Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,18,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(146.577669876\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{83281}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 20820 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-143.792\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9311.53 | 0.819390 | 0.409695 | − | 0.912223i | \(-0.365635\pi\) | ||||
0.409695 | + | 0.912223i | \(0.365635\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 390625. | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.48655e7 | 1.63029 | 0.815144 | − | 0.579258i | \(-0.196658\pi\) | ||||
0.815144 | + | 0.579258i | \(0.196658\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.24355e7 | −0.328600 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.90392e8 | 0.267801 | 0.133900 | − | 0.990995i | \(-0.457250\pi\) | ||||
0.133900 | + | 0.990995i | \(0.457250\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.57377e7 | −0.00535085 | −0.00267543 | − | 0.999996i | \(-0.500852\pi\) | ||||
−0.00267543 | + | 0.999996i | \(0.500852\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.63732e9 | 0.366442 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.25502e10 | −0.784032 | −0.392016 | − | 0.919958i | \(-0.628222\pi\) | ||||
−0.392016 | + | 0.919958i | \(0.628222\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.27984e11 | −1.72882 | −0.864408 | − | 0.502791i | \(-0.832306\pi\) | ||||
−0.864408 | + | 0.502791i | \(0.832306\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.31536e11 | 1.33584 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59325e11 | −0.690490 | −0.345245 | − | 0.938513i | \(-0.612204\pi\) | ||||
−0.345245 | + | 0.938513i | \(0.612204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.59763e12 | −1.08864 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.57953e12 | −0.957542 | −0.478771 | − | 0.877940i | \(-0.658918\pi\) | ||||
−0.478771 | + | 0.877940i | \(0.658918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.91253e12 | −1.66625 | −0.833126 | − | 0.553083i | \(-0.813451\pi\) | ||||
−0.833126 | + | 0.553083i | \(0.813451\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.77285e12 | 0.219433 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.71310e12 | 0.729087 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.09888e13 | −0.982367 | −0.491184 | − | 0.871056i | \(-0.663436\pi\) | ||||
−0.491184 | + | 0.871056i | \(0.663436\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.46542e11 | −0.00438444 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.98123e13 | 0.387499 | 0.193750 | − | 0.981051i | \(-0.437935\pi\) | ||||
0.193750 | + | 0.981051i | \(0.437935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.60777e13 | 0.601186 | 0.300593 | − | 0.953753i | \(-0.402815\pi\) | ||||
0.300593 | + | 0.953753i | \(0.402815\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.65764e13 | −0.146955 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.66827e14 | −1.63455 | −0.817274 | − | 0.576250i | \(-0.804516\pi\) | ||||
−0.817274 | + | 0.576250i | \(0.804516\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.85664e14 | 1.65784 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.09977e14 | −0.642428 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.00045e14 | 0.882599 | 0.441300 | − | 0.897360i | \(-0.354518\pi\) | ||||
0.441300 | + | 0.897360i | \(0.354518\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.43721e13 | 0.119764 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.19172e15 | −1.41657 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.82611e15 | −1.61914 | −0.809570 | − | 0.587024i | \(-0.800299\pi\) | ||||
−0.809570 | + | 0.587024i | \(0.800299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.48236e15 | −0.990035 | −0.495017 | − | 0.868883i | \(-0.664838\pi\) | ||||
−0.495017 | + | 0.868883i | \(0.664838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.05518e15 | −0.535713 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.14754e12 | −0.00239297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.71410e15 | 0.816563 | 0.408282 | − | 0.912856i | \(-0.366128\pi\) | ||||
0.408282 | + | 0.912856i | \(0.366128\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.41471e15 | −0.565780 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.87337e15 | 0.711858 | 0.355929 | − | 0.934513i | \(-0.384164\pi\) | ||||
0.355929 | + | 0.934513i | \(0.384164\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.85786e15 | −0.414759 | −0.207380 | − | 0.978261i | \(-0.566494\pi\) | ||||
−0.207380 | + | 0.978261i | \(0.566494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.42083e15 | 0.163878 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.73421e15 | 0.436593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.80988e15 | −0.208381 | −0.104190 | − | 0.994557i | \(-0.533225\pi\) | ||||
−0.104190 | + | 0.994557i | \(0.533225\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.39628e15 | −0.563422 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.04230e15 | 0.343203 | 0.171601 | − | 0.985166i | \(-0.445106\pi\) | ||||
0.171601 | + | 0.985166i | \(0.445106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.80866e15 | −0.350630 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.40194e16 | −0.784600 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.51966e16 | 1.48627 | 0.743135 | − | 0.669142i | \(-0.233338\pi\) | ||||
0.743135 | + | 0.669142i | \(0.233338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.91327e14 | −0.00872343 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.36778e16 | −1.36531 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.99936e16 | −0.773150 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.42662e16 | 0.832574 | 0.416287 | − | 0.909233i | \(-0.363331\pi\) | ||||
0.416287 | + | 0.909233i | \(0.363331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.07940e15 | −0.0879994 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.56405e17 | −1.43721 | −0.718603 | − | 0.695421i | \(-0.755218\pi\) | ||||
−0.718603 | + | 0.695421i | \(0.755218\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.33166e17 | 1.81363 | 0.906816 | − | 0.421527i | \(-0.138506\pi\) | ||||
0.906816 | + | 0.421527i | \(0.138506\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.04438e16 | 0.597407 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.05397e17 | 0.593017 | 0.296509 | − | 0.955030i | \(-0.404178\pi\) | ||||
0.296509 | + | 0.955030i | \(0.404178\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.51895e17 | 1.21086 | 0.605431 | − | 0.795898i | \(-0.293001\pi\) | ||||
0.605431 | + | 0.795898i | \(0.293001\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.95438e17 | −0.804942 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.09395e17 | 1.44869 | 0.724346 | − | 0.689436i | \(-0.242142\pi\) | ||||
0.724346 | + | 0.689436i | \(0.242142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.01299e17 | −0.308796 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.67838e14 | 0.00175829 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.60722e17 | −1.27820 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.69198e17 | −0.928283 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.84482e17 | 0.317513 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.96046e16 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.42410e17 | 0.842327 | 0.421164 | − | 0.906985i | \(-0.361622\pi\) | ||||
0.421164 | + | 0.906985i | \(0.361622\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.29054e17 | 0.492606 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.57323e17 | −0.359961 | −0.179980 | − | 0.983670i | \(-0.557603\pi\) | ||||
−0.179980 | + | 0.983670i | \(0.557603\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.18238e18 | −2.81847 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.24075e17 | −0.486855 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.23821e18 | −0.852454 | −0.426227 | − | 0.904616i | \(-0.640158\pi\) | ||||
−0.426227 | + | 0.904616i | \(0.640158\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.95129e18 | −1.18767 | −0.593836 | − | 0.804586i | \(-0.702387\pi\) | ||||
−0.593836 | + | 0.804586i | \(0.702387\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.48457e18 | −1.33933 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.99634e15 | −0.00143296 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00763e18 | −0.428226 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.59112e18 | 1.35842 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.86793e18 | 0.629908 | 0.314954 | − | 0.949107i | \(-0.398011\pi\) | ||||
0.314954 | + | 0.949107i | \(0.398011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.18884e18 | −1.56231 | −0.781154 | − | 0.624339i | \(-0.785368\pi\) | ||||
−0.781154 | + | 0.624339i | \(0.785368\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.56927e17 | 0.257633 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.09083e18 | −0.745171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.78987e18 | 1.68416 | 0.842080 | − | 0.539353i | \(-0.181331\pi\) | ||||
0.842080 | + | 0.539353i | \(0.181331\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.72503e18 | 0.723193 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.44825e18 | −1.12570 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.16891e18 | −0.969647 | −0.484824 | − | 0.874612i | \(-0.661116\pi\) | ||||
−0.484824 | + | 0.874612i | \(0.661116\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.92518e17 | 0.0981336 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.24726e19 | −1.59539 | −0.797693 | − | 0.603064i | \(-0.793946\pi\) | ||||
−0.797693 | + | 0.603064i | \(0.793946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.65017e18 | −0.999971 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.43105e18 | 0.568089 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.64494e19 | 1.55869 | 0.779344 | − | 0.626596i | \(-0.215552\pi\) | ||||
0.779344 | + | 0.626596i | \(0.215552\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.79418e18 | 0.326058 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.70039e19 | −1.32671 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.53067e18 | 0.108550 | 0.0542751 | − | 0.998526i | \(-0.482715\pi\) | ||||
0.0542751 | + | 0.998526i | \(0.482715\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.51444e18 | −0.549399 | −0.274700 | − | 0.961530i | \(-0.588578\pi\) | ||||
−0.274700 | + | 0.961530i | \(0.588578\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.38031e19 | −0.811224 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.19877e18 | −0.439328 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.29338e18 | −0.209965 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.97260e19 | −1.77480 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.05921e19 | −0.432710 | −0.216355 | − | 0.976315i | \(-0.569417\pi\) | ||||
−0.216355 | + | 0.976315i | \(0.569417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.55768e19 | −0.582425 | −0.291213 | − | 0.956658i | \(-0.594059\pi\) | ||||
−0.291213 | + | 0.956658i | \(0.594059\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.72431e16 | −0.00196078 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.47320e18 | 0.266124 | 0.133062 | − | 0.991108i | \(-0.457519\pi\) | ||||
0.133062 | + | 0.991108i | \(0.457519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.48640e18 | −0.273433 | −0.136716 | − | 0.990610i | \(-0.543655\pi\) | ||||
−0.136716 | + | 0.990610i | \(0.543655\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.52724e19 | 0.669083 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.41414e19 | −1.56107 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.73916e18 | 0.173295 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.10046e19 | 0.226895 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.43671e19 | −0.462978 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.06102e19 | 0.886824 | 0.443412 | − | 0.896318i | \(-0.353768\pi\) | ||||
0.443412 | + | 0.896318i | \(0.353768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.60671e19 | 0.583289 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.79991e19 | 0.268858 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.96749e20 | −2.71647 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.66110e19 | −0.339849 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.54888e17 | 0.00419524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.13017e20 | −1.23752 | −0.618759 | − | 0.785581i | \(-0.712364\pi\) | ||||
−0.618759 | + | 0.785581i | \(0.712364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.47514e18 | −0.0657201 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.34057e20 | −1.26203 | −0.631016 | − | 0.775770i | \(-0.717362\pi\) | ||||
−0.631016 | + | 0.775770i | \(0.717362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.53092e20 | −1.33768 | −0.668840 | − | 0.743406i | \(-0.733209\pi\) | ||||
−0.668840 | + | 0.743406i | \(0.733209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.40828e19 | 0.357740 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.54095e20 | 1.16215 | 0.581076 | − | 0.813849i | \(-0.302632\pi\) | ||||
0.581076 | + | 0.813849i | \(0.302632\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.04229e20 | −0.730992 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.61643e19 | −0.170745 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.10626e20 | −0.672161 | −0.336081 | − | 0.941833i | \(-0.609101\pi\) | ||||
−0.336081 | + | 0.941833i | \(0.609101\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.68590e20 | −0.954303 | −0.477152 | − | 0.878821i | \(-0.658331\pi\) | ||||
−0.477152 | + | 0.878821i | \(0.658331\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.18825e20 | 0.626980 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.50650e20 | 0.741408 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.01417e18 | 0.00925064 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.55746e19 | 0.281217 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.71684e19 | 0.349247 | 0.174623 | − | 0.984635i | \(-0.444129\pi\) | ||||
0.174623 | + | 0.984635i | \(0.444129\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.93735e19 | −0.184914 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.20221e19 | −0.287303 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.57989e20 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361046\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.21899e20 | −1.60154 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.09464e20 | 0.314648 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.12838e20 | 1.11213 | 0.556065 | − | 0.831139i | \(-0.312311\pi\) | ||||
0.556065 | + | 0.831139i | \(0.312311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.56267e20 | 0.394710 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.13965e20 | 1.21783 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.61622e20 | 0.804194 | 0.402097 | − | 0.915597i | \(-0.368282\pi\) | ||||
0.402097 | + | 0.915597i | \(0.368282\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.61685e20 | 1.38170 | 0.690848 | − | 0.723000i | \(-0.257238\pi\) | ||||
0.690848 | + | 0.723000i | \(0.257238\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.64385e18 | −0.00714789 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.90516e19 | 0.0535602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.43700e20 | 0.422452 | 0.211226 | − | 0.977437i | \(-0.432254\pi\) | ||||
0.211226 | + | 0.977437i | \(0.432254\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.35772e20 | 0.547531 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.47052e20 | −1.45335 | −0.726675 | − | 0.686981i | \(-0.758935\pi\) | ||||
−0.726675 | + | 0.686981i | \(0.758935\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.67504e20 | 0.530979 | 0.265489 | − | 0.964114i | \(-0.414466\pi\) | ||||
0.265489 | + | 0.964114i | \(0.414466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.65517e20 | −0.633511 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.92642e20 | 0.631736 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.18730e20 | −0.385293 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.98417e20 | 0.682203 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.20904e21 | 1.30037 | 0.650183 | − | 0.759778i | \(-0.274692\pi\) | ||||
0.650183 | + | 0.759778i | \(0.274692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.13323e20 | −0.724101 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.04177e20 | −0.291539 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.08118e18 | 0.00369471 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.14575e21 | 0.980106 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.45637e21 | −1.17763 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.79047e20 | −0.442757 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.76931e20 | 0.344969 | 0.172484 | − | 0.985012i | \(-0.444821\pi\) | ||||
0.172484 | + | 0.985012i | \(0.444821\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.17114e21 | 1.48607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.50418e20 | −0.227051 | −0.113525 | − | 0.993535i | \(-0.536214\pi\) | ||||
−0.113525 | + | 0.993535i | \(0.536214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.04751e21 | 1.25631 | 0.628157 | − | 0.778087i | \(-0.283810\pi\) | ||||
0.628157 | + | 0.778087i | \(0.283810\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.12180e20 | −0.239578 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.31663e21 | 0.725205 | 0.362602 | − | 0.931944i | \(-0.381888\pi\) | ||||
0.362602 | + | 0.931944i | \(0.381888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.91123e20 | −0.256430 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.81411e20 | 0.485912 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.88605e21 | 1.35545 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.40138e18 | −0.00107017 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.34553e21 | 0.992167 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.63479e21 | −2.66478 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.85862e21 | −1.47195 | −0.735977 | − | 0.677007i | \(-0.763277\pi\) | ||||
−0.735977 | + | 0.677007i | \(0.763277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.90672e20 | 0.322806 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.06019e21 | 0.365178 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.69149e21 | 1.53623 | 0.768115 | − | 0.640312i | \(-0.221195\pi\) | ||||
0.768115 | + | 0.640312i | \(0.221195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.81210e21 | 1.18704 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.50649e21 | −0.446224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.80526e21 | 1.07247 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.43246e20 | −0.253025 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.51637e21 | −0.642648 | −0.321324 | − | 0.946969i | \(-0.604128\pi\) | ||||
−0.321324 | + | 0.946969i | \(0.604128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.20222e21 | −0.535606 | −0.267803 | − | 0.963474i | \(-0.586298\pi\) | ||||
−0.267803 | + | 0.963474i | \(0.586298\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.51431e19 | 0.00582516 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.30214e21 | 0.287456 | 0.143728 | − | 0.989617i | \(-0.454091\pi\) | ||||
0.143728 | + | 0.989617i | \(0.454091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.51304e21 | 0.318353 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.22118e21 | −1.04734 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.07162e21 | −0.396285 | −0.198143 | − | 0.980173i | \(-0.563491\pi\) | ||||
−0.198143 | + | 0.980173i | \(0.563491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.08994e22 | 1.98880 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.36895e21 | −0.760625 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.11635e21 | −0.185486 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.69137e21 | −0.744111 | −0.372056 | − | 0.928210i | \(-0.621347\pi\) | ||||
−0.372056 | + | 0.928210i | \(0.621347\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.40743e20 | −0.127332 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.94732e21 | 1.43889 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.77652e20 | −0.107463 | −0.0537317 | − | 0.998555i | \(-0.517112\pi\) | ||||
−0.0537317 | + | 0.998555i | \(0.517112\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.55011e20 | 0.0732885 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.05959e19 | 0.00512367 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.50054e20 | −0.0422379 | −0.0211189 | − | 0.999777i | \(-0.506723\pi\) | ||||
−0.0211189 | + | 0.999777i | \(0.506723\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.98183e21 | 0.690194 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.02315e22 | 1.12914 | 0.564570 | − | 0.825385i | \(-0.309042\pi\) | ||||
0.564570 | + | 0.825385i | \(0.309042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.84930e21 | 0.195250 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.95533e21 | −0.197550 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.13104e21 | −0.399473 | −0.199737 | − | 0.979850i | \(-0.564009\pi\) | ||||
−0.199737 | + | 0.979850i | \(0.564009\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.84781e21 | 0.541366 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.32723e21 | −0.294948 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.09761e21 | −0.0931907 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.65334e21 | −0.622489 | −0.311244 | − | 0.950330i | \(-0.600746\pi\) | ||||
−0.311244 | + | 0.950330i | \(0.600746\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.96328e22 | −2.30942 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.08273e20 | −0.0304947 | −0.0152473 | − | 0.999884i | \(-0.504854\pi\) | ||||
−0.0152473 | + | 0.999884i | \(0.504854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.24525e20 | 0.00891588 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.67042e21 | −0.251970 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.99612e21 | −0.263079 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00923e22 | 1.26877 | 0.634383 | − | 0.773019i | \(-0.281254\pi\) | ||||
0.634383 | + | 0.773019i | \(0.281254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.15297e22 | −0.698493 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.54071e22 | −2.63966 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.75090e21 | 0.153485 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.81695e22 | −0.973167 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.31114e22 | −1.70278 | −0.851390 | − | 0.524533i | \(-0.824240\pi\) | ||||
−0.851390 | + | 0.524533i | \(0.824240\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31325e22 | −1.14242 | −0.571208 | − | 0.820805i | \(-0.693525\pi\) | ||||
−0.571208 | + | 0.820805i | \(0.693525\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.13229e22 | 0.537113 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.44088e21 | −0.156806 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.68597e22 | −1.61404 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.79005e19 | −0.00117416 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.44596e22 | −1.79849 | −0.899247 | − | 0.437440i | \(-0.855885\pi\) | ||||
−0.899247 | + | 0.437440i | \(0.855885\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.85304e22 | 1.10959 | 0.554793 | − | 0.831989i | \(-0.312798\pi\) | ||||
0.554793 | + | 0.831989i | \(0.312798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.38257e21 | −0.350884 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.31893e22 | 1.19373 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.28578e22 | 1.48279 | 0.741397 | − | 0.671066i | \(-0.234163\pi\) | ||||
0.741397 | + | 0.671066i | \(0.234163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.63658e22 | −0.544767 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.40464e22 | 0.449919 | 0.224959 | − | 0.974368i | \(-0.427775\pi\) | ||||
0.224959 | + | 0.974368i | \(0.427775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.15612e22 | 0.664680 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.73933e22 | 0.516140 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.88401e22 | −1.10965 | −0.554826 | − | 0.831966i | \(-0.687215\pi\) | ||||
−0.554826 | + | 0.831966i | \(0.687215\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.77210e21 | 0.103773 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.83161e22 | −1.28014 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.52862e20 | −0.00390124 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.21160e22 | −0.543774 | −0.271887 | − | 0.962329i | \(-0.587648\pi\) | ||||
−0.271887 | + | 0.962329i | \(0.587648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.60269e22 | 0.853530 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.69257e22 | 0.386446 | 0.193223 | − | 0.981155i | \(-0.438106\pi\) | ||||
0.193223 | + | 0.981155i | \(0.438106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.00810e22 | −1.10213 | −0.551067 | − | 0.834461i | \(-0.685779\pi\) | ||||
−0.551067 | + | 0.834461i | \(0.685779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.87804e22 | −0.610585 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.87611e22 | 1.40653 | 0.703266 | − | 0.710927i | \(-0.251724\pi\) | ||||
0.703266 | + | 0.710927i | \(0.251724\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.74875e22 | 1.33123 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.25357e22 | 1.37998 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.77284e21 | 0.160998 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.95287e22 | −0.345763 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.69761e22 | −0.290022 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.44291e22 | 0.567641 | 0.283821 | − | 0.958877i | \(-0.408398\pi\) | ||||
0.283821 | + | 0.958877i | \(0.408398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.30316e20 | 0.00525650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00431e22 | −0.922385 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.51040e22 | 0.372338 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.83844e20 | −0.0126584 | −0.00632921 | − | 0.999980i | \(-0.502015\pi\) | ||||
−0.00632921 | + | 0.999980i | \(0.502015\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.74420e22 | −0.794519 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04515e23 | −1.39632 | −0.698158 | − | 0.715943i | \(-0.745997\pi\) | ||||
−0.698158 | + | 0.715943i | \(0.745997\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.81688e22 | 0.750744 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.15602e21 | −0.0393545 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.63135e22 | 1.16053 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.12067e22 | 0.596310 | 0.298155 | − | 0.954518i | \(-0.403629\pi\) | ||||
0.298155 | + | 0.954518i | \(0.403629\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.16139e23 | −1.30724 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.06660e22 | −0.551301 | −0.275650 | − | 0.961258i | \(-0.588893\pi\) | ||||
−0.275650 | + | 0.961258i | \(0.588893\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.10957e22 | −0.642738 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.05463e22 | −0.819366 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.68111e23 | 1.65385 | 0.826923 | − | 0.562316i | \(-0.190089\pi\) | ||||
0.826923 | + | 0.562316i | \(0.190089\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.10621e22 | −0.676177 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.04471e23 | 1.88206 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.10805e22 | 0.811081 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.08018e22 | −0.437733 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.53170e23 | 1.27717 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.13516e23 | 0.916085 | 0.458042 | − | 0.888930i | \(-0.348551\pi\) | ||||
0.458042 | + | 0.888930i | \(0.348551\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.13139e22 | −0.244609 | −0.122305 | − | 0.992493i | \(-0.539028\pi\) | ||||
−0.122305 | + | 0.992493i | \(0.539028\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.53296e22 | 0.267168 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.78429e23 | 1.30640 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.38008e22 | −0.523224 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.74918e22 | 0.532050 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.11800e20 | −0.00207345 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.11708e22 | 0.265205 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.42529e22 | 0.0889449 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.34275e22 | 0.443971 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.32903e23 | −0.778680 | −0.389340 | − | 0.921094i | \(-0.627297\pi\) | ||||
−0.389340 | + | 0.921094i | \(0.627297\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.92825e22 | −0.450172 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.83965e22 | 0.541514 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.86923e22 | −0.206411 | −0.103205 | − | 0.994660i | \(-0.532910\pi\) | ||||
−0.103205 | + | 0.994660i | \(0.532910\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.29047e22 | 0.325326 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.30138e23 | 1.65541 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.98692e22 | −0.339721 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.63431e22 | −0.359981 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.53384e23 | −0.701475 | −0.350737 | − | 0.936474i | \(-0.614069\pi\) | ||||
−0.350737 | + | 0.936474i | \(0.614069\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.25157e20 | −0.00321686 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.99780e22 | −0.172043 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.19252e23 | 0.497904 | 0.248952 | − | 0.968516i | \(-0.419914\pi\) | ||||
0.248952 | + | 0.968516i | \(0.419914\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.59920e23 | 0.647875 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.33644e23 | −0.918540 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.07363e23 | −0.409638 | −0.204819 | − | 0.978800i | \(-0.565661\pi\) | ||||
−0.204819 | + | 0.978800i | \(0.565661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.25644e23 | 0.835634 | 0.417817 | − | 0.908531i | \(-0.362795\pi\) | ||||
0.417817 | + | 0.908531i | \(0.362795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.86284e22 | −0.354558 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.95698e22 | −0.138098 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.29594e23 | −0.439127 | −0.219563 | − | 0.975598i | \(-0.570463\pi\) | ||||
−0.219563 | + | 0.975598i | \(0.570463\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.45044e23 | −0.477233 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.75111e23 | 0.559519 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.61655e22 | 0.236361 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.60874e20 | 0.000786332 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.21537e23 | −0.941471 | −0.470735 | − | 0.882274i | \(-0.656011\pi\) | ||||
−0.470735 | + | 0.882274i | \(0.656011\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.01267e24 | 2.88064 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.88985e22 | 0.218060 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.23836e22 | −0.221246 | −0.110623 | − | 0.993862i | \(-0.535285\pi\) | ||||
−0.110623 | + | 0.993862i | \(0.535285\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.19032e23 | −0.571628 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.83330e22 | −0.224048 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.29015e22 | 0.179725 | 0.0898625 | − | 0.995954i | \(-0.471357\pi\) | ||||
0.0898625 | + | 0.995954i | \(0.471357\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.79880e23 | 0.910361 | 0.455180 | − | 0.890399i | \(-0.349575\pi\) | ||||
0.455180 | + | 0.890399i | \(0.349575\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.15174e23 | −0.268323 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.83280e23 | −0.415141 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.76245e23 | 0.828641 | 0.414321 | − | 0.910131i | \(-0.364019\pi\) | ||||
0.414321 | + | 0.910131i | \(0.364019\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.97255e23 | −1.27912 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.19924e21 | 0.00874623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.60370e23 | −0.932595 | −0.466298 | − | 0.884628i | \(-0.654412\pi\) | ||||
−0.466298 | + | 0.884628i | \(0.654412\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.20635e22 | 0.141996 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.36863e23 | −0.645698 | −0.322849 | − | 0.946451i | \(-0.604641\pi\) | ||||
−0.322849 | + | 0.946451i | \(0.604641\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.49640e23 | −0.279047 | −0.139523 | − | 0.990219i | \(-0.544557\pi\) | ||||
−0.139523 | + | 0.990219i | \(0.544557\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.14306e23 | 0.751696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.37249e24 | 2.42305 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.26895e23 | −0.379360 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.73302e23 | 0.770208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.17252e21 | 0.00977717 | 0.00488858 | − | 0.999988i | \(-0.498444\pi\) | ||||
0.00488858 | + | 0.999988i | \(0.498444\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.71259e23 | 0.726654 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.50942e23 | 0.376700 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.06947e21 | −0.00887086 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.64369e23 | −0.233917 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.59514e23 | −0.221057 | −0.110529 | − | 0.993873i | \(-0.535254\pi\) | ||||
−0.110529 | + | 0.993873i | \(0.535254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.37854e24 | −1.86049 | −0.930244 | − | 0.366941i | \(-0.880405\pi\) | ||||
−0.930244 | + | 0.366941i | \(0.880405\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.67599e23 | 0.220300 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.15056e23 | −0.403369 | −0.201684 | − | 0.979451i | \(-0.564641\pi\) | ||||
−0.201684 | + | 0.979451i | \(0.564641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.47677e23 | −0.433607 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.83204e24 | −2.22585 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.27963e23 | −0.269838 | −0.134919 | − | 0.990857i | \(-0.543077\pi\) | ||||
−0.134919 | + | 0.990857i | \(0.543077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.39579e23 | −0.160979 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.21275e23 | 0.136290 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.18670e24 | −1.29961 | −0.649806 | − | 0.760100i | \(-0.725150\pi\) | ||||
−0.649806 | + | 0.760100i | \(0.725150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50237e24 | −1.60348 | −0.801741 | − | 0.597672i | \(-0.796092\pi\) | ||||
−0.801741 | + | 0.597672i | \(0.796092\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.30455e21 | 0.00343754 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.24312e24 | −1.26046 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.68936e23 | 0.661173 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.05236e24 | −1.01401 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.82230e23 | −0.265132 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.53432e23 | 0.232131 | 0.116065 | − | 0.993242i | \(-0.462972\pi\) | ||||
0.116065 | + | 0.993242i | \(0.462972\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.43779e23 | −0.217728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.60323e23 | 0.400921 | 0.200460 | − | 0.979702i | \(-0.435756\pi\) | ||||
0.200460 | + | 0.979702i | \(0.435756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.59801e24 | 1.35734 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.24828e24 | −1.03410 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.27345e23 | 0.506910 | 0.253455 | − | 0.967347i | \(-0.418433\pi\) | ||||
0.253455 | + | 0.967347i | \(0.418433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.83678e23 | −0.381229 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.42553e24 | −1.09608 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.29579e21 | −0.00472266 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.11645e23 | −0.301272 | −0.150636 | − | 0.988589i | \(-0.548132\pi\) | ||||
−0.150636 | + | 0.988589i | \(0.548132\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00899e23 | −0.143464 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.62224e23 | −0.531144 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.46770e23 | −0.303812 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.43486e24 | 0.952255 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.88292e23 | 0.186737 | 0.0933683 | − | 0.995632i | \(-0.470237\pi\) | ||||
0.0933683 | + | 0.995632i | \(0.470237\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.68623e24 | 1.69833 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.70534e23 | −0.598967 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.88909e24 | −2.34306 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.85869e24 | −1.68141 | −0.840707 | − | 0.541491i | \(-0.817860\pi\) | ||||
−0.840707 | + | 0.541491i | \(0.817860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.19239e23 | 0.0684740 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.05191e24 | 1.15053 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.17045e21 | −0.000640841 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.03009e24 | −0.550762 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.21983e24 | 0.636946 | 0.318473 | − | 0.947932i | \(-0.396830\pi\) | ||||
0.318473 | + | 0.947932i | \(0.396830\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.79780e24 | 2.95674 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.56983e24 | −0.781947 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.93605e23 | −0.191508 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.28060e24 | 1.08394 | 0.541972 | − | 0.840396i | \(-0.317678\pi\) | ||||
0.541972 | + | 0.840396i | \(0.317678\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.31988e24 | 1.07716 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.03906e24 | −0.471349 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.50533e23 | −0.376970 | −0.188485 | − | 0.982076i | \(-0.560358\pi\) | ||||
−0.188485 | + | 0.982076i | \(0.560358\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.40278e24 | 0.607503 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.16744e23 | 0.218676 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.14385e24 | −0.886578 | −0.443289 | − | 0.896379i | \(-0.646188\pi\) | ||||
−0.443289 | + | 0.896379i | \(0.646188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.87550e22 | 0.00757988 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.23446e24 | −0.882606 | −0.441303 | − | 0.897358i | \(-0.645484\pi\) | ||||
−0.441303 | + | 0.897358i | \(0.645484\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.29660e23 | 0.281703 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.98843e23 | −0.112777 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.62076e24 | 0.966789 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71798e24 | 0.619555 | 0.309778 | − | 0.950809i | \(-0.399745\pi\) | ||||
0.309778 | + | 0.950809i | \(0.399745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.11671e23 | 0.286169 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.02689e24 | −0.698685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.09729e24 | −0.369832 | −0.184916 | − | 0.982754i | \(-0.559201\pi\) | ||||
−0.184916 | + | 0.982754i | \(0.559201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.59743e23 | −0.151516 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.70967e24 | −0.550990 | −0.275495 | − | 0.961302i | \(-0.588842\pi\) | ||||
−0.275495 | + | 0.961302i | \(0.588842\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.26350e24 | 1.97405 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.73800e23 | 0.115217 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.87388e22 | 0.00866378 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.22119e24 | 0.360090 | 0.180045 | − | 0.983658i | \(-0.442376\pi\) | ||||
0.180045 | + | 0.983658i | \(0.442376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.40228e24 | 0.692884 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.59069e24 | 0.730952 | 0.365476 | − | 0.930821i | \(-0.380906\pi\) | ||||
0.365476 | + | 0.930821i | \(0.380906\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.20736e24 | −0.333251 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.85968e24 | −1.31229 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.53564e24 | −0.669915 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.37461e23 | 0.190636 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.12114e24 | 1.04242 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.04292e24 | 0.753179 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.64413e24 | −0.640467 | −0.320234 | − | 0.947339i | \(-0.603761\pi\) | ||||
−0.320234 | + | 0.947339i | \(0.603761\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.84415e24 | 0.911268 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.01798e25 | 2.36179 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.33290e22 | 0.00529753 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.45509e24 | 0.323422 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.24909e24 | −1.35963 | −0.679815 | − | 0.733383i | \(-0.737940\pi\) | ||||
−0.679815 | + | 0.733383i | \(0.737940\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.01699e24 | 1.28154 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.34230e24 | −0.488388 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.44114e23 | −0.111073 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.51885e24 | −0.503427 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.36726e24 | 0.658948 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.76985e24 | 1.10561 | 0.552805 | − | 0.833311i | \(-0.313557\pi\) | ||||
0.552805 | + | 0.833311i | \(0.313557\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.03433e24 | −0.569359 | −0.284679 | − | 0.958623i | \(-0.591887\pi\) | ||||
−0.284679 | + | 0.958623i | \(0.591887\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.16130e24 | 1.13215 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.40973e24 | −0.433639 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.89719e24 | −1.03934 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.66061e22 | 0.00286652 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.15299e24 | 0.702172 | 0.351086 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351086 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.22848e23 | −0.152838 | −0.0764191 | − | 0.997076i | \(-0.524349\pi\) | ||||
−0.0764191 | + | 0.997076i | \(0.524349\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.70515e23 | 0.0438867 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.67636e24 | −1.22000 | −0.609998 | − | 0.792403i | \(-0.708830\pi\) | ||||
−0.609998 | + | 0.792403i | \(0.708830\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.23009e23 | 0.128142 | 0.0640709 | − | 0.997945i | \(-0.479592\pi\) | ||||
0.0640709 | + | 0.997945i | \(0.479592\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.26922e24 | 0.346153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.69679e24 | −1.29980 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.87209e24 | −0.713478 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.26413e25 | 1.81395 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.57083e24 | 1.34578 | 0.672888 | − | 0.739744i | \(-0.265053\pi\) | ||||
0.672888 | + | 0.739744i | \(0.265053\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.03171e23 | −0.0831140 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.81851e24 | −1.19086 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.37897e24 | −0.447201 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.16669e25 | −1.51337 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.42203e24 | 0.435079 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.44292e24 | 0.678314 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.48597e24 | 0.303690 | 0.151845 | − | 0.988404i | \(-0.451479\pi\) | ||||
0.151845 | + | 0.988404i | \(0.451479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.12150e24 | 0.254057 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.10495e24 | −0.247118 | −0.123559 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123559 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.58565e23 | 0.0873074 | 0.0436537 | − | 0.999047i | \(-0.486100\pi\) | ||||
0.0436537 | + | 0.999047i | \(0.486100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.58725e24 | 0.517638 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.83299e24 | 0.645356 | 0.322678 | − | 0.946509i | \(-0.395417\pi\) | ||||
0.322678 | + | 0.946509i | \(0.395417\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.42556e24 | 0.697067 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.96787e24 | −0.315706 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.34980e23 | −0.0558046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.27137e22 | −0.00436931 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.72717e24 | −0.273584 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.48210e24 | 0.145817 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.53835e25 | −1.48443 | −0.742214 | − | 0.670163i | \(-0.766224\pi\) | ||||
−0.742214 | + | 0.670163i | \(0.766224\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.12580e25 | 1.06551 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.57727e25 | −1.46424 | −0.732118 | − | 0.681178i | \(-0.761468\pi\) | ||||
−0.732118 | + | 0.681178i | \(0.761468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75208e25 | −1.59547 | −0.797734 | − | 0.603009i | \(-0.793968\pi\) | ||||
−0.797734 | + | 0.603009i | \(0.793968\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.64213e24 | −0.593321 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.05988e25 | 0.928764 | 0.464382 | − | 0.885635i | \(-0.346276\pi\) | ||||
0.464382 | + | 0.885635i | \(0.346276\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.59739e25 | 1.37324 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78898e24 | −0.150885 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.41494e25 | 2.82583 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.97918e23 | 0.0485451 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.80020e22 | 0.00302741 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.04106e25 | 1.59551 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.02107e24 | −0.691986 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.06687e25 | 0.803089 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.32595e24 | −0.245699 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.72762e24 | −0.487753 | −0.243876 | − | 0.969806i | \(-0.578419\pi\) | ||||
−0.243876 | + | 0.969806i | \(0.578419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.63712e24 | 0.472266 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.90734e25 | −1.33205 | −0.666027 | − | 0.745928i | \(-0.732006\pi\) | ||||
−0.666027 | + | 0.745928i | \(0.732006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.34080e24 | 0.0919100 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.39182e24 | −0.362791 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.88503e24 | −0.586840 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.73304e25 | 1.12364 | 0.561818 | − | 0.827261i | \(-0.310102\pi\) | ||||
0.561818 | + | 0.827261i | \(0.310102\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.44096e24 | 0.282664 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.09580e22 | −0.00380905 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.20264e24 | −0.196473 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.89452e24 | −0.595960 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.38514e24 | −0.377605 | −0.188802 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188802 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.93587e25 | −2.86610 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.26293e24 | −0.186043 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.67710e24 | −0.0938990 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.87864e25 | −1.58271 | −0.791354 | − | 0.611358i | \(-0.790624\pi\) | ||||
−0.791354 | + | 0.611358i | \(0.790624\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.90654e25 | 1.02941 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.31234e25 | −1.22614 | −0.613071 | − | 0.790028i | \(-0.710066\pi\) | ||||
−0.613071 | + | 0.790028i | \(0.710066\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.13781e24 | −0.267564 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.55180e25 | −0.793714 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.60999e25 | −0.808816 | −0.404408 | − | 0.914579i | \(-0.632522\pi\) | ||||
−0.404408 | + | 0.914579i | \(0.632522\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.49761e22 | 0.00221932 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.22599e25 | 0.594225 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.12344e25 | −0.534883 | −0.267441 | − | 0.963574i | \(-0.586178\pi\) | ||||
−0.267441 | + | 0.963574i | \(0.586178\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.13753e24 | −0.193514 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.57311e24 | −0.210117 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.07889e25 | −1.38975 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.00580e25 | 1.77640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.47259e24 | −0.194866 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.08468e24 | −0.260469 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.40854e24 | −0.101305 | −0.0506524 | − | 0.998716i | \(-0.516130\pi\) | ||||
−0.0506524 | + | 0.998716i | \(0.516130\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.68736e25 | 1.11064 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.55647e25 | 1.03819 | 0.519095 | − | 0.854716i | \(-0.326269\pi\) | ||||
0.519095 | + | 0.854716i | \(0.326269\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.85200e25 | −1.93625 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.23606e22 | −0.000876887 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.30301e25 | −0.887547 | −0.443774 | − | 0.896139i | \(-0.646361\pi\) | ||||
−0.443774 | + | 0.896139i | \(0.646361\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.05090e25 | 0.398024 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.06893e25 | −0.397889 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.04718e25 | 0.748949 | 0.374474 | − | 0.927237i | \(-0.377823\pi\) | ||||
0.374474 | + | 0.927237i | \(0.377823\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.30984e24 | 0.119014 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.17801e25 | −2.18350 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.19491e25 | −0.415113 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.20622e25 | −0.411907 | −0.205954 | − | 0.978562i | \(-0.566030\pi\) | ||||
−0.205954 | + | 0.978562i | \(0.566030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.59297e25 | −1.20610 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.70563e24 | −0.122283 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.73789e23 | −0.00563786 | −0.00281893 | − | 0.999996i | \(-0.500897\pi\) | ||||
−0.00281893 | + | 0.999996i | \(0.500897\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.35325e25 | 1.06945 |
(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 | 80.18.a.d.1.2 | 2 | ||
4.3 | odd | 2 | 10.18.a.c.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 90.18.a.k.1.1 | 2 | |||
20.3 | even | 4 | 50.18.b.d.49.3 | 4 | |||
20.7 | even | 4 | 50.18.b.d.49.2 | 4 | |||
20.19 | odd | 2 | 50.18.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
50.18.a.f.1.2 | 2 | 20.19 | odd | 2 | |||
50.18.b.d.49.2 | 4 | 20.7 | even | 4 | |||
50.18.b.d.49.3 | 4 | 20.3 | even | 4 | |||
80.18.a.d.1.2 | 2 | 1.1 | even | 1 | trivial | ||
90.18.a.k.1.1 | 2 | 12.11 | even | 2 |