Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 28.6118 | 0.316119 | 0.158060 | − | 0.987430i | \(-0.449476\pi\) | ||||
0.158060 | + | 0.987430i | \(0.449476\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −7373.36 | −0.900069 | ||||||||
\(5\) | 60045.3 | 1.71860 | 0.859298 | − | 0.511475i | \(-0.170901\pi\) | ||||
0.859298 | + | 0.511475i | \(0.170901\pi\) | |||||||
\(6\) | 20858.0 | 0.182511 | ||||||||
\(7\) | 428045. | 1.37516 | 0.687578 | − | 0.726110i | \(-0.258674\pi\) | ||||
0.687578 | + | 0.726110i | \(0.258674\pi\) | |||||||
\(8\) | −445354. | −0.600648 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 1.71801e6 | 0.543281 | ||||||||
\(11\) | −5.05028e6 | −0.859535 | −0.429767 | − | 0.902940i | \(-0.641404\pi\) | ||||
−0.429767 | + | 0.902940i | \(0.641404\pi\) | |||||||
\(12\) | −5.37518e6 | −0.519655 | ||||||||
\(13\) | 8.30885e6 | 0.477430 | 0.238715 | − | 0.971090i | \(-0.423274\pi\) | ||||
0.238715 | + | 0.971090i | \(0.423274\pi\) | |||||||
\(14\) | 1.22472e7 | 0.434713 | ||||||||
\(15\) | 4.37730e7 | 0.992232 | ||||||||
\(16\) | 4.76602e7 | 0.710193 | ||||||||
\(17\) | −3.21092e7 | −0.322635 | −0.161318 | − | 0.986903i | \(-0.551574\pi\) | ||||
−0.161318 | + | 0.986903i | \(0.551574\pi\) | |||||||
\(18\) | 1.52055e7 | 0.105373 | ||||||||
\(19\) | 9.20230e7 | 0.448744 | 0.224372 | − | 0.974504i | \(-0.427967\pi\) | ||||
0.224372 | + | 0.974504i | \(0.427967\pi\) | |||||||
\(20\) | −4.42736e8 | −1.54685 | ||||||||
\(21\) | 3.12045e8 | 0.793947 | ||||||||
\(22\) | −1.44498e8 | −0.271715 | ||||||||
\(23\) | 2.82456e8 | 0.397851 | 0.198925 | − | 0.980015i | \(-0.436255\pi\) | ||||
0.198925 | + | 0.980015i | \(0.436255\pi\) | |||||||
\(24\) | −3.24663e8 | −0.346784 | ||||||||
\(25\) | 2.38473e9 | 1.95357 | ||||||||
\(26\) | 2.37732e8 | 0.150925 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −3.15613e9 | −1.23774 | ||||||||
\(29\) | −1.86463e9 | −0.582110 | −0.291055 | − | 0.956706i | \(-0.594006\pi\) | ||||
−0.291055 | + | 0.956706i | \(0.594006\pi\) | |||||||
\(30\) | 1.25243e9 | 0.313663 | ||||||||
\(31\) | −1.29741e9 | −0.262558 | −0.131279 | − | 0.991345i | \(-0.541908\pi\) | ||||
−0.131279 | + | 0.991345i | \(0.541908\pi\) | |||||||
\(32\) | 5.01198e9 | 0.825153 | ||||||||
\(33\) | −3.68166e9 | −0.496253 | ||||||||
\(34\) | −9.18703e8 | −0.101991 | ||||||||
\(35\) | 2.57021e10 | 2.36334 | ||||||||
\(36\) | −3.91851e9 | −0.300023 | ||||||||
\(37\) | −5.91028e9 | −0.378701 | −0.189351 | − | 0.981910i | \(-0.560638\pi\) | ||||
−0.189351 | + | 0.981910i | \(0.560638\pi\) | |||||||
\(38\) | 2.63295e9 | 0.141856 | ||||||||
\(39\) | 6.05716e9 | 0.275644 | ||||||||
\(40\) | −2.67414e10 | −1.03227 | ||||||||
\(41\) | 4.67448e10 | 1.53687 | 0.768437 | − | 0.639926i | \(-0.221035\pi\) | ||||
0.768437 | + | 0.639926i | \(0.221035\pi\) | |||||||
\(42\) | 8.92817e9 | 0.250982 | ||||||||
\(43\) | 5.00850e10 | 1.20827 | 0.604134 | − | 0.796883i | \(-0.293519\pi\) | ||||
0.604134 | + | 0.796883i | \(0.293519\pi\) | |||||||
\(44\) | 3.72376e10 | 0.773640 | ||||||||
\(45\) | 3.19105e10 | 0.572865 | ||||||||
\(46\) | 8.08158e9 | 0.125768 | ||||||||
\(47\) | 5.50206e10 | 0.744542 | 0.372271 | − | 0.928124i | \(-0.378579\pi\) | ||||
0.372271 | + | 0.928124i | \(0.378579\pi\) | |||||||
\(48\) | 3.47443e10 | 0.410030 | ||||||||
\(49\) | 8.63335e10 | 0.891056 | ||||||||
\(50\) | 6.82315e10 | 0.617561 | ||||||||
\(51\) | −2.34076e10 | −0.186273 | ||||||||
\(52\) | −6.12642e10 | −0.429720 | ||||||||
\(53\) | −5.12531e10 | −0.317634 | −0.158817 | − | 0.987308i | \(-0.550768\pi\) | ||||
−0.158817 | + | 0.987308i | \(0.550768\pi\) | |||||||
\(54\) | 1.10848e10 | 0.0608371 | ||||||||
\(55\) | −3.03246e11 | −1.47719 | ||||||||
\(56\) | −1.90631e11 | −0.825985 | ||||||||
\(57\) | 6.70848e10 | 0.259082 | ||||||||
\(58\) | −5.33504e10 | −0.184016 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −3.22754e11 | −0.893077 | ||||||||
\(61\) | 4.21271e11 | 1.04693 | 0.523465 | − | 0.852047i | \(-0.324639\pi\) | ||||
0.523465 | + | 0.852047i | \(0.324639\pi\) | |||||||
\(62\) | −3.71212e10 | −0.0829996 | ||||||||
\(63\) | 2.27481e11 | 0.458386 | ||||||||
\(64\) | −2.47031e11 | −0.449346 | ||||||||
\(65\) | 4.98907e11 | 0.820509 | ||||||||
\(66\) | −1.05339e11 | −0.156875 | ||||||||
\(67\) | −6.77755e9 | −0.00915348 | −0.00457674 | − | 0.999990i | \(-0.501457\pi\) | ||||
−0.00457674 | + | 0.999990i | \(0.501457\pi\) | |||||||
\(68\) | 2.36753e11 | 0.290394 | ||||||||
\(69\) | 2.05910e11 | 0.229699 | ||||||||
\(70\) | 7.35384e11 | 0.747096 | ||||||||
\(71\) | 6.84243e11 | 0.633915 | 0.316958 | − | 0.948440i | \(-0.397339\pi\) | ||||
0.316958 | + | 0.948440i | \(0.397339\pi\) | |||||||
\(72\) | −2.36679e11 | −0.200216 | ||||||||
\(73\) | −1.74954e12 | −1.35308 | −0.676542 | − | 0.736404i | \(-0.736522\pi\) | ||||
−0.676542 | + | 0.736404i | \(0.736522\pi\) | |||||||
\(74\) | −1.69104e11 | −0.119715 | ||||||||
\(75\) | 1.73847e12 | 1.12790 | ||||||||
\(76\) | −6.78519e11 | −0.403900 | ||||||||
\(77\) | −2.16175e12 | −1.18199 | ||||||||
\(78\) | 1.73306e11 | 0.0871364 | ||||||||
\(79\) | −4.15612e12 | −1.92359 | −0.961794 | − | 0.273773i | \(-0.911728\pi\) | ||||
−0.961794 | + | 0.273773i | \(0.911728\pi\) | |||||||
\(80\) | 2.86177e12 | 1.22053 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 1.33745e12 | 0.485835 | ||||||||
\(83\) | 1.01331e12 | 0.340201 | 0.170101 | − | 0.985427i | \(-0.445591\pi\) | ||||
0.170101 | + | 0.985427i | \(0.445591\pi\) | |||||||
\(84\) | −2.30082e12 | −0.714607 | ||||||||
\(85\) | −1.92801e12 | −0.554479 | ||||||||
\(86\) | 1.43302e12 | 0.381956 | ||||||||
\(87\) | −1.35931e12 | −0.336081 | ||||||||
\(88\) | 2.24916e12 | 0.516278 | ||||||||
\(89\) | −4.21516e12 | −0.899039 | −0.449520 | − | 0.893270i | \(-0.648405\pi\) | ||||
−0.449520 | + | 0.893270i | \(0.648405\pi\) | |||||||
\(90\) | 9.13018e11 | 0.181094 | ||||||||
\(91\) | 3.55656e12 | 0.656541 | ||||||||
\(92\) | −2.08265e12 | −0.358093 | ||||||||
\(93\) | −9.45810e11 | −0.151588 | ||||||||
\(94\) | 1.57424e12 | 0.235364 | ||||||||
\(95\) | 5.52555e12 | 0.771209 | ||||||||
\(96\) | 3.65373e12 | 0.476402 | ||||||||
\(97\) | −3.08119e12 | −0.375580 | −0.187790 | − | 0.982209i | \(-0.560132\pi\) | ||||
−0.187790 | + | 0.982209i | \(0.560132\pi\) | |||||||
\(98\) | 2.47016e12 | 0.281680 | ||||||||
\(99\) | −2.68393e12 | −0.286512 | ||||||||
\(100\) | −1.75835e13 | −1.75835 | ||||||||
\(101\) | 3.98600e12 | 0.373635 | 0.186818 | − | 0.982395i | \(-0.440183\pi\) | ||||
0.186818 | + | 0.982395i | \(0.440183\pi\) | |||||||
\(102\) | −6.69734e11 | −0.0588846 | ||||||||
\(103\) | −6.75982e12 | −0.557818 | −0.278909 | − | 0.960317i | \(-0.589973\pi\) | ||||
−0.278909 | + | 0.960317i | \(0.589973\pi\) | |||||||
\(104\) | −3.70038e12 | −0.286767 | ||||||||
\(105\) | 1.87368e13 | 1.36447 | ||||||||
\(106\) | −1.46644e12 | −0.100410 | ||||||||
\(107\) | 1.94180e13 | 1.25086 | 0.625432 | − | 0.780279i | \(-0.284923\pi\) | ||||
0.625432 | + | 0.780279i | \(0.284923\pi\) | |||||||
\(108\) | −2.85659e12 | −0.173218 | ||||||||
\(109\) | 3.32706e13 | 1.90015 | 0.950076 | − | 0.312018i | \(-0.101005\pi\) | ||||
0.950076 | + | 0.312018i | \(0.101005\pi\) | |||||||
\(110\) | −8.67642e12 | −0.466969 | ||||||||
\(111\) | −4.30859e12 | −0.218643 | ||||||||
\(112\) | 2.04007e13 | 0.976626 | ||||||||
\(113\) | 2.33760e13 | 1.05623 | 0.528116 | − | 0.849172i | \(-0.322899\pi\) | ||||
0.528116 | + | 0.849172i | \(0.322899\pi\) | |||||||
\(114\) | 1.91942e12 | 0.0819008 | ||||||||
\(115\) | 1.69602e13 | 0.683744 | ||||||||
\(116\) | 1.37486e13 | 0.523939 | ||||||||
\(117\) | 4.41567e12 | 0.159143 | ||||||||
\(118\) | −1.20686e12 | −0.0411552 | ||||||||
\(119\) | −1.37442e13 | −0.443674 | ||||||||
\(120\) | −1.94945e13 | −0.595982 | ||||||||
\(121\) | −9.01734e12 | −0.261200 | ||||||||
\(122\) | 1.20533e13 | 0.330955 | ||||||||
\(123\) | 3.40769e13 | 0.887314 | ||||||||
\(124\) | 9.56625e12 | 0.236320 | ||||||||
\(125\) | 6.98944e13 | 1.63881 | ||||||||
\(126\) | 6.50864e12 | 0.144904 | ||||||||
\(127\) | −2.01180e13 | −0.425461 | −0.212730 | − | 0.977111i | \(-0.568236\pi\) | ||||
−0.212730 | + | 0.977111i | \(0.568236\pi\) | |||||||
\(128\) | −4.81261e13 | −0.967200 | ||||||||
\(129\) | 3.65120e13 | 0.697593 | ||||||||
\(130\) | 1.42747e13 | 0.259378 | ||||||||
\(131\) | −1.03263e14 | −1.78517 | −0.892587 | − | 0.450876i | \(-0.851112\pi\) | ||||
−0.892587 | + | 0.450876i | \(0.851112\pi\) | |||||||
\(132\) | 2.71462e13 | 0.446661 | ||||||||
\(133\) | 3.93900e13 | 0.617093 | ||||||||
\(134\) | −1.93918e11 | −0.00289359 | ||||||||
\(135\) | 2.32628e13 | 0.330744 | ||||||||
\(136\) | 1.42999e13 | 0.193790 | ||||||||
\(137\) | −3.98625e13 | −0.515088 | −0.257544 | − | 0.966267i | \(-0.582913\pi\) | ||||
−0.257544 | + | 0.966267i | \(0.582913\pi\) | |||||||
\(138\) | 5.89148e12 | 0.0726123 | ||||||||
\(139\) | 8.28297e13 | 0.974069 | 0.487035 | − | 0.873383i | \(-0.338079\pi\) | ||||
0.487035 | + | 0.873383i | \(0.338079\pi\) | |||||||
\(140\) | −1.89511e14 | −2.12717 | ||||||||
\(141\) | 4.01100e13 | 0.429862 | ||||||||
\(142\) | 1.95774e13 | 0.200393 | ||||||||
\(143\) | −4.19621e13 | −0.410367 | ||||||||
\(144\) | 2.53286e13 | 0.236731 | ||||||||
\(145\) | −1.11962e14 | −1.00041 | ||||||||
\(146\) | −5.00575e13 | −0.427735 | ||||||||
\(147\) | 6.29371e13 | 0.514451 | ||||||||
\(148\) | 4.35786e13 | 0.340857 | ||||||||
\(149\) | 1.89703e14 | 1.42024 | 0.710122 | − | 0.704079i | \(-0.248640\pi\) | ||||
0.710122 | + | 0.704079i | \(0.248640\pi\) | |||||||
\(150\) | 4.97408e13 | 0.356549 | ||||||||
\(151\) | 4.48388e12 | 0.0307825 | 0.0153913 | − | 0.999882i | \(-0.495101\pi\) | ||||
0.0153913 | + | 0.999882i | \(0.495101\pi\) | |||||||
\(152\) | −4.09828e13 | −0.269537 | ||||||||
\(153\) | −1.70641e13 | −0.107545 | ||||||||
\(154\) | −6.18516e13 | −0.373651 | ||||||||
\(155\) | −7.79032e13 | −0.451231 | ||||||||
\(156\) | −4.46616e13 | −0.248099 | ||||||||
\(157\) | 1.71354e14 | 0.913159 | 0.456579 | − | 0.889683i | \(-0.349074\pi\) | ||||
0.456579 | + | 0.889683i | \(0.349074\pi\) | |||||||
\(158\) | −1.18914e14 | −0.608083 | ||||||||
\(159\) | −3.73635e13 | −0.183386 | ||||||||
\(160\) | 3.00946e14 | 1.41811 | ||||||||
\(161\) | 1.20904e14 | 0.547107 | ||||||||
\(162\) | 8.08083e12 | 0.0351243 | ||||||||
\(163\) | 3.63350e14 | 1.51742 | 0.758709 | − | 0.651429i | \(-0.225830\pi\) | ||||
0.758709 | + | 0.651429i | \(0.225830\pi\) | |||||||
\(164\) | −3.44666e14 | −1.38329 | ||||||||
\(165\) | −2.21066e14 | −0.852858 | ||||||||
\(166\) | 2.89927e13 | 0.107544 | ||||||||
\(167\) | −2.08346e14 | −0.743240 | −0.371620 | − | 0.928385i | \(-0.621197\pi\) | ||||
−0.371620 | + | 0.928385i | \(0.621197\pi\) | |||||||
\(168\) | −1.38970e14 | −0.476883 | ||||||||
\(169\) | −2.33838e14 | −0.772061 | ||||||||
\(170\) | −5.51638e13 | −0.175281 | ||||||||
\(171\) | 4.89048e13 | 0.149581 | ||||||||
\(172\) | −3.69295e14 | −1.08752 | ||||||||
\(173\) | 1.06883e14 | 0.303115 | 0.151558 | − | 0.988448i | \(-0.451571\pi\) | ||||
0.151558 | + | 0.988448i | \(0.451571\pi\) | |||||||
\(174\) | −3.88924e13 | −0.106242 | ||||||||
\(175\) | 1.02077e15 | 2.68647 | ||||||||
\(176\) | −2.40698e14 | −0.610435 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | −1.20603e14 | −0.284203 | ||||||||
\(179\) | 7.38037e13 | 0.167700 | 0.0838501 | − | 0.996478i | \(-0.473278\pi\) | ||||
0.0838501 | + | 0.996478i | \(0.473278\pi\) | |||||||
\(180\) | −2.35288e14 | −0.515618 | ||||||||
\(181\) | 4.34002e13 | 0.0917446 | 0.0458723 | − | 0.998947i | \(-0.485393\pi\) | ||||
0.0458723 | + | 0.998947i | \(0.485393\pi\) | |||||||
\(182\) | 1.01760e14 | 0.207545 | ||||||||
\(183\) | 3.07107e14 | 0.604445 | ||||||||
\(184\) | −1.25793e14 | −0.238968 | ||||||||
\(185\) | −3.54884e14 | −0.650834 | ||||||||
\(186\) | −2.70613e13 | −0.0479198 | ||||||||
\(187\) | 1.62161e14 | 0.277316 | ||||||||
\(188\) | −4.05687e14 | −0.670139 | ||||||||
\(189\) | 1.65833e14 | 0.264649 | ||||||||
\(190\) | 1.58096e14 | 0.243794 | ||||||||
\(191\) | 6.53880e14 | 0.974498 | 0.487249 | − | 0.873263i | \(-0.338000\pi\) | ||||
0.487249 | + | 0.873263i | \(0.338000\pi\) | |||||||
\(192\) | −1.80085e14 | −0.259430 | ||||||||
\(193\) | 2.02162e14 | 0.281564 | 0.140782 | − | 0.990041i | \(-0.455038\pi\) | ||||
0.140782 | + | 0.990041i | \(0.455038\pi\) | |||||||
\(194\) | −8.81585e13 | −0.118728 | ||||||||
\(195\) | 3.63704e14 | 0.473721 | ||||||||
\(196\) | −6.36568e14 | −0.802012 | ||||||||
\(197\) | −5.32924e14 | −0.649583 | −0.324791 | − | 0.945786i | \(-0.605294\pi\) | ||||
−0.324791 | + | 0.945786i | \(0.605294\pi\) | |||||||
\(198\) | −7.67921e13 | −0.0905718 | ||||||||
\(199\) | −5.68355e14 | −0.648746 | −0.324373 | − | 0.945929i | \(-0.605153\pi\) | ||||
−0.324373 | + | 0.945929i | \(0.605153\pi\) | |||||||
\(200\) | −1.06205e15 | −1.17341 | ||||||||
\(201\) | −4.94083e12 | −0.00528477 | ||||||||
\(202\) | 1.14047e14 | 0.118113 | ||||||||
\(203\) | −7.98144e14 | −0.800492 | ||||||||
\(204\) | 1.72593e14 | 0.167659 | ||||||||
\(205\) | 2.80680e15 | 2.64126 | ||||||||
\(206\) | −1.93411e14 | −0.176337 | ||||||||
\(207\) | 1.50109e14 | 0.132617 | ||||||||
\(208\) | 3.96002e14 | 0.339067 | ||||||||
\(209\) | −4.64743e14 | −0.385711 | ||||||||
\(210\) | 5.36095e14 | 0.431336 | ||||||||
\(211\) | 1.67860e15 | 1.30952 | 0.654758 | − | 0.755839i | \(-0.272771\pi\) | ||||
0.654758 | + | 0.755839i | \(0.272771\pi\) | |||||||
\(212\) | 3.77908e14 | 0.285892 | ||||||||
\(213\) | 4.98813e14 | 0.365991 | ||||||||
\(214\) | 5.55584e14 | 0.395422 | ||||||||
\(215\) | 3.00737e15 | 2.07652 | ||||||||
\(216\) | −1.72539e14 | −0.115595 | ||||||||
\(217\) | −5.55349e14 | −0.361058 | ||||||||
\(218\) | 9.51933e14 | 0.600674 | ||||||||
\(219\) | −1.27541e15 | −0.781203 | ||||||||
\(220\) | 2.23594e15 | 1.32958 | ||||||||
\(221\) | −2.66791e14 | −0.154036 | ||||||||
\(222\) | −1.23277e14 | −0.0691173 | ||||||||
\(223\) | 3.31081e15 | 1.80282 | 0.901410 | − | 0.432966i | \(-0.142533\pi\) | ||||
0.901410 | + | 0.432966i | \(0.142533\pi\) | |||||||
\(224\) | 2.14535e15 | 1.13472 | ||||||||
\(225\) | 1.26734e15 | 0.651191 | ||||||||
\(226\) | 6.68829e14 | 0.333895 | ||||||||
\(227\) | 1.02924e15 | 0.499287 | 0.249643 | − | 0.968338i | \(-0.419687\pi\) | ||||
0.249643 | + | 0.968338i | \(0.419687\pi\) | |||||||
\(228\) | −4.94641e14 | −0.233192 | ||||||||
\(229\) | 9.90704e14 | 0.453955 | 0.226978 | − | 0.973900i | \(-0.427116\pi\) | ||||
0.226978 | + | 0.973900i | \(0.427116\pi\) | |||||||
\(230\) | 4.85261e14 | 0.216145 | ||||||||
\(231\) | −1.57592e15 | −0.682425 | ||||||||
\(232\) | 8.30418e14 | 0.349643 | ||||||||
\(233\) | 1.52144e15 | 0.622931 | 0.311466 | − | 0.950257i | \(-0.399180\pi\) | ||||
0.311466 | + | 0.950257i | \(0.399180\pi\) | |||||||
\(234\) | 1.26340e14 | 0.0503082 | ||||||||
\(235\) | 3.30373e15 | 1.27957 | ||||||||
\(236\) | 3.11012e14 | 0.117179 | ||||||||
\(237\) | −3.02981e15 | −1.11058 | ||||||||
\(238\) | −3.93246e14 | −0.140254 | ||||||||
\(239\) | −1.07681e15 | −0.373726 | −0.186863 | − | 0.982386i | \(-0.559832\pi\) | ||||
−0.186863 | + | 0.982386i | \(0.559832\pi\) | |||||||
\(240\) | 2.08623e15 | 0.704676 | ||||||||
\(241\) | 2.34050e15 | 0.769481 | 0.384741 | − | 0.923025i | \(-0.374291\pi\) | ||||
0.384741 | + | 0.923025i | \(0.374291\pi\) | |||||||
\(242\) | −2.58002e14 | −0.0825703 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −3.10618e15 | −0.942309 | ||||||||
\(245\) | 5.18392e15 | 1.53137 | ||||||||
\(246\) | 9.75004e14 | 0.280497 | ||||||||
\(247\) | 7.64606e14 | 0.214243 | ||||||||
\(248\) | 5.77805e14 | 0.157705 | ||||||||
\(249\) | 7.38705e14 | 0.196415 | ||||||||
\(250\) | 1.99981e15 | 0.518058 | ||||||||
\(251\) | 3.17723e15 | 0.801992 | 0.400996 | − | 0.916080i | \(-0.368664\pi\) | ||||
0.400996 | + | 0.916080i | \(0.368664\pi\) | |||||||
\(252\) | −1.67730e15 | −0.412579 | ||||||||
\(253\) | −1.42648e15 | −0.341966 | ||||||||
\(254\) | −5.75611e14 | −0.134496 | ||||||||
\(255\) | −1.40552e15 | −0.320129 | ||||||||
\(256\) | 6.46697e14 | 0.143596 | ||||||||
\(257\) | 2.52119e15 | 0.545809 | 0.272905 | − | 0.962041i | \(-0.412016\pi\) | ||||
0.272905 | + | 0.962041i | \(0.412016\pi\) | |||||||
\(258\) | 1.04467e15 | 0.220523 | ||||||||
\(259\) | −2.52986e15 | −0.520773 | ||||||||
\(260\) | −3.67863e15 | −0.738514 | ||||||||
\(261\) | −9.90939e14 | −0.194037 | ||||||||
\(262\) | −2.95454e15 | −0.564327 | ||||||||
\(263\) | −9.14713e14 | −0.170440 | −0.0852202 | − | 0.996362i | \(-0.527159\pi\) | ||||
−0.0852202 | + | 0.996362i | \(0.527159\pi\) | |||||||
\(264\) | 1.63964e15 | 0.298073 | ||||||||
\(265\) | −3.07750e15 | −0.545884 | ||||||||
\(266\) | 1.12702e15 | 0.195075 | ||||||||
\(267\) | −3.07285e15 | −0.519061 | ||||||||
\(268\) | 4.99733e13 | 0.00823876 | ||||||||
\(269\) | 9.66114e15 | 1.55467 | 0.777336 | − | 0.629086i | \(-0.216571\pi\) | ||||
0.777336 | + | 0.629086i | \(0.216571\pi\) | |||||||
\(270\) | 6.65590e14 | 0.104554 | ||||||||
\(271\) | −1.13859e16 | −1.74610 | −0.873048 | − | 0.487635i | \(-0.837860\pi\) | ||||
−0.873048 | + | 0.487635i | \(0.837860\pi\) | |||||||
\(272\) | −1.53033e15 | −0.229133 | ||||||||
\(273\) | 2.59274e15 | 0.379054 | ||||||||
\(274\) | −1.14054e15 | −0.162829 | ||||||||
\(275\) | −1.20436e16 | −1.67916 | ||||||||
\(276\) | −1.51825e15 | −0.206745 | ||||||||
\(277\) | −1.05903e16 | −1.40861 | −0.704304 | − | 0.709899i | \(-0.748741\pi\) | ||||
−0.704304 | + | 0.709899i | \(0.748741\pi\) | |||||||
\(278\) | 2.36991e15 | 0.307922 | ||||||||
\(279\) | −6.89495e14 | −0.0875193 | ||||||||
\(280\) | −1.14465e16 | −1.41953 | ||||||||
\(281\) | −9.53225e15 | −1.15506 | −0.577529 | − | 0.816370i | \(-0.695983\pi\) | ||||
−0.577529 | + | 0.816370i | \(0.695983\pi\) | |||||||
\(282\) | 1.14762e15 | 0.135887 | ||||||||
\(283\) | −4.46032e15 | −0.516124 | −0.258062 | − | 0.966128i | \(-0.583084\pi\) | ||||
−0.258062 | + | 0.966128i | \(0.583084\pi\) | |||||||
\(284\) | −5.04517e15 | −0.570567 | ||||||||
\(285\) | 4.02813e15 | 0.445258 | ||||||||
\(286\) | −1.20061e15 | −0.129725 | ||||||||
\(287\) | 2.00089e16 | 2.11344 | ||||||||
\(288\) | 2.66357e15 | 0.275051 | ||||||||
\(289\) | −8.87358e15 | −0.895907 | ||||||||
\(290\) | −3.20344e15 | −0.316249 | ||||||||
\(291\) | −2.24619e15 | −0.216841 | ||||||||
\(292\) | 1.29000e16 | 1.21787 | ||||||||
\(293\) | 1.77460e16 | 1.63855 | 0.819277 | − | 0.573398i | \(-0.194375\pi\) | ||||
0.819277 | + | 0.573398i | \(0.194375\pi\) | |||||||
\(294\) | 1.80075e15 | 0.162628 | ||||||||
\(295\) | −2.53274e15 | −0.223742 | ||||||||
\(296\) | 2.63216e15 | 0.227466 | ||||||||
\(297\) | −1.95658e15 | −0.165418 | ||||||||
\(298\) | 5.42774e15 | 0.448966 | ||||||||
\(299\) | 2.34689e15 | 0.189946 | ||||||||
\(300\) | −1.28184e16 | −1.01518 | ||||||||
\(301\) | 2.14386e16 | 1.66156 | ||||||||
\(302\) | 1.28292e14 | 0.00973094 | ||||||||
\(303\) | 2.90579e15 | 0.215718 | ||||||||
\(304\) | 4.38584e15 | 0.318694 | ||||||||
\(305\) | 2.52953e16 | 1.79925 | ||||||||
\(306\) | −4.88236e14 | −0.0339970 | ||||||||
\(307\) | 1.42327e16 | 0.970259 | 0.485129 | − | 0.874442i | \(-0.338772\pi\) | ||||
0.485129 | + | 0.874442i | \(0.338772\pi\) | |||||||
\(308\) | 1.59394e16 | 1.06388 | ||||||||
\(309\) | −4.92791e15 | −0.322057 | ||||||||
\(310\) | −2.22895e15 | −0.142643 | ||||||||
\(311\) | 6.96725e15 | 0.436636 | 0.218318 | − | 0.975878i | \(-0.429943\pi\) | ||||
0.218318 | + | 0.975878i | \(0.429943\pi\) | |||||||
\(312\) | −2.69758e15 | −0.165565 | ||||||||
\(313\) | −1.86288e16 | −1.11981 | −0.559907 | − | 0.828556i | \(-0.689163\pi\) | ||||
−0.559907 | + | 0.828556i | \(0.689163\pi\) | |||||||
\(314\) | 4.90275e15 | 0.288667 | ||||||||
\(315\) | 1.36591e16 | 0.787780 | ||||||||
\(316\) | 3.06446e16 | 1.73136 | ||||||||
\(317\) | 2.34802e15 | 0.129962 | 0.0649810 | − | 0.997887i | \(-0.479301\pi\) | ||||
0.0649810 | + | 0.997887i | \(0.479301\pi\) | |||||||
\(318\) | −1.06904e15 | −0.0579718 | ||||||||
\(319\) | 9.41690e15 | 0.500344 | ||||||||
\(320\) | −1.48330e16 | −0.772244 | ||||||||
\(321\) | 1.41557e16 | 0.722186 | ||||||||
\(322\) | 3.45928e15 | 0.172951 | ||||||||
\(323\) | −2.95479e15 | −0.144780 | ||||||||
\(324\) | −2.08246e15 | −0.100008 | ||||||||
\(325\) | 1.98144e16 | 0.932693 | ||||||||
\(326\) | 1.03961e16 | 0.479685 | ||||||||
\(327\) | 2.42543e16 | 1.09705 | ||||||||
\(328\) | −2.08180e16 | −0.923120 | ||||||||
\(329\) | 2.35513e16 | 1.02386 | ||||||||
\(330\) | −6.32511e15 | −0.269605 | ||||||||
\(331\) | −2.75150e16 | −1.14997 | −0.574986 | − | 0.818163i | \(-0.694992\pi\) | ||||
−0.574986 | + | 0.818163i | \(0.694992\pi\) | |||||||
\(332\) | −7.47152e15 | −0.306204 | ||||||||
\(333\) | −3.14096e15 | −0.126234 | ||||||||
\(334\) | −5.96117e15 | −0.234952 | ||||||||
\(335\) | −4.06960e14 | −0.0157311 | ||||||||
\(336\) | 1.48721e16 | 0.563855 | ||||||||
\(337\) | 3.01597e16 | 1.12159 | 0.560794 | − | 0.827956i | \(-0.310496\pi\) | ||||
0.560794 | + | 0.827956i | \(0.310496\pi\) | |||||||
\(338\) | −6.69053e15 | −0.244063 | ||||||||
\(339\) | 1.70411e16 | 0.609816 | ||||||||
\(340\) | 1.42159e16 | 0.499069 | ||||||||
\(341\) | 6.55227e15 | 0.225678 | ||||||||
\(342\) | 1.39926e15 | 0.0472855 | ||||||||
\(343\) | −4.51822e15 | −0.149815 | ||||||||
\(344\) | −2.23055e16 | −0.725743 | ||||||||
\(345\) | 1.23640e16 | 0.394760 | ||||||||
\(346\) | 3.05811e15 | 0.0958205 | ||||||||
\(347\) | 2.92206e16 | 0.898562 | 0.449281 | − | 0.893391i | \(-0.351680\pi\) | ||||
0.449281 | + | 0.893391i | \(0.351680\pi\) | |||||||
\(348\) | 1.00227e16 | 0.302496 | ||||||||
\(349\) | 2.57396e16 | 0.762494 | 0.381247 | − | 0.924473i | \(-0.375495\pi\) | ||||
0.381247 | + | 0.924473i | \(0.375495\pi\) | |||||||
\(350\) | 2.92062e16 | 0.849244 | ||||||||
\(351\) | 3.21902e15 | 0.0918814 | ||||||||
\(352\) | −2.53119e16 | −0.709248 | ||||||||
\(353\) | 1.98344e16 | 0.545610 | 0.272805 | − | 0.962069i | \(-0.412049\pi\) | ||||
0.272805 | + | 0.962069i | \(0.412049\pi\) | |||||||
\(354\) | −8.79803e14 | −0.0237610 | ||||||||
\(355\) | 4.10856e16 | 1.08944 | ||||||||
\(356\) | 3.10799e16 | 0.809197 | ||||||||
\(357\) | −1.00195e16 | −0.256155 | ||||||||
\(358\) | 2.11166e15 | 0.0530132 | ||||||||
\(359\) | −6.75022e16 | −1.66419 | −0.832097 | − | 0.554630i | \(-0.812860\pi\) | ||||
−0.832097 | + | 0.554630i | \(0.812860\pi\) | |||||||
\(360\) | −1.42115e16 | −0.344090 | ||||||||
\(361\) | −3.35847e16 | −0.798629 | ||||||||
\(362\) | 1.24176e15 | 0.0290022 | ||||||||
\(363\) | −6.57364e15 | −0.150804 | ||||||||
\(364\) | −2.62238e16 | −0.590932 | ||||||||
\(365\) | −1.05051e17 | −2.32540 | ||||||||
\(366\) | 8.78688e15 | 0.191077 | ||||||||
\(367\) | 6.55766e16 | 1.40094 | 0.700470 | − | 0.713682i | \(-0.252974\pi\) | ||||
0.700470 | + | 0.713682i | \(0.252974\pi\) | |||||||
\(368\) | 1.34619e16 | 0.282550 | ||||||||
\(369\) | 2.48421e16 | 0.512291 | ||||||||
\(370\) | −1.01539e16 | −0.205741 | ||||||||
\(371\) | −2.19386e16 | −0.436796 | ||||||||
\(372\) | 6.97380e15 | 0.136440 | ||||||||
\(373\) | 3.93729e16 | 0.756989 | 0.378495 | − | 0.925603i | \(-0.376442\pi\) | ||||
0.378495 | + | 0.925603i | \(0.376442\pi\) | |||||||
\(374\) | 4.63971e15 | 0.0876649 | ||||||||
\(375\) | 5.09530e16 | 0.946165 | ||||||||
\(376\) | −2.45036e16 | −0.447208 | ||||||||
\(377\) | −1.54929e16 | −0.277917 | ||||||||
\(378\) | 4.74480e15 | 0.0836606 | ||||||||
\(379\) | −2.09052e16 | −0.362326 | −0.181163 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181163 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(380\) | −4.07419e16 | −0.694141 | ||||||||
\(381\) | −1.46660e16 | −0.245640 | ||||||||
\(382\) | 1.87087e16 | 0.308057 | ||||||||
\(383\) | −4.89324e16 | −0.792145 | −0.396073 | − | 0.918219i | \(-0.629627\pi\) | ||||
−0.396073 | + | 0.918219i | \(0.629627\pi\) | |||||||
\(384\) | −3.50840e16 | −0.558413 | ||||||||
\(385\) | −1.29803e17 | −2.03137 | ||||||||
\(386\) | 5.78423e15 | 0.0890078 | ||||||||
\(387\) | 2.66172e16 | 0.402756 | ||||||||
\(388\) | 2.27187e16 | 0.338048 | ||||||||
\(389\) | 6.05798e15 | 0.0886452 | 0.0443226 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443226 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(390\) | 1.04062e16 | 0.149752 | ||||||||
\(391\) | −9.06944e15 | −0.128361 | ||||||||
\(392\) | −3.84489e16 | −0.535211 | ||||||||
\(393\) | −7.52786e16 | −1.03067 | ||||||||
\(394\) | −1.52479e16 | −0.205346 | ||||||||
\(395\) | −2.49556e17 | −3.30587 | ||||||||
\(396\) | 1.97896e16 | 0.257880 | ||||||||
\(397\) | −1.10851e16 | −0.142103 | −0.0710513 | − | 0.997473i | \(-0.522635\pi\) | ||||
−0.0710513 | + | 0.997473i | \(0.522635\pi\) | |||||||
\(398\) | −1.62617e16 | −0.205081 | ||||||||
\(399\) | 2.87153e16 | 0.356279 | ||||||||
\(400\) | 1.13657e17 | 1.38741 | ||||||||
\(401\) | −1.48299e17 | −1.78115 | −0.890574 | − | 0.454838i | \(-0.849697\pi\) | ||||
−0.890574 | + | 0.454838i | \(0.849697\pi\) | |||||||
\(402\) | −1.41366e14 | −0.00167062 | ||||||||
\(403\) | −1.07800e16 | −0.125353 | ||||||||
\(404\) | −2.93902e16 | −0.336298 | ||||||||
\(405\) | 1.69586e16 | 0.190955 | ||||||||
\(406\) | −2.28364e16 | −0.253051 | ||||||||
\(407\) | 2.98486e16 | 0.325507 | ||||||||
\(408\) | 1.04247e16 | 0.111885 | ||||||||
\(409\) | −6.53952e16 | −0.690787 | −0.345393 | − | 0.938458i | \(-0.612255\pi\) | ||||
−0.345393 | + | 0.938458i | \(0.612255\pi\) | |||||||
\(410\) | 8.03078e16 | 0.834954 | ||||||||
\(411\) | −2.90598e16 | −0.297386 | ||||||||
\(412\) | 4.98426e16 | 0.502075 | ||||||||
\(413\) | −1.80552e16 | −0.179030 | ||||||||
\(414\) | 4.29489e15 | 0.0419227 | ||||||||
\(415\) | 6.08446e16 | 0.584668 | ||||||||
\(416\) | 4.16438e16 | 0.393953 | ||||||||
\(417\) | 6.03828e16 | 0.562379 | ||||||||
\(418\) | −1.32971e16 | −0.121930 | ||||||||
\(419\) | −2.96994e16 | −0.268137 | −0.134069 | − | 0.990972i | \(-0.542804\pi\) | ||||
−0.134069 | + | 0.990972i | \(0.542804\pi\) | |||||||
\(420\) | −1.38153e17 | −1.22812 | ||||||||
\(421\) | −3.74709e16 | −0.327990 | −0.163995 | − | 0.986461i | \(-0.552438\pi\) | ||||
−0.163995 | + | 0.986461i | \(0.552438\pi\) | |||||||
\(422\) | 4.80277e16 | 0.413963 | ||||||||
\(423\) | 2.92402e16 | 0.248181 | ||||||||
\(424\) | 2.28257e16 | 0.190786 | ||||||||
\(425\) | −7.65718e16 | −0.630291 | ||||||||
\(426\) | 1.42720e16 | 0.115697 | ||||||||
\(427\) | 1.80323e17 | 1.43969 | ||||||||
\(428\) | −1.43176e17 | −1.12586 | ||||||||
\(429\) | −3.05904e16 | −0.236926 | ||||||||
\(430\) | 8.60463e16 | 0.656428 | ||||||||
\(431\) | 2.25892e17 | 1.69745 | 0.848727 | − | 0.528831i | \(-0.177369\pi\) | ||||
0.848727 | + | 0.528831i | \(0.177369\pi\) | |||||||
\(432\) | 1.84645e16 | 0.136677 | ||||||||
\(433\) | −3.17126e16 | −0.231238 | −0.115619 | − | 0.993294i | \(-0.536885\pi\) | ||||
−0.115619 | + | 0.993294i | \(0.536885\pi\) | |||||||
\(434\) | −1.58895e16 | −0.114137 | ||||||||
\(435\) | −8.16203e16 | −0.577588 | ||||||||
\(436\) | −2.45316e17 | −1.71027 | ||||||||
\(437\) | 2.59925e16 | 0.178533 | ||||||||
\(438\) | −3.64919e16 | −0.246953 | ||||||||
\(439\) | −5.45505e16 | −0.363730 | −0.181865 | − | 0.983324i | \(-0.558213\pi\) | ||||
−0.181865 | + | 0.983324i | \(0.558213\pi\) | |||||||
\(440\) | 1.35052e17 | 0.887273 | ||||||||
\(441\) | 4.58812e16 | 0.297019 | ||||||||
\(442\) | −7.63337e15 | −0.0486936 | ||||||||
\(443\) | 5.75290e16 | 0.361628 | 0.180814 | − | 0.983517i | \(-0.442127\pi\) | ||||
0.180814 | + | 0.983517i | \(0.442127\pi\) | |||||||
\(444\) | 3.17688e16 | 0.196794 | ||||||||
\(445\) | −2.53100e17 | −1.54509 | ||||||||
\(446\) | 9.47283e16 | 0.569906 | ||||||||
\(447\) | 1.38293e17 | 0.819978 | ||||||||
\(448\) | −1.05740e17 | −0.617921 | ||||||||
\(449\) | −2.78144e17 | −1.60202 | −0.801011 | − | 0.598649i | \(-0.795704\pi\) | ||||
−0.801011 | + | 0.598649i | \(0.795704\pi\) | |||||||
\(450\) | 3.62610e16 | 0.205854 | ||||||||
\(451\) | −2.36074e17 | −1.32100 | ||||||||
\(452\) | −1.72359e17 | −0.950682 | ||||||||
\(453\) | 3.26875e15 | 0.0177723 | ||||||||
\(454\) | 2.94485e16 | 0.157834 | ||||||||
\(455\) | 2.13555e17 | 1.12833 | ||||||||
\(456\) | −2.98764e16 | −0.155617 | ||||||||
\(457\) | −3.44104e17 | −1.76699 | −0.883496 | − | 0.468438i | \(-0.844817\pi\) | ||||
−0.883496 | + | 0.468438i | \(0.844817\pi\) | |||||||
\(458\) | 2.83459e16 | 0.143504 | ||||||||
\(459\) | −1.24398e16 | −0.0620911 | ||||||||
\(460\) | −1.25053e17 | −0.615417 | ||||||||
\(461\) | 2.94568e17 | 1.42932 | 0.714660 | − | 0.699472i | \(-0.246582\pi\) | ||||
0.714660 | + | 0.699472i | \(0.246582\pi\) | |||||||
\(462\) | −4.50898e16 | −0.215728 | ||||||||
\(463\) | 2.54307e16 | 0.119972 | 0.0599862 | − | 0.998199i | \(-0.480894\pi\) | ||||
0.0599862 | + | 0.998199i | \(0.480894\pi\) | |||||||
\(464\) | −8.88685e16 | −0.413410 | ||||||||
\(465\) | −5.67914e16 | −0.260518 | ||||||||
\(466\) | 4.35311e16 | 0.196920 | ||||||||
\(467\) | −8.60939e16 | −0.384072 | −0.192036 | − | 0.981388i | \(-0.561509\pi\) | ||||
−0.192036 | + | 0.981388i | \(0.561509\pi\) | |||||||
\(468\) | −3.25583e16 | −0.143240 | ||||||||
\(469\) | −2.90110e15 | −0.0125875 | ||||||||
\(470\) | 9.45257e16 | 0.404496 | ||||||||
\(471\) | 1.24917e17 | 0.527212 | ||||||||
\(472\) | 1.87852e16 | 0.0781977 | ||||||||
\(473\) | −2.52944e17 | −1.03855 | ||||||||
\(474\) | −8.66885e16 | −0.351077 | ||||||||
\(475\) | 2.19450e17 | 0.876653 | ||||||||
\(476\) | 1.01341e17 | 0.399337 | ||||||||
\(477\) | −2.72380e16 | −0.105878 | ||||||||
\(478\) | −3.08096e16 | −0.118142 | ||||||||
\(479\) | −1.88707e17 | −0.713852 | −0.356926 | − | 0.934133i | \(-0.616175\pi\) | ||||
−0.356926 | + | 0.934133i | \(0.616175\pi\) | |||||||
\(480\) | 2.19390e17 | 0.818743 | ||||||||
\(481\) | −4.91076e16 | −0.180803 | ||||||||
\(482\) | 6.69660e16 | 0.243248 | ||||||||
\(483\) | 8.81390e16 | 0.315872 | ||||||||
\(484\) | 6.64881e16 | 0.235098 | ||||||||
\(485\) | −1.85011e17 | −0.645470 | ||||||||
\(486\) | 5.89092e15 | 0.0202790 | ||||||||
\(487\) | −4.58622e17 | −1.55782 | −0.778908 | − | 0.627138i | \(-0.784226\pi\) | ||||
−0.778908 | + | 0.627138i | \(0.784226\pi\) | |||||||
\(488\) | −1.87615e17 | −0.628836 | ||||||||
\(489\) | 2.64882e17 | 0.876082 | ||||||||
\(490\) | 1.48321e17 | 0.484094 | ||||||||
\(491\) | −4.21466e17 | −1.35748 | −0.678739 | − | 0.734380i | \(-0.737473\pi\) | ||||
−0.678739 | + | 0.734380i | \(0.737473\pi\) | |||||||
\(492\) | −2.51262e17 | −0.798644 | ||||||||
\(493\) | 5.98717e16 | 0.187809 | ||||||||
\(494\) | 2.18768e16 | 0.0677264 | ||||||||
\(495\) | −1.61157e17 | −0.492398 | ||||||||
\(496\) | −6.18347e16 | −0.186467 | ||||||||
\(497\) | 2.92887e17 | 0.871733 | ||||||||
\(498\) | 2.11357e16 | 0.0620906 | ||||||||
\(499\) | 4.93358e17 | 1.43057 | 0.715285 | − | 0.698833i | \(-0.246297\pi\) | ||||
0.715285 | + | 0.698833i | \(0.246297\pi\) | |||||||
\(500\) | −5.15357e17 | −1.47504 | ||||||||
\(501\) | −1.51884e17 | −0.429110 | ||||||||
\(502\) | 9.09065e16 | 0.253525 | ||||||||
\(503\) | −3.34056e17 | −0.919661 | −0.459831 | − | 0.888007i | \(-0.652090\pi\) | ||||
−0.459831 | + | 0.888007i | \(0.652090\pi\) | |||||||
\(504\) | −1.01309e17 | −0.275328 | ||||||||
\(505\) | 2.39340e17 | 0.642128 | ||||||||
\(506\) | −4.08143e16 | −0.108102 | ||||||||
\(507\) | −1.70468e17 | −0.445750 | ||||||||
\(508\) | 1.48337e17 | 0.382944 | ||||||||
\(509\) | 6.63987e17 | 1.69236 | 0.846182 | − | 0.532894i | \(-0.178896\pi\) | ||||
0.846182 | + | 0.532894i | \(0.178896\pi\) | |||||||
\(510\) | −4.02144e16 | −0.101199 | ||||||||
\(511\) | −7.48881e17 | −1.86070 | ||||||||
\(512\) | 4.12753e17 | 1.01259 | ||||||||
\(513\) | 3.56516e16 | 0.0863607 | ||||||||
\(514\) | 7.21360e16 | 0.172541 | ||||||||
\(515\) | −4.05895e17 | −0.958665 | ||||||||
\(516\) | −2.69216e17 | −0.627882 | ||||||||
\(517\) | −2.77870e17 | −0.639960 | ||||||||
\(518\) | −7.23840e16 | −0.164626 | ||||||||
\(519\) | 7.79175e16 | 0.175004 | ||||||||
\(520\) | −2.22190e17 | −0.492837 | ||||||||
\(521\) | −2.59732e17 | −0.568958 | −0.284479 | − | 0.958682i | \(-0.591821\pi\) | ||||
−0.284479 | + | 0.958682i | \(0.591821\pi\) | |||||||
\(522\) | −2.83526e16 | −0.0613387 | ||||||||
\(523\) | −2.00639e17 | −0.428701 | −0.214350 | − | 0.976757i | \(-0.568763\pi\) | ||||
−0.214350 | + | 0.976757i | \(0.568763\pi\) | |||||||
\(524\) | 7.61394e17 | 1.60678 | ||||||||
\(525\) | 7.44143e17 | 1.55103 | ||||||||
\(526\) | −2.61716e16 | −0.0538795 | ||||||||
\(527\) | 4.16587e16 | 0.0847104 | ||||||||
\(528\) | −1.75469e17 | −0.352435 | ||||||||
\(529\) | −4.24255e17 | −0.841715 | ||||||||
\(530\) | −8.80530e16 | −0.172564 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | −2.90437e17 | −0.555426 | ||||||||
\(533\) | 3.88396e17 | 0.733749 | ||||||||
\(534\) | −8.79198e16 | −0.164085 | ||||||||
\(535\) | 1.16596e18 | 2.14973 | ||||||||
\(536\) | 3.01840e15 | 0.00549802 | ||||||||
\(537\) | 5.38029e16 | 0.0968217 | ||||||||
\(538\) | 2.76423e17 | 0.491461 | ||||||||
\(539\) | −4.36009e17 | −0.765894 | ||||||||
\(540\) | −1.71525e17 | −0.297692 | ||||||||
\(541\) | −2.36614e17 | −0.405750 | −0.202875 | − | 0.979205i | \(-0.565028\pi\) | ||||
−0.202875 | + | 0.979205i | \(0.565028\pi\) | |||||||
\(542\) | −3.25772e17 | −0.551974 | ||||||||
\(543\) | 3.16387e16 | 0.0529688 | ||||||||
\(544\) | −1.60931e17 | −0.266223 | ||||||||
\(545\) | 1.99774e18 | 3.26559 | ||||||||
\(546\) | 7.41829e16 | 0.119826 | ||||||||
\(547\) | 2.15614e17 | 0.344159 | 0.172079 | − | 0.985083i | \(-0.444951\pi\) | ||||
0.172079 | + | 0.985083i | \(0.444951\pi\) | |||||||
\(548\) | 2.93921e17 | 0.463614 | ||||||||
\(549\) | 2.23881e17 | 0.348977 | ||||||||
\(550\) | −3.44589e17 | −0.530815 | ||||||||
\(551\) | −1.71589e17 | −0.261218 | ||||||||
\(552\) | −9.17030e16 | −0.137968 | ||||||||
\(553\) | −1.77901e18 | −2.64524 | ||||||||
\(554\) | −3.03008e17 | −0.445288 | ||||||||
\(555\) | −2.58711e17 | −0.375759 | ||||||||
\(556\) | −6.10733e17 | −0.876729 | ||||||||
\(557\) | −8.75029e17 | −1.24155 | −0.620774 | − | 0.783990i | \(-0.713182\pi\) | ||||
−0.620774 | + | 0.783990i | \(0.713182\pi\) | |||||||
\(558\) | −1.97277e16 | −0.0276665 | ||||||||
\(559\) | 4.16149e17 | 0.576863 | ||||||||
\(560\) | 1.22497e18 | 1.67843 | ||||||||
\(561\) | 1.18215e17 | 0.160108 | ||||||||
\(562\) | −2.72735e17 | −0.365136 | ||||||||
\(563\) | 9.12606e17 | 1.20775 | 0.603877 | − | 0.797077i | \(-0.293622\pi\) | ||||
0.603877 | + | 0.797077i | \(0.293622\pi\) | |||||||
\(564\) | −2.95746e17 | −0.386905 | ||||||||
\(565\) | 1.40362e18 | 1.81524 | ||||||||
\(566\) | −1.27618e17 | −0.163157 | ||||||||
\(567\) | 1.20893e17 | 0.152795 | ||||||||
\(568\) | −3.04730e17 | −0.380760 | ||||||||
\(569\) | −4.32429e17 | −0.534177 | −0.267089 | − | 0.963672i | \(-0.586062\pi\) | ||||
−0.267089 | + | 0.963672i | \(0.586062\pi\) | |||||||
\(570\) | 1.15252e17 | 0.140754 | ||||||||
\(571\) | −3.05605e17 | −0.368999 | −0.184500 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184500 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(572\) | 3.09402e17 | 0.369359 | ||||||||
\(573\) | 4.76678e17 | 0.562627 | ||||||||
\(574\) | 5.72490e17 | 0.668099 | ||||||||
\(575\) | 6.73582e17 | 0.777230 | ||||||||
\(576\) | −1.31282e17 | −0.149782 | ||||||||
\(577\) | 2.04890e17 | 0.231141 | 0.115571 | − | 0.993299i | \(-0.463130\pi\) | ||||
0.115571 | + | 0.993299i | \(0.463130\pi\) | |||||||
\(578\) | −2.53889e17 | −0.283213 | ||||||||
\(579\) | 1.47376e17 | 0.162561 | ||||||||
\(580\) | 8.25537e17 | 0.900440 | ||||||||
\(581\) | 4.33743e17 | 0.467830 | ||||||||
\(582\) | −6.42676e16 | −0.0685476 | ||||||||
\(583\) | 2.58843e17 | 0.273017 | ||||||||
\(584\) | 7.79162e17 | 0.812727 | ||||||||
\(585\) | 2.65140e17 | 0.273503 | ||||||||
\(586\) | 5.07745e17 | 0.517978 | ||||||||
\(587\) | −8.18615e17 | −0.825909 | −0.412954 | − | 0.910752i | \(-0.635503\pi\) | ||||
−0.412954 | + | 0.910752i | \(0.635503\pi\) | |||||||
\(588\) | −4.64058e17 | −0.463042 | ||||||||
\(589\) | −1.19391e17 | −0.117821 | ||||||||
\(590\) | −7.24664e16 | −0.0707292 | ||||||||
\(591\) | −3.88501e17 | −0.375037 | ||||||||
\(592\) | −2.81685e17 | −0.268951 | ||||||||
\(593\) | −2.63935e17 | −0.249254 | −0.124627 | − | 0.992204i | \(-0.539773\pi\) | ||||
−0.124627 | + | 0.992204i | \(0.539773\pi\) | |||||||
\(594\) | −5.59814e16 | −0.0522916 | ||||||||
\(595\) | −8.25273e17 | −0.762496 | ||||||||
\(596\) | −1.39875e18 | −1.27832 | ||||||||
\(597\) | −4.14331e17 | −0.374554 | ||||||||
\(598\) | 6.71487e16 | 0.0600454 | ||||||||
\(599\) | 6.06960e17 | 0.536890 | 0.268445 | − | 0.963295i | \(-0.413490\pi\) | ||||
0.268445 | + | 0.963295i | \(0.413490\pi\) | |||||||
\(600\) | −7.74234e17 | −0.677468 | ||||||||
\(601\) | −9.28222e17 | −0.803467 | −0.401733 | − | 0.915757i | \(-0.631592\pi\) | ||||
−0.401733 | + | 0.915757i | \(0.631592\pi\) | |||||||
\(602\) | 6.13399e17 | 0.525250 | ||||||||
\(603\) | −3.60187e15 | −0.00305116 | ||||||||
\(604\) | −3.30613e16 | −0.0277064 | ||||||||
\(605\) | −5.41448e17 | −0.448897 | ||||||||
\(606\) | 8.31400e16 | 0.0681927 | ||||||||
\(607\) | −1.02008e18 | −0.827766 | −0.413883 | − | 0.910330i | \(-0.635828\pi\) | ||||
−0.413883 | + | 0.910330i | \(0.635828\pi\) | |||||||
\(608\) | 4.61218e17 | 0.370282 | ||||||||
\(609\) | −5.81847e17 | −0.462165 | ||||||||
\(610\) | 7.23746e17 | 0.568777 | ||||||||
\(611\) | 4.57158e17 | 0.355466 | ||||||||
\(612\) | 1.25820e17 | 0.0967979 | ||||||||
\(613\) | 1.38898e18 | 1.05731 | 0.528655 | − | 0.848837i | \(-0.322697\pi\) | ||||
0.528655 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(614\) | 4.07223e17 | 0.306717 | ||||||||
\(615\) | 2.04616e18 | 1.52493 | ||||||||
\(616\) | 9.62743e17 | 0.709963 | ||||||||
\(617\) | 1.27962e18 | 0.933740 | 0.466870 | − | 0.884326i | \(-0.345382\pi\) | ||||
0.466870 | + | 0.884326i | \(0.345382\pi\) | |||||||
\(618\) | −1.40996e17 | −0.101808 | ||||||||
\(619\) | 7.14427e17 | 0.510468 | 0.255234 | − | 0.966879i | \(-0.417847\pi\) | ||||
0.255234 | + | 0.966879i | \(0.417847\pi\) | |||||||
\(620\) | 5.74408e17 | 0.406139 | ||||||||
\(621\) | 1.09429e17 | 0.0765664 | ||||||||
\(622\) | 1.99346e17 | 0.138029 | ||||||||
\(623\) | −1.80428e18 | −1.23632 | ||||||||
\(624\) | 2.88685e17 | 0.195760 | ||||||||
\(625\) | 1.28578e18 | 0.862873 | ||||||||
\(626\) | −5.33003e17 | −0.353994 | ||||||||
\(627\) | −3.38797e17 | −0.222690 | ||||||||
\(628\) | −1.26345e18 | −0.821906 | ||||||||
\(629\) | 1.89774e17 | 0.122182 | ||||||||
\(630\) | 3.90813e17 | 0.249032 | ||||||||
\(631\) | 1.73070e18 | 1.09152 | 0.545758 | − | 0.837943i | \(-0.316242\pi\) | ||||
0.545758 | + | 0.837943i | \(0.316242\pi\) | |||||||
\(632\) | 1.85094e18 | 1.15540 | ||||||||
\(633\) | 1.22370e18 | 0.756049 | ||||||||
\(634\) | 6.71811e16 | 0.0410835 | ||||||||
\(635\) | −1.20799e18 | −0.731195 | ||||||||
\(636\) | 2.75495e17 | 0.165060 | ||||||||
\(637\) | 7.17333e17 | 0.425417 | ||||||||
\(638\) | 2.69435e17 | 0.158168 | ||||||||
\(639\) | 3.63635e17 | 0.211305 | ||||||||
\(640\) | −2.88975e18 | −1.66223 | ||||||||
\(641\) | 1.48780e18 | 0.847163 | 0.423581 | − | 0.905858i | \(-0.360773\pi\) | ||||
0.423581 | + | 0.905858i | \(0.360773\pi\) | |||||||
\(642\) | 4.05021e17 | 0.228297 | ||||||||
\(643\) | 1.41403e18 | 0.789016 | 0.394508 | − | 0.918892i | \(-0.370915\pi\) | ||||
0.394508 | + | 0.918892i | \(0.370915\pi\) | |||||||
\(644\) | −8.91468e17 | −0.492434 | ||||||||
\(645\) | 2.19237e18 | 1.19888 | ||||||||
\(646\) | −8.45418e16 | −0.0457678 | ||||||||
\(647\) | 2.03762e18 | 1.09206 | 0.546029 | − | 0.837766i | \(-0.316139\pi\) | ||||
0.546029 | + | 0.837766i | \(0.316139\pi\) | |||||||
\(648\) | −1.25781e17 | −0.0667387 | ||||||||
\(649\) | 2.13024e17 | 0.111902 | ||||||||
\(650\) | 5.66926e17 | 0.294842 | ||||||||
\(651\) | −4.04849e17 | −0.208457 | ||||||||
\(652\) | −2.67911e18 | −1.36578 | ||||||||
\(653\) | −9.92522e17 | −0.500962 | −0.250481 | − | 0.968122i | \(-0.580589\pi\) | ||||
−0.250481 | + | 0.968122i | \(0.580589\pi\) | |||||||
\(654\) | 6.93959e17 | 0.346800 | ||||||||
\(655\) | −6.20044e18 | −3.06799 | ||||||||
\(656\) | 2.22787e18 | 1.09148 | ||||||||
\(657\) | −9.29776e17 | −0.451028 | ||||||||
\(658\) | 6.73846e17 | 0.323662 | ||||||||
\(659\) | 1.22480e17 | 0.0582520 | 0.0291260 | − | 0.999576i | \(-0.490728\pi\) | ||||
0.0291260 | + | 0.999576i | \(0.490728\pi\) | |||||||
\(660\) | 1.63000e18 | 0.767631 | ||||||||
\(661\) | 3.12167e17 | 0.145572 | 0.0727860 | − | 0.997348i | \(-0.476811\pi\) | ||||
0.0727860 | + | 0.997348i | \(0.476811\pi\) | |||||||
\(662\) | −7.87254e17 | −0.363528 | ||||||||
\(663\) | −1.94490e17 | −0.0889325 | ||||||||
\(664\) | −4.51282e17 | −0.204341 | ||||||||
\(665\) | 2.36518e18 | 1.06053 | ||||||||
\(666\) | −8.98687e16 | −0.0399049 | ||||||||
\(667\) | −5.26675e17 | −0.231593 | ||||||||
\(668\) | 1.53621e18 | 0.668967 | ||||||||
\(669\) | 2.41358e18 | 1.04086 | ||||||||
\(670\) | −1.16439e16 | −0.00497291 | ||||||||
\(671\) | −2.12754e18 | −0.899873 | ||||||||
\(672\) | 1.56396e18 | 0.655128 | ||||||||
\(673\) | −2.67413e18 | −1.10939 | −0.554696 | − | 0.832053i | \(-0.687166\pi\) | ||||
−0.554696 | + | 0.832053i | \(0.687166\pi\) | |||||||
\(674\) | 8.62925e17 | 0.354555 | ||||||||
\(675\) | 9.23894e17 | 0.375965 | ||||||||
\(676\) | 1.72417e18 | 0.694908 | ||||||||
\(677\) | −4.28300e18 | −1.70971 | −0.854854 | − | 0.518868i | \(-0.826354\pi\) | ||||
−0.854854 | + | 0.518868i | \(0.826354\pi\) | |||||||
\(678\) | 4.87576e17 | 0.192774 | ||||||||
\(679\) | −1.31889e18 | −0.516481 | ||||||||
\(680\) | 8.58644e17 | 0.333047 | ||||||||
\(681\) | 7.50319e17 | 0.288263 | ||||||||
\(682\) | 1.87473e17 | 0.0713410 | ||||||||
\(683\) | −7.31913e17 | −0.275883 | −0.137941 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137941 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(684\) | −3.60593e17 | −0.134633 | ||||||||
\(685\) | −2.39356e18 | −0.885228 | ||||||||
\(686\) | −1.29275e17 | −0.0473594 | ||||||||
\(687\) | 7.22223e17 | 0.262091 | ||||||||
\(688\) | 2.38706e18 | 0.858102 | ||||||||
\(689\) | −4.25854e17 | −0.151648 | ||||||||
\(690\) | 3.53755e17 | 0.124791 | ||||||||
\(691\) | 7.91680e17 | 0.276657 | 0.138329 | − | 0.990386i | \(-0.455827\pi\) | ||||
0.138329 | + | 0.990386i | \(0.455827\pi\) | |||||||
\(692\) | −7.88085e17 | −0.272825 | ||||||||
\(693\) | −1.14884e18 | −0.393998 | ||||||||
\(694\) | 8.36055e17 | 0.284052 | ||||||||
\(695\) | 4.97353e18 | 1.67403 | ||||||||
\(696\) | 6.05375e17 | 0.201867 | ||||||||
\(697\) | −1.50094e18 | −0.495849 | ||||||||
\(698\) | 7.36457e17 | 0.241039 | ||||||||
\(699\) | 1.10913e18 | 0.359650 | ||||||||
\(700\) | −7.52653e18 | −2.41801 | ||||||||
\(701\) | 1.65035e18 | 0.525302 | 0.262651 | − | 0.964891i | \(-0.415403\pi\) | ||||
0.262651 | + | 0.964891i | \(0.415403\pi\) | |||||||
\(702\) | 9.21021e16 | 0.0290455 | ||||||||
\(703\) | −5.43882e17 | −0.169940 | ||||||||
\(704\) | 1.24757e18 | 0.386228 | ||||||||
\(705\) | 2.40842e18 | 0.738758 | ||||||||
\(706\) | 5.67497e17 | 0.172478 | ||||||||
\(707\) | 1.70619e18 | 0.513807 | ||||||||
\(708\) | 2.26728e17 | 0.0676533 | ||||||||
\(709\) | −6.24771e18 | −1.84723 | −0.923614 | − | 0.383324i | \(-0.874779\pi\) | ||||
−0.923614 | + | 0.383324i | \(0.874779\pi\) | |||||||
\(710\) | 1.17553e18 | 0.344394 | ||||||||
\(711\) | −2.20873e18 | −0.641196 | ||||||||
\(712\) | 1.87723e18 | 0.540006 | ||||||||
\(713\) | −3.66460e17 | −0.104459 | ||||||||
\(714\) | −2.86676e17 | −0.0809755 | ||||||||
\(715\) | −2.51962e18 | −0.705256 | ||||||||
\(716\) | −5.44182e17 | −0.150942 | ||||||||
\(717\) | −7.84996e17 | −0.215771 | ||||||||
\(718\) | −1.93136e18 | −0.526083 | ||||||||
\(719\) | 5.85211e18 | 1.57970 | 0.789850 | − | 0.613300i | \(-0.210158\pi\) | ||||
0.789850 | + | 0.613300i | \(0.210158\pi\) | |||||||
\(720\) | 1.52086e18 | 0.406845 | ||||||||
\(721\) | −2.89351e18 | −0.767088 | ||||||||
\(722\) | −9.60921e17 | −0.252462 | ||||||||
\(723\) | 1.70623e18 | 0.444260 | ||||||||
\(724\) | −3.20005e17 | −0.0825765 | ||||||||
\(725\) | −4.44664e18 | −1.13719 | ||||||||
\(726\) | −1.88084e17 | −0.0476720 | ||||||||
\(727\) | 1.76655e17 | 0.0443765 | 0.0221882 | − | 0.999754i | \(-0.492937\pi\) | ||||
0.0221882 | + | 0.999754i | \(0.492937\pi\) | |||||||
\(728\) | −1.58393e18 | −0.394350 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −3.00571e18 | −0.735104 | ||||||||
\(731\) | −1.60819e18 | −0.389829 | ||||||||
\(732\) | −2.26441e18 | −0.544042 | ||||||||
\(733\) | 3.03756e18 | 0.723350 | 0.361675 | − | 0.932304i | \(-0.382205\pi\) | ||||
0.361675 | + | 0.932304i | \(0.382205\pi\) | |||||||
\(734\) | 1.87627e18 | 0.442864 | ||||||||
\(735\) | 3.77908e18 | 0.884134 | ||||||||
\(736\) | 1.41566e18 | 0.328288 | ||||||||
\(737\) | 3.42285e16 | 0.00786774 | ||||||||
\(738\) | 7.10778e17 | 0.161945 | ||||||||
\(739\) | −4.10920e18 | −0.928044 | −0.464022 | − | 0.885824i | \(-0.653594\pi\) | ||||
−0.464022 | + | 0.885824i | \(0.653594\pi\) | |||||||
\(740\) | 2.61669e18 | 0.585795 | ||||||||
\(741\) | 5.57398e17 | 0.123694 | ||||||||
\(742\) | −6.27704e17 | −0.138080 | ||||||||
\(743\) | −7.88870e18 | −1.72020 | −0.860098 | − | 0.510128i | \(-0.829598\pi\) | ||||
−0.860098 | + | 0.510128i | \(0.829598\pi\) | |||||||
\(744\) | 4.21220e17 | 0.0910510 | ||||||||
\(745\) | 1.13908e19 | 2.44083 | ||||||||
\(746\) | 1.12653e18 | 0.239299 | ||||||||
\(747\) | 5.38516e17 | 0.113400 | ||||||||
\(748\) | −1.19567e18 | −0.249603 | ||||||||
\(749\) | 8.31178e18 | 1.72013 | ||||||||
\(750\) | 1.45786e18 | 0.299101 | ||||||||
\(751\) | −2.55663e18 | −0.520006 | −0.260003 | − | 0.965608i | \(-0.583724\pi\) | ||||
−0.260003 | + | 0.965608i | \(0.583724\pi\) | |||||||
\(752\) | 2.62229e18 | 0.528768 | ||||||||
\(753\) | 2.31620e18 | 0.463030 | ||||||||
\(754\) | −4.43281e17 | −0.0878547 | ||||||||
\(755\) | 2.69236e17 | 0.0529027 | ||||||||
\(756\) | −1.22275e18 | −0.238202 | ||||||||
\(757\) | 5.09571e18 | 0.984195 | 0.492098 | − | 0.870540i | \(-0.336230\pi\) | ||||
0.492098 | + | 0.870540i | \(0.336230\pi\) | |||||||
\(758\) | −5.98136e17 | −0.114538 | ||||||||
\(759\) | −1.03991e18 | −0.197434 | ||||||||
\(760\) | −2.46082e18 | −0.463225 | ||||||||
\(761\) | −3.34517e18 | −0.624336 | −0.312168 | − | 0.950027i | \(-0.601055\pi\) | ||||
−0.312168 | + | 0.950027i | \(0.601055\pi\) | |||||||
\(762\) | −4.19621e17 | −0.0776515 | ||||||||
\(763\) | 1.42413e19 | 2.61301 | ||||||||
\(764\) | −4.82129e18 | −0.877115 | ||||||||
\(765\) | −1.02462e18 | −0.184826 | ||||||||
\(766\) | −1.40005e18 | −0.250412 | ||||||||
\(767\) | −3.50472e17 | −0.0621560 | ||||||||
\(768\) | 4.71442e17 | 0.0829049 | ||||||||
\(769\) | 3.54959e18 | 0.618952 | 0.309476 | − | 0.950907i | \(-0.399846\pi\) | ||||
0.309476 | + | 0.950907i | \(0.399846\pi\) | |||||||
\(770\) | −3.71390e18 | −0.642155 | ||||||||
\(771\) | 1.83795e18 | 0.315123 | ||||||||
\(772\) | −1.49062e18 | −0.253427 | ||||||||
\(773\) | −2.46328e18 | −0.415285 | −0.207643 | − | 0.978205i | \(-0.566579\pi\) | ||||
−0.207643 | + | 0.978205i | \(0.566579\pi\) | |||||||
\(774\) | 7.61568e17 | 0.127319 | ||||||||
\(775\) | −3.09397e18 | −0.512926 | ||||||||
\(776\) | 1.37222e18 | 0.225591 | ||||||||
\(777\) | −1.84427e18 | −0.300669 | ||||||||
\(778\) | 1.73330e17 | 0.0280224 | ||||||||
\(779\) | 4.30160e18 | 0.689662 | ||||||||
\(780\) | −2.68172e18 | −0.426381 | ||||||||
\(781\) | −3.45562e18 | −0.544872 | ||||||||
\(782\) | −2.59493e17 | −0.0405772 | ||||||||
\(783\) | −7.22395e17 | −0.112027 | ||||||||
\(784\) | 4.11467e18 | 0.632821 | ||||||||
\(785\) | 1.02890e19 | 1.56935 | ||||||||
\(786\) | −2.15386e18 | −0.325815 | ||||||||
\(787\) | −5.08722e18 | −0.763211 | −0.381605 | − | 0.924325i | \(-0.624629\pi\) | ||||
−0.381605 | + | 0.924325i | \(0.624629\pi\) | |||||||
\(788\) | 3.92944e18 | 0.584669 | ||||||||
\(789\) | −6.66826e17 | −0.0984038 | ||||||||
\(790\) | −7.14024e18 | −1.04505 | ||||||||
\(791\) | 1.00060e19 | 1.45248 | ||||||||
\(792\) | 1.19530e18 | 0.172093 | ||||||||
\(793\) | 3.50028e18 | 0.499835 | ||||||||
\(794\) | −3.17166e17 | −0.0449214 | ||||||||
\(795\) | −2.24350e18 | −0.315166 | ||||||||
\(796\) | 4.19069e18 | 0.583916 | ||||||||
\(797\) | −9.51239e18 | −1.31465 | −0.657325 | − | 0.753607i | \(-0.728312\pi\) | ||||
−0.657325 | + | 0.753607i | \(0.728312\pi\) | |||||||
\(798\) | 8.21598e17 | 0.112626 | ||||||||
\(799\) | −1.76667e18 | −0.240215 | ||||||||
\(800\) | 1.19522e19 | 1.61200 | ||||||||
\(801\) | −2.24011e18 | −0.299680 | ||||||||
\(802\) | −4.24311e18 | −0.563055 | ||||||||
\(803\) | 8.83566e18 | 1.16302 | ||||||||
\(804\) | 3.64306e16 | 0.00475665 | ||||||||
\(805\) | 7.25971e18 | 0.940256 | ||||||||
\(806\) | −3.08435e17 | −0.0396265 | ||||||||
\(807\) | 7.04297e18 | 0.897590 | ||||||||
\(808\) | −1.77518e18 | −0.224423 | ||||||||
\(809\) | 4.48219e18 | 0.562114 | 0.281057 | − | 0.959691i | \(-0.409315\pi\) | ||||
0.281057 | + | 0.959691i | \(0.409315\pi\) | |||||||
\(810\) | 4.85215e17 | 0.0603645 | ||||||||
\(811\) | −1.01306e19 | −1.25025 | −0.625127 | − | 0.780523i | \(-0.714953\pi\) | ||||
−0.625127 | + | 0.780523i | \(0.714953\pi\) | |||||||
\(812\) | 5.88501e18 | 0.720498 | ||||||||
\(813\) | −8.30034e18 | −1.00811 | ||||||||
\(814\) | 8.54022e17 | 0.102899 | ||||||||
\(815\) | 2.18174e19 | 2.60783 | ||||||||
\(816\) | −1.11561e18 | −0.132290 | ||||||||
\(817\) | 4.60898e18 | 0.542202 | ||||||||
\(818\) | −1.87108e18 | −0.218371 | ||||||||
\(819\) | 1.89010e18 | 0.218847 | ||||||||
\(820\) | −2.06956e19 | −2.37732 | ||||||||
\(821\) | −1.44455e19 | −1.64627 | −0.823136 | − | 0.567845i | \(-0.807777\pi\) | ||||
−0.823136 | + | 0.567845i | \(0.807777\pi\) | |||||||
\(822\) | −8.31454e17 | −0.0940094 | ||||||||
\(823\) | −1.87229e18 | −0.210026 | −0.105013 | − | 0.994471i | \(-0.533488\pi\) | ||||
−0.105013 | + | 0.994471i | \(0.533488\pi\) | |||||||
\(824\) | 3.01051e18 | 0.335053 | ||||||||
\(825\) | −8.77977e18 | −0.969465 | ||||||||
\(826\) | −5.16591e17 | −0.0565948 | ||||||||
\(827\) | −8.21859e18 | −0.893329 | −0.446665 | − | 0.894701i | \(-0.647388\pi\) | ||||
−0.446665 | + | 0.894701i | \(0.647388\pi\) | |||||||
\(828\) | −1.10681e18 | −0.119364 | ||||||||
\(829\) | −6.85548e18 | −0.733557 | −0.366778 | − | 0.930308i | \(-0.619539\pi\) | ||||
−0.366778 | + | 0.930308i | \(0.619539\pi\) | |||||||
\(830\) | 1.74088e18 | 0.184825 | ||||||||
\(831\) | −7.72033e18 | −0.813260 | ||||||||
\(832\) | −2.05254e18 | −0.214531 | ||||||||
\(833\) | −2.77210e18 | −0.287486 | ||||||||
\(834\) | 1.72766e18 | 0.177779 | ||||||||
\(835\) | −1.25102e19 | −1.27733 | ||||||||
\(836\) | 3.42672e18 | 0.347166 | ||||||||
\(837\) | −5.02642e17 | −0.0505293 | ||||||||
\(838\) | −8.49755e17 | −0.0847633 | ||||||||
\(839\) | −1.29934e19 | −1.28608 | −0.643041 | − | 0.765832i | \(-0.722327\pi\) | ||||
−0.643041 | + | 0.765832i | \(0.722327\pi\) | |||||||
\(840\) | −8.34451e18 | −0.819569 | ||||||||
\(841\) | −6.78379e18 | −0.661148 | ||||||||
\(842\) | −1.07211e18 | −0.103684 | ||||||||
\(843\) | −6.94901e18 | −0.666874 | ||||||||
\(844\) | −1.23769e19 | −1.17865 | ||||||||
\(845\) | −1.40409e19 | −1.32686 | ||||||||
\(846\) | 8.36616e17 | 0.0784546 | ||||||||
\(847\) | −3.85983e18 | −0.359191 | ||||||||
\(848\) | −2.44273e18 | −0.225581 | ||||||||
\(849\) | −3.25157e18 | −0.297984 | ||||||||
\(850\) | −2.19086e18 | −0.199247 | ||||||||
\(851\) | −1.66939e18 | −0.150666 | ||||||||
\(852\) | −3.67793e18 | −0.329417 | ||||||||
\(853\) | −6.44498e18 | −0.572866 | −0.286433 | − | 0.958100i | \(-0.592470\pi\) | ||||
−0.286433 | + | 0.958100i | \(0.592470\pi\) | |||||||
\(854\) | 5.15937e18 | 0.455114 | ||||||||
\(855\) | 2.93650e18 | 0.257070 | ||||||||
\(856\) | −8.64787e18 | −0.751329 | ||||||||
\(857\) | −1.91734e19 | −1.65319 | −0.826596 | − | 0.562795i | \(-0.809726\pi\) | ||||
−0.826596 | + | 0.562795i | \(0.809726\pi\) | |||||||
\(858\) | −8.75246e17 | −0.0748967 | ||||||||
\(859\) | 1.33684e19 | 1.13533 | 0.567667 | − | 0.823259i | \(-0.307846\pi\) | ||||
0.567667 | + | 0.823259i | \(0.307846\pi\) | |||||||
\(860\) | −2.21744e19 | −1.86901 | ||||||||
\(861\) | 1.45865e19 | 1.22020 | ||||||||
\(862\) | 6.46318e18 | 0.536598 | ||||||||
\(863\) | 1.08501e19 | 0.894056 | 0.447028 | − | 0.894520i | \(-0.352482\pi\) | ||||
0.447028 | + | 0.894520i | \(0.352482\pi\) | |||||||
\(864\) | 1.94174e18 | 0.158801 | ||||||||
\(865\) | 6.41780e18 | 0.520933 | ||||||||
\(866\) | −9.07354e17 | −0.0730989 | ||||||||
\(867\) | −6.46884e18 | −0.517252 | ||||||||
\(868\) | 4.09479e18 | 0.324977 | ||||||||
\(869\) | 2.09896e19 | 1.65339 | ||||||||
\(870\) | −2.33531e18 | −0.182587 | ||||||||
\(871\) | −5.63137e16 | −0.00437014 | ||||||||
\(872\) | −1.48172e19 | −1.14132 | ||||||||
\(873\) | −1.63747e18 | −0.125193 | ||||||||
\(874\) | 7.43692e17 | 0.0564376 | ||||||||
\(875\) | 2.99180e19 | 2.25361 | ||||||||
\(876\) | 9.40408e18 | 0.703136 | ||||||||
\(877\) | −7.91821e18 | −0.587665 | −0.293832 | − | 0.955857i | \(-0.594931\pi\) | ||||
−0.293832 | + | 0.955857i | \(0.594931\pi\) | |||||||
\(878\) | −1.56079e18 | −0.114982 | ||||||||
\(879\) | 1.29368e19 | 0.946020 | ||||||||
\(880\) | −1.44528e19 | −1.04909 | ||||||||
\(881\) | 2.63411e18 | 0.189797 | 0.0948987 | − | 0.995487i | \(-0.469747\pi\) | ||||
0.0948987 | + | 0.995487i | \(0.469747\pi\) | |||||||
\(882\) | 1.31274e18 | 0.0938933 | ||||||||
\(883\) | 2.30340e19 | 1.63540 | 0.817702 | − | 0.575641i | \(-0.195248\pi\) | ||||
0.817702 | + | 0.575641i | \(0.195248\pi\) | |||||||
\(884\) | 1.96714e18 | 0.138643 | ||||||||
\(885\) | −1.84637e18 | −0.129178 | ||||||||
\(886\) | 1.64601e18 | 0.114318 | ||||||||
\(887\) | 4.21937e18 | 0.290901 | 0.145450 | − | 0.989366i | \(-0.453537\pi\) | ||||
0.145450 | + | 0.989366i | \(0.453537\pi\) | |||||||
\(888\) | 1.91885e18 | 0.131328 | ||||||||
\(889\) | −8.61139e18 | −0.585075 | ||||||||
\(890\) | −7.24166e18 | −0.488431 | ||||||||
\(891\) | −1.42635e18 | −0.0955039 | ||||||||
\(892\) | −2.44118e19 | −1.62266 | ||||||||
\(893\) | 5.06316e18 | 0.334108 | ||||||||
\(894\) | 3.95683e18 | 0.259211 | ||||||||
\(895\) | 4.43156e18 | 0.288209 | ||||||||
\(896\) | −2.06002e19 | −1.33005 | ||||||||
\(897\) | 1.71088e18 | 0.109665 | ||||||||
\(898\) | −7.95821e18 | −0.506430 | ||||||||
\(899\) | 2.41918e18 | 0.152838 | ||||||||
\(900\) | −9.34459e18 | −0.586116 | ||||||||
\(901\) | 1.64570e18 | 0.102480 | ||||||||
\(902\) | −6.75452e18 | −0.417592 | ||||||||
\(903\) | 1.56288e19 | 0.959300 | ||||||||
\(904\) | −1.04106e19 | −0.634424 | ||||||||
\(905\) | 2.60598e18 | 0.157672 | ||||||||
\(906\) | 9.35249e16 | 0.00561816 | ||||||||
\(907\) | −2.00406e18 | −0.119526 | −0.0597631 | − | 0.998213i | \(-0.519035\pi\) | ||||
−0.0597631 | + | 0.998213i | \(0.519035\pi\) | |||||||
\(908\) | −7.58899e18 | −0.449392 | ||||||||
\(909\) | 2.11832e18 | 0.124545 | ||||||||
\(910\) | 6.11020e18 | 0.356686 | ||||||||
\(911\) | 1.33766e19 | 0.775311 | 0.387656 | − | 0.921804i | \(-0.373285\pi\) | ||||
0.387656 | + | 0.921804i | \(0.373285\pi\) | |||||||
\(912\) | 3.19728e18 | 0.183998 | ||||||||
\(913\) | −5.11752e18 | −0.292415 | ||||||||
\(914\) | −9.84545e18 | −0.558580 | ||||||||
\(915\) | 1.84403e19 | 1.03880 | ||||||||
\(916\) | −7.30482e18 | −0.408591 | ||||||||
\(917\) | −4.42011e19 | −2.45489 | ||||||||
\(918\) | −3.55924e17 | −0.0196282 | ||||||||
\(919\) | −5.46503e18 | −0.299255 | −0.149628 | − | 0.988742i | \(-0.547808\pi\) | ||||
−0.149628 | + | 0.988742i | \(0.547808\pi\) | |||||||
\(920\) | −7.55326e18 | −0.410690 | ||||||||
\(921\) | 1.03756e19 | 0.560179 | ||||||||
\(922\) | 8.42812e18 | 0.451835 | ||||||||
\(923\) | 5.68528e18 | 0.302650 | ||||||||
\(924\) | 1.16198e19 | 0.614229 | ||||||||
\(925\) | −1.40944e19 | −0.739820 | ||||||||
\(926\) | 7.27618e17 | 0.0379256 | ||||||||
\(927\) | −3.59244e18 | −0.185939 | ||||||||
\(928\) | −9.34548e18 | −0.480330 | ||||||||
\(929\) | 2.03703e19 | 1.03967 | 0.519834 | − | 0.854267i | \(-0.325994\pi\) | ||||
0.519834 | + | 0.854267i | \(0.325994\pi\) | |||||||
\(930\) | −1.62491e18 | −0.0823548 | ||||||||
\(931\) | 7.94467e18 | 0.399856 | ||||||||
\(932\) | −1.12181e19 | −0.560681 | ||||||||
\(933\) | 5.07913e18 | 0.252092 | ||||||||
\(934\) | −2.46331e18 | −0.121413 | ||||||||
\(935\) | 9.73698e18 | 0.476594 | ||||||||
\(936\) | −1.96653e18 | −0.0955890 | ||||||||
\(937\) | −2.26477e19 | −1.09324 | −0.546621 | − | 0.837380i | \(-0.684086\pi\) | ||||
−0.546621 | + | 0.837380i | \(0.684086\pi\) | |||||||
\(938\) | −8.30057e16 | −0.00397914 | ||||||||
\(939\) | −1.35804e19 | −0.646525 | ||||||||
\(940\) | −2.43596e19 | −1.15170 | ||||||||
\(941\) | −4.52873e17 | −0.0212639 | −0.0106320 | − | 0.999943i | \(-0.503384\pi\) | ||||
−0.0106320 | + | 0.999943i | \(0.503384\pi\) | |||||||
\(942\) | 3.57410e18 | 0.166662 | ||||||||
\(943\) | 1.32033e19 | 0.611446 | ||||||||
\(944\) | −2.01033e18 | −0.0924592 | ||||||||
\(945\) | 9.95751e18 | 0.454825 | ||||||||
\(946\) | −7.23718e18 | −0.328305 | ||||||||
\(947\) | 2.29988e19 | 1.03617 | 0.518083 | − | 0.855330i | \(-0.326646\pi\) | ||||
0.518083 | + | 0.855330i | \(0.326646\pi\) | |||||||
\(948\) | 2.23399e19 | 0.999602 | ||||||||
\(949\) | −1.45366e19 | −0.646002 | ||||||||
\(950\) | 6.27887e18 | 0.277127 | ||||||||
\(951\) | 1.71171e18 | 0.0750336 | ||||||||
\(952\) | 6.12102e18 | 0.266492 | ||||||||
\(953\) | 3.27952e19 | 1.41810 | 0.709050 | − | 0.705158i | \(-0.249124\pi\) | ||||
0.709050 | + | 0.705158i | \(0.249124\pi\) | |||||||
\(954\) | −7.79329e17 | −0.0334700 | ||||||||
\(955\) | 3.92624e19 | 1.67477 | ||||||||
\(956\) | 7.93973e18 | 0.336379 | ||||||||
\(957\) | 6.86492e18 | 0.288874 | ||||||||
\(958\) | −5.39927e18 | −0.225662 | ||||||||
\(959\) | −1.70630e19 | −0.708326 | ||||||||
\(960\) | −1.08133e19 | −0.445855 | ||||||||
\(961\) | −2.27343e19 | −0.931063 | ||||||||
\(962\) | −1.40506e18 | −0.0571553 | ||||||||
\(963\) | 1.03195e19 | 0.416954 | ||||||||
\(964\) | −1.72574e19 | −0.692586 | ||||||||
\(965\) | 1.21389e19 | 0.483895 | ||||||||
\(966\) | 2.52182e18 | 0.0998532 | ||||||||
\(967\) | 2.96901e19 | 1.16772 | 0.583861 | − | 0.811853i | \(-0.301541\pi\) | ||||
0.583861 | + | 0.811853i | \(0.301541\pi\) | |||||||
\(968\) | 4.01590e18 | 0.156889 | ||||||||
\(969\) | −2.15404e18 | −0.0835890 | ||||||||
\(970\) | −5.29350e18 | −0.204045 | ||||||||
\(971\) | −1.17847e19 | −0.451225 | −0.225613 | − | 0.974217i | \(-0.572438\pi\) | ||||
−0.225613 | + | 0.974217i | \(0.572438\pi\) | |||||||
\(972\) | −1.51811e18 | −0.0577394 | ||||||||
\(973\) | 3.54548e19 | 1.33950 | ||||||||
\(974\) | −1.31220e19 | −0.492455 | ||||||||
\(975\) | 1.44447e19 | 0.538491 | ||||||||
\(976\) | 2.00779e19 | 0.743522 | ||||||||
\(977\) | −4.47194e19 | −1.64506 | −0.822529 | − | 0.568723i | \(-0.807438\pi\) | ||||
−0.822529 | + | 0.568723i | \(0.807438\pi\) | |||||||
\(978\) | 7.57876e18 | 0.276946 | ||||||||
\(979\) | 2.12877e19 | 0.772755 | ||||||||
\(980\) | −3.82229e19 | −1.37833 | ||||||||
\(981\) | 1.76814e19 | 0.633384 | ||||||||
\(982\) | −1.20589e19 | −0.429125 | ||||||||
\(983\) | −1.95000e19 | −0.689345 | −0.344673 | − | 0.938723i | \(-0.612010\pi\) | ||||
−0.344673 | + | 0.938723i | \(0.612010\pi\) | |||||||
\(984\) | −1.51763e19 | −0.532963 | ||||||||
\(985\) | −3.19996e19 | −1.11637 | ||||||||
\(986\) | 1.71304e18 | 0.0593700 | ||||||||
\(987\) | 1.71689e19 | 0.591127 | ||||||||
\(988\) | −5.63772e18 | −0.192834 | ||||||||
\(989\) | 1.41468e19 | 0.480710 | ||||||||
\(990\) | −4.61100e18 | −0.155656 | ||||||||
\(991\) | 3.83680e18 | 0.128674 | 0.0643369 | − | 0.997928i | \(-0.479507\pi\) | ||||
0.0643369 | + | 0.997928i | \(0.479507\pi\) | |||||||
\(992\) | −6.50258e18 | −0.216651 | ||||||||
\(993\) | −2.00584e19 | −0.663936 | ||||||||
\(994\) | 8.38003e18 | 0.275571 | ||||||||
\(995\) | −3.41270e19 | −1.11493 | ||||||||
\(996\) | −5.44674e18 | −0.176787 | ||||||||
\(997\) | −9.82416e18 | −0.316794 | −0.158397 | − | 0.987376i | \(-0.550633\pi\) | ||||
−0.158397 | + | 0.987376i | \(0.550633\pi\) | |||||||
\(998\) | 1.41159e19 | 0.452230 | ||||||||
\(999\) | −2.28976e18 | −0.0728811 |
(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 | 177.14.a.c.1.17 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.17 | ✓ | 31 | 1.1 | even | 1 | trivial |