LMFDB - Embedded newform 2.48.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,48,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, 48, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 48);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 48 $
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:	$27.9815325310$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+8.38861e6 q^{2} -1.96635e11 q^{3} +7.03687e13 q^{4} +2.06700e16 q^{5} -1.64949e18 q^{6} -5.11729e19 q^{7} +5.90296e20 q^{8} +1.20763e22 q^{9} +O(q^{10})$

\(q+8.38861e6 q^{2} -1.96635e11 q^{3} +7.03687e13 q^{4} +2.06700e16 q^{5} -1.64949e18 q^{6} -5.11729e19 q^{7} +5.90296e20 q^{8} +1.20763e22 q^{9} +1.73392e23 q^{10} +5.29743e24 q^{11} -1.38369e25 q^{12} -1.25094e26 q^{13} -4.29269e26 q^{14} -4.06443e27 q^{15} +4.95176e27 q^{16} -4.48300e28 q^{17} +1.01304e29 q^{18} -1.11132e30 q^{19} +1.45452e30 q^{20} +1.00624e31 q^{21} +4.44381e31 q^{22} -1.78238e32 q^{23} -1.16073e32 q^{24} -2.83295e32 q^{25} -1.04937e33 q^{26} +2.85365e33 q^{27} -3.60097e33 q^{28} -3.05341e34 q^{29} -3.40949e34 q^{30} -1.10802e35 q^{31} +4.15384e34 q^{32} -1.04166e36 q^{33} -3.76062e35 q^{34} -1.05774e36 q^{35} +8.49797e35 q^{36} +6.20377e36 q^{37} -9.32243e36 q^{38} +2.45978e37 q^{39} +1.22014e37 q^{40} -3.56698e37 q^{41} +8.44092e37 q^{42} +3.38085e38 q^{43} +3.72774e38 q^{44} +2.49618e38 q^{45} -1.49517e39 q^{46} -2.29839e39 q^{47} -9.73687e38 q^{48} -2.62467e39 q^{49} -2.37645e39 q^{50} +8.81513e39 q^{51} -8.80272e39 q^{52} -2.95957e40 q^{53} +2.39382e40 q^{54} +1.09498e41 q^{55} -3.02071e40 q^{56} +2.18524e41 q^{57} -2.56139e41 q^{58} +4.02898e41 q^{59} -2.86009e41 q^{60} +5.75153e41 q^{61} -9.29472e41 q^{62} -6.17981e41 q^{63} +3.48449e41 q^{64} -2.58569e42 q^{65} -8.73806e42 q^{66} -1.86803e42 q^{67} -3.15463e42 q^{68} +3.50478e43 q^{69} -8.87298e42 q^{70} +5.52020e43 q^{71} +7.12862e42 q^{72} -7.91827e43 q^{73} +5.20410e43 q^{74} +5.57057e43 q^{75} -7.82022e43 q^{76} -2.71085e44 q^{77} +2.06342e44 q^{78} +8.82751e43 q^{79} +1.02353e44 q^{80} -8.82223e44 q^{81} -2.99220e44 q^{82} -7.37731e44 q^{83} +7.08076e44 q^{84} -9.26635e44 q^{85} +2.83607e45 q^{86} +6.00406e45 q^{87} +3.12705e45 q^{88} -8.27703e45 q^{89} +2.09394e45 q^{90} +6.40143e45 q^{91} -1.25424e46 q^{92} +2.17874e46 q^{93} -1.92803e46 q^{94} -2.29709e46 q^{95} -8.16788e45 q^{96} -6.19542e46 q^{97} -2.20174e46 q^{98} +6.39736e46 q^{99} +O(q^{100})\)

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 $

$2$	8.38861e6	0.707107
$2$	8.38861e6	0.707107
$3$	−1.96635e11	−1.20590	−0.602949	−	0.797780i	$-0.706008\pi$
$3$	−1.96635e11	−1.20590	−0.602949	+	0.797780i	$0.706008\pi$
$4$	7.03687e13	0.500000
$5$	2.06700e16	0.775434	0.387717	−	0.921779i	$-0.373264\pi$
$5$	2.06700e16	0.775434	0.387717	+	0.921779i	$0.373264\pi$
$6$	−1.64949e18	−0.852698
$7$	−5.11729e19	−0.706701	−0.353351	−	0.935491i	$-0.614958\pi$
$7$	−5.11729e19	−0.706701	−0.353351	+	0.935491i	$0.614958\pi$
$8$	5.90296e20	0.353553
$9$	1.20763e22	0.454189
$10$	1.73392e23	0.548314
$11$	5.29743e24	1.78376	0.891882	−	0.452269i	$-0.149385\pi$
$11$	5.29743e24	1.78376	0.891882	+	0.452269i	$0.149385\pi$
$12$	−1.38369e25	−0.602949
$13$	−1.25094e26	−0.830937	−0.415469	−	0.909608i	$-0.636382\pi$
$13$	−1.25094e26	−0.830937	−0.415469	+	0.909608i	$0.636382\pi$
$14$	−4.29269e26	−0.499713
$15$	−4.06443e27	−0.935093
$16$	4.95176e27	0.250000
$17$	−4.48300e28	−0.544527	−0.272263	−	0.962223i	$-0.587772\pi$
$17$	−4.48300e28	−0.544527	−0.272263	+	0.962223i	$0.587772\pi$
$18$	1.01304e29	0.321160
$19$	−1.11132e30	−0.988848	−0.494424	−	0.869221i	$-0.664621\pi$
$19$	−1.11132e30	−0.988848	−0.494424	+	0.869221i	$0.664621\pi$
$20$	1.45452e30	0.387717
$21$	1.00624e31	0.852209
$22$	4.44381e31	1.26131
$23$	−1.78238e32	−1.77990	−0.889952	−	0.456055i	$-0.849262\pi$
$23$	−1.78238e32	−1.77990	−0.889952	+	0.456055i	$0.849262\pi$
$24$	−1.16073e32	−0.426349
$25$	−2.83295e32	−0.398703
$26$	−1.04937e33	−0.587561
$27$	2.85365e33	0.658192
$28$	−3.60097e33	−0.353351
$29$	−3.05341e34	−1.31351	−0.656753	−	0.754105i	$-0.728071\pi$
$29$	−3.05341e34	−1.31351	−0.656753	+	0.754105i	$0.728071\pi$
$30$	−3.40949e34	−0.661211
$31$	−1.10802e35	−0.994367	−0.497183	−	0.867645i	$-0.665632\pi$
$31$	−1.10802e35	−0.994367	−0.497183	+	0.867645i	$0.665632\pi$
$32$	4.15384e34	0.176777
$33$	−1.04166e36	−2.15104
$34$	−3.76062e35	−0.385039
$35$	−1.05774e36	−0.548000
$36$	8.49797e35	0.227094
$37$	6.20377e36	0.870793	0.435397	−	0.900239i	$-0.356608\pi$
$37$	6.20377e36	0.870793	0.435397	+	0.900239i	$0.356608\pi$
$38$	−9.32243e36	−0.699221
$39$	2.45978e37	1.00203
$40$	1.22014e37	0.274157
$41$	−3.56698e37	−0.448621	−0.224311	−	0.974518i	$-0.572013\pi$
$41$	−3.56698e37	−0.448621	−0.224311	+	0.974518i	$0.572013\pi$
$42$	8.44092e37	0.602603
$43$	3.38085e38	1.38841	0.694205	−	0.719777i	$-0.255756\pi$
$43$	3.38085e38	1.38841	0.694205	+	0.719777i	$0.255756\pi$
$44$	3.72774e38	0.891882
$45$	2.49618e38	0.352193
$46$	−1.49517e39	−1.25858
$47$	−2.29839e39	−1.16714	−0.583571	−	0.812062i	$-0.698345\pi$
$47$	−2.29839e39	−1.16714	−0.583571	+	0.812062i	$0.698345\pi$
$48$	−9.73687e38	−0.301474
$49$	−2.62467e39	−0.500573
$50$	−2.37645e39	−0.281925
$51$	8.81513e39	0.656644
$52$	−8.80272e39	−0.415469
$53$	−2.95957e40	−0.892781	−0.446391	−	0.894838i	$-0.647291\pi$
$53$	−2.95957e40	−0.892781	−0.446391	+	0.894838i	$0.647291\pi$
$54$	2.39382e40	0.465412
$55$	1.09498e41	1.38319
$56$	−3.02071e40	−0.249857
$57$	2.18524e41	1.19245
$58$	−2.56139e41	−0.928790
$59$	4.02898e41	0.977626	0.488813	−	0.872389i	$-0.337430\pi$
$59$	4.02898e41	0.977626	0.488813	+	0.872389i	$0.337430\pi$
$60$	−2.86009e41	−0.467547
$61$	5.75153e41	0.637577	0.318788	−	0.947826i	$-0.396724\pi$
$61$	5.75153e41	0.637577	0.318788	+	0.947826i	$0.396724\pi$
$62$	−9.29472e41	−0.703124
$63$	−6.17981e41	−0.320976
$64$	3.48449e41	0.125000
$65$	−2.58569e42	−0.644337
$66$	−8.73806e42	−1.52101
$67$	−1.86803e42	−0.228364	−0.114182	−	0.993460i	$-0.536425\pi$
$67$	−1.86803e42	−0.228364	−0.114182	+	0.993460i	$0.536425\pi$
$68$	−3.15463e42	−0.272263
$69$	3.50478e43	2.14638
$70$	−8.87298e42	−0.387494
$71$	5.52020e43	1.72736	0.863681	−	0.504038i	$-0.168153\pi$
$71$	5.52020e43	1.72736	0.863681	+	0.504038i	$0.168153\pi$
$72$	7.12862e42	0.160580
$73$	−7.91827e43	−1.28986	−0.644931	−	0.764241i	$-0.723114\pi$
$73$	−7.91827e43	−1.28986	−0.644931	+	0.764241i	$0.723114\pi$
$74$	5.20410e43	0.615744
$75$	5.57057e43	0.480795
$76$	−7.82022e43	−0.494424
$77$	−2.71085e44	−1.26059
$78$	2.06342e44	0.708539
$79$	8.82751e43	0.224699	0.112350	−	0.993669i	$-0.464162\pi$
$79$	8.82751e43	0.224699	0.112350	+	0.993669i	$0.464162\pi$
$80$	1.02353e44	0.193858
$81$	−8.82223e44	−1.24790
$82$	−2.99220e44	−0.317223
$83$	−7.37731e44	−0.588251	−0.294125	−	0.955767i	$-0.595028\pi$
$83$	−7.37731e44	−0.588251	−0.294125	+	0.955767i	$0.595028\pi$
$84$	7.08076e44	0.426105
$85$	−9.26635e44	−0.422244
$86$	2.83607e45	0.981754
$87$	6.00406e45	1.58395
$88$	3.12705e45	0.630655
$89$	−8.27703e45	−1.28000	−0.639999	−	0.768375i	$-0.721065\pi$
$89$	−8.27703e45	−1.28000	−0.639999	+	0.768375i	$0.721065\pi$
$90$	2.09394e45	0.249038
$91$	6.40143e45	0.587224
$92$	−1.25424e46	−0.889952
$93$	2.17874e46	1.19910
$94$	−1.92803e46	−0.825293
$95$	−2.29709e46	−0.766786
$96$	−8.16788e45	−0.213175
$97$	−6.19542e46	−1.26746	−0.633731	−	0.773554i	$-0.718477\pi$
$97$	−6.19542e46	−1.26746	−0.633731	+	0.773554i	$0.718477\pi$
$98$	−2.20174e46	−0.353959
$99$	6.39736e46	0.810165
$100$	−1.99351e46	−0.199351
$101$	1.21967e47	0.965363	0.482682	−	0.875796i	$-0.339663\pi$
$101$	1.21967e47	0.965363	0.482682	+	0.875796i	$0.339663\pi$
$102$	7.39467e46	0.464317
$103$	1.65592e47	0.826732	0.413366	−	0.910565i	$-0.364353\pi$
$103$	1.65592e47	0.826732	0.413366	+	0.910565i	$0.364353\pi$
$104$	−7.38425e46	−0.293781
$105$	2.07989e47	0.660832
$106$	−2.48266e47	−0.631292
$107$	−4.61678e47	−0.941500	−0.470750	−	0.882267i	$-0.656017\pi$
$107$	−4.61678e47	−0.941500	−0.470750	+	0.882267i	$0.656017\pi$
$108$	2.00808e47	0.329096
$109$	2.51311e47	0.331657	0.165829	−	0.986155i	$-0.446970\pi$
$109$	2.51311e47	0.331657	0.165829	+	0.986155i	$0.446970\pi$
$110$	9.18533e47	0.978063
$111$	−1.21988e48	−1.05009
$112$	−2.53396e47	−0.176675
$113$	−8.86375e47	−0.501504	−0.250752	−	0.968051i	$-0.580678\pi$
$113$	−8.86375e47	−0.501504	−0.250752	+	0.968051i	$0.580678\pi$
$114$	1.83311e48	0.843189
$115$	−3.68417e48	−1.38020
$116$	−2.14865e48	−0.656753
$117$	−1.51068e48	−0.377402
$118$	3.37975e48	0.691286
$119$	2.29408e48	0.384818
$120$	−2.39922e48	−0.330605
$121$	1.92430e49	2.18181
$122$	4.82474e48	0.450835
$123$	7.01391e48	0.540991
$124$	−7.79698e48	−0.497183
$125$	−2.05426e49	−1.08460
$126$	−5.18400e48	−0.226964
$127$	2.35947e49	0.857883	0.428941	−	0.903332i	$-0.358887\pi$
$127$	2.35947e49	0.857883	0.428941	+	0.903332i	$0.358887\pi$
$128$	2.92300e48	0.0883883
$129$	−6.64793e49	−1.67428
$130$	−2.16903e49	−0.455615
$131$	3.57925e49	0.627938	0.313969	−	0.949433i	$-0.398341\pi$
$131$	3.57925e49	0.627938	0.313969	+	0.949433i	$0.398341\pi$
$132$	−7.33002e49	−1.07552
$133$	5.68694e49	0.698820
$134$	−1.56702e49	−0.161477
$135$	5.89849e49	0.510384
$136$	−2.64630e49	−0.192519
$137$	−1.00526e50	−0.615665	−0.307832	−	0.951441i	$-0.599604\pi$
$137$	−1.00526e50	−0.615665	−0.307832	+	0.951441i	$0.599604\pi$
$138$	2.94002e50	1.51772
$139$	−5.50254e49	−0.239726	−0.119863	−	0.992790i	$-0.538246\pi$
$139$	−5.50254e49	−0.239726	−0.119863	+	0.992790i	$0.538246\pi$
$140$	−7.44319e49	−0.274000
$141$	4.51942e50	1.40745
$142$	4.63068e50	1.22143
$143$	−6.62677e50	−1.48219
$144$	5.97992e49	0.113547
$145$	−6.31139e50	−1.01854
$146$	−6.64233e50	−0.912070
$147$	5.16102e50	0.603640
$148$	4.36551e50	0.435397
$149$	3.78314e48	0.00322089	0.00161044	−	0.999999i	$-0.499487\pi$
$149$	3.78314e48	0.00322089	0.00161044	+	0.999999i	$0.499487\pi$
$150$	4.67293e50	0.339973
$151$	−8.86913e50	−0.551979	−0.275990	−	0.961161i	$-0.589006\pi$
$151$	−8.86913e50	−0.551979	−0.275990	+	0.961161i	$0.589006\pi$
$152$	−6.56007e50	−0.349610
$153$	−5.41383e50	−0.247318
$154$	−2.27402e51	−0.891370
$155$	−2.29027e51	−0.771065
$156$	1.73092e51	0.501013
$157$	5.52046e51	1.37510	0.687548	−	0.726139i	$-0.258687\pi$
$157$	5.52046e51	1.37510	0.687548	+	0.726139i	$0.258687\pi$
$158$	7.40505e50	0.158886
$159$	5.81953e51	1.07660
$160$	8.58597e50	0.137079
$161$	9.12096e51	1.25786
$162$	−7.40062e51	−0.882400
$163$	7.64913e51	0.789229	0.394615	−	0.918847i	$-0.370878\pi$
$163$	7.64913e51	0.789229	0.394615	+	0.918847i	$0.370878\pi$
$164$	−2.51004e51	−0.224311
$165$	−2.15310e52	−1.66799
$166$	−6.18853e51	−0.415956
$167$	−1.01020e52	−0.589615	−0.294807	−	0.955557i	$-0.595255\pi$
$167$	−1.01020e52	−0.589615	−0.294807	+	0.955557i	$0.595255\pi$
$168$	5.93977e51	0.301302
$169$	−7.01551e51	−0.309543
$170$	−7.77318e51	−0.298572
$171$	−1.34207e52	−0.449124
$172$	2.37906e52	0.694205
$173$	−1.26608e52	−0.322387	−0.161193	−	0.986923i	$-0.551534\pi$
$173$	−1.26608e52	−0.322387	−0.161193	+	0.986923i	$0.551534\pi$
$174$	5.03657e52	1.12003
$175$	1.44970e52	0.281764
$176$	2.62316e52	0.445941
$177$	−7.92236e52	−1.17892
$178$	−6.94328e52	−0.905096
$179$	1.53886e53	1.75854	0.879269	−	0.476325i	$-0.158031\pi$
$179$	1.53886e53	1.75854	0.879269	+	0.476325i	$0.158031\pi$
$180$	1.75653e52	0.176097
$181$	6.25255e52	0.550314	0.275157	−	0.961399i	$-0.411270\pi$
$181$	6.25255e52	0.550314	0.275157	+	0.961399i	$0.411270\pi$
$182$	5.36991e52	0.415230
$183$	−1.13095e53	−0.768852
$184$	−1.05213e53	−0.629291
$185$	1.28232e53	0.675242
$186$	1.82766e53	0.847895
$187$	−2.37484e53	−0.971307
$188$	−1.61735e53	−0.583571
$189$	−1.46030e53	−0.465145
$190$	−1.92694e53	−0.542199
$191$	−1.11993e52	−0.0278553	−0.0139276	−	0.999903i	$-0.504433\pi$
$191$	−1.11993e52	−0.0278553	−0.0139276	+	0.999903i	$0.504433\pi$
$192$	−6.85172e52	−0.150737
$193$	3.30249e53	0.643050	0.321525	−	0.946901i	$-0.395805\pi$
$193$	3.30249e53	0.643050	0.321525	+	0.946901i	$0.395805\pi$
$194$	−5.19709e53	−0.896231
$195$	5.08436e53	0.777004
$196$	−1.84695e53	−0.250287
$197$	3.35582e53	0.403499	0.201749	−	0.979437i	$-0.435337\pi$
$197$	3.35582e53	0.403499	0.201749	+	0.979437i	$0.435337\pi$
$198$	5.36649e53	0.572873
$199$	−4.53521e53	−0.430081	−0.215041	−	0.976605i	$-0.568988\pi$
$199$	−4.53521e53	−0.430081	−0.215041	+	0.976605i	$0.568988\pi$
$200$	−1.67228e53	−0.140963
$201$	3.67320e53	0.275383
$202$	1.02313e54	0.682615
$203$	1.56252e54	0.928257
$204$	6.20310e53	0.328322
$205$	−7.37293e53	−0.347876
$206$	1.38909e54	0.584588
$207$	−2.15246e54	−0.808412
$208$	−6.19436e53	−0.207734
$209$	−5.88714e54	−1.76387
$210$	1.74473e54	0.467279
$211$	2.34865e54	0.562574	0.281287	−	0.959624i	$-0.409239\pi$
$211$	2.34865e54	0.562574	0.281287	+	0.959624i	$0.409239\pi$
$212$	−2.08261e54	−0.446391
$213$	−1.08546e55	−2.08302
$214$	−3.87284e54	−0.665741
$215$	6.98821e54	1.07662
$216$	1.68450e54	0.232706
$217$	5.67004e54	0.702720
$218$	2.10815e54	0.234517
$219$	1.55701e55	1.55544
$220$	7.70521e54	0.691595
$221$	5.60797e54	0.452468
$222$	−1.02331e55	−0.742524
$223$	−1.63862e55	−1.06983	−0.534913	−	0.844907i	$-0.679656\pi$
$223$	−1.63862e55	−1.06983	−0.534913	+	0.844907i	$0.679656\pi$
$224$	−2.12564e54	−0.124928
$225$	−3.42117e54	−0.181086
$226$	−7.43546e54	−0.354617
$227$	6.42416e54	0.276190	0.138095	−	0.990419i	$-0.455902\pi$
$227$	6.42416e54	0.276190	0.138095	+	0.990419i	$0.455902\pi$
$228$	1.53773e55	0.596225
$229$	2.68073e55	0.937819	0.468910	−	0.883246i	$-0.344647\pi$
$229$	2.68073e55	0.937819	0.468910	+	0.883246i	$0.344647\pi$
$230$	−3.09051e55	−0.975946
$231$	5.33046e55	1.52014
$232$	−1.80242e55	−0.464395
$233$	−6.96307e55	−1.62157	−0.810787	−	0.585341i	$-0.800961\pi$
$233$	−6.96307e55	−1.62157	−0.810787	+	0.585341i	$0.800961\pi$
$234$	−1.26725e55	−0.266864
$235$	−4.75076e55	−0.905040
$236$	2.83514e55	0.488813
$237$	−1.73579e55	−0.270964
$238$	1.92442e55	0.272107
$239$	−1.13696e54	−0.0145678	−0.00728390	−	0.999973i	$-0.502319\pi$
$239$	−1.13696e54	−0.0145678	−0.00728390	+	0.999973i	$0.502319\pi$
$240$	−2.01261e55	−0.233773
$241$	−1.08595e56	−1.14396	−0.571979	−	0.820268i	$-0.693824\pi$
$241$	−1.08595e56	−1.14396	−0.571979	+	0.820268i	$0.693824\pi$
$242$	1.61422e56	1.54277
$243$	9.76002e55	0.846649
$244$	4.04728e55	0.318788
$245$	−5.42519e55	−0.388161
$246$	5.88369e55	0.382538
$247$	1.39020e56	0.821670
$248$	−6.54058e55	−0.351562
$249$	1.45063e56	0.709370
$250$	−1.72324e56	−0.766929
$251$	3.63653e56	1.47352	0.736758	−	0.676156i	$-0.236356\pi$
$251$	3.63653e56	1.47352	0.736758	+	0.676156i	$0.236356\pi$
$252$	−4.34866e55	−0.160488
$253$	−9.44204e56	−3.17493
$254$	1.97927e56	0.606615
$255$	1.82208e56	0.509184
$256$	2.45199e55	0.0625000
$257$	2.18320e56	0.507769	0.253884	−	0.967235i	$-0.418292\pi$
$257$	2.18320e56	0.507769	0.253884	+	0.967235i	$0.418292\pi$
$258$	−5.57669e56	−1.18389
$259$	−3.17465e56	−0.615391
$260$	−1.81952e56	−0.322168
$261$	−3.68740e56	−0.596580
$262$	3.00249e56	0.444019
$263$	1.02288e57	1.38314	0.691570	−	0.722309i	$-0.256919\pi$
$263$	1.02288e57	1.38314	0.691570	+	0.722309i	$0.256919\pi$
$264$	−6.14886e56	−0.760506
$265$	−6.11741e56	−0.692292
$266$	4.77055e56	0.494140
$267$	1.62755e57	1.54355
$268$	−1.31451e56	−0.114182
$269$	5.80374e56	0.461880	0.230940	−	0.972968i	$-0.425820\pi$
$269$	5.80374e56	0.461880	0.230940	+	0.972968i	$0.425820\pi$
$270$	4.94801e56	0.360896
$271$	1.66765e57	1.11513	0.557565	−	0.830133i	$-0.311736\pi$
$271$	1.66765e57	1.11513	0.557565	+	0.830133i	$0.311736\pi$
$272$	−2.21988e56	−0.136132
$273$	−1.25874e57	−0.708132
$274$	−8.43272e56	−0.435341
$275$	−1.50074e57	−0.711191
$276$	2.46627e57	1.07319
$277$	−3.42098e57	−1.36734	−0.683669	−	0.729792i	$-0.739617\pi$
$277$	−3.42098e57	−1.36734	−0.683669	+	0.729792i	$0.739617\pi$
$278$	−4.61586e56	−0.169512
$279$	−1.33808e57	−0.451630
$280$	−6.24380e56	−0.193747
$281$	1.12913e57	0.322214	0.161107	−	0.986937i	$-0.448494\pi$
$281$	1.12913e57	0.322214	0.161107	+	0.986937i	$0.448494\pi$
$282$	3.79117e57	0.995219
$283$	−7.01471e57	−1.69445	−0.847225	−	0.531234i	$-0.821728\pi$
$283$	−7.01471e57	−1.69445	−0.847225	+	0.531234i	$0.821728\pi$
$284$	3.88449e57	0.863681
$285$	4.51688e57	0.924665
$286$	−5.55894e57	−1.04807
$287$	1.82532e57	0.317041
$288$	5.01632e56	0.0802900
$289$	−4.76823e57	−0.703490
$290$	−5.29438e57	−0.720215
$291$	1.21823e58	1.52843
$292$	−5.57199e57	−0.644931
$293$	−7.39186e57	−0.789523	−0.394761	−	0.918784i	$-0.629173\pi$
$293$	−7.39186e57	−0.789523	−0.394761	+	0.918784i	$0.629173\pi$
$294$	4.32938e57	0.426838
$295$	8.32788e57	0.758084
$296$	3.66206e57	0.307872
$297$	1.51170e58	1.17406
$298$	3.17353e55	0.00227751
$299$	2.22965e58	1.47899
$300$	3.91994e57	0.240397
$301$	−1.73008e58	−0.981191
$302$	−7.43997e57	−0.390308
$303$	−2.39830e58	−1.16413
$304$	−5.50299e57	−0.247212
$305$	1.18884e58	0.494398
$306$	−4.54145e57	−0.174880
$307$	−2.91735e58	−1.04049	−0.520243	−	0.854018i	$-0.674159\pi$
$307$	−2.91735e58	−1.04049	−0.520243	+	0.854018i	$0.674159\pi$
$308$	−1.90759e58	−0.630294
$309$	−3.25611e58	−0.996954
$310$	−1.92122e58	−0.545226
$311$	1.96485e58	0.516964	0.258482	−	0.966016i	$-0.416778\pi$
$311$	1.96485e58	0.516964	0.258482	+	0.966016i	$0.416778\pi$
$312$	1.45200e58	0.354269
$313$	5.30059e58	1.19959	0.599794	−	0.800155i	$-0.295249\pi$
$313$	5.30059e58	1.19959	0.599794	+	0.800155i	$0.295249\pi$
$314$	4.63089e58	0.972340
$315$	−1.27737e58	−0.248895
$316$	6.21181e57	0.112350
$317$	1.71533e58	0.288041	0.144020	−	0.989575i	$-0.453997\pi$
$317$	1.71533e58	0.288041	0.144020	+	0.989575i	$0.453997\pi$
$318$	4.88177e58	0.761273
$319$	−1.61752e59	−2.34298
$320$	7.20243e57	0.0969292
$321$	9.07819e58	1.13535
$322$	7.65121e58	0.889441
$323$	4.98205e58	0.538454
$324$	−6.20809e58	−0.623951
$325$	3.54386e58	0.331297
$326$	6.41655e58	0.558069
$327$	−4.94165e58	−0.399944
$328$	−2.10557e58	−0.158612
$329$	1.17615e59	0.824820
$330$	−1.80615e59	−1.17944
$331$	−3.07803e59	−1.87204	−0.936020	−	0.351947i	$-0.885520\pi$
$331$	−3.07803e59	−1.87204	−0.936020	+	0.351947i	$0.885520\pi$
$332$	−5.19132e58	−0.294125
$333$	7.49188e58	0.395505
$334$	−8.47413e58	−0.416921
$335$	−3.86122e58	−0.177081
$336$	4.98264e58	0.213052
$337$	2.88763e59	1.15143	0.575716	−	0.817650i	$-0.304723\pi$
$337$	2.88763e59	1.15143	0.575716	+	0.817650i	$0.304723\pi$
$338$	−5.88504e58	−0.218880
$339$	1.74292e59	0.604762
$340$	−6.52061e58	−0.211122
$341$	−5.86964e59	−1.77371
$342$	−1.12581e59	−0.317578
$343$	4.02629e59	1.06046
$344$	1.99570e59	0.490877
$345$	7.24436e59	1.66438
$346$	−1.06206e59	−0.227962
$347$	−3.66533e59	−0.735141	−0.367570	−	0.929996i	$-0.619810\pi$
$347$	−3.66533e59	−0.735141	−0.367570	+	0.929996i	$0.619810\pi$
$348$	4.22498e59	0.791977
$349$	−3.54128e59	−0.620530	−0.310265	−	0.950650i	$-0.600418\pi$
$349$	−3.54128e59	−0.620530	−0.310265	+	0.950650i	$0.600418\pi$
$350$	1.21610e59	0.199237
$351$	−3.56975e59	−0.546916
$352$	2.20047e59	0.315328
$353$	4.56710e59	0.612259	0.306129	−	0.951990i	$-0.400966\pi$
$353$	4.56710e59	0.612259	0.306129	+	0.951990i	$0.400966\pi$
$354$	−6.64576e59	−0.833620
$355$	1.14102e60	1.33945
$356$	−5.82444e59	−0.639999
$357$	−4.51096e59	−0.464051
$358$	1.29089e60	1.24347
$359$	−9.09804e59	−0.820783	−0.410391	−	0.911910i	$-0.634608\pi$
$359$	−9.09804e59	−0.820783	−0.410391	+	0.911910i	$0.634608\pi$
$360$	1.47348e59	0.124519
$361$	−2.80144e58	−0.0221800
$362$	5.24502e59	0.389131
$363$	−3.78384e60	−2.63104
$364$	4.50460e59	0.293612
$365$	−1.63670e60	−1.00020
$366$	−9.48710e59	−0.543661
$367$	1.74699e60	0.938939	0.469470	−	0.882949i	$-0.344445\pi$
$367$	1.74699e60	0.938939	0.469470	+	0.882949i	$0.344445\pi$
$368$	−8.82592e59	−0.444976
$369$	−4.30760e59	−0.203759
$370$	1.07569e60	0.477468
$371$	1.51449e60	0.630930
$372$	1.53316e60	0.599552
$373$	4.07052e60	1.49449	0.747243	−	0.664551i	$-0.231377\pi$
$373$	4.07052e60	1.49449	0.747243	+	0.664551i	$0.231377\pi$
$374$	−1.99216e60	−0.686818
$375$	4.03938e60	1.30792
$376$	−1.35673e60	−0.412647
$377$	3.81964e60	1.09144
$378$	−1.22499e60	−0.328907
$379$	2.62308e60	0.661896	0.330948	−	0.943649i	$-0.392632\pi$
$379$	2.62308e60	0.661896	0.330948	+	0.943649i	$0.392632\pi$
$380$	−1.61644e60	−0.383393
$381$	−4.63954e60	−1.03452
$382$	−9.39467e58	−0.0196967
$383$	−4.33638e60	−0.854981	−0.427491	−	0.904020i	$-0.640602\pi$
$383$	−4.33638e60	−0.854981	−0.427491	+	0.904020i	$0.640602\pi$
$384$	−5.74764e59	−0.106587
$385$	−5.60331e60	−0.977502
$386$	2.77033e60	0.454705
$387$	4.08284e60	0.630600
$388$	−4.35964e60	−0.633731
$389$	−8.25352e60	−1.12934	−0.564668	−	0.825318i	$-0.690996\pi$
$389$	−8.25352e60	−1.12934	−0.564668	+	0.825318i	$0.690996\pi$
$390$	4.26507e60	0.549425
$391$	7.99042e60	0.969205
$392$	−1.54933e60	−0.176979
$393$	−7.03804e60	−0.757228
$394$	2.81506e60	0.285317
$395$	1.82464e60	0.174239
$396$	4.50174e60	0.405083
$397$	−2.22502e60	−0.188693	−0.0943467	−	0.995539i	$-0.530076\pi$
$397$	−2.22502e60	−0.188693	−0.0943467	+	0.995539i	$0.530076\pi$
$398$	−3.80441e60	−0.304113
$399$	−1.11825e61	−0.842705
$400$	−1.40281e60	−0.0996757
$401$	1.02772e61	0.688626	0.344313	−	0.938855i	$-0.388112\pi$
$401$	1.02772e61	0.688626	0.344313	+	0.938855i	$0.388112\pi$
$402$	3.08130e60	0.194725
$403$	1.38606e61	0.826256
$404$	8.58268e60	0.482682
$405$	−1.82355e61	−0.967665
$406$	1.31074e61	0.656377
$407$	3.28640e61	1.55329
$408$	5.20354e60	0.232159
$409$	−2.81920e61	−1.18749	−0.593743	−	0.804655i	$-0.702350\pi$
$409$	−2.81920e61	−1.18749	−0.593743	+	0.804655i	$0.702350\pi$
$410$	−6.18486e60	−0.245985
$411$	1.97668e61	0.742428
$412$	1.16525e61	0.413366
$413$	−2.06174e61	−0.690889
$414$	−1.80562e61	−0.571634
$415$	−1.52489e61	−0.456149
$416$	−5.19621e60	−0.146890
$417$	1.08199e61	0.289085
$418$	−4.93849e61	−1.24724
$419$	−3.13668e61	−0.748928	−0.374464	−	0.927241i	$-0.622173\pi$
$419$	−3.13668e61	−0.748928	−0.374464	+	0.927241i	$0.622173\pi$
$420$	1.46359e61	0.330416
$421$	6.99827e61	1.49404	0.747018	−	0.664803i	$-0.231485\pi$
$421$	6.99827e61	1.49404	0.747018	+	0.664803i	$0.231485\pi$
$422$	1.97019e61	0.397800
$423$	−2.77561e61	−0.530103
$424$	−1.74702e61	−0.315646
$425$	1.27001e61	0.217104
$426$	−9.10551e61	−1.47292
$427$	−2.94323e61	−0.450576
$428$	−3.24877e61	−0.470750
$429$	1.30305e62	1.78738
$430$	5.86214e61	0.761285
$431$	−2.82940e61	−0.347920	−0.173960	−	0.984753i	$-0.555656\pi$
$431$	−2.82940e61	−0.347920	−0.173960	+	0.984753i	$0.555656\pi$
$432$	1.41306e61	0.164548
$433$	−1.51590e62	−1.67188	−0.835938	−	0.548823i	$-0.815076\pi$
$433$	−1.51590e62	−1.67188	−0.835938	+	0.548823i	$0.815076\pi$
$434$	4.75638e61	0.496898
$435$	1.24104e62	1.22825
$436$	1.76845e61	0.165829
$437$	1.98080e62	1.76005
$438$	1.30611e62	1.09986
$439$	−1.10003e62	−0.877986	−0.438993	−	0.898490i	$-0.644665\pi$
$439$	−1.10003e62	−0.877986	−0.438993	+	0.898490i	$0.644665\pi$
$440$	6.46360e61	0.489031
$441$	−3.16965e61	−0.227355
$442$	4.70431e61	0.319943
$443$	−1.34508e62	−0.867481	−0.433741	−	0.901038i	$-0.642807\pi$
$443$	−1.34508e62	−0.867481	−0.433741	+	0.901038i	$0.642807\pi$
$444$	−8.58411e61	−0.525044
$445$	−1.71086e62	−0.992554
$446$	−1.37457e62	−0.756482
$447$	−7.43896e59	−0.00388406
$448$	−1.78311e61	−0.0883377
$449$	−7.92587e61	−0.372613	−0.186306	−	0.982492i	$-0.559652\pi$
$449$	−7.92587e61	−0.372613	−0.186306	+	0.982492i	$0.559652\pi$
$450$	−2.86989e61	−0.128047
$451$	−1.88958e62	−0.800234
$452$	−6.23731e61	−0.250752
$453$	1.74398e62	0.665631
$454$	5.38898e61	0.195296
$455$	1.32317e62	0.455354
$456$	1.28994e62	0.421594
$457$	−3.26630e62	−1.01397	−0.506985	−	0.861955i	$-0.669240\pi$
$457$	−3.26630e62	−1.01397	−0.506985	+	0.861955i	$0.669240\pi$
$458$	2.24876e62	0.663138
$459$	−1.27929e62	−0.358403
$460$	−2.59251e62	−0.690098
$461$	5.58029e62	1.41151	0.705757	−	0.708454i	$-0.250607\pi$
$461$	5.58029e62	1.41151	0.705757	+	0.708454i	$0.250607\pi$
$462$	4.47152e62	1.07490
$463$	5.76010e62	1.31606	0.658031	−	0.752991i	$-0.271390\pi$
$463$	5.76010e62	1.31606	0.658031	+	0.752991i	$0.271390\pi$
$464$	−1.51198e62	−0.328377
$465$	4.50346e62	0.929826
$466$	−5.84105e62	−1.14663
$467$	−4.90192e62	−0.914997	−0.457499	−	0.889210i	$-0.651255\pi$
$467$	−4.90192e62	−0.914997	−0.457499	+	0.889210i	$0.651255\pi$
$468$	−1.06305e62	−0.188701
$469$	9.55926e61	0.161385
$470$	−3.98522e62	−0.639960
$471$	−1.08551e63	−1.65823
$472$	2.37829e62	0.345643
$473$	1.79098e63	2.47659
$474$	−1.45609e62	−0.191601
$475$	3.14832e62	0.394256
$476$	1.61432e62	0.192409
$477$	−3.57407e62	−0.405491
$478$	−9.53750e60	−0.0103010
$479$	4.76619e62	0.490103	0.245051	−	0.969510i	$-0.421195\pi$
$479$	4.76619e62	0.490103	0.245051	+	0.969510i	$0.421195\pi$
$480$	−1.68830e62	−0.165303
$481$	−7.76055e62	−0.723574
$482$	−9.10962e62	−0.808900
$483$	−1.79350e63	−1.51685
$484$	1.35411e63	1.09091
$485$	−1.28059e63	−0.982832
$486$	8.18730e62	0.598671
$487$	−9.40089e62	−0.654996	−0.327498	−	0.944852i	$-0.606205\pi$
$487$	−9.40089e62	−0.654996	−0.327498	+	0.944852i	$0.606205\pi$
$488$	3.39511e62	0.225417
$489$	−1.50408e63	−0.951730
$490$	−4.55098e62	−0.274471
$491$	2.46181e63	1.41527	0.707634	−	0.706579i	$-0.249763\pi$
$491$	2.46181e63	1.41527	0.707634	+	0.706579i	$0.249763\pi$
$492$	4.93560e62	0.270496
$493$	1.36885e63	0.715240
$494$	1.16618e63	0.581009
$495$	1.32233e63	0.628229
$496$	−5.48664e62	−0.248592
$497$	−2.82484e63	−1.22073
$498$	1.21688e63	0.501601
$499$	3.13630e63	1.23326	0.616630	−	0.787253i	$-0.288498\pi$
$499$	3.13630e63	1.23326	0.616630	+	0.787253i	$0.288498\pi$
$500$	−1.44556e63	−0.542301
$501$	1.98639e63	0.711015
$502$	3.05054e63	1.04193
$503$	−2.01256e63	−0.655997	−0.327998	−	0.944678i	$-0.606374\pi$
$503$	−2.01256e63	−0.655997	−0.327998	+	0.944678i	$0.606374\pi$
$504$	−3.64792e62	−0.113482
$505$	2.52106e63	0.748575
$506$	−7.92056e63	−2.24501
$507$	1.37949e63	0.373278
$508$	1.66033e63	0.428941
$509$	−7.12023e63	−1.75641	−0.878206	−	0.478283i	$-0.841259\pi$
$509$	−7.12023e63	−1.75641	−0.878206	+	0.478283i	$0.841259\pi$
$510$	1.52848e63	0.360047
$511$	4.05201e63	0.911547
$512$	2.05688e62	0.0441942
$513$	−3.17132e63	−0.650852
$514$	1.83140e63	0.359047
$515$	3.42278e63	0.641076
$516$	−4.67806e63	−0.837140
$517$	−1.21755e64	−2.08190
$518$	−2.66309e63	−0.435147
$519$	2.48955e63	0.388765
$520$	−1.52632e63	−0.227807
$521$	1.00318e64	1.43117	0.715585	−	0.698526i	$-0.246160\pi$
$521$	1.00318e64	1.43117	0.715585	+	0.698526i	$0.246160\pi$
$522$	−3.09322e63	−0.421846
$523$	−2.57269e63	−0.335427	−0.167714	−	0.985836i	$-0.553638\pi$
$523$	−2.57269e63	−0.335427	−0.167714	+	0.985836i	$0.553638\pi$
$524$	2.51867e63	0.313969
$525$	−2.85062e63	−0.339778
$526$	8.58057e63	0.978028
$527$	4.96724e63	0.541460
$528$	−5.15804e63	−0.537759
$529$	2.17410e64	2.16806
$530$	−5.13166e63	−0.489525
$531$	4.86553e63	0.444027
$532$	4.00183e63	0.349410
$533$	4.46208e63	0.372776
$534$	1.36529e64	1.09145
$535$	−9.54287e63	−0.730071
$536$	−1.10269e63	−0.0807387
$537$	−3.02592e64	−2.12062
$538$	4.86853e63	0.326599
$539$	−1.39040e64	−0.892904
$540$	4.15069e63	0.255192
$541$	−1.17177e64	−0.689774	−0.344887	−	0.938644i	$-0.612083\pi$
$541$	−1.17177e64	−0.689774	−0.344887	+	0.938644i	$0.612083\pi$
$542$	1.39892e64	0.788516
$543$	−1.22947e64	−0.663622
$544$	−1.86217e63	−0.0962597
$545$	5.19459e63	0.257178
$546$	−1.05591e64	−0.500725
$547$	7.70176e63	0.349855	0.174927	−	0.984581i	$-0.444031\pi$
$547$	7.70176e63	0.349855	0.174927	+	0.984581i	$0.444031\pi$
$548$	−7.07387e63	−0.307832
$549$	6.94575e63	0.289580
$550$	−1.25891e64	−0.502888
$551$	3.39332e64	1.29886
$552$	2.06886e64	0.758860
$553$	−4.51729e63	−0.158795
$554$	−2.86973e64	−0.966854
$555$	−2.52148e64	−0.814273
$556$	−3.87207e63	−0.119863
$557$	1.83973e64	0.545957	0.272978	−	0.962020i	$-0.411991\pi$
$557$	1.83973e64	0.545957	0.272978	+	0.962020i	$0.411991\pi$
$558$	−1.12246e64	−0.319351
$559$	−4.22925e64	−1.15368
$560$	−5.23768e63	−0.137000
$561$	4.66976e64	1.17130
$562$	9.47181e63	0.227840
$563$	3.16333e64	0.729790	0.364895	−	0.931049i	$-0.381105\pi$
$563$	3.16333e64	0.729790	0.364895	+	0.931049i	$0.381105\pi$
$564$	3.18026e64	0.703726
$565$	−1.83213e64	−0.388883
$566$	−5.88437e64	−1.19816
$567$	4.51459e64	0.881894
$568$	3.25855e64	0.610715
$569$	8.24261e64	1.48227	0.741133	−	0.671358i	$-0.234289\pi$
$569$	8.24261e64	1.48227	0.741133	+	0.671358i	$0.234289\pi$
$570$	3.78903e64	0.653837
$571$	−4.09282e64	−0.677756	−0.338878	−	0.940830i	$-0.610047\pi$
$571$	−4.09282e64	−0.677756	−0.338878	+	0.940830i	$0.610047\pi$
$572$	−4.66318e64	−0.741097
$573$	2.20217e63	0.0335906
$574$	1.53119e64	0.224182
$575$	5.04940e64	0.709652
$576$	4.20799e63	0.0567736
$577$	−1.08012e65	−1.39907	−0.699534	−	0.714599i	$-0.746609\pi$
$577$	−1.08012e65	−1.39907	−0.699534	+	0.714599i	$0.746609\pi$
$578$	−3.99988e64	−0.497443
$579$	−6.49384e64	−0.775453
$580$	−4.44125e64	−0.509269
$581$	3.77518e64	0.415718
$582$	1.02193e65	1.08076
$583$	−1.56781e65	−1.59251
$584$	−4.67412e64	−0.456035
$585$	−3.12257e64	−0.292650
$586$	−6.20074e64	−0.558277
$587$	−8.27524e64	−0.715789	−0.357895	−	0.933762i	$-0.616505\pi$
$587$	−8.27524e64	−0.715789	−0.357895	+	0.933762i	$0.616505\pi$
$588$	3.63174e64	0.301820
$589$	1.23136e65	0.983278
$590$	6.98593e64	0.536046
$591$	−6.59870e64	−0.486578
$592$	3.07196e64	0.217698
$593$	9.13374e64	0.622104	0.311052	−	0.950393i	$-0.399319\pi$
$593$	9.13374e64	0.622104	0.311052	+	0.950393i	$0.399319\pi$
$594$	1.26811e65	0.830185
$595$	4.74186e64	0.298401
$596$	2.66215e62	0.00161044
$597$	8.91780e64	0.518634
$598$	1.87037e65	1.04580
$599$	−9.38897e64	−0.504763	−0.252382	−	0.967628i	$-0.581214\pi$
$599$	−9.38897e64	−0.504763	−0.252382	+	0.967628i	$0.581214\pi$
$600$	3.28828e64	0.169987
$601$	−8.67884e64	−0.431431	−0.215716	−	0.976456i	$-0.569208\pi$
$601$	−8.67884e64	−0.431431	−0.215716	+	0.976456i	$0.569208\pi$
$602$	−1.45130e65	−0.693807
$603$	−2.25590e64	−0.103720
$604$	−6.24110e64	−0.275990
$605$	3.97752e65	1.69185
$606$	−2.01184e65	−0.823163
$607$	5.32801e64	0.209716	0.104858	−	0.994487i	$-0.466561\pi$
$607$	5.32801e64	0.209716	0.104858	+	0.994487i	$0.466561\pi$
$608$	−4.61624e64	−0.174805
$609$	−3.07245e65	−1.11938
$610$	9.97271e64	0.349593
$611$	2.87515e65	0.969821
$612$	−3.80964e64	−0.123659
$613$	1.74087e65	0.543807	0.271903	−	0.962325i	$-0.412347\pi$
$613$	1.74087e65	0.543807	0.271903	+	0.962325i	$0.412347\pi$
$614$	−2.44725e65	−0.735735
$615$	1.44977e65	0.419503
$616$	−1.60020e65	−0.445685
$617$	−4.55160e65	−1.22029	−0.610144	−	0.792290i	$-0.708888\pi$
$617$	−4.55160e65	−1.22029	−0.610144	+	0.792290i	$0.708888\pi$
$618$	−2.73143e65	−0.704953
$619$	−2.56378e65	−0.637017	−0.318509	−	0.947920i	$-0.603182\pi$
$619$	−2.56378e65	−0.637017	−0.318509	+	0.947920i	$0.603182\pi$
$620$	−1.61163e65	−0.385533
$621$	−5.08630e65	−1.17152
$622$	1.64824e65	0.365549
$623$	4.23560e65	0.904577
$624$	1.21803e65	0.250506
$625$	−2.23321e65	−0.442333
$626$	4.44645e65	0.848237
$627$	1.15762e66	2.12705
$628$	3.88468e65	0.687548
$629$	−2.78115e65	−0.474170
$630$	−1.07153e65	−0.175996
$631$	−4.23671e65	−0.670407	−0.335203	−	0.942146i	$-0.608805\pi$
$631$	−4.23671e65	−0.670407	−0.335203	+	0.942146i	$0.608805\pi$
$632$	5.21084e64	0.0794432
$633$	−4.61825e65	−0.678407
$634$	1.43892e65	0.203676
$635$	4.87703e65	0.665231
$636$	4.09513e65	0.538301
$637$	3.28331e65	0.415945
$638$	−1.35688e66	−1.65674
$639$	6.66638e65	0.784549
$640$	6.04184e64	0.0685393
$641$	2.49269e65	0.272587	0.136293	−	0.990669i	$-0.456481\pi$
$641$	2.49269e65	0.272587	0.136293	+	0.990669i	$0.456481\pi$
$642$	7.61534e65	0.802816
$643$	−9.57846e65	−0.973505	−0.486752	−	0.873540i	$-0.661819\pi$
$643$	−9.57846e65	−0.973505	−0.486752	+	0.873540i	$0.661819\pi$
$644$	6.41830e65	0.628930
$645$	−1.37412e66	−1.29829
$646$	4.17925e65	0.380745
$647$	−3.65746e65	−0.321313	−0.160657	−	0.987010i	$-0.551361\pi$
$647$	−3.65746e65	−0.321313	−0.160657	+	0.987010i	$0.551361\pi$
$648$	−5.20772e65	−0.441200
$649$	2.13432e66	1.74385
$650$	2.97280e65	0.234262
$651$	−1.11493e66	−0.847409
$652$	5.38259e65	0.394615
$653$	−1.29709e66	−0.917301	−0.458650	−	0.888617i	$-0.651667\pi$
$653$	−1.29709e66	−0.917301	−0.458650	+	0.888617i	$0.651667\pi$
$654$	−4.14535e65	−0.282803
$655$	7.39830e65	0.486924
$656$	−1.76628e65	−0.112155
$657$	−9.56237e65	−0.585841
$658$	9.86627e65	0.583236
$659$	−1.65954e66	−0.946628	−0.473314	−	0.880894i	$-0.656942\pi$
$659$	−1.65954e66	−0.946628	−0.473314	+	0.880894i	$0.656942\pi$
$660$	−1.51511e66	−0.833993
$661$	−3.53637e65	−0.187855	−0.0939275	−	0.995579i	$-0.529942\pi$
$661$	−3.53637e65	−0.187855	−0.0939275	+	0.995579i	$0.529942\pi$
$662$	−2.58204e66	−1.32373
$663$	−1.10272e66	−0.545630
$664$	−4.35479e65	−0.207978
$665$	1.17549e66	0.541889
$666$	6.28465e65	0.279664
$667$	5.44234e66	2.33792
$668$	−7.10862e65	−0.294807
$669$	3.22209e66	1.29010
$670$	−3.23902e65	−0.125215
$671$	3.04684e66	1.13729
$672$	4.17974e65	0.150651
$673$	−7.59962e65	−0.264507	−0.132254	−	0.991216i	$-0.542221\pi$
$673$	−7.59962e65	−0.264507	−0.132254	+	0.991216i	$0.542221\pi$
$674$	2.42232e66	0.814186
$675$	−8.08427e65	−0.262423
$676$	−4.93673e65	−0.154772
$677$	1.68304e65	0.0509637	0.0254818	−	0.999675i	$-0.491888\pi$
$677$	1.68304e65	0.0509637	0.0254818	+	0.999675i	$0.491888\pi$
$678$	1.46207e66	0.427632
$679$	3.17037e66	0.895717
$680$	−5.46989e65	−0.149286
$681$	−1.26321e66	−0.333057
$682$	−4.92381e66	−1.25421
$683$	−6.47982e66	−1.59469	−0.797345	−	0.603524i	$-0.793763\pi$
$683$	−6.47982e66	−1.59469	−0.797345	+	0.603524i	$0.793763\pi$
$684$	−9.44396e65	−0.224562
$685$	−2.07786e66	−0.477407
$686$	3.37750e66	0.749856
$687$	−5.27124e66	−1.13091
$688$	1.67412e66	0.347102
$689$	3.70224e66	0.741845
$690$	6.07701e66	1.17689
$691$	−8.13920e66	−1.52352	−0.761759	−	0.647861i	$-0.775664\pi$
$691$	−8.13920e66	−1.52352	−0.761759	+	0.647861i	$0.775664\pi$
$692$	−8.90923e65	−0.161193
$693$	−3.27371e66	−0.572545
$694$	−3.07470e66	−0.519823
$695$	−1.13737e66	−0.185892
$696$	3.54417e66	0.560013
$697$	1.59908e66	0.244286
$698$	−2.97064e66	−0.438781
$699$	1.36918e67	1.95545
$700$	1.02014e66	0.140882
$701$	−4.13550e66	−0.552274	−0.276137	−	0.961118i	$-0.589054\pi$
$701$	−4.13550e66	−0.552274	−0.276137	+	0.961118i	$0.589054\pi$
$702$	−2.99453e66	−0.386728
$703$	−6.89437e66	−0.861082
$704$	1.84589e66	0.222970
$705$	9.34163e66	1.09139
$706$	3.83116e66	0.432932
$707$	−6.24141e66	−0.682223
$708$	−5.57487e66	−0.589458
$709$	5.79936e66	0.593190	0.296595	−	0.955003i	$-0.404149\pi$
$709$	5.79936e66	0.593190	0.296595	+	0.955003i	$0.404149\pi$
$710$	9.57159e66	0.947138
$711$	1.06604e66	0.102056
$712$	−4.88590e66	−0.452548
$713$	1.97491e67	1.76988
$714$	−3.78407e66	−0.328134
$715$	−1.36975e67	−1.14934
$716$	1.08287e67	0.879269
$717$	2.23565e65	0.0175673
$718$	−7.63199e66	−0.580381
$719$	−3.81716e66	−0.280939	−0.140469	−	0.990085i	$-0.544861\pi$
$719$	−3.81716e66	−0.280939	−0.140469	+	0.990085i	$0.544861\pi$
$720$	1.23605e66	0.0880483
$721$	−8.47383e66	−0.584253
$722$	−2.35002e65	−0.0156836
$723$	2.13536e67	1.37950
$724$	4.39984e66	0.275157
$725$	8.65017e66	0.523699
$726$	−3.17412e67	−1.86043
$727$	−1.41840e67	−0.804898	−0.402449	−	0.915442i	$-0.631841\pi$
$727$	−1.41840e67	−0.804898	−0.402449	+	0.915442i	$0.631841\pi$
$728$	3.77874e66	0.207615
$729$	4.26568e66	0.226930
$730$	−1.37297e67	−0.707250
$731$	−1.51564e67	−0.756027
$732$	−7.95836e66	−0.384426
$733$	−3.13854e66	−0.146820	−0.0734098	−	0.997302i	$-0.523388\pi$
$733$	−3.13854e66	−0.146820	−0.0734098	+	0.997302i	$0.523388\pi$
$734$	1.46548e67	0.663930
$735$	1.06678e67	0.468083
$736$	−7.40372e66	−0.314645
$737$	−9.89578e66	−0.407346
$738$	−3.61348e66	−0.144079
$739$	3.40636e67	1.31567	0.657835	−	0.753162i	$-0.271473\pi$
$739$	3.40636e67	1.31567	0.657835	+	0.753162i	$0.271473\pi$
$740$	9.02350e66	0.337621
$741$	−2.73361e67	−0.990850
$742$	1.27045e67	0.446135
$743$	−1.68868e67	−0.574526	−0.287263	−	0.957852i	$-0.592745\pi$
$743$	−1.68868e67	−0.574526	−0.287263	+	0.957852i	$0.592745\pi$
$744$	1.28610e67	0.423948
$745$	7.81974e64	0.00249758
$746$	3.41460e67	1.05676
$747$	−8.90909e66	−0.267177
$748$	−1.67114e67	−0.485653
$749$	2.36254e67	0.665360
$750$	3.38848e67	0.924838
$751$	5.49068e66	0.145240	0.0726202	−	0.997360i	$-0.476864\pi$
$751$	5.49068e66	0.145240	0.0726202	+	0.997360i	$0.476864\pi$
$752$	−1.13811e67	−0.291785
$753$	−7.15068e67	−1.77691
$754$	3.20414e67	0.771766
$755$	−1.83325e67	−0.428023
$756$	−1.02759e67	−0.232573
$757$	4.95348e67	1.08682	0.543410	−	0.839468i	$-0.317133\pi$
$757$	4.95348e67	1.08682	0.543410	+	0.839468i	$0.317133\pi$
$758$	2.20040e67	0.468031
$759$	1.85663e68	3.82863
$760$	−1.35596e67	−0.271100
$761$	−9.42386e67	−1.82679	−0.913397	−	0.407070i	$-0.866550\pi$
$761$	−9.42386e67	−1.82679	−0.913397	+	0.407070i	$0.866550\pi$
$762$	−3.89193e67	−0.731515
$763$	−1.28603e67	−0.234382
$764$	−7.88082e65	−0.0139276
$765$	−1.11904e67	−0.191779
$766$	−3.63762e67	−0.604563
$767$	−5.04001e67	−0.812345
$768$	−4.82147e66	−0.0753686
$769$	−7.17781e67	−1.08824	−0.544118	−	0.839009i	$-0.683136\pi$
$769$	−7.17781e67	−1.08824	−0.544118	+	0.839009i	$0.683136\pi$
$770$	−4.70040e67	−0.691198
$771$	−4.29293e67	−0.612317
$772$	2.32392e67	0.321525
$773$	−9.60953e67	−1.28969	−0.644843	−	0.764315i	$-0.723077\pi$
$773$	−9.60953e67	−1.28969	−0.644843	+	0.764315i	$0.723077\pi$
$774$	3.42493e67	0.445902
$775$	3.13896e67	0.396457
$776$	−3.65713e67	−0.448115
$777$	6.24245e67	0.742098
$778$	−6.92355e67	−0.798562
$779$	3.96405e67	0.443618
$780$	3.57780e67	0.388502
$781$	2.92429e68	3.08121
$782$	6.70285e67	0.685332
$783$	−8.71338e67	−0.864540
$784$	−1.29968e67	−0.125143
$785$	1.14108e68	1.06630
$786$	−5.90394e67	−0.535441
$787$	8.61160e67	0.758015	0.379008	−	0.925394i	$-0.376265\pi$
$787$	8.61160e67	0.758015	0.379008	+	0.925394i	$0.376265\pi$
$788$	2.36145e67	0.201749
$789$	−2.01134e68	−1.66793
$790$	1.53062e67	0.123206
$791$	4.53584e67	0.354413
$792$	3.77633e67	0.286437
$793$	−7.19483e67	−0.529786
$794$	−1.86648e67	−0.133426
$795$	1.20289e68	0.834834
$796$	−3.19137e67	−0.215041
$797$	−1.65301e67	−0.108144	−0.0540722	−	0.998537i	$-0.517220\pi$
$797$	−1.65301e67	−0.108144	−0.0540722	+	0.998537i	$0.517220\pi$
$798$	−9.38056e67	−0.595883
$799$	1.03037e68	0.635540
$800$	−1.17676e67	−0.0704814
$801$	−9.99563e67	−0.581361
$802$	8.62116e67	0.486932
$803$	−4.19465e68	−2.30081
$804$	2.58478e67	0.137691
$805$	1.88530e68	0.975387
$806$	1.16272e68	0.584252
$807$	−1.14122e68	−0.556980
$808$	7.19967e67	0.341307
$809$	2.92290e68	1.34593	0.672966	−	0.739673i	$-0.265020\pi$
$809$	2.92290e68	1.34593	0.672966	+	0.739673i	$0.265020\pi$
$810$	−1.52971e68	−0.684242
$811$	−2.83385e68	−1.23137	−0.615683	−	0.787994i	$-0.711120\pi$
$811$	−2.83385e68	−1.23137	−0.615683	+	0.787994i	$0.711120\pi$
$812$	1.09952e68	0.464129
$813$	−3.27917e68	−1.34473
$814$	2.75683e68	1.09834
$815$	1.58107e68	0.611995
$816$	4.36504e67	0.164161
$817$	−3.75721e68	−1.37293
$818$	−2.36492e68	−0.839679
$819$	7.73058e67	0.266711
$820$	−5.18824e67	−0.173938
$821$	−1.55031e68	−0.505072	−0.252536	−	0.967588i	$-0.581265\pi$
$821$	−1.55031e68	−0.505072	−0.252536	+	0.967588i	$0.581265\pi$
$822$	1.65816e68	0.524976
$823$	−2.72599e68	−0.838740	−0.419370	−	0.907815i	$-0.637749\pi$
$823$	−2.72599e68	−0.838740	−0.419370	+	0.907815i	$0.637749\pi$
$824$	9.77483e67	0.292294
$825$	2.95097e68	0.857624
$826$	−1.72952e68	−0.488533
$827$	4.52263e68	1.24169	0.620843	−	0.783935i	$-0.286790\pi$
$827$	4.52263e68	1.24169	0.620843	+	0.783935i	$0.286790\pi$
$828$	−1.51466e68	−0.404206
$829$	7.53936e68	1.95570	0.977852	−	0.209296i	$-0.0671171\pi$
$829$	7.53936e68	1.95570	0.977852	+	0.209296i	$0.0671171\pi$
$830$	−1.27917e68	−0.322546
$831$	6.72683e68	1.64887
$832$	−4.35889e67	−0.103867
$833$	1.17664e68	0.272576
$834$	9.07638e67	0.204414
$835$	−2.08807e68	−0.457207
$836$	−4.14271e68	−0.881935
$837$	−3.16190e68	−0.654485
$838$	−2.63123e68	−0.529572
$839$	−1.96939e68	−0.385413	−0.192706	−	0.981256i	$-0.561726\pi$
$839$	−1.96939e68	−0.385413	−0.192706	+	0.981256i	$0.561726\pi$
$840$	1.22775e68	0.233639
$841$	3.91944e68	0.725300
$842$	5.87057e68	1.05644
$843$	−2.22026e68	−0.388557
$844$	1.65271e68	0.281287
$845$	−1.45010e68	−0.240030
$846$	−2.32835e68	−0.374839
$847$	−9.84721e68	−1.54189
$848$	−1.46551e68	−0.223195
$849$	1.37934e69	2.04333
$850$	1.06536e68	0.153516
$851$	−1.10575e69	−1.54993
$852$	−7.63826e68	−1.04151
$853$	−3.49668e68	−0.463824	−0.231912	−	0.972737i	$-0.574498\pi$
$853$	−3.49668e68	−0.463824	−0.231912	+	0.972737i	$0.574498\pi$
$854$	−2.46896e68	−0.318606
$855$	−2.77405e68	−0.348266
$856$	−2.72527e68	−0.332871
$857$	5.38103e68	0.639464	0.319732	−	0.947508i	$-0.396407\pi$
$857$	5.38103e68	0.639464	0.319732	+	0.947508i	$0.396407\pi$
$858$	1.09308e69	1.26387
$859$	−8.79126e68	−0.989036	−0.494518	−	0.869167i	$-0.664655\pi$
$859$	−8.79126e68	−0.989036	−0.494518	+	0.869167i	$0.664655\pi$
$860$	4.91752e68	0.538310
$861$	−3.58922e68	−0.382319
$862$	−2.37348e68	−0.246016
$863$	9.57146e68	0.965438	0.482719	−	0.875775i	$-0.339649\pi$
$863$	9.57146e68	0.965438	0.482719	+	0.875775i	$0.339649\pi$
$864$	1.18536e68	0.116353
$865$	−2.61698e68	−0.249989
$866$	−1.27163e69	−1.18220
$867$	9.37600e68	0.848337
$868$	3.98994e68	0.351360
$869$	4.67631e68	0.400810
$870$	1.04106e69	0.868505
$871$	2.33680e68	0.189756
$872$	1.48348e68	0.117258
$873$	−7.48180e68	−0.575667
$874$	1.66161e69	1.24455
$875$	1.05122e69	0.766489
$876$	1.09565e69	0.777720
$877$	−1.79736e69	−1.24207	−0.621033	−	0.783784i	$-0.713287\pi$
$877$	−1.79736e69	−1.24207	−0.621033	+	0.783784i	$0.713287\pi$
$878$	−9.22771e68	−0.620830
$879$	1.45350e69	0.952084
$880$	5.42206e68	0.345797
$881$	−7.63566e67	−0.0474146	−0.0237073	−	0.999719i	$-0.507547\pi$
$881$	−7.63566e67	−0.0474146	−0.0237073	+	0.999719i	$0.507547\pi$
$882$	−2.65889e68	−0.160764
$883$	−1.09005e69	−0.641757	−0.320879	−	0.947120i	$-0.603978\pi$
$883$	−1.09005e69	−0.641757	−0.320879	+	0.947120i	$0.603978\pi$
$884$	3.94626e68	0.226234
$885$	−1.63755e69	−0.914171
$886$	−1.12833e69	−0.613402
$887$	2.23120e69	1.18123	0.590613	−	0.806955i	$-0.298886\pi$
$887$	2.23120e69	1.18123	0.590613	+	0.806955i	$0.298886\pi$
$888$	−7.20087e68	−0.371262
$889$	−1.20741e69	−0.606267
$890$	−1.43517e69	−0.701842
$891$	−4.67351e69	−2.22596
$892$	−1.15307e69	−0.534913
$893$	2.55424e69	1.15412
$894$	−6.24026e66	−0.00274644
$895$	3.18081e69	1.36363
$896$	−1.49579e68	−0.0624642
$897$	−4.38427e69	−1.78351
$898$	−6.64870e68	−0.263477
$899$	3.38323e69	1.30611
$900$	−2.40744e68	−0.0905432
$901$	1.32677e69	0.486143
$902$	−1.58510e69	−0.565851
$903$	3.40194e69	1.18322
$904$	−5.23224e68	−0.177308
$905$	1.29240e69	0.426732
$906$	1.46295e69	0.470672
$907$	3.40839e68	0.106851	0.0534255	−	0.998572i	$-0.482986\pi$
$907$	3.40839e68	0.106851	0.0534255	+	0.998572i	$0.482986\pi$
$908$	4.52060e68	0.138095
$909$	1.47292e69	0.438457
$910$	1.10996e69	0.321984
$911$	−1.74063e69	−0.492068	−0.246034	−	0.969261i	$-0.579127\pi$
$911$	−1.74063e69	−0.492068	−0.246034	+	0.969261i	$0.579127\pi$
$912$	1.08208e69	0.298112
$913$	−3.90808e69	−1.04930
$914$	−2.73997e69	−0.716984
$915$	−2.33767e69	−0.596194
$916$	1.88640e69	0.468910
$917$	−1.83161e69	−0.443764
$918$	−1.07315e69	−0.253429
$919$	5.31109e69	1.22256	0.611279	−	0.791415i	$-0.290655\pi$
$919$	5.31109e69	1.22256	0.611279	+	0.791415i	$0.290655\pi$
$920$	−2.17475e69	−0.487973
$921$	5.73652e69	1.25472
$922$	4.68109e69	0.998091
$923$	−6.90544e69	−1.43533
$924$	3.75098e69	0.760070
$925$	−1.75750e69	−0.347188
$926$	4.83192e69	0.930596
$927$	1.99975e69	0.375493
$928$	−1.26834e69	−0.232197
$929$	2.19849e69	0.392424	0.196212	−	0.980562i	$-0.437136\pi$
$929$	2.19849e69	0.392424	0.196212	+	0.980562i	$0.437136\pi$
$930$	3.77777e69	0.657486
$931$	2.91685e69	0.494991
$932$	−4.89983e69	−0.810787
$933$	−3.86357e69	−0.623406
$934$	−4.11203e69	−0.647001
$935$	−4.90878e69	−0.753184
$936$	−8.91748e68	−0.133432
$937$	−3.73566e69	−0.545113	−0.272557	−	0.962140i	$-0.587869\pi$
$937$	−3.73566e69	−0.545113	−0.272557	+	0.962140i	$0.587869\pi$
$938$	8.01889e68	0.114116
$939$	−1.04228e70	−1.44658
$940$	−3.34305e69	−0.452520
$941$	−3.51161e69	−0.463607	−0.231804	−	0.972763i	$-0.574463\pi$
$941$	−3.51161e69	−0.463607	−0.231804	+	0.972763i	$0.574463\pi$
$942$	−9.10594e69	−1.17254
$943$	6.35771e69	0.798502
$944$	1.99505e69	0.244406
$945$	−3.01843e69	−0.360689
$946$	1.50239e70	1.75122
$947$	−1.80829e69	−0.205610	−0.102805	−	0.994702i	$-0.532782\pi$
$947$	−1.80829e69	−0.205610	−0.102805	+	0.994702i	$0.532782\pi$
$948$	−1.22146e69	−0.135482
$949$	9.90529e69	1.07179
$950$	2.64100e69	0.278781
$951$	−3.37293e69	−0.347348
$952$	1.35419e69	0.136054
$953$	−5.47380e69	−0.536544	−0.268272	−	0.963343i	$-0.586453\pi$
$953$	−5.47380e69	−0.536544	−0.268272	+	0.963343i	$0.586453\pi$
$954$	−2.99815e69	−0.286726
$955$	−2.31490e68	−0.0215999
$956$	−8.00063e67	−0.00728390
$957$	3.18061e70	2.82540
$958$	3.99817e69	0.346555
$959$	5.14419e69	0.435091
$960$	−1.41625e69	−0.116887
$961$	−1.39491e68	−0.0112343
$962$	−6.51002e69	−0.511644
$963$	−5.57538e69	−0.427619
$964$	−7.64171e69	−0.571979
$965$	6.82624e69	0.498643
$966$	−1.50449e70	−1.07258
$967$	2.03692e70	1.41727	0.708633	−	0.705577i	$-0.249312\pi$
$967$	2.03692e70	1.41727	0.708633	+	0.705577i	$0.249312\pi$
$968$	1.13591e70	0.771386
$969$	−9.79643e69	−0.649321
$970$	−1.07424e70	−0.694967
$971$	6.08262e69	0.384095	0.192047	−	0.981386i	$-0.438487\pi$
$971$	6.08262e69	0.384095	0.192047	+	0.981386i	$0.438487\pi$
$972$	6.86800e69	0.423324
$973$	2.81581e69	0.169415
$974$	−7.88604e69	−0.463152
$975$	−6.96845e69	−0.399510
$976$	2.84802e69	0.159394
$977$	−1.09440e70	−0.597935	−0.298968	−	0.954263i	$-0.596642\pi$
$977$	−1.09440e70	−0.597935	−0.298968	+	0.954263i	$0.596642\pi$
$978$	−1.26172e70	−0.672974
$979$	−4.38470e70	−2.28321
$980$	−3.81764e69	−0.194081
$981$	3.03492e69	0.150635
$982$	2.06511e70	1.00075
$983$	2.00353e70	0.947958	0.473979	−	0.880536i	$-0.342817\pi$
$983$	2.00353e70	0.947958	0.473979	+	0.880536i	$0.342817\pi$
$984$	4.14028e69	0.191269
$985$	6.93646e69	0.312886
$986$	1.14827e70	0.505751
$987$	−2.31272e70	−0.994649
$988$	9.78263e69	0.410835
$989$	−6.02597e70	−2.47124
$990$	1.10925e70	0.444225
$991$	−1.91105e70	−0.747379	−0.373690	−	0.927554i	$-0.621908\pi$
$991$	−1.91105e70	−0.747379	−0.373690	+	0.927554i	$0.621908\pi$
$992$	−4.60252e69	−0.175781
$993$	6.05247e70	2.25749
$994$	−2.36965e70	−0.863186
$995$	−9.37427e69	−0.333499
$996$	1.02079e70	0.354685
$997$	1.24124e70	0.421229	0.210614	−	0.977569i	$-0.432454\pi$
$997$	1.24124e70	0.421229	0.210614	+	0.977569i	$0.432454\pi$
$998$	2.63092e70	0.872046
$999$	1.77034e70	0.573149

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.48.a.a.1.1	✓	1
4.3	odd	2		16.48.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.48.a.a.1.1	✓	1	1.1	even	1	trivial
16.48.a.a.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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 48 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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