LMFDB - Embedded newform 6.20.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,20,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	6.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:	$13.7290017934$
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	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+512.000 q^{2} +19683.0 q^{3} +262144. q^{4} +1.95339e6 q^{5} +1.00777e7 q^{6} +4.04888e7 q^{7} +1.34218e8 q^{8} +3.87420e8 q^{9} +O(q^{10})$

\(q+512.000 q^{2} +19683.0 q^{3} +262144. q^{4} +1.95339e6 q^{5} +1.00777e7 q^{6} +4.04888e7 q^{7} +1.34218e8 q^{8} +3.87420e8 q^{9} +1.00014e9 q^{10} +1.91686e9 q^{11} +5.15978e9 q^{12} +3.13248e9 q^{13} +2.07303e10 q^{14} +3.84486e10 q^{15} +6.87195e10 q^{16} +6.07660e11 q^{17} +1.98359e11 q^{18} +2.50751e12 q^{19} +5.12069e11 q^{20} +7.96941e11 q^{21} +9.81433e11 q^{22} -1.35888e13 q^{23} +2.64181e12 q^{24} -1.52578e13 q^{25} +1.60383e12 q^{26} +7.62560e12 q^{27} +1.06139e13 q^{28} -9.51299e13 q^{29} +1.96857e13 q^{30} -1.28131e14 q^{31} +3.51844e13 q^{32} +3.77296e13 q^{33} +3.11122e14 q^{34} +7.90904e13 q^{35} +1.01560e14 q^{36} -3.06931e14 q^{37} +1.28385e15 q^{38} +6.16566e13 q^{39} +2.62180e14 q^{40} +1.92851e15 q^{41} +4.08034e14 q^{42} -6.03647e15 q^{43} +5.02493e14 q^{44} +7.56783e14 q^{45} -6.95749e15 q^{46} -2.20540e15 q^{47} +1.35261e15 q^{48} -9.75955e15 q^{49} -7.81197e15 q^{50} +1.19606e16 q^{51} +8.21161e14 q^{52} +3.05615e16 q^{53} +3.90431e15 q^{54} +3.74438e15 q^{55} +5.43431e15 q^{56} +4.93553e16 q^{57} -4.87065e16 q^{58} +5.11229e16 q^{59} +1.00791e16 q^{60} -6.21405e16 q^{61} -6.56032e16 q^{62} +1.56862e16 q^{63} +1.80144e16 q^{64} +6.11896e15 q^{65} +1.93175e16 q^{66} -1.37732e17 q^{67} +1.59294e17 q^{68} -2.67469e17 q^{69} +4.04943e16 q^{70} -1.38269e17 q^{71} +5.19987e16 q^{72} -3.31152e17 q^{73} -1.57149e17 q^{74} -3.00318e17 q^{75} +6.57329e17 q^{76} +7.76113e16 q^{77} +3.15682e16 q^{78} +1.69508e18 q^{79} +1.34236e17 q^{80} +1.50095e17 q^{81} +9.87396e17 q^{82} +3.36651e17 q^{83} +2.08913e17 q^{84} +1.18700e18 q^{85} -3.09067e18 q^{86} -1.87244e18 q^{87} +2.57277e17 q^{88} -2.05991e18 q^{89} +3.87473e17 q^{90} +1.26830e17 q^{91} -3.56223e18 q^{92} -2.52201e18 q^{93} -1.12917e18 q^{94} +4.89815e18 q^{95} +6.92534e17 q^{96} -2.80899e18 q^{97} -4.99689e18 q^{98} +7.42631e17 q^{99} +O(q^{100})\)

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 $

$2$	512.000	0.707107
$2$	512.000	0.707107
$3$	19683.0	0.577350
$3$	19683.0	0.577350
$4$	262144.	0.500000
$5$	1.95339e6	0.447274	0.223637	−	0.974672i	$-0.428207\pi$
$5$	1.95339e6	0.447274	0.223637	+	0.974672i	$0.428207\pi$
$6$	1.00777e7	0.408248
$7$	4.04888e7	0.379231	0.189615	−	0.981858i	$-0.439276\pi$
$7$	4.04888e7	0.379231	0.189615	+	0.981858i	$0.439276\pi$
$8$	1.34218e8	0.353553
$9$	3.87420e8	0.333333
$10$	1.00014e9	0.316271
$11$	1.91686e9	0.245109	0.122555	−	0.992462i	$-0.460891\pi$
$11$	1.91686e9	0.245109	0.122555	+	0.992462i	$0.460891\pi$
$12$	5.15978e9	0.288675
$13$	3.13248e9	0.0819269	0.0409634	−	0.999161i	$-0.486957\pi$
$13$	3.13248e9	0.0819269	0.0409634	+	0.999161i	$0.486957\pi$
$14$	2.07303e10	0.268156
$15$	3.84486e10	0.258234
$16$	6.87195e10	0.250000
$17$	6.07660e11	1.24278	0.621392	−	0.783500i	$-0.286567\pi$
$17$	6.07660e11	1.24278	0.621392	+	0.783500i	$0.286567\pi$
$18$	1.98359e11	0.235702
$19$	2.50751e12	1.78272	0.891361	−	0.453294i	$-0.149751\pi$
$19$	2.50751e12	1.78272	0.891361	+	0.453294i	$0.149751\pi$
$20$	5.12069e11	0.223637
$21$	7.96941e11	0.218949
$22$	9.81433e11	0.173319
$23$	−1.35888e13	−1.57314	−0.786571	−	0.617500i	$-0.788146\pi$
$23$	−1.35888e13	−1.57314	−0.786571	+	0.617500i	$0.788146\pi$
$24$	2.64181e12	0.204124
$25$	−1.52578e13	−0.799946
$26$	1.60383e12	0.0579311
$27$	7.62560e12	0.192450
$28$	1.06139e13	0.189615
$29$	−9.51299e13	−1.21769	−0.608844	−	0.793290i	$-0.708367\pi$
$29$	−9.51299e13	−1.21769	−0.608844	+	0.793290i	$0.708367\pi$
$30$	1.96857e13	0.182599
$31$	−1.28131e14	−0.870400	−0.435200	−	0.900334i	$-0.643322\pi$
$31$	−1.28131e14	−0.870400	−0.435200	+	0.900334i	$0.643322\pi$
$32$	3.51844e13	0.176777
$33$	3.77296e13	0.141514
$34$	3.11122e14	0.878781
$35$	7.90904e13	0.169620
$36$	1.01560e14	0.166667
$37$	−3.06931e14	−0.388262	−0.194131	−	0.980976i	$-0.562189\pi$
$37$	−3.06931e14	−0.388262	−0.194131	+	0.980976i	$0.562189\pi$
$38$	1.28385e15	1.26057
$39$	6.16566e13	0.0473005
$40$	2.62180e14	0.158135
$41$	1.92851e15	0.919972	0.459986	−	0.887926i	$-0.347854\pi$
$41$	1.92851e15	0.919972	0.459986	+	0.887926i	$0.347854\pi$
$42$	4.08034e14	0.154820
$43$	−6.03647e15	−1.83161	−0.915805	−	0.401623i	$-0.868446\pi$
$43$	−6.03647e15	−1.83161	−0.915805	+	0.401623i	$0.868446\pi$
$44$	5.02493e14	0.122555
$45$	7.56783e14	0.149091
$46$	−6.95749e15	−1.11238
$47$	−2.20540e15	−0.287447	−0.143724	−	0.989618i	$-0.545908\pi$
$47$	−2.20540e15	−0.287447	−0.143724	+	0.989618i	$0.545908\pi$
$48$	1.35261e15	0.144338
$49$	−9.75955e15	−0.856184
$50$	−7.81197e15	−0.565647
$51$	1.19606e16	0.717522
$52$	8.21161e14	0.0409634
$53$	3.05615e16	1.27220	0.636098	−	0.771608i	$-0.280547\pi$
$53$	3.05615e16	1.27220	0.636098	+	0.771608i	$0.280547\pi$
$54$	3.90431e15	0.136083
$55$	3.74438e15	0.109631
$56$	5.43431e15	0.134078
$57$	4.93553e16	1.02926
$58$	−4.87065e16	−0.861036
$59$	5.11229e16	0.768284	0.384142	−	0.923274i	$-0.374497\pi$
$59$	5.11229e16	0.768284	0.384142	+	0.923274i	$0.374497\pi$
$60$	1.00791e16	0.129117
$61$	−6.21405e16	−0.680364	−0.340182	−	0.940360i	$-0.610489\pi$
$61$	−6.21405e16	−0.680364	−0.340182	+	0.940360i	$0.610489\pi$
$62$	−6.56032e16	−0.615465
$63$	1.56862e16	0.126410
$64$	1.80144e16	0.125000
$65$	6.11896e15	0.0366438
$66$	1.93175e16	0.100065
$67$	−1.37732e17	−0.618480	−0.309240	−	0.950984i	$-0.600075\pi$
$67$	−1.37732e17	−0.618480	−0.309240	+	0.950984i	$0.600075\pi$
$68$	1.59294e17	0.621392
$69$	−2.67469e17	−0.908254
$70$	4.04943e16	0.119939
$71$	−1.38269e17	−0.357907	−0.178953	−	0.983858i	$-0.557271\pi$
$71$	−1.38269e17	−0.357907	−0.178953	+	0.983858i	$0.557271\pi$
$72$	5.19987e16	0.117851
$73$	−3.31152e17	−0.658355	−0.329178	−	0.944268i	$-0.606771\pi$
$73$	−3.31152e17	−0.658355	−0.329178	+	0.944268i	$0.606771\pi$
$74$	−1.57149e17	−0.274543
$75$	−3.00318e17	−0.461849
$76$	6.57329e17	0.891361
$77$	7.76113e16	0.0929530
$78$	3.15682e16	0.0334465
$79$	1.69508e18	1.59123	0.795616	−	0.605802i	$-0.207147\pi$
$79$	1.69508e18	1.59123	0.795616	+	0.605802i	$0.207147\pi$
$80$	1.34236e17	0.111819
$81$	1.50095e17	0.111111
$82$	9.87396e17	0.650519
$83$	3.36651e17	0.197669	0.0988344	−	0.995104i	$-0.468489\pi$
$83$	3.36651e17	0.197669	0.0988344	+	0.995104i	$0.468489\pi$
$84$	2.08913e17	0.109474
$85$	1.18700e18	0.555866
$86$	−3.09067e18	−1.29514
$87$	−1.87244e18	−0.703033
$88$	2.57277e17	0.0866593
$89$	−2.05991e18	−0.623222	−0.311611	−	0.950210i	$-0.600869\pi$
$89$	−2.05991e18	−0.623222	−0.311611	+	0.950210i	$0.600869\pi$
$90$	3.87473e17	0.105424
$91$	1.26830e17	0.0310692
$92$	−3.56223e18	−0.786571
$93$	−2.52201e18	−0.502525
$94$	−1.12917e18	−0.203256
$95$	4.89815e18	0.797366
$96$	6.92534e17	0.102062
$97$	−2.80899e18	−0.375163	−0.187581	−	0.982249i	$-0.560065\pi$
$97$	−2.80899e18	−0.375163	−0.187581	+	0.982249i	$0.560065\pi$
$98$	−4.99689e18	−0.605414
$99$	7.42631e17	0.0817031
$100$	−3.99973e18	−0.399973
$101$	1.95319e19	1.77702	0.888508	−	0.458860i	$-0.151742\pi$
$101$	1.95319e19	1.77702	0.888508	+	0.458860i	$0.151742\pi$
$102$	6.12381e18	0.507365
$103$	−3.67429e18	−0.277472	−0.138736	−	0.990329i	$-0.544304\pi$
$103$	−3.67429e18	−0.277472	−0.138736	+	0.990329i	$0.544304\pi$
$104$	4.20434e17	0.0289655
$105$	1.55674e18	0.0979302
$106$	1.56475e19	0.899578
$107$	2.31416e19	1.21688	0.608439	−	0.793600i	$-0.291796\pi$
$107$	2.31416e19	1.21688	0.608439	+	0.793600i	$0.291796\pi$
$108$	1.99900e18	0.0962250
$109$	−3.98979e19	−1.75954	−0.879769	−	0.475401i	$-0.842303\pi$
$109$	−3.98979e19	−1.75954	−0.879769	+	0.475401i	$0.842303\pi$
$110$	1.91712e18	0.0775209
$111$	−6.04133e18	−0.224163
$112$	2.78237e18	0.0948076
$113$	−2.09577e19	−0.656294	−0.328147	−	0.944627i	$-0.606424\pi$
$113$	−2.09577e19	−0.656294	−0.328147	+	0.944627i	$0.606424\pi$
$114$	2.52699e19	0.727793
$115$	−2.65443e19	−0.703626
$116$	−2.49377e19	−0.608844
$117$	1.21359e18	0.0273090
$118$	2.61749e19	0.543259
$119$	2.46034e19	0.471302
$120$	5.16048e18	0.0912995
$121$	−5.74847e19	−0.939921
$122$	−3.18159e19	−0.481090
$123$	3.79588e19	0.531146
$124$	−3.35888e19	−0.435200
$125$	−6.70623e19	−0.805069
$126$	8.03132e18	0.0893855
$127$	9.05478e19	0.934852	0.467426	−	0.884032i	$-0.345182\pi$
$127$	9.05478e19	0.934852	0.467426	+	0.884032i	$0.345182\pi$
$128$	9.22337e18	0.0883883
$129$	−1.18816e20	−1.05748
$130$	3.13291e18	0.0259111
$131$	1.71493e20	1.31877	0.659384	−	0.751806i	$-0.270817\pi$
$131$	1.71493e20	1.31877	0.659384	+	0.751806i	$0.270817\pi$
$132$	9.89058e18	0.0707570
$133$	1.01526e20	0.676063
$134$	−7.05190e19	−0.437331
$135$	1.48958e19	0.0860780
$136$	8.15587e19	0.439391
$137$	5.99415e19	0.301219	0.150609	−	0.988593i	$-0.451876\pi$
$137$	5.99415e19	0.301219	0.150609	+	0.988593i	$0.451876\pi$
$138$	−1.36944e20	−0.642233
$139$	3.92231e20	1.71752	0.858759	−	0.512380i	$-0.171236\pi$
$139$	3.92231e20	1.71752	0.858759	+	0.512380i	$0.171236\pi$
$140$	2.07331e19	0.0848100
$141$	−4.34089e19	−0.165958
$142$	−7.07937e19	−0.253078
$143$	6.00453e18	0.0200811
$144$	2.66233e19	0.0833333
$145$	−1.85826e20	−0.544641
$146$	−1.69550e20	−0.465527
$147$	−1.92097e20	−0.494318
$148$	−8.04602e19	−0.194131
$149$	−8.21882e20	−1.86012	−0.930058	−	0.367412i	$-0.880244\pi$
$149$	−8.21882e20	−1.86012	−0.930058	+	0.367412i	$0.880244\pi$
$150$	−1.53763e20	−0.326576
$151$	−2.10572e20	−0.419875	−0.209937	−	0.977715i	$-0.567326\pi$
$151$	−2.10572e20	−0.419875	−0.209937	+	0.977715i	$0.567326\pi$
$152$	3.36552e20	0.630287
$153$	2.35420e20	0.414262
$154$	3.97370e19	0.0657277
$155$	−2.50290e20	−0.389307
$156$	1.61629e19	0.0236503
$157$	8.19056e19	0.112789	0.0563945	−	0.998409i	$-0.482040\pi$
$157$	8.19056e19	0.112789	0.0563945	+	0.998409i	$0.482040\pi$
$158$	8.67882e20	1.12517
$159$	6.01542e20	0.734503
$160$	6.87288e19	0.0790677
$161$	−5.50196e20	−0.596584
$162$	7.68485e19	0.0785674
$163$	7.91414e20	0.763170	0.381585	−	0.924334i	$-0.375378\pi$
$163$	7.91414e20	0.763170	0.381585	+	0.924334i	$0.375378\pi$
$164$	5.05547e20	0.459986
$165$	7.37006e19	0.0632956
$166$	1.72365e20	0.139773
$167$	4.14346e20	0.317363	0.158682	−	0.987330i	$-0.449276\pi$
$167$	4.14346e20	0.317363	0.158682	+	0.987330i	$0.449276\pi$
$168$	1.06964e20	0.0774101
$169$	−1.45211e21	−0.993288
$170$	6.07742e20	0.393056
$171$	9.71461e20	0.594241
$172$	−1.58243e21	−0.915805
$173$	2.98194e20	0.163328	0.0816642	−	0.996660i	$-0.473977\pi$
$173$	2.98194e20	0.163328	0.0816642	+	0.996660i	$0.473977\pi$
$174$	−9.58690e20	−0.497119
$175$	−6.17768e20	−0.303364
$176$	1.31726e20	0.0612774
$177$	1.00625e21	0.443569
$178$	−1.05467e21	−0.440684
$179$	1.70052e21	0.673717	0.336859	−	0.941555i	$-0.390636\pi$
$179$	1.70052e21	0.673717	0.336859	+	0.941555i	$0.390636\pi$
$180$	1.98386e20	0.0745457
$181$	−2.61570e21	−0.932485	−0.466242	−	0.884657i	$-0.654393\pi$
$181$	−2.61570e21	−0.932485	−0.466242	+	0.884657i	$0.654393\pi$
$182$	6.49371e19	0.0219692
$183$	−1.22311e21	−0.392808
$184$	−1.82386e21	−0.556190
$185$	−5.99557e20	−0.173660
$186$	−1.29127e21	−0.355339
$187$	1.16480e21	0.304618
$188$	−5.78133e20	−0.143724
$189$	3.08751e20	0.0729829
$190$	2.50785e21	0.563823
$191$	−3.89096e21	−0.832223	−0.416111	−	0.909314i	$-0.636607\pi$
$191$	−3.89096e21	−0.832223	−0.416111	+	0.909314i	$0.636607\pi$
$192$	3.54577e20	0.0721688
$193$	8.91713e21	1.72755	0.863775	−	0.503877i	$-0.168094\pi$
$193$	8.91713e21	1.72755	0.863775	+	0.503877i	$0.168094\pi$
$194$	−1.43821e21	−0.265280
$195$	1.20439e20	0.0211563
$196$	−2.55841e21	−0.428092
$197$	2.91067e21	0.464049	0.232025	−	0.972710i	$-0.425465\pi$
$197$	2.91067e21	0.464049	0.232025	+	0.972710i	$0.425465\pi$
$198$	3.80227e20	0.0577728
$199$	3.12683e21	0.452897	0.226449	−	0.974023i	$-0.427288\pi$
$199$	3.12683e21	0.452897	0.226449	+	0.974023i	$0.427288\pi$
$200$	−2.04786e21	−0.282824
$201$	−2.71099e21	−0.357079
$202$	1.00003e22	1.25654
$203$	−3.85169e21	−0.461785
$204$	3.13539e21	0.358761
$205$	3.76713e21	0.411480
$206$	−1.88124e21	−0.196203
$207$	−5.26460e21	−0.524381
$208$	2.15262e20	0.0204817
$209$	4.80655e21	0.436962
$210$	7.97049e20	0.0692471
$211$	−8.08091e21	−0.671084	−0.335542	−	0.942025i	$-0.608919\pi$
$211$	−8.08091e21	−0.671084	−0.335542	+	0.942025i	$0.608919\pi$
$212$	8.01151e21	0.636098
$213$	−2.72155e21	−0.206638
$214$	1.18485e22	0.860463
$215$	−1.17916e22	−0.819232
$216$	1.02349e21	0.0680414
$217$	−5.18787e21	−0.330082
$218$	−2.04277e22	−1.24418
$219$	−6.51807e21	−0.380102
$220$	9.81566e20	0.0548156
$221$	1.90348e21	0.101817
$222$	−3.09316e21	−0.158507
$223$	−3.95350e22	−1.94127	−0.970634	−	0.240562i	$-0.922668\pi$
$223$	−3.95350e22	−1.94127	−0.970634	+	0.240562i	$0.922668\pi$
$224$	1.42457e21	0.0670391
$225$	−5.91117e21	−0.266649
$226$	−1.07303e22	−0.464070
$227$	2.77053e22	1.14899	0.574496	−	0.818507i	$-0.305198\pi$
$227$	2.77053e22	1.14899	0.574496	+	0.818507i	$0.305198\pi$
$228$	1.29382e22	0.514628
$229$	3.56961e22	1.36202	0.681010	−	0.732274i	$-0.261541\pi$
$229$	3.56961e22	1.36202	0.681010	+	0.732274i	$0.261541\pi$
$230$	−1.35907e22	−0.497539
$231$	1.52762e21	0.0536664
$232$	−1.27681e22	−0.430518
$233$	5.24103e22	1.69643	0.848214	−	0.529654i	$-0.177678\pi$
$233$	5.24103e22	1.69643	0.848214	+	0.529654i	$0.177678\pi$
$234$	6.21357e20	0.0193104
$235$	−4.30801e21	−0.128568
$236$	1.34016e22	0.384142
$237$	3.33643e22	0.918698
$238$	1.25969e22	0.333261
$239$	3.14251e22	0.798907	0.399454	−	0.916753i	$-0.369200\pi$
$239$	3.14251e22	0.798907	0.399454	+	0.916753i	$0.369200\pi$
$240$	2.64217e21	0.0645585
$241$	−3.24727e22	−0.762705	−0.381353	−	0.924430i	$-0.624542\pi$
$241$	−3.24727e22	−0.762705	−0.381353	+	0.924430i	$0.624542\pi$
$242$	−2.94322e22	−0.664625
$243$	2.95431e21	0.0641500
$244$	−1.62897e22	−0.340182
$245$	−1.90642e22	−0.382949
$246$	1.94349e22	0.375577
$247$	7.85473e21	0.146053
$248$	−1.71975e22	−0.307733
$249$	6.62630e21	0.114124
$250$	−3.43359e22	−0.569270
$251$	−6.38522e22	−1.01924	−0.509619	−	0.860400i	$-0.670214\pi$
$251$	−6.38522e22	−1.01924	−0.509619	+	0.860400i	$0.670214\pi$
$252$	4.11204e21	0.0632051
$253$	−2.60479e22	−0.385592
$254$	4.63605e22	0.661040
$255$	2.33637e22	0.320929
$256$	4.72237e21	0.0625000
$257$	−7.41244e22	−0.945359	−0.472679	−	0.881234i	$-0.656713\pi$
$257$	−7.41244e22	−0.945359	−0.472679	+	0.881234i	$0.656713\pi$
$258$	−6.08337e22	−0.747752
$259$	−1.24273e22	−0.147241
$260$	1.60405e21	0.0183219
$261$	−3.68553e22	−0.405896
$262$	8.78043e22	0.932510
$263$	1.84734e22	0.189221	0.0946103	−	0.995514i	$-0.469839\pi$
$263$	1.84734e22	0.189221	0.0946103	+	0.995514i	$0.469839\pi$
$264$	5.06398e21	0.0500327
$265$	5.96985e22	0.569020
$266$	5.19813e22	0.478048
$267$	−4.05452e22	−0.359817
$268$	−3.61057e22	−0.309240
$269$	−3.35623e22	−0.277463	−0.138731	−	0.990330i	$-0.544302\pi$
$269$	−3.35623e22	−0.277463	−0.138731	+	0.990330i	$0.544302\pi$
$270$	7.62663e21	0.0608663
$271$	5.08530e22	0.391840	0.195920	−	0.980620i	$-0.437231\pi$
$271$	5.08530e22	0.391840	0.195920	+	0.980620i	$0.437231\pi$
$272$	4.17581e22	0.310696
$273$	2.49640e21	0.0179378
$274$	3.06901e22	0.212994
$275$	−2.92470e22	−0.196074
$276$	−7.01154e22	−0.454127
$277$	−2.07544e22	−0.129883	−0.0649414	−	0.997889i	$-0.520686\pi$
$277$	−2.07544e22	−0.129883	−0.0649414	+	0.997889i	$0.520686\pi$
$278$	2.00822e23	1.21447
$279$	−4.96406e22	−0.290133
$280$	1.06153e22	0.0599697
$281$	−1.28771e23	−0.703245	−0.351622	−	0.936142i	$-0.614370\pi$
$281$	−1.28771e23	−0.703245	−0.351622	+	0.936142i	$0.614370\pi$
$282$	−2.22254e22	−0.117350
$283$	3.15394e23	1.61021	0.805106	−	0.593131i	$-0.202108\pi$
$283$	3.15394e23	1.61021	0.805106	+	0.593131i	$0.202108\pi$
$284$	−3.62464e22	−0.178953
$285$	9.64102e22	0.460359
$286$	3.07432e21	0.0141994
$287$	7.80829e22	0.348882
$288$	1.36311e22	0.0589256
$289$	1.30178e23	0.544514
$290$	−9.51428e22	−0.385119
$291$	−5.52894e22	−0.216600
$292$	−8.68095e22	−0.329178
$293$	−2.58168e23	−0.947678	−0.473839	−	0.880612i	$-0.657132\pi$
$293$	−2.58168e23	−0.947678	−0.473839	+	0.880612i	$0.657132\pi$
$294$	−9.83538e22	−0.349536
$295$	9.98631e22	0.343634
$296$	−4.11956e22	−0.137271
$297$	1.46172e22	0.0471713
$298$	−4.20804e23	−1.31530
$299$	−4.25668e22	−0.128883
$300$	−7.87267e22	−0.230924
$301$	−2.44409e23	−0.694602
$302$	−1.07813e23	−0.296896
$303$	3.84446e23	1.02596
$304$	1.72315e23	0.445681
$305$	−1.21385e23	−0.304309
$306$	1.20535e23	0.292927
$307$	−4.56110e23	−1.07462	−0.537310	−	0.843385i	$-0.680559\pi$
$307$	−4.56110e23	−1.07462	−0.537310	+	0.843385i	$0.680559\pi$
$308$	2.03453e22	0.0464765
$309$	−7.23210e22	−0.160199
$310$	−1.28149e23	−0.275282
$311$	6.92775e23	1.44334	0.721670	−	0.692237i	$-0.243375\pi$
$311$	6.92775e23	1.44334	0.721670	+	0.692237i	$0.243375\pi$
$312$	8.27541e21	0.0167233
$313$	−1.51886e23	−0.297746	−0.148873	−	0.988856i	$-0.547565\pi$
$313$	−1.51886e23	−0.297746	−0.148873	+	0.988856i	$0.547565\pi$
$314$	4.19356e22	0.0797539
$315$	3.06412e22	0.0565400
$316$	4.44356e23	0.795616
$317$	−3.33119e23	−0.578811	−0.289405	−	0.957207i	$-0.593458\pi$
$317$	−3.33119e23	−0.578811	−0.289405	+	0.957207i	$0.593458\pi$
$318$	3.07990e23	0.519372
$319$	−1.82351e23	−0.298467
$320$	3.51891e22	0.0559093
$321$	4.55496e23	0.702565
$322$	−2.81700e23	−0.421848
$323$	1.52371e24	2.21554
$324$	3.93464e22	0.0555556
$325$	−4.77946e22	−0.0655371
$326$	4.05204e23	0.539643
$327$	−7.85311e23	−1.01587
$328$	2.58840e23	0.325259
$329$	−8.92940e22	−0.109009
$330$	3.77347e22	0.0447567
$331$	−1.80526e23	−0.208053	−0.104026	−	0.994575i	$-0.533173\pi$
$331$	−1.80526e23	−0.208053	−0.104026	+	0.994575i	$0.533173\pi$
$332$	8.82511e22	0.0988344
$333$	−1.18911e23	−0.129421
$334$	2.12145e23	0.224410
$335$	−2.69045e23	−0.276630
$336$	5.47653e22	0.0547372
$337$	−9.39972e23	−0.913337	−0.456668	−	0.889637i	$-0.650957\pi$
$337$	−9.39972e23	−0.913337	−0.456668	+	0.889637i	$0.650957\pi$
$338$	−7.43479e23	−0.702361
$339$	−4.12510e23	−0.378912
$340$	3.11164e23	0.277933
$341$	−2.45610e23	−0.213343
$342$	4.97388e23	0.420192
$343$	−8.56680e23	−0.703922
$344$	−8.10202e23	−0.647572
$345$	−5.22472e23	−0.406239
$346$	1.52676e23	0.115491
$347$	−2.04729e24	−1.50678	−0.753389	−	0.657575i	$-0.771582\pi$
$347$	−2.04729e24	−1.50678	−0.753389	+	0.657575i	$0.771582\pi$
$348$	−4.90850e23	−0.351516
$349$	2.12521e24	1.48102	0.740511	−	0.672045i	$-0.234584\pi$
$349$	2.12521e24	1.48102	0.740511	+	0.672045i	$0.234584\pi$
$350$	−3.16297e23	−0.214511
$351$	2.38870e22	0.0157668
$352$	6.74435e22	0.0433296
$353$	9.34149e23	0.584193	0.292097	−	0.956389i	$-0.405647\pi$
$353$	9.34149e23	0.584193	0.292097	+	0.956389i	$0.405647\pi$
$354$	5.15202e23	0.313651
$355$	−2.70093e23	−0.160083
$356$	−5.39992e23	−0.311611
$357$	4.84269e23	0.272106
$358$	8.70665e23	0.476390
$359$	2.35288e24	1.25373	0.626864	−	0.779129i	$-0.284338\pi$
$359$	2.35288e24	1.25373	0.626864	+	0.779129i	$0.284338\pi$
$360$	1.01574e23	0.0527118
$361$	4.30919e24	2.17810
$362$	−1.33924e24	−0.659366
$363$	−1.13147e24	−0.542664
$364$	3.32478e22	0.0155346
$365$	−6.46869e23	−0.294465
$366$	−6.26233e23	−0.277757
$367$	−7.57752e23	−0.327491	−0.163745	−	0.986503i	$-0.552358\pi$
$367$	−7.57752e23	−0.327491	−0.163745	+	0.986503i	$0.552358\pi$
$368$	−9.33818e23	−0.393286
$369$	7.47143e23	0.306657
$370$	−3.06973e23	−0.122796
$371$	1.23740e24	0.482455
$372$	−6.61129e23	−0.251263
$373$	1.39078e23	0.0515258	0.0257629	−	0.999668i	$-0.491799\pi$
$373$	1.39078e23	0.0515258	0.0257629	+	0.999668i	$0.491799\pi$
$374$	5.96377e23	0.215398
$375$	−1.31999e24	−0.464807
$376$	−2.96004e23	−0.101628
$377$	−2.97993e23	−0.0997614
$378$	1.58081e23	0.0516067
$379$	1.64384e24	0.523342	0.261671	−	0.965157i	$-0.415726\pi$
$379$	1.64384e24	0.523342	0.261671	+	0.965157i	$0.415726\pi$
$380$	1.28402e24	0.398683
$381$	1.78225e24	0.539737
$382$	−1.99217e24	−0.588470
$383$	−1.85425e24	−0.534295	−0.267147	−	0.963656i	$-0.586081\pi$
$383$	−1.85425e24	−0.534295	−0.267147	+	0.963656i	$0.586081\pi$
$384$	1.81544e23	0.0510310
$385$	1.51605e23	0.0415755
$386$	4.56557e24	1.22156
$387$	−2.33865e24	−0.610537
$388$	−7.36361e23	−0.187581
$389$	−1.13735e24	−0.282730	−0.141365	−	0.989958i	$-0.545149\pi$
$389$	−1.13735e24	−0.282730	−0.141365	+	0.989958i	$0.545149\pi$
$390$	6.16650e22	0.0149598
$391$	−8.25739e24	−1.95508
$392$	−1.30991e24	−0.302707
$393$	3.37549e24	0.761391
$394$	1.49026e24	0.328132
$395$	3.31116e24	0.711717
$396$	1.94676e23	0.0408516
$397$	−8.47561e24	−1.73645	−0.868223	−	0.496174i	$-0.834738\pi$
$397$	−8.47561e24	−1.73645	−0.868223	+	0.496174i	$0.834738\pi$
$398$	1.60094e24	0.320247
$399$	1.99834e24	0.390325
$400$	−1.04850e24	−0.199986
$401$	−8.26281e24	−1.53906	−0.769532	−	0.638609i	$-0.779510\pi$
$401$	−8.26281e24	−1.53906	−0.769532	+	0.638609i	$0.779510\pi$
$402$	−1.38802e24	−0.252493
$403$	−4.01368e23	−0.0713091
$404$	5.12017e24	0.888508
$405$	2.93193e23	0.0496971
$406$	−1.97207e24	−0.326531
$407$	−5.88345e23	−0.0951667
$408$	1.60532e24	0.253682
$409$	8.40720e24	1.29802	0.649008	−	0.760782i	$-0.275184\pi$
$409$	8.40720e24	1.29802	0.649008	+	0.760782i	$0.275184\pi$
$410$	1.92877e24	0.290960
$411$	1.17983e24	0.173909
$412$	−9.63193e23	−0.138736
$413$	2.06991e24	0.291357
$414$	−2.69547e24	−0.370793
$415$	6.57611e23	0.0884122
$416$	1.10214e23	0.0144828
$417$	7.72028e24	0.991609
$418$	2.46095e24	0.308979
$419$	3.89215e24	0.477701	0.238850	−	0.971056i	$-0.423229\pi$
$419$	3.89215e24	0.477701	0.238850	+	0.971056i	$0.423229\pi$
$420$	4.08089e23	0.0489651
$421$	8.63572e24	1.01302	0.506511	−	0.862234i	$-0.330935\pi$
$421$	8.63572e24	1.01302	0.506511	+	0.862234i	$0.330935\pi$
$422$	−4.13743e24	−0.474528
$423$	−8.54418e23	−0.0958157
$424$	4.10190e24	0.449789
$425$	−9.27153e24	−0.994160
$426$	−1.39343e24	−0.146115
$427$	−2.51599e24	−0.258015
$428$	6.06643e24	0.608439
$429$	1.18187e23	0.0115938
$430$	−6.03729e24	−0.579285
$431$	1.49165e25	1.40001	0.700006	−	0.714137i	$-0.253181\pi$
$431$	1.49165e25	1.40001	0.700006	+	0.714137i	$0.253181\pi$
$432$	5.24027e23	0.0481125
$433$	6.10046e24	0.547933	0.273966	−	0.961739i	$-0.411664\pi$
$433$	6.10046e24	0.547933	0.273966	+	0.961739i	$0.411664\pi$
$434$	−2.65619e24	−0.233403
$435$	−3.65761e24	−0.314448
$436$	−1.04590e25	−0.879769
$437$	−3.40742e25	−2.80448
$438$	−3.33725e24	−0.268772
$439$	3.38497e24	0.266773	0.133387	−	0.991064i	$-0.457415\pi$
$439$	3.38497e24	0.266773	0.133387	+	0.991064i	$0.457415\pi$
$440$	5.02562e23	0.0387605
$441$	−3.78105e24	−0.285395
$442$	9.74583e23	0.0719958
$443$	9.74089e24	0.704309	0.352154	−	0.935942i	$-0.385449\pi$
$443$	9.74089e24	0.704309	0.352154	+	0.935942i	$0.385449\pi$
$444$	−1.58370e24	−0.112082
$445$	−4.02380e24	−0.278751
$446$	−2.02419e25	−1.37268
$447$	−1.61771e25	−1.07394
$448$	7.29381e23	0.0474038
$449$	3.05582e25	1.94441	0.972205	−	0.234132i	$-0.0752249\pi$
$449$	3.05582e25	1.94441	0.972205	+	0.234132i	$0.0752249\pi$
$450$	−3.02652e24	−0.188549
$451$	3.69668e24	0.225494
$452$	−5.49394e24	−0.328147
$453$	−4.14469e24	−0.242415
$454$	1.41851e25	0.812460
$455$	2.47749e23	0.0138964
$456$	6.62436e24	0.363897
$457$	2.58040e23	0.0138830	0.00694148	−	0.999976i	$-0.497790\pi$
$457$	2.58040e23	0.0138830	0.00694148	+	0.999976i	$0.497790\pi$
$458$	1.82764e25	0.963094
$459$	4.63377e24	0.239174
$460$	−6.95843e24	−0.351813
$461$	−3.13742e25	−1.55387	−0.776935	−	0.629581i	$-0.783226\pi$
$461$	−3.13742e25	−1.55387	−0.776935	+	0.629581i	$0.783226\pi$
$462$	7.82143e23	0.0379479
$463$	2.56417e25	1.21879	0.609393	−	0.792868i	$-0.291413\pi$
$463$	2.56417e25	1.21879	0.609393	+	0.792868i	$0.291413\pi$
$464$	−6.53728e24	−0.304422
$465$	−4.92646e24	−0.224767
$466$	2.68341e25	1.19956
$467$	2.83701e25	1.24266	0.621328	−	0.783551i	$-0.286594\pi$
$467$	2.83701e25	1.24266	0.621328	+	0.783551i	$0.286594\pi$
$468$	3.18135e23	0.0136545
$469$	−5.57661e24	−0.234546
$470$	−2.20570e24	−0.0909111
$471$	1.61215e24	0.0651187
$472$	6.86161e24	0.271629
$473$	−1.15711e25	−0.448945
$474$	1.70825e25	0.649618
$475$	−3.82590e25	−1.42608
$476$	6.44964e24	0.235651
$477$	1.18402e25	0.424065
$478$	1.60896e25	0.564913
$479$	2.37829e25	0.818609	0.409305	−	0.912398i	$-0.365771\pi$
$479$	2.37829e25	0.818609	0.409305	+	0.912398i	$0.365771\pi$
$480$	1.35279e24	0.0456497
$481$	−9.61456e23	−0.0318091
$482$	−1.66260e25	−0.539314
$483$	−1.08295e25	−0.344438
$484$	−1.50693e25	−0.469961
$485$	−5.48706e24	−0.167801
$486$	1.51261e24	0.0453609
$487$	−3.19675e25	−0.940120	−0.470060	−	0.882634i	$-0.655768\pi$
$487$	−3.19675e25	−0.940120	−0.470060	+	0.882634i	$0.655768\pi$
$488$	−8.34035e24	−0.240545
$489$	1.55774e25	0.440617
$490$	−9.76088e24	−0.270786
$491$	−8.38522e24	−0.228160	−0.114080	−	0.993472i	$-0.536392\pi$
$491$	−8.38522e24	−0.228160	−0.114080	+	0.993472i	$0.536392\pi$
$492$	9.95068e24	0.265573
$493$	−5.78066e25	−1.51332
$494$	4.02162e24	0.103275
$495$	1.45065e24	0.0365437
$496$	−8.80511e24	−0.217600
$497$	−5.59834e24	−0.135729
$498$	3.39267e24	0.0806980
$499$	1.45147e25	0.338729	0.169364	−	0.985554i	$-0.445829\pi$
$499$	1.45147e25	0.338729	0.169364	+	0.985554i	$0.445829\pi$
$500$	−1.75800e25	−0.402535
$501$	8.15558e24	0.183230
$502$	−3.26923e25	−0.720710
$503$	8.10116e25	1.75247	0.876237	−	0.481881i	$-0.160046\pi$
$503$	8.10116e25	1.75247	0.876237	+	0.481881i	$0.160046\pi$
$504$	2.10536e24	0.0446927
$505$	3.81534e25	0.794814
$506$	−1.33365e25	−0.272655
$507$	−2.85818e25	−0.573475
$508$	2.37366e25	0.467426
$509$	−2.10287e25	−0.406437	−0.203219	−	0.979133i	$-0.565140\pi$
$509$	−2.10287e25	−0.406437	−0.203219	+	0.979133i	$0.565140\pi$
$510$	1.19622e25	0.226931
$511$	−1.34079e25	−0.249668
$512$	2.41785e24	0.0441942
$513$	1.91213e25	0.343085
$514$	−3.79517e25	−0.668470
$515$	−7.17732e24	−0.124106
$516$	−3.11469e25	−0.528740
$517$	−4.22745e24	−0.0704560
$518$	−6.36276e24	−0.104115
$519$	5.86936e24	0.0942977
$520$	8.21272e23	0.0129555
$521$	1.06276e26	1.64618	0.823092	−	0.567908i	$-0.192247\pi$
$521$	1.06276e26	1.64618	0.823092	+	0.567908i	$0.192247\pi$
$522$	−1.88699e25	−0.287012
$523$	−2.15543e25	−0.321935	−0.160968	−	0.986960i	$-0.551462\pi$
$523$	−2.15543e25	−0.321935	−0.160968	+	0.986960i	$0.551462\pi$
$524$	4.49558e25	0.659384
$525$	−1.21595e25	−0.175147
$526$	9.45841e24	0.133799
$527$	−7.78602e25	−1.08172
$528$	2.59276e24	0.0353785
$529$	1.10041e26	1.47478
$530$	3.05656e25	0.402358
$531$	1.98061e25	0.256095
$532$	2.66144e25	0.338031
$533$	6.04101e24	0.0753705
$534$	−2.07591e25	−0.254429
$535$	4.52046e25	0.544279
$536$	−1.84861e25	−0.218666
$537$	3.34713e25	0.388971
$538$	−1.71839e25	−0.196196
$539$	−1.87077e25	−0.209859
$540$	3.90484e24	0.0430390
$541$	6.77309e25	0.733521	0.366761	−	0.930315i	$-0.380467\pi$
$541$	6.77309e25	0.733521	0.366761	+	0.930315i	$0.380467\pi$
$542$	2.60368e25	0.277073
$543$	−5.14849e25	−0.538370
$544$	2.13801e25	0.219695
$545$	−7.79362e25	−0.786996
$546$	1.27816e24	0.0126839
$547$	−6.18652e25	−0.603346	−0.301673	−	0.953411i	$-0.597545\pi$
$547$	−6.18652e25	−0.603346	−0.301673	+	0.953411i	$0.597545\pi$
$548$	1.57133e25	0.150609
$549$	−2.40745e25	−0.226788
$550$	−1.49745e25	−0.138645
$551$	−2.38539e26	−2.17080
$552$	−3.58991e25	−0.321116
$553$	6.86318e25	0.603444
$554$	−1.06262e25	−0.0918411
$555$	−1.18011e25	−0.100262
$556$	1.02821e26	0.858759
$557$	−2.01945e26	−1.65810	−0.829048	−	0.559178i	$-0.811117\pi$
$557$	−2.01945e26	−1.65810	−0.829048	+	0.559178i	$0.811117\pi$
$558$	−2.54160e25	−0.205155
$559$	−1.89091e25	−0.150058
$560$	5.43505e24	0.0424050
$561$	2.29267e25	0.175871
$562$	−6.59305e25	−0.497269
$563$	−1.25430e26	−0.930188	−0.465094	−	0.885261i	$-0.653979\pi$
$563$	−1.25430e26	−0.930188	−0.465094	+	0.885261i	$0.653979\pi$
$564$	−1.13794e25	−0.0829789
$565$	−4.09386e25	−0.293543
$566$	1.61482e26	1.13859
$567$	6.07715e24	0.0421367
$568$	−1.85581e25	−0.126539
$569$	2.15171e26	1.44284	0.721418	−	0.692500i	$-0.243491\pi$
$569$	2.15171e26	1.44284	0.721418	+	0.692500i	$0.243491\pi$
$570$	4.93620e25	0.325523
$571$	2.78328e25	0.180515	0.0902575	−	0.995918i	$-0.471231\pi$
$571$	2.78328e25	0.180515	0.0902575	+	0.995918i	$0.471231\pi$
$572$	1.57405e24	0.0100405
$573$	−7.65857e25	−0.480484
$574$	3.99785e25	0.246697
$575$	2.07335e26	1.25843
$576$	6.97915e24	0.0416667
$577$	9.14714e25	0.537174	0.268587	−	0.963255i	$-0.413443\pi$
$577$	9.14714e25	0.537174	0.268587	+	0.963255i	$0.413443\pi$
$578$	6.66512e25	0.385029
$579$	1.75516e26	0.997402
$580$	−4.87131e25	−0.272320
$581$	1.36306e25	0.0749621
$582$	−2.83082e25	−0.153159
$583$	5.85821e25	0.311827
$584$	−4.44465e25	−0.232764
$585$	2.37061e24	0.0122146
$586$	−1.32182e26	−0.670109
$587$	1.62458e26	0.810362	0.405181	−	0.914236i	$-0.367208\pi$
$587$	1.62458e26	0.810362	0.405181	+	0.914236i	$0.367208\pi$
$588$	−5.03572e25	−0.247159
$589$	−3.21290e26	−1.55168
$590$	5.11299e25	0.242986
$591$	5.72907e25	0.267919
$592$	−2.10922e25	−0.0970655
$593$	3.63544e26	1.64641	0.823204	−	0.567746i	$-0.192184\pi$
$593$	3.63544e26	1.64641	0.823204	+	0.567746i	$0.192184\pi$
$594$	7.48401e24	0.0333552
$595$	4.80601e25	0.210801
$596$	−2.15452e26	−0.930058
$597$	6.15453e25	0.261480
$598$	−2.17942e25	−0.0911338
$599$	−1.25044e26	−0.514645	−0.257322	−	0.966326i	$-0.582840\pi$
$599$	−1.25044e26	−0.514645	−0.257322	+	0.966326i	$0.582840\pi$
$600$	−4.03080e25	−0.163288
$601$	1.66232e25	0.0662836	0.0331418	−	0.999451i	$-0.489449\pi$
$601$	1.66232e25	0.0662836	0.0331418	+	0.999451i	$0.489449\pi$
$602$	−1.25138e26	−0.491158
$603$	−5.33603e25	−0.206160
$604$	−5.52002e25	−0.209937
$605$	−1.12290e26	−0.420403
$606$	1.96837e26	0.725464
$607$	−1.54786e26	−0.561616	−0.280808	−	0.959764i	$-0.590602\pi$
$607$	−1.54786e26	−0.561616	−0.280808	+	0.959764i	$0.590602\pi$
$608$	8.82252e25	0.315144
$609$	−7.58129e25	−0.266611
$610$	−6.21489e25	−0.215179
$611$	−6.90838e24	−0.0235497
$612$	6.17139e25	0.207131
$613$	−5.04580e26	−1.66746	−0.833730	−	0.552172i	$-0.813799\pi$
$613$	−5.04580e26	−1.66746	−0.833730	+	0.552172i	$0.813799\pi$
$614$	−2.33528e26	−0.759871
$615$	7.41484e25	0.237568
$616$	1.04168e25	0.0328638
$617$	1.75529e26	0.545306	0.272653	−	0.962112i	$-0.412099\pi$
$617$	1.75529e26	0.545306	0.272653	+	0.962112i	$0.412099\pi$
$618$	−3.70284e25	−0.113278
$619$	4.90142e25	0.147659	0.0738297	−	0.997271i	$-0.476478\pi$
$619$	4.90142e25	0.147659	0.0738297	+	0.997271i	$0.476478\pi$
$620$	−6.56121e25	−0.194654
$621$	−1.03623e26	−0.302751
$622$	3.54701e26	1.02060
$623$	−8.34031e25	−0.236345
$624$	4.23701e24	0.0118251
$625$	1.60020e26	0.439859
$626$	−7.77655e25	−0.210538
$627$	9.46073e25	0.252280
$628$	2.14711e25	0.0563945
$629$	−1.86510e26	−0.482526
$630$	1.56883e25	0.0399798
$631$	3.22240e26	0.808909	0.404455	−	0.914558i	$-0.367461\pi$
$631$	3.22240e26	0.808909	0.404455	+	0.914558i	$0.367461\pi$
$632$	2.27510e26	0.562585
$633$	−1.59057e26	−0.387451
$634$	−1.70557e26	−0.409281
$635$	1.76875e26	0.418135
$636$	1.57691e26	0.367251
$637$	−3.05716e25	−0.0701445
$638$	−9.33636e25	−0.211048
$639$	−5.35682e25	−0.119302
$640$	1.80168e25	0.0395338
$641$	−6.56092e25	−0.141845	−0.0709224	−	0.997482i	$-0.522594\pi$
$641$	−6.56092e25	−0.141845	−0.0709224	+	0.997482i	$0.522594\pi$
$642$	2.33214e26	0.496789
$643$	1.15304e26	0.242014	0.121007	−	0.992652i	$-0.461388\pi$
$643$	1.15304e26	0.242014	0.121007	+	0.992652i	$0.461388\pi$
$644$	−1.44230e26	−0.298292
$645$	−2.32094e26	−0.472984
$646$	7.80142e26	1.56662
$647$	−1.92053e26	−0.380041	−0.190020	−	0.981780i	$-0.560855\pi$
$647$	−1.92053e26	−0.380041	−0.190020	+	0.981780i	$0.560855\pi$
$648$	2.01454e25	0.0392837
$649$	9.79956e25	0.188314
$650$	−2.44708e25	−0.0463417
$651$	−1.02113e26	−0.190573
$652$	2.07464e26	0.381585
$653$	5.35603e26	0.970884	0.485442	−	0.874269i	$-0.338659\pi$
$653$	5.35603e26	0.970884	0.485442	+	0.874269i	$0.338659\pi$
$654$	−4.02079e26	−0.718328
$655$	3.34992e26	0.589851
$656$	1.32526e26	0.229993
$657$	−1.28295e26	−0.219452
$658$	−4.57185e25	−0.0770808
$659$	−3.30621e26	−0.549439	−0.274719	−	0.961524i	$-0.588585\pi$
$659$	−3.30621e26	−0.549439	−0.274719	+	0.961524i	$0.588585\pi$
$660$	1.93202e25	0.0316478
$661$	−7.36962e26	−1.18996	−0.594978	−	0.803742i	$-0.702839\pi$
$661$	−7.36962e26	−1.18996	−0.594978	+	0.803742i	$0.702839\pi$
$662$	−9.24292e25	−0.147115
$663$	3.74663e25	0.0587844
$664$	4.51845e25	0.0698865
$665$	1.98320e26	0.302385
$666$	−6.08827e25	−0.0915142
$667$	1.29271e27	1.91560
$668$	1.08618e26	0.158682
$669$	−7.78167e26	−1.12079
$670$	−1.37751e26	−0.195607
$671$	−1.19115e26	−0.166764
$672$	2.80399e25	0.0387051
$673$	−8.62818e26	−1.17429	−0.587146	−	0.809481i	$-0.699749\pi$
$673$	−8.62818e26	−1.17429	−0.587146	+	0.809481i	$0.699749\pi$
$674$	−4.81266e26	−0.645827
$675$	−1.16349e26	−0.153950
$676$	−3.80661e26	−0.496644
$677$	5.83017e26	0.750048	0.375024	−	0.927015i	$-0.377634\pi$
$677$	5.83017e26	0.750048	0.375024	+	0.927015i	$0.377634\pi$
$678$	−2.11205e26	−0.267931
$679$	−1.13733e26	−0.142273
$680$	1.59316e26	0.196528
$681$	5.45323e26	0.663371
$682$	−1.25752e26	−0.150856
$683$	−1.23753e27	−1.46406	−0.732029	−	0.681274i	$-0.761426\pi$
$683$	−1.23753e27	−1.46406	−0.732029	+	0.681274i	$0.761426\pi$
$684$	2.54663e26	0.297120
$685$	1.17089e26	0.134727
$686$	−4.38620e26	−0.497748
$687$	7.02606e26	0.786363
$688$	−4.14823e26	−0.457903
$689$	9.57333e25	0.104227
$690$	−2.67505e26	−0.287254
$691$	−4.14903e26	−0.439445	−0.219723	−	0.975562i	$-0.570515\pi$
$691$	−4.14903e26	−0.439445	−0.219723	+	0.975562i	$0.570515\pi$
$692$	7.81699e25	0.0816642
$693$	3.00682e25	0.0309843
$694$	−1.04821e27	−1.06545
$695$	7.66180e26	0.768201
$696$	−2.51315e26	−0.248560
$697$	1.17188e27	1.14333
$698$	1.08811e27	1.04724
$699$	1.03159e27	0.979433
$700$	−1.61944e26	−0.151682
$701$	−1.42197e27	−1.31392	−0.656962	−	0.753924i	$-0.728159\pi$
$701$	−1.42197e27	−1.31392	−0.656962	+	0.753924i	$0.728159\pi$
$702$	1.22302e25	0.0111488
$703$	−7.69634e26	−0.692163
$704$	3.45311e25	0.0306387
$705$	−8.47946e25	−0.0742286
$706$	4.78284e26	0.413087
$707$	7.90823e26	0.673899
$708$	2.63783e26	0.221784
$709$	1.03545e27	0.858991	0.429495	−	0.903069i	$-0.358691\pi$
$709$	1.03545e27	0.858991	0.429495	+	0.903069i	$0.358691\pi$
$710$	−1.38288e26	−0.113195
$711$	6.56710e26	0.530411
$712$	−2.76476e26	−0.220342
$713$	1.74115e27	1.36926
$714$	2.47946e26	0.192408
$715$	1.17292e25	0.00898174
$716$	4.45781e26	0.336859
$717$	6.18540e26	0.461249
$718$	1.20468e27	0.886519
$719$	−2.01904e27	−1.46629	−0.733147	−	0.680070i	$-0.761949\pi$
$719$	−2.01904e27	−1.46629	−0.733147	+	0.680070i	$0.761949\pi$
$720$	5.20058e25	0.0372729
$721$	−1.48767e26	−0.105226
$722$	2.20631e27	1.54015
$723$	−6.39161e26	−0.440348
$724$	−6.85691e26	−0.466242
$725$	1.45147e27	0.974085
$726$	−5.79314e26	−0.383721
$727$	−1.23132e27	−0.804996	−0.402498	−	0.915421i	$-0.631858\pi$
$727$	−1.23132e27	−0.804996	−0.402498	+	0.915421i	$0.631858\pi$
$728$	1.70229e25	0.0109846
$729$	5.81497e25	0.0370370
$730$	−3.31197e26	−0.208218
$731$	−3.66812e27	−2.27630
$732$	−3.20631e26	−0.196404
$733$	−1.89076e27	−1.14327	−0.571636	−	0.820507i	$-0.693691\pi$
$733$	−1.89076e27	−1.14327	−0.571636	+	0.820507i	$0.693691\pi$
$734$	−3.87969e26	−0.231571
$735$	−3.75241e26	−0.221096
$736$	−4.78115e26	−0.278095
$737$	−2.64014e26	−0.151595
$738$	3.82537e26	0.216840
$739$	−1.41231e27	−0.790328	−0.395164	−	0.918611i	$-0.629312\pi$
$739$	−1.41231e27	−0.790328	−0.395164	+	0.918611i	$0.629312\pi$
$740$	−1.57170e26	−0.0868298
$741$	1.54605e26	0.0843237
$742$	6.33548e26	0.341148
$743$	6.03755e26	0.320972	0.160486	−	0.987038i	$-0.448694\pi$
$743$	6.03755e26	0.320972	0.160486	+	0.987038i	$0.448694\pi$
$744$	−3.38498e26	−0.177670
$745$	−1.60546e27	−0.831982
$746$	7.12080e25	0.0364343
$747$	1.30426e26	0.0658896
$748$	3.05345e26	0.152309
$749$	9.36975e26	0.461478
$750$	−6.75833e26	−0.328668
$751$	2.52152e27	1.21083	0.605414	−	0.795911i	$-0.293008\pi$
$751$	2.52152e27	1.21083	0.605414	+	0.795911i	$0.293008\pi$
$752$	−1.51554e26	−0.0718618
$753$	−1.25680e27	−0.588457
$754$	−1.52572e26	−0.0705420
$755$	−4.11329e26	−0.187799
$756$	8.09373e25	0.0364915
$757$	3.73262e27	1.66189	0.830945	−	0.556354i	$-0.187800\pi$
$757$	3.73262e27	1.66189	0.830945	+	0.556354i	$0.187800\pi$
$758$	8.41644e26	0.370059
$759$	−5.12701e26	−0.222622
$760$	6.57418e26	0.281911
$761$	3.28161e26	0.138974	0.0694868	−	0.997583i	$-0.477864\pi$
$761$	3.28161e26	0.138974	0.0694868	+	0.997583i	$0.477864\pi$
$762$	9.12513e26	0.381652
$763$	−1.61542e27	−0.667270
$764$	−1.01999e27	−0.416111
$765$	4.59867e26	0.185289
$766$	−9.49378e26	−0.377803
$767$	1.60142e26	0.0629431
$768$	9.29503e25	0.0360844
$769$	4.26787e27	1.63648	0.818240	−	0.574877i	$-0.194950\pi$
$769$	4.26787e27	1.63648	0.818240	+	0.574877i	$0.194950\pi$
$770$	7.76219e25	0.0293983
$771$	−1.45899e27	−0.545803
$772$	2.33757e27	0.863775
$773$	−2.84675e27	−1.03907	−0.519535	−	0.854449i	$-0.673895\pi$
$773$	−2.84675e27	−1.03907	−0.519535	+	0.854449i	$0.673895\pi$
$774$	−1.19739e27	−0.431715
$775$	1.95499e27	0.696272
$776$	−3.77017e26	−0.132640
$777$	−2.44606e26	−0.0850095
$778$	−5.82322e26	−0.199920
$779$	4.83575e27	1.64006
$780$	3.15725e25	0.0105782
$781$	−2.65042e26	−0.0877264
$782$	−4.22779e27	−1.38245
$783$	−7.25423e26	−0.234344
$784$	−6.70671e26	−0.214046
$785$	1.59993e26	0.0504476
$786$	1.72825e27	0.538385
$787$	1.96941e27	0.606145	0.303072	−	0.952968i	$-0.401988\pi$
$787$	1.96941e27	0.606145	0.303072	+	0.952968i	$0.401988\pi$
$788$	7.63015e26	0.232025
$789$	3.63613e26	0.109247
$790$	1.69531e27	0.503260
$791$	−8.48552e26	−0.248887
$792$	9.96742e25	0.0288864
$793$	−1.94654e26	−0.0557401
$794$	−4.33951e27	−1.22785
$795$	1.17505e27	0.328524
$796$	8.19679e26	0.226449
$797$	2.61905e27	0.714973	0.357487	−	0.933918i	$-0.383634\pi$
$797$	2.61905e27	0.714973	0.357487	+	0.933918i	$0.383634\pi$
$798$	1.02315e27	0.276001
$799$	−1.34013e27	−0.357235
$800$	−5.36834e26	−0.141412
$801$	−7.98050e26	−0.207741
$802$	−4.23056e27	−1.08828
$803$	−6.34772e26	−0.161369
$804$	−7.10669e26	−0.178540
$805$	−1.07475e27	−0.266836
$806$	−2.05501e26	−0.0504232
$807$	−6.60607e26	−0.160193
$808$	2.62153e27	0.628270
$809$	−2.28409e27	−0.541007	−0.270503	−	0.962719i	$-0.587190\pi$
$809$	−2.28409e27	−0.541007	−0.270503	+	0.962719i	$0.587190\pi$
$810$	1.50115e26	0.0351412
$811$	1.58288e27	0.366226	0.183113	−	0.983092i	$-0.441383\pi$
$811$	1.58288e27	0.366226	0.183113	+	0.983092i	$0.441383\pi$
$812$	−1.00970e27	−0.230892
$813$	1.00094e27	0.226229
$814$	−3.01232e26	−0.0672930
$815$	1.54594e27	0.341346
$816$	8.21924e26	0.179381
$817$	−1.51365e28	−3.26525
$818$	4.30449e27	0.917836
$819$	4.91367e25	0.0103564
$820$	9.87530e26	0.205740
$821$	3.43110e27	0.706599	0.353299	−	0.935510i	$-0.385060\pi$
$821$	3.43110e27	0.706599	0.353299	+	0.935510i	$0.385060\pi$
$822$	6.04072e26	0.122972
$823$	−5.85623e27	−1.17847	−0.589236	−	0.807961i	$-0.700571\pi$
$823$	−5.85623e27	−1.17847	−0.589236	+	0.807961i	$0.700571\pi$
$824$	−4.93155e26	−0.0981013
$825$	−5.75668e26	−0.113204
$826$	1.05979e27	0.206020
$827$	3.98611e27	0.766033	0.383016	−	0.923742i	$-0.374885\pi$
$827$	3.98611e27	0.766033	0.383016	+	0.923742i	$0.374885\pi$
$828$	−1.38008e27	−0.262190
$829$	4.32633e26	0.0812553	0.0406277	−	0.999174i	$-0.487064\pi$
$829$	4.32633e26	0.0812553	0.0406277	+	0.999174i	$0.487064\pi$
$830$	3.36697e26	0.0625169
$831$	−4.08508e26	−0.0749879
$832$	5.64297e25	0.0102409
$833$	−5.93049e27	−1.06405
$834$	3.95278e27	0.701174
$835$	8.09380e26	0.141949
$836$	1.26001e27	0.218481
$837$	−9.77077e26	−0.167508
$838$	1.99278e27	0.337785
$839$	9.81280e27	1.64458	0.822289	−	0.569071i	$-0.192697\pi$
$839$	9.81280e27	1.64458	0.822289	+	0.569071i	$0.192697\pi$
$840$	2.08942e26	0.0346235
$841$	2.94644e27	0.482765
$842$	4.42149e27	0.716314
$843$	−2.53459e27	−0.406018
$844$	−2.11836e27	−0.335542
$845$	−2.83653e27	−0.444272
$846$	−4.37462e26	−0.0677520
$847$	−2.32749e27	−0.356447
$848$	2.10017e27	0.318049
$849$	6.20791e27	0.929656
$850$	−4.74702e27	−0.702977
$851$	4.17084e27	0.610791
$852$	−7.13437e26	−0.103319
$853$	7.51513e27	1.07627	0.538134	−	0.842859i	$-0.319129\pi$
$853$	7.51513e27	1.07627	0.538134	+	0.842859i	$0.319129\pi$
$854$	−1.28819e27	−0.182444
$855$	1.89764e27	0.265789
$856$	3.10601e27	0.430232
$857$	−1.15398e28	−1.58081	−0.790404	−	0.612586i	$-0.790129\pi$
$857$	−1.15398e28	−1.58081	−0.790404	+	0.612586i	$0.790129\pi$
$858$	6.05118e25	0.00819806
$859$	−7.59446e26	−0.101756	−0.0508782	−	0.998705i	$-0.516202\pi$
$859$	−7.59446e26	−0.101756	−0.0508782	+	0.998705i	$0.516202\pi$
$860$	−3.09109e27	−0.409616
$861$	1.53691e27	0.201427
$862$	7.63723e27	0.989958
$863$	5.04238e27	0.646448	0.323224	−	0.946323i	$-0.395233\pi$
$863$	5.04238e27	0.646448	0.323224	+	0.946323i	$0.395233\pi$
$864$	2.68302e26	0.0340207
$865$	5.82490e26	0.0730526
$866$	3.12343e27	0.387447
$867$	2.56230e27	0.314375
$868$	−1.35997e27	−0.165041
$869$	3.24924e27	0.390026
$870$	−1.87270e27	−0.222349
$871$	−4.31444e26	−0.0506701
$872$	−5.35501e27	−0.622091
$873$	−1.08826e27	−0.125054
$874$	−1.74460e28	−1.98306
$875$	−2.71527e27	−0.305307
$876$	−1.70867e27	−0.190051
$877$	2.27276e27	0.250068	0.125034	−	0.992152i	$-0.460096\pi$
$877$	2.27276e27	0.250068	0.125034	+	0.992152i	$0.460096\pi$
$878$	1.73311e27	0.188637
$879$	−5.08153e27	−0.547142
$880$	2.57312e26	0.0274078
$881$	−1.41624e28	−1.49233	−0.746165	−	0.665761i	$-0.768107\pi$
$881$	−1.41624e28	−1.49233	−0.746165	+	0.665761i	$0.768107\pi$
$882$	−1.93590e27	−0.201805
$883$	7.16419e27	0.738823	0.369412	−	0.929266i	$-0.379559\pi$
$883$	7.16419e27	0.738823	0.369412	+	0.929266i	$0.379559\pi$
$884$	4.98987e26	0.0509087
$885$	1.96560e27	0.198397
$886$	4.98733e27	0.498021
$887$	−1.80721e28	−1.78539	−0.892697	−	0.450658i	$-0.851189\pi$
$887$	−1.80721e28	−1.78539	−0.892697	+	0.450658i	$0.851189\pi$
$888$	−8.10854e26	−0.0792536
$889$	3.66617e27	0.354524
$890$	−2.06019e27	−0.197107
$891$	2.87710e26	0.0272344
$892$	−1.03639e28	−0.970634
$893$	−5.53007e27	−0.512439
$894$	−8.28268e27	−0.759389
$895$	3.32178e27	0.301336
$896$	3.73443e26	0.0335196
$897$	−8.37842e26	−0.0744104
$898$	1.56458e28	1.37491
$899$	1.21891e28	1.05988
$900$	−1.54958e27	−0.133324
$901$	1.85710e28	1.58107
$902$	1.89270e27	0.159448
$903$	−4.81071e27	−0.401029
$904$	−2.81290e27	−0.232035
$905$	−5.10949e27	−0.417077
$906$	−2.12208e27	−0.171413
$907$	−9.38782e27	−0.750404	−0.375202	−	0.926943i	$-0.622427\pi$
$907$	−9.38782e27	−0.750404	−0.375202	+	0.926943i	$0.622427\pi$
$908$	7.26277e27	0.574496
$909$	7.56706e27	0.592339
$910$	1.26847e26	0.00982627
$911$	1.16380e28	0.892181	0.446091	−	0.894988i	$-0.352816\pi$
$911$	1.16380e28	0.892181	0.446091	+	0.894988i	$0.352816\pi$
$912$	3.39167e27	0.257314
$913$	6.45313e26	0.0484505
$914$	1.32116e26	0.00981674
$915$	−2.38921e27	−0.175693
$916$	9.35752e27	0.681010
$917$	6.94353e27	0.500117
$918$	2.37249e27	0.169122
$919$	2.45968e28	1.73532	0.867662	−	0.497154i	$-0.165622\pi$
$919$	2.45968e28	1.73532	0.867662	+	0.497154i	$0.165622\pi$
$920$	−3.56272e27	−0.248769
$921$	−8.97761e27	−0.620432
$922$	−1.60636e28	−1.09875
$923$	−4.33125e26	−0.0293222
$924$	4.00457e26	0.0268332
$925$	4.68308e27	0.310588
$926$	1.31286e28	0.861812
$927$	−1.42349e27	−0.0924907
$928$	−3.34709e27	−0.215259
$929$	1.30187e27	0.0828739	0.0414370	−	0.999141i	$-0.486806\pi$
$929$	1.30187e27	0.0828739	0.0414370	+	0.999141i	$0.486806\pi$
$930$	−2.52235e27	−0.158934
$931$	−2.44722e28	−1.52634
$932$	1.37390e28	0.848214
$933$	1.36359e28	0.833313
$934$	1.45255e28	0.878690
$935$	2.27531e27	0.136248
$936$	1.62885e26	0.00965518
$937$	−1.51773e28	−0.890569	−0.445285	−	0.895389i	$-0.646898\pi$
$937$	−1.51773e28	−0.890569	−0.445285	+	0.895389i	$0.646898\pi$
$938$	−2.85523e27	−0.165849
$939$	−2.98957e27	−0.171904
$940$	−1.12932e27	−0.0642839
$941$	−1.63925e28	−0.923729	−0.461865	−	0.886950i	$-0.652819\pi$
$941$	−1.63925e28	−0.923729	−0.461865	+	0.886950i	$0.652819\pi$
$942$	8.25419e26	0.0460459
$943$	−2.62062e28	−1.44725
$944$	3.51314e27	0.192071
$945$	6.03111e26	0.0326434
$946$	−5.92439e27	−0.317452
$947$	−1.44359e28	−0.765808	−0.382904	−	0.923788i	$-0.625076\pi$
$947$	−1.44359e28	−0.765808	−0.382904	+	0.923788i	$0.625076\pi$
$948$	8.74625e27	0.459349
$949$	−1.03733e27	−0.0539370
$950$	−1.95886e28	−1.00839
$951$	−6.55678e27	−0.334177
$952$	3.30221e27	0.166630
$953$	7.49006e27	0.374199	0.187100	−	0.982341i	$-0.440091\pi$
$953$	7.49006e27	0.374199	0.187100	+	0.982341i	$0.440091\pi$
$954$	6.06216e27	0.299859
$955$	−7.60056e27	−0.372232
$956$	8.23790e27	0.399454
$957$	−3.58921e27	−0.172320
$958$	1.21768e28	0.578844
$959$	2.42696e27	0.114231
$960$	6.92628e26	0.0322792
$961$	−5.25306e27	−0.242404
$962$	−4.92266e26	−0.0224924
$963$	8.96553e27	0.405626
$964$	−8.51253e27	−0.381353
$965$	1.74186e28	0.772689
$966$	−5.54470e27	−0.243554
$967$	−1.31496e28	−0.571954	−0.285977	−	0.958237i	$-0.592318\pi$
$967$	−1.31496e28	−0.571954	−0.285977	+	0.958237i	$0.592318\pi$
$968$	−7.71547e27	−0.332312
$969$	2.99913e28	1.27914
$970$	−2.80938e27	−0.118653
$971$	−4.50091e27	−0.188242	−0.0941212	−	0.995561i	$-0.530004\pi$
$971$	−4.50091e27	−0.188242	−0.0941212	+	0.995561i	$0.530004\pi$
$972$	7.74455e26	0.0320750
$973$	1.58809e28	0.651335
$974$	−1.63674e28	−0.664765
$975$	−9.40741e26	−0.0378378
$976$	−4.27026e27	−0.170091
$977$	2.02948e27	0.0800546	0.0400273	−	0.999199i	$-0.487256\pi$
$977$	2.02948e27	0.0800546	0.0400273	+	0.999199i	$0.487256\pi$
$978$	7.97563e27	0.311563
$979$	−3.94855e27	−0.152758
$980$	−4.99757e27	−0.191475
$981$	−1.54573e28	−0.586513
$982$	−4.29323e27	−0.161334
$983$	−1.67910e28	−0.624911	−0.312456	−	0.949932i	$-0.601152\pi$
$983$	−1.67910e28	−0.624911	−0.312456	+	0.949932i	$0.601152\pi$
$984$	5.09475e27	0.187789
$985$	5.68567e27	0.207557
$986$	−2.95970e28	−1.07008
$987$	−1.75757e27	−0.0629362
$988$	2.05907e27	0.0730264
$989$	8.20287e28	2.88138
$990$	7.42732e26	0.0258403
$991$	5.00531e26	0.0172477	0.00862386	−	0.999963i	$-0.497255\pi$
$991$	5.00531e26	0.0172477	0.00862386	+	0.999963i	$0.497255\pi$
$992$	−4.50821e27	−0.153866
$993$	−3.55329e27	−0.120119
$994$	−2.86635e27	−0.0959751
$995$	6.10791e27	0.202569
$996$	1.73705e27	0.0570621
$997$	−2.97628e28	−0.968434	−0.484217	−	0.874948i	$-0.660895\pi$
$997$	−2.97628e28	−0.968434	−0.484217	+	0.874948i	$0.660895\pi$
$998$	7.43151e27	0.239517
$999$	−2.34053e27	−0.0747210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.20.a.c.1.1	✓	1
3.2	odd	2		18.20.a.a.1.1		1
4.3	odd	2		48.20.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.20.a.c.1.1	✓	1	1.1	even	1	trivial
18.20.a.a.1.1		1	3.2	odd	2
48.20.a.b.1.1		1	4.3	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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