LMFDB - Embedded newform 666.2.bs.b.17.1

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			17.1
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.b.431.1

$q$-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	−0.787520	−	0.616289i	$-0.788635\pi$
$5$	−3.25585	+	0.284850i	−1.45606	+	0.127389i	−0.668538	+	0.743678i	$0.733080\pi$
$6$		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	$0.100072\pi$
$11$	2.46523	+	4.26991i	0.743295	+	1.28743i	−0.207692	+	0.978194i	$0.566595\pi$
$12$		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	−0.526962	−	0.849889i	$-0.676669\pi$
$17$	−0.884960	+	0.412663i	−0.214634	+	0.100086i	0.312328	+	0.949974i	$0.398891\pi$
$18$		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	$-0.837286\pi$
$23$	−1.73346	−	6.46937i	−0.361452	−	1.34896i	0.510715	−	0.859750i	$-0.329381\pi$
$24$		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	$-0.769170\pi$
$29$	1.24596	−	4.64998i	0.231369	−	0.863479i	0.979752	−	0.200213i	$-0.0641636\pi$
$30$		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	0.311207	−	0.950342i	$-0.399267\pi$
$41$	7.43066	−	2.70454i	1.16047	−	0.422378i	0.849267	+	0.527964i	$0.177045\pi$
$42$		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	0.755980	−	0.654594i	$-0.227160\pi$
$47$	3.88767	+	2.24455i	0.567075	+	0.327401i	−0.188905	+	0.981995i	$0.560494\pi$
$48$		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	$-0.949906\pi$
$53$	−7.06523	−	8.42001i	−0.970484	−	1.15658i	0.0171585	−	0.999853i	$-0.494538\pi$
$54$		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	$0.208628\pi$
$59$	−0.720442	+	8.23470i	−0.0937936	+	1.07207i	−0.886583	+	0.462570i	$0.846927\pi$
$60$		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	−0.135513	−	0.990776i	$-0.543268\pi$
$71$	−5.07018	−	0.894009i	−0.601719	−	0.106099i	−0.466206	+	0.884676i	$0.654379\pi$
$72$		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	$-0.723529\pi$
$83$	3.09377	−	8.50007i	0.339586	−	0.933004i	0.985512	−	0.169605i	$-0.0542490\pi$
$84$		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	−0.230718	−	0.973021i	$-0.574107\pi$
$89$	−5.91410	−	0.517417i	−0.626893	−	0.0548461i	−0.396176	+	0.918175i	$0.629663\pi$
$90$		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	$-0.531605\pi$
$101$	8.16247	−	14.1378i	0.812196	−	1.40676i	0.911324	−	0.411690i	$-0.135061\pi$
$102$		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	0.886602	−	0.462533i	$-0.153059\pi$
$107$	−0.929777	−	2.55454i	−0.0898850	−	0.246957i	−0.976487	+	0.215576i	$0.930837\pi$
$108$		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	−0.551892	−	0.833916i	$-0.686094\pi$
$113$	4.46988	−	6.38365i	0.420491	−	0.600523i	0.972383	+	0.233393i	$0.0749828\pi$
$114$		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	0.839870	−	0.542788i	$-0.182631\pi$
$131$	−1.32526	−	2.84202i	−0.115788	−	0.248308i	−0.955658	+	0.294480i	$0.904854\pi$
$132$		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	−0.637621	−	0.770350i	$-0.720081\pi$
$137$	−3.38604	+	1.95493i	−0.289289	+	0.167021i	0.348332	+	0.937371i	$0.386748\pi$
$138$		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	$-0.832543\pi$
$149$		−	12.2590i		−	1.00430i	0.864781	−	0.502150i	$-0.167457\pi$
$150$		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	$-0.944173\pi$
$167$	−10.4914	−	14.9833i	−0.811852	−	1.15944i	0.172808	−	0.984956i	$-0.444716\pi$
$168$		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	$0.317612\pi$
$173$	4.21012	+	23.8768i	0.320090	+	1.81532i	−0.222055	+	0.975034i	$0.571277\pi$
$174$		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	0.731568	−	0.681769i	$-0.238789\pi$
$179$	0.666266	+	0.666266i	0.0497991	+	0.0497991i	−0.681769	+	0.731568i	$0.738789\pi$
$180$		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	−0.647148	−	0.762364i	$-0.724038\pi$
$191$	1.59232	−	1.59232i	0.115216	−	0.115216i	0.762364	+	0.647148i	$0.224038\pi$
$192$		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	−0.955488	−	0.295029i	$-0.904671\pi$
$197$	−24.5968	+	4.33708i	−1.75245	+	0.309004i	−0.796960	+	0.604032i	$0.793560\pi$
$198$		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	−0.313715	−	0.949517i	$-0.601574\pi$
$227$	−6.89719	+	0.603426i	−0.457783	+	0.0400508i	−0.144067	+	0.989568i	$0.546018\pi$
$228$		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	0.746950	−	0.664880i	$-0.231518\pi$
$233$	−3.08841	−	5.34928i	−0.202328	−	0.350443i	−0.949278	+	0.314437i	$0.898184\pi$
$234$		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	−0.192656	−	0.981266i	$-0.561710\pi$
$239$	6.72804	−	3.13734i	0.435201	−	0.202937i	0.627857	+	0.778329i	$0.283932\pi$
$240$		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	−0.940501	−	0.339790i	$-0.889644\pi$
$251$	0.695379	−	2.59519i	0.0438919	−	0.163807i	0.984393	+	0.175984i	$0.0563105\pi$
$252$		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	0.167003	−	0.985956i	$-0.446591\pi$
$257$	−11.2599	−	7.88429i	−0.702375	−	0.491808i	−0.869378	+	0.494148i	$0.835480\pi$
$258$		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	0.118998	−	0.992894i	$-0.462032\pi$
$263$	13.7584	−	5.00763i	0.848377	−	0.308784i	0.729378	+	0.684111i	$0.239809\pi$
$264$		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	$0.0577133\pi$
$269$	26.7598	+	15.4498i	1.63157	+	0.941989i	0.647966	+	0.761670i	$0.275620\pi$
$270$		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	$-0.884386\pi$
$281$	0.796118	−	9.09967i	0.0474924	−	0.542841i	0.982253	−	0.187562i	$-0.0600585\pi$
$282$		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	0.826534	−	0.562887i	$-0.190309\pi$
$293$	24.1474	+	4.25783i	1.41070	+	0.248745i	0.584169	+	0.811632i	$0.301420\pi$
$294$		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	0.301663	−	0.953415i	$-0.402458\pi$
$311$	7.63928	+	0.668350i	0.433184	+	0.0378987i	0.131521	+	0.991313i	$0.458014\pi$
$312$		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	−0.424688	−	0.905340i	$-0.639616\pi$
$317$	6.99987	−	5.87359i	0.393152	−	0.329894i	0.817840	+	0.575446i	$0.195172\pi$
$318$		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	−0.0831702	−	0.996535i	$-0.526505\pi$
$347$	6.39069	−	1.71238i	0.343070	−	0.0919253i	0.426240	+	0.904610i	$0.359838\pi$
$348$		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	$0.00721084\pi$
$353$	7.03571	+	15.0881i	0.374473	+	0.803060i	−0.625271	+	0.780408i	$0.715011\pi$
$354$		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	−0.984897	−	0.173144i	$-0.944607\pi$
$359$	−25.1506	+	14.5207i	−1.32740	+	0.766373i	−0.342501	+	0.939517i	$0.611274\pi$
$360$		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	$0.341486\pi$
$383$	−9.83179	+	21.0843i	−0.502381	+	1.07736i	−0.980038	+	0.198813i	$0.936292\pi$
$384$		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	0.866612	−	0.498982i	$-0.166293\pi$
$389$	1.99842	+	2.85404i	0.101324	+	0.144705i	−0.765289	+	0.643687i	$0.777404\pi$
$390$		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	0.535892	−	0.844287i	$-0.319976\pi$
$401$	−6.17561	−	6.17561i	−0.308395	−	0.308395i	−0.844287	+	0.535892i	$0.819976\pi$
$402$		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	−0.216016	−	0.976390i	$-0.569306\pi$
$419$	−1.74113	+	0.307009i	−0.0850599	+	0.0149983i	0.130956	+	0.991388i	$0.458195\pi$
$420$		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	0.237250	−	0.971449i	$-0.423754\pi$
$431$	−7.35797	−	3.43108i	−0.354421	−	0.165269i	−0.591671	+	0.806179i	$0.701532\pi$
$432$		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	$-0.219855\pi$
$443$	32.4471			1.54161			0.770804	+	0.637072i	$0.219855\pi$
$444$		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	−0.194422	−	0.980918i	$-0.562283\pi$
$449$	−4.56754	+	0.399608i	−0.215555	+	0.0188587i	−0.0211335	+	0.999777i	$0.506728\pi$
$450$		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	−0.706255	−	0.707958i	$-0.749617\pi$
$461$	−13.2669	+	6.18644i	−0.617899	+	0.288131i	0.0883554	+	0.996089i	$0.471839\pi$
$462$		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	$0.186353\pi$
$467$	8.38364	+	31.2882i	0.387948	+	1.44784i	−0.445518	+	0.895273i	$0.646980\pi$
$468$		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	0.548596	−	0.836088i	$-0.315163\pi$
$479$	−1.08202	−	0.757635i	−0.0494385	−	0.0346172i	−0.598034	+	0.801470i	$0.704051\pi$
$480$		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	$0.00601465\pi$
$491$	33.5944	+	19.3958i	1.51610	+	0.875318i	0.516274	+	0.856424i	$0.327319\pi$
$492$		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	$-0.829993\pi$
$503$	1.68927	−	19.3085i	0.0753210	−	0.860924i	0.936052	−	0.351863i	$-0.114452\pi$
$504$		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	0.532342	−	0.846529i	$-0.321312\pi$
$509$	8.93419	+	3.25178i	0.396001	+	0.144133i	−0.136341	+	0.990662i	$0.543534\pi$
$510$		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	$-0.616237\pi$
$521$	6.80043	−	38.5671i	0.297932	−	1.68966i	0.655040	−	0.755594i	$-0.272652\pi$
$522$		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	−0.458526	−	0.888681i	$-0.651622\pi$
$557$	12.5884	−	17.9780i	0.533386	−	0.761754i	0.991912	+	0.126927i	$0.0405113\pi$
$558$		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	−0.0909944	−	0.995851i	$-0.529005\pi$
$563$	−15.8435	−	4.24525i	−0.667724	−	0.178916i	−0.576729	+	0.816935i	$0.695671\pi$
$564$		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	0.325728	−	0.945463i	$-0.394391\pi$
$569$	25.7751	−	6.90642i	1.08055	−	0.289532i	0.754821	+	0.655931i	$0.227724\pi$
$570$		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	$-0.882232\pi$
$587$	−1.86447	−	21.3109i	−0.0769548	−	0.879597i	0.855380	−	0.518001i	$-0.173324\pi$
$588$		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	$0.144082\pi$
$593$			21.3003i			0.874697i	−0.899292	+	0.437349i	$0.855918\pi$
$594$		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	−0.989833	−	0.142233i	$-0.954572\pi$
$599$	−16.5907	+	19.7720i	−0.677878	+	0.807864i	0.311955	+	0.950097i	$0.399016\pi$
$600$		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	$0.00683252\pi$
$617$	1.68000	+	9.52777i	0.0676344	+	0.383574i	−0.932135	+	0.362110i	$0.882056\pi$
$618$		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	−0.414087	−	0.910237i	$-0.635899\pi$
$641$	−12.4535	+	2.19588i	−0.491883	+	0.0867322i	−0.0777954	+	0.996969i	$0.524788\pi$
$642$		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	−0.959954	−	0.280158i	$-0.909613\pi$
$647$	−26.0725	+	18.2561i	−1.02501	+	0.717723i	−0.0650609	+	0.997881i	$0.520724\pi$
$648$		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	−0.308564	−	0.951204i	$-0.599848\pi$
$653$	−31.5736	−	14.7230i	−1.23557	−	0.576156i	−0.927005	+	0.375048i	$0.877626\pi$
$654$		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	0.926641	−	0.375948i	$-0.122683\pi$
$659$	18.4141	+	15.4513i	0.717313	+	0.601897i	−0.209327	+	0.977846i	$0.567127\pi$
$660$		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	0.883308	−	0.468794i	$-0.155311\pi$
$677$	0.928012	+	1.60736i	0.0356664	+	0.0617760i	−0.847641	+	0.530570i	$0.821978\pi$
$678$		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	−0.558391	−	0.829578i	$-0.688581\pi$
$683$	−7.36526	+	3.43448i	−0.281824	+	0.131417i	0.276567	+	0.960995i	$0.410803\pi$
$684$		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	0.687769	−	0.725929i	$-0.258590\pi$
$701$	6.37683	+	4.46511i	0.240850	+	0.168645i	−0.446920	+	0.894574i	$0.647479\pi$
$702$		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	$0.0114498\pi$
$719$	23.0933	+	27.5215i	0.861234	+	1.02638i	−0.138119	+	0.990416i	$0.544106\pi$
$720$		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	$-0.848577\pi$
$743$	2.80822	−	15.9262i	0.103023	−	0.584275i	0.991991	−	0.126306i	$-0.0403120\pi$
$744$		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	−0.866799	−	0.498657i	$-0.833827\pi$
$761$	−14.5169	+	12.1811i	−0.526236	+	0.441565i	0.340563	+	0.940222i	$0.389382\pi$
$762$		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	$0.195312\pi$
$773$	15.6085	+	42.8841i	0.561400	+	1.54243i	−0.256187	+	0.966627i	$0.582466\pi$
$774$		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	$-0.929142\pi$
$797$	−14.6102	−	31.3317i	−0.517521	−	1.10983i	0.457804	−	0.889053i	$-0.348636\pi$
$798$		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	$0.128118\pi$
$809$	2.33228	+	26.6581i	0.0819986	+	0.937249i	−0.838088	+	0.545535i	$0.816327\pi$
$810$		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	−0.924816	−	0.380415i	$-0.875781\pi$
$821$	−11.1629	+	13.3034i	−0.389588	+	0.464293i	0.535228	+	0.844708i	$0.320226\pi$
$822$		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	$-0.707198\pi$
$827$	11.3005	−	24.2341i	0.392958	−	0.842701i	0.998886	−	0.0471820i	$-0.0150241\pi$
$828$		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	$-0.790897\pi$
$839$	−7.43313	−	42.1554i	−0.256620	−	1.45536i	0.535260	−	0.844688i	$-0.320214\pi$
$840$		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	−0.959753	−	0.280844i	$-0.909386\pi$
$857$	−19.8748	+	19.8748i	−0.678910	+	0.678910i	0.280844	+	0.959753i	$0.409386\pi$
$858$		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	0.143412	−	0.989663i	$-0.454193\pi$
$863$	18.1155	−	3.19426i	0.616660	−	0.108734i	0.473248	+	0.880929i	$0.343081\pi$
$864$		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	0.122334	−	0.992489i	$-0.460962\pi$
$881$	−24.7495	−	20.7673i	−0.833833	−	0.699669i	−0.956168	+	0.292820i	$0.905406\pi$
$882$		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	$-0.558233\pi$
$887$	−10.8365			−0.363853			−0.181926	+	0.983312i	$0.558233\pi$
$888$		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	$0.156214\pi$
$911$	10.6790	+	39.8545i	0.353810	+	1.32044i	−0.528165	+	0.849142i	$0.677120\pi$
$912$		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	−0.478742	−	0.877956i	$-0.658907\pi$
$929$	−8.56900	+	3.11886i	−0.281140	+	0.102327i	0.197602	+	0.980282i	$0.436685\pi$
$930$		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	0.952741	−	0.303783i	$-0.0982498\pi$
$941$	14.9738	+	17.8451i	0.488132	+	0.581733i	−0.464610	+	0.885516i	$0.653805\pi$
$942$		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	−0.990851	−	0.134957i	$-0.956910\pi$
$947$	0.257936	−	2.94822i	0.00838179	−	0.0958043i	0.999233	+	0.0391528i	$0.0124659\pi$
$948$		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	0.294217	−	0.955739i	$-0.404941\pi$
$953$	−2.92460	−	1.06447i	−0.0947372	−	0.0344815i	−0.388954	+	0.921257i	$0.627163\pi$
$954$		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	$-0.739763\pi$
$971$	9.62475	−	26.4438i	0.308873	−	0.848621i	0.992877	−	0.119143i	$-0.0380147\pi$
$972$		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	0.895170	−	0.445724i	$-0.147054\pi$
$977$	53.1163	+	4.64708i	1.69934	+	0.148673i	0.804172	+	0.594397i	$0.202609\pi$
$978$		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	−0.767240	−	0.641360i	$-0.778371\pi$
$983$	−8.42935	+	7.07306i	−0.268854	+	0.225596i	0.498386	+	0.866955i	$0.333926\pi$
$984$		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.17.1	✓	96
3.2	odd	2	inner	666.2.bs.b.17.8	yes	96
37.24	odd	36	inner	666.2.bs.b.431.8	yes	96
111.98	even	36	inner	666.2.bs.b.431.1	yes	96

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

Varieties

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Database

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