Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [261,12,Mod(1,261)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(261, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("261.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 261 = 3^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 261.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: | \(200.537570126\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} - 388180519304 x^{4} + 193065378004825 x^{3} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-82.7218\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 261.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 85.7218 | 1.89420 | 0.947101 | − | 0.320934i | \(-0.103997\pi\) | ||||
0.947101 | + | 0.320934i | \(0.103997\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5300.23 | 2.58800 | ||||||||
\(5\) | 1506.26 | 0.215559 | 0.107780 | − | 0.994175i | \(-0.465626\pi\) | ||||
0.107780 | + | 0.994175i | \(0.465626\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7069.49 | −0.158982 | −0.0794912 | − | 0.996836i | \(-0.525330\pi\) | ||||
−0.0794912 | + | 0.996836i | \(0.525330\pi\) | |||||||
\(8\) | 278787. | 3.00800 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 129120. | 0.408313 | ||||||||
\(11\) | −598395. | −1.12028 | −0.560142 | − | 0.828397i | \(-0.689253\pi\) | ||||
−0.560142 | + | 0.828397i | \(0.689253\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −284167. | −0.212268 | −0.106134 | − | 0.994352i | \(-0.533847\pi\) | ||||
−0.106134 | + | 0.994352i | \(0.533847\pi\) | |||||||
\(14\) | −606010. | −0.301145 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.30433e7 | 3.10976 | ||||||||
\(17\) | −6.02872e6 | −1.02981 | −0.514904 | − | 0.857248i | \(-0.672172\pi\) | ||||
−0.514904 | + | 0.857248i | \(0.672172\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.04134e7 | −0.964825 | −0.482413 | − | 0.875944i | \(-0.660239\pi\) | ||||
−0.482413 | + | 0.875944i | \(0.660239\pi\) | |||||||
\(20\) | 7.98356e6 | 0.557868 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.12955e7 | −2.12204 | ||||||||
\(23\) | −3.07410e7 | −0.995897 | −0.497949 | − | 0.867207i | \(-0.665913\pi\) | ||||
−0.497949 | + | 0.867207i | \(0.665913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.65593e7 | −0.953534 | ||||||||
\(26\) | −2.43593e7 | −0.402079 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.74700e7 | −0.411447 | ||||||||
\(29\) | −2.05111e7 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00119e7 | 0.125545 | 0.0627725 | − | 0.998028i | \(-0.480006\pi\) | ||||
0.0627725 | + | 0.998028i | \(0.480006\pi\) | |||||||
\(32\) | 5.47138e8 | 2.88252 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.16793e8 | −1.95066 | ||||||||
\(35\) | −1.06485e7 | −0.0342701 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.29372e8 | −0.780867 | −0.390433 | − | 0.920631i | \(-0.627675\pi\) | ||||
−0.390433 | + | 0.920631i | \(0.627675\pi\) | |||||||
\(38\) | −8.92657e8 | −1.82757 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.19928e8 | 0.648402 | ||||||||
\(41\) | 1.33409e8 | 0.179834 | 0.0899172 | − | 0.995949i | \(-0.471340\pi\) | ||||
0.0899172 | + | 0.995949i | \(0.471340\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.51972e8 | −0.157647 | −0.0788236 | − | 0.996889i | \(-0.525116\pi\) | ||||
−0.0788236 | + | 0.996889i | \(0.525116\pi\) | |||||||
\(44\) | −3.17163e9 | −2.89930 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.63517e9 | −1.88643 | ||||||||
\(47\) | −5.65222e8 | −0.359485 | −0.179743 | − | 0.983714i | \(-0.557526\pi\) | ||||
−0.179743 | + | 0.983714i | \(0.557526\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.92735e9 | −0.974725 | ||||||||
\(50\) | −3.99115e9 | −1.80619 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.50615e9 | −0.549351 | ||||||||
\(53\) | 5.83151e9 | 1.91542 | 0.957709 | − | 0.287738i | \(-0.0929032\pi\) | ||||
0.957709 | + | 0.287738i | \(0.0929032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.01341e8 | −0.241487 | ||||||||
\(56\) | −1.97089e9 | −0.478220 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.75825e9 | −0.351745 | ||||||||
\(59\) | 8.59503e9 | 1.56517 | 0.782585 | − | 0.622544i | \(-0.213901\pi\) | ||||
0.782585 | + | 0.622544i | \(0.213901\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.25836e10 | −1.90761 | −0.953807 | − | 0.300419i | \(-0.902873\pi\) | ||||
−0.953807 | + | 0.300419i | \(0.902873\pi\) | |||||||
\(62\) | 1.71546e9 | 0.237808 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.01890e10 | 2.35031 | ||||||||
\(65\) | −4.28030e8 | −0.0457563 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.31795e10 | 1.19258 | 0.596291 | − | 0.802768i | \(-0.296640\pi\) | ||||
0.596291 | + | 0.802768i | \(0.296640\pi\) | |||||||
\(68\) | −3.19536e10 | −2.66515 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9.12811e8 | −0.0649145 | ||||||||
\(71\) | 4.99850e9 | 0.328790 | 0.164395 | − | 0.986395i | \(-0.447433\pi\) | ||||
0.164395 | + | 0.986395i | \(0.447433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.78444e9 | 0.213661 | 0.106831 | − | 0.994277i | \(-0.465930\pi\) | ||||
0.106831 | + | 0.994277i | \(0.465930\pi\) | |||||||
\(74\) | −2.82344e10 | −1.47912 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.51936e10 | −2.49697 | ||||||||
\(77\) | 4.23035e9 | 0.178105 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.61053e10 | −1.32015 | −0.660074 | − | 0.751201i | \(-0.729475\pi\) | ||||
−0.660074 | + | 0.751201i | \(0.729475\pi\) | |||||||
\(80\) | 1.96467e10 | 0.670338 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.14360e10 | 0.340643 | ||||||||
\(83\) | 3.39624e10 | 0.946387 | 0.473193 | − | 0.880959i | \(-0.343101\pi\) | ||||
0.473193 | + | 0.880959i | \(0.343101\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.08085e9 | −0.221984 | ||||||||
\(86\) | −1.30273e10 | −0.298616 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.66825e11 | −3.36982 | ||||||||
\(89\) | −8.21218e10 | −1.55888 | −0.779441 | − | 0.626475i | \(-0.784497\pi\) | ||||
−0.779441 | + | 0.626475i | \(0.784497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00891e9 | 0.0337469 | ||||||||
\(92\) | −1.62934e11 | −2.57739 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.84519e10 | −0.680938 | ||||||||
\(95\) | −1.56854e10 | −0.207977 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.18025e10 | −0.494262 | −0.247131 | − | 0.968982i | \(-0.579488\pi\) | ||||
−0.247131 | + | 0.968982i | \(0.579488\pi\) | |||||||
\(98\) | −1.65216e11 | −1.84633 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.46775e11 | −2.46775 | ||||||||
\(101\) | 1.93279e11 | 1.82986 | 0.914930 | − | 0.403613i | \(-0.132246\pi\) | ||||
0.914930 | + | 0.403613i | \(0.132246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.18942e11 | 1.01095 | 0.505475 | − | 0.862841i | \(-0.331317\pi\) | ||||
0.505475 | + | 0.862841i | \(0.331317\pi\) | |||||||
\(104\) | −7.92221e10 | −0.638503 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.99888e11 | 3.62819 | ||||||||
\(107\) | −1.74684e11 | −1.20404 | −0.602022 | − | 0.798480i | \(-0.705638\pi\) | ||||
−0.602022 | + | 0.798480i | \(0.705638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.14362e10 | −0.257949 | −0.128975 | − | 0.991648i | \(-0.541169\pi\) | ||||
−0.128975 | + | 0.991648i | \(0.541169\pi\) | |||||||
\(110\) | −7.72646e10 | −0.457426 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.22095e10 | −0.494398 | ||||||||
\(113\) | 7.24493e10 | 0.369916 | 0.184958 | − | 0.982746i | \(-0.440785\pi\) | ||||
0.184958 | + | 0.982746i | \(0.440785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.63040e10 | −0.214675 | ||||||||
\(116\) | −1.08714e11 | −0.480580 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.36782e11 | 2.96475 | ||||||||
\(119\) | 4.26200e10 | 0.163721 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.27646e10 | 0.255036 | ||||||||
\(122\) | −1.07869e12 | −3.61341 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.06068e11 | 0.324911 | ||||||||
\(125\) | −1.43679e11 | −0.421102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.62132e11 | 0.435460 | 0.217730 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217730 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(128\) | 6.10103e11 | 1.56945 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.66915e10 | −0.0866718 | ||||||||
\(131\) | −4.23024e10 | −0.0958016 | −0.0479008 | − | 0.998852i | \(-0.515253\pi\) | ||||
−0.0479008 | + | 0.998852i | \(0.515253\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.36176e10 | 0.153390 | ||||||||
\(134\) | 1.12977e12 | 2.25899 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.68073e12 | −3.09766 | ||||||||
\(137\) | 9.90449e11 | 1.75335 | 0.876676 | − | 0.481082i | \(-0.159756\pi\) | ||||
0.876676 | + | 0.481082i | \(0.159756\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.58932e10 | 0.0913646 | 0.0456823 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456823 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(140\) | −5.64397e10 | −0.0886912 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.28480e11 | 0.622795 | ||||||||
\(143\) | 1.70044e11 | 0.237801 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.08952e10 | −0.0400283 | ||||||||
\(146\) | 3.24409e11 | 0.404718 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.74575e12 | −2.02089 | ||||||||
\(149\) | −5.84976e11 | −0.652550 | −0.326275 | − | 0.945275i | \(-0.605794\pi\) | ||||
−0.326275 | + | 0.945275i | \(0.605794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.14354e12 | 1.18543 | 0.592716 | − | 0.805412i | \(-0.298056\pi\) | ||||
0.592716 | + | 0.805412i | \(0.298056\pi\) | |||||||
\(152\) | −2.90313e12 | −2.90220 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.62633e11 | 0.337368 | ||||||||
\(155\) | 3.01433e10 | 0.0270624 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.19892e12 | −1.00309 | −0.501547 | − | 0.865130i | \(-0.667236\pi\) | ||||
−0.501547 | + | 0.865130i | \(0.667236\pi\) | |||||||
\(158\) | −3.09502e12 | −2.50063 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.24135e11 | 0.621353 | ||||||||
\(161\) | 2.17323e11 | 0.158330 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.10135e12 | −1.43043 | −0.715216 | − | 0.698904i | \(-0.753671\pi\) | ||||
−0.715216 | + | 0.698904i | \(0.753671\pi\) | |||||||
\(164\) | 7.07097e11 | 0.465413 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.91132e12 | 1.79265 | ||||||||
\(167\) | −2.49583e12 | −1.48688 | −0.743438 | − | 0.668805i | \(-0.766806\pi\) | ||||
−0.743438 | + | 0.668805i | \(0.766806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.71141e12 | −0.954942 | ||||||||
\(170\) | −7.78427e11 | −0.420483 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.05485e11 | −0.407992 | ||||||||
\(173\) | 1.72047e11 | 0.0844100 | 0.0422050 | − | 0.999109i | \(-0.486562\pi\) | ||||
0.0422050 | + | 0.999109i | \(0.486562\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.29151e11 | 0.151595 | ||||||||
\(176\) | −7.80504e12 | −3.48382 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.03963e12 | −2.95284 | ||||||||
\(179\) | 3.23099e12 | 1.31415 | 0.657074 | − | 0.753826i | \(-0.271794\pi\) | ||||
0.657074 | + | 0.753826i | \(0.271794\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.32931e12 | 0.891239 | 0.445620 | − | 0.895222i | \(-0.352983\pi\) | ||||
0.445620 | + | 0.895222i | \(0.352983\pi\) | |||||||
\(182\) | 1.72208e11 | 0.0639235 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.57020e12 | −2.99566 | ||||||||
\(185\) | −4.96121e11 | −0.168323 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.60755e12 | 1.15368 | ||||||||
\(188\) | −2.99581e12 | −0.930349 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.34458e12 | −0.393950 | ||||||||
\(191\) | −8.46740e11 | −0.241028 | −0.120514 | − | 0.992712i | \(-0.538454\pi\) | ||||
−0.120514 | + | 0.992712i | \(0.538454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.76009e12 | −0.741921 | −0.370960 | − | 0.928649i | \(-0.620971\pi\) | ||||
−0.370960 | + | 0.928649i | \(0.620971\pi\) | |||||||
\(194\) | −3.58339e12 | −0.936233 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.02154e13 | −2.52259 | ||||||||
\(197\) | −4.20436e12 | −1.00957 | −0.504785 | − | 0.863245i | \(-0.668428\pi\) | ||||
−0.504785 | + | 0.863245i | \(0.668428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.87735e12 | −1.78932 | −0.894661 | − | 0.446746i | \(-0.852583\pi\) | ||||
−0.894661 | + | 0.446746i | \(0.852583\pi\) | |||||||
\(200\) | −1.29801e13 | −2.86823 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.65683e13 | 3.46613 | ||||||||
\(203\) | 1.45003e11 | 0.0295223 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00949e11 | 0.0387650 | ||||||||
\(206\) | 1.01959e13 | 1.91494 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.70647e12 | −0.660104 | ||||||||
\(209\) | 6.23134e12 | 1.08088 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03418e13 | 1.70233 | 0.851165 | − | 0.524899i | \(-0.175897\pi\) | ||||
0.851165 | + | 0.524899i | \(0.175897\pi\) | |||||||
\(212\) | 3.09084e13 | 4.95711 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.49742e13 | −2.28070 | ||||||||
\(215\) | −2.28910e11 | −0.0339823 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.41474e11 | −0.0199595 | ||||||||
\(218\) | −3.55199e12 | −0.488608 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.77732e12 | −0.624970 | ||||||||
\(221\) | 1.71316e12 | 0.218595 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.02014e12 | 0.488162 | 0.244081 | − | 0.969755i | \(-0.421514\pi\) | ||||
0.244081 | + | 0.969755i | \(0.421514\pi\) | |||||||
\(224\) | −3.86799e12 | −0.458270 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.21049e12 | 0.700696 | ||||||||
\(227\) | −1.61832e13 | −1.78206 | −0.891030 | − | 0.453944i | \(-0.850017\pi\) | ||||
−0.891030 | + | 0.453944i | \(0.850017\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.45521e13 | 1.52697 | 0.763485 | − | 0.645826i | \(-0.223487\pi\) | ||||
0.763485 | + | 0.645826i | \(0.223487\pi\) | |||||||
\(230\) | −3.96927e12 | −0.406637 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.71825e12 | −0.558572 | ||||||||
\(233\) | −1.36170e13 | −1.29904 | −0.649520 | − | 0.760344i | \(-0.725030\pi\) | ||||
−0.649520 | + | 0.760344i | \(0.725030\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.51374e11 | −0.0774903 | ||||||||
\(236\) | 4.55557e13 | 4.05067 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.65346e12 | 0.310121 | ||||||||
\(239\) | −3.48235e12 | −0.288858 | −0.144429 | − | 0.989515i | \(-0.546135\pi\) | ||||
−0.144429 | + | 0.989515i | \(0.546135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.57570e12 | −0.441780 | −0.220890 | − | 0.975299i | \(-0.570896\pi\) | ||||
−0.220890 | + | 0.975299i | \(0.570896\pi\) | |||||||
\(242\) | 6.23752e12 | 0.483089 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.66960e13 | −4.93691 | ||||||||
\(245\) | −2.90310e12 | −0.210111 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.95915e12 | 0.204802 | ||||||||
\(248\) | 5.57908e12 | 0.377640 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.23164e13 | −0.797653 | ||||||||
\(251\) | 1.23140e13 | 0.780177 | 0.390088 | − | 0.920777i | \(-0.372444\pi\) | ||||
0.390088 | + | 0.920777i | \(0.372444\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.83952e13 | 1.11569 | ||||||||
\(254\) | 1.38982e13 | 0.824849 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.09519e13 | 0.622546 | ||||||||
\(257\) | −2.71133e13 | −1.50852 | −0.754258 | − | 0.656578i | \(-0.772003\pi\) | ||||
−0.754258 | + | 0.656578i | \(0.772003\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.32849e12 | 0.124144 | ||||||||
\(260\) | −2.26866e12 | −0.118418 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.62624e12 | −0.181468 | ||||||||
\(263\) | −1.68153e13 | −0.824038 | −0.412019 | − | 0.911175i | \(-0.635176\pi\) | ||||
−0.412019 | + | 0.911175i | \(0.635176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.78380e12 | 0.412886 | ||||||||
\(266\) | 6.31064e12 | 0.290552 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.98546e13 | 3.08641 | ||||||||
\(269\) | 3.03478e13 | 1.31368 | 0.656840 | − | 0.754030i | \(-0.271893\pi\) | ||||
0.656840 | + | 0.754030i | \(0.271893\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.31818e13 | −0.547826 | −0.273913 | − | 0.961754i | \(-0.588318\pi\) | ||||
−0.273913 | + | 0.961754i | \(0.588318\pi\) | |||||||
\(272\) | −7.86344e13 | −3.20246 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.49031e13 | 3.32120 | ||||||||
\(275\) | 2.78608e13 | 1.06823 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.85013e13 | 1.78696 | 0.893480 | − | 0.449103i | \(-0.148256\pi\) | ||||
0.893480 | + | 0.449103i | \(0.148256\pi\) | |||||||
\(278\) | 4.79127e12 | 0.173063 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.96868e12 | −0.103085 | ||||||||
\(281\) | 1.57905e13 | 0.537663 | 0.268832 | − | 0.963187i | \(-0.413362\pi\) | ||||
0.268832 | + | 0.963187i | \(0.413362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.55960e13 | −1.16567 | −0.582836 | − | 0.812590i | \(-0.698057\pi\) | ||||
−0.582836 | + | 0.812590i | \(0.698057\pi\) | |||||||
\(284\) | 2.64932e13 | 0.850910 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.45765e13 | 0.450442 | ||||||||
\(287\) | −9.43132e11 | −0.0285905 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.07357e12 | 0.0605036 | ||||||||
\(290\) | −2.64840e12 | −0.0758218 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00584e13 | 0.552957 | ||||||||
\(293\) | 6.08679e13 | 1.64671 | 0.823354 | − | 0.567528i | \(-0.192100\pi\) | ||||
0.823354 | + | 0.567528i | \(0.192100\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.29464e13 | 0.337387 | ||||||||
\(296\) | −9.18247e13 | −2.34885 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.01452e13 | −1.23606 | ||||||||
\(299\) | 8.73556e12 | 0.211397 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.07436e12 | 0.0250631 | ||||||||
\(302\) | 9.80260e13 | 2.24545 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.35825e14 | −3.00038 | ||||||||
\(305\) | −1.89542e13 | −0.411204 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.27841e12 | 0.0267552 | 0.0133776 | − | 0.999911i | \(-0.495742\pi\) | ||||
0.0133776 | + | 0.999911i | \(0.495742\pi\) | |||||||
\(308\) | 2.24218e13 | 0.460938 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.58394e12 | 0.0512616 | ||||||||
\(311\) | 5.67748e13 | 1.10656 | 0.553278 | − | 0.832996i | \(-0.313377\pi\) | ||||
0.553278 | + | 0.832996i | \(0.313377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.35116e13 | −0.630524 | −0.315262 | − | 0.949005i | \(-0.602092\pi\) | ||||
−0.315262 | + | 0.949005i | \(0.602092\pi\) | |||||||
\(314\) | −1.02774e14 | −1.90006 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.91367e14 | −3.41655 | ||||||||
\(317\) | 1.98376e13 | 0.348066 | 0.174033 | − | 0.984740i | \(-0.444320\pi\) | ||||
0.174033 | + | 0.984740i | \(0.444320\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.22738e13 | 0.208031 | ||||||||
\(320\) | 3.04100e13 | 0.506632 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.86293e13 | 0.299909 | ||||||||
\(323\) | 6.27796e13 | 0.993584 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.32306e13 | 0.202405 | ||||||||
\(326\) | −1.80132e14 | −2.70953 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.71927e13 | 0.540943 | ||||||||
\(329\) | 3.99583e12 | 0.0571518 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.54179e13 | −0.628309 | −0.314155 | − | 0.949372i | \(-0.601721\pi\) | ||||
−0.314155 | + | 0.949372i | \(0.601721\pi\) | |||||||
\(332\) | 1.80009e14 | 2.44925 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.13947e14 | −2.81644 | ||||||||
\(335\) | 1.98519e13 | 0.257072 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.95830e13 | 0.997369 | 0.498685 | − | 0.866784i | \(-0.333817\pi\) | ||||
0.498685 | + | 0.866784i | \(0.333817\pi\) | |||||||
\(338\) | −1.46705e14 | −1.80885 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.81306e13 | −0.574497 | ||||||||
\(341\) | −1.19750e13 | −0.140646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.76041e13 | 0.313946 | ||||||||
\(344\) | −4.23678e13 | −0.474203 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47482e13 | 0.159890 | ||||||||
\(347\) | 5.46578e13 | 0.583230 | 0.291615 | − | 0.956536i | \(-0.405807\pi\) | ||||
0.291615 | + | 0.956536i | \(0.405807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.78873e13 | −1.01201 | −0.506007 | − | 0.862530i | \(-0.668879\pi\) | ||||
−0.506007 | + | 0.862530i | \(0.668879\pi\) | |||||||
\(350\) | 2.82154e13 | 0.287152 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.27405e14 | −3.22924 | ||||||||
\(353\) | −1.31032e14 | −1.27238 | −0.636189 | − | 0.771533i | \(-0.719490\pi\) | ||||
−0.636189 | + | 0.771533i | \(0.719490\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.52906e12 | 0.0708736 | ||||||||
\(356\) | −4.35265e14 | −4.03440 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.76967e14 | 2.48926 | ||||||||
\(359\) | −2.77646e13 | −0.245738 | −0.122869 | − | 0.992423i | \(-0.539210\pi\) | ||||
−0.122869 | + | 0.992423i | \(0.539210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.05095e12 | −0.0691127 | ||||||||
\(362\) | 1.99672e14 | 1.68819 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.06477e13 | 0.0873371 | ||||||||
\(365\) | 5.70037e12 | 0.0460567 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.08509e14 | −0.850754 | −0.425377 | − | 0.905016i | \(-0.639858\pi\) | ||||
−0.425377 | + | 0.905016i | \(0.639858\pi\) | |||||||
\(368\) | −4.00964e14 | −3.09700 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.25284e13 | −0.318838 | ||||||||
\(371\) | −4.12258e13 | −0.304518 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.02186e13 | −0.288422 | −0.144211 | − | 0.989547i | \(-0.546064\pi\) | ||||
−0.144211 | + | 0.989547i | \(0.546064\pi\) | |||||||
\(374\) | 3.09246e14 | 2.18530 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.57577e14 | −1.08133 | ||||||||
\(377\) | 5.82859e12 | 0.0394172 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.80219e14 | −1.18382 | −0.591908 | − | 0.806005i | \(-0.701625\pi\) | ||||
−0.591908 | + | 0.806005i | \(0.701625\pi\) | |||||||
\(380\) | −8.31361e13 | −0.538245 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.25841e13 | −0.456555 | ||||||||
\(383\) | 1.41856e14 | 0.879535 | 0.439768 | − | 0.898112i | \(-0.355061\pi\) | ||||
0.439768 | + | 0.898112i | \(0.355061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.37202e12 | 0.0383922 | ||||||||
\(386\) | −2.36600e14 | −1.40535 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.21563e14 | −1.27915 | ||||||||
\(389\) | −2.91132e14 | −1.65717 | −0.828586 | − | 0.559862i | \(-0.810854\pi\) | ||||
−0.828586 | + | 0.559862i | \(0.810854\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85329e14 | 1.02558 | ||||||||
\(392\) | −5.37321e14 | −2.93197 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.60406e14 | −1.91233 | ||||||||
\(395\) | −5.43842e13 | −0.284570 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.35401e14 | 0.689086 | 0.344543 | − | 0.938771i | \(-0.388034\pi\) | ||||
0.344543 | + | 0.938771i | \(0.388034\pi\) | |||||||
\(398\) | −6.75261e14 | −3.38934 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.07286e14 | −2.96527 | ||||||||
\(401\) | −9.06673e12 | −0.0436673 | −0.0218337 | − | 0.999762i | \(-0.506950\pi\) | ||||
−0.0218337 | + | 0.999762i | \(0.506950\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.68673e12 | −0.0266492 | ||||||||
\(404\) | 1.02443e15 | 4.73569 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.24300e13 | 0.0559212 | ||||||||
\(407\) | 1.97094e14 | 0.874792 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.87571e13 | 0.383464 | 0.191732 | − | 0.981447i | \(-0.438589\pi\) | ||||
0.191732 | + | 0.981447i | \(0.438589\pi\) | |||||||
\(410\) | 1.72257e13 | 0.0734287 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.30419e14 | 2.61634 | ||||||||
\(413\) | −6.07625e13 | −0.248834 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.11563e13 | 0.204002 | ||||||||
\(416\) | −1.55479e14 | −0.611867 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.34162e14 | 2.04740 | ||||||||
\(419\) | 2.74320e13 | 0.103772 | 0.0518860 | − | 0.998653i | \(-0.483477\pi\) | ||||
0.0518860 | + | 0.998653i | \(0.483477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.33872e14 | 1.59886 | 0.799429 | − | 0.600760i | \(-0.205135\pi\) | ||||
0.799429 | + | 0.600760i | \(0.205135\pi\) | |||||||
\(422\) | 8.86520e14 | 3.22456 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.62575e15 | 5.76158 | ||||||||
\(425\) | 2.80693e14 | 0.981957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.89596e13 | 0.303277 | ||||||||
\(428\) | −9.25865e14 | −3.11607 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.96225e13 | −0.0643693 | ||||||||
\(431\) | −3.83089e14 | −1.24072 | −0.620361 | − | 0.784316i | \(-0.713014\pi\) | ||||
−0.620361 | + | 0.784316i | \(0.713014\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.06861e13 | 0.286324 | 0.143162 | − | 0.989699i | \(-0.454273\pi\) | ||||
0.143162 | + | 0.989699i | \(0.454273\pi\) | |||||||
\(434\) | −1.21274e13 | −0.0378073 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.19621e14 | −0.667573 | ||||||||
\(437\) | 3.20119e14 | 0.960867 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.09425e14 | −0.613019 | −0.306510 | − | 0.951868i | \(-0.599161\pi\) | ||||
−0.306510 | + | 0.951868i | \(0.599161\pi\) | |||||||
\(440\) | −2.51283e14 | −0.726395 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.46855e14 | 0.414064 | ||||||||
\(443\) | 1.56421e14 | 0.435585 | 0.217793 | − | 0.975995i | \(-0.430114\pi\) | ||||
0.217793 | + | 0.975995i | \(0.430114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.23697e14 | −0.336031 | ||||||||
\(446\) | 3.44614e14 | 0.924678 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.42726e14 | −0.373659 | ||||||||
\(449\) | 4.22292e14 | 1.09209 | 0.546045 | − | 0.837756i | \(-0.316133\pi\) | ||||
0.546045 | + | 0.837756i | \(0.316133\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.98311e13 | −0.201466 | ||||||||
\(452\) | 3.83998e14 | 0.957344 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.38725e15 | −3.37558 | ||||||||
\(455\) | 3.02596e12 | 0.00727445 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.05203e14 | 0.950898 | 0.475449 | − | 0.879743i | \(-0.342286\pi\) | ||||
0.475449 | + | 0.879743i | \(0.342286\pi\) | |||||||
\(458\) | 1.24743e15 | 2.89239 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.45422e14 | −0.555579 | ||||||||
\(461\) | 5.53814e14 | 1.23882 | 0.619410 | − | 0.785067i | \(-0.287372\pi\) | ||||
0.619410 | + | 0.785067i | \(0.287372\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.46478e14 | −0.538372 | −0.269186 | − | 0.963088i | \(-0.586755\pi\) | ||||
−0.269186 | + | 0.963088i | \(0.586755\pi\) | |||||||
\(464\) | −2.67533e14 | −0.577469 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.16727e15 | −2.46065 | ||||||||
\(467\) | −3.13903e14 | −0.653961 | −0.326981 | − | 0.945031i | \(-0.606031\pi\) | ||||
−0.326981 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.31726e13 | −0.189600 | ||||||||
\(470\) | −7.29814e13 | −0.146782 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.39619e15 | 4.70803 | ||||||||
\(473\) | 9.09390e13 | 0.176610 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.84841e14 | 0.919994 | ||||||||
\(476\) | 2.25896e14 | 0.423711 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.98514e14 | −0.547156 | ||||||||
\(479\) | −2.29175e14 | −0.415262 | −0.207631 | − | 0.978207i | \(-0.566575\pi\) | ||||
−0.207631 | + | 0.978207i | \(0.566575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.35965e13 | 0.165753 | ||||||||
\(482\) | −4.77959e14 | −0.836821 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.85669e14 | 0.660033 | ||||||||
\(485\) | −6.29656e13 | −0.106543 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.16926e14 | −0.358841 | −0.179420 | − | 0.983773i | \(-0.557422\pi\) | ||||
−0.179420 | + | 0.983773i | \(0.557422\pi\) | |||||||
\(488\) | −3.50815e15 | −5.73811 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.48859e14 | −0.397992 | ||||||||
\(491\) | 1.19339e15 | 1.88727 | 0.943637 | − | 0.330982i | \(-0.107380\pi\) | ||||
0.943637 | + | 0.330982i | \(0.107380\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.23656e14 | 0.191230 | ||||||||
\(494\) | 2.53664e14 | 0.387936 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.61022e14 | 0.390416 | ||||||||
\(497\) | −3.53368e13 | −0.0522718 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.45455e14 | 0.355156 | 0.177578 | − | 0.984107i | \(-0.443174\pi\) | ||||
0.177578 | + | 0.984107i | \(0.443174\pi\) | |||||||
\(500\) | −7.61531e14 | −1.08981 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.05558e15 | 1.47781 | ||||||||
\(503\) | −2.39448e13 | −0.0331579 | −0.0165790 | − | 0.999863i | \(-0.505277\pi\) | ||||
−0.0165790 | + | 0.999863i | \(0.505277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91130e14 | 0.394443 | ||||||||
\(506\) | 1.57687e15 | 2.11334 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.59337e14 | 1.12697 | ||||||||
\(509\) | −7.32323e14 | −0.950069 | −0.475034 | − | 0.879967i | \(-0.657564\pi\) | ||||
−0.475034 | + | 0.879967i | \(0.657564\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.67541e13 | −0.0339684 | ||||||||
\(512\) | −3.10669e14 | −0.390223 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.32420e15 | −2.85744 | ||||||||
\(515\) | 1.79158e14 | 0.217919 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.38226e14 | 0.402725 | ||||||||
\(518\) | 1.99603e14 | 0.235154 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.19329e14 | −0.137635 | ||||||||
\(521\) | −3.34135e14 | −0.381341 | −0.190671 | − | 0.981654i | \(-0.561066\pi\) | ||||
−0.190671 | + | 0.981654i | \(0.561066\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.01114e13 | −0.0448238 | −0.0224119 | − | 0.999749i | \(-0.507135\pi\) | ||||
−0.0224119 | + | 0.999749i | \(0.507135\pi\) | |||||||
\(524\) | −2.24213e14 | −0.247935 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.44144e15 | −1.56090 | ||||||||
\(527\) | −1.20646e14 | −0.129287 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.80235e12 | −0.00818878 | ||||||||
\(530\) | 7.52963e14 | 0.782090 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.90190e14 | 0.396975 | ||||||||
\(533\) | −3.79103e13 | −0.0381731 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.63120e14 | −0.259542 | ||||||||
\(536\) | 3.67429e15 | 3.58729 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.60147e15 | 2.48838 | ||||||||
\(539\) | 1.15332e15 | 1.09197 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.82729e14 | 0.355063 | 0.177532 | − | 0.984115i | \(-0.443189\pi\) | ||||
0.177532 | + | 0.984115i | \(0.443189\pi\) | |||||||
\(542\) | −1.12997e15 | −1.03769 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.29854e15 | −2.96844 | ||||||||
\(545\) | −6.24139e13 | −0.0556033 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.10953e15 | 0.968742 | 0.484371 | − | 0.874863i | \(-0.339048\pi\) | ||||
0.484371 | + | 0.874863i | \(0.339048\pi\) | |||||||
\(548\) | 5.24961e15 | 4.53768 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.38828e15 | 2.02344 | ||||||||
\(551\) | 2.13591e14 | 0.179164 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.55246e14 | 0.209880 | ||||||||
\(554\) | 4.15762e15 | 3.38486 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.96247e14 | 0.236452 | ||||||||
\(557\) | −9.17117e14 | −0.724805 | −0.362402 | − | 0.932022i | \(-0.618043\pi\) | ||||
−0.362402 | + | 0.932022i | \(0.618043\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.31853e13 | 0.0334635 | ||||||||
\(560\) | −1.38892e14 | −0.106572 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.35359e15 | 1.01844 | ||||||||
\(563\) | 1.33076e15 | 0.991522 | 0.495761 | − | 0.868459i | \(-0.334889\pi\) | ||||
0.495761 | + | 0.868459i | \(0.334889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.09128e14 | 0.0797387 | ||||||||
\(566\) | −3.05136e15 | −2.20802 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.39352e15 | 0.989001 | ||||||||
\(569\) | 1.00669e15 | 0.707584 | 0.353792 | − | 0.935324i | \(-0.384892\pi\) | ||||
0.353792 | + | 0.935324i | \(0.384892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.06731e15 | −1.42530 | −0.712652 | − | 0.701518i | \(-0.752506\pi\) | ||||
−0.712652 | + | 0.701518i | \(0.752506\pi\) | |||||||
\(572\) | 9.01272e14 | 0.615429 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.08470e13 | −0.0541562 | ||||||||
\(575\) | 1.43128e15 | 0.949622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.80901e14 | 0.508310 | 0.254155 | − | 0.967163i | \(-0.418203\pi\) | ||||
0.254155 | + | 0.967163i | \(0.418203\pi\) | |||||||
\(578\) | 1.77750e14 | 0.114606 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.63752e14 | −0.103593 | ||||||||
\(581\) | −2.40097e14 | −0.150459 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.48954e15 | −2.14581 | ||||||||
\(584\) | 1.05506e15 | 0.642694 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.21771e15 | 3.11920 | ||||||||
\(587\) | −2.95350e15 | −1.74915 | −0.874574 | − | 0.484891i | \(-0.838859\pi\) | ||||
−0.874574 | + | 0.484891i | \(0.838859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.08393e14 | −0.121129 | ||||||||
\(590\) | 1.10979e15 | 0.639079 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.29609e15 | −2.42831 | ||||||||
\(593\) | 1.10716e14 | 0.0620026 | 0.0310013 | − | 0.999519i | \(-0.490130\pi\) | ||||
0.0310013 | + | 0.999519i | \(0.490130\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.41970e13 | 0.0352916 | ||||||||
\(596\) | −3.10051e15 | −1.68880 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.48828e14 | 0.400429 | ||||||||
\(599\) | 2.23003e14 | 0.118158 | 0.0590791 | − | 0.998253i | \(-0.481184\pi\) | ||||
0.0590791 | + | 0.998253i | \(0.481184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.38409e15 | 1.24026 | 0.620130 | − | 0.784499i | \(-0.287080\pi\) | ||||
0.620130 | + | 0.784499i | \(0.287080\pi\) | |||||||
\(602\) | 9.20963e13 | 0.0474746 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.06101e15 | 3.06790 | ||||||||
\(605\) | 1.09603e14 | 0.0549752 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.55050e14 | 0.470423 | 0.235211 | − | 0.971944i | \(-0.424422\pi\) | ||||
0.235211 | + | 0.971944i | \(0.424422\pi\) | |||||||
\(608\) | −5.69758e15 | −2.78113 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.62479e15 | −0.778903 | ||||||||
\(611\) | 1.60617e14 | 0.0763073 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.30769e15 | 1.54345 | 0.771725 | − | 0.635956i | \(-0.219394\pi\) | ||||
0.771725 | + | 0.635956i | \(0.219394\pi\) | |||||||
\(614\) | 1.09587e14 | 0.0506798 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.17937e15 | 0.535742 | ||||||||
\(617\) | 4.36956e15 | 1.96730 | 0.983648 | − | 0.180104i | \(-0.0576434\pi\) | ||||
0.983648 | + | 0.180104i | \(0.0576434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.19128e13 | −0.00969169 | −0.00484585 | − | 0.999988i | \(-0.501542\pi\) | ||||
−0.00484585 | + | 0.999988i | \(0.501542\pi\) | |||||||
\(620\) | 1.59766e14 | 0.0700376 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.86684e15 | 2.09604 | ||||||||
\(623\) | 5.80560e14 | 0.247835 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.05698e15 | 0.862762 | ||||||||
\(626\) | −2.87268e15 | −1.19434 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.35455e15 | −2.59601 | ||||||||
\(629\) | 1.98569e15 | 0.804143 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.46904e15 | −0.982577 | −0.491288 | − | 0.870997i | \(-0.663474\pi\) | ||||
−0.491288 | + | 0.870997i | \(0.663474\pi\) | |||||||
\(632\) | −1.00657e16 | −3.97101 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.70051e15 | 0.659308 | ||||||||
\(635\) | 2.44214e14 | 0.0938673 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.47688e14 | 0.206903 | ||||||||
\(638\) | 1.05213e15 | 0.394054 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.18976e14 | 0.338310 | ||||||||
\(641\) | −4.93142e14 | −0.179992 | −0.0899959 | − | 0.995942i | \(-0.528685\pi\) | ||||
−0.0899959 | + | 0.995942i | \(0.528685\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.23186e15 | −1.15956 | −0.579779 | − | 0.814774i | \(-0.696861\pi\) | ||||
−0.579779 | + | 0.814774i | \(0.696861\pi\) | |||||||
\(644\) | 1.15186e15 | 0.409759 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.38158e15 | 1.88205 | ||||||||
\(647\) | 3.57806e15 | 1.24072 | 0.620361 | − | 0.784317i | \(-0.286986\pi\) | ||||
0.620361 | + | 0.784317i | \(0.286986\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.14322e15 | −1.75343 | ||||||||
\(650\) | 1.13415e15 | 0.383396 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.11377e16 | −3.70196 | ||||||||
\(653\) | −1.86179e15 | −0.613631 | −0.306816 | − | 0.951769i | \(-0.599264\pi\) | ||||
−0.306816 | + | 0.951769i | \(0.599264\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.37186e13 | −0.0206509 | ||||||||
\(656\) | 1.74009e15 | 0.559243 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.42530e14 | 0.108257 | ||||||||
\(659\) | −2.15375e15 | −0.675034 | −0.337517 | − | 0.941319i | \(-0.609587\pi\) | ||||
−0.337517 | + | 0.941319i | \(0.609587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.87662e14 | 0.304439 | 0.152219 | − | 0.988347i | \(-0.451358\pi\) | ||||
0.152219 | + | 0.988347i | \(0.451358\pi\) | |||||||
\(662\) | −3.89331e15 | −1.19014 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.46829e15 | 2.84673 | ||||||||
\(665\) | 1.10888e14 | 0.0330646 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.30533e14 | 0.184933 | ||||||||
\(668\) | −1.32285e16 | −3.84804 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.70174e15 | 0.486947 | ||||||||
\(671\) | 7.52996e15 | 2.13707 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.49944e15 | −0.977048 | −0.488524 | − | 0.872550i | \(-0.662465\pi\) | ||||
−0.488524 | + | 0.872550i | \(0.662465\pi\) | |||||||
\(674\) | 6.82200e15 | 1.88922 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.07087e15 | −2.47139 | ||||||||
\(677\) | 1.40384e14 | 0.0379386 | 0.0189693 | − | 0.999820i | \(-0.493962\pi\) | ||||
0.0189693 | + | 0.999820i | \(0.493962\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.95522e14 | 0.0785790 | ||||||||
\(680\) | −2.53163e15 | −0.667730 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.02652e15 | −0.266412 | ||||||||
\(683\) | 4.41379e15 | 1.13631 | 0.568157 | − | 0.822920i | \(-0.307657\pi\) | ||||
0.568157 | + | 0.822920i | \(0.307657\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.49188e15 | 0.377951 | ||||||||
\(686\) | 2.36627e15 | 0.594678 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.98221e15 | −0.490245 | ||||||||
\(689\) | −1.65712e15 | −0.406582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.16695e15 | −1.00621 | −0.503105 | − | 0.864225i | \(-0.667809\pi\) | ||||
−0.503105 | + | 0.864225i | \(0.667809\pi\) | |||||||
\(692\) | 9.11891e14 | 0.218454 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.68536e15 | 1.10476 | ||||||||
\(695\) | 8.41900e13 | 0.0196945 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.04284e14 | −0.185195 | ||||||||
\(698\) | −8.39108e15 | −1.91696 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.74457e15 | 0.392329 | ||||||||
\(701\) | −1.15347e14 | −0.0257369 | −0.0128685 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128685 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.42989e15 | 0.753400 | ||||||||
\(704\) | −1.20810e16 | −2.63302 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.12323e16 | −2.41014 | ||||||||
\(707\) | −1.36639e15 | −0.290916 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.73974e15 | 1.83208 | 0.916039 | − | 0.401088i | \(-0.131368\pi\) | ||||
0.916039 | + | 0.401088i | \(0.131368\pi\) | |||||||
\(710\) | 6.45405e14 | 0.134249 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.28945e16 | −4.68912 | ||||||||
\(713\) | −6.15186e14 | −0.125030 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.56131e14 | 0.0512601 | ||||||||
\(716\) | 1.71250e16 | 3.40102 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.38004e15 | −0.465478 | ||||||||
\(719\) | 7.62293e14 | 0.147949 | 0.0739747 | − | 0.997260i | \(-0.476432\pi\) | ||||
0.0739747 | + | 0.997260i | \(0.476432\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.40858e14 | −0.160723 | ||||||||
\(722\) | −6.90143e14 | −0.130913 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.23459e16 | 2.30653 | ||||||||
\(725\) | 9.54985e14 | 0.177067 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.14284e15 | −0.939212 | −0.469606 | − | 0.882876i | \(-0.655604\pi\) | ||||
−0.469606 | + | 0.882876i | \(0.655604\pi\) | |||||||
\(728\) | 5.60060e14 | 0.101511 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.88646e14 | 0.0872407 | ||||||||
\(731\) | 9.16195e14 | 0.162346 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.01404e15 | −0.700663 | −0.350332 | − | 0.936626i | \(-0.613931\pi\) | ||||
−0.350332 | + | 0.936626i | \(0.613931\pi\) | |||||||
\(734\) | −9.30162e15 | −1.61150 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.68196e16 | −2.87069 | ||||||||
\(737\) | −7.88656e15 | −1.33603 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.88766e15 | 0.648850 | 0.324425 | − | 0.945911i | \(-0.394829\pi\) | ||||
0.324425 | + | 0.945911i | \(0.394829\pi\) | |||||||
\(740\) | −2.62956e15 | −0.435621 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.53395e15 | −0.576819 | ||||||||
\(743\) | −2.10387e15 | −0.340863 | −0.170432 | − | 0.985370i | \(-0.554516\pi\) | ||||
−0.170432 | + | 0.985370i | \(0.554516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.81129e14 | −0.140663 | ||||||||
\(746\) | −3.44761e15 | −0.546329 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.91209e16 | 2.98572 | ||||||||
\(749\) | 1.23493e15 | 0.191422 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.83508e15 | 0.738557 | 0.369279 | − | 0.929319i | \(-0.379605\pi\) | ||||
0.369279 | + | 0.929319i | \(0.379605\pi\) | |||||||
\(752\) | −7.37236e15 | −1.11791 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.99637e14 | 0.0746642 | ||||||||
\(755\) | 1.72247e15 | 0.255531 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.12261e15 | −1.18759 | −0.593797 | − | 0.804615i | \(-0.702372\pi\) | ||||
−0.593797 | + | 0.804615i | \(0.702372\pi\) | |||||||
\(758\) | −1.54487e16 | −2.24239 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.37288e15 | −0.625595 | ||||||||
\(761\) | −3.35823e15 | −0.476974 | −0.238487 | − | 0.971146i | \(-0.576651\pi\) | ||||
−0.238487 | + | 0.971146i | \(0.576651\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.92933e14 | 0.0410094 | ||||||||
\(764\) | −4.48792e15 | −0.623780 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.21601e16 | 1.66602 | ||||||||
\(767\) | −2.44242e15 | −0.332236 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.21660e14 | −0.0163137 | −0.00815686 | − | 0.999967i | \(-0.502596\pi\) | ||||
−0.00815686 | + | 0.999967i | \(0.502596\pi\) | |||||||
\(770\) | 5.46222e14 | 0.0727227 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.46291e16 | −1.92009 | ||||||||
\(773\) | 3.05158e15 | 0.397684 | 0.198842 | − | 0.980032i | \(-0.436282\pi\) | ||||
0.198842 | + | 0.980032i | \(0.436282\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.31742e14 | −0.119712 | ||||||||
\(776\) | −1.16540e16 | −1.48674 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.49564e16 | −3.13902 | ||||||||
\(779\) | −1.38924e15 | −0.173509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.99107e15 | −0.368338 | ||||||||
\(782\) | 1.58867e16 | 1.94266 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.51390e16 | −3.03116 | ||||||||
\(785\) | −1.80589e15 | −0.216226 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.93889e15 | 1.17348 | 0.586742 | − | 0.809774i | \(-0.300410\pi\) | ||||
0.586742 | + | 0.809774i | \(0.300410\pi\) | |||||||
\(788\) | −2.22841e16 | −2.61277 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.66191e15 | −0.539033 | ||||||||
\(791\) | −5.12180e14 | −0.0588101 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.57584e15 | 0.404926 | ||||||||
\(794\) | 1.16068e16 | 1.30527 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.17518e16 | −4.63077 | ||||||||
\(797\) | −6.66631e15 | −0.734285 | −0.367143 | − | 0.930165i | \(-0.619664\pi\) | ||||
−0.367143 | + | 0.930165i | \(0.619664\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.40757e15 | 0.370201 | ||||||||
\(800\) | −2.54744e16 | −2.74858 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.77217e14 | −0.0827148 | ||||||||
\(803\) | −2.26459e15 | −0.239361 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.27346e14 | 0.0341295 | ||||||||
\(806\) | −4.87477e14 | −0.0504790 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.38839e16 | 5.50422 | ||||||||
\(809\) | 1.50060e16 | 1.52246 | 0.761232 | − | 0.648479i | \(-0.224595\pi\) | ||||
0.761232 | + | 0.648479i | \(0.224595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.15416e15 | 0.916229 | 0.458115 | − | 0.888893i | \(-0.348525\pi\) | ||||
0.458115 | + | 0.888893i | \(0.348525\pi\) | |||||||
\(812\) | 7.68552e14 | 0.0764038 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.68953e16 | 1.65703 | ||||||||
\(815\) | −3.16519e15 | −0.308342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.58254e15 | 0.152102 | ||||||||
\(818\) | 7.60843e15 | 0.726360 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.06508e15 | 0.100324 | ||||||||
\(821\) | −1.78031e16 | −1.66574 | −0.832872 | − | 0.553466i | \(-0.813305\pi\) | ||||
−0.832872 | + | 0.553466i | \(0.813305\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.32521e16 | 1.22345 | 0.611724 | − | 0.791071i | \(-0.290476\pi\) | ||||
0.611724 | + | 0.791071i | \(0.290476\pi\) | |||||||
\(824\) | 3.31595e16 | 3.04094 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.20867e15 | −0.471343 | ||||||||
\(827\) | 1.40611e16 | 1.26398 | 0.631989 | − | 0.774977i | \(-0.282239\pi\) | ||||
0.631989 | + | 0.774977i | \(0.282239\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.03566e16 | −0.918686 | −0.459343 | − | 0.888259i | \(-0.651915\pi\) | ||||
−0.459343 | + | 0.888259i | \(0.651915\pi\) | |||||||
\(830\) | 4.38522e15 | 0.386422 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.73705e15 | −0.498897 | ||||||||
\(833\) | 1.16194e16 | 1.00378 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.75938e15 | −0.320510 | ||||||||
\(836\) | 3.30275e16 | 2.79732 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.35152e15 | 0.196565 | ||||||||
\(839\) | −9.68827e15 | −0.804554 | −0.402277 | − | 0.915518i | \(-0.631781\pi\) | ||||
−0.402277 | + | 0.915518i | \(0.631781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | 3.71923e16 | 3.02856 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.48141e16 | 4.40564 | ||||||||
\(845\) | −2.57784e15 | −0.205846 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.14409e14 | −0.0405462 | ||||||||
\(848\) | 7.60621e16 | 5.95650 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.40615e16 | 1.86003 | ||||||||
\(851\) | 1.01252e16 | 0.777663 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.46435e16 | 1.11026 | 0.555132 | − | 0.831762i | \(-0.312668\pi\) | ||||
0.555132 | + | 0.831762i | \(0.312668\pi\) | |||||||
\(854\) | 7.62578e15 | 0.574468 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.86997e16 | −3.62177 | ||||||||
\(857\) | 9.45909e15 | 0.698964 | 0.349482 | − | 0.936943i | \(-0.386358\pi\) | ||||
0.349482 | + | 0.936943i | \(0.386358\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.86873e15 | 0.355184 | 0.177592 | − | 0.984104i | \(-0.443169\pi\) | ||||
0.177592 | + | 0.984104i | \(0.443169\pi\) | |||||||
\(860\) | −1.21327e15 | −0.0879463 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.28391e16 | −2.35018 | ||||||||
\(863\) | 1.48573e15 | 0.105652 | 0.0528262 | − | 0.998604i | \(-0.483177\pi\) | ||||
0.0528262 | + | 0.998604i | \(0.483177\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.59149e14 | 0.0181954 | ||||||||
\(866\) | 7.77378e15 | 0.542355 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.49846e14 | −0.0516552 | ||||||||
\(869\) | 2.16052e16 | 1.47894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.74518e15 | −0.253147 | ||||||||
\(872\) | −1.15519e16 | −0.775912 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.74412e16 | 1.82008 | ||||||||
\(875\) | 1.01574e15 | 0.0669478 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.05639e16 | −0.687583 | −0.343791 | − | 0.939046i | \(-0.611711\pi\) | ||||
−0.343791 | + | 0.939046i | \(0.611711\pi\) | |||||||
\(878\) | −1.79523e16 | −1.16118 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.17565e16 | −0.750968 | ||||||||
\(881\) | 8.44930e15 | 0.536356 | 0.268178 | − | 0.963369i | \(-0.413578\pi\) | ||||
0.268178 | + | 0.963369i | \(0.413578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.60928e16 | −1.63583 | −0.817913 | − | 0.575342i | \(-0.804869\pi\) | ||||
−0.817913 | + | 0.575342i | \(0.804869\pi\) | |||||||
\(884\) | 9.08016e15 | 0.565726 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.34087e16 | 0.825087 | ||||||||
\(887\) | −2.69034e16 | −1.64523 | −0.822615 | − | 0.568598i | \(-0.807486\pi\) | ||||
−0.822615 | + | 0.568598i | \(0.807486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.14619e15 | −0.0692304 | ||||||||
\(890\) | −1.06036e16 | −0.636512 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.13077e16 | 1.26337 | ||||||||
\(893\) | 5.88590e15 | 0.346840 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.86673e15 | 0.283277 | ||||||||
\(896\) | −4.31312e15 | −0.249515 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.61997e16 | 2.06864 | ||||||||
\(899\) | −4.10468e14 | −0.0233131 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.51565e16 | −1.97251 | ||||||||
\(902\) | −6.84327e15 | −0.381617 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.01980e16 | 1.11271 | ||||||||
\(905\) | 3.50855e15 | 0.192115 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.07428e15 | 0.112209 | 0.0561045 | − | 0.998425i | \(-0.482132\pi\) | ||||
0.0561045 | + | 0.998425i | \(0.482132\pi\) | |||||||
\(908\) | −8.57748e16 | −4.61198 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.59391e14 | 0.0137793 | ||||||||
\(911\) | −1.42172e16 | −0.750696 | −0.375348 | − | 0.926884i | \(-0.622477\pi\) | ||||
−0.375348 | + | 0.926884i | \(0.622477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.03229e16 | −1.06022 | ||||||||
\(914\) | 3.47348e16 | 1.80119 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.71295e16 | 3.95180 | ||||||||
\(917\) | 2.99056e14 | 0.0152308 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.08777e16 | −1.55385 | −0.776925 | − | 0.629593i | \(-0.783222\pi\) | ||||
−0.776925 | + | 0.629593i | \(0.783222\pi\) | |||||||
\(920\) | −1.29090e16 | −0.645742 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.74739e16 | 2.34658 | ||||||||
\(923\) | −1.42041e15 | −0.0697916 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.53353e16 | 0.744583 | ||||||||
\(926\) | −2.11285e16 | −1.01979 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.12224e16 | −0.535270 | ||||||||
\(929\) | −3.68373e16 | −1.74663 | −0.873315 | − | 0.487156i | \(-0.838034\pi\) | ||||
−0.873315 | + | 0.487156i | \(0.838034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00703e16 | 0.940439 | ||||||||
\(932\) | −7.21731e16 | −3.36192 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.69083e16 | −1.23874 | ||||||||
\(935\) | 5.43393e15 | 0.248685 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.33816e16 | −1.96217 | −0.981087 | − | 0.193565i | \(-0.937995\pi\) | ||||
−0.981087 | + | 0.193565i | \(0.937995\pi\) | |||||||
\(938\) | −7.98693e15 | −0.359140 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.51248e15 | −0.200545 | ||||||||
\(941\) | −1.78920e16 | −0.790528 | −0.395264 | − | 0.918568i | \(-0.629347\pi\) | ||||
−0.395264 | + | 0.918568i | \(0.629347\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.10111e15 | −0.179097 | ||||||||
\(944\) | 1.12108e17 | 4.86731 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.79546e15 | 0.334534 | ||||||||
\(947\) | 9.07033e15 | 0.386989 | 0.193494 | − | 0.981101i | \(-0.438018\pi\) | ||||
0.193494 | + | 0.981101i | \(0.438018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.07541e15 | −0.0453535 | ||||||||
\(950\) | 4.15615e16 | 1.74265 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.18819e16 | 0.492474 | ||||||||
\(953\) | 1.41782e16 | 0.584266 | 0.292133 | − | 0.956378i | \(-0.405635\pi\) | ||||
0.292133 | + | 0.956378i | \(0.405635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.27542e15 | −0.0519557 | ||||||||
\(956\) | −1.84573e16 | −0.747566 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.96453e16 | −0.786590 | ||||||||
\(959\) | −7.00197e15 | −0.278752 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50080e16 | −0.984238 | ||||||||
\(962\) | 8.02327e15 | 0.313970 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.95525e16 | −1.14333 | ||||||||
\(965\) | −4.15742e15 | −0.159928 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.91949e16 | −0.730028 | −0.365014 | − | 0.931002i | \(-0.618936\pi\) | ||||
−0.365014 | + | 0.931002i | \(0.618936\pi\) | |||||||
\(968\) | 2.02859e16 | 0.767148 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.39753e15 | −0.201814 | ||||||||
\(971\) | −3.56830e16 | −1.32665 | −0.663324 | − | 0.748332i | \(-0.730855\pi\) | ||||
−0.663324 | + | 0.748332i | \(0.730855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.95137e14 | −0.0145254 | ||||||||
\(974\) | −1.85953e16 | −0.679717 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.64131e17 | −5.93223 | ||||||||
\(977\) | −3.12998e16 | −1.12492 | −0.562460 | − | 0.826824i | \(-0.690145\pi\) | ||||
−0.562460 | + | 0.826824i | \(0.690145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.91413e16 | 1.74639 | ||||||||
\(980\) | −1.53871e16 | −0.543768 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.02300e17 | 3.57488 | ||||||||
\(983\) | −4.86496e16 | −1.69058 | −0.845289 | − | 0.534310i | \(-0.820572\pi\) | ||||
−0.845289 | + | 0.534310i | \(0.820572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.33289e15 | −0.217622 | ||||||||
\(986\) | 1.06000e16 | 0.362229 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.56842e16 | 0.530027 | ||||||||
\(989\) | 4.67176e15 | 0.157000 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.35365e16 | 0.449885 | 0.224942 | − | 0.974372i | \(-0.427781\pi\) | ||||
0.224942 | + | 0.974372i | \(0.427781\pi\) | |||||||
\(992\) | 1.09493e16 | 0.361886 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.02914e15 | −0.0990134 | ||||||||
\(995\) | −1.18654e16 | −0.385704 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.72028e15 | 0.119606 | 0.0598028 | − | 0.998210i | \(-0.480953\pi\) | ||||
0.0598028 | + | 0.998210i | \(0.480953\pi\) | |||||||
\(998\) | 2.10409e16 | 0.672738 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(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 | 261.12.a.a.1.11 | 11 | ||
3.2 | odd | 2 | 29.12.a.a.1.1 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.1 | ✓ | 11 | 3.2 | odd | 2 | ||
261.12.a.a.1.11 | 11 | 1.1 | even | 1 | trivial |