LMFDB - Embedded newform 666.2.bs.b.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

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

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

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bs (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.b.431.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.25585 - 0.284850i) q^{5} +(-0.761384 - 0.638877i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.25585 - 0.284850i) q^{5} +(-0.761384 - 0.638877i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.63414 - 2.83042i) q^{10} +(-2.46523 - 4.26991i) q^{11} +(-3.00612 - 1.40178i) q^{13} +(-0.960050 + 0.257245i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.884960 - 0.412663i) q^{17} +(6.51313 - 4.56054i) q^{19} +(-1.38124 - 2.96207i) q^{20} +(-4.91170 - 0.429718i) q^{22} +(1.73346 + 6.46937i) q^{23} +(5.59535 - 0.986611i) q^{25} +(-2.87251 + 1.65844i) q^{26} +(-0.339940 + 0.933976i) q^{28} +(-1.24596 + 4.64998i) q^{29} +(7.57767 - 7.57767i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.169558 - 0.961611i) q^{34} +(-2.66093 - 1.86321i) q^{35} +(2.37105 + 5.60162i) q^{37} -7.95106i q^{38} +(-3.21863 - 0.567531i) q^{40} +(-7.43066 + 2.70454i) q^{41} +(-1.60293 - 1.60293i) q^{43} +(-3.16924 + 3.77695i) q^{44} +(6.29367 + 2.29071i) q^{46} +(-3.88767 - 2.24455i) q^{47} +(-1.04400 - 5.92079i) q^{49} +(2.40118 - 5.14934i) q^{50} +(-0.289085 + 3.30426i) q^{52} +(7.06523 + 8.42001i) q^{53} +(-9.24269 - 13.1999i) q^{55} +(0.570087 + 0.814169i) q^{56} +(3.09439 + 3.68775i) q^{58} +(0.720442 - 8.23470i) q^{59} +(-3.71848 + 7.97431i) q^{61} +(-1.86089 - 10.5536i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-10.1867 - 3.70767i) q^{65} +(-1.59175 + 1.89697i) q^{67} +(-0.690451 - 0.690451i) q^{68} +(-3.05250 + 1.11102i) q^{70} +(5.07018 + 0.894009i) q^{71} +5.03089i q^{73} +(5.94856 + 1.27071i) q^{74} +(-6.51313 - 4.56054i) q^{76} +(-0.850958 + 4.82602i) q^{77} +(0.278754 + 3.18617i) q^{79} +(-2.31102 + 2.31102i) q^{80} +(-2.04662 + 7.63810i) q^{82} +(-3.09377 + 8.50007i) q^{83} +(2.76375 - 1.59565i) q^{85} +(-2.23245 + 0.393642i) q^{86} +(1.27610 + 4.76246i) q^{88} +(5.91410 + 0.517417i) q^{89} +(1.39325 + 2.98783i) q^{91} +(5.48634 - 3.84158i) q^{92} +(-4.06850 + 1.89717i) q^{94} +(19.9067 - 16.7037i) q^{95} +(11.4622 - 3.07130i) q^{97} +(-5.44884 - 2.54084i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) $ 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{7}{36}\right)$

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 $

$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$2$	0.573576	−	0.819152i	0.405580	−	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	3.25585	−	0.284850i	1.45606	−	0.127389i	0.668538	−	0.743678i	$-0.266920\pi$
$5$	3.25585	−	0.284850i	1.45606	−	0.127389i	0.787520	+	0.616289i	$0.211365\pi$
$6$		0			0
$7$	−0.761384	−	0.638877i	−0.287776	−	0.241473i	0.487459	−	0.873146i	$-0.337924\pi$
$7$	−0.761384	−	0.638877i	−0.287776	−	0.241473i	−0.775235	+	0.631673i	$0.782368\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	1.63414	−	2.83042i	0.516761	−	0.895056i
$11$	−2.46523	−	4.26991i	−0.743295	−	1.28743i	−0.950987	−	0.309231i	$-0.899928\pi$
$11$	−2.46523	−	4.26991i	−0.743295	−	1.28743i	0.207692	−	0.978194i	$-0.433405\pi$
$12$		0			0
$13$	−3.00612	−	1.40178i	−0.833747	−	0.388783i	−0.0416160	−	0.999134i	$-0.513251\pi$
$13$	−3.00612	−	1.40178i	−0.833747	−	0.388783i	−0.792131	+	0.610351i	$0.791028\pi$
$14$	−0.960050	+	0.257245i	−0.256584	+	0.0687515i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	0.884960	−	0.412663i	0.214634	−	0.100086i	−0.312328	−	0.949974i	$-0.601109\pi$
$17$	0.884960	−	0.412663i	0.214634	−	0.100086i	0.526962	+	0.849889i	$0.323331\pi$
$18$		0			0
$19$	6.51313	−	4.56054i	1.49421	−	1.04626i	0.511894	−	0.859049i	$-0.328944\pi$
$19$	6.51313	−	4.56054i	1.49421	−	1.04626i	0.982320	−	0.187211i	$-0.0599449\pi$
$20$	−1.38124	−	2.96207i	−0.308854	−	0.662339i
$21$		0			0
$22$	−4.91170	−	0.429718i	−1.04718	−	0.0916162i
$23$	1.73346	+	6.46937i	0.361452	+	1.34896i	0.872167	+	0.489207i	$0.162714\pi$
$23$	1.73346	+	6.46937i	0.361452	+	1.34896i	−0.510715	+	0.859750i	$0.670619\pi$
$24$		0			0
$25$	5.59535	−	0.986611i	1.11907	−	0.197322i
$26$	−2.87251	+	1.65844i	−0.563345	+	0.325247i
$27$		0			0
$28$	−0.339940	+	0.933976i	−0.0642425	+	0.176505i
$29$	−1.24596	+	4.64998i	−0.231369	+	0.863479i	0.748384	+	0.663266i	$0.230830\pi$
$29$	−1.24596	+	4.64998i	−0.231369	+	0.863479i	−0.979752	+	0.200213i	$0.935836\pi$
$30$		0			0
$31$	7.57767	−	7.57767i	1.36099	−	1.36099i	0.488332	−	0.872658i	$-0.337605\pi$
$31$	7.57767	−	7.57767i	1.36099	−	1.36099i	0.872658	−	0.488332i	$-0.162395\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$		0			0
$34$	0.169558	−	0.961611i	0.0290789	−	0.164915i
$35$	−2.66093	−	1.86321i	−0.449780	−	0.314939i
$36$		0			0
$37$	2.37105	+	5.60162i	0.389798	+	0.920900i
$37$	2.37105	+	5.60162i	0.389798	+	0.920900i
$38$		−	7.95106i		−	1.28983i
$39$		0			0
$40$	−3.21863	−	0.567531i	−0.508910	−	0.0897346i
$41$	−7.43066	+	2.70454i	−1.16047	+	0.422378i	−0.849267	−	0.527964i	$-0.822955\pi$
$41$	−7.43066	+	2.70454i	−1.16047	+	0.422378i	−0.311207	+	0.950342i	$0.600733\pi$
$42$		0			0
$43$	−1.60293	−	1.60293i	−0.244445	−	0.244445i	0.574241	−	0.818686i	$-0.305297\pi$
$43$	−1.60293	−	1.60293i	−0.244445	−	0.244445i	−0.818686	+	0.574241i	$0.805297\pi$
$44$	−3.16924	+	3.77695i	−0.477781	+	0.569397i
$45$		0			0
$46$	6.29367	+	2.29071i	0.927951	+	0.337747i
$47$	−3.88767	−	2.24455i	−0.567075	−	0.327401i	0.188905	−	0.981995i	$-0.439506\pi$
$47$	−3.88767	−	2.24455i	−0.567075	−	0.327401i	−0.755980	+	0.654594i	$0.772840\pi$
$48$		0			0
$49$	−1.04400	−	5.92079i	−0.149142	−	0.845827i
$50$	2.40118	−	5.14934i	0.339578	−	0.728227i
$51$		0			0
$52$	−0.289085	+	3.30426i	−0.0400889	+	0.458219i
$53$	7.06523	+	8.42001i	0.970484	+	1.15658i	0.987642	+	0.156725i	$0.0500936\pi$
$53$	7.06523	+	8.42001i	0.970484	+	1.15658i	−0.0171585	+	0.999853i	$0.505462\pi$
$54$		0			0
$55$	−9.24269	−	13.1999i	−1.24628	−	1.77988i
$56$	0.570087	+	0.814169i	0.0761811	+	0.108798i
$57$		0			0
$58$	3.09439	+	3.68775i	0.406313	+	0.484225i
$59$	0.720442	−	8.23470i	0.0937936	−	1.07207i	−0.792789	−	0.609496i	$-0.791372\pi$
$59$	0.720442	−	8.23470i	0.0937936	−	1.07207i	0.886583	−	0.462570i	$-0.153073\pi$
$60$		0			0
$61$	−3.71848	+	7.97431i	−0.476103	+	1.02101i	0.510801	+	0.859699i	$0.329349\pi$
$61$	−3.71848	+	7.97431i	−0.476103	+	1.02101i	−0.986904	+	0.161307i	$0.948429\pi$
$62$	−1.86089	−	10.5536i	−0.236333	−	1.34031i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−10.1867	−	3.70767i	−1.26351	−	0.459880i
$66$		0			0
$67$	−1.59175	+	1.89697i	−0.194463	+	0.231752i	−0.854461	−	0.519515i	$-0.826113\pi$
$67$	−1.59175	+	1.89697i	−0.194463	+	0.231752i	0.659998	+	0.751267i	$0.270557\pi$
$68$	−0.690451	−	0.690451i	−0.0837295	−	0.0837295i
$69$		0			0
$70$	−3.05250	+	1.11102i	−0.364843	+	0.132792i
$71$	5.07018	+	0.894009i	0.601719	+	0.106099i	0.466206	−	0.884676i	$-0.345621\pi$
$71$	5.07018	+	0.894009i	0.601719	+	0.106099i	0.135513	+	0.990776i	$0.456732\pi$
$72$		0			0
$73$			5.03089i			0.588822i	0.955679	+	0.294411i	$0.0951234\pi$
$73$			5.03089i			0.588822i	−0.955679	+	0.294411i	$0.904877\pi$
$74$	5.94856	+	1.27071i	0.691505	+	0.147717i
$75$		0			0
$76$	−6.51313	−	4.56054i	−0.747107	−	0.523130i
$77$	−0.850958	+	4.82602i	−0.0969756	+	0.549976i
$78$		0			0
$79$	0.278754	+	3.18617i	0.0313622	+	0.358472i	0.995619	+	0.0935025i	$0.0298063\pi$
$79$	0.278754	+	3.18617i	0.0313622	+	0.358472i	−0.964257	+	0.264969i	$0.914638\pi$
$80$	−2.31102	+	2.31102i	−0.258380	+	0.258380i
$81$		0			0
$82$	−2.04662	+	7.63810i	−0.226012	+	0.843487i
$83$	−3.09377	+	8.50007i	−0.339586	+	0.933004i	0.645926	+	0.763400i	$0.276471\pi$
$83$	−3.09377	+	8.50007i	−0.339586	+	0.933004i	−0.985512	+	0.169605i	$0.945751\pi$
$84$		0			0
$85$	2.76375	−	1.59565i	0.299770	−	0.173072i
$86$	−2.23245	+	0.393642i	−0.240732	+	0.0424475i
$87$		0			0
$88$	1.27610	+	4.76246i	0.136032	+	0.507680i
$89$	5.91410	+	0.517417i	0.626893	+	0.0548461i	0.396176	−	0.918175i	$-0.370337\pi$
$89$	5.91410	+	0.517417i	0.626893	+	0.0548461i	0.230718	+	0.973021i	$0.425893\pi$
$90$		0			0
$91$	1.39325	+	2.98783i	0.146052	+	0.313210i
$92$	5.48634	−	3.84158i	0.571991	−	0.400512i
$93$		0			0
$94$	−4.06850	+	1.89717i	−0.419634	+	0.195679i
$95$	19.9067	−	16.7037i	2.04238	−	1.71376i
$96$		0			0
$97$	11.4622	−	3.07130i	1.16381	−	0.311843i	0.375326	−	0.926893i	$-0.377531\pi$
$97$	11.4622	−	3.07130i	1.16381	−	0.311843i	0.788489	+	0.615049i	$0.210864\pi$
$98$	−5.44884	−	2.54084i	−0.550416	−	0.256663i
$99$		0			0
$100$	−2.84083	−	4.92047i	−0.284083	−	0.492047i
$101$	−8.16247	+	14.1378i	−0.812196	+	1.40676i	0.0991277	+	0.995075i	$0.468395\pi$
$101$	−8.16247	+	14.1378i	−0.812196	+	1.40676i	−0.911324	+	0.411690i	$0.864939\pi$
$102$		0			0
$103$	5.39516	+	1.44563i	0.531601	+	0.142442i	0.514628	−	0.857414i	$-0.327930\pi$
$103$	5.39516	+	1.44563i	0.531601	+	0.142442i	0.0169737	+	0.999856i	$0.494597\pi$
$104$	2.54088	+	2.13205i	0.249154	+	0.209065i
$105$		0			0
$106$	10.9497	−	0.957976i	1.06353	−	0.0930469i
$107$	0.929777	+	2.55454i	0.0898850	+	0.246957i	0.976487	−	0.215576i	$-0.0691629\pi$
$107$	0.929777	+	2.55454i	0.0898850	+	0.246957i	−0.886602	+	0.462533i	$0.846941\pi$
$108$		0			0
$109$	4.45426	−	6.36134i	0.426641	−	0.609306i	−0.547072	−	0.837086i	$-0.684258\pi$
$109$	4.45426	−	6.36134i	0.426641	−	0.609306i	0.973713	+	0.227779i	$0.0731465\pi$
$110$	−16.1141			−1.53642
$111$		0			0
$112$	0.993917			0.0939163
$113$	−4.46988	+	6.38365i	−0.420491	+	0.600523i	−0.972383	−	0.233393i	$-0.925017\pi$
$113$	−4.46988	+	6.38365i	−0.420491	+	0.600523i	0.551892	+	0.833916i	$0.313906\pi$
$114$		0			0
$115$	7.48669	+	20.5695i	0.698137	+	1.91812i
$116$	4.79569	−	0.419569i	0.445269	−	0.0389560i
$117$		0			0
$118$	−6.33224	−	5.31338i	−0.582930	−	0.489136i
$119$	−0.937436	−	0.251185i	−0.0859346	−	0.0230261i
$120$		0			0
$121$	−6.65474	+	11.5263i	−0.604976	+	1.04785i
$122$	4.39934	+	7.61988i	0.398298	+	0.689872i
$123$		0			0
$124$	−9.71240	−	4.52897i	−0.872199	−	0.406713i
$125$	2.15197	−	0.576620i	0.192478	−	0.0515744i
$126$		0			0
$127$	−6.77831	+	5.68767i	−0.601477	+	0.504699i	−0.891920	−	0.452193i	$-0.850642\pi$
$127$	−6.77831	+	5.68767i	−0.601477	+	0.504699i	0.290443	+	0.956892i	$0.406197\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$		0			0
$130$	−8.88003	+	6.21786i	−0.778830	+	0.545343i
$131$	1.32526	+	2.84202i	0.115788	+	0.248308i	0.955658	−	0.294480i	$-0.0951464\pi$
$131$	1.32526	+	2.84202i	0.115788	+	0.248308i	−0.839870	+	0.542788i	$0.817369\pi$
$132$		0			0
$133$	−7.87262	−	0.688765i	−0.682643	−	0.0597235i
$134$	0.640919	+	2.39194i	0.0553669	+	0.206632i
$135$		0			0
$136$	−0.961611	+	0.169558i	−0.0824574	+	0.0145395i
$137$	3.38604	−	1.95493i	0.289289	−	0.167021i	−0.348332	−	0.937371i	$-0.613252\pi$
$137$	3.38604	−	1.95493i	0.289289	−	0.167021i	0.637621	+	0.770350i	$0.279919\pi$
$138$		0			0
$139$	−3.35111	+	9.20711i	−0.284238	+	0.780937i	0.712607	+	0.701563i	$0.247514\pi$
$139$	−3.35111	+	9.20711i	−0.284238	+	0.780937i	−0.996845	+	0.0793735i	$0.974708\pi$
$140$	−0.840748	+	3.13771i	−0.0710562	+	0.265185i
$141$		0			0
$142$	3.64046	−	3.64046i	0.305501	−	0.305501i
$143$	1.42533	+	16.2915i	0.119192	+	1.36237i
$144$		0			0
$145$	−2.73210	+	15.4945i	−0.226889	+	1.28675i
$146$	4.12107	+	2.88560i	0.341062	+	0.238814i
$147$		0			0
$148$	4.45285	−	4.14392i	0.366022	−	0.340628i
$149$			12.2590i			1.00430i	0.864781	+	0.502150i	$0.167457\pi$
$149$			12.2590i			1.00430i	−0.864781	+	0.502150i	$0.832543\pi$
$150$		0			0
$151$	−18.3089	−	3.22835i	−1.48995	−	0.262719i	−0.631406	−	0.775452i	$-0.717522\pi$
$151$	−18.3089	−	3.22835i	−1.48995	−	0.262719i	−0.858548	+	0.512733i	$0.828633\pi$
$152$	−7.47155	+	2.71942i	−0.606023	+	0.220574i
$153$		0			0
$154$	3.46516	+	3.46516i	0.279230	+	0.279230i
$155$	22.5132	−	26.8302i	1.80831	−	2.15506i
$156$		0			0
$157$	3.55197	+	1.29281i	0.283478	+	0.103178i	0.479846	−	0.877353i	$-0.340693\pi$
$157$	3.55197	+	1.29281i	0.283478	+	0.103178i	−0.196368	+	0.980530i	$0.562915\pi$
$158$	2.76984	+	1.59917i	0.220357	+	0.127223i
$159$		0			0
$160$	0.567531	+	3.21863i	0.0448673	+	0.254455i
$161$	2.81330	−	6.03315i	0.221719	−	0.475479i
$162$		0			0
$163$	0.754612	−	8.62526i	0.0591058	−	0.675582i	−0.907624	−	0.419784i	$-0.862106\pi$
$163$	0.754612	−	8.62526i	0.0591058	−	0.675582i	0.966730	−	0.255799i	$-0.0823385\pi$
$164$	5.08287	+	6.05753i	0.396905	+	0.473013i
$165$		0			0
$166$	5.18834	+	7.40971i	0.402693	+	0.575105i
$167$	10.4914	+	14.9833i	0.811852	+	1.15944i	0.984659	+	0.174489i	$0.0558272\pi$
$167$	10.4914	+	14.9833i	0.811852	+	1.15944i	−0.172808	+	0.984956i	$0.555284\pi$
$168$		0			0
$169$	−1.28447	−	1.53077i	−0.0988055	−	0.117752i
$170$	0.278140	−	3.17915i	0.0213324	−	0.243830i
$171$		0			0
$172$	−0.958030	+	2.05450i	−0.0730491	+	0.156654i
$173$	−4.21012	−	23.8768i	−0.320090	−	1.81532i	−0.542145	−	0.840285i	$-0.682388\pi$
$173$	−4.21012	−	23.8768i	−0.320090	−	1.81532i	0.222055	−	0.975034i	$-0.428723\pi$
$174$		0			0
$175$	−4.89054	−	2.82355i	−0.369690	−	0.213441i
$176$	4.63312	+	1.68632i	0.349235	+	0.127111i
$177$		0			0
$178$	3.81603	−	4.54777i	0.286024	−	0.340870i
$179$	−0.666266	−	0.666266i	−0.0497991	−	0.0497991i	0.681769	−	0.731568i	$-0.261211\pi$
$179$	−0.666266	−	0.666266i	−0.0497991	−	0.0497991i	−0.731568	+	0.681769i	$0.761211\pi$
$180$		0			0
$181$	6.55132	−	2.38448i	0.486956	−	0.177237i	−0.0868622	−	0.996220i	$-0.527684\pi$
$181$	6.55132	−	2.38448i	0.486956	−	0.177237i	0.573818	+	0.818983i	$0.305462\pi$
$182$	3.24662	+	0.572467i	0.240656	+	0.0424341i
$183$		0			0
$184$		−	6.69759i		−	0.493753i
$185$	9.31539	+	17.5626i	0.684881	+	1.29123i
$186$		0			0
$187$	−3.94367	−	2.76138i	−0.288389	−	0.201932i
$188$	−0.779524	+	4.42090i	−0.0568526	+	0.322427i
$189$		0			0
$190$	−2.26486	−	25.8874i	−0.164310	−	1.87807i
$191$	−1.59232	+	1.59232i	−0.115216	+	0.115216i	−0.762364	−	0.647148i	$-0.775962\pi$
$191$	−1.59232	+	1.59232i	−0.115216	+	0.115216i	0.647148	+	0.762364i	$0.275962\pi$
$192$		0			0
$193$	5.43132	−	20.2700i	0.390955	−	1.45906i	−0.437607	−	0.899166i	$-0.644174\pi$
$193$	5.43132	−	20.2700i	0.390955	−	1.45906i	0.828562	−	0.559897i	$-0.189159\pi$
$194$	4.05861	−	11.1509i	0.291391	−	0.800591i
$195$		0			0
$196$	−5.20666	+	3.00606i	−0.371904	+	0.214719i
$197$	24.5968	−	4.33708i	1.75245	−	0.309004i	0.796960	−	0.604032i	$-0.206440\pi$
$197$	24.5968	−	4.33708i	1.75245	−	0.309004i	0.955488	+	0.295029i	$0.0953291\pi$
$198$		0			0
$199$	−5.29922	−	19.7770i	−0.375652	−	1.40195i	−0.852390	−	0.522906i	$-0.824848\pi$
$199$	−5.29922	−	19.7770i	−0.375652	−	1.40195i	0.476738	−	0.879045i	$-0.341819\pi$
$200$	−5.66005	−	0.495190i	−0.400226	−	0.0350152i
$201$		0			0
$202$	6.89922	+	14.7954i	0.485427	+	1.04100i
$203$	3.91942	−	2.74441i	0.275089	−	0.192620i
$204$		0			0
$205$	−23.4227	+	10.9222i	−1.63591	+	0.762838i
$206$	4.27873	−	3.59028i	0.298113	−	0.250147i
$207$		0			0
$208$	3.20386	−	0.858473i	0.222148	−	0.0595244i
$209$	−35.5295	−	16.5677i	−2.45762	−	1.14601i
$210$		0			0
$211$	10.3724	+	17.9655i	0.714066	+	1.23680i	0.963319	+	0.268360i	$0.0864816\pi$
$211$	10.3724	+	17.9655i	0.714066	+	1.23680i	−0.249253	+	0.968438i	$0.580185\pi$
$212$	5.49577	−	9.51896i	0.377451	−	0.653765i
$213$		0			0
$214$	2.62586	+	0.703596i	0.179500	+	0.0480969i
$215$	−5.67550	−	4.76231i	−0.387066	−	0.324787i
$216$		0			0
$217$	−10.6107	+	0.928318i	−0.720303	+	0.0630183i
$218$	−2.65605	−	7.29743i	−0.179890	−	0.494244i
$219$		0			0
$220$	−9.24269	+	13.1999i	−0.623142	+	0.889940i
$221$	−3.23875			−0.217862
$222$		0			0
$223$	−10.8550			−0.726905			−0.363452	−	0.931613i	$-0.618402\pi$
$223$	−10.8550			−0.726905			−0.363452	+	0.931613i	$0.618402\pi$
$224$	0.570087	−	0.814169i	0.0380906	−	0.0543989i
$225$		0			0
$226$	2.66536	+	7.32302i	0.177297	+	0.487120i
$227$	6.89719	−	0.603426i	0.457783	−	0.0400508i	0.144067	−	0.989568i	$-0.453982\pi$
$227$	6.89719	−	0.603426i	0.457783	−	0.0400508i	0.313715	+	0.949517i	$0.398426\pi$
$228$		0			0
$229$	18.5107	+	15.5323i	1.22322	+	1.02640i	0.998650	+	0.0519448i	$0.0165420\pi$
$229$	18.5107	+	15.5323i	1.22322	+	1.02640i	0.224569	+	0.974458i	$0.427902\pi$
$230$	21.1437	+	5.66545i	1.39418	+	0.373568i
$231$		0			0
$232$	2.40701	−	4.16906i	0.158028	−	0.273712i
$233$	3.08841	+	5.34928i	0.202328	+	0.350443i	0.949278	−	0.314437i	$-0.101816\pi$
$233$	3.08841	+	5.34928i	0.202328	+	0.350443i	−0.746950	+	0.664880i	$0.768482\pi$
$234$		0			0
$235$	−13.2970	−	6.20050i	−0.867402	−	0.404476i
$236$	−7.98449	+	2.13944i	−0.519746	+	0.139265i
$237$		0			0
$238$	−0.743450	+	0.623829i	−0.0481907	+	0.0404368i
$239$	−6.72804	+	3.13734i	−0.435201	+	0.202937i	−0.627857	−	0.778329i	$-0.716068\pi$
$239$	−6.72804	+	3.13734i	−0.435201	+	0.202937i	0.192656	+	0.981266i	$0.438290\pi$
$240$		0			0
$241$	9.36053	−	6.55431i	0.602965	−	0.422200i	−0.231834	−	0.972755i	$-0.574473\pi$
$241$	9.36053	−	6.55431i	0.602965	−	0.422200i	0.834799	+	0.550555i	$0.185584\pi$
$242$	5.62483	+	12.0625i	0.361577	+	0.775405i
$243$		0			0
$244$	8.76520	+	0.766856i	0.561134	+	0.0490929i
$245$	−5.08562	−	18.9798i	−0.324909	−	1.21258i
$246$		0			0
$247$	−25.9721	+	4.57958i	−1.65256	+	0.291392i
$248$	−9.28071	+	5.35822i	−0.589326	+	0.340247i
$249$		0			0
$250$	0.761982	−	2.09353i	0.0481920	−	0.132406i
$251$	−0.695379	+	2.59519i	−0.0438919	+	0.163807i	−0.984393	−	0.175984i	$-0.943689\pi$
$251$	−0.695379	+	2.59519i	−0.0438919	+	0.163807i	0.940501	+	0.339790i	$0.110356\pi$
$252$		0			0
$253$	23.3502	−	23.3502i	1.46802	−	1.46802i
$254$	0.771193	+	8.81478i	0.0483890	+	0.553088i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	11.2599	+	7.88429i	0.702375	+	0.491808i	0.869378	−	0.494148i	$-0.164520\pi$
$257$	11.2599	+	7.88429i	0.702375	+	0.491808i	−0.167003	+	0.985956i	$0.553409\pi$
$258$		0			0
$259$	1.77347	−	5.77979i	0.110198	−	0.359139i
$260$			10.8405i			0.672300i
$261$		0			0
$262$	3.08818	+	0.544530i	0.190789	+	0.0336412i
$263$	−13.7584	+	5.00763i	−0.848377	+	0.308784i	−0.729378	−	0.684111i	$-0.760191\pi$
$263$	−13.7584	+	5.00763i	−0.848377	+	0.308784i	−0.118998	+	0.992894i	$0.537968\pi$
$264$		0			0
$265$	25.4017	+	25.4017i	1.56042	+	1.56042i
$266$	−5.07975	+	6.05381i	−0.311460	+	0.371183i
$267$		0			0
$268$	2.32698	+	0.846951i	0.142143	+	0.0517358i
$269$	−26.7598	−	15.4498i	−1.63157	−	0.941989i	−0.983608	−	0.180320i	$-0.942287\pi$
$269$	−26.7598	−	15.4498i	−1.63157	−	0.941989i	−0.647966	−	0.761670i	$-0.724380\pi$
$270$		0			0
$271$	0.248366	+	1.40855i	0.0150871	+	0.0855634i	0.991422	−	0.130703i	$-0.0417233\pi$
$271$	0.248366	+	1.40855i	0.0150871	+	0.0855634i	−0.976334	+	0.216266i	$0.930612\pi$
$272$	−0.412663	+	0.884960i	−0.0250214	+	0.0536586i
$273$		0			0
$274$	0.340766	−	3.89498i	0.0205865	−	0.235304i
$275$	−18.0066	−	21.4594i	−1.08584	−	1.29405i
$276$		0			0
$277$	4.12948	+	5.89751i	0.248116	+	0.354347i	0.923820	−	0.382826i	$-0.125049\pi$
$277$	4.12948	+	5.89751i	0.248116	+	0.354347i	−0.675704	+	0.737173i	$0.736160\pi$
$278$	5.61990	+	8.02605i	0.337059	+	0.481371i
$279$		0			0
$280$	2.08803	+	2.48842i	0.124784	+	0.148711i
$281$	−0.796118	+	9.09967i	−0.0474924	+	0.542841i	0.934760	+	0.355279i	$0.115614\pi$
$281$	−0.796118	+	9.09967i	−0.0474924	+	0.542841i	−0.982253	+	0.187562i	$0.939941\pi$
$282$		0			0
$283$	5.69526	−	12.2135i	0.338548	−	0.726019i	−0.661158	−	0.750246i	$-0.729935\pi$
$283$	5.69526	−	12.2135i	0.338548	−	0.726019i	0.999706	+	0.0242275i	$0.00771260\pi$
$284$	−0.894009	−	5.07018i	−0.0530497	−	0.300860i
$285$		0			0
$286$	14.1628	+	8.17689i	0.837463	+	0.483509i
$287$	7.38545	+	2.68809i	0.435950	+	0.158673i
$288$		0			0
$289$	−10.3145	+	12.2924i	−0.606737	+	0.723081i
$290$	11.1253	+	11.1253i	0.653300	+	0.653300i
$291$		0			0
$292$	4.72749	−	1.72067i	0.276656	−	0.100694i
$293$	−24.1474	−	4.25783i	−1.41070	−	0.248745i	−0.584169	−	0.811632i	$-0.698580\pi$
$293$	−24.1474	−	4.25783i	−1.41070	−	0.248745i	−0.826534	+	0.562887i	$0.809691\pi$
$294$		0			0
$295$		−	27.0161i		−	1.57294i
$296$	−0.840453	−	6.02442i	−0.0488503	−	0.350162i
$297$		0			0
$298$	10.0420	+	7.03150i	0.581718	+	0.407324i
$299$	3.85761	−	21.8776i	0.223092	−	1.26522i
$300$		0			0
$301$	0.196371	+	2.24453i	0.0113186	+	0.129372i
$302$	−13.1460	+	13.1460i	−0.756469	+	0.756469i
$303$		0			0
$304$	−2.05789	+	7.68013i	−0.118028	+	0.440486i
$305$	−9.83533	+	27.0223i	−0.563169	+	1.54729i
$306$		0			0
$307$	−10.8486	+	6.26344i	−0.619162	+	0.357473i	−0.776543	−	0.630065i	$-0.783028\pi$
$307$	−10.8486	+	6.26344i	−0.619162	+	0.357473i	0.157381	+	0.987538i	$0.449695\pi$
$308$	4.82602	−	0.850958i	0.274988	−	0.0484878i
$309$		0			0
$310$	−9.06497	−	33.8309i	−0.514856	−	1.92147i
$311$	−7.63928	−	0.668350i	−0.433184	−	0.0378987i	−0.131521	−	0.991313i	$-0.541986\pi$
$311$	−7.63928	−	0.668350i	−0.433184	−	0.0378987i	−0.301663	+	0.953415i	$0.597542\pi$
$312$		0			0
$313$	3.92846	+	8.42461i	0.222050	+	0.476187i	0.985499	−	0.169680i	$-0.0542735\pi$
$313$	3.92846	+	8.42461i	0.222050	+	0.476187i	−0.763449	+	0.645868i	$0.776496\pi$
$314$	3.09634	−	2.16808i	0.174736	−	0.122352i
$315$		0			0
$316$	2.89868	−	1.35168i	0.163063	−	0.0760377i
$317$	−6.99987	+	5.87359i	−0.393152	+	0.329894i	−0.817840	−	0.575446i	$-0.804828\pi$
$317$	−6.99987	+	5.87359i	−0.393152	+	0.329894i	0.424688	+	0.905340i	$0.360384\pi$
$318$		0			0
$319$	22.9266	−	6.14315i	1.28364	−	0.343950i
$320$	2.96207	+	1.38124i	0.165585	+	0.0772134i
$321$		0			0
$322$	−3.32842	−	5.76500i	−0.185486	−	0.321271i
$323$	3.88189	−	6.72362i	0.215994	−	0.374112i
$324$		0			0
$325$	−18.2033	−	4.87756i	−1.00974	−	0.270558i
$326$	−6.63257	−	5.56539i	−0.367344	−	0.308238i
$327$		0			0
$328$	7.87745	−	0.689188i	0.434959	−	0.0380540i
$329$	1.52602	+	4.19271i	0.0841323	+	0.231152i
$330$		0			0
$331$	−5.35923	+	7.65378i	−0.294570	+	0.420690i	−0.938970	−	0.343999i	$-0.888218\pi$
$331$	−5.35923	+	7.65378i	−0.294570	+	0.420690i	0.644400	+	0.764689i	$0.277107\pi$
$332$	9.04559			0.496441
$333$		0			0
$334$	18.2913			1.00085
$335$	−4.64213	+	6.62965i	−0.253627	+	0.362217i
$336$		0			0
$337$	2.12008	+	5.82487i	0.115488	+	0.317301i	0.983947	−	0.178460i	$-0.0571115\pi$
$337$	2.12008	+	5.82487i	0.115488	+	0.317301i	−0.868459	+	0.495761i	$0.834889\pi$
$338$	−1.99068	+	0.174162i	−0.108279	+	0.00947315i
$339$		0			0
$340$	−2.44468	−	2.05133i	−0.132581	−	0.111249i
$341$	−51.0367	−	13.6752i	−2.76379	−	0.740555i
$342$		0			0
$343$	−6.46649	+	11.2003i	−0.349157	+	0.604758i
$344$	1.13345	+	1.96319i	0.0611113	+	0.105848i
$345$		0			0
$346$	−21.9736	−	10.2464i	−1.18131	−	0.550852i
$347$	−6.39069	+	1.71238i	−0.343070	+	0.0919253i	−0.426240	−	0.904610i	$-0.640162\pi$
$347$	−6.39069	+	1.71238i	−0.343070	+	0.0919253i	0.0831702	+	0.996535i	$0.473495\pi$
$348$		0			0
$349$	9.63233	−	8.08248i	0.515607	−	0.432645i	−0.347490	−	0.937684i	$-0.612966\pi$
$349$	9.63233	−	8.08248i	0.515607	−	0.432645i	0.863097	+	0.505038i	$0.168522\pi$
$350$	−5.11802	+	2.38657i	−0.273569	+	0.127568i
$351$		0			0
$352$	4.03880	−	2.82800i	0.215269	−	0.150733i
$353$	−7.03571	−	15.0881i	−0.374473	−	0.803060i	−0.999743	−	0.0226516i	$-0.992789\pi$
$353$	−7.03571	−	15.0881i	−0.374473	−	0.803060i	0.625271	−	0.780408i	$-0.284989\pi$
$354$		0			0
$355$	16.7624	+	1.46652i	0.889654	+	0.0778347i
$356$	−1.53653	−	5.73440i	−0.0814358	−	0.303923i
$357$		0			0
$358$	−0.927928	+	0.163619i	−0.0490425	+	0.00864751i
$359$	25.1506	−	14.5207i	1.32740	−	0.766373i	0.342501	−	0.939517i	$-0.388726\pi$
$359$	25.1506	−	14.5207i	1.32740	−	0.766373i	0.984897	+	0.173144i	$0.0553926\pi$
$360$		0			0
$361$	15.1239	−	41.5526i	0.795995	−	2.18698i
$362$	1.80443	−	6.73421i	0.0948385	−	0.353942i
$363$		0			0
$364$	2.33112	−	2.33112i	0.122184	−	0.122184i
$365$	1.43305	+	16.3798i	0.0750092	+	0.857359i
$366$		0			0
$367$	3.80260	−	21.5656i	0.198494	−	1.12572i	−0.708860	−	0.705349i	$-0.750790\pi$
$367$	3.80260	−	21.5656i	0.198494	−	1.12572i	0.907354	−	0.420367i	$-0.138099\pi$
$368$	−5.48634	−	3.84158i	−0.285995	−	0.200256i
$369$		0			0
$370$	19.7295	+	2.44278i	1.02569	+	0.126994i
$371$		−	10.9247i		−	0.567181i
$372$		0			0
$373$	−16.6650	−	2.93849i	−0.862881	−	0.152149i	−0.275343	−	0.961346i	$-0.588792\pi$
$373$	−16.6650	−	2.93849i	−0.862881	−	0.152149i	−0.587538	+	0.809197i	$0.699903\pi$
$374$	−4.52399	+	1.64660i	−0.233930	+	0.0851435i
$375$		0			0
$376$	3.17427	+	3.17427i	0.163701	+	0.163701i
$377$	10.2637	−	12.2318i	0.528609	−	0.629971i
$378$		0			0
$379$	−27.2065	−	9.90236i	−1.39750	−	0.508650i	−0.470068	−	0.882630i	$-0.655771\pi$
$379$	−27.2065	−	9.90236i	−1.39750	−	0.508650i	−0.927437	+	0.373980i	$0.877993\pi$
$380$	−22.5048	−	12.9932i	−1.15447	−	0.666535i
$381$		0			0
$382$	0.391035	+	2.21767i	0.0200071	+	0.113466i
$383$	9.83179	−	21.0843i	0.502381	−	1.07736i	−0.477657	−	0.878547i	$-0.658514\pi$
$383$	9.83179	−	21.0843i	0.502381	−	1.07736i	0.980038	−	0.198813i	$-0.0637085\pi$
$384$		0			0
$385$	−1.39590	+	15.9552i	−0.0711415	+	0.813151i
$386$	−13.4889	−	16.0754i	−0.686567	−	0.818219i
$387$		0			0
$388$	−6.80640	−	9.72054i	−0.345542	−	0.493486i
$389$	−1.99842	−	2.85404i	−0.101324	−	0.144705i	0.765289	−	0.643687i	$-0.222596\pi$
$389$	−1.99842	−	2.85404i	−0.101324	−	0.144705i	−0.866612	+	0.498982i	$0.833707\pi$
$390$		0			0
$391$	4.20372	+	5.00980i	0.212591	+	0.253356i
$392$	−0.523992	+	5.98925i	−0.0264656	+	0.302503i
$393$		0			0
$394$	10.5554	−	22.6361i	0.531774	−	1.14039i
$395$	1.81516	+	10.2943i	0.0913305	+	0.517961i
$396$		0			0
$397$	14.0980	+	8.13949i	0.707558	+	0.408509i	0.810156	−	0.586214i	$-0.199382\pi$
$397$	14.0980	+	8.13949i	0.707558	+	0.408509i	−0.102598	+	0.994723i	$0.532715\pi$
$398$	−19.2398	−	7.00273i	−0.964406	−	0.351015i
$399$		0			0
$400$	−3.65211	+	4.35241i	−0.182605	+	0.217621i
$401$	6.17561	+	6.17561i	0.308395	+	0.308395i	0.844287	−	0.535892i	$-0.180024\pi$
$401$	6.17561	+	6.17561i	0.308395	+	0.308395i	−0.535892	+	0.844287i	$0.680024\pi$
$402$		0			0
$403$	−33.4016	+	12.1572i	−1.66385	+	0.605592i
$404$	16.0769	+	2.83480i	0.799857	+	0.141036i
$405$		0			0
$406$		−	4.78473i		−	0.237462i
$407$	18.0732	−	23.9334i	0.895855	−	1.18634i
$408$		0			0
$409$	−26.5845	−	18.6147i	−1.31452	−	0.920435i	−0.314929	−	0.949115i	$-0.601981\pi$
$409$	−26.5845	−	18.6147i	−1.31452	−	0.920435i	−0.999589	+	0.0286800i	$0.990870\pi$
$410$	−4.48778	+	25.4514i	−0.221635	+	1.25696i
$411$		0			0
$412$	−0.486807	−	5.56423i	−0.0239833	−	0.274130i
$413$	−5.80949	+	5.80949i	−0.285867	+	0.285867i
$414$		0			0
$415$	−7.65161	+	28.5562i	−0.375603	+	1.40177i
$416$	1.13444	−	3.11685i	0.0556205	−	0.152816i
$417$		0			0
$418$	−33.9503	+	19.6012i	−1.66056	+	0.958726i
$419$	1.74113	−	0.307009i	0.0850599	−	0.0149983i	−0.130956	−	0.991388i	$-0.541805\pi$
$419$	1.74113	−	0.307009i	0.0850599	−	0.0149983i	0.216016	+	0.976390i	$0.430694\pi$
$420$		0			0
$421$	−2.12875	−	7.94461i	−0.103749	−	0.387197i	0.894451	−	0.447166i	$-0.147567\pi$
$421$	−2.12875	−	7.94461i	−0.103749	−	0.387197i	−0.998200	+	0.0599689i	$0.980900\pi$
$422$	20.6659	+	1.80803i	1.00600	+	0.0880135i
$423$		0			0
$424$	−4.64523	−	9.96172i	−0.225592	−	0.483784i
$425$	4.54452	−	3.18211i	0.220442	−	0.154355i
$426$		0			0
$427$	7.92580	−	3.69586i	0.383556	−	0.178855i
$428$	2.08248	−	1.74741i	0.100661	−	0.0844643i
$429$		0			0
$430$	−7.15639	+	1.91755i	−0.345112	+	0.0924725i
$431$	7.35797	+	3.43108i	0.354421	+	0.165269i	0.591671	−	0.806179i	$-0.298468\pi$
$431$	7.35797	+	3.43108i	0.354421	+	0.165269i	−0.237250	+	0.971449i	$0.576246\pi$
$432$		0			0
$433$	−12.8888	−	22.3240i	−0.619395	−	1.07282i	−0.989596	−	0.143871i	$-0.954045\pi$
$433$	−12.8888	−	22.3240i	−0.619395	−	1.07282i	0.370202	−	0.928951i	$-0.379289\pi$
$434$	−5.32563	+	9.22426i	−0.255638	+	0.442778i
$435$		0			0
$436$	−7.50115	−	2.00993i	−0.359240	−	0.0962581i
$437$	40.7941	+	34.2303i	1.95145	+	1.63746i
$438$		0			0
$439$	5.50739	−	0.481834i	0.262853	−	0.0229967i	0.0450327	−	0.998986i	$-0.485661\pi$
$439$	5.50739	−	0.481834i	0.262853	−	0.0229967i	0.217821	+	0.975989i	$0.430105\pi$
$440$	5.51136	+	15.1423i	0.262744	+	0.721883i
$441$		0			0
$442$	−1.85767	+	2.65303i	−0.0883605	+	0.126192i
$443$	−32.4471			−1.54161			−0.770804	−	0.637072i	$-0.780145\pi$
$443$	−32.4471			−1.54161			−0.770804	+	0.637072i	$0.780145\pi$
$444$		0			0
$445$	19.4028			0.919780
$446$	−6.22617	+	8.89189i	−0.294818	+	0.421043i
$447$		0			0
$448$	−0.339940	−	0.933976i	−0.0160606	−	0.0441262i
$449$	4.56754	−	0.399608i	0.215555	−	0.0188587i	0.0211335	−	0.999777i	$-0.493272\pi$
$449$	4.56754	−	0.399608i	0.215555	−	0.0188587i	0.194422	+	0.980918i	$0.437717\pi$
$450$		0			0
$451$	29.8664	+	25.0609i	1.40635	+	1.18007i
$452$	7.52745	+	2.01698i	0.354062	+	0.0948705i
$453$		0			0
$454$	3.46177	−	5.99596i	0.162469	−	0.281404i
$455$	5.38728	+	9.33105i	0.252560	+	0.437446i
$456$		0			0
$457$	30.9632	+	14.4384i	1.44840	+	0.675399i	0.978296	−	0.207212i	$-0.0664391\pi$
$457$	30.9632	+	14.4384i	1.44840	+	0.675399i	0.470103	+	0.882612i	$0.344217\pi$
$458$	23.3406	−	6.25409i	1.09063	−	0.292235i
$459$		0			0
$460$	16.7684	−	14.0704i	0.781831	−	0.656034i
$461$	13.2669	−	6.18644i	0.617899	−	0.288131i	−0.0883554	−	0.996089i	$-0.528161\pi$
$461$	13.2669	−	6.18644i	0.617899	−	0.288131i	0.706255	+	0.707958i	$0.250383\pi$
$462$		0			0
$463$	30.0006	−	21.0067i	1.39425	−	0.976263i	0.395930	−	0.918281i	$-0.370422\pi$
$463$	30.0006	−	21.0067i	1.39425	−	0.976263i	0.998318	−	0.0579821i	$-0.0184666\pi$
$464$	−2.03449	−	4.36298i	−0.0944488	−	0.202546i
$465$		0			0
$466$	6.15331	+	0.538345i	0.285047	+	0.0249384i
$467$	−8.38364	−	31.2882i	−0.387948	−	1.44784i	−0.833466	−	0.552570i	$-0.813647\pi$
$467$	−8.38364	−	31.2882i	−0.387948	−	1.44784i	0.445518	−	0.895273i	$-0.353020\pi$
$468$		0			0
$469$	2.42386	−	0.427392i	0.111924	−	0.0197352i
$470$	−12.7060	+	7.33582i	−0.586085	+	0.338376i
$471$		0			0
$472$	−2.82719	+	7.76764i	−0.130132	+	0.357535i
$473$	−2.89278	+	10.7960i	−0.133010	+	0.496400i
$474$		0			0
$475$	31.9438	−	31.9438i	1.46568	−	1.46568i
$476$	0.0845851	+	0.966812i	0.00387695	+	0.0443138i
$477$		0			0
$478$	−1.28909	+	7.31079i	−0.0589616	+	0.334388i
$479$	1.08202	+	0.757635i	0.0494385	+	0.0346172i	0.598034	−	0.801470i	$-0.295949\pi$
$479$	1.08202	+	0.757635i	0.0494385	+	0.0346172i	−0.548596	+	0.836088i	$0.684837\pi$
$480$		0			0
$481$	0.724556	−	20.1628i	0.0330369	−	0.919345i
$482$		−	11.4271i		−	0.520490i
$483$		0			0
$484$	13.1073	+	2.31117i	0.595785	+	0.105053i
$485$	36.4444	−	13.2647i	1.65486	−	0.602319i
$486$		0			0
$487$	−13.4766	−	13.4766i	−0.610682	−	0.610682i	0.332442	−	0.943124i	$-0.392127\pi$
$487$	−13.4766	−	13.4766i	−0.610682	−	0.610682i	−0.943124	+	0.332442i	$0.892127\pi$
$488$	5.65568	−	6.74018i	0.256021	−	0.305114i
$489$		0			0
$490$	−18.4643	−	6.72047i	−0.834134	−	0.303600i
$491$	−33.5944	−	19.3958i	−1.51610	−	0.875318i	−0.999821	−	0.0188945i	$-0.993985\pi$
$491$	−33.5944	−	19.3958i	−1.51610	−	0.875318i	−0.516274	−	0.856424i	$-0.672681\pi$
$492$		0			0
$493$	0.816254	+	4.62921i	0.0367622	+	0.208489i
$494$	−11.1456	+	23.9018i	−0.501464	+	1.07539i
$495$		0			0
$496$	−0.934000	+	10.6757i	−0.0419378	+	0.479352i
$497$	−3.28919	−	3.91990i	−0.147540	−	0.175832i
$498$		0			0
$499$	−5.63615	−	8.04926i	−0.252309	−	0.360334i	0.672939	−	0.739698i	$-0.265032\pi$
$499$	−5.63615	−	8.04926i	−0.252309	−	0.360334i	−0.925248	+	0.379364i	$0.876143\pi$
$500$	−1.27786	−	1.82498i	−0.0571478	−	0.0816155i
$501$		0			0
$502$	1.72700	+	2.05816i	0.0770798	+	0.0918602i
$503$	−1.68927	+	19.3085i	−0.0753210	+	0.860924i	0.860731	+	0.509061i	$0.170007\pi$
$503$	−1.68927	+	19.3085i	−0.0753210	+	0.860924i	−0.936052	+	0.351863i	$0.885548\pi$
$504$		0			0
$505$	−22.5486	+	48.3556i	−1.00340	+	2.15180i
$506$	−5.73425	−	32.5205i	−0.254918	−	1.44571i
$507$		0			0
$508$	7.66298	+	4.42422i	0.339990	+	0.196293i
$509$	−8.93419	−	3.25178i	−0.396001	−	0.144133i	0.136341	−	0.990662i	$-0.456466\pi$
$509$	−8.93419	−	3.25178i	−0.396001	−	0.144133i	−0.532342	+	0.846529i	$0.678688\pi$
$510$		0			0
$511$	3.21412	−	3.83044i	0.142184	−	0.169449i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	12.9169	−	4.70135i	0.569738	−	0.207368i
$515$	17.9776	+	3.16994i	0.792188	+	0.139684i
$516$		0			0
$517$			22.1333i			0.973423i
$518$	−3.71731	−	4.76789i	−0.163329	−	0.209489i
$519$		0			0
$520$	8.88003	+	6.21786i	0.389415	+	0.272671i
$521$	−6.80043	+	38.5671i	−0.297932	+	1.68966i	0.357108	+	0.934063i	$0.383763\pi$
$521$	−6.80043	+	38.5671i	−0.297932	+	1.68966i	−0.655040	+	0.755594i	$0.727348\pi$
$522$		0			0
$523$	3.54430	+	40.5115i	0.154981	+	1.77145i	0.533451	+	0.845831i	$0.320895\pi$
$523$	3.54430	+	40.5115i	0.154981	+	1.77145i	−0.378469	+	0.925614i	$0.623549\pi$
$524$	2.21736	−	2.21736i	0.0968659	−	0.0968659i
$525$		0			0
$526$	−3.78946	+	14.1424i	−0.165228	+	0.616640i
$527$	3.57891	−	9.83296i	0.155900	−	0.428331i
$528$		0			0
$529$	−18.9293	+	10.9288i	−0.823013	+	0.475167i
$530$	35.3777	−	6.23805i	1.53671	−	0.270963i
$531$		0			0
$532$	2.04537	+	7.63341i	0.0886779	+	0.330950i
$533$	26.1286	+	2.28595i	1.13175	+	0.0990157i
$534$		0			0
$535$	3.75487	+	8.05235i	0.162337	+	0.348133i
$536$	2.02848	−	1.42036i	0.0876171	−	0.0613501i
$537$		0			0
$538$	−28.0045	+	13.0587i	−1.20736	+	0.563001i
$539$	−22.7075	+	19.0539i	−0.978083	+	0.820709i
$540$		0			0
$541$	−23.7858	+	6.37340i	−1.02263	+	0.274014i	−0.730899	−	0.682486i	$-0.760899\pi$
$541$	−23.7858	+	6.37340i	−1.02263	+	0.274014i	−0.291734	+	0.956499i	$0.594232\pi$
$542$	1.29627	+	0.604463i	0.0556798	+	0.0259639i
$543$		0			0
$544$	0.488223	+	0.845626i	0.0209324	+	0.0362559i
$545$	12.6904	−	21.9803i	0.543595	−	0.941534i
$546$		0			0
$547$	−16.6299	−	4.45598i	−0.711044	−	0.190524i	−0.114872	−	0.993380i	$-0.536646\pi$
$547$	−16.6299	−	4.45598i	−0.711044	−	0.190524i	−0.596172	+	0.802857i	$0.703312\pi$
$548$	−2.99512	−	2.51321i	−0.127945	−	0.107359i
$549$		0			0
$550$	−27.9067	+	2.44152i	−1.18994	+	0.104107i
$551$	13.0913	+	35.9682i	0.557710	+	1.53229i
$552$		0			0
$553$	1.82333	−	2.60399i	0.0775360	−	0.110733i
$554$	7.19953			0.305879
$555$		0			0
$556$	9.79800			0.415528
$557$	−12.5884	+	17.9780i	−0.533386	+	0.761754i	−0.991912	−	0.126927i	$-0.959489\pi$
$557$	−12.5884	+	17.9780i	−0.533386	+	0.761754i	0.458526	+	0.888681i	$0.348378\pi$
$558$		0			0
$559$	2.57166	+	7.06557i	0.108769	+	0.298842i
$560$	3.23604	−	0.283117i	0.136748	−	0.0119639i
$561$		0			0
$562$	6.99738	+	5.87150i	0.295167	+	0.247674i
$563$	15.8435	+	4.24525i	0.667724	+	0.178916i	0.576729	−	0.816935i	$-0.304329\pi$
$563$	15.8435	+	4.24525i	0.667724	+	0.178916i	0.0909944	+	0.995851i	$0.470995\pi$
$564$		0			0
$565$	−12.7349	+	22.0574i	−0.535759	+	0.927962i
$566$	−6.73807	−	11.6707i	−0.283222	−	0.490555i
$567$		0			0
$568$	−4.66603	−	2.17580i	−0.195782	−	0.0912947i
$569$	−25.7751	+	6.90642i	−1.08055	+	0.289532i	−0.754821	−	0.655931i	$-0.772276\pi$
$569$	−25.7751	+	6.90642i	−1.08055	+	0.289532i	−0.325728	+	0.945463i	$0.605609\pi$
$570$		0			0
$571$	−9.81239	+	8.23357i	−0.410636	+	0.344564i	−0.824587	−	0.565735i	$-0.808593\pi$
$571$	−9.81239	+	8.23357i	−0.410636	+	0.344564i	0.413952	+	0.910299i	$0.364148\pi$
$572$	14.8216	−	6.91140i	0.619720	−	0.288980i
$573$		0			0
$574$	6.43807	−	4.50799i	0.268720	−	0.188160i
$575$	16.0821	+	34.4882i	0.670670	+	1.43826i
$576$		0			0
$577$	−26.1333	−	2.28637i	−1.08794	−	0.0951827i	−0.470956	−	0.882156i	$-0.656091\pi$
$577$	−26.1333	−	2.28637i	−1.08794	−	0.0951827i	−0.616986	+	0.786974i	$0.711647\pi$
$578$	4.15315	+	15.4998i	0.172748	+	0.644706i
$579$		0			0
$580$	15.4945	−	2.73210i	0.643375	−	0.113444i
$581$	7.78605	−	4.49528i	0.323020	−	0.186496i
$582$		0			0
$583$	18.5352	−	50.9251i	0.767651	−	2.10910i
$584$	1.30209	−	4.85947i	0.0538809	−	0.201086i
$585$		0			0
$586$	−17.3382	+	17.3382i	−0.716233	+	0.716233i
$587$	1.86447	+	21.3109i	0.0769548	+	0.879597i	0.932335	+	0.361596i	$0.117768\pi$
$587$	1.86447	+	21.3109i	0.0769548	+	0.879597i	−0.855380	+	0.518001i	$0.826676\pi$
$588$		0			0
$589$	14.7961	−	83.9126i	0.609661	−	3.45756i
$590$	−22.1303	−	15.4958i	−0.911090	−	0.637952i
$591$		0			0
$592$	−5.41698	−	2.76701i	−0.222637	−	0.113723i
$593$		−	21.3003i		−	0.874697i	−0.899292	−	0.437349i	$-0.855918\pi$
$593$		−	21.3003i		−	0.874697i	0.899292	−	0.437349i	$-0.144082\pi$
$594$		0			0
$595$	−3.12370	−	0.550792i	−0.128059	−	0.0225803i
$596$	11.5197	−	4.19284i	0.471867	−	0.171745i
$597$		0			0
$598$	−15.7085	−	15.7085i	−0.642367	−	0.642367i
$599$	16.5907	−	19.7720i	0.677878	−	0.807864i	−0.311955	−	0.950097i	$-0.600984\pi$
$599$	16.5907	−	19.7720i	0.677878	−	0.807864i	0.989833	+	0.142233i	$0.0454283\pi$
$600$		0			0
$601$	20.3844	+	7.41930i	0.831495	+	0.302640i	0.722472	−	0.691400i	$-0.243006\pi$
$601$	20.3844	+	7.41930i	0.831495	+	0.302640i	0.109023	+	0.994039i	$0.465228\pi$
$602$	1.95124	+	1.12655i	0.0795268	+	0.0459148i
$603$		0			0
$604$	3.22835	+	18.3089i	0.131360	+	0.744977i
$605$	−18.3835	+	39.4236i	−0.747396	+	1.60280i
$606$		0			0
$607$	1.11780	−	12.7765i	0.0453700	−	0.518582i	−0.939174	−	0.343442i	$-0.888407\pi$
$607$	1.11780	−	12.7765i	0.0453700	−	0.518582i	0.984544	−	0.175139i	$-0.0560375\pi$
$608$	5.11084	+	6.09087i	0.207272	+	0.247017i
$609$		0			0
$610$	16.4941	+	23.5560i	0.667826	+	0.953755i
$611$	8.54045	+	12.1970i	0.345510	+	0.493439i
$612$		0			0
$613$	25.8434	+	30.7989i	1.04380	+	1.24396i	0.969078	+	0.246753i	$0.0793636\pi$
$613$	25.8434	+	30.7989i	1.04380	+	1.24396i	0.0747255	+	0.997204i	$0.476192\pi$
$614$	−1.09179	+	12.4792i	−0.0440610	+	0.503620i
$615$		0			0
$616$	2.07103	−	4.44133i	0.0834441	−	0.178946i
$617$	−1.68000	−	9.52777i	−0.0676344	−	0.383574i	−0.999770	−	0.0214633i	$-0.993167\pi$
$617$	−1.68000	−	9.52777i	−0.0676344	−	0.383574i	0.932135	−	0.362110i	$-0.117944\pi$
$618$		0			0
$619$	−29.7334	−	17.1666i	−1.19509	−	0.689984i	−0.235631	−	0.971842i	$-0.575716\pi$
$619$	−29.7334	−	17.1666i	−1.19509	−	0.689984i	−0.959456	+	0.281858i	$0.909049\pi$
$620$	−32.9121	−	11.9790i	−1.32178	−	0.481090i
$621$		0			0
$622$	−4.92919	+	5.87438i	−0.197643	+	0.235541i
$623$	−4.17234	−	4.17234i	−0.167161	−	0.167161i
$624$		0			0
$625$	−19.8529	+	7.22585i	−0.794115	+	0.289034i
$626$	9.15431	+	1.61415i	0.365880	+	0.0645145i
$627$		0			0
$628$		−	3.77993i		−	0.150836i
$629$	4.40987	+	3.97876i	0.175833	+	0.158644i
$630$		0			0
$631$	25.6688	+	17.9735i	1.02186	+	0.715513i	0.959260	−	0.282525i	$-0.0911721\pi$
$631$	25.6688	+	17.9735i	1.02186	+	0.715513i	0.0625993	+	0.998039i	$0.480061\pi$
$632$	0.555386	−	3.14975i	0.0220921	−	0.125290i
$633$		0			0
$634$	0.796402	+	9.10291i	0.0316292	+	0.361523i
$635$	−20.4490	+	20.4490i	−0.811493	+	0.811493i
$636$		0			0
$637$	−5.16125	+	19.2620i	−0.204496	+	0.763190i
$638$	8.11796	−	22.3039i	0.321393	−	0.883020i
$639$		0			0
$640$	2.83042	−	1.63414i	0.111882	−	0.0645951i
$641$	12.4535	−	2.19588i	0.491883	−	0.0867322i	0.0777954	−	0.996969i	$-0.475212\pi$
$641$	12.4535	−	2.19588i	0.491883	−	0.0867322i	0.414087	+	0.910237i	$0.364101\pi$
$642$		0			0
$643$	−2.03426	−	7.59195i	−0.0802232	−	0.299397i	0.914144	−	0.405390i	$-0.132864\pi$
$643$	−2.03426	−	7.59195i	−0.0802232	−	0.299397i	−0.994367	+	0.105993i	$0.966198\pi$
$644$	−6.63151	−	0.580182i	−0.261318	−	0.0228624i
$645$		0			0
$646$	−3.28111	−	7.03637i	−0.129094	−	0.276842i
$647$	26.0725	−	18.2561i	1.02501	−	0.717723i	0.0650609	−	0.997881i	$-0.479276\pi$
$647$	26.0725	−	18.2561i	1.02501	−	0.717723i	0.959954	+	0.280158i	$0.0903869\pi$
$648$		0			0
$649$	−36.9374	+	17.2242i	−1.44992	+	0.676109i
$650$	−14.4364	+	12.1136i	−0.566244	+	0.475135i
$651$		0			0
$652$	−8.36318	+	2.24091i	−0.327528	+	0.0877607i
$653$	31.5736	+	14.7230i	1.23557	+	0.576156i	0.927005	−	0.375048i	$-0.122374\pi$
$653$	31.5736	+	14.7230i	1.23557	+	0.576156i	0.308564	+	0.951204i	$0.400152\pi$
$654$		0			0
$655$	5.12438	+	8.87568i	0.200226	+	0.346801i
$656$	3.95377	−	6.84813i	0.154369	−	0.267375i
$657$		0			0
$658$	4.30976	+	1.15480i	0.168012	+	0.0450186i
$659$	−18.4141	−	15.4513i	−0.717313	−	0.601897i	0.209327	−	0.977846i	$-0.432873\pi$
$659$	−18.4141	−	15.4513i	−0.717313	−	0.601897i	−0.926641	+	0.375948i	$0.877317\pi$
$660$		0			0
$661$	−19.9528	+	1.74565i	−0.776076	+	0.0678978i	−0.468310	−	0.883564i	$-0.655137\pi$
$661$	−19.9528	+	1.74565i	−0.776076	+	0.0678978i	−0.307766	+	0.951462i	$0.599581\pi$
$662$	3.19568	+	8.78005i	0.124204	+	0.341247i
$663$		0			0
$664$	5.18834	−	7.40971i	0.201346	−	0.287553i
$665$	−25.8282			−1.00158
$666$		0			0
$667$	−32.2423			−1.24843
$668$	10.4914	−	14.9833i	0.405926	−	0.579722i
$669$		0			0
$670$	2.76808	+	7.60522i	0.106940	+	0.293815i
$671$	43.2165	−	3.78095i	1.66835	−	0.145962i
$672$		0			0
$673$	−9.80797	−	8.22986i	−0.378069	−	0.317238i	0.433875	−	0.900973i	$-0.357146\pi$
$673$	−9.80797	−	8.22986i	−0.378069	−	0.317238i	−0.811944	+	0.583735i	$0.801591\pi$
$674$	5.98748	+	1.60434i	0.230629	+	0.0617969i
$675$		0			0
$676$	−0.999141	+	1.73056i	−0.0384285	+	0.0665601i
$677$	−0.928012	−	1.60736i	−0.0356664	−	0.0617760i	0.847641	−	0.530570i	$-0.178022\pi$
$677$	−0.928012	−	1.60736i	−0.0356664	−	0.0617760i	−0.883308	+	0.468794i	$0.844689\pi$
$678$		0			0
$679$	−10.6894	−	4.98453i	−0.410220	−	0.191289i
$680$	−3.08256	+	0.825969i	−0.118211	+	0.0316745i
$681$		0			0
$682$	−40.4755	+	33.9630i	−1.54989	+	1.30051i
$683$	7.36526	−	3.43448i	0.281824	−	0.131417i	−0.276567	−	0.960995i	$-0.589197\pi$
$683$	7.36526	−	3.43448i	0.281824	−	0.131417i	0.558391	+	0.829578i	$0.311419\pi$
$684$		0			0
$685$	10.4675	−	7.32946i	0.399944	−	0.280044i
$686$	5.46571	+	11.7213i	0.208682	+	0.447520i
$687$		0			0
$688$	2.25827	+	0.197573i	0.0860956	+	0.00753239i
$689$	−9.43594	−	35.2154i	−0.359481	−	1.34160i
$690$		0			0
$691$	27.8831	−	4.91655i	1.06072	−	0.187034i	0.384047	−	0.923314i	$-0.374530\pi$
$691$	27.8831	−	4.91655i	1.06072	−	0.187034i	0.676678	+	0.736279i	$0.263419\pi$
$692$	−20.9969	+	12.1226i	−0.798182	+	0.460831i
$693$		0			0
$694$	−2.26285	+	6.21712i	−0.0858965	+	0.235999i
$695$	−8.28807	+	30.9315i	−0.314384	+	1.17330i
$696$		0			0
$697$	−5.45977	+	5.45977i	−0.206803	+	0.206803i
$698$	−1.09591	−	12.5263i	−0.0414807	−	0.474126i
$699$		0			0
$700$	−0.980610	+	5.56131i	−0.0370636	+	0.210198i
$701$	−6.37683	−	4.46511i	−0.240850	−	0.168645i	0.446920	−	0.894574i	$-0.352521\pi$
$701$	−6.37683	−	4.46511i	−0.240850	−	0.168645i	−0.687769	+	0.725929i	$0.741410\pi$
$702$		0			0
$703$	40.9894	+	25.6708i	1.54594	+	0.968192i
$704$		−	4.93046i		−	0.185824i
$705$		0			0
$706$	−16.3950	−	2.89088i	−0.617033	−	0.108800i
$707$	15.2471	−	5.54949i	0.573426	−	0.208710i
$708$		0			0
$709$	14.9687	+	14.9687i	0.562160	+	0.562160i	0.929921	−	0.367761i	$-0.119875\pi$
$709$	14.9687	+	14.9687i	0.562160	+	0.562160i	−0.367761	+	0.929921i	$0.619875\pi$
$710$	10.8158	−	12.8898i	0.405910	−	0.483744i
$711$		0			0
$712$	−5.57866	−	2.03047i	−0.209069	−	0.0760950i
$713$	62.1584	+	35.8872i	2.32785	+	1.34398i
$714$		0			0
$715$	9.28128	+	52.6367i	0.347100	+	1.96850i
$716$	−0.398209	+	0.853962i	−0.0148818	+	0.0319140i
$717$		0			0
$718$	2.53113	−	28.9309i	0.0944608	−	1.07969i
$719$	−23.0933	−	27.5215i	−0.861234	−	1.02638i	−0.999353	−	0.0359629i	$-0.988550\pi$
$719$	−23.0933	−	27.5215i	−0.861234	−	1.02638i	0.138119	−	0.990416i	$-0.455894\pi$
$720$		0			0
$721$	−3.18421	−	4.54753i	−0.118586	−	0.169359i
$722$	−25.3632	−	36.2224i	−0.943920	−	1.34806i
$723$		0			0
$724$	−4.48136	−	5.34068i	−0.166549	−	0.198485i
$725$	−2.38385	+	27.2475i	−0.0885340	+	1.01195i
$726$		0			0
$727$	−2.99890	+	6.43116i	−0.111223	+	0.238519i	−0.954039	−	0.299684i	$-0.903119\pi$
$727$	−2.99890	+	6.43116i	−0.111223	+	0.238519i	0.842815	+	0.538203i	$0.180897\pi$
$728$	−0.572467	−	3.24662i	−0.0212170	−	0.120328i
$729$		0			0
$730$	14.2395	+	8.22119i	0.527028	+	0.304280i
$731$	−2.08001	−	0.757060i	−0.0769318	−	0.0280009i
$732$		0			0
$733$	8.48914	−	10.1170i	0.313554	−	0.373679i	−0.586133	−	0.810215i	$-0.699350\pi$
$733$	8.48914	−	10.1170i	0.313554	−	0.373679i	0.899687	+	0.436536i	$0.143795\pi$
$734$	−15.4844	−	15.4844i	−0.571541	−	0.571541i
$735$		0			0
$736$	−6.29367	+	2.29071i	−0.231988	+	0.0844367i
$737$	12.0239	+	2.12014i	0.442907	+	0.0780964i
$738$		0			0
$739$		−	29.4464i		−	1.08320i	−0.840635	−	0.541602i	$-0.817818\pi$
$739$		−	29.4464i		−	1.08320i	0.840635	−	0.541602i	$-0.182182\pi$
$740$	13.3174	−	14.7604i	0.489557	−	0.542602i
$741$		0			0
$742$	−8.94897	−	6.26614i	−0.328527	−	0.230037i
$743$	−2.80822	+	15.9262i	−0.103023	+	0.584275i	0.888968	+	0.457969i	$0.151423\pi$
$743$	−2.80822	+	15.9262i	−0.103023	+	0.584275i	−0.991991	+	0.126306i	$0.959688\pi$
$744$		0			0
$745$	3.49198	+	39.9135i	0.127936	+	1.46232i
$746$	−11.9657	+	11.9657i	−0.438096	+	0.438096i
$747$		0			0
$748$	−1.24604	+	4.65028i	−0.0455597	+	0.170031i
$749$	0.924121	−	2.53900i	0.0337667	−	0.0927731i
$750$		0			0
$751$	−31.5713	+	18.2277i	−1.15205	+	0.665139i	−0.949387	−	0.314109i	$-0.898294\pi$
$751$	−31.5713	+	18.2277i	−1.15205	+	0.665139i	−0.202667	+	0.979248i	$0.564961\pi$
$752$	4.42090	−	0.779524i	0.161214	−	0.0284263i
$753$		0			0
$754$	−4.13270	−	15.4234i	−0.150504	−	0.561689i
$755$	−60.5304	−	5.29573i	−2.20293	−	0.192731i
$756$		0			0
$757$	21.6168	+	46.3574i	0.785676	+	1.68489i	0.727028	+	0.686608i	$0.240901\pi$
$757$	21.6168	+	46.3574i	0.785676	+	1.68489i	0.0586481	+	0.998279i	$0.481321\pi$
$758$	−23.7166	+	16.6065i	−0.861424	+	0.603176i
$759$		0			0
$760$	−23.5516	+	10.9823i	−0.854306	+	0.398369i
$761$	14.5169	−	12.1811i	0.526236	−	0.441565i	−0.340563	−	0.940222i	$-0.610618\pi$
$761$	14.5169	−	12.1811i	0.526236	−	0.441565i	0.866799	+	0.498657i	$0.166173\pi$
$762$		0			0
$763$	−7.45552	+	1.99770i	−0.269908	+	0.0723216i
$764$	2.04090	+	0.951685i	0.0738370	+	0.0344308i
$765$		0			0
$766$	−11.6320	−	20.1472i	−0.420281	−	0.727948i
$767$	−13.7089	+	23.7446i	−0.495001	+	0.857366i
$768$		0			0
$769$	31.8507	+	8.53437i	1.14857	+	0.307757i	0.782390	−	0.622789i	$-0.214000\pi$
$769$	31.8507	+	8.53437i	1.14857	+	0.307757i	0.366175	+	0.930546i	$0.380667\pi$
$770$	12.2691	+	10.2950i	0.442146	+	0.371005i
$771$		0			0
$772$	−20.9052	+	1.82896i	−0.752393	+	0.0658259i
$773$	−15.6085	−	42.8841i	−0.561400	−	1.54243i	−0.817587	−	0.575806i	$-0.804688\pi$
$773$	−15.6085	−	42.8841i	−0.561400	−	1.54243i	0.256187	−	0.966627i	$-0.417534\pi$
$774$		0			0
$775$	34.9235	−	49.8760i	1.25449	−	1.79160i
$776$	−11.8666			−0.425986
$777$		0			0
$778$	−3.48414			−0.124912
$779$	−36.0627	+	51.5028i	−1.29208	+	1.84528i
$780$		0			0
$781$	−8.68182	−	23.8531i	−0.310660	−	0.853532i
$782$	6.51494	−	0.569983i	0.232974	−	0.0203826i
$783$		0			0
$784$	4.60556	+	3.86452i	0.164484	+	0.138019i
$785$	11.9329	+	3.19742i	0.425904	+	0.114121i
$786$		0			0
$787$	−4.30594	+	7.45810i	−0.153490	+	0.265853i	−0.932508	−	0.361149i	$-0.882385\pi$
$787$	−4.30594	+	7.45810i	−0.153490	+	0.265853i	0.779018	+	0.627001i	$0.215718\pi$
$788$	−12.4881	−	21.6300i	−0.444871	−	0.770539i
$789$		0			0
$790$	9.47370	+	4.41766i	0.337059	+	0.157173i
$791$	7.48166	−	2.00471i	0.266017	−	0.0712791i
$792$		0			0
$793$	22.3564	−	18.7592i	0.793899	−	0.666160i
$794$	14.7538	−	6.87979i	0.523591	−	0.244155i
$795$		0			0
$796$	−16.7718	+	11.7438i	−0.594461	+	0.416246i
$797$	14.6102	+	31.3317i	0.517521	+	1.10983i	0.975325	+	0.220774i	$0.0708583\pi$
$797$	14.6102	+	31.3317i	0.517521	+	1.10983i	−0.457804	+	0.889053i	$0.651364\pi$
$798$		0			0
$799$	−4.36668	−	0.382035i	−0.154482	−	0.0135154i
$800$	1.47052	+	5.48807i	0.0519909	+	0.194033i
$801$		0			0
$802$	8.60095	−	1.51658i	0.303710	−	0.0535523i
$803$	21.4814	−	12.4023i	0.758064	−	0.437668i
$804$		0			0
$805$	7.44114	−	20.4444i	0.262266	−	0.720569i
$806$	−9.19978	+	34.3340i	−0.324048	+	1.20936i
$807$		0			0
$808$	11.5435	−	11.5435i	0.406098	−	0.406098i
$809$	−2.33228	−	26.6581i	−0.0819986	−	0.937249i	−0.920087	−	0.391714i	$-0.871882\pi$
$809$	−2.33228	−	26.6581i	−0.0819986	−	0.937249i	0.838088	−	0.545535i	$-0.183673\pi$
$810$		0			0
$811$	−7.50082	+	42.5393i	−0.263389	+	1.49376i	0.510193	+	0.860060i	$0.329574\pi$
$811$	−7.50082	+	42.5393i	−0.263389	+	1.49376i	−0.773582	+	0.633696i	$0.781537\pi$
$812$	−3.91942	−	2.74441i	−0.137545	−	0.0963098i
$813$		0			0
$814$	−9.23877	−	28.5324i	−0.323819	−	1.00006i
$815$		−	28.2975i		−	0.991217i
$816$		0			0
$817$	−17.7504	−	3.12987i	−0.621007	−	0.109500i
$818$	−30.4965	+	11.0998i	−1.06628	+	0.388096i
$819$		0			0
$820$	18.2745	+	18.2745i	0.638174	+	0.638174i
$821$	11.1629	−	13.3034i	0.389588	−	0.464293i	−0.535228	−	0.844708i	$-0.679774\pi$
$821$	11.1629	−	13.3034i	0.389588	−	0.464293i	0.924816	+	0.380415i	$0.124219\pi$
$822$		0			0
$823$	52.2284	+	19.0096i	1.82057	+	0.662632i	0.995180	+	0.0980637i	$0.0312649\pi$
$823$	52.2284	+	19.0096i	1.82057	+	0.662632i	0.825386	+	0.564568i	$0.190957\pi$
$824$	−4.83717	−	2.79274i	−0.168511	−	0.0972898i
$825$		0			0
$826$	1.42667	+	8.09105i	0.0496402	+	0.281524i
$827$	−11.3005	+	24.2341i	−0.392958	+	0.842701i	0.605928	+	0.795519i	$0.292802\pi$
$827$	−11.3005	+	24.2341i	−0.392958	+	0.842701i	−0.998886	+	0.0471820i	$0.984976\pi$
$828$		0			0
$829$	−1.65183	+	18.8805i	−0.0573704	+	0.655747i	0.912008	+	0.410173i	$0.134532\pi$
$829$	−1.65183	+	18.8805i	−0.0573704	+	0.655747i	−0.969378	+	0.245573i	$0.921024\pi$
$830$	19.0031	+	22.6470i	0.659606	+	0.786088i
$831$		0			0
$832$	−1.90249	−	2.71703i	−0.0659568	−	0.0941961i
$833$	−3.36719	−	4.80884i	−0.116666	−	0.166617i
$834$		0			0
$835$	38.4265	+	45.7949i	1.32980	+	1.58480i
$836$	−3.41672	+	39.0532i	−0.118170	+	1.35068i
$837$		0			0
$838$	0.747185	−	1.60234i	0.0258111	−	0.0553521i
$839$	7.43313	+	42.1554i	0.256620	+	1.45536i	0.791880	+	0.610677i	$0.209103\pi$
$839$	7.43313	+	42.1554i	0.256620	+	1.45536i	−0.535260	+	0.844688i	$0.679786\pi$
$840$		0			0
$841$	5.04484	+	2.91264i	0.173960	+	0.100436i
$842$	−7.72885	−	2.81307i	−0.266354	−	0.0969448i
$843$		0			0
$844$	13.3345	−	15.8914i	0.458993	−	0.547006i
$845$	−4.61808	−	4.61808i	−0.158867	−	0.158867i
$846$		0			0
$847$	12.4307	−	4.52441i	0.427125	−	0.155461i
$848$	−10.8246	−	1.90866i	−0.371717	−	0.0655437i
$849$		0			0
$850$		−	5.54784i		−	0.190289i
$851$	−32.1288	+	25.0494i	−1.10136	+	0.858682i
$852$		0			0
$853$	−40.7979	−	28.5670i	−1.39689	−	0.978116i	−0.998134	−	0.0610607i	$-0.980552\pi$
$853$	−40.7979	−	28.5670i	−1.39689	−	0.978116i	−0.398760	−	0.917055i	$-0.630559\pi$
$854$	1.51858	−	8.61230i	0.0519648	−	0.294707i
$855$		0			0
$856$	−0.236932	−	2.70814i	−0.00809816	−	0.0925624i
$857$	19.8748	−	19.8748i	0.678910	−	0.678910i	−0.280844	−	0.959753i	$-0.590614\pi$
$857$	19.8748	−	19.8748i	0.678910	−	0.678910i	0.959753	+	0.280844i	$0.0906143\pi$
$858$		0			0
$859$	5.82849	−	21.7522i	0.198865	−	0.742176i	−0.792367	−	0.610045i	$-0.791151\pi$
$859$	5.82849	−	21.7522i	0.198865	−	0.742176i	0.991232	−	0.132131i	$-0.0421819\pi$
$860$	−2.53397	+	6.96204i	−0.0864078	+	0.237403i
$861$		0			0
$862$	7.03094	−	4.05931i	0.239475	−	0.138261i
$863$	−18.1155	+	3.19426i	−0.616660	+	0.108734i	−0.473248	−	0.880929i	$-0.656919\pi$
$863$	−18.1155	+	3.19426i	−0.616660	+	0.108734i	−0.143412	+	0.989663i	$0.545807\pi$
$864$		0			0
$865$	−20.5088	−	76.5399i	−0.697320	−	2.60243i
$866$	−25.6794	−	2.24666i	−0.872623	−	0.0763446i
$867$		0			0
$868$	4.50141	+	9.65331i	0.152788	+	0.327655i
$869$	12.9174	−	9.04489i	0.438194	−	0.306827i
$870$		0			0
$871$	7.44411	−	3.47124i	0.252234	−	0.117619i
$872$	−5.94892	+	4.99174i	−0.201456	+	0.169042i
$873$		0			0
$874$	51.4384	−	13.7829i	1.73993	−	0.466212i
$875$	−2.00687	−	0.935818i	−0.0678445	−	0.0316364i
$876$		0			0
$877$	−16.4337	−	28.4640i	−0.554926	−	0.961160i	−0.997909	−	0.0646302i	$-0.979413\pi$
$877$	−16.4337	−	28.4640i	−0.554926	−	0.961160i	0.442983	−	0.896530i	$-0.353920\pi$
$878$	2.76421	−	4.78776i	0.0932877	−	0.161579i
$879$		0			0
$880$	15.5651	+	4.17065i	0.524698	+	0.140593i
$881$	24.7495	+	20.7673i	0.833833	+	0.699669i	0.956168	−	0.292820i	$-0.0945935\pi$
$881$	24.7495	+	20.7673i	0.833833	+	0.699669i	−0.122334	+	0.992489i	$0.539038\pi$
$882$		0			0
$883$	−10.2855	+	0.899861i	−0.346133	+	0.0302827i	−0.258897	−	0.965905i	$-0.583359\pi$
$883$	−10.2855	+	0.899861i	−0.346133	+	0.0302827i	−0.0872363	+	0.996188i	$0.527804\pi$
$884$	1.10772	+	3.04343i	0.0372566	+	0.102362i
$885$		0			0
$886$	−18.6109	+	26.5791i	−0.625245	+	0.892943i
$887$	10.8365			0.363853			0.181926	−	0.983312i	$-0.441767\pi$
$887$	10.8365			0.363853			0.181926	+	0.983312i	$0.441767\pi$
$888$		0			0
$889$	8.79462			0.294962
$890$	11.1290	−	15.8938i	0.373044	−	0.532762i
$891$		0			0
$892$	3.71263	+	10.2004i	0.124308	+	0.341533i
$893$	−35.5573	+	3.11086i	−1.18988	+	0.104101i
$894$		0			0
$895$	−2.35904	−	1.97947i	−0.0788542	−	0.0661665i
$896$	−0.960050	−	0.257245i	−0.0320730	−	0.00859394i
$897$		0			0
$898$	2.29249	−	3.97071i	0.0765015	−	0.132504i
$899$	25.7946	+	44.6775i	0.860297	+	1.49008i
$900$		0			0
$901$	9.72707	+	4.53581i	0.324056	+	0.151110i
$902$	37.6594	−	10.0908i	1.25392	−	0.335987i
$903$		0			0
$904$	5.96978	−	5.00924i	0.198552	−	0.166605i
$905$	20.6509	−	9.62965i	0.686458	−	0.320100i
$906$		0			0
$907$	−47.9336	+	33.5635i	−1.59161	+	1.11446i	−0.659842	+	0.751405i	$0.729377\pi$
$907$	−47.9336	+	33.5635i	−1.59161	+	1.11446i	−0.931768	+	0.363053i	$0.881734\pi$
$908$	−2.92601	−	6.27486i	−0.0971032	−	0.208238i
$909$		0			0
$910$	10.7336	+	0.939065i	0.355814	+	0.0311297i
$911$	−10.6790	−	39.8545i	−0.353810	−	1.32044i	−0.881975	−	0.471296i	$-0.843786\pi$
$911$	−10.6790	−	39.8545i	−0.353810	−	1.32044i	0.528165	−	0.849142i	$-0.322880\pi$
$912$		0			0
$913$	43.9214	−	7.74452i	1.45359	−	0.256306i
$914$	29.5870	−	17.0821i	0.978651	−	0.565025i
$915$		0			0
$916$	8.26456	−	22.7067i	0.273069	−	0.750250i
$917$	0.806673	−	3.01055i	0.0266387	−	0.0994170i
$918$		0			0
$919$	11.1299	−	11.1299i	0.367141	−	0.367141i	−0.499292	−	0.866434i	$-0.666407\pi$
$919$	11.1299	−	11.1299i	0.367141	−	0.367141i	0.866434	+	0.499292i	$0.166407\pi$
$920$	−1.90780	−	21.8063i	−0.0628985	−	0.718933i
$921$		0			0
$922$	2.54192	−	14.4160i	0.0837138	−	0.474765i
$923$	−13.9883	−	9.79474i	−0.460432	−	0.322398i
$924$		0			0
$925$	18.7935	+	29.0037i	0.617926	+	0.953636i
$926$		−	36.6240i		−	1.20354i
$927$		0			0
$928$	−4.74088	−	0.835945i	−0.155627	−	0.0274412i
$929$	8.56900	−	3.11886i	0.281140	−	0.102327i	−0.197602	−	0.980282i	$-0.563315\pi$
$929$	8.56900	−	3.11886i	0.281140	−	0.102327i	0.478742	+	0.877956i	$0.341093\pi$
$930$		0			0
$931$	−33.8017	−	33.8017i	−1.10781	−	1.10781i
$932$	3.97038	−	4.73172i	0.130054	−	0.154993i
$933$		0			0
$934$	−30.4384	−	11.0787i	−0.995975	−	0.362505i
$935$	−13.6265	−	7.86729i	−0.445636	−	0.257288i
$936$		0			0
$937$	1.97710	+	11.2127i	0.0645892	+	0.366304i	0.999921	+	0.0125330i	$0.00398949\pi$
$937$	1.97710	+	11.2127i	0.0645892	+	0.366304i	−0.935332	+	0.353770i	$0.884899\pi$
$938$	1.04017	−	2.23065i	0.0339628	−	0.0728335i
$939$		0			0
$940$	−1.27872	+	14.6158i	−0.0417072	+	0.476715i
$941$	−14.9738	−	17.8451i	−0.488132	−	0.581733i	0.464610	−	0.885516i	$-0.346195\pi$
$941$	−14.9738	−	17.8451i	−0.488132	−	0.581733i	−0.952741	+	0.303783i	$0.901750\pi$
$942$		0			0
$943$	−30.3774	−	43.3835i	−0.989225	−	1.41276i
$944$	4.74127	+	6.77123i	0.154315	+	0.220385i
$945$		0			0
$946$	7.18433	+	8.56195i	0.233583	+	0.278373i
$947$	−0.257936	+	2.94822i	−0.00838179	+	0.0958043i	−0.999233	−	0.0391528i	$-0.987534\pi$
$947$	−0.257936	+	2.94822i	−0.00838179	+	0.0958043i	0.990851	+	0.134957i	$0.0430897\pi$
$948$		0			0
$949$	7.05218	−	15.1235i	0.228924	−	0.490928i
$950$	−7.84461	−	44.4890i	−0.254513	−	1.44341i
$951$		0			0
$952$	0.840482	+	0.485252i	0.0272402	+	0.0157271i
$953$	2.92460	+	1.06447i	0.0947372	+	0.0344815i	0.388954	−	0.921257i	$-0.372837\pi$
$953$	2.92460	+	1.06447i	0.0947372	+	0.0344815i	−0.294217	+	0.955739i	$0.595059\pi$
$954$		0			0
$955$	−4.73077	+	5.63792i	−0.153084	+	0.182439i
$956$	5.24926	+	5.24926i	0.169773	+	0.169773i
$957$		0			0
$958$	1.24124	−	0.451773i	0.0401026	−	0.0145961i
$959$	−3.82703	−	0.674809i	−0.123581	−	0.0217907i
$960$		0			0
$961$		−	83.8422i		−	2.70459i
$962$	−16.1008	−	12.1584i	−0.519111	−	0.392003i
$963$		0			0
$964$	−9.36053	−	6.55431i	−0.301482	−	0.211100i
$965$	11.9096	−	67.5430i	0.383385	−	2.17429i
$966$		0			0
$967$	5.26495	+	60.1786i	0.169309	+	1.93521i	0.321593	+	0.946878i	$0.395782\pi$
$967$	5.26495	+	60.1786i	0.169309	+	1.93521i	−0.152284	+	0.988337i	$0.548663\pi$
$968$	9.41122	−	9.41122i	0.302488	−	0.302488i
$969$		0			0
$970$	10.0379	−	37.4619i	0.322297	−	1.20283i
$971$	−9.62475	+	26.4438i	−0.308873	+	0.848621i	0.684004	+	0.729478i	$0.260237\pi$
$971$	−9.62475	+	26.4438i	−0.308873	+	0.848621i	−0.992877	+	0.119143i	$0.961985\pi$
$972$		0			0
$973$	8.43370	−	4.86920i	0.270372	−	0.156099i
$974$	−18.7692	+	3.30952i	−0.601404	+	0.106044i
$975$		0			0
$976$	−2.27727	−	8.49887i	−0.0728935	−	0.272042i
$977$	−53.1163	−	4.64708i	−1.69934	−	0.148673i	−0.804172	−	0.594397i	$-0.797391\pi$
$977$	−53.1163	−	4.64708i	−1.69934	−	0.148673i	−0.895170	+	0.445724i	$0.852946\pi$
$978$		0			0
$979$	−12.3703	−	26.5282i	−0.395357	−	0.847845i
$980$	−16.0958	+	11.2704i	−0.514161	+	0.360020i
$981$		0			0
$982$	−35.1570	+	16.3940i	−1.12191	+	0.523153i
$983$	8.42935	−	7.07306i	0.268854	−	0.225596i	−0.498386	−	0.866955i	$-0.666074\pi$
$983$	8.42935	−	7.07306i	0.268854	−	0.225596i	0.767240	+	0.641360i	$0.221629\pi$
$984$		0			0
$985$	78.8479	−	21.1272i	2.51230	−	0.673170i
$986$	4.26021	+	1.98657i	0.135673	+	0.0632652i
$987$		0			0
$988$	13.1864	+	22.8395i	0.419514	+	0.726620i
$989$	7.59135	−	13.1486i	0.241391	−	0.418101i
$990$		0			0
$991$	−35.9689	−	9.63784i	−1.14259	−	0.306156i	−0.362598	−	0.931946i	$-0.618110\pi$
$991$	−35.9689	−	9.63784i	−1.14259	−	0.306156i	−0.779992	+	0.625790i	$0.784777\pi$
$992$	8.20927	+	6.88840i	0.260645	+	0.218707i
$993$		0			0
$994$	−5.09760	+	0.445982i	−0.161686	+	0.0141457i
$995$	−22.8869	−	62.8812i	−0.725563	−	1.99347i
$996$		0			0
$997$	−4.44695	+	6.35090i	−0.140836	+	0.201135i	−0.883373	−	0.468670i	$-0.844733\pi$
$997$	−4.44695	+	6.35090i	−0.140836	+	0.201135i	0.742537	+	0.669805i	$0.233622\pi$
$998$	−9.82633			−0.311047
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.17.8	yes	96
3.2	odd	2	inner	666.2.bs.b.17.1	✓	96
37.24	odd	36	inner	666.2.bs.b.431.1	yes	96
111.98	even	36	inner	666.2.bs.b.431.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.17.1	✓	96	3.2	odd	2	inner
666.2.bs.b.17.8	yes	96	1.1	even	1	trivial
666.2.bs.b.431.1	yes	96	37.24	odd	36	inner
666.2.bs.b.431.8	yes	96	111.98	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bs (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.25585 - 0.284850i) q^{5} +(-0.761384 - 0.638877i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(3.25585 - 0.284850i) q^{5} +(-0.761384 - 0.638877i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(1.63414 - 2.83042i) q^{10} +(-2.46523 - 4.26991i) q^{11} +(-3.00612 - 1.40178i) q^{13} +(-0.960050 + 0.257245i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(0.884960 - 0.412663i) q^{17} +(6.51313 - 4.56054i) q^{19} +(-1.38124 - 2.96207i) q^{20} +(-4.91170 - 0.429718i) q^{22} +(1.73346 + 6.46937i) q^{23} +(5.59535 - 0.986611i) q^{25} +(-2.87251 + 1.65844i) q^{26} +(-0.339940 + 0.933976i) q^{28} +(-1.24596 + 4.64998i) q^{29} +(7.57767 - 7.57767i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.169558 - 0.961611i) q^{34} +(-2.66093 - 1.86321i) q^{35} +(2.37105 + 5.60162i) q^{37} -7.95106i q^{38} +(-3.21863 - 0.567531i) q^{40} +(-7.43066 + 2.70454i) q^{41} +(-1.60293 - 1.60293i) q^{43} +(-3.16924 + 3.77695i) q^{44} +(6.29367 + 2.29071i) q^{46} +(-3.88767 - 2.24455i) q^{47} +(-1.04400 - 5.92079i) q^{49} +(2.40118 - 5.14934i) q^{50} +(-0.289085 + 3.30426i) q^{52} +(7.06523 + 8.42001i) q^{53} +(-9.24269 - 13.1999i) q^{55} +(0.570087 + 0.814169i) q^{56} +(3.09439 + 3.68775i) q^{58} +(0.720442 - 8.23470i) q^{59} +(-3.71848 + 7.97431i) q^{61} +(-1.86089 - 10.5536i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-10.1867 - 3.70767i) q^{65} +(-1.59175 + 1.89697i) q^{67} +(-0.690451 - 0.690451i) q^{68} +(-3.05250 + 1.11102i) q^{70} +(5.07018 + 0.894009i) q^{71} +5.03089i q^{73} +(5.94856 + 1.27071i) q^{74} +(-6.51313 - 4.56054i) q^{76} +(-0.850958 + 4.82602i) q^{77} +(0.278754 + 3.18617i) q^{79} +(-2.31102 + 2.31102i) q^{80} +(-2.04662 + 7.63810i) q^{82} +(-3.09377 + 8.50007i) q^{83} +(2.76375 - 1.59565i) q^{85} +(-2.23245 + 0.393642i) q^{86} +(1.27610 + 4.76246i) q^{88} +(5.91410 + 0.517417i) q^{89} +(1.39325 + 2.98783i) q^{91} +(5.48634 - 3.84158i) q^{92} +(-4.06850 + 1.89717i) q^{94} +(19.9067 - 16.7037i) q^{95} +(11.4622 - 3.07130i) q^{97} +(-5.44884 - 2.54084i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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