LMFDB - Embedded newform 666.2.bs.b.17.2

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			17.2
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.b.431.2

$q$-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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$2$	−0.573576	+	0.819152i	−0.405580	+	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	−	0.939693i	−0.171010	−	0.469846i
$5$	−1.60885	+	0.140756i	−0.719498	+	0.0629479i	−0.441023	−	0.897496i	$-0.645384\pi$
$5$	−1.60885	+	0.140756i	−0.719498	+	0.0629479i	−0.278474	+	0.960444i	$0.589829\pi$
$6$		0			0
$7$	1.53998	+	1.29220i	0.582058	+	0.488405i	0.885622	−	0.464406i	$-0.153732\pi$
$7$	1.53998	+	1.29220i	0.582058	+	0.488405i	−0.303564	+	0.952811i	$0.598177\pi$
$8$	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	−0.921473	−	0.388442i	$-0.873013\pi$
$11$	−2.64381	−	4.57920i	−0.797137	−	1.38068i	0.124336	−	0.992240i	$-0.460320\pi$
$12$		0			0
$13$	4.54133	+	2.11766i	1.25954	+	0.587332i	0.933687	−	0.358089i	$-0.116572\pi$
$13$	4.54133	+	2.11766i	1.25954	+	0.587332i	0.325851	+	0.945421i	$0.394349\pi$
$14$	−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	0.305752	−	0.952111i	$-0.401092\pi$
$17$	5.07820	−	2.36800i	1.23164	−	0.574325i	0.925893	+	0.377786i	$0.123314\pi$
$18$		0			0
$19$	−0.363361	+	0.254428i	−0.0833608	+	0.0583698i	−0.614514	−	0.788906i	$-0.710648\pi$
$19$	−0.363361	+	0.254428i	−0.0833608	+	0.0583698i	0.531153	+	0.847276i	$0.321759\pi$
$20$	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	0.923415	+	0.383803i	$0.125386\pi$
$23$	1.51364	+	5.64898i	0.315616	+	1.17789i	−0.607800	+	0.794090i	$0.707948\pi$
$24$		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	0.522729	+	0.852499i	$0.324914\pi$
$29$	−1.91829	+	7.15914i	−0.356217	+	1.32942i	−0.878946	+	0.476921i	$0.841753\pi$
$30$		0			0
$31$	5.12102	−	5.12102i	0.919762	−	0.919762i	−0.0772495	−	0.997012i	$-0.524614\pi$
$31$	5.12102	−	5.12102i	0.919762	−	0.919762i	0.997012	+	0.0772495i	$0.0246138\pi$
$32$	−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	0.211561	−	0.977365i	$-0.432145\pi$
$41$	6.41507	−	2.33489i	1.00186	−	0.364649i	0.790303	+	0.612716i	$0.209923\pi$
$42$		0			0
$43$	7.63098	+	7.63098i	1.16371	+	1.16371i	0.983656	+	0.180057i	$0.0576281\pi$
$43$	7.63098	+	7.63098i	1.16371	+	1.16371i	0.180057	+	0.983656i	$0.442372\pi$
$44$	−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	0.782318	−	0.622880i	$-0.214037\pi$
$47$	4.34681	+	2.50963i	0.634047	+	0.366067i	−0.148271	+	0.988947i	$0.547371\pi$
$48$		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	0.967049	+	0.254590i	$0.0819405\pi$
$53$	7.64299	+	9.10856i	1.04985	+	1.25116i	0.0827960	+	0.996567i	$0.473615\pi$
$54$		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	−0.844441	−	0.535649i	$-0.820067\pi$
$59$	0.615917	−	7.03996i	0.0801855	−	0.916525i	0.924626	−	0.380876i	$-0.124377\pi$
$60$		0			0
$61$	−2.86510	+	6.14423i	−0.366839	+	0.786688i	0.633082	+	0.774085i	$0.281790\pi$
$61$	−2.86510	+	6.14423i	−0.366839	+	0.786688i	−0.999921	+	0.0126035i	$0.995988\pi$
$62$	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	−0.951839	−	0.306597i	$-0.900810\pi$
$67$	−3.96674	+	4.72738i	−0.484615	+	0.577541i	0.467224	+	0.884139i	$0.345254\pi$
$68$	−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	0.0843922	−	0.996433i	$-0.473105\pi$
$71$	−1.49231	−	0.263135i	−0.177105	−	0.0312284i	−0.261497	+	0.965204i	$0.584216\pi$
$72$		0			0
$73$		−	8.32062i		−	0.973855i	−0.873442	−	0.486928i	$-0.838118\pi$
$73$		−	8.32062i		−	0.973855i	0.873442	−	0.486928i	$-0.161882\pi$
$74$	−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	−0.633184	−	0.774002i	$-0.718252\pi$
$79$	−1.28011	−	14.6317i	−0.144023	−	1.64620i	0.489160	−	0.872194i	$-0.337303\pi$
$80$	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	0.498814	+	0.866709i	$0.333769\pi$
$83$	−4.01232	+	11.0238i	−0.440409	+	1.21002i	−0.939224	+	0.343306i	$0.888453\pi$
$84$		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	0.0548445	−	0.998495i	$-0.482534\pi$
$89$	−0.608784	−	0.0532617i	−0.0645310	−	0.00564573i	−0.119376	+	0.992849i	$0.538089\pi$
$90$		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	−0.728883	−	0.684638i	$-0.759960\pi$
$97$	−10.0241	+	2.68596i	−1.01780	+	0.272717i	−0.288912	+	0.957356i	$0.593294\pi$
$98$	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	−0.949360	−	0.314190i	$-0.898267\pi$
$101$	−2.03594	+	3.52635i	−0.202584	+	0.350885i	0.746777	+	0.665075i	$0.231600\pi$
$102$		0			0
$103$	−4.60559	−	1.23406i	−0.453802	−	0.121596i	0.0246758	−	0.999696i	$-0.492145\pi$
$103$	−4.60559	−	1.23406i	−0.453802	−	0.121596i	−0.478478	+	0.878100i	$0.658811\pi$
$104$	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	−0.985653	−	0.168783i	$-0.946016\pi$
$107$	−3.50758	−	9.63701i	−0.339091	−	0.931645i	0.646562	−	0.762861i	$-0.276206\pi$
$108$		0			0
$109$	−3.38772	+	4.83817i	−0.324485	+	0.463412i	−0.947941	−	0.318446i	$-0.896839\pi$
$109$	−3.38772	+	4.83817i	−0.324485	+	0.463412i	0.623456	+	0.781858i	$0.285728\pi$
$110$	−8.53944			−0.814204
$111$		0			0
$112$	−2.01030			−0.189956
$113$	11.1455	−	15.9174i	1.04848	−	1.49738i	0.191862	−	0.981422i	$-0.438547\pi$
$113$	11.1455	−	15.9174i	1.04848	−	1.49738i	0.856614	−	0.515957i	$-0.172564\pi$
$114$		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	−0.589350	−	0.807878i	$-0.700616\pi$
$127$	1.17105	−	0.982631i	0.103914	−	0.0871944i	0.693265	+	0.720683i	$0.256172\pi$
$128$	−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	0.970405	−	0.241482i	$-0.0776334\pi$
$131$	1.85023	+	3.96782i	0.161655	+	0.346670i	−0.808750	+	0.588152i	$0.799856\pi$
$132$		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	−0.351288	−	0.936267i	$-0.614256\pi$
$137$	3.32296	−	1.91851i	0.283899	−	0.163909i	0.635187	+	0.772358i	$0.280923\pi$
$138$		0			0
$139$	4.92800	−	13.5396i	0.417987	−	1.14841i	−0.534854	−	0.844944i	$-0.679634\pi$
$139$	4.92800	−	13.5396i	0.417987	−	1.14841i	0.952842	−	0.303467i	$-0.0981442\pi$
$140$	−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	$-0.962904\pi$
$149$		−	2.83869i		−	0.232555i	0.993217	−	0.116277i	$-0.0370962\pi$
$150$		0			0
$151$	−0.603963	−	0.106495i	−0.0491499	−	0.00866644i	0.149019	−	0.988834i	$-0.452388\pi$
$151$	−0.603963	−	0.106495i	−0.0491499	−	0.00866644i	−0.198169	+	0.980168i	$0.563499\pi$
$152$	−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	0.595328	−	0.803483i	$-0.297022\pi$
$157$	6.70235	+	2.43946i	0.534906	+	0.194690i	−0.0604216	+	0.998173i	$0.519245\pi$
$158$	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	−0.883599	−	0.468245i	$-0.844887\pi$
$163$	0.866710	−	9.90654i	0.0678860	−	0.775940i	0.951485	−	0.307696i	$-0.0995578\pi$
$164$	−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	−0.837466	−	0.546489i	$-0.815964\pi$
$167$	−13.7572	−	19.6474i	−1.06457	−	1.52036i	−0.227102	−	0.973871i	$-0.572925\pi$
$168$		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	0.951213	+	0.308534i	$0.0998384\pi$
$173$	2.14248	+	12.1506i	0.162890	+	0.923795i	−0.788323	+	0.615261i	$0.789051\pi$
$174$		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	0.387148	−	0.922018i	$-0.373460\pi$
$179$	−7.15607	−	7.15607i	−0.534870	−	0.534870i	−0.922018	+	0.387148i	$0.873460\pi$
$180$		0			0
$181$	−22.2657	+	8.10406i	−1.65500	+	0.602370i	−0.989565	−	0.144087i	$-0.953975\pi$
$181$	−22.2657	+	8.10406i	−1.65500	+	0.602370i	−0.665433	+	0.746457i	$0.731753\pi$
$182$	−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	−0.588165	−	0.808741i	$-0.700150\pi$
$191$	3.04841	−	3.04841i	0.220575	−	0.220575i	0.808741	+	0.588165i	$0.200150\pi$
$192$		0			0
$193$	−2.77230	+	10.3464i	−0.199555	+	0.744748i	0.791486	+	0.611187i	$0.209308\pi$
$193$	−2.77230	+	10.3464i	−0.199555	+	0.744748i	−0.991041	+	0.133561i	$0.957359\pi$
$194$	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	−0.317277	−	0.948333i	$-0.602768\pi$
$197$	−4.08537	+	0.720361i	−0.291070	+	0.0513236i	0.0262063	+	0.999657i	$0.491657\pi$
$198$		0			0
$199$	−2.91327	−	10.8725i	−0.206516	−	0.770729i	−0.988982	−	0.148036i	$-0.952705\pi$
$199$	−2.91327	−	10.8725i	−0.206516	−	0.770729i	0.782466	−	0.622694i	$-0.213962\pi$
$200$	−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	0.818391	−	0.574661i	$-0.194866\pi$
$211$	−1.28518	−	2.22600i	−0.0884757	−	0.153244i	−0.906867	+	0.421417i	$0.861533\pi$
$212$	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	−0.573641	−	0.819107i	$-0.694470\pi$
$227$	−15.0112	+	1.31331i	−0.996331	+	0.0871677i	−0.422690	+	0.906274i	$0.638914\pi$
$228$		0			0
$229$	19.5108	+	16.3715i	1.28931	+	1.08186i	0.991888	+	0.127116i	$0.0405720\pi$
$229$	19.5108	+	16.3715i	1.28931	+	1.08186i	0.297424	+	0.954745i	$0.403872\pi$
$230$	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	0.995507	−	0.0946850i	$-0.0301844\pi$
$233$	6.34621	+	10.9920i	0.415754	+	0.720107i	−0.579753	+	0.814792i	$0.696851\pi$
$234$		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	−0.842916	−	0.538045i	$-0.819163\pi$
$239$	−15.0355	+	7.01117i	−0.972565	+	0.453515i	−0.129649	+	0.991560i	$0.541385\pi$
$240$		0			0
$241$	4.85829	−	3.40181i	0.312950	−	0.219130i	−0.406540	−	0.913633i	$-0.633265\pi$
$241$	4.85829	−	3.40181i	0.312950	−	0.219130i	0.719490	+	0.694503i	$0.244376\pi$
$242$	−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	−0.753450	−	0.657505i	$-0.771612\pi$
$251$	3.60918	−	13.4696i	0.227809	−	0.850195i	0.981260	−	0.192691i	$-0.0617214\pi$
$252$		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	0.925729	−	0.378187i	$-0.123452\pi$
$257$	14.2192	+	9.95637i	0.886967	+	0.621061i	−0.0387618	+	0.999248i	$0.512341\pi$
$258$		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	−0.811273	−	0.584667i	$-0.801225\pi$
$263$	−17.1405	+	6.23863i	−1.05693	+	0.384690i	−0.245655	+	0.969357i	$0.579003\pi$
$264$		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	0.941120	−	0.338072i	$-0.109775\pi$
$269$	18.3513	+	10.5952i	1.11890	+	0.645998i	0.177781	+	0.984070i	$0.443108\pi$
$270$		0			0
$271$	−1.33346	−	7.56242i	−0.0810018	−	0.459384i	−0.998148	−	0.0608331i	$-0.980624\pi$
$271$	−1.33346	−	7.56242i	−0.0810018	−	0.459384i	0.917146	−	0.398551i	$-0.130487\pi$
$272$	−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	−0.988800	−	0.149249i	$-0.952314\pi$
$277$	−13.1625	−	18.7980i	−0.790858	−	1.12946i	0.197941	−	0.980214i	$-0.436574\pi$
$278$	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	0.808912	+	0.587930i	$0.200057\pi$
$281$	−1.50538	+	17.2066i	−0.0898037	+	1.02646i	−0.898716	+	0.438532i	$0.855499\pi$
$282$		0			0
$283$	−11.9844	+	25.7006i	−0.712398	+	1.52774i	0.131546	+	0.991310i	$0.458006\pi$
$283$	−11.9844	+	25.7006i	−0.712398	+	1.52774i	−0.843944	+	0.536432i	$0.819772\pi$
$284$	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	−0.0529698	−	0.998596i	$-0.516869\pi$
$293$	−7.60493	−	1.34096i	−0.444285	−	0.0783394i	−0.391315	+	0.920257i	$0.627980\pi$
$294$		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	−0.960337	−	0.278841i	$-0.910050\pi$
$307$	−21.0086	+	12.1293i	−1.19902	+	0.692256i	−0.238685	+	0.971097i	$0.576716\pi$
$308$	−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	0.0329249	−	0.999458i	$-0.489518\pi$
$311$	−1.90821	−	0.166946i	−0.108204	−	0.00946667i	−0.141129	+	0.989991i	$0.545073\pi$
$312$		0			0
$313$	7.60147	+	16.3014i	0.429661	+	0.921410i	0.995307	+	0.0967626i	$0.0308488\pi$
$313$	7.60147	+	16.3014i	0.429661	+	0.921410i	−0.565647	+	0.824648i	$0.691373\pi$
$314$	−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	−0.947155	−	0.320775i	$-0.896057\pi$
$317$	−14.1675	+	11.8879i	−0.795725	+	0.667693i	0.151430	+	0.988468i	$0.451612\pi$
$318$		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	−0.562977	−	0.826472i	$-0.690344\pi$
$331$	7.39020	−	10.5543i	0.406202	−	0.580117i	0.969180	+	0.246356i	$0.0792331\pi$
$332$	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	0.978611	−	0.205719i	$-0.0659533\pi$
$337$	1.77550	+	4.87816i	0.0967179	+	0.265730i	−0.881893	+	0.471449i	$0.843731\pi$
$338$	−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	−0.151641	−	0.988436i	$-0.548456\pi$
$347$	3.93518	−	1.05443i	0.211252	−	0.0566047i	0.362893	+	0.931831i	$0.381789\pi$
$348$		0			0
$349$	10.4267	−	8.74905i	0.558129	−	0.468326i	−0.319554	−	0.947568i	$-0.603533\pi$
$349$	10.4267	−	8.74905i	0.558129	−	0.468326i	0.877683	+	0.479242i	$0.159088\pi$
$350$	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	0.887252	−	0.461286i	$-0.152612\pi$
$353$	−0.684424	−	1.46775i	−0.0364282	−	0.0781205i	−0.923680	+	0.383165i	$0.874834\pi$
$354$		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	−0.436220	−	0.899840i	$-0.643683\pi$
$359$	2.36755	−	1.36690i	0.124954	−	0.0721424i	0.561174	+	0.827698i	$0.310350\pi$
$360$		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	−0.958245	−	0.285949i	$-0.907691\pi$
$367$	0.766502	−	4.34705i	0.0400111	−	0.226914i	0.998256	+	0.0590349i	$0.0188023\pi$
$368$	−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	−0.862879	−	0.505410i	$-0.831341\pi$
$373$	−35.6634	−	6.28842i	−1.84658	−	0.325602i	−0.983702	+	0.179808i	$0.942452\pi$
$374$	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	0.547746	−	0.836645i	$-0.315486\pi$
$379$	8.36262	+	3.04374i	0.429559	+	0.156347i	−0.118187	+	0.992991i	$0.537708\pi$
$380$	−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	−0.723409	−	0.690419i	$-0.757426\pi$
$383$	5.29342	−	11.3518i	0.270481	−	0.580049i	0.993890	+	0.110371i	$0.0352038\pi$
$384$		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	0.634391	−	0.773012i	$-0.281251\pi$
$389$	−6.09399	−	8.70312i	−0.308978	−	0.441266i	−0.943369	+	0.331747i	$0.892362\pi$
$390$		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	0.610535	−	0.791990i	$-0.290955\pi$
$397$	4.58110	+	2.64490i	0.229919	+	0.132744i	−0.380616	+	0.924733i	$0.624288\pi$
$398$	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	0.963523	−	0.267624i	$-0.0862387\pi$
$401$	13.9354	+	13.9354i	0.695899	+	0.695899i	−0.267624	+	0.963523i	$0.586239\pi$
$402$		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	0.893928	−	0.448211i	$-0.147939\pi$
$409$	15.7440	+	11.0240i	0.778489	+	0.545104i	−0.115439	+	0.993315i	$0.536827\pi$
$410$	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	−0.247614	−	0.968859i	$-0.579646\pi$
$419$	−3.04843	+	0.537521i	−0.148926	+	0.0262596i	0.0986883	+	0.995118i	$0.468535\pi$
$420$		0			0
$421$	−8.45077	−	31.5387i	−0.411865	−	1.53710i	−0.791033	−	0.611774i	$-0.790456\pi$
$421$	−8.45077	−	31.5387i	−0.411865	−	1.53710i	0.379167	−	0.925328i	$-0.376211\pi$
$422$	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	0.986012	−	0.166674i	$-0.0533027\pi$
$431$	30.9774	+	14.4450i	1.49213	+	0.695791i	0.506117	+	0.862465i	$0.331081\pi$
$432$		0			0
$433$	−0.983226	−	1.70300i	−0.0472508	−	0.0818408i	0.841433	−	0.540362i	$-0.181713\pi$
$433$	−0.983226	−	1.70300i	−0.0472508	−	0.0818408i	−0.888684	+	0.458521i	$0.848379\pi$
$434$	−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	−0.907359	−	0.420357i	$-0.861905\pi$
$439$	−36.2043	+	3.16747i	−1.72794	+	0.151175i	−0.820579	+	0.571532i	$0.806349\pi$
$440$	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	−0.516376	−	0.856362i	$-0.672719\pi$
$449$	−18.5664	+	1.62435i	−0.876200	+	0.0766576i	−0.359825	+	0.933020i	$0.617164\pi$
$450$		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	−0.0501015	−	0.998744i	$-0.515954\pi$
$457$	−18.1151	−	8.44721i	−0.847388	−	0.395144i	−0.797287	+	0.603600i	$0.793732\pi$
$458$	−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	−0.543421	−	0.839460i	$-0.682871\pi$
$461$	−5.36047	+	2.49963i	−0.249662	+	0.116419i	0.293759	+	0.955879i	$0.405094\pi$
$462$		0			0
$463$	13.4573	−	9.42294i	0.625416	−	0.437921i	−0.217430	−	0.976076i	$-0.569767\pi$
$463$	13.4573	−	9.42294i	0.625416	−	0.437921i	0.842846	+	0.538155i	$0.180878\pi$
$464$	−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	0.993520	−	0.113661i	$-0.0362579\pi$
$467$	1.64833	+	6.15166i	0.0762757	+	0.284665i	−0.917244	+	0.398326i	$0.869591\pi$
$468$		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	0.178879	−	0.983871i	$-0.442753\pi$
$479$	−14.9805	−	10.4895i	−0.684478	−	0.479276i	−0.863356	+	0.504595i	$0.831642\pi$
$480$		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	0.979504	+	0.201423i	$0.0645566\pi$
$487$	26.0608	+	26.0608i	1.18093	+	1.18093i	0.201423	+	0.979504i	$0.435443\pi$
$488$	−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	0.173633	−	0.984810i	$-0.444449\pi$
$491$	−13.1272	−	7.57897i	−0.592421	−	0.342034i	−0.766054	+	0.642776i	$0.777783\pi$
$492$		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	−0.997995	−	0.0632929i	$-0.979840\pi$
$499$	−15.9973	−	22.8465i	−0.716136	−	1.02275i	0.281859	−	0.959456i	$-0.409049\pi$
$500$	−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	−0.999016	−	0.0443563i	$-0.985876\pi$
$503$	−0.167644	+	1.91618i	−0.00747490	+	0.0854385i	0.991541	+	0.129795i	$0.0414319\pi$
$504$		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	0.314360	−	0.949304i	$-0.398210\pi$
$509$	−1.24147	−	0.451859i	−0.0550273	−	0.0200283i	−0.369387	+	0.929276i	$0.620432\pi$
$510$		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	−0.888228	−	0.459402i	$-0.848064\pi$
$521$	2.36376	−	13.4055i	0.103558	−	0.587308i	0.991786	−	0.127905i	$-0.0408253\pi$
$522$		0			0
$523$	3.09092	+	35.3294i	0.135156	+	1.54485i	0.696679	+	0.717383i	$0.254660\pi$
$523$	3.09092	+	35.3294i	0.135156	+	1.54485i	−0.561522	+	0.827462i	$0.689784\pi$
$524$	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	0.455852	−	0.890055i	$-0.349334\pi$
$541$	30.1363	−	8.07499i	1.29566	−	0.347171i	0.839807	+	0.542884i	$0.182668\pi$
$542$	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	−0.100553	−	0.994932i	$-0.532061\pi$
$547$	−16.0232	−	4.29339i	−0.685101	−	0.183572i	−0.584547	+	0.811360i	$0.698728\pi$
$548$	−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	−0.538163	−	0.842841i	$-0.680882\pi$
$557$	10.3351	−	14.7600i	0.437910	−	0.625401i	0.976074	+	0.217440i	$0.0697705\pi$
$558$		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	0.758316	−	0.651887i	$-0.226022\pi$
$563$	25.8416	+	6.92423i	1.08909	+	0.291822i	0.330777	+	0.943709i	$0.392689\pi$
$564$		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	−0.0875387	−	0.996161i	$-0.527900\pi$
$569$	7.98458	−	2.13946i	0.334731	−	0.0896909i	0.422270	+	0.906470i	$0.361233\pi$
$570$		0			0
$571$	−5.51840	+	4.63049i	−0.230938	+	0.193780i	−0.750912	−	0.660402i	$-0.770386\pi$
$571$	−5.51840	+	4.63049i	−0.230938	+	0.193780i	0.519974	+	0.854182i	$0.325941\pi$
$572$	−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	−0.783504	−	0.621387i	$-0.786570\pi$
$577$	−39.9468	−	3.49489i	−1.66301	−	0.145494i	−0.879504	+	0.475892i	$0.842125\pi$
$578$	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	−0.900544	−	0.434766i	$-0.856831\pi$
$587$	−2.16060	−	24.6958i	−0.0891776	−	1.01930i	0.811366	−	0.584539i	$-0.198724\pi$
$588$		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	$0.0391052\pi$
$593$			5.96828i			0.245088i	−0.992463	+	0.122544i	$0.960895\pi$
$594$		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	0.0102905	+	0.999947i	$0.496724\pi$
$599$	−23.8933	+	28.4749i	−0.976252	+	1.16345i	−0.986543	+	0.163505i	$0.947720\pi$
$600$		0			0
$601$	−42.7015	−	15.5421i	−1.74183	−	0.633974i	−0.742474	−	0.669875i	$-0.766348\pi$
$601$	−42.7015	−	15.5421i	−1.74183	−	0.633974i	−0.999355	+	0.0359013i	$0.988570\pi$
$602$	−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	0.871976	+	0.489549i	$0.162839\pi$
$607$	−1.76803	+	20.2086i	−0.0717620	+	0.820243i	−0.943738	+	0.330695i	$0.892717\pi$
$608$	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	0.577174	−	0.816621i	$-0.304155\pi$
$613$	−8.10272	−	9.65644i	−0.327266	−	0.390020i	−0.904440	+	0.426601i	$0.859711\pi$
$614$	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	−0.880818	−	0.473456i	$-0.843006\pi$
$617$	−5.34176	−	30.2946i	−0.215051	−	1.21962i	0.665767	−	0.746160i	$-0.268105\pi$
$618$		0			0
$619$	4.52235	+	2.61098i	0.181768	+	0.104944i	0.588123	−	0.808771i	$-0.299867\pi$
$619$	4.52235	+	2.61098i	0.181768	+	0.104944i	−0.406355	+	0.913715i	$0.633200\pi$
$620$	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	0.306341	−	0.951922i	$-0.400895\pi$
$631$	−12.1428	−	8.50250i	−0.483399	−	0.338479i	−0.789739	+	0.613443i	$0.789784\pi$
$632$	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	−0.425031	−	0.905179i	$-0.639737\pi$
$641$	−13.0347	+	2.29837i	−0.514839	+	0.0907801i	−0.0898087	+	0.995959i	$0.528626\pi$
$642$		0			0
$643$	−1.97118	−	7.35655i	−0.0777358	−	0.290114i	0.916104	−	0.400941i	$-0.131317\pi$
$643$	−1.97118	−	7.35655i	−0.0777358	−	0.290114i	−0.993840	+	0.110827i	$0.964650\pi$
$644$	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	−0.0767281	−	0.997052i	$-0.524447\pi$
$647$	21.2126	−	14.8532i	0.833952	−	0.583939i	0.910680	+	0.413113i	$0.135558\pi$
$648$		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	0.483834	−	0.875160i	$-0.339244\pi$
$653$	3.17955	+	1.48265i	0.124425	+	0.0580205i	−0.359409	+	0.933180i	$0.617022\pi$
$654$		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	−0.149270	−	0.988797i	$-0.547692\pi$
$659$	−29.4951	−	24.7493i	−1.14896	−	0.964096i	−0.999695	+	0.0247007i	$0.992137\pi$
$660$		0			0
$661$	29.0548	−	2.54197i	1.13010	−	0.0988711i	0.493272	−	0.869875i	$-0.335801\pi$
$661$	29.0548	−	2.54197i	1.13010	−	0.0988711i	0.636830	+	0.771004i	$0.280245\pi$
$662$	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	0.999227	+	0.0393187i	$0.0125188\pi$
$673$	31.4280	+	26.3713i	1.21146	+	1.01654i	0.212235	+	0.977219i	$0.431926\pi$
$674$	−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	0.652502	−	0.757787i	$-0.273719\pi$
$677$	−8.58666	−	14.8725i	−0.330012	−	0.571598i	−0.982514	+	0.186190i	$0.940386\pi$
$678$		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	−0.985890	−	0.167394i	$-0.946465\pi$
$683$	−38.9760	+	18.1748i	−1.49138	+	0.695440i	−0.505487	+	0.862834i	$0.668687\pi$
$684$		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	0.554419	−	0.832238i	$-0.312940\pi$
$691$	35.7513	−	6.30392i	1.36004	−	0.239813i	0.805626	+	0.592425i	$0.201829\pi$
$692$	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	0.325918	−	0.945398i	$-0.394327\pi$
$701$	−11.9407	−	8.36099i	−0.450995	−	0.315790i	−0.776913	+	0.629608i	$0.783216\pi$
$702$		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	0.840913	−	0.541170i	$-0.182018\pi$
$709$	7.98129	+	7.98129i	0.299744	+	0.299744i	−0.541170	+	0.840913i	$0.682018\pi$
$710$	−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	0.370392	−	0.928876i	$-0.379223\pi$
$719$	−16.3215	−	19.4512i	−0.608690	−	0.725408i	−0.979082	+	0.203467i	$0.934779\pi$
$720$		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	−0.963335	−	0.268303i	$-0.913537\pi$
$727$	−3.73661	+	8.01319i	−0.138583	+	0.297193i	0.824751	+	0.565496i	$0.191315\pi$
$728$	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	0.100311	+	0.994956i	$0.468016\pi$
$733$	−24.2840	+	28.9405i	−0.896948	+	1.06894i	−0.997259	+	0.0739853i	$0.976428\pi$
$734$	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	$-0.617829\pi$
$739$		−	50.6865i		−	1.86453i	0.361773	−	0.932266i	$-0.382171\pi$
$740$	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	−0.697204	−	0.716873i	$-0.745573\pi$
$743$	5.53715	−	31.4028i	0.203139	−	1.15206i	0.900342	−	0.435183i	$-0.143316\pi$
$744$		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	−0.945076	−	0.326851i	$-0.894012\pi$
$751$	−31.0917	+	17.9508i	−1.13455	+	0.655034i	−0.189476	+	0.981885i	$0.560679\pi$
$752$	−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	−0.927452	−	0.373943i	$-0.878006\pi$
$757$	−16.9967	−	36.4495i	−0.617754	−	1.32478i	0.309697	−	0.950835i	$-0.399772\pi$
$758$	−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	−0.635246	−	0.772310i	$-0.719101\pi$
$761$	0.414396	−	0.347720i	0.0150219	−	0.0126048i	0.650268	+	0.759705i	$0.274657\pi$
$762$		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	0.872836	−	0.488013i	$-0.162278\pi$
$769$	38.3997	+	10.2892i	1.38473	+	0.371037i	0.511891	+	0.859050i	$0.328945\pi$
$770$	−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	0.866773	−	0.498703i	$-0.166190\pi$
$773$	−3.27444	−	8.99645i	−0.117773	−	0.323580i	−0.984547	+	0.175123i	$0.943968\pi$
$774$		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

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

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