LMFDB - Embedded newform 10.20.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,20,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, 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("10.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	10.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:	$22.8816696556$
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	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-512.000 q^{2} +38628.0 q^{3} +262144. q^{4} +1.95312e6 q^{5} -1.97775e7 q^{6} -1.44186e8 q^{7} -1.34218e8 q^{8} +3.29861e8 q^{9} +O(q^{10})$

\(q-512.000 q^{2} +38628.0 q^{3} +262144. q^{4} +1.95312e6 q^{5} -1.97775e7 q^{6} -1.44186e8 q^{7} -1.34218e8 q^{8} +3.29861e8 q^{9} -1.00000e9 q^{10} -5.15650e9 q^{11} +1.01261e10 q^{12} +3.43552e9 q^{13} +7.38231e10 q^{14} +7.54453e10 q^{15} +6.87195e10 q^{16} +3.66348e11 q^{17} -1.68889e11 q^{18} -1.60438e12 q^{19} +5.12000e11 q^{20} -5.56961e12 q^{21} +2.64013e12 q^{22} -1.36497e13 q^{23} -5.18456e12 q^{24} +3.81470e12 q^{25} -1.75898e12 q^{26} -3.21540e13 q^{27} -3.77974e13 q^{28} +5.01714e13 q^{29} -3.86280e13 q^{30} -1.35507e14 q^{31} -3.51844e13 q^{32} -1.99185e14 q^{33} -1.87570e14 q^{34} -2.81613e14 q^{35} +8.64711e13 q^{36} +9.12687e13 q^{37} +8.21442e14 q^{38} +1.32707e14 q^{39} -2.62144e14 q^{40} +8.27682e14 q^{41} +2.85164e15 q^{42} -5.87140e15 q^{43} -1.35175e15 q^{44} +6.44260e14 q^{45} +6.98863e15 q^{46} +1.31806e16 q^{47} +2.65450e15 q^{48} +9.39064e15 q^{49} -1.95312e15 q^{50} +1.41513e16 q^{51} +9.00600e14 q^{52} -3.64075e16 q^{53} +1.64628e16 q^{54} -1.00713e16 q^{55} +1.93523e16 q^{56} -6.19740e16 q^{57} -2.56878e16 q^{58} -1.22070e17 q^{59} +1.97775e16 q^{60} -7.11219e16 q^{61} +6.93795e16 q^{62} -4.75613e16 q^{63} +1.80144e16 q^{64} +6.70999e15 q^{65} +1.01983e17 q^{66} +3.16005e17 q^{67} +9.60359e16 q^{68} -5.27260e17 q^{69} +1.44186e17 q^{70} -2.47514e17 q^{71} -4.42732e16 q^{72} +3.70318e17 q^{73} -4.67296e16 q^{74} +1.47354e17 q^{75} -4.20578e17 q^{76} +7.43494e17 q^{77} -6.79460e16 q^{78} +1.68187e18 q^{79} +1.34218e17 q^{80} -1.62543e18 q^{81} -4.23773e17 q^{82} +1.85271e18 q^{83} -1.46004e18 q^{84} +7.15523e17 q^{85} +3.00615e18 q^{86} +1.93802e18 q^{87} +6.92094e17 q^{88} -3.08948e18 q^{89} -3.29861e17 q^{90} -4.95353e17 q^{91} -3.57818e18 q^{92} -5.23436e18 q^{93} -6.74847e18 q^{94} -3.13355e18 q^{95} -1.35910e18 q^{96} +6.98270e18 q^{97} -4.80801e18 q^{98} -1.70093e18 q^{99} +O(q^{100})\)

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
$3$	38628.0	1.13305	0.566527	−	0.824043i	$-0.308287\pi$
$3$	38628.0	1.13305	0.566527	+	0.824043i	$0.308287\pi$
$4$	262144.	0.500000
$5$	1.95312e6	0.447214
$5$	1.95312e6	0.447214
$6$	−1.97775e7	−0.801190
$7$	−1.44186e8	−1.35049	−0.675244	−	0.737594i	$-0.735962\pi$
$7$	−1.44186e8	−1.35049	−0.675244	+	0.737594i	$0.735962\pi$
$8$	−1.34218e8	−0.353553
$9$	3.29861e8	0.283810
$10$	−1.00000e9	−0.316228
$11$	−5.15650e9	−0.659363	−0.329681	−	0.944092i	$-0.606941\pi$
$11$	−5.15650e9	−0.659363	−0.329681	+	0.944092i	$0.606941\pi$
$12$	1.01261e10	0.566527
$13$	3.43552e9	0.0898525	0.0449262	−	0.998990i	$-0.485695\pi$
$13$	3.43552e9	0.0898525	0.0449262	+	0.998990i	$0.485695\pi$
$14$	7.38231e10	0.954940
$15$	7.54453e10	0.506717
$16$	6.87195e10	0.250000
$17$	3.66348e11	0.749254	0.374627	−	0.927176i	$-0.377771\pi$
$17$	3.66348e11	0.749254	0.374627	+	0.927176i	$0.377771\pi$
$18$	−1.68889e11	−0.200684
$19$	−1.60438e12	−1.14064	−0.570319	−	0.821423i	$-0.693180\pi$
$19$	−1.60438e12	−1.14064	−0.570319	+	0.821423i	$0.693180\pi$
$20$	5.12000e11	0.223607
$21$	−5.56961e12	−1.53018
$22$	2.64013e12	0.466240
$23$	−1.36497e13	−1.58018	−0.790092	−	0.612988i	$-0.789968\pi$
$23$	−1.36497e13	−1.58018	−0.790092	+	0.612988i	$0.789968\pi$
$24$	−5.18456e12	−0.400595
$25$	3.81470e12	0.200000
$26$	−1.75898e12	−0.0635353
$27$	−3.21540e13	−0.811482
$28$	−3.77974e13	−0.675244
$29$	5.01714e13	0.642208	0.321104	−	0.947044i	$-0.395946\pi$
$29$	5.01714e13	0.642208	0.321104	+	0.947044i	$0.395946\pi$
$30$	−3.86280e13	−0.358303
$31$	−1.35507e14	−0.920502	−0.460251	−	0.887789i	$-0.652241\pi$
$31$	−1.35507e14	−0.920502	−0.460251	+	0.887789i	$0.652241\pi$
$32$	−3.51844e13	−0.176777
$33$	−1.99185e14	−0.747093
$34$	−1.87570e14	−0.529802
$35$	−2.81613e14	−0.603957
$36$	8.64711e13	0.141905
$37$	9.12687e13	0.115453	0.0577265	−	0.998332i	$-0.481615\pi$
$37$	9.12687e13	0.115453	0.0577265	+	0.998332i	$0.481615\pi$
$38$	8.21442e14	0.806553
$39$	1.32707e14	0.101808
$40$	−2.62144e14	−0.158114
$41$	8.27682e14	0.394836	0.197418	−	0.980319i	$-0.436744\pi$
$41$	8.27682e14	0.394836	0.197418	+	0.980319i	$0.436744\pi$
$42$	2.85164e15	1.08200
$43$	−5.87140e15	−1.78152	−0.890761	−	0.454473i	$-0.849828\pi$
$43$	−5.87140e15	−1.78152	−0.890761	+	0.454473i	$0.849828\pi$
$44$	−1.35175e15	−0.329681
$45$	6.44260e14	0.126923
$46$	6.98863e15	1.11736
$47$	1.31806e16	1.71793	0.858966	−	0.512033i	$-0.171107\pi$
$47$	1.31806e16	1.71793	0.858966	+	0.512033i	$0.171107\pi$
$48$	2.65450e15	0.283263
$49$	9.39064e15	0.823820
$50$	−1.95312e15	−0.141421
$51$	1.41513e16	0.848944
$52$	9.00600e14	0.0449262
$53$	−3.64075e16	−1.51555	−0.757776	−	0.652515i	$-0.773714\pi$
$53$	−3.64075e16	−1.51555	−0.757776	+	0.652515i	$0.773714\pi$
$54$	1.64628e16	0.573804
$55$	−1.00713e16	−0.294876
$56$	1.93523e16	0.477470
$57$	−6.19740e16	−1.29240
$58$	−2.56878e16	−0.454110
$59$	−1.22070e17	−1.83449	−0.917244	−	0.398326i	$-0.869591\pi$
$59$	−1.22070e17	−1.83449	−0.917244	+	0.398326i	$0.869591\pi$
$60$	1.97775e16	0.253358
$61$	−7.11219e16	−0.778699	−0.389350	−	0.921090i	$-0.627300\pi$
$61$	−7.11219e16	−0.778699	−0.389350	+	0.921090i	$0.627300\pi$
$62$	6.93795e16	0.650893
$63$	−4.75613e16	−0.383282
$64$	1.80144e16	0.125000
$65$	6.70999e15	0.0401833
$66$	1.01983e17	0.528275
$67$	3.16005e17	1.41900	0.709502	−	0.704704i	$-0.248920\pi$
$67$	3.16005e17	1.41900	0.709502	+	0.704704i	$0.248920\pi$
$68$	9.60359e16	0.374627
$69$	−5.27260e17	−1.79043
$70$	1.44186e17	0.427062
$71$	−2.47514e17	−0.640686	−0.320343	−	0.947302i	$-0.603798\pi$
$71$	−2.47514e17	−0.640686	−0.320343	+	0.947302i	$0.603798\pi$
$72$	−4.42732e16	−0.100342
$73$	3.70318e17	0.736219	0.368110	−	0.929782i	$-0.380005\pi$
$73$	3.70318e17	0.736219	0.368110	+	0.929782i	$0.380005\pi$
$74$	−4.67296e16	−0.0816376
$75$	1.47354e17	0.226611
$76$	−4.20578e17	−0.570319
$77$	7.43494e17	0.890462
$78$	−6.79460e16	−0.0719889
$79$	1.68187e18	1.57883	0.789416	−	0.613858i	$-0.210383\pi$
$79$	1.68187e18	1.57883	0.789416	+	0.613858i	$0.210383\pi$
$80$	1.34218e17	0.111803
$81$	−1.62543e18	−1.20326
$82$	−4.23773e17	−0.279191
$83$	1.85271e18	1.08784	0.543922	−	0.839136i	$-0.316939\pi$
$83$	1.85271e18	1.08784	0.543922	+	0.839136i	$0.316939\pi$
$84$	−1.46004e18	−0.765088
$85$	7.15523e17	0.335076
$86$	3.00615e18	1.25973
$87$	1.93802e18	0.727656
$88$	6.92094e17	0.233120
$89$	−3.08948e18	−0.934719	−0.467359	−	0.884067i	$-0.654795\pi$
$89$	−3.08948e18	−0.934719	−0.467359	+	0.884067i	$0.654795\pi$
$90$	−3.29861e17	−0.0897485
$91$	−4.95353e17	−0.121345
$92$	−3.57818e18	−0.790092
$93$	−5.23436e18	−1.04298
$94$	−6.74847e18	−1.21476
$95$	−3.13355e18	−0.510109
$96$	−1.35910e18	−0.200297
$97$	6.98270e18	0.932592	0.466296	−	0.884629i	$-0.345588\pi$
$97$	6.98270e18	0.932592	0.466296	+	0.884629i	$0.345588\pi$
$98$	−4.80801e18	−0.582529
$99$	−1.70093e18	−0.187134
$100$	1.00000e18	0.100000
$101$	9.03682e18	0.822172	0.411086	−	0.911597i	$-0.365150\pi$
$101$	9.03682e18	0.822172	0.411086	+	0.911597i	$0.365150\pi$
$102$	−7.24546e18	−0.600294
$103$	5.98000e18	0.451593	0.225797	−	0.974174i	$-0.427502\pi$
$103$	5.98000e18	0.451593	0.225797	+	0.974174i	$0.427502\pi$
$104$	−4.61107e17	−0.0317677
$105$	−1.08781e19	−0.684315
$106$	1.86407e19	1.07166
$107$	−6.01677e18	−0.316386	−0.158193	−	0.987408i	$-0.550567\pi$
$107$	−6.01677e18	−0.316386	−0.158193	+	0.987408i	$0.550567\pi$
$108$	−8.42897e18	−0.405741
$109$	1.93841e19	0.854858	0.427429	−	0.904049i	$-0.359419\pi$
$109$	1.93841e19	0.854858	0.427429	+	0.904049i	$0.359419\pi$
$110$	5.15650e18	0.208509
$111$	3.52553e18	0.130814
$112$	−9.90837e18	−0.337622
$113$	4.32649e19	1.35485	0.677424	−	0.735593i	$-0.263096\pi$
$113$	4.32649e19	1.35485	0.677424	+	0.735593i	$0.263096\pi$
$114$	3.17307e19	0.913867
$115$	−2.66595e19	−0.706680
$116$	1.31521e19	0.321104
$117$	1.13324e18	0.0255010
$118$	6.24998e19	1.29718
$119$	−5.28221e19	−1.01186
$120$	−1.01261e19	−0.179151
$121$	−3.45696e19	−0.565240
$122$	3.64144e19	0.550624
$123$	3.19717e19	0.447370
$124$	−3.55223e19	−0.460251
$125$	7.45058e18	0.0894427
$126$	2.43514e19	0.271021
$127$	−2.21459e19	−0.228643	−0.114321	−	0.993444i	$-0.536469\pi$
$127$	−2.21459e19	−0.228643	−0.114321	+	0.993444i	$0.536469\pi$
$128$	−9.22337e18	−0.0883883
$129$	−2.26800e20	−2.01856
$130$	−3.43552e18	−0.0284139
$131$	−1.11766e20	−0.859475	−0.429737	−	0.902954i	$-0.641394\pi$
$131$	−1.11766e20	−0.859475	−0.429737	+	0.902954i	$0.641394\pi$
$132$	−5.22152e19	−0.373547
$133$	2.31329e20	1.54042
$134$	−1.61795e20	−1.00339
$135$	−6.28007e19	−0.362906
$136$	−4.91704e19	−0.264901
$137$	−2.37729e20	−1.19464	−0.597319	−	0.802004i	$-0.703767\pi$
$137$	−2.37729e20	−1.19464	−0.597319	+	0.802004i	$0.703767\pi$
$138$	2.69957e20	1.26603
$139$	−5.71447e19	−0.250228	−0.125114	−	0.992142i	$-0.539930\pi$
$139$	−5.71447e19	−0.250228	−0.125114	+	0.992142i	$0.539930\pi$
$140$	−7.38231e19	−0.301979
$141$	5.09141e20	1.94651
$142$	1.26727e20	0.453033
$143$	−1.77152e19	−0.0592454
$144$	2.26679e19	0.0709524
$145$	9.79911e19	0.287204
$146$	−1.89603e20	−0.520586
$147$	3.62742e20	0.933432
$148$	2.39255e19	0.0577265
$149$	−5.24530e20	−1.18714	−0.593568	−	0.804784i	$-0.702281\pi$
$149$	−5.24530e20	−1.18714	−0.593568	+	0.804784i	$0.702281\pi$
$150$	−7.54453e19	−0.160238
$151$	3.72810e20	0.743373	0.371687	−	0.928358i	$-0.378780\pi$
$151$	3.72810e20	0.743373	0.371687	+	0.928358i	$0.378780\pi$
$152$	2.15336e20	0.403276
$153$	1.20844e20	0.212645
$154$	−3.80669e20	−0.629652
$155$	−2.64662e20	−0.411661
$156$	3.47884e19	0.0509038
$157$	7.83112e20	1.07839	0.539197	−	0.842180i	$-0.318728\pi$
$157$	7.83112e20	1.07839	0.539197	+	0.842180i	$0.318728\pi$
$158$	−8.61120e20	−1.11640
$159$	−1.40635e21	−1.71720
$160$	−6.87195e19	−0.0790569
$161$	1.96809e21	2.13402
$162$	8.32219e20	0.850835
$163$	1.65420e21	1.59517	0.797583	−	0.603210i	$-0.206112\pi$
$163$	1.65420e21	1.59517	0.797583	+	0.603210i	$0.206112\pi$
$164$	2.16972e20	0.197418
$165$	−3.89034e20	−0.334110
$166$	−9.48590e20	−0.769222
$167$	1.54429e21	1.18283	0.591414	−	0.806368i	$-0.298570\pi$
$167$	1.54429e21	1.18283	0.591414	+	0.806368i	$0.298570\pi$
$168$	7.47540e20	0.540999
$169$	−1.45012e21	−0.991927
$170$	−3.66348e20	−0.236935
$171$	−5.29222e20	−0.323724
$172$	−1.53915e21	−0.890761
$173$	−5.24523e20	−0.287294	−0.143647	−	0.989629i	$-0.545883\pi$
$173$	−5.24523e20	−0.287294	−0.143647	+	0.989629i	$0.545883\pi$
$174$	−9.92267e20	−0.514530
$175$	−5.50025e20	−0.270098
$176$	−3.54352e20	−0.164841
$177$	−4.71532e21	−2.07857
$178$	1.58182e21	0.660946
$179$	−3.84886e20	−0.152485	−0.0762427	−	0.997089i	$-0.524292\pi$
$179$	−3.84886e20	−0.152485	−0.0762427	+	0.997089i	$0.524292\pi$
$180$	1.68889e20	0.0634617
$181$	−1.77525e21	−0.632868	−0.316434	−	0.948615i	$-0.602486\pi$
$181$	−1.77525e21	−0.632868	−0.316434	+	0.948615i	$0.602486\pi$
$182$	2.53620e20	0.0858037
$183$	−2.74730e21	−0.882308
$184$	1.83203e21	0.558680
$185$	1.78259e20	0.0516322
$186$	2.67999e21	0.737497
$187$	−1.88907e21	−0.494030
$188$	3.45522e21	0.858966
$189$	4.63614e21	1.09590
$190$	1.60438e21	0.360701
$191$	−6.03775e21	−1.29139	−0.645696	−	0.763594i	$-0.723433\pi$
$191$	−6.03775e21	−1.29139	−0.645696	+	0.763594i	$0.723433\pi$
$192$	6.95860e20	0.141632
$193$	7.61778e21	1.47582	0.737911	−	0.674898i	$-0.235812\pi$
$193$	7.61778e21	1.47582	0.737911	+	0.674898i	$0.235812\pi$
$194$	−3.57514e21	−0.659442
$195$	2.59194e20	0.0455298
$196$	2.46170e21	0.411910
$197$	5.13589e21	0.818817	0.409408	−	0.912351i	$-0.365735\pi$
$197$	5.13589e21	0.818817	0.409408	+	0.912351i	$0.365735\pi$
$198$	8.70875e20	0.132323
$199$	2.90011e21	0.420059	0.210029	−	0.977695i	$-0.432644\pi$
$199$	2.90011e21	0.420059	0.210029	+	0.977695i	$0.432644\pi$
$200$	−5.12000e20	−0.0707107
$201$	1.22066e22	1.60781
$202$	−4.62685e21	−0.581363
$203$	−7.23401e21	−0.867295
$204$	3.70967e21	0.424472
$205$	1.61657e21	0.176576
$206$	−3.06176e21	−0.319325
$207$	−4.50249e21	−0.448472
$208$	2.36087e20	0.0224631
$209$	8.27298e21	0.752094
$210$	5.56961e21	0.483884
$211$	−1.74216e22	−1.44679	−0.723394	−	0.690435i	$-0.757419\pi$
$211$	−1.74216e22	−1.44679	−0.723394	+	0.690435i	$0.757419\pi$
$212$	−9.54402e21	−0.757776
$213$	−9.56096e21	−0.725931
$214$	3.08059e21	0.223719
$215$	−1.14676e22	−0.796721
$216$	4.31563e21	0.286902
$217$	1.95381e22	1.24313
$218$	−9.92466e21	−0.604476
$219$	1.43046e22	0.834176
$220$	−2.64013e21	−0.147438
$221$	1.25859e21	0.0673223
$222$	−1.80507e21	−0.0924998
$223$	−3.33534e22	−1.63774	−0.818868	−	0.573982i	$-0.805398\pi$
$223$	−3.33534e22	−1.63774	−0.818868	+	0.573982i	$0.805398\pi$
$224$	5.07309e21	0.238735
$225$	1.25832e21	0.0567619
$226$	−2.21516e22	−0.958022
$227$	−1.06658e22	−0.442332	−0.221166	−	0.975236i	$-0.570986\pi$
$227$	−1.06658e22	−0.442332	−0.221166	+	0.975236i	$0.570986\pi$
$228$	−1.62461e22	−0.646202
$229$	1.87612e22	0.715851	0.357925	−	0.933750i	$-0.383484\pi$
$229$	1.87612e22	0.715851	0.357925	+	0.933750i	$0.383484\pi$
$230$	1.36497e22	0.499698
$231$	2.87197e22	1.00894
$232$	−6.73390e21	−0.227055
$233$	−5.36405e22	−1.73625	−0.868124	−	0.496348i	$-0.834674\pi$
$233$	−5.36405e22	−1.73625	−0.868124	+	0.496348i	$0.834674\pi$
$234$	−5.80220e20	−0.0180319
$235$	2.57434e22	0.768283
$236$	−3.19999e22	−0.917244
$237$	6.49674e22	1.78890
$238$	2.70449e22	0.715492
$239$	−6.95763e21	−0.176881	−0.0884405	−	0.996081i	$-0.528188\pi$
$239$	−6.95763e21	−0.176881	−0.0884405	+	0.996081i	$0.528188\pi$
$240$	5.18456e21	0.126679
$241$	1.38664e22	0.325687	0.162844	−	0.986652i	$-0.447933\pi$
$241$	1.38664e22	0.325687	0.162844	+	0.986652i	$0.447933\pi$
$242$	1.76996e22	0.399685
$243$	−2.54157e22	−0.551878
$244$	−1.86442e22	−0.389350
$245$	1.83411e22	0.368424
$246$	−1.63695e22	−0.316339
$247$	−5.51187e21	−0.102489
$248$	1.81874e22	0.325447
$249$	7.15667e22	1.23259
$250$	−3.81470e21	−0.0632456
$251$	−2.14896e22	−0.343026	−0.171513	−	0.985182i	$-0.554866\pi$
$251$	−2.14896e22	−0.343026	−0.171513	+	0.985182i	$0.554866\pi$
$252$	−1.24679e22	−0.191641
$253$	7.03846e22	1.04192
$254$	1.13387e22	0.161675
$255$	2.76392e22	0.379659
$256$	4.72237e21	0.0625000
$257$	−1.28920e23	−1.64420	−0.822099	−	0.569345i	$-0.807197\pi$
$257$	−1.28920e23	−1.64420	−0.822099	+	0.569345i	$0.807197\pi$
$258$	1.16122e23	1.42734
$259$	−1.31596e22	−0.155918
$260$	1.75898e21	0.0200916
$261$	1.65496e22	0.182265
$262$	5.72243e22	0.607741
$263$	−1.58385e23	−1.62231	−0.811155	−	0.584831i	$-0.801161\pi$
$263$	−1.58385e23	−1.62231	−0.811155	+	0.584831i	$0.801161\pi$
$264$	2.67342e22	0.264137
$265$	−7.11085e22	−0.677775
$266$	−1.18440e23	−1.08924
$267$	−1.19341e23	−1.05909
$268$	8.28388e22	0.709502
$269$	−7.85068e22	−0.649024	−0.324512	−	0.945882i	$-0.605200\pi$
$269$	−7.85068e22	−0.649024	−0.324512	+	0.945882i	$0.605200\pi$
$270$	3.21540e22	0.256613
$271$	1.45558e23	1.12157	0.560785	−	0.827961i	$-0.310499\pi$
$271$	1.45558e23	1.12157	0.560785	+	0.827961i	$0.310499\pi$
$272$	2.51752e22	0.187313
$273$	−1.91345e22	−0.137490
$274$	1.21717e23	0.844737
$275$	−1.96705e22	−0.131873
$276$	−1.38218e23	−0.895217
$277$	2.71383e23	1.69834	0.849170	−	0.528120i	$-0.177103\pi$
$277$	2.71383e23	1.69834	0.849170	+	0.528120i	$0.177103\pi$
$278$	2.92581e22	0.176938
$279$	−4.46984e22	−0.261247
$280$	3.77974e22	0.213531
$281$	−4.97575e22	−0.271737	−0.135869	−	0.990727i	$-0.543382\pi$
$281$	−4.97575e22	−0.271737	−0.135869	+	0.990727i	$0.543382\pi$
$282$	−2.60680e23	−1.37639
$283$	−2.62367e23	−1.33949	−0.669743	−	0.742593i	$-0.733596\pi$
$283$	−2.62367e23	−1.33949	−0.669743	+	0.742593i	$0.733596\pi$
$284$	−6.48843e22	−0.320343
$285$	−1.21043e23	−0.577980
$286$	9.07020e21	0.0418928
$287$	−1.19340e23	−0.533222
$288$	−1.16059e22	−0.0501709
$289$	−1.04862e23	−0.438619
$290$	−5.01714e22	−0.203084
$291$	2.69728e23	1.05668
$292$	9.70765e22	0.368110
$293$	2.62435e23	0.963340	0.481670	−	0.876353i	$-0.340030\pi$
$293$	2.62435e23	0.963340	0.481670	+	0.876353i	$0.340030\pi$
$294$	−1.85724e23	−0.660036
$295$	−2.38418e23	−0.820408
$296$	−1.22499e22	−0.0408188
$297$	1.65802e23	0.535061
$298$	2.68559e23	0.839432
$299$	−4.68937e22	−0.141984
$300$	3.86280e22	0.113305
$301$	8.46572e23	2.40592
$302$	−1.90879e23	−0.525644
$303$	3.49074e23	0.931564
$304$	−1.10252e23	−0.285159
$305$	−1.38910e23	−0.348245
$306$	−6.18720e22	−0.150363
$307$	4.42378e23	1.04227	0.521133	−	0.853475i	$-0.325510\pi$
$307$	4.42378e23	1.04227	0.521133	+	0.853475i	$0.325510\pi$
$308$	1.94903e23	0.445231
$309$	2.30995e23	0.511679
$310$	1.35507e23	0.291088
$311$	−2.66011e22	−0.0554212	−0.0277106	−	0.999616i	$-0.508822\pi$
$311$	−2.66011e22	−0.0554212	−0.0277106	+	0.999616i	$0.508822\pi$
$312$	−1.78116e22	−0.0359944
$313$	−8.22865e22	−0.161308	−0.0806542	−	0.996742i	$-0.525701\pi$
$313$	−8.22865e22	−0.161308	−0.0806542	+	0.996742i	$0.525701\pi$
$314$	−4.00953e23	−0.762539
$315$	−9.28931e22	−0.171409
$316$	4.40893e23	0.789416
$317$	3.38377e22	0.0587946	0.0293973	−	0.999568i	$-0.490641\pi$
$317$	3.38377e22	0.0587946	0.0293973	+	0.999568i	$0.490641\pi$
$318$	7.20052e23	1.21424
$319$	−2.58709e23	−0.423448
$320$	3.51844e22	0.0559017
$321$	−2.32416e23	−0.358482
$322$	−1.00766e24	−1.50898
$323$	−5.87761e23	−0.854627
$324$	−4.26096e23	−0.601631
$325$	1.31055e22	0.0179705
$326$	−8.46950e23	−1.12795
$327$	7.48769e23	0.968600
$328$	−1.11090e23	−0.139596
$329$	−1.90046e24	−2.32005
$330$	1.99185e23	0.236252
$331$	−1.15635e24	−1.33267	−0.666334	−	0.745654i	$-0.732137\pi$
$331$	−1.15635e24	−1.33267	−0.666334	+	0.745654i	$0.732137\pi$
$332$	4.85678e23	0.543922
$333$	3.01060e22	0.0327667
$334$	−7.90676e23	−0.836386
$335$	6.17197e23	0.634598
$336$	−3.82741e23	−0.382544
$337$	4.69484e22	0.0456181	0.0228090	−	0.999740i	$-0.492739\pi$
$337$	4.69484e22	0.0456181	0.0228090	+	0.999740i	$0.492739\pi$
$338$	7.42460e23	0.701398
$339$	1.67124e24	1.53512
$340$	1.87570e23	0.167538
$341$	6.98741e23	0.606945
$342$	2.70962e23	0.228907
$343$	2.89561e23	0.237929
$344$	7.88045e23	0.629863
$345$	−1.02980e24	−0.800706
$346$	2.68556e23	0.203148
$347$	8.58393e23	0.631766	0.315883	−	0.948798i	$-0.397699\pi$
$347$	8.58393e23	0.631766	0.315883	+	0.948798i	$0.397699\pi$
$348$	5.08041e23	0.363828
$349$	−2.63396e24	−1.83556	−0.917778	−	0.397093i	$-0.870019\pi$
$349$	−2.63396e24	−1.83556	−0.917778	+	0.397093i	$0.870019\pi$
$350$	2.81613e23	0.190988
$351$	−1.10465e23	−0.0729137
$352$	1.81428e23	0.116560
$353$	−1.08981e24	−0.681539	−0.340770	−	0.940147i	$-0.610688\pi$
$353$	−1.08981e24	−0.681539	−0.340770	+	0.940147i	$0.610688\pi$
$354$	2.41424e24	1.46977
$355$	−4.83425e23	−0.286523
$356$	−8.09890e23	−0.467359
$357$	−2.04041e24	−1.14649
$358$	1.97062e23	0.107823
$359$	2.73245e24	1.45598	0.727988	−	0.685590i	$-0.240456\pi$
$359$	2.73245e24	1.45598	0.727988	+	0.685590i	$0.240456\pi$
$360$	−8.64711e22	−0.0448742
$361$	5.95612e23	0.301055
$362$	9.08928e23	0.447505
$363$	−1.33535e24	−0.640447
$364$	−1.29854e23	−0.0606724
$365$	7.23277e23	0.329247
$366$	1.40662e24	0.623886
$367$	−4.02190e23	−0.173821	−0.0869107	−	0.996216i	$-0.527699\pi$
$367$	−4.02190e23	−0.173821	−0.0869107	+	0.996216i	$0.527699\pi$
$368$	−9.37999e23	−0.395046
$369$	2.73020e23	0.112058
$370$	−9.12687e22	−0.0365095
$371$	5.24945e24	2.04674
$372$	−1.37215e24	−0.521489
$373$	−4.52397e23	−0.167605	−0.0838023	−	0.996482i	$-0.526706\pi$
$373$	−4.52397e23	−0.167605	−0.0838023	+	0.996482i	$0.526706\pi$
$374$	9.67205e23	0.349332
$375$	2.87801e23	0.101343
$376$	−1.76907e24	−0.607381
$377$	1.72365e23	0.0577040
$378$	−2.37371e24	−0.774916
$379$	4.14922e24	1.32097	0.660487	−	0.750837i	$-0.270350\pi$
$379$	4.14922e24	1.32097	0.660487	+	0.750837i	$0.270350\pi$
$380$	−8.21442e23	−0.255054
$381$	−8.55450e23	−0.259064
$382$	3.09133e24	0.913152
$383$	−4.46499e24	−1.28657	−0.643283	−	0.765629i	$-0.722428\pi$
$383$	−4.46499e24	−1.28657	−0.643283	+	0.765629i	$0.722428\pi$
$384$	−3.56280e23	−0.100149
$385$	1.45214e24	0.398227
$386$	−3.90031e24	−1.04356
$387$	−1.93674e24	−0.505613
$388$	1.83047e24	0.466296
$389$	3.12087e24	0.775809	0.387905	−	0.921699i	$-0.373199\pi$
$389$	3.12087e24	0.775809	0.387905	+	0.921699i	$0.373199\pi$
$390$	−1.32707e23	−0.0321944
$391$	−5.00053e24	−1.18396
$392$	−1.26039e24	−0.291265
$393$	−4.31731e24	−0.973831
$394$	−2.62958e24	−0.578991
$395$	3.28491e24	0.706075
$396$	−4.45888e23	−0.0935668
$397$	−4.73788e24	−0.970676	−0.485338	−	0.874327i	$-0.661303\pi$
$397$	−4.73788e24	−0.970676	−0.485338	+	0.874327i	$0.661303\pi$
$398$	−1.48486e24	−0.297027
$399$	8.93576e24	1.74538
$400$	2.62144e23	0.0500000
$401$	2.82785e24	0.526726	0.263363	−	0.964697i	$-0.415168\pi$
$401$	2.82785e24	0.526726	0.263363	+	0.964697i	$0.415168\pi$
$402$	−6.24980e24	−1.13689
$403$	−4.65536e23	−0.0827094
$404$	2.36895e24	0.411086
$405$	−3.17466e24	−0.538115
$406$	3.70381e24	0.613270
$407$	−4.70627e23	−0.0761255
$408$	−1.89935e24	−0.300147
$409$	−4.78789e24	−0.739219	−0.369610	−	0.929187i	$-0.620509\pi$
$409$	−4.78789e24	−0.739219	−0.369610	+	0.929187i	$0.620509\pi$
$410$	−8.27682e23	−0.124858
$411$	−9.18299e24	−1.35359
$412$	1.56762e24	0.225797
$413$	1.76008e25	2.47745
$414$	2.30528e24	0.317117
$415$	3.61858e24	0.486499
$416$	−1.20876e23	−0.0158838
$417$	−2.20739e24	−0.283521
$418$	−4.23577e24	−0.531811
$419$	−3.43496e24	−0.421588	−0.210794	−	0.977530i	$-0.567605\pi$
$419$	−3.43496e24	−0.421588	−0.210794	+	0.977530i	$0.567605\pi$
$420$	−2.85164e24	−0.342158
$421$	−1.05815e25	−1.24128	−0.620639	−	0.784096i	$-0.713127\pi$
$421$	−1.05815e25	−1.24128	−0.620639	+	0.784096i	$0.713127\pi$
$422$	8.91987e24	1.02303
$423$	4.34777e24	0.487566
$424$	4.88654e24	0.535828
$425$	1.39751e24	0.149851
$426$	4.89521e24	0.513311
$427$	1.02548e25	1.05162
$428$	−1.57726e24	−0.158193
$429$	−6.84304e23	−0.0671282
$430$	5.87140e24	0.563367
$431$	3.94872e23	0.0370614	0.0185307	−	0.999828i	$-0.494101\pi$
$431$	3.94872e23	0.0370614	0.0185307	+	0.999828i	$0.494101\pi$
$432$	−2.20960e24	−0.202870
$433$	2.87274e24	0.258024	0.129012	−	0.991643i	$-0.458819\pi$
$433$	2.87274e24	0.258024	0.129012	+	0.991643i	$0.458819\pi$
$434$	−1.00035e25	−0.879024
$435$	3.78520e24	0.325417
$436$	5.08143e24	0.427429
$437$	2.18993e25	1.80242
$438$	−7.32397e24	−0.589851
$439$	−5.64514e24	−0.444900	−0.222450	−	0.974944i	$-0.571405\pi$
$439$	−5.64514e24	−0.444900	−0.222450	+	0.974944i	$0.571405\pi$
$440$	1.35175e24	0.104254
$441$	3.09761e24	0.233808
$442$	−6.44400e23	−0.0476041
$443$	−6.27178e24	−0.453477	−0.226739	−	0.973956i	$-0.572806\pi$
$443$	−6.27178e24	−0.453477	−0.226739	+	0.973956i	$0.572806\pi$
$444$	9.24195e23	0.0654072
$445$	−6.03415e24	−0.418019
$446$	1.70769e25	1.15805
$447$	−2.02615e25	−1.34509
$448$	−2.59742e24	−0.168811
$449$	−1.16630e25	−0.742116	−0.371058	−	0.928610i	$-0.621005\pi$
$449$	−1.16630e25	−0.742116	−0.371058	+	0.928610i	$0.621005\pi$
$450$	−6.44260e23	−0.0401367
$451$	−4.26794e24	−0.260340
$452$	1.13416e25	0.677424
$453$	1.44009e25	0.842281
$454$	5.46090e24	0.312776
$455$	−9.67485e23	−0.0542670
$456$	8.31800e24	0.456934
$457$	7.08522e24	0.381197	0.190599	−	0.981668i	$-0.438957\pi$
$457$	7.08522e24	0.381197	0.190599	+	0.981668i	$0.438957\pi$
$458$	−9.60571e24	−0.506183
$459$	−1.17795e25	−0.608006
$460$	−6.98863e24	−0.353340
$461$	−2.36610e25	−1.17185	−0.585927	−	0.810364i	$-0.699269\pi$
$461$	−2.36610e25	−1.17185	−0.585927	+	0.810364i	$0.699269\pi$
$462$	−1.47045e25	−0.713429
$463$	−2.89073e25	−1.37400	−0.687002	−	0.726655i	$-0.741074\pi$
$463$	−2.89073e25	−1.37400	−0.687002	+	0.726655i	$0.741074\pi$
$464$	3.44776e24	0.160552
$465$	−1.02234e25	−0.466434
$466$	2.74639e25	1.22771
$467$	−2.31100e25	−1.01225	−0.506127	−	0.862459i	$-0.668923\pi$
$467$	−2.31100e25	−1.01225	−0.506127	+	0.862459i	$0.668923\pi$
$468$	2.97073e23	0.0127505
$469$	−4.55634e25	−1.91635
$470$	−1.31806e25	−0.543258
$471$	3.02500e25	1.22188
$472$	1.63840e25	0.648589
$473$	3.02759e25	1.17467
$474$	−3.32633e25	−1.26494
$475$	−6.12022e24	−0.228128
$476$	−1.38470e25	−0.505929
$477$	−1.20094e25	−0.430128
$478$	3.56231e24	0.125074
$479$	1.35926e25	0.467858	0.233929	−	0.972254i	$-0.424842\pi$
$479$	1.35926e25	0.467858	0.233929	+	0.972254i	$0.424842\pi$
$480$	−2.65450e24	−0.0895757
$481$	3.13555e23	0.0103737
$482$	−7.09958e24	−0.230296
$483$	7.60233e25	2.41796
$484$	−9.06221e24	−0.282620
$485$	1.36381e25	0.417068
$486$	1.30128e25	0.390236
$487$	1.94699e25	0.572582	0.286291	−	0.958143i	$-0.407578\pi$
$487$	1.94699e25	0.572582	0.286291	+	0.958143i	$0.407578\pi$
$488$	9.54582e24	0.275312
$489$	6.38984e25	1.80741
$490$	−9.39064e24	−0.260515
$491$	−3.22833e25	−0.878423	−0.439212	−	0.898384i	$-0.644742\pi$
$491$	−3.22833e25	−0.878423	−0.439212	+	0.898384i	$0.644742\pi$
$492$	8.38119e24	0.223685
$493$	1.83802e25	0.481177
$494$	2.82208e24	0.0724708
$495$	−3.32213e24	−0.0836887
$496$	−9.31195e24	−0.230126
$497$	3.56880e25	0.865239
$498$	−3.66421e25	−0.871569
$499$	−2.02682e25	−0.473000	−0.236500	−	0.971632i	$-0.576000\pi$
$499$	−2.02682e25	−0.473000	−0.236500	+	0.971632i	$0.576000\pi$
$500$	1.95313e24	0.0447214
$501$	5.96528e25	1.34021
$502$	1.10027e25	0.242556
$503$	6.40462e25	1.38547	0.692735	−	0.721192i	$-0.256405\pi$
$503$	6.40462e25	1.38547	0.692735	+	0.721192i	$0.256405\pi$
$504$	6.38356e24	0.135511
$505$	1.76500e25	0.367686
$506$	−3.60369e25	−0.736745
$507$	−5.60151e25	−1.12391
$508$	−5.80540e24	−0.114321
$509$	−7.11151e25	−1.37449	−0.687247	−	0.726424i	$-0.741181\pi$
$509$	−7.11151e25	−1.37449	−0.687247	+	0.726424i	$0.741181\pi$
$510$	−1.41513e25	−0.268460
$511$	−5.33945e25	−0.994256
$512$	−2.41785e24	−0.0441942
$513$	5.15872e25	0.925607
$514$	6.60068e25	1.16262
$515$	1.16797e25	0.201959
$516$	−5.94543e25	−1.00928
$517$	−6.79658e25	−1.13274
$518$	6.73774e24	0.110251
$519$	−2.02613e25	−0.325520
$520$	−9.00600e23	−0.0142069
$521$	5.41363e25	0.838552	0.419276	−	0.907859i	$-0.362284\pi$
$521$	5.41363e25	0.838552	0.419276	+	0.907859i	$0.362284\pi$
$522$	−8.47339e24	−0.128881
$523$	−1.17133e26	−1.74950	−0.874750	−	0.484574i	$-0.838975\pi$
$523$	−1.17133e26	−1.74950	−0.874750	+	0.484574i	$0.838975\pi$
$524$	−2.92988e25	−0.429737
$525$	−2.12464e25	−0.306035
$526$	8.10930e25	1.14715
$527$	−4.96426e25	−0.689690
$528$	−1.36879e25	−0.186773
$529$	1.11698e26	1.49698
$530$	3.64075e25	0.479259
$531$	−4.02661e25	−0.520645
$532$	6.06414e25	0.770209
$533$	2.84351e24	0.0354770
$534$	6.11024e25	0.748887
$535$	−1.17515e25	−0.141492
$536$	−4.24135e25	−0.501693
$537$	−1.48674e25	−0.172774
$538$	4.01955e25	0.458929
$539$	−4.84229e25	−0.543197
$540$	−1.64628e25	−0.181453
$541$	6.75042e25	0.731066	0.365533	−	0.930798i	$-0.380887\pi$
$541$	6.75042e25	0.731066	0.365533	+	0.930798i	$0.380887\pi$
$542$	−7.45255e25	−0.793070
$543$	−6.85743e25	−0.717073
$544$	−1.28897e25	−0.132451
$545$	3.78596e25	0.382304
$546$	9.79685e24	0.0972202
$547$	1.20857e26	1.17867	0.589337	−	0.807887i	$-0.299389\pi$
$547$	1.20857e26	1.17867	0.589337	+	0.807887i	$0.299389\pi$
$548$	−6.23192e25	−0.597319
$549$	−2.34603e25	−0.221002
$550$	1.00713e25	0.0932480
$551$	−8.04940e25	−0.732527
$552$	7.07676e25	0.633014
$553$	−2.42502e26	−2.13220
$554$	−1.38948e26	−1.20091
$555$	6.88579e24	0.0585020
$556$	−1.49801e25	−0.125114
$557$	4.67858e25	0.384140	0.192070	−	0.981381i	$-0.438480\pi$
$557$	4.67858e25	0.384140	0.192070	+	0.981381i	$0.438480\pi$
$558$	2.28856e25	0.184730
$559$	−2.01713e25	−0.160074
$560$	−1.93523e25	−0.150989
$561$	−7.29711e25	−0.559762
$562$	2.54759e25	0.192147
$563$	−1.02745e26	−0.761957	−0.380979	−	0.924584i	$-0.624413\pi$
$563$	−1.02745e26	−0.761957	−0.380979	+	0.924584i	$0.624413\pi$
$564$	1.33468e26	0.973254
$565$	8.45018e25	0.605907
$566$	1.34332e26	0.947160
$567$	2.34364e26	1.62499
$568$	3.32207e25	0.226517
$569$	1.79422e26	1.20312	0.601560	−	0.798827i	$-0.294546\pi$
$569$	1.79422e26	1.20312	0.601560	+	0.798827i	$0.294546\pi$
$570$	6.19740e25	0.408694
$571$	1.55654e26	1.00953	0.504763	−	0.863258i	$-0.331580\pi$
$571$	1.55654e26	1.00953	0.504763	+	0.863258i	$0.331580\pi$
$572$	−4.64394e24	−0.0296227
$573$	−2.33226e26	−1.46322
$574$	6.11021e25	0.377045
$575$	−5.20694e25	−0.316037
$576$	5.94225e24	0.0354762
$577$	−7.74779e25	−0.454996	−0.227498	−	0.973779i	$-0.573055\pi$
$577$	−7.74779e25	−0.454996	−0.227498	+	0.973779i	$0.573055\pi$
$578$	5.36892e25	0.310150
$579$	2.94260e26	1.67219
$580$	2.56878e25	0.143602
$581$	−2.67135e26	−1.46912
$582$	−1.38101e26	−0.747183
$583$	1.87736e26	0.999299
$584$	−4.97032e25	−0.260293
$585$	2.21336e24	0.0114044
$586$	−1.34367e26	−0.681185
$587$	2.63212e25	0.131294	0.0656468	−	0.997843i	$-0.479089\pi$
$587$	2.63212e25	0.131294	0.0656468	+	0.997843i	$0.479089\pi$
$588$	9.50906e25	0.466716
$589$	2.17404e26	1.04996
$590$	1.22070e26	0.580116
$591$	1.98389e26	0.927763
$592$	6.27193e24	0.0288633
$593$	−1.91142e26	−0.865639	−0.432820	−	0.901480i	$-0.642481\pi$
$593$	−1.91142e26	−0.865639	−0.432820	+	0.901480i	$0.642481\pi$
$594$	−8.48906e25	−0.378345
$595$	−1.03168e26	−0.452517
$596$	−1.37502e26	−0.593568
$597$	1.12025e26	0.475949
$598$	2.40096e25	0.100398
$599$	1.31313e26	0.540445	0.270223	−	0.962798i	$-0.412903\pi$
$599$	1.31313e26	0.540445	0.270223	+	0.962798i	$0.412903\pi$
$600$	−1.97775e25	−0.0801190
$601$	−2.78498e26	−1.11049	−0.555246	−	0.831686i	$-0.687376\pi$
$601$	−2.78498e26	−1.11049	−0.555246	+	0.831686i	$0.687376\pi$
$602$	−4.33445e26	−1.70125
$603$	1.04238e26	0.402727
$604$	9.77300e25	0.371687
$605$	−6.75187e25	−0.252783
$606$	−1.78726e26	−0.658715
$607$	−3.00611e26	−1.09072	−0.545358	−	0.838203i	$-0.683606\pi$
$607$	−3.00611e26	−1.09072	−0.545358	+	0.838203i	$0.683606\pi$
$608$	5.64491e25	0.201638
$609$	−2.79435e26	−0.982691
$610$	7.11219e25	0.246246
$611$	4.52822e25	0.154360
$612$	3.16785e25	0.106323
$613$	2.74671e26	0.907690	0.453845	−	0.891081i	$-0.350052\pi$
$613$	2.74671e26	0.907690	0.453845	+	0.891081i	$0.350052\pi$
$614$	−2.26497e26	−0.736993
$615$	6.24447e25	0.200070
$616$	−9.97901e25	−0.314826
$617$	−1.81117e26	−0.562666	−0.281333	−	0.959610i	$-0.590776\pi$
$617$	−1.81117e26	−0.562666	−0.281333	+	0.959610i	$0.590776\pi$
$618$	−1.18270e26	−0.361812
$619$	−5.54073e26	−1.66919	−0.834595	−	0.550864i	$-0.814298\pi$
$619$	−5.54073e26	−1.66919	−0.834595	+	0.550864i	$0.814298\pi$
$620$	−6.93795e25	−0.205831
$621$	4.38891e26	1.28229
$622$	1.36198e25	0.0391887
$623$	4.45460e26	1.26233
$624$	9.11956e24	0.0254519
$625$	1.45519e25	0.0400000
$626$	4.21307e25	0.114062
$627$	3.19569e26	0.852163
$628$	2.05288e26	0.539197
$629$	3.34361e25	0.0865036
$630$	4.75613e25	0.121204
$631$	4.62565e26	1.16116	0.580582	−	0.814202i	$-0.302825\pi$
$631$	4.62565e26	1.16116	0.580582	+	0.814202i	$0.302825\pi$
$632$	−2.25737e26	−0.558202
$633$	−6.72962e26	−1.63929
$634$	−1.73249e25	−0.0415741
$635$	−4.32536e25	−0.102252
$636$	−3.68666e26	−0.858600
$637$	3.22617e25	0.0740223
$638$	1.32459e26	0.299423
$639$	−8.16451e25	−0.181833
$640$	−1.80144e25	−0.0395285
$641$	−2.67276e26	−0.577841	−0.288921	−	0.957353i	$-0.593296\pi$
$641$	−2.67276e26	−0.577841	−0.288921	+	0.957353i	$0.593296\pi$
$642$	1.18997e26	0.253485
$643$	−3.55315e26	−0.745778	−0.372889	−	0.927876i	$-0.621633\pi$
$643$	−3.55315e26	−0.745778	−0.372889	+	0.927876i	$0.621633\pi$
$644$	5.15923e26	1.06701
$645$	−4.42969e26	−0.902727
$646$	3.00934e26	0.604313
$647$	−1.19511e26	−0.236492	−0.118246	−	0.992984i	$-0.537727\pi$
$647$	−1.19511e26	−0.236492	−0.118246	+	0.992984i	$0.537727\pi$
$648$	2.18161e26	0.425417
$649$	6.29454e26	1.20959
$650$	−6.70999e24	−0.0127071
$651$	7.54720e26	1.40853
$652$	4.33638e26	0.797583
$653$	2.70579e26	0.490478	0.245239	−	0.969463i	$-0.421134\pi$
$653$	2.70579e26	0.490478	0.245239	+	0.969463i	$0.421134\pi$
$654$	−3.83370e26	−0.684904
$655$	−2.18293e26	−0.384369
$656$	5.68779e25	0.0987090
$657$	1.22153e26	0.208946
$658$	9.73034e26	1.64052
$659$	8.98491e25	0.149315	0.0746573	−	0.997209i	$-0.476214\pi$
$659$	8.98491e25	0.149315	0.0746573	+	0.997209i	$0.476214\pi$
$660$	−1.01983e26	−0.167055
$661$	5.20525e26	0.840481	0.420240	−	0.907413i	$-0.361946\pi$
$661$	5.20525e26	0.840481	0.420240	+	0.907413i	$0.361946\pi$
$662$	5.92049e26	0.942338
$663$	4.86170e25	0.0762798
$664$	−2.48667e26	−0.384611
$665$	4.51814e26	0.688896
$666$	−1.54143e25	−0.0231695
$667$	−6.84824e26	−1.01481
$668$	4.04826e26	0.591414
$669$	−1.28837e27	−1.85564
$670$	−3.16005e26	−0.448728
$671$	3.66740e26	0.513446
$672$	1.95963e26	0.270499
$673$	−1.06152e27	−1.44472	−0.722361	−	0.691516i	$-0.756943\pi$
$673$	−1.06152e27	−1.44472	−0.722361	+	0.691516i	$0.756943\pi$
$674$	−2.40376e25	−0.0322569
$675$	−1.22658e26	−0.162296
$676$	−3.80140e26	−0.495963
$677$	8.28733e26	1.06616	0.533080	−	0.846065i	$-0.321035\pi$
$677$	8.28733e26	1.06616	0.533080	+	0.846065i	$0.321035\pi$
$678$	−8.55673e26	−1.08549
$679$	−1.00681e27	−1.25946
$680$	−9.60359e25	−0.118467
$681$	−4.11999e26	−0.501186
$682$	−3.57755e26	−0.429175
$683$	1.03335e27	1.22251	0.611253	−	0.791435i	$-0.290666\pi$
$683$	1.03335e27	1.22251	0.611253	+	0.791435i	$0.290666\pi$
$684$	−1.38732e26	−0.161862
$685$	−4.64314e26	−0.534258
$686$	−1.48255e26	−0.168241
$687$	7.24706e26	0.811097
$688$	−4.03479e26	−0.445380
$689$	−1.25079e26	−0.136176
$690$	5.27260e26	0.566185
$691$	−7.59795e26	−0.804739	−0.402369	−	0.915477i	$-0.631813\pi$
$691$	−7.59795e26	−0.804739	−0.402369	+	0.915477i	$0.631813\pi$
$692$	−1.37501e26	−0.143647
$693$	2.45250e26	0.252722
$694$	−4.39497e26	−0.446726
$695$	−1.11611e26	−0.111905
$696$	−2.60117e26	−0.257265
$697$	3.03219e26	0.295832
$698$	1.34859e27	1.29793
$699$	−2.07203e27	−1.96726
$700$	−1.44186e26	−0.135049
$701$	1.31938e26	0.121912	0.0609561	−	0.998140i	$-0.480585\pi$
$701$	1.31938e26	0.121912	0.0609561	+	0.998140i	$0.480585\pi$
$702$	5.65583e25	0.0515577
$703$	−1.46430e26	−0.131690
$704$	−9.28913e25	−0.0824204
$705$	9.94416e26	0.870505
$706$	5.57982e26	0.481921
$707$	−1.30298e27	−1.11033
$708$	−1.23609e27	−1.03929
$709$	−4.33944e25	−0.0359993	−0.0179997	−	0.999838i	$-0.505730\pi$
$709$	−4.33944e25	−0.0359993	−0.0179997	+	0.999838i	$0.505730\pi$
$710$	2.47514e26	0.202603
$711$	5.54785e26	0.448088
$712$	4.14664e26	0.330473
$713$	1.84962e27	1.45456
$714$	1.04469e27	0.810691
$715$	−3.46001e25	−0.0264954
$716$	−1.00896e26	−0.0762427
$717$	−2.68759e26	−0.200416
$718$	−1.39901e27	−1.02953
$719$	2.15268e27	1.56334	0.781672	−	0.623690i	$-0.214367\pi$
$719$	2.15268e27	1.56334	0.781672	+	0.623690i	$0.214367\pi$
$720$	4.42732e25	0.0317309
$721$	−8.62231e26	−0.609872
$722$	−3.04954e26	−0.212878
$723$	5.35630e26	0.369021
$724$	−4.65371e26	−0.316434
$725$	1.91389e26	0.128442
$726$	6.83701e26	0.452865
$727$	1.13933e27	0.744855	0.372427	−	0.928061i	$-0.378526\pi$
$727$	1.13933e27	0.744855	0.372427	+	0.928061i	$0.378526\pi$
$728$	6.64851e25	0.0429019
$729$	9.07414e26	0.577955
$730$	−3.70318e26	−0.232813
$731$	−2.15097e27	−1.33481
$732$	−7.20187e26	−0.441154
$733$	1.40325e27	0.848491	0.424246	−	0.905547i	$-0.360539\pi$
$733$	1.40325e27	0.848491	0.424246	+	0.905547i	$0.360539\pi$
$734$	2.05921e26	0.122910
$735$	7.08480e26	0.417444
$736$	4.80255e26	0.279340
$737$	−1.62948e27	−0.935638
$738$	−1.39786e26	−0.0792371
$739$	2.87318e27	1.60783	0.803916	−	0.594743i	$-0.202746\pi$
$739$	2.87318e27	1.60783	0.803916	+	0.594743i	$0.202746\pi$
$740$	4.67296e25	0.0258161
$741$	−2.12912e26	−0.116126
$742$	−2.68772e27	−1.44726
$743$	−7.07202e26	−0.375967	−0.187984	−	0.982172i	$-0.560195\pi$
$743$	−7.07202e26	−0.375967	−0.187984	+	0.982172i	$0.560195\pi$
$744$	7.02543e26	0.368748
$745$	−1.02447e27	−0.530903
$746$	2.31627e26	0.118514
$747$	6.11138e26	0.308741
$748$	−4.95209e26	−0.247015
$749$	8.67533e26	0.427276
$750$	−1.47354e26	−0.0716606
$751$	−6.60347e26	−0.317097	−0.158549	−	0.987351i	$-0.550681\pi$
$751$	−6.60347e26	−0.317097	−0.158549	+	0.987351i	$0.550681\pi$
$752$	9.05765e26	0.429483
$753$	−8.30099e26	−0.388667
$754$	−8.82508e25	−0.0408029
$755$	7.28145e26	0.332447
$756$	1.21534e27	0.547949
$757$	1.83362e27	0.816391	0.408195	−	0.912895i	$-0.366158\pi$
$757$	1.83362e27	0.816391	0.408195	+	0.912895i	$0.366158\pi$
$758$	−2.12440e27	−0.934070
$759$	2.71881e27	1.18055
$760$	4.20578e26	0.180351
$761$	2.15732e27	0.913607	0.456803	−	0.889568i	$-0.348994\pi$
$761$	2.15732e27	0.913607	0.456803	+	0.889568i	$0.348994\pi$
$762$	4.37991e26	0.183186
$763$	−2.79491e27	−1.15448
$764$	−1.58276e27	−0.645696
$765$	2.36023e26	0.0950979
$766$	2.28607e27	0.909739
$767$	−4.19373e26	−0.164833
$768$	1.82416e26	0.0708158
$769$	2.32459e27	0.891346	0.445673	−	0.895196i	$-0.352964\pi$
$769$	2.32459e27	0.891346	0.445673	+	0.895196i	$0.352964\pi$
$770$	−7.43494e26	−0.281589
$771$	−4.97990e27	−1.86296
$772$	1.99696e27	0.737911
$773$	−9.93299e26	−0.362556	−0.181278	−	0.983432i	$-0.558023\pi$
$773$	−9.93299e26	−0.362556	−0.181278	+	0.983432i	$0.558023\pi$
$774$	9.91613e26	0.357522
$775$	−5.16917e26	−0.184100
$776$	−9.37202e26	−0.329721
$777$	−5.08331e26	−0.176663
$778$	−1.59789e27	−0.548580
$779$	−1.32792e27	−0.450365
$780$	6.79460e25	0.0227649
$781$	1.27630e27	0.422444
$782$	2.56027e27	0.837186
$783$	−1.61321e27	−0.521140
$784$	6.45320e26	0.205955
$785$	1.52952e27	0.482272
$786$	2.21046e27	0.688602
$787$	−5.19069e27	−1.59759	−0.798795	−	0.601603i	$-0.794529\pi$
$787$	−5.19069e27	−1.59759	−0.798795	+	0.601603i	$0.794529\pi$
$788$	1.34634e27	0.409408
$789$	−6.11809e27	−1.83816
$790$	−1.68187e27	−0.499271
$791$	−6.23819e27	−1.82971
$792$	2.28295e26	0.0661617
$793$	−2.44340e26	−0.0699681
$794$	2.42579e27	0.686372
$795$	−2.74678e27	−0.767955
$796$	7.60246e26	0.210029
$797$	−3.60791e27	−0.984920	−0.492460	−	0.870335i	$-0.663902\pi$
$797$	−3.60791e27	−0.984920	−0.492460	+	0.870335i	$0.663902\pi$
$798$	−4.57511e27	−1.23417
$799$	4.82869e27	1.28717
$800$	−1.34218e26	−0.0353553
$801$	−1.01910e27	−0.265282
$802$	−1.44786e27	−0.372452
$803$	−1.90954e27	−0.485436
$804$	3.19990e27	0.803903
$805$	3.84392e27	0.954364
$806$	2.38354e26	0.0584844
$807$	−3.03256e27	−0.735379
$808$	−1.21290e27	−0.290682
$809$	2.01292e27	0.476777	0.238388	−	0.971170i	$-0.423381\pi$
$809$	2.01292e27	0.476777	0.238388	+	0.971170i	$0.423381\pi$
$810$	1.62543e27	0.380505
$811$	2.48444e27	0.574818	0.287409	−	0.957808i	$-0.407206\pi$
$811$	2.48444e27	0.574818	0.287409	+	0.957808i	$0.407206\pi$
$812$	−1.89635e27	−0.433647
$813$	5.62260e27	1.27080
$814$	2.40961e26	0.0538288
$815$	3.23086e27	0.713379
$816$	9.72469e26	0.212236
$817$	9.41994e27	2.03207
$818$	2.45140e27	0.522707
$819$	−1.63397e26	−0.0344388
$820$	4.23773e26	0.0882880
$821$	1.35921e27	0.279916	0.139958	−	0.990157i	$-0.455303\pi$
$821$	1.35921e27	0.279916	0.139958	+	0.990157i	$0.455303\pi$
$822$	4.70169e27	0.957132
$823$	7.84246e27	1.57817	0.789085	−	0.614283i	$-0.210555\pi$
$823$	7.84246e27	1.57817	0.789085	+	0.614283i	$0.210555\pi$
$824$	−8.02622e26	−0.159662
$825$	−7.59832e26	−0.149419
$826$	−9.01159e27	−1.75183
$827$	−4.10888e27	−0.789625	−0.394813	−	0.918762i	$-0.629190\pi$
$827$	−4.10888e27	−0.789625	−0.394813	+	0.918762i	$0.629190\pi$
$828$	−1.18030e27	−0.224236
$829$	−7.04484e27	−1.32313	−0.661566	−	0.749887i	$-0.730108\pi$
$829$	−7.04484e27	−1.32313	−0.661566	+	0.749887i	$0.730108\pi$
$830$	−1.85271e27	−0.344007
$831$	1.04830e28	1.92431
$832$	6.18888e25	0.0112316
$833$	3.44024e27	0.617251
$834$	1.13018e27	0.200480
$835$	3.01619e27	0.528977
$836$	2.16871e27	0.376047
$837$	4.35708e27	0.746971
$838$	1.75870e27	0.298108
$839$	−6.12481e27	−1.02649	−0.513245	−	0.858242i	$-0.671557\pi$
$839$	−6.12481e27	−1.02649	−0.513245	+	0.858242i	$0.671557\pi$
$840$	1.46004e27	0.241942
$841$	−3.58609e27	−0.587569
$842$	5.41775e27	0.877716
$843$	−1.92203e27	−0.307893
$844$	−4.56697e27	−0.723394
$845$	−2.83226e27	−0.443603
$846$	−2.22606e27	−0.344761
$847$	4.98444e27	0.763351
$848$	−2.50191e27	−0.378888
$849$	−1.01347e28	−1.51771
$850$	−7.15523e26	−0.105960
$851$	−1.24579e27	−0.182437
$852$	−2.50635e27	−0.362966
$853$	6.50654e27	0.931824	0.465912	−	0.884831i	$-0.345726\pi$
$853$	6.50654e27	0.931824	0.465912	+	0.884831i	$0.345726\pi$
$854$	−5.25044e27	−0.743611
$855$	−1.03364e27	−0.144774
$856$	8.07557e26	0.111859
$857$	−3.05270e26	−0.0418183	−0.0209092	−	0.999781i	$-0.506656\pi$
$857$	−3.05270e26	−0.0418183	−0.0209092	+	0.999781i	$0.506656\pi$
$858$	3.50364e26	0.0474668
$859$	7.64949e27	1.02494	0.512469	−	0.858706i	$-0.328731\pi$
$859$	7.64949e27	1.02494	0.512469	+	0.858706i	$0.328731\pi$
$860$	−3.00615e27	−0.398360
$861$	−4.60986e27	−0.604169
$862$	−2.02174e26	−0.0262064
$863$	−1.58074e27	−0.202656	−0.101328	−	0.994853i	$-0.532309\pi$
$863$	−1.58074e27	−0.202656	−0.101328	+	0.994853i	$0.532309\pi$
$864$	1.13132e27	0.143451
$865$	−1.02446e27	−0.128482
$866$	−1.47084e27	−0.182451
$867$	−4.05060e27	−0.496979
$868$	5.12181e27	0.621564
$869$	−8.67258e27	−1.04102
$870$	−1.93802e27	−0.230105
$871$	1.08564e27	0.127501
$872$	−2.60169e27	−0.302238
$873$	2.30332e27	0.264679
$874$	−1.12124e28	−1.27450
$875$	−1.07427e27	−0.120791
$876$	3.74987e27	0.417088
$877$	1.83506e26	0.0201908	0.0100954	−	0.999949i	$-0.496786\pi$
$877$	1.83506e26	0.0201908	0.0100954	+	0.999949i	$0.496786\pi$
$878$	2.89031e27	0.314592
$879$	1.01373e28	1.09152
$880$	−6.92094e26	−0.0737190
$881$	8.90803e27	0.938665	0.469332	−	0.883022i	$-0.344495\pi$
$881$	8.90803e27	0.938665	0.469332	+	0.883022i	$0.344495\pi$
$882$	−1.58597e27	−0.165327
$883$	−8.37742e27	−0.863940	−0.431970	−	0.901888i	$-0.642181\pi$
$883$	−8.37742e27	−0.863940	−0.431970	+	0.901888i	$0.642181\pi$
$884$	3.29933e26	0.0336612
$885$	−9.20961e27	−0.929566
$886$	3.21115e27	0.320657
$887$	−3.59767e27	−0.355424	−0.177712	−	0.984083i	$-0.556870\pi$
$887$	−3.59767e27	−0.355424	−0.177712	+	0.984083i	$0.556870\pi$
$888$	−4.73188e26	−0.0462499
$889$	3.19312e27	0.308779
$890$	3.08948e27	0.295584
$891$	8.38152e27	0.793386
$892$	−8.74339e27	−0.818868
$893$	−2.11467e28	−1.95954
$894$	1.03739e28	0.951121
$895$	−7.51730e26	−0.0681935
$896$	1.32988e27	0.119367
$897$	−1.81141e27	−0.160875
$898$	5.97148e27	0.524755
$899$	−6.79857e27	−0.591154
$900$	3.29861e26	0.0283810
$901$	−1.33378e28	−1.13553
$902$	2.18519e27	0.184088
$903$	3.27014e28	2.72604
$904$	−5.80692e27	−0.479011
$905$	−3.46728e27	−0.283027
$906$	−7.37327e27	−0.595583
$907$	5.20747e27	0.416253	0.208127	−	0.978102i	$-0.433263\pi$
$907$	5.20747e27	0.416253	0.208127	+	0.978102i	$0.433263\pi$
$908$	−2.79598e27	−0.221166
$909$	2.98089e27	0.233340
$910$	4.95353e26	0.0383726
$911$	1.96939e28	1.50975	0.754877	−	0.655866i	$-0.227697\pi$
$911$	1.96939e28	1.50975	0.754877	+	0.655866i	$0.227697\pi$
$912$	−4.25882e27	−0.323101
$913$	−9.55352e27	−0.717284
$914$	−3.62764e27	−0.269547
$915$	−5.36581e27	−0.394580
$916$	4.91813e27	0.357925
$917$	1.61151e28	1.16071
$918$	6.03112e27	0.429925
$919$	6.46913e27	0.456403	0.228201	−	0.973614i	$-0.426716\pi$
$919$	6.46913e27	0.456403	0.228201	+	0.973614i	$0.426716\pi$
$920$	3.57818e27	0.249849
$921$	1.70882e28	1.18094
$922$	1.21144e28	0.828626
$923$	−8.50338e26	−0.0575672
$924$	7.52869e27	0.504471
$925$	3.48162e26	0.0230906
$926$	1.48005e28	0.971568
$927$	1.97257e27	0.128166
$928$	−1.76525e27	−0.113527
$929$	−2.06946e28	−1.31737	−0.658686	−	0.752418i	$-0.728888\pi$
$929$	−2.06946e28	−1.31737	−0.658686	+	0.752418i	$0.728888\pi$
$930$	5.23436e27	0.329819
$931$	−1.50662e28	−0.939681
$932$	−1.40615e28	−0.868124
$933$	−1.02755e27	−0.0627951
$934$	1.18323e28	0.715771
$935$	−3.68960e27	−0.220937
$936$	−1.52101e26	−0.00901596
$937$	−4.86106e27	−0.285236	−0.142618	−	0.989778i	$-0.545552\pi$
$937$	−4.86106e27	−0.285236	−0.142618	+	0.989778i	$0.545552\pi$
$938$	2.33285e28	1.35506
$939$	−3.17856e27	−0.182771
$940$	6.74847e27	0.384141
$941$	−2.02926e28	−1.14350	−0.571751	−	0.820427i	$-0.693736\pi$
$941$	−2.02926e28	−1.14350	−0.571751	+	0.820427i	$0.693736\pi$
$942$	−1.54880e28	−0.863997
$943$	−1.12976e28	−0.623914
$944$	−8.38858e27	−0.458622
$945$	9.05497e27	0.490100
$946$	−1.55012e28	−0.830617
$947$	−1.43284e28	−0.760101	−0.380051	−	0.924966i	$-0.624093\pi$
$947$	−1.43284e28	−0.760101	−0.380051	+	0.924966i	$0.624093\pi$
$948$	1.70308e28	0.894451
$949$	1.27223e27	0.0661511
$950$	3.13355e27	0.161311
$951$	1.30708e27	0.0666174
$952$	7.08967e27	0.357746
$953$	−1.10181e28	−0.550460	−0.275230	−	0.961378i	$-0.588754\pi$
$953$	−1.10181e28	−0.550460	−0.275230	+	0.961378i	$0.588754\pi$
$954$	6.14883e27	0.304146
$955$	−1.17925e28	−0.577528
$956$	−1.82390e27	−0.0884405
$957$	−9.99341e27	−0.479789
$958$	−6.95939e27	−0.330825
$959$	3.42771e28	1.61335
$960$	1.35910e27	0.0633396
$961$	−3.30858e27	−0.152675
$962$	−1.60540e26	−0.00733534
$963$	−1.98470e27	−0.0897934
$964$	3.63498e27	0.162844
$965$	1.48785e28	0.660008
$966$	−3.89240e28	−1.70976
$967$	1.66259e28	0.723158	0.361579	−	0.932341i	$-0.382238\pi$
$967$	1.66259e28	0.723158	0.361579	+	0.932341i	$0.382238\pi$
$968$	4.63985e27	0.199843
$969$	−2.27040e28	−0.968338
$970$	−6.98270e27	−0.294912
$971$	−4.53510e27	−0.189673	−0.0948363	−	0.995493i	$-0.530233\pi$
$971$	−4.53510e27	−0.189673	−0.0948363	+	0.995493i	$0.530233\pi$
$972$	−6.66258e27	−0.275939
$973$	8.23946e27	0.337930
$974$	−9.96857e27	−0.404877
$975$	5.06237e26	0.0203615
$976$	−4.88746e27	−0.194675
$977$	3.50587e28	1.38292	0.691461	−	0.722414i	$-0.256968\pi$
$977$	3.50587e28	1.38292	0.691461	+	0.722414i	$0.256968\pi$
$978$	−3.27160e28	−1.27803
$979$	1.59309e28	0.616319
$980$	4.80801e27	0.184212
$981$	6.39406e27	0.242617
$982$	1.65291e28	0.621139
$983$	−1.72428e28	−0.641724	−0.320862	−	0.947126i	$-0.603973\pi$
$983$	−1.72428e28	−0.641724	−0.320862	+	0.947126i	$0.603973\pi$
$984$	−4.29117e27	−0.158169
$985$	1.00310e28	0.366186
$986$	−9.41066e27	−0.340243
$987$	−7.34109e28	−2.62874
$988$	−1.44490e27	−0.0512446
$989$	8.01427e28	2.81513
$990$	1.70093e27	0.0591768
$991$	−2.09706e27	−0.0722622	−0.0361311	−	0.999347i	$-0.511503\pi$
$991$	−2.09706e27	−0.0722622	−0.0361311	+	0.999347i	$0.511503\pi$
$992$	4.76772e27	0.162723
$993$	−4.46673e28	−1.50998
$994$	−1.82722e28	−0.611816
$995$	5.66428e27	0.187856
$996$	1.87608e28	0.616293
$997$	4.00417e28	1.30289	0.651446	−	0.758695i	$-0.274163\pi$
$997$	4.00417e28	1.30289	0.651446	+	0.758695i	$0.274163\pi$
$998$	1.03773e28	0.334461
$999$	−2.93465e27	−0.0936880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.20.a.b.1.1	✓	1
3.2	odd	2		90.20.a.c.1.1		1
4.3	odd	2		80.20.a.a.1.1		1
5.2	odd	4		50.20.b.b.49.1		2
5.3	odd	4		50.20.b.b.49.2		2
5.4	even	2		50.20.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.20.a.b.1.1	✓	1	1.1	even	1	trivial
50.20.a.c.1.1		1	5.4	even	2
50.20.b.b.49.1		2	5.2	odd	4
50.20.b.b.49.2		2	5.3	odd	4
80.20.a.a.1.1		1	4.3	odd	2
90.20.a.c.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more