LMFDB - Embedded newform 666.2.bs.a.557.5

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:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.5
Character	$\chi$	$=$	666.557
Dual form			666.2.bs.a.611.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(0.309586 + 0.144362i) q^{5} +(-2.12726 + 0.774261i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})$	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(0.309586 + 0.144362i) q^{5} +(-2.12726 + 0.774261i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.170795 - 0.295826i) q^{10} +(2.53348 + 4.38812i) q^{11} +(0.447015 + 0.638404i) q^{13} +(0.585911 + 2.18665i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.48398 + 4.97563i) q^{17} +(5.68686 - 0.497536i) q^{19} +(-0.279814 - 0.195928i) q^{20} +(4.59223 - 2.14139i) q^{22} +(-2.40525 + 0.644485i) q^{23} +(-3.13894 - 3.74084i) q^{25} +(0.674935 - 0.389674i) q^{26} +(2.22940 - 0.393103i) q^{28} +(10.2511 + 2.74678i) q^{29} +(4.79672 + 4.79672i) q^{31} +(0.422618 - 0.906308i) q^{32} +(4.65305 + 3.90437i) q^{34} +(-0.770346 - 0.0673965i) q^{35} +(-4.86851 - 3.64659i) q^{37} -5.70858i q^{38} +(-0.219570 + 0.261673i) q^{40} +(-1.94300 + 11.0193i) q^{41} +(5.24522 - 5.24522i) q^{43} +(-1.73300 - 4.76138i) q^{44} +(0.432401 + 2.45227i) q^{46} +(-1.12230 - 0.647958i) q^{47} +(-1.43654 + 1.20540i) q^{49} +(-4.00018 + 2.80096i) q^{50} +(-0.329366 - 0.706329i) q^{52} +(-1.91222 + 5.25379i) q^{53} +(0.150851 + 1.72424i) q^{55} +(-0.197302 - 2.25517i) q^{56} +(3.62978 - 9.97273i) q^{58} +(-0.911581 - 1.95489i) q^{59} +(2.57678 - 1.80428i) q^{61} +(5.19653 - 4.36040i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.0462282 + 0.262173i) q^{65} +(-1.75464 - 4.82082i) q^{67} +(4.29506 - 4.29506i) q^{68} +(-0.134280 + 0.761540i) q^{70} +(6.66465 - 7.94262i) q^{71} +14.3898i q^{73} +(-4.05704 + 4.53216i) q^{74} +(-5.68686 - 0.497536i) q^{76} +(-8.78693 - 7.37311i) q^{77} +(-1.92544 + 4.12911i) q^{79} +(0.241541 + 0.241541i) q^{80} +(10.8080 + 2.89600i) q^{82} +(4.84692 - 0.854643i) q^{83} +(-1.79688 + 1.03743i) q^{85} +(-4.76811 - 5.68241i) q^{86} +(-4.89431 + 1.31143i) q^{88} +(-8.92392 + 4.16129i) q^{89} +(-1.44521 - 1.01195i) q^{91} +(2.48062 - 0.217026i) q^{92} +(-0.743307 + 1.06155i) q^{94} +(1.83240 + 0.666938i) q^{95} +(-2.93104 - 10.9388i) q^{97} +(1.07561 + 1.53613i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q+O(q^{10}) $ 72 * q	$ 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) $ 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$2$	0.0871557	−	0.996195i	0.0616284	−	0.704416i
$3$		0			0
$3$		0			0
$4$	−0.984808	−	0.173648i	−0.492404	−	0.0868241i
$5$	0.309586	+	0.144362i	0.138451	+	0.0645608i	0.490609	−	0.871380i	$-0.336774\pi$
$5$	0.309586	+	0.144362i	0.138451	+	0.0645608i	−0.352158	+	0.935941i	$0.614552\pi$
$6$		0			0
$7$	−2.12726	+	0.774261i	−0.804031	+	0.292643i	−0.711156	−	0.703035i	$-0.751828\pi$
$7$	−2.12726	+	0.774261i	−0.804031	+	0.292643i	−0.0928749	+	0.995678i	$0.529606\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	0.170795	−	0.295826i	0.0540102	−	0.0935484i
$11$	2.53348	+	4.38812i	0.763873	+	1.32307i	0.940840	+	0.338850i	$0.110038\pi$
$11$	2.53348	+	4.38812i	0.763873	+	1.32307i	−0.176967	+	0.984217i	$0.556629\pi$
$12$		0			0
$13$	0.447015	+	0.638404i	0.123980	+	0.177061i	0.876344	−	0.481686i	$-0.159975\pi$
$13$	0.447015	+	0.638404i	0.123980	+	0.177061i	−0.752364	+	0.658748i	$0.771087\pi$
$14$	0.585911	+	2.18665i	0.156591	+	0.584407i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−3.48398	+	4.97563i	−0.844989	+	1.20677i	0.131525	+	0.991313i	$0.458013\pi$
$17$	−3.48398	+	4.97563i	−0.844989	+	1.20677i	−0.976514	+	0.215456i	$0.930876\pi$
$18$		0			0
$19$	5.68686	−	0.497536i	1.30466	−	0.114143i	0.586457	−	0.809981i	$-0.300522\pi$
$19$	5.68686	−	0.497536i	1.30466	−	0.114143i	0.718199	+	0.695838i	$0.244967\pi$
$20$	−0.279814	−	0.195928i	−0.0625684	−	0.0438109i
$21$		0			0
$22$	4.59223	−	2.14139i	0.979066	−	0.456546i
$23$	−2.40525	+	0.644485i	−0.501529	+	0.134384i	−0.500710	−	0.865615i	$-0.666928\pi$
$23$	−2.40525	+	0.644485i	−0.501529	+	0.134384i	−0.000819621		1.00000i	$0.500261\pi$
$24$		0			0
$25$	−3.13894	−	3.74084i	−0.627787	−	0.748167i
$26$	0.674935	−	0.389674i	0.132366	−	0.0764213i
$27$		0			0
$28$	2.22940	−	0.393103i	0.421316	−	0.0742894i
$29$	10.2511	+	2.74678i	1.90359	+	0.510065i	0.995905	+	0.0904086i	$0.0288173\pi$
$29$	10.2511	+	2.74678i	1.90359	+	0.510065i	0.907683	+	0.419656i	$0.137849\pi$
$30$		0			0
$31$	4.79672	+	4.79672i	0.861516	+	0.861516i	0.991514	−	0.129998i	$-0.0414972\pi$
$31$	4.79672	+	4.79672i	0.861516	+	0.861516i	−0.129998	+	0.991514i	$0.541497\pi$
$32$	0.422618	−	0.906308i	0.0747091	−	0.160214i
$33$		0			0
$34$	4.65305	+	3.90437i	0.797992	+	0.669595i
$35$	−0.770346	−	0.0673965i	−0.130212	−	0.0113921i
$36$		0			0
$37$	−4.86851	−	3.64659i	−0.800377	−	0.599496i
$37$	−4.86851	−	3.64659i	−0.800377	−	0.599496i
$38$		−	5.70858i		−	0.926055i
$39$		0			0
$40$	−0.219570	+	0.261673i	−0.0347171	+	0.0413742i
$41$	−1.94300	+	11.0193i	−0.303445	+	1.72092i	0.327289	+	0.944924i	$0.393865\pi$
$41$	−1.94300	+	11.0193i	−0.303445	+	1.72092i	−0.630735	+	0.775999i	$0.717246\pi$
$42$		0			0
$43$	5.24522	−	5.24522i	0.799888	−	0.799888i	−0.183190	−	0.983078i	$-0.558642\pi$
$43$	5.24522	−	5.24522i	0.799888	−	0.799888i	0.983078	+	0.183190i	$0.0586422\pi$
$44$	−1.73300	−	4.76138i	−0.261260	−	0.717806i
$45$		0			0
$46$	0.432401	+	2.45227i	0.0637540	+	0.361567i
$47$	−1.12230	−	0.647958i	−0.163704	−	0.0945144i	0.415910	−	0.909406i	$-0.363463\pi$
$47$	−1.12230	−	0.647958i	−0.163704	−	0.0945144i	−0.579614	+	0.814891i	$0.696797\pi$
$48$		0			0
$49$	−1.43654	+	1.20540i	−0.205219	+	0.172199i
$50$	−4.00018	+	2.80096i	−0.565711	+	0.396115i
$51$		0			0
$52$	−0.329366	−	0.706329i	−0.0456749	−	0.0979502i
$53$	−1.91222	+	5.25379i	−0.262664	+	0.721663i	0.736322	+	0.676632i	$0.236561\pi$
$53$	−1.91222	+	5.25379i	−0.262664	+	0.721663i	−0.998986	+	0.0450316i	$0.985661\pi$
$54$		0			0
$55$	0.150851	+	1.72424i	0.0203408	+	0.232496i
$56$	−0.197302	−	2.25517i	−0.0263656	−	0.301360i
$57$		0			0
$58$	3.62978	−	9.97273i	0.476613	−	1.30948i
$59$	−0.911581	−	1.95489i	−0.118678	−	0.254505i	0.837991	−	0.545684i	$-0.183730\pi$
$59$	−0.911581	−	1.95489i	−0.118678	−	0.254505i	−0.956669	+	0.291179i	$0.905952\pi$
$60$		0			0
$61$	2.57678	−	1.80428i	0.329922	−	0.231014i	−0.396864	−	0.917877i	$-0.629902\pi$
$61$	2.57678	−	1.80428i	0.329922	−	0.231014i	0.726787	+	0.686863i	$0.241013\pi$
$62$	5.19653	−	4.36040i	0.659959	−	0.553772i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	0.0462282	+	0.262173i	0.00573390	+	0.0325186i
$66$		0			0
$67$	−1.75464	−	4.82082i	−0.214363	−	0.588957i	0.785177	−	0.619271i	$-0.212572\pi$
$67$	−1.75464	−	4.82082i	−0.214363	−	0.588957i	−0.999540	+	0.0303134i	$0.990349\pi$
$68$	4.29506	−	4.29506i	0.520852	−	0.520852i
$69$		0			0
$70$	−0.134280	+	0.761540i	−0.0160495	+	0.0910215i
$71$	6.66465	−	7.94262i	0.790949	−	0.942616i	−0.208424	−	0.978039i	$-0.566833\pi$
$71$	6.66465	−	7.94262i	0.790949	−	0.942616i	0.999372	+	0.0354228i	$0.0112778\pi$
$72$		0			0
$73$			14.3898i			1.68420i	0.539319	+	0.842101i	$0.318682\pi$
$73$			14.3898i			1.68420i	−0.539319	+	0.842101i	$0.681318\pi$
$74$	−4.05704	+	4.53216i	−0.471621	+	0.526853i
$75$		0			0
$76$	−5.68686	−	0.497536i	−0.652328	−	0.0570713i
$77$	−8.78693	−	7.37311i	−1.00136	−	0.840244i
$78$		0			0
$79$	−1.92544	+	4.12911i	−0.216629	+	0.464562i	−0.984351	−	0.176222i	$-0.943612\pi$
$79$	−1.92544	+	4.12911i	−0.216629	+	0.464562i	0.767722	+	0.640783i	$0.221390\pi$
$80$	0.241541	+	0.241541i	0.0270051	+	0.0270051i
$81$		0			0
$82$	10.8080	+	2.89600i	1.19354	+	0.319809i
$83$	4.84692	−	0.854643i	0.532018	−	0.0938092i	0.0988158	−	0.995106i	$-0.468495\pi$
$83$	4.84692	−	0.854643i	0.532018	−	0.0938092i	0.433203	+	0.901297i	$0.357383\pi$
$84$		0			0
$85$	−1.79688	+	1.03743i	−0.194900	+	0.112525i
$86$	−4.76811	−	5.68241i	−0.514158	−	0.612750i
$87$		0			0
$88$	−4.89431	+	1.31143i	−0.521735	+	0.139798i
$89$	−8.92392	+	4.16129i	−0.945933	+	0.441096i	−0.833473	−	0.552560i	$-0.813651\pi$
$89$	−8.92392	+	4.16129i	−0.945933	+	0.441096i	−0.112460	+	0.993656i	$0.535873\pi$
$90$		0			0
$91$	−1.44521	−	1.01195i	−0.151499	−	0.106081i
$92$	2.48062	−	0.217026i	0.258623	−	0.0226266i
$93$		0			0
$94$	−0.743307	+	1.06155i	−0.0766663	+	0.109491i
$95$	1.83240	+	0.666938i	0.188000	+	0.0684264i
$96$		0			0
$97$	−2.93104	−	10.9388i	−0.297603	−	1.11067i	−0.939128	−	0.343566i	$-0.888365\pi$
$97$	−2.93104	−	10.9388i	−0.297603	−	1.11067i	0.641526	−	0.767101i	$-0.278302\pi$
$98$	1.07561	+	1.53613i	0.108653	+	0.155172i
$99$		0			0
$100$	2.44166	+	4.22908i	0.244166	+	0.422908i
$101$	5.77814	−	10.0080i	0.574946	−	0.995836i	−0.421101	−	0.907014i	$-0.638356\pi$
$101$	5.77814	−	10.0080i	0.574946	−	0.995836i	0.996047	−	0.0888223i	$-0.0283103\pi$
$102$		0			0
$103$	1.15240	−	4.30083i	0.113550	−	0.423774i	−0.885625	−	0.464402i	$-0.846269\pi$
$103$	1.15240	−	4.30083i	0.113550	−	0.423774i	0.999174	+	0.0406283i	$0.0129360\pi$
$104$	−0.732347	+	0.266553i	−0.0718125	+	0.0261376i
$105$		0			0
$106$	5.06713	+	2.36284i	0.492164	+	0.229500i
$107$	2.17068	+	0.382750i	0.209848	+	0.0370019i	0.277584	−	0.960701i	$-0.410466\pi$
$107$	2.17068	+	0.382750i	0.209848	+	0.0370019i	−0.0677358	+	0.997703i	$0.521578\pi$
$108$		0			0
$109$	−0.0347412	+	0.397093i	−0.00332760	+	0.0380347i	−0.997677	−	0.0681225i	$-0.978299\pi$
$109$	−0.0347412	+	0.397093i	−0.00332760	+	0.0380347i	0.994349	+	0.106157i	$0.0338547\pi$
$110$	1.73082			0.165028
$111$		0			0
$112$	−2.26379			−0.213908
$113$	−1.04794	+	11.9780i	−0.0985820	+	1.12680i	0.772284	+	0.635277i	$0.219114\pi$
$113$	−1.04794	+	11.9780i	−0.0985820	+	1.12680i	−0.870866	+	0.491520i	$0.836441\pi$
$114$		0			0
$115$	−0.837671	−	0.147704i	−0.0781132	−	0.0137735i
$116$	−9.61842	−	4.48514i	−0.893048	−	0.416435i
$117$		0			0
$118$	−2.02690	+	0.737732i	−0.186592	+	0.0679138i
$119$	3.55890	−	13.2820i	0.326244	−	1.21756i
$120$		0			0
$121$	−7.33704	+	12.7081i	−0.667004	+	1.15528i
$122$	−1.57283	−	2.72422i	−0.142397	−	0.246640i
$123$		0			0
$124$	−3.89090	−	5.55678i	−0.349413	−	0.499014i
$125$	−0.873785	−	3.26101i	−0.0781537	−	0.291674i
$126$		0			0
$127$	−16.2722	−	5.92261i	−1.44393	−	0.525546i	−0.503039	−	0.864264i	$-0.667785\pi$
$127$	−16.2722	−	5.92261i	−1.44393	−	0.525546i	−0.940888	+	0.338717i	$0.890007\pi$
$128$	−0.573576	+	0.819152i	−0.0506975	+	0.0724035i
$129$		0			0
$130$	0.265205	−	0.0232024i	0.0232600	−	0.00203498i
$131$	−11.9410	−	8.36120i	−1.04329	−	0.730522i	−0.0794084	−	0.996842i	$-0.525303\pi$
$131$	−11.9410	−	8.36120i	−1.04329	−	0.730522i	−0.963884	+	0.266321i	$0.914192\pi$
$132$		0			0
$133$	−11.7122	+	5.46151i	−1.01558	+	0.473573i
$134$	−4.95541	+	1.32780i	−0.428082	+	0.114704i
$135$		0			0
$136$	−3.90437	−	4.65305i	−0.334797	−	0.398996i
$137$	1.17284	−	0.677141i	0.100203	−	0.0578520i	−0.449061	−	0.893501i	$-0.648242\pi$
$137$	1.17284	−	0.677141i	0.100203	−	0.0578520i	0.549264	+	0.835649i	$0.314908\pi$
$138$		0			0
$139$	−16.2072	+	2.85776i	−1.37467	+	0.242392i	−0.811696	−	0.584079i	$-0.801456\pi$
$139$	−16.2072	+	2.85776i	−1.37467	+	0.242392i	−0.562978	+	0.826472i	$0.690345\pi$
$140$	0.746939	+	0.200142i	0.0631279	+	0.0169151i
$141$		0			0
$142$	−7.33154	−	7.33154i	−0.615249	−	0.615249i
$143$	−1.66889	+	3.57894i	−0.139559	+	0.299286i
$144$		0			0
$145$	2.77708	+	2.33024i	0.230624	+	0.193516i
$146$	14.3351	+	1.25416i	1.18638	+	0.103795i
$147$		0			0
$148$	4.16132	+	4.43660i	0.342058	+	0.364686i
$149$			13.4310i			1.10031i	0.835063	+	0.550154i	$0.185431\pi$
$149$			13.4310i			1.10031i	−0.835063	+	0.550154i	$0.814569\pi$
$150$		0			0
$151$	4.28184	−	5.10290i	0.348451	−	0.415268i	−0.563143	−	0.826360i	$-0.690408\pi$
$151$	4.28184	−	5.10290i	0.348451	−	0.415268i	0.911594	+	0.411092i	$0.134852\pi$
$152$	−0.991285	+	5.62186i	−0.0804039	+	0.455993i
$153$		0			0
$154$	−8.11088	+	8.11088i	−0.653594	+	0.653594i
$155$	0.792531	+	2.17746i	0.0636576	+	0.174898i
$156$		0			0
$157$	−2.82884	−	16.0431i	−0.225766	−	1.28038i	−0.861216	−	0.508239i	$-0.830297\pi$
$157$	−2.82884	−	16.0431i	−0.225766	−	1.28038i	0.635450	−	0.772142i	$-0.280815\pi$
$158$	3.94559	+	2.27799i	0.313894	+	0.181227i
$159$		0			0
$160$	0.261673	−	0.219570i	0.0206871	−	0.0173585i
$161$	4.61760	−	3.23328i	0.363918	−	0.254818i
$162$		0			0
$163$	9.60004	+	20.5874i	0.751933	+	1.61253i	0.789891	+	0.613247i	$0.210137\pi$
$163$	9.60004	+	20.5874i	0.751933	+	1.61253i	−0.0379582	+	0.999279i	$0.512085\pi$
$164$	3.82696	−	10.5145i	0.298835	−	0.821043i
$165$		0			0
$166$	−0.428954	−	4.90296i	−0.0332933	−	0.380544i
$167$	0.0349366	+	0.399328i	0.00270348	+	0.0309009i	0.997427	−	0.0716948i	$-0.0228408\pi$
$167$	0.0349366	+	0.399328i	0.00270348	+	0.0309009i	−0.994723	+	0.102596i	$0.967285\pi$
$168$		0			0
$169$	4.23852	−	11.6453i	0.326040	−	0.895789i
$170$	0.876875	+	1.88047i	0.0672533	+	0.144225i
$171$		0			0
$172$	−6.07635	+	4.25471i	−0.463317	+	0.324418i
$173$	8.98813	−	7.54194i	0.683355	−	0.573403i	−0.233630	−	0.972326i	$-0.575060\pi$
$173$	8.98813	−	7.54194i	0.683355	−	0.573403i	0.916984	+	0.398923i	$0.130616\pi$
$174$		0			0
$175$	9.57373	+	5.52740i	0.723706	+	0.417832i
$176$	0.879868	+	4.98998i	0.0663226	+	0.376134i
$177$		0			0
$178$	3.36768	+	9.25264i	0.252419	+	0.693514i
$179$	3.02271	−	3.02271i	0.225928	−	0.225928i	−0.585061	−	0.810989i	$-0.698930\pi$
$179$	3.02271	−	3.02271i	0.225928	−	0.225928i	0.810989	+	0.585061i	$0.198930\pi$
$180$		0			0
$181$	−2.44365	+	13.8586i	−0.181635	+	1.03010i	0.748568	+	0.663058i	$0.230742\pi$
$181$	−2.44365	+	13.8586i	−0.181635	+	1.03010i	−0.930203	+	0.367045i	$0.880369\pi$
$182$	−1.13406	+	1.35151i	−0.0840618	+	0.100181i
$183$		0			0
$184$		−	2.49010i		−	0.183572i
$185$	−0.980790	−	1.83176i	−0.0721091	−	0.134674i
$186$		0			0
$187$	−30.6602	−	2.68242i	−2.24210	−	0.196158i
$188$	0.992729	+	0.832999i	0.0724022	+	0.0607527i
$189$		0			0
$190$	0.824105	−	1.76730i	0.0597868	−	0.128213i
$191$	−13.4153	−	13.4153i	−0.970695	−	0.970695i	0.0288874	−	0.999583i	$-0.490804\pi$
$191$	−13.4153	−	13.4153i	−0.970695	−	0.970695i	−0.999583	+	0.0288874i	$0.990804\pi$
$192$		0			0
$193$	−0.0113745	−	0.00304780i	−0.000818756	−	0.000219385i	0.258410	−	0.966035i	$-0.416802\pi$
$193$	−0.0113745	−	0.00304780i	−0.000818756	−	0.000219385i	−0.259228	+	0.965816i	$0.583468\pi$
$194$	−11.1526	+	1.96651i	−0.800713	+	0.141187i
$195$		0			0
$196$	1.62403	−	0.937632i	0.116002	−	0.0669737i
$197$	7.53780	+	8.98320i	0.537046	+	0.640026i	0.964523	−	0.264000i	$-0.0850419\pi$
$197$	7.53780	+	8.98320i	0.537046	+	0.640026i	−0.427477	+	0.904026i	$0.640597\pi$
$198$		0			0
$199$	14.6608	−	3.92834i	1.03927	−	0.278473i	0.301462	−	0.953478i	$-0.402525\pi$
$199$	14.6608	−	3.92834i	1.03927	−	0.278473i	0.737813	+	0.675006i	$0.235859\pi$
$200$	4.42579	−	2.06378i	0.312950	−	0.145931i
$201$		0			0
$202$	−9.46635	−	6.62841i	−0.666050	−	0.466373i
$203$	−23.9336	+	2.09392i	−1.67981	+	0.146964i
$204$		0			0
$205$	−2.19229	+	3.13092i	−0.153116	+	0.218673i
$206$	−4.18403	−	1.52286i	−0.291515	−	0.106103i
$207$		0			0
$208$	0.201710	+	0.752792i	0.0139861	+	0.0521967i
$209$	16.5908	+	23.6941i	1.14761	+	1.63896i
$210$		0			0
$211$	4.00528	+	6.93735i	0.275735	+	0.477587i	0.970320	−	0.241824i	$-0.0777455\pi$
$211$	4.00528	+	6.93735i	0.275735	+	0.477587i	−0.694585	+	0.719410i	$0.744412\pi$
$212$	2.79548	−	4.84192i	0.191995	−	0.332544i
$213$		0			0
$214$	0.570481	−	2.12907i	0.0389973	−	0.145540i
$215$	2.38106	−	0.866634i	0.162387	−	0.0591039i
$216$		0			0
$217$	−13.9178	−	6.48998i	−0.944802	−	0.440568i
$218$	0.392554	+	0.0692179i	0.0265871	+	0.00468803i
$219$		0			0
$220$	0.150851	−	1.72424i	0.0101704	−	0.116248i
$221$	−4.73386			−0.318434
$222$		0			0
$223$	20.9461			1.40265			0.701326	−	0.712841i	$-0.252592\pi$
$223$	20.9461			1.40265			0.701326	+	0.712841i	$0.252592\pi$
$224$	−0.197302	+	2.25517i	−0.0131828	+	0.150680i
$225$		0			0
$226$	11.8411	+	2.08791i	0.787658	+	0.138885i
$227$	4.11182	+	1.91737i	0.272911	+	0.127261i	0.554256	−	0.832346i	$-0.313003\pi$
$227$	4.11182	+	1.91737i	0.272911	+	0.127261i	−0.281345	+	0.959607i	$0.590781\pi$
$228$		0			0
$229$	7.50358	−	2.73108i	0.495850	−	0.180475i	−0.0819763	−	0.996634i	$-0.526123\pi$
$229$	7.50358	−	2.73108i	0.495850	−	0.180475i	0.577827	+	0.816160i	$0.303901\pi$
$230$	−0.220150	+	0.821610i	−0.0145162	+	0.0541754i
$231$		0			0
$232$	−5.30638	+	9.19092i	−0.348381	+	0.603413i
$233$	−9.02974	−	15.6400i	−0.591558	−	1.02461i	−0.994023	−	0.109173i	$-0.965180\pi$
$233$	−9.02974	−	15.6400i	−0.591558	−	1.02461i	0.402465	−	0.915435i	$-0.368153\pi$
$234$		0			0
$235$	−0.253907	−	0.362616i	−0.0165630	−	0.0236545i
$236$	0.558269	+	2.08349i	0.0363402	+	0.135623i
$237$		0			0
$238$	−12.9213	−	4.70296i	−0.837562	−	0.304848i
$239$	5.52851	−	7.89553i	0.357609	−	0.510719i	−0.599528	−	0.800354i	$-0.704645\pi$
$239$	5.52851	−	7.89553i	0.357609	−	0.510719i	0.957137	+	0.289635i	$0.0935338\pi$
$240$		0			0
$241$	−6.30139	+	0.551300i	−0.405908	+	0.0355124i	−0.288282	−	0.957546i	$-0.593084\pi$
$241$	−6.30139	+	0.551300i	−0.405908	+	0.0355124i	−0.117626	+	0.993058i	$0.537529\pi$
$242$	12.0203	+	8.41671i	0.772694	+	0.541046i
$243$		0			0
$244$	−2.85094	+	1.32941i	−0.182513	+	0.0851071i
$245$	−0.618745	+	0.165792i	−0.0395302	+	0.0105921i
$246$		0			0
$247$	2.85974	+	3.40811i	0.181961	+	0.216853i
$248$	−5.87475	+	3.39179i	−0.373047	+	0.215379i
$249$		0			0
$250$	−3.32476	+	0.586244i	−0.210276	+	0.0370773i
$251$	18.1723	+	4.86925i	1.14702	+	0.307344i	0.781772	−	0.623564i	$-0.214316\pi$
$251$	18.1723	+	4.86925i	1.14702	+	0.307344i	0.365252	+	0.930909i	$0.380983\pi$
$252$		0			0
$253$	−8.92173	−	8.92173i	−0.560904	−	0.560904i
$254$	−7.31829	+	15.6941i	−0.459190	+	0.984737i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−1.56209	−	0.136666i	−0.0974408	−	0.00852497i	0.0383310	−	0.999265i	$-0.487796\pi$
$257$	−1.56209	−	0.136666i	−0.0974408	−	0.00852497i	−0.135772	+	0.990740i	$0.543351\pi$
$258$		0			0
$259$	13.1800	+	3.98778i	0.818966	+	0.247788i
$260$		−	0.266218i		−	0.0165101i
$261$		0			0
$262$	−9.37011	+	11.1669i	−0.578888	+	0.689891i
$263$	1.39543	−	7.91389i	0.0860461	−	0.487991i	−0.911080	−	0.412230i	$-0.864750\pi$
$263$	1.39543	−	7.91389i	0.0860461	−	0.487991i	0.997126	−	0.0757617i	$-0.0241388\pi$
$264$		0			0
$265$	−1.35045	+	1.35045i	−0.0829573	+	0.0829573i
$266$	4.41994	+	12.1437i	0.271004	+	0.744576i
$267$		0			0
$268$	0.890852	+	5.05227i	0.0544175	+	0.308617i
$269$	−21.4858	−	12.4048i	−1.31001	−	0.756337i	−0.327916	−	0.944707i	$-0.606346\pi$
$269$	−21.4858	−	12.4048i	−1.31001	−	0.756337i	−0.982098	+	0.188370i	$0.939680\pi$
$270$		0			0
$271$	23.5933	−	19.7971i	1.43319	−	1.20259i	0.489391	−	0.872065i	$-0.337219\pi$
$271$	23.5933	−	19.7971i	1.43319	−	1.20259i	0.943798	−	0.330523i	$-0.107225\pi$
$272$	−4.97563	+	3.48398i	−0.301692	+	0.211247i
$273$		0			0
$274$	−0.572344	−	1.22740i	−0.0345766	−	0.0741497i
$275$	8.46280	−	23.2513i	0.510326	−	1.40211i
$276$		0			0
$277$	0.271006	+	3.09761i	0.0162832	+	0.186117i	0.999980	+	0.00628411i	$0.00200031\pi$
$277$	0.271006	+	3.09761i	0.0162832	+	0.186117i	−0.983697	+	0.179833i	$0.942444\pi$
$278$	1.43434	+	16.3946i	0.0860260	+	0.983281i
$279$		0			0
$280$	0.264480	−	0.726653i	0.0158057	−	0.0434258i
$281$	−9.80568	−	21.0283i	−0.584958	−	1.25445i	−0.946685	−	0.322162i	$-0.895591\pi$
$281$	−9.80568	−	21.0283i	−0.584958	−	1.25445i	0.361727	−	0.932284i	$-0.382187\pi$
$282$		0			0
$283$	15.9412	−	11.1622i	0.947607	−	0.663522i	0.00590970	−	0.999983i	$-0.498119\pi$
$283$	15.9412	−	11.1622i	0.947607	−	0.663522i	0.941697	+	0.336461i	$0.109230\pi$
$284$	−7.94262	+	6.66465i	−0.471308	+	0.395474i
$285$		0			0
$286$	3.41987	+	1.97446i	0.202221	+	0.116752i
$287$	−4.39853	−	24.9453i	−0.259637	−	1.47248i
$288$		0			0
$289$	−6.80450	−	18.6952i	−0.400265	−	1.09972i
$290$	2.56341	−	2.56341i	0.150529	−	0.150529i
$291$		0			0
$292$	2.49877	−	14.1712i	0.146229	−	0.829308i
$293$	−4.96420	+	5.91611i	−0.290012	+	0.345623i	−0.891304	−	0.453407i	$-0.850208\pi$
$293$	−4.96420	+	5.91611i	−0.290012	+	0.345623i	0.601292	+	0.799030i	$0.294653\pi$
$294$		0			0
$295$		−	0.736805i		−	0.0428985i
$296$	4.78240	−	3.75881i	0.277971	−	0.218476i
$297$		0			0
$298$	13.3799	+	1.17059i	0.775074	+	0.0678102i
$299$	−1.48663	−	1.24743i	−0.0859738	−	0.0721406i
$300$		0			0
$301$	−7.09680	+	15.2191i	−0.409053	+	0.877216i
$302$	−4.71029	−	4.71029i	−0.271047	−	0.271047i
$303$		0			0
$304$	5.51407	+	1.47749i	0.316254	+	0.0847399i
$305$	1.05820	−	0.186590i	0.0605926	−	0.0106841i
$306$		0			0
$307$	22.8458	−	13.1900i	1.30388	−	0.752796i	0.322813	−	0.946463i	$-0.395371\pi$
$307$	22.8458	−	13.1900i	1.30388	−	0.752796i	0.981067	+	0.193667i	$0.0620382\pi$
$308$	7.37311	+	8.78693i	0.420122	+	0.500682i
$309$		0			0
$310$	2.23825	−	0.599737i	0.127124	−	0.0340628i
$311$	24.8659	−	11.5952i	1.41002	−	0.657502i	0.439436	−	0.898274i	$-0.355178\pi$
$311$	24.8659	−	11.5952i	1.41002	−	0.657502i	0.970582	+	0.240772i	$0.0774005\pi$
$312$		0			0
$313$	3.40090	+	2.38133i	0.192230	+	0.134601i	0.665729	−	0.746193i	$-0.268121\pi$
$313$	3.40090	+	2.38133i	0.192230	+	0.134601i	−0.473499	+	0.880794i	$0.657009\pi$
$314$	−16.2286	+	1.41982i	−0.915835	+	0.0801251i
$315$		0			0
$316$	2.61320	−	3.73203i	0.147004	−	0.209943i
$317$	21.0857	+	7.67458i	1.18429	+	0.431047i	0.857716	−	0.514124i	$-0.171883\pi$
$317$	21.0857	+	7.67458i	1.18429	+	0.431047i	0.326576	+	0.945171i	$0.394105\pi$
$318$		0			0
$319$	13.9178	+	51.9421i	0.779249	+	2.90820i
$320$	−0.195928	−	0.279814i	−0.0109527	−	0.0156421i
$321$		0			0
$322$	−2.81853	−	4.88183i	−0.157070	−	0.272054i
$323$	−17.3373	+	30.0292i	−0.964675	+	1.67087i
$324$		0			0
$325$	0.985014	−	3.67612i	0.0546387	−	0.203914i
$326$	21.3457	−	7.76920i	1.18223	−	0.430296i
$327$		0			0
$328$	−10.1409	−	4.72879i	−0.559939	−	0.261104i
$329$	2.88911	+	0.509428i	0.159282	+	0.0280857i
$330$		0			0
$331$	0.699671	−	7.99727i	0.0384574	−	0.439570i	−0.952419	−	0.304793i	$-0.901413\pi$
$331$	0.699671	−	7.99727i	0.0384574	−	0.439570i	0.990876	−	0.134777i	$-0.0430318\pi$
$332$	−4.92169			−0.270113
$333$		0			0
$334$	0.400853			0.0219337
$335$	0.152734	−	1.74576i	0.00834478	−	0.0953812i
$336$		0			0
$337$	21.1895	+	3.73628i	1.15427	+	0.203528i	0.717837	−	0.696211i	$-0.245132\pi$
$337$	21.1895	+	3.73628i	1.15427	+	0.203528i	0.436428	+	0.899739i	$0.356243\pi$
$338$	−11.2315	−	5.23735i	−0.610914	−	0.284874i
$339$		0			0
$340$	1.94973	−	0.709645i	0.105739	−	0.0384859i
$341$	−8.89616	+	33.2009i	−0.481754	+	1.79793i
$342$		0			0
$343$	10.0459	−	17.3999i	0.542425	−	0.939508i
$344$	3.70893	+	6.42405i	0.199972	+	0.346362i
$345$		0			0
$346$	−6.72987	−	9.61125i	−0.361800	−	0.516704i
$347$	2.45271	+	9.15364i	0.131668	+	0.491393i	0.999989	−	0.00460965i	$-0.00146730\pi$
$347$	2.45271	+	9.15364i	0.131668	+	0.491393i	−0.868321	+	0.496003i	$0.834801\pi$
$348$		0			0
$349$	21.7238	+	7.90681i	1.16285	+	0.423242i	0.850114	−	0.526599i	$-0.176533\pi$
$349$	21.7238	+	7.90681i	1.16285	+	0.423242i	0.312733	+	0.949841i	$0.398755\pi$
$350$	6.34077	−	9.05556i	0.338928	−	0.484040i
$351$		0			0
$352$	5.04768	−	0.441615i	0.269042	−	0.0235381i
$353$	1.93917	+	1.35782i	0.103211	+	0.0722694i	0.624043	−	0.781390i	$-0.285489\pi$
$353$	1.93917	+	1.35782i	0.103211	+	0.0722694i	−0.520831	+	0.853660i	$0.674378\pi$
$354$		0			0
$355$	3.20990	−	1.49680i	0.170364	−	0.0794419i
$356$	9.51094	−	2.54845i	0.504079	−	0.135068i
$357$		0			0
$358$	−2.74776	−	3.27465i	−0.145223	−	0.173071i
$359$	−17.4532	+	10.0766i	−0.921144	+	0.531823i	−0.884000	−	0.467487i	$-0.845159\pi$
$359$	−17.4532	+	10.0766i	−0.921144	+	0.531823i	−0.0371441	+	0.999310i	$0.511826\pi$
$360$		0			0
$361$	13.3815	−	2.35952i	0.704290	−	0.124185i
$362$	13.5929	+	3.64221i	0.714427	+	0.191430i
$363$		0			0
$364$	1.24753	+	1.24753i	0.0653885	+	0.0653885i
$365$	−2.07735	+	4.45489i	−0.108733	+	0.233180i
$366$		0			0
$367$	17.1498	+	14.3904i	0.895212	+	0.751172i	0.969249	−	0.246083i	$-0.0791436\pi$
$367$	17.1498	+	14.3904i	0.895212	+	0.751172i	−0.0740363	+	0.997256i	$0.523588\pi$
$368$	−2.48062	−	0.217026i	−0.129311	−	0.0113133i
$369$		0			0
$370$	−1.91027	+	0.817409i	−0.0993104	+	0.0424951i
$371$		−	12.6568i		−	0.657106i
$372$		0			0
$373$	9.33849	−	11.1292i	0.483529	−	0.576247i	−0.468031	−	0.883712i	$-0.655036\pi$
$373$	9.33849	−	11.1292i	0.483529	−	0.576247i	0.951559	+	0.307465i	$0.0994807\pi$
$374$	−5.34443	+	30.3098i	−0.276354	+	1.56728i
$375$		0			0
$376$	0.916351	−	0.916351i	0.0472572	−	0.0472572i
$377$	2.82886	+	7.77222i	0.145694	+	0.400290i
$378$		0			0
$379$	−4.05138	−	22.9765i	−0.208105	−	1.18022i	−0.892478	−	0.451091i	$-0.851035\pi$
$379$	−4.05138	−	22.9765i	−0.208105	−	1.18022i	0.684372	−	0.729133i	$-0.260076\pi$
$380$	−1.68875	−	0.974999i	−0.0866309	−	0.0500164i
$381$		0			0
$382$	−14.5334	+	12.1950i	−0.743596	+	0.623951i
$383$	−5.98356	+	4.18973i	−0.305745	+	0.214085i	−0.716372	−	0.697718i	$-0.754199\pi$
$383$	−5.98356	+	4.18973i	−0.305745	+	0.214085i	0.410627	+	0.911803i	$0.365310\pi$
$384$		0			0
$385$	−1.65591	−	3.55111i	−0.0843931	−	0.180981i
$386$	−0.00402755	+	0.0110656i	−0.000204997	+	0.000563225i
$387$		0			0
$388$	0.987012	+	11.2816i	0.0501079	+	0.572736i
$389$	1.30017	+	14.8610i	0.0659211	+	0.753482i	0.955170	+	0.296058i	$0.0956721\pi$
$389$	1.30017	+	14.8610i	0.0659211	+	0.753482i	−0.889249	+	0.457424i	$0.848772\pi$
$390$		0			0
$391$	5.17311	−	14.2130i	0.261616	−	0.718783i
$392$	−0.792521	−	1.69957i	−0.0400283	−	0.0858411i
$393$		0			0
$394$	9.60597	−	6.72618i	0.483942	−	0.338860i
$395$	−1.19218	+	1.00036i	−0.0599849	+	0.0503333i
$396$		0			0
$397$	−4.15013	−	2.39608i	−0.208289	−	0.120256i	0.392227	−	0.919868i	$-0.371705\pi$
$397$	−4.15013	−	2.39608i	−0.208289	−	0.120256i	−0.600516	+	0.799613i	$0.705038\pi$
$398$	−2.63562	−	14.9474i	−0.132112	−	0.749243i
$399$		0			0
$400$	−1.67019	−	4.58882i	−0.0835096	−	0.229441i
$401$	−4.96675	+	4.96675i	−0.248027	+	0.248027i	−0.820161	−	0.572133i	$-0.806116\pi$
$401$	−4.96675	+	4.96675i	−0.248027	+	0.248027i	0.572133	+	0.820161i	$0.306116\pi$
$402$		0			0
$403$	−0.918038	+	5.20645i	−0.0457307	+	0.259352i
$404$	−7.42823	+	8.85262i	−0.369568	+	0.440434i
$405$		0			0
$406$			24.0250i			1.19234i
$407$	3.66742	−	30.6021i	0.181787	−	1.51689i
$408$		0			0
$409$	−14.1609	−	1.23892i	−0.700210	−	0.0612604i	−0.268509	−	0.963277i	$-0.586531\pi$
$409$	−14.1609	−	1.23892i	−0.700210	−	0.0612604i	−0.431701	+	0.902017i	$0.642086\pi$
$410$	2.92794	+	2.45683i	0.144600	+	0.121334i
$411$		0			0
$412$	−1.88173	+	4.03538i	−0.0927061	+	0.198809i
$413$	3.45277	+	3.45277i	0.169900	+	0.169900i
$414$		0			0
$415$	1.62392	+	0.435127i	0.0797149	+	0.0213595i
$416$	0.767507	−	0.135332i	0.0376301	−	0.00663521i
$417$		0			0
$418$	25.0499	−	14.4626i	1.22523	−	0.707388i
$419$	5.58059	+	6.65069i	0.272630	+	0.324907i	0.884936	−	0.465714i	$-0.154202\pi$
$419$	5.58059	+	6.65069i	0.272630	+	0.324907i	−0.612306	+	0.790621i	$0.709758\pi$
$420$		0			0
$421$	30.3902	−	8.14302i	1.48113	−	0.396866i	0.574396	−	0.818578i	$-0.305237\pi$
$421$	30.3902	−	8.14302i	1.48113	−	0.396866i	0.906730	+	0.421711i	$0.138570\pi$
$422$	7.26003	−	3.38541i	0.353413	−	0.164799i
$423$		0			0
$424$	−4.57985	−	3.20685i	−0.222417	−	0.155738i
$425$	29.5490	−	2.58520i	1.43334	−	0.125401i
$426$		0			0
$427$	−4.08450	+	5.83328i	−0.197663	+	0.282292i
$428$	−2.07124	−	0.753871i	−0.100117	−	0.0364397i
$429$		0			0
$430$	−0.655813	−	2.44753i	−0.0316261	−	0.118030i
$431$	−0.593085	−	0.847013i	−0.0285679	−	0.0407992i	0.804614	−	0.593798i	$-0.202372\pi$
$431$	−0.593085	−	0.847013i	−0.0285679	−	0.0407992i	−0.833182	+	0.552999i	$0.813483\pi$
$432$		0			0
$433$	3.98008	+	6.89370i	0.191270	+	0.331290i	0.945672	−	0.325124i	$-0.105406\pi$
$433$	3.98008	+	6.89370i	0.191270	+	0.331290i	−0.754401	+	0.656414i	$0.772073\pi$
$434$	−7.67830	+	13.2992i	−0.368570	+	0.638382i
$435$		0			0
$436$	0.103168	−	0.385028i	0.00494085	−	0.0184395i
$437$	−13.3577	+	4.86179i	−0.638984	+	0.232571i
$438$		0			0
$439$	10.6925	+	4.98598i	0.510324	+	0.237968i	0.660685	−	0.750663i	$-0.270266\pi$
$439$	10.6925	+	4.98598i	0.510324	+	0.237968i	−0.150361	+	0.988631i	$0.548044\pi$
$440$	−1.70453	−	0.300555i	−0.0812603	−	0.0143284i
$441$		0			0
$442$	−0.412583	+	4.71584i	−0.0196246	+	0.224310i
$443$	7.03829			0.334399			0.167200	−	0.985923i	$-0.446528\pi$
$443$	7.03829			0.334399			0.167200	+	0.985923i	$0.446528\pi$
$444$		0			0
$445$	−3.36345			−0.159443
$446$	1.82557	−	20.8664i	0.0864432	−	0.988051i
$447$		0			0
$448$	2.22940	+	0.393103i	0.105329	+	0.0185724i
$449$	−36.9916	−	17.2495i	−1.74574	−	0.814054i	−0.986606	−	0.163124i	$-0.947843\pi$
$449$	−36.9916	−	17.2495i	−1.74574	−	0.814054i	−0.759138	−	0.650930i	$-0.774379\pi$
$450$		0			0
$451$	−53.2764	+	19.3910i	−2.50869	+	0.913088i
$452$	3.11198	−	11.6141i	0.146375	−	0.546280i
$453$		0			0
$454$	2.26845	−	3.92907i	0.106464	−	0.184400i
$455$	−0.301330	−	0.521919i	−0.0141266	−	0.0244679i
$456$		0			0
$457$	−11.5615	−	16.5115i	−0.540822	−	0.772375i	0.451994	−	0.892021i	$-0.350713\pi$
$457$	−11.5615	−	16.5115i	−0.540822	−	0.772375i	−0.992817	+	0.119646i	$0.961824\pi$
$458$	−2.06671	−	7.71305i	−0.0965708	−	0.360407i
$459$		0			0
$460$	0.799296	+	0.290920i	0.0372674	+	0.0135642i
$461$	−10.5405	+	15.0534i	−0.490921	+	0.701108i	−0.985813	−	0.167846i	$-0.946319\pi$
$461$	−10.5405	+	15.0534i	−0.490921	+	0.701108i	0.494892	+	0.868955i	$0.335208\pi$
$462$		0			0
$463$	−8.60748	+	0.753057i	−0.400023	+	0.0349975i	−0.285393	−	0.958411i	$-0.592124\pi$
$463$	−8.60748	+	0.753057i	−0.400023	+	0.0349975i	−0.114631	+	0.993408i	$0.536568\pi$
$464$	8.69346	+	6.08723i	0.403584	+	0.282592i
$465$		0			0
$466$	−16.3674	+	7.63226i	−0.758207	+	0.353558i
$467$	26.6178	−	7.13221i	1.23172	−	0.330039i	0.416473	−	0.909148i	$-0.363266\pi$
$467$	26.6178	−	7.13221i	1.23172	−	0.330039i	0.815250	+	0.579109i	$0.196599\pi$
$468$		0			0
$469$	7.46515	+	8.89662i	0.344709	+	0.410808i
$470$	−0.383366	+	0.221336i	−0.0176833	+	0.0102095i
$471$		0			0
$472$	2.12422	−	0.374557i	0.0977749	−	0.0172404i
$473$	36.3053	+	9.72797i	1.66932	+	0.447292i
$474$		0			0
$475$	−19.7119	−	19.7119i	−0.904444	−	0.904444i
$476$	−5.81123	+	12.4622i	−0.266357	+	0.571205i
$477$		0			0
$478$	−7.38364	−	6.19561i	−0.337720	−	0.283381i
$479$	20.5910	+	1.80148i	0.940826	+	0.0823116i	0.547239	−	0.836976i	$-0.315679\pi$
$479$	20.5910	+	1.80148i	0.940826	+	0.0823116i	0.393586	+	0.919288i	$0.371234\pi$
$480$		0			0
$481$	0.151704	−	4.73816i	0.00691711	−	0.216041i
$482$			6.32546i			0.288117i
$483$		0			0
$484$	9.43232	−	11.2410i	0.428742	−	0.510955i
$485$	0.671741	−	3.80963i	0.0305022	−	0.172987i
$486$		0			0
$487$	−23.7014	+	23.7014i	−1.07401	+	1.07401i	−0.0769788	+	0.997033i	$0.524527\pi$
$487$	−23.7014	+	23.7014i	−1.07401	+	1.07401i	−0.997033	+	0.0769788i	$0.975473\pi$
$488$	1.07588	+	2.95596i	0.0487028	+	0.133810i
$489$		0			0
$490$	0.111234	+	0.630840i	0.00502505	+	0.0284985i
$491$	−20.3797	−	11.7662i	−0.919723	−	0.531002i	−0.0361765	−	0.999345i	$-0.511518\pi$
$491$	−20.3797	−	11.7662i	−0.919723	−	0.531002i	−0.883547	+	0.468343i	$0.844851\pi$
$492$		0			0
$493$	−49.3817	+	41.4362i	−2.22404	+	1.86619i
$494$	3.64438	−	2.55183i	0.163969	−	0.114812i
$495$		0			0
$496$	2.86687	+	6.14801i	0.128726	+	0.276054i
$497$	−8.02782	+	22.0562i	−0.360097	+	0.989358i
$498$		0			0
$499$	2.80588	+	32.0714i	0.125609	+	1.43571i	0.753518	+	0.657427i	$0.228355\pi$
$499$	2.80588	+	32.0714i	0.125609	+	1.43571i	−0.627910	+	0.778286i	$0.716089\pi$
$500$	0.294242	+	3.36320i	0.0131589	+	0.150407i
$501$		0			0
$502$	6.43454	−	17.6788i	0.287188	−	0.789041i
$503$	−6.50544	−	13.9510i	−0.290063	−	0.622042i	0.706238	−	0.707975i	$-0.250391\pi$
$503$	−6.50544	−	13.9510i	−0.290063	−	0.622042i	−0.996301	+	0.0859323i	$0.972613\pi$
$504$		0			0
$505$	3.23361	−	2.26420i	0.143894	−	0.100756i
$506$	−9.66536	+	8.11020i	−0.429677	+	0.360542i
$507$		0			0
$508$	14.9966	+	8.65827i	0.665365	+	0.384149i
$509$	−0.856968	−	4.86011i	−0.0379845	−	0.215421i	0.959908	−	0.280317i	$-0.0904395\pi$
$509$	−0.856968	−	4.86011i	−0.0379845	−	0.215421i	−0.997892	+	0.0648962i	$0.979328\pi$
$510$		0			0
$511$	−11.1415	−	30.6110i	−0.492870	−	1.35415i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−0.272291	+	1.54424i	−0.0120102	+	0.0681135i
$515$	0.977647	−	1.16511i	0.0430803	−	0.0513411i
$516$		0			0
$517$		−	6.56636i		−	0.288788i
$518$	5.12132	−	12.7823i	0.225018	−	0.561622i
$519$		0			0
$520$	−0.265205	−	0.0232024i	−0.0116300	−	0.00101749i
$521$	−2.00664	−	1.68377i	−0.0879126	−	0.0737674i	0.597772	−	0.801666i	$-0.296053\pi$
$521$	−2.00664	−	1.68377i	−0.0879126	−	0.0737674i	−0.685685	+	0.727899i	$0.740497\pi$
$522$		0			0
$523$	0.915997	−	1.96436i	0.0400538	−	0.0858956i	−0.885263	−	0.465091i	$-0.846022\pi$
$523$	0.915997	−	1.96436i	0.0400538	−	0.0858956i	0.925316	+	0.379196i	$0.123799\pi$
$524$	10.3077	+	10.3077i	0.450295	+	0.450295i
$525$		0			0
$526$	−7.76216	−	2.07986i	−0.338446	−	0.0906864i
$527$	−40.5784	+	7.15506i	−1.76762	+	0.311679i
$528$		0			0
$529$	−14.5487	+	8.39971i	−0.632553	+	0.365205i
$530$	1.22761	+	1.46301i	0.0533239	+	0.0635490i
$531$		0			0
$532$	12.4827	−	3.34473i	0.541193	−	0.145012i
$533$	−7.90330	+	3.68537i	−0.342330	+	0.159631i
$534$		0			0
$535$	0.616759	+	0.431859i	0.0266648	+	0.0186709i
$536$	5.11069	−	0.447128i	0.220748	−	0.0193130i
$537$		0			0
$538$	−14.2303	+	20.3229i	−0.613510	+	0.876183i
$539$	−8.92885	−	3.24984i	−0.384593	−	0.139980i
$540$		0			0
$541$	−4.36140	−	16.2769i	−0.187511	−	0.699801i	−0.994079	−	0.108659i	$-0.965344\pi$
$541$	−4.36140	−	16.2769i	−0.187511	−	0.699801i	0.806568	−	0.591141i	$-0.201322\pi$
$542$	−17.6655	−	25.2289i	−0.758797	−	1.08367i
$543$		0			0
$544$	3.03706	+	5.26035i	0.130213	+	0.225536i
$545$	−0.0680807	+	0.117919i	−0.00291626	+	0.00505111i
$546$		0			0
$547$	11.2565	−	42.0097i	0.481292	−	1.79621i	−0.114914	−	0.993375i	$-0.536659\pi$
$547$	11.2565	−	42.0097i	0.481292	−	1.79621i	0.596206	−	0.802832i	$-0.296674\pi$
$548$	−1.27261	+	0.463191i	−0.0543631	+	0.0197866i
$549$		0			0
$550$	−22.4253	−	10.4571i	−0.956217	−	0.445892i
$551$	59.6634	+	10.5203i	2.54175	+	0.448179i
$552$		0			0
$553$	0.898903	−	10.2745i	0.0382252	−	0.436917i
$554$	3.10944			0.132108
$555$		0			0
$556$	16.4572			0.697941
$557$	0.364366	−	4.16472i	0.0154387	−	0.176465i	−0.984560	−	0.175046i	$-0.943993\pi$
$557$	0.364366	−	4.16472i	0.0154387	−	0.176465i	0.999999	−	0.00141923i	$-0.000451754\pi$
$558$		0			0
$559$	5.69326	+	1.00388i	0.240799	+	0.0424594i
$560$	−0.700837	−	0.326806i	−0.0296158	−	0.0138101i
$561$		0			0
$562$	−21.8029	+	7.93562i	−0.919702	+	0.334744i
$563$	−11.3722	+	42.4417i	−0.479282	+	1.78871i	0.125250	+	0.992125i	$0.460027\pi$
$563$	−11.3722	+	42.4417i	−0.479282	+	1.78871i	−0.604532	+	0.796581i	$0.706640\pi$
$564$		0			0
$565$	−2.05360	+	3.55694i	−0.0863957	+	0.149642i
$566$	−9.73032	−	16.8534i	−0.408996	−	0.708401i
$567$		0			0
$568$	5.94705	+	8.49326i	0.249532	+	0.356369i
$569$	−0.398555	−	1.48743i	−0.0167083	−	0.0623562i	0.957068	−	0.289862i	$-0.0936095\pi$
$569$	−0.398555	−	1.48743i	−0.0167083	−	0.0623562i	−0.973777	+	0.227506i	$0.926943\pi$
$570$		0			0
$571$	−18.9366	−	6.89235i	−0.792472	−	0.288436i	−0.0861085	−	0.996286i	$-0.527443\pi$
$571$	−18.9366	−	6.89235i	−0.792472	−	0.288436i	−0.706363	+	0.707850i	$0.749665\pi$
$572$	2.26501	−	3.23477i	0.0947048	−	0.135252i
$573$		0			0
$574$	−25.2338	+	2.20767i	−1.05324	+	0.0921463i
$575$	9.96084	+	6.97465i	0.415396	+	0.290863i
$576$		0			0
$577$	−34.7913	+	16.2235i	−1.44838	+	0.675392i	−0.978293	−	0.207227i	$-0.933556\pi$
$577$	−34.7913	+	16.2235i	−1.44838	+	0.675392i	−0.470090	+	0.882619i	$0.655778\pi$
$578$	−19.2171	+	5.14921i	−0.799327	+	0.214179i
$579$		0			0
$580$	−2.33024	−	2.77708i	−0.0967581	−	0.115312i
$581$	−9.64896	+	5.57083i	−0.400306	+	0.231117i
$582$		0			0
$583$	−27.8988	+	4.91931i	−1.15545	+	0.203737i
$584$	−13.8995	−	3.72436i	−0.575166	−	0.154115i
$585$		0			0
$586$	5.46094	+	5.46094i	0.225589	+	0.225589i
$587$	−2.70746	+	5.80617i	−0.111749	+	0.239646i	−0.954226	−	0.299085i	$-0.903318\pi$
$587$	−2.70746	+	5.80617i	−0.111749	+	0.239646i	0.842478	+	0.538731i	$0.181096\pi$
$588$		0			0
$589$	29.6648	+	24.8917i	1.22232	+	1.02565i
$590$	−0.734002	−	0.0642168i	−0.0302184	−	0.00264376i
$591$		0			0
$592$	−3.32769	−	5.09181i	−0.136767	−	0.209272i
$593$			15.1947i			0.623972i	0.950087	+	0.311986i	$0.100994\pi$
$593$			15.1947i			0.623972i	−0.950087	+	0.311986i	$0.899006\pi$
$594$		0			0
$595$	3.01921	−	3.59815i	0.123775	−	0.147510i
$596$	2.33226	−	13.2269i	0.0955332	−	0.541796i
$597$		0			0
$598$	−1.37225	+	1.37225i	−0.0561154	+	0.0561154i
$599$	−13.5715	−	37.2874i	−0.554517	−	1.52352i	−0.827479	−	0.561497i	$-0.810226\pi$
$599$	−13.5715	−	37.2874i	−0.554517	−	1.52352i	0.272962	−	0.962025i	$-0.411997\pi$
$600$		0			0
$601$	6.04006	+	34.2549i	0.246379	+	1.39729i	0.817268	+	0.576258i	$0.195488\pi$
$601$	6.04006	+	34.2549i	0.246379	+	1.39729i	−0.570889	+	0.821027i	$0.693401\pi$
$602$	14.5427	+	8.39623i	0.592716	+	0.342205i
$603$		0			0
$604$	−5.10290	+	4.28184i	−0.207634	+	0.174226i
$605$	−4.10602	+	2.87507i	−0.166933	+	0.116888i
$606$		0			0
$607$	5.06737	+	10.8670i	0.205678	+	0.441079i	0.981905	−	0.189376i	$-0.0606464\pi$
$607$	5.06737	+	10.8670i	0.205678	+	0.441079i	−0.776226	+	0.630454i	$0.782869\pi$
$608$	1.95245	−	5.36432i	0.0791823	−	0.217552i
$609$		0			0
$610$	−0.0936513	−	1.07044i	−0.00379183	−	0.0433408i
$611$	−0.0880246	−	1.00613i	−0.00356109	−	0.0407035i
$612$		0			0
$613$	15.4356	−	42.4089i	0.623437	−	1.71288i	−0.0749788	−	0.997185i	$-0.523889\pi$
$613$	15.4356	−	42.4089i	0.623437	−	1.71288i	0.698415	−	0.715693i	$-0.253889\pi$
$614$	−11.1487	−	23.9085i	−0.449925	−	0.964868i
$615$		0			0
$616$	9.39610	−	6.57922i	0.378580	−	0.265084i
$617$	24.4406	−	20.5081i	0.983943	−	0.825626i	−0.000736589	−	1.00000i	$-0.500234\pi$
$617$	24.4406	−	20.5081i	0.983943	−	0.825626i	0.984680	+	0.174374i	$0.0557900\pi$
$618$		0			0
$619$	30.4254	+	17.5661i	1.22290	+	0.706042i	0.965535	−	0.260272i	$-0.0838123\pi$
$619$	30.4254	+	17.5661i	1.22290	+	0.706042i	0.257365	+	0.966314i	$0.417146\pi$
$620$	−0.402379	−	2.28200i	−0.0161599	−	0.0916474i
$621$		0			0
$622$	−9.38385	−	25.7819i	−0.376258	−	1.03376i
$623$	15.7616	−	15.7616i	0.631475	−	0.631475i
$624$		0			0
$625$	−4.03964	+	22.9099i	−0.161586	+	0.916397i
$626$	2.66868	−	3.18041i	0.106662	−	0.127115i
$627$		0			0
$628$			16.2906i			0.650067i
$629$	35.1059	−	11.5193i	1.39976	−	0.459303i
$630$		0			0
$631$	12.7024	+	1.11132i	0.505675	+	0.0442409i	0.337140	−	0.941455i	$-0.390541\pi$
$631$	12.7024	+	1.11132i	0.505675	+	0.0442409i	0.168536	+	0.985696i	$0.446096\pi$
$632$	−3.49008	−	2.92852i	−0.138828	−	0.116490i
$633$		0			0
$634$	9.48311	−	20.3366i	0.376623	−	0.807670i
$635$	−4.18265	−	4.18265i	−0.165984	−	0.165984i
$636$		0			0
$637$	−1.41168	−	0.378259i	−0.0559329	−	0.0149872i
$638$	52.9575	−	9.33783i	2.09661	−	0.369688i
$639$		0			0
$640$	−0.295826	+	0.170795i	−0.0116935	+	0.00675127i
$641$	−13.9207	−	16.5901i	−0.549836	−	0.655269i	0.417527	−	0.908665i	$-0.362897\pi$
$641$	−13.9207	−	16.5901i	−0.549836	−	0.655269i	−0.967363	+	0.253395i	$0.918453\pi$
$642$		0			0
$643$	−10.7792	+	2.88828i	−0.425090	+	0.113903i	−0.465021	−	0.885300i	$-0.653953\pi$
$643$	−10.7792	+	2.88828i	−0.425090	+	0.113903i	0.0399303	+	0.999202i	$0.487286\pi$
$644$	−5.10891	+	2.38232i	−0.201319	+	0.0938766i
$645$		0			0
$646$	28.4038	+	19.8886i	1.11753	+	0.782506i
$647$	−21.5171	+	1.88250i	−0.845924	+	0.0740087i	−0.501872	−	0.864942i	$-0.667355\pi$
$647$	−21.5171	+	1.88250i	−0.845924	+	0.0740087i	−0.344052	+	0.938951i	$0.611800\pi$
$648$		0			0
$649$	6.26882	−	8.95280i	0.246073	−	0.351428i
$650$	−3.57628	−	1.30166i	−0.140273	−	0.0510553i
$651$		0			0
$652$	−5.87924	−	21.9416i	−0.230249	−	0.859300i
$653$	−13.4979	−	19.2769i	−0.528212	−	0.754365i	0.463042	−	0.886336i	$-0.346758\pi$
$653$	−13.4979	−	19.2769i	−0.528212	−	0.754365i	−0.991253	+	0.131972i	$0.957869\pi$
$654$		0			0
$655$	−2.48973	−	4.31235i	−0.0972820	−	0.168497i
$656$	−5.59464	+	9.69019i	−0.218434	+	0.378339i
$657$		0			0
$658$	0.759292	−	2.83372i	0.0296003	−	0.110470i
$659$	−8.73571	+	3.17954i	−0.340295	+	0.123857i	−0.506514	−	0.862232i	$-0.669066\pi$
$659$	−8.73571	+	3.17954i	−0.340295	+	0.123857i	0.166219	+	0.986089i	$0.446844\pi$
$660$		0			0
$661$	−20.9000	−	9.74581i	−0.812914	−	0.379068i	−0.0287229	−	0.999587i	$-0.509144\pi$
$661$	−20.9000	−	9.74581i	−0.812914	−	0.379068i	−0.784191	+	0.620519i	$0.786922\pi$
$662$	−7.90586	−	1.39402i	−0.307270	−	0.0541800i
$663$		0			0
$664$	−0.428954	+	4.90296i	−0.0166466	+	0.190272i
$665$	−4.41438			−0.171182
$666$		0			0
$667$	−26.4268			−1.02325
$668$	0.0349366	−	0.399328i	0.00135174	−	0.0154504i
$669$		0			0
$670$	−1.72581	−	0.304307i	−0.0666738	−	0.0117564i
$671$	14.4456	+	6.73609i	0.557666	+	0.260044i
$672$		0			0
$673$	−2.84854	+	1.03679i	−0.109803	+	0.0399651i	−0.396338	−	0.918105i	$-0.629719\pi$
$673$	−2.84854	+	1.03679i	−0.109803	+	0.0399651i	0.286534	+	0.958070i	$0.407497\pi$
$674$	5.56885	−	20.7832i	0.214504	−	0.800540i
$675$		0			0
$676$	−6.19631	+	10.7323i	−0.238320	+	0.412782i
$677$	−9.88875	−	17.1278i	−0.380056	−	0.658275i	0.611014	−	0.791620i	$-0.290762\pi$
$677$	−9.88875	−	17.1278i	−0.380056	−	0.658275i	−0.991070	+	0.133344i	$0.957428\pi$
$678$		0			0
$679$	14.7046	+	21.0003i	0.564311	+	0.805919i
$680$	−0.537014	−	2.00416i	−0.0205936	−	0.0768562i
$681$		0			0
$682$	32.2992	+	11.7560i	1.23680	+	0.450159i
$683$	−15.9350	+	22.7576i	−0.609737	+	0.870795i	−0.998727	−	0.0504472i	$-0.983935\pi$
$683$	−15.9350	+	22.7576i	−0.609737	+	0.870795i	0.388990	+	0.921242i	$0.372824\pi$
$684$		0			0
$685$	0.460849	−	0.0403191i	0.0176081	−	0.00154051i
$686$	−16.4582	−	11.5241i	−0.628376	−	0.439994i
$687$		0			0
$688$	6.72286	−	3.13492i	0.256307	−	0.119518i
$689$	−4.20883	+	1.12775i	−0.160344	+	0.0429640i
$690$		0			0
$691$	−3.33918	−	3.97948i	−0.127029	−	0.151387i	0.698781	−	0.715335i	$-0.253726\pi$
$691$	−3.33918	−	3.97948i	−0.127029	−	0.151387i	−0.825810	+	0.563949i	$0.809282\pi$
$692$	−10.1612	+	5.86658i	−0.386272	+	0.223014i
$693$		0			0
$694$	9.33257	−	1.64558i	0.354260	−	0.0624655i
$695$	−5.43007	−	1.45498i	−0.205974	−	0.0551906i
$696$		0			0
$697$	−48.0586	−	48.0586i	−1.82035	−	1.82035i
$698$	9.77007	−	20.9520i	0.369803	−	0.793044i
$699$		0			0
$700$	−8.46846	−	7.10588i	−0.320078	−	0.268577i
$701$	12.9140	+	1.12983i	0.487755	+	0.0426731i	0.328381	−	0.944545i	$-0.393497\pi$
$701$	12.9140	+	1.12983i	0.487755	+	0.0426731i	0.159374	+	0.987218i	$0.449052\pi$
$702$		0			0
$703$	−29.5008	−	18.3154i	−1.11264	−	0.690779i
$704$		−	5.06696i		−	0.190968i
$705$		0			0
$706$	1.52166	−	1.81345i	0.0572685	−	0.0682499i
$707$	−4.54280	+	25.7635i	−0.170850	+	0.968937i
$708$		0			0
$709$	−30.7993	+	30.7993i	−1.15669	+	1.15669i	−0.171509	+	0.985183i	$0.554864\pi$
$709$	−30.7993	+	30.7993i	−1.15669	+	1.15669i	−0.985183	+	0.171509i	$0.945136\pi$
$710$	−1.21134	−	3.32814i	−0.0454609	−	0.124903i
$711$		0			0
$712$	−1.70982	−	9.69686i	−0.0640781	−	0.363405i
$713$	−14.6287	−	8.44589i	−0.547850	−	0.316301i
$714$		0			0
$715$	−1.03333	+	0.867065i	−0.0386443	+	0.0324264i
$716$	−3.50167	+	2.45190i	−0.130864	+	0.0916317i
$717$		0			0
$718$	8.51711	+	18.2650i	0.317856	+	0.681644i
$719$	4.04555	−	11.1150i	0.150873	−	0.414521i	−0.841114	−	0.540858i	$-0.818100\pi$
$719$	4.04555	−	11.1150i	0.150873	−	0.414521i	0.991987	+	0.126337i	$0.0403219\pi$
$720$		0			0
$721$	0.878498	+	10.0413i	0.0327170	+	0.373957i
$722$	−1.18427	−	13.5362i	−0.0440739	−	0.503766i
$723$		0			0
$724$	4.81305	−	13.2237i	0.178876	−	0.491457i
$725$	−21.9024	−	46.9698i	−0.813434	−	1.74441i
$726$		0			0
$727$	−13.7148	+	9.60318i	−0.508652	+	0.356162i	−0.799557	−	0.600590i	$-0.794933\pi$
$727$	−13.7148	+	9.60318i	−0.508652	+	0.356162i	0.290905	+	0.956752i	$0.406044\pi$
$728$	1.35151	−	1.13406i	0.0500905	−	0.0420309i
$729$		0			0
$730$	4.25689	+	2.45771i	0.157554	+	0.0909641i
$731$	7.82407	+	44.3725i	0.289384	+	1.64118i
$732$		0			0
$733$	−5.97847	−	16.4257i	−0.220820	−	0.606697i	0.778973	−	0.627057i	$-0.215741\pi$
$733$	−5.97847	−	16.4257i	−0.220820	−	0.606697i	−0.999793	+	0.0203603i	$0.993519\pi$
$734$	15.8303	−	15.8303i	0.584308	−	0.584308i
$735$		0			0
$736$	−0.432401	+	2.45227i	−0.0159385	+	0.0903918i
$737$	16.7090	−	19.9130i	0.615484	−	0.733505i
$738$		0			0
$739$			8.65316i			0.318312i	0.987253	+	0.159156i	$0.0508772\pi$
$739$			8.65316i			0.318312i	−0.987253	+	0.159156i	$0.949123\pi$
$740$	0.647808	+	1.97425i	0.0238139	+	0.0725748i
$741$		0			0
$742$	−12.6086	−	1.10311i	−0.462876	−	0.0404964i
$743$	4.76947	+	4.00206i	0.174975	+	0.146821i	0.726069	−	0.687622i	$-0.241345\pi$
$743$	4.76947	+	4.00206i	0.174975	+	0.146821i	−0.551094	+	0.834443i	$0.685790\pi$
$744$		0			0
$745$	−1.93893	+	4.15804i	−0.0710367	+	0.152339i
$746$	−10.2729	−	10.2729i	−0.376119	−	0.376119i
$747$		0			0
$748$	29.7287	+	7.96577i	1.08699	+	0.291257i
$749$	−4.91397	+	0.866465i	−0.179553	+	0.0316600i
$750$		0			0
$751$	3.09145	−	1.78485i	0.112809	−	0.0651300i	−0.442534	−	0.896752i	$-0.645920\pi$
$751$	3.09145	−	1.78485i	0.112809	−	0.0651300i	0.555343	+	0.831622i	$0.312587\pi$
$752$	−0.832999	−	0.992729i	−0.0303763	−	0.0362011i
$753$		0			0
$754$	7.98920	−	2.14070i	0.290949	−	0.0779596i
$755$	2.06226	−	0.961649i	0.0750535	−	0.0349980i
$756$		0			0
$757$	−42.6822	−	29.8864i	−1.55131	−	1.08624i	−0.960076	−	0.279740i	$-0.909752\pi$
$757$	−42.6822	−	29.8864i	−1.55131	−	1.08624i	−0.591235	−	0.806499i	$-0.701360\pi$
$758$	−23.2422	+	2.03343i	−0.844194	+	0.0738574i
$759$		0			0
$760$	−1.11847	+	1.59734i	−0.0405713	+	0.0579418i
$761$	24.4657	+	8.90480i	0.886882	+	0.322799i	0.744984	−	0.667082i	$-0.232457\pi$
$761$	24.4657	+	8.90480i	0.886882	+	0.322799i	0.141898	+	0.989881i	$0.454679\pi$
$762$		0			0
$763$	−0.233550	−	0.871622i	−0.00845509	−	0.0315548i
$764$	10.8819	+	15.5410i	0.393694	+	0.562254i
$765$		0			0
$766$	3.65229	+	6.32595i	0.131962	+	0.228566i
$767$	0.840520	−	1.45582i	0.0303494	−	0.0525668i
$768$		0			0
$769$	−2.99406	+	11.1740i	−0.107969	+	0.402944i	−0.998665	−	0.0516544i	$-0.983551\pi$
$769$	−2.99406	+	11.1740i	−0.107969	+	0.402944i	0.890696	+	0.454598i	$0.150217\pi$
$770$	−3.68192	+	1.34011i	−0.132687	+	0.0482942i
$771$		0			0
$772$	0.0106725	+	0.00497666i	0.000384111	+	0.000179114i
$773$	31.2170	+	5.50440i	1.12280	+	0.197979i	0.704069	−	0.710132i	$-0.251365\pi$
$773$	31.2170	+	5.50440i	1.12280	+	0.197979i	0.418729	+	0.908111i	$0.362476\pi$
$774$		0			0
$775$	2.88715	−	33.0003i	0.103710	−	1.18541i
$776$	11.3247			0.406533
$777$		0			0
$778$	14.9177			0.534827
$779$	−5.56707	+	63.6319i	−0.199461	+	2.27985i
$780$		0			0
$781$	51.7379	+	9.12279i	1.85133	+	0.326439i
$782$	−13.7081	−	6.39218i	−0.490199	−	0.228584i
$783$		0			0
$784$	−1.76217	+	0.641378i	−0.0629347	+	0.0229064i
$785$	1.44026	−	5.37511i	0.0514049	−	0.191846i
$786$		0			0
$787$	−23.1577	+	40.1103i	−0.825483	+	1.42978i	0.0760674	+	0.997103i	$0.475764\pi$
$787$	−23.1577	+	40.1103i	−0.825483	+	1.42978i	−0.901550	+	0.432675i	$0.857570\pi$
$788$	−5.86336	−	10.1556i	−0.208874	−	0.361780i
$789$		0			0
$790$	0.892643	+	1.27483i	0.0317588	+	0.0453563i
$791$	−7.04486	−	26.2918i	−0.250487	−	0.934829i
$792$		0			0
$793$	2.30372	+	0.838484i	0.0818074	+	0.0297755i
$794$	−2.74867	+	3.92551i	−0.0975466	+	0.139311i
$795$		0			0
$796$	−15.1202	+	1.32284i	−0.535921	+	0.0468870i
$797$	18.7617	+	13.1371i	0.664573	+	0.465339i	0.856553	−	0.516060i	$-0.172602\pi$
$797$	18.7617	+	13.1371i	0.664573	+	0.465339i	−0.191979	+	0.981399i	$0.561491\pi$
$798$		0			0
$799$	7.13406	−	3.32667i	0.252385	−	0.117689i
$800$	−4.71692	+	1.26390i	−0.166768	+	0.0446854i
$801$		0			0
$802$	4.51497	+	5.38073i	0.159429	+	0.190000i
$803$	−63.1443	+	36.4564i	−2.22831	+	1.28652i
$804$		0			0
$805$	1.89631	−	0.334371i	0.0668361	−	0.0117850i
$806$	5.10663	+	1.36832i	0.179873	+	0.0481969i
$807$		0			0
$808$	8.17152	+	8.17152i	0.287473	+	0.287473i
$809$	−3.55849	+	7.63122i	−0.125110	+	0.268299i	−0.958880	−	0.283813i	$-0.908400\pi$
$809$	−3.55849	+	7.63122i	−0.125110	+	0.268299i	0.833770	+	0.552113i	$0.186178\pi$
$810$		0			0
$811$	−8.81396	−	7.39579i	−0.309500	−	0.259701i	0.474785	−	0.880102i	$-0.342526\pi$
$811$	−8.81396	−	7.39579i	−0.309500	−	0.259701i	−0.784285	+	0.620400i	$0.786970\pi$
$812$	23.9336	+	2.09392i	0.839905	+	0.0734822i
$813$		0			0
$814$	−30.1661	−	6.32061i	−1.05732	−	0.221537i
$815$			7.75944i			0.271801i
$816$		0			0
$817$	27.2191	−	32.4385i	0.952277	−	1.13488i
$818$	−2.46840	+	13.9990i	−0.0863056	+	0.489464i
$819$		0			0
$820$	2.70267	−	2.70267i	0.0943812	−	0.0943812i
$821$	−5.19730	−	14.2795i	−0.181387	−	0.498356i	0.815360	−	0.578955i	$-0.196539\pi$
$821$	−5.19730	−	14.2795i	−0.181387	−	0.498356i	−0.996747	+	0.0805982i	$0.974317\pi$
$822$		0			0
$823$	3.73530	+	21.1839i	0.130204	+	0.738426i	0.978080	+	0.208230i	$0.0667703\pi$
$823$	3.73530	+	21.1839i	0.130204	+	0.738426i	−0.847875	+	0.530195i	$0.822119\pi$
$824$	3.85602	+	2.22627i	0.134331	+	0.0775560i
$825$		0			0
$826$	3.74056	−	3.13870i	0.130151	−	0.109209i
$827$	21.0621	−	14.7479i	0.732403	−	0.512834i	−0.146868	−	0.989156i	$-0.546919\pi$
$827$	21.0621	−	14.7479i	0.732403	−	0.512834i	0.879271	+	0.476322i	$0.158030\pi$
$828$		0			0
$829$	9.96036	+	21.3601i	0.345938	+	0.741866i	0.999892	−	0.0146680i	$-0.00466915\pi$
$829$	9.96036	+	21.3601i	0.345938	+	0.741866i	−0.653955	+	0.756534i	$0.726891\pi$
$830$	0.575005	−	1.57981i	0.0199587	−	0.0548361i
$831$		0			0
$832$	−0.0679246	−	0.776382i	−0.00235486	−	0.0269162i
$833$	−0.992756	−	11.3473i	−0.0343969	−	0.393159i
$834$		0			0
$835$	−0.0468320	+	0.128670i	−0.00162069	+	0.00445280i
$836$	−12.2243	−	26.2151i	−0.422786	−	0.906668i
$837$		0			0
$838$	7.11176	−	4.97971i	0.245672	−	0.172021i
$839$	8.93263	−	7.49537i	0.308389	−	0.258769i	−0.475437	−	0.879750i	$-0.657710\pi$
$839$	8.93263	−	7.49537i	0.308389	−	0.258769i	0.783826	+	0.620981i	$0.213266\pi$
$840$		0			0
$841$	72.4262	+	41.8153i	2.49746	+	1.44191i
$842$	−5.46336	−	30.9842i	−0.188280	−	1.06779i
$843$		0			0
$844$	−2.73977	−	7.52746i	−0.0943068	−	0.259106i
$845$	2.99332	−	2.99332i	0.102973	−	0.102973i
$846$		0			0
$847$	5.76842	−	32.7143i	0.198205	−	1.12408i
$848$	−3.59380	+	4.28293i	−0.123412	+	0.147076i
$849$		0			0
$850$		−	29.6619i		−	1.01739i
$851$	14.0601	+	5.63329i	0.481976	+	0.193107i
$852$		0			0
$853$	−1.49700	−	0.130971i	−0.0512563	−	0.00448435i	0.0614987	−	0.998107i	$-0.480412\pi$
$853$	−1.49700	−	0.130971i	−0.0512563	−	0.00448435i	−0.112755	+	0.993623i	$0.535968\pi$
$854$	5.45509	+	4.57736i	0.186669	+	0.156634i
$855$		0			0
$856$	−0.931523	+	1.99766i	−0.0318388	+	0.0682785i
$857$	−33.1828	−	33.1828i	−1.13350	−	1.13350i	−0.989591	−	0.143911i	$-0.954032\pi$
$857$	−33.1828	−	33.1828i	−1.13350	−	1.13350i	−0.143911	−	0.989591i	$-0.545968\pi$
$858$		0			0
$859$	32.8407	+	8.79963i	1.12051	+	0.300240i	0.771090	−	0.636727i	$-0.219712\pi$
$859$	32.8407	+	8.79963i	1.12051	+	0.300240i	0.349420	+	0.936966i	$0.386379\pi$
$860$	−2.49537	+	0.440002i	−0.0850915	+	0.0150039i
$861$		0			0
$862$	−0.895481	+	0.517006i	−0.0305002	+	0.0176093i
$863$	−23.4703	−	27.9708i	−0.798938	−	0.952137i	0.200683	−	0.979656i	$-0.435684\pi$
$863$	−23.4703	−	27.9708i	−0.798938	−	0.952137i	−0.999621	+	0.0275190i	$0.991239\pi$
$864$		0			0
$865$	3.87137	−	1.03733i	0.131631	−	0.0352703i
$866$	7.21436	−	3.36411i	0.245154	−	0.114317i
$867$		0			0
$868$	12.5794	+	8.80818i	0.426972	+	0.298969i
$869$	−22.9971	+	2.01198i	−0.780123	+	0.0682519i
$870$		0			0
$871$	2.29328	−	3.27515i	0.0777050	−	0.110974i
$872$	−0.374571	−	0.136333i	−0.0126846	−	0.00461681i
$873$		0			0
$874$	3.67910	+	13.7306i	0.124447	+	0.464444i
$875$	4.38364	+	6.26049i	0.148194	+	0.211643i
$876$		0			0
$877$	−6.30842	−	10.9265i	−0.213020	−	0.368962i	0.739638	−	0.673005i	$-0.234997\pi$
$877$	−6.30842	−	10.9265i	−0.213020	−	0.368962i	−0.952658	+	0.304043i	$0.901663\pi$
$878$	5.89892	−	10.2172i	0.199079	−	0.344815i
$879$		0			0
$880$	−0.447970	+	1.67185i	−0.0151011	+	0.0563580i
$881$	21.4926	−	7.82265i	0.724103	−	0.263552i	0.0464363	−	0.998921i	$-0.485214\pi$
$881$	21.4926	−	7.82265i	0.724103	−	0.263552i	0.677666	+	0.735369i	$0.262991\pi$
$882$		0			0
$883$	−15.2505	−	7.11143i	−0.513221	−	0.239319i	0.148714	−	0.988880i	$-0.452487\pi$
$883$	−15.2505	−	7.11143i	−0.513221	−	0.239319i	−0.661935	+	0.749561i	$0.730264\pi$
$884$	4.66194	+	0.822026i	0.156798	+	0.0276477i
$885$		0			0
$886$	0.613427	−	7.01151i	0.0206085	−	0.235556i
$887$	29.2457			0.981975			0.490988	−	0.871167i	$-0.336636\pi$
$887$	29.2457			0.981975			0.490988	+	0.871167i	$0.336636\pi$
$888$		0			0
$889$	39.2010			1.31476
$890$	−0.293144	+	3.35065i	−0.00982622	+	0.112314i
$891$		0			0
$892$	−20.6278	−	3.63725i	−0.690671	−	0.121784i
$893$	−6.70473	−	3.12647i	−0.224365	−	0.104623i
$894$		0			0
$895$	1.37215	−	0.499422i	0.0458660	−	0.0166939i
$896$	0.585911	−	2.18665i	0.0195739	−	0.0730509i
$897$		0			0
$898$	−20.4079	+	35.3475i	−0.681020	+	1.17956i
$899$	35.9962	+	62.3473i	1.20054	+	2.07940i
$900$		0			0
$901$	−19.4788	−	27.8186i	−0.648933	−	0.926772i
$902$	14.6739	+	54.7637i	0.488587	+	1.82343i
$903$		0			0
$904$	−11.2986	−	4.11237i	−0.375787	−	0.136775i
$905$	−2.75718	+	3.93766i	−0.0916518	+	0.130892i
$906$		0			0
$907$	−33.2303	+	2.90727i	−1.10339	+	0.0965344i	−0.624267	−	0.781211i	$-0.714602\pi$
$907$	−33.2303	+	2.90727i	−1.10339	+	0.0965344i	−0.479127	+	0.877746i	$0.659047\pi$
$908$	−3.71641	−	2.60226i	−0.123333	−	0.0863589i
$909$		0			0
$910$	−0.546196	+	0.254695i	−0.0181062	+	0.00844306i
$911$	−42.2984	+	11.3338i	−1.40141	+	0.375506i	−0.878850	−	0.477097i	$-0.841689\pi$
$911$	−42.2984	+	11.3338i	−1.40141	+	0.375506i	−0.522558	+	0.852604i	$0.675022\pi$
$912$		0			0
$913$	16.0298	+	19.1036i	0.530510	+	0.632238i
$914$	−17.4563	+	10.0784i	−0.577403	+	0.333364i
$915$		0			0
$916$	−7.86383	+	1.38660i	−0.259828	+	0.0458147i
$917$	31.8755	+	8.54101i	1.05262	+	0.282049i
$918$		0			0
$919$	13.0279	+	13.0279i	0.429750	+	0.429750i	0.888543	−	0.458793i	$-0.151718\pi$
$919$	13.0279	+	13.0279i	0.429750	+	0.429750i	−0.458793	+	0.888543i	$0.651718\pi$
$920$	0.359476	−	0.770899i	0.0118516	−	0.0254158i
$921$		0			0
$922$	14.0775	+	11.8124i	0.463617	+	0.389021i
$923$	8.04980	+	0.704267i	0.264963	+	0.0231812i
$924$		0			0
$925$	1.64061	+	29.6587i	0.0539428	+	0.975172i
$926$			8.64036i			0.283940i
$927$		0			0
$928$	6.82175	−	8.12984i	0.223935	−	0.266875i
$929$	−9.82741	+	55.7340i	−0.322427	+	1.82857i	0.204746	+	0.978815i	$0.434363\pi$
$929$	−9.82741	+	55.7340i	−0.322427	+	1.82857i	−0.527172	+	0.849758i	$0.676748\pi$
$930$		0			0
$931$	−7.56965	+	7.56965i	−0.248085	+	0.248085i
$932$	6.17670	+	16.9704i	0.202325	+	0.555882i
$933$		0			0
$934$	−4.78518	−	27.1381i	−0.156576	−	0.887985i
$935$	−9.10474	−	5.25663i	−0.297757	−	0.171910i
$936$		0			0
$937$	28.8706	−	24.2253i	0.943160	−	0.791406i	−0.0349721	−	0.999388i	$-0.511134\pi$
$937$	28.8706	−	24.2253i	0.943160	−	0.791406i	0.978132	+	0.207983i	$0.0666898\pi$
$938$	9.51340	−	6.66135i	0.310624	−	0.217501i
$939$		0			0
$940$	0.187081	+	0.401198i	0.00610193	+	0.0130856i
$941$	4.07683	−	11.2010i	0.132901	−	0.365142i	−0.855336	−	0.518074i	$-0.826649\pi$
$941$	4.07683	−	11.2010i	0.132901	−	0.365142i	0.988237	+	0.152932i	$0.0488715\pi$
$942$		0			0
$943$	−2.42837	−	27.7564i	−0.0790785	−	0.903871i
$944$	−0.187994	−	2.14878i	−0.00611867	−	0.0699367i
$945$		0			0
$946$	12.8552	−	35.3193i	0.417957	−	1.14833i
$947$	8.01939	+	17.1976i	0.260595	+	0.558848i	0.992455	−	0.122607i	$-0.0391254\pi$
$947$	8.01939	+	17.1976i	0.260595	+	0.558848i	−0.731860	+	0.681455i	$0.761348\pi$
$948$		0			0
$949$	−9.18653	+	6.43248i	−0.298207	+	0.208807i
$950$	−21.3549	+	17.9189i	−0.692844	+	0.581365i
$951$		0			0
$952$	11.9083	+	6.87527i	0.385951	+	0.222829i
$953$	5.52559	+	31.3372i	0.178992	+	1.01511i	0.933435	+	0.358747i	$0.116796\pi$
$953$	5.52559	+	31.3372i	0.178992	+	1.01511i	−0.754443	+	0.656365i	$0.772093\pi$
$954$		0			0
$955$	−2.21652	−	6.08984i	−0.0717249	−	0.197063i
$956$	−6.81556	+	6.81556i	−0.220431	+	0.220431i
$957$		0			0
$958$	3.58924	−	20.3556i	0.115963	−	0.657660i
$959$	−1.97066	+	2.34854i	−0.0636360	+	0.0758384i
$960$		0			0
$961$			15.0170i			0.484419i
$962$	−4.70691	−	0.564084i	−0.151757	−	0.0181868i
$963$		0			0
$964$	6.30139	+	0.551300i	0.202954	+	0.0177562i
$965$	−0.00308141	−	0.00258561i	−9.91940e−5	−	8.32337e-5i
$966$		0			0
$967$	1.04225	−	2.23511i	0.0335165	−	0.0718764i	−0.888837	−	0.458224i	$-0.848486\pi$
$967$	1.04225	−	2.23511i	0.0335165	−	0.0718764i	0.922353	+	0.386348i	$0.126264\pi$
$968$	−10.3761	−	10.3761i	−0.333502	−	0.333502i
$969$		0			0
$970$	−3.73659	−	1.00122i	−0.119975	−	0.0321471i
$971$	−15.1997	+	2.68012i	−0.487783	+	0.0860092i	−0.412130	−	0.911125i	$-0.635215\pi$
$971$	−15.1997	+	2.68012i	−0.487783	+	0.0860092i	−0.0756525	+	0.997134i	$0.524104\pi$
$972$		0			0
$973$	32.2643	−	18.6278i	1.03435	−	0.597180i
$974$	21.5455	+	25.6769i	0.690361	+	0.822741i
$975$		0			0
$976$	3.03848	−	0.814157i	0.0972593	−	0.0260605i
$977$	−23.8785	+	11.1347i	−0.763940	+	0.356231i	−0.765221	−	0.643768i	$-0.777370\pi$
$977$	−23.8785	+	11.1347i	−0.763940	+	0.356231i	0.00128034	+	0.999999i	$0.499592\pi$
$978$		0			0
$979$	−40.8688	−	28.6166i	−1.30617	−	0.914591i
$980$	0.638135	−	0.0558295i	0.0203845	−	0.00178341i
$981$		0			0
$982$	−13.4977	+	19.2767i	−0.430728	+	0.615143i
$983$	45.8053	+	16.6718i	1.46096	+	0.531747i	0.945630	−	0.325243i	$-0.105446\pi$
$983$	45.8053	+	16.6718i	1.46096	+	0.531747i	0.515333	+	0.856990i	$0.327668\pi$
$984$		0			0
$985$	1.03676	+	3.86925i	0.0330340	+	0.123284i
$986$	36.9746	+	52.8052i	1.17751	+	1.68166i
$987$		0			0
$988$	−2.22449	−	3.85292i	−0.0707703	−	0.122578i
$989$	−9.23559	+	15.9965i	−0.293675	+	0.508660i
$990$		0			0
$991$	−13.5185	+	50.4517i	−0.429429	+	1.60265i	0.324629	+	0.945842i	$0.394761\pi$
$991$	−13.5185	+	50.4517i	−0.429429	+	1.60265i	−0.754057	+	0.656809i	$0.771906\pi$
$992$	6.37448	−	2.32012i	0.202390	−	0.0736639i
$993$		0			0
$994$	21.2726	+	9.91960i	0.674727	+	0.314630i
$995$	5.10587	+	0.900303i	0.161867	+	0.0285415i
$996$		0			0
$997$	0.169293	−	1.93503i	0.00536157	−	0.0612831i	−0.993043	−	0.117756i	$-0.962430\pi$
$997$	0.169293	−	1.93503i	0.00536157	−	0.0612831i	0.998404	+	0.0564730i	$0.0179855\pi$
$998$	32.1939			1.01908
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.a.557.5	yes	72
3.2	odd	2	inner	666.2.bs.a.557.2	✓	72
37.19	odd	36	inner	666.2.bs.a.611.2	yes	72
111.56	even	36	inner	666.2.bs.a.611.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.a.557.2	✓	72	3.2	odd	2	inner
666.2.bs.a.557.5	yes	72	1.1	even	1	trivial
666.2.bs.a.611.2	yes	72	37.19	odd	36	inner
666.2.bs.a.611.5	yes	72	111.56	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)

\(f(q)\)	\(=\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(0.309586 + 0.144362i) q^{5} +(-2.12726 + 0.774261i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\)	\(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(0.309586 + 0.144362i) q^{5} +(-2.12726 + 0.774261i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.170795 - 0.295826i) q^{10} +(2.53348 + 4.38812i) q^{11} +(0.447015 + 0.638404i) q^{13} +(0.585911 + 2.18665i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-3.48398 + 4.97563i) q^{17} +(5.68686 - 0.497536i) q^{19} +(-0.279814 - 0.195928i) q^{20} +(4.59223 - 2.14139i) q^{22} +(-2.40525 + 0.644485i) q^{23} +(-3.13894 - 3.74084i) q^{25} +(0.674935 - 0.389674i) q^{26} +(2.22940 - 0.393103i) q^{28} +(10.2511 + 2.74678i) q^{29} +(4.79672 + 4.79672i) q^{31} +(0.422618 - 0.906308i) q^{32} +(4.65305 + 3.90437i) q^{34} +(-0.770346 - 0.0673965i) q^{35} +(-4.86851 - 3.64659i) q^{37} -5.70858i q^{38} +(-0.219570 + 0.261673i) q^{40} +(-1.94300 + 11.0193i) q^{41} +(5.24522 - 5.24522i) q^{43} +(-1.73300 - 4.76138i) q^{44} +(0.432401 + 2.45227i) q^{46} +(-1.12230 - 0.647958i) q^{47} +(-1.43654 + 1.20540i) q^{49} +(-4.00018 + 2.80096i) q^{50} +(-0.329366 - 0.706329i) q^{52} +(-1.91222 + 5.25379i) q^{53} +(0.150851 + 1.72424i) q^{55} +(-0.197302 - 2.25517i) q^{56} +(3.62978 - 9.97273i) q^{58} +(-0.911581 - 1.95489i) q^{59} +(2.57678 - 1.80428i) q^{61} +(5.19653 - 4.36040i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(0.0462282 + 0.262173i) q^{65} +(-1.75464 - 4.82082i) q^{67} +(4.29506 - 4.29506i) q^{68} +(-0.134280 + 0.761540i) q^{70} +(6.66465 - 7.94262i) q^{71} +14.3898i q^{73} +(-4.05704 + 4.53216i) q^{74} +(-5.68686 - 0.497536i) q^{76} +(-8.78693 - 7.37311i) q^{77} +(-1.92544 + 4.12911i) q^{79} +(0.241541 + 0.241541i) q^{80} +(10.8080 + 2.89600i) q^{82} +(4.84692 - 0.854643i) q^{83} +(-1.79688 + 1.03743i) q^{85} +(-4.76811 - 5.68241i) q^{86} +(-4.89431 + 1.31143i) q^{88} +(-8.92392 + 4.16129i) q^{89} +(-1.44521 - 1.01195i) q^{91} +(2.48062 - 0.217026i) q^{92} +(-0.743307 + 1.06155i) q^{94} +(1.83240 + 0.666938i) q^{95} +(-2.93104 - 10.9388i) q^{97} +(1.07561 + 1.53613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q+O(q^{10}) \) 72 * q	\( 72 q + 12 q^{13} - 24 q^{19} - 12 q^{22} + 72 q^{34} + 72 q^{37} + 24 q^{40} + 24 q^{43} + 36 q^{46} - 48 q^{49} - 12 q^{52} + 60 q^{55} + 120 q^{61} + 60 q^{67} - 60 q^{70} + 24 q^{76} - 12 q^{79} - 48 q^{82} + 108 q^{85} - 24 q^{88} - 168 q^{91} - 84 q^{94} - 264 q^{97}+O(q^{100}) \) 72 * q + 12 * q^13 - 24 * q^19 - 12 * q^22 + 72 * q^34 + 72 * q^37 + 24 * q^40 + 24 * q^43 + 36 * q^46 - 48 * q^49 - 12 * q^52 + 60 * q^55 + 120 * q^61 + 60 * q^67 - 60 * q^70 + 24 * q^76 - 12 * q^79 - 48 * q^82 + 108 * q^85 - 24 * q^88 - 168 * q^91 - 84 * q^94 - 264 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more