Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,8,Mod(1,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.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: | \(134.950331009\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 54) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 432.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 105.000 | 0.375659 | 0.187830 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187830 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 937.000 | 1.03252 | 0.516258 | − | 0.856433i | \(-0.327325\pi\) | ||||
0.516258 | + | 0.856433i | \(0.327325\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5943.00 | −1.34627 | −0.673134 | − | 0.739521i | \(-0.735052\pi\) | ||||
−0.673134 | + | 0.739521i | \(0.735052\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 68.0000 | 0.00858435 | 0.00429217 | − | 0.999991i | \(-0.498634\pi\) | ||||
0.00429217 | + | 0.999991i | \(0.498634\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5400.00 | −0.266577 | −0.133288 | − | 0.991077i | \(-0.542554\pi\) | ||||
−0.133288 | + | 0.991077i | \(0.542554\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 48382.0 | 1.61825 | 0.809126 | − | 0.587635i | \(-0.199941\pi\) | ||||
0.809126 | + | 0.587635i | \(0.199941\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 642.000 | 0.0110024 | 0.00550120 | − | 0.999985i | \(-0.498249\pi\) | ||||
0.00550120 | + | 0.999985i | \(0.498249\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −67100.0 | −0.858880 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −125934. | −0.958849 | −0.479424 | − | 0.877583i | \(-0.659154\pi\) | ||||
−0.479424 | + | 0.877583i | \(0.659154\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 161275. | 0.972302 | 0.486151 | − | 0.873875i | \(-0.338401\pi\) | ||||
0.486151 | + | 0.873875i | \(0.338401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 98385.0 | 0.387874 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −414286. | −1.34460 | −0.672302 | − | 0.740277i | \(-0.734694\pi\) | ||||
−0.672302 | + | 0.740277i | \(0.734694\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −627474. | −1.42184 | −0.710922 | − | 0.703270i | \(-0.751722\pi\) | ||||
−0.710922 | + | 0.703270i | \(0.751722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −570590. | −1.09442 | −0.547211 | − | 0.836995i | \(-0.684310\pi\) | ||||
−0.547211 | + | 0.836995i | \(0.684310\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −538698. | −0.756838 | −0.378419 | − | 0.925634i | \(-0.623532\pi\) | ||||
−0.378419 | + | 0.925634i | \(0.623532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 54426.0 | 0.0660876 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 356283. | 0.328723 | 0.164361 | − | 0.986400i | \(-0.447444\pi\) | ||||
0.164361 | + | 0.986400i | \(0.447444\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −624015. | −0.505738 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.91083e6 | 1.84516 | 0.922581 | − | 0.385803i | \(-0.126076\pi\) | ||||
0.922581 | + | 0.385803i | \(0.126076\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.68417e6 | 1.51410 | 0.757051 | − | 0.653356i | \(-0.226639\pi\) | ||||
0.757051 | + | 0.653356i | \(0.226639\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7140.00 | 0.00322479 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.68108e6 | −1.08905 | −0.544525 | − | 0.838745i | \(-0.683290\pi\) | ||||
−0.544525 | + | 0.838745i | \(0.683290\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.70548e6 | 1.22868 | 0.614342 | − | 0.789040i | \(-0.289422\pi\) | ||||
0.614342 | + | 0.789040i | \(0.289422\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −153151. | −0.0460776 | −0.0230388 | − | 0.999735i | \(-0.507334\pi\) | ||||
−0.0230388 | + | 0.999735i | \(0.507334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.56859e6 | −1.39004 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.57929e6 | 1.72955 | 0.864776 | − | 0.502158i | \(-0.167460\pi\) | ||||
0.864776 | + | 0.502158i | \(0.167460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.34600e6 | −1.79412 | −0.897062 | − | 0.441905i | \(-0.854303\pi\) | ||||
−0.897062 | + | 0.441905i | \(0.854303\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −567000. | −0.100142 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.03360e6 | 0.606496 | 0.303248 | − | 0.952912i | \(-0.401929\pi\) | ||||
0.303248 | + | 0.952912i | \(0.401929\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 63716.0 | 0.00886347 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.08011e6 | 0.607912 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.75410e6 | −0.640142 | −0.320071 | − | 0.947394i | \(-0.603707\pi\) | ||||
−0.320071 | + | 0.947394i | \(0.603707\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.87922e6 | 0.857532 | 0.428766 | − | 0.903416i | \(-0.358949\pi\) | ||||
0.428766 | + | 0.903416i | \(0.358949\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.65565e6 | 0.239464 | 0.119732 | − | 0.992806i | \(-0.461796\pi\) | ||||
0.119732 | + | 0.992806i | \(0.461796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.11234e7 | −1.66694 | −0.833471 | − | 0.552564i | \(-0.813650\pi\) | ||||
−0.833471 | + | 0.552564i | \(0.813650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.84213e7 | −1.36247 | −0.681237 | − | 0.732063i | \(-0.738558\pi\) | ||||
−0.681237 | + | 0.732063i | \(0.738558\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.86285e7 | −1.21452 | −0.607258 | − | 0.794505i | \(-0.707730\pi\) | ||||
−0.607258 | + | 0.794505i | \(0.707730\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 67410.0 | 0.00413316 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.05980e6 | −0.275245 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.58321e7 | 0.812436 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.52486e7 | −0.698306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.58380e6 | 0.111930 | 0.0559649 | − | 0.998433i | \(-0.482177\pi\) | ||||
0.0559649 | + | 0.998433i | \(0.482177\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.19283e7 | −1.62951 | −0.814757 | − | 0.579803i | \(-0.803129\pi\) | ||||
−0.814757 | + | 0.579803i | \(0.803129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.53339e7 | 1.67087 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.26662e6 | 0.0420846 | 0.0210423 | − | 0.999779i | \(-0.493302\pi\) | ||||
0.0210423 | + | 0.999779i | \(0.493302\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.30561e7 | −0.728173 | −0.364086 | − | 0.931365i | \(-0.618619\pi\) | ||||
−0.364086 | + | 0.931365i | \(0.618619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −404124. | −0.0115568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32231e7 | −0.360200 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.38266e7 | 0.590080 | 0.295040 | − | 0.955485i | \(-0.404667\pi\) | ||||
0.295040 | + | 0.955485i | \(0.404667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50493e7 | −1.06480 | −0.532401 | − | 0.846492i | \(-0.678710\pi\) | ||||
−0.532401 | + | 0.846492i | \(0.678710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.69339e7 | 0.365254 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.52575e7 | 0.727115 | 0.363558 | − | 0.931572i | \(-0.381562\pi\) | ||||
0.363558 | + | 0.931572i | \(0.381562\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 601554. | 0.0113601 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.55009e7 | 1.18465 | 0.592326 | − | 0.805699i | \(-0.298210\pi\) | ||||
0.592326 | + | 0.805699i | \(0.298210\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.28090e7 | −0.877405 | −0.438703 | − | 0.898632i | \(-0.644562\pi\) | ||||
−0.438703 | + | 0.898632i | \(0.644562\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.27439e7 | −0.999926 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.10733e8 | −1.62598 | −0.812991 | − | 0.582277i | \(-0.802162\pi\) | ||||
−0.812991 | + | 0.582277i | \(0.802162\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.28727e7 | −0.886807 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.19427e7 | 0.155639 | 0.0778195 | − | 0.996967i | \(-0.475204\pi\) | ||||
0.0778195 | + | 0.996967i | \(0.475204\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.95226e7 | −0.996817 | −0.498408 | − | 0.866942i | \(-0.666082\pi\) | ||||
−0.498408 | + | 0.866942i | \(0.666082\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.35000e7 | −0.505113 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.20922e7 | 0.358884 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.02315e6 | 0.0625470 | 0.0312735 | − | 0.999511i | \(-0.490044\pi\) | ||||
0.0312735 | + | 0.999511i | \(0.490044\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.85850e7 | −0.586591 | −0.293296 | − | 0.956022i | \(-0.594752\pi\) | ||||
−0.293296 | + | 0.956022i | \(0.594752\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.68414e8 | −1.56945 | −0.784725 | − | 0.619844i | \(-0.787196\pi\) | ||||
−0.784725 | + | 0.619844i | \(0.787196\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01669e8 | 0.914543 | 0.457271 | − | 0.889327i | \(-0.348827\pi\) | ||||
0.457271 | + | 0.889327i | \(0.348827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.18000e8 | −0.990026 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.58848e7 | −0.534129 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.87534e8 | −2.17860 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.63820e7 | 0.633045 | 0.316523 | − | 0.948585i | \(-0.397485\pi\) | ||||
0.316523 | + | 0.948585i | \(0.397485\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.99120e7 | −0.411130 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.51115e8 | 1.00392 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −367200. | −0.00228839 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.16173e7 | −0.251308 | −0.125654 | − | 0.992074i | \(-0.540103\pi\) | ||||
−0.125654 | + | 0.992074i | \(0.540103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.09315e8 | −1.18771 | −0.593855 | − | 0.804572i | \(-0.702395\pi\) | ||||
−0.593855 | + | 0.804572i | \(0.702395\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.32919e8 | 1.83195 | 0.915976 | − | 0.401233i | \(-0.131418\pi\) | ||||
0.915976 | + | 0.401233i | \(0.131418\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.95428e7 | 0.411960 | 0.205980 | − | 0.978556i | \(-0.433962\pi\) | ||||
0.205980 | + | 0.978556i | \(0.433962\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.65633e7 | −0.284313 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.46900e8 | −0.696034 | −0.348017 | − | 0.937488i | \(-0.613145\pi\) | ||||
−0.348017 | + | 0.937488i | \(0.613145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.03055e7 | −0.139464 | −0.0697320 | − | 0.997566i | \(-0.522214\pi\) | ||||
−0.0697320 | + | 0.997566i | \(0.522214\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.71473e6 | 0.0248264 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.28998e6 | 0.0138916 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.47027e8 | −0.586866 | −0.293433 | − | 0.955980i | \(-0.594798\pi\) | ||||
−0.293433 | + | 0.955980i | \(0.594798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.81541e6 | −0.0148122 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.67776e8 | −1.35150 | −0.675752 | − | 0.737129i | \(-0.736181\pi\) | ||||
−0.675752 | + | 0.737129i | \(0.736181\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.88186e8 | −1.38832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.25857e8 | −1.10454 | −0.552270 | − | 0.833665i | \(-0.686238\pi\) | ||||
−0.552270 | + | 0.833665i | \(0.686238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.74097e7 | 0.123488 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.39029e8 | −1.06195 | −0.530976 | − | 0.847387i | \(-0.678174\pi\) | ||||
−0.530976 | + | 0.847387i | \(0.678174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.50778e6 | 0.00765416 | 0.00382708 | − | 0.999993i | \(-0.498782\pi\) | ||||
0.00382708 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.98775e8 | 1.15628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.28585e7 | −0.149429 | −0.0747146 | − | 0.997205i | \(-0.523805\pi\) | ||||
−0.0747146 | + | 0.997205i | \(0.523805\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.39552e8 | 1.45064 | 0.725322 | − | 0.688409i | \(-0.241691\pi\) | ||||
0.725322 | + | 0.688409i | \(0.241691\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.58565e7 | −0.172721 | −0.0863607 | − | 0.996264i | \(-0.527524\pi\) | ||||
−0.0863607 | + | 0.996264i | \(0.527524\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.87943e8 | −1.46808 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.81179e8 | −0.928937 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.52583e7 | −0.0818889 | −0.0409444 | − | 0.999161i | \(-0.513037\pi\) | ||||
−0.0409444 | + | 0.999161i | \(0.513037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.05637e8 | 0.693152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43656.0 | 9.44484e−5 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.34643e8 | −1.13001 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.81838e8 | 0.568787 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.14259e8 | −0.225376 | −0.112688 | − | 0.993630i | \(-0.535946\pi\) | ||||
−0.112688 | + | 0.993630i | \(0.535946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.55463e8 | −0.293066 | −0.146533 | − | 0.989206i | \(-0.546811\pi\) | ||||
−0.146533 | + | 0.989206i | \(0.546811\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.82299e8 | 0.704690 | 0.352345 | − | 0.935870i | \(-0.385384\pi\) | ||||
0.352345 | + | 0.935870i | \(0.385384\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.44887e8 | 0.784408 | 0.392204 | − | 0.919878i | \(-0.371713\pi\) | ||||
0.392204 | + | 0.919878i | \(0.371713\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.48426e8 | 1.29087 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.61263e8 | −0.431389 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.56280e6 | −0.00737292 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.04760e8 | −0.781447 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.50888e8 | 0.834960 | 0.417480 | − | 0.908686i | \(-0.362913\pi\) | ||||
0.417480 | + | 0.908686i | \(0.362913\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.81513e8 | −0.409112 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.96793e8 | −0.707084 | −0.353542 | − | 0.935419i | \(-0.615023\pi\) | ||||
−0.353542 | + | 0.935419i | \(0.615023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.58457e8 | −1.30898 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.20663e8 | −0.964279 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.51162e8 | 0.322701 | 0.161350 | − | 0.986897i | \(-0.448415\pi\) | ||||
0.161350 | + | 0.986897i | \(0.448415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.82914e8 | −0.608108 | −0.304054 | − | 0.952655i | \(-0.598340\pi\) | ||||
−0.304054 | + | 0.952655i | \(0.598340\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.86935e8 | −0.589195 | −0.294598 | − | 0.955621i | \(-0.595186\pi\) | ||||
−0.294598 | + | 0.955621i | \(0.595186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.89075e8 | 0.461567 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.59969e8 | 0.524684 | 0.262342 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262342 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44695e9 | 1.61874 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.60809e7 | −0.0173095 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.52503e8 | −0.689051 | −0.344526 | − | 0.938777i | \(-0.611960\pi\) | ||||
−0.344526 | + | 0.938777i | \(0.611960\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.33837e8 | 0.339411 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91791e9 | 1.91358 | 0.956791 | − | 0.290775i | \(-0.0939131\pi\) | ||||
0.956791 | + | 0.290775i | \(0.0939131\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.56351e6 | −0.00823109 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.43151e9 | −1.35070 | −0.675348 | − | 0.737499i | \(-0.736007\pi\) | ||||
−0.675348 | + | 0.737499i | \(0.736007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.39859e8 | 0.127203 | 0.0636013 | − | 0.997975i | \(-0.479741\pi\) | ||||
0.0636013 | + | 0.997975i | \(0.479741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.84702e8 | −0.522182 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.77592e9 | −1.52968 | −0.764838 | − | 0.644222i | \(-0.777181\pi\) | ||||
−0.764838 | + | 0.644222i | \(0.777181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.46680e6 | −0.00293299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.95825e8 | 0.649722 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.05301e9 | −0.844630 | −0.422315 | − | 0.906449i | \(-0.638782\pi\) | ||||
−0.422315 | + | 0.906449i | \(0.638782\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.33012e9 | 1.80457 | 0.902284 | − | 0.431142i | \(-0.141889\pi\) | ||||
0.902284 | + | 0.431142i | \(0.141889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.09667e7 | 0.00834658 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.46210e9 | 1.81020 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.50422e8 | −0.108712 | −0.0543562 | − | 0.998522i | \(-0.517311\pi\) | ||||
−0.0543562 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.72745e9 | 1.90516 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.81330e8 | −0.673980 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.11432e8 | −0.605306 | −0.302653 | − | 0.953101i | \(-0.597872\pi\) | ||||
−0.302653 | + | 0.953101i | \(0.597872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.53482e8 | −0.492137 | −0.246068 | − | 0.969252i | \(-0.579139\pi\) | ||||
−0.246068 | + | 0.969252i | \(0.579139\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.62340e8 | 0.228958 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.51507e9 | 1.56333 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.72892e9 | 1.64180 | 0.820900 | − | 0.571072i | \(-0.193472\pi\) | ||||
0.820900 | + | 0.571072i | \(0.193472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.84699e9 | 1.09335 | 0.546673 | − | 0.837346i | \(-0.315894\pi\) | ||||
0.546673 | + | 0.837346i | \(0.315894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.10612e7 | 0.0178047 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.50066e9 | −0.846557 | −0.423279 | − | 0.906000i | \(-0.639121\pi\) | ||||
−0.423279 | + | 0.906000i | \(0.639121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.31690e9 | −0.719680 | −0.359840 | − | 0.933014i | \(-0.617169\pi\) | ||||
−0.359840 | + | 0.933014i | \(0.617169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.23528e8 | 0.227836 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.71216e8 | 0.141401 | 0.0707006 | − | 0.997498i | \(-0.477477\pi\) | ||||
0.0707006 | + | 0.997498i | \(0.477477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.72908e9 | 1.91418 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.69018e6 | 0.00332964 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.15061e9 | −1.05404 | −0.527018 | − | 0.849854i | \(-0.676690\pi\) | ||||
−0.527018 | + | 0.849854i | \(0.676690\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.84188e8 | 0.467870 | 0.233935 | − | 0.972252i | \(-0.424840\pi\) | ||||
0.233935 | + | 0.972252i | \(0.424840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.56748e9 | 1.20219 | 0.601096 | − | 0.799177i | \(-0.294731\pi\) | ||||
0.601096 | + | 0.799177i | \(0.294731\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.97867e8 | 0.317076 | 0.158538 | − | 0.987353i | \(-0.449322\pi\) | ||||
0.158538 | + | 0.987353i | \(0.449322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51217e9 | −1.12446 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.39102e9 | 1.47338 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.24643e9 | −1.38988 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.07066e9 | 1.27661 | 0.638304 | − | 0.769785i | \(-0.279636\pi\) | ||||
0.638304 | + | 0.769785i | \(0.279636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.81714e7 | −0.0115425 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.04180e8 | −0.240475 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.74254e9 | 0.683646 | 0.341823 | − | 0.939764i | \(-0.388956\pi\) | ||||
0.341823 | + | 0.939764i | \(0.388956\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01054e9 | 0.385272 | 0.192636 | − | 0.981270i | \(-0.438296\pi\) | ||||
0.192636 | + | 0.981270i | \(0.438296\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.80044e8 | 0.255607 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.47203e9 | 1.26864 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.56087e9 | −0.562361 | −0.281181 | − | 0.959655i | \(-0.590726\pi\) | ||||
−0.281181 | + | 0.959655i | \(0.590726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.63663e9 | −0.573407 | −0.286704 | − | 0.958019i | \(-0.592559\pi\) | ||||
−0.286704 | + | 0.958019i | \(0.592559\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.32318e8 | 0.322140 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.28526e8 | −0.177645 | −0.0888227 | − | 0.996047i | \(-0.528310\pi\) | ||||
−0.0888227 | + | 0.996047i | \(0.528310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.43502e8 | −0.0475758 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.78843e8 | 0.0899570 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.20148e9 | 1.01891 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.50707e9 | 1.39625 | 0.698124 | − | 0.715977i | \(-0.254018\pi\) | ||||
0.698124 | + | 0.715977i | \(0.254018\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.60454e9 | −1.10178 | −0.550888 | − | 0.834579i | \(-0.685711\pi\) | ||||
−0.550888 | + | 0.834579i | \(0.685711\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.70885e8 | −0.259193 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.40441e9 | −0.999879 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.26682e7 | −0.0122056 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.21796e9 | −0.626202 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.23454e8 | −0.0889716 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.24714e9 | −0.610154 | −0.305077 | − | 0.952328i | \(-0.598682\pi\) | ||||
−0.305077 | + | 0.952328i | \(0.598682\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.93424e9 | −0.511827 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.26741e9 | −1.11483 | −0.557415 | − | 0.830234i | \(-0.688207\pi\) | ||||
−0.557415 | + | 0.830234i | \(0.688207\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.09294e9 | −1.55166 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.10179e9 | 1.78579 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.18311e8 | 0.176124 | 0.0880622 | − | 0.996115i | \(-0.471933\pi\) | ||||
0.0880622 | + | 0.996115i | \(0.471933\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.88001e7 | −0.00939489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.71155e9 | 1.34888 | 0.674442 | − | 0.738328i | \(-0.264384\pi\) | ||||
0.674442 | + | 0.738328i | \(0.264384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.95599e9 | −0.456244 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.36000e9 | 1.44732 | 0.723660 | − | 0.690157i | \(-0.242458\pi\) | ||||
0.723660 | + | 0.690157i | \(0.242458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.74950e9 | 1.06763 | 0.533816 | − | 0.845600i | \(-0.320757\pi\) | ||||
0.533816 | + | 0.845600i | \(0.320757\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.30782e7 | −0.00944975 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.95938e8 | −0.194161 | −0.0970807 | − | 0.995277i | \(-0.530950\pi\) | ||||
−0.0970807 | + | 0.995277i | \(0.530950\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.75720e9 | −1.85246 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.11739e9 | −0.442549 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.42764e9 | 1.31165 | 0.655826 | − | 0.754912i | \(-0.272321\pi\) | ||||
0.655826 | + | 0.754912i | \(0.272321\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.80281e9 | 1.57343 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.89741e9 | −1.35830 | −0.679148 | − | 0.734001i | \(-0.737651\pi\) | ||||
−0.679148 | + | 0.734001i | \(0.737651\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.31279e8 | −0.103398 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.50564e9 | 1.61701 | 0.808506 | − | 0.588488i | \(-0.200277\pi\) | ||||
0.808506 | + | 0.588488i | \(0.200277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.03680e9 | −1.32225 | −0.661126 | − | 0.750275i | \(-0.729921\pi\) | ||||
−0.661126 | + | 0.750275i | \(0.729921\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.66237e9 | 0.305199 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.16881e9 | 1.66400 | 0.831999 | − | 0.554778i | \(-0.187197\pi\) | ||||
0.831999 | + | 0.554778i | \(0.187197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.66315e7 | −0.00649696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.89814e9 | 0.332826 | 0.166413 | − | 0.986056i | \(-0.446781\pi\) | ||||
0.166413 | + | 0.986056i | \(0.446781\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.00801e10 | 1.72769 | 0.863847 | − | 0.503755i | \(-0.168049\pi\) | ||||
0.863847 | + | 0.503755i | \(0.168049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.07797e9 | 0.352145 | 0.176073 | − | 0.984377i | \(-0.443661\pi\) | ||||
0.176073 | + | 0.984377i | \(0.443661\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.77949e9 | 0.626216 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.64108e9 | 0.596555 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.23714e9 | 0.358440 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.91619e9 | 1.41279 | 0.706393 | − | 0.707820i | \(-0.250321\pi\) | ||||
0.706393 | + | 0.707820i | \(0.250321\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.71299e8 | 0.0420475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.70097e6 | 0.000567319 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.87905e9 | −0.281796 | −0.140898 | − | 0.990024i | \(-0.544999\pi\) | ||||
−0.140898 | + | 0.990024i | \(0.544999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.30520e9 | 0.341956 | 0.170978 | − | 0.985275i | \(-0.445307\pi\) | ||||
0.170978 | + | 0.985275i | \(0.445307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.73867e9 | 0.833002 | 0.416501 | − | 0.909135i | \(-0.363256\pi\) | ||||
0.416501 | + | 0.909135i | \(0.363256\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.72991e10 | −2.48408 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.36875e9 | −1.03561 | −0.517807 | − | 0.855497i | \(-0.673251\pi\) | ||||
−0.517807 | + | 0.855497i | \(0.673251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.40247e9 | −0.612142 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.24540e10 | −1.69515 | −0.847577 | − | 0.530672i | \(-0.821940\pi\) | ||||
−0.847577 | + | 0.530672i | \(0.821940\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.53207e9 | −0.745045 | −0.372523 | − | 0.928023i | \(-0.621507\pi\) | ||||
−0.372523 | + | 0.928023i | \(0.621507\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.76006e9 | 0.627678 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.08496e7 | −0.0105496 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.59520e10 | −2.03839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.11788e10 | 1.41366 | 0.706829 | − | 0.707385i | \(-0.250125\pi\) | ||||
0.706829 | + | 0.707385i | \(0.250125\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.60037e10 | −1.98226 | −0.991130 | − | 0.132893i | \(-0.957573\pi\) | ||||
−0.991130 | + | 0.132893i | \(0.957573\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.39159e9 | −0.660956 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.70052e8 | −0.116499 | −0.0582496 | − | 0.998302i | \(-0.518552\pi\) | ||||
−0.0582496 | + | 0.998302i | \(0.518552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.32995e8 | 0.0158095 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.42272e7 | 0.00282187 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.09761e8 | −0.0241853 | −0.0120927 | − | 0.999927i | \(-0.503849\pi\) | ||||
−0.0120927 | + | 0.999927i | \(0.503849\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.42089e9 | −0.273545 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.38836e9 | 0.379031 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.65792e10 | −1.81782 | −0.908910 | − | 0.416993i | \(-0.863084\pi\) | ||||
−0.908910 | + | 0.416993i | \(0.863084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.00440e10 | −2.17591 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.31983e9 | 0.885414 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.78901e9 | −1.03152 | −0.515759 | − | 0.856734i | \(-0.672490\pi\) | ||||
−0.515759 | + | 0.856734i | \(0.672490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.03539e8 | 0.0106977 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.24330e7 | −0.00434143 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.08605e10 | −1.08968 | −0.544838 | − | 0.838541i | \(-0.683409\pi\) | ||||
−0.544838 | + | 0.838541i | \(0.683409\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48835e9 | 0.247251 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.45017e9 | 0.823536 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.01058e9 | −0.773203 | −0.386602 | − | 0.922247i | \(-0.626351\pi\) | ||||
−0.386602 | + | 0.922247i | \(0.626351\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.08119e9 | 0.291747 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.67173e10 | 1.56784 | 0.783921 | − | 0.620860i | \(-0.213217\pi\) | ||||
0.783921 | + | 0.620860i | \(0.213217\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.59336e10 | 1.46615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.35702e9 | 0.852869 | 0.426434 | − | 0.904519i | \(-0.359770\pi\) | ||||
0.426434 | + | 0.904519i | \(0.359770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.58318e10 | −1.41602 | −0.708012 | − | 0.706201i | \(-0.750408\pi\) | ||||
−0.708012 | + | 0.706201i | \(0.750408\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.50180e9 | 0.221669 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.97926e10 | −1.72114 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50540e10 | 1.29692 | 0.648458 | − | 0.761250i | \(-0.275414\pi\) | ||||
0.648458 | + | 0.761250i | \(0.275414\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.73018e9 | −0.400003 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.81448e9 | 0.570949 | 0.285474 | − | 0.958386i | \(-0.407849\pi\) | ||||
0.285474 | + | 0.958386i | \(0.407849\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.42269e9 | 0.281527 | 0.140764 | − | 0.990043i | \(-0.455044\pi\) | ||||
0.140764 | + | 0.990043i | \(0.455044\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.72608e10 | −1.40678 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.97936e8 | 0.0158395 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.62370e9 | 0.763133 | 0.381566 | − | 0.924341i | \(-0.375385\pi\) | ||||
0.381566 | + | 0.924341i | \(0.375385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.46796e10 | −1.92181 | −0.960905 | − | 0.276880i | \(-0.910700\pi\) | ||||
−0.960905 | + | 0.276880i | \(0.910700\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.08216e10 | −0.835091 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.03584e10 | −2.30090 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.20217e10 | −1.65414 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.70204e9 | 0.273148 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.46260e10 | 1.80087 | 0.900436 | − | 0.434988i | \(-0.143247\pi\) | ||||
0.900436 | + | 0.434988i | \(0.143247\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.74549e10 | −1.25401 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.82523e8 | 0.0129976 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.46329e9 | 0.312285 | 0.156142 | − | 0.987735i | \(-0.450094\pi\) | ||||
0.156142 | + | 0.987735i | \(0.450094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.90897e9 | 0.201756 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.10176e8 | 0.0620328 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.31632e7 | 0.00426755 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.56496e9 | −0.170318 | −0.0851590 | − | 0.996367i | \(-0.527140\pi\) | ||||
−0.0851590 | + | 0.996367i | \(0.527140\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.95820e9 | −0.260570 | −0.130285 | − | 0.991477i | \(-0.541589\pi\) | ||||
−0.130285 | + | 0.991477i | \(0.541589\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.87759e9 | 0.445026 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.76063e10 | −1.77105 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.58510e10 | 0.999669 | 0.499835 | − | 0.866121i | \(-0.333394\pi\) | ||||
0.499835 | + | 0.866121i | \(0.333394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.57453e10 | 0.984583 | 0.492292 | − | 0.870430i | \(-0.336159\pi\) | ||||
0.492292 | + | 0.870430i | \(0.336159\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.15640e9 | 0.132574 | 0.0662872 | − | 0.997801i | \(-0.478885\pi\) | ||||
0.0662872 | + | 0.997801i | \(0.478885\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.95703e10 | 1.80267 | 0.901333 | − | 0.433126i | \(-0.142589\pi\) | ||||
0.901333 | + | 0.433126i | \(0.142589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.93900e8 | −0.0176174 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.54494e9 | −0.329605 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.11982e9 | 0.182374 | 0.0911869 | − | 0.995834i | \(-0.470934\pi\) | ||||
0.0911869 | + | 0.995834i | \(0.470934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.39050e9 | −0.0806095 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.58811e9 | −0.375632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.48347e10 | 0.838852 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.65972e8 | −0.0147939 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.43942e10 | −0.794082 | −0.397041 | − | 0.917801i | \(-0.629963\pi\) | ||||
−0.397041 | + | 0.917801i | \(0.629963\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.73201e9 | 0.256810 | 0.128405 | − | 0.991722i | \(-0.459014\pi\) | ||||
0.128405 | + | 0.991722i | \(0.459014\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.83735e9 | 0.260394 | 0.130197 | − | 0.991488i | \(-0.458439\pi\) | ||||
0.130197 | + | 0.991488i | \(0.458439\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.90890e10 | 1.01099 | 0.505493 | − | 0.862831i | \(-0.331311\pi\) | ||||
0.505493 | + | 0.862831i | \(0.331311\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.16270e10 | −0.610815 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.50437e10 | −2.32844 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.82313e8 | −0.00934878 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.42880e10 | −0.721011 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.36363e10 | −1.68388 | −0.841938 | − | 0.539575i | \(-0.818585\pi\) | ||||
−0.841938 | + | 0.539575i | \(0.818585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.81256e10 | 1.38575 | 0.692876 | − | 0.721057i | \(-0.256343\pi\) | ||||
0.692876 | + | 0.721057i | \(0.256343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.99944e10 | −0.977341 | −0.488671 | − | 0.872468i | \(-0.662518\pi\) | ||||
−0.488671 | + | 0.872468i | \(0.662518\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.22676e10 | 1.55251 | 0.776255 | − | 0.630419i | \(-0.217117\pi\) | ||||
0.776255 | + | 0.630419i | \(0.217117\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.42102e9 | 0.115569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.60633e10 | −1.22475 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.25399e9 | 0.0584672 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.03100e10 | −0.932290 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.92393e9 | −0.0876299 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.34987e9 | −0.374464 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.15232e10 | −0.512801 | −0.256400 | − | 0.966571i | \(-0.582537\pi\) | ||||
−0.256400 | + | 0.966571i | \(0.582537\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.89709e9 | 0.258418 | 0.129209 | − | 0.991617i | \(-0.458756\pi\) | ||||
0.129209 | + | 0.991617i | \(0.458756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.55433e10 | 2.41537 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.92868e10 | −1.68250 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.37679e9 | −0.186017 | −0.0930083 | − | 0.995665i | \(-0.529648\pi\) | ||||
−0.0930083 | + | 0.995665i | \(0.529648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.51973e8 | 0.0105474 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.77986e10 | 1.15485 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.03024e10 | 1.24000 | 0.620000 | − | 0.784602i | \(-0.287133\pi\) | ||||
0.620000 | + | 0.784602i | \(0.287133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.63324e9 | 0.106946 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.36968e9 | 0.134818 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.61397e10 | 1.03804 | 0.519018 | − | 0.854763i | \(-0.326298\pi\) | ||||
0.519018 | + | 0.854763i | \(0.326298\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.42439e10 | −0.948505 | −0.474253 | − | 0.880389i | \(-0.657282\pi\) | ||||
−0.474253 | + | 0.880389i | \(0.657282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.02838e8 | −0.0156437 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.57755e10 | −0.986237 | −0.493119 | − | 0.869962i | \(-0.664143\pi\) | ||||
−0.493119 | + | 0.869962i | \(0.664143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.04143e7 | −0.000395546 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.22288e10 | 0.831937 | 0.415968 | − | 0.909379i | \(-0.363443\pi\) | ||||
0.415968 | + | 0.909379i | \(0.363443\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.32431e8 | 0.0234964 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.18682e9 | 0.0434530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.50299e9 | −0.0546291 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.15142e9 | −0.220358 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.09410e9 | 0.110038 | 0.0550189 | − | 0.998485i | \(-0.482478\pi\) | ||||
0.0550189 | + | 0.998485i | \(0.482478\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.62621e10 | 0.570044 | 0.285022 | − | 0.958521i | \(-0.407999\pi\) | ||||
0.285022 | + | 0.958521i | \(0.407999\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.16036e10 | −0.751850 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.42256e9 | 0.151720 | 0.0758601 | − | 0.997118i | \(-0.475830\pi\) | ||||
0.0758601 | + | 0.997118i | \(0.475830\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.39717e10 | −0.816506 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.73847e10 | −1.25533 | −0.627663 | − | 0.778485i | \(-0.715988\pi\) | ||||
−0.627663 | + | 0.778485i | \(0.715988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.76835e10 | −0.589579 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.66319e8 | −0.0120413 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.24473e10 | 0.406273 | 0.203136 | − | 0.979150i | \(-0.434887\pi\) | ||||
0.203136 | + | 0.979150i | \(0.434887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.06753e10 | 0.343557 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.84335e10 | 0.908652 | 0.454326 | − | 0.890836i | \(-0.349880\pi\) | ||||
0.454326 | + | 0.890836i | \(0.349880\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 432.8.a.f.1.1 | 1 | ||
3.2 | odd | 2 | 432.8.a.c.1.1 | 1 | |||
4.3 | odd | 2 | 54.8.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 54.8.a.e.1.1 | yes | 1 | ||
36.7 | odd | 6 | 162.8.c.j.109.1 | 2 | |||
36.11 | even | 6 | 162.8.c.c.109.1 | 2 | |||
36.23 | even | 6 | 162.8.c.c.55.1 | 2 | |||
36.31 | odd | 6 | 162.8.c.j.55.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.8.a.b.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
54.8.a.e.1.1 | yes | 1 | 12.11 | even | 2 | ||
162.8.c.c.55.1 | 2 | 36.23 | even | 6 | |||
162.8.c.c.109.1 | 2 | 36.11 | even | 6 | |||
162.8.c.j.55.1 | 2 | 36.31 | odd | 6 | |||
162.8.c.j.109.1 | 2 | 36.7 | odd | 6 | |||
432.8.a.c.1.1 | 1 | 3.2 | odd | 2 | |||
432.8.a.f.1.1 | 1 | 1.1 | even | 1 | trivial |