Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.10784448.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 11x^{4} - 4x^{3} + 31x^{2} + 22x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.58124\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 2.81361 | 1.62444 | 0.812218 | − | 0.583354i | \(-0.198260\pi\) | ||||
0.812218 | + | 0.583354i | \(0.198260\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.81361 | −1.14865 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.91638 | 1.63879 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 2.81361 | 0.812218 | ||||||||
\(13\) | −0.500855 | −0.138912 | −0.0694560 | − | 0.997585i | \(-0.522126\pi\) | ||||
−0.0694560 | + | 0.997585i | \(0.522126\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 2.81361 | 0.726470 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.39194 | 0.580132 | 0.290066 | − | 0.957007i | \(-0.406323\pi\) | ||||
0.290066 | + | 0.957007i | \(0.406323\pi\) | |||||||
\(18\) | −4.91638 | −1.15880 | ||||||||
\(19\) | 3.43043 | 0.786994 | 0.393497 | − | 0.919326i | \(-0.371265\pi\) | ||||
0.393497 | + | 0.919326i | \(0.371265\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.81361 | −0.613979 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.60363 | 0.751409 | 0.375704 | − | 0.926740i | \(-0.377401\pi\) | ||||
0.375704 | + | 0.926740i | \(0.377401\pi\) | |||||||
\(24\) | −2.81361 | −0.574325 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.500855 | 0.0982257 | ||||||||
\(27\) | 5.39194 | 1.03768 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −4.27139 | −0.793177 | −0.396589 | − | 0.917996i | \(-0.629806\pi\) | ||||
−0.396589 | + | 0.917996i | \(0.629806\pi\) | |||||||
\(30\) | −2.81361 | −0.513692 | ||||||||
\(31\) | 3.10278 | 0.557275 | 0.278637 | − | 0.960396i | \(-0.410117\pi\) | ||||
0.278637 | + | 0.960396i | \(0.410117\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.39194 | −0.410215 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 4.91638 | 0.819397 | ||||||||
\(37\) | −2.27139 | −0.373414 | −0.186707 | − | 0.982416i | \(-0.559782\pi\) | ||||
−0.186707 | + | 0.982416i | \(0.559782\pi\) | |||||||
\(38\) | −3.43043 | −0.556489 | ||||||||
\(39\) | −1.40921 | −0.225654 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −0.0899376 | −0.0140459 | −0.00702295 | − | 0.999975i | \(-0.502235\pi\) | ||||
−0.00702295 | + | 0.999975i | \(0.502235\pi\) | |||||||
\(42\) | 2.81361 | 0.434149 | ||||||||
\(43\) | 3.19923 | 0.487878 | 0.243939 | − | 0.969791i | \(-0.421560\pi\) | ||||
0.243939 | + | 0.969791i | \(0.421560\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.91638 | 0.732891 | ||||||||
\(46\) | −3.60363 | −0.531326 | ||||||||
\(47\) | −1.29720 | −0.189216 | −0.0946078 | − | 0.995515i | \(-0.530160\pi\) | ||||
−0.0946078 | + | 0.995515i | \(0.530160\pi\) | |||||||
\(48\) | 2.81361 | 0.406109 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 6.72999 | 0.942387 | ||||||||
\(52\) | −0.500855 | −0.0694560 | ||||||||
\(53\) | 8.60536 | 1.18204 | 0.591019 | − | 0.806658i | \(-0.298726\pi\) | ||||
0.591019 | + | 0.806658i | \(0.298726\pi\) | |||||||
\(54\) | −5.39194 | −0.733751 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 9.65187 | 1.27842 | ||||||||
\(58\) | 4.27139 | 0.560861 | ||||||||
\(59\) | 5.89109 | 0.766954 | 0.383477 | − | 0.923550i | \(-0.374726\pi\) | ||||
0.383477 | + | 0.923550i | \(0.374726\pi\) | |||||||
\(60\) | 2.81361 | 0.363235 | ||||||||
\(61\) | −9.25687 | −1.18522 | −0.592610 | − | 0.805489i | \(-0.701903\pi\) | ||||
−0.592610 | + | 0.805489i | \(0.701903\pi\) | |||||||
\(62\) | −3.10278 | −0.394053 | ||||||||
\(63\) | −4.91638 | −0.619406 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.500855 | −0.0621234 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.90762 | 0.477391 | 0.238696 | − | 0.971094i | \(-0.423280\pi\) | ||||
0.238696 | + | 0.971094i | \(0.423280\pi\) | |||||||
\(68\) | 2.39194 | 0.290066 | ||||||||
\(69\) | 10.1392 | 1.22062 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 15.5063 | 1.84026 | 0.920131 | − | 0.391610i | \(-0.128082\pi\) | ||||
0.920131 | + | 0.391610i | \(0.128082\pi\) | |||||||
\(72\) | −4.91638 | −0.579401 | ||||||||
\(73\) | −7.66162 | −0.896725 | −0.448363 | − | 0.893852i | \(-0.647993\pi\) | ||||
−0.448363 | + | 0.893852i | \(0.647993\pi\) | |||||||
\(74\) | 2.27139 | 0.264044 | ||||||||
\(75\) | 2.81361 | 0.324887 | ||||||||
\(76\) | 3.43043 | 0.393497 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.40921 | 0.159561 | ||||||||
\(79\) | 10.3606 | 1.16566 | 0.582832 | − | 0.812593i | \(-0.301945\pi\) | ||||
0.582832 | + | 0.812593i | \(0.301945\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0.421663 | 0.0468514 | ||||||||
\(82\) | 0.0899376 | 0.00993194 | ||||||||
\(83\) | −4.19309 | −0.460252 | −0.230126 | − | 0.973161i | \(-0.573914\pi\) | ||||
−0.230126 | + | 0.973161i | \(0.573914\pi\) | |||||||
\(84\) | −2.81361 | −0.306990 | ||||||||
\(85\) | 2.39194 | 0.259443 | ||||||||
\(86\) | −3.19923 | −0.344982 | ||||||||
\(87\) | −12.0180 | −1.28847 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.2856 | −1.72627 | −0.863135 | − | 0.504973i | \(-0.831503\pi\) | ||||
−0.863135 | + | 0.504973i | \(0.831503\pi\) | |||||||
\(90\) | −4.91638 | −0.518232 | ||||||||
\(91\) | 0.500855 | 0.0525038 | ||||||||
\(92\) | 3.60363 | 0.375704 | ||||||||
\(93\) | 8.72999 | 0.905258 | ||||||||
\(94\) | 1.29720 | 0.133796 | ||||||||
\(95\) | 3.43043 | 0.351954 | ||||||||
\(96\) | −2.81361 | −0.287163 | ||||||||
\(97\) | 15.9907 | 1.62360 | 0.811802 | − | 0.583932i | \(-0.198487\pi\) | ||||
0.811802 | + | 0.583932i | \(0.198487\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 10.2349 | 1.01841 | 0.509207 | − | 0.860644i | \(-0.329939\pi\) | ||||
0.509207 | + | 0.860644i | \(0.329939\pi\) | |||||||
\(102\) | −6.72999 | −0.666368 | ||||||||
\(103\) | 2.15822 | 0.212656 | 0.106328 | − | 0.994331i | \(-0.466091\pi\) | ||||
0.106328 | + | 0.994331i | \(0.466091\pi\) | |||||||
\(104\) | 0.500855 | 0.0491128 | ||||||||
\(105\) | −2.81361 | −0.274580 | ||||||||
\(106\) | −8.60536 | −0.835826 | ||||||||
\(107\) | 4.14362 | 0.400579 | 0.200290 | − | 0.979737i | \(-0.435812\pi\) | ||||
0.200290 | + | 0.979737i | \(0.435812\pi\) | |||||||
\(108\) | 5.39194 | 0.518840 | ||||||||
\(109\) | 8.55011 | 0.818952 | 0.409476 | − | 0.912321i | \(-0.365711\pi\) | ||||
0.409476 | + | 0.912321i | \(0.365711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.39079 | −0.606587 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −17.6102 | −1.65663 | −0.828313 | − | 0.560266i | \(-0.810699\pi\) | ||||
−0.828313 | + | 0.560266i | \(0.810699\pi\) | |||||||
\(114\) | −9.65187 | −0.903981 | ||||||||
\(115\) | 3.60363 | 0.336040 | ||||||||
\(116\) | −4.27139 | −0.396589 | ||||||||
\(117\) | −2.46239 | −0.227648 | ||||||||
\(118\) | −5.89109 | −0.542319 | ||||||||
\(119\) | −2.39194 | −0.219269 | ||||||||
\(120\) | −2.81361 | −0.256846 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.25687 | 0.838078 | ||||||||
\(123\) | −0.253049 | −0.0228167 | ||||||||
\(124\) | 3.10278 | 0.278637 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.91638 | 0.437986 | ||||||||
\(127\) | 12.6352 | 1.12120 | 0.560598 | − | 0.828088i | \(-0.310571\pi\) | ||||
0.560598 | + | 0.828088i | \(0.310571\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 9.00138 | 0.792527 | ||||||||
\(130\) | 0.500855 | 0.0439279 | ||||||||
\(131\) | 6.16025 | 0.538224 | 0.269112 | − | 0.963109i | \(-0.413270\pi\) | ||||
0.269112 | + | 0.963109i | \(0.413270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.43043 | −0.297456 | ||||||||
\(134\) | −3.90762 | −0.337567 | ||||||||
\(135\) | 5.39194 | 0.464065 | ||||||||
\(136\) | −2.39194 | −0.205107 | ||||||||
\(137\) | 4.37378 | 0.373677 | 0.186839 | − | 0.982391i | \(-0.440176\pi\) | ||||
0.186839 | + | 0.982391i | \(0.440176\pi\) | |||||||
\(138\) | −10.1392 | −0.863106 | ||||||||
\(139\) | −12.2300 | −1.03734 | −0.518670 | − | 0.854975i | \(-0.673572\pi\) | ||||
−0.518670 | + | 0.854975i | \(0.673572\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | −3.64980 | −0.307369 | ||||||||
\(142\) | −15.5063 | −1.30126 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.91638 | 0.409698 | ||||||||
\(145\) | −4.27139 | −0.354720 | ||||||||
\(146\) | 7.66162 | 0.634080 | ||||||||
\(147\) | 2.81361 | 0.232062 | ||||||||
\(148\) | −2.27139 | −0.186707 | ||||||||
\(149\) | −7.45847 | −0.611021 | −0.305511 | − | 0.952189i | \(-0.598827\pi\) | ||||
−0.305511 | + | 0.952189i | \(0.598827\pi\) | |||||||
\(150\) | −2.81361 | −0.229730 | ||||||||
\(151\) | −8.99272 | −0.731817 | −0.365908 | − | 0.930651i | \(-0.619242\pi\) | ||||
−0.365908 | + | 0.930651i | \(0.619242\pi\) | |||||||
\(152\) | −3.43043 | −0.278244 | ||||||||
\(153\) | 11.7597 | 0.950716 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.10278 | 0.249221 | ||||||||
\(156\) | −1.40921 | −0.112827 | ||||||||
\(157\) | −1.14513 | −0.0913915 | −0.0456958 | − | 0.998955i | \(-0.514550\pi\) | ||||
−0.0456958 | + | 0.998955i | \(0.514550\pi\) | |||||||
\(158\) | −10.3606 | −0.824248 | ||||||||
\(159\) | 24.2121 | 1.92014 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.60363 | −0.284006 | ||||||||
\(162\) | −0.421663 | −0.0331290 | ||||||||
\(163\) | −5.36940 | −0.420564 | −0.210282 | − | 0.977641i | \(-0.567438\pi\) | ||||
−0.210282 | + | 0.977641i | \(0.567438\pi\) | |||||||
\(164\) | −0.0899376 | −0.00702295 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.19309 | 0.325447 | ||||||||
\(167\) | 23.4652 | 1.81579 | 0.907897 | − | 0.419194i | \(-0.137687\pi\) | ||||
0.907897 | + | 0.419194i | \(0.137687\pi\) | |||||||
\(168\) | 2.81361 | 0.217074 | ||||||||
\(169\) | −12.7491 | −0.980703 | ||||||||
\(170\) | −2.39194 | −0.183454 | ||||||||
\(171\) | 16.8653 | 1.28972 | ||||||||
\(172\) | 3.19923 | 0.243939 | ||||||||
\(173\) | −14.0465 | −1.06793 | −0.533966 | − | 0.845506i | \(-0.679299\pi\) | ||||
−0.533966 | + | 0.845506i | \(0.679299\pi\) | |||||||
\(174\) | 12.0180 | 0.911083 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.5752 | 1.24587 | ||||||||
\(178\) | 16.2856 | 1.22066 | ||||||||
\(179\) | −6.46206 | −0.482997 | −0.241499 | − | 0.970401i | \(-0.577639\pi\) | ||||
−0.241499 | + | 0.970401i | \(0.577639\pi\) | |||||||
\(180\) | 4.91638 | 0.366445 | ||||||||
\(181\) | 13.1930 | 0.980629 | 0.490314 | − | 0.871546i | \(-0.336882\pi\) | ||||
0.490314 | + | 0.871546i | \(0.336882\pi\) | |||||||
\(182\) | −0.500855 | −0.0371258 | ||||||||
\(183\) | −26.0452 | −1.92532 | ||||||||
\(184\) | −3.60363 | −0.265663 | ||||||||
\(185\) | −2.27139 | −0.166996 | ||||||||
\(186\) | −8.72999 | −0.640114 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.29720 | −0.0946078 | ||||||||
\(189\) | −5.39194 | −0.392206 | ||||||||
\(190\) | −3.43043 | −0.248869 | ||||||||
\(191\) | −12.3673 | −0.894867 | −0.447434 | − | 0.894317i | \(-0.647662\pi\) | ||||
−0.447434 | + | 0.894317i | \(0.647662\pi\) | |||||||
\(192\) | 2.81361 | 0.203055 | ||||||||
\(193\) | 12.2658 | 0.882909 | 0.441455 | − | 0.897284i | \(-0.354463\pi\) | ||||
0.441455 | + | 0.897284i | \(0.354463\pi\) | |||||||
\(194\) | −15.9907 | −1.14806 | ||||||||
\(195\) | −1.40921 | −0.100915 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 8.65314 | 0.616511 | 0.308255 | − | 0.951304i | \(-0.400255\pi\) | ||||
0.308255 | + | 0.951304i | \(0.400255\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4838 | 0.884954 | 0.442477 | − | 0.896780i | \(-0.354100\pi\) | ||||
0.442477 | + | 0.896780i | \(0.354100\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 10.9945 | 0.775492 | ||||||||
\(202\) | −10.2349 | −0.720128 | ||||||||
\(203\) | 4.27139 | 0.299793 | ||||||||
\(204\) | 6.72999 | 0.471193 | ||||||||
\(205\) | −0.0899376 | −0.00628151 | ||||||||
\(206\) | −2.15822 | −0.150370 | ||||||||
\(207\) | 17.7168 | 1.23140 | ||||||||
\(208\) | −0.500855 | −0.0347280 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.81361 | 0.194157 | ||||||||
\(211\) | −6.76072 | −0.465427 | −0.232714 | − | 0.972545i | \(-0.574761\pi\) | ||||
−0.232714 | + | 0.972545i | \(0.574761\pi\) | |||||||
\(212\) | 8.60536 | 0.591019 | ||||||||
\(213\) | 43.6287 | 2.98939 | ||||||||
\(214\) | −4.14362 | −0.283252 | ||||||||
\(215\) | 3.19923 | 0.218186 | ||||||||
\(216\) | −5.39194 | −0.366875 | ||||||||
\(217\) | −3.10278 | −0.210630 | ||||||||
\(218\) | −8.55011 | −0.579087 | ||||||||
\(219\) | −21.5568 | −1.45667 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.19802 | −0.0805873 | ||||||||
\(222\) | 6.39079 | 0.428922 | ||||||||
\(223\) | −6.14794 | −0.411696 | −0.205848 | − | 0.978584i | \(-0.565995\pi\) | ||||
−0.205848 | + | 0.978584i | \(0.565995\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 4.91638 | 0.327759 | ||||||||
\(226\) | 17.6102 | 1.17141 | ||||||||
\(227\) | 11.2377 | 0.745870 | 0.372935 | − | 0.927858i | \(-0.378351\pi\) | ||||
0.372935 | + | 0.927858i | \(0.378351\pi\) | |||||||
\(228\) | 9.65187 | 0.639211 | ||||||||
\(229\) | −17.2115 | −1.13737 | −0.568685 | − | 0.822555i | \(-0.692548\pi\) | ||||
−0.568685 | + | 0.822555i | \(0.692548\pi\) | |||||||
\(230\) | −3.60363 | −0.237616 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.27139 | 0.280430 | ||||||||
\(233\) | 7.59338 | 0.497459 | 0.248729 | − | 0.968573i | \(-0.419987\pi\) | ||||
0.248729 | + | 0.968573i | \(0.419987\pi\) | |||||||
\(234\) | 2.46239 | 0.160972 | ||||||||
\(235\) | −1.29720 | −0.0846198 | ||||||||
\(236\) | 5.89109 | 0.383477 | ||||||||
\(237\) | 29.1508 | 1.89355 | ||||||||
\(238\) | 2.39194 | 0.155047 | ||||||||
\(239\) | 28.8381 | 1.86538 | 0.932691 | − | 0.360676i | \(-0.117454\pi\) | ||||
0.932691 | + | 0.360676i | \(0.117454\pi\) | |||||||
\(240\) | 2.81361 | 0.181618 | ||||||||
\(241\) | 15.3781 | 0.990589 | 0.495295 | − | 0.868725i | \(-0.335060\pi\) | ||||
0.495295 | + | 0.868725i | \(0.335060\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9894 | −0.961573 | ||||||||
\(244\) | −9.25687 | −0.592610 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0.253049 | 0.0161338 | ||||||||
\(247\) | −1.71815 | −0.109323 | ||||||||
\(248\) | −3.10278 | −0.197026 | ||||||||
\(249\) | −11.7977 | −0.747650 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 9.22254 | 0.582122 | 0.291061 | − | 0.956705i | \(-0.405992\pi\) | ||||
0.291061 | + | 0.956705i | \(0.405992\pi\) | |||||||
\(252\) | −4.91638 | −0.309703 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.6352 | −0.792806 | ||||||||
\(255\) | 6.72999 | 0.421448 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.000868886 0 | 5.41996e−5 0 | 2.70998e−5 | − | 1.00000i | \(-0.499991\pi\) | ||||
2.70998e−5 | 1.00000i | \(0.499991\pi\) | ||||||||
\(258\) | −9.00138 | −0.560401 | ||||||||
\(259\) | 2.27139 | 0.141137 | ||||||||
\(260\) | −0.500855 | −0.0310617 | ||||||||
\(261\) | −20.9998 | −1.29985 | ||||||||
\(262\) | −6.16025 | −0.380582 | ||||||||
\(263\) | 5.23650 | 0.322896 | 0.161448 | − | 0.986881i | \(-0.448384\pi\) | ||||
0.161448 | + | 0.986881i | \(0.448384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.60536 | 0.528623 | ||||||||
\(266\) | 3.43043 | 0.210333 | ||||||||
\(267\) | −45.8213 | −2.80422 | ||||||||
\(268\) | 3.90762 | 0.238696 | ||||||||
\(269\) | −27.8809 | −1.69993 | −0.849963 | − | 0.526842i | \(-0.823376\pi\) | ||||
−0.849963 | + | 0.526842i | \(0.823376\pi\) | |||||||
\(270\) | −5.39194 | −0.328143 | ||||||||
\(271\) | −7.08659 | −0.430479 | −0.215240 | − | 0.976561i | \(-0.569053\pi\) | ||||
−0.215240 | + | 0.976561i | \(0.569053\pi\) | |||||||
\(272\) | 2.39194 | 0.145033 | ||||||||
\(273\) | 1.40921 | 0.0852891 | ||||||||
\(274\) | −4.37378 | −0.264230 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.1392 | 0.610308 | ||||||||
\(277\) | 21.2777 | 1.27846 | 0.639228 | − | 0.769018i | \(-0.279254\pi\) | ||||
0.639228 | + | 0.769018i | \(0.279254\pi\) | |||||||
\(278\) | 12.2300 | 0.733509 | ||||||||
\(279\) | 15.2544 | 0.913259 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 30.4417 | 1.81600 | 0.908001 | − | 0.418969i | \(-0.137608\pi\) | ||||
0.908001 | + | 0.418969i | \(0.137608\pi\) | |||||||
\(282\) | 3.64980 | 0.217343 | ||||||||
\(283\) | 14.8159 | 0.880711 | 0.440356 | − | 0.897823i | \(-0.354852\pi\) | ||||
0.440356 | + | 0.897823i | \(0.354852\pi\) | |||||||
\(284\) | 15.5063 | 0.920131 | ||||||||
\(285\) | 9.65187 | 0.571728 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0899376 | 0.00530885 | ||||||||
\(288\) | −4.91638 | −0.289701 | ||||||||
\(289\) | −11.2786 | −0.663447 | ||||||||
\(290\) | 4.27139 | 0.250825 | ||||||||
\(291\) | 44.9914 | 2.63744 | ||||||||
\(292\) | −7.66162 | −0.448363 | ||||||||
\(293\) | −31.4790 | −1.83902 | −0.919511 | − | 0.393065i | \(-0.871415\pi\) | ||||
−0.919511 | + | 0.393065i | \(0.871415\pi\) | |||||||
\(294\) | −2.81361 | −0.164093 | ||||||||
\(295\) | 5.89109 | 0.342992 | ||||||||
\(296\) | 2.27139 | 0.132022 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.45847 | 0.432057 | ||||||||
\(299\) | −1.80489 | −0.104380 | ||||||||
\(300\) | 2.81361 | 0.162444 | ||||||||
\(301\) | −3.19923 | −0.184401 | ||||||||
\(302\) | 8.99272 | 0.517473 | ||||||||
\(303\) | 28.7971 | 1.65435 | ||||||||
\(304\) | 3.43043 | 0.196748 | ||||||||
\(305\) | −9.25687 | −0.530047 | ||||||||
\(306\) | −11.7597 | −0.672258 | ||||||||
\(307\) | −10.6499 | −0.607823 | −0.303911 | − | 0.952700i | \(-0.598293\pi\) | ||||
−0.303911 | + | 0.952700i | \(0.598293\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.07239 | 0.345446 | ||||||||
\(310\) | −3.10278 | −0.176226 | ||||||||
\(311\) | 0.450689 | 0.0255562 | 0.0127781 | − | 0.999918i | \(-0.495932\pi\) | ||||
0.0127781 | + | 0.999918i | \(0.495932\pi\) | |||||||
\(312\) | 1.40921 | 0.0797807 | ||||||||
\(313\) | −26.5206 | −1.49903 | −0.749517 | − | 0.661985i | \(-0.769714\pi\) | ||||
−0.749517 | + | 0.661985i | \(0.769714\pi\) | |||||||
\(314\) | 1.14513 | 0.0646236 | ||||||||
\(315\) | −4.91638 | −0.277007 | ||||||||
\(316\) | 10.3606 | 0.582832 | ||||||||
\(317\) | 29.2492 | 1.64280 | 0.821399 | − | 0.570354i | \(-0.193194\pi\) | ||||
0.821399 | + | 0.570354i | \(0.193194\pi\) | |||||||
\(318\) | −24.2121 | −1.35775 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 11.6585 | 0.650715 | ||||||||
\(322\) | 3.60363 | 0.200822 | ||||||||
\(323\) | 8.20539 | 0.456560 | ||||||||
\(324\) | 0.421663 | 0.0234257 | ||||||||
\(325\) | −0.500855 | −0.0277824 | ||||||||
\(326\) | 5.36940 | 0.297383 | ||||||||
\(327\) | 24.0567 | 1.33034 | ||||||||
\(328\) | 0.0899376 | 0.00496597 | ||||||||
\(329\) | 1.29720 | 0.0715168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.5049 | −0.907191 | −0.453596 | − | 0.891208i | \(-0.649859\pi\) | ||||
−0.453596 | + | 0.891208i | \(0.649859\pi\) | |||||||
\(332\) | −4.19309 | −0.230126 | ||||||||
\(333\) | −11.1670 | −0.611949 | ||||||||
\(334\) | −23.4652 | −1.28396 | ||||||||
\(335\) | 3.90762 | 0.213496 | ||||||||
\(336\) | −2.81361 | −0.153495 | ||||||||
\(337\) | −26.9655 | −1.46890 | −0.734452 | − | 0.678660i | \(-0.762561\pi\) | ||||
−0.734452 | + | 0.678660i | \(0.762561\pi\) | |||||||
\(338\) | 12.7491 | 0.693462 | ||||||||
\(339\) | −49.5481 | −2.69108 | ||||||||
\(340\) | 2.39194 | 0.129721 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −16.8653 | −0.911970 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.19923 | −0.172491 | ||||||||
\(345\) | 10.1392 | 0.545876 | ||||||||
\(346\) | 14.0465 | 0.755142 | ||||||||
\(347\) | 11.4888 | 0.616751 | 0.308375 | − | 0.951265i | \(-0.400215\pi\) | ||||
0.308375 | + | 0.951265i | \(0.400215\pi\) | |||||||
\(348\) | −12.0180 | −0.644233 | ||||||||
\(349\) | 12.0767 | 0.646452 | 0.323226 | − | 0.946322i | \(-0.395233\pi\) | ||||
0.323226 | + | 0.946322i | \(0.395233\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | −2.70058 | −0.144146 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.27099 | −0.0676477 | −0.0338239 | − | 0.999428i | \(-0.510769\pi\) | ||||
−0.0338239 | + | 0.999428i | \(0.510769\pi\) | |||||||
\(354\) | −16.5752 | −0.880962 | ||||||||
\(355\) | 15.5063 | 0.822990 | ||||||||
\(356\) | −16.2856 | −0.863135 | ||||||||
\(357\) | −6.72999 | −0.356189 | ||||||||
\(358\) | 6.46206 | 0.341530 | ||||||||
\(359\) | 0.866556 | 0.0457351 | 0.0228675 | − | 0.999739i | \(-0.492720\pi\) | ||||
0.0228675 | + | 0.999739i | \(0.492720\pi\) | |||||||
\(360\) | −4.91638 | −0.259116 | ||||||||
\(361\) | −7.23217 | −0.380641 | ||||||||
\(362\) | −13.1930 | −0.693409 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.500855 | 0.0262519 | ||||||||
\(365\) | −7.66162 | −0.401028 | ||||||||
\(366\) | 26.0452 | 1.36140 | ||||||||
\(367\) | 18.3256 | 0.956588 | 0.478294 | − | 0.878200i | \(-0.341255\pi\) | ||||
0.478294 | + | 0.878200i | \(0.341255\pi\) | |||||||
\(368\) | 3.60363 | 0.187852 | ||||||||
\(369\) | −0.442167 | −0.0230183 | ||||||||
\(370\) | 2.27139 | 0.118084 | ||||||||
\(371\) | −8.60536 | −0.446768 | ||||||||
\(372\) | 8.72999 | 0.452629 | ||||||||
\(373\) | 19.1453 | 0.991308 | 0.495654 | − | 0.868520i | \(-0.334928\pi\) | ||||
0.495654 | + | 0.868520i | \(0.334928\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.81361 | 0.145294 | ||||||||
\(376\) | 1.29720 | 0.0668978 | ||||||||
\(377\) | 2.13934 | 0.110182 | ||||||||
\(378\) | 5.39194 | 0.277332 | ||||||||
\(379\) | −6.30548 | −0.323891 | −0.161945 | − | 0.986800i | \(-0.551777\pi\) | ||||
−0.161945 | + | 0.986800i | \(0.551777\pi\) | |||||||
\(380\) | 3.43043 | 0.175977 | ||||||||
\(381\) | 35.5506 | 1.82131 | ||||||||
\(382\) | 12.3673 | 0.632767 | ||||||||
\(383\) | −8.05894 | −0.411792 | −0.205896 | − | 0.978574i | \(-0.566011\pi\) | ||||
−0.205896 | + | 0.978574i | \(0.566011\pi\) | |||||||
\(384\) | −2.81361 | −0.143581 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.2658 | −0.624311 | ||||||||
\(387\) | 15.7286 | 0.799532 | ||||||||
\(388\) | 15.9907 | 0.811802 | ||||||||
\(389\) | 33.7643 | 1.71192 | 0.855958 | − | 0.517046i | \(-0.172968\pi\) | ||||
0.855958 | + | 0.517046i | \(0.172968\pi\) | |||||||
\(390\) | 1.40921 | 0.0713580 | ||||||||
\(391\) | 8.61968 | 0.435916 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 17.3325 | 0.874310 | ||||||||
\(394\) | −8.65314 | −0.435939 | ||||||||
\(395\) | 10.3606 | 0.521300 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.64243 | 0.232997 | 0.116498 | − | 0.993191i | \(-0.462833\pi\) | ||||
0.116498 | + | 0.993191i | \(0.462833\pi\) | |||||||
\(398\) | −12.4838 | −0.625757 | ||||||||
\(399\) | −9.65187 | −0.483198 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 18.2561 | 0.911668 | 0.455834 | − | 0.890065i | \(-0.349341\pi\) | ||||
0.455834 | + | 0.890065i | \(0.349341\pi\) | |||||||
\(402\) | −10.9945 | −0.548356 | ||||||||
\(403\) | −1.55404 | −0.0774122 | ||||||||
\(404\) | 10.2349 | 0.509207 | ||||||||
\(405\) | 0.421663 | 0.0209526 | ||||||||
\(406\) | −4.27139 | −0.211985 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.72999 | −0.333184 | ||||||||
\(409\) | 7.94680 | 0.392944 | 0.196472 | − | 0.980509i | \(-0.437052\pi\) | ||||
0.196472 | + | 0.980509i | \(0.437052\pi\) | |||||||
\(410\) | 0.0899376 | 0.00444170 | ||||||||
\(411\) | 12.3061 | 0.607015 | ||||||||
\(412\) | 2.15822 | 0.106328 | ||||||||
\(413\) | −5.89109 | −0.289882 | ||||||||
\(414\) | −17.7168 | −0.870734 | ||||||||
\(415\) | −4.19309 | −0.205831 | ||||||||
\(416\) | 0.500855 | 0.0245564 | ||||||||
\(417\) | −34.4105 | −1.68509 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.4201 | −1.04644 | −0.523221 | − | 0.852197i | \(-0.675270\pi\) | ||||
−0.523221 | + | 0.852197i | \(0.675270\pi\) | |||||||
\(420\) | −2.81361 | −0.137290 | ||||||||
\(421\) | 0.894942 | 0.0436168 | 0.0218084 | − | 0.999762i | \(-0.493058\pi\) | ||||
0.0218084 | + | 0.999762i | \(0.493058\pi\) | |||||||
\(422\) | 6.76072 | 0.329107 | ||||||||
\(423\) | −6.37751 | −0.310085 | ||||||||
\(424\) | −8.60536 | −0.417913 | ||||||||
\(425\) | 2.39194 | 0.116026 | ||||||||
\(426\) | −43.6287 | −2.11382 | ||||||||
\(427\) | 9.25687 | 0.447971 | ||||||||
\(428\) | 4.14362 | 0.200290 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.19923 | −0.154281 | ||||||||
\(431\) | −37.2082 | −1.79226 | −0.896128 | − | 0.443796i | \(-0.853631\pi\) | ||||
−0.896128 | + | 0.443796i | \(0.853631\pi\) | |||||||
\(432\) | 5.39194 | 0.259420 | ||||||||
\(433\) | 37.0912 | 1.78249 | 0.891245 | − | 0.453522i | \(-0.149833\pi\) | ||||
0.891245 | + | 0.453522i | \(0.149833\pi\) | |||||||
\(434\) | 3.10278 | 0.148938 | ||||||||
\(435\) | −12.0180 | −0.576219 | ||||||||
\(436\) | 8.55011 | 0.409476 | ||||||||
\(437\) | 12.3620 | 0.591354 | ||||||||
\(438\) | 21.5568 | 1.03002 | ||||||||
\(439\) | −16.6322 | −0.793813 | −0.396907 | − | 0.917859i | \(-0.629916\pi\) | ||||
−0.396907 | + | 0.917859i | \(0.629916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.91638 | 0.234113 | ||||||||
\(442\) | 1.19802 | 0.0569838 | ||||||||
\(443\) | 18.9936 | 0.902411 | 0.451206 | − | 0.892420i | \(-0.350994\pi\) | ||||
0.451206 | + | 0.892420i | \(0.350994\pi\) | |||||||
\(444\) | −6.39079 | −0.303294 | ||||||||
\(445\) | −16.2856 | −0.772012 | ||||||||
\(446\) | 6.14794 | 0.291113 | ||||||||
\(447\) | −20.9852 | −0.992565 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −15.0632 | −0.710877 | −0.355439 | − | 0.934700i | \(-0.615669\pi\) | ||||
−0.355439 | + | 0.934700i | \(0.615669\pi\) | |||||||
\(450\) | −4.91638 | −0.231760 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −17.6102 | −0.828313 | ||||||||
\(453\) | −25.3020 | −1.18879 | ||||||||
\(454\) | −11.2377 | −0.527410 | ||||||||
\(455\) | 0.500855 | 0.0234804 | ||||||||
\(456\) | −9.65187 | −0.451990 | ||||||||
\(457\) | −13.0743 | −0.611590 | −0.305795 | − | 0.952097i | \(-0.598922\pi\) | ||||
−0.305795 | + | 0.952097i | \(0.598922\pi\) | |||||||
\(458\) | 17.2115 | 0.804242 | ||||||||
\(459\) | 12.8972 | 0.601991 | ||||||||
\(460\) | 3.60363 | 0.168020 | ||||||||
\(461\) | 40.0901 | 1.86718 | 0.933591 | − | 0.358342i | \(-0.116658\pi\) | ||||
0.933591 | + | 0.358342i | \(0.116658\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.38625 | 0.203846 | 0.101923 | − | 0.994792i | \(-0.467500\pi\) | ||||
0.101923 | + | 0.994792i | \(0.467500\pi\) | |||||||
\(464\) | −4.27139 | −0.198294 | ||||||||
\(465\) | 8.72999 | 0.404844 | ||||||||
\(466\) | −7.59338 | −0.351756 | ||||||||
\(467\) | −2.76704 | −0.128043 | −0.0640217 | − | 0.997949i | \(-0.520393\pi\) | ||||
−0.0640217 | + | 0.997949i | \(0.520393\pi\) | |||||||
\(468\) | −2.46239 | −0.113824 | ||||||||
\(469\) | −3.90762 | −0.180437 | ||||||||
\(470\) | 1.29720 | 0.0598352 | ||||||||
\(471\) | −3.22195 | −0.148460 | ||||||||
\(472\) | −5.89109 | −0.271159 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −29.1508 | −1.33894 | ||||||||
\(475\) | 3.43043 | 0.157399 | ||||||||
\(476\) | −2.39194 | −0.109635 | ||||||||
\(477\) | 42.3072 | 1.93712 | ||||||||
\(478\) | −28.8381 | −1.31902 | ||||||||
\(479\) | 2.13584 | 0.0975889 | 0.0487945 | − | 0.998809i | \(-0.484462\pi\) | ||||
0.0487945 | + | 0.998809i | \(0.484462\pi\) | |||||||
\(480\) | −2.81361 | −0.128423 | ||||||||
\(481\) | 1.13764 | 0.0518717 | ||||||||
\(482\) | −15.3781 | −0.700452 | ||||||||
\(483\) | −10.1392 | −0.461349 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.9907 | 0.726098 | ||||||||
\(486\) | 14.9894 | 0.679935 | ||||||||
\(487\) | −30.0879 | −1.36341 | −0.681707 | − | 0.731625i | \(-0.738762\pi\) | ||||
−0.681707 | + | 0.731625i | \(0.738762\pi\) | |||||||
\(488\) | 9.25687 | 0.419039 | ||||||||
\(489\) | −15.1074 | −0.683179 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | −14.1922 | −0.640484 | −0.320242 | − | 0.947336i | \(-0.603764\pi\) | ||||
−0.320242 | + | 0.947336i | \(0.603764\pi\) | |||||||
\(492\) | −0.253049 | −0.0114083 | ||||||||
\(493\) | −10.2169 | −0.460147 | ||||||||
\(494\) | 1.71815 | 0.0773030 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.10278 | 0.139319 | ||||||||
\(497\) | −15.5063 | −0.695554 | ||||||||
\(498\) | 11.7977 | 0.528668 | ||||||||
\(499\) | 17.9339 | 0.802831 | 0.401416 | − | 0.915896i | \(-0.368518\pi\) | ||||
0.401416 | + | 0.915896i | \(0.368518\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 66.0219 | 2.94964 | ||||||||
\(502\) | −9.22254 | −0.411622 | ||||||||
\(503\) | −4.82298 | −0.215046 | −0.107523 | − | 0.994203i | \(-0.534292\pi\) | ||||
−0.107523 | + | 0.994203i | \(0.534292\pi\) | |||||||
\(504\) | 4.91638 | 0.218993 | ||||||||
\(505\) | 10.2349 | 0.455449 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.8711 | −1.59309 | ||||||||
\(508\) | 12.6352 | 0.560598 | ||||||||
\(509\) | 35.9415 | 1.59308 | 0.796540 | − | 0.604586i | \(-0.206662\pi\) | ||||
0.796540 | + | 0.604586i | \(0.206662\pi\) | |||||||
\(510\) | −6.72999 | −0.298009 | ||||||||
\(511\) | 7.66162 | 0.338930 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 18.4967 | 0.816648 | ||||||||
\(514\) | −0.000868886 0 | −3.83249e−5 0 | ||||||||
\(515\) | 2.15822 | 0.0951026 | ||||||||
\(516\) | 9.00138 | 0.396264 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −2.27139 | −0.0997991 | ||||||||
\(519\) | −39.5212 | −1.73479 | ||||||||
\(520\) | 0.500855 | 0.0219639 | ||||||||
\(521\) | 14.6257 | 0.640766 | 0.320383 | − | 0.947288i | \(-0.396188\pi\) | ||||
0.320383 | + | 0.947288i | \(0.396188\pi\) | |||||||
\(522\) | 20.9998 | 0.919135 | ||||||||
\(523\) | −22.6277 | −0.989439 | −0.494720 | − | 0.869053i | \(-0.664729\pi\) | ||||
−0.494720 | + | 0.869053i | \(0.664729\pi\) | |||||||
\(524\) | 6.16025 | 0.269112 | ||||||||
\(525\) | −2.81361 | −0.122796 | ||||||||
\(526\) | −5.23650 | −0.228322 | ||||||||
\(527\) | 7.42166 | 0.323293 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0139 | −0.435385 | ||||||||
\(530\) | −8.60536 | −0.373793 | ||||||||
\(531\) | 28.9628 | 1.25688 | ||||||||
\(532\) | −3.43043 | −0.148728 | ||||||||
\(533\) | 0.0450457 | 0.00195114 | ||||||||
\(534\) | 45.8213 | 1.98288 | ||||||||
\(535\) | 4.14362 | 0.179144 | ||||||||
\(536\) | −3.90762 | −0.168783 | ||||||||
\(537\) | −18.1817 | −0.784598 | ||||||||
\(538\) | 27.8809 | 1.20203 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.39194 | 0.232032 | ||||||||
\(541\) | 25.8522 | 1.11147 | 0.555737 | − | 0.831358i | \(-0.312436\pi\) | ||||
0.555737 | + | 0.831358i | \(0.312436\pi\) | |||||||
\(542\) | 7.08659 | 0.304395 | ||||||||
\(543\) | 37.1199 | 1.59297 | ||||||||
\(544\) | −2.39194 | −0.102554 | ||||||||
\(545\) | 8.55011 | 0.366247 | ||||||||
\(546\) | −1.40921 | −0.0603085 | ||||||||
\(547\) | 32.9722 | 1.40979 | 0.704896 | − | 0.709311i | \(-0.250994\pi\) | ||||
0.704896 | + | 0.709311i | \(0.250994\pi\) | |||||||
\(548\) | 4.37378 | 0.186839 | ||||||||
\(549\) | −45.5103 | −1.94233 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.6527 | −0.624226 | ||||||||
\(552\) | −10.1392 | −0.431553 | ||||||||
\(553\) | −10.3606 | −0.440579 | ||||||||
\(554\) | −21.2777 | −0.904004 | ||||||||
\(555\) | −6.39079 | −0.271274 | ||||||||
\(556\) | −12.2300 | −0.518670 | ||||||||
\(557\) | −10.6402 | −0.450840 | −0.225420 | − | 0.974262i | \(-0.572375\pi\) | ||||
−0.225420 | + | 0.974262i | \(0.572375\pi\) | |||||||
\(558\) | −15.2544 | −0.645771 | ||||||||
\(559\) | −1.60235 | −0.0677722 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.4417 | −1.28411 | ||||||||
\(563\) | −27.8178 | −1.17238 | −0.586190 | − | 0.810174i | \(-0.699373\pi\) | ||||
−0.586190 | + | 0.810174i | \(0.699373\pi\) | |||||||
\(564\) | −3.64980 | −0.153684 | ||||||||
\(565\) | −17.6102 | −0.740866 | ||||||||
\(566\) | −14.8159 | −0.622757 | ||||||||
\(567\) | −0.421663 | −0.0177082 | ||||||||
\(568\) | −15.5063 | −0.650631 | ||||||||
\(569\) | −23.2943 | −0.976547 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(570\) | −9.65187 | −0.404272 | ||||||||
\(571\) | −22.9549 | −0.960633 | −0.480317 | − | 0.877095i | \(-0.659478\pi\) | ||||
−0.480317 | + | 0.877095i | \(0.659478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34.7968 | −1.45366 | ||||||||
\(574\) | −0.0899376 | −0.00375392 | ||||||||
\(575\) | 3.60363 | 0.150282 | ||||||||
\(576\) | 4.91638 | 0.204849 | ||||||||
\(577\) | −45.7343 | −1.90394 | −0.951972 | − | 0.306184i | \(-0.900948\pi\) | ||||
−0.951972 | + | 0.306184i | \(0.900948\pi\) | |||||||
\(578\) | 11.2786 | 0.469128 | ||||||||
\(579\) | 34.5110 | 1.43423 | ||||||||
\(580\) | −4.27139 | −0.177360 | ||||||||
\(581\) | 4.19309 | 0.173959 | ||||||||
\(582\) | −44.9914 | −1.86495 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.66162 | 0.317040 | ||||||||
\(585\) | −2.46239 | −0.101807 | ||||||||
\(586\) | 31.4790 | 1.30038 | ||||||||
\(587\) | −29.5719 | −1.22056 | −0.610282 | − | 0.792184i | \(-0.708944\pi\) | ||||
−0.610282 | + | 0.792184i | \(0.708944\pi\) | |||||||
\(588\) | 2.81361 | 0.116031 | ||||||||
\(589\) | 10.6438 | 0.438572 | ||||||||
\(590\) | −5.89109 | −0.242532 | ||||||||
\(591\) | 24.3465 | 1.00148 | ||||||||
\(592\) | −2.27139 | −0.0933535 | ||||||||
\(593\) | 30.8187 | 1.26557 | 0.632786 | − | 0.774327i | \(-0.281911\pi\) | ||||
0.632786 | + | 0.774327i | \(0.281911\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.39194 | −0.0980601 | ||||||||
\(596\) | −7.45847 | −0.305511 | ||||||||
\(597\) | 35.1246 | 1.43755 | ||||||||
\(598\) | 1.80489 | 0.0738076 | ||||||||
\(599\) | 0.426966 | 0.0174454 | 0.00872268 | − | 0.999962i | \(-0.497223\pi\) | ||||
0.00872268 | + | 0.999962i | \(0.497223\pi\) | |||||||
\(600\) | −2.81361 | −0.114865 | ||||||||
\(601\) | −34.6294 | −1.41256 | −0.706282 | − | 0.707931i | \(-0.749629\pi\) | ||||
−0.706282 | + | 0.707931i | \(0.749629\pi\) | |||||||
\(602\) | 3.19923 | 0.130391 | ||||||||
\(603\) | 19.2113 | 0.782346 | ||||||||
\(604\) | −8.99272 | −0.365908 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −28.7971 | −1.16980 | ||||||||
\(607\) | −8.77207 | −0.356047 | −0.178024 | − | 0.984026i | \(-0.556970\pi\) | ||||
−0.178024 | + | 0.984026i | \(0.556970\pi\) | |||||||
\(608\) | −3.43043 | −0.139122 | ||||||||
\(609\) | 12.0180 | 0.486994 | ||||||||
\(610\) | 9.25687 | 0.374800 | ||||||||
\(611\) | 0.649707 | 0.0262843 | ||||||||
\(612\) | 11.7597 | 0.475358 | ||||||||
\(613\) | 14.3859 | 0.581043 | 0.290521 | − | 0.956868i | \(-0.406171\pi\) | ||||
0.290521 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(614\) | 10.6499 | 0.429795 | ||||||||
\(615\) | −0.253049 | −0.0102039 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.5656 | −1.15001 | −0.575005 | − | 0.818150i | \(-0.695000\pi\) | ||||
−0.575005 | + | 0.818150i | \(0.695000\pi\) | |||||||
\(618\) | −6.07239 | −0.244267 | ||||||||
\(619\) | 14.5070 | 0.583084 | 0.291542 | − | 0.956558i | \(-0.405832\pi\) | ||||
0.291542 | + | 0.956558i | \(0.405832\pi\) | |||||||
\(620\) | 3.10278 | 0.124610 | ||||||||
\(621\) | 19.4306 | 0.779722 | ||||||||
\(622\) | −0.450689 | −0.0180710 | ||||||||
\(623\) | 16.2856 | 0.652469 | ||||||||
\(624\) | −1.40921 | −0.0564135 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.5206 | 1.05998 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.14513 | −0.0456958 | ||||||||
\(629\) | −5.43303 | −0.216629 | ||||||||
\(630\) | 4.91638 | 0.195873 | ||||||||
\(631\) | −29.3973 | −1.17029 | −0.585143 | − | 0.810930i | \(-0.698962\pi\) | ||||
−0.585143 | + | 0.810930i | \(0.698962\pi\) | |||||||
\(632\) | −10.3606 | −0.412124 | ||||||||
\(633\) | −19.0220 | −0.756057 | ||||||||
\(634\) | −29.2492 | −1.16163 | ||||||||
\(635\) | 12.6352 | 0.501414 | ||||||||
\(636\) | 24.2121 | 0.960072 | ||||||||
\(637\) | −0.500855 | −0.0198446 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 76.2350 | 3.01581 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −21.4821 | −0.848491 | −0.424245 | − | 0.905547i | \(-0.639461\pi\) | ||||
−0.424245 | + | 0.905547i | \(0.639461\pi\) | |||||||
\(642\) | −11.6585 | −0.460125 | ||||||||
\(643\) | 6.62789 | 0.261379 | 0.130689 | − | 0.991423i | \(-0.458281\pi\) | ||||
0.130689 | + | 0.991423i | \(0.458281\pi\) | |||||||
\(644\) | −3.60363 | −0.142003 | ||||||||
\(645\) | 9.00138 | 0.354429 | ||||||||
\(646\) | −8.20539 | −0.322837 | ||||||||
\(647\) | −40.0796 | −1.57569 | −0.787847 | − | 0.615871i | \(-0.788804\pi\) | ||||
−0.787847 | + | 0.615871i | \(0.788804\pi\) | |||||||
\(648\) | −0.421663 | −0.0165645 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.500855 | 0.0196451 | ||||||||
\(651\) | −8.72999 | −0.342155 | ||||||||
\(652\) | −5.36940 | −0.210282 | ||||||||
\(653\) | 1.08840 | 0.0425923 | 0.0212962 | − | 0.999773i | \(-0.493221\pi\) | ||||
0.0212962 | + | 0.999773i | \(0.493221\pi\) | |||||||
\(654\) | −24.0567 | −0.940690 | ||||||||
\(655\) | 6.16025 | 0.240701 | ||||||||
\(656\) | −0.0899376 | −0.00351147 | ||||||||
\(657\) | −37.6675 | −1.46955 | ||||||||
\(658\) | −1.29720 | −0.0505700 | ||||||||
\(659\) | −38.5368 | −1.50118 | −0.750591 | − | 0.660767i | \(-0.770231\pi\) | ||||
−0.750591 | + | 0.660767i | \(0.770231\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.8017 | 0.925777 | 0.462889 | − | 0.886416i | \(-0.346813\pi\) | ||||
0.462889 | + | 0.886416i | \(0.346813\pi\) | |||||||
\(662\) | 16.5049 | 0.641481 | ||||||||
\(663\) | −3.37075 | −0.130909 | ||||||||
\(664\) | 4.19309 | 0.162724 | ||||||||
\(665\) | −3.43043 | −0.133026 | ||||||||
\(666\) | 11.1670 | 0.432713 | ||||||||
\(667\) | −15.3925 | −0.596000 | ||||||||
\(668\) | 23.4652 | 0.907897 | ||||||||
\(669\) | −17.2979 | −0.668775 | ||||||||
\(670\) | −3.90762 | −0.150964 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.81361 | 0.108537 | ||||||||
\(673\) | −9.60964 | −0.370424 | −0.185212 | − | 0.982699i | \(-0.559297\pi\) | ||||
−0.185212 | + | 0.982699i | \(0.559297\pi\) | |||||||
\(674\) | 26.9655 | 1.03867 | ||||||||
\(675\) | 5.39194 | 0.207536 | ||||||||
\(676\) | −12.7491 | −0.490352 | ||||||||
\(677\) | −4.45989 | −0.171407 | −0.0857037 | − | 0.996321i | \(-0.527314\pi\) | ||||
−0.0857037 | + | 0.996321i | \(0.527314\pi\) | |||||||
\(678\) | 49.5481 | 1.90288 | ||||||||
\(679\) | −15.9907 | −0.613665 | ||||||||
\(680\) | −2.39194 | −0.0917268 | ||||||||
\(681\) | 31.6184 | 1.21162 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.0977 | −0.807281 | −0.403641 | − | 0.914918i | \(-0.632255\pi\) | ||||
−0.403641 | + | 0.914918i | \(0.632255\pi\) | |||||||
\(684\) | 16.8653 | 0.644860 | ||||||||
\(685\) | 4.37378 | 0.167114 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −48.4265 | −1.84759 | ||||||||
\(688\) | 3.19923 | 0.121970 | ||||||||
\(689\) | −4.31003 | −0.164199 | ||||||||
\(690\) | −10.1392 | −0.385993 | ||||||||
\(691\) | −36.7936 | −1.39969 | −0.699847 | − | 0.714293i | \(-0.746748\pi\) | ||||
−0.699847 | + | 0.714293i | \(0.746748\pi\) | |||||||
\(692\) | −14.0465 | −0.533966 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.4888 | −0.436109 | ||||||||
\(695\) | −12.2300 | −0.463912 | ||||||||
\(696\) | 12.0180 | 0.455541 | ||||||||
\(697\) | −0.215126 | −0.00814846 | ||||||||
\(698\) | −12.0767 | −0.457110 | ||||||||
\(699\) | 21.3648 | 0.808090 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −38.3577 | −1.44875 | −0.724374 | − | 0.689407i | \(-0.757871\pi\) | ||||
−0.724374 | + | 0.689407i | \(0.757871\pi\) | |||||||
\(702\) | 2.70058 | 0.101927 | ||||||||
\(703\) | −7.79183 | −0.293875 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.64980 | −0.137459 | ||||||||
\(706\) | 1.27099 | 0.0478342 | ||||||||
\(707\) | −10.2349 | −0.384924 | ||||||||
\(708\) | 16.5752 | 0.622934 | ||||||||
\(709\) | −37.3501 | −1.40271 | −0.701357 | − | 0.712811i | \(-0.747422\pi\) | ||||
−0.701357 | + | 0.712811i | \(0.747422\pi\) | |||||||
\(710\) | −15.5063 | −0.581942 | ||||||||
\(711\) | 50.9369 | 1.91028 | ||||||||
\(712\) | 16.2856 | 0.610329 | ||||||||
\(713\) | 11.1813 | 0.418741 | ||||||||
\(714\) | 6.72999 | 0.251863 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.46206 | −0.241499 | ||||||||
\(717\) | 81.1391 | 3.03020 | ||||||||
\(718\) | −0.866556 | −0.0323396 | ||||||||
\(719\) | −33.1232 | −1.23529 | −0.617644 | − | 0.786458i | \(-0.711913\pi\) | ||||
−0.617644 | + | 0.786458i | \(0.711913\pi\) | |||||||
\(720\) | 4.91638 | 0.183223 | ||||||||
\(721\) | −2.15822 | −0.0803764 | ||||||||
\(722\) | 7.23217 | 0.269153 | ||||||||
\(723\) | 43.2679 | 1.60915 | ||||||||
\(724\) | 13.1930 | 0.490314 | ||||||||
\(725\) | −4.27139 | −0.158635 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.85088 | 0.216997 | 0.108498 | − | 0.994097i | \(-0.465396\pi\) | ||||
0.108498 | + | 0.994097i | \(0.465396\pi\) | |||||||
\(728\) | −0.500855 | −0.0185629 | ||||||||
\(729\) | −43.4394 | −1.60887 | ||||||||
\(730\) | 7.66162 | 0.283569 | ||||||||
\(731\) | 7.65238 | 0.283033 | ||||||||
\(732\) | −26.0452 | −0.962658 | ||||||||
\(733\) | 5.37537 | 0.198544 | 0.0992719 | − | 0.995060i | \(-0.468349\pi\) | ||||
0.0992719 | + | 0.995060i | \(0.468349\pi\) | |||||||
\(734\) | −18.3256 | −0.676410 | ||||||||
\(735\) | 2.81361 | 0.103781 | ||||||||
\(736\) | −3.60363 | −0.132832 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.442167 | 0.0162764 | ||||||||
\(739\) | −25.0957 | −0.923159 | −0.461580 | − | 0.887099i | \(-0.652717\pi\) | ||||
−0.461580 | + | 0.887099i | \(0.652717\pi\) | |||||||
\(740\) | −2.27139 | −0.0834979 | ||||||||
\(741\) | −4.83418 | −0.177588 | ||||||||
\(742\) | 8.60536 | 0.315913 | ||||||||
\(743\) | −28.8312 | −1.05772 | −0.528858 | − | 0.848711i | \(-0.677379\pi\) | ||||
−0.528858 | + | 0.848711i | \(0.677379\pi\) | |||||||
\(744\) | −8.72999 | −0.320057 | ||||||||
\(745\) | −7.45847 | −0.273257 | ||||||||
\(746\) | −19.1453 | −0.700960 | ||||||||
\(747\) | −20.6149 | −0.754258 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.14362 | −0.151405 | ||||||||
\(750\) | −2.81361 | −0.102738 | ||||||||
\(751\) | 29.2067 | 1.06577 | 0.532884 | − | 0.846188i | \(-0.321108\pi\) | ||||
0.532884 | + | 0.846188i | \(0.321108\pi\) | |||||||
\(752\) | −1.29720 | −0.0473039 | ||||||||
\(753\) | 25.9486 | 0.945620 | ||||||||
\(754\) | −2.13934 | −0.0779103 | ||||||||
\(755\) | −8.99272 | −0.327278 | ||||||||
\(756\) | −5.39194 | −0.196103 | ||||||||
\(757\) | −9.52403 | −0.346157 | −0.173078 | − | 0.984908i | \(-0.555371\pi\) | ||||
−0.173078 | + | 0.984908i | \(0.555371\pi\) | |||||||
\(758\) | 6.30548 | 0.229025 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.43043 | −0.124435 | ||||||||
\(761\) | −29.0101 | −1.05162 | −0.525808 | − | 0.850604i | \(-0.676237\pi\) | ||||
−0.525808 | + | 0.850604i | \(0.676237\pi\) | |||||||
\(762\) | −35.5506 | −1.28786 | ||||||||
\(763\) | −8.55011 | −0.309535 | ||||||||
\(764\) | −12.3673 | −0.447434 | ||||||||
\(765\) | 11.7597 | 0.425173 | ||||||||
\(766\) | 8.05894 | 0.291181 | ||||||||
\(767\) | −2.95058 | −0.106539 | ||||||||
\(768\) | 2.81361 | 0.101527 | ||||||||
\(769\) | 6.81244 | 0.245663 | 0.122831 | − | 0.992428i | \(-0.460803\pi\) | ||||
0.122831 | + | 0.992428i | \(0.460803\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.00244470 | 8.80438e−5 0 | ||||||||
\(772\) | 12.2658 | 0.441455 | ||||||||
\(773\) | 40.1042 | 1.44245 | 0.721224 | − | 0.692702i | \(-0.243580\pi\) | ||||
0.721224 | + | 0.692702i | \(0.243580\pi\) | |||||||
\(774\) | −15.7286 | −0.565354 | ||||||||
\(775\) | 3.10278 | 0.111455 | ||||||||
\(776\) | −15.9907 | −0.574031 | ||||||||
\(777\) | 6.39079 | 0.229268 | ||||||||
\(778\) | −33.7643 | −1.21051 | ||||||||
\(779\) | −0.308524 | −0.0110540 | ||||||||
\(780\) | −1.40921 | −0.0504577 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.61968 | −0.308239 | ||||||||
\(783\) | −23.0311 | −0.823064 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −1.14513 | −0.0408715 | ||||||||
\(786\) | −17.3325 | −0.618231 | ||||||||
\(787\) | 24.0127 | 0.855962 | 0.427981 | − | 0.903788i | \(-0.359225\pi\) | ||||
0.427981 | + | 0.903788i | \(0.359225\pi\) | |||||||
\(788\) | 8.65314 | 0.308255 | ||||||||
\(789\) | 14.7334 | 0.524525 | ||||||||
\(790\) | −10.3606 | −0.368615 | ||||||||
\(791\) | 17.6102 | 0.626146 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.63635 | 0.164641 | ||||||||
\(794\) | −4.64243 | −0.164754 | ||||||||
\(795\) | 24.2121 | 0.858715 | ||||||||
\(796\) | 12.4838 | 0.442477 | ||||||||
\(797\) | −25.6941 | −0.910133 | −0.455066 | − | 0.890458i | \(-0.650384\pi\) | ||||
−0.455066 | + | 0.890458i | \(0.650384\pi\) | |||||||
\(798\) | 9.65187 | 0.341673 | ||||||||
\(799\) | −3.10282 | −0.109770 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −80.0662 | −2.82900 | ||||||||
\(802\) | −18.2561 | −0.644647 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 10.9945 | 0.387746 | ||||||||
\(805\) | −3.60363 | −0.127011 | ||||||||
\(806\) | 1.55404 | 0.0547387 | ||||||||
\(807\) | −78.4458 | −2.76142 | ||||||||
\(808\) | −10.2349 | −0.360064 | ||||||||
\(809\) | 15.0751 | 0.530013 | 0.265007 | − | 0.964247i | \(-0.414626\pi\) | ||||
0.265007 | + | 0.964247i | \(0.414626\pi\) | |||||||
\(810\) | −0.421663 | −0.0148157 | ||||||||
\(811\) | −32.4904 | −1.14089 | −0.570447 | − | 0.821335i | \(-0.693230\pi\) | ||||
−0.570447 | + | 0.821335i | \(0.693230\pi\) | |||||||
\(812\) | 4.27139 | 0.149896 | ||||||||
\(813\) | −19.9389 | −0.699287 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.36940 | −0.188082 | ||||||||
\(816\) | 6.72999 | 0.235597 | ||||||||
\(817\) | 10.9747 | 0.383957 | ||||||||
\(818\) | −7.94680 | −0.277853 | ||||||||
\(819\) | 2.46239 | 0.0860430 | ||||||||
\(820\) | −0.0899376 | −0.00314076 | ||||||||
\(821\) | 39.6858 | 1.38504 | 0.692521 | − | 0.721398i | \(-0.256500\pi\) | ||||
0.692521 | + | 0.721398i | \(0.256500\pi\) | |||||||
\(822\) | −12.3061 | −0.429225 | ||||||||
\(823\) | 47.5189 | 1.65641 | 0.828203 | − | 0.560429i | \(-0.189364\pi\) | ||||
0.828203 | + | 0.560429i | \(0.189364\pi\) | |||||||
\(824\) | −2.15822 | −0.0751852 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.89109 | 0.204977 | ||||||||
\(827\) | −10.6297 | −0.369630 | −0.184815 | − | 0.982773i | \(-0.559169\pi\) | ||||
−0.184815 | + | 0.982773i | \(0.559169\pi\) | |||||||
\(828\) | 17.7168 | 0.615702 | ||||||||
\(829\) | −4.00818 | −0.139210 | −0.0696050 | − | 0.997575i | \(-0.522174\pi\) | ||||
−0.0696050 | + | 0.997575i | \(0.522174\pi\) | |||||||
\(830\) | 4.19309 | 0.145544 | ||||||||
\(831\) | 59.8672 | 2.07677 | ||||||||
\(832\) | −0.500855 | −0.0173640 | ||||||||
\(833\) | 2.39194 | 0.0828759 | ||||||||
\(834\) | 34.4105 | 1.19154 | ||||||||
\(835\) | 23.4652 | 0.812048 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.7300 | 0.578273 | ||||||||
\(838\) | 21.4201 | 0.739946 | ||||||||
\(839\) | 24.5933 | 0.849055 | 0.424527 | − | 0.905415i | \(-0.360440\pi\) | ||||
0.424527 | + | 0.905415i | \(0.360440\pi\) | |||||||
\(840\) | 2.81361 | 0.0970786 | ||||||||
\(841\) | −10.7552 | −0.370870 | ||||||||
\(842\) | −0.894942 | −0.0308417 | ||||||||
\(843\) | 85.6510 | 2.94998 | ||||||||
\(844\) | −6.76072 | −0.232714 | ||||||||
\(845\) | −12.7491 | −0.438584 | ||||||||
\(846\) | 6.37751 | 0.219263 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.60536 | 0.295509 | ||||||||
\(849\) | 41.6860 | 1.43066 | ||||||||
\(850\) | −2.39194 | −0.0820430 | ||||||||
\(851\) | −8.18524 | −0.280587 | ||||||||
\(852\) | 43.6287 | 1.49469 | ||||||||
\(853\) | −9.44511 | −0.323395 | −0.161697 | − | 0.986840i | \(-0.551697\pi\) | ||||
−0.161697 | + | 0.986840i | \(0.551697\pi\) | |||||||
\(854\) | −9.25687 | −0.316764 | ||||||||
\(855\) | 16.8653 | 0.576781 | ||||||||
\(856\) | −4.14362 | −0.141626 | ||||||||
\(857\) | 5.17154 | 0.176656 | 0.0883282 | − | 0.996091i | \(-0.471848\pi\) | ||||
0.0883282 | + | 0.996091i | \(0.471848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8136 | −1.18782 | −0.593912 | − | 0.804530i | \(-0.702417\pi\) | ||||
−0.593912 | + | 0.804530i | \(0.702417\pi\) | |||||||
\(860\) | 3.19923 | 0.109093 | ||||||||
\(861\) | 0.253049 | 0.00862389 | ||||||||
\(862\) | 37.2082 | 1.26732 | ||||||||
\(863\) | −12.0780 | −0.411140 | −0.205570 | − | 0.978642i | \(-0.565905\pi\) | ||||
−0.205570 | + | 0.978642i | \(0.565905\pi\) | |||||||
\(864\) | −5.39194 | −0.183438 | ||||||||
\(865\) | −14.0465 | −0.477594 | ||||||||
\(866\) | −37.0912 | −1.26041 | ||||||||
\(867\) | −31.7336 | −1.07773 | ||||||||
\(868\) | −3.10278 | −0.105315 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 12.0180 | 0.407449 | ||||||||
\(871\) | −1.95715 | −0.0663154 | ||||||||
\(872\) | −8.55011 | −0.289543 | ||||||||
\(873\) | 78.6161 | 2.66075 | ||||||||
\(874\) | −12.3620 | −0.418151 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −21.5568 | −0.728337 | ||||||||
\(877\) | 22.5704 | 0.762149 | 0.381074 | − | 0.924544i | \(-0.375554\pi\) | ||||
0.381074 | + | 0.924544i | \(0.375554\pi\) | |||||||
\(878\) | 16.6322 | 0.561311 | ||||||||
\(879\) | −88.5695 | −2.98737 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.5330 | 0.893920 | 0.446960 | − | 0.894554i | \(-0.352507\pi\) | ||||
0.446960 | + | 0.894554i | \(0.352507\pi\) | |||||||
\(882\) | −4.91638 | −0.165543 | ||||||||
\(883\) | −19.5994 | −0.659572 | −0.329786 | − | 0.944056i | \(-0.606977\pi\) | ||||
−0.329786 | + | 0.944056i | \(0.606977\pi\) | |||||||
\(884\) | −1.19802 | −0.0402936 | ||||||||
\(885\) | 16.5752 | 0.557169 | ||||||||
\(886\) | −18.9936 | −0.638101 | ||||||||
\(887\) | −16.1610 | −0.542635 | −0.271317 | − | 0.962490i | \(-0.587459\pi\) | ||||
−0.271317 | + | 0.962490i | \(0.587459\pi\) | |||||||
\(888\) | 6.39079 | 0.214461 | ||||||||
\(889\) | −12.6352 | −0.423772 | ||||||||
\(890\) | 16.2856 | 0.545895 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.14794 | −0.205848 | ||||||||
\(893\) | −4.44994 | −0.148912 | ||||||||
\(894\) | 20.9852 | 0.701850 | ||||||||
\(895\) | −6.46206 | −0.216003 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −5.07826 | −0.169558 | ||||||||
\(898\) | 15.0632 | 0.502666 | ||||||||
\(899\) | −13.2532 | −0.442018 | ||||||||
\(900\) | 4.91638 | 0.163879 | ||||||||
\(901\) | 20.5835 | 0.685737 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.00138 | −0.299547 | ||||||||
\(904\) | 17.6102 | 0.585706 | ||||||||
\(905\) | 13.1930 | 0.438551 | ||||||||
\(906\) | 25.3020 | 0.840601 | ||||||||
\(907\) | 49.8041 | 1.65372 | 0.826859 | − | 0.562410i | \(-0.190126\pi\) | ||||
0.826859 | + | 0.562410i | \(0.190126\pi\) | |||||||
\(908\) | 11.2377 | 0.372935 | ||||||||
\(909\) | 50.3189 | 1.66897 | ||||||||
\(910\) | −0.500855 | −0.0166032 | ||||||||
\(911\) | 44.4515 | 1.47274 | 0.736372 | − | 0.676577i | \(-0.236538\pi\) | ||||
0.736372 | + | 0.676577i | \(0.236538\pi\) | |||||||
\(912\) | 9.65187 | 0.319605 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 13.0743 | 0.432459 | ||||||||
\(915\) | −26.0452 | −0.861028 | ||||||||
\(916\) | −17.2115 | −0.568685 | ||||||||
\(917\) | −6.16025 | −0.203429 | ||||||||
\(918\) | −12.8972 | −0.425672 | ||||||||
\(919\) | 25.2876 | 0.834162 | 0.417081 | − | 0.908869i | \(-0.363053\pi\) | ||||
0.417081 | + | 0.908869i | \(0.363053\pi\) | |||||||
\(920\) | −3.60363 | −0.118808 | ||||||||
\(921\) | −29.9647 | −0.987369 | ||||||||
\(922\) | −40.0901 | −1.32030 | ||||||||
\(923\) | −7.76642 | −0.255635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.27139 | −0.0746828 | ||||||||
\(926\) | −4.38625 | −0.144141 | ||||||||
\(927\) | 10.6106 | 0.348499 | ||||||||
\(928\) | 4.27139 | 0.140215 | ||||||||
\(929\) | 58.4872 | 1.91890 | 0.959452 | − | 0.281873i | \(-0.0909558\pi\) | ||||
0.959452 | + | 0.281873i | \(0.0909558\pi\) | |||||||
\(930\) | −8.72999 | −0.286268 | ||||||||
\(931\) | 3.43043 | 0.112428 | ||||||||
\(932\) | 7.59338 | 0.248729 | ||||||||
\(933\) | 1.26806 | 0.0415144 | ||||||||
\(934\) | 2.76704 | 0.0905404 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.46239 | 0.0804858 | ||||||||
\(937\) | −4.14373 | −0.135370 | −0.0676849 | − | 0.997707i | \(-0.521561\pi\) | ||||
−0.0676849 | + | 0.997707i | \(0.521561\pi\) | |||||||
\(938\) | 3.90762 | 0.127588 | ||||||||
\(939\) | −74.6186 | −2.43509 | ||||||||
\(940\) | −1.29720 | −0.0423099 | ||||||||
\(941\) | 5.11048 | 0.166597 | 0.0832985 | − | 0.996525i | \(-0.473455\pi\) | ||||
0.0832985 | + | 0.996525i | \(0.473455\pi\) | |||||||
\(942\) | 3.22195 | 0.104977 | ||||||||
\(943\) | −0.324102 | −0.0105542 | ||||||||
\(944\) | 5.89109 | 0.191739 | ||||||||
\(945\) | −5.39194 | −0.175400 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.4259 | 0.468779 | 0.234389 | − | 0.972143i | \(-0.424691\pi\) | ||||
0.234389 | + | 0.972143i | \(0.424691\pi\) | |||||||
\(948\) | 29.1508 | 0.946773 | ||||||||
\(949\) | 3.83736 | 0.124566 | ||||||||
\(950\) | −3.43043 | −0.111298 | ||||||||
\(951\) | 82.2957 | 2.66862 | ||||||||
\(952\) | 2.39194 | 0.0775233 | ||||||||
\(953\) | −37.3047 | −1.20842 | −0.604208 | − | 0.796827i | \(-0.706510\pi\) | ||||
−0.604208 | + | 0.796827i | \(0.706510\pi\) | |||||||
\(954\) | −42.3072 | −1.36975 | ||||||||
\(955\) | −12.3673 | −0.400197 | ||||||||
\(956\) | 28.8381 | 0.932691 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.13584 | −0.0690058 | ||||||||
\(959\) | −4.37378 | −0.141237 | ||||||||
\(960\) | 2.81361 | 0.0908088 | ||||||||
\(961\) | −21.3728 | −0.689445 | ||||||||
\(962\) | −1.13764 | −0.0366788 | ||||||||
\(963\) | 20.3716 | 0.656467 | ||||||||
\(964\) | 15.3781 | 0.495295 | ||||||||
\(965\) | 12.2658 | 0.394849 | ||||||||
\(966\) | 10.1392 | 0.326223 | ||||||||
\(967\) | 55.7048 | 1.79135 | 0.895673 | − | 0.444712i | \(-0.146694\pi\) | ||||
0.895673 | + | 0.444712i | \(0.146694\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.0867 | 0.741653 | ||||||||
\(970\) | −15.9907 | −0.513429 | ||||||||
\(971\) | 0.975158 | 0.0312943 | 0.0156471 | − | 0.999878i | \(-0.495019\pi\) | ||||
0.0156471 | + | 0.999878i | \(0.495019\pi\) | |||||||
\(972\) | −14.9894 | −0.480786 | ||||||||
\(973\) | 12.2300 | 0.392077 | ||||||||
\(974\) | 30.0879 | 0.964079 | ||||||||
\(975\) | −1.40921 | −0.0451308 | ||||||||
\(976\) | −9.25687 | −0.296305 | ||||||||
\(977\) | 14.8373 | 0.474688 | 0.237344 | − | 0.971426i | \(-0.423723\pi\) | ||||
0.237344 | + | 0.971426i | \(0.423723\pi\) | |||||||
\(978\) | 15.1074 | 0.483080 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 42.0356 | 1.34209 | ||||||||
\(982\) | 14.1922 | 0.452891 | ||||||||
\(983\) | −9.04686 | −0.288550 | −0.144275 | − | 0.989538i | \(-0.546085\pi\) | ||||
−0.144275 | + | 0.989538i | \(0.546085\pi\) | |||||||
\(984\) | 0.253049 | 0.00806691 | ||||||||
\(985\) | 8.65314 | 0.275712 | ||||||||
\(986\) | 10.2169 | 0.325373 | ||||||||
\(987\) | 3.64980 | 0.116174 | ||||||||
\(988\) | −1.71815 | −0.0546615 | ||||||||
\(989\) | 11.5288 | 0.366596 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.7717 | −1.10456 | −0.552280 | − | 0.833659i | \(-0.686242\pi\) | ||||
−0.552280 | + | 0.833659i | \(0.686242\pi\) | |||||||
\(992\) | −3.10278 | −0.0985132 | ||||||||
\(993\) | −46.4383 | −1.47367 | ||||||||
\(994\) | 15.5063 | 0.491831 | ||||||||
\(995\) | 12.4838 | 0.395764 | ||||||||
\(996\) | −11.7977 | −0.373825 | ||||||||
\(997\) | −23.5849 | −0.746942 | −0.373471 | − | 0.927642i | \(-0.621832\pi\) | ||||
−0.373471 | + | 0.927642i | \(0.621832\pi\) | |||||||
\(998\) | −17.9339 | −0.567688 | ||||||||
\(999\) | −12.2472 | −0.387484 |
(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 | 8470.2.a.cz.1.5 | ✓ | 6 | |
11.10 | odd | 2 | 8470.2.a.df.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cz.1.5 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8470.2.a.df.1.6 | yes | 6 | 11.10 | odd | 2 |