LMFDB - Embedded newform 666.2.bs.b.17.3

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			17.3
Character	$\chi$	$=$	666.17
Dual form			666.2.bs.b.431.3

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

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

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	0.210267	−	0.977644i	$-0.432567\pi$
$5$	1.31281	−	0.114856i	0.587105	−	0.0513650i	0.376838	+	0.926279i	$0.377011\pi$
$6$		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	0.609102	−	0.793092i	$-0.291530\pi$
$11$	−1.26790	−	2.19607i	−0.382287	−	0.662141i	−0.991389	+	0.130951i	$0.958197\pi$
$12$		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	−0.667820	−	0.744322i	$-0.732773\pi$
$17$	−2.17248	+	1.01304i	−0.526903	+	0.245699i	0.140917	+	0.990021i	$0.454995\pi$
$18$		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	$0.205998\pi$
$23$	1.95836	+	7.30871i	0.408347	+	1.52397i	−0.389452	+	0.921047i	$0.627335\pi$
$24$		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	$-0.613191\pi$
$29$	2.27295	−	8.48275i	0.422075	−	1.57521i	0.770228	−	0.637769i	$-0.220143\pi$
$30$		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	−0.981241	−	0.192787i	$-0.938247\pi$
$41$	−10.3026	+	3.74984i	−1.60899	+	0.585626i	−0.627753	+	0.778412i	$0.716025\pi$
$42$		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	0.995459	−	0.0951926i	$-0.0303467\pi$
$47$	9.67161	+	5.58391i	1.41075	+	0.814496i	0.415290	+	0.909689i	$0.363680\pi$
$48$		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	0.678126	−	0.734946i	$-0.262792\pi$
$53$	−1.18964	−	1.41776i	−0.163409	−	0.194744i	−0.841536	+	0.540202i	$0.818348\pi$
$54$		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	$-0.779609\pi$
$59$	0.761646	−	8.70565i	0.0991579	−	1.13338i	0.868887	−	0.495010i	$-0.164835\pi$
$60$		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	−0.0710580	−	0.997472i	$-0.522638\pi$
$71$	−4.03601	−	0.711657i	−0.478986	−	0.0844582i	−0.407928	+	0.913014i	$0.633749\pi$
$72$		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	−0.916572	−	0.399870i	$-0.869055\pi$
$83$	0.388056	−	1.06617i	0.0425947	−	0.117028i	0.959166	+	0.282842i	$0.0912774\pi$
$84$		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	0.103974	−	0.994580i	$-0.466844\pi$
$89$	0.317556	+	0.0277825i	0.0336609	+	0.00294494i	−0.0703129	+	0.997525i	$0.522400\pi$
$90$		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	−0.863647	−	0.504098i	$-0.831825\pi$
$101$	0.0476198	−	0.0824799i	0.00473834	−	0.00820705i	0.868385	+	0.495891i	$0.165158\pi$
$102$		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	$0.0491835\pi$
$107$	3.41452	+	9.38130i	0.330094	+	0.906925i	−0.657993	+	0.753024i	$0.728594\pi$
$108$		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	−0.532748	−	0.846274i	$-0.678841\pi$
$113$	4.72723	−	6.75118i	0.444700	−	0.635098i	0.977448	+	0.211176i	$0.0677295\pi$
$114$		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	0.890744	−	0.454506i	$-0.150184\pi$
$131$	−0.343220	−	0.736037i	−0.0299873	−	0.0643079i	−0.920731	+	0.390198i	$0.872406\pi$
$132$		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	−0.820837	−	0.571162i	$-0.806493\pi$
$137$	−8.62186	+	4.97783i	−0.736615	+	0.425285i	0.0842223	+	0.996447i	$0.473159\pi$
$138$		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	$0.244484\pi$
$149$			16.9610i			1.38950i	−0.719252	+	0.694749i	$0.755516\pi$
$150$		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	0.993059	−	0.117614i	$-0.0375246\pi$
$167$	7.01571	+	10.0195i	0.542892	+	0.775330i	−0.450167	+	0.892944i	$0.648636\pi$
$168$		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	$-0.988919\pi$
$173$	−0.949307	−	5.38379i	−0.0721745	−	0.409322i	0.927220	−	0.374518i	$-0.122192\pi$
$174$		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	0.896831	−	0.442373i	$-0.145863\pi$
$179$	6.08023	+	6.08023i	0.454458	+	0.454458i	−0.442373	+	0.896831i	$0.645863\pi$
$180$		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	−0.0936599	−	0.995604i	$-0.529857\pi$
$191$	12.4651	−	12.4651i	0.901944	−	0.901944i	0.995604	+	0.0936599i	$0.0298566\pi$
$192$		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	−0.679968	−	0.733242i	$-0.738006\pi$
$197$	−14.9921	+	2.64352i	−1.06815	+	0.188343i	−0.388177	+	0.921585i	$0.626895\pi$
$198$		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	0.434902	−	0.900478i	$-0.356783\pi$
$227$	15.3613	−	1.34394i	1.01956	−	0.0892003i	0.584662	+	0.811277i	$0.301227\pi$
$228$		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	$-0.910511\pi$
$233$	−11.0002	−	19.0529i	−0.720647	−	1.24820i	0.240093	−	0.970750i	$-0.422822\pi$
$234$		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	−0.742337	−	0.670027i	$-0.766283\pi$
$239$	−10.9181	+	5.09118i	−0.706232	+	0.329321i	0.0361053	+	0.999348i	$0.488505\pi$
$240$		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	$-0.789076\pi$
$251$	3.19993	−	11.9423i	0.201977	−	0.753790i	0.990350	−	0.138592i	$-0.0442575\pi$
$252$		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	0.753166	−	0.657830i	$-0.228526\pi$
$257$	6.29396	+	4.40708i	0.392606	+	0.274906i	−0.360560	+	0.932736i	$0.617414\pi$
$258$		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	−0.208272	−	0.978071i	$-0.566784\pi$
$263$	4.23067	−	1.53984i	0.260874	−	0.0949504i	0.469146	+	0.883120i	$0.344562\pi$
$264$		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	0.608898	−	0.793248i	$-0.291612\pi$
$269$	3.71281	+	2.14359i	0.226374	+	0.130697i	−0.382524	+	0.923946i	$0.624945\pi$
$270$		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	$-0.798361\pi$
$281$	1.51781	−	17.3487i	0.0905451	−	1.03494i	0.896525	−	0.442993i	$-0.146083\pi$
$282$		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	0.0190163	−	0.999819i	$-0.493947\pi$
$293$	−5.22200	−	0.920779i	−0.305072	−	0.0537925i	−0.324089	+	0.946027i	$0.605058\pi$
$294$		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	−0.445853	−	0.895106i	$-0.647100\pi$
$311$	−18.3471	−	1.60516i	−1.04037	−	0.0910202i	−0.594513	+	0.804086i	$0.702655\pi$
$312$		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	−0.413614	−	0.910452i	$-0.635734\pi$
$317$	7.32092	−	6.14298i	0.411184	−	0.345024i	0.824797	+	0.565428i	$0.191289\pi$
$318$		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	0.488328	−	0.872660i	$-0.337607\pi$
$347$	25.1023	−	6.72615i	1.34756	−	0.361078i	0.859235	+	0.511582i	$0.170940\pi$
$348$		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	0.837089	−	0.547067i	$-0.184256\pi$
$353$	−2.25571	−	4.83739i	−0.120059	−	0.257468i	−0.957148	+	0.289599i	$0.906478\pi$
$354$		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	−0.429363	−	0.903132i	$-0.641262\pi$
$359$	2.61646	−	1.51062i	0.138092	−	0.0797273i	0.567454	+	0.823405i	$0.307928\pi$
$360$		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	−0.820111	−	0.572205i	$-0.806088\pi$
$383$	2.84516	−	6.10146i	0.145381	−	0.311770i	0.965491	+	0.260435i	$0.0838659\pi$
$384$		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	0.377195	−	0.926134i	$-0.376889\pi$
$389$	−12.2696	−	17.5228i	−0.622095	−	0.888443i	−0.999289	+	0.0376907i	$0.988000\pi$
$390$		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	0.628697	−	0.777651i	$-0.283589\pi$
$401$	−2.98281	−	2.98281i	−0.148954	−	0.148954i	−0.777651	+	0.628697i	$0.783589\pi$
$402$		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	0.213622	−	0.976916i	$-0.431474\pi$
$419$	15.3211	−	2.70153i	0.748487	−	0.131978i	0.534864	+	0.844938i	$0.320363\pi$
$420$		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	0.728996	−	0.684518i	$-0.239987\pi$
$431$	13.9763	+	6.51724i	0.673214	+	0.313925i	−0.0557821	+	0.998443i	$0.517765\pi$
$432$		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	$-0.588691\pi$
$443$	−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	0.722049	−	0.691842i	$-0.243201\pi$
$449$	32.9131	−	2.87952i	1.55327	−	0.135893i	0.831216	+	0.555949i	$0.187645\pi$
$450$		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	−0.806127	−	0.591742i	$-0.798440\pi$
$461$	−18.7010	+	8.72044i	−0.870995	+	0.406152i	−0.0648676	+	0.997894i	$0.520663\pi$
$462$		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	$0.258388\pi$
$467$	9.83159	+	36.6920i	0.454952	+	1.69790i	−0.233278	+	0.972410i	$0.574945\pi$
$468$		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	$-0.990279\pi$
$479$	−29.9858	−	20.9963i	−1.37009	−	0.959345i	−0.370553	−	0.928811i	$-0.620832\pi$
$480$		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	0.892960	−	0.450137i	$-0.148625\pi$
$491$	21.0419	+	12.1486i	0.949609	+	0.548257i	0.0566498	+	0.998394i	$0.481958\pi$
$492$		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	$-0.894757\pi$
$503$	0.942043	−	10.7676i	0.0420036	−	0.480104i	0.987842	−	0.155464i	$-0.0496874\pi$
$504$		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	0.342483	−	0.939524i	$-0.388732\pi$
$509$	0.0209050	+	0.00760879i	0.000926597	+	0.000337254i	−0.341557	+	0.939861i	$0.610954\pi$
$510$		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	$0.337293\pi$
$521$	−6.13550	+	34.7961i	−0.268801	+	1.52445i	−0.757989	+	0.652268i	$0.773818\pi$
$522$		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	−0.995347	−	0.0963569i	$-0.969281\pi$
$557$	−13.3197	+	19.0225i	−0.564372	+	0.806007i	0.430975	+	0.902364i	$0.358170\pi$
$558$		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	−0.542605	−	0.839988i	$-0.682562\pi$
$563$	−33.9900	−	9.10760i	−1.43251	−	0.383840i	−0.889904	+	0.456148i	$0.849229\pi$
$564$		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	−0.289276	−	0.957246i	$-0.593415\pi$
$569$	−1.45924	+	0.391001i	−0.0611744	+	0.0163916i	0.228102	+	0.973637i	$0.426748\pi$
$570$		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	$-0.952640\pi$
$587$	−0.987670	−	11.2891i	−0.0407655	−	0.465952i	0.948186	−	0.317715i	$-0.102915\pi$
$588$		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	$0.0179469\pi$
$593$			2.74452i			0.112704i	−0.998411	+	0.0563519i	$0.982053\pi$
$594$		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	$0.559476\pi$
$599$	−27.4401	+	32.7018i	−1.12117	+	1.33616i	−0.935409	+	0.353567i	$0.884969\pi$
$600$		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	$0.176300\pi$
$617$	5.74253	+	32.5675i	0.231186	+	1.31112i	−0.619314	+	0.785143i	$0.712589\pi$
$618$		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	−0.870591	−	0.492007i	$-0.836264\pi$
$641$	−38.4935	+	6.78745i	−1.52040	+	0.268088i	−0.649812	+	0.760095i	$0.725152\pi$
$642$		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	$0.734851\pi$
$647$	−40.6484	+	28.4623i	−1.59805	+	1.11897i	−0.925387	+	0.379022i	$0.876260\pi$
$648$		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	0.725172	−	0.688567i	$-0.241760\pi$
$653$	16.9635	+	7.91019i	0.663831	+	0.309550i	−0.0613413	+	0.998117i	$0.519538\pi$
$654$		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	0.625217	−	0.780451i	$-0.285010\pi$
$659$	−0.893583	−	0.749805i	−0.0348090	−	0.0292083i	−0.660026	+	0.751243i	$0.729455\pi$
$660$		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	0.637843	−	0.770166i	$-0.279827\pi$
$677$	−9.05630	−	15.6860i	−0.348062	−	0.602861i	−0.985905	+	0.167305i	$0.946493\pi$
$678$		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	−0.383478	−	0.923550i	$-0.625274\pi$
$683$	2.02560	−	0.944551i	0.0775073	−	0.0361422i	0.460985	+	0.887408i	$0.347496\pi$
$684$		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	0.460035	−	0.887901i	$-0.347837\pi$
$701$	−5.74480	−	4.02255i	−0.216978	−	0.151930i	−0.677013	+	0.735971i	$0.736726\pi$
$702$		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	$0.0108443\pi$
$719$	23.0445	+	27.4634i	0.859416	+	1.02421i	−0.140003	+	0.990151i	$0.544711\pi$
$720$		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	$0.178917\pi$
$743$	−3.57765	+	20.2899i	−0.131251	+	0.744363i	−0.977397	+	0.211412i	$0.932194\pi$
$744$		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	−0.419497	−	0.907757i	$-0.637794\pi$
$761$	11.0793	−	9.29662i	0.401624	−	0.337002i	0.821121	+	0.570754i	$0.193349\pi$
$762$		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	$-0.912592\pi$
$773$	−11.1070	−	30.5161i	−0.399489	−	1.09759i	0.563045	−	0.826427i	$-0.309630\pi$
$774$		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

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

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