Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.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: | \(127.444125612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 141x^{2} + 200x + 3500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 1080) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(9.55367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.40438 | 0.129824 | 0.0649121 | − | 0.997891i | \(-0.479323\pi\) | ||||
0.0649121 | + | 0.997891i | \(0.479323\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.3282 | −0.474968 | −0.237484 | − | 0.971391i | \(-0.576323\pi\) | ||||
−0.237484 | + | 0.971391i | \(0.576323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 71.2940 | 1.52103 | 0.760515 | − | 0.649320i | \(-0.224946\pi\) | ||||
0.760515 | + | 0.649320i | \(0.224946\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 111.164 | 1.58595 | 0.792974 | − | 0.609255i | \(-0.208532\pi\) | ||||
0.792974 | + | 0.609255i | \(0.208532\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 86.2397 | 1.04130 | 0.520651 | − | 0.853769i | \(-0.325689\pi\) | ||||
0.520651 | + | 0.853769i | \(0.325689\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 148.266 | 1.34416 | 0.672080 | − | 0.740479i | \(-0.265401\pi\) | ||||
0.672080 | + | 0.740479i | \(0.265401\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 71.1182 | 0.455390 | 0.227695 | − | 0.973732i | \(-0.426881\pi\) | ||||
0.227695 | + | 0.973732i | \(0.426881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212.038 | −1.22849 | −0.614244 | − | 0.789116i | \(-0.710539\pi\) | ||||
−0.614244 | + | 0.789116i | \(0.710539\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.0219 | 0.0580591 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −132.980 | −0.590859 | −0.295430 | − | 0.955365i | \(-0.595463\pi\) | ||||
−0.295430 | + | 0.955365i | \(0.595463\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29.6830 | −0.113066 | −0.0565330 | − | 0.998401i | \(-0.518005\pi\) | ||||
−0.0565330 | + | 0.998401i | \(0.518005\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 126.879 | 0.449973 | 0.224987 | − | 0.974362i | \(-0.427766\pi\) | ||||
0.224987 | + | 0.974362i | \(0.427766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 103.317 | 0.320647 | 0.160323 | − | 0.987065i | \(-0.448746\pi\) | ||||
0.160323 | + | 0.987065i | \(0.448746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −337.219 | −0.983146 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −298.464 | −0.773531 | −0.386765 | − | 0.922178i | \(-0.626408\pi\) | ||||
−0.386765 | + | 0.922178i | \(0.626408\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −86.6410 | −0.212412 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −893.675 | −1.97198 | −0.985988 | − | 0.166817i | \(-0.946651\pi\) | ||||
−0.985988 | + | 0.166817i | \(0.946651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 752.720 | 1.57993 | 0.789966 | − | 0.613150i | \(-0.210098\pi\) | ||||
0.789966 | + | 0.613150i | \(0.210098\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 356.470 | 0.680226 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −477.167 | −0.870078 | −0.435039 | − | 0.900412i | \(-0.643265\pi\) | ||||
−0.435039 | + | 0.900412i | \(0.643265\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 58.7339 | 0.0981751 | 0.0490875 | − | 0.998794i | \(-0.484369\pi\) | ||||
0.0490875 | + | 0.998794i | \(0.484369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 873.851 | 1.40105 | 0.700524 | − | 0.713628i | \(-0.252949\pi\) | ||||
0.700524 | + | 0.713628i | \(0.252949\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −41.6635 | −0.0616623 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −819.768 | −1.16748 | −0.583741 | − | 0.811940i | \(-0.698412\pi\) | ||||
−0.583741 | + | 0.811940i | \(0.698412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 959.392 | 1.26876 | 0.634379 | − | 0.773022i | \(-0.281256\pi\) | ||||
0.634379 | + | 0.773022i | \(0.281256\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 555.818 | 0.709258 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −406.735 | −0.484425 | −0.242212 | − | 0.970223i | \(-0.577873\pi\) | ||||
−0.242212 | + | 0.970223i | \(0.577873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 171.418 | 0.197467 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 431.199 | 0.465685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 623.748 | 0.652908 | 0.326454 | − | 0.945213i | \(-0.394146\pi\) | ||||
0.326454 | + | 0.945213i | \(0.394146\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −468.202 | −0.461266 | −0.230633 | − | 0.973041i | \(-0.574080\pi\) | ||||
−0.230633 | + | 0.973041i | \(0.574080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 949.097 | 0.907935 | 0.453967 | − | 0.891018i | \(-0.350008\pi\) | ||||
0.453967 | + | 0.891018i | \(0.350008\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 649.086 | 0.586444 | 0.293222 | − | 0.956044i | \(-0.405273\pi\) | ||||
0.293222 | + | 0.956044i | \(0.405273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1152.44 | 1.01269 | 0.506346 | − | 0.862330i | \(-0.330996\pi\) | ||||
0.506346 | + | 0.862330i | \(0.330996\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1537.75 | 1.28017 | 0.640087 | − | 0.768302i | \(-0.278898\pi\) | ||||
0.640087 | + | 0.768302i | \(0.278898\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 741.331 | 0.601126 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 267.279 | 0.205894 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1030.73 | −0.774405 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1950.33 | −1.36271 | −0.681353 | − | 0.731955i | \(-0.738608\pi\) | ||||
−0.681353 | + | 0.731955i | \(0.738608\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1219.32 | 0.813222 | 0.406611 | − | 0.913601i | \(-0.366710\pi\) | ||||
0.406611 | + | 0.913601i | \(0.366710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 207.353 | 0.135186 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2632.77 | 1.64185 | 0.820924 | − | 0.571038i | \(-0.193459\pi\) | ||||
0.820924 | + | 0.571038i | \(0.193459\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −943.117 | −0.575498 | −0.287749 | − | 0.957706i | \(-0.592907\pi\) | ||||
−0.287749 | + | 0.957706i | \(0.592907\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1235.40 | −0.722441 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 355.591 | 0.203657 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −833.371 | −0.458204 | −0.229102 | − | 0.973402i | \(-0.573579\pi\) | ||||
−0.229102 | + | 0.973402i | \(0.573579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2413.13 | −1.30052 | −0.650258 | − | 0.759714i | \(-0.725339\pi\) | ||||
−0.650258 | + | 0.759714i | \(0.725339\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1060.19 | −0.549396 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1085.41 | 0.551755 | 0.275877 | − | 0.961193i | \(-0.411032\pi\) | ||||
0.275877 | + | 0.961193i | \(0.411032\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 356.488 | 0.174504 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3657.89 | −1.75772 | −0.878859 | − | 0.477082i | \(-0.841694\pi\) | ||||
−0.878859 | + | 0.477082i | \(0.841694\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1506.46 | 0.698043 | 0.349022 | − | 0.937115i | \(-0.386514\pi\) | ||||
0.349022 | + | 0.937115i | \(0.386514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2885.84 | 1.31353 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −83.8876 | −0.0368662 | −0.0184331 | − | 0.999830i | \(-0.505868\pi\) | ||||
−0.0184331 | + | 0.999830i | \(0.505868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 60.1094 | 0.0259648 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4698.85 | 1.96206 | 0.981030 | − | 0.193855i | \(-0.0620990\pi\) | ||||
0.981030 | + | 0.193855i | \(0.0620990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2160.95 | −0.887413 | −0.443707 | − | 0.896172i | \(-0.646337\pi\) | ||||
−0.443707 | + | 0.896172i | \(0.646337\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −664.900 | −0.264240 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1926.26 | −0.753275 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 160.758 | 0.0609009 | 0.0304504 | − | 0.999536i | \(-0.490306\pi\) | ||||
0.0304504 | + | 0.999536i | \(0.490306\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3743.78 | 1.39628 | 0.698142 | − | 0.715959i | \(-0.254010\pi\) | ||||
0.698142 | + | 0.715959i | \(0.254010\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3812.48 | 1.37882 | 0.689411 | − | 0.724371i | \(-0.257870\pi\) | ||||
0.689411 | + | 0.724371i | \(0.257870\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 52.1965 | 0.0185935 | 0.00929676 | − | 0.999957i | \(-0.497041\pi\) | ||||
0.00929676 | + | 0.999957i | \(0.497041\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 170.995 | 0.0591206 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −148.415 | −0.0505646 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1494.38 | −0.494585 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2781.76 | −0.907603 | −0.453802 | − | 0.891103i | \(-0.649933\pi\) | ||||
−0.453802 | + | 0.891103i | \(0.649933\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 634.395 | 0.201234 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −509.819 | −0.159487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7925.29 | 2.41228 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1310.27 | −0.393462 | −0.196731 | − | 0.980458i | \(-0.563032\pi\) | ||||
−0.196731 | + | 0.980458i | \(0.563032\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3413.82 | −0.998163 | −0.499082 | − | 0.866555i | \(-0.666329\pi\) | ||||
−0.499082 | + | 0.866555i | \(0.666329\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4317.15 | −1.24579 | −0.622894 | − | 0.782306i | \(-0.714043\pi\) | ||||
−0.622894 | + | 0.782306i | \(0.714043\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2244.87 | 0.631185 | 0.315593 | − | 0.948895i | \(-0.397797\pi\) | ||||
0.315593 | + | 0.948895i | \(0.397797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 516.587 | 0.143398 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −924.054 | −0.250092 | −0.125046 | − | 0.992151i | \(-0.539908\pi\) | ||||
−0.125046 | + | 0.992151i | \(0.539908\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5505.32 | 1.47149 | 0.735744 | − | 0.677260i | \(-0.236833\pi\) | ||||
0.735744 | + | 0.677260i | \(0.236833\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1686.09 | −0.439676 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6148.37 | 1.58385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1654.48 | 0.416056 | 0.208028 | − | 0.978123i | \(-0.433295\pi\) | ||||
0.208028 | + | 0.978123i | \(0.433295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2569.19 | −0.638433 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5099.06 | −1.23763 | −0.618814 | − | 0.785538i | \(-0.712387\pi\) | ||||
−0.618814 | + | 0.785538i | \(0.712387\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −319.734 | −0.0767078 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4300.91 | 1.00838 | 0.504192 | − | 0.863591i | \(-0.331790\pi\) | ||||
0.504192 | + | 0.863591i | \(0.331790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1492.32 | −0.345933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5589.55 | 1.26692 | 0.633459 | − | 0.773776i | \(-0.281634\pi\) | ||||
0.633459 | + | 0.773776i | \(0.281634\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3435.85 | −0.770158 | −0.385079 | − | 0.922884i | \(-0.625826\pi\) | ||||
−0.385079 | + | 0.922884i | \(0.625826\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −433.205 | −0.0949936 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4652.36 | 1.00914 | 0.504572 | − | 0.863369i | \(-0.331650\pi\) | ||||
0.504572 | + | 0.863369i | \(0.331650\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3173.95 | −0.673814 | −0.336907 | − | 0.941538i | \(-0.609381\pi\) | ||||
−0.336907 | + | 0.941538i | \(0.609381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4344.90 | 0.912641 | 0.456321 | − | 0.889815i | \(-0.349167\pi\) | ||||
0.456321 | + | 0.889815i | \(0.349167\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −71.3691 | −0.0146787 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7444.33 | 1.51523 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3010.86 | −0.600329 | −0.300165 | − | 0.953887i | \(-0.597042\pi\) | ||||
−0.300165 | + | 0.953887i | \(0.597042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4468.37 | −0.881894 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 10570.5 | 2.04451 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 305.065 | 0.0584174 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3763.60 | 0.706567 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1083.82 | 0.201487 | 0.100744 | − | 0.994912i | \(-0.467878\pi\) | ||||
0.100744 | + | 0.994912i | \(0.467878\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7202.17 | 1.31318 | 0.656588 | − | 0.754249i | \(-0.271999\pi\) | ||||
0.656588 | + | 0.754249i | \(0.271999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 55.5588 | 0.0100331 | 0.00501656 | − | 0.999987i | \(-0.498403\pi\) | ||||
0.00501656 | + | 0.999987i | \(0.498403\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6762.76 | 1.19822 | 0.599108 | − | 0.800668i | \(-0.295522\pi\) | ||||
0.599108 | + | 0.800668i | \(0.295522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1232.35 | −0.216296 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9586.71 | 1.65145 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1782.35 | 0.304206 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 248.414 | 0.0416277 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4689.11 | 0.778660 | 0.389330 | − | 0.921098i | \(-0.372707\pi\) | ||||
0.389330 | + | 0.921098i | \(0.372707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2385.84 | −0.389111 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11110.1 | −1.79587 | −0.897935 | − | 0.440128i | \(-0.854933\pi\) | ||||
−0.897935 | + | 0.440128i | \(0.854933\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3674.23 | 0.583492 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1635.50 | −0.257460 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8190.20 | −1.26707 | −0.633535 | − | 0.773714i | \(-0.718397\pi\) | ||||
−0.633535 | + | 0.773714i | \(0.718397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2804.03 | −0.430075 | −0.215037 | − | 0.976606i | \(-0.568987\pi\) | ||||
−0.215037 | + | 0.976606i | \(0.568987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5285.46 | 0.796931 | 0.398466 | − | 0.917183i | \(-0.369543\pi\) | ||||
0.398466 | + | 0.917183i | \(0.369543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 293.669 | 0.0439052 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3078.37 | 0.452563 | 0.226281 | − | 0.974062i | \(-0.427343\pi\) | ||||
0.226281 | + | 0.974062i | \(0.427343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 578.288 | 0.0843109 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4369.26 | 0.626568 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 81.5000 | 0.0115920 | 0.00579600 | − | 0.999983i | \(-0.498155\pi\) | ||||
0.00579600 | + | 0.999983i | \(0.498155\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −717.619 | −0.100423 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11888.6 | −1.65032 | −0.825160 | − | 0.564899i | \(-0.808915\pi\) | ||||
−0.825160 | + | 0.564899i | \(0.808915\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5070.30 | 0.692662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10663.7 | 1.44527 | 0.722636 | − | 0.691229i | \(-0.242930\pi\) | ||||
0.722636 | + | 0.691229i | \(0.242930\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6178.97 | 0.824362 | 0.412181 | − | 0.911102i | \(-0.364767\pi\) | ||||
0.412181 | + | 0.911102i | \(0.364767\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −208.318 | −0.0275762 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7948.36 | 1.03598 | 0.517992 | − | 0.855386i | \(-0.326680\pi\) | ||||
0.517992 | + | 0.855386i | \(0.326680\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16481.8 | 2.13177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4098.84 | −0.522114 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11191.2 | 1.41478 | 0.707392 | − | 0.706822i | \(-0.249872\pi\) | ||||
0.707392 | + | 0.706822i | \(0.249872\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9357.36 | −1.16530 | −0.582649 | − | 0.812724i | \(-0.697984\pi\) | ||||
−0.582649 | + | 0.812724i | \(0.697984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15117.0 | −1.86857 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2304.31 | 0.280639 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3229.59 | −0.390447 | −0.195224 | − | 0.980759i | \(-0.562543\pi\) | ||||
−0.195224 | + | 0.980759i | \(0.562543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2148.73 | −0.256010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4796.96 | 0.567406 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4305.10 | 0.501951 | 0.250976 | − | 0.967993i | \(-0.419249\pi\) | ||||
0.250976 | + | 0.967993i | \(0.419249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4330.36 | −0.501304 | −0.250652 | − | 0.968077i | \(-0.580645\pi\) | ||||
−0.250652 | + | 0.968077i | \(0.580645\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2779.09 | 0.317190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1809.82 | 0.205113 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2774.39 | 0.310064 | 0.155032 | − | 0.987909i | \(-0.450452\pi\) | ||||
0.155032 | + | 0.987909i | \(0.450452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16958.3 | −1.88213 | −0.941065 | − | 0.338225i | \(-0.890173\pi\) | ||||
−0.941065 | + | 0.338225i | \(0.890173\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12786.4 | 1.39968 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1334.39 | −0.145072 | −0.0725362 | − | 0.997366i | \(-0.523109\pi\) | ||||
−0.0725362 | + | 0.997366i | \(0.523109\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1990.19 | −0.213447 | −0.106723 | − | 0.994289i | \(-0.534036\pi\) | ||||
−0.106723 | + | 0.994289i | \(0.534036\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2033.67 | −0.216641 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5858.34 | −0.615751 | −0.307876 | − | 0.951427i | \(-0.599618\pi\) | ||||
−0.307876 | + | 0.951427i | \(0.599618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 514.353 | 0.0537027 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 857.088 | 0.0883097 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1838.53 | 0.188190 | 0.0940952 | − | 0.995563i | \(-0.470004\pi\) | ||||
0.0940952 | + | 0.995563i | \(0.470004\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2805.80 | 0.283469 | 0.141735 | − | 0.989905i | \(-0.454732\pi\) | ||||
0.141735 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9647.34 | 0.968359 | 0.484179 | − | 0.874969i | \(-0.339118\pi\) | ||||
0.484179 | + | 0.874969i | \(0.339118\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8339.39 | 0.826340 | 0.413170 | − | 0.910654i | \(-0.364421\pi\) | ||||
0.413170 | + | 0.910654i | \(0.364421\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1147.29 | −0.112957 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2198.58 | −0.213723 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2155.99 | 0.208260 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2842.91 | 0.271181 | 0.135591 | − | 0.990765i | \(-0.456707\pi\) | ||||
0.135591 | + | 0.990765i | \(0.456707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9480.68 | −0.898715 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3118.74 | 0.291989 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −55.8309 | −0.00519495 | −0.00259747 | − | 0.999997i | \(-0.500827\pi\) | ||||
−0.00259747 | + | 0.999997i | \(0.500827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10131.2 | −0.931188 | −0.465594 | − | 0.884998i | \(-0.654159\pi\) | ||||
−0.465594 | + | 0.884998i | \(0.654159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7905.75 | 0.722225 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 141.218 | 0.0127455 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18760.6 | 1.68305 | 0.841524 | − | 0.540219i | \(-0.181659\pi\) | ||||
0.841524 | + | 0.540219i | \(0.181659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1263.21 | −0.111975 | −0.0559877 | − | 0.998431i | \(-0.517831\pi\) | ||||
−0.0559877 | + | 0.998431i | \(0.517831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2341.01 | −0.206284 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20105.1 | −1.75077 | −0.875386 | − | 0.483424i | \(-0.839393\pi\) | ||||
−0.875386 | + | 0.483424i | \(0.839393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2101.07 | 0.181890 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4745.48 | 0.406041 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1790.31 | −0.152297 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1644.53 | 0.138288 | 0.0691440 | − | 0.997607i | \(-0.477973\pi\) | ||||
0.0691440 | + | 0.997607i | \(0.477973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4830.92 | −0.403903 | −0.201952 | − | 0.979395i | \(-0.564728\pi\) | ||||
−0.201952 | + | 0.979395i | \(0.564728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −23570.9 | −1.94832 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9815.89 | 0.806764 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2116.22 | −0.171977 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3245.43 | 0.262266 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5843.40 | 0.466963 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 159.541 | 0.0126787 | 0.00633936 | − | 0.999980i | \(-0.497982\pi\) | ||||
0.00633936 | + | 0.999980i | \(0.497982\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5762.18 | 0.452890 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3217.83 | −0.251526 | −0.125763 | − | 0.992060i | \(-0.540138\pi\) | ||||
−0.125763 | + | 0.992060i | \(0.540138\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6133.21 | 0.474199 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1971.03 | −0.151567 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21394.0 | 1.62745 | 0.813727 | − | 0.581247i | \(-0.197435\pi\) | ||||
0.813727 | + | 0.581247i | \(0.197435\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9045.71 | 0.684423 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3427.87 | −0.256603 | −0.128302 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128302 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7688.77 | 0.572511 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12420.8 | −0.915128 | −0.457564 | − | 0.889177i | \(-0.651278\pi\) | ||||
−0.457564 | + | 0.889177i | \(0.651278\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3954.37 | 0.289816 | 0.144908 | − | 0.989445i | \(-0.453711\pi\) | ||||
0.144908 | + | 0.989445i | \(0.453711\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3706.66 | 0.268832 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24982.7 | −1.80250 | −0.901250 | − | 0.433299i | \(-0.857349\pi\) | ||||
−0.901250 | + | 0.433299i | \(0.857349\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2306.74 | 0.164715 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5171.84 | 0.367402 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7981.44 | −0.561208 | −0.280604 | − | 0.959824i | \(-0.590535\pi\) | ||||
−0.280604 | + | 0.959824i | \(0.590535\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18286.1 | −1.27923 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2465.27 | 0.170719 | 0.0853597 | − | 0.996350i | \(-0.472796\pi\) | ||||
0.0853597 | + | 0.996350i | \(0.472796\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1336.40 | 0.0920788 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21413.6 | 1.46066 | 0.730331 | − | 0.683093i | \(-0.239366\pi\) | ||||
0.730331 | + | 0.683093i | \(0.239366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −307.813 | −0.0208918 | −0.0104459 | − | 0.999945i | \(-0.503325\pi\) | ||||
−0.0104459 | + | 0.999945i | \(0.503325\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5153.67 | −0.346325 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3953.10 | −0.264335 | −0.132168 | − | 0.991227i | \(-0.542194\pi\) | ||||
−0.132168 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7365.92 | 0.487714 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8356.90 | −0.550623 | −0.275311 | − | 0.961355i | \(-0.588781\pi\) | ||||
−0.275311 | + | 0.961355i | \(0.588781\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25301.3 | 1.65088 | 0.825439 | − | 0.564491i | \(-0.190928\pi\) | ||||
0.825439 | + | 0.564491i | \(0.190928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1542.86 | −0.100182 | −0.0500912 | − | 0.998745i | \(-0.515951\pi\) | ||||
−0.0500912 | + | 0.998745i | \(0.515951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −977.944 | −0.0628900 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14782.5 | −0.937072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12888.9 | −0.813152 | −0.406576 | − | 0.913617i | \(-0.633277\pi\) | ||||
−0.406576 | + | 0.913617i | \(0.633277\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9751.64 | −0.609420 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24041.7 | −1.49539 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4590.77 | −0.282878 | −0.141439 | − | 0.989947i | \(-0.545173\pi\) | ||||
−0.141439 | + | 0.989947i | \(0.545173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12085.3 | 0.741209 | 0.370605 | − | 0.928791i | \(-0.379150\pi\) | ||||
0.370605 | + | 0.928791i | \(0.379150\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6233.43 | 0.378766 | 0.189383 | − | 0.981903i | \(-0.439351\pi\) | ||||
0.189383 | + | 0.981903i | \(0.439351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15485.8 | 0.936625 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24307.8 | −1.45672 | −0.728361 | − | 0.685194i | \(-0.759718\pi\) | ||||
−0.728361 | + | 0.685194i | \(0.759718\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6096.58 | 0.363684 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1445.94 | −0.0854719 | −0.0427359 | − | 0.999086i | \(-0.513607\pi\) | ||||
−0.0427359 | + | 0.999086i | \(0.513607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11159.3 | −0.656654 | −0.328327 | − | 0.944564i | \(-0.606485\pi\) | ||||
−0.328327 | + | 0.944564i | \(0.606485\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1036.76 | 0.0604571 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10544.4 | 0.612117 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13043.3 | −0.750418 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4473.63 | −0.256234 | −0.128117 | − | 0.991759i | \(-0.540893\pi\) | ||||
−0.128117 | + | 0.991759i | \(0.540893\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19997.2 | 1.13523 | 0.567617 | − | 0.823292i | \(-0.307865\pi\) | ||||
0.567617 | + | 0.823292i | \(0.307865\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1499.73 | 0.0847632 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21261.5 | 1.19114 | 0.595571 | − | 0.803303i | \(-0.296926\pi\) | ||||
0.595571 | + | 0.803303i | \(0.296926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13163.9 | 0.734256 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21278.7 | −1.17656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −31303.9 | −1.72338 | −0.861691 | − | 0.507434i | \(-0.830594\pi\) | ||||
−0.861691 | + | 0.507434i | \(0.830594\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4715.59 | −0.257370 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3299.67 | −0.179317 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30288.1 | 1.63190 | 0.815952 | − | 0.578120i | \(-0.196214\pi\) | ||||
0.815952 | + | 0.578120i | \(0.196214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11468.2 | −0.615263 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1125.73 | −0.0598835 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26181.8 | 1.38685 | 0.693426 | − | 0.720528i | \(-0.256101\pi\) | ||||
0.693426 | + | 0.720528i | \(0.256101\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31438.1 | −1.65128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6176.98 | −0.323085 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32762.6 | 1.69936 | 0.849679 | − | 0.527301i | \(-0.176796\pi\) | ||||
0.849679 | + | 0.527301i | \(0.176796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2281.99 | 0.117872 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1777.95 | 0.0910780 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19439.8 | −0.991721 | −0.495861 | − | 0.868402i | \(-0.665147\pi\) | ||||
−0.495861 | + | 0.868402i | \(0.665147\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14104.3 | 0.713634 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16886.4 | −0.850906 | −0.425453 | − | 0.904981i | \(-0.639885\pi\) | ||||
−0.425453 | + | 0.904981i | \(0.639885\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8268.45 | 0.413259 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9048.46 | −0.450410 | −0.225205 | − | 0.974311i | \(-0.572305\pi\) | ||||
−0.225205 | + | 0.974311i | \(0.572305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22272.8 | −1.09975 | −0.549873 | − | 0.835249i | \(-0.685324\pi\) | ||||
−0.549873 | + | 0.835249i | \(0.685324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4166.85 | −0.204915 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1560.65 | 0.0761346 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2223.89 | −0.108057 | −0.0540284 | − | 0.998539i | \(-0.517206\pi\) | ||||
−0.0540284 | + | 0.998539i | \(0.517206\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12065.7 | −0.581608 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21253.7 | 1.02045 | 0.510225 | − | 0.860041i | \(-0.329562\pi\) | ||||
0.510225 | + | 0.860041i | \(0.329562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36585.2 | −1.74272 | −0.871362 | − | 0.490640i | \(-0.836763\pi\) | ||||
−0.871362 | + | 0.490640i | \(0.836763\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2770.89 | 0.131472 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63713.7 | −2.99944 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14952.5 | 0.701171 | 0.350585 | − | 0.936531i | \(-0.385983\pi\) | ||||
0.350585 | + | 0.936531i | \(0.385983\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41504.0 | 1.93117 | 0.965586 | − | 0.260082i | \(-0.0837497\pi\) | ||||
0.965586 | + | 0.260082i | \(0.0837497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5300.94 | −0.245697 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2559.85 | −0.117736 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1017.75 | −0.0466300 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5427.07 | 0.246752 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34867.0 | 1.57926 | 0.789628 | − | 0.613585i | \(-0.210273\pi\) | ||||
0.789628 | + | 0.613585i | \(0.210273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3697.34 | 0.166198 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 53664.4 | 2.40313 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14744.4 | −0.655299 | −0.327649 | − | 0.944799i | \(-0.606257\pi\) | ||||
−0.327649 | + | 0.944799i | \(0.606257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11485.1 | 0.508529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15142.3 | −0.665454 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1782.44 | 0.0780407 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26179.5 | −1.13773 | −0.568864 | − | 0.822431i | \(-0.692617\pi\) | ||||
−0.568864 | + | 0.822431i | \(0.692617\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1162.53 | 0.0503354 | 0.0251677 | − | 0.999683i | \(-0.491988\pi\) | ||||
0.0251677 | + | 0.999683i | \(0.491988\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18289.4 | −0.786075 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10942.0 | 0.468558 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35989.7 | −1.52990 | −0.764951 | − | 0.644088i | \(-0.777237\pi\) | ||||
−0.764951 | + | 0.644088i | \(0.777237\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36003.6 | −1.52492 | −0.762459 | − | 0.647036i | \(-0.776008\pi\) | ||||
−0.762459 | + | 0.647036i | \(0.776008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22096.7 | −0.929114 | −0.464557 | − | 0.885543i | \(-0.653786\pi\) | ||||
−0.464557 | + | 0.885543i | \(0.653786\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.9350 | 0.000625710 0 | 0.000312855 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000312855 | 1.00000i | \(0.499900\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37486.5 | −1.55922 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7532.29 | 0.312174 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41995.0 | −1.72804 | −0.864022 | − | 0.503453i | \(-0.832063\pi\) | ||||
−0.864022 | + | 0.503453i | \(0.832063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19331.2 | −0.792620 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14429.2 | 0.587430 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2478.27 | −0.100537 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19716.5 | −0.794209 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9809.11 | 0.393737 | 0.196868 | − | 0.980430i | \(-0.436923\pi\) | ||||
0.196868 | + | 0.980430i | \(0.436923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31063.8 | −1.23818 | −0.619089 | − | 0.785321i | \(-0.712498\pi\) | ||||
−0.619089 | + | 0.785321i | \(0.712498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5957.06 | 0.236615 | 0.118307 | − | 0.992977i | \(-0.462253\pi\) | ||||
0.118307 | + | 0.992977i | \(0.462253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31548.8 | 1.24442 | 0.622210 | − | 0.782850i | \(-0.286235\pi\) | ||||
0.622210 | + | 0.782850i | \(0.286235\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −419.438 | −0.0164871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14205.1 | 0.554517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34019.2 | −1.32342 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 300.547 | 0.0116118 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44007.7 | 1.69445 | 0.847226 | − | 0.531233i | \(-0.178271\pi\) | ||||
0.847226 | + | 0.531233i | \(0.178271\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8635.87 | 0.330250 | 0.165125 | − | 0.986273i | \(-0.447197\pi\) | ||||
0.165125 | + | 0.986273i | \(0.447197\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25587.5 | 0.975184 | 0.487592 | − | 0.873072i | \(-0.337875\pi\) | ||||
0.487592 | + | 0.873072i | \(0.337875\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22534.0 | −0.853007 | −0.426503 | − | 0.904486i | \(-0.640255\pi\) | ||||
−0.426503 | + | 0.904486i | \(0.640255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4689.32 | −0.176912 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8910.07 | 0.333890 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23494.3 | 0.877460 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15079.7 | −0.559441 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33178.3 | −1.22678 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10804.7 | −0.396863 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44792.3 | −1.63980 | −0.819902 | − | 0.572504i | \(-0.805972\pi\) | ||||
−0.819902 | + | 0.572504i | \(0.805972\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44378.6 | 1.61397 | 0.806986 | − | 0.590571i | \(-0.201097\pi\) | ||||
0.806986 | + | 0.590571i | \(0.201097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16624.5 | −0.602620 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2931.69 | 0.105576 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19542.4 | 0.701462 | 0.350731 | − | 0.936476i | \(-0.385933\pi\) | ||||
0.350731 | + | 0.936476i | \(0.385933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4187.37 | 0.149327 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3324.50 | −0.118172 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23231.5 | −0.820453 | −0.410227 | − | 0.911984i | \(-0.634550\pi\) | ||||
−0.410227 | + | 0.911984i | \(0.634550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29081.7 | −1.02375 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9631.32 | −0.336875 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14026.4 | −0.489032 | −0.244516 | − | 0.969645i | \(-0.578629\pi\) | ||||
−0.244516 | + | 0.969645i | \(0.578629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −986.880 | −0.0341885 | −0.0170943 | − | 0.999854i | \(-0.505442\pi\) | ||||
−0.0170943 | + | 0.999854i | \(0.505442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4400.99 | −0.151979 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34679.9 | −1.19002 | −0.595008 | − | 0.803720i | \(-0.702851\pi\) | ||||
−0.595008 | + | 0.803720i | \(0.702851\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62300.4 | 2.13104 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52384.1 | −1.78058 | −0.890288 | − | 0.455398i | \(-0.849497\pi\) | ||||
−0.890288 | + | 0.455398i | \(0.849497\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 803.792 | 0.0272357 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6330.18 | 0.213151 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15169.0 | 0.509181 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18718.9 | 0.624437 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29842.4 | −0.992417 | −0.496208 | − | 0.868203i | \(-0.665275\pi\) | ||||
−0.496208 | + | 0.868203i | \(0.665275\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21134.5 | −0.698494 | −0.349247 | − | 0.937031i | \(-0.613563\pi\) | ||||
−0.349247 | + | 0.937031i | \(0.613563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2267.61 | −0.0747135 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11583.6 | −0.379318 | −0.189659 | − | 0.981850i | \(-0.560738\pi\) | ||||
−0.189659 | + | 0.981850i | \(0.560738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7047.98 | 0.230086 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54382.8 | 1.76454 | 0.882269 | − | 0.470745i | \(-0.156015\pi\) | ||||
0.882269 | + | 0.470745i | \(0.156015\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19062.4 | 0.616628 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18811.9 | 0.604836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8319.58 | −0.266680 | −0.133340 | − | 0.991070i | \(-0.542570\pi\) | ||||
−0.133340 | + | 0.991070i | \(0.542570\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 260.982 | 0.00831527 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 33697.8 | 1.07043 | 0.535216 | − | 0.844715i | \(-0.320230\pi\) | ||||
0.535216 | + | 0.844715i | \(0.320230\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2160.4.a.bv.1.3 | 4 | ||
3.2 | odd | 2 | 2160.4.a.bu.1.3 | 4 | |||
4.3 | odd | 2 | 1080.4.a.p.1.2 | yes | 4 | ||
12.11 | even | 2 | 1080.4.a.o.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.o.1.2 | ✓ | 4 | 12.11 | even | 2 | ||
1080.4.a.p.1.2 | yes | 4 | 4.3 | odd | 2 | ||
2160.4.a.bu.1.3 | 4 | 3.2 | odd | 2 | |||
2160.4.a.bv.1.3 | 4 | 1.1 | even | 1 | trivial |