LMFDB - Embedded newform 360.2.w.e.163.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.10
Character	$\chi$	$=$	360.163
Dual form			360.2.w.e.307.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16309 - 0.804501i) q^{2} +(0.705556 - 1.87141i) q^{4} +(1.51371 - 1.64581i) q^{5} +(3.43671 + 3.43671i) q^{7} +(-0.684930 - 2.74424i) q^{8} +O(q^{10})$	\(q+(1.16309 - 0.804501i) q^{2} +(0.705556 - 1.87141i) q^{4} +(1.51371 - 1.64581i) q^{5} +(3.43671 + 3.43671i) q^{7} +(-0.684930 - 2.74424i) q^{8} +(0.436527 - 3.13200i) q^{10} -3.48120 q^{11} +(-2.05033 + 2.05033i) q^{13} +(6.76204 + 1.23237i) q^{14} +(-3.00438 - 2.64077i) q^{16} +(1.64963 - 1.64963i) q^{17} -0.642023i q^{19} +(-2.01198 - 3.99399i) q^{20} +(-4.04895 + 2.80063i) q^{22} +(-2.31024 + 2.31024i) q^{23} +(-0.417363 - 4.98255i) q^{25} +(-0.735225 + 4.03421i) q^{26} +(8.85630 - 4.00672i) q^{28} -0.699613 q^{29} +1.56863i q^{31} +(-5.61887 - 0.654430i) q^{32} +(0.591537 - 3.24579i) q^{34} +(10.8583 - 0.453979i) q^{35} +(-5.31751 - 5.31751i) q^{37} +(-0.516509 - 0.746731i) q^{38} +(-5.55328 - 3.02673i) q^{40} -4.92316 q^{41} +(3.56519 + 3.56519i) q^{43} +(-2.45618 + 6.51477i) q^{44} +(-0.828427 + 4.54561i) q^{46} +(6.85586 + 6.85586i) q^{47} +16.6220i q^{49} +(-4.49390 - 5.45938i) q^{50} +(2.39039 + 5.28364i) q^{52} +(-1.94008 + 1.94008i) q^{53} +(-5.26953 + 5.72939i) q^{55} +(7.07726 - 11.7851i) q^{56} +(-0.813713 + 0.562839i) q^{58} +2.74121i q^{59} +5.20943i q^{61} +(1.26196 + 1.82446i) q^{62} +(-7.06174 + 3.75923i) q^{64} +(0.270842 + 6.47805i) q^{65} +(6.92316 - 6.92316i) q^{67} +(-1.92323 - 4.25104i) q^{68} +(12.2640 - 9.26357i) q^{70} +11.1548i q^{71} +(-6.56519 - 6.56519i) q^{73} +(-10.4627 - 1.90680i) q^{74} +(-1.20149 - 0.452983i) q^{76} +(-11.9639 - 11.9639i) q^{77} +2.09702 q^{79} +(-8.89397 + 0.947265i) q^{80} +(-5.72608 + 3.96069i) q^{82} +(-6.64648 - 6.64648i) q^{83} +(-0.217911 - 5.21202i) q^{85} +(7.01483 + 1.27844i) q^{86} +(2.38438 + 9.55327i) q^{88} +0.733690i q^{89} -14.0928 q^{91} +(2.69342 + 5.95343i) q^{92} +(13.4895 + 2.45843i) q^{94} +(-1.05665 - 0.971837i) q^{95} +(8.79083 - 8.79083i) q^{97} +(13.3724 + 19.3328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.16309	−	0.804501i	0.822429	−	0.568868i
$2$	1.16309	−	0.804501i	0.822429	−	0.568868i
$3$		0			0
$3$		0			0
$4$	0.705556	−	1.87141i	0.352778	−	0.935707i
$5$	1.51371	−	1.64581i	0.676952	−	0.736027i
$5$	1.51371	−	1.64581i	0.676952	−	0.736027i
$6$		0			0
$7$	3.43671	+	3.43671i	1.29895	+	1.29895i	0.929083	+	0.369871i	$0.120598\pi$
$7$	3.43671	+	3.43671i	1.29895	+	1.29895i	0.369871	+	0.929083i	$0.379402\pi$
$8$	−0.684930	−	2.74424i	−0.242159	−	0.970237i
$9$		0			0
$10$	0.436527	−	3.13200i	0.138042	−	0.990426i
$11$	−3.48120			−1.04962			−0.524811	−	0.851219i	$-0.675864\pi$
$11$	−3.48120			−1.04962			−0.524811	+	0.851219i	$0.675864\pi$
$12$		0			0
$13$	−2.05033	+	2.05033i	−0.568659	+	0.568659i	−0.931753	−	0.363093i	$-0.881721\pi$
$13$	−2.05033	+	2.05033i	−0.568659	+	0.568659i	0.363093	+	0.931753i	$0.381721\pi$
$14$	6.76204	+	1.23237i	1.80723	+	0.329364i
$15$		0			0
$16$	−3.00438	−	2.64077i	−0.751095	−	0.660194i
$17$	1.64963	−	1.64963i	0.400093	−	0.400093i	−0.478173	−	0.878266i	$-0.658701\pi$
$17$	1.64963	−	1.64963i	0.400093	−	0.400093i	0.878266	+	0.478173i	$0.158701\pi$
$18$		0			0
$19$		−	0.642023i		−	0.147290i	−0.997285	−	0.0736451i	$-0.976537\pi$
$19$		−	0.642023i		−	0.147290i	0.997285	−	0.0736451i	$-0.0234632\pi$
$20$	−2.01198	−	3.99399i	−0.449892	−	0.893083i
$21$		0			0
$22$	−4.04895	+	2.80063i	−0.863239	+	0.597097i
$23$	−2.31024	+	2.31024i	−0.481719	+	0.481719i	−0.905680	−	0.423961i	$-0.860639\pi$
$23$	−2.31024	+	2.31024i	−0.481719	+	0.481719i	0.423961	+	0.905680i	$0.360639\pi$
$24$		0			0
$25$	−0.417363	−	4.98255i	−0.0834726	−	0.996510i
$26$	−0.735225	+	4.03421i	−0.144190	+	0.791174i
$27$		0			0
$28$	8.85630	−	4.00672i	1.67368	−	0.757198i
$29$	−0.699613			−0.129915			−0.0649574	−	0.997888i	$-0.520691\pi$
$29$	−0.699613			−0.129915			−0.0649574	+	0.997888i	$0.520691\pi$
$30$		0			0
$31$			1.56863i			0.281734i	0.990029	+	0.140867i	$0.0449890\pi$
$31$			1.56863i			0.281734i	−0.990029	+	0.140867i	$0.955011\pi$
$32$	−5.61887	−	0.654430i	−0.993286	−	0.115688i
$33$		0			0
$34$	0.591537	−	3.24579i	0.101448	−	0.556648i
$35$	10.8583	−	0.453979i	1.83540	−	0.0767365i
$36$		0			0
$37$	−5.31751	−	5.31751i	−0.874193	−	0.874193i	0.118733	−	0.992926i	$-0.462117\pi$
$37$	−5.31751	−	5.31751i	−0.874193	−	0.874193i	−0.992926	+	0.118733i	$0.962117\pi$
$38$	−0.516509	−	0.746731i	−0.0837888	−	0.121136i
$39$		0			0
$40$	−5.55328	−	3.02673i	−0.878051	−	0.478568i
$41$	−4.92316			−0.768869			−0.384435	−	0.923152i	$-0.625604\pi$
$41$	−4.92316			−0.768869			−0.384435	+	0.923152i	$0.625604\pi$
$42$		0			0
$43$	3.56519	+	3.56519i	0.543686	+	0.543686i	0.924607	−	0.380921i	$-0.124393\pi$
$43$	3.56519	+	3.56519i	0.543686	+	0.543686i	−0.380921	+	0.924607i	$0.624393\pi$
$44$	−2.45618	+	6.51477i	−0.370284	+	0.982139i
$45$		0			0
$46$	−0.828427	+	4.54561i	−0.122145	+	0.670214i
$47$	6.85586	+	6.85586i	1.00003	+	1.00003i	1.00000		2.93703e-5i	$9.34887e-6\pi$
$47$	6.85586	+	6.85586i	1.00003	+	1.00003i	2.93703e−5		1.00000i	$0.499991\pi$
$48$		0			0
$49$			16.6220i			2.37457i
$50$	−4.49390	−	5.45938i	−0.635533	−	0.772074i
$51$		0			0
$52$	2.39039	+	5.28364i	0.331488	+	0.732709i
$53$	−1.94008	+	1.94008i	−0.266490	+	0.266490i	−0.827684	−	0.561194i	$-0.810342\pi$
$53$	−1.94008	+	1.94008i	−0.266490	+	0.266490i	0.561194	+	0.827684i	$0.310342\pi$
$54$		0			0
$55$	−5.26953	+	5.72939i	−0.710544	+	0.772551i
$56$	7.07726	−	11.7851i	0.945739	−	1.57485i
$57$		0			0
$58$	−0.813713	+	0.562839i	−0.106846	+	0.0739044i
$59$			2.74121i			0.356876i	0.983951	+	0.178438i	$0.0571043\pi$
$59$			2.74121i			0.356876i	−0.983951	+	0.178438i	$0.942896\pi$
$60$		0			0
$61$			5.20943i			0.666999i	0.942750	+	0.333500i	$0.108230\pi$
$61$			5.20943i			0.666999i	−0.942750	+	0.333500i	$0.891770\pi$
$62$	1.26196	+	1.82446i	0.160269	+	0.231706i
$63$		0			0
$64$	−7.06174	+	3.75923i	−0.882718	+	0.469903i
$65$	0.270842	+	6.47805i	0.0335939	+	0.803504i
$66$		0			0
$67$	6.92316	−	6.92316i	0.845799	−	0.845799i	−0.143807	−	0.989606i	$-0.545934\pi$
$67$	6.92316	−	6.92316i	0.845799	−	0.845799i	0.989606	+	0.143807i	$0.0459344\pi$
$68$	−1.92323	−	4.25104i	−0.233226	−	0.515514i
$69$		0			0
$70$	12.2640	−	9.26357i	1.46583	−	1.10721i
$71$			11.1548i			1.32384i	0.749576	+	0.661918i	$0.230257\pi$
$71$			11.1548i			1.32384i	−0.749576	+	0.661918i	$0.769743\pi$
$72$		0			0
$73$	−6.56519	−	6.56519i	−0.768397	−	0.768397i	0.209427	−	0.977824i	$-0.432840\pi$
$73$	−6.56519	−	6.56519i	−0.768397	−	0.768397i	−0.977824	+	0.209427i	$0.932840\pi$
$74$	−10.4627	−	1.90680i	−1.21626	−	0.221661i
$75$		0			0
$76$	−1.20149	−	0.452983i	−0.137821	−	0.0519608i
$77$	−11.9639	−	11.9639i	−1.36341	−	1.36341i
$78$		0			0
$79$	2.09702			0.235933			0.117966	−	0.993018i	$-0.462363\pi$
$79$	2.09702			0.235933			0.117966	+	0.993018i	$0.462363\pi$
$80$	−8.89397	+	0.947265i	−0.994376	+	0.105907i
$81$		0			0
$82$	−5.72608	+	3.96069i	−0.632340	+	0.437385i
$83$	−6.64648	−	6.64648i	−0.729546	−	0.729546i	0.240984	−	0.970529i	$-0.422530\pi$
$83$	−6.64648	−	6.64648i	−0.729546	−	0.729546i	−0.970529	+	0.240984i	$0.922530\pi$
$84$		0			0
$85$	−0.217911	−	5.21202i	−0.0236357	−	0.565323i
$86$	7.01483	+	1.27844i	0.756429	+	0.137857i
$87$		0			0
$88$	2.38438	+	9.55327i	0.254176	+	1.01838i
$89$			0.733690i			0.0777710i	0.999244	+	0.0388855i	$0.0123808\pi$
$89$			0.733690i			0.0777710i	−0.999244	+	0.0388855i	$0.987619\pi$
$90$		0			0
$91$	−14.0928			−1.47732
$92$	2.69342	+	5.95343i	0.280808	+	0.620688i
$93$		0			0
$94$	13.4895	+	2.45843i	1.39134	+	0.253568i
$95$	−1.05665	−	0.971837i	−0.108410	−	0.0997084i
$96$		0			0
$97$	8.79083	−	8.79083i	0.892574	−	0.892574i	−0.102191	−	0.994765i	$-0.532585\pi$
$97$	8.79083	−	8.79083i	0.892574	−	0.892574i	0.994765	+	0.102191i	$0.0325853\pi$
$98$	13.3724	+	19.3328i	1.35081	+	1.95291i
$99$		0			0
$100$	−9.61889	−	2.73441i	−0.961889	−	0.273441i
$101$		−	1.40933i		−	0.140233i	−0.997539	−	0.0701167i	$-0.977663\pi$
$101$		−	1.40933i		−	0.140233i	0.997539	−	0.0701167i	$-0.0223372\pi$
$102$		0			0
$103$	2.41334	−	2.41334i	0.237793	−	0.237793i	−0.578143	−	0.815936i	$-0.696222\pi$
$103$	2.41334	−	2.41334i	0.237793	−	0.237793i	0.815936	+	0.578143i	$0.196222\pi$
$104$	7.03094	+	4.22227i	0.689440	+	0.414028i
$105$		0			0
$106$	−0.695690	+	3.81728i	−0.0675714	+	0.370767i
$107$	−1.56073	+	1.56073i	−0.150882	+	0.150882i	−0.778512	−	0.627630i	$-0.784025\pi$
$107$	−1.56073	+	1.56073i	−0.150882	+	0.150882i	0.627630	+	0.778512i	$0.284025\pi$
$108$		0			0
$109$	14.6177			1.40012			0.700060	−	0.714084i	$-0.253157\pi$
$109$	14.6177			1.40012			0.700060	+	0.714084i	$0.253157\pi$
$110$	−1.51964	+	10.9031i	−0.144892	+	1.03957i
$111$		0			0
$112$	−1.24961	−	19.4008i	−0.118077	−	1.83320i
$113$	4.55758	+	4.55758i	0.428742	+	0.428742i	0.888199	−	0.459458i	$-0.151956\pi$
$113$	4.55758	+	4.55758i	0.428742	+	0.428742i	−0.459458	+	0.888199i	$0.651956\pi$
$114$		0			0
$115$	0.305176	+	7.29925i	0.0284578	+	0.680659i
$116$	−0.493616	+	1.30927i	−0.0458311	+	0.121562i
$117$		0			0
$118$	2.20531	+	3.18828i	0.203015	+	0.293505i
$119$	11.3386			1.03941
$120$		0			0
$121$	1.11877			0.101707
$122$	4.19099	+	6.05904i	0.379435	+	0.548559i
$123$		0			0
$124$	2.93555	+	1.10675i	0.263620	+	0.0993895i
$125$	−8.83208	−	6.85524i	−0.789966	−	0.613151i
$126$		0			0
$127$	−9.62582	−	9.62582i	−0.854154	−	0.854154i	0.136488	−	0.990642i	$-0.456418\pi$
$127$	−9.62582	−	9.62582i	−0.854154	−	0.854154i	−0.990642	+	0.136488i	$0.956418\pi$
$128$	−5.18914	+	10.0535i	−0.458659	+	0.888612i
$129$		0			0
$130$	5.52662	+	7.31667i	0.484716	+	0.641714i
$131$	−1.26769			−0.110759			−0.0553794	−	0.998465i	$-0.517637\pi$
$131$	−1.26769			−0.110759			−0.0553794	+	0.998465i	$0.517637\pi$
$132$		0			0
$133$	2.20645	−	2.20645i	0.191323	−	0.191323i
$134$	2.48257	−	13.6220i	0.214461	−	1.17676i
$135$		0			0
$136$	−5.65685	−	3.39710i	−0.485071	−	0.291299i
$137$	12.2296	−	12.2296i	1.04485	−	1.04485i	0.0459032	−	0.998946i	$-0.485383\pi$
$137$	12.2296	−	12.2296i	1.04485	−	1.04485i	0.998946	−	0.0459032i	$-0.0146166\pi$
$138$		0			0
$139$		−	8.13630i		−	0.690112i	−0.938582	−	0.345056i	$-0.887860\pi$
$139$		−	8.13630i		−	0.690112i	0.938582	−	0.345056i	$-0.112140\pi$
$140$	6.81159	−	20.6408i	0.575684	−	1.74446i
$141$		0			0
$142$	8.97408	+	12.9741i	0.753088	+	1.08876i
$143$	7.13761	−	7.13761i	0.596877	−	0.596877i
$144$		0			0
$145$	−1.05901	+	1.15143i	−0.0879461	+	0.0956209i
$146$	−12.9176	−	2.35420i	−1.06907	−	0.194835i
$147$		0			0
$148$	−13.7031	+	6.19946i	−1.12638	+	0.509592i
$149$	−2.75071			−0.225347			−0.112674	−	0.993632i	$-0.535941\pi$
$149$	−2.75071			−0.225347			−0.112674	+	0.993632i	$0.535941\pi$
$150$		0			0
$151$			10.2020i			0.830226i	0.909770	+	0.415113i	$0.136258\pi$
$151$			10.2020i			0.830226i	−0.909770	+	0.415113i	$0.863742\pi$
$152$	−1.76187	+	0.439741i	−0.142906	+	0.0356677i
$153$		0			0
$154$	−23.5400	−	4.29011i	−1.89691	−	0.345707i
$155$	2.58166	+	2.37445i	0.207364	+	0.190720i
$156$		0			0
$157$	1.29115	+	1.29115i	0.103045	+	0.103045i	0.756750	−	0.653705i	$-0.226786\pi$
$157$	1.29115	+	1.29115i	0.103045	+	0.103045i	−0.653705	+	0.756750i	$0.726786\pi$
$158$	2.43902	−	1.68705i	0.194038	−	0.134215i
$159$		0			0
$160$	−9.58241	+	8.25696i	−0.757556	+	0.652770i
$161$	−15.8793			−1.25146
$162$		0			0
$163$	9.30787	+	9.30787i	0.729049	+	0.729049i	0.970430	−	0.241382i	$-0.0776005\pi$
$163$	9.30787	+	9.30787i	0.729049	+	0.729049i	−0.241382	+	0.970430i	$0.577601\pi$
$164$	−3.47357	+	9.21328i	−0.271240	+	0.719436i
$165$		0			0
$166$	−13.0775	−	2.38335i	−1.01501	−	0.184984i
$167$	−11.8845	−	11.8845i	−0.919652	−	0.919652i	0.0773515	−	0.997004i	$-0.475354\pi$
$167$	−11.8845	−	11.8845i	−0.919652	−	0.919652i	−0.997004	+	0.0773515i	$0.975354\pi$
$168$		0			0
$169$			4.59229i			0.353253i
$170$	−4.44653	−	5.88674i	−0.341033	−	0.451492i
$171$		0			0
$172$	9.18738	−	4.15650i	0.700531	−	0.316930i
$173$	13.2536	−	13.2536i	1.00765	−	1.00765i	0.00768426	−	0.999970i	$-0.497554\pi$
$173$	13.2536	−	13.2536i	1.00765	−	1.00765i	0.999970	−	0.00768426i	$-0.00244600\pi$
$174$		0			0
$175$	15.6892	−	18.5579i	1.18599	−	1.40285i
$176$	10.4589	+	9.19307i	0.788366	+	0.692954i
$177$		0			0
$178$	0.590255	+	0.853348i	0.0442414	+	0.0639611i
$179$			3.61084i			0.269887i	0.990853	+	0.134943i	$0.0430853\pi$
$179$			3.61084i			0.269887i	−0.990853	+	0.134943i	$0.956915\pi$
$180$		0			0
$181$		−	21.8993i		−	1.62776i	−0.581032	−	0.813881i	$-0.697351\pi$
$181$		−	21.8993i		−	1.62776i	0.581032	−	0.813881i	$-0.302649\pi$
$182$	−16.3912	+	11.3377i	−1.21499	+	0.840403i
$183$		0			0
$184$	7.92222	+	4.75751i	0.584034	+	0.350729i
$185$	−16.8008	+	0.702427i	−1.23522	+	0.0516434i
$186$		0			0
$187$	−5.74268	+	5.74268i	−0.419947	+	0.419947i
$188$	17.6673	−	7.99296i	1.28852	−	0.582946i
$189$		0			0
$190$	−2.01082	−	0.280261i	−0.145880	−	0.0203323i
$191$		−	10.1309i		−	0.733045i	−0.930409	−	0.366522i	$-0.880548\pi$
$191$		−	10.1309i		−	0.733045i	0.930409	−	0.366522i	$-0.119452\pi$
$192$		0			0
$193$	−14.3560	−	14.3560i	−1.03337	−	1.03337i	−0.999424	−	0.0339453i	$-0.989193\pi$
$193$	−14.3560	−	14.3560i	−1.03337	−	1.03337i	−0.0339453	−	0.999424i	$-0.510807\pi$
$194$	3.15229	−	17.2968i	0.226321	−	1.24184i
$195$		0			0
$196$	31.1066	+	11.7277i	2.22190	+	0.837694i
$197$	14.6884	+	14.6884i	1.04650	+	1.04650i	0.998865	+	0.0476396i	$0.0151699\pi$
$197$	14.6884	+	14.6884i	1.04650	+	1.04650i	0.0476396	+	0.998865i	$0.484830\pi$
$198$		0			0
$199$	−5.08593			−0.360532			−0.180266	−	0.983618i	$-0.557696\pi$
$199$	−5.08593			−0.360532			−0.180266	+	0.983618i	$0.557696\pi$
$200$	−13.3875	+	4.55804i	−0.946637	+	0.322302i
$201$		0			0
$202$	−1.13381	−	1.63918i	−0.0797744	−	0.115332i
$203$	−2.40437	−	2.40437i	−0.168753	−	0.168753i
$204$		0			0
$205$	−7.45224	+	8.10258i	−0.520487	+	0.565909i
$206$	0.865395	−	4.74846i	0.0602950	−	0.330841i
$207$		0			0
$208$	11.5744	−	0.745514i	0.802543	−	0.0516921i
$209$			2.23501i			0.154599i
$210$		0			0
$211$	−21.7932			−1.50030			−0.750151	−	0.661266i	$-0.770019\pi$
$211$	−21.7932			−1.50030			−0.750151	+	0.661266i	$0.770019\pi$
$212$	2.26186	+	4.99952i	0.155345	+	0.343369i
$213$		0			0
$214$	−0.559662	+	3.07089i	−0.0382577	+	0.209921i
$215$	11.2643	−	0.470951i	0.768217	−	0.0321186i
$216$		0			0
$217$	−5.39092	+	5.39092i	−0.365959	+	0.365959i
$218$	17.0017	−	11.7599i	1.15150	−	0.796484i
$219$		0			0
$220$	7.00411	+	13.9039i	0.472217	+	0.937399i
$221$			6.76456i			0.455033i
$222$		0			0
$223$	7.63273	−	7.63273i	0.511126	−	0.511126i	−0.403746	−	0.914871i	$-0.632292\pi$
$223$	7.63273	−	7.63273i	0.511126	−	0.511126i	0.914871	+	0.403746i	$0.132292\pi$
$224$	−17.0613	−	21.5595i	−1.13996	−	1.44051i
$225$		0			0
$226$	8.96746	+	1.63430i	0.596507	+	0.108712i
$227$	8.84363	−	8.84363i	0.586973	−	0.586973i	−0.349838	−	0.936810i	$-0.613763\pi$
$227$	8.84363	−	8.84363i	0.586973	−	0.586973i	0.936810	+	0.349838i	$0.113763\pi$
$228$		0			0
$229$	−23.9520			−1.58279			−0.791397	−	0.611302i	$-0.790646\pi$
$229$	−23.9520			−1.58279			−0.791397	+	0.611302i	$0.790646\pi$
$230$	6.22720	+	8.24417i	0.410610	+	0.543605i
$231$		0			0
$232$	0.479186	+	1.91991i	0.0314601	+	0.126048i
$233$	−4.38332	−	4.38332i	−0.287161	−	0.287161i	0.548796	−	0.835956i	$-0.315086\pi$
$233$	−4.38332	−	4.38332i	−0.287161	−	0.287161i	−0.835956	+	0.548796i	$0.815086\pi$
$234$		0			0
$235$	21.6612	−	0.905638i	1.41302	−	0.0590773i
$236$	5.12995	+	1.93408i	0.333931	+	0.125898i
$237$		0			0
$238$	13.1878	−	9.12190i	0.854837	−	0.591285i
$239$	−16.7993			−1.08666			−0.543328	−	0.839521i	$-0.682836\pi$
$239$	−16.7993			−1.08666			−0.543328	+	0.839521i	$0.682836\pi$
$240$		0			0
$241$	3.47277			0.223701			0.111850	−	0.993725i	$-0.464322\pi$
$241$	3.47277			0.223701			0.111850	+	0.993725i	$0.464322\pi$
$242$	1.30123	−	0.900054i	0.0836464	−	0.0578576i
$243$		0			0
$244$	9.74900	+	3.67555i	0.624116	+	0.235303i
$245$	27.3565	+	25.1608i	1.74774	+	1.60747i
$246$		0			0
$247$	1.31636	+	1.31636i	0.0837580	+	0.0837580i
$248$	4.30470	−	1.07440i	0.273348	−	0.0682245i
$249$		0			0
$250$	−15.7876	−	0.867838i	−0.998493	−	0.0548869i
$251$	−10.6116			−0.669797			−0.334898	−	0.942254i	$-0.608702\pi$
$251$	−10.6116			−0.669797			−0.334898	+	0.942254i	$0.608702\pi$
$252$		0			0
$253$	8.04242	−	8.04242i	0.505623	−	0.505623i
$254$	−18.9397	−	3.45171i	−1.18838	−	0.216580i
$255$		0			0
$256$	2.05262	+	15.8678i	0.128289	+	0.991737i
$257$	16.4495	−	16.4495i	1.02609	−	1.02609i	0.0264382	−	0.999650i	$-0.491583\pi$
$257$	16.4495	−	16.4495i	1.02609	−	1.02609i	0.999650	−	0.0264382i	$-0.00841653\pi$
$258$		0			0
$259$		−	36.5495i		−	2.27107i
$260$	12.3142	+	4.06377i	0.763695	+	0.252024i
$261$		0			0
$262$	−1.47444	+	1.01986i	−0.0910913	+	0.0630072i
$263$	−17.3101	+	17.3101i	−1.06739	+	1.06739i	−0.0698281	+	0.997559i	$0.522245\pi$
$263$	−17.3101	+	17.3101i	−1.06739	+	1.06739i	−0.997559	+	0.0698281i	$0.977755\pi$
$264$		0			0
$265$	0.256279	+	6.12971i	0.0157431	+	0.376545i
$266$	0.791208	−	4.34139i	0.0485121	−	0.266188i
$267$		0			0
$268$	−8.07143	−	17.8408i	−0.493041	−	1.08980i
$269$	17.2178			1.04979			0.524895	−	0.851167i	$-0.324105\pi$
$269$	17.2178			1.04979			0.524895	+	0.851167i	$0.324105\pi$
$270$		0			0
$271$		−	8.37293i		−	0.508619i	−0.967123	−	0.254310i	$-0.918152\pi$
$271$		−	8.37293i		−	0.508619i	0.967123	−	0.254310i	$-0.0818482\pi$
$272$	−9.31240	+	0.599815i	−0.564647	+	0.0363691i
$273$		0			0
$274$	4.38541	−	24.0629i	0.264932	−	1.45370i
$275$	1.45292	+	17.3453i	0.0876146	+	1.04596i
$276$		0			0
$277$	11.2504	+	11.2504i	0.675971	+	0.675971i	0.959086	−	0.283115i	$-0.0913678\pi$
$277$	11.2504	+	11.2504i	0.675971	+	0.675971i	−0.283115	+	0.959086i	$0.591368\pi$
$278$	−6.54566	−	9.46325i	−0.392583	−	0.567568i
$279$		0			0
$280$	−8.68303	−	29.4870i	−0.518910	−	1.76219i
$281$	25.9447			1.54773			0.773864	−	0.633352i	$-0.218321\pi$
$281$	25.9447			1.54773			0.773864	+	0.633352i	$0.218321\pi$
$282$		0			0
$283$	0.0392414	+	0.0392414i	0.00233266	+	0.00233266i	0.708272	−	0.705939i	$-0.249475\pi$
$283$	0.0392414	+	0.0392414i	0.00233266	+	0.00233266i	−0.705939	+	0.708272i	$0.749475\pi$
$284$	20.8753	+	7.87036i	1.23872	+	0.467020i
$285$		0			0
$286$	2.55947	−	14.0439i	0.151345	−	0.830434i
$287$	−16.9195	−	16.9195i	−0.998726	−	0.998726i
$288$		0			0
$289$			11.5575i			0.679851i
$290$	−0.305400	+	2.19119i	−0.0179337	+	0.128671i
$291$		0			0
$292$	−16.9183	+	7.65408i	−0.990068	+	0.447921i
$293$	−21.6367	+	21.6367i	−1.26403	+	1.26403i	−0.314905	+	0.949123i	$0.601973\pi$
$293$	−21.6367	+	21.6367i	−1.26403	+	1.26403i	−0.949123	+	0.314905i	$0.898027\pi$
$294$		0			0
$295$	4.51151	+	4.14940i	0.262670	+	0.241588i
$296$	−10.9504	+	18.2347i	−0.636480	+	1.05987i
$297$		0			0
$298$	−3.19933	+	2.21295i	−0.185332	+	0.128193i
$299$		−	9.47352i		−	0.547868i
$300$		0			0
$301$			24.5050i			1.41245i
$302$	8.20751	+	11.8658i	0.472289	+	0.682802i
$303$		0			0
$304$	−1.69544	+	1.92888i	−0.0972401	+	0.110629i
$305$	8.57372	+	7.88557i	0.490930	+	0.451526i
$306$		0			0
$307$	−18.1166	+	18.1166i	−1.03397	+	1.03397i	−0.0345669	+	0.999402i	$0.511005\pi$
$307$	−18.1166	+	18.1166i	−1.03397	+	1.03397i	−0.999402	+	0.0345669i	$0.988995\pi$
$308$	−30.8306	+	13.9482i	−1.75674	+	0.794772i
$309$		0			0
$310$	4.91295	+	0.684749i	0.279037	+	0.0388911i
$311$		−	9.63648i		−	0.546435i	−0.961952	−	0.273217i	$-0.911912\pi$
$311$		−	9.63648i		−	0.546435i	0.961952	−	0.273217i	$-0.0880878\pi$
$312$		0			0
$313$	18.2372	+	18.2372i	1.03083	+	1.03083i	0.999509	+	0.0313208i	$0.00997135\pi$
$313$	18.2372	+	18.2372i	1.03083	+	1.03083i	0.0313208	+	0.999509i	$0.490029\pi$
$314$	2.54046	+	0.462992i	0.143366	+	0.0261282i
$315$		0			0
$316$	1.47956	−	3.92439i	0.0832319	−	0.220764i
$317$	−0.866839	−	0.866839i	−0.0486865	−	0.0486865i	0.682344	−	0.731031i	$-0.260960\pi$
$317$	−0.866839	−	0.866839i	−0.0486865	−	0.0486865i	−0.731031	+	0.682344i	$0.760960\pi$
$318$		0			0
$319$	2.43549			0.136362
$320$	−4.50247	+	17.3126i	−0.251696	+	0.967806i
$321$		0			0
$322$	−18.4690	+	12.7749i	−1.02924	+	0.711917i
$323$	−1.05910	−	1.05910i	−0.0589298	−	0.0589298i
$324$		0			0
$325$	11.0716	+	9.36014i	0.614142	+	0.519207i
$326$	18.3141	+	3.33770i	1.01432	+	0.184858i
$327$		0			0
$328$	3.37202	+	13.5104i	0.186189	+	0.745985i
$329$			47.1232i			2.59799i
$330$		0			0
$331$	14.4884			0.796352			0.398176	−	0.917309i	$-0.369643\pi$
$331$	14.4884			0.796352			0.398176	+	0.917309i	$0.369643\pi$
$332$	−17.1278	+	7.74885i	−0.940009	+	0.425273i
$333$		0			0
$334$	−23.3839	−	4.26166i	−1.27951	−	0.233188i
$335$	−0.914529	−	21.8739i	−0.0499661	−	1.19510i
$336$		0			0
$337$	21.9977	−	21.9977i	1.19829	−	1.19829i	0.223611	−	0.974679i	$-0.428216\pi$
$337$	21.9977	−	21.9977i	1.19829	−	1.19829i	0.974679	−	0.223611i	$-0.0717845\pi$
$338$	3.69451	+	5.34125i	0.200955	+	0.290526i
$339$		0			0
$340$	−9.90760	−	3.26957i	−0.537315	−	0.177317i
$341$		−	5.46071i		−	0.295714i
$342$		0			0
$343$	−33.0679	+	33.0679i	−1.78550	+	1.78550i
$344$	7.34184	−	12.2256i	0.395845	−	0.659163i
$345$		0			0
$346$	4.75260	−	26.0777i	0.255501	−	1.40195i
$347$	−3.52917	+	3.52917i	−0.189456	+	0.189456i	−0.795461	−	0.606005i	$-0.792771\pi$
$347$	−3.52917	+	3.52917i	−0.189456	+	0.189456i	0.606005	+	0.795461i	$0.292771\pi$
$348$		0			0
$349$	−3.26043			−0.174527			−0.0872635	−	0.996185i	$-0.527812\pi$
$349$	−3.26043			−0.174527			−0.0872635	+	0.996185i	$0.527812\pi$
$350$	3.31810	−	34.2065i	0.177360	−	1.82842i
$351$		0			0
$352$	19.5604	+	2.27820i	1.04257	+	0.121429i
$353$	−22.6567	−	22.6567i	−1.20589	−	1.20589i	−0.972346	−	0.233547i	$-0.924967\pi$
$353$	−22.6567	−	22.6567i	−1.20589	−	1.20589i	−0.233547	−	0.972346i	$-0.575033\pi$
$354$		0			0
$355$	18.3587	+	16.8852i	0.974379	+	0.896173i
$356$	1.37304	+	0.517659i	0.0727709	+	0.0274359i
$357$		0			0
$358$	2.90492	+	4.19973i	0.153530	+	0.221963i
$359$	−16.9181			−0.892903			−0.446451	−	0.894808i	$-0.647312\pi$
$359$	−16.9181			−0.892903			−0.446451	+	0.894808i	$0.647312\pi$
$360$		0			0
$361$	18.5878			0.978306
$362$	−17.6180	−	25.4708i	−0.925982	−	1.33872i
$363$		0			0
$364$	−9.94325	+	26.3734i	−0.521168	+	1.38234i
$365$	−20.7428	+	0.867242i	−1.08573	+	0.0453935i
$366$		0			0
$367$	2.82093	+	2.82093i	0.147252	+	0.147252i	0.776889	−	0.629637i	$-0.216797\pi$
$367$	2.82093	+	2.82093i	0.147252	+	0.147252i	−0.629637	+	0.776889i	$0.716797\pi$
$368$	13.0417	−	0.840020i	0.679845	−	0.0437891i
$369$		0			0
$370$	−18.9757	+	14.3332i	−0.986499	+	0.745148i
$371$	−13.3350			−0.692318
$372$		0			0
$373$	−22.7300	+	22.7300i	−1.17691	+	1.17691i	−0.196388	+	0.980526i	$0.562921\pi$
$373$	−22.7300	+	22.7300i	−1.17691	+	1.17691i	−0.980526	+	0.196388i	$0.937079\pi$
$374$	−2.05926	+	11.2993i	−0.106482	+	0.584270i
$375$		0			0
$376$	14.1184	−	23.5099i	0.728099	−	1.21243i
$377$	1.43444	−	1.43444i	0.0738773	−	0.0738773i
$378$		0			0
$379$		−	2.55793i		−	0.131392i	−0.997840	−	0.0656959i	$-0.979073\pi$
$379$		−	2.55793i		−	0.131392i	0.997840	−	0.0656959i	$-0.0209267\pi$
$380$	−2.56423	+	1.29174i	−0.131542	+	0.0662648i
$381$		0			0
$382$	−8.15030	−	11.7831i	−0.417006	−	0.602877i
$383$	5.48289	−	5.48289i	0.280163	−	0.280163i	−0.553011	−	0.833174i	$-0.686521\pi$
$383$	5.48289	−	5.48289i	0.280163	−	0.280163i	0.833174	+	0.553011i	$0.186521\pi$
$384$		0			0
$385$	−37.8001	+	1.58039i	−1.92647	+	0.0805443i
$386$	−28.2468	−	5.14791i	−1.43772	−	0.262022i
$387$		0			0
$388$	−10.2489	−	22.6537i	−0.520307	−	1.15007i
$389$	−5.02529			−0.254792			−0.127396	−	0.991852i	$-0.540662\pi$
$389$	−5.02529			−0.254792			−0.127396	+	0.991852i	$0.540662\pi$
$390$		0			0
$391$			7.62208i			0.385465i
$392$	45.6147	−	11.3849i	2.30389	−	0.575023i
$393$		0			0
$394$	28.9007	+	5.26709i	1.45600	+	0.265352i
$395$	3.17427	−	3.45128i	0.159715	−	0.173653i
$396$		0			0
$397$	8.56361	+	8.56361i	0.429795	+	0.429795i	0.888558	−	0.458763i	$-0.151707\pi$
$397$	8.56361	+	8.56361i	0.429795	+	0.429795i	−0.458763	+	0.888558i	$0.651707\pi$
$398$	−5.91539	+	4.09163i	−0.296512	+	0.205095i
$399$		0			0
$400$	−11.9039	+	16.0716i	−0.595194	+	0.803582i
$401$	12.5710			0.627763			0.313882	−	0.949462i	$-0.398370\pi$
$401$	12.5710			0.627763			0.313882	+	0.949462i	$0.398370\pi$
$402$		0			0
$403$	−3.21620	−	3.21620i	−0.160211	−	0.160211i
$404$	−2.63744	−	0.994361i	−0.131217	−	0.0494713i
$405$		0			0
$406$	−4.73081	−	0.862179i	−0.234786	−	0.0427892i
$407$	18.5113	+	18.5113i	0.917572	+	0.917572i
$408$		0			0
$409$		−	9.94711i		−	0.491853i	−0.969288	−	0.245927i	$-0.920908\pi$
$409$		−	9.94711i		−	0.491853i	0.969288	−	0.245927i	$-0.0790922\pi$
$410$	−2.14910	+	15.4194i	−0.106136	+	0.761508i
$411$		0			0
$412$	−2.81361	−	6.21910i	−0.138617	−	0.306393i
$413$	−9.42076	+	9.42076i	−0.463565	+	0.463565i
$414$		0			0
$415$	−20.9997	+	0.877980i	−1.03083	+	0.0430983i
$416$	12.8623	−	10.1787i	0.630628	−	0.499054i
$417$		0			0
$418$	1.79807	+	2.59952i	0.0879465	+	0.127147i
$419$			1.92920i			0.0942475i	0.998889	+	0.0471238i	$0.0150055\pi$
$419$			1.92920i			0.0942475i	−0.998889	+	0.0471238i	$0.984994\pi$
$420$		0			0
$421$		−	0.454084i		−	0.0221307i	−0.999939	−	0.0110654i	$-0.996478\pi$
$421$		−	0.454084i		−	0.0221307i	0.999939	−	0.0110654i	$-0.00352229\pi$
$422$	−25.3474	+	17.5326i	−1.23389	+	0.853474i
$423$		0			0
$424$	6.65287	+	3.99523i	0.323092	+	0.194026i
$425$	−8.90784	−	7.53085i	−0.432094	−	0.365300i
$426$		0			0
$427$	−17.9033	+	17.9033i	−0.866402	+	0.866402i
$428$	1.81959	+	4.02196i	0.0879534	+	0.194409i
$429$		0			0
$430$	12.7225	−	9.60988i	0.613532	−	0.463429i
$431$			7.07961i			0.341013i	0.985357	+	0.170506i	$0.0545403\pi$
$431$			7.07961i			0.341013i	−0.985357	+	0.170506i	$0.945460\pi$
$432$		0			0
$433$	−15.1484	−	15.1484i	−0.727987	−	0.727987i	0.242231	−	0.970219i	$-0.422121\pi$
$433$	−15.1484	−	15.1484i	−0.727987	−	0.727987i	−0.970219	+	0.242231i	$0.922121\pi$
$434$	−1.93312	+	10.6071i	−0.0927929	+	0.509158i
$435$		0			0
$436$	10.3136	−	27.3557i	0.493931	−	1.31010i
$437$	1.48323	+	1.48323i	0.0709525	+	0.0709525i
$438$		0			0
$439$	−25.2936			−1.20720			−0.603599	−	0.797288i	$-0.706267\pi$
$439$	−25.2936			−1.20720			−0.603599	+	0.797288i	$0.706267\pi$
$440$	19.3321	+	10.5366i	0.921621	+	0.502315i
$441$		0			0
$442$	5.44209	+	7.86779i	0.258854	+	0.374232i
$443$	26.9275	+	26.9275i	1.27936	+	1.27936i	0.941024	+	0.338341i	$0.109866\pi$
$443$	26.9275	+	26.9275i	1.27936	+	1.27936i	0.338341	+	0.941024i	$0.390134\pi$
$444$		0			0
$445$	1.20751	+	1.11059i	0.0572416	+	0.0526472i
$446$	2.73701	−	15.0181i	0.129601	−	0.711127i
$447$		0			0
$448$	−37.1885	−	11.3498i	−1.75699	−	0.536227i
$449$		−	22.4863i		−	1.06120i	−0.847624	−	0.530598i	$-0.821967\pi$
$449$		−	22.4863i		−	1.06120i	0.847624	−	0.530598i	$-0.178033\pi$
$450$		0			0
$451$	17.1385			0.807022
$452$	11.7448	−	5.31350i	0.552427	−	0.249926i
$453$		0			0
$454$	3.17123	−	17.4007i	0.148833	−	0.816653i
$455$	−21.3324	+	23.1940i	−1.00008	+	1.08735i
$456$		0			0
$457$	−0.0735546	+	0.0735546i	−0.00344074	+	0.00344074i	−0.708825	−	0.705384i	$-0.750774\pi$
$457$	−0.0735546	+	0.0735546i	−0.00344074	+	0.00344074i	0.705384	+	0.708825i	$0.250774\pi$
$458$	−27.8584	+	19.2694i	−1.30174	+	0.900401i
$459$		0			0
$460$	13.8752	+	4.57892i	0.646937	+	0.213493i
$461$			33.7901i			1.57376i	0.617105	+	0.786881i	$0.288305\pi$
$461$			33.7901i			1.57376i	−0.617105	+	0.786881i	$0.711695\pi$
$462$		0			0
$463$	27.4189	−	27.4189i	1.27427	−	1.27427i	0.330439	−	0.943827i	$-0.392803\pi$
$463$	27.4189	−	27.4189i	1.27427	−	1.27427i	0.943827	−	0.330439i	$-0.107197\pi$
$464$	2.10190	+	1.84752i	0.0975784	+	0.0857690i
$465$		0			0
$466$	−8.62457	−	1.57181i	−0.399526	−	0.0728126i
$467$	−11.8191	+	11.8191i	−0.546923	+	0.546923i	−0.925550	−	0.378626i	$-0.876397\pi$
$467$	−11.8191	+	11.8191i	−0.546923	+	0.546923i	0.378626	+	0.925550i	$0.376397\pi$
$468$		0			0
$469$	47.5858			2.19731
$470$	24.4653	−	18.4798i	1.12850	−	0.852409i
$471$		0			0
$472$	7.52256	−	1.87754i	0.346254	−	0.0864207i
$473$	−12.4111	−	12.4111i	−0.570665	−	0.570665i
$474$		0			0
$475$	−3.19891	+	0.267957i	−0.146776	+	0.0122947i
$476$	8.00000	−	21.2192i	0.366679	−	0.972579i
$477$		0			0
$478$	−19.5391	+	13.5150i	−0.893697	+	0.618164i
$479$	39.9242			1.82418			0.912091	−	0.409988i	$-0.134467\pi$
$479$	39.9242			1.82418			0.912091	+	0.409988i	$0.134467\pi$
$480$		0			0
$481$	21.8053			0.994236
$482$	4.03914	−	2.79385i	0.183978	−	0.127256i
$483$		0			0
$484$	0.789357	−	2.09369i	0.0358798	−	0.0951676i
$485$	−1.16124	−	27.7748i	−0.0527293	−	1.26119i
$486$		0			0
$487$	10.5650	+	10.5650i	0.478745	+	0.478745i	0.904730	−	0.425985i	$-0.140072\pi$
$487$	10.5650	+	10.5650i	0.478745	+	0.478745i	−0.425985	+	0.904730i	$0.640072\pi$
$488$	14.2959	−	3.56809i	0.647147	−	0.161520i
$489$		0			0
$490$	52.0600	+	7.25594i	2.35183	+	0.327790i
$491$	27.7875			1.25403			0.627016	−	0.779006i	$-0.284276\pi$
$491$	27.7875			1.25403			0.627016	+	0.779006i	$0.284276\pi$
$492$		0			0
$493$	−1.15410	+	1.15410i	−0.0519780	+	0.0519780i
$494$	2.59006	+	0.472032i	0.116532	+	0.0212377i
$495$		0			0
$496$	4.14239	−	4.71276i	0.185999	−	0.211609i
$497$	−38.3360	+	38.3360i	−1.71960	+	1.71960i
$498$		0			0
$499$			19.6133i			0.878014i	0.898484	+	0.439007i	$0.144670\pi$
$499$			19.6133i			0.878014i	−0.898484	+	0.439007i	$0.855330\pi$
$500$	−19.0605	+	11.6917i	−0.852412	+	0.522870i
$501$		0			0
$502$	−12.3422	+	8.53703i	−0.550860	+	0.381026i
$503$	24.2004	−	24.2004i	1.07904	−	1.07904i	0.0824469	−	0.996595i	$-0.473727\pi$
$503$	24.2004	−	24.2004i	1.07904	−	1.07904i	0.996595	−	0.0824469i	$-0.0262735\pi$
$504$		0			0
$505$	−2.31948	−	2.13332i	−0.103216	−	0.0949313i
$506$	2.88392	−	15.8242i	0.128206	−	0.703472i
$507$		0			0
$508$	−24.8055	+	11.2223i	−1.10056	+	0.497911i
$509$	10.8167			0.479444			0.239722	−	0.970842i	$-0.422944\pi$
$509$	10.8167			0.479444			0.239722	+	0.970842i	$0.422944\pi$
$510$		0			0
$511$		−	45.1253i		−	1.99623i
$512$	15.1530	+	16.8043i	0.669676	+	0.742654i
$513$		0			0
$514$	5.89859	−	32.3658i	0.260176	−	1.42759i
$515$	−0.318795	−	7.62498i	−0.0140478	−	0.335997i
$516$		0			0
$517$	−23.8666	−	23.8666i	−1.04965	−	1.04965i
$518$	−29.4041	−	42.5103i	−1.29194	−	1.86780i
$519$		0			0
$520$	17.5918	−	5.18027i	0.771454	−	0.227170i
$521$	29.5691			1.29544			0.647722	−	0.761877i	$-0.275722\pi$
$521$	29.5691			1.29544			0.647722	+	0.761877i	$0.275722\pi$
$522$		0			0
$523$	−26.2357	−	26.2357i	−1.14721	−	1.14721i	−0.987100	−	0.160106i	$-0.948816\pi$
$523$	−26.2357	−	26.2357i	−1.14721	−	1.14721i	−0.160106	−	0.987100i	$-0.551184\pi$
$524$	−0.894429	+	2.37238i	−0.0390733	+	0.103638i
$525$		0			0
$526$	−6.20721	+	34.0592i	−0.270647	+	1.48505i
$527$	2.58765	+	2.58765i	0.112720	+	0.112720i
$528$		0			0
$529$			12.3256i			0.535894i
$530$	5.22944	+	6.92323i	0.227152	+	0.300726i
$531$		0			0
$532$	−2.57241	−	5.68595i	−0.111528	−	0.246517i
$533$	10.0941	−	10.0941i	0.437224	−	0.437224i
$534$		0			0
$535$	0.206168	+	4.93117i	0.00891343	+	0.213193i
$536$	−23.7407	−	14.2570i	−1.02544	−	0.615807i
$537$		0			0
$538$	20.0259	−	13.8518i	0.863378	−	0.597192i
$539$		−	57.8644i		−	2.49240i
$540$		0			0
$541$		−	9.66967i		−	0.415731i	−0.978157	−	0.207866i	$-0.933348\pi$
$541$		−	9.66967i		−	0.415731i	0.978157	−	0.207866i	$-0.0666517\pi$
$542$	−6.73603	−	9.73847i	−0.289337	−	0.418303i
$543$		0			0
$544$	−10.3486	+	8.18947i	−0.443693	+	0.351121i
$545$	22.1269	−	24.0579i	0.947814	−	1.03053i
$546$		0			0
$547$	4.45632	−	4.45632i	0.190538	−	0.190538i	−0.605390	−	0.795929i	$-0.706983\pi$
$547$	4.45632	−	4.45632i	0.190538	−	0.190538i	0.795929	+	0.605390i	$0.206983\pi$
$548$	−14.2580	−	31.5154i	−0.609073	−	1.34627i
$549$		0			0
$550$	15.6442	+	19.0052i	0.667070	+	0.810386i
$551$			0.449168i			0.0191352i
$552$		0			0
$553$	7.20684	+	7.20684i	0.306466	+	0.306466i
$554$	22.1362	+	4.03427i	0.940476	+	0.171400i
$555$		0			0
$556$	−15.2264	−	5.74061i	−0.645743	−	0.243456i
$557$	7.10582	+	7.10582i	0.301083	+	0.301083i	0.841438	−	0.540354i	$-0.181710\pi$
$557$	7.10582	+	7.10582i	0.301083	+	0.301083i	−0.540354	+	0.841438i	$0.681710\pi$
$558$		0			0
$559$	−14.6196			−0.618344
$560$	−33.8215	−	27.3105i	−1.42922	−	1.15408i
$561$		0			0
$562$	30.1760	−	20.8725i	1.27290	−	0.880453i
$563$	−12.1395	−	12.1395i	−0.511620	−	0.511620i	0.403403	−	0.915023i	$-0.367827\pi$
$563$	−12.1395	−	12.1395i	−0.511620	−	0.511620i	−0.915023	+	0.403403i	$0.867827\pi$
$564$		0			0
$565$	14.3998	−	0.602043i	0.605803	−	0.0253282i
$566$	0.0772109	+	0.0140715i	0.00324542	+	0.000591470i
$567$		0			0
$568$	30.6116	−	7.64028i	1.28443	−	0.320579i
$569$		−	9.17667i		−	0.384706i	−0.981326	−	0.192353i	$-0.938388\pi$
$569$		−	9.17667i		−	0.384706i	0.981326	−	0.192353i	$-0.0616118\pi$
$570$		0			0
$571$	14.1460			0.591990			0.295995	−	0.955190i	$-0.404349\pi$
$571$	14.1460			0.591990			0.295995	+	0.955190i	$0.404349\pi$
$572$	−8.32145	−	18.3934i	−0.347937	−	0.769067i
$573$		0			0
$574$	−33.2906	−	6.06714i	−1.38952	−	0.253237i
$575$	12.4751	+	10.5467i	0.520248	+	0.439827i
$576$		0			0
$577$	6.88789	−	6.88789i	0.286747	−	0.286747i	−0.549046	−	0.835792i	$-0.685009\pi$
$577$	6.88789	−	6.88789i	0.286747	−	0.286747i	0.835792	+	0.549046i	$0.185009\pi$
$578$	9.29799	+	13.4424i	0.386746	+	0.559129i
$579$		0			0
$580$	1.40761	+	2.79425i	0.0584477	+	0.116025i
$581$		−	45.6840i		−	1.89529i
$582$		0			0
$583$	6.75381	−	6.75381i	0.279714	−	0.279714i
$584$	−13.5198	+	22.5132i	−0.559452	+	0.931601i
$585$		0			0
$586$	−7.75867	+	42.5721i	−0.320508	+	1.75864i
$587$	−5.90740	+	5.90740i	−0.243824	+	0.243824i	−0.818430	−	0.574606i	$-0.805155\pi$
$587$	−5.90740	+	5.90740i	−0.243824	+	0.243824i	0.574606	+	0.818430i	$0.305155\pi$
$588$		0			0
$589$	1.00710			0.0414967
$590$	8.58549	+	1.19661i	0.353459	+	0.0492638i
$591$		0			0
$592$	1.93348	+	30.0182i	0.0794656	+	1.23374i
$593$	22.6480	+	22.6480i	0.930042	+	0.930042i	0.997708	−	0.0676664i	$-0.0215554\pi$
$593$	22.6480	+	22.6480i	0.930042	+	0.930042i	−0.0676664	+	0.997708i	$0.521555\pi$
$594$		0			0
$595$	17.1633	−	18.6611i	0.703627	−	0.765031i
$596$	−1.94078	+	5.14772i	−0.0794975	+	0.210859i
$597$		0			0
$598$	−7.62146	−	11.0186i	−0.311665	−	0.450582i
$599$	−17.4493			−0.712958			−0.356479	−	0.934303i	$-0.616023\pi$
$599$	−17.4493			−0.712958			−0.356479	+	0.934303i	$0.616023\pi$
$600$		0			0
$601$	−26.2079			−1.06904			−0.534521	−	0.845155i	$-0.679508\pi$
$601$	−26.2079			−1.06904			−0.534521	+	0.845155i	$0.679508\pi$
$602$	19.7143	+	28.5016i	0.803496	+	1.16164i
$603$		0			0
$604$	19.0921	+	7.19807i	0.776848	+	0.292885i
$605$	1.69350	−	1.84128i	0.0688505	−	0.0748588i
$606$		0			0
$607$	8.79177	+	8.79177i	0.356847	+	0.356847i	0.862649	−	0.505802i	$-0.168804\pi$
$607$	8.79177	+	8.79177i	0.356847	+	0.356847i	−0.505802	+	0.862649i	$0.668804\pi$
$608$	−0.420160	+	3.60745i	−0.0170397	+	0.146301i
$609$		0			0
$610$	16.3160	+	2.27406i	0.660614	+	0.0920740i
$611$	−28.1135			−1.13735
$612$		0			0
$613$	10.9270	−	10.9270i	0.441339	−	0.441339i	−0.451123	−	0.892462i	$-0.648976\pi$
$613$	10.9270	−	10.9270i	0.441339	−	0.441339i	0.892462	+	0.451123i	$0.148976\pi$
$614$	−6.49641	+	35.6461i	−0.262174	+	1.43856i
$615$		0			0
$616$	−24.6374	+	41.0262i	−0.992669	+	1.65299i
$617$	−13.6319	+	13.6319i	−0.548799	+	0.548799i	−0.926093	−	0.377294i	$-0.876855\pi$
$617$	−13.6319	+	13.6319i	−0.548799	+	0.548799i	0.377294	+	0.926093i	$0.376855\pi$
$618$		0			0
$619$		−	1.50796i		−	0.0606100i	−0.999541	−	0.0303050i	$-0.990352\pi$
$619$		−	1.50796i		−	0.0606100i	0.999541	−	0.0303050i	$-0.00964785\pi$
$620$	6.26508	−	3.15605i	0.251612	−	0.126750i
$621$		0			0
$622$	−7.75256	−	11.2081i	−0.310849	−	0.449404i
$623$	−2.52148	+	2.52148i	−0.101021	+	0.101021i
$624$		0			0
$625$	−24.6516	+	4.15906i	−0.986065	+	0.166362i
$626$	35.8834	+	6.53967i	1.43419	+	0.261378i
$627$		0			0
$628$	3.32726	−	1.50530i	0.132772	−	0.0600679i
$629$	−17.5438			−0.699517
$630$		0			0
$631$			42.8319i			1.70511i	0.522638	+	0.852555i	$0.324948\pi$
$631$			42.8319i			1.70511i	−0.522638	+	0.852555i	$0.675052\pi$
$632$	−1.43631	−	5.75472i	−0.0571333	−	0.228911i
$633$		0			0
$634$	−1.70558	−	0.310839i	−0.0677374	−	0.0123450i
$635$	−30.4130	+	1.27154i	−1.20690	+	0.0504596i
$636$		0			0
$637$	−34.0805	−	34.0805i	−1.35032	−	1.35032i
$638$	2.83270	−	1.95936i	0.112148	−	0.0775717i
$639$		0			0
$640$	8.69127	+	23.7584i	0.343553	+	0.939133i
$641$	−9.93597			−0.392447			−0.196224	−	0.980559i	$-0.562868\pi$
$641$	−9.93597			−0.392447			−0.196224	+	0.980559i	$0.562868\pi$
$642$		0			0
$643$	−20.3751	−	20.3751i	−0.803517	−	0.803517i	0.180127	−	0.983643i	$-0.442349\pi$
$643$	−20.3751	−	20.3751i	−0.803517	−	0.803517i	−0.983643	+	0.180127i	$0.942349\pi$
$644$	−11.2037	+	29.7167i	−0.441488	+	1.17100i
$645$		0			0
$646$	−2.08387	−	0.379781i	−0.0819889	−	0.0149423i
$647$	25.4648	+	25.4648i	1.00112	+	1.00112i	0.999999	+	0.00112374i	$0.000357696\pi$
$647$	25.4648	+	25.4648i	1.00112	+	1.00112i	0.00112374	+	0.999999i	$0.499642\pi$
$648$		0			0
$649$		−	9.54272i		−	0.374585i
$650$	20.4075	+	1.97957i	0.800449	+	0.0776450i
$651$		0			0
$652$	23.9861	−	10.8517i	0.939368	−	0.424984i
$653$	16.9677	−	16.9677i	0.663999	−	0.663999i	−0.292321	−	0.956320i	$-0.594428\pi$
$653$	16.9677	−	16.9677i	0.663999	−	0.663999i	0.956320	+	0.292321i	$0.0944276\pi$
$654$		0			0
$655$	−1.91892	+	2.08638i	−0.0749784	+	0.0815216i
$656$	14.7911	+	13.0010i	0.577494	+	0.507603i
$657$		0			0
$658$	37.9107	+	54.8085i	1.47791	+	2.13666i
$659$			0.958005i			0.0373186i	0.999826	+	0.0186593i	$0.00593978\pi$
$659$			0.958005i			0.0373186i	−0.999826	+	0.0186593i	$0.994060\pi$
$660$		0			0
$661$			5.22656i			0.203289i	0.994821	+	0.101645i	$0.0324105\pi$
$661$			5.22656i			0.203289i	−0.994821	+	0.101645i	$0.967590\pi$
$662$	16.8513	−	11.6559i	0.654943	−	0.453019i
$663$		0			0
$664$	−13.6872	+	22.7919i	−0.531166	+	0.884498i
$665$	−0.291465	−	6.97131i	−0.0113025	−	0.270336i
$666$		0			0
$667$	1.61628	−	1.61628i	0.0625824	−	0.0625824i
$668$	−30.6261	+	13.8557i	−1.18496	+	0.536092i
$669$		0			0
$670$	−18.6612	−	24.7055i	−0.720946	−	0.954458i
$671$		−	18.1351i		−	0.700097i
$672$		0			0
$673$	16.3145	+	16.3145i	0.628876	+	0.628876i	0.947785	−	0.318909i	$-0.103316\pi$
$673$	16.3145	+	16.3145i	0.628876	+	0.628876i	−0.318909	+	0.947785i	$0.603316\pi$
$674$	7.88812	−	43.2824i	0.303839	−	1.66718i
$675$		0			0
$676$	8.59408	+	3.24012i	0.330542	+	0.124620i
$677$	−21.9712	−	21.9712i	−0.844423	−	0.844423i	0.145008	−	0.989431i	$-0.453679\pi$
$677$	−21.9712	−	21.9712i	−0.844423	−	0.844423i	−0.989431	+	0.145008i	$0.953679\pi$
$678$		0			0
$679$	60.4231			2.31883
$680$	−14.1538	+	4.16787i	−0.542774	+	0.159831i
$681$		0			0
$682$	−4.39315	−	6.35130i	−0.168222	−	0.243204i
$683$	27.9871	+	27.9871i	1.07090	+	1.07090i	0.997287	+	0.0736087i	$0.0234516\pi$
$683$	27.9871	+	27.9871i	1.07090	+	1.07090i	0.0736087	+	0.997287i	$0.476548\pi$
$684$		0			0
$685$	−1.61550	−	38.6398i	−0.0617251	−	1.47635i
$686$	−11.8578	+	65.0640i	−0.452732	+	2.48416i
$687$		0			0
$688$	−1.29633	−	20.1260i	−0.0494220	−	0.767298i
$689$		−	7.95560i		−	0.303084i
$690$		0			0
$691$	−39.3415			−1.49662			−0.748310	−	0.663349i	$-0.769134\pi$
$691$	−39.3415			−1.49662			−0.748310	+	0.663349i	$0.769134\pi$
$692$	−15.4519	−	34.1542i	−0.587391	−	1.29835i
$693$		0			0
$694$	−1.26552	+	6.94397i	−0.0480386	+	0.263590i
$695$	−13.3908	−	12.3160i	−0.507941	−	0.467172i
$696$		0			0
$697$	−8.12138	+	8.12138i	−0.307619	+	0.307619i
$698$	−3.79218	+	2.62302i	−0.143536	+	0.0992829i
$699$		0			0
$700$	−23.6600	−	42.4547i	−0.894262	−	1.60464i
$701$		−	10.3150i		−	0.389594i	−0.980844	−	0.194797i	$-0.937595\pi$
$701$		−	10.3150i		−	0.389594i	0.980844	−	0.194797i	$-0.0624048\pi$
$702$		0			0
$703$	−3.41396	+	3.41396i	−0.128760	+	0.128760i
$704$	24.5834	−	13.0866i	0.926520	−	0.493221i
$705$		0			0
$706$	−44.5790	−	8.12442i	−1.67775	−	0.305767i
$707$	4.84346	−	4.84346i	0.182157	−	0.182157i
$708$		0			0
$709$	−45.3404			−1.70279			−0.851397	−	0.524522i	$-0.824244\pi$
$709$	−45.3404			−1.70279			−0.851397	+	0.524522i	$0.824244\pi$
$710$	34.9370	+	4.86939i	1.31116	+	0.182745i
$711$		0			0
$712$	2.01342	−	0.502526i	0.0754563	−	0.0188330i
$713$	−3.62391	−	3.62391i	−0.135717	−	0.135717i
$714$		0			0
$715$	−0.942858	−	22.5514i	−0.0352609	−	0.843375i
$716$	6.75738	+	2.54765i	0.252535	+	0.0952101i
$717$		0			0
$718$	−19.6773	+	13.6106i	−0.734349	+	0.507944i
$719$	−43.8494			−1.63531			−0.817653	−	0.575711i	$-0.804725\pi$
$719$	−43.8494			−1.63531			−0.817653	+	0.575711i	$0.804725\pi$
$720$		0			0
$721$	16.5879			0.617765
$722$	21.6193	−	14.9539i	0.804587	−	0.556527i
$723$		0			0
$724$	−40.9826	−	15.4512i	−1.52311	−	0.574238i
$725$	0.291992	+	3.48586i	0.0108443	+	0.129461i
$726$		0			0
$727$	2.07567	+	2.07567i	0.0769824	+	0.0769824i	0.744550	−	0.667567i	$-0.232664\pi$
$727$	2.07567	+	2.07567i	0.0769824	+	0.0769824i	−0.667567	+	0.744550i	$0.732664\pi$
$728$	9.65256	+	38.6740i	0.357748	+	1.43335i
$729$		0			0
$730$	−23.4281	+	17.6963i	−0.867112	+	0.654970i
$731$	11.7625			0.435050
$732$		0			0
$733$	−2.13221	+	2.13221i	−0.0787549	+	0.0787549i	−0.745387	−	0.666632i	$-0.767735\pi$
$733$	−2.13221	+	2.13221i	−0.0787549	+	0.0787549i	0.666632	+	0.745387i	$0.267735\pi$
$734$	5.55045	+	1.01156i	0.204871	+	0.0373372i
$735$		0			0
$736$	14.4929	−	11.4691i	0.534214	−	0.422755i
$737$	−24.1009	+	24.1009i	−0.887769	+	0.887769i
$738$		0			0
$739$			32.9512i			1.21213i	0.795416	+	0.606064i	$0.207253\pi$
$739$			32.9512i			1.21213i	−0.795416	+	0.606064i	$0.792747\pi$
$740$	−10.5393	+	31.9368i	−0.387434	+	1.17402i
$741$		0			0
$742$	−15.5098	+	10.7280i	−0.569382	+	0.393837i
$743$	−17.0344	+	17.0344i	−0.624931	+	0.624931i	−0.946788	−	0.321857i	$-0.895693\pi$
$743$	−17.0344	+	17.0344i	−0.624931	+	0.624931i	0.321857	+	0.946788i	$0.395693\pi$
$744$		0			0
$745$	−4.16378	+	4.52714i	−0.152549	+	0.165862i
$746$	−8.15072	+	44.7233i	−0.298419	+	1.63744i
$747$		0			0
$748$	6.69515	+	14.7987i	0.244799	+	0.541095i
$749$	−10.7276			−0.391977
$750$		0			0
$751$		−	38.0634i		−	1.38895i	−0.719515	−	0.694477i	$-0.755636\pi$
$751$		−	38.0634i		−	1.38895i	0.719515	−	0.694477i	$-0.244364\pi$
$752$	−2.49284	−	38.7024i	−0.0909043	−	1.41133i
$753$		0			0
$754$	0.514373	−	2.82239i	0.0187324	−	0.102785i
$755$	16.7905	+	15.4429i	0.611069	+	0.562023i
$756$		0			0
$757$	31.5125	+	31.5125i	1.14534	+	1.14534i	0.987458	+	0.157885i	$0.0504674\pi$
$757$	31.5125	+	31.5125i	1.14534	+	1.14534i	0.157885	+	0.987458i	$0.449533\pi$
$758$	−2.05786	−	2.97510i	−0.0747447	−	0.108060i
$759$		0			0
$760$	−1.94323	+	3.56534i	−0.0704883	+	0.129328i
$761$	−36.1731			−1.31128			−0.655638	−	0.755076i	$-0.727600\pi$
$761$	−36.1731			−1.31128			−0.655638	+	0.755076i	$0.727600\pi$
$762$		0			0
$763$	50.2367	+	50.2367i	1.81869	+	1.81869i
$764$	−18.9591	−	7.14790i	−0.685915	−	0.258602i
$765$		0			0
$766$	1.96610	−	10.7881i	0.0710382	−	0.389789i
$767$	−5.62039	−	5.62039i	−0.202941	−	0.202941i
$768$		0			0
$769$			29.7981i			1.07455i	0.843408	+	0.537273i	$0.180546\pi$
$769$			29.7981i			1.07455i	−0.843408	+	0.537273i	$0.819454\pi$
$770$	−42.6935	+	32.2484i	−1.53857	+	1.16215i
$771$		0			0
$772$	−36.9950	+	16.7371i	−1.33148	+	0.602381i
$773$	−4.11081	+	4.11081i	−0.147856	+	0.147856i	−0.777159	−	0.629304i	$-0.783340\pi$
$773$	−4.11081	+	4.11081i	−0.147856	+	0.147856i	0.629304	+	0.777159i	$0.283340\pi$
$774$		0			0
$775$	7.81577	−	0.654687i	0.280751	−	0.0235170i
$776$	−30.1453	−	18.1031i	−1.08215	−	0.649863i
$777$		0			0
$778$	−5.84487	+	4.04285i	−0.209549	+	0.144943i
$779$			3.16079i			0.113247i
$780$		0			0
$781$		−	38.8323i		−	1.38953i
$782$	6.13197	+	8.86516i	0.219279	+	0.317017i
$783$		0			0
$784$	43.8948	−	49.9387i	1.56767	−	1.78352i
$785$	4.07941	−	0.170557i	0.145600	−	0.00608744i
$786$		0			0
$787$	14.4907	−	14.4907i	0.516537	−	0.516537i	−0.399985	−	0.916522i	$-0.630985\pi$
$787$	14.4907	−	14.4907i	0.516537	−	0.516537i	0.916522	+	0.399985i	$0.130985\pi$
$788$	37.8515	−	17.1246i	1.34840	−	0.610038i
$789$		0			0
$790$	0.915405	−	6.56786i	0.0325686	−	0.233674i
$791$			31.3262i			1.11383i
$792$		0			0
$793$	−10.6811	−	10.6811i	−0.379295	−	0.379295i
$794$	16.8497	+	3.07081i	0.597973	+	0.108979i
$795$		0			0
$796$	−3.58841	+	9.51788i	−0.127188	+	0.337352i
$797$	3.99359	+	3.99359i	0.141460	+	0.141460i	0.774291	−	0.632830i	$-0.218107\pi$
$797$	3.99359	+	3.99359i	0.141460	+	0.141460i	−0.632830	+	0.774291i	$0.718107\pi$
$798$		0			0
$799$	22.6192			0.800210
$800$	−0.915623	+	28.2694i	−0.0323722	+	0.999476i
$801$		0			0
$802$	14.6211	−	10.1133i	0.516291	−	0.357115i
$803$	22.8547	+	22.8547i	0.806527	+	0.806527i
$804$		0			0
$805$	−24.0366	+	26.1342i	−0.847179	+	0.921110i
$806$	−6.32818	−	1.15329i	−0.222900	−	0.0406231i
$807$		0			0
$808$	−3.86754	+	0.965291i	−0.136060	+	0.0339588i
$809$		−	1.83726i		−	0.0645947i	−0.999478	−	0.0322974i	$-0.989718\pi$
$809$		−	1.83726i		−	0.0645947i	0.999478	−	0.0322974i	$-0.0102824\pi$
$810$		0			0
$811$	19.2559			0.676166			0.338083	−	0.941116i	$-0.390222\pi$
$811$	19.2559			0.676166			0.338083	+	0.941116i	$0.390222\pi$
$812$	−6.19598	+	2.80315i	−0.217436	+	0.0983713i
$813$		0			0
$814$	36.4227	+	6.63795i	1.27662	+	0.232660i
$815$	29.4084	−	1.22954i	1.03013	−	0.0430690i
$816$		0			0
$817$	2.28893	−	2.28893i	0.0800797	−	0.0800797i
$818$	−8.00246	−	11.5694i	−0.279800	−	0.404514i
$819$		0			0
$820$	9.90531	+	19.6631i	0.345908	+	0.686664i
$821$		−	29.3331i		−	1.02373i	−0.859066	−	0.511865i	$-0.828955\pi$
$821$		−	29.3331i		−	1.02373i	0.859066	−	0.511865i	$-0.171045\pi$
$822$		0			0
$823$	−11.8788	+	11.8788i	−0.414067	+	0.414067i	−0.883153	−	0.469085i	$-0.844584\pi$
$823$	−11.8788	+	11.8788i	−0.414067	+	0.414067i	0.469085	+	0.883153i	$0.344584\pi$
$824$	−8.27575	−	4.96982i	−0.288299	−	0.173132i
$825$		0			0
$826$	−3.37818	+	18.5362i	−0.117542	+	0.644957i
$827$	−24.1429	+	24.1429i	−0.839530	+	0.839530i	−0.988797	−	0.149267i	$-0.952309\pi$
$827$	−24.1429	+	24.1429i	−0.839530	+	0.839530i	0.149267	+	0.988797i	$0.452309\pi$
$828$		0			0
$829$	−30.6528			−1.06462			−0.532309	−	0.846550i	$-0.678675\pi$
$829$	−30.6528			−1.06462			−0.532309	+	0.846550i	$0.678675\pi$
$830$	−23.7182	+	17.9154i	−0.823269	+	0.621853i
$831$		0			0
$832$	6.77125	−	22.1866i	0.234751	−	0.769181i
$833$	27.4200	+	27.4200i	0.950047	+	0.950047i
$834$		0			0
$835$	−37.5494	+	1.56991i	−1.29945	+	0.0543290i
$836$	4.18264	+	1.57693i	0.144660	+	0.0545392i
$837$		0			0
$838$	1.55204	+	2.24383i	0.0536144	+	0.0775119i
$839$	−2.59796			−0.0896914			−0.0448457	−	0.998994i	$-0.514280\pi$
$839$	−2.59796			−0.0896914			−0.0448457	+	0.998994i	$0.514280\pi$
$840$		0			0
$841$	−28.5105			−0.983122
$842$	−0.365311	−	0.528141i	−0.0125895	−	0.0182009i
$843$		0			0
$844$	−15.3763	+	40.7840i	−0.529274	+	1.40384i
$845$	7.55803	+	6.95140i	0.260004	+	0.239135i
$846$		0			0
$847$	3.84490	+	3.84490i	0.132112	+	0.132112i
$848$	10.9520	−	0.705426i	0.376095	−	0.0242244i
$849$		0			0
$850$	−16.4192	−	1.59269i	−0.563174	−	0.0546289i
$851$	24.5695			0.842230
$852$		0			0
$853$	20.7909	−	20.7909i	0.711866	−	0.711866i	−0.255059	−	0.966925i	$-0.582095\pi$
$853$	20.7909	−	20.7909i	0.711866	−	0.711866i	0.966925	+	0.255059i	$0.0820949\pi$
$854$	−6.41992	+	35.2264i	−0.219685	+	1.20542i
$855$		0			0
$856$	5.35203	+	3.21404i	0.182929	+	0.109854i
$857$	33.7632	−	33.7632i	1.15333	−	1.15333i	0.167446	−	0.985881i	$-0.446448\pi$
$857$	33.7632	−	33.7632i	1.15333	−	1.15333i	0.985881	−	0.167446i	$-0.0535521\pi$
$858$		0			0
$859$		−	31.9834i		−	1.09126i	−0.838027	−	0.545629i	$-0.816291\pi$
$859$		−	31.9834i		−	1.09126i	0.838027	−	0.545629i	$-0.183709\pi$
$860$	7.06623	−	21.4124i	0.240956	−	0.730157i
$861$		0			0
$862$	5.69555	+	8.23422i	0.193991	+	0.280459i
$863$	−2.78203	+	2.78203i	−0.0947013	+	0.0947013i	−0.752870	−	0.658169i	$-0.771331\pi$
$863$	−2.78203	+	2.78203i	−0.0947013	+	0.0947013i	0.658169	+	0.752870i	$0.271331\pi$
$864$		0			0
$865$	−1.75076	−	41.8751i	−0.0595278	−	1.42380i
$866$	−29.8059	−	5.43206i	−1.01285	−	0.184589i
$867$		0			0
$868$	6.28505	+	13.8922i	0.213328	+	0.471533i
$869$	−7.30014			−0.247640
$870$		0			0
$871$			28.3895i			0.961943i
$872$	−10.0121	−	40.1145i	−0.339052	−	1.35845i
$873$		0			0
$874$	2.91839	+	0.531870i	0.0987160	+	0.0179908i
$875$	−6.79384	−	53.9128i	−0.229674	−	1.82258i
$876$		0			0
$877$	−3.46500	−	3.46500i	−0.117005	−	0.117005i	0.646180	−	0.763185i	$-0.276365\pi$
$877$	−3.46500	−	3.46500i	−0.117005	−	0.117005i	−0.763185	+	0.646180i	$0.776365\pi$
$878$	−29.4187	+	20.3487i	−0.992834	+	0.686736i
$879$		0			0
$880$	30.9617	−	3.29762i	1.04372	−	0.111163i
$881$	−11.9117			−0.401316			−0.200658	−	0.979661i	$-0.564308\pi$
$881$	−11.9117			−0.401316			−0.200658	+	0.979661i	$0.564308\pi$
$882$		0			0
$883$	14.6270	+	14.6270i	0.492237	+	0.492237i	0.909010	−	0.416774i	$-0.136839\pi$
$883$	14.6270	+	14.6270i	0.492237	+	0.492237i	−0.416774	+	0.909010i	$0.636839\pi$
$884$	12.6593	+	4.77277i	0.425778	+	0.160526i
$885$		0			0
$886$	52.9823	+	9.65590i	1.77998	+	0.324396i
$887$	5.84575	+	5.84575i	0.196281	+	0.196281i	0.798404	−	0.602123i	$-0.205678\pi$
$887$	5.84575	+	5.84575i	0.196281	+	0.196281i	−0.602123	+	0.798404i	$0.705678\pi$
$888$		0			0
$889$		−	66.1623i		−	2.21901i
$890$	2.29792	+	0.320276i	0.0770264	+	0.0107357i
$891$		0			0
$892$	−8.89868	−	19.6693i	−0.297950	−	0.658578i
$893$	4.40162	−	4.40162i	0.147295	−	0.147295i
$894$		0			0
$895$	5.94274	+	5.46576i	0.198644	+	0.182700i
$896$	−52.3845	+	16.7174i	−1.75004	+	0.558489i
$897$		0			0
$898$	−18.0903	−	26.1536i	−0.603681	−	0.872758i
$899$		−	1.09743i		−	0.0366014i
$900$		0			0
$901$			6.40081i			0.213242i
$902$	19.9337	−	13.7880i	0.663718	−	0.459089i
$903$		0			0
$904$	9.38550	−	15.6287i	0.312157	−	0.519804i
$905$	−36.0420	−	33.1492i	−1.19808	−	1.10192i
$906$		0			0
$907$	−19.5550	+	19.5550i	−0.649314	+	0.649314i	−0.952827	−	0.303513i	$-0.901840\pi$
$907$	−19.5550	+	19.5550i	−0.649314	+	0.649314i	0.303513	+	0.952827i	$0.401840\pi$
$908$	−10.3104	−	22.7898i	−0.342163	−	0.756305i
$909$		0			0
$910$	−6.15188	+	44.1386i	−0.203933	+	1.46318i
$911$			20.2174i			0.669832i	0.942248	+	0.334916i	$0.108708\pi$
$911$			20.2174i			0.669832i	−0.942248	+	0.334916i	$0.891292\pi$
$912$		0			0
$913$	23.1377	+	23.1377i	0.765747	+	0.765747i
$914$	−0.0263758	+	0.144725i	−0.000872435	+	0.00478709i
$915$		0			0
$916$	−16.8995	+	44.8242i	−0.558375	+	1.48103i
$917$	−4.35669	−	4.35669i	−0.143871	−	0.143871i
$918$		0			0
$919$	−58.3013			−1.92318			−0.961591	−	0.274485i	$-0.911493\pi$
$919$	−58.3013			−1.92318			−0.961591	+	0.274485i	$0.911493\pi$
$920$	19.8219	−	5.83695i	0.653509	−	0.192439i
$921$		0			0
$922$	27.1842	+	39.3009i	0.895263	+	1.29431i
$923$	−22.8711	−	22.8711i	−0.752812	−	0.752812i
$924$		0			0
$925$	−24.2754	+	28.7141i	−0.798171	+	0.944113i
$926$	9.83212	−	53.9493i	0.323104	−	1.77288i
$927$		0			0
$928$	3.93104	+	0.457848i	0.129043	+	0.0150296i
$929$			5.05985i			0.166008i	0.996549	+	0.0830041i	$0.0264515\pi$
$929$			5.05985i			0.166008i	−0.996549	+	0.0830041i	$0.973549\pi$
$930$		0			0
$931$	10.6717			0.349750
$932$	−11.2957	+	5.11033i	−0.370002	+	0.167394i
$933$		0			0
$934$	−4.23820	+	23.2552i	−0.138678	+	0.760933i
$935$	0.758591	+	18.1441i	0.0248086	+	0.593376i
$936$		0			0
$937$	−10.0055	+	10.0055i	−0.326864	+	0.326864i	−0.851393	−	0.524529i	$-0.824242\pi$
$937$	−10.0055	+	10.0055i	−0.326864	+	0.326864i	0.524529	+	0.851393i	$0.324242\pi$
$938$	55.3466	−	38.2828i	1.80713	−	1.24998i
$939$		0			0
$940$	13.5884	−	41.1760i	0.443204	−	1.34301i
$941$			23.9169i			0.779667i	0.920885	+	0.389834i	$0.127468\pi$
$941$			23.9169i			0.779667i	−0.920885	+	0.389834i	$0.872532\pi$
$942$		0			0
$943$	11.3737	−	11.3737i	0.370379	−	0.370379i
$944$	7.23893	−	8.23565i	0.235607	−	0.268048i
$945$		0			0
$946$	−24.4200	−	4.45050i	−0.793964	−	0.144698i
$947$	24.5395	−	24.5395i	0.797426	−	0.797426i	−0.185263	−	0.982689i	$-0.559314\pi$
$947$	24.5395	−	24.5395i	0.797426	−	0.797426i	0.982689	+	0.185263i	$0.0593136\pi$
$948$		0			0
$949$	26.9216			0.873912
$950$	−3.50505	+	2.88519i	−0.113719	+	0.0936079i
$951$		0			0
$952$	−7.76613	−	31.1158i	−0.251702	−	1.00847i
$953$	0.855191	+	0.855191i	0.0277023	+	0.0277023i	0.720822	−	0.693120i	$-0.243764\pi$
$953$	0.855191	+	0.855191i	0.0277023	+	0.0277023i	−0.693120	+	0.720822i	$0.743764\pi$
$954$		0			0
$955$	−16.6735	−	15.3352i	−0.539541	−	0.496236i
$956$	−11.8528	+	31.4384i	−0.383348	+	1.01679i
$957$		0			0
$958$	46.4354	−	32.1190i	1.50026	−	1.03772i
$959$	84.0595			2.71442
$960$		0			0
$961$	28.5394			0.920626
$962$	25.3615	−	17.5424i	0.817688	−	0.565589i
$963$		0			0
$964$	2.45023	−	6.49899i	0.0789167	−	0.209318i
$965$	−45.3581	+	1.89639i	−1.46013	+	0.0610469i
$966$		0			0
$967$	−15.5174	−	15.5174i	−0.499007	−	0.499007i	0.412122	−	0.911129i	$-0.364788\pi$
$967$	−15.5174	−	15.5174i	−0.499007	−	0.499007i	−0.911129	+	0.412122i	$0.864788\pi$
$968$	−0.766281	−	3.07018i	−0.0246292	−	0.0986795i
$969$		0			0
$970$	−23.6955	−	31.3704i	−0.760816	−	1.00724i
$971$	11.2086			0.359701			0.179851	−	0.983694i	$-0.442439\pi$
$971$	11.2086			0.359701			0.179851	+	0.983694i	$0.442439\pi$
$972$		0			0
$973$	27.9621	−	27.9621i	0.896424	−	0.896424i
$974$	20.7876	+	3.78848i	0.666076	+	0.121391i
$975$		0			0
$976$	13.7569	−	15.6511i	0.440349	−	0.500980i
$977$	19.3780	−	19.3780i	0.619957	−	0.619957i	−0.325563	−	0.945520i	$-0.605554\pi$
$977$	19.3780	−	19.3780i	0.619957	−	0.619957i	0.945520	+	0.325563i	$0.105554\pi$
$978$		0			0
$979$		−	2.55412i		−	0.0816302i
$980$	66.3879	−	33.4430i	2.12068	−	1.06830i
$981$		0			0
$982$	32.3194	−	22.3551i	1.03135	−	0.713379i
$983$	14.1500	−	14.1500i	0.451314	−	0.451314i	−0.444476	−	0.895791i	$-0.646610\pi$
$983$	14.1500	−	14.1500i	0.451314	−	0.451314i	0.895791	+	0.444476i	$0.146610\pi$
$984$		0			0
$985$	46.4082	−	1.94029i	1.47869	−	0.0618228i
$986$	−0.413847	+	2.27080i	−0.0131796	+	0.0723169i
$987$		0			0
$988$	3.39222	−	1.53469i	0.107921	−	0.0488250i
$989$	−16.4729			−0.523808
$990$		0			0
$991$			45.3242i			1.43977i	0.694093	+	0.719885i	$0.255805\pi$
$991$			45.3242i			1.43977i	−0.694093	+	0.719885i	$0.744195\pi$
$992$	1.02656	−	8.81392i	0.0325932	−	0.279842i
$993$		0			0
$994$	−13.7468	+	75.4295i	−0.436023	+	2.39248i
$995$	−7.69862	+	8.37046i	−0.244063	+	0.265361i
$996$		0			0
$997$	14.5950	+	14.5950i	0.462228	+	0.462228i	0.899385	−	0.437157i	$-0.144015\pi$
$997$	14.5950	+	14.5950i	0.462228	+	0.462228i	−0.437157	+	0.899385i	$0.644015\pi$
$998$	15.7790	+	22.8121i	0.499474	+	0.722104i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.e.163.10		24
3.2	odd	2		120.2.v.a.43.3	✓	24
4.3	odd	2		1440.2.bi.e.1423.10		24
5.2	odd	4	inner	360.2.w.e.307.8		24
8.3	odd	2	inner	360.2.w.e.163.8		24
8.5	even	2		1440.2.bi.e.1423.3		24
12.11	even	2		480.2.bh.a.463.8		24
15.2	even	4		120.2.v.a.67.5	yes	24
15.8	even	4		600.2.v.b.307.8		24
15.14	odd	2		600.2.v.b.43.10		24
20.7	even	4		1440.2.bi.e.847.3		24
24.5	odd	2		480.2.bh.a.463.11		24
24.11	even	2		120.2.v.a.43.5	yes	24
40.27	even	4	inner	360.2.w.e.307.10		24
40.37	odd	4		1440.2.bi.e.847.10		24
60.23	odd	4		2400.2.bh.b.1807.5		24
60.47	odd	4		480.2.bh.a.367.11		24
60.59	even	2		2400.2.bh.b.943.6		24
120.29	odd	2		2400.2.bh.b.943.5		24
120.53	even	4		2400.2.bh.b.1807.6		24
120.59	even	2		600.2.v.b.43.8		24
120.77	even	4		480.2.bh.a.367.8		24
120.83	odd	4		600.2.v.b.307.10		24
120.107	odd	4		120.2.v.a.67.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.3	✓	24	3.2	odd	2
120.2.v.a.43.5	yes	24	24.11	even	2
120.2.v.a.67.3	yes	24	120.107	odd	4
120.2.v.a.67.5	yes	24	15.2	even	4
360.2.w.e.163.8		24	8.3	odd	2	inner
360.2.w.e.163.10		24	1.1	even	1	trivial
360.2.w.e.307.8		24	5.2	odd	4	inner
360.2.w.e.307.10		24	40.27	even	4	inner
480.2.bh.a.367.8		24	120.77	even	4
480.2.bh.a.367.11		24	60.47	odd	4
480.2.bh.a.463.8		24	12.11	even	2
480.2.bh.a.463.11		24	24.5	odd	2
600.2.v.b.43.8		24	120.59	even	2
600.2.v.b.43.10		24	15.14	odd	2
600.2.v.b.307.8		24	15.8	even	4
600.2.v.b.307.10		24	120.83	odd	4
1440.2.bi.e.847.3		24	20.7	even	4
1440.2.bi.e.847.10		24	40.37	odd	4
1440.2.bi.e.1423.3		24	8.5	even	2
1440.2.bi.e.1423.10		24	4.3	odd	2
2400.2.bh.b.943.5		24	120.29	odd	2
2400.2.bh.b.943.6		24	60.59	even	2
2400.2.bh.b.1807.5		24	60.23	odd	4
2400.2.bh.b.1807.6		24	120.53	even	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16309 - 0.804501i) q^{2} +(0.705556 - 1.87141i) q^{4} +(1.51371 - 1.64581i) q^{5} +(3.43671 + 3.43671i) q^{7} +(-0.684930 - 2.74424i) q^{8} +O(q^{10})\)	\(q+(1.16309 - 0.804501i) q^{2} +(0.705556 - 1.87141i) q^{4} +(1.51371 - 1.64581i) q^{5} +(3.43671 + 3.43671i) q^{7} +(-0.684930 - 2.74424i) q^{8} +(0.436527 - 3.13200i) q^{10} -3.48120 q^{11} +(-2.05033 + 2.05033i) q^{13} +(6.76204 + 1.23237i) q^{14} +(-3.00438 - 2.64077i) q^{16} +(1.64963 - 1.64963i) q^{17} -0.642023i q^{19} +(-2.01198 - 3.99399i) q^{20} +(-4.04895 + 2.80063i) q^{22} +(-2.31024 + 2.31024i) q^{23} +(-0.417363 - 4.98255i) q^{25} +(-0.735225 + 4.03421i) q^{26} +(8.85630 - 4.00672i) q^{28} -0.699613 q^{29} +1.56863i q^{31} +(-5.61887 - 0.654430i) q^{32} +(0.591537 - 3.24579i) q^{34} +(10.8583 - 0.453979i) q^{35} +(-5.31751 - 5.31751i) q^{37} +(-0.516509 - 0.746731i) q^{38} +(-5.55328 - 3.02673i) q^{40} -4.92316 q^{41} +(3.56519 + 3.56519i) q^{43} +(-2.45618 + 6.51477i) q^{44} +(-0.828427 + 4.54561i) q^{46} +(6.85586 + 6.85586i) q^{47} +16.6220i q^{49} +(-4.49390 - 5.45938i) q^{50} +(2.39039 + 5.28364i) q^{52} +(-1.94008 + 1.94008i) q^{53} +(-5.26953 + 5.72939i) q^{55} +(7.07726 - 11.7851i) q^{56} +(-0.813713 + 0.562839i) q^{58} +2.74121i q^{59} +5.20943i q^{61} +(1.26196 + 1.82446i) q^{62} +(-7.06174 + 3.75923i) q^{64} +(0.270842 + 6.47805i) q^{65} +(6.92316 - 6.92316i) q^{67} +(-1.92323 - 4.25104i) q^{68} +(12.2640 - 9.26357i) q^{70} +11.1548i q^{71} +(-6.56519 - 6.56519i) q^{73} +(-10.4627 - 1.90680i) q^{74} +(-1.20149 - 0.452983i) q^{76} +(-11.9639 - 11.9639i) q^{77} +2.09702 q^{79} +(-8.89397 + 0.947265i) q^{80} +(-5.72608 + 3.96069i) q^{82} +(-6.64648 - 6.64648i) q^{83} +(-0.217911 - 5.21202i) q^{85} +(7.01483 + 1.27844i) q^{86} +(2.38438 + 9.55327i) q^{88} +0.733690i q^{89} -14.0928 q^{91} +(2.69342 + 5.95343i) q^{92} +(13.4895 + 2.45843i) q^{94} +(-1.05665 - 0.971837i) q^{95} +(8.79083 - 8.79083i) q^{97} +(13.3724 + 19.3328i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

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