LMFDB - Embedded newform 2.18.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,18,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$3.66444174689$
Analytic rank:	$0$
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	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+256.000 q^{2} +6084.00 q^{3} +65536.0 q^{4} +1.25511e6 q^{5} +1.55750e6 q^{6} -2.24659e7 q^{7} +1.67772e7 q^{8} -9.21251e7 q^{9} +O(q^{10})$

\(q+256.000 q^{2} +6084.00 q^{3} +65536.0 q^{4} +1.25511e6 q^{5} +1.55750e6 q^{6} -2.24659e7 q^{7} +1.67772e7 q^{8} -9.21251e7 q^{9} +3.21308e8 q^{10} +1.72400e8 q^{11} +3.98721e8 q^{12} -2.18015e9 q^{13} -5.75127e9 q^{14} +7.63609e9 q^{15} +4.29497e9 q^{16} +3.01639e10 q^{17} -2.35840e10 q^{18} -7.62758e10 q^{19} +8.22549e10 q^{20} -1.36683e11 q^{21} +4.41343e10 q^{22} +1.30467e11 q^{23} +1.02073e11 q^{24} +8.12362e11 q^{25} -5.58118e11 q^{26} -1.34618e12 q^{27} -1.47233e12 q^{28} +8.03134e11 q^{29} +1.95484e12 q^{30} +2.04534e12 q^{31} +1.09951e12 q^{32} +1.04888e12 q^{33} +7.72197e12 q^{34} -2.81972e13 q^{35} -6.03751e12 q^{36} +3.38554e13 q^{37} -1.95266e13 q^{38} -1.32640e13 q^{39} +2.10573e13 q^{40} +5.32064e13 q^{41} -3.49907e13 q^{42} +2.65904e13 q^{43} +1.12984e13 q^{44} -1.15627e14 q^{45} +3.33994e13 q^{46} -2.32565e14 q^{47} +2.61306e13 q^{48} +2.72087e14 q^{49} +2.07965e14 q^{50} +1.83517e14 q^{51} -1.42878e14 q^{52} -1.63278e14 q^{53} -3.44622e14 q^{54} +2.16381e14 q^{55} -3.76915e14 q^{56} -4.64062e14 q^{57} +2.05602e14 q^{58} +6.97821e14 q^{59} +5.00439e14 q^{60} -8.98968e14 q^{61} +5.23606e14 q^{62} +2.06967e15 q^{63} +2.81475e14 q^{64} -2.73633e15 q^{65} +2.68513e14 q^{66} -2.66700e15 q^{67} +1.97682e15 q^{68} +7.93759e14 q^{69} -7.21848e15 q^{70} +3.91064e15 q^{71} -1.54560e15 q^{72} +5.85593e15 q^{73} +8.66697e15 q^{74} +4.94241e15 q^{75} -4.99881e15 q^{76} -3.87312e15 q^{77} -3.39559e15 q^{78} -2.38217e16 q^{79} +5.39066e15 q^{80} +3.70690e15 q^{81} +1.36208e16 q^{82} -1.39157e16 q^{83} -8.95763e15 q^{84} +3.78591e16 q^{85} +6.80713e15 q^{86} +4.88627e15 q^{87} +2.89239e15 q^{88} -3.07227e16 q^{89} -2.96005e16 q^{90} +4.89790e16 q^{91} +8.55026e15 q^{92} +1.24438e16 q^{93} -5.95367e16 q^{94} -9.57345e16 q^{95} +6.68943e15 q^{96} +5.76491e16 q^{97} +6.96542e16 q^{98} -1.58823e16 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	6084.00	0.535376	0.267688	−	0.963506i	$-0.413740\pi$
$3$	6084.00	0.535376	0.267688	+	0.963506i	$0.413740\pi$
$4$	65536.0	0.500000
$5$	1.25511e6	1.43693	0.718467	−	0.695561i	$-0.244844\pi$
$5$	1.25511e6	1.43693	0.718467	+	0.695561i	$0.244844\pi$
$6$	1.55750e6	0.378568
$7$	−2.24659e7	−1.47296	−0.736480	−	0.676460i	$-0.763513\pi$
$7$	−2.24659e7	−1.47296	−0.736480	+	0.676460i	$0.763513\pi$
$8$	1.67772e7	0.353553
$9$	−9.21251e7	−0.713373
$10$	3.21308e8	1.01607
$11$	1.72400e8	0.242493	0.121246	−	0.992622i	$-0.461311\pi$
$11$	1.72400e8	0.242493	0.121246	+	0.992622i	$0.461311\pi$
$12$	3.98721e8	0.267688
$13$	−2.18015e9	−0.741255	−0.370628	−	0.928782i	$-0.620857\pi$
$13$	−2.18015e9	−0.741255	−0.370628	+	0.928782i	$0.620857\pi$
$14$	−5.75127e9	−1.04154
$15$	7.63609e9	0.769299
$16$	4.29497e9	0.250000
$17$	3.01639e10	1.04875	0.524375	−	0.851487i	$-0.324299\pi$
$17$	3.01639e10	1.04875	0.524375	+	0.851487i	$0.324299\pi$
$18$	−2.35840e10	−0.504431
$19$	−7.62758e10	−1.03034	−0.515170	−	0.857088i	$-0.672271\pi$
$19$	−7.62758e10	−1.03034	−0.515170	+	0.857088i	$0.672271\pi$
$20$	8.22549e10	0.718467
$21$	−1.36683e11	−0.788586
$22$	4.41343e10	0.171468
$23$	1.30467e11	0.347386	0.173693	−	0.984800i	$-0.444430\pi$
$23$	1.30467e11	0.347386	0.173693	+	0.984800i	$0.444430\pi$
$24$	1.02073e11	0.189284
$25$	8.12362e11	1.06478
$26$	−5.58118e11	−0.524147
$27$	−1.34618e12	−0.917298
$28$	−1.47233e12	−0.736480
$29$	8.03134e11	0.298130	0.149065	−	0.988827i	$-0.452374\pi$
$29$	8.03134e11	0.298130	0.149065	+	0.988827i	$0.452374\pi$
$30$	1.95484e12	0.543977
$31$	2.04534e12	0.430715	0.215358	−	0.976535i	$-0.430908\pi$
$31$	2.04534e12	0.430715	0.215358	+	0.976535i	$0.430908\pi$
$32$	1.09951e12	0.176777
$33$	1.04888e12	0.129825
$34$	7.72197e12	0.741579
$35$	−2.81972e13	−2.11654
$36$	−6.03751e12	−0.356687
$37$	3.38554e13	1.58458	0.792288	−	0.610148i	$-0.208890\pi$
$37$	3.38554e13	1.58458	0.792288	+	0.610148i	$0.208890\pi$
$38$	−1.95266e13	−0.728561
$39$	−1.32640e13	−0.396850
$40$	2.10573e13	0.508033
$41$	5.32064e13	1.04064	0.520321	−	0.853971i	$-0.325812\pi$
$41$	5.32064e13	1.04064	0.520321	+	0.853971i	$0.325812\pi$
$42$	−3.49907e13	−0.557615
$43$	2.65904e13	0.346930	0.173465	−	0.984840i	$-0.444504\pi$
$43$	2.65904e13	0.346930	0.173465	+	0.984840i	$0.444504\pi$
$44$	1.12984e13	0.121246
$45$	−1.15627e14	−1.02507
$46$	3.33994e13	0.245639
$47$	−2.32565e14	−1.42467	−0.712333	−	0.701841i	$-0.752362\pi$
$47$	−2.32565e14	−1.42467	−0.712333	+	0.701841i	$0.752362\pi$
$48$	2.61306e13	0.133844
$49$	2.72087e14	1.16961
$50$	2.07965e14	0.752912
$51$	1.83517e14	0.561475
$52$	−1.42878e14	−0.370628
$53$	−1.63278e14	−0.360232	−0.180116	−	0.983645i	$-0.557647\pi$
$53$	−1.63278e14	−0.360232	−0.180116	+	0.983645i	$0.557647\pi$
$54$	−3.44622e14	−0.648628
$55$	2.16381e14	0.348446
$56$	−3.76915e14	−0.520770
$57$	−4.64062e14	−0.551619
$58$	2.05602e14	0.210810
$59$	6.97821e14	0.618731	0.309365	−	0.950943i	$-0.399883\pi$
$59$	6.97821e14	0.618731	0.309365	+	0.950943i	$0.399883\pi$
$60$	5.00439e14	0.384650
$61$	−8.98968e14	−0.600400	−0.300200	−	0.953876i	$-0.597053\pi$
$61$	−8.98968e14	−0.600400	−0.300200	+	0.953876i	$0.597053\pi$
$62$	5.23606e14	0.304562
$63$	2.06967e15	1.05077
$64$	2.81475e14	0.125000
$65$	−2.73633e15	−1.06513
$66$	2.68513e14	0.0917999
$67$	−2.66700e15	−0.802394	−0.401197	−	0.915992i	$-0.631406\pi$
$67$	−2.66700e15	−0.802394	−0.401197	+	0.915992i	$0.631406\pi$
$68$	1.97682e15	0.524375
$69$	7.93759e14	0.185982
$70$	−7.21848e15	−1.49662
$71$	3.91064e15	0.718707	0.359353	−	0.933202i	$-0.382997\pi$
$71$	3.91064e15	0.718707	0.359353	+	0.933202i	$0.382997\pi$
$72$	−1.54560e15	−0.252215
$73$	5.85593e15	0.849868	0.424934	−	0.905224i	$-0.360297\pi$
$73$	5.85593e15	0.849868	0.424934	+	0.905224i	$0.360297\pi$
$74$	8.66697e15	1.12046
$75$	4.94241e15	0.570056
$76$	−4.99881e15	−0.515170
$77$	−3.87312e15	−0.357182
$78$	−3.39559e15	−0.280615
$79$	−2.38217e16	−1.76662	−0.883310	−	0.468789i	$-0.844690\pi$
$79$	−2.38217e16	−1.76662	−0.883310	+	0.468789i	$0.844690\pi$
$80$	5.39066e15	0.359233
$81$	3.70690e15	0.222274
$82$	1.36208e16	0.735845
$83$	−1.39157e16	−0.678176	−0.339088	−	0.940755i	$-0.610119\pi$
$83$	−1.39157e16	−0.678176	−0.339088	+	0.940755i	$0.610119\pi$
$84$	−8.95763e15	−0.394293
$85$	3.78591e16	1.50698
$86$	6.80713e15	0.245317
$87$	4.88627e15	0.159611
$88$	2.89239e15	0.0857341
$89$	−3.07227e16	−0.827266	−0.413633	−	0.910444i	$-0.635740\pi$
$89$	−3.07227e16	−0.827266	−0.413633	+	0.910444i	$0.635740\pi$
$90$	−2.96005e16	−0.724834
$91$	4.89790e16	1.09184
$92$	8.55026e15	0.173693
$93$	1.24438e16	0.230594
$94$	−5.95367e16	−1.00739
$95$	−9.57345e16	−1.48053
$96$	6.68943e15	0.0946419
$97$	5.76491e16	0.746849	0.373424	−	0.927661i	$-0.378183\pi$
$97$	5.76491e16	0.746849	0.373424	+	0.927661i	$0.378183\pi$
$98$	6.96542e16	0.827038
$99$	−1.58823e16	−0.172988
$100$	5.32389e16	0.532389
$101$	−3.80153e16	−0.349323	−0.174661	−	0.984629i	$-0.555883\pi$
$101$	−3.80153e16	−0.349323	−0.174661	+	0.984629i	$0.555883\pi$
$102$	4.69804e16	0.397023
$103$	1.43913e17	1.11940	0.559700	−	0.828696i	$-0.310917\pi$
$103$	1.43913e17	1.11940	0.559700	+	0.828696i	$0.310917\pi$
$104$	−3.65768e16	−0.262073
$105$	−1.71552e17	−1.13315
$106$	−4.17991e16	−0.254723
$107$	9.14309e16	0.514435	0.257218	−	0.966353i	$-0.417194\pi$
$107$	9.14309e16	0.514435	0.257218	+	0.966353i	$0.417194\pi$
$108$	−8.82231e16	−0.458649
$109$	−3.74881e17	−1.80205	−0.901027	−	0.433762i	$-0.857186\pi$
$109$	−3.74881e17	−1.80205	−0.901027	+	0.433762i	$0.857186\pi$
$110$	5.53934e16	0.246388
$111$	2.05976e17	0.848343
$112$	−9.64904e16	−0.368240
$113$	4.32401e17	1.53010	0.765051	−	0.643970i	$-0.222714\pi$
$113$	4.32401e17	1.53010	0.765051	+	0.643970i	$0.222714\pi$
$114$	−1.18800e17	−0.390054
$115$	1.63750e17	0.499171
$116$	5.26342e16	0.149065
$117$	2.00846e17	0.528791
$118$	1.78642e17	0.437509
$119$	−6.77660e17	−1.54477
$120$	1.28112e17	0.271988
$121$	−4.75725e17	−0.941197
$122$	−2.30136e17	−0.424547
$123$	3.23708e17	0.557134
$124$	1.34043e17	0.215358
$125$	6.20303e16	0.0930827
$126$	5.29837e17	0.743006
$127$	−1.20057e18	−1.57418	−0.787091	−	0.616836i	$-0.788414\pi$
$127$	−1.20057e18	−1.57418	−0.787091	+	0.616836i	$0.788414\pi$
$128$	7.20576e16	0.0883883
$129$	1.61776e17	0.185738
$130$	−7.00500e17	−0.753164
$131$	1.75544e18	1.76840	0.884198	−	0.467112i	$-0.154705\pi$
$131$	1.75544e18	1.76840	0.884198	+	0.467112i	$0.154705\pi$
$132$	6.87394e16	0.0649123
$133$	1.71360e18	1.51765
$134$	−6.82753e17	−0.567378
$135$	−1.68960e18	−1.31810
$136$	5.06067e17	0.370789
$137$	4.29231e17	0.295506	0.147753	−	0.989024i	$-0.452796\pi$
$137$	4.29231e17	0.295506	0.147753	+	0.989024i	$0.452796\pi$
$138$	2.03202e17	0.131509
$139$	−8.28362e17	−0.504190	−0.252095	−	0.967702i	$-0.581120\pi$
$139$	−8.28362e17	−0.504190	−0.252095	+	0.967702i	$0.581120\pi$
$140$	−1.84793e18	−1.05827
$141$	−1.41493e18	−0.762732
$142$	1.00112e18	0.508202
$143$	−3.75857e17	−0.179749
$144$	−3.95674e17	−0.178343
$145$	1.00802e18	0.428393
$146$	1.49912e18	0.600948
$147$	1.65538e18	0.626180
$148$	2.21875e18	0.792288
$149$	−3.84279e17	−0.129587	−0.0647937	−	0.997899i	$-0.520639\pi$
$149$	−3.84279e17	−0.129587	−0.0647937	+	0.997899i	$0.520639\pi$
$150$	1.26526e18	0.403091
$151$	−8.97916e17	−0.270353	−0.135177	−	0.990822i	$-0.543160\pi$
$151$	−8.97916e17	−0.270353	−0.135177	+	0.990822i	$0.543160\pi$
$152$	−1.27970e18	−0.364281
$153$	−2.77886e18	−0.748150
$154$	−9.91518e17	−0.252566
$155$	2.56712e18	0.618909
$156$	−8.69271e17	−0.198425
$157$	3.59596e16	0.00777442	0.00388721	−	0.999992i	$-0.498763\pi$
$157$	3.59596e16	0.00777442	0.00388721	+	0.999992i	$0.498763\pi$
$158$	−6.09837e18	−1.24919
$159$	−9.93383e17	−0.192859
$160$	1.38001e18	0.254016
$161$	−2.93105e18	−0.511686
$162$	9.48968e17	0.157171
$163$	1.15191e19	1.81060	0.905301	−	0.424771i	$-0.139646\pi$
$163$	1.15191e19	1.81060	0.905301	+	0.424771i	$0.139646\pi$
$164$	3.48694e18	0.520321
$165$	1.31646e18	0.186549
$166$	−3.56243e18	−0.479543
$167$	−4.51883e18	−0.578011	−0.289006	−	0.957327i	$-0.593325\pi$
$167$	−4.51883e18	−0.578011	−0.289006	+	0.957327i	$0.593325\pi$
$168$	−2.29315e18	−0.278807
$169$	−3.89736e18	−0.450541
$170$	9.69192e18	1.06560
$171$	7.02691e18	0.735017
$172$	1.74263e18	0.173465
$173$	−6.30747e18	−0.597673	−0.298837	−	0.954304i	$-0.596599\pi$
$173$	−6.30747e18	−0.597673	−0.298837	+	0.954304i	$0.596599\pi$
$174$	1.25089e18	0.112862
$175$	−1.82504e19	−1.56838
$176$	7.40451e17	0.0606232
$177$	4.24554e18	0.331253
$178$	−7.86502e18	−0.584965
$179$	4.69485e18	0.332944	0.166472	−	0.986046i	$-0.446763\pi$
$179$	4.69485e18	0.332944	0.166472	+	0.986046i	$0.446763\pi$
$180$	−7.57774e18	−0.512535
$181$	−7.61795e18	−0.491553	−0.245776	−	0.969327i	$-0.579043\pi$
$181$	−7.61795e18	−0.491553	−0.245776	+	0.969327i	$0.579043\pi$
$182$	1.25386e19	0.772047
$183$	−5.46932e18	−0.321440
$184$	2.18887e18	0.122820
$185$	4.24922e19	2.27693
$186$	3.18562e18	0.163055
$187$	5.20025e18	0.254314
$188$	−1.52414e19	−0.712333
$189$	3.02431e19	1.35114
$190$	−2.45080e19	−1.04689
$191$	−3.26501e19	−1.33383	−0.666916	−	0.745133i	$-0.732386\pi$
$191$	−3.26501e19	−1.33383	−0.666916	+	0.745133i	$0.732386\pi$
$192$	1.71249e18	0.0669219
$193$	−2.16468e19	−0.809386	−0.404693	−	0.914453i	$-0.632622\pi$
$193$	−2.16468e19	−0.809386	−0.404693	+	0.914453i	$0.632622\pi$
$194$	1.47582e19	0.528102
$195$	−1.66478e19	−0.570247
$196$	1.78315e19	0.584804
$197$	−4.59530e19	−1.44328	−0.721641	−	0.692268i	$-0.756612\pi$
$197$	−4.59530e19	−1.44328	−0.721641	+	0.692268i	$0.756612\pi$
$198$	−4.06588e18	−0.122321
$199$	5.74258e19	1.65522	0.827610	−	0.561303i	$-0.189700\pi$
$199$	5.74258e19	1.65522	0.827610	+	0.561303i	$0.189700\pi$
$200$	1.36292e19	0.376456
$201$	−1.62260e19	−0.429582
$202$	−9.73191e18	−0.247008
$203$	−1.80431e19	−0.439133
$204$	1.20270e19	0.280738
$205$	6.67799e19	1.49533
$206$	3.68418e19	0.791535
$207$	−1.20192e19	−0.247816
$208$	−9.36367e18	−0.185314
$209$	−1.31499e19	−0.249850
$210$	−4.39172e19	−0.801255
$211$	−2.94651e19	−0.516305	−0.258153	−	0.966104i	$-0.583114\pi$
$211$	−2.94651e19	−0.516305	−0.258153	+	0.966104i	$0.583114\pi$
$212$	−1.07006e19	−0.180116
$213$	2.37923e19	0.384778
$214$	2.34063e19	0.363761
$215$	3.33738e19	0.498516
$216$	−2.25851e19	−0.324314
$217$	−4.59503e19	−0.634426
$218$	−9.59695e19	−1.27425
$219$	3.56275e19	0.454999
$220$	1.41807e19	0.174223
$221$	−6.57619e19	−0.777392
$222$	5.27299e19	0.599869
$223$	1.27173e20	1.39252	0.696262	−	0.717788i	$-0.254845\pi$
$223$	1.27173e20	1.39252	0.696262	+	0.717788i	$0.254845\pi$
$224$	−2.47015e19	−0.260385
$225$	−7.48389e19	−0.759584
$226$	1.10695e20	1.08195
$227$	8.30214e19	0.781574	0.390787	−	0.920481i	$-0.372203\pi$
$227$	8.30214e19	0.781574	0.390787	+	0.920481i	$0.372203\pi$
$228$	−3.04128e19	−0.275810
$229$	−6.40290e19	−0.559468	−0.279734	−	0.960078i	$-0.590246\pi$
$229$	−6.40290e19	−0.559468	−0.279734	+	0.960078i	$0.590246\pi$
$230$	4.19200e19	0.352967
$231$	−2.35640e19	−0.191226
$232$	1.34744e19	0.105405
$233$	1.53412e20	1.15700	0.578501	−	0.815682i	$-0.303638\pi$
$233$	1.53412e20	1.15700	0.578501	+	0.815682i	$0.303638\pi$
$234$	5.14167e19	0.373912
$235$	−2.91895e20	−2.04715
$236$	4.57324e19	0.309365
$237$	−1.44931e20	−0.945805
$238$	−1.73481e20	−1.09231
$239$	−5.35334e19	−0.325269	−0.162635	−	0.986686i	$-0.551999\pi$
$239$	−5.35334e19	−0.325269	−0.162635	+	0.986686i	$0.551999\pi$
$240$	3.27968e19	0.192325
$241$	7.12230e19	0.403158	0.201579	−	0.979472i	$-0.435393\pi$
$241$	7.12230e19	0.403158	0.201579	+	0.979472i	$0.435393\pi$
$242$	−1.21786e20	−0.665527
$243$	1.96398e20	1.03630
$244$	−5.89148e19	−0.300200
$245$	3.41499e20	1.68065
$246$	8.28692e19	0.393954
$247$	1.66293e20	0.763746
$248$	3.43150e19	0.152281
$249$	−8.46634e19	−0.363079
$250$	1.58798e19	0.0658194
$251$	−3.66706e20	−1.46924	−0.734618	−	0.678481i	$-0.762639\pi$
$251$	−3.66706e20	−1.46924	−0.734618	+	0.678481i	$0.762639\pi$
$252$	1.35638e20	0.525385
$253$	2.24924e19	0.0842386
$254$	−3.07345e20	−1.11312
$255$	2.30334e20	0.806803
$256$	1.84467e19	0.0625000
$257$	2.48604e20	0.814849	0.407425	−	0.913239i	$-0.366427\pi$
$257$	2.48604e20	0.814849	0.407425	+	0.913239i	$0.366427\pi$
$258$	4.14146e19	0.131337
$259$	−7.60592e20	−2.33401
$260$	−1.79328e20	−0.532567
$261$	−7.39888e19	−0.212678
$262$	4.49392e20	1.25045
$263$	9.04042e19	0.243537	0.121768	−	0.992559i	$-0.461143\pi$
$263$	9.04042e19	0.243537	0.121768	+	0.992559i	$0.461143\pi$
$264$	1.75973e19	0.0458999
$265$	−2.04932e20	−0.517630
$266$	4.38683e20	1.07314
$267$	−1.86917e20	−0.442898
$268$	−1.74785e20	−0.401197
$269$	2.89996e19	0.0644908	0.0322454	−	0.999480i	$-0.489734\pi$
$269$	2.89996e19	0.0644908	0.0322454	+	0.999480i	$0.489734\pi$
$270$	−4.32538e20	−0.932035
$271$	7.70455e20	1.60882	0.804412	−	0.594072i	$-0.202481\pi$
$271$	7.70455e20	1.60882	0.804412	+	0.594072i	$0.202481\pi$
$272$	1.29553e20	0.262188
$273$	2.97989e20	0.584544
$274$	1.09883e20	0.208954
$275$	1.40051e20	0.258201
$276$	5.20198e19	0.0929911
$277$	−1.55171e20	−0.268988	−0.134494	−	0.990914i	$-0.542941\pi$
$277$	−1.55171e20	−0.268988	−0.134494	+	0.990914i	$0.542941\pi$
$278$	−2.12061e20	−0.356516
$279$	−1.88427e20	−0.307261
$280$	−4.73070e20	−0.748312
$281$	−4.97825e20	−0.763964	−0.381982	−	0.924170i	$-0.624758\pi$
$281$	−4.97825e20	−0.763964	−0.381982	+	0.924170i	$0.624758\pi$
$282$	−3.62222e20	−0.539333
$283$	1.19056e21	1.72016	0.860078	−	0.510163i	$-0.170415\pi$
$283$	1.19056e21	1.72016	0.860078	+	0.510163i	$0.170415\pi$
$284$	2.56288e20	0.359353
$285$	−5.82449e20	−0.792641
$286$	−9.62194e19	−0.127102
$287$	−1.19533e21	−1.53282
$288$	−1.01293e20	−0.126108
$289$	8.26226e19	0.0998774
$290$	2.58054e20	0.302919
$291$	3.50737e20	0.399845
$292$	3.83774e20	0.424934
$293$	5.21973e20	0.561401	0.280701	−	0.959795i	$-0.409433\pi$
$293$	5.21973e20	0.561401	0.280701	+	0.959795i	$0.409433\pi$
$294$	4.23776e20	0.442776
$295$	8.75842e20	0.889075
$296$	5.67999e20	0.560232
$297$	−2.32081e20	−0.222438
$298$	−9.83753e19	−0.0916322
$299$	−2.84437e20	−0.257502
$300$	3.23906e20	0.285028
$301$	−5.97377e20	−0.511014
$302$	−2.29866e20	−0.191169
$303$	−2.31285e20	−0.187019
$304$	−3.27602e20	−0.257585
$305$	−1.12830e21	−0.862735
$306$	−7.11387e20	−0.529022
$307$	−1.85651e20	−0.134283	−0.0671416	−	0.997743i	$-0.521388\pi$
$307$	−1.85651e20	−0.134283	−0.0671416	+	0.997743i	$0.521388\pi$
$308$	−2.53829e20	−0.178591
$309$	8.75569e20	0.599299
$310$	6.57183e20	0.437635
$311$	−1.00184e21	−0.649136	−0.324568	−	0.945862i	$-0.605219\pi$
$311$	−1.00184e21	−0.649136	−0.324568	+	0.945862i	$0.605219\pi$
$312$	−2.22533e20	−0.140308
$313$	−4.18947e20	−0.257059	−0.128529	−	0.991706i	$-0.541026\pi$
$313$	−4.18947e20	−0.257059	−0.128529	+	0.991706i	$0.541026\pi$
$314$	9.20566e18	0.00549734
$315$	2.59767e21	1.50989
$316$	−1.56118e21	−0.883310
$317$	3.02177e21	1.66440	0.832199	−	0.554478i	$-0.187082\pi$
$317$	3.02177e21	1.66440	0.832199	+	0.554478i	$0.187082\pi$
$318$	−2.54306e20	−0.136372
$319$	1.38460e20	0.0722943
$320$	3.53282e20	0.179617
$321$	5.56266e20	0.275416
$322$	−7.50349e20	−0.361817
$323$	−2.30078e21	−1.08057
$324$	2.42936e20	0.111137
$325$	−1.77107e21	−0.789273
$326$	2.94888e21	1.28029
$327$	−2.28077e21	−0.964776
$328$	8.92656e20	0.367923
$329$	5.22479e21	2.09848
$330$	3.37014e20	0.131910
$331$	−1.94091e21	−0.740401	−0.370200	−	0.928952i	$-0.620711\pi$
$331$	−1.94091e21	−0.740401	−0.370200	+	0.928952i	$0.620711\pi$
$332$	−9.11982e20	−0.339088
$333$	−3.11893e21	−1.13039
$334$	−1.15682e21	−0.408716
$335$	−3.34738e21	−1.15299
$336$	−5.87047e20	−0.197147
$337$	−1.79576e20	−0.0588022	−0.0294011	−	0.999568i	$-0.509360\pi$
$337$	−1.79576e20	−0.0588022	−0.0294011	+	0.999568i	$0.509360\pi$
$338$	−9.97725e20	−0.318580
$339$	2.63073e21	0.819179
$340$	2.48113e21	0.753492
$341$	3.52615e20	0.104445
$342$	1.79889e21	0.519736
$343$	−8.86419e20	−0.249827
$344$	4.46112e20	0.122658
$345$	9.96255e20	0.267244
$346$	−1.61471e21	−0.422619
$347$	7.43959e21	1.89998	0.949989	−	0.312283i	$-0.101094\pi$
$347$	7.43959e21	1.89998	0.949989	+	0.312283i	$0.101094\pi$
$348$	3.20227e20	0.0798057
$349$	6.07435e20	0.147735	0.0738675	−	0.997268i	$-0.476466\pi$
$349$	6.07435e20	0.147735	0.0738675	+	0.997268i	$0.476466\pi$
$350$	−4.67211e21	−1.10901
$351$	2.93487e21	0.679952
$352$	1.89555e20	0.0428671
$353$	−5.66609e21	−1.25083	−0.625416	−	0.780292i	$-0.715071\pi$
$353$	−5.66609e21	−1.25083	−0.625416	+	0.780292i	$0.715071\pi$
$354$	1.08686e21	0.234232
$355$	4.90828e21	1.03273
$356$	−2.01345e21	−0.413633
$357$	−4.12289e21	−0.827030
$358$	1.20188e21	0.235427
$359$	−7.99486e21	−1.52935	−0.764677	−	0.644414i	$-0.777101\pi$
$359$	−7.99486e21	−1.52935	−0.764677	+	0.644414i	$0.777101\pi$
$360$	−1.93990e21	−0.362417
$361$	3.37606e20	0.0616025
$362$	−1.95020e21	−0.347580
$363$	−2.89431e21	−0.503894
$364$	3.20989e21	0.545919
$365$	7.34984e21	1.22120
$366$	−1.40015e21	−0.227292
$367$	1.36525e21	0.216547	0.108273	−	0.994121i	$-0.465468\pi$
$367$	1.36525e21	0.216547	0.108273	+	0.994121i	$0.465468\pi$
$368$	5.60350e20	0.0868466
$369$	−4.90165e21	−0.742366
$370$	1.08780e22	1.61003
$371$	3.66819e21	0.530607
$372$	8.15518e20	0.115297
$373$	−1.82317e21	−0.251942	−0.125971	−	0.992034i	$-0.540205\pi$
$373$	−1.82317e21	−0.251942	−0.125971	+	0.992034i	$0.540205\pi$
$374$	1.33126e21	0.179827
$375$	3.77392e20	0.0498342
$376$	−3.90180e21	−0.503696
$377$	−1.75095e21	−0.220990
$378$	7.74224e21	0.955402
$379$	5.95497e21	0.718532	0.359266	−	0.933235i	$-0.383027\pi$
$379$	5.95497e21	0.718532	0.359266	+	0.933235i	$0.383027\pi$
$380$	−6.27405e21	−0.740266
$381$	−7.30426e21	−0.842779
$382$	−8.35843e21	−0.943161
$383$	2.83557e21	0.312933	0.156466	−	0.987683i	$-0.449990\pi$
$383$	2.83557e21	0.312933	0.156466	+	0.987683i	$0.449990\pi$
$384$	4.38398e20	0.0473210
$385$	−4.86119e21	−0.513247
$386$	−5.54157e21	−0.572322
$387$	−2.44964e21	−0.247491
$388$	3.77809e21	0.373424
$389$	1.16641e22	1.12793	0.563963	−	0.825800i	$-0.309276\pi$
$389$	1.16641e22	1.12793	0.563963	+	0.825800i	$0.309276\pi$
$390$	−4.26184e21	−0.403226
$391$	3.93539e21	0.364322
$392$	4.56486e21	0.413519
$393$	1.06801e22	0.946756
$394$	−1.17640e22	−1.02055
$395$	−2.98989e22	−2.53852
$396$	−1.04087e21	−0.0864939
$397$	−2.09530e21	−0.170423	−0.0852113	−	0.996363i	$-0.527157\pi$
$397$	−2.09530e21	−0.170423	−0.0852113	+	0.996363i	$0.527157\pi$
$398$	1.47010e22	1.17042
$399$	1.04256e22	0.812513
$400$	3.48907e21	0.266195
$401$	2.60385e22	1.94486	0.972430	−	0.233194i	$-0.0749176\pi$
$401$	2.60385e22	1.94486	0.972430	+	0.233194i	$0.0749176\pi$
$402$	−4.15387e21	−0.303760
$403$	−4.45914e21	−0.319270
$404$	−2.49137e21	−0.174661
$405$	4.65257e21	0.319393
$406$	−4.61905e21	−0.310514
$407$	5.83665e21	0.384248
$408$	3.07891e21	0.198512
$409$	−2.74091e22	−1.73080	−0.865400	−	0.501082i	$-0.832935\pi$
$409$	−2.74091e22	−1.73080	−0.865400	+	0.501082i	$0.832935\pi$
$410$	1.70957e22	1.05736
$411$	2.61144e21	0.158207
$412$	9.43151e21	0.559700
$413$	−1.56772e22	−0.911365
$414$	−3.07693e21	−0.175232
$415$	−1.74658e22	−0.974495
$416$	−2.39710e21	−0.131037
$417$	−5.03975e21	−0.269931
$418$	−3.36638e21	−0.176671
$419$	−3.15789e22	−1.62397	−0.811985	−	0.583679i	$-0.801613\pi$
$419$	−3.15789e22	−1.62397	−0.811985	+	0.583679i	$0.801613\pi$
$420$	−1.12428e22	−0.566573
$421$	2.96704e22	1.46530	0.732648	−	0.680608i	$-0.238284\pi$
$421$	2.96704e22	1.46530	0.732648	+	0.680608i	$0.238284\pi$
$422$	−7.54306e21	−0.365083
$423$	2.14251e22	1.01632
$424$	−2.73935e21	−0.127361
$425$	2.45040e22	1.11669
$426$	6.09083e21	0.272079
$427$	2.01961e22	0.884365
$428$	5.99202e21	0.257218
$429$	−2.28671e21	−0.0962332
$430$	8.54370e21	0.352504
$431$	−1.92658e21	−0.0779346	−0.0389673	−	0.999240i	$-0.512407\pi$
$431$	−1.92658e21	−0.0779346	−0.0389673	+	0.999240i	$0.512407\pi$
$432$	−5.78179e21	−0.229325
$433$	3.02417e21	0.117614	0.0588070	−	0.998269i	$-0.481270\pi$
$433$	3.02417e21	0.117614	0.0588070	+	0.998269i	$0.481270\pi$
$434$	−1.17633e22	−0.448607
$435$	6.13281e21	0.229351
$436$	−2.45682e22	−0.901027
$437$	−9.95144e21	−0.357926
$438$	9.12064e21	0.321733
$439$	2.18819e22	0.757071	0.378536	−	0.925587i	$-0.376428\pi$
$439$	2.18819e22	0.757071	0.378536	+	0.925587i	$0.376428\pi$
$440$	3.63026e21	0.123194
$441$	−2.50660e22	−0.834367
$442$	−1.68350e22	−0.549699
$443$	−2.01050e21	−0.0643979	−0.0321990	−	0.999481i	$-0.510251\pi$
$443$	−2.01050e21	−0.0643979	−0.0321990	+	0.999481i	$0.510251\pi$
$444$	1.34988e22	0.424171
$445$	−3.85604e22	−1.18873
$446$	3.25562e22	0.984663
$447$	−2.33795e21	−0.0693779
$448$	−6.32359e21	−0.184120
$449$	−4.78968e22	−1.36840	−0.684200	−	0.729295i	$-0.739848\pi$
$449$	−4.78968e22	−1.36840	−0.684200	+	0.729295i	$0.739848\pi$
$450$	−1.91588e22	−0.537107
$451$	9.17277e21	0.252348
$452$	2.83379e22	0.765051
$453$	−5.46292e21	−0.144740
$454$	2.12535e22	0.552656
$455$	6.14741e22	1.56890
$456$	−7.78566e21	−0.195027
$457$	6.48444e22	1.59435	0.797177	−	0.603746i	$-0.206326\pi$
$457$	6.48444e22	1.59435	0.797177	+	0.603746i	$0.206326\pi$
$458$	−1.63914e22	−0.395603
$459$	−4.06060e22	−0.962017
$460$	1.07315e22	0.249586
$461$	−4.94636e22	−1.12935	−0.564674	−	0.825314i	$-0.690998\pi$
$461$	−4.94636e22	−1.12935	−0.564674	+	0.825314i	$0.690998\pi$
$462$	−6.03239e21	−0.135218
$463$	3.26536e21	0.0718609	0.0359305	−	0.999354i	$-0.488561\pi$
$463$	3.26536e21	0.0718609	0.0359305	+	0.999354i	$0.488561\pi$
$464$	3.44944e21	0.0745324
$465$	1.56184e22	0.331349
$466$	3.92735e22	0.818124
$467$	−1.09833e22	−0.224667	−0.112333	−	0.993671i	$-0.535832\pi$
$467$	−1.09833e22	−0.224667	−0.112333	+	0.993671i	$0.535832\pi$
$468$	1.31627e22	0.264396
$469$	5.99166e22	1.18189
$470$	−7.47252e22	−1.44755
$471$	2.18778e20	0.00416223
$472$	1.17075e22	0.218754
$473$	4.58417e21	0.0841281
$474$	−3.71025e22	−0.668785
$475$	−6.19635e22	−1.09709
$476$	−4.44111e22	−0.772383
$477$	1.50420e22	0.256980
$478$	−1.37046e22	−0.230000
$479$	5.84533e22	0.963734	0.481867	−	0.876244i	$-0.339959\pi$
$479$	5.84533e22	0.963734	0.481867	+	0.876244i	$0.339959\pi$
$480$	8.39597e21	0.135994
$481$	−7.38098e22	−1.17457
$482$	1.82331e22	0.285076
$483$	−1.78325e22	−0.273944
$484$	−3.11771e22	−0.470599
$485$	7.23560e22	1.07317
$486$	5.02780e22	0.732773
$487$	−8.54084e22	−1.22322	−0.611610	−	0.791160i	$-0.709478\pi$
$487$	−8.54084e22	−1.22322	−0.611610	+	0.791160i	$0.709478\pi$
$488$	−1.50822e22	−0.212274
$489$	7.00820e22	0.969352
$490$	8.74237e22	1.18840
$491$	4.73139e22	0.632115	0.316058	−	0.948740i	$-0.397641\pi$
$491$	4.73139e22	0.632115	0.316058	+	0.948740i	$0.397641\pi$
$492$	2.12145e22	0.278567
$493$	2.42257e22	0.312664
$494$	4.25709e22	0.540050
$495$	−1.99341e22	−0.248572
$496$	8.78465e21	0.107679
$497$	−8.78560e22	−1.05863
$498$	−2.16738e22	−0.256736
$499$	7.86063e22	0.915382	0.457691	−	0.889111i	$-0.348677\pi$
$499$	7.86063e22	0.915382	0.457691	+	0.889111i	$0.348677\pi$
$500$	4.06522e21	0.0465413
$501$	−2.74926e22	−0.309453
$502$	−9.38768e22	−1.03891
$503$	−1.44291e23	−1.57004	−0.785022	−	0.619468i	$-0.787348\pi$
$503$	−1.44291e23	−1.57004	−0.785022	+	0.619468i	$0.787348\pi$
$504$	3.47234e22	0.371503
$505$	−4.77134e22	−0.501953
$506$	5.75805e21	0.0595657
$507$	−2.37116e22	−0.241208
$508$	−7.86804e22	−0.787091
$509$	8.61175e22	0.847208	0.423604	−	0.905847i	$-0.360765\pi$
$509$	8.61175e22	0.847208	0.423604	+	0.905847i	$0.360765\pi$
$510$	5.89656e22	0.570496
$511$	−1.31559e23	−1.25182
$512$	4.72237e21	0.0441942
$513$	1.02681e23	0.945130
$514$	6.36427e22	0.576185
$515$	1.80627e23	1.60850
$516$	1.06021e22	0.0928690
$517$	−4.00942e22	−0.345471
$518$	−1.94711e23	−1.65040
$519$	−3.83747e22	−0.319980
$520$	−4.59080e22	−0.376582
$521$	1.98567e23	1.60246	0.801229	−	0.598358i	$-0.204180\pi$
$521$	1.98567e23	1.60246	0.801229	+	0.598358i	$0.204180\pi$
$522$	−1.89411e22	−0.150386
$523$	1.21175e23	0.946563	0.473282	−	0.880911i	$-0.343069\pi$
$523$	1.21175e23	0.946563	0.473282	+	0.880911i	$0.343069\pi$
$524$	1.15044e23	0.884198
$525$	−1.11036e23	−0.839670
$526$	2.31435e22	0.172207
$527$	6.16954e22	0.451713
$528$	4.50490e21	0.0324562
$529$	−1.24029e23	−0.879323
$530$	−5.24625e22	−0.366019
$531$	−6.42868e22	−0.441386
$532$	1.12303e23	0.758825
$533$	−1.15998e23	−0.771381
$534$	−4.78508e22	−0.313176
$535$	1.14756e23	0.739210
$536$	−4.47449e22	−0.283689
$537$	2.85635e22	0.178250
$538$	7.42390e21	0.0456019
$539$	4.69077e22	0.283622
$540$	−1.10730e23	−0.659048
$541$	−1.67082e23	−0.978932	−0.489466	−	0.872022i	$-0.662808\pi$
$541$	−1.67082e23	−0.978932	−0.489466	+	0.872022i	$0.662808\pi$
$542$	1.97237e23	1.13761
$543$	−4.63476e22	−0.263165
$544$	3.31656e22	0.185395
$545$	−4.70517e23	−2.58943
$546$	7.62851e22	0.413335
$547$	4.10773e22	0.219134	0.109567	−	0.993979i	$-0.465054\pi$
$547$	4.10773e22	0.219134	0.109567	+	0.993979i	$0.465054\pi$
$548$	2.81301e22	0.147753
$549$	8.28176e22	0.428309
$550$	3.58530e22	0.182576
$551$	−6.12597e22	−0.307175
$552$	1.33171e22	0.0657546
$553$	5.35177e23	2.60216
$554$	−3.97238e22	−0.190203
$555$	2.58523e23	1.21901
$556$	−5.42875e22	−0.252095
$557$	−1.50464e23	−0.688118	−0.344059	−	0.938948i	$-0.611802\pi$
$557$	−1.50464e23	−0.688118	−0.344059	+	0.938948i	$0.611802\pi$
$558$	−4.82373e22	−0.217266
$559$	−5.79710e22	−0.257164
$560$	−1.21106e23	−0.529136
$561$	3.16383e22	0.136154
$562$	−1.27443e23	−0.540204
$563$	−1.14744e22	−0.0479082	−0.0239541	−	0.999713i	$-0.507626\pi$
$563$	−1.14744e22	−0.0479082	−0.0239541	+	0.999713i	$0.507626\pi$
$564$	−9.27287e22	−0.381366
$565$	5.42711e23	2.19865
$566$	3.04784e23	1.21633
$567$	−8.32790e22	−0.327401
$568$	6.56096e22	0.254101
$569$	−4.09528e23	−1.56253	−0.781267	−	0.624197i	$-0.785426\pi$
$569$	−4.09528e23	−1.56253	−0.781267	+	0.624197i	$0.785426\pi$
$570$	−1.49107e23	−0.560481
$571$	−2.45795e23	−0.910260	−0.455130	−	0.890425i	$-0.650407\pi$
$571$	−2.45795e23	−0.910260	−0.455130	+	0.890425i	$0.650407\pi$
$572$	−2.46322e22	−0.0898745
$573$	−1.98643e23	−0.714101
$574$	−3.06005e23	−1.08387
$575$	1.05986e23	0.369890
$576$	−2.59309e22	−0.0891716
$577$	−8.68049e22	−0.294137	−0.147069	−	0.989126i	$-0.546984\pi$
$577$	−8.68049e22	−0.294137	−0.147069	+	0.989126i	$0.546984\pi$
$578$	2.11514e22	0.0706240
$579$	−1.31699e23	−0.433326
$580$	6.60617e22	0.214196
$581$	3.12630e23	0.998926
$582$	8.97887e22	0.282733
$583$	−2.81491e22	−0.0873537
$584$	9.82462e22	0.300474
$585$	2.52084e23	0.759838
$586$	1.33625e23	0.396971
$587$	3.99552e23	1.16990	0.584951	−	0.811069i	$-0.301114\pi$
$587$	3.99552e23	1.16990	0.584951	+	0.811069i	$0.301114\pi$
$588$	1.08487e23	0.313090
$589$	−1.56010e23	−0.443784
$590$	2.24215e23	0.628671
$591$	−2.79578e23	−0.772698
$592$	1.45408e23	0.396144
$593$	2.25692e23	0.606110	0.303055	−	0.952973i	$-0.401993\pi$
$593$	2.25692e23	0.606110	0.303055	+	0.952973i	$0.401993\pi$
$594$	−5.94126e22	−0.157287
$595$	−8.50538e23	−2.21973
$596$	−2.51841e22	−0.0647937
$597$	3.49379e23	0.886165
$598$	−7.28158e22	−0.182081
$599$	−3.25464e23	−0.802370	−0.401185	−	0.915997i	$-0.631402\pi$
$599$	−3.25464e23	−0.802370	−0.401185	+	0.915997i	$0.631402\pi$
$600$	8.29199e22	0.201545
$601$	3.08585e23	0.739506	0.369753	−	0.929130i	$-0.379442\pi$
$601$	3.08585e23	0.739506	0.369753	+	0.929130i	$0.379442\pi$
$602$	−1.52928e23	−0.361342
$603$	2.45698e23	0.572406
$604$	−5.88458e22	−0.135177
$605$	−5.97088e23	−1.35244
$606$	−5.92090e22	−0.132242
$607$	4.99444e22	0.109998	0.0549988	−	0.998486i	$-0.482485\pi$
$607$	4.99444e22	0.109998	0.0549988	+	0.998486i	$0.482485\pi$
$608$	−8.38661e22	−0.182140
$609$	−1.09775e23	−0.235101
$610$	−2.88846e23	−0.610046
$611$	5.07027e23	1.05604
$612$	−1.82115e23	−0.374075
$613$	5.20372e22	0.105414	0.0527072	−	0.998610i	$-0.483215\pi$
$613$	5.20372e22	0.105414	0.0527072	+	0.998610i	$0.483215\pi$
$614$	−4.75268e22	−0.0949526
$615$	4.06289e23	0.800565
$616$	−6.49801e22	−0.126283
$617$	−1.26687e23	−0.242833	−0.121416	−	0.992602i	$-0.538744\pi$
$617$	−1.26687e23	−0.242833	−0.121416	+	0.992602i	$0.538744\pi$
$618$	2.24146e23	0.423768
$619$	−7.40213e22	−0.138034	−0.0690170	−	0.997615i	$-0.521986\pi$
$619$	−7.40213e22	−0.138034	−0.0690170	+	0.997615i	$0.521986\pi$
$620$	1.68239e23	0.309455
$621$	−1.75631e23	−0.318657
$622$	−2.56471e23	−0.459008
$623$	6.90214e23	1.21853
$624$	−5.69686e22	−0.0992125
$625$	−5.41928e23	−0.931025
$626$	−1.07250e23	−0.181768
$627$	−8.00041e22	−0.133764
$628$	2.35665e21	0.00388721
$629$	1.02121e24	1.66182
$630$	6.65003e23	1.06765
$631$	8.00054e23	1.26727	0.633636	−	0.773631i	$-0.281562\pi$
$631$	8.00054e23	1.26727	0.633636	+	0.773631i	$0.281562\pi$
$632$	−3.99662e23	−0.624595
$633$	−1.79266e23	−0.276417
$634$	7.73572e23	1.17691
$635$	−1.50685e24	−2.26200
$636$	−6.51023e22	−0.0964297
$637$	−5.93190e23	−0.866979
$638$	3.54458e22	0.0511198
$639$	−3.60268e23	−0.512706
$640$	9.04402e22	0.127008
$641$	−2.73379e23	−0.378854	−0.189427	−	0.981895i	$-0.560663\pi$
$641$	−2.73379e23	−0.378854	−0.189427	+	0.981895i	$0.560663\pi$
$642$	1.42404e23	0.194749
$643$	−4.94746e23	−0.667712	−0.333856	−	0.942624i	$-0.608350\pi$
$643$	−4.94746e23	−0.667712	−0.333856	+	0.942624i	$0.608350\pi$
$644$	−1.92089e23	−0.255843
$645$	2.03046e23	0.266893
$646$	−5.88999e23	−0.764079
$647$	5.85656e23	0.749818	0.374909	−	0.927062i	$-0.377674\pi$
$647$	5.85656e23	0.749818	0.374909	+	0.927062i	$0.377674\pi$
$648$	6.21915e22	0.0785857
$649$	1.20304e23	0.150038
$650$	−4.53394e23	−0.558100
$651$	−2.79562e23	−0.339656
$652$	7.54914e23	0.905301
$653$	−1.33857e24	−1.58446	−0.792229	−	0.610224i	$-0.791079\pi$
$653$	−1.33857e24	−1.58446	−0.792229	+	0.610224i	$0.791079\pi$
$654$	−5.83878e23	−0.682200
$655$	2.20327e24	2.54107
$656$	2.28520e23	0.260161
$657$	−5.39478e23	−0.606273
$658$	1.33755e24	1.48385
$659$	9.95800e23	1.09055	0.545276	−	0.838257i	$-0.316425\pi$
$659$	9.95800e23	1.09055	0.545276	+	0.838257i	$0.316425\pi$
$660$	8.62755e22	0.0932747
$661$	−3.55898e23	−0.379851	−0.189925	−	0.981799i	$-0.560825\pi$
$661$	−3.55898e23	−0.379851	−0.189925	+	0.981799i	$0.560825\pi$
$662$	−4.96872e23	−0.523542
$663$	−4.00095e23	−0.416197
$664$	−2.33467e23	−0.239772
$665$	2.15076e24	2.18076
$666$	−7.98446e23	−0.799309
$667$	1.04782e23	0.103566
$668$	−2.96146e23	−0.289006
$669$	7.73719e23	0.745523
$670$	−8.56930e23	−0.815285
$671$	−1.54982e23	−0.145593
$672$	−1.50284e23	−0.139404
$673$	−8.19644e23	−0.750753	−0.375377	−	0.926872i	$-0.622487\pi$
$673$	−8.19644e23	−0.750753	−0.375377	+	0.926872i	$0.622487\pi$
$674$	−4.59714e22	−0.0415794
$675$	−1.09358e24	−0.976719
$676$	−2.55418e23	−0.225270
$677$	−3.76541e23	−0.327950	−0.163975	−	0.986464i	$-0.552432\pi$
$677$	−3.76541e23	−0.327950	−0.163975	+	0.986464i	$0.552432\pi$
$678$	6.73467e23	0.579247
$679$	−1.29514e24	−1.10008
$680$	6.35170e23	0.532800
$681$	5.05102e23	0.418436
$682$	9.02695e22	0.0738540
$683$	−1.24736e24	−1.00789	−0.503946	−	0.863735i	$-0.668119\pi$
$683$	−1.24736e24	−1.00789	−0.503946	+	0.863735i	$0.668119\pi$
$684$	4.60516e23	0.367509
$685$	5.38732e23	0.424622
$686$	−2.26923e23	−0.176654
$687$	−3.89552e23	−0.299525
$688$	1.14205e23	0.0867326
$689$	3.55970e23	0.267024
$690$	2.55041e23	0.188970
$691$	9.48314e23	0.694047	0.347023	−	0.937856i	$-0.387192\pi$
$691$	9.48314e23	0.694047	0.347023	+	0.937856i	$0.387192\pi$
$692$	−4.13367e23	−0.298837
$693$	3.56811e23	0.254804
$694$	1.90454e24	1.34349
$695$	−1.03969e24	−0.724488
$696$	8.19780e22	0.0564311
$697$	1.60492e24	1.09137
$698$	1.55503e23	0.104464
$699$	9.33359e23	0.619431
$700$	−1.19606e24	−0.784188
$701$	−1.86029e23	−0.120498	−0.0602488	−	0.998183i	$-0.519189\pi$
$701$	−1.86029e23	−0.120498	−0.0602488	+	0.998183i	$0.519189\pi$
$702$	7.51326e23	0.480799
$703$	−2.58234e24	−1.63265
$704$	4.85262e22	0.0303116
$705$	−1.77589e24	−1.09600
$706$	−1.45052e24	−0.884471
$707$	8.54048e23	0.514538
$708$	2.78236e23	0.165627
$709$	1.93226e24	1.13651	0.568253	−	0.822854i	$-0.307619\pi$
$709$	1.93226e24	1.13651	0.568253	+	0.822854i	$0.307619\pi$
$710$	1.25652e24	0.730253
$711$	2.19458e24	1.26026
$712$	−5.15442e23	−0.292483
$713$	2.66848e23	0.149625
$714$	−1.05546e24	−0.584799
$715$	−4.71742e23	−0.258287
$716$	3.07682e23	0.166472
$717$	−3.25697e23	−0.174141
$718$	−2.04668e24	−1.08142
$719$	−1.37714e24	−0.719089	−0.359545	−	0.933128i	$-0.617068\pi$
$719$	−1.37714e24	−0.719089	−0.359545	+	0.933128i	$0.617068\pi$
$720$	−4.96615e23	−0.256267
$721$	−3.23315e24	−1.64883
$722$	8.64270e22	0.0435596
$723$	4.33321e23	0.215841
$724$	−4.99250e23	−0.245776
$725$	6.52436e23	0.317442
$726$	−7.40944e23	−0.356307
$727$	2.26138e24	1.07481	0.537404	−	0.843325i	$-0.319405\pi$
$727$	2.26138e24	1.07481	0.537404	+	0.843325i	$0.319405\pi$
$728$	8.21732e23	0.386023
$729$	7.16178e23	0.332535
$730$	1.88156e24	0.863522
$731$	8.02070e23	0.363843
$732$	−3.58438e23	−0.160720
$733$	−2.27165e23	−0.100683	−0.0503416	−	0.998732i	$-0.516031\pi$
$733$	−2.27165e23	−0.100683	−0.0503416	+	0.998732i	$0.516031\pi$
$734$	3.49505e23	0.153122
$735$	2.07768e24	0.899779
$736$	1.43450e23	0.0614098
$737$	−4.59790e23	−0.194575
$738$	−1.25482e24	−0.524932
$739$	−6.37558e23	−0.263659	−0.131829	−	0.991272i	$-0.542085\pi$
$739$	−6.37558e23	−0.263659	−0.131829	+	0.991272i	$0.542085\pi$
$740$	2.78477e24	1.13846
$741$	1.01172e24	0.408891
$742$	9.39056e23	0.375196
$743$	−1.43514e24	−0.566876	−0.283438	−	0.958991i	$-0.591475\pi$
$743$	−1.43514e24	−0.566876	−0.283438	+	0.958991i	$0.591475\pi$
$744$	2.08773e23	0.0815274
$745$	−4.82312e23	−0.186209
$746$	−4.66731e23	−0.178150
$747$	1.28199e24	0.483793
$748$	3.40804e23	0.127157
$749$	−2.05408e24	−0.757742
$750$	9.66124e22	0.0352381
$751$	−3.45967e24	−1.24766	−0.623829	−	0.781561i	$-0.714424\pi$
$751$	−3.45967e24	−1.24766	−0.623829	+	0.781561i	$0.714424\pi$
$752$	−9.98861e23	−0.356167
$753$	−2.23104e24	−0.786593
$754$	−4.48244e23	−0.156264
$755$	−1.12698e24	−0.388480
$756$	1.98201e24	0.675571
$757$	−4.54182e24	−1.53079	−0.765395	−	0.643561i	$-0.777456\pi$
$757$	−4.54182e24	−1.53079	−0.765395	+	0.643561i	$0.777456\pi$
$758$	1.52447e24	0.508079
$759$	1.36844e23	0.0450993
$760$	−1.60616e24	−0.523447
$761$	3.84040e24	1.23768	0.618838	−	0.785519i	$-0.287604\pi$
$761$	3.84040e24	1.23768	0.618838	+	0.785519i	$0.287604\pi$
$762$	−1.86989e24	−0.595935
$763$	8.42204e24	2.65435
$764$	−2.13976e24	−0.666916
$765$	−3.48777e24	−1.07504
$766$	7.25906e23	0.221277
$767$	−1.52135e24	−0.458637
$768$	1.12230e23	0.0334610
$769$	5.15334e24	1.51955	0.759775	−	0.650186i	$-0.225309\pi$
$769$	5.15334e24	1.51955	0.759775	+	0.650186i	$0.225309\pi$
$770$	−1.24446e24	−0.362920
$771$	1.51251e24	0.436250
$772$	−1.41864e24	−0.404693
$773$	5.28998e24	1.49255	0.746274	−	0.665639i	$-0.231841\pi$
$773$	5.28998e24	1.49255	0.746274	+	0.665639i	$0.231841\pi$
$774$	−6.27108e23	−0.175002
$775$	1.66155e24	0.458616
$776$	9.67191e23	0.264051
$777$	−4.62744e24	−1.24957
$778$	2.98602e24	0.797564
$779$	−4.05836e24	−1.07222
$780$	−1.09103e24	−0.285124
$781$	6.74193e23	0.174281
$782$	1.00746e24	0.257614
$783$	−1.08116e24	−0.273474
$784$	1.16860e24	0.292402
$785$	4.51333e22	0.0111713
$786$	2.73410e24	0.669458
$787$	5.81069e24	1.40748	0.703740	−	0.710457i	$-0.251512\pi$
$787$	5.81069e24	1.40748	0.703740	+	0.710457i	$0.251512\pi$
$788$	−3.01158e24	−0.721641
$789$	5.50019e23	0.130384
$790$	−7.65412e24	−1.79500
$791$	−9.71429e24	−2.25378
$792$	−2.66461e23	−0.0611604
$793$	1.95989e24	0.445050
$794$	−5.36397e23	−0.120507
$795$	−1.24680e24	−0.277126
$796$	3.76346e24	0.827610
$797$	1.38132e24	0.300538	0.150269	−	0.988645i	$-0.451986\pi$
$797$	1.38132e24	0.300538	0.150269	+	0.988645i	$0.451986\pi$
$798$	2.66895e24	0.574533
$799$	−7.01509e24	−1.49412
$800$	8.93201e23	0.188228
$801$	2.83034e24	0.590149
$802$	6.66585e24	1.37522
$803$	1.00956e24	0.206087
$804$	−1.06339e24	−0.214791
$805$	−3.67879e24	−0.735259
$806$	−1.14154e24	−0.225758
$807$	1.76434e23	0.0345268
$808$	−6.37791e23	−0.123504
$809$	−3.50030e24	−0.670723	−0.335362	−	0.942089i	$-0.608858\pi$
$809$	−3.50030e24	−0.670723	−0.335362	+	0.942089i	$0.608858\pi$
$810$	1.19106e24	0.225845
$811$	−2.96509e24	−0.556365	−0.278183	−	0.960528i	$-0.589732\pi$
$811$	−2.96509e24	−0.556365	−0.278183	+	0.960528i	$0.589732\pi$
$812$	−1.18248e24	−0.219566
$813$	4.68745e24	0.861325
$814$	1.49418e24	0.271704
$815$	1.44577e25	2.60171
$816$	7.88201e23	0.140369
$817$	−2.02820e24	−0.357457
$818$	−7.01673e24	−1.22386
$819$	−4.51220e24	−0.778888
$820$	4.37649e24	0.747667
$821$	8.29888e24	1.40315	0.701573	−	0.712598i	$-0.252482\pi$
$821$	8.29888e24	1.40315	0.701573	+	0.712598i	$0.252482\pi$
$822$	6.68529e23	0.111869
$823$	−1.89319e24	−0.313541	−0.156771	−	0.987635i	$-0.550108\pi$
$823$	−1.89319e24	−0.313541	−0.156771	+	0.987635i	$0.550108\pi$
$824$	2.41447e24	0.395767
$825$	8.52070e23	0.138235
$826$	−4.01336e24	−0.644433
$827$	−1.23165e24	−0.195745	−0.0978724	−	0.995199i	$-0.531204\pi$
$827$	−1.23165e24	−0.195745	−0.0978724	+	0.995199i	$0.531204\pi$
$828$	−7.87694e23	−0.123908
$829$	−3.32086e24	−0.517055	−0.258528	−	0.966004i	$-0.583237\pi$
$829$	−3.32086e24	−0.517055	−0.258528	+	0.966004i	$0.583237\pi$
$830$	−4.47124e24	−0.689072
$831$	−9.44062e23	−0.144010
$832$	−6.13658e23	−0.0926569
$833$	8.20720e24	1.22663
$834$	−1.29018e24	−0.190870
$835$	−5.67163e24	−0.830564
$836$	−8.61793e23	−0.124925
$837$	−2.75339e24	−0.395094
$838$	−8.08420e24	−1.14832
$839$	−7.24116e23	−0.101820	−0.0509098	−	0.998703i	$-0.516212\pi$
$839$	−7.24116e23	−0.101820	−0.0509098	+	0.998703i	$0.516212\pi$
$840$	−2.87816e24	−0.400628
$841$	−6.61212e24	−0.911119
$842$	7.59562e24	1.03612
$843$	−3.02877e24	−0.409007
$844$	−1.93102e24	−0.258153
$845$	−4.89162e24	−0.647397
$846$	5.48483e24	0.718646
$847$	1.06876e25	1.38635
$848$	−7.01273e23	−0.0900580
$849$	7.24338e24	0.920929
$850$	6.27303e24	0.789617
$851$	4.41699e24	0.550460
$852$	1.55925e24	0.192389
$853$	−8.97587e23	−0.109650	−0.0548251	−	0.998496i	$-0.517460\pi$
$853$	−8.97587e23	−0.109650	−0.0548251	+	0.998496i	$0.517460\pi$
$854$	5.17021e24	0.625340
$855$	8.81955e24	1.05617
$856$	1.53396e24	0.181880
$857$	−1.01446e25	−1.19097	−0.595483	−	0.803368i	$-0.703039\pi$
$857$	−1.01446e25	−1.19097	−0.595483	+	0.803368i	$0.703039\pi$
$858$	−5.85399e23	−0.0680472
$859$	8.66799e23	0.0997646	0.0498823	−	0.998755i	$-0.484115\pi$
$859$	8.66799e23	0.0997646	0.0498823	+	0.998755i	$0.484115\pi$
$860$	2.18719e24	0.249258
$861$	−7.27240e24	−0.820636
$862$	−4.93204e23	−0.0551081
$863$	2.24930e24	0.248860	0.124430	−	0.992228i	$-0.460290\pi$
$863$	2.24930e24	0.248860	0.124430	+	0.992228i	$0.460290\pi$
$864$	−1.48014e24	−0.162157
$865$	−7.91657e24	−0.858817
$866$	7.74187e23	0.0831656
$867$	5.02676e23	0.0534719
$868$	−3.01140e24	−0.317213
$869$	−4.10686e24	−0.428393
$870$	1.57000e24	0.162176
$871$	5.81446e24	0.594779
$872$	−6.28946e24	−0.637123
$873$	−5.31093e24	−0.532782
$874$	−2.54757e24	−0.253092
$875$	−1.39357e24	−0.137107
$876$	2.33488e24	0.227499
$877$	7.32275e24	0.706606	0.353303	−	0.935509i	$-0.385058\pi$
$877$	7.32275e24	0.706606	0.353303	+	0.935509i	$0.385058\pi$
$878$	5.60177e24	0.535330
$879$	3.17568e24	0.300560
$880$	9.29348e23	0.0871115
$881$	−8.73491e24	−0.810893	−0.405446	−	0.914119i	$-0.632884\pi$
$881$	−8.73491e24	−0.810893	−0.405446	+	0.914119i	$0.632884\pi$
$882$	−6.41690e24	−0.589987
$883$	−1.80866e25	−1.64699	−0.823496	−	0.567323i	$-0.807979\pi$
$883$	−1.80866e25	−1.64699	−0.823496	+	0.567323i	$0.807979\pi$
$884$	−4.30977e24	−0.388696
$885$	5.32862e24	0.475989
$886$	−5.14687e23	−0.0455362
$887$	−2.95323e24	−0.258790	−0.129395	−	0.991593i	$-0.541303\pi$
$887$	−2.95323e24	−0.258790	−0.129395	+	0.991593i	$0.541303\pi$
$888$	3.45570e24	0.299934
$889$	2.69719e25	2.31871
$890$	−9.87147e24	−0.840556
$891$	6.39069e23	0.0538998
$892$	8.33439e24	0.696262
$893$	1.77391e25	1.46789
$894$	−5.98515e23	−0.0490576
$895$	5.89255e24	0.478418
$896$	−1.61884e24	−0.130192
$897$	−1.73051e24	−0.137860
$898$	−1.22616e25	−0.967604
$899$	1.64268e24	0.128409
$900$	−4.90464e24	−0.379792
$901$	−4.92510e24	−0.377794
$902$	2.34823e24	0.178437
$903$	−3.63444e24	−0.273585
$904$	7.25449e24	0.540973
$905$	−9.56137e24	−0.706329
$906$	−1.39851e24	−0.102347
$907$	1.14361e25	0.829116	0.414558	−	0.910023i	$-0.363936\pi$
$907$	1.14361e25	0.829116	0.414558	+	0.910023i	$0.363936\pi$
$908$	5.44089e24	0.390787
$909$	3.50216e24	0.249197
$910$	1.57374e25	1.10938
$911$	−7.42471e24	−0.518529	−0.259265	−	0.965806i	$-0.583480\pi$
$911$	−7.42471e24	−0.518529	−0.259265	+	0.965806i	$0.583480\pi$
$912$	−1.99313e24	−0.137905
$913$	−2.39907e24	−0.164453
$914$	1.66002e25	1.12738
$915$	−6.86460e24	−0.461887
$916$	−4.19620e24	−0.279734
$917$	−3.94375e25	−2.60478
$918$	−1.03951e25	−0.680249
$919$	2.07572e24	0.134582	0.0672910	−	0.997733i	$-0.478564\pi$
$919$	2.07572e24	0.134582	0.0672910	+	0.997733i	$0.478564\pi$
$920$	2.74727e24	0.176484
$921$	−1.12950e24	−0.0718920
$922$	−1.26627e25	−0.798569
$923$	−8.52577e24	−0.532745
$924$	−1.54429e24	−0.0956132
$925$	2.75028e25	1.68722
$926$	8.35932e23	0.0508133
$927$	−1.32580e25	−0.798549
$928$	8.83056e23	0.0527024
$929$	2.31300e25	1.36786	0.683930	−	0.729548i	$-0.260269\pi$
$929$	2.31300e25	1.36786	0.683930	+	0.729548i	$0.260269\pi$
$930$	3.99830e24	0.234299
$931$	−2.07536e25	−1.20510
$932$	1.00540e25	0.578501
$933$	−6.09520e24	−0.347532
$934$	−2.81172e24	−0.158863
$935$	6.52689e24	0.365433
$936$	3.36965e24	0.186956
$937$	6.85999e24	0.377170	0.188585	−	0.982057i	$-0.439610\pi$
$937$	6.85999e24	0.377170	0.188585	+	0.982057i	$0.439610\pi$
$938$	1.53387e25	0.835725
$939$	−2.54887e24	−0.137623
$940$	−1.91296e25	−1.02358
$941$	1.00555e25	0.533204	0.266602	−	0.963807i	$-0.414099\pi$
$941$	1.00555e25	0.533204	0.266602	+	0.963807i	$0.414099\pi$
$942$	5.60072e22	0.00294314
$943$	6.94166e24	0.361505
$944$	2.99712e24	0.154683
$945$	3.79584e25	1.94150
$946$	1.17355e24	0.0594875
$947$	2.54151e25	1.27678	0.638392	−	0.769712i	$-0.279600\pi$
$947$	2.54151e25	1.27678	0.638392	+	0.769712i	$0.279600\pi$
$948$	−9.49823e24	−0.472903
$949$	−1.27668e25	−0.629969
$950$	−1.58627e25	−0.775756
$951$	1.83844e25	0.891078
$952$	−1.13693e25	−0.546157
$953$	−1.52541e25	−0.726266	−0.363133	−	0.931737i	$-0.618293\pi$
$953$	−1.52541e25	−0.726266	−0.363133	+	0.931737i	$0.618293\pi$
$954$	3.85075e24	0.181712
$955$	−4.09795e25	−1.91663
$956$	−3.50837e24	−0.162635
$957$	8.42391e23	0.0387046
$958$	1.49640e25	0.681463
$959$	−9.64306e24	−0.435268
$960$	2.14937e24	0.0961624
$961$	−1.83667e25	−0.814484
$962$	−1.88953e25	−0.830550
$963$	−8.42308e24	−0.366984
$964$	4.66767e24	0.201579
$965$	−2.71691e25	−1.16303
$966$	−4.56512e24	−0.193708
$967$	2.94437e25	1.23842	0.619209	−	0.785226i	$-0.287453\pi$
$967$	2.94437e25	1.23842	0.619209	+	0.785226i	$0.287453\pi$
$968$	−7.98135e24	−0.332763
$969$	−1.39979e25	−0.578511
$970$	1.85231e25	0.758848
$971$	4.42559e25	1.79725	0.898623	−	0.438722i	$-0.144569\pi$
$971$	4.42559e25	1.79725	0.898623	+	0.438722i	$0.144569\pi$
$972$	1.28712e25	0.518149
$973$	1.86099e25	0.742651
$974$	−2.18646e25	−0.864947
$975$	−1.07752e25	−0.422557
$976$	−3.86104e24	−0.150100
$977$	−4.39121e24	−0.169231	−0.0846157	−	0.996414i	$-0.526966\pi$
$977$	−4.39121e24	−0.169231	−0.0846157	+	0.996414i	$0.526966\pi$
$978$	1.79410e25	0.685435
$979$	−5.29659e24	−0.200606
$980$	2.23805e25	0.840325
$981$	3.45359e25	1.28554
$982$	1.21124e25	0.446973
$983$	−3.24550e25	−1.18734	−0.593672	−	0.804707i	$-0.702322\pi$
$983$	−3.24550e25	−1.18734	−0.593672	+	0.804707i	$0.702322\pi$
$984$	5.43092e24	0.196977
$985$	−5.76761e25	−2.07390
$986$	6.20178e24	0.221087
$987$	3.17876e25	1.12347
$988$	1.08981e25	0.381873
$989$	3.46915e24	0.120519
$990$	−5.10313e24	−0.175767
$991$	−1.34212e25	−0.458315	−0.229157	−	0.973389i	$-0.573597\pi$
$991$	−1.34212e25	−0.458315	−0.229157	+	0.973389i	$0.573597\pi$
$992$	2.24887e24	0.0761404
$993$	−1.18085e25	−0.396393
$994$	−2.24911e25	−0.748561
$995$	7.20757e25	2.37844
$996$	−5.54850e24	−0.181540
$997$	−2.02909e25	−0.658252	−0.329126	−	0.944286i	$-0.606754\pi$
$997$	−2.02909e25	−0.658252	−0.329126	+	0.944286i	$0.606754\pi$
$998$	2.01232e25	0.647273
$999$	−4.55753e25	−1.45353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.18.a.a.1.1	✓	1
3.2	odd	2		18.18.a.a.1.1		1
4.3	odd	2		16.18.a.a.1.1		1
5.2	odd	4		50.18.b.b.49.2		2
5.3	odd	4		50.18.b.b.49.1		2
5.4	even	2		50.18.a.a.1.1		1
7.6	odd	2		98.18.a.a.1.1		1
8.3	odd	2		64.18.a.e.1.1		1
8.5	even	2		64.18.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.18.a.a.1.1	✓	1	1.1	even	1	trivial
16.18.a.a.1.1		1	4.3	odd	2
18.18.a.a.1.1		1	3.2	odd	2
50.18.a.a.1.1		1	5.4	even	2
50.18.b.b.49.1		2	5.3	odd	4
50.18.b.b.49.2		2	5.2	odd	4
64.18.a.a.1.1		1	8.5	even	2
64.18.a.e.1.1		1	8.3	odd	2
98.18.a.a.1.1		1	7.6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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