Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,4,Mod(1,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1680.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.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: | \(99.1232088096\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93774 | 0.0805239 | 0.0402619 | − | 0.999189i | \(-0.487181\pi\) | ||||
0.0402619 | + | 0.999189i | \(0.487181\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.0623 | −0.406686 | −0.203343 | − | 0.979108i | \(-0.565181\pi\) | ||||
−0.203343 | + | 0.979108i | \(0.565181\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 122.498 | 1.74766 | 0.873828 | − | 0.486236i | \(-0.161630\pi\) | ||||
0.873828 | + | 0.486236i | \(0.161630\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −107.436 | −1.29723 | −0.648617 | − | 0.761115i | \(-0.724652\pi\) | ||||
−0.648617 | + | 0.761115i | \(0.724652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −210.623 | −1.90947 | −0.954736 | − | 0.297455i | \(-0.903862\pi\) | ||||
−0.954736 | + | 0.297455i | \(0.903862\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 95.4942 | 0.611477 | 0.305738 | − | 0.952116i | \(-0.401097\pi\) | ||||
0.305738 | + | 0.952116i | \(0.401097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 94.3074 | 0.546391 | 0.273195 | − | 0.961959i | \(-0.411919\pi\) | ||||
0.273195 | + | 0.961959i | \(0.411919\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.81323 | −0.0464905 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.0000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 97.1206 | 0.431528 | 0.215764 | − | 0.976446i | \(-0.430776\pi\) | ||||
0.215764 | + | 0.976446i | \(0.430776\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 57.1868 | 0.234800 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −491.113 | −1.87071 | −0.935353 | − | 0.353716i | \(-0.884918\pi\) | ||||
−0.935353 | + | 0.353716i | \(0.884918\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.0039 | 0.152512 | 0.0762562 | − | 0.997088i | \(-0.475703\pi\) | ||||
0.0762562 | + | 0.997088i | \(0.475703\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 45.0000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −473.494 | −1.46949 | −0.734747 | − | 0.678341i | \(-0.762699\pi\) | ||||
−0.734747 | + | 0.678341i | \(0.762699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −367.494 | −1.00901 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −183.677 | −0.476038 | −0.238019 | − | 0.971261i | \(-0.576498\pi\) | ||||
−0.238019 | + | 0.971261i | \(0.576498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.6887 | 0.0360114 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 322.307 | 0.748959 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 760.615 | 1.67837 | 0.839183 | − | 0.543849i | \(-0.183034\pi\) | ||||
0.839183 | + | 0.543849i | \(0.183034\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −198.747 | −0.417163 | −0.208582 | − | 0.978005i | \(-0.566885\pi\) | ||||
−0.208582 | + | 0.978005i | \(0.566885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −95.3113 | −0.181876 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 309.992 | 0.565247 | 0.282624 | − | 0.959231i | \(-0.408795\pi\) | ||||
0.282624 | + | 0.959231i | \(0.408795\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 631.868 | 1.10243 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −665.693 | −1.11272 | −0.556360 | − | 0.830941i | \(-0.687803\pi\) | ||||
−0.556360 | + | 0.830941i | \(0.687803\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 621.288 | 0.996113 | 0.498057 | − | 0.867145i | \(-0.334047\pi\) | ||||
0.498057 | + | 0.867145i | \(0.334047\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.5642 | 0.0304352 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.7626 | 0.0352659 | 0.0176330 | − | 0.999845i | \(-0.494387\pi\) | ||||
0.0176330 | + | 0.999845i | \(0.494387\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 406.724 | 0.537876 | 0.268938 | − | 0.963157i | \(-0.413327\pi\) | ||||
0.268938 | + | 0.963157i | \(0.413327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 612.490 | 0.781575 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −286.483 | −0.353036 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 261.751 | 0.311748 | 0.155874 | − | 0.987777i | \(-0.450181\pi\) | ||||
0.155874 | + | 0.987777i | \(0.450181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −133.436 | −0.153713 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −282.922 | −0.315459 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −537.179 | −0.580141 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1004.77 | −1.05175 | −0.525873 | − | 0.850563i | \(-0.676261\pi\) | ||||
−0.525873 | + | 0.850563i | \(0.676261\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 26.4397 | 0.0268413 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −128.872 | −0.126962 | −0.0634812 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634812 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −806.008 | −0.771051 | −0.385526 | − | 0.922697i | \(-0.625980\pi\) | ||||
−0.385526 | + | 0.922697i | \(0.625980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −105.000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 769.712 | 0.695429 | 0.347714 | − | 0.937600i | \(-0.386958\pi\) | ||||
0.347714 | + | 0.937600i | \(0.386958\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −780.856 | −0.686169 | −0.343085 | − | 0.939304i | \(-0.611472\pi\) | ||||
−0.343085 | + | 0.939304i | \(0.611472\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −291.362 | −0.249143 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1115.65 | −0.928771 | −0.464386 | − | 0.885633i | \(-0.653725\pi\) | ||||
−0.464386 | + | 0.885633i | \(0.653725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1053.11 | −0.853942 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −171.560 | −0.135562 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 857.486 | 0.660552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1322.37 | −0.993516 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1473.34 | 1.08005 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1875.98 | 1.31076 | 0.655381 | − | 0.755299i | \(-0.272508\pi\) | ||||
0.655381 | + | 0.755299i | \(0.272508\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −129.012 | −0.0880530 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −364.203 | −0.242905 | −0.121452 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121452 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −752.051 | −0.490309 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1603.13 | 0.999743 | 0.499872 | − | 0.866099i | \(-0.333380\pi\) | ||||
0.499872 | + | 0.866099i | \(0.333380\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2431.12 | −1.48349 | −0.741746 | − | 0.670681i | \(-0.766002\pi\) | ||||
−0.741746 | + | 0.670681i | \(0.766002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1420.48 | 0.848413 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −56.0000 | −0.0327479 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 477.471 | 0.273461 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2341.57 | 1.28744 | 0.643722 | − | 0.765260i | \(-0.277389\pi\) | ||||
0.643722 | + | 0.765260i | \(0.277389\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2104.07 | 1.13395 | 0.566976 | − | 0.823734i | \(-0.308113\pi\) | ||||
0.566976 | + | 0.823734i | \(0.308113\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1102.48 | 0.582552 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 471.537 | 0.244353 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −593.467 | −0.301680 | −0.150840 | − | 0.988558i | \(-0.548198\pi\) | ||||
−0.150840 | + | 0.988558i | \(0.548198\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 551.031 | 0.274840 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1474.36 | −0.721712 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2178.71 | −1.04693 | −0.523465 | − | 0.852047i | \(-0.675361\pi\) | ||||
−0.523465 | + | 0.852047i | \(0.675361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −44.0661 | −0.0207912 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −799.502 | −0.370463 | −0.185231 | − | 0.982695i | \(-0.559303\pi\) | ||||
−0.185231 | + | 0.982695i | \(0.559303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1833.63 | −0.834606 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −966.922 | −0.432412 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1444.36 | −0.634754 | −0.317377 | − | 0.948299i | \(-0.602802\pi\) | ||||
−0.317377 | + | 0.948299i | \(0.602802\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2281.84 | −0.969005 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3343.49 | −1.39611 | −0.698056 | − | 0.716043i | \(-0.745952\pi\) | ||||
−0.698056 | + | 0.716043i | \(0.745952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2251.81 | 0.924729 | 0.462365 | − | 0.886690i | \(-0.347001\pi\) | ||||
0.462365 | + | 0.886690i | \(0.347001\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 596.241 | 0.240849 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 485.603 | 0.192985 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 359.868 | 0.140728 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1001.93 | 0.379565 | 0.189782 | − | 0.981826i | \(-0.439222\pi\) | ||||
0.189782 | + | 0.981826i | \(0.439222\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4054.97 | −1.51235 | −0.756173 | − | 0.654372i | \(-0.772933\pi\) | ||||
−0.756173 | + | 0.654372i | \(0.772933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 285.934 | 0.105006 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5140.23 | −1.85902 | −0.929508 | − | 0.368802i | \(-0.879768\pi\) | ||||
−0.929508 | + | 0.368802i | \(0.879768\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −585.631 | −0.208614 | −0.104307 | − | 0.994545i | \(-0.533263\pi\) | ||||
−0.104307 | + | 0.994545i | \(0.533263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −929.977 | −0.326346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 668.459 | 0.231116 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2455.56 | −0.836605 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1895.60 | −0.636490 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −315.619 | −0.104458 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1055.16 | 0.344266 | 0.172133 | − | 0.985074i | \(-0.444934\pi\) | ||||
0.172133 | + | 0.985074i | \(0.444934\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1997.08 | 0.642430 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 215.019 | 0.0682056 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 660.152 | 0.206516 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1863.86 | −0.575106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2335.09 | −0.710747 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4675.85 | −1.40412 | −0.702059 | − | 0.712119i | \(-0.747736\pi\) | ||||
−0.702059 | + | 0.712119i | \(0.747736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5443.11 | −1.59151 | −0.795754 | − | 0.605621i | \(-0.792925\pi\) | ||||
−0.795754 | + | 0.605621i | \(0.792925\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −536.303 | −0.154759 | −0.0773797 | − | 0.997002i | \(-0.524655\pi\) | ||||
−0.0773797 | + | 0.997002i | \(0.524655\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −61.6926 | −0.0175717 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −183.490 | −0.0515916 | −0.0257958 | − | 0.999667i | \(-0.508212\pi\) | ||||
−0.0257958 | + | 0.999667i | \(0.508212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2367.47 | −0.657178 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −74.2878 | −0.0203608 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −643.218 | −0.174085 | −0.0870425 | − | 0.996205i | \(-0.527742\pi\) | ||||
−0.0870425 | + | 0.996205i | \(0.527742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5755.61 | −1.53839 | −0.769194 | − | 0.639015i | \(-0.779342\pi\) | ||||
−0.769194 | + | 0.639015i | \(0.779342\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 245.000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2047.97 | 0.527567 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1220.17 | −0.310543 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5132.27 | 1.29062 | 0.645311 | − | 0.763920i | \(-0.276728\pi\) | ||||
0.645311 | + | 0.763920i | \(0.276728\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −618.755 | −0.153758 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1837.47 | −0.451243 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5041.74 | 1.22372 | 0.611859 | − | 0.790967i | \(-0.290422\pi\) | ||||
0.611859 | + | 0.790967i | \(0.290422\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 679.844 | 0.163102 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 859.448 | 0.203826 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7577.00 | −1.77649 | −0.888246 | − | 0.459367i | \(-0.848076\pi\) | ||||
−0.888246 | + | 0.459367i | \(0.848076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −918.385 | −0.212890 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −785.253 | −0.179988 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1023.10 | 0.231893 | 0.115947 | − | 0.993255i | \(-0.463010\pi\) | ||||
0.115947 | + | 0.993255i | \(0.463010\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2251.98 | 0.504790 | 0.252395 | − | 0.967624i | \(-0.418782\pi\) | ||||
0.252395 | + | 0.967624i | \(0.418782\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 400.307 | 0.0887462 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 73.4436 | 0.0161048 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8630.72 | −1.87209 | −0.936047 | − | 0.351875i | \(-0.885544\pi\) | ||||
−0.936047 | + | 0.351875i | \(0.885544\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 848.767 | 0.182130 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7521.62 | −1.59680 | −0.798402 | − | 0.602124i | \(-0.794321\pi\) | ||||
−0.798402 | + | 0.602124i | \(0.794321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.8169 | −0.00311226 | −0.00155613 | − | 0.999999i | \(-0.500495\pi\) | ||||
−0.00155613 | + | 0.999999i | \(0.500495\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1611.54 | 0.334945 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3437.79 | −0.707060 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10092.8 | 2.05430 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3014.32 | 0.607226 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6913.39 | 1.37844 | 0.689222 | − | 0.724550i | \(-0.257952\pi\) | ||||
0.689222 | + | 0.724550i | \(0.257952\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3803.07 | 0.750588 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −79.3190 | −0.0154968 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4014.94 | 0.776555 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 301.027 | 0.0576442 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 386.615 | 0.0733018 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −993.735 | −0.186561 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7644.12 | 1.42108 | 0.710542 | − | 0.703655i | \(-0.248450\pi\) | ||||
0.710542 | + | 0.703655i | \(0.248450\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2418.02 | 0.445167 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7593.99 | −1.38462 | −0.692308 | − | 0.721602i | \(-0.743406\pi\) | ||||
−0.692308 | + | 0.721602i | \(0.743406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9127.84 | −1.64836 | −0.824179 | − | 0.566329i | \(-0.808363\pi\) | ||||
−0.824179 | + | 0.566329i | \(0.808363\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 315.000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4929.81 | −0.873456 | −0.436728 | − | 0.899593i | \(-0.643863\pi\) | ||||
−0.436728 | + | 0.899593i | \(0.643863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 280.537 | 0.0492385 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2309.14 | −0.401506 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13160.7 | −2.26712 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −476.556 | −0.0813372 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2342.57 | 0.396160 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3314.46 | −0.555417 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1221.67 | −0.202867 | −0.101433 | − | 0.994842i | \(-0.532343\pi\) | ||||
−0.101433 | + | 0.994842i | \(0.532343\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 874.086 | 0.143843 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1549.96 | 0.252786 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8744.83 | −1.41354 | −0.706768 | − | 0.707446i | \(-0.749847\pi\) | ||||
−0.706768 | + | 0.707446i | \(0.749847\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3346.94 | 0.536226 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 277.051 | 0.0439975 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3159.34 | 0.493023 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4589.56 | −0.710031 | −0.355015 | − | 0.934860i | \(-0.615524\pi\) | ||||
−0.355015 | + | 0.934860i | \(0.615524\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3989.89 | −0.611960 | −0.305980 | − | 0.952038i | \(-0.598984\pi\) | ||||
−0.305980 | + | 0.952038i | \(0.598984\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 514.681 | 0.0782668 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2416.35 | 0.364333 | 0.182166 | − | 0.983268i | \(-0.441689\pi\) | ||||
0.182166 | + | 0.983268i | \(0.441689\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3328.46 | −0.497624 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2572.46 | −0.381370 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2756.24 | 0.405206 | 0.202603 | − | 0.979261i | \(-0.435060\pi\) | ||||
0.202603 | + | 0.979261i | \(0.435060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4683.45 | 0.682818 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3967.11 | 0.573607 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3106.44 | 0.445475 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11112.8 | −1.58061 | −0.790307 | − | 0.612711i | \(-0.790079\pi\) | ||||
−0.790307 | + | 0.612711i | \(0.790079\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4420.02 | −0.623569 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1285.74 | −0.179925 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6091.09 | 0.845535 | 0.422768 | − | 0.906238i | \(-0.361059\pi\) | ||||
0.422768 | + | 0.906238i | \(0.361059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1820.33 | −0.248679 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3984.29 | −0.539998 | −0.269999 | − | 0.962861i | \(-0.587023\pi\) | ||||
−0.269999 | + | 0.962861i | \(0.587023\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5627.95 | −0.756768 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −318.475 | −0.0424890 | −0.0212445 | − | 0.999774i | \(-0.506763\pi\) | ||||
−0.0212445 | + | 0.999774i | \(0.506763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 102.821 | 0.0136110 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 387.035 | 0.0508374 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3885.46 | 0.506429 | 0.253214 | − | 0.967410i | \(-0.418512\pi\) | ||||
0.253214 | + | 0.967410i | \(0.418512\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25800.9 | −3.33710 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1092.61 | 0.140241 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 123.813 | 0.0157714 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4806.04 | 0.607578 | 0.303789 | − | 0.952739i | \(-0.401748\pi\) | ||||
0.303789 | + | 0.952739i | \(0.401748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2256.15 | 0.283080 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3618.59 | 0.450633 | 0.225316 | − | 0.974286i | \(-0.427658\pi\) | ||||
0.225316 | + | 0.974286i | \(0.427658\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1797.71 | −0.222209 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 285.315 | 0.0347483 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2109.05 | −0.254978 | −0.127489 | − | 0.991840i | \(-0.540692\pi\) | ||||
−0.127489 | + | 0.991840i | \(0.540692\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4809.40 | −0.577202 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5324.30 | 0.634363 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2033.62 | 0.240546 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7293.37 | 0.856494 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6905.91 | 0.805193 | 0.402597 | − | 0.915377i | \(-0.368108\pi\) | ||||
0.402597 | + | 0.915377i | \(0.368108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9647.54 | −1.11685 | −0.558423 | − | 0.829556i | \(-0.688593\pi\) | ||||
−0.558423 | + | 0.829556i | \(0.688593\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4261.45 | −0.489831 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3062.45 | 0.349531 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1391.23 | −0.157673 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 168.000 | 0.0189070 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13002.7 | 1.45318 | 0.726589 | − | 0.687073i | \(-0.241105\pi\) | ||||
0.726589 | + | 0.687073i | \(0.241105\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7356.07 | 0.816420 | 0.408210 | − | 0.912888i | \(-0.366153\pi\) | ||||
0.408210 | + | 0.912888i | \(0.366153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1432.41 | −0.157883 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22628.4 | 2.47703 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6909.21 | −0.751159 | −0.375579 | − | 0.926790i | \(-0.622556\pi\) | ||||
−0.375579 | + | 0.926790i | \(0.622556\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14812.6 | 1.58864 | 0.794318 | − | 0.607502i | \(-0.207828\pi\) | ||||
0.794318 | + | 0.607502i | \(0.207828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1308.75 | 0.139418 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7024.72 | −0.743306 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10654.5 | −1.11986 | −0.559932 | − | 0.828538i | \(-0.689173\pi\) | ||||
−0.559932 | + | 0.828538i | \(0.689173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1442.76 | −0.150636 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6312.21 | −0.654688 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −667.179 | −0.0687425 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5855.16 | −0.599328 | −0.299664 | − | 0.954045i | \(-0.596875\pi\) | ||||
−0.299664 | + | 0.954045i | \(0.596875\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3307.45 | −0.336336 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3204.74 | 0.323774 | 0.161887 | − | 0.986809i | \(-0.448242\pi\) | ||||
0.161887 | + | 0.986809i | \(0.448242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −371.658 | −0.0373054 | −0.0186527 | − | 0.999826i | \(-0.505938\pi\) | ||||
−0.0186527 | + | 0.999826i | \(0.505938\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1414.61 | −0.141077 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 19752.3 | 1.95723 | 0.978614 | − | 0.205703i | \(-0.0659482\pi\) | ||||
0.978614 | + | 0.205703i | \(0.0659482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2169.95 | 0.213643 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1780.40 | 0.174175 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 126.334 | 0.0122809 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2685.90 | −0.259447 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1653.09 | −0.158679 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20762.0 | 1.98046 | 0.990232 | − | 0.139433i | \(-0.0445279\pi\) | ||||
0.990232 | + | 0.139433i | \(0.0445279\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1851.34 | −0.175496 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4423.07 | 0.416681 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5023.87 | −0.470355 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17647.6 | −1.64207 | −0.821035 | − | 0.570878i | \(-0.806603\pi\) | ||||
−0.821035 | + | 0.570878i | \(0.806603\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6536.12 | 0.604445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5637.46 | 0.518157 | 0.259078 | − | 0.965856i | \(-0.416581\pi\) | ||||
0.259078 | + | 0.965856i | \(0.416581\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11697.9 | 1.06865 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 132.198 | 0.0120038 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4659.85 | −0.420569 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17474.1 | 1.56764 | 0.783818 | − | 0.620991i | \(-0.213270\pi\) | ||||
0.783818 | + | 0.620991i | \(0.213270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2398.51 | 0.213887 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7444.81 | −0.659936 | −0.329968 | − | 0.943992i | \(-0.607038\pi\) | ||||
−0.329968 | + | 0.943992i | \(0.607038\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −644.358 | −0.0567793 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5500.89 | 0.481860 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3384.48 | −0.294724 | −0.147362 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147362 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4349.02 | 0.376495 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2900.77 | 0.249653 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4030.04 | −0.344825 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1391.00 | −0.118329 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4333.07 | 0.366476 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2973.12 | 0.250009 | 0.125005 | − | 0.992156i | \(-0.460105\pi\) | ||||
0.125005 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2689.02 | −0.224823 | −0.112412 | − | 0.993662i | \(-0.535858\pi\) | ||||
−0.112412 | + | 0.993662i | \(0.535858\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11552.5 | 0.954903 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32194.9 | 2.64608 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6845.53 | 0.559455 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9361.72 | 0.760790 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3848.56 | 0.311005 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10030.5 | 0.806046 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 143.949 | 0.0115034 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14429.5 | −1.14671 | −0.573356 | − | 0.819306i | \(-0.694359\pi\) | ||||
−0.573356 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6755.44 | −0.533893 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3904.28 | −0.306864 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13811.2 | −1.07957 | −0.539784 | − | 0.841804i | \(-0.681494\pi\) | ||||
−0.539784 | + | 0.841804i | \(0.681494\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1788.72 | −0.139054 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10259.5 | −0.793229 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 173.338 | 0.0133293 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1456.81 | −0.111420 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6033.26 | −0.458954 | −0.229477 | − | 0.973314i | \(-0.573702\pi\) | ||||
−0.229477 | + | 0.973314i | \(0.573702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −819.751 | −0.0620246 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1079.60 | −0.0812493 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6958.47 | 0.520896 | 0.260448 | − | 0.965488i | \(-0.416130\pi\) | ||||
0.260448 | + | 0.965488i | \(0.416130\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5578.23 | −0.415359 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13396.4 | −0.987009 | −0.493505 | − | 0.869743i | \(-0.664284\pi\) | ||||
−0.493505 | + | 0.869743i | \(0.664284\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8055.84 | 0.590414 | 0.295207 | − | 0.955433i | \(-0.404611\pi\) | ||||
0.295207 | + | 0.955433i | \(0.404611\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3005.78 | −0.219142 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5265.56 | −0.381894 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21456.9 | −1.54812 | −0.774059 | − | 0.633114i | \(-0.781777\pi\) | ||||
−0.774059 | + | 0.633114i | \(0.781777\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12164.9 | 0.873153 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2847.07 | 0.203298 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −539.596 | −0.0383324 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −857.802 | −0.0606252 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20156.3 | −1.41728 | −0.708638 | − | 0.705572i | \(-0.750690\pi\) | ||||
−0.708638 | + | 0.705572i | \(0.750690\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10132.0 | −0.708797 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15420.7 | 1.07330 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 599.307 | 0.0415018 | 0.0207509 | − | 0.999785i | \(-0.493394\pi\) | ||||
0.0207509 | + | 0.999785i | \(0.493394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4287.43 | 0.295408 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1756.89 | 0.120444 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5493.05 | 0.374691 | 0.187346 | − | 0.982294i | \(-0.440012\pi\) | ||||
0.187346 | + | 0.982294i | \(0.440012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24292.8 | 1.64879 | 0.824396 | − | 0.566014i | \(-0.191515\pi\) | ||||
0.824396 | + | 0.566014i | \(0.191515\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2789.93 | 0.188416 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6611.85 | −0.444314 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3029.50 | −0.202576 | −0.101288 | − | 0.994857i | \(-0.532296\pi\) | ||||
−0.101288 | + | 0.994857i | \(0.532296\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2005.38 | −0.133435 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9025.87 | 0.597623 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19339.6 | −1.27426 | −0.637129 | − | 0.770757i | \(-0.719878\pi\) | ||||
−0.637129 | + | 0.770757i | \(0.719878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7366.69 | 0.483014 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5743.91 | −0.374783 | −0.187391 | − | 0.982285i | \(-0.560003\pi\) | ||||
−0.187391 | + | 0.982285i | \(0.560003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8243.35 | 0.535264 | 0.267632 | − | 0.963521i | \(-0.413759\pi\) | ||||
0.267632 | + | 0.963521i | \(0.413759\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5686.81 | 0.367478 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1832.26 | 0.117830 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 946.856 | 0.0603091 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11897.1 | 0.754162 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4376.56 | 0.276114 | 0.138057 | − | 0.990424i | \(-0.455914\pi\) | ||||
0.138057 | + | 0.990424i | \(0.455914\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3165.48 | −0.198762 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9379.92 | 0.586190 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −934.051 | −0.0580980 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5991.23 | −0.370907 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11836.6 | 0.729357 | 0.364678 | − | 0.931133i | \(-0.381179\pi\) | ||||
0.364678 | + | 0.931133i | \(0.381179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1448.21 | −0.0888209 | −0.0444104 | − | 0.999013i | \(-0.514141\pi\) | ||||
−0.0444104 | + | 0.999013i | \(0.514141\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −645.058 | −0.0393785 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8732.95 | 0.530646 | 0.265323 | − | 0.964160i | \(-0.414521\pi\) | ||||
0.265323 | + | 0.964160i | \(0.414521\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2234.49 | 0.135149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1980.46 | −0.119232 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21978.4 | −1.31712 | −0.658562 | − | 0.752527i | \(-0.728835\pi\) | ||||
−0.658562 | + | 0.752527i | \(0.728835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1821.01 | −0.108630 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5591.59 | 0.332038 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27761.7 | 1.64103 | 0.820516 | − | 0.571623i | \(-0.193686\pi\) | ||||
0.820516 | + | 0.571623i | \(0.193686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8573.72 | −0.504507 | −0.252254 | − | 0.967661i | \(-0.581172\pi\) | ||||
−0.252254 | + | 0.967661i | \(0.581172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7005.27 | 0.410350 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3760.25 | −0.219273 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20113.2 | −1.16760 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14027.6 | 0.810668 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −583.868 | −0.0335916 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27159.2 | 1.55559 | 0.777795 | − | 0.628518i | \(-0.216338\pi\) | ||||
0.777795 | + | 0.628518i | \(0.216338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1392.30 | −0.0790404 | −0.0395202 | − | 0.999219i | \(-0.512583\pi\) | ||||
−0.0395202 | + | 0.999219i | \(0.512583\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7033.42 | −0.397523 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16329.3 | 0.918857 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8675.09 | 0.486007 | 0.243004 | − | 0.970025i | \(-0.421867\pi\) | ||||
0.243004 | + | 0.970025i | \(0.421867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8015.66 | 0.447099 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1608.91 | 0.0893504 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3501.30 | 0.193598 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21426.0 | 1.17957 | 0.589785 | − | 0.807561i | \(-0.299213\pi\) | ||||
0.589785 | + | 0.807561i | \(0.299213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 185.078 | 0.0101451 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12155.6 | −0.663438 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −60160.4 | −3.26935 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 550.470 | 0.0297864 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24840.5 | 1.33839 | 0.669197 | − | 0.743085i | \(-0.266638\pi\) | ||||
0.669197 | + | 0.743085i | \(0.266638\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10434.2 | −0.559793 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7102.41 | 0.379422 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −902.101 | −0.0479873 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12525.0 | 0.663450 | 0.331725 | − | 0.943376i | \(-0.392369\pi\) | ||||
0.331725 | + | 0.943376i | \(0.392369\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 222.863 | 0.0117553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19863.3 | −1.04332 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −280.000 | −0.0146453 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1929.65 | 0.100508 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28085.0 | −1.45674 | −0.728369 | − | 0.685185i | \(-0.759721\pi\) | ||||
−0.728369 | + | 0.685185i | \(0.759721\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5642.05 | −0.291430 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17266.8 | 0.888189 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2387.35 | 0.122295 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14326.2 | 0.730851 | 0.365426 | − | 0.930841i | \(-0.380923\pi\) | ||||
0.365426 | + | 0.930841i | \(0.380923\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5267.89 | 0.266539 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6727.85 | 0.339016 | 0.169508 | − | 0.985529i | \(-0.445782\pi\) | ||||
0.169508 | + | 0.985529i | \(0.445782\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −735.000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 910.677 | 0.0455159 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3418.51 | 0.170165 | 0.0850826 | − | 0.996374i | \(-0.472885\pi\) | ||||
0.0850826 | + | 0.996374i | \(0.472885\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6143.91 | −0.304591 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8095.50 | −0.399724 | −0.199862 | − | 0.979824i | \(-0.564049\pi\) | ||||
−0.199862 | + | 0.979824i | \(0.564049\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11707.9 | 0.575762 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3660.51 | 0.179292 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5387.99 | 0.262847 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13446.8 | −0.653371 | −0.326686 | − | 0.945133i | \(-0.605932\pi\) | ||||
−0.326686 | + | 0.945133i | \(0.605932\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15396.8 | −0.745141 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10520.4 | 0.507119 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2593.24 | −0.124508 | −0.0622541 | − | 0.998060i | \(-0.519829\pi\) | ||||
−0.0622541 | + | 0.998060i | \(0.519829\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1856.26 | 0.0887722 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27079.4 | 1.28992 | 0.644959 | − | 0.764217i | \(-0.276875\pi\) | ||||
0.644959 | + | 0.764217i | \(0.276875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5465.99 | −0.259348 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5512.41 | 0.260525 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14499.0 | −0.682568 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2138.72 | 0.100292 | 0.0501458 | − | 0.998742i | \(-0.484031\pi\) | ||||
0.0501458 | + | 0.998742i | \(0.484031\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15125.2 | −0.706513 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25864.0 | 1.20345 | 0.601724 | − | 0.798704i | \(-0.294481\pi\) | ||||
0.601724 | + | 0.798704i | \(0.294481\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2357.69 | 0.109278 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2039.53 | −0.0941671 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 52763.1 | 2.42675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1955.63 | −0.0896006 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2578.34 | −0.117679 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2967.33 | −0.134916 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32371.3 | 1.46621 | 0.733107 | − | 0.680113i | \(-0.238069\pi\) | ||||
0.733107 | + | 0.680113i | \(0.238069\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22731.0 | 1.02566 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7809.52 | −0.351043 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3788.57 | 0.169654 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2755.16 | 0.122912 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2024.33 | 0.0899691 | 0.0449845 | − | 0.998988i | \(-0.485676\pi\) | ||||
0.0449845 | + | 0.998988i | \(0.485676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −58002.1 | −2.56817 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2355.76 | 0.103916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1825.18 | 0.0802109 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7371.79 | −0.322760 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3069.29 | −0.133884 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12391.7 | 0.538526 | 0.269263 | − | 0.963067i | \(-0.413220\pi\) | ||||
0.269263 | + | 0.963067i | \(0.413220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14654.5 | −0.634511 | −0.317256 | − | 0.948340i | \(-0.602761\pi\) | ||||
−0.317256 | + | 0.948340i | \(0.602761\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6755.94 | −0.291441 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10893.5 | −0.468201 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4620.16 | −0.197844 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1200.92 | −0.0512376 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23887.9 | 1.01546 | 0.507731 | − | 0.861516i | \(-0.330485\pi\) | ||||
0.507731 | + | 0.861516i | \(0.330485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4008.41 | 0.169774 | 0.0848871 | − | 0.996391i | \(-0.472947\pi\) | ||||
0.0848871 | + | 0.996391i | \(0.472947\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −220.331 | −0.00929810 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 45110.4 | 1.89679 | 0.948394 | − | 0.317096i | \(-0.102708\pi\) | ||||
0.948394 | + | 0.317096i | \(0.102708\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16165.4 | 0.677260 | 0.338630 | − | 0.940920i | \(-0.390036\pi\) | ||||
0.338630 | + | 0.940920i | \(0.390036\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25892.2 | 1.08085 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6002.41 | 0.249665 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3997.51 | −0.165676 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2546.30 | −0.105153 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25244.4 | 1.03878 | 0.519388 | − | 0.854538i | \(-0.326160\pi\) | ||||
0.519388 | + | 0.854538i | \(0.326160\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15269.9 | −0.626096 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22564.9 | 0.921916 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9168.15 | −0.373247 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9256.59 | −0.375514 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 44.4506 | 0.00179687 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20455.8 | −0.823990 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30168.1 | −1.21094 | −0.605472 | − | 0.795867i | \(-0.707016\pi\) | ||||
−0.605472 | + | 0.795867i | \(0.707016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4834.61 | −0.193380 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13393.6 | −0.533857 | −0.266929 | − | 0.963716i | \(-0.586009\pi\) | ||||
−0.266929 | + | 0.963716i | \(0.586009\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19060.4 | −0.757081 | −0.378541 | − | 0.925585i | \(-0.623574\pi\) | ||||
−0.378541 | + | 0.925585i | \(0.623574\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10313.4 | 0.408222 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9466.86 | 0.373413 | 0.186707 | − | 0.982416i | \(-0.440219\pi\) | ||||
0.186707 | + | 0.982416i | \(0.440219\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7221.79 | −0.283871 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30278.3 | −1.18605 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 72.7461 | 0.00283975 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5909.15 | −0.229878 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9042.97 | −0.350582 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 875.000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37740.6 | 1.45315 | 0.726573 | − | 0.687090i | \(-0.241112\pi\) | ||||
0.726573 | + | 0.687090i | \(0.241112\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20740.2 | −0.795845 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25991.5 | 0.993957 | 0.496979 | − | 0.867763i | \(-0.334443\pi\) | ||||
0.496979 | + | 0.867763i | \(0.334443\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39420.3 | −1.50238 | −0.751189 | − | 0.660087i | \(-0.770519\pi\) | ||||
−0.751189 | + | 0.660087i | \(0.770519\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11409.2 | −0.433352 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46005.2 | −1.74149 | −0.870745 | − | 0.491735i | \(-0.836363\pi\) | ||||
−0.870745 | + | 0.491735i | \(0.836363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13131.9 | 0.495421 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 237.957 | 0.00894710 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 50870.2 | 1.90628 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16717.5 | −0.624361 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12044.8 | −0.448345 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9005.81 | 0.334105 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22500.1 | −0.831950 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −903.081 | −0.0332809 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11259.1 | 0.413551 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2838.97 | 0.103932 | 0.0519661 | − | 0.998649i | \(-0.483451\pi\) | ||||
0.0519661 | + | 0.998649i | \(0.483451\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1159.84 | −0.0423208 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39890.9 | −1.45076 | −0.725382 | − | 0.688347i | \(-0.758337\pi\) | ||||
−0.725382 | + | 0.688347i | \(0.758337\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1194.85 | 0.0433119 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2981.21 | 0.107711 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2549.42 | −0.0918094 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 646.475 | 0.0232048 | 0.0116024 | − | 0.999933i | \(-0.496307\pi\) | ||||
0.0116024 | + | 0.999933i | \(0.496307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22932.4 | −0.820463 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12689.6 | 0.452528 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2428.02 | 0.0863056 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7254.07 | −0.257017 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51188.2 | 1.80778 | 0.903892 | − | 0.427760i | \(-0.140697\pi\) | ||||
0.903892 | + | 0.427760i | \(0.140697\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5264.35 | −0.185319 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22782.0 | 0.799409 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1799.34 | 0.0629355 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29786.1 | 1.03849 | 0.519247 | − | 0.854624i | \(-0.326212\pi\) | ||||
0.519247 | + | 0.854624i | \(0.326212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27383.5 | 0.951680 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44817.4 | −1.55261 | −0.776304 | − | 0.630358i | \(-0.782908\pi\) | ||||
−0.776304 | + | 0.630358i | \(0.782908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 103439. | 3.57206 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −945.000 | −0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54697.1 | −1.87689 | −0.938446 | − | 0.345425i | \(-0.887735\pi\) | ||||
−0.938446 | + | 0.345425i | \(0.887735\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11843.2 | −0.405105 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14789.4 | 0.504290 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7577.51 | −0.257565 | −0.128783 | − | 0.991673i | \(-0.541107\pi\) | ||||
−0.128783 | + | 0.991673i | \(0.541107\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5009.63 | 0.169746 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −841.612 | −0.0284278 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11221.9 | 0.377868 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20897.1 | −0.701457 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6927.41 | 0.231810 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20274.8 | −0.676342 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50779.0 | −1.68867 | −0.844334 | − | 0.535817i | \(-0.820004\pi\) | ||||
−0.844334 | + | 0.535817i | \(0.820004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 39482.0 | 1.30892 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15313.2 | 0.506102 | 0.253051 | − | 0.967453i | \(-0.418566\pi\) | ||||
0.253051 | + | 0.967453i | \(0.418566\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17017.9 | −0.560707 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1429.67 | 0.0469601 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 46620.4 | 1.52663 | 0.763316 | − | 0.646025i | \(-0.223570\pi\) | ||||
0.763316 | + | 0.646025i | \(0.223570\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 768.957 | 0.0251031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7027.70 | −0.228723 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2824.37 | 0.0916414 | 0.0458207 | − | 0.998950i | \(-0.485410\pi\) | ||||
0.0458207 | + | 0.998950i | \(0.485410\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25701.1 | −0.831377 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9943.38 | 0.320670 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9057.59 | −0.291218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16951.4 | −0.543370 | −0.271685 | − | 0.962386i | \(-0.587581\pi\) | ||||
−0.271685 | + | 0.962386i | \(0.587581\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3665.00 | 0.117125 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2928.15 | −0.0932952 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23847.8 | 0.757540 | 0.378770 | − | 0.925491i | \(-0.376347\pi\) | ||||
0.378770 | + | 0.925491i | \(0.376347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2622.26 | −0.0830476 |
(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 | 1680.4.a.bg.1.1 | 2 | ||
4.3 | odd | 2 | 105.4.a.f.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 315.4.a.i.1.2 | 2 | |||
20.3 | even | 4 | 525.4.d.h.274.3 | 4 | |||
20.7 | even | 4 | 525.4.d.h.274.2 | 4 | |||
20.19 | odd | 2 | 525.4.a.k.1.2 | 2 | |||
28.27 | even | 2 | 735.4.a.p.1.1 | 2 | |||
60.59 | even | 2 | 1575.4.a.w.1.1 | 2 | |||
84.83 | odd | 2 | 2205.4.a.z.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.f.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
315.4.a.i.1.2 | 2 | 12.11 | even | 2 | |||
525.4.a.k.1.2 | 2 | 20.19 | odd | 2 | |||
525.4.d.h.274.2 | 4 | 20.7 | even | 4 | |||
525.4.d.h.274.3 | 4 | 20.3 | even | 4 | |||
735.4.a.p.1.1 | 2 | 28.27 | even | 2 | |||
1575.4.a.w.1.1 | 2 | 60.59 | even | 2 | |||
1680.4.a.bg.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2205.4.a.z.1.2 | 2 | 84.83 | odd | 2 |