Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.34 | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 39.9305 | 1.76470 | 0.882348 | − | 0.470598i | \(-0.155962\pi\) | ||||
0.882348 | + | 0.470598i | \(0.155962\pi\) | |||||||
\(3\) | −192.155 | −1.36964 | −0.684821 | − | 0.728712i | \(-0.740119\pi\) | ||||
−0.684821 | + | 0.728712i | \(0.740119\pi\) | |||||||
\(4\) | 1082.44 | 2.11415 | ||||||||
\(5\) | 2270.02 | 1.62430 | 0.812148 | − | 0.583451i | \(-0.198298\pi\) | ||||
0.812148 | + | 0.583451i | \(0.198298\pi\) | |||||||
\(6\) | −7672.86 | −2.41700 | ||||||||
\(7\) | −10525.4 | −1.65691 | −0.828453 | − | 0.560058i | \(-0.810779\pi\) | ||||
−0.828453 | + | 0.560058i | \(0.810779\pi\) | |||||||
\(8\) | 22778.2 | 1.96614 | ||||||||
\(9\) | 17240.7 | 0.875917 | ||||||||
\(10\) | 90643.1 | 2.86639 | ||||||||
\(11\) | −26182.4 | −0.539191 | −0.269596 | − | 0.962974i | \(-0.586890\pi\) | ||||
−0.269596 | + | 0.962974i | \(0.586890\pi\) | |||||||
\(12\) | −207998. | −2.89563 | ||||||||
\(13\) | 130709. | 1.26929 | 0.634643 | − | 0.772805i | \(-0.281147\pi\) | ||||
0.634643 | + | 0.772805i | \(0.281147\pi\) | |||||||
\(14\) | −420285. | −2.92394 | ||||||||
\(15\) | −436197. | −2.22470 | ||||||||
\(16\) | 355331. | 1.35548 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 688429. | 1.54573 | ||||||||
\(19\) | −446045. | −0.785213 | −0.392607 | − | 0.919707i | \(-0.628427\pi\) | ||||
−0.392607 | + | 0.919707i | \(0.628427\pi\) | |||||||
\(20\) | 2.45717e6 | 3.43401 | ||||||||
\(21\) | 2.02251e6 | 2.26937 | ||||||||
\(22\) | −1.04548e6 | −0.951509 | ||||||||
\(23\) | 340450. | 0.253675 | 0.126838 | − | 0.991923i | \(-0.459517\pi\) | ||||
0.126838 | + | 0.991923i | \(0.459517\pi\) | |||||||
\(24\) | −4.37694e6 | −2.69290 | ||||||||
\(25\) | 3.19988e6 | 1.63834 | ||||||||
\(26\) | 5.21927e6 | 2.23990 | ||||||||
\(27\) | 469307. | 0.169949 | ||||||||
\(28\) | −1.13932e7 | −3.50295 | ||||||||
\(29\) | −3.01654e6 | −0.791986 | −0.395993 | − | 0.918253i | \(-0.629600\pi\) | ||||
−0.395993 | + | 0.918253i | \(0.629600\pi\) | |||||||
\(30\) | −1.74176e7 | −3.92592 | ||||||||
\(31\) | −1.67993e6 | −0.326711 | −0.163355 | − | 0.986567i | \(-0.552232\pi\) | ||||
−0.163355 | + | 0.986567i | \(0.552232\pi\) | |||||||
\(32\) | 2.52614e6 | 0.425876 | ||||||||
\(33\) | 5.03109e6 | 0.738499 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.38929e7 | −2.69131 | ||||||||
\(36\) | 1.86621e7 | 1.85182 | ||||||||
\(37\) | −1.57112e7 | −1.37817 | −0.689083 | − | 0.724683i | \(-0.741986\pi\) | ||||
−0.689083 | + | 0.724683i | \(0.741986\pi\) | |||||||
\(38\) | −1.78108e7 | −1.38566 | ||||||||
\(39\) | −2.51164e7 | −1.73847 | ||||||||
\(40\) | 5.17069e7 | 3.19359 | ||||||||
\(41\) | −1.68228e7 | −0.929762 | −0.464881 | − | 0.885373i | \(-0.653903\pi\) | ||||
−0.464881 | + | 0.885373i | \(0.653903\pi\) | |||||||
\(42\) | 8.07600e7 | 4.00474 | ||||||||
\(43\) | −4.62151e6 | −0.206146 | −0.103073 | − | 0.994674i | \(-0.532868\pi\) | ||||
−0.103073 | + | 0.994674i | \(0.532868\pi\) | |||||||
\(44\) | −2.83410e7 | −1.13993 | ||||||||
\(45\) | 3.91367e7 | 1.42275 | ||||||||
\(46\) | 1.35943e7 | 0.447660 | ||||||||
\(47\) | −5.82190e6 | −0.174030 | −0.0870151 | − | 0.996207i | \(-0.527733\pi\) | ||||
−0.0870151 | + | 0.996207i | \(0.527733\pi\) | |||||||
\(48\) | −6.82788e7 | −1.85652 | ||||||||
\(49\) | 7.04308e7 | 1.74534 | ||||||||
\(50\) | 1.27773e8 | 2.89117 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41485e8 | 2.68346 | ||||||||
\(53\) | 2.06125e7 | 0.358831 | 0.179416 | − | 0.983773i | \(-0.442579\pi\) | ||||
0.179416 | + | 0.983773i | \(0.442579\pi\) | |||||||
\(54\) | 1.87397e7 | 0.299909 | ||||||||
\(55\) | −5.94347e7 | −0.875806 | ||||||||
\(56\) | −2.39750e8 | −3.25770 | ||||||||
\(57\) | 8.57099e7 | 1.07546 | ||||||||
\(58\) | −1.20452e8 | −1.39761 | ||||||||
\(59\) | −5.56955e7 | −0.598393 | −0.299196 | − | 0.954192i | \(-0.596719\pi\) | ||||
−0.299196 | + | 0.954192i | \(0.596719\pi\) | |||||||
\(60\) | −4.72159e8 | −4.70336 | ||||||||
\(61\) | 1.23184e8 | 1.13912 | 0.569562 | − | 0.821949i | \(-0.307113\pi\) | ||||
0.569562 | + | 0.821949i | \(0.307113\pi\) | |||||||
\(62\) | −6.70805e7 | −0.576545 | ||||||||
\(63\) | −1.81465e8 | −1.45131 | ||||||||
\(64\) | −8.10595e7 | −0.603940 | ||||||||
\(65\) | 2.96712e8 | 2.06170 | ||||||||
\(66\) | 2.00894e8 | 1.30323 | ||||||||
\(67\) | −1.03447e8 | −0.627166 | −0.313583 | − | 0.949561i | \(-0.601529\pi\) | ||||
−0.313583 | + | 0.949561i | \(0.601529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.54193e7 | −0.347444 | ||||||||
\(70\) | −9.54057e8 | −4.74934 | ||||||||
\(71\) | −2.91931e8 | −1.36338 | −0.681691 | − | 0.731640i | \(-0.738755\pi\) | ||||
−0.681691 | + | 0.731640i | \(0.738755\pi\) | |||||||
\(72\) | 3.92711e8 | 1.72217 | ||||||||
\(73\) | −2.25028e8 | −0.927436 | −0.463718 | − | 0.885983i | \(-0.653485\pi\) | ||||
−0.463718 | + | 0.885983i | \(0.653485\pi\) | |||||||
\(74\) | −6.27356e8 | −2.43204 | ||||||||
\(75\) | −6.14874e8 | −2.24393 | ||||||||
\(76\) | −4.82819e8 | −1.66006 | ||||||||
\(77\) | 2.75581e8 | 0.893390 | ||||||||
\(78\) | −1.00291e9 | −3.06786 | ||||||||
\(79\) | 6.19743e8 | 1.79015 | 0.895075 | − | 0.445915i | \(-0.147122\pi\) | ||||
0.895075 | + | 0.445915i | \(0.147122\pi\) | |||||||
\(80\) | 8.06610e8 | 2.20170 | ||||||||
\(81\) | −4.29528e8 | −1.10869 | ||||||||
\(82\) | −6.71744e8 | −1.64075 | ||||||||
\(83\) | 1.60147e8 | 0.370398 | 0.185199 | − | 0.982701i | \(-0.440707\pi\) | ||||
0.185199 | + | 0.982701i | \(0.440707\pi\) | |||||||
\(84\) | 2.18926e9 | 4.79778 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.84539e8 | −0.363786 | ||||||||
\(87\) | 5.79644e8 | 1.08474 | ||||||||
\(88\) | −5.96387e8 | −1.06012 | ||||||||
\(89\) | 6.09272e8 | 1.02933 | 0.514667 | − | 0.857390i | \(-0.327915\pi\) | ||||
0.514667 | + | 0.857390i | \(0.327915\pi\) | |||||||
\(90\) | 1.56275e9 | 2.51072 | ||||||||
\(91\) | −1.37576e9 | −2.10309 | ||||||||
\(92\) | 3.68519e8 | 0.536308 | ||||||||
\(93\) | 3.22808e8 | 0.447477 | ||||||||
\(94\) | −2.32472e8 | −0.307110 | ||||||||
\(95\) | −1.01253e9 | −1.27542 | ||||||||
\(96\) | −4.85411e8 | −0.583297 | ||||||||
\(97\) | −5.75873e8 | −0.660471 | −0.330236 | − | 0.943899i | \(-0.607128\pi\) | ||||
−0.330236 | + | 0.943899i | \(0.607128\pi\) | |||||||
\(98\) | 2.81234e9 | 3.07999 | ||||||||
\(99\) | −4.51403e8 | −0.472287 | ||||||||
\(100\) | 3.46369e9 | 3.46369 | ||||||||
\(101\) | −8.22534e8 | −0.786516 | −0.393258 | − | 0.919428i | \(-0.628652\pi\) | ||||
−0.393258 | + | 0.919428i | \(0.628652\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.21303e8 | −0.631466 | −0.315733 | − | 0.948848i | \(-0.602250\pi\) | ||||
−0.315733 | + | 0.948848i | \(0.602250\pi\) | |||||||
\(104\) | 2.97730e9 | 2.49559 | ||||||||
\(105\) | 4.59115e9 | 3.68613 | ||||||||
\(106\) | 8.23069e8 | 0.633228 | ||||||||
\(107\) | −2.46308e9 | −1.81657 | −0.908283 | − | 0.418357i | \(-0.862606\pi\) | ||||
−0.908283 | + | 0.418357i | \(0.862606\pi\) | |||||||
\(108\) | 5.07999e8 | 0.359299 | ||||||||
\(109\) | 2.68309e8 | 0.182061 | 0.0910304 | − | 0.995848i | \(-0.470984\pi\) | ||||
0.0910304 | + | 0.995848i | \(0.470984\pi\) | |||||||
\(110\) | −2.37326e9 | −1.54553 | ||||||||
\(111\) | 3.01899e9 | 1.88759 | ||||||||
\(112\) | −3.74001e9 | −2.24591 | ||||||||
\(113\) | −2.59778e9 | −1.49882 | −0.749409 | − | 0.662107i | \(-0.769662\pi\) | ||||
−0.749409 | + | 0.662107i | \(0.769662\pi\) | |||||||
\(114\) | 3.42244e9 | 1.89786 | ||||||||
\(115\) | 7.72830e8 | 0.412044 | ||||||||
\(116\) | −3.26524e9 | −1.67438 | ||||||||
\(117\) | 2.25351e9 | 1.11179 | ||||||||
\(118\) | −2.22395e9 | −1.05598 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −9.93576e9 | −4.37407 | ||||||||
\(121\) | −1.67243e9 | −0.709273 | ||||||||
\(122\) | 4.91881e9 | 2.01021 | ||||||||
\(123\) | 3.23260e9 | 1.27344 | ||||||||
\(124\) | −1.81843e9 | −0.690716 | ||||||||
\(125\) | 2.83016e9 | 1.03685 | ||||||||
\(126\) | −7.24600e9 | −2.56112 | ||||||||
\(127\) | −2.80736e9 | −0.957595 | −0.478797 | − | 0.877925i | \(-0.658927\pi\) | ||||
−0.478797 | + | 0.877925i | \(0.658927\pi\) | |||||||
\(128\) | −4.53013e9 | −1.49165 | ||||||||
\(129\) | 8.88047e8 | 0.282347 | ||||||||
\(130\) | 1.18479e10 | 3.63827 | ||||||||
\(131\) | −4.93021e9 | −1.46266 | −0.731332 | − | 0.682022i | \(-0.761101\pi\) | ||||
−0.731332 | + | 0.682022i | \(0.761101\pi\) | |||||||
\(132\) | 5.44588e9 | 1.56130 | ||||||||
\(133\) | 4.69481e9 | 1.30103 | ||||||||
\(134\) | −4.13070e9 | −1.10676 | ||||||||
\(135\) | 1.06534e9 | 0.276048 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.50097e9 | −1.57665 | −0.788325 | − | 0.615259i | \(-0.789051\pi\) | ||||
−0.788325 | + | 0.615259i | \(0.789051\pi\) | |||||||
\(138\) | −2.61223e9 | −0.613133 | ||||||||
\(139\) | 6.50760e9 | 1.47861 | 0.739306 | − | 0.673370i | \(-0.235154\pi\) | ||||
0.739306 | + | 0.673370i | \(0.235154\pi\) | |||||||
\(140\) | −2.58628e10 | −5.68983 | ||||||||
\(141\) | 1.11871e9 | 0.238359 | ||||||||
\(142\) | −1.16569e10 | −2.40595 | ||||||||
\(143\) | −3.42227e9 | −0.684388 | ||||||||
\(144\) | 6.12615e9 | 1.18729 | ||||||||
\(145\) | −6.84761e9 | −1.28642 | ||||||||
\(146\) | −8.98548e9 | −1.63664 | ||||||||
\(147\) | −1.35336e10 | −2.39049 | ||||||||
\(148\) | −1.70065e10 | −2.91365 | ||||||||
\(149\) | −5.06101e9 | −0.841199 | −0.420600 | − | 0.907246i | \(-0.638180\pi\) | ||||
−0.420600 | + | 0.907246i | \(0.638180\pi\) | |||||||
\(150\) | −2.45522e10 | −3.95986 | ||||||||
\(151\) | −1.65176e9 | −0.258553 | −0.129277 | − | 0.991609i | \(-0.541266\pi\) | ||||
−0.129277 | + | 0.991609i | \(0.541266\pi\) | |||||||
\(152\) | −1.01601e10 | −1.54384 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.10041e10 | 1.57656 | ||||||||
\(155\) | −3.81348e9 | −0.530675 | ||||||||
\(156\) | −2.71871e10 | −3.67538 | ||||||||
\(157\) | 1.14123e10 | 1.49908 | 0.749542 | − | 0.661957i | \(-0.230274\pi\) | ||||
0.749542 | + | 0.661957i | \(0.230274\pi\) | |||||||
\(158\) | 2.47466e10 | 3.15907 | ||||||||
\(159\) | −3.96081e9 | −0.491470 | ||||||||
\(160\) | 5.73440e9 | 0.691748 | ||||||||
\(161\) | −3.58338e9 | −0.420317 | ||||||||
\(162\) | −1.71513e10 | −1.95649 | ||||||||
\(163\) | 6.03422e9 | 0.669541 | 0.334770 | − | 0.942300i | \(-0.391341\pi\) | ||||
0.334770 | + | 0.942300i | \(0.391341\pi\) | |||||||
\(164\) | −1.82098e10 | −1.96566 | ||||||||
\(165\) | 1.14207e10 | 1.19954 | ||||||||
\(166\) | 6.39476e9 | 0.653639 | ||||||||
\(167\) | 9.15503e8 | 0.0910827 | 0.0455413 | − | 0.998962i | \(-0.485499\pi\) | ||||
0.0455413 | + | 0.998962i | \(0.485499\pi\) | |||||||
\(168\) | 4.60692e10 | 4.46189 | ||||||||
\(169\) | 6.48028e9 | 0.611088 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.69012e9 | −0.687781 | ||||||||
\(172\) | −5.00253e9 | −0.435824 | ||||||||
\(173\) | −1.14509e10 | −0.971920 | −0.485960 | − | 0.873981i | \(-0.661530\pi\) | ||||
−0.485960 | + | 0.873981i | \(0.661530\pi\) | |||||||
\(174\) | 2.31455e10 | 1.91423 | ||||||||
\(175\) | −3.36801e10 | −2.71457 | ||||||||
\(176\) | −9.30344e9 | −0.730864 | ||||||||
\(177\) | 1.07022e10 | 0.819583 | ||||||||
\(178\) | 2.43286e10 | 1.81646 | ||||||||
\(179\) | −8.16576e9 | −0.594508 | −0.297254 | − | 0.954798i | \(-0.596071\pi\) | ||||
−0.297254 | + | 0.954798i | \(0.596071\pi\) | |||||||
\(180\) | 4.23633e10 | 3.00790 | ||||||||
\(181\) | 1.94229e10 | 1.34512 | 0.672561 | − | 0.740042i | \(-0.265194\pi\) | ||||
0.672561 | + | 0.740042i | \(0.265194\pi\) | |||||||
\(182\) | −5.49349e10 | −3.71131 | ||||||||
\(183\) | −2.36705e10 | −1.56019 | ||||||||
\(184\) | 7.75483e9 | 0.498760 | ||||||||
\(185\) | −3.56648e10 | −2.23855 | ||||||||
\(186\) | 1.28899e10 | 0.789660 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.30189e9 | −0.367926 | ||||||||
\(189\) | −4.93965e9 | −0.281590 | ||||||||
\(190\) | −4.04309e10 | −2.25073 | ||||||||
\(191\) | −2.56201e10 | −1.39293 | −0.696467 | − | 0.717588i | \(-0.745246\pi\) | ||||
−0.696467 | + | 0.717588i | \(0.745246\pi\) | |||||||
\(192\) | 1.55760e10 | 0.827182 | ||||||||
\(193\) | 3.24728e10 | 1.68466 | 0.842329 | − | 0.538963i | \(-0.181184\pi\) | ||||
0.842329 | + | 0.538963i | \(0.181184\pi\) | |||||||
\(194\) | −2.29949e10 | −1.16553 | ||||||||
\(195\) | −5.70148e10 | −2.82378 | ||||||||
\(196\) | 7.62374e10 | 3.68991 | ||||||||
\(197\) | 3.93713e10 | 1.86244 | 0.931219 | − | 0.364461i | \(-0.118747\pi\) | ||||
0.931219 | + | 0.364461i | \(0.118747\pi\) | |||||||
\(198\) | −1.80247e10 | −0.833442 | ||||||||
\(199\) | −2.57185e9 | −0.116254 | −0.0581268 | − | 0.998309i | \(-0.518513\pi\) | ||||
−0.0581268 | + | 0.998309i | \(0.518513\pi\) | |||||||
\(200\) | 7.28873e10 | 3.22119 | ||||||||
\(201\) | 1.98779e10 | 0.858992 | ||||||||
\(202\) | −3.28442e10 | −1.38796 | ||||||||
\(203\) | 3.17503e10 | 1.31225 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.81882e10 | −1.51021 | ||||||||
\(206\) | −2.88020e10 | −1.11435 | ||||||||
\(207\) | 5.86959e9 | 0.222199 | ||||||||
\(208\) | 4.64449e10 | 1.72049 | ||||||||
\(209\) | 1.16785e10 | 0.423380 | ||||||||
\(210\) | 1.83327e11 | 6.50489 | ||||||||
\(211\) | 1.81456e10 | 0.630231 | 0.315116 | − | 0.949053i | \(-0.397957\pi\) | ||||
0.315116 | + | 0.949053i | \(0.397957\pi\) | |||||||
\(212\) | 2.23120e10 | 0.758623 | ||||||||
\(213\) | 5.60961e10 | 1.86734 | ||||||||
\(214\) | −9.83519e10 | −3.20569 | ||||||||
\(215\) | −1.04909e10 | −0.334843 | ||||||||
\(216\) | 1.06899e10 | 0.334144 | ||||||||
\(217\) | 1.76820e10 | 0.541330 | ||||||||
\(218\) | 1.07137e10 | 0.321282 | ||||||||
\(219\) | 4.32403e10 | 1.27025 | ||||||||
\(220\) | −6.43348e10 | −1.85159 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.20550e11 | 3.33103 | ||||||||
\(223\) | −1.42142e10 | −0.384903 | −0.192451 | − | 0.981307i | \(-0.561644\pi\) | ||||
−0.192451 | + | 0.981307i | \(0.561644\pi\) | |||||||
\(224\) | −2.65887e10 | −0.705636 | ||||||||
\(225\) | 5.51680e10 | 1.43505 | ||||||||
\(226\) | −1.03731e11 | −2.64496 | ||||||||
\(227\) | −7.38003e10 | −1.84477 | −0.922384 | − | 0.386274i | \(-0.873762\pi\) | ||||
−0.922384 | + | 0.386274i | \(0.873762\pi\) | |||||||
\(228\) | 9.27763e10 | 2.27368 | ||||||||
\(229\) | 1.62402e10 | 0.390240 | 0.195120 | − | 0.980779i | \(-0.437490\pi\) | ||||
0.195120 | + | 0.980779i | \(0.437490\pi\) | |||||||
\(230\) | 3.08595e10 | 0.727132 | ||||||||
\(231\) | −5.29544e10 | −1.22362 | ||||||||
\(232\) | −6.87112e10 | −1.55715 | ||||||||
\(233\) | 1.91917e10 | 0.426590 | 0.213295 | − | 0.976988i | \(-0.431580\pi\) | ||||
0.213295 | + | 0.976988i | \(0.431580\pi\) | |||||||
\(234\) | 8.99836e10 | 1.96197 | ||||||||
\(235\) | −1.32159e10 | −0.282677 | ||||||||
\(236\) | −6.02874e10 | −1.26509 | ||||||||
\(237\) | −1.19087e11 | −2.45186 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.13762e10 | 0.423780 | 0.211890 | − | 0.977294i | \(-0.432038\pi\) | ||||
0.211890 | + | 0.977294i | \(0.432038\pi\) | |||||||
\(240\) | −1.54994e11 | −3.01554 | ||||||||
\(241\) | −6.20535e10 | −1.18492 | −0.592461 | − | 0.805599i | \(-0.701844\pi\) | ||||
−0.592461 | + | 0.805599i | \(0.701844\pi\) | |||||||
\(242\) | −6.67809e10 | −1.25165 | ||||||||
\(243\) | 7.32987e10 | 1.34855 | ||||||||
\(244\) | 1.33340e11 | 2.40828 | ||||||||
\(245\) | 1.59879e11 | 2.83495 | ||||||||
\(246\) | 1.29079e11 | 2.24723 | ||||||||
\(247\) | −5.83020e10 | −0.996660 | ||||||||
\(248\) | −3.82657e10 | −0.642358 | ||||||||
\(249\) | −3.07732e10 | −0.507312 | ||||||||
\(250\) | 1.13010e11 | 1.82972 | ||||||||
\(251\) | −5.99268e10 | −0.952992 | −0.476496 | − | 0.879177i | \(-0.658093\pi\) | ||||
−0.476496 | + | 0.879177i | \(0.658093\pi\) | |||||||
\(252\) | −1.96426e11 | −3.06829 | ||||||||
\(253\) | −8.91382e9 | −0.136780 | ||||||||
\(254\) | −1.12099e11 | −1.68986 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39388e11 | −2.02836 | ||||||||
\(257\) | 1.24917e10 | 0.178616 | 0.0893081 | − | 0.996004i | \(-0.471534\pi\) | ||||
0.0893081 | + | 0.996004i | \(0.471534\pi\) | |||||||
\(258\) | 3.54602e10 | 0.498256 | ||||||||
\(259\) | 1.65367e11 | 2.28349 | ||||||||
\(260\) | 3.21174e11 | 4.35874 | ||||||||
\(261\) | −5.20071e10 | −0.693714 | ||||||||
\(262\) | −1.96866e11 | −2.58116 | ||||||||
\(263\) | 5.97877e10 | 0.770569 | 0.385284 | − | 0.922798i | \(-0.374103\pi\) | ||||
0.385284 | + | 0.922798i | \(0.374103\pi\) | |||||||
\(264\) | 1.14599e11 | 1.45199 | ||||||||
\(265\) | 4.67910e10 | 0.582848 | ||||||||
\(266\) | 1.87466e11 | 2.29591 | ||||||||
\(267\) | −1.17075e11 | −1.40982 | ||||||||
\(268\) | −1.11976e11 | −1.32592 | ||||||||
\(269\) | 4.76191e10 | 0.554493 | 0.277246 | − | 0.960799i | \(-0.410578\pi\) | ||||
0.277246 | + | 0.960799i | \(0.410578\pi\) | |||||||
\(270\) | 4.25394e10 | 0.487141 | ||||||||
\(271\) | 2.21456e10 | 0.249417 | 0.124709 | − | 0.992193i | \(-0.460200\pi\) | ||||
0.124709 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.64360e11 | 2.88048 | ||||||||
\(274\) | −2.59587e11 | −2.78231 | ||||||||
\(275\) | −8.37806e10 | −0.883378 | ||||||||
\(276\) | −7.08128e10 | −0.734549 | ||||||||
\(277\) | 9.60150e10 | 0.979896 | 0.489948 | − | 0.871752i | \(-0.337016\pi\) | ||||
0.489948 | + | 0.871752i | \(0.337016\pi\) | |||||||
\(278\) | 2.59852e11 | 2.60930 | ||||||||
\(279\) | −2.89631e10 | −0.286172 | ||||||||
\(280\) | −5.44237e11 | −5.29148 | ||||||||
\(281\) | 5.47493e10 | 0.523842 | 0.261921 | − | 0.965089i | \(-0.415644\pi\) | ||||
0.261921 | + | 0.965089i | \(0.415644\pi\) | |||||||
\(282\) | 4.46707e10 | 0.420631 | ||||||||
\(283\) | 1.95278e11 | 1.80973 | 0.904865 | − | 0.425699i | \(-0.139972\pi\) | ||||
0.904865 | + | 0.425699i | \(0.139972\pi\) | |||||||
\(284\) | −3.15999e11 | −2.88239 | ||||||||
\(285\) | 1.94564e11 | 1.74687 | ||||||||
\(286\) | −1.36653e11 | −1.20774 | ||||||||
\(287\) | 1.77067e11 | 1.54053 | ||||||||
\(288\) | 4.35524e10 | 0.373032 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −2.73428e11 | −2.27014 | ||||||||
\(291\) | 1.10657e11 | 0.904608 | ||||||||
\(292\) | −2.43580e11 | −1.96074 | ||||||||
\(293\) | −7.82174e10 | −0.620010 | −0.310005 | − | 0.950735i | \(-0.600331\pi\) | ||||
−0.310005 | + | 0.950735i | \(0.600331\pi\) | |||||||
\(294\) | −5.40405e11 | −4.21849 | ||||||||
\(295\) | −1.26430e11 | −0.971967 | ||||||||
\(296\) | −3.57872e11 | −2.70966 | ||||||||
\(297\) | −1.22876e10 | −0.0916353 | ||||||||
\(298\) | −2.02089e11 | −1.48446 | ||||||||
\(299\) | 4.44998e10 | 0.321987 | ||||||||
\(300\) | −6.65567e11 | −4.74402 | ||||||||
\(301\) | 4.86433e10 | 0.341565 | ||||||||
\(302\) | −6.59555e10 | −0.456268 | ||||||||
\(303\) | 1.58054e11 | 1.07724 | ||||||||
\(304\) | −1.58494e11 | −1.06434 | ||||||||
\(305\) | 2.79631e11 | 1.85027 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.90235e11 | −1.22227 | −0.611136 | − | 0.791526i | \(-0.709287\pi\) | ||||
−0.611136 | + | 0.791526i | \(0.709287\pi\) | |||||||
\(308\) | 2.98301e11 | 1.88876 | ||||||||
\(309\) | 1.38602e11 | 0.864882 | ||||||||
\(310\) | −1.52274e11 | −0.936480 | ||||||||
\(311\) | 8.33297e10 | 0.505101 | 0.252550 | − | 0.967584i | \(-0.418731\pi\) | ||||
0.252550 | + | 0.967584i | \(0.418731\pi\) | |||||||
\(312\) | −5.72105e11 | −3.41806 | ||||||||
\(313\) | 2.01585e11 | 1.18716 | 0.593580 | − | 0.804775i | \(-0.297714\pi\) | ||||
0.593580 | + | 0.804775i | \(0.297714\pi\) | |||||||
\(314\) | 4.55700e11 | 2.64543 | ||||||||
\(315\) | −4.11930e11 | −2.35736 | ||||||||
\(316\) | 6.70838e11 | 3.78465 | ||||||||
\(317\) | 1.02689e10 | 0.0571158 | 0.0285579 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285579 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(318\) | −1.58157e11 | −0.867295 | ||||||||
\(319\) | 7.89803e10 | 0.427032 | ||||||||
\(320\) | −1.84007e11 | −0.980978 | ||||||||
\(321\) | 4.73294e11 | 2.48804 | ||||||||
\(322\) | −1.43086e11 | −0.741731 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.64940e11 | −2.34393 | ||||||||
\(325\) | 4.18252e11 | 2.07952 | ||||||||
\(326\) | 2.40949e11 | 1.18154 | ||||||||
\(327\) | −5.15571e10 | −0.249358 | ||||||||
\(328\) | −3.83193e11 | −1.82804 | ||||||||
\(329\) | 6.12780e10 | 0.288352 | ||||||||
\(330\) | 4.56034e11 | 2.11682 | ||||||||
\(331\) | 4.20342e10 | 0.192476 | 0.0962380 | − | 0.995358i | \(-0.469319\pi\) | ||||
0.0962380 | + | 0.995358i | \(0.469319\pi\) | |||||||
\(332\) | 1.73351e11 | 0.783076 | ||||||||
\(333\) | −2.70871e11 | −1.20716 | ||||||||
\(334\) | 3.65565e10 | 0.160733 | ||||||||
\(335\) | −2.34828e11 | −1.01870 | ||||||||
\(336\) | 7.18663e11 | 3.07609 | ||||||||
\(337\) | 1.17165e11 | 0.494840 | 0.247420 | − | 0.968908i | \(-0.420417\pi\) | ||||
0.247420 | + | 0.968908i | \(0.420417\pi\) | |||||||
\(338\) | 2.58761e11 | 1.07838 | ||||||||
\(339\) | 4.99177e11 | 2.05284 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.39847e10 | 0.176160 | ||||||||
\(342\) | −3.07070e11 | −1.21372 | ||||||||
\(343\) | −3.16575e11 | −1.23496 | ||||||||
\(344\) | −1.05269e11 | −0.405312 | ||||||||
\(345\) | −1.48503e11 | −0.564352 | ||||||||
\(346\) | −4.57239e11 | −1.71514 | ||||||||
\(347\) | −8.63930e10 | −0.319886 | −0.159943 | − | 0.987126i | \(-0.551131\pi\) | ||||
−0.159943 | + | 0.987126i | \(0.551131\pi\) | |||||||
\(348\) | 6.27432e11 | 2.29330 | ||||||||
\(349\) | 7.38933e10 | 0.266619 | 0.133309 | − | 0.991074i | \(-0.457440\pi\) | ||||
0.133309 | + | 0.991074i | \(0.457440\pi\) | |||||||
\(350\) | −1.34486e12 | −4.79040 | ||||||||
\(351\) | 6.13425e10 | 0.215715 | ||||||||
\(352\) | −6.61405e10 | −0.229628 | ||||||||
\(353\) | 5.59145e10 | 0.191663 | 0.0958315 | − | 0.995398i | \(-0.469449\pi\) | ||||
0.0958315 | + | 0.995398i | \(0.469449\pi\) | |||||||
\(354\) | 4.27344e11 | 1.44632 | ||||||||
\(355\) | −6.62690e11 | −2.21454 | ||||||||
\(356\) | 6.59504e11 | 2.17617 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.26063e11 | −1.04913 | ||||||||
\(359\) | 1.53879e11 | 0.488937 | 0.244469 | − | 0.969657i | \(-0.421387\pi\) | ||||
0.244469 | + | 0.969657i | \(0.421387\pi\) | |||||||
\(360\) | 8.91462e11 | 2.79732 | ||||||||
\(361\) | −1.23731e11 | −0.383440 | ||||||||
\(362\) | 7.75568e11 | 2.37373 | ||||||||
\(363\) | 3.21366e11 | 0.971449 | ||||||||
\(364\) | −1.48919e12 | −4.44625 | ||||||||
\(365\) | −5.10819e11 | −1.50643 | ||||||||
\(366\) | −9.45175e11 | −2.75326 | ||||||||
\(367\) | −2.65608e11 | −0.764265 | −0.382132 | − | 0.924108i | \(-0.624810\pi\) | ||||
−0.382132 | + | 0.924108i | \(0.624810\pi\) | |||||||
\(368\) | 1.20973e11 | 0.343852 | ||||||||
\(369\) | −2.90037e11 | −0.814394 | ||||||||
\(370\) | −1.42411e12 | −3.95036 | ||||||||
\(371\) | −2.16956e11 | −0.594550 | ||||||||
\(372\) | 3.49421e11 | 0.946033 | ||||||||
\(373\) | −1.61393e11 | −0.431713 | −0.215857 | − | 0.976425i | \(-0.569254\pi\) | ||||
−0.215857 | + | 0.976425i | \(0.569254\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.43830e11 | −1.42011 | ||||||||
\(376\) | −1.32612e11 | −0.342167 | ||||||||
\(377\) | −3.94288e11 | −1.00526 | ||||||||
\(378\) | −1.97243e11 | −0.496921 | ||||||||
\(379\) | 1.58023e11 | 0.393408 | 0.196704 | − | 0.980463i | \(-0.436976\pi\) | ||||
0.196704 | + | 0.980463i | \(0.436976\pi\) | |||||||
\(380\) | −1.09601e12 | −2.69643 | ||||||||
\(381\) | 5.39450e11 | 1.31156 | ||||||||
\(382\) | −1.02302e12 | −2.45811 | ||||||||
\(383\) | 4.20992e11 | 0.999722 | 0.499861 | − | 0.866106i | \(-0.333384\pi\) | ||||
0.499861 | + | 0.866106i | \(0.333384\pi\) | |||||||
\(384\) | 8.70489e11 | 2.04302 | ||||||||
\(385\) | 6.25575e11 | 1.45113 | ||||||||
\(386\) | 1.29666e12 | 2.97291 | ||||||||
\(387\) | −7.96779e10 | −0.180567 | ||||||||
\(388\) | −6.23351e11 | −1.39634 | ||||||||
\(389\) | −5.78199e11 | −1.28028 | −0.640139 | − | 0.768259i | \(-0.721123\pi\) | ||||
−0.640139 | + | 0.768259i | \(0.721123\pi\) | |||||||
\(390\) | −2.27663e12 | −4.98312 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.60428e12 | 3.43158 | ||||||||
\(393\) | 9.47366e11 | 2.00332 | ||||||||
\(394\) | 1.57212e12 | 3.28663 | ||||||||
\(395\) | 1.40683e12 | 2.90773 | ||||||||
\(396\) | −4.88619e11 | −0.998485 | ||||||||
\(397\) | 6.39613e11 | 1.29229 | 0.646145 | − | 0.763215i | \(-0.276380\pi\) | ||||
0.646145 | + | 0.763215i | \(0.276380\pi\) | |||||||
\(398\) | −1.02695e11 | −0.205152 | ||||||||
\(399\) | −9.02133e11 | −1.78194 | ||||||||
\(400\) | 1.13702e12 | 2.22074 | ||||||||
\(401\) | −5.74794e11 | −1.11010 | −0.555051 | − | 0.831816i | \(-0.687301\pi\) | ||||
−0.555051 | + | 0.831816i | \(0.687301\pi\) | |||||||
\(402\) | 7.93736e11 | 1.51586 | ||||||||
\(403\) | −2.19582e11 | −0.414690 | ||||||||
\(404\) | −8.90347e11 | −1.66281 | ||||||||
\(405\) | −9.75038e11 | −1.80084 | ||||||||
\(406\) | 1.26781e12 | 2.31572 | ||||||||
\(407\) | 4.11357e11 | 0.743095 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.11632e11 | −0.550664 | −0.275332 | − | 0.961349i | \(-0.588788\pi\) | ||||
−0.275332 | + | 0.961349i | \(0.588788\pi\) | |||||||
\(410\) | −1.52487e12 | −2.66506 | ||||||||
\(411\) | 1.24920e12 | 2.15944 | ||||||||
\(412\) | −7.80770e11 | −1.33501 | ||||||||
\(413\) | 5.86219e11 | 0.991481 | ||||||||
\(414\) | 2.34376e11 | 0.392113 | ||||||||
\(415\) | 3.63538e11 | 0.601635 | ||||||||
\(416\) | 3.30189e11 | 0.540558 | ||||||||
\(417\) | −1.25047e12 | −2.02517 | ||||||||
\(418\) | 4.66330e11 | 0.747137 | ||||||||
\(419\) | −2.81135e11 | −0.445608 | −0.222804 | − | 0.974863i | \(-0.571521\pi\) | ||||
−0.222804 | + | 0.974863i | \(0.571521\pi\) | |||||||
\(420\) | 4.96967e12 | 7.79302 | ||||||||
\(421\) | 1.12765e12 | 1.74947 | 0.874733 | − | 0.484605i | \(-0.161037\pi\) | ||||
0.874733 | + | 0.484605i | \(0.161037\pi\) | |||||||
\(422\) | 7.24562e11 | 1.11217 | ||||||||
\(423\) | −1.00374e11 | −0.152436 | ||||||||
\(424\) | 4.69516e11 | 0.705511 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.23995e12 | 3.29529 | ||||||||
\(427\) | −1.29657e12 | −1.88742 | ||||||||
\(428\) | −2.66615e12 | −3.84049 | ||||||||
\(429\) | 6.57608e11 | 0.937366 | ||||||||
\(430\) | −4.18908e11 | −0.590895 | ||||||||
\(431\) | 4.10369e10 | 0.0572831 | 0.0286416 | − | 0.999590i | \(-0.490882\pi\) | ||||
0.0286416 | + | 0.999590i | \(0.490882\pi\) | |||||||
\(432\) | 1.66759e11 | 0.230363 | ||||||||
\(433\) | 9.68299e11 | 1.32377 | 0.661887 | − | 0.749604i | \(-0.269756\pi\) | ||||
0.661887 | + | 0.749604i | \(0.269756\pi\) | |||||||
\(434\) | 7.06050e11 | 0.955282 | ||||||||
\(435\) | 1.31580e12 | 1.76193 | ||||||||
\(436\) | 2.90430e11 | 0.384904 | ||||||||
\(437\) | −1.51856e11 | −0.199189 | ||||||||
\(438\) | 1.72661e12 | 2.24161 | ||||||||
\(439\) | 1.39595e12 | 1.79382 | 0.896912 | − | 0.442208i | \(-0.145805\pi\) | ||||
0.896912 | + | 0.442208i | \(0.145805\pi\) | |||||||
\(440\) | −1.35381e12 | −1.72195 | ||||||||
\(441\) | 1.21427e12 | 1.52877 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.85808e11 | 0.352580 | 0.176290 | − | 0.984338i | \(-0.443590\pi\) | ||||
0.176290 | + | 0.984338i | \(0.443590\pi\) | |||||||
\(444\) | 3.26789e12 | 3.99065 | ||||||||
\(445\) | 1.38306e12 | 1.67194 | ||||||||
\(446\) | −5.67580e11 | −0.679236 | ||||||||
\(447\) | 9.72500e11 | 1.15214 | ||||||||
\(448\) | 8.53185e11 | 1.00067 | ||||||||
\(449\) | 4.26432e11 | 0.495156 | 0.247578 | − | 0.968868i | \(-0.420365\pi\) | ||||
0.247578 | + | 0.968868i | \(0.420365\pi\) | |||||||
\(450\) | 2.20289e12 | 2.53242 | ||||||||
\(451\) | 4.40463e11 | 0.501320 | ||||||||
\(452\) | −2.81195e12 | −3.16873 | ||||||||
\(453\) | 3.17394e11 | 0.354125 | ||||||||
\(454\) | −2.94688e12 | −3.25545 | ||||||||
\(455\) | −3.12302e12 | −3.41604 | ||||||||
\(456\) | 1.95231e12 | 2.11450 | ||||||||
\(457\) | 9.18833e11 | 0.985403 | 0.492701 | − | 0.870198i | \(-0.336010\pi\) | ||||
0.492701 | + | 0.870198i | \(0.336010\pi\) | |||||||
\(458\) | 6.48479e11 | 0.688654 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.36546e11 | 0.871123 | ||||||||
\(461\) | 1.32769e12 | 1.36912 | 0.684559 | − | 0.728957i | \(-0.259995\pi\) | ||||
0.684559 | + | 0.728957i | \(0.259995\pi\) | |||||||
\(462\) | −2.11449e12 | −2.15932 | ||||||||
\(463\) | −2.36101e11 | −0.238772 | −0.119386 | − | 0.992848i | \(-0.538093\pi\) | ||||
−0.119386 | + | 0.992848i | \(0.538093\pi\) | |||||||
\(464\) | −1.07187e12 | −1.07352 | ||||||||
\(465\) | 7.32781e11 | 0.726835 | ||||||||
\(466\) | 7.66333e11 | 0.752802 | ||||||||
\(467\) | 2.97347e11 | 0.289293 | 0.144647 | − | 0.989483i | \(-0.453795\pi\) | ||||
0.144647 | + | 0.989483i | \(0.453795\pi\) | |||||||
\(468\) | 2.43930e12 | 2.35049 | ||||||||
\(469\) | 1.08883e12 | 1.03916 | ||||||||
\(470\) | −5.27716e11 | −0.498838 | ||||||||
\(471\) | −2.19294e12 | −2.05321 | ||||||||
\(472\) | −1.26864e12 | −1.17652 | ||||||||
\(473\) | 1.21002e11 | 0.111152 | ||||||||
\(474\) | −4.75520e12 | −4.32679 | ||||||||
\(475\) | −1.42729e12 | −1.28644 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.55374e11 | 0.314306 | ||||||||
\(478\) | 8.53563e11 | 0.747842 | ||||||||
\(479\) | 3.85863e11 | 0.334906 | 0.167453 | − | 0.985880i | \(-0.446446\pi\) | ||||
0.167453 | + | 0.985880i | \(0.446446\pi\) | |||||||
\(480\) | −1.10190e12 | −0.947447 | ||||||||
\(481\) | −2.05359e12 | −1.74929 | ||||||||
\(482\) | −2.47783e12 | −2.09103 | ||||||||
\(483\) | 6.88566e11 | 0.575683 | ||||||||
\(484\) | −1.81031e12 | −1.49951 | ||||||||
\(485\) | −1.30724e12 | −1.07280 | ||||||||
\(486\) | 2.92685e12 | 2.37979 | ||||||||
\(487\) | 3.74600e11 | 0.301778 | 0.150889 | − | 0.988551i | \(-0.451786\pi\) | ||||
0.150889 | + | 0.988551i | \(0.451786\pi\) | |||||||
\(488\) | 2.80591e12 | 2.23967 | ||||||||
\(489\) | −1.15951e12 | −0.917030 | ||||||||
\(490\) | 6.38407e12 | 5.00282 | ||||||||
\(491\) | −2.24428e12 | −1.74265 | −0.871324 | − | 0.490708i | \(-0.836738\pi\) | ||||
−0.871324 | + | 0.490708i | \(0.836738\pi\) | |||||||
\(492\) | 3.49911e12 | 2.69224 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.32803e12 | −1.75880 | ||||||||
\(495\) | −1.02469e12 | −0.767133 | ||||||||
\(496\) | −5.96932e11 | −0.442851 | ||||||||
\(497\) | 3.07269e12 | 2.25900 | ||||||||
\(498\) | −1.22879e12 | −0.895251 | ||||||||
\(499\) | 2.05931e12 | 1.48686 | 0.743429 | − | 0.668815i | \(-0.233198\pi\) | ||||
0.743429 | + | 0.668815i | \(0.233198\pi\) | |||||||
\(500\) | 3.06349e12 | 2.19206 | ||||||||
\(501\) | −1.75919e11 | −0.124751 | ||||||||
\(502\) | −2.39291e12 | −1.68174 | ||||||||
\(503\) | −6.76592e11 | −0.471271 | −0.235636 | − | 0.971841i | \(-0.575717\pi\) | ||||
−0.235636 | + | 0.971841i | \(0.575717\pi\) | |||||||
\(504\) | −4.13344e12 | −2.85348 | ||||||||
\(505\) | −1.86717e12 | −1.27753 | ||||||||
\(506\) | −3.55933e11 | −0.241374 | ||||||||
\(507\) | −1.24522e12 | −0.836971 | ||||||||
\(508\) | −3.03882e12 | −2.02450 | ||||||||
\(509\) | −1.65744e12 | −1.09448 | −0.547240 | − | 0.836976i | \(-0.684321\pi\) | ||||
−0.547240 | + | 0.836976i | \(0.684321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.36851e12 | 1.53667 | ||||||||
\(512\) | −3.24640e12 | −2.08779 | ||||||||
\(513\) | −2.09332e11 | −0.133447 | ||||||||
\(514\) | 4.98798e11 | 0.315203 | ||||||||
\(515\) | −1.63737e12 | −1.02569 | ||||||||
\(516\) | 9.61262e11 | 0.596923 | ||||||||
\(517\) | 1.52432e11 | 0.0938356 | ||||||||
\(518\) | 6.60318e12 | 4.02967 | ||||||||
\(519\) | 2.20034e12 | 1.33118 | ||||||||
\(520\) | 6.75855e12 | 4.05358 | ||||||||
\(521\) | −3.35020e11 | −0.199205 | −0.0996027 | − | 0.995027i | \(-0.531757\pi\) | ||||
−0.0996027 | + | 0.995027i | \(0.531757\pi\) | |||||||
\(522\) | −2.07667e12 | −1.22419 | ||||||||
\(523\) | −1.54766e12 | −0.904519 | −0.452260 | − | 0.891886i | \(-0.649382\pi\) | ||||
−0.452260 | + | 0.891886i | \(0.649382\pi\) | |||||||
\(524\) | −5.33668e12 | −3.09229 | ||||||||
\(525\) | 6.47180e12 | 3.71799 | ||||||||
\(526\) | 2.38735e12 | 1.35982 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.78770e12 | 1.00102 | ||||||||
\(529\) | −1.68525e12 | −0.935649 | ||||||||
\(530\) | 1.86839e12 | 1.02855 | ||||||||
\(531\) | −9.60229e11 | −0.524142 | ||||||||
\(532\) | 5.08187e12 | 2.75056 | ||||||||
\(533\) | −2.19889e12 | −1.18013 | ||||||||
\(534\) | −4.67486e12 | −2.48790 | ||||||||
\(535\) | −5.59124e12 | −2.95064 | ||||||||
\(536\) | −2.35634e12 | −1.23309 | ||||||||
\(537\) | 1.56909e12 | 0.814263 | ||||||||
\(538\) | 1.90145e12 | 0.978511 | ||||||||
\(539\) | −1.84405e12 | −0.941072 | ||||||||
\(540\) | 1.15317e12 | 0.583607 | ||||||||
\(541\) | −1.39774e11 | −0.0701518 | −0.0350759 | − | 0.999385i | \(-0.511167\pi\) | ||||
−0.0350759 | + | 0.999385i | \(0.511167\pi\) | |||||||
\(542\) | 8.84287e11 | 0.440145 | ||||||||
\(543\) | −3.73222e12 | −1.84233 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.09068e11 | 0.295721 | ||||||||
\(546\) | 1.05560e13 | 5.08317 | ||||||||
\(547\) | −2.71387e12 | −1.29612 | −0.648062 | − | 0.761587i | \(-0.724420\pi\) | ||||
−0.648062 | + | 0.761587i | \(0.724420\pi\) | |||||||
\(548\) | −7.03694e12 | −3.33328 | ||||||||
\(549\) | 2.12378e12 | 0.997777 | ||||||||
\(550\) | −3.34540e12 | −1.55889 | ||||||||
\(551\) | 1.34551e12 | 0.621878 | ||||||||
\(552\) | −1.49013e12 | −0.683123 | ||||||||
\(553\) | −6.52305e12 | −2.96611 | ||||||||
\(554\) | 3.83393e12 | 1.72922 | ||||||||
\(555\) | 6.85317e12 | 3.06601 | ||||||||
\(556\) | 7.04412e12 | 3.12601 | ||||||||
\(557\) | 1.13986e12 | 0.501769 | 0.250884 | − | 0.968017i | \(-0.419279\pi\) | ||||
0.250884 | + | 0.968017i | \(0.419279\pi\) | |||||||
\(558\) | −1.15651e12 | −0.505006 | ||||||||
\(559\) | −6.04072e11 | −0.261659 | ||||||||
\(560\) | −8.48991e12 | −3.64802 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.18617e12 | 0.924421 | ||||||||
\(563\) | 1.30558e12 | 0.547667 | 0.273834 | − | 0.961777i | \(-0.411708\pi\) | ||||
0.273834 | + | 0.961777i | \(0.411708\pi\) | |||||||
\(564\) | 1.21094e12 | 0.503927 | ||||||||
\(565\) | −5.89701e12 | −2.43452 | ||||||||
\(566\) | 7.79753e12 | 3.19362 | ||||||||
\(567\) | 4.52096e12 | 1.83699 | ||||||||
\(568\) | −6.64965e12 | −2.68059 | ||||||||
\(569\) | 1.81208e12 | 0.724722 | 0.362361 | − | 0.932038i | \(-0.381971\pi\) | ||||
0.362361 | + | 0.932038i | \(0.381971\pi\) | |||||||
\(570\) | 7.76902e12 | 3.08269 | ||||||||
\(571\) | −5.00343e12 | −1.96972 | −0.984862 | − | 0.173340i | \(-0.944544\pi\) | ||||
−0.984862 | + | 0.173340i | \(0.944544\pi\) | |||||||
\(572\) | −3.70442e12 | −1.44690 | ||||||||
\(573\) | 4.92304e12 | 1.90782 | ||||||||
\(574\) | 7.07039e12 | 2.71856 | ||||||||
\(575\) | 1.08940e12 | 0.415606 | ||||||||
\(576\) | −1.39752e12 | −0.529002 | ||||||||
\(577\) | 2.87243e11 | 0.107884 | 0.0539422 | − | 0.998544i | \(-0.482821\pi\) | ||||
0.0539422 | + | 0.998544i | \(0.482821\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.23982e12 | −2.30738 | ||||||||
\(580\) | −7.41216e12 | −2.71969 | ||||||||
\(581\) | −1.68562e12 | −0.613714 | ||||||||
\(582\) | 4.41859e12 | 1.59636 | ||||||||
\(583\) | −5.39687e11 | −0.193479 | ||||||||
\(584\) | −5.12572e12 | −1.82346 | ||||||||
\(585\) | 5.11551e12 | 1.80587 | ||||||||
\(586\) | −3.12326e12 | −1.09413 | ||||||||
\(587\) | 2.18972e12 | 0.761232 | 0.380616 | − | 0.924733i | \(-0.375712\pi\) | ||||
0.380616 | + | 0.924733i | \(0.375712\pi\) | |||||||
\(588\) | −1.46494e13 | −5.05386 | ||||||||
\(589\) | 7.49325e11 | 0.256538 | ||||||||
\(590\) | −5.04842e12 | −1.71523 | ||||||||
\(591\) | −7.56540e12 | −2.55087 | ||||||||
\(592\) | −5.58268e12 | −1.86808 | ||||||||
\(593\) | 7.91217e11 | 0.262754 | 0.131377 | − | 0.991332i | \(-0.458060\pi\) | ||||
0.131377 | + | 0.991332i | \(0.458060\pi\) | |||||||
\(594\) | −4.90650e11 | −0.161708 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.47826e12 | −1.77842 | ||||||||
\(597\) | 4.94194e11 | 0.159226 | ||||||||
\(598\) | 1.77690e12 | 0.568209 | ||||||||
\(599\) | 3.64233e12 | 1.15600 | 0.578001 | − | 0.816036i | \(-0.303833\pi\) | ||||
0.578001 | + | 0.816036i | \(0.303833\pi\) | |||||||
\(600\) | −1.40057e13 | −4.41188 | ||||||||
\(601\) | −6.61320e11 | −0.206765 | −0.103382 | − | 0.994642i | \(-0.532967\pi\) | ||||
−0.103382 | + | 0.994642i | \(0.532967\pi\) | |||||||
\(602\) | 1.94235e12 | 0.602759 | ||||||||
\(603\) | −1.78350e12 | −0.549345 | ||||||||
\(604\) | −1.78794e12 | −0.546620 | ||||||||
\(605\) | −3.79645e12 | −1.15207 | ||||||||
\(606\) | 6.31118e12 | 1.90101 | ||||||||
\(607\) | 6.37807e11 | 0.190695 | 0.0953477 | − | 0.995444i | \(-0.469604\pi\) | ||||
0.0953477 | + | 0.995444i | \(0.469604\pi\) | |||||||
\(608\) | −1.12677e12 | −0.334403 | ||||||||
\(609\) | −6.10099e12 | −1.79731 | ||||||||
\(610\) | 1.11658e13 | 3.26517 | ||||||||
\(611\) | −7.60974e11 | −0.220894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.20031e12 | 1.20146 | 0.600729 | − | 0.799452i | \(-0.294877\pi\) | ||||
0.600729 | + | 0.799452i | \(0.294877\pi\) | |||||||
\(614\) | −7.59618e12 | −2.15694 | ||||||||
\(615\) | 7.33807e12 | 2.06844 | ||||||||
\(616\) | 6.27723e12 | 1.75653 | ||||||||
\(617\) | 5.36107e12 | 1.48925 | 0.744625 | − | 0.667483i | \(-0.232628\pi\) | ||||
0.744625 | + | 0.667483i | \(0.232628\pi\) | |||||||
\(618\) | 5.53445e12 | 1.52625 | ||||||||
\(619\) | 5.27140e10 | 0.0144317 | 0.00721586 | − | 0.999974i | \(-0.497703\pi\) | ||||
0.00721586 | + | 0.999974i | \(0.497703\pi\) | |||||||
\(620\) | −4.12788e12 | −1.12193 | ||||||||
\(621\) | 1.59776e11 | 0.0431120 | ||||||||
\(622\) | 3.32740e12 | 0.891349 | ||||||||
\(623\) | −6.41285e12 | −1.70551 | ||||||||
\(624\) | −8.92464e12 | −2.35646 | ||||||||
\(625\) | 1.74762e11 | 0.0458129 | ||||||||
\(626\) | 8.04940e12 | 2.09498 | ||||||||
\(627\) | −2.24409e12 | −0.579879 | ||||||||
\(628\) | 1.23532e13 | 3.16929 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.64486e13 | −4.16002 | ||||||||
\(631\) | 4.08326e12 | 1.02536 | 0.512678 | − | 0.858581i | \(-0.328653\pi\) | ||||
0.512678 | + | 0.858581i | \(0.328653\pi\) | |||||||
\(632\) | 1.41166e13 | 3.51968 | ||||||||
\(633\) | −3.48677e12 | −0.863191 | ||||||||
\(634\) | 4.10041e11 | 0.100792 | ||||||||
\(635\) | −6.37278e12 | −1.55542 | ||||||||
\(636\) | −4.28736e12 | −1.03904 | ||||||||
\(637\) | 9.20592e12 | 2.21534 | ||||||||
\(638\) | 3.15372e12 | 0.753582 | ||||||||
\(639\) | −5.03309e12 | −1.19421 | ||||||||
\(640\) | −1.02835e13 | −2.42288 | ||||||||
\(641\) | 1.09935e12 | 0.257203 | 0.128601 | − | 0.991696i | \(-0.458951\pi\) | ||||
0.128601 | + | 0.991696i | \(0.458951\pi\) | |||||||
\(642\) | 1.88988e13 | 4.39064 | ||||||||
\(643\) | −7.93048e12 | −1.82957 | −0.914787 | − | 0.403937i | \(-0.867642\pi\) | ||||
−0.914787 | + | 0.403937i | \(0.867642\pi\) | |||||||
\(644\) | −3.87881e12 | −0.888612 | ||||||||
\(645\) | 2.01589e12 | 0.458614 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.70401e12 | −1.27971 | −0.639854 | − | 0.768496i | \(-0.721005\pi\) | ||||
−0.639854 | + | 0.768496i | \(0.721005\pi\) | |||||||
\(648\) | −9.78385e12 | −2.17983 | ||||||||
\(649\) | 1.45824e12 | 0.322648 | ||||||||
\(650\) | 1.67010e13 | 3.66972 | ||||||||
\(651\) | −3.39768e12 | −0.741427 | ||||||||
\(652\) | 6.53171e12 | 1.41551 | ||||||||
\(653\) | 1.03269e12 | 0.222260 | 0.111130 | − | 0.993806i | \(-0.464553\pi\) | ||||
0.111130 | + | 0.993806i | \(0.464553\pi\) | |||||||
\(654\) | −2.05870e12 | −0.440041 | ||||||||
\(655\) | −1.11917e13 | −2.37580 | ||||||||
\(656\) | −5.97768e12 | −1.26027 | ||||||||
\(657\) | −3.87963e12 | −0.812356 | ||||||||
\(658\) | 2.44686e12 | 0.508853 | ||||||||
\(659\) | 3.77448e12 | 0.779601 | 0.389801 | − | 0.920899i | \(-0.372544\pi\) | ||||
0.389801 | + | 0.920899i | \(0.372544\pi\) | |||||||
\(660\) | 1.23623e13 | 2.53601 | ||||||||
\(661\) | −6.49086e12 | −1.32250 | −0.661250 | − | 0.750166i | \(-0.729974\pi\) | ||||
−0.661250 | + | 0.750166i | \(0.729974\pi\) | |||||||
\(662\) | 1.67845e12 | 0.339662 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.64786e12 | 0.728252 | ||||||||
\(665\) | 1.06573e13 | 2.11325 | ||||||||
\(666\) | −1.08160e13 | −2.13027 | ||||||||
\(667\) | −1.02698e12 | −0.200907 | ||||||||
\(668\) | 9.90982e11 | 0.192562 | ||||||||
\(669\) | 2.73134e12 | 0.527178 | ||||||||
\(670\) | −9.37679e12 | −1.79770 | ||||||||
\(671\) | −3.22526e12 | −0.614206 | ||||||||
\(672\) | 5.10916e12 | 0.966468 | ||||||||
\(673\) | −3.32644e12 | −0.625045 | −0.312523 | − | 0.949910i | \(-0.601174\pi\) | ||||
−0.312523 | + | 0.949910i | \(0.601174\pi\) | |||||||
\(674\) | 4.67847e12 | 0.873242 | ||||||||
\(675\) | 1.50172e12 | 0.278435 | ||||||||
\(676\) | 7.01454e12 | 1.29193 | ||||||||
\(677\) | −7.88907e12 | −1.44337 | −0.721683 | − | 0.692224i | \(-0.756631\pi\) | ||||
−0.721683 | + | 0.692224i | \(0.756631\pi\) | |||||||
\(678\) | 1.99324e13 | 3.62264 | ||||||||
\(679\) | 6.06130e12 | 1.09434 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.41811e13 | 2.52667 | ||||||||
\(682\) | 1.75633e12 | 0.310868 | ||||||||
\(683\) | −5.91580e12 | −1.04021 | −0.520105 | − | 0.854103i | \(-0.674107\pi\) | ||||
−0.520105 | + | 0.854103i | \(0.674107\pi\) | |||||||
\(684\) | −8.32413e12 | −1.45407 | ||||||||
\(685\) | −1.47573e13 | −2.56095 | ||||||||
\(686\) | −1.26410e13 | −2.17933 | ||||||||
\(687\) | −3.12064e12 | −0.534488 | ||||||||
\(688\) | −1.64217e12 | −0.279428 | ||||||||
\(689\) | 2.69424e12 | 0.455460 | ||||||||
\(690\) | −5.92981e12 | −0.995910 | ||||||||
\(691\) | 5.47987e12 | 0.914363 | 0.457182 | − | 0.889373i | \(-0.348859\pi\) | ||||
0.457182 | + | 0.889373i | \(0.348859\pi\) | |||||||
\(692\) | −1.23949e13 | −2.05479 | ||||||||
\(693\) | 4.75120e12 | 0.782535 | ||||||||
\(694\) | −3.44971e12 | −0.564502 | ||||||||
\(695\) | 1.47724e13 | 2.40170 | ||||||||
\(696\) | 1.32032e13 | 2.13274 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 2.95060e12 | 0.470501 | ||||||||
\(699\) | −3.68778e12 | −0.584275 | ||||||||
\(700\) | −3.64568e13 | −5.73902 | ||||||||
\(701\) | 1.96914e12 | 0.307997 | 0.153998 | − | 0.988071i | \(-0.450785\pi\) | ||||
0.153998 | + | 0.988071i | \(0.450785\pi\) | |||||||
\(702\) | 2.44944e12 | 0.380670 | ||||||||
\(703\) | 7.00790e12 | 1.08215 | ||||||||
\(704\) | 2.12234e12 | 0.325639 | ||||||||
\(705\) | 2.53950e12 | 0.387166 | ||||||||
\(706\) | 2.23269e12 | 0.338227 | ||||||||
\(707\) | 8.65751e12 | 1.30318 | ||||||||
\(708\) | 1.15845e13 | 1.73272 | ||||||||
\(709\) | −3.28723e12 | −0.488565 | −0.244283 | − | 0.969704i | \(-0.578552\pi\) | ||||
−0.244283 | + | 0.969704i | \(0.578552\pi\) | |||||||
\(710\) | −2.64615e13 | −3.90798 | ||||||||
\(711\) | 1.06848e13 | 1.56802 | ||||||||
\(712\) | 1.38781e13 | 2.02381 | ||||||||
\(713\) | −5.71933e11 | −0.0828785 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.76864e12 | −1.11165 | ||||||||
\(716\) | −8.83899e12 | −1.25688 | ||||||||
\(717\) | −4.10755e12 | −0.580426 | ||||||||
\(718\) | 6.14445e12 | 0.862825 | ||||||||
\(719\) | 1.73463e12 | 0.242062 | 0.121031 | − | 0.992649i | \(-0.461380\pi\) | ||||
0.121031 | + | 0.992649i | \(0.461380\pi\) | |||||||
\(720\) | 1.39065e13 | 1.92851 | ||||||||
\(721\) | 7.59201e12 | 1.04628 | ||||||||
\(722\) | −4.94066e12 | −0.676655 | ||||||||
\(723\) | 1.19239e13 | 1.62292 | ||||||||
\(724\) | 2.10243e13 | 2.84379 | ||||||||
\(725\) | −9.65255e12 | −1.29754 | ||||||||
\(726\) | 1.28323e13 | 1.71431 | ||||||||
\(727\) | −4.39497e12 | −0.583514 | −0.291757 | − | 0.956492i | \(-0.594240\pi\) | ||||
−0.291757 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(728\) | −3.13374e13 | −4.13496 | ||||||||
\(729\) | −5.63034e12 | −0.738347 | ||||||||
\(730\) | −2.03972e13 | −2.65839 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2.56220e13 | −3.29848 | ||||||||
\(733\) | −7.92679e12 | −1.01421 | −0.507107 | − | 0.861883i | \(-0.669285\pi\) | ||||
−0.507107 | + | 0.861883i | \(0.669285\pi\) | |||||||
\(734\) | −1.06059e13 | −1.34869 | ||||||||
\(735\) | −3.07217e13 | −3.88286 | ||||||||
\(736\) | 8.60025e11 | 0.108034 | ||||||||
\(737\) | 2.70850e12 | 0.338162 | ||||||||
\(738\) | −1.15813e13 | −1.43716 | ||||||||
\(739\) | 2.29373e12 | 0.282906 | 0.141453 | − | 0.989945i | \(-0.454823\pi\) | ||||
0.141453 | + | 0.989945i | \(0.454823\pi\) | |||||||
\(740\) | −3.86051e13 | −4.73263 | ||||||||
\(741\) | 1.12030e13 | 1.36507 | ||||||||
\(742\) | −8.66315e12 | −1.04920 | ||||||||
\(743\) | −2.14410e11 | −0.0258104 | −0.0129052 | − | 0.999917i | \(-0.504108\pi\) | ||||
−0.0129052 | + | 0.999917i | \(0.504108\pi\) | |||||||
\(744\) | 7.35296e12 | 0.879800 | ||||||||
\(745\) | −1.14886e13 | −1.36636 | ||||||||
\(746\) | −6.44451e12 | −0.761842 | ||||||||
\(747\) | 2.76105e12 | 0.324437 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.59249e13 | 3.00988 | ||||||||
\(750\) | −2.17154e13 | −2.50606 | ||||||||
\(751\) | 6.59796e12 | 0.756885 | 0.378442 | − | 0.925625i | \(-0.376460\pi\) | ||||
0.378442 | + | 0.925625i | \(0.376460\pi\) | |||||||
\(752\) | −2.06870e12 | −0.235895 | ||||||||
\(753\) | 1.15152e13 | 1.30526 | ||||||||
\(754\) | −1.57441e13 | −1.77397 | ||||||||
\(755\) | −3.74953e12 | −0.419967 | ||||||||
\(756\) | −5.34690e12 | −0.595325 | ||||||||
\(757\) | 7.92736e12 | 0.877399 | 0.438700 | − | 0.898634i | \(-0.355439\pi\) | ||||
0.438700 | + | 0.898634i | \(0.355439\pi\) | |||||||
\(758\) | 6.30993e12 | 0.694246 | ||||||||
\(759\) | 1.71284e12 | 0.187339 | ||||||||
\(760\) | −2.30636e13 | −2.50765 | ||||||||
\(761\) | 1.21277e13 | 1.31084 | 0.655419 | − | 0.755266i | \(-0.272492\pi\) | ||||
0.655419 | + | 0.755266i | \(0.272492\pi\) | |||||||
\(762\) | 2.15405e13 | 2.31451 | ||||||||
\(763\) | −2.82407e12 | −0.301658 | ||||||||
\(764\) | −2.77324e13 | −2.94487 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.68104e13 | 1.76421 | ||||||||
\(767\) | −7.27989e12 | −0.759532 | ||||||||
\(768\) | 2.67841e13 | 2.77813 | ||||||||
\(769\) | 8.69590e12 | 0.896697 | 0.448349 | − | 0.893859i | \(-0.352012\pi\) | ||||
0.448349 | + | 0.893859i | \(0.352012\pi\) | |||||||
\(770\) | 2.49795e13 | 2.56080 | ||||||||
\(771\) | −2.40034e12 | −0.244640 | ||||||||
\(772\) | 3.51500e13 | 3.56162 | ||||||||
\(773\) | −8.84251e12 | −0.890775 | −0.445387 | − | 0.895338i | \(-0.646934\pi\) | ||||
−0.445387 | + | 0.895338i | \(0.646934\pi\) | |||||||
\(774\) | −3.18158e12 | −0.318646 | ||||||||
\(775\) | −5.37557e12 | −0.535263 | ||||||||
\(776\) | −1.31173e13 | −1.29858 | ||||||||
\(777\) | −3.17761e13 | −3.12756 | ||||||||
\(778\) | −2.30878e13 | −2.25930 | ||||||||
\(779\) | 7.50374e12 | 0.730061 | ||||||||
\(780\) | −6.17153e13 | −5.96991 | ||||||||
\(781\) | 7.64346e12 | 0.735124 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.41568e12 | −0.134598 | ||||||||
\(784\) | 2.50263e13 | 2.36578 | ||||||||
\(785\) | 2.59062e13 | 2.43496 | ||||||||
\(786\) | 3.78288e13 | 3.53526 | ||||||||
\(787\) | −1.58211e13 | −1.47011 | −0.735054 | − | 0.678008i | \(-0.762843\pi\) | ||||
−0.735054 | + | 0.678008i | \(0.762843\pi\) | |||||||
\(788\) | 4.26173e13 | 3.93747 | ||||||||
\(789\) | −1.14885e13 | −1.05540 | ||||||||
\(790\) | 5.61754e13 | 5.13127 | ||||||||
\(791\) | 2.73427e13 | 2.48340 | ||||||||
\(792\) | −1.02821e13 | −0.928580 | ||||||||
\(793\) | 1.61013e13 | 1.44587 | ||||||||
\(794\) | 2.55401e13 | 2.28050 | ||||||||
\(795\) | −8.99113e12 | −0.798293 | ||||||||
\(796\) | −2.78388e12 | −0.245778 | ||||||||
\(797\) | −7.81310e12 | −0.685900 | −0.342950 | − | 0.939354i | \(-0.611426\pi\) | ||||
−0.342950 | + | 0.939354i | \(0.611426\pi\) | |||||||
\(798\) | −3.60226e13 | −3.14458 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 8.08334e12 | 0.697728 | ||||||||
\(801\) | 1.05043e13 | 0.901611 | ||||||||
\(802\) | −2.29518e13 | −1.95899 | ||||||||
\(803\) | 5.89178e12 | 0.500065 | ||||||||
\(804\) | 2.15168e13 | 1.81604 | ||||||||
\(805\) | −8.13436e12 | −0.682719 | ||||||||
\(806\) | −8.76800e12 | −0.731801 | ||||||||
\(807\) | −9.15026e12 | −0.759456 | ||||||||
\(808\) | −1.87358e13 | −1.54640 | ||||||||
\(809\) | −1.10974e13 | −0.910862 | −0.455431 | − | 0.890271i | \(-0.650515\pi\) | ||||
−0.455431 | + | 0.890271i | \(0.650515\pi\) | |||||||
\(810\) | −3.89338e13 | −3.17793 | ||||||||
\(811\) | −2.59323e12 | −0.210497 | −0.105249 | − | 0.994446i | \(-0.533564\pi\) | ||||
−0.105249 | + | 0.994446i | \(0.533564\pi\) | |||||||
\(812\) | 3.43680e13 | 2.77429 | ||||||||
\(813\) | −4.25540e12 | −0.341612 | ||||||||
\(814\) | 1.64257e13 | 1.31134 | ||||||||
\(815\) | 1.36978e13 | 1.08753 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.06140e12 | 0.161869 | ||||||||
\(818\) | −1.24436e13 | −0.971755 | ||||||||
\(819\) | −2.37191e13 | −1.84213 | ||||||||
\(820\) | −4.13366e13 | −3.19281 | ||||||||
\(821\) | −5.84654e12 | −0.449112 | −0.224556 | − | 0.974461i | \(-0.572093\pi\) | ||||
−0.224556 | + | 0.974461i | \(0.572093\pi\) | |||||||
\(822\) | 4.98810e13 | 3.81076 | ||||||||
\(823\) | −2.17086e13 | −1.64942 | −0.824711 | − | 0.565554i | \(-0.808662\pi\) | ||||
−0.824711 | + | 0.565554i | \(0.808662\pi\) | |||||||
\(824\) | −1.64299e13 | −1.24155 | ||||||||
\(825\) | 1.60989e13 | 1.20991 | ||||||||
\(826\) | 2.34080e13 | 1.74966 | ||||||||
\(827\) | 2.04178e13 | 1.51787 | 0.758935 | − | 0.651167i | \(-0.225720\pi\) | ||||
0.758935 | + | 0.651167i | \(0.225720\pi\) | |||||||
\(828\) | 6.35351e12 | 0.469761 | ||||||||
\(829\) | 1.14245e13 | 0.840119 | 0.420060 | − | 0.907496i | \(-0.362009\pi\) | ||||
0.420060 | + | 0.907496i | \(0.362009\pi\) | |||||||
\(830\) | 1.45163e13 | 1.06170 | ||||||||
\(831\) | −1.84498e13 | −1.34211 | ||||||||
\(832\) | −1.05952e13 | −0.766573 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −4.99319e13 | −3.57380 | ||||||||
\(835\) | 2.07821e12 | 0.147945 | ||||||||
\(836\) | 1.26414e13 | 0.895089 | ||||||||
\(837\) | −7.88403e11 | −0.0555244 | ||||||||
\(838\) | −1.12259e13 | −0.786362 | ||||||||
\(839\) | −2.33259e13 | −1.62521 | −0.812607 | − | 0.582813i | \(-0.801952\pi\) | ||||
−0.812607 | + | 0.582813i | \(0.801952\pi\) | |||||||
\(840\) | 1.04578e14 | 7.24742 | ||||||||
\(841\) | −5.40765e12 | −0.372758 | ||||||||
\(842\) | 4.50277e13 | 3.08727 | ||||||||
\(843\) | −1.05204e13 | −0.717475 | ||||||||
\(844\) | 1.96416e13 | 1.33240 | ||||||||
\(845\) | 1.47104e13 | 0.992587 | ||||||||
\(846\) | −4.00797e12 | −0.269003 | ||||||||
\(847\) | 1.76030e13 | 1.17520 | ||||||||
\(848\) | 7.32428e12 | 0.486389 | ||||||||
\(849\) | −3.75236e13 | −2.47868 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.34888e12 | −0.349607 | ||||||||
\(852\) | 6.07209e13 | 3.94785 | ||||||||
\(853\) | −1.94665e12 | −0.125897 | −0.0629486 | − | 0.998017i | \(-0.520050\pi\) | ||||
−0.0629486 | + | 0.998017i | \(0.520050\pi\) | |||||||
\(854\) | −5.17725e13 | −3.33072 | ||||||||
\(855\) | −1.74567e13 | −1.11716 | ||||||||
\(856\) | −5.61044e13 | −3.57162 | ||||||||
\(857\) | 1.09250e13 | 0.691842 | 0.345921 | − | 0.938264i | \(-0.387567\pi\) | ||||
0.345921 | + | 0.938264i | \(0.387567\pi\) | |||||||
\(858\) | 2.62586e13 | 1.65417 | ||||||||
\(859\) | 1.59827e13 | 1.00157 | 0.500783 | − | 0.865573i | \(-0.333045\pi\) | ||||
0.500783 | + | 0.865573i | \(0.333045\pi\) | |||||||
\(860\) | −1.13559e13 | −0.707908 | ||||||||
\(861\) | −3.40244e13 | −2.10997 | ||||||||
\(862\) | 1.63862e12 | 0.101087 | ||||||||
\(863\) | 8.53563e12 | 0.523826 | 0.261913 | − | 0.965091i | \(-0.415647\pi\) | ||||
0.261913 | + | 0.965091i | \(0.415647\pi\) | |||||||
\(864\) | 1.18553e12 | 0.0723773 | ||||||||
\(865\) | −2.59937e13 | −1.57869 | ||||||||
\(866\) | 3.86646e13 | 2.33606 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.91398e13 | 1.14445 | ||||||||
\(869\) | −1.62264e13 | −0.965234 | ||||||||
\(870\) | 5.25407e13 | 3.10928 | ||||||||
\(871\) | −1.35215e13 | −0.796053 | ||||||||
\(872\) | 6.11159e12 | 0.357956 | ||||||||
\(873\) | −9.92843e12 | −0.578518 | ||||||||
\(874\) | −6.06369e12 | −0.351508 | ||||||||
\(875\) | −2.97886e13 | −1.71796 | ||||||||
\(876\) | 4.68053e13 | 2.68551 | ||||||||
\(877\) | 1.45232e13 | 0.829021 | 0.414511 | − | 0.910044i | \(-0.363953\pi\) | ||||
0.414511 | + | 0.910044i | \(0.363953\pi\) | |||||||
\(878\) | 5.57411e13 | 3.16555 | ||||||||
\(879\) | 1.50299e13 | 0.849192 | ||||||||
\(880\) | −2.11190e13 | −1.18714 | ||||||||
\(881\) | 2.79317e13 | 1.56209 | 0.781044 | − | 0.624476i | \(-0.214688\pi\) | ||||
0.781044 | + | 0.624476i | \(0.214688\pi\) | |||||||
\(882\) | 4.84866e13 | 2.69782 | ||||||||
\(883\) | −1.95980e13 | −1.08490 | −0.542450 | − | 0.840088i | \(-0.682503\pi\) | ||||
−0.542450 | + | 0.840088i | \(0.682503\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.42942e13 | 1.33125 | ||||||||
\(886\) | 1.14124e13 | 0.622196 | ||||||||
\(887\) | −1.87122e13 | −1.01501 | −0.507504 | − | 0.861650i | \(-0.669432\pi\) | ||||
−0.507504 | + | 0.861650i | \(0.669432\pi\) | |||||||
\(888\) | 6.87670e13 | 3.71126 | ||||||||
\(889\) | 2.95487e13 | 1.58665 | ||||||||
\(890\) | 5.52264e13 | 2.95047 | ||||||||
\(891\) | 1.12461e13 | 0.597794 | ||||||||
\(892\) | −1.53861e13 | −0.813742 | ||||||||
\(893\) | 2.59683e12 | 0.136651 | ||||||||
\(894\) | 3.88324e13 | 2.03318 | ||||||||
\(895\) | −1.85365e13 | −0.965658 | ||||||||
\(896\) | 4.76815e13 | 2.47152 | ||||||||
\(897\) | −8.55088e12 | −0.441006 | ||||||||
\(898\) | 1.70277e13 | 0.873799 | ||||||||
\(899\) | 5.06757e12 | 0.258751 | ||||||||
\(900\) | 5.97164e13 | 3.03391 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.75879e13 | 0.884676 | ||||||||
\(903\) | −9.34707e12 | −0.467822 | ||||||||
\(904\) | −5.91726e13 | −2.94688 | ||||||||
\(905\) | 4.40905e13 | 2.18487 | ||||||||
\(906\) | 1.26737e13 | 0.624923 | ||||||||
\(907\) | 1.04166e12 | 0.0511085 | 0.0255542 | − | 0.999673i | \(-0.491865\pi\) | ||||
0.0255542 | + | 0.999673i | \(0.491865\pi\) | |||||||
\(908\) | −7.98848e13 | −3.90012 | ||||||||
\(909\) | −1.41810e13 | −0.688922 | ||||||||
\(910\) | −1.24704e14 | −6.02827 | ||||||||
\(911\) | 2.23220e13 | 1.07374 | 0.536871 | − | 0.843665i | \(-0.319606\pi\) | ||||
0.536871 | + | 0.843665i | \(0.319606\pi\) | |||||||
\(912\) | 3.04554e13 | 1.45777 | ||||||||
\(913\) | −4.19305e12 | −0.199715 | ||||||||
\(914\) | 3.66895e13 | 1.73894 | ||||||||
\(915\) | −5.37326e13 | −2.53421 | ||||||||
\(916\) | 1.75791e13 | 0.825025 | ||||||||
\(917\) | 5.18925e13 | 2.42350 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.33385e13 | 1.07933 | 0.539665 | − | 0.841880i | \(-0.318551\pi\) | ||||
0.539665 | + | 0.841880i | \(0.318551\pi\) | |||||||
\(920\) | 1.76036e13 | 0.810135 | ||||||||
\(921\) | 3.65547e13 | 1.67407 | ||||||||
\(922\) | 5.30152e13 | 2.41608 | ||||||||
\(923\) | −3.81579e13 | −1.73052 | ||||||||
\(924\) | −5.73202e13 | −2.58692 | ||||||||
\(925\) | −5.02739e13 | −2.25790 | ||||||||
\(926\) | −9.42764e12 | −0.421360 | ||||||||
\(927\) | −1.24357e13 | −0.553112 | ||||||||
\(928\) | −7.62020e12 | −0.337288 | ||||||||
\(929\) | −3.89397e13 | −1.71523 | −0.857614 | − | 0.514293i | \(-0.828054\pi\) | ||||
−0.857614 | + | 0.514293i | \(0.828054\pi\) | |||||||
\(930\) | 2.92603e13 | 1.28264 | ||||||||
\(931\) | −3.14153e13 | −1.37046 | ||||||||
\(932\) | 2.07739e13 | 0.901876 | ||||||||
\(933\) | −1.60122e13 | −0.691807 | ||||||||
\(934\) | 1.18732e13 | 0.510514 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.13307e13 | 2.18593 | ||||||||
\(937\) | −4.23162e13 | −1.79340 | −0.896702 | − | 0.442634i | \(-0.854044\pi\) | ||||
−0.896702 | + | 0.442634i | \(0.854044\pi\) | |||||||
\(938\) | 4.34774e13 | 1.83379 | ||||||||
\(939\) | −3.87357e13 | −1.62598 | ||||||||
\(940\) | −1.43054e13 | −0.597621 | ||||||||
\(941\) | −4.34990e13 | −1.80853 | −0.904266 | − | 0.426970i | \(-0.859581\pi\) | ||||
−0.904266 | + | 0.426970i | \(0.859581\pi\) | |||||||
\(942\) | −8.75652e13 | −3.62328 | ||||||||
\(943\) | −5.72734e12 | −0.235858 | ||||||||
\(944\) | −1.97904e13 | −0.811110 | ||||||||
\(945\) | −1.12131e13 | −0.457386 | ||||||||
\(946\) | 4.83168e12 | 0.196150 | ||||||||
\(947\) | −3.51130e13 | −1.41871 | −0.709354 | − | 0.704853i | \(-0.751013\pi\) | ||||
−0.709354 | + | 0.704853i | \(0.751013\pi\) | |||||||
\(948\) | −1.28905e14 | −5.18361 | ||||||||
\(949\) | −2.94131e13 | −1.17718 | ||||||||
\(950\) | −5.69924e13 | −2.27018 | ||||||||
\(951\) | −1.97322e12 | −0.0782281 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.36351e12 | 0.210635 | 0.105318 | − | 0.994439i | \(-0.466414\pi\) | ||||
0.105318 | + | 0.994439i | \(0.466414\pi\) | |||||||
\(954\) | 1.41903e13 | 0.554655 | ||||||||
\(955\) | −5.81582e13 | −2.26254 | ||||||||
\(956\) | 2.31386e13 | 0.895934 | ||||||||
\(957\) | −1.51765e13 | −0.584881 | ||||||||
\(958\) | 1.54077e13 | 0.591008 | ||||||||
\(959\) | 6.84254e13 | 2.61236 | ||||||||
\(960\) | 3.53579e13 | 1.34359 | ||||||||
\(961\) | −2.36175e13 | −0.893260 | ||||||||
\(962\) | −8.20009e13 | −3.08696 | ||||||||
\(963\) | −4.24651e13 | −1.59116 | ||||||||
\(964\) | −6.71695e13 | −2.50510 | ||||||||
\(965\) | 7.37140e13 | 2.73638 | ||||||||
\(966\) | 2.74948e13 | 1.01590 | ||||||||
\(967\) | 3.98866e13 | 1.46693 | 0.733463 | − | 0.679729i | \(-0.237903\pi\) | ||||
0.733463 | + | 0.679729i | \(0.237903\pi\) | |||||||
\(968\) | −3.80948e13 | −1.39453 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.21989e13 | −1.89317 | ||||||||
\(971\) | −2.58744e13 | −0.934079 | −0.467039 | − | 0.884237i | \(-0.654679\pi\) | ||||
−0.467039 | + | 0.884237i | \(0.654679\pi\) | |||||||
\(972\) | 7.93418e13 | 2.85104 | ||||||||
\(973\) | −6.84952e13 | −2.44992 | ||||||||
\(974\) | 1.49580e13 | 0.532546 | ||||||||
\(975\) | −8.03694e13 | −2.84820 | ||||||||
\(976\) | 4.37712e13 | 1.54406 | ||||||||
\(977\) | −4.14893e13 | −1.45684 | −0.728418 | − | 0.685133i | \(-0.759744\pi\) | ||||
−0.728418 | + | 0.685133i | \(0.759744\pi\) | |||||||
\(978\) | −4.62997e13 | −1.61828 | ||||||||
\(979\) | −1.59522e13 | −0.555008 | ||||||||
\(980\) | 1.73061e14 | 5.99351 | ||||||||
\(981\) | 4.62583e12 | 0.159470 | ||||||||
\(982\) | −8.96151e13 | −3.07524 | ||||||||
\(983\) | −2.21812e13 | −0.757695 | −0.378847 | − | 0.925459i | \(-0.623679\pi\) | ||||
−0.378847 | + | 0.925459i | \(0.623679\pi\) | |||||||
\(984\) | 7.36326e13 | 2.50376 | ||||||||
\(985\) | 8.93737e13 | 3.02515 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.17749e13 | −0.394939 | ||||||||
\(988\) | −6.31087e13 | −2.10709 | ||||||||
\(989\) | −1.57339e12 | −0.0522943 | ||||||||
\(990\) | −4.09166e13 | −1.35376 | ||||||||
\(991\) | −1.15492e13 | −0.380382 | −0.190191 | − | 0.981747i | \(-0.560911\pi\) | ||||
−0.190191 | + | 0.981747i | \(0.560911\pi\) | |||||||
\(992\) | −4.24374e12 | −0.139138 | ||||||||
\(993\) | −8.07709e12 | −0.263623 | ||||||||
\(994\) | 1.22694e14 | 3.98644 | ||||||||
\(995\) | −5.83816e12 | −0.188830 | ||||||||
\(996\) | −3.33102e13 | −1.07253 | ||||||||
\(997\) | −2.07044e13 | −0.663643 | −0.331821 | − | 0.943342i | \(-0.607663\pi\) | ||||
−0.331821 | + | 0.943342i | \(0.607663\pi\) | |||||||
\(998\) | 8.22293e13 | 2.62385 | ||||||||
\(999\) | −7.37337e12 | −0.234218 |
(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 | 289.10.a.g.1.34 | ✓ | 36 | |
17.16 | even | 2 | 289.10.a.h.1.34 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.10.a.g.1.34 | ✓ | 36 | 1.1 | even | 1 | trivial | |
289.10.a.h.1.34 | yes | 36 | 17.16 | even | 2 |