Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,12,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, 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("16.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(12.2934908890\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 8) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 36.0000 | 0.0855334 | 0.0427667 | − | 0.999085i | \(-0.486383\pi\) | ||||
0.0427667 | + | 0.999085i | \(0.486383\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3490.00 | −0.499448 | −0.249724 | − | 0.968317i | \(-0.580340\pi\) | ||||
−0.249724 | + | 0.968317i | \(0.580340\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 55464.0 | 1.24730 | 0.623652 | − | 0.781703i | \(-0.285648\pi\) | ||||
0.623652 | + | 0.781703i | \(0.285648\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −175851. | −0.992684 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 597004. | 1.11768 | 0.558840 | − | 0.829276i | \(-0.311247\pi\) | ||||
0.558840 | + | 0.829276i | \(0.311247\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.37388e6 | 1.02627 | 0.513133 | − | 0.858309i | \(-0.328485\pi\) | ||||
0.513133 | + | 0.858309i | \(0.328485\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −125640. | −0.0427195 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.01408e7 | 1.73223 | 0.866114 | − | 0.499846i | \(-0.166610\pi\) | ||||
0.866114 | + | 0.499846i | \(0.166610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.29740e6 | 0.676119 | 0.338059 | − | 0.941125i | \(-0.390229\pi\) | ||||
0.338059 | + | 0.941125i | \(0.390229\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.99670e6 | 0.106686 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.20575e7 | 1.03855 | 0.519273 | − | 0.854608i | \(-0.326203\pi\) | ||||
0.519273 | + | 0.854608i | \(0.326203\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.66480e7 | −0.750552 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.27079e7 | −0.170441 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.36054e7 | −0.123175 | −0.0615875 | − | 0.998102i | \(-0.519616\pi\) | ||||
−0.0615875 | + | 0.998102i | \(0.519616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.33161e8 | −1.46274 | −0.731368 | − | 0.681983i | \(-0.761118\pi\) | ||||
−0.731368 | + | 0.681983i | \(0.761118\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.14921e7 | 0.0955989 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.93569e8 | −0.622963 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.57786e8 | −0.611153 | −0.305577 | − | 0.952167i | \(-0.598849\pi\) | ||||
−0.305577 | + | 0.952167i | \(0.598849\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.94596e7 | 0.0877800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.21439e8 | −0.298498 | −0.149249 | − | 0.988800i | \(-0.547686\pi\) | ||||
−0.149249 | + | 0.988800i | \(0.547686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.69776e9 | 1.76116 | 0.880581 | − | 0.473895i | \(-0.157152\pi\) | ||||
0.880581 | + | 0.473895i | \(0.157152\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.13720e8 | 0.495794 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.27509e8 | −0.335500 | −0.167750 | − | 0.985830i | \(-0.553650\pi\) | ||||
−0.167750 | + | 0.985830i | \(0.553650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.09893e9 | 0.555765 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.65071e8 | 0.148163 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.27738e9 | 1.07649 | 0.538244 | − | 0.842789i | \(-0.319088\pi\) | ||||
0.538244 | + | 0.842789i | \(0.319088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.08354e9 | −0.558223 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.62706e8 | 0.0578307 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.00191e9 | 0.546653 | 0.273326 | − | 0.961921i | \(-0.411876\pi\) | ||||
0.273326 | + | 0.961921i | \(0.411876\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.16300e10 | −1.76306 | −0.881529 | − | 0.472130i | \(-0.843485\pi\) | ||||
−0.881529 | + | 0.472130i | \(0.843485\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.75340e9 | −1.23818 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.79483e9 | −0.512566 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.71890e10 | 1.55539 | 0.777695 | − | 0.628642i | \(-0.216389\pi\) | ||||
0.777695 | + | 0.628642i | \(0.216389\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.15407e9 | 0.0888304 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.61695e10 | −1.72137 | −0.860687 | − | 0.509135i | \(-0.829966\pi\) | ||||
−0.860687 | + | 0.509135i | \(0.829966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.03902e9 | −0.397408 | −0.198704 | − | 0.980060i | \(-0.563673\pi\) | ||||
−0.198704 | + | 0.980060i | \(0.563673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.31933e9 | −0.0641972 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.31122e10 | 1.39409 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.19991e9 | 0.153565 | 0.0767823 | − | 0.997048i | \(-0.475535\pi\) | ||||
0.0767823 | + | 0.997048i | \(0.475535\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.06940e10 | 0.978106 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.97399e10 | 1.10738 | 0.553691 | − | 0.832722i | \(-0.313219\pi\) | ||||
0.553691 | + | 0.832722i | \(0.313219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.53916e10 | −0.865159 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.89794e8 | −0.0105356 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.05653e10 | 0.200557 | 0.100279 | − | 0.994959i | \(-0.468027\pi\) | ||||
0.100279 | + | 0.994959i | \(0.468027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.62008e10 | 1.28006 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.39379e9 | −0.125113 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.54679e10 | −0.337686 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.98516e10 | −0.825909 | −0.412954 | − | 0.910752i | \(-0.635503\pi\) | ||||
−0.412954 | + | 0.910752i | \(0.635503\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.04984e11 | −1.10950 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.45194e10 | 0.705508 | 0.352754 | − | 0.935716i | \(-0.385245\pi\) | ||||
0.352754 | + | 0.935716i | \(0.385245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.86642e10 | −0.668609 | −0.334304 | − | 0.942465i | \(-0.608501\pi\) | ||||
−0.334304 | + | 0.942465i | \(0.608501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.96850e9 | −0.0532841 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.88490e10 | −0.543482 | −0.271741 | − | 0.962370i | \(-0.587599\pi\) | ||||
−0.271741 | + | 0.962370i | \(0.587599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.08680e10 | −0.441169 | −0.220584 | − | 0.975368i | \(-0.570796\pi\) | ||||
−0.220584 | + | 0.975368i | \(0.570796\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.28030e9 | −0.0522740 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.96816e10 | 0.100491 | 0.0502457 | − | 0.998737i | \(-0.484000\pi\) | ||||
0.0502457 | + | 0.998737i | \(0.484000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.11881e11 | −0.518700 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.41598e11 | −1.01876 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.62452e11 | 2.16061 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.11021e10 | 0.249209 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.97179e9 | −0.0255316 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.98312e11 | 0.874310 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.90252e11 | 0.510985 | 0.255492 | − | 0.966811i | \(-0.417762\pi\) | ||||
0.255492 | + | 0.966811i | \(0.417762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.11193e10 | 0.150638 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.14525e11 | −0.259363 | −0.129681 | − | 0.991556i | \(-0.541395\pi\) | ||||
−0.129681 | + | 0.991556i | \(0.541395\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.04743e11 | 0.843325 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.43507e10 | 0.0851264 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.17101e11 | 0.207299 | 0.103650 | − | 0.994614i | \(-0.466948\pi\) | ||||
0.103650 | + | 0.994614i | \(0.466948\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.89561e11 | −1.61756 | −0.808781 | − | 0.588110i | \(-0.799872\pi\) | ||||
−0.808781 | + | 0.588110i | \(0.799872\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.89903e10 | −0.0286964 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.20211e11 | 1.14704 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.74829e10 | 0.0615195 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.95614e10 | 0.0475364 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.97579e11 | −0.889712 | −0.444856 | − | 0.895602i | \(-0.646745\pi\) | ||||
−0.444856 | + | 0.895602i | \(0.646745\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.18323e12 | −1.22658 | −0.613290 | − | 0.789858i | \(-0.710154\pi\) | ||||
−0.613290 | + | 0.789858i | \(0.710154\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.78328e12 | −1.71956 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.13731e11 | 0.730561 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.53512e11 | −0.630438 | −0.315219 | − | 0.949019i | \(-0.602078\pi\) | ||||
−0.315219 | + | 0.949019i | \(0.602078\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.17986e11 | 0.0920757 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.77804e12 | 1.29538 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.34305e11 | −0.567928 | −0.283964 | − | 0.958835i | \(-0.591650\pi\) | ||||
−0.283964 | + | 0.958835i | \(0.591650\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.50076e10 | −0.0477467 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.01514e12 | 0.604761 | 0.302380 | − | 0.953187i | \(-0.402219\pi\) | ||||
0.302380 | + | 0.953187i | \(0.402219\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.53804e10 | 0.0532209 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.28325e12 | −0.671172 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.89496e12 | 1.42033 | 0.710165 | − | 0.704035i | \(-0.248620\pi\) | ||||
0.710165 | + | 0.704035i | \(0.248620\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.03265e12 | −0.936165 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.08069e11 | 0.0467570 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.09263e12 | 1.66461 | 0.832303 | − | 0.554322i | \(-0.187022\pi\) | ||||
0.832303 | + | 0.554322i | \(0.187022\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.08615e11 | 0.194606 | 0.0973032 | − | 0.995255i | \(-0.468978\pi\) | ||||
0.0973032 | + | 0.995255i | \(0.468978\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.18681e11 | −0.150800 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.99674e11 | 0.305239 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.05413e12 | 1.93608 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.04833e11 | −0.212592 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.99951e12 | −0.853822 | −0.426911 | − | 0.904294i | \(-0.640398\pi\) | ||||
−0.426911 | + | 0.904294i | \(0.640398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.18193e12 | −0.586509 | −0.293255 | − | 0.956034i | \(-0.594738\pi\) | ||||
−0.293255 | + | 0.956034i | \(0.594738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.72614e11 | −0.0438415 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.77475e12 | −1.14653 | −0.573267 | − | 0.819369i | \(-0.694324\pi\) | ||||
−0.573267 | + | 0.819369i | \(0.694324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.95210e11 | −0.0670563 | −0.0335281 | − | 0.999438i | \(-0.510674\pi\) | ||||
−0.0335281 | + | 0.999438i | \(0.510674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.18804e11 | 0.133038 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.54610e11 | −0.153636 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.72821e11 | 0.149085 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.63734e12 | −1.03095 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.35657e12 | 0.755685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.76886e12 | −0.784984 | −0.392492 | − | 0.919755i | \(-0.628387\pi\) | ||||
−0.392492 | + | 0.919755i | \(0.628387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.42103e11 | −0.147235 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.92518e12 | −0.879609 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.29320e13 | −1.82448 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.53405e11 | −0.0339916 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.39323e13 | 1.77773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.21455e12 | 1.11892 | 0.559458 | − | 0.828859i | \(-0.311009\pi\) | ||||
0.559458 | + | 0.828859i | \(0.311009\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.44459e12 | 0.745061 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.85444e12 | 0.644678 | 0.322339 | − | 0.946624i | \(-0.395531\pi\) | ||||
0.322339 | + | 0.946624i | \(0.395531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.40273e13 | −1.47191 | −0.735953 | − | 0.677033i | \(-0.763266\pi\) | ||||
−0.735953 | + | 0.677033i | \(0.763266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.19204e12 | 0.119241 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.29610e12 | −0.505241 | −0.252621 | − | 0.967565i | \(-0.581292\pi\) | ||||
−0.252621 | + | 0.967565i | \(0.581292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.84101e12 | 0.167565 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.51197e11 | 0.0131349 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.31646e13 | 1.09199 | 0.545997 | − | 0.837787i | \(-0.316151\pi\) | ||||
0.545997 | + | 0.837787i | \(0.316151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.25897e13 | 1.78985 | 0.894924 | − | 0.446219i | \(-0.147230\pi\) | ||||
0.894924 | + | 0.446219i | \(0.147230\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.35616e12 | 0.254102 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.83526e12 | −0.277576 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00257e13 | 0.693878 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.43064e12 | 0.0947182 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.61185e13 | −1.65479 | −0.827396 | − | 0.561619i | \(-0.810179\pi\) | ||||
−0.827396 | + | 0.561619i | \(0.810179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.91384e13 | 1.16076 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.27410e12 | −0.0739999 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.26580e13 | −0.704259 | −0.352129 | − | 0.935951i | \(-0.614542\pi\) | ||||
−0.352129 | + | 0.935951i | \(0.614542\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.42979e13 | −0.762293 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.39252e12 | 0.122274 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.37023e12 | −0.263170 | −0.131585 | − | 0.991305i | \(-0.542007\pi\) | ||||
−0.131585 | + | 0.991305i | \(0.542007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.14381e13 | −0.537650 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.80352e11 | 0.0171543 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.60140e12 | −0.372333 | −0.186167 | − | 0.982518i | \(-0.559606\pi\) | ||||
−0.186167 | + | 0.982518i | \(0.559606\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.01371e12 | 0.249926 | 0.124963 | − | 0.992161i | \(-0.460119\pi\) | ||||
0.124963 | + | 0.992161i | \(0.460119\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.74323e12 | 0.109488 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.18790e13 | −0.838876 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.63312e13 | −0.970134 | −0.485067 | − | 0.874477i | \(-0.661205\pi\) | ||||
−0.485067 | + | 0.874477i | \(0.661205\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.10016e13 | 1.45204 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.11748e13 | −1.74250 | −0.871248 | − | 0.490843i | \(-0.836689\pi\) | ||||
−0.871248 | + | 0.490843i | \(0.836689\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.94896e12 | −0.293054 | −0.146527 | − | 0.989207i | \(-0.546809\pi\) | ||||
−0.146527 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.16845e11 | −0.0288835 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.22819e13 | −0.372318 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.85649e13 | 2.00062 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.51466e12 | −0.0706428 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.68480e13 | −0.726339 | −0.363170 | − | 0.931723i | \(-0.618305\pi\) | ||||
−0.363170 | + | 0.931723i | \(0.618305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.04767e13 | −0.273025 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.58668e12 | −0.190498 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.40430e13 | 1.06582 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.41645e13 | 2.19670 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.68270e12 | 0.0603445 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.05888e13 | 0.880556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.62433e12 | −0.138638 | −0.0693188 | − | 0.997595i | \(-0.522083\pi\) | ||||
−0.0693188 | + | 0.997595i | \(0.522083\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.83191e12 | −0.0571884 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.02852e13 | −0.785170 | −0.392585 | − | 0.919716i | \(-0.628419\pi\) | ||||
−0.392585 | + | 0.919716i | \(0.628419\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.15423e13 | −0.405320 | −0.202660 | − | 0.979249i | \(-0.564959\pi\) | ||||
−0.202660 | + | 0.979249i | \(0.564959\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.40394e13 | 0.618406 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.79479e12 | −0.0490369 | −0.0245184 | − | 0.999699i | \(-0.507805\pi\) | ||||
−0.0245184 | + | 0.999699i | \(0.507805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.12248e12 | −0.137670 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.83856e12 | −0.0464859 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.40018e13 | 1.17119 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.03499e13 | −0.770265 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.55125e12 | −0.0377346 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.92578e13 | −0.418470 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.48560e13 | 0.620536 | 0.310268 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310268 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.53320e13 | 0.606682 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.99896e13 | −0.776836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.23428e13 | −0.655982 | −0.327991 | − | 0.944681i | \(-0.606372\pi\) | ||||
−0.327991 | + | 0.944681i | \(0.606372\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.08538e11 | 0.00859537 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.39198e14 | −1.63487 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.87195e13 | −0.554096 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.02770e12 | −0.0443662 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.62475e14 | −1.73370 | −0.866849 | − | 0.498571i | \(-0.833858\pi\) | ||||
−0.866849 | + | 0.498571i | \(0.833858\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.60706e13 | 0.579689 | 0.289845 | − | 0.957074i | \(-0.406396\pi\) | ||||
0.289845 | + | 0.957074i | \(0.406396\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.74591e13 | −0.174918 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.21433e14 | 1.17917 | 0.589585 | − | 0.807707i | \(-0.299291\pi\) | ||||
0.589585 | + | 0.807707i | \(0.299291\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.13317e13 | 0.859737 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.02483e13 | 0.184805 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.93082e13 | −0.878953 | −0.439476 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439476 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.32383e13 | −0.542863 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.55968e12 | 0.0213156 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.45662e13 | 0.198485 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.80965e13 | −0.455498 | −0.227749 | − | 0.973720i | \(-0.573137\pi\) | ||||
−0.227749 | + | 0.973720i | \(0.573137\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.89402e13 | 0.296315 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.81777e14 | 1.34271 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.06336e13 | 0.0762576 | 0.0381288 | − | 0.999273i | \(-0.487860\pi\) | ||||
0.0381288 | + | 0.999273i | \(0.487860\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.07392e13 | 0.0747827 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.86922e13 | −0.126410 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.94564e14 | 1.27805 | 0.639023 | − | 0.769188i | \(-0.279339\pi\) | ||||
0.639023 | + | 0.769188i | \(0.279339\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.84906e12 | 0.0437062 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.19102e14 | 1.35848 | 0.679240 | − | 0.733916i | \(-0.262309\pi\) | ||||
0.679240 | + | 0.733916i | \(0.262309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.15562e14 | −0.696273 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.98553e14 | −1.74828 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.58688e14 | 1.47250 | 0.736248 | − | 0.676712i | \(-0.236596\pi\) | ||||
0.736248 | + | 0.676712i | \(0.236596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.25090e14 | 1.79900 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.12289e12 | −0.0221842 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.46577e13 | −0.0766975 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.53970e14 | −1.29251 | −0.646256 | − | 0.763121i | \(-0.723666\pi\) | ||||
−0.646256 | + | 0.763121i | \(0.723666\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.45707e13 | 0.0721324 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.76194e14 | 0.848590 | 0.424295 | − | 0.905524i | \(-0.360522\pi\) | ||||
0.424295 | + | 0.905524i | \(0.360522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.20334e14 | −1.50116 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.07122e14 | −0.488513 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.53899e14 | −0.683074 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.54652e14 | 1.10019 | 0.550097 | − | 0.835101i | \(-0.314591\pi\) | ||||
0.550097 | + | 0.835101i | \(0.314591\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.21564e12 | 0.0177310 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.66498e14 | 0.681841 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.38692e14 | −0.553080 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.56242e13 | −0.138356 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.09764e13 | 0.0415224 | 0.0207612 | − | 0.999784i | \(-0.493391\pi\) | ||||
0.0207612 | + | 0.999784i | \(0.493391\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.06791e14 | −1.13056 | −0.565278 | − | 0.824901i | \(-0.691231\pi\) | ||||
−0.565278 | + | 0.824901i | \(0.691231\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.27631e13 | 0.333045 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.71642e14 | −1.30013 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.45048e14 | −2.19907 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.95276e13 | 0.0981099 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.94137e14 | 0.628756 | 0.314378 | − | 0.949298i | \(-0.398204\pi\) | ||||
0.314378 | + | 0.949298i | \(0.398204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.97021e14 | −0.622055 | −0.311027 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311027 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.70938e12 | 0.00526197 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.33936e14 | 0.702181 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.81833e14 | 1.41040 | 0.705199 | − | 0.709009i | \(-0.250857\pi\) | ||||
0.705199 | + | 0.709009i | \(0.250857\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.93248e14 | −0.551699 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.72499e14 | 1.31577 | 0.657886 | − | 0.753118i | \(-0.271451\pi\) | ||||
0.657886 | + | 0.753118i | \(0.271451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.68730e13 | −0.100168 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.87129e13 | −0.0761001 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.52414e13 | −0.0911377 | −0.0455688 | − | 0.998961i | \(-0.514510\pi\) | ||||
−0.0455688 | + | 0.998961i | \(0.514510\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.32200e14 | −0.333626 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.25962e13 | −0.104913 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.65941e14 | −0.639326 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.41522e14 | 1.27080 | 0.635400 | − | 0.772183i | \(-0.280835\pi\) | ||||
0.635400 | + | 0.772183i | \(0.280835\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.28869e14 | −0.295243 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.63903e14 | −0.590322 | −0.295161 | − | 0.955447i | \(-0.595373\pi\) | ||||
−0.295161 | + | 0.955447i | \(0.595373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.44968e13 | 0.0753499 | 0.0376750 | − | 0.999290i | \(-0.488005\pi\) | ||||
0.0376750 | + | 0.999290i | \(0.488005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.92943e13 | 0.0624874 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.88838e14 | 1.22674 | 0.613370 | − | 0.789795i | \(-0.289813\pi\) | ||||
0.613370 | + | 0.789795i | \(0.289813\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.53371e14 | 1.94004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.71264e13 | −0.0539235 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.01357e15 | 1.96842 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.67435e14 | −0.507462 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.76331e14 | −1.06861 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.73690e14 | 0.314723 | 0.157362 | − | 0.987541i | \(-0.449701\pi\) | ||||
0.157362 | + | 0.987541i | \(0.449701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.54167e14 | −0.627206 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.40093e13 | 0.110798 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.43782e14 | 0.412499 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.42617e14 | −1.39387 | −0.696933 | − | 0.717136i | \(-0.745453\pi\) | ||||
−0.696933 | + | 0.717136i | \(0.745453\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.00350e13 | −0.0485768 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.38408e14 | 0.851458 | 0.425729 | − | 0.904851i | \(-0.360018\pi\) | ||||
0.425729 | + | 0.904851i | \(0.360018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.37970e14 | −0.213367 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.66393e14 | 0.554139 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.45147e15 | −2.14707 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.36234e14 | 0.197121 | 0.0985603 | − | 0.995131i | \(-0.468576\pi\) | ||||
0.0985603 | + | 0.995131i | \(0.468576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.65449e13 | 0.0517272 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.88252e14 | −0.676115 | −0.338057 | − | 0.941125i | \(-0.609770\pi\) | ||||
−0.338057 | + | 0.941125i | \(0.609770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.60073e14 | −0.352365 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.43369e12 | 0.00455216 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.88014e14 | −0.633117 | −0.316559 | − | 0.948573i | \(-0.602527\pi\) | ||||
−0.316559 | + | 0.948573i | \(0.602527\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.90412e14 | −0.495688 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.27348e13 | −0.115238 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.74538e14 | 0.333935 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.14925e14 | −0.374981 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.04219e14 | 0.121486 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.10790e15 | 1.26442 | 0.632211 | − | 0.774796i | \(-0.282148\pi\) | ||||
0.632211 | + | 0.774796i | \(0.282148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.18140e14 | 0.690761 | 0.345380 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345380 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.31753e13 | −0.0800734 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.36445e15 | −2.53380 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.48712e13 | 0.0785794 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.27889e14 | −0.542653 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.04230e14 | −0.306339 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.75183e14 | 0.271441 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.47335e14 | 0.142379 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.56065e14 | 0.621167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.61295e14 | 0.706265 | 0.353133 | − | 0.935573i | \(-0.385116\pi\) | ||||
0.353133 | + | 0.935573i | \(0.385116\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.83101e13 | 0.0166453 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.47329e14 | 0.220341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.65709e14 | 0.493927 | 0.246964 | − | 0.969025i | \(-0.420567\pi\) | ||||
0.246964 | + | 0.969025i | \(0.420567\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.04515e15 | 1.75016 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.92840e13 | −0.0832809 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.32944e14 | 0.191542 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.23883e13 | 0.0261082 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.88089e15 | −1.48649 | −0.743243 | − | 0.669021i | \(-0.766713\pi\) | ||||
−0.743243 | + | 0.669021i | \(0.766713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.33251e15 | 1.80742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.17949e14 | 0.165599 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.76231e14 | 0.131306 | 0.0656531 | − | 0.997843i | \(-0.479087\pi\) | ||||
0.0656531 | + | 0.997843i | \(0.479087\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.86888e13 | −0.0501903 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.70241e15 | 1.21999 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.91855e14 | −0.345716 | −0.172858 | − | 0.984947i | \(-0.555300\pi\) | ||||
−0.172858 | + | 0.984947i | \(0.555300\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.18553e14 | −0.633295 | −0.316647 | − | 0.948543i | \(-0.602557\pi\) | ||||
−0.316647 | + | 0.948543i | \(0.602557\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.07982e14 | −0.0730303 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.17484e15 | −0.779483 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.53842e15 | −1.00140 | −0.500701 | − | 0.865620i | \(-0.666924\pi\) | ||||
−0.500701 | + | 0.865620i | \(0.666924\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.85493e13 | −0.0501661 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.20414e15 | 1.38124 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.95661e15 | 1.20317 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 8.43176e14 | 0.508816 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.66027e12 | −0.00335218 | −0.00167609 | − | 0.999999i | \(-0.500534\pi\) | ||||
−0.00167609 | + | 0.999999i | \(0.500534\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.70147e15 | −0.988984 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.71891e14 | −0.0980668 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.11514e14 | −0.230454 | −0.115227 | − | 0.993339i | \(-0.536760\pi\) | ||||
−0.115227 | + | 0.993339i | \(0.536760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.96296e15 | −1.07911 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.06276e13 | −0.00573555 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.35375e15 | −1.77698 | −0.888492 | − | 0.458893i | \(-0.848246\pi\) | ||||
−0.888492 | + | 0.458893i | \(0.848246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.02502e15 | 0.533240 | 0.266620 | − | 0.963802i | \(-0.414093\pi\) | ||||
0.266620 | + | 0.963802i | \(0.414093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.02270e15 | −1.54401 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.48146e14 | −0.124467 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.99079e15 | 0.980591 | 0.490296 | − | 0.871556i | \(-0.336889\pi\) | ||||
0.490296 | + | 0.871556i | \(0.336889\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.71660e13 | −0.0131410 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.24734e14 | −0.344312 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.16975e14 | −0.241233 | −0.120617 | − | 0.992699i | \(-0.538487\pi\) | ||||
−0.120617 | + | 0.992699i | \(0.538487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.78215e13 | 0.0127517 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.78133e14 | −0.305314 | −0.152657 | − | 0.988279i | \(-0.548783\pi\) | ||||
−0.152657 | + | 0.988279i | \(0.548783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.55793e14 | 0.290047 | 0.145023 | − | 0.989428i | \(-0.453674\pi\) | ||||
0.145023 | + | 0.989428i | \(0.453674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.07384e14 | −0.177011 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.85996e14 | 0.250156 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.48346e14 | 0.313879 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.56837e14 | 0.0646363 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.61417e15 | −1.05866 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.36388e14 | −0.133869 | −0.0669343 | − | 0.997757i | \(-0.521322\pi\) | ||||
−0.0669343 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.71679e14 | −0.0671423 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.63978e14 | −0.255210 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50979e15 | 0.570362 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.60194e15 | 1.70878 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.68016e15 | −0.978233 | −0.489116 | − | 0.872218i | \(-0.662681\pi\) | ||||
−0.489116 | + | 0.872218i | \(0.662681\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.63908e14 | −0.0588085 | −0.0294043 | − | 0.999568i | \(-0.509361\pi\) | ||||
−0.0294043 | + | 0.999568i | \(0.509361\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.13306e14 | −0.0752360 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.11319e15 | 1.07952 | 0.539762 | − | 0.841818i | \(-0.318514\pi\) | ||||
0.539762 | + | 0.841818i | \(0.318514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.79215e15 | 0.610983 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.65553e14 | −0.156054 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.15674e15 | 1.04044 | 0.520218 | − | 0.854033i | \(-0.325851\pi\) | ||||
0.520218 | + | 0.854033i | \(0.325851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.99691e14 | 0.129538 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.23782e15 | 0.394501 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.21997e15 | 0.695787 | 0.347894 | − | 0.937534i | \(-0.386897\pi\) | ||||
0.347894 | + | 0.937534i | \(0.386897\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.94533e15 | 0.907873 | 0.453937 | − | 0.891034i | \(-0.350019\pi\) | ||||
0.453937 | + | 0.891034i | \(0.350019\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.01562e14 | 0.152055 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.41255e15 | −0.421197 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.36155e14 | −0.127923 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.31724e14 | 0.0957046 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.94317e15 | −1.97053 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.03972e15 | 0.569492 | 0.284746 | − | 0.958603i | \(-0.408091\pi\) | ||||
0.284746 | + | 0.958603i | \(0.408091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.65720e14 | 0.127925 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.47929e14 | 0.0399775 | 0.0199887 | − | 0.999800i | \(-0.493637\pi\) | ||||
0.0199887 | + | 0.999800i | \(0.493637\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.87425e15 | −1.03016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.10760e14 | 0.0551415 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.94016e15 | 1.27183 | 0.635913 | − | 0.771761i | \(-0.280624\pi\) | ||||
0.635913 | + | 0.771761i | \(0.280624\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.08683e14 | −0.103535 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.04984e14 | −0.125897 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.50272e15 | 1.10476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.96403e15 | −0.715737 | −0.357868 | − | 0.933772i | \(-0.616496\pi\) | ||||
−0.357868 | + | 0.933772i | \(0.616496\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.82282e15 | −1.38389 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.45357e15 | 0.807888 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.24558e15 | −0.517068 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.90660e14 | −0.0432150 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.45018e14 | 0.188546 | 0.0942729 | − | 0.995546i | \(-0.469947\pi\) | ||||
0.0942729 | + | 0.995546i | \(0.469947\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.88117e15 | −0.413212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.62763e13 | 0.0143324 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.13314e15 | 0.879982 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.16194e15 | −1.29171 | −0.645853 | − | 0.763462i | \(-0.723498\pi\) | ||||
−0.645853 | + | 0.763462i | \(0.723498\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.38558e14 | −0.152441 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.47454e15 | −1.51912 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.86254e15 | −0.572885 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.73927e14 | 0.0934019 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.67467e15 | −1.48954 | −0.744768 | − | 0.667324i | \(-0.767440\pi\) | ||||
−0.744768 | + | 0.667324i | \(0.767440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.36303e15 | −0.833958 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.13228e14 | 0.153092 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.98611e14 | 0.0924491 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.55382e15 | −0.466391 | −0.233196 | − | 0.972430i | \(-0.574918\pi\) | ||||
−0.233196 | + | 0.972430i | \(0.574918\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.31653e15 | −0.956371 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.72167e16 | 3.05074 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.06639e16 | 1.86142 | 0.930709 | − | 0.365760i | \(-0.119191\pi\) | ||||
0.930709 | + | 0.365760i | \(0.119191\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.38069e14 | −0.0237420 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.02619e16 | 1.73843 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.93967e15 | −0.824430 | −0.412215 | − | 0.911087i | \(-0.635245\pi\) | ||||
−0.412215 | + | 0.911087i | \(0.635245\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.60926e14 | 0.0593497 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.04838e16 | −1.69855 | −0.849277 | − | 0.527948i | \(-0.822961\pi\) | ||||
−0.849277 | + | 0.527948i | \(0.822961\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.78355e15 | 0.444365 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.98831e15 | −1.09928 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.37328e15 | −0.677887 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.78697e15 | 1.49496 | 0.747478 | − | 0.664287i | \(-0.231265\pi\) | ||||
0.747478 | + | 0.664287i | \(0.231265\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.40268e14 | −0.141540 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.12947e15 | 0.612613 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.93317e14 | −0.0721271 | −0.0360636 | − | 0.999349i | \(-0.511482\pi\) | ||||
−0.0360636 | + | 0.999349i | \(0.511482\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.88984e14 | 0.0992840 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.97168e15 | 1.27426 | 0.637130 | − | 0.770756i | \(-0.280121\pi\) | ||||
0.637130 | + | 0.770756i | \(0.280121\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.93062e15 | −0.550271 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.22364e15 | 0.858829 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.12426e15 | 0.561011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.72650e15 | 0.499697 | 0.249849 | − | 0.968285i | \(-0.419619\pi\) | ||||
0.249849 | + | 0.968285i | \(0.419619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.55687e14 | −0.0602376 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.12337e15 | 0.146399 | 0.0731993 | − | 0.997317i | \(-0.476679\pi\) | ||||
0.0731993 | + | 0.997317i | \(0.476679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.54488e15 | 1.09786 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.14723e14 | −0.0652015 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.61593e15 | −0.201820 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.56233e16 | −1.92394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.72896e14 | 0.0209941 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.62976e15 | 0.314871 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.39683e16 | 1.64923 | 0.824617 | − | 0.565692i | \(-0.191391\pi\) | ||||
0.824617 | + | 0.565692i | \(0.191391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.93328e14 | −0.0225098 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.09162e15 | 0.125343 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.59782e16 | −1.80937 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.11770e14 | −0.0459870 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.77226e16 | 1.95213 | 0.976063 | − | 0.217490i | \(-0.0697869\pi\) | ||||
0.976063 | + | 0.217490i | \(0.0697869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.34939e15 | −0.581162 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.85792e15 | −0.199090 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.20232e15 | −0.444175 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.20534e15 | −0.646976 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.09650e14 | −0.0318469 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.35271e16 | −1.37242 | −0.686211 | − | 0.727402i | \(-0.740727\pi\) | ||||
−0.686211 | + | 0.727402i | \(0.740727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.11634e16 | −1.11733 | −0.558666 | − | 0.829393i | \(-0.688687\pi\) | ||||
−0.558666 | + | 0.829393i | \(0.688687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.16494e14 | 0.0213770 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.91173e15 | 0.283651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.23892e16 | 1.19076 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.34000e16 | −1.27070 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.29639e16 | −1.21297 | −0.606483 | − | 0.795097i | \(-0.707420\pi\) | ||||
−0.606483 | + | 0.795097i | \(0.707420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.20238e15 | 0.295647 | 0.147824 | − | 0.989014i | \(-0.452773\pi\) | ||||
0.147824 | + | 0.989014i | \(0.452773\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.87645e14 | −0.0717519 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.92879e15 | −0.892516 | −0.446258 | − | 0.894904i | \(-0.647244\pi\) | ||||
−0.446258 | + | 0.894904i | \(0.647244\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.17935e16 | 1.04615 | 0.523073 | − | 0.852288i | \(-0.324785\pi\) | ||||
0.523073 | + | 0.852288i | \(0.324785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.47923e14 | −0.0829789 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.11441e16 | 0.962712 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.54282e15 | −0.302047 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.96299e15 | 0.249310 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.90602e14 | 0.0241328 | 0.0120664 | − | 0.999927i | \(-0.496159\pi\) | ||||
0.0120664 | + | 0.999927i | \(0.496159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20154e16 | −0.984828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.84229e15 | −0.149042 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.32877e14 | −0.0265811 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.94361e15 | 0.310839 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.22162e14 | −0.0250659 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.26397e15 | −0.634711 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.57981e16 | −1.19780 | −0.598902 | − | 0.800823i | \(-0.704396\pi\) | ||||
−0.598902 | + | 0.800823i | \(0.704396\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.47856e15 | 0.335216 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.64826e16 | 1.21796 | 0.608978 | − | 0.793187i | \(-0.291580\pi\) | ||||
0.608978 | + | 0.793187i | \(0.291580\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.21838e13 | 0.00453644 | 0.00226822 | − | 0.999997i | \(-0.499278\pi\) | ||||
0.00226822 | + | 0.999997i | \(0.499278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.42147e14 | −0.0318456 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.77134e16 | 1.25963 | 0.629815 | − | 0.776745i | \(-0.283131\pi\) | ||||
0.629815 | + | 0.776745i | \(0.283131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.01034e16 | −0.709382 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.46834e15 | 0.171120 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.50736e15 | 0.171636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.36156e16 | 1.59624 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.22835e16 | 0.819867 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.65456e16 | 1.09053 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.21556e15 | 0.534736 | 0.267368 | − | 0.963595i | \(-0.413846\pi\) | ||||
0.267368 | + | 0.963595i | \(0.413846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.66527e14 | −0.0621263 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.91858e16 | −1.21790 | −0.608950 | − | 0.793209i | \(-0.708409\pi\) | ||||
−0.608950 | + | 0.793209i | \(0.708409\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.04412e16 | −0.654584 | −0.327292 | − | 0.944923i | \(-0.606136\pi\) | ||||
−0.327292 | + | 0.944923i | \(0.606136\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.77160e14 | −0.0233527 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.33912e15 | −0.571118 | −0.285559 | − | 0.958361i | \(-0.592179\pi\) | ||||
−0.285559 | + | 0.958361i | \(0.592179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.05521e16 | 0.637353 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.83244e16 | 1.09321 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.84944e15 | −0.226838 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.42833e16 | −0.831384 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.58555e15 | 0.0911636 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.17225e15 | 0.180173 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.32354e16 | 1.86472 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.38992e15 | 0.187891 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.77507e15 | −0.0971958 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.35976e16 | 0.735565 | 0.367782 | − | 0.929912i | \(-0.380117\pi\) | ||||
0.367782 | + | 0.929912i | \(0.380117\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.31043e16 | −0.700346 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.44918e16 | −1.29321 | −0.646607 | − | 0.762823i | \(-0.723813\pi\) | ||||
−0.646607 | + | 0.762823i | \(0.723813\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.37249e16 | 1.23770 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.46120e15 | 0.0753169 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.35200e15 | −0.323504 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.94715e16 | −0.979860 | −0.489930 | − | 0.871762i | \(-0.662978\pi\) | ||||
−0.489930 | + | 0.871762i | \(0.662978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.38476e14 | −0.0118581 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.59538e16 | −1.76659 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.44735e15 | 0.458702 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.38332e16 | 0.663717 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.72465e16 | −1.76604 | −0.883018 | − | 0.469340i | \(-0.844492\pi\) | ||||
−0.883018 | + | 0.469340i | \(0.844492\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.01932e15 | 0.375763 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.45027e15 | −0.0671582 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.11289e16 | −0.966970 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.42521e15 | −0.154924 | −0.0774622 | − | 0.996995i | \(-0.524682\pi\) | ||||
−0.0774622 | + | 0.996995i | \(0.524682\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.75523e14 | −0.0346684 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.69228e16 | −1.18954 | −0.594768 | − | 0.803898i | \(-0.702756\pi\) | ||||
−0.594768 | + | 0.803898i | \(0.702756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.09876e15 | −0.310005 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.45987e15 | 0.106178 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.87322e16 | 1.22587 | 0.612935 | − | 0.790133i | \(-0.289989\pi\) | ||||
0.612935 | + | 0.790133i | \(0.289989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.67076e15 | −0.407846 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00612e14 | −0.00419429 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.77454e16 | −0.731265 | −0.365633 | − | 0.930759i | \(-0.619147\pi\) | ||||
−0.365633 | + | 0.930759i | \(0.619147\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.04683e16 | 0.426440 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.92409e14 | −0.0117754 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.49490e15 | 0.258565 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.89555e16 | 1.13960 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.38657e16 | 0.539506 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.61492e15 | 0.292931 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.45602e16 | −0.934086 | −0.467043 | − | 0.884235i | \(-0.654681\pi\) | ||||
−0.467043 | + | 0.884235i | \(0.654681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.66406e15 | 0.100176 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.69158e15 | 0.174427 | 0.0872135 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872135 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.48850e16 | −2.01759 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.81260e15 | −0.0658834 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.77872e16 | −0.998676 | −0.499338 | − | 0.866407i | \(-0.666423\pi\) | ||||
−0.499338 | + | 0.866407i | \(0.666423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.30755e15 | 0.224159 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.24622e16 | 0.437941 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.09519e16 | 0.380581 | 0.190290 | − | 0.981728i | \(-0.439057\pi\) | ||||
0.190290 | + | 0.981728i | \(0.439057\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.66639e16 | 0.572634 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.05328e15 | −0.0357931 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.44258e16 | 1.82905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.36280e16 | −1.11762 | −0.558811 | − | 0.829295i | \(-0.688742\pi\) | ||||
−0.558811 | + | 0.829295i | \(0.688742\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.61482e15 | 0.0530765 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.03028e15 | 0.0334911 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.27110e16 | 1.69464 | 0.847321 | − | 0.531082i | \(-0.178214\pi\) | ||||
0.847321 | + | 0.531082i | \(0.178214\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.27593e15 | 0.104166 |
(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 | 16.12.a.b.1.1 | 1 | ||
3.2 | odd | 2 | 144.12.a.j.1.1 | 1 | |||
4.3 | odd | 2 | 8.12.a.a.1.1 | ✓ | 1 | ||
8.3 | odd | 2 | 64.12.a.e.1.1 | 1 | |||
8.5 | even | 2 | 64.12.a.c.1.1 | 1 | |||
12.11 | even | 2 | 72.12.a.c.1.1 | 1 | |||
16.3 | odd | 4 | 256.12.b.g.129.1 | 2 | |||
16.5 | even | 4 | 256.12.b.a.129.1 | 2 | |||
16.11 | odd | 4 | 256.12.b.g.129.2 | 2 | |||
16.13 | even | 4 | 256.12.b.a.129.2 | 2 | |||
20.3 | even | 4 | 200.12.c.b.49.1 | 2 | |||
20.7 | even | 4 | 200.12.c.b.49.2 | 2 | |||
20.19 | odd | 2 | 200.12.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.12.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
16.12.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
64.12.a.c.1.1 | 1 | 8.5 | even | 2 | |||
64.12.a.e.1.1 | 1 | 8.3 | odd | 2 | |||
72.12.a.c.1.1 | 1 | 12.11 | even | 2 | |||
144.12.a.j.1.1 | 1 | 3.2 | odd | 2 | |||
200.12.a.b.1.1 | 1 | 20.19 | odd | 2 | |||
200.12.c.b.49.1 | 2 | 20.3 | even | 4 | |||
200.12.c.b.49.2 | 2 | 20.7 | even | 4 | |||
256.12.b.a.129.1 | 2 | 16.5 | even | 4 | |||
256.12.b.a.129.2 | 2 | 16.13 | even | 4 | |||
256.12.b.g.129.1 | 2 | 16.3 | odd | 4 | |||
256.12.b.g.129.2 | 2 | 16.11 | odd | 4 |