LMFDB - Embedded newform 460.2.x.a.333.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			333.6
Character	$\chi$	$=$	460.333
Dual form			460.2.x.a.297.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.412482 + 0.308781i) q^{3} +(-1.14759 + 1.91912i) q^{5} +(0.218363 - 3.05312i) q^{7} +(-0.770401 + 2.62375i) q^{9} +O(q^{10})$	\(q+(-0.412482 + 0.308781i) q^{3} +(-1.14759 + 1.91912i) q^{5} +(0.218363 - 3.05312i) q^{7} +(-0.770401 + 2.62375i) q^{9} +(-1.30741 + 2.03437i) q^{11} +(-0.155000 + 0.0110858i) q^{13} +(-0.119228 - 1.14596i) q^{15} +(-1.84552 + 4.94803i) q^{17} +(-0.917639 + 2.00935i) q^{19} +(0.852673 + 1.32678i) q^{21} +(-4.48053 + 1.71022i) q^{23} +(-2.36608 - 4.40473i) q^{25} +(-1.03257 - 2.76844i) q^{27} +(-3.67210 + 1.67699i) q^{29} +(0.161302 + 1.12188i) q^{31} +(-0.0888899 - 1.24284i) q^{33} +(5.60873 + 3.92279i) q^{35} +(0.622782 + 1.14054i) q^{37} +(0.0605116 - 0.0524336i) q^{39} +(-11.6377 + 3.41715i) q^{41} +(3.54563 + 4.73641i) q^{43} +(-4.15119 - 4.48948i) q^{45} +(6.85700 - 6.85700i) q^{47} +(-2.34511 - 0.337176i) q^{49} +(-0.766610 - 2.61083i) q^{51} +(10.4809 + 0.749612i) q^{53} +(-2.40384 - 4.84370i) q^{55} +(-0.241938 - 1.11217i) q^{57} +(7.94805 + 6.88702i) q^{59} +(-3.34965 + 0.481607i) q^{61} +(7.84238 + 2.92506i) q^{63} +(0.156601 - 0.310186i) q^{65} +(4.21490 + 0.916895i) q^{67} +(1.32006 - 2.08894i) q^{69} +(-5.76111 + 3.70244i) q^{71} +(4.68224 - 1.74639i) q^{73} +(2.33606 + 1.08628i) q^{75} +(5.92568 + 4.43591i) q^{77} +(8.94885 - 10.3275i) q^{79} +(-5.62050 - 3.61207i) q^{81} +(2.49105 - 1.36022i) q^{83} +(-7.37798 - 9.22008i) q^{85} +(0.996855 - 1.82560i) q^{87} +(0.438889 - 3.05254i) q^{89} +0.475654i q^{91} +(-0.412948 - 0.412948i) q^{93} +(-2.80312 - 4.06697i) q^{95} +(-14.4425 - 7.88622i) q^{97} +(-4.33043 - 4.99759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.412482	+	0.308781i	−0.238147	+	0.178275i	−0.711685	−	0.702499i	$-0.752068\pi$
$3$	−0.412482	+	0.308781i	−0.238147	+	0.178275i	0.473538	+	0.880773i	$0.342977\pi$
$4$		0			0
$5$	−1.14759	+	1.91912i	−0.513218	+	0.858259i
$5$	−1.14759	+	1.91912i	−0.513218	+	0.858259i
$6$		0			0
$7$	0.218363	−	3.05312i	0.0825336	−	1.15397i	−0.772366	−	0.635178i	$-0.780927\pi$
$7$	0.218363	−	3.05312i	0.0825336	−	1.15397i	0.854900	−	0.518793i	$-0.173619\pi$
$8$		0			0
$9$	−0.770401	+	2.62375i	−0.256800	+	0.874582i
$10$		0			0
$11$	−1.30741	+	2.03437i	−0.394199	+	0.613385i	−0.980456	−	0.196740i	$-0.936964\pi$
$11$	−1.30741	+	2.03437i	−0.394199	+	0.613385i	0.586257	+	0.810125i	$0.300601\pi$
$12$		0			0
$13$	−0.155000	+	0.0110858i	−0.0429892	+	0.00307465i	−0.0928172	−	0.995683i	$-0.529587\pi$
$13$	−0.155000	+	0.0110858i	−0.0429892	+	0.00307465i	0.0498280	+	0.998758i	$0.484133\pi$
$14$		0			0
$15$	−0.119228	−	1.14596i	−0.0307845	−	0.295885i
$16$		0			0
$17$	−1.84552	+	4.94803i	−0.447604	+	1.20007i	0.495803	+	0.868435i	$0.334874\pi$
$17$	−1.84552	+	4.94803i	−0.447604	+	1.20007i	−0.943407	+	0.331637i	$0.892399\pi$
$18$		0			0
$19$	−0.917639	+	2.00935i	−0.210521	+	0.460976i	−0.985207	−	0.171370i	$-0.945181\pi$
$19$	−0.917639	+	2.00935i	−0.210521	+	0.460976i	0.774686	+	0.632346i	$0.217908\pi$
$20$		0			0
$21$	0.852673	+	1.32678i	0.186068	+	0.289528i
$22$		0			0
$23$	−4.48053	+	1.71022i	−0.934255	+	0.356606i
$23$	−4.48053	+	1.71022i	−0.934255	+	0.356606i
$24$		0			0
$25$	−2.36608	−	4.40473i	−0.473215	−	0.880947i
$26$		0			0
$27$	−1.03257	−	2.76844i	−0.198719	−	0.532786i
$28$		0			0
$29$	−3.67210	+	1.67699i	−0.681892	+	0.311410i	−0.726077	−	0.687614i	$-0.758658\pi$
$29$	−3.67210	+	1.67699i	−0.681892	+	0.311410i	0.0441845	+	0.999023i	$0.485931\pi$
$30$		0			0
$31$	0.161302	+	1.12188i	0.0289706	+	0.201495i	0.999166	−	0.0408282i	$-0.0129996\pi$
$31$	0.161302	+	1.12188i	0.0289706	+	0.201495i	−0.970196	+	0.242323i	$0.922091\pi$
$32$		0			0
$33$	−0.0888899	−	1.24284i	−0.0154737	−	0.216351i
$34$		0			0
$35$	5.60873	+	3.92279i	0.948048	+	0.663073i
$36$		0			0
$37$	0.622782	+	1.14054i	0.102385	+	0.187504i	0.923850	−	0.382755i	$-0.125025\pi$
$37$	0.622782	+	1.14054i	0.102385	+	0.187504i	−0.821465	+	0.570259i	$0.806843\pi$
$38$		0			0
$39$	0.0605116	−	0.0524336i	0.00968961	−	0.00839610i
$40$		0			0
$41$	−11.6377	+	3.41715i	−1.81751	+	0.533669i	−0.999157	−	0.0410499i	$-0.986930\pi$
$41$	−11.6377	+	3.41715i	−1.81751	+	0.533669i	−0.818351	+	0.574718i	$0.805112\pi$
$42$		0			0
$43$	3.54563	+	4.73641i	0.540704	+	0.722296i	0.984802	−	0.173682i	$-0.0555666\pi$
$43$	3.54563	+	4.73641i	0.540704	+	0.722296i	−0.444098	+	0.895978i	$0.646476\pi$
$44$		0			0
$45$	−4.15119	−	4.48948i	−0.618823	−	0.669252i
$46$		0			0
$47$	6.85700	−	6.85700i	1.00020	−	1.00020i	0.000196434	−	1.00000i	$-0.499937\pi$
$47$	6.85700	−	6.85700i	1.00020	−	1.00020i	1.00000		0.000196434i	$-6.25269e-5\pi$
$48$		0			0
$49$	−2.34511	−	0.337176i	−0.335015	−	0.0481680i
$50$		0			0
$51$	−0.766610	−	2.61083i	−0.107347	−	0.365590i
$52$		0			0
$53$	10.4809	+	0.749612i	1.43967	+	0.102967i	0.769218	−	0.638987i	$-0.220646\pi$
$53$	10.4809	+	0.749612i	1.43967	+	0.102967i	0.670451	+	0.741954i	$0.266101\pi$
$54$		0			0
$55$	−2.40384	−	4.84370i	−0.324133	−	0.653124i
$56$		0			0
$57$	−0.241938	−	1.11217i	−0.0320454	−	0.147311i
$58$		0			0
$59$	7.94805	+	6.88702i	1.03475	+	0.896614i	0.994724	−	0.102585i	$-0.0327113\pi$
$59$	7.94805	+	6.88702i	1.03475	+	0.896614i	0.0400234	+	0.999199i	$0.487257\pi$
$60$		0			0
$61$	−3.34965	+	0.481607i	−0.428878	+	0.0616634i	−0.353374	−	0.935482i	$-0.614966\pi$
$61$	−3.34965	+	0.481607i	−0.428878	+	0.0616634i	−0.0755043	+	0.997145i	$0.524057\pi$
$62$		0			0
$63$	7.84238	+	2.92506i	0.988047	+	0.368523i
$64$		0			0
$65$	0.156601	−	0.310186i	0.0194240	−	0.0384738i
$66$		0			0
$67$	4.21490	+	0.916895i	0.514932	+	0.112017i	0.462520	−	0.886609i	$-0.346945\pi$
$67$	4.21490	+	0.916895i	0.514932	+	0.112017i	0.0524121	+	0.998626i	$0.483309\pi$
$68$		0			0
$69$	1.32006	−	2.08894i	0.158916	−	0.251478i
$70$		0			0
$71$	−5.76111	+	3.70244i	−0.683718	+	0.439399i	−0.835847	−	0.548962i	$-0.815023\pi$
$71$	−5.76111	+	3.70244i	−0.683718	+	0.439399i	0.152130	+	0.988361i	$0.451387\pi$
$72$		0			0
$73$	4.68224	−	1.74639i	0.548015	−	0.204399i	−0.0601787	−	0.998188i	$-0.519167\pi$
$73$	4.68224	−	1.74639i	0.548015	−	0.204399i	0.608194	+	0.793789i	$0.291894\pi$
$74$		0			0
$75$	2.33606	+	1.08628i	0.269745	+	0.125432i
$76$		0			0
$77$	5.92568	+	4.43591i	0.675294	+	0.505519i
$78$		0			0
$79$	8.94885	−	10.3275i	1.00682	−	1.16194i	0.0200558	−	0.999799i	$-0.493616\pi$
$79$	8.94885	−	10.3275i	1.00682	−	1.16194i	0.986768	−	0.162138i	$-0.0518389\pi$
$80$		0			0
$81$	−5.62050	−	3.61207i	−0.624500	−	0.401342i
$82$		0			0
$83$	2.49105	−	1.36022i	0.273428	−	0.149303i	−0.336685	−	0.941617i	$-0.609306\pi$
$83$	2.49105	−	1.36022i	0.273428	−	0.149303i	0.610113	+	0.792314i	$0.291124\pi$
$84$		0			0
$85$	−7.37798	−	9.22008i	−0.800254	−	1.00006i
$86$		0			0
$87$	0.996855	−	1.82560i	0.106874	−	0.195725i
$88$		0			0
$89$	0.438889	−	3.05254i	0.0465222	−	0.323569i	−0.953249	−	0.302185i	$-0.902284\pi$
$89$	0.438889	−	3.05254i	0.0465222	−	0.323569i	0.999771	−	0.0213834i	$-0.00680708\pi$
$90$		0			0
$91$			0.475654i			0.0498620i
$92$		0			0
$93$	−0.412948	−	0.412948i	−0.0428207	−	0.0428207i
$94$		0			0
$95$	−2.80312	−	4.06697i	−0.287594	−	0.417262i
$96$		0			0
$97$	−14.4425	−	7.88622i	−1.46642	−	0.800724i	−0.469789	−	0.882779i	$-0.655670\pi$
$97$	−14.4425	−	7.88622i	−1.46642	−	0.800724i	−0.996628	+	0.0820549i	$0.973852\pi$
$98$		0			0
$99$	−4.33043	−	4.99759i	−0.435225	−	0.502276i
$100$		0			0
$101$	−2.53394	−	0.744031i	−0.252136	−	0.0740339i	0.153222	−	0.988192i	$-0.451035\pi$
$101$	−2.53394	−	0.744031i	−0.252136	−	0.0740339i	−0.405358	+	0.914158i	$0.632853\pi$
$102$		0			0
$103$	2.02418	−	0.440333i	0.199448	−	0.0433873i	−0.111731	−	0.993738i	$-0.535640\pi$
$103$	2.02418	−	0.440333i	0.199448	−	0.0433873i	0.311179	+	0.950351i	$0.399276\pi$
$104$		0			0
$105$	−3.52478	+	0.113781i	−0.343984	+	0.0111039i
$106$		0			0
$107$	5.67950	−	7.58693i	0.549058	−	0.733456i	−0.437072	−	0.899426i	$-0.643985\pi$
$107$	5.67950	−	7.58693i	0.549058	−	0.733456i	0.986131	+	0.165970i	$0.0530756\pi$
$108$		0			0
$109$	7.84971	+	17.1885i	0.751866	+	1.64636i	0.762983	+	0.646419i	$0.223734\pi$
$109$	7.84971	+	17.1885i	0.751866	+	1.64636i	−0.0111168	+	0.999938i	$0.503539\pi$
$110$		0			0
$111$	−0.609063	−	0.278150i	−0.0578097	−	0.0264008i
$112$		0			0
$113$	2.05592	−	9.45091i	0.193405	−	0.889067i	−0.773474	−	0.633829i	$-0.781482\pi$
$113$	2.05592	−	9.45091i	0.193405	−	0.889067i	0.966878	−	0.255238i	$-0.0821539\pi$
$114$		0			0
$115$	1.85968	−	10.5613i	0.173416	−	0.984849i
$116$		0			0
$117$	0.0903257	−	0.415220i	0.00835061	−	0.0383871i
$118$		0			0
$119$	14.7039	+	6.71506i	1.34791	+	0.615568i
$120$		0			0
$121$	2.14023	+	4.68645i	0.194566	+	0.426041i
$122$		0			0
$123$	3.74521	−	5.00302i	0.337694	−	0.451107i
$124$		0			0
$125$	11.1685	+	0.514030i	0.998943	+	0.0459763i
$126$		0			0
$127$	−10.0978	+	2.19664i	−0.896034	+	0.194920i	−0.636923	−	0.770927i	$-0.719793\pi$
$127$	−10.0978	+	2.19664i	−0.896034	+	0.194920i	−0.259111	+	0.965848i	$0.583430\pi$
$128$		0			0
$129$	−2.92502	−	0.858864i	−0.257534	−	0.0756188i
$130$		0			0
$131$	−2.62307	−	3.02718i	−0.229179	−	0.264486i	0.629500	−	0.777000i	$-0.283260\pi$
$131$	−2.62307	−	3.02718i	−0.229179	−	0.264486i	−0.858679	+	0.512514i	$0.828714\pi$
$132$		0			0
$133$	5.93440	+	3.24043i	0.514578	+	0.280981i
$134$		0			0
$135$	6.49795	+	1.19539i	0.559254	+	0.102883i
$136$		0			0
$137$	7.39047	+	7.39047i	0.631411	+	0.631411i	0.948422	−	0.317011i	$-0.102679\pi$
$137$	7.39047	+	7.39047i	0.631411	+	0.631411i	−0.317011	+	0.948422i	$0.602679\pi$
$138$		0			0
$139$			6.96785i			0.591005i	0.955342	+	0.295503i	$0.0954871\pi$
$139$			6.96785i			0.591005i	−0.955342	+	0.295503i	$0.904513\pi$
$140$		0			0
$141$	−0.711084	+	4.94570i	−0.0598841	+	0.416503i
$142$		0			0
$143$	0.180095	−	0.329820i	0.0150603	−	0.0275809i
$144$		0			0
$145$	0.995708	−	8.97172i	0.0826890	−	0.745061i
$146$		0			0
$147$	1.07143	−	0.585045i	0.0883700	−	0.0482537i
$148$		0			0
$149$	17.0245	+	10.9410i	1.39470	+	0.896319i	0.999749	−	0.0223842i	$-0.00712571\pi$
$149$	17.0245	+	10.9410i	1.39470	+	0.896319i	0.394950	+	0.918703i	$0.370762\pi$
$150$		0			0
$151$	5.56077	−	6.41747i	0.452529	−	0.522246i	−0.482941	−	0.875653i	$-0.660431\pi$
$151$	5.56077	−	6.41747i	0.452529	−	0.522246i	0.935470	+	0.353407i	$0.114977\pi$
$152$		0			0
$153$	−11.5606	−	8.65413i	−0.934617	−	0.699645i
$154$		0			0
$155$	−2.33813	−	0.977897i	−0.187803	−	0.0785466i
$156$		0			0
$157$	2.87735	−	1.07320i	0.229638	−	0.0856504i	−0.232011	−	0.972713i	$-0.574531\pi$
$157$	2.87735	−	1.07320i	0.229638	−	0.0856504i	0.461649	+	0.887063i	$0.347258\pi$
$158$		0			0
$159$	−4.55467	+	2.92711i	−0.361209	+	0.232135i
$160$		0			0
$161$	4.24313	+	14.0530i	0.334406	+	1.10753i
$162$		0			0
$163$	−6.36626	−	1.38489i	−0.498644	−	0.108473i	−0.0437923	−	0.999041i	$-0.513944\pi$
$163$	−6.36626	−	1.38489i	−0.498644	−	0.108473i	−0.454851	+	0.890567i	$0.650308\pi$
$164$		0			0
$165$	2.48718	+	1.25568i	0.193627	+	0.0977548i
$166$		0			0
$167$	−0.285532	−	0.106498i	−0.0220951	−	0.00824105i	0.338392	−	0.941005i	$-0.390117\pi$
$167$	−0.285532	−	0.106498i	−0.0220951	−	0.00824105i	−0.360487	+	0.932764i	$0.617390\pi$
$168$		0			0
$169$	−12.8438	+	1.84666i	−0.987983	+	0.142050i
$170$		0			0
$171$	−4.56507	−	3.95566i	−0.349100	−	0.302497i
$172$		0			0
$173$	2.65518	+	12.2056i	0.201869	+	0.927978i	0.960894	+	0.276916i	$0.0893125\pi$
$173$	2.65518	+	12.2056i	0.201869	+	0.927978i	−0.759025	+	0.651062i	$0.774324\pi$
$174$		0			0
$175$	−13.9648	+	6.26208i	−1.05564	+	0.473369i
$176$		0			0
$177$	−5.40501	−	0.386574i	−0.406265	−	0.0290567i
$178$		0			0
$179$	−6.26707	−	21.3437i	−0.468423	−	1.59530i	−0.767485	−	0.641067i	$-0.778492\pi$
$179$	−6.26707	−	21.3437i	−0.468423	−	1.59530i	0.299062	−	0.954234i	$-0.403326\pi$
$180$		0			0
$181$	−6.64640	−	0.955608i	−0.494023	−	0.0710298i	−0.109199	−	0.994020i	$-0.534829\pi$
$181$	−6.64640	−	0.955608i	−0.494023	−	0.0710298i	−0.384824	+	0.922990i	$0.625738\pi$
$182$		0			0
$183$	1.23296	−	1.23296i	0.0911431	−	0.0911431i
$184$		0			0
$185$	−2.90354	−	0.113676i	−0.213472	−	0.00835760i
$186$		0			0
$187$	−7.65326	−	10.2236i	−0.559662	−	0.747620i
$188$		0			0
$189$	−8.67785	+	2.54805i	−0.631220	+	0.185343i
$190$		0			0
$191$	−7.98374	+	6.91795i	−0.577683	+	0.500565i	−0.893987	−	0.448092i	$-0.852104\pi$
$191$	−7.98374	+	6.91795i	−0.577683	+	0.500565i	0.316304	+	0.948658i	$0.397558\pi$
$192$		0			0
$193$	1.28367	+	2.35086i	0.0924003	+	0.169219i	0.919791	−	0.392408i	$-0.128358\pi$
$193$	1.28367	+	2.35086i	0.0924003	+	0.169219i	−0.827391	+	0.561626i	$0.810176\pi$
$194$		0			0
$195$	0.0311841	+	0.176302i	0.00223314	+	0.0126252i
$196$		0			0
$197$	0.200486	+	2.80316i	0.0142840	+	0.199717i	0.999583	+	0.0288778i	$0.00919335\pi$
$197$	0.200486	+	2.80316i	0.0142840	+	0.199717i	−0.985299	+	0.170839i	$0.945352\pi$
$198$		0			0
$199$	2.96058	+	20.5913i	0.209870	+	1.45968i	0.773577	+	0.633702i	$0.218465\pi$
$199$	2.96058	+	20.5913i	0.209870	+	1.45968i	−0.563708	+	0.825974i	$0.690626\pi$
$200$		0			0
$201$	−2.02169	+	0.923276i	−0.142599	+	0.0651228i
$202$		0			0
$203$	4.31821	+	11.5776i	0.303079	+	0.812586i
$204$		0			0
$205$	6.79741	−	26.2557i	0.474752	−	1.83378i
$206$		0			0
$207$	−1.03538	−	13.0733i	−0.0719642	−	0.908659i
$208$		0			0
$209$	−2.88802	−	4.49385i	−0.199769	−	0.310846i
$210$		0			0
$211$	−2.77784	+	6.08263i	−0.191235	+	0.418745i	−0.980825	−	0.194888i	$-0.937566\pi$
$211$	−2.77784	+	6.08263i	−0.191235	+	0.418745i	0.789591	+	0.613634i	$0.210293\pi$
$212$		0			0
$213$	1.23311	−	3.30611i	0.0844916	−	0.226531i
$214$		0			0
$215$	−13.1587	+	1.36906i	−0.897415	+	0.0933688i
$216$		0			0
$217$	3.46045	−	0.247496i	0.234911	−	0.0168011i
$218$		0			0
$219$	−1.39209	+	2.16614i	−0.0940690	+	0.146374i
$220$		0			0
$221$	0.231202	−	0.787402i	0.0155523	−	0.0529664i
$222$		0			0
$223$	−1.57337	+	21.9986i	−0.105361	+	1.47314i	0.619910	+	0.784673i	$0.287169\pi$
$223$	−1.57337	+	21.9986i	−0.105361	+	1.47314i	−0.725270	+	0.688464i	$0.758285\pi$
$224$		0			0
$225$	13.3797	−	2.81457i	0.891982	−	0.187638i
$226$		0			0
$227$	−12.9388	+	9.68587i	−0.858779	+	0.642874i	−0.935168	−	0.354204i	$-0.884752\pi$
$227$	−12.9388	+	9.68587i	−0.858779	+	0.642874i	0.0763890	+	0.997078i	$0.475661\pi$
$228$		0			0
$229$	−18.2967			−1.20908			−0.604539	−	0.796576i	$-0.706642\pi$
$229$	−18.2967			−1.20908			−0.604539	+	0.796576i	$0.706642\pi$
$230$		0			0
$231$	−3.81396			−0.250940
$232$		0			0
$233$	−19.0227	+	14.2402i	−1.24622	+	0.932908i	−0.999347	−	0.0361399i	$-0.988494\pi$
$233$	−19.0227	+	14.2402i	−1.24622	+	0.932908i	−0.246873	+	0.969048i	$0.579403\pi$
$234$		0			0
$235$	5.29042	+	21.0285i	0.345109	+	1.37175i
$236$		0			0
$237$	−0.502306	+	7.02315i	−0.0326283	+	0.456203i
$238$		0			0
$239$	6.27379	−	21.3666i	0.405818	−	1.38209i	−0.462737	−	0.886496i	$-0.653133\pi$
$239$	6.27379	−	21.3666i	0.405818	−	1.38209i	0.868555	−	0.495593i	$-0.165049\pi$
$240$		0			0
$241$	−0.173684	+	0.270258i	−0.0111880	+	0.0174089i	−0.846802	−	0.531907i	$-0.821475\pi$
$241$	−0.173684	+	0.270258i	−0.0111880	+	0.0174089i	0.835614	+	0.549316i	$0.185112\pi$
$242$		0			0
$243$	12.2753	−	0.877948i	0.787462	−	0.0563204i
$244$		0			0
$245$	3.33830	−	4.11362i	0.213276	−	0.262809i
$246$		0			0
$247$	0.119959	−	0.321621i	0.00763278	−	0.0204643i
$248$		0			0
$249$	−0.607507	+	1.33025i	−0.0384992	+	0.0843014i
$250$		0			0
$251$	13.6380	+	21.2212i	0.860824	+	1.33947i	0.939493	+	0.342568i	$0.111297\pi$
$251$	13.6380	+	21.2212i	0.860824	+	1.33947i	−0.0786689	+	0.996901i	$0.525067\pi$
$252$		0			0
$253$	2.37866	−	11.3510i	0.149545	−	0.713631i
$254$		0			0
$255$	5.89027	+	1.52495i	0.368863	+	0.0954958i
$256$		0			0
$257$	3.76580	+	10.0965i	0.234904	+	0.629803i	0.999899	−	0.0142340i	$-0.00453098\pi$
$257$	3.76580	+	10.0965i	0.234904	+	0.629803i	−0.764994	+	0.644037i	$0.777258\pi$
$258$		0			0
$259$	3.61820	−	1.65238i	0.224824	−	0.102674i
$260$		0			0
$261$	−1.57101	−	10.9266i	−0.0972431	−	0.676341i
$262$		0			0
$263$	0.107360	+	1.50110i	0.00662013	+	0.0925615i	0.999688	−	0.0249816i	$-0.00795271\pi$
$263$	0.107360	+	1.50110i	0.00662013	+	0.0925615i	−0.993068	+	0.117543i	$0.962498\pi$
$264$		0			0
$265$	−13.4664	+	19.2540i	−0.827236	+	1.18276i
$266$		0			0
$267$	0.761531	+	1.39464i	0.0466050	+	0.0853506i
$268$		0			0
$269$	−11.7173	+	10.1531i	−0.714419	+	0.619047i	−0.934304	−	0.356478i	$-0.883977\pi$
$269$	−11.7173	+	10.1531i	−0.714419	+	0.619047i	0.219885	+	0.975526i	$0.429432\pi$
$270$		0			0
$271$	15.0825	−	4.42861i	0.916195	−	0.269019i	0.210549	−	0.977583i	$-0.432475\pi$
$271$	15.0825	−	4.42861i	0.916195	−	0.269019i	0.705646	+	0.708564i	$0.250657\pi$
$272$		0			0
$273$	−0.146873	−	0.196199i	−0.00888913	−	0.0118745i
$274$		0			0
$275$	12.0543	+	0.945317i	0.726900	+	0.0570048i
$276$		0			0
$277$	20.6153	−	20.6153i	1.23865	−	1.23865i	0.278098	−	0.960553i	$-0.410296\pi$
$277$	20.6153	−	20.6153i	1.23865	−	1.23865i	0.960553	−	0.278098i	$-0.0897041\pi$
$278$		0			0
$279$	−3.06779	−	0.441081i	−0.183664	−	0.0264068i
$280$		0			0
$281$	4.30282	+	14.6541i	0.256685	+	0.874188i	0.982494	+	0.186292i	$0.0596472\pi$
$281$	4.30282	+	14.6541i	0.256685	+	0.874188i	−0.725810	+	0.687896i	$0.758535\pi$
$282$		0			0
$283$	−18.6719	−	1.33544i	−1.10993	−	0.0793836i	−0.495686	−	0.868502i	$-0.665083\pi$
$283$	−18.6719	−	1.33544i	−1.10993	−	0.0793836i	−0.614242	+	0.789118i	$0.710538\pi$
$284$		0			0
$285$	2.41204	+	0.812006i	0.142877	+	0.0480991i
$286$		0			0
$287$	7.89170	+	36.2776i	0.465832	+	2.14140i
$288$		0			0
$289$	−8.22927	−	7.13071i	−0.484075	−	0.419453i
$290$		0			0
$291$	8.39240	−	1.20664i	0.491971	−	0.0707348i
$292$		0			0
$293$	11.5224	+	4.29764i	0.673147	+	0.251071i	0.662711	−	0.748875i	$-0.269406\pi$
$293$	11.5224	+	4.29764i	0.673147	+	0.251071i	0.0104352	+	0.999946i	$0.496678\pi$
$294$		0			0
$295$	−22.3381	+	7.34982i	−1.30058	+	0.427923i
$296$		0			0
$297$	6.98201	+	1.51884i	0.405138	+	0.0881323i
$298$		0			0
$299$	0.675522	−	0.314754i	0.0390664	−	0.0182027i
$300$		0			0
$301$	15.2351	−	9.79098i	0.878135	−	0.564343i
$302$		0			0
$303$	1.27495	−	0.475531i	0.0732438	−	0.0273185i
$304$		0			0
$305$	2.91976	−	6.98108i	0.167185	−	0.399735i
$306$		0			0
$307$	−26.4023	−	19.7645i	−1.50686	−	1.12802i	−0.955979	−	0.293435i	$-0.905202\pi$
$307$	−26.4023	−	19.7645i	−1.50686	−	1.12802i	−0.550879	−	0.834585i	$-0.685707\pi$
$308$		0			0
$309$	−0.698971	+	0.806656i	−0.0397631	+	0.0458891i
$310$		0			0
$311$	−25.4823	−	16.3765i	−1.44497	−	0.928626i	−0.999444	−	0.0333565i	$-0.989380\pi$
$311$	−25.4823	−	16.3765i	−1.44497	−	0.928626i	−0.445526	−	0.895269i	$-0.646983\pi$
$312$		0			0
$313$	−4.16512	+	2.27433i	−0.235426	+	0.128553i	−0.592632	−	0.805473i	$-0.701911\pi$
$313$	−4.16512	+	2.27433i	−0.235426	+	0.128553i	0.357206	+	0.934026i	$0.383729\pi$
$314$		0			0
$315$	−14.6134	+	11.6937i	−0.823371	+	0.658868i
$316$		0			0
$317$	3.05280	−	5.59078i	0.171462	−	0.314010i	−0.777791	−	0.628523i	$-0.783660\pi$
$317$	3.05280	−	5.59078i	0.171462	−	0.314010i	0.949253	+	0.314514i	$0.101841\pi$
$318$		0			0
$319$	1.38932	−	9.66292i	0.0777869	−	0.541020i
$320$		0			0
$321$			4.88320i			0.272553i
$322$		0			0
$323$	−8.24879	−	8.24879i	−0.458975	−	0.458975i
$324$		0			0
$325$	0.415571	+	0.656503i	0.0230517	+	0.0364162i
$326$		0			0
$327$	−8.54533	−	4.66611i	−0.472558	−	0.258036i
$328$		0			0
$329$	−19.4379	−	22.4326i	−1.07165	−	1.23675i
$330$		0			0
$331$	−8.29012	−	2.43420i	−0.455666	−	0.133796i	0.0458417	−	0.998949i	$-0.485403\pi$
$331$	−8.29012	−	2.43420i	−0.455666	−	0.133796i	−0.501508	+	0.865153i	$0.667221\pi$
$332$		0			0
$333$	−3.47228	+	0.755348i	−0.190280	+	0.0413928i
$334$		0			0
$335$	−6.59661	+	7.03670i	−0.360411	+	0.384456i
$336$		0			0
$337$	5.67236	−	7.57738i	0.308993	−	0.412766i	−0.618984	−	0.785403i	$-0.712455\pi$
$337$	5.67236	−	7.57738i	0.308993	−	0.412766i	0.927977	+	0.372637i	$0.121546\pi$
$338$		0			0
$339$	2.07023	+	4.53316i	0.112439	+	0.246208i
$340$		0			0
$341$	−2.49320	−	1.13861i	−0.135014	−	0.0616589i
$342$		0			0
$343$	3.01299	−	13.8505i	0.162686	−	0.747857i
$344$		0			0
$345$	2.49405	+	4.93059i	0.134275	+	0.265454i
$346$		0			0
$347$	0.772593	−	3.55155i	0.0414750	−	0.190657i	−0.951748	−	0.306880i	$-0.900715\pi$
$347$	0.772593	−	3.55155i	0.0414750	−	0.190657i	0.993223	+	0.116223i	$0.0370786\pi$
$348$		0			0
$349$	25.7406	+	11.7554i	1.37786	+	0.629250i	0.960190	−	0.279347i	$-0.0901179\pi$
$349$	25.7406	+	11.7554i	1.37786	+	0.629250i	0.417675	+	0.908597i	$0.362845\pi$
$350$		0			0
$351$	0.190739	+	0.417660i	0.0101809	+	0.0222930i
$352$		0			0
$353$	−11.1098	+	14.8410i	−0.591316	+	0.789906i	−0.991990	−	0.126314i	$-0.959685\pi$
$353$	−11.1098	+	14.8410i	−0.591316	+	0.789906i	0.400674	+	0.916221i	$0.368776\pi$
$354$		0			0
$355$	−0.494055	−	15.3052i	−0.0262217	−	0.812314i
$356$		0			0
$357$	−8.13859	+	1.77044i	−0.430740	+	0.0937017i
$358$		0			0
$359$	18.1276	+	5.32274i	0.956737	+	0.280923i	0.722589	−	0.691278i	$-0.242952\pi$
$359$	18.1276	+	5.32274i	0.956737	+	0.280923i	0.234148	+	0.972201i	$0.424770\pi$
$360$		0			0
$361$	9.24693	+	10.6715i	0.486681	+	0.561659i
$362$		0			0
$363$	−2.32989	−	1.27222i	−0.122288	−	0.0667741i
$364$		0			0
$365$	−2.02176	+	10.9899i	−0.105824	+	0.575240i
$366$		0			0
$367$	22.4061	+	22.4061i	1.16959	+	1.16959i	0.982305	+	0.187286i	$0.0599691\pi$
$367$	22.4061	+	22.4061i	1.16959	+	1.16959i	0.187286	+	0.982305i	$0.440031\pi$
$368$		0			0
$369$		−	33.1670i		−	1.72661i
$370$		0			0
$371$	4.57731	−	31.8359i	0.237642	−	1.65284i
$372$		0			0
$373$	6.86913	−	12.5799i	0.355670	−	0.651362i	−0.637182	−	0.770714i	$-0.719900\pi$
$373$	6.86913	−	12.5799i	0.355670	−	0.651362i	0.992852	+	0.119352i	$0.0380817\pi$
$374$		0			0
$375$	−4.76554	+	3.23659i	−0.246091	+	0.167137i
$376$		0			0
$377$	0.550584	−	0.300642i	0.0283565	−	0.0154838i
$378$		0			0
$379$	30.5836	+	19.6549i	1.57097	+	1.00960i	0.979053	+	0.203604i	$0.0652657\pi$
$379$	30.5836	+	19.6549i	1.57097	+	1.00960i	0.591919	+	0.805998i	$0.298371\pi$
$380$		0			0
$381$	3.48688	−	4.02408i	0.178638	−	0.206160i
$382$		0			0
$383$	−20.4374	−	15.2992i	−1.04430	−	0.781755i	−0.0678953	−	0.997692i	$-0.521628\pi$
$383$	−20.4374	−	15.2992i	−1.04430	−	0.781755i	−0.976407	+	0.215937i	$0.930719\pi$
$384$		0			0
$385$	−15.3133	+	6.28151i	−0.780438	+	0.320136i
$386$		0			0
$387$	−15.1587	+	5.65390i	−0.770560	+	0.287404i
$388$		0			0
$389$	−3.90796	+	2.51149i	−0.198141	+	0.127338i	−0.635949	−	0.771731i	$-0.719391\pi$
$389$	−3.90796	+	2.51149i	−0.198141	+	0.127338i	0.437808	+	0.899068i	$0.355755\pi$
$390$		0			0
$391$	−0.193329	−	25.3260i	−0.00977706	−	1.28079i
$392$		0			0
$393$	2.01671	+	0.438707i	0.101729	+	0.0221299i
$394$		0			0
$395$	9.55019	+	29.0257i	0.480522	+	1.46044i
$396$		0			0
$397$	16.5688	+	6.17984i	0.831564	+	0.310157i	0.728952	−	0.684564i	$-0.240008\pi$
$397$	16.5688	+	6.17984i	0.831564	+	0.310157i	0.102611	+	0.994722i	$0.467280\pi$
$398$		0			0
$399$	−3.44842	+	0.495808i	−0.172637	+	0.0248214i
$400$		0			0
$401$	18.7572	+	16.2532i	0.936692	+	0.811648i	0.982301	−	0.187311i	$-0.0599774\pi$
$401$	18.7572	+	16.2532i	0.936692	+	0.811648i	−0.0456089	+	0.998959i	$0.514523\pi$
$402$		0			0
$403$	−0.0374386	−	0.172103i	−0.00186495	−	0.00857304i
$404$		0			0
$405$	13.3820	−	6.64126i	0.664959	−	0.330007i
$406$		0			0
$407$	−3.13451	−	0.224185i	−0.155372	−	0.0111124i
$408$		0			0
$409$	−6.28714	−	21.4120i	−0.310879	−	1.05876i	−0.955680	−	0.294407i	$-0.904878\pi$
$409$	−6.28714	−	21.4120i	−0.310879	−	1.05876i	0.644801	−	0.764350i	$-0.276940\pi$
$410$		0			0
$411$	−5.33047	−	0.766406i	−0.262933	−	0.0378040i
$412$		0			0
$413$	22.7625	−	22.7625i	1.12007	−	1.12007i
$414$		0			0
$415$	−0.248279	+	6.34161i	−0.0121875	+	0.311297i
$416$		0			0
$417$	−2.15154	−	2.87412i	−0.105361	−	0.140746i
$418$		0			0
$419$	−5.97319	+	1.75389i	−0.291809	+	0.0856830i	−0.424361	−	0.905493i	$-0.639501\pi$
$419$	−5.97319	+	1.75389i	−0.291809	+	0.0856830i	0.132551	+	0.991176i	$0.457683\pi$
$420$		0			0
$421$	8.24216	−	7.14187i	0.401698	−	0.348074i	−0.430462	−	0.902609i	$-0.641649\pi$
$421$	8.24216	−	7.14187i	0.401698	−	0.348074i	0.832160	+	0.554535i	$0.187104\pi$
$422$		0			0
$423$	12.7084	+	23.2737i	0.617903	+	1.13160i
$424$		0			0
$425$	26.1614	−	3.57839i	1.26901	−	0.173578i
$426$		0			0
$427$	0.738962	+	10.3320i	0.0357609	+	0.500003i
$428$		0			0
$429$	0.0275558	+	0.191655i	0.00133041	+	0.00925319i
$430$		0			0
$431$	29.5276	−	13.4848i	1.42230	−	0.649541i	0.452123	−	0.891956i	$-0.350667\pi$
$431$	29.5276	−	13.4848i	1.42230	−	0.649541i	0.970173	+	0.242415i	$0.0779395\pi$
$432$		0			0
$433$	−5.88777	−	15.7857i	−0.282948	−	0.758613i	−0.998213	−	0.0597597i	$-0.980967\pi$
$433$	−5.88777	−	15.7857i	−0.282948	−	0.758613i	0.715265	−	0.698854i	$-0.246306\pi$
$434$		0			0
$435$	2.35958	+	4.00813i	0.113133	+	0.192175i
$436$		0			0
$437$	0.675073	−	10.5723i	0.0322931	−	0.505742i
$438$		0			0
$439$	−2.19769	−	3.41967i	−0.104890	−	0.163212i	0.784841	−	0.619697i	$-0.212745\pi$
$439$	−2.19769	−	3.41967i	−0.104890	−	0.163212i	−0.889731	+	0.456485i	$0.849108\pi$
$440$		0			0
$441$	2.69134	−	5.89321i	0.128159	−	0.280629i
$442$		0			0
$443$	8.74865	−	23.4560i	0.415661	−	1.11443i	−0.545420	−	0.838163i	$-0.683630\pi$
$443$	8.74865	−	23.4560i	0.415661	−	1.11443i	0.961081	−	0.276267i	$-0.0890975\pi$
$444$		0			0
$445$	5.35454	+	4.34535i	0.253830	+	0.205989i
$446$		0			0
$447$	−10.4007	+	0.743869i	−0.491934	+	0.0351838i
$448$		0			0
$449$	−10.1916	+	15.8584i	−0.480969	+	0.748403i	−0.993931	−	0.110009i	$-0.964912\pi$
$449$	−10.1916	+	15.8584i	−0.480969	+	0.748403i	0.512961	+	0.858412i	$0.328548\pi$
$450$		0			0
$451$	8.26354	−	28.1430i	0.389115	−	1.32520i
$452$		0			0
$453$	−0.312130	+	4.36415i	−0.0146651	+	0.205046i
$454$		0			0
$455$	−0.912838	−	0.545855i	−0.0427945	−	0.0255901i
$456$		0			0
$457$	18.7125	−	14.0080i	0.875335	−	0.655267i	−0.0641194	−	0.997942i	$-0.520424\pi$
$457$	18.7125	−	14.0080i	0.875335	−	0.655267i	0.939454	+	0.342675i	$0.111333\pi$
$458$		0			0
$459$	15.6039			0.728329
$460$		0			0
$461$	−9.03119			−0.420624			−0.210312	−	0.977634i	$-0.567448\pi$
$461$	−9.03119			−0.420624			−0.210312	+	0.977634i	$0.567448\pi$
$462$		0			0
$463$	−12.2683	+	9.18391i	−0.570155	+	0.426813i	−0.845070	−	0.534656i	$-0.820441\pi$
$463$	−12.2683	+	9.18391i	−0.570155	+	0.426813i	0.274915	+	0.961469i	$0.411350\pi$
$464$		0			0
$465$	1.26639	−	0.318604i	0.0587276	−	0.0147749i
$466$		0			0
$467$	−0.535139	+	7.48222i	−0.0247633	+	0.346236i	0.969932	+	0.243374i	$0.0782544\pi$
$467$	−0.535139	+	7.48222i	−0.0247633	+	0.346236i	−0.994696	+	0.102862i	$0.967200\pi$
$468$		0			0
$469$	3.71977	−	12.6684i	0.171763	−	0.584971i
$470$		0			0
$471$	−0.855475	+	1.33114i	−0.0394182	+	0.0613359i
$472$		0			0
$473$	−14.2712	+	1.02070i	−0.656190	+	0.0469316i
$474$		0			0
$475$	11.0218	−	0.712319i	0.505717	−	0.0326834i
$476$		0			0
$477$	−10.0413	+	26.9218i	−0.459761	+	1.23267i
$478$		0			0
$479$	2.41387	−	5.28564i	0.110293	−	0.241507i	−0.846435	−	0.532492i	$-0.821256\pi$
$479$	2.41387	−	5.28564i	0.110293	−	0.241507i	0.956728	+	0.290985i	$0.0939830\pi$
$480$		0			0
$481$	−0.109175	−	0.169879i	−0.00497795	−	0.00774584i
$482$		0			0
$483$	−6.08952	−	4.48644i	−0.277083	−	0.204140i
$484$		0			0
$485$	31.7087	−	18.6669i	1.43982	−	0.847619i
$486$		0			0
$487$	−5.86311	−	15.7196i	−0.265683	−	0.712323i	−0.999458	−	0.0329304i	$-0.989516\pi$
$487$	−5.86311	−	15.7196i	−0.265683	−	0.712323i	0.733775	−	0.679393i	$-0.237757\pi$
$488$		0			0
$489$	3.05360	−	1.39453i	0.138088	−	0.0630629i
$490$		0			0
$491$	0.379109	+	2.63676i	0.0171090	+	0.118995i	0.996586	−	0.0825598i	$-0.0263095\pi$
$491$	0.379109	+	2.63676i	0.0171090	+	0.118995i	−0.979477	+	0.201555i	$0.935400\pi$
$492$		0			0
$493$	−1.52087	−	21.2646i	−0.0684967	−	0.957708i
$494$		0			0
$495$	14.5606	−	2.57546i	0.654448	−	0.115758i
$496$		0			0
$497$	10.0460	+	18.3978i	0.450624	+	0.825255i
$498$		0			0
$499$	−32.4103	+	28.0837i	−1.45089	+	1.25720i	−0.541854	+	0.840473i	$0.682278\pi$
$499$	−32.4103	+	28.0837i	−1.45089	+	1.25720i	−0.909032	+	0.416727i	$0.863177\pi$
$500$		0			0
$501$	0.150661	−	0.0442381i	0.00673105	−	0.00197641i
$502$		0			0
$503$	−6.78863	−	9.06855i	−0.302690	−	0.404347i	0.623247	−	0.782025i	$-0.285813\pi$
$503$	−6.78863	−	9.06855i	−0.302690	−	0.404347i	−0.925937	+	0.377679i	$0.876722\pi$
$504$		0			0
$505$	4.33581	−	4.00910i	0.192941	−	0.178403i
$506$		0			0
$507$	4.72762	−	4.72762i	0.209961	−	0.209961i
$508$		0			0
$509$	−25.6859	−	3.69307i	−1.13851	−	0.163692i	−0.452828	−	0.891598i	$-0.649585\pi$
$509$	−25.6859	−	3.69307i	−1.13851	−	0.163692i	−0.685677	+	0.727905i	$0.740494\pi$
$510$		0			0
$511$	−4.30950	−	14.6768i	−0.190641	−	0.649263i
$512$		0			0
$513$	6.51028	+	0.465625i	0.287436	+	0.0205578i
$514$		0			0
$515$	−1.47787	+	4.38997i	−0.0651228	+	0.193445i
$516$		0			0
$517$	4.98476	+	22.9146i	0.219229	+	1.00778i
$518$		0			0
$519$	−4.86408	−	4.21475i	−0.213509	−	0.185007i
$520$		0			0
$521$	18.8651	−	2.71240i	0.826497	−	0.118832i	0.283930	−	0.958845i	$-0.408362\pi$
$521$	18.8651	−	2.71240i	0.826497	−	0.118832i	0.542567	+	0.840013i	$0.317453\pi$
$522$		0			0
$523$	−29.1164	−	10.8598i	−1.27317	−	0.474868i	−0.380166	−	0.924918i	$-0.624133\pi$
$523$	−29.1164	−	10.8598i	−1.27317	−	0.474868i	−0.893003	+	0.450051i	$0.851406\pi$
$524$		0			0
$525$	3.82664	−	6.89507i	0.167008	−	0.300926i
$526$		0			0
$527$	−5.84876	−	1.27232i	−0.254776	−	0.0554231i
$528$		0			0
$529$	17.1503	−	15.3254i	0.745664	−	0.666322i
$530$		0			0
$531$	−24.1930	+	15.5479i	−1.04989	+	0.674721i
$532$		0			0
$533$	1.76596	−	0.658670i	0.0764924	−	0.0285302i
$534$		0			0
$535$	8.04252	+	19.6064i	0.347709	+	0.847657i
$536$		0			0
$537$	9.17556	+	6.86874i	0.395955	+	0.296408i
$538$		0			0
$539$	3.75195	−	4.32999i	0.161608	−	0.186506i
$540$		0			0
$541$	33.6029	+	21.5952i	1.44470	+	0.928452i	0.999454	+	0.0330435i	$0.0105200\pi$
$541$	33.6029	+	21.5952i	1.44470	+	0.928452i	0.445246	+	0.895409i	$0.353116\pi$
$542$		0			0
$543$	3.03660	−	1.65811i	0.130313	−	0.0711562i
$544$		0			0
$545$	−41.9951	−	4.66074i	−1.79887	−	0.199644i
$546$		0			0
$547$	1.30362	−	2.38741i	0.0557389	−	0.102078i	−0.848324	−	0.529477i	$-0.822388\pi$
$547$	1.30362	−	2.38741i	0.0557389	−	0.102078i	0.904063	+	0.427399i	$0.140570\pi$
$548$		0			0
$549$	1.31696	−	9.15965i	0.0562065	−	0.390925i
$550$		0			0
$551$		−	8.91741i		−	0.379894i
$552$		0			0
$553$	−29.5771	−	29.5771i	−1.25774	−	1.25774i
$554$		0			0
$555$	1.23276	−	0.849667i	0.0523277	−	0.0360663i
$556$		0			0
$557$	−22.7881	−	12.4432i	−0.965562	−	0.527237i	−0.0825500	−	0.996587i	$-0.526306\pi$
$557$	−22.7881	−	12.4432i	−0.965562	−	0.527237i	−0.883012	+	0.469350i	$0.844488\pi$
$558$		0			0
$559$	−0.602079	−	0.694836i	−0.0254652	−	0.0293884i
$560$		0			0
$561$	6.31367	+	1.85386i	0.266563	+	0.0782700i
$562$		0			0
$563$	4.50277	−	0.979517i	0.189769	−	0.0412817i	−0.116676	−	0.993170i	$-0.537224\pi$
$563$	4.50277	−	0.979517i	0.189769	−	0.0412817i	0.306445	+	0.951888i	$0.400860\pi$
$564$		0			0
$565$	15.7781	+	14.7913i	0.663790	+	0.622276i
$566$		0			0
$567$	−12.2554	+	16.3713i	−0.514679	+	0.687530i
$568$		0			0
$569$	8.98891	+	19.6830i	0.376835	+	0.825153i	0.999103	+	0.0423487i	$0.0134840\pi$
$569$	8.98891	+	19.6830i	0.376835	+	0.825153i	−0.622268	+	0.782804i	$0.713789\pi$
$570$		0			0
$571$	15.6390	+	7.14209i	0.654472	+	0.298887i	0.714839	−	0.699289i	$-0.246500\pi$
$571$	15.6390	+	7.14209i	0.654472	+	0.298887i	−0.0603674	+	0.998176i	$0.519227\pi$
$572$		0			0
$573$	1.15702	−	5.31876i	0.0483354	−	0.222194i
$574$		0			0
$575$	18.1344	+	15.6890i	0.756255	+	0.654277i
$576$		0			0
$577$	−8.46280	+	38.9029i	−0.352311	+	1.61955i	0.370729	+	0.928741i	$0.379108\pi$
$577$	−8.46280	+	38.9029i	−0.352311	+	1.61955i	−0.723040	+	0.690806i	$0.757256\pi$
$578$		0			0
$579$	−1.25539	−	0.573317i	−0.0521722	−	0.0238262i
$580$		0			0
$581$	−3.60895	−	7.90250i	−0.149725	−	0.327851i
$582$		0			0
$583$	−15.2279	+	20.3421i	−0.630674	+	0.842482i
$584$		0			0
$585$	0.693203	+	0.649849i	0.0286604	+	0.0268679i
$586$		0			0
$587$	−19.0681	+	4.14801i	−0.787024	+	0.171207i	−0.588079	−	0.808804i	$-0.700115\pi$
$587$	−19.0681	+	4.14801i	−0.787024	+	0.171207i	−0.198946	+	0.980010i	$0.563752\pi$
$588$		0			0
$589$	−2.40226	−	0.705367i	−0.0989834	−	0.0290641i
$590$		0			0
$591$	−0.948259	−	1.09435i	−0.0390062	−	0.0450155i
$592$		0			0
$593$	14.9463	+	8.16127i	0.613769	+	0.335143i	0.755883	−	0.654707i	$-0.227208\pi$
$593$	14.9463	+	8.16127i	0.613769	+	0.335143i	−0.142113	+	0.989850i	$0.545390\pi$
$594$		0			0
$595$	−29.7611	+	20.5125i	−1.22009	+	0.840932i
$596$		0			0
$597$	−7.57937	−	7.57937i	−0.310203	−	0.310203i
$598$		0			0
$599$		−	38.3759i		−	1.56800i	−0.620762	−	0.783999i	$-0.713177\pi$
$599$		−	38.3759i		−	1.56800i	0.620762	−	0.783999i	$-0.286823\pi$
$600$		0			0
$601$	1.39135	−	9.67704i	0.0567543	−	0.394735i	−0.941568	−	0.336824i	$-0.890647\pi$
$601$	1.39135	−	9.67704i	0.0567543	−	0.394735i	0.998322	−	0.0579103i	$-0.0184437\pi$
$602$		0			0
$603$	−5.65286	+	10.3524i	−0.230202	+	0.421584i
$604$		0			0
$605$	−11.4500	−	1.27075i	−0.465508	−	0.0516635i
$606$		0			0
$607$	11.8719	−	6.48254i	0.481865	−	0.263118i	−0.219906	−	0.975521i	$-0.570575\pi$
$607$	11.8719	−	6.48254i	0.481865	−	0.263118i	0.701770	+	0.712403i	$0.252393\pi$
$608$		0			0
$609$	−5.35611	−	3.44216i	−0.217041	−	0.139484i
$610$		0			0
$611$	−0.986818	+	1.13885i	−0.0399224	+	0.0460729i
$612$		0			0
$613$	10.7544	+	8.05063i	0.434366	+	0.325162i	0.793985	−	0.607937i	$-0.208003\pi$
$613$	10.7544	+	8.05063i	0.434366	+	0.325162i	−0.359620	+	0.933099i	$0.617094\pi$
$614$		0			0
$615$	5.30345	+	12.9289i	0.213856	+	0.521345i
$616$		0			0
$617$	−15.4493	+	5.76229i	−0.621965	+	0.231981i	−0.640636	−	0.767845i	$-0.721329\pi$
$617$	−15.4493	+	5.76229i	−0.621965	+	0.231981i	0.0186709	+	0.999826i	$0.494057\pi$
$618$		0			0
$619$	3.13460	−	2.01449i	0.125990	−	0.0809691i	−0.476128	−	0.879376i	$-0.657960\pi$
$619$	3.13460	−	2.01449i	0.125990	−	0.0809691i	0.602118	+	0.798407i	$0.294324\pi$
$620$		0			0
$621$	9.36112	+	10.6381i	0.375649	+	0.426893i
$622$		0			0
$623$	−9.22394	−	2.00655i	−0.369549	−	0.0803905i
$624$		0			0
$625$	−13.8034	+	20.8439i	−0.552134	+	0.833755i
$626$		0			0
$627$	2.57887	+	0.961870i	0.102990	+	0.0384134i
$628$		0			0
$629$	−6.79278	+	0.976654i	−0.270846	+	0.0389418i
$630$		0			0
$631$	11.6585	+	10.1021i	0.464116	+	0.402158i	0.855283	−	0.518161i	$-0.173383\pi$
$631$	11.6585	+	10.1021i	0.464116	+	0.402158i	−0.391167	+	0.920320i	$0.627929\pi$
$632$		0			0
$633$	−0.732385	−	3.36672i	−0.0291097	−	0.133815i
$634$		0			0
$635$	7.37249	−	21.8998i	0.292568	−	0.869065i
$636$		0			0
$637$	0.367229	+	0.0262647i	0.0145501	+	0.00104065i
$638$		0			0
$639$	−5.27589	−	17.9680i	−0.208711	−	0.710805i
$640$		0			0
$641$	12.0722	+	1.73572i	0.476824	+	0.0685569i	0.376537	−	0.926402i	$-0.377115\pi$
$641$	12.0722	+	1.73572i	0.476824	+	0.0685569i	0.100287	+	0.994959i	$0.468024\pi$
$642$		0			0
$643$	−30.8383	+	30.8383i	−1.21614	+	1.21614i	−0.247171	+	0.968972i	$0.579501\pi$
$643$	−30.8383	+	30.8383i	−1.21614	+	1.21614i	−0.968972	+	0.247171i	$0.920499\pi$
$644$		0			0
$645$	5.00499	−	4.62786i	0.197071	−	0.182222i
$646$		0			0
$647$	−26.8658	−	35.8885i	−1.05620	−	1.41092i	−0.906506	−	0.422192i	$-0.861261\pi$
$647$	−26.8658	−	35.8885i	−1.05620	−	1.41092i	−0.149698	−	0.988732i	$-0.547830\pi$
$648$		0			0
$649$	−24.4021	+	7.16510i	−0.957866	+	0.281255i
$650$		0			0
$651$	−1.35095	+	1.17061i	−0.0529480	+	0.0458797i
$652$		0			0
$653$	19.2519	+	35.2571i	0.753383	+	1.37972i	0.919292	+	0.393577i	$0.128763\pi$
$653$	19.2519	+	35.2571i	0.753383	+	1.37972i	−0.165908	+	0.986141i	$0.553056\pi$
$654$		0			0
$655$	8.81975	−	1.56003i	0.344616	−	0.0609555i
$656$		0			0
$657$	0.974868	+	13.6304i	0.0380332	+	0.531774i
$658$		0			0
$659$	−4.45234	−	30.9667i	−0.173439	−	1.20629i	−0.871551	−	0.490304i	$-0.836886\pi$
$659$	−4.45234	−	30.9667i	−0.173439	−	1.20629i	0.698113	−	0.715988i	$-0.254023\pi$
$660$		0			0
$661$	−38.9653	+	17.7949i	−1.51558	+	0.692141i	−0.987582	−	0.157107i	$-0.949783\pi$
$661$	−38.9653	+	17.7949i	−1.51558	+	0.692141i	−0.527995	+	0.849248i	$0.677056\pi$
$662$		0			0
$663$	0.147768	+	0.396180i	0.00573882	+	0.0153864i
$664$		0			0
$665$	−13.0290	+	7.67018i	−0.505245	+	0.297437i
$666$		0			0
$667$	13.5849	−	13.7939i	0.526011	−	0.534103i
$668$		0			0
$669$	−6.14376	−	9.55988i	−0.237531	−	0.369606i
$670$		0			0
$671$	3.39959	−	7.44407i	0.131240	−	0.287375i
$672$		0			0
$673$	−1.36506	+	3.65987i	−0.0526192	+	0.141078i	−0.960600	−	0.277934i	$-0.910350\pi$
$673$	−1.36506	+	3.65987i	−0.0526192	+	0.141078i	0.907981	+	0.419011i	$0.137623\pi$
$674$		0			0
$675$	−9.75108	+	11.0985i	−0.375319	+	0.427183i
$676$		0			0
$677$	45.1782	−	3.23121i	1.73634	−	0.124186i	0.833045	−	0.553205i	$-0.186595\pi$
$677$	45.1782	−	3.23121i	1.73634	−	0.124186i	0.903295	+	0.429019i	$0.141141\pi$
$678$		0			0
$679$	−27.2313	+	42.3727i	−1.04504	+	1.62612i
$680$		0			0
$681$	2.34622	−	7.99051i	0.0899075	−	0.306197i
$682$		0			0
$683$	−1.98961	+	27.8183i	−0.0761301	+	1.06444i	0.805530	+	0.592554i	$0.201880\pi$
$683$	−1.98961	+	27.8183i	−0.0761301	+	1.06444i	−0.881661	+	0.471884i	$0.843574\pi$
$684$		0			0
$685$	−22.6645	+	5.70201i	−0.865964	+	0.217862i
$686$		0			0
$687$	7.54705	−	5.64965i	0.287938	−	0.215548i
$688$		0			0
$689$	−1.63285			−0.0622068
$690$		0			0
$691$	33.4965			1.27427			0.637133	−	0.770754i	$-0.280120\pi$
$691$	33.4965			1.27427			0.637133	+	0.770754i	$0.280120\pi$
$692$		0			0
$693$	−16.2038	+	12.1300i	−0.615533	+	0.460782i
$694$		0			0
$695$	−13.3722	−	7.99623i	−0.507235	−	0.303314i
$696$		0			0
$697$	4.56952	−	63.8902i	0.173083	−	2.42001i
$698$		0			0
$699$	3.44943	−	11.7477i	0.130469	−	0.444338i
$700$		0			0
$701$	2.68952	−	4.18498i	0.101582	−	0.158064i	−0.786742	−	0.617282i	$-0.788234\pi$
$701$	2.68952	−	4.18498i	0.101582	−	0.158064i	0.888324	+	0.459218i	$0.151870\pi$
$702$		0			0
$703$	−2.86323	+	0.204782i	−0.107989	+	0.00772352i
$704$		0			0
$705$	−8.67538	−	7.04029i	−0.326734	−	0.265153i
$706$		0			0
$707$	−2.82494	+	7.57395i	−0.106243	+	0.284848i
$708$		0			0
$709$	−9.92767	+	21.7386i	−0.372842	+	0.816409i	0.626475	+	0.779442i	$0.284497\pi$
$709$	−9.92767	+	21.7386i	−0.372842	+	0.816409i	−0.999316	+	0.0369676i	$0.988230\pi$
$710$		0			0
$711$	20.2026	+	31.4358i	0.757656	+	1.17894i
$712$		0			0
$713$	−2.64138	−	4.75074i	−0.0989203	−	0.177917i
$714$		0			0
$715$	0.426290	+	0.724124i	0.0159424	+	0.0270807i
$716$		0			0
$717$	4.00975	+	10.7506i	0.149747	+	0.401487i
$718$		0			0
$719$	−1.10251	+	0.503502i	−0.0411169	+	0.0187774i	−0.435867	−	0.900011i	$-0.643558\pi$
$719$	−1.10251	+	0.503502i	−0.0411169	+	0.0187774i	0.394750	+	0.918788i	$0.370831\pi$
$720$		0			0
$721$	−0.902382	−	6.27621i	−0.0336065	−	0.233738i
$722$		0			0
$723$	−0.0118087	−	0.165107i	−0.000439170	−	0.00614040i
$724$		0			0
$725$	16.0752	+	12.2067i	0.597017	+	0.453347i
$726$		0			0
$727$	6.80626	+	12.4647i	0.252430	+	0.462291i	0.972910	−	0.231185i	$-0.0742601\pi$
$727$	6.80626	+	12.4647i	0.252430	+	0.462291i	−0.720480	+	0.693476i	$0.756078\pi$
$728$		0			0
$729$	10.3555	−	8.97305i	0.383535	−	0.332335i
$730$		0			0
$731$	−29.9794	+	8.80275i	−1.10883	+	0.325581i
$732$		0			0
$733$	21.6979	+	28.9850i	0.801431	+	1.07059i	0.995970	+	0.0896913i	$0.0285880\pi$
$733$	21.6979	+	28.9850i	0.801431	+	1.07059i	−0.194539	+	0.980895i	$0.562321\pi$
$734$		0			0
$735$	−0.106787	+	2.72760i	−0.00393892	+	0.100609i
$736$		0			0
$737$	−7.37590	+	7.37590i	−0.271695	+	0.271695i
$738$		0			0
$739$	38.6361	+	5.55504i	1.42125	+	0.204345i	0.809694	−	0.586853i	$-0.199633\pi$
$739$	38.6361	+	5.55504i	1.42125	+	0.204345i	0.611560	+	0.791198i	$0.290542\pi$
$740$		0			0
$741$	0.0498296	+	0.169704i	0.00183054	+	0.00623423i
$742$		0			0
$743$	5.25915	+	0.376142i	0.192939	+	0.0137993i	0.167474	−	0.985876i	$-0.446439\pi$
$743$	5.25915	+	0.376142i	0.192939	+	0.0137993i	0.0254649	+	0.999676i	$0.491893\pi$
$744$		0			0
$745$	−40.5342	+	20.1163i	−1.48506	+	0.737006i
$746$		0			0
$747$	1.64975	+	7.58380i	0.0603614	+	0.277477i
$748$		0			0
$749$	−21.9236	−	18.9969i	−0.801071	−	0.694132i
$750$		0			0
$751$	11.1128	−	1.59778i	0.405512	−	0.0583038i	0.0634590	−	0.997984i	$-0.479787\pi$
$751$	11.1128	−	1.59778i	0.405512	−	0.0583038i	0.342053	+	0.939681i	$0.388878\pi$
$752$		0			0
$753$	−12.1781	−	4.54221i	−0.443796	−	0.165527i
$754$		0			0
$755$	5.93444	+	18.0364i	0.215976	+	0.656412i
$756$		0			0
$757$	6.44399	+	1.40180i	0.234211	+	0.0509494i	0.328139	−	0.944630i	$-0.393579\pi$
$757$	6.44399	+	1.40180i	0.234211	+	0.0509494i	−0.0939279	+	0.995579i	$0.529942\pi$
$758$		0			0
$759$	2.52381	+	5.41657i	0.0916086	+	0.196609i
$760$		0			0
$761$	5.23408	−	3.36374i	0.189735	−	0.121935i	−0.442325	−	0.896855i	$-0.645846\pi$
$761$	5.23408	−	3.36374i	0.189735	−	0.121935i	0.632060	+	0.774920i	$0.282210\pi$
$762$		0			0
$763$	54.1926	−	20.2128i	1.96190	−	0.731752i
$764$		0			0
$765$	29.8752	−	12.2548i	1.08014	−	0.443072i
$766$		0			0
$767$	−1.30829	−	0.979376i	−0.0472397	−	0.0353632i
$768$		0			0
$769$	−3.34891	+	3.86484i	−0.120765	+	0.139370i	−0.812912	−	0.582386i	$-0.802119\pi$
$769$	−3.34891	+	3.86484i	−0.120765	+	0.139370i	0.692148	+	0.721756i	$0.256665\pi$
$770$		0			0
$771$	−4.67093	−	3.00183i	−0.168220	−	0.108108i
$772$		0			0
$773$	−30.6746	+	16.7496i	−1.10329	+	0.602440i	−0.924398	−	0.381429i	$-0.875432\pi$
$773$	−30.6746	+	16.7496i	−1.10329	+	0.602440i	−0.178889	+	0.983869i	$0.557250\pi$
$774$		0			0
$775$	4.55992	−	3.36494i	0.163797	−	0.120872i
$776$		0			0
$777$	−0.982222	+	1.79881i	−0.0352370	+	0.0645318i
$778$		0			0
$779$	3.81300	−	26.5200i	0.136615	−	0.950176i
$780$		0			0
$781$		−	16.5608i		−	0.592592i
$782$		0			0
$783$	8.43437	+	8.43437i	0.301420	+	0.301420i
$784$		0			0
$785$	−1.24242	+	6.75358i	−0.0443439	+	0.241046i
$786$		0			0
$787$	−12.1140	−	6.61476i	−0.431819	−	0.235791i	0.248612	−	0.968603i	$-0.420026\pi$
$787$	−12.1140	−	6.61476i	−0.431819	−	0.235791i	−0.680431	+	0.732812i	$0.738207\pi$
$788$		0			0
$789$	−0.507793	−	0.586025i	−0.0180779	−	0.0208630i
$790$		0			0
$791$	−28.4058	−	8.34070i	−1.00999	−	0.296561i
$792$		0			0
$793$	0.513856	−	0.111782i	0.0182475	−	0.00396951i
$794$		0			0
$795$	−0.390595	−	12.1001i	−0.0138530	−	0.429147i
$796$		0			0
$797$	−12.8803	+	17.2061i	−0.456244	+	0.609471i	−0.968394	−	0.249425i	$-0.919758\pi$
$797$	−12.8803	+	17.2061i	−0.456244	+	0.609471i	0.512150	+	0.858896i	$0.328849\pi$
$798$		0			0
$799$	21.2739	+	46.5833i	0.752616	+	1.64800i
$800$		0			0
$801$	7.67097	+	3.50322i	0.271041	+	0.123780i
$802$		0			0
$803$	−2.56881	+	11.8086i	−0.0906515	+	0.416718i
$804$		0			0
$805$	−31.8389	−	7.98403i	−1.12217	−	0.281400i
$806$		0			0
$807$	1.69811	−	7.80608i	0.0597762	−	0.274787i
$808$		0			0
$809$	−25.7934	−	11.7795i	−0.906848	−	0.414144i	−0.0932977	−	0.995638i	$-0.529741\pi$
$809$	−25.7934	−	11.7795i	−0.906848	−	0.414144i	−0.813550	+	0.581495i	$0.802468\pi$
$810$		0			0
$811$	2.75839	+	6.04003i	0.0968602	+	0.212094i	0.951859	−	0.306535i	$-0.0991697\pi$
$811$	2.75839	+	6.04003i	0.0968602	+	0.212094i	−0.854999	+	0.518629i	$0.826442\pi$
$812$		0			0
$813$	−4.85379	+	6.48390i	−0.170230	+	0.227400i
$814$		0			0
$815$	9.96363	−	10.6283i	0.349011	−	0.372295i
$816$		0			0
$817$	−12.7707	+	2.77810i	−0.446791	+	0.0971933i
$818$		0			0
$819$	−1.24799	−	0.366444i	−0.0436084	−	0.0128046i
$820$		0			0
$821$	−17.8095	−	20.5533i	−0.621557	−	0.717315i	0.354445	−	0.935077i	$-0.384670\pi$
$821$	−17.8095	−	20.5533i	−0.621557	−	0.717315i	−0.976002	+	0.217762i	$0.930124\pi$
$822$		0			0
$823$	−36.9966	−	20.2016i	−1.28962	−	0.704185i	−0.319678	−	0.947526i	$-0.603575\pi$
$823$	−36.9966	−	20.2016i	−1.28962	−	0.704185i	−0.969941	+	0.243341i	$0.921757\pi$
$824$		0			0
$825$	−5.26407	+	3.33220i	−0.183272	+	0.116012i
$826$		0			0
$827$	−10.4829	−	10.4829i	−0.364526	−	0.364526i	0.500950	−	0.865476i	$-0.332984\pi$
$827$	−10.4829	−	10.4829i	−0.364526	−	0.364526i	−0.865476	+	0.500950i	$0.832984\pi$
$828$		0			0
$829$			22.9706i			0.797803i	0.916994	+	0.398902i	$0.130608\pi$
$829$			22.9706i			0.797803i	−0.916994	+	0.398902i	$0.869392\pi$
$830$		0			0
$831$	−2.13784	+	14.8690i	−0.0741609	+	0.515801i
$832$		0			0
$833$	5.99629	−	10.9814i	0.207759	−	0.380483i
$834$		0			0
$835$	0.532056	−	0.425755i	0.0184125	−	0.0147339i
$836$		0			0
$837$	2.93929	−	1.60497i	0.101597	−	0.0554760i
$838$		0			0
$839$	18.4962	+	11.8868i	0.638560	+	0.410378i	0.819470	−	0.573122i	$-0.194268\pi$
$839$	18.4962	+	11.8868i	0.638560	+	0.410378i	−0.180910	+	0.983500i	$0.557904\pi$
$840$		0			0
$841$	−8.31893	+	9.60056i	−0.286860	+	0.331054i
$842$		0			0
$843$	−6.29973	−	4.71592i	−0.216974	−	0.162425i
$844$		0			0
$845$	11.1954	−	26.7680i	0.385134	−	0.920847i
$846$		0			0
$847$	14.7756	−	5.51103i	0.507697	−	0.189361i
$848$		0			0
$849$	8.11418	−	5.21467i	0.278478	−	0.178967i
$850$		0			0
$851$	−4.74097	−	4.04513i	−0.162518	−	0.138665i
$852$		0			0
$853$	−16.1166	−	3.50595i	−0.551822	−	0.120041i	−0.0719954	−	0.997405i	$-0.522937\pi$
$853$	−16.1166	−	3.50595i	−0.551822	−	0.120041i	−0.479826	+	0.877364i	$0.659300\pi$
$854$		0			0
$855$	12.8302	−	4.22147i	0.438784	−	0.144371i
$856$		0			0
$857$	−47.7941	−	17.8263i	−1.63262	−	0.608934i	−0.644770	−	0.764376i	$-0.723047\pi$
$857$	−47.7941	−	17.8263i	−1.63262	−	0.608934i	−0.987845	+	0.155442i	$0.950320\pi$
$858$		0			0
$859$	35.0459	−	5.03883i	1.19575	−	0.171923i	0.484454	−	0.874817i	$-0.339018\pi$
$859$	35.0459	−	5.03883i	1.19575	−	0.171923i	0.711295	+	0.702894i	$0.248109\pi$
$860$		0			0
$861$	−14.4570	−	12.5271i	−0.492693	−	0.426921i
$862$		0			0
$863$	−4.22834	−	19.4374i	−0.143935	−	0.661656i	−0.991407	−	0.130816i	$-0.958240\pi$
$863$	−4.22834	−	19.4374i	−0.143935	−	0.661656i	0.847472	−	0.530840i	$-0.178123\pi$
$864$		0			0
$865$	−26.4712	−	8.91146i	−0.900048	−	0.302999i
$866$		0			0
$867$	5.59625	+	0.400252i	0.190059	+	0.0135933i
$868$		0			0
$869$	9.31017	+	31.7075i	0.315826	+	1.07560i
$870$		0			0
$871$	−0.663473	−	0.0953930i	−0.0224809	−	0.00323227i
$872$		0			0
$873$	31.8180	−	31.8180i	1.07688	−	1.07688i
$874$		0			0
$875$	4.00819	−	33.9866i	0.135502	−	1.14896i
$876$		0			0
$877$	21.7113	+	29.0029i	0.733140	+	0.979360i	0.999878	+	0.0155909i	$0.00496294\pi$
$877$	21.7113	+	29.0029i	0.733140	+	0.979360i	−0.266739	+	0.963769i	$0.585946\pi$
$878$		0			0
$879$	−6.07982	+	1.78520i	−0.205067	+	0.0602132i
$880$		0			0
$881$	5.14228	−	4.45581i	0.173248	−	0.150120i	−0.563921	−	0.825829i	$-0.690708\pi$
$881$	5.14228	−	4.45581i	0.173248	−	0.150120i	0.737169	+	0.675709i	$0.236162\pi$
$882$		0			0
$883$	−2.72198	−	4.98493i	−0.0916019	−	0.167756i	0.827861	−	0.560934i	$-0.189558\pi$
$883$	−2.72198	−	4.98493i	−0.0916019	−	0.167756i	−0.919463	+	0.393177i	$0.871376\pi$
$884$		0			0
$885$	6.94461	−	9.92926i	0.233441	−	0.333768i
$886$		0			0
$887$	−1.22370	−	17.1095i	−0.0410877	−	0.574481i	−0.975742	−	0.218923i	$-0.929746\pi$
$887$	−1.22370	−	17.1095i	−0.0410877	−	0.574481i	0.934654	−	0.355558i	$-0.115709\pi$
$888$		0			0
$889$	4.50162	+	31.3094i	0.150979	+	1.05008i
$890$		0			0
$891$	14.6966	−	6.71170i	0.492354	−	0.224850i
$892$		0			0
$893$	7.48586	+	20.0704i	0.250505	+	0.671629i
$894$		0			0
$895$	48.1532	+	12.4665i	1.60958	+	0.416709i
$896$		0			0
$897$	−0.181451	+	0.338419i	−0.00605847	+	0.0112995i
$898$		0			0
$899$	−2.47370	−	3.84915i	−0.0825024	−	0.128376i
$900$		0			0
$901$	−23.0519	+	50.4766i	−0.767969	+	1.68162i
$902$		0			0
$903$	−3.26093	+	8.74290i	−0.108517	+	0.290946i
$904$		0			0
$905$	9.46127	−	11.6586i	0.314503	−	0.387546i
$906$		0			0
$907$	36.6178	−	2.61896i	1.21587	−	0.0869611i	0.551380	−	0.834254i	$-0.314101\pi$
$907$	36.6178	−	2.61896i	1.21587	−	0.0869611i	0.664495	+	0.747293i	$0.268647\pi$
$908$		0			0
$909$	3.90430	−	6.07521i	0.129497	−	0.201502i
$910$		0			0
$911$	−3.57411	+	12.1723i	−0.118416	+	0.403287i	−0.997273	−	0.0737975i	$-0.976488\pi$
$911$	−3.57411	+	12.1723i	−0.118416	+	0.403287i	0.878858	+	0.477084i	$0.158306\pi$
$912$		0			0
$913$	−0.489641	+	6.84607i	−0.0162047	+	0.226572i
$914$		0			0
$915$	0.951272	+	3.78114i	0.0314481	+	0.125001i
$916$		0			0
$917$	−9.81514	+	7.34752i	−0.324124	+	0.242636i
$918$		0			0
$919$	−30.2113			−0.996580			−0.498290	−	0.867010i	$-0.666038\pi$
$919$	−30.2113			−0.996580			−0.498290	+	0.867010i	$0.666038\pi$
$920$		0			0
$921$	16.9934			0.559951
$922$		0			0
$923$	0.851926	−	0.637744i	0.0280415	−	0.0209916i
$924$		0			0
$925$	3.55023	−	5.44180i	0.116731	−	0.178925i
$926$		0			0
$927$	−0.404107	+	5.65016i	−0.0132726	+	0.185576i
$928$		0			0
$929$	4.38753	−	14.9425i	0.143950	−	0.490249i	−0.855678	−	0.517508i	$-0.826860\pi$
$929$	4.38753	−	14.9425i	0.143950	−	0.490249i	0.999628	+	0.0272591i	$0.00867793\pi$
$930$		0			0
$931$	2.82947	−	4.40273i	0.0927320	−	0.144294i
$932$		0			0
$933$	15.5677	−	1.11343i	0.509665	−	0.0364520i
$934$		0			0
$935$	28.4031	−	2.95511i	0.928880	−	0.0966424i
$936$		0			0
$937$	1.16762	−	3.13051i	0.0381444	−	0.102269i	−0.916481	−	0.400078i	$-0.868983\pi$
$937$	1.16762	−	3.13051i	0.0381444	−	0.102269i	0.954626	+	0.297809i	$0.0962558\pi$
$938$		0			0
$939$	1.01577	−	2.22423i	0.0331484	−	0.0725849i
$940$		0			0
$941$	−25.4398	−	39.5851i	−0.829313	−	1.29044i	−0.954472	−	0.298300i	$-0.903581\pi$
$941$	−25.4398	−	39.5851i	−0.829313	−	1.29044i	0.125159	−	0.992137i	$-0.460056\pi$
$942$		0			0
$943$	46.2991	−	35.2137i	1.50771	−	1.14672i
$944$		0			0
$945$	5.06859	−	19.5780i	0.164881	−	0.636872i
$946$		0			0
$947$	−11.0777	−	29.7004i	−0.359976	−	0.965133i	−0.983110	−	0.183017i	$-0.941414\pi$
$947$	−11.0777	−	29.7004i	−0.359976	−	0.965133i	0.623134	−	0.782115i	$-0.285859\pi$
$948$		0			0
$949$	−0.706386	+	0.322596i	−0.0229303	+	0.0104719i
$950$		0			0
$951$	0.467099	+	3.24875i	0.0151467	+	0.105348i
$952$		0			0
$953$	−3.69820	−	51.7076i	−0.119796	−	1.67497i	−0.601680	−	0.798738i	$-0.705502\pi$
$953$	−3.69820	−	51.7076i	−0.119796	−	1.67497i	0.481883	−	0.876235i	$-0.339953\pi$
$954$		0			0
$955$	−4.11435	−	23.2608i	−0.133137	−	0.752701i
$956$		0			0
$957$	2.41065	+	4.41478i	0.0779253	+	0.142710i
$958$		0			0
$959$	24.1778	−	20.9502i	0.780742	−	0.676517i
$960$		0			0
$961$	28.5117	−	8.37179i	0.919732	−	0.270058i
$962$		0			0
$963$	15.5307	+	20.7466i	0.500469	+	0.668548i
$964$		0			0
$965$	−5.98471	−	0.234306i	−0.192655	−	0.00754258i
$966$		0			0
$967$	−5.74062	+	5.74062i	−0.184606	+	0.184606i	−0.793359	−	0.608754i	$-0.791670\pi$
$967$	−5.74062	+	5.74062i	−0.184606	+	0.184606i	0.608754	+	0.793359i	$0.291670\pi$
$968$		0			0
$969$	5.94955	+	0.855416i	0.191127	+	0.0274799i
$970$		0			0
$971$	10.7713	+	36.6837i	0.345667	+	1.17724i	0.930565	+	0.366128i	$0.119317\pi$
$971$	10.7713	+	36.6837i	0.345667	+	1.17724i	−0.584897	+	0.811107i	$0.698865\pi$
$972$		0			0
$973$	21.2737	+	1.52152i	0.682003	+	0.0487778i
$974$		0			0
$975$	−0.374131	−	0.142476i	−0.0119818	−	0.00456287i
$976$		0			0
$977$	6.25817	+	28.7683i	0.200217	+	0.920381i	0.962106	+	0.272674i	$0.0879081\pi$
$977$	6.25817	+	28.7683i	0.200217	+	0.920381i	−0.761890	+	0.647707i	$0.775728\pi$
$978$		0			0
$979$	5.63619	+	4.88378i	0.180133	+	0.156086i
$980$		0			0
$981$	−51.1456	+	7.35363i	−1.63295	+	0.234783i
$982$		0			0
$983$	30.5960	+	11.4117i	0.975860	+	0.363977i	0.786268	−	0.617886i	$-0.212011\pi$
$983$	30.5960	+	11.4117i	0.975860	+	0.363977i	0.189592	+	0.981863i	$0.439283\pi$
$984$		0			0
$985$	−5.60969	−	2.83212i	−0.178740	−	0.0902389i
$986$		0			0
$987$	14.9445	+	3.25099i	0.475690	+	0.103480i
$988$		0			0
$989$	−23.9866	−	15.1578i	−0.762730	−	0.481990i
$990$		0			0
$991$	26.9542	−	17.3224i	0.856227	−	0.550264i	−0.0372842	−	0.999305i	$-0.511871\pi$
$991$	26.9542	−	17.3224i	0.856227	−	0.550264i	0.893511	+	0.449041i	$0.148234\pi$
$992$		0			0
$993$	4.17116	−	1.55576i	0.132368	−	0.0493707i
$994$		0			0
$995$	−42.9147	−	17.9486i	−1.36049	−	0.569009i
$996$		0			0
$997$	−6.45988	−	4.83581i	−0.204586	−	0.153152i	0.492072	−	0.870555i	$-0.336240\pi$
$997$	−6.45988	−	4.83581i	−0.204586	−	0.153152i	−0.696658	+	0.717403i	$0.745331\pi$
$998$		0			0
$999$	2.51445	−	2.90183i	0.0795536	−	0.0918097i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.333.6	yes	240
5.2	odd	4	inner	460.2.x.a.57.7	✓	240
23.21	odd	22	inner	460.2.x.a.113.7	yes	240
115.67	even	44	inner	460.2.x.a.297.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.57.7	✓	240	5.2	odd	4	inner
460.2.x.a.113.7	yes	240	23.21	odd	22	inner
460.2.x.a.297.6	yes	240	115.67	even	44	inner
460.2.x.a.333.6	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.412482 + 0.308781i) q^{3} +(-1.14759 + 1.91912i) q^{5} +(0.218363 - 3.05312i) q^{7} +(-0.770401 + 2.62375i) q^{9} +O(q^{10})\)	\(q+(-0.412482 + 0.308781i) q^{3} +(-1.14759 + 1.91912i) q^{5} +(0.218363 - 3.05312i) q^{7} +(-0.770401 + 2.62375i) q^{9} +(-1.30741 + 2.03437i) q^{11} +(-0.155000 + 0.0110858i) q^{13} +(-0.119228 - 1.14596i) q^{15} +(-1.84552 + 4.94803i) q^{17} +(-0.917639 + 2.00935i) q^{19} +(0.852673 + 1.32678i) q^{21} +(-4.48053 + 1.71022i) q^{23} +(-2.36608 - 4.40473i) q^{25} +(-1.03257 - 2.76844i) q^{27} +(-3.67210 + 1.67699i) q^{29} +(0.161302 + 1.12188i) q^{31} +(-0.0888899 - 1.24284i) q^{33} +(5.60873 + 3.92279i) q^{35} +(0.622782 + 1.14054i) q^{37} +(0.0605116 - 0.0524336i) q^{39} +(-11.6377 + 3.41715i) q^{41} +(3.54563 + 4.73641i) q^{43} +(-4.15119 - 4.48948i) q^{45} +(6.85700 - 6.85700i) q^{47} +(-2.34511 - 0.337176i) q^{49} +(-0.766610 - 2.61083i) q^{51} +(10.4809 + 0.749612i) q^{53} +(-2.40384 - 4.84370i) q^{55} +(-0.241938 - 1.11217i) q^{57} +(7.94805 + 6.88702i) q^{59} +(-3.34965 + 0.481607i) q^{61} +(7.84238 + 2.92506i) q^{63} +(0.156601 - 0.310186i) q^{65} +(4.21490 + 0.916895i) q^{67} +(1.32006 - 2.08894i) q^{69} +(-5.76111 + 3.70244i) q^{71} +(4.68224 - 1.74639i) q^{73} +(2.33606 + 1.08628i) q^{75} +(5.92568 + 4.43591i) q^{77} +(8.94885 - 10.3275i) q^{79} +(-5.62050 - 3.61207i) q^{81} +(2.49105 - 1.36022i) q^{83} +(-7.37798 - 9.22008i) q^{85} +(0.996855 - 1.82560i) q^{87} +(0.438889 - 3.05254i) q^{89} +0.475654i q^{91} +(-0.412948 - 0.412948i) q^{93} +(-2.80312 - 4.06697i) q^{95} +(-14.4425 - 7.88622i) q^{97} +(-4.33043 - 4.99759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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