Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,12,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(172.877215626\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 34.0000 | 0.751301 | 0.375650 | − | 0.926761i | \(-0.377419\pi\) | ||||
0.375650 | + | 0.926761i | \(0.377419\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −892.000 | −0.435547 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17556.0 | 0.394808 | 0.197404 | − | 0.980322i | \(-0.436749\pi\) | ||||
0.197404 | + | 0.980322i | \(0.436749\pi\) | |||||||
\(8\) | −99960.0 | −1.07853 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 468788. | 0.877641 | 0.438820 | − | 0.898575i | \(-0.355396\pi\) | ||||
0.438820 | + | 0.898575i | \(0.355396\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 374042. | 0.279404 | 0.139702 | − | 0.990194i | \(-0.455386\pi\) | ||||
0.139702 | + | 0.990194i | \(0.455386\pi\) | |||||||
\(14\) | 596904. | 0.296620 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.57182e6 | −0.374752 | ||||||||
\(17\) | −3.72429e6 | −0.636171 | −0.318086 | − | 0.948062i | \(-0.603040\pi\) | ||||
−0.318086 | + | 0.948062i | \(0.603040\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −379460. | −0.0351578 | −0.0175789 | − | 0.999845i | \(-0.505596\pi\) | ||||
−0.0175789 | + | 0.999845i | \(0.505596\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.59388e7 | 0.659372 | ||||||||
\(23\) | −3.24581e7 | −1.05153 | −0.525763 | − | 0.850631i | \(-0.676220\pi\) | ||||
−0.525763 | + | 0.850631i | \(0.676220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.27174e7 | 0.209916 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.56600e7 | −0.171958 | ||||||||
\(29\) | −6.96967e7 | −0.630991 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.71449e8 | 1.07558 | 0.537792 | − | 0.843077i | \(-0.319258\pi\) | ||||
0.537792 | + | 0.843077i | \(0.319258\pi\) | |||||||
\(32\) | 1.51276e8 | 0.796976 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.26626e8 | −0.477956 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.91341e8 | 0.690703 | 0.345352 | − | 0.938473i | \(-0.387760\pi\) | ||||
0.345352 | + | 0.938473i | \(0.387760\pi\) | |||||||
\(38\) | −1.29016e7 | −0.0264141 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.91343e8 | −0.257930 | −0.128965 | − | 0.991649i | \(-0.541165\pi\) | ||||
−0.128965 | + | 0.991649i | \(0.541165\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.75986e9 | 1.82558 | 0.912790 | − | 0.408429i | \(-0.133923\pi\) | ||||
0.912790 | + | 0.408429i | \(0.133923\pi\) | |||||||
\(44\) | −4.18159e8 | −0.382254 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.10358e9 | −0.790012 | ||||||||
\(47\) | 1.62347e9 | 1.03254 | 0.516269 | − | 0.856426i | \(-0.327320\pi\) | ||||
0.516269 | + | 0.856426i | \(0.327320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.66911e9 | −0.844126 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.33645e8 | −0.121693 | ||||||||
\(53\) | −6.44889e8 | −0.211820 | −0.105910 | − | 0.994376i | \(-0.533776\pi\) | ||||
−0.105910 | + | 0.994376i | \(0.533776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.75490e9 | −0.425812 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.36969e9 | −0.474064 | ||||||||
\(59\) | −9.25569e8 | −0.168548 | −0.0842739 | − | 0.996443i | \(-0.526857\pi\) | ||||
−0.0842739 | + | 0.996443i | \(0.526857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08986e10 | −1.65218 | −0.826088 | − | 0.563541i | \(-0.809439\pi\) | ||||
−0.826088 | + | 0.563541i | \(0.809439\pi\) | |||||||
\(62\) | 5.82925e9 | 0.808088 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.36248e9 | 0.973521 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.79567e9 | −0.343461 | −0.171731 | − | 0.985144i | \(-0.554936\pi\) | ||||
−0.171731 | + | 0.985144i | \(0.554936\pi\) | |||||||
\(68\) | 3.32206e9 | 0.277082 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.29669e10 | 1.51071 | 0.755357 | − | 0.655313i | \(-0.227463\pi\) | ||||
0.755357 | + | 0.655313i | \(0.227463\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.88082e9 | −0.557850 | −0.278925 | − | 0.960313i | \(-0.589978\pi\) | ||||
−0.278925 | + | 0.960313i | \(0.589978\pi\) | |||||||
\(74\) | 9.90558e9 | 0.518926 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.38478e8 | 0.0153129 | ||||||||
\(77\) | 8.23004e9 | 0.346500 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.07689e10 | −0.759389 | −0.379694 | − | 0.925112i | \(-0.623971\pi\) | ||||
−0.379694 | + | 0.925112i | \(0.623971\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.50567e9 | −0.193783 | ||||||||
\(83\) | 3.20486e9 | 0.0893058 | 0.0446529 | − | 0.999003i | \(-0.485782\pi\) | ||||
0.0446529 | + | 0.999003i | \(0.485782\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.98352e10 | 1.37156 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.68600e10 | −0.946560 | ||||||||
\(89\) | −6.31763e10 | −1.19925 | −0.599624 | − | 0.800282i | \(-0.704683\pi\) | ||||
−0.599624 | + | 0.800282i | \(0.704683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.56668e9 | 0.110311 | ||||||||
\(92\) | 2.89526e10 | 0.457989 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.51980e10 | 0.775747 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.26494e11 | −1.49564 | −0.747820 | − | 0.663902i | \(-0.768899\pi\) | ||||
−0.747820 | + | 0.663902i | \(0.768899\pi\) | |||||||
\(98\) | −5.67499e10 | −0.634193 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.28905e10 | −0.311389 | −0.155694 | − | 0.987805i | \(-0.549762\pi\) | ||||
−0.155694 | + | 0.987805i | \(0.549762\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.62224e10 | −0.647855 | −0.323928 | − | 0.946082i | \(-0.605003\pi\) | ||||
−0.323928 | + | 0.946082i | \(0.605003\pi\) | |||||||
\(104\) | −3.73892e10 | −0.301344 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.19262e10 | −0.159141 | ||||||||
\(107\) | 5.58566e10 | 0.385002 | 0.192501 | − | 0.981297i | \(-0.438340\pi\) | ||||
0.192501 | + | 0.981297i | \(0.438340\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.66137e11 | −1.03424 | −0.517119 | − | 0.855914i | \(-0.672995\pi\) | ||||
−0.517119 | + | 0.855914i | \(0.672995\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.75949e10 | −0.147955 | ||||||||
\(113\) | −1.79452e11 | −0.916254 | −0.458127 | − | 0.888887i | \(-0.651480\pi\) | ||||
−0.458127 | + | 0.888887i | \(0.651480\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.21695e10 | 0.274826 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.14694e10 | −0.126630 | ||||||||
\(119\) | −6.53836e10 | −0.251166 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.55495e10 | −0.229747 | ||||||||
\(122\) | −3.70552e11 | −1.24128 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.52932e11 | −0.468468 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.37949e10 | 0.144484 | 0.0722421 | − | 0.997387i | \(-0.476985\pi\) | ||||
0.0722421 | + | 0.997387i | \(0.476985\pi\) | |||||||
\(128\) | −2.54890e10 | −0.0655689 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.31507e11 | −1.20370 | −0.601848 | − | 0.798610i | \(-0.705569\pi\) | ||||
−0.601848 | + | 0.798610i | \(0.705569\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.66180e9 | −0.0138806 | ||||||||
\(134\) | −1.29053e11 | −0.258043 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.72280e11 | 0.686128 | ||||||||
\(137\) | 3.92828e11 | 0.695407 | 0.347703 | − | 0.937605i | \(-0.386962\pi\) | ||||
0.347703 | + | 0.937605i | \(0.386962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.04604e12 | −1.70988 | −0.854940 | − | 0.518727i | \(-0.826406\pi\) | ||||
−0.854940 | + | 0.518727i | \(0.826406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.80876e11 | 1.13500 | ||||||||
\(143\) | 1.75346e11 | 0.245216 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.35948e11 | −0.419113 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.59876e11 | −0.300834 | ||||||||
\(149\) | −4.45289e11 | −0.496727 | −0.248363 | − | 0.968667i | \(-0.579893\pi\) | ||||
−0.248363 | + | 0.968667i | \(0.579893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.66615e11 | 0.276383 | 0.138191 | − | 0.990406i | \(-0.455871\pi\) | ||||
0.138191 | + | 0.990406i | \(0.455871\pi\) | |||||||
\(152\) | 3.79308e10 | 0.0379186 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.79821e11 | 0.260326 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.61959e12 | 1.35505 | 0.677526 | − | 0.735498i | \(-0.263052\pi\) | ||||
0.677526 | + | 0.735498i | \(0.263052\pi\) | |||||||
\(158\) | −7.06142e11 | −0.570530 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.69834e11 | −0.415151 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.55712e12 | −1.05996 | −0.529980 | − | 0.848010i | \(-0.677801\pi\) | ||||
−0.529980 | + | 0.848010i | \(0.677801\pi\) | |||||||
\(164\) | 1.70678e11 | 0.112341 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.08965e11 | 0.0670956 | ||||||||
\(167\) | −8.10194e11 | −0.482668 | −0.241334 | − | 0.970442i | \(-0.577585\pi\) | ||||
−0.241334 | + | 0.970442i | \(0.577585\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.65225e12 | −0.921934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.56979e12 | −0.795126 | ||||||||
\(173\) | −3.62920e12 | −1.78056 | −0.890281 | − | 0.455412i | \(-0.849492\pi\) | ||||
−0.890281 | + | 0.455412i | \(0.849492\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.36852e11 | −0.328898 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.14799e12 | −0.900997 | ||||||||
\(179\) | 3.78383e12 | 1.53900 | 0.769502 | − | 0.638644i | \(-0.220504\pi\) | ||||
0.769502 | + | 0.638644i | \(0.220504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.63828e10 | −0.0100946 | −0.00504729 | − | 0.999987i | \(-0.501607\pi\) | ||||
−0.00504729 | + | 0.999987i | \(0.501607\pi\) | |||||||
\(182\) | 2.23267e11 | 0.0828767 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.24451e12 | 1.13410 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.74590e12 | −0.558330 | ||||||||
\(188\) | −1.44814e12 | −0.449719 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.18849e12 | −0.907615 | −0.453807 | − | 0.891100i | \(-0.649935\pi\) | ||||
−0.453807 | + | 0.891100i | \(0.649935\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.17255e12 | 0.583990 | 0.291995 | − | 0.956420i | \(-0.405681\pi\) | ||||
0.291995 | + | 0.956420i | \(0.405681\pi\) | |||||||
\(194\) | −4.30081e12 | −1.12368 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.48885e12 | 0.367657 | ||||||||
\(197\) | 3.09042e12 | 0.742085 | 0.371043 | − | 0.928616i | \(-0.379000\pi\) | ||||
0.371043 | + | 0.928616i | \(0.379000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.50627e12 | 1.02359 | 0.511794 | − | 0.859108i | \(-0.328981\pi\) | ||||
0.511794 | + | 0.859108i | \(0.328981\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.11828e12 | −0.233947 | ||||||||
\(203\) | −1.22360e12 | −0.249121 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.59156e12 | −0.486734 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.87928e11 | −0.104707 | ||||||||
\(209\) | −1.77886e11 | −0.0308559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.04739e13 | −1.72408 | −0.862038 | − | 0.506843i | \(-0.830812\pi\) | ||||
−0.862038 | + | 0.506843i | \(0.830812\pi\) | |||||||
\(212\) | 5.75241e11 | 0.0922576 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.89912e12 | 0.289253 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.00995e12 | 0.424650 | ||||||||
\(218\) | −5.64865e12 | −0.777023 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.39304e12 | −0.177748 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.63798e12 | 0.441757 | 0.220879 | − | 0.975301i | \(-0.429108\pi\) | ||||
0.220879 | + | 0.975301i | \(0.429108\pi\) | |||||||
\(224\) | 2.65580e12 | 0.314653 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.10136e12 | −0.688383 | ||||||||
\(227\) | 1.65864e13 | 1.82646 | 0.913229 | − | 0.407446i | \(-0.133581\pi\) | ||||
0.913229 | + | 0.407446i | \(0.133581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.02798e13 | −1.07867 | −0.539336 | − | 0.842091i | \(-0.681325\pi\) | ||||
−0.539336 | + | 0.842091i | \(0.681325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.96688e12 | 0.680541 | ||||||||
\(233\) | 2.92760e12 | 0.279289 | 0.139645 | − | 0.990202i | \(-0.455404\pi\) | ||||
0.139645 | + | 0.990202i | \(0.455404\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.25608e11 | 0.0734104 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.22304e12 | −0.188701 | ||||||||
\(239\) | −1.33960e13 | −1.11119 | −0.555593 | − | 0.831454i | \(-0.687509\pi\) | ||||
−0.555593 | + | 0.831454i | \(0.687509\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.67282e13 | −1.32543 | −0.662713 | − | 0.748874i | \(-0.730595\pi\) | ||||
−0.662713 | + | 0.748874i | \(0.730595\pi\) | |||||||
\(242\) | −2.22868e12 | −0.172609 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.72154e12 | 0.719600 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.41934e11 | −0.00982320 | ||||||||
\(248\) | −1.71380e13 | −1.16005 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.88339e13 | −1.19326 | −0.596629 | − | 0.802517i | \(-0.703494\pi\) | ||||
−0.596629 | + | 0.802517i | \(0.703494\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.52160e13 | −0.922862 | ||||||||
\(254\) | 1.82903e12 | 0.108551 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.79930e13 | −1.02278 | ||||||||
\(257\) | −1.20156e12 | −0.0668520 | −0.0334260 | − | 0.999441i | \(-0.510642\pi\) | ||||
−0.0334260 | + | 0.999441i | \(0.510642\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.11477e12 | 0.272695 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.80712e13 | −0.904339 | ||||||||
\(263\) | 3.79660e12 | 0.186054 | 0.0930268 | − | 0.995664i | \(-0.470346\pi\) | ||||
0.0930268 | + | 0.995664i | \(0.470346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.26501e11 | −0.0104285 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.38574e12 | 0.149593 | ||||||||
\(269\) | 2.57422e13 | 1.11432 | 0.557159 | − | 0.830406i | \(-0.311892\pi\) | ||||
0.557159 | + | 0.830406i | \(0.311892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.60144e13 | 0.665550 | 0.332775 | − | 0.943006i | \(-0.392015\pi\) | ||||
0.332775 | + | 0.943006i | \(0.392015\pi\) | |||||||
\(272\) | 5.85392e12 | 0.238406 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.33561e13 | 0.522460 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.31620e13 | 0.853369 | 0.426684 | − | 0.904401i | \(-0.359681\pi\) | ||||
0.426684 | + | 0.904401i | \(0.359681\pi\) | |||||||
\(278\) | −3.55653e13 | −1.28463 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.71797e13 | −1.26596 | −0.632981 | − | 0.774167i | \(-0.718169\pi\) | ||||
−0.632981 | + | 0.774167i | \(0.718169\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.57806e12 | −0.313655 | −0.156827 | − | 0.987626i | \(-0.550127\pi\) | ||||
−0.156827 | + | 0.987626i | \(0.550127\pi\) | |||||||
\(284\) | −2.04865e13 | −0.657987 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.96178e12 | 0.184231 | ||||||||
\(287\) | −3.35922e12 | −0.101833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.04016e13 | −0.595286 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.81369e12 | 0.242970 | ||||||||
\(293\) | −6.51052e13 | −1.76134 | −0.880672 | − | 0.473727i | \(-0.842908\pi\) | ||||
−0.880672 | + | 0.473727i | \(0.842908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.91224e13 | −0.744943 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.51398e13 | −0.373191 | ||||||||
\(299\) | −1.21407e13 | −0.293800 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.08961e13 | 0.720754 | ||||||||
\(302\) | 9.06490e12 | 0.207647 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.96444e11 | 0.0131754 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.37872e13 | 0.707116 | 0.353558 | − | 0.935413i | \(-0.384972\pi\) | ||||
0.353558 | + | 0.935413i | \(0.384972\pi\) | |||||||
\(308\) | −7.34120e12 | −0.150917 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.13268e13 | −0.610568 | −0.305284 | − | 0.952261i | \(-0.598751\pi\) | ||||
−0.305284 | + | 0.952261i | \(0.598751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.39027e13 | −1.20234 | −0.601168 | − | 0.799123i | \(-0.705298\pi\) | ||||
−0.601168 | + | 0.799123i | \(0.705298\pi\) | |||||||
\(314\) | 5.50660e13 | 1.01805 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.85258e13 | 0.330749 | ||||||||
\(317\) | 1.15517e13 | 0.202685 | 0.101342 | − | 0.994852i | \(-0.467686\pi\) | ||||
0.101342 | + | 0.994852i | \(0.467686\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.26730e13 | −0.553783 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.93744e13 | −0.311903 | ||||||||
\(323\) | 1.41322e12 | 0.0223664 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.29420e13 | −0.796349 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.91267e13 | 0.278185 | ||||||||
\(329\) | 2.85016e13 | 0.407655 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.17396e14 | 1.62406 | 0.812028 | − | 0.583618i | \(-0.198363\pi\) | ||||
0.812028 | + | 0.583618i | \(0.198363\pi\) | |||||||
\(332\) | −2.85874e12 | −0.0388969 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.75466e13 | −0.362629 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.67400e12 | −0.0460441 | −0.0230221 | − | 0.999735i | \(-0.507329\pi\) | ||||
−0.0230221 | + | 0.999735i | \(0.507329\pi\) | |||||||
\(338\) | −5.61766e13 | −0.692650 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.03731e13 | 0.943977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.40169e13 | −0.728077 | ||||||||
\(344\) | −1.75915e14 | −1.96894 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.23393e14 | −1.33774 | ||||||||
\(347\) | −5.92966e13 | −0.632729 | −0.316364 | − | 0.948638i | \(-0.602462\pi\) | ||||
−0.316364 | + | 0.948638i | \(0.602462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.69156e13 | −1.00197 | −0.500984 | − | 0.865457i | \(-0.667028\pi\) | ||||
−0.500984 | + | 0.865457i | \(0.667028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.09164e13 | 0.699459 | ||||||||
\(353\) | 3.93594e13 | 0.382197 | 0.191099 | − | 0.981571i | \(-0.438795\pi\) | ||||
0.191099 | + | 0.981571i | \(0.438795\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.63533e13 | 0.522329 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.28650e14 | 1.15626 | ||||||||
\(359\) | 5.38495e13 | 0.476609 | 0.238305 | − | 0.971190i | \(-0.423408\pi\) | ||||
0.238305 | + | 0.971190i | \(0.423408\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.16346e14 | −0.998764 | ||||||||
\(362\) | −8.97014e11 | −0.00758406 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.85748e12 | −0.0480456 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.55671e13 | −0.357263 | −0.178632 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178632 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(368\) | 5.10184e13 | 0.394061 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.13217e13 | −0.0836284 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.69341e14 | −1.21441 | −0.607203 | − | 0.794547i | \(-0.707709\pi\) | ||||
−0.607203 | + | 0.794547i | \(0.707709\pi\) | |||||||
\(374\) | −5.93606e13 | −0.419474 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.62282e14 | −1.11362 | ||||||||
\(377\) | −2.60695e13 | −0.176301 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.93802e13 | −0.390055 | −0.195028 | − | 0.980798i | \(-0.562480\pi\) | ||||
−0.195028 | + | 0.980798i | \(0.562480\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.08409e14 | −0.681892 | ||||||||
\(383\) | 1.21003e14 | 0.750242 | 0.375121 | − | 0.926976i | \(-0.377601\pi\) | ||||
0.375121 | + | 0.926976i | \(0.377601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.38668e13 | 0.438752 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.12833e14 | 0.651421 | ||||||||
\(389\) | −1.53362e14 | −0.872960 | −0.436480 | − | 0.899714i | \(-0.643775\pi\) | ||||
−0.436480 | + | 0.899714i | \(0.643775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.20883e14 | 0.668950 | ||||||||
\(392\) | 1.66845e14 | 0.910414 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.05074e14 | 0.557529 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.33061e14 | −0.677180 | −0.338590 | − | 0.940934i | \(-0.609950\pi\) | ||||
−0.338590 | + | 0.940934i | \(0.609950\pi\) | |||||||
\(398\) | 1.53213e14 | 0.769023 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.25080e14 | 0.602411 | 0.301205 | − | 0.953559i | \(-0.402611\pi\) | ||||
0.301205 | + | 0.953559i | \(0.402611\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.41290e13 | 0.300522 | ||||||||
\(404\) | 2.93383e13 | 0.135624 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.16022e13 | −0.187165 | ||||||||
\(407\) | 1.36577e14 | 0.606189 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.91902e14 | 0.829087 | 0.414544 | − | 0.910029i | \(-0.363941\pi\) | ||||
0.414544 | + | 0.910029i | \(0.363941\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.79904e13 | 0.282171 | ||||||||
\(413\) | −1.62493e13 | −0.0665440 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.65836e13 | 0.222678 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.04813e12 | −0.0231821 | ||||||||
\(419\) | 3.39088e14 | 1.28273 | 0.641366 | − | 0.767235i | \(-0.278368\pi\) | ||||
0.641366 | + | 0.767235i | \(0.278368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.09835e14 | 1.51028 | 0.755139 | − | 0.655564i | \(-0.227569\pi\) | ||||
0.755139 | + | 0.655564i | \(0.227569\pi\) | |||||||
\(422\) | −3.56114e14 | −1.29530 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.44631e13 | 0.228454 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.91336e14 | −0.652293 | ||||||||
\(428\) | −4.98241e13 | −0.167687 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.58968e14 | 1.81035 | 0.905173 | − | 0.425043i | \(-0.139741\pi\) | ||||
0.905173 | + | 0.425043i | \(0.139741\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.26000e14 | 1.02928 | 0.514640 | − | 0.857406i | \(-0.327925\pi\) | ||||
0.514640 | + | 0.857406i | \(0.327925\pi\) | |||||||
\(434\) | 1.02338e14 | 0.319040 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.48194e14 | 0.450459 | ||||||||
\(437\) | 1.23165e13 | 0.0369693 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.91336e13 | 0.260908 | 0.130454 | − | 0.991454i | \(-0.458357\pi\) | ||||
0.130454 | + | 0.991454i | \(0.458357\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.73633e13 | −0.133543 | ||||||||
\(443\) | 5.55014e14 | 1.54555 | 0.772776 | − | 0.634679i | \(-0.218868\pi\) | ||||
0.772776 | + | 0.634679i | \(0.218868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.23691e14 | 0.331893 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.46812e14 | 0.384354 | ||||||||
\(449\) | 2.41405e14 | 0.624296 | 0.312148 | − | 0.950033i | \(-0.398952\pi\) | ||||
0.312148 | + | 0.950033i | \(0.398952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.96994e13 | −0.226370 | ||||||||
\(452\) | 1.60071e14 | 0.399072 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.63937e14 | 1.37222 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.60954e13 | −0.0847057 | −0.0423529 | − | 0.999103i | \(-0.513485\pi\) | ||||
−0.0423529 | + | 0.999103i | \(0.513485\pi\) | |||||||
\(458\) | −3.49513e14 | −0.810407 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.58827e14 | −0.578968 | −0.289484 | − | 0.957183i | \(-0.593484\pi\) | ||||
−0.289484 | + | 0.957183i | \(0.593484\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.64823e14 | 1.23372 | 0.616860 | − | 0.787073i | \(-0.288404\pi\) | ||||
0.616860 | + | 0.787073i | \(0.288404\pi\) | |||||||
\(464\) | 1.09551e14 | 0.236465 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.95384e13 | 0.209830 | ||||||||
\(467\) | −3.88270e14 | −0.808892 | −0.404446 | − | 0.914562i | \(-0.632536\pi\) | ||||
−0.404446 | + | 0.914562i | \(0.632536\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.66369e13 | −0.135601 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.25199e13 | 0.181783 | ||||||||
\(473\) | 8.25000e14 | 1.60220 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.83221e13 | 0.109394 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.55464e14 | −0.834836 | ||||||||
\(479\) | −2.64819e14 | −0.479848 | −0.239924 | − | 0.970792i | \(-0.577122\pi\) | ||||
−0.239924 | + | 0.970792i | \(0.577122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.08974e14 | 0.192985 | ||||||||
\(482\) | −5.68759e14 | −0.995794 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.84701e13 | 0.100066 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.60424e14 | 1.58874 | 0.794372 | − | 0.607432i | \(-0.207800\pi\) | ||||
0.794372 | + | 0.607432i | \(0.207800\pi\) | |||||||
\(488\) | 1.08942e15 | 1.78192 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.37920e14 | −0.376255 | −0.188127 | − | 0.982145i | \(-0.560242\pi\) | ||||
−0.188127 | + | 0.982145i | \(0.560242\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.59570e14 | 0.401418 | ||||||||
\(494\) | −4.82576e12 | −0.00738018 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.69487e14 | −0.403078 | ||||||||
\(497\) | 4.03208e14 | 0.596443 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.26509e14 | −1.34059 | −0.670296 | − | 0.742094i | \(-0.733833\pi\) | ||||
−0.670296 | + | 0.742094i | \(0.733833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.40352e14 | −0.896496 | ||||||||
\(503\) | −2.21172e14 | −0.306272 | −0.153136 | − | 0.988205i | \(-0.548937\pi\) | ||||
−0.153136 | + | 0.988205i | \(0.548937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.17343e14 | −0.693347 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.79850e13 | −0.0629297 | ||||||||
\(509\) | 2.22667e14 | 0.288873 | 0.144437 | − | 0.989514i | \(-0.453863\pi\) | ||||
0.144437 | + | 0.989514i | \(0.453863\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.73468e14 | −0.220244 | ||||||||
\(512\) | −5.59560e14 | −0.702849 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.08531e13 | −0.0502260 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.61063e14 | 0.906197 | ||||||||
\(518\) | 1.73902e14 | 0.204876 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.00449e15 | 1.14641 | 0.573203 | − | 0.819413i | \(-0.305701\pi\) | ||||
0.573203 | + | 0.819413i | \(0.305701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.01954e15 | 1.13932 | 0.569658 | − | 0.821882i | \(-0.307076\pi\) | ||||
0.569658 | + | 0.821882i | \(0.307076\pi\) | |||||||
\(524\) | 4.74104e14 | 0.524266 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.29084e14 | 0.139782 | ||||||||
\(527\) | −6.38524e14 | −0.684256 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00718e14 | 0.105706 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.94233e12 | 0.00604564 | ||||||||
\(533\) | −7.15704e13 | −0.0720666 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.79416e14 | 0.370432 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.75236e14 | 0.837188 | ||||||||
\(539\) | −7.82460e14 | −0.740840 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.57672e15 | 1.46275 | 0.731376 | − | 0.681975i | \(-0.238879\pi\) | ||||
0.731376 | + | 0.681975i | \(0.238879\pi\) | |||||||
\(542\) | 5.44491e14 | 0.500028 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.63395e14 | −0.507013 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.73964e14 | 0.239201 | 0.119600 | − | 0.992822i | \(-0.461839\pi\) | ||||
0.119600 | + | 0.992822i | \(0.461839\pi\) | |||||||
\(548\) | −3.50402e14 | −0.302882 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.64471e13 | 0.0221842 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.64619e14 | −0.299813 | ||||||||
\(554\) | 7.87507e14 | 0.641137 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.33065e14 | 0.744733 | ||||||||
\(557\) | 9.10005e13 | 0.0719184 | 0.0359592 | − | 0.999353i | \(-0.488551\pi\) | ||||
0.0359592 | + | 0.999353i | \(0.488551\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.58261e14 | 0.510074 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.26411e15 | −0.951119 | ||||||||
\(563\) | 1.02926e14 | 0.0766886 | 0.0383443 | − | 0.999265i | \(-0.487792\pi\) | ||||
0.0383443 | + | 0.999265i | \(0.487792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.25654e14 | −0.235649 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.29578e15 | −1.62935 | ||||||||
\(569\) | −2.33956e15 | −1.64443 | −0.822216 | − | 0.569175i | \(-0.807263\pi\) | ||||
−0.822216 | + | 0.569175i | \(0.807263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.26931e14 | −0.156457 | −0.0782286 | − | 0.996935i | \(-0.524926\pi\) | ||||
−0.0782286 | + | 0.996935i | \(0.524926\pi\) | |||||||
\(572\) | −1.56409e14 | −0.106803 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.14214e14 | −0.0765072 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.42151e15 | −1.57623 | −0.788115 | − | 0.615528i | \(-0.788943\pi\) | ||||
−0.788115 | + | 0.615528i | \(0.788943\pi\) | |||||||
\(578\) | −6.93654e14 | −0.447239 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.62646e13 | 0.0352587 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.02316e14 | −0.185902 | ||||||||
\(584\) | 9.87687e14 | 0.601656 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.21358e15 | −1.32330 | ||||||||
\(587\) | 1.60425e15 | 0.950087 | 0.475044 | − | 0.879962i | \(-0.342432\pi\) | ||||
0.475044 | + | 0.879962i | \(0.342432\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.50579e13 | −0.0378152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.57936e14 | −0.258842 | ||||||||
\(593\) | −2.02053e15 | −1.13153 | −0.565763 | − | 0.824568i | \(-0.691418\pi\) | ||||
−0.565763 | + | 0.824568i | \(0.691418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.97198e14 | 0.216348 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.12783e14 | −0.220732 | ||||||||
\(599\) | −1.25788e15 | −0.666486 | −0.333243 | − | 0.942841i | \(-0.608143\pi\) | ||||
−0.333243 | + | 0.942841i | \(0.608143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50070e14 | −0.442227 | −0.221113 | − | 0.975248i | \(-0.570969\pi\) | ||||
−0.221113 | + | 0.975248i | \(0.570969\pi\) | |||||||
\(602\) | 1.05047e15 | 0.541503 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.37820e14 | −0.120378 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.25771e15 | 1.11207 | 0.556033 | − | 0.831160i | \(-0.312323\pi\) | ||||
0.556033 | + | 0.831160i | \(0.312323\pi\) | |||||||
\(608\) | −5.74032e13 | −0.0280199 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.07246e14 | 0.288495 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.37583e15 | −1.57525 | −0.787623 | − | 0.616157i | \(-0.788689\pi\) | ||||
−0.787623 | + | 0.616157i | \(0.788689\pi\) | |||||||
\(614\) | 1.14876e15 | 0.531257 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.22675e14 | −0.373710 | ||||||||
\(617\) | −1.76114e15 | −0.792915 | −0.396457 | − | 0.918053i | \(-0.629761\pi\) | ||||
−0.396457 | + | 0.918053i | \(0.629761\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.36923e14 | −0.237472 | −0.118736 | − | 0.992926i | \(-0.537884\pi\) | ||||
−0.118736 | + | 0.992926i | \(0.537884\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.06511e15 | −0.458720 | ||||||||
\(623\) | −1.10912e15 | −0.473473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.17269e15 | −0.903316 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.44467e15 | −0.590189 | ||||||||
\(629\) | −1.08504e15 | −0.439405 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.36152e15 | −0.541830 | −0.270915 | − | 0.962603i | \(-0.587326\pi\) | ||||
−0.270915 | + | 0.962603i | \(0.587326\pi\) | |||||||
\(632\) | 2.07606e15 | 0.819022 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.92758e14 | 0.152277 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.24319e14 | −0.235852 | ||||||||
\(638\) | −1.11088e15 | −0.416058 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.14896e15 | 0.784348 | 0.392174 | − | 0.919891i | \(-0.371723\pi\) | ||||
0.392174 | + | 0.919891i | \(0.371723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.57356e14 | 0.199973 | 0.0999867 | − | 0.994989i | \(-0.468120\pi\) | ||||
0.0999867 | + | 0.994989i | \(0.468120\pi\) | |||||||
\(644\) | 5.08292e14 | 0.180818 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.80494e13 | 0.0168039 | ||||||||
\(647\) | 2.41894e14 | 0.0838787 | 0.0419394 | − | 0.999120i | \(-0.486646\pi\) | ||||
0.0419394 | + | 0.999120i | \(0.486646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.33896e14 | −0.147924 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.38895e15 | 0.461663 | ||||||||
\(653\) | −3.13959e15 | −1.03478 | −0.517392 | − | 0.855748i | \(-0.673097\pi\) | ||||
−0.517392 | + | 0.855748i | \(0.673097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00758e14 | 0.0966598 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.69056e14 | 0.306271 | ||||||||
\(659\) | −1.06199e15 | −0.332851 | −0.166425 | − | 0.986054i | \(-0.553223\pi\) | ||||
−0.166425 | + | 0.986054i | \(0.553223\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.87576e14 | −0.273588 | −0.136794 | − | 0.990599i | \(-0.543680\pi\) | ||||
−0.136794 | + | 0.990599i | \(0.543680\pi\) | |||||||
\(662\) | 3.99148e15 | 1.22016 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.20358e14 | −0.0963188 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.26222e15 | 0.663503 | ||||||||
\(668\) | 7.22693e14 | 0.210224 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.10913e15 | −1.45002 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.92399e15 | 0.816380 | 0.408190 | − | 0.912897i | \(-0.366160\pi\) | ||||
0.408190 | + | 0.912897i | \(0.366160\pi\) | |||||||
\(674\) | −1.24916e14 | −0.0345930 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.47381e15 | 0.401545 | ||||||||
\(677\) | −3.20144e15 | −0.865181 | −0.432591 | − | 0.901590i | \(-0.642400\pi\) | ||||
−0.432591 | + | 0.901590i | \(0.642400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.22074e15 | −0.590491 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.73268e15 | 0.709211 | ||||||||
\(683\) | 2.37436e15 | 0.611269 | 0.305634 | − | 0.952149i | \(-0.401131\pi\) | ||||
0.305634 | + | 0.952149i | \(0.401131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.17657e15 | −0.547005 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.76619e15 | −0.684140 | ||||||||
\(689\) | −2.41215e14 | −0.0591833 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.46382e14 | −0.107790 | −0.0538949 | − | 0.998547i | \(-0.517164\pi\) | ||||
−0.0538949 | + | 0.998547i | \(0.517164\pi\) | |||||||
\(692\) | 3.23724e15 | 0.775518 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.01608e15 | −0.475370 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.12617e14 | 0.164088 | ||||||||
\(698\) | −3.29513e15 | −0.752780 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.79930e15 | −1.29398 | −0.646988 | − | 0.762500i | \(-0.723972\pi\) | ||||
−0.646988 | + | 0.762500i | \(0.723972\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.10552e14 | −0.0242836 | ||||||||
\(704\) | 3.92023e15 | 0.854402 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.33822e15 | 0.287145 | ||||||||
\(707\) | −5.77426e14 | −0.122939 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.71150e15 | 0.778027 | 0.389014 | − | 0.921232i | \(-0.372816\pi\) | ||||
0.389014 | + | 0.921232i | \(0.372816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.31511e15 | 1.29342 | ||||||||
\(713\) | −5.56490e15 | −1.13101 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.37518e15 | −0.670309 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.83088e15 | 0.358077 | ||||||||
\(719\) | −2.54074e14 | −0.0493118 | −0.0246559 | − | 0.999696i | \(-0.507849\pi\) | ||||
−0.0246559 | + | 0.999696i | \(0.507849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.33816e15 | −0.255779 | ||||||||
\(722\) | −3.95577e15 | −0.750372 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.35334e13 | 0.00439666 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.40726e15 | −0.622251 | −0.311126 | − | 0.950369i | \(-0.600706\pi\) | ||||
−0.311126 | + | 0.950369i | \(0.600706\pi\) | |||||||
\(728\) | −6.56405e14 | −0.118973 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.55421e15 | −1.16138 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.16708e15 | 0.552825 | 0.276412 | − | 0.961039i | \(-0.410854\pi\) | ||||
0.276412 | + | 0.961039i | \(0.410854\pi\) | |||||||
\(734\) | −1.54928e15 | −0.268412 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.91013e15 | −0.838041 | ||||||||
\(737\) | −1.77937e15 | −0.301435 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.82593e15 | 0.638547 | 0.319273 | − | 0.947663i | \(-0.396561\pi\) | ||||
0.319273 | + | 0.947663i | \(0.396561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.84937e14 | −0.0628301 | ||||||||
\(743\) | −2.20995e15 | −0.358051 | −0.179025 | − | 0.983844i | \(-0.557294\pi\) | ||||
−0.179025 | + | 0.983844i | \(0.557294\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.75760e15 | −0.912385 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.55734e15 | 0.243179 | ||||||||
\(749\) | 9.80618e14 | 0.152002 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22606e15 | 0.187281 | 0.0936405 | − | 0.995606i | \(-0.470150\pi\) | ||||
0.0936405 | + | 0.995606i | \(0.470150\pi\) | |||||||
\(752\) | −2.55181e15 | −0.386946 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.86363e14 | −0.132455 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.70929e15 | −0.980955 | −0.490478 | − | 0.871454i | \(-0.663178\pi\) | ||||
−0.490478 | + | 0.871454i | \(0.663178\pi\) | |||||||
\(758\) | −2.01893e15 | −0.293049 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.22698e15 | 0.742396 | 0.371198 | − | 0.928554i | \(-0.378947\pi\) | ||||
0.371198 | + | 0.928554i | \(0.378947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.91670e15 | −0.408325 | ||||||||
\(764\) | 2.84413e15 | 0.395309 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.11409e15 | 0.563657 | ||||||||
\(767\) | −3.46202e14 | −0.0470928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.72252e15 | 1.30372 | 0.651859 | − | 0.758340i | \(-0.273989\pi\) | ||||
0.651859 | + | 0.758340i | \(0.273989\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.93792e15 | −0.254355 | ||||||||
\(773\) | 9.82829e15 | 1.28083 | 0.640414 | − | 0.768030i | \(-0.278763\pi\) | ||||
0.640414 | + | 0.768030i | \(0.278763\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.26444e16 | 1.61309 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.21430e15 | −0.655855 | ||||||||
\(779\) | 7.26071e13 | 0.00906824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07666e16 | 1.32586 | ||||||||
\(782\) | 4.11003e15 | 0.502583 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.62355e15 | 0.316338 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.54031e15 | −0.299934 | −0.149967 | − | 0.988691i | \(-0.547917\pi\) | ||||
−0.149967 | + | 0.988691i | \(0.547917\pi\) | |||||||
\(788\) | −2.75666e15 | −0.323213 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.15045e15 | −0.361745 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.07653e15 | −0.461624 | ||||||||
\(794\) | −4.52408e15 | −0.508766 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.01960e15 | −0.445821 | ||||||||
\(797\) | −3.63405e15 | −0.400285 | −0.200143 | − | 0.979767i | \(-0.564141\pi\) | ||||
−0.200143 | + | 0.979767i | \(0.564141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.04627e15 | −0.656871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.25271e15 | 0.452592 | ||||||||
\(803\) | −4.63201e15 | −0.489592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.18039e15 | 0.225783 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.28774e15 | 0.335842 | ||||||||
\(809\) | 4.02489e15 | 0.408355 | 0.204177 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204177 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.12095e16 | −1.12194 | −0.560970 | − | 0.827836i | \(-0.689572\pi\) | ||||
−0.560970 | + | 0.827836i | \(0.689572\pi\) | |||||||
\(812\) | 1.09145e15 | 0.108504 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.64362e15 | 0.455430 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.67795e14 | −0.0641833 | ||||||||
\(818\) | 6.52465e15 | 0.622894 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.11427e16 | 1.97821 | 0.989106 | − | 0.147204i | \(-0.0470274\pi\) | ||||
0.989106 | + | 0.147204i | \(0.0470274\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.76589e15 | 0.347671 | 0.173836 | − | 0.984775i | \(-0.444384\pi\) | ||||
0.173836 | + | 0.984775i | \(0.444384\pi\) | |||||||
\(824\) | 7.61919e15 | 0.698730 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.52476e14 | −0.0499946 | ||||||||
\(827\) | 1.79419e15 | 0.161282 | 0.0806412 | − | 0.996743i | \(-0.474303\pi\) | ||||
0.0806412 | + | 0.996743i | \(0.474303\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.11615e16 | −0.990084 | −0.495042 | − | 0.868869i | \(-0.664847\pi\) | ||||
−0.495042 | + | 0.868869i | \(0.664847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.12792e15 | 0.272005 | ||||||||
\(833\) | 6.21626e15 | 0.537009 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.58675e14 | 0.0134392 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.15290e16 | 0.963717 | ||||||||
\(839\) | −3.47514e15 | −0.288590 | −0.144295 | − | 0.989535i | \(-0.546091\pi\) | ||||
−0.144295 | + | 0.989535i | \(0.546091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.34288e15 | −0.601850 | ||||||||
\(842\) | 1.39344e16 | 1.13467 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.34275e15 | 0.750916 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.15079e15 | −0.0907060 | ||||||||
\(848\) | 1.01365e15 | 0.0793801 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.45636e15 | −0.726292 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.64122e16 | −1.24436 | −0.622182 | − | 0.782873i | \(-0.713754\pi\) | ||||
−0.622182 | + | 0.782873i | \(0.713754\pi\) | |||||||
\(854\) | −6.50541e15 | −0.490068 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.58342e15 | −0.415236 | ||||||||
\(857\) | 4.91921e15 | 0.363497 | 0.181748 | − | 0.983345i | \(-0.441824\pi\) | ||||
0.181748 | + | 0.983345i | \(0.441824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.96890e16 | −1.43635 | −0.718176 | − | 0.695861i | \(-0.755023\pi\) | ||||
−0.718176 | + | 0.695861i | \(0.755023\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.90049e16 | 1.36012 | ||||||||
\(863\) | 2.44068e16 | 1.73560 | 0.867802 | − | 0.496910i | \(-0.165532\pi\) | ||||
0.867802 | + | 0.496910i | \(0.165532\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.10840e16 | 0.773299 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.68488e15 | −0.184955 | ||||||||
\(869\) | −9.73620e15 | −0.666470 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.41974e15 | −0.0959642 | ||||||||
\(872\) | 1.66070e16 | 1.11545 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.18763e14 | 0.0277751 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.88744e16 | −1.87938 | −0.939691 | − | 0.342025i | \(-0.888887\pi\) | ||||
−0.939691 | + | 0.342025i | \(0.888887\pi\) | |||||||
\(878\) | 3.03054e15 | 0.196020 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.51928e15 | 0.159922 | 0.0799610 | − | 0.996798i | \(-0.474520\pi\) | ||||
0.0799610 | + | 0.996798i | \(0.474520\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.29479e16 | 1.43866 | 0.719330 | − | 0.694668i | \(-0.244449\pi\) | ||||
0.719330 | + | 0.694668i | \(0.244449\pi\) | |||||||
\(884\) | 1.24259e15 | 0.0774178 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.88705e16 | 1.16117 | ||||||||
\(887\) | −3.12029e16 | −1.90816 | −0.954080 | − | 0.299553i | \(-0.903163\pi\) | ||||
−0.954080 | + | 0.299553i | \(0.903163\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.44423e14 | 0.0570436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.24508e15 | −0.192406 | ||||||||
\(893\) | −6.16042e14 | −0.0363017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.47485e14 | −0.0258872 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.20775e15 | 0.469034 | ||||||||
\(899\) | −1.19494e16 | −0.678685 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.40175e15 | 0.134754 | ||||||||
\(902\) | −3.04978e15 | −0.170072 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.79380e16 | 0.988206 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.97131e15 | −0.431211 | −0.215605 | − | 0.976481i | \(-0.569173\pi\) | ||||
−0.215605 | + | 0.976481i | \(0.569173\pi\) | |||||||
\(908\) | −1.47951e16 | −0.795508 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.15018e16 | 1.13533 | 0.567666 | − | 0.823259i | \(-0.307846\pi\) | ||||
0.567666 | + | 0.823259i | \(0.307846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.50240e15 | 0.0783784 | ||||||||
\(914\) | −1.22724e15 | −0.0636395 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.16958e15 | 0.469812 | ||||||||
\(917\) | −9.33114e15 | −0.475230 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.93638e16 | −0.974442 | −0.487221 | − | 0.873279i | \(-0.661989\pi\) | ||||
−0.487221 | + | 0.873279i | \(0.661989\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.80012e15 | −0.434979 | ||||||||
\(923\) | 8.59060e15 | 0.422099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.92040e16 | 0.926896 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.05434e16 | −0.502885 | ||||||||
\(929\) | 1.78505e16 | 0.846379 | 0.423189 | − | 0.906041i | \(-0.360911\pi\) | ||||
0.423189 | + | 0.906041i | \(0.360911\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.33362e14 | 0.0296776 | ||||||||
\(932\) | −2.61142e15 | −0.121644 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.32012e16 | −0.607722 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.46505e15 | −0.337649 | −0.168824 | − | 0.985646i | \(-0.553997\pi\) | ||||
−0.168824 | + | 0.985646i | \(0.553997\pi\) | |||||||
\(938\) | −2.26565e15 | −0.101877 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.05984e16 | −1.35194 | −0.675968 | − | 0.736931i | \(-0.736274\pi\) | ||||
−0.675968 | + | 0.736931i | \(0.736274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.21064e15 | 0.271220 | ||||||||
\(944\) | 1.45483e15 | 0.0631636 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.80500e16 | 1.20374 | ||||||||
\(947\) | −2.35138e16 | −1.00322 | −0.501611 | − | 0.865093i | \(-0.667259\pi\) | ||||
−0.501611 | + | 0.865093i | \(0.667259\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.69584e15 | −0.155865 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.53574e15 | 0.270889 | ||||||||
\(953\) | 1.48744e16 | 0.612956 | 0.306478 | − | 0.951878i | \(-0.400849\pi\) | ||||
0.306478 | + | 0.951878i | \(0.400849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.19492e16 | 0.483974 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.00384e15 | −0.360510 | ||||||||
\(959\) | 6.89648e15 | 0.274552 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.98616e15 | 0.156883 | ||||||||
\(962\) | 3.70510e15 | 0.144990 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.49216e16 | 0.577285 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.74039e16 | 1.80289 | 0.901444 | − | 0.432896i | \(-0.142508\pi\) | ||||
0.901444 | + | 0.432896i | \(0.142508\pi\) | |||||||
\(968\) | 6.55233e15 | 0.247788 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.21083e16 | 0.450171 | 0.225086 | − | 0.974339i | \(-0.427734\pi\) | ||||
0.225086 | + | 0.974339i | \(0.427734\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.83642e16 | −0.675075 | ||||||||
\(974\) | 3.26544e16 | 1.19362 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.71307e16 | 0.619156 | ||||||||
\(977\) | −5.23952e16 | −1.88309 | −0.941546 | − | 0.336885i | \(-0.890627\pi\) | ||||
−0.941546 | + | 0.336885i | \(0.890627\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.96163e16 | −1.05251 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.08927e15 | −0.282681 | ||||||||
\(983\) | 3.64254e16 | 1.26578 | 0.632892 | − | 0.774240i | \(-0.281868\pi\) | ||||
0.632892 | + | 0.774240i | \(0.281868\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.82540e15 | 0.301586 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.26605e14 | 0.00427847 | ||||||||
\(989\) | −5.71216e16 | −1.91964 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.21088e16 | 1.39948 | 0.699742 | − | 0.714396i | \(-0.253298\pi\) | ||||
0.699742 | + | 0.714396i | \(0.253298\pi\) | |||||||
\(992\) | 2.59361e16 | 0.857216 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.37091e16 | 0.448108 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.75209e16 | −0.884789 | −0.442394 | − | 0.896821i | \(-0.645871\pi\) | ||||
−0.442394 | + | 0.896821i | \(0.645871\pi\) | |||||||
\(998\) | −3.15013e16 | −1.00719 | ||||||||
\(999\) | 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 | 225.12.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 25.12.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 225.12.b.c.199.2 | 2 | |||
5.3 | odd | 4 | 225.12.b.c.199.1 | 2 | |||
5.4 | even | 2 | 45.12.a.a.1.1 | 1 | |||
15.2 | even | 4 | 25.12.b.a.24.1 | 2 | |||
15.8 | even | 4 | 25.12.b.a.24.2 | 2 | |||
15.14 | odd | 2 | 5.12.a.a.1.1 | ✓ | 1 | ||
60.59 | even | 2 | 80.12.a.f.1.1 | 1 | |||
105.104 | even | 2 | 245.12.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.12.a.a.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
25.12.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
25.12.b.a.24.1 | 2 | 15.2 | even | 4 | |||
25.12.b.a.24.2 | 2 | 15.8 | even | 4 | |||
45.12.a.a.1.1 | 1 | 5.4 | even | 2 | |||
80.12.a.f.1.1 | 1 | 60.59 | even | 2 | |||
225.12.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.12.b.c.199.1 | 2 | 5.3 | odd | 4 | |||
225.12.b.c.199.2 | 2 | 5.2 | odd | 4 | |||
245.12.a.a.1.1 | 1 | 105.104 | even | 2 |