Properties

Label 289.10.a.e.1.3
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [289,10,Mod(1,289)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(289, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("289.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.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: \(148.845356651\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5 x^{11} - 4542 x^{10} + 30079 x^{9} + 7481825 x^{8} - 58373994 x^{7} - 5553197164 x^{6} + 45662797046 x^{5} + 1825619566875 x^{4} + \cdots + 245077910606835 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{12}\cdot 3^{5}\cdot 17 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-31.5756\) of defining polynomial
Character \(\chi\) \(=\) 289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-30.5756 q^{2} +194.921 q^{3} +422.865 q^{4} -941.135 q^{5} -5959.81 q^{6} +4513.44 q^{7} +2725.35 q^{8} +18311.1 q^{9} +O(q^{10})\) \(q-30.5756 q^{2} +194.921 q^{3} +422.865 q^{4} -941.135 q^{5} -5959.81 q^{6} +4513.44 q^{7} +2725.35 q^{8} +18311.1 q^{9} +28775.7 q^{10} -41597.1 q^{11} +82425.2 q^{12} +101290. q^{13} -138001. q^{14} -183447. q^{15} -299836. q^{16} -559873. q^{18} +878675. q^{19} -397973. q^{20} +879763. q^{21} +1.27185e6 q^{22} +1.58058e6 q^{23} +531227. q^{24} -1.06739e6 q^{25} -3.09699e6 q^{26} -267410. q^{27} +1.90858e6 q^{28} -1.94618e6 q^{29} +5.60899e6 q^{30} +4.44805e6 q^{31} +7.77228e6 q^{32} -8.10814e6 q^{33} -4.24775e6 q^{35} +7.74313e6 q^{36} -9.92035e6 q^{37} -2.68660e7 q^{38} +1.97434e7 q^{39} -2.56492e6 q^{40} +3.03121e7 q^{41} -2.68993e7 q^{42} -4.15989e7 q^{43} -1.75900e7 q^{44} -1.72332e7 q^{45} -4.83272e7 q^{46} +2.96697e7 q^{47} -5.84443e7 q^{48} -1.99825e7 q^{49} +3.26361e7 q^{50} +4.28318e7 q^{52} -1.85086e7 q^{53} +8.17620e6 q^{54} +3.91485e7 q^{55} +1.23007e7 q^{56} +1.71272e8 q^{57} +5.95055e7 q^{58} +3.51354e7 q^{59} -7.75732e7 q^{60} +1.88656e8 q^{61} -1.36002e8 q^{62} +8.26461e7 q^{63} -8.41258e7 q^{64} -9.53271e7 q^{65} +2.47911e8 q^{66} +2.08556e8 q^{67} +3.08088e8 q^{69} +1.29878e8 q^{70} -4.89810e7 q^{71} +4.99041e7 q^{72} -1.30289e8 q^{73} +3.03320e8 q^{74} -2.08057e8 q^{75} +3.71561e8 q^{76} -1.87746e8 q^{77} -6.03667e8 q^{78} -2.59845e8 q^{79} +2.82186e8 q^{80} -4.12541e8 q^{81} -9.26809e8 q^{82} +4.12715e8 q^{83} +3.72021e8 q^{84} +1.27191e9 q^{86} -3.79351e8 q^{87} -1.13366e8 q^{88} +1.05219e9 q^{89} +5.26916e8 q^{90} +4.57164e8 q^{91} +6.68373e8 q^{92} +8.67017e8 q^{93} -9.07169e8 q^{94} -8.26952e8 q^{95} +1.51498e9 q^{96} -1.29676e9 q^{97} +6.10975e8 q^{98} -7.61689e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 17 q^{2} + 74 q^{3} + 2987 q^{4} + 454 q^{5} + 2674 q^{6} - 5524 q^{7} - 12036 q^{8} + 71898 q^{9} - 2449 q^{10} + 152886 q^{11} + 41717 q^{12} + 23478 q^{13} + 492839 q^{14} - 149346 q^{15} + 272743 q^{16} + 1610378 q^{18} + 1053982 q^{19} - 2477218 q^{20} - 1395256 q^{21} + 2391095 q^{22} + 2012428 q^{23} + 708393 q^{24} + 6123166 q^{25} - 733144 q^{26} + 3231638 q^{27} - 5978216 q^{28} + 12772842 q^{29} + 181633 q^{30} + 5535814 q^{31} - 5277485 q^{32} - 16526054 q^{33} + 23712622 q^{35} - 37692723 q^{36} + 1352872 q^{37} + 3704404 q^{38} - 1380780 q^{39} + 44739331 q^{40} + 40941240 q^{41} - 73649073 q^{42} - 14142490 q^{43} + 148233417 q^{44} - 79449336 q^{45} + 31855859 q^{46} + 133558002 q^{47} - 80444894 q^{48} + 184488050 q^{49} + 103322437 q^{50} + 179597031 q^{52} - 299319258 q^{53} - 50215469 q^{54} - 91197532 q^{55} + 267350757 q^{56} + 49507694 q^{57} + 367048088 q^{58} - 106431852 q^{59} + 103650215 q^{60} + 262041240 q^{61} - 314328847 q^{62} + 218532626 q^{63} + 595820098 q^{64} + 330279796 q^{65} - 117450322 q^{66} - 489635100 q^{67} + 661586712 q^{69} - 226277420 q^{70} + 204290852 q^{71} - 208030791 q^{72} + 673538852 q^{73} + 1274510282 q^{74} + 588895258 q^{75} - 403517977 q^{76} - 705301770 q^{77} + 165043245 q^{78} + 434002980 q^{79} + 599590757 q^{80} - 389011392 q^{81} - 180073450 q^{82} + 411781442 q^{83} - 475971445 q^{84} + 492988379 q^{86} + 1513399800 q^{87} - 262108460 q^{88} + 911678128 q^{89} - 2734590475 q^{90} - 560105446 q^{91} - 847049266 q^{92} - 1228562570 q^{93} + 2009871759 q^{94} - 1116511966 q^{95} + 2204198979 q^{96} - 3589270998 q^{97} - 2677144485 q^{98} + 2056683494 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −30.5756 −1.35126 −0.675631 0.737240i \(-0.736129\pi\)
−0.675631 + 0.737240i \(0.736129\pi\)
\(3\) 194.921 1.38935 0.694676 0.719322i \(-0.255548\pi\)
0.694676 + 0.719322i \(0.255548\pi\)
\(4\) 422.865 0.825909
\(5\) −941.135 −0.673421 −0.336711 0.941608i \(-0.609314\pi\)
−0.336711 + 0.941608i \(0.609314\pi\)
\(6\) −5959.81 −1.87738
\(7\) 4513.44 0.710504 0.355252 0.934771i \(-0.384395\pi\)
0.355252 + 0.934771i \(0.384395\pi\)
\(8\) 2725.35 0.235243
\(9\) 18311.1 0.930301
\(10\) 28775.7 0.909968
\(11\) −41597.1 −0.856635 −0.428317 0.903628i \(-0.640894\pi\)
−0.428317 + 0.903628i \(0.640894\pi\)
\(12\) 82425.2 1.14748
\(13\) 101290. 0.983602 0.491801 0.870708i \(-0.336339\pi\)
0.491801 + 0.870708i \(0.336339\pi\)
\(14\) −138001. −0.960077
\(15\) −183447. −0.935620
\(16\) −299836. −1.14378
\(17\) 0 0
\(18\) −559873. −1.25708
\(19\) 878675. 1.54681 0.773405 0.633912i \(-0.218552\pi\)
0.773405 + 0.633912i \(0.218552\pi\)
\(20\) −397973. −0.556184
\(21\) 879763. 0.987140
\(22\) 1.27185e6 1.15754
\(23\) 1.58058e6 1.17772 0.588860 0.808235i \(-0.299577\pi\)
0.588860 + 0.808235i \(0.299577\pi\)
\(24\) 531227. 0.326836
\(25\) −1.06739e6 −0.546504
\(26\) −3.09699e6 −1.32910
\(27\) −267410. −0.0968367
\(28\) 1.90858e6 0.586811
\(29\) −1.94618e6 −0.510966 −0.255483 0.966814i \(-0.582234\pi\)
−0.255483 + 0.966814i \(0.582234\pi\)
\(30\) 5.60899e6 1.26427
\(31\) 4.44805e6 0.865051 0.432525 0.901622i \(-0.357623\pi\)
0.432525 + 0.901622i \(0.357623\pi\)
\(32\) 7.77228e6 1.31031
\(33\) −8.10814e6 −1.19017
\(34\) 0 0
\(35\) −4.24775e6 −0.478468
\(36\) 7.74313e6 0.768344
\(37\) −9.92035e6 −0.870200 −0.435100 0.900382i \(-0.643287\pi\)
−0.435100 + 0.900382i \(0.643287\pi\)
\(38\) −2.68660e7 −2.09015
\(39\) 1.97434e7 1.36657
\(40\) −2.56492e6 −0.158418
\(41\) 3.03121e7 1.67528 0.837642 0.546220i \(-0.183934\pi\)
0.837642 + 0.546220i \(0.183934\pi\)
\(42\) −2.68993e7 −1.33389
\(43\) −4.15989e7 −1.85555 −0.927777 0.373135i \(-0.878283\pi\)
−0.927777 + 0.373135i \(0.878283\pi\)
\(44\) −1.75900e7 −0.707502
\(45\) −1.72332e7 −0.626484
\(46\) −4.83272e7 −1.59141
\(47\) 2.96697e7 0.886897 0.443449 0.896300i \(-0.353755\pi\)
0.443449 + 0.896300i \(0.353755\pi\)
\(48\) −5.84443e7 −1.58912
\(49\) −1.99825e7 −0.495184
\(50\) 3.26361e7 0.738470
\(51\) 0 0
\(52\) 4.28318e7 0.812366
\(53\) −1.85086e7 −0.322204 −0.161102 0.986938i \(-0.551505\pi\)
−0.161102 + 0.986938i \(0.551505\pi\)
\(54\) 8.17620e6 0.130852
\(55\) 3.91485e7 0.576876
\(56\) 1.23007e7 0.167141
\(57\) 1.71272e8 2.14907
\(58\) 5.95055e7 0.690448
\(59\) 3.51354e7 0.377495 0.188747 0.982026i \(-0.439557\pi\)
0.188747 + 0.982026i \(0.439557\pi\)
\(60\) −7.75732e7 −0.772736
\(61\) 1.88656e8 1.74456 0.872279 0.489009i \(-0.162641\pi\)
0.872279 + 0.489009i \(0.162641\pi\)
\(62\) −1.36002e8 −1.16891
\(63\) 8.26461e7 0.660982
\(64\) −8.41258e7 −0.626786
\(65\) −9.53271e7 −0.662379
\(66\) 2.47911e8 1.60823
\(67\) 2.08556e8 1.26440 0.632201 0.774804i \(-0.282152\pi\)
0.632201 + 0.774804i \(0.282152\pi\)
\(68\) 0 0
\(69\) 3.08088e8 1.63627
\(70\) 1.29878e8 0.646536
\(71\) −4.89810e7 −0.228752 −0.114376 0.993438i \(-0.536487\pi\)
−0.114376 + 0.993438i \(0.536487\pi\)
\(72\) 4.99041e7 0.218847
\(73\) −1.30289e8 −0.536978 −0.268489 0.963283i \(-0.586524\pi\)
−0.268489 + 0.963283i \(0.586524\pi\)
\(74\) 3.03320e8 1.17587
\(75\) −2.08057e8 −0.759287
\(76\) 3.71561e8 1.27752
\(77\) −1.87746e8 −0.608642
\(78\) −6.03667e8 −1.84659
\(79\) −2.59845e8 −0.750571 −0.375286 0.926909i \(-0.622455\pi\)
−0.375286 + 0.926909i \(0.622455\pi\)
\(80\) 2.82186e8 0.770248
\(81\) −4.12541e8 −1.06484
\(82\) −9.26809e8 −2.26375
\(83\) 4.12715e8 0.954550 0.477275 0.878754i \(-0.341625\pi\)
0.477275 + 0.878754i \(0.341625\pi\)
\(84\) 3.72021e8 0.815288
\(85\) 0 0
\(86\) 1.27191e9 2.50734
\(87\) −3.79351e8 −0.709912
\(88\) −1.13366e8 −0.201517
\(89\) 1.05219e9 1.77763 0.888815 0.458267i \(-0.151530\pi\)
0.888815 + 0.458267i \(0.151530\pi\)
\(90\) 5.26916e8 0.846544
\(91\) 4.57164e8 0.698853
\(92\) 6.68373e8 0.972689
\(93\) 8.67017e8 1.20186
\(94\) −9.07169e8 −1.19843
\(95\) −8.26952e8 −1.04166
\(96\) 1.51498e9 1.82048
\(97\) −1.29676e9 −1.48726 −0.743628 0.668594i \(-0.766896\pi\)
−0.743628 + 0.668594i \(0.766896\pi\)
\(98\) 6.10975e8 0.669124
\(99\) −7.61689e8 −0.796928
\(100\) −4.51362e8 −0.451362
\(101\) 5.40379e8 0.516717 0.258358 0.966049i \(-0.416818\pi\)
0.258358 + 0.966049i \(0.416818\pi\)
\(102\) 0 0
\(103\) −2.13430e9 −1.86848 −0.934238 0.356649i \(-0.883919\pi\)
−0.934238 + 0.356649i \(0.883919\pi\)
\(104\) 2.76049e8 0.231386
\(105\) −8.27976e8 −0.664761
\(106\) 5.65910e8 0.435382
\(107\) 5.12879e6 0.00378258 0.00189129 0.999998i \(-0.499398\pi\)
0.00189129 + 0.999998i \(0.499398\pi\)
\(108\) −1.13078e8 −0.0799783
\(109\) −4.25009e8 −0.288389 −0.144195 0.989549i \(-0.546059\pi\)
−0.144195 + 0.989549i \(0.546059\pi\)
\(110\) −1.19699e9 −0.779511
\(111\) −1.93368e9 −1.20902
\(112\) −1.35329e9 −0.812663
\(113\) −7.28636e8 −0.420395 −0.210197 0.977659i \(-0.567411\pi\)
−0.210197 + 0.977659i \(0.567411\pi\)
\(114\) −5.23674e9 −2.90395
\(115\) −1.48754e9 −0.793101
\(116\) −8.22971e8 −0.422011
\(117\) 1.85472e9 0.915046
\(118\) −1.07429e9 −0.510095
\(119\) 0 0
\(120\) −4.99956e8 −0.220098
\(121\) −6.27630e8 −0.266177
\(122\) −5.76825e9 −2.35735
\(123\) 5.90845e9 2.32756
\(124\) 1.88092e9 0.714453
\(125\) 2.84271e9 1.04145
\(126\) −2.52695e9 −0.893160
\(127\) −2.52131e9 −0.860022 −0.430011 0.902824i \(-0.641490\pi\)
−0.430011 + 0.902824i \(0.641490\pi\)
\(128\) −1.40721e9 −0.463356
\(129\) −8.10849e9 −2.57802
\(130\) 2.91468e9 0.895047
\(131\) 5.51873e9 1.63726 0.818631 0.574320i \(-0.194733\pi\)
0.818631 + 0.574320i \(0.194733\pi\)
\(132\) −3.42865e9 −0.982970
\(133\) 3.96585e9 1.09902
\(134\) −6.37671e9 −1.70854
\(135\) 2.51668e8 0.0652119
\(136\) 0 0
\(137\) 9.40891e8 0.228190 0.114095 0.993470i \(-0.463603\pi\)
0.114095 + 0.993470i \(0.463603\pi\)
\(138\) −9.41998e9 −2.21103
\(139\) −8.97314e8 −0.203881 −0.101941 0.994790i \(-0.532505\pi\)
−0.101941 + 0.994790i \(0.532505\pi\)
\(140\) −1.79623e9 −0.395171
\(141\) 5.78325e9 1.23221
\(142\) 1.49762e9 0.309104
\(143\) −4.21335e9 −0.842588
\(144\) −5.49033e9 −1.06406
\(145\) 1.83162e9 0.344095
\(146\) 3.98367e9 0.725598
\(147\) −3.89500e9 −0.687986
\(148\) −4.19497e9 −0.718706
\(149\) −1.30561e9 −0.217009 −0.108504 0.994096i \(-0.534606\pi\)
−0.108504 + 0.994096i \(0.534606\pi\)
\(150\) 6.36145e9 1.02599
\(151\) −6.19193e9 −0.969236 −0.484618 0.874726i \(-0.661041\pi\)
−0.484618 + 0.874726i \(0.661041\pi\)
\(152\) 2.39469e9 0.363876
\(153\) 0 0
\(154\) 5.74044e9 0.822435
\(155\) −4.18621e9 −0.582544
\(156\) 8.34881e9 1.12866
\(157\) 1.28176e10 1.68367 0.841834 0.539736i \(-0.181476\pi\)
0.841834 + 0.539736i \(0.181476\pi\)
\(158\) 7.94490e9 1.01422
\(159\) −3.60770e9 −0.447655
\(160\) −7.31476e9 −0.882389
\(161\) 7.13386e9 0.836774
\(162\) 1.26137e10 1.43888
\(163\) 9.23048e9 1.02419 0.512095 0.858929i \(-0.328870\pi\)
0.512095 + 0.858929i \(0.328870\pi\)
\(164\) 1.28179e10 1.38363
\(165\) 7.63085e9 0.801485
\(166\) −1.26190e10 −1.28985
\(167\) −2.26110e9 −0.224955 −0.112477 0.993654i \(-0.535879\pi\)
−0.112477 + 0.993654i \(0.535879\pi\)
\(168\) 2.39766e9 0.232218
\(169\) −3.44926e8 −0.0325264
\(170\) 0 0
\(171\) 1.60895e10 1.43900
\(172\) −1.75907e10 −1.53252
\(173\) 6.75290e8 0.0573169 0.0286585 0.999589i \(-0.490876\pi\)
0.0286585 + 0.999589i \(0.490876\pi\)
\(174\) 1.15989e10 0.959276
\(175\) −4.81760e9 −0.388293
\(176\) 1.24723e10 0.979805
\(177\) 6.84862e9 0.524474
\(178\) −3.21715e10 −2.40204
\(179\) 1.70190e10 1.23907 0.619533 0.784971i \(-0.287322\pi\)
0.619533 + 0.784971i \(0.287322\pi\)
\(180\) −7.28733e9 −0.517419
\(181\) −9.47430e9 −0.656136 −0.328068 0.944654i \(-0.606397\pi\)
−0.328068 + 0.944654i \(0.606397\pi\)
\(182\) −1.39781e10 −0.944334
\(183\) 3.67729e10 2.42381
\(184\) 4.30763e9 0.277050
\(185\) 9.33639e9 0.586011
\(186\) −2.65095e10 −1.62403
\(187\) 0 0
\(188\) 1.25463e10 0.732496
\(189\) −1.20694e9 −0.0688028
\(190\) 2.52845e10 1.40755
\(191\) −5.23707e8 −0.0284733 −0.0142367 0.999899i \(-0.504532\pi\)
−0.0142367 + 0.999899i \(0.504532\pi\)
\(192\) −1.63979e10 −0.870827
\(193\) 1.35576e10 0.703355 0.351678 0.936121i \(-0.385611\pi\)
0.351678 + 0.936121i \(0.385611\pi\)
\(194\) 3.96491e10 2.00967
\(195\) −1.85812e10 −0.920278
\(196\) −8.44989e9 −0.408977
\(197\) −2.22167e10 −1.05095 −0.525474 0.850810i \(-0.676112\pi\)
−0.525474 + 0.850810i \(0.676112\pi\)
\(198\) 2.32891e10 1.07686
\(199\) 1.58102e10 0.714659 0.357329 0.933978i \(-0.383687\pi\)
0.357329 + 0.933978i \(0.383687\pi\)
\(200\) −2.90901e9 −0.128561
\(201\) 4.06518e10 1.75670
\(202\) −1.65224e10 −0.698220
\(203\) −8.78396e9 −0.363043
\(204\) 0 0
\(205\) −2.85278e10 −1.12817
\(206\) 6.52574e10 2.52480
\(207\) 2.89422e10 1.09563
\(208\) −3.03703e10 −1.12503
\(209\) −3.65503e10 −1.32505
\(210\) 2.53158e10 0.898267
\(211\) 4.76983e10 1.65666 0.828328 0.560244i \(-0.189293\pi\)
0.828328 + 0.560244i \(0.189293\pi\)
\(212\) −7.82663e9 −0.266111
\(213\) −9.54742e9 −0.317818
\(214\) −1.56816e8 −0.00511125
\(215\) 3.91502e10 1.24957
\(216\) −7.28784e8 −0.0227802
\(217\) 2.00760e10 0.614622
\(218\) 1.29949e10 0.389690
\(219\) −2.53961e10 −0.746052
\(220\) 1.65545e10 0.476447
\(221\) 0 0
\(222\) 5.91234e10 1.63370
\(223\) 4.45882e10 1.20739 0.603696 0.797215i \(-0.293694\pi\)
0.603696 + 0.797215i \(0.293694\pi\)
\(224\) 3.50797e10 0.930979
\(225\) −1.95451e10 −0.508413
\(226\) 2.22784e10 0.568064
\(227\) 6.65541e10 1.66364 0.831818 0.555048i \(-0.187300\pi\)
0.831818 + 0.555048i \(0.187300\pi\)
\(228\) 7.24250e10 1.77493
\(229\) 3.55296e10 0.853749 0.426875 0.904311i \(-0.359615\pi\)
0.426875 + 0.904311i \(0.359615\pi\)
\(230\) 4.54824e10 1.07169
\(231\) −3.65956e10 −0.845619
\(232\) −5.30401e9 −0.120201
\(233\) −4.02652e10 −0.895010 −0.447505 0.894281i \(-0.647687\pi\)
−0.447505 + 0.894281i \(0.647687\pi\)
\(234\) −5.67092e10 −1.23647
\(235\) −2.79232e10 −0.597256
\(236\) 1.48575e10 0.311776
\(237\) −5.06491e10 −1.04281
\(238\) 0 0
\(239\) 1.30898e10 0.259503 0.129752 0.991547i \(-0.458582\pi\)
0.129752 + 0.991547i \(0.458582\pi\)
\(240\) 5.50039e10 1.07015
\(241\) 3.29841e10 0.629836 0.314918 0.949119i \(-0.398023\pi\)
0.314918 + 0.949119i \(0.398023\pi\)
\(242\) 1.91902e10 0.359674
\(243\) −7.51494e10 −1.38260
\(244\) 7.97759e10 1.44085
\(245\) 1.88062e10 0.333468
\(246\) −1.80654e11 −3.14514
\(247\) 8.90006e10 1.52145
\(248\) 1.21225e10 0.203497
\(249\) 8.04467e10 1.32621
\(250\) −8.69175e10 −1.40727
\(251\) −5.32797e10 −0.847285 −0.423643 0.905829i \(-0.639249\pi\)
−0.423643 + 0.905829i \(0.639249\pi\)
\(252\) 3.49482e10 0.545911
\(253\) −6.57476e10 −1.00888
\(254\) 7.70905e10 1.16212
\(255\) 0 0
\(256\) 8.60987e10 1.25290
\(257\) 3.34024e10 0.477615 0.238808 0.971067i \(-0.423243\pi\)
0.238808 + 0.971067i \(0.423243\pi\)
\(258\) 2.47922e11 3.48358
\(259\) −4.47749e10 −0.618281
\(260\) −4.03105e10 −0.547064
\(261\) −3.56367e10 −0.475352
\(262\) −1.68738e11 −2.21237
\(263\) 2.58102e10 0.332653 0.166326 0.986071i \(-0.446810\pi\)
0.166326 + 0.986071i \(0.446810\pi\)
\(264\) −2.20975e10 −0.279979
\(265\) 1.74190e10 0.216979
\(266\) −1.21258e11 −1.48506
\(267\) 2.05095e11 2.46975
\(268\) 8.81909e10 1.04428
\(269\) −3.02035e10 −0.351700 −0.175850 0.984417i \(-0.556267\pi\)
−0.175850 + 0.984417i \(0.556267\pi\)
\(270\) −7.69490e9 −0.0881183
\(271\) −7.25899e10 −0.817550 −0.408775 0.912635i \(-0.634044\pi\)
−0.408775 + 0.912635i \(0.634044\pi\)
\(272\) 0 0
\(273\) 8.91108e10 0.970954
\(274\) −2.87683e10 −0.308345
\(275\) 4.44003e10 0.468154
\(276\) 1.30280e11 1.35141
\(277\) 8.69284e9 0.0887161 0.0443581 0.999016i \(-0.485876\pi\)
0.0443581 + 0.999016i \(0.485876\pi\)
\(278\) 2.74359e10 0.275497
\(279\) 8.14487e10 0.804758
\(280\) −1.15766e10 −0.112556
\(281\) 1.30456e10 0.124820 0.0624100 0.998051i \(-0.480121\pi\)
0.0624100 + 0.998051i \(0.480121\pi\)
\(282\) −1.76826e11 −1.66504
\(283\) 1.25572e11 1.16374 0.581869 0.813282i \(-0.302321\pi\)
0.581869 + 0.813282i \(0.302321\pi\)
\(284\) −2.07124e10 −0.188929
\(285\) −1.61190e11 −1.44723
\(286\) 1.28826e11 1.13856
\(287\) 1.36812e11 1.19030
\(288\) 1.42319e11 1.21898
\(289\) 0 0
\(290\) −5.60027e10 −0.464963
\(291\) −2.52765e11 −2.06632
\(292\) −5.50949e10 −0.443495
\(293\) 2.09036e11 1.65698 0.828488 0.560006i \(-0.189201\pi\)
0.828488 + 0.560006i \(0.189201\pi\)
\(294\) 1.19092e11 0.929649
\(295\) −3.30672e10 −0.254213
\(296\) −2.70364e10 −0.204709
\(297\) 1.11235e10 0.0829537
\(298\) 3.99199e10 0.293235
\(299\) 1.60096e11 1.15841
\(300\) −8.79799e10 −0.627101
\(301\) −1.87754e11 −1.31838
\(302\) 1.89322e11 1.30969
\(303\) 1.05331e11 0.717902
\(304\) −2.63458e11 −1.76922
\(305\) −1.77550e11 −1.17482
\(306\) 0 0
\(307\) 1.44198e11 0.926484 0.463242 0.886232i \(-0.346686\pi\)
0.463242 + 0.886232i \(0.346686\pi\)
\(308\) −7.93912e10 −0.502683
\(309\) −4.16019e11 −2.59597
\(310\) 1.27996e11 0.787169
\(311\) 3.05482e11 1.85167 0.925836 0.377925i \(-0.123362\pi\)
0.925836 + 0.377925i \(0.123362\pi\)
\(312\) 5.38077e10 0.321476
\(313\) 1.97546e11 1.16337 0.581685 0.813414i \(-0.302394\pi\)
0.581685 + 0.813414i \(0.302394\pi\)
\(314\) −3.91904e11 −2.27508
\(315\) −7.77811e10 −0.445120
\(316\) −1.09879e11 −0.619903
\(317\) 2.53026e11 1.40734 0.703670 0.710527i \(-0.251543\pi\)
0.703670 + 0.710527i \(0.251543\pi\)
\(318\) 1.10308e11 0.604899
\(319\) 8.09554e10 0.437711
\(320\) 7.91737e10 0.422091
\(321\) 9.99708e8 0.00525534
\(322\) −2.18122e11 −1.13070
\(323\) 0 0
\(324\) −1.74449e11 −0.879462
\(325\) −1.08115e11 −0.537542
\(326\) −2.82227e11 −1.38395
\(327\) −8.28432e10 −0.400675
\(328\) 8.26109e10 0.394099
\(329\) 1.33913e11 0.630144
\(330\) −2.33318e11 −1.08302
\(331\) 4.14467e11 1.89786 0.948930 0.315486i \(-0.102167\pi\)
0.948930 + 0.315486i \(0.102167\pi\)
\(332\) 1.74523e11 0.788371
\(333\) −1.81653e11 −0.809548
\(334\) 6.91343e10 0.303973
\(335\) −1.96279e11 −0.851475
\(336\) −2.63785e11 −1.12907
\(337\) −1.55413e11 −0.656375 −0.328187 0.944613i \(-0.606438\pi\)
−0.328187 + 0.944613i \(0.606438\pi\)
\(338\) 1.05463e10 0.0439517
\(339\) −1.42026e11 −0.584077
\(340\) 0 0
\(341\) −1.85026e11 −0.741033
\(342\) −4.91946e11 −1.94447
\(343\) −2.72323e11 −1.06233
\(344\) −1.13371e11 −0.436506
\(345\) −2.89953e11 −1.10190
\(346\) −2.06474e10 −0.0774501
\(347\) −1.69024e11 −0.625844 −0.312922 0.949779i \(-0.601308\pi\)
−0.312922 + 0.949779i \(0.601308\pi\)
\(348\) −1.60414e11 −0.586322
\(349\) −2.15573e11 −0.777823 −0.388911 0.921275i \(-0.627149\pi\)
−0.388911 + 0.921275i \(0.627149\pi\)
\(350\) 1.47301e11 0.524686
\(351\) −2.70858e10 −0.0952488
\(352\) −3.23304e11 −1.12246
\(353\) 3.02994e11 1.03860 0.519299 0.854593i \(-0.326193\pi\)
0.519299 + 0.854593i \(0.326193\pi\)
\(354\) −2.09401e11 −0.708701
\(355\) 4.60978e10 0.154047
\(356\) 4.44937e11 1.46816
\(357\) 0 0
\(358\) −5.20364e11 −1.67430
\(359\) −2.90075e11 −0.921692 −0.460846 0.887480i \(-0.652454\pi\)
−0.460846 + 0.887480i \(0.652454\pi\)
\(360\) −4.69665e10 −0.147376
\(361\) 4.49383e11 1.39262
\(362\) 2.89682e11 0.886611
\(363\) −1.22338e11 −0.369813
\(364\) 1.93319e11 0.577189
\(365\) 1.22620e11 0.361612
\(366\) −1.12435e12 −3.27520
\(367\) −1.41373e11 −0.406789 −0.203394 0.979097i \(-0.565197\pi\)
−0.203394 + 0.979097i \(0.565197\pi\)
\(368\) −4.73915e11 −1.34706
\(369\) 5.55048e11 1.55852
\(370\) −2.85465e11 −0.791855
\(371\) −8.35372e10 −0.228927
\(372\) 3.66631e11 0.992627
\(373\) 1.79070e11 0.478998 0.239499 0.970897i \(-0.423017\pi\)
0.239499 + 0.970897i \(0.423017\pi\)
\(374\) 0 0
\(375\) 5.54104e11 1.44694
\(376\) 8.08603e10 0.208636
\(377\) −1.97128e11 −0.502587
\(378\) 3.69028e10 0.0929707
\(379\) 2.66182e11 0.662677 0.331338 0.943512i \(-0.392500\pi\)
0.331338 + 0.943512i \(0.392500\pi\)
\(380\) −3.49689e11 −0.860312
\(381\) −4.91456e11 −1.19487
\(382\) 1.60126e10 0.0384749
\(383\) 6.18970e11 1.46986 0.734928 0.678145i \(-0.237216\pi\)
0.734928 + 0.678145i \(0.237216\pi\)
\(384\) −2.74295e11 −0.643765
\(385\) 1.76694e11 0.409873
\(386\) −4.14531e11 −0.950417
\(387\) −7.61722e11 −1.72622
\(388\) −5.48353e11 −1.22834
\(389\) −1.72722e11 −0.382450 −0.191225 0.981546i \(-0.561246\pi\)
−0.191225 + 0.981546i \(0.561246\pi\)
\(390\) 5.68132e11 1.24354
\(391\) 0 0
\(392\) −5.44592e10 −0.116489
\(393\) 1.07572e12 2.27473
\(394\) 6.79288e11 1.42011
\(395\) 2.44549e11 0.505451
\(396\) −3.22092e11 −0.658190
\(397\) −5.98018e9 −0.0120825 −0.00604125 0.999982i \(-0.501923\pi\)
−0.00604125 + 0.999982i \(0.501923\pi\)
\(398\) −4.83406e11 −0.965691
\(399\) 7.73026e11 1.52692
\(400\) 3.20042e11 0.625082
\(401\) 2.91381e9 0.00562745 0.00281372 0.999996i \(-0.499104\pi\)
0.00281372 + 0.999996i \(0.499104\pi\)
\(402\) −1.24295e12 −2.37376
\(403\) 4.50541e11 0.850866
\(404\) 2.28508e11 0.426761
\(405\) 3.88257e11 0.717087
\(406\) 2.68575e11 0.490566
\(407\) 4.12658e11 0.745444
\(408\) 0 0
\(409\) 4.39771e11 0.777091 0.388546 0.921430i \(-0.372978\pi\)
0.388546 + 0.921430i \(0.372978\pi\)
\(410\) 8.72252e11 1.52446
\(411\) 1.83399e11 0.317037
\(412\) −9.02521e11 −1.54319
\(413\) 1.58582e11 0.268212
\(414\) −8.84925e11 −1.48049
\(415\) −3.88420e11 −0.642814
\(416\) 7.87251e11 1.28882
\(417\) −1.74905e11 −0.283263
\(418\) 1.11755e12 1.79049
\(419\) 8.88321e11 1.40801 0.704006 0.710194i \(-0.251393\pi\)
0.704006 + 0.710194i \(0.251393\pi\)
\(420\) −3.50122e11 −0.549032
\(421\) 3.91195e11 0.606910 0.303455 0.952846i \(-0.401860\pi\)
0.303455 + 0.952846i \(0.401860\pi\)
\(422\) −1.45840e12 −2.23858
\(423\) 5.43286e11 0.825081
\(424\) −5.04422e10 −0.0757963
\(425\) 0 0
\(426\) 2.91918e11 0.429455
\(427\) 8.51485e11 1.23951
\(428\) 2.16879e9 0.00312406
\(429\) −8.21269e11 −1.17065
\(430\) −1.19704e12 −1.68850
\(431\) 7.81278e11 1.09058 0.545291 0.838247i \(-0.316419\pi\)
0.545291 + 0.838247i \(0.316419\pi\)
\(432\) 8.01790e10 0.110760
\(433\) 9.03790e11 1.23558 0.617791 0.786342i \(-0.288028\pi\)
0.617791 + 0.786342i \(0.288028\pi\)
\(434\) −6.13835e11 −0.830515
\(435\) 3.57020e11 0.478070
\(436\) −1.79722e11 −0.238183
\(437\) 1.38882e12 1.82171
\(438\) 7.76501e11 1.00811
\(439\) −5.14908e11 −0.661667 −0.330834 0.943689i \(-0.607330\pi\)
−0.330834 + 0.943689i \(0.607330\pi\)
\(440\) 1.06693e11 0.135706
\(441\) −3.65901e11 −0.460670
\(442\) 0 0
\(443\) −1.59851e12 −1.97196 −0.985981 0.166856i \(-0.946638\pi\)
−0.985981 + 0.166856i \(0.946638\pi\)
\(444\) −8.17687e11 −0.998536
\(445\) −9.90257e11 −1.19709
\(446\) −1.36331e12 −1.63150
\(447\) −2.54491e11 −0.301501
\(448\) −3.79697e11 −0.445334
\(449\) 8.81603e11 1.02368 0.511840 0.859081i \(-0.328964\pi\)
0.511840 + 0.859081i \(0.328964\pi\)
\(450\) 5.97603e11 0.686999
\(451\) −1.26089e12 −1.43511
\(452\) −3.08115e11 −0.347208
\(453\) −1.20694e12 −1.34661
\(454\) −2.03493e12 −2.24801
\(455\) −4.30253e11 −0.470623
\(456\) 4.66776e11 0.505553
\(457\) −4.45550e11 −0.477830 −0.238915 0.971041i \(-0.576792\pi\)
−0.238915 + 0.971041i \(0.576792\pi\)
\(458\) −1.08634e12 −1.15364
\(459\) 0 0
\(460\) −6.29029e11 −0.655029
\(461\) 1.05555e12 1.08849 0.544247 0.838925i \(-0.316815\pi\)
0.544247 + 0.838925i \(0.316815\pi\)
\(462\) 1.11893e12 1.14265
\(463\) −6.82069e11 −0.689785 −0.344892 0.938642i \(-0.612085\pi\)
−0.344892 + 0.938642i \(0.612085\pi\)
\(464\) 5.83534e11 0.584434
\(465\) −8.15980e11 −0.809359
\(466\) 1.23113e12 1.20939
\(467\) −1.14817e12 −1.11707 −0.558533 0.829482i \(-0.688636\pi\)
−0.558533 + 0.829482i \(0.688636\pi\)
\(468\) 7.84298e11 0.755745
\(469\) 9.41303e11 0.898363
\(470\) 8.53768e11 0.807049
\(471\) 2.49841e12 2.33921
\(472\) 9.57562e10 0.0888031
\(473\) 1.73039e12 1.58953
\(474\) 1.54863e12 1.40911
\(475\) −9.37889e11 −0.845338
\(476\) 0 0
\(477\) −3.38912e11 −0.299747
\(478\) −4.00228e11 −0.350657
\(479\) −1.39726e11 −0.121274 −0.0606369 0.998160i \(-0.519313\pi\)
−0.0606369 + 0.998160i \(0.519313\pi\)
\(480\) −1.42580e12 −1.22595
\(481\) −1.00483e12 −0.855931
\(482\) −1.00851e12 −0.851074
\(483\) 1.39054e12 1.16257
\(484\) −2.65403e11 −0.219837
\(485\) 1.22042e12 1.00155
\(486\) 2.29774e12 1.86826
\(487\) −6.54778e11 −0.527489 −0.263745 0.964593i \(-0.584958\pi\)
−0.263745 + 0.964593i \(0.584958\pi\)
\(488\) 5.14152e11 0.410395
\(489\) 1.79921e12 1.42296
\(490\) −5.75010e11 −0.450602
\(491\) −1.33697e11 −0.103814 −0.0519069 0.998652i \(-0.516530\pi\)
−0.0519069 + 0.998652i \(0.516530\pi\)
\(492\) 2.49848e12 1.92235
\(493\) 0 0
\(494\) −2.72124e12 −2.05587
\(495\) 7.16852e11 0.536668
\(496\) −1.33368e12 −0.989431
\(497\) −2.21073e11 −0.162529
\(498\) −2.45970e12 −1.79205
\(499\) −7.51123e11 −0.542323 −0.271162 0.962534i \(-0.587408\pi\)
−0.271162 + 0.962534i \(0.587408\pi\)
\(500\) 1.20208e12 0.860141
\(501\) −4.40735e11 −0.312541
\(502\) 1.62906e12 1.14490
\(503\) 3.90993e10 0.0272341 0.0136170 0.999907i \(-0.495665\pi\)
0.0136170 + 0.999907i \(0.495665\pi\)
\(504\) 2.25239e11 0.155491
\(505\) −5.08570e11 −0.347968
\(506\) 2.01027e12 1.36326
\(507\) −6.72332e10 −0.0451906
\(508\) −1.06617e12 −0.710300
\(509\) −1.04082e12 −0.687296 −0.343648 0.939098i \(-0.611663\pi\)
−0.343648 + 0.939098i \(0.611663\pi\)
\(510\) 0 0
\(511\) −5.88054e11 −0.381525
\(512\) −1.91202e12 −1.22964
\(513\) −2.34966e11 −0.149788
\(514\) −1.02130e12 −0.645383
\(515\) 2.00866e12 1.25827
\(516\) −3.42880e12 −2.12921
\(517\) −1.23417e12 −0.759747
\(518\) 1.36902e12 0.835459
\(519\) 1.31628e11 0.0796334
\(520\) −2.59799e11 −0.155820
\(521\) −2.49791e12 −1.48528 −0.742638 0.669693i \(-0.766426\pi\)
−0.742638 + 0.669693i \(0.766426\pi\)
\(522\) 1.08961e12 0.642325
\(523\) 2.04811e11 0.119700 0.0598501 0.998207i \(-0.480938\pi\)
0.0598501 + 0.998207i \(0.480938\pi\)
\(524\) 2.33368e12 1.35223
\(525\) −9.39050e11 −0.539476
\(526\) −7.89162e11 −0.449501
\(527\) 0 0
\(528\) 2.43111e12 1.36129
\(529\) 6.97088e11 0.387023
\(530\) −5.32597e11 −0.293196
\(531\) 6.43369e11 0.351184
\(532\) 1.67702e12 0.907686
\(533\) 3.07030e12 1.64781
\(534\) −6.27088e12 −3.33728
\(535\) −4.82688e9 −0.00254727
\(536\) 5.68386e11 0.297442
\(537\) 3.31735e12 1.72150
\(538\) 9.23489e11 0.475238
\(539\) 8.31213e11 0.424192
\(540\) 1.06422e11 0.0538591
\(541\) 2.24094e12 1.12471 0.562357 0.826894i \(-0.309895\pi\)
0.562357 + 0.826894i \(0.309895\pi\)
\(542\) 2.21948e12 1.10472
\(543\) −1.84674e12 −0.911604
\(544\) 0 0
\(545\) 3.99991e11 0.194208
\(546\) −2.72461e12 −1.31201
\(547\) 1.94999e12 0.931300 0.465650 0.884969i \(-0.345821\pi\)
0.465650 + 0.884969i \(0.345821\pi\)
\(548\) 3.97870e11 0.188464
\(549\) 3.45449e12 1.62296
\(550\) −1.35756e12 −0.632599
\(551\) −1.71006e12 −0.790367
\(552\) 8.39647e11 0.384921
\(553\) −1.17279e12 −0.533284
\(554\) −2.65788e11 −0.119879
\(555\) 1.81986e12 0.814177
\(556\) −3.79443e11 −0.168387
\(557\) −3.69055e12 −1.62459 −0.812293 0.583250i \(-0.801781\pi\)
−0.812293 + 0.583250i \(0.801781\pi\)
\(558\) −2.49034e12 −1.08744
\(559\) −4.21353e12 −1.82513
\(560\) 1.27363e12 0.547264
\(561\) 0 0
\(562\) −3.98876e11 −0.168665
\(563\) −7.69327e11 −0.322718 −0.161359 0.986896i \(-0.551588\pi\)
−0.161359 + 0.986896i \(0.551588\pi\)
\(564\) 2.44553e12 1.01770
\(565\) 6.85744e11 0.283103
\(566\) −3.83945e12 −1.57252
\(567\) −1.86198e12 −0.756574
\(568\) −1.33490e11 −0.0538124
\(569\) 4.75620e11 0.190219 0.0951097 0.995467i \(-0.469680\pi\)
0.0951097 + 0.995467i \(0.469680\pi\)
\(570\) 4.92848e12 1.95558
\(571\) −3.53469e12 −1.39152 −0.695759 0.718276i \(-0.744932\pi\)
−0.695759 + 0.718276i \(0.744932\pi\)
\(572\) −1.78168e12 −0.695901
\(573\) −1.02081e11 −0.0395595
\(574\) −4.18310e12 −1.60840
\(575\) −1.68710e12 −0.643628
\(576\) −1.54044e12 −0.583099
\(577\) −6.21322e11 −0.233360 −0.116680 0.993170i \(-0.537225\pi\)
−0.116680 + 0.993170i \(0.537225\pi\)
\(578\) 0 0
\(579\) 2.64266e12 0.977209
\(580\) 7.74527e11 0.284191
\(581\) 1.86276e12 0.678211
\(582\) 7.72842e12 2.79214
\(583\) 7.69902e11 0.276011
\(584\) −3.55084e11 −0.126320
\(585\) −1.74555e12 −0.616212
\(586\) −6.39139e12 −2.23901
\(587\) −5.46826e12 −1.90098 −0.950490 0.310756i \(-0.899418\pi\)
−0.950490 + 0.310756i \(0.899418\pi\)
\(588\) −1.64706e12 −0.568213
\(589\) 3.90839e12 1.33807
\(590\) 1.01105e12 0.343509
\(591\) −4.33049e12 −1.46014
\(592\) 2.97448e12 0.995321
\(593\) 1.92966e12 0.640819 0.320410 0.947279i \(-0.396179\pi\)
0.320410 + 0.947279i \(0.396179\pi\)
\(594\) −3.40106e11 −0.112092
\(595\) 0 0
\(596\) −5.52099e11 −0.179229
\(597\) 3.08174e12 0.992913
\(598\) −4.89504e12 −1.56531
\(599\) −4.29083e12 −1.36182 −0.680911 0.732366i \(-0.738416\pi\)
−0.680911 + 0.732366i \(0.738416\pi\)
\(600\) −5.67026e11 −0.178617
\(601\) −1.72436e12 −0.539128 −0.269564 0.962982i \(-0.586880\pi\)
−0.269564 + 0.962982i \(0.586880\pi\)
\(602\) 5.74069e12 1.78147
\(603\) 3.81888e12 1.17627
\(604\) −2.61835e12 −0.800500
\(605\) 5.90685e11 0.179249
\(606\) −3.22056e12 −0.970073
\(607\) −3.54265e12 −1.05920 −0.529602 0.848246i \(-0.677659\pi\)
−0.529602 + 0.848246i \(0.677659\pi\)
\(608\) 6.82931e12 2.02680
\(609\) −1.71218e12 −0.504395
\(610\) 5.42870e12 1.58749
\(611\) 3.00523e12 0.872354
\(612\) 0 0
\(613\) −2.75371e12 −0.787674 −0.393837 0.919180i \(-0.628853\pi\)
−0.393837 + 0.919180i \(0.628853\pi\)
\(614\) −4.40895e12 −1.25192
\(615\) −5.56065e12 −1.56743
\(616\) −5.11673e11 −0.143179
\(617\) 6.84976e12 1.90280 0.951398 0.307963i \(-0.0996474\pi\)
0.951398 + 0.307963i \(0.0996474\pi\)
\(618\) 1.27200e13 3.50784
\(619\) −6.91984e11 −0.189447 −0.0947235 0.995504i \(-0.530197\pi\)
−0.0947235 + 0.995504i \(0.530197\pi\)
\(620\) −1.77020e12 −0.481128
\(621\) −4.22663e11 −0.114046
\(622\) −9.34029e12 −2.50209
\(623\) 4.74902e12 1.26301
\(624\) −5.91979e12 −1.56306
\(625\) −5.90629e11 −0.154830
\(626\) −6.04007e12 −1.57202
\(627\) −7.12442e12 −1.84097
\(628\) 5.42010e12 1.39056
\(629\) 0 0
\(630\) 2.37820e12 0.601473
\(631\) 2.99016e12 0.750866 0.375433 0.926850i \(-0.377494\pi\)
0.375433 + 0.926850i \(0.377494\pi\)
\(632\) −7.08167e11 −0.176567
\(633\) 9.29740e12 2.30168
\(634\) −7.73643e12 −1.90169
\(635\) 2.37289e12 0.579157
\(636\) −1.52557e12 −0.369722
\(637\) −2.02402e12 −0.487065
\(638\) −2.47526e12 −0.591462
\(639\) −8.96897e11 −0.212808
\(640\) 1.32438e12 0.312034
\(641\) −3.46519e12 −0.810711 −0.405356 0.914159i \(-0.632852\pi\)
−0.405356 + 0.914159i \(0.632852\pi\)
\(642\) −3.05666e10 −0.00710133
\(643\) 3.07922e10 0.00710381 0.00355190 0.999994i \(-0.498869\pi\)
0.00355190 + 0.999994i \(0.498869\pi\)
\(644\) 3.01666e12 0.691099
\(645\) 7.63118e12 1.73609
\(646\) 0 0
\(647\) −8.58031e11 −0.192501 −0.0962506 0.995357i \(-0.530685\pi\)
−0.0962506 + 0.995357i \(0.530685\pi\)
\(648\) −1.12432e12 −0.250496
\(649\) −1.46153e12 −0.323375
\(650\) 3.30569e12 0.726361
\(651\) 3.91323e12 0.853927
\(652\) 3.90325e12 0.845887
\(653\) 7.56711e12 1.62862 0.814312 0.580428i \(-0.197115\pi\)
0.814312 + 0.580428i \(0.197115\pi\)
\(654\) 2.53298e12 0.541416
\(655\) −5.19387e12 −1.10257
\(656\) −9.08865e12 −1.91616
\(657\) −2.38575e12 −0.499551
\(658\) −4.09445e12 −0.851489
\(659\) 1.21600e12 0.251159 0.125580 0.992084i \(-0.459921\pi\)
0.125580 + 0.992084i \(0.459921\pi\)
\(660\) 3.22682e12 0.661953
\(661\) −6.17442e11 −0.125803 −0.0629013 0.998020i \(-0.520035\pi\)
−0.0629013 + 0.998020i \(0.520035\pi\)
\(662\) −1.26726e13 −2.56451
\(663\) 0 0
\(664\) 1.12479e12 0.224551
\(665\) −3.73240e12 −0.740100
\(666\) 5.55413e12 1.09391
\(667\) −3.07610e12 −0.601774
\(668\) −9.56139e11 −0.185792
\(669\) 8.69117e12 1.67749
\(670\) 6.00134e12 1.15057
\(671\) −7.84752e12 −1.49445
\(672\) 6.83776e12 1.29346
\(673\) −4.43202e12 −0.832786 −0.416393 0.909185i \(-0.636706\pi\)
−0.416393 + 0.909185i \(0.636706\pi\)
\(674\) 4.75183e12 0.886934
\(675\) 2.85430e11 0.0529216
\(676\) −1.45857e11 −0.0268638
\(677\) −7.03236e12 −1.28663 −0.643313 0.765603i \(-0.722441\pi\)
−0.643313 + 0.765603i \(0.722441\pi\)
\(678\) 4.34253e12 0.789241
\(679\) −5.85283e12 −1.05670
\(680\) 0 0
\(681\) 1.29728e13 2.31138
\(682\) 5.65727e12 1.00133
\(683\) 3.12019e12 0.548640 0.274320 0.961638i \(-0.411547\pi\)
0.274320 + 0.961638i \(0.411547\pi\)
\(684\) 6.80370e12 1.18848
\(685\) −8.85505e11 −0.153668
\(686\) 8.32644e12 1.43549
\(687\) 6.92545e12 1.18616
\(688\) 1.24728e13 2.12235
\(689\) −1.87472e12 −0.316921
\(690\) 8.86547e12 1.48895
\(691\) −7.61866e10 −0.0127124 −0.00635620 0.999980i \(-0.502023\pi\)
−0.00635620 + 0.999980i \(0.502023\pi\)
\(692\) 2.85557e11 0.0473385
\(693\) −3.43784e12 −0.566221
\(694\) 5.16801e12 0.845679
\(695\) 8.44493e11 0.137298
\(696\) −1.03386e12 −0.167002
\(697\) 0 0
\(698\) 6.59128e12 1.05104
\(699\) −7.84852e12 −1.24348
\(700\) −2.03720e12 −0.320695
\(701\) −4.55938e12 −0.713139 −0.356570 0.934269i \(-0.616054\pi\)
−0.356570 + 0.934269i \(0.616054\pi\)
\(702\) 8.28163e11 0.128706
\(703\) −8.71677e12 −1.34604
\(704\) 3.49939e12 0.536927
\(705\) −5.44282e12 −0.829799
\(706\) −9.26420e12 −1.40342
\(707\) 2.43897e12 0.367129
\(708\) 2.89605e12 0.433167
\(709\) 9.54492e12 1.41861 0.709307 0.704899i \(-0.249008\pi\)
0.709307 + 0.704899i \(0.249008\pi\)
\(710\) −1.40947e12 −0.208157
\(711\) −4.75804e12 −0.698257
\(712\) 2.86760e12 0.418175
\(713\) 7.03050e12 1.01879
\(714\) 0 0
\(715\) 3.96533e12 0.567417
\(716\) 7.19673e12 1.02336
\(717\) 2.55148e12 0.360541
\(718\) 8.86922e12 1.24545
\(719\) 1.65457e12 0.230890 0.115445 0.993314i \(-0.463171\pi\)
0.115445 + 0.993314i \(0.463171\pi\)
\(720\) 5.16714e12 0.716563
\(721\) −9.63303e12 −1.32756
\(722\) −1.37401e13 −1.88180
\(723\) 6.42928e12 0.875065
\(724\) −4.00635e12 −0.541908
\(725\) 2.07733e12 0.279245
\(726\) 3.74056e12 0.499714
\(727\) −2.21622e12 −0.294244 −0.147122 0.989118i \(-0.547001\pi\)
−0.147122 + 0.989118i \(0.547001\pi\)
\(728\) 1.24593e12 0.164400
\(729\) −6.52814e12 −0.856082
\(730\) −3.74918e12 −0.488633
\(731\) 0 0
\(732\) 1.55500e13 2.00184
\(733\) 2.96185e11 0.0378961 0.0189481 0.999820i \(-0.493968\pi\)
0.0189481 + 0.999820i \(0.493968\pi\)
\(734\) 4.32255e12 0.549678
\(735\) 3.66572e12 0.463304
\(736\) 1.22847e13 1.54318
\(737\) −8.67530e12 −1.08313
\(738\) −1.69709e13 −2.10597
\(739\) −4.82363e12 −0.594941 −0.297470 0.954731i \(-0.596143\pi\)
−0.297470 + 0.954731i \(0.596143\pi\)
\(740\) 3.94803e12 0.483992
\(741\) 1.73481e13 2.11383
\(742\) 2.55420e12 0.309341
\(743\) 4.52977e12 0.545288 0.272644 0.962115i \(-0.412102\pi\)
0.272644 + 0.962115i \(0.412102\pi\)
\(744\) 2.36292e12 0.282729
\(745\) 1.22876e12 0.146138
\(746\) −5.47518e12 −0.647252
\(747\) 7.55726e12 0.888018
\(748\) 0 0
\(749\) 2.31485e10 0.00268754
\(750\) −1.69420e13 −1.95519
\(751\) 1.65211e13 1.89522 0.947610 0.319430i \(-0.103491\pi\)
0.947610 + 0.319430i \(0.103491\pi\)
\(752\) −8.89606e12 −1.01442
\(753\) −1.03853e13 −1.17718
\(754\) 6.02729e12 0.679127
\(755\) 5.82744e12 0.652704
\(756\) −5.10372e11 −0.0568249
\(757\) 1.53269e13 1.69638 0.848192 0.529690i \(-0.177692\pi\)
0.848192 + 0.529690i \(0.177692\pi\)
\(758\) −8.13865e12 −0.895450
\(759\) −1.28156e13 −1.40168
\(760\) −2.25373e12 −0.245042
\(761\) 2.48205e12 0.268274 0.134137 0.990963i \(-0.457174\pi\)
0.134137 + 0.990963i \(0.457174\pi\)
\(762\) 1.50265e13 1.61459
\(763\) −1.91825e12 −0.204902
\(764\) −2.21457e11 −0.0235164
\(765\) 0 0
\(766\) −1.89254e13 −1.98616
\(767\) 3.55885e12 0.371305
\(768\) 1.67824e13 1.74072
\(769\) 1.57447e13 1.62356 0.811778 0.583967i \(-0.198500\pi\)
0.811778 + 0.583967i \(0.198500\pi\)
\(770\) −5.40253e12 −0.553845
\(771\) 6.51082e12 0.663576
\(772\) 5.73304e12 0.580907
\(773\) −1.47271e11 −0.0148357 −0.00741786 0.999972i \(-0.502361\pi\)
−0.00741786 + 0.999972i \(0.502361\pi\)
\(774\) 2.32901e13 2.33258
\(775\) −4.74780e12 −0.472754
\(776\) −3.53411e12 −0.349866
\(777\) −8.72756e12 −0.859010
\(778\) 5.28108e12 0.516790
\(779\) 2.66345e13 2.59135
\(780\) −7.85736e12 −0.760065
\(781\) 2.03747e12 0.195957
\(782\) 0 0
\(783\) 5.20427e11 0.0494802
\(784\) 5.99147e12 0.566384
\(785\) −1.20630e13 −1.13382
\(786\) −3.28906e13 −3.07376
\(787\) −1.64023e13 −1.52412 −0.762059 0.647508i \(-0.775811\pi\)
−0.762059 + 0.647508i \(0.775811\pi\)
\(788\) −9.39466e12 −0.867987
\(789\) 5.03095e12 0.462172
\(790\) −7.47722e12 −0.682996
\(791\) −3.28865e12 −0.298692
\(792\) −2.07587e12 −0.187472
\(793\) 1.91088e13 1.71595
\(794\) 1.82847e11 0.0163266
\(795\) 3.39533e12 0.301461
\(796\) 6.68559e12 0.590243
\(797\) −3.29266e12 −0.289058 −0.144529 0.989501i \(-0.546167\pi\)
−0.144529 + 0.989501i \(0.546167\pi\)
\(798\) −2.36357e13 −2.06327
\(799\) 0 0
\(800\) −8.29605e12 −0.716088
\(801\) 1.92669e13 1.65373
\(802\) −8.90914e10 −0.00760416
\(803\) 5.41966e12 0.459994
\(804\) 1.71902e13 1.45087
\(805\) −6.71393e12 −0.563501
\(806\) −1.37755e13 −1.14974
\(807\) −5.88729e12 −0.488635
\(808\) 1.47272e12 0.121554
\(809\) 1.55916e13 1.27974 0.639870 0.768483i \(-0.278988\pi\)
0.639870 + 0.768483i \(0.278988\pi\)
\(810\) −1.18712e13 −0.968972
\(811\) −1.51604e11 −0.0123060 −0.00615301 0.999981i \(-0.501959\pi\)
−0.00615301 + 0.999981i \(0.501959\pi\)
\(812\) −3.71443e12 −0.299840
\(813\) −1.41493e13 −1.13587
\(814\) −1.26172e13 −1.00729
\(815\) −8.68713e12 −0.689711
\(816\) 0 0
\(817\) −3.65519e13 −2.87019
\(818\) −1.34463e13 −1.05005
\(819\) 8.37119e12 0.650144
\(820\) −1.20634e13 −0.931767
\(821\) 1.44623e13 1.11095 0.555475 0.831533i \(-0.312536\pi\)
0.555475 + 0.831533i \(0.312536\pi\)
\(822\) −5.60754e12 −0.428399
\(823\) 2.42578e13 1.84311 0.921557 0.388243i \(-0.126918\pi\)
0.921557 + 0.388243i \(0.126918\pi\)
\(824\) −5.81670e12 −0.439546
\(825\) 8.65455e12 0.650431
\(826\) −4.84872e12 −0.362424
\(827\) −6.48867e12 −0.482371 −0.241185 0.970479i \(-0.577536\pi\)
−0.241185 + 0.970479i \(0.577536\pi\)
\(828\) 1.22387e13 0.904893
\(829\) −1.83303e12 −0.134795 −0.0673977 0.997726i \(-0.521470\pi\)
−0.0673977 + 0.997726i \(0.521470\pi\)
\(830\) 1.18762e13 0.868610
\(831\) 1.69441e12 0.123258
\(832\) −8.52106e12 −0.616508
\(833\) 0 0
\(834\) 5.34782e12 0.382763
\(835\) 2.12800e12 0.151489
\(836\) −1.54559e13 −1.09437
\(837\) −1.18945e12 −0.0837687
\(838\) −2.71609e13 −1.90259
\(839\) −2.21690e13 −1.54461 −0.772303 0.635254i \(-0.780895\pi\)
−0.772303 + 0.635254i \(0.780895\pi\)
\(840\) −2.25652e12 −0.156380
\(841\) −1.07195e13 −0.738914
\(842\) −1.19610e13 −0.820094
\(843\) 2.54285e12 0.173419
\(844\) 2.01700e13 1.36825
\(845\) 3.24622e11 0.0219040
\(846\) −1.66113e13 −1.11490
\(847\) −2.83277e12 −0.189119
\(848\) 5.54953e12 0.368532
\(849\) 2.44767e13 1.61684
\(850\) 0 0
\(851\) −1.56799e13 −1.02485
\(852\) −4.03727e12 −0.262488
\(853\) −1.03748e13 −0.670979 −0.335489 0.942044i \(-0.608902\pi\)
−0.335489 + 0.942044i \(0.608902\pi\)
\(854\) −2.60346e13 −1.67491
\(855\) −1.51424e13 −0.969053
\(856\) 1.39777e10 0.000889825 0
\(857\) 6.86176e12 0.434532 0.217266 0.976112i \(-0.430286\pi\)
0.217266 + 0.976112i \(0.430286\pi\)
\(858\) 2.51108e13 1.58186
\(859\) −1.74774e13 −1.09524 −0.547619 0.836728i \(-0.684466\pi\)
−0.547619 + 0.836728i \(0.684466\pi\)
\(860\) 1.65552e13 1.03203
\(861\) 2.66674e13 1.65374
\(862\) −2.38880e13 −1.47366
\(863\) 2.44274e13 1.49910 0.749548 0.661950i \(-0.230271\pi\)
0.749548 + 0.661950i \(0.230271\pi\)
\(864\) −2.07838e12 −0.126886
\(865\) −6.35539e11 −0.0385984
\(866\) −2.76339e13 −1.66960
\(867\) 0 0
\(868\) 8.48944e12 0.507622
\(869\) 1.08088e13 0.642965
\(870\) −1.09161e13 −0.645997
\(871\) 2.11245e13 1.24367
\(872\) −1.15830e12 −0.0678416
\(873\) −2.37450e13 −1.38359
\(874\) −4.24639e13 −2.46161
\(875\) 1.28304e13 0.739953
\(876\) −1.07391e13 −0.616171
\(877\) −2.67317e13 −1.52591 −0.762953 0.646454i \(-0.776251\pi\)
−0.762953 + 0.646454i \(0.776251\pi\)
\(878\) 1.57436e13 0.894086
\(879\) 4.07454e13 2.30212
\(880\) −1.17381e13 −0.659822
\(881\) 1.44360e13 0.807338 0.403669 0.914905i \(-0.367735\pi\)
0.403669 + 0.914905i \(0.367735\pi\)
\(882\) 1.11876e13 0.622486
\(883\) 4.32149e12 0.239227 0.119613 0.992821i \(-0.461834\pi\)
0.119613 + 0.992821i \(0.461834\pi\)
\(884\) 0 0
\(885\) −6.44548e12 −0.353192
\(886\) 4.88754e13 2.66464
\(887\) 1.12787e13 0.611792 0.305896 0.952065i \(-0.401044\pi\)
0.305896 + 0.952065i \(0.401044\pi\)
\(888\) −5.26995e12 −0.284412
\(889\) −1.13798e13 −0.611049
\(890\) 3.02777e13 1.61759
\(891\) 1.71605e13 0.912180
\(892\) 1.88548e13 0.997195
\(893\) 2.60701e13 1.37186
\(894\) 7.78122e12 0.407407
\(895\) −1.60171e13 −0.834413
\(896\) −6.35137e12 −0.329216
\(897\) 3.12061e13 1.60944
\(898\) −2.69555e13 −1.38326
\(899\) −8.65669e12 −0.442011
\(900\) −8.26494e12 −0.419903
\(901\) 0 0
\(902\) 3.85526e13 1.93920
\(903\) −3.65972e13 −1.83169
\(904\) −1.98578e12 −0.0988950
\(905\) 8.91659e12 0.441856
\(906\) 3.69027e13 1.81962
\(907\) −5.70352e12 −0.279840 −0.139920 0.990163i \(-0.544685\pi\)
−0.139920 + 0.990163i \(0.544685\pi\)
\(908\) 2.81434e13 1.37401
\(909\) 9.89495e12 0.480702
\(910\) 1.31552e13 0.635934
\(911\) 3.37049e13 1.62129 0.810643 0.585540i \(-0.199118\pi\)
0.810643 + 0.585540i \(0.199118\pi\)
\(912\) −5.13535e13 −2.45807
\(913\) −1.71677e13 −0.817701
\(914\) 1.36229e13 0.645673
\(915\) −3.46082e13 −1.63224
\(916\) 1.50242e13 0.705119
\(917\) 2.49084e13 1.16328
\(918\) 0 0
\(919\) −2.15276e13 −0.995577 −0.497789 0.867298i \(-0.665854\pi\)
−0.497789 + 0.867298i \(0.665854\pi\)
\(920\) −4.05406e12 −0.186572
\(921\) 2.81073e13 1.28721
\(922\) −3.22742e13 −1.47084
\(923\) −4.96127e12 −0.225001
\(924\) −1.54750e13 −0.698404
\(925\) 1.05889e13 0.475568
\(926\) 2.08546e13 0.932080
\(927\) −3.90814e13 −1.73825
\(928\) −1.51262e13 −0.669522
\(929\) −3.52619e13 −1.55323 −0.776613 0.629978i \(-0.783064\pi\)
−0.776613 + 0.629978i \(0.783064\pi\)
\(930\) 2.49490e13 1.09366
\(931\) −1.75581e13 −0.765957
\(932\) −1.70267e13 −0.739196
\(933\) 5.95448e13 2.57263
\(934\) 3.51059e13 1.50945
\(935\) 0 0
\(936\) 5.05477e12 0.215258
\(937\) −6.89322e12 −0.292142 −0.146071 0.989274i \(-0.546663\pi\)
−0.146071 + 0.989274i \(0.546663\pi\)
\(938\) −2.87809e13 −1.21392
\(939\) 3.85058e13 1.61633
\(940\) −1.18078e13 −0.493279
\(941\) 5.81040e12 0.241575 0.120788 0.992678i \(-0.461458\pi\)
0.120788 + 0.992678i \(0.461458\pi\)
\(942\) −7.63902e13 −3.16088
\(943\) 4.79107e13 1.97301
\(944\) −1.05349e13 −0.431773
\(945\) 1.13589e12 0.0463333
\(946\) −5.29077e13 −2.14788
\(947\) −2.09948e13 −0.848277 −0.424139 0.905597i \(-0.639423\pi\)
−0.424139 + 0.905597i \(0.639423\pi\)
\(948\) −2.14178e13 −0.861264
\(949\) −1.31970e13 −0.528173
\(950\) 2.86765e13 1.14227
\(951\) 4.93201e13 1.95529
\(952\) 0 0
\(953\) 4.60372e13 1.80797 0.903984 0.427567i \(-0.140629\pi\)
0.903984 + 0.427567i \(0.140629\pi\)
\(954\) 1.03624e13 0.405036
\(955\) 4.92879e11 0.0191745
\(956\) 5.53522e12 0.214326
\(957\) 1.57799e13 0.608135
\(958\) 4.27220e12 0.163873
\(959\) 4.24666e12 0.162130
\(960\) 1.54326e13 0.586433
\(961\) −6.65451e12 −0.251687
\(962\) 3.07232e13 1.15659
\(963\) 9.39138e10 0.00351894
\(964\) 1.39478e13 0.520187
\(965\) −1.27595e13 −0.473655
\(966\) −4.25165e13 −1.57094
\(967\) −3.36646e13 −1.23809 −0.619047 0.785354i \(-0.712481\pi\)
−0.619047 + 0.785354i \(0.712481\pi\)
\(968\) −1.71051e12 −0.0626162
\(969\) 0 0
\(970\) −3.73151e13 −1.35336
\(971\) −4.32838e13 −1.56257 −0.781284 0.624175i \(-0.785435\pi\)
−0.781284 + 0.624175i \(0.785435\pi\)
\(972\) −3.17781e13 −1.14190
\(973\) −4.04997e12 −0.144859
\(974\) 2.00202e13 0.712776
\(975\) −2.10740e13 −0.746836
\(976\) −5.65657e13 −1.99540
\(977\) −2.72015e13 −0.955141 −0.477570 0.878593i \(-0.658482\pi\)
−0.477570 + 0.878593i \(0.658482\pi\)
\(978\) −5.50120e13 −1.92279
\(979\) −4.37682e13 −1.52278
\(980\) 7.95249e12 0.275414
\(981\) −7.78240e12 −0.268289
\(982\) 4.08787e12 0.140280
\(983\) −3.51517e13 −1.20076 −0.600379 0.799716i \(-0.704984\pi\)
−0.600379 + 0.799716i \(0.704984\pi\)
\(984\) 1.61026e13 0.547542
\(985\) 2.09089e13 0.707731
\(986\) 0 0
\(987\) 2.61023e13 0.875492
\(988\) 3.76353e13 1.25658
\(989\) −6.57505e13 −2.18532
\(990\) −2.19182e13 −0.725180
\(991\) 2.19268e13 0.722177 0.361088 0.932532i \(-0.382405\pi\)
0.361088 + 0.932532i \(0.382405\pi\)
\(992\) 3.45715e13 1.13348
\(993\) 8.07883e13 2.63680
\(994\) 6.75943e12 0.219620
\(995\) −1.48795e13 −0.481266
\(996\) 3.40181e13 1.09532
\(997\) 5.52175e13 1.76990 0.884949 0.465688i \(-0.154193\pi\)
0.884949 + 0.465688i \(0.154193\pi\)
\(998\) 2.29660e13 0.732821
\(999\) 2.65280e12 0.0842673
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 289.10.a.e.1.3 yes 12
17.16 even 2 289.10.a.d.1.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.d.1.3 12 17.16 even 2
289.10.a.e.1.3 yes 12 1.1 even 1 trivial