LMFDB - Embedded newform 114.12.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,12,Mod(1,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("114.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	114.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:	$87.5911225838$
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	$\chi$	$=$	114.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} -1575.00 q^{5} +7776.00 q^{6} -81697.0 q^{7} -32768.0 q^{8} +59049.0 q^{9} +O(q^{10})$

\(q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} -1575.00 q^{5} +7776.00 q^{6} -81697.0 q^{7} -32768.0 q^{8} +59049.0 q^{9} +50400.0 q^{10} -284151. q^{11} -248832. q^{12} +1.45565e6 q^{13} +2.61430e6 q^{14} +382725. q^{15} +1.04858e6 q^{16} +1.28993e6 q^{17} -1.88957e6 q^{18} +2.47610e6 q^{19} -1.61280e6 q^{20} +1.98524e7 q^{21} +9.09283e6 q^{22} +9.73460e6 q^{23} +7.96262e6 q^{24} -4.63475e7 q^{25} -4.65808e7 q^{26} -1.43489e7 q^{27} -8.36577e7 q^{28} +1.82737e7 q^{29} -1.22472e7 q^{30} +1.30820e8 q^{31} -3.35544e7 q^{32} +6.90487e7 q^{33} -4.12778e7 q^{34} +1.28673e8 q^{35} +6.04662e7 q^{36} +1.03015e8 q^{37} -7.92352e7 q^{38} -3.53723e8 q^{39} +5.16096e7 q^{40} +1.73001e8 q^{41} -6.35276e8 q^{42} +6.31545e8 q^{43} -2.90971e8 q^{44} -9.30022e7 q^{45} -3.11507e8 q^{46} +2.11628e9 q^{47} -2.54804e8 q^{48} +4.69707e9 q^{49} +1.48312e9 q^{50} -3.13453e8 q^{51} +1.49059e9 q^{52} +4.98148e8 q^{53} +4.59165e8 q^{54} +4.47538e8 q^{55} +2.67705e9 q^{56} -6.01692e8 q^{57} -5.84759e8 q^{58} -4.19899e9 q^{59} +3.91910e8 q^{60} +3.55393e9 q^{61} -4.18625e9 q^{62} -4.82413e9 q^{63} +1.07374e9 q^{64} -2.29265e9 q^{65} -2.20956e9 q^{66} +1.30099e9 q^{67} +1.32089e9 q^{68} -2.36551e9 q^{69} -4.11753e9 q^{70} -1.83120e10 q^{71} -1.93492e9 q^{72} +7.84737e9 q^{73} -3.29648e9 q^{74} +1.12624e10 q^{75} +2.53553e9 q^{76} +2.32143e10 q^{77} +1.13191e10 q^{78} -2.99554e10 q^{79} -1.65151e9 q^{80} +3.48678e9 q^{81} -5.53604e9 q^{82} +2.53145e10 q^{83} +2.03288e10 q^{84} -2.03164e9 q^{85} -2.02094e10 q^{86} -4.44052e9 q^{87} +9.31106e9 q^{88} +4.02870e10 q^{89} +2.97607e9 q^{90} -1.18922e11 q^{91} +9.96823e9 q^{92} -3.17894e10 q^{93} -6.77209e10 q^{94} -3.89986e9 q^{95} +8.15373e9 q^{96} -1.14275e11 q^{97} -1.50306e11 q^{98} -1.67788e10 q^{99} +O(q^{100})\)

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 $

$2$	−32.0000	−0.707107
$2$	−32.0000	−0.707107
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	1024.00	0.500000
$5$	−1575.00	−0.225396	−0.112698	−	0.993629i	$-0.535949\pi$
$5$	−1575.00	−0.225396	−0.112698	+	0.993629i	$0.535949\pi$
$6$	7776.00	0.408248
$7$	−81697.0	−1.83724	−0.918622	−	0.395137i	$-0.870697\pi$
$7$	−81697.0	−1.83724	−0.918622	+	0.395137i	$0.870697\pi$
$8$	−32768.0	−0.353553
$9$	59049.0	0.333333
$10$	50400.0	0.159379
$11$	−284151.	−0.531973	−0.265986	−	0.963977i	$-0.585698\pi$
$11$	−284151.	−0.531973	−0.265986	+	0.963977i	$0.585698\pi$
$12$	−248832.	−0.288675
$13$	1.45565e6	1.08735	0.543674	−	0.839297i	$-0.317033\pi$
$13$	1.45565e6	1.08735	0.543674	+	0.839297i	$0.317033\pi$
$14$	2.61430e6	1.29913
$15$	382725.	0.130132
$16$	1.04858e6	0.250000
$17$	1.28993e6	0.220342	0.110171	−	0.993913i	$-0.464860\pi$
$17$	1.28993e6	0.220342	0.110171	+	0.993913i	$0.464860\pi$
$18$	−1.88957e6	−0.235702
$19$	2.47610e6	0.229416
$19$	2.47610e6	0.229416
$20$	−1.61280e6	−0.112698
$21$	1.98524e7	1.06073
$22$	9.09283e6	0.376162
$23$	9.73460e6	0.315366	0.157683	−	0.987490i	$-0.449598\pi$
$23$	9.73460e6	0.315366	0.157683	+	0.987490i	$0.449598\pi$
$24$	7.96262e6	0.204124
$25$	−4.63475e7	−0.949197
$26$	−4.65808e7	−0.768871
$27$	−1.43489e7	−0.192450
$28$	−8.36577e7	−0.918622
$29$	1.82737e7	0.165439	0.0827195	−	0.996573i	$-0.473639\pi$
$29$	1.82737e7	0.165439	0.0827195	+	0.996573i	$0.473639\pi$
$30$	−1.22472e7	−0.0920174
$31$	1.30820e8	0.820703	0.410352	−	0.911927i	$-0.365406\pi$
$31$	1.30820e8	0.820703	0.410352	+	0.911927i	$0.365406\pi$
$32$	−3.35544e7	−0.176777
$33$	6.90487e7	0.307135
$34$	−4.12778e7	−0.155805
$35$	1.28673e8	0.414107
$36$	6.04662e7	0.166667
$37$	1.03015e8	0.244226	0.122113	−	0.992516i	$-0.461033\pi$
$37$	1.03015e8	0.244226	0.122113	+	0.992516i	$0.461033\pi$
$38$	−7.92352e7	−0.162221
$39$	−3.53723e8	−0.627781
$40$	5.16096e7	0.0796894
$41$	1.73001e8	0.233205	0.116603	−	0.993179i	$-0.462800\pi$
$41$	1.73001e8	0.233205	0.116603	+	0.993179i	$0.462800\pi$
$42$	−6.35276e8	−0.750052
$43$	6.31545e8	0.655130	0.327565	−	0.944829i	$-0.393772\pi$
$43$	6.31545e8	0.655130	0.327565	+	0.944829i	$0.393772\pi$
$44$	−2.90971e8	−0.265986
$45$	−9.30022e7	−0.0751319
$46$	−3.11507e8	−0.222998
$47$	2.11628e9	1.34597	0.672984	−	0.739657i	$-0.265012\pi$
$47$	2.11628e9	1.34597	0.672984	+	0.739657i	$0.265012\pi$
$48$	−2.54804e8	−0.144338
$49$	4.69707e9	2.37547
$50$	1.48312e9	0.671183
$51$	−3.13453e8	−0.127215
$52$	1.49059e9	0.543674
$53$	4.98148e8	0.163622	0.0818108	−	0.996648i	$-0.473930\pi$
$53$	4.98148e8	0.163622	0.0818108	+	0.996648i	$0.473930\pi$
$54$	4.59165e8	0.136083
$55$	4.47538e8	0.119904
$56$	2.67705e9	0.649564
$57$	−6.01692e8	−0.132453
$58$	−5.84759e8	−0.116983
$59$	−4.19899e9	−0.764643	−0.382322	−	0.924029i	$-0.624875\pi$
$59$	−4.19899e9	−0.764643	−0.382322	+	0.924029i	$0.624875\pi$
$60$	3.91910e8	0.0650661
$61$	3.55393e9	0.538760	0.269380	−	0.963034i	$-0.413181\pi$
$61$	3.55393e9	0.538760	0.269380	+	0.963034i	$0.413181\pi$
$62$	−4.18625e9	−0.580325
$63$	−4.82413e9	−0.612415
$64$	1.07374e9	0.125000
$65$	−2.29265e9	−0.245083
$66$	−2.20956e9	−0.217177
$67$	1.30099e9	0.117723	0.0588616	−	0.998266i	$-0.481253\pi$
$67$	1.30099e9	0.117723	0.0588616	+	0.998266i	$0.481253\pi$
$68$	1.32089e9	0.110171
$69$	−2.36551e9	−0.182077
$70$	−4.11753e9	−0.292818
$71$	−1.83120e10	−1.20452	−0.602260	−	0.798300i	$-0.705733\pi$
$71$	−1.83120e10	−1.20452	−0.602260	+	0.798300i	$0.705733\pi$
$72$	−1.93492e9	−0.117851
$73$	7.84737e9	0.443046	0.221523	−	0.975155i	$-0.428897\pi$
$73$	7.84737e9	0.443046	0.221523	+	0.975155i	$0.428897\pi$
$74$	−3.29648e9	−0.172694
$75$	1.12624e10	0.548019
$76$	2.53553e9	0.114708
$77$	2.32143e10	0.977364
$78$	1.13191e10	0.443908
$79$	−2.99554e10	−1.09528	−0.547641	−	0.836713i	$-0.684474\pi$
$79$	−2.99554e10	−1.09528	−0.547641	+	0.836713i	$0.684474\pi$
$80$	−1.65151e9	−0.0563489
$81$	3.48678e9	0.111111
$82$	−5.53604e9	−0.164901
$83$	2.53145e10	0.705408	0.352704	−	0.935735i	$-0.385262\pi$
$83$	2.53145e10	0.705408	0.352704	+	0.935735i	$0.385262\pi$
$84$	2.03288e10	0.530367
$85$	−2.03164e9	−0.0496641
$86$	−2.02094e10	−0.463247
$87$	−4.44052e9	−0.0955163
$88$	9.31106e9	0.188081
$89$	4.02870e10	0.764751	0.382376	−	0.924007i	$-0.375106\pi$
$89$	4.02870e10	0.764751	0.382376	+	0.924007i	$0.375106\pi$
$90$	2.97607e9	0.0531263
$91$	−1.18922e11	−1.99772
$92$	9.96823e9	0.157683
$93$	−3.17894e10	−0.473833
$94$	−6.77209e10	−0.951743
$95$	−3.89986e9	−0.0517093
$96$	8.15373e9	0.102062
$97$	−1.14275e11	−1.35115	−0.675577	−	0.737289i	$-0.736105\pi$
$97$	−1.14275e11	−1.35115	−0.675577	+	0.737289i	$0.736105\pi$
$98$	−1.50306e11	−1.67971
$99$	−1.67788e10	−0.177324
$100$	−4.74598e10	−0.474598
$101$	1.32797e11	1.25725	0.628626	−	0.777708i	$-0.283618\pi$
$101$	1.32797e11	1.25725	0.628626	+	0.777708i	$0.283618\pi$
$102$	1.00305e10	0.0899543
$103$	−6.54584e10	−0.556366	−0.278183	−	0.960528i	$-0.589732\pi$
$103$	−6.54584e10	−0.556366	−0.278183	+	0.960528i	$0.589732\pi$
$104$	−4.76987e10	−0.384436
$105$	−3.12675e10	−0.239085
$106$	−1.59407e10	−0.115698
$107$	−7.78205e10	−0.536393	−0.268197	−	0.963364i	$-0.586428\pi$
$107$	−7.78205e10	−0.536393	−0.268197	+	0.963364i	$0.586428\pi$
$108$	−1.46933e10	−0.0962250
$109$	−7.58468e10	−0.472162	−0.236081	−	0.971733i	$-0.575863\pi$
$109$	−7.58468e10	−0.472162	−0.236081	+	0.971733i	$0.575863\pi$
$110$	−1.43212e10	−0.0847852
$111$	−2.50327e10	−0.141004
$112$	−8.56655e10	−0.459311
$113$	9.24778e10	0.472179	0.236089	−	0.971731i	$-0.424134\pi$
$113$	9.24778e10	0.472179	0.236089	+	0.971731i	$0.424134\pi$
$114$	1.92541e10	0.0936586
$115$	−1.53320e10	−0.0710822
$116$	1.87123e10	0.0827195
$117$	8.59547e10	0.362449
$118$	1.34368e11	0.540684
$119$	−1.05383e11	−0.404822
$120$	−1.25411e10	−0.0460087
$121$	−2.04570e11	−0.717005
$122$	−1.13726e11	−0.380961
$123$	−4.20393e10	−0.134641
$124$	1.33960e11	0.410352
$125$	1.49902e11	0.439340
$126$	1.54372e11	0.433043
$127$	−4.17857e11	−1.12230	−0.561148	−	0.827716i	$-0.689640\pi$
$127$	−4.17857e11	−1.12230	−0.561148	+	0.827716i	$0.689640\pi$
$128$	−3.43597e10	−0.0883883
$129$	−1.53465e11	−0.378240
$130$	7.33648e10	0.173300
$131$	−7.62516e11	−1.72686	−0.863430	−	0.504469i	$-0.831688\pi$
$131$	−7.62516e11	−1.72686	−0.863430	+	0.504469i	$0.831688\pi$
$132$	7.07059e10	0.153567
$133$	−2.02290e11	−0.421493
$134$	−4.16316e10	−0.0832429
$135$	2.25995e10	0.0433774
$136$	−4.22685e10	−0.0779027
$137$	3.75744e11	0.665165	0.332583	−	0.943074i	$-0.392080\pi$
$137$	3.75744e11	0.665165	0.332583	+	0.943074i	$0.392080\pi$
$138$	7.56963e10	0.128748
$139$	−4.36760e11	−0.713939	−0.356969	−	0.934116i	$-0.616190\pi$
$139$	−4.36760e11	−0.713939	−0.356969	+	0.934116i	$0.616190\pi$
$140$	1.31761e11	0.207053
$141$	−5.14256e11	−0.777095
$142$	5.85983e11	0.851724
$143$	−4.13624e11	−0.578440
$144$	6.19174e10	0.0833333
$145$	−2.87811e10	−0.0372893
$146$	−2.51116e11	−0.313280
$147$	−1.14139e12	−1.37148
$148$	1.05487e11	0.122113
$149$	−1.27943e12	−1.42722	−0.713610	−	0.700544i	$-0.752941\pi$
$149$	−1.27943e12	−1.42722	−0.713610	+	0.700544i	$0.752941\pi$
$150$	−3.60398e11	−0.387508
$151$	−1.01648e11	−0.105372	−0.0526858	−	0.998611i	$-0.516778\pi$
$151$	−1.01648e11	−0.105372	−0.0526858	+	0.998611i	$0.516778\pi$
$152$	−8.11368e10	−0.0811107
$153$	7.61691e10	0.0734474
$154$	−7.42857e11	−0.691101
$155$	−2.06042e11	−0.184983
$156$	−3.62212e11	−0.313890
$157$	9.19718e10	0.0769497	0.0384748	−	0.999260i	$-0.487750\pi$
$157$	9.19718e10	0.0769497	0.0384748	+	0.999260i	$0.487750\pi$
$158$	9.58572e11	0.774481
$159$	−1.21050e11	−0.0944670
$160$	5.28482e10	0.0398447
$161$	−7.95288e11	−0.579405
$162$	−1.11577e11	−0.0785674
$163$	−2.16774e12	−1.47562	−0.737810	−	0.675008i	$-0.764140\pi$
$163$	−2.16774e12	−1.47562	−0.737810	+	0.675008i	$0.764140\pi$
$164$	1.77153e11	0.116603
$165$	−1.08752e11	−0.0692268
$166$	−8.10065e11	−0.498799
$167$	1.81454e12	1.08100	0.540502	−	0.841343i	$-0.318235\pi$
$167$	1.81454e12	1.08100	0.540502	+	0.841343i	$0.318235\pi$
$168$	−6.50522e11	−0.375026
$169$	3.26757e11	0.182325
$170$	6.50125e10	0.0351179
$171$	1.46211e11	0.0764719
$172$	6.46702e11	0.327565
$173$	4.32606e11	0.212246	0.106123	−	0.994353i	$-0.466156\pi$
$173$	4.32606e11	0.212246	0.106123	+	0.994353i	$0.466156\pi$
$174$	1.42096e11	0.0675402
$175$	3.78645e12	1.74391
$176$	−2.97954e11	−0.132993
$177$	1.02035e12	0.441467
$178$	−1.28919e12	−0.540761
$179$	−4.40340e11	−0.179101	−0.0895503	−	0.995982i	$-0.528543\pi$
$179$	−4.40340e11	−0.179101	−0.0895503	+	0.995982i	$0.528543\pi$
$180$	−9.52342e10	−0.0375659
$181$	4.27118e12	1.63424	0.817120	−	0.576467i	$-0.195569\pi$
$181$	4.27118e12	1.63424	0.817120	+	0.576467i	$0.195569\pi$
$182$	3.80551e12	1.41260
$183$	−8.63606e11	−0.311053
$184$	−3.18984e11	−0.111499
$185$	−1.62249e11	−0.0550474
$186$	1.01726e12	0.335051
$187$	−3.66535e11	−0.117216
$188$	2.16707e12	0.672984
$189$	1.17226e12	0.353578
$190$	1.24795e11	0.0365640
$191$	3.85809e12	1.09822	0.549109	−	0.835751i	$-0.314967\pi$
$191$	3.85809e12	1.09822	0.549109	+	0.835751i	$0.314967\pi$
$192$	−2.60919e11	−0.0721688
$193$	−2.81845e12	−0.757610	−0.378805	−	0.925477i	$-0.623665\pi$
$193$	−2.81845e12	−0.757610	−0.378805	+	0.925477i	$0.623665\pi$
$194$	3.65678e12	0.955410
$195$	5.57114e11	0.141499
$196$	4.80980e12	1.18773
$197$	3.19891e11	0.0768135	0.0384068	−	0.999262i	$-0.487772\pi$
$197$	3.19891e11	0.0768135	0.0384068	+	0.999262i	$0.487772\pi$
$198$	5.36923e11	0.125387
$199$	−7.17408e12	−1.62958	−0.814788	−	0.579759i	$-0.803147\pi$
$199$	−7.17408e12	−1.62958	−0.814788	+	0.579759i	$0.803147\pi$
$200$	1.51871e12	0.335592
$201$	−3.16140e11	−0.0679675
$202$	−4.24952e12	−0.889011
$203$	−1.49291e12	−0.303952
$204$	−3.20976e11	−0.0636073
$205$	−2.72477e11	−0.0525634
$206$	2.09467e12	0.393410
$207$	5.74819e11	0.105122
$208$	1.52636e12	0.271837
$209$	−7.03586e11	−0.122043
$210$	1.00056e12	0.169058
$211$	−4.06289e12	−0.668777	−0.334389	−	0.942435i	$-0.608530\pi$
$211$	−4.06289e12	−0.668777	−0.334389	+	0.942435i	$0.608530\pi$
$212$	5.10103e11	0.0818108
$213$	4.44980e12	0.695430
$214$	2.49026e12	0.379287
$215$	−9.94683e11	−0.147664
$216$	4.70185e11	0.0680414
$217$	−1.06876e13	−1.50783
$218$	2.42710e12	0.333869
$219$	−1.90691e12	−0.255792
$220$	4.58279e11	0.0599522
$221$	1.87769e12	0.239588
$222$	8.01045e11	0.0997047
$223$	4.66718e12	0.566732	0.283366	−	0.959012i	$-0.408549\pi$
$223$	4.66718e12	0.566732	0.283366	+	0.959012i	$0.408549\pi$
$224$	2.74130e12	0.324782
$225$	−2.73677e12	−0.316399
$226$	−2.95929e12	−0.333881
$227$	8.08013e12	0.889767	0.444883	−	0.895589i	$-0.353245\pi$
$227$	8.08013e12	0.889767	0.444883	+	0.895589i	$0.353245\pi$
$228$	−6.16133e11	−0.0662266
$229$	−1.01312e13	−1.06308	−0.531541	−	0.847033i	$-0.678387\pi$
$229$	−1.01312e13	−1.06308	−0.531541	+	0.847033i	$0.678387\pi$
$230$	4.90624e11	0.0502627
$231$	−5.64107e12	−0.564281
$232$	−5.98793e11	−0.0584915
$233$	9.94526e12	0.948765	0.474382	−	0.880319i	$-0.342671\pi$
$233$	9.94526e12	0.948765	0.474382	+	0.880319i	$0.342671\pi$
$234$	−2.75055e12	−0.256290
$235$	−3.33314e12	−0.303375
$236$	−4.29977e12	−0.382322
$237$	7.27916e12	0.632361
$238$	3.37227e12	0.286253
$239$	2.68961e12	0.223101	0.111550	−	0.993759i	$-0.464418\pi$
$239$	2.68961e12	0.223101	0.111550	+	0.993759i	$0.464418\pi$
$240$	4.01316e11	0.0325331
$241$	1.52574e13	1.20889	0.604444	−	0.796647i	$-0.293395\pi$
$241$	1.52574e13	1.20889	0.604444	+	0.796647i	$0.293395\pi$
$242$	6.54624e12	0.506999
$243$	−8.47289e11	−0.0641500
$244$	3.63923e12	0.269380
$245$	−7.39789e12	−0.535420
$246$	1.34526e12	0.0952056
$247$	3.60433e12	0.249455
$248$	−4.28672e12	−0.290162
$249$	−6.15143e12	−0.407267
$250$	−4.79685e12	−0.310661
$251$	1.84458e13	1.16867	0.584336	−	0.811512i	$-0.301355\pi$
$251$	1.84458e13	1.16867	0.584336	+	0.811512i	$0.301355\pi$
$252$	−4.93991e12	−0.306207
$253$	−2.76610e12	−0.167766
$254$	1.33714e13	0.793583
$255$	4.93689e11	0.0286736
$256$	1.09951e12	0.0625000
$257$	2.61901e12	0.145715	0.0728575	−	0.997342i	$-0.476788\pi$
$257$	2.61901e12	0.145715	0.0728575	+	0.997342i	$0.476788\pi$
$258$	4.91089e12	0.267456
$259$	−8.41602e12	−0.448702
$260$	−2.34767e12	−0.122542
$261$	1.07905e12	0.0551464
$262$	2.44005e13	1.22107
$263$	5.21786e11	0.0255703	0.0127852	−	0.999918i	$-0.495930\pi$
$263$	5.21786e11	0.0255703	0.0127852	+	0.999918i	$0.495930\pi$
$264$	−2.26259e12	−0.108588
$265$	−7.84582e11	−0.0368796
$266$	6.47328e12	0.298040
$267$	−9.78975e12	−0.441529
$268$	1.33221e12	0.0588616
$269$	−4.27663e13	−1.85124	−0.925622	−	0.378449i	$-0.876458\pi$
$269$	−4.27663e13	−1.85124	−0.925622	+	0.378449i	$0.876458\pi$
$270$	−7.23185e11	−0.0306725
$271$	8.59364e12	0.357146	0.178573	−	0.983927i	$-0.442852\pi$
$271$	8.59364e12	0.357146	0.178573	+	0.983927i	$0.442852\pi$
$272$	1.35259e12	0.0550855
$273$	2.88981e13	1.15339
$274$	−1.20238e13	−0.470343
$275$	1.31697e13	0.504947
$276$	−2.42228e12	−0.0910384
$277$	5.42990e12	0.200057	0.100028	−	0.994985i	$-0.468107\pi$
$277$	5.42990e12	0.200057	0.100028	+	0.994985i	$0.468107\pi$
$278$	1.39763e13	0.504831
$279$	7.72482e12	0.273568
$280$	−4.21635e12	−0.146409
$281$	5.01776e12	0.170854	0.0854270	−	0.996344i	$-0.472775\pi$
$281$	5.01776e12	0.170854	0.0854270	+	0.996344i	$0.472775\pi$
$282$	1.64562e13	0.549489
$283$	−3.94321e13	−1.29129	−0.645646	−	0.763637i	$-0.723412\pi$
$283$	−3.94321e13	−1.29129	−0.645646	+	0.763637i	$0.723412\pi$
$284$	−1.87514e13	−0.602260
$285$	9.47665e11	0.0298544
$286$	1.32360e13	0.409018
$287$	−1.41337e13	−0.428455
$288$	−1.98136e12	−0.0589256
$289$	−3.26080e13	−0.951449
$290$	9.20996e11	0.0263675
$291$	2.77687e13	0.780089
$292$	8.03571e12	0.221523
$293$	−2.89456e13	−0.783088	−0.391544	−	0.920159i	$-0.628059\pi$
$293$	−2.89456e13	−0.783088	−0.391544	+	0.920159i	$0.628059\pi$
$294$	3.65244e13	0.969780
$295$	6.61341e12	0.172347
$296$	−3.37560e12	−0.0863468
$297$	4.07726e12	0.102378
$298$	4.09416e13	1.00920
$299$	1.41702e13	0.342913
$300$	1.15327e13	0.274010
$301$	−5.15953e13	−1.20363
$302$	3.25272e12	0.0745090
$303$	−3.22698e13	−0.725874
$304$	2.59638e12	0.0573539
$305$	−5.59745e12	−0.121434
$306$	−2.43741e12	−0.0519351
$307$	−3.31102e13	−0.692949	−0.346474	−	0.938059i	$-0.612621\pi$
$307$	−3.31102e13	−0.692949	−0.346474	+	0.938059i	$0.612621\pi$
$308$	2.37714e13	0.488682
$309$	1.59064e13	0.321218
$310$	6.59335e12	0.130803
$311$	7.44360e13	1.45078	0.725389	−	0.688339i	$-0.241660\pi$
$311$	7.44360e13	1.45078	0.725389	+	0.688339i	$0.241660\pi$
$312$	1.15908e13	0.221954
$313$	−5.28984e13	−0.995289	−0.497644	−	0.867381i	$-0.665802\pi$
$313$	−5.28984e13	−0.995289	−0.497644	+	0.867381i	$0.665802\pi$
$314$	−2.94310e12	−0.0544116
$315$	7.59800e12	0.138036
$316$	−3.06743e13	−0.547641
$317$	1.05201e14	1.84585	0.922923	−	0.384984i	$-0.125793\pi$
$317$	1.05201e14	1.84585	0.922923	+	0.384984i	$0.125793\pi$
$318$	3.87360e12	0.0667983
$319$	−5.19250e12	−0.0880091
$320$	−1.69114e12	−0.0281745
$321$	1.89104e13	0.309687
$322$	2.54492e13	0.409701
$323$	3.19400e12	0.0505499
$324$	3.57047e12	0.0555556
$325$	−6.74657e13	−1.03211
$326$	6.93676e13	1.04342
$327$	1.84308e13	0.272603
$328$	−5.66890e12	−0.0824504
$329$	−1.72894e14	−2.47287
$330$	3.48005e12	0.0489507
$331$	−9.43547e13	−1.30530	−0.652649	−	0.757660i	$-0.726342\pi$
$331$	−9.43547e13	−1.30530	−0.652649	+	0.757660i	$0.726342\pi$
$332$	2.59221e13	0.352704
$333$	6.08294e12	0.0814085
$334$	−5.80654e13	−0.764385
$335$	−2.04906e12	−0.0265343
$336$	2.08167e13	0.265183
$337$	8.25931e13	1.03509	0.517546	−	0.855655i	$-0.326846\pi$
$337$	8.25931e13	1.03509	0.517546	+	0.855655i	$0.326846\pi$
$338$	−1.04562e13	−0.128924
$339$	−2.24721e13	−0.272612
$340$	−2.08040e12	−0.0248321
$341$	−3.71728e13	−0.436592
$342$	−4.67876e12	−0.0540738
$343$	−2.22195e14	−2.52707
$344$	−2.06945e13	−0.231624
$345$	3.72568e12	0.0410393
$346$	−1.38434e13	−0.150080
$347$	−1.83815e14	−1.96141	−0.980707	−	0.195485i	$-0.937372\pi$
$347$	−1.83815e14	−1.96141	−0.980707	+	0.195485i	$0.937372\pi$
$348$	−4.54709e12	−0.0477582
$349$	8.57658e13	0.886695	0.443348	−	0.896350i	$-0.353791\pi$
$349$	8.57658e13	0.886695	0.443348	+	0.896350i	$0.353791\pi$
$350$	−1.21166e14	−1.23313
$351$	−2.08870e13	−0.209260
$352$	9.53453e12	0.0940404
$353$	1.72694e14	1.67694	0.838468	−	0.544950i	$-0.183452\pi$
$353$	1.72694e14	1.67694	0.838468	+	0.544950i	$0.183452\pi$
$354$	−3.26513e13	−0.312164
$355$	2.88413e13	0.271493
$356$	4.12539e13	0.382376
$357$	2.56082e13	0.233724
$358$	1.40909e13	0.126643
$359$	−1.70137e14	−1.50584	−0.752921	−	0.658111i	$-0.771356\pi$
$359$	−1.70137e14	−1.50584	−0.752921	+	0.658111i	$0.771356\pi$
$360$	3.04750e12	0.0265631
$361$	6.13107e12	0.0526316
$362$	−1.36678e14	−1.15558
$363$	4.97105e13	0.413963
$364$	−1.21776e14	−0.998862
$365$	−1.23596e13	−0.0998605
$366$	2.76354e13	0.219948
$367$	−1.29709e14	−1.01697	−0.508483	−	0.861072i	$-0.669794\pi$
$367$	−1.29709e14	−1.01697	−0.508483	+	0.861072i	$0.669794\pi$
$368$	1.02075e13	0.0788416
$369$	1.02156e13	0.0777350
$370$	5.19196e12	0.0389244
$371$	−4.06972e13	−0.300613
$372$	−3.25523e13	−0.236917
$373$	−5.13469e12	−0.0368227	−0.0184113	−	0.999830i	$-0.505861\pi$
$373$	−5.13469e12	−0.0368227	−0.0184113	+	0.999830i	$0.505861\pi$
$374$	1.17291e13	0.0828842
$375$	−3.64261e13	−0.253653
$376$	−6.93462e13	−0.475872
$377$	2.66001e13	0.179890
$378$	−3.75124e13	−0.250017
$379$	−1.87623e13	−0.123245	−0.0616226	−	0.998100i	$-0.519628\pi$
$379$	−1.87623e13	−0.123245	−0.0616226	+	0.998100i	$0.519628\pi$
$380$	−3.99345e12	−0.0258547
$381$	1.01539e14	0.647958
$382$	−1.23459e14	−0.776558
$383$	1.06070e14	0.657658	0.328829	−	0.944389i	$-0.393346\pi$
$383$	1.06070e14	0.657658	0.328829	+	0.944389i	$0.393346\pi$
$384$	8.34942e12	0.0510310
$385$	−3.65625e13	−0.220294
$386$	9.01905e13	0.535711
$387$	3.72921e13	0.218377
$388$	−1.17017e14	−0.675577
$389$	−1.04503e14	−0.594850	−0.297425	−	0.954745i	$-0.596128\pi$
$389$	−1.04503e14	−0.594850	−0.297425	+	0.954745i	$0.596128\pi$
$390$	−1.78276e13	−0.100055
$391$	1.25570e13	0.0694884
$392$	−1.53914e14	−0.839854
$393$	1.85291e14	0.997003
$394$	−1.02365e13	−0.0543154
$395$	4.71797e13	0.246872
$396$	−1.71815e13	−0.0886621
$397$	1.99719e14	1.01642	0.508208	−	0.861235i	$-0.330308\pi$
$397$	1.99719e14	1.01642	0.508208	+	0.861235i	$0.330308\pi$
$398$	2.29571e14	1.15228
$399$	4.91564e13	0.243349
$400$	−4.85989e13	−0.237299
$401$	−2.99218e14	−1.44110	−0.720549	−	0.693404i	$-0.756110\pi$
$401$	−2.99218e14	−1.44110	−0.720549	+	0.693404i	$0.756110\pi$
$402$	1.01165e13	0.0480603
$403$	1.90429e14	0.892390
$404$	1.35985e14	0.628626
$405$	−5.49169e12	−0.0250440
$406$	4.77731e13	0.214927
$407$	−2.92718e13	−0.129921
$408$	1.02712e13	0.0449771
$409$	2.25711e14	0.975158	0.487579	−	0.873079i	$-0.337880\pi$
$409$	2.25711e14	0.975158	0.487579	+	0.873079i	$0.337880\pi$
$410$	8.71926e12	0.0371679
$411$	−9.13059e13	−0.384033
$412$	−6.70294e13	−0.278183
$413$	3.43045e14	1.40484
$414$	−1.83942e13	−0.0743325
$415$	−3.98704e13	−0.158996
$416$	−4.88435e13	−0.192218
$417$	1.06133e14	0.412193
$418$	2.25148e13	0.0862974
$419$	−1.32845e14	−0.502537	−0.251269	−	0.967917i	$-0.580848\pi$
$419$	−1.32845e14	−0.502537	−0.251269	+	0.967917i	$0.580848\pi$
$420$	−3.20179e13	−0.119542
$421$	−2.34636e14	−0.864657	−0.432328	−	0.901716i	$-0.642308\pi$
$421$	−2.34636e14	−0.864657	−0.432328	+	0.901716i	$0.642308\pi$
$422$	1.30013e14	0.472897
$423$	1.24964e14	0.448656
$424$	−1.63233e13	−0.0578490
$425$	−5.97851e13	−0.209148
$426$	−1.42394e14	−0.491743
$427$	−2.90346e14	−0.989834
$428$	−7.96882e13	−0.268197
$429$	1.00511e14	0.333962
$430$	3.18299e13	0.104414
$431$	2.79604e14	0.905564	0.452782	−	0.891621i	$-0.350432\pi$
$431$	2.79604e14	0.905564	0.452782	+	0.891621i	$0.350432\pi$
$432$	−1.50459e13	−0.0481125
$433$	2.02092e14	0.638066	0.319033	−	0.947744i	$-0.396642\pi$
$433$	2.02092e14	0.638066	0.319033	+	0.947744i	$0.396642\pi$
$434$	3.42004e14	1.06620
$435$	6.99381e12	0.0215290
$436$	−7.76671e13	−0.236081
$437$	2.41038e13	0.0723500
$438$	6.10211e13	0.180873
$439$	−5.25206e14	−1.53736	−0.768679	−	0.639635i	$-0.779086\pi$
$439$	−5.25206e14	−1.53736	−0.768679	+	0.639635i	$0.779086\pi$
$440$	−1.46649e13	−0.0423926
$441$	2.77357e14	0.791822
$442$	−6.00860e13	−0.169415
$443$	3.27935e14	0.913202	0.456601	−	0.889672i	$-0.349067\pi$
$443$	3.27935e14	0.913202	0.456601	+	0.889672i	$0.349067\pi$
$444$	−2.56334e13	−0.0705019
$445$	−6.34521e13	−0.172372
$446$	−1.49350e14	−0.400740
$447$	3.10900e14	0.824005
$448$	−8.77215e13	−0.229656
$449$	1.22405e14	0.316553	0.158276	−	0.987395i	$-0.449406\pi$
$449$	1.22405e14	0.316553	0.158276	+	0.987395i	$0.449406\pi$
$450$	8.75768e13	0.223728
$451$	−4.91585e13	−0.124059
$452$	9.46973e13	0.236089
$453$	2.47004e13	0.0608363
$454$	−2.58564e14	−0.629160
$455$	1.87303e14	0.450278
$456$	1.97162e13	0.0468293
$457$	5.99527e14	1.40692	0.703460	−	0.710735i	$-0.251637\pi$
$457$	5.99527e14	1.40692	0.703460	+	0.710735i	$0.251637\pi$
$458$	3.24199e14	0.751712
$459$	−1.85091e13	−0.0424048
$460$	−1.57000e13	−0.0355411
$461$	3.06101e14	0.684715	0.342358	−	0.939570i	$-0.388775\pi$
$461$	3.06101e14	0.684715	0.342358	+	0.939570i	$0.388775\pi$
$462$	1.80514e14	0.399007
$463$	3.05612e14	0.667536	0.333768	−	0.942655i	$-0.391680\pi$
$463$	3.05612e14	0.667536	0.333768	+	0.942655i	$0.391680\pi$
$464$	1.91614e13	0.0413598
$465$	5.00682e13	0.106800
$466$	−3.18248e14	−0.670878
$467$	8.26320e14	1.72149	0.860747	−	0.509033i	$-0.169997\pi$
$467$	8.26320e14	1.72149	0.860747	+	0.509033i	$0.169997\pi$
$468$	8.80176e13	0.181225
$469$	−1.06287e14	−0.216286
$470$	1.06660e14	0.214519
$471$	−2.23492e13	−0.0444269
$472$	1.37593e14	0.270342
$473$	−1.79454e14	−0.348511
$474$	−2.32933e14	−0.447147
$475$	−1.14761e14	−0.217761
$476$	−1.07913e14	−0.202411
$477$	2.94151e13	0.0545405
$478$	−8.60676e13	−0.157756
$479$	6.98439e14	1.26556	0.632780	−	0.774331i	$-0.281914\pi$
$479$	6.98439e14	1.26556	0.632780	+	0.774331i	$0.281914\pi$
$480$	−1.28421e13	−0.0230043
$481$	1.49954e14	0.265558
$482$	−4.88236e14	−0.854813
$483$	1.93255e14	0.334520
$484$	−2.09480e14	−0.358502
$485$	1.79982e14	0.304544
$486$	2.71132e13	0.0453609
$487$	3.58402e14	0.592872	0.296436	−	0.955053i	$-0.404202\pi$
$487$	3.58402e14	0.592872	0.296436	+	0.955053i	$0.404202\pi$
$488$	−1.16455e14	−0.190480
$489$	5.26760e14	0.851950
$490$	2.36732e14	0.378599
$491$	4.32599e14	0.684128	0.342064	−	0.939677i	$-0.388874\pi$
$491$	4.32599e14	0.684128	0.342064	+	0.939677i	$0.388874\pi$
$492$	−4.30482e13	−0.0673205
$493$	2.35718e13	0.0364532
$494$	−1.15339e14	−0.176391
$495$	2.64267e13	0.0399681
$496$	1.37175e14	0.205176
$497$	1.49603e15	2.21300
$498$	1.96846e14	0.287982
$499$	−5.25519e14	−0.760389	−0.380194	−	0.924907i	$-0.624143\pi$
$499$	−5.25519e14	−0.760389	−0.380194	+	0.924907i	$0.624143\pi$
$500$	1.53499e14	0.219670
$501$	−4.40934e14	−0.624117
$502$	−5.90267e14	−0.826376
$503$	4.21701e14	0.583957	0.291979	−	0.956425i	$-0.405686\pi$
$503$	4.21701e14	0.583957	0.291979	+	0.956425i	$0.405686\pi$
$504$	1.58077e14	0.216521
$505$	−2.09156e14	−0.283379
$506$	8.85151e13	0.118629
$507$	−7.94018e13	−0.105266
$508$	−4.27886e14	−0.561148
$509$	−9.76752e14	−1.26717	−0.633587	−	0.773671i	$-0.718418\pi$
$509$	−9.76752e14	−1.26717	−0.633587	+	0.773671i	$0.718418\pi$
$510$	−1.57980e13	−0.0202753
$511$	−6.41107e14	−0.813983
$512$	−3.51844e13	−0.0441942
$513$	−3.55293e13	−0.0441511
$514$	−8.38082e13	−0.103036
$515$	1.03097e14	0.125402
$516$	−1.57149e14	−0.189120
$517$	−6.01343e14	−0.716018
$518$	2.69313e14	0.317280
$519$	−1.05123e14	−0.122540
$520$	7.51255e13	0.0866501
$521$	−6.03595e14	−0.688871	−0.344435	−	0.938810i	$-0.611930\pi$
$521$	−6.03595e14	−0.688871	−0.344435	+	0.938810i	$0.611930\pi$
$522$	−3.45294e13	−0.0389944
$523$	9.63850e14	1.07709	0.538543	−	0.842598i	$-0.318975\pi$
$523$	9.63850e14	1.07709	0.538543	+	0.842598i	$0.318975\pi$
$524$	−7.80817e14	−0.863430
$525$	−9.20108e14	−1.00684
$526$	−1.66972e13	−0.0180809
$527$	1.68749e14	0.180835
$528$	7.24028e13	0.0767837
$529$	−8.58047e14	−0.900544
$530$	2.51066e13	0.0260778
$531$	−2.47946e14	−0.254881
$532$	−2.07145e14	−0.210746
$533$	2.51829e14	0.253575
$534$	3.13272e14	0.312208
$535$	1.22567e14	0.120901
$536$	−4.26308e13	−0.0416214
$537$	1.07003e14	0.103404
$538$	1.36852e15	1.30903
$539$	−1.33468e15	−1.26368
$540$	2.31419e13	0.0216887
$541$	−1.36863e15	−1.26970	−0.634848	−	0.772637i	$-0.718937\pi$
$541$	−1.36863e15	−1.26970	−0.634848	+	0.772637i	$0.718937\pi$
$542$	−2.74996e14	−0.252540
$543$	−1.03790e15	−0.943529
$544$	−4.32829e13	−0.0389513
$545$	1.19459e14	0.106423
$546$	−9.24739e14	−0.815567
$547$	−7.33057e14	−0.640041	−0.320020	−	0.947411i	$-0.603690\pi$
$547$	−7.33057e14	−0.640041	−0.320020	+	0.947411i	$0.603690\pi$
$548$	3.84762e14	0.332583
$549$	2.09856e14	0.179587
$550$	−4.21430e14	−0.357051
$551$	4.52476e13	0.0379543
$552$	7.75130e13	0.0643739
$553$	2.44727e15	2.01230
$554$	−1.73757e14	−0.141461
$555$	3.94264e13	0.0317816
$556$	−4.47242e14	−0.356969
$557$	−1.25283e15	−0.990125	−0.495062	−	0.868857i	$-0.664855\pi$
$557$	−1.25283e15	−0.990125	−0.495062	+	0.868857i	$0.664855\pi$
$558$	−2.47194e14	−0.193442
$559$	9.19308e14	0.712355
$560$	1.34923e14	0.103527
$561$	8.90680e13	0.0676747
$562$	−1.60568e14	−0.120812
$563$	−4.49986e13	−0.0335276	−0.0167638	−	0.999859i	$-0.505336\pi$
$563$	−4.49986e13	−0.0335276	−0.0167638	+	0.999859i	$0.505336\pi$
$564$	−5.26598e14	−0.388548
$565$	−1.45653e14	−0.106427
$566$	1.26183e15	0.913081
$567$	−2.84860e14	−0.204138
$568$	6.00046e14	0.425862
$569$	−1.32126e15	−0.928687	−0.464344	−	0.885655i	$-0.653710\pi$
$569$	−1.32126e15	−0.928687	−0.464344	+	0.885655i	$0.653710\pi$
$570$	−3.03253e13	−0.0211102
$571$	2.52834e15	1.74316	0.871578	−	0.490257i	$-0.163097\pi$
$571$	2.52834e15	1.74316	0.871578	+	0.490257i	$0.163097\pi$
$572$	−4.23551e14	−0.289220
$573$	−9.37516e14	−0.634057
$574$	4.52278e14	0.302963
$575$	−4.51175e14	−0.299345
$576$	6.34034e13	0.0416667
$577$	1.07625e15	0.700560	0.350280	−	0.936645i	$-0.386086\pi$
$577$	1.07625e15	0.700560	0.350280	+	0.936645i	$0.386086\pi$
$578$	1.04346e15	0.672776
$579$	6.84884e14	0.437406
$580$	−2.94719e13	−0.0186446
$581$	−2.06812e15	−1.29601
$582$	−8.88599e14	−0.551606
$583$	−1.41549e14	−0.0870423
$584$	−2.57143e14	−0.156640
$585$	−1.35379e14	−0.0816945
$586$	9.26260e14	0.553727
$587$	1.36436e15	0.808015	0.404007	−	0.914756i	$-0.367617\pi$
$587$	1.36436e15	0.808015	0.404007	+	0.914756i	$0.367617\pi$
$588$	−1.16878e15	−0.685738
$589$	3.23924e14	0.188282
$590$	−2.11629e14	−0.121868
$591$	−7.77335e13	−0.0443483
$592$	1.08019e14	0.0610564
$593$	−2.90646e15	−1.62766	−0.813829	−	0.581104i	$-0.802621\pi$
$593$	−2.90646e15	−1.62766	−0.813829	+	0.581104i	$0.802621\pi$
$594$	−1.30472e14	−0.0723923
$595$	1.65979e14	0.0912452
$596$	−1.31013e15	−0.713610
$597$	1.74330e15	0.940836
$598$	−4.53446e14	−0.242476
$599$	−2.32189e15	−1.23025	−0.615125	−	0.788430i	$-0.710894\pi$
$599$	−2.32189e15	−1.23025	−0.615125	+	0.788430i	$0.710894\pi$
$600$	−3.69048e14	−0.193754
$601$	6.09144e14	0.316891	0.158446	−	0.987368i	$-0.449352\pi$
$601$	6.09144e14	0.316891	0.158446	+	0.987368i	$0.449352\pi$
$602$	1.65105e15	0.851098
$603$	7.68221e13	0.0392411
$604$	−1.04087e14	−0.0526858
$605$	3.22198e14	0.161610
$606$	1.03263e15	0.513271
$607$	−1.46907e15	−0.723608	−0.361804	−	0.932254i	$-0.617839\pi$
$607$	−1.46907e15	−0.723608	−0.361804	+	0.932254i	$0.617839\pi$
$608$	−8.30841e13	−0.0405554
$609$	3.62777e14	0.175487
$610$	1.79118e14	0.0858669
$611$	3.08056e15	1.46354
$612$	7.79972e13	0.0367237
$613$	−3.14486e15	−1.46747	−0.733735	−	0.679436i	$-0.762225\pi$
$613$	−3.14486e15	−1.46747	−0.733735	+	0.679436i	$0.762225\pi$
$614$	1.05953e15	0.489989
$615$	6.62119e13	0.0303475
$616$	−7.60686e14	−0.345550
$617$	−8.50314e14	−0.382834	−0.191417	−	0.981509i	$-0.561308\pi$
$617$	−8.50314e14	−0.382834	−0.191417	+	0.981509i	$0.561308\pi$
$618$	−5.09004e14	−0.227135
$619$	−3.52921e15	−1.56092	−0.780458	−	0.625209i	$-0.785014\pi$
$619$	−3.52921e15	−1.56092	−0.780458	+	0.625209i	$0.785014\pi$
$620$	−2.10987e14	−0.0924915
$621$	−1.39681e14	−0.0606923
$622$	−2.38195e15	−1.02585
$623$	−3.29133e15	−1.40504
$624$	−3.70905e14	−0.156945
$625$	2.02697e15	0.850171
$626$	1.69275e15	0.703775
$627$	1.70971e14	0.0704615
$628$	9.41791e13	0.0384748
$629$	1.32882e14	0.0538132
$630$	−2.43136e14	−0.0976059
$631$	−4.88972e15	−1.94591	−0.972954	−	0.230997i	$-0.925801\pi$
$631$	−4.88972e15	−1.94591	−0.972954	+	0.230997i	$0.925801\pi$
$632$	9.81578e14	0.387241
$633$	9.87282e14	0.386119
$634$	−3.36644e15	−1.30521
$635$	6.58125e14	0.252961
$636$	−1.23955e14	−0.0472335
$637$	6.83729e15	2.58296
$638$	1.66160e14	0.0622318
$639$	−1.08130e15	−0.401506
$640$	5.41166e13	0.0199223
$641$	1.64296e15	0.599665	0.299832	−	0.953992i	$-0.403069\pi$
$641$	1.64296e15	0.599665	0.299832	+	0.953992i	$0.403069\pi$
$642$	−6.05132e14	−0.218982
$643$	1.20407e13	0.00432006	0.00216003	−	0.999998i	$-0.499312\pi$
$643$	1.20407e13	0.00432006	0.00216003	+	0.999998i	$0.499312\pi$
$644$	−8.14375e14	−0.289702
$645$	2.41708e14	0.0852536
$646$	−1.02208e14	−0.0357442
$647$	−3.41403e15	−1.18384	−0.591922	−	0.805996i	$-0.701630\pi$
$647$	−3.41403e15	−1.18384	−0.591922	+	0.805996i	$0.701630\pi$
$648$	−1.14255e14	−0.0392837
$649$	1.19315e15	0.406769
$650$	2.15890e15	0.729810
$651$	2.59710e15	0.870548
$652$	−2.21976e15	−0.737810
$653$	−4.00240e15	−1.31916	−0.659580	−	0.751634i	$-0.729266\pi$
$653$	−4.00240e15	−1.31916	−0.659580	+	0.751634i	$0.729266\pi$
$654$	−5.89784e14	−0.192759
$655$	1.20096e15	0.389227
$656$	1.81405e14	0.0583013
$657$	4.63379e14	0.147682
$658$	5.53260e15	1.74858
$659$	−1.49131e15	−0.467410	−0.233705	−	0.972308i	$-0.575085\pi$
$659$	−1.49131e15	−0.467410	−0.233705	+	0.972308i	$0.575085\pi$
$660$	−1.11362e14	−0.0346134
$661$	−7.54624e14	−0.232607	−0.116303	−	0.993214i	$-0.537104\pi$
$661$	−7.54624e14	−0.232607	−0.116303	+	0.993214i	$0.537104\pi$
$662$	3.01935e15	0.922985
$663$	−4.56278e14	−0.138326
$664$	−8.29507e14	−0.249399
$665$	3.18607e14	0.0950026
$666$	−1.94654e14	−0.0575645
$667$	1.77887e14	0.0521739
$668$	1.85809e15	0.540502
$669$	−1.13413e15	−0.327203
$670$	6.55698e13	0.0187626
$671$	−1.00985e15	−0.286606
$672$	−6.66135e14	−0.187513
$673$	4.29185e15	1.19829	0.599145	−	0.800640i	$-0.295507\pi$
$673$	4.29185e15	1.19829	0.599145	+	0.800640i	$0.295507\pi$
$674$	−2.64298e15	−0.731921
$675$	6.65036e14	0.182673
$676$	3.34599e14	0.0911627
$677$	−2.59063e15	−0.700113	−0.350057	−	0.936729i	$-0.613838\pi$
$677$	−2.59063e15	−0.700113	−0.350057	+	0.936729i	$0.613838\pi$
$678$	7.19108e14	0.192766
$679$	9.33588e15	2.48240
$680$	6.65728e13	0.0175589
$681$	−1.96347e15	−0.513707
$682$	1.18953e15	0.308717
$683$	−3.78762e15	−0.975109	−0.487554	−	0.873093i	$-0.662111\pi$
$683$	−3.78762e15	−0.975109	−0.487554	+	0.873093i	$0.662111\pi$
$684$	1.49720e14	0.0382360
$685$	−5.91797e14	−0.149925
$686$	7.11024e15	1.78691
$687$	2.46189e15	0.613771
$688$	6.62223e14	0.163783
$689$	7.25128e14	0.177914
$690$	−1.19222e14	−0.0290192
$691$	−3.29478e15	−0.795605	−0.397802	−	0.917471i	$-0.630227\pi$
$691$	−3.29478e15	−0.795605	−0.397802	+	0.917471i	$0.630227\pi$
$692$	4.42988e14	0.106123
$693$	1.37078e15	0.325788
$694$	5.88208e15	1.38693
$695$	6.87896e14	0.160919
$696$	1.45507e14	0.0337701
$697$	2.23160e14	0.0513849
$698$	−2.74451e15	−0.626988
$699$	−2.41670e15	−0.547769
$700$	3.87733e15	0.871953
$701$	−4.73903e15	−1.05740	−0.528701	−	0.848808i	$-0.677321\pi$
$701$	−4.73903e15	−1.05740	−0.528701	+	0.848808i	$0.677321\pi$
$702$	6.68384e14	0.147969
$703$	2.55075e14	0.0560292
$704$	−3.05105e14	−0.0664966
$705$	8.09953e14	0.175154
$706$	−5.52621e15	−1.18577
$707$	−1.08491e16	−2.30988
$708$	1.04484e15	0.220733
$709$	−3.30737e15	−0.693311	−0.346655	−	0.937993i	$-0.612683\pi$
$709$	−3.30737e15	−0.693311	−0.346655	+	0.937993i	$0.612683\pi$
$710$	−9.22923e14	−0.191975
$711$	−1.76884e15	−0.365094
$712$	−1.32013e15	−0.270380
$713$	1.27349e15	0.258822
$714$	−8.19462e14	−0.165268
$715$	6.51458e14	0.130378
$716$	−4.50909e14	−0.0895503
$717$	−6.53576e14	−0.128807
$718$	5.44439e15	1.06479
$719$	−9.24756e15	−1.79481	−0.897405	−	0.441208i	$-0.854550\pi$
$719$	−9.24756e15	−1.79481	−0.897405	+	0.441208i	$0.854550\pi$
$720$	−9.75198e13	−0.0187830
$721$	5.34775e15	1.02218
$722$	−1.96194e14	−0.0372161
$723$	−3.70754e15	−0.697952
$724$	4.37369e15	0.817120
$725$	−8.46942e14	−0.157034
$726$	−1.59074e15	−0.292716
$727$	4.50859e15	0.823382	0.411691	−	0.911323i	$-0.364938\pi$
$727$	4.50859e15	0.823382	0.411691	+	0.911323i	$0.364938\pi$
$728$	3.89684e15	0.706302
$729$	2.05891e14	0.0370370
$730$	3.95507e14	0.0706121
$731$	8.14649e14	0.144353
$732$	−8.84333e14	−0.155527
$733$	8.88641e14	0.155115	0.0775576	−	0.996988i	$-0.475288\pi$
$733$	8.88641e14	0.155115	0.0775576	+	0.996988i	$0.475288\pi$
$734$	4.15069e15	0.719104
$735$	1.79769e15	0.309125
$736$	−3.26639e14	−0.0557494
$737$	−3.69677e14	−0.0626256
$738$	−3.26898e14	−0.0549670
$739$	6.81741e15	1.13782	0.568912	−	0.822398i	$-0.307364\pi$
$739$	6.81741e15	1.13782	0.568912	+	0.822398i	$0.307364\pi$
$740$	−1.66143e14	−0.0275237
$741$	−8.75853e14	−0.144023
$742$	1.30231e15	0.212565
$743$	−6.50528e15	−1.05397	−0.526984	−	0.849875i	$-0.676677\pi$
$743$	−6.50528e15	−1.05397	−0.526984	+	0.849875i	$0.676677\pi$
$744$	1.04167e15	0.167525
$745$	2.01510e15	0.321689
$746$	1.64310e14	0.0260376
$747$	1.49480e15	0.235136
$748$	−3.75332e14	−0.0586080
$749$	6.35770e15	0.985485
$750$	1.16563e15	0.179360
$751$	1.02212e16	1.56129	0.780643	−	0.624977i	$-0.214892\pi$
$751$	1.02212e16	1.56129	0.780643	+	0.624977i	$0.214892\pi$
$752$	2.21908e15	0.336492
$753$	−4.48234e15	−0.674733
$754$	−8.51205e14	−0.127201
$755$	1.60095e14	0.0237503
$756$	1.20040e15	0.176789
$757$	2.22230e15	0.324919	0.162459	−	0.986715i	$-0.448057\pi$
$757$	2.22230e15	0.324919	0.162459	+	0.986715i	$0.448057\pi$
$758$	6.00393e14	0.0871475
$759$	6.72162e14	0.0968599
$760$	1.27790e14	0.0182820
$761$	1.29775e16	1.84321	0.921605	−	0.388129i	$-0.126879\pi$
$761$	1.29775e16	1.84321	0.921605	+	0.388129i	$0.126879\pi$
$762$	−3.24926e15	−0.458175
$763$	6.19645e15	0.867477
$764$	3.95068e15	0.549109
$765$	−1.19966e14	−0.0165547
$766$	−3.39425e15	−0.465035
$767$	−6.11226e15	−0.831433
$768$	−2.67181e14	−0.0360844
$769$	−1.41051e15	−0.189139	−0.0945693	−	0.995518i	$-0.530147\pi$
$769$	−1.41051e15	−0.189139	−0.0945693	+	0.995518i	$0.530147\pi$
$770$	1.17000e15	0.155771
$771$	−6.36418e14	−0.0841286
$772$	−2.88610e15	−0.378805
$773$	1.05466e15	0.137443	0.0687217	−	0.997636i	$-0.478108\pi$
$773$	1.05466e15	0.137443	0.0687217	+	0.997636i	$0.478108\pi$
$774$	−1.19335e15	−0.154416
$775$	−6.06320e15	−0.779009
$776$	3.74455e15	0.477705
$777$	2.04509e15	0.259058
$778$	3.34411e15	0.420623
$779$	4.28368e14	0.0535009
$780$	5.70484e14	0.0707495
$781$	5.20336e15	0.640772
$782$	−4.01823e14	−0.0491358
$783$	−2.62208e14	−0.0318388
$784$	4.92524e15	0.593867
$785$	−1.44856e14	−0.0173441
$786$	−5.92933e15	−0.704987
$787$	−5.80215e15	−0.685059	−0.342530	−	0.939507i	$-0.611284\pi$
$787$	−5.80215e15	−0.685059	−0.342530	+	0.939507i	$0.611284\pi$
$788$	3.27568e14	0.0384068
$789$	−1.26794e14	−0.0147630
$790$	−1.50975e15	−0.174565
$791$	−7.55516e15	−0.867507
$792$	5.49809e14	0.0626936
$793$	5.17329e15	0.585820
$794$	−6.39100e15	−0.718714
$795$	1.90654e14	0.0212924
$796$	−7.34626e15	−0.814788
$797$	1.27896e16	1.40876	0.704381	−	0.709822i	$-0.251225\pi$
$797$	1.27896e16	1.40876	0.704381	+	0.709822i	$0.251225\pi$
$798$	−1.57301e15	−0.172074
$799$	2.72985e15	0.296573
$800$	1.55516e15	0.167796
$801$	2.37891e15	0.254917
$802$	9.57497e15	1.01901
$803$	−2.22984e15	−0.235688
$804$	−3.23728e14	−0.0339838
$805$	1.25258e15	0.130595
$806$	−6.09372e15	−0.631015
$807$	1.03922e16	1.06882
$808$	−4.35150e15	−0.444505
$809$	2.15092e15	0.218226	0.109113	−	0.994029i	$-0.465199\pi$
$809$	2.15092e15	0.218226	0.109113	+	0.994029i	$0.465199\pi$
$810$	1.75734e14	0.0177088
$811$	−8.83221e15	−0.884005	−0.442002	−	0.897014i	$-0.645732\pi$
$811$	−8.83221e15	−0.884005	−0.442002	+	0.897014i	$0.645732\pi$
$812$	−1.52874e15	−0.151976
$813$	−2.08825e15	−0.206198
$814$	9.36699e14	0.0918683
$815$	3.41419e15	0.332598
$816$	−3.28680e14	−0.0318036
$817$	1.56377e15	0.150297
$818$	−7.22276e15	−0.689541
$819$	−7.02224e15	−0.665908
$820$	−2.79016e14	−0.0262817
$821$	1.49848e15	0.140205	0.0701025	−	0.997540i	$-0.477667\pi$
$821$	1.49848e15	0.140205	0.0701025	+	0.997540i	$0.477667\pi$
$822$	2.92179e15	0.271553
$823$	−1.25236e16	−1.15619	−0.578094	−	0.815970i	$-0.696203\pi$
$823$	−1.25236e16	−1.15619	−0.578094	+	0.815970i	$0.696203\pi$
$824$	2.14494e15	0.196705
$825$	−3.20023e15	−0.291531
$826$	−1.09774e16	−0.993369
$827$	7.65998e14	0.0688569	0.0344284	−	0.999407i	$-0.489039\pi$
$827$	7.65998e14	0.0688569	0.0344284	+	0.999407i	$0.489039\pi$
$828$	5.88614e14	0.0525610
$829$	1.00407e16	0.890664	0.445332	−	0.895366i	$-0.353086\pi$
$829$	1.00407e16	0.890664	0.445332	+	0.895366i	$0.353086\pi$
$830$	1.27585e15	0.112427
$831$	−1.31947e15	−0.115503
$832$	1.56299e15	0.135918
$833$	6.05890e15	0.523415
$834$	−3.39624e15	−0.291464
$835$	−2.85791e15	−0.243653
$836$	−7.20472e14	−0.0610215
$837$	−1.87713e15	−0.157944
$838$	4.25104e15	0.355347
$839$	−3.45775e15	−0.287146	−0.143573	−	0.989640i	$-0.545859\pi$
$839$	−3.45775e15	−0.287146	−0.143573	+	0.989640i	$0.545859\pi$
$840$	1.02457e15	0.0845292
$841$	−1.18666e16	−0.972630
$842$	7.50836e15	0.611405
$843$	−1.21932e15	−0.0986426
$844$	−4.16040e15	−0.334389
$845$	−5.14642e14	−0.0410954
$846$	−3.99885e15	−0.317248
$847$	1.67127e16	1.31731
$848$	5.22346e14	0.0409054
$849$	9.58200e15	0.745528
$850$	1.91312e15	0.147890
$851$	1.00281e15	0.0770205
$852$	4.55660e15	0.347715
$853$	−1.38092e16	−1.04700	−0.523501	−	0.852025i	$-0.675374\pi$
$853$	−1.38092e16	−1.04700	−0.523501	+	0.852025i	$0.675374\pi$
$854$	9.29107e15	0.699918
$855$	−2.30283e14	−0.0172364
$856$	2.55002e15	0.189644
$857$	−1.97762e16	−1.46133	−0.730666	−	0.682735i	$-0.760790\pi$
$857$	−1.97762e16	−1.46133	−0.730666	+	0.682735i	$0.760790\pi$
$858$	−3.21634e15	−0.236147
$859$	1.40367e16	1.02401	0.512003	−	0.858984i	$-0.328904\pi$
$859$	1.40367e16	1.02401	0.512003	+	0.858984i	$0.328904\pi$
$860$	−1.01856e15	−0.0738318
$861$	3.43448e15	0.247368
$862$	−8.94734e15	−0.640330
$863$	−2.52332e16	−1.79438	−0.897188	−	0.441648i	$-0.854394\pi$
$863$	−2.52332e16	−1.79438	−0.897188	+	0.441648i	$0.854394\pi$
$864$	4.81469e14	0.0340207
$865$	−6.81354e14	−0.0478392
$866$	−6.46694e15	−0.451181
$867$	7.92374e15	0.549320
$868$	−1.09441e16	−0.753916
$869$	8.51185e15	0.582660
$870$	−2.23802e14	−0.0152233
$871$	1.89378e15	0.128006
$872$	2.48535e15	0.166935
$873$	−6.74780e15	−0.450385
$874$	−7.71323e14	−0.0511592
$875$	−1.22465e16	−0.807176
$876$	−1.95268e15	−0.127896
$877$	−1.47015e15	−0.0956895	−0.0478447	−	0.998855i	$-0.515235\pi$
$877$	−1.47015e15	−0.0956895	−0.0478447	+	0.998855i	$0.515235\pi$
$878$	1.68066e16	1.08708
$879$	7.03378e15	0.452116
$880$	4.69277e14	0.0299761
$881$	−7.39238e15	−0.469263	−0.234632	−	0.972084i	$-0.575388\pi$
$881$	−7.39238e15	−0.469263	−0.234632	+	0.972084i	$0.575388\pi$
$882$	−8.87544e15	−0.559903
$883$	−2.62622e16	−1.64645	−0.823223	−	0.567719i	$-0.807826\pi$
$883$	−2.62622e16	−1.64645	−0.823223	+	0.567719i	$0.807826\pi$
$884$	1.92275e15	0.119794
$885$	−1.60706e15	−0.0995047
$886$	−1.04939e16	−0.645731
$887$	2.88943e16	1.76698	0.883491	−	0.468449i	$-0.155187\pi$
$887$	2.88943e16	1.76698	0.883491	+	0.468449i	$0.155187\pi$
$888$	8.20270e14	0.0498523
$889$	3.41377e16	2.06193
$890$	2.03047e15	0.121885
$891$	−9.90773e14	−0.0591081
$892$	4.77919e15	0.283366
$893$	5.24012e15	0.308786
$894$	−9.94882e15	−0.582660
$895$	6.93536e14	0.0403685
$896$	2.80709e15	0.162391
$897$	−3.44335e15	−0.197981
$898$	−3.91697e15	−0.223836
$899$	2.39058e15	0.135776
$900$	−2.80246e15	−0.158199
$901$	6.42576e14	0.0360527
$902$	1.57307e15	0.0877228
$903$	1.25377e16	0.694919
$904$	−3.03031e15	−0.166940
$905$	−6.72711e15	−0.368351
$906$	−7.90411e14	−0.0430178
$907$	9.60114e14	0.0519377	0.0259688	−	0.999663i	$-0.491733\pi$
$907$	9.60114e14	0.0519377	0.0259688	+	0.999663i	$0.491733\pi$
$908$	8.27405e15	0.444883
$909$	7.84155e15	0.419084
$910$	−5.99368e15	−0.318395
$911$	1.16460e16	0.614931	0.307466	−	0.951559i	$-0.400519\pi$
$911$	1.16460e16	0.614931	0.307466	+	0.951559i	$0.400519\pi$
$912$	−6.30920e14	−0.0331133
$913$	−7.19315e15	−0.375258
$914$	−1.91849e16	−0.994843
$915$	1.36018e15	0.0701101
$916$	−1.03744e16	−0.531541
$917$	6.22953e16	3.17266
$918$	5.92291e14	0.0299848
$919$	5.12286e15	0.257796	0.128898	−	0.991658i	$-0.458856\pi$
$919$	5.12286e15	0.257796	0.128898	+	0.991658i	$0.458856\pi$
$920$	5.02399e14	0.0251313
$921$	8.04579e15	0.400074
$922$	−9.79524e15	−0.484167
$923$	−2.66558e16	−1.30973
$924$	−5.77646e15	−0.282141
$925$	−4.77449e15	−0.231818
$926$	−9.77957e15	−0.472019
$927$	−3.86525e15	−0.185455
$928$	−6.13164e14	−0.0292458
$929$	−4.03636e15	−0.191383	−0.0956915	−	0.995411i	$-0.530506\pi$
$929$	−4.03636e15	−0.191383	−0.0956915	+	0.995411i	$0.530506\pi$
$930$	−1.60218e15	−0.0755190
$931$	1.16304e16	0.544969
$932$	1.01839e16	0.474382
$933$	−1.80879e16	−0.837607
$934$	−2.64423e16	−1.21728
$935$	5.77293e14	0.0264200
$936$	−2.81656e15	−0.128145
$937$	−4.04911e16	−1.83144	−0.915719	−	0.401820i	$-0.868378\pi$
$937$	−4.04911e16	−1.83144	−0.915719	+	0.401820i	$0.868378\pi$
$938$	3.40118e15	0.152938
$939$	1.28543e16	0.574630
$940$	−3.41314e15	−0.151688
$941$	2.03868e16	0.900755	0.450378	−	0.892838i	$-0.351289\pi$
$941$	2.03868e16	0.900755	0.450378	+	0.892838i	$0.351289\pi$
$942$	7.15173e14	0.0314146
$943$	1.68410e15	0.0735450
$944$	−4.40296e15	−0.191161
$945$	−1.84631e15	−0.0796949
$946$	5.74253e15	0.246435
$947$	−1.07658e16	−0.459325	−0.229662	−	0.973270i	$-0.573762\pi$
$947$	−1.07658e16	−0.459325	−0.229662	+	0.973270i	$0.573762\pi$
$948$	7.45386e15	0.316181
$949$	1.14230e16	0.481745
$950$	3.67235e15	0.153980
$951$	−2.55639e16	−1.06570
$952$	3.45321e15	0.143126
$953$	−3.70615e16	−1.52726	−0.763629	−	0.645655i	$-0.776584\pi$
$953$	−3.70615e16	−1.52726	−0.763629	+	0.645655i	$0.776584\pi$
$954$	−9.41284e14	−0.0385660
$955$	−6.07649e15	−0.247534
$956$	2.75416e15	0.111550
$957$	1.26178e15	0.0508121
$958$	−2.23500e16	−0.894886
$959$	−3.06972e16	−1.22207
$960$	4.10948e14	0.0162665
$961$	−8.29449e15	−0.326446
$962$	−4.79852e15	−0.187778
$963$	−4.59522e15	−0.178798
$964$	1.56236e16	0.604444
$965$	4.43906e15	0.170762
$966$	−6.18416e15	−0.236541
$967$	−2.62211e16	−0.997253	−0.498627	−	0.866817i	$-0.666162\pi$
$967$	−2.62211e16	−0.997253	−0.498627	+	0.866817i	$0.666162\pi$
$968$	6.70335e15	0.253500
$969$	−7.76141e14	−0.0291850
$970$	−5.75944e15	−0.215345
$971$	−3.99758e16	−1.48625	−0.743124	−	0.669154i	$-0.766657\pi$
$971$	−3.99758e16	−1.48625	−0.743124	+	0.669154i	$0.766657\pi$
$972$	−8.67624e14	−0.0320750
$973$	3.56819e16	1.31168
$974$	−1.14689e16	−0.419224
$975$	1.63942e16	0.595887
$976$	3.72657e15	0.134690
$977$	4.56719e15	0.164146	0.0820728	−	0.996626i	$-0.473846\pi$
$977$	4.56719e15	0.164146	0.0820728	+	0.996626i	$0.473846\pi$
$978$	−1.68563e16	−0.602420
$979$	−1.14476e16	−0.406827
$980$	−7.57544e15	−0.267710
$981$	−4.47867e15	−0.157387
$982$	−1.38432e16	−0.483752
$983$	−3.50209e16	−1.21698	−0.608489	−	0.793562i	$-0.708224\pi$
$983$	−3.50209e16	−1.21698	−0.608489	+	0.793562i	$0.708224\pi$
$984$	1.37754e15	0.0476028
$985$	−5.03828e14	−0.0173134
$986$	−7.54299e14	−0.0257763
$987$	4.20132e16	1.42771
$988$	3.69084e15	0.124727
$989$	6.14784e15	0.206606
$990$	−8.45653e14	−0.0282617
$991$	−4.91086e16	−1.63212	−0.816060	−	0.577967i	$-0.803846\pi$
$991$	−4.91086e16	−1.63212	−0.816060	+	0.577967i	$0.803846\pi$
$992$	−4.38961e15	−0.145081
$993$	2.29282e16	0.753614
$994$	−4.78730e16	−1.56482
$995$	1.12992e16	0.367299
$996$	−6.29907e15	−0.203634
$997$	−2.85344e16	−0.917370	−0.458685	−	0.888599i	$-0.651679\pi$
$997$	−2.85344e16	−0.917370	−0.458685	+	0.888599i	$0.651679\pi$
$998$	1.68166e16	0.537676
$999$	−1.47815e15	−0.0470012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.12.a.a.1.1	✓	1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.12.a.a.1.1	✓	1	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	114.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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