LMFDB - Embedded newform 2548.2.bb.g.569.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(569,2548)] 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("2548.569"); 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, 2, 5])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,0,0,-8,0,0,0,0] 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			569.5
Character	$\chi$	$=$	2548.569
Dual form			2548.2.bb.g.1733.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.450600 + 0.780462i) q^{3} +(1.46259 + 0.844424i) q^{5} +(1.09392 + 1.89472i) q^{9} +(-1.07390 - 0.620015i) q^{11} +(3.32131 + 1.40318i) q^{13} +(-1.31808 + 0.760994i) q^{15} -3.60518 q^{17} +(-6.45050 + 3.72420i) q^{19} -8.37298 q^{23} +(-1.07390 - 1.86004i) q^{25} -4.67528 q^{27} +(3.09257 + 5.35649i) q^{29} +(-1.13472 + 0.655128i) q^{31} +(0.967795 - 0.558757i) q^{33} -10.2809i q^{37} +(-2.59171 + 1.95988i) q^{39} +(1.40793 - 0.812871i) q^{41} +(-4.78041 + 8.27991i) q^{43} +3.69493i q^{45} +(10.3435 + 5.97181i) q^{47} +(1.62449 - 2.81370i) q^{51} +(-4.95371 - 8.58008i) q^{53} +(-1.04711 - 1.81365i) q^{55} -6.71250i q^{57} -4.74824i q^{59} +(6.19715 + 10.7338i) q^{61} +(3.67282 + 4.85686i) q^{65} +(-4.69645 - 2.71149i) q^{67} +(3.77286 - 6.53479i) q^{69} +(3.90075 + 2.25210i) q^{71} +(-4.42116 + 2.55256i) q^{73} +1.93559 q^{75} +(3.11082 - 5.38810i) q^{79} +(-1.17508 + 2.03530i) q^{81} +17.4323i q^{83} +(-5.27288 - 3.04430i) q^{85} -5.57404 q^{87} -5.86217i q^{89} -1.18080i q^{93} -12.5792 q^{95} +(-1.64789 - 0.951408i) q^{97} -2.71298i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{9} - 12 q^{15} - 32 q^{23} + 24 q^{29} - 28 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} + 32 q^{65} - 24 q^{71} + 24 q^{79} + 4 q^{81} + 12 q^{85} + 40 q^{95}+O(q^{100}) $ 24 * q - 8 * q^9 - 12 * q^15 - 32 * q^23 + 24 * q^29 - 28 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 + 32 * q^65 - 24 * q^71 + 24 * q^79 + 4 * q^81 + 12 * q^85 + 40 * q^95

Character values

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

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

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
$3$	−0.450600	+	0.780462i	−0.260154	+	0.450600i	−0.966283	−	0.257484i	$-0.917107\pi$
$3$	−0.450600	+	0.780462i	−0.260154	+	0.450600i	0.706129	+	0.708083i	$0.250440\pi$
$4$		0			0
$5$	1.46259	+	0.844424i	0.654088	+	0.377638i	0.790021	−	0.613080i	$-0.210070\pi$
$5$	1.46259	+	0.844424i	0.654088	+	0.377638i	−0.135933	+	0.990718i	$0.543403\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.09392	+	1.89472i	0.364640	+	0.631575i
$10$		0			0
$11$	−1.07390	−	0.620015i	−0.323792	−	0.186941i	0.329290	−	0.944229i	$-0.393191\pi$
$11$	−1.07390	−	0.620015i	−0.323792	−	0.186941i	−0.653082	+	0.757288i	$0.726524\pi$
$12$		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
$17$	−3.60518			−0.874384			−0.437192	−	0.899368i	$-0.644027\pi$
$17$	−3.60518			−0.874384			−0.437192	+	0.899368i	$0.644027\pi$
$18$		0			0
$19$	−6.45050	+	3.72420i	−1.47985	+	0.854390i	−0.999740	−	0.0228194i	$-0.992736\pi$
$19$	−6.45050	+	3.72420i	−1.47985	+	0.854390i	−0.480108	+	0.877210i	$0.659402\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−8.37298			−1.74589			−0.872943	−	0.487822i	$-0.837792\pi$
$23$	−8.37298			−1.74589			−0.872943	+	0.487822i	$0.837792\pi$
$24$		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	−0.598427	−	0.801177i	$-0.704207\pi$
$31$	−1.13472	+	0.655128i	−0.203801	+	0.117664i	0.394626	+	0.918842i	$0.370874\pi$
$32$		0			0
$33$	0.967795	−	0.558757i	0.168472	−	0.0972671i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	10.2809i		−	1.69018i	−0.534628	−	0.845088i	$-0.679548\pi$
$37$		−	10.2809i		−	1.69018i	0.534628	−	0.845088i	$-0.320452\pi$
$38$		0			0
$39$	−2.59171	+	1.95988i	−0.415006	+	0.313832i
$40$		0			0
$41$	1.40793	−	0.812871i	0.219882	−	0.126949i	−0.386013	−	0.922493i	$-0.626148\pi$
$41$	1.40793	−	0.812871i	0.219882	−	0.126949i	0.605896	+	0.795544i	$0.292815\pi$
$42$		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
$45$			3.69493i			0.550807i
$46$		0			0
$47$	10.3435	+	5.97181i	1.50875	+	0.871077i	0.999948	+	0.0101938i	$0.00324484\pi$
$47$	10.3435	+	5.97181i	1.50875	+	0.871077i	0.508802	+	0.860884i	$0.330088\pi$
$48$		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	−0.974845	−	0.222883i	$-0.928453\pi$
$53$	−4.95371	−	8.58008i	−0.680445	−	1.17857i	0.294400	−	0.955682i	$-0.404880\pi$
$54$		0			0
$55$	−1.04711	−	1.81365i	−0.141192	−	0.244552i
$56$		0			0
$57$		−	6.71250i		−	0.889092i
$58$		0			0
$59$		−	4.74824i		−	0.618169i	−0.951035	−	0.309084i	$-0.899977\pi$
$59$		−	4.74824i		−	0.618169i	0.951035	−	0.309084i	$-0.100023\pi$
$60$		0			0
$61$	6.19715	+	10.7338i	0.793464	+	1.37432i	0.923810	+	0.382851i	$0.125058\pi$
$61$	6.19715	+	10.7338i	0.793464	+	1.37432i	−0.130346	+	0.991469i	$0.541609\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.67282	+	4.85686i	0.455557	+	0.602420i
$66$		0			0
$67$	−4.69645	−	2.71149i	−0.573762	−	0.331262i	0.184888	−	0.982760i	$-0.440808\pi$
$67$	−4.69645	−	2.71149i	−0.573762	−	0.331262i	−0.758651	+	0.651498i	$0.774141\pi$
$68$		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	−0.735894	−	0.677097i	$-0.763238\pi$
$73$	−4.42116	+	2.55256i	−0.517458	+	0.298754i	0.218436	+	0.975851i	$0.429904\pi$
$74$		0			0
$75$	1.93559			0.223503
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.11082	−	5.38810i	0.349994	−	0.606208i	−0.636254	−	0.771480i	$-0.719517\pi$
$79$	3.11082	−	5.38810i	0.349994	−	0.606208i	0.986248	+	0.165272i	$0.0528502\pi$
$80$		0			0
$81$	−1.17508	+	2.03530i	−0.130564	+	0.226144i
$82$		0			0
$83$			17.4323i			1.91345i	0.290998	+	0.956724i	$0.406013\pi$
$83$			17.4323i			1.91345i	−0.290998	+	0.956724i	$0.593987\pi$
$84$		0			0
$85$	−5.27288	−	3.04430i	−0.571924	−	0.330200i
$86$		0			0
$87$	−5.57404			−0.597600
$88$		0			0
$89$		−	5.86217i		−	0.621389i	−0.950510	−	0.310694i	$-0.899438\pi$
$89$		−	5.86217i		−	0.621389i	0.950510	−	0.310694i	$-0.100562\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		−	1.18080i		−	0.122443i
$94$		0			0
$95$	−12.5792			−1.29060
$96$		0			0
$97$	−1.64789	−	0.951408i	−0.167318	−	0.0966009i	0.414003	−	0.910276i	$-0.364130\pi$
$97$	−1.64789	−	0.951408i	−0.167318	−	0.0966009i	−0.581320	+	0.813675i	$0.697464\pi$
$98$		0			0
$99$		−	2.71298i		−	0.272665i
$100$		0			0
$101$	−0.332051	+	0.575130i	−0.0330403	+	0.0572276i	−0.882073	−	0.471113i	$-0.843852\pi$
$101$	−0.332051	+	0.575130i	−0.0330403	+	0.0572276i	0.849032	+	0.528341i	$0.177186\pi$
$102$		0			0
$103$	2.39306	−	4.14489i	0.235795	−	0.408409i	−0.723709	−	0.690106i	$-0.757564\pi$
$103$	2.39306	−	4.14489i	0.235795	−	0.408409i	0.959503	+	0.281697i	$0.0908973\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.19848			−0.502556			−0.251278	−	0.967915i	$-0.580851\pi$
$107$	−5.19848			−0.502556			−0.251278	+	0.967915i	$0.580851\pi$
$108$		0			0
$109$	−13.8406	+	7.99089i	−1.32569	+	0.765388i	−0.984630	−	0.174653i	$-0.944120\pi$
$109$	−13.8406	+	7.99089i	−1.32569	+	0.765388i	−0.341062	+	0.940041i	$0.610786\pi$
$110$		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
$115$	−12.2462	−	7.07034i	−1.14196	−	0.659313i
$116$		0			0
$117$	0.974603	+	7.82793i	0.0901021	+	0.723692i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.73116	−	8.19462i	−0.430106	−	0.744965i
$122$		0			0
$123$			1.46512i			0.132105i
$124$		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	0.462927	+	0.886396i	$0.346799\pi$
$131$	−6.13684	+	10.6293i	−0.536178	+	0.928687i	−0.999105	+	0.0422911i	$0.986534\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−6.83799	−	3.94792i	−0.588521	−	0.339783i
$136$		0			0
$137$			1.87971i			0.160595i	0.996771	+	0.0802973i	$0.0255870\pi$
$137$			1.87971i			0.160595i	−0.996771	+	0.0802973i	$0.974413\pi$
$138$		0			0
$139$	7.11986	−	12.3320i	0.603899	−	1.04598i	−0.388326	−	0.921522i	$-0.626946\pi$
$139$	7.11986	−	12.3320i	0.603899	−	1.04598i	0.992225	−	0.124461i	$-0.0397202\pi$
$140$		0			0
$141$	−9.32153	+	5.38179i	−0.785014	+	0.453228i
$142$		0			0
$143$	−2.69675	−	3.56613i	−0.225513	−	0.298215i
$144$		0			0
$145$			10.4458i			0.867473i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	13.1397	−	7.58619i	1.07644	−	0.621485i	0.146509	−	0.989209i	$-0.453196\pi$
$149$	13.1397	−	7.58619i	1.07644	−	0.621485i	0.929935	+	0.367725i	$0.119863\pi$
$150$		0			0
$151$	−2.67238	+	1.54290i	−0.217475	+	0.125559i	−0.604781	−	0.796392i	$-0.706739\pi$
$151$	−2.67238	+	1.54290i	−0.217475	+	0.125559i	0.387305	+	0.921951i	$0.373406\pi$
$152$		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	0.944442	+	0.328678i	$0.106603\pi$
$157$	9.48349	+	16.4259i	0.756865	+	1.31093i	−0.187577	+	0.982250i	$0.560064\pi$
$158$		0			0
$159$	8.92857			0.708082
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−10.5171	+	6.07203i	−0.823759	+	0.475598i	−0.851711	−	0.524012i	$-0.824435\pi$
$163$	−10.5171	+	6.07203i	−0.823759	+	0.475598i	0.0279517	+	0.999609i	$0.491102\pi$
$164$		0			0
$165$	1.88731			0.146927
$166$		0			0
$167$	0.740822	−	0.427714i	0.0573265	−	0.0330975i	−0.471063	−	0.882100i	$-0.656129\pi$
$167$	0.740822	−	0.427714i	0.0573265	−	0.0330975i	0.528389	+	0.849002i	$0.322796\pi$
$168$		0			0
$169$	9.06217	+	9.32079i	0.697090	+	0.716984i
$170$		0			0
$171$	−14.1127	−	8.14795i	−1.07922	−	0.623090i
$172$		0			0
$173$	4.96885	+	8.60630i	0.377774	+	0.654325i	0.990738	−	0.135787i	$-0.0433561\pi$
$173$	4.96885	+	8.60630i	0.377774	+	0.654325i	−0.612964	+	0.790111i	$0.710023\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	3.70582	+	2.13956i	0.278547	+	0.160819i
$178$		0			0
$179$	−4.34095	+	7.51875i	−0.324458	+	0.561978i	−0.981403	−	0.191961i	$-0.938515\pi$
$179$	−4.34095	+	7.51875i	−0.324458	+	0.561978i	0.656944	+	0.753939i	$0.271849\pi$
$180$		0			0
$181$	−8.29857			−0.616828			−0.308414	−	0.951252i	$-0.599798\pi$
$181$	−8.29857			−0.616828			−0.308414	+	0.951252i	$0.599798\pi$
$182$		0			0
$183$	−11.1697			−0.825691
$184$		0			0
$185$	8.68147	−	15.0367i	0.638274	−	1.10552i
$186$		0			0
$187$	3.87159	+	2.23526i	0.283118	+	0.163459i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.75700	+	3.04321i	0.127132	+	0.220199i	0.922564	−	0.385843i	$-0.126090\pi$
$191$	1.75700	+	3.04321i	0.127132	+	0.220199i	−0.795432	+	0.606042i	$0.792756\pi$
$192$		0			0
$193$	−6.91243	−	3.99089i	−0.497568	−	0.287271i	0.230141	−	0.973157i	$-0.426081\pi$
$193$	−6.91243	−	3.99089i	−0.497568	−	0.287271i	−0.727709	+	0.685886i	$0.759415\pi$
$194$		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
$199$	19.5938			1.38897			0.694483	−	0.719509i	$-0.255633\pi$
$199$	19.5938			1.38897			0.694483	+	0.719509i	$0.255633\pi$
$200$		0			0
$201$	4.23243	−	2.44360i	0.298533	−	0.172358i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	2.74563			0.191763
$206$		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
$215$	−13.9835	+	8.07338i	−0.953667	+	0.550600i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		−	4.60073i		−	0.310888i
$220$		0			0
$221$	−11.9739	−	5.05871i	−0.805452	−	0.340286i
$222$		0			0
$223$	−8.28564	+	4.78371i	−0.554847	+	0.320341i	−0.751075	−	0.660217i	$-0.770464\pi$
$223$	−8.28564	+	4.78371i	−0.554847	+	0.320341i	0.196228	+	0.980558i	$0.437131\pi$
$224$		0			0
$225$	2.34951	−	4.06948i	0.156634	−	0.271298i
$226$		0			0
$227$			2.76881i			0.183772i	0.995770	+	0.0918862i	$0.0292896\pi$
$227$			2.76881i			0.183772i	−0.995770	+	0.0918862i	$0.970710\pi$
$228$		0			0
$229$	−2.51003	−	1.44917i	−0.165867	−	0.0957636i	0.414768	−	0.909927i	$-0.363863\pi$
$229$	−2.51003	−	1.44917i	−0.165867	−	0.0957636i	−0.580636	+	0.814163i	$0.697196\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.04198	−	13.9291i	0.526847	−	0.912526i	−0.472663	−	0.881243i	$-0.656707\pi$
$233$	8.04198	−	13.9291i	0.526847	−	0.912526i	0.999511	−	0.0312833i	$-0.00995941\pi$
$234$		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
$241$			19.4763i			1.25458i	0.778785	+	0.627290i	$0.215836\pi$
$241$			19.4763i			1.25458i	−0.778785	+	0.627290i	$0.784164\pi$
$242$		0			0
$243$	−8.07190	−	13.9809i	−0.517813	−	0.896878i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−26.6498	+	3.31799i	−1.69569	+	0.211119i
$248$		0			0
$249$	−13.6053	−	7.85501i	−0.862199	−	0.497791i
$250$		0			0
$251$	−1.27911	+	2.21549i	−0.0807369	+	0.139840i	−0.903567	−	0.428448i	$-0.859061\pi$
$251$	−1.27911	+	2.21549i	−0.0807369	+	0.139840i	0.822830	+	0.568288i	$0.192394\pi$
$252$		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
$257$	−1.67795			−0.104668			−0.0523338	−	0.998630i	$-0.516666\pi$
$257$	−1.67795			−0.104668			−0.0523338	+	0.998630i	$0.516666\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−6.76605	+	11.7191i	−0.418808	+	0.725396i
$262$		0			0
$263$	−2.61679	+	4.53242i	−0.161358	+	0.279481i	−0.935356	−	0.353708i	$-0.884921\pi$
$263$	−2.61679	+	4.53242i	−0.161358	+	0.279481i	0.773998	+	0.633188i	$0.218254\pi$
$264$		0			0
$265$		−	16.7321i		−	1.02785i
$266$		0			0
$267$	4.57520	+	2.64149i	0.279998	+	0.161657i
$268$		0			0
$269$	−25.3217			−1.54389			−0.771947	−	0.635687i	$-0.780717\pi$
$269$	−25.3217			−1.54389			−0.771947	+	0.635687i	$0.780717\pi$
$270$		0			0
$271$			10.7596i			0.653596i	0.945094	+	0.326798i	$0.105970\pi$
$271$			10.7596i			0.653596i	−0.945094	+	0.326798i	$0.894030\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			2.66333i			0.160605i
$276$		0			0
$277$	27.5554			1.65565			0.827823	−	0.560990i	$-0.189579\pi$
$277$	27.5554			1.65565			0.827823	+	0.560990i	$0.189579\pi$
$278$		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
$283$	−2.22475	+	3.85339i	−0.132248	+	0.229060i	−0.924543	−	0.381078i	$-0.875553\pi$
$283$	−2.22475	+	3.85339i	−0.132248	+	0.229060i	0.792295	+	0.610138i	$0.208886\pi$
$284$		0			0
$285$	5.66819	−	9.81760i	0.335755	−	0.581544i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.00270			−0.235453
$290$		0			0
$291$	1.48508	−	0.857409i	0.0870567	−	0.0502622i
$292$		0			0
$293$	−16.8402	−	9.72271i	−0.983816	−	0.568007i	−0.0803960	−	0.996763i	$-0.525618\pi$
$293$	−16.8402	−	9.72271i	−0.983816	−	0.568007i	−0.903420	+	0.428756i	$0.858952\pi$
$294$		0			0
$295$	4.00953	−	6.94471i	0.233444	−	0.404337i
$296$		0			0
$297$	5.02077	+	2.89874i	0.291334	+	0.168202i
$298$		0			0
$299$	−27.8092	−	11.7488i	−1.60825	−	0.679451i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−0.299244	−	0.518307i	−0.0171911	−	0.0297759i
$304$		0			0
$305$			20.9321i			1.19857i
$306$		0			0
$307$			10.9479i			0.624830i	0.949946	+	0.312415i	$0.101138\pi$
$307$			10.9479i			0.624830i	−0.949946	+	0.312415i	$0.898862\pi$
$308$		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	$-0.00979450\pi$
$311$	8.34356	+	14.4515i	0.473120	+	0.819467i	−0.526407	+	0.850233i	$0.676461\pi$
$312$		0			0
$313$	−1.67149	+	2.89510i	−0.0944780	+	0.163641i	−0.909391	−	0.415943i	$-0.863452\pi$
$313$	−1.67149	+	2.89510i	−0.0944780	+	0.163641i	0.814913	+	0.579584i	$0.196785\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	27.9207	+	16.1200i	1.56818	+	0.905390i	0.996381	+	0.0849965i	$0.0270879\pi$
$317$	27.9207	+	16.1200i	1.56818	+	0.905390i	0.571800	+	0.820393i	$0.306245\pi$
$318$		0			0
$319$		−	7.66975i		−	0.429424i
$320$		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
$325$	−0.956764	−	7.68465i	−0.0530717	−	0.426268i
$326$		0			0
$327$		−	14.4028i		−	0.796475i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	26.5382	−	15.3218i	1.45867	−	0.842163i	0.459724	−	0.888062i	$-0.347948\pi$
$331$	26.5382	−	15.3218i	1.45867	−	0.842163i	0.998946	+	0.0458987i	$0.0146151\pi$
$332$		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
$341$	1.62476			0.0879854
$342$		0			0
$343$		0			0
$344$		0			0
$345$	11.0363	−	6.37179i	0.594172	−	0.343046i
$346$		0			0
$347$	−12.4460			−0.668135			−0.334067	−	0.942549i	$-0.608421\pi$
$347$	−12.4460			−0.668135			−0.334067	+	0.942549i	$0.608421\pi$
$348$		0			0
$349$	−16.3534	+	9.44164i	−0.875378	+	0.505400i	−0.869132	−	0.494581i	$-0.835322\pi$
$349$	−16.3534	+	9.44164i	−0.875378	+	0.505400i	−0.00624626	+	0.999980i	$0.501988\pi$
$350$		0			0
$351$	−15.5280	−	6.56026i	−0.828825	−	0.350161i
$352$		0			0
$353$	−12.5661	−	7.25502i	−0.668824	−	0.386146i	0.126807	−	0.991927i	$-0.459527\pi$
$353$	−12.5661	−	7.25502i	−0.668824	−	0.386146i	−0.795631	+	0.605782i	$0.792860\pi$
$354$		0			0
$355$	3.80346	+	6.58778i	0.201867	+	0.349643i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−23.8583	−	13.7746i	−1.25919	−	0.726995i	−0.286275	−	0.958147i	$-0.592417\pi$
$359$	−23.8583	−	13.7746i	−1.25919	−	0.726995i	−0.972918	+	0.231152i	$0.925750\pi$
$360$		0			0
$361$	18.2393	−	31.5915i	0.959965	−	1.66271i
$362$		0			0
$363$	8.52745			0.447575
$364$		0			0
$365$	−8.62176			−0.451284
$366$		0			0
$367$	8.60996	−	14.9129i	0.449436	−	0.778447i	−0.548913	−	0.835879i	$-0.684958\pi$
$367$	8.60996	−	14.9129i	0.449436	−	0.778447i	0.998349	+	0.0574328i	$0.0182915\pi$
$368$		0			0
$369$	3.08033	+	1.77843i	0.160356	+	0.0925814i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.0227	+	17.3598i	0.518956	+	0.898859i	0.999757	+	0.0220290i	$0.00701261\pi$
$373$	10.0227	+	17.3598i	0.518956	+	0.898859i	−0.480801	+	0.876830i	$0.659654\pi$
$374$		0			0
$375$	9.42137	+	5.43943i	0.486517	+	0.280891i
$376$		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
$381$	10.4026			0.532941
$382$		0			0
$383$	5.90309	−	3.40815i	0.301634	−	0.174148i	−0.341543	−	0.939866i	$-0.610949\pi$
$383$	5.90309	−	3.40815i	0.301634	−	0.174148i	0.643177	+	0.765718i	$0.277616\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−20.9175			−1.06330
$388$		0			0
$389$	8.01572	+	13.8836i	0.406413	+	0.703928i	0.994485	−	0.104881i	$-0.0334461\pi$
$389$	8.01572	+	13.8836i	0.406413	+	0.703928i	−0.588072	+	0.808809i	$0.700113\pi$
$390$		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
$397$	10.7304	−	6.19522i	0.538545	−	0.310929i	−0.205944	−	0.978564i	$-0.566026\pi$
$397$	10.7304	−	6.19522i	0.538545	−	0.310929i	0.744489	+	0.667635i	$0.232693\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			29.7609i			1.48619i	0.669186	+	0.743095i	$0.266643\pi$
$401$			29.7609i			1.48619i	−0.669186	+	0.743095i	$0.733357\pi$
$402$		0			0
$403$	−4.68800	+	0.583672i	−0.233526	+	0.0290747i
$404$		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
$409$			34.7812i			1.71982i	0.510445	+	0.859910i	$0.329481\pi$
$409$			34.7812i			1.71982i	−0.510445	+	0.859910i	$0.670519\pi$
$410$		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	$0.232430\pi$
$419$	19.4496	+	33.6877i	0.950176	+	1.64575i	0.205134	+	0.978734i	$0.434237\pi$
$420$		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
$423$			26.1307i			1.27052i
$424$		0			0
$425$	3.87159	+	6.70579i	0.187800	+	0.325278i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	3.99838	−	0.497812i	0.193044	−	0.0240346i
$430$		0			0
$431$	24.7995	+	14.3180i	1.19455	+	0.689674i	0.959335	−	0.282270i	$-0.0910874\pi$
$431$	24.7995	+	14.3180i	1.19455	+	0.689674i	0.235215	+	0.971943i	$0.424421\pi$
$432$		0			0
$433$	6.70789	−	11.6184i	0.322361	−	0.558345i	−0.658614	−	0.752481i	$-0.728857\pi$
$433$	6.70789	−	11.6184i	0.322361	−	0.558345i	0.980975	+	0.194136i	$0.0621902\pi$
$434$		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
$439$	−6.60203			−0.315098			−0.157549	−	0.987511i	$-0.550359\pi$
$439$	−6.60203			−0.315098			−0.157549	+	0.987511i	$0.550359\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.64747	+	4.58555i	−0.125785	+	0.217866i	−0.922040	−	0.387096i	$-0.873478\pi$
$443$	−2.64747	+	4.58555i	−0.125785	+	0.217866i	0.796255	+	0.604962i	$0.206812\pi$
$444$		0			0
$445$	4.95016	−	8.57392i	0.234660	−	0.406443i
$446$		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
$451$	−2.01597			−0.0949282
$452$		0			0
$453$		−	2.78092i		−	0.130659i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	18.2682i		−	0.854549i	−0.904122	−	0.427275i	$-0.859474\pi$
$457$		−	18.2682i		−	0.854549i	0.904122	−	0.427275i	$-0.140526\pi$
$458$		0			0
$459$	16.8552			0.786734
$460$		0			0
$461$	1.32125	+	0.762824i	0.0615367	+	0.0355282i	0.530453	−	0.847715i	$-0.322022\pi$
$461$	1.32125	+	0.762824i	0.0615367	+	0.0355282i	−0.468916	+	0.883243i	$0.655355\pi$
$462$		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
$465$	0.997098	−	1.72702i	0.0462393	−	0.0800888i
$466$		0			0
$467$	10.6415	−	18.4316i	0.492428	−	0.852911i	−0.507534	−	0.861632i	$-0.669443\pi$
$467$	10.6415	−	18.4316i	0.492428	−	0.852911i	0.999962	+	0.00872095i	$0.00277600\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−17.0930			−0.787605
$472$		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
$479$	15.7631	+	9.10086i	0.720236	+	0.415829i	0.814840	−	0.579686i	$-0.196825\pi$
$479$	15.7631	+	9.10086i	0.720236	+	0.415829i	−0.0946033	+	0.995515i	$0.530158\pi$
$480$		0			0
$481$	14.4260	−	34.1461i	0.657769	−	1.55693i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.60678	−	2.78303i	−0.0729603	−	0.126371i
$486$		0			0
$487$		−	7.41946i		−	0.336208i	−0.985769	−	0.168104i	$-0.946236\pi$
$487$		−	7.41946i		−	0.336208i	0.985769	−	0.168104i	$-0.0537644\pi$
$488$		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	$-0.210210\pi$
$499$	14.5955	+	8.42670i	0.653383	+	0.377231i	−0.136368	+	0.990658i	$0.543543\pi$
$500$		0			0
$501$			0.770911i			0.0344418i
$502$		0			0
$503$	−3.04565	+	5.27522i	−0.135799	+	0.235211i	−0.925902	−	0.377763i	$-0.876693\pi$
$503$	−3.04565	+	5.27522i	−0.135799	+	0.235211i	0.790103	+	0.612974i	$0.210027\pi$
$504$		0			0
$505$	−0.971307	+	0.560784i	−0.0432226	+	0.0249546i
$506$		0			0
$507$	−11.3579	+	2.87273i	−0.504423	+	0.127582i
$508$		0			0
$509$		−	32.6347i		−	1.44651i	−0.690582	−	0.723254i	$-0.742646\pi$
$509$		−	32.6347i		−	1.44651i	0.690582	−	0.723254i	$-0.257354\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	30.1579	−	17.4117i	1.33150	−	0.768744i
$514$		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	$-0.177913\pi$
$521$	−0.806311	−	1.39657i	−0.0353251	−	0.0611849i	−0.883147	+	0.469095i	$0.844580\pi$
$522$		0			0
$523$	−15.1636			−0.663058			−0.331529	−	0.943445i	$-0.607564\pi$
$523$	−15.1636			−0.663058			−0.331529	+	0.943445i	$0.607564\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.09085	−	2.36185i	0.178200	−	0.102884i
$528$		0			0
$529$	47.1068			2.04812
$530$		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
$535$	−7.60322	−	4.38972i	−0.328716	−	0.189784i
$536$		0			0
$537$	−3.91207	−	6.77590i	−0.168818	−	0.292401i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	22.9733	+	13.2637i	0.987701	+	0.570250i	0.904586	−	0.426290i	$-0.140180\pi$
$541$	22.9733	+	13.2637i	0.987701	+	0.570250i	0.0831149	+	0.996540i	$0.473513\pi$
$542$		0			0
$543$	3.73933	−	6.47671i	0.160470	−	0.277942i
$544$		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
$549$	−13.5584	+	23.4838i	−0.578657	+	1.00226i
$550$		0			0
$551$	−39.8973	−	23.0347i	−1.69968	−	0.981311i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	7.82373	+	13.5511i	0.332099	+	0.575212i
$556$		0			0
$557$	2.53541	+	1.46382i	0.107429	+	0.0620239i	0.552752	−	0.833346i	$-0.313578\pi$
$557$	2.53541	+	1.46382i	0.107429	+	0.0620239i	−0.445323	+	0.895370i	$0.646911\pi$
$558$		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
$563$	43.0334			1.81364			0.906820	−	0.421518i	$-0.138503\pi$
$563$	43.0334			1.81364			0.906820	+	0.421518i	$0.138503\pi$
$564$		0			0
$565$	−20.9992	+	12.1239i	−0.883443	+	0.510056i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.293422			0.0123009			0.00615044	−	0.999981i	$-0.498042\pi$
$569$	0.293422			0.0123009			0.00615044	+	0.999981i	$0.498042\pi$
$570$		0			0
$571$	−8.07299	−	13.9828i	−0.337844	−	0.585163i	0.646183	−	0.763182i	$-0.276364\pi$
$571$	−8.07299	−	13.9828i	−0.337844	−	0.585163i	−0.984027	+	0.178020i	$0.943031\pi$
$572$		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	−0.812586	−	0.582841i	$-0.801941\pi$
$577$	−17.1538	+	9.90377i	−0.714124	+	0.412299i	0.0984625	+	0.995141i	$0.468608\pi$
$578$		0			0
$579$	6.22948	−	3.59659i	0.258888	−	0.149469i
$580$		0			0
$581$		0			0
$582$		0			0
$583$			12.2855i			0.508813i
$584$		0			0
$585$	−5.18465	+	12.2720i	−0.214359	+	0.507384i
$586$		0			0
$587$	2.23571	−	1.29079i	0.0922775	−	0.0532764i	−0.453151	−	0.891434i	$-0.649700\pi$
$587$	2.23571	−	1.29079i	0.0922775	−	0.0532764i	0.545429	+	0.838157i	$0.316367\pi$
$588$		0			0
$589$	4.87966	−	8.45181i	0.201063	−	0.348251i
$590$		0			0
$591$			14.1841i			0.583455i
$592$		0			0
$593$	11.6618	+	6.73296i	0.478894	+	0.276489i	0.719955	−	0.694020i	$-0.244162\pi$
$593$	11.6618	+	6.73296i	0.478894	+	0.276489i	−0.241062	+	0.970510i	$0.577496\pi$
$594$		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	0.967758	−	0.251881i	$-0.0810493\pi$
$599$	6.50393	+	11.2651i	0.265743	+	0.460281i	−0.702015	+	0.712162i	$0.747716\pi$
$600$		0			0
$601$	−20.3117	−	35.1808i	−0.828530	−	1.43506i	−0.899192	−	0.437555i	$-0.855845\pi$
$601$	−20.3117	−	35.1808i	−0.828530	−	1.43506i	0.0706620	−	0.997500i	$-0.477489\pi$
$602$		0			0
$603$		−	11.8646i		−	0.483165i
$604$		0			0
$605$		−	15.9804i		−	0.649697i
$606$		0			0
$607$	−10.5622	−	18.2942i	−0.428705	−	0.742538i	0.568054	−	0.822991i	$-0.307697\pi$
$607$	−10.5622	−	18.2942i	−0.428705	−	0.742538i	−0.996758	+	0.0804533i	$0.974363\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	25.9743	+	34.3480i	1.05081	+	1.38957i
$612$		0			0
$613$	18.1301	+	10.4674i	0.732267	+	0.422774i	0.819251	−	0.573435i	$-0.194390\pi$
$613$	18.1301	+	10.4674i	0.732267	+	0.422774i	−0.0869841	+	0.996210i	$0.527723\pi$
$614$		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	−0.725828	−	0.687876i	$-0.758543\pi$
$619$	−12.2663	+	7.08194i	−0.493024	+	0.284647i	0.232804	+	0.972524i	$0.425210\pi$
$620$		0			0
$621$	39.1460			1.57088
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.82401	−	8.35543i	0.192960	−	0.334217i
$626$		0			0
$627$	−4.16184	+	7.20853i	−0.166208	+	0.287881i
$628$		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
$633$	12.6366			0.502259
$634$		0			0
$635$		−	19.4945i		−	0.773614i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			9.85447i			0.389837i
$640$		0			0
$641$	12.3721			0.488669			0.244334	−	0.969691i	$-0.421431\pi$
$641$	12.3721			0.488669			0.244334	+	0.969691i	$0.421431\pi$
$642$		0			0
$643$	33.8520	+	19.5445i	1.33499	+	0.770758i	0.986060	−	0.166389i	$-0.0532109\pi$
$643$	33.8520	+	19.5445i	1.33499	+	0.770758i	0.348933	+	0.937148i	$0.386544\pi$
$644$		0			0
$645$		−	14.5515i		−	0.572963i
$646$		0			0
$647$	19.8756	−	34.4255i	0.781389	−	1.35340i	−0.149744	−	0.988725i	$-0.547845\pi$
$647$	19.8756	−	34.4255i	0.781389	−	1.35340i	0.931133	−	0.364680i	$-0.118822\pi$
$648$		0			0
$649$	−2.94398	+	5.09912i	−0.115561	+	0.200158i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.34868			−0.170177			−0.0850884	−	0.996373i	$-0.527117\pi$
$653$	−4.34868			−0.170177			−0.0850884	+	0.996373i	$0.527117\pi$
$654$		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
$661$	−9.26534	−	5.34934i	−0.360380	−	0.208065i	0.308868	−	0.951105i	$-0.400050\pi$
$661$	−9.26534	−	5.34934i	−0.360380	−	0.208065i	−0.669247	+	0.743040i	$0.733383\pi$
$662$		0			0
$663$	9.34357	−	7.06572i	0.362874	−	0.274410i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−25.8940	−	44.8498i	−1.00262	−	1.73659i
$668$		0			0
$669$		−	8.62216i		−	0.333352i
$670$		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	$-0.955274\pi$
$677$	−9.72565	+	16.8453i	−0.373787	+	0.647418i	0.616358	+	0.787466i	$0.288608\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.16095	−	1.24763i	−0.0828078	−	0.0478091i
$682$		0			0
$683$			13.6193i			0.521127i	0.965457	+	0.260564i	$0.0839084\pi$
$683$			13.6193i			0.521127i	−0.965457	+	0.260564i	$0.916092\pi$
$684$		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
$689$	−4.41340	−	35.4481i	−0.168137	−	1.35046i
$690$		0			0
$691$			6.86331i			0.261093i	0.991442	+	0.130546i	$0.0416731\pi$
$691$			6.86331i			0.261093i	−0.991442	+	0.130546i	$0.958327\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	20.8268	−	12.0244i	0.790006	−	0.456110i
$696$		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
$705$	−18.1780			−0.684625
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.3451	+	10.0142i	−0.651408	+	0.376091i	−0.788996	−	0.614399i	$-0.789399\pi$
$709$	−17.3451	+	10.0142i	−0.651408	+	0.376091i	0.137587	+	0.990490i	$0.456065\pi$
$710$		0			0
$711$	13.6119			0.510488
$712$		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
$717$	−5.83062	−	3.36631i	−0.217749	−	0.125717i
$718$		0			0
$719$	4.87905	+	8.45076i	0.181958	+	0.315160i	0.942547	−	0.334073i	$-0.108423\pi$
$719$	4.87905	+	8.45076i	0.181958	+	0.315160i	−0.760589	+	0.649233i	$0.775090\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−15.2005	−	8.77603i	−0.565314	−	0.326384i
$724$		0			0
$725$	6.64220	−	11.5046i	0.246685	−	0.427271i
$726$		0			0
$727$	−48.2982			−1.79128			−0.895640	−	0.444779i	$-0.853282\pi$
$727$	−48.2982			−1.79128			−0.895640	+	0.444779i	$0.853282\pi$
$728$		0			0
$729$	7.49830			0.277715
$730$		0			0
$731$	17.2342	−	29.8505i	0.637431	−	1.10406i
$732$		0			0
$733$	−30.0068	−	17.3244i	−1.10833	−	0.639893i	−0.169931	−	0.985456i	$-0.554354\pi$
$733$	−30.0068	−	17.3244i	−1.10833	−	0.639893i	−0.938395	+	0.345563i	$0.887688\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.36233	+	5.82373i	0.123853	+	0.214520i
$738$		0			0
$739$	−0.669535	−	0.386556i	−0.0246292	−	0.0142197i	0.487635	−	0.873048i	$-0.337860\pi$
$739$	−0.669535	−	0.386556i	−0.0246292	−	0.0142197i	−0.512264	+	0.858828i	$0.671193\pi$
$740$		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
$745$	25.6238			0.938785
$746$		0			0
$747$	−33.0295	+	19.0696i	−1.20849	+	0.697719i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−20.8360			−0.760315			−0.380157	−	0.924922i	$-0.624130\pi$
$751$	−20.8360			−0.760315			−0.380157	+	0.924922i	$0.624130\pi$
$752$		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
$761$	−14.9060	+	8.60600i	−0.540343	+	0.311967i	−0.745218	−	0.666821i	$-0.767655\pi$
$761$	−14.9060	+	8.60600i	−0.540343	+	0.311967i	0.204875	+	0.978788i	$0.434321\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		−	13.3209i		−	0.481617i
$766$		0			0
$767$	6.66264	−	15.7704i	0.240574	−	0.569435i
$768$		0			0
$769$	25.8086	−	14.9006i	0.930681	−	0.537329i	0.0436540	−	0.999047i	$-0.486100\pi$
$769$	25.8086	−	14.9006i	0.930681	−	0.537329i	0.887027	+	0.461718i	$0.152767\pi$
$770$		0			0
$771$	0.756083	−	1.30958i	0.0272297	−	0.0471632i
$772$		0			0
$773$			33.8103i			1.21607i	0.793910	+	0.608036i	$0.208042\pi$
$773$			33.8103i			1.21607i	−0.793910	+	0.608036i	$0.791958\pi$
$774$		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
$787$		−	19.7112i		−	0.702629i	−0.936258	−	0.351314i	$-0.885735\pi$
$787$		−	19.7112i		−	0.702629i	0.936258	−	0.351314i	$-0.114265\pi$
$788$		0			0
$789$	−2.35825	−	4.08461i	−0.0839560	−	0.145416i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	5.52121	+	44.3459i	0.196064	+	1.57477i
$794$		0			0
$795$	13.0588	+	7.53950i	0.463148	+	0.267398i
$796$		0			0
$797$	7.72839	−	13.3860i	0.273754	−	0.474155i	−0.696066	−	0.717978i	$-0.745068\pi$
$797$	7.72839	−	13.3860i	0.273754	−	0.474155i	0.969820	+	0.243822i	$0.0784013\pi$
$798$		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
$803$	6.33049			0.223398
$804$		0			0
$805$		0			0
$806$		0			0
$807$	11.4100	−	19.7626i	0.401650	−	0.695678i
$808$		0			0
$809$	20.0405	−	34.7111i	0.704586	−	1.22038i	−0.262255	−	0.964999i	$-0.584466\pi$
$809$	20.0405	−	34.7111i	0.704586	−	1.22038i	0.966841	−	0.255380i	$-0.0822005\pi$
$810$		0			0
$811$		−	33.5484i		−	1.17804i	−0.808117	−	0.589022i	$-0.799513\pi$
$811$		−	33.5484i		−	1.17804i	0.808117	−	0.589022i	$-0.200487\pi$
$812$		0			0
$813$	−8.39742	−	4.84825i	−0.294510	−	0.170036i
$814$		0			0
$815$	−20.5095			−0.718415
$816$		0			0
$817$		−	71.2128i		−	2.49142i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			41.0071i			1.43116i	0.698532	+	0.715579i	$0.253837\pi$
$821$			41.0071i			1.43116i	−0.698532	+	0.715579i	$0.746163\pi$
$822$		0			0
$823$	11.2858			0.393398			0.196699	−	0.980464i	$-0.436978\pi$
$823$	11.2858			0.393398			0.196699	+	0.980464i	$0.436978\pi$
$824$		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
$829$	−10.7528	+	18.6244i	−0.373459	+	0.646851i	−0.990095	−	0.140398i	$-0.955162\pi$
$829$	−10.7528	+	18.6244i	−0.373459	+	0.646851i	0.616636	+	0.787249i	$0.288495\pi$
$830$		0			0
$831$	−12.4165	+	21.5060i	−0.430723	+	0.746033i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	1.44469			0.0499954
$836$		0			0
$837$	5.30511	−	3.06291i	0.183371	−	0.105870i
$838$		0			0
$839$	8.99327	+	5.19227i	0.310482	+	0.179257i	0.647142	−	0.762369i	$-0.275964\pi$
$839$	8.99327	+	5.19227i	0.310482	+	0.179257i	−0.336660	+	0.941626i	$0.609297\pi$
$840$		0			0
$841$	−4.62797	+	8.01588i	−0.159585	+	0.276410i
$842$		0			0
$843$	−22.0974	−	12.7580i	−0.761076	−	0.439407i
$844$		0			0
$845$	5.38349	+	21.2848i	0.185198	+	0.732218i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−2.00495	−	3.47267i	−0.0688096	−	0.119182i
$850$		0			0
$851$			86.0820i			2.95085i
$852$		0			0
$853$		−	11.0193i		−	0.377295i	−0.982045	−	0.188647i	$-0.939590\pi$
$853$		−	11.0193i		−	0.377295i	0.982045	−	0.188647i	$-0.0604103\pi$
$854$		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	$-0.122617\pi$
$857$	4.03831	+	6.99457i	0.137946	+	0.238930i	−0.788773	+	0.614685i	$0.789283\pi$
$858$		0			0
$859$	2.26526	−	3.92355i	0.0772898	−	0.133870i	−0.824790	−	0.565439i	$-0.808707\pi$
$859$	2.26526	−	3.92355i	0.0772898	−	0.133870i	0.902080	+	0.431569i	$0.142040\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.89597	−	2.24934i	−0.132620	−	0.0765685i	0.432222	−	0.901767i	$-0.357730\pi$
$863$	−3.89597	−	2.24934i	−0.132620	−	0.0765685i	−0.564842	+	0.825199i	$0.691063\pi$
$864$		0			0
$865$			16.7833i			0.570648i
$866$		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
$871$	−11.7936	−	15.5957i	−0.399612	−	0.528439i
$872$		0			0
$873$		−	4.16306i		−	0.140898i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.08070	−	1.20129i	0.0702601	−	0.0405647i	−0.464458	−	0.885595i	$-0.653751\pi$
$877$	2.08070	−	1.20129i	0.0702601	−	0.0405647i	0.534719	+	0.845030i	$0.320418\pi$
$878$		0			0
$879$	15.1764	−	8.76210i	0.511887	−	0.295538i
$880$		0			0
$881$	10.0166	+	17.3493i	0.337468	+	0.584512i	0.983956	−	0.178413i	$-0.0570962\pi$
$881$	10.0166	+	17.3493i	0.337468	+	0.584512i	−0.646488	+	0.762924i	$0.723763\pi$
$882$		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
$887$	7.94061			0.266620			0.133310	−	0.991074i	$-0.457439\pi$
$887$	7.94061			0.266620			0.133310	+	0.991074i	$0.457439\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	2.52383	−	1.45713i	0.0845514	−	0.0488158i
$892$		0			0
$893$	−88.9608			−2.97696
$894$		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
$899$	−7.01837	−	4.05206i	−0.234076	−	0.135144i
$900$		0			0
$901$	17.8590	+	30.9327i	0.594970	+	1.03052i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.1374	−	7.00751i	−0.403459	−	0.232937i
$906$		0			0
$907$	−4.36173	+	7.55474i	−0.144829	+	0.250851i	−0.929309	−	0.369303i	$-0.879597\pi$
$907$	−4.36173	+	7.55474i	−0.144829	+	0.250851i	0.784480	+	0.620154i	$0.212930\pi$
$908$		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
$913$	10.8083	−	18.7205i	0.357703	−	0.619559i
$914$		0			0
$915$	−16.3367	−	9.43199i	−0.540074	−	0.311812i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	10.1837	+	17.6388i	0.335931	+	0.581849i	0.983663	−	0.180019i	$-0.0576158\pi$
$919$	10.1837	+	17.6388i	0.335931	+	0.581849i	−0.647732	+	0.761868i	$0.724282\pi$
$920$		0			0
$921$	−8.54442	−	4.93312i	−0.281548	−	0.162552i
$922$		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
$927$	10.4712			0.343921
$928$		0			0
$929$	−16.5214	+	9.53862i	−0.542049	+	0.312952i	−0.745909	−	0.666048i	$-0.767985\pi$
$929$	−16.5214	+	9.53862i	−0.542049	+	0.312952i	0.203860	+	0.979000i	$0.434651\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−15.0384			−0.492336
$934$		0			0
$935$	3.77502	+	6.53852i	0.123456	+	0.213833i
$936$		0			0
$937$	−46.2095			−1.50960			−0.754800	−	0.655955i	$-0.772266\pi$
$937$	−46.2095			−1.50960			−0.754800	+	0.655955i	$0.772266\pi$
$938$		0			0
$939$	−1.50634	−	2.60906i	−0.0491576	−	0.0851435i
$940$		0			0
$941$	−5.89182	+	3.40164i	−0.192068	+	0.110890i	−0.592950	−	0.805239i	$-0.702037\pi$
$941$	−5.89182	+	3.40164i	−0.192068	+	0.110890i	0.400882	+	0.916130i	$0.368704\pi$
$942$		0			0
$943$	−11.7886	+	6.80615i	−0.383890	+	0.221639i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	41.2178i		−	1.33940i	−0.742633	−	0.669699i	$-0.766423\pi$
$947$		−	41.2178i		−	1.33940i	0.742633	−	0.669699i	$-0.233577\pi$
$948$		0			0
$949$	−18.2657	+	2.27414i	−0.592931	+	0.0738218i
$950$		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
$955$			5.93460i			0.192039i
$956$		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
$969$			24.1997i			0.777407i
$970$		0			0
$971$	8.90802	+	15.4291i	0.285872	+	0.495145i	0.972820	−	0.231562i	$-0.0743835\pi$
$971$	8.90802	+	15.4291i	0.285872	+	0.495145i	−0.686948	+	0.726706i	$0.741050\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.42869	+	2.71598i	0.205883	+	0.0869811i
$976$		0			0
$977$	−42.6835	−	24.6433i	−1.36556	−	0.788409i	−0.375207	−	0.926941i	$-0.622428\pi$
$977$	−42.6835	−	24.6433i	−1.36556	−	0.788409i	−0.990358	+	0.138532i	$0.955762\pi$
$978$		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	−0.299143	−	0.954208i	$-0.596701\pi$
$983$	11.8405	−	6.83612i	0.377653	−	0.218038i	0.676797	+	0.736170i	$0.263368\pi$
$984$		0			0
$985$	26.5810			0.846940
$986$		0			0
$987$		0			0
$988$		0			0
$989$	40.0263	−	69.3275i	1.27276	−	2.20449i
$990$		0			0
$991$	11.0959	−	19.2186i	0.352472	−	0.610499i	−0.634210	−	0.773161i	$-0.718675\pi$
$991$	11.0959	−	19.2186i	0.352472	−	0.610499i	0.986682	+	0.162662i	$0.0520080\pi$
$992$		0			0
$993$			27.6160i			0.876368i
$994$		0			0
$995$	28.6576	+	16.5455i	0.908506	+	0.524526i
$996$		0			0
$997$	−18.0449			−0.571489			−0.285745	−	0.958306i	$-0.592241\pi$
$997$	−18.0449			−0.571489			−0.285745	+	0.958306i	$0.592241\pi$
$998$		0			0
$999$			48.0662i			1.52075i

Twists

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

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

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.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.450600 + 0.780462i) q^{3} +(1.46259 + 0.844424i) q^{5} +(1.09392 + 1.89472i) q^{9} +(-1.07390 - 0.620015i) q^{11} +(3.32131 + 1.40318i) q^{13} +(-1.31808 + 0.760994i) q^{15} -3.60518 q^{17} +(-6.45050 + 3.72420i) q^{19} -8.37298 q^{23} +(-1.07390 - 1.86004i) q^{25} -4.67528 q^{27} +(3.09257 + 5.35649i) q^{29} +(-1.13472 + 0.655128i) q^{31} +(0.967795 - 0.558757i) q^{33} -10.2809i q^{37} +(-2.59171 + 1.95988i) q^{39} +(1.40793 - 0.812871i) q^{41} +(-4.78041 + 8.27991i) q^{43} +3.69493i q^{45} +(10.3435 + 5.97181i) q^{47} +(1.62449 - 2.81370i) q^{51} +(-4.95371 - 8.58008i) q^{53} +(-1.04711 - 1.81365i) q^{55} -6.71250i q^{57} -4.74824i q^{59} +(6.19715 + 10.7338i) q^{61} +(3.67282 + 4.85686i) q^{65} +(-4.69645 - 2.71149i) q^{67} +(3.77286 - 6.53479i) q^{69} +(3.90075 + 2.25210i) q^{71} +(-4.42116 + 2.55256i) q^{73} +1.93559 q^{75} +(3.11082 - 5.38810i) q^{79} +(-1.17508 + 2.03530i) q^{81} +17.4323i q^{83} +(-5.27288 - 3.04430i) q^{85} -5.57404 q^{87} -5.86217i q^{89} -1.18080i q^{93} -12.5792 q^{95} +(-1.64789 - 0.951408i) q^{97} -2.71298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{9} - 12 q^{15} - 32 q^{23} + 24 q^{29} - 28 q^{39} + 4 q^{43} - 40 q^{51} + 24 q^{53} + 32 q^{65} - 24 q^{71} + 24 q^{79} + 4 q^{81} + 12 q^{85} + 40 q^{95}+O(q^{100}) \) 24 * q - 8 * q^9 - 12 * q^15 - 32 * q^23 + 24 * q^29 - 28 * q^39 + 4 * q^43 - 40 * q^51 + 24 * q^53 + 32 * q^65 - 24 * q^71 + 24 * q^79 + 4 * q^81 + 12 * q^85 + 40 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more