LMFDB - Embedded newform 666.2.bs.b.17.6

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			17.6
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.b.431.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.31281 + 0.114856i) q^{5} +(-1.79970 - 1.51012i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.31281 + 0.114856i) q^{5} +(-1.79970 - 1.51012i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-0.658910 + 1.14127i) q^{10} +(1.26790 + 2.19607i) q^{11} +(-5.68512 - 2.65102i) q^{13} +(-2.26929 + 0.608053i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.17248 - 1.01304i) q^{17} +(-5.10508 + 3.57462i) q^{19} +(0.556935 + 1.19435i) q^{20} +(2.52616 + 0.221010i) q^{22} +(-1.95836 - 7.30871i) q^{23} +(-3.21377 + 0.566675i) q^{25} +(-5.43244 + 3.13642i) q^{26} +(-0.803520 + 2.20765i) q^{28} +(-2.27295 + 8.48275i) q^{29} +(1.77815 - 1.77815i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.416246 - 2.36065i) q^{34} +(2.53610 + 1.77580i) q^{35} +(-6.02076 + 0.866319i) q^{37} +6.23215i q^{38} +(1.29780 + 0.228837i) q^{40} +(10.3026 - 3.74984i) q^{41} +(-0.789016 - 0.789016i) q^{43} +(1.62998 - 1.94254i) q^{44} +(-7.11021 - 2.58791i) q^{46} +(-9.67161 - 5.58391i) q^{47} +(-0.257106 - 1.45812i) q^{49} +(-1.37915 + 2.95760i) q^{50} +(-0.546714 + 6.24897i) q^{52} +(1.18964 + 1.41776i) q^{53} +(-1.91674 - 2.73739i) q^{55} +(1.34752 + 1.92446i) q^{56} +(5.64495 + 6.72739i) q^{58} +(-0.761646 + 8.70565i) q^{59} +(4.69196 - 10.0620i) q^{61} +(-0.436671 - 2.47649i) q^{62} +(0.866025 + 0.500000i) q^{64} +(7.76795 + 2.82730i) q^{65} +(5.02896 - 5.99328i) q^{67} +(-1.69498 - 1.69498i) q^{68} +(2.90929 - 1.05890i) q^{70} +(4.03601 + 0.711657i) q^{71} -10.8547i q^{73} +(-2.74372 + 5.42881i) q^{74} +(5.10508 + 3.57462i) q^{76} +(1.03450 - 5.86695i) q^{77} +(0.818534 + 9.35588i) q^{79} +(0.931840 - 0.931840i) q^{80} +(2.83764 - 10.5902i) q^{82} +(-0.388056 + 1.06617i) q^{83} +(-2.73569 + 1.57945i) q^{85} +(-1.09888 + 0.193763i) q^{86} +(-0.656315 - 2.44940i) q^{88} +(-0.317556 - 0.0277825i) q^{89} +(6.22813 + 13.3563i) q^{91} +(-6.19814 + 4.33998i) q^{92} +(-10.1215 + 4.71972i) q^{94} +(6.29142 - 5.27913i) q^{95} +(12.8298 - 3.43773i) q^{97} +(-1.34189 - 0.625736i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.31281	+	0.114856i	−0.587105	+	0.0513650i	−0.376838	−	0.926279i	$-0.622989\pi$
$5$	−1.31281	+	0.114856i	−0.587105	+	0.0513650i	−0.210267	+	0.977644i	$0.567433\pi$
$6$		0			0
$7$	−1.79970	−	1.51012i	−0.680221	−	0.570773i	0.235850	−	0.971790i	$-0.424213\pi$
$7$	−1.79970	−	1.51012i	−0.680221	−	0.570773i	−0.916071	+	0.401016i	$0.868657\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	−0.658910	+	1.14127i	−0.208366	+	0.360900i
$11$	1.26790	+	2.19607i	0.382287	+	0.662141i	0.991389	−	0.130951i	$-0.0418032\pi$
$11$	1.26790	+	2.19607i	0.382287	+	0.662141i	−0.609102	+	0.793092i	$0.708470\pi$
$12$		0			0
$13$	−5.68512	−	2.65102i	−1.57677	−	0.735260i	−0.579928	−	0.814668i	$-0.696919\pi$
$13$	−5.68512	−	2.65102i	−1.57677	−	0.735260i	−0.996842	+	0.0794083i	$0.974697\pi$
$14$	−2.26929	+	0.608053i	−0.606492	+	0.162509i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	2.17248	−	1.01304i	0.526903	−	0.245699i	−0.140917	−	0.990021i	$-0.545005\pi$
$17$	2.17248	−	1.01304i	0.526903	−	0.245699i	0.667820	+	0.744322i	$0.267227\pi$
$18$		0			0
$19$	−5.10508	+	3.57462i	−1.17119	+	0.820073i	−0.986666	−	0.162755i	$-0.947962\pi$
$19$	−5.10508	+	3.57462i	−1.17119	+	0.820073i	−0.184520	+	0.982829i	$0.559073\pi$
$20$	0.556935	+	1.19435i	0.124534	+	0.267065i
$21$		0			0
$22$	2.52616	+	0.221010i	0.538578	+	0.0471195i
$23$	−1.95836	−	7.30871i	−0.408347	−	1.52397i	−0.797799	−	0.602924i	$-0.794002\pi$
$23$	−1.95836	−	7.30871i	−0.408347	−	1.52397i	0.389452	−	0.921047i	$-0.372665\pi$
$24$		0			0
$25$	−3.21377	+	0.566675i	−0.642754	+	0.113335i
$26$	−5.43244	+	3.13642i	−1.06539	+	0.615103i
$27$		0			0
$28$	−0.803520	+	2.20765i	−0.151851	+	0.417207i
$29$	−2.27295	+	8.48275i	−0.422075	+	1.57521i	0.348152	+	0.937438i	$0.386809\pi$
$29$	−2.27295	+	8.48275i	−0.422075	+	1.57521i	−0.770228	+	0.637769i	$0.779857\pi$
$30$		0			0
$31$	1.77815	−	1.77815i	0.319366	−	0.319366i	−0.529158	−	0.848524i	$-0.677492\pi$
$31$	1.77815	−	1.77815i	0.319366	−	0.319366i	0.848524	+	0.529158i	$0.177492\pi$
$32$	0.0871557	+	0.996195i	0.0154071	+	0.176104i
$33$		0			0
$34$	0.416246	−	2.36065i	0.0713856	−	0.404848i
$35$	2.53610	+	1.77580i	0.428679	+	0.300164i
$36$		0			0
$37$	−6.02076	+	0.866319i	−0.989806	+	0.142422i
$37$	−6.02076	+	0.866319i	−0.989806	+	0.142422i
$38$			6.23215i			1.01099i
$39$		0			0
$40$	1.29780	+	0.228837i	0.205200	+	0.0361823i
$41$	10.3026	−	3.74984i	1.60899	−	0.585626i	0.627753	−	0.778412i	$-0.283975\pi$
$41$	10.3026	−	3.74984i	1.60899	−	0.585626i	0.981241	+	0.192787i	$0.0617525\pi$
$42$		0			0
$43$	−0.789016	−	0.789016i	−0.120324	−	0.120324i	0.644381	−	0.764705i	$-0.277115\pi$
$43$	−0.789016	−	0.789016i	−0.120324	−	0.120324i	−0.764705	+	0.644381i	$0.777115\pi$
$44$	1.62998	−	1.94254i	0.245729	−	0.292849i
$45$		0			0
$46$	−7.11021	−	2.58791i	−1.04834	−	0.381566i
$47$	−9.67161	−	5.58391i	−1.41075	−	0.814496i	−0.415290	−	0.909689i	$-0.636320\pi$
$47$	−9.67161	−	5.58391i	−1.41075	−	0.814496i	−0.995459	+	0.0951926i	$0.969653\pi$
$48$		0			0
$49$	−0.257106	−	1.45812i	−0.0367295	−	0.208303i
$50$	−1.37915	+	2.95760i	−0.195041	+	0.418268i
$51$		0			0
$52$	−0.546714	+	6.24897i	−0.0758156	+	0.866576i
$53$	1.18964	+	1.41776i	0.163409	+	0.194744i	0.841536	−	0.540202i	$-0.181652\pi$
$53$	1.18964	+	1.41776i	0.163409	+	0.194744i	−0.678126	+	0.734946i	$0.737208\pi$
$54$		0			0
$55$	−1.91674	−	2.73739i	−0.258453	−	0.369110i
$56$	1.34752	+	1.92446i	0.180070	+	0.257167i
$57$		0			0
$58$	5.64495	+	6.72739i	0.741219	+	0.883350i
$59$	−0.761646	+	8.70565i	−0.0991579	+	1.13338i	0.769730	+	0.638370i	$0.220391\pi$
$59$	−0.761646	+	8.70565i	−0.0991579	+	1.13338i	−0.868887	+	0.495010i	$0.835165\pi$
$60$		0			0
$61$	4.69196	−	10.0620i	0.600745	−	1.28830i	−0.337173	−	0.941443i	$-0.609471\pi$
$61$	4.69196	−	10.0620i	0.600745	−	1.28830i	0.937918	−	0.346858i	$-0.112751\pi$
$62$	−0.436671	−	2.47649i	−0.0554573	−	0.314514i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	7.76795	+	2.82730i	0.963496	+	0.350684i
$66$		0			0
$67$	5.02896	−	5.99328i	0.614385	−	0.732196i	−0.365709	−	0.930729i	$-0.619173\pi$
$67$	5.02896	−	5.99328i	0.614385	−	0.732196i	0.980094	+	0.198534i	$0.0636179\pi$
$68$	−1.69498	−	1.69498i	−0.205547	−	0.205547i
$69$		0			0
$70$	2.90929	−	1.05890i	0.347727	−	0.126562i
$71$	4.03601	+	0.711657i	0.478986	+	0.0844582i	0.407928	−	0.913014i	$-0.366251\pi$
$71$	4.03601	+	0.711657i	0.478986	+	0.0844582i	0.0710580	+	0.997472i	$0.477362\pi$
$72$		0			0
$73$		−	10.8547i		−	1.27044i	−0.772330	−	0.635222i	$-0.780909\pi$
$73$		−	10.8547i		−	1.27044i	0.772330	−	0.635222i	$-0.219091\pi$
$74$	−2.74372	+	5.42881i	−0.318951	+	0.631087i
$75$		0			0
$76$	5.10508	+	3.57462i	0.585593	+	0.410037i
$77$	1.03450	−	5.86695i	0.117892	−	0.668601i
$78$		0			0
$79$	0.818534	+	9.35588i	0.0920922	+	1.05262i	0.891861	+	0.452310i	$0.149400\pi$
$79$	0.818534	+	9.35588i	0.0920922	+	1.05262i	−0.799768	+	0.600309i	$0.795044\pi$
$80$	0.931840	−	0.931840i	0.104183	−	0.104183i
$81$		0			0
$82$	2.83764	−	10.5902i	0.313365	−	1.16949i
$83$	−0.388056	+	1.06617i	−0.0425947	+	0.117028i	−0.959166	−	0.282842i	$-0.908723\pi$
$83$	−0.388056	+	1.06617i	−0.0425947	+	0.117028i	0.916572	+	0.399870i	$0.130945\pi$
$84$		0			0
$85$	−2.73569	+	1.57945i	−0.296727	+	0.171315i
$86$	−1.09888	+	0.193763i	−0.118496	+	0.0208940i
$87$		0			0
$88$	−0.656315	−	2.44940i	−0.0699634	−	0.261107i
$89$	−0.317556	−	0.0277825i	−0.0336609	−	0.00294494i	0.0703129	−	0.997525i	$-0.477600\pi$
$89$	−0.317556	−	0.0277825i	−0.0336609	−	0.00294494i	−0.103974	+	0.994580i	$0.533156\pi$
$90$		0			0
$91$	6.22813	+	13.3563i	0.652886	+	1.40012i
$92$	−6.19814	+	4.33998i	−0.646201	+	0.452475i
$93$		0			0
$94$	−10.1215	+	4.71972i	−1.04395	+	0.486802i
$95$	6.29142	−	5.27913i	0.645486	−	0.541627i
$96$		0			0
$97$	12.8298	−	3.43773i	1.30267	−	0.349049i	0.460209	−	0.887811i	$-0.347774\pi$
$97$	12.8298	−	3.43773i	1.30267	−	0.349049i	0.842458	+	0.538762i	$0.181108\pi$
$98$	−1.34189	−	0.625736i	−0.135552	−	0.0632088i
$99$		0			0
$100$	1.63167	+	2.82614i	0.163167	+	0.282614i
$101$	−0.0476198	+	0.0824799i	−0.00473834	+	0.00820705i	−0.868385	−	0.495891i	$-0.834842\pi$
$101$	−0.0476198	+	0.0824799i	−0.00473834	+	0.00820705i	0.863647	+	0.504098i	$0.168175\pi$
$102$		0			0
$103$	−6.75270	−	1.80938i	−0.665364	−	0.178284i	−0.0896982	−	0.995969i	$-0.528590\pi$
$103$	−6.75270	−	1.80938i	−0.665364	−	0.178284i	−0.575665	+	0.817685i	$0.695257\pi$
$104$	4.80527	+	4.03210i	0.471196	+	0.395380i
$105$		0			0
$106$	1.84371	−	0.161303i	0.179077	−	0.0156672i
$107$	−3.41452	−	9.38130i	−0.330094	−	0.906925i	−0.988086	−	0.153901i	$-0.950816\pi$
$107$	−3.41452	−	9.38130i	−0.330094	−	0.906925i	0.657993	−	0.753024i	$-0.271406\pi$
$108$		0			0
$109$	−1.53963	+	2.19883i	−0.147470	+	0.210609i	−0.886090	−	0.463513i	$-0.846589\pi$
$109$	−1.53963	+	2.19883i	−0.147470	+	0.210609i	0.738620	+	0.674122i	$0.235478\pi$
$110$	−3.34174			−0.318622
$111$		0			0
$112$	2.34934			0.221991
$113$	−4.72723	+	6.75118i	−0.444700	+	0.635098i	−0.977448	−	0.211176i	$-0.932271\pi$
$113$	−4.72723	+	6.75118i	−0.444700	+	0.635098i	0.532748	+	0.846274i	$0.321159\pi$
$114$		0			0
$115$	3.41040	+	9.36999i	0.318021	+	0.873756i
$116$	8.74857	−	0.765401i	0.812284	−	0.0710657i
$117$		0			0
$118$	6.69439	+	5.61726i	0.616269	+	0.517111i
$119$	−5.43962	−	1.45754i	−0.498649	−	0.133613i
$120$		0			0
$121$	2.28485	−	3.95747i	0.207713	−	0.359770i
$122$	−5.55107	−	9.61473i	−0.502570	−	0.870477i
$123$		0			0
$124$	−2.27908	−	1.06275i	−0.204668	−	0.0954381i
$125$	10.5186	−	2.81844i	0.940808	−	0.252089i
$126$		0			0
$127$	−10.4018	+	8.72817i	−0.923013	+	0.774500i	−0.974550	−	0.224171i	$-0.928033\pi$
$127$	−10.4018	+	8.72817i	−0.923013	+	0.774500i	0.0515366	+	0.998671i	$0.483588\pi$
$128$	0.906308	−	0.422618i	0.0801070	−	0.0373545i
$129$		0			0
$130$	6.77150	−	4.74146i	0.593900	−	0.415853i
$131$	0.343220	+	0.736037i	0.0299873	+	0.0643079i	0.920731	−	0.390198i	$-0.127594\pi$
$131$	0.343220	+	0.736037i	0.0299873	+	0.0643079i	−0.890744	+	0.454506i	$0.849816\pi$
$132$		0			0
$133$	14.5857	+	1.27608i	1.26474	+	0.110651i
$134$	−2.02492	−	7.55709i	−0.174926	−	0.652833i
$135$		0			0
$136$	−2.36065	+	0.416246i	−0.202424	+	0.0356928i
$137$	8.62186	−	4.97783i	0.736615	−	0.425285i	−0.0842223	−	0.996447i	$-0.526841\pi$
$137$	8.62186	−	4.97783i	0.736615	−	0.425285i	0.820837	+	0.571162i	$0.193507\pi$
$138$		0			0
$139$	4.48900	−	12.3334i	0.380752	−	1.04611i	−0.590289	−	0.807192i	$-0.700986\pi$
$139$	4.48900	−	12.3334i	0.380752	−	1.04611i	0.971041	−	0.238915i	$-0.0767916\pi$
$140$	0.801305	−	2.99051i	0.0677226	−	0.252744i
$141$		0			0
$142$	2.89792	−	2.89792i	0.243188	−	0.243188i
$143$	−1.38636	−	15.8462i	−0.115933	−	1.32512i
$144$		0			0
$145$	2.00965	−	11.3973i	0.166892	−	0.946491i
$146$	−8.89163	−	6.22599i	−0.735877	−	0.515266i
$147$		0			0
$148$	2.87329	+	5.36136i	0.236183	+	0.440701i
$149$		−	16.9610i		−	1.38950i	−0.719252	−	0.694749i	$-0.755516\pi$
$149$		−	16.9610i		−	1.38950i	0.719252	−	0.694749i	$-0.244484\pi$
$150$		0			0
$151$	−11.5457	−	2.03582i	−0.939579	−	0.165673i	−0.317173	−	0.948368i	$-0.602734\pi$
$151$	−11.5457	−	2.03582i	−0.939579	−	0.165673i	−0.622406	+	0.782695i	$0.713845\pi$
$152$	5.85631	−	2.13152i	0.475009	−	0.172889i
$153$		0			0
$154$	−4.21256	−	4.21256i	−0.339458	−	0.339458i
$155$	−2.13014	+	2.53860i	−0.171097	+	0.203905i
$156$		0			0
$157$	12.3075	+	4.47958i	0.982248	+	0.357509i	0.782714	−	0.622382i	$-0.213835\pi$
$157$	12.3075	+	4.47958i	0.982248	+	0.357509i	0.199534	+	0.979891i	$0.436057\pi$
$158$	8.13338	+	4.69581i	0.647057	+	0.373579i
$159$		0			0
$160$	−0.228837	−	1.29780i	−0.0180912	−	0.102600i
$161$	−7.51260	+	16.1108i	−0.592076	+	1.26971i
$162$		0			0
$163$	−1.11467	+	12.7407i	−0.0873078	+	0.997932i	0.818574	+	0.574401i	$0.194765\pi$
$163$	−1.11467	+	12.7407i	−0.0873078	+	0.997932i	−0.905882	+	0.423531i	$0.860790\pi$
$164$	−7.04739	−	8.39875i	−0.550308	−	0.655832i
$165$		0			0
$166$	0.650780	+	0.929409i	0.0505103	+	0.0721362i
$167$	−7.01571	−	10.0195i	−0.542892	−	0.775330i	0.450167	−	0.892944i	$-0.351364\pi$
$167$	−7.01571	−	10.0195i	−0.542892	−	0.775330i	−0.993059	+	0.117614i	$0.962475\pi$
$168$		0			0
$169$	16.9365	+	20.1841i	1.30281	+	1.55263i
$170$	−0.275316	+	3.14688i	−0.0211158	+	0.241355i
$171$		0			0
$172$	−0.471573	+	1.01129i	−0.0359571	+	0.0771102i
$173$	0.949307	+	5.38379i	0.0721745	+	0.409322i	0.999394	+	0.0348039i	$0.0110807\pi$
$173$	0.949307	+	5.38379i	0.0721745	+	0.409322i	−0.927220	+	0.374518i	$0.877808\pi$
$174$		0			0
$175$	6.63956	+	3.83335i	0.501904	+	0.289774i
$176$	−2.38288	−	0.867297i	−0.179616	−	0.0653749i
$177$		0			0
$178$	−0.204901	+	0.244191i	−0.0153580	+	0.0183029i
$179$	−6.08023	−	6.08023i	−0.454458	−	0.454458i	0.442373	−	0.896831i	$-0.354137\pi$
$179$	−6.08023	−	6.08023i	−0.454458	−	0.454458i	−0.896831	+	0.442373i	$0.854137\pi$
$180$		0			0
$181$	−6.05881	+	2.20523i	−0.450348	+	0.163913i	−0.557230	−	0.830358i	$-0.688136\pi$
$181$	−6.05881	+	2.20523i	−0.450348	+	0.163913i	0.106881	+	0.994272i	$0.465913\pi$
$182$	14.5131	+	2.55906i	1.07578	+	0.189690i
$183$		0			0
$184$			7.56653i			0.557812i
$185$	7.80458	−	1.82883i	0.573804	−	0.134458i
$186$		0			0
$187$	4.97921	+	3.48648i	0.364116	+	0.254956i
$188$	−1.93927	+	10.9981i	−0.141436	+	0.802122i
$189$		0			0
$190$	−0.715798	−	8.18161i	−0.0519295	−	0.593556i
$191$	−12.4651	+	12.4651i	−0.901944	+	0.901944i	−0.995604	−	0.0936599i	$-0.970143\pi$
$191$	−12.4651	+	12.4651i	−0.901944	+	0.901944i	0.0936599	+	0.995604i	$0.470143\pi$
$192$		0			0
$193$	−5.29840	+	19.7739i	−0.381387	+	1.42336i	0.462396	+	0.886673i	$0.346990\pi$
$193$	−5.29840	+	19.7739i	−0.381387	+	1.42336i	−0.843783	+	0.536684i	$0.819677\pi$
$194$	4.54284	−	12.4813i	0.326157	−	0.896108i
$195$		0			0
$196$	−1.28225	+	0.740308i	−0.0915894	+	0.0528792i
$197$	14.9921	−	2.64352i	1.06815	−	0.188343i	0.388177	−	0.921585i	$-0.373105\pi$
$197$	14.9921	−	2.64352i	1.06815	−	0.188343i	0.679968	+	0.733242i	$0.261994\pi$
$198$		0			0
$199$	−6.16077	−	22.9923i	−0.436726	−	1.62988i	−0.736903	−	0.675999i	$-0.763712\pi$
$199$	−6.16077	−	22.9923i	−0.436726	−	1.62988i	0.300177	−	0.953883i	$-0.402954\pi$
$200$	3.25093	+	0.284420i	0.229875	+	0.0201115i
$201$		0			0
$202$	0.0402500	+	0.0863163i	0.00283198	+	0.00607320i
$203$	16.9006	−	11.8339i	1.18619	−	0.830580i
$204$		0			0
$205$	−13.0946	+	6.10612i	−0.914567	+	0.426470i
$206$	−5.35535	+	4.49367i	−0.373125	+	0.313089i
$207$		0			0
$208$	6.05910	−	1.62353i	0.420123	−	0.112572i
$209$	−14.3229	−	6.67886i	−0.990733	−	0.461987i
$210$		0			0
$211$	−10.9534	−	18.9719i	−0.754065	−	1.30608i	−0.945838	−	0.324639i	$-0.894757\pi$
$211$	−10.9534	−	18.9719i	−0.754065	−	1.30608i	0.191773	−	0.981439i	$-0.438576\pi$
$212$	0.925375	−	1.60280i	0.0635550	−	0.110080i
$213$		0			0
$214$	−9.64320	−	2.58389i	−0.659196	−	0.176631i
$215$	1.12645	+	0.945201i	0.0768231	+	0.0644622i
$216$		0			0
$217$	−5.88537	+	0.514903i	−0.399525	+	0.0349539i
$218$	0.918075	+	2.52239i	0.0621799	+	0.170838i
$219$		0			0
$220$	−1.91674	+	2.73739i	−0.129227	+	0.184555i
$221$	−15.0364			−1.01146
$222$		0			0
$223$	−16.7142			−1.11926			−0.559632	−	0.828741i	$-0.689057\pi$
$223$	−16.7142			−1.11926			−0.559632	+	0.828741i	$0.689057\pi$
$224$	1.34752	−	1.92446i	0.0900352	−	0.128584i
$225$		0			0
$226$	2.81882	+	7.74464i	0.187505	+	0.515165i
$227$	−15.3613	+	1.34394i	−1.01956	+	0.0892003i	−0.584662	−	0.811277i	$-0.698773\pi$
$227$	−15.3613	+	1.34394i	−1.01956	+	0.0892003i	−0.434902	+	0.900478i	$0.643217\pi$
$228$		0			0
$229$	−8.27385	−	6.94259i	−0.546751	−	0.458779i	0.327088	−	0.944994i	$-0.393933\pi$
$229$	−8.27385	−	6.94259i	−0.546751	−	0.458779i	−0.873839	+	0.486215i	$0.838377\pi$
$230$	9.63157	+	2.58077i	0.635087	+	0.170171i
$231$		0			0
$232$	4.39099	−	7.60542i	0.288283	−	0.499321i
$233$	11.0002	+	19.0529i	0.720647	+	1.24820i	0.960741	+	0.277448i	$0.0894887\pi$
$233$	11.0002	+	19.0529i	0.720647	+	1.24820i	−0.240093	+	0.970750i	$0.577178\pi$
$234$		0			0
$235$	13.3383	+	6.21975i	0.870094	+	0.405732i
$236$	8.44114	−	2.26180i	0.549471	−	0.147230i
$237$		0			0
$238$	−4.31399	+	3.61987i	−0.279634	+	0.234641i
$239$	10.9181	−	5.09118i	0.706232	−	0.329321i	−0.0361053	−	0.999348i	$-0.511495\pi$
$239$	10.9181	−	5.09118i	0.706232	−	0.329321i	0.742337	+	0.670027i	$0.233717\pi$
$240$		0			0
$241$	12.3898	−	8.67541i	0.798095	−	0.558832i	−0.101868	−	0.994798i	$-0.532482\pi$
$241$	12.3898	−	8.67541i	0.798095	−	0.558832i	0.899963	+	0.435966i	$0.143593\pi$
$242$	−1.93123	−	4.14155i	−0.124144	−	0.266229i
$243$		0			0
$244$	−11.0599	−	0.967615i	−0.708037	−	0.0619452i
$245$	0.505004	+	1.88470i	0.0322636	+	0.120409i
$246$		0			0
$247$	38.4994	−	6.78848i	2.44966	−	0.431941i
$248$	−2.17778	+	1.25734i	−0.138289	+	0.0798415i
$249$		0			0
$250$	3.72447	−	10.2329i	0.235556	−	0.647185i
$251$	−3.19993	+	11.9423i	−0.201977	+	0.753790i	0.788372	+	0.615199i	$0.210924\pi$
$251$	−3.19993	+	11.9423i	−0.201977	+	0.753790i	−0.990350	+	0.138592i	$0.955742\pi$
$252$		0			0
$253$	13.5674	−	13.5674i	0.852977	−	0.852977i
$254$	1.18346	+	13.5270i	0.0742566	+	0.848757i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−6.29396	−	4.40708i	−0.392606	−	0.274906i	0.360560	−	0.932736i	$-0.382586\pi$
$257$	−6.29396	−	4.40708i	−0.392606	−	0.274906i	−0.753166	+	0.657830i	$0.771474\pi$
$258$		0			0
$259$	12.1438	+	7.53298i	0.754578	+	0.468077i
$260$		−	8.26648i		−	0.512665i
$261$		0			0
$262$	0.799789	+	0.141024i	0.0494111	+	0.00871252i
$263$	−4.23067	+	1.53984i	−0.260874	+	0.0949504i	−0.469146	−	0.883120i	$-0.655438\pi$
$263$	−4.23067	+	1.53984i	−0.260874	+	0.0949504i	0.208272	+	0.978071i	$0.433216\pi$
$264$		0			0
$265$	−1.72460	−	1.72460i	−0.105941	−	0.105941i
$266$	9.41133	−	11.2160i	0.577046	−	0.687696i
$267$		0			0
$268$	−7.35185	−	2.67585i	−0.449086	−	0.163454i
$269$	−3.71281	−	2.14359i	−0.226374	−	0.130697i	0.382524	−	0.923946i	$-0.375055\pi$
$269$	−3.71281	−	2.14359i	−0.226374	−	0.130697i	−0.608898	+	0.793248i	$0.708388\pi$
$270$		0			0
$271$	3.01658	+	17.1079i	0.183244	+	1.03923i	0.928191	+	0.372105i	$0.121364\pi$
$271$	3.01658	+	17.1079i	0.183244	+	1.03923i	−0.744947	+	0.667124i	$0.767525\pi$
$272$	−1.01304	+	2.17248i	−0.0614248	+	0.131726i
$273$		0			0
$274$	0.867693	−	9.91778i	0.0524193	−	0.599155i
$275$	−5.31921	−	6.33918i	−0.320760	−	0.382267i
$276$		0			0
$277$	−0.592556	−	0.846257i	−0.0356032	−	0.0508467i	0.800956	−	0.598723i	$-0.204325\pi$
$277$	−0.592556	−	0.846257i	−0.0356032	−	0.0508467i	−0.836559	+	0.547877i	$0.815436\pi$
$278$	−7.52816	−	10.7513i	−0.451509	−	0.644822i
$279$		0			0
$280$	−1.99007	−	2.37168i	−0.118930	−	0.141735i
$281$	−1.51781	+	17.3487i	−0.0905451	+	1.03494i	0.805980	+	0.591943i	$0.201639\pi$
$281$	−1.51781	+	17.3487i	−0.0905451	+	1.03494i	−0.896525	+	0.442993i	$0.853917\pi$
$282$		0			0
$283$	−8.61652	+	18.4782i	−0.512199	+	1.09841i	0.464848	+	0.885390i	$0.346109\pi$
$283$	−8.61652	+	18.4782i	−0.512199	+	1.09841i	−0.977047	+	0.213024i	$0.931669\pi$
$284$	−0.711657	−	4.03601i	−0.0422291	−	0.239493i
$285$		0			0
$286$	−13.7756	−	7.95335i	−0.814569	−	0.470292i
$287$	−24.2042	−	8.80963i	−1.42873	−	0.520016i
$288$		0			0
$289$	−7.23399	+	8.62113i	−0.425529	+	0.507125i
$290$	−8.18341	−	8.18341i	−0.480546	−	0.480546i
$291$		0			0
$292$	−10.2001	+	3.71252i	−0.596914	+	0.217259i
$293$	5.22200	+	0.920779i	0.305072	+	0.0537925i	0.324089	−	0.946027i	$-0.394942\pi$
$293$	5.22200	+	0.920779i	0.305072	+	0.0537925i	−0.0190163	+	0.999819i	$0.506053\pi$
$294$		0			0
$295$		−	11.5163i		−	0.670506i
$296$	6.03982	+	0.721486i	0.351058	+	0.0419355i
$297$		0			0
$298$	−13.8936	−	9.72842i	−0.804836	−	0.563552i
$299$	−8.24198	+	46.7426i	−0.476646	+	2.70319i
$300$		0			0
$301$	0.228477	+	2.61150i	0.0131692	+	0.150524i
$302$	−8.29001	+	8.29001i	−0.477037	+	0.477037i
$303$		0			0
$304$	1.61300	−	6.01980i	0.0925119	−	0.345259i
$305$	−5.00397	+	13.7483i	−0.286526	+	0.787225i
$306$		0			0
$307$	−14.5787	+	8.41700i	−0.832049	+	0.480384i	−0.854554	−	0.519363i	$-0.826169\pi$
$307$	−14.5787	+	8.41700i	−0.832049	+	0.480384i	0.0225047	+	0.999747i	$0.492836\pi$
$308$	−5.86695	+	1.03450i	−0.334301	+	0.0589462i
$309$		0			0
$310$	0.857703	+	3.20099i	0.0487143	+	0.181804i
$311$	18.3471	+	1.60516i	1.04037	+	0.0910202i	0.594513	−	0.804086i	$-0.297345\pi$
$311$	18.3471	+	1.60516i	1.04037	+	0.0910202i	0.445853	+	0.895106i	$0.352900\pi$
$312$		0			0
$313$	−10.8404	−	23.2473i	−0.612734	−	1.31401i	−0.930656	−	0.365896i	$-0.880763\pi$
$313$	−10.8404	−	23.2473i	−0.612734	−	1.31401i	0.317921	−	0.948117i	$-0.397015\pi$
$314$	10.7288	−	7.51236i	0.605459	−	0.423947i
$315$		0			0
$316$	8.51170	−	3.96907i	0.478820	−	0.223278i
$317$	−7.32092	+	6.14298i	−0.411184	+	0.345024i	−0.824797	−	0.565428i	$-0.808711\pi$
$317$	−7.32092	+	6.14298i	−0.411184	+	0.345024i	0.413614	+	0.910452i	$0.364266\pi$
$318$		0			0
$319$	−21.5106	+	5.76375i	−1.20436	+	0.322708i
$320$	−1.19435	−	0.556935i	−0.0667663	−	0.0311336i
$321$		0			0
$322$	8.88817	+	15.3948i	0.495318	+	0.857916i
$323$	−7.46944	+	12.9374i	−0.415611	+	0.719859i
$324$		0			0
$325$	19.7729	+	5.29815i	1.09681	+	0.293888i
$326$	9.79726	+	8.22088i	0.542620	+	0.455312i
$327$		0			0
$328$	−10.9221	+	0.955557i	−0.603070	+	0.0527618i
$329$	8.97357	+	24.6547i	0.494729	+	1.35926i
$330$		0			0
$331$	−4.54433	+	6.48997i	−0.249779	+	0.356721i	−0.924388	−	0.381454i	$-0.875423\pi$
$331$	−4.54433	+	6.48997i	−0.249779	+	0.356721i	0.674609	+	0.738175i	$0.264312\pi$
$332$	1.13460			0.0622692
$333$		0			0
$334$	−12.2315			−0.669279
$335$	−5.91369	+	8.44562i	−0.323099	+	0.461433i
$336$		0			0
$337$	−2.09974	−	5.76900i	−0.114380	−	0.314257i	0.869272	−	0.494333i	$-0.164588\pi$
$337$	−2.09974	−	5.76900i	−0.114380	−	0.314257i	−0.983653	+	0.180076i	$0.942366\pi$
$338$	26.2483	−	2.29643i	1.42772	−	0.124909i
$339$		0			0
$340$	2.41986	+	2.03050i	0.131235	+	0.110119i
$341$	6.15948	+	1.65043i	0.333555	+	0.0893757i
$342$		0			0
$343$	−9.96191	+	17.2545i	−0.537893	+	0.931658i
$344$	0.557918	+	0.966343i	0.0300809	+	0.0521017i
$345$		0			0
$346$	4.95464	+	2.31039i	0.266363	+	0.124207i
$347$	−25.1023	+	6.72615i	−1.34756	+	0.361078i	−0.859235	−	0.511582i	$-0.829060\pi$
$347$	−25.1023	+	6.72615i	−1.34756	+	0.361078i	−0.488328	+	0.872660i	$0.662393\pi$
$348$		0			0
$349$	10.7419	−	9.01354i	0.575002	−	0.482484i	−0.308300	−	0.951289i	$-0.599760\pi$
$349$	10.7419	−	9.01354i	0.575002	−	0.482484i	0.883301	+	0.468806i	$0.155316\pi$
$350$	6.94839	−	3.24009i	0.371407	−	0.173190i
$351$		0			0
$352$	−2.07721	+	1.45448i	−0.110716	+	0.0775240i
$353$	2.25571	+	4.83739i	0.120059	+	0.257468i	0.957148	−	0.289599i	$-0.0935219\pi$
$353$	2.25571	+	4.83739i	0.120059	+	0.257468i	−0.837089	+	0.547067i	$0.815744\pi$
$354$		0			0
$355$	−5.38024	−	0.470710i	−0.285553	−	0.0249827i
$356$	0.0825035	+	0.307907i	0.00437268	+	0.0163190i
$357$		0			0
$358$	−8.46811	+	1.49316i	−0.447553	+	0.0789157i
$359$	−2.61646	+	1.51062i	−0.138092	+	0.0797273i	−0.567454	−	0.823405i	$-0.692072\pi$
$359$	−2.61646	+	1.51062i	−0.138092	+	0.0797273i	0.429363	+	0.903132i	$0.358738\pi$
$360$		0			0
$361$	6.78560	−	18.6433i	0.357137	−	0.981225i
$362$	−1.66878	+	6.22796i	−0.0877089	+	0.327334i
$363$		0			0
$364$	10.4206	−	10.4206i	0.546190	−	0.546190i
$365$	1.24672	+	14.2501i	0.0652564	+	0.745884i
$366$		0			0
$367$	−1.08395	+	6.14738i	−0.0565817	+	0.320891i	−0.999941	−	0.0108828i	$-0.996536\pi$
$367$	−1.08395	+	6.14738i	−0.0565817	+	0.320891i	0.943359	+	0.331773i	$0.107647\pi$
$368$	6.19814	+	4.33998i	0.323100	+	0.226237i
$369$		0			0
$370$	2.97844	−	7.44211i	0.154842	−	0.386897i
$371$		−	4.34803i		−	0.225739i
$372$		0			0
$373$	−36.7948	−	6.48792i	−1.90516	−	0.335932i	−0.908522	−	0.417836i	$-0.862789\pi$
$373$	−36.7948	−	6.48792i	−1.90516	−	0.335932i	−0.996640	+	0.0819046i	$0.973900\pi$
$374$	5.71191	−	2.07897i	0.295356	−	0.107501i
$375$		0			0
$376$	7.89684	+	7.89684i	0.407248	+	0.407248i
$377$	35.4099	−	42.1999i	1.82370	−	2.17340i
$378$		0			0
$379$	−3.73631	−	1.35990i	−0.191921	−	0.0698536i	0.244272	−	0.969707i	$-0.421451\pi$
$379$	−3.73631	−	1.35990i	−0.191921	−	0.0698536i	−0.436193	+	0.899853i	$0.643673\pi$
$380$	−7.11255	−	4.10643i	−0.364866	−	0.210655i
$381$		0			0
$382$	3.06113	+	17.3605i	0.156621	+	0.888242i
$383$	−2.84516	+	6.10146i	−0.145381	+	0.311770i	−0.965491	−	0.260435i	$-0.916134\pi$
$383$	−2.84516	+	6.10146i	−0.145381	+	0.311770i	0.820111	+	0.572205i	$0.193912\pi$
$384$		0			0
$385$	−0.684248	+	7.82099i	−0.0348725	+	0.398595i
$386$	13.1588	+	15.6820i	0.669765	+	0.798195i
$387$		0			0
$388$	−7.61845	−	10.8803i	−0.386768	−	0.552362i
$389$	12.2696	+	17.5228i	0.622095	+	0.888443i	0.999289	−	0.0376907i	$-0.0120002\pi$
$389$	12.2696	+	17.5228i	0.622095	+	0.888443i	−0.377195	+	0.926134i	$0.623111\pi$
$390$		0			0
$391$	−11.6585	−	13.8941i	−0.589597	−	0.702655i
$392$	−0.129044	+	1.47498i	−0.00651772	+	0.0744979i
$393$		0			0
$394$	6.43369	−	13.7971i	0.324125	−	0.695088i
$395$	−2.14915	−	12.1884i	−0.108136	−	0.613267i
$396$		0			0
$397$	20.4209	+	11.7900i	1.02490	+	0.591724i	0.915518	−	0.402276i	$-0.131781\pi$
$397$	20.4209	+	11.7900i	1.02490	+	0.591724i	0.109378	+	0.994000i	$0.465114\pi$
$398$	−22.3679	−	8.14124i	−1.12120	−	0.408084i
$399$		0			0
$400$	2.09764	−	2.49987i	0.104882	−	0.124993i
$401$	2.98281	+	2.98281i	0.148954	+	0.148954i	0.777651	−	0.628697i	$-0.216411\pi$
$401$	2.98281	+	2.98281i	0.148954	+	0.148954i	−0.628697	+	0.777651i	$0.716411\pi$
$402$		0			0
$403$	−14.8229	+	5.39511i	−0.738383	+	0.268750i
$404$	0.0937926	+	0.0165382i	0.00466636	+	0.000822805i
$405$		0			0
$406$		−	20.6318i		−	1.02394i
$407$	−9.53623	−	12.1236i	−0.472693	−	0.600945i
$408$		0			0
$409$	−6.82901	−	4.78172i	−0.337673	−	0.236441i	0.392425	−	0.919784i	$-0.371636\pi$
$409$	−6.82901	−	4.78172i	−0.337673	−	0.236441i	−0.730097	+	0.683343i	$0.760525\pi$
$410$	−2.50892	+	14.2288i	−0.123907	+	0.702710i
$411$		0			0
$412$	0.609298	+	6.96431i	0.0300180	+	0.343107i
$413$	14.5174	−	14.5174i	0.714352	−	0.714352i
$414$		0			0
$415$	0.386986	−	1.44425i	0.0189964	−	0.0708955i
$416$	2.14544	−	5.89454i	0.105189	−	0.289004i
$417$		0			0
$418$	−13.6863	+	7.90177i	−0.669417	+	0.386488i
$419$	−15.3211	+	2.70153i	−0.748487	+	0.131978i	−0.534864	−	0.844938i	$-0.679637\pi$
$419$	−15.3211	+	2.70153i	−0.748487	+	0.131978i	−0.213622	+	0.976916i	$0.568526\pi$
$420$		0			0
$421$	−4.33319	−	16.1717i	−0.211187	−	0.788160i	−0.987474	−	0.157781i	$-0.949566\pi$
$421$	−4.33319	−	16.1717i	−0.211187	−	0.788160i	0.776287	−	0.630379i	$-0.217101\pi$
$422$	−21.8235	−	1.90931i	−1.06235	−	0.0929436i
$423$		0			0
$424$	−0.782161	−	1.67735i	−0.0379851	−	0.0814593i
$425$	−6.40778	+	4.48678i	−0.310823	+	0.217641i
$426$		0			0
$427$	−23.6389	+	11.0230i	−1.14397	+	0.533441i
$428$	−7.64771	+	6.41719i	−0.369666	+	0.310187i
$429$		0			0
$430$	1.42037	−	0.380586i	0.0684962	−	0.0183535i
$431$	−13.9763	−	6.51724i	−0.673214	−	0.313925i	0.0557821	−	0.998443i	$-0.482235\pi$
$431$	−13.9763	−	6.51724i	−0.673214	−	0.313925i	−0.728996	+	0.684518i	$0.760013\pi$
$432$		0			0
$433$	−1.08383	−	1.87724i	−0.0520854	−	0.0902145i	0.838807	−	0.544429i	$-0.183253\pi$
$433$	−1.08383	−	1.87724i	−0.0520854	−	0.0902145i	−0.890893	+	0.454214i	$0.849920\pi$
$434$	−2.95393	+	5.11635i	−0.141793	+	0.245593i
$435$		0			0
$436$	2.59281	+	0.694740i	0.124173	+	0.0332720i
$437$	36.1234	+	30.3112i	1.72802	+	1.44998i
$438$		0			0
$439$	−12.0667	+	1.05570i	−0.575910	+	0.0503856i	−0.371390	−	0.928477i	$-0.621119\pi$
$439$	−12.0667	+	1.05570i	−0.575910	+	0.0503856i	−0.204520	+	0.978862i	$0.565563\pi$
$440$	1.14294	+	3.14021i	0.0544876	+	0.149703i
$441$		0			0
$442$	−8.62452	+	12.3171i	−0.410227	+	0.585865i
$443$	11.5779			0.550081			0.275040	−	0.961433i	$-0.411309\pi$
$443$	11.5779			0.550081			0.275040	+	0.961433i	$0.411309\pi$
$444$		0			0
$445$	0.420080			0.0199137
$446$	−9.58686	+	13.6915i	−0.453951	+	0.648309i
$447$		0			0
$448$	−0.803520	−	2.20765i	−0.0379628	−	0.104302i
$449$	−32.9131	+	2.87952i	−1.55327	+	0.135893i	−0.831216	−	0.555949i	$-0.812355\pi$
$449$	−32.9131	+	2.87952i	−1.55327	+	0.135893i	−0.722049	+	0.691842i	$0.756799\pi$
$450$		0			0
$451$	21.2976	+	17.8708i	1.00286	+	0.841503i
$452$	7.96084	+	2.13310i	0.374446	+	0.100333i
$453$		0			0
$454$	−7.70998	+	13.3541i	−0.361847	+	0.626738i
$455$	−9.71037	−	16.8189i	−0.455229	−	0.788480i
$456$		0			0
$457$	−22.9391	−	10.6967i	−1.07304	−	0.500369i	−0.195914	−	0.980621i	$-0.562767\pi$
$457$	−22.9391	−	10.6967i	−1.07304	−	0.500369i	−0.877130	+	0.480252i	$0.840545\pi$
$458$	−10.4327	+	2.79544i	−0.487489	+	0.130622i
$459$		0			0
$460$	7.63848	−	6.40945i	0.356146	−	0.298842i
$461$	18.7010	−	8.72044i	0.870995	−	0.406152i	0.0648676	−	0.997894i	$-0.479337\pi$
$461$	18.7010	−	8.72044i	0.870995	−	0.406152i	0.806127	+	0.591742i	$0.201560\pi$
$462$		0			0
$463$	24.4192	−	17.0985i	1.13486	−	0.794635i	0.153751	−	0.988110i	$-0.450865\pi$
$463$	24.4192	−	17.0985i	1.13486	−	0.794635i	0.981105	+	0.193475i	$0.0619757\pi$
$464$	−3.71143	−	7.95918i	−0.172299	−	0.369496i
$465$		0			0
$466$	21.9167	+	1.91746i	1.01527	+	0.0888247i
$467$	−9.83159	−	36.6920i	−0.454952	−	1.69790i	−0.688229	−	0.725493i	$-0.741612\pi$
$467$	−9.83159	−	36.6920i	−0.454952	−	1.69790i	0.233278	−	0.972410i	$-0.425055\pi$
$468$		0			0
$469$	−18.1012	+	3.19173i	−0.835836	+	0.147380i
$470$	12.7454	−	7.35859i	0.587904	−	0.339426i
$471$		0			0
$472$	2.98888	−	8.21189i	0.137574	−	0.377983i
$473$	0.732340	−	2.73313i	0.0336730	−	0.125669i
$474$		0			0
$475$	14.3809	−	14.3809i	0.659842	−	0.659842i
$476$	0.490818	+	5.61008i	0.0224966	+	0.257138i
$477$		0			0
$478$	2.09190	−	11.8637i	0.0956812	−	0.542635i
$479$	29.9858	+	20.9963i	1.37009	+	0.959345i	0.999534	+	0.0305337i	$0.00972068\pi$
$479$	29.9858	+	20.9963i	1.37009	+	0.959345i	0.370553	+	0.928811i	$0.379168\pi$
$480$		0			0
$481$	36.5254	+	11.0360i	1.66541	+	0.503198i
$482$		−	15.1251i		−	0.688930i
$483$		0			0
$484$	−4.50027	−	0.793518i	−0.204558	−	0.0360690i
$485$	−16.4482	+	5.98664i	−0.746873	+	0.271840i
$486$		0			0
$487$	17.6239	+	17.6239i	0.798617	+	0.798617i	0.982877	−	0.184261i	$-0.0589890\pi$
$487$	17.6239	+	17.6239i	0.798617	+	0.798617i	−0.184261	+	0.982877i	$0.558989\pi$
$488$	−7.13631	+	8.50473i	−0.323046	+	0.384991i
$489$		0			0
$490$	1.83352	+	0.667345i	0.0828298	+	0.0301476i
$491$	−21.0419	−	12.1486i	−0.949609	−	0.548257i	−0.0566498	−	0.998394i	$-0.518042\pi$
$491$	−21.0419	−	12.1486i	−0.949609	−	0.548257i	−0.892960	+	0.450137i	$0.851375\pi$
$492$		0			0
$493$	3.65547	+	20.7312i	0.164634	+	0.933685i
$494$	16.5215	−	35.4306i	0.743340	−	1.59410i
$495$		0			0
$496$	−0.219170	+	2.50512i	−0.00984101	+	0.112483i
$497$	−6.18890	−	7.37564i	−0.277610	−	0.330843i
$498$		0			0
$499$	−1.85420	−	2.64808i	−0.0830056	−	0.118544i	0.775502	−	0.631345i	$-0.217497\pi$
$499$	−1.85420	−	2.64808i	−0.0830056	−	0.118544i	−0.858508	+	0.512801i	$0.828608\pi$
$500$	−6.24602	−	8.92025i	−0.279331	−	0.398926i
$501$		0			0
$502$	7.94714	+	9.47104i	0.354698	+	0.422713i
$503$	−0.942043	+	10.7676i	−0.0420036	+	0.480104i	0.945838	+	0.324639i	$0.105243\pi$
$503$	−0.942043	+	10.7676i	−0.0420036	+	0.480104i	−0.987842	+	0.155464i	$0.950313\pi$
$504$		0			0
$505$	0.0530422	−	0.113749i	0.00236035	−	0.00506178i
$506$	−3.33183	−	18.8958i	−0.148118	−	0.840019i
$507$		0			0
$508$	11.7594	+	6.78931i	0.521741	+	0.301227i
$509$	−0.0209050	−	0.00760879i	−0.000926597	−	0.000337254i	0.341557	−	0.939861i	$-0.389046\pi$
$509$	−0.0209050	−	0.00760879i	−0.000926597	−	0.000337254i	−0.342483	+	0.939524i	$0.611268\pi$
$510$		0			0
$511$	−16.3919	+	19.5351i	−0.725136	+	0.864183i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−7.22013	+	2.62791i	−0.318466	+	0.115912i
$515$	9.07281	+	1.59978i	0.399796	+	0.0704948i
$516$		0			0
$517$		−	28.3194i		−	1.24549i
$518$	13.1360	−	5.62686i	0.577165	−	0.247230i
$519$		0			0
$520$	−6.77150	−	4.74146i	−0.296950	−	0.207927i
$521$	6.13550	−	34.7961i	0.268801	−	1.52445i	−0.489188	−	0.872179i	$-0.662707\pi$
$521$	6.13550	−	34.7961i	0.268801	−	1.52445i	0.757989	−	0.652268i	$-0.226182\pi$
$522$		0			0
$523$	−1.20573	−	13.7815i	−0.0527227	−	0.602623i	−0.975896	−	0.218238i	$-0.929969\pi$
$523$	−1.20573	−	13.7815i	−0.0527227	−	0.602623i	0.923173	−	0.384385i	$-0.125586\pi$
$524$	0.574261	−	0.574261i	0.0250867	−	0.0250867i
$525$		0			0
$526$	−1.16525	+	4.34878i	−0.0508074	+	0.189616i
$527$	2.06165	−	5.66435i	0.0898070	−	0.246743i
$528$		0			0
$529$	−29.6634	+	17.1262i	−1.28972	+	0.744617i
$530$	−2.40190	+	0.423520i	−0.104332	+	0.0183965i
$531$		0			0
$532$	−3.78948	−	14.1425i	−0.164295	−	0.613157i
$533$	−68.5124	−	5.99406i	−2.96760	−	0.259631i
$534$		0			0
$535$	5.56009	+	11.9237i	0.240384	+	0.515505i
$536$	−6.40878	+	4.48747i	−0.276817	+	0.193829i
$537$		0			0
$538$	−3.88551	+	1.81184i	−0.167516	+	0.0781141i
$539$	2.87616	−	2.41338i	0.123885	−	0.103952i
$540$		0			0
$541$	23.2053	−	6.21785i	0.997675	−	0.267326i	0.277204	−	0.960811i	$-0.410592\pi$
$541$	23.2053	−	6.21785i	0.997675	−	0.267326i	0.720471	+	0.693485i	$0.243926\pi$
$542$	15.7442	+	7.34163i	0.676271	+	0.315350i
$543$		0			0
$544$	1.19853	+	2.07592i	0.0513866	+	0.0890043i
$545$	1.76869	−	3.06347i	0.0757625	−	0.131225i
$546$		0			0
$547$	12.1411	+	3.25320i	0.519116	+	0.139097i	0.508858	−	0.860851i	$-0.330068\pi$
$547$	12.1411	+	3.25320i	0.519116	+	0.139097i	0.0102585	+	0.999947i	$0.496735\pi$
$548$	−7.62648	−	6.39938i	−0.325787	−	0.273368i
$549$		0			0
$550$	−8.24373	+	0.721233i	−0.351514	+	0.0307535i
$551$	−18.7190	−	51.4300i	−0.797456	−	2.19099i
$552$		0			0
$553$	12.6554	−	18.0738i	0.538164	−	0.768578i
$554$	−1.03309			−0.0438917
$555$		0			0
$556$	−13.1249			−0.556622
$557$	13.3197	−	19.0225i	0.564372	−	0.806007i	−0.430975	−	0.902364i	$-0.641830\pi$
$557$	13.3197	−	19.0225i	0.564372	−	0.806007i	0.995347	+	0.0963569i	$0.0307190\pi$
$558$		0			0
$559$	2.39396	+	6.57734i	0.101254	+	0.278192i
$560$	−3.08422	+	0.269835i	−0.130332	+	0.0114026i
$561$		0			0
$562$	13.3406	+	11.1941i	0.562740	+	0.472195i
$563$	33.9900	+	9.10760i	1.43251	+	0.383840i	0.889904	−	0.456148i	$-0.150771\pi$
$563$	33.9900	+	9.10760i	1.43251	+	0.383840i	0.542605	+	0.839988i	$0.317438\pi$
$564$		0			0
$565$	5.43052	−	9.40594i	0.228464	−	0.395711i
$566$	10.1942	+	17.6569i	0.428495	+	0.742175i
$567$		0			0
$568$	−3.71430	−	1.73200i	−0.155848	−	0.0726733i
$569$	1.45924	−	0.391001i	0.0611744	−	0.0163916i	−0.228102	−	0.973637i	$-0.573252\pi$
$569$	1.45924	−	0.391001i	0.0611744	−	0.0163916i	0.289276	+	0.957246i	$0.406585\pi$
$570$		0			0
$571$	22.7016	−	19.0489i	0.950034	−	0.797173i	−0.0292690	−	0.999572i	$-0.509318\pi$
$571$	22.7016	−	19.0489i	0.950034	−	0.797173i	0.979303	+	0.202398i	$0.0648735\pi$
$572$	−14.4164	+	6.72246i	−0.602779	+	0.281080i
$573$		0			0
$574$	−21.0994	+	14.7740i	−0.880672	+	0.616653i
$575$	10.4354	+	22.3788i	0.435186	+	0.933259i
$576$		0			0
$577$	−2.35290	−	0.205852i	−0.0979525	−	0.00856973i	0.0380741	−	0.999275i	$-0.487878\pi$
$577$	−2.35290	−	0.205852i	−0.0979525	−	0.00856973i	−0.136027	+	0.990705i	$0.543433\pi$
$578$	2.91277	+	10.8706i	0.121155	+	0.452158i
$579$		0			0
$580$	−11.3973	+	2.00965i	−0.473246	+	0.0834460i
$581$	2.30844	−	1.33278i	0.0957702	−	0.0552930i
$582$		0			0
$583$	−1.60515	+	4.41011i	−0.0664785	+	0.182648i
$584$	−2.80940	+	10.4848i	−0.116254	+	0.433865i
$585$		0			0
$586$	3.74947	−	3.74947i	0.154889	−	0.154889i
$587$	0.987670	+	11.2891i	0.0407655	+	0.465952i	0.988952	+	0.148237i	$0.0473598\pi$
$587$	0.987670	+	11.2891i	0.0407655	+	0.465952i	−0.948186	+	0.317715i	$0.897085\pi$
$588$		0			0
$589$	−2.72140	+	15.4338i	−0.112133	+	0.635940i
$590$	−9.43361	−	6.60549i	−0.388376	−	0.271944i
$591$		0			0
$592$	4.05531	−	4.53371i	0.166672	−	0.186334i
$593$		−	2.74452i		−	0.112704i	−0.998411	−	0.0563519i	$-0.982053\pi$
$593$		−	2.74452i		−	0.112704i	0.998411	−	0.0563519i	$-0.0179469\pi$
$594$		0			0
$595$	7.30857	+	1.28870i	0.299622	+	0.0528315i
$596$	−15.9381	+	5.80100i	−0.652850	+	0.237618i
$597$		0			0
$598$	33.5619	+	33.5619i	1.37245	+	1.37245i
$599$	27.4401	−	32.7018i	1.12117	−	1.33616i	0.185763	−	0.982595i	$-0.440524\pi$
$599$	27.4401	−	32.7018i	1.12117	−	1.33616i	0.935409	−	0.353567i	$-0.115031\pi$
$600$		0			0
$601$	−5.25901	−	1.91412i	−0.214519	−	0.0780787i	0.232525	−	0.972590i	$-0.425301\pi$
$601$	−5.25901	−	1.91412i	−0.214519	−	0.0780787i	−0.447044	+	0.894512i	$0.647523\pi$
$602$	2.27026	+	1.31074i	0.0925291	+	0.0534217i
$603$		0			0
$604$	2.03582	+	11.5457i	0.0828365	+	0.469789i
$605$	−2.54502	+	5.45782i	−0.103470	+	0.221892i
$606$		0			0
$607$	1.05141	−	12.0177i	0.0426754	−	0.487782i	−0.944541	−	0.328394i	$-0.893493\pi$
$607$	1.05141	−	12.0177i	0.0426754	−	0.487782i	0.987216	−	0.159388i	$-0.0509519\pi$
$608$	−4.00595	−	4.77411i	−0.162463	−	0.193616i
$609$		0			0
$610$	8.39178	+	11.9847i	0.339773	+	0.485247i
$611$	40.1813	+	57.3848i	1.62556	+	2.32154i
$612$		0			0
$613$	27.0267	+	32.2092i	1.09160	+	1.30092i	0.950433	+	0.310930i	$0.100641\pi$
$613$	27.0267	+	32.2092i	1.09160	+	1.30092i	0.141166	+	0.989986i	$0.454915\pi$
$614$	−1.46718	+	16.7699i	−0.0592106	+	0.676780i
$615$		0			0
$616$	−2.51773	+	5.39929i	−0.101442	+	0.217544i
$617$	−5.74253	−	32.5675i	−0.231186	−	1.31112i	−0.850500	−	0.525976i	$-0.823700\pi$
$617$	−5.74253	−	32.5675i	−0.231186	−	1.31112i	0.619314	−	0.785143i	$-0.287411\pi$
$618$		0			0
$619$	5.29830	+	3.05897i	0.212957	+	0.122951i	0.602685	−	0.797979i	$-0.294098\pi$
$619$	5.29830	+	3.05897i	0.212957	+	0.122951i	−0.389728	+	0.920930i	$0.627431\pi$
$620$	3.11406	+	1.13342i	0.125064	+	0.0455194i
$621$		0			0
$622$	11.8383	−	14.1083i	0.474673	−	0.565693i
$623$	0.529549	+	0.529549i	0.0212159	+	0.0212159i
$624$		0			0
$625$	1.84761	−	0.672475i	0.0739044	−	0.0268990i
$626$	−25.2608	−	4.45417i	−1.00963	−	0.178024i
$627$		0			0
$628$		−	13.0974i		−	0.522643i
$629$	−12.2023	+	7.98134i	−0.486539	+	0.318237i
$630$		0			0
$631$	−35.6483	−	24.9612i	−1.41914	−	0.993690i	−0.996160	−	0.0875491i	$-0.972097\pi$
$631$	−35.6483	−	24.9612i	−1.41914	−	0.993690i	−0.422976	−	0.906141i	$-0.639015\pi$
$632$	1.63084	−	9.24894i	0.0648712	−	0.367903i
$633$		0			0
$634$	0.832928	+	9.52041i	0.0330798	+	0.378104i
$635$	12.6531	−	12.6531i	0.502123	−	0.502123i
$636$		0			0
$637$	−2.40383	+	8.97120i	−0.0952431	+	0.355452i
$638$	−7.61659	+	20.9264i	−0.301544	+	0.828484i
$639$		0			0
$640$	−1.14127	+	0.658910i	−0.0451125	+	0.0260457i
$641$	38.4935	−	6.78745i	1.52040	−	0.268088i	0.649812	−	0.760095i	$-0.274848\pi$
$641$	38.4935	−	6.78745i	1.52040	−	0.268088i	0.870591	+	0.492007i	$0.163736\pi$
$642$		0			0
$643$	−10.4218	−	38.8946i	−0.410995	−	1.53385i	−0.792725	−	0.609579i	$-0.791338\pi$
$643$	−10.4218	−	38.8946i	−0.410995	−	1.53385i	0.381731	−	0.924274i	$-0.375328\pi$
$644$	17.7087	+	1.54931i	0.697820	+	0.0610513i
$645$		0			0
$646$	6.31344	+	13.5392i	0.248399	+	0.532693i
$647$	40.6484	−	28.4623i	1.59805	−	1.11897i	0.672666	−	0.739946i	$-0.265149\pi$
$647$	40.6484	−	28.4623i	1.59805	−	1.11897i	0.925387	−	0.379022i	$-0.123740\pi$
$648$		0			0
$649$	−20.0839	+	9.36529i	−0.788364	+	0.367620i
$650$	15.6813	−	13.1582i	0.615071	−	0.516106i
$651$		0			0
$652$	12.3536	−	3.31014i	0.483805	−	0.129635i
$653$	−16.9635	−	7.91019i	−0.663831	−	0.309550i	0.0613413	−	0.998117i	$-0.480462\pi$
$653$	−16.9635	−	7.91019i	−0.663831	−	0.309550i	−0.725172	+	0.688567i	$0.758240\pi$
$654$		0			0
$655$	−0.535119	−	0.926853i	−0.0209088	−	0.0362152i
$656$	−5.48189	+	9.49492i	−0.214032	+	0.370714i
$657$		0			0
$658$	25.3429	+	6.79062i	0.987971	+	0.264726i
$659$	0.893583	+	0.749805i	0.0348090	+	0.0292083i	0.660026	−	0.751243i	$-0.270545\pi$
$659$	0.893583	+	0.749805i	0.0348090	+	0.0292083i	−0.625217	+	0.780451i	$0.714990\pi$
$660$		0			0
$661$	−22.2984	+	1.95086i	−0.867309	+	0.0758797i	−0.512119	−	0.858915i	$-0.671139\pi$
$661$	−22.2984	+	1.95086i	−0.867309	+	0.0758797i	−0.355190	+	0.934794i	$0.615584\pi$
$662$	2.70976	+	7.44499i	0.105318	+	0.289358i
$663$		0			0
$664$	0.650780	−	0.929409i	0.0252551	−	0.0360681i
$665$	−19.2948			−0.748220
$666$		0			0
$667$	66.4492			2.57292
$668$	−7.01571	+	10.0195i	−0.271446	+	0.387665i
$669$		0			0
$670$	3.52630	+	9.68842i	0.136233	+	0.374296i
$671$	28.0457	−	2.45368i	1.08269	−	0.0947234i
$672$		0			0
$673$	14.2359	+	11.9454i	0.548755	+	0.460460i	0.874519	−	0.484991i	$-0.161177\pi$
$673$	14.2359	+	11.9454i	0.548755	+	0.460460i	−0.325764	+	0.945451i	$0.605621\pi$
$674$	−5.93005	−	1.58895i	−0.228417	−	0.0612042i
$675$		0			0
$676$	13.1743	−	22.8185i	0.506702	−	0.877634i
$677$	9.05630	+	15.6860i	0.348062	+	0.602861i	0.985905	−	0.167305i	$-0.0535066\pi$
$677$	9.05630	+	15.6860i	0.348062	+	0.602861i	−0.637843	+	0.770166i	$0.720173\pi$
$678$		0			0
$679$	−28.2811	−	13.1877i	−1.08533	−	0.506097i
$680$	3.05126	−	0.817584i	0.117011	−	0.0313529i
$681$		0			0
$682$	4.88488	−	4.09890i	0.187052	−	0.156955i
$683$	−2.02560	+	0.944551i	−0.0775073	+	0.0361422i	−0.460985	−	0.887408i	$-0.652504\pi$
$683$	−2.02560	+	0.944551i	−0.0775073	+	0.0361422i	0.383478	+	0.923550i	$0.374726\pi$
$684$		0			0
$685$	−10.7471	+	7.52520i	−0.410625	+	0.287523i
$686$	8.42017	+	18.0571i	0.321484	+	0.689424i
$687$		0			0
$688$	1.11159	+	0.0972516i	0.0423790	+	0.00370768i
$689$	−3.00475	−	11.2139i	−0.114472	−	0.427215i
$690$		0			0
$691$	43.5634	−	7.68141i	1.65723	−	0.292215i	0.734774	−	0.678312i	$-0.237288\pi$
$691$	43.5634	−	7.68141i	1.65723	−	0.292215i	0.922458	+	0.386098i	$0.126177\pi$
$692$	4.73442	−	2.73342i	0.179976	−	0.103909i
$693$		0			0
$694$	−8.88836	+	24.4206i	−0.337398	+	0.926992i
$695$	−4.47662	+	16.7070i	−0.169808	+	0.633732i
$696$		0			0
$697$	18.5834	−	18.5834i	0.703896	−	0.703896i
$698$	−1.22215	−	13.9692i	−0.0462590	−	0.528743i
$699$		0			0
$700$	1.33131	−	7.55023i	0.0503188	−	0.285372i
$701$	5.74480	+	4.02255i	0.216978	+	0.151930i	0.677013	−	0.735971i	$-0.263274\pi$
$701$	5.74480	+	4.02255i	0.216978	+	0.151930i	−0.460035	+	0.887901i	$0.652163\pi$
$702$		0			0
$703$	27.6397	−	25.9445i	1.04245	−	0.978516i
$704$			2.53581i			0.0955718i
$705$		0			0
$706$	5.25638	+	0.926842i	0.197827	+	0.0348822i
$707$	0.210256	−	0.0765269i	0.00790749	−	0.00287809i
$708$		0			0
$709$	−12.1883	−	12.1883i	−0.457742	−	0.457742i	0.440172	−	0.897914i	$-0.354918\pi$
$709$	−12.1883	−	12.1883i	−0.457742	−	0.457742i	−0.897914	+	0.440172i	$0.854918\pi$
$710$	−3.47156	+	4.13724i	−0.130285	+	0.155268i
$711$		0			0
$712$	0.299545	+	0.109025i	0.0112259	+	0.00408590i
$713$	−16.4783	−	9.51374i	−0.617116	−	0.356292i
$714$		0			0
$715$	3.64005	+	20.6437i	0.136130	+	0.772031i
$716$	−3.63398	+	7.79310i	−0.135808	+	0.291242i
$717$		0			0
$718$	−0.263318	+	3.00974i	−0.00982693	+	0.112322i
$719$	−23.0445	−	27.4634i	−0.859416	−	1.02421i	−0.999420	−	0.0340616i	$-0.989156\pi$
$719$	−23.0445	−	27.4634i	−0.859416	−	1.02421i	0.140003	−	0.990151i	$-0.455289\pi$
$720$		0			0
$721$	9.42043	+	13.4538i	0.350835	+	0.501044i
$722$	−11.3796	−	16.2518i	−0.423505	−	0.604828i
$723$		0			0
$724$	4.14447	+	4.93919i	0.154028	+	0.183564i
$725$	2.49777	−	28.5496i	0.0927648	−	1.06031i
$726$		0			0
$727$	0.923111	−	1.97962i	0.0342363	−	0.0734200i	−0.888446	−	0.458981i	$-0.848214\pi$
$727$	0.923111	−	1.97962i	0.0342363	−	0.0734200i	0.922682	+	0.385561i	$0.125992\pi$
$728$	−2.55906	−	14.5131i	−0.0948449	−	0.537892i
$729$		0			0
$730$	12.3881	+	7.15226i	0.458503	+	0.264717i
$731$	−2.51343	−	0.914812i	−0.0929624	−	0.0338355i
$732$		0			0
$733$	23.1990	−	27.6475i	0.856873	−	1.02118i	−0.142633	−	0.989776i	$-0.545557\pi$
$733$	23.1990	−	27.6475i	0.856873	−	1.02118i	0.999507	−	0.0314064i	$-0.00999862\pi$
$734$	4.41391	+	4.41391i	0.162920	+	0.162920i
$735$		0			0
$736$	7.11021	−	2.58791i	0.262086	−	0.0953915i
$737$	19.5379	+	3.44506i	0.719688	+	0.126900i
$738$		0			0
$739$			20.3972i			0.750324i	0.926959	+	0.375162i	$0.122413\pi$
$739$			20.3972i			0.750324i	−0.926959	+	0.375162i	$0.877587\pi$
$740$	−4.38786	−	6.70841i	−0.161301	−	0.246606i
$741$		0			0
$742$	−3.56170	−	2.49393i	−0.130754	−	0.0915550i
$743$	3.57765	−	20.2899i	0.131251	−	0.744363i	−0.846146	−	0.532951i	$-0.821083\pi$
$743$	3.57765	−	20.2899i	0.131251	−	0.744363i	0.977397	−	0.211412i	$-0.0678061\pi$
$744$		0			0
$745$	1.94806	+	22.2665i	0.0713716	+	0.815781i
$746$	−26.4192	+	26.4192i	−0.967276	+	0.967276i
$747$		0			0
$748$	1.57323	−	5.87137i	0.0575229	−	0.214678i
$749$	−8.02185	+	22.0398i	−0.293112	+	0.805318i
$750$		0			0
$751$	1.33664	−	0.771711i	0.0487748	−	0.0281601i	−0.475414	−	0.879762i	$-0.657702\pi$
$751$	1.33664	−	0.771711i	0.0487748	−	0.0281601i	0.524189	+	0.851602i	$0.324369\pi$
$752$	10.9981	−	1.93927i	0.401061	−	0.0707179i
$753$		0			0
$754$	−14.2578	−	53.2109i	−0.519239	−	1.93783i
$755$	15.3911	+	1.34655i	0.560141	+	0.0490060i
$756$		0			0
$757$	11.1804	+	23.9764i	0.406358	+	0.871438i	0.997876	+	0.0651456i	$0.0207512\pi$
$757$	11.1804	+	23.9764i	0.406358	+	0.871438i	−0.591518	+	0.806292i	$0.701471\pi$
$758$	−3.25703	+	2.28059i	−0.118300	+	0.0828349i
$759$		0			0
$760$	−7.44338	+	3.47091i	−0.270000	+	0.125903i
$761$	−11.0793	+	9.29662i	−0.401624	+	0.337002i	−0.821121	−	0.570754i	$-0.806651\pi$
$761$	−11.0793	+	9.29662i	−0.401624	+	0.337002i	0.419497	+	0.907757i	$0.362206\pi$
$762$		0			0
$763$	6.09137	−	1.63218i	0.220523	−	0.0590888i
$764$	15.9767	+	7.45006i	0.578017	+	0.269534i
$765$		0			0
$766$	3.36611	+	5.83027i	0.121622	+	0.210656i
$767$	27.4089	−	47.4736i	0.989678	−	1.71417i
$768$		0			0
$769$	−17.0925	−	4.57993i	−0.616373	−	0.165157i	−0.0628946	−	0.998020i	$-0.520033\pi$
$769$	−17.0925	−	4.57993i	−0.616373	−	0.165157i	−0.553478	+	0.832864i	$0.686700\pi$
$770$	6.01411	+	5.04644i	0.216734	+	0.181861i
$771$		0			0
$772$	20.3936	−	1.78421i	0.733980	−	0.0642149i
$773$	11.1070	+	30.5161i	0.399489	+	1.09759i	0.962534	+	0.271161i	$0.0874077\pi$
$773$	11.1070	+	30.5161i	0.399489	+	1.09759i	−0.563045	+	0.826427i	$0.690370\pi$
$774$		0			0
$775$	−4.70694	+	6.72221i	−0.169078	+	0.241469i
$776$	−13.2824			−0.476809
$777$		0			0
$778$	21.3914			0.766920
$779$	−39.1913	+	55.9710i	−1.40418	+	2.00537i
$780$		0			0
$781$	3.55442	+	9.76568i	0.127187	+	0.349444i
$782$	−18.0684	+	1.58078i	−0.646126	+	0.0565287i
$783$		0			0
$784$	1.13422	+	0.951722i	0.0405078	+	0.0339901i
$785$	−16.6719	−	4.46722i	−0.595046	−	0.159442i
$786$		0			0
$787$	−10.9753	+	19.0098i	−0.391227	+	0.677625i	−0.992612	−	0.121335i	$-0.961283\pi$
$787$	−10.9753	+	19.0098i	−0.391227	+	0.677625i	0.601385	+	0.798960i	$0.294616\pi$
$788$	−7.61171	−	13.1839i	−0.271156	−	0.469656i
$789$		0			0
$790$	−11.2169	−	5.23052i	−0.399079	−	0.186094i
$791$	18.7027	−	5.01137i	0.664991	−	0.178184i
$792$		0			0
$793$	−53.3488	+	44.7650i	−1.89447	+	1.58965i
$794$	21.3708	−	9.96536i	0.758420	−	0.353657i
$795$		0			0
$796$	−19.4986	+	13.6531i	−0.691110	+	0.483920i
$797$	2.25822	+	4.84277i	0.0799902	+	0.171540i	0.942235	−	0.334952i	$-0.108720\pi$
$797$	2.25822	+	4.84277i	0.0799902	+	0.171540i	−0.862245	+	0.506491i	$0.830942\pi$
$798$		0			0
$799$	−26.6681	−	2.33316i	−0.943449	−	0.0825411i
$800$	−0.844617	−	3.15215i	−0.0298617	−	0.111445i
$801$		0			0
$802$	4.15424	−	0.732504i	0.146691	−	0.0258656i
$803$	23.8377	−	13.7627i	0.841213	−	0.485674i
$804$		0			0
$805$	8.01217	−	22.0133i	0.282392	−	0.775865i
$806$	−4.08268	+	15.2368i	−0.143806	+	0.536692i
$807$		0			0
$808$	0.0673445	−	0.0673445i	0.00236917	−	0.00236917i
$809$	2.96421	+	33.8811i	0.104216	+	1.19119i	0.850649	+	0.525734i	$0.176209\pi$
$809$	2.96421	+	33.8811i	0.104216	+	1.19119i	−0.746433	+	0.665461i	$0.768235\pi$
$810$		0			0
$811$	6.51751	−	36.9626i	0.228861	−	1.29793i	−0.626305	−	0.779578i	$-0.715433\pi$
$811$	6.51751	−	36.9626i	0.228861	−	1.29793i	0.855166	−	0.518355i	$-0.173455\pi$
$812$	−16.9006	−	11.8339i	−0.593096	−	0.415290i
$813$		0			0
$814$	−15.4008	+	0.857810i	−0.539799	+	0.0300662i
$815$		−	16.8542i		−	0.590375i
$816$		0			0
$817$	6.84842	+	1.20756i	0.239596	+	0.0422472i
$818$	−7.83392	+	2.85131i	−0.273906	+	0.0996938i
$819$		0			0
$820$	10.2165	+	10.2165i	0.356775	+	0.356775i
$821$	24.8711	−	29.6402i	0.868008	−	1.03445i	−0.131064	−	0.991374i	$-0.541839\pi$
$821$	24.8711	−	29.6402i	0.868008	−	1.03445i	0.999072	−	0.0430776i	$-0.0137163\pi$
$822$		0			0
$823$	−31.4307	−	11.4398i	−1.09560	−	0.398767i	−0.269910	−	0.962885i	$-0.586994\pi$
$823$	−31.4307	−	11.4398i	−1.09560	−	0.398767i	−0.825694	+	0.564118i	$0.809216\pi$
$824$	6.05431	+	3.49546i	0.210912	+	0.121770i
$825$		0			0
$826$	−3.56511	−	20.2187i	−0.124046	−	0.703500i
$827$	−20.1528	+	43.2179i	−0.700782	+	1.50283i	0.156331	+	0.987705i	$0.450033\pi$
$827$	−20.1528	+	43.2179i	−0.700782	+	1.50283i	−0.857113	+	0.515128i	$0.827745\pi$
$828$		0			0
$829$	4.41492	−	50.4628i	0.153337	−	1.75265i	−0.397106	−	0.917773i	$-0.629985\pi$
$829$	4.41492	−	50.4628i	0.153337	−	1.75265i	0.550442	−	0.834873i	$-0.314459\pi$
$830$	−0.961095	−	1.14539i	−0.0333601	−	0.0397570i
$831$		0			0
$832$	−3.59795	−	5.13841i	−0.124737	−	0.178142i
$833$	−2.03570	−	2.90728i	−0.0705328	−	0.100731i
$834$		0			0
$835$	10.3611	+	12.3478i	0.358559	+	0.427314i
$836$	−1.37737	+	15.7434i	−0.0476373	+	0.544497i
$837$		0			0
$838$	−6.57488	+	14.0999i	−0.227126	+	0.487072i
$839$	3.52228	+	19.9758i	0.121603	+	0.689642i	0.983268	+	0.182165i	$0.0583107\pi$
$839$	3.52228	+	19.9758i	0.121603	+	0.689642i	−0.861665	+	0.507477i	$0.830578\pi$
$840$		0			0
$841$	−41.6760	−	24.0617i	−1.43710	−	0.829712i
$842$	−15.7325	−	5.72616i	−0.542178	−	0.197336i
$843$		0			0
$844$	−14.0814	+	16.7816i	−0.484703	+	0.577647i
$845$	−24.5526	−	24.5526i	−0.844635	−	0.844635i
$846$		0			0
$847$	−10.0883	+	3.67184i	−0.346638	+	0.126166i
$848$	−1.82263	−	0.321379i	−0.0625895	−	0.0110362i
$849$		0			0
$850$			7.82245i			0.268308i
$851$	18.1225	+	42.3074i	0.621231	+	1.45028i
$852$		0			0
$853$	−0.677954	−	0.474709i	−0.0232127	−	0.0162537i	0.561913	−	0.827197i	$-0.310066\pi$
$853$	−0.677954	−	0.474709i	−0.0232127	−	0.0162537i	−0.585125	+	0.810943i	$0.698955\pi$
$854$	−4.52920	+	25.6864i	−0.154986	+	0.878970i
$855$		0			0
$856$	0.870108	+	9.94539i	0.0297397	+	0.339926i
$857$	−12.2467	+	12.2467i	−0.418339	+	0.418339i	−0.884631	−	0.466292i	$-0.845590\pi$
$857$	−12.2467	+	12.2467i	−0.418339	+	0.418339i	0.466292	+	0.884631i	$0.345590\pi$
$858$		0			0
$859$	7.67775	−	28.6538i	0.261961	−	0.977654i	−0.702123	−	0.712056i	$-0.747764\pi$
$859$	7.67775	−	28.6538i	0.261961	−	0.977654i	0.964084	−	0.265597i	$-0.0855692\pi$
$860$	0.502931	−	1.38179i	0.0171498	−	0.0471187i
$861$		0			0
$862$	−13.3551	+	7.71056i	−0.454876	+	0.262623i
$863$	15.7822	−	2.78283i	0.537232	−	0.0947285i	0.101552	−	0.994830i	$-0.467619\pi$
$863$	15.7822	−	2.78283i	0.537232	−	0.0947285i	0.435680	+	0.900102i	$0.356508\pi$
$864$		0			0
$865$	−1.86461	−	6.95884i	−0.0633988	−	0.236608i
$866$	−2.15940	−	0.188923i	−0.0733796	−	0.00641988i
$867$		0			0
$868$	2.49677	+	5.35433i	0.0847458	+	0.181738i
$869$	−19.5084	+	13.6599i	−0.661776	+	0.463381i
$870$		0			0
$871$	−44.4785	+	20.7407i	−1.50710	+	0.702771i
$872$	2.05627	−	1.72542i	0.0696341	−	0.0584299i
$873$		0			0
$874$	45.5490	−	12.2048i	1.54072	−	0.412834i
$875$	−23.1864	−	10.8120i	−0.783844	−	0.365512i
$876$		0			0
$877$	4.18478	+	7.24825i	0.141310	+	0.244756i	0.927990	−	0.372605i	$-0.121535\pi$
$877$	4.18478	+	7.24825i	0.141310	+	0.244756i	−0.786680	+	0.617361i	$0.788202\pi$
$878$	−6.05638	+	10.4900i	−0.204393	+	0.354019i
$879$		0			0
$880$	3.22787	+	0.864905i	0.108811	+	0.0291559i
$881$	−27.2866	−	22.8962i	−0.919309	−	0.771392i	0.0545578	−	0.998511i	$-0.482625\pi$
$881$	−27.2866	−	22.8962i	−0.919309	−	0.771392i	−0.973867	+	0.227119i	$0.927070\pi$
$882$		0			0
$883$	−17.9967	+	1.57451i	−0.605638	+	0.0529864i	−0.385850	−	0.922561i	$-0.626092\pi$
$883$	−17.9967	+	1.57451i	−0.605638	+	0.0529864i	−0.219787	+	0.975548i	$0.570536\pi$
$884$	5.14275	+	14.1296i	0.172969	+	0.475230i
$885$		0			0
$886$	6.64079	−	9.48403i	0.223102	−	0.318622i
$887$	−54.5653			−1.83212			−0.916062	−	0.401037i	$-0.868650\pi$
$887$	−54.5653			−1.83212			−0.916062	+	0.401037i	$0.868650\pi$
$888$		0			0
$889$	31.9008			1.06992
$890$	0.240948	−	0.344110i	0.00807660	−	0.0115346i
$891$		0			0
$892$	5.71658	+	15.7062i	0.191405	+	0.525882i
$893$	69.3347	−	6.06600i	2.32020	−	0.202991i
$894$		0			0
$895$	8.68051	+	7.28381i	0.290157	+	0.243471i
$896$	−2.26929	−	0.608053i	−0.0758115	−	0.0203136i
$897$		0			0
$898$	−16.5194	+	28.6125i	−0.551260	+	0.954810i
$899$	11.0420	+	19.1253i	0.368271	+	0.637864i
$900$		0			0
$901$	4.02071	+	1.87489i	0.133949	+	0.0624616i
$902$	26.8547	−	7.19569i	0.894164	−	0.239590i
$903$		0			0
$904$	6.31348	−	5.29764i	0.209983	−	0.176197i
$905$	7.70076	−	3.59093i	0.255982	−	0.119366i
$906$		0			0
$907$	−4.13334	+	2.89420i	−0.137245	+	0.0961003i	−0.640183	−	0.768222i	$-0.721141\pi$
$907$	−4.13334	+	2.89420i	−0.137245	+	0.0961003i	0.502938	+	0.864323i	$0.332253\pi$
$908$	6.51676	+	13.9752i	0.216266	+	0.463784i
$909$		0			0
$910$	−19.3468	−	1.69263i	−0.641342	−	0.0561101i
$911$	−8.23073	−	30.7175i	−0.272696	−	1.01772i	−0.957370	−	0.288866i	$-0.906722\pi$
$911$	−8.23073	−	30.7175i	−0.272696	−	1.01772i	0.684673	−	0.728850i	$-0.259945\pi$
$912$		0			0
$913$	−2.83341	+	0.499607i	−0.0937723	+	0.0165346i
$914$	−21.9195	+	12.6552i	−0.725033	+	0.418598i
$915$		0			0
$916$	−3.69407	+	10.1494i	−0.122056	+	0.335345i
$917$	0.493816	−	1.84295i	0.0163073	−	0.0608595i
$918$		0			0
$919$	6.16884	−	6.16884i	0.203491	−	0.203491i	−0.598003	−	0.801494i	$-0.704039\pi$
$919$	6.16884	−	6.16884i	0.203491	−	0.203491i	0.801494	+	0.598003i	$0.204039\pi$
$920$	−0.869059	−	9.93339i	−0.0286520	−	0.327494i
$921$		0			0
$922$	3.58311	−	20.3208i	0.118004	−	0.669231i
$923$	−21.0586	−	14.7454i	−0.693152	−	0.485350i
$924$		0			0
$925$	18.8584	−	6.19596i	0.620061	−	0.203722i
$926$		−	29.8103i		−	0.979628i
$927$		0			0
$928$	−8.64857	−	1.52498i	−0.283903	−	0.0500598i
$929$	30.5093	−	11.1045i	1.00098	−	0.364326i	0.211016	−	0.977483i	$-0.432323\pi$
$929$	30.5093	−	11.1045i	1.00098	−	0.364326i	0.789961	+	0.613157i	$0.210101\pi$
$930$		0			0
$931$	6.52478	+	6.52478i	0.213841	+	0.213841i
$932$	14.1416	−	16.8533i	0.463223	−	0.552048i
$933$		0			0
$934$	−35.6955	−	12.9921i	−1.16799	−	0.425114i
$935$	−6.93717	−	4.00518i	−0.226870	−	0.130983i
$936$		0			0
$937$	−3.07577	−	17.4436i	−0.100481	−	0.569857i	−0.992929	−	0.118707i	$-0.962125\pi$
$937$	−3.07577	−	17.4436i	−0.100481	−	0.569857i	0.892448	−	0.451150i	$-0.148986\pi$
$938$	−7.76791	+	16.6583i	−0.253631	+	0.543914i
$939$		0			0
$940$	1.28269	−	14.6612i	0.0418366	−	0.478195i
$941$	14.2805	+	17.0189i	0.465532	+	0.554799i	0.946820	−	0.321763i	$-0.104275\pi$
$941$	14.2805	+	17.0189i	0.465532	+	0.554799i	−0.481288	+	0.876562i	$0.659831\pi$
$942$		0			0
$943$	−47.5827	−	67.9551i	−1.54950	−	2.21292i
$944$	−5.01243	−	7.15850i	−0.163141	−	0.232989i
$945$		0			0
$946$	−1.81880	−	2.16756i	−0.0591342	−	0.0704733i
$947$	1.16399	−	13.3045i	0.0378247	−	0.432339i	−0.953546	−	0.301248i	$-0.902597\pi$
$947$	1.16399	−	13.3045i	0.0378247	−	0.432339i	0.991370	−	0.131090i	$-0.0418478\pi$
$948$		0			0
$949$	−28.7759	+	61.7102i	−0.934107	+	2.00320i
$950$	−3.53160	−	20.0287i	−0.114580	−	0.649817i
$951$		0			0
$952$	4.87703	+	2.81576i	0.158065	+	0.0912591i
$953$	3.29224	+	1.19828i	0.106646	+	0.0388160i	0.394792	−	0.918771i	$-0.370817\pi$
$953$	3.29224	+	1.19828i	0.106646	+	0.0388160i	−0.288146	+	0.957586i	$0.593039\pi$
$954$		0			0
$955$	14.9326	−	17.7960i	0.483207	−	0.575864i
$956$	−8.51835	−	8.51835i	−0.275503	−	0.275503i
$957$		0			0
$958$	34.3983	−	12.5200i	1.11136	−	0.404502i
$959$	−23.0339	−	4.06149i	−0.743803	−	0.131152i
$960$		0			0
$961$			24.6763i			0.796011i
$962$	29.9902	−	23.5898i	0.966924	−	0.760567i
$963$		0			0
$964$	−12.3898	−	8.67541i	−0.399048	−	0.279416i
$965$	4.68463	−	26.5679i	0.150804	−	0.855250i
$966$		0			0
$967$	3.63781	+	41.5803i	0.116984	+	1.33713i	0.797020	+	0.603953i	$0.206409\pi$
$967$	3.63781	+	41.5803i	0.116984	+	1.33713i	−0.680036	+	0.733179i	$0.738036\pi$
$968$	−3.23126	+	3.23126i	−0.103857	+	0.103857i
$969$		0			0
$970$	−4.53031	+	16.9074i	−0.145460	+	0.542862i
$971$	−15.6214	+	42.9195i	−0.501315	+	1.37735i	0.388676	+	0.921374i	$0.372933\pi$
$971$	−15.6214	+	42.9195i	−0.501315	+	1.37735i	−0.889991	+	0.455978i	$0.849290\pi$
$972$		0			0
$973$	−26.7038	+	15.4175i	−0.856085	+	0.494261i
$974$	24.5454	−	4.32801i	0.786484	−	0.138678i
$975$		0			0
$976$	2.87344	+	10.7238i	0.0919767	+	0.343262i
$977$	−15.0255	−	1.31456i	−0.480710	−	0.0420567i	−0.155774	−	0.987793i	$-0.549787\pi$
$977$	−15.0255	−	1.31456i	−0.480710	−	0.0420567i	−0.324936	+	0.945736i	$0.605343\pi$
$978$		0			0
$979$	−0.341618	−	0.732601i	−0.0109181	−	0.0234140i
$980$	1.59832	−	1.11916i	0.0510564	−	0.0357501i
$981$		0			0
$982$	−22.0207	+	10.2684i	−0.702708	+	0.327678i
$983$	45.4440	−	38.1320i	1.44944	−	1.21622i	0.516450	−	0.856317i	$-0.327253\pi$
$983$	45.4440	−	38.1320i	1.44944	−	1.21622i	0.932989	−	0.359906i	$-0.117191\pi$
$984$		0			0
$985$	−19.3781	+	5.19236i	−0.617439	+	0.165442i
$986$	19.0787	+	8.89653i	0.607589	+	0.283323i
$987$		0			0
$988$	−19.5467	−	33.8558i	−0.621862	−	1.07710i
$989$	−4.22151	+	7.31186i	−0.134236	+	0.232504i
$990$		0			0
$991$	−42.6867	−	11.4379i	−1.35599	−	0.363336i	−0.493647	−	0.869663i	$-0.664336\pi$
$991$	−42.6867	−	11.4379i	−1.35599	−	0.363336i	−0.862342	+	0.506327i	$0.831003\pi$
$992$	1.92636	+	1.61641i	0.0611621	+	0.0513211i
$993$		0			0
$994$	−9.59158	+	0.839155i	−0.304226	+	0.0266164i
$995$	10.7287	+	29.4769i	0.340123	+	0.934479i
$996$		0			0
$997$	9.94656	−	14.2052i	0.315011	−	0.449882i	−0.630157	−	0.776468i	$-0.717009\pi$
$997$	9.94656	−	14.2052i	0.315011	−	0.449882i	0.945167	+	0.326586i	$0.105898\pi$
$998$	−3.23271			−0.102330
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bs.b.17.6	yes	96
3.2	odd	2	inner	666.2.bs.b.17.3	✓	96
37.24	odd	36	inner	666.2.bs.b.431.3	yes	96
111.98	even	36	inner	666.2.bs.b.431.6	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.17.3	✓	96	3.2	odd	2	inner
666.2.bs.b.17.6	yes	96	1.1	even	1	trivial
666.2.bs.b.431.3	yes	96	37.24	odd	36	inner
666.2.bs.b.431.6	yes	96	111.98	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.31281 + 0.114856i) q^{5} +(-1.79970 - 1.51012i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.31281 + 0.114856i) q^{5} +(-1.79970 - 1.51012i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-0.658910 + 1.14127i) q^{10} +(1.26790 + 2.19607i) q^{11} +(-5.68512 - 2.65102i) q^{13} +(-2.26929 + 0.608053i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.17248 - 1.01304i) q^{17} +(-5.10508 + 3.57462i) q^{19} +(0.556935 + 1.19435i) q^{20} +(2.52616 + 0.221010i) q^{22} +(-1.95836 - 7.30871i) q^{23} +(-3.21377 + 0.566675i) q^{25} +(-5.43244 + 3.13642i) q^{26} +(-0.803520 + 2.20765i) q^{28} +(-2.27295 + 8.48275i) q^{29} +(1.77815 - 1.77815i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.416246 - 2.36065i) q^{34} +(2.53610 + 1.77580i) q^{35} +(-6.02076 + 0.866319i) q^{37} +6.23215i q^{38} +(1.29780 + 0.228837i) q^{40} +(10.3026 - 3.74984i) q^{41} +(-0.789016 - 0.789016i) q^{43} +(1.62998 - 1.94254i) q^{44} +(-7.11021 - 2.58791i) q^{46} +(-9.67161 - 5.58391i) q^{47} +(-0.257106 - 1.45812i) q^{49} +(-1.37915 + 2.95760i) q^{50} +(-0.546714 + 6.24897i) q^{52} +(1.18964 + 1.41776i) q^{53} +(-1.91674 - 2.73739i) q^{55} +(1.34752 + 1.92446i) q^{56} +(5.64495 + 6.72739i) q^{58} +(-0.761646 + 8.70565i) q^{59} +(4.69196 - 10.0620i) q^{61} +(-0.436671 - 2.47649i) q^{62} +(0.866025 + 0.500000i) q^{64} +(7.76795 + 2.82730i) q^{65} +(5.02896 - 5.99328i) q^{67} +(-1.69498 - 1.69498i) q^{68} +(2.90929 - 1.05890i) q^{70} +(4.03601 + 0.711657i) q^{71} -10.8547i q^{73} +(-2.74372 + 5.42881i) q^{74} +(5.10508 + 3.57462i) q^{76} +(1.03450 - 5.86695i) q^{77} +(0.818534 + 9.35588i) q^{79} +(0.931840 - 0.931840i) q^{80} +(2.83764 - 10.5902i) q^{82} +(-0.388056 + 1.06617i) q^{83} +(-2.73569 + 1.57945i) q^{85} +(-1.09888 + 0.193763i) q^{86} +(-0.656315 - 2.44940i) q^{88} +(-0.317556 - 0.0277825i) q^{89} +(6.22813 + 13.3563i) q^{91} +(-6.19814 + 4.33998i) q^{92} +(-10.1215 + 4.71972i) q^{94} +(6.29142 - 5.27913i) q^{95} +(12.8298 - 3.43773i) q^{97} +(-1.34189 - 0.625736i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 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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