LMFDB - Embedded newform 666.2.bs.b.431.2

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			431.2
Character	$\chi$	$=$	666.431
Dual form			666.2.bs.b.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-1.60885 - 0.140756i) q^{5} +(1.53998 - 1.29220i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-1.60885 - 0.140756i) q^{5} +(1.53998 - 1.29220i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.807495 + 1.39862i) q^{10} +(-2.64381 + 4.57920i) q^{11} +(4.54133 - 2.11766i) q^{13} +(-1.94180 - 0.520305i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(5.07820 + 2.36800i) q^{17} +(-0.363361 - 0.254428i) q^{19} +(0.682525 - 1.46368i) q^{20} +(5.26749 - 0.460846i) q^{22} +(1.51364 - 5.64898i) q^{23} +(-2.35547 - 0.415332i) q^{25} +(-4.33948 - 2.50540i) q^{26} +(0.687564 + 1.88907i) q^{28} +(-1.91829 - 7.15914i) q^{29} +(5.12102 + 5.12102i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-0.972981 - 5.51805i) q^{34} +(-2.65948 + 1.86218i) q^{35} +(6.05499 + 0.580588i) q^{37} +0.443582i q^{38} +(-1.59046 + 0.280440i) q^{40} +(6.41507 + 2.33489i) q^{41} +(7.63098 - 7.63098i) q^{43} +(-3.39881 - 4.05054i) q^{44} +(-5.49556 + 2.00022i) q^{46} +(4.34681 - 2.50963i) q^{47} +(-0.513770 + 2.91374i) q^{49} +(1.01082 + 2.16771i) q^{50} +(0.436720 + 4.99173i) q^{52} +(7.64299 - 9.10856i) q^{53} +(4.89802 - 6.99510i) q^{55} +(1.15306 - 1.64674i) q^{56} +(-4.76414 + 5.67769i) q^{58} +(0.615917 + 7.03996i) q^{59} +(-2.86510 - 6.14423i) q^{61} +(1.25760 - 7.13219i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-7.60437 + 2.76776i) q^{65} +(-3.96674 - 4.72738i) q^{67} +(-3.96204 + 3.96204i) q^{68} +(3.05082 + 1.11041i) q^{70} +(-1.49231 + 0.263135i) q^{71} +8.32062i q^{73} +(-2.99741 - 5.29297i) q^{74} +(0.363361 - 0.254428i) q^{76} +(1.84583 + 10.4682i) q^{77} +(-1.28011 + 14.6317i) q^{79} +(1.14197 + 1.14197i) q^{80} +(-1.76690 - 6.59415i) q^{82} +(-4.01232 - 11.0238i) q^{83} +(-7.83673 - 4.52454i) q^{85} +(-10.6279 - 1.87398i) q^{86} +(-1.36853 + 5.10744i) q^{88} +(-0.608784 + 0.0532617i) q^{89} +(4.25713 - 9.12944i) q^{91} +(4.79061 + 3.35442i) q^{92} +(-4.54900 - 2.12123i) q^{94} +(0.548780 + 0.460481i) q^{95} +(-10.0241 - 2.68596i) q^{97} +(2.68148 - 1.25039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$-1$	$e\left(\frac{29}{36}\right)$

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
$5$	−1.60885	−	0.140756i	−0.719498	−	0.0629479i	−0.278474	−	0.960444i	$-0.589829\pi$
$5$	−1.60885	−	0.140756i	−0.719498	−	0.0629479i	−0.441023	+	0.897496i	$0.645384\pi$
$6$		0			0
$7$	1.53998	−	1.29220i	0.582058	−	0.488405i	−0.303564	−	0.952811i	$-0.598177\pi$
$7$	1.53998	−	1.29220i	0.582058	−	0.488405i	0.885622	+	0.464406i	$0.153732\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$		0			0
$10$	0.807495	+	1.39862i	0.255352	+	0.442283i
$11$	−2.64381	+	4.57920i	−0.797137	+	1.38068i	0.124336	+	0.992240i	$0.460320\pi$
$11$	−2.64381	+	4.57920i	−0.797137	+	1.38068i	−0.921473	+	0.388442i	$0.873013\pi$
$12$		0			0
$13$	4.54133	−	2.11766i	1.25954	−	0.587332i	0.325851	−	0.945421i	$-0.394349\pi$
$13$	4.54133	−	2.11766i	1.25954	−	0.587332i	0.933687	+	0.358089i	$0.116572\pi$
$14$	−1.94180	−	0.520305i	−0.518969	−	0.139057i
$15$		0			0
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	5.07820	+	2.36800i	1.23164	+	0.574325i	0.925893	−	0.377786i	$-0.123314\pi$
$17$	5.07820	+	2.36800i	1.23164	+	0.574325i	0.305752	+	0.952111i	$0.401092\pi$
$18$		0			0
$19$	−0.363361	−	0.254428i	−0.0833608	−	0.0583698i	0.531153	−	0.847276i	$-0.321759\pi$
$19$	−0.363361	−	0.254428i	−0.0833608	−	0.0583698i	−0.614514	+	0.788906i	$0.710648\pi$
$20$	0.682525	−	1.46368i	0.152617	−	0.327289i
$21$		0			0
$22$	5.26749	−	0.460846i	1.12303	−	0.0982526i
$23$	1.51364	−	5.64898i	0.315616	−	1.17789i	−0.607800	−	0.794090i	$-0.707948\pi$
$23$	1.51364	−	5.64898i	0.315616	−	1.17789i	0.923415	−	0.383803i	$-0.125386\pi$
$24$		0			0
$25$	−2.35547	−	0.415332i	−0.471093	−	0.0830665i
$26$	−4.33948	−	2.50540i	−0.851042	−	0.491350i
$27$		0			0
$28$	0.687564	+	1.88907i	0.129937	+	0.357000i
$29$	−1.91829	−	7.15914i	−0.356217	−	1.32942i	−0.878946	−	0.476921i	$-0.841753\pi$
$29$	−1.91829	−	7.15914i	−0.356217	−	1.32942i	0.522729	−	0.852499i	$-0.324914\pi$
$30$		0			0
$31$	5.12102	+	5.12102i	0.919762	+	0.919762i	0.997012	−	0.0772495i	$-0.0246138\pi$
$31$	5.12102	+	5.12102i	0.919762	+	0.919762i	−0.0772495	+	0.997012i	$0.524614\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$		0			0
$34$	−0.972981	−	5.51805i	−0.166865	−	0.946338i
$35$	−2.65948	+	1.86218i	−0.449533	+	0.314767i
$36$		0			0
$37$	6.05499	+	0.580588i	0.995434	+	0.0954481i
$37$	6.05499	+	0.580588i	0.995434	+	0.0954481i
$38$			0.443582i			0.0719585i
$39$		0			0
$40$	−1.59046	+	0.280440i	−0.251473	+	0.0443415i
$41$	6.41507	+	2.33489i	1.00186	+	0.364649i	0.790303	−	0.612716i	$-0.209923\pi$
$41$	6.41507	+	2.33489i	1.00186	+	0.364649i	0.211561	+	0.977365i	$0.432145\pi$
$42$		0			0
$43$	7.63098	−	7.63098i	1.16371	−	1.16371i	0.180057	−	0.983656i	$-0.442372\pi$
$43$	7.63098	−	7.63098i	1.16371	−	1.16371i	0.983656	−	0.180057i	$-0.0576281\pi$
$44$	−3.39881	−	4.05054i	−0.512390	−	0.610643i
$45$		0			0
$46$	−5.49556	+	2.00022i	−0.810276	+	0.294916i
$47$	4.34681	−	2.50963i	0.634047	−	0.366067i	−0.148271	−	0.988947i	$-0.547371\pi$
$47$	4.34681	−	2.50963i	0.634047	−	0.366067i	0.782318	+	0.622880i	$0.214037\pi$
$48$		0			0
$49$	−0.513770	+	2.91374i	−0.0733957	+	0.416248i
$50$	1.01082	+	2.16771i	0.142952	+	0.306561i
$51$		0			0
$52$	0.436720	+	4.99173i	0.0605622	+	0.692229i
$53$	7.64299	−	9.10856i	1.04985	−	1.25116i	0.0827960	−	0.996567i	$-0.473615\pi$
$53$	7.64299	−	9.10856i	1.04985	−	1.25116i	0.967049	−	0.254590i	$-0.0819405\pi$
$54$		0			0
$55$	4.89802	−	6.99510i	0.660449	−	0.943219i
$56$	1.15306	−	1.64674i	0.154084	−	0.220055i
$57$		0			0
$58$	−4.76414	+	5.67769i	−0.625563	+	0.745517i
$59$	0.615917	+	7.03996i	0.0801855	+	0.916525i	0.924626	+	0.380876i	$0.124377\pi$
$59$	0.615917	+	7.03996i	0.0801855	+	0.916525i	−0.844441	+	0.535649i	$0.820067\pi$
$60$		0			0
$61$	−2.86510	−	6.14423i	−0.366839	−	0.786688i	−0.999921	−	0.0126035i	$-0.995988\pi$
$61$	−2.86510	−	6.14423i	−0.366839	−	0.786688i	0.633082	−	0.774085i	$-0.281790\pi$
$62$	1.25760	−	7.13219i	0.159715	−	0.905789i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−7.60437	+	2.76776i	−0.943206	+	0.343299i
$66$		0			0
$67$	−3.96674	−	4.72738i	−0.484615	−	0.577541i	0.467224	−	0.884139i	$-0.345254\pi$
$67$	−3.96674	−	4.72738i	−0.484615	−	0.577541i	−0.951839	+	0.306597i	$0.900810\pi$
$68$	−3.96204	+	3.96204i	−0.480468	+	0.480468i
$69$		0			0
$70$	3.05082	+	1.11041i	0.364643	+	0.132719i
$71$	−1.49231	+	0.263135i	−0.177105	+	0.0312284i	−0.261497	−	0.965204i	$-0.584216\pi$
$71$	−1.49231	+	0.263135i	−0.177105	+	0.0312284i	0.0843922	+	0.996433i	$0.473105\pi$
$72$		0			0
$73$			8.32062i			0.973855i	0.873442	+	0.486928i	$0.161882\pi$
$73$			8.32062i			0.973855i	−0.873442	+	0.486928i	$0.838118\pi$
$74$	−2.99741	−	5.29297i	−0.348442	−	0.615295i
$75$		0			0
$76$	0.363361	−	0.254428i	0.0416804	−	0.0291849i
$77$	1.84583	+	10.4682i	0.210352	+	1.19296i
$78$		0			0
$79$	−1.28011	+	14.6317i	−0.144023	+	1.64620i	0.489160	+	0.872194i	$0.337303\pi$
$79$	−1.28011	+	14.6317i	−0.144023	+	1.64620i	−0.633184	+	0.774002i	$0.718252\pi$
$80$	1.14197	+	1.14197i	0.127676	+	0.127676i
$81$		0			0
$82$	−1.76690	−	6.59415i	−0.195121	−	0.728202i
$83$	−4.01232	−	11.0238i	−0.440409	−	1.21002i	−0.939224	−	0.343306i	$-0.888453\pi$
$83$	−4.01232	−	11.0238i	−0.440409	−	1.21002i	0.498814	−	0.866709i	$-0.333769\pi$
$84$		0			0
$85$	−7.83673	−	4.52454i	−0.850013	−	0.490755i
$86$	−10.6279	−	1.87398i	−1.14603	−	0.202077i
$87$		0			0
$88$	−1.36853	+	5.10744i	−0.145886	+	0.544455i
$89$	−0.608784	+	0.0532617i	−0.0645310	+	0.00564573i	−0.119376	−	0.992849i	$-0.538089\pi$
$89$	−0.608784	+	0.0532617i	−0.0645310	+	0.00564573i	0.0548445	+	0.998495i	$0.482534\pi$
$90$		0			0
$91$	4.25713	−	9.12944i	0.446268	−	0.957026i
$92$	4.79061	+	3.35442i	0.499455	+	0.349722i
$93$		0			0
$94$	−4.54900	−	2.12123i	−0.469193	−	0.218788i
$95$	0.548780	+	0.460481i	0.0563036	+	0.0472443i
$96$		0			0
$97$	−10.0241	−	2.68596i	−1.01780	−	0.272717i	−0.288912	−	0.957356i	$-0.593294\pi$
$97$	−10.0241	−	2.68596i	−1.01780	−	0.272717i	−0.728883	+	0.684638i	$0.759960\pi$
$98$	2.68148	−	1.25039i	0.270870	−	0.126309i
$99$		0			0
$100$	1.19590	−	2.07136i	0.119590	−	0.207136i
$101$	−2.03594	−	3.52635i	−0.202584	−	0.350885i	0.746777	−	0.665075i	$-0.231600\pi$
$101$	−2.03594	−	3.52635i	−0.202584	−	0.350885i	−0.949360	+	0.314190i	$0.898267\pi$
$102$		0			0
$103$	−4.60559	+	1.23406i	−0.453802	+	0.121596i	−0.478478	−	0.878100i	$-0.658811\pi$
$103$	−4.60559	+	1.23406i	−0.453802	+	0.121596i	0.0246758	+	0.999696i	$0.492145\pi$
$104$	3.83850	−	3.22088i	0.376396	−	0.315833i
$105$		0			0
$106$	−11.8451	−	1.03631i	−1.15050	−	0.100656i
$107$	−3.50758	+	9.63701i	−0.339091	+	0.931645i	0.646562	+	0.762861i	$0.276206\pi$
$107$	−3.50758	+	9.63701i	−0.339091	+	0.931645i	−0.985653	+	0.168783i	$0.946016\pi$
$108$		0			0
$109$	−3.38772	−	4.83817i	−0.324485	−	0.463412i	0.623456	−	0.781858i	$-0.285728\pi$
$109$	−3.38772	−	4.83817i	−0.324485	−	0.463412i	−0.947941	+	0.318446i	$0.896839\pi$
$110$	−8.53944			−0.814204
$111$		0			0
$112$	−2.01030			−0.189956
$113$	11.1455	+	15.9174i	1.04848	+	1.49738i	0.856614	+	0.515957i	$0.172564\pi$
$113$	11.1455	+	15.9174i	1.04848	+	1.49738i	0.191862	+	0.981422i	$0.438547\pi$
$114$		0			0
$115$	−3.23034	+	8.87528i	−0.301231	+	0.827624i
$116$	7.38349	+	0.645972i	0.685540	+	0.0599770i
$117$		0			0
$118$	5.41352	−	4.54249i	0.498355	−	0.418170i
$119$	10.8803	−	2.91536i	0.997392	−	0.267250i
$120$		0			0
$121$	−8.47941	−	14.6868i	−0.770856	−	1.33516i
$122$	−3.38971	+	5.87114i	−0.306890	+	0.531548i
$123$		0			0
$124$	−6.56368	+	3.06069i	−0.589436	+	0.274858i
$125$	11.5309	+	3.08970i	1.03136	+	0.276351i
$126$		0			0
$127$	1.17105	+	0.982631i	0.103914	+	0.0871944i	0.693265	−	0.720683i	$-0.256172\pi$
$127$	1.17105	+	0.982631i	0.103914	+	0.0871944i	−0.589350	+	0.807878i	$0.700616\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$		0			0
$130$	6.62891	+	4.64161i	0.581394	+	0.407096i
$131$	1.85023	−	3.96782i	0.161655	−	0.346670i	−0.808750	−	0.588152i	$-0.799856\pi$
$131$	1.85023	−	3.96782i	0.161655	−	0.346670i	0.970405	+	0.241482i	$0.0776334\pi$
$132$		0			0
$133$	−0.888341	+	0.0777197i	−0.0770289	+	0.00673916i
$134$	−1.59721	+	5.96088i	−0.137978	+	0.514942i
$135$		0			0
$136$	5.51805	+	0.972981i	0.473169	+	0.0834324i
$137$	3.32296	+	1.91851i	0.283899	+	0.163909i	0.635187	−	0.772358i	$-0.280923\pi$
$137$	3.32296	+	1.91851i	0.283899	+	0.163909i	−0.351288	+	0.936267i	$0.614256\pi$
$138$		0			0
$139$	4.92800	+	13.5396i	0.417987	+	1.14841i	0.952842	+	0.303467i	$0.0981442\pi$
$139$	4.92800	+	13.5396i	0.417987	+	1.14841i	−0.534854	+	0.844944i	$0.679634\pi$
$140$	−0.840287	−	3.13599i	−0.0710172	−	0.265040i
$141$		0			0
$142$	1.07150	+	1.07150i	0.0899186	+	0.0899186i
$143$	−2.30921	+	26.3943i	−0.193106	+	2.20721i
$144$		0			0
$145$	2.07854	+	11.7880i	0.172613	+	0.978937i
$146$	6.81586	−	4.77251i	0.564084	−	0.394976i
$147$		0			0
$148$	−2.61650	+	5.49126i	−0.215075	+	0.451379i
$149$			2.83869i			0.232555i	0.993217	+	0.116277i	$0.0370962\pi$
$149$			2.83869i			0.232555i	−0.993217	+	0.116277i	$0.962904\pi$
$150$		0			0
$151$	−0.603963	+	0.106495i	−0.0491499	+	0.00866644i	−0.198169	−	0.980168i	$-0.563499\pi$
$151$	−0.603963	+	0.106495i	−0.0491499	+	0.00866644i	0.149019	+	0.988834i	$0.452388\pi$
$152$	−0.416831	−	0.151714i	−0.0338094	−	0.0123056i
$153$		0			0
$154$	7.51633	−	7.51633i	0.605683	−	0.605683i
$155$	−7.51812	−	8.95974i	−0.603870	−	0.719664i
$156$		0			0
$157$	6.70235	−	2.43946i	0.534906	−	0.194690i	−0.0604216	−	0.998173i	$-0.519245\pi$
$157$	6.70235	−	2.43946i	0.534906	−	0.194690i	0.595328	+	0.803483i	$0.297022\pi$
$158$	12.7198	−	7.34380i	1.01194	−	0.584241i
$159$		0			0
$160$	0.280440	−	1.59046i	0.0221707	−	0.125737i
$161$	−4.96862	−	10.6552i	−0.391582	−	0.839750i
$162$		0			0
$163$	0.866710	+	9.90654i	0.0678860	+	0.775940i	0.951485	+	0.307696i	$0.0995578\pi$
$163$	0.866710	+	9.90654i	0.0678860	+	0.775940i	−0.883599	+	0.468245i	$0.844887\pi$
$164$	−4.38816	+	5.22961i	−0.342658	+	0.408364i
$165$		0			0
$166$	−6.72876	+	9.60967i	−0.522253	+	0.745855i
$167$	−13.7572	+	19.6474i	−1.06457	+	1.52036i	−0.227102	+	0.973871i	$0.572925\pi$
$167$	−13.7572	+	19.6474i	−1.06457	+	1.52036i	−0.837466	+	0.546489i	$0.815964\pi$
$168$		0			0
$169$	7.78296	−	9.27537i	0.598689	−	0.713490i
$170$	0.788679	+	9.01464i	0.0604889	+	0.691392i
$171$		0			0
$172$	4.56082	+	9.78072i	0.347760	+	0.745773i
$173$	2.14248	−	12.1506i	0.162890	−	0.923795i	−0.788323	−	0.615261i	$-0.789051\pi$
$173$	2.14248	−	12.1506i	0.162890	−	0.923795i	0.951213	−	0.308534i	$-0.0998384\pi$
$174$		0			0
$175$	−4.16407	+	2.40412i	−0.314774	+	0.181735i
$176$	4.96873	−	1.80847i	0.374532	−	0.136318i
$177$		0			0
$178$	0.392814	+	0.468137i	0.0294426	+	0.0350884i
$179$	−7.15607	+	7.15607i	−0.534870	+	0.534870i	−0.922018	−	0.387148i	$-0.873460\pi$
$179$	−7.15607	+	7.15607i	−0.534870	+	0.534870i	0.387148	+	0.922018i	$0.373460\pi$
$180$		0			0
$181$	−22.2657	−	8.10406i	−1.65500	−	0.602370i	−0.665433	−	0.746457i	$-0.731753\pi$
$181$	−22.2657	−	8.10406i	−1.65500	−	0.602370i	−0.989565	+	0.144087i	$0.953975\pi$
$182$	−9.92019	+	1.74920i	−0.735334	+	0.129659i
$183$		0			0
$184$		−	5.84825i		−	0.431139i
$185$	−9.65982	−	1.78635i	−0.710204	−	0.131335i
$186$		0			0
$187$	−24.2694	+	16.9936i	−1.77475	+	1.24269i
$188$	0.871586	+	4.94301i	0.0635669	+	0.360506i
$189$		0			0
$190$	0.0624367	−	0.713655i	0.00452964	−	0.0517740i
$191$	3.04841	+	3.04841i	0.220575	+	0.220575i	0.808741	−	0.588165i	$-0.200150\pi$
$191$	3.04841	+	3.04841i	0.220575	+	0.220575i	−0.588165	+	0.808741i	$0.700150\pi$
$192$		0			0
$193$	−2.77230	−	10.3464i	−0.199555	−	0.744748i	−0.991041	−	0.133561i	$-0.957359\pi$
$193$	−2.77230	−	10.3464i	−0.199555	−	0.744748i	0.791486	−	0.611187i	$-0.209308\pi$
$194$	3.54939	+	9.75188i	0.254832	+	0.700144i
$195$		0			0
$196$	−2.56230	−	1.47934i	−0.183021	−	0.105667i
$197$	−4.08537	−	0.720361i	−0.291070	−	0.0513236i	0.0262063	−	0.999657i	$-0.491657\pi$
$197$	−4.08537	−	0.720361i	−0.291070	−	0.0513236i	−0.317277	+	0.948333i	$0.602768\pi$
$198$		0			0
$199$	−2.91327	+	10.8725i	−0.206516	+	0.770729i	0.782466	+	0.622694i	$0.213962\pi$
$199$	−2.91327	+	10.8725i	−0.206516	+	0.770729i	−0.988982	+	0.148036i	$0.952705\pi$
$200$	−2.38270	+	0.208459i	−0.168483	+	0.0147403i
$201$		0			0
$202$	−1.72085	+	3.69038i	−0.121079	+	0.259654i
$203$	−12.2052	−	8.54614i	−0.856634	−	0.599821i
$204$		0			0
$205$	−9.99220	−	4.65944i	−0.697885	−	0.325429i
$206$	3.65254	+	3.06485i	0.254485	+	0.213538i
$207$		0			0
$208$	−4.84006	−	1.29689i	−0.335598	−	0.0899232i
$209$	2.12573	−	0.991246i	0.147040	−	0.0685660i
$210$		0			0
$211$	−1.28518	+	2.22600i	−0.0884757	+	0.153244i	−0.906867	−	0.421417i	$-0.861533\pi$
$211$	−1.28518	+	2.22600i	−0.0884757	+	0.153244i	0.818391	+	0.574661i	$0.194866\pi$
$212$	5.94519	+	10.2974i	0.408317	+	0.707226i
$213$		0			0
$214$	9.90604	−	2.65432i	0.677163	−	0.181445i
$215$	−13.3512	+	11.2030i	−0.910542	+	0.764035i
$216$		0			0
$217$	14.5036	+	1.26890i	0.984571	+	0.0861388i
$218$	−2.02008	+	5.55012i	−0.136817	+	0.375901i
$219$		0			0
$220$	4.89802	+	6.99510i	0.330225	+	0.471610i
$221$	28.0764			1.88862
$222$		0			0
$223$	8.99214			0.602158			0.301079	−	0.953599i	$-0.402653\pi$
$223$	8.99214			0.602158			0.301079	+	0.953599i	$0.402653\pi$
$224$	1.15306	+	1.64674i	0.0770422	+	0.110028i
$225$		0			0
$226$	6.64597	−	18.2596i	0.442083	−	1.21461i
$227$	−15.0112	−	1.31331i	−0.996331	−	0.0871677i	−0.422690	−	0.906274i	$-0.638914\pi$
$227$	−15.0112	−	1.31331i	−0.996331	−	0.0871677i	−0.573641	+	0.819107i	$0.694470\pi$
$228$		0			0
$229$	19.5108	−	16.3715i	1.28931	−	1.08186i	0.297424	−	0.954745i	$-0.403872\pi$
$229$	19.5108	−	16.3715i	1.28931	−	1.08186i	0.991888	−	0.127116i	$-0.0405720\pi$
$230$	9.12305	−	2.44451i	0.601556	−	0.161186i
$231$		0			0
$232$	−3.70585	−	6.41871i	−0.243301	−	0.421409i
$233$	6.34621	−	10.9920i	0.415754	−	0.720107i	−0.579753	−	0.814792i	$-0.696851\pi$
$233$	6.34621	−	10.9920i	0.415754	−	0.720107i	0.995507	+	0.0946850i	$0.0301844\pi$
$234$		0			0
$235$	−7.34659	+	3.42577i	−0.479238	+	0.223473i
$236$	−6.82606	−	1.82904i	−0.444338	−	0.119060i
$237$		0			0
$238$	−8.62878	−	7.24041i	−0.559321	−	0.469326i
$239$	−15.0355	−	7.01117i	−0.972565	−	0.453515i	−0.129649	−	0.991560i	$-0.541385\pi$
$239$	−15.0355	−	7.01117i	−0.972565	−	0.453515i	−0.842916	+	0.538045i	$0.819163\pi$
$240$		0			0
$241$	4.85829	+	3.40181i	0.312950	+	0.219130i	0.719490	−	0.694503i	$-0.244376\pi$
$241$	4.85829	+	3.40181i	0.312950	+	0.219130i	−0.406540	+	0.913633i	$0.633265\pi$
$242$	−7.16711	+	15.3699i	−0.460719	+	0.988015i
$243$		0			0
$244$	6.75361	−	0.590865i	0.432356	−	0.0378262i
$245$	1.23670	−	4.61543i	0.0790100	−	0.294869i
$246$		0			0
$247$	−2.18893	−	0.385968i	−0.139279	−	0.0245586i
$248$	6.27194	+	3.62111i	0.398269	+	0.229941i
$249$		0			0
$250$	−4.08293	−	11.2178i	−0.258227	−	0.709474i
$251$	3.60918	+	13.4696i	0.227809	+	0.850195i	0.981260	+	0.192691i	$0.0617214\pi$
$251$	3.60918	+	13.4696i	0.227809	+	0.850195i	−0.753450	+	0.657505i	$0.771612\pi$
$252$		0			0
$253$	21.8661	+	21.8661i	1.37471	+	1.37471i
$254$	0.133235	−	1.52289i	0.00835992	−	0.0955543i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	14.2192	−	9.95637i	0.886967	−	0.621061i	−0.0387618	−	0.999248i	$-0.512341\pi$
$257$	14.2192	−	9.95637i	0.886967	−	0.621061i	0.925729	+	0.378187i	$0.123452\pi$
$258$		0			0
$259$	10.0748	−	6.93015i	0.626018	−	0.430618i
$260$		−	8.09240i		−	0.501869i
$261$		0			0
$262$	−4.31150	+	0.760233i	−0.266365	+	0.0469674i
$263$	−17.1405	−	6.23863i	−1.05693	−	0.384690i	−0.245655	−	0.969357i	$-0.579003\pi$
$263$	−17.1405	−	6.23863i	−1.05693	−	0.384690i	−0.811273	+	0.584667i	$0.801225\pi$
$264$		0			0
$265$	−13.5785	+	13.5785i	−0.834119	+	0.834119i
$266$	0.573196	+	0.683108i	0.0351449	+	0.0418840i
$267$		0			0
$268$	5.79899	−	2.11066i	0.354230	−	0.128929i
$269$	18.3513	−	10.5952i	1.11890	−	0.645998i	0.177781	−	0.984070i	$-0.443108\pi$
$269$	18.3513	−	10.5952i	1.11890	−	0.645998i	0.941120	+	0.338072i	$0.109775\pi$
$270$		0			0
$271$	−1.33346	+	7.56242i	−0.0810018	+	0.459384i	0.917146	+	0.398551i	$0.130487\pi$
$271$	−1.33346	+	7.56242i	−0.0810018	+	0.459384i	−0.998148	+	0.0608331i	$0.980624\pi$
$272$	−2.36800	−	5.07820i	−0.143581	−	0.307911i
$273$		0			0
$274$	−0.334418	−	3.82242i	−0.0202029	−	0.230921i
$275$	8.12929	−	9.68811i	0.490215	−	0.584215i
$276$		0			0
$277$	−13.1625	+	18.7980i	−0.790858	+	1.12946i	0.197941	+	0.980214i	$0.436574\pi$
$277$	−13.1625	+	18.7980i	−0.790858	+	1.12946i	−0.988800	+	0.149249i	$0.952314\pi$
$278$	8.26438	−	11.8028i	0.495665	−	0.707882i
$279$		0			0
$280$	−2.08689	+	2.48706i	−0.124715	+	0.148630i
$281$	−1.50538	−	17.2066i	−0.0898037	−	1.02646i	−0.898716	−	0.438532i	$-0.855499\pi$
$281$	−1.50538	−	17.2066i	−0.0898037	−	1.02646i	0.808912	−	0.587930i	$-0.200057\pi$
$282$		0			0
$283$	−11.9844	−	25.7006i	−0.712398	−	1.52774i	−0.843944	−	0.536432i	$-0.819772\pi$
$283$	−11.9844	−	25.7006i	−0.712398	−	1.52774i	0.131546	−	0.991310i	$-0.458006\pi$
$284$	0.263135	−	1.49231i	0.0156142	−	0.0885525i
$285$		0			0
$286$	22.9455	−	13.2476i	1.35680	−	0.783346i
$287$	12.8962	−	4.69384i	0.761240	−	0.277069i
$288$		0			0
$289$	9.25330	+	11.0276i	0.544311	+	0.648685i
$290$	8.46394	−	8.46394i	0.497020	−	0.497020i
$291$		0			0
$292$	−7.81883	−	2.84582i	−0.457562	−	0.166539i
$293$	−7.60493	+	1.34096i	−0.444285	+	0.0783394i	−0.391315	−	0.920257i	$-0.627980\pi$
$293$	−7.60493	+	1.34096i	−0.444285	+	0.0783394i	−0.0529698	+	0.998596i	$0.516869\pi$
$294$		0			0
$295$		−	11.4129i		−	0.664485i
$296$	5.99894	−	1.00634i	0.348681	−	0.0584924i
$297$		0			0
$298$	2.32532	−	1.62821i	0.134702	−	0.0943195i
$299$	−5.08866	−	28.8592i	−0.294285	−	1.66897i
$300$		0			0
$301$	1.89083	−	21.6123i	0.108986	−	1.24571i
$302$	0.433655	+	0.433655i	0.0249540	+	0.0249540i
$303$		0			0
$304$	0.114807	+	0.428467i	0.00658466	+	0.0245743i
$305$	3.74467	+	10.2884i	0.214419	+	0.589112i
$306$		0			0
$307$	−21.0086	−	12.1293i	−1.19902	−	0.692256i	−0.238685	−	0.971097i	$-0.576716\pi$
$307$	−21.0086	−	12.1293i	−1.19902	−	0.692256i	−0.960337	+	0.278841i	$0.910050\pi$
$308$	−10.4682	−	1.84583i	−0.596481	−	0.105176i
$309$		0			0
$310$	−3.02718	+	11.2976i	−0.171932	+	0.641659i
$311$	−1.90821	+	0.166946i	−0.108204	+	0.00946667i	−0.141129	−	0.989991i	$-0.545073\pi$
$311$	−1.90821	+	0.166946i	−0.108204	+	0.00946667i	0.0329249	+	0.999458i	$0.489518\pi$
$312$		0			0
$313$	7.60147	−	16.3014i	0.429661	−	0.921410i	−0.565647	−	0.824648i	$-0.691373\pi$
$313$	7.60147	−	16.3014i	0.429661	−	0.921410i	0.995307	−	0.0967626i	$-0.0308488\pi$
$314$	−5.84260	−	4.09103i	−0.329717	−	0.230870i
$315$		0			0
$316$	−13.3115	−	6.20725i	−0.748830	−	0.349185i
$317$	−14.1675	−	11.8879i	−0.795725	−	0.667693i	0.151430	−	0.988468i	$-0.451612\pi$
$317$	−14.1675	−	11.8879i	−0.795725	−	0.667693i	−0.947155	+	0.320775i	$0.896057\pi$
$318$		0			0
$319$	37.8548	+	10.1432i	2.11946	+	0.567908i
$320$	−1.46368	+	0.682525i	−0.0818221	+	0.0381543i
$321$		0			0
$322$	−5.87838	+	10.1816i	−0.327589	+	0.567401i
$323$	−1.24273	−	2.15248i	−0.0691476	−	0.119767i
$324$		0			0
$325$	−11.5765	+	3.10191i	−0.642148	+	0.172063i
$326$	7.61784	−	6.39213i	0.421913	−	0.354027i
$327$		0			0
$328$	6.80079	+	0.594992i	0.375511	+	0.0328529i
$329$	3.45106	−	9.48172i	0.190263	−	0.522744i
$330$		0			0
$331$	7.39020	+	10.5543i	0.406202	+	0.580117i	0.969180	−	0.246356i	$-0.0792331\pi$
$331$	7.39020	+	10.5543i	0.406202	+	0.580117i	−0.562977	+	0.826472i	$0.690344\pi$
$332$	11.7312			0.643836
$333$		0			0
$334$	23.9850			1.31240
$335$	5.71647	+	8.16397i	0.312324	+	0.446045i
$336$		0			0
$337$	1.77550	−	4.87816i	0.0967179	−	0.265730i	−0.881893	−	0.471449i	$-0.843731\pi$
$337$	1.77550	−	4.87816i	0.0967179	−	0.265730i	0.978611	+	0.205719i	$0.0659533\pi$
$338$	−12.0621	−	1.05529i	−0.656090	−	0.0574004i
$339$		0			0
$340$	6.93200	−	5.81663i	0.375940	−	0.315451i
$341$	−36.9892	+	9.91122i	−2.00308	+	0.536723i
$342$		0			0
$343$	10.0100	+	17.3378i	0.540488	+	0.936153i
$344$	5.39591	−	9.34600i	0.290928	−	0.503902i
$345$		0			0
$346$	−11.1821	+	5.21430i	−0.601153	+	0.280322i
$347$	3.93518	+	1.05443i	0.211252	+	0.0566047i	0.362893	−	0.931831i	$-0.381789\pi$
$347$	3.93518	+	1.05443i	0.211252	+	0.0566047i	−0.151641	+	0.988436i	$0.548456\pi$
$348$		0			0
$349$	10.4267	+	8.74905i	0.558129	+	0.468326i	0.877683	−	0.479242i	$-0.159088\pi$
$349$	10.4267	+	8.74905i	0.558129	+	0.468326i	−0.319554	+	0.947568i	$0.603533\pi$
$350$	4.35775	+	2.03205i	0.232932	+	0.108618i
$351$		0			0
$352$	−4.33136	−	3.03285i	−0.230862	−	0.161651i
$353$	−0.684424	+	1.46775i	−0.0364282	+	0.0781205i	−0.923680	−	0.383165i	$-0.874834\pi$
$353$	−0.684424	+	1.46775i	−0.0364282	+	0.0781205i	0.887252	+	0.461286i	$0.152612\pi$
$354$		0			0
$355$	2.43794	−	0.213292i	0.129392	−	0.0113204i
$356$	0.158167	−	0.590287i	0.00838283	−	0.0312851i
$357$		0			0
$358$	9.96647	+	1.75736i	0.526744	+	0.0928792i
$359$	2.36755	+	1.36690i	0.124954	+	0.0721424i	0.561174	−	0.827698i	$-0.310350\pi$
$359$	2.36755	+	1.36690i	0.124954	+	0.0721424i	−0.436220	+	0.899840i	$0.643683\pi$
$360$		0			0
$361$	−6.43109	−	17.6693i	−0.338478	−	0.929961i
$362$	6.13264	+	22.8873i	0.322324	+	1.20293i
$363$		0			0
$364$	7.12285	+	7.12285i	0.373339	+	0.373339i
$365$	1.17118	−	13.3866i	0.0613021	−	0.700687i
$366$		0			0
$367$	0.766502	+	4.34705i	0.0400111	+	0.226914i	0.998256	−	0.0590349i	$-0.0188023\pi$
$367$	0.766502	+	4.34705i	0.0400111	+	0.226914i	−0.958245	+	0.285949i	$0.907691\pi$
$368$	−4.79061	+	3.35442i	−0.249728	+	0.174861i
$369$		0			0
$370$	4.07735	+	8.93747i	0.211972	+	0.464637i
$371$		−	23.9033i		−	1.24100i
$372$		0			0
$373$	−35.6634	+	6.28842i	−1.84658	+	0.325602i	−0.983702	−	0.179808i	$-0.942452\pi$
$373$	−35.6634	+	6.28842i	−1.84658	+	0.325602i	−0.862879	+	0.505410i	$0.831341\pi$
$374$	27.8407	+	10.1332i	1.43961	+	0.523974i
$375$		0			0
$376$	3.54915	−	3.54915i	0.183034	−	0.183034i
$377$	−23.8722	−	28.4498i	−1.22948	−	1.46524i
$378$		0			0
$379$	8.36262	−	3.04374i	0.429559	−	0.156347i	−0.118187	−	0.992991i	$-0.537708\pi$
$379$	8.36262	−	3.04374i	0.429559	−	0.156347i	0.547746	+	0.836645i	$0.315486\pi$
$380$	−0.620404	+	0.358190i	−0.0318261	+	0.0183748i
$381$		0			0
$382$	0.748615	−	4.24561i	0.0383025	−	0.217224i
$383$	5.29342	+	11.3518i	0.270481	+	0.580049i	0.993890	−	0.110371i	$-0.0352038\pi$
$383$	5.29342	+	11.3518i	0.270481	+	0.580049i	−0.723409	+	0.690419i	$0.757426\pi$
$384$		0			0
$385$	−1.49619	−	17.1015i	−0.0762529	−	0.871575i
$386$	−6.88513	+	8.20537i	−0.350444	+	0.417643i
$387$		0			0
$388$	5.95242	−	8.50094i	0.302189	−	0.431570i
$389$	−6.09399	+	8.70312i	−0.308978	+	0.441266i	−0.943369	−	0.331747i	$-0.892362\pi$
$389$	−6.09399	+	8.70312i	−0.308978	+	0.441266i	0.634391	+	0.773012i	$0.281251\pi$
$390$		0			0
$391$	21.0634	−	25.1023i	1.06522	−	1.26948i
$392$	0.257866	+	2.94743i	0.0130242	+	0.148868i
$393$		0			0
$394$	1.75319	+	3.75972i	0.0883243	+	0.189412i
$395$	4.11899	−	23.3600i	0.207249	−	1.17537i
$396$		0			0
$397$	4.58110	−	2.64490i	0.229919	−	0.132744i	−0.380616	−	0.924733i	$-0.624288\pi$
$397$	4.58110	−	2.64490i	0.229919	−	0.132744i	0.610535	+	0.791990i	$0.290955\pi$
$398$	10.5772	−	3.84978i	0.530187	−	0.192972i
$399$		0			0
$400$	1.53742	+	1.83223i	0.0768711	+	0.0916114i
$401$	13.9354	−	13.9354i	0.695899	−	0.695899i	−0.267624	−	0.963523i	$-0.586239\pi$
$401$	13.9354	−	13.9354i	0.695899	−	0.695899i	0.963523	+	0.267624i	$0.0862387\pi$
$402$		0			0
$403$	34.1008	+	12.4117i	1.69868	+	0.618270i
$404$	4.01002	−	0.707074i	0.199506	−	0.0351783i
$405$		0			0
$406$			14.8997i			0.739462i
$407$	−18.6668	+	26.1921i	−0.925281	+	1.29829i
$408$		0			0
$409$	15.7440	−	11.0240i	0.778489	−	0.545104i	−0.115439	−	0.993315i	$-0.536827\pi$
$409$	15.7440	−	11.0240i	0.778489	−	0.545104i	0.893928	+	0.448211i	$0.147939\pi$
$410$	1.91450	+	10.8577i	0.0945505	+	0.536222i
$411$		0			0
$412$	0.415563	−	4.74991i	0.0204733	−	0.234011i
$413$	10.0455	+	10.0455i	0.494308	+	0.494308i
$414$		0			0
$415$	4.90355	+	18.3003i	0.240706	+	0.898326i
$416$	1.71380	+	4.70861i	0.0840257	+	0.230859i
$417$		0			0
$418$	−2.03125	−	1.17274i	−0.0993518	−	0.0573608i
$419$	−3.04843	−	0.537521i	−0.148926	−	0.0262596i	0.0986883	−	0.995118i	$-0.468535\pi$
$419$	−3.04843	−	0.537521i	−0.148926	−	0.0262596i	−0.247614	+	0.968859i	$0.579646\pi$
$420$		0			0
$421$	−8.45077	+	31.5387i	−0.411865	+	1.53710i	0.379167	+	0.925328i	$0.376211\pi$
$421$	−8.45077	+	31.5387i	−0.411865	+	1.53710i	−0.791033	+	0.611774i	$0.790456\pi$
$422$	2.56059	−	0.224022i	0.124647	−	0.0109052i
$423$		0			0
$424$	5.02509	−	10.7763i	0.244040	−	0.523345i
$425$	−10.9780	−	7.68690i	−0.532513	−	0.372869i
$426$		0			0
$427$	−12.3518	−	5.75972i	−0.597744	−	0.278733i
$428$	−7.85616	−	6.59210i	−0.379742	−	0.318641i
$429$		0			0
$430$	16.8348	+	4.51088i	0.811848	+	0.217534i
$431$	30.9774	−	14.4450i	1.49213	−	0.695791i	0.506117	−	0.862465i	$-0.331081\pi$
$431$	30.9774	−	14.4450i	1.49213	−	0.695791i	0.986012	+	0.166674i	$0.0533027\pi$
$432$		0			0
$433$	−0.983226	+	1.70300i	−0.0472508	+	0.0818408i	−0.888684	−	0.458521i	$-0.848379\pi$
$433$	−0.983226	+	1.70300i	−0.0472508	+	0.0818408i	0.841433	+	0.540362i	$0.181713\pi$
$434$	−7.27952	−	12.6085i	−0.349428	−	0.605227i
$435$		0			0
$436$	5.70506	−	1.52867i	0.273223	−	0.0732098i
$437$	−1.98726	+	1.66751i	−0.0950634	+	0.0797677i
$438$		0			0
$439$	−36.2043	−	3.16747i	−1.72794	−	0.151175i	−0.820579	−	0.571532i	$-0.806349\pi$
$439$	−36.2043	−	3.16747i	−1.72794	−	0.151175i	−0.907359	+	0.420357i	$0.861905\pi$
$440$	2.92066	−	8.02445i	0.139237	−	0.382551i
$441$		0			0
$442$	−16.1040	−	22.9988i	−0.765987	−	1.09394i
$443$	2.18977			0.104039			0.0520196	−	0.998646i	$-0.483434\pi$
$443$	2.18977			0.104039			0.0520196	+	0.998646i	$0.483434\pi$
$444$		0			0
$445$	0.986937			0.0467853
$446$	−5.15768	−	7.36593i	−0.244223	−	0.348787i
$447$		0			0
$448$	0.687564	−	1.88907i	0.0324843	−	0.0892500i
$449$	−18.5664	−	1.62435i	−0.876200	−	0.0766576i	−0.359825	−	0.933020i	$-0.617164\pi$
$449$	−18.5664	−	1.62435i	−0.876200	−	0.0766576i	−0.516376	+	0.856362i	$0.672719\pi$
$450$		0			0
$451$	−27.6521	+	23.2029i	−1.30209	+	1.09258i
$452$	−18.7694	+	5.02924i	−0.882838	+	0.236556i
$453$		0			0
$454$	7.53429	+	13.0498i	0.353602	+	0.612456i
$455$	−8.13409	+	14.0886i	−0.381332	+	0.660486i
$456$		0			0
$457$	−18.1151	+	8.44721i	−0.847388	+	0.395144i	−0.797287	−	0.603600i	$-0.793732\pi$
$457$	−18.1151	+	8.44721i	−0.847388	+	0.395144i	−0.0501015	+	0.998744i	$0.515954\pi$
$458$	−24.6017	−	6.59201i	−1.14956	−	0.308025i
$459$		0			0
$460$	−7.23519	−	6.07105i	−0.337343	−	0.283064i
$461$	−5.36047	−	2.49963i	−0.249662	−	0.116419i	0.293759	−	0.955879i	$-0.405094\pi$
$461$	−5.36047	−	2.49963i	−0.249662	−	0.116419i	−0.543421	+	0.839460i	$0.682871\pi$
$462$		0			0
$463$	13.4573	+	9.42294i	0.625416	+	0.437921i	0.842846	−	0.538155i	$-0.180878\pi$
$463$	13.4573	+	9.42294i	0.625416	+	0.437921i	−0.217430	+	0.976076i	$0.569767\pi$
$464$	−3.13232	+	6.71727i	−0.145414	+	0.311842i
$465$		0			0
$466$	−12.6441	+	1.10622i	−0.585728	+	0.0512445i
$467$	1.64833	−	6.15166i	0.0762757	−	0.284665i	−0.917244	−	0.398326i	$-0.869591\pi$
$467$	1.64833	−	6.15166i	0.0762757	−	0.284665i	0.993520	+	0.113661i	$0.0362579\pi$
$468$		0			0
$469$	−12.2174	−	2.15426i	−0.564148	−	0.0994745i
$470$	7.02006	+	4.05303i	0.323811	+	0.186952i
$471$		0			0
$472$	2.41701	+	6.64067i	0.111252	+	0.305662i
$473$	14.7690	+	55.1186i	0.679079	+	2.53436i
$474$		0			0
$475$	0.750213	+	0.750213i	0.0344221	+	0.0344221i
$476$	−0.981729	+	11.2212i	−0.0449975	+	0.514323i
$477$		0			0
$478$	2.88079	+	16.3378i	0.131764	+	0.747273i
$479$	−14.9805	+	10.4895i	−0.684478	+	0.479276i	−0.863356	−	0.504595i	$-0.831642\pi$
$479$	−14.9805	+	10.4895i	−0.684478	+	0.479276i	0.178879	+	0.983871i	$0.442753\pi$
$480$		0			0
$481$	28.7272	−	10.1857i	1.30985	−	0.464430i
$482$		−	5.93088i		−	0.270144i
$483$		0			0
$484$	16.7012	−	2.94487i	0.759145	−	0.133858i
$485$	15.7492	+	5.73224i	0.715134	+	0.260288i
$486$		0			0
$487$	26.0608	−	26.0608i	1.18093	−	1.18093i	0.201423	−	0.979504i	$-0.435443\pi$
$487$	26.0608	−	26.0608i	1.18093	−	1.18093i	0.979504	−	0.201423i	$-0.0645566\pi$
$488$	−4.35772	−	5.19333i	−0.197265	−	0.235091i
$489$		0			0
$490$	−4.49009	+	1.63426i	−0.202841	+	0.0738282i
$491$	−13.1272	+	7.57897i	−0.592421	+	0.342034i	−0.766054	−	0.642776i	$-0.777783\pi$
$491$	−13.1272	+	7.57897i	−0.592421	+	0.342034i	0.173633	+	0.984810i	$0.444449\pi$
$492$		0			0
$493$	7.21144	−	40.8981i	0.324787	−	1.84196i
$494$	0.939354	+	2.01445i	0.0422636	+	0.0906345i
$495$		0			0
$496$	−0.631201	−	7.21466i	−0.0283417	−	0.323948i
$497$	−1.95811	+	2.33359i	−0.0878333	+	0.104676i
$498$		0			0
$499$	−15.9973	+	22.8465i	−0.716136	+	1.02275i	0.281859	+	0.959456i	$0.409049\pi$
$499$	−15.9973	+	22.8465i	−0.716136	+	1.02275i	−0.997995	+	0.0632929i	$0.979840\pi$
$500$	−6.84718	+	9.77879i	−0.306215	+	0.437321i
$501$		0			0
$502$	8.96354	−	10.6823i	0.400062	−	0.476776i
$503$	−0.167644	−	1.91618i	−0.00747490	−	0.0854385i	0.991541	−	0.129795i	$-0.0414319\pi$
$503$	−0.167644	−	1.91618i	−0.00747490	−	0.0854385i	−0.999016	+	0.0443563i	$0.985876\pi$
$504$		0			0
$505$	2.77916	+	5.95992i	0.123671	+	0.265213i
$506$	5.36977	−	30.4535i	0.238715	−	1.35382i
$507$		0			0
$508$	−1.32390	+	0.764351i	−0.0587384	+	0.0339126i
$509$	−1.24147	+	0.451859i	−0.0550273	+	0.0200283i	−0.369387	−	0.929276i	$-0.620432\pi$
$509$	−1.24147	+	0.451859i	−0.0550273	+	0.0200283i	0.314360	+	0.949304i	$0.398210\pi$
$510$		0			0
$511$	10.7519	+	12.8136i	0.475636	+	0.566840i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−16.3116	−	5.93692i	−0.719472	−	0.261866i
$515$	7.58338	−	1.33715i	0.334164	−	0.0589221i
$516$		0			0
$517$			26.5399i			1.16722i
$518$	−11.4555	−	4.27783i	−0.503326	−	0.187957i
$519$		0			0
$520$	−6.62891	+	4.64161i	−0.290697	+	0.203548i
$521$	2.36376	+	13.4055i	0.103558	+	0.587308i	0.991786	+	0.127905i	$0.0408253\pi$
$521$	2.36376	+	13.4055i	0.103558	+	0.587308i	−0.888228	+	0.459402i	$0.848064\pi$
$522$		0			0
$523$	3.09092	−	35.3294i	0.135156	−	1.54485i	−0.561522	−	0.827462i	$-0.689784\pi$
$523$	3.09092	−	35.3294i	0.135156	−	1.54485i	0.696679	−	0.717383i	$-0.254660\pi$
$524$	3.09572	+	3.09572i	0.135237	+	0.135237i
$525$		0			0
$526$	4.72100	+	17.6190i	0.205845	+	0.768225i
$527$	13.8790	+	38.1322i	0.604578	+	1.66106i
$528$		0			0
$529$	−9.70126	−	5.60103i	−0.421794	−	0.243523i
$530$	18.9111	+	3.33454i	0.821446	+	0.144843i
$531$		0			0
$532$	0.230798	−	0.861349i	0.0100064	−	0.0373442i
$533$	34.0774	−	2.98139i	1.47606	−	0.129138i
$534$		0			0
$535$	6.99962	−	15.0107i	0.302620	−	0.648971i
$536$	−5.05512	−	3.53963i	−0.218348	−	0.152889i
$537$		0			0
$538$	−19.2049	−	8.95541i	−0.827984	−	0.386095i
$539$	−11.9843	−	10.0560i	−0.516200	−	0.433143i
$540$		0			0
$541$	30.1363	+	8.07499i	1.29566	+	0.347171i	0.839807	−	0.542884i	$-0.182668\pi$
$541$	30.1363	+	8.07499i	1.29566	+	0.347171i	0.455852	+	0.890055i	$0.349334\pi$
$542$	6.95961	−	3.24532i	0.298941	−	0.139398i
$543$		0			0
$544$	−2.80159	+	4.85249i	−0.120117	+	0.208049i
$545$	4.76932	+	8.26070i	0.204295	+	0.353850i
$546$		0			0
$547$	−16.0232	+	4.29339i	−0.685101	+	0.183572i	−0.584547	−	0.811360i	$-0.698728\pi$
$547$	−16.0232	+	4.29339i	−0.685101	+	0.183572i	−0.100553	+	0.994932i	$0.532061\pi$
$548$	−2.93933	+	2.46639i	−0.125562	+	0.105359i
$549$		0			0
$550$	−12.5988	−	1.10225i	−0.537215	−	0.0470002i
$551$	−1.12446	+	3.08942i	−0.0479035	+	0.131614i
$552$		0			0
$553$	16.9357	+	24.1867i	0.720180	+	1.02852i
$554$	22.9481			0.974972
$555$		0			0
$556$	−14.4085			−0.611057
$557$	10.3351	+	14.7600i	0.437910	+	0.625401i	0.976074	−	0.217440i	$-0.0697705\pi$
$557$	10.3351	+	14.7600i	0.437910	+	0.625401i	−0.538163	+	0.842841i	$0.680882\pi$
$558$		0			0
$559$	18.4950	−	50.8146i	0.782255	−	2.14923i
$560$	3.23427	+	0.282962i	0.136673	+	0.0119573i
$561$		0			0
$562$	−13.2314	+	11.1025i	−0.558132	+	0.468329i
$563$	25.8416	−	6.92423i	1.08909	−	0.291822i	0.330777	−	0.943709i	$-0.392689\pi$
$563$	25.8416	−	6.92423i	1.08909	−	0.291822i	0.758316	+	0.651887i	$0.226022\pi$
$564$		0			0
$565$	−15.6909	−	27.1774i	−0.660119	−	1.14336i
$566$	−14.1787	+	24.5583i	−0.595977	+	1.03226i
$567$		0			0
$568$	−1.37336	+	0.640408i	−0.0576249	+	0.0268709i
$569$	7.98458	+	2.13946i	0.334731	+	0.0896909i	0.422270	−	0.906470i	$-0.361233\pi$
$569$	7.98458	+	2.13946i	0.334731	+	0.0896909i	−0.0875387	+	0.996161i	$0.527900\pi$
$570$		0			0
$571$	−5.51840	−	4.63049i	−0.230938	−	0.193780i	0.519974	−	0.854182i	$-0.325941\pi$
$571$	−5.51840	−	4.63049i	−0.230938	−	0.193780i	−0.750912	+	0.660402i	$0.770386\pi$
$572$	−24.0128	−	11.1973i	−1.00402	−	0.468184i
$573$		0			0
$574$	−11.2419	−	7.87169i	−0.469229	−	0.328558i
$575$	−5.91153	+	12.6773i	−0.246528	+	0.528681i
$576$		0			0
$577$	−39.9468	+	3.49489i	−1.66301	+	0.145494i	−0.879504	−	0.475892i	$-0.842125\pi$
$577$	−39.9468	+	3.49489i	−1.66301	+	0.145494i	−0.783504	+	0.621387i	$0.786570\pi$
$578$	3.72585	−	13.9051i	0.154975	−	0.578374i
$579$		0			0
$580$	−11.7880	−	2.07854i	−0.489469	−	0.0863065i
$581$	−20.4238	−	11.7917i	−0.847321	−	0.489201i
$582$		0			0
$583$	21.5034	+	59.0801i	0.890579	+	2.44685i
$584$	2.15354	+	8.03711i	0.0891140	+	0.332578i
$585$		0			0
$586$	5.46046	+	5.46046i	0.225569	+	0.225569i
$587$	−2.16060	+	24.6958i	−0.0891776	+	1.01930i	0.811366	+	0.584539i	$0.198724\pi$
$587$	−2.16060	+	24.6958i	−0.0891776	+	1.01930i	−0.900544	+	0.434766i	$0.856831\pi$
$588$		0			0
$589$	−0.557848	−	3.16371i	−0.0229857	−	0.130358i
$590$	−9.34890	+	6.54617i	−0.384888	+	0.269502i
$591$		0			0
$592$	−4.26520	−	4.33683i	−0.175299	−	0.178243i
$593$		−	5.96828i		−	0.245088i	−0.992463	−	0.122544i	$-0.960895\pi$
$593$		−	5.96828i		−	0.245088i	0.992463	−	0.122544i	$-0.0391052\pi$
$594$		0			0
$595$	−17.9150	+	3.15890i	−0.734444	+	0.129502i
$596$	−2.66750	−	0.970890i	−0.109265	−	0.0397692i
$597$		0			0
$598$	−20.7214	+	20.7214i	−0.847360	+	0.847360i
$599$	−23.8933	−	28.4749i	−0.976252	−	1.16345i	−0.986543	−	0.163505i	$-0.947720\pi$
$599$	−23.8933	−	28.4749i	−0.976252	−	1.16345i	0.0102905	−	0.999947i	$-0.496724\pi$
$600$		0			0
$601$	−42.7015	+	15.5421i	−1.74183	+	0.633974i	−0.999355	−	0.0359013i	$-0.988570\pi$
$601$	−42.7015	+	15.5421i	−1.74183	+	0.633974i	−0.742474	+	0.669875i	$0.766348\pi$
$602$	−18.7883	+	10.8474i	−0.765753	+	0.442108i
$603$		0			0
$604$	0.106495	−	0.603963i	0.00433322	−	0.0245749i
$605$	11.5748	+	24.8223i	0.470583	+	1.00917i
$606$		0			0
$607$	−1.76803	−	20.2086i	−0.0717620	−	0.820243i	−0.943738	−	0.330695i	$-0.892717\pi$
$607$	−1.76803	−	20.2086i	−0.0717620	−	0.820243i	0.871976	−	0.489549i	$-0.162839\pi$
$608$	0.285129	−	0.339804i	0.0115635	−	0.0137809i
$609$		0			0
$610$	6.27991	−	8.96864i	0.254266	−	0.363130i
$611$	14.4257	−	20.6021i	0.583603	−	0.833472i
$612$		0			0
$613$	−8.10272	+	9.65644i	−0.327266	+	0.390020i	−0.904440	−	0.426601i	$-0.859711\pi$
$613$	−8.10272	+	9.65644i	−0.327266	+	0.390020i	0.577174	+	0.816621i	$0.304155\pi$
$614$	2.11428	+	24.1663i	0.0853253	+	0.975272i
$615$		0			0
$616$	4.49230	+	9.63378i	0.181000	+	0.388156i
$617$	−5.34176	+	30.2946i	−0.215051	+	1.21962i	0.665767	+	0.746160i	$0.268105\pi$
$617$	−5.34176	+	30.2946i	−0.215051	+	1.21962i	−0.880818	+	0.473456i	$0.843006\pi$
$618$		0			0
$619$	4.52235	−	2.61098i	0.181768	−	0.104944i	−0.406355	−	0.913715i	$-0.633200\pi$
$619$	4.52235	−	2.61098i	0.181768	−	0.104944i	0.588123	+	0.808771i	$0.299867\pi$
$620$	10.9908	−	4.00031i	0.441399	−	0.160656i
$621$		0			0
$622$	1.23126	+	1.46736i	0.0493689	+	0.0588356i
$623$	−0.868691	+	0.868691i	−0.0348034	+	0.0348034i
$624$		0			0
$625$	−6.87879	−	2.50367i	−0.275151	−	0.100147i
$626$	−17.7134	+	3.12334i	−0.707968	+	0.124834i
$627$		0			0
$628$			7.13250i			0.284618i
$629$	29.3736	+	17.2866i	1.17120	+	0.689261i
$630$		0			0
$631$	−12.1428	+	8.50250i	−0.483399	+	0.338479i	−0.789739	−	0.613443i	$-0.789784\pi$
$631$	−12.1428	+	8.50250i	−0.483399	+	0.338479i	0.306341	+	0.951922i	$0.400895\pi$
$632$	2.55047	+	14.4645i	0.101452	+	0.575365i
$633$		0			0
$634$	−1.61189	+	18.4240i	−0.0640162	+	0.731709i
$635$	−1.74573	−	1.74573i	−0.0692773	−	0.0692773i
$636$		0			0
$637$	3.83709	+	14.3202i	0.152031	+	0.567388i
$638$	−13.4038	−	36.8267i	−0.530662	−	1.45798i
$639$		0			0
$640$	1.39862	+	0.807495i	0.0552854	+	0.0319191i
$641$	−13.0347	−	2.29837i	−0.514839	−	0.0907801i	−0.0898087	−	0.995959i	$-0.528626\pi$
$641$	−13.0347	−	2.29837i	−0.514839	−	0.0907801i	−0.425031	+	0.905179i	$0.639737\pi$
$642$		0			0
$643$	−1.97118	+	7.35655i	−0.0777358	+	0.290114i	−0.993840	−	0.110827i	$-0.964650\pi$
$643$	−1.97118	+	7.35655i	−0.0777358	+	0.290114i	0.916104	+	0.400941i	$0.131317\pi$
$644$	11.7120	−	1.02467i	0.461518	−	0.0403776i
$645$		0			0
$646$	−1.05040	+	2.25260i	−0.0413276	+	0.0886273i
$647$	21.2126	+	14.8532i	0.833952	+	0.583939i	0.910680	−	0.413113i	$-0.135558\pi$
$647$	21.2126	+	14.8532i	0.833952	+	0.583939i	−0.0767281	+	0.997052i	$0.524447\pi$
$648$		0			0
$649$	−33.8658	−	15.7919i	−1.32935	−	0.619885i
$650$	9.18093	+	7.70372i	0.360106	+	0.302165i
$651$		0			0
$652$	−9.60554	−	2.57380i	−0.376182	−	0.100798i
$653$	3.17955	−	1.48265i	0.124425	−	0.0580205i	−0.359409	−	0.933180i	$-0.617022\pi$
$653$	3.17955	−	1.48265i	0.124425	−	0.0580205i	0.483834	+	0.875160i	$0.339244\pi$
$654$		0			0
$655$	−3.53522	+	6.12319i	−0.138133	+	0.239253i
$656$	−3.41338	−	5.91216i	−0.133270	−	0.230831i
$657$		0			0
$658$	−9.74642	+	2.61154i	−0.379955	+	0.101809i
$659$	−29.4951	+	24.7493i	−1.14896	+	0.964096i	−0.999695	−	0.0247007i	$-0.992137\pi$
$659$	−29.4951	+	24.7493i	−1.14896	+	0.964096i	−0.149270	+	0.988797i	$0.547692\pi$
$660$		0			0
$661$	29.0548	+	2.54197i	1.13010	+	0.0988711i	0.636830	−	0.771004i	$-0.280245\pi$
$661$	29.0548	+	2.54197i	1.13010	+	0.0988711i	0.493272	+	0.869875i	$0.335801\pi$
$662$	4.40673	−	12.1074i	0.171272	−	0.470567i
$663$		0			0
$664$	−6.72876	−	9.60967i	−0.261127	−	0.372928i
$665$	1.44014			0.0558463
$666$		0			0
$667$	−43.3454			−1.67834
$668$	−13.7572	−	19.6474i	−0.532284	−	0.760180i
$669$		0			0
$670$	3.40870	−	9.36532i	0.131689	−	0.361814i
$671$	35.7105	+	3.12426i	1.37859	+	0.120611i
$672$		0			0
$673$	31.4280	−	26.3713i	1.21146	−	1.01654i	0.212235	−	0.977219i	$-0.431926\pi$
$673$	31.4280	−	26.3713i	1.21146	−	1.01654i	0.999227	−	0.0393187i	$-0.0125188\pi$
$674$	−5.01434	+	1.34359i	−0.193145	+	0.0517531i
$675$		0			0
$676$	6.05407	+	10.4860i	0.232849	+	0.403306i
$677$	−8.58666	+	14.8725i	−0.330012	+	0.571598i	−0.982514	−	0.186190i	$-0.940386\pi$
$677$	−8.58666	+	14.8725i	−0.330012	+	0.571598i	0.652502	+	0.757787i	$0.273719\pi$
$678$		0			0
$679$	−18.9077	+	8.81683i	−0.725613	+	0.338359i
$680$	−8.74074	−	2.34207i	−0.335192	−	0.0898144i
$681$		0			0
$682$	29.3349	+	24.6149i	1.12329	+	0.942554i
$683$	−38.9760	−	18.1748i	−1.49138	−	0.695440i	−0.505487	−	0.862834i	$-0.668687\pi$
$683$	−38.9760	−	18.1748i	−1.49138	−	0.695440i	−0.985890	+	0.167394i	$0.946465\pi$
$684$		0			0
$685$	−5.07608	−	3.55431i	−0.193947	−	0.135803i
$686$	8.46080	−	18.1443i	0.323035	−	0.692751i
$687$		0			0
$688$	−10.7508	+	0.940570i	−0.409869	+	0.0358589i
$689$	15.4205	−	57.5502i	0.587475	−	2.19249i
$690$		0			0
$691$	35.7513	+	6.30392i	1.36004	+	0.239813i	0.805626	−	0.592425i	$-0.201829\pi$
$691$	35.7513	+	6.30392i	1.36004	+	0.239813i	0.554419	+	0.832238i	$0.312940\pi$
$692$	10.6851	+	6.16904i	0.406186	+	0.234512i
$693$		0			0
$694$	−1.39339	−	3.82831i	−0.0528924	−	0.145321i
$695$	−6.02262	−	22.4767i	−0.228451	−	0.852590i
$696$		0			0
$697$	27.0480	+	27.0480i	1.02451	+	1.02451i
$698$	1.18629	−	13.5593i	0.0449016	−	0.513227i
$699$		0			0
$700$	−0.834944	−	4.73520i	−0.0315579	−	0.178974i
$701$	−11.9407	+	8.36099i	−0.450995	+	0.315790i	−0.776913	−	0.629608i	$-0.783216\pi$
$701$	−11.9407	+	8.36099i	−0.450995	+	0.315790i	0.325918	+	0.945398i	$0.394327\pi$
$702$		0			0
$703$	−2.05243	−	1.75152i	−0.0774089	−	0.0660600i
$704$			5.28761i			0.199284i
$705$		0			0
$706$	1.59488	−	0.281221i	0.0600241	−	0.0105839i
$707$	−7.69205	−	2.79968i	−0.289289	−	0.105293i
$708$		0			0
$709$	7.98129	−	7.98129i	0.299744	−	0.299744i	−0.541170	−	0.840913i	$-0.682018\pi$
$709$	7.98129	−	7.98129i	0.299744	−	0.299744i	0.840913	+	0.541170i	$0.182018\pi$
$710$	−1.57306	−	1.87470i	−0.0590360	−	0.0703564i
$711$		0			0
$712$	−0.574255	+	0.209012i	−0.0215211	+	0.00783305i
$713$	36.6799	−	21.1772i	1.37367	−	0.793091i
$714$		0			0
$715$	7.43031	−	42.1394i	0.277878	−	1.57592i
$716$	−4.27699	−	9.17203i	−0.159839	−	0.342775i
$717$		0			0
$718$	−0.238267	−	2.72340i	−0.00889205	−	0.101637i
$719$	−16.3215	+	19.4512i	−0.608690	+	0.725408i	−0.979082	−	0.203467i	$-0.934779\pi$
$719$	−16.3215	+	19.4512i	−0.608690	+	0.725408i	0.370392	+	0.928876i	$0.379223\pi$
$720$		0			0
$721$	−5.49786	+	7.85176i	−0.204751	+	0.292415i
$722$	−10.7851	+	15.4027i	−0.401380	+	0.573229i
$723$		0			0
$724$	15.2307	−	18.1512i	0.566043	−	0.674583i
$725$	1.54504	+	17.6599i	0.0573812	+	0.655871i
$726$		0			0
$727$	−3.73661	−	8.01319i	−0.138583	−	0.297193i	0.824751	−	0.565496i	$-0.191315\pi$
$727$	−3.73661	−	8.01319i	−0.138583	−	0.297193i	−0.963335	+	0.268303i	$0.913537\pi$
$728$	1.74920	−	9.92019i	0.0648296	−	0.367667i
$729$		0			0
$730$	−11.6374	+	6.71887i	−0.430720	+	0.248676i
$731$	56.8218	−	20.6814i	2.10163	−	0.764931i
$732$		0			0
$733$	−24.2840	−	28.9405i	−0.896948	−	1.06894i	−0.997259	−	0.0739853i	$-0.976428\pi$
$733$	−24.2840	−	28.9405i	−0.896948	−	1.06894i	0.100311	−	0.994956i	$-0.468016\pi$
$734$	3.12125	−	3.12125i	0.115207	−	0.115207i
$735$		0			0
$736$	5.49556	+	2.00022i	0.202569	+	0.0737291i
$737$	32.1349	−	5.66626i	1.18371	−	0.208719i
$738$		0			0
$739$			50.6865i			1.86453i	0.361773	+	0.932266i	$0.382171\pi$
$739$			50.6865i			1.86453i	−0.361773	+	0.932266i	$0.617829\pi$
$740$	4.98248	−	8.46630i	0.183159	−	0.311227i
$741$		0			0
$742$	−19.5804	+	13.7103i	−0.718819	+	0.503322i
$743$	5.53715	+	31.4028i	0.203139	+	1.15206i	0.900342	+	0.435183i	$0.143316\pi$
$743$	5.53715	+	31.4028i	0.203139	+	1.15206i	−0.697204	+	0.716873i	$0.745573\pi$
$744$		0			0
$745$	0.399562	−	4.56702i	0.0146388	−	0.167323i
$746$	25.6069	+	25.6069i	0.937534	+	0.937534i
$747$		0			0
$748$	−7.66814	−	28.6179i	−0.280375	−	1.04637i
$749$	7.05130	+	19.3733i	0.257649	+	0.707885i
$750$		0			0
$751$	−31.0917	−	17.9508i	−1.13455	−	0.655034i	−0.189476	−	0.981885i	$-0.560679\pi$
$751$	−31.0917	−	17.9508i	−1.13455	−	0.655034i	−0.945076	+	0.326851i	$0.894012\pi$
$752$	−4.94301	−	0.871586i	−0.180253	−	0.0317835i
$753$		0			0
$754$	−9.61216	+	35.8731i	−0.350054	+	1.30642i
$755$	0.986674	−	0.0863228i	0.0359087	−	0.00314161i
$756$		0			0
$757$	−16.9967	+	36.4495i	−0.617754	+	1.32478i	0.309697	+	0.950835i	$0.399772\pi$
$757$	−16.9967	+	36.4495i	−0.617754	+	1.32478i	−0.927452	+	0.373943i	$0.878006\pi$
$758$	−7.28989	−	5.10443i	−0.264781	−	0.185401i
$759$		0			0
$760$	0.649262	+	0.302756i	0.0235512	+	0.0109821i
$761$	0.414396	+	0.347720i	0.0150219	+	0.0126048i	0.650268	−	0.759705i	$-0.274657\pi$
$761$	0.414396	+	0.347720i	0.0150219	+	0.0126048i	−0.635246	+	0.772310i	$0.719101\pi$
$762$		0			0
$763$	−11.4689	−	3.07308i	−0.415202	−	0.111253i
$764$	−3.90719	+	1.82195i	−0.141357	+	0.0659159i
$765$		0			0
$766$	6.26265	−	10.8472i	0.226279	−	0.391926i
$767$	17.7053	+	30.6665i	0.639301	+	1.10730i
$768$		0			0
$769$	38.3997	−	10.2892i	1.38473	−	0.371037i	0.511891	−	0.859050i	$-0.328945\pi$
$769$	38.3997	−	10.2892i	1.38473	−	0.371037i	0.872836	+	0.488013i	$0.162278\pi$
$770$	−13.1506	+	11.0346i	−0.473914	+	0.397661i
$771$		0			0
$772$	10.6706	+	0.933556i	0.384043	+	0.0335994i
$773$	−3.27444	+	8.99645i	−0.117773	+	0.323580i	−0.984547	−	0.175123i	$-0.943968\pi$
$773$	−3.27444	+	8.99645i	−0.117773	+	0.323580i	0.866773	+	0.498703i	$0.166190\pi$
$774$		0			0
$775$	−9.93547	−	14.1893i	−0.356893	−	0.509695i
$776$	−10.3777			−0.372539
$777$		0			0
$778$	10.6246			0.380909
$779$	−1.73692	−	2.48058i	−0.0622317	−	0.0888761i
$780$		0			0
$781$	2.74044	−	7.52929i	0.0980605	−	0.269419i
$782$	−32.6441	−	2.85599i	−1.16735	−	0.102130i
$783$		0			0
$784$	2.26648	−	1.90181i	0.0809459	−	0.0679216i
$785$	−11.1264	+	2.98131i	−0.397119	+	0.106408i
$786$		0			0
$787$	−19.2930	−	33.4164i	−0.687720	−	1.19117i	−0.972574	−	0.232595i	$-0.925278\pi$
$787$	−19.2930	−	33.4164i	−0.687720	−	1.19117i	0.284854	−	0.958571i	$-0.408055\pi$
$788$	2.07420	−	3.59261i	0.0738902	−	0.127982i
$789$		0			0
$790$	−21.4979	+	10.0246i	−0.764862	+	0.356661i
$791$	37.7322	+	10.1103i	1.34160	+	0.359481i
$792$		0			0
$793$	−26.0228	−	21.8357i	−0.924095	−	0.775408i
$794$	−4.79419	−	2.23557i	−0.170139	−	0.0793373i
$795$		0			0
$796$	−9.22039	−	6.45619i	−0.326808	−	0.228833i
$797$	−10.7437	+	23.0399i	−0.380560	+	0.816114i	0.618968	+	0.785416i	$0.287551\pi$
$797$	−10.7437	+	23.0399i	−0.380560	+	0.816114i	−0.999529	+	0.0306983i	$0.990227\pi$
$798$		0			0
$799$	28.0168	−	2.45115i	0.991162	−	0.0867155i
$800$	0.619044	−	2.31031i	0.0218865	−	0.0816816i
$801$		0			0
$802$	−19.4082	−	3.42219i	−0.685327	−	0.120842i
$803$	−38.1018	−	21.9981i	−1.34458	−	0.776296i
$804$		0			0
$805$	6.49395	+	17.8420i	0.228882	+	0.628848i
$806$	−9.39236	−	35.0528i	−0.330832	−	1.23468i
$807$		0			0
$808$	−2.87925	−	2.87925i	−0.101292	−	0.101292i
$809$	3.50975	−	40.1166i	0.123396	−	1.41042i	−0.641921	−	0.766771i	$-0.721862\pi$
$809$	3.50975	−	40.1166i	0.123396	−	1.41042i	0.765317	−	0.643653i	$-0.222582\pi$
$810$		0			0
$811$	3.64567	+	20.6756i	0.128017	+	0.726019i	0.979470	+	0.201589i	$0.0646104\pi$
$811$	3.64567	+	20.6756i	0.128017	+	0.726019i	−0.851454	+	0.524430i	$0.824278\pi$
$812$	12.2052	−	8.54614i	0.428317	−	0.299911i
$813$		0			0
$814$	32.1622	+	0.267827i	1.12728	+	0.00938733i
$815$		−	16.0601i		−	0.562560i
$816$		0			0
$817$	−4.71434	+	0.831265i	−0.164934	+	0.0290823i
$818$	−18.0607	−	6.57357i	−0.631479	−	0.229840i
$819$		0			0
$820$	7.79597	−	7.79597i	0.272247	−	0.272247i
$821$	−16.7207	−	19.9269i	−0.583556	−	0.695454i	0.390798	−	0.920476i	$-0.372199\pi$
$821$	−16.7207	−	19.9269i	−0.583556	−	0.695454i	−0.974354	+	0.225022i	$0.927755\pi$
$822$		0			0
$823$	3.26998	−	1.19018i	0.113984	−	0.0414869i	−0.284398	−	0.958706i	$-0.591794\pi$
$823$	3.26998	−	1.19018i	0.113984	−	0.0414869i	0.398383	+	0.917219i	$0.369572\pi$
$824$	−4.12926	+	2.38403i	−0.143850	+	0.0830515i
$825$		0			0
$826$	2.46693	−	13.9907i	0.0858356	−	0.486798i
$827$	20.3961	+	43.7397i	0.709243	+	1.52098i	0.847624	+	0.530598i	$0.178032\pi$
$827$	20.3961	+	43.7397i	0.709243	+	1.52098i	−0.138381	+	0.990379i	$0.544190\pi$
$828$		0			0
$829$	2.92322	+	33.4125i	0.101528	+	1.16047i	0.860538	+	0.509387i	$0.170128\pi$
$829$	2.92322	+	33.4125i	0.101528	+	1.16047i	−0.759010	+	0.651079i	$0.774317\pi$
$830$	12.1782	−	14.5134i	0.422710	−	0.503766i
$831$		0			0
$832$	2.87408	−	4.10461i	0.0996407	−	0.142302i
$833$	−9.50877	+	13.5799i	−0.329459	+	0.470517i
$834$		0			0
$835$	24.8988	−	29.6732i	0.861657	−	1.02688i
$836$	0.204423	+	2.33656i	0.00707011	+	0.0808117i
$837$		0			0
$838$	1.30820	+	2.80544i	0.0451909	+	0.0969123i
$839$	2.81254	−	15.9507i	0.0970997	−	0.550680i	−0.896984	−	0.442063i	$-0.854247\pi$
$839$	2.81254	−	15.9507i	0.0970997	−	0.550680i	0.994084	−	0.108617i	$-0.0346422\pi$
$840$		0			0
$841$	−22.4588	+	12.9666i	−0.774441	+	0.447124i
$842$	30.6822	−	11.1674i	1.05738	−	0.384854i
$843$		0			0
$844$	−1.65220	−	1.96902i	−0.0568711	−	0.0677764i
$845$	−13.8271	+	13.8271i	−0.475668	+	0.475668i
$846$		0			0
$847$	−32.0363	−	11.6603i	−1.10078	−	0.400652i
$848$	−11.7097	+	2.06474i	−0.402114	+	0.0709035i
$849$		0			0
$850$			13.4017i			0.459674i
$851$	12.4448	−	33.3257i	0.426602	−	1.14239i
$852$		0			0
$853$	36.1467	−	25.3102i	1.23764	−	0.866605i	0.243003	−	0.970026i	$-0.421867\pi$
$853$	36.1467	−	25.3102i	1.23764	−	0.866605i	0.994638	+	0.103420i	$0.0329786\pi$
$854$	2.36659	+	13.4216i	0.0809831	+	0.459278i
$855$		0			0
$856$	−0.893825	+	10.2165i	−0.0305503	+	0.349191i
$857$	25.1749	+	25.1749i	0.859959	+	0.859959i	0.991333	−	0.131374i	$-0.0419390\pi$
$857$	25.1749	+	25.1749i	0.859959	+	0.859959i	−0.131374	+	0.991333i	$0.541939\pi$
$858$		0			0
$859$	−11.8608	−	44.2652i	−0.404686	−	1.51031i	−0.804635	−	0.593770i	$-0.797639\pi$
$859$	−11.8608	−	44.2652i	−0.404686	−	1.51031i	0.399949	−	0.916537i	$-0.369028\pi$
$860$	−5.96097	−	16.3776i	−0.203267	−	0.558472i
$861$		0			0
$862$	−29.6006	−	17.0899i	−1.00820	−	0.582084i
$863$	−17.7169	−	3.12397i	−0.603090	−	0.106341i	−0.136237	−	0.990676i	$-0.543501\pi$
$863$	−17.7169	−	3.12397i	−0.603090	−	0.106341i	−0.466852	+	0.884335i	$0.654612\pi$
$864$		0			0
$865$	−5.15720	+	19.2469i	−0.175350	+	0.654415i
$866$	1.95897	−	0.171388i	0.0665685	−	0.00582398i
$867$		0			0
$868$	−6.15292	+	13.1950i	−0.208844	+	0.447867i
$869$	−63.6172	−	44.5453i	−2.15807	−	1.51109i
$870$		0			0
$871$	−28.0253	−	13.0684i	−0.949600	−	0.442806i
$872$	−4.52450	−	3.79650i	−0.153219	−	0.128566i
$873$		0			0
$874$	2.50579	+	0.671423i	0.0847594	+	0.0227112i
$875$	21.7499	−	10.1422i	0.735281	−	0.342867i
$876$		0			0
$877$	6.37127	−	11.0354i	0.215143	−	0.372638i	−0.738174	−	0.674610i	$-0.764312\pi$
$877$	6.37127	−	11.0354i	0.215143	−	0.372638i	0.953317	+	0.301972i	$0.0976451\pi$
$878$	18.1713	+	31.4736i	0.613252	+	1.06218i
$879$		0			0
$880$	−8.24847	+	2.21017i	−0.278056	+	0.0745048i
$881$	−38.9554	+	32.6875i	−1.31244	+	1.10127i	−0.324592	+	0.945854i	$0.605227\pi$
$881$	−38.9554	+	32.6875i	−1.31244	+	1.10127i	−0.987849	+	0.155415i	$0.950329\pi$
$882$		0			0
$883$	−39.7065	−	3.47387i	−1.33623	−	0.116905i	−0.603467	−	0.797388i	$-0.706214\pi$
$883$	−39.7065	−	3.47387i	−1.33623	−	0.116905i	−0.732764	+	0.680483i	$0.761770\pi$
$884$	−9.60270	+	26.3832i	−0.322974	+	0.887363i
$885$		0			0
$886$	−1.25600	−	1.79376i	−0.0421962	−	0.0602625i
$887$	−28.3940			−0.953378			−0.476689	−	0.879072i	$-0.658163\pi$
$887$	−28.3940			−0.953378			−0.476689	+	0.879072i	$0.658163\pi$
$888$		0			0
$889$	3.07315			0.103070
$890$	−0.566084	−	0.808451i	−0.0189752	−	0.0270993i
$891$		0			0
$892$	−3.07549	+	8.44985i	−0.102975	+	0.282922i
$893$	−2.21798	−	0.194048i	−0.0742219	−	0.00649358i
$894$		0			0
$895$	12.5203	−	10.5058i	0.418507	−	0.351169i
$896$	−1.94180	+	0.520305i	−0.0648711	+	0.0173822i
$897$		0			0
$898$	9.31864	+	16.1404i	0.310967	+	0.538611i
$899$	26.8385	−	46.4857i	0.895115	−	1.55039i
$900$		0			0
$901$	60.3817	−	28.1565i	2.01161	−	0.938028i
$902$	34.8673	+	9.34267i	1.16095	+	0.311077i
$903$		0			0
$904$	14.8854	+	12.4903i	0.495081	+	0.415422i
$905$	34.6814	+	16.1722i	1.15285	+	0.537582i
$906$		0			0
$907$	46.2137	+	32.3592i	1.53450	+	1.07447i	0.968171	+	0.250289i	$0.0805256\pi$
$907$	46.2137	+	32.3592i	1.53450	+	1.07447i	0.566329	+	0.824179i	$0.308363\pi$
$908$	6.36826	−	13.6568i	0.211338	−	0.453216i
$909$		0			0
$910$	16.2063	−	1.41786i	0.537232	−	0.0470018i
$911$	2.07080	−	7.72832i	0.0686086	−	0.256051i	−0.923100	−	0.384561i	$-0.874353\pi$
$911$	2.07080	−	7.72832i	0.0686086	−	0.256051i	0.991708	+	0.128510i	$0.0410195\pi$
$912$		0			0
$913$	61.0879	+	10.7714i	2.02171	+	0.356483i
$914$	17.3099	+	9.99390i	0.572562	+	0.330569i
$915$		0			0
$916$	8.71111	+	23.9336i	0.287823	+	0.790788i
$917$	−2.27790	−	8.50123i	−0.0752228	−	0.280735i
$918$		0			0
$919$	34.0204	+	34.0204i	1.12223	+	1.12223i	0.991406	+	0.130823i	$0.0417620\pi$
$919$	34.0204	+	34.0204i	1.12223	+	1.12223i	0.130823	+	0.991406i	$0.458238\pi$
$920$	−0.823175	+	9.40893i	−0.0271393	+	0.310203i
$921$		0			0
$922$	1.02706	+	5.82477i	0.0338246	+	0.191829i
$923$	−6.21986	+	4.35519i	−0.204729	+	0.143353i
$924$		0			0
$925$	−14.0212	−	3.88239i	−0.461014	−	0.127652i
$926$		−	16.4284i		−	0.539870i
$927$		0			0
$928$	7.29909	−	1.28703i	0.239604	−	0.0422487i
$929$	−48.6559	−	17.7093i	−1.59635	−	0.581023i	−0.617672	−	0.786436i	$-0.711924\pi$
$929$	−48.6559	−	17.7093i	−1.59635	−	0.581023i	−0.978675	+	0.205413i	$0.934146\pi$
$930$		0			0
$931$	0.928021	−	0.928021i	0.0304147	−	0.0304147i
$932$	8.15853	+	9.72296i	0.267242	+	0.318486i
$933$		0			0
$934$	−5.98459	+	2.17821i	−0.195822	+	0.0712733i
$935$	41.4376	−	23.9240i	1.35515	−	0.782398i
$936$		0			0
$937$	6.99876	−	39.6919i	0.228640	−	1.29668i	−0.626964	−	0.779048i	$-0.715703\pi$
$937$	6.99876	−	39.6919i	0.228640	−	1.29668i	0.855604	−	0.517631i	$-0.173186\pi$
$938$	5.24296	+	11.2436i	0.171189	+	0.367115i
$939$		0			0
$940$	−0.706490	−	8.07522i	−0.0230432	−	0.263384i
$941$	4.06282	−	4.84188i	0.132444	−	0.157841i	−0.695746	−	0.718288i	$-0.744926\pi$
$941$	4.06282	−	4.84188i	0.132444	−	0.157841i	0.828190	+	0.560447i	$0.189371\pi$
$942$		0			0
$943$	22.8999	−	32.7044i	0.745722	−	1.06500i
$944$	4.05338	−	5.78883i	0.131926	−	0.188410i
$945$		0			0
$946$	36.6794	−	43.7128i	1.19255	−	1.42123i
$947$	3.87291	+	44.2676i	0.125853	+	1.43850i	0.752187	+	0.658949i	$0.228999\pi$
$947$	3.87291	+	44.2676i	0.125853	+	1.43850i	−0.626335	+	0.779554i	$0.715446\pi$
$948$		0			0
$949$	17.6202	+	37.7867i	0.571977	+	1.22661i
$950$	0.184234	−	1.04484i	0.00597734	−	0.0338992i
$951$		0			0
$952$	9.75498	−	5.63204i	0.316161	−	0.182535i
$953$	−25.8223	+	9.39854i	−0.836465	+	0.304448i	−0.724510	−	0.689265i	$-0.757934\pi$
$953$	−25.8223	+	9.39854i	−0.836465	+	0.304448i	−0.111956	+	0.993713i	$0.535711\pi$
$954$		0			0
$955$	−4.47534	−	5.33350i	−0.144819	−	0.172588i
$956$	11.7308	−	11.7308i	0.379401	−	0.379401i
$957$		0			0
$958$	17.1850	+	6.25481i	0.555221	+	0.202084i
$959$	7.59638	−	1.33945i	0.245300	−	0.0432530i
$960$		0			0
$961$			21.4497i			0.691925i
$962$	−24.8209	−	17.6896i	−0.800259	−	0.570337i
$963$		0			0
$964$	−4.85829	+	3.40181i	−0.156475	+	0.109565i
$965$	3.00390	+	17.0359i	0.0966988	+	0.548406i
$966$		0			0
$967$	3.54538	−	40.5239i	0.114012	−	1.30316i	−0.696550	−	0.717508i	$-0.745282\pi$
$967$	3.54538	−	40.5239i	0.114012	−	1.30316i	0.810562	−	0.585653i	$-0.199162\pi$
$968$	−11.9917	−	11.9917i	−0.385428	−	0.385428i
$969$		0			0
$970$	−4.33779	−	16.1889i	−0.139278	−	0.519793i
$971$	0.0161464	+	0.0443619i	0.000518162	+	0.00142364i	0.939951	−	0.341308i	$-0.110870\pi$
$971$	0.0161464	+	0.0443619i	0.000518162	+	0.00142364i	−0.939433	+	0.342732i	$0.888648\pi$
$972$		0			0
$973$	25.0848	+	14.4827i	0.804182	+	0.464295i
$974$	−36.2956	−	6.39990i	−1.16299	−	0.205066i
$975$		0			0
$976$	−1.75464	+	6.54841i	−0.0561647	+	0.209609i
$977$	−50.8959	+	4.45281i	−1.62830	+	0.142458i	−0.864377	−	0.502845i	$-0.832287\pi$
$977$	−50.8959	+	4.45281i	−1.62830	+	0.142458i	−0.763927	+	0.645303i	$0.776731\pi$
$978$		0			0
$979$	1.36561	−	2.92856i	0.0436451	−	0.0935972i
$980$	3.91411	+	2.74069i	0.125032	+	0.0875482i
$981$		0			0
$982$	13.7378	+	6.40602i	0.438390	+	0.204424i
$983$	35.1130	+	29.4633i	1.11993	+	0.939734i	0.998601	−	0.0528776i	$-0.0168393\pi$
$983$	35.1130	+	29.4633i	1.11993	+	0.939734i	0.121331	+	0.992612i	$0.461284\pi$
$984$		0			0
$985$	6.47133	+	1.73399i	0.206194	+	0.0552495i
$986$	−37.6381	+	17.5509i	−1.19864	+	0.558935i
$987$		0			0
$988$	1.11135	−	1.92492i	0.0353568	−	0.0612397i
$989$	−31.5567	−	54.6578i	−1.00344	−	1.73802i
$990$		0			0
$991$	14.9237	−	3.99880i	0.474067	−	0.127026i	−0.0138715	−	0.999904i	$-0.504416\pi$
$991$	14.9237	−	3.99880i	0.474067	−	0.127026i	0.487939	+	0.872878i	$0.337749\pi$
$992$	−5.54786	+	4.65521i	−0.176145	+	0.147803i
$993$		0			0
$994$	3.03469	+	0.265501i	0.0962545	+	0.00842118i
$995$	6.21737	−	17.0821i	0.197104	−	0.541538i
$996$		0			0
$997$	−2.17999	−	3.11335i	−0.0690409	−	0.0986007i	0.783147	−	0.621837i	$-0.213613\pi$
$997$	−2.17999	−	3.11335i	−0.0690409	−	0.0986007i	−0.852188	+	0.523236i	$0.824724\pi$
$998$	27.8904			0.882855
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.431.2	yes	96
3.2	odd	2	inner	666.2.bs.b.431.7	yes	96
37.17	odd	36	inner	666.2.bs.b.17.7	yes	96
111.17	even	36	inner	666.2.bs.b.17.2	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.17.2	✓	96	111.17	even	36	inner
666.2.bs.b.17.7	yes	96	37.17	odd	36	inner
666.2.bs.b.431.2	yes	96	1.1	even	1	trivial
666.2.bs.b.431.7	yes	96	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-1.60885 - 0.140756i) q^{5} +(1.53998 - 1.29220i) q^{7} +(0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(-1.60885 - 0.140756i) q^{5} +(1.53998 - 1.29220i) q^{7} +(0.965926 - 0.258819i) q^{8} +(0.807495 + 1.39862i) q^{10} +(-2.64381 + 4.57920i) q^{11} +(4.54133 - 2.11766i) q^{13} +(-1.94180 - 0.520305i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(5.07820 + 2.36800i) q^{17} +(-0.363361 - 0.254428i) q^{19} +(0.682525 - 1.46368i) q^{20} +(5.26749 - 0.460846i) q^{22} +(1.51364 - 5.64898i) q^{23} +(-2.35547 - 0.415332i) q^{25} +(-4.33948 - 2.50540i) q^{26} +(0.687564 + 1.88907i) q^{28} +(-1.91829 - 7.15914i) q^{29} +(5.12102 + 5.12102i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-0.972981 - 5.51805i) q^{34} +(-2.65948 + 1.86218i) q^{35} +(6.05499 + 0.580588i) q^{37} +0.443582i q^{38} +(-1.59046 + 0.280440i) q^{40} +(6.41507 + 2.33489i) q^{41} +(7.63098 - 7.63098i) q^{43} +(-3.39881 - 4.05054i) q^{44} +(-5.49556 + 2.00022i) q^{46} +(4.34681 - 2.50963i) q^{47} +(-0.513770 + 2.91374i) q^{49} +(1.01082 + 2.16771i) q^{50} +(0.436720 + 4.99173i) q^{52} +(7.64299 - 9.10856i) q^{53} +(4.89802 - 6.99510i) q^{55} +(1.15306 - 1.64674i) q^{56} +(-4.76414 + 5.67769i) q^{58} +(0.615917 + 7.03996i) q^{59} +(-2.86510 - 6.14423i) q^{61} +(1.25760 - 7.13219i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-7.60437 + 2.76776i) q^{65} +(-3.96674 - 4.72738i) q^{67} +(-3.96204 + 3.96204i) q^{68} +(3.05082 + 1.11041i) q^{70} +(-1.49231 + 0.263135i) q^{71} +8.32062i q^{73} +(-2.99741 - 5.29297i) q^{74} +(0.363361 - 0.254428i) q^{76} +(1.84583 + 10.4682i) q^{77} +(-1.28011 + 14.6317i) q^{79} +(1.14197 + 1.14197i) q^{80} +(-1.76690 - 6.59415i) q^{82} +(-4.01232 - 11.0238i) q^{83} +(-7.83673 - 4.52454i) q^{85} +(-10.6279 - 1.87398i) q^{86} +(-1.36853 + 5.10744i) q^{88} +(-0.608784 + 0.0532617i) q^{89} +(4.25713 - 9.12944i) q^{91} +(4.79061 + 3.35442i) q^{92} +(-4.54900 - 2.12123i) q^{94} +(0.548780 + 0.460481i) q^{95} +(-10.0241 - 2.68596i) q^{97} +(2.68148 - 1.25039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) 96 * q - 12 * q^13 + 24 * q^19 + 12 * q^22 + 48 * q^31 + 72 * q^34 + 24 * q^37 + 72 * q^43 + 60 * q^46 + 12 * q^52 - 60 * q^55 + 12 * q^58 - 120 * q^61 + 36 * q^67 + 12 * q^70 - 24 * q^76 + 60 * q^79 + 96 * q^82 - 108 * q^85 - 24 * q^88 + 216 * q^91 - 60 * q^94 + 24 * q^97

Introduction

L-functions

Modular forms

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Database

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