Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.85932\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 1.85932 | 1.07348 | 0.536740 | − | 0.843748i | \(-0.319656\pi\) | ||||
0.536740 | + | 0.843748i | \(0.319656\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.13919 | 0.509460 | 0.254730 | − | 0.967012i | \(-0.418013\pi\) | ||||
0.254730 | + | 0.967012i | \(0.418013\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.457073 | 0.152358 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.11812 | 0.546895 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.43965 | −0.591701 | −0.295850 | − | 0.955234i | \(-0.595603\pi\) | ||||
−0.295850 | + | 0.955234i | \(0.595603\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.36447 | −1.00128 | −0.500639 | − | 0.865656i | \(-0.666902\pi\) | ||||
−0.500639 | + | 0.865656i | \(0.666902\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.85932 | 0.405737 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.06162 | 0.846907 | 0.423454 | − | 0.905918i | \(-0.360818\pi\) | ||||
0.423454 | + | 0.905918i | \(0.360818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.70225 | −0.740450 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.72812 | −0.909927 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.412473 | −0.0765943 | −0.0382972 | − | 0.999266i | \(-0.512193\pi\) | ||||
−0.0382972 | + | 0.999266i | \(0.512193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.12679 | −1.45961 | −0.729807 | − | 0.683653i | \(-0.760390\pi\) | ||||
−0.729807 | + | 0.683653i | \(0.760390\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.85932 | −0.323666 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.13919 | 0.192558 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.51813 | −1.23597 | −0.617986 | − | 0.786189i | \(-0.712051\pi\) | ||||
−0.617986 | + | 0.786189i | \(0.712051\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.85932 | −0.297730 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.210128 | −0.0328165 | −0.0164083 | − | 0.999865i | \(-0.505223\pi\) | ||||
−0.0164083 | + | 0.999865i | \(0.505223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.57641 | 1.30789 | 0.653945 | − | 0.756542i | \(-0.273113\pi\) | ||||
0.653945 | + | 0.756542i | \(0.273113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.520692 | 0.0776201 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.98496 | −1.31059 | −0.655296 | − | 0.755372i | \(-0.727456\pi\) | ||||
−0.655296 | + | 0.755372i | \(0.727456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.53608 | −0.635179 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.77822 | 1.20578 | 0.602891 | − | 0.797824i | \(-0.294016\pi\) | ||||
0.602891 | + | 0.797824i | \(0.294016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.13919 | −0.153608 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.11495 | −1.07485 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.23049 | −0.290385 | −0.145192 | − | 0.989403i | \(-0.546380\pi\) | ||||
−0.145192 | + | 0.989403i | \(0.546380\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.23803 | −0.798698 | −0.399349 | − | 0.916799i | \(-0.630764\pi\) | ||||
−0.399349 | + | 0.916799i | \(0.630764\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.457073 | 0.0575857 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.13919 | −0.141299 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2185 | 1.37056 | 0.685281 | − | 0.728279i | \(-0.259679\pi\) | ||||
0.685281 | + | 0.728279i | \(0.259679\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.55186 | 0.909137 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.84719 | −0.931290 | −0.465645 | − | 0.884972i | \(-0.654178\pi\) | ||||
−0.465645 | + | 0.884972i | \(0.654178\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.8894 | −1.85971 | −0.929857 | − | 0.367921i | \(-0.880070\pi\) | ||||
−0.929857 | + | 0.367921i | \(0.880070\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.88367 | −0.794858 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.38936 | −0.606351 | −0.303175 | − | 0.952935i | \(-0.598047\pi\) | ||||
−0.303175 | + | 0.952935i | \(0.598047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.1623 | −1.12914 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.74479 | −0.630572 | −0.315286 | − | 0.948997i | \(-0.602100\pi\) | ||||
−0.315286 | + | 0.948997i | \(0.602100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.77921 | −0.301448 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.766920 | −0.0822224 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.577855 | 0.0612525 | 0.0306262 | − | 0.999531i | \(-0.490250\pi\) | ||||
0.0306262 | + | 0.999531i | \(0.490250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.1103 | −1.56687 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.97195 | −0.510111 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.41830 | −0.245541 | −0.122770 | − | 0.992435i | \(-0.539178\pi\) | ||||
−0.122770 | + | 0.992435i | \(0.539178\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.457073 | −0.0459375 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.57116 | 0.355344 | 0.177672 | − | 0.984090i | \(-0.443143\pi\) | ||||
0.177672 | + | 0.984090i | \(0.443143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8044 | −1.06459 | −0.532295 | − | 0.846559i | \(-0.678670\pi\) | ||||
−0.532295 | + | 0.846559i | \(0.678670\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.11812 | 0.206707 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.8099 | 1.33505 | 0.667526 | − | 0.744587i | \(-0.267353\pi\) | ||||
0.667526 | + | 0.744587i | \(0.267353\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.49058 | −0.525903 | −0.262951 | − | 0.964809i | \(-0.584696\pi\) | ||||
−0.262951 | + | 0.964809i | \(0.584696\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.9786 | −1.32679 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.64277 | 0.813043 | 0.406522 | − | 0.913641i | \(-0.366742\pi\) | ||||
0.406522 | + | 0.913641i | \(0.366742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.62695 | 0.431466 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.457073 | −0.0422564 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.43965 | −0.223642 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.390696 | −0.0352279 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.91350 | −0.886690 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.6357 | 1.65365 | 0.826824 | − | 0.562460i | \(-0.190145\pi\) | ||||
0.826824 | + | 0.562460i | \(0.190145\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.9463 | 1.40399 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.760163 | −0.0664157 | −0.0332079 | − | 0.999448i | \(-0.510572\pi\) | ||||
−0.0332079 | + | 0.999448i | \(0.510572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.36447 | −0.378447 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.38621 | −0.463572 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1918 | 1.29792 | 0.648962 | − | 0.760821i | \(-0.275203\pi\) | ||||
0.648962 | + | 0.760821i | \(0.275203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.1907 | −1.20364 | −0.601820 | − | 0.798632i | \(-0.705558\pi\) | ||||
−0.601820 | + | 0.798632i | \(0.705558\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.7059 | −1.40689 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.469884 | −0.0390218 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.85932 | 0.153354 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.84598 | −0.560845 | −0.280422 | − | 0.959877i | \(-0.590475\pi\) | ||||
−0.280422 | + | 0.959877i | \(0.590475\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.713259 | 0.0580442 | 0.0290221 | − | 0.999579i | \(-0.490761\pi\) | ||||
0.0290221 | + | 0.999579i | \(0.490761\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.11509 | −0.0901501 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.25794 | −0.743616 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6338 | 0.848673 | 0.424337 | − | 0.905505i | \(-0.360507\pi\) | ||||
0.424337 | + | 0.905505i | \(0.360507\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.3215 | 1.29438 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.06162 | 0.320101 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2140 | 0.878350 | 0.439175 | − | 0.898401i | \(-0.355271\pi\) | ||||
0.439175 | + | 0.898401i | \(0.355271\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.11812 | −0.164895 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.40870 | 0.263773 | 0.131887 | − | 0.991265i | \(-0.457896\pi\) | ||||
0.131887 | + | 0.991265i | \(0.457896\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.99488 | −0.152552 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50127 | −0.570311 | −0.285155 | − | 0.958481i | \(-0.592045\pi\) | ||||
−0.285155 | + | 0.958481i | \(0.592045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.70225 | −0.279864 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.14719 | −0.311722 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.0679 | −1.20097 | −0.600485 | − | 0.799636i | \(-0.705026\pi\) | ||||
−0.600485 | + | 0.799636i | \(0.705026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.1109 | −1.19751 | −0.598756 | − | 0.800931i | \(-0.704338\pi\) | ||||
−0.598756 | + | 0.800931i | \(0.704338\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.5985 | −0.857386 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.56456 | −0.629679 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.43965 | 0.178405 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.72812 | −0.343920 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.59700 | −0.260270 | −0.130135 | − | 0.991496i | \(-0.541541\pi\) | ||||
−0.130135 | + | 0.991496i | \(0.541541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.52564 | −0.325762 | −0.162881 | − | 0.986646i | \(-0.552079\pi\) | ||||
−0.162881 | + | 0.986646i | \(0.552079\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.11812 | −0.151681 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1491 | 1.07933 | 0.539666 | − | 0.841879i | \(-0.318551\pi\) | ||||
0.539666 | + | 0.841879i | \(0.318551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.59654 | −0.325840 | −0.162920 | − | 0.986639i | \(-0.552091\pi\) | ||||
−0.162920 | + | 0.986639i | \(0.552091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 20.8588 | 1.47127 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.412473 | −0.0289499 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.239376 | −0.0167187 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.85646 | 0.129033 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.36447 | 0.301897 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.54087 | −0.519135 | −0.259568 | − | 0.965725i | \(-0.583580\pi\) | ||||
−0.259568 | + | 0.965725i | \(0.583580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −14.5904 | −0.999720 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.77014 | 0.666318 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.12679 | −0.551682 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −29.5435 | −1.99636 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.43965 | 0.164108 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8067 | −1.79511 | −0.897555 | − | 0.440902i | \(-0.854659\pi\) | ||||
−0.897555 | + | 0.440902i | \(0.854659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.69220 | −0.112813 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.96930 | −0.130707 | −0.0653535 | − | 0.997862i | \(-0.520818\pi\) | ||||
−0.0653535 | + | 0.997862i | \(0.520818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.9526 | 1.38459 | 0.692294 | − | 0.721616i | \(-0.256600\pi\) | ||||
0.692294 | + | 0.721616i | \(0.256600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.85932 | −0.122334 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.7952 | −1.03478 | −0.517389 | − | 0.855750i | \(-0.673096\pi\) | ||||
−0.517389 | + | 0.855750i | \(0.673096\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.2356 | −0.667694 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.0206 | −0.650905 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4833 | 1.58369 | 0.791845 | − | 0.610722i | \(-0.209121\pi\) | ||||
0.791845 | + | 0.610722i | \(0.209121\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0133 | 0.709426 | 0.354713 | − | 0.934975i | \(-0.384579\pi\) | ||||
0.354713 | + | 0.934975i | \(0.384579\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.71063 | −0.302187 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.13919 | 0.0727801 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.36447 | 0.277704 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.6814 | −0.676906 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.01223 | 0.253250 | 0.126625 | − | 0.991951i | \(-0.459586\pi\) | ||||
0.126625 | + | 0.991951i | \(0.459586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.06162 | −0.255352 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.16745 | −0.323598 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.02186 | −0.188498 | −0.0942492 | − | 0.995549i | \(-0.530045\pi\) | ||||
−0.0942492 | + | 0.995549i | \(0.530045\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.51813 | −0.467154 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.188530 | −0.0116697 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.513650 | −0.0316730 | −0.0158365 | − | 0.999875i | \(-0.505041\pi\) | ||||
−0.0158365 | + | 0.999875i | \(0.505041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | 0.614298 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.07442 | 0.0657532 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −26.5185 | −1.61686 | −0.808429 | − | 0.588593i | \(-0.799682\pi\) | ||||
−0.808429 | + | 0.588593i | \(0.799682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.5252 | 1.91502 | 0.957509 | − | 0.288404i | \(-0.0931247\pi\) | ||||
0.957509 | + | 0.288404i | \(0.0931247\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.85932 | −0.112531 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.70225 | 0.223254 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.9907 | 1.68180 | 0.840899 | − | 0.541192i | \(-0.182027\pi\) | ||||
0.840899 | + | 0.541192i | \(0.182027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.71453 | −0.222383 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.3440 | 1.63120 | 0.815602 | − | 0.578613i | \(-0.196406\pi\) | ||||
0.815602 | + | 0.578613i | \(0.196406\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.18505 | 0.308219 | 0.154110 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154110 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.24445 | −0.547594 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.210128 | −0.0124035 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0481 | −0.649890 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.49639 | −0.263583 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.6760 | −1.67527 | −0.837636 | − | 0.546229i | \(-0.816063\pi\) | ||||
−0.837636 | + | 0.546229i | \(0.816063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.54094 | −0.147939 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.72812 | 0.274353 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.06162 | −0.234890 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.57641 | 0.494336 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.63994 | 0.381454 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.10629 | −0.406905 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.21096 | −0.0691130 | −0.0345565 | − | 0.999403i | \(-0.511002\pi\) | ||||
−0.0345565 | + | 0.999403i | \(0.511002\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.0889 | −1.14282 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.12676 | −0.177302 | −0.0886512 | − | 0.996063i | \(-0.528256\pi\) | ||||
−0.0886512 | + | 0.996063i | \(0.528256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1075 | −0.966972 | −0.483486 | − | 0.875352i | \(-0.660630\pi\) | ||||
−0.483486 | + | 0.875352i | \(0.660630\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.520692 | 0.0293377 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.7586 | 1.61524 | 0.807621 | − | 0.589702i | \(-0.200755\pi\) | ||||
0.807621 | + | 0.589702i | \(0.200755\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.412473 | 0.0230941 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.6770 | 1.43315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.6478 | 0.592457 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.70225 | 0.205364 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.2088 | −0.564545 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.98496 | −0.495357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.1599 | −1.71270 | −0.856352 | − | 0.516392i | \(-0.827275\pi\) | ||||
−0.856352 | + | 0.516392i | \(0.827275\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.43633 | −0.188310 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7800 | 0.698247 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.21637 | −0.175207 | −0.0876034 | − | 0.996155i | \(-0.527921\pi\) | ||||
−0.0876034 | + | 0.996155i | \(0.527921\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.0697 | 0.872785 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.12679 | 0.440090 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.60299 | 0.463169 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.25621 | 0.174802 | 0.0874012 | − | 0.996173i | \(-0.472144\pi\) | ||||
0.0874012 | + | 0.996173i | \(0.472144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.70551 | 0.251880 | 0.125940 | − | 0.992038i | \(-0.459805\pi\) | ||||
0.125940 | + | 0.992038i | \(0.459805\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.72812 | 0.252368 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.76977 | −0.307094 | −0.153547 | − | 0.988141i | \(-0.549070\pi\) | ||||
−0.153547 | + | 0.988141i | \(0.549070\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.93942 | −0.474455 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.53608 | −0.240075 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.48183 | −0.500432 | −0.250216 | − | 0.968190i | \(-0.580502\pi\) | ||||
−0.250216 | + | 0.968190i | \(0.580502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.0485854 | 0.00255712 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.85932 | 0.0975890 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.1010 | −0.947451 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0919 | 1.46638 | 0.733192 | − | 0.680022i | \(-0.238030\pi\) | ||||
0.733192 | + | 0.680022i | \(0.238030\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0960439 | −0.00499985 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.77822 | 0.455743 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.47251 | 0.335134 | 0.167567 | − | 0.985861i | \(-0.446409\pi\) | ||||
0.167567 | + | 0.985861i | \(0.446409\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.4324 | −0.951844 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.412473 | 0.0212434 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6820 | −1.16510 | −0.582549 | − | 0.812796i | \(-0.697945\pi\) | ||||
−0.582549 | + | 0.812796i | \(0.697945\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 34.6497 | 1.77516 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.3230 | −1.24285 | −0.621424 | − | 0.783475i | \(-0.713446\pi\) | ||||
−0.621424 | + | 0.783475i | \(0.713446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.13919 | −0.0580584 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.92004 | 0.199267 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.23244 | 0.468103 | 0.234052 | − | 0.972224i | \(-0.424802\pi\) | ||||
0.234052 | + | 0.972224i | \(0.424802\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.90892 | −0.501116 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.41339 | −0.0712959 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.13950 | −0.308912 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7358 | 0.538814 | 0.269407 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269407 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.11495 | −0.406255 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.44508 | −0.271914 | −0.135957 | − | 0.990715i | \(-0.543411\pi\) | ||||
−0.135957 | + | 0.990715i | \(0.543411\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.12679 | 0.404824 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.5768 | −0.575255 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.51813 | 0.372660 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.7840 | 1.22549 | 0.612744 | − | 0.790281i | \(-0.290066\pi\) | ||||
0.612744 | + | 0.790281i | \(0.290066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.2465 | 1.39329 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.23049 | −0.109755 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.54439 | −0.321252 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.3851 | −1.29208 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.58148 | 0.419233 | 0.209616 | − | 0.977784i | \(-0.432778\pi\) | ||||
0.209616 | + | 0.977784i | \(0.432778\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.89799 | 0.336187 | 0.168094 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168094 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.10678 | −0.199678 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.03218 | 0.438125 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.23803 | −0.301880 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.85932 | 0.0897688 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.8518 | −1.10073 | −0.550367 | − | 0.834923i | \(-0.685512\pi\) | ||||
−0.550367 | + | 0.834923i | \(0.685512\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.9326 | 1.15013 | 0.575063 | − | 0.818109i | \(-0.304977\pi\) | ||||
0.575063 | + | 0.818109i | \(0.304977\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.873666 | −0.0418891 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.7268 | −0.847989 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.28669 | −0.204593 | −0.102296 | − | 0.994754i | \(-0.532619\pi\) | ||||
−0.102296 | + | 0.994754i | \(0.532619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.457073 | 0.0217654 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.9434 | 0.757494 | 0.378747 | − | 0.925500i | \(-0.376355\pi\) | ||||
0.378747 | + | 0.925500i | \(0.376355\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.658285 | 0.0312057 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.7289 | −0.602055 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.69766 | −0.174504 | −0.0872518 | − | 0.996186i | \(-0.527808\pi\) | ||||
−0.0872518 | + | 0.996186i | \(0.527808\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.210128 | 0.00989456 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.32618 | 0.0623093 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.13919 | −0.0534060 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.2958 | −1.18329 | −0.591644 | − | 0.806200i | \(-0.701521\pi\) | ||||
−0.591644 | + | 0.806200i | \(0.701521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11.5349 | 0.538404 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.3046 | 1.64430 | 0.822149 | − | 0.569273i | \(-0.192775\pi\) | ||||
0.822149 | + | 0.569273i | \(0.192775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.9855 | 0.928806 | 0.464403 | − | 0.885624i | \(-0.346269\pi\) | ||||
0.464403 | + | 0.885624i | \(0.346269\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −17.2135 | −0.798256 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.8835 | 1.47539 | 0.737695 | − | 0.675134i | \(-0.235914\pi\) | ||||
0.737695 | + | 0.675134i | \(0.235914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.2185 | 0.518024 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.7717 | 0.911033 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.57641 | −0.394344 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.1584 | 0.741396 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.01228 | 0.183710 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.9578 | −1.64295 | −0.821477 | − | 0.570241i | \(-0.806850\pi\) | ||||
−0.821477 | + | 0.570241i | \(0.806850\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.51813 | 0.342797 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.55186 | 0.343622 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.75489 | −0.125093 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.1605 | −1.04950 | −0.524752 | − | 0.851255i | \(-0.675842\pi\) | ||||
−0.524752 | + | 0.851255i | \(0.675842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.8505 | 0.942891 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.3914 | −1.32642 | −0.663208 | − | 0.748435i | \(-0.730806\pi\) | ||||
−0.663208 | + | 0.748435i | \(0.730806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.00629 | 0.0453209 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.520692 | −0.0234034 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.84719 | −0.351994 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.1855 | −1.08269 | −0.541346 | − | 0.840800i | \(-0.682085\pi\) | ||||
−0.541346 | + | 0.840800i | \(0.682085\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.33787 | 0.283155 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.0053 | 1.15952 | 0.579760 | − | 0.814787i | \(-0.303146\pi\) | ||||
0.579760 | + | 0.814787i | \(0.303146\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.06823 | 0.181034 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.85932 | 0.0825753 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.3224 | −0.900773 | −0.450387 | − | 0.892834i | \(-0.648714\pi\) | ||||
−0.450387 | + | 0.892834i | \(0.648714\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.8894 | −0.702906 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.6357 | 0.911089 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3083 | −0.542367 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.98496 | 0.395158 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.9473 | −0.612217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.3536 | −1.46125 | −0.730625 | − | 0.682779i | \(-0.760771\pi\) | ||||
−0.730625 | + | 0.682779i | \(0.760771\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.3051 | −0.800428 | −0.400214 | − | 0.916422i | \(-0.631064\pi\) | ||||
−0.400214 | + | 0.916422i | \(0.631064\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.88367 | −0.300428 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.8265 | 0.863655 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50320 | −0.282748 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.01949 | −0.0442423 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.210128 | 0.00910167 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.7321 | 0.680156 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.8753 | −1.28922 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.53976 | −0.324160 | −0.162080 | − | 0.986778i | \(-0.551820\pi\) | ||||
−0.162080 | + | 0.986778i | \(0.551820\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −29.9553 | −1.28550 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.25481 | −0.267927 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.12726 | 0.304740 | 0.152370 | − | 0.988324i | \(-0.451310\pi\) | ||||
0.152370 | + | 0.988324i | \(0.451310\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.85123 | −0.121688 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.80023 | 0.0766922 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.38936 | −0.229179 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.9243 | −0.675947 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.7729 | 0.795433 | 0.397717 | − | 0.917508i | \(-0.369803\pi\) | ||||
0.397717 | + | 0.917508i | \(0.369803\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.57641 | −0.362743 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.53608 | 0.191514 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.8497 | −0.794420 | −0.397210 | − | 0.917728i | \(-0.630022\pi\) | ||||
−0.397210 | + | 0.917728i | \(0.630022\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.84574 | 0.414213 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.1623 | −0.426777 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.8921 | 0.540463 | 0.270232 | − | 0.962795i | \(-0.412900\pi\) | ||||
0.270232 | + | 0.962795i | \(0.412900\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.4783 | 1.65212 | 0.826058 | − | 0.563585i | \(-0.190578\pi\) | ||||
0.826058 | + | 0.563585i | \(0.190578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.68798 | −0.279394 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.0372 | −0.627093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.9135 | −0.495966 | −0.247983 | − | 0.968764i | \(-0.579768\pi\) | ||||
−0.247983 | + | 0.968764i | \(0.579768\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.41461 | −0.349699 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.74479 | −0.238334 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.77822 | −0.363557 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.520692 | −0.0215280 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.9659 | −0.700259 | −0.350130 | − | 0.936701i | \(-0.613862\pi\) | ||||
−0.350130 | + | 0.936701i | \(0.613862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.4691 | 1.46148 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.1671 | 1.15864 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.95059 | 0.285426 | 0.142713 | − | 0.989764i | \(-0.454417\pi\) | ||||
0.142713 | + | 0.989764i | \(0.454417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.77921 | −0.113937 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.54645 | −0.349783 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −42.4976 | −1.73640 | −0.868202 | − | 0.496210i | \(-0.834724\pi\) | ||||
−0.868202 | + | 0.496210i | \(0.834724\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.23112 | 0.254173 | 0.127086 | − | 0.991892i | \(-0.459437\pi\) | ||||
0.127086 | + | 0.991892i | \(0.459437\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.12768 | 0.208815 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.13919 | 0.0463146 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6593 | 1.00089 | 0.500445 | − | 0.865768i | \(-0.333170\pi\) | ||||
0.500445 | + | 0.865768i | \(0.333170\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.766920 | −0.0310772 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.98496 | 0.363493 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.7158 | 0.634756 | 0.317378 | − | 0.948299i | \(-0.397198\pi\) | ||||
0.317378 | + | 0.948299i | \(0.397198\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.445076 | −0.0179472 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.5791 | 0.466158 | 0.233079 | − | 0.972458i | \(-0.425120\pi\) | ||||
0.233079 | + | 0.972458i | \(0.425120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.22023 | 0.290205 | 0.145103 | − | 0.989417i | \(-0.453649\pi\) | ||||
0.145103 | + | 0.989417i | \(0.453649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.2038 | −0.770623 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.577855 | 0.0231513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.21791 | 0.288716 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.11495 | 0.324080 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.3416 | 0.731326 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2384 | 0.885298 | 0.442649 | − | 0.896695i | \(-0.354039\pi\) | ||||
0.442649 | + | 0.896695i | \(0.354039\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0209 | −0.557281 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.2295 | 0.842468 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.58673 | −0.141889 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.6804 | −1.25130 | −0.625651 | − | 0.780103i | \(-0.715167\pi\) | ||||
−0.625651 | + | 0.780103i | \(0.715167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −37.3281 | −1.47208 | −0.736038 | − | 0.676941i | \(-0.763305\pi\) | ||||
−0.736038 | + | 0.676941i | \(0.763305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.1658 | 0.715279 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.0364 | 1.25948 | 0.629739 | − | 0.776806i | \(-0.283162\pi\) | ||||
0.629739 | + | 0.776806i | \(0.283162\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.23049 | 0.0875542 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.1103 | −0.592220 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.4097 | −1.58135 | −0.790676 | − | 0.612235i | \(-0.790271\pi\) | ||||
−0.790676 | + | 0.612235i | \(0.790271\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.865968 | −0.0338362 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7.26261 | −0.283341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.45813 | −0.329482 | −0.164741 | − | 0.986337i | \(-0.552679\pi\) | ||||
−0.164741 | + | 0.986337i | \(0.552679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.1707 | −0.667862 | −0.333931 | − | 0.942597i | \(-0.608375\pi\) | ||||
−0.333931 | + | 0.942597i | \(0.608375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.53608 | 0.176167 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.97195 | −0.192804 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.67531 | −0.0648683 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −49.8423 | −1.92701 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.23803 | 0.240817 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.3578 | 1.17021 | 0.585104 | − | 0.810958i | \(-0.301054\pi\) | ||||
0.585104 | + | 0.810958i | \(0.301054\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.5047 | 0.673755 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.6466 | 0.524482 | 0.262241 | − | 0.965002i | \(-0.415539\pi\) | ||||
0.262241 | + | 0.965002i | \(0.415539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.41830 | −0.0928057 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.66156 | −0.140311 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.0332 | −1.64662 | −0.823310 | − | 0.567592i | \(-0.807875\pi\) | ||||
−0.823310 | + | 0.567592i | \(0.807875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.3063 | 0.661241 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 38.9576 | 1.48633 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.77822 | −0.334424 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3082 | −0.430183 | −0.215092 | − | 0.976594i | \(-0.569005\pi\) | ||||
−0.215092 | + | 0.976594i | \(0.569005\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.457073 | −0.0173628 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.1659 | −0.613207 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.512639 | 0.0194176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −29.3684 | −1.11081 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.0712 | 1.02246 | 0.511232 | − | 0.859442i | \(-0.329189\pi\) | ||||
0.511232 | + | 0.859442i | \(0.329189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32.8126 | 1.23755 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19.0312 | −0.716756 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.57116 | 0.134307 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.6143 | 1.07463 | 0.537316 | − | 0.843381i | \(-0.319438\pi\) | ||||
0.537316 | + | 0.843381i | \(0.319438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.46333 | −0.0923821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.0080 | −1.23616 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.13919 | 0.0426032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 45.5222 | 1.70006 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.89921 | 0.294591 | 0.147295 | − | 0.989093i | \(-0.452943\pi\) | ||||
0.147295 | + | 0.989093i | \(0.452943\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.8044 | −0.402377 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.4772 | 0.761554 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.52708 | 0.0567143 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.67249 | −0.0620292 | −0.0310146 | − | 0.999519i | \(-0.509874\pi\) | ||||
−0.0310146 | + | 0.999519i | \(0.509874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21.7283 | 0.804753 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.9234 | −0.773880 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7021 | 1.31869 | 0.659344 | − | 0.751841i | \(-0.270834\pi\) | ||||
0.659344 | + | 0.751841i | \(0.270834\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.11812 | 0.0781279 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.2185 | −0.413240 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.9259 | −0.916915 | −0.458457 | − | 0.888716i | \(-0.651598\pi\) | ||||
−0.458457 | + | 0.888716i | \(0.651598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.11495 | 0.298110 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.9776 | 0.402729 | 0.201365 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201365 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.79886 | −0.285728 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.62578 | −0.0960724 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.8099 | 0.504602 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.54131 | 0.0562431 | 0.0281215 | − | 0.999605i | \(-0.491047\pi\) | ||||
0.0281215 | + | 0.999605i | \(0.491047\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.46002 | 0.271858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.812537 | 0.0295712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.8138 | 0.756490 | 0.378245 | − | 0.925705i | \(-0.376528\pi\) | ||||
0.378245 | + | 0.925705i | \(0.376528\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.55186 | −0.274115 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.52690 | 0.236600 | 0.118300 | − | 0.992978i | \(-0.462256\pi\) | ||||
0.118300 | + | 0.992978i | \(0.462256\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.49058 | −0.198772 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.27030 | −0.0459279 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.23049 | 0.0805382 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9745 | 1.04485 | 0.522424 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522424 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.61861 | −0.202349 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.4044 | −0.374220 | −0.187110 | − | 0.982339i | \(-0.559912\pi\) | ||||
−0.187110 | + | 0.982339i | \(0.559912\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.0874 | 1.08077 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.9786 | −0.501480 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.917099 | 0.0328585 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.84719 | 0.280794 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.95022 | 0.0696952 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.1139 | 0.432365 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.2258 | 0.400155 | 0.200078 | − | 0.979780i | \(-0.435881\pi\) | ||||
0.200078 | + | 0.979780i | \(0.435881\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.955040 | −0.0340003 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.64277 | 0.307301 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.23803 | 0.221519 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.5933 | 0.659436 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.2894 | 0.647845 | 0.323922 | − | 0.946084i | \(-0.394998\pi\) | ||||
0.323922 | + | 0.946084i | \(0.394998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.9201 | 0.775478 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.264122 | 0.00933228 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.8894 | 0.560725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.62695 | 0.163079 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49.3063 | −1.73566 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.09275 | −0.143893 | −0.0719467 | − | 0.997408i | \(-0.522921\pi\) | ||||
−0.0719467 | + | 0.997408i | \(0.522921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.3329 | −1.87277 | −0.936385 | − | 0.350973i | \(-0.885851\pi\) | ||||
−0.936385 | + | 0.350973i | \(0.885851\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 58.6154 | 2.05573 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.7749 | 0.447485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4315 | −1.30956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.457073 | −0.0159714 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.4574 | −1.09787 | −0.548935 | − | 0.835865i | \(-0.684966\pi\) | ||||
−0.548935 | + | 0.835865i | \(0.684966\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 55.3033 | 1.92775 | 0.963876 | − | 0.266351i | \(-0.0858179\pi\) | ||||
0.963876 | + | 0.266351i | \(0.0858179\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.88367 | 0.239659 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.1998 | −1.81516 | −0.907582 | − | 0.419875i | \(-0.862074\pi\) | ||||
−0.907582 | + | 0.419875i | \(0.862074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.2170 | 0.667435 | 0.333717 | − | 0.942673i | \(-0.391697\pi\) | ||||
0.333717 | + | 0.942673i | \(0.391697\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.0437 | 1.80537 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.43965 | −0.0845287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.88316 | 0.134382 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.4244 | 1.32814 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.5682 | −1.15890 | −0.579451 | − | 0.815007i | \(-0.696733\pi\) | ||||
−0.579451 | + | 0.815007i | \(0.696733\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8299 | −0.994133 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 50.8412 | 1.75106 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.13919 | 0.0391893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.64067 | 0.330867 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.5358 | −1.04675 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.2442 | 0.967064 | 0.483532 | − | 0.875327i | \(-0.339354\pi\) | ||||
0.483532 | + | 0.875327i | \(0.339354\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.27254 | −0.0777193 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.6777 | 0.364742 | 0.182371 | − | 0.983230i | \(-0.441623\pi\) | ||||
0.182371 | + | 0.983230i | \(0.441623\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.0048 | −1.02375 | −0.511875 | − | 0.859060i | \(-0.671049\pi\) | ||||
−0.511875 | + | 0.859060i | \(0.671049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.390696 | −0.0133149 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −58.1989 | −1.98112 | −0.990558 | − | 0.137097i | \(-0.956223\pi\) | ||||
−0.990558 | + | 0.137097i | \(0.956223\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.54535 | −0.290551 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20.5420 | −0.697643 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.38936 | 0.182822 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.2185 | −0.380125 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.10534 | −0.0374100 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.91350 | −0.335137 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.8675 | −1.34623 | −0.673115 | − | 0.739538i | \(-0.735044\pi\) | ||||
−0.673115 | + | 0.739538i | \(0.735044\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −53.3179 | −1.79837 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.3519 | −0.820437 | −0.410218 | − | 0.911987i | \(-0.634547\pi\) | ||||
−0.410218 | + | 0.911987i | \(0.634547\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.3434 | −0.516345 | −0.258173 | − | 0.966099i | \(-0.583120\pi\) | ||||
−0.258173 | + | 0.966099i | \(0.583120\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.72443 | −0.158810 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7397 | −0.427757 | −0.213878 | − | 0.976860i | \(-0.568610\pi\) | ||||
−0.213878 | + | 0.976860i | \(0.568610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6357 | 0.625020 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.1623 | 0.340450 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 39.2146 | 1.31227 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.3043 | −0.611846 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.55186 | −0.252149 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.35208 | 0.111798 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.4157 | −0.713462 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.9463 | 0.530659 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.3533 | −0.610085 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.2984 | −0.972839 | −0.486419 | − | 0.873725i | \(-0.661697\pi\) | ||||
−0.486419 | + | 0.873725i | \(0.661697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.63228 | 0.0541393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.0771 | −0.863973 | −0.431987 | − | 0.901880i | \(-0.642187\pi\) | ||||
−0.431987 | + | 0.901880i | \(0.642187\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.74479 | 0.190125 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.2129 | −0.436804 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.760163 | −0.0251028 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.38215 | −0.243515 | −0.121757 | − | 0.992560i | \(-0.538853\pi\) | ||||
−0.121757 | + | 0.992560i | \(0.538853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.25156 | −0.0741913 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.84719 | 0.258293 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.8340 | 0.915176 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.93840 | −0.162198 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −41.2805 | −1.35437 | −0.677185 | − | 0.735813i | \(-0.736800\pi\) | ||||
−0.677185 | + | 0.735813i | \(0.736800\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.36447 | −0.143040 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.81365 | −0.190330 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.77921 | 0.0908900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.6346 | −0.902782 | −0.451391 | − | 0.892326i | \(-0.649072\pi\) | ||||
−0.451391 | + | 0.892326i | \(0.649072\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.8083 | −1.03802 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.2613 | 0.595303 | 0.297651 | − | 0.954675i | \(-0.403797\pi\) | ||||
0.297651 | + | 0.954675i | \(0.403797\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.853463 | −0.0277926 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.38621 | −0.175214 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.38628 | −0.175031 | −0.0875153 | − | 0.996163i | \(-0.527893\pi\) | ||||
−0.0875153 | + | 0.996163i | \(0.527893\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.8894 | 0.515792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53.4714 | 1.73393 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.4840 | 0.857900 | 0.428950 | − | 0.903328i | \(-0.358884\pi\) | ||||
0.428950 | + | 0.903328i | \(0.358884\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.09766 | −0.132597 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.766920 | 0.0247910 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.1918 | 0.490569 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.0447 | 1.13047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.31212 | 0.203405 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.15555 | −0.165963 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.4189 | −0.849574 | −0.424787 | − | 0.905293i | \(-0.639651\pi\) | ||||
−0.424787 | + | 0.905293i | \(0.639651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.7976 | 0.635990 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.54863 | 0.242247 | 0.121123 | − | 0.992637i | \(-0.461350\pi\) | ||||
0.121123 | + | 0.992637i | \(0.461350\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.1907 | −0.454933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.88367 | 0.220454 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.3574 | 0.715277 | 0.357639 | − | 0.933860i | \(-0.383582\pi\) | ||||
0.357639 | + | 0.933860i | \(0.383582\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.577855 | −0.0184683 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.50960 | −0.0801252 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29.6401 | 0.945373 | 0.472687 | − | 0.881231i | \(-0.343284\pi\) | ||||
0.472687 | + | 0.881231i | \(0.343284\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.2577 | 0.549877 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.7059 | −0.531755 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.8342 | 1.10766 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.4495 | −1.28492 | −0.642461 | − | 0.766318i | \(-0.722087\pi\) | ||||
−0.642461 | + | 0.766318i | \(0.722087\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −57.9363 | −1.83855 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.23633 | −0.166003 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0197 | −0.697372 | −0.348686 | − | 0.937240i | \(-0.613372\pi\) | ||||
−0.348686 | + | 0.937240i | \(0.613372\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.5466 | 1.12464 |
(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 | 8008.2.a.y.1.11 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.11 | ✓ | 14 | 1.1 | even | 1 | trivial |