Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.461844.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 14x^{2} - 12x + 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.32424\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.32424 | 1.25645 | 0.628223 | − | 0.778033i | \(-0.283783\pi\) | ||||
0.628223 | + | 0.778033i | \(0.283783\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.84395 | 1.46051 | 0.730253 | − | 0.683176i | \(-0.239402\pi\) | ||||
0.730253 | + | 0.683176i | \(0.239402\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.11760 | −0.271058 | −0.135529 | − | 0.990773i | \(-0.543273\pi\) | ||||
−0.135529 | + | 0.990773i | \(0.543273\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.05060 | 0.929271 | 0.464635 | − | 0.885502i | \(-0.346185\pi\) | ||||
0.464635 | + | 0.885502i | \(0.346185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.32424 | 0.725409 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.16820 | −0.869129 | −0.434565 | − | 0.900641i | \(-0.643098\pi\) | ||||
−0.434565 | + | 0.900641i | \(0.643098\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.64849 | 1.04890 | 0.524449 | − | 0.851442i | \(-0.324271\pi\) | ||||
0.524449 | + | 0.851442i | \(0.324271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.49244 | −1.34568 | −0.672841 | − | 0.739787i | \(-0.734926\pi\) | ||||
−0.672841 | + | 0.739787i | \(0.734926\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.84395 | 0.843224 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.69908 | −1.43012 | −0.715060 | − | 0.699063i | \(-0.753601\pi\) | ||||
−0.715060 | + | 0.699063i | \(0.753601\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.63731 | 0.880400 | 0.440200 | − | 0.897900i | \(-0.354908\pi\) | ||||
0.440200 | + | 0.897900i | \(0.354908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.8167 | 1.95453 | 0.977263 | − | 0.212030i | \(-0.0680076\pi\) | ||||
0.977263 | + | 0.212030i | \(0.0680076\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.89455 | −1.00567 | −0.502837 | − | 0.864381i | \(-0.667710\pi\) | ||||
−0.502837 | + | 0.864381i | \(0.667710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.05060 | 0.578657 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.11760 | −0.156495 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2300 | 1.67992 | 0.839958 | − | 0.542651i | \(-0.182580\pi\) | ||||
0.839958 | + | 0.542651i | \(0.182580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.05060 | 0.536515 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.910956 | 0.118596 | 0.0592982 | − | 0.998240i | \(-0.481114\pi\) | ||||
0.0592982 | + | 0.998240i | \(0.481114\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.46911 | 0.316137 | 0.158069 | − | 0.987428i | \(-0.449473\pi\) | ||||
0.158069 | + | 0.987428i | \(0.449473\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.32424 | 0.418815 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0233 | 1.22454 | 0.612272 | − | 0.790647i | \(-0.290256\pi\) | ||||
0.612272 | + | 0.790647i | \(0.290256\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.16820 | −0.501792 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.05060 | 0.955430 | 0.477715 | − | 0.878515i | \(-0.341465\pi\) | ||||
0.477715 | + | 0.878515i | \(0.341465\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4034 | 1.21763 | 0.608813 | − | 0.793314i | \(-0.291646\pi\) | ||||
0.608813 | + | 0.793314i | \(0.291646\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.1025 | 1.83505 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.6991 | −1.20374 | −0.601871 | − | 0.798594i | \(-0.705578\pi\) | ||||
−0.601871 | + | 0.798594i | \(0.705578\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.67576 | 0.293702 | 0.146851 | − | 0.989159i | \(-0.453086\pi\) | ||||
0.146851 | + | 0.989159i | \(0.453086\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.64849 | 0.605581 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.68791 | −0.390917 | −0.195459 | − | 0.980712i | \(-0.562620\pi\) | ||||
−0.195459 | + | 0.980712i | \(0.562620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.32424 | 0.348475 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.49244 | −0.776930 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.64849 | −0.675052 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.84395 | 0.486836 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.6991 | 1.16410 | 0.582051 | − | 0.813152i | \(-0.302250\pi\) | ||||
0.582051 | + | 0.813152i | \(0.302250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.1531 | −1.88721 | −0.943604 | − | 0.331075i | \(-0.892589\pi\) | ||||
−0.943604 | + | 0.331075i | \(0.892589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.8673 | −1.24393 | −0.621964 | − | 0.783046i | \(-0.713665\pi\) | ||||
−0.621964 | + | 0.783046i | \(0.713665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.1124 | −1.06437 | −0.532186 | − | 0.846627i | \(-0.678629\pi\) | ||||
−0.532186 | + | 0.846627i | \(0.678629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.69908 | −0.825681 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.7497 | −1.01125 | −0.505623 | − | 0.862755i | \(-0.668737\pi\) | ||||
−0.505623 | + | 0.862755i | \(0.668737\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.71518 | −0.340570 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.4639 | 1.13308 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.63731 | 0.508299 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3476 | −1.00693 | −0.503467 | − | 0.864014i | \(-0.667942\pi\) | ||||
−0.503467 | + | 0.864014i | \(0.667942\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.8167 | 1.12845 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.38699 | −0.732775 | −0.366387 | − | 0.930462i | \(-0.619406\pi\) | ||||
−0.366387 | + | 0.930462i | \(0.619406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.4652 | 1.16758 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.80551 | 0.837741 | 0.418870 | − | 0.908046i | \(-0.362426\pi\) | ||||
0.418870 | + | 0.908046i | \(0.362426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.2352 | −0.868138 | −0.434069 | − | 0.900880i | \(-0.642923\pi\) | ||||
−0.434069 | + | 0.900880i | \(0.642923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.89455 | −0.580626 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.84395 | 0.405072 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.05060 | 0.334088 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6485 | 0.872358 | 0.436179 | − | 0.899860i | \(-0.356331\pi\) | ||||
0.436179 | + | 0.899860i | \(0.356331\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.42544 | −0.441516 | −0.220758 | − | 0.975329i | \(-0.570853\pi\) | ||||
−0.220758 | + | 0.975329i | \(0.570853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.11760 | −0.0903526 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.94940 | −0.554623 | −0.277311 | − | 0.960780i | \(-0.589443\pi\) | ||||
−0.277311 | + | 0.960780i | \(0.589443\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.2300 | 0.969900 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.8561 | −1.09201 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.2694 | 1.43097 | 0.715485 | − | 0.698629i | \(-0.246206\pi\) | ||||
0.715485 | + | 0.698629i | \(0.246206\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.9961 | 1.39258 | 0.696288 | − | 0.717762i | \(-0.254833\pi\) | ||||
0.696288 | + | 0.717762i | \(0.254833\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.05060 | 0.309757 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.9573 | −1.44130 | −0.720648 | − | 0.693301i | \(-0.756156\pi\) | ||||
−0.720648 | + | 0.693301i | \(0.756156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.910956 | 0.0684717 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.7773 | −0.880274 | −0.440137 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440137 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5979 | 0.862064 | 0.431032 | − | 0.902337i | \(-0.358150\pi\) | ||||
0.431032 | + | 0.902337i | \(0.358150\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.46911 | 0.182522 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.41360 | −0.395882 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.32424 | 0.241803 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.2970 | 1.68571 | 0.842855 | − | 0.538141i | \(-0.180873\pi\) | ||||
0.842855 | + | 0.538141i | \(0.180873\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6386 | −0.909746 | −0.454873 | − | 0.890556i | \(-0.650315\pi\) | ||||
−0.454873 | + | 0.890556i | \(0.650315\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.0913 | −1.71643 | −0.858217 | − | 0.513287i | \(-0.828428\pi\) | ||||
−0.858217 | + | 0.513287i | \(0.828428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1176 | −0.858994 | −0.429497 | − | 0.903068i | \(-0.641309\pi\) | ||||
−0.429497 | + | 0.903068i | \(0.641309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0233 | 0.706991 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.7770 | 1.31788 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.16820 | −0.289710 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.6209 | 1.35721 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.168197 | −0.0115792 | −0.00578959 | − | 0.999983i | \(-0.501843\pi\) | ||||
−0.00578959 | + | 0.999983i | \(0.501843\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.05060 | 0.551618 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.9067 | −1.69078 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.4034 | 0.702996 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.11760 | −0.0751779 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.5440 | −1.71055 | −0.855277 | − | 0.518171i | \(-0.826613\pi\) | ||||
−0.855277 | + | 0.518171i | \(0.826613\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.70995 | 0.445355 | 0.222677 | − | 0.974892i | \(-0.428520\pi\) | ||||
0.222677 | + | 0.974892i | \(0.428520\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.92182 | 0.193079 | 0.0965396 | − | 0.995329i | \(-0.469223\pi\) | ||||
0.0965396 | + | 0.995329i | \(0.469223\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.1025 | 1.05947 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.68791 | −0.110578 | −0.0552892 | − | 0.998470i | \(-0.517608\pi\) | ||||
−0.0552892 | + | 0.998470i | \(0.517608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.6991 | −0.694980 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.2079 | −1.04840 | −0.524202 | − | 0.851594i | \(-0.675636\pi\) | ||||
−0.524202 | + | 0.851594i | \(0.675636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1682 | 0.783822 | 0.391911 | − | 0.920003i | \(-0.371814\pi\) | ||||
0.391911 | + | 0.920003i | \(0.371814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.05060 | 0.257733 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.67576 | 0.169569 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.6373 | 0.987018 | 0.493509 | − | 0.869741i | \(-0.335714\pi\) | ||||
0.493509 | + | 0.869741i | \(0.335714\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.1906 | −1.26937 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5210 | −0.718660 | −0.359330 | − | 0.933211i | \(-0.616995\pi\) | ||||
−0.359330 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −28.9179 | −1.79687 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.64849 | 0.349633 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.41852 | 0.0874694 | 0.0437347 | − | 0.999043i | \(-0.486074\pi\) | ||||
0.0437347 | + | 0.999043i | \(0.486074\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.68791 | −0.225696 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.3982 | 1.60952 | 0.804762 | − | 0.593597i | \(-0.202293\pi\) | ||||
0.804762 | + | 0.593597i | \(0.202293\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.1133 | 1.64702 | 0.823509 | − | 0.567303i | \(-0.192013\pi\) | ||||
0.823509 | + | 0.567303i | \(0.192013\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.32424 | 0.201192 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0861 | 0.666098 | 0.333049 | − | 0.942910i | \(-0.391923\pi\) | ||||
0.333049 | + | 0.942910i | \(0.391923\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.49244 | −0.448561 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.17938 | 0.547596 | 0.273798 | − | 0.961787i | \(-0.411720\pi\) | ||||
0.273798 | + | 0.961787i | \(0.411720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.8686 | 1.89439 | 0.947195 | − | 0.320658i | \(-0.103904\pi\) | ||||
0.947195 | + | 0.320658i | \(0.103904\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.7398 | 1.10617 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7510 | −0.926528 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.64849 | −0.389741 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.14061 | 0.534000 | 0.267000 | − | 0.963696i | \(-0.413968\pi\) | ||||
0.267000 | + | 0.963696i | \(0.413968\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.84395 | 0.281075 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.16820 | −0.241053 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.6058 | 2.45576 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.6991 | 0.672095 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.40211 | −0.422461 | −0.211230 | − | 0.977436i | \(-0.567747\pi\) | ||||
−0.211230 | + | 0.977436i | \(0.567747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.1531 | −1.08958 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.5098 | 1.21971 | 0.609855 | − | 0.792513i | \(-0.291228\pi\) | ||||
0.609855 | + | 0.792513i | \(0.291228\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.1458 | 0.630000 | 0.315000 | − | 0.949092i | \(-0.397995\pi\) | ||||
0.315000 | + | 0.949092i | \(0.397995\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.0960 | −1.52186 | −0.760931 | − | 0.648833i | \(-0.775257\pi\) | ||||
−0.760931 | + | 0.648833i | \(0.775257\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.3610 | 1.53192 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8673 | −0.718182 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.52695 | −0.251886 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.1124 | −0.614516 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.9192 | −1.26357 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0670 | 0.553333 | 0.276666 | − | 0.960966i | \(-0.410770\pi\) | ||||
0.276666 | + | 0.960966i | \(0.410770\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.69908 | −0.476707 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.0749 | −1.91065 | −0.955326 | − | 0.295555i | \(-0.904495\pi\) | ||||
−0.955326 | + | 0.295555i | \(0.904495\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7497 | −0.583843 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.2930 | −1.96538 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.80453 | −0.529395 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.15702 | 0.169478 | 0.0847388 | − | 0.996403i | \(-0.472994\pi\) | ||||
0.0847388 | + | 0.996403i | \(0.472994\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.3883 | 1.68018 | 0.840088 | − | 0.542450i | \(-0.182503\pi\) | ||||
0.840088 | + | 0.542450i | \(0.182503\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.3325 | 1.29509 | 0.647543 | − | 0.762029i | \(-0.275797\pi\) | ||||
0.647543 | + | 0.762029i | \(0.275797\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.71518 | −0.196628 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.1915 | 1.38234 | 0.691168 | − | 0.722694i | \(-0.257096\pi\) | ||||
0.691168 | + | 0.722694i | \(0.257096\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.59266 | −0.136456 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.4639 | 0.654184 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.2806 | 1.00644 | 0.503219 | − | 0.864159i | \(-0.332149\pi\) | ||||
0.503219 | + | 0.864159i | \(0.332149\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.63731 | 0.293467 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 40.6554 | 2.11072 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.8331 | −1.02692 | −0.513459 | − | 0.858114i | \(-0.671636\pi\) | ||||
−0.513459 | + | 0.858114i | \(0.671636\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.64849 | 0.290912 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.5936 | −1.10919 | −0.554595 | − | 0.832120i | \(-0.687127\pi\) | ||||
−0.554595 | + | 0.832120i | \(0.687127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.3476 | −0.581354 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.81540 | 0.399348 | 0.199674 | − | 0.979862i | \(-0.436012\pi\) | ||||
0.199674 | + | 0.979862i | \(0.436012\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.8167 | 0.651509 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.7043 | 0.999048 | 0.499524 | − | 0.866300i | \(-0.333508\pi\) | ||||
0.499524 | + | 0.866300i | \(0.333508\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.65838 | 0.235584 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.38699 | −0.423068 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.96848 | 0.249361 | 0.124680 | − | 0.992197i | \(-0.460209\pi\) | ||||
0.124680 | + | 0.992197i | \(0.460209\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.4652 | 0.674102 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.6209 | −1.27945 | −0.639723 | − | 0.768605i | \(-0.720951\pi\) | ||||
−0.639723 | + | 0.768605i | \(0.720951\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.49244 | −0.373225 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −42.1380 | −2.08870 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6761 | 0.676238 | 0.338119 | − | 0.941103i | \(-0.390209\pi\) | ||||
0.338119 | + | 0.941103i | \(0.390209\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.80551 | 0.483670 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.02824 | 0.149010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2352 | −0.501220 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.50330 | 0.366560 | 0.183280 | − | 0.983061i | \(-0.441328\pi\) | ||||
0.183280 | + | 0.983061i | \(0.441328\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.39817 | −0.458039 | −0.229019 | − | 0.973422i | \(-0.573552\pi\) | ||||
−0.229019 | + | 0.973422i | \(0.573552\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.89455 | −0.335225 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.20793 | 0.397210 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.84395 | 0.233868 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.77598 | 0.230051 | 0.115025 | − | 0.993363i | \(-0.463305\pi\) | ||||
0.115025 | + | 0.993363i | \(0.463305\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.50853 | −0.120552 | −0.0602762 | − | 0.998182i | \(-0.519198\pi\) | ||||
−0.0602762 | + | 0.998182i | \(0.519198\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.8837 | −0.807656 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0900 | −0.624752 | −0.312376 | − | 0.949958i | \(-0.601125\pi\) | ||||
−0.312376 | + | 0.949958i | \(0.601125\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.05060 | 0.192886 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.2089 | 1.81536 | 0.907680 | − | 0.419663i | \(-0.137852\pi\) | ||||
0.907680 | + | 0.419663i | \(0.137852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.6485 | 0.503656 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.29103 | 0.438471 | 0.219235 | − | 0.975672i | \(-0.429644\pi\) | ||||
0.219235 | + | 0.975672i | \(0.429644\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.3069 | 1.28583 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.42544 | −0.254909 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.05189 | 0.236317 | 0.118159 | − | 0.992995i | \(-0.462301\pi\) | ||||
0.118159 | + | 0.992995i | \(0.462301\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.11760 | −0.0521651 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.89881 | −0.461033 | −0.230517 | − | 0.973068i | \(-0.574042\pi\) | ||||
−0.230517 | + | 0.973068i | \(0.574042\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.8906 | 1.15676 | 0.578382 | − | 0.815766i | \(-0.303684\pi\) | ||||
0.578382 | + | 0.815766i | \(0.303684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7333 | −1.23707 | −0.618534 | − | 0.785758i | \(-0.712273\pi\) | ||||
−0.618534 | + | 0.785758i | \(0.712273\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.3200 | 1.53857 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.94940 | −0.320212 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 62.0834 | 2.85460 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.2300 | 0.559972 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.8827 | 0.497244 | 0.248622 | − | 0.968601i | \(-0.420022\pi\) | ||||
0.248622 | + | 0.968601i | \(0.420022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.69908 | −0.396644 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −13.8561 | −0.630475 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.88337 | −0.0853438 | −0.0426719 | − | 0.999089i | \(-0.513587\pi\) | ||||
−0.0426719 | + | 0.999089i | \(0.513587\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.2694 | 0.826170 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.2050 | −1.45339 | −0.726695 | − | 0.686960i | \(-0.758945\pi\) | ||||
−0.726695 | + | 0.686960i | \(0.758945\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.31275 | −0.284312 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.7621 | 1.20045 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.03516 | 0.359703 | 0.179852 | − | 0.983694i | \(-0.442438\pi\) | ||||
0.179852 | + | 0.983694i | \(0.442438\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.9961 | 0.804005 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.40340 | 0.107162 | 0.0535811 | − | 0.998564i | \(-0.482936\pi\) | ||||
0.0535811 | + | 0.998564i | \(0.482936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.91064 | −0.0846877 | −0.0423438 | − | 0.999103i | \(-0.513482\pi\) | ||||
−0.0423438 | + | 0.999103i | \(0.513482\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.5834 | 1.52988 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.05060 | 0.178838 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.3969 | −1.46879 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.9573 | −0.832133 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0618 | −0.659868 | −0.329934 | − | 0.944004i | \(-0.607027\pi\) | ||||
−0.329934 | + | 0.944004i | \(0.607027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.1649 | −1.45020 | −0.725100 | − | 0.688643i | \(-0.758207\pi\) | ||||
−0.725100 | + | 0.688643i | \(0.758207\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.37355 | 0.364758 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.62613 | −0.244614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.910956 | 0.0395321 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.63731 | 0.244179 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.7773 | −0.508227 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.6209 | 0.845132 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.50459 | −0.279654 | −0.139827 | − | 0.990176i | \(-0.544655\pi\) | ||||
−0.139827 | + | 0.990176i | \(0.544655\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.5979 | 0.497713 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.5118 | −1.77492 | −0.887459 | − | 0.460887i | \(-0.847531\pi\) | ||||
−0.887459 | + | 0.460887i | \(0.847531\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.46911 | 0.105379 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.8797 | 0.974710 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35.5664 | −1.51244 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.7004 | −0.580503 | −0.290252 | − | 0.956950i | \(-0.593739\pi\) | ||||
−0.290252 | + | 0.956950i | \(0.593739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8167 | 0.542088 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.41360 | −0.228562 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.3476 | 1.48972 | 0.744861 | − | 0.667219i | \(-0.232516\pi\) | ||||
0.744861 | + | 0.667219i | \(0.232516\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.32424 | 0.139605 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 36.2483 | 1.51961 | 0.759804 | − | 0.650152i | \(-0.225295\pi\) | ||||
0.759804 | + | 0.650152i | \(0.225295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.96581 | 0.333359 | 0.166679 | − | 0.986011i | \(-0.446696\pi\) | ||||
0.166679 | + | 0.986011i | \(0.446696\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.2970 | 0.973245 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.8219 | −0.908458 | −0.454229 | − | 0.890885i | \(-0.650085\pi\) | ||||
−0.454229 | + | 0.890885i | \(0.650085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6386 | −0.525242 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.89487 | 0.369021 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 59.2414 | 2.45353 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.3518 | −1.08766 | −0.543828 | − | 0.839197i | \(-0.683026\pi\) | ||||
−0.543828 | + | 0.839197i | \(0.683026\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.3489 | −1.25050 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.0913 | −0.990984 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21.8522 | −0.897361 | −0.448680 | − | 0.893692i | \(-0.648106\pi\) | ||||
−0.448680 | + | 0.893692i | \(0.648106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −12.1176 | −0.495940 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.4822 | 0.836881 | 0.418441 | − | 0.908244i | \(-0.362577\pi\) | ||||
0.418441 | + | 0.908244i | \(0.362577\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.1380 | 1.27014 | 0.635072 | − | 0.772453i | \(-0.280970\pi\) | ||||
0.635072 | + | 0.772453i | \(0.280970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0233 | 0.408181 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.6715 | −0.473732 | −0.236866 | − | 0.971542i | \(-0.576120\pi\) | ||||
−0.236866 | + | 0.971542i | \(0.576120\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.7770 | 0.760880 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.89455 | −0.278924 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.3758 | −1.67115 | −0.835577 | − | 0.549374i | \(-0.814866\pi\) | ||||
−0.835577 | + | 0.549374i | \(0.814866\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.7359 | 1.72048 | 0.860240 | − | 0.509889i | \(-0.170313\pi\) | ||||
0.860240 | + | 0.509889i | \(0.170313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.44087 | 0.299074 | 0.149537 | − | 0.988756i | \(-0.452222\pi\) | ||||
0.149537 | + | 0.988756i | \(0.452222\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.16820 | −0.167264 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.2595 | −0.491167 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.6209 | 0.783583 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.72210 | 0.387645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7221 | −0.705506 | −0.352753 | − | 0.935717i | \(-0.614754\pi\) | ||||
−0.352753 | + | 0.935717i | \(0.614754\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.168197 | −0.00668524 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.05060 | 0.160491 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.05060 | 0.318477 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.4764 | −1.24324 | −0.621621 | − | 0.783319i | \(-0.713525\pi\) | ||||
−0.621621 | + | 0.783319i | \(0.713525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −40.7234 | −1.60597 | −0.802987 | − | 0.595997i | \(-0.796757\pi\) | ||||
−0.802987 | + | 0.595997i | \(0.796757\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.1255 | 1.73475 | 0.867376 | − | 0.497653i | \(-0.165805\pi\) | ||||
0.867376 | + | 0.497653i | \(0.165805\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.41263 | 0.173211 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −24.9067 | −0.976171 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.02301 | 0.235699 | 0.117849 | − | 0.993031i | \(-0.462400\pi\) | ||||
0.117849 | + | 0.993031i | \(0.462400\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.4034 | 0.405875 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.26810 | −0.205216 | −0.102608 | − | 0.994722i | \(-0.532719\pi\) | ||||
−0.102608 | + | 0.994722i | \(0.532719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.72144 | 0.339225 | 0.169612 | − | 0.985511i | \(-0.445748\pi\) | ||||
0.169612 | + | 0.985511i | \(0.445748\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.11760 | −0.0434040 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.5440 | −0.911628 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.5440 | −0.987589 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.9603 | 0.461721 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.04931 | 0.233184 | 0.116592 | − | 0.993180i | \(-0.462803\pi\) | ||||
0.116592 | + | 0.993180i | \(0.462803\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.6636 | −0.525135 | −0.262568 | − | 0.964914i | \(-0.584569\pi\) | ||||
−0.262568 | + | 0.964914i | \(0.584569\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.1012 | −0.848166 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.70995 | 0.257126 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.41555 | −0.130692 | −0.0653462 | − | 0.997863i | \(-0.520815\pi\) | ||||
−0.0653462 | + | 0.997863i | \(0.520815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.92182 | 0.111474 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.2300 | 0.465925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.6153 | 0.784242 | 0.392121 | − | 0.919914i | \(-0.371741\pi\) | ||||
0.392121 | + | 0.919914i | \(0.371741\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.1025 | 0.611683 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.30026 | −0.238639 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.68791 | −0.0638425 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.5861 | −0.513138 | −0.256569 | − | 0.966526i | \(-0.582592\pi\) | ||||
−0.256569 | + | 0.966526i | \(0.582592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.2365 | −1.32897 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 38.8906 | 1.46263 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.39616 | −0.0524339 | −0.0262169 | − | 0.999656i | \(-0.508346\pi\) | ||||
−0.0262169 | + | 0.999656i | \(0.508346\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.6991 | −0.401247 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.2300 | 1.16957 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.2079 | −0.605296 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.6130 | −1.40273 | −0.701365 | − | 0.712803i | \(-0.747425\pi\) | ||||
−0.701365 | + | 0.712803i | \(0.747425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −63.6695 | −2.37118 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.1682 | 0.452540 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.0191 | 1.29879 | 0.649393 | − | 0.760453i | \(-0.275023\pi\) | ||||
0.649393 | + | 0.760453i | \(0.275023\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.3239 | −0.529790 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.8824 | −0.660502 | −0.330251 | − | 0.943893i | \(-0.607133\pi\) | ||||
−0.330251 | + | 0.943893i | \(0.607133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 48.5525 | 1.78846 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.2034 | 1.25819 | 0.629095 | − | 0.777328i | \(-0.283425\pi\) | ||||
0.629095 | + | 0.777328i | \(0.283425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.05060 | 0.148802 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.96155 | −0.182022 | −0.0910109 | − | 0.995850i | \(-0.529010\pi\) | ||||
−0.0910109 | + | 0.995850i | \(0.529010\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.67576 | 0.0979008 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.7740 | −1.56293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.8574 | −1.12600 | −0.563001 | − | 0.826456i | \(-0.690353\pi\) | ||||
−0.563001 | + | 0.826456i | \(0.690353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.6373 | 0.569855 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.9534 | −1.27040 | −0.635201 | − | 0.772347i | \(-0.719083\pi\) | ||||
−0.635201 | + | 0.772347i | \(0.719083\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.1906 | −0.732871 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.79304 | −0.354997 | −0.177499 | − | 0.984121i | \(-0.556801\pi\) | ||||
−0.177499 | + | 0.984121i | \(0.556801\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −36.9402 | −1.33733 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.910956 | 0.0328927 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.66555 | 0.0600613 | 0.0300306 | − | 0.999549i | \(-0.490440\pi\) | ||||
0.0300306 | + | 0.999549i | \(0.490440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5210 | −0.414919 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.7273 | −1.17712 | −0.588560 | − | 0.808454i | \(-0.700305\pi\) | ||||
−0.588560 | + | 0.808454i | \(0.700305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −28.9179 | −1.03742 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.8345 | 0.818130 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.9967 | 1.39541 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.64849 | 0.201860 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4484 | 0.479382 | 0.239691 | − | 0.970849i | \(-0.422954\pi\) | ||||
0.239691 | + | 0.970849i | \(0.422954\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.41852 | 0.0505005 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −35.7346 | −1.27057 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.46911 | 0.0876808 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.6544 | −0.908727 | −0.454363 | − | 0.890816i | \(-0.650133\pi\) | ||||
−0.454363 | + | 0.890816i | \(0.650133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.70535 | 0.272596 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.68791 | −0.130306 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 50.3936 | 1.77835 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.3982 | 0.929260 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.9915 | −1.05444 | −0.527222 | − | 0.849727i | \(-0.676766\pi\) | ||||
−0.527222 | + | 0.849727i | \(0.676766\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.1133 | 0.390242 | 0.195121 | − | 0.980779i | \(-0.437490\pi\) | ||||
0.195121 | + | 0.980779i | \(0.437490\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.1133 | 0.950907 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.9152 | 1.81628 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.32424 | 0.116158 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.62090 | −0.0565699 | −0.0282850 | − | 0.999600i | \(-0.509005\pi\) | ||||
−0.0282850 | + | 0.999600i | \(0.509005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.5007 | −1.41176 | −0.705882 | − | 0.708329i | \(-0.749449\pi\) | ||||
−0.705882 | + | 0.708329i | \(0.749449\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.95560 | −0.172323 | −0.0861616 | − | 0.996281i | \(-0.527460\pi\) | ||||
−0.0861616 | + | 0.996281i | \(0.527460\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.2588 | −0.912007 | −0.456004 | − | 0.889978i | \(-0.650720\pi\) | ||||
−0.456004 | + | 0.889978i | \(0.650720\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0861 | 0.384572 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.52695 | −0.156849 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.49244 | −0.258977 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.0565 | 1.10671 | 0.553357 | − | 0.832944i | \(-0.313346\pi\) | ||||
0.553357 | + | 0.832944i | \(0.313346\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.90541 | 0.100187 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.17938 | 0.316154 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.4330 | 1.42365 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.8686 | 1.09373 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.2595 | 1.24296 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.5775 | −1.80022 | −0.900110 | − | 0.435662i | \(-0.856514\pi\) | ||||
−0.900110 | + | 0.435662i | \(0.856514\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.5940 | −0.566839 | −0.283419 | − | 0.958996i | \(-0.591469\pi\) | ||||
−0.283419 | + | 0.958996i | \(0.591469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.0742 | 0.923761 | 0.461881 | − | 0.886942i | \(-0.347175\pi\) | ||||
0.461881 | + | 0.886942i | \(0.347175\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.7398 | 0.638650 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.99903 | −0.340371 | −0.170185 | − | 0.985412i | \(-0.554437\pi\) | ||||
−0.170185 | + | 0.985412i | \(0.554437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.7510 | −0.534931 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.8259 | −1.75807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0233 | 0.339628 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.64849 | −0.225017 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.10248 | 0.104763 | 0.0523817 | − | 0.998627i | \(-0.483319\pi\) | ||||
0.0523817 | + | 0.998627i | \(0.483319\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.14061 | 0.308305 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.19121 | 0.275969 | 0.137984 | − | 0.990434i | \(-0.455938\pi\) | ||||
0.137984 | + | 0.990434i | \(0.455938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.1649 | 1.31800 | 0.659002 | − | 0.752141i | \(-0.270979\pi\) | ||||
0.659002 | + | 0.752141i | \(0.270979\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.2543 | −0.713649 | −0.356824 | − | 0.934172i | \(-0.616141\pi\) | ||||
−0.356824 | + | 0.934172i | \(0.616141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.7221 | −1.26516 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.84395 | 0.162279 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.9270 | −0.934543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.16820 | −0.139172 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42.3210 | −1.41148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.6682 | −0.455354 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 42.6058 | 1.41783 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0618 | 0.832163 | 0.416081 | − | 0.909327i | \(-0.363403\pi\) | ||||
0.416081 | + | 0.909327i | \(0.363403\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.6991 | 0.388034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3246 | 0.342068 | 0.171034 | − | 0.985265i | \(-0.445289\pi\) | ||||
0.171034 | + | 0.985265i | \(0.445289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.9612 | 0.428954 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.8804 | −0.920692 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0605 | −0.661734 | −0.330867 | − | 0.943677i | \(-0.607341\pi\) | ||||
−0.330867 | + | 0.943677i | \(0.607341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.40211 | −0.243908 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.05060 | 0.264989 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.1531 | −0.629070 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.8692 | 1.27526 | 0.637629 | − | 0.770344i | \(-0.279915\pi\) | ||||
0.637629 | + | 0.770344i | \(0.279915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.4073 | 0.537729 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.5098 | 0.704200 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.5007 | −1.74779 | −0.873895 | − | 0.486115i | \(-0.838414\pi\) | ||||
−0.873895 | + | 0.486115i | \(0.838414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11.1458 | 0.363731 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.1906 | −0.658193 | −0.329097 | − | 0.944296i | \(-0.606744\pi\) | ||||
−0.329097 | + | 0.944296i | \(0.606744\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.4974 | −0.765181 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.4839 | −1.15307 | −0.576536 | − | 0.817071i | \(-0.695596\pi\) | ||||
−0.576536 | + | 0.817071i | \(0.695596\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4034 | 0.337709 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.0960 | −0.878647 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.02630 | 0.0332450 | 0.0166225 | − | 0.999862i | \(-0.494709\pi\) | ||||
0.0166225 | + | 0.999862i | \(0.494709\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.3610 | 0.884456 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.5959 | 1.05258 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.1367 | 0.810860 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.8673 | −0.414642 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.8465 | −0.541748 | −0.270874 | − | 0.962615i | \(-0.587313\pi\) | ||||
−0.270874 | + | 0.962615i | \(0.587313\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.52695 | −0.145427 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.3153 | 1.64679 | 0.823394 | − | 0.567471i | \(-0.192078\pi\) | ||||
0.823394 | + | 0.567471i | \(0.192078\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.0243 | −1.09077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.2733 | −1.60839 | −0.804193 | − | 0.594368i | \(-0.797402\pi\) | ||||
−0.804193 | + | 0.594368i | \(0.797402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.8640 | −0.570937 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.1124 | −0.354791 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.5319 | 0.973815 | 0.486908 | − | 0.873454i | \(-0.338125\pi\) | ||||
0.486908 | + | 0.873454i | \(0.338125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.9192 | −0.729525 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.4225 | −1.69874 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.8876 | −0.663517 | −0.331759 | − | 0.943364i | \(-0.607642\pi\) | ||||
−0.331759 | + | 0.943364i | \(0.607642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.0670 | 0.319467 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.7727 | 0.467856 | 0.233928 | − | 0.972254i | \(-0.424842\pi\) | ||||
0.233928 | + | 0.972254i | \(0.424842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.69908 | −0.275227 |
(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 | 7800.2.a.bx.1.4 | yes | 4 | |
5.4 | even | 2 | 7800.2.a.bu.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bu.1.1 | ✓ | 4 | 5.4 | even | 2 | ||
7800.2.a.bx.1.4 | yes | 4 | 1.1 | even | 1 | trivial |