Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,14,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(80.4231967139\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 12.0000 | 0.132583 | 0.0662913 | − | 0.997800i | \(-0.478883\pi\) | ||||
0.0662913 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −8048.00 | −0.982422 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 8748.00 | 0.0765466 | ||||||||
\(7\) | −235088. | −0.755254 | −0.377627 | − | 0.925958i | \(-0.623260\pi\) | ||||
−0.377627 | + | 0.925958i | \(0.623260\pi\) | |||||||
\(8\) | −194880. | −0.262834 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.11829e7 | −1.90328 | −0.951639 | − | 0.307218i | \(-0.900602\pi\) | ||||
−0.951639 | + | 0.307218i | \(0.900602\pi\) | |||||||
\(12\) | −5.86699e6 | −0.567202 | ||||||||
\(13\) | −8.04961e6 | −0.462534 | −0.231267 | − | 0.972890i | \(-0.574287\pi\) | ||||
−0.231267 | + | 0.972890i | \(0.574287\pi\) | |||||||
\(14\) | −2.82106e6 | −0.100134 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.35907e7 | 0.947575 | ||||||||
\(17\) | 1.17495e8 | 1.18059 | 0.590296 | − | 0.807187i | \(-0.299011\pi\) | ||||
0.590296 | + | 0.807187i | \(0.299011\pi\) | |||||||
\(18\) | 6.37729e6 | 0.0441942 | ||||||||
\(19\) | −2.14061e8 | −1.04385 | −0.521927 | − | 0.852990i | \(-0.674787\pi\) | ||||
−0.521927 | + | 0.852990i | \(0.674787\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.71379e8 | −0.436046 | ||||||||
\(22\) | −1.34195e8 | −0.252341 | ||||||||
\(23\) | −8.30556e8 | −1.16987 | −0.584935 | − | 0.811080i | \(-0.698880\pi\) | ||||
−0.584935 | + | 0.811080i | \(0.698880\pi\) | |||||||
\(24\) | −1.42068e8 | −0.151748 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.65954e7 | −0.0613239 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 1.89199e9 | 0.741978 | ||||||||
\(29\) | −1.25240e9 | −0.390981 | −0.195491 | − | 0.980706i | \(-0.562630\pi\) | ||||
−0.195491 | + | 0.980706i | \(0.562630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.15935e9 | 1.24648 | 0.623238 | − | 0.782032i | \(-0.285817\pi\) | ||||
0.623238 | + | 0.782032i | \(0.285817\pi\) | |||||||
\(32\) | 2.35954e9 | 0.388466 | ||||||||
\(33\) | −8.15234e9 | −1.09886 | ||||||||
\(34\) | 1.40994e9 | 0.156526 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.27704e9 | −0.327474 | ||||||||
\(37\) | 5.49819e9 | 0.352297 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(38\) | −2.56874e9 | −0.138397 | ||||||||
\(39\) | −5.86817e9 | −0.267044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.67869e9 | −0.153826 | −0.0769129 | − | 0.997038i | \(-0.524506\pi\) | ||||
−0.0769129 | + | 0.997038i | \(0.524506\pi\) | |||||||
\(42\) | −2.05655e9 | −0.0578121 | ||||||||
\(43\) | −7.11501e9 | −0.171645 | −0.0858224 | − | 0.996310i | \(-0.527352\pi\) | ||||
−0.0858224 | + | 0.996310i | \(0.527352\pi\) | |||||||
\(44\) | 9.00000e10 | 1.86982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.96667e9 | −0.155104 | ||||||||
\(47\) | 2.95288e10 | 0.399585 | 0.199793 | − | 0.979838i | \(-0.435973\pi\) | ||||
0.199793 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(48\) | 4.63576e10 | 0.547082 | ||||||||
\(49\) | −4.16226e10 | −0.429591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.56536e10 | 0.681615 | ||||||||
\(52\) | 6.47833e10 | 0.454403 | ||||||||
\(53\) | 2.04125e11 | 1.26504 | 0.632518 | − | 0.774545i | \(-0.282021\pi\) | ||||
0.632518 | + | 0.774545i | \(0.282021\pi\) | |||||||
\(54\) | 4.64905e9 | 0.0255155 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.58139e10 | 0.198507 | ||||||||
\(57\) | −1.56051e11 | −0.602670 | ||||||||
\(58\) | −1.50288e10 | −0.0518373 | ||||||||
\(59\) | −2.99098e10 | −0.0923157 | −0.0461579 | − | 0.998934i | \(-0.514698\pi\) | ||||
−0.0461579 | + | 0.998934i | \(0.514698\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.34392e11 | −0.333987 | −0.166993 | − | 0.985958i | \(-0.553406\pi\) | ||||
−0.166993 | + | 0.985958i | \(0.553406\pi\) | |||||||
\(62\) | 7.39122e10 | 0.165261 | ||||||||
\(63\) | −1.24935e11 | −0.251751 | ||||||||
\(64\) | −4.92620e11 | −0.896071 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.78281e10 | −0.145689 | ||||||||
\(67\) | −3.48519e11 | −0.470695 | −0.235348 | − | 0.971911i | \(-0.575623\pi\) | ||||
−0.235348 | + | 0.971911i | \(0.575623\pi\) | |||||||
\(68\) | −9.45597e11 | −1.15984 | ||||||||
\(69\) | −6.05475e11 | −0.675425 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.31434e12 | 1.21766 | 0.608831 | − | 0.793300i | \(-0.291639\pi\) | ||||
0.608831 | + | 0.793300i | \(0.291639\pi\) | |||||||
\(72\) | −1.03567e11 | −0.0876115 | ||||||||
\(73\) | 1.17888e12 | 0.911737 | 0.455868 | − | 0.890047i | \(-0.349329\pi\) | ||||
0.455868 | + | 0.890047i | \(0.349329\pi\) | |||||||
\(74\) | 6.59783e10 | 0.0467084 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.72277e12 | 1.02551 | ||||||||
\(77\) | 2.62897e12 | 1.43746 | ||||||||
\(78\) | −7.04180e10 | −0.0354054 | ||||||||
\(79\) | −1.07242e12 | −0.496351 | −0.248176 | − | 0.968715i | \(-0.579831\pi\) | ||||
−0.248176 | + | 0.968715i | \(0.579831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −5.61443e10 | −0.0203946 | ||||||||
\(83\) | −1.12403e12 | −0.377371 | −0.188685 | − | 0.982038i | \(-0.560423\pi\) | ||||
−0.188685 | + | 0.982038i | \(0.560423\pi\) | |||||||
\(84\) | 1.37926e12 | 0.428381 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.53802e10 | −0.0227571 | ||||||||
\(87\) | −9.13000e11 | −0.225733 | ||||||||
\(88\) | 2.17933e12 | 0.500247 | ||||||||
\(89\) | 2.23561e12 | 0.476827 | 0.238414 | − | 0.971164i | \(-0.423373\pi\) | ||||
0.238414 | + | 0.971164i | \(0.423373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.89237e12 | 0.349330 | ||||||||
\(92\) | 6.68431e12 | 1.14931 | ||||||||
\(93\) | 4.49017e12 | 0.719653 | ||||||||
\(94\) | 3.54345e11 | 0.0529780 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.72011e12 | 0.224281 | ||||||||
\(97\) | 1.42153e13 | 1.73276 | 0.866380 | − | 0.499385i | \(-0.166441\pi\) | ||||
0.866380 | + | 0.499385i | \(0.166441\pi\) | |||||||
\(98\) | −4.99472e11 | −0.0569563 | ||||||||
\(99\) | −5.94306e12 | −0.634426 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.70194e13 | 1.59535 | 0.797675 | − | 0.603088i | \(-0.206063\pi\) | ||||
0.797675 | + | 0.603088i | \(0.206063\pi\) | |||||||
\(102\) | 1.02784e12 | 0.0903703 | ||||||||
\(103\) | −1.09904e13 | −0.906928 | −0.453464 | − | 0.891275i | \(-0.649812\pi\) | ||||
−0.453464 | + | 0.891275i | \(0.649812\pi\) | |||||||
\(104\) | 1.56871e12 | 0.121570 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.44950e12 | 0.167722 | ||||||||
\(107\) | 1.96403e13 | 1.26519 | 0.632593 | − | 0.774485i | \(-0.281991\pi\) | ||||
0.632593 | + | 0.774485i | \(0.281991\pi\) | |||||||
\(108\) | −3.11796e12 | −0.189067 | ||||||||
\(109\) | −9.82099e12 | −0.560897 | −0.280448 | − | 0.959869i | \(-0.590483\pi\) | ||||
−0.280448 | + | 0.959869i | \(0.590483\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00818e12 | 0.203399 | ||||||||
\(112\) | −1.49494e13 | −0.715660 | ||||||||
\(113\) | 1.70267e13 | 0.769344 | 0.384672 | − | 0.923053i | \(-0.374315\pi\) | ||||
0.384672 | + | 0.923053i | \(0.374315\pi\) | |||||||
\(114\) | −1.87261e12 | −0.0799035 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00793e13 | 0.384109 | ||||||||
\(117\) | −4.27789e12 | −0.154178 | ||||||||
\(118\) | −3.58918e11 | −0.0122395 | ||||||||
\(119\) | −2.76216e13 | −0.891648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.05347e13 | 2.62247 | ||||||||
\(122\) | −1.61270e12 | −0.0442808 | ||||||||
\(123\) | −3.41076e12 | −0.0888113 | ||||||||
\(124\) | −4.95705e13 | −1.22457 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.49922e12 | −0.0333778 | ||||||||
\(127\) | 4.49347e13 | 0.950292 | 0.475146 | − | 0.879907i | \(-0.342395\pi\) | ||||
0.475146 | + | 0.879907i | \(0.342395\pi\) | |||||||
\(128\) | −2.52408e13 | −0.507270 | ||||||||
\(129\) | −5.18685e12 | −0.0990992 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.20182e12 | −0.0207768 | −0.0103884 | − | 0.999946i | \(-0.503307\pi\) | ||||
−0.0103884 | + | 0.999946i | \(0.503307\pi\) | |||||||
\(132\) | 6.56100e13 | 1.07954 | ||||||||
\(133\) | 5.03233e13 | 0.788375 | ||||||||
\(134\) | −4.18223e12 | −0.0624060 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.28974e13 | −0.310300 | ||||||||
\(137\) | −1.71562e13 | −0.221685 | −0.110842 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110842 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(138\) | −7.26570e12 | −0.0895495 | ||||||||
\(139\) | 1.05644e14 | 1.24236 | 0.621182 | − | 0.783666i | \(-0.286653\pi\) | ||||
0.621182 | + | 0.783666i | \(0.286653\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.15265e13 | 0.230701 | ||||||||
\(142\) | 1.57720e13 | 0.161441 | ||||||||
\(143\) | 9.00181e13 | 0.880330 | ||||||||
\(144\) | 3.37947e13 | 0.315858 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.41465e13 | 0.120880 | ||||||||
\(147\) | −3.03429e13 | −0.248024 | ||||||||
\(148\) | −4.42494e13 | −0.346104 | ||||||||
\(149\) | −8.53533e13 | −0.639012 | −0.319506 | − | 0.947584i | \(-0.603517\pi\) | ||||
−0.319506 | + | 0.947584i | \(0.603517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.16414e13 | −0.423177 | −0.211589 | − | 0.977359i | \(-0.567864\pi\) | ||||
−0.211589 | + | 0.977359i | \(0.567864\pi\) | |||||||
\(152\) | 4.17163e13 | 0.274361 | ||||||||
\(153\) | 6.24415e13 | 0.393531 | ||||||||
\(154\) | 3.15476e13 | 0.190582 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.72270e13 | 0.262350 | ||||||||
\(157\) | 1.18021e14 | 0.628942 | 0.314471 | − | 0.949267i | \(-0.398173\pi\) | ||||
0.314471 | + | 0.949267i | \(0.398173\pi\) | |||||||
\(158\) | −1.28690e13 | −0.0658075 | ||||||||
\(159\) | 1.48807e14 | 0.730369 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.95254e14 | 0.883550 | ||||||||
\(162\) | 3.38915e12 | 0.0147314 | ||||||||
\(163\) | −1.54710e14 | −0.646099 | −0.323050 | − | 0.946382i | \(-0.604708\pi\) | ||||
−0.323050 | + | 0.946382i | \(0.604708\pi\) | |||||||
\(164\) | 3.76541e13 | 0.151122 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.34883e13 | −0.0500328 | ||||||||
\(167\) | −3.76012e14 | −1.34136 | −0.670679 | − | 0.741748i | \(-0.733997\pi\) | ||||
−0.670679 | + | 0.741748i | \(0.733997\pi\) | |||||||
\(168\) | 3.33984e13 | 0.114608 | ||||||||
\(169\) | −2.38079e14 | −0.786063 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.13761e14 | −0.347951 | ||||||||
\(172\) | 5.72616e13 | 0.168628 | ||||||||
\(173\) | −3.73562e14 | −1.05941 | −0.529704 | − | 0.848182i | \(-0.677697\pi\) | ||||
−0.529704 | + | 0.848182i | \(0.677697\pi\) | |||||||
\(174\) | −1.09560e13 | −0.0299283 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.11128e14 | −1.80350 | ||||||||
\(177\) | −2.18043e13 | −0.0532985 | ||||||||
\(178\) | 2.68273e13 | 0.0632190 | ||||||||
\(179\) | 4.23349e13 | 0.0961952 | 0.0480976 | − | 0.998843i | \(-0.484684\pi\) | ||||
0.0480976 | + | 0.998843i | \(0.484684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.10447e14 | −0.656261 | −0.328130 | − | 0.944632i | \(-0.606419\pi\) | ||||
−0.328130 | + | 0.944632i | \(0.606419\pi\) | |||||||
\(182\) | 2.27084e13 | 0.0463151 | ||||||||
\(183\) | −9.79718e13 | −0.192827 | ||||||||
\(184\) | 1.61859e14 | 0.307482 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.38820e13 | 0.0954134 | ||||||||
\(187\) | −1.31393e15 | −2.24700 | ||||||||
\(188\) | −2.37648e14 | −0.392561 | ||||||||
\(189\) | −9.10779e13 | −0.145349 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.62273e14 | −1.28507 | −0.642537 | − | 0.766255i | \(-0.722118\pi\) | ||||
−0.642537 | + | 0.766255i | \(0.722118\pi\) | |||||||
\(192\) | −3.59120e14 | −0.517347 | ||||||||
\(193\) | 9.37837e14 | 1.30618 | 0.653092 | − | 0.757278i | \(-0.273471\pi\) | ||||
0.653092 | + | 0.757278i | \(0.273471\pi\) | |||||||
\(194\) | 1.70583e14 | 0.229734 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.34979e14 | 0.422040 | ||||||||
\(197\) | 6.71715e14 | 0.818756 | 0.409378 | − | 0.912365i | \(-0.365746\pi\) | ||||
0.409378 | + | 0.912365i | \(0.365746\pi\) | |||||||
\(198\) | −7.13167e13 | −0.0841138 | ||||||||
\(199\) | −4.36451e13 | −0.0498185 | −0.0249093 | − | 0.999690i | \(-0.507930\pi\) | ||||
−0.0249093 | + | 0.999690i | \(0.507930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.54070e14 | −0.271756 | ||||||||
\(202\) | 2.04233e14 | 0.211515 | ||||||||
\(203\) | 2.94424e14 | 0.295290 | ||||||||
\(204\) | −6.89340e14 | −0.669634 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.31885e14 | −0.120243 | ||||||||
\(207\) | −4.41391e14 | −0.389957 | ||||||||
\(208\) | −5.11880e14 | −0.438285 | ||||||||
\(209\) | 2.39383e15 | 1.98675 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.62162e15 | −1.26507 | −0.632534 | − | 0.774533i | \(-0.717985\pi\) | ||||
−0.632534 | + | 0.774533i | \(0.717985\pi\) | |||||||
\(212\) | −1.64280e15 | −1.24280 | ||||||||
\(213\) | 9.58151e14 | 0.703018 | ||||||||
\(214\) | 2.35684e14 | 0.167742 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −7.55005e13 | −0.0505825 | ||||||||
\(217\) | −1.44799e15 | −0.941406 | ||||||||
\(218\) | −1.17852e14 | −0.0743651 | ||||||||
\(219\) | 8.59401e14 | 0.526392 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.45786e14 | −0.546064 | ||||||||
\(222\) | 4.80982e13 | 0.0269671 | ||||||||
\(223\) | −1.47333e15 | −0.802266 | −0.401133 | − | 0.916020i | \(-0.631383\pi\) | ||||
−0.401133 | + | 0.916020i | \(0.631383\pi\) | |||||||
\(224\) | −5.54701e14 | −0.293391 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.04320e14 | 0.102002 | ||||||||
\(227\) | 3.74889e15 | 1.81859 | 0.909294 | − | 0.416153i | \(-0.136622\pi\) | ||||
0.909294 | + | 0.416153i | \(0.136622\pi\) | |||||||
\(228\) | 1.25590e15 | 0.592076 | ||||||||
\(229\) | −1.47993e13 | −0.00678126 | −0.00339063 | − | 0.999994i | \(-0.501079\pi\) | ||||
−0.00339063 | + | 0.999994i | \(0.501079\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.91652e15 | 0.829917 | ||||||||
\(232\) | 2.44068e14 | 0.102763 | ||||||||
\(233\) | −3.63053e15 | −1.48647 | −0.743236 | − | 0.669030i | \(-0.766710\pi\) | ||||
−0.743236 | + | 0.669030i | \(0.766710\pi\) | |||||||
\(234\) | −5.13347e13 | −0.0204413 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.40714e14 | 0.0906930 | ||||||||
\(237\) | −7.81795e14 | −0.286569 | ||||||||
\(238\) | −3.31459e14 | −0.118217 | ||||||||
\(239\) | −4.33900e15 | −1.50592 | −0.752962 | − | 0.658063i | \(-0.771376\pi\) | ||||
−0.752962 | + | 0.658063i | \(0.771376\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.02372e15 | 0.994103 | 0.497051 | − | 0.867721i | \(-0.334416\pi\) | ||||
0.497051 | + | 0.867721i | \(0.334416\pi\) | |||||||
\(242\) | 1.08642e15 | 0.347693 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 1.08159e15 | 0.328116 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.09292e13 | −0.0117748 | ||||||||
\(247\) | 1.72311e15 | 0.482818 | ||||||||
\(248\) | −1.20033e15 | −0.327617 | ||||||||
\(249\) | −8.19414e14 | −0.217875 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.75146e15 | −0.442099 | −0.221050 | − | 0.975263i | \(-0.570948\pi\) | ||||
−0.221050 | + | 0.975263i | \(0.570948\pi\) | |||||||
\(252\) | 1.00548e15 | 0.247326 | ||||||||
\(253\) | 9.28803e15 | 2.22659 | ||||||||
\(254\) | 5.39216e14 | 0.125992 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.73265e15 | 0.828816 | ||||||||
\(257\) | −4.87604e15 | −1.05561 | −0.527803 | − | 0.849367i | \(-0.676984\pi\) | ||||
−0.527803 | + | 0.849367i | \(0.676984\pi\) | |||||||
\(258\) | −6.22421e13 | −0.0131388 | ||||||||
\(259\) | −1.29256e15 | −0.266074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.65577e14 | −0.130327 | ||||||||
\(262\) | −1.44219e13 | −0.00275463 | ||||||||
\(263\) | −4.67882e15 | −0.871815 | −0.435907 | − | 0.899992i | \(-0.643572\pi\) | ||||
−0.435907 | + | 0.899992i | \(0.643572\pi\) | |||||||
\(264\) | 1.58873e15 | 0.288818 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.03879e14 | 0.104525 | ||||||||
\(267\) | 1.62976e15 | 0.275296 | ||||||||
\(268\) | 2.80488e15 | 0.462422 | ||||||||
\(269\) | −1.80262e15 | −0.290078 | −0.145039 | − | 0.989426i | \(-0.546331\pi\) | ||||
−0.145039 | + | 0.989426i | \(0.546331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.10016e15 | 0.935494 | 0.467747 | − | 0.883862i | \(-0.345066\pi\) | ||||
0.467747 | + | 0.883862i | \(0.345066\pi\) | |||||||
\(272\) | 7.47156e15 | 1.11870 | ||||||||
\(273\) | 1.37954e15 | 0.201686 | ||||||||
\(274\) | −2.05874e14 | −0.0293915 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.87286e15 | 0.663552 | ||||||||
\(277\) | 1.07023e16 | 1.42351 | 0.711754 | − | 0.702428i | \(-0.247901\pi\) | ||||
0.711754 | + | 0.702428i | \(0.247901\pi\) | |||||||
\(278\) | 1.26773e15 | 0.164716 | ||||||||
\(279\) | 3.27333e15 | 0.415492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.45460e15 | −0.297433 | −0.148717 | − | 0.988880i | \(-0.547514\pi\) | ||||
−0.148717 | + | 0.988880i | \(0.547514\pi\) | |||||||
\(282\) | 2.58318e14 | 0.0305869 | ||||||||
\(283\) | −4.01155e15 | −0.464195 | −0.232098 | − | 0.972692i | \(-0.574559\pi\) | ||||
−0.232098 | + | 0.972692i | \(0.574559\pi\) | |||||||
\(284\) | −1.05778e16 | −1.19626 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.08022e15 | 0.116716 | ||||||||
\(287\) | 1.09990e15 | 0.116178 | ||||||||
\(288\) | 1.25396e15 | 0.129489 | ||||||||
\(289\) | 3.90041e15 | 0.393799 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.03629e16 | 1.00041 | ||||||||
\(292\) | −9.48759e15 | −0.895710 | ||||||||
\(293\) | −2.08187e15 | −0.192227 | −0.0961133 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961133 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(294\) | −3.64115e14 | −0.0328837 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.07149e15 | −0.0925957 | ||||||||
\(297\) | −4.33249e15 | −0.366286 | ||||||||
\(298\) | −1.02424e15 | −0.0847219 | ||||||||
\(299\) | 6.68565e15 | 0.541104 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.67265e15 | 0.129636 | ||||||||
\(302\) | −7.39697e14 | −0.0561059 | ||||||||
\(303\) | 1.24072e16 | 0.921075 | ||||||||
\(304\) | −1.36123e16 | −0.989130 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.49298e14 | 0.0521753 | ||||||||
\(307\) | 1.32352e16 | 0.902260 | 0.451130 | − | 0.892458i | \(-0.351021\pi\) | ||||
0.451130 | + | 0.892458i | \(0.351021\pi\) | |||||||
\(308\) | −2.11579e16 | −1.41219 | ||||||||
\(309\) | −8.01202e15 | −0.523615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.09301e15 | −0.507187 | −0.253593 | − | 0.967311i | \(-0.581612\pi\) | ||||
−0.253593 | + | 0.967311i | \(0.581612\pi\) | |||||||
\(312\) | 1.14359e15 | 0.0701883 | ||||||||
\(313\) | 1.48181e16 | 0.890748 | 0.445374 | − | 0.895345i | \(-0.353071\pi\) | ||||
0.445374 | + | 0.895345i | \(0.353071\pi\) | |||||||
\(314\) | 1.41625e15 | 0.0833868 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.63084e15 | 0.487626 | ||||||||
\(317\) | 2.43171e16 | 1.34594 | 0.672970 | − | 0.739670i | \(-0.265018\pi\) | ||||
0.672970 | + | 0.739670i | \(0.265018\pi\) | |||||||
\(318\) | 1.78569e15 | 0.0968342 | ||||||||
\(319\) | 1.40055e16 | 0.744147 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.43178e16 | 0.730455 | ||||||||
\(322\) | 2.34304e15 | 0.117143 | ||||||||
\(323\) | −2.51511e16 | −1.23237 | ||||||||
\(324\) | −2.27299e15 | −0.109158 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.85652e15 | −0.0856615 | ||||||||
\(327\) | −7.15950e15 | −0.323834 | ||||||||
\(328\) | 9.11783e14 | 0.0404307 | ||||||||
\(329\) | −6.94186e15 | −0.301788 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.16232e16 | 0.485783 | 0.242892 | − | 0.970053i | \(-0.421904\pi\) | ||||
0.242892 | + | 0.970053i | \(0.421904\pi\) | |||||||
\(332\) | 9.04615e15 | 0.370737 | ||||||||
\(333\) | 2.92196e15 | 0.117432 | ||||||||
\(334\) | −4.51214e15 | −0.177841 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.08981e16 | −0.413186 | ||||||||
\(337\) | −4.62652e16 | −1.72052 | −0.860262 | − | 0.509853i | \(-0.829700\pi\) | ||||
−0.860262 | + | 0.509853i | \(0.829700\pi\) | |||||||
\(338\) | −2.85695e15 | −0.104218 | ||||||||
\(339\) | 1.24125e16 | 0.444181 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.88795e16 | −2.37239 | ||||||||
\(342\) | −1.36513e15 | −0.0461323 | ||||||||
\(343\) | 3.25624e16 | 1.07970 | ||||||||
\(344\) | 1.38657e15 | 0.0451142 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.48275e15 | −0.140459 | ||||||||
\(347\) | −4.79404e15 | −0.147421 | −0.0737106 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737106 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(348\) | 7.34782e15 | 0.221765 | ||||||||
\(349\) | 3.76900e16 | 1.11651 | 0.558253 | − | 0.829671i | \(-0.311472\pi\) | ||||
0.558253 | + | 0.829671i | \(0.311472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11859e15 | −0.0890146 | ||||||||
\(352\) | −2.63866e16 | −0.739360 | ||||||||
\(353\) | −4.80179e16 | −1.32089 | −0.660446 | − | 0.750873i | \(-0.729633\pi\) | ||||
−0.660446 | + | 0.750873i | \(0.729633\pi\) | |||||||
\(354\) | −2.61651e14 | −0.00706645 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.79922e16 | −0.468446 | ||||||||
\(357\) | −2.01361e16 | −0.514793 | ||||||||
\(358\) | 5.08018e14 | 0.0127538 | ||||||||
\(359\) | 4.06616e16 | 1.00247 | 0.501234 | − | 0.865312i | \(-0.332880\pi\) | ||||
0.501234 | + | 0.865312i | \(0.332880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.76929e15 | 0.0896320 | ||||||||
\(362\) | −3.72536e15 | −0.0870087 | ||||||||
\(363\) | 6.59998e16 | 1.51408 | ||||||||
\(364\) | −1.52298e16 | −0.343190 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.17566e15 | −0.0255656 | ||||||||
\(367\) | −2.96733e16 | −0.633923 | −0.316961 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316961 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(368\) | −5.28156e16 | −1.10854 | ||||||||
\(369\) | −2.48645e15 | −0.0512752 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.79873e16 | −0.955424 | ||||||||
\(372\) | −3.61369e16 | −0.707003 | ||||||||
\(373\) | 9.01346e16 | 1.73294 | 0.866471 | − | 0.499227i | \(-0.166383\pi\) | ||||
0.866471 | + | 0.499227i | \(0.166383\pi\) | |||||||
\(374\) | −1.57672e16 | −0.297912 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.75457e15 | −0.105025 | ||||||||
\(377\) | 1.00813e16 | 0.180842 | ||||||||
\(378\) | −1.09293e15 | −0.0192707 | ||||||||
\(379\) | −1.54841e16 | −0.268369 | −0.134184 | − | 0.990956i | \(-0.542841\pi\) | ||||
−0.134184 | + | 0.990956i | \(0.542841\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.27574e16 | 0.548652 | ||||||||
\(382\) | −1.03473e16 | −0.170378 | ||||||||
\(383\) | −9.37088e15 | −0.151701 | −0.0758505 | − | 0.997119i | \(-0.524167\pi\) | ||||
−0.0758505 | + | 0.997119i | \(0.524167\pi\) | |||||||
\(384\) | −1.84006e16 | −0.292872 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.12540e16 | 0.173177 | ||||||||
\(387\) | −3.78121e15 | −0.0572150 | ||||||||
\(388\) | −1.14404e17 | −1.70230 | ||||||||
\(389\) | 2.95806e16 | 0.432847 | 0.216423 | − | 0.976300i | \(-0.430561\pi\) | ||||
0.216423 | + | 0.976300i | \(0.430561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.75858e16 | −1.38114 | ||||||||
\(392\) | 8.11142e15 | 0.112911 | ||||||||
\(393\) | −8.76130e14 | −0.0119955 | ||||||||
\(394\) | 8.06058e15 | 0.108553 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.78297e16 | 0.623274 | ||||||||
\(397\) | −1.80617e16 | −0.231538 | −0.115769 | − | 0.993276i | \(-0.536933\pi\) | ||||
−0.115769 | + | 0.993276i | \(0.536933\pi\) | |||||||
\(398\) | −5.23742e14 | −0.00660507 | ||||||||
\(399\) | 3.66857e16 | 0.455169 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.20412e17 | −1.44621 | −0.723107 | − | 0.690736i | \(-0.757287\pi\) | ||||
−0.723107 | + | 0.690736i | \(0.757287\pi\) | |||||||
\(402\) | −3.04884e15 | −0.0360301 | ||||||||
\(403\) | −4.95804e16 | −0.576537 | ||||||||
\(404\) | −1.36972e17 | −1.56731 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.53309e15 | 0.0391503 | ||||||||
\(407\) | −6.14858e16 | −0.670519 | ||||||||
\(408\) | −1.66922e16 | −0.179152 | ||||||||
\(409\) | −1.77522e16 | −0.187521 | −0.0937606 | − | 0.995595i | \(-0.529889\pi\) | ||||
−0.0937606 | + | 0.995595i | \(0.529889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.25068e16 | −0.127990 | ||||||||
\(412\) | 8.84510e16 | 0.890986 | ||||||||
\(413\) | 7.03144e15 | 0.0697219 | ||||||||
\(414\) | −5.29670e15 | −0.0517015 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.89934e16 | −0.179679 | ||||||||
\(417\) | 7.70145e16 | 0.717279 | ||||||||
\(418\) | 2.87259e16 | 0.263408 | ||||||||
\(419\) | 1.75670e17 | 1.58602 | 0.793008 | − | 0.609212i | \(-0.208514\pi\) | ||||
0.793008 | + | 0.609212i | \(0.208514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.84473e17 | 1.61473 | 0.807365 | − | 0.590052i | \(-0.200893\pi\) | ||||
0.807365 | + | 0.590052i | \(0.200893\pi\) | |||||||
\(422\) | −1.94595e16 | −0.167726 | ||||||||
\(423\) | 1.56928e16 | 0.133195 | ||||||||
\(424\) | −3.97799e16 | −0.332495 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.14978e16 | 0.0932079 | ||||||||
\(427\) | 3.15939e16 | 0.252245 | ||||||||
\(428\) | −1.58065e17 | −1.24295 | ||||||||
\(429\) | 6.56232e16 | 0.508259 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.05532e16 | 0.605314 | 0.302657 | − | 0.953100i | \(-0.402126\pi\) | ||||
0.302657 | + | 0.953100i | \(0.402126\pi\) | |||||||
\(432\) | 2.46363e16 | 0.182361 | ||||||||
\(433\) | 1.97092e17 | 1.43714 | 0.718568 | − | 0.695457i | \(-0.244798\pi\) | ||||
0.718568 | + | 0.695457i | \(0.244798\pi\) | |||||||
\(434\) | −1.73759e16 | −0.124814 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.90393e16 | 0.551037 | ||||||||
\(437\) | 1.77790e17 | 1.22117 | ||||||||
\(438\) | 1.03128e16 | 0.0697903 | ||||||||
\(439\) | 9.89007e16 | 0.659447 | 0.329724 | − | 0.944078i | \(-0.393044\pi\) | ||||
0.329724 | + | 0.944078i | \(0.393044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.21200e16 | −0.143197 | ||||||||
\(442\) | −1.13494e16 | −0.0723985 | ||||||||
\(443\) | 1.25104e17 | 0.786404 | 0.393202 | − | 0.919452i | \(-0.371367\pi\) | ||||
0.393202 | + | 0.919452i | \(0.371367\pi\) | |||||||
\(444\) | −3.22578e16 | −0.199823 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.76800e16 | −0.106366 | ||||||||
\(447\) | −6.22225e16 | −0.368934 | ||||||||
\(448\) | 1.15809e17 | 0.676761 | ||||||||
\(449\) | −1.80095e17 | −1.03729 | −0.518645 | − | 0.854990i | \(-0.673563\pi\) | ||||
−0.518645 | + | 0.854990i | \(0.673563\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.23213e16 | 0.292773 | ||||||||
\(452\) | −1.37031e17 | −0.755820 | ||||||||
\(453\) | −4.49366e16 | −0.244322 | ||||||||
\(454\) | 4.49867e16 | 0.241113 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.04112e16 | 0.158402 | ||||||||
\(457\) | 9.43597e16 | 0.484542 | 0.242271 | − | 0.970209i | \(-0.422108\pi\) | ||||
0.242271 | + | 0.970209i | \(0.422108\pi\) | |||||||
\(458\) | −1.77592e14 | −0.000899076 0 | ||||||||
\(459\) | 4.55198e16 | 0.227205 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.00500e16 | 0.388423 | 0.194212 | − | 0.980960i | \(-0.437785\pi\) | ||||
0.194212 | + | 0.980960i | \(0.437785\pi\) | |||||||
\(462\) | 2.29982e16 | 0.110033 | ||||||||
\(463\) | −2.14174e17 | −1.01039 | −0.505196 | − | 0.863004i | \(-0.668580\pi\) | ||||
−0.505196 | + | 0.863004i | \(0.668580\pi\) | |||||||
\(464\) | −7.96410e16 | −0.370484 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.35663e16 | −0.197080 | ||||||||
\(467\) | 1.80681e17 | 0.806031 | 0.403015 | − | 0.915193i | \(-0.367962\pi\) | ||||
0.403015 | + | 0.915193i | \(0.367962\pi\) | |||||||
\(468\) | 3.44285e16 | 0.151468 | ||||||||
\(469\) | 8.19326e16 | 0.355495 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.60372e16 | 0.363120 | ||||||||
\(472\) | 5.82883e15 | 0.0242638 | ||||||||
\(473\) | 7.95665e16 | 0.326688 | ||||||||
\(474\) | −9.38154e15 | −0.0379940 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.22298e17 | 0.875974 | ||||||||
\(477\) | 1.08480e17 | 0.421679 | ||||||||
\(478\) | −5.20680e16 | −0.199659 | ||||||||
\(479\) | −2.66712e17 | −1.00893 | −0.504466 | − | 0.863431i | \(-0.668311\pi\) | ||||
−0.504466 | + | 0.863431i | \(0.668311\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.42583e16 | −0.162949 | ||||||||
\(482\) | 3.62847e16 | 0.131801 | ||||||||
\(483\) | 1.42340e17 | 0.510118 | ||||||||
\(484\) | −7.28623e17 | −2.57637 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.47069e15 | 0.00850517 | ||||||||
\(487\) | 2.63552e17 | 0.895216 | 0.447608 | − | 0.894230i | \(-0.352276\pi\) | ||||
0.447608 | + | 0.894230i | \(0.352276\pi\) | |||||||
\(488\) | 2.61903e16 | 0.0877833 | ||||||||
\(489\) | −1.12784e17 | −0.373026 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.11733e17 | 1.32613 | 0.663065 | − | 0.748562i | \(-0.269255\pi\) | ||||
0.663065 | + | 0.748562i | \(0.269255\pi\) | |||||||
\(492\) | 2.74498e16 | 0.0872502 | ||||||||
\(493\) | −1.47150e17 | −0.461590 | ||||||||
\(494\) | 2.06773e16 | 0.0640132 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.91677e17 | 1.18113 | ||||||||
\(497\) | −3.08984e17 | −0.919645 | ||||||||
\(498\) | −9.83297e15 | −0.0288864 | ||||||||
\(499\) | 3.99658e17 | 1.15887 | 0.579435 | − | 0.815018i | \(-0.303273\pi\) | ||||
0.579435 | + | 0.815018i | \(0.303273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.74113e17 | −0.774433 | ||||||||
\(502\) | −2.10175e16 | −0.0586146 | ||||||||
\(503\) | 2.83581e17 | 0.780702 | 0.390351 | − | 0.920666i | \(-0.372354\pi\) | ||||
0.390351 | + | 0.920666i | \(0.372354\pi\) | |||||||
\(504\) | 2.43474e16 | 0.0661690 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.11456e17 | 0.295207 | ||||||||
\(507\) | −1.73559e17 | −0.453834 | ||||||||
\(508\) | −3.61634e17 | −0.933588 | ||||||||
\(509\) | 6.40327e17 | 1.63206 | 0.816030 | − | 0.578009i | \(-0.196170\pi\) | ||||
0.816030 | + | 0.578009i | \(0.196170\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.77140e17 | −0.688593 | ||||||||
\(512\) | 2.51565e17 | 0.617156 | ||||||||
\(513\) | −8.29318e16 | −0.200890 | ||||||||
\(514\) | −5.85124e16 | −0.139955 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.17437e16 | 0.0973572 | ||||||||
\(517\) | −3.30218e17 | −0.760522 | ||||||||
\(518\) | −1.55107e16 | −0.0352767 | ||||||||
\(519\) | −2.72327e17 | −0.611650 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.01348e17 | −0.879175 | −0.439588 | − | 0.898200i | \(-0.644875\pi\) | ||||
−0.439588 | + | 0.898200i | \(0.644875\pi\) | |||||||
\(522\) | −7.98692e15 | −0.0172791 | ||||||||
\(523\) | 5.05985e17 | 1.08113 | 0.540564 | − | 0.841303i | \(-0.318211\pi\) | ||||
0.540564 | + | 0.841303i | \(0.318211\pi\) | |||||||
\(524\) | 9.67228e15 | 0.0204115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.61459e16 | −0.115587 | ||||||||
\(527\) | 7.23691e17 | 1.47158 | ||||||||
\(528\) | −5.18413e17 | −1.04125 | ||||||||
\(529\) | 1.85786e17 | 0.368597 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.58953e16 | −0.0307719 | ||||||||
\(532\) | −4.05002e17 | −0.774517 | ||||||||
\(533\) | 3.76616e16 | 0.0711496 | ||||||||
\(534\) | 1.95571e16 | 0.0364995 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.79193e16 | 0.123715 | ||||||||
\(537\) | 3.08621e16 | 0.0555383 | ||||||||
\(538\) | −2.16314e16 | −0.0384592 | ||||||||
\(539\) | 4.65462e17 | 0.817631 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.69124e17 | −0.290017 | −0.145009 | − | 0.989430i | \(-0.546321\pi\) | ||||
−0.145009 | + | 0.989430i | \(0.546321\pi\) | |||||||
\(542\) | 7.32020e16 | 0.124030 | ||||||||
\(543\) | −2.26316e17 | −0.378892 | ||||||||
\(544\) | 2.77234e17 | 0.458620 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.65544e16 | 0.0267400 | ||||||||
\(547\) | 4.32104e17 | 0.689717 | 0.344858 | − | 0.938655i | \(-0.387927\pi\) | ||||
0.344858 | + | 0.938655i | \(0.387927\pi\) | |||||||
\(548\) | 1.38073e17 | 0.217788 | ||||||||
\(549\) | −7.14214e16 | −0.111329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.68091e17 | 0.408128 | ||||||||
\(552\) | 1.17995e17 | 0.177525 | ||||||||
\(553\) | 2.52113e17 | 0.374871 | ||||||||
\(554\) | 1.28428e17 | 0.188732 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.50224e17 | −1.22053 | ||||||||
\(557\) | −1.36804e18 | −1.94107 | −0.970534 | − | 0.240966i | \(-0.922536\pi\) | ||||
−0.970534 | + | 0.240966i | \(0.922536\pi\) | |||||||
\(558\) | 3.92800e16 | 0.0550870 | ||||||||
\(559\) | 5.72731e16 | 0.0793915 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.57856e17 | −1.29730 | ||||||||
\(562\) | −2.94552e16 | −0.0394345 | ||||||||
\(563\) | 9.52405e17 | 1.26043 | 0.630213 | − | 0.776422i | \(-0.282968\pi\) | ||||
0.630213 | + | 0.776422i | \(0.282968\pi\) | |||||||
\(564\) | −1.73245e17 | −0.226645 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.81386e16 | −0.0615442 | ||||||||
\(567\) | −6.63958e16 | −0.0839171 | ||||||||
\(568\) | −2.56138e17 | −0.320044 | ||||||||
\(569\) | 1.53632e17 | 0.189780 | 0.0948902 | − | 0.995488i | \(-0.469750\pi\) | ||||
0.0948902 | + | 0.995488i | \(0.469750\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.27956e18 | −1.54500 | −0.772498 | − | 0.635017i | \(-0.780993\pi\) | ||||
−0.772498 | + | 0.635017i | \(0.780993\pi\) | |||||||
\(572\) | −7.24466e17 | −0.864856 | ||||||||
\(573\) | −6.28597e17 | −0.741938 | ||||||||
\(574\) | 1.31988e16 | 0.0154031 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.61799e17 | −0.298690 | ||||||||
\(577\) | −3.56770e17 | −0.402481 | −0.201241 | − | 0.979542i | \(-0.564497\pi\) | ||||
−0.201241 | + | 0.979542i | \(0.564497\pi\) | |||||||
\(578\) | 4.68049e16 | 0.0522108 | ||||||||
\(579\) | 6.83683e17 | 0.754126 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.64245e17 | 0.285011 | ||||||||
\(582\) | 1.24355e17 | 0.132637 | ||||||||
\(583\) | −2.28271e18 | −2.40772 | ||||||||
\(584\) | −2.29739e17 | −0.239636 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.49824e16 | −0.0254859 | ||||||||
\(587\) | −1.28968e18 | −1.30118 | −0.650588 | − | 0.759431i | \(-0.725477\pi\) | ||||
−0.650588 | + | 0.759431i | \(0.725477\pi\) | |||||||
\(588\) | 2.44200e17 | 0.243665 | ||||||||
\(589\) | −1.31848e18 | −1.30114 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.89680e17 | 0.472709 | ||||||||
\(592\) | 3.49634e17 | 0.333827 | ||||||||
\(593\) | 1.88640e18 | 1.78147 | 0.890735 | − | 0.454523i | \(-0.150190\pi\) | ||||
0.890735 | + | 0.454523i | \(0.150190\pi\) | |||||||
\(594\) | −5.19899e16 | −0.0485631 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.86923e17 | 0.627780 | ||||||||
\(597\) | −3.18173e16 | −0.0287627 | ||||||||
\(598\) | 8.02278e16 | 0.0717410 | ||||||||
\(599\) | −1.44668e18 | −1.27967 | −0.639834 | − | 0.768513i | \(-0.720997\pi\) | ||||
−0.639834 | + | 0.768513i | \(0.720997\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.44358e16 | −0.0384635 | −0.0192317 | − | 0.999815i | \(-0.506122\pi\) | ||||
−0.0192317 | + | 0.999815i | \(0.506122\pi\) | |||||||
\(602\) | 2.00719e16 | 0.0171874 | ||||||||
\(603\) | −1.85217e17 | −0.156898 | ||||||||
\(604\) | 4.96090e17 | 0.415739 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.48886e17 | 0.122118 | ||||||||
\(607\) | −2.98050e16 | −0.0241860 | −0.0120930 | − | 0.999927i | \(-0.503849\pi\) | ||||
−0.0120930 | + | 0.999927i | \(0.503849\pi\) | |||||||
\(608\) | −5.05087e17 | −0.405502 | ||||||||
\(609\) | 2.14635e17 | 0.170486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.37695e17 | −0.184822 | ||||||||
\(612\) | −5.02529e17 | −0.386613 | ||||||||
\(613\) | 8.84082e17 | 0.672976 | 0.336488 | − | 0.941688i | \(-0.390761\pi\) | ||||
0.336488 | + | 0.941688i | \(0.390761\pi\) | |||||||
\(614\) | 1.58823e17 | 0.119624 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.12333e17 | −0.377814 | ||||||||
\(617\) | −1.43684e18 | −1.04846 | −0.524232 | − | 0.851575i | \(-0.675648\pi\) | ||||
−0.524232 | + | 0.851575i | \(0.675648\pi\) | |||||||
\(618\) | −9.61443e16 | −0.0694222 | ||||||||
\(619\) | 1.68862e18 | 1.20654 | 0.603272 | − | 0.797535i | \(-0.293863\pi\) | ||||
0.603272 | + | 0.797535i | \(0.293863\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.21774e17 | −0.225142 | ||||||||
\(622\) | −9.71162e16 | −0.0672441 | ||||||||
\(623\) | −5.25565e17 | −0.360126 | ||||||||
\(624\) | −3.73161e17 | −0.253044 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.77817e17 | 0.118098 | ||||||||
\(627\) | 1.74510e18 | 1.14705 | ||||||||
\(628\) | −9.49831e17 | −0.617887 | ||||||||
\(629\) | 6.46008e17 | 0.415919 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.53490e17 | −0.222939 | −0.111470 | − | 0.993768i | \(-0.535556\pi\) | ||||
−0.111470 | + | 0.993768i | \(0.535556\pi\) | |||||||
\(632\) | 2.08993e17 | 0.130458 | ||||||||
\(633\) | −1.18216e18 | −0.730387 | ||||||||
\(634\) | 2.91805e17 | 0.178448 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.19760e18 | −0.717531 | ||||||||
\(637\) | 3.35046e17 | 0.198700 | ||||||||
\(638\) | 1.68066e17 | 0.0986608 | ||||||||
\(639\) | 6.98492e17 | 0.405888 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.61802e18 | 0.921313 | 0.460656 | − | 0.887579i | \(-0.347614\pi\) | ||||
0.460656 | + | 0.887579i | \(0.347614\pi\) | |||||||
\(642\) | 1.71814e17 | 0.0968456 | ||||||||
\(643\) | 1.96065e18 | 1.09403 | 0.547015 | − | 0.837123i | \(-0.315764\pi\) | ||||
0.547015 | + | 0.837123i | \(0.315764\pi\) | |||||||
\(644\) | −1.57140e18 | −0.868018 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.01813e17 | −0.163390 | ||||||||
\(647\) | 5.96114e17 | 0.319486 | 0.159743 | − | 0.987159i | \(-0.448933\pi\) | ||||
0.159743 | + | 0.987159i | \(0.448933\pi\) | |||||||
\(648\) | −5.50399e16 | −0.0292038 | ||||||||
\(649\) | 3.34479e17 | 0.175703 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.05558e18 | −0.543521 | ||||||||
\(652\) | 1.24511e18 | 0.634742 | ||||||||
\(653\) | 2.58318e18 | 1.30382 | 0.651912 | − | 0.758295i | \(-0.273967\pi\) | ||||
0.651912 | + | 0.758295i | \(0.273967\pi\) | |||||||
\(654\) | −8.59140e16 | −0.0429347 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.97521e17 | −0.145761 | ||||||||
\(657\) | 6.26503e17 | 0.303912 | ||||||||
\(658\) | −8.33023e16 | −0.0400119 | ||||||||
\(659\) | 2.64137e18 | 1.25624 | 0.628121 | − | 0.778116i | \(-0.283824\pi\) | ||||
0.628121 | + | 0.778116i | \(0.283824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.12451e18 | 1.92337 | 0.961685 | − | 0.274156i | \(-0.0883983\pi\) | ||||
0.961685 | + | 0.274156i | \(0.0883983\pi\) | |||||||
\(662\) | 1.39478e17 | 0.0644064 | ||||||||
\(663\) | −6.89478e17 | −0.315270 | ||||||||
\(664\) | 2.19050e17 | 0.0991861 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.50636e16 | 0.0155695 | ||||||||
\(667\) | 1.04019e18 | 0.457398 | ||||||||
\(668\) | 3.02614e18 | 1.31778 | ||||||||
\(669\) | −1.07406e18 | −0.463189 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50289e18 | 0.635670 | ||||||||
\(672\) | −4.04377e17 | −0.169389 | ||||||||
\(673\) | −2.79726e18 | −1.16047 | −0.580236 | − | 0.814449i | \(-0.697039\pi\) | ||||
−0.580236 | + | 0.814449i | \(0.697039\pi\) | |||||||
\(674\) | −5.55183e17 | −0.228111 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.91606e18 | 0.772245 | ||||||||
\(677\) | 4.25553e18 | 1.69874 | 0.849372 | − | 0.527795i | \(-0.176981\pi\) | ||||
0.849372 | + | 0.527795i | \(0.176981\pi\) | |||||||
\(678\) | 1.48950e17 | 0.0588906 | ||||||||
\(679\) | −3.34184e18 | −1.30867 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.73294e18 | 1.04996 | ||||||||
\(682\) | −8.26553e17 | −0.314538 | ||||||||
\(683\) | −1.60893e18 | −0.606461 | −0.303230 | − | 0.952917i | \(-0.598065\pi\) | ||||
−0.303230 | + | 0.952917i | \(0.598065\pi\) | |||||||
\(684\) | 9.15548e17 | 0.341835 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.90749e17 | 0.143150 | ||||||||
\(687\) | −1.07887e16 | −0.00391516 | ||||||||
\(688\) | −4.52448e17 | −0.162646 | ||||||||
\(689\) | −1.64313e18 | −0.585122 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.06331e18 | −1.07049 | −0.535247 | − | 0.844696i | \(-0.679782\pi\) | ||||
−0.535247 | + | 0.844696i | \(0.679782\pi\) | |||||||
\(692\) | 3.00643e18 | 1.04079 | ||||||||
\(693\) | 1.39714e18 | 0.479153 | ||||||||
\(694\) | −5.75285e16 | −0.0195455 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.77925e17 | 0.0593305 | ||||||||
\(697\) | −5.49721e17 | −0.181606 | ||||||||
\(698\) | 4.52280e17 | 0.148029 | ||||||||
\(699\) | −2.64666e18 | −0.858214 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.99144e18 | 0.952166 | 0.476083 | − | 0.879400i | \(-0.342056\pi\) | ||||
0.476083 | + | 0.879400i | \(0.342056\pi\) | |||||||
\(702\) | −3.74230e16 | −0.0118018 | ||||||||
\(703\) | −1.17695e18 | −0.367747 | ||||||||
\(704\) | 5.50893e18 | 1.70547 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.76215e17 | −0.175127 | ||||||||
\(707\) | −4.00106e18 | −1.20489 | ||||||||
\(708\) | 1.75481e17 | 0.0523616 | ||||||||
\(709\) | −5.31694e18 | −1.57203 | −0.786015 | − | 0.618207i | \(-0.787859\pi\) | ||||
−0.786015 | + | 0.618207i | \(0.787859\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.69928e17 | −0.165450 | ||||||||
\(712\) | −4.35676e17 | −0.125327 | ||||||||
\(713\) | −5.11568e18 | −1.45822 | ||||||||
\(714\) | −2.41634e17 | −0.0682525 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.40711e17 | −0.0945043 | ||||||||
\(717\) | −3.16313e18 | −0.869446 | ||||||||
\(718\) | 4.87939e17 | 0.132910 | ||||||||
\(719\) | −4.03153e18 | −1.08826 | −0.544129 | − | 0.839001i | \(-0.683140\pi\) | ||||
−0.544129 | + | 0.839001i | \(0.683140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.58372e18 | 0.684961 | ||||||||
\(722\) | 4.52315e16 | 0.0118836 | ||||||||
\(723\) | 2.20429e18 | 0.573945 | ||||||||
\(724\) | 2.49848e18 | 0.644725 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.91998e17 | 0.200741 | ||||||||
\(727\) | 4.77643e18 | 1.19986 | 0.599928 | − | 0.800054i | \(-0.295196\pi\) | ||||
0.599928 | + | 0.800054i | \(0.295196\pi\) | |||||||
\(728\) | −3.68785e17 | −0.0918161 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.35976e17 | −0.202643 | ||||||||
\(732\) | 7.88477e17 | 0.189438 | ||||||||
\(733\) | −1.71668e18 | −0.408803 | −0.204401 | − | 0.978887i | \(-0.565525\pi\) | ||||
−0.204401 | + | 0.978887i | \(0.565525\pi\) | |||||||
\(734\) | −3.56080e17 | −0.0840471 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.95973e18 | −0.454455 | ||||||||
\(737\) | 3.89745e18 | 0.895864 | ||||||||
\(738\) | −2.98374e16 | −0.00679820 | ||||||||
\(739\) | −8.69723e17 | −0.196423 | −0.0982114 | − | 0.995166i | \(-0.531312\pi\) | ||||
−0.0982114 | + | 0.995166i | \(0.531312\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.25615e18 | 0.278755 | ||||||||
\(742\) | −5.75848e17 | −0.126673 | ||||||||
\(743\) | −2.40272e18 | −0.523933 | −0.261966 | − | 0.965077i | \(-0.584371\pi\) | ||||
−0.261966 | + | 0.965077i | \(0.584371\pi\) | |||||||
\(744\) | −8.75044e17 | −0.189150 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.08161e18 | 0.229758 | ||||||||
\(747\) | −5.97353e17 | −0.125790 | ||||||||
\(748\) | 1.05745e19 | 2.20750 | ||||||||
\(749\) | −4.61721e18 | −0.955537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.37175e18 | 1.90617 | 0.953084 | − | 0.302706i | \(-0.0978899\pi\) | ||||
0.953084 | + | 0.302706i | \(0.0978899\pi\) | |||||||
\(752\) | 1.87775e18 | 0.378637 | ||||||||
\(753\) | −1.27681e18 | −0.255246 | ||||||||
\(754\) | 1.20976e17 | 0.0239765 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.32995e17 | 0.142794 | ||||||||
\(757\) | −3.09120e18 | −0.597040 | −0.298520 | − | 0.954403i | \(-0.596493\pi\) | ||||
−0.298520 | + | 0.954403i | \(0.596493\pi\) | |||||||
\(758\) | −1.85810e17 | −0.0355810 | ||||||||
\(759\) | 6.77097e18 | 1.28552 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.97787e18 | −1.48897 | −0.744486 | − | 0.667638i | \(-0.767306\pi\) | ||||
−0.744486 | + | 0.667638i | \(0.767306\pi\) | |||||||
\(762\) | 3.93088e17 | 0.0727416 | ||||||||
\(763\) | 2.30880e18 | 0.423620 | ||||||||
\(764\) | 6.93957e18 | 1.26248 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.12451e17 | −0.0201129 | ||||||||
\(767\) | 2.40763e17 | 0.0426991 | ||||||||
\(768\) | 2.72110e18 | 0.478517 | ||||||||
\(769\) | 7.37344e18 | 1.28573 | 0.642863 | − | 0.765981i | \(-0.277746\pi\) | ||||
0.642863 | + | 0.765981i | \(0.277746\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.55463e18 | −0.609454 | ||||||||
\(772\) | −7.54771e18 | −1.28322 | ||||||||
\(773\) | 1.67335e18 | 0.282111 | 0.141056 | − | 0.990002i | \(-0.454950\pi\) | ||||
0.141056 | + | 0.990002i | \(0.454950\pi\) | |||||||
\(774\) | −4.53745e16 | −0.00758570 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.77027e18 | −0.455429 | ||||||||
\(777\) | −9.42275e17 | −0.153618 | ||||||||
\(778\) | 3.54967e17 | 0.0573879 | ||||||||
\(779\) | 1.00153e18 | 0.160572 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.46981e19 | −2.31755 | ||||||||
\(782\) | −1.17103e18 | −0.183115 | ||||||||
\(783\) | −4.85206e17 | −0.0752444 | ||||||||
\(784\) | −2.64681e18 | −0.407069 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.05136e16 | −0.00159039 | ||||||||
\(787\) | 3.75359e18 | 0.563133 | 0.281566 | − | 0.959542i | \(-0.409146\pi\) | ||||
0.281566 | + | 0.959542i | \(0.409146\pi\) | |||||||
\(788\) | −5.40596e18 | −0.804363 | ||||||||
\(789\) | −3.41086e18 | −0.503342 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.00277e18 | −0.581050 | ||||||||
\(792\) | 1.15818e18 | 0.166749 | ||||||||
\(793\) | 1.08180e18 | 0.154480 | ||||||||
\(794\) | −2.16741e17 | −0.0306978 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.51256e17 | 0.0489428 | ||||||||
\(797\) | −3.38853e18 | −0.468309 | −0.234154 | − | 0.972199i | \(-0.575232\pi\) | ||||
−0.234154 | + | 0.972199i | \(0.575232\pi\) | |||||||
\(798\) | 4.40228e17 | 0.0603474 | ||||||||
\(799\) | 3.46947e18 | 0.471747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.18810e18 | 0.158942 | ||||||||
\(802\) | −1.44495e18 | −0.191743 | ||||||||
\(803\) | −1.31833e19 | −1.73529 | ||||||||
\(804\) | 2.04476e18 | 0.266979 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.94965e17 | −0.0764387 | ||||||||
\(807\) | −1.31411e18 | −0.167476 | ||||||||
\(808\) | −3.31674e18 | −0.419313 | ||||||||
\(809\) | −3.13119e18 | −0.392685 | −0.196343 | − | 0.980535i | \(-0.562906\pi\) | ||||
−0.196343 | + | 0.980535i | \(0.562906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.04731e19 | 1.29253 | 0.646264 | − | 0.763114i | \(-0.276331\pi\) | ||||
0.646264 | + | 0.763114i | \(0.276331\pi\) | |||||||
\(812\) | −2.36953e18 | −0.290100 | ||||||||
\(813\) | 4.44702e18 | 0.540108 | ||||||||
\(814\) | −7.37829e17 | −0.0888991 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.44677e18 | 0.645881 | ||||||||
\(817\) | 1.52305e18 | 0.179172 | ||||||||
\(818\) | −2.13026e17 | −0.0248620 | ||||||||
\(819\) | 1.00568e18 | 0.116443 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.85162e18 | −0.780841 | −0.390421 | − | 0.920637i | \(-0.627670\pi\) | ||||
−0.390421 | + | 0.920637i | \(0.627670\pi\) | |||||||
\(822\) | −1.50082e17 | −0.0169692 | ||||||||
\(823\) | −3.06934e17 | −0.0344308 | −0.0172154 | − | 0.999852i | \(-0.505480\pi\) | ||||
−0.0172154 | + | 0.999852i | \(0.505480\pi\) | |||||||
\(824\) | 2.14181e18 | 0.238372 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.43773e16 | 0.00924390 | ||||||||
\(827\) | −7.75365e18 | −0.842792 | −0.421396 | − | 0.906877i | \(-0.638460\pi\) | ||||
−0.421396 | + | 0.906877i | \(0.638460\pi\) | |||||||
\(828\) | 3.55232e18 | 0.383102 | ||||||||
\(829\) | 2.34336e18 | 0.250747 | 0.125373 | − | 0.992110i | \(-0.459987\pi\) | ||||
0.125373 | + | 0.992110i | \(0.459987\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.80200e18 | 0.821863 | ||||||||
\(832\) | 3.96540e18 | 0.414463 | ||||||||
\(833\) | −4.89044e18 | −0.507172 | ||||||||
\(834\) | 9.24174e17 | 0.0950987 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.92655e19 | −1.95182 | ||||||||
\(837\) | 2.38626e18 | 0.239884 | ||||||||
\(838\) | 2.10804e18 | 0.210278 | ||||||||
\(839\) | −1.63297e19 | −1.61632 | −0.808158 | − | 0.588965i | \(-0.799535\pi\) | ||||
−0.808158 | + | 0.588965i | \(0.799535\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.69212e18 | −0.847134 | ||||||||
\(842\) | 2.21368e18 | 0.214085 | ||||||||
\(843\) | −1.78940e18 | −0.171723 | ||||||||
\(844\) | 1.30508e19 | 1.24283 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.88314e17 | 0.0176593 | ||||||||
\(847\) | −2.12836e19 | −1.98063 | ||||||||
\(848\) | 1.29804e19 | 1.19872 | ||||||||
\(849\) | −2.92442e18 | −0.268003 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.56655e18 | −0.412142 | ||||||||
\(852\) | −7.71120e18 | −0.690660 | ||||||||
\(853\) | −1.93794e19 | −1.72255 | −0.861276 | − | 0.508137i | \(-0.830334\pi\) | ||||
−0.861276 | + | 0.508137i | \(0.830334\pi\) | |||||||
\(854\) | 3.79127e17 | 0.0334433 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.82751e18 | −0.332534 | ||||||||
\(857\) | −1.20537e19 | −1.03931 | −0.519656 | − | 0.854376i | \(-0.673940\pi\) | ||||
−0.519656 | + | 0.854376i | \(0.673940\pi\) | |||||||
\(858\) | 7.87478e17 | 0.0673862 | ||||||||
\(859\) | −1.00612e19 | −0.854465 | −0.427232 | − | 0.904142i | \(-0.640511\pi\) | ||||
−0.427232 | + | 0.904142i | \(0.640511\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.01830e17 | 0.0670751 | ||||||||
\(862\) | 9.66639e17 | 0.0802541 | ||||||||
\(863\) | −8.01407e18 | −0.660363 | −0.330182 | − | 0.943917i | \(-0.607110\pi\) | ||||
−0.330182 | + | 0.943917i | \(0.607110\pi\) | |||||||
\(864\) | 9.14136e17 | 0.0747604 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.36510e18 | 0.190539 | ||||||||
\(867\) | 2.84340e18 | 0.227360 | ||||||||
\(868\) | 1.16534e19 | 0.924858 | ||||||||
\(869\) | 1.19928e19 | 0.944694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.80544e18 | 0.217712 | ||||||||
\(872\) | 1.91391e18 | 0.147423 | ||||||||
\(873\) | 7.55457e18 | 0.577587 | ||||||||
\(874\) | 2.13348e18 | 0.161906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −6.91646e18 | −0.517139 | ||||||||
\(877\) | −8.87791e17 | −0.0658891 | −0.0329445 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329445 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(878\) | 1.18681e18 | 0.0874312 | ||||||||
\(879\) | −1.51768e18 | −0.110982 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.78774e18 | 0.272921 | 0.136460 | − | 0.990646i | \(-0.456427\pi\) | ||||
0.136460 | + | 0.990646i | \(0.456427\pi\) | |||||||
\(882\) | −2.65440e17 | −0.0189854 | ||||||||
\(883\) | 2.75428e19 | 1.95553 | 0.977763 | − | 0.209712i | \(-0.0672526\pi\) | ||||
0.977763 | + | 0.209712i | \(0.0672526\pi\) | |||||||
\(884\) | 7.61169e18 | 0.536465 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.50124e18 | 0.104263 | ||||||||
\(887\) | 2.84165e19 | 1.95914 | 0.979572 | − | 0.201092i | \(-0.0644489\pi\) | ||||
0.979572 | + | 0.201092i | \(0.0644489\pi\) | |||||||
\(888\) | −7.81114e17 | −0.0534602 | ||||||||
\(889\) | −1.05636e19 | −0.717712 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.15838e18 | −0.211475 | ||||||||
\(892\) | 1.18574e19 | 0.788164 | ||||||||
\(893\) | −6.32097e18 | −0.417109 | ||||||||
\(894\) | −7.46670e17 | −0.0489142 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5.93382e18 | 0.383118 | ||||||||
\(897\) | 4.87384e18 | 0.312407 | ||||||||
\(898\) | −2.16114e18 | −0.137527 | ||||||||
\(899\) | −7.71397e18 | −0.487349 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.39836e19 | 1.49349 | ||||||||
\(902\) | 6.27856e17 | 0.0388166 | ||||||||
\(903\) | 1.21937e18 | 0.0748451 | ||||||||
\(904\) | −3.31816e18 | −0.202210 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.39239e17 | −0.0323928 | ||||||||
\(907\) | −7.51023e18 | −0.447926 | −0.223963 | − | 0.974598i | \(-0.571899\pi\) | ||||
−0.223963 | + | 0.974598i | \(0.571899\pi\) | |||||||
\(908\) | −3.01711e19 | −1.78662 | ||||||||
\(909\) | 9.04482e18 | 0.531783 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.34028e19 | −1.35643 | −0.678216 | − | 0.734863i | \(-0.737247\pi\) | ||||
−0.678216 | + | 0.734863i | \(0.737247\pi\) | |||||||
\(912\) | −9.92337e18 | −0.571074 | ||||||||
\(913\) | 1.25699e19 | 0.718242 | ||||||||
\(914\) | 1.13232e18 | 0.0642418 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.19105e17 | 0.00666206 | ||||||||
\(917\) | 2.82535e17 | 0.0156917 | ||||||||
\(918\) | 5.46238e17 | 0.0301234 | ||||||||
\(919\) | 2.20881e19 | 1.20950 | 0.604752 | − | 0.796414i | \(-0.293272\pi\) | ||||
0.604752 | + | 0.796414i | \(0.293272\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.64848e18 | 0.520920 | ||||||||
\(922\) | 9.60600e17 | 0.0514982 | ||||||||
\(923\) | −1.05799e19 | −0.563210 | ||||||||
\(924\) | −1.54241e19 | −0.815329 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.57009e18 | −0.133960 | ||||||||
\(927\) | −5.84077e18 | −0.302309 | ||||||||
\(928\) | −2.95509e18 | −0.151883 | ||||||||
\(929\) | −1.05632e19 | −0.539132 | −0.269566 | − | 0.962982i | \(-0.586880\pi\) | ||||
−0.269566 | + | 0.962982i | \(0.586880\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.90980e18 | 0.448430 | ||||||||
\(932\) | 2.92185e19 | 1.46034 | ||||||||
\(933\) | −5.89981e18 | −0.292824 | ||||||||
\(934\) | 2.16817e18 | 0.106866 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.33676e17 | 0.0405233 | ||||||||
\(937\) | 1.72833e19 | 0.834294 | 0.417147 | − | 0.908839i | \(-0.363030\pi\) | ||||
0.417147 | + | 0.908839i | \(0.363030\pi\) | |||||||
\(938\) | 9.83191e17 | 0.0471324 | ||||||||
\(939\) | 1.08024e19 | 0.514273 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.14038e19 | 1.00498 | 0.502490 | − | 0.864583i | \(-0.332417\pi\) | ||||
0.502490 | + | 0.864583i | \(0.332417\pi\) | |||||||
\(942\) | 1.03245e18 | 0.0481434 | ||||||||
\(943\) | 3.88591e18 | 0.179956 | ||||||||
\(944\) | −1.90199e18 | −0.0874760 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.54799e17 | 0.0433131 | ||||||||
\(947\) | 5.91308e17 | 0.0266403 | 0.0133202 | − | 0.999911i | \(-0.495760\pi\) | ||||
0.0133202 | + | 0.999911i | \(0.495760\pi\) | |||||||
\(948\) | 6.29188e18 | 0.281531 | ||||||||
\(949\) | −9.48950e18 | −0.421709 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.77271e19 | 0.777079 | ||||||||
\(952\) | 5.38289e18 | 0.234356 | ||||||||
\(953\) | 2.39396e19 | 1.03517 | 0.517587 | − | 0.855631i | \(-0.326830\pi\) | ||||
0.517587 | + | 0.855631i | \(0.326830\pi\) | |||||||
\(954\) | 1.30177e18 | 0.0559073 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.49203e19 | 1.47945 | ||||||||
\(957\) | 1.02100e19 | 0.429633 | ||||||||
\(958\) | −3.20055e18 | −0.133767 | ||||||||
\(959\) | 4.03321e18 | 0.167429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.35201e19 | 0.553702 | ||||||||
\(962\) | −5.31100e17 | −0.0216042 | ||||||||
\(963\) | 1.04377e19 | 0.421729 | ||||||||
\(964\) | −2.43349e19 | −0.976628 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.70808e18 | 0.0676327 | ||||||||
\(967\) | −1.99045e18 | −0.0782853 | −0.0391427 | − | 0.999234i | \(-0.512463\pi\) | ||||
−0.0391427 | + | 0.999234i | \(0.512463\pi\) | |||||||
\(968\) | −1.76434e19 | −0.689275 | ||||||||
\(969\) | −1.83351e19 | −0.711507 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.12385e19 | 1.57898 | 0.789492 | − | 0.613761i | \(-0.210344\pi\) | ||||
0.789492 | + | 0.613761i | \(0.210344\pi\) | |||||||
\(972\) | −1.65701e18 | −0.0630224 | ||||||||
\(973\) | −2.48357e19 | −0.938301 | ||||||||
\(974\) | 3.16262e18 | 0.118690 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.54608e18 | −0.316478 | ||||||||
\(977\) | 1.25374e19 | 0.461202 | 0.230601 | − | 0.973048i | \(-0.425931\pi\) | ||||
0.230601 | + | 0.973048i | \(0.425931\pi\) | |||||||
\(978\) | −1.35340e18 | −0.0494567 | ||||||||
\(979\) | −2.50006e19 | −0.907535 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.21928e18 | −0.186966 | ||||||||
\(982\) | 4.94080e18 | 0.175822 | ||||||||
\(983\) | 1.83966e19 | 0.650340 | 0.325170 | − | 0.945656i | \(-0.394578\pi\) | ||||
0.325170 | + | 0.945656i | \(0.394578\pi\) | |||||||
\(984\) | 6.64690e17 | 0.0233427 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.76580e18 | −0.0611987 | ||||||||
\(987\) | −5.06062e18 | −0.174238 | ||||||||
\(988\) | −1.38676e19 | −0.474331 | ||||||||
\(989\) | 5.90941e18 | 0.200802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.43064e19 | −1.15053 | −0.575263 | − | 0.817969i | \(-0.695100\pi\) | ||||
−0.575263 | + | 0.817969i | \(0.695100\pi\) | |||||||
\(992\) | 1.45333e19 | 0.484214 | ||||||||
\(993\) | 8.47329e18 | 0.280467 | ||||||||
\(994\) | −3.70781e18 | −0.121929 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.59465e18 | 0.214045 | ||||||||
\(997\) | 5.72458e19 | 1.84597 | 0.922985 | − | 0.384835i | \(-0.125742\pi\) | ||||
0.922985 | + | 0.384835i | \(0.125742\pi\) | |||||||
\(998\) | 4.79589e18 | 0.153646 | ||||||||
\(999\) | 2.13011e18 | 0.0677995 |
(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 | 75.14.a.a.1.1 | 1 | ||
5.2 | odd | 4 | 75.14.b.b.49.2 | 2 | |||
5.3 | odd | 4 | 75.14.b.b.49.1 | 2 | |||
5.4 | even | 2 | 3.14.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 9.14.a.a.1.1 | 1 | |||
20.19 | odd | 2 | 48.14.a.c.1.1 | 1 | |||
35.34 | odd | 2 | 147.14.a.a.1.1 | 1 | |||
40.19 | odd | 2 | 192.14.a.e.1.1 | 1 | |||
40.29 | even | 2 | 192.14.a.j.1.1 | 1 | |||
60.59 | even | 2 | 144.14.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.14.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
9.14.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
48.14.a.c.1.1 | 1 | 20.19 | odd | 2 | |||
75.14.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
75.14.b.b.49.1 | 2 | 5.3 | odd | 4 | |||
75.14.b.b.49.2 | 2 | 5.2 | odd | 4 | |||
144.14.a.k.1.1 | 1 | 60.59 | even | 2 | |||
147.14.a.a.1.1 | 1 | 35.34 | odd | 2 | |||
192.14.a.e.1.1 | 1 | 40.19 | odd | 2 | |||
192.14.a.j.1.1 | 1 | 40.29 | even | 2 |