−	0.609779i	−0.125085	−	0.0265876i
$527$	−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
$533$	4.59513	+	21.6184i	0.199037	+	0.936396i
$534$		0			0
$535$	0.0545871	−	0.00573733i	0.00236000	−	0.000248046i
$536$	−17.6181	+	7.84407i	−0.760984	+	0.338812i
$537$		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	$0.401549\pi$
$542$	10.8809	+	1.14363i	0.467377	+	0.0491233i
$543$		0			0
$544$	16.6112	+	18.4486i	0.712198	+	0.790976i
$545$	−0.197113	−	0.218916i	−0.00844338	−	0.00937733i
$546$		0			0
$547$	16.3731	+	1.72088i	0.700062	+	0.0735795i	0.447871	−	0.894098i	$-0.352182\pi$
$547$	16.3731	+	1.72088i	0.700062	+	0.0735795i	0.252191	+	0.967678i	$0.418849\pi$
$548$	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
$553$	0.679002	−	0.302311i	0.0288741	−	0.0128556i
$554$	−7.76318	+	0.815943i	−0.329826	+	0.0346661i
$555$		0			0
$556$	−1.22402	−	5.75858i	−0.0519102	−	0.244218i
$557$	−21.2624	+	15.4481i	−0.900919	+	0.654556i	−0.938702	−	0.344730i	$-0.887970\pi$
$557$	−21.2624	+	15.4481i	−0.900919	+	0.654556i	0.0377832	+	0.999286i	$0.487970\pi$
$558$		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
$563$	35.5711	+	7.56087i	1.49914	+	0.318653i	0.883147	−	0.469097i	$-0.155421\pi$
$563$	35.5711	+	7.56087i	1.49914	+	0.318653i	0.615996	+	0.787750i	$0.288754\pi$
$564$		0			0
$565$	−0.0193664	−	0.00862248i	−0.000814751	−	0.000362750i
$566$	17.3898	+	5.65030i	0.730949	+	0.237500i
$567$		0			0
$568$	−4.74846	−	6.53570i	−0.199241	−	0.274232i
$569$	2.11468	−	20.1198i	0.0886520	−	0.843468i	−0.856348	−	0.516399i	$-0.827272\pi$
$569$	2.11468	−	20.1198i	0.0886520	−	0.843468i	0.945000	−	0.327069i	$-0.106061\pi$
$570$		0			0
$571$	−21.1312	−	12.2001i	−0.884313	−	0.510558i	−0.0122350	−	0.999925i	$-0.503895\pi$
$571$	−21.1312	−	12.2001i	−0.884313	−	0.510558i	−0.872078	+	0.489367i	$0.837228\pi$
$572$	8.06533	+	8.40720i	0.337228	+	0.351523i
$573$		0			0
$574$	1.21249	+	1.09173i	0.0506085	+	0.0455681i
$575$	−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	$0.968386\pi$
$578$	−0.865784	+	0.184028i	−0.0360118	+	0.00765455i
$579$		0			0
$580$	0.139328	+	0.312935i	0.00578526	+	0.0129939i
$581$	−0.271691	+	1.27821i	−0.0112717	+	0.0530290i
$582$		0			0
$583$	27.5401	+	11.2327i	1.14059	+	0.465211i
$584$		−	28.7700i		−	1.19051i
$585$		0			0
$586$	−14.6641	−	10.6541i	−0.605769	−	0.440117i
$587$	−7.78344	+	17.4819i	−0.321257	+	0.721555i	−0.999917	−	0.0128978i	$-0.995894\pi$
$587$	−7.78344	+	17.4819i	−0.321257	+	0.721555i	0.678660	+	0.734453i	$0.262561\pi$
$588$		0			0
$589$	22.1040	−	19.9026i	0.910781	−	0.820071i
$590$	0.00804615	+	0.0765540i	0.000331255	+	0.00315168i
$591$		0			0
$592$	−3.72739	+	4.13968i	−0.153195	+	0.170140i
$593$	14.9885			0.615503			0.307751	−	0.951467i	$-0.400423\pi$
$593$	14.9885			0.615503			0.307751	+	0.951467i	$0.400423\pi$
$594$		0			0
$595$	−0.0423378			−0.00173568
$596$	10.4884	−	11.6485i	0.429620	−	0.477142i
$597$		0			0
$598$	−1.12595	−	10.7127i	−0.0460437	−	0.438076i
$599$	24.7771	−	22.3094i	1.01236	−	0.911537i	0.0162732	−	0.999868i	$-0.494820\pi$
$599$	24.7771	−	22.3094i	1.01236	−	0.911537i	0.996091	+	0.0883306i	$0.0281532\pi$
$600$		0			0
$601$	−17.1940	+	38.6183i	−0.701357	+	1.57527i	0.112133	+	0.993693i	$0.464232\pi$
$601$	−17.1940	+	38.6183i	−0.701357	+	1.57527i	−0.813490	+	0.581579i	$0.802435\pi$
$602$	−0.141807	−	0.103029i	−0.00577962	−	0.00419914i
$603$		0			0
$604$		−	13.3859i		−	0.544664i
$605$	0.345868	+	0.273915i	0.0140615	+	0.0111362i
$606$		0			0
$607$	6.42154	−	30.2110i	0.260642	−	1.22623i	−0.631824	−	0.775112i	$-0.717694\pi$
$607$	6.42154	−	30.2110i	0.260642	−	1.22623i	0.892467	−	0.451114i	$-0.148973\pi$
$608$	−14.6399	−	32.8817i	−0.593726	−	1.33353i
$609$		0			0
$610$	−0.229109	+	0.0486986i	−0.00927634	+	0.00197175i
$611$	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	$0.304558\pi$
$614$	−13.3032	−	11.9783i	−0.536875	−	0.483404i
$615$		0			0
$616$	1.95573	+	0.351502i	0.0787985	+	0.0141624i
$617$	2.28088	+	1.31687i	0.0918248	+	0.0530151i	0.545209	−	0.838300i	$-0.316450\pi$
$617$	2.28088	+	1.31687i	0.0918248	+	0.0530151i	−0.453384	+	0.891315i	$0.649784\pi$
$618$		0			0
$619$	−2.11664	+	20.1385i	−0.0850751	+	0.809436i	0.865910	+	0.500200i	$0.166740\pi$
$619$	−2.11664	+	20.1385i	−0.0850751	+	0.809436i	−0.950985	+	0.309236i	$0.899927\pi$
$620$	−0.172619	−	0.237590i	−0.00693255	−	0.00954184i
$621$		0			0
$622$	8.72244	+	2.83409i	0.349738	+	0.113637i
$623$	−1.92678	−	0.857858i	−0.0771949	−	0.0343694i
$624$		0			0
$625$	−24.4301	−	5.19278i	−0.977204	−	0.207711i
$626$	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	$0.353732\pi$
$632$	1.51941	+	7.14828i	0.0604390	+	0.284343i
$633$		0			0
$634$	7.49730	−	0.787998i	0.297756	−	0.0312954i
$635$	0.467976	−	0.208356i	0.0185711	−	0.00826837i
$636$		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
$641$	−32.1374	−	3.37778i	−1.26935	−	0.133414i	−0.554200	−	0.832383i	$-0.686976\pi$
$641$	−32.1374	−	3.37778i	−1.26935	−	0.133414i	−0.715152	+	0.698969i	$0.753643\pi$
$642$		0			0
$643$	9.21842	+	10.2381i	0.363539	+	0.403751i	0.896969	−	0.442093i	$-0.145764\pi$
$643$	9.21842	+	10.2381i	0.363539	+	0.403751i	−0.533430	+	0.845844i	$0.679097\pi$
$644$	1.71422	+	1.90383i	0.0675497	+	0.0750216i
$645$		0			0
$646$	18.1485	+	1.90748i	0.714042	+	0.0750488i
$647$	−8.11003	+	2.63511i	−0.318838	+	0.103597i	−0.464064	−	0.885802i	$-0.653609\pi$
$647$	−8.11003	+	2.63511i	−0.318838	+	0.103597i	0.145226	+	0.989399i	$0.453609\pi$
$648$		0			0
$649$	−7.64968	−	5.19656i	−0.300276	−	0.203983i
$650$	6.85722	−	3.95902i	0.268962	−	0.155285i
$651$		0			0
$652$	12.7966	−	5.69739i	0.501152	−	0.223127i
$653$	1.20137	−	0.126269i	0.0470132	−	0.00494129i	−0.0809927	−	0.996715i	$-0.525809\pi$
$653$	1.20137	−	0.126269i	0.0470132	−	0.00494129i	0.128006	+	0.991773i	$0.459142\pi$
$654$		0			0
$655$	−0.151382	−	0.712198i	−0.00591499	−	0.0278279i
$656$	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	$-0.225342\pi$
$659$	−4.70527	−	8.14977i	−0.183291	−	0.317470i	−0.942999	+	0.332794i	$0.892009\pi$
$660$		0			0
$661$	−7.55133	+	13.0793i	−0.293713	+	0.508725i	−0.974685	−	0.223584i	$-0.928224\pi$
$661$	−7.55133	+	13.0793i	−0.293713	+	0.508725i	0.680972	+	0.732309i	$0.261558\pi$
$662$	−2.84977	−	0.605737i	−0.110759	−	0.0235426i
$663$		0			0
$664$	−11.7377	−	5.22596i	−0.455511	−	0.202807i
$665$	0.0583807	+	0.0189690i	0.00226391	+	0.000735588i
$666$		0			0
$667$	22.3653	+	30.7832i	0.865988	+	1.19193i
$668$	1.21397	−	11.5502i	0.0469700	−	0.446889i
$669$		0			0
$670$	0.189970	+	0.109679i	0.00733916	+	0.00423727i
$671$	13.2927	−	24.8023i	0.513161	−	0.957484i
$672$		0			0
$673$	−30.9140	−	27.8351i	−1.19165	−	1.07296i	−0.995727	−	0.0923433i	$-0.970564\pi$
$673$	−30.9140	−	27.8351i	−1.19165	−	1.07296i	−0.195919	−	0.980620i	$-0.562769\pi$
$674$	1.07711	−	1.48252i	0.0414888	−	0.0571045i
$675$		0			0
$676$	−3.63303	+	11.1813i	−0.139732	+	0.430051i
$677$	−4.42177	+	0.939877i	−0.169943	+	0.0361224i	−0.292097	−	0.956389i	$-0.594353\pi$
$677$	−4.42177	+	0.939877i	−0.169943	+	0.0361224i	0.122154	+	0.992511i	$0.461020\pi$
$678$		0			0
$679$	0.304042	+	0.682890i	0.0116681	+	0.0262069i
$680$	0.0865492	−	0.407182i	0.00331901	−	0.0156147i
$681$		0			0
$682$	−10.9222	−	0.799960i	−0.418233	−	0.0306320i
$683$			34.7783i			1.33075i	0.746507	+	0.665377i	$0.231729\pi$
$683$			34.7783i			1.33075i	−0.746507	+	0.665377i	$0.768271\pi$
$684$		0			0
$685$	−0.521547	−	0.378926i	−0.0199273	−	0.0144780i
$686$	0.963272	−	2.16354i	0.0367779	−	0.0826045i
$687$		0			0
$688$	−1.05952	+	0.953996i	−0.0403938	+	0.0363707i
$689$	−2.15741	−	20.5264i	−0.0821909	−	0.781995i
$690$		0			0
$691$	−11.9664	+	13.2900i	−0.455223	+	0.505576i	−0.926441	−	0.376441i	$-0.877148\pi$
$691$	−11.9664	+	13.2900i	−0.455223	+	0.505576i	0.471218	+	0.882017i	$0.343815\pi$
$692$	−25.3670			−0.964308
$693$		0			0
$694$	11.4278			0.433794
$695$	−0.103522	+	0.114973i	−0.00392682	+	0.00436118i
$696$		0			0
$697$	4.29237	+	40.8392i	0.162585	+	1.54689i
$698$	7.04579	−	6.34406i	0.266687	−	0.240126i
$699$		0			0
$700$	−0.765950	+	1.72035i	−0.0289502	+	0.0650232i
$701$	14.1345	+	10.2693i	0.533852	+	0.387866i	0.821797	−	0.569781i	$-0.192972\pi$
$701$	14.1345	+	10.2693i	0.533852	+	0.387866i	−0.287945	+	0.957647i	$0.592972\pi$
$702$		0			0
$703$			24.9914i			0.942568i
$704$	−1.54298	+	3.78304i	−0.0581532	+	0.142579i
$705$		0			0
$706$	1.57770	−	7.42251i	0.0593776	−	0.279350i
$707$	−0.697994	−	1.56772i	−0.0262507	−	0.0589601i
$708$		0			0
$709$	−8.15627	+	1.73367i	−0.306315	+	0.0651093i	−0.358505	−	0.933528i	$-0.616713\pi$
$709$	−8.15627	+	1.73367i	−0.306315	+	0.0651093i	0.0521896	+	0.998637i	$0.483380\pi$
$710$	−0.0283950	+	0.0873909i	−0.00106565	+	0.00327972i
$711$		0			0
$712$	12.1893	−	16.7771i	0.456812	−	0.628747i
$713$	−24.2424	−	21.8280i	−0.907886	−	0.817464i
$714$		0			0
$715$	0.0541584	−	0.301333i	0.00202541	−	0.0112692i
$716$	9.31824	+	5.37989i	0.348239	+	0.201056i
$717$		0			0
$718$	1.36800	−	13.0156i	0.0510532	−	0.485739i
$719$	13.8736	+	19.0953i	0.517397	+	0.712136i	0.985145	−	0.171726i	$-0.0549344\pi$
$719$	13.8736	+	19.0953i	0.517397	+	0.712136i	−0.467748	+	0.883862i	$0.654934\pi$
$720$		0			0
$721$	−3.08000	−	1.00075i	−0.114705	−	0.0372699i
$722$	−12.2239	−	5.44241i	−0.454925	−	0.202546i
$723$		0			0
$724$	−31.5355	−	6.70308i	−1.17201	−	0.249118i
$725$	−13.9849	+	24.2225i	−0.519384	+	0.899600i
$726$		0			0
$727$	−0.952312	−	1.64945i	−0.0353193	−	0.0611748i	0.847825	−	0.530275i	$-0.177911\pi$
$727$	−0.952312	−	1.64945i	−0.0353193	−	0.0611748i	−0.883145	+	0.469101i	$0.844578\pi$
$728$	−0.426102	−	1.31141i	−0.0157924	−	0.0486039i
$729$		0			0
$730$	−0.264742	+	0.192346i	−0.00979854	+	0.00711905i
$731$	−0.917225	−	4.31521i	−0.0339248	−	0.159604i
$732$		0			0
$733$	17.5153	−	1.84093i	0.646943	−	0.0679964i	0.224626	−	0.974445i	$-0.427884\pi$
$733$	17.5153	−	1.84093i	0.646943	−	0.0679964i	0.422316	+	0.906449i	$0.361217\pi$
$734$	−3.58230	+	1.59494i	−0.132225	+	0.0588704i
$735$		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	$0.428006\pi$
$740$	0.245401	+	0.0257927i	0.00902113	+	0.000948159i
$741$		0			0
$742$	−1.01952	−	1.13229i	−0.0374278	−	0.0415678i
$743$	−1.22970	−	1.36573i	−0.0451135	−	0.0501036i	0.720166	−	0.693802i	$-0.244066\pi$
$743$	−1.22970	−	1.36573i	−0.0451135	−	0.0501036i	−0.765279	+	0.643698i	$0.777399\pi$
$744$		0			0
$745$	−0.409660	−	0.0430570i	−0.0150088	−	0.00157749i
$746$	−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
$751$	−34.6641	+	15.4334i	−1.26491	+	0.563174i	−0.925957	−	0.377629i	$-0.876740\pi$
$751$	−34.6641	+	15.4334i	−1.26491	+	0.563174i	−0.338953	+	0.940803i	$0.610073\pi$
$752$	−15.2918	+	1.60723i	−0.557635	+	0.0586098i
$753$		0			0
$754$	−1.84299	−	8.67060i	−0.0671179	−	0.315765i
$755$	−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
$761$	−30.1908	−	6.41724i	−1.09441	−	0.232625i	−0.374874	−	0.927076i	$-0.622314\pi$
$761$	−30.1908	−	6.41724i	−1.09441	−	0.232625i	−0.719540	+	0.694451i	$0.755647\pi$
$762$		0			0
$763$	−1.65625	−	0.737408i	−0.0599601	−	0.0266960i
$764$	19.8402	+	6.44648i	0.717794	+	0.233225i
$765$		0			0
$766$	5.12362	+	7.05205i	0.185124	+	0.254801i
$767$	−0.670798	+	6.38222i	−0.0242211	+	0.230449i
$768$		0			0
$769$	16.7276	+	9.65771i	0.603214	+	0.348266i	0.770305	−	0.637676i	$-0.220104\pi$
$769$	16.7276	+	9.65771i	0.603214	+	0.348266i	−0.167091	+	0.985942i	$0.553437\pi$
$770$	−0.00984080	−	0.0203467i	−0.000354638	−	0.000733243i
$771$		0			0
$772$	28.3953	+	25.5672i	1.02197	+	0.920185i
$773$	1.72928	−	2.38015i	0.0621980	−	0.0856082i	−0.776785	−	0.629766i	$-0.783151\pi$
$773$	1.72928	−	2.38015i	0.0621980	−	0.0856082i	0.838983	+	0.544158i	$0.183151\pi$
$774$		0			0
$775$	7.40997	−	22.8056i	0.266174	−	0.819200i
$776$	−7.18920	+	1.52811i	−0.258077	+	0.0548560i
$777$		0			0
$778$	6.66249	+	14.9642i	0.238862	+	0.536493i
$779$	12.3787	−	58.2374i	0.443515	−	2.08657i
$780$		0			0
$781$	−5.81908	−	9.38117i	−0.208223	−	0.335685i
$782$		−	20.0138i		−	0.715693i
$783$		0			0
$784$	−7.75811	−	5.63660i	−0.277075	−	0.201307i
$785$	−0.212581	+	0.477465i	−0.00758735	+	0.0170415i
$786$		0			0
$787$	5.97911	−	5.38362i	0.213132	−	0.191905i	−0.555649	−	0.831417i	$-0.687530\pi$
$787$	5.97911	−	5.38362i	0.213132	−	0.191905i	0.768781	+	0.639512i	$0.220863\pi$
$788$	−3.35733	−	31.9429i	−0.119600	−	1.13792i
$789$		0			0
$790$	0.0556203	−	0.0617726i	0.00197888	−	0.00219777i
$791$	−0.130470			−0.00463897
$792$		0			0
$793$	−19.5272			−0.693433
$794$	2.30507	−	2.56004i	0.0818039	−	0.0908524i
$795$		0			0
$796$	−1.65455	−	15.7420i	−0.0586440	−	0.557960i
$797$	−40.8149	+	36.7499i	−1.44574	+	1.30175i	−0.567634	+	0.823281i	$0.692141\pi$
$797$	−40.8149	+	36.7499i	−1.44574	+	1.30175i	−0.878105	+	0.478468i	$0.841192\pi$
$798$		0			0
$799$	19.3517	−	43.4647i	0.684615	−	1.53767i
$800$	−23.4757	−	17.0561i	−0.829991	−	0.603024i
$801$		0			0
$802$			2.92121i			0.103152i
$803$	2.87174	−	39.2092i	0.101342	−	1.38366i
$804$		0			0
$805$	0.0139974	−	0.0658524i	0.000493342	−	0.00232099i
$806$	3.09104	+	6.94259i	0.108877	+	0.244542i
$807$		0			0
$808$	16.5044	−	3.50811i	0.580621	−	0.123415i
$809$	−7.52538	+	23.1607i	−0.264578	+	0.814288i	0.727212	+	0.686413i	$0.240816\pi$
$809$	−7.52538	+	23.1607i	−0.264578	+	0.814288i	−0.991790	+	0.127875i	$0.959184\pi$
$810$		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	$0.318759\pi$
$812$	1.56671	+	1.41067i	0.0549807	+	0.0495048i
$813$		0			0
$814$	6.64014	−	6.37012i	0.232737	−	0.223273i
$815$	−0.318790	−	0.184054i	−0.0111667	−	0.00644712i
$816$		0			0
$817$	−0.668601	+	6.36131i	−0.0233914	+	0.222554i
$818$	−4.77615	−	6.57380i	−0.166994	−	0.229848i
$819$		0			0
$820$	−0.559083	−	0.181657i	−0.0195240	−	0.00634374i
$821$	−26.1615	−	11.6478i	−0.913042	−	0.406513i	−0.104212	−	0.994555i	$-0.533232\pi$
$821$	−26.1615	−	11.6478i	−0.913042	−	0.406513i	−0.808830	+	0.588043i	$0.799899\pi$
$822$		0			0
$823$	−2.43348	−	0.517251i	−0.0848256	−	0.0180302i	0.165303	−	0.986243i	$-0.447140\pi$
$823$	−2.43348	−	0.517251i	−0.0848256	−	0.0180302i	−0.250129	+	0.968213i	$0.580473\pi$
$824$	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	$0.0360024\pi$
$827$	7.36490	+	22.6668i	0.256103	+	0.788202i	−0.737508	+	0.675338i	$0.763998\pi$
$828$		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	$0.0506601\pi$
$830$	0.0303849	+	0.142950i	0.00105467	+	0.00496185i
$831$		0			0
$832$	2.81961	−	0.296353i	0.0977525	−	0.0102742i
$833$	27.1075	−	12.0691i	0.939221	−	0.418168i
$834$		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
$839$	−56.9097	−	5.98145i	−1.96474	−	0.206503i	−0.966081	−	0.258240i	$-0.916857\pi$
$839$	−56.9097	−	5.98145i	−1.96474	−	0.206503i	−0.998661	+	0.0517373i	$0.983524\pi$
$840$		0			0
$841$	1.54724	+	1.71839i	0.0533532	+	0.0592548i
$842$	−1.28025	−	1.42186i	−0.0441202	−	0.0490004i
$843$		0			0
$844$	28.4508	+	2.99030i	0.979318	+	0.102930i
$845$	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
$850$	13.4398	−	5.98377i	0.460980	−	0.205242i
$851$	27.2589	−	2.86503i	0.934425	−	0.0982120i
$852$		0			0
$853$	6.34987	+	29.8738i	0.217415	+	1.02286i	0.942502	+	0.334201i	$0.108466\pi$
$853$	6.34987	+	29.8738i	0.217415	+	1.02286i	−0.725087	+	0.688658i	$0.758200\pi$
$854$	−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	$-0.200152\pi$
$857$	−3.07390	−	5.32416i	−0.105003	−	0.181870i	−0.913739	+	0.406301i	$0.866818\pi$
$858$		0			0
$859$	13.7994	−	23.9013i	0.470830	−	0.815501i	−0.528614	−	0.848863i	$-0.677288\pi$
$859$	13.7994	−	23.9013i	0.470830	−	0.815501i	0.999443	+	0.0333614i	$0.0106212\pi$
$860$	0.0617744	+	0.0131306i	0.00210649	+	0.000447748i
$861$		0			0
$862$	17.5615	+	7.81887i	0.598146	+	0.266312i
$863$	−40.7061	−	13.2262i	−1.38565	−	0.450226i	−0.481129	−	0.876650i	$-0.659773\pi$
$863$	−40.7061	−	13.2262i	−1.38565	−	0.450226i	−0.904523	+	0.426424i	$0.859773\pi$
$864$		0			0
$865$	0.391832	+	0.539310i	0.0133227	+	0.0183371i
$866$	0.659608	−	6.27575i	0.0224144	−	0.213259i
$867$		0			0
$868$	−1.56528	−	0.903714i	−0.0531290	−	0.0306741i
$869$	1.35721	+	9.89371i	0.0460403	+	0.335621i
$870$		0			0
$871$	13.5903	+	12.2368i	0.460491	+	0.414628i
$872$	10.4778	−	14.4214i	0.354822	−	0.488371i
$873$		0			0
$874$	−8.96700	+	27.5976i	−0.303313	+	0.933503i
$875$	0.0968285	−	0.0205815i	0.00327340	−	0.000695783i
$876$		0			0
$877$	4.56785	+	10.2596i	0.154245	+	0.346441i	0.974095	−	0.226138i	$-0.0726099\pi$
$877$	4.56785	+	10.2596i	0.154245	+	0.346441i	−0.819850	+	0.572578i	$0.805943\pi$
$878$	−0.419453	+	1.97337i	−0.0141559	+	0.0665981i
$879$		0			0
$880$	−0.178522	+	0.0438857i	−0.00601797	+	0.00147939i
$881$			47.3136i			1.59403i	0.603957	+	0.797017i	$0.293590\pi$
$881$			47.3136i			1.59403i	−0.603957	+	0.797017i	$0.706410\pi$
$882$		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	$0.799418\pi$
$884$	6.10963	−	13.7224i	0.205489	−	0.461536i
$885$		0			0
$886$	18.3329	−	16.5070i	0.615905	−	0.554563i
$887$	4.25539	+	40.4873i	0.142882	+	1.35943i	0.797430	+	0.603411i	$0.206192\pi$
$887$	4.25539	+	40.4873i	0.142882	+	1.35943i	−0.654548	+	0.756020i	$0.727141\pi$
$888$		0			0
$889$	2.10958	−	2.34292i	0.0707529	−	0.0785791i
$890$	−0.235876			−0.00790658
$891$		0			0
$892$	−14.7573			−0.494110
$893$	−46.1586	+	51.2643i	−1.54464	+	1.71549i
$894$		0			0
$895$	−0.0295563	−	0.281209i	−0.000987958	−	0.00939979i
$896$	−1.97438	+	1.77774i	−0.0659595	+	0.0593902i
$897$		0			0
$898$	3.97929	−	8.93763i	0.132791	−	0.298253i
$899$	−21.7180	−	15.7790i	−0.724335	−	0.526260i
$900$		0			0
$901$		−	38.3480i		−	1.27756i
$902$	−18.6288	+	11.5553i	−0.620270	+	0.384750i
$903$		0			0
$904$	0.266713	−	1.25479i	0.00887075	−	0.0417336i
$905$	0.344604	+	0.773994i	0.0114550	+	0.0257284i
$906$		0			0
$907$	−1.15589	+	0.245691i	−0.0383806	+	0.00815804i	−0.227062	−	0.973880i	$-0.572912\pi$
$907$	−1.15589	+	0.245691i	−0.0383806	+	0.00815804i	0.188681	+	0.982038i	$0.439579\pi$
$908$	5.52581	−	17.0067i	0.183380	−	0.564387i
$909$		0			0
$910$	−0.00921881	+	0.0126886i	−0.000305601	+	0.000420623i
$911$	15.7280	+	14.1615i	0.521092	+	0.469193i	0.887204	−	0.461378i	$-0.152645\pi$
$911$	15.7280	+	14.1615i	0.521092	+	0.469193i	−0.366112	+	0.930571i	$0.619311\pi$
$912$		0			0
$913$	−15.4751	−	8.29384i	−0.512152	−	0.274486i
$914$	−12.1596	−	7.02032i	−0.402202	−	0.232212i
$915$		0			0
$916$	3.26735	−	31.0867i	0.107956	−	1.02713i
$917$	−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	$0.674659\pi$
$920$	0.604719	+	0.269238i	0.0199370	+	0.00887653i
$921$		0			0
$922$	−0.518641	−	0.110241i	−0.0170805	−	0.00363058i
$923$	−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
$929$	−7.08681	−	33.3408i	−0.232511	−	1.09388i	−0.927200	−	0.374567i	$-0.877791\pi$
$929$	−7.08681	−	33.3408i	−0.232511	−	1.09388i	0.694689	−	0.719310i	$-0.255542\pi$
$930$		0			0
$931$	−42.7868	+	4.49707i	−1.40228	+	0.147386i
$932$	22.5081	−	10.0212i	0.737276	−	0.328256i
$933$		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	$0.364832\pi$
$938$	1.34264	+	0.141117i	0.0438386	+	0.00460763i
$939$		0			0
$940$	0.455748	+	0.506159i	0.0148648	+	0.0165091i
$941$	−22.2806	−	24.7451i	−0.726328	−	0.806669i	0.261004	−	0.965338i	$-0.415946\pi$
$941$	−22.2806	−	24.7451i	−0.726328	−	0.806669i	−0.987332	+	0.158669i	$0.949280\pi$
$942$		0			0
$943$	−64.9407	−	6.82554i	−2.11476	−	0.222270i
$944$	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	−0.489392	−	0.872064i	$-0.662781\pi$
$947$	0.650586	−	0.375616i	0.0211412	−	0.0122059i	0.510533	+	0.859858i	$0.329448\pi$
$948$		0			0
$949$	−24.9229	+	11.0964i	−0.809032	+	0.360204i
$950$	−21.2134	+	2.22962i	−0.688255	+	0.0723385i
$951$		0			0
$952$	−0.532664	−	2.50599i	−0.0172638	−	0.0812196i
$953$	3.76491	−	2.73537i	0.121957	−	0.0886073i	−0.525134	−	0.851019i	$-0.675985\pi$
$953$	3.76491	−	2.73537i	0.121957	−	0.0886073i	0.647092	+	0.762412i	$0.275985\pi$
$954$		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
$959$	−3.88088	−	0.824907i	−0.125320	−	0.0266376i
$960$		0			0
$961$	−7.29480	−	3.24785i	−0.235316	−	0.104769i
$962$	−6.07281	−	1.97318i	−0.195795	−	0.0636177i
$963$		0			0
$964$	−12.8874	−	17.7379i	−0.415074	−	0.571300i
$965$	0.104959	−	0.998617i	0.00337875	−	0.0321466i
$966$		0			0
$967$	−18.8385	−	10.8764i	−0.605807	−	0.349763i	0.165516	−	0.986207i	$-0.447071\pi$
$967$	−18.8385	−	10.8764i	−0.605807	−	0.349763i	−0.771323	+	0.636444i	$0.780404\pi$
$968$	−11.8616	+	23.9183i	−0.381248	+	0.768763i
$969$		0			0
$970$	0.0621263	+	0.0559387i	0.00199475	+	0.00179608i
$971$	−3.45215	+	4.75147i	−0.110785	+	0.152482i	−0.860809	−	0.508928i	$-0.830042\pi$
$971$	−3.45215	+	4.75147i	−0.110785	+	0.152482i	0.750024	+	0.661410i	$0.230042\pi$
$972$		0			0
$973$	−0.294236	+	0.905565i	−0.00943277	+	0.0290311i
$974$	−9.82799	+	2.08900i	−0.314909	+	0.0669360i
$975$		0			0
$976$	4.76910	+	10.7116i	0.152655	+	0.342869i
$977$	−0.191277	+	0.899889i	−0.00611950	+	0.0287900i	−0.981101	−	0.193494i	$-0.938018\pi$
$977$	−0.191277	+	0.899889i	−0.00611950	+	0.0287900i	0.974982	+	0.222284i	$0.0713513\pi$
$978$		0			0
$979$	18.2868	−	21.6480i	0.584448	−	0.691872i
$980$			0.424783i			0.0135692i
$981$		0			0
$982$	13.9446	+	10.1313i	0.444989	+	0.323304i
$983$	18.9685	−	42.6040i	0.605002	−	1.35886i	−0.308188	−	0.951325i	$-0.599723\pi$
$983$	18.9685	−	42.6040i	0.605002	−	1.35886i	0.913191	−	0.407532i	$-0.133611\pi$
$984$		0			0
$985$	−0.627256	+	0.564784i	−0.0199860	+	0.0179955i
$986$	−1.72157	−	16.3796i	−0.0548258	−	0.521633i
$987$		0			0
$988$	−14.5729	+	16.1849i	−0.463627	+	0.514910i
$989$	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	$0.468548\pi$
$992$	18.6357	−	20.6970i	0.591683	−	0.657131i
$993$		0			0
$994$	0.0591133	+	0.562425i	0.00187496	+	0.0178390i
$995$	−0.309123	+	0.278335i	−0.00979984	+	0.00882382i
$996$		0			0
$997$	−11.6192	+	26.0971i	−0.367982	+	0.826502i	0.630741	+	0.775993i	$0.282751\pi$
$997$	−11.6192	+	26.0971i	−0.367982	+	0.826502i	−0.998724	+	0.0505088i	$0.983916\pi$
$998$	−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.215.3		32
3.2	odd	2	inner	891.2.u.c.215.2		32
9.2	odd	6	inner	891.2.u.c.512.3		32
9.4	even	3		99.2.j.a.17.3	yes	16
9.5	odd	6		99.2.j.a.17.2	✓	16
9.7	even	3	inner	891.2.u.c.512.2		32
11.2	odd	10	inner	891.2.u.c.134.3		32
33.2	even	10	inner	891.2.u.c.134.2		32
36.23	even	6		1584.2.cd.c.17.3		16
36.31	odd	6		1584.2.cd.c.17.2		16
99.2	even	30	inner	891.2.u.c.431.3		32
99.13	odd	30		99.2.j.a.35.2	yes	16
99.14	odd	30		1089.2.d.g.1088.6		16
99.41	even	30		1089.2.d.g.1088.12		16
99.58	even	15		1089.2.d.g.1088.11		16
99.68	even	30		99.2.j.a.35.3	yes	16
99.79	odd	30	inner	891.2.u.c.431.2		32
99.85	odd	30		1089.2.d.g.1088.5		16
396.167	odd	30		1584.2.cd.c.1025.2		16
396.211	even	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	9.5	odd	6
99.2.j.a.17.3	yes	16	9.4	even	3
99.2.j.a.35.2	yes	16	99.13	odd	30
99.2.j.a.35.3	yes	16	99.68	even	30
891.2.u.c.134.2		32	33.2	even	10	inner
891.2.u.c.134.3		32	11.2	odd	10	inner
891.2.u.c.215.2		32	3.2	odd	2	inner
891.2.u.c.215.3		32	1.1	even	1	trivial
891.2.u.c.431.2		32	99.79	odd	30	inner
891.2.u.c.431.3		32	99.2	even	30	inner
891.2.u.c.512.2		32	9.7	even	3	inner
891.2.u.c.512.3		32	9.2	odd	6	inner
1089.2.d.g.1088.5		16	99.85	odd	30
1089.2.d.g.1088.6		16	99.14	odd	30
1089.2.d.g.1088.11		16	99.58	even	15
1089.2.d.g.1088.12		16	99.41	even	30
1584.2.cd.c.17.2		16	36.31	odd	6
1584.2.cd.c.17.3		16	36.23	even	6
1584.2.cd.c.1025.2		16	396.167	odd	30
1584.2.cd.c.1025.3		16	396.211	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.460557 - 0.511500i) q^{2} +(0.159537 + 1.51789i) q^{4} +(0.0298066 - 0.0268380i) q^{5} +(0.100402 - 0.225507i) q^{7} +(1.96356 + 1.42661i) q^{8} -0.0276065i q^{10} +(2.53364 + 2.14025i) q^{11} +(0.478513 - 2.25123i) q^{13} +(-0.0691059 - 0.155214i) q^{14} +(-1.35177 + 0.287327i) q^{16} +(1.32142 - 4.06692i) q^{17} +(-3.64429 + 5.01593i) q^{19} +(0.0454925 + 0.0409616i) q^{20} +(2.26162 - 0.310248i) q^{22} +(5.88883 + 3.39992i) q^{23} +(-0.522474 + 4.97101i) q^{25} +(-0.931121 - 1.28158i) q^{26} +(0.358314 + 0.116423i) q^{28} +(5.11196 + 2.27599i) q^{29} +(-4.69255 - 0.997431i) q^{31} +(-2.90269 + 5.02760i) q^{32} +(-1.47164 - 2.54895i) q^{34} +(-0.00305951 - 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(0.887248 + 4.17418i) q^{38} +(0.0968143 - 0.0101756i) q^{40} +(-8.77271 + 3.90586i) q^{41} +(0.893447 - 0.515832i) q^{43} +(-2.84447 + 4.18724i) q^{44} +(4.45120 - 1.44628i) q^{46} +(11.0653 + 1.16301i) q^{47} +(4.64314 + 5.15673i) q^{49} +(2.30204 + 2.55668i) q^{50} +(3.49347 + 0.367178i) q^{52} +(8.52885 - 2.77119i) q^{53} +(0.132959 - 0.00420408i) q^{55} +(0.518855 - 0.299561i) q^{56} +(3.51852 - 1.56655i) q^{58} +(-2.77304 + 0.291459i) q^{59} +(-1.76403 - 8.29909i) q^{61} +(-2.67137 + 1.94086i) q^{62} +(0.380665 + 1.17156i) q^{64} +(-0.0461556 - 0.0799438i) q^{65} +(-3.97294 + 6.88133i) q^{67} +(6.38397 + 1.35695i) q^{68} +(-0.00622546 - 0.00277175i) q^{70} +(-3.16559 - 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(0.290003 - 2.75920i) q^{74} +(-8.19506 - 4.73142i) q^{76} +(0.737025 - 0.356467i) q^{77} +(2.23761 + 2.01475i) q^{79} +(-0.0325803 + 0.0448429i) q^{80} +(-2.04248 + 6.28611i) q^{82} +(-5.17811 + 1.10064i) q^{83} +(-0.0697608 - 0.156685i) q^{85} +(0.147635 - 0.694568i) q^{86} +(1.92164 + 7.81702i) q^{88} -8.54422i q^{89} +(-0.459624 - 0.333936i) q^{91} +(-4.22123 + 9.48104i) q^{92} +(5.69106 - 5.12425i) q^{94} +(0.0259937 + 0.247313i) q^{95} +(-2.02629 + 2.25042i) q^{97} +4.77610 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{4} + 20 q^{16} + 48 q^{22} + 32 q^{25} + 80 q^{28} - 16 q^{31} - 40 q^{34} - 24 q^{37} - 60 q^{40} - 80 q^{46} + 24 q^{49} + 40 q^{52} + 32 q^{55} - 12 q^{58} + 72 q^{64} - 96 q^{67} - 76 q^{70}+ \cdots - 60 q^{97}+O(q^{100}) \) 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

Varieties

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Database

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