LMFDB - Embedded newform 216.2.t.a.205.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, 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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			205.24
Character	$\chi$	$=$	216.205
Dual form			216.2.t.a.157.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.770006 - 1.18621i) q^{2} +(0.759610 + 1.55660i) q^{3} +(-0.814182 - 1.82678i) q^{4} +(0.857221 - 2.35519i) q^{5} +(2.43135 + 0.297532i) q^{6} +(0.442985 - 2.51229i) q^{7} +(-2.79386 - 0.440839i) q^{8} +(-1.84598 + 2.36481i) q^{9} +O(q^{10})$	\(q+(0.770006 - 1.18621i) q^{2} +(0.759610 + 1.55660i) q^{3} +(-0.814182 - 1.82678i) q^{4} +(0.857221 - 2.35519i) q^{5} +(2.43135 + 0.297532i) q^{6} +(0.442985 - 2.51229i) q^{7} +(-2.79386 - 0.440839i) q^{8} +(-1.84598 + 2.36481i) q^{9} +(-2.13369 - 2.83036i) q^{10} +(1.32995 + 3.65402i) q^{11} +(2.22509 - 2.65499i) q^{12} +(1.81187 + 2.15930i) q^{13} +(-2.63900 - 2.45995i) q^{14} +(4.31724 - 0.454683i) q^{15} +(-2.67422 + 2.97465i) q^{16} +(-3.79287 - 6.56945i) q^{17} +(1.38374 + 4.01064i) q^{18} +(4.25574 + 2.45705i) q^{19} +(-5.00034 + 0.351606i) q^{20} +(4.24712 - 1.21881i) q^{21} +(5.35850 + 1.23601i) q^{22} +(0.488755 + 2.77187i) q^{23} +(-1.43604 - 4.68378i) q^{24} +(-0.981892 - 0.823905i) q^{25} +(3.95653 - 0.486580i) q^{26} +(-5.08329 - 1.07712i) q^{27} +(-4.95007 + 1.23623i) q^{28} +(-1.68216 + 2.00472i) q^{29} +(2.78495 - 5.47126i) q^{30} +(0.605101 + 3.43170i) q^{31} +(1.46940 + 5.46268i) q^{32} +(-4.67758 + 4.84583i) q^{33} +(-10.7133 - 0.559376i) q^{34} +(-5.53721 - 3.19691i) q^{35} +(5.82295 + 1.44681i) q^{36} +(-6.91267 + 3.99103i) q^{37} +(6.19153 - 3.15625i) q^{38} +(-1.98485 + 4.46058i) q^{39} +(-3.43322 + 6.20219i) q^{40} +(-7.68334 + 6.44709i) q^{41} +(1.82454 - 5.97647i) q^{42} +(1.38824 + 3.81417i) q^{43} +(5.59224 - 5.40456i) q^{44} +(3.98718 + 6.37482i) q^{45} +(3.66436 + 1.55459i) q^{46} +(1.48461 - 8.41962i) q^{47} +(-6.66170 - 1.90310i) q^{48} +(0.462463 + 0.168323i) q^{49} +(-1.73339 + 0.530317i) q^{50} +(7.34487 - 10.8942i) q^{51} +(2.46937 - 5.06794i) q^{52} -11.8427i q^{53} +(-5.19185 + 5.20045i) q^{54} +9.74598 q^{55} +(-2.34516 + 6.82372i) q^{56} +(-0.591936 + 8.49088i) q^{57} +(1.08274 + 3.53904i) q^{58} +(0.584688 - 1.60642i) q^{59} +(-4.34562 - 7.51644i) q^{60} +(0.343677 + 0.0605995i) q^{61} +(4.53664 + 1.92465i) q^{62} +(5.12336 + 5.68523i) q^{63} +(7.61132 + 2.46328i) q^{64} +(6.63875 - 2.41631i) q^{65} +(2.14640 + 9.27990i) q^{66} +(-1.45040 - 1.72852i) q^{67} +(-8.91282 + 12.2774i) q^{68} +(-3.94342 + 2.86633i) q^{69} +(-8.05588 + 4.10664i) q^{70} +(-2.53118 - 4.38413i) q^{71} +(6.19993 - 5.79318i) q^{72} +(1.34818 - 2.33512i) q^{73} +(-0.588601 + 11.2730i) q^{74} +(0.536633 - 2.15426i) q^{75} +(1.02354 - 9.77477i) q^{76} +(9.76911 - 1.72256i) q^{77} +(3.76283 + 5.78912i) q^{78} +(-0.652898 - 0.547847i) q^{79} +(4.71349 + 8.84824i) q^{80} +(-2.18468 - 8.73082i) q^{81} +(1.73137 + 14.0783i) q^{82} +(-5.59873 + 6.67230i) q^{83} +(-5.68443 - 6.76620i) q^{84} +(-18.7237 + 3.30149i) q^{85} +(5.59336 + 1.29019i) q^{86} +(-4.39832 - 1.09564i) q^{87} +(-2.10487 - 10.7951i) q^{88} +(3.02691 - 5.24277i) q^{89} +(10.6320 + 0.179025i) q^{90} +(6.22743 - 3.59541i) q^{91} +(4.66564 - 3.14965i) q^{92} +(-4.88213 + 3.54865i) q^{93} +(-8.84427 - 8.24421i) q^{94} +(9.43495 - 7.91686i) q^{95} +(-7.38702 + 6.43677i) q^{96} +(4.71115 - 1.71472i) q^{97} +(0.555765 - 0.418968i) q^{98} +(-11.0961 - 3.60017i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.770006	−	1.18621i	0.544476	−	0.838776i
$2$	0.770006	−	1.18621i	0.544476	−	0.838776i
$3$	0.759610	+	1.55660i	0.438561	+	0.898701i
$3$	0.759610	+	1.55660i	0.438561	+	0.898701i
$4$	−0.814182	−	1.82678i	−0.407091	−	0.913388i
$5$	0.857221	−	2.35519i	0.383361	−	1.05328i	−0.586571	−	0.809898i	$-0.699522\pi$
$5$	0.857221	−	2.35519i	0.383361	−	1.05328i	0.969932	−	0.243377i	$-0.0782553\pi$
$6$	2.43135	+	0.297532i	0.992595	+	0.121467i
$7$	0.442985	−	2.51229i	0.167433	−	0.949558i	−0.779088	−	0.626915i	$-0.784317\pi$
$7$	0.442985	−	2.51229i	0.167433	−	0.949558i	0.946521	−	0.322643i	$-0.104571\pi$
$8$	−2.79386	−	0.440839i	−0.987779	−	0.155860i
$9$	−1.84598	+	2.36481i	−0.615328	+	0.788271i
$10$	−2.13369	−	2.83036i	−0.674731	−	0.895037i
$11$	1.32995	+	3.65402i	0.400996	+	1.10173i	0.961794	+	0.273774i	$0.0882722\pi$
$11$	1.32995	+	3.65402i	0.400996	+	1.10173i	−0.560798	+	0.827953i	$0.689506\pi$
$12$	2.22509	−	2.65499i	0.642329	−	0.766429i
$13$	1.81187	+	2.15930i	0.502522	+	0.598883i	0.956356	−	0.292204i	$-0.0943885\pi$
$13$	1.81187	+	2.15930i	0.502522	+	0.598883i	−0.453834	+	0.891086i	$0.649944\pi$
$14$	−2.63900	−	2.45995i	−0.705303	−	0.657450i
$15$	4.31724	−	0.454683i	1.11471	−	0.117399i
$16$	−2.67422	+	2.97465i	−0.668554	+	0.743663i
$17$	−3.79287	−	6.56945i	−0.919907	−	1.59333i	−0.799554	−	0.600594i	$-0.794931\pi$
$17$	−3.79287	−	6.56945i	−0.919907	−	1.59333i	−0.120352	−	0.992731i	$-0.538402\pi$
$18$	1.38374	+	4.01064i	0.326151	+	0.945318i
$19$	4.25574	+	2.45705i	0.976334	+	0.563687i	0.901161	−	0.433484i	$-0.142716\pi$
$19$	4.25574	+	2.45705i	0.976334	+	0.563687i	0.0751728	+	0.997171i	$0.476049\pi$
$20$	−5.00034	+	0.351606i	−1.11811	+	0.0786216i
$21$	4.24712	−	1.21881i	0.926798	−	0.265967i
$22$	5.35850	+	1.23601i	1.14244	+	0.263519i
$23$	0.488755	+	2.77187i	0.101912	+	0.577974i	0.992409	+	0.122984i	$0.0392463\pi$
$23$	0.488755	+	2.77187i	0.101912	+	0.577974i	−0.890496	+	0.454991i	$0.849643\pi$
$24$	−1.43604	−	4.68378i	−0.293130	−	0.956073i
$25$	−0.981892	−	0.823905i	−0.196378	−	0.164781i
$26$	3.95653	−	0.486580i	0.775940	−	0.0954262i
$27$	−5.08329	−	1.07712i	−0.978279	−	0.207291i
$28$	−4.95007	+	1.23623i	−0.935475	+	0.233625i
$29$	−1.68216	+	2.00472i	−0.312369	+	0.372267i	−0.899272	−	0.437391i	$-0.855903\pi$
$29$	−1.68216	+	2.00472i	−0.312369	+	0.372267i	0.586903	+	0.809658i	$0.300347\pi$
$30$	2.78495	−	5.47126i	0.508460	−	0.998910i
$31$	0.605101	+	3.43170i	0.108679	+	0.616351i	0.989687	+	0.143249i	$0.0457549\pi$
$31$	0.605101	+	3.43170i	0.108679	+	0.616351i	−0.881007	+	0.473103i	$0.843134\pi$
$32$	1.46940	+	5.46268i	0.259755	+	0.965675i
$33$	−4.67758	+	4.84583i	−0.814262	+	0.843550i
$34$	−10.7133	−	0.559376i	−1.83731	−	0.0959322i
$35$	−5.53721	−	3.19691i	−0.935958	−	0.540376i
$36$	5.82295	+	1.44681i	0.970491	+	0.241135i
$37$	−6.91267	+	3.99103i	−1.13644	+	0.656121i	−0.945545	−	0.325490i	$-0.894471\pi$
$37$	−6.91267	+	3.99103i	−1.13644	+	0.656121i	−0.190890	+	0.981611i	$0.561137\pi$
$38$	6.19153	−	3.15625i	1.00440	−	0.512012i
$39$	−1.98485	+	4.46058i	−0.317830	+	0.714264i
$40$	−3.43322	+	6.20219i	−0.542839	+	0.980652i
$41$	−7.68334	+	6.44709i	−1.19994	+	1.00687i	−0.200305	+	0.979734i	$0.564193\pi$
$41$	−7.68334	+	6.44709i	−1.19994	+	1.00687i	−0.999632	+	0.0271328i	$0.991362\pi$
$42$	1.82454	−	5.97647i	0.281533	−	0.922189i
$43$	1.38824	+	3.81417i	0.211705	+	0.581655i	0.999408	−	0.0343999i	$-0.0109520\pi$
$43$	1.38824	+	3.81417i	0.211705	+	0.581655i	−0.787703	+	0.616055i	$0.788730\pi$
$44$	5.59224	−	5.40456i	0.843062	−	0.814768i
$45$	3.98718	+	6.37482i	0.594373	+	0.950302i
$46$	3.66436	+	1.55459i	0.540280	+	0.229212i
$47$	1.48461	−	8.41962i	0.216552	−	1.22813i	−0.661641	−	0.749821i	$-0.730140\pi$
$47$	1.48461	−	8.41962i	0.216552	−	1.22813i	0.878193	−	0.478307i	$-0.158749\pi$
$48$	−6.66170	−	1.90310i	−0.961533	−	0.274689i
$49$	0.462463	+	0.168323i	0.0660661	+	0.0240461i
$50$	−1.73339	+	0.530317i	−0.245138	+	0.0749981i
$51$	7.34487	−	10.8942i	1.02849	−	1.52549i
$52$	2.46937	−	5.06794i	0.342440	−	0.702797i
$53$		−	11.8427i		−	1.62672i	−0.581762	−	0.813359i	$-0.697637\pi$
$53$		−	11.8427i		−	1.62672i	0.581762	−	0.813359i	$-0.302363\pi$
$54$	−5.19185	+	5.20045i	−0.706521	+	0.707692i
$55$	9.74598			1.31415
$56$	−2.34516	+	6.82372i	−0.313385	+	0.911857i
$57$	−0.591936	+	8.49088i	−0.0784039	+	1.12464i
$58$	1.08274	+	3.53904i	0.142171	+	0.464698i
$59$	0.584688	−	1.60642i	0.0761199	−	0.209138i	−0.895796	−	0.444465i	$-0.853394\pi$
$59$	0.584688	−	1.60642i	0.0761199	−	0.209138i	0.971916	+	0.235327i	$0.0756161\pi$
$60$	−4.34562	−	7.51644i	−0.561017	−	0.970368i
$61$	0.343677	+	0.0605995i	0.0440033	+	0.00775897i	0.195606	−	0.980682i	$-0.437332\pi$
$61$	0.343677	+	0.0605995i	0.0440033	+	0.00775897i	−0.151603	+	0.988441i	$0.548444\pi$
$62$	4.53664	+	1.92465i	0.576154	+	0.244431i
$63$	5.12336	+	5.68523i	0.645483	+	0.716272i
$64$	7.61132	+	2.46328i	0.951415	+	0.307911i
$65$	6.63875	−	2.41631i	0.823436	−	0.299706i
$66$	2.14640	+	9.27990i	0.264203	+	1.14228i
$67$	−1.45040	−	1.72852i	−0.177195	−	0.211173i	0.670135	−	0.742239i	$-0.266236\pi$
$67$	−1.45040	−	1.72852i	−0.177195	−	0.211173i	−0.847330	+	0.531066i	$0.821792\pi$
$68$	−8.91282	+	12.2774i	−1.08084	+	1.48886i
$69$	−3.94342	+	2.86633i	−0.474731	+	0.345066i
$70$	−8.05588	+	4.10664i	−0.962862	+	0.490838i
$71$	−2.53118	−	4.38413i	−0.300396	−	0.520301i	0.675830	−	0.737058i	$-0.263785\pi$
$71$	−2.53118	−	4.38413i	−0.300396	−	0.520301i	−0.976226	+	0.216757i	$0.930452\pi$
$72$	6.19993	−	5.79318i	0.730668	−	0.682733i
$73$	1.34818	−	2.33512i	0.157793	−	0.273305i	−0.776280	−	0.630389i	$-0.782895\pi$
$73$	1.34818	−	2.33512i	0.157793	−	0.273305i	0.934072	+	0.357083i	$0.116229\pi$
$74$	−0.588601	+	11.2730i	−0.0684234	+	1.31046i
$75$	0.536633	−	2.15426i	0.0619650	−	0.248752i
$76$	1.02354	−	9.77477i	0.117408	−	1.12124i
$77$	9.76911	−	1.72256i	1.11329	−	0.196304i
$78$	3.76283	+	5.78912i	0.426057	+	0.655488i
$79$	−0.652898	−	0.547847i	−0.0734568	−	0.0616376i	0.605320	−	0.795982i	$-0.293045\pi$
$79$	−0.652898	−	0.547847i	−0.0734568	−	0.0616376i	−0.678777	+	0.734345i	$0.737490\pi$
$80$	4.71349	+	8.84824i	0.526985	+	0.989263i
$81$	−2.18468	−	8.73082i	−0.242742	−	0.970091i
$82$	1.73137	+	14.0783i	0.191198	+	1.55469i
$83$	−5.59873	+	6.67230i	−0.614540	+	0.732380i	−0.980121	−	0.198399i	$-0.936426\pi$
$83$	−5.59873	+	6.67230i	−0.614540	+	0.732380i	0.365581	+	0.930779i	$0.380870\pi$
$84$	−5.68443	−	6.76620i	−0.620222	−	0.738253i
$85$	−18.7237	+	3.30149i	−2.03087	+	0.358096i
$86$	5.59336	+	1.29019i	0.603147	+	0.139124i
$87$	−4.39832	−	1.09564i	−0.471550	−	0.117465i
$88$	−2.10487	−	10.7951i	−0.224380	−	1.15076i
$89$	3.02691	−	5.24277i	0.320852	−	0.555732i	−0.659812	−	0.751431i	$-0.729364\pi$
$89$	3.02691	−	5.24277i	0.320852	−	0.555732i	0.980664	+	0.195698i	$0.0626974\pi$
$90$	10.6320	+	0.179025i	1.12071	+	0.0188709i
$91$	6.22743	−	3.59541i	0.652812	−	0.376901i
$92$	4.66564	−	3.14965i	0.486427	−	0.328374i
$93$	−4.88213	+	3.54865i	−0.506253	+	0.367978i
$94$	−8.84427	−	8.24421i	−0.912217	−	0.850325i
$95$	9.43495	−	7.91686i	0.968006	−	0.812253i
$96$	−7.38702	+	6.43677i	−0.753934	+	0.656950i
$97$	4.71115	−	1.71472i	0.478344	−	0.174103i	−0.0915842	−	0.995797i	$-0.529193\pi$
$97$	4.71115	−	1.71472i	0.478344	−	0.174103i	0.569929	+	0.821694i	$0.306971\pi$
$98$	0.555765	−	0.418968i	0.0561408	−	0.0423222i
$99$	−11.0961	−	3.60017i	−1.11520	−	0.361830i
$100$	−0.705651	+	2.46450i	−0.0705651	+	0.246450i
$101$	−1.06482	−	0.187757i	−0.105954	−	0.0186825i	0.120420	−	0.992723i	$-0.461576\pi$
$101$	−1.06482	−	0.187757i	−0.105954	−	0.0186825i	−0.226374	+	0.974041i	$0.572687\pi$
$102$	−7.26719	−	17.1011i	−0.719559	−	1.69327i
$103$	10.4356	+	3.79825i	1.02825	+	0.374252i	0.800414	−	0.599447i	$-0.204613\pi$
$103$	10.4356	+	3.79825i	1.02825	+	0.374252i	0.227836	+	0.973700i	$0.426835\pi$
$104$	−4.11021	−	6.83153i	−0.403039	−	0.669887i
$105$	0.770176	−	11.0476i	0.0751615	−	1.07814i
$106$	−14.0479	−	9.11894i	−1.36445	−	0.885709i
$107$			12.1144i			1.17114i	0.810622	+	0.585570i	$0.199129\pi$
$107$			12.1144i			1.17114i	−0.810622	+	0.585570i	$0.800871\pi$
$108$	2.17107	+	10.1630i	0.208911	+	0.977935i
$109$		−	19.5560i		−	1.87312i	−0.350502	−	0.936562i	$-0.613989\pi$
$109$		−	19.5560i		−	1.87312i	0.350502	−	0.936562i	$-0.386011\pi$
$110$	7.50446	−	11.5608i	0.715522	−	1.10228i
$111$	−11.4634	−	7.72861i	−1.08805	−	0.733567i
$112$	6.28857	+	8.03615i	0.594214	+	0.759344i
$113$	−5.58697	−	2.03349i	−0.525578	−	0.191295i	0.0655850	−	0.997847i	$-0.479109\pi$
$113$	−5.58697	−	2.03349i	−0.525578	−	0.191295i	−0.591163	+	0.806552i	$0.701331\pi$
$114$	9.61616	+	7.24019i	0.900636	+	0.678106i
$115$	6.94726	+	1.22499i	0.647835	+	0.114231i
$116$	5.03176	+	1.44072i	0.467187	+	0.133768i
$117$	−8.45103	+	0.298694i	−0.781298	+	0.0276143i
$118$	−1.45533	−	1.93051i	−0.133974	−	0.177718i
$119$	−18.1846	+	6.61864i	−1.66698	+	0.606730i
$120$	−12.2622	−	0.632886i	−1.11938	−	0.0577743i
$121$	−3.15656	+	2.64867i	−0.286960	+	0.240788i
$122$	0.336517	−	0.361010i	0.0304668	−	0.0326843i
$123$	−15.8719	−	7.06259i	−1.43112	−	0.636812i
$124$	5.77628	−	3.89941i	0.518725	−	0.350177i
$125$	8.07064	−	4.65959i	0.721860	−	0.416766i
$126$	10.6889	−	1.69971i	0.952242	−	0.151422i
$127$	6.21113	−	10.7580i	0.551148	−	0.954617i	−0.447044	−	0.894512i	$-0.647523\pi$
$127$	6.21113	−	10.7580i	0.551148	−	0.954617i	0.998192	−	0.0601050i	$-0.0191435\pi$
$128$	8.78273	−	7.13187i	0.776291	−	0.630374i
$129$	−4.88260	+	5.05822i	−0.429889	+	0.445351i
$130$	2.24563	−	9.73551i	0.196955	−	0.853861i
$131$	0.306951	−	0.0541237i	0.0268184	−	0.00472881i	−0.160223	−	0.987081i	$-0.551221\pi$
$131$	0.306951	−	0.0541237i	0.0268184	−	0.00472881i	0.187041	+	0.982352i	$0.440110\pi$
$132$	12.6606	+	4.59951i	1.10197	+	0.400336i
$133$	8.05807	−	9.60324i	0.698724	−	0.832706i
$134$	−3.16721	+	0.389507i	−0.273605	+	0.0336483i
$135$	−6.89432	+	11.0488i	−0.593369	+	0.950930i
$136$	7.70069	+	20.0262i	0.660329	+	1.71723i
$137$	4.88568	+	4.09957i	0.417412	+	0.350250i	0.827177	−	0.561941i	$-0.189945\pi$
$137$	4.88568	+	4.09957i	0.417412	+	0.350250i	−0.409766	+	0.912191i	$0.634390\pi$
$138$	0.363615	+	6.88481i	0.0309530	+	0.586074i
$139$	5.04955	−	0.890371i	0.428297	−	0.0755203i	0.0446555	−	0.999002i	$-0.485781\pi$
$139$	5.04955	−	0.890371i	0.428297	−	0.0755203i	0.383641	+	0.923482i	$0.374670\pi$
$140$	−1.33174	+	12.7181i	−0.112553	+	1.07488i
$141$	14.2337	−	4.08470i	1.19869	−	0.343994i
$142$	−7.14952	−	0.373301i	−0.599975	−	0.0313267i
$143$	−5.48042	+	9.49237i	−0.458296	+	0.793792i
$144$	−2.09794	−	11.8152i	−0.174828	−	0.984599i
$145$	3.27952	+	5.68030i	0.272350	+	0.471723i
$146$	−1.73183	−	3.39728i	−0.143327	−	0.281161i
$147$	0.0892810	+	0.847728i	0.00736377	+	0.0699194i
$148$	12.9189	+	9.37847i	1.06193	+	0.770905i
$149$	1.33347	+	1.58917i	0.109242	+	0.130190i	0.817895	−	0.575368i	$-0.195141\pi$
$149$	1.33347	+	1.58917i	0.109242	+	0.130190i	−0.708653	+	0.705558i	$0.750697\pi$
$150$	−2.14219	−	2.29535i	−0.174909	−	0.187414i
$151$	−22.6819	+	8.25555i	−1.84583	+	0.671827i	−0.858572	+	0.512693i	$0.828648\pi$
$151$	−22.6819	+	8.25555i	−1.84583	+	0.671827i	−0.987257	+	0.159134i	$0.949130\pi$
$152$	−10.8068	−	8.74076i	−0.876546	−	0.708970i
$153$	22.5371	+	3.15767i	1.82202	+	0.255282i
$154$	5.47896	−	12.9146i	0.441507	−	1.04069i
$155$	8.60102	+	1.51659i	0.690851	+	0.121816i
$156$	9.76450	−	0.00584982i	0.781786	−	0.000468361i
$157$	−2.97797	+	8.18190i	−0.237668	+	0.652987i	0.762316	+	0.647206i	$0.224062\pi$
$157$	−2.97797	+	8.18190i	−0.237668	+	0.652987i	−0.999983	+	0.00578127i	$0.998160\pi$
$158$	−1.15260	+	0.352628i	−0.0916956	+	0.0280536i
$159$	18.4343	−	8.99582i	1.46193	−	0.713415i
$160$	14.1253	+	1.22201i	1.11670	+	0.0966081i
$161$	7.18026			0.565883
$162$	−12.0388	−	4.13130i	−0.945856	−	0.324585i
$163$		−	6.44084i		−	0.504485i	−0.967664	−	0.252243i	$-0.918832\pi$
$163$		−	6.44084i		−	0.504485i	0.967664	−	0.252243i	$-0.0811681\pi$
$164$	18.0330	+	8.78664i	1.40814	+	0.686121i
$165$	7.40315	+	15.1706i	0.576334	+	1.18103i
$166$	3.60369	+	11.7790i	0.279701	+	0.914225i
$167$	−13.4013	−	4.87768i	−1.03703	−	0.377446i	−0.233273	−	0.972411i	$-0.574944\pi$
$167$	−13.4013	−	4.87768i	−1.03703	−	0.377446i	−0.803752	+	0.594965i	$0.797166\pi$
$168$	−12.4032	+	1.53290i	−0.956926	+	0.118266i
$169$	0.877712	−	4.97775i	0.0675163	−	0.382904i
$170$	−10.5011	+	24.7523i	−0.805396	+	1.89842i
$171$	−13.6665	+	5.52835i	−1.04510	+	0.422764i
$172$	5.83735	−	5.64144i	0.445094	−	0.430156i
$173$	3.39321	+	9.32276i	0.257981	+	0.708796i	0.999292	+	0.0376343i	$0.0119822\pi$
$173$	3.39321	+	9.32276i	0.257981	+	0.708796i	−0.741311	+	0.671162i	$0.765796\pi$
$174$	−4.68639	+	4.37368i	−0.355274	+	0.331568i
$175$	−2.50486	+	2.10182i	−0.189349	+	0.158883i
$176$	−14.4260	−	5.81548i	−1.08740	−	0.438358i
$177$	2.94468	−	0.310127i	0.221335	−	0.0233106i
$178$	−3.88828	−	7.62752i	−0.291439	−	0.571706i
$179$	−8.28116	+	4.78113i	−0.618963	+	0.357359i	−0.776465	−	0.630160i	$-0.782989\pi$
$179$	−8.28116	+	4.78113i	−0.618963	+	0.357359i	0.157502	+	0.987519i	$0.449656\pi$
$180$	8.39908	−	12.4739i	0.626030	−	0.929753i
$181$	−4.60888	−	2.66094i	−0.342575	−	0.197786i	0.318835	−	0.947810i	$-0.396708\pi$
$181$	−4.60888	−	2.66094i	−0.342575	−	0.197786i	−0.661410	+	0.750024i	$0.730042\pi$
$182$	0.530254	−	10.1555i	0.0393051	−	0.752778i
$183$	0.166731	+	0.580998i	0.0123251	+	0.0429486i
$184$	−0.143567	−	7.95967i	−0.0105839	−	0.586795i
$185$	3.47397	+	19.7019i	0.255411	+	1.44851i
$186$	0.450172	+	8.52370i	0.0330082	+	0.624988i
$187$	18.9605	−	22.5963i	1.38653	−	1.65240i
$188$	−16.5895	+	4.14306i	−1.20991	+	0.302164i
$189$	−4.95786	+	12.2936i	−0.360631	+	0.894225i
$190$	−2.12608	−	17.2879i	−0.154242	−	1.25419i
$191$	3.17518	+	2.66429i	0.229748	+	0.192781i	0.750393	−	0.660992i	$-0.229864\pi$
$191$	3.17518	+	2.66429i	0.229748	+	0.192781i	−0.520645	+	0.853773i	$0.674309\pi$
$192$	1.94730	+	13.7189i	0.140534	+	0.990076i
$193$	−3.12735	−	17.7361i	−0.225112	−	1.27667i	−0.862472	−	0.506106i	$-0.831085\pi$
$193$	−3.12735	−	17.7361i	−0.225112	−	1.27667i	0.637360	−	0.770566i	$-0.280027\pi$
$194$	1.59360	−	6.90874i	0.114414	−	0.496019i
$195$	8.80408	+	8.49840i	0.630473	+	0.608583i
$196$	−0.0690410	−	0.981861i	−0.00493150	−	0.0701329i
$197$	−13.4165	−	7.74604i	−0.955888	−	0.551882i	−0.0609831	−	0.998139i	$-0.519424\pi$
$197$	−13.4165	−	7.74604i	−0.955888	−	0.551882i	−0.894905	+	0.446256i	$0.852757\pi$
$198$	−12.8146	+	10.3902i	−0.910697	+	0.738398i
$199$	−8.79403	−	15.2317i	−0.623392	−	1.07975i	−0.988849	−	0.148919i	$-0.952421\pi$
$199$	−8.79403	−	15.2317i	−0.623392	−	1.07975i	0.365457	−	0.930828i	$-0.380913\pi$
$200$	2.38006	+	2.73473i	0.168296	+	0.193375i
$201$	1.58887	−	3.57070i	0.112070	−	0.251857i
$202$	−1.04264	+	1.11853i	−0.0733597	+	0.0786993i
$203$	4.29127	+	5.11414i	0.301188	+	0.358942i
$204$	−25.8813	−	4.54759i	−1.81205	−	0.318395i
$205$	8.59783	+	23.6223i	0.600499	+	1.64986i
$206$	12.5410	−	9.45412i	0.873772	−	0.658700i
$207$	−7.45718	−	3.96101i	−0.518310	−	0.275309i
$208$	−11.2685	−	0.384757i	−0.781331	−	0.0266781i
$209$	−3.31818	+	18.8183i	−0.229523	+	1.30169i
$210$	−12.5117	−	9.42031i	−0.863390	−	0.650063i
$211$	−8.41203	+	23.1119i	−0.579108	+	1.59109i	0.210579	+	0.977577i	$0.432465\pi$
$211$	−8.41203	+	23.1119i	−0.579108	+	1.59109i	−0.789687	+	0.613510i	$0.789757\pi$
$212$	−21.6339	+	9.64209i	−1.48582	+	0.662222i
$213$	4.90162	−	7.27026i	0.335853	−	0.498150i
$214$	14.3702	+	9.32813i	0.982324	+	0.637658i
$215$	10.1731			0.693803
$216$	13.7272	+	5.25023i	0.934015	+	0.357233i
$217$	8.88949			0.603458
$218$	−23.1975	−	15.0582i	−1.57113	−	1.01987i
$219$	4.65894	+	0.324795i	0.314822	+	0.0219476i
$220$	−7.93500	−	17.8037i	−0.534977	−	1.20033i
$221$	7.31323	−	20.0929i	0.491941	−	1.35160i
$222$	−17.9946	+	7.64686i	−1.20772	+	0.513224i
$223$	−2.95087	+	16.7352i	−0.197605	+	1.12067i	0.711055	+	0.703136i	$0.248218\pi$
$223$	−2.95087	+	16.7352i	−0.197605	+	1.12067i	−0.908660	+	0.417537i	$0.862893\pi$
$224$	14.3748	−	1.27167i	0.960455	−	0.0849671i
$225$	3.76094	−	0.801074i	0.250729	−	0.0534050i
$226$	−6.71414	+	5.06151i	−0.446618	+	0.336687i
$227$	3.04973	+	8.37907i	0.202418	+	0.556138i	0.998817	−	0.0486333i	$-0.0154866\pi$
$227$	3.04973	+	8.37907i	0.202418	+	0.556138i	−0.796399	+	0.604772i	$0.793264\pi$
$228$	15.9929	−	5.83178i	1.05915	−	0.386219i
$229$	1.06473	+	1.26890i	0.0703594	+	0.0838511i	0.800076	−	0.599899i	$-0.204792\pi$
$229$	1.06473	+	1.26890i	0.0703594	+	0.0838511i	−0.729717	+	0.683750i	$0.760348\pi$
$230$	6.80252	−	7.29765i	0.448545	−	0.481193i
$231$	10.1020	+	13.8981i	0.664666	+	0.914427i
$232$	5.58348	−	4.85935i	0.366573	−	0.319032i
$233$	−7.11806	−	12.3288i	−0.466320	−	0.807689i	0.532940	−	0.846153i	$-0.321087\pi$
$233$	−7.11806	−	12.3288i	−0.466320	−	0.807689i	−0.999260	+	0.0384635i	$0.987754\pi$
$234$	−6.15303	+	10.2547i	−0.402236	+	0.670369i
$235$	−18.5572	−	10.7140i	−1.21054	−	0.698905i
$236$	−3.41060	+	0.239821i	−0.222011	+	0.0156110i
$237$	0.356828	−	1.43245i	0.0231785	−	0.0930475i
$238$	−6.15114	+	26.6671i	−0.398719	+	1.72857i
$239$	3.00714	+	17.0544i	0.194516	+	1.10316i	0.913106	+	0.407722i	$0.133677\pi$
$239$	3.00714	+	17.0544i	0.194516	+	1.10316i	−0.718590	+	0.695434i	$0.755212\pi$
$240$	−10.1927	+	14.0582i	−0.657937	+	0.907454i
$241$	16.9856	+	14.2526i	1.09414	+	0.918090i	0.997017	−	0.0771832i	$-0.0245926\pi$
$241$	16.9856	+	14.2526i	1.09414	+	0.918090i	0.0971195	+	0.995273i	$0.469037\pi$
$242$	0.711304	+	5.78384i	0.0457244	+	0.371799i
$243$	11.9309	−	10.0327i	0.765365	−	0.643597i
$244$	−0.169114	−	0.677159i	−0.0108264	−	0.0433507i
$245$	0.792866	−	0.944900i	0.0506543	−	0.0603675i
$246$	−20.5991	+	13.3891i	−1.31335	+	0.853658i
$247$	2.40533	+	13.6413i	0.153047	+	0.867975i
$248$	−0.177743	−	9.85444i	−0.0112867	−	0.625758i
$249$	−14.6389	−	3.64661i	−0.927705	−	0.231094i
$250$	0.687200	−	13.1614i	0.0434623	−	0.832398i
$251$	−5.87413	−	3.39143i	−0.370772	−	0.214065i	0.303024	−	0.952983i	$-0.402004\pi$
$251$	−5.87413	−	3.39143i	−0.370772	−	0.214065i	−0.673796	+	0.738918i	$0.735337\pi$
$252$	6.21430	−	13.9880i	0.391464	−	0.881164i
$253$	−9.47842	+	5.47237i	−0.595903	+	0.344045i
$254$	−7.97861	−	15.6514i	−0.500623	−	0.982057i
$255$	−19.3618	−	26.6373i	−1.21248	−	1.66809i
$256$	−1.69713	−	15.9097i	−0.106071	−	0.994359i
$257$	17.7134	−	14.8633i	1.10493	−	0.927148i	0.107185	−	0.994239i	$-0.465816\pi$
$257$	17.7134	−	14.8633i	1.10493	−	0.927148i	0.997747	+	0.0670910i	$0.0213718\pi$
$258$	2.24047	+	9.68664i	0.139486	+	0.603064i
$259$	6.96443	+	19.1346i	0.432749	+	1.18897i
$260$	−9.81920	−	10.1602i	−0.608961	−	0.630108i
$261$	−1.63555	−	7.67867i	−0.101238	−	0.475298i
$262$	0.172152	−	0.405783i	0.0106356	−	0.0250694i
$263$	0.367614	−	2.08484i	0.0226680	−	0.128557i	−0.971374	−	0.237556i	$-0.923654\pi$
$263$	0.367614	−	2.08484i	0.0226680	−	0.128557i	0.994042	+	0.108999i	$0.0347647\pi$
$264$	15.2047	−	11.4765i	0.935787	−	0.706330i
$265$	−27.8918	−	10.1518i	−1.71338	−	0.623620i
$266$	−5.18668	−	16.9531i	−0.318016	−	1.03946i
$267$	10.4602	+	0.729223i	0.640151	+	0.0446277i
$268$	−1.97673	+	4.05689i	−0.120748	+	0.247814i
$269$			25.6896i			1.56632i	0.621820	+	0.783161i	$0.286394\pi$
$269$			25.6896i			1.56632i	−0.621820	+	0.783161i	$0.713606\pi$
$270$	7.79752	+	16.6857i	0.474542	+	1.01546i
$271$	−27.3036			−1.65857			−0.829287	−	0.558823i	$-0.811253\pi$
$271$	−27.3036			−1.65857			−0.829287	+	0.558823i	$0.811253\pi$
$272$	29.6848	+	6.28564i	1.79991	+	0.381123i
$273$	10.3270	+	6.96249i	0.625020	+	0.421389i
$274$	8.62495	−	2.63874i	0.521052	−	0.159412i
$275$	1.70469	−	4.68360i	0.102797	−	0.282432i
$276$	8.44680	+	4.87002i	0.508438	+	0.293141i
$277$	−16.2093	−	2.85814i	−0.973923	−	0.171729i	−0.336028	−	0.941852i	$-0.609084\pi$
$277$	−16.2093	−	2.85814i	−0.973923	−	0.171729i	−0.637895	+	0.770123i	$0.720195\pi$
$278$	2.83201	−	6.67540i	0.169853	−	0.400364i
$279$	−9.23233	−	4.90391i	−0.552725	−	0.293590i
$280$	14.0609	+	11.3727i	0.840297	+	0.679651i
$281$	27.1438	−	9.87955i	1.61927	−	0.589364i	0.636023	−	0.771670i	$-0.280578\pi$
$281$	27.1438	−	9.87955i	1.61927	−	0.589364i	0.983242	+	0.182305i	$0.0583560\pi$
$282$	6.11471	−	20.0293i	0.364126	−	1.19273i
$283$	2.37158	+	2.82634i	0.140976	+	0.168009i	0.831913	−	0.554907i	$-0.187246\pi$
$283$	2.37158	+	2.82634i	0.140976	+	0.168009i	−0.690937	+	0.722915i	$0.742802\pi$
$284$	−5.94799	+	8.19338i	−0.352948	+	0.486188i
$285$	19.4902	+	8.67268i	1.15450	+	0.513725i
$286$	7.03997	+	13.8101i	0.416282	+	0.816609i
$287$	12.7934	+	22.1588i	0.755169	+	1.30799i
$288$	−15.6307	−	6.60918i	−0.921048	−	0.389449i
$289$	−20.2718	+	35.1117i	−1.19246	+	2.06540i
$290$	9.26327	+	0.483667i	0.543958	+	0.0284019i
$291$	6.24776	+	6.03084i	0.366250	+	0.353534i
$292$	−5.36341	−	0.561615i	−0.313870	−	0.0328660i
$293$	−12.6127	+	2.22395i	−0.736840	+	0.129925i	−0.529459	−	0.848336i	$-0.677605\pi$
$293$	−12.6127	+	2.22395i	−0.736840	+	0.129925i	−0.207381	+	0.978260i	$0.566494\pi$
$294$	1.07433	+	0.546850i	0.0626561	+	0.0318929i
$295$	−3.28222	−	2.75411i	−0.191098	−	0.160350i
$296$	21.0724	−	8.10301i	1.22481	−	0.470978i
$297$	−2.82473	−	20.0069i	−0.163907	−	1.16092i
$298$	2.91186	−	0.358105i	0.168680	−	0.0207445i
$299$	−5.09974	+	6.07763i	−0.294926	+	0.351479i
$300$	−4.37226	+	0.773648i	−0.252432	+	0.0446666i
$301$	10.1973	−	1.79806i	0.587762	−	0.103638i
$302$	−7.67242	+	33.2623i	−0.441498	+	1.91403i
$303$	−0.516588	−	1.80012i	−0.0296772	−	0.103414i
$304$	−18.6897	+	6.08867i	−1.07193	+	0.349209i
$305$	0.437330	−	0.757478i	0.0250415	−	0.0433731i
$306$	21.0994	−	24.3023i	1.20617	−	1.38927i
$307$	16.6782	−	9.62914i	0.951873	−	0.549564i	0.0582108	−	0.998304i	$-0.481460\pi$
$307$	16.6782	−	9.62914i	0.951873	−	0.549564i	0.893662	+	0.448740i	$0.148127\pi$
$308$	−11.1006	−	16.4435i	−0.632513	−	0.936955i
$309$	2.01465	+	19.1292i	0.114609	+	1.08822i
$310$	8.42183	−	9.03482i	0.478328	−	0.513143i
$311$	24.4635	−	20.5273i	1.38720	−	1.16400i	0.420740	−	0.907181i	$-0.361770\pi$
$311$	24.4635	−	20.5273i	1.38720	−	1.16400i	0.966460	−	0.256818i	$-0.0826740\pi$
$312$	7.51179	−	11.5872i	0.425271	−	0.655998i
$313$	5.47887	−	1.99414i	0.309684	−	0.112716i	−0.182503	−	0.983205i	$-0.558420\pi$
$313$	5.47887	−	1.99414i	0.309684	−	0.112716i	0.492187	+	0.870490i	$0.336198\pi$
$314$	7.41239	+	9.83261i	0.418305	+	0.554886i
$315$	17.7817	−	7.19301i	1.00188	−	0.405280i
$316$	−0.469215	+	1.63874i	−0.0263954	+	0.0921866i
$317$	10.5865	+	1.86668i	0.594595	+	0.104843i	0.462844	−	0.886440i	$-0.346829\pi$
$317$	10.5865	+	1.86668i	0.594595	+	0.104843i	0.131751	+	0.991283i	$0.457940\pi$
$318$	3.52358	−	28.7937i	0.197593	−	1.61467i
$319$	−9.56247	−	3.48045i	−0.535395	−	0.194868i
$320$	12.3261	−	15.8146i	0.689050	−	0.884061i
$321$	−18.8572	+	9.20220i	−1.05251	+	0.513616i
$322$	5.52884	−	8.51728i	0.308110	−	0.474650i
$323$		−	37.2772i		−	2.07416i
$324$	−14.1705	+	11.0994i	−0.787251	+	0.616633i
$325$		−	3.61301i		−	0.200414i
$326$	−7.64017	−	4.95948i	−0.423150	−	0.274680i
$327$	30.4408	−	14.8549i	1.68338	−	0.821479i
$328$	24.3083	−	14.6252i	1.34220	−	0.807539i
$329$	−20.4949	−	7.45953i	−1.12992	−	0.411257i
$330$	23.6959	+	2.89975i	1.30442	+	0.159626i
$331$	−17.6652	−	3.11484i	−0.970965	−	0.171207i	−0.334400	−	0.942431i	$-0.608534\pi$
$331$	−17.6652	−	3.11484i	−0.970965	−	0.171207i	−0.636564	+	0.771224i	$0.719645\pi$
$332$	16.7472	+	4.79515i	0.919121	+	0.263168i
$333$	3.32264	−	23.7145i	0.182079	−	1.29955i
$334$	−16.1050	+	12.1409i	−0.881229	+	0.664321i
$335$	−5.31432	+	1.93426i	−0.290353	+	0.105680i
$336$	−7.73218	+	15.8931i	−0.421825	+	0.867040i
$337$	1.36202	−	1.14287i	0.0741941	−	0.0622562i	−0.604936	−	0.796274i	$-0.706801\pi$
$337$	1.36202	−	1.14287i	0.0741941	−	0.0622562i	0.679130	+	0.734018i	$0.262357\pi$
$338$	−5.22881	−	4.87405i	−0.284410	−	0.265113i
$339$	−1.07859	−	10.2413i	−0.0585812	−	0.556232i
$340$	21.2755	+	31.5159i	1.15383	+	1.70919i
$341$	−11.7347	+	6.77505i	−0.635471	+	0.366889i
$342$	−3.96552	+	20.4682i	−0.214431	+	1.10679i
$343$	9.55642	−	16.5522i	0.515998	−	0.893735i
$344$	−2.19713	−	11.2683i	−0.118461	−	0.607543i
$345$	3.37039	+	11.7446i	0.181456	+	0.632307i
$346$	13.6715	+	3.15353i	0.734986	+	0.169535i
$347$	3.34069	−	0.589055i	0.179338	−	0.0316221i	−0.0832579	−	0.996528i	$-0.526533\pi$
$347$	3.34069	−	0.589055i	0.179338	−	0.0316221i	0.262596	+	0.964906i	$0.415421\pi$
$348$	1.57955	+	8.92680i	0.0846728	+	0.478527i
$349$	1.19141	−	1.41987i	0.0637747	−	0.0760038i	−0.733214	−	0.679998i	$-0.761981\pi$
$349$	1.19141	−	1.41987i	0.0637747	−	0.0760038i	0.796989	+	0.603994i	$0.206425\pi$
$350$	0.564447	+	4.58970i	0.0301710	+	0.245330i
$351$	−6.88443	−	12.9280i	−0.367464	−	0.690043i
$352$	−18.0065	+	12.6343i	−0.959749	+	0.673411i
$353$	−10.5282	−	8.83425i	−0.560362	−	0.470200i	0.318070	−	0.948067i	$-0.396965\pi$
$353$	−10.5282	−	8.83425i	−0.560362	−	0.470200i	−0.878432	+	0.477868i	$0.841410\pi$
$354$	1.89954	−	3.73180i	0.100960	−	0.198343i
$355$	−12.4953	+	2.20325i	−0.663180	+	0.116937i
$356$	−12.0418	−	1.26093i	−0.638215	−	0.0668290i
$357$	−24.1157	−	23.2784i	−1.27634	−	1.23203i
$358$	−0.705126	+	13.5047i	−0.0372670	+	0.713745i
$359$	−5.37668	+	9.31267i	−0.283770	+	0.491504i	−0.972310	−	0.233694i	$-0.924919\pi$
$359$	−5.37668	+	9.31267i	−0.283770	+	0.491504i	0.688540	+	0.725198i	$0.258252\pi$
$360$	−8.32935	−	19.5681i	−0.438996	−	1.03133i
$361$	2.57423	+	4.45870i	0.135486	+	0.234668i
$362$	−6.70529	+	3.41815i	−0.352422	+	0.179654i
$363$	−6.52067	−	2.90154i	−0.342247	−	0.152291i
$364$	−11.6383	−	8.44881i	−0.610011	−	0.442838i
$365$	−4.34397	−	5.17695i	−0.227374	−	0.270974i
$366$	0.817569	+	0.249594i	0.0427350	+	0.0130465i
$367$	−10.2024	+	3.71337i	−0.532562	+	0.193837i	−0.594282	−	0.804257i	$-0.702564\pi$
$367$	−10.2024	+	3.71337i	−0.532562	+	0.193837i	0.0617202	+	0.998093i	$0.480341\pi$
$368$	−9.55238	−	5.95870i	−0.497952	−	0.310619i
$369$	−1.06283	−	30.0709i	−0.0553286	−	1.56543i
$370$	26.0455	+	11.0497i	1.35404	+	0.574447i
$371$	−29.7523	−	5.24613i	−1.54466	−	0.272366i
$372$	10.4575	+	6.02931i	0.542198	+	0.312605i
$373$	7.89812	−	21.6999i	0.408949	−	1.12358i	−0.548795	−	0.835957i	$-0.684913\pi$
$373$	7.89812	−	21.6999i	0.408949	−	1.12358i	0.957744	−	0.287621i	$-0.0928645\pi$
$374$	−12.2042	−	39.8904i	−0.631063	−	2.06268i
$375$	13.3836	+	9.02326i	0.691128	+	0.465959i
$376$	−7.85948	+	22.8688i	−0.405322	+	1.17937i
$377$	−7.37665			−0.379917
$378$	10.7652	+	15.3472i	0.553700	+	0.789373i
$379$			19.1947i			0.985963i	0.870040	+	0.492982i	$0.164093\pi$
$379$			19.1947i			0.985963i	−0.870040	+	0.492982i	$0.835907\pi$
$380$	−22.1441	−	10.7898i	−1.13597	−	0.553504i
$381$	21.4639	+	1.49634i	1.09963	+	0.0766599i
$382$	5.60531	−	1.71490i	0.286792	−	0.0877421i
$383$	23.4828	+	8.54705i	1.19992	+	0.436734i	0.863195	−	0.504870i	$-0.168460\pi$
$383$	23.4828	+	8.54705i	1.19992	+	0.436734i	0.336722	+	0.941604i	$0.390682\pi$
$384$	17.7729	+	8.25373i	0.906969	+	0.421196i
$385$	4.31733	−	24.4848i	0.220031	−	1.24786i
$386$	−23.4468	−	9.94721i	−1.19341	−	0.506299i
$387$	−11.5825	−	3.75796i	−0.588770	−	0.191028i
$388$	−6.96813	−	7.21012i	−0.353753	−	0.366038i
$389$	0.272464	+	0.748588i	0.0138145	+	0.0379549i	0.946408	−	0.322973i	$-0.104682\pi$
$389$	0.272464	+	0.748588i	0.0138145	+	0.0379549i	−0.932594	+	0.360928i	$0.882460\pi$
$390$	16.8601	−	3.89965i	0.853743	−	0.197467i
$391$	16.3559	−	13.7242i	0.827151	−	0.694062i
$392$	−1.21785	−	0.674142i	−0.0615109	−	0.0340493i
$393$	0.317412	+	0.436685i	0.0160113	+	0.0220279i
$394$	−19.5192	+	9.95031i	−0.983364	+	0.501289i
$395$	−1.84996	+	1.06808i	−0.0930817	+	0.0537408i
$396$	2.45757	+	23.2013i	0.123498	+	1.16591i
$397$	26.8054	+	15.4761i	1.34532	+	0.776723i	0.987583	−	0.157099i	$-0.0502141\pi$
$397$	26.8054	+	15.4761i	1.34532	+	0.776723i	0.357740	+	0.933821i	$0.383547\pi$
$398$	−24.8394	−	1.29695i	−1.24509	−	0.0650103i
$399$	21.0694	+	5.24845i	1.05479	+	0.262751i
$400$	5.07662	−	0.717488i	0.253831	−	0.0358744i
$401$	5.68481	+	32.2401i	0.283886	+	1.61000i	0.709239	+	0.704968i	$0.249039\pi$
$401$	5.68481	+	32.2401i	0.283886	+	1.61000i	−0.425353	+	0.905028i	$0.639850\pi$
$402$	−3.01215	−	4.63419i	−0.150232	−	0.231132i
$403$	−6.31371	+	7.52439i	−0.314508	+	0.374816i
$404$	0.523969	+	2.09806i	0.0260684	+	0.104382i
$405$	−22.4355	−	2.33889i	−1.11483	−	0.116220i
$406$	9.37074	−	1.15243i	0.465062	−	0.0571940i
$407$	−23.7768	−	19.9511i	−1.17857	−	0.988940i
$408$	−25.3231	+	27.1990i	−1.25368	+	1.34655i
$409$	0.478133	+	2.71163i	0.0236422	+	0.134081i	0.994344	−	0.106205i	$-0.0338699\pi$
$409$	0.478133	+	2.71163i	0.0236422	+	0.134081i	−0.970702	+	0.240286i	$0.922759\pi$
$410$	34.6414	+	7.99053i	1.71082	+	0.394624i
$411$	−2.67017	+	10.7191i	−0.131710	+	0.528735i
$412$	−1.55793	−	22.1560i	−0.0767536	−	1.09155i
$413$	−3.77678	−	2.18053i	−0.185843	−	0.107297i
$414$	−10.4407	+	5.79577i	−0.513130	+	0.284847i
$415$	10.9152	+	18.9057i	0.535807	+	0.928046i
$416$	−9.13322	+	13.0705i	−0.447793	+	0.640836i
$417$	5.22163	+	7.18377i	0.255705	+	0.351791i
$418$	19.7674	+	18.4263i	0.966857	+	0.901258i
$419$	16.1377	+	19.2321i	0.788376	+	0.939551i	0.999279	−	0.0379565i	$-0.0120848\pi$
$419$	16.1377	+	19.2321i	0.788376	+	0.939551i	−0.210903	+	0.977507i	$0.567640\pi$
$420$	−20.8085	+	7.58781i	−1.01535	+	0.370247i
$421$	−2.33021	−	6.40219i	−0.113567	−	0.312024i	0.869868	−	0.493285i	$-0.164204\pi$
$421$	−2.33021	−	6.40219i	−0.113567	−	0.312024i	−0.983435	+	0.181262i	$0.941982\pi$
$422$	20.9382	+	27.7747i	1.01925	+	1.35205i
$423$	17.1703	+	19.0533i	0.834847	+	0.926404i
$424$	−5.22071	+	33.0868i	−0.253540	+	1.60684i
$425$	−1.68841	+	9.57545i	−0.0819000	+	0.464478i
$426$	−4.84977	−	11.4125i	−0.234972	−	0.552937i
$427$	0.304487	−	0.836572i	0.0147352	−	0.0404846i
$428$	22.1302	−	9.86329i	1.06970	−	0.476760i
$429$	−18.9388	−	1.32031i	−0.914373	−	0.0637449i
$430$	7.83338	−	12.0675i	0.377759	−	0.581945i
$431$	2.93816			0.141526			0.0707631	−	0.997493i	$-0.477457\pi$
$431$	2.93816			0.141526			0.0707631	+	0.997493i	$0.477457\pi$
$432$	16.7979	−	12.2406i	0.808188	−	0.588925i
$433$	−31.2403			−1.50131			−0.750656	−	0.660694i	$-0.770262\pi$
$433$	−31.2403			−1.50131			−0.750656	+	0.660694i	$0.770262\pi$
$434$	6.84496	−	10.5448i	0.328568	−	0.506166i
$435$	−6.35078	+	9.41971i	−0.304496	+	0.451640i
$436$	−35.7244	+	15.9221i	−1.71089	+	0.762531i
$437$	−4.73061	+	12.9972i	−0.226296	+	0.621743i
$438$	3.97268	−	5.27637i	0.189822	−	0.252115i
$439$	1.21855	−	6.91073i	0.0581581	−	0.329831i	−0.941822	−	0.336112i	$-0.890888\pi$
$439$	1.21855	−	6.91073i	0.0581581	−	0.329831i	0.999980	+	0.00628055i	$0.00199917\pi$
$440$	−27.2289	−	4.29641i	−1.29809	−	0.204823i
$441$	−1.25175	+	0.782917i	−0.0596072	+	0.0372818i
$442$	−18.2032	−	24.1467i	−0.865837	−	1.14854i
$443$	−7.15814	−	19.6668i	−0.340093	−	0.934399i	−0.985367	−	0.170447i	$-0.945479\pi$
$443$	−7.15814	−	19.6668i	−0.340093	−	0.934399i	0.645273	−	0.763952i	$-0.276743\pi$
$444$	−4.78517	+	27.2335i	−0.227094	+	1.29244i
$445$	−9.75301	−	11.6232i	−0.462337	−	0.550992i
$446$	17.5793	+	16.3866i	0.832403	+	0.775926i
$447$	−1.46077	+	3.28282i	−0.0690923	+	0.155272i
$448$	9.56020	−	18.0307i	0.451677	−	0.851870i
$449$	7.57475	+	13.1198i	0.357474	+	0.619164i	0.987538	−	0.157380i	$-0.0503046\pi$
$449$	7.57475	+	13.1198i	0.357474	+	0.619164i	−0.630064	+	0.776543i	$0.716971\pi$
$450$	1.94570	−	5.07809i	0.0917214	−	0.239383i
$451$	−33.7763	−	19.5007i	−1.59046	−	0.918253i
$452$	0.834077	+	11.8618i	0.0392317	+	0.557930i
$453$	−30.0800	−	29.0356i	−1.41328	−	1.36421i
$454$	12.2876	+	2.83432i	0.576687	+	0.133021i
$455$	−3.12961	−	17.7489i	−0.146718	−	0.832080i
$456$	5.39690	−	23.4614i	0.252733	−	1.09868i
$457$	0.729228	+	0.611895i	0.0341118	+	0.0286232i	0.659684	−	0.751543i	$-0.270690\pi$
$457$	0.729228	+	0.611895i	0.0341118	+	0.0286232i	−0.625572	+	0.780166i	$0.715134\pi$
$458$	2.32503	−	0.285935i	0.108641	−	0.0133609i
$459$	12.2042	+	37.4798i	0.569643	+	1.74941i
$460$	−3.41855	−	13.6884i	−0.159391	−	0.638227i
$461$	2.82485	−	3.36653i	0.131567	−	0.156795i	−0.696239	−	0.717810i	$-0.745145\pi$
$461$	2.82485	−	3.36653i	0.131567	−	0.156795i	0.827806	+	0.561015i	$0.189589\pi$
$462$	24.2647	−	1.28152i	1.12889	−	0.0596216i
$463$	−0.0157534	−	0.0893420i	−0.000732123	−	0.00415207i	0.984440	−	0.175724i	$-0.0562266\pi$
$463$	−0.0157534	−	0.0893420i	−0.000732123	−	0.00415207i	−0.985172	+	0.171572i	$0.945115\pi$
$464$	−1.46489	−	10.3649i	−0.0680057	−	0.481178i
$465$	4.17270	+	14.5403i	0.193504	+	0.674292i
$466$	−20.1055	−	1.04978i	−0.931370	−	0.0486300i
$467$	8.84291	+	5.10545i	0.409201	+	0.236252i	0.690446	−	0.723384i	$-0.257414\pi$
$467$	8.84291	+	5.10545i	0.409201	+	0.236252i	−0.281245	+	0.959636i	$0.590748\pi$
$468$	7.42632	+	15.1949i	0.343282	+	0.702387i
$469$	−4.98507	+	2.87813i	−0.230189	+	0.132900i
$470$	−26.9982	+	13.7629i	−1.24533	+	0.634834i
$471$	−14.9980	+	1.57956i	−0.691072	+	0.0727823i
$472$	−2.34171	+	4.23035i	−0.107786	+	0.194718i
$473$	−12.0907	+	10.1453i	−0.555933	+	0.466483i
$474$	−1.42442	−	1.52627i	−0.0654259	−	0.0701037i
$475$	−2.15430	−	5.91889i	−0.0988460	−	0.271577i
$476$	26.8963	+	27.8303i	1.23279	+	1.27560i
$477$	28.0057	+	21.8614i	1.28229	+	1.00097i
$478$	22.5456	+	9.56486i	1.03121	+	0.437487i
$479$	0.385466	−	2.18609i	0.0176124	−	0.0998848i	−0.974734	−	0.223367i	$-0.928295\pi$
$479$	0.385466	−	2.18609i	0.0176124	−	0.0998848i	0.992347	+	0.123482i	$0.0394062\pi$
$480$	8.82753	+	22.9156i	0.402920	+	1.04595i
$481$	−21.1427	−	7.69531i	−0.964024	−	0.350876i
$482$	29.9855	−	9.17385i	1.36580	−	0.417857i
$483$	5.45420	+	11.1768i	0.248175	+	0.508560i
$484$	7.40855	+	3.60983i	0.336752	+	0.164083i
$485$		−	12.5656i		−	0.570573i
$486$	−2.71403	−	21.8777i	−0.123111	−	0.992393i
$487$	41.4817			1.87971			0.939857	−	0.341569i	$-0.110958\pi$
$487$	41.4817			1.87971			0.939857	+	0.341569i	$0.110958\pi$
$488$	−0.933470	−	0.320812i	−0.0422562	−	0.0145225i
$489$	10.0258	−	4.89252i	0.453382	−	0.221248i
$490$	−0.510338	−	1.66808i	−0.0230547	−	0.0753563i
$491$	1.96933	−	5.41068i	0.0888745	−	0.244181i	−0.887290	−	0.461211i	$-0.847415\pi$
$491$	1.96933	−	5.41068i	0.0888745	−	0.244181i	0.976165	+	0.217031i	$0.0696372\pi$
$492$	0.0208152	+	34.7446i	0.000938420	+	1.56641i
$493$	19.5501	+	3.44721i	0.880493	+	0.155255i
$494$	18.0335	+	7.65066i	0.811367	+	0.344219i
$495$	−17.9909	+	23.0474i	−0.808632	+	1.03590i
$496$	−11.8263	−	7.37714i	−0.531016	−	0.331243i
$497$	−12.1355	+	4.41696i	−0.544352	+	0.198128i
$498$	−15.5977	+	14.5569i	−0.698950	+	0.652311i
$499$	−8.64536	−	10.3031i	−0.387019	−	0.461232i	0.536997	−	0.843584i	$-0.319559\pi$
$499$	−8.64536	−	10.3031i	−0.387019	−	0.461232i	−0.924017	+	0.382352i	$0.875114\pi$
$500$	−15.0830	−	10.9495i	−0.674532	−	0.489676i
$501$	−2.58720	−	24.5656i	−0.115587	−	1.09751i
$502$	−8.54606	+	4.35652i	−0.381429	+	0.194441i
$503$	9.82946	+	17.0251i	0.438274	+	0.759113i	0.997557	−	0.0698643i	$-0.0222566\pi$
$503$	9.82946	+	17.0251i	0.438274	+	0.759113i	−0.559282	+	0.828977i	$0.688923\pi$
$504$	−11.8077	−	18.1423i	−0.525956	−	0.808124i
$505$	−1.35499	+	2.34691i	−0.0602963	+	0.104436i
$506$	−0.807070	+	15.4571i	−0.0358786	+	0.687154i
$507$	8.41507	−	2.41491i	0.373726	−	0.107250i
$508$	−24.7094	−	2.58738i	−1.09630	−	0.114796i
$509$	−8.99761	+	1.58652i	−0.398812	+	0.0703213i	−0.369457	−	0.929248i	$-0.620456\pi$
$509$	−8.99761	+	1.58652i	−0.398812	+	0.0703213i	−0.0293547	+	0.999569i	$0.509345\pi$
$510$	−46.5061	+	2.45618i	−2.05932	+	0.108761i
$511$	−5.26929	−	4.42146i	−0.233100	−	0.195594i
$512$	−20.1791	−	10.2374i	−0.891797	−	0.452435i
$513$	−18.9866	−	17.0738i	−0.838280	−	0.753829i
$514$	−3.99156	−	32.4566i	−0.176060	−	1.43160i
$515$	17.8912	−	21.3219i	0.788381	−	0.939556i
$516$	13.2155	+	4.80110i	0.581782	+	0.211357i
$517$	32.7399	−	5.77292i	1.43990	−	0.253893i
$518$	28.0603	+	6.47250i	1.23290	+	0.284385i
$519$	−11.9343	+	12.3635i	−0.523856	+	0.542698i
$520$	−19.6129	+	3.82421i	−0.860085	+	0.167703i
$521$	13.8130	−	23.9247i	0.605157	−	1.04816i	−0.386870	−	0.922134i	$-0.626444\pi$
$521$	13.8130	−	23.9247i	0.605157	−	1.04816i	0.992027	−	0.126028i	$-0.0402229\pi$
$522$	−10.3679	−	3.97253i	−0.453790	−	0.173873i
$523$	2.64626	−	1.52782i	0.115713	−	0.0668068i	−0.441027	−	0.897494i	$-0.645386\pi$
$523$	2.64626	−	1.52782i	0.115713	−	0.0668068i	0.556739	+	0.830687i	$0.312052\pi$
$524$	−0.348785	−	0.516663i	−0.0152368	−	0.0225705i
$525$	−5.17440	−	2.30248i	−0.225830	−	0.100489i
$526$	−2.18999	−	2.04141i	−0.0954882	−	0.0890096i
$527$	20.2493	−	16.9912i	0.882073	−	0.740147i
$528$	−1.90579	−	26.8730i	−0.0829389	−	1.16950i
$529$	14.1686	−	5.15694i	0.616025	−	0.224215i
$530$	−33.5190	+	25.2686i	−1.45597	+	1.09760i
$531$	2.71955	+	4.34810i	0.118018	+	0.188691i
$532$	−24.1037	−	6.90151i	−1.04503	−	0.299218i
$533$	−27.8424	−	4.90937i	−1.20599	−	0.212649i
$534$	8.91939	−	11.8464i	0.385980	−	0.512644i
$535$	28.5317	+	10.3847i	1.23353	+	0.448969i
$536$	3.29022	+	5.46865i	0.142116	+	0.236210i
$537$	−13.7327	−	9.25863i	−0.592612	−	0.399539i
$538$	30.4732	+	19.7811i	1.31379	+	0.852825i
$539$			1.91371i			0.0824292i
$540$	25.7969	+	3.59864i	1.11012	+	0.154861i
$541$		−	12.4110i		−	0.533592i	−0.963753	−	0.266796i	$-0.914035\pi$
$541$		−	12.4110i		−	0.533592i	0.963753	−	0.266796i	$-0.0859650\pi$
$542$	−21.0239	+	32.3877i	−0.903054	+	1.39117i
$543$	0.641054	−	9.19544i	0.0275103	−	0.394614i
$544$	30.3136	−	30.3724i	1.29968	−	1.30220i
$545$	−46.0581	−	16.7638i	−1.97291	−	0.718082i
$546$	16.2108	−	6.88885i	0.693760	−	0.294815i
$547$	0.791575	+	0.139576i	0.0338453	+	0.00596784i	0.190545	−	0.981678i	$-0.438974\pi$
$547$	0.791575	+	0.139576i	0.0338453	+	0.00596784i	−0.156700	+	0.987646i	$0.550086\pi$
$548$	3.51117	−	12.2628i	0.149990	−	0.523842i
$549$	−0.777728	+	0.700865i	−0.0331926	+	0.0299122i
$550$	−4.24311	−	5.62852i	−0.180927	−	0.240001i
$551$	−12.0845	+	4.39841i	−0.514819	+	0.187379i
$552$	12.2809	−	6.26973i	0.522712	−	0.266857i
$553$	−1.66558	+	1.39758i	−0.0708275	+	0.0594313i
$554$	−15.8716	+	17.0268i	−0.674320	+	0.723401i
$555$	−28.0290	+	20.3733i	−1.18976	+	0.864799i
$556$	−5.73775	−	8.49946i	−0.243335	−	0.360457i
$557$	−15.6214	+	9.01902i	−0.661900	+	0.382148i	−0.793000	−	0.609221i	$-0.791482\pi$
$557$	−15.6214	+	9.01902i	−0.661900	+	0.382148i	0.131101	+	0.991369i	$0.458149\pi$
$558$	−12.9260	+	7.17543i	−0.547202	+	0.303760i
$559$	−5.72063	+	9.90842i	−0.241957	+	0.419081i
$560$	24.3174	−	7.92205i	1.02760	−	0.334768i
$561$	49.5759	+	12.3495i	2.09310	+	0.521397i
$562$	9.18171	−	39.8056i	0.387307	−	1.67910i
$563$	20.6986	−	3.64973i	0.872344	−	0.153818i	0.280484	−	0.959859i	$-0.409505\pi$
$563$	20.6986	−	3.64973i	0.872344	−	0.153818i	0.591860	+	0.806041i	$0.298394\pi$
$564$	−19.0506	−	22.6760i	−0.802176	−	0.954833i
$565$	−9.57853	+	11.4152i	−0.402972	+	0.480243i
$566$	5.17876	−	0.636891i	0.217680	−	0.0267705i
$567$	−22.9022	+	1.62094i	−0.961800	+	0.0680729i
$568$	5.13907	+	13.3645i	0.215631	+	0.560762i
$569$	18.1237	+	15.2076i	0.759785	+	0.637535i	0.938071	−	0.346444i	$-0.112611\pi$
$569$	18.1237	+	15.2076i	0.759785	+	0.637535i	−0.178286	+	0.983979i	$0.557055\pi$
$570$	25.2952	−	16.4415i	1.05950	−	0.688658i
$571$	−3.45440	+	0.609103i	−0.144562	+	0.0254902i	−0.245461	−	0.969407i	$-0.578939\pi$
$571$	−3.45440	+	0.609103i	−0.144562	+	0.0254902i	0.100899	+	0.994897i	$0.467828\pi$
$572$	21.8025	+	2.28299i	0.911608	+	0.0954565i
$573$	−1.73533	+	6.96629i	−0.0724943	+	0.291021i
$574$	36.1359	+	1.88678i	1.50828	+	0.0787526i
$575$	1.80385	−	3.12436i	0.0752258	−	0.130295i
$576$	−19.8756	+	13.4522i	−0.828150	+	0.560507i
$577$	8.52365	+	14.7634i	0.354844	+	0.614608i	0.987091	−	0.160159i	$-0.0512006\pi$
$577$	8.52365	+	14.7634i	0.354844	+	0.614608i	−0.632247	+	0.774767i	$0.717867\pi$
$578$	26.0404	+	51.0828i	1.08314	+	2.12476i
$579$	25.2324	−	18.3405i	1.04862	−	0.762207i
$580$	7.70650	−	10.6157i	0.319995	−	0.440795i
$581$	14.2826	+	17.0214i	0.592543	+	0.706166i
$582$	11.9646	−	2.76736i	0.495950	−	0.114711i
$583$	43.2733	−	15.7502i	1.79220	−	0.652307i
$584$	−4.79605	+	5.92967i	−0.198462	+	0.245372i
$585$	−6.54092	+	20.1599i	−0.270434	+	0.833508i
$586$	−7.07375	+	16.6737i	−0.292214	+	0.688785i
$587$	36.9148	+	6.50908i	1.52364	+	0.268658i	0.871861	−	0.489753i	$-0.162913\pi$
$587$	36.9148	+	6.50908i	1.52364	+	0.268658i	0.651776	+	0.758412i	$0.274024\pi$
$588$	1.47592	−	0.853301i	0.0608658	−	0.0351895i
$589$	−5.85671	+	16.0912i	−0.241322	+	0.663026i
$590$	−5.79427	+	1.77271i	−0.238546	+	0.0729815i
$591$	1.86612	−	26.7681i	0.0767620	−	1.10109i
$592$	6.61404	−	31.2357i	0.271835	−	1.28378i
$593$	−16.4642			−0.676103			−0.338051	−	0.941128i	$-0.609768\pi$
$593$	−16.4642			−0.676103			−0.338051	+	0.941128i	$0.609768\pi$
$594$	−25.9074	−	12.0547i	−1.06300	−	0.494612i
$595$			48.5018i			1.98838i
$596$	1.81737	−	3.72982i	0.0744422	−	0.152779i
$597$	17.0296	−	25.2589i	0.696974	−	1.03378i
$598$	3.28251	+	10.7292i	0.134232	+	0.438748i
$599$	−20.2683	−	7.37705i	−0.828139	−	0.301418i	−0.107044	−	0.994254i	$-0.534139\pi$
$599$	−20.2683	−	7.37705i	−0.828139	−	0.301418i	−0.721095	+	0.692836i	$0.756361\pi$
$600$	−2.44896	+	5.78212i	−0.0999782	+	0.236054i
$601$	−3.05008	+	17.2979i	−0.124415	+	0.705595i	0.857238	+	0.514920i	$0.172179\pi$
$601$	−3.05008	+	17.2979i	−0.124415	+	0.705595i	−0.981653	+	0.190674i	$0.938933\pi$
$602$	5.71910	−	13.4806i	0.233093	−	0.549429i
$603$	6.76506	−	0.239105i	0.275494	−	0.00973709i
$604$	33.5482	+	34.7133i	1.36506	+	1.41246i
$605$	3.53227	+	9.70482i	0.143607	+	0.394557i
$606$	−2.53309	−	0.773322i	−0.102900	−	0.0314140i
$607$	−17.1550	+	14.3947i	−0.696299	+	0.584264i	−0.920718	−	0.390229i	$-0.872396\pi$
$607$	−17.1550	+	14.3947i	−0.696299	+	0.584264i	0.224419	+	0.974493i	$0.427951\pi$
$608$	−7.16872	+	26.8581i	−0.290730	+	1.08924i
$609$	−4.70096	+	10.5645i	−0.190492	+	0.428096i
$610$	−0.561780	−	1.10203i	−0.0227458	−	0.0446198i
$611$	20.8704	−	12.0495i	0.844327	−	0.487472i
$612$	−12.5809	−	43.7411i	−0.508554	−	1.76813i
$613$	20.3462	+	11.7469i	0.821774	+	0.474451i	0.851028	−	0.525121i	$-0.175980\pi$
$613$	20.3462	+	11.7469i	0.821774	+	0.474451i	−0.0292540	+	0.999572i	$0.509313\pi$
$614$	1.42011	−	27.1983i	0.0573112	−	1.09763i
$615$	−30.2395	+	31.3271i	−1.21937	+	1.26323i
$616$	−28.0529	+	0.505985i	−1.13028	+	0.0203867i
$617$	−0.911711	−	5.17057i	−0.0367041	−	0.208159i	0.960940	−	0.276755i	$-0.0892591\pi$
$617$	−0.911711	−	5.17057i	−0.0367041	−	0.208159i	−0.997645	+	0.0685961i	$0.978148\pi$
$618$	24.2425	+	12.3398i	0.975177	+	0.496380i
$619$	−14.0073	+	16.6933i	−0.563001	+	0.670958i	−0.970179	−	0.242390i	$-0.922068\pi$
$619$	−14.0073	+	16.6933i	−0.563001	+	0.670958i	0.407178	+	0.913349i	$0.366513\pi$
$620$	−4.23232	−	16.9469i	−0.169974	−	0.680605i
$621$	0.501144	−	14.6166i	0.0201102	−	0.586546i
$622$	−5.51264	−	44.8250i	−0.221037	−	1.79732i
$623$	−11.8305	−	9.92697i	−0.473979	−	0.397716i
$624$	−7.96076	−	17.8328i	−0.318686	−	0.713883i
$625$	−5.16880	−	29.3137i	−0.206752	−	1.17255i
$626$	1.85329	−	8.03458i	0.0740723	−	0.321127i
$627$	−31.8130	+	9.12952i	−1.27049	+	0.364598i
$628$	17.3711	−	1.22147i	0.693183	−	0.0487421i
$629$	52.4377	+	30.2749i	2.09083	+	1.20714i
$630$	5.15959	−	26.6314i	0.205563	−	1.06102i
$631$	−18.2913	−	31.6814i	−0.728164	−	1.26122i	−0.957658	−	0.287908i	$-0.907040\pi$
$631$	−18.2913	−	31.6814i	−0.728164	−	1.26122i	0.229494	−	0.973310i	$-0.426293\pi$
$632$	1.58259	+	1.81843i	0.0629522	+	0.0723333i
$633$	−42.3657	+	4.46187i	−1.68389	+	0.177343i
$634$	10.3659	−	11.1204i	0.411683	−	0.441647i
$635$	−20.0128	−	23.8504i	−0.794186	−	0.946474i
$636$	−31.4422	−	26.3511i	−1.24676	−	1.04489i
$637$	0.474463	+	1.30358i	0.0187989	+	0.0516496i
$638$	−11.4917	+	8.66311i	−0.454961	+	0.342976i
$639$	15.0402	+	2.10728i	0.594980	+	0.0833625i
$640$	−9.26820	−	26.7986i	−0.366358	−	1.05931i
$641$	2.53575	−	14.3809i	0.100156	−	0.568012i	−0.892889	−	0.450277i	$-0.851325\pi$
$641$	2.53575	−	14.3809i	0.100156	−	0.568012i	0.993045	−	0.117736i	$-0.0375636\pi$
$642$	−3.60442	+	29.4543i	−0.142255	+	1.16247i
$643$	16.8828	−	46.3851i	0.665793	−	1.82925i	0.117300	−	0.993097i	$-0.462576\pi$
$643$	16.8828	−	46.3851i	0.665793	−	1.82925i	0.548494	−	0.836155i	$-0.315202\pi$
$644$	−5.84603	−	13.1167i	−0.230366	−	0.516871i
$645$	7.72762	+	15.8355i	0.304275	+	0.623521i
$646$	−44.2185	−	28.7036i	−1.73975	−	1.12933i
$647$	−23.5483			−0.925778			−0.462889	−	0.886416i	$-0.653187\pi$
$647$	−23.5483			−0.925778			−0.462889	+	0.886416i	$0.653187\pi$
$648$	2.25481	+	25.3558i	0.0885773	+	0.996069i
$649$	6.64748			0.260936
$650$	−4.28578	−	2.78204i	−0.168102	−	0.109121i
$651$	6.75254	+	13.8373i	0.264653	+	0.542328i
$652$	−11.7660	+	5.24401i	−0.460791	+	0.205371i
$653$	−9.17895	+	25.2190i	−0.359200	+	0.986894i	0.620108	+	0.784517i	$0.287089\pi$
$653$	−9.17895	+	25.2190i	−0.359200	+	0.986894i	−0.979308	+	0.202377i	$0.935133\pi$
$654$	5.81854	−	47.5475i	0.227523	−	1.85925i
$655$	0.135653	−	0.769324i	0.00530039	−	0.0300600i
$656$	1.36906	−	40.0962i	0.0534529	−	1.56549i
$657$	3.03340	+	7.49880i	0.118344	+	0.292556i
$658$	−24.6298	+	18.5673i	−0.960168	+	0.723830i
$659$	−2.27329	−	6.24582i	−0.0885548	−	0.243302i	0.887508	−	0.460793i	$-0.152435\pi$
$659$	−2.27329	−	6.24582i	−0.0885548	−	0.243302i	−0.976062	+	0.217491i	$0.930213\pi$
$660$	21.6857	−	25.8755i	0.844115	−	1.00720i
$661$	19.3288	+	23.0352i	0.751803	+	0.895964i	0.997300	−	0.0734332i	$-0.0233956\pi$
$661$	19.3288	+	23.0352i	0.751803	+	0.895964i	−0.245497	+	0.969397i	$0.578951\pi$
$662$	−17.2971	+	18.5561i	−0.672272	+	0.721204i
$663$	36.8318	−	3.87905i	1.43043	−	0.150650i
$664$	18.5835	−	16.1734i	0.721179	−	0.627648i
$665$	−15.7099	−	27.2104i	−0.609206	−	1.05517i
$666$	−25.5719	−	22.2017i	−0.990893	−	0.860298i
$667$	−6.37898	−	3.68291i	−0.246995	−	0.142603i
$668$	2.00068	+	28.4525i	0.0774086	+	1.10086i
$669$	−28.2915	+	8.11893i	−1.09381	+	0.313896i
$670$	−1.79763	+	7.79328i	−0.0694485	+	0.301081i
$671$	0.235642	+	1.33639i	0.00909687	+	0.0515909i
$672$	12.8987	+	21.4098i	0.497578	+	0.825899i
$673$	17.8623	+	14.9883i	0.688543	+	0.577756i	0.918489	−	0.395447i	$-0.129410\pi$
$673$	17.8623	+	14.9883i	0.688543	+	0.577756i	−0.229946	+	0.973203i	$0.573855\pi$
$674$	−0.306920	−	2.49566i	−0.0118221	−	0.0961293i
$675$	4.10380	+	5.24576i	0.157955	+	0.201909i
$676$	−9.80785	+	2.44941i	−0.377225	+	0.0942081i
$677$	−27.4963	+	32.7688i	−1.05677	+	1.25941i	−0.0921554	+	0.995745i	$0.529376\pi$
$677$	−27.4963	+	32.7688i	−1.05677	+	1.25941i	−0.964614	+	0.263665i	$0.915069\pi$
$678$	−12.9789	−	6.60643i	−0.498450	−	0.253719i
$679$	−2.22091	−	12.5954i	−0.0852305	−	0.483366i
$680$	53.7667	−	0.969780i	2.06186	−	0.0371893i
$681$	−10.7262	+	11.1120i	−0.411030	+	0.425814i
$682$	−0.999190	+	19.1367i	−0.0382610	+	0.732780i
$683$	9.59344	+	5.53878i	0.367083	+	0.211935i	0.672183	−	0.740385i	$-0.265357\pi$
$683$	9.59344	+	5.53878i	0.367083	+	0.211935i	−0.305100	+	0.952320i	$0.598690\pi$
$684$	21.2261	+	20.4646i	0.811599	+	0.782482i
$685$	13.8434	−	7.99249i	0.528929	−	0.305377i
$686$	−12.2759	−	24.0812i	−0.468695	−	0.919424i
$687$	−1.16638	+	2.62122i	−0.0445002	+	0.100006i
$688$	−15.0583	−	6.07037i	−0.574092	−	0.231431i
$689$	25.5719	−	21.4574i	0.974213	−	0.817462i
$690$	16.5268	+	5.04541i	0.629163	+	0.192076i
$691$	−15.4467	−	42.4396i	−0.587622	−	1.61448i	−0.774839	−	0.632158i	$-0.782169\pi$
$691$	−15.4467	−	42.4396i	−0.587622	−	1.61448i	0.187218	−	0.982318i	$-0.440053\pi$
$692$	14.2679	−	13.7890i	0.542384	−	0.524181i
$693$	−13.9601	+	26.2819i	−0.530300	+	0.998368i
$694$	1.87361	−	4.41634i	0.0711214	−	0.167642i
$695$	2.23158	−	12.6559i	0.0846486	−	0.480066i
$696$	11.8053	+	5.00001i	0.447479	+	0.189525i
$697$	71.4958	+	26.0223i	2.70810	+	0.985666i
$698$	−0.766866	−	2.50657i	−0.0290263	−	0.0948750i
$699$	13.7841	−	20.4451i	0.521362	−	0.773303i
$700$	5.87897	+	2.86454i	0.222204	+	0.108270i
$701$		−	10.1103i		−	0.381863i	−0.981603	−	0.190931i	$-0.938849\pi$
$701$		−	10.1103i		−	0.381863i	0.981603	−	0.190931i	$-0.0611508\pi$
$702$	−20.6363	−	1.78823i	−0.778867	−	0.0674922i
$703$	−39.2247			−1.47939
$704$	1.12182	+	31.0879i	0.0422801	+	1.17167i
$705$	2.58114	−	37.0246i	0.0972115	−	1.39443i
$706$	−18.5861	+	5.68627i	−0.699496	+	0.214006i
$707$	−0.943400	+	2.59197i	−0.0354802	+	0.0974811i
$708$	−2.96403	−	5.12676i	−0.111395	−	0.192676i
$709$	−9.89080	−	1.74401i	−0.371457	−	0.0654978i	−0.0151963	−	0.999885i	$-0.504837\pi$
$709$	−9.89080	−	1.74401i	−0.371457	−	0.0654978i	−0.356260	+	0.934387i	$0.615948\pi$
$710$	−7.00792	+	16.5185i	−0.263002	+	0.619929i
$711$	2.50079	−	0.532665i	0.0937871	−	0.0199765i
$712$	−10.7680	+	13.3132i	−0.403548	+	0.498933i
$713$	−9.21647	+	3.35452i	−0.345159	+	0.125628i
$714$	−46.1824	+	10.6818i	−1.72833	+	0.399755i
$715$	17.6584	+	21.0445i	0.660389	+	0.787020i
$716$	15.4764	+	11.2351i	0.578381	+	0.419876i
$717$	−24.2625	+	17.6356i	−0.906100	+	0.658613i
$718$	6.90670	+	13.5487i	0.257756	+	0.505632i
$719$	12.6792	+	21.9611i	0.472856	+	0.819010i	0.999517	−	0.0310648i	$-0.00988984\pi$
$719$	12.6792	+	21.9611i	0.472856	+	0.819010i	−0.526662	+	0.850075i	$0.676557\pi$
$720$	−29.6255	−	5.18718i	−1.10408	−	0.193315i
$721$	14.1651	−	24.5347i	0.527537	−	0.913721i
$722$	7.27111	+	0.379650i	0.270603	+	0.0141291i
$723$	−9.28311	+	37.2661i	−0.345243	+	1.38594i
$724$	−1.10847	+	10.5859i	−0.0411960	+	0.393421i
$725$	3.30340	−	0.582478i	0.122685	−	0.0216327i
$726$	−8.46279	+	5.50068i	−0.314083	+	0.204149i
$727$	10.0163	+	8.40466i	0.371483	+	0.311712i	0.809348	−	0.587329i	$-0.199821\pi$
$727$	10.0163	+	8.40466i	0.371483	+	0.311712i	−0.437865	+	0.899041i	$0.644265\pi$
$728$	−18.9836	+	7.29978i	−0.703578	+	0.270548i
$729$	24.6796	+	10.9506i	0.914061	+	0.405578i
$730$	−9.48583	+	1.16658i	−0.351086	+	0.0431770i
$731$	19.7916	−	23.5867i	0.732017	−	0.872384i
$732$	0.925603	−	0.777618i	0.0342113	−	0.0287416i
$733$	8.57953	−	1.51280i	0.316892	−	0.0558766i	−0.0129398	−	0.999916i	$-0.504119\pi$
$733$	8.57953	−	1.51280i	0.316892	−	0.0558766i	0.329832	+	0.944040i	$0.393008\pi$
$734$	−3.45108	+	14.9615i	−0.127382	+	0.552239i
$735$	2.07310	+	0.516416i	0.0764673	+	0.0190483i
$736$	−14.4236	+	6.74289i	−0.531663	+	0.248546i
$737$	4.38708	−	7.59865i	0.161600	−	0.279900i
$738$	−36.4887	−	21.8940i	−1.34317	−	0.805931i
$739$	36.1627	−	20.8786i	1.33027	−	0.768031i	0.344927	−	0.938629i	$-0.387904\pi$
$739$	36.1627	−	20.8786i	1.33027	−	0.768031i	0.985341	+	0.170599i	$0.0545702\pi$
$740$	33.1624	−	22.3871i	1.21908	−	0.822965i
$741$	−19.4069	+	14.1062i	−0.712930	+	0.518204i
$742$	−29.1325	+	31.2529i	−1.06949	+	1.14733i
$743$	−9.46740	+	7.94409i	−0.347325	+	0.291441i	−0.799715	−	0.600380i	$-0.795016\pi$
$743$	−9.46740	+	7.94409i	−0.347325	+	0.291441i	0.452390	+	0.891820i	$0.350572\pi$
$744$	15.2044	−	7.76221i	0.557419	−	0.284576i
$745$	4.88588	−	1.77831i	0.179005	−	0.0651524i
$746$	−19.6590	−	26.0779i	−0.719768	−	0.954779i
$747$	−5.44358	−	25.5569i	−0.199170	−	0.935078i
$748$	−56.7156	−	16.2391i	−2.07373	−	0.593762i
$749$	30.4348	+	5.36648i	1.11207	+	0.196087i
$750$	21.0089	−	8.92782i	0.767138	−	0.325998i
$751$	23.4602	+	8.53880i	0.856074	+	0.311585i	0.732514	−	0.680752i	$-0.238347\pi$
$751$	23.4602	+	8.53880i	0.856074	+	0.311585i	0.123560	+	0.992337i	$0.460569\pi$
$752$	21.0753	+	26.9321i	0.768537	+	0.982112i
$753$	0.817040	−	11.7198i	0.0297746	−	0.427094i
$754$	−5.68006	+	8.75024i	−0.206856	+	0.318665i
$755$			60.4972i			2.20172i
$756$	26.4942	−	0.952305i	0.963584	−	0.0346350i
$757$		−	8.24126i		−	0.299534i	−0.988721	−	0.149767i	$-0.952148\pi$
$757$		−	8.24126i		−	0.299534i	0.988721	−	0.149767i	$-0.0478523\pi$
$758$	22.7689	+	14.7800i	0.827003	+	0.536834i
$759$	−15.7182	−	10.5972i	−0.570534	−	0.384654i
$760$	−29.8500	+	17.9593i	−1.08277	+	0.651453i
$761$	6.01155	+	2.18802i	0.217918	+	0.0793158i	0.448672	−	0.893696i	$-0.351897\pi$
$761$	6.01155	+	2.18802i	0.217918	+	0.0793158i	−0.230754	+	0.973012i	$0.574119\pi$
$762$	18.3023	−	24.3084i	0.663022	−	0.880602i
$763$	−49.1304	−	8.66301i	−1.77864	−	0.313622i
$764$	2.28189	−	7.96955i	0.0825558	−	0.288328i
$765$	26.7562	−	50.3724i	0.967372	−	1.82122i
$766$	28.2205	−	21.2743i	1.01965	−	0.768670i
$767$	4.52812	−	1.64810i	0.163501	−	0.0595094i
$768$	23.4759	−	14.7269i	0.847113	−	0.531413i
$769$	22.1762	−	18.6080i	0.799693	−	0.671022i	−0.148431	−	0.988923i	$-0.547422\pi$
$769$	22.1762	−	18.6080i	0.799693	−	0.671022i	0.948124	+	0.317900i	$0.102978\pi$
$770$	−25.7197	−	23.9747i	−0.926873	−	0.863987i
$771$	36.5915	+	16.2823i	1.31781	+	0.586393i
$772$	−29.8536	+	20.1534i	−1.07446	+	0.725336i
$773$	20.3275	−	11.7361i	0.731130	−	0.422118i	−0.0877057	−	0.996146i	$-0.527954\pi$
$773$	20.3275	−	11.7361i	0.731130	−	0.422118i	0.818835	+	0.574029i	$0.194620\pi$
$774$	−13.3763	+	10.8456i	−0.480801	+	0.389836i
$775$	2.23325	−	3.86810i	0.0802207	−	0.138946i
$776$	−13.9182	+	2.71383i	−0.499634	+	0.0974207i
$777$	−24.4946	+	25.3757i	−0.878740	+	0.910347i
$778$	1.09778	+	0.253218i	0.0393573	+	0.00907832i
$779$	−48.5392	+	8.55877i	−1.73910	+	0.306650i
$780$	8.35656	−	23.0023i	0.299213	−	0.823615i
$781$	12.6533	−	15.0797i	0.452772	−	0.539593i
$782$	−3.68565	−	29.9692i	−0.131798	−	1.07169i
$783$	10.7102	−	8.37868i	0.382752	−	0.299430i
$784$	−1.73743	+	0.925536i	−0.0620510	+	0.0330548i
$785$	16.7172	+	14.0274i	0.596662	+	0.500659i
$786$	0.762409	−	0.0402660i	0.0271942	−	0.00143624i
$787$	−6.50488	+	1.14699i	−0.231874	+	0.0408856i	−0.288378	−	0.957517i	$-0.593116\pi$
$787$	−6.50488	+	1.14699i	−0.231874	+	0.0408856i	0.0565038	+	0.998402i	$0.482005\pi$
$788$	−3.22678	+	30.8157i	−0.114949	+	1.09776i
$789$	3.52450	−	1.01144i	0.125476	−	0.0360082i
$790$	−0.157521	+	3.01687i	−0.00560434	+	0.107335i
$791$	−7.58367	+	13.1353i	−0.269644	+	0.467037i
$792$	29.4140	+	14.9500i	1.04518	+	0.531224i
$793$	0.491845	+	0.851900i	0.0174659	+	0.0302519i
$794$	38.9982	−	19.8801i	1.38399	−	0.705518i
$795$	−5.38467	−	51.1277i	−0.190974	−	1.81331i
$796$	−20.6650	+	28.4661i	−0.732450	+	1.00895i
$797$	8.42383	+	10.0391i	0.298387	+	0.355604i	0.894318	−	0.447432i	$-0.147661\pi$
$797$	8.42383	+	10.0391i	0.298387	+	0.355604i	−0.595931	+	0.803036i	$0.703217\pi$
$798$	22.4493	−	20.9513i	0.794696	−	0.741669i
$799$	−60.9432	+	22.1815i	−2.15601	+	0.784725i
$800$	3.05794	−	6.57440i	0.108115	−	0.232440i
$801$	6.81053	+	16.8362i	0.240638	+	0.594876i
$802$	42.6209	+	18.0817i	1.50500	+	0.638488i
$803$	10.3256	+	1.82068i	0.364382	+	0.0642504i
$804$	−7.81649	+	0.00468279i	−0.275666	+	0.000165149i
$805$	6.15506	−	16.9109i	0.216938	−	0.596031i
$806$	4.06390	+	13.2832i	0.143145	+	0.467881i
$807$	−39.9883	+	19.5141i	−1.40765	+	0.686928i
$808$	2.89219	+	0.993981i	0.101747	+	0.0349681i
$809$	−2.66482			−0.0936902			−0.0468451	−	0.998902i	$-0.514917\pi$
$809$	−2.66482			−0.0936902			−0.0468451	+	0.998902i	$0.514917\pi$
$810$	−20.0499	+	24.8123i	−0.704482	+	0.871814i
$811$			55.4951i			1.94870i	0.225042	+	0.974349i	$0.427748\pi$
$811$			55.4951i			1.94870i	−0.225042	+	0.974349i	$0.572252\pi$
$812$	5.84851	−	12.0030i	0.205242	−	0.421224i
$813$	−20.7401	−	42.5006i	−0.727386	−	1.49056i
$814$	−41.9745	+	12.8418i	−1.47120	+	0.450104i
$815$	−15.1694	−	5.52122i	−0.531362	−	0.193400i
$816$	12.7647	+	50.9819i	0.446852	+	1.78472i
$817$	−3.46361	+	19.6431i	−0.121176	+	0.687226i
$818$	3.58472	+	1.52080i	0.125337	+	0.0531737i
$819$	−2.99327	+	21.3638i	−0.104593	+	0.746511i
$820$	36.1525	−	34.9392i	1.26250	−	1.22013i
$821$	−17.2927	−	47.5113i	−0.603519	−	1.65815i	−0.744086	−	0.668083i	$-0.767115\pi$
$821$	−17.2927	−	47.5113i	−0.603519	−	1.65815i	0.140568	−	0.990071i	$-0.455107\pi$
$822$	10.6591	+	11.4212i	0.371777	+	0.398358i
$823$	7.96652	−	6.68471i	0.277696	−	0.233014i	−0.493293	−	0.869863i	$-0.664207\pi$
$823$	7.96652	−	6.68471i	0.277696	−	0.233014i	0.770989	+	0.636849i	$0.219763\pi$
$824$	−27.4812	−	15.2122i	−0.957353	−	0.529942i
$825$	8.58538	−	0.904195i	0.298905	−	0.0314800i
$826$	−5.49470	+	2.80103i	−0.191185	+	0.0974604i
$827$	2.28479	−	1.31912i	0.0794498	−	0.0458703i	−0.459749	−	0.888049i	$-0.652061\pi$
$827$	2.28479	−	1.31912i	0.0794498	−	0.0458703i	0.539199	+	0.842179i	$0.318727\pi$
$828$	−1.16438	+	16.8476i	−0.0404649	+	0.585494i
$829$	12.8874	+	7.44056i	0.447599	+	0.258421i	0.706816	−	0.707398i	$-0.250131\pi$
$829$	12.8874	+	7.44056i	0.447599	+	0.258421i	−0.259217	+	0.965819i	$0.583464\pi$
$830$	30.8309	+	1.60979i	1.07016	+	0.0558765i
$831$	−7.86379	−	27.4024i	−0.272792	−	0.950580i
$832$	8.47175	+	20.8983i	0.293705	+	0.724518i
$833$	−0.648275	−	3.67655i	−0.0224614	−	0.127385i
$834$	12.5421	−	0.662402i	0.434299	−	0.0229371i
$835$	−22.9758	+	27.3815i	−0.795109	+	0.947574i
$836$	37.0784	−	9.25996i	1.28238	−	0.320262i
$837$	0.620439	−	18.0961i	0.0214455	−	0.625492i
$838$	35.2394	−	4.33379i	1.21732	−	0.149708i
$839$	3.12853	+	2.62515i	0.108009	+	0.0906302i	0.695193	−	0.718823i	$-0.255319\pi$
$839$	3.12853	+	2.62515i	0.108009	+	0.0906302i	−0.587184	+	0.809454i	$0.699763\pi$
$840$	−7.02198	+	30.5259i	−0.242281	+	1.05324i
$841$	3.84656	+	21.8149i	0.132640	+	0.752238i
$842$	−9.38861	−	2.16561i	−0.323553	−	0.0746320i
$843$	35.9972	+	34.7474i	1.23981	+	1.19676i
$844$	49.0691	−	3.45036i	1.68903	−	0.118766i
$845$	−10.9712	−	6.33421i	−0.377420	−	0.217904i
$846$	35.8224	−	5.69636i	1.23160	−	0.195845i
$847$	5.25593	+	9.10354i	0.180596	+	0.312801i
$848$	35.2279	+	31.6699i	1.20973	+	1.08755i
$849$	−2.59800	+	5.83851i	−0.0891630	+	0.200377i
$850$	10.0584	+	9.37596i	0.345000	+	0.321593i
$851$	−14.4412	−	17.2104i	−0.495038	−	0.589964i
$852$	−17.2719	−	3.03484i	−0.591727	−	0.103972i
$853$	−6.86679	−	18.8664i	−0.235115	−	0.645972i	−0.999998	−	0.00180361i	$-0.999426\pi$
$853$	−6.86679	−	18.8664i	−0.235115	−	0.645972i	0.764884	−	0.644168i	$-0.222796\pi$
$854$	−0.757892	−	1.00535i	−0.0259345	−	0.0344024i
$855$	1.30513	+	36.9263i	0.0446344	+	1.26285i
$856$	5.34048	−	33.8459i	0.182534	−	1.15683i
$857$	7.94304	−	45.0472i	0.271329	−	1.53878i	−0.479057	−	0.877784i	$-0.659021\pi$
$857$	7.94304	−	45.0472i	0.271329	−	1.53878i	0.750386	−	0.661000i	$-0.229868\pi$
$858$	−16.1491	+	21.4487i	−0.551322	+	0.732246i
$859$	4.92364	−	13.5276i	0.167992	−	0.461555i	−0.826918	−	0.562323i	$-0.809908\pi$
$859$	4.92364	−	13.5276i	0.167992	−	0.461555i	0.994910	+	0.100768i	$0.0321300\pi$
$860$	−8.28279	−	18.5840i	−0.282441	−	0.633711i
$861$	−24.7743	+	36.7462i	−0.844306	+	1.25231i
$862$	2.26240	−	3.48527i	0.0770577	−	0.118709i
$863$	−6.80168			−0.231532			−0.115766	−	0.993277i	$-0.536932\pi$
$863$	−6.80168			−0.231532			−0.115766	+	0.993277i	$0.536932\pi$
$864$	−1.58542	−	29.3511i	−0.0539371	−	0.998544i
$865$	24.8656			0.845457
$866$	−24.0552	+	37.0575i	−0.817429	+	1.25926i
$867$	−70.0534	−	4.88373i	−2.37914	−	0.165860i
$868$	−7.23766	−	16.2391i	−0.245662	−	0.551191i
$869$	1.13352	−	3.11431i	0.0384519	−	0.105646i
$870$	6.28360	+	14.7866i	0.213034	+	0.501312i
$871$	1.10446	−	6.26372i	0.0374233	−	0.212238i
$872$	−8.62104	+	54.6367i	−0.291945	+	1.85023i
$873$	−4.64172	+	14.3063i	−0.157098	+	0.484196i
$874$	11.7748	+	15.6195i	0.398290	+	0.528336i
$875$	−8.13108	−	22.3399i	−0.274881	−	0.755228i
$876$	−3.19989	−	8.77527i	−0.108114	−	0.296489i
$877$	−26.6118	−	31.7147i	−0.898615	−	1.07093i	−0.997124	−	0.0757918i	$-0.975852\pi$
$877$	−26.6118	−	31.7147i	−0.898615	−	1.07093i	0.0985084	−	0.995136i	$-0.468593\pi$
$878$	−7.25928	−	6.76675i	−0.244989	−	0.228367i
$879$	−13.0425	−	17.9435i	−0.439913	−	0.605219i
$880$	−26.0629	+	28.9909i	−0.878579	+	0.977284i
$881$	14.8677	+	25.7517i	0.500907	+	0.867596i	0.999999	+	0.00104741i	$0.000333401\pi$
$881$	14.8677	+	25.7517i	0.500907	+	0.867596i	−0.499093	+	0.866549i	$0.666333\pi$
$882$	−0.0351530	+	2.08769i	−0.00118366	+	0.0702961i
$883$	−2.83903	−	1.63911i	−0.0955408	−	0.0551605i	0.451468	−	0.892287i	$-0.350900\pi$
$883$	−2.83903	−	1.63911i	−0.0955408	−	0.0551605i	−0.547009	+	0.837127i	$0.684234\pi$
$884$	−42.6596	+	2.99967i	−1.43480	+	0.100890i
$885$	1.79383	−	7.20113i	0.0602989	−	0.242063i
$886$	−28.8408	−	6.65253i	−0.968925	−	0.223496i
$887$	2.48943	+	14.1182i	0.0835867	+	0.474044i	0.997653	+	0.0684782i	$0.0218144\pi$
$887$	2.48943	+	14.1182i	0.0835867	+	0.474044i	−0.914066	+	0.405566i	$0.867075\pi$
$888$	28.6200	+	26.6461i	0.960423	+	0.894186i
$889$	−24.2758	−	20.3698i	−0.814184	−	0.683181i
$890$	−21.2974	+	2.61918i	−0.713890	+	0.0877952i
$891$	28.9970	−	19.5944i	0.971437	−	0.656438i
$892$	32.9740	−	8.23493i	1.10405	−	0.275726i
$893$	27.0056	−	32.1840i	0.903707	−	1.07700i
$894$	2.76931	+	4.26058i	0.0926194	+	0.142495i
$895$	4.16171	+	23.6022i	0.139111	+	0.788936i
$896$	−14.0267	−	25.2241i	−0.468600	−	0.842679i
$897$	−13.3342	−	3.32160i	−0.445217	−	0.110905i
$898$	21.3955	+	1.11713i	0.713976	+	0.0372791i
$899$	−7.89747	−	4.55961i	−0.263395	−	0.152071i
$900$	−4.52547	−	6.21817i	−0.150849	−	0.207272i
$901$	−77.7999	+	44.9178i	−2.59189	+	1.49643i
$902$	−49.1399	+	25.0500i	−1.63618	+	0.834074i
$903$	10.5448	+	14.5072i	0.350909	+	0.482771i
$904$	14.7128	+	8.14424i	0.489339	+	0.270873i
$905$	−10.2179	+	8.57380i	−0.339653	+	0.285003i
$906$	−57.6040	+	13.3235i	−1.91377	+	0.442645i
$907$	9.86338	+	27.0994i	0.327508	+	0.899822i	0.988741	+	0.149640i	$0.0478116\pi$
$907$	9.86338	+	27.0994i	0.327508	+	0.899822i	−0.661232	+	0.750181i	$0.729966\pi$
$908$	12.8236	−	12.3933i	0.425568	−	0.411285i
$909$	2.40965	−	2.17151i	0.0799232	−	0.0720244i
$910$	−23.4637	−	9.95438i	−0.777814	−	0.329984i
$911$	−8.43557	+	47.8405i	−0.279483	+	1.58503i	0.444869	+	0.895595i	$0.353250\pi$
$911$	−8.43557	+	47.8405i	−0.279483	+	1.58503i	−0.724352	+	0.689430i	$0.757861\pi$
$912$	−23.6745	−	24.4672i	−0.783939	−	0.810192i
$913$	−31.8267	−	11.5840i	−1.05331	−	0.383374i
$914$	1.28734	−	0.393854i	0.0425816	−	0.0130275i
$915$	1.51129	+	0.105359i	0.0499616	+	0.00348305i
$916$	1.45111	−	2.97814i	0.0479459	−	0.0984004i
$917$		−	0.795126i		−	0.0262574i
$918$	53.8561	+	14.3829i	1.77752	+	0.474707i
$919$	3.55196			0.117168			0.0585842	−	0.998282i	$-0.481341\pi$
$919$	3.55196			0.117168			0.0585842	+	0.998282i	$0.481341\pi$
$920$	−18.8697	−	6.48507i	−0.622114	−	0.213806i
$921$	27.6576	+	18.6468i	0.911349	+	0.614432i
$922$	−1.81825	−	5.94311i	−0.0598809	−	0.195726i
$923$	4.88050	−	13.4091i	0.160644	−	0.441365i
$924$	17.1638	−	29.7697i	0.564647	−	0.979352i
$925$	10.0757	+	1.77662i	0.331288	+	0.0584150i
$926$	−0.118108	−	0.0501070i	−0.00388128	−	0.00164662i
$927$	−28.2461	+	17.6667i	−0.927723	+	0.580251i
$928$	−13.4229	−	6.24337i	−0.440628	−	0.204949i
$929$	−15.0376	+	5.47325i	−0.493369	+	0.179572i	−0.576709	−	0.816950i	$-0.695663\pi$
$929$	−15.0376	+	5.47325i	−0.493369	+	0.179572i	0.0833403	+	0.996521i	$0.473441\pi$
$930$	20.4609	+	6.24645i	0.670939	+	0.204829i
$931$	1.55454	+	1.85263i	0.0509482	+	0.0607176i
$932$	−16.7266	+	23.0410i	−0.547899	+	0.754733i
$933$	50.5355	+	22.4871i	1.65446	+	0.736194i
$934$	12.8652	−	6.55830i	0.420963	−	0.214594i
$935$	−36.9653	−	64.0257i	−1.20889	−	2.09386i
$936$	23.7427	+	2.89103i	0.776054	+	0.0944964i
$937$	−3.30668	+	5.72734i	−0.108025	+	0.187104i	−0.914970	−	0.403522i	$-0.867786\pi$
$937$	−3.30668	+	5.72734i	−0.108025	+	0.187104i	0.806945	+	0.590626i	$0.201119\pi$
$938$	−0.424469	+	8.12950i	−0.0138594	+	0.265438i
$939$	7.26588	+	7.01361i	0.237113	+	0.228881i
$940$	−4.46315	+	42.6230i	−0.145572	+	1.39021i
$941$	−55.8790	+	9.85298i	−1.82160	+	0.321198i	−0.976845	−	0.213950i	$-0.931367\pi$
$941$	−55.8790	+	9.85298i	−1.82160	+	0.321198i	−0.844759	+	0.535148i	$0.820256\pi$
$942$	−9.67487	+	19.0070i	−0.315224	+	0.619283i
$943$	−21.6258	−	18.1462i	−0.704231	−	0.590920i
$944$	3.21495	+	6.03515i	0.104638	+	0.196427i
$945$	24.7038	+	22.2150i	0.803614	+	0.722655i
$946$	2.72454	+	22.1541i	0.0885825	+	0.720292i
$947$	1.48059	−	1.76450i	0.0481128	−	0.0573386i	−0.741451	−	0.671007i	$-0.765862\pi$
$947$	1.48059	−	1.76450i	0.0481128	−	0.0573386i	0.789564	+	0.613668i	$0.210307\pi$
$948$	−2.90728	+	0.514429i	−0.0944242	+	0.0167079i
$949$	7.48497	−	1.31980i	0.242972	−	0.0428426i
$950$	−8.67986	−	2.00213i	−0.281612	−	0.0649577i
$951$	5.13592	+	17.8968i	0.166543	+	0.580343i
$952$	53.7229	−	10.4751i	1.74117	−	0.339500i
$953$	−8.85341	+	15.3346i	−0.286790	+	0.496735i	−0.973042	−	0.230629i	$-0.925922\pi$
$953$	−8.85341	+	15.3346i	−0.286790	+	0.496735i	0.686252	+	0.727364i	$0.259255\pi$
$954$	47.4968	−	16.3872i	1.53776	−	0.530556i
$955$	8.99675	−	5.19427i	0.291128	−	0.168083i
$956$	28.7061	−	19.3787i	0.928423	−	0.626753i
$957$	−1.84609	−	17.5287i	−0.0596755	−	0.566622i
$958$	−2.29634	−	2.14054i	−0.0741915	−	0.0691578i
$959$	12.4636	−	10.4582i	0.402471	−	0.337713i
$960$	33.9799	+	7.17386i	1.09670	+	0.231535i
$961$	17.7201	−	6.44958i	0.571615	−	0.208051i
$962$	−25.4082	+	19.1542i	−0.819195	+	0.617557i
$963$	−28.6482	−	22.3629i	−0.923176	−	0.720635i
$964$	12.2069	−	42.6330i	0.393159	−	1.37312i
$965$	−44.4528	−	7.83822i	−1.43099	−	0.252321i
$966$	17.4577	+	2.13636i	0.561693	+	0.0687362i
$967$	−40.5193	−	14.7478i	−1.30301	−	0.474257i	−0.405035	−	0.914301i	$-0.632741\pi$
$967$	−40.5193	−	14.7478i	−1.30301	−	0.474257i	−0.897976	+	0.440044i	$0.854963\pi$
$968$	9.98664	−	6.00849i	0.320983	−	0.193120i
$969$	58.0255	−	28.3161i	1.86405	−	0.909645i
$970$	−14.9054	−	9.67555i	−0.478583	−	0.310663i
$971$		−	28.3313i		−	0.909195i	−0.890697	−	0.454598i	$-0.849783\pi$
$971$		−	28.3313i		−	0.909195i	0.890697	−	0.454598i	$-0.150217\pi$
$972$	−28.0413	−	13.6266i	−0.899426	−	0.437072i
$973$		−	13.0804i		−	0.419337i
$974$	31.9411	−	49.2059i	1.02346	−	1.57666i
$975$	5.62400	−	2.74448i	0.180112	−	0.0878937i
$976$	−1.09933	+	0.860263i	−0.0351886	+	0.0275363i
$977$	2.02803	+	0.738143i	0.0648824	+	0.0236153i	0.374257	−	0.927325i	$-0.377898\pi$
$977$	2.02803	+	0.738143i	0.0648824	+	0.0236153i	−0.309375	+	0.950940i	$0.600120\pi$
$978$	1.91636	−	15.6599i	0.0612784	−	0.500750i
$979$	23.1828	+	4.08776i	0.740926	+	0.130645i
$980$	−2.37166	−	0.679067i	−0.0757598	−	0.0216920i
$981$	46.2462	+	36.1001i	1.47653	+	1.15259i
$982$	−4.90180	−	6.50229i	−0.156423	−	0.207496i
$983$	38.8354	−	14.1349i	1.23866	−	0.450834i	0.362103	−	0.932138i	$-0.382059\pi$
$983$	38.8354	−	14.1349i	1.23866	−	0.450834i	0.876554	+	0.481304i	$0.159837\pi$
$984$	41.2303	+	26.7288i	1.31437	+	0.852084i
$985$	−29.7444	+	24.9585i	−0.947734	+	0.795243i
$986$	19.1428	−	20.5361i	0.609632	−	0.654004i
$987$	−3.95665	−	37.5686i	−0.125942	−	1.19582i
$988$	22.9612	−	15.5005i	0.730493	−	0.493136i
$989$	−9.89386	+	5.71222i	−0.314606	+	0.181638i
$990$	13.4859	+	39.0876i	0.428611	+	1.24229i
$991$	18.3797	−	31.8346i	0.583851	−	1.01126i	−0.411167	−	0.911560i	$-0.634879\pi$
$991$	18.3797	−	31.8346i	0.583851	−	1.01126i	0.995018	−	0.0996989i	$-0.0317880\pi$
$992$	−17.8571	+	8.34800i	−0.566965	+	0.265049i
$993$	−8.57008	−	29.8636i	−0.271963	−	0.947692i
$994$	−4.10497	+	17.7963i	−0.130202	+	0.564466i
$995$	−43.4120	+	7.65472i	−1.37625	+	0.242671i
$996$	5.25721	+	29.7110i	0.166581	+	0.941430i
$997$	−1.91885	+	2.28679i	−0.0607705	+	0.0724234i	−0.795573	−	0.605857i	$-0.792830\pi$
$997$	−1.91885	+	2.28679i	−0.0607705	+	0.0724234i	0.734803	+	0.678281i	$0.237275\pi$
$998$	−18.8786	+	2.32172i	−0.597593	+	0.0734928i
$999$	39.4379	−	12.8418i	1.24776	−	0.406297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.205.24	yes	204
3.2	odd	2		648.2.t.a.613.11		204
4.3	odd	2		864.2.bf.a.529.12		204
8.3	odd	2		864.2.bf.a.529.23		204
8.5	even	2	inner	216.2.t.a.205.9	yes	204
24.5	odd	2		648.2.t.a.613.26		204
27.5	odd	18		648.2.t.a.37.26		204
27.22	even	9	inner	216.2.t.a.157.9	✓	204
108.103	odd	18		864.2.bf.a.49.23		204
216.5	odd	18		648.2.t.a.37.11		204
216.157	even	18	inner	216.2.t.a.157.24	yes	204
216.211	odd	18		864.2.bf.a.49.12		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.9	✓	204	27.22	even	9	inner
216.2.t.a.157.24	yes	204	216.157	even	18	inner
216.2.t.a.205.9	yes	204	8.5	even	2	inner
216.2.t.a.205.24	yes	204	1.1	even	1	trivial
648.2.t.a.37.11		204	216.5	odd	18
648.2.t.a.37.26		204	27.5	odd	18
648.2.t.a.613.11		204	3.2	odd	2
648.2.t.a.613.26		204	24.5	odd	2
864.2.bf.a.49.12		204	216.211	odd	18
864.2.bf.a.49.23		204	108.103	odd	18
864.2.bf.a.529.12		204	4.3	odd	2
864.2.bf.a.529.23		204	8.3	odd	2

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.770006 - 1.18621i) q^{2} +(0.759610 + 1.55660i) q^{3} +(-0.814182 - 1.82678i) q^{4} +(0.857221 - 2.35519i) q^{5} +(2.43135 + 0.297532i) q^{6} +(0.442985 - 2.51229i) q^{7} +(-2.79386 - 0.440839i) q^{8} +(-1.84598 + 2.36481i) q^{9} +O(q^{10})\)	\(q+(0.770006 - 1.18621i) q^{2} +(0.759610 + 1.55660i) q^{3} +(-0.814182 - 1.82678i) q^{4} +(0.857221 - 2.35519i) q^{5} +(2.43135 + 0.297532i) q^{6} +(0.442985 - 2.51229i) q^{7} +(-2.79386 - 0.440839i) q^{8} +(-1.84598 + 2.36481i) q^{9} +(-2.13369 - 2.83036i) q^{10} +(1.32995 + 3.65402i) q^{11} +(2.22509 - 2.65499i) q^{12} +(1.81187 + 2.15930i) q^{13} +(-2.63900 - 2.45995i) q^{14} +(4.31724 - 0.454683i) q^{15} +(-2.67422 + 2.97465i) q^{16} +(-3.79287 - 6.56945i) q^{17} +(1.38374 + 4.01064i) q^{18} +(4.25574 + 2.45705i) q^{19} +(-5.00034 + 0.351606i) q^{20} +(4.24712 - 1.21881i) q^{21} +(5.35850 + 1.23601i) q^{22} +(0.488755 + 2.77187i) q^{23} +(-1.43604 - 4.68378i) q^{24} +(-0.981892 - 0.823905i) q^{25} +(3.95653 - 0.486580i) q^{26} +(-5.08329 - 1.07712i) q^{27} +(-4.95007 + 1.23623i) q^{28} +(-1.68216 + 2.00472i) q^{29} +(2.78495 - 5.47126i) q^{30} +(0.605101 + 3.43170i) q^{31} +(1.46940 + 5.46268i) q^{32} +(-4.67758 + 4.84583i) q^{33} +(-10.7133 - 0.559376i) q^{34} +(-5.53721 - 3.19691i) q^{35} +(5.82295 + 1.44681i) q^{36} +(-6.91267 + 3.99103i) q^{37} +(6.19153 - 3.15625i) q^{38} +(-1.98485 + 4.46058i) q^{39} +(-3.43322 + 6.20219i) q^{40} +(-7.68334 + 6.44709i) q^{41} +(1.82454 - 5.97647i) q^{42} +(1.38824 + 3.81417i) q^{43} +(5.59224 - 5.40456i) q^{44} +(3.98718 + 6.37482i) q^{45} +(3.66436 + 1.55459i) q^{46} +(1.48461 - 8.41962i) q^{47} +(-6.66170 - 1.90310i) q^{48} +(0.462463 + 0.168323i) q^{49} +(-1.73339 + 0.530317i) q^{50} +(7.34487 - 10.8942i) q^{51} +(2.46937 - 5.06794i) q^{52} -11.8427i q^{53} +(-5.19185 + 5.20045i) q^{54} +9.74598 q^{55} +(-2.34516 + 6.82372i) q^{56} +(-0.591936 + 8.49088i) q^{57} +(1.08274 + 3.53904i) q^{58} +(0.584688 - 1.60642i) q^{59} +(-4.34562 - 7.51644i) q^{60} +(0.343677 + 0.0605995i) q^{61} +(4.53664 + 1.92465i) q^{62} +(5.12336 + 5.68523i) q^{63} +(7.61132 + 2.46328i) q^{64} +(6.63875 - 2.41631i) q^{65} +(2.14640 + 9.27990i) q^{66} +(-1.45040 - 1.72852i) q^{67} +(-8.91282 + 12.2774i) q^{68} +(-3.94342 + 2.86633i) q^{69} +(-8.05588 + 4.10664i) q^{70} +(-2.53118 - 4.38413i) q^{71} +(6.19993 - 5.79318i) q^{72} +(1.34818 - 2.33512i) q^{73} +(-0.588601 + 11.2730i) q^{74} +(0.536633 - 2.15426i) q^{75} +(1.02354 - 9.77477i) q^{76} +(9.76911 - 1.72256i) q^{77} +(3.76283 + 5.78912i) q^{78} +(-0.652898 - 0.547847i) q^{79} +(4.71349 + 8.84824i) q^{80} +(-2.18468 - 8.73082i) q^{81} +(1.73137 + 14.0783i) q^{82} +(-5.59873 + 6.67230i) q^{83} +(-5.68443 - 6.76620i) q^{84} +(-18.7237 + 3.30149i) q^{85} +(5.59336 + 1.29019i) q^{86} +(-4.39832 - 1.09564i) q^{87} +(-2.10487 - 10.7951i) q^{88} +(3.02691 - 5.24277i) q^{89} +(10.6320 + 0.179025i) q^{90} +(6.22743 - 3.59541i) q^{91} +(4.66564 - 3.14965i) q^{92} +(-4.88213 + 3.54865i) q^{93} +(-8.84427 - 8.24421i) q^{94} +(9.43495 - 7.91686i) q^{95} +(-7.38702 + 6.43677i) q^{96} +(4.71115 - 1.71472i) q^{97} +(0.555765 - 0.418968i) q^{98} +(-11.0961 - 3.60017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

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