LMFDB - Embedded newform 360.2.w.e.307.8

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			307.8
Character	$\chi$	$=$	360.307
Dual form			360.2.w.e.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.804501 + 1.16309i) q^{2} +(-0.705556 + 1.87141i) q^{4} +(-1.51371 - 1.64581i) q^{5} +(-3.43671 + 3.43671i) q^{7} +(-2.74424 + 0.684930i) q^{8} +O(q^{10})$	\(q+(0.804501 + 1.16309i) q^{2} +(-0.705556 + 1.87141i) q^{4} +(-1.51371 - 1.64581i) q^{5} +(-3.43671 + 3.43671i) q^{7} +(-2.74424 + 0.684930i) q^{8} +(0.696440 - 3.08463i) q^{10} -3.48120 q^{11} +(2.05033 + 2.05033i) q^{13} +(-6.76204 - 1.23237i) q^{14} +(-3.00438 - 2.64077i) q^{16} +(1.64963 + 1.64963i) q^{17} +0.642023i q^{19} +(4.14799 - 1.67157i) q^{20} +(-2.80063 - 4.04895i) q^{22} +(2.31024 + 2.31024i) q^{23} +(-0.417363 + 4.98255i) q^{25} +(-0.735225 + 4.03421i) q^{26} +(-4.00672 - 8.85630i) q^{28} +0.699613 q^{29} +1.56863i q^{31} +(0.654430 - 5.61887i) q^{32} +(-0.591537 + 3.24579i) q^{34} +(10.8583 + 0.453979i) q^{35} +(5.31751 - 5.31751i) q^{37} +(-0.746731 + 0.516509i) q^{38} +(5.28125 + 3.47971i) q^{40} -4.92316 q^{41} +(3.56519 - 3.56519i) q^{43} +(2.45618 - 6.51477i) q^{44} +(-0.828427 + 4.54561i) q^{46} +(-6.85586 + 6.85586i) q^{47} -16.6220i q^{49} +(-6.13092 + 3.52304i) q^{50} +(-5.28364 + 2.39039i) q^{52} +(1.94008 + 1.94008i) q^{53} +(5.26953 + 5.72939i) q^{55} +(7.07726 - 11.7851i) q^{56} +(0.562839 + 0.813713i) q^{58} -2.74121i q^{59} +5.20943i q^{61} +(-1.82446 + 1.26196i) q^{62} +(7.06174 - 3.75923i) q^{64} +(0.270842 - 6.47805i) q^{65} +(6.92316 + 6.92316i) q^{67} +(-4.25104 + 1.92323i) q^{68} +(8.20753 + 12.9945i) q^{70} +11.1548i q^{71} +(-6.56519 + 6.56519i) q^{73} +(10.4627 + 1.90680i) q^{74} +(-1.20149 - 0.452983i) q^{76} +(11.9639 - 11.9639i) q^{77} -2.09702 q^{79} +(0.201557 + 8.94200i) q^{80} +(-3.96069 - 5.72608i) q^{82} +(-6.64648 + 6.64648i) q^{83} +(0.217911 - 5.21202i) q^{85} +(7.01483 + 1.27844i) q^{86} +(9.55327 - 2.38438i) q^{88} -0.733690i q^{89} -14.0928 q^{91} +(-5.95343 + 2.69342i) q^{92} +(-13.4895 - 2.45843i) q^{94} +(1.05665 - 0.971837i) q^{95} +(8.79083 + 8.79083i) q^{97} +(19.3328 - 13.3724i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.804501	+	1.16309i	0.568868	+	0.822429i
$2$	0.804501	+	1.16309i	0.568868	+	0.822429i
$3$		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	−0.369871	+	0.929083i	$0.620598\pi$
$7$	−3.43671	+	3.43671i	−1.29895	+	1.29895i	−0.929083	+	0.369871i	$0.879402\pi$
$8$	−2.74424	+	0.684930i	−0.970237	+	0.242159i
$9$		0			0
$10$	0.696440	−	3.08463i	0.220234	−	0.975447i
$11$	−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	$-0.118279\pi$
$13$	2.05033	+	2.05033i	0.568659	+	0.568659i	−0.363093	+	0.931753i	$0.618279\pi$
$14$	−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	0.878266	−	0.478173i	$-0.158701\pi$
$17$	1.64963	+	1.64963i	0.400093	+	0.400093i	−0.478173	+	0.878266i	$0.658701\pi$
$18$		0			0
$19$			0.642023i			0.147290i	0.997285	+	0.0736451i	$0.0234632\pi$
$19$			0.642023i			0.147290i	−0.997285	+	0.0736451i	$0.976537\pi$
$20$	4.14799	−	1.67157i	0.927520	−	0.373774i
$21$		0			0
$22$	−2.80063	−	4.04895i	−0.597097	−	0.863239i
$23$	2.31024	+	2.31024i	0.481719	+	0.481719i	0.905680	−	0.423961i	$-0.139361\pi$
$23$	2.31024	+	2.31024i	0.481719	+	0.481719i	−0.423961	+	0.905680i	$0.639361\pi$
$24$		0			0
$25$	−0.417363	+	4.98255i	−0.0834726	+	0.996510i
$26$	−0.735225	+	4.03421i	−0.144190	+	0.791174i
$27$		0			0
$28$	−4.00672	−	8.85630i	−0.757198	−	1.67368i
$29$	0.699613			0.129915			0.0649574	−	0.997888i	$-0.479309\pi$
$29$	0.699613			0.129915			0.0649574	+	0.997888i	$0.479309\pi$
$30$		0			0
$31$			1.56863i			0.281734i	0.990029	+	0.140867i	$0.0449890\pi$
$31$			1.56863i			0.281734i	−0.990029	+	0.140867i	$0.955011\pi$
$32$	0.654430	−	5.61887i	0.115688	−	0.993286i
$33$		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	$-0.537883\pi$
$37$	5.31751	−	5.31751i	0.874193	−	0.874193i	0.992926	+	0.118733i	$0.0378834\pi$
$38$	−0.746731	+	0.516509i	−0.121136	+	0.0837888i
$39$		0			0
$40$	5.28125	+	3.47971i	0.835039	+	0.550191i
$41$	−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	−0.380921	−	0.924607i	$-0.624393\pi$
$43$	3.56519	−	3.56519i	0.543686	−	0.543686i	0.924607	+	0.380921i	$0.124393\pi$
$44$	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	−2.93703e−5		1.00000i	$0.500009\pi$
$47$	−6.85586	+	6.85586i	−1.00003	+	1.00003i	−1.00000		2.93703e-5i	$0.999991\pi$
$48$		0			0
$49$		−	16.6220i		−	2.37457i
$50$	−6.13092	+	3.52304i	−0.867043	+	0.498233i
$51$		0			0
$52$	−5.28364	+	2.39039i	−0.732709	+	0.331488i
$53$	1.94008	+	1.94008i	0.266490	+	0.266490i	0.827684	−	0.561194i	$-0.189658\pi$
$53$	1.94008	+	1.94008i	0.266490	+	0.266490i	−0.561194	+	0.827684i	$0.689658\pi$
$54$		0			0
$55$	5.26953	+	5.72939i	0.710544	+	0.772551i
$56$	7.07726	−	11.7851i	0.945739	−	1.57485i
$57$		0			0
$58$	0.562839	+	0.813713i	0.0739044	+	0.106846i
$59$		−	2.74121i		−	0.356876i	−0.983951	−	0.178438i	$-0.942896\pi$
$59$		−	2.74121i		−	0.356876i	0.983951	−	0.178438i	$-0.0571043\pi$
$60$		0			0
$61$			5.20943i			0.666999i	0.942750	+	0.333500i	$0.108230\pi$
$61$			5.20943i			0.666999i	−0.942750	+	0.333500i	$0.891770\pi$
$62$	−1.82446	+	1.26196i	−0.231706	+	0.160269i
$63$		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	0.989606	−	0.143807i	$-0.0459344\pi$
$67$	6.92316	+	6.92316i	0.845799	+	0.845799i	−0.143807	+	0.989606i	$0.545934\pi$
$68$	−4.25104	+	1.92323i	−0.515514	+	0.233226i
$69$		0			0
$70$	8.20753	+	12.9945i	0.980988	+	1.55313i
$71$			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	−0.977824	−	0.209427i	$-0.932840\pi$
$73$	−6.56519	+	6.56519i	−0.768397	+	0.768397i	0.209427	+	0.977824i	$0.432840\pi$
$74$	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	$-0.537637\pi$
$79$	−2.09702			−0.235933			−0.117966	+	0.993018i	$0.537637\pi$
$80$	0.201557	+	8.94200i	0.0225347	+	0.999746i
$81$		0			0
$82$	−3.96069	−	5.72608i	−0.437385	−	0.632340i
$83$	−6.64648	+	6.64648i	−0.729546	+	0.729546i	−0.970529	−	0.240984i	$-0.922530\pi$
$83$	−6.64648	+	6.64648i	−0.729546	+	0.729546i	0.240984	+	0.970529i	$0.422530\pi$
$84$		0			0
$85$	0.217911	−	5.21202i	0.0236357	−	0.565323i
$86$	7.01483	+	1.27844i	0.756429	+	0.137857i
$87$		0			0
$88$	9.55327	−	2.38438i	1.01838	−	0.254176i
$89$		−	0.733690i		−	0.0777710i	−0.999244	−	0.0388855i	$-0.987619\pi$
$89$		−	0.733690i		−	0.0777710i	0.999244	−	0.0388855i	$-0.0123808\pi$
$90$		0			0
$91$	−14.0928			−1.47732
$92$	−5.95343	+	2.69342i	−0.620688	+	0.280808i
$93$		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	0.994765	−	0.102191i	$-0.0325853\pi$
$97$	8.79083	+	8.79083i	0.892574	+	0.892574i	−0.102191	+	0.994765i	$0.532585\pi$
$98$	19.3328	−	13.3724i	1.95291	−	1.35081i
$99$		0			0
$100$	−9.02994	−	4.29653i	−0.902994	−	0.429653i
$101$		−	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	$-0.303778\pi$
$103$	−2.41334	−	2.41334i	−0.237793	−	0.237793i	−0.815936	+	0.578143i	$0.803778\pi$
$104$	−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	0.627630	−	0.778512i	$-0.284025\pi$
$107$	−1.56073	−	1.56073i	−0.150882	−	0.150882i	−0.778512	+	0.627630i	$0.784025\pi$
$108$		0			0
$109$	−14.6177			−1.40012			−0.700060	−	0.714084i	$-0.746843\pi$
$109$	−14.6177			−1.40012			−0.700060	+	0.714084i	$0.746843\pi$
$110$	−2.42445	+	10.7382i	−0.231162	+	1.02385i
$111$		0			0
$112$	19.4008	−	1.24961i	1.83320	−	0.118077i
$113$	4.55758	−	4.55758i	0.428742	−	0.428742i	−0.459458	−	0.888199i	$-0.651956\pi$
$113$	4.55758	−	4.55758i	0.428742	−	0.428742i	0.888199	+	0.459458i	$0.151956\pi$
$114$		0			0
$115$	0.305176	−	7.29925i	0.0284578	−	0.680659i
$116$	−0.493616	+	1.30927i	−0.0458311	+	0.121562i
$117$		0			0
$118$	3.18828	−	2.20531i	0.293505	−	0.203015i
$119$	−11.3386			−1.03941
$120$		0			0
$121$	1.11877			0.101707
$122$	−6.05904	+	4.19099i	−0.548559	+	0.379435i
$123$		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	$-0.543582\pi$
$127$	9.62582	−	9.62582i	0.854154	−	0.854154i	0.990642	+	0.136488i	$0.0435815\pi$
$128$	10.0535	+	5.18914i	0.888612	+	0.458659i
$129$		0			0
$130$	7.75245	−	4.89659i	0.679935	−	0.429459i
$131$	−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	0.998946	+	0.0459032i	$0.0146166\pi$
$137$	12.2296	+	12.2296i	1.04485	+	1.04485i	0.0459032	+	0.998946i	$0.485383\pi$
$138$		0			0
$139$			8.13630i			0.690112i	0.938582	+	0.345056i	$0.112140\pi$
$139$			8.13630i			0.690112i	−0.938582	+	0.345056i	$0.887860\pi$
$140$	−8.51075	+	20.0002i	−0.719290	+	1.69032i
$141$		0			0
$142$	−12.9741	+	8.97408i	−1.08876	+	0.753088i
$143$	−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
$148$	6.19946	+	13.7031i	0.509592	+	1.12638i
$149$	2.75071			0.225347			0.112674	−	0.993632i	$-0.464059\pi$
$149$	2.75071			0.225347			0.112674	+	0.993632i	$0.464059\pi$
$150$		0			0
$151$			10.2020i			0.830226i	0.909770	+	0.415113i	$0.136258\pi$
$151$			10.2020i			0.830226i	−0.909770	+	0.415113i	$0.863742\pi$
$152$	−0.439741	−	1.76187i	−0.0356677	−	0.142906i
$153$		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	$-0.773214\pi$
$157$	−1.29115	+	1.29115i	−0.103045	+	0.103045i	0.653705	+	0.756750i	$0.273214\pi$
$158$	−1.68705	−	2.43902i	−0.134215	−	0.194038i
$159$		0			0
$160$	−10.2382	+	7.42828i	−0.809401	+	0.587257i
$161$	−15.8793			−1.25146
$162$		0			0
$163$	9.30787	−	9.30787i	0.729049	−	0.729049i	−0.241382	−	0.970430i	$-0.577601\pi$
$163$	9.30787	−	9.30787i	0.729049	−	0.729049i	0.970430	+	0.241382i	$0.0776005\pi$
$164$	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	$-0.524646\pi$
$167$	11.8845	−	11.8845i	0.919652	−	0.919652i	0.997004	+	0.0773515i	$0.0246464\pi$
$168$		0			0
$169$		−	4.59229i		−	0.353253i
$170$	6.23736	−	3.93963i	0.478384	−	0.302156i
$171$		0			0
$172$	4.15650	+	9.18738i	0.316930	+	0.700531i
$173$	−13.2536	−	13.2536i	−1.00765	−	1.00765i	−0.999970	−	0.00768426i	$-0.997554\pi$
$173$	−13.2536	−	13.2536i	−1.00765	−	1.00765i	−0.00768426	−	0.999970i	$-0.502446\pi$
$174$		0			0
$175$	−15.6892	−	18.5579i	−1.18599	−	1.40285i
$176$	10.4589	+	9.19307i	0.788366	+	0.692954i
$177$		0			0
$178$	0.853348	−	0.590255i	0.0639611	−	0.0442414i
$179$		−	3.61084i		−	0.269887i	−0.990853	−	0.134943i	$-0.956915\pi$
$179$		−	3.61084i		−	0.269887i	0.990853	−	0.134943i	$-0.0430853\pi$
$180$		0			0
$181$		−	21.8993i		−	1.62776i	−0.581032	−	0.813881i	$-0.697351\pi$
$181$		−	21.8993i		−	1.62776i	0.581032	−	0.813881i	$-0.302649\pi$
$182$	−11.3377	−	16.3912i	−0.840403	−	1.21499i
$183$		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
$188$	−7.99296	−	17.6673i	−0.582946	−	1.28852i
$189$		0			0
$190$	1.98041	+	0.447131i	0.143674	+	0.0324383i
$191$		−	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	−0.0339453	+	0.999424i	$0.510807\pi$
$193$	−14.3560	+	14.3560i	−1.03337	+	1.03337i	−0.999424	+	0.0339453i	$0.989193\pi$
$194$	−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	−0.0476396	+	0.998865i	$0.515170\pi$
$197$	−14.6884	+	14.6884i	−1.04650	+	1.04650i	−0.998865	+	0.0476396i	$0.984830\pi$
$198$		0			0
$199$	5.08593			0.360532			0.180266	−	0.983618i	$-0.442304\pi$
$199$	5.08593			0.360532			0.180266	+	0.983618i	$0.442304\pi$
$200$	−2.26735	−	13.9592i	−0.160326	−	0.987064i
$201$		0			0
$202$	1.63918	−	1.13381i	0.115332	−	0.0797744i
$203$	−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
$208$	−0.745514	−	11.5744i	−0.0516921	−	0.802543i
$209$		−	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	$0.770019\pi$
$212$	−4.99952	+	2.26186i	−0.343369	+	0.155345i
$213$		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
$218$	−11.7599	−	17.0017i	−0.796484	−	1.15150i
$219$		0			0
$220$	−14.4400	+	5.81907i	−0.973545	+	0.392322i
$221$			6.76456i			0.455033i
$222$		0			0
$223$	−7.63273	−	7.63273i	−0.511126	−	0.511126i	0.403746	−	0.914871i	$-0.367708\pi$
$223$	−7.63273	−	7.63273i	−0.511126	−	0.511126i	−0.914871	+	0.403746i	$0.867708\pi$
$224$	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	0.936810	−	0.349838i	$-0.113763\pi$
$227$	8.84363	+	8.84363i	0.586973	+	0.586973i	−0.349838	+	0.936810i	$0.613763\pi$
$228$		0			0
$229$	23.9520			1.58279			0.791397	−	0.611302i	$-0.209354\pi$
$229$	23.9520			1.58279			0.791397	+	0.611302i	$0.209354\pi$
$230$	8.73520	−	5.51731i	0.575982	−	0.363801i
$231$		0			0
$232$	−1.91991	+	0.479186i	−0.126048	+	0.0314601i
$233$	−4.38332	+	4.38332i	−0.287161	+	0.287161i	−0.835956	−	0.548796i	$-0.815086\pi$
$233$	−4.38332	+	4.38332i	−0.287161	+	0.287161i	0.548796	+	0.835956i	$0.315086\pi$
$234$		0			0
$235$	21.6612	+	0.905638i	1.41302	+	0.0590773i
$236$	5.12995	+	1.93408i	0.333931	+	0.125898i
$237$		0			0
$238$	−9.12190	−	13.1878i	−0.591285	−	0.854837i
$239$	16.7993			1.08666			0.543328	−	0.839521i	$-0.317164\pi$
$239$	16.7993			1.08666			0.543328	+	0.839521i	$0.317164\pi$
$240$		0			0
$241$	3.47277			0.223701			0.111850	−	0.993725i	$-0.464322\pi$
$241$	3.47277			0.223701			0.111850	+	0.993725i	$0.464322\pi$
$242$	0.900054	+	1.30123i	0.0578576	+	0.0836464i
$243$		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
$248$	−1.07440	−	4.30470i	−0.0682245	−	0.273348i
$249$		0			0
$250$	15.0787	+	4.75746i	0.953659	+	0.300888i
$251$	−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	0.999650	+	0.0264382i	$0.00841653\pi$
$257$	16.4495	+	16.4495i	1.02609	+	1.02609i	0.0264382	+	0.999650i	$0.491583\pi$
$258$		0			0
$259$			36.5495i			2.27107i
$260$	11.9320	+	5.07749i	0.739993	+	0.314892i
$261$		0			0
$262$	−1.01986	−	1.47444i	−0.0630072	−	0.0910913i
$263$	17.3101	+	17.3101i	1.06739	+	1.06739i	0.997559	+	0.0698281i	$0.0222451\pi$
$263$	17.3101	+	17.3101i	1.06739	+	1.06739i	0.0698281	+	0.997559i	$0.477755\pi$
$264$		0			0
$265$	0.256279	−	6.12971i	0.0157431	−	0.376545i
$266$	0.791208	−	4.34139i	0.0485121	−	0.266188i
$267$		0			0
$268$	−17.8408	+	8.07143i	−1.08980	+	0.493041i
$269$	−17.2178			−1.04979			−0.524895	−	0.851167i	$-0.675895\pi$
$269$	−17.2178			−1.04979			−0.524895	+	0.851167i	$0.675895\pi$
$270$		0			0
$271$		−	8.37293i		−	0.508619i	−0.967123	−	0.254310i	$-0.918152\pi$
$271$		−	8.37293i		−	0.508619i	0.967123	−	0.254310i	$-0.0818482\pi$
$272$	−0.599815	−	9.31240i	−0.0363691	−	0.564647i
$273$		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	$-0.908632\pi$
$277$	−11.2504	+	11.2504i	−0.675971	+	0.675971i	0.283115	+	0.959086i	$0.408632\pi$
$278$	−9.46325	+	6.54566i	−0.567568	+	0.392583i
$279$		0			0
$280$	−30.1089	+	6.19137i	−1.79935	+	0.370005i
$281$	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	−0.705939	−	0.708272i	$-0.749475\pi$
$283$	0.0392414	−	0.0392414i	0.00233266	−	0.00233266i	0.708272	+	0.705939i	$0.249475\pi$
$284$	−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
$290$	0.487239	−	2.15805i	0.0286116	−	0.126725i
$291$		0			0
$292$	−7.65408	−	16.9183i	−0.447921	−	0.990068i
$293$	21.6367	+	21.6367i	1.26403	+	1.26403i	0.949123	+	0.314905i	$0.101973\pi$
$293$	21.6367	+	21.6367i	1.26403	+	1.26403i	0.314905	+	0.949123i	$0.398027\pi$
$294$		0			0
$295$	−4.51151	+	4.14940i	−0.262670	+	0.241588i
$296$	−10.9504	+	18.2347i	−0.636480	+	1.05987i
$297$		0			0
$298$	2.21295	+	3.19933i	0.128193	+	0.185332i
$299$			9.47352i			0.547868i
$300$		0			0
$301$			24.5050i			1.41245i
$302$	−11.8658	+	8.20751i	−0.682802	+	0.472289i
$303$		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	−0.999402	−	0.0345669i	$-0.988995\pi$
$307$	−18.1166	−	18.1166i	−1.03397	−	1.03397i	−0.0345669	−	0.999402i	$-0.511005\pi$
$308$	13.9482	+	30.8306i	0.794772	+	1.75674i
$309$		0			0
$310$	4.83864	+	1.09246i	0.274817	+	0.0620473i
$311$		−	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	0.0313208	−	0.999509i	$-0.490029\pi$
$313$	18.2372	−	18.2372i	1.03083	−	1.03083i	0.999509	−	0.0313208i	$-0.00997135\pi$
$314$	−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	$-0.739040\pi$
$317$	0.866839	−	0.866839i	0.0486865	−	0.0486865i	0.731031	+	0.682344i	$0.239040\pi$
$318$		0			0
$319$	−2.43549			−0.136362
$320$	−16.8764	−	5.93189i	−0.943419	−	0.331603i
$321$		0			0
$322$	−12.7749	−	18.4690i	−0.711917	−	1.02924i
$323$	−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
$328$	13.5104	−	3.37202i	0.745985	−	0.186189i
$329$		−	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	$0.369643\pi$
$332$	−7.74885	−	17.1278i	−0.425273	−	0.940009i
$333$		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	0.974679	+	0.223611i	$0.0717845\pi$
$337$	21.9977	+	21.9977i	1.19829	+	1.19829i	0.223611	+	0.974679i	$0.428216\pi$
$338$	5.34125	−	3.69451i	0.290526	−	0.200955i
$339$		0			0
$340$	9.60011	+	4.08518i	0.520639	+	0.221550i
$341$		−	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	0.606005	−	0.795461i	$-0.292771\pi$
$347$	−3.52917	−	3.52917i	−0.189456	−	0.189456i	−0.795461	+	0.606005i	$0.792771\pi$
$348$		0			0
$349$	3.26043			0.174527			0.0872635	−	0.996185i	$-0.472188\pi$
$349$	3.26043			0.174527			0.0872635	+	0.996185i	$0.472188\pi$
$350$	8.96255	−	33.1779i	0.479068	−	1.77343i
$351$		0			0
$352$	−2.27820	+	19.5604i	−0.121429	+	1.04257i
$353$	−22.6567	+	22.6567i	−1.20589	+	1.20589i	−0.233547	+	0.972346i	$0.575033\pi$
$353$	−22.6567	+	22.6567i	−1.20589	+	1.20589i	−0.972346	+	0.233547i	$0.924967\pi$
$354$		0			0
$355$	18.3587	−	16.8852i	0.974379	−	0.896173i
$356$	1.37304	+	0.517659i	0.0727709	+	0.0274359i
$357$		0			0
$358$	4.19973	−	2.90492i	0.221963	−	0.153530i
$359$	16.9181			0.892903			0.446451	−	0.894808i	$-0.352688\pi$
$359$	16.9181			0.892903			0.446451	+	0.894808i	$0.352688\pi$
$360$		0			0
$361$	18.5878			0.978306
$362$	25.4708	−	17.6180i	1.33872	−	0.925982i
$363$		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	$-0.783203\pi$
$367$	−2.82093	+	2.82093i	−0.147252	+	0.147252i	0.629637	+	0.776889i	$0.283203\pi$
$368$	−0.840020	−	13.0417i	−0.0437891	−	0.679845i
$369$		0			0
$370$	−12.6992	−	20.1059i	−0.660202	−	1.04526i
$371$	−13.3350			−0.692318
$372$		0			0
$373$	22.7300	+	22.7300i	1.17691	+	1.17691i	0.980526	+	0.196388i	$0.0629213\pi$
$373$	22.7300	+	22.7300i	1.17691	+	1.17691i	0.196388	+	0.980526i	$0.437079\pi$
$374$	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	$0.0209267\pi$
$379$			2.55793i			0.131392i	−0.997840	+	0.0656959i	$0.979073\pi$
$380$	1.07319	+	2.66311i	0.0550533	+	0.136615i
$381$		0			0
$382$	11.7831	−	8.15030i	0.602877	−	0.417006i
$383$	−5.48289	−	5.48289i	−0.280163	−	0.280163i	0.553011	−	0.833174i	$-0.313479\pi$
$383$	−5.48289	−	5.48289i	−0.280163	−	0.280163i	−0.833174	+	0.553011i	$0.813479\pi$
$384$		0			0
$385$	−37.8001	−	1.58039i	−1.92647	−	0.0805443i
$386$	−28.2468	−	5.14791i	−1.43772	−	0.262022i
$387$		0			0
$388$	−22.6537	+	10.2489i	−1.15007	+	0.520307i
$389$	5.02529			0.254792			0.127396	−	0.991852i	$-0.459338\pi$
$389$	5.02529			0.254792			0.127396	+	0.991852i	$0.459338\pi$
$390$		0			0
$391$			7.62208i			0.385465i
$392$	11.3849	+	45.6147i	0.575023	+	2.30389i
$393$		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	$-0.848293\pi$
$397$	−8.56361	+	8.56361i	−0.429795	+	0.429795i	0.458763	+	0.888558i	$0.348293\pi$
$398$	4.09163	+	5.91539i	0.205095	+	0.296512i
$399$		0			0
$400$	14.4117	−	13.8673i	0.720586	−	0.693366i
$401$	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	$0.0790922\pi$
$409$			9.94711i			0.491853i	−0.969288	+	0.245927i	$0.920908\pi$
$410$	−3.42869	+	15.1862i	−0.169331	+	0.749991i
$411$		0			0
$412$	6.21910	−	2.81361i	0.306393	−	0.138617i
$413$	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
$418$	2.59952	−	1.79807i	0.127147	−	0.0879465i
$419$		−	1.92920i		−	0.0942475i	−0.998889	−	0.0471238i	$-0.984994\pi$
$419$		−	1.92920i		−	0.0942475i	0.998889	−	0.0471238i	$-0.0150055\pi$
$420$		0			0
$421$		−	0.454084i		−	0.0221307i	−0.999939	−	0.0110654i	$-0.996478\pi$
$421$		−	0.454084i		−	0.0221307i	0.999939	−	0.0110654i	$-0.00352229\pi$
$422$	−17.5326	−	25.3474i	−0.853474	−	1.23389i
$423$		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
$428$	4.02196	−	1.81959i	0.194409	−	0.0879534i
$429$		0			0
$430$	−8.51436	−	13.4802i	−0.410599	−	0.650075i
$431$			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	−0.970219	−	0.242231i	$-0.922121\pi$
$433$	−15.1484	+	15.1484i	−0.727987	+	0.727987i	0.242231	+	0.970219i	$0.422121\pi$
$434$	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	$-0.293733\pi$
$439$	25.2936			1.20720			0.603599	+	0.797288i	$0.293733\pi$
$440$	−18.3851	−	12.1136i	−0.876476	−	0.577492i
$441$		0			0
$442$	−7.86779	+	5.44209i	−0.374232	+	0.258854i
$443$	26.9275	−	26.9275i	1.27936	−	1.27936i	0.338341	−	0.941024i	$-0.390134\pi$
$443$	26.9275	−	26.9275i	1.27936	−	1.27936i	0.941024	−	0.338341i	$-0.109866\pi$
$444$		0			0
$445$	−1.20751	+	1.11059i	−0.0572416	+	0.0526472i
$446$	2.73701	−	15.0181i	0.129601	−	0.711127i
$447$		0			0
$448$	−11.3498	+	37.1885i	−0.536227	+	1.75699i
$449$			22.4863i			1.06120i	0.847624	+	0.530598i	$0.178033\pi$
$449$			22.4863i			1.06120i	−0.847624	+	0.530598i	$0.821967\pi$
$450$		0			0
$451$	17.1385			0.807022
$452$	5.31350	+	11.7448i	0.249926	+	0.552427i
$453$		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	0.705384	−	0.708825i	$-0.250774\pi$
$457$	−0.0735546	−	0.0735546i	−0.00344074	−	0.00344074i	−0.708825	+	0.705384i	$0.750774\pi$
$458$	19.2694	+	27.8584i	0.900401	+	1.30174i
$459$		0			0
$460$	13.4446	+	5.72114i	0.626858	+	0.266750i
$461$			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	−0.943827	−	0.330439i	$-0.892803\pi$
$463$	−27.4189	−	27.4189i	−1.27427	−	1.27427i	−0.330439	−	0.943827i	$-0.607197\pi$
$464$	−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	0.378626	−	0.925550i	$-0.376397\pi$
$467$	−11.8191	−	11.8191i	−0.546923	−	0.546923i	−0.925550	+	0.378626i	$0.876397\pi$
$468$		0			0
$469$	−47.5858			−2.19731
$470$	16.3731	+	25.9225i	0.755236	+	1.19572i
$471$		0			0
$472$	1.87754	+	7.52256i	0.0864207	+	0.346254i
$473$	−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
$478$	13.5150	+	19.5391i	0.618164	+	0.893697i
$479$	−39.9242			−1.82418			−0.912091	−	0.409988i	$-0.865533\pi$
$479$	−39.9242			−1.82418			−0.912091	+	0.409988i	$0.865533\pi$
$480$		0			0
$481$	21.8053			0.994236
$482$	2.79385	+	4.03914i	0.127256	+	0.183978i
$483$		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	$-0.859928\pi$
$487$	−10.5650	+	10.5650i	−0.478745	+	0.478745i	0.425985	+	0.904730i	$0.359928\pi$
$488$	−3.56809	−	14.2959i	−0.161520	−	0.647147i
$489$		0			0
$490$	−51.2727	−	11.5762i	−2.31626	−	0.522959i
$491$	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	$-0.855330\pi$
$499$		−	19.6133i		−	0.878014i	0.898484	−	0.439007i	$-0.144670\pi$
$500$	6.59746	+	21.3652i	0.295047	+	0.955483i
$501$		0			0
$502$	−8.53703	−	12.3422i	−0.381026	−	0.550860i
$503$	−24.2004	−	24.2004i	−1.07904	−	1.07904i	−0.996595	−	0.0824469i	$-0.973727\pi$
$503$	−24.2004	−	24.2004i	−1.07904	−	1.07904i	−0.0824469	−	0.996595i	$-0.526273\pi$
$504$		0			0
$505$	−2.31948	+	2.13332i	−0.103216	+	0.0949313i
$506$	2.88392	−	15.8242i	0.128206	−	0.703472i
$507$		0			0
$508$	11.2223	+	24.8055i	0.497911	+	1.10056i
$509$	−10.8167			−0.479444			−0.239722	−	0.970842i	$-0.577056\pi$
$509$	−10.8167			−0.479444			−0.239722	+	0.970842i	$0.577056\pi$
$510$		0			0
$511$		−	45.1253i		−	1.99623i
$512$	−16.8043	+	15.1530i	−0.742654	+	0.669676i
$513$		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
$518$	−42.5103	+	29.4041i	−1.86780	+	1.29194i
$519$		0			0
$520$	3.69375	+	17.9629i	0.161982	+	0.787724i
$521$	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	−0.160106	+	0.987100i	$0.551184\pi$
$523$	−26.2357	+	26.2357i	−1.14721	+	1.14721i	−0.987100	+	0.160106i	$0.948816\pi$
$524$	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
$530$	7.33558	−	4.63329i	0.318637	−	0.201257i
$531$		0			0
$532$	5.68595	−	2.57241i	0.246517	−	0.111528i
$533$	−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
$538$	−13.8518	−	20.0259i	−0.597192	−	0.863378i
$539$			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	$-0.0666517\pi$
$542$	9.73847	−	6.73603i	0.418303	−	0.289337i
$543$		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	0.795929	−	0.605390i	$-0.206983\pi$
$547$	4.45632	+	4.45632i	0.190538	+	0.190538i	−0.605390	+	0.795929i	$0.706983\pi$
$548$	−31.5154	+	14.2580i	−1.34627	+	0.609073i
$549$		0			0
$550$	21.3430	−	12.2644i	0.910068	−	0.522956i
$551$			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	$-0.818290\pi$
$557$	−7.10582	+	7.10582i	−0.301083	+	0.301083i	0.540354	+	0.841438i	$0.318290\pi$
$558$		0			0
$559$	14.6196			0.618344
$560$	−31.4238	−	30.0384i	−1.32790	−	1.26935i
$561$		0			0
$562$	20.8725	+	30.1760i	0.880453	+	1.27290i
$563$	−12.1395	+	12.1395i	−0.511620	+	0.511620i	−0.915023	−	0.403403i	$-0.867827\pi$
$563$	−12.1395	+	12.1395i	−0.511620	+	0.511620i	0.403403	+	0.915023i	$0.367827\pi$
$564$		0			0
$565$	−14.3998	−	0.602043i	−0.605803	−	0.0253282i
$566$	0.0772109	+	0.0140715i	0.00324542	+	0.000591470i
$567$		0			0
$568$	−7.64028	−	30.6116i	−0.320579	−	1.28443i
$569$			9.17667i			0.384706i	0.981326	+	0.192353i	$0.0616118\pi$
$569$			9.17667i			0.384706i	−0.981326	+	0.192353i	$0.938388\pi$
$570$		0			0
$571$	14.1460			0.591990			0.295995	−	0.955190i	$-0.404349\pi$
$571$	14.1460			0.591990			0.295995	+	0.955190i	$0.404349\pi$
$572$	18.3934	−	8.32145i	0.769067	−	0.347937i
$573$		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	0.835792	−	0.549046i	$-0.185009\pi$
$577$	6.88789	+	6.88789i	0.286747	+	0.286747i	−0.549046	+	0.835792i	$0.685009\pi$
$578$	13.4424	−	9.29799i	0.559129	−	0.386746i
$579$		0			0
$580$	2.90199	−	1.16945i	0.120499	−	0.0485588i
$581$		−	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	0.574606	−	0.818430i	$-0.305155\pi$
$587$	−5.90740	−	5.90740i	−0.243824	−	0.243824i	−0.818430	+	0.574606i	$0.805155\pi$
$588$		0			0
$589$	−1.00710			−0.0414967
$590$	−8.45564	−	1.90909i	−0.348113	−	0.0785961i
$591$		0			0
$592$	−30.0182	+	1.93348i	−1.23374	+	0.0794656i
$593$	22.6480	−	22.6480i	0.930042	−	0.930042i	−0.0676664	−	0.997708i	$-0.521555\pi$
$593$	22.6480	−	22.6480i	0.930042	−	0.930042i	0.997708	+	0.0676664i	$0.0215554\pi$
$594$		0			0
$595$	17.1633	+	18.6611i	0.703627	+	0.765031i
$596$	−1.94078	+	5.14772i	−0.0794975	+	0.210859i
$597$		0			0
$598$	−11.0186	+	7.62146i	−0.450582	+	0.311665i
$599$	17.4493			0.712958			0.356479	−	0.934303i	$-0.383977\pi$
$599$	17.4493			0.712958			0.356479	+	0.934303i	$0.383977\pi$
$600$		0			0
$601$	−26.2079			−1.06904			−0.534521	−	0.845155i	$-0.679508\pi$
$601$	−26.2079			−1.06904			−0.534521	+	0.845155i	$0.679508\pi$
$602$	−28.5016	+	19.7143i	−1.16164	+	0.803496i
$603$		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	$-0.831196\pi$
$607$	−8.79177	+	8.79177i	−0.356847	+	0.356847i	0.505802	+	0.862649i	$0.331196\pi$
$608$	3.60745	+	0.420160i	0.146301	+	0.0170397i
$609$		0			0
$610$	16.0692	+	3.62806i	0.650623	+	0.146896i
$611$	−28.1135			−1.13735
$612$		0			0
$613$	−10.9270	−	10.9270i	−0.441339	−	0.441339i	0.451123	−	0.892462i	$-0.351024\pi$
$613$	−10.9270	−	10.9270i	−0.441339	−	0.441339i	−0.892462	+	0.451123i	$0.851024\pi$
$614$	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	0.377294	−	0.926093i	$-0.376855\pi$
$617$	−13.6319	−	13.6319i	−0.548799	−	0.548799i	−0.926093	+	0.377294i	$0.876855\pi$
$618$		0			0
$619$			1.50796i			0.0606100i	0.999541	+	0.0303050i	$0.00964785\pi$
$619$			1.50796i			0.0606100i	−0.999541	+	0.0303050i	$0.990352\pi$
$620$	2.62207	+	6.50666i	0.105305	+	0.261314i
$621$		0			0
$622$	11.2081	−	7.75256i	0.449404	−	0.310849i
$623$	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
$628$	−1.50530	−	3.32726i	−0.0600679	−	0.132772i
$629$	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	$0.675052\pi$
$632$	5.75472	−	1.43631i	0.228911	−	0.0571333i
$633$		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
$638$	−1.95936	−	2.83270i	−0.0775717	−	0.112148i
$639$		0			0
$640$	−6.67776	−	24.4010i	−0.263962	−	0.964533i
$641$	−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	−0.983643	−	0.180127i	$-0.942349\pi$
$643$	−20.3751	+	20.3751i	−0.803517	+	0.803517i	0.180127	+	0.983643i	$0.442349\pi$
$644$	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	−0.00112374	+	0.999999i	$0.500358\pi$
$647$	−25.4648	+	25.4648i	−1.00112	+	1.00112i	−0.999999	+	0.00112374i	$0.999642\pi$
$648$		0			0
$649$			9.54272i			0.374585i
$650$	−19.7938	−	5.34703i	−0.776377	−	0.209728i
$651$		0			0
$652$	10.8517	+	23.9861i	0.424984	+	0.939368i
$653$	−16.9677	−	16.9677i	−0.663999	−	0.663999i	0.292321	−	0.956320i	$-0.405572\pi$
$653$	−16.9677	−	16.9677i	−0.663999	−	0.663999i	−0.956320	+	0.292321i	$0.905572\pi$
$654$		0			0
$655$	1.91892	+	2.08638i	0.0749784	+	0.0815216i
$656$	14.7911	+	13.0010i	0.577494	+	0.507603i
$657$		0			0
$658$	54.8085	−	37.9107i	2.13666	−	1.47791i
$659$		−	0.958005i		−	0.0373186i	−0.999826	−	0.0186593i	$-0.994060\pi$
$659$		−	0.958005i		−	0.0373186i	0.999826	−	0.0186593i	$-0.00593978\pi$
$660$		0			0
$661$			5.22656i			0.203289i	0.994821	+	0.101645i	$0.0324105\pi$
$661$			5.22656i			0.203289i	−0.994821	+	0.101645i	$0.967590\pi$
$662$	11.6559	+	16.8513i	0.453019	+	0.654943i
$663$		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
$668$	13.8557	+	30.6261i	0.536092	+	1.18496i
$669$		0			0
$670$	26.1770	−	16.5339i	1.01131	−	0.638759i
$671$		−	18.1351i		−	0.700097i
$672$		0			0
$673$	16.3145	−	16.3145i	0.628876	−	0.628876i	−0.318909	−	0.947785i	$-0.603316\pi$
$673$	16.3145	−	16.3145i	0.628876	−	0.628876i	0.947785	+	0.318909i	$0.103316\pi$
$674$	−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	$-0.546321\pi$
$677$	21.9712	−	21.9712i	0.844423	−	0.844423i	0.989431	+	0.145008i	$0.0463207\pi$
$678$		0			0
$679$	−60.4231			−2.31883
$680$	2.97187	+	14.4523i	0.113966	+	0.554221i
$681$		0			0
$682$	6.35130	−	4.39315i	0.243204	−	0.168222i
$683$	27.9871	−	27.9871i	1.07090	−	1.07090i	0.0736087	−	0.997287i	$-0.476548\pi$
$683$	27.9871	−	27.9871i	1.07090	−	1.07090i	0.997287	−	0.0736087i	$-0.0234516\pi$
$684$		0			0
$685$	1.61550	−	38.6398i	0.0617251	−	1.47635i
$686$	−11.8578	+	65.0640i	−0.452732	+	2.48416i
$687$		0			0
$688$	−20.1260	+	1.29633i	−0.767298	+	0.0494220i
$689$			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	$0.769134\pi$
$692$	34.1542	−	15.4519i	1.29835	−	0.587391i
$693$		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
$698$	2.62302	+	3.79218i	0.0992829	+	0.143536i
$699$		0			0
$700$	45.7992	−	16.2674i	1.73105	−	0.614849i
$701$		−	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	$-0.175756\pi$
$709$	45.3404			1.70279			0.851397	+	0.524522i	$0.175756\pi$
$710$	34.4086	+	7.76868i	1.29133	+	0.291553i
$711$		0			0
$712$	0.502526	+	2.01342i	0.0188330	+	0.0754563i
$713$	−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
$718$	13.6106	+	19.6773i	0.507944	+	0.734349i
$719$	43.8494			1.63531			0.817653	−	0.575711i	$-0.195275\pi$
$719$	43.8494			1.63531			0.817653	+	0.575711i	$0.195275\pi$
$720$		0			0
$721$	16.5879			0.617765
$722$	14.9539	+	21.6193i	0.556527	+	0.804587i
$723$		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	$-0.767336\pi$
$727$	−2.07567	+	2.07567i	−0.0769824	+	0.0769824i	0.667567	+	0.744550i	$0.267336\pi$
$728$	38.6740	−	9.65256i	1.43335	−	0.357748i
$729$		0			0
$730$	15.6789	+	24.8235i	0.580304	+	0.918758i
$731$	11.7625			0.435050
$732$		0			0
$733$	2.13221	+	2.13221i	0.0787549	+	0.0787549i	0.745387	−	0.666632i	$-0.232265\pi$
$733$	2.13221	+	2.13221i	0.0787549	+	0.0787549i	−0.666632	+	0.745387i	$0.732265\pi$
$734$	−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	$-0.792747\pi$
$739$		−	32.9512i		−	1.21213i	0.795416	−	0.606064i	$-0.207253\pi$
$740$	13.1684	−	30.9456i	0.484080	−	1.13758i
$741$		0			0
$742$	−10.7280	−	15.5098i	−0.393837	−	0.569382i
$743$	17.0344	+	17.0344i	0.624931	+	0.624931i	0.946788	−	0.321857i	$-0.104307\pi$
$743$	17.0344	+	17.0344i	0.624931	+	0.624931i	−0.321857	+	0.946788i	$0.604307\pi$
$744$		0			0
$745$	−4.16378	−	4.52714i	−0.152549	−	0.165862i
$746$	−8.15072	+	44.7233i	−0.298419	+	1.63744i
$747$		0			0
$748$	14.7987	−	6.69515i	0.541095	−	0.244799i
$749$	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	$-0.244364\pi$
$752$	38.7024	−	2.49284i	1.41133	−	0.0909043i
$753$		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	−0.157885	+	0.987458i	$0.550467\pi$
$757$	−31.5125	+	31.5125i	−1.14534	+	1.14534i	−0.987458	+	0.157885i	$0.949533\pi$
$758$	−2.97510	+	2.05786i	−0.108060	+	0.0747447i
$759$		0			0
$760$	−2.23406	+	3.39069i	−0.0810377	+	0.122993i
$761$	−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	$-0.819454\pi$
$769$		−	29.7981i		−	1.07455i	0.843408	−	0.537273i	$-0.180546\pi$
$770$	−28.5721	−	45.2363i	−1.02967	−	1.63020i
$771$		0			0
$772$	−16.7371	−	36.9950i	−0.602381	−	1.33148i
$773$	4.11081	+	4.11081i	0.147856	+	0.147856i	0.777159	−	0.629304i	$-0.216660\pi$
$773$	4.11081	+	4.11081i	0.147856	+	0.147856i	−0.629304	+	0.777159i	$0.716660\pi$
$774$		0			0
$775$	−7.81577	−	0.654687i	−0.280751	−	0.0235170i
$776$	−30.1453	−	18.1031i	−1.08215	−	0.649863i
$777$		0			0
$778$	4.04285	+	5.84487i	0.144943	+	0.209549i
$779$		−	3.16079i		−	0.113247i
$780$		0			0
$781$		−	38.8323i		−	1.38953i
$782$	−8.86516	+	6.13197i	−0.317017	+	0.219279i
$783$		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	0.916522	−	0.399985i	$-0.130985\pi$
$787$	14.4907	+	14.4907i	0.516537	+	0.516537i	−0.399985	+	0.916522i	$0.630985\pi$
$788$	−17.1246	−	37.8515i	−0.610038	−	1.34840i
$789$		0			0
$790$	−1.46045	+	6.46853i	−0.0519603	+	0.230140i
$791$			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	$-0.781893\pi$
$797$	−3.99359	+	3.99359i	−0.141460	+	0.141460i	0.632830	+	0.774291i	$0.281893\pi$
$798$		0			0
$799$	−22.6192			−0.800210
$800$	27.7232	+	5.60584i	0.980162	+	0.198196i
$801$		0			0
$802$	10.1133	+	14.6211i	0.357115	+	0.516291i
$803$	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
$808$	0.965291	+	3.86754i	0.0339588	+	0.136060i
$809$			1.83726i			0.0645947i	0.999478	+	0.0322974i	$0.0102824\pi$
$809$			1.83726i			0.0645947i	−0.999478	+	0.0322974i	$0.989718\pi$
$810$		0			0
$811$	19.2559			0.676166			0.338083	−	0.941116i	$-0.390222\pi$
$811$	19.2559			0.676166			0.338083	+	0.941116i	$0.390222\pi$
$812$	−2.80315	−	6.19598i	−0.0983713	−	0.217436i
$813$		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
$818$	−11.5694	+	8.00246i	−0.404514	+	0.279800i
$819$		0			0
$820$	−20.4213	+	8.22941i	−0.713141	+	0.287384i
$821$		−	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	$-0.155416\pi$
$823$	11.8788	+	11.8788i	0.414067	+	0.414067i	−0.469085	+	0.883153i	$0.655416\pi$
$824$	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	0.149267	−	0.988797i	$-0.452309\pi$
$827$	−24.1429	−	24.1429i	−0.839530	−	0.839530i	−0.988797	+	0.149267i	$0.952309\pi$
$828$		0			0
$829$	30.6528			1.06462			0.532309	−	0.846550i	$-0.321325\pi$
$829$	30.6528			1.06462			0.532309	+	0.846550i	$0.321325\pi$
$830$	15.8731	+	25.1308i	0.550963	+	0.872304i
$831$		0			0
$832$	22.1866	+	6.77125i	0.769181	+	0.234751i
$833$	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
$838$	2.24383	−	1.55204i	0.0775119	−	0.0536144i
$839$	2.59796			0.0896914			0.0448457	−	0.998994i	$-0.485720\pi$
$839$	2.59796			0.0896914			0.0448457	+	0.998994i	$0.485720\pi$
$840$		0			0
$841$	−28.5105			−0.983122
$842$	0.528141	−	0.365311i	0.0182009	−	0.0125895i
$843$		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
$848$	−0.705426	−	10.9520i	−0.0242244	−	0.376095i
$849$		0			0
$850$	−15.9254	−	4.30204i	−0.546238	−	0.147559i
$851$	24.5695			0.842230
$852$		0			0
$853$	−20.7909	−	20.7909i	−0.711866	−	0.711866i	0.255059	−	0.966925i	$-0.417905\pi$
$853$	−20.7909	−	20.7909i	−0.711866	−	0.711866i	−0.966925	+	0.255059i	$0.917905\pi$
$854$	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	0.985881	+	0.167446i	$0.0535521\pi$
$857$	33.7632	+	33.7632i	1.15333	+	1.15333i	0.167446	+	0.985881i	$0.446448\pi$
$858$		0			0
$859$			31.9834i			1.09126i	0.838027	+	0.545629i	$0.183709\pi$
$859$			31.9834i			1.09126i	−0.838027	+	0.545629i	$0.816291\pi$
$860$	8.82892	−	20.7478i	0.301064	−	0.707495i
$861$		0			0
$862$	−8.23422	+	5.69555i	−0.280459	+	0.193991i
$863$	2.78203	+	2.78203i	0.0947013	+	0.0947013i	0.752870	−	0.658169i	$-0.228669\pi$
$863$	2.78203	+	2.78203i	0.0947013	+	0.0947013i	−0.658169	+	0.752870i	$0.728669\pi$
$864$		0			0
$865$	−1.75076	+	41.8751i	−0.0595278	+	1.42380i
$866$	−29.8059	−	5.43206i	−1.01285	−	0.184589i
$867$		0			0
$868$	13.8922	−	6.28505i	0.471533	−	0.213328i
$869$	7.30014			0.247640
$870$		0			0
$871$			28.3895i			0.961943i
$872$	40.1145	−	10.0121i	1.35845	−	0.339052i
$873$		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	$-0.723635\pi$
$877$	3.46500	−	3.46500i	0.117005	−	0.117005i	0.763185	+	0.646180i	$0.223635\pi$
$878$	20.3487	+	29.4187i	0.686736	+	0.992834i
$879$		0			0
$880$	−0.701660	−	31.1289i	−0.0236529	−	1.04936i
$881$	−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	−0.416774	−	0.909010i	$-0.636839\pi$
$883$	14.6270	−	14.6270i	0.492237	−	0.492237i	0.909010	+	0.416774i	$0.136839\pi$
$884$	−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	$-0.794322\pi$
$887$	−5.84575	+	5.84575i	−0.196281	+	0.196281i	0.602123	+	0.798404i	$0.294322\pi$
$888$		0			0
$889$			66.1623i			2.21901i
$890$	−2.26317	−	0.510971i	−0.0758615	−	0.0171278i
$891$		0			0
$892$	19.6693	−	8.89868i	0.658578	−	0.297950i
$893$	−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
$898$	−26.1536	+	18.0903i	−0.872758	+	0.603681i
$899$			1.09743i			0.0366014i
$900$		0			0
$901$			6.40081i			0.213242i
$902$	13.7880	+	19.9337i	0.459089	+	0.663718i
$903$		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	0.303513	−	0.952827i	$-0.401840\pi$
$907$	−19.5550	−	19.5550i	−0.649314	−	0.649314i	−0.952827	+	0.303513i	$0.901840\pi$
$908$	−22.7898	+	10.3104i	−0.756305	+	0.342163i
$909$		0			0
$910$	−9.81478	+	43.4711i	−0.325357	+	1.44105i
$911$			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	$-0.0885074\pi$
$919$	58.3013			1.92318			0.961591	+	0.274485i	$0.0885074\pi$
$920$	4.16200	+	20.2399i	0.137217	+	0.667291i
$921$		0			0
$922$	−39.3009	+	27.1842i	−1.29431	+	0.895263i
$923$	−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
$928$	0.457848	−	3.93104i	0.0150296	−	0.129043i
$929$		−	5.05985i		−	0.166008i	−0.996549	−	0.0830041i	$-0.973549\pi$
$929$		−	5.05985i		−	0.166008i	0.996549	−	0.0830041i	$-0.0264515\pi$
$930$		0			0
$931$	10.6717			0.349750
$932$	−5.11033	−	11.2957i	−0.167394	−	0.370002i
$933$		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	0.524529	−	0.851393i	$-0.324242\pi$
$937$	−10.0055	−	10.0055i	−0.326864	−	0.326864i	−0.851393	+	0.524529i	$0.824242\pi$
$938$	−38.2828	−	55.3466i	−1.24998	−	1.80713i
$939$		0			0
$940$	−16.9780	+	39.8981i	−0.553762	+	1.30133i
$941$			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	0.982689	−	0.185263i	$-0.0593136\pi$
$947$	24.5395	+	24.5395i	0.797426	+	0.797426i	−0.185263	+	0.982689i	$0.559314\pi$
$948$		0			0
$949$	−26.9216			−0.873912
$950$	−2.26187	−	3.93620i	−0.0733848	−	0.127707i
$951$		0			0
$952$	31.1158	−	7.76613i	1.00847	−	0.251702i
$953$	0.855191	−	0.855191i	0.0277023	−	0.0277023i	−0.693120	−	0.720822i	$-0.743764\pi$
$953$	0.855191	−	0.855191i	0.0277023	−	0.0277023i	0.720822	+	0.693120i	$0.243764\pi$
$954$		0			0
$955$	−16.6735	+	15.3352i	−0.539541	+	0.496236i
$956$	−11.8528	+	31.4384i	−0.383348	+	1.01679i
$957$		0			0
$958$	−32.1190	−	46.4354i	−1.03772	−	1.50026i
$959$	−84.0595			−2.71442
$960$		0			0
$961$	28.5394			0.920626
$962$	17.5424	+	25.3615i	0.565589	+	0.817688i
$963$		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	$-0.635212\pi$
$967$	15.5174	−	15.5174i	0.499007	−	0.499007i	0.911129	+	0.412122i	$0.135212\pi$
$968$	−3.07018	+	0.766281i	−0.0986795	+	0.0246292i
$969$		0			0
$970$	33.2388	−	20.9942i	1.06723	−	0.674084i
$971$	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	0.945520	−	0.325563i	$-0.105554\pi$
$977$	19.3780	+	19.3780i	0.619957	+	0.619957i	−0.325563	+	0.945520i	$0.605554\pi$
$978$		0			0
$979$			2.55412i			0.0816302i
$980$	−27.7848	−	68.9478i	−0.887551	−	2.20246i
$981$		0			0
$982$	22.3551	+	32.3194i	0.713379	+	1.03135i
$983$	−14.1500	−	14.1500i	−0.451314	−	0.451314i	0.444476	−	0.895791i	$-0.353390\pi$
$983$	−14.1500	−	14.1500i	−0.451314	−	0.451314i	−0.895791	+	0.444476i	$0.853390\pi$
$984$		0			0
$985$	46.4082	+	1.94029i	1.47869	+	0.0618228i
$986$	−0.413847	+	2.27080i	−0.0131796	+	0.0723169i
$987$		0			0
$988$	−1.53469	−	3.39222i	−0.0488250	−	0.107921i
$989$	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	$0.744195\pi$
$992$	8.81392	+	1.02656i	0.279842	+	0.0325932i
$993$		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	$-0.855985\pi$
$997$	−14.5950	+	14.5950i	−0.462228	+	0.462228i	0.437157	+	0.899385i	$0.355985\pi$
$998$	22.8121	−	15.7790i	0.722104	−	0.499474i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.3	✓	24	15.8	even	4
120.2.v.a.43.5	yes	24	120.83	odd	4
120.2.v.a.67.3	yes	24	24.11	even	2
120.2.v.a.67.5	yes	24	3.2	odd	2
360.2.w.e.163.8		24	40.3	even	4	inner
360.2.w.e.163.10		24	5.3	odd	4	inner
360.2.w.e.307.8		24	1.1	even	1	trivial
360.2.w.e.307.10		24	8.3	odd	2	inner
480.2.bh.a.367.8		24	24.5	odd	2
480.2.bh.a.367.11		24	12.11	even	2
480.2.bh.a.463.8		24	60.23	odd	4
480.2.bh.a.463.11		24	120.53	even	4
600.2.v.b.43.8		24	120.107	odd	4
600.2.v.b.43.10		24	15.2	even	4
600.2.v.b.307.8		24	15.14	odd	2
600.2.v.b.307.10		24	120.59	even	2
1440.2.bi.e.847.3		24	4.3	odd	2
1440.2.bi.e.847.10		24	8.5	even	2
1440.2.bi.e.1423.3		24	40.13	odd	4
1440.2.bi.e.1423.10		24	20.3	even	4
2400.2.bh.b.943.5		24	120.77	even	4
2400.2.bh.b.943.6		24	60.47	odd	4
2400.2.bh.b.1807.5		24	60.59	even	2
2400.2.bh.b.1807.6		24	120.29	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.804501 + 1.16309i) q^{2} +(-0.705556 + 1.87141i) q^{4} +(-1.51371 - 1.64581i) q^{5} +(-3.43671 + 3.43671i) q^{7} +(-2.74424 + 0.684930i) q^{8} +O(q^{10})\)	\(q+(0.804501 + 1.16309i) q^{2} +(-0.705556 + 1.87141i) q^{4} +(-1.51371 - 1.64581i) q^{5} +(-3.43671 + 3.43671i) q^{7} +(-2.74424 + 0.684930i) q^{8} +(0.696440 - 3.08463i) q^{10} -3.48120 q^{11} +(2.05033 + 2.05033i) q^{13} +(-6.76204 - 1.23237i) q^{14} +(-3.00438 - 2.64077i) q^{16} +(1.64963 + 1.64963i) q^{17} +0.642023i q^{19} +(4.14799 - 1.67157i) q^{20} +(-2.80063 - 4.04895i) q^{22} +(2.31024 + 2.31024i) q^{23} +(-0.417363 + 4.98255i) q^{25} +(-0.735225 + 4.03421i) q^{26} +(-4.00672 - 8.85630i) q^{28} +0.699613 q^{29} +1.56863i q^{31} +(0.654430 - 5.61887i) q^{32} +(-0.591537 + 3.24579i) q^{34} +(10.8583 + 0.453979i) q^{35} +(5.31751 - 5.31751i) q^{37} +(-0.746731 + 0.516509i) q^{38} +(5.28125 + 3.47971i) q^{40} -4.92316 q^{41} +(3.56519 - 3.56519i) q^{43} +(2.45618 - 6.51477i) q^{44} +(-0.828427 + 4.54561i) q^{46} +(-6.85586 + 6.85586i) q^{47} -16.6220i q^{49} +(-6.13092 + 3.52304i) q^{50} +(-5.28364 + 2.39039i) q^{52} +(1.94008 + 1.94008i) q^{53} +(5.26953 + 5.72939i) q^{55} +(7.07726 - 11.7851i) q^{56} +(0.562839 + 0.813713i) q^{58} -2.74121i q^{59} +5.20943i q^{61} +(-1.82446 + 1.26196i) q^{62} +(7.06174 - 3.75923i) q^{64} +(0.270842 - 6.47805i) q^{65} +(6.92316 + 6.92316i) q^{67} +(-4.25104 + 1.92323i) q^{68} +(8.20753 + 12.9945i) q^{70} +11.1548i q^{71} +(-6.56519 + 6.56519i) q^{73} +(10.4627 + 1.90680i) q^{74} +(-1.20149 - 0.452983i) q^{76} +(11.9639 - 11.9639i) q^{77} -2.09702 q^{79} +(0.201557 + 8.94200i) q^{80} +(-3.96069 - 5.72608i) q^{82} +(-6.64648 + 6.64648i) q^{83} +(0.217911 - 5.21202i) q^{85} +(7.01483 + 1.27844i) q^{86} +(9.55327 - 2.38438i) q^{88} -0.733690i q^{89} -14.0928 q^{91} +(-5.95343 + 2.69342i) q^{92} +(-13.4895 - 2.45843i) q^{94} +(1.05665 - 0.971837i) q^{95} +(8.79083 + 8.79083i) q^{97} +(19.3328 - 13.3724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 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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