LMFDB - Embedded newform 14.14.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,14,Mod(1,14)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("14.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	14.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$15.0123300533$
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	$\chi$	$=$	14.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$

$=$

\(q-64.0000 q^{2} +1626.00 q^{3} +4096.00 q^{4} -36400.0 q^{5} -104064. q^{6} -117649. q^{7} -262144. q^{8} +1.04955e6 q^{9} +2.32960e6 q^{10} +2.60529e6 q^{11} +6.66010e6 q^{12} -1.26245e7 q^{13} +7.52954e6 q^{14} -5.91864e7 q^{15} +1.67772e7 q^{16} -1.30752e8 q^{17} -6.71714e7 q^{18} -2.49436e8 q^{19} -1.49094e8 q^{20} -1.91297e8 q^{21} -1.66738e8 q^{22} +4.89054e8 q^{23} -4.26246e8 q^{24} +1.04257e8 q^{25} +8.07966e8 q^{26} -8.85796e8 q^{27} -4.81890e8 q^{28} -1.12116e8 q^{29} +3.78793e9 q^{30} -9.10307e9 q^{31} -1.07374e9 q^{32} +4.23620e9 q^{33} +8.36815e9 q^{34} +4.28242e9 q^{35} +4.29897e9 q^{36} +1.83082e10 q^{37} +1.59639e10 q^{38} -2.05274e10 q^{39} +9.54204e9 q^{40} +1.30824e10 q^{41} +1.22430e10 q^{42} -6.71235e10 q^{43} +1.06713e10 q^{44} -3.82037e10 q^{45} -3.12995e10 q^{46} +1.05240e11 q^{47} +2.72798e10 q^{48} +1.38413e10 q^{49} -6.67244e9 q^{50} -2.12603e11 q^{51} -5.17098e10 q^{52} -2.52217e10 q^{53} +5.66909e10 q^{54} -9.48325e10 q^{55} +3.08410e10 q^{56} -4.05583e11 q^{57} +7.17542e9 q^{58} -2.76775e11 q^{59} -2.42427e11 q^{60} +7.59389e11 q^{61} +5.82596e11 q^{62} -1.23479e11 q^{63} +6.87195e10 q^{64} +4.59531e11 q^{65} -2.71117e11 q^{66} +1.03966e12 q^{67} -5.35562e11 q^{68} +7.95202e11 q^{69} -2.74075e11 q^{70} +1.81709e12 q^{71} -2.75134e11 q^{72} +4.00342e11 q^{73} -1.17172e12 q^{74} +1.69522e11 q^{75} -1.02169e12 q^{76} -3.06510e11 q^{77} +1.31375e12 q^{78} -3.59780e12 q^{79} -6.10691e11 q^{80} -3.11363e12 q^{81} -8.37272e11 q^{82} -1.30903e12 q^{83} -7.83554e11 q^{84} +4.75939e12 q^{85} +4.29590e12 q^{86} -1.82300e11 q^{87} -6.82961e11 q^{88} +1.65329e12 q^{89} +2.44504e12 q^{90} +1.48526e12 q^{91} +2.00317e12 q^{92} -1.48016e13 q^{93} -6.73536e12 q^{94} +9.07947e12 q^{95} -1.74590e12 q^{96} -1.27369e13 q^{97} -8.85842e11 q^{98} +2.73439e12 q^{99} +O(q^{100})\)

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 $

$2$	−64.0000	−0.707107
$2$	−64.0000	−0.707107
$3$	1626.00	1.28775	0.643876	−	0.765130i	$-0.277325\pi$
$3$	1626.00	1.28775	0.643876	+	0.765130i	$0.277325\pi$
$4$	4096.00	0.500000
$5$	−36400.0	−1.04183	−0.520914	−	0.853609i	$-0.674409\pi$
$5$	−36400.0	−1.04183	−0.520914	+	0.853609i	$0.674409\pi$
$6$	−104064.	−0.910578
$7$	−117649.	−0.377964
$7$	−117649.	−0.377964
$8$	−262144.	−0.353553
$9$	1.04955e6	0.658306
$10$	2.32960e6	0.736684
$11$	2.60529e6	0.443408	0.221704	−	0.975114i	$-0.428838\pi$
$11$	2.60529e6	0.443408	0.221704	+	0.975114i	$0.428838\pi$
$12$	6.66010e6	0.643876
$13$	−1.26245e7	−0.725406	−0.362703	−	0.931905i	$-0.618146\pi$
$13$	−1.26245e7	−0.725406	−0.362703	+	0.931905i	$0.618146\pi$
$14$	7.52954e6	0.267261
$15$	−5.91864e7	−1.34162
$16$	1.67772e7	0.250000
$17$	−1.30752e8	−1.31381	−0.656903	−	0.753975i	$-0.728134\pi$
$17$	−1.30752e8	−1.31381	−0.656903	+	0.753975i	$0.728134\pi$
$18$	−6.71714e7	−0.465493
$19$	−2.49436e8	−1.21636	−0.608178	−	0.793801i	$-0.708099\pi$
$19$	−2.49436e8	−1.21636	−0.608178	+	0.793801i	$0.708099\pi$
$20$	−1.49094e8	−0.520914
$21$	−1.91297e8	−0.486725
$22$	−1.66738e8	−0.313537
$23$	4.89054e8	0.688852	0.344426	−	0.938813i	$-0.388074\pi$
$23$	4.89054e8	0.688852	0.344426	+	0.938813i	$0.388074\pi$
$24$	−4.26246e8	−0.455289
$25$	1.04257e8	0.0854072
$26$	8.07966e8	0.512940
$27$	−8.85796e8	−0.440017
$28$	−4.81890e8	−0.188982
$29$	−1.12116e8	−0.0350010	−0.0175005	−	0.999847i	$-0.505571\pi$
$29$	−1.12116e8	−0.0350010	−0.0175005	+	0.999847i	$0.505571\pi$
$30$	3.78793e9	0.948667
$31$	−9.10307e9	−1.84220	−0.921100	−	0.389326i	$-0.872708\pi$
$31$	−9.10307e9	−1.84220	−0.921100	+	0.389326i	$0.872708\pi$
$32$	−1.07374e9	−0.176777
$33$	4.23620e9	0.570999
$34$	8.36815e9	0.929002
$35$	4.28242e9	0.393774
$36$	4.29897e9	0.329153
$37$	1.83082e10	1.17310	0.586548	−	0.809914i	$-0.300486\pi$
$37$	1.83082e10	1.17310	0.586548	+	0.809914i	$0.300486\pi$
$38$	1.59639e10	0.860094
$39$	−2.05274e10	−0.934144
$40$	9.54204e9	0.368342
$41$	1.30824e10	0.430122	0.215061	−	0.976601i	$-0.431005\pi$
$41$	1.30824e10	0.430122	0.215061	+	0.976601i	$0.431005\pi$
$42$	1.22430e10	0.344166
$43$	−6.71235e10	−1.61931	−0.809654	−	0.586908i	$-0.800345\pi$
$43$	−6.71235e10	−1.61931	−0.809654	+	0.586908i	$0.800345\pi$
$44$	1.06713e10	0.221704
$45$	−3.82037e10	−0.685843
$46$	−3.12995e10	−0.487092
$47$	1.05240e11	1.42411	0.712057	−	0.702122i	$-0.247764\pi$
$47$	1.05240e11	1.42411	0.712057	+	0.702122i	$0.247764\pi$
$48$	2.72798e10	0.321938
$49$	1.38413e10	0.142857
$50$	−6.67244e9	−0.0603920
$51$	−2.12603e11	−1.69186
$52$	−5.17098e10	−0.362703
$53$	−2.52217e10	−0.156308	−0.0781541	−	0.996941i	$-0.524903\pi$
$53$	−2.52217e10	−0.156308	−0.0781541	+	0.996941i	$0.524903\pi$
$54$	5.66909e10	0.311139
$55$	−9.48325e10	−0.461955
$56$	3.08410e10	0.133631
$57$	−4.05583e11	−1.56637
$58$	7.17542e9	0.0247494
$59$	−2.76775e11	−0.854256	−0.427128	−	0.904191i	$-0.640475\pi$
$59$	−2.76775e11	−0.854256	−0.427128	+	0.904191i	$0.640475\pi$
$60$	−2.42427e11	−0.670809
$61$	7.59389e11	1.88721	0.943605	−	0.331074i	$-0.107411\pi$
$61$	7.59389e11	1.88721	0.943605	+	0.331074i	$0.107411\pi$
$62$	5.82596e11	1.30263
$63$	−1.23479e11	−0.248816
$64$	6.87195e10	0.125000
$65$	4.59531e11	0.755749
$66$	−2.71117e11	−0.403758
$67$	1.03966e12	1.40413	0.702065	−	0.712113i	$-0.252262\pi$
$67$	1.03966e12	1.40413	0.702065	+	0.712113i	$0.252262\pi$
$68$	−5.35562e11	−0.656903
$69$	7.95202e11	0.887071
$70$	−2.74075e11	−0.278440
$71$	1.81709e12	1.68343	0.841717	−	0.539918i	$-0.181545\pi$
$71$	1.81709e12	1.68343	0.841717	+	0.539918i	$0.181545\pi$
$72$	−2.75134e11	−0.232746
$73$	4.00342e11	0.309623	0.154811	−	0.987944i	$-0.450523\pi$
$73$	4.00342e11	0.309623	0.154811	+	0.987944i	$0.450523\pi$
$74$	−1.17172e12	−0.829504
$75$	1.69522e11	0.109983
$76$	−1.02169e12	−0.608178
$77$	−3.06510e11	−0.167592
$78$	1.31375e12	0.660539
$79$	−3.59780e12	−1.66518	−0.832589	−	0.553891i	$-0.813142\pi$
$79$	−3.59780e12	−1.66518	−0.832589	+	0.553891i	$0.813142\pi$
$80$	−6.10691e11	−0.260457
$81$	−3.11363e12	−1.22494
$82$	−8.37272e11	−0.304142
$83$	−1.30903e12	−0.439483	−0.219742	−	0.975558i	$-0.570521\pi$
$83$	−1.30903e12	−0.439483	−0.219742	+	0.975558i	$0.570521\pi$
$84$	−7.83554e11	−0.243362
$85$	4.75939e12	1.36876
$86$	4.29590e12	1.14502
$87$	−1.82300e11	−0.0450726
$88$	−6.82961e11	−0.156768
$89$	1.65329e12	0.352625	0.176313	−	0.984334i	$-0.443583\pi$
$89$	1.65329e12	0.352625	0.176313	+	0.984334i	$0.443583\pi$
$90$	2.44504e12	0.484964
$91$	1.48526e12	0.274178
$92$	2.00317e12	0.344426
$93$	−1.48016e13	−2.37230
$94$	−6.73536e12	−1.00700
$95$	9.07947e12	1.26723
$96$	−1.74590e12	−0.227645
$97$	−1.27369e13	−1.55256	−0.776279	−	0.630390i	$-0.782895\pi$
$97$	−1.27369e13	−1.55256	−0.776279	+	0.630390i	$0.782895\pi$
$98$	−8.85842e11	−0.101015
$99$	2.73439e12	0.291898
$100$	4.27036e11	0.0427036
$101$	9.55627e11	0.0895776	0.0447888	−	0.998996i	$-0.485739\pi$
$101$	9.55627e11	0.0895776	0.0447888	+	0.998996i	$0.485739\pi$
$102$	1.36066e13	1.19632
$103$	6.32113e11	0.0521618	0.0260809	−	0.999660i	$-0.491697\pi$
$103$	6.32113e11	0.0521618	0.0260809	+	0.999660i	$0.491697\pi$
$104$	3.30943e12	0.256470
$105$	6.96322e12	0.507084
$106$	1.61419e12	0.110527
$107$	5.45940e12	0.351682	0.175841	−	0.984419i	$-0.443736\pi$
$107$	5.45940e12	0.351682	0.175841	+	0.984419i	$0.443736\pi$
$108$	−3.62822e12	−0.220008
$109$	−1.08453e12	−0.0619395	−0.0309698	−	0.999520i	$-0.509860\pi$
$109$	−1.08453e12	−0.0619395	−0.0309698	+	0.999520i	$0.509860\pi$
$110$	6.06928e12	0.326651
$111$	2.97691e13	1.51066
$112$	−1.97382e12	−0.0944911
$113$	−1.49550e13	−0.675733	−0.337867	−	0.941194i	$-0.609705\pi$
$113$	−1.49550e13	−0.675733	−0.337867	+	0.941194i	$0.609705\pi$
$114$	2.59573e13	1.10759
$115$	−1.78016e13	−0.717666
$116$	−4.59227e11	−0.0175005
$117$	−1.32500e13	−0.477540
$118$	1.77136e13	0.604050
$119$	1.53829e13	0.496572
$120$	1.55154e13	0.474333
$121$	−2.77352e13	−0.803390
$122$	−4.86009e13	−1.33446
$123$	2.12719e13	0.553890
$124$	−3.72862e13	−0.921100
$125$	4.06386e13	0.952849
$126$	7.90265e12	0.175940
$127$	−3.30223e13	−0.698366	−0.349183	−	0.937054i	$-0.613541\pi$
$127$	−3.30223e13	−0.698366	−0.349183	+	0.937054i	$0.613541\pi$
$128$	−4.39805e12	−0.0883883
$129$	−1.09143e14	−2.08527
$130$	−2.94100e13	−0.534395
$131$	−4.33190e13	−0.748885	−0.374443	−	0.927250i	$-0.622166\pi$
$131$	−4.33190e13	−0.748885	−0.374443	+	0.927250i	$0.622166\pi$
$132$	1.73515e13	0.285500
$133$	2.93459e13	0.459739
$134$	−6.65385e13	−0.992869
$135$	3.22430e13	0.458422
$136$	3.42759e13	0.464501
$137$	1.20048e14	1.55121	0.775606	−	0.631217i	$-0.217444\pi$
$137$	1.20048e14	1.55121	0.775606	+	0.631217i	$0.217444\pi$
$138$	−5.08929e13	−0.627254
$139$	−2.21339e13	−0.260293	−0.130146	−	0.991495i	$-0.541545\pi$
$139$	−2.21339e13	−0.260293	−0.130146	+	0.991495i	$0.541545\pi$
$140$	1.75408e13	0.196887
$141$	1.71120e14	1.83391
$142$	−1.16294e14	−1.19037
$143$	−3.28904e13	−0.321651
$144$	1.76086e13	0.164577
$145$	4.08102e12	0.0364650
$146$	−2.56219e13	−0.218936
$147$	2.25059e13	0.183965
$148$	7.49903e13	0.586548
$149$	−5.37812e13	−0.402643	−0.201321	−	0.979525i	$-0.564524\pi$
$149$	−5.37812e13	−0.402643	−0.201321	+	0.979525i	$0.564524\pi$
$150$	−1.08494e13	−0.0777700
$151$	2.03010e14	1.39369	0.696845	−	0.717222i	$-0.254586\pi$
$151$	2.03010e14	1.39369	0.696845	+	0.717222i	$0.254586\pi$
$152$	6.53882e13	0.430047
$153$	−1.37232e14	−0.864887
$154$	1.96166e13	0.118506
$155$	3.31352e14	1.91926
$156$	−8.40802e13	−0.467072
$157$	−3.02016e14	−1.60947	−0.804734	−	0.593635i	$-0.797692\pi$
$157$	−3.02016e14	−1.60947	−0.804734	+	0.593635i	$0.797692\pi$
$158$	2.30259e14	1.17746
$159$	−4.10105e13	−0.201286
$160$	3.90842e13	0.184171
$161$	−5.75367e13	−0.260362
$162$	1.99272e14	0.866163
$163$	2.97351e13	0.124180	0.0620898	−	0.998071i	$-0.480223\pi$
$163$	2.97351e13	0.124180	0.0620898	+	0.998071i	$0.480223\pi$
$164$	5.35854e13	0.215061
$165$	−1.54198e14	−0.594884
$166$	8.37780e13	0.310761
$167$	2.27827e14	0.812732	0.406366	−	0.913710i	$-0.366796\pi$
$167$	2.27827e14	0.812732	0.406366	+	0.913710i	$0.366796\pi$
$168$	5.01474e13	0.172083
$169$	−1.43498e14	−0.473786
$170$	−3.04601e14	−0.967861
$171$	−2.61796e14	−0.800735
$172$	−2.74938e14	−0.809654
$173$	−3.07503e14	−0.872066	−0.436033	−	0.899931i	$-0.643617\pi$
$173$	−3.07503e14	−0.872066	−0.436033	+	0.899931i	$0.643617\pi$
$174$	1.16672e13	0.0318711
$175$	−1.22657e13	−0.0322809
$176$	4.37095e13	0.110852
$177$	−4.50036e14	−1.10007
$178$	−1.05810e14	−0.249344
$179$	−3.72906e14	−0.847334	−0.423667	−	0.905818i	$-0.639257\pi$
$179$	−3.72906e14	−0.847334	−0.423667	+	0.905818i	$0.639257\pi$
$180$	−1.56482e14	−0.342921
$181$	1.03356e14	0.218487	0.109244	−	0.994015i	$-0.465157\pi$
$181$	1.03356e14	0.218487	0.109244	+	0.994015i	$0.465157\pi$
$182$	−9.50564e13	−0.193873
$183$	1.23477e15	2.43026
$184$	−1.28203e14	−0.243546
$185$	−6.66417e14	−1.22217
$186$	9.47302e14	1.67747
$187$	−3.40648e14	−0.582552
$188$	4.31063e14	0.712057
$189$	1.04213e14	0.166311
$190$	−5.81086e14	−0.896070
$191$	1.06898e15	1.59314	0.796570	−	0.604546i	$-0.206646\pi$
$191$	1.06898e15	1.59314	0.796570	+	0.604546i	$0.206646\pi$
$192$	1.11738e14	0.160969
$193$	−8.32297e14	−1.15919	−0.579596	−	0.814904i	$-0.696790\pi$
$193$	−8.32297e14	−1.15919	−0.579596	+	0.814904i	$0.696790\pi$
$194$	8.15162e14	1.09782
$195$	7.47197e14	0.973218
$196$	5.66939e13	0.0714286
$197$	−1.07329e15	−1.30823	−0.654117	−	0.756394i	$-0.726960\pi$
$197$	−1.07329e15	−1.30823	−0.654117	+	0.756394i	$0.726960\pi$
$198$	−1.75001e14	−0.206403
$199$	−7.90785e14	−0.902638	−0.451319	−	0.892363i	$-0.649046\pi$
$199$	−7.90785e14	−0.902638	−0.451319	+	0.892363i	$0.649046\pi$
$200$	−2.73303e13	−0.0301960
$201$	1.69049e15	1.80817
$202$	−6.11601e13	−0.0633409
$203$	1.31903e13	0.0132291
$204$	−8.70823e14	−0.845929
$205$	−4.76198e14	−0.448113
$206$	−4.04552e13	−0.0368840
$207$	5.13288e14	0.453476
$208$	−2.11803e14	−0.181352
$209$	−6.49853e14	−0.539342
$210$	−4.45646e14	−0.358562
$211$	−8.38652e14	−0.654253	−0.327127	−	0.944981i	$-0.606080\pi$
$211$	−8.38652e14	−0.654253	−0.327127	+	0.944981i	$0.606080\pi$
$212$	−1.03308e14	−0.0781541
$213$	2.95458e15	2.16785
$214$	−3.49401e14	−0.248677
$215$	2.44329e15	1.68704
$216$	2.32206e14	0.155569
$217$	1.07097e15	0.696286
$218$	6.94097e13	0.0437979
$219$	6.50956e14	0.398717
$220$	−3.88434e14	−0.230977
$221$	1.65068e15	0.953044
$222$	−1.90522e15	−1.06820
$223$	−1.97980e15	−1.07805	−0.539026	−	0.842289i	$-0.681208\pi$
$223$	−1.97980e15	−1.07805	−0.539026	+	0.842289i	$0.681208\pi$
$224$	1.26325e14	0.0668153
$225$	1.09423e14	0.0562241
$226$	9.57117e14	0.477816
$227$	5.88094e13	0.0285285	0.0142642	−	0.999898i	$-0.495459\pi$
$227$	5.88094e13	0.0285285	0.0142642	+	0.999898i	$0.495459\pi$
$228$	−1.66127e15	−0.783183
$229$	−2.62300e15	−1.20190	−0.600948	−	0.799288i	$-0.705210\pi$
$229$	−2.62300e15	−1.20190	−0.600948	+	0.799288i	$0.705210\pi$
$230$	1.13930e15	0.507467
$231$	−4.98384e14	−0.215817
$232$	2.93905e13	0.0123747
$233$	1.51560e15	0.620543	0.310272	−	0.950648i	$-0.399580\pi$
$233$	1.51560e15	0.620543	0.310272	+	0.950648i	$0.399580\pi$
$234$	8.48003e14	0.337671
$235$	−3.83074e15	−1.48368
$236$	−1.13367e15	−0.427128
$237$	−5.85002e15	−2.14434
$238$	−9.84505e14	−0.351130
$239$	−1.14306e15	−0.396718	−0.198359	−	0.980129i	$-0.563561\pi$
$239$	−1.14306e15	−0.396718	−0.198359	+	0.980129i	$0.563561\pi$
$240$	−9.92983e14	−0.335404
$241$	3.44644e15	1.13308	0.566539	−	0.824035i	$-0.308282\pi$
$241$	3.44644e15	1.13308	0.566539	+	0.824035i	$0.308282\pi$
$242$	1.77505e15	0.568082
$243$	−3.65052e15	−1.13740
$244$	3.11046e15	0.943605
$245$	−5.03823e14	−0.148833
$246$	−1.36140e15	−0.391660
$247$	3.14900e15	0.882352
$248$	2.38631e15	0.651316
$249$	−2.12848e15	−0.565945
$250$	−2.60087e15	−0.673766
$251$	−6.23540e15	−1.57393	−0.786964	−	0.616999i	$-0.788348\pi$
$251$	−6.23540e15	−1.57393	−0.786964	+	0.616999i	$0.788348\pi$
$252$	−5.05769e14	−0.124408
$253$	1.27413e15	0.305442
$254$	2.11343e15	0.493820
$255$	7.73876e15	1.76263
$256$	2.81475e14	0.0625000
$257$	6.90707e15	1.49530	0.747650	−	0.664093i	$-0.231182\pi$
$257$	6.90707e15	1.49530	0.747650	+	0.664093i	$0.231182\pi$
$258$	6.98514e15	1.47451
$259$	−2.15394e15	−0.443389
$260$	1.88224e15	0.377875
$261$	−1.17672e14	−0.0230414
$262$	2.77242e15	0.529542
$263$	2.59151e15	0.482881	0.241440	−	0.970416i	$-0.422380\pi$
$263$	2.59151e15	0.482881	0.241440	+	0.970416i	$0.422380\pi$
$264$	−1.11049e15	−0.201879
$265$	9.18071e14	0.162846
$266$	−1.87814e15	−0.325085
$267$	2.68825e15	0.454094
$268$	4.25847e15	0.702065
$269$	−1.79933e15	−0.289548	−0.144774	−	0.989465i	$-0.546246\pi$
$269$	−1.79933e15	−0.289548	−0.144774	+	0.989465i	$0.546246\pi$
$270$	−2.06355e15	−0.324153
$271$	−2.02210e15	−0.310100	−0.155050	−	0.987907i	$-0.549554\pi$
$271$	−2.02210e15	−0.310100	−0.155050	+	0.987907i	$0.549554\pi$
$272$	−2.19366e15	−0.328452
$273$	2.41503e15	0.353073
$274$	−7.68307e15	−1.09687
$275$	2.71619e14	0.0378702
$276$	3.25715e15	0.443536
$277$	3.01889e15	0.401540	0.200770	−	0.979638i	$-0.435656\pi$
$277$	3.01889e15	0.401540	0.200770	+	0.979638i	$0.435656\pi$
$278$	1.41657e15	0.184055
$279$	−9.55415e15	−1.21273
$280$	−1.12261e15	−0.139220
$281$	−1.33443e16	−1.61698	−0.808490	−	0.588510i	$-0.799715\pi$
$281$	−1.33443e16	−1.61698	−0.808490	+	0.588510i	$0.799715\pi$
$282$	−1.09517e16	−1.29677
$283$	3.01223e15	0.348559	0.174279	−	0.984696i	$-0.444240\pi$
$283$	3.01223e15	0.348559	0.174279	+	0.984696i	$0.444240\pi$
$284$	7.44279e15	0.841717
$285$	1.47632e16	1.63188
$286$	2.10498e15	0.227441
$287$	−1.53913e15	−0.162571
$288$	−1.12695e15	−0.116373
$289$	7.19160e15	0.726089
$290$	−2.61185e14	−0.0257847
$291$	−2.07102e16	−1.99931
$292$	1.63980e15	0.154811
$293$	−2.13650e15	−0.197271	−0.0986355	−	0.995124i	$-0.531448\pi$
$293$	−2.13650e15	−0.197271	−0.0986355	+	0.995124i	$0.531448\pi$
$294$	−1.44038e15	−0.130083
$295$	1.00746e16	0.889989
$296$	−4.79938e15	−0.414752
$297$	−2.30775e15	−0.195107
$298$	3.44200e15	0.284711
$299$	−6.17405e15	−0.499698
$300$	6.94361e14	0.0549917
$301$	7.89701e15	0.612041
$302$	−1.29926e16	−0.985488
$303$	1.55385e15	0.115354
$304$	−4.18484e15	−0.304089
$305$	−2.76417e16	−1.96615
$306$	8.78282e15	0.611568
$307$	1.19582e16	0.815205	0.407602	−	0.913159i	$-0.366365\pi$
$307$	1.19582e16	0.815205	0.407602	+	0.913159i	$0.366365\pi$
$308$	−1.25546e15	−0.0837962
$309$	1.02782e15	0.0671715
$310$	−2.12065e16	−1.35712
$311$	−2.39264e16	−1.49946	−0.749730	−	0.661743i	$-0.769817\pi$
$311$	−2.39264e16	−1.49946	−0.749730	+	0.661743i	$0.769817\pi$
$312$	5.38113e15	0.330270
$313$	2.49550e16	1.50010	0.750049	−	0.661382i	$-0.230030\pi$
$313$	2.49550e16	1.50010	0.750049	+	0.661382i	$0.230030\pi$
$314$	1.93290e16	1.13807
$315$	4.49463e15	0.259224
$316$	−1.47366e16	−0.832589
$317$	2.96100e16	1.63891	0.819453	−	0.573147i	$-0.194278\pi$
$317$	2.96100e16	1.63891	0.819453	+	0.573147i	$0.194278\pi$
$318$	2.62467e15	0.142331
$319$	−2.92094e14	−0.0155197
$320$	−2.50139e15	−0.130229
$321$	8.87698e15	0.452879
$322$	3.68235e15	0.184103
$323$	3.26144e16	1.59806
$324$	−1.27534e16	−0.612470
$325$	−1.31619e15	−0.0619549
$326$	−1.90305e15	−0.0878082
$327$	−1.76344e15	−0.0797628
$328$	−3.42947e15	−0.152071
$329$	−1.23814e16	−0.538264
$330$	9.86865e15	0.420646
$331$	2.46215e16	1.02904	0.514521	−	0.857478i	$-0.327970\pi$
$331$	2.46215e16	1.02904	0.514521	+	0.857478i	$0.327970\pi$
$332$	−5.36179e15	−0.219742
$333$	1.92154e16	0.772257
$334$	−1.45809e16	−0.574689
$335$	−3.78438e16	−1.46286
$336$	−3.20944e15	−0.121681
$337$	2.57418e16	0.957292	0.478646	−	0.878008i	$-0.341128\pi$
$337$	2.57418e16	0.957292	0.478646	+	0.878008i	$0.341128\pi$
$338$	9.18387e15	0.335017
$339$	−2.43168e16	−0.870177
$340$	1.94944e16	0.684381
$341$	−2.37161e16	−0.816846
$342$	1.67550e16	0.566205
$343$	−1.62841e15	−0.0539949
$344$	1.75960e16	0.572512
$345$	−2.89454e16	−0.924176
$346$	1.96802e16	0.616644
$347$	3.18822e16	0.980407	0.490203	−	0.871608i	$-0.336922\pi$
$347$	3.18822e16	0.980407	0.490203	+	0.871608i	$0.336922\pi$
$348$	−7.46703e14	−0.0225363
$349$	1.35002e16	0.399923	0.199961	−	0.979804i	$-0.435918\pi$
$349$	1.35002e16	0.399923	0.199961	+	0.979804i	$0.435918\pi$
$350$	7.85006e14	0.0228260
$351$	1.11827e16	0.319191
$352$	−2.79741e15	−0.0783842
$353$	−6.28259e16	−1.72824	−0.864119	−	0.503288i	$-0.832123\pi$
$353$	−6.28259e16	−1.72824	−0.864119	+	0.503288i	$0.832123\pi$
$354$	2.88023e16	0.777867
$355$	−6.61419e16	−1.75385
$356$	6.77187e15	0.176313
$357$	2.50126e16	0.639462
$358$	2.38660e16	0.599156
$359$	−7.15356e16	−1.76363	−0.881817	−	0.471592i	$-0.843680\pi$
$359$	−7.15356e16	−1.76363	−0.881817	+	0.471592i	$0.843680\pi$
$360$	1.00149e16	0.242482
$361$	2.01654e16	0.479523
$362$	−6.61480e15	−0.154494
$363$	−4.50974e16	−1.03457
$364$	6.08361e15	0.137089
$365$	−1.45725e16	−0.322574
$366$	−7.90250e16	−1.71845
$367$	9.06336e15	0.193624	0.0968121	−	0.995303i	$-0.469135\pi$
$367$	9.06336e15	0.193624	0.0968121	+	0.995303i	$0.469135\pi$
$368$	8.20497e15	0.172213
$369$	1.37306e16	0.283152
$370$	4.26507e16	0.864202
$371$	2.96731e15	0.0590789
$372$	−6.06273e16	−1.18615
$373$	3.66363e16	0.704376	0.352188	−	0.935929i	$-0.385438\pi$
$373$	3.66363e16	0.704376	0.352188	+	0.935929i	$0.385438\pi$
$374$	2.18014e16	0.411927
$375$	6.60784e16	1.22703
$376$	−2.75880e16	−0.503500
$377$	1.41540e15	0.0253899
$378$	−6.66963e15	−0.117599
$379$	8.68107e16	1.50459	0.752295	−	0.658826i	$-0.228947\pi$
$379$	8.68107e16	1.50459	0.752295	+	0.658826i	$0.228947\pi$
$380$	3.71895e16	0.633617
$381$	−5.36943e16	−0.899323
$382$	−6.84149e16	−1.12652
$383$	1.02864e16	0.166522	0.0832612	−	0.996528i	$-0.473466\pi$
$383$	1.02864e16	0.166522	0.0832612	+	0.996528i	$0.473466\pi$
$384$	−7.15122e15	−0.113822
$385$	1.11569e16	0.174603
$386$	5.32670e16	0.819673
$387$	−7.04496e16	−1.06600
$388$	−5.21704e16	−0.776279
$389$	−6.34705e16	−0.928752	−0.464376	−	0.885638i	$-0.653721\pi$
$389$	−6.34705e16	−0.928752	−0.464376	+	0.885638i	$0.653721\pi$
$390$	−4.78206e16	−0.688169
$391$	−6.39450e16	−0.905019
$392$	−3.62841e15	−0.0505076
$393$	−7.04367e16	−0.964379
$394$	6.86904e16	0.925061
$395$	1.30960e17	1.73483
$396$	1.12001e16	0.145949
$397$	−6.02014e16	−0.771735	−0.385867	−	0.922554i	$-0.626098\pi$
$397$	−6.02014e16	−0.771735	−0.385867	+	0.922554i	$0.626098\pi$
$398$	5.06102e16	0.638261
$399$	4.77164e16	0.592031
$400$	1.74914e15	0.0213518
$401$	6.40950e16	0.769814	0.384907	−	0.922955i	$-0.374233\pi$
$401$	6.40950e16	0.769814	0.384907	+	0.922955i	$0.374233\pi$
$402$	−1.08192e17	−1.27857
$403$	1.14921e17	1.33634
$404$	3.91425e15	0.0447888
$405$	1.13336e17	1.27618
$406$	−8.44181e14	−0.00935441
$407$	4.76981e16	0.520160
$408$	5.57327e16	0.598162
$409$	−1.10649e17	−1.16881	−0.584407	−	0.811461i	$-0.698673\pi$
$409$	−1.10649e17	−1.16881	−0.584407	+	0.811461i	$0.698673\pi$
$410$	3.04767e16	0.316864
$411$	1.95198e17	1.99758
$412$	2.58914e15	0.0260809
$413$	3.25623e16	0.322879
$414$	−3.28504e16	−0.320656
$415$	4.76487e16	0.457866
$416$	1.35554e16	0.128235
$417$	−3.59897e16	−0.335193
$418$	4.15906e16	0.381372
$419$	1.50452e17	1.35834	0.679169	−	0.733982i	$-0.262341\pi$
$419$	1.50452e17	1.35834	0.679169	+	0.733982i	$0.262341\pi$
$420$	2.85214e16	0.253542
$421$	−1.55902e17	−1.36464	−0.682322	−	0.731052i	$-0.739030\pi$
$421$	−1.55902e17	−1.36464	−0.682322	+	0.731052i	$0.739030\pi$
$422$	5.36737e16	0.462627
$423$	1.10455e17	0.937503
$424$	6.61172e15	0.0552633
$425$	−1.36318e16	−0.112209
$426$	−1.89093e17	−1.53290
$427$	−8.93413e16	−0.713298
$428$	2.23617e16	0.175841
$429$	−5.34797e16	−0.414207
$430$	−1.56371e17	−1.19292
$431$	−1.94922e17	−1.46474	−0.732368	−	0.680909i	$-0.761585\pi$
$431$	−1.94922e17	−1.46474	−0.732368	+	0.680909i	$0.761585\pi$
$432$	−1.48612e16	−0.110004
$433$	−5.45291e16	−0.397610	−0.198805	−	0.980039i	$-0.563706\pi$
$433$	−5.45291e16	−0.397610	−0.198805	+	0.980039i	$0.563706\pi$
$434$	−6.85419e16	−0.492349
$435$	6.63574e15	0.0469579
$436$	−4.44222e15	−0.0309698
$437$	−1.21988e17	−0.837890
$438$	−4.16612e16	−0.281936
$439$	−3.61086e16	−0.240764	−0.120382	−	0.992728i	$-0.538412\pi$
$439$	−3.61086e16	−0.240764	−0.120382	+	0.992728i	$0.538412\pi$
$440$	2.48598e16	0.163326
$441$	1.45272e16	0.0940438
$442$	−1.05643e17	−0.673904
$443$	−8.50250e16	−0.534469	−0.267235	−	0.963632i	$-0.586110\pi$
$443$	−8.50250e16	−0.534469	−0.267235	+	0.963632i	$0.586110\pi$
$444$	1.21934e17	0.755329
$445$	−6.01797e16	−0.367375
$446$	1.26707e17	0.762298
$447$	−8.74482e16	−0.518504
$448$	−8.08478e15	−0.0472456
$449$	−2.55741e17	−1.47298	−0.736492	−	0.676446i	$-0.763519\pi$
$449$	−2.55741e17	−1.47298	−0.736492	+	0.676446i	$0.763519\pi$
$450$	−7.00308e15	−0.0397565
$451$	3.40834e16	0.190719
$452$	−6.12555e16	−0.337867
$453$	3.30094e17	1.79473
$454$	−3.76380e15	−0.0201727
$455$	−5.40633e16	−0.285646
$456$	1.06321e17	0.553794
$457$	−3.92621e16	−0.201613	−0.100806	−	0.994906i	$-0.532142\pi$
$457$	−3.92621e16	−0.201613	−0.100806	+	0.994906i	$0.532142\pi$
$458$	1.67872e17	0.849869
$459$	1.15820e17	0.578097
$460$	−7.29152e16	−0.358833
$461$	7.33616e16	0.355969	0.177985	−	0.984033i	$-0.443042\pi$
$461$	7.33616e16	0.355969	0.177985	+	0.984033i	$0.443042\pi$
$462$	3.18966e16	0.152606
$463$	2.93826e17	1.38616	0.693082	−	0.720859i	$-0.256252\pi$
$463$	2.93826e17	1.38616	0.693082	+	0.720859i	$0.256252\pi$
$464$	−1.88099e15	−0.00875025
$465$	5.38778e17	2.47153
$466$	−9.69986e16	−0.438790
$467$	−3.65608e17	−1.63101	−0.815504	−	0.578752i	$-0.803540\pi$
$467$	−3.65608e17	−1.63101	−0.815504	+	0.578752i	$0.803540\pi$
$468$	−5.42722e16	−0.238770
$469$	−1.22315e17	−0.530711
$470$	2.45167e17	1.04912
$471$	−4.91078e17	−2.07260
$472$	7.25548e16	0.302025
$473$	−1.74876e17	−0.718014
$474$	3.74401e17	1.51628
$475$	−2.60054e16	−0.103886
$476$	6.30083e16	0.248286
$477$	−2.64715e16	−0.102899
$478$	7.31557e16	0.280522
$479$	2.81548e17	1.06506	0.532528	−	0.846413i	$-0.321242\pi$
$479$	2.81548e17	1.06506	0.532528	+	0.846413i	$0.321242\pi$
$480$	6.35509e16	0.237167
$481$	−2.31131e17	−0.850972
$482$	−2.20572e17	−0.801208
$483$	−9.35547e16	−0.335281
$484$	−1.13603e17	−0.401695
$485$	4.63623e17	1.61750
$486$	2.33633e17	0.804264
$487$	−4.03204e16	−0.136958	−0.0684789	−	0.997653i	$-0.521815\pi$
$487$	−4.03204e16	−0.136958	−0.0684789	+	0.997653i	$0.521815\pi$
$488$	−1.99069e17	−0.667229
$489$	4.83493e16	0.159913
$490$	3.22447e16	0.105241
$491$	−2.51587e17	−0.810325	−0.405163	−	0.914245i	$-0.632785\pi$
$491$	−2.51587e17	−0.810325	−0.405163	+	0.914245i	$0.632785\pi$
$492$	8.71299e16	0.276945
$493$	1.46594e16	0.0459845
$494$	−2.01536e17	−0.623917
$495$	−9.95317e16	−0.304108
$496$	−1.52724e17	−0.460550
$497$	−2.13778e17	−0.636278
$498$	1.36223e17	0.400184
$499$	3.09361e17	0.897040	0.448520	−	0.893773i	$-0.351951\pi$
$499$	3.09361e17	0.897040	0.448520	+	0.893773i	$0.351951\pi$
$500$	1.66456e17	0.476425
$501$	3.70446e17	1.04660
$502$	3.99065e17	1.11294
$503$	2.26269e17	0.622921	0.311460	−	0.950259i	$-0.399182\pi$
$503$	2.26269e17	0.622921	0.311460	+	0.950259i	$0.399182\pi$
$504$	3.23692e16	0.0879699
$505$	−3.47848e16	−0.0933245
$506$	−8.15441e16	−0.215980
$507$	−2.33328e17	−0.610119
$508$	−1.35259e17	−0.349183
$509$	2.83018e17	0.721354	0.360677	−	0.932691i	$-0.382546\pi$
$509$	2.83018e17	0.721354	0.360677	+	0.932691i	$0.382546\pi$
$510$	−4.95281e17	−1.24637
$511$	−4.70999e16	−0.117026
$512$	−1.80144e16	−0.0441942
$513$	2.20949e17	0.535217
$514$	−4.42052e17	−1.05734
$515$	−2.30089e16	−0.0543437
$516$	−4.47049e17	−1.04263
$517$	2.74180e17	0.631463
$518$	1.37852e17	0.313523
$519$	−4.99999e17	−1.12301
$520$	−1.20463e17	−0.267198
$521$	−9.63330e16	−0.211023	−0.105512	−	0.994418i	$-0.533648\pi$
$521$	−9.63330e16	−0.211023	−0.105512	+	0.994418i	$0.533648\pi$
$522$	7.53098e15	0.0162927
$523$	1.66074e16	0.0354847	0.0177424	−	0.999843i	$-0.494352\pi$
$523$	1.66074e16	0.0354847	0.0177424	+	0.999843i	$0.494352\pi$
$524$	−1.77435e17	−0.374443
$525$	−1.99441e16	−0.0415698
$526$	−1.65856e17	−0.341448
$527$	1.19025e18	2.42030
$528$	7.10716e16	0.142750
$529$	−2.64862e17	−0.525483
$530$	−5.87565e16	−0.115150
$531$	−2.90490e17	−0.562362
$532$	1.20201e17	0.229870
$533$	−1.65158e17	−0.312013
$534$	−1.72048e17	−0.321093
$535$	−1.98722e17	−0.366392
$536$	−2.72542e17	−0.496435
$537$	−6.06345e17	−1.09116
$538$	1.15157e17	0.204741
$539$	3.60605e16	0.0633440
$540$	1.32067e17	0.229211
$541$	−7.44804e17	−1.27720	−0.638601	−	0.769538i	$-0.720487\pi$
$541$	−7.44804e17	−1.27720	−0.638601	+	0.769538i	$0.720487\pi$
$542$	1.29414e17	0.219274
$543$	1.68057e17	0.281358
$544$	1.40394e17	0.232250
$545$	3.94768e16	0.0645304
$546$	−1.54562e17	−0.249660
$547$	−4.39431e17	−0.701411	−0.350706	−	0.936486i	$-0.614058\pi$
$547$	−4.39431e17	−0.701411	−0.350706	+	0.936486i	$0.614058\pi$
$548$	4.91717e17	0.775606
$549$	7.97019e17	1.24236
$550$	−1.73836e16	−0.0267783
$551$	2.79658e16	0.0425737
$552$	−2.08457e17	−0.313627
$553$	4.23277e17	0.629378
$554$	−1.93209e17	−0.283931
$555$	−1.08359e18	−1.57385
$556$	−9.06605e16	−0.130146
$557$	3.73860e17	0.530456	0.265228	−	0.964186i	$-0.414553\pi$
$557$	3.73860e17	0.530456	0.265228	+	0.964186i	$0.414553\pi$
$558$	6.11466e17	0.857531
$559$	8.47398e17	1.17466
$560$	7.18471e16	0.0984436
$561$	−5.53893e17	−0.750183
$562$	8.54035e17	1.14338
$563$	3.42075e17	0.452706	0.226353	−	0.974045i	$-0.427320\pi$
$563$	3.42075e17	0.452706	0.226353	+	0.974045i	$0.427320\pi$
$564$	7.00908e17	0.916953
$565$	5.44360e17	0.703998
$566$	−1.92783e17	−0.246468
$567$	3.66316e17	0.462983
$568$	−4.76338e17	−0.595184
$569$	−6.77917e17	−0.837427	−0.418713	−	0.908118i	$-0.637519\pi$
$569$	−6.77917e17	−0.837427	−0.418713	+	0.908118i	$0.637519\pi$
$570$	−9.44846e17	−1.15392
$571$	4.56708e17	0.551448	0.275724	−	0.961237i	$-0.411082\pi$
$571$	4.56708e17	0.551448	0.275724	+	0.961237i	$0.411082\pi$
$572$	−1.34719e17	−0.160825
$573$	1.73817e18	2.05157
$574$	9.85042e16	0.114955
$575$	5.09873e16	0.0588330
$576$	7.21247e16	0.0822883
$577$	−6.86010e17	−0.773905	−0.386953	−	0.922100i	$-0.626472\pi$
$577$	−6.86010e17	−0.773905	−0.386953	+	0.922100i	$0.626472\pi$
$578$	−4.60263e17	−0.513422
$579$	−1.35331e18	−1.49275
$580$	1.67159e16	0.0182325
$581$	1.54006e17	0.166109
$582$	1.32545e18	1.41373
$583$	−6.57098e16	−0.0693082
$584$	−1.04947e17	−0.109468
$585$	4.82302e17	0.497514
$586$	1.36736e17	0.139492
$587$	1.74269e17	0.175822	0.0879109	−	0.996128i	$-0.471981\pi$
$587$	1.74269e17	0.175822	0.0879109	+	0.996128i	$0.471981\pi$
$588$	9.21843e16	0.0919823
$589$	2.27063e18	2.24077
$590$	−6.44774e17	−0.629317
$591$	−1.74516e18	−1.68468
$592$	3.07160e17	0.293274
$593$	6.59417e17	0.622737	0.311368	−	0.950289i	$-0.399213\pi$
$593$	6.59417e17	0.622737	0.311368	+	0.950289i	$0.399213\pi$
$594$	1.47696e17	0.137961
$595$	−5.59937e17	−0.517343
$596$	−2.20288e17	−0.201321
$597$	−1.28582e18	−1.16237
$598$	3.95139e17	0.353340
$599$	−6.86248e17	−0.607025	−0.303513	−	0.952827i	$-0.598159\pi$
$599$	−6.86248e17	−0.607025	−0.303513	+	0.952827i	$0.598159\pi$
$600$	−4.44391e16	−0.0388850
$601$	−1.67864e18	−1.45303	−0.726514	−	0.687151i	$-0.758861\pi$
$601$	−1.67864e18	−1.45303	−0.726514	+	0.687151i	$0.758861\pi$
$602$	−5.05409e17	−0.432778
$603$	1.09118e18	0.924347
$604$	8.31527e17	0.696845
$605$	1.00956e18	0.836994
$606$	−9.94463e16	−0.0815674
$607$	1.36994e17	0.111167	0.0555833	−	0.998454i	$-0.482298\pi$
$607$	1.36994e17	0.111167	0.0555833	+	0.998454i	$0.482298\pi$
$608$	2.67830e17	0.215023
$609$	2.14475e16	0.0170358
$610$	1.76907e18	1.39028
$611$	−1.32860e18	−1.03306
$612$	−5.62100e17	−0.432444
$613$	1.06871e18	0.813520	0.406760	−	0.913535i	$-0.366659\pi$
$613$	1.06871e18	0.813520	0.406760	+	0.913535i	$0.366659\pi$
$614$	−7.65325e17	−0.576437
$615$	−7.74299e17	−0.577059
$616$	8.03496e16	0.0592529
$617$	−1.16717e18	−0.851690	−0.425845	−	0.904796i	$-0.640023\pi$
$617$	−1.16717e18	−0.851690	−0.425845	+	0.904796i	$0.640023\pi$
$618$	−6.57802e16	−0.0474975
$619$	−1.69459e18	−1.21081	−0.605404	−	0.795918i	$-0.706988\pi$
$619$	−1.69459e18	−1.21081	−0.605404	+	0.795918i	$0.706988\pi$
$620$	1.35722e18	0.959629
$621$	−4.33202e17	−0.303107
$622$	1.53129e18	1.06028
$623$	−1.94508e17	−0.133280
$624$	−3.44392e17	−0.233536
$625$	−1.60651e18	−1.07811
$626$	−1.59712e18	−1.06073
$627$	−1.05666e18	−0.694539
$628$	−1.23706e18	−0.804734
$629$	−2.39384e18	−1.54122
$630$	−2.87656e17	−0.183299
$631$	8.08906e17	0.510161	0.255081	−	0.966920i	$-0.417898\pi$
$631$	8.08906e17	0.510161	0.255081	+	0.966920i	$0.417898\pi$
$632$	9.43141e17	0.588729
$633$	−1.36365e18	−0.842516
$634$	−1.89504e18	−1.15888
$635$	1.20201e18	0.727578
$636$	−1.67979e17	−0.100643
$637$	−1.74739e17	−0.103629
$638$	1.86940e16	0.0109741
$639$	1.90713e18	1.10822
$640$	1.60089e17	0.0920855
$641$	1.47947e18	0.842418	0.421209	−	0.906964i	$-0.361606\pi$
$641$	1.47947e18	0.842418	0.421209	+	0.906964i	$0.361606\pi$
$642$	−5.68127e17	−0.320234
$643$	2.22617e18	1.24219	0.621095	−	0.783735i	$-0.286688\pi$
$643$	2.22617e18	1.24219	0.621095	+	0.783735i	$0.286688\pi$
$644$	−2.35670e17	−0.130181
$645$	3.97280e18	2.17249
$646$	−2.08732e18	−1.13000
$647$	−1.23935e18	−0.664227	−0.332114	−	0.943239i	$-0.607762\pi$
$647$	−1.23935e18	−0.664227	−0.332114	+	0.943239i	$0.607762\pi$
$648$	8.16220e17	0.433081
$649$	−7.21078e17	−0.378784
$650$	8.42360e16	0.0438088
$651$	1.74139e18	0.896644
$652$	1.21795e17	0.0620898
$653$	1.99854e18	1.00874	0.504368	−	0.863489i	$-0.331726\pi$
$653$	1.99854e18	1.00874	0.504368	+	0.863489i	$0.331726\pi$
$654$	1.12860e17	0.0564008
$655$	1.57681e18	0.780210
$656$	2.19486e17	0.107530
$657$	4.20180e17	0.203827
$658$	7.92408e17	0.380610
$659$	−6.60133e17	−0.313962	−0.156981	−	0.987602i	$-0.550176\pi$
$659$	−6.60133e17	−0.313962	−0.156981	+	0.987602i	$0.550176\pi$
$660$	−6.31593e17	−0.297442
$661$	2.77431e18	1.29373	0.646867	−	0.762603i	$-0.276079\pi$
$661$	2.77431e18	1.29373	0.646867	+	0.762603i	$0.276079\pi$
$662$	−1.57578e18	−0.727643
$663$	2.68400e18	1.22728
$664$	3.43154e17	0.155381
$665$	−1.06819e18	−0.478970
$666$	−1.22979e18	−0.546068
$667$	−5.48308e16	−0.0241105
$668$	9.33178e17	0.406366
$669$	−3.21916e18	−1.38827
$670$	2.42200e18	1.03440
$671$	1.97843e18	0.836803
$672$	2.05404e17	0.0860416
$673$	8.48529e17	0.352021	0.176011	−	0.984388i	$-0.443681\pi$
$673$	8.48529e17	0.352021	0.176011	+	0.984388i	$0.443681\pi$
$674$	−1.64747e18	−0.676907
$675$	−9.23503e16	−0.0375806
$676$	−5.87767e17	−0.236893
$677$	6.48470e17	0.258859	0.129430	−	0.991589i	$-0.458685\pi$
$677$	6.48470e17	0.258859	0.129430	+	0.991589i	$0.458685\pi$
$678$	1.55627e18	0.615308
$679$	1.49848e18	0.586812
$680$	−1.24764e18	−0.483930
$681$	9.56241e16	0.0367376
$682$	1.51783e18	0.577597
$683$	2.66861e18	1.00589	0.502945	−	0.864318i	$-0.332250\pi$
$683$	2.66861e18	1.00589	0.502945	+	0.864318i	$0.332250\pi$
$684$	−1.07232e18	−0.400368
$685$	−4.36975e18	−1.61610
$686$	1.04218e17	0.0381802
$687$	−4.26499e18	−1.54774
$688$	−1.12614e18	−0.404827
$689$	3.18411e17	0.113387
$690$	1.85250e18	0.653491
$691$	1.75642e18	0.613793	0.306897	−	0.951743i	$-0.400709\pi$
$691$	1.75642e18	0.613793	0.306897	+	0.951743i	$0.400709\pi$
$692$	−1.25953e18	−0.436033
$693$	−3.21698e17	−0.110327
$694$	−2.04046e18	−0.693252
$695$	8.05675e17	0.271180
$696$	4.77890e16	0.0159356
$697$	−1.71055e18	−0.565097
$698$	−8.64015e17	−0.282788
$699$	2.46437e18	0.799106
$700$	−5.02404e16	−0.0161404
$701$	−4.38123e18	−1.39453	−0.697267	−	0.716812i	$-0.745601\pi$
$701$	−4.38123e18	−1.39453	−0.697267	+	0.716812i	$0.745601\pi$
$702$	−7.15693e17	−0.225702
$703$	−4.56672e18	−1.42690
$704$	1.79034e17	0.0554260
$705$	−6.22878e18	−1.91062
$706$	4.02086e18	1.22205
$707$	−1.12429e17	−0.0338571
$708$	−1.84335e18	−0.550035
$709$	4.97050e18	1.46960	0.734801	−	0.678283i	$-0.237276\pi$
$709$	4.97050e18	1.46960	0.734801	+	0.678283i	$0.237276\pi$
$710$	4.23308e18	1.24016
$711$	−3.77608e18	−1.09620
$712$	−4.33400e17	−0.124672
$713$	−4.45189e18	−1.26900
$714$	−1.60080e18	−0.452168
$715$	1.19721e18	0.335105
$716$	−1.52742e18	−0.423667
$717$	−1.85861e18	−0.510874
$718$	4.57828e18	1.24708
$719$	2.62307e18	0.708063	0.354032	−	0.935233i	$-0.384811\pi$
$719$	2.62307e18	0.708063	0.354032	+	0.935233i	$0.384811\pi$
$720$	−6.40952e17	−0.171461
$721$	−7.43675e16	−0.0197153
$722$	−1.29058e18	−0.339074
$723$	5.60391e18	1.45913
$724$	4.23347e17	0.109244
$725$	−1.16889e16	−0.00298934
$726$	2.88623e18	0.731549
$727$	−3.57761e18	−0.898710	−0.449355	−	0.893353i	$-0.648346\pi$
$727$	−3.57761e18	−0.898710	−0.449355	+	0.893353i	$0.648346\pi$
$728$	−3.89351e17	−0.0969365
$729$	−9.71610e17	−0.239753
$730$	9.32637e17	0.228094
$731$	8.77655e18	2.12746
$732$	5.05760e18	1.21513
$733$	−4.01369e18	−0.955803	−0.477901	−	0.878414i	$-0.658602\pi$
$733$	−4.01369e18	−0.955803	−0.477901	+	0.878414i	$0.658602\pi$
$734$	−5.80055e17	−0.136913
$735$	−8.19216e17	−0.191660
$736$	−5.25118e17	−0.121773
$737$	2.70863e18	0.622602
$738$	−8.78761e17	−0.200219
$739$	−4.48595e18	−1.01313	−0.506566	−	0.862201i	$-0.669085\pi$
$739$	−4.48595e18	−1.01313	−0.506566	+	0.862201i	$0.669085\pi$
$740$	−2.72965e18	−0.611083
$741$	5.12027e18	1.13625
$742$	−1.89908e17	−0.0417751
$743$	−2.22911e18	−0.486076	−0.243038	−	0.970017i	$-0.578144\pi$
$743$	−2.22911e18	−0.486076	−0.243038	+	0.970017i	$0.578144\pi$
$744$	3.88015e18	0.838734
$745$	1.95764e18	0.419485
$746$	−2.34472e18	−0.498069
$747$	−1.37390e18	−0.289315
$748$	−1.39529e18	−0.291276
$749$	−6.42292e17	−0.132923
$750$	−4.22902e18	−0.867644
$751$	7.89050e17	0.160489	0.0802445	−	0.996775i	$-0.474430\pi$
$751$	7.89050e17	0.160489	0.0802445	+	0.996775i	$0.474430\pi$
$752$	1.76563e18	0.356028
$753$	−1.01388e19	−2.02683
$754$	−9.05859e16	−0.0179534
$755$	−7.38955e18	−1.45199
$756$	4.26857e17	0.0831554
$757$	1.89356e18	0.365727	0.182863	−	0.983138i	$-0.441463\pi$
$757$	1.89356e18	0.365727	0.182863	+	0.983138i	$0.441463\pi$
$758$	−5.55588e18	−1.06391
$759$	2.07173e18	0.393334
$760$	−2.38013e18	−0.448035
$761$	2.66760e18	0.497875	0.248938	−	0.968520i	$-0.419919\pi$
$761$	2.66760e18	0.497875	0.248938	+	0.968520i	$0.419919\pi$
$762$	3.43643e18	0.635917
$763$	1.27593e17	0.0234109
$764$	4.37855e18	0.796570
$765$	4.99523e18	0.901065
$766$	−6.58332e17	−0.117749
$767$	3.49413e18	0.619683
$768$	4.57678e17	0.0804845
$769$	−6.63834e18	−1.15755	−0.578773	−	0.815489i	$-0.696468\pi$
$769$	−6.63834e18	−1.15755	−0.578773	+	0.815489i	$0.696468\pi$
$770$	−7.14045e17	−0.123463
$771$	1.12309e19	1.92558
$772$	−3.40909e18	−0.579596
$773$	9.95954e18	1.67908	0.839542	−	0.543295i	$-0.182823\pi$
$773$	9.95954e18	1.67908	0.839542	+	0.543295i	$0.182823\pi$
$774$	4.50878e18	0.753776
$775$	−9.49057e17	−0.157337
$776$	3.33890e18	0.548912
$777$	−3.50230e18	−0.570975
$778$	4.06211e18	0.656727
$779$	−3.26322e18	−0.523181
$780$	3.06052e18	0.486609
$781$	4.73403e18	0.746448
$782$	4.09248e18	0.639945
$783$	9.93118e16	0.0154010
$784$	2.32218e17	0.0357143
$785$	1.09934e19	1.67679
$786$	4.50795e18	0.681919
$787$	−3.71459e17	−0.0557282	−0.0278641	−	0.999612i	$-0.508871\pi$
$787$	−3.71459e17	−0.0557282	−0.0278641	+	0.999612i	$0.508871\pi$
$788$	−4.39618e18	−0.654117
$789$	4.21379e18	0.621831
$790$	−8.38143e18	−1.22671
$791$	1.75944e18	0.255403
$792$	−7.16803e17	−0.103202
$793$	−9.58688e18	−1.36899
$794$	3.85289e18	0.545699
$795$	1.49278e18	0.209706
$796$	−3.23906e18	−0.451319
$797$	1.16492e18	0.160997	0.0804987	−	0.996755i	$-0.474349\pi$
$797$	1.16492e18	0.160997	0.0804987	+	0.996755i	$0.474349\pi$
$798$	−3.05385e18	−0.418629
$799$	−1.37604e19	−1.87101
$800$	−1.11945e17	−0.0150980
$801$	1.73521e18	0.232136
$802$	−4.10208e18	−0.544341
$803$	1.04301e18	0.137289
$804$	6.92427e18	0.904085
$805$	2.09434e18	0.271252
$806$	−7.35497e18	−0.944938
$807$	−2.92571e18	−0.372866
$808$	−2.50512e17	−0.0316705
$809$	−8.50877e18	−1.06709	−0.533545	−	0.845771i	$-0.679141\pi$
$809$	−8.50877e18	−1.06709	−0.533545	+	0.845771i	$0.679141\pi$
$810$	−7.25351e18	−0.902393
$811$	−1.22872e19	−1.51641	−0.758205	−	0.652016i	$-0.773923\pi$
$811$	−1.22872e19	−1.51641	−0.758205	+	0.652016i	$0.773923\pi$
$812$	5.40276e16	0.00661457
$813$	−3.28793e18	−0.399332
$814$	−3.05268e18	−0.367809
$815$	−1.08236e18	−0.129374
$816$	−3.56689e18	−0.422965
$817$	1.67430e19	1.96966
$818$	7.08153e18	0.826476
$819$	1.55885e18	0.180493
$820$	−1.95051e18	−0.224057
$821$	4.48891e18	0.511576	0.255788	−	0.966733i	$-0.417665\pi$
$821$	4.48891e18	0.511576	0.255788	+	0.966733i	$0.417665\pi$
$822$	−1.24927e19	−1.41250
$823$	1.51768e18	0.170247	0.0851236	−	0.996370i	$-0.472871\pi$
$823$	1.51768e18	0.170247	0.0851236	+	0.996370i	$0.472871\pi$
$824$	−1.65705e17	−0.0184420
$825$	4.41653e17	0.0487675
$826$	−2.08398e18	−0.228310
$827$	−3.09315e18	−0.336213	−0.168107	−	0.985769i	$-0.553765\pi$
$827$	−3.09315e18	−0.336213	−0.168107	+	0.985769i	$0.553765\pi$
$828$	2.10243e18	0.226738
$829$	4.99805e18	0.534806	0.267403	−	0.963585i	$-0.413835\pi$
$829$	4.99805e18	0.534806	0.267403	+	0.963585i	$0.413835\pi$
$830$	−3.04952e18	−0.323760
$831$	4.90871e18	0.517084
$832$	−8.67547e17	−0.0906758
$833$	−1.80978e18	−0.187687
$834$	2.30334e18	0.237017
$835$	−8.29289e18	−0.846728
$836$	−2.66180e18	−0.269671
$837$	8.06346e18	0.810599
$838$	−9.62894e18	−0.960489
$839$	1.14481e19	1.13313	0.566565	−	0.824017i	$-0.308272\pi$
$839$	1.14481e19	1.13313	0.566565	+	0.824017i	$0.308272\pi$
$840$	−1.82537e18	−0.179281
$841$	−1.02481e19	−0.998775
$842$	9.97776e18	0.964949
$843$	−2.16978e19	−2.08227
$844$	−3.43512e18	−0.327127
$845$	5.22332e18	0.493604
$846$	−7.06912e18	−0.662915
$847$	3.26302e18	0.303653
$848$	−4.23150e17	−0.0390770
$849$	4.89789e18	0.448858
$850$	8.72437e17	0.0793435
$851$	8.95369e18	0.808090
$852$	1.21020e19	1.08392
$853$	5.69574e18	0.506269	0.253134	−	0.967431i	$-0.418538\pi$
$853$	5.69574e18	0.506269	0.253134	+	0.967431i	$0.418538\pi$
$854$	5.71784e18	0.504378
$855$	9.52939e18	0.834229
$856$	−1.43115e18	−0.124338
$857$	−1.42907e19	−1.23220	−0.616098	−	0.787670i	$-0.711287\pi$
$857$	−1.42907e19	−1.23220	−0.616098	+	0.787670i	$0.711287\pi$
$858$	3.42270e18	0.292888
$859$	−1.06350e18	−0.0903196	−0.0451598	−	0.998980i	$-0.514380\pi$
$859$	−1.06350e18	−0.0903196	−0.0451598	+	0.998980i	$0.514380\pi$
$860$	1.00077e19	0.843521
$861$	−2.50262e18	−0.209351
$862$	1.24750e19	1.03572
$863$	−2.03035e19	−1.67302	−0.836508	−	0.547954i	$-0.815407\pi$
$863$	−2.03035e19	−1.67302	−0.836508	+	0.547954i	$0.815407\pi$
$864$	9.51116e17	0.0777847
$865$	1.11931e19	0.908543
$866$	3.48986e18	0.281152
$867$	1.16935e19	0.935022
$868$	4.38668e18	0.348143
$869$	−9.37330e18	−0.738353
$870$	−4.24687e17	−0.0332043
$871$	−1.31252e19	−1.01856
$872$	2.84302e17	0.0218989
$873$	−1.33681e19	−1.02206
$874$	7.80721e18	0.592477
$875$	−4.78110e18	−0.360143
$876$	2.66632e18	0.199359
$877$	1.71374e19	1.27189	0.635943	−	0.771736i	$-0.280611\pi$
$877$	1.71374e19	1.27189	0.635943	+	0.771736i	$0.280611\pi$
$878$	2.31095e18	0.170246
$879$	−3.47395e18	−0.254036
$880$	−1.59103e18	−0.115489
$881$	9.92794e18	0.715345	0.357673	−	0.933847i	$-0.383570\pi$
$881$	9.92794e18	0.715345	0.357673	+	0.933847i	$0.383570\pi$
$882$	−9.29739e17	−0.0664990
$883$	1.59915e19	1.13539	0.567695	−	0.823239i	$-0.307835\pi$
$883$	1.59915e19	1.13539	0.567695	+	0.823239i	$0.307835\pi$
$884$	6.76118e18	0.476522
$885$	1.63813e19	1.14609
$886$	5.44160e18	0.377927
$887$	−1.06464e19	−0.734006	−0.367003	−	0.930220i	$-0.619616\pi$
$887$	−1.06464e19	−0.734006	−0.367003	+	0.930220i	$0.619616\pi$
$888$	−7.80379e18	−0.534098
$889$	3.88504e18	0.263958
$890$	3.85150e18	0.259774
$891$	−8.11191e18	−0.543147
$892$	−8.10927e18	−0.539026
$893$	−2.62506e19	−1.73223
$894$	5.59669e18	0.366638
$895$	1.35738e19	0.882777
$896$	5.17426e17	0.0334077
$897$	−1.00390e19	−0.643487
$898$	1.63674e19	1.04156
$899$	1.02060e18	0.0644788
$900$	4.48197e17	0.0281121
$901$	3.29780e18	0.205359
$902$	−2.18133e18	−0.134859
$903$	1.28405e19	0.788157
$904$	3.92035e18	0.238908
$905$	−3.76217e18	−0.227626
$906$	−2.11260e19	−1.26906
$907$	1.76638e19	1.05350	0.526752	−	0.850019i	$-0.323410\pi$
$907$	1.76638e19	1.05350	0.526752	+	0.850019i	$0.323410\pi$
$908$	2.40883e17	0.0142642
$909$	1.00298e18	0.0589695
$910$	3.46005e18	0.201982
$911$	6.94199e18	0.402359	0.201180	−	0.979554i	$-0.435522\pi$
$911$	6.94199e18	0.402359	0.201180	+	0.979554i	$0.435522\pi$
$912$	−6.80455e18	−0.391591
$913$	−3.41040e18	−0.194870
$914$	2.51277e18	0.142562
$915$	−4.49455e19	−2.53191
$916$	−1.07438e19	−0.600948
$917$	5.09644e18	0.283052
$918$	−7.41247e18	−0.408776
$919$	8.32534e17	0.0455881	0.0227940	−	0.999740i	$-0.492744\pi$
$919$	8.32534e17	0.0455881	0.0227940	+	0.999740i	$0.492744\pi$
$920$	4.66658e18	0.253733
$921$	1.94440e19	1.04978
$922$	−4.69514e18	−0.251708
$923$	−2.29397e19	−1.22117
$924$	−2.04138e18	−0.107909
$925$	1.90875e18	0.100191
$926$	−1.88049e19	−0.980166
$927$	6.63436e17	0.0343385
$928$	1.20384e17	0.00618736
$929$	−1.05532e19	−0.538621	−0.269311	−	0.963053i	$-0.586796\pi$
$929$	−1.05532e19	−0.538621	−0.269311	+	0.963053i	$0.586796\pi$
$930$	−3.44818e19	−1.74763
$931$	−3.45252e18	−0.173765
$932$	6.20791e18	0.310272
$933$	−3.89044e19	−1.93093
$934$	2.33989e19	1.15330
$935$	1.23996e19	0.606920
$936$	3.47342e18	0.168836
$937$	−2.69244e19	−1.29969	−0.649843	−	0.760068i	$-0.725166\pi$
$937$	−2.69244e19	−1.29969	−0.649843	+	0.760068i	$0.725166\pi$
$938$	7.82819e18	0.375269
$939$	4.05769e19	1.93176
$940$	−1.56907e19	−0.741841
$941$	−6.75264e18	−0.317059	−0.158530	−	0.987354i	$-0.550675\pi$
$941$	−6.75264e18	−0.317059	−0.158530	+	0.987354i	$0.550675\pi$
$942$	3.14290e19	1.46555
$943$	6.39799e18	0.296290
$944$	−4.64351e18	−0.213564
$945$	−3.79335e18	−0.173267
$946$	1.11921e19	0.507712
$947$	−1.01728e19	−0.458316	−0.229158	−	0.973389i	$-0.573597\pi$
$947$	−1.01728e19	−0.458316	−0.229158	+	0.973389i	$0.573597\pi$
$948$	−2.39617e19	−1.07217
$949$	−5.05411e18	−0.224602
$950$	1.66435e18	0.0734582
$951$	4.81459e19	2.11050
$952$	−4.03253e18	−0.175565
$953$	−2.73673e19	−1.18339	−0.591696	−	0.806161i	$-0.701541\pi$
$953$	−2.73673e19	−1.18339	−0.591696	+	0.806161i	$0.701541\pi$
$954$	1.69418e18	0.0727603
$955$	−3.89110e19	−1.65978
$956$	−4.68196e18	−0.198359
$957$	−4.74945e17	−0.0199855
$958$	−1.80191e19	−0.753108
$959$	−1.41235e19	−0.586303
$960$	−4.06726e18	−0.167702
$961$	5.84483e19	2.39370
$962$	1.47924e19	0.601728
$963$	5.72992e18	0.231514
$964$	1.41166e19	0.566539
$965$	3.02956e19	1.20768
$966$	5.98750e18	0.237080
$967$	1.58703e19	0.624184	0.312092	−	0.950052i	$-0.398970\pi$
$967$	1.58703e19	0.624184	0.312092	+	0.950052i	$0.398970\pi$
$968$	7.27061e18	0.284041
$969$	5.30309e19	2.05790
$970$	−2.96719e19	−1.14374
$971$	−4.10298e19	−1.57099	−0.785496	−	0.618867i	$-0.787592\pi$
$971$	−4.10298e19	−1.57099	−0.785496	+	0.618867i	$0.787592\pi$
$972$	−1.49525e19	−0.568701
$973$	2.60403e18	0.0983814
$974$	2.58051e18	0.0968438
$975$	−2.14012e18	−0.0797826
$976$	1.27404e19	0.471802
$977$	4.77987e19	1.75833	0.879166	−	0.476515i	$-0.158100\pi$
$977$	4.77987e19	1.75833	0.879166	+	0.476515i	$0.158100\pi$
$978$	−3.09436e18	−0.113075
$979$	4.30729e18	0.156357
$980$	−2.06366e18	−0.0744163
$981$	−1.13827e18	−0.0407752
$982$	1.61016e19	0.572986
$983$	−2.56658e19	−0.907312	−0.453656	−	0.891177i	$-0.649881\pi$
$983$	−2.56658e19	−0.907312	−0.453656	+	0.891177i	$0.649881\pi$
$984$	−5.57631e18	−0.195830
$985$	3.90676e19	1.36296
$986$	−9.38203e17	−0.0325160
$987$	−2.01321e19	−0.693151
$988$	1.28983e19	0.441176
$989$	−3.28270e19	−1.11546
$990$	6.37003e18	0.215037
$991$	2.82488e18	0.0947373	0.0473687	−	0.998877i	$-0.484916\pi$
$991$	2.82488e18	0.0947373	0.0473687	+	0.998877i	$0.484916\pi$
$992$	9.77435e18	0.325658
$993$	4.00346e19	1.32515
$994$	1.36818e19	0.449917
$995$	2.87846e19	0.940394
$996$	−8.71827e18	−0.282973
$997$	−1.41169e19	−0.455221	−0.227610	−	0.973752i	$-0.573091\pi$
$997$	−1.41169e19	−0.455221	−0.227610	+	0.973752i	$0.573091\pi$
$998$	−1.97991e19	−0.634303
$999$	−1.62173e19	−0.516182

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.a.a.1.1	✓	1
3.2	odd	2		126.14.a.e.1.1		1
4.3	odd	2		112.14.a.a.1.1		1
7.2	even	3		98.14.c.f.67.1		2
7.3	odd	6		98.14.c.g.79.1		2
7.4	even	3		98.14.c.f.79.1		2
7.5	odd	6		98.14.c.g.67.1		2
7.6	odd	2		98.14.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.a.a.1.1	✓	1	1.1	even	1	trivial
98.14.a.a.1.1		1	7.6	odd	2
98.14.c.f.67.1		2	7.2	even	3
98.14.c.f.79.1		2	7.4	even	3
98.14.c.g.67.1		2	7.5	odd	6
98.14.c.g.79.1		2	7.3	odd	6
112.14.a.a.1.1		1	4.3	odd	2
126.14.a.e.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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more