LMFDB - Embedded newform 2240.2.bd.a.561.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(561,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.bd (of order $4$, degree $2$, not 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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.4
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63220 + 1.63220i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -2.32815i q^{9} +O(q^{10})$	\(q+(-1.63220 + 1.63220i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -2.32815i q^{9} +(0.230290 + 0.230290i) q^{11} +(-1.57890 + 1.57890i) q^{13} +2.30828 q^{15} +4.13766 q^{17} +(-0.553790 + 0.553790i) q^{19} +(1.63220 + 1.63220i) q^{21} +0.651345i q^{23} +1.00000i q^{25} +(-1.09659 - 1.09659i) q^{27} +(-5.41931 + 5.41931i) q^{29} -4.74322 q^{31} -0.751759 q^{33} +(-0.707107 + 0.707107i) q^{35} +(4.34473 + 4.34473i) q^{37} -5.15418i q^{39} -6.29786i q^{41} +(-1.77592 - 1.77592i) q^{43} +(-1.64625 + 1.64625i) q^{45} +2.06198 q^{47} -1.00000 q^{49} +(-6.75348 + 6.75348i) q^{51} +(-3.94676 - 3.94676i) q^{53} -0.325680i q^{55} -1.80779i q^{57} +(-10.2275 - 10.2275i) q^{59} +(-3.32236 + 3.32236i) q^{61} -2.32815 q^{63} +2.23291 q^{65} +(10.7536 - 10.7536i) q^{67} +(-1.06313 - 1.06313i) q^{69} +2.53417i q^{71} -10.8492i q^{73} +(-1.63220 - 1.63220i) q^{75} +(0.230290 - 0.230290i) q^{77} -6.25359 q^{79} +10.5642 q^{81} +(-4.72764 + 4.72764i) q^{83} +(-2.92577 - 2.92577i) q^{85} -17.6908i q^{87} -9.25664i q^{89} +(1.57890 + 1.57890i) q^{91} +(7.74189 - 7.74189i) q^{93} +0.783177 q^{95} -2.47273 q^{97} +(0.536151 - 0.536151i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−1.63220	+	1.63220i	−0.942351	+	0.942351i	−0.998427	−	0.0560756i	$-0.982141\pi$
$3$	−1.63220	+	1.63220i	−0.942351	+	0.942351i	0.0560756	+	0.998427i	$0.482141\pi$
$4$		0			0
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$5$	−0.707107	−	0.707107i	−0.316228	−	0.316228i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$		−	2.32815i		−	0.776051i
$10$		0			0
$11$	0.230290	+	0.230290i	0.0694351	+	0.0694351i	0.740972	−	0.671536i	$-0.234365\pi$
$11$	0.230290	+	0.230290i	0.0694351	+	0.0694351i	−0.671536	+	0.740972i	$0.734365\pi$
$12$		0			0
$13$	−1.57890	+	1.57890i	−0.437909	+	0.437909i	−0.891308	−	0.453399i	$-0.850211\pi$
$13$	−1.57890	+	1.57890i	−0.437909	+	0.437909i	0.453399	+	0.891308i	$0.350211\pi$
$14$		0			0
$15$	2.30828			0.595995
$16$		0			0
$17$	4.13766			1.00353			0.501765	−	0.865004i	$-0.332684\pi$
$17$	4.13766			1.00353			0.501765	+	0.865004i	$0.332684\pi$
$18$		0			0
$19$	−0.553790	+	0.553790i	−0.127048	+	0.127048i	−0.767772	−	0.640724i	$-0.778634\pi$
$19$	−0.553790	+	0.553790i	−0.127048	+	0.127048i	0.640724	+	0.767772i	$0.278634\pi$
$20$		0			0
$21$	1.63220	+	1.63220i	0.356175	+	0.356175i
$22$		0			0
$23$			0.651345i			0.135815i	0.997692	+	0.0679074i	$0.0216322\pi$
$23$			0.651345i			0.135815i	−0.997692	+	0.0679074i	$0.978368\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−1.09659	−	1.09659i	−0.211039	−	0.211039i
$28$		0			0
$29$	−5.41931	+	5.41931i	−1.00634	+	1.00634i	−0.00636148	+	0.999980i	$0.502025\pi$
$29$	−5.41931	+	5.41931i	−1.00634	+	1.00634i	−0.999980	+	0.00636148i	$0.997975\pi$
$30$		0			0
$31$	−4.74322			−0.851908			−0.425954	−	0.904745i	$-0.640061\pi$
$31$	−4.74322			−0.851908			−0.425954	+	0.904745i	$0.640061\pi$
$32$		0			0
$33$	−0.751759			−0.130865
$34$		0			0
$35$	−0.707107	+	0.707107i	−0.119523	+	0.119523i
$36$		0			0
$37$	4.34473	+	4.34473i	0.714269	+	0.714269i	0.967425	−	0.253156i	$-0.0814687\pi$
$37$	4.34473	+	4.34473i	0.714269	+	0.714269i	−0.253156	+	0.967425i	$0.581469\pi$
$38$		0			0
$39$		−	5.15418i		−	0.825329i
$40$		0			0
$41$		−	6.29786i		−	0.983560i	−0.870720	−	0.491780i	$-0.836346\pi$
$41$		−	6.29786i		−	0.983560i	0.870720	−	0.491780i	$-0.163654\pi$
$42$		0			0
$43$	−1.77592	−	1.77592i	−0.270826	−	0.270826i	0.558607	−	0.829433i	$-0.311336\pi$
$43$	−1.77592	−	1.77592i	−0.270826	−	0.270826i	−0.829433	+	0.558607i	$0.811336\pi$
$44$		0			0
$45$	−1.64625	+	1.64625i	−0.245409	+	0.245409i
$46$		0			0
$47$	2.06198			0.300771			0.150385	−	0.988627i	$-0.451949\pi$
$47$	2.06198			0.300771			0.150385	+	0.988627i	$0.451949\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−6.75348	+	6.75348i	−0.945677	+	0.945677i
$52$		0			0
$53$	−3.94676	−	3.94676i	−0.542129	−	0.542129i	0.382024	−	0.924152i	$-0.375227\pi$
$53$	−3.94676	−	3.94676i	−0.542129	−	0.542129i	−0.924152	+	0.382024i	$0.875227\pi$
$54$		0			0
$55$		−	0.325680i		−	0.0439146i
$56$		0			0
$57$		−	1.80779i		−	0.239448i
$58$		0			0
$59$	−10.2275	−	10.2275i	−1.33151	−	1.33151i	−0.904021	−	0.427487i	$-0.859399\pi$
$59$	−10.2275	−	10.2275i	−1.33151	−	1.33151i	−0.427487	−	0.904021i	$-0.640601\pi$
$60$		0			0
$61$	−3.32236	+	3.32236i	−0.425385	+	0.425385i	−0.887053	−	0.461668i	$-0.847251\pi$
$61$	−3.32236	+	3.32236i	−0.425385	+	0.425385i	0.461668	+	0.887053i	$0.347251\pi$
$62$		0			0
$63$	−2.32815			−0.293320
$64$		0			0
$65$	2.23291			0.276958
$66$		0			0
$67$	10.7536	−	10.7536i	1.31376	−	1.31376i	0.395132	−	0.918624i	$-0.370699\pi$
$67$	10.7536	−	10.7536i	1.31376	−	1.31376i	0.918624	−	0.395132i	$-0.129301\pi$
$68$		0			0
$69$	−1.06313	−	1.06313i	−0.127985	−	0.127985i
$70$		0			0
$71$			2.53417i			0.300750i	0.988629	+	0.150375i	$0.0480482\pi$
$71$			2.53417i			0.300750i	−0.988629	+	0.150375i	$0.951952\pi$
$72$		0			0
$73$		−	10.8492i		−	1.26981i	−0.772591	−	0.634904i	$-0.781040\pi$
$73$		−	10.8492i		−	1.26981i	0.772591	−	0.634904i	$-0.218960\pi$
$74$		0			0
$75$	−1.63220	−	1.63220i	−0.188470	−	0.188470i
$76$		0			0
$77$	0.230290	−	0.230290i	0.0262440	−	0.0262440i
$78$		0			0
$79$	−6.25359			−0.703584			−0.351792	−	0.936078i	$-0.614428\pi$
$79$	−6.25359			−0.703584			−0.351792	+	0.936078i	$0.614428\pi$
$80$		0			0
$81$	10.5642			1.17380
$82$		0			0
$83$	−4.72764	+	4.72764i	−0.518926	+	0.518926i	−0.917246	−	0.398320i	$-0.869593\pi$
$83$	−4.72764	+	4.72764i	−0.518926	+	0.518926i	0.398320	+	0.917246i	$0.369593\pi$
$84$		0			0
$85$	−2.92577	−	2.92577i	−0.317344	−	0.317344i
$86$		0			0
$87$		−	17.6908i		−	1.89665i
$88$		0			0
$89$		−	9.25664i		−	0.981202i	−0.871384	−	0.490601i	$-0.836777\pi$
$89$		−	9.25664i		−	0.981202i	0.871384	−	0.490601i	$-0.163223\pi$
$90$		0			0
$91$	1.57890	+	1.57890i	0.165514	+	0.165514i
$92$		0			0
$93$	7.74189	−	7.74189i	0.802796	−	0.802796i
$94$		0			0
$95$	0.783177			0.0803523
$96$		0			0
$97$	−2.47273			−0.251068			−0.125534	−	0.992089i	$-0.540064\pi$
$97$	−2.47273			−0.251068			−0.125534	+	0.992089i	$0.540064\pi$
$98$		0			0
$99$	0.536151	−	0.536151i	0.0538852	−	0.0538852i
$100$		0			0
$101$	2.80716	+	2.80716i	0.279323	+	0.279323i	0.832839	−	0.553516i	$-0.186714\pi$
$101$	2.80716	+	2.80716i	0.279323	+	0.279323i	−0.553516	+	0.832839i	$0.686714\pi$
$102$		0			0
$103$		−	0.603916i		−	0.0595056i	−0.999557	−	0.0297528i	$-0.990528\pi$
$103$		−	0.603916i		−	0.0595056i	0.999557	−	0.0297528i	$-0.00947201\pi$
$104$		0			0
$105$		−	2.30828i		−	0.225265i
$106$		0			0
$107$	8.82899	+	8.82899i	0.853531	+	0.853531i	0.990566	−	0.137035i	$-0.0437574\pi$
$107$	8.82899	+	8.82899i	0.853531	+	0.853531i	−0.137035	+	0.990566i	$0.543757\pi$
$108$		0			0
$109$	−6.93357	+	6.93357i	−0.664115	+	0.664115i	−0.956347	−	0.292232i	$-0.905602\pi$
$109$	−6.93357	+	6.93357i	−0.664115	+	0.664115i	0.292232	+	0.956347i	$0.405602\pi$
$110$		0			0
$111$	−14.1829			−1.34618
$112$		0			0
$113$	−3.29485			−0.309953			−0.154977	−	0.987918i	$-0.549530\pi$
$113$	−3.29485			−0.309953			−0.154977	+	0.987918i	$0.549530\pi$
$114$		0			0
$115$	0.460570	−	0.460570i	0.0429484	−	0.0429484i
$116$		0			0
$117$	3.67593	+	3.67593i	0.339840	+	0.339840i
$118$		0			0
$119$		−	4.13766i		−	0.379298i
$120$		0			0
$121$		−	10.8939i		−	0.990358i
$122$		0			0
$123$	10.2794	+	10.2794i	0.926858	+	0.926858i
$124$		0			0
$125$	0.707107	−	0.707107i	0.0632456	−	0.0632456i
$126$		0			0
$127$	19.8246			1.75915			0.879575	−	0.475761i	$-0.157827\pi$
$127$	19.8246			1.75915			0.879575	+	0.475761i	$0.157827\pi$
$128$		0			0
$129$	5.79732			0.510425
$130$		0			0
$131$	2.58904	−	2.58904i	0.226206	−	0.226206i	−0.584900	−	0.811105i	$-0.698866\pi$
$131$	2.58904	−	2.58904i	0.226206	−	0.226206i	0.811105	+	0.584900i	$0.198866\pi$
$132$		0			0
$133$	0.553790	+	0.553790i	0.0480197	+	0.0480197i
$134$		0			0
$135$			1.55081i			0.133473i
$136$		0			0
$137$		−	10.5885i		−	0.904632i	−0.891858	−	0.452316i	$-0.850598\pi$
$137$		−	10.5885i		−	0.904632i	0.891858	−	0.452316i	$-0.149402\pi$
$138$		0			0
$139$	−14.8992	−	14.8992i	−1.26373	−	1.26373i	−0.949271	−	0.314460i	$-0.898177\pi$
$139$	−14.8992	−	14.8992i	−1.26373	−	1.26373i	−0.314460	−	0.949271i	$-0.601823\pi$
$140$		0			0
$141$	−3.36557	+	3.36557i	−0.283432	+	0.283432i
$142$		0			0
$143$	−0.727213			−0.0608126
$144$		0			0
$145$	7.66407			0.636466
$146$		0			0
$147$	1.63220	−	1.63220i	0.134622	−	0.134622i
$148$		0			0
$149$	2.28193	+	2.28193i	0.186943	+	0.186943i	0.794373	−	0.607430i	$-0.207799\pi$
$149$	2.28193	+	2.28193i	0.186943	+	0.186943i	−0.607430	+	0.794373i	$0.707799\pi$
$150$		0			0
$151$		−	18.0434i		−	1.46835i	−0.678959	−	0.734176i	$-0.737568\pi$
$151$		−	18.0434i		−	1.46835i	0.678959	−	0.734176i	$-0.262432\pi$
$152$		0			0
$153$		−	9.63309i		−	0.778789i
$154$		0			0
$155$	3.35396	+	3.35396i	0.269397	+	0.269397i
$156$		0			0
$157$	−7.26110	+	7.26110i	−0.579499	+	0.579499i	−0.934765	−	0.355266i	$-0.884390\pi$
$157$	−7.26110	+	7.26110i	−0.579499	+	0.579499i	0.355266	+	0.934765i	$0.384390\pi$
$158$		0			0
$159$	12.8838			1.02175
$160$		0			0
$161$	0.651345			0.0513332
$162$		0			0
$163$	4.81521	−	4.81521i	0.377157	−	0.377157i	−0.492919	−	0.870075i	$-0.664070\pi$
$163$	4.81521	−	4.81521i	0.377157	−	0.377157i	0.870075	+	0.492919i	$0.164070\pi$
$164$		0			0
$165$	0.531574	+	0.531574i	0.0413830	+	0.0413830i
$166$		0			0
$167$		−	22.7491i		−	1.76038i	−0.474625	−	0.880188i	$-0.657416\pi$
$167$		−	22.7491i		−	1.76038i	0.474625	−	0.880188i	$-0.342584\pi$
$168$		0			0
$169$			8.01412i			0.616471i
$170$		0			0
$171$	1.28931	+	1.28931i	0.0985958	+	0.0985958i
$172$		0			0
$173$	16.3387	−	16.3387i	1.24221	−	1.24221i	0.283124	−	0.959083i	$-0.408629\pi$
$173$	16.3387	−	16.3387i	1.24221	−	1.24221i	0.959083	−	0.283124i	$-0.0913710\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	33.3867			2.50950
$178$		0			0
$179$	13.8259	−	13.8259i	1.03339	−	1.03339i	0.0339721	−	0.999423i	$-0.489184\pi$
$179$	13.8259	−	13.8259i	1.03339	−	1.03339i	0.999423	−	0.0339721i	$-0.0108157\pi$
$180$		0			0
$181$	−12.1646	−	12.1646i	−0.904189	−	0.904189i	0.0916061	−	0.995795i	$-0.470800\pi$
$181$	−12.1646	−	12.1646i	−0.904189	−	0.904189i	−0.995795	+	0.0916061i	$0.970800\pi$
$182$		0			0
$183$		−	10.8455i		−	0.801724i
$184$		0			0
$185$		−	6.14438i		−	0.451744i
$186$		0			0
$187$	0.952862	+	0.952862i	0.0696802	+	0.0696802i
$188$		0			0
$189$	−1.09659	+	1.09659i	−0.0797652	+	0.0797652i
$190$		0			0
$191$	−8.62130			−0.623816			−0.311908	−	0.950112i	$-0.600968\pi$
$191$	−8.62130			−0.623816			−0.311908	+	0.950112i	$0.600968\pi$
$192$		0			0
$193$	−15.0833			−1.08572			−0.542861	−	0.839822i	$-0.682659\pi$
$193$	−15.0833			−1.08572			−0.542861	+	0.839822i	$0.682659\pi$
$194$		0			0
$195$	−3.64455	+	3.64455i	−0.260992	+	0.260992i
$196$		0			0
$197$	−5.90488	−	5.90488i	−0.420705	−	0.420705i	0.464741	−	0.885446i	$-0.346147\pi$
$197$	−5.90488	−	5.90488i	−0.420705	−	0.420705i	−0.885446	+	0.464741i	$0.846147\pi$
$198$		0			0
$199$			0.126378i			0.00895868i	0.999990	+	0.00447934i	$0.00142582\pi$
$199$			0.126378i			0.00895868i	−0.999990	+	0.00447934i	$0.998574\pi$
$200$		0			0
$201$			35.1039i			2.47604i
$202$		0			0
$203$	5.41931	+	5.41931i	0.380361	+	0.380361i
$204$		0			0
$205$	−4.45326	+	4.45326i	−0.311029	+	0.311029i
$206$		0			0
$207$	1.51643			0.105399
$208$		0			0
$209$	−0.255065			−0.0176432
$210$		0			0
$211$	−0.680388	+	0.680388i	−0.0468399	+	0.0468399i	−0.730139	−	0.683299i	$-0.760545\pi$
$211$	−0.680388	+	0.680388i	−0.0468399	+	0.0468399i	0.683299	+	0.730139i	$0.260545\pi$
$212$		0			0
$213$	−4.13627	−	4.13627i	−0.283412	−	0.283412i
$214$		0			0
$215$			2.51153i			0.171285i
$216$		0			0
$217$			4.74322i			0.321991i
$218$		0			0
$219$	17.7081	+	17.7081i	1.19661	+	1.19661i
$220$		0			0
$221$	−6.53297	+	6.53297i	−0.439455	+	0.439455i
$222$		0			0
$223$	−17.7352			−1.18763			−0.593817	−	0.804600i	$-0.702380\pi$
$223$	−17.7352			−1.18763			−0.593817	+	0.804600i	$0.702380\pi$
$224$		0			0
$225$	2.32815			0.155210
$226$		0			0
$227$	0.767624	−	0.767624i	0.0509490	−	0.0509490i	−0.681173	−	0.732122i	$-0.738530\pi$
$227$	0.767624	−	0.767624i	0.0509490	−	0.0509490i	0.732122	+	0.681173i	$0.238530\pi$
$228$		0			0
$229$	−10.1735	−	10.1735i	−0.672282	−	0.672282i	0.285960	−	0.958242i	$-0.407688\pi$
$229$	−10.1735	−	10.1735i	−0.672282	−	0.672282i	−0.958242	+	0.285960i	$0.907688\pi$
$230$		0			0
$231$			0.751759i			0.0494621i
$232$		0			0
$233$		−	15.7556i		−	1.03218i	−0.856534	−	0.516091i	$-0.827387\pi$
$233$		−	15.7556i		−	1.03218i	0.856534	−	0.516091i	$-0.172613\pi$
$234$		0			0
$235$	−1.45804	−	1.45804i	−0.0951121	−	0.0951121i
$236$		0			0
$237$	10.2071	−	10.2071i	0.663023	−	0.663023i
$238$		0			0
$239$	1.32563			0.0857476			0.0428738	−	0.999080i	$-0.486349\pi$
$239$	1.32563			0.0857476			0.0428738	+	0.999080i	$0.486349\pi$
$240$		0			0
$241$	−22.0952			−1.42328			−0.711638	−	0.702546i	$-0.752046\pi$
$241$	−22.0952			−1.42328			−0.711638	+	0.702546i	$0.752046\pi$
$242$		0			0
$243$	−13.9531	+	13.9531i	−0.895089	+	0.895089i
$244$		0			0
$245$	0.707107	+	0.707107i	0.0451754	+	0.0451754i
$246$		0			0
$247$		−	1.74876i		−	0.111271i
$248$		0			0
$249$		−	15.4329i		−	0.978021i
$250$		0			0
$251$	3.02111	+	3.02111i	0.190691	+	0.190691i	0.795995	−	0.605304i	$-0.206948\pi$
$251$	3.02111	+	3.02111i	0.190691	+	0.190691i	−0.605304	+	0.795995i	$0.706948\pi$
$252$		0			0
$253$	−0.149998	+	0.149998i	−0.00943032	+	0.00943032i
$254$		0			0
$255$	9.55087			0.598098
$256$		0			0
$257$	18.7247			1.16801			0.584006	−	0.811749i	$-0.301484\pi$
$257$	18.7247			1.16801			0.584006	+	0.811749i	$0.301484\pi$
$258$		0			0
$259$	4.34473	−	4.34473i	0.269968	−	0.269968i
$260$		0			0
$261$	12.6170	+	12.6170i	0.780972	+	0.780972i
$262$		0			0
$263$			14.7136i			0.907277i	0.891186	+	0.453639i	$0.149874\pi$
$263$			14.7136i			0.907277i	−0.891186	+	0.453639i	$0.850126\pi$
$264$		0			0
$265$			5.58156i			0.342872i
$266$		0			0
$267$	15.1087	+	15.1087i	0.924637	+	0.924637i
$268$		0			0
$269$	−13.6150	+	13.6150i	−0.830120	+	0.830120i	−0.987533	−	0.157413i	$-0.949685\pi$
$269$	−13.6150	+	13.6150i	−0.830120	+	0.830120i	0.157413	+	0.987533i	$0.449685\pi$
$270$		0			0
$271$	0.376705			0.0228832			0.0114416	−	0.999935i	$-0.496358\pi$
$271$	0.376705			0.0228832			0.0114416	+	0.999935i	$0.496358\pi$
$272$		0			0
$273$	−5.15418			−0.311945
$274$		0			0
$275$	−0.230290	+	0.230290i	−0.0138870	+	0.0138870i
$276$		0			0
$277$	−18.7924	−	18.7924i	−1.12913	−	1.12913i	−0.990319	−	0.138807i	$-0.955673\pi$
$277$	−18.7924	−	18.7924i	−1.12913	−	1.12913i	−0.138807	−	0.990319i	$-0.544327\pi$
$278$		0			0
$279$			11.0429i			0.661124i
$280$		0			0
$281$			4.41374i			0.263301i	0.991296	+	0.131651i	$0.0420277\pi$
$281$			4.41374i			0.263301i	−0.991296	+	0.131651i	$0.957972\pi$
$282$		0			0
$283$	11.8977	+	11.8977i	0.707247	+	0.707247i	0.965955	−	0.258709i	$-0.0832970\pi$
$283$	11.8977	+	11.8977i	0.707247	+	0.707247i	−0.258709	+	0.965955i	$0.583297\pi$
$284$		0			0
$285$	−1.27830	+	1.27830i	−0.0757201	+	0.0757201i
$286$		0			0
$287$	−6.29786			−0.371751
$288$		0			0
$289$	0.120206			0.00707093
$290$		0			0
$291$	4.03599	−	4.03599i	0.236594	−	0.236594i
$292$		0			0
$293$	−17.0375	−	17.0375i	−0.995341	−	0.995341i	0.00464837	−	0.999989i	$-0.498520\pi$
$293$	−17.0375	−	17.0375i	−0.995341	−	0.995341i	−0.999989	+	0.00464837i	$0.998520\pi$
$294$		0			0
$295$			14.4639i			0.842120i
$296$		0			0
$297$		−	0.505068i		−	0.0293070i
$298$		0			0
$299$	−1.02841	−	1.02841i	−0.0594746	−	0.0594746i
$300$		0			0
$301$	−1.77592	+	1.77592i	−0.102362	+	0.102362i
$302$		0			0
$303$	−9.16370			−0.526441
$304$		0			0
$305$	4.69853			0.269037
$306$		0			0
$307$	−15.1063	+	15.1063i	−0.862161	+	0.862161i	−0.991589	−	0.129428i	$-0.958686\pi$
$307$	−15.1063	+	15.1063i	−0.862161	+	0.862161i	0.129428	+	0.991589i	$0.458686\pi$
$308$		0			0
$309$	0.985711	+	0.985711i	0.0560751	+	0.0560751i
$310$		0			0
$311$			14.3484i			0.813622i	0.913512	+	0.406811i	$0.133359\pi$
$311$			14.3484i			0.813622i	−0.913512	+	0.406811i	$0.866641\pi$
$312$		0			0
$313$			33.0767i			1.86961i	0.355168	+	0.934803i	$0.384424\pi$
$313$			33.0767i			1.86961i	−0.355168	+	0.934803i	$0.615576\pi$
$314$		0			0
$315$	1.64625	+	1.64625i	0.0927558	+	0.0927558i
$316$		0			0
$317$	10.4503	−	10.4503i	0.586946	−	0.586946i	−0.349857	−	0.936803i	$-0.613770\pi$
$317$	10.4503	−	10.4503i	0.586946	−	0.586946i	0.936803	+	0.349857i	$0.113770\pi$
$318$		0			0
$319$	−2.49603			−0.139751
$320$		0			0
$321$	−28.8213			−1.60865
$322$		0			0
$323$	−2.29139	+	2.29139i	−0.127497	+	0.127497i
$324$		0			0
$325$	−1.57890	−	1.57890i	−0.0875819	−	0.0875819i
$326$		0			0
$327$		−	22.6339i		−	1.25166i
$328$		0			0
$329$		−	2.06198i		−	0.113681i
$330$		0			0
$331$	−2.54269	−	2.54269i	−0.139759	−	0.139759i	0.633766	−	0.773525i	$-0.281508\pi$
$331$	−2.54269	−	2.54269i	−0.139759	−	0.139759i	−0.773525	+	0.633766i	$0.781508\pi$
$332$		0			0
$333$	10.1152	−	10.1152i	0.554309	−	0.554309i
$334$		0			0
$335$	−15.2078			−0.830893
$336$		0			0
$337$	−2.32450			−0.126623			−0.0633117	−	0.997994i	$-0.520166\pi$
$337$	−2.32450			−0.126623			−0.0633117	+	0.997994i	$0.520166\pi$
$338$		0			0
$339$	5.37785	−	5.37785i	0.292085	−	0.292085i
$340$		0			0
$341$	−1.09232	−	1.09232i	−0.0591523	−	0.0591523i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			1.50349i			0.0809450i
$346$		0			0
$347$	21.2887	+	21.2887i	1.14284	+	1.14284i	0.987928	+	0.154911i	$0.0495091\pi$
$347$	21.2887	+	21.2887i	1.14284	+	1.14284i	0.154911	+	0.987928i	$0.450491\pi$
$348$		0			0
$349$	−8.87199	+	8.87199i	−0.474907	+	0.474907i	−0.903498	−	0.428592i	$-0.859010\pi$
$349$	−8.87199	+	8.87199i	−0.474907	+	0.474907i	0.428592	+	0.903498i	$0.359010\pi$
$350$		0			0
$351$	3.46282			0.184832
$352$		0			0
$353$	2.88022			0.153298			0.0766492	−	0.997058i	$-0.475578\pi$
$353$	2.88022			0.153298			0.0766492	+	0.997058i	$0.475578\pi$
$354$		0			0
$355$	1.79193	−	1.79193i	0.0951056	−	0.0951056i
$356$		0			0
$357$	6.75348	+	6.75348i	0.357432	+	0.357432i
$358$		0			0
$359$			33.6342i			1.77514i	0.460668	+	0.887572i	$0.347610\pi$
$359$			33.6342i			1.77514i	−0.460668	+	0.887572i	$0.652390\pi$
$360$		0			0
$361$			18.3866i			0.967718i
$362$		0			0
$363$	17.7811	+	17.7811i	0.933264	+	0.933264i
$364$		0			0
$365$	−7.67158	+	7.67158i	−0.401549	+	0.401549i
$366$		0			0
$367$	−9.32047			−0.486525			−0.243262	−	0.969961i	$-0.578218\pi$
$367$	−9.32047			−0.486525			−0.243262	+	0.969961i	$0.578218\pi$
$368$		0			0
$369$	−14.6624			−0.763292
$370$		0			0
$371$	−3.94676	+	3.94676i	−0.204905	+	0.204905i
$372$		0			0
$373$	−10.0834	−	10.0834i	−0.522098	−	0.522098i	0.396107	−	0.918205i	$-0.370361\pi$
$373$	−10.0834	−	10.0834i	−0.522098	−	0.522098i	−0.918205	+	0.396107i	$0.870361\pi$
$374$		0			0
$375$			2.30828i			0.119199i
$376$		0			0
$377$		−	17.1132i		−	0.881372i
$378$		0			0
$379$	−20.4770	−	20.4770i	−1.05183	−	1.05183i	−0.998581	−	0.0532538i	$-0.983041\pi$
$379$	−20.4770	−	20.4770i	−1.05183	−	1.05183i	−0.0532538	−	0.998581i	$-0.516959\pi$
$380$		0			0
$381$	−32.3577	+	32.3577i	−1.65774	+	1.65774i
$382$		0			0
$383$	13.9720			0.713937			0.356968	−	0.934116i	$-0.383810\pi$
$383$	13.9720			0.713937			0.356968	+	0.934116i	$0.383810\pi$
$384$		0			0
$385$	−0.325680			−0.0165982
$386$		0			0
$387$	−4.13462	+	4.13462i	−0.210174	+	0.210174i
$388$		0			0
$389$	24.0214	+	24.0214i	1.21793	+	1.21793i	0.968355	+	0.249577i	$0.0802915\pi$
$389$	24.0214	+	24.0214i	1.21793	+	1.21793i	0.249577	+	0.968355i	$0.419709\pi$
$390$		0			0
$391$			2.69504i			0.136294i
$392$		0			0
$393$			8.45166i			0.426330i
$394$		0			0
$395$	4.42196	+	4.42196i	0.222493	+	0.222493i
$396$		0			0
$397$	13.1166	−	13.1166i	0.658301	−	0.658301i	−0.296677	−	0.954978i	$-0.595878\pi$
$397$	13.1166	−	13.1166i	0.658301	−	0.658301i	0.954978	+	0.296677i	$0.0958785\pi$
$398$		0			0
$399$	−1.80779			−0.0905028
$400$		0			0
$401$	−3.30366			−0.164977			−0.0824885	−	0.996592i	$-0.526287\pi$
$401$	−3.30366			−0.164977			−0.0824885	+	0.996592i	$0.526287\pi$
$402$		0			0
$403$	7.48910	−	7.48910i	0.373058	−	0.373058i
$404$		0			0
$405$	−7.46999	−	7.46999i	−0.371187	−	0.371187i
$406$		0			0
$407$			2.00110i			0.0991908i
$408$		0			0
$409$		−	22.8364i		−	1.12919i	−0.825370	−	0.564593i	$-0.809033\pi$
$409$		−	22.8364i		−	1.12919i	0.825370	−	0.564593i	$-0.190967\pi$
$410$		0			0
$411$	17.2825	+	17.2825i	0.852481	+	0.852481i
$412$		0			0
$413$	−10.2275	+	10.2275i	−0.503263	+	0.503263i
$414$		0			0
$415$	6.68590			0.328198
$416$		0			0
$417$	48.6368			2.38176
$418$		0			0
$419$	2.88606	−	2.88606i	0.140993	−	0.140993i	−0.633087	−	0.774081i	$-0.718213\pi$
$419$	2.88606	−	2.88606i	0.140993	−	0.140993i	0.774081	+	0.633087i	$0.218213\pi$
$420$		0			0
$421$	−5.62573	−	5.62573i	−0.274181	−	0.274181i	0.556600	−	0.830781i	$-0.312106\pi$
$421$	−5.62573	−	5.62573i	−0.274181	−	0.274181i	−0.830781	+	0.556600i	$0.812106\pi$
$422$		0			0
$423$		−	4.80060i		−	0.233413i
$424$		0			0
$425$			4.13766i			0.200706i
$426$		0			0
$427$	3.32236	+	3.32236i	0.160780	+	0.160780i
$428$		0			0
$429$	1.18696	−	1.18696i	0.0573068	−	0.0573068i
$430$		0			0
$431$	−37.1003			−1.78706			−0.893528	−	0.449007i	$-0.851778\pi$
$431$	−37.1003			−1.78706			−0.893528	+	0.449007i	$0.851778\pi$
$432$		0			0
$433$	−19.4955			−0.936893			−0.468447	−	0.883492i	$-0.655186\pi$
$433$	−19.4955			−0.936893			−0.468447	+	0.883492i	$0.655186\pi$
$434$		0			0
$435$	−12.5093	+	12.5093i	−0.599774	+	0.599774i
$436$		0			0
$437$	−0.360708	−	0.360708i	−0.0172550	−	0.0172550i
$438$		0			0
$439$			7.74362i			0.369583i	0.982778	+	0.184791i	$0.0591609\pi$
$439$			7.74362i			0.369583i	−0.982778	+	0.184791i	$0.940839\pi$
$440$		0			0
$441$			2.32815i			0.110864i
$442$		0			0
$443$	17.0700	+	17.0700i	0.811019	+	0.811019i	0.984787	−	0.173768i	$-0.0555943\pi$
$443$	17.0700	+	17.0700i	0.811019	+	0.811019i	−0.173768	+	0.984787i	$0.555594\pi$
$444$		0			0
$445$	−6.54544	+	6.54544i	−0.310283	+	0.310283i
$446$		0			0
$447$	−7.44914			−0.352332
$448$		0			0
$449$	23.3884			1.10377			0.551884	−	0.833921i	$-0.313909\pi$
$449$	23.3884			1.10377			0.551884	+	0.833921i	$0.313909\pi$
$450$		0			0
$451$	1.45033	−	1.45033i	0.0682936	−	0.0682936i
$452$		0			0
$453$	29.4505	+	29.4505i	1.38370	+	1.38370i
$454$		0			0
$455$		−	2.23291i		−	0.104680i
$456$		0			0
$457$			3.34635i			0.156536i	0.996932	+	0.0782678i	$0.0249389\pi$
$457$			3.34635i			0.156536i	−0.996932	+	0.0782678i	$0.975061\pi$
$458$		0			0
$459$	−4.53732	−	4.53732i	−0.211784	−	0.211784i
$460$		0			0
$461$	23.4062	−	23.4062i	1.09013	−	1.09013i	0.0946217	−	0.995513i	$-0.469836\pi$
$461$	23.4062	−	23.4062i	1.09013	−	1.09013i	0.995513	−	0.0946217i	$-0.0301641\pi$
$462$		0			0
$463$	−32.8655			−1.52739			−0.763695	−	0.645578i	$-0.776617\pi$
$463$	−32.8655			−1.52739			−0.763695	+	0.645578i	$0.776617\pi$
$464$		0			0
$465$	−10.9487			−0.507733
$466$		0			0
$467$	−7.76809	+	7.76809i	−0.359464	+	0.359464i	−0.863615	−	0.504151i	$-0.831805\pi$
$467$	−7.76809	+	7.76809i	−0.359464	+	0.359464i	0.504151	+	0.863615i	$0.331805\pi$
$468$		0			0
$469$	−10.7536	−	10.7536i	−0.496553	−	0.496553i
$470$		0			0
$471$		−	23.7031i		−	1.09218i
$472$		0			0
$473$		−	0.817955i		−	0.0376096i
$474$		0			0
$475$	−0.553790	−	0.553790i	−0.0254096	−	0.0254096i
$476$		0			0
$477$	−9.18865	+	9.18865i	−0.420719	+	0.420719i
$478$		0			0
$479$	−16.7204			−0.763976			−0.381988	−	0.924167i	$-0.624760\pi$
$479$	−16.7204			−0.763976			−0.381988	+	0.924167i	$0.624760\pi$
$480$		0			0
$481$	−13.7198			−0.625570
$482$		0			0
$483$	−1.06313	+	1.06313i	−0.0483739	+	0.0483739i
$484$		0			0
$485$	1.74849	+	1.74849i	0.0793947	+	0.0793947i
$486$		0			0
$487$		−	8.40976i		−	0.381083i	−0.981679	−	0.190541i	$-0.938976\pi$
$487$		−	8.40976i		−	0.381083i	0.981679	−	0.190541i	$-0.0610243\pi$
$488$		0			0
$489$			15.7188i			0.710828i
$490$		0			0
$491$	−27.7902	−	27.7902i	−1.25415	−	1.25415i	−0.953841	−	0.300312i	$-0.902909\pi$
$491$	−27.7902	−	27.7902i	−1.25415	−	1.25415i	−0.300312	−	0.953841i	$-0.597091\pi$
$492$		0			0
$493$	−22.4233	+	22.4233i	−1.00989	+	1.00989i
$494$		0			0
$495$	−0.758232			−0.0340800
$496$		0			0
$497$	2.53417			0.113673
$498$		0			0
$499$	−11.6936	+	11.6936i	−0.523477	+	0.523477i	−0.918620	−	0.395143i	$-0.870695\pi$
$499$	−11.6936	+	11.6936i	−0.523477	+	0.523477i	0.395143	+	0.918620i	$0.370695\pi$
$500$		0			0
$501$	37.1310	+	37.1310i	1.65889	+	1.65889i
$502$		0			0
$503$		−	8.71880i		−	0.388752i	−0.980927	−	0.194376i	$-0.937732\pi$
$503$		−	8.71880i		−	0.388752i	0.980927	−	0.194376i	$-0.0622682\pi$
$504$		0			0
$505$		−	3.96993i		−	0.176659i
$506$		0			0
$507$	−13.0806	−	13.0806i	−0.580932	−	0.580932i
$508$		0			0
$509$	24.0041	−	24.0041i	1.06396	−	1.06396i	0.0661535	−	0.997809i	$-0.478927\pi$
$509$	24.0041	−	24.0041i	1.06396	−	1.06396i	0.997809	−	0.0661535i	$-0.0210727\pi$
$510$		0			0
$511$	−10.8492			−0.479942
$512$		0			0
$513$	1.21456			0.0536242
$514$		0			0
$515$	−0.427033	+	0.427033i	−0.0188173	+	0.0188173i
$516$		0			0
$517$	0.474854	+	0.474854i	0.0208841	+	0.0208841i
$518$		0			0
$519$			53.3360i			2.34119i
$520$		0			0
$521$			37.0452i			1.62298i	0.584366	+	0.811490i	$0.301343\pi$
$521$			37.0452i			1.62298i	−0.584366	+	0.811490i	$0.698657\pi$
$522$		0			0
$523$	−0.169768	−	0.169768i	−0.00742346	−	0.00742346i	0.703385	−	0.710809i	$-0.251671\pi$
$523$	−0.169768	−	0.169768i	−0.00742346	−	0.00742346i	−0.710809	+	0.703385i	$0.751671\pi$
$524$		0			0
$525$	−1.63220	+	1.63220i	−0.0712350	+	0.0712350i
$526$		0			0
$527$	−19.6258			−0.854914
$528$		0			0
$529$	22.5757			0.981554
$530$		0			0
$531$	−23.8112	+	23.8112i	−1.03332	+	1.03332i
$532$		0			0
$533$	9.94371	+	9.94371i	0.430710	+	0.430710i
$534$		0			0
$535$		−	12.4861i		−	0.539820i
$536$		0			0
$537$			45.1332i			1.94764i
$538$		0			0
$539$	−0.230290	−	0.230290i	−0.00991930	−	0.00991930i
$540$		0			0
$541$	−20.6083	+	20.6083i	−0.886020	+	0.886020i	−0.994138	−	0.108118i	$-0.965518\pi$
$541$	−20.6083	+	20.6083i	−0.886020	+	0.886020i	0.108118	+	0.994138i	$0.465518\pi$
$542$		0			0
$543$	39.7102			1.70413
$544$		0			0
$545$	9.80555			0.420023
$546$		0			0
$547$	7.38571	−	7.38571i	0.315790	−	0.315790i	−0.531357	−	0.847148i	$-0.678318\pi$
$547$	7.38571	−	7.38571i	0.315790	−	0.315790i	0.847148	+	0.531357i	$0.178318\pi$
$548$		0			0
$549$	7.73497	+	7.73497i	0.330120	+	0.330120i
$550$		0			0
$551$		−	6.00232i		−	0.255708i
$552$		0			0
$553$			6.25359i			0.265930i
$554$		0			0
$555$	10.0288	+	10.0288i	0.425701	+	0.425701i
$556$		0			0
$557$	−17.0066	+	17.0066i	−0.720595	+	0.720595i	−0.968726	−	0.248132i	$-0.920183\pi$
$557$	−17.0066	+	17.0066i	−0.720595	+	0.720595i	0.248132	+	0.968726i	$0.420183\pi$
$558$		0			0
$559$	5.60802			0.237194
$560$		0			0
$561$	−3.11052			−0.131326
$562$		0			0
$563$	12.9934	−	12.9934i	0.547605	−	0.547605i	−0.378142	−	0.925747i	$-0.623437\pi$
$563$	12.9934	−	12.9934i	0.547605	−	0.547605i	0.925747	+	0.378142i	$0.123437\pi$
$564$		0			0
$565$	2.32981	+	2.32981i	0.0980159	+	0.0980159i
$566$		0			0
$567$		−	10.5642i		−	0.443653i
$568$		0			0
$569$		−	20.4908i		−	0.859020i	−0.903062	−	0.429510i	$-0.858686\pi$
$569$		−	20.4908i		−	0.859020i	0.903062	−	0.429510i	$-0.141314\pi$
$570$		0			0
$571$	14.5167	+	14.5167i	0.607505	+	0.607505i	0.942293	−	0.334788i	$-0.108665\pi$
$571$	14.5167	+	14.5167i	0.607505	+	0.607505i	−0.334788	+	0.942293i	$0.608665\pi$
$572$		0			0
$573$	14.0717	−	14.0717i	0.587853	−	0.587853i
$574$		0			0
$575$	−0.651345			−0.0271630
$576$		0			0
$577$	−6.82911			−0.284300			−0.142150	−	0.989845i	$-0.545401\pi$
$577$	−6.82911			−0.284300			−0.142150	+	0.989845i	$0.545401\pi$
$578$		0			0
$579$	24.6190	−	24.6190i	1.02313	−	1.02313i
$580$		0			0
$581$	4.72764	+	4.72764i	0.196136	+	0.196136i
$582$		0			0
$583$		−	1.81780i		−	0.0752856i
$584$		0			0
$585$		−	5.19855i		−	0.214934i
$586$		0			0
$587$	−27.3521	−	27.3521i	−1.12894	−	1.12894i	−0.990349	−	0.138595i	$-0.955741\pi$
$587$	−27.3521	−	27.3521i	−1.12894	−	1.12894i	−0.138595	−	0.990349i	$-0.544259\pi$
$588$		0			0
$589$	2.62675	−	2.62675i	0.108233	−	0.108233i
$590$		0			0
$591$	19.2759			0.792904
$592$		0			0
$593$	−32.6330			−1.34008			−0.670039	−	0.742326i	$-0.733723\pi$
$593$	−32.6330			−1.34008			−0.670039	+	0.742326i	$0.733723\pi$
$594$		0			0
$595$	−2.92577	+	2.92577i	−0.119945	+	0.119945i
$596$		0			0
$597$	−0.206274	−	0.206274i	−0.00844222	−	0.00844222i
$598$		0			0
$599$		−	14.9206i		−	0.609640i	−0.952410	−	0.304820i	$-0.901404\pi$
$599$		−	14.9206i		−	0.609640i	0.952410	−	0.304820i	$-0.0985962\pi$
$600$		0			0
$601$			45.2291i			1.84493i	0.386076	+	0.922467i	$0.373830\pi$
$601$			45.2291i			1.84493i	−0.386076	+	0.922467i	$0.626170\pi$
$602$		0			0
$603$	−25.0359	−	25.0359i	−1.01954	−	1.01954i
$604$		0			0
$605$	−7.70317	+	7.70317i	−0.313179	+	0.313179i
$606$		0			0
$607$	38.3803			1.55781			0.778905	−	0.627142i	$-0.215775\pi$
$607$	38.3803			1.55781			0.778905	+	0.627142i	$0.215775\pi$
$608$		0			0
$609$	−17.6908			−0.716868
$610$		0			0
$611$	−3.25567	+	3.25567i	−0.131710	+	0.131710i
$612$		0			0
$613$	31.3491	+	31.3491i	1.26618	+	1.26618i	0.948047	+	0.318130i	$0.103055\pi$
$613$	31.3491	+	31.3491i	1.26618	+	1.26618i	0.318130	+	0.948047i	$0.396945\pi$
$614$		0			0
$615$		−	14.5372i		−	0.586197i
$616$		0			0
$617$		−	5.21884i		−	0.210102i	−0.994467	−	0.105051i	$-0.966499\pi$
$617$		−	5.21884i		−	0.210102i	0.994467	−	0.105051i	$-0.0335007\pi$
$618$		0			0
$619$	−27.6631	−	27.6631i	−1.11187	−	1.11187i	−0.992897	−	0.118976i	$-0.962039\pi$
$619$	−27.6631	−	27.6631i	−1.11187	−	1.11187i	−0.118976	−	0.992897i	$-0.537961\pi$
$620$		0			0
$621$	0.714259	−	0.714259i	0.0286622	−	0.0286622i
$622$		0			0
$623$	−9.25664			−0.370860
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	0.416317	−	0.416317i	0.0166261	−	0.0166261i
$628$		0			0
$629$	17.9770	+	17.9770i	0.716790	+	0.716790i
$630$		0			0
$631$			24.6642i			0.981866i	0.871197	+	0.490933i	$0.163344\pi$
$631$			24.6642i			0.981866i	−0.871197	+	0.490933i	$0.836656\pi$
$632$		0			0
$633$		−	2.22106i		−	0.0882792i
$634$		0			0
$635$	−14.0181	−	14.0181i	−0.556292	−	0.556292i
$636$		0			0
$637$	1.57890	−	1.57890i	0.0625585	−	0.0625585i
$638$		0			0
$639$	5.89993			0.233397
$640$		0			0
$641$	35.3131			1.39478			0.697391	−	0.716691i	$-0.254344\pi$
$641$	35.3131			1.39478			0.697391	+	0.716691i	$0.254344\pi$
$642$		0			0
$643$	5.35915	−	5.35915i	0.211344	−	0.211344i	−0.593494	−	0.804838i	$-0.702252\pi$
$643$	5.35915	−	5.35915i	0.211344	−	0.211344i	0.804838	+	0.593494i	$0.202252\pi$
$644$		0			0
$645$	−4.09932	−	4.09932i	−0.161411	−	0.161411i
$646$		0			0
$647$			27.9823i			1.10010i	0.835132	+	0.550049i	$0.185391\pi$
$647$			27.9823i			1.10010i	−0.835132	+	0.550049i	$0.814609\pi$
$648$		0			0
$649$		−	4.71059i		−	0.184907i
$650$		0			0
$651$	−7.74189	−	7.74189i	−0.303428	−	0.303428i
$652$		0			0
$653$	23.2765	−	23.2765i	0.910880	−	0.910880i	−0.0854616	−	0.996341i	$-0.527236\pi$
$653$	23.2765	−	23.2765i	0.910880	−	0.910880i	0.996341	+	0.0854616i	$0.0272365\pi$
$654$		0			0
$655$	−3.66146			−0.143065
$656$		0			0
$657$	−25.2587			−0.985435
$658$		0			0
$659$	9.53678	−	9.53678i	0.371500	−	0.371500i	−0.496523	−	0.868023i	$-0.665390\pi$
$659$	9.53678	−	9.53678i	0.371500	−	0.371500i	0.868023	+	0.496523i	$0.165390\pi$
$660$		0			0
$661$	−19.8255	−	19.8255i	−0.771123	−	0.771123i	0.207180	−	0.978303i	$-0.433571\pi$
$661$	−19.8255	−	19.8255i	−0.771123	−	0.771123i	−0.978303	+	0.207180i	$0.933571\pi$
$662$		0			0
$663$		−	21.3262i		−	0.828241i
$664$		0			0
$665$		−	0.783177i		−	0.0303703i
$666$		0			0
$667$	−3.52984	−	3.52984i	−0.136676	−	0.136676i
$668$		0			0
$669$	28.9473	−	28.9473i	1.11917	−	1.11917i
$670$		0			0
$671$	−1.53022			−0.0590733
$672$		0			0
$673$	46.7380			1.80162			0.900810	−	0.434214i	$-0.142974\pi$
$673$	46.7380			1.80162			0.900810	+	0.434214i	$0.142974\pi$
$674$		0			0
$675$	1.09659	−	1.09659i	0.0422078	−	0.0422078i
$676$		0			0
$677$	−15.1286	−	15.1286i	−0.581438	−	0.581438i	0.353860	−	0.935298i	$-0.384869\pi$
$677$	−15.1286	−	15.1286i	−0.581438	−	0.581438i	−0.935298	+	0.353860i	$0.884869\pi$
$678$		0			0
$679$			2.47273i			0.0948948i
$680$		0			0
$681$			2.50583i			0.0960236i
$682$		0			0
$683$	−15.4767	−	15.4767i	−0.592201	−	0.592201i	0.346025	−	0.938225i	$-0.387531\pi$
$683$	−15.4767	−	15.4767i	−0.592201	−	0.592201i	−0.938225	+	0.346025i	$0.887531\pi$
$684$		0			0
$685$	−7.48717	+	7.48717i	−0.286070	+	0.286070i
$686$		0			0
$687$	33.2103			1.26705
$688$		0			0
$689$	12.4631			0.474806
$690$		0			0
$691$	−8.56494	+	8.56494i	−0.325826	+	0.325826i	−0.850997	−	0.525171i	$-0.824001\pi$
$691$	−8.56494	+	8.56494i	−0.325826	+	0.325826i	0.525171	+	0.850997i	$0.324001\pi$
$692$		0			0
$693$	−0.536151	−	0.536151i	−0.0203667	−	0.0203667i
$694$		0			0
$695$			21.0706i			0.799253i
$696$		0			0
$697$		−	26.0584i		−	0.987031i
$698$		0			0
$699$	25.7162	+	25.7162i	0.972677	+	0.972677i
$700$		0			0
$701$	8.01447	−	8.01447i	0.302702	−	0.302702i	−0.539368	−	0.842070i	$-0.681337\pi$
$701$	8.01447	−	8.01447i	0.302702	−	0.302702i	0.842070	+	0.539368i	$0.181337\pi$
$702$		0			0
$703$	−4.81214			−0.181493
$704$		0			0
$705$	4.75963			0.179258
$706$		0			0
$707$	2.80716	−	2.80716i	0.105574	−	0.105574i
$708$		0			0
$709$	26.6629	+	26.6629i	1.00135	+	1.00135i	0.999999	+	0.00134836i	$0.000429195\pi$
$709$	26.6629	+	26.6629i	1.00135	+	1.00135i	0.00134836	+	0.999999i	$0.499571\pi$
$710$		0			0
$711$			14.5593i			0.546017i
$712$		0			0
$713$		−	3.08947i		−	0.115702i
$714$		0			0
$715$	0.514217	+	0.514217i	0.0192306	+	0.0192306i
$716$		0			0
$717$	−2.16369	+	2.16369i	−0.0808043	+	0.0808043i
$718$		0			0
$719$	31.4729			1.17374			0.586870	−	0.809681i	$-0.300360\pi$
$719$	31.4729			1.17374			0.586870	+	0.809681i	$0.300360\pi$
$720$		0			0
$721$	−0.603916			−0.0224910
$722$		0			0
$723$	36.0637	−	36.0637i	1.34123	−	1.34123i
$724$		0			0
$725$	−5.41931	−	5.41931i	−0.201268	−	0.201268i
$726$		0			0
$727$		−	33.2740i		−	1.23406i	−0.786938	−	0.617032i	$-0.788335\pi$
$727$		−	33.2740i		−	1.23406i	0.786938	−	0.617032i	$-0.211665\pi$
$728$		0			0
$729$		−	13.8558i		−	0.513180i
$730$		0			0
$731$	−7.34816	−	7.34816i	−0.271781	−	0.271781i
$732$		0			0
$733$	13.7601	−	13.7601i	0.508241	−	0.508241i	−0.405745	−	0.913986i	$-0.632988\pi$
$733$	13.7601	−	13.7601i	0.508241	−	0.508241i	0.913986	+	0.405745i	$0.132988\pi$
$734$		0			0
$735$	−2.30828			−0.0851422
$736$		0			0
$737$	4.95288			0.182442
$738$		0			0
$739$	−9.92020	+	9.92020i	−0.364921	+	0.364921i	−0.865621	−	0.500700i	$-0.833076\pi$
$739$	−9.92020	+	9.92020i	−0.364921	+	0.364921i	0.500700	+	0.865621i	$0.333076\pi$
$740$		0			0
$741$	2.85433	+	2.85433i	0.104856	+	0.104856i
$742$		0			0
$743$			25.4224i			0.932657i	0.884612	+	0.466328i	$0.154423\pi$
$743$			25.4224i			0.932657i	−0.884612	+	0.466328i	$0.845577\pi$
$744$		0			0
$745$		−	3.22714i		−	0.118233i
$746$		0			0
$747$	11.0067	+	11.0067i	0.402713	+	0.402713i
$748$		0			0
$749$	8.82899	−	8.82899i	0.322604	−	0.322604i
$750$		0			0
$751$	7.22036			0.263475			0.131737	−	0.991285i	$-0.457944\pi$
$751$	7.22036			0.263475			0.131737	+	0.991285i	$0.457944\pi$
$752$		0			0
$753$	−9.86212			−0.359396
$754$		0			0
$755$	−12.7586	+	12.7586i	−0.464334	+	0.464334i
$756$		0			0
$757$	−37.7483	−	37.7483i	−1.37198	−	1.37198i	−0.857500	−	0.514484i	$-0.827984\pi$
$757$	−37.7483	−	37.7483i	−1.37198	−	1.37198i	−0.514484	−	0.857500i	$-0.672016\pi$
$758$		0			0
$759$		−	0.489655i		−	0.0177733i
$760$		0			0
$761$		−	26.6726i		−	0.966880i	−0.875378	−	0.483440i	$-0.839387\pi$
$761$		−	26.6726i		−	0.966880i	0.875378	−	0.483440i	$-0.160613\pi$
$762$		0			0
$763$	6.93357	+	6.93357i	0.251012	+	0.251012i
$764$		0			0
$765$	−6.81163	+	6.81163i	−0.246275	+	0.246275i
$766$		0			0
$767$	32.2965			1.16616
$768$		0			0
$769$	3.76130			0.135636			0.0678179	−	0.997698i	$-0.478396\pi$
$769$	3.76130			0.135636			0.0678179	+	0.997698i	$0.478396\pi$
$770$		0			0
$771$	−30.5624	+	30.5624i	−1.10068	+	1.10068i
$772$		0			0
$773$	17.8852	+	17.8852i	0.643285	+	0.643285i	0.951362	−	0.308076i	$-0.0996852\pi$
$773$	17.8852	+	17.8852i	0.643285	+	0.643285i	−0.308076	+	0.951362i	$0.599685\pi$
$774$		0			0
$775$		−	4.74322i		−	0.170382i
$776$		0			0
$777$			14.1829i			0.508810i
$778$		0			0
$779$	3.48769	+	3.48769i	0.124959	+	0.124959i
$780$		0			0
$781$	−0.583594	+	0.583594i	−0.0208826	+	0.0208826i
$782$		0			0
$783$	11.8855			0.424754
$784$		0			0
$785$	10.2687			0.366507
$786$		0			0
$787$	−24.1958	+	24.1958i	−0.862486	+	0.862486i	−0.991626	−	0.129141i	$-0.958778\pi$
$787$	−24.1958	+	24.1958i	−0.862486	+	0.862486i	0.129141	+	0.991626i	$0.458778\pi$
$788$		0			0
$789$	−24.0155	−	24.0155i	−0.854974	−	0.854974i
$790$		0			0
$791$			3.29485i			0.117151i
$792$		0			0
$793$		−	10.4914i		−	0.372560i
$794$		0			0
$795$	−9.11021	−	9.11021i	−0.323106	−	0.323106i
$796$		0			0
$797$	−21.9739	+	21.9739i	−0.778355	+	0.778355i	−0.979551	−	0.201196i	$-0.935517\pi$
$797$	−21.9739	+	21.9739i	−0.778355	+	0.778355i	0.201196	+	0.979551i	$0.435517\pi$
$798$		0			0
$799$	8.53177			0.301832
$800$		0			0
$801$	−21.5509			−0.761463
$802$		0			0
$803$	2.49848	−	2.49848i	0.0881693	−	0.0881693i
$804$		0			0
$805$	−0.460570	−	0.460570i	−0.0162330	−	0.0162330i
$806$		0			0
$807$		−	44.4447i		−	1.56453i
$808$		0			0
$809$		−	9.61310i		−	0.337979i	−0.985618	−	0.168989i	$-0.945950\pi$
$809$		−	9.61310i		−	0.337979i	0.985618	−	0.168989i	$-0.0540504\pi$
$810$		0			0
$811$	5.47100	+	5.47100i	0.192113	+	0.192113i	0.796609	−	0.604496i	$-0.206625\pi$
$811$	5.47100	+	5.47100i	0.192113	+	0.192113i	−0.604496	+	0.796609i	$0.706625\pi$
$812$		0			0
$813$	−0.614858	+	0.614858i	−0.0215640	+	0.0215640i
$814$		0			0
$815$	−6.80974			−0.238535
$816$		0			0
$817$	1.96698			0.0688158
$818$		0			0
$819$	3.67593	−	3.67593i	0.128447	−	0.128447i
$820$		0			0
$821$	2.76610	+	2.76610i	0.0965377	+	0.0965377i	0.753726	−	0.657189i	$-0.228254\pi$
$821$	2.76610	+	2.76610i	0.0965377	+	0.0965377i	−0.657189	+	0.753726i	$0.728254\pi$
$822$		0			0
$823$			43.6725i			1.52233i	0.648560	+	0.761164i	$0.275372\pi$
$823$			43.6725i			1.52233i	−0.648560	+	0.761164i	$0.724628\pi$
$824$		0			0
$825$		−	0.751759i		−	0.0261729i
$826$		0			0
$827$	−3.63397	−	3.63397i	−0.126365	−	0.126365i	0.641096	−	0.767461i	$-0.278480\pi$
$827$	−3.63397	−	3.63397i	−0.126365	−	0.126365i	−0.767461	+	0.641096i	$0.778480\pi$
$828$		0			0
$829$	30.7319	−	30.7319i	1.06736	−	1.06736i	0.0698021	−	0.997561i	$-0.477763\pi$
$829$	30.7319	−	30.7319i	1.06736	−	1.06736i	0.997561	−	0.0698021i	$-0.0222368\pi$
$830$		0			0
$831$	61.3459			2.12807
$832$		0			0
$833$	−4.13766			−0.143361
$834$		0			0
$835$	−16.0860	+	16.0860i	−0.556680	+	0.556680i
$836$		0			0
$837$	5.20137	+	5.20137i	0.179786	+	0.179786i
$838$		0			0
$839$			51.6444i			1.78296i	0.453059	+	0.891480i	$0.350333\pi$
$839$			51.6444i			1.78296i	−0.453059	+	0.891480i	$0.649667\pi$
$840$		0			0
$841$		−	29.7379i		−	1.02545i
$842$		0			0
$843$	−7.20410	−	7.20410i	−0.248122	−	0.248122i
$844$		0			0
$845$	5.66684	−	5.66684i	0.194945	−	0.194945i
$846$		0			0
$847$	−10.8939			−0.374320
$848$		0			0
$849$	−38.8389			−1.33295
$850$		0			0
$851$	−2.82992	+	2.82992i	−0.0970083	+	0.0970083i
$852$		0			0
$853$	10.5486	+	10.5486i	0.361178	+	0.361178i	0.864246	−	0.503069i	$-0.167796\pi$
$853$	10.5486	+	10.5486i	0.361178	+	0.361178i	−0.503069	+	0.864246i	$0.667796\pi$
$854$		0			0
$855$		−	1.82336i		−	0.0623575i
$856$		0			0
$857$		−	27.9469i		−	0.954647i	−0.878728	−	0.477323i	$-0.841607\pi$
$857$		−	27.9469i		−	0.954647i	0.878728	−	0.477323i	$-0.158393\pi$
$858$		0			0
$859$	−19.2150	−	19.2150i	−0.655608	−	0.655608i	0.298730	−	0.954338i	$-0.403437\pi$
$859$	−19.2150	−	19.2150i	−0.655608	−	0.655608i	−0.954338	+	0.298730i	$0.903437\pi$
$860$		0			0
$861$	10.2794	−	10.2794i	0.350320	−	0.350320i
$862$		0			0
$863$	−0.340094			−0.0115769			−0.00578846	−	0.999983i	$-0.501843\pi$
$863$	−0.340094			−0.0115769			−0.00578846	+	0.999983i	$0.501843\pi$
$864$		0			0
$865$	−23.1064			−0.785641
$866$		0			0
$867$	−0.196200	+	0.196200i	−0.00666330	+	0.00666330i
$868$		0			0
$869$	−1.44014	−	1.44014i	−0.0488535	−	0.0488535i
$870$		0			0
$871$			33.9577i			1.15061i
$872$		0			0
$873$			5.75690i			0.194841i
$874$		0			0
$875$	−0.707107	−	0.707107i	−0.0239046	−	0.0239046i
$876$		0			0
$877$	2.47604	−	2.47604i	0.0836098	−	0.0836098i	−0.664065	−	0.747675i	$-0.731170\pi$
$877$	2.47604	−	2.47604i	0.0836098	−	0.0836098i	0.747675	+	0.664065i	$0.231170\pi$
$878$		0			0
$879$	55.6172			1.87592
$880$		0			0
$881$	−27.6372			−0.931120			−0.465560	−	0.885016i	$-0.654147\pi$
$881$	−27.6372			−0.931120			−0.465560	+	0.885016i	$0.654147\pi$
$882$		0			0
$883$	−7.06999	+	7.06999i	−0.237924	+	0.237924i	−0.815990	−	0.578066i	$-0.803808\pi$
$883$	−7.06999	+	7.06999i	−0.237924	+	0.237924i	0.578066	+	0.815990i	$0.303808\pi$
$884$		0			0
$885$	−23.6080	−	23.6080i	−0.793573	−	0.793573i
$886$		0			0
$887$			8.02331i			0.269396i	0.990887	+	0.134698i	$0.0430065\pi$
$887$			8.02331i			0.269396i	−0.990887	+	0.134698i	$0.956994\pi$
$888$		0			0
$889$		−	19.8246i		−	0.664896i
$890$		0			0
$891$	2.43282	+	2.43282i	0.0815027	+	0.0815027i
$892$		0			0
$893$	−1.14190	+	1.14190i	−0.0382124	+	0.0382124i
$894$		0			0
$895$	−19.5527			−0.653576
$896$		0			0
$897$	3.35715			0.112092
$898$		0			0
$899$	25.7050	−	25.7050i	0.857310	−	0.857310i
$900$		0			0
$901$	−16.3303	−	16.3303i	−0.544042	−	0.544042i
$902$		0			0
$903$		−	5.79732i		−	0.192923i
$904$		0			0
$905$			17.2034i			0.571859i
$906$		0			0
$907$	−13.1127	−	13.1127i	−0.435398	−	0.435398i	0.455062	−	0.890460i	$-0.349617\pi$
$907$	−13.1127	−	13.1127i	−0.435398	−	0.435398i	−0.890460	+	0.455062i	$0.849617\pi$
$908$		0			0
$909$	6.53550	−	6.53550i	0.216769	−	0.216769i
$910$		0			0
$911$	10.7278			0.355426			0.177713	−	0.984082i	$-0.443130\pi$
$911$	10.7278			0.355426			0.177713	+	0.984082i	$0.443130\pi$
$912$		0			0
$913$	−2.17746			−0.0720634
$914$		0			0
$915$	−7.66894	+	7.66894i	−0.253527	+	0.253527i
$916$		0			0
$917$	−2.58904	−	2.58904i	−0.0854977	−	0.0854977i
$918$		0			0
$919$			18.1540i			0.598844i	0.954121	+	0.299422i	$0.0967939\pi$
$919$			18.1540i			0.598844i	−0.954121	+	0.299422i	$0.903206\pi$
$920$		0			0
$921$		−	49.3129i		−	1.62492i
$922$		0			0
$923$	−4.00121	−	4.00121i	−0.131701	−	0.131701i
$924$		0			0
$925$	−4.34473	+	4.34473i	−0.142854	+	0.142854i
$926$		0			0
$927$	−1.40601			−0.0461793
$928$		0			0
$929$	5.83056			0.191294			0.0956472	−	0.995415i	$-0.469508\pi$
$929$	5.83056			0.191294			0.0956472	+	0.995415i	$0.469508\pi$
$930$		0			0
$931$	0.553790	−	0.553790i	0.0181497	−	0.0181497i
$932$		0			0
$933$	−23.4194	−	23.4194i	−0.766718	−	0.766718i
$934$		0			0
$935$		−	1.34755i		−	0.0440696i
$936$		0			0
$937$			20.6391i			0.674249i	0.941460	+	0.337124i	$0.109454\pi$
$937$			20.6391i			0.674249i	−0.941460	+	0.337124i	$0.890546\pi$
$938$		0			0
$939$	−53.9878	−	53.9878i	−1.76182	−	1.76182i
$940$		0			0
$941$	12.0696	−	12.0696i	0.393458	−	0.393458i	−0.482460	−	0.875918i	$-0.660257\pi$
$941$	12.0696	−	12.0696i	0.393458	−	0.393458i	0.875918	+	0.482460i	$0.160257\pi$
$942$		0			0
$943$	4.10208			0.133582
$944$		0			0
$945$	1.55081			0.0504480
$946$		0			0
$947$	−10.6980	+	10.6980i	−0.347639	+	0.347639i	−0.859229	−	0.511590i	$-0.829057\pi$
$947$	−10.6980	+	10.6980i	−0.347639	+	0.347639i	0.511590	+	0.859229i	$0.329057\pi$
$948$		0			0
$949$	17.1299	+	17.1299i	0.556061	+	0.556061i
$950$		0			0
$951$			34.1139i			1.10622i
$952$		0			0
$953$		−	31.4313i		−	1.01816i	−0.860719	−	0.509080i	$-0.829986\pi$
$953$		−	31.4313i		−	1.01816i	0.860719	−	0.509080i	$-0.170014\pi$
$954$		0			0
$955$	6.09618	+	6.09618i	0.197268	+	0.197268i
$956$		0			0
$957$	4.07402	−	4.07402i	0.131694	−	0.131694i
$958$		0			0
$959$	−10.5885			−0.341919
$960$		0			0
$961$	−8.50184			−0.274253
$962$		0			0
$963$	20.5552	−	20.5552i	0.662383	−	0.662383i
$964$		0			0
$965$	10.6655	+	10.6655i	0.343336	+	0.343336i
$966$		0			0
$967$		−	4.02128i		−	0.129316i	−0.997907	−	0.0646579i	$-0.979404\pi$
$967$		−	4.02128i		−	0.129316i	0.997907	−	0.0646579i	$-0.0205956\pi$
$968$		0			0
$969$		−	7.48002i		−	0.240293i
$970$		0			0
$971$	16.8706	+	16.8706i	0.541403	+	0.541403i	0.923940	−	0.382537i	$-0.124950\pi$
$971$	16.8706	+	16.8706i	0.541403	+	0.541403i	−0.382537	+	0.923940i	$0.624950\pi$
$972$		0			0
$973$	−14.8992	+	14.8992i	−0.477645	+	0.477645i
$974$		0			0
$975$	5.15418			0.165066
$976$		0			0
$977$	−17.1717			−0.549371			−0.274685	−	0.961534i	$-0.588574\pi$
$977$	−17.1717			−0.549371			−0.274685	+	0.961534i	$0.588574\pi$
$978$		0			0
$979$	2.13171	−	2.13171i	0.0681299	−	0.0681299i
$980$		0			0
$981$	16.1424	+	16.1424i	0.515387	+	0.515387i
$982$		0			0
$983$			22.4151i			0.714929i	0.933927	+	0.357465i	$0.116359\pi$
$983$			22.4151i			0.714929i	−0.933927	+	0.357465i	$0.883641\pi$
$984$		0			0
$985$			8.35076i			0.266077i
$986$		0			0
$987$	3.36557	+	3.36557i	0.107127	+	0.107127i
$988$		0			0
$989$	1.15674	−	1.15674i	0.0367821	−	0.0367821i
$990$		0			0
$991$	−16.5712			−0.526402			−0.263201	−	0.964741i	$-0.584778\pi$
$991$	−16.5712			−0.526402			−0.263201	+	0.964741i	$0.584778\pi$
$992$		0			0
$993$	8.30036			0.263404
$994$		0			0
$995$	0.0893625	−	0.0893625i	0.00283298	−	0.00283298i
$996$		0			0
$997$	−12.7525	−	12.7525i	−0.403874	−	0.403874i	0.475722	−	0.879596i	$-0.342187\pi$
$997$	−12.7525	−	12.7525i	−0.403874	−	0.403874i	−0.879596	+	0.475722i	$0.842187\pi$
$998$		0			0
$999$		−	9.52878i		−	0.301477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.4		44
4.3	odd	2		560.2.bd.a.421.18	yes	44
16.3	odd	4		560.2.bd.a.141.18	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.4		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.18	✓	44	16.3	odd	4
560.2.bd.a.421.18	yes	44	4.3	odd	2
2240.2.bd.a.561.4		44	1.1	even	1	trivial
2240.2.bd.a.1681.4		44	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.63220 + 1.63220i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -2.32815i q^{9} +O(q^{10})\)	\(q+(-1.63220 + 1.63220i) q^{3} +(-0.707107 - 0.707107i) q^{5} -1.00000i q^{7} -2.32815i q^{9} +(0.230290 + 0.230290i) q^{11} +(-1.57890 + 1.57890i) q^{13} +2.30828 q^{15} +4.13766 q^{17} +(-0.553790 + 0.553790i) q^{19} +(1.63220 + 1.63220i) q^{21} +0.651345i q^{23} +1.00000i q^{25} +(-1.09659 - 1.09659i) q^{27} +(-5.41931 + 5.41931i) q^{29} -4.74322 q^{31} -0.751759 q^{33} +(-0.707107 + 0.707107i) q^{35} +(4.34473 + 4.34473i) q^{37} -5.15418i q^{39} -6.29786i q^{41} +(-1.77592 - 1.77592i) q^{43} +(-1.64625 + 1.64625i) q^{45} +2.06198 q^{47} -1.00000 q^{49} +(-6.75348 + 6.75348i) q^{51} +(-3.94676 - 3.94676i) q^{53} -0.325680i q^{55} -1.80779i q^{57} +(-10.2275 - 10.2275i) q^{59} +(-3.32236 + 3.32236i) q^{61} -2.32815 q^{63} +2.23291 q^{65} +(10.7536 - 10.7536i) q^{67} +(-1.06313 - 1.06313i) q^{69} +2.53417i q^{71} -10.8492i q^{73} +(-1.63220 - 1.63220i) q^{75} +(0.230290 - 0.230290i) q^{77} -6.25359 q^{79} +10.5642 q^{81} +(-4.72764 + 4.72764i) q^{83} +(-2.92577 - 2.92577i) q^{85} -17.6908i q^{87} -9.25664i q^{89} +(1.57890 + 1.57890i) q^{91} +(7.74189 - 7.74189i) q^{93} +0.783177 q^{95} -2.47273 q^{97} +(0.536151 - 0.536151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) \) 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more