LMFDB - Embedded newform 14.16.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,16,Mod(1,14)] 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("14.1"); S:= CuspForms(chi, 16); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 16, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-128] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$19.9770907140$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-128.000 q^{2} +1350.00 q^{3} +16384.0 q^{4} -81060.0 q^{5} -172800. q^{6} +823543. q^{7} -2.09715e6 q^{8} -1.25264e7 q^{9} +1.03757e7 q^{10} +7.01212e7 q^{11} +2.21184e7 q^{12} +1.51470e8 q^{13} -1.05414e8 q^{14} -1.09431e8 q^{15} +2.68435e8 q^{16} -2.49757e8 q^{17} +1.60338e9 q^{18} -6.47686e9 q^{19} -1.32809e9 q^{20} +1.11178e9 q^{21} -8.97551e9 q^{22} -2.11292e10 q^{23} -2.83116e9 q^{24} -2.39469e10 q^{25} -1.93881e10 q^{26} -3.62817e10 q^{27} +1.34929e10 q^{28} +7.79483e9 q^{29} +1.40072e10 q^{30} -9.50321e10 q^{31} -3.43597e10 q^{32} +9.46636e10 q^{33} +3.19688e10 q^{34} -6.67564e10 q^{35} -2.05233e11 q^{36} -8.70082e11 q^{37} +8.29038e11 q^{38} +2.04484e11 q^{39} +1.69995e11 q^{40} +1.00767e12 q^{41} -1.42308e11 q^{42} +1.55008e11 q^{43} +1.14887e12 q^{44} +1.01539e12 q^{45} +2.70454e12 q^{46} -2.55197e12 q^{47} +3.62388e11 q^{48} +6.78223e11 q^{49} +3.06520e12 q^{50} -3.37171e11 q^{51} +2.48168e12 q^{52} +4.04765e12 q^{53} +4.64405e12 q^{54} -5.68402e12 q^{55} -1.72709e12 q^{56} -8.74376e12 q^{57} -9.97738e11 q^{58} -1.25992e13 q^{59} -1.79292e12 q^{60} -3.99250e13 q^{61} +1.21641e13 q^{62} -1.03160e13 q^{63} +4.39805e12 q^{64} -1.22781e13 q^{65} -1.21169e13 q^{66} -4.84238e13 q^{67} -4.09201e12 q^{68} -2.85244e13 q^{69} +8.54482e12 q^{70} +3.76931e13 q^{71} +2.62698e13 q^{72} +1.41416e14 q^{73} +1.11371e14 q^{74} -3.23283e13 q^{75} -1.06117e14 q^{76} +5.77478e13 q^{77} -2.61739e13 q^{78} +2.47021e14 q^{79} -2.17594e13 q^{80} +1.30760e14 q^{81} -1.28981e14 q^{82} +2.78879e12 q^{83} +1.82155e13 q^{84} +2.02453e13 q^{85} -1.98410e13 q^{86} +1.05230e13 q^{87} -1.47055e14 q^{88} -5.83963e12 q^{89} -1.29970e14 q^{90} +1.24742e14 q^{91} -3.46181e14 q^{92} -1.28293e14 q^{93} +3.26652e14 q^{94} +5.25014e14 q^{95} -4.63856e13 q^{96} +2.78027e14 q^{97} -8.68126e13 q^{98} -8.78366e14 q^{99} +O(q^{100})\)

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 $

$2$	−128.000	−0.707107
$2$	−128.000	−0.707107
$3$	1350.00	0.356389	0.178195	−	0.983995i	$-0.442974\pi$
$3$	1350.00	0.356389	0.178195	+	0.983995i	$0.442974\pi$
$4$	16384.0	0.500000
$5$	−81060.0	−0.464015	−0.232007	−	0.972714i	$-0.574529\pi$
$5$	−81060.0	−0.464015	−0.232007	+	0.972714i	$0.574529\pi$
$6$	−172800.	−0.252005
$7$	823543.	0.377964
$7$	823543.	0.377964
$8$	−2.09715e6	−0.353553
$9$	−1.25264e7	−0.872987
$10$	1.03757e7	0.328108
$11$	7.01212e7	1.08494	0.542468	−	0.840076i	$-0.317490\pi$
$11$	7.01212e7	1.08494	0.542468	+	0.840076i	$0.317490\pi$
$12$	2.21184e7	0.178195
$13$	1.51470e8	0.669499	0.334750	−	0.942307i	$-0.391348\pi$
$13$	1.51470e8	0.669499	0.334750	+	0.942307i	$0.391348\pi$
$14$	−1.05414e8	−0.267261
$15$	−1.09431e8	−0.165370
$16$	2.68435e8	0.250000
$17$	−2.49757e8	−0.147622	−0.0738108	−	0.997272i	$-0.523516\pi$
$17$	−2.49757e8	−0.147622	−0.0738108	+	0.997272i	$0.523516\pi$
$18$	1.60338e9	0.617295
$19$	−6.47686e9	−1.66231	−0.831155	−	0.556040i	$-0.812320\pi$
$19$	−6.47686e9	−1.66231	−0.831155	+	0.556040i	$0.812320\pi$
$20$	−1.32809e9	−0.232007
$21$	1.11178e9	0.134702
$22$	−8.97551e9	−0.767166
$23$	−2.11292e10	−1.29397	−0.646985	−	0.762503i	$-0.723970\pi$
$23$	−2.11292e10	−1.29397	−0.646985	+	0.762503i	$0.723970\pi$
$24$	−2.83116e9	−0.126003
$25$	−2.39469e10	−0.784691
$26$	−1.93881e10	−0.473408
$27$	−3.62817e10	−0.667512
$28$	1.34929e10	0.188982
$29$	7.79483e9	0.0839115	0.0419557	−	0.999119i	$-0.486641\pi$
$29$	7.79483e9	0.0839115	0.0419557	+	0.999119i	$0.486641\pi$
$30$	1.40072e10	0.116934
$31$	−9.50321e10	−0.620379	−0.310190	−	0.950675i	$-0.600393\pi$
$31$	−9.50321e10	−0.620379	−0.310190	+	0.950675i	$0.600393\pi$
$32$	−3.43597e10	−0.176777
$33$	9.46636e10	0.386659
$34$	3.19688e10	0.104384
$35$	−6.67564e10	−0.175381
$36$	−2.05233e11	−0.436493
$37$	−8.70082e11	−1.50677	−0.753386	−	0.657579i	$-0.771581\pi$
$37$	−8.70082e11	−1.50677	−0.753386	+	0.657579i	$0.771581\pi$
$38$	8.29038e11	1.17543
$39$	2.04484e11	0.238602
$40$	1.69995e11	0.164054
$41$	1.00767e12	0.808049	0.404025	−	0.914748i	$-0.367611\pi$
$41$	1.00767e12	0.808049	0.404025	+	0.914748i	$0.367611\pi$
$42$	−1.42308e11	−0.0952490
$43$	1.55008e11	0.0869640	0.0434820	−	0.999054i	$-0.486155\pi$
$43$	1.55008e11	0.0869640	0.0434820	+	0.999054i	$0.486155\pi$
$44$	1.14887e12	0.542468
$45$	1.01539e12	0.405079
$46$	2.70454e12	0.914975
$47$	−2.55197e12	−0.734753	−0.367377	−	0.930072i	$-0.619744\pi$
$47$	−2.55197e12	−0.734753	−0.367377	+	0.930072i	$0.619744\pi$
$48$	3.62388e11	0.0890973
$49$	6.78223e11	0.142857
$50$	3.06520e12	0.554860
$51$	−3.37171e11	−0.0526107
$52$	2.48168e12	0.334750
$53$	4.04765e12	0.473297	0.236648	−	0.971595i	$-0.423951\pi$
$53$	4.04765e12	0.473297	0.236648	+	0.971595i	$0.423951\pi$
$54$	4.64405e12	0.472002
$55$	−5.68402e12	−0.503426
$56$	−1.72709e12	−0.133631
$57$	−8.74376e12	−0.592429
$58$	−9.97738e11	−0.0593344
$59$	−1.25992e13	−0.659105	−0.329552	−	0.944137i	$-0.606898\pi$
$59$	−1.25992e13	−0.659105	−0.329552	+	0.944137i	$0.606898\pi$
$60$	−1.79292e12	−0.0826848
$61$	−3.99250e13	−1.62657	−0.813283	−	0.581869i	$-0.802322\pi$
$61$	−3.99250e13	−1.62657	−0.813283	+	0.581869i	$0.802322\pi$
$62$	1.21641e13	0.438675
$63$	−1.03160e13	−0.329958
$64$	4.39805e12	0.125000
$65$	−1.22781e13	−0.310657
$66$	−1.21169e13	−0.273409
$67$	−4.84238e13	−0.976108	−0.488054	−	0.872814i	$-0.662293\pi$
$67$	−4.84238e13	−0.976108	−0.488054	+	0.872814i	$0.662293\pi$
$68$	−4.09201e12	−0.0738108
$69$	−2.85244e13	−0.461157
$70$	8.54482e12	0.124013
$71$	3.76931e13	0.491840	0.245920	−	0.969290i	$-0.420910\pi$
$71$	3.76931e13	0.491840	0.245920	+	0.969290i	$0.420910\pi$
$72$	2.62698e13	0.308647
$73$	1.41416e14	1.49823	0.749114	−	0.662442i	$-0.230480\pi$
$73$	1.41416e14	1.49823	0.749114	+	0.662442i	$0.230480\pi$
$74$	1.11371e14	1.06545
$75$	−3.23283e13	−0.279655
$76$	−1.06117e14	−0.831155
$77$	5.77478e13	0.410067
$78$	−2.61739e13	−0.168717
$79$	2.47021e14	1.44720	0.723602	−	0.690217i	$-0.242485\pi$
$79$	2.47021e14	1.44720	0.723602	+	0.690217i	$0.242485\pi$
$80$	−2.17594e13	−0.116004
$81$	1.30760e14	0.635093
$82$	−1.28981e14	−0.571377
$83$	2.78879e12	0.0112805	0.00564027	−	0.999984i	$-0.498205\pi$
$83$	2.78879e12	0.0112805	0.00564027	+	0.999984i	$0.498205\pi$
$84$	1.82155e13	0.0673512
$85$	2.02453e13	0.0684986
$86$	−1.98410e13	−0.0614928
$87$	1.05230e13	0.0299051
$88$	−1.47055e14	−0.383583
$89$	−5.83963e12	−0.0139946	−0.00699730	−	0.999976i	$-0.502227\pi$
$89$	−5.83963e12	−0.0139946	−0.00699730	+	0.999976i	$0.502227\pi$
$90$	−1.29970e14	−0.286434
$91$	1.24742e14	0.253047
$92$	−3.46181e14	−0.646985
$93$	−1.28293e14	−0.221096
$94$	3.26652e14	0.519549
$95$	5.25014e14	0.771336
$96$	−4.63856e13	−0.0630013
$97$	2.78027e14	0.349381	0.174690	−	0.984623i	$-0.444108\pi$
$97$	2.78027e14	0.349381	0.174690	+	0.984623i	$0.444108\pi$
$98$	−8.68126e13	−0.101015
$99$	−8.78366e14	−0.947135
$100$	−3.92345e14	−0.392345
$101$	1.59112e14	0.147670	0.0738350	−	0.997270i	$-0.476476\pi$
$101$	1.59112e14	0.147670	0.0738350	+	0.997270i	$0.476476\pi$
$102$	4.31579e13	0.0372014
$103$	−1.70968e15	−1.36973	−0.684864	−	0.728671i	$-0.740138\pi$
$103$	−1.70968e15	−1.36973	−0.684864	+	0.728671i	$0.740138\pi$
$104$	−3.17655e14	−0.236704
$105$	−9.01211e13	−0.0625039
$106$	−5.18099e14	−0.334671
$107$	2.16914e15	1.30590	0.652950	−	0.757401i	$-0.273531\pi$
$107$	2.16914e15	1.30590	0.652950	+	0.757401i	$0.273531\pi$
$108$	−5.94439e14	−0.333756
$109$	−8.01543e14	−0.419979	−0.209990	−	0.977704i	$-0.567343\pi$
$109$	−8.01543e14	−0.419979	−0.209990	+	0.977704i	$0.567343\pi$
$110$	7.27555e14	0.355976
$111$	−1.17461e15	−0.536997
$112$	2.21068e14	0.0944911
$113$	−1.94568e15	−0.778008	−0.389004	−	0.921236i	$-0.627181\pi$
$113$	−1.94568e15	−0.778008	−0.389004	+	0.921236i	$0.627181\pi$
$114$	1.11920e15	0.418911
$115$	1.71273e15	0.600421
$116$	1.27710e14	0.0419557
$117$	−1.89737e15	−0.584464
$118$	1.61270e15	0.466058
$119$	−2.05685e14	−0.0557957
$120$	2.29493e14	0.0584670
$121$	7.39732e14	0.177086
$122$	5.11040e15	1.15016
$123$	1.36035e15	0.287980
$124$	−1.55701e15	−0.310190
$125$	4.41489e15	0.828122
$126$	1.32045e15	0.233316
$127$	−9.42390e14	−0.156929	−0.0784645	−	0.996917i	$-0.525002\pi$
$127$	−9.42390e14	−0.156929	−0.0784645	+	0.996917i	$0.525002\pi$
$128$	−5.62950e14	−0.0883883
$129$	2.09260e14	0.0309930
$130$	1.57160e15	0.219668
$131$	1.11917e16	1.47693	0.738467	−	0.674289i	$-0.235550\pi$
$131$	1.11917e16	1.47693	0.738467	+	0.674289i	$0.235550\pi$
$132$	1.55097e15	0.193330
$133$	−5.33397e15	−0.628294
$134$	6.19824e15	0.690212
$135$	2.94099e15	0.309735
$136$	5.23777e14	0.0521921
$137$	−1.52428e16	−1.43768	−0.718839	−	0.695177i	$-0.755326\pi$
$137$	−1.52428e16	−1.43768	−0.718839	+	0.695177i	$0.755326\pi$
$138$	3.65113e15	0.326087
$139$	−2.30670e16	−1.95155	−0.975775	−	0.218775i	$-0.929794\pi$
$139$	−2.30670e16	−1.95155	−0.975775	+	0.218775i	$0.929794\pi$
$140$	−1.09374e15	−0.0876905
$141$	−3.44516e15	−0.261858
$142$	−4.82472e15	−0.347784
$143$	1.06212e16	0.726364
$144$	−3.36253e15	−0.218247
$145$	−6.31849e14	−0.0389361
$146$	−1.81013e16	−1.05941
$147$	9.15601e14	0.0509127
$148$	−1.42554e16	−0.753386
$149$	−5.22922e15	−0.262748	−0.131374	−	0.991333i	$-0.541939\pi$
$149$	−5.22922e15	−0.262748	−0.131374	+	0.991333i	$0.541939\pi$
$150$	4.13802e15	0.197746
$151$	−1.02631e16	−0.466605	−0.233303	−	0.972404i	$-0.574953\pi$
$151$	−1.02631e16	−0.466605	−0.233303	+	0.972404i	$0.574953\pi$
$152$	1.35830e16	0.587716
$153$	3.12855e15	0.128872
$154$	−7.39172e15	−0.289961
$155$	7.70330e15	0.287865
$156$	3.35026e15	0.119301
$157$	2.60653e16	0.884739	0.442369	−	0.896833i	$-0.354138\pi$
$157$	2.60653e16	0.884739	0.442369	+	0.896833i	$0.354138\pi$
$158$	−3.16186e16	−1.02333
$159$	5.46432e15	0.168678
$160$	2.78520e15	0.0820270
$161$	−1.74008e16	−0.489075
$162$	−1.67373e16	−0.449078
$163$	4.28113e16	1.09686	0.548431	−	0.836196i	$-0.315226\pi$
$163$	4.28113e16	1.09686	0.548431	+	0.836196i	$0.315226\pi$
$164$	1.65096e16	0.404025
$165$	−7.67343e15	−0.179416
$166$	−3.56965e14	−0.00797655
$167$	4.85639e16	1.03738	0.518692	−	0.854961i	$-0.326419\pi$
$167$	4.85639e16	1.03738	0.518692	+	0.854961i	$0.326419\pi$
$168$	−2.33158e15	−0.0476245
$169$	−2.82429e16	−0.551771
$170$	−2.59139e15	−0.0484358
$171$	8.11317e16	1.45118
$172$	2.53964e15	0.0434820
$173$	9.78932e16	1.60475	0.802374	−	0.596822i	$-0.203570\pi$
$173$	9.78932e16	1.60475	0.802374	+	0.596822i	$0.203570\pi$
$174$	−1.34695e15	−0.0211461
$175$	−1.97213e16	−0.296585
$176$	1.88230e16	0.271234
$177$	−1.70090e16	−0.234898
$178$	7.47473e14	0.00989568
$179$	−7.28657e16	−0.924965	−0.462483	−	0.886628i	$-0.653041\pi$
$179$	−7.28657e16	−0.924965	−0.462483	+	0.886628i	$0.653041\pi$
$180$	1.66362e16	0.202539
$181$	−4.51786e16	−0.527647	−0.263823	−	0.964571i	$-0.584984\pi$
$181$	−4.51786e16	−0.527647	−0.263823	+	0.964571i	$0.584984\pi$
$182$	−1.59669e16	−0.178931
$183$	−5.38988e16	−0.579690
$184$	4.43111e16	0.457487
$185$	7.05289e16	0.699164
$186$	1.64215e16	0.156339
$187$	−1.75132e16	−0.160160
$188$	−4.18115e16	−0.367377
$189$	−2.98795e16	−0.252296
$190$	−6.72018e16	−0.545417
$191$	1.15946e17	0.904699	0.452350	−	0.891841i	$-0.350586\pi$
$191$	1.15946e17	0.904699	0.452350	+	0.891841i	$0.350586\pi$
$192$	5.93736e15	0.0445486
$193$	−2.40107e17	−1.73271	−0.866354	−	0.499431i	$-0.833542\pi$
$193$	−2.40107e17	−1.73271	−0.866354	+	0.499431i	$0.833542\pi$
$194$	−3.55875e16	−0.247050
$195$	−1.65755e16	−0.110715
$196$	1.11120e16	0.0714286
$197$	−3.08577e17	−1.90927	−0.954634	−	0.297783i	$-0.903753\pi$
$197$	−3.08577e17	−1.90927	−0.954634	+	0.297783i	$0.903753\pi$
$198$	1.12431e17	0.669725
$199$	3.11535e17	1.78693	0.893466	−	0.449130i	$-0.148266\pi$
$199$	3.11535e17	1.78693	0.893466	+	0.449130i	$0.148266\pi$
$200$	5.02202e16	0.277430
$201$	−6.53721e16	−0.347874
$202$	−2.03663e16	−0.104419
$203$	6.41937e15	0.0317156
$204$	−5.52422e15	−0.0263054
$205$	−8.16815e16	−0.374947
$206$	2.18838e17	0.968544
$207$	2.64673e17	1.12962
$208$	4.06598e16	0.167375
$209$	−4.54165e17	−1.80350
$210$	1.15355e16	0.0441969
$211$	−3.71643e17	−1.37407	−0.687033	−	0.726626i	$-0.741087\pi$
$211$	−3.71643e17	−1.37407	−0.687033	+	0.726626i	$0.741087\pi$
$212$	6.63166e16	0.236648
$213$	5.08857e16	0.175287
$214$	−2.77650e17	−0.923410
$215$	−1.25649e16	−0.0403526
$216$	7.60882e16	0.236001
$217$	−7.82630e16	−0.234481
$218$	1.02597e17	0.296970
$219$	1.90912e17	0.533952
$220$	−9.31270e16	−0.251713
$221$	−3.78305e16	−0.0988326
$222$	1.50350e17	0.379714
$223$	−7.62007e15	−0.0186068	−0.00930341	−	0.999957i	$-0.502961\pi$
$223$	−7.62007e15	−0.0186068	−0.00930341	+	0.999957i	$0.502961\pi$
$224$	−2.82967e16	−0.0668153
$225$	2.99968e17	0.685025
$226$	2.49048e17	0.550135
$227$	7.15322e17	1.52865	0.764324	−	0.644832i	$-0.223073\pi$
$227$	7.15322e17	1.52865	0.764324	+	0.644832i	$0.223073\pi$
$228$	−1.43258e17	−0.296215
$229$	−3.85984e17	−0.772331	−0.386166	−	0.922429i	$-0.626201\pi$
$229$	−3.85984e17	−0.772331	−0.386166	+	0.922429i	$0.626201\pi$
$230$	−2.19230e17	−0.424562
$231$	7.79595e16	0.146143
$232$	−1.63469e16	−0.0296672
$233$	7.08260e17	1.24458	0.622290	−	0.782786i	$-0.286202\pi$
$233$	7.08260e17	1.24458	0.622290	+	0.782786i	$0.286202\pi$
$234$	2.42863e17	0.413279
$235$	2.06863e17	0.340936
$236$	−2.06426e17	−0.329552
$237$	3.33478e17	0.515768
$238$	2.63277e16	0.0394535
$239$	4.09559e17	0.594747	0.297373	−	0.954761i	$-0.403889\pi$
$239$	4.09559e17	0.594747	0.297373	+	0.954761i	$0.403889\pi$
$240$	−2.93752e16	−0.0413424
$241$	−9.94946e16	−0.135729	−0.0678643	−	0.997695i	$-0.521619\pi$
$241$	−9.94946e16	−0.135729	−0.0678643	+	0.997695i	$0.521619\pi$
$242$	−9.46857e16	−0.125219
$243$	6.97128e17	0.893852
$244$	−6.54132e17	−0.813283
$245$	−5.49768e16	−0.0662878
$246$	−1.74125e17	−0.203633
$247$	−9.81047e17	−1.11292
$248$	1.99297e17	0.219337
$249$	3.76487e15	0.00402026
$250$	−5.65106e17	−0.585571
$251$	1.04654e18	1.05246	0.526228	−	0.850344i	$-0.323606\pi$
$251$	1.04654e18	1.05246	0.526228	+	0.850344i	$0.323606\pi$
$252$	−1.69018e17	−0.164979
$253$	−1.48160e18	−1.40387
$254$	1.20626e17	0.110965
$255$	2.73311e16	0.0244121
$256$	7.20576e16	0.0625000
$257$	−1.38920e18	−1.17021	−0.585106	−	0.810957i	$-0.698947\pi$
$257$	−1.38920e18	−1.17021	−0.585106	+	0.810957i	$0.698947\pi$
$258$	−2.67853e16	−0.0219154
$259$	−7.16550e17	−0.569506
$260$	−2.01165e17	−0.155329
$261$	−9.76412e16	−0.0732536
$262$	−1.43254e18	−1.04435
$263$	4.64879e17	0.329361	0.164680	−	0.986347i	$-0.447341\pi$
$263$	4.64879e17	0.329361	0.164680	+	0.986347i	$0.447341\pi$
$264$	−1.98524e17	−0.136705
$265$	−3.28102e17	−0.219617
$266$	6.82748e17	0.444271
$267$	−7.88351e15	−0.00498752
$268$	−7.93375e17	−0.488054
$269$	−6.09641e17	−0.364697	−0.182348	−	0.983234i	$-0.558370\pi$
$269$	−6.09641e17	−0.364697	−0.182348	+	0.983234i	$0.558370\pi$
$270$	−3.76447e17	−0.219016
$271$	1.79864e18	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$271$	1.79864e18	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$272$	−6.70435e16	−0.0369054
$273$	1.68401e17	0.0901832
$274$	1.95108e18	1.01659
$275$	−1.67918e18	−0.851339
$276$	−4.67344e17	−0.230578
$277$	−6.65764e17	−0.319685	−0.159842	−	0.987143i	$-0.551099\pi$
$277$	−6.65764e17	−0.319685	−0.159842	+	0.987143i	$0.551099\pi$
$278$	2.95257e18	1.37995
$279$	1.19041e18	0.541583
$280$	1.39998e17	0.0620065
$281$	3.07586e18	1.32638	0.663191	−	0.748450i	$-0.269202\pi$
$281$	3.07586e18	1.32638	0.663191	+	0.748450i	$0.269202\pi$
$282$	4.40980e17	0.185162
$283$	−2.28687e18	−0.935066	−0.467533	−	0.883976i	$-0.654857\pi$
$283$	−2.28687e18	−0.935066	−0.467533	+	0.883976i	$0.654857\pi$
$284$	6.17564e17	0.245920
$285$	7.08769e17	0.274896
$286$	−1.35952e18	−0.513617
$287$	8.29857e17	0.305414
$288$	4.30404e17	0.154324
$289$	−2.80004e18	−0.978208
$290$	8.08766e16	0.0275320
$291$	3.75337e17	0.124516
$292$	2.31696e18	0.749114
$293$	6.01478e18	1.89545	0.947726	−	0.319086i	$-0.103376\pi$
$293$	6.01478e18	1.89545	0.947726	+	0.319086i	$0.103376\pi$
$294$	−1.17197e17	−0.0360007
$295$	1.02130e18	0.305834
$296$	1.82469e18	0.532724
$297$	−2.54411e18	−0.724208
$298$	6.69340e17	0.185791
$299$	−3.20043e18	−0.866312
$300$	−5.29666e17	−0.139828
$301$	1.27655e17	0.0328693
$302$	1.31367e18	0.329940
$303$	2.14801e17	0.0526280
$304$	−1.73862e18	−0.415578
$305$	3.23632e18	0.754750
$306$	−4.00455e17	−0.0911261
$307$	4.78608e17	0.106278	0.0531388	−	0.998587i	$-0.483077\pi$
$307$	4.78608e17	0.106278	0.0531388	+	0.998587i	$0.483077\pi$
$308$	9.46140e17	0.205034
$309$	−2.30806e18	−0.488156
$310$	−9.86022e17	−0.203551
$311$	−7.55326e18	−1.52206	−0.761030	−	0.648717i	$-0.775306\pi$
$311$	−7.55326e18	−1.52206	−0.761030	+	0.648717i	$0.775306\pi$
$312$	−4.28834e17	−0.0843586
$313$	−3.06006e18	−0.587688	−0.293844	−	0.955853i	$-0.594935\pi$
$313$	−3.06006e18	−0.587688	−0.293844	+	0.955853i	$0.594935\pi$
$314$	−3.33636e18	−0.625605
$315$	8.36218e17	0.153105
$316$	4.04718e18	0.723602
$317$	−3.99150e18	−0.696934	−0.348467	−	0.937321i	$-0.613298\pi$
$317$	−3.99150e18	−0.696934	−0.348467	+	0.937321i	$0.613298\pi$
$318$	−6.99433e17	−0.119273
$319$	5.46582e17	0.0910386
$320$	−3.56506e17	−0.0580018
$321$	2.92834e18	0.465408
$322$	2.22730e18	0.345828
$323$	1.61764e18	0.245393
$324$	2.14237e18	0.317546
$325$	−3.62722e18	−0.525350
$326$	−5.47985e18	−0.775598
$327$	−1.08208e18	−0.149676
$328$	−2.11323e18	−0.285689
$329$	−2.10166e18	−0.277711
$330$	9.82199e17	0.126866
$331$	−6.58270e18	−0.831179	−0.415589	−	0.909552i	$-0.636425\pi$
$331$	−6.58270e18	−0.831179	−0.415589	+	0.909552i	$0.636425\pi$
$332$	4.56915e16	0.00564027
$333$	1.08990e19	1.31539
$334$	−6.21618e18	−0.733542
$335$	3.92523e18	0.452928
$336$	2.98442e17	0.0336756
$337$	8.40974e18	0.928022	0.464011	−	0.885829i	$-0.346410\pi$
$337$	8.40974e18	0.928022	0.464011	+	0.885829i	$0.346410\pi$
$338$	3.61509e18	0.390161
$339$	−2.62667e18	−0.277273
$340$	3.31698e17	0.0342493
$341$	−6.66376e18	−0.673072
$342$	−1.03849e19	−1.02614
$343$	5.58546e17	0.0539949
$344$	−3.25074e17	−0.0307464
$345$	2.31219e18	0.213983
$346$	−1.25303e19	−1.13473
$347$	7.42259e18	0.657785	0.328893	−	0.944367i	$-0.393325\pi$
$347$	7.42259e18	0.657785	0.328893	+	0.944367i	$0.393325\pi$
$348$	1.72409e17	0.0149526
$349$	1.87993e19	1.59570	0.797850	−	0.602856i	$-0.205971\pi$
$349$	1.87993e19	1.59570	0.797850	+	0.602856i	$0.205971\pi$
$350$	2.52432e18	0.209717
$351$	−5.49557e18	−0.446899
$352$	−2.40935e18	−0.191791
$353$	7.98787e18	0.622473	0.311237	−	0.950332i	$-0.399257\pi$
$353$	7.98787e18	0.622473	0.311237	+	0.950332i	$0.399257\pi$
$354$	2.17715e18	0.166098
$355$	−3.05540e18	−0.228221
$356$	−9.56766e16	−0.00699730
$357$	−2.77675e17	−0.0198850
$358$	9.32681e18	0.654049
$359$	−2.19394e19	−1.50666	−0.753332	−	0.657640i	$-0.771555\pi$
$359$	−2.19394e19	−1.50666	−0.753332	+	0.657640i	$0.771555\pi$
$360$	−2.12943e18	−0.143217
$361$	2.67685e19	1.76328
$362$	5.78286e18	0.373103
$363$	9.98639e17	0.0631115
$364$	2.04377e18	0.126523
$365$	−1.14632e19	−0.695199
$366$	6.89905e18	0.409903
$367$	2.74267e19	1.59654	0.798268	−	0.602302i	$-0.205750\pi$
$367$	2.74267e19	1.59654	0.798268	+	0.602302i	$0.205750\pi$
$368$	−5.67183e18	−0.323492
$369$	−1.26224e19	−0.705417
$370$	−9.02770e18	−0.494384
$371$	3.33341e18	0.178889
$372$	−2.10196e18	−0.110548
$373$	2.29342e19	1.18214	0.591068	−	0.806622i	$-0.298706\pi$
$373$	2.29342e19	1.18214	0.591068	+	0.806622i	$0.298706\pi$
$374$	2.24169e18	0.113250
$375$	5.96010e18	0.295134
$376$	5.35187e18	0.259775
$377$	1.18068e18	0.0561787
$378$	3.82458e18	0.178400
$379$	−3.03498e19	−1.38791	−0.693955	−	0.720018i	$-0.744133\pi$
$379$	−3.03498e19	−1.38791	−0.693955	+	0.720018i	$0.744133\pi$
$380$	8.60183e18	0.385668
$381$	−1.27223e18	−0.0559277
$382$	−1.48410e19	−0.639719
$383$	−2.47308e19	−1.04532	−0.522659	−	0.852542i	$-0.675060\pi$
$383$	−2.47308e19	−1.04532	−0.522659	+	0.852542i	$0.675060\pi$
$384$	−7.59982e17	−0.0315006
$385$	−4.68104e18	−0.190277
$386$	3.07337e19	1.22521
$387$	−1.94169e18	−0.0759184
$388$	4.55520e18	0.174690
$389$	−3.78552e19	−1.42398	−0.711989	−	0.702190i	$-0.752206\pi$
$389$	−3.78552e19	−1.42398	−0.711989	+	0.702190i	$0.752206\pi$
$390$	2.12166e18	0.0782873
$391$	5.27716e18	0.191018
$392$	−1.42234e18	−0.0505076
$393$	1.51088e19	0.526363
$394$	3.94978e19	1.35006
$395$	−2.00235e19	−0.671524
$396$	−1.43912e19	−0.473567
$397$	5.34934e19	1.72731	0.863657	−	0.504080i	$-0.168168\pi$
$397$	5.34934e19	1.72731	0.863657	+	0.504080i	$0.168168\pi$
$398$	−3.98764e19	−1.26355
$399$	−7.20086e18	−0.223917
$400$	−6.42818e18	−0.196173
$401$	−4.98878e19	−1.49421	−0.747105	−	0.664706i	$-0.768557\pi$
$401$	−4.98878e19	−1.49421	−0.747105	+	0.664706i	$0.768557\pi$
$402$	8.36763e18	0.245984
$403$	−1.43945e19	−0.415344
$404$	2.60689e18	0.0738350
$405$	−1.05994e19	−0.294692
$406$	−8.21680e17	−0.0224263
$407$	−6.10112e19	−1.63475
$408$	7.07100e17	0.0186007
$409$	8.75158e18	0.226028	0.113014	−	0.993593i	$-0.463950\pi$
$409$	8.75158e18	0.226028	0.113014	+	0.993593i	$0.463950\pi$
$410$	1.04552e19	0.265127
$411$	−2.05778e19	−0.512372
$412$	−2.80113e19	−0.684864
$413$	−1.03760e19	−0.249118
$414$	−3.38781e19	−0.798761
$415$	−2.26059e17	−0.00523434
$416$	−5.20445e18	−0.118352
$417$	−3.11404e19	−0.695511
$418$	5.81331e19	1.27527
$419$	5.18994e19	1.11830	0.559148	−	0.829068i	$-0.311128\pi$
$419$	5.18994e19	1.11830	0.559148	+	0.829068i	$0.311128\pi$
$420$	−1.47654e18	−0.0312519
$421$	1.64745e19	0.342528	0.171264	−	0.985225i	$-0.445215\pi$
$421$	1.64745e19	0.342528	0.171264	+	0.985225i	$0.445215\pi$
$422$	4.75703e19	0.971612
$423$	3.19670e19	0.641430
$424$	−8.48853e18	−0.167336
$425$	5.98088e18	0.115837
$426$	−6.51337e18	−0.123946
$427$	−3.28800e19	−0.614784
$428$	3.55392e19	0.652950
$429$	1.43387e19	0.258868
$430$	1.60831e18	0.0285336
$431$	2.94589e18	0.0513614	0.0256807	−	0.999670i	$-0.491825\pi$
$431$	2.94589e18	0.0513614	0.0256807	+	0.999670i	$0.491825\pi$
$432$	−9.73929e18	−0.166878
$433$	5.16768e19	0.870234	0.435117	−	0.900374i	$-0.356707\pi$
$433$	5.16768e19	0.870234	0.435117	+	0.900374i	$0.356707\pi$
$434$	1.00177e19	0.165803
$435$	−8.52996e17	−0.0138764
$436$	−1.31325e19	−0.209990
$437$	1.36851e20	2.15098
$438$	−2.44367e19	−0.377561
$439$	8.39088e19	1.27445	0.637226	−	0.770677i	$-0.280082\pi$
$439$	8.39088e19	1.27445	0.637226	+	0.770677i	$0.280082\pi$
$440$	1.19203e19	0.177988
$441$	−8.49570e18	−0.124712
$442$	4.84231e18	0.0698852
$443$	7.29528e19	1.03518	0.517588	−	0.855630i	$-0.326830\pi$
$443$	7.29528e19	1.03518	0.517588	+	0.855630i	$0.326830\pi$
$444$	−1.92448e19	−0.268498
$445$	4.73361e17	0.00649370
$446$	9.75368e17	0.0131570
$447$	−7.05945e18	−0.0936406
$448$	3.62198e18	0.0472456
$449$	−9.36146e19	−1.20087	−0.600435	−	0.799673i	$-0.705006\pi$
$449$	−9.36146e19	−1.20087	−0.600435	+	0.799673i	$0.705006\pi$
$450$	−3.83959e19	−0.484385
$451$	7.06588e19	0.876682
$452$	−3.18781e19	−0.389004
$453$	−1.38551e19	−0.166293
$454$	−9.15612e19	−1.08092
$455$	−1.01116e19	−0.117417
$456$	1.83370e19	0.209455
$457$	−7.61708e19	−0.855889	−0.427944	−	0.903805i	$-0.640762\pi$
$457$	−7.61708e19	−0.855889	−0.427944	+	0.903805i	$0.640762\pi$
$458$	4.94060e19	0.546121
$459$	9.06159e18	0.0985392
$460$	2.80614e19	0.300210
$461$	−1.23736e20	−1.30238	−0.651192	−	0.758913i	$-0.725731\pi$
$461$	−1.23736e20	−1.30238	−0.651192	+	0.758913i	$0.725731\pi$
$462$	−9.97882e18	−0.103339
$463$	1.35828e19	0.138399	0.0691993	−	0.997603i	$-0.477956\pi$
$463$	1.35828e19	0.138399	0.0691993	+	0.997603i	$0.477956\pi$
$464$	2.09241e18	0.0209779
$465$	1.03995e19	0.102592
$466$	−9.06572e19	−0.880052
$467$	5.50577e18	0.0525947	0.0262973	−	0.999654i	$-0.491628\pi$
$467$	5.50577e18	0.0525947	0.0262973	+	0.999654i	$0.491628\pi$
$468$	−3.10865e19	−0.292232
$469$	−3.98791e19	−0.368934
$470$	−2.64784e19	−0.241078
$471$	3.51881e19	0.315311
$472$	2.64225e19	0.233029
$473$	1.08693e19	0.0943504
$474$	−4.26851e19	−0.364703
$475$	1.55100e20	1.30440
$476$	−3.36995e18	−0.0278979
$477$	−5.07025e19	−0.413182
$478$	−5.24235e19	−0.420550
$479$	−9.96289e18	−0.0786809	−0.0393404	−	0.999226i	$-0.512526\pi$
$479$	−9.96289e18	−0.0786809	−0.0393404	+	0.999226i	$0.512526\pi$
$480$	3.76002e18	0.0292335
$481$	−1.31791e20	−1.00878
$482$	1.27353e19	0.0959747
$483$	−2.34911e19	−0.174301
$484$	1.21198e19	0.0885430
$485$	−2.25369e19	−0.162118
$486$	−8.92324e19	−0.632049
$487$	−9.48341e19	−0.661451	−0.330725	−	0.943727i	$-0.607293\pi$
$487$	−9.48341e19	−0.661451	−0.330725	+	0.943727i	$0.607293\pi$
$488$	8.37289e19	0.575078
$489$	5.77953e19	0.390909
$490$	7.03703e18	0.0468725
$491$	−9.79269e18	−0.0642378	−0.0321189	−	0.999484i	$-0.510226\pi$
$491$	−9.79269e18	−0.0642378	−0.0321189	+	0.999484i	$0.510226\pi$
$492$	2.22880e19	0.143990
$493$	−1.94681e18	−0.0123871
$494$	1.25574e20	0.786951
$495$	7.12004e19	0.439484
$496$	−2.55100e19	−0.155095
$497$	3.10419e19	0.185898
$498$	−4.81903e17	−0.00284275
$499$	2.29903e19	0.133595	0.0667976	−	0.997767i	$-0.478722\pi$
$499$	2.29903e19	0.133595	0.0667976	+	0.997767i	$0.478722\pi$
$500$	7.23335e19	0.414061
$501$	6.55612e19	0.369712
$502$	−1.33957e20	−0.744198
$503$	−1.80850e20	−0.989824	−0.494912	−	0.868943i	$-0.664800\pi$
$503$	−1.80850e20	−0.989824	−0.494912	+	0.868943i	$0.664800\pi$
$504$	2.16343e19	0.116658
$505$	−1.28976e19	−0.0685211
$506$	1.89645e20	0.992689
$507$	−3.81279e19	−0.196645
$508$	−1.54401e19	−0.0784645
$509$	−2.41838e20	−1.21099	−0.605495	−	0.795849i	$-0.707025\pi$
$509$	−2.41838e20	−1.21099	−0.605495	+	0.795849i	$0.707025\pi$
$510$	−3.49838e18	−0.0172620
$511$	1.16462e20	0.566277
$512$	−9.22337e18	−0.0441942
$513$	2.34991e20	1.10961
$514$	1.77817e20	0.827465
$515$	1.38586e20	0.635574
$516$	3.42852e18	0.0154965
$517$	−1.78947e20	−0.797160
$518$	9.17184e19	0.402702
$519$	1.32156e20	0.571915
$520$	2.57491e19	0.109834
$521$	−4.08212e20	−1.71634	−0.858170	−	0.513365i	$-0.828399\pi$
$521$	−4.08212e20	−1.71634	−0.858170	+	0.513365i	$0.828399\pi$
$522$	1.24981e19	0.0517981
$523$	1.04211e20	0.425747	0.212874	−	0.977080i	$-0.431718\pi$
$523$	1.04211e20	0.425747	0.212874	+	0.977080i	$0.431718\pi$
$524$	1.83365e20	0.738467
$525$	−2.66237e19	−0.105700
$526$	−5.95045e19	−0.232893
$527$	2.37349e19	0.0915814
$528$	2.54111e19	0.0966648
$529$	1.79808e20	0.674358
$530$	4.19971e19	0.155292
$531$	1.57823e20	0.575390
$532$	−8.73918e19	−0.314147
$533$	1.52631e20	0.540989
$534$	1.00909e18	0.00352671
$535$	−1.75831e20	−0.605956
$536$	1.01552e20	0.345106
$537$	−9.83687e19	−0.329648
$538$	7.80341e19	0.257880
$539$	4.75578e19	0.154991
$540$	4.81852e19	0.154868
$541$	−3.30898e20	−1.04885	−0.524426	−	0.851456i	$-0.675720\pi$
$541$	−3.30898e20	−1.04885	−0.524426	+	0.851456i	$0.675720\pi$
$542$	−2.30225e20	−0.719712
$543$	−6.09911e19	−0.188048
$544$	8.58157e18	0.0260961
$545$	6.49731e19	0.194877
$546$	−2.15554e19	−0.0637691
$547$	−1.38512e20	−0.404188	−0.202094	−	0.979366i	$-0.564775\pi$
$547$	−1.38512e20	−0.404188	−0.202094	+	0.979366i	$0.564775\pi$
$548$	−2.49739e20	−0.718839
$549$	5.00117e20	1.41997
$550$	2.14935e20	0.601988
$551$	−5.04860e19	−0.139487
$552$	5.98200e19	0.163044
$553$	2.03432e20	0.546992
$554$	8.52178e19	0.226051
$555$	9.52140e19	0.249174
$556$	−3.77929e20	−0.975775
$557$	−1.99131e19	−0.0507254	−0.0253627	−	0.999678i	$-0.508074\pi$
$557$	−1.99131e19	−0.0507254	−0.0253627	+	0.999678i	$0.508074\pi$
$558$	−1.52373e20	−0.382957
$559$	2.34789e19	0.0582224
$560$	−1.79198e19	−0.0438453
$561$	−2.36429e19	−0.0570793
$562$	−3.93709e20	−0.937893
$563$	−3.18834e20	−0.749466	−0.374733	−	0.927133i	$-0.622266\pi$
$563$	−3.18834e20	−0.749466	−0.374733	+	0.927133i	$0.622266\pi$
$564$	−5.64455e19	−0.130929
$565$	1.57717e20	0.361007
$566$	2.92719e20	0.661192
$567$	1.07686e20	0.240043
$568$	−7.90482e19	−0.173892
$569$	−7.58166e20	−1.64597	−0.822986	−	0.568061i	$-0.807694\pi$
$569$	−7.58166e20	−1.64597	−0.822986	+	0.568061i	$0.807694\pi$
$570$	−9.07224e19	−0.194381
$571$	−2.32331e20	−0.491288	−0.245644	−	0.969360i	$-0.578999\pi$
$571$	−2.32331e20	−0.491288	−0.245644	+	0.969360i	$0.578999\pi$
$572$	1.74018e20	0.363182
$573$	1.56527e20	0.322425
$574$	−1.06222e20	−0.215960
$575$	5.05978e20	1.01537
$576$	−5.50917e19	−0.109123
$577$	−8.20976e20	−1.60514	−0.802568	−	0.596560i	$-0.796534\pi$
$577$	−8.20976e20	−1.60514	−0.802568	+	0.596560i	$0.796534\pi$
$578$	3.58406e20	0.691697
$579$	−3.24145e20	−0.617518
$580$	−1.03522e19	−0.0194681
$581$	2.29669e18	0.00426365
$582$	−4.80431e19	−0.0880458
$583$	2.83826e20	0.513497
$584$	−2.96571e20	−0.529703
$585$	1.53801e20	0.271200
$586$	−7.69892e20	−1.34029
$587$	−4.63376e19	−0.0796431	−0.0398215	−	0.999207i	$-0.512679\pi$
$587$	−4.63376e19	−0.0796431	−0.0398215	+	0.999207i	$0.512679\pi$
$588$	1.50012e19	0.0254564
$589$	6.15509e20	1.03126
$590$	−1.30726e20	−0.216257
$591$	−4.16579e20	−0.680442
$592$	−2.33561e20	−0.376693
$593$	7.13658e20	1.13653	0.568264	−	0.822846i	$-0.307615\pi$
$593$	7.13658e20	1.13653	0.568264	+	0.822846i	$0.307615\pi$
$594$	3.25647e20	0.512092
$595$	1.66728e19	0.0258900
$596$	−8.56756e19	−0.131374
$597$	4.20572e20	0.636843
$598$	4.09655e20	0.612575
$599$	6.12330e20	0.904241	0.452120	−	0.891957i	$-0.350668\pi$
$599$	6.12330e20	0.904241	0.452120	+	0.891957i	$0.350668\pi$
$600$	6.77973e19	0.0988730
$601$	−7.54383e20	−1.08651	−0.543254	−	0.839568i	$-0.682808\pi$
$601$	−7.54383e20	−1.08651	−0.543254	+	0.839568i	$0.682808\pi$
$602$	−1.63399e19	−0.0232421
$603$	6.06576e20	0.852129
$604$	−1.68150e20	−0.233303
$605$	−5.99627e19	−0.0821705
$606$	−2.74945e19	−0.0372136
$607$	3.80950e20	0.509276	0.254638	−	0.967036i	$-0.418044\pi$
$607$	3.80950e20	0.509276	0.254638	+	0.967036i	$0.418044\pi$
$608$	2.22543e20	0.293858
$609$	8.66615e18	0.0113031
$610$	−4.14249e20	−0.533689
$611$	−3.86546e20	−0.491917
$612$	5.12582e19	0.0644359
$613$	5.14778e19	0.0639243	0.0319622	−	0.999489i	$-0.489824\pi$
$613$	5.14778e19	0.0639243	0.0319622	+	0.999489i	$0.489824\pi$
$614$	−6.12618e19	−0.0751497
$615$	−1.10270e20	−0.133627
$616$	−1.21106e20	−0.144981
$617$	1.63289e21	1.93116	0.965579	−	0.260110i	$-0.0837588\pi$
$617$	1.63289e21	1.93116	0.965579	+	0.260110i	$0.0837588\pi$
$618$	2.95432e20	0.345179
$619$	1.04021e20	0.120072	0.0600358	−	0.998196i	$-0.480879\pi$
$619$	1.04021e20	0.120072	0.0600358	+	0.998196i	$0.480879\pi$
$620$	1.26211e20	0.143933
$621$	7.66603e20	0.863741
$622$	9.66817e20	1.07626
$623$	−4.80919e18	−0.00528946
$624$	5.48907e19	0.0596506
$625$	3.72929e20	0.400430
$626$	3.91687e20	0.415558
$627$	−6.13123e20	−0.642748
$628$	4.27054e20	0.442369
$629$	2.17309e20	0.222432
$630$	−1.07036e20	−0.108262
$631$	−7.03288e20	−0.702932	−0.351466	−	0.936201i	$-0.614317\pi$
$631$	−7.03288e20	−0.702932	−0.351466	+	0.936201i	$0.614317\pi$
$632$	−5.18040e20	−0.511664
$633$	−5.01718e20	−0.489702
$634$	5.10912e20	0.492807
$635$	7.63902e19	0.0728173
$636$	8.95274e19	0.0843389
$637$	1.02730e20	0.0956428
$638$	−6.99625e19	−0.0643740
$639$	−4.72159e20	−0.429370
$640$	4.56327e19	0.0410135
$641$	−1.48507e21	−1.31921	−0.659603	−	0.751615i	$-0.729275\pi$
$641$	−1.48507e21	−1.31921	−0.659603	+	0.751615i	$0.729275\pi$
$642$	−3.74828e20	−0.329093
$643$	−6.21927e20	−0.539706	−0.269853	−	0.962901i	$-0.586975\pi$
$643$	−6.21927e20	−0.539706	−0.269853	+	0.962901i	$0.586975\pi$
$644$	−2.85095e20	−0.244537
$645$	−1.69626e19	−0.0143812
$646$	−2.07058e20	−0.173519
$647$	−1.19457e21	−0.989535	−0.494767	−	0.869025i	$-0.664747\pi$
$647$	−1.19457e21	−0.989535	−0.494767	+	0.869025i	$0.664747\pi$
$648$	−2.74224e20	−0.224539
$649$	−8.83474e20	−0.715087
$650$	4.64284e20	0.371478
$651$	−1.05655e20	−0.0835666
$652$	7.01421e20	0.548431
$653$	1.72344e21	1.33213	0.666066	−	0.745893i	$-0.267977\pi$
$653$	1.72344e21	1.33213	0.666066	+	0.745893i	$0.267977\pi$
$654$	1.38507e20	0.105837
$655$	−9.07199e20	−0.685319
$656$	2.70493e20	0.202012
$657$	−1.77144e21	−1.30793
$658$	2.69012e20	0.196371
$659$	−2.23540e21	−1.61330	−0.806648	−	0.591033i	$-0.798720\pi$
$659$	−2.23540e21	−1.61330	−0.806648	+	0.591033i	$0.798720\pi$
$660$	−1.25721e20	−0.0897078
$661$	1.40118e21	0.988511	0.494255	−	0.869317i	$-0.335441\pi$
$661$	1.40118e21	0.988511	0.494255	+	0.869317i	$0.335441\pi$
$662$	8.42586e20	0.587732
$663$	−5.10712e19	−0.0352229
$664$	−5.84852e18	−0.00398827
$665$	4.32372e20	0.291538
$666$	−1.39507e21	−0.930122
$667$	−1.64698e20	−0.108579
$668$	7.95670e20	0.518692
$669$	−1.02871e19	−0.00663127
$670$	−5.02430e20	−0.320269
$671$	−2.79959e21	−1.76472
$672$	−3.82006e19	−0.0238122
$673$	−6.24855e20	−0.385182	−0.192591	−	0.981279i	$-0.561689\pi$
$673$	−6.24855e20	−0.385182	−0.192591	+	0.981279i	$0.561689\pi$
$674$	−1.07645e21	−0.656211
$675$	8.68832e20	0.523790
$676$	−4.62731e20	−0.275885
$677$	5.97594e19	0.0352364	0.0176182	−	0.999845i	$-0.494392\pi$
$677$	5.97594e19	0.0352364	0.0176182	+	0.999845i	$0.494392\pi$
$678$	3.36214e20	0.196062
$679$	2.28967e20	0.132054
$680$	−4.24574e19	−0.0242179
$681$	9.65685e20	0.544794
$682$	8.52961e20	0.475934
$683$	1.92947e21	1.06484	0.532418	−	0.846481i	$-0.321283\pi$
$683$	1.92947e21	1.06484	0.532418	+	0.846481i	$0.321283\pi$
$684$	1.32926e21	0.725588
$685$	1.23558e21	0.667103
$686$	−7.14939e19	−0.0381802
$687$	−5.21079e20	−0.275250
$688$	4.16095e19	0.0217410
$689$	6.13095e20	0.316872
$690$	−2.95960e20	−0.151309
$691$	−5.76171e20	−0.291384	−0.145692	−	0.989330i	$-0.546541\pi$
$691$	−5.76171e20	−0.291384	−0.145692	+	0.989330i	$0.546541\pi$
$692$	1.60388e21	0.802374
$693$	−7.23373e20	−0.357983
$694$	−9.50091e20	−0.465125
$695$	1.86981e21	0.905548
$696$	−2.20684e19	−0.0105731
$697$	−2.51671e20	−0.119286
$698$	−2.40631e21	−1.12833
$699$	9.56151e20	0.443555
$700$	−3.23113e20	−0.148293
$701$	−2.73524e20	−0.124197	−0.0620983	−	0.998070i	$-0.519779\pi$
$701$	−2.73524e20	−0.124197	−0.0620983	+	0.998070i	$0.519779\pi$
$702$	7.03433e20	0.316005
$703$	5.63540e21	2.50472
$704$	3.08396e20	0.135617
$705$	2.79265e20	0.121506
$706$	−1.02245e21	−0.440155
$707$	1.31036e20	0.0558140
$708$	−2.78675e20	−0.117449
$709$	3.60600e21	1.50376	0.751880	−	0.659300i	$-0.229147\pi$
$709$	3.60600e21	1.50376	0.751880	+	0.659300i	$0.229147\pi$
$710$	3.91092e20	0.161377
$711$	−3.09428e21	−1.26339
$712$	1.22466e19	0.00494784
$713$	2.00795e21	0.802752
$714$	3.55424e19	0.0140608
$715$	−8.60956e20	−0.337043
$716$	−1.19383e21	−0.462483
$717$	5.52905e20	0.211961
$718$	2.80824e21	1.06537
$719$	2.62332e20	0.0984882	0.0492441	−	0.998787i	$-0.484319\pi$
$719$	2.62332e20	0.0984882	0.0492441	+	0.998787i	$0.484319\pi$
$720$	2.72567e20	0.101270
$721$	−1.40799e21	−0.517709
$722$	−3.42637e21	−1.24683
$723$	−1.34318e20	−0.0483722
$724$	−7.40206e20	−0.263823
$725$	−1.86662e20	−0.0658445
$726$	−1.27826e20	−0.0446266
$727$	−2.79986e21	−0.967449	−0.483725	−	0.875220i	$-0.660716\pi$
$727$	−2.79986e21	−0.967449	−0.483725	+	0.875220i	$0.660716\pi$
$728$	−2.61602e20	−0.0894656
$729$	−9.35140e20	−0.316534
$730$	1.46729e21	0.491580
$731$	−3.87142e19	−0.0128378
$732$	−8.83078e20	−0.289845
$733$	3.35119e21	1.08873	0.544364	−	0.838849i	$-0.316771\pi$
$733$	3.35119e21	1.08873	0.544364	+	0.838849i	$0.316771\pi$
$734$	−3.51062e21	−1.12892
$735$	−7.42186e19	−0.0236242
$736$	7.25994e20	0.228744
$737$	−3.39553e21	−1.05901
$738$	1.61567e21	0.498805
$739$	−1.57752e21	−0.482105	−0.241053	−	0.970512i	$-0.577493\pi$
$739$	−1.57752e21	−0.482105	−0.241053	+	0.970512i	$0.577493\pi$
$740$	1.15555e21	0.349582
$741$	−1.32441e21	−0.396631
$742$	−4.26677e20	−0.126494
$743$	5.98403e21	1.75621	0.878107	−	0.478465i	$-0.158806\pi$
$743$	5.98403e21	1.75621	0.878107	+	0.478465i	$0.158806\pi$
$744$	2.69050e20	0.0781694
$745$	4.23881e20	0.121919
$746$	−2.93558e21	−0.835897
$747$	−3.49335e19	−0.00984777
$748$	−2.86937e20	−0.0800800
$749$	1.78638e21	0.493584
$750$	−7.62892e20	−0.208691
$751$	4.92530e21	1.33393	0.666965	−	0.745089i	$-0.267593\pi$
$751$	4.92530e21	1.33393	0.666965	+	0.745089i	$0.267593\pi$
$752$	−6.85039e20	−0.183688
$753$	1.41283e21	0.375084
$754$	−1.51127e20	−0.0397243
$755$	8.31924e20	0.216512
$756$	−4.89546e20	−0.126148
$757$	−3.93959e21	−1.00515	−0.502576	−	0.864533i	$-0.667614\pi$
$757$	−3.93959e21	−1.00515	−0.502576	+	0.864533i	$0.667614\pi$
$758$	3.88477e21	0.981401
$759$	−2.00017e21	−0.500326
$760$	−1.10103e21	−0.272709
$761$	−7.54503e21	−1.85044	−0.925222	−	0.379427i	$-0.876121\pi$
$761$	−7.54503e21	−1.85044	−0.925222	+	0.379427i	$0.876121\pi$
$762$	1.62845e20	0.0395469
$763$	−6.60105e20	−0.158737
$764$	1.89965e21	0.452350
$765$	−2.53600e20	−0.0597984
$766$	3.16555e21	0.739151
$767$	−1.90840e21	−0.441270
$768$	9.72778e19	0.0222743
$769$	−2.81569e21	−0.638465	−0.319232	−	0.947676i	$-0.603425\pi$
$769$	−2.81569e21	−0.638465	−0.319232	+	0.947676i	$0.603425\pi$
$770$	5.99173e20	0.134546
$771$	−1.87541e21	−0.417051
$772$	−3.93391e21	−0.866354
$773$	−2.20729e20	−0.0481409	−0.0240704	−	0.999710i	$-0.507663\pi$
$773$	−2.20729e20	−0.0481409	−0.0240704	+	0.999710i	$0.507663\pi$
$774$	2.48536e20	0.0536824
$775$	2.27572e21	0.486806
$776$	−5.83065e20	−0.123525
$777$	−9.67343e20	−0.202966
$778$	4.84546e21	1.00690
$779$	−6.52651e21	−1.34323
$780$	−2.71572e20	−0.0553575
$781$	2.64308e21	0.533615
$782$	−6.75476e20	−0.135070
$783$	−2.82809e20	−0.0560119
$784$	1.82059e20	0.0357143
$785$	−2.11285e21	−0.410532
$786$	−1.93393e21	−0.372195
$787$	3.27072e21	0.623494	0.311747	−	0.950165i	$-0.399086\pi$
$787$	3.27072e21	0.623494	0.311747	+	0.950165i	$0.399086\pi$
$788$	−5.05572e21	−0.954634
$789$	6.27587e20	0.117381
$790$	2.56301e21	0.474839
$791$	−1.60235e21	−0.294059
$792$	1.84207e21	0.334863
$793$	−6.04743e21	−1.08898
$794$	−6.84715e21	−1.22140
$795$	−4.42938e20	−0.0782689
$796$	5.10418e21	0.893466
$797$	3.12348e21	0.541628	0.270814	−	0.962632i	$-0.412707\pi$
$797$	3.12348e21	0.541628	0.270814	+	0.962632i	$0.412707\pi$
$798$	9.21710e20	0.158333
$799$	6.37371e20	0.108465
$800$	8.22808e20	0.138715
$801$	7.31496e19	0.0122171
$802$	6.38564e21	1.05657
$803$	9.91627e21	1.62548
$804$	−1.07106e21	−0.173937
$805$	1.41051e21	0.226938
$806$	1.84249e21	0.293692
$807$	−8.23016e20	−0.129974
$808$	−3.33682e20	−0.0522093
$809$	−3.33107e21	−0.516381	−0.258191	−	0.966094i	$-0.583126\pi$
$809$	−3.33107e21	−0.516381	−0.258191	+	0.966094i	$0.583126\pi$
$810$	1.35672e21	0.208379
$811$	7.28612e21	1.10877	0.554383	−	0.832262i	$-0.312954\pi$
$811$	7.28612e21	1.10877	0.554383	+	0.832262i	$0.312954\pi$
$812$	1.05175e20	0.0158578
$813$	2.42816e21	0.362742
$814$	7.80943e21	1.15594
$815$	−3.47029e21	−0.508959
$816$	−9.05087e19	−0.0131527
$817$	−1.00396e21	−0.144561
$818$	−1.12020e21	−0.159826
$819$	−1.56257e21	−0.220907
$820$	−1.33827e21	−0.187473
$821$	−1.80178e21	−0.250108	−0.125054	−	0.992150i	$-0.539910\pi$
$821$	−1.80178e21	−0.250108	−0.125054	+	0.992150i	$0.539910\pi$
$822$	2.63396e21	0.362302
$823$	5.07686e21	0.691985	0.345992	−	0.938237i	$-0.387542\pi$
$823$	5.07686e21	0.691985	0.345992	+	0.938237i	$0.387542\pi$
$824$	3.58545e21	0.484272
$825$	−2.26690e21	−0.303408
$826$	1.32813e21	0.176153
$827$	8.67477e21	1.14016	0.570081	−	0.821588i	$-0.306912\pi$
$827$	8.67477e21	1.14016	0.570081	+	0.821588i	$0.306912\pi$
$828$	4.33640e21	0.564809
$829$	−1.05326e22	−1.35950	−0.679748	−	0.733446i	$-0.737911\pi$
$829$	−1.05326e22	−1.35950	−0.679748	+	0.733446i	$0.737911\pi$
$830$	2.89356e19	0.00370123
$831$	−8.98781e20	−0.113932
$832$	6.66170e20	0.0836874
$833$	−1.69391e20	−0.0210888
$834$	3.98597e21	0.491801
$835$	−3.93659e21	−0.481361
$836$	−7.44104e21	−0.901750
$837$	3.44792e21	0.414111
$838$	−6.64312e21	−0.790755
$839$	9.80857e21	1.15715	0.578577	−	0.815628i	$-0.303608\pi$
$839$	9.80857e21	1.15715	0.578577	+	0.815628i	$0.303608\pi$
$840$	1.88998e20	0.0220985
$841$	−8.56843e21	−0.992959
$842$	−2.10874e21	−0.242204
$843$	4.15240e21	0.472708
$844$	−6.08900e21	−0.687033
$845$	2.28937e21	0.256030
$846$	−4.09178e21	−0.453560
$847$	6.09201e20	0.0669322
$848$	1.08653e21	0.118324
$849$	−3.08727e21	−0.333247
$850$	−7.65553e20	−0.0819093
$851$	1.83841e22	1.94972
$852$	8.33711e20	0.0876433
$853$	1.50526e22	1.56853	0.784265	−	0.620426i	$-0.213040\pi$
$853$	1.50526e22	1.56853	0.784265	+	0.620426i	$0.213040\pi$
$854$	4.20864e21	0.434718
$855$	−6.57654e21	−0.673367
$856$	−4.54902e21	−0.461705
$857$	−1.44340e22	−1.45222	−0.726109	−	0.687580i	$-0.758673\pi$
$857$	−1.44340e22	−1.45222	−0.726109	+	0.687580i	$0.758673\pi$
$858$	−1.83535e21	−0.183047
$859$	−1.52942e22	−1.51209	−0.756046	−	0.654518i	$-0.772872\pi$
$859$	−1.52942e22	−1.51209	−0.756046	+	0.654518i	$0.772872\pi$
$860$	−2.05864e20	−0.0201763
$861$	1.12031e21	0.108846
$862$	−3.77073e20	−0.0363180
$863$	−6.51823e21	−0.622370	−0.311185	−	0.950349i	$-0.600726\pi$
$863$	−6.51823e21	−0.622370	−0.311185	+	0.950349i	$0.600726\pi$
$864$	1.24663e21	0.118001
$865$	−7.93522e21	−0.744626
$866$	−6.61462e21	−0.615348
$867$	−3.78006e21	−0.348623
$868$	−1.28226e21	−0.117241
$869$	1.73214e22	1.57012
$870$	1.09183e20	0.00981211
$871$	−7.33473e21	−0.653503
$872$	1.68096e21	0.148485
$873$	−3.48268e21	−0.305005
$874$	−1.75169e22	−1.52097
$875$	3.63585e21	0.313001
$876$	3.12790e21	0.266976
$877$	−6.55580e21	−0.554790	−0.277395	−	0.960756i	$-0.589471\pi$
$877$	−6.55580e21	−0.554790	−0.277395	+	0.960756i	$0.589471\pi$
$878$	−1.07403e22	−0.901174
$879$	8.11996e21	0.675518
$880$	−1.52579e21	−0.125857
$881$	1.19476e22	0.977147	0.488573	−	0.872523i	$-0.337517\pi$
$881$	1.19476e22	0.977147	0.488573	+	0.872523i	$0.337517\pi$
$882$	1.08745e21	0.0881850
$883$	−1.26909e22	−1.02044	−0.510219	−	0.860044i	$-0.670436\pi$
$883$	−1.26909e22	−1.02044	−0.510219	+	0.860044i	$0.670436\pi$
$884$	−6.19815e20	−0.0494163
$885$	1.37875e21	0.108996
$886$	−9.33795e21	−0.731979
$887$	−1.63386e22	−1.26995	−0.634977	−	0.772531i	$-0.718991\pi$
$887$	−1.63386e22	−1.26995	−0.634977	+	0.772531i	$0.718991\pi$
$888$	2.46334e21	0.189857
$889$	−7.76099e20	−0.0593136
$890$	−6.05902e19	−0.00459174
$891$	9.16905e21	0.689035
$892$	−1.24847e20	−0.00930341
$893$	1.65287e22	1.22139
$894$	9.03609e20	0.0662139
$895$	5.90649e21	0.429197
$896$	−4.63613e20	−0.0334077
$897$	−4.32058e21	−0.308744
$898$	1.19827e22	0.849144
$899$	−7.40758e20	−0.0520570
$900$	4.91468e21	0.342512
$901$	−1.01093e21	−0.0698688
$902$	−9.04432e21	−0.619908
$903$	1.72335e20	0.0117143
$904$	4.08039e21	0.275067
$905$	3.66218e21	0.244836
$906$	1.77346e21	0.117587
$907$	−6.84061e21	−0.449821	−0.224911	−	0.974379i	$-0.572209\pi$
$907$	−6.84061e21	−0.449821	−0.224911	+	0.974379i	$0.572209\pi$
$908$	1.17198e22	0.764324
$909$	−1.99310e21	−0.128914
$910$	1.29428e21	0.0830267
$911$	1.43474e22	0.912819	0.456409	−	0.889770i	$-0.349135\pi$
$911$	1.43474e22	0.912819	0.456409	+	0.889770i	$0.349135\pi$
$912$	−2.34713e21	−0.148107
$913$	1.95553e20	0.0122387
$914$	9.74987e21	0.605205
$915$	4.36904e21	0.268985
$916$	−6.32397e21	−0.386166
$917$	9.21684e21	0.558229
$918$	−1.15988e21	−0.0696777
$919$	−7.95365e21	−0.473915	−0.236957	−	0.971520i	$-0.576150\pi$
$919$	−7.95365e21	−0.473915	−0.236957	+	0.971520i	$0.576150\pi$
$920$	−3.59186e21	−0.212281
$921$	6.46121e20	0.0378762
$922$	1.58382e22	0.920924
$923$	5.70936e21	0.329287
$924$	1.27729e21	0.0730717
$925$	2.08357e22	1.18235
$926$	−1.73860e21	−0.0978626
$927$	2.14161e22	1.19575
$928$	−2.67828e20	−0.0148336
$929$	−4.97478e20	−0.0273310	−0.0136655	−	0.999907i	$-0.504350\pi$
$929$	−4.97478e20	−0.0273310	−0.0136655	+	0.999907i	$0.504350\pi$
$930$	−1.33113e21	−0.0725435
$931$	−4.39275e21	−0.237473
$932$	1.16041e22	0.622290
$933$	−1.01969e22	−0.542445
$934$	−7.04739e20	−0.0371900
$935$	1.41962e21	0.0743166
$936$	3.97907e21	0.206639
$937$	−1.53684e22	−0.791740	−0.395870	−	0.918307i	$-0.629557\pi$
$937$	−1.53684e22	−0.791740	−0.395870	+	0.918307i	$0.629557\pi$
$938$	5.10452e21	0.260876
$939$	−4.13108e21	−0.209446
$940$	3.38924e21	0.170468
$941$	3.84108e21	0.191660	0.0958300	−	0.995398i	$-0.469449\pi$
$941$	3.84108e21	0.191660	0.0958300	+	0.995398i	$0.469449\pi$
$942$	−4.50408e21	−0.222959
$943$	−2.12912e22	−1.04559
$944$	−3.38209e21	−0.164776
$945$	2.42203e21	0.117069
$946$	−1.39127e21	−0.0667158
$947$	2.30784e22	1.09795	0.548973	−	0.835840i	$-0.315019\pi$
$947$	2.30784e22	1.09795	0.548973	+	0.835840i	$0.315019\pi$
$948$	5.46370e21	0.257884
$949$	2.14202e22	1.00306
$950$	−1.98528e22	−0.922350
$951$	−5.38853e21	−0.248380
$952$	4.31353e20	0.0197268
$953$	−4.05784e22	−1.84119	−0.920595	−	0.390519i	$-0.872296\pi$
$953$	−4.05784e22	−1.84119	−0.920595	+	0.390519i	$0.872296\pi$
$954$	6.48991e21	0.292164
$955$	−9.39856e21	−0.419794
$956$	6.71021e21	0.297373
$957$	7.37886e20	0.0324452
$958$	1.27525e21	0.0556358
$959$	−1.25531e22	−0.543391
$960$	−4.81283e20	−0.0206712
$961$	−1.44342e22	−0.615129
$962$	1.68692e22	0.713317
$963$	−2.71716e22	−1.14003
$964$	−1.63012e21	−0.0678643
$965$	1.94631e22	0.804001
$966$	3.00686e21	0.123249
$967$	−1.46021e22	−0.593905	−0.296953	−	0.954892i	$-0.595970\pi$
$967$	−1.46021e22	−0.593905	−0.296953	+	0.954892i	$0.595970\pi$
$968$	−1.55133e21	−0.0626094
$969$	2.18381e21	0.0874554
$970$	2.88472e21	0.114635
$971$	−9.78867e21	−0.385993	−0.192997	−	0.981199i	$-0.561821\pi$
$971$	−9.78867e21	−0.385993	−0.192997	+	0.981199i	$0.561821\pi$
$972$	1.14218e22	0.446926
$973$	−1.89967e22	−0.737617
$974$	1.21388e22	0.467716
$975$	−4.89675e21	−0.187229
$976$	−1.07173e22	−0.406641
$977$	−4.80677e21	−0.180986	−0.0904929	−	0.995897i	$-0.528844\pi$
$977$	−4.80677e21	−0.180986	−0.0904929	+	0.995897i	$0.528844\pi$
$978$	−7.39780e21	−0.276415
$979$	−4.09482e20	−0.0151832
$980$	−9.00739e20	−0.0331439
$981$	1.00405e22	0.366636
$982$	1.25346e21	0.0454230
$983$	−5.40159e21	−0.194254	−0.0971270	−	0.995272i	$-0.530965\pi$
$983$	−5.40159e21	−0.194254	−0.0971270	+	0.995272i	$0.530965\pi$
$984$	−2.85286e21	−0.101816
$985$	2.50132e22	0.885928
$986$	2.49192e20	0.00875904
$987$	−2.83724e21	−0.0989731
$988$	−1.60735e22	−0.556458
$989$	−3.27519e21	−0.112529
$990$	−9.11365e21	−0.310762
$991$	−2.66832e22	−0.902995	−0.451498	−	0.892272i	$-0.649110\pi$
$991$	−2.66832e22	−0.902995	−0.451498	+	0.892272i	$0.649110\pi$
$992$	3.26528e21	0.109669
$993$	−8.88665e21	−0.296223
$994$	−3.97336e21	−0.131450
$995$	−2.52530e22	−0.829163
$996$	6.16836e19	0.00201013
$997$	2.32396e22	0.751648	0.375824	−	0.926691i	$-0.377360\pi$
$997$	2.32396e22	0.751648	0.375824	+	0.926691i	$0.377360\pi$
$998$	−2.94276e21	−0.0944661
$999$	3.15680e22	1.00579

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.16.a.a.1.1	✓	1
3.2	odd	2		126.16.a.e.1.1		1
4.3	odd	2		112.16.a.a.1.1		1
7.2	even	3		98.16.c.b.67.1		2
7.3	odd	6		98.16.c.c.79.1		2
7.4	even	3		98.16.c.b.79.1		2
7.5	odd	6		98.16.c.c.67.1		2
7.6	odd	2		98.16.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.16.a.a.1.1	✓	1	1.1	even	1	trivial
98.16.a.b.1.1		1	7.6	odd	2
98.16.c.b.67.1		2	7.2	even	3
98.16.c.b.79.1		2	7.4	even	3
98.16.c.c.67.1		2	7.5	odd	6
98.16.c.c.79.1		2	7.3	odd	6
112.16.a.a.1.1		1	4.3	odd	2
126.16.a.e.1.1		1	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:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more