LMFDB - Embedded newform 192.4.j.a.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,4,Mod(49,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.49"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	192.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.3283667211$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	192.49
Dual form			192.4.j.a.145.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.12132 - 2.12132i) q^{3} +(-11.7719 - 11.7719i) q^{5} -14.7089i q^{7} -9.00000i q^{9} +(24.9380 + 24.9380i) q^{11} +(-58.1345 + 58.1345i) q^{13} -49.9441 q^{15} -75.8798 q^{17} +(-51.8464 + 51.8464i) q^{19} +(-31.2023 - 31.2023i) q^{21} -149.444i q^{23} +152.157i q^{25} +(-19.0919 - 19.0919i) q^{27} +(48.5419 - 48.5419i) q^{29} -29.6074 q^{31} +105.803 q^{33} +(-173.153 + 173.153i) q^{35} +(-147.751 - 147.751i) q^{37} +246.644i q^{39} -225.232i q^{41} +(-81.7640 - 81.7640i) q^{43} +(-105.947 + 105.947i) q^{45} -46.5418 q^{47} +126.648 q^{49} +(-160.965 + 160.965i) q^{51} +(-156.105 - 156.105i) q^{53} -587.137i q^{55} +219.965i q^{57} +(238.199 + 238.199i) q^{59} +(-594.013 + 594.013i) q^{61} -132.380 q^{63} +1368.71 q^{65} +(-299.623 + 299.623i) q^{67} +(-317.018 - 317.018i) q^{69} -693.932i q^{71} -462.446i q^{73} +(322.774 + 322.774i) q^{75} +(366.811 - 366.811i) q^{77} +878.797 q^{79} -81.0000 q^{81} +(926.380 - 926.380i) q^{83} +(893.252 + 893.252i) q^{85} -205.946i q^{87} +350.770i q^{89} +(855.096 + 855.096i) q^{91} +(-62.8068 + 62.8068i) q^{93} +1220.66 q^{95} -766.194 q^{97} +(224.442 - 224.442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 40 q^{11} - 120 q^{15} - 24 q^{19} + 400 q^{29} + 744 q^{31} + 456 q^{35} + 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} + 752 q^{53} + 1376 q^{59} - 912 q^{61} + 504 q^{63} + 976 q^{65} + 2256 q^{67}+ \cdots + 360 q^{99}+O(q^{100}) $ 24 * q + 40 * q^11 - 120 * q^15 - 24 * q^19 + 400 * q^29 + 744 * q^31 + 456 * q^35 + 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 + 752 * q^53 + 1376 * q^59 - 912 * q^61 + 504 * q^63 + 976 * q^65 + 2256 * q^67 - 528 * q^69 - 1104 * q^75 + 1904 * q^77 - 5992 * q^79 - 1944 * q^81 - 2680 * q^83 - 240 * q^85 + 3496 * q^91 + 7728 * q^95 + 360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$		0			0
$5$	−11.7719	−	11.7719i	−1.05291	−	1.05291i	−0.998520	−	0.0543947i	$-0.982677\pi$
$5$	−11.7719	−	11.7719i	−1.05291	−	1.05291i	−0.0543947	−	0.998520i	$-0.517323\pi$
$6$		0			0
$7$		−	14.7089i		−	0.794207i	−0.917774	−	0.397104i	$-0.870015\pi$
$7$		−	14.7089i		−	0.794207i	0.917774	−	0.397104i	$-0.129985\pi$
$8$		0			0
$9$		−	9.00000i		−	0.333333i
$10$		0			0
$11$	24.9380	+	24.9380i	0.683553	+	0.683553i	0.960799	−	0.277246i	$-0.0894216\pi$
$11$	24.9380	+	24.9380i	0.683553	+	0.683553i	−0.277246	+	0.960799i	$0.589422\pi$
$12$		0			0
$13$	−58.1345	+	58.1345i	−1.24028	+	1.24028i	−0.280393	+	0.959885i	$0.590465\pi$
$13$	−58.1345	+	58.1345i	−1.24028	+	1.24028i	−0.959885	+	0.280393i	$0.909535\pi$
$14$		0			0
$15$	−49.9441			−0.859701
$16$		0			0
$17$	−75.8798			−1.08256			−0.541281	−	0.840842i	$-0.682060\pi$
$17$	−75.8798			−1.08256			−0.541281	+	0.840842i	$0.682060\pi$
$18$		0			0
$19$	−51.8464	+	51.8464i	−0.626020	+	0.626020i	−0.947064	−	0.321045i	$-0.895966\pi$
$19$	−51.8464	+	51.8464i	−0.626020	+	0.626020i	0.321045	+	0.947064i	$0.395966\pi$
$20$		0			0
$21$	−31.2023	−	31.2023i	−0.324234	−	0.324234i
$22$		0			0
$23$		−	149.444i		−	1.35483i	−0.735600	−	0.677416i	$-0.763100\pi$
$23$		−	149.444i		−	1.35483i	0.735600	−	0.677416i	$-0.236900\pi$
$24$		0			0
$25$			152.157i			1.21726i
$26$		0			0
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$		0			0
$29$	48.5419	−	48.5419i	0.310828	−	0.310828i	−0.534402	−	0.845230i	$-0.679463\pi$
$29$	48.5419	−	48.5419i	0.310828	−	0.310828i	0.845230	+	0.534402i	$0.179463\pi$
$30$		0			0
$31$	−29.6074			−0.171537			−0.0857685	−	0.996315i	$-0.527335\pi$
$31$	−29.6074			−0.171537			−0.0857685	+	0.996315i	$0.527335\pi$
$32$		0			0
$33$	105.803			0.558119
$34$		0			0
$35$	−173.153	+	173.153i	−0.836232	+	0.836232i
$36$		0			0
$37$	−147.751	−	147.751i	−0.656489	−	0.656489i	0.298058	−	0.954548i	$-0.403661\pi$
$37$	−147.751	−	147.751i	−0.656489	−	0.656489i	−0.954548	+	0.298058i	$0.903661\pi$
$38$		0			0
$39$			246.644i			1.01268i
$40$		0			0
$41$		−	225.232i		−	0.857933i	−0.903320	−	0.428967i	$-0.858878\pi$
$41$		−	225.232i		−	0.857933i	0.903320	−	0.428967i	$-0.141122\pi$
$42$		0			0
$43$	−81.7640	−	81.7640i	−0.289974	−	0.289974i	0.547096	−	0.837070i	$-0.315733\pi$
$43$	−81.7640	−	81.7640i	−0.289974	−	0.289974i	−0.837070	+	0.547096i	$0.815733\pi$
$44$		0			0
$45$	−105.947	+	105.947i	−0.350971	+	0.350971i
$46$		0			0
$47$	−46.5418			−0.144443			−0.0722215	−	0.997389i	$-0.523009\pi$
$47$	−46.5418			−0.144443			−0.0722215	+	0.997389i	$0.523009\pi$
$48$		0			0
$49$	126.648			0.369235
$50$		0			0
$51$	−160.965	+	160.965i	−0.441954	+	0.441954i
$52$		0			0
$53$	−156.105	−	156.105i	−0.404578	−	0.404578i	0.475265	−	0.879843i	$-0.342352\pi$
$53$	−156.105	−	156.105i	−0.404578	−	0.404578i	−0.879843	+	0.475265i	$0.842352\pi$
$54$		0			0
$55$		−	587.137i		−	1.43945i
$56$		0			0
$57$			219.965i			0.511143i
$58$		0			0
$59$	238.199	+	238.199i	0.525608	+	0.525608i	0.919260	−	0.393652i	$-0.128788\pi$
$59$	238.199	+	238.199i	0.525608	+	0.525608i	−0.393652	+	0.919260i	$0.628788\pi$
$60$		0			0
$61$	−594.013	+	594.013i	−1.24681	+	1.24681i	−0.289692	+	0.957120i	$0.593553\pi$
$61$	−594.013	+	594.013i	−1.24681	+	1.24681i	−0.957120	+	0.289692i	$0.906447\pi$
$62$		0			0
$63$	−132.380			−0.264736
$64$		0			0
$65$	1368.71			2.61181
$66$		0			0
$67$	−299.623	+	299.623i	−0.546339	+	0.546339i	−0.925380	−	0.379041i	$-0.876254\pi$
$67$	−299.623	+	299.623i	−0.546339	+	0.546339i	0.379041	+	0.925380i	$0.376254\pi$
$68$		0			0
$69$	−317.018	−	317.018i	−0.553108	−	0.553108i
$70$		0			0
$71$		−	693.932i		−	1.15992i	−0.814644	−	0.579962i	$-0.803067\pi$
$71$		−	693.932i		−	1.15992i	0.814644	−	0.579962i	$-0.196933\pi$
$72$		0			0
$73$		−	462.446i		−	0.741441i	−0.928745	−	0.370720i	$-0.879111\pi$
$73$		−	462.446i		−	0.741441i	0.928745	−	0.370720i	$-0.120889\pi$
$74$		0			0
$75$	322.774	+	322.774i	0.496943	+	0.496943i
$76$		0			0
$77$	366.811	−	366.811i	0.542883	−	0.542883i
$78$		0			0
$79$	878.797			1.25155			0.625775	−	0.780004i	$-0.284783\pi$
$79$	878.797			1.25155			0.625775	+	0.780004i	$0.284783\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	926.380	−	926.380i	1.22510	−	1.22510i	0.259306	−	0.965795i	$-0.416506\pi$
$83$	926.380	−	926.380i	1.22510	−	1.22510i	0.965795	−	0.259306i	$-0.0834938\pi$
$84$		0			0
$85$	893.252	+	893.252i	1.13984	+	1.13984i
$86$		0			0
$87$		−	205.946i		−	0.253790i
$88$		0			0
$89$			350.770i			0.417770i	0.977940	+	0.208885i	$0.0669834\pi$
$89$			350.770i			0.417770i	−0.977940	+	0.208885i	$0.933017\pi$
$90$		0			0
$91$	855.096	+	855.096i	0.985038	+	0.985038i
$92$		0			0
$93$	−62.8068	+	62.8068i	−0.0700296	+	0.0700296i
$94$		0			0
$95$	1220.66			1.31829
$96$		0			0
$97$	−766.194			−0.802013			−0.401006	−	0.916075i	$-0.631339\pi$
$97$	−766.194			−0.802013			−0.401006	+	0.916075i	$0.631339\pi$
$98$		0			0
$99$	224.442	−	224.442i	0.227851	−	0.227851i
$100$		0			0
$101$	−983.994	−	983.994i	−0.969417	−	0.969417i	0.0301291	−	0.999546i	$-0.490408\pi$
$101$	−983.994	−	983.994i	−0.969417	−	0.969417i	−0.999546	+	0.0301291i	$0.990408\pi$
$102$		0			0
$103$			512.291i			0.490074i	0.969514	+	0.245037i	$0.0788000\pi$
$103$			512.291i			0.490074i	−0.969514	+	0.245037i	$0.921200\pi$
$104$		0			0
$105$			734.624i			0.682781i
$106$		0			0
$107$	−633.097	−	633.097i	−0.571998	−	0.571998i	0.360688	−	0.932686i	$-0.382542\pi$
$107$	−633.097	−	633.097i	−0.571998	−	0.571998i	−0.932686	+	0.360688i	$0.882542\pi$
$108$		0			0
$109$	983.894	−	983.894i	0.864587	−	0.864587i	−0.127280	−	0.991867i	$-0.540625\pi$
$109$	983.894	−	983.894i	0.864587	−	0.864587i	0.991867	+	0.127280i	$0.0406246\pi$
$110$		0			0
$111$	−626.854			−0.536021
$112$		0			0
$113$	332.042			0.276424			0.138212	−	0.990403i	$-0.455864\pi$
$113$	332.042			0.276424			0.138212	+	0.990403i	$0.455864\pi$
$114$		0			0
$115$	−1759.24	+	1759.24i	−1.42652	+	1.42652i
$116$		0			0
$117$	523.211	+	523.211i	0.413426	+	0.413426i
$118$		0			0
$119$			1116.11i			0.859778i
$120$		0			0
$121$		−	87.1933i		−	0.0655096i
$122$		0			0
$123$	−477.788	−	477.788i	−0.350250	−	0.350250i
$124$		0			0
$125$	319.692	−	319.692i	0.228753	−	0.228753i
$126$		0			0
$127$	−712.949			−0.498141			−0.249071	−	0.968485i	$-0.580125\pi$
$127$	−712.949			−0.498141			−0.249071	+	0.968485i	$0.580125\pi$
$128$		0			0
$129$	−346.895			−0.236763
$130$		0			0
$131$	2039.63	−	2039.63i	1.36033	−	1.36033i	0.486843	−	0.873489i	$-0.338148\pi$
$131$	2039.63	−	2039.63i	1.36033	−	1.36033i	0.873489	−	0.486843i	$-0.161852\pi$
$132$		0			0
$133$	762.604	+	762.604i	0.497189	+	0.497189i
$134$		0			0
$135$			449.497i			0.286567i
$136$		0			0
$137$		−	761.248i		−	0.474728i	−0.971421	−	0.237364i	$-0.923717\pi$
$137$		−	761.248i		−	0.474728i	0.971421	−	0.237364i	$-0.0762835\pi$
$138$		0			0
$139$	−1277.92	−	1277.92i	−0.779798	−	0.779798i	0.199998	−	0.979796i	$-0.435906\pi$
$139$	−1277.92	−	1277.92i	−0.779798	−	0.779798i	−0.979796	+	0.199998i	$0.935906\pi$
$140$		0			0
$141$	−98.7302	+	98.7302i	−0.0589686	+	0.0589686i
$142$		0			0
$143$	−2899.52			−1.69559
$144$		0			0
$145$	−1142.86			−0.654550
$146$		0			0
$147$	268.660	−	268.660i	0.150740	−	0.150740i
$148$		0			0
$149$	746.651	+	746.651i	0.410524	+	0.410524i	0.881921	−	0.471397i	$-0.156250\pi$
$149$	746.651	+	746.651i	0.410524	+	0.410524i	−0.471397	+	0.881921i	$0.656250\pi$
$150$		0			0
$151$		−	1186.11i		−	0.639234i	−0.947547	−	0.319617i	$-0.896446\pi$
$151$		−	1186.11i		−	0.639234i	0.947547	−	0.319617i	$-0.103554\pi$
$152$		0			0
$153$			682.918i			0.360854i
$154$		0			0
$155$	348.536	+	348.536i	0.180614	+	0.180614i
$156$		0			0
$157$	219.416	−	219.416i	0.111537	−	0.111537i	−0.649136	−	0.760673i	$-0.724869\pi$
$157$	219.416	−	219.416i	0.111537	−	0.111537i	0.760673	+	0.649136i	$0.224869\pi$
$158$		0			0
$159$	−662.297			−0.330337
$160$		0			0
$161$	−2198.15			−1.07602
$162$		0			0
$163$	−1321.49	+	1321.49i	−0.635011	+	0.635011i	−0.949321	−	0.314309i	$-0.898227\pi$
$163$	−1321.49	+	1321.49i	−0.635011	+	0.635011i	0.314309	+	0.949321i	$0.398227\pi$
$164$		0			0
$165$	−1245.51	−	1245.51i	−0.587651	−	0.587651i
$166$		0			0
$167$			1180.83i			0.547160i	0.961849	+	0.273580i	$0.0882078\pi$
$167$			1180.83i			0.547160i	−0.961849	+	0.273580i	$0.911792\pi$
$168$		0			0
$169$		−	4562.25i		−	2.07658i
$170$		0			0
$171$	466.617	+	466.617i	0.208673	+	0.208673i
$172$		0			0
$173$	−1559.35	+	1559.35i	−0.685289	+	0.685289i	−0.961187	−	0.275898i	$-0.911025\pi$
$173$	−1559.35	+	1559.35i	−0.685289	+	0.685289i	0.275898	+	0.961187i	$0.411025\pi$
$174$		0			0
$175$	2238.07			0.966754
$176$		0			0
$177$	1010.59			0.429157
$178$		0			0
$179$	−1718.83	+	1718.83i	−0.717717	+	0.717717i	−0.968137	−	0.250420i	$-0.919431\pi$
$179$	−1718.83	+	1718.83i	−0.717717	+	0.717717i	0.250420	+	0.968137i	$0.419431\pi$
$180$		0			0
$181$	703.803	+	703.803i	0.289023	+	0.289023i	0.836694	−	0.547671i	$-0.184485\pi$
$181$	703.803	+	703.803i	0.289023	+	0.289023i	−0.547671	+	0.836694i	$0.684485\pi$
$182$		0			0
$183$			2520.18i			1.01802i
$184$		0			0
$185$			3478.63i			1.38245i
$186$		0			0
$187$	−1892.29	−	1892.29i	−0.739989	−	0.739989i
$188$		0			0
$189$	−280.821	+	280.821i	−0.108078	+	0.108078i
$190$		0			0
$191$	−290.013			−0.109867			−0.0549335	−	0.998490i	$-0.517495\pi$
$191$	−290.013			−0.109867			−0.0549335	+	0.998490i	$0.517495\pi$
$192$		0			0
$193$	−4295.94			−1.60222			−0.801111	−	0.598516i	$-0.795757\pi$
$193$	−4295.94			−1.60222			−0.801111	+	0.598516i	$0.795757\pi$
$194$		0			0
$195$	2903.48	−	2903.48i	1.06627	−	1.06627i
$196$		0			0
$197$	936.690	+	936.690i	0.338764	+	0.338764i	0.855902	−	0.517138i	$-0.173003\pi$
$197$	936.690	+	936.690i	0.338764	+	0.338764i	−0.517138	+	0.855902i	$0.673003\pi$
$198$		0			0
$199$			3333.18i			1.18735i	0.804705	+	0.593675i	$0.202324\pi$
$199$			3333.18i			1.18735i	−0.804705	+	0.593675i	$0.797676\pi$
$200$		0			0
$201$			1271.19i			0.446084i
$202$		0			0
$203$	−713.999	−	713.999i	−0.246862	−	0.246862i
$204$		0			0
$205$	−2651.41	+	2651.41i	−0.903330	+	0.903330i
$206$		0			0
$207$	−1344.99			−0.451611
$208$		0			0
$209$	−2585.89			−0.855836
$210$		0			0
$211$	3810.99	−	3810.99i	1.24341	−	1.24341i	0.284831	−	0.958578i	$-0.408063\pi$
$211$	3810.99	−	3810.99i	1.24341	−	1.24341i	0.958578	−	0.284831i	$-0.0919375\pi$
$212$		0			0
$213$	−1472.05	−	1472.05i	−0.473537	−	0.473537i
$214$		0			0
$215$			1925.04i			0.610636i
$216$		0			0
$217$			435.493i			0.136236i
$218$		0			0
$219$	−980.996	−	980.996i	−0.302692	−	0.302692i
$220$		0			0
$221$	4411.23	−	4411.23i	1.34268	−	1.34268i
$222$		0			0
$223$	3093.27			0.928882			0.464441	−	0.885604i	$-0.346255\pi$
$223$	3093.27			0.928882			0.464441	+	0.885604i	$0.346255\pi$
$224$		0			0
$225$	1369.41			0.405752
$226$		0			0
$227$	−97.5310	+	97.5310i	−0.0285170	+	0.0285170i	−0.721222	−	0.692705i	$-0.756419\pi$
$227$	−97.5310	+	97.5310i	−0.0285170	+	0.0285170i	0.692705	+	0.721222i	$0.256419\pi$
$228$		0			0
$229$	2867.04	+	2867.04i	0.827334	+	0.827334i	0.987147	−	0.159813i	$-0.0510892\pi$
$229$	2867.04	+	2867.04i	0.827334	+	0.827334i	−0.159813	+	0.987147i	$0.551089\pi$
$230$		0			0
$231$		−	1556.25i		−	0.443262i
$232$		0			0
$233$		−	260.384i		−	0.0732116i	−0.999330	−	0.0366058i	$-0.988345\pi$
$233$		−	260.384i		−	0.0732116i	0.999330	−	0.0366058i	$-0.0116546\pi$
$234$		0			0
$235$	547.888	+	547.888i	0.152086	+	0.152086i
$236$		0			0
$237$	1864.21	−	1864.21i	0.510943	−	0.510943i
$238$		0			0
$239$	−1133.63			−0.306814			−0.153407	−	0.988163i	$-0.549025\pi$
$239$	−1133.63			−0.306814			−0.153407	+	0.988163i	$0.549025\pi$
$240$		0			0
$241$	2717.65			0.726386			0.363193	−	0.931714i	$-0.381686\pi$
$241$	2717.65			0.726386			0.363193	+	0.931714i	$0.381686\pi$
$242$		0			0
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−1490.89	−	1490.89i	−0.388773	−	0.388773i
$246$		0			0
$247$		−	6028.13i		−	1.55288i
$248$		0			0
$249$		−	3930.30i		−	1.00029i
$250$		0			0
$251$	−902.500	−	902.500i	−0.226953	−	0.226953i	0.584465	−	0.811419i	$-0.301304\pi$
$251$	−902.500	−	902.500i	−0.226953	−	0.226953i	−0.811419	+	0.584465i	$0.801304\pi$
$252$		0			0
$253$	3726.82	−	3726.82i	0.926101	−	0.926101i
$254$		0			0
$255$	3789.75			0.930679
$256$		0			0
$257$	−49.0728			−0.0119108			−0.00595541	−	0.999982i	$-0.501896\pi$
$257$	−49.0728			−0.0119108			−0.00595541	+	0.999982i	$0.501896\pi$
$258$		0			0
$259$	−2173.26	+	2173.26i	−0.521388	+	0.521388i
$260$		0			0
$261$	−436.877	−	436.877i	−0.103609	−	0.103609i
$262$		0			0
$263$		−	448.347i		−	0.105119i	−0.998618	−	0.0525594i	$-0.983262\pi$
$263$		−	448.347i		−	0.105119i	0.998618	−	0.0525594i	$-0.0167379\pi$
$264$		0			0
$265$			3675.31i			0.851973i
$266$		0			0
$267$	744.095	+	744.095i	0.170554	+	0.170554i
$268$		0			0
$269$	−4691.01	+	4691.01i	−1.06326	+	1.06326i	−0.0653970	+	0.997859i	$0.520831\pi$
$269$	−4691.01	+	4691.01i	−1.06326	+	1.06326i	−0.997859	+	0.0653970i	$0.979169\pi$
$270$		0			0
$271$	−310.218			−0.0695365			−0.0347683	−	0.999395i	$-0.511069\pi$
$271$	−310.218			−0.0695365			−0.0347683	+	0.999395i	$0.511069\pi$
$272$		0			0
$273$	3627.87			0.804280
$274$		0			0
$275$	−3794.49	+	3794.49i	−0.832060	+	0.832060i
$276$		0			0
$277$	3523.42	+	3523.42i	0.764267	+	0.764267i	0.977091	−	0.212823i	$-0.0682659\pi$
$277$	3523.42	+	3523.42i	0.764267	+	0.764267i	−0.212823	+	0.977091i	$0.568266\pi$
$278$		0			0
$279$			266.467i			0.0571790i
$280$		0			0
$281$			1369.74i			0.290789i	0.989374	+	0.145395i	$0.0464452\pi$
$281$			1369.74i			0.290789i	−0.989374	+	0.145395i	$0.953555\pi$
$282$		0			0
$283$	5575.17	+	5575.17i	1.17106	+	1.17106i	0.981958	+	0.189100i	$0.0605570\pi$
$283$	5575.17	+	5575.17i	1.17106	+	1.17106i	0.189100	+	0.981958i	$0.439443\pi$
$284$		0			0
$285$	2589.42	−	2589.42i	0.538190	−	0.538190i
$286$		0			0
$287$	−3312.91			−0.681377
$288$		0			0
$289$	844.738			0.171939
$290$		0			0
$291$	−1625.34	+	1625.34i	−0.327420	+	0.327420i
$292$		0			0
$293$	−1651.17	−	1651.17i	−0.329222	−	0.329222i	0.523068	−	0.852291i	$-0.324787\pi$
$293$	−1651.17	−	1651.17i	−0.329222	−	0.329222i	−0.852291	+	0.523068i	$0.824787\pi$
$294$		0			0
$295$		−	5608.13i		−	1.10684i
$296$		0			0
$297$		−	952.226i		−	0.186040i
$298$		0			0
$299$	8687.84	+	8687.84i	1.68037	+	1.68037i
$300$		0			0
$301$	−1202.66	+	1202.66i	−0.230300	+	0.230300i
$302$		0			0
$303$	−4174.73			−0.791526
$304$		0			0
$305$	13985.4			2.62557
$306$		0			0
$307$	1930.51	−	1930.51i	0.358892	−	0.358892i	−0.504512	−	0.863404i	$-0.668328\pi$
$307$	1930.51	−	1930.51i	0.358892	−	0.358892i	0.863404	+	0.504512i	$0.168328\pi$
$308$		0			0
$309$	1086.73	+	1086.73i	0.200072	+	0.200072i
$310$		0			0
$311$			3967.14i			0.723331i	0.932308	+	0.361665i	$0.117792\pi$
$311$			3967.14i			0.723331i	−0.932308	+	0.361665i	$0.882208\pi$
$312$		0			0
$313$		−	7329.46i		−	1.32360i	−0.749682	−	0.661798i	$-0.769794\pi$
$313$		−	7329.46i		−	1.32360i	0.749682	−	0.661798i	$-0.230206\pi$
$314$		0			0
$315$	1558.37	+	1558.37i	0.278744	+	0.278744i
$316$		0			0
$317$	−3264.85	+	3264.85i	−0.578461	+	0.578461i	−0.934479	−	0.356018i	$-0.884134\pi$
$317$	−3264.85	+	3264.85i	−0.578461	+	0.578461i	0.356018	+	0.934479i	$0.384134\pi$
$318$		0			0
$319$	2421.07			0.424935
$320$		0			0
$321$	−2686.00			−0.467035
$322$		0			0
$323$	3934.09	−	3934.09i	0.677705	−	0.677705i
$324$		0			0
$325$	−8845.58	−	8845.58i	−1.50974	−	1.50974i
$326$		0			0
$327$		−	4174.31i		−	0.705932i
$328$		0			0
$329$			684.580i			0.114718i
$330$		0			0
$331$	−7640.33	−	7640.33i	−1.26873	−	1.26873i	−0.946743	−	0.321991i	$-0.895648\pi$
$331$	−7640.33	−	7640.33i	−1.26873	−	1.26873i	−0.321991	−	0.946743i	$-0.604352\pi$
$332$		0			0
$333$	−1329.76	+	1329.76i	−0.218830	+	0.218830i
$334$		0			0
$335$	7054.28			1.15050
$336$		0			0
$337$	10375.8			1.67716			0.838582	−	0.544775i	$-0.183385\pi$
$337$	10375.8			1.67716			0.838582	+	0.544775i	$0.183385\pi$
$338$		0			0
$339$	704.368	−	704.368i	0.112850	−	0.112850i
$340$		0			0
$341$	−738.349	−	738.349i	−0.117255	−	0.117255i
$342$		0			0
$343$		−	6908.01i		−	1.08746i
$344$		0			0
$345$			7463.83i			1.16475i
$346$		0			0
$347$	−3827.22	−	3827.22i	−0.592092	−	0.592092i	0.346104	−	0.938196i	$-0.387504\pi$
$347$	−3827.22	−	3827.22i	−0.592092	−	0.592092i	−0.938196	+	0.346104i	$0.887504\pi$
$348$		0			0
$349$	783.575	−	783.575i	0.120183	−	0.120183i	−0.644457	−	0.764640i	$-0.722917\pi$
$349$	783.575	−	783.575i	0.120183	−	0.120183i	0.764640	+	0.644457i	$0.222917\pi$
$350$		0			0
$351$	2219.80			0.337561
$352$		0			0
$353$	−9151.32			−1.37982			−0.689909	−	0.723896i	$-0.742349\pi$
$353$	−9151.32			−1.37982			−0.689909	+	0.723896i	$0.742349\pi$
$354$		0			0
$355$	−8168.92	+	8168.92i	−1.22130	+	1.22130i
$356$		0			0
$357$	2367.63	+	2367.63i	0.351003	+	0.351003i
$358$		0			0
$359$		−	290.943i		−	0.0427727i	−0.999771	−	0.0213863i	$-0.993192\pi$
$359$		−	290.943i		−	0.0427727i	0.999771	−	0.0213863i	$-0.00680800\pi$
$360$		0			0
$361$			1482.91i			0.216199i
$362$		0			0
$363$	−184.965	−	184.965i	−0.0267442	−	0.0267442i
$364$		0			0
$365$	−5443.88	+	5443.88i	−0.780674	+	0.780674i
$366$		0			0
$367$	5526.68			0.786077			0.393039	−	0.919522i	$-0.371424\pi$
$367$	5526.68			0.786077			0.393039	+	0.919522i	$0.371424\pi$
$368$		0			0
$369$	−2027.08			−0.285978
$370$		0			0
$371$	−2296.13	+	2296.13i	−0.321319	+	0.321319i
$372$		0			0
$373$	−978.030	−	978.030i	−0.135765	−	0.135765i	0.635958	−	0.771724i	$-0.280605\pi$
$373$	−978.030	−	978.030i	−0.135765	−	0.135765i	−0.771724	+	0.635958i	$0.780605\pi$
$374$		0			0
$375$		−	1356.34i		−	0.186776i
$376$		0			0
$377$			5643.92i			0.771026i
$378$		0			0
$379$	4408.79	+	4408.79i	0.597531	+	0.597531i	0.939655	−	0.342124i	$-0.111146\pi$
$379$	4408.79	+	4408.79i	0.597531	+	0.597531i	−0.342124	+	0.939655i	$0.611146\pi$
$380$		0			0
$381$	−1512.39	+	1512.39i	−0.203365	+	0.203365i
$382$		0			0
$383$	−6799.13			−0.907101			−0.453550	−	0.891231i	$-0.649843\pi$
$383$	−6799.13			−0.907101			−0.453550	+	0.891231i	$0.649843\pi$
$384$		0			0
$385$	−8636.15			−1.14322
$386$		0			0
$387$	−735.876	+	735.876i	−0.0966581	+	0.0966581i
$388$		0			0
$389$	−5520.37	−	5520.37i	−0.719521	−	0.719521i	0.248986	−	0.968507i	$-0.419903\pi$
$389$	−5520.37	−	5520.37i	−0.719521	−	0.719521i	−0.968507	+	0.248986i	$0.919903\pi$
$390$		0			0
$391$			11339.7i			1.46669i
$392$		0			0
$393$		−	8653.43i		−	1.11071i
$394$		0			0
$395$	−10345.1	−	10345.1i	−1.31777	−	1.31777i
$396$		0			0
$397$	−4743.70	+	4743.70i	−0.599696	+	0.599696i	−0.940232	−	0.340536i	$-0.889392\pi$
$397$	−4743.70	+	4743.70i	−0.599696	+	0.599696i	0.340536	+	0.940232i	$0.389392\pi$
$398$		0			0
$399$	3235.45			0.405953
$400$		0			0
$401$	−1674.92			−0.208582			−0.104291	−	0.994547i	$-0.533257\pi$
$401$	−1674.92			−0.208582			−0.104291	+	0.994547i	$0.533257\pi$
$402$		0			0
$403$	1721.21	−	1721.21i	0.212754	−	0.212754i
$404$		0			0
$405$	953.527	+	953.527i	0.116990	+	0.116990i
$406$		0			0
$407$		−	7369.22i		−	0.897491i
$408$		0			0
$409$			11918.0i			1.44084i	0.693536	+	0.720422i	$0.256052\pi$
$409$			11918.0i			1.44084i	−0.693536	+	0.720422i	$0.743948\pi$
$410$		0			0
$411$	−1614.85	−	1614.85i	−0.193807	−	0.193807i
$412$		0			0
$413$	3503.65	−	3503.65i	0.417442	−	0.417442i
$414$		0			0
$415$	−21810.6			−2.57985
$416$		0			0
$417$	−5421.76			−0.636702
$418$		0			0
$419$	−4342.25	+	4342.25i	−0.506284	+	0.506284i	−0.913384	−	0.407100i	$-0.866540\pi$
$419$	−4342.25	+	4342.25i	−0.506284	+	0.506284i	0.407100	+	0.913384i	$0.366540\pi$
$420$		0			0
$421$	−8933.14	−	8933.14i	−1.03414	−	1.03414i	−0.999396	−	0.0347474i	$-0.988937\pi$
$421$	−8933.14	−	8933.14i	−1.03414	−	1.03414i	−0.0347474	−	0.999396i	$-0.511063\pi$
$422$		0			0
$423$			418.877i			0.0481477i
$424$		0			0
$425$		−	11545.6i		−	1.31776i
$426$		0			0
$427$	8737.28	+	8737.28i	0.990227	+	0.990227i
$428$		0			0
$429$	−6150.80	+	6150.80i	−0.692223	+	0.692223i
$430$		0			0
$431$	6175.68			0.690191			0.345095	−	0.938568i	$-0.387847\pi$
$431$	6175.68			0.690191			0.345095	+	0.938568i	$0.387847\pi$
$432$		0			0
$433$	7.68815			0.000853276			0.000426638	−	1.00000i	$-0.499864\pi$
$433$	7.68815			0.000853276			0.000426638		1.00000i	$0.499864\pi$
$434$		0			0
$435$	−2424.38	+	2424.38i	−0.267219	+	0.267219i
$436$		0			0
$437$	7748.11	+	7748.11i	0.848152	+	0.848152i
$438$		0			0
$439$			15185.1i			1.65090i	0.564477	+	0.825449i	$0.309078\pi$
$439$			15185.1i			1.65090i	−0.564477	+	0.825449i	$0.690922\pi$
$440$		0			0
$441$		−	1139.83i		−	0.123078i
$442$		0			0
$443$	3404.98	+	3404.98i	0.365182	+	0.365182i	0.865716	−	0.500535i	$-0.166863\pi$
$443$	3404.98	+	3404.98i	0.365182	+	0.365182i	−0.500535	+	0.865716i	$0.666863\pi$
$444$		0			0
$445$	4129.24	−	4129.24i	0.439876	−	0.439876i
$446$		0			0
$447$	3167.77			0.335191
$448$		0			0
$449$	6766.99			0.711257			0.355628	−	0.934627i	$-0.384267\pi$
$449$	6766.99			0.711257			0.355628	+	0.934627i	$0.384267\pi$
$450$		0			0
$451$	5616.82	−	5616.82i	0.586443	−	0.586443i
$452$		0			0
$453$	−2516.12	−	2516.12i	−0.260966	−	0.260966i
$454$		0			0
$455$		−	20132.3i		−	2.07432i
$456$		0			0
$457$		−	7528.20i		−	0.770578i	−0.922796	−	0.385289i	$-0.874102\pi$
$457$		−	7528.20i		−	0.770578i	0.922796	−	0.385289i	$-0.125898\pi$
$458$		0			0
$459$	1448.69	+	1448.69i	0.147318	+	0.147318i
$460$		0			0
$461$	9029.85	−	9029.85i	0.912282	−	0.912282i	−0.0841690	−	0.996451i	$-0.526824\pi$
$461$	9029.85	−	9029.85i	0.912282	−	0.912282i	0.996451	+	0.0841690i	$0.0268236\pi$
$462$		0			0
$463$	−8555.19			−0.858733			−0.429367	−	0.903130i	$-0.641263\pi$
$463$	−8555.19			−0.858733			−0.429367	+	0.903130i	$0.641263\pi$
$464$		0			0
$465$	1478.71			0.147470
$466$		0			0
$467$	−1326.73	+	1326.73i	−0.131464	+	0.131464i	−0.769777	−	0.638313i	$-0.779632\pi$
$467$	−1326.73	+	1326.73i	−0.131464	+	0.131464i	0.638313	+	0.769777i	$0.279632\pi$
$468$		0			0
$469$	4407.13	+	4407.13i	0.433907	+	0.433907i
$470$		0			0
$471$		−	930.901i		−	0.0910693i
$472$		0			0
$473$		−	4078.06i		−	0.396426i
$474$		0			0
$475$	−7888.79	−	7888.79i	−0.762027	−	0.762027i
$476$		0			0
$477$	−1404.94	+	1404.94i	−0.134859	+	0.134859i
$478$		0			0
$479$	6121.90			0.583960			0.291980	−	0.956424i	$-0.405686\pi$
$479$	6121.90			0.583960			0.291980	+	0.956424i	$0.405686\pi$
$480$		0			0
$481$	17178.9			1.62846
$482$		0			0
$483$	−4662.99	+	4662.99i	−0.439282	+	0.439282i
$484$		0			0
$485$	9019.59	+	9019.59i	0.844450	+	0.844450i
$486$		0			0
$487$			6508.23i			0.605577i	0.953058	+	0.302789i	$0.0979177\pi$
$487$			6508.23i			0.605577i	−0.953058	+	0.302789i	$0.902082\pi$
$488$		0			0
$489$			5606.59i			0.518484i
$490$		0			0
$491$	8093.67	+	8093.67i	0.743915	+	0.743915i	0.973329	−	0.229414i	$-0.0736811\pi$
$491$	8093.67	+	8093.67i	0.743915	+	0.743915i	−0.229414	+	0.973329i	$0.573681\pi$
$492$		0			0
$493$	−3683.35	+	3683.35i	−0.336490	+	0.336490i
$494$		0			0
$495$	−5284.23			−0.479815
$496$		0			0
$497$	−10207.0			−0.921219
$498$		0			0
$499$	6772.14	−	6772.14i	0.607540	−	0.607540i	−0.334762	−	0.942303i	$-0.608656\pi$
$499$	6772.14	−	6772.14i	0.607540	−	0.607540i	0.942303	+	0.334762i	$0.108656\pi$
$500$		0			0
$501$	2504.93	+	2504.93i	0.223377	+	0.223377i
$502$		0			0
$503$			3296.12i			0.292180i	0.989271	+	0.146090i	$0.0466689\pi$
$503$			3296.12i			0.292180i	−0.989271	+	0.146090i	$0.953331\pi$
$504$		0			0
$505$			23167.0i			2.04143i
$506$		0			0
$507$	−9677.99	−	9677.99i	−0.847761	−	0.847761i
$508$		0			0
$509$	6445.02	−	6445.02i	0.561239	−	0.561239i	−0.368421	−	0.929659i	$-0.620101\pi$
$509$	6445.02	−	6445.02i	0.561239	−	0.561239i	0.929659	+	0.368421i	$0.120101\pi$
$510$		0			0
$511$	−6802.08			−0.588858
$512$		0			0
$513$	1979.69			0.170381
$514$		0			0
$515$	6030.66	−	6030.66i	0.516005	−	0.516005i
$516$		0			0
$517$	−1160.66	−	1160.66i	−0.0987346	−	0.0987346i
$518$		0			0
$519$			6615.75i			0.559536i
$520$		0			0
$521$		−	15572.4i		−	1.30948i	−0.755854	−	0.654740i	$-0.772778\pi$
$521$		−	15572.4i		−	1.30948i	0.755854	−	0.654740i	$-0.227222\pi$
$522$		0			0
$523$	−2333.98	−	2333.98i	−0.195139	−	0.195139i	0.602773	−	0.797913i	$-0.294062\pi$
$523$	−2333.98	−	2333.98i	−0.195139	−	0.195139i	−0.797913	+	0.602773i	$0.794062\pi$
$524$		0			0
$525$	4747.66	−	4747.66i	0.394676	−	0.394676i
$526$		0			0
$527$	2246.60			0.185699
$528$		0			0
$529$	−10166.4			−0.835572
$530$		0			0
$531$	2143.79	−	2143.79i	0.175203	−	0.175203i
$532$		0			0
$533$	13093.7	+	13093.7i	1.06408	+	1.06408i
$534$		0			0
$535$			14905.6i			1.20453i
$536$		0			0
$537$			7292.38i			0.586014i
$538$		0			0
$539$	3158.34	+	3158.34i	0.252392	+	0.252392i
$540$		0			0
$541$	8320.06	−	8320.06i	0.661196	−	0.661196i	−0.294466	−	0.955662i	$-0.595142\pi$
$541$	8320.06	−	8320.06i	0.661196	−	0.661196i	0.955662	+	0.294466i	$0.0951417\pi$
$542$		0			0
$543$	2985.98			0.235987
$544$		0			0
$545$	−23164.7			−1.82067
$546$		0			0
$547$	10206.5	−	10206.5i	0.797801	−	0.797801i	−0.184947	−	0.982748i	$-0.559211\pi$
$547$	10206.5	−	10206.5i	0.797801	−	0.797801i	0.982748	+	0.184947i	$0.0592113\pi$
$548$		0			0
$549$	5346.11	+	5346.11i	0.415604	+	0.415604i
$550$		0			0
$551$			5033.44i			0.389168i
$552$		0			0
$553$		−	12926.2i		−	0.993989i
$554$		0			0
$555$	7379.29	+	7379.29i	0.564384	+	0.564384i
$556$		0			0
$557$	9984.48	−	9984.48i	0.759526	−	0.759526i	−0.216710	−	0.976236i	$-0.569533\pi$
$557$	9984.48	−	9984.48i	0.759526	−	0.759526i	0.976236	+	0.216710i	$0.0695325\pi$
$558$		0			0
$559$	9506.63			0.719298
$560$		0			0
$561$	−8028.30			−0.604198
$562$		0			0
$563$	12193.3	−	12193.3i	0.912761	−	0.912761i	−0.0837279	−	0.996489i	$-0.526683\pi$
$563$	12193.3	−	12193.3i	0.912761	−	0.912761i	0.996489	+	0.0837279i	$0.0266827\pi$
$564$		0			0
$565$	−3908.78	−	3908.78i	−0.291051	−	0.291051i
$566$		0			0
$567$			1191.42i			0.0882452i
$568$		0			0
$569$			4990.14i			0.367659i	0.982958	+	0.183829i	$0.0588494\pi$
$569$			4990.14i			0.367659i	−0.982958	+	0.183829i	$0.941151\pi$
$570$		0			0
$571$	−6896.58	−	6896.58i	−0.505451	−	0.505451i	0.407676	−	0.913127i	$-0.366339\pi$
$571$	−6896.58	−	6896.58i	−0.505451	−	0.505451i	−0.913127	+	0.407676i	$0.866339\pi$
$572$		0			0
$573$	−615.211	+	615.211i	−0.0448530	+	0.0448530i
$574$		0			0
$575$	22738.9			1.64918
$576$		0			0
$577$	−12824.7			−0.925299			−0.462649	−	0.886541i	$-0.653101\pi$
$577$	−12824.7			−0.925299			−0.462649	+	0.886541i	$0.653101\pi$
$578$		0			0
$579$	−9113.07	+	9113.07i	−0.654104	+	0.654104i
$580$		0			0
$581$	−13626.0	−	13626.0i	−0.972984	−	0.972984i
$582$		0			0
$583$		−	7785.88i		−	0.553102i
$584$		0			0
$585$		−	12318.4i		−	0.870605i
$586$		0			0
$587$	−15610.1	−	15610.1i	−1.09761	−	1.09761i	−0.994690	−	0.102920i	$-0.967181\pi$
$587$	−15610.1	−	15610.1i	−1.09761	−	1.09761i	−0.102920	−	0.994690i	$-0.532819\pi$
$588$		0			0
$589$	1535.04	−	1535.04i	0.107385	−	0.107385i
$590$		0			0
$591$	3974.04			0.276599
$592$		0			0
$593$	16469.9			1.14054			0.570268	−	0.821458i	$-0.306839\pi$
$593$	16469.9			1.14054			0.570268	+	0.821458i	$0.306839\pi$
$594$		0			0
$595$	13138.8	−	13138.8i	0.905272	−	0.905272i
$596$		0			0
$597$	7070.74	+	7070.74i	0.484734	+	0.484734i
$598$		0			0
$599$			10220.6i			0.697164i	0.937278	+	0.348582i	$0.113337\pi$
$599$			10220.6i			0.697164i	−0.937278	+	0.348582i	$0.886663\pi$
$600$		0			0
$601$			16286.3i			1.10538i	0.833387	+	0.552690i	$0.186399\pi$
$601$			16286.3i			1.10538i	−0.833387	+	0.552690i	$0.813601\pi$
$602$		0			0
$603$	2696.60	+	2696.60i	0.182113	+	0.182113i
$604$		0			0
$605$	−1026.43	+	1026.43i	−0.0689760	+	0.0689760i
$606$		0			0
$607$	21362.6			1.42847			0.714235	−	0.699906i	$-0.246775\pi$
$607$	21362.6			1.42847			0.714235	+	0.699906i	$0.246775\pi$
$608$		0			0
$609$	−3029.24			−0.201562
$610$		0			0
$611$	2705.69	−	2705.69i	0.179150	−	0.179150i
$612$		0			0
$613$	1189.98	+	1189.98i	0.0784057	+	0.0784057i	0.745222	−	0.666816i	$-0.232343\pi$
$613$	1189.98	+	1189.98i	0.0784057	+	0.0784057i	−0.666816	+	0.745222i	$0.732343\pi$
$614$		0			0
$615$			11249.0i			0.737566i
$616$		0			0
$617$		−	1361.21i		−	0.0888173i	−0.999013	−	0.0444087i	$-0.985860\pi$
$617$		−	1361.21i		−	0.0888173i	0.999013	−	0.0444087i	$-0.0141404\pi$
$618$		0			0
$619$	5468.68	+	5468.68i	0.355097	+	0.355097i	0.862002	−	0.506905i	$-0.169211\pi$
$619$	5468.68	+	5468.68i	0.355097	+	0.355097i	−0.506905	+	0.862002i	$0.669211\pi$
$620$		0			0
$621$	−2853.16	+	2853.16i	−0.184369	+	0.184369i
$622$		0			0
$623$	5159.44			0.331796
$624$		0			0
$625$	11492.9			0.735543
$626$		0			0
$627$	−5485.50	+	5485.50i	−0.349393	+	0.349393i
$628$		0			0
$629$	11211.3	+	11211.3i	0.710690	+	0.710690i
$630$		0			0
$631$		−	11369.6i		−	0.717303i	−0.933472	−	0.358651i	$-0.883237\pi$
$631$		−	11369.6i		−	0.717303i	0.933472	−	0.358651i	$-0.116763\pi$
$632$		0			0
$633$		−	16168.7i		−	1.01524i
$634$		0			0
$635$	8392.79	+	8392.79i	0.524500	+	0.524500i
$636$		0			0
$637$	−7362.60	+	7362.60i	−0.457954	+	0.457954i
$638$		0			0
$639$	−6245.39			−0.386641
$640$		0			0
$641$	9280.18			0.571833			0.285917	−	0.958255i	$-0.407702\pi$
$641$	9280.18			0.571833			0.285917	+	0.958255i	$0.407702\pi$
$642$		0			0
$643$	9377.81	−	9377.81i	0.575155	−	0.575155i	−0.358409	−	0.933565i	$-0.616681\pi$
$643$	9377.81	−	9377.81i	0.575155	−	0.575155i	0.933565	+	0.358409i	$0.116681\pi$
$644$		0			0
$645$	4083.63	+	4083.63i	0.249291	+	0.249291i
$646$		0			0
$647$			1950.32i			0.118508i	0.998243	+	0.0592542i	$0.0188723\pi$
$647$			1950.32i			0.118508i	−0.998243	+	0.0592542i	$0.981128\pi$
$648$		0			0
$649$			11880.4i			0.718562i
$650$		0			0
$651$	923.820	+	923.820i	0.0556180	+	0.0556180i
$652$		0			0
$653$	−8699.36	+	8699.36i	−0.521336	+	0.521336i	−0.917975	−	0.396639i	$-0.870177\pi$
$653$	−8699.36	+	8699.36i	−0.521336	+	0.521336i	0.396639	+	0.917975i	$0.370177\pi$
$654$		0			0
$655$	−48020.9			−2.86463
$656$		0			0
$657$	−4162.01			−0.247147
$658$		0			0
$659$	−7958.47	+	7958.47i	−0.470437	+	0.470437i	−0.902056	−	0.431619i	$-0.857942\pi$
$659$	−7958.47	+	7958.47i	−0.470437	+	0.470437i	0.431619	+	0.902056i	$0.357942\pi$
$660$		0			0
$661$	7483.62	+	7483.62i	0.440362	+	0.440362i	0.892134	−	0.451772i	$-0.149208\pi$
$661$	7483.62	+	7483.62i	0.440362	+	0.440362i	−0.451772	+	0.892134i	$0.649208\pi$
$662$		0			0
$663$		−	18715.3i		−	1.09629i
$664$		0			0
$665$		−	17954.7i		−	1.04700i
$666$		0			0
$667$	−7254.28	−	7254.28i	−0.421120	−	0.421120i
$668$		0			0
$669$	6561.82	−	6561.82i	0.379215	−	0.379215i
$670$		0			0
$671$	−29627.0			−1.70452
$672$		0			0
$673$	3592.82			0.205785			0.102892	−	0.994692i	$-0.467190\pi$
$673$	3592.82			0.205785			0.102892	+	0.994692i	$0.467190\pi$
$674$		0			0
$675$	2904.97	−	2904.97i	0.165648	−	0.165648i
$676$		0			0
$677$	−16494.8	−	16494.8i	−0.936408	−	0.936408i	0.0616872	−	0.998096i	$-0.480352\pi$
$677$	−16494.8	−	16494.8i	−0.936408	−	0.936408i	−0.998096	+	0.0616872i	$0.980352\pi$
$678$		0			0
$679$			11269.9i			0.636964i
$680$		0			0
$681$			413.789i			0.0232840i
$682$		0			0
$683$	−20875.1	−	20875.1i	−1.16949	−	1.16949i	−0.982328	−	0.187166i	$-0.940070\pi$
$683$	−20875.1	−	20875.1i	−1.16949	−	1.16949i	−0.187166	−	0.982328i	$-0.559930\pi$
$684$		0			0
$685$	−8961.36	+	8961.36i	−0.499848	+	0.499848i
$686$		0			0
$687$	12163.8			0.675515
$688$		0			0
$689$	18150.2			1.00358
$690$		0			0
$691$	−22267.3	+	22267.3i	−1.22589	+	1.22589i	−0.260382	+	0.965506i	$0.583849\pi$
$691$	−22267.3	+	22267.3i	−1.22589	+	1.22589i	−0.965506	+	0.260382i	$0.916151\pi$
$692$		0			0
$693$	−3301.30	−	3301.30i	−0.180961	−	0.180961i
$694$		0			0
$695$			30087.2i			1.64212i
$696$		0			0
$697$			17090.5i			0.928765i
$698$		0			0
$699$	−552.357	−	552.357i	−0.0298885	−	0.0298885i
$700$		0			0
$701$	−12419.0	+	12419.0i	−0.669129	+	0.669129i	−0.957515	−	0.288385i	$-0.906882\pi$
$701$	−12419.0	+	12419.0i	−0.669129	+	0.669129i	0.288385	+	0.957515i	$0.406882\pi$
$702$		0			0
$703$	15320.7			0.821950
$704$		0			0
$705$	2324.49			0.124178
$706$		0			0
$707$	−14473.5	+	14473.5i	−0.769918	+	0.769918i
$708$		0			0
$709$	−17027.9	−	17027.9i	−0.901970	−	0.901970i	0.0936362	−	0.995606i	$-0.470151\pi$
$709$	−17027.9	−	17027.9i	−0.901970	−	0.901970i	−0.995606	+	0.0936362i	$0.970151\pi$
$710$		0			0
$711$		−	7909.17i		−	0.417183i
$712$		0			0
$713$			4424.64i			0.232404i
$714$		0			0
$715$	34132.9	+	34132.9i	1.78531	+	1.78531i
$716$		0			0
$717$	−2404.79	+	2404.79i	−0.125256	+	0.125256i
$718$		0			0
$719$	−9987.52			−0.518041			−0.259021	−	0.965872i	$-0.583400\pi$
$719$	−9987.52			−0.518041			−0.259021	+	0.965872i	$0.583400\pi$
$720$		0			0
$721$	7535.25			0.389220
$722$		0			0
$723$	5765.00	−	5765.00i	0.296546	−	0.296546i
$724$		0			0
$725$	7385.99	+	7385.99i	0.378357	+	0.378357i
$726$		0			0
$727$		−	18495.4i		−	0.943545i	−0.881720	−	0.471772i	$-0.843614\pi$
$727$		−	18495.4i		−	0.943545i	0.881720	−	0.471772i	$-0.156386\pi$
$728$		0			0
$729$			729.000i			0.0370370i
$730$		0			0
$731$	6204.24	+	6204.24i	0.313915	+	0.313915i
$732$		0			0
$733$	3852.08	−	3852.08i	0.194106	−	0.194106i	−0.603362	−	0.797468i	$-0.706172\pi$
$733$	3852.08	−	3852.08i	0.194106	−	0.194106i	0.797468	+	0.603362i	$0.206172\pi$
$734$		0			0
$735$	−6325.30			−0.317432
$736$		0			0
$737$	−14944.0			−0.746904
$738$		0			0
$739$	−16168.9	+	16168.9i	−0.804846	+	0.804846i	−0.983849	−	0.179003i	$-0.942713\pi$
$739$	−16168.9	+	16168.9i	−0.804846	+	0.804846i	0.179003	+	0.983849i	$0.442713\pi$
$740$		0			0
$741$	−12787.6	−	12787.6i	−0.633959	−	0.633959i
$742$		0			0
$743$		−	36990.3i		−	1.82644i	−0.407471	−	0.913218i	$-0.633589\pi$
$743$		−	36990.3i		−	1.82644i	0.407471	−	0.913218i	$-0.366411\pi$
$744$		0			0
$745$		−	17579.1i		−	0.864492i
$746$		0			0
$747$	−8337.42	−	8337.42i	−0.408367	−	0.408367i
$748$		0			0
$749$	−9312.18	+	9312.18i	−0.454285	+	0.454285i
$750$		0			0
$751$	10125.3			0.491981			0.245990	−	0.969272i	$-0.420887\pi$
$751$	10125.3			0.491981			0.245990	+	0.969272i	$0.420887\pi$
$752$		0			0
$753$	−3828.98			−0.185307
$754$		0			0
$755$	−13962.8	+	13962.8i	−0.673059	+	0.673059i
$756$		0			0
$757$	−8998.60	−	8998.60i	−0.432047	−	0.432047i	0.457277	−	0.889324i	$-0.348825\pi$
$757$	−8998.60	−	8998.60i	−0.432047	−	0.432047i	−0.889324	+	0.457277i	$0.848825\pi$
$758$		0			0
$759$		−	15811.6i		−	0.756158i
$760$		0			0
$761$			25265.9i			1.20353i	0.798672	+	0.601766i	$0.205536\pi$
$761$			25265.9i			1.20353i	−0.798672	+	0.601766i	$0.794464\pi$
$762$		0			0
$763$	−14472.0	−	14472.0i	−0.686661	−	0.686661i
$764$		0			0
$765$	8039.27	−	8039.27i	0.379948	−	0.379948i
$766$		0			0
$767$	−27695.2			−1.30380
$768$		0			0
$769$	−28077.3			−1.31664			−0.658318	−	0.752740i	$-0.728732\pi$
$769$	−28077.3			−1.31664			−0.658318	+	0.752740i	$0.728732\pi$
$770$		0			0
$771$	−104.099	+	104.099i	−0.00486257	+	0.00486257i
$772$		0			0
$773$	−8413.75	−	8413.75i	−0.391490	−	0.391490i	0.483728	−	0.875218i	$-0.339282\pi$
$773$	−8413.75	−	8413.75i	−0.391490	−	0.391490i	−0.875218	+	0.483728i	$0.839282\pi$
$774$		0			0
$775$		−	4504.97i		−	0.208804i
$776$		0			0
$777$			9220.35i			0.425712i
$778$		0			0
$779$	11677.4	+	11677.4i	0.537083	+	0.537083i
$780$		0			0
$781$	17305.3	−	17305.3i	0.792870	−	0.792870i
$782$		0			0
$783$	−1853.51			−0.0845966
$784$		0			0
$785$	−5165.89			−0.234877
$786$		0			0
$787$	−8677.71	+	8677.71i	−0.393046	+	0.393046i	−0.875772	−	0.482726i	$-0.839647\pi$
$787$	−8677.71	+	8677.71i	−0.393046	+	0.393046i	0.482726	+	0.875772i	$0.339647\pi$
$788$		0			0
$789$	−951.088	−	951.088i	−0.0429146	−	0.0429146i
$790$		0			0
$791$		−	4883.98i		−	0.219538i
$792$		0			0
$793$		−	69065.3i		−	3.09279i
$794$		0			0
$795$	7796.52	+	7796.52i	0.347816	+	0.347816i
$796$		0			0
$797$	16951.1	−	16951.1i	0.753374	−	0.753374i	−0.221733	−	0.975107i	$-0.571171\pi$
$797$	16951.1	−	16951.1i	0.753374	−	0.753374i	0.975107	+	0.221733i	$0.0711715\pi$
$798$		0			0
$799$	3531.58			0.156369
$800$		0			0
$801$	3156.93			0.139257
$802$		0			0
$803$	11532.5	−	11532.5i	0.506814	−	0.506814i
$804$		0			0
$805$	25876.5	+	25876.5i	1.13295	+	1.13295i
$806$		0			0
$807$			19902.3i			0.868145i
$808$		0			0
$809$			39305.4i			1.70816i	0.520138	+	0.854082i	$0.325880\pi$
$809$			39305.4i			1.70816i	−0.520138	+	0.854082i	$0.674120\pi$
$810$		0			0
$811$	−25524.4	−	25524.4i	−1.10516	−	1.10516i	−0.993778	−	0.111378i	$-0.964474\pi$
$811$	−25524.4	−	25524.4i	−1.10516	−	1.10516i	−0.111378	−	0.993778i	$-0.535526\pi$
$812$		0			0
$813$	−658.072	+	658.072i	−0.0283882	+	0.0283882i
$814$		0			0
$815$	31112.9			1.33722
$816$		0			0
$817$	8478.34			0.363059
$818$		0			0
$819$	7695.87	−	7695.87i	0.328346	−	0.328346i
$820$		0			0
$821$	−20817.5	−	20817.5i	−0.884939	−	0.884939i	0.109093	−	0.994032i	$-0.465206\pi$
$821$	−20817.5	−	20817.5i	−0.884939	−	0.884939i	−0.994032	+	0.109093i	$0.965206\pi$
$822$		0			0
$823$			8625.74i			0.365339i	0.983174	+	0.182670i	$0.0584739\pi$
$823$			8625.74i			0.365339i	−0.983174	+	0.182670i	$0.941526\pi$
$824$		0			0
$825$			16098.7i			0.679374i
$826$		0			0
$827$	16592.0	+	16592.0i	0.697654	+	0.697654i	0.963904	−	0.266250i	$-0.0857848\pi$
$827$	16592.0	+	16592.0i	0.697654	+	0.697654i	−0.266250	+	0.963904i	$0.585785\pi$
$828$		0			0
$829$	−11523.3	+	11523.3i	−0.482777	+	0.482777i	−0.906018	−	0.423240i	$-0.860893\pi$
$829$	−11523.3	+	11523.3i	−0.482777	+	0.482777i	0.423240	+	0.906018i	$0.360893\pi$
$830$		0			0
$831$	14948.6			0.624022
$832$		0			0
$833$	−9609.99			−0.399720
$834$		0			0
$835$	13900.7	−	13900.7i	0.576112	−	0.576112i
$836$		0			0
$837$	565.261	+	565.261i	0.0233432	+	0.0233432i
$838$		0			0
$839$		−	1709.60i		−	0.0703482i	−0.999381	−	0.0351741i	$-0.988801\pi$
$839$		−	1709.60i		−	0.0703482i	0.999381	−	0.0351741i	$-0.0111986\pi$
$840$		0			0
$841$			19676.4i			0.806772i
$842$		0			0
$843$	2905.66	+	2905.66i	0.118714	+	0.118714i
$844$		0			0
$845$	−53706.5	+	53706.5i	−2.18646	+	2.18646i
$846$		0			0
$847$	−1282.52			−0.0520282
$848$		0			0
$849$	23653.4			0.956165
$850$		0			0
$851$	−22080.4	+	22080.4i	−0.889433	+	0.889433i
$852$		0			0
$853$	−27950.1	−	27950.1i	−1.12191	−	1.12191i	−0.991453	−	0.130462i	$-0.958354\pi$
$853$	−27950.1	−	27950.1i	−1.12191	−	1.12191i	−0.130462	−	0.991453i	$-0.541646\pi$
$854$		0			0
$855$		−	10986.0i		−	0.439430i
$856$		0			0
$857$			20208.0i			0.805477i	0.915315	+	0.402739i	$0.131942\pi$
$857$			20208.0i			0.805477i	−0.915315	+	0.402739i	$0.868058\pi$
$858$		0			0
$859$	6906.75	+	6906.75i	0.274337	+	0.274337i	0.830843	−	0.556507i	$-0.187859\pi$
$859$	6906.75	+	6906.75i	0.274337	+	0.274337i	−0.556507	+	0.830843i	$0.687859\pi$
$860$		0			0
$861$	−7027.75	+	7027.75i	−0.278171	+	0.278171i
$862$		0			0
$863$	−16342.0			−0.644599			−0.322300	−	0.946638i	$-0.604456\pi$
$863$	−16342.0			−0.644599			−0.322300	+	0.946638i	$0.604456\pi$
$864$		0			0
$865$	36713.1			1.44310
$866$		0			0
$867$	1791.96	−	1791.96i	0.0701939	−	0.0701939i
$868$		0			0
$869$	21915.4	+	21915.4i	0.855501	+	0.855501i
$870$		0			0
$871$		−	34836.9i		−	1.35523i
$872$		0			0
$873$			6895.75i			0.267338i
$874$		0			0
$875$	−4702.32	−	4702.32i	−0.181677	−	0.181677i
$876$		0			0
$877$	517.041	−	517.041i	0.0199079	−	0.0199079i	−0.697083	−	0.716991i	$-0.745519\pi$
$877$	517.041	−	517.041i	0.0199079	−	0.0199079i	0.716991	+	0.697083i	$0.245519\pi$
$878$		0			0
$879$	−7005.31			−0.268809
$880$		0			0
$881$	−22171.2			−0.847861			−0.423931	−	0.905695i	$-0.639350\pi$
$881$	−22171.2			−0.847861			−0.423931	+	0.905695i	$0.639350\pi$
$882$		0			0
$883$	−589.293	+	589.293i	−0.0224590	+	0.0224590i	−0.718247	−	0.695788i	$-0.755055\pi$
$883$	−589.293	+	589.293i	−0.0224590	+	0.0224590i	0.695788	+	0.718247i	$0.255055\pi$
$884$		0			0
$885$	−11896.6	−	11896.6i	−0.451866	−	0.451866i
$886$		0			0
$887$		−	13685.0i		−	0.518034i	−0.965873	−	0.259017i	$-0.916601\pi$
$887$		−	13685.0i		−	0.518034i	0.965873	−	0.259017i	$-0.0833985\pi$
$888$		0			0
$889$			10486.7i			0.395627i
$890$		0			0
$891$	−2019.98	−	2019.98i	−0.0759504	−	0.0759504i
$892$		0			0
$893$	2413.03	−	2413.03i	0.0904242	−	0.0904242i
$894$		0			0
$895$	40467.9			1.51139
$896$		0			0
$897$	36859.4			1.37202
$898$		0			0
$899$	−1437.20	+	1437.20i	−0.0533184	+	0.0533184i
$900$		0			0
$901$	11845.2	+	11845.2i	0.437981	+	0.437981i
$902$		0			0
$903$			5102.46i			0.188039i
$904$		0			0
$905$		−	16570.2i		−	0.608634i
$906$		0			0
$907$	32330.9	+	32330.9i	1.18361	+	1.18361i	0.978803	+	0.204804i	$0.0656557\pi$
$907$	32330.9	+	32330.9i	1.18361	+	1.18361i	0.204804	+	0.978803i	$0.434344\pi$
$908$		0			0
$909$	−8855.95	+	8855.95i	−0.323139	+	0.323139i
$910$		0			0
$911$	36436.3			1.32513			0.662563	−	0.749006i	$-0.269469\pi$
$911$	36436.3			1.32513			0.662563	+	0.749006i	$0.269469\pi$
$912$		0			0
$913$	46204.1			1.67484
$914$		0			0
$915$	29667.4	−	29667.4i	1.07189	−	1.07189i
$916$		0			0
$917$	−30000.8	−	30000.8i	−1.08039	−	1.08039i
$918$		0			0
$919$		−	18351.8i		−	0.658726i	−0.944203	−	0.329363i	$-0.893166\pi$
$919$		−	18351.8i		−	0.658726i	0.944203	−	0.329363i	$-0.106834\pi$
$920$		0			0
$921$		−	8190.45i		−	0.293034i
$922$		0			0
$923$	40341.4	+	40341.4i	1.43863	+	1.43863i
$924$		0			0
$925$	22481.4	−	22481.4i	0.799116	−	0.799116i
$926$		0			0
$927$	4610.62			0.163358
$928$		0			0
$929$	25908.3			0.914989			0.457495	−	0.889212i	$-0.348747\pi$
$929$	25908.3			0.914989			0.457495	+	0.889212i	$0.348747\pi$
$930$		0			0
$931$	−6566.22	+	6566.22i	−0.231148	+	0.231148i
$932$		0			0
$933$	8415.58	+	8415.58i	0.295299	+	0.295299i
$934$		0			0
$935$			44551.8i			1.55829i
$936$		0			0
$937$		−	41822.4i		−	1.45814i	−0.684438	−	0.729071i	$-0.739953\pi$
$937$		−	41822.4i		−	1.45814i	0.684438	−	0.729071i	$-0.260047\pi$
$938$		0			0
$939$	−15548.1	−	15548.1i	−0.540356	−	0.540356i
$940$		0			0
$941$	35805.6	−	35805.6i	1.24041	−	1.24041i	0.280585	−	0.959829i	$-0.409471\pi$
$941$	35805.6	−	35805.6i	1.24041	−	1.24041i	0.959829	−	0.280585i	$-0.0905285\pi$
$942$		0			0
$943$	−33659.4			−1.16236
$944$		0			0
$945$	6611.62			0.227594
$946$		0			0
$947$	−4833.07	+	4833.07i	−0.165844	+	0.165844i	−0.785150	−	0.619306i	$-0.787414\pi$
$947$	−4833.07	+	4833.07i	−0.165844	+	0.165844i	0.619306	+	0.785150i	$0.287414\pi$
$948$		0			0
$949$	26884.1	+	26884.1i	0.919593	+	0.919593i
$950$		0			0
$951$			13851.6i			0.472312i
$952$		0			0
$953$		−	54695.5i		−	1.85914i	−0.368645	−	0.929570i	$-0.620178\pi$
$953$		−	54695.5i		−	1.85914i	0.368645	−	0.929570i	$-0.379822\pi$
$954$		0			0
$955$	3414.02	+	3414.02i	0.115681	+	0.115681i
$956$		0			0
$957$	5135.87	−	5135.87i	0.173479	−	0.173479i
$958$		0			0
$959$	−11197.1			−0.377033
$960$		0			0
$961$	−28914.4			−0.970575
$962$		0			0
$963$	−5697.88	+	5697.88i	−0.190666	+	0.190666i
$964$		0			0
$965$	50571.6	+	50571.6i	1.68700	+	1.68700i
$966$		0			0
$967$			11587.6i			0.385350i	0.981263	+	0.192675i	$0.0617163\pi$
$967$			11587.6i			0.385350i	−0.981263	+	0.192675i	$0.938284\pi$
$968$		0			0
$969$		−	16690.9i		−	0.553343i
$970$		0			0
$971$	−36545.7	−	36545.7i	−1.20784	−	1.20784i	−0.971727	−	0.236109i	$-0.924128\pi$
$971$	−36545.7	−	36545.7i	−1.20784	−	1.20784i	−0.236109	−	0.971727i	$-0.575872\pi$
$972$		0			0
$973$	−18796.8	+	18796.8i	−0.619321	+	0.619321i
$974$		0			0
$975$	−37528.6			−1.23270
$976$		0			0
$977$	11161.4			0.365490			0.182745	−	0.983160i	$-0.441502\pi$
$977$	11161.4			0.365490			0.182745	+	0.983160i	$0.441502\pi$
$978$		0			0
$979$	−8747.49	+	8747.49i	−0.285568	+	0.285568i
$980$		0			0
$981$	−8855.05	−	8855.05i	−0.288196	−	0.288196i
$982$		0			0
$983$		−	52855.9i		−	1.71500i	−0.514486	−	0.857499i	$-0.672017\pi$
$983$		−	52855.9i		−	1.71500i	0.514486	−	0.857499i	$-0.327983\pi$
$984$		0			0
$985$		−	22053.3i		−	0.713378i
$986$		0			0
$987$	1452.21	+	1452.21i	0.0468333	+	0.0468333i
$988$		0			0
$989$	−12219.1	+	12219.1i	−0.392867	+	0.392867i
$990$		0			0
$991$	50245.9			1.61061			0.805305	−	0.592861i	$-0.202002\pi$
$991$	50245.9			1.61061			0.805305	+	0.592861i	$0.202002\pi$
$992$		0			0
$993$	−32415.2			−1.03592
$994$		0			0
$995$	39238.0	−	39238.0i	1.25018	−	1.25018i
$996$		0			0
$997$	−3886.25	−	3886.25i	−0.123449	−	0.123449i	0.642683	−	0.766132i	$-0.277821\pi$
$997$	−3886.25	−	3886.25i	−0.123449	−	0.123449i	−0.766132	+	0.642683i	$0.777821\pi$
$998$		0			0
$999$			5641.69i			0.178674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.4.j.a.49.7		24
3.2	odd	2		576.4.k.b.433.11		24
4.3	odd	2		48.4.j.a.37.6	yes	24
8.3	odd	2		384.4.j.b.97.12		24
8.5	even	2		384.4.j.a.97.1		24
12.11	even	2		144.4.k.b.37.7		24
16.3	odd	4		48.4.j.a.13.6	✓	24
16.5	even	4		384.4.j.a.289.1		24
16.11	odd	4		384.4.j.b.289.12		24
16.13	even	4	inner	192.4.j.a.145.7		24
48.29	odd	4		576.4.k.b.145.11		24
48.35	even	4		144.4.k.b.109.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.6	✓	24	16.3	odd	4
48.4.j.a.37.6	yes	24	4.3	odd	2
144.4.k.b.37.7		24	12.11	even	2
144.4.k.b.109.7		24	48.35	even	4
192.4.j.a.49.7		24	1.1	even	1	trivial
192.4.j.a.145.7		24	16.13	even	4	inner
384.4.j.a.97.1		24	8.5	even	2
384.4.j.a.289.1		24	16.5	even	4
384.4.j.b.97.12		24	8.3	odd	2
384.4.j.b.289.12		24	16.11	odd	4
576.4.k.b.145.11		24	48.29	odd	4
576.4.k.b.433.11		24	3.2	odd	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.12132 - 2.12132i) q^{3} +(-11.7719 - 11.7719i) q^{5} -14.7089i q^{7} -9.00000i q^{9} +(24.9380 + 24.9380i) q^{11} +(-58.1345 + 58.1345i) q^{13} -49.9441 q^{15} -75.8798 q^{17} +(-51.8464 + 51.8464i) q^{19} +(-31.2023 - 31.2023i) q^{21} -149.444i q^{23} +152.157i q^{25} +(-19.0919 - 19.0919i) q^{27} +(48.5419 - 48.5419i) q^{29} -29.6074 q^{31} +105.803 q^{33} +(-173.153 + 173.153i) q^{35} +(-147.751 - 147.751i) q^{37} +246.644i q^{39} -225.232i q^{41} +(-81.7640 - 81.7640i) q^{43} +(-105.947 + 105.947i) q^{45} -46.5418 q^{47} +126.648 q^{49} +(-160.965 + 160.965i) q^{51} +(-156.105 - 156.105i) q^{53} -587.137i q^{55} +219.965i q^{57} +(238.199 + 238.199i) q^{59} +(-594.013 + 594.013i) q^{61} -132.380 q^{63} +1368.71 q^{65} +(-299.623 + 299.623i) q^{67} +(-317.018 - 317.018i) q^{69} -693.932i q^{71} -462.446i q^{73} +(322.774 + 322.774i) q^{75} +(366.811 - 366.811i) q^{77} +878.797 q^{79} -81.0000 q^{81} +(926.380 - 926.380i) q^{83} +(893.252 + 893.252i) q^{85} -205.946i q^{87} +350.770i q^{89} +(855.096 + 855.096i) q^{91} +(-62.8068 + 62.8068i) q^{93} +1220.66 q^{95} -766.194 q^{97} +(224.442 - 224.442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 40 q^{11} - 120 q^{15} - 24 q^{19} + 400 q^{29} + 744 q^{31} + 456 q^{35} + 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} + 752 q^{53} + 1376 q^{59} - 912 q^{61} + 504 q^{63} + 976 q^{65} + 2256 q^{67}+ \cdots + 360 q^{99}+O(q^{100}) \) 24 * q + 40 * q^11 - 120 * q^15 - 24 * q^19 + 400 * q^29 + 744 * q^31 + 456 * q^35 + 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 + 752 * q^53 + 1376 * q^59 - 912 * q^61 + 504 * q^63 + 976 * q^65 + 2256 * q^67 - 528 * q^69 - 1104 * q^75 + 1904 * q^77 - 5992 * q^79 - 1944 * q^81 - 2680 * q^83 - 240 * q^85 + 3496 * q^91 + 7728 * q^95 + 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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