Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,14,Mod(1,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("192.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.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: | \(205.883383588\) |
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 | \(\chi\) | \(=\) | 192.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 30210.0 | 0.864661 | 0.432330 | − | 0.901715i | \(-0.357691\pi\) | ||||
0.432330 | + | 0.901715i | \(0.357691\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 235088. | 0.755254 | 0.377627 | − | 0.925958i | \(-0.376740\pi\) | ||||
0.377627 | + | 0.925958i | \(0.376740\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.11829e7 | 1.90328 | 0.951639 | − | 0.307218i | \(-0.0993981\pi\) | ||||
0.951639 | + | 0.307218i | \(0.0993981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.04961e6 | −0.462534 | −0.231267 | − | 0.972890i | \(-0.574287\pi\) | ||||
−0.231267 | + | 0.972890i | \(0.574287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.20231e7 | 0.499212 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.17495e8 | −1.18059 | −0.590296 | − | 0.807187i | \(-0.700989\pi\) | ||||
−0.590296 | + | 0.807187i | \(0.700989\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.14061e8 | 1.04385 | 0.521927 | − | 0.852990i | \(-0.325213\pi\) | ||||
0.521927 | + | 0.852990i | \(0.325213\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.71379e8 | 0.436046 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.30556e8 | 1.16987 | 0.584935 | − | 0.811080i | \(-0.301120\pi\) | ||||
0.584935 | + | 0.811080i | \(0.301120\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.08059e8 | −0.252362 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.25240e9 | 0.390981 | 0.195491 | − | 0.980706i | \(-0.437370\pi\) | ||||
0.195491 | + | 0.980706i | \(0.437370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.15935e9 | 1.24648 | 0.623238 | − | 0.782032i | \(-0.285817\pi\) | ||||
0.623238 | + | 0.782032i | \(0.285817\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.15234e9 | 1.09886 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.10201e9 | 0.653039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.49819e9 | 0.352297 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.86817e9 | −0.267044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.67869e9 | −0.153826 | −0.0769129 | − | 0.997038i | \(-0.524506\pi\) | ||||
−0.0769129 | + | 0.997038i | \(0.524506\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.11501e9 | −0.171645 | −0.0858224 | − | 0.996310i | \(-0.527352\pi\) | ||||
−0.0858224 | + | 0.996310i | \(0.527352\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.60548e10 | 0.288220 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.95288e10 | −0.399585 | −0.199793 | − | 0.979838i | \(-0.564027\pi\) | ||||
−0.199793 | + | 0.979838i | \(0.564027\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.16226e10 | −0.429591 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.56536e10 | −0.681615 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.04125e11 | 1.26504 | 0.632518 | − | 0.774545i | \(-0.282021\pi\) | ||||
0.632518 | + | 0.774545i | \(0.282021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.37836e11 | 1.64569 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.56051e11 | 0.602670 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.99098e10 | 0.0923157 | 0.0461579 | − | 0.998934i | \(-0.485302\pi\) | ||||
0.0461579 | + | 0.998934i | \(0.485302\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.34392e11 | 0.333987 | 0.166993 | − | 0.985958i | \(-0.446594\pi\) | ||||
0.166993 | + | 0.985958i | \(0.446594\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.24935e11 | 0.251751 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.43179e11 | −0.399935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.48519e11 | −0.470695 | −0.235348 | − | 0.971911i | \(-0.575623\pi\) | ||||
−0.235348 | + | 0.971911i | \(0.575623\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.05475e11 | 0.675425 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.31434e12 | 1.21766 | 0.608831 | − | 0.793300i | \(-0.291639\pi\) | ||||
0.608831 | + | 0.793300i | \(0.291639\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.17888e12 | −0.911737 | −0.455868 | − | 0.890047i | \(-0.650671\pi\) | ||||
−0.455868 | + | 0.890047i | \(0.650671\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.24575e11 | −0.145701 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.62897e12 | 1.43746 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.12403e12 | −0.377371 | −0.188685 | − | 0.982038i | \(-0.560423\pi\) | ||||
−0.188685 | + | 0.982038i | \(0.560423\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.54951e12 | −1.02081 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.13000e11 | 0.225733 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.49017e12 | 0.719653 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.46679e12 | 0.902580 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.42153e13 | −1.73276 | −0.866380 | − | 0.499385i | \(-0.833559\pi\) | ||||
−0.866380 | + | 0.499385i | \(0.833559\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.94306e12 | 0.634426 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.70194e13 | −1.59535 | −0.797675 | − | 0.603088i | \(-0.793937\pi\) | ||||
−0.797675 | + | 0.603088i | \(0.793937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.09904e13 | 0.906928 | 0.453464 | − | 0.891275i | \(-0.350188\pi\) | ||||
0.453464 | + | 0.891275i | \(0.350188\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.17736e12 | 0.377032 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.96403e13 | 1.26519 | 0.632593 | − | 0.774485i | \(-0.281991\pi\) | ||||
0.632593 | + | 0.774485i | \(0.281991\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.82099e12 | 0.560897 | 0.280448 | − | 0.959869i | \(-0.409517\pi\) | ||||
0.280448 | + | 0.959869i | \(0.409517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00818e12 | 0.203399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.70267e13 | −0.769344 | −0.384672 | − | 0.923053i | \(-0.625685\pi\) | ||||
−0.384672 | + | 0.923053i | \(0.625685\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.50911e13 | 1.01154 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.27789e12 | −0.154178 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.76216e13 | −0.891648 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.05347e13 | 2.62247 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41076e12 | −0.0888113 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.61839e13 | −1.08287 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.49347e13 | −0.950292 | −0.475146 | − | 0.879907i | \(-0.657605\pi\) | ||||
−0.475146 | + | 0.879907i | \(0.657605\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.18685e12 | −0.0990992 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.20182e12 | 0.0207768 | 0.0103884 | − | 0.999946i | \(-0.496693\pi\) | ||||
0.0103884 | + | 0.999946i | \(0.496693\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.03233e13 | 0.788375 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.17040e13 | 0.166404 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.71562e13 | 0.221685 | 0.110842 | − | 0.993838i | \(-0.464645\pi\) | ||||
0.110842 | + | 0.993838i | \(0.464645\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.05644e14 | −1.24236 | −0.621182 | − | 0.783666i | \(-0.713347\pi\) | ||||
−0.621182 | + | 0.783666i | \(0.713347\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.15265e13 | −0.230701 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.00181e13 | −0.880330 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.78350e13 | 0.338066 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.03429e13 | −0.248024 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.53533e13 | 0.639012 | 0.319506 | − | 0.947584i | \(-0.396483\pi\) | ||||
0.319506 | + | 0.947584i | \(0.396483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.16414e13 | −0.423177 | −0.211589 | − | 0.977359i | \(-0.567864\pi\) | ||||
−0.211589 | + | 0.977359i | \(0.567864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.24415e13 | −0.393531 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.86074e14 | 1.07778 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.18021e14 | 0.628942 | 0.314471 | − | 0.949267i | \(-0.398173\pi\) | ||||
0.314471 | + | 0.949267i | \(0.398173\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.48807e14 | 0.730369 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.95254e14 | 0.883550 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.54710e14 | −0.646099 | −0.323050 | − | 0.946382i | \(-0.604708\pi\) | ||||
−0.323050 | + | 0.946382i | \(0.604708\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.46282e14 | 0.950139 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.76012e14 | 1.34136 | 0.670679 | − | 0.741748i | \(-0.266003\pi\) | ||||
0.670679 | + | 0.741748i | \(0.266003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.38079e14 | −0.786063 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.13761e14 | 0.347951 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.73562e14 | −1.05941 | −0.529704 | − | 0.848182i | \(-0.677697\pi\) | ||||
−0.529704 | + | 0.848182i | \(0.677697\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.24210e13 | −0.190597 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.18043e13 | 0.0532985 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.23349e13 | −0.0961952 | −0.0480976 | − | 0.998843i | \(-0.515316\pi\) | ||||
−0.0480976 | + | 0.998843i | \(0.515316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.10447e14 | 0.656261 | 0.328130 | − | 0.944632i | \(-0.393581\pi\) | ||||
0.328130 | + | 0.944632i | \(0.393581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.79718e13 | 0.192827 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.66100e14 | 0.304617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.31393e15 | −2.24700 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.10779e13 | 0.145349 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.62273e14 | −1.28507 | −0.642537 | − | 0.766255i | \(-0.722118\pi\) | ||||
−0.642537 | + | 0.766255i | \(0.722118\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.37837e14 | −1.30618 | −0.653092 | − | 0.757278i | \(-0.726529\pi\) | ||||
−0.653092 | + | 0.757278i | \(0.726529\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.77277e14 | −0.230902 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.71715e14 | 0.818756 | 0.409378 | − | 0.912365i | \(-0.365746\pi\) | ||||
0.409378 | + | 0.912365i | \(0.365746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −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 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.94424e14 | 0.295290 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.41343e14 | −0.133007 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.41391e14 | 0.389957 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.39383e15 | 1.98675 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.62162e15 | 1.26507 | 0.632534 | − | 0.774533i | \(-0.282015\pi\) | ||||
0.632534 | + | 0.774533i | \(0.282015\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.58151e14 | 0.703018 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.14945e14 | −0.148415 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.44799e15 | 0.941406 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.59401e14 | −0.526392 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.45786e14 | 0.546064 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.47333e15 | 0.802266 | 0.401133 | − | 0.916020i | \(-0.368617\pi\) | ||||
0.401133 | + | 0.916020i | \(0.368617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.63715e14 | −0.0841207 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.74889e15 | 1.81859 | 0.909294 | − | 0.416153i | \(-0.136622\pi\) | ||||
0.909294 | + | 0.416153i | \(0.136622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.47993e13 | 0.00678126 | 0.00339063 | − | 0.999994i | \(-0.498921\pi\) | ||||
0.00339063 | + | 0.999994i | \(0.498921\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.91652e15 | 0.829917 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.63053e15 | 1.48647 | 0.743236 | − | 0.669030i | \(-0.233290\pi\) | ||||
0.743236 | + | 0.669030i | \(0.233290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.92064e14 | −0.345506 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.81795e14 | −0.286569 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.334416\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.25742e15 | −0.371450 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.72311e15 | −0.482818 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.19414e14 | −0.217875 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.75146e15 | 0.442099 | 0.221050 | − | 0.975263i | \(-0.429052\pi\) | ||||
0.221050 | + | 0.975263i | \(0.429052\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.28803e15 | 2.22659 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.58759e15 | −0.589366 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.87604e15 | 1.05561 | 0.527803 | − | 0.849367i | \(-0.323016\pi\) | ||||
0.527803 | + | 0.849367i | \(0.323016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.29256e15 | 0.266074 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.65577e14 | 0.130327 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.67882e15 | 0.871815 | 0.435907 | − | 0.899992i | \(-0.356428\pi\) | ||||
0.435907 | + | 0.899992i | \(0.356428\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.16662e15 | 1.09383 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.62976e15 | 0.275296 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.80262e15 | 0.290078 | 0.145039 | − | 0.989426i | \(-0.453669\pi\) | ||||
0.145039 | + | 0.989426i | \(0.453669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.10016e15 | 0.935494 | 0.467747 | − | 0.883862i | \(-0.345066\pi\) | ||||
0.467747 | + | 0.883862i | \(0.345066\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.37954e15 | −0.201686 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.44500e15 | −0.480315 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.07023e16 | 1.42351 | 0.711754 | − | 0.702428i | \(-0.247901\pi\) | ||||
0.711754 | + | 0.702428i | \(0.247901\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.27333e15 | 0.415492 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.45460e15 | −0.297433 | −0.148717 | − | 0.988880i | \(-0.547514\pi\) | ||||
−0.148717 | + | 0.988880i | \(0.547514\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.01155e15 | −0.464195 | −0.232098 | − | 0.972692i | \(-0.574559\pi\) | ||||
−0.232098 | + | 0.972692i | \(0.574559\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.71429e15 | 0.521105 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.09990e15 | −0.116178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.90041e15 | 0.393799 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.03629e16 | −1.00041 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.08187e15 | −0.192227 | −0.0961133 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961133 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.03576e14 | 0.0798218 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.33249e15 | 0.366286 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.68565e15 | −0.541104 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.67265e15 | −0.129636 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.24072e16 | −0.921075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.05998e15 | 0.288785 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.32352e16 | 0.902260 | 0.451130 | − | 0.892458i | \(-0.351021\pi\) | ||||
0.451130 | + | 0.892458i | \(0.351021\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.01202e15 | 0.523615 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.09301e15 | −0.507187 | −0.253593 | − | 0.967311i | \(-0.581612\pi\) | ||||
−0.253593 | + | 0.967311i | \(0.581612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.48181e16 | −0.890748 | −0.445374 | − | 0.895345i | \(-0.646929\pi\) | ||||
−0.445374 | + | 0.895345i | \(0.646929\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.77430e15 | 0.217680 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.43171e16 | 1.34594 | 0.672970 | − | 0.739670i | \(-0.265018\pi\) | ||||
0.672970 | + | 0.739670i | \(0.265018\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.40055e16 | 0.744147 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.43178e16 | 0.730455 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.51511e16 | −1.23237 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.47976e15 | 0.116726 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.15950e15 | 0.323834 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.94186e15 | −0.301788 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.16232e16 | −0.485783 | −0.242892 | − | 0.970053i | \(-0.578096\pi\) | ||||
−0.242892 | + | 0.970053i | \(0.578096\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.92196e15 | 0.117432 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.05288e16 | −0.406992 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.62652e16 | 1.72052 | 0.860262 | − | 0.509853i | \(-0.170300\pi\) | ||||
0.860262 | + | 0.509853i | \(0.170300\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.24125e16 | −0.444181 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.88795e16 | 2.37239 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.25624e16 | −1.07970 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.82914e16 | 0.584013 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.79404e15 | −0.147421 | −0.0737106 | − | 0.997280i | \(-0.523484\pi\) | ||||
−0.0737106 | + | 0.997280i | \(0.523484\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.76900e16 | −1.11651 | −0.558253 | − | 0.829671i | \(-0.688528\pi\) | ||||
−0.558253 | + | 0.829671i | \(0.688528\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.11859e15 | −0.0890146 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.80179e16 | 1.32089 | 0.660446 | − | 0.750873i | \(-0.270367\pi\) | ||||
0.660446 | + | 0.750873i | \(0.270367\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.97061e16 | 1.05286 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.01361e16 | −0.514793 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.59998e16 | 1.51408 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.56138e16 | −0.788343 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.96733e16 | 0.633923 | 0.316961 | − | 0.948438i | \(-0.397337\pi\) | ||||
0.316961 | + | 0.948438i | \(0.397337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.48645e15 | −0.0512752 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.79873e16 | 0.955424 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.01346e16 | 1.73294 | 0.866471 | − | 0.499227i | \(-0.166383\pi\) | ||||
0.866471 | + | 0.499227i | \(0.166383\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.36681e16 | −0.625194 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00813e16 | −0.180842 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54841e16 | 0.268369 | 0.134184 | − | 0.990956i | \(-0.457159\pi\) | ||||
0.134184 | + | 0.990956i | \(0.457159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.27574e16 | −0.548652 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.37088e15 | 0.151701 | 0.0758505 | − | 0.997119i | \(-0.475833\pi\) | ||||
0.0758505 | + | 0.997119i | \(0.475833\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.94211e16 | 1.24291 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.78121e15 | −0.0572150 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.95806e16 | −0.432847 | −0.216423 | − | 0.976300i | \(-0.569439\pi\) | ||||
−0.216423 | + | 0.976300i | \(0.569439\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.75858e16 | −1.38114 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.76130e14 | 0.0119955 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.23978e16 | −0.429175 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.80617e16 | −0.231538 | −0.115769 | − | 0.993276i | \(-0.536933\pi\) | ||||
−0.115769 | + | 0.993276i | \(0.536933\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.66857e16 | 0.455169 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.20412e17 | −1.44621 | −0.723107 | − | 0.690736i | \(-0.757287\pi\) | ||||
−0.723107 | + | 0.690736i | \(0.757287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.95804e16 | −0.576537 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.53220e15 | 0.0960734 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.14858e16 | 0.670519 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −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 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.03144e15 | 0.0697219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.39568e16 | −0.326298 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.70145e16 | −0.717279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.75670e17 | −1.58602 | −0.793008 | − | 0.609212i | \(-0.791486\pi\) | ||||
−0.793008 | + | 0.609212i | \(0.791486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.84473e17 | −1.61473 | −0.807365 | − | 0.590052i | \(-0.799107\pi\) | ||||
−0.807365 | + | 0.590052i | \(0.799107\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.56928e16 | −0.133195 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.61953e16 | 0.297937 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.15939e16 | 0.252245 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.56232e16 | −0.508259 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.05532e16 | 0.605314 | 0.302657 | − | 0.953100i | \(-0.402126\pi\) | ||||
0.302657 | + | 0.953100i | \(0.402126\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.97092e17 | −1.43714 | −0.718568 | − | 0.695457i | \(-0.755202\pi\) | ||||
−0.718568 | + | 0.695457i | \(0.755202\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.75817e16 | 0.195183 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.77790e17 | 1.22117 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 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 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.25104e17 | 0.786404 | 0.393202 | − | 0.919452i | \(-0.371367\pi\) | ||||
0.393202 | + | 0.919452i | \(0.371367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.75378e16 | 0.412294 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.22225e16 | 0.368934 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.49366e16 | −0.244322 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.71684e16 | −0.302052 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.43597e16 | −0.484542 | −0.242271 | − | 0.970209i | \(-0.577892\pi\) | ||||
−0.242271 | + | 0.970209i | \(0.577892\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.55198e16 | −0.227205 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.00500e16 | −0.388423 | −0.194212 | − | 0.980960i | \(-0.562215\pi\) | ||||
−0.194212 | + | 0.980960i | \(0.562215\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.14174e17 | 1.01039 | 0.505196 | − | 0.863004i | \(-0.331420\pi\) | ||||
0.505196 | + | 0.863004i | \(0.331420\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.35648e17 | 0.622256 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.80681e17 | 0.806031 | 0.403015 | − | 0.915193i | \(-0.367962\pi\) | ||||
0.403015 | + | 0.915193i | \(0.367962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.19326e16 | −0.355495 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.60372e16 | 0.363120 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.95665e16 | −0.326688 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.59435e16 | −0.263429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.08480e17 | 0.421679 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.42340e17 | 0.510118 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.29443e17 | −1.49825 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.63552e17 | −0.895216 | −0.447608 | − | 0.894230i | \(-0.647724\pi\) | ||||
−0.447608 | + | 0.894230i | \(0.647724\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.12784e17 | −0.373026 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.11733e17 | −1.32613 | −0.663065 | − | 0.748562i | \(-0.730745\pi\) | ||||
−0.663065 | + | 0.748562i | \(0.730745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.47150e17 | −0.461590 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.79540e17 | 0.548563 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.08984e17 | 0.919645 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.99658e17 | −1.15887 | −0.579435 | − | 0.815018i | \(-0.696727\pi\) | ||||
−0.579435 | + | 0.815018i | \(0.696727\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.74113e17 | 0.774433 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.83581e17 | −0.780702 | −0.390351 | − | 0.920666i | \(-0.627646\pi\) | ||||
−0.390351 | + | 0.920666i | \(0.627646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.14157e17 | −1.37944 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.73559e17 | −0.453834 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.40327e17 | −1.63206 | −0.816030 | − | 0.578009i | \(-0.803830\pi\) | ||||
−0.816030 | + | 0.578009i | \(0.803830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.77140e17 | −0.688593 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.29318e16 | 0.200890 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.32021e17 | 0.784185 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.30218e17 | −0.760522 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.72327e17 | −0.611650 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.01348e17 | −0.879175 | −0.439588 | − | 0.898200i | \(-0.644875\pi\) | ||||
−0.439588 | + | 0.898200i | \(0.644875\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.05985e17 | 1.08113 | 0.540564 | − | 0.841303i | \(-0.318211\pi\) | ||||
0.540564 | + | 0.841303i | \(0.318211\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.27949e16 | −0.110041 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.23691e17 | −1.47158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.85786e17 | 0.368597 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.58953e16 | 0.0307719 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.76616e16 | 0.0711496 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.93334e17 | 1.09396 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.08621e16 | −0.0555383 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.65462e17 | −0.817631 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.69124e17 | 0.290017 | 0.145009 | − | 0.989430i | \(-0.453679\pi\) | ||||
0.145009 | + | 0.989430i | \(0.453679\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.26316e17 | 0.378892 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.96692e17 | 0.484986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.32104e17 | 0.689717 | 0.344858 | − | 0.938655i | \(-0.387927\pi\) | ||||
0.344858 | + | 0.938655i | \(0.387927\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.14214e16 | 0.111329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.68091e17 | 0.408128 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.52113e17 | −0.374871 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.21087e17 | 0.175871 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.36804e18 | −1.94107 | −0.970534 | − | 0.240966i | \(-0.922536\pi\) | ||||
−0.970534 | + | 0.240966i | \(0.922536\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.72731e16 | 0.0793915 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.57856e17 | −1.29730 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.52405e17 | 1.26043 | 0.630213 | − | 0.776422i | \(-0.282968\pi\) | ||||
0.630213 | + | 0.776422i | \(0.282968\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.14377e17 | −0.665221 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.63958e16 | 0.0839171 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 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 | \(-0.219007\pi\) | ||||
0.772498 | + | 0.635017i | \(0.219007\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.28597e17 | −0.741938 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.55860e17 | −0.295231 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.56770e17 | 0.402481 | 0.201241 | − | 0.979542i | \(-0.435503\pi\) | ||||
0.201241 | + | 0.979542i | \(0.435503\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.83683e17 | −0.754126 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.64245e17 | −0.285011 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.28271e18 | 2.40772 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.29235e17 | −0.133312 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.28968e18 | −1.30118 | −0.650588 | − | 0.759431i | \(-0.725477\pi\) | ||||
−0.650588 | + | 0.759431i | \(0.725477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31848e18 | 1.30114 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.89680e17 | 0.472709 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.88640e18 | −1.78147 | −0.890735 | − | 0.454523i | \(-0.849810\pi\) | ||||
−0.890735 | + | 0.454523i | \(0.849810\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.34448e17 | −0.770973 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.18173e16 | −0.0287627 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(0.506122\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.85217e17 | −0.156898 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.73505e18 | 2.26755 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.98050e16 | 0.0241860 | 0.0120930 | − | 0.999927i | \(-0.496151\pi\) | ||||
0.0120930 | + | 0.999927i | \(0.496151\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.14635e17 | 0.170486 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.37695e17 | 0.184822 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.84082e17 | 0.672976 | 0.336488 | − | 0.941688i | \(-0.390761\pi\) | ||||
0.336488 | + | 0.941688i | \(0.390761\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.03039e17 | −0.0767917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.43684e18 | 1.04846 | 0.524232 | − | 0.851575i | \(-0.324352\pi\) | ||||
0.524232 | + | 0.851575i | \(0.324352\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.68862e18 | −1.20654 | −0.603272 | − | 0.797535i | \(-0.706137\pi\) | ||||
−0.603272 | + | 0.797535i | \(0.706137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.21774e17 | 0.225142 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.25565e17 | 0.360126 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.01917e18 | −0.683951 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.74510e18 | 1.14705 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.46008e17 | −0.415919 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.53490e17 | −0.222939 | −0.111470 | − | 0.993768i | \(-0.535556\pi\) | ||||
−0.111470 | + | 0.993768i | \(0.535556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.18216e18 | 0.730387 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.35748e18 | −0.821680 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.35046e17 | 0.198700 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.98492e17 | 0.405888 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.61802e18 | 0.921313 | 0.460656 | − | 0.887579i | \(-0.347614\pi\) | ||||
0.460656 | + | 0.887579i | \(0.347614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.96065e18 | 1.09403 | 0.547015 | − | 0.837123i | \(-0.315764\pi\) | ||||
0.547015 | + | 0.837123i | \(0.315764\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.56695e17 | −0.0856872 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.96114e17 | −0.319486 | −0.159743 | − | 0.987159i | \(-0.551067\pi\) | ||||
−0.159743 | + | 0.987159i | \(0.551067\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.34479e17 | 0.175703 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.05558e18 | 0.543521 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.58318e18 | 1.30382 | 0.651912 | − | 0.758295i | \(-0.273967\pi\) | ||||
0.651912 | + | 0.758295i | \(0.273967\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.63071e16 | 0.0179648 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.26503e17 | −0.303912 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.64137e18 | −1.25624 | −0.628121 | − | 0.778116i | \(-0.716176\pi\) | ||||
−0.628121 | + | 0.778116i | \(0.716176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.12451e18 | −1.92337 | −0.961685 | − | 0.274156i | \(-0.911602\pi\) | ||||
−0.961685 | + | 0.274156i | \(0.911602\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.89478e17 | 0.315270 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.52027e18 | 0.681677 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.04019e18 | 0.457398 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.07406e18 | 0.463189 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.50289e18 | 0.635670 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.79726e18 | 1.16047 | 0.580236 | − | 0.814449i | \(-0.302961\pi\) | ||||
0.580236 | + | 0.814449i | \(0.302961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.19348e17 | −0.0485671 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.25553e18 | 1.69874 | 0.849372 | − | 0.527795i | \(-0.176981\pi\) | ||||
0.849372 | + | 0.527795i | \(0.176981\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.34184e18 | −1.30867 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.73294e18 | 1.04996 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.60893e18 | −0.606461 | −0.303230 | − | 0.952917i | \(-0.598065\pi\) | ||||
−0.303230 | + | 0.952917i | \(0.598065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.18287e17 | 0.191682 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.07887e16 | 0.00391516 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.64313e18 | −0.585122 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.06331e18 | 1.07049 | 0.535247 | − | 0.844696i | \(-0.320218\pi\) | ||||
0.535247 | + | 0.844696i | \(0.320218\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.39714e18 | 0.479153 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.19151e18 | −1.07422 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.49721e17 | 0.181606 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.64666e18 | 0.858214 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.99144e18 | −0.952166 | −0.476083 | − | 0.879400i | \(-0.657944\pi\) | ||||
−0.476083 | + | 0.879400i | \(0.657944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.17695e18 | 0.367747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.50315e17 | −0.199478 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.00106e18 | −1.20489 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.31694e18 | 1.57203 | 0.786015 | − | 0.618207i | \(-0.212141\pi\) | ||||
0.786015 | + | 0.618207i | \(0.212141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.69928e17 | −0.165450 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.11568e18 | 1.45822 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.71945e18 | −0.761187 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.16313e18 | −0.869446 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.20429e18 | 0.573945 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.85813e17 | −0.0986688 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.77643e18 | −1.19986 | −0.599928 | − | 0.800054i | \(-0.704804\pi\) | ||||
−0.599928 | + | 0.800054i | \(0.704804\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.35976e17 | 0.202643 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.71668e18 | −0.408803 | −0.204401 | − | 0.978887i | \(-0.565525\pi\) | ||||
−0.204401 | + | 0.978887i | \(0.565525\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.16659e17 | −0.214457 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.89745e18 | −0.895864 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.69723e17 | 0.196423 | 0.0982114 | − | 0.995166i | \(-0.468688\pi\) | ||||
0.0982114 | + | 0.995166i | \(0.468688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.25615e18 | −0.278755 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.40272e18 | 0.523933 | 0.261966 | − | 0.965077i | \(-0.415629\pi\) | ||||
0.261966 | + | 0.965077i | \(0.415629\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.57852e18 | 0.552529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.97353e17 | −0.125790 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.61721e18 | 0.955537 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.37175e18 | 1.90617 | 0.953084 | − | 0.302706i | \(-0.0978899\pi\) | ||||
0.953084 | + | 0.302706i | \(0.0978899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.27681e18 | 0.255246 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.86219e18 | −0.365905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.09120e18 | −0.597040 | −0.298520 | − | 0.954403i | \(-0.596493\pi\) | ||||
−0.298520 | + | 0.954403i | \(0.596493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.77097e18 | 1.28552 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.97787e18 | −1.48897 | −0.744486 | − | 0.667638i | \(-0.767306\pi\) | ||||
−0.744486 | + | 0.667638i | \(0.767306\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.30880e18 | 0.423620 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.88636e18 | −0.340271 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.40763e17 | −0.0426991 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.67335e18 | 0.282111 | 0.141056 | − | 0.990002i | \(-0.454950\pi\) | ||||
0.141056 | + | 0.990002i | \(0.454950\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.89744e18 | −0.314563 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.42275e17 | 0.153618 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.00153e18 | −0.160572 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.46981e19 | 2.31755 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.85206e17 | 0.0752444 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.56541e18 | 0.543822 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.75359e18 | 0.563133 | 0.281566 | − | 0.959542i | \(-0.409146\pi\) | ||||
0.281566 | + | 0.959542i | \(0.409146\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.41086e18 | 0.503342 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.00277e18 | −0.581050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.08180e18 | −0.154480 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.49546e18 | 0.631522 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.38853e18 | −0.468309 | −0.234154 | − | 0.972199i | \(-0.575232\pi\) | ||||
−0.234154 | + | 0.972199i | \(0.575232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.46947e18 | 0.471747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.18810e18 | 0.158942 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.31833e19 | −1.73529 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.89861e18 | 0.763971 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.31411e18 | 0.167476 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −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 | \(-0.723669\pi\) | ||||
−0.646264 | + | 0.763114i | \(0.723669\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.44702e18 | 0.540108 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.67379e18 | −0.558657 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.52305e18 | −0.179172 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00568e18 | −0.116443 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.85162e18 | 0.780841 | 0.390421 | − | 0.920637i | \(-0.372330\pi\) | ||||
0.390421 | + | 0.920637i | \(0.372330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.06934e17 | 0.0344308 | 0.0172154 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172154 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.51140e18 | −0.277310 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.75365e18 | −0.842792 | −0.421396 | − | 0.906877i | \(-0.638460\pi\) | ||||
−0.421396 | + | 0.906877i | \(0.638460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34336e18 | −0.250747 | −0.125373 | − | 0.992110i | \(-0.540013\pi\) | ||||
−0.125373 | + | 0.992110i | \(0.540013\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.80200e18 | 0.821863 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.89044e18 | 0.507172 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.13593e19 | 1.15982 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.38626e18 | 0.239884 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.78940e18 | −0.171723 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.19236e18 | −0.679677 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12836e19 | 1.98063 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.92442e18 | −0.268003 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.56655e18 | 0.412142 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.93794e19 | −1.72255 | −0.861276 | − | 0.508137i | \(-0.830334\pi\) | ||||
−0.861276 | + | 0.508137i | \(0.830334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.43672e18 | 0.300860 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.20537e19 | 1.03931 | 0.519656 | − | 0.854376i | \(-0.326060\pi\) | ||||
0.519656 | + | 0.854376i | \(0.326060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.00612e19 | 0.854465 | 0.427232 | − | 0.904142i | \(-0.359489\pi\) | ||||
0.427232 | + | 0.904142i | \(0.359489\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.01830e17 | −0.0670751 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.01407e18 | 0.660363 | 0.330182 | − | 0.943917i | \(-0.392890\pi\) | ||||
0.330182 | + | 0.943917i | \(0.392890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.12853e19 | −0.916029 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.84340e18 | 0.227360 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.19928e19 | −0.944694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.80544e18 | 0.217712 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.55457e18 | −0.577587 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.08573e19 | −0.817841 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.87791e17 | −0.0658891 | −0.0329445 | − | 0.999457i | \(-0.510488\pi\) | ||||
−0.0329445 | + | 0.999457i | \(0.510488\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.51768e18 | −0.110982 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.78774e18 | 0.272921 | 0.136460 | − | 0.990646i | \(-0.456427\pi\) | ||||
0.136460 | + | 0.990646i | \(0.456427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.75428e19 | 1.95553 | 0.977763 | − | 0.209712i | \(-0.0672526\pi\) | ||||
0.977763 | + | 0.209712i | \(0.0672526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.58707e17 | 0.0460851 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.84165e19 | −1.95914 | −0.979572 | − | 0.201092i | \(-0.935551\pi\) | ||||
−0.979572 | + | 0.201092i | \(0.935551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.05636e19 | −0.717712 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.15838e18 | 0.211475 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.32097e18 | −0.417109 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.27894e18 | −0.0831762 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.87384e18 | −0.312407 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.71397e18 | 0.487349 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.39836e19 | −1.49349 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.21937e18 | −0.0748451 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.37860e18 | 0.567443 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.51023e18 | −0.447926 | −0.223963 | − | 0.974598i | \(-0.571899\pi\) | ||||
−0.223963 | + | 0.974598i | \(0.571899\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.04482e18 | −0.531783 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.34028e19 | −1.35643 | −0.678216 | − | 0.734863i | \(-0.737247\pi\) | ||||
−0.678216 | + | 0.734863i | \(0.737247\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.25699e19 | −0.718242 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.95973e18 | 0.166730 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.82535e17 | 0.0156917 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 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 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.05799e19 | −0.563210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.69377e18 | −0.0889063 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.84077e18 | 0.302309 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.89981e18 | −0.292824 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.96939e19 | −1.94289 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.72833e19 | −0.834294 | −0.417147 | − | 0.908839i | \(-0.636970\pi\) | ||||
−0.417147 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.08024e19 | −0.514273 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.14038e19 | −1.00498 | −0.502490 | − | 0.864583i | \(-0.667583\pi\) | ||||
−0.502490 | + | 0.864583i | \(0.667583\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.88591e18 | −0.179956 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.75146e18 | 0.125677 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.91308e17 | 0.0266403 | 0.0133202 | − | 0.999911i | \(-0.495760\pi\) | ||||
0.0133202 | + | 0.999911i | \(0.495760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.48950e18 | 0.421709 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.77271e19 | 0.777079 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.39396e19 | −1.03517 | −0.517587 | − | 0.855631i | \(-0.673170\pi\) | ||||
−0.517587 | + | 0.855631i | \(0.673170\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.60493e19 | −1.11115 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.02100e19 | 0.429633 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.03321e18 | 0.167429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.35201e19 | 0.553702 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.04377e19 | 0.421729 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.83320e19 | −1.12941 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.99045e18 | 0.0782853 | 0.0391427 | − | 0.999234i | \(-0.487537\pi\) | ||||
0.0391427 | + | 0.999234i | \(0.487537\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.83351e19 | −0.711507 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.12385e19 | −1.57898 | −0.789492 | − | 0.613761i | \(-0.789656\pi\) | ||||
−0.789492 | + | 0.613761i | \(0.789656\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.48357e19 | −0.938301 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.80774e18 | 0.0673917 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.25374e19 | −0.461202 | −0.230601 | − | 0.973048i | \(-0.574069\pi\) | ||||
−0.230601 | + | 0.973048i | \(0.574069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50006e19 | 0.907535 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.21928e18 | 0.186966 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.83966e19 | −0.650340 | −0.325170 | − | 0.945656i | \(-0.605422\pi\) | ||||
−0.325170 | + | 0.945656i | \(0.605422\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.02925e19 | 0.707946 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.06062e18 | −0.174238 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.90941e18 | −0.200802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.43064e19 | −1.15053 | −0.575263 | − | 0.817969i | \(-0.695100\pi\) | ||||
−0.575263 | + | 0.817969i | \(0.695100\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.47329e18 | −0.280467 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.31852e18 | −0.0430761 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.72458e19 | 1.84597 | 0.922985 | − | 0.384835i | \(-0.125742\pi\) | ||||
0.922985 | + | 0.384835i | \(0.125742\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 192.14.a.j.1.1 | 1 | ||
4.3 | odd | 2 | 192.14.a.e.1.1 | 1 | |||
8.3 | odd | 2 | 48.14.a.c.1.1 | 1 | |||
8.5 | even | 2 | 3.14.a.a.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 9.14.a.a.1.1 | 1 | |||
24.11 | even | 2 | 144.14.a.k.1.1 | 1 | |||
40.13 | odd | 4 | 75.14.b.b.49.2 | 2 | |||
40.29 | even | 2 | 75.14.a.a.1.1 | 1 | |||
40.37 | odd | 4 | 75.14.b.b.49.1 | 2 | |||
56.13 | odd | 2 | 147.14.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.14.a.a.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
9.14.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
48.14.a.c.1.1 | 1 | 8.3 | odd | 2 | |||
75.14.a.a.1.1 | 1 | 40.29 | even | 2 | |||
75.14.b.b.49.1 | 2 | 40.37 | odd | 4 | |||
75.14.b.b.49.2 | 2 | 40.13 | odd | 4 | |||
144.14.a.k.1.1 | 1 | 24.11 | even | 2 | |||
147.14.a.a.1.1 | 1 | 56.13 | odd | 2 | |||
192.14.a.e.1.1 | 1 | 4.3 | odd | 2 | |||
192.14.a.j.1.1 | 1 | 1.1 | even | 1 | trivial |