LMFDB - Embedded newform 2548.2.bq.g.361.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(361,2548)] 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("2548.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,16,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.5
Character	$\chi$	$=$	2548.361
Dual form			2548.2.bq.g.1941.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.901200 q^{3} +(1.46259 - 0.844424i) q^{5} -2.18784 q^{9} +1.24003i q^{11} +(-3.32131 - 1.40318i) q^{13} +(-1.31808 + 0.760994i) q^{15} +(-1.80259 - 3.12217i) q^{17} +7.44840i q^{19} +(4.18649 - 7.25121i) q^{23} +(-1.07390 + 1.86004i) q^{25} +4.67528 q^{27} +(3.09257 + 5.35649i) q^{29} +(-1.13472 - 0.655128i) q^{31} -1.11751i q^{33} +(8.90355 + 5.14047i) q^{37} +(2.99316 + 1.26455i) q^{39} +(-1.40793 + 0.812871i) q^{41} +(-4.78041 + 8.27991i) q^{43} +(-3.19990 + 1.84746i) q^{45} +(10.3435 - 5.97181i) q^{47} +(1.62449 + 2.81370i) q^{51} +(-4.95371 + 8.58008i) q^{53} +(1.04711 + 1.81365i) q^{55} -6.71250i q^{57} +(4.11210 - 2.37412i) q^{59} +12.3943 q^{61} +(-6.04257 + 0.752320i) q^{65} +5.42299i q^{67} +(-3.77286 + 6.53479i) q^{69} +(3.90075 + 2.25210i) q^{71} +(-4.42116 - 2.55256i) q^{73} +(0.967795 - 1.67627i) q^{75} +(3.11082 + 5.38810i) q^{79} +2.35016 q^{81} -17.4323i q^{83} +(-5.27288 - 3.04430i) q^{85} +(-2.78702 - 4.82726i) q^{87} +(-5.07679 - 2.93109i) q^{89} +(1.02260 + 0.590401i) q^{93} +(6.28961 + 10.8939i) q^{95} +(1.64789 + 0.951408i) q^{97} -2.71298i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 20 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} - 40 q^{65} - 24 q^{71} + 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 20 q^{95}+O(q^{100}) $ 24 * q + 16 * q^9 - 12 * q^15 + 16 * q^23 + 24 * q^29 + 20 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 - 40 * q^65 - 24 * q^71 + 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 20 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	−0.901200			−0.520308			−0.260154	−	0.965567i	$-0.583773\pi$
$3$	−0.901200			−0.520308			−0.260154	+	0.965567i	$0.583773\pi$
$4$		0			0
$5$	1.46259	−	0.844424i	0.654088	−	0.377638i	−0.135933	−	0.990718i	$-0.543403\pi$
$5$	1.46259	−	0.844424i	0.654088	−	0.377638i	0.790021	+	0.613080i	$0.210070\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.18784			−0.729280
$10$		0			0
$11$			1.24003i			0.373883i	0.982371	+	0.186941i	$0.0598575\pi$
$11$			1.24003i			0.373883i	−0.982371	+	0.186941i	$0.940143\pi$
$12$		0			0
$13$	−3.32131	−	1.40318i	−0.921165	−	0.389172i
$13$	−3.32131	−	1.40318i	−0.921165	−	0.389172i
$14$		0			0
$15$	−1.31808	+	0.760994i	−0.340327	+	0.196488i
$16$		0			0
$17$	−1.80259	−	3.12217i	−0.437192	−	0.757239i	0.560280	−	0.828303i	$-0.310694\pi$
$17$	−1.80259	−	3.12217i	−0.437192	−	0.757239i	−0.997472	+	0.0710648i	$0.977360\pi$
$18$		0			0
$19$			7.44840i			1.70878i	0.519632	+	0.854390i	$0.326069\pi$
$19$			7.44840i			1.70878i	−0.519632	+	0.854390i	$0.673931\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.18649	−	7.25121i	0.872943	−	1.51198i	0.0140058	−	0.999902i	$-0.495542\pi$
$23$	4.18649	−	7.25121i	0.872943	−	1.51198i	0.858938	−	0.512080i	$-0.171125\pi$
$24$		0			0
$25$	−1.07390	+	1.86004i	−0.214779	+	0.372009i
$26$		0			0
$27$	4.67528			0.899758
$28$		0			0
$29$	3.09257	+	5.35649i	0.574276	+	0.994675i	0.996120	+	0.0880064i	$0.0280496\pi$
$29$	3.09257	+	5.35649i	0.574276	+	0.994675i	−0.421844	+	0.906668i	$0.638617\pi$
$30$		0			0
$31$	−1.13472	−	0.655128i	−0.203801	−	0.117664i	0.394626	−	0.918842i	$-0.370874\pi$
$31$	−1.13472	−	0.655128i	−0.203801	−	0.117664i	−0.598427	+	0.801177i	$0.704207\pi$
$32$		0			0
$33$		−	1.11751i		−	0.194534i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	8.90355	+	5.14047i	1.46373	+	0.845088i	0.999181	−	0.0404575i	$-0.0128815\pi$
$37$	8.90355	+	5.14047i	1.46373	+	0.845088i	0.464553	+	0.885545i	$0.346215\pi$
$38$		0			0
$39$	2.99316	+	1.26455i	0.479289	+	0.202489i
$40$		0			0
$41$	−1.40793	+	0.812871i	−0.219882	+	0.126949i	−0.605896	−	0.795544i	$-0.707185\pi$
$41$	−1.40793	+	0.812871i	−0.219882	+	0.126949i	0.386013	+	0.922493i	$0.373852\pi$
$42$		0			0
$43$	−4.78041	+	8.27991i	−0.729006	+	1.26267i	0.228298	+	0.973591i	$0.426684\pi$
$43$	−4.78041	+	8.27991i	−0.729006	+	1.26267i	−0.957304	+	0.289083i	$0.906650\pi$
$44$		0			0
$45$	−3.19990	+	1.84746i	−0.477013	+	0.275404i
$46$		0			0
$47$	10.3435	−	5.97181i	1.50875	−	0.871077i	0.508802	−	0.860884i	$-0.330088\pi$
$47$	10.3435	−	5.97181i	1.50875	−	0.871077i	0.999948	−	0.0101938i	$-0.00324484\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	1.62449	+	2.81370i	0.227474	+	0.393997i
$52$		0			0
$53$	−4.95371	+	8.58008i	−0.680445	+	1.17857i	0.294400	+	0.955682i	$0.404880\pi$
$53$	−4.95371	+	8.58008i	−0.680445	+	1.17857i	−0.974845	+	0.222883i	$0.928453\pi$
$54$		0			0
$55$	1.04711	+	1.81365i	0.141192	+	0.244552i
$56$		0			0
$57$		−	6.71250i		−	0.889092i
$58$		0			0
$59$	4.11210	−	2.37412i	0.535350	−	0.309084i	−0.207842	−	0.978162i	$-0.566644\pi$
$59$	4.11210	−	2.37412i	0.535350	−	0.309084i	0.743192	+	0.669078i	$0.233311\pi$
$60$		0			0
$61$	12.3943			1.58693			0.793464	−	0.608617i	$-0.208275\pi$
$61$	12.3943			1.58693			0.793464	+	0.608617i	$0.208275\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.04257	+	0.752320i	−0.749489	+	0.0933139i
$66$		0			0
$67$			5.42299i			0.662523i	0.943539	+	0.331262i	$0.107474\pi$
$67$			5.42299i			0.662523i	−0.943539	+	0.331262i	$0.892526\pi$
$68$		0			0
$69$	−3.77286	+	6.53479i	−0.454199	+	0.786696i
$70$		0			0
$71$	3.90075	+	2.25210i	0.462934	+	0.267275i	0.713277	−	0.700882i	$-0.247210\pi$
$71$	3.90075	+	2.25210i	0.462934	+	0.267275i	−0.250343	+	0.968157i	$0.580543\pi$
$72$		0			0
$73$	−4.42116	−	2.55256i	−0.517458	−	0.298754i	0.218436	−	0.975851i	$-0.429904\pi$
$73$	−4.42116	−	2.55256i	−0.517458	−	0.298754i	−0.735894	+	0.677097i	$0.763238\pi$
$74$		0			0
$75$	0.967795	−	1.67627i	0.111751	−	0.193559i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.11082	+	5.38810i	0.349994	+	0.606208i	0.986248	−	0.165272i	$-0.0528502\pi$
$79$	3.11082	+	5.38810i	0.349994	+	0.606208i	−0.636254	+	0.771480i	$0.719517\pi$
$80$		0			0
$81$	2.35016			0.261129
$82$		0			0
$83$		−	17.4323i		−	1.91345i	−0.290998	−	0.956724i	$-0.593987\pi$
$83$		−	17.4323i		−	1.91345i	0.290998	−	0.956724i	$-0.406013\pi$
$84$		0			0
$85$	−5.27288	−	3.04430i	−0.571924	−	0.330200i
$86$		0			0
$87$	−2.78702	−	4.82726i	−0.298800	−	0.517537i
$88$		0			0
$89$	−5.07679	−	2.93109i	−0.538139	−	0.310694i	0.206186	−	0.978513i	$-0.433895\pi$
$89$	−5.07679	−	2.93109i	−0.538139	−	0.310694i	−0.744324	+	0.667818i	$0.767228\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.02260	+	0.590401i	0.106039	+	0.0612217i
$94$		0			0
$95$	6.28961	+	10.8939i	0.645300	+	1.11769i
$96$		0			0
$97$	1.64789	+	0.951408i	0.167318	+	0.0966009i	0.581320	−	0.813675i	$-0.302536\pi$
$97$	1.64789	+	0.951408i	0.167318	+	0.0966009i	−0.414003	+	0.910276i	$0.635870\pi$
$98$		0			0
$99$		−	2.71298i		−	0.272665i
$100$		0			0
$101$	−0.664103			−0.0660807			−0.0330403	−	0.999454i	$-0.510519\pi$
$101$	−0.664103			−0.0660807			−0.0330403	+	0.999454i	$0.510519\pi$
$102$		0			0
$103$	−2.39306	−	4.14489i	−0.235795	−	0.408409i	0.723709	−	0.690106i	$-0.242436\pi$
$103$	−2.39306	−	4.14489i	−0.235795	−	0.408409i	−0.959503	+	0.281697i	$0.909103\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.59924	−	4.50202i	0.251278	−	0.435226i	−0.712600	−	0.701571i	$-0.752482\pi$
$107$	2.59924	−	4.50202i	0.251278	−	0.435226i	0.963878	+	0.266344i	$0.0858158\pi$
$108$		0			0
$109$	13.8406	+	7.99089i	1.32569	+	0.765388i	0.984630	−	0.174653i	$-0.0558802\pi$
$109$	13.8406	+	7.99089i	1.32569	+	0.765388i	0.341062	+	0.940041i	$0.389214\pi$
$110$		0			0
$111$	−8.02388	−	4.63259i	−0.761593	−	0.439706i
$112$		0			0
$113$	−7.17880	+	12.4340i	−0.675324	+	1.16970i	0.301050	+	0.953608i	$0.402663\pi$
$113$	−7.17880	+	12.4340i	−0.675324	+	1.16970i	−0.976374	+	0.216088i	$0.930670\pi$
$114$		0			0
$115$		−	14.1407i		−	1.31863i
$116$		0			0
$117$	7.26649	+	3.06993i	0.671787	+	0.283815i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	9.46233			0.860212
$122$		0			0
$123$	1.26883	−	0.732559i	0.114406	−	0.0660526i
$124$		0			0
$125$			12.0715i			1.07971i
$126$		0			0
$127$	−5.77153	−	9.99658i	−0.512140	−	0.887053i	−0.999901	−	0.0140755i	$-0.995519\pi$
$127$	−5.77153	−	9.99658i	−0.512140	−	0.887053i	0.487761	−	0.872977i	$-0.337814\pi$
$128$		0			0
$129$	4.30810	−	7.46185i	0.379307	−	0.656979i
$130$		0			0
$131$	6.13684	+	10.6293i	0.536178	+	0.928687i	0.999105	+	0.0422911i	$0.0134657\pi$
$131$	6.13684	+	10.6293i	0.536178	+	0.928687i	−0.462927	+	0.886396i	$0.653201\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	6.83799	−	3.94792i	0.588521	−	0.339783i
$136$		0			0
$137$	1.62788	−	0.939855i	0.139079	−	0.0802973i	−0.428846	−	0.903378i	$-0.641080\pi$
$137$	1.62788	−	0.939855i	0.139079	−	0.0802973i	0.567925	+	0.823080i	$0.307746\pi$
$138$		0			0
$139$	−7.11986	+	12.3320i	−0.603899	+	1.04598i	0.388326	+	0.921522i	$0.373054\pi$
$139$	−7.11986	+	12.3320i	−0.603899	+	1.04598i	−0.992225	+	0.124461i	$0.960280\pi$
$140$		0			0
$141$	−9.32153	+	5.38179i	−0.785014	+	0.453228i
$142$		0			0
$143$	1.73998	−	4.11852i	0.145505	−	0.344408i
$144$		0			0
$145$	9.04629	+	5.22288i	0.751254	+	0.433736i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			15.1724i			1.24297i	0.783426	+	0.621485i	$0.213470\pi$
$149$			15.1724i			1.24297i	−0.783426	+	0.621485i	$0.786530\pi$
$150$		0			0
$151$	2.67238	+	1.54290i	0.217475	+	0.125559i	0.604781	−	0.796392i	$-0.293261\pi$
$151$	2.67238	+	1.54290i	0.217475	+	0.125559i	−0.387305	+	0.921951i	$0.626594\pi$
$152$		0			0
$153$	3.94377	+	6.83082i	0.318835	+	0.552239i
$154$		0			0
$155$	−2.21282			−0.177738
$156$		0			0
$157$	−9.48349	+	16.4259i	−0.756865	+	1.31093i	0.187577	+	0.982250i	$0.439936\pi$
$157$	−9.48349	+	16.4259i	−0.756865	+	1.31093i	−0.944442	+	0.328678i	$0.893397\pi$
$158$		0			0
$159$	4.46428	−	7.73237i	0.354041	−	0.613217i
$160$		0			0
$161$		0			0
$162$		0			0
$163$		−	12.1441i		−	0.951196i	−0.879663	−	0.475598i	$-0.842232\pi$
$163$		−	12.1441i		−	0.951196i	0.879663	−	0.475598i	$-0.157768\pi$
$164$		0			0
$165$	−0.943655	−	1.63446i	−0.0734635	−	0.127242i
$166$		0			0
$167$	−0.740822	+	0.427714i	−0.0573265	+	0.0330975i	−0.528389	−	0.849002i	$-0.677204\pi$
$167$	−0.740822	+	0.427714i	−0.0573265	+	0.0330975i	0.471063	+	0.882100i	$0.343871\pi$
$168$		0			0
$169$	9.06217	+	9.32079i	0.697090	+	0.716984i
$170$		0			0
$171$		−	16.2959i		−	1.24618i
$172$		0			0
$173$	9.93769			0.755549			0.377774	−	0.925898i	$-0.376689\pi$
$173$	9.93769			0.755549			0.377774	+	0.925898i	$0.376689\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.70582	+	2.13956i	−0.278547	+	0.160819i
$178$		0			0
$179$	8.68191			0.648916			0.324458	−	0.945900i	$-0.394818\pi$
$179$	8.68191			0.648916			0.324458	+	0.945900i	$0.394818\pi$
$180$		0			0
$181$	8.29857			0.616828			0.308414	−	0.951252i	$-0.400202\pi$
$181$	8.29857			0.616828			0.308414	+	0.951252i	$0.400202\pi$
$182$		0			0
$183$	−11.1697			−0.825691
$184$		0			0
$185$	17.3629			1.27655
$186$		0			0
$187$	3.87159	−	2.23526i	0.283118	−	0.163459i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.51400			−0.254264			−0.127132	−	0.991886i	$-0.540577\pi$
$191$	−3.51400			−0.254264			−0.127132	+	0.991886i	$0.540577\pi$
$192$		0			0
$193$			7.98179i			0.574542i	0.957849	+	0.287271i	$0.0927480\pi$
$193$			7.98179i			0.574542i	−0.957849	+	0.287271i	$0.907252\pi$
$194$		0			0
$195$	5.44556	−	0.677991i	0.389965	−	0.0485519i
$196$		0			0
$197$	13.6305	−	7.86955i	0.971130	−	0.560682i	0.0715497	−	0.997437i	$-0.477206\pi$
$197$	13.6305	−	7.86955i	0.971130	−	0.560682i	0.899581	+	0.436755i	$0.143872\pi$
$198$		0			0
$199$	9.79689	+	16.9687i	0.694483	+	1.20288i	0.970355	+	0.241686i	$0.0777003\pi$
$199$	9.79689	+	16.9687i	0.694483	+	1.20288i	−0.275871	+	0.961195i	$0.588966\pi$
$200$		0			0
$201$		−	4.88719i		−	0.344716i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.37281	+	2.37779i	−0.0958816	+	0.166072i
$206$		0			0
$207$	−9.15937	+	15.8645i	−0.636620	+	1.10266i
$208$		0			0
$209$	−9.23623			−0.638884
$210$		0			0
$211$	−7.01098	−	12.1434i	−0.482656	−	0.835984i	0.517146	−	0.855897i	$-0.326994\pi$
$211$	−7.01098	−	12.1434i	−0.482656	−	0.835984i	−0.999802	+	0.0199129i	$0.993661\pi$
$212$		0			0
$213$	−3.51536	−	2.02959i	−0.240868	−	0.139065i
$214$		0			0
$215$			16.1468i			1.10120i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.98435	+	2.30036i	0.269237	+	0.155444i
$220$		0			0
$221$	1.60598	+	12.8991i	0.108030	+	0.867685i
$222$		0			0
$223$	8.28564	−	4.78371i	0.554847	−	0.320341i	−0.196228	−	0.980558i	$-0.562869\pi$
$223$	8.28564	−	4.78371i	0.554847	−	0.320341i	0.751075	+	0.660217i	$0.229536\pi$
$224$		0			0
$225$	2.34951	−	4.06948i	0.156634	−	0.271298i
$226$		0			0
$227$	−2.39786	+	1.38441i	−0.159152	+	0.0918862i	−0.577461	−	0.816419i	$-0.695956\pi$
$227$	−2.39786	+	1.38441i	−0.159152	+	0.0918862i	0.418309	+	0.908305i	$0.362623\pi$
$228$		0			0
$229$	−2.51003	+	1.44917i	−0.165867	+	0.0957636i	−0.580636	−	0.814163i	$-0.697196\pi$
$229$	−2.51003	+	1.44917i	−0.165867	+	0.0957636i	0.414768	+	0.909927i	$0.363863\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.04198	+	13.9291i	0.526847	+	0.912526i	0.999511	+	0.0312833i	$0.00995941\pi$
$233$	8.04198	+	13.9291i	0.526847	+	0.912526i	−0.472663	+	0.881243i	$0.656707\pi$
$234$		0			0
$235$	10.0855	−	17.4685i	0.657903	−	1.13952i
$236$		0			0
$237$	−2.80347	−	4.85575i	−0.182105	−	0.315415i
$238$		0			0
$239$			7.47074i			0.483242i	0.970371	+	0.241621i	$0.0776790\pi$
$239$			7.47074i			0.483242i	−0.970371	+	0.241621i	$0.922321\pi$
$240$		0			0
$241$	−16.8670	+	9.73817i	−1.08650	+	0.627290i	−0.932642	−	0.360803i	$-0.882503\pi$
$241$	−16.8670	+	9.73817i	−1.08650	+	0.627290i	−0.153857	+	0.988093i	$0.549169\pi$
$242$		0			0
$243$	−16.1438			−1.03563
$244$		0			0
$245$		0			0
$246$		0			0
$247$	10.4515	−	24.7384i	0.665010	−	1.57407i
$248$		0			0
$249$			15.7100i			0.995582i
$250$		0			0
$251$	1.27911	−	2.21549i	0.0807369	−	0.139840i	−0.822830	−	0.568288i	$-0.807606\pi$
$251$	1.27911	−	2.21549i	0.0807369	−	0.139840i	0.903567	+	0.428448i	$0.140939\pi$
$252$		0			0
$253$	8.99171	+	5.19137i	0.565304	+	0.326379i
$254$		0			0
$255$	4.75191	+	2.74352i	0.297576	+	0.171806i
$256$		0			0
$257$	−0.838975	+	1.45315i	−0.0523338	+	0.0906448i	−0.891006	−	0.453992i	$-0.849999\pi$
$257$	−0.838975	+	1.45315i	−0.0523338	+	0.0906448i	0.838672	+	0.544637i	$0.183333\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−6.76605	−	11.7191i	−0.418808	−	0.725396i
$262$		0			0
$263$	5.23358			0.322717			0.161358	−	0.986896i	$-0.448413\pi$
$263$	5.23358			0.322717			0.161358	+	0.986896i	$0.448413\pi$
$264$		0			0
$265$			16.7321i			1.02785i
$266$		0			0
$267$	4.57520	+	2.64149i	0.279998	+	0.161657i
$268$		0			0
$269$	−12.6609	−	21.9293i	−0.771947	−	1.33705i	−0.936495	−	0.350682i	$-0.885950\pi$
$269$	−12.6609	−	21.9293i	−0.771947	−	1.33705i	0.164548	−	0.986369i	$-0.447383\pi$
$270$		0			0
$271$	9.31805	+	5.37978i	0.566031	+	0.326798i	0.755563	−	0.655076i	$-0.227364\pi$
$271$	9.31805	+	5.37978i	0.566031	+	0.326798i	−0.189531	+	0.981875i	$0.560697\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.30651	−	1.33166i	−0.139088	−	0.0803023i
$276$		0			0
$277$	−13.7777	−	23.8637i	−0.827823	−	1.43383i	−0.899743	−	0.436421i	$-0.856246\pi$
$277$	−13.7777	−	23.8637i	−0.827823	−	1.43383i	0.0719201	−	0.997410i	$-0.477087\pi$
$278$		0			0
$279$	2.48257	+	1.43331i	0.148628	+	0.0858103i
$280$		0			0
$281$			28.3133i			1.68903i	0.535534	+	0.844514i	$0.320111\pi$
$281$			28.3133i			1.68903i	−0.535534	+	0.844514i	$0.679889\pi$
$282$		0			0
$283$	−4.44951			−0.264496			−0.132248	−	0.991217i	$-0.542220\pi$
$283$	−4.44951			−0.264496			−0.132248	+	0.991217i	$0.542220\pi$
$284$		0			0
$285$	−5.66819	−	9.81760i	−0.335755	−	0.581544i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	2.00135	−	3.46644i	0.117726	−	0.203908i
$290$		0			0
$291$	−1.48508	−	0.857409i	−0.0870567	−	0.0502622i
$292$		0			0
$293$	16.8402	+	9.72271i	0.983816	+	0.568007i	0.903420	−	0.428756i	$-0.141048\pi$
$293$	16.8402	+	9.72271i	0.983816	+	0.568007i	0.0803960	+	0.996763i	$0.474382\pi$
$294$		0			0
$295$	4.00953	−	6.94471i	0.233444	−	0.404337i
$296$		0			0
$297$			5.79748i			0.336404i
$298$		0			0
$299$	−24.0794	+	18.2091i	−1.39255	+	1.05306i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.598489			0.0343823
$304$		0			0
$305$	18.1277	−	10.4660i	1.03799	−	0.599284i
$306$		0			0
$307$		−	10.9479i		−	0.624830i	−0.949946	−	0.312415i	$-0.898862\pi$
$307$		−	10.9479i		−	0.624830i	0.949946	−	0.312415i	$-0.101138\pi$
$308$		0			0
$309$	2.15662	+	3.73538i	0.122686	+	0.212498i
$310$		0			0
$311$	−8.34356	+	14.4515i	−0.473120	+	0.819467i	−0.999527	−	0.0307655i	$-0.990206\pi$
$311$	−8.34356	+	14.4515i	−0.473120	+	0.819467i	0.526407	+	0.850233i	$0.323539\pi$
$312$		0			0
$313$	1.67149	+	2.89510i	0.0944780	+	0.163641i	0.909391	−	0.415943i	$-0.136548\pi$
$313$	1.67149	+	2.89510i	0.0944780	+	0.163641i	−0.814913	+	0.579584i	$0.803215\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−27.9207	+	16.1200i	−1.56818	+	0.905390i	−0.571800	+	0.820393i	$0.693755\pi$
$317$	−27.9207	+	16.1200i	−1.56818	+	0.905390i	−0.996381	+	0.0849965i	$0.972912\pi$
$318$		0			0
$319$	−6.64220	+	3.83488i	−0.371892	+	0.214712i
$320$		0			0
$321$	−2.34243	+	4.05722i	−0.130742	+	0.226452i
$322$		0			0
$323$	23.2552	−	13.4264i	1.29395	−	0.747065i
$324$		0			0
$325$	6.17672	−	4.67091i	0.342623	−	0.259095i
$326$		0			0
$327$	−12.4732	−	7.20139i	−0.689768	−	0.398238i
$328$		0			0
$329$		0			0
$330$		0			0
$331$			30.6436i			1.68433i	0.539222	+	0.842163i	$0.318718\pi$
$331$			30.6436i			1.68433i	−0.539222	+	0.842163i	$0.681282\pi$
$332$		0			0
$333$	−19.4795	−	11.2465i	−1.06747	−	0.616305i
$334$		0			0
$335$	4.57930	+	7.93158i	0.250194	+	0.433349i
$336$		0			0
$337$	−10.0120			−0.545391			−0.272695	−	0.962100i	$-0.587915\pi$
$337$	−10.0120			−0.545391			−0.272695	+	0.962100i	$0.587915\pi$
$338$		0			0
$339$	6.46953	−	11.2056i	0.351377	−	0.608602i
$340$		0			0
$341$	0.812378	−	1.40708i	0.0439927	−	0.0761976i
$342$		0			0
$343$		0			0
$344$		0			0
$345$			12.7436i			0.686091i
$346$		0			0
$347$	6.22299	+	10.7785i	0.334067	+	0.578622i	0.983305	−	0.181964i	$-0.0582453\pi$
$347$	6.22299	+	10.7785i	0.334067	+	0.578622i	−0.649238	+	0.760585i	$0.724912\pi$
$348$		0			0
$349$	16.3534	−	9.44164i	0.875378	−	0.505400i	0.00624626	−	0.999980i	$-0.498012\pi$
$349$	16.3534	−	9.44164i	0.875378	−	0.505400i	0.869132	+	0.494581i	$0.164678\pi$
$350$		0			0
$351$	−15.5280	−	6.56026i	−0.828825	−	0.350161i
$352$		0			0
$353$		−	14.5100i		−	0.772292i	−0.922438	−	0.386146i	$-0.873806\pi$
$353$		−	14.5100i		−	0.772292i	0.922438	−	0.386146i	$-0.126194\pi$
$354$		0			0
$355$	7.60691			0.403733
$356$		0			0
$357$		0			0
$358$		0			0
$359$	23.8583	−	13.7746i	1.25919	−	0.726995i	0.286275	−	0.958147i	$-0.407583\pi$
$359$	23.8583	−	13.7746i	1.25919	−	0.726995i	0.972918	+	0.231152i	$0.0742496\pi$
$360$		0			0
$361$	−36.4787			−1.91993
$362$		0			0
$363$	−8.52745			−0.447575
$364$		0			0
$365$	−8.62176			−0.451284
$366$		0			0
$367$	17.2199			0.898873			0.449436	−	0.893312i	$-0.351625\pi$
$367$	17.2199			0.898873			0.449436	+	0.893312i	$0.351625\pi$
$368$		0			0
$369$	3.08033	−	1.77843i	0.160356	−	0.0925814i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−20.0454			−1.03791			−0.518956	−	0.854801i	$-0.673679\pi$
$373$	−20.0454			−1.03791			−0.518956	+	0.854801i	$0.673679\pi$
$374$		0			0
$375$		−	10.8789i		−	0.561782i
$376$		0			0
$377$	−2.75525	−	22.1300i	−0.141903	−	1.13975i
$378$		0			0
$379$	29.6299	−	17.1068i	1.52198	−	0.878718i	0.522321	−	0.852749i	$-0.325066\pi$
$379$	29.6299	−	17.1068i	1.52198	−	0.878718i	0.999663	−	0.0259690i	$-0.00826713\pi$
$380$		0			0
$381$	5.20130	+	9.00891i	0.266471	+	0.461541i
$382$		0			0
$383$		−	6.81630i		−	0.348297i	−0.984719	−	0.174148i	$-0.944283\pi$
$383$		−	6.81630i		−	0.348297i	0.984719	−	0.174148i	$-0.0557173\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	10.4588	−	18.1151i	0.531649	−	0.920843i
$388$		0			0
$389$	8.01572	−	13.8836i	0.406413	−	0.703928i	−0.588072	−	0.808809i	$-0.700113\pi$
$389$	8.01572	−	13.8836i	0.406413	−	0.703928i	0.994485	+	0.104881i	$0.0334461\pi$
$390$		0			0
$391$	−30.1861			−1.52658
$392$		0			0
$393$	−5.53051	−	9.57913i	−0.278978	−	0.483203i
$394$		0			0
$395$	9.09967	+	5.25370i	0.457854	+	0.264342i
$396$		0			0
$397$		−	12.3904i		−	0.621859i	−0.950433	−	0.310929i	$-0.899360\pi$
$397$		−	12.3904i		−	0.621859i	0.950433	−	0.310929i	$-0.100640\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.7737	−	14.8805i	−1.28708	−	0.743095i	−0.308947	−	0.951079i	$-0.599976\pi$
$401$	−25.7737	−	14.8805i	−1.28708	−	0.743095i	−0.978132	+	0.207984i	$0.933310\pi$
$402$		0			0
$403$	2.84947	+	3.76809i	0.141942	+	0.187702i
$404$		0			0
$405$	3.43731	−	1.98453i	0.170801	−	0.0986121i
$406$		0			0
$407$	−6.37433	+	11.0407i	−0.315964	+	0.547265i
$408$		0			0
$409$	−30.1214	+	17.3906i	−1.48941	+	0.859910i	−0.999927	−	0.0121036i	$-0.996147\pi$
$409$	−30.1214	+	17.3906i	−1.48941	+	0.859910i	−0.489481	+	0.872014i	$0.662814\pi$
$410$		0			0
$411$	−1.46704	+	0.846997i	−0.0723639	+	0.0417793i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−14.7203	−	25.4963i	−0.722590	−	1.25156i
$416$		0			0
$417$	6.41641	−	11.1136i	0.314213	−	0.544233i
$418$		0			0
$419$	−19.4496	−	33.6877i	−0.950176	−	1.64575i	−0.745041	−	0.667018i	$-0.767570\pi$
$419$	−19.4496	−	33.6877i	−0.950176	−	1.64575i	−0.205134	−	0.978734i	$-0.565763\pi$
$420$		0			0
$421$			5.22668i			0.254733i	0.991856	+	0.127366i	$0.0406524\pi$
$421$			5.22668i			0.254733i	−0.991856	+	0.127366i	$0.959348\pi$
$422$		0			0
$423$	−22.6299	+	13.0654i	−1.10030	+	0.635259i
$424$		0			0
$425$	7.74317			0.375599
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.56807	+	3.71161i	−0.0757073	+	0.179198i
$430$		0			0
$431$		−	28.6360i		−	1.37935i	−0.724120	−	0.689674i	$-0.757754\pi$
$431$		−	28.6360i		−	1.37935i	0.724120	−	0.689674i	$-0.242246\pi$
$432$		0			0
$433$	−6.70789	+	11.6184i	−0.322361	+	0.558345i	−0.980975	−	0.194136i	$-0.937810\pi$
$433$	−6.70789	+	11.6184i	−0.322361	+	0.558345i	0.658614	+	0.752481i	$0.271143\pi$
$434$		0			0
$435$	−8.15251	−	4.70686i	−0.390883	−	0.225676i
$436$		0			0
$437$	54.0099	+	31.1827i	2.58365	+	1.49167i
$438$		0			0
$439$	−3.30101	+	5.71753i	−0.157549	+	0.272883i	−0.933984	−	0.357314i	$-0.883693\pi$
$439$	−3.30101	+	5.71753i	−0.157549	+	0.272883i	0.776435	+	0.630197i	$0.217026\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.64747	−	4.58555i	−0.125785	−	0.217866i	0.796255	−	0.604962i	$-0.206812\pi$
$443$	−2.64747	−	4.58555i	−0.125785	−	0.217866i	−0.922040	+	0.387096i	$0.873478\pi$
$444$		0			0
$445$	−9.90032			−0.469320
$446$		0			0
$447$		−	13.6733i		−	0.646727i
$448$		0			0
$449$	−9.52908	−	5.50162i	−0.449705	−	0.259637i	0.258001	−	0.966145i	$-0.416936\pi$
$449$	−9.52908	−	5.50162i	−0.449705	−	0.259637i	−0.707706	+	0.706507i	$0.750270\pi$
$450$		0			0
$451$	−1.00798	−	1.74588i	−0.0474641	−	0.0822102i
$452$		0			0
$453$	−2.40835	−	1.39046i	−0.113154	−	0.0653295i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	15.8207	+	9.13409i	0.740062	+	0.427275i	0.822092	−	0.569355i	$-0.192807\pi$
$457$	15.8207	+	9.13409i	0.740062	+	0.427275i	−0.0820301	+	0.996630i	$0.526140\pi$
$458$		0			0
$459$	−8.42760	−	14.5970i	−0.393367	−	0.681331i
$460$		0			0
$461$	−1.32125	−	0.762824i	−0.0615367	−	0.0355282i	0.468916	−	0.883243i	$-0.344645\pi$
$461$	−1.32125	−	0.762824i	−0.0615367	−	0.0355282i	−0.530453	+	0.847715i	$0.677978\pi$
$462$		0			0
$463$		−	10.1463i		−	0.471539i	−0.971809	−	0.235770i	$-0.924239\pi$
$463$		−	10.1463i		−	0.471539i	0.971809	−	0.235770i	$-0.0757611\pi$
$464$		0			0
$465$	1.99420			0.0924786
$466$		0			0
$467$	−10.6415	−	18.4316i	−0.492428	−	0.852911i	0.507534	−	0.861632i	$-0.330557\pi$
$467$	−10.6415	−	18.4316i	−0.492428	−	0.852911i	−0.999962	+	0.00872095i	$0.997224\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	8.54651	−	14.8030i	0.393803	−	0.682086i
$472$		0			0
$473$	−10.2673	−	5.92785i	−0.472092	−	0.272563i
$474$		0			0
$475$	−13.8544	−	7.99881i	−0.635681	−	0.367011i
$476$		0			0
$477$	10.8379	−	18.7718i	0.496235	−	0.859504i
$478$		0			0
$479$			18.2017i			0.831657i	0.909443	+	0.415829i	$0.136508\pi$
$479$			18.2017i			0.831657i	−0.909443	+	0.415829i	$0.863492\pi$
$480$		0			0
$481$	−22.3584	−	29.5664i	−1.01946	−	1.34811i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.21357			0.145921
$486$		0			0
$487$	−6.42544	+	3.70973i	−0.291165	+	0.168104i	−0.638467	−	0.769649i	$-0.720431\pi$
$487$	−6.42544	+	3.70973i	−0.291165	+	0.168104i	0.347302	+	0.937753i	$0.387098\pi$
$488$		0			0
$489$			10.9442i			0.494914i
$490$		0			0
$491$	8.47626	+	14.6813i	0.382528	+	0.662559i	0.991423	−	0.130693i	$-0.0417201\pi$
$491$	8.47626	+	14.6813i	0.382528	+	0.662559i	−0.608895	+	0.793251i	$0.708387\pi$
$492$		0			0
$493$	11.1493	−	19.3111i	0.502137	−	0.869728i
$494$		0			0
$495$	−2.29091	−	3.96797i	−0.102969	−	0.178347i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−14.5955	+	8.42670i	−0.653383	+	0.377231i	−0.789751	−	0.613427i	$-0.789790\pi$
$499$	−14.5955	+	8.42670i	−0.653383	+	0.377231i	0.136368	+	0.990658i	$0.456457\pi$
$500$		0			0
$501$	0.667628	−	0.385455i	0.0298274	−	0.0172209i
$502$		0			0
$503$	3.04565	−	5.27522i	0.135799	−	0.235211i	−0.790103	−	0.612974i	$-0.789973\pi$
$503$	3.04565	−	5.27522i	0.135799	−	0.235211i	0.925902	+	0.377763i	$0.123307\pi$
$504$		0			0
$505$	−0.971307	+	0.560784i	−0.0432226	+	0.0249546i
$506$		0			0
$507$	−8.16682	−	8.39989i	−0.362701	−	0.373052i
$508$		0			0
$509$	−28.2625	−	16.3174i	−1.25271	−	0.723254i	−0.281065	−	0.959689i	$-0.590688\pi$
$509$	−28.2625	−	16.3174i	−1.25271	−	0.723254i	−0.971647	+	0.236435i	$0.924021\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			34.8233i			1.53749i
$514$		0			0
$515$	−7.00010	−	4.04151i	−0.308461	−	0.178090i
$516$		0			0
$517$	7.40521	+	12.8262i	0.325681	+	0.564096i
$518$		0			0
$519$	−8.95585			−0.393118
$520$		0			0
$521$	0.806311	−	1.39657i	0.0353251	−	0.0611849i	−0.847822	−	0.530280i	$-0.822087\pi$
$521$	0.806311	−	1.39657i	0.0353251	−	0.0611849i	0.883147	+	0.469095i	$0.155420\pi$
$522$		0			0
$523$	−7.58180	+	13.1321i	−0.331529	+	0.574225i	−0.982812	−	0.184610i	$-0.940898\pi$
$523$	−7.58180	+	13.1321i	−0.331529	+	0.574225i	0.651283	+	0.758835i	$0.274231\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			4.72370i			0.205768i
$528$		0			0
$529$	−23.5534	−	40.7957i	−1.02406	−	1.77372i
$530$		0			0
$531$	−8.99661	+	5.19420i	−0.390420	+	0.225409i
$532$		0			0
$533$	5.81678	−	0.724209i	0.251953	−	0.0313690i
$534$		0			0
$535$		−	8.77944i		−	0.379568i
$536$		0			0
$537$	−7.82413			−0.337636
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−22.9733	+	13.2637i	−0.987701	+	0.570250i	−0.904586	−	0.426290i	$-0.859820\pi$
$541$	−22.9733	+	13.2637i	−0.987701	+	0.570250i	−0.0831149	+	0.996540i	$0.526487\pi$
$542$		0			0
$543$	−7.47866			−0.320940
$544$		0			0
$545$	26.9908			1.15616
$546$		0			0
$547$	−1.62348			−0.0694149			−0.0347075	−	0.999398i	$-0.511050\pi$
$547$	−1.62348			−0.0694149			−0.0347075	+	0.999398i	$0.511050\pi$
$548$		0			0
$549$	−27.1167			−1.15731
$550$		0			0
$551$	−39.8973	+	23.0347i	−1.69968	+	0.981311i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−15.6475			−0.664198
$556$		0			0
$557$		−	2.92764i		−	0.124048i	−0.998075	−	0.0620239i	$-0.980244\pi$
$557$		−	2.92764i		−	0.124048i	0.998075	−	0.0620239i	$-0.0197555\pi$
$558$		0			0
$559$	27.4954	−	20.7924i	1.16293	−	0.879423i
$560$		0			0
$561$	−3.48907	+	2.01442i	−0.147309	+	0.0850488i
$562$		0			0
$563$	21.5167	+	37.2680i	0.906820	+	1.57066i	0.818455	+	0.574570i	$0.194831\pi$
$563$	21.5167	+	37.2680i	0.906820	+	1.57066i	0.0883645	+	0.996088i	$0.471836\pi$
$564$		0			0
$565$			24.2478i			1.02011i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.146711	+	0.254111i	−0.00615044	+	0.0106529i	−0.869084	−	0.494664i	$-0.835291\pi$
$569$	−0.146711	+	0.254111i	−0.00615044	+	0.0106529i	0.862934	+	0.505317i	$0.168624\pi$
$570$		0			0
$571$	−8.07299	+	13.9828i	−0.337844	+	0.585163i	−0.984027	−	0.178020i	$-0.943031\pi$
$571$	−8.07299	+	13.9828i	−0.337844	+	0.585163i	0.646183	+	0.763182i	$0.276364\pi$
$572$		0			0
$573$	3.16681			0.132295
$574$		0			0
$575$	8.99171	+	15.5741i	0.374980	+	0.649485i
$576$		0			0
$577$	−17.1538	−	9.90377i	−0.714124	−	0.412299i	0.0984625	−	0.995141i	$-0.468608\pi$
$577$	−17.1538	−	9.90377i	−0.714124	−	0.412299i	−0.812586	+	0.582841i	$0.801941\pi$
$578$		0			0
$579$		−	7.19318i		−	0.298939i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−10.6396	−	6.14275i	−0.440645	−	0.254407i
$584$		0			0
$585$	13.2202	−	1.64596i	0.546587	−	0.0680519i
$586$		0			0
$587$	−2.23571	+	1.29079i	−0.0922775	+	0.0532764i	−0.545429	−	0.838157i	$-0.683633\pi$
$587$	−2.23571	+	1.29079i	−0.0922775	+	0.0532764i	0.453151	+	0.891434i	$0.350300\pi$
$588$		0			0
$589$	4.87966	−	8.45181i	0.201063	−	0.348251i
$590$		0			0
$591$	−12.2838	+	7.09204i	−0.505287	+	0.291727i
$592$		0			0
$593$	11.6618	−	6.73296i	0.478894	−	0.276489i	−0.241062	−	0.970510i	$-0.577496\pi$
$593$	11.6618	−	6.73296i	0.478894	−	0.276489i	0.719955	+	0.694020i	$0.244162\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.82895	−	15.2922i	−0.361345	−	0.625868i
$598$		0			0
$599$	6.50393	−	11.2651i	0.265743	−	0.460281i	−0.702015	−	0.712162i	$-0.747716\pi$
$599$	6.50393	−	11.2651i	0.265743	−	0.460281i	0.967758	+	0.251881i	$0.0810493\pi$
$600$		0			0
$601$	20.3117	+	35.1808i	0.828530	+	1.43506i	0.899192	+	0.437555i	$0.144155\pi$
$601$	20.3117	+	35.1808i	0.828530	+	1.43506i	−0.0706620	+	0.997500i	$0.522511\pi$
$602$		0			0
$603$		−	11.8646i		−	0.483165i
$604$		0			0
$605$	13.8395	−	7.99022i	0.562654	−	0.324848i
$606$		0			0
$607$	−21.1243			−0.857409			−0.428705	−	0.903445i	$-0.641030\pi$
$607$	−21.1243			−0.857409			−0.428705	+	0.903445i	$0.641030\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−42.7334	+	5.32044i	−1.72881	+	0.215242i
$612$		0			0
$613$		−	20.9348i		−	0.845549i	−0.906235	−	0.422774i	$-0.861056\pi$
$613$		−	20.9348i		−	0.845549i	0.906235	−	0.422774i	$-0.138944\pi$
$614$		0			0
$615$	1.23718	−	2.14286i	0.0498879	−	0.0864084i
$616$		0			0
$617$	31.6854	+	18.2936i	1.27561	+	0.736471i	0.976037	−	0.217603i	$-0.0698240\pi$
$617$	31.6854	+	18.2936i	1.27561	+	0.736471i	0.299568	+	0.954075i	$0.403157\pi$
$618$		0			0
$619$	−12.2663	−	7.08194i	−0.493024	−	0.284647i	0.232804	−	0.972524i	$-0.425210\pi$
$619$	−12.2663	−	7.08194i	−0.493024	−	0.284647i	−0.725828	+	0.687876i	$0.758543\pi$
$620$		0			0
$621$	19.5730	−	33.9014i	0.785438	−	1.36042i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.82401	+	8.35543i	0.192960	+	0.334217i
$626$		0			0
$627$	8.32369			0.332416
$628$		0			0
$629$		−	37.0646i		−	1.47786i
$630$		0			0
$631$	−29.0904	−	16.7954i	−1.15807	−	0.668612i	−0.207230	−	0.978292i	$-0.566445\pi$
$631$	−29.0904	−	16.7954i	−1.15807	−	0.668612i	−0.950841	+	0.309680i	$0.899778\pi$
$632$		0			0
$633$	6.31829	+	10.9436i	0.251130	+	0.434969i
$634$		0			0
$635$	−16.8827	−	9.74723i	−0.669969	−	0.386807i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−8.53423	−	4.92724i	−0.337609	−	0.194918i
$640$		0			0
$641$	−6.18605	−	10.7146i	−0.244334	−	0.423200i	0.717610	−	0.696445i	$-0.245236\pi$
$641$	−6.18605	−	10.7146i	−0.244334	−	0.423200i	−0.961944	+	0.273246i	$0.911903\pi$
$642$		0			0
$643$	−33.8520	−	19.5445i	−1.33499	−	0.770758i	−0.348933	−	0.937148i	$-0.613456\pi$
$643$	−33.8520	−	19.5445i	−1.33499	−	0.770758i	−0.986060	+	0.166389i	$0.946789\pi$
$644$		0			0
$645$		−	14.5515i		−	0.572963i
$646$		0			0
$647$	39.7511			1.56278			0.781389	−	0.624045i	$-0.214512\pi$
$647$	39.7511			1.56278			0.781389	+	0.624045i	$0.214512\pi$
$648$		0			0
$649$	2.94398	+	5.09912i	0.115561	+	0.200158i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.17434	−	3.76606i	0.0850884	−	0.147377i	−0.820340	−	0.571875i	$-0.806216\pi$
$653$	2.17434	−	3.76606i	0.0850884	−	0.147377i	0.905429	+	0.424498i	$0.139549\pi$
$654$		0			0
$655$	17.9513	+	10.3642i	0.701415	+	0.404962i
$656$		0			0
$657$	9.67279	+	5.58459i	0.377371	+	0.217875i
$658$		0			0
$659$	12.6807	−	21.9637i	0.493971	−	0.855583i	−0.506005	−	0.862531i	$-0.668878\pi$
$659$	12.6807	−	21.9637i	0.493971	−	0.855583i	0.999976	+	0.00694774i	$0.00221155\pi$
$660$		0			0
$661$		−	10.6987i		−	0.416131i	−0.978115	−	0.208065i	$-0.933283\pi$
$661$		−	10.6987i		−	0.416131i	0.978115	−	0.208065i	$-0.0667167\pi$
$662$		0			0
$663$	−1.44730	−	11.6246i	−0.0562086	−	0.451463i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	51.7880			2.00524
$668$		0			0
$669$	−7.46701	+	4.31108i	−0.288691	+	0.166676i
$670$		0			0
$671$			15.3693i			0.593325i
$672$		0			0
$673$	−15.3911	−	26.6582i	−0.593284	−	1.02760i	−0.993787	−	0.111302i	$-0.964498\pi$
$673$	−15.3911	−	26.6582i	−0.593284	−	1.02760i	0.400503	−	0.916296i	$-0.368836\pi$
$674$		0			0
$675$	−5.02077	+	8.69622i	−0.193249	+	0.334718i
$676$		0			0
$677$	9.72565	+	16.8453i	0.373787	+	0.647418i	0.990145	−	0.140048i	$-0.0447257\pi$
$677$	9.72565	+	16.8453i	0.373787	+	0.647418i	−0.616358	+	0.787466i	$0.711392\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	2.16095	−	1.24763i	0.0828078	−	0.0478091i
$682$		0			0
$683$	11.7946	−	6.80964i	0.451310	−	0.260564i	−0.257074	−	0.966392i	$-0.582758\pi$
$683$	11.7946	−	6.80964i	0.451310	−	0.260564i	0.708383	+	0.705828i	$0.249425\pi$
$684$		0			0
$685$	1.58727	−	2.74924i	0.0606466	−	0.105043i
$686$		0			0
$687$	2.26204	−	1.30599i	0.0863021	−	0.0498266i
$688$		0			0
$689$	28.4922	−	21.5461i	1.08547	−	0.820843i
$690$		0			0
$691$	5.94380	+	3.43165i	0.226113	+	0.130546i	0.608777	−	0.793341i	$-0.291660\pi$
$691$	5.94380	+	3.43165i	0.226113	+	0.130546i	−0.382665	+	0.923887i	$0.624994\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			24.0487i			0.912220i
$696$		0			0
$697$	5.07585	+	2.93054i	0.192261	+	0.111002i
$698$		0			0
$699$	−7.24743	−	12.5529i	−0.274123	−	0.474795i
$700$		0			0
$701$	44.0990			1.66560			0.832799	−	0.553576i	$-0.186737\pi$
$701$	44.0990			1.66560			0.832799	+	0.553576i	$0.186737\pi$
$702$		0			0
$703$	−38.2883	+	66.3172i	−1.44407	+	2.50120i
$704$		0			0
$705$	−9.08902	+	15.7426i	−0.342312	+	0.592902i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		−	20.0284i		−	0.752182i	−0.926583	−	0.376091i	$-0.877268\pi$
$709$		−	20.0284i		−	0.752182i	0.926583	−	0.376091i	$-0.122732\pi$
$710$		0			0
$711$	−6.80597	−	11.7883i	−0.255244	−	0.442095i
$712$		0			0
$713$	−9.50094	+	5.48537i	−0.355813	+	0.205429i
$714$		0			0
$715$	−0.932899	−	7.49297i	−0.0348884	−	0.280221i
$716$		0			0
$717$		−	6.73262i		−	0.251434i
$718$		0			0
$719$	9.75810			0.363916			0.181958	−	0.983306i	$-0.441757\pi$
$719$	9.75810			0.363916			0.181958	+	0.983306i	$0.441757\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	15.2005	−	8.77603i	0.565314	−	0.326384i
$724$		0			0
$725$	−13.2844			−0.493370
$726$		0			0
$727$	48.2982			1.79128			0.895640	−	0.444779i	$-0.146718\pi$
$727$	48.2982			1.79128			0.895640	+	0.444779i	$0.146718\pi$
$728$		0			0
$729$	7.49830			0.277715
$730$		0			0
$731$	34.4684			1.27486
$732$		0			0
$733$	−30.0068	+	17.3244i	−1.10833	+	0.639893i	−0.938395	−	0.345563i	$-0.887688\pi$
$733$	−30.0068	+	17.3244i	−1.10833	+	0.639893i	−0.169931	+	0.985456i	$0.554354\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.72466			−0.247706
$738$		0			0
$739$			0.773112i			0.0284394i	0.999899	+	0.0142197i	$0.00452642\pi$
$739$			0.773112i			0.0284394i	−0.999899	+	0.0142197i	$0.995474\pi$
$740$		0			0
$741$	−9.41884	+	22.2943i	−0.346010	+	0.819000i
$742$		0			0
$743$	4.28498	−	2.47393i	0.157201	−	0.0907598i	−0.419336	−	0.907831i	$-0.637737\pi$
$743$	4.28498	−	2.47393i	0.157201	−	0.0907598i	0.576537	+	0.817071i	$0.304404\pi$
$744$		0			0
$745$	12.8119	+	22.1909i	0.469392	+	0.813011i
$746$		0			0
$747$			38.1392i			1.39544i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	10.4180	−	18.0445i	0.380157	−	0.658452i	−0.610927	−	0.791687i	$-0.709203\pi$
$751$	10.4180	−	18.0445i	0.380157	−	0.658452i	0.991084	+	0.133235i	$0.0425365\pi$
$752$		0			0
$753$	−1.15274	+	1.99660i	−0.0420080	+	0.0727600i
$754$		0			0
$755$	5.21144			0.189664
$756$		0			0
$757$	24.0402	+	41.6388i	0.873754	+	1.51339i	0.858084	+	0.513510i	$0.171655\pi$
$757$	24.0402	+	41.6388i	0.873754	+	1.51339i	0.0156704	+	0.999877i	$0.495012\pi$
$758$		0			0
$759$	−8.10333	−	4.67846i	−0.294132	−	0.169817i
$760$		0			0
$761$			17.2120i			0.623934i	0.950093	+	0.311967i	$0.100988\pi$
$761$			17.2120i			0.623934i	−0.950093	+	0.311967i	$0.899012\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.5362	+	6.66043i	0.417093	+	0.240808i
$766$		0			0
$767$	−16.9889	+	2.11517i	−0.613433	+	0.0763744i
$768$		0			0
$769$	−25.8086	+	14.9006i	−0.930681	+	0.537329i	−0.887027	−	0.461718i	$-0.847233\pi$
$769$	−25.8086	+	14.9006i	−0.930681	+	0.537329i	−0.0436540	+	0.999047i	$0.513900\pi$
$770$		0			0
$771$	0.756083	−	1.30958i	0.0272297	−	0.0471632i
$772$		0			0
$773$	−29.2806	+	16.9051i	−1.05315	+	0.608036i	−0.923529	−	0.383528i	$-0.874709\pi$
$773$	−29.2806	+	16.9051i	−1.05315	+	0.608036i	−0.129619	+	0.991564i	$0.541376\pi$
$774$		0			0
$775$	2.43713	−	1.40708i	0.0875444	−	0.0505438i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.05459	−	10.4869i	−0.216928	−	0.375730i
$780$		0			0
$781$	−2.79267	+	4.83705i	−0.0999296	+	0.173083i
$782$		0			0
$783$	14.4586	+	25.0431i	0.516709	+	0.894966i
$784$		0			0
$785$			32.0323i			1.14328i
$786$		0			0
$787$	17.0704	−	9.85561i	0.608494	−	0.351314i	−0.163882	−	0.986480i	$-0.552402\pi$
$787$	17.0704	−	9.85561i	0.608494	−	0.351314i	0.772376	+	0.635166i	$0.219068\pi$
$788$		0			0
$789$	−4.71650			−0.167912
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−41.1653	−	17.3914i	−1.46182	−	0.617588i
$794$		0			0
$795$		−	15.0790i		−	0.534797i
$796$		0			0
$797$	−7.72839	+	13.3860i	−0.273754	+	0.474155i	−0.969820	−	0.243822i	$-0.921599\pi$
$797$	−7.72839	+	13.3860i	−0.273754	+	0.474155i	0.696066	+	0.717978i	$0.254932\pi$
$798$		0			0
$799$	−37.2900	−	21.5294i	−1.31923	−	0.761656i
$800$		0			0
$801$	11.1072	+	6.41275i	0.392454	+	0.226583i
$802$		0			0
$803$	3.16525	−	5.48237i	0.111699	−	0.193469i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.4100	+	19.7626i	0.401650	+	0.695678i
$808$		0			0
$809$	−40.0810			−1.40917			−0.704586	−	0.709619i	$-0.748867\pi$
$809$	−40.0810			−1.40917			−0.704586	+	0.709619i	$0.748867\pi$
$810$		0			0
$811$			33.5484i			1.17804i	0.808117	+	0.589022i	$0.200487\pi$
$811$			33.5484i			1.17804i	−0.808117	+	0.589022i	$0.799513\pi$
$812$		0			0
$813$	−8.39742	−	4.84825i	−0.294510	−	0.170036i
$814$		0			0
$815$	−10.2547	−	17.7617i	−0.359207	−	0.622166i
$816$		0			0
$817$	−61.6721	−	35.6064i	−2.15763	−	1.24571i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−35.5132	−	20.5035i	−1.23942	−	0.715579i	−0.270443	−	0.962736i	$-0.587170\pi$
$821$	−35.5132	−	20.5035i	−1.23942	−	0.715579i	−0.968975	+	0.247157i	$0.920504\pi$
$822$		0			0
$823$	−5.64290	−	9.77379i	−0.196699	−	0.340693i	0.750757	−	0.660578i	$-0.229689\pi$
$823$	−5.64290	−	9.77379i	−0.196699	−	0.340693i	−0.947456	+	0.319885i	$0.896356\pi$
$824$		0			0
$825$	2.07862	+	1.20009i	0.0723684	+	0.0417819i
$826$		0			0
$827$			36.8099i			1.28000i	0.768373	+	0.640002i	$0.221066\pi$
$827$			36.8099i			1.28000i	−0.768373	+	0.640002i	$0.778934\pi$
$828$		0			0
$829$	−21.5055			−0.746919			−0.373459	−	0.927647i	$-0.621828\pi$
$829$	−21.5055			−0.746919			−0.373459	+	0.927647i	$0.621828\pi$
$830$		0			0
$831$	12.4165	+	21.5060i	0.430723	+	0.746033i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−0.722343	+	1.25114i	−0.0249977	+	0.0432973i
$836$		0			0
$837$	−5.30511	−	3.06291i	−0.183371	−	0.105870i
$838$		0			0
$839$	−8.99327	−	5.19227i	−0.310482	−	0.179257i	0.336660	−	0.941626i	$-0.390703\pi$
$839$	−8.99327	−	5.19227i	−0.310482	−	0.179257i	−0.647142	+	0.762369i	$0.724036\pi$
$840$		0			0
$841$	−4.62797	+	8.01588i	−0.159585	+	0.276410i
$842$		0			0
$843$		−	25.5159i		−	0.878814i
$844$		0			0
$845$	21.1249	+	5.98014i	0.726718	+	0.205723i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.00990			0.137619
$850$		0			0
$851$	74.5492	−	43.0410i	2.55551	−	1.47543i
$852$		0			0
$853$			11.0193i			0.377295i	0.982045	+	0.188647i	$0.0604103\pi$
$853$			11.0193i			0.377295i	−0.982045	+	0.188647i	$0.939590\pi$
$854$		0			0
$855$	−13.7607	−	23.8341i	−0.470604	−	0.815111i
$856$		0			0
$857$	−4.03831	+	6.99457i	−0.137946	+	0.238930i	−0.926719	−	0.375755i	$-0.877383\pi$
$857$	−4.03831	+	6.99457i	−0.137946	+	0.238930i	0.788773	+	0.614685i	$0.210717\pi$
$858$		0			0
$859$	−2.26526	−	3.92355i	−0.0772898	−	0.133870i	0.824790	−	0.565439i	$-0.191293\pi$
$859$	−2.26526	−	3.92355i	−0.0772898	−	0.133870i	−0.902080	+	0.431569i	$0.857960\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.89597	−	2.24934i	0.132620	−	0.0765685i	−0.432222	−	0.901767i	$-0.642270\pi$
$863$	3.89597	−	2.24934i	0.132620	−	0.0765685i	0.564842	+	0.825199i	$0.308937\pi$
$864$		0			0
$865$	14.5347	−	8.39163i	0.494195	−	0.285324i
$866$		0			0
$867$	−1.80362	+	3.12395i	−0.0612540	+	0.106095i
$868$		0			0
$869$	−6.68139	+	3.85750i	−0.226651	+	0.130857i
$870$		0			0
$871$	7.60943	−	18.0114i	0.257836	−	0.610293i
$872$		0			0
$873$	−3.60531	−	2.08153i	−0.122021	−	0.0704491i
$874$		0			0
$875$		0			0
$876$		0			0
$877$			2.40258i			0.0811294i	0.999177	+	0.0405647i	$0.0129157\pi$
$877$			2.40258i			0.0811294i	−0.999177	+	0.0405647i	$0.987084\pi$
$878$		0			0
$879$	−15.1764	−	8.76210i	−0.511887	−	0.295538i
$880$		0			0
$881$	−10.0166	−	17.3493i	−0.337468	−	0.584512i	0.646488	−	0.762924i	$-0.276237\pi$
$881$	−10.0166	−	17.3493i	−0.337468	−	0.584512i	−0.983956	+	0.178413i	$0.942904\pi$
$882$		0			0
$883$	15.1929			0.511282			0.255641	−	0.966772i	$-0.417713\pi$
$883$	15.1929			0.511282			0.255641	+	0.966772i	$0.417713\pi$
$884$		0			0
$885$	−3.61339	+	6.25857i	−0.121463	+	0.210380i
$886$		0			0
$887$	3.97030	−	6.87677i	0.133310	−	0.230899i	−0.791641	−	0.610987i	$-0.790773\pi$
$887$	3.97030	−	6.87677i	0.133310	−	0.230899i	0.924951	+	0.380088i	$0.124106\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			2.91427i			0.0976316i
$892$		0			0
$893$	44.4804	+	77.0423i	1.48848	+	2.57812i
$894$		0			0
$895$	12.6980	−	7.33121i	0.424448	−	0.245055i
$896$		0			0
$897$	21.7003	−	16.4100i	0.724553	−	0.547915i
$898$		0			0
$899$		−	8.10412i		−	0.270287i
$900$		0			0
$901$	35.7180			1.18994
$902$		0			0
$903$		0			0
$904$		0			0
$905$	12.1374	−	7.00751i	0.403459	−	0.232937i
$906$		0			0
$907$	8.72347			0.289658			0.144829	−	0.989457i	$-0.453737\pi$
$907$	8.72347			0.289658			0.144829	+	0.989457i	$0.453737\pi$
$908$		0			0
$909$	1.45295			0.0481913
$910$		0			0
$911$	−11.5182			−0.381616			−0.190808	−	0.981627i	$-0.561111\pi$
$911$	−11.5182			−0.381616			−0.190808	+	0.981627i	$0.561111\pi$
$912$		0			0
$913$	21.6166			0.715405
$914$		0			0
$915$	−16.3367	+	9.43199i	−0.540074	+	0.311812i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−20.3675			−0.671862			−0.335931	−	0.941887i	$-0.609051\pi$
$919$	−20.3675			−0.671862			−0.335931	+	0.941887i	$0.609051\pi$
$920$		0			0
$921$			9.86624i			0.325104i
$922$		0			0
$923$	−9.79550	−	12.9534i	−0.322423	−	0.426366i
$924$		0			0
$925$	−19.1230	+	11.0407i	−0.628760	+	0.363015i
$926$		0			0
$927$	5.23562	+	9.06836i	0.171960	+	0.297844i
$928$		0			0
$929$			19.0772i			0.625904i	0.949769	+	0.312952i	$0.101318\pi$
$929$			19.0772i			0.625904i	−0.949769	+	0.312952i	$0.898682\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	7.51921	−	13.0237i	0.246168	−	0.426375i
$934$		0			0
$935$	3.77502	−	6.53852i	0.123456	−	0.213833i
$936$		0			0
$937$	46.2095			1.50960			0.754800	−	0.655955i	$-0.227734\pi$
$937$	46.2095			1.50960			0.754800	+	0.655955i	$0.227734\pi$
$938$		0			0
$939$	−1.50634	−	2.60906i	−0.0491576	−	0.0851435i
$940$		0			0
$941$	−5.89182	−	3.40164i	−0.192068	−	0.110890i	0.400882	−	0.916130i	$-0.368704\pi$
$941$	−5.89182	−	3.40164i	−0.192068	−	0.110890i	−0.592950	+	0.805239i	$0.702037\pi$
$942$		0			0
$943$			13.6123i			0.443277i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.6956	+	20.6089i	1.15995	+	0.669699i	0.951292	−	0.308290i	$-0.0997567\pi$
$947$	35.6956	+	20.6089i	1.15995	+	0.669699i	0.208659	+	0.977988i	$0.433090\pi$
$948$		0			0
$949$	11.1023	+	14.6815i	0.360397	+	0.476582i
$950$		0			0
$951$	25.1621	−	14.5273i	0.815937	−	0.471081i
$952$		0			0
$953$	−21.0646	+	36.4850i	−0.682350	+	1.18187i	0.291911	+	0.956445i	$0.405709\pi$
$953$	−21.0646	+	36.4850i	−0.682350	+	1.18187i	−0.974262	+	0.225420i	$0.927625\pi$
$954$		0			0
$955$	−5.13952	+	2.96730i	−0.166311	+	0.0960196i
$956$		0			0
$957$	5.98595	−	3.45599i	0.193498	−	0.111716i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−14.6416	−	25.3600i	−0.472310	−	0.818065i
$962$		0			0
$963$	−5.68672	+	9.84969i	−0.183252	+	0.317402i
$964$		0			0
$965$	6.74001	+	11.6740i	0.216969	+	0.375801i
$966$		0			0
$967$		−	33.5435i		−	1.07869i	−0.842086	−	0.539343i	$-0.818673\pi$
$967$		−	33.5435i		−	1.07869i	0.842086	−	0.539343i	$-0.181327\pi$
$968$		0			0
$969$	−20.9576	+	12.0999i	−0.673255	+	0.388704i
$970$		0			0
$971$	17.8160			0.571744			0.285872	−	0.958268i	$-0.407717\pi$
$971$	17.8160			0.571744			0.285872	+	0.958268i	$0.407717\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−5.56646	+	4.20942i	−0.178269	+	0.134809i
$976$		0			0
$977$			49.2866i			1.57682i	0.615151	+	0.788409i	$0.289095\pi$
$977$			49.2866i			1.57682i	−0.615151	+	0.788409i	$0.710905\pi$
$978$		0			0
$979$	3.63463	−	6.29537i	0.116163	−	0.201201i
$980$		0			0
$981$	−30.2811	−	17.4828i	−0.966800	−	0.558182i
$982$		0			0
$983$	11.8405	+	6.83612i	0.377653	+	0.218038i	0.676797	−	0.736170i	$-0.263368\pi$
$983$	11.8405	+	6.83612i	0.377653	+	0.218038i	−0.299143	+	0.954208i	$0.596701\pi$
$984$		0			0
$985$	13.2905	−	23.0198i	0.423470	−	0.733471i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	40.0263	+	69.3275i	1.27276	+	2.20449i
$990$		0			0
$991$	−22.1917			−0.704943			−0.352472	−	0.935823i	$-0.614659\pi$
$991$	−22.1917			−0.704943			−0.352472	+	0.935823i	$0.614659\pi$
$992$		0			0
$993$		−	27.6160i		−	0.876368i
$994$		0			0
$995$	28.6576	+	16.5455i	0.908506	+	0.524526i
$996$		0			0
$997$	−9.02247	−	15.6274i	−0.285745	−	0.494924i	0.687045	−	0.726615i	$-0.258908\pi$
$997$	−9.02247	−	15.6274i	−0.285745	−	0.494924i	−0.972789	+	0.231691i	$0.925574\pi$
$998$		0			0
$999$	41.6266	+	24.0331i	1.31701	+	0.760374i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bq.g.361.5		24
7.2	even	3		2548.2.bb.g.569.8		24
7.3	odd	6		2548.2.u.f.1765.5	yes	24
7.4	even	3		2548.2.u.f.1765.8	yes	24
7.5	odd	6		2548.2.bb.g.569.5		24
7.6	odd	2	inner	2548.2.bq.g.361.8		24
13.4	even	6		2548.2.bb.g.1733.8		24
91.4	even	6		2548.2.u.f.589.8	yes	24
91.17	odd	6		2548.2.u.f.589.5	✓	24
91.30	even	6	inner	2548.2.bq.g.1941.5		24
91.69	odd	6		2548.2.bb.g.1733.5		24
91.82	odd	6	inner	2548.2.bq.g.1941.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2548.2.u.f.589.5	✓	24	91.17	odd	6
2548.2.u.f.589.8	yes	24	91.4	even	6
2548.2.u.f.1765.5	yes	24	7.3	odd	6
2548.2.u.f.1765.8	yes	24	7.4	even	3
2548.2.bb.g.569.5		24	7.5	odd	6
2548.2.bb.g.569.8		24	7.2	even	3
2548.2.bb.g.1733.5		24	91.69	odd	6
2548.2.bb.g.1733.8		24	13.4	even	6
2548.2.bq.g.361.5		24	1.1	even	1	trivial
2548.2.bq.g.361.8		24	7.6	odd	2	inner
2548.2.bq.g.1941.5		24	91.30	even	6	inner
2548.2.bq.g.1941.8		24	91.82	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.901200 q^{3} +(1.46259 - 0.844424i) q^{5} -2.18784 q^{9} +1.24003i q^{11} +(-3.32131 - 1.40318i) q^{13} +(-1.31808 + 0.760994i) q^{15} +(-1.80259 - 3.12217i) q^{17} +7.44840i q^{19} +(4.18649 - 7.25121i) q^{23} +(-1.07390 + 1.86004i) q^{25} +4.67528 q^{27} +(3.09257 + 5.35649i) q^{29} +(-1.13472 - 0.655128i) q^{31} -1.11751i q^{33} +(8.90355 + 5.14047i) q^{37} +(2.99316 + 1.26455i) q^{39} +(-1.40793 + 0.812871i) q^{41} +(-4.78041 + 8.27991i) q^{43} +(-3.19990 + 1.84746i) q^{45} +(10.3435 - 5.97181i) q^{47} +(1.62449 + 2.81370i) q^{51} +(-4.95371 + 8.58008i) q^{53} +(1.04711 + 1.81365i) q^{55} -6.71250i q^{57} +(4.11210 - 2.37412i) q^{59} +12.3943 q^{61} +(-6.04257 + 0.752320i) q^{65} +5.42299i q^{67} +(-3.77286 + 6.53479i) q^{69} +(3.90075 + 2.25210i) q^{71} +(-4.42116 - 2.55256i) q^{73} +(0.967795 - 1.67627i) q^{75} +(3.11082 + 5.38810i) q^{79} +2.35016 q^{81} -17.4323i q^{83} +(-5.27288 - 3.04430i) q^{85} +(-2.78702 - 4.82726i) q^{87} +(-5.07679 - 2.93109i) q^{89} +(1.02260 + 0.590401i) q^{93} +(6.28961 + 10.8939i) q^{95} +(1.64789 + 0.951408i) q^{97} -2.71298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{9} - 12 q^{15} + 16 q^{23} + 24 q^{29} + 20 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} - 40 q^{65} - 24 q^{71} + 24 q^{79} - 8 q^{81} + 12 q^{85} - 48 q^{93} - 20 q^{95}+O(q^{100}) \) 24 * q + 16 * q^9 - 12 * q^15 + 16 * q^23 + 24 * q^29 + 20 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 - 40 * q^65 - 24 * q^71 + 24 * q^79 - 8 * q^81 + 12 * q^85 - 48 * q^93 - 20 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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