LMFDB - Embedded newform 666.2.bs.b.431.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(17,666)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([18, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("666.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			431.3
Character	$\chi$	$=$	666.431
Dual form			666.2.bs.b.17.3

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

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

Coefficient data

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

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

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

$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	1.31281	+	0.114856i	0.587105	+	0.0513650i	0.376838	−	0.926279i	$-0.377011\pi$
$5$	1.31281	+	0.114856i	0.587105	+	0.0513650i	0.210267	+	0.977644i	$0.432567\pi$
$6$		0			0
$7$	−1.79970	+	1.51012i	−0.680221	+	0.570773i	−0.916071	−	0.401016i	$-0.868657\pi$
$7$	−1.79970	+	1.51012i	−0.680221	+	0.570773i	0.235850	+	0.971790i	$0.424213\pi$
$8$	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	$-0.958197\pi$
$11$	−1.26790	+	2.19607i	−0.382287	+	0.662141i	0.609102	+	0.793092i	$0.291530\pi$
$12$		0			0
$13$	−5.68512	+	2.65102i	−1.57677	+	0.735260i	−0.996842	−	0.0794083i	$-0.974697\pi$
$13$	−5.68512	+	2.65102i	−1.57677	+	0.735260i	−0.579928	+	0.814668i	$0.696919\pi$
$14$	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	$-0.454995\pi$
$17$	−2.17248	−	1.01304i	−0.526903	−	0.245699i	−0.667820	+	0.744322i	$0.732773\pi$
$18$		0			0
$19$	−5.10508	−	3.57462i	−1.17119	−	0.820073i	−0.184520	−	0.982829i	$-0.559073\pi$
$19$	−5.10508	−	3.57462i	−1.17119	−	0.820073i	−0.986666	+	0.162755i	$0.947962\pi$
$20$	−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	−0.389452	−	0.921047i	$-0.627335\pi$
$23$	1.95836	−	7.30871i	0.408347	−	1.52397i	0.797799	−	0.602924i	$-0.205998\pi$
$24$		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	0.770228	+	0.637769i	$0.220143\pi$
$29$	2.27295	+	8.48275i	0.422075	+	1.57521i	−0.348152	+	0.937438i	$0.613191\pi$
$30$		0			0
$31$	1.77815	+	1.77815i	0.319366	+	0.319366i	0.848524	−	0.529158i	$-0.177492\pi$
$31$	1.77815	+	1.77815i	0.319366	+	0.319366i	−0.529158	+	0.848524i	$0.677492\pi$
$32$	−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	$-0.716025\pi$
$41$	−10.3026	−	3.74984i	−1.60899	−	0.585626i	−0.981241	+	0.192787i	$0.938247\pi$
$42$		0			0
$43$	−0.789016	+	0.789016i	−0.120324	+	0.120324i	−0.764705	−	0.644381i	$-0.777115\pi$
$43$	−0.789016	+	0.789016i	−0.120324	+	0.120324i	0.644381	+	0.764705i	$0.277115\pi$
$44$	−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	$-0.363680\pi$
$47$	9.67161	−	5.58391i	1.41075	−	0.814496i	0.995459	+	0.0951926i	$0.0303467\pi$
$48$		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	$-0.818348\pi$
$53$	−1.18964	+	1.41776i	−0.163409	+	0.194744i	0.678126	+	0.734946i	$0.262792\pi$
$54$		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	0.868887	+	0.495010i	$0.164835\pi$
$59$	0.761646	+	8.70565i	0.0991579	+	1.13338i	−0.769730	+	0.638370i	$0.779609\pi$
$60$		0			0
$61$	4.69196	+	10.0620i	0.600745	+	1.28830i	0.937918	+	0.346858i	$0.112751\pi$
$61$	4.69196	+	10.0620i	0.600745	+	1.28830i	−0.337173	+	0.941443i	$0.609471\pi$
$62$	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	0.980094	−	0.198534i	$-0.0636179\pi$
$67$	5.02896	+	5.99328i	0.614385	+	0.732196i	−0.365709	+	0.930729i	$0.619173\pi$
$68$	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	$-0.633749\pi$
$71$	−4.03601	+	0.711657i	−0.478986	+	0.0844582i	−0.0710580	+	0.997472i	$0.522638\pi$
$72$		0			0
$73$			10.8547i			1.27044i	0.772330	+	0.635222i	$0.219091\pi$
$73$			10.8547i			1.27044i	−0.772330	+	0.635222i	$0.780909\pi$
$74$	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	−0.799768	−	0.600309i	$-0.795044\pi$
$79$	0.818534	−	9.35588i	0.0920922	−	1.05262i	0.891861	−	0.452310i	$-0.149400\pi$
$80$	−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	$-0.0912774\pi$
$83$	0.388056	+	1.06617i	0.0425947	+	0.117028i	−0.916572	+	0.399870i	$0.869055\pi$
$84$		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	$-0.522400\pi$
$89$	0.317556	−	0.0277825i	0.0336609	−	0.00294494i	0.103974	+	0.994580i	$0.466844\pi$
$90$		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	0.842458	−	0.538762i	$-0.181108\pi$
$97$	12.8298	+	3.43773i	1.30267	+	0.349049i	0.460209	+	0.887811i	$0.347774\pi$
$98$	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	$-0.165158\pi$
$101$	0.0476198	+	0.0824799i	0.00473834	+	0.00820705i	−0.863647	+	0.504098i	$0.831825\pi$
$102$		0			0
$103$	−6.75270	+	1.80938i	−0.665364	+	0.178284i	−0.575665	−	0.817685i	$-0.695257\pi$
$103$	−6.75270	+	1.80938i	−0.665364	+	0.178284i	−0.0896982	+	0.995969i	$0.528590\pi$
$104$	−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	−0.657993	−	0.753024i	$-0.728594\pi$
$107$	3.41452	−	9.38130i	0.330094	−	0.906925i	0.988086	−	0.153901i	$-0.0491835\pi$
$108$		0			0
$109$	−1.53963	−	2.19883i	−0.147470	−	0.210609i	0.738620	−	0.674122i	$-0.235478\pi$
$109$	−1.53963	−	2.19883i	−0.147470	−	0.210609i	−0.886090	+	0.463513i	$0.846589\pi$
$110$	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	$-0.0677295\pi$
$113$	4.72723	+	6.75118i	0.444700	+	0.635098i	−0.532748	+	0.846274i	$0.678841\pi$
$114$		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	0.0515366	−	0.998671i	$-0.483588\pi$
$127$	−10.4018	−	8.72817i	−0.923013	−	0.774500i	−0.974550	+	0.224171i	$0.928033\pi$
$128$	−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	$-0.872406\pi$
$131$	−0.343220	+	0.736037i	−0.0299873	+	0.0643079i	0.890744	+	0.454506i	$0.150184\pi$
$132$		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	$-0.473159\pi$
$137$	−8.62186	−	4.97783i	−0.736615	−	0.425285i	−0.820837	+	0.571162i	$0.806493\pi$
$138$		0			0
$139$	4.48900	+	12.3334i	0.380752	+	1.04611i	0.971041	+	0.238915i	$0.0767916\pi$
$139$	4.48900	+	12.3334i	0.380752	+	1.04611i	−0.590289	+	0.807192i	$0.700986\pi$
$140$	−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	−0.622406	−	0.782695i	$-0.713845\pi$
$151$	−11.5457	+	2.03582i	−0.939579	+	0.165673i	−0.317173	+	0.948368i	$0.602734\pi$
$152$	−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	0.199534	−	0.979891i	$-0.436057\pi$
$157$	12.3075	−	4.47958i	0.982248	−	0.357509i	0.782714	+	0.622382i	$0.213835\pi$
$158$	−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	−0.905882	−	0.423531i	$-0.860790\pi$
$163$	−1.11467	−	12.7407i	−0.0873078	−	0.997932i	0.818574	−	0.574401i	$-0.194765\pi$
$164$	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	$-0.648636\pi$
$167$	7.01571	−	10.0195i	0.542892	−	0.775330i	0.993059	+	0.117614i	$0.0375246\pi$
$168$		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	0.927220	+	0.374518i	$0.122192\pi$
$173$	−0.949307	+	5.38379i	−0.0721745	+	0.409322i	−0.999394	+	0.0348039i	$0.988919\pi$
$174$		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	$-0.645863\pi$
$179$	6.08023	−	6.08023i	0.454458	−	0.454458i	0.896831	+	0.442373i	$0.145863\pi$
$180$		0			0
$181$	−6.05881	−	2.20523i	−0.450348	−	0.163913i	0.106881	−	0.994272i	$-0.465913\pi$
$181$	−6.05881	−	2.20523i	−0.450348	−	0.163913i	−0.557230	+	0.830358i	$0.688136\pi$
$182$	−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	$-0.0298566\pi$
$191$	12.4651	+	12.4651i	0.901944	+	0.901944i	−0.0936599	+	0.995604i	$0.529857\pi$
$192$		0			0
$193$	−5.29840	−	19.7739i	−0.381387	−	1.42336i	−0.843783	−	0.536684i	$-0.819677\pi$
$193$	−5.29840	−	19.7739i	−0.381387	−	1.42336i	0.462396	−	0.886673i	$-0.346990\pi$
$194$	−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	$-0.626895\pi$
$197$	−14.9921	−	2.64352i	−1.06815	−	0.188343i	−0.679968	+	0.733242i	$0.738006\pi$
$198$		0			0
$199$	−6.16077	+	22.9923i	−0.436726	+	1.62988i	0.300177	+	0.953883i	$0.402954\pi$
$199$	−6.16077	+	22.9923i	−0.436726	+	1.62988i	−0.736903	+	0.675999i	$0.763712\pi$
$200$	−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	0.191773	+	0.981439i	$0.438576\pi$
$211$	−10.9534	+	18.9719i	−0.754065	+	1.30608i	−0.945838	+	0.324639i	$0.894757\pi$
$212$	−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	$-0.301227\pi$
$227$	15.3613	+	1.34394i	1.01956	+	0.0892003i	0.434902	+	0.900478i	$0.356783\pi$
$228$		0			0
$229$	−8.27385	+	6.94259i	−0.546751	+	0.458779i	−0.873839	−	0.486215i	$-0.838377\pi$
$229$	−8.27385	+	6.94259i	−0.546751	+	0.458779i	0.327088	+	0.944994i	$0.393933\pi$
$230$	−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	0.240093	+	0.970750i	$0.422822\pi$
$233$	−11.0002	+	19.0529i	−0.720647	+	1.24820i	−0.960741	+	0.277448i	$0.910511\pi$
$234$		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	$-0.488505\pi$
$239$	−10.9181	−	5.09118i	−0.706232	−	0.329321i	−0.742337	+	0.670027i	$0.766283\pi$
$240$		0			0
$241$	12.3898	+	8.67541i	0.798095	+	0.558832i	0.899963	−	0.435966i	$-0.143593\pi$
$241$	12.3898	+	8.67541i	0.798095	+	0.558832i	−0.101868	+	0.994798i	$0.532482\pi$
$242$	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	0.990350	+	0.138592i	$0.0442575\pi$
$251$	3.19993	+	11.9423i	0.201977	+	0.753790i	−0.788372	+	0.615199i	$0.789076\pi$
$252$		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	$-0.617414\pi$
$257$	6.29396	−	4.40708i	0.392606	−	0.274906i	0.753166	+	0.657830i	$0.228526\pi$
$258$		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	$-0.344562\pi$
$263$	4.23067	+	1.53984i	0.260874	+	0.0949504i	−0.208272	+	0.978071i	$0.566784\pi$
$264$		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	$-0.624945\pi$
$269$	3.71281	−	2.14359i	0.226374	−	0.130697i	0.608898	+	0.793248i	$0.291612\pi$
$270$		0			0
$271$	3.01658	−	17.1079i	0.183244	−	1.03923i	−0.744947	−	0.667124i	$-0.767525\pi$
$271$	3.01658	−	17.1079i	0.183244	−	1.03923i	0.928191	−	0.372105i	$-0.121364\pi$
$272$	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	−0.836559	−	0.547877i	$-0.815436\pi$
$277$	−0.592556	+	0.846257i	−0.0356032	+	0.0508467i	0.800956	+	0.598723i	$0.204325\pi$
$278$	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	0.896525	+	0.442993i	$0.146083\pi$
$281$	1.51781	+	17.3487i	0.0905451	+	1.03494i	−0.805980	+	0.591943i	$0.798361\pi$
$282$		0			0
$283$	−8.61652	−	18.4782i	−0.512199	−	1.09841i	−0.977047	−	0.213024i	$-0.931669\pi$
$283$	−8.61652	−	18.4782i	−0.512199	−	1.09841i	0.464848	−	0.885390i	$-0.346109\pi$
$284$	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	$-0.605058\pi$
$293$	−5.22200	+	0.920779i	−0.305072	+	0.0537925i	0.0190163	+	0.999819i	$0.493947\pi$
$294$		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	0.0225047	−	0.999747i	$-0.492836\pi$
$307$	−14.5787	−	8.41700i	−0.832049	−	0.480384i	−0.854554	+	0.519363i	$0.826169\pi$
$308$	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	$-0.702655\pi$
$311$	−18.3471	+	1.60516i	−1.04037	+	0.0910202i	−0.445853	+	0.895106i	$0.647100\pi$
$312$		0			0
$313$	−10.8404	+	23.2473i	−0.612734	+	1.31401i	0.317921	+	0.948117i	$0.397015\pi$
$313$	−10.8404	+	23.2473i	−0.612734	+	1.31401i	−0.930656	+	0.365896i	$0.880763\pi$
$314$	−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	$-0.191289\pi$
$317$	7.32092	+	6.14298i	0.411184	+	0.345024i	−0.413614	+	0.910452i	$0.635734\pi$
$318$		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	0.674609	−	0.738175i	$-0.264312\pi$
$331$	−4.54433	−	6.48997i	−0.249779	−	0.356721i	−0.924388	+	0.381454i	$0.875423\pi$
$332$	−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	−0.983653	−	0.180076i	$-0.942366\pi$
$337$	−2.09974	+	5.76900i	−0.114380	+	0.314257i	0.869272	+	0.494333i	$0.164588\pi$
$338$	−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	$-0.170940\pi$
$347$	25.1023	+	6.72615i	1.34756	+	0.361078i	0.488328	+	0.872660i	$0.337607\pi$
$348$		0			0
$349$	10.7419	+	9.01354i	0.575002	+	0.482484i	0.883301	−	0.468806i	$-0.155316\pi$
$349$	10.7419	+	9.01354i	0.575002	+	0.482484i	−0.308300	+	0.951289i	$0.599760\pi$
$350$	−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	$-0.906478\pi$
$353$	−2.25571	+	4.83739i	−0.120059	+	0.257468i	0.837089	+	0.547067i	$0.184256\pi$
$354$		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	$-0.307928\pi$
$359$	2.61646	+	1.51062i	0.138092	+	0.0797273i	−0.429363	+	0.903132i	$0.641262\pi$
$360$		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	0.943359	−	0.331773i	$-0.107647\pi$
$367$	−1.08395	−	6.14738i	−0.0565817	−	0.320891i	−0.999941	+	0.0108828i	$0.996536\pi$
$368$	−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	−0.996640	−	0.0819046i	$-0.973900\pi$
$373$	−36.7948	+	6.48792i	−1.90516	+	0.335932i	−0.908522	+	0.417836i	$0.862789\pi$
$374$	−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	−0.436193	−	0.899853i	$-0.643673\pi$
$379$	−3.73631	+	1.35990i	−0.191921	+	0.0698536i	0.244272	+	0.969707i	$0.421451\pi$
$380$	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	$-0.0838659\pi$
$383$	2.84516	+	6.10146i	0.145381	+	0.311770i	−0.820111	+	0.572205i	$0.806088\pi$
$384$		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	$-0.988000\pi$
$389$	−12.2696	+	17.5228i	−0.622095	+	0.888443i	0.377195	+	0.926134i	$0.376889\pi$
$390$		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	0.109378	−	0.994000i	$-0.465114\pi$
$397$	20.4209	−	11.7900i	1.02490	−	0.591724i	0.915518	+	0.402276i	$0.131781\pi$
$398$	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	$-0.783589\pi$
$401$	−2.98281	+	2.98281i	−0.148954	+	0.148954i	0.628697	+	0.777651i	$0.283589\pi$
$402$		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	−0.730097	−	0.683343i	$-0.760525\pi$
$409$	−6.82901	+	4.78172i	−0.337673	+	0.236441i	0.392425	+	0.919784i	$0.371636\pi$
$410$	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	$-0.320363\pi$
$419$	15.3211	+	2.70153i	0.748487	+	0.131978i	0.213622	+	0.976916i	$0.431474\pi$
$420$		0			0
$421$	−4.33319	+	16.1717i	−0.211187	+	0.788160i	0.776287	+	0.630379i	$0.217101\pi$
$421$	−4.33319	+	16.1717i	−0.211187	+	0.788160i	−0.987474	+	0.157781i	$0.949566\pi$
$422$	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	$-0.517765\pi$
$431$	13.9763	−	6.51724i	0.673214	−	0.313925i	0.728996	+	0.684518i	$0.239987\pi$
$432$		0			0
$433$	−1.08383	+	1.87724i	−0.0520854	+	0.0902145i	−0.890893	−	0.454214i	$-0.849920\pi$
$433$	−1.08383	+	1.87724i	−0.0520854	+	0.0902145i	0.838807	+	0.544429i	$0.183253\pi$
$434$	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	−0.204520	−	0.978862i	$-0.565563\pi$
$439$	−12.0667	−	1.05570i	−0.575910	−	0.0503856i	−0.371390	+	0.928477i	$0.621119\pi$
$440$	−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	$-0.588691\pi$
$443$	−11.5779			−0.550081			−0.275040	+	0.961433i	$0.588691\pi$
$444$		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	$-0.187645\pi$
$449$	32.9131	+	2.87952i	1.55327	+	0.135893i	0.722049	+	0.691842i	$0.243201\pi$
$450$		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	−0.877130	−	0.480252i	$-0.840545\pi$
$457$	−22.9391	+	10.6967i	−1.07304	+	0.500369i	−0.195914	+	0.980621i	$0.562767\pi$
$458$	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	$-0.520663\pi$
$461$	−18.7010	−	8.72044i	−0.870995	−	0.406152i	−0.806127	+	0.591742i	$0.798440\pi$
$462$		0			0
$463$	24.4192	+	17.0985i	1.13486	+	0.794635i	0.981105	−	0.193475i	$-0.0619757\pi$
$463$	24.4192	+	17.0985i	1.13486	+	0.794635i	0.153751	+	0.988110i	$0.450865\pi$
$464$	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	−0.233278	−	0.972410i	$-0.574945\pi$
$467$	9.83159	−	36.6920i	0.454952	−	1.69790i	0.688229	−	0.725493i	$-0.258388\pi$
$468$		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	−0.370553	+	0.928811i	$0.620832\pi$
$479$	−29.9858	+	20.9963i	−1.37009	+	0.959345i	−0.999534	+	0.0305337i	$0.990279\pi$
$480$		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	−0.184261	−	0.982877i	$-0.558989\pi$
$487$	17.6239	−	17.6239i	0.798617	−	0.798617i	0.982877	+	0.184261i	$0.0589890\pi$
$488$	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	$-0.481958\pi$
$491$	21.0419	−	12.1486i	0.949609	−	0.548257i	0.892960	+	0.450137i	$0.148625\pi$
$492$		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	−0.858508	−	0.512801i	$-0.828608\pi$
$499$	−1.85420	+	2.64808i	−0.0830056	+	0.118544i	0.775502	+	0.631345i	$0.217497\pi$
$500$	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	0.987842	+	0.155464i	$0.0496874\pi$
$503$	0.942043	+	10.7676i	0.0420036	+	0.480104i	−0.945838	+	0.324639i	$0.894757\pi$
$504$		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	$-0.610954\pi$
$509$	0.0209050	−	0.00760879i	0.000926597	−	0.000337254i	0.342483	+	0.939524i	$0.388732\pi$
$510$		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	−0.757989	−	0.652268i	$-0.773818\pi$
$521$	−6.13550	−	34.7961i	−0.268801	−	1.52445i	0.489188	−	0.872179i	$-0.337293\pi$
$522$		0			0
$523$	−1.20573	+	13.7815i	−0.0527227	+	0.602623i	0.923173	+	0.384385i	$0.125586\pi$
$523$	−1.20573	+	13.7815i	−0.0527227	+	0.602623i	−0.975896	+	0.218238i	$0.929969\pi$
$524$	−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	0.720471	−	0.693485i	$-0.243926\pi$
$541$	23.2053	+	6.21785i	0.997675	+	0.267326i	0.277204	+	0.960811i	$0.410592\pi$
$542$	−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	0.0102585	−	0.999947i	$-0.496735\pi$
$547$	12.1411	−	3.25320i	0.519116	−	0.139097i	0.508858	+	0.860851i	$0.330068\pi$
$548$	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	$-0.358170\pi$
$557$	−13.3197	−	19.0225i	−0.564372	−	0.806007i	−0.995347	+	0.0963569i	$0.969281\pi$
$558$		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	$-0.849229\pi$
$563$	−33.9900	+	9.10760i	−1.43251	+	0.383840i	−0.542605	+	0.839988i	$0.682562\pi$
$564$		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	$-0.426748\pi$
$569$	−1.45924	−	0.391001i	−0.0611744	−	0.0163916i	−0.289276	+	0.957246i	$0.593415\pi$
$570$		0			0
$571$	22.7016	+	19.0489i	0.950034	+	0.797173i	0.979303	−	0.202398i	$-0.0648735\pi$
$571$	22.7016	+	19.0489i	0.950034	+	0.797173i	−0.0292690	+	0.999572i	$0.509318\pi$
$572$	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	−0.136027	−	0.990705i	$-0.543433\pi$
$577$	−2.35290	+	0.205852i	−0.0979525	+	0.00856973i	0.0380741	+	0.999275i	$0.487878\pi$
$578$	−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	0.948186	+	0.317715i	$0.102915\pi$
$587$	−0.987670	+	11.2891i	−0.0407655	+	0.465952i	−0.988952	+	0.148237i	$0.952640\pi$
$588$		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	−0.935409	−	0.353567i	$-0.884969\pi$
$599$	−27.4401	−	32.7018i	−1.12117	−	1.33616i	−0.185763	−	0.982595i	$-0.559476\pi$
$600$		0			0
$601$	−5.25901	+	1.91412i	−0.214519	+	0.0780787i	−0.447044	−	0.894512i	$-0.647523\pi$
$601$	−5.25901	+	1.91412i	−0.214519	+	0.0780787i	0.232525	+	0.972590i	$0.425301\pi$
$602$	−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	0.987216	+	0.159388i	$0.0509519\pi$
$607$	1.05141	+	12.0177i	0.0426754	+	0.487782i	−0.944541	+	0.328394i	$0.893493\pi$
$608$	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	0.141166	−	0.989986i	$-0.454915\pi$
$613$	27.0267	−	32.2092i	1.09160	−	1.30092i	0.950433	−	0.310930i	$-0.100641\pi$
$614$	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	−0.619314	−	0.785143i	$-0.712589\pi$
$617$	5.74253	−	32.5675i	0.231186	−	1.31112i	0.850500	−	0.525976i	$-0.176300\pi$
$618$		0			0
$619$	5.29830	−	3.05897i	0.212957	−	0.122951i	−0.389728	−	0.920930i	$-0.627431\pi$
$619$	5.29830	−	3.05897i	0.212957	−	0.122951i	0.602685	+	0.797979i	$0.294098\pi$
$620$	−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	−0.422976	+	0.906141i	$0.639015\pi$
$631$	−35.6483	+	24.9612i	−1.41914	+	0.993690i	−0.996160	+	0.0875491i	$0.972097\pi$
$632$	−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	$-0.725152\pi$
$641$	−38.4935	−	6.78745i	−1.52040	−	0.268088i	−0.870591	+	0.492007i	$0.836264\pi$
$642$		0			0
$643$	−10.4218	+	38.8946i	−0.410995	+	1.53385i	0.381731	+	0.924274i	$0.375328\pi$
$643$	−10.4218	+	38.8946i	−0.410995	+	1.53385i	−0.792725	+	0.609579i	$0.791338\pi$
$644$	−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	−0.925387	−	0.379022i	$-0.876260\pi$
$647$	−40.6484	−	28.4623i	−1.59805	−	1.11897i	−0.672666	−	0.739946i	$-0.734851\pi$
$648$		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	$-0.519538\pi$
$653$	16.9635	−	7.91019i	0.663831	−	0.309550i	0.725172	+	0.688567i	$0.241760\pi$
$654$		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	$-0.729455\pi$
$659$	−0.893583	+	0.749805i	−0.0348090	+	0.0292083i	0.625217	+	0.780451i	$0.285010\pi$
$660$		0			0
$661$	−22.2984	−	1.95086i	−0.867309	−	0.0758797i	−0.355190	−	0.934794i	$-0.615584\pi$
$661$	−22.2984	−	1.95086i	−0.867309	−	0.0758797i	−0.512119	+	0.858915i	$0.671139\pi$
$662$	−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	−0.325764	−	0.945451i	$-0.605621\pi$
$673$	14.2359	−	11.9454i	0.548755	−	0.460460i	0.874519	+	0.484991i	$0.161177\pi$
$674$	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	$-0.946493\pi$
$677$	−9.05630	+	15.6860i	−0.348062	+	0.602861i	0.637843	+	0.770166i	$0.279827\pi$
$678$		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	$-0.347496\pi$
$683$	2.02560	+	0.944551i	0.0775073	+	0.0361422i	−0.383478	+	0.923550i	$0.625274\pi$
$684$		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	0.922458	−	0.386098i	$-0.126177\pi$
$691$	43.5634	+	7.68141i	1.65723	+	0.292215i	0.734774	+	0.678312i	$0.237288\pi$
$692$	−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	$-0.736726\pi$
$701$	−5.74480	+	4.02255i	−0.216978	+	0.151930i	0.460035	+	0.887901i	$0.347837\pi$
$702$		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	−0.897914	−	0.440172i	$-0.854918\pi$
$709$	−12.1883	+	12.1883i	−0.457742	+	0.457742i	0.440172	+	0.897914i	$0.354918\pi$
$710$	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	−0.140003	−	0.990151i	$-0.544711\pi$
$719$	23.0445	−	27.4634i	0.859416	−	1.02421i	0.999420	−	0.0340616i	$-0.0108443\pi$
$720$		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	0.922682	−	0.385561i	$-0.125992\pi$
$727$	0.923111	+	1.97962i	0.0342363	+	0.0734200i	−0.888446	+	0.458981i	$0.848214\pi$
$728$	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	0.999507	+	0.0314064i	$0.00999862\pi$
$733$	23.1990	+	27.6475i	0.856873	+	1.02118i	−0.142633	+	0.989776i	$0.545557\pi$
$734$	−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	$-0.877587\pi$
$739$		−	20.3972i		−	0.750324i	0.926959	−	0.375162i	$-0.122413\pi$
$740$	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	−0.977397	−	0.211412i	$-0.932194\pi$
$743$	−3.57765	−	20.2899i	−0.131251	−	0.744363i	0.846146	−	0.532951i	$-0.178917\pi$
$744$		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	0.524189	−	0.851602i	$-0.324369\pi$
$751$	1.33664	+	0.771711i	0.0487748	+	0.0281601i	−0.475414	+	0.879762i	$0.657702\pi$
$752$	−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	−0.591518	−	0.806292i	$-0.701471\pi$
$757$	11.1804	−	23.9764i	0.406358	−	0.871438i	0.997876	−	0.0651456i	$-0.0207512\pi$
$758$	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	$-0.193349\pi$
$761$	11.0793	+	9.29662i	0.401624	+	0.337002i	−0.419497	+	0.907757i	$0.637794\pi$
$762$		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	−0.553478	−	0.832864i	$-0.686700\pi$
$769$	−17.0925	+	4.57993i	−0.616373	+	0.165157i	−0.0628946	+	0.998020i	$0.520033\pi$
$770$	−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	0.563045	+	0.826427i	$0.309630\pi$
$773$	−11.1070	+	30.5161i	−0.399489	+	1.09759i	−0.962534	+	0.271161i	$0.912592\pi$
$774$		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	0.601385	−	0.798960i	$-0.294616\pi$
$787$	−10.9753	−	19.0098i	−0.391227	−	0.677625i	−0.992612	+	0.121335i	$0.961283\pi$
$788$	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	$-0.891280\pi$
$797$	−2.25822	+	4.84277i	−0.0799902	+	0.171540i	0.862245	+	0.506491i	$0.169058\pi$
$798$		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	0.746433	+	0.665461i	$0.231765\pi$
$809$	−2.96421	+	33.8811i	−0.104216	+	1.19119i	−0.850649	+	0.525734i	$0.823791\pi$
$810$		0			0
$811$	6.51751	+	36.9626i	0.228861	+	1.29793i	0.855166	+	0.518355i	$0.173455\pi$
$811$	6.51751	+	36.9626i	0.228861	+	1.29793i	−0.626305	+	0.779578i	$0.715433\pi$
$812$	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	−0.999072	−	0.0430776i	$-0.986284\pi$
$821$	−24.8711	−	29.6402i	−0.868008	−	1.03445i	0.131064	−	0.991374i	$-0.458161\pi$
$822$		0			0
$823$	−31.4307	+	11.4398i	−1.09560	+	0.398767i	−0.825694	−	0.564118i	$-0.809216\pi$
$823$	−31.4307	+	11.4398i	−1.09560	+	0.398767i	−0.269910	+	0.962885i	$0.586994\pi$
$824$	−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	0.857113	+	0.515128i	$0.172255\pi$
$827$	20.1528	+	43.2179i	0.700782	+	1.50283i	−0.156331	+	0.987705i	$0.549967\pi$
$828$		0			0
$829$	4.41492	+	50.4628i	0.153337	+	1.75265i	0.550442	+	0.834873i	$0.314459\pi$
$829$	4.41492	+	50.4628i	0.153337	+	1.75265i	−0.397106	+	0.917773i	$0.629985\pi$
$830$	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	0.861665	+	0.507477i	$0.169422\pi$
$839$	−3.52228	+	19.9758i	−0.121603	+	0.689642i	−0.983268	+	0.182165i	$0.941689\pi$
$840$		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	−0.585125	−	0.810943i	$-0.698955\pi$
$853$	−0.677954	+	0.474709i	−0.0232127	+	0.0162537i	0.561913	+	0.827197i	$0.310066\pi$
$854$	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	$-0.154410\pi$
$857$	12.2467	+	12.2467i	0.418339	+	0.418339i	−0.466292	+	0.884631i	$0.654410\pi$
$858$		0			0
$859$	7.67775	+	28.6538i	0.261961	+	0.977654i	0.964084	+	0.265597i	$0.0855692\pi$
$859$	7.67775	+	28.6538i	0.261961	+	0.977654i	−0.702123	+	0.712056i	$0.747764\pi$
$860$	−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	$-0.532381\pi$
$863$	−15.7822	−	2.78283i	−0.537232	−	0.0947285i	−0.435680	+	0.900102i	$0.643492\pi$
$864$		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	−0.786680	−	0.617361i	$-0.788202\pi$
$877$	4.18478	−	7.24825i	0.141310	−	0.244756i	0.927990	+	0.372605i	$0.121535\pi$
$878$	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	$-0.517375\pi$
$881$	27.2866	−	22.8962i	0.919309	−	0.771392i	0.973867	+	0.227119i	$0.0729305\pi$
$882$		0			0
$883$	−17.9967	−	1.57451i	−0.605638	−	0.0529864i	−0.219787	−	0.975548i	$-0.570536\pi$
$883$	−17.9967	−	1.57451i	−0.605638	−	0.0529864i	−0.385850	+	0.922561i	$0.626092\pi$
$884$	−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	$-0.131350\pi$
$887$	54.5653			1.83212			0.916062	+	0.401037i	$0.131350\pi$
$888$		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	0.502938	−	0.864323i	$-0.332253\pi$
$907$	−4.13334	−	2.89420i	−0.137245	−	0.0961003i	−0.640183	+	0.768222i	$0.721141\pi$
$908$	−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	−0.684673	−	0.728850i	$-0.740055\pi$
$911$	8.23073	−	30.7175i	0.272696	−	1.01772i	0.957370	−	0.288866i	$-0.0932782\pi$
$912$		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	0.801494	−	0.598003i	$-0.204039\pi$
$919$	6.16884	+	6.16884i	0.203491	+	0.203491i	−0.598003	+	0.801494i	$0.704039\pi$
$920$	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	$-0.567677\pi$
$929$	−30.5093	−	11.1045i	−1.00098	−	0.364326i	−0.789961	+	0.613157i	$0.789899\pi$
$930$		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	0.892448	+	0.451150i	$0.148986\pi$
$937$	−3.07577	+	17.4436i	−0.100481	+	0.569857i	−0.992929	+	0.118707i	$0.962125\pi$
$938$	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	$-0.895725\pi$
$941$	−14.2805	+	17.0189i	−0.465532	+	0.554799i	0.481288	+	0.876562i	$0.340169\pi$
$942$		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	−0.991370	−	0.131090i	$-0.958152\pi$
$947$	−1.16399	−	13.3045i	−0.0378247	−	0.432339i	0.953546	−	0.301248i	$-0.0974033\pi$
$948$		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	$-0.629183\pi$
$953$	−3.29224	+	1.19828i	−0.106646	+	0.0388160i	0.288146	+	0.957586i	$0.406961\pi$
$954$		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	−0.680036	−	0.733179i	$-0.738036\pi$
$967$	3.63781	−	41.5803i	0.116984	−	1.33713i	0.797020	−	0.603953i	$-0.206409\pi$
$968$	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	0.889991	+	0.455978i	$0.150710\pi$
$971$	15.6214	+	42.9195i	0.501315	+	1.37735i	−0.388676	+	0.921374i	$0.627067\pi$
$972$		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	$-0.450213\pi$
$977$	15.0255	−	1.31456i	0.480710	−	0.0420567i	0.324936	+	0.945736i	$0.394657\pi$
$978$		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	−0.932989	−	0.359906i	$-0.882809\pi$
$983$	−45.4440	−	38.1320i	−1.44944	−	1.21622i	−0.516450	−	0.856317i	$-0.672747\pi$
$984$		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	−0.862342	−	0.506327i	$-0.831003\pi$
$991$	−42.6867	+	11.4379i	−1.35599	+	0.363336i	−0.493647	+	0.869663i	$0.664336\pi$
$992$	−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	0.945167	−	0.326586i	$-0.105898\pi$
$997$	9.94656	+	14.2052i	0.315011	+	0.449882i	−0.630157	+	0.776468i	$0.717009\pi$
$998$	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.431.3	yes	96
3.2	odd	2	inner	666.2.bs.b.431.6	yes	96
37.17	odd	36	inner	666.2.bs.b.17.6	yes	96
111.17	even	36	inner	666.2.bs.b.17.3	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.bs.b.17.3	✓	96	111.17	even	36	inner
666.2.bs.b.17.6	yes	96	37.17	odd	36	inner
666.2.bs.b.431.3	yes	96	1.1	even	1	trivial
666.2.bs.b.431.6	yes	96	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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