LMFDB - Embedded newform 1860.2.s.a.1177.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1860,2,Mod(433,1860)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1860.433"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1860, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1860.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8521747760$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1177.27
Character	$\chi$	$=$	1860.1177
Dual form			1860.2.s.a.433.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{3} +(-1.64250 - 1.51730i) q^{5} +(0.674956 + 0.674956i) q^{7} +1.00000i q^{9} +1.09513i q^{11} +(-2.63427 - 2.63427i) q^{13} +(-0.0885319 - 2.23431i) q^{15} +(1.41591 - 1.41591i) q^{17} +2.52916i q^{19} +0.954532i q^{21} +(5.53381 + 5.53381i) q^{23} +(0.395616 + 4.98432i) q^{25} +(-0.707107 + 0.707107i) q^{27} +5.18978 q^{29} +(1.26807 - 5.42144i) q^{31} +(-0.774371 + 0.774371i) q^{33} +(-0.0845065 - 2.13272i) q^{35} +(3.34017 - 3.34017i) q^{37} -3.72543i q^{39} +4.37610 q^{41} +(3.16760 + 3.16760i) q^{43} +(1.51730 - 1.64250i) q^{45} +(7.37506 + 7.37506i) q^{47} -6.08887i q^{49} +2.00240 q^{51} +(-3.45807 - 3.45807i) q^{53} +(1.66163 - 1.79875i) q^{55} +(-1.78839 + 1.78839i) q^{57} +11.6212i q^{59} -4.88626i q^{61} +(-0.674956 + 0.674956i) q^{63} +(0.329819 + 8.32377i) q^{65} +(3.63817 + 3.63817i) q^{67} +7.82599i q^{69} +15.2051 q^{71} +(-5.18122 - 5.18122i) q^{73} +(-3.24471 + 3.80419i) q^{75} +(-0.739162 + 0.739162i) q^{77} -8.53262 q^{79} -1.00000 q^{81} +(0.755959 + 0.755959i) q^{83} +(-4.47399 + 0.177276i) q^{85} +(3.66973 + 3.66973i) q^{87} +6.58476 q^{89} -3.55604i q^{91} +(4.73020 - 2.93688i) q^{93} +(3.83750 - 4.15415i) q^{95} +(4.81663 + 4.81663i) q^{97} -1.09513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1860\mathbb{Z}\right)^\times$.

$n$	$931$	$1117$	$1241$	$1801$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$	−1.64250	−	1.51730i	−0.734549	−	0.678556i
$5$	−1.64250	−	1.51730i	−0.734549	−	0.678556i
$6$		0			0
$7$	0.674956	+	0.674956i	0.255109	+	0.255109i	0.823062	−	0.567952i	$-0.192264\pi$
$7$	0.674956	+	0.674956i	0.255109	+	0.255109i	−0.567952	+	0.823062i	$0.692264\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$			1.09513i			0.330193i	0.986277	+	0.165097i	$0.0527936\pi$
$11$			1.09513i			0.330193i	−0.986277	+	0.165097i	$0.947206\pi$
$12$		0			0
$13$	−2.63427	−	2.63427i	−0.730616	−	0.730616i	0.240126	−	0.970742i	$-0.422811\pi$
$13$	−2.63427	−	2.63427i	−0.730616	−	0.730616i	−0.970742	+	0.240126i	$0.922811\pi$
$14$		0			0
$15$	−0.0885319	−	2.23431i	−0.0228588	−	0.576898i
$16$		0			0
$17$	1.41591	−	1.41591i	0.343409	−	0.343409i	−0.514239	−	0.857647i	$-0.671925\pi$
$17$	1.41591	−	1.41591i	0.343409	−	0.343409i	0.857647	+	0.514239i	$0.171925\pi$
$18$		0			0
$19$			2.52916i			0.580230i	0.956992	+	0.290115i	$0.0936936\pi$
$19$			2.52916i			0.580230i	−0.956992	+	0.290115i	$0.906306\pi$
$20$		0			0
$21$			0.954532i			0.208296i
$22$		0			0
$23$	5.53381	+	5.53381i	1.15388	+	1.15388i	0.985768	+	0.168112i	$0.0537671\pi$
$23$	5.53381	+	5.53381i	1.15388	+	1.15388i	0.168112	+	0.985768i	$0.446233\pi$
$24$		0			0
$25$	0.395616	+	4.98432i	0.0791232	+	0.996865i
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	5.18978			0.963718			0.481859	−	0.876249i	$-0.339962\pi$
$29$	5.18978			0.963718			0.481859	+	0.876249i	$0.339962\pi$
$30$		0			0
$31$	1.26807	−	5.42144i	0.227752	−	0.973719i
$31$	1.26807	−	5.42144i	0.227752	−	0.973719i
$32$		0			0
$33$	−0.774371	+	0.774371i	−0.134801	+	0.134801i
$34$		0			0
$35$	−0.0845065	−	2.13272i	−0.0142842	−	0.360496i
$36$		0			0
$37$	3.34017	−	3.34017i	0.549121	−	0.549121i	−0.377066	−	0.926187i	$-0.623067\pi$
$37$	3.34017	−	3.34017i	0.549121	−	0.549121i	0.926187	+	0.377066i	$0.123067\pi$
$38$		0			0
$39$		−	3.72543i		−	0.596545i
$40$		0			0
$41$	4.37610			0.683431			0.341716	−	0.939803i	$-0.388992\pi$
$41$	4.37610			0.683431			0.341716	+	0.939803i	$0.388992\pi$
$42$		0			0
$43$	3.16760	+	3.16760i	0.483054	+	0.483054i	0.906106	−	0.423051i	$-0.139041\pi$
$43$	3.16760	+	3.16760i	0.483054	+	0.483054i	−0.423051	+	0.906106i	$0.639041\pi$
$44$		0			0
$45$	1.51730	−	1.64250i	0.226185	−	0.244850i
$46$		0			0
$47$	7.37506	+	7.37506i	1.07576	+	1.07576i	0.996884	+	0.0788794i	$0.0251342\pi$
$47$	7.37506	+	7.37506i	1.07576	+	1.07576i	0.0788794	+	0.996884i	$0.474866\pi$
$48$		0			0
$49$		−	6.08887i		−	0.869838i
$50$		0			0
$51$	2.00240			0.280392
$52$		0			0
$53$	−3.45807	−	3.45807i	−0.475003	−	0.475003i	0.428526	−	0.903529i	$-0.359033\pi$
$53$	−3.45807	−	3.45807i	−0.475003	−	0.475003i	−0.903529	+	0.428526i	$0.859033\pi$
$54$		0			0
$55$	1.66163	−	1.79875i	0.224054	−	0.242543i
$56$		0			0
$57$	−1.78839	+	1.78839i	−0.236878	+	0.236878i
$58$		0			0
$59$			11.6212i			1.51295i	0.654024	+	0.756473i	$0.273079\pi$
$59$			11.6212i			1.51295i	−0.654024	+	0.756473i	$0.726921\pi$
$60$		0			0
$61$		−	4.88626i		−	0.625622i	−0.949815	−	0.312811i	$-0.898729\pi$
$61$		−	4.88626i		−	0.625622i	0.949815	−	0.312811i	$-0.101271\pi$
$62$		0			0
$63$	−0.674956	+	0.674956i	−0.0850364	+	0.0850364i
$64$		0			0
$65$	0.329819	+	8.32377i	0.0409090	+	1.03244i
$66$		0			0
$67$	3.63817	+	3.63817i	0.444473	+	0.444473i	0.893512	−	0.449039i	$-0.148234\pi$
$67$	3.63817	+	3.63817i	0.444473	+	0.444473i	−0.449039	+	0.893512i	$0.648234\pi$
$68$		0			0
$69$			7.82599i			0.942139i
$70$		0			0
$71$	15.2051			1.80451			0.902254	−	0.431205i	$-0.141911\pi$
$71$	15.2051			1.80451			0.902254	+	0.431205i	$0.141911\pi$
$72$		0			0
$73$	−5.18122	−	5.18122i	−0.606416	−	0.606416i	0.335592	−	0.942007i	$-0.391064\pi$
$73$	−5.18122	−	5.18122i	−0.606416	−	0.606416i	−0.942007	+	0.335592i	$0.891064\pi$
$74$		0			0
$75$	−3.24471	+	3.80419i	−0.374666	+	0.439270i
$76$		0			0
$77$	−0.739162	+	0.739162i	−0.0842353	+	0.0842353i
$78$		0			0
$79$	−8.53262			−0.959995			−0.479997	−	0.877270i	$-0.659362\pi$
$79$	−8.53262			−0.959995			−0.479997	+	0.877270i	$0.659362\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	0.755959	+	0.755959i	0.0829773	+	0.0829773i	0.747377	−	0.664400i	$-0.231313\pi$
$83$	0.755959	+	0.755959i	0.0829773	+	0.0829773i	−0.664400	+	0.747377i	$0.731313\pi$
$84$		0			0
$85$	−4.47399	+	0.177276i	−0.485272	+	0.0192283i
$86$		0			0
$87$	3.66973	+	3.66973i	0.393436	+	0.393436i
$88$		0			0
$89$	6.58476			0.697984			0.348992	−	0.937126i	$-0.386524\pi$
$89$	6.58476			0.697984			0.348992	+	0.937126i	$0.386524\pi$
$90$		0			0
$91$		−	3.55604i		−	0.372774i
$92$		0			0
$93$	4.73020	−	2.93688i	0.490498	−	0.304540i
$94$		0			0
$95$	3.83750	−	4.15415i	0.393719	−	0.426207i
$96$		0			0
$97$	4.81663	+	4.81663i	0.489055	+	0.489055i	0.908008	−	0.418953i	$-0.137603\pi$
$97$	4.81663	+	4.81663i	0.489055	+	0.489055i	−0.418953	+	0.908008i	$0.637603\pi$
$98$		0			0
$99$	−1.09513			−0.110064
$100$		0			0
$101$	5.57055			0.554291			0.277145	−	0.960828i	$-0.410612\pi$
$101$	5.57055			0.554291			0.277145	+	0.960828i	$0.410612\pi$
$102$		0			0
$103$	5.51344	−	5.51344i	0.543256	−	0.543256i	−0.381226	−	0.924482i	$-0.624498\pi$
$103$	5.51344	−	5.51344i	0.543256	−	0.543256i	0.924482	+	0.381226i	$0.124498\pi$
$104$		0			0
$105$	1.44831	−	1.56782i	0.141340	−	0.153003i
$106$		0			0
$107$	−7.40337	−	7.40337i	−0.715711	−	0.715711i	0.252013	−	0.967724i	$-0.418907\pi$
$107$	−7.40337	−	7.40337i	−0.715711	−	0.715711i	−0.967724	+	0.252013i	$0.918907\pi$
$108$		0			0
$109$			12.7983i			1.22586i	0.790139	+	0.612928i	$0.210008\pi$
$109$			12.7983i			1.22586i	−0.790139	+	0.612928i	$0.789992\pi$
$110$		0			0
$111$	4.72372			0.448355
$112$		0			0
$113$	−3.41147	+	3.41147i	−0.320924	+	0.320924i	−0.849122	−	0.528197i	$-0.822868\pi$
$113$	−3.41147	+	3.41147i	−0.320924	+	0.320924i	0.528197	+	0.849122i	$0.322868\pi$
$114$		0			0
$115$	−0.692850	−	17.4857i	−0.0646086	−	1.63055i
$116$		0			0
$117$	2.63427	−	2.63427i	0.243539	−	0.243539i
$118$		0			0
$119$	1.91135			0.175213
$120$		0			0
$121$	9.80070			0.890973
$122$		0			0
$123$	3.09437	+	3.09437i	0.279010	+	0.279010i
$124$		0			0
$125$	6.91290	−	8.78702i	0.618309	−	0.785935i
$126$		0			0
$127$	7.87121	−	7.87121i	0.698457	−	0.698457i	−0.265621	−	0.964078i	$-0.585577\pi$
$127$	7.87121	−	7.87121i	0.698457	−	0.698457i	0.964078	+	0.265621i	$0.0855770\pi$
$128$		0			0
$129$			4.47966i			0.394412i
$130$		0			0
$131$	2.41281			0.210808			0.105404	−	0.994429i	$-0.466386\pi$
$131$	2.41281			0.210808			0.105404	+	0.994429i	$0.466386\pi$
$132$		0			0
$133$	−1.70707	+	1.70707i	−0.148022	+	0.148022i
$134$		0			0
$135$	2.23431	−	0.0885319i	0.192299	−	0.00761961i
$136$		0			0
$137$	5.04954	−	5.04954i	0.431411	−	0.431411i	−0.457697	−	0.889108i	$-0.651326\pi$
$137$	5.04954	−	5.04954i	0.431411	−	0.431411i	0.889108	+	0.457697i	$0.151326\pi$
$138$		0			0
$139$	−1.34745			−0.114289			−0.0571447	−	0.998366i	$-0.518200\pi$
$139$	−1.34745			−0.114289			−0.0571447	+	0.998366i	$0.518200\pi$
$140$		0			0
$141$			10.4299i			0.878357i
$142$		0			0
$143$	2.88486	−	2.88486i	0.241244	−	0.241244i
$144$		0			0
$145$	−8.52422	−	7.87444i	−0.707898	−	0.653937i
$146$		0			0
$147$	4.30548	−	4.30548i	0.355110	−	0.355110i
$148$		0			0
$149$			17.8665i			1.46368i	0.681474	+	0.731842i	$0.261339\pi$
$149$			17.8665i			1.46368i	−0.681474	+	0.731842i	$0.738661\pi$
$150$		0			0
$151$			13.8290i			1.12539i	0.826664	+	0.562696i	$0.190236\pi$
$151$			13.8290i			1.12539i	−0.826664	+	0.562696i	$0.809764\pi$
$152$		0			0
$153$	1.41591	+	1.41591i	0.114470	+	0.114470i
$154$		0			0
$155$	−10.3087	+	6.98068i	−0.828018	+	0.560702i
$156$		0			0
$157$	−11.1983	−	11.1983i	−0.893725	−	0.893725i	0.101147	−	0.994872i	$-0.467749\pi$
$157$	−11.1983	−	11.1983i	−0.893725	−	0.893725i	−0.994872	+	0.101147i	$0.967749\pi$
$158$		0			0
$159$		−	4.89045i		−	0.387838i
$160$		0			0
$161$			7.47016i			0.588731i
$162$		0			0
$163$	−5.93305	+	5.93305i	−0.464713	+	0.464713i	−0.900196	−	0.435484i	$-0.856577\pi$
$163$	−5.93305	+	5.93305i	−0.464713	+	0.464713i	0.435484	+	0.900196i	$0.356577\pi$
$164$		0			0
$165$	2.44686	−	0.0969536i	0.190488	−	0.00754782i
$166$		0			0
$167$	−10.2689	+	10.2689i	−0.794634	+	0.794634i	−0.982244	−	0.187609i	$-0.939926\pi$
$167$	−10.2689	+	10.2689i	−0.794634	+	0.794634i	0.187609	+	0.982244i	$0.439926\pi$
$168$		0			0
$169$			0.878795i			0.0675996i
$170$		0			0
$171$	−2.52916			−0.193410
$172$		0			0
$173$	−9.99494	+	9.99494i	−0.759901	+	0.759901i	−0.976304	−	0.216403i	$-0.930568\pi$
$173$	−9.99494	+	9.99494i	−0.759901	+	0.759901i	0.216403	+	0.976304i	$0.430568\pi$
$174$		0			0
$175$	−3.09718	+	3.63122i	−0.234124	+	0.274495i
$176$		0			0
$177$	−8.21740	+	8.21740i	−0.617658	+	0.617658i
$178$		0			0
$179$	−24.0536			−1.79785			−0.898924	−	0.438105i	$-0.855650\pi$
$179$	−24.0536			−1.79785			−0.898924	+	0.438105i	$0.855650\pi$
$180$		0			0
$181$			1.25030i			0.0929339i	0.998920	+	0.0464670i	$0.0147962\pi$
$181$			1.25030i			0.0929339i	−0.998920	+	0.0464670i	$0.985204\pi$
$182$		0			0
$183$	3.45511	−	3.45511i	0.255409	−	0.255409i
$184$		0			0
$185$	−10.5543	+	0.418199i	−0.775965	+	0.0307466i
$186$		0			0
$187$	1.55060	+	1.55060i	0.113391	+	0.113391i
$188$		0			0
$189$	−0.954532			−0.0694320
$190$		0			0
$191$	17.8442			1.29116			0.645579	−	0.763693i	$-0.276616\pi$
$191$	17.8442			1.29116			0.645579	+	0.763693i	$0.276616\pi$
$192$		0			0
$193$	−14.6393	+	14.6393i	−1.05376	+	1.05376i	−0.0552868	+	0.998471i	$0.517607\pi$
$193$	−14.6393	+	14.6393i	−1.05376	+	1.05376i	−0.998471	+	0.0552868i	$0.982393\pi$
$194$		0			0
$195$	−5.65258	+	6.11901i	−0.404790	+	0.438192i
$196$		0			0
$197$	17.9405	−	17.9405i	1.27821	−	1.27821i	0.336536	−	0.941671i	$-0.390745\pi$
$197$	17.9405	−	17.9405i	1.27821	−	1.27821i	0.941671	−	0.336536i	$-0.109255\pi$
$198$		0			0
$199$	12.4017			0.879134			0.439567	−	0.898210i	$-0.355132\pi$
$199$	12.4017			0.879134			0.439567	+	0.898210i	$0.355132\pi$
$200$		0			0
$201$			5.14515i			0.362911i
$202$		0			0
$203$	3.50287	+	3.50287i	0.245853	+	0.245853i
$204$		0			0
$205$	−7.18774	−	6.63984i	−0.502013	−	0.463746i
$206$		0			0
$207$	−5.53381	+	5.53381i	−0.384627	+	0.384627i
$208$		0			0
$209$	−2.76975			−0.191588
$210$		0			0
$211$	12.9668			0.892674			0.446337	−	0.894865i	$-0.352728\pi$
$211$	12.9668			0.892674			0.446337	+	0.894865i	$0.352728\pi$
$212$		0			0
$213$	10.7516	+	10.7516i	0.736687	+	0.736687i
$214$		0			0
$215$	−0.396593	−	10.0090i	−0.0270474	−	0.682606i
$216$		0			0
$217$	4.51512	−	2.80334i	0.306506	−	0.190303i
$218$		0			0
$219$		−	7.32735i		−	0.495136i
$220$		0			0
$221$	−7.45979			−0.501800
$222$		0			0
$223$	−1.27168	−	1.27168i	−0.0851581	−	0.0851581i	0.663245	−	0.748403i	$-0.269179\pi$
$223$	−1.27168	−	1.27168i	−0.0851581	−	0.0851581i	−0.748403	+	0.663245i	$0.769179\pi$
$224$		0			0
$225$	−4.98432	+	0.395616i	−0.332288	+	0.0263744i
$226$		0			0
$227$	−14.9881	−	14.9881i	−0.994798	−	0.994798i	0.00518898	−	0.999987i	$-0.498348\pi$
$227$	−14.9881	−	14.9881i	−0.994798	−	0.994798i	−0.999987	+	0.00518898i	$0.998348\pi$
$228$		0			0
$229$	−9.42360			−0.622729			−0.311364	−	0.950291i	$-0.600786\pi$
$229$	−9.42360			−0.622729			−0.311364	+	0.950291i	$0.600786\pi$
$230$		0			0
$231$	−1.04533			−0.0687778
$232$		0			0
$233$	−11.8768	+	11.8768i	−0.778072	+	0.778072i	−0.979503	−	0.201431i	$-0.935441\pi$
$233$	−11.8768	+	11.8768i	−0.778072	+	0.778072i	0.201431	+	0.979503i	$0.435441\pi$
$234$		0			0
$235$	−0.923380	−	23.3037i	−0.0602346	−	1.52017i
$236$		0			0
$237$	−6.03347	−	6.03347i	−0.391916	−	0.391916i
$238$		0			0
$239$	6.87543			0.444735			0.222367	−	0.974963i	$-0.428622\pi$
$239$	6.87543			0.444735			0.222367	+	0.974963i	$0.428622\pi$
$240$		0			0
$241$		−	27.2401i		−	1.75469i	−0.479859	−	0.877346i	$-0.659312\pi$
$241$		−	27.2401i		−	1.75469i	0.479859	−	0.877346i	$-0.340688\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−9.23863	+	10.0010i	−0.590234	+	0.638939i
$246$		0			0
$247$	6.66251	−	6.66251i	0.423925	−	0.423925i
$248$		0			0
$249$			1.06909i			0.0677507i
$250$		0			0
$251$			21.4917i			1.35654i	0.734812	+	0.678271i	$0.237270\pi$
$251$			21.4917i			1.35654i	−0.734812	+	0.678271i	$0.762730\pi$
$252$		0			0
$253$	−6.06023	+	6.06023i	−0.381003	+	0.381003i
$254$		0			0
$255$	−3.28894	−	3.03824i	−0.205961	−	0.190262i
$256$		0			0
$257$	−5.94155	−	5.94155i	−0.370624	−	0.370624i	0.497080	−	0.867704i	$-0.334405\pi$
$257$	−5.94155	−	5.94155i	−0.370624	−	0.370624i	−0.867704	+	0.497080i	$0.834405\pi$
$258$		0			0
$259$	4.50894			0.280172
$260$		0			0
$261$			5.18978i			0.321239i
$262$		0			0
$263$	−1.25620	−	1.25620i	−0.0774607	−	0.0774607i	0.667315	−	0.744776i	$-0.267444\pi$
$263$	−1.25620	−	1.25620i	−0.0774607	−	0.0774607i	−0.744776	+	0.667315i	$0.767444\pi$
$264$		0			0
$265$	0.432961	+	10.9268i	0.0265966	+	0.671229i
$266$		0			0
$267$	4.65613	+	4.65613i	0.284951	+	0.284951i
$268$		0			0
$269$	8.10846			0.494381			0.247191	−	0.968967i	$-0.420493\pi$
$269$	8.10846			0.494381			0.247191	+	0.968967i	$0.420493\pi$
$270$		0			0
$271$		−	25.9070i		−	1.57374i	−0.617122	−	0.786868i	$-0.711701\pi$
$271$		−	25.9070i		−	1.57374i	0.617122	−	0.786868i	$-0.288299\pi$
$272$		0			0
$273$	2.51450	−	2.51450i	0.152184	−	0.152184i
$274$		0			0
$275$	−5.45846	+	0.433250i	−0.329158	+	0.0261259i
$276$		0			0
$277$	2.49814	−	2.49814i	0.150099	−	0.150099i	−0.628063	−	0.778162i	$-0.716152\pi$
$277$	2.49814	−	2.49814i	0.150099	−	0.150099i	0.778162	+	0.628063i	$0.216152\pi$
$278$		0			0
$279$	5.42144	+	1.26807i	0.324573	+	0.0759172i
$280$		0			0
$281$	−1.72691			−0.103019			−0.0515093	−	0.998673i	$-0.516403\pi$
$281$	−1.72691			−0.103019			−0.0515093	+	0.998673i	$0.516403\pi$
$282$		0			0
$283$	−2.59071	+	2.59071i	−0.154001	+	0.154001i	−0.779902	−	0.625901i	$-0.784731\pi$
$283$	−2.59071	+	2.59071i	−0.154001	+	0.154001i	0.625901	+	0.779902i	$0.284731\pi$
$284$		0			0
$285$	5.65095	−	0.223912i	0.334733	−	0.0132634i
$286$		0			0
$287$	2.95367	+	2.95367i	0.174350	+	0.174350i
$288$		0			0
$289$			12.9904i			0.764141i
$290$		0			0
$291$			6.81175i			0.399312i
$292$		0			0
$293$	10.6069	−	10.6069i	0.619665	−	0.619665i	−0.325781	−	0.945445i	$-0.605627\pi$
$293$	10.6069	−	10.6069i	0.619665	−	0.619665i	0.945445	+	0.325781i	$0.105627\pi$
$294$		0			0
$295$	17.6328	−	19.0878i	1.02662	−	1.11133i
$296$		0			0
$297$	−0.774371	−	0.774371i	−0.0449336	−	0.0449336i
$298$		0			0
$299$		−	29.1552i		−	1.68609i
$300$		0			0
$301$			4.27598i			0.246463i
$302$		0			0
$303$	3.93897	+	3.93897i	0.226288	+	0.226288i
$304$		0			0
$305$	−7.41392	+	8.02569i	−0.424520	+	0.459550i
$306$		0			0
$307$	−22.2521	−	22.2521i	−1.26999	−	1.26999i	−0.946090	−	0.323904i	$-0.895005\pi$
$307$	−22.2521	−	22.2521i	−1.26999	−	1.26999i	−0.323904	−	0.946090i	$-0.604995\pi$
$308$		0			0
$309$	7.79719			0.443567
$310$		0			0
$311$	−13.2621			−0.752026			−0.376013	−	0.926614i	$-0.622705\pi$
$311$	−13.2621			−0.752026			−0.376013	+	0.926614i	$0.622705\pi$
$312$		0			0
$313$	9.01445	+	9.01445i	0.509527	+	0.509527i	0.914381	−	0.404854i	$-0.132678\pi$
$313$	9.01445	+	9.01445i	0.509527	+	0.509527i	−0.404854	+	0.914381i	$0.632678\pi$
$314$		0			0
$315$	2.13272	−	0.0845065i	0.120165	−	0.00476140i
$316$		0			0
$317$	2.34914	+	2.34914i	0.131941	+	0.131941i	0.769993	−	0.638052i	$-0.220260\pi$
$317$	2.34914	+	2.34914i	0.131941	+	0.131941i	−0.638052	+	0.769993i	$0.720260\pi$
$318$		0			0
$319$			5.68347i			0.318213i
$320$		0			0
$321$		−	10.4699i		−	0.584376i
$322$		0			0
$323$	3.58107	+	3.58107i	0.199256	+	0.199256i
$324$		0			0
$325$	12.0879	−	14.1722i	0.670517	−	0.786134i
$326$		0			0
$327$	−9.04977	+	9.04977i	−0.500453	+	0.500453i
$328$		0			0
$329$			9.95568i			0.548875i
$330$		0			0
$331$		−	26.5502i		−	1.45933i	−0.683804	−	0.729666i	$-0.739676\pi$
$331$		−	26.5502i		−	1.45933i	0.683804	−	0.729666i	$-0.260324\pi$
$332$		0			0
$333$	3.34017	+	3.34017i	0.183040	+	0.183040i
$334$		0			0
$335$	−0.455509	−	11.4959i	−0.0248871	−	0.628087i
$336$		0			0
$337$	−18.8301	+	18.8301i	−1.02574	+	1.02574i	−0.0260815	+	0.999660i	$0.508303\pi$
$337$	−18.8301	+	18.8301i	−1.02574	+	1.02574i	−0.999660	+	0.0260815i	$0.991697\pi$
$338$		0			0
$339$	−4.82455			−0.262034
$340$		0			0
$341$	5.93716	+	1.38869i	0.321515	+	0.0752020i
$342$		0			0
$343$	8.83441	−	8.83441i	0.477013	−	0.477013i
$344$		0			0
$345$	11.8744	−	12.8542i	0.639294	−	0.692047i
$346$		0			0
$347$	−2.66638	+	2.66638i	−0.143139	+	0.143139i	−0.775045	−	0.631906i	$-0.782273\pi$
$347$	−2.66638	+	2.66638i	−0.143139	+	0.143139i	0.631906	+	0.775045i	$0.282273\pi$
$348$		0			0
$349$			26.3012i			1.40787i	0.710265	+	0.703934i	$0.248575\pi$
$349$			26.3012i			1.40787i	−0.710265	+	0.703934i	$0.751425\pi$
$350$		0			0
$351$	3.72543			0.198848
$352$		0			0
$353$	4.13690	+	4.13690i	0.220185	+	0.220185i	0.808576	−	0.588391i	$-0.200239\pi$
$353$	4.13690	+	4.13690i	0.220185	+	0.220185i	−0.588391	+	0.808576i	$0.700239\pi$
$354$		0			0
$355$	−24.9743	−	23.0706i	−1.32550	−	1.22446i
$356$		0			0
$357$	1.35153	+	1.35153i	0.0715306	+	0.0715306i
$358$		0			0
$359$		−	4.28123i		−	0.225955i	−0.993598	−	0.112977i	$-0.963961\pi$
$359$		−	4.28123i		−	0.225955i	0.993598	−	0.112977i	$-0.0360388\pi$
$360$		0			0
$361$	12.6033			0.663333
$362$		0			0
$363$	6.93014	+	6.93014i	0.363738	+	0.363738i
$364$		0			0
$365$	0.648704	+	16.3716i	0.0339547	+	0.856929i
$366$		0			0
$367$	−8.88242	+	8.88242i	−0.463659	+	0.463659i	−0.899853	−	0.436194i	$-0.856326\pi$
$367$	−8.88242	+	8.88242i	−0.463659	+	0.463659i	0.436194	+	0.899853i	$0.356326\pi$
$368$		0			0
$369$			4.37610i			0.227810i
$370$		0			0
$371$		−	4.66809i		−	0.242355i
$372$		0			0
$373$	−14.3672	+	14.3672i	−0.743905	+	0.743905i	−0.973327	−	0.229422i	$-0.926317\pi$
$373$	−14.3672	+	14.3672i	−0.743905	+	0.743905i	0.229422	+	0.973327i	$0.426317\pi$
$374$		0			0
$375$	11.1015	−	1.32520i	0.573280	−	0.0684331i
$376$		0			0
$377$	−13.6713	−	13.6713i	−0.704108	−	0.704108i
$378$		0			0
$379$		−	12.0851i		−	0.620772i	−0.950611	−	0.310386i	$-0.899542\pi$
$379$		−	12.0851i		−	0.620772i	0.950611	−	0.310386i	$-0.100458\pi$
$380$		0			0
$381$	11.1316			0.570287
$382$		0			0
$383$	−25.0270	−	25.0270i	−1.27882	−	1.27882i	−0.941330	−	0.337489i	$-0.890422\pi$
$383$	−25.0270	−	25.0270i	−1.27882	−	1.27882i	−0.337489	−	0.941330i	$-0.609578\pi$
$384$		0			0
$385$	2.33560	−	0.0925452i	0.119033	−	0.00471654i
$386$		0			0
$387$	−3.16760	+	3.16760i	−0.161018	+	0.161018i
$388$		0			0
$389$	20.0881			1.01851			0.509254	−	0.860616i	$-0.329921\pi$
$389$	20.0881			1.01851			0.509254	+	0.860616i	$0.329921\pi$
$390$		0			0
$391$	15.6708			0.792505
$392$		0			0
$393$	1.70611	+	1.70611i	0.0860621	+	0.0860621i
$394$		0			0
$395$	14.0148	+	12.9465i	0.705163	+	0.651410i
$396$		0			0
$397$	−24.3552	−	24.3552i	−1.22235	−	1.22235i	−0.966794	−	0.255558i	$-0.917741\pi$
$397$	−24.3552	−	24.3552i	−1.22235	−	1.22235i	−0.255558	−	0.966794i	$-0.582259\pi$
$398$		0			0
$399$	−2.41417			−0.120860
$400$		0			0
$401$		−	19.8177i		−	0.989649i	−0.868993	−	0.494824i	$-0.835232\pi$
$401$		−	19.8177i		−	0.989649i	0.868993	−	0.494824i	$-0.164768\pi$
$402$		0			0
$403$	−17.6220	+	10.9411i	−0.877814	+	0.545016i
$404$		0			0
$405$	1.64250	+	1.51730i	0.0816165	+	0.0753951i
$406$		0			0
$407$	3.65791	+	3.65791i	0.181316	+	0.181316i
$408$		0			0
$409$	−23.2433			−1.14931			−0.574655	−	0.818396i	$-0.694864\pi$
$409$	−23.2433			−1.14931			−0.574655	+	0.818396i	$0.694864\pi$
$410$		0			0
$411$	7.14112			0.352246
$412$		0			0
$413$	−7.84377	+	7.84377i	−0.385967	+	0.385967i
$414$		0			0
$415$	−0.0946483	−	2.38868i	−0.00464610	−	0.117256i
$416$		0			0
$417$	−0.952792	−	0.952792i	−0.0466584	−	0.0466584i
$418$		0			0
$419$		−	14.1658i		−	0.692042i	−0.938227	−	0.346021i	$-0.887533\pi$
$419$		−	14.1658i		−	0.692042i	0.938227	−	0.346021i	$-0.112467\pi$
$420$		0			0
$421$	−15.1661			−0.739150			−0.369575	−	0.929201i	$-0.620497\pi$
$421$	−15.1661			−0.739150			−0.369575	+	0.929201i	$0.620497\pi$
$422$		0			0
$423$	−7.37506	+	7.37506i	−0.358588	+	0.358588i
$424$		0			0
$425$	7.61751	+	6.49720i	0.369504	+	0.315160i
$426$		0			0
$427$	3.29801	−	3.29801i	0.159602	−	0.159602i
$428$		0			0
$429$	4.07981			0.196975
$430$		0			0
$431$	11.6559			0.561447			0.280723	−	0.959789i	$-0.409426\pi$
$431$	11.6559			0.561447			0.280723	+	0.959789i	$0.409426\pi$
$432$		0			0
$433$	−10.0234	−	10.0234i	−0.481694	−	0.481694i	0.423978	−	0.905672i	$-0.360633\pi$
$433$	−10.0234	−	10.0234i	−0.481694	−	0.481694i	−0.905672	+	0.423978i	$0.860633\pi$
$434$		0			0
$435$	−0.459461	−	11.5956i	−0.0220295	−	0.555967i
$436$		0			0
$437$	−13.9959	+	13.9959i	−0.669516	+	0.669516i
$438$		0			0
$439$		−	25.4921i		−	1.21667i	−0.793680	−	0.608336i	$-0.791837\pi$
$439$		−	25.4921i		−	1.21667i	0.793680	−	0.608336i	$-0.208163\pi$
$440$		0			0
$441$	6.08887			0.289946
$442$		0			0
$443$	−10.0568	+	10.0568i	−0.477813	+	0.477813i	−0.904432	−	0.426619i	$-0.859705\pi$
$443$	−10.0568	+	10.0568i	−0.477813	+	0.477813i	0.426619	+	0.904432i	$0.359705\pi$
$444$		0			0
$445$	−10.8155	−	9.99105i	−0.512703	−	0.473621i
$446$		0			0
$447$	−12.6336	+	12.6336i	−0.597547	+	0.597547i
$448$		0			0
$449$	27.5805			1.30160			0.650802	−	0.759247i	$-0.274433\pi$
$449$	27.5805			1.30160			0.650802	+	0.759247i	$0.274433\pi$
$450$		0			0
$451$			4.79238i			0.225664i
$452$		0			0
$453$	−9.77861	+	9.77861i	−0.459439	+	0.459439i
$454$		0			0
$455$	−5.39557	+	5.84079i	−0.252948	+	0.273821i
$456$		0			0
$457$	−8.75134	+	8.75134i	−0.409371	+	0.409371i	−0.881519	−	0.472148i	$-0.843479\pi$
$457$	−8.75134	+	8.75134i	−0.409371	+	0.409371i	0.472148	+	0.881519i	$0.343479\pi$
$458$		0			0
$459$			2.00240i			0.0934640i
$460$		0			0
$461$			11.8628i			0.552506i	0.961085	+	0.276253i	$0.0890928\pi$
$461$			11.8628i			0.552506i	−0.961085	+	0.276253i	$0.910907\pi$
$462$		0			0
$463$	−10.6990	−	10.6990i	−0.497227	−	0.497227i	0.413347	−	0.910574i	$-0.364360\pi$
$463$	−10.6990	−	10.6990i	−0.497227	−	0.497227i	−0.910574	+	0.413347i	$0.864360\pi$
$464$		0			0
$465$	−12.2255	−	2.35329i	−0.566942	−	0.109131i
$466$		0			0
$467$	2.66393	+	2.66393i	0.123272	+	0.123272i	0.766051	−	0.642779i	$-0.222219\pi$
$467$	2.66393	+	2.66393i	0.123272	+	0.123272i	−0.642779	+	0.766051i	$0.722219\pi$
$468$		0			0
$469$			4.91121i			0.226778i
$470$		0			0
$471$		−	15.8368i		−	0.729723i
$472$		0			0
$473$	−3.46892	+	3.46892i	−0.159501	+	0.159501i
$474$		0			0
$475$	−12.6062	+	1.00058i	−0.578411	+	0.0459097i
$476$		0			0
$477$	3.45807	−	3.45807i	0.158334	−	0.158334i
$478$		0			0
$479$		−	4.74464i		−	0.216788i	−0.994108	−	0.108394i	$-0.965429\pi$
$479$		−	4.74464i		−	0.216788i	0.994108	−	0.108394i	$-0.0345708\pi$
$480$		0			0
$481$	−17.5979			−0.802393
$482$		0			0
$483$	−5.28220	+	5.28220i	−0.240348	+	0.240348i
$484$		0			0
$485$	−0.603057	−	15.2196i	−0.0273834	−	0.691086i
$486$		0			0
$487$	8.34525	−	8.34525i	0.378159	−	0.378159i	−0.492278	−	0.870438i	$-0.663836\pi$
$487$	8.34525	−	8.34525i	0.378159	−	0.378159i	0.870438	+	0.492278i	$0.163836\pi$
$488$		0			0
$489$	−8.39060			−0.379436
$490$		0			0
$491$			31.4346i			1.41863i	0.704894	+	0.709313i	$0.250995\pi$
$491$			31.4346i			1.41863i	−0.704894	+	0.709313i	$0.749005\pi$
$492$		0			0
$493$	7.34826	−	7.34826i	0.330949	−	0.330949i
$494$		0			0
$495$	1.79875	+	1.66163i	0.0808476	+	0.0746848i
$496$		0			0
$497$	10.2627	+	10.2627i	0.460347	+	0.460347i
$498$		0			0
$499$	14.0066			0.627022			0.313511	−	0.949585i	$-0.398495\pi$
$499$	14.0066			0.627022			0.313511	+	0.949585i	$0.398495\pi$
$500$		0			0
$501$	−14.5225			−0.648816
$502$		0			0
$503$	−3.51443	+	3.51443i	−0.156701	+	0.156701i	−0.781103	−	0.624402i	$-0.785343\pi$
$503$	−3.51443	+	3.51443i	−0.156701	+	0.156701i	0.624402	+	0.781103i	$0.285343\pi$
$504$		0			0
$505$	−9.14963	−	8.45218i	−0.407153	−	0.376117i
$506$		0			0
$507$	−0.621402	+	0.621402i	−0.0275974	+	0.0275974i
$508$		0			0
$509$	−2.64688			−0.117321			−0.0586604	−	0.998278i	$-0.518683\pi$
$509$	−2.64688			−0.117321			−0.0586604	+	0.998278i	$0.518683\pi$
$510$		0			0
$511$		−	6.99418i		−	0.309404i
$512$		0			0
$513$	−1.78839	−	1.78839i	−0.0789593	−	0.0789593i
$514$		0			0
$515$	−17.4214	+	0.690299i	−0.767677	+	0.0304182i
$516$		0			0
$517$	−8.07663	+	8.07663i	−0.355210	+	0.355210i
$518$		0			0
$519$	−14.1350			−0.620457
$520$		0			0
$521$	−1.76978			−0.0775353			−0.0387676	−	0.999248i	$-0.512343\pi$
$521$	−1.76978			−0.0775353			−0.0387676	+	0.999248i	$0.512343\pi$
$522$		0			0
$523$	5.25909	+	5.25909i	0.229964	+	0.229964i	0.812678	−	0.582714i	$-0.198009\pi$
$523$	5.25909	+	5.25909i	0.229964	+	0.229964i	−0.582714	+	0.812678i	$0.698009\pi$
$524$		0			0
$525$	−4.75770	+	0.377628i	−0.207643	+	0.0164810i
$526$		0			0
$527$	−5.88080	−	9.47174i	−0.256172	−	0.412595i
$528$		0			0
$529$			38.2462i			1.66288i
$530$		0			0
$531$	−11.6212			−0.504316
$532$		0			0
$533$	−11.5278	−	11.5278i	−0.499326	−	0.499326i
$534$		0			0
$535$	0.926924	+	23.3932i	0.0400744	+	1.01137i
$536$		0			0
$537$	−17.0084	−	17.0084i	−0.733968	−	0.733968i
$538$		0			0
$539$	6.66808			0.287215
$540$		0			0
$541$	−10.1801			−0.437679			−0.218839	−	0.975761i	$-0.570227\pi$
$541$	−10.1801			−0.437679			−0.218839	+	0.975761i	$0.570227\pi$
$542$		0			0
$543$	−0.884094	+	0.884094i	−0.0379401	+	0.0379401i
$544$		0			0
$545$	19.4188	−	21.0212i	0.831812	−	0.900450i
$546$		0			0
$547$	−28.4175	−	28.4175i	−1.21504	−	1.21504i	−0.969346	−	0.245698i	$-0.920983\pi$
$547$	−28.4175	−	28.4175i	−1.21504	−	1.21504i	−0.245698	−	0.969346i	$-0.579017\pi$
$548$		0			0
$549$	4.88626			0.208541
$550$		0			0
$551$			13.1258i			0.559178i
$552$		0			0
$553$	−5.75914	−	5.75914i	−0.244904	−	0.244904i
$554$		0			0
$555$	−7.75871	−	7.16728i	−0.329339	−	0.304234i
$556$		0			0
$557$	0.676207	−	0.676207i	0.0286518	−	0.0286518i	−0.692636	−	0.721288i	$-0.743551\pi$
$557$	0.676207	−	0.676207i	0.0286518	−	0.0286518i	0.721288	+	0.692636i	$0.243551\pi$
$558$		0			0
$559$		−	16.6886i		−	0.705854i
$560$		0			0
$561$			2.19288i			0.0925835i
$562$		0			0
$563$	14.8036	−	14.8036i	0.623897	−	0.623897i	−0.322629	−	0.946526i	$-0.604566\pi$
$563$	14.8036	−	14.8036i	0.623897	−	0.623897i	0.946526	+	0.322629i	$0.104566\pi$
$564$		0			0
$565$	10.7796	−	0.427126i	0.453500	−	0.0179693i
$566$		0			0
$567$	−0.674956	−	0.674956i	−0.0283455	−	0.0283455i
$568$		0			0
$569$	19.5754			0.820642			0.410321	−	0.911941i	$-0.365417\pi$
$569$	19.5754			0.820642			0.410321	+	0.911941i	$0.365417\pi$
$570$		0			0
$571$		−	10.5827i		−	0.442871i	−0.975175	−	0.221436i	$-0.928926\pi$
$571$		−	10.5827i		−	0.442871i	0.975175	−	0.221436i	$-0.0710743\pi$
$572$		0			0
$573$	12.6177	+	12.6177i	0.527113	+	0.527113i
$574$		0			0
$575$	−25.3931	+	29.7716i	−1.05896	+	1.24156i
$576$		0			0
$577$	2.42237	+	2.42237i	0.100845	+	0.100845i	0.755729	−	0.654884i	$-0.227283\pi$
$577$	2.42237	+	2.42237i	0.100845	+	0.100845i	−0.654884	+	0.755729i	$0.727283\pi$
$578$		0			0
$579$	−20.7030			−0.860389
$580$		0			0
$581$			1.02048i			0.0423365i
$582$		0			0
$583$	3.78703	−	3.78703i	0.156843	−	0.156843i
$584$		0			0
$585$	−8.32377	+	0.329819i	−0.344146	+	0.0136363i
$586$		0			0
$587$	31.2971	−	31.2971i	1.29177	−	1.29177i	0.358079	−	0.933691i	$-0.383432\pi$
$587$	31.2971	−	31.2971i	1.29177	−	1.29177i	0.933691	−	0.358079i	$-0.116568\pi$
$588$		0			0
$589$	13.7117	+	3.20715i	0.564981	+	0.132148i
$590$		0			0
$591$	25.3717			1.04365
$592$		0			0
$593$	−16.1223	+	16.1223i	−0.662062	+	0.662062i	−0.955866	−	0.293803i	$-0.905079\pi$
$593$	−16.1223	+	16.1223i	−0.662062	+	0.662062i	0.293803	+	0.955866i	$0.405079\pi$
$594$		0			0
$595$	−3.13940	−	2.90009i	−0.128703	−	0.118892i
$596$		0			0
$597$	8.76933	+	8.76933i	0.358905	+	0.358905i
$598$		0			0
$599$			34.4127i			1.40607i	0.711157	+	0.703033i	$0.248171\pi$
$599$			34.4127i			1.40607i	−0.711157	+	0.703033i	$0.751829\pi$
$600$		0			0
$601$			43.9721i			1.79366i	0.442375	+	0.896830i	$0.354136\pi$
$601$			43.9721i			1.79366i	−0.442375	+	0.896830i	$0.645864\pi$
$602$		0			0
$603$	−3.63817	+	3.63817i	−0.148158	+	0.148158i
$604$		0			0
$605$	−16.0977	−	14.8706i	−0.654463	−	0.604575i
$606$		0			0
$607$	18.9315	+	18.9315i	0.768407	+	0.768407i	0.977826	−	0.209419i	$-0.0671572\pi$
$607$	18.9315	+	18.9315i	0.768407	+	0.768407i	−0.209419	+	0.977826i	$0.567157\pi$
$608$		0			0
$609$			4.95381i			0.200739i
$610$		0			0
$611$		−	38.8559i		−	1.57194i
$612$		0			0
$613$	4.11508	+	4.11508i	0.166207	+	0.166207i	0.785310	−	0.619103i	$-0.212504\pi$
$613$	4.11508	+	4.11508i	0.166207	+	0.166207i	−0.619103	+	0.785310i	$0.712504\pi$
$614$		0			0
$615$	−0.387424	−	9.77757i	−0.0156224	−	0.394270i
$616$		0			0
$617$	−28.7713	−	28.7713i	−1.15829	−	1.15829i	−0.984843	−	0.173447i	$-0.944510\pi$
$617$	−28.7713	−	28.7713i	−1.15829	−	1.15829i	−0.173447	−	0.984843i	$-0.555490\pi$
$618$		0			0
$619$	−10.9506			−0.440143			−0.220071	−	0.975484i	$-0.570629\pi$
$619$	−10.9506			−0.440143			−0.220071	+	0.975484i	$0.570629\pi$
$620$		0			0
$621$	−7.82599			−0.314046
$622$		0			0
$623$	4.44442	+	4.44442i	0.178062	+	0.178062i
$624$		0			0
$625$	−24.6870	+	3.94376i	−0.987479	+	0.157750i
$626$		0			0
$627$	−1.95851	−	1.95851i	−0.0782155	−	0.0782155i
$628$		0			0
$629$		−	9.45877i		−	0.377146i
$630$		0			0
$631$		−	37.6162i		−	1.49748i	−0.662866	−	0.748738i	$-0.730660\pi$
$631$		−	37.6162i		−	1.49748i	0.662866	−	0.748738i	$-0.269340\pi$
$632$		0			0
$633$	9.16894	+	9.16894i	0.364433	+	0.364433i
$634$		0			0
$635$	−24.8714	+	0.985498i	−0.986992	+	0.0391083i
$636$		0			0
$637$	−16.0397	+	16.0397i	−0.635518	+	0.635518i
$638$		0			0
$639$			15.2051i			0.601503i
$640$		0			0
$641$			33.6101i			1.32752i	0.747945	+	0.663761i	$0.231041\pi$
$641$			33.6101i			1.32752i	−0.747945	+	0.663761i	$0.768959\pi$
$642$		0			0
$643$	26.6316	+	26.6316i	1.05025	+	1.05025i	0.998669	+	0.0515772i	$0.0164248\pi$
$643$	26.6316	+	26.6316i	1.05025	+	1.05025i	0.0515772	+	0.998669i	$0.483575\pi$
$644$		0			0
$645$	6.79698	−	7.35785i	0.267631	−	0.289715i
$646$		0			0
$647$	−9.07490	+	9.07490i	−0.356771	+	0.356771i	−0.862621	−	0.505850i	$-0.831179\pi$
$647$	−9.07490	+	9.07490i	−0.356771	+	0.356771i	0.505850	+	0.862621i	$0.331179\pi$
$648$		0			0
$649$	−12.7266			−0.499564
$650$		0			0
$651$	5.17494	+	1.21041i	0.202822	+	0.0474397i
$652$		0			0
$653$	−19.2462	+	19.2462i	−0.753163	+	0.753163i	−0.975068	−	0.221905i	$-0.928772\pi$
$653$	−19.2462	+	19.2462i	−0.753163	+	0.753163i	0.221905	+	0.975068i	$0.428772\pi$
$654$		0			0
$655$	−3.96304	−	3.66095i	−0.154849	−	0.143045i
$656$		0			0
$657$	5.18122	−	5.18122i	0.202139	−	0.202139i
$658$		0			0
$659$		−	6.30466i		−	0.245595i	−0.992432	−	0.122797i	$-0.960813\pi$
$659$		−	6.30466i		−	0.245595i	0.992432	−	0.122797i	$-0.0391865\pi$
$660$		0			0
$661$	30.4139			1.18296			0.591482	−	0.806318i	$-0.298543\pi$
$661$	30.4139			1.18296			0.591482	+	0.806318i	$0.298543\pi$
$662$		0			0
$663$	−5.27487	−	5.27487i	−0.204859	−	0.204859i
$664$		0			0
$665$	5.39401	−	0.213731i	0.209171	−	0.00828812i
$666$		0			0
$667$	28.7193	+	28.7193i	1.11202	+	1.11202i
$668$		0			0
$669$		−	1.79843i		−	0.0695313i
$670$		0			0
$671$	5.35108			0.206576
$672$		0			0
$673$	−3.14867	−	3.14867i	−0.121372	−	0.121372i	0.643812	−	0.765184i	$-0.277352\pi$
$673$	−3.14867	−	3.14867i	−0.121372	−	0.121372i	−0.765184	+	0.643812i	$0.777352\pi$
$674$		0			0
$675$	−3.80419	−	3.24471i	−0.146423	−	0.124889i
$676$		0			0
$677$	−8.64677	+	8.64677i	−0.332322	+	0.332322i	−0.853468	−	0.521146i	$-0.825505\pi$
$677$	−8.64677	+	8.64677i	−0.332322	+	0.332322i	0.521146	+	0.853468i	$0.325505\pi$
$678$		0			0
$679$			6.50203i			0.249525i
$680$		0			0
$681$		−	21.1964i		−	0.812249i
$682$		0			0
$683$	−23.1432	+	23.1432i	−0.885550	+	0.885550i	−0.994092	−	0.108542i	$-0.965382\pi$
$683$	−23.1432	+	23.1432i	−0.885550	+	0.885550i	0.108542	+	0.994092i	$0.465382\pi$
$684$		0			0
$685$	−15.9555	+	0.632217i	−0.609629	+	0.0241558i
$686$		0			0
$687$	−6.66349	−	6.66349i	−0.254228	−	0.254228i
$688$		0			0
$689$			18.2190i			0.694089i
$690$		0			0
$691$	−8.97183			−0.341304			−0.170652	−	0.985331i	$-0.554587\pi$
$691$	−8.97183			−0.341304			−0.170652	+	0.985331i	$0.554587\pi$
$692$		0			0
$693$	−0.739162	−	0.739162i	−0.0280784	−	0.0280784i
$694$		0			0
$695$	2.21319	+	2.04449i	0.0839511	+	0.0775518i
$696$		0			0
$697$	6.19616	−	6.19616i	0.234696	−	0.234696i
$698$		0			0
$699$	−16.7963			−0.635293
$700$		0			0
$701$	26.9783			1.01895			0.509477	−	0.860484i	$-0.329839\pi$
$701$	26.9783			1.01895			0.509477	+	0.860484i	$0.329839\pi$
$702$		0			0
$703$	8.44785	+	8.44785i	0.318617	+	0.318617i
$704$		0			0
$705$	15.8253	−	17.1311i	0.596015	−	0.645196i
$706$		0			0
$707$	3.75988	+	3.75988i	0.141405	+	0.141405i
$708$		0			0
$709$	−43.0218			−1.61572			−0.807860	−	0.589375i	$-0.799374\pi$
$709$	−43.0218			−1.61572			−0.807860	+	0.589375i	$0.799374\pi$
$710$		0			0
$711$		−	8.53262i		−	0.319998i
$712$		0			0
$713$	37.0185	−	22.9840i	1.38635	−	0.860757i
$714$		0			0
$715$	−9.11558	+	0.361193i	−0.340903	+	0.0135079i
$716$		0			0
$717$	4.86166	+	4.86166i	0.181562	+	0.181562i
$718$		0			0
$719$	2.07067			0.0772230			0.0386115	−	0.999254i	$-0.487707\pi$
$719$	2.07067			0.0772230			0.0386115	+	0.999254i	$0.487707\pi$
$720$		0			0
$721$	7.44266			0.277179
$722$		0			0
$723$	19.2617	−	19.2617i	0.716350	−	0.716350i
$724$		0			0
$725$	2.05316	+	25.8676i	0.0762525	+	0.960697i
$726$		0			0
$727$	29.8835	+	29.8835i	1.10832	+	1.10832i	0.993372	+	0.114947i	$0.0366697\pi$
$727$	29.8835	+	29.8835i	1.10832	+	1.10832i	0.114947	+	0.993372i	$0.463330\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	8.97007			0.331770
$732$		0			0
$733$	27.5334	−	27.5334i	1.01697	−	1.01697i	0.0171174	−	0.999853i	$-0.494551\pi$
$733$	27.5334	−	27.5334i	1.01697	−	1.01697i	0.999853	−	0.0171174i	$-0.00544889\pi$
$734$		0			0
$735$	−13.6045	+	0.539059i	−0.501808	+	0.0198835i
$736$		0			0
$737$	−3.98425	+	3.98425i	−0.146762	+	0.146762i
$738$		0			0
$739$	−5.02503			−0.184849			−0.0924244	−	0.995720i	$-0.529462\pi$
$739$	−5.02503			−0.184849			−0.0924244	+	0.995720i	$0.529462\pi$
$740$		0			0
$741$	9.42221			0.346134
$742$		0			0
$743$	−34.7705	−	34.7705i	−1.27561	−	1.27561i	−0.943102	−	0.332504i	$-0.892106\pi$
$743$	−34.7705	−	34.7705i	−1.27561	−	1.27561i	−0.332504	−	0.943102i	$-0.607894\pi$
$744$		0			0
$745$	27.1089	−	29.3458i	0.993192	−	1.07515i
$746$		0			0
$747$	−0.755959	+	0.755959i	−0.0276591	+	0.0276591i
$748$		0			0
$749$		−	9.99390i		−	0.365169i
$750$		0			0
$751$	14.4725			0.528108			0.264054	−	0.964508i	$-0.414940\pi$
$751$	14.4725			0.528108			0.264054	+	0.964508i	$0.414940\pi$
$752$		0			0
$753$	−15.1969	+	15.1969i	−0.553806	+	0.553806i
$754$		0			0
$755$	20.9828	−	22.7142i	0.763642	−	0.826655i
$756$		0			0
$757$	19.9293	−	19.9293i	0.724345	−	0.724345i	−0.245143	−	0.969487i	$-0.578835\pi$
$757$	19.9293	−	19.9293i	0.724345	−	0.724345i	0.969487	+	0.245143i	$0.0788348\pi$
$758$		0			0
$759$	−8.57045			−0.311088
$760$		0			0
$761$			2.59554i			0.0940881i	0.998893	+	0.0470441i	$0.0149801\pi$
$761$			2.59554i			0.0940881i	−0.998893	+	0.0470441i	$0.985020\pi$
$762$		0			0
$763$	−8.63829	+	8.63829i	−0.312727	+	0.312727i
$764$		0			0
$765$	−0.177276	−	4.47399i	−0.00640943	−	0.161757i
$766$		0			0
$767$	30.6133	−	30.6133i	1.10538	−	1.10538i
$768$		0			0
$769$		−	17.1689i		−	0.619125i	−0.950879	−	0.309563i	$-0.899817\pi$
$769$		−	17.1689i		−	0.619125i	0.950879	−	0.309563i	$-0.100183\pi$
$770$		0			0
$771$		−	8.40263i		−	0.302613i
$772$		0			0
$773$	−16.1071	−	16.1071i	−0.579331	−	0.579331i	0.355388	−	0.934719i	$-0.384349\pi$
$773$	−16.1071	−	16.1071i	−0.579331	−	0.579331i	−0.934719	+	0.355388i	$0.884349\pi$
$774$		0			0
$775$	27.5239	+	4.17565i	0.988687	+	0.149994i
$776$		0			0
$777$	3.18830	+	3.18830i	0.114380	+	0.114380i
$778$		0			0
$779$			11.0679i			0.396547i
$780$		0			0
$781$			16.6515i			0.595836i
$782$		0			0
$783$	−3.66973	+	3.66973i	−0.131145	+	0.131145i
$784$		0			0
$785$	1.40207	+	35.3845i	0.0500419	+	1.26293i
$786$		0			0
$787$	−27.2835	+	27.2835i	−0.972552	+	0.972552i	−0.999633	−	0.0270816i	$-0.991379\pi$
$787$	−27.2835	+	27.2835i	−0.972552	+	0.972552i	0.0270816	+	0.999633i	$0.491379\pi$
$788$		0			0
$789$		−	1.77654i		−	0.0632464i
$790$		0			0
$791$	−4.60519			−0.163742
$792$		0			0
$793$	−12.8718	+	12.8718i	−0.457089	+	0.457089i
$794$		0			0
$795$	−7.42027	+	8.03257i	−0.263170	+	0.284886i
$796$		0			0
$797$	−0.223267	+	0.223267i	−0.00790851	+	0.00790851i	−0.711050	−	0.703141i	$-0.751780\pi$
$797$	−0.223267	+	0.223267i	−0.00790851	+	0.00790851i	0.703141	+	0.711050i	$0.251780\pi$
$798$		0			0
$799$	20.8849			0.738853
$800$		0			0
$801$			6.58476i			0.232661i
$802$		0			0
$803$	5.67409	−	5.67409i	0.200234	−	0.200234i
$804$		0			0
$805$	11.3345	−	12.2697i	0.399487	−	0.432452i
$806$		0			0
$807$	5.73355	+	5.73355i	0.201830	+	0.201830i
$808$		0			0
$809$	49.3759			1.73597			0.867983	−	0.496594i	$-0.165416\pi$
$809$	49.3759			1.73597			0.867983	+	0.496594i	$0.165416\pi$
$810$		0			0
$811$	35.7963			1.25698			0.628488	−	0.777819i	$-0.283674\pi$
$811$	35.7963			1.25698			0.628488	+	0.777819i	$0.283674\pi$
$812$		0			0
$813$	18.3190	−	18.3190i	0.642475	−	0.642475i
$814$		0			0
$815$	18.7472	−	0.742836i	0.656687	−	0.0260204i
$816$		0			0
$817$	−8.01138	+	8.01138i	−0.280283	+	0.280283i
$818$		0			0
$819$	3.55604			0.124258
$820$		0			0
$821$		−	44.5903i		−	1.55621i	−0.628132	−	0.778106i	$-0.716180\pi$
$821$		−	44.5903i		−	1.55621i	0.628132	−	0.778106i	$-0.283820\pi$
$822$		0			0
$823$	29.3364	+	29.3364i	1.02260	+	1.02260i	0.999739	+	0.0228648i	$0.00727873\pi$
$823$	29.3364	+	29.3364i	1.02260	+	1.02260i	0.0228648	+	0.999739i	$0.492721\pi$
$824$		0			0
$825$	−4.16607	−	3.55336i	−0.145044	−	0.123712i
$826$		0			0
$827$	−14.1963	+	14.1963i	−0.493652	+	0.493652i	−0.909455	−	0.415803i	$-0.863501\pi$
$827$	−14.1963	+	14.1963i	−0.493652	+	0.493652i	0.415803	+	0.909455i	$0.363501\pi$
$828$		0			0
$829$	5.58289			0.193902			0.0969508	−	0.995289i	$-0.469091\pi$
$829$	5.58289			0.193902			0.0969508	+	0.995289i	$0.469091\pi$
$830$		0			0
$831$	3.53291			0.122555
$832$		0			0
$833$	−8.62129	−	8.62129i	−0.298710	−	0.298710i
$834$		0			0
$835$	32.4478	−	1.28570i	1.12290	−	0.0444935i
$836$		0			0
$837$	2.93688	+	4.73020i	0.101513	+	0.163499i
$838$		0			0
$839$			29.4670i			1.01732i	0.860969	+	0.508658i	$0.169858\pi$
$839$			29.4670i			1.01732i	−0.860969	+	0.508658i	$0.830142\pi$
$840$		0			0
$841$	−2.06617			−0.0712472
$842$		0			0
$843$	−1.22111	−	1.22111i	−0.0420572	−	0.0420572i
$844$		0			0
$845$	1.33339	−	1.44342i	0.0458701	−	0.0496552i
$846$		0			0
$847$	6.61504	+	6.61504i	0.227295	+	0.227295i
$848$		0			0
$849$	−3.66381			−0.125742
$850$		0			0
$851$	36.9678			1.26724
$852$		0			0
$853$	14.9270	−	14.9270i	0.511090	−	0.511090i	−0.403770	−	0.914860i	$-0.632300\pi$
$853$	14.9270	−	14.9270i	0.511090	−	0.511090i	0.914860	+	0.403770i	$0.132300\pi$
$854$		0			0
$855$	4.15415	+	3.83750i	0.142069	+	0.131240i
$856$		0			0
$857$	14.8493	+	14.8493i	0.507243	+	0.507243i	0.913679	−	0.406436i	$-0.133229\pi$
$857$	14.8493	+	14.8493i	0.507243	+	0.507243i	−0.406436	+	0.913679i	$0.633229\pi$
$858$		0			0
$859$	1.41434			0.0482565			0.0241283	−	0.999709i	$-0.492319\pi$
$859$	1.41434			0.0482565			0.0241283	+	0.999709i	$0.492319\pi$
$860$		0			0
$861$			4.17712i			0.142356i
$862$		0			0
$863$	13.1106	+	13.1106i	0.446289	+	0.446289i	0.894119	−	0.447830i	$-0.147803\pi$
$863$	13.1106	+	13.1106i	0.446289	+	0.446289i	−0.447830	+	0.894119i	$0.647803\pi$
$864$		0			0
$865$	31.5820	−	1.25140i	1.07382	−	0.0425487i
$866$		0			0
$867$	−9.18560	+	9.18560i	−0.311959	+	0.311959i
$868$		0			0
$869$		−	9.34430i		−	0.316984i
$870$		0			0
$871$		−	19.1679i		−	0.649478i
$872$		0			0
$873$	−4.81663	+	4.81663i	−0.163018	+	0.163018i
$874$		0			0
$875$	10.5968	−	1.26495i	0.358236	−	0.0427630i
$876$		0			0
$877$	22.8529	+	22.8529i	0.771689	+	0.771689i	0.978402	−	0.206713i	$-0.0662766\pi$
$877$	22.8529	+	22.8529i	0.771689	+	0.771689i	−0.206713	+	0.978402i	$0.566277\pi$
$878$		0			0
$879$	15.0005			0.505954
$880$		0			0
$881$		−	10.6141i		−	0.357597i	−0.983886	−	0.178798i	$-0.942779\pi$
$881$		−	10.6141i		−	0.357597i	0.983886	−	0.178798i	$-0.0572210\pi$
$882$		0			0
$883$	−1.13603	−	1.13603i	−0.0382305	−	0.0382305i	0.687733	−	0.725964i	$-0.258606\pi$
$883$	−1.13603	−	1.13603i	−0.0382305	−	0.0382305i	−0.725964	+	0.687733i	$0.758606\pi$
$884$		0			0
$885$	25.9653	−	1.02884i	0.872815	−	0.0345842i
$886$		0			0
$887$	8.48910	+	8.48910i	0.285036	+	0.285036i	0.835114	−	0.550078i	$-0.185402\pi$
$887$	8.48910	+	8.48910i	0.285036	+	0.285036i	−0.550078	+	0.835114i	$0.685402\pi$
$888$		0			0
$889$	10.6254			0.356366
$890$		0			0
$891$		−	1.09513i		−	0.0366881i
$892$		0			0
$893$	−18.6528	+	18.6528i	−0.624191	+	0.624191i
$894$		0			0
$895$	39.5080	+	36.4964i	1.32061	+	1.21994i
$896$		0			0
$897$	20.6158	−	20.6158i	0.688342	−	0.688342i
$898$		0			0
$899$	6.58099	−	28.1361i	0.219488	−	0.938391i
$900$		0			0
$901$	−9.79264			−0.326240
$902$		0			0
$903$	−3.02357	+	3.02357i	−0.100618	+	0.100618i
$904$		0			0
$905$	1.89707	−	2.05362i	0.0630609	−	0.0682645i
$906$		0			0
$907$	−22.5564	−	22.5564i	−0.748972	−	0.748972i	0.225314	−	0.974286i	$-0.427659\pi$
$907$	−22.5564	−	22.5564i	−0.748972	−	0.748972i	−0.974286	+	0.225314i	$0.927659\pi$
$908$		0			0
$909$			5.57055i			0.184764i
$910$		0			0
$911$			9.99495i			0.331148i	0.986197	+	0.165574i	$0.0529476\pi$
$911$			9.99495i			0.331148i	−0.986197	+	0.165574i	$0.947052\pi$
$912$		0			0
$913$	−0.827870	+	0.827870i	−0.0273985	+	0.0273985i
$914$		0			0
$915$	−10.9175	+	0.432590i	−0.360920	+	0.0143010i
$916$		0			0
$917$	1.62854	+	1.62854i	0.0537791	+	0.0537791i
$918$		0			0
$919$			25.4139i			0.838328i	0.907911	+	0.419164i	$0.137677\pi$
$919$			25.4139i			0.838328i	−0.907911	+	0.419164i	$0.862323\pi$
$920$		0			0
$921$		−	31.4692i		−	1.03695i
$922$		0			0
$923$	−40.0543	−	40.0543i	−1.31840	−	1.31840i
$924$		0			0
$925$	17.9699	+	15.3271i	0.590848	+	0.503951i
$926$		0			0
$927$	5.51344	+	5.51344i	0.181085	+	0.181085i
$928$		0			0
$929$	33.1942			1.08907			0.544533	−	0.838740i	$-0.316707\pi$
$929$	33.1942			1.08907			0.544533	+	0.838740i	$0.316707\pi$
$930$		0			0
$931$	15.3998			0.504707
$932$		0			0
$933$	−9.37774	−	9.37774i	−0.307014	−	0.307014i
$934$		0			0
$935$	−0.194140	−	4.89958i	−0.00634905	−	0.160234i
$936$		0			0
$937$	2.85795	+	2.85795i	0.0933651	+	0.0933651i	0.752247	−	0.658882i	$-0.228970\pi$
$937$	2.85795	+	2.85795i	0.0933651	+	0.0933651i	−0.658882	+	0.752247i	$0.728970\pi$
$938$		0			0
$939$			12.7484i			0.416027i
$940$		0			0
$941$			10.4526i			0.340746i	0.985380	+	0.170373i	$0.0544973\pi$
$941$			10.4526i			0.340746i	−0.985380	+	0.170373i	$0.945503\pi$
$942$		0			0
$943$	24.2165	+	24.2165i	0.788598	+	0.788598i
$944$		0			0
$945$	1.56782	+	1.44831i	0.0510011	+	0.0471135i
$946$		0			0
$947$	−2.08838	+	2.08838i	−0.0678632	+	0.0678632i	−0.740224	−	0.672361i	$-0.765280\pi$
$947$	−2.08838	+	2.08838i	−0.0678632	+	0.0678632i	0.672361	+	0.740224i	$0.265280\pi$
$948$		0			0
$949$			27.2975i			0.886114i
$950$		0			0
$951$			3.32218i			0.107729i
$952$		0			0
$953$	−43.1572	−	43.1572i	−1.39800	−	1.39800i	−0.805772	−	0.592225i	$-0.798250\pi$
$953$	−43.1572	−	43.1572i	−1.39800	−	1.39800i	−0.592225	−	0.805772i	$-0.701750\pi$
$954$		0			0
$955$	−29.3090	−	27.0749i	−0.948418	−	0.876123i
$956$		0			0
$957$	−4.01882	+	4.01882i	−0.129910	+	0.129910i
$958$		0			0
$959$	6.81643			0.220114
$960$		0			0
$961$	−27.7840	−	13.7495i	−0.896258	−	0.443532i
$962$		0			0
$963$	7.40337	−	7.40337i	0.238570	−	0.238570i
$964$		0			0
$965$	46.2571	−	1.83288i	1.48907	−	0.0590025i
$966$		0			0
$967$	−15.0000	+	15.0000i	−0.482369	+	0.482369i	−0.905887	−	0.423518i	$-0.860795\pi$
$967$	−15.0000	+	15.0000i	−0.482369	+	0.482369i	0.423518	+	0.905887i	$0.360795\pi$
$968$		0			0
$969$			5.06440i			0.162692i
$970$		0			0
$971$	−10.0013			−0.320957			−0.160479	−	0.987039i	$-0.551304\pi$
$971$	−10.0013			−0.320957			−0.160479	+	0.987039i	$0.551304\pi$
$972$		0			0
$973$	−0.909471	−	0.909471i	−0.0291563	−	0.0291563i
$974$		0			0
$975$	18.5687	−	1.47384i	0.594675	−	0.0472006i
$976$		0			0
$977$	13.3907	+	13.3907i	0.428406	+	0.428406i	0.888085	−	0.459679i	$-0.152036\pi$
$977$	13.3907	+	13.3907i	0.428406	+	0.428406i	−0.459679	+	0.888085i	$0.652036\pi$
$978$		0			0
$979$			7.21115i			0.230469i
$980$		0			0
$981$	−12.7983			−0.408619
$982$		0			0
$983$	−0.201467	−	0.201467i	−0.00642579	−	0.00642579i	0.703887	−	0.710312i	$-0.251446\pi$
$983$	−0.201467	−	0.201467i	−0.00642579	−	0.00642579i	−0.710312	+	0.703887i	$0.751446\pi$
$984$		0			0
$985$	−56.6883	+	2.24620i	−1.80624	+	0.0715699i
$986$		0			0
$987$	−7.03973	+	7.03973i	−0.224077	+	0.224077i
$988$		0			0
$989$			35.0578i			1.11477i
$990$		0			0
$991$			49.2420i			1.56422i	0.623137	+	0.782112i	$0.285858\pi$
$991$			49.2420i			1.56422i	−0.623137	+	0.782112i	$0.714142\pi$
$992$		0			0
$993$	18.7738	−	18.7738i	0.595770	−	0.595770i
$994$		0			0
$995$	−20.3698	−	18.8171i	−0.645766	−	0.596541i
$996$		0			0
$997$	−10.2384	−	10.2384i	−0.324252	−	0.324252i	0.526144	−	0.850396i	$-0.323637\pi$
$997$	−10.2384	−	10.2384i	−0.324252	−	0.324252i	−0.850396	+	0.526144i	$0.823637\pi$
$998$		0			0
$999$			4.72372i			0.149452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1860.2.s.a.1177.27	yes	64
5.3	odd	4	inner	1860.2.s.a.433.7	✓	64
31.30	odd	2	inner	1860.2.s.a.1177.7	yes	64
155.123	even	4	inner	1860.2.s.a.433.27	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1860.2.s.a.433.7	✓	64	5.3	odd	4	inner
1860.2.s.a.433.27	yes	64	155.123	even	4	inner
1860.2.s.a.1177.7	yes	64	31.30	odd	2	inner
1860.2.s.a.1177.27	yes	64	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1860.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.64250 - 1.51730i) q^{5} +(0.674956 + 0.674956i) q^{7} +1.00000i q^{9} +1.09513i q^{11} +(-2.63427 - 2.63427i) q^{13} +(-0.0885319 - 2.23431i) q^{15} +(1.41591 - 1.41591i) q^{17} +2.52916i q^{19} +0.954532i q^{21} +(5.53381 + 5.53381i) q^{23} +(0.395616 + 4.98432i) q^{25} +(-0.707107 + 0.707107i) q^{27} +5.18978 q^{29} +(1.26807 - 5.42144i) q^{31} +(-0.774371 + 0.774371i) q^{33} +(-0.0845065 - 2.13272i) q^{35} +(3.34017 - 3.34017i) q^{37} -3.72543i q^{39} +4.37610 q^{41} +(3.16760 + 3.16760i) q^{43} +(1.51730 - 1.64250i) q^{45} +(7.37506 + 7.37506i) q^{47} -6.08887i q^{49} +2.00240 q^{51} +(-3.45807 - 3.45807i) q^{53} +(1.66163 - 1.79875i) q^{55} +(-1.78839 + 1.78839i) q^{57} +11.6212i q^{59} -4.88626i q^{61} +(-0.674956 + 0.674956i) q^{63} +(0.329819 + 8.32377i) q^{65} +(3.63817 + 3.63817i) q^{67} +7.82599i q^{69} +15.2051 q^{71} +(-5.18122 - 5.18122i) q^{73} +(-3.24471 + 3.80419i) q^{75} +(-0.739162 + 0.739162i) q^{77} -8.53262 q^{79} -1.00000 q^{81} +(0.755959 + 0.755959i) q^{83} +(-4.47399 + 0.177276i) q^{85} +(3.66973 + 3.66973i) q^{87} +6.58476 q^{89} -3.55604i q^{91} +(4.73020 - 2.93688i) q^{93} +(3.83750 - 4.15415i) q^{95} +(4.81663 + 4.81663i) q^{97} -1.09513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 8 q^{31} - 8 q^{33} + 24 q^{35} + 16 q^{41} + 56 q^{47} + 8 q^{63} - 32 q^{67} - 16 q^{71} - 64 q^{81} - 32 q^{87} - 32 q^{95} + 64 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 8 * q^31 - 8 * q^33 + 24 * q^35 + 16 * q^41 + 56 * q^47 + 8 * q^63 - 32 * q^67 - 16 * q^71 - 64 * q^81 - 32 * q^87 - 32 * q^95 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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