Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, 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("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.571993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.24482 | 1.60439 | 0.802195 | − | 0.597062i | \(-0.203665\pi\) | ||||
0.802195 | + | 0.597062i | \(0.203665\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.42801 | 0.430560 | 0.215280 | − | 0.976552i | \(-0.430934\pi\) | ||||
0.215280 | + | 0.976552i | \(0.430934\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.91764 | −1.91861 | −0.959304 | − | 0.282375i | \(-0.908878\pi\) | ||||
−0.959304 | + | 0.282375i | \(0.908878\pi\) | |||||||
\(14\) | 4.24482 | 1.13448 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.10083 | −1.23713 | −0.618567 | − | 0.785732i | \(-0.712286\pi\) | ||||
−0.618567 | + | 0.785732i | \(0.712286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.42801 | 0.304452 | ||||||||
\(23\) | 3.67282 | 0.765837 | 0.382918 | − | 0.923782i | \(-0.374919\pi\) | ||||
0.382918 | + | 0.923782i | \(0.374919\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.91764 | −1.35666 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.24482 | 0.802195 | ||||||||
\(29\) | 8.10083 | 1.50429 | 0.752143 | − | 0.659000i | \(-0.229020\pi\) | ||||
0.752143 | + | 0.659000i | \(0.229020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.28797 | −0.231327 | −0.115663 | − | 0.993288i | \(-0.536899\pi\) | ||||
−0.115663 | + | 0.993288i | \(0.536899\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.10083 | −0.874785 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.856013 | −0.140728 | −0.0703639 | − | 0.997521i | \(-0.522416\pi\) | ||||
−0.0703639 | + | 0.997521i | \(0.522416\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.01847 | −1.25227 | −0.626137 | − | 0.779713i | \(-0.715365\pi\) | ||||
−0.626137 | + | 0.779713i | \(0.715365\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.57199 | 0.544724 | 0.272362 | − | 0.962195i | \(-0.412195\pi\) | ||||
0.272362 | + | 0.962195i | \(0.412195\pi\) | |||||||
\(44\) | 1.42801 | 0.215280 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.67282 | 0.541528 | ||||||||
\(47\) | −3.81681 | −0.556739 | −0.278369 | − | 0.960474i | \(-0.589794\pi\) | ||||
−0.278369 | + | 0.960474i | \(0.589794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0185 | 1.57407 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.91764 | −0.959304 | ||||||||
\(53\) | 9.06163 | 1.24471 | 0.622355 | − | 0.782735i | \(-0.286176\pi\) | ||||
0.622355 | + | 0.782735i | \(0.286176\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.24482 | 0.567238 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.10083 | 1.06369 | ||||||||
\(59\) | 12.3496 | 1.60778 | 0.803891 | − | 0.594777i | \(-0.202760\pi\) | ||||
0.803891 | + | 0.594777i | \(0.202760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.20561 | 1.05062 | 0.525311 | − | 0.850911i | \(-0.323949\pi\) | ||||
0.525311 | + | 0.850911i | \(0.323949\pi\) | |||||||
\(62\) | −1.28797 | −0.163573 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.38880 | 0.536178 | 0.268089 | − | 0.963394i | \(-0.413608\pi\) | ||||
0.268089 | + | 0.963394i | \(0.413608\pi\) | |||||||
\(68\) | −5.10083 | −0.618567 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1008 | 1.31743 | 0.658713 | − | 0.752394i | \(-0.271101\pi\) | ||||
0.658713 | + | 0.752394i | \(0.271101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.38485 | 0.630249 | 0.315125 | − | 0.949050i | \(-0.397954\pi\) | ||||
0.315125 | + | 0.949050i | \(0.397954\pi\) | |||||||
\(74\) | −0.856013 | −0.0995095 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 6.06163 | 0.690787 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.14399 | 0.241217 | 0.120609 | − | 0.992700i | \(-0.461515\pi\) | ||||
0.120609 | + | 0.992700i | \(0.461515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.01847 | −0.885492 | ||||||||
\(83\) | 1.04316 | 0.114501 | 0.0572506 | − | 0.998360i | \(-0.481767\pi\) | ||||
0.0572506 | + | 0.998360i | \(0.481767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.57199 | 0.385178 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.42801 | 0.152226 | ||||||||
\(89\) | 16.7305 | 1.77343 | 0.886715 | − | 0.462317i | \(-0.152982\pi\) | ||||
0.886715 | + | 0.462317i | \(0.152982\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29.3641 | −3.07820 | ||||||||
\(92\) | 3.67282 | 0.382918 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.81681 | −0.393674 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.81286 | 0.691741 | 0.345870 | − | 0.938282i | \(-0.387584\pi\) | ||||
0.345870 | + | 0.938282i | \(0.387584\pi\) | |||||||
\(98\) | 11.0185 | 1.11303 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7737 | 1.17152 | 0.585761 | − | 0.810484i | \(-0.300796\pi\) | ||||
0.585761 | + | 0.810484i | \(0.300796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.32718 | 0.426369 | 0.213185 | − | 0.977012i | \(-0.431616\pi\) | ||||
0.213185 | + | 0.977012i | \(0.431616\pi\) | |||||||
\(104\) | −6.91764 | −0.678330 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.06163 | 0.880143 | ||||||||
\(107\) | −4.14003 | −0.400232 | −0.200116 | − | 0.979772i | \(-0.564132\pi\) | ||||
−0.200116 | + | 0.979772i | \(0.564132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.48963 | −0.238464 | −0.119232 | − | 0.992866i | \(-0.538043\pi\) | ||||
−0.119232 | + | 0.992866i | \(0.538043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.24482 | 0.401098 | ||||||||
\(113\) | 11.0185 | 1.03653 | 0.518265 | − | 0.855220i | \(-0.326578\pi\) | ||||
0.518265 | + | 0.855220i | \(0.326578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.10083 | 0.752143 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.3496 | 1.13687 | ||||||||
\(119\) | −21.6521 | −1.98484 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.96080 | −0.814618 | ||||||||
\(122\) | 8.20561 | 0.742901 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.28797 | −0.115663 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.05767 | 0.537532 | 0.268766 | − | 0.963206i | \(-0.413384\pi\) | ||||
0.268766 | + | 0.963206i | \(0.413384\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.44648 | −0.825343 | −0.412671 | − | 0.910880i | \(-0.635404\pi\) | ||||
−0.412671 | + | 0.910880i | \(0.635404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.24482 | 0.368072 | ||||||||
\(134\) | 4.38880 | 0.379135 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.10083 | −0.437393 | ||||||||
\(137\) | 4.20166 | 0.358972 | 0.179486 | − | 0.983761i | \(-0.442557\pi\) | ||||
0.179486 | + | 0.983761i | \(0.442557\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.40727 | −0.458639 | −0.229320 | − | 0.973351i | \(-0.573650\pi\) | ||||
−0.229320 | + | 0.973351i | \(0.573650\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.1008 | 0.931561 | ||||||||
\(143\) | −9.87844 | −0.826076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.38485 | 0.445653 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.856013 | −0.0703639 | ||||||||
\(149\) | 1.51037 | 0.123734 | 0.0618670 | − | 0.998084i | \(-0.480295\pi\) | ||||
0.0618670 | + | 0.998084i | \(0.480295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4504 | −1.25734 | −0.628669 | − | 0.777673i | \(-0.716400\pi\) | ||||
−0.628669 | + | 0.777673i | \(0.716400\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.06163 | 0.488460 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.16246 | −0.731244 | −0.365622 | − | 0.930763i | \(-0.619144\pi\) | ||||
−0.365622 | + | 0.930763i | \(0.619144\pi\) | |||||||
\(158\) | 2.14399 | 0.170566 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.5905 | 1.22870 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6913 | −0.994059 | −0.497029 | − | 0.867734i | \(-0.665576\pi\) | ||||
−0.497029 | + | 0.867734i | \(0.665576\pi\) | |||||||
\(164\) | −8.01847 | −0.626137 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.04316 | 0.0809646 | ||||||||
\(167\) | 16.3249 | 1.26326 | 0.631630 | − | 0.775270i | \(-0.282386\pi\) | ||||
0.631630 | + | 0.775270i | \(0.282386\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 34.8538 | 2.68106 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.57199 | 0.272362 | ||||||||
\(173\) | 3.32322 | 0.252660 | 0.126330 | − | 0.991988i | \(-0.459680\pi\) | ||||
0.126330 | + | 0.991988i | \(0.459680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.42801 | 0.107640 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.7305 | 1.25400 | ||||||||
\(179\) | −5.54731 | −0.414625 | −0.207313 | − | 0.978275i | \(-0.566472\pi\) | ||||
−0.207313 | + | 0.978275i | \(0.566472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.2840 | −1.28471 | −0.642356 | − | 0.766407i | \(-0.722043\pi\) | ||||
−0.642356 | + | 0.766407i | \(0.722043\pi\) | |||||||
\(182\) | −29.3641 | −2.17661 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.67282 | 0.270764 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.28402 | −0.532660 | ||||||||
\(188\) | −3.81681 | −0.278369 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6336 | 1.63771 | 0.818856 | − | 0.573999i | \(-0.194609\pi\) | ||||
0.818856 | + | 0.573999i | \(0.194609\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.24482 | 0.305549 | 0.152774 | − | 0.988261i | \(-0.451179\pi\) | ||||
0.152774 | + | 0.988261i | \(0.451179\pi\) | |||||||
\(194\) | 6.81286 | 0.489135 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.0185 | 0.787034 | ||||||||
\(197\) | −5.00395 | −0.356517 | −0.178258 | − | 0.983984i | \(-0.557046\pi\) | ||||
−0.178258 | + | 0.983984i | \(0.557046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −27.3826 | −1.94110 | −0.970550 | − | 0.240899i | \(-0.922558\pi\) | ||||
−0.970550 | + | 0.240899i | \(0.922558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.7737 | 0.828391 | ||||||||
\(203\) | 34.3865 | 2.41346 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.32718 | 0.301489 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.91764 | −0.479652 | ||||||||
\(209\) | 1.42801 | 0.0987773 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.14003 | −0.353855 | −0.176927 | − | 0.984224i | \(-0.556616\pi\) | ||||
−0.176927 | + | 0.984224i | \(0.556616\pi\) | |||||||
\(212\) | 9.06163 | 0.622355 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.14003 | −0.283007 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.46721 | −0.371138 | ||||||||
\(218\) | −2.48963 | −0.168619 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 35.2857 | 2.37357 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1625 | 0.680528 | 0.340264 | − | 0.940330i | \(-0.389483\pi\) | ||||
0.340264 | + | 0.940330i | \(0.389483\pi\) | |||||||
\(224\) | 4.24482 | 0.283619 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.0185 | 0.732938 | ||||||||
\(227\) | −7.92159 | −0.525775 | −0.262887 | − | 0.964827i | \(-0.584675\pi\) | ||||
−0.262887 | + | 0.964827i | \(0.584675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.44648 | −0.492077 | −0.246039 | − | 0.969260i | \(-0.579129\pi\) | ||||
−0.246039 | + | 0.969260i | \(0.579129\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.10083 | 0.531846 | ||||||||
\(233\) | −28.4834 | −1.86601 | −0.933005 | − | 0.359862i | \(-0.882824\pi\) | ||||
−0.933005 | + | 0.359862i | \(0.882824\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.3496 | 0.803891 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −21.6521 | −1.40350 | ||||||||
\(239\) | 3.24086 | 0.209634 | 0.104817 | − | 0.994492i | \(-0.466574\pi\) | ||||
0.104817 | + | 0.994492i | \(0.466574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.9938 | 1.67441 | 0.837203 | − | 0.546892i | \(-0.184189\pi\) | ||||
0.837203 | + | 0.546892i | \(0.184189\pi\) | |||||||
\(242\) | −8.96080 | −0.576022 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.20561 | 0.525311 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.91764 | −0.440159 | ||||||||
\(248\) | −1.28797 | −0.0817864 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.98153 | 0.251312 | 0.125656 | − | 0.992074i | \(-0.459896\pi\) | ||||
0.125656 | + | 0.992074i | \(0.459896\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.24482 | 0.329739 | ||||||||
\(254\) | 6.05767 | 0.380092 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.1625 | −0.883430 | −0.441715 | − | 0.897155i | \(-0.645630\pi\) | ||||
−0.441715 | + | 0.897155i | \(0.645630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.63362 | −0.225782 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.44648 | −0.583605 | ||||||||
\(263\) | −21.3434 | −1.31609 | −0.658045 | − | 0.752979i | \(-0.728616\pi\) | ||||
−0.658045 | + | 0.752979i | \(0.728616\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.24482 | 0.260266 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.38880 | 0.268089 | ||||||||
\(269\) | 24.4112 | 1.48838 | 0.744189 | − | 0.667969i | \(-0.232836\pi\) | ||||
0.744189 | + | 0.667969i | \(0.232836\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.8129 | −0.899817 | −0.449909 | − | 0.893075i | \(-0.648543\pi\) | ||||
−0.449909 | + | 0.893075i | \(0.648543\pi\) | |||||||
\(272\) | −5.10083 | −0.309283 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.20166 | 0.253832 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.2633 | 0.917082 | 0.458541 | − | 0.888673i | \(-0.348372\pi\) | ||||
0.458541 | + | 0.888673i | \(0.348372\pi\) | |||||||
\(278\) | −5.40727 | −0.324307 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.83528 | −0.169139 | −0.0845694 | − | 0.996418i | \(-0.526951\pi\) | ||||
−0.0845694 | + | 0.996418i | \(0.526951\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.942326 | 0.0560154 | 0.0280077 | − | 0.999608i | \(-0.491084\pi\) | ||||
0.0280077 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(284\) | 11.1008 | 0.658713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.87844 | −0.584124 | ||||||||
\(287\) | −34.0369 | −2.00914 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.01847 | 0.530498 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.38485 | 0.315125 | ||||||||
\(293\) | −13.5513 | −0.791673 | −0.395837 | − | 0.918321i | \(-0.629545\pi\) | ||||
−0.395837 | + | 0.918321i | \(0.629545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.856013 | −0.0497548 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.51037 | 0.0874932 | ||||||||
\(299\) | −25.4073 | −1.46934 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.1625 | 0.873950 | ||||||||
\(302\) | −15.4504 | −0.889072 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.7921 | −1.52911 | −0.764554 | − | 0.644560i | \(-0.777041\pi\) | ||||
−0.764554 | + | 0.644560i | \(0.777041\pi\) | |||||||
\(308\) | 6.06163 | 0.345393 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.03920 | 0.285747 | 0.142873 | − | 0.989741i | \(-0.454366\pi\) | ||||
0.142873 | + | 0.989741i | \(0.454366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0185 | −0.848894 | −0.424447 | − | 0.905453i | \(-0.639532\pi\) | ||||
−0.424447 | + | 0.905453i | \(0.639532\pi\) | |||||||
\(314\) | −9.16246 | −0.517067 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.14399 | 0.120609 | ||||||||
\(317\) | −20.1008 | −1.12898 | −0.564488 | − | 0.825442i | \(-0.690926\pi\) | ||||
−0.564488 | + | 0.825442i | \(0.690926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.5680 | 0.647686 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.5905 | 0.868823 | ||||||||
\(323\) | −5.10083 | −0.283818 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.6913 | −0.702906 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.01847 | −0.442746 | ||||||||
\(329\) | −16.2017 | −0.893226 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.5697 | −1.40544 | −0.702720 | − | 0.711467i | \(-0.748031\pi\) | ||||
−0.702720 | + | 0.711467i | \(0.748031\pi\) | |||||||
\(332\) | 1.04316 | 0.0572506 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.3249 | 0.893260 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.9137 | −0.757927 | −0.378963 | − | 0.925412i | \(-0.623719\pi\) | ||||
−0.378963 | + | 0.925412i | \(0.623719\pi\) | |||||||
\(338\) | 34.8538 | 1.89579 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.83923 | −0.0996001 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0577 | 0.921028 | ||||||||
\(344\) | 3.57199 | 0.192589 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.32322 | 0.178658 | ||||||||
\(347\) | −2.56804 | −0.137860 | −0.0689298 | − | 0.997622i | \(-0.521958\pi\) | ||||
−0.0689298 | + | 0.997622i | \(0.521958\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.23691 | −0.280325 | −0.140163 | − | 0.990128i | \(-0.544763\pi\) | ||||
−0.140163 | + | 0.990128i | \(0.544763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.42801 | 0.0761130 | ||||||||
\(353\) | −12.2818 | −0.653692 | −0.326846 | − | 0.945078i | \(-0.605986\pi\) | ||||
−0.326846 | + | 0.945078i | \(0.605986\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.7305 | 0.886715 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.54731 | −0.293184 | ||||||||
\(359\) | 33.7753 | 1.78259 | 0.891297 | − | 0.453419i | \(-0.149796\pi\) | ||||
0.891297 | + | 0.453419i | \(0.149796\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −17.2840 | −0.908428 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −29.3641 | −1.53910 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.3681 | −1.58520 | −0.792600 | − | 0.609742i | \(-0.791273\pi\) | ||||
−0.792600 | + | 0.609742i | \(0.791273\pi\) | |||||||
\(368\) | 3.67282 | 0.191459 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 38.4649 | 1.99700 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.7322 | 1.33236 | 0.666181 | − | 0.745790i | \(-0.267928\pi\) | ||||
0.666181 | + | 0.745790i | \(0.267928\pi\) | |||||||
\(374\) | −7.28402 | −0.376648 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.81681 | −0.196837 | ||||||||
\(377\) | −56.0386 | −2.88614 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.2593 | 1.91388 | 0.956942 | − | 0.290280i | \(-0.0937485\pi\) | ||||
0.956942 | + | 0.290280i | \(0.0937485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.6336 | 1.15804 | ||||||||
\(383\) | 31.9154 | 1.63080 | 0.815400 | − | 0.578898i | \(-0.196517\pi\) | ||||
0.815400 | + | 0.578898i | \(0.196517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.24482 | 0.216055 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.81286 | 0.345870 | ||||||||
\(389\) | −4.48963 | −0.227633 | −0.113817 | − | 0.993502i | \(-0.536308\pi\) | ||||
−0.113817 | + | 0.993502i | \(0.536308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.7345 | −0.947442 | ||||||||
\(392\) | 11.0185 | 0.556517 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.00395 | −0.252096 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.6873 | −1.74091 | −0.870454 | − | 0.492250i | \(-0.836175\pi\) | ||||
−0.870454 | + | 0.492250i | \(0.836175\pi\) | |||||||
\(398\) | −27.3826 | −1.37257 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.03694 | −0.351408 | −0.175704 | − | 0.984443i | \(-0.556220\pi\) | ||||
−0.175704 | + | 0.984443i | \(0.556220\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.90973 | 0.443826 | ||||||||
\(404\) | 11.7737 | 0.585761 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.3865 | 1.70658 | ||||||||
\(407\) | −1.22239 | −0.0605918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4112 | 1.30595 | 0.652976 | − | 0.757379i | \(-0.273520\pi\) | ||||
0.652976 | + | 0.757379i | \(0.273520\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.32718 | 0.213185 | ||||||||
\(413\) | 52.4218 | 2.57951 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.91764 | −0.339165 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.42801 | 0.0698461 | ||||||||
\(419\) | −16.4896 | −0.805571 | −0.402786 | − | 0.915294i | \(-0.631958\pi\) | ||||
−0.402786 | + | 0.915294i | \(0.631958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 39.0162 | 1.90153 | 0.950767 | − | 0.309907i | \(-0.100298\pi\) | ||||
0.950767 | + | 0.309907i | \(0.100298\pi\) | |||||||
\(422\) | −5.14003 | −0.250213 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.06163 | 0.440072 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.8313 | 1.68561 | ||||||||
\(428\) | −4.14003 | −0.200116 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −39.8722 | −1.92058 | −0.960289 | − | 0.279008i | \(-0.909994\pi\) | ||||
−0.960289 | + | 0.279008i | \(0.909994\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.3681 | −1.45940 | −0.729698 | − | 0.683769i | \(-0.760339\pi\) | ||||
−0.729698 | + | 0.683769i | \(0.760339\pi\) | |||||||
\(434\) | −5.46721 | −0.262434 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.48963 | −0.119232 | ||||||||
\(437\) | 3.67282 | 0.175695 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.4033 | 0.926070 | 0.463035 | − | 0.886340i | \(-0.346760\pi\) | ||||
0.463035 | + | 0.886340i | \(0.346760\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.2857 | 1.67837 | ||||||||
\(443\) | 20.8705 | 0.991589 | 0.495794 | − | 0.868440i | \(-0.334877\pi\) | ||||
0.495794 | + | 0.868440i | \(0.334877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.1625 | 0.481206 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.24482 | 0.200549 | ||||||||
\(449\) | −30.7753 | −1.45238 | −0.726189 | − | 0.687495i | \(-0.758710\pi\) | ||||
−0.726189 | + | 0.687495i | \(0.758710\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.4504 | −0.539180 | ||||||||
\(452\) | 11.0185 | 0.518265 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.92159 | −0.371779 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.5658 | 1.28947 | 0.644736 | − | 0.764405i | \(-0.276967\pi\) | ||||
0.644736 | + | 0.764405i | \(0.276967\pi\) | |||||||
\(458\) | −7.44648 | −0.347951 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.3042 | 1.45798 | 0.728991 | − | 0.684524i | \(-0.239990\pi\) | ||||
0.728991 | + | 0.684524i | \(0.239990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.1440 | 0.517905 | 0.258952 | − | 0.965890i | \(-0.416623\pi\) | ||||
0.258952 | + | 0.965890i | \(0.416623\pi\) | |||||||
\(464\) | 8.10083 | 0.376072 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.4834 | −1.31947 | ||||||||
\(467\) | −36.3289 | −1.68110 | −0.840550 | − | 0.541734i | \(-0.817768\pi\) | ||||
−0.840550 | + | 0.541734i | \(0.817768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.6297 | 0.860238 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.3496 | 0.568436 | ||||||||
\(473\) | 5.10083 | 0.234536 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −21.6521 | −0.992422 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.24086 | 0.148234 | ||||||||
\(479\) | 17.0185 | 0.777594 | 0.388797 | − | 0.921323i | \(-0.372891\pi\) | ||||
0.388797 | + | 0.921323i | \(0.372891\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.92159 | 0.270001 | ||||||||
\(482\) | 25.9938 | 1.18398 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.96080 | −0.407309 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −27.3536 | −1.23951 | −0.619754 | − | 0.784796i | \(-0.712768\pi\) | ||||
−0.619754 | + | 0.784796i | \(0.712768\pi\) | |||||||
\(488\) | 8.20561 | 0.371451 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.7697 | 0.576289 | 0.288144 | − | 0.957587i | \(-0.406962\pi\) | ||||
0.288144 | + | 0.957587i | \(0.406962\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −41.3210 | −1.86100 | ||||||||
\(494\) | −6.91764 | −0.311239 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.28797 | −0.0578317 | ||||||||
\(497\) | 47.1210 | 2.11367 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.8969 | −1.51743 | −0.758717 | − | 0.651420i | \(-0.774173\pi\) | ||||
−0.758717 | + | 0.651420i | \(0.774173\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.98153 | 0.177704 | ||||||||
\(503\) | −35.6706 | −1.59047 | −0.795236 | − | 0.606300i | \(-0.792653\pi\) | ||||
−0.795236 | + | 0.606300i | \(0.792653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.24482 | 0.233161 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.05767 | 0.268766 | ||||||||
\(509\) | 24.2347 | 1.07418 | 0.537091 | − | 0.843524i | \(-0.319523\pi\) | ||||
0.537091 | + | 0.843524i | \(0.319523\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.8577 | 1.01117 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.1625 | −0.624679 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.45043 | −0.239710 | ||||||||
\(518\) | −3.63362 | −0.159652 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4689 | 1.51011 | 0.755055 | − | 0.655661i | \(-0.227610\pi\) | ||||
0.755055 | + | 0.655661i | \(0.227610\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.3905 | 1.54752 | 0.773759 | − | 0.633480i | \(-0.218374\pi\) | ||||
0.773759 | + | 0.633480i | \(0.218374\pi\) | |||||||
\(524\) | −9.44648 | −0.412671 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −21.3434 | −0.930616 | ||||||||
\(527\) | 6.56973 | 0.286182 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.51037 | −0.413494 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.24482 | 0.184036 | ||||||||
\(533\) | 55.4689 | 2.40262 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.38880 | 0.189567 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 24.4112 | 1.05244 | ||||||||
\(539\) | 15.7345 | 0.677731 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.6560 | −0.931066 | −0.465533 | − | 0.885031i | \(-0.654137\pi\) | ||||
−0.465533 | + | 0.885031i | \(0.654137\pi\) | |||||||
\(542\) | −14.8129 | −0.636267 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.10083 | −0.218696 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.21844 | −0.137611 | −0.0688053 | − | 0.997630i | \(-0.521919\pi\) | ||||
−0.0688053 | + | 0.997630i | \(0.521919\pi\) | |||||||
\(548\) | 4.20166 | 0.179486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.10083 | 0.345107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.10083 | 0.387007 | ||||||||
\(554\) | 15.2633 | 0.648475 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.40727 | −0.229320 | ||||||||
\(557\) | 40.3865 | 1.71123 | 0.855616 | − | 0.517611i | \(-0.173178\pi\) | ||||
0.855616 | + | 0.517611i | \(0.173178\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.7098 | −1.04511 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.83528 | −0.119599 | ||||||||
\(563\) | 9.65831 | 0.407049 | 0.203525 | − | 0.979070i | \(-0.434760\pi\) | ||||
0.203525 | + | 0.979070i | \(0.434760\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.942326 | 0.0396089 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1008 | 0.465780 | ||||||||
\(569\) | 18.6992 | 0.783911 | 0.391956 | − | 0.919984i | \(-0.371799\pi\) | ||||
0.391956 | + | 0.919984i | \(0.371799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.34169 | 0.181694 | 0.0908471 | − | 0.995865i | \(-0.471043\pi\) | ||||
0.0908471 | + | 0.995865i | \(0.471043\pi\) | |||||||
\(572\) | −9.87844 | −0.413038 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −34.0369 | −1.42067 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.03694 | 0.126430 | 0.0632148 | − | 0.998000i | \(-0.479865\pi\) | ||||
0.0632148 | + | 0.998000i | \(0.479865\pi\) | |||||||
\(578\) | 9.01847 | 0.375119 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.42801 | 0.183705 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.9401 | 0.535923 | ||||||||
\(584\) | 5.38485 | 0.222827 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5513 | −0.559797 | ||||||||
\(587\) | −33.7345 | −1.39237 | −0.696185 | − | 0.717863i | \(-0.745121\pi\) | ||||
−0.696185 | + | 0.717863i | \(0.745121\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.28797 | −0.0530700 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.856013 | −0.0351819 | ||||||||
\(593\) | 34.7361 | 1.42644 | 0.713221 | − | 0.700939i | \(-0.247236\pi\) | ||||
0.713221 | + | 0.700939i | \(0.247236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.51037 | 0.0618670 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −25.4073 | −1.03898 | ||||||||
\(599\) | −6.28176 | −0.256666 | −0.128333 | − | 0.991731i | \(-0.540963\pi\) | ||||
−0.128333 | + | 0.991731i | \(0.540963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4544 | 0.752770 | 0.376385 | − | 0.926463i | \(-0.377167\pi\) | ||||
0.376385 | + | 0.926463i | \(0.377167\pi\) | |||||||
\(602\) | 15.1625 | 0.617976 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.4504 | −0.628669 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20.5367 | −0.833561 | −0.416780 | − | 0.909007i | \(-0.636842\pi\) | ||||
−0.416780 | + | 0.909007i | \(0.636842\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.4033 | 1.06816 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.9216 | −0.481509 | −0.240754 | − | 0.970586i | \(-0.577395\pi\) | ||||
−0.240754 | + | 0.970586i | \(0.577395\pi\) | |||||||
\(614\) | −26.7921 | −1.08124 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.06163 | 0.244230 | ||||||||
\(617\) | 17.5473 | 0.706428 | 0.353214 | − | 0.935543i | \(-0.385089\pi\) | ||||
0.353214 | + | 0.935543i | \(0.385089\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.7322 | −1.35581 | −0.677906 | − | 0.735149i | \(-0.737112\pi\) | ||||
−0.677906 | + | 0.735149i | \(0.737112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5.03920 | 0.202054 | ||||||||
\(623\) | 71.0179 | 2.84527 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.0185 | −0.600259 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.16246 | −0.365622 | ||||||||
\(629\) | 4.36638 | 0.174099 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.4033 | 0.891862 | 0.445931 | − | 0.895067i | \(-0.352873\pi\) | ||||
0.445931 | + | 0.895067i | \(0.352873\pi\) | |||||||
\(632\) | 2.14399 | 0.0852832 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −20.1008 | −0.798306 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −76.2218 | −3.02002 | ||||||||
\(638\) | 11.5680 | 0.457983 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.2778 | −0.998413 | −0.499207 | − | 0.866483i | \(-0.666375\pi\) | ||||
−0.499207 | + | 0.866483i | \(0.666375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.4320 | −0.529705 | −0.264852 | − | 0.964289i | \(-0.585323\pi\) | ||||
−0.264852 | + | 0.964289i | \(0.585323\pi\) | |||||||
\(644\) | 15.5905 | 0.614350 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.10083 | −0.200689 | ||||||||
\(647\) | 5.95289 | 0.234032 | 0.117016 | − | 0.993130i | \(-0.462667\pi\) | ||||
0.117016 | + | 0.993130i | \(0.462667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.6353 | 0.692247 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.6913 | −0.497029 | ||||||||
\(653\) | 35.3826 | 1.38463 | 0.692314 | − | 0.721597i | \(-0.256591\pi\) | ||||
0.692314 | + | 0.721597i | \(0.256591\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.01847 | −0.313069 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.2017 | −0.631606 | ||||||||
\(659\) | 46.2218 | 1.80055 | 0.900273 | − | 0.435325i | \(-0.143367\pi\) | ||||
0.900273 | + | 0.435325i | \(0.143367\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.5843 | −1.46186 | −0.730929 | − | 0.682454i | \(-0.760913\pi\) | ||||
−0.730929 | + | 0.682454i | \(0.760913\pi\) | |||||||
\(662\) | −25.5697 | −0.993796 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.04316 | 0.0404823 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29.7529 | 1.15204 | ||||||||
\(668\) | 16.3249 | 0.631630 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.7177 | 0.452356 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.4257 | −1.67394 | −0.836970 | − | 0.547249i | \(-0.815675\pi\) | ||||
−0.836970 | + | 0.547249i | \(0.815675\pi\) | |||||||
\(674\) | −13.9137 | −0.535935 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.8538 | 1.34053 | ||||||||
\(677\) | 25.2218 | 0.969353 | 0.484677 | − | 0.874693i | \(-0.338937\pi\) | ||||
0.484677 | + | 0.874693i | \(0.338937\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.9193 | 1.10982 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.83923 | −0.0704279 | ||||||||
\(683\) | −18.0616 | −0.691109 | −0.345554 | − | 0.938399i | \(-0.612309\pi\) | ||||
−0.345554 | + | 0.938399i | \(0.612309\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 17.0577 | 0.651265 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.57199 | 0.136181 | ||||||||
\(689\) | −62.6851 | −2.38811 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.36243 | −0.356163 | −0.178082 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178082 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(692\) | 3.32322 | 0.126330 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.56804 | −0.0974815 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.9009 | 1.54923 | ||||||||
\(698\) | −5.23691 | −0.198220 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −52.5714 | −1.98560 | −0.992798 | − | 0.119803i | \(-0.961774\pi\) | ||||
−0.992798 | + | 0.119803i | \(0.961774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.856013 | −0.0322852 | ||||||||
\(704\) | 1.42801 | 0.0538200 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.2818 | −0.462230 | ||||||||
\(707\) | 49.9770 | 1.87958 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.3025 | 0.537141 | 0.268571 | − | 0.963260i | \(-0.413449\pi\) | ||||
0.268571 | + | 0.963260i | \(0.413449\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 16.7305 | 0.627002 | ||||||||
\(713\) | −4.73050 | −0.177159 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.54731 | −0.207313 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.7753 | 1.26048 | ||||||||
\(719\) | 50.6706 | 1.88969 | 0.944847 | − | 0.327513i | \(-0.106211\pi\) | ||||
0.944847 | + | 0.327513i | \(0.106211\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.3681 | 0.684063 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.2840 | −0.642356 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −43.0083 | −1.59509 | −0.797545 | − | 0.603260i | \(-0.793868\pi\) | ||||
−0.797545 | + | 0.603260i | \(0.793868\pi\) | |||||||
\(728\) | −29.3641 | −1.08831 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.2201 | −0.673896 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.77592 | −0.0655949 | −0.0327975 | − | 0.999462i | \(-0.510442\pi\) | ||||
−0.0327975 | + | 0.999462i | \(0.510442\pi\) | |||||||
\(734\) | −30.3681 | −1.12091 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.67282 | 0.135382 | ||||||||
\(737\) | 6.26724 | 0.230857 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.43196 | 0.199818 | 0.0999089 | − | 0.994997i | \(-0.468145\pi\) | ||||
0.0999089 | + | 0.994997i | \(0.468145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 38.4649 | 1.41209 | ||||||||
\(743\) | −0.769701 | −0.0282376 | −0.0141188 | − | 0.999900i | \(-0.504494\pi\) | ||||
−0.0141188 | + | 0.999900i | \(0.504494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 25.7322 | 0.942122 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.28402 | −0.266330 | ||||||||
\(749\) | −17.5737 | −0.642128 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.6683 | 1.55699 | 0.778494 | − | 0.627652i | \(-0.215984\pi\) | ||||
0.778494 | + | 0.627652i | \(0.215984\pi\) | |||||||
\(752\) | −3.81681 | −0.139185 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −56.0386 | −2.04081 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.2448 | −1.42638 | −0.713189 | − | 0.700972i | \(-0.752750\pi\) | ||||
−0.713189 | + | 0.700972i | \(0.752750\pi\) | |||||||
\(758\) | 37.2593 | 1.35332 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.38090 | 0.0500575 | 0.0250288 | − | 0.999687i | \(-0.492032\pi\) | ||||
0.0250288 | + | 0.999687i | \(0.492032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.5680 | −0.382589 | ||||||||
\(764\) | 22.6336 | 0.818856 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.9154 | 1.15315 | ||||||||
\(767\) | −85.4301 | −3.08470 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.9691 | 1.18890 | 0.594448 | − | 0.804134i | \(-0.297371\pi\) | ||||
0.594448 | + | 0.804134i | \(0.297371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.24482 | 0.152774 | ||||||||
\(773\) | −32.4975 | −1.16886 | −0.584428 | − | 0.811446i | \(-0.698681\pi\) | ||||
−0.584428 | + | 0.811446i | \(0.698681\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.81286 | 0.244567 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.48963 | −0.160961 | ||||||||
\(779\) | −8.01847 | −0.287292 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8521 | 0.567231 | ||||||||
\(782\) | −18.7345 | −0.669943 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.0185 | 0.393517 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.187143 | 0.00667091 | 0.00333546 | − | 0.999994i | \(-0.498938\pi\) | ||||
0.00333546 | + | 0.999994i | \(0.498938\pi\) | |||||||
\(788\) | −5.00395 | −0.178258 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 46.7714 | 1.66300 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.7635 | −2.01573 | ||||||||
\(794\) | −34.6873 | −1.23101 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.3826 | −0.970550 | ||||||||
\(797\) | −33.9691 | −1.20325 | −0.601624 | − | 0.798780i | \(-0.705479\pi\) | ||||
−0.601624 | + | 0.798780i | \(0.705479\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.4689 | 0.688760 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.03694 | −0.248483 | ||||||||
\(803\) | 7.68960 | 0.271360 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.90973 | 0.313832 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.7737 | 0.414196 | ||||||||
\(809\) | 34.2897 | 1.20556 | 0.602780 | − | 0.797907i | \(-0.294060\pi\) | ||||
0.602780 | + | 0.797907i | \(0.294060\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7737 | −0.659232 | −0.329616 | − | 0.944115i | \(-0.606919\pi\) | ||||
−0.329616 | + | 0.944115i | \(0.606919\pi\) | |||||||
\(812\) | 34.3865 | 1.20673 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.22239 | −0.0428449 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.57199 | 0.124968 | ||||||||
\(818\) | 26.4112 | 0.923447 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.16077 | 0.0405110 | 0.0202555 | − | 0.999795i | \(-0.493552\pi\) | ||||
0.0202555 | + | 0.999795i | \(0.493552\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 4.32718 | 0.150744 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 52.4218 | 1.82399 | ||||||||
\(827\) | 35.4857 | 1.23396 | 0.616979 | − | 0.786980i | \(-0.288356\pi\) | ||||
0.616979 | + | 0.786980i | \(0.288356\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.9546 | −0.380468 | −0.190234 | − | 0.981739i | \(-0.560925\pi\) | ||||
−0.190234 | + | 0.981739i | \(0.560925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.91764 | −0.239826 | ||||||||
\(833\) | −56.2034 | −1.94733 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.42801 | 0.0493886 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.4896 | −0.569625 | ||||||||
\(839\) | −0.417441 | −0.0144117 | −0.00720584 | − | 0.999974i | \(-0.502294\pi\) | ||||
−0.00720584 | + | 0.999974i | \(0.502294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36.6235 | 1.26288 | ||||||||
\(842\) | 39.0162 | 1.34459 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.14003 | −0.176927 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −38.0369 | −1.30696 | ||||||||
\(848\) | 9.06163 | 0.311178 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.14399 | −0.107774 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.7776 | −1.53316 | −0.766578 | − | 0.642151i | \(-0.778042\pi\) | ||||
−0.766578 | + | 0.642151i | \(0.778042\pi\) | |||||||
\(854\) | 34.8313 | 1.19190 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.14003 | −0.141503 | ||||||||
\(857\) | −43.3720 | −1.48156 | −0.740780 | − | 0.671748i | \(-0.765544\pi\) | ||||
−0.740780 | + | 0.671748i | \(0.765544\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.36638 | −0.0807398 | −0.0403699 | − | 0.999185i | \(-0.512854\pi\) | ||||
−0.0403699 | + | 0.999185i | \(0.512854\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −39.8722 | −1.35805 | ||||||||
\(863\) | −19.9921 | −0.680539 | −0.340269 | − | 0.940328i | \(-0.610518\pi\) | ||||
−0.340269 | + | 0.940328i | \(0.610518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −30.3681 | −1.03195 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.46721 | −0.185569 | ||||||||
\(869\) | 3.06163 | 0.103859 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.3602 | −1.02871 | ||||||||
\(872\) | −2.48963 | −0.0843096 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.67282 | 0.124235 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.0946 | 0.644779 | 0.322390 | − | 0.946607i | \(-0.395514\pi\) | ||||
0.322390 | + | 0.946607i | \(0.395514\pi\) | |||||||
\(878\) | 19.4033 | 0.654830 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.1233 | 0.610588 | 0.305294 | − | 0.952258i | \(-0.401245\pi\) | ||||
0.305294 | + | 0.952258i | \(0.401245\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7737 | 0.665436 | 0.332718 | − | 0.943026i | \(-0.392034\pi\) | ||||
0.332718 | + | 0.943026i | \(0.392034\pi\) | |||||||
\(884\) | 35.2857 | 1.18679 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.8705 | 0.701159 | ||||||||
\(887\) | 35.5473 | 1.19356 | 0.596781 | − | 0.802404i | \(-0.296446\pi\) | ||||
0.596781 | + | 0.802404i | \(0.296446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.7137 | 0.862410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.1625 | 0.340264 | ||||||||
\(893\) | −3.81681 | −0.127725 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.24482 | 0.141809 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.7753 | −1.02699 | ||||||||
\(899\) | −10.4337 | −0.347982 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −46.2218 | −1.53987 | ||||||||
\(902\) | −11.4504 | −0.381258 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 11.0185 | 0.366469 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0554 | 1.06438 | 0.532191 | − | 0.846624i | \(-0.321369\pi\) | ||||
0.532191 | + | 0.846624i | \(0.321369\pi\) | |||||||
\(908\) | −7.92159 | −0.262887 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9714 | −0.562286 | −0.281143 | − | 0.959666i | \(-0.590714\pi\) | ||||
−0.281143 | + | 0.959666i | \(0.590714\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.48963 | 0.0492997 | ||||||||
\(914\) | 27.5658 | 0.911795 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.44648 | −0.246039 | ||||||||
\(917\) | −40.0986 | −1.32417 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.4465 | 1.07031 | 0.535155 | − | 0.844754i | \(-0.320253\pi\) | ||||
0.535155 | + | 0.844754i | \(0.320253\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.3042 | 1.03095 | ||||||||
\(923\) | −76.7916 | −2.52762 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.1440 | 0.366214 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.10083 | 0.265923 | ||||||||
\(929\) | −13.9631 | −0.458113 | −0.229057 | − | 0.973413i | \(-0.573564\pi\) | ||||
−0.229057 | + | 0.973413i | \(0.573564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.0185 | 0.361116 | ||||||||
\(932\) | −28.4834 | −0.933005 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.3289 | −1.18872 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.5058 | 0.637228 | 0.318614 | − | 0.947885i | \(-0.396783\pi\) | ||||
0.318614 | + | 0.947885i | \(0.396783\pi\) | |||||||
\(938\) | 18.6297 | 0.608280 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.48568 | −0.276625 | −0.138313 | − | 0.990389i | \(-0.544168\pi\) | ||||
−0.138313 | + | 0.990389i | \(0.544168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.4504 | −0.959038 | ||||||||
\(944\) | 12.3496 | 0.401945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.10083 | 0.165842 | ||||||||
\(947\) | −5.06558 | −0.164609 | −0.0823046 | − | 0.996607i | \(-0.526228\pi\) | ||||
−0.0823046 | + | 0.996607i | \(0.526228\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.2505 | −1.20920 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.6521 | −0.701748 | ||||||||
\(953\) | 4.46890 | 0.144762 | 0.0723810 | − | 0.997377i | \(-0.476940\pi\) | ||||
0.0723810 | + | 0.997377i | \(0.476940\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.24086 | 0.104817 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.0185 | 0.549842 | ||||||||
\(959\) | 17.8353 | 0.575931 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3411 | −0.946488 | ||||||||
\(962\) | 5.92159 | 0.190920 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.9938 | 0.837203 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.9872 | −0.353324 | −0.176662 | − | 0.984272i | \(-0.556530\pi\) | ||||
−0.176662 | + | 0.984272i | \(0.556530\pi\) | |||||||
\(968\) | −8.96080 | −0.288011 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8969 | −0.381790 | −0.190895 | − | 0.981610i | \(-0.561139\pi\) | ||||
−0.190895 | + | 0.981610i | \(0.561139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.9529 | −0.735836 | ||||||||
\(974\) | −27.3536 | −0.876464 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.20561 | 0.262655 | ||||||||
\(977\) | 29.9031 | 0.956686 | 0.478343 | − | 0.878173i | \(-0.341238\pi\) | ||||
0.478343 | + | 0.878173i | \(0.341238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.8913 | 0.763568 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.7697 | 0.407498 | ||||||||
\(983\) | 6.89917 | 0.220049 | 0.110025 | − | 0.993929i | \(-0.464907\pi\) | ||||
0.110025 | + | 0.993929i | \(0.464907\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −41.3210 | −1.31593 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.91764 | −0.220079 | ||||||||
\(989\) | 13.1193 | 0.417170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.3720 | 0.393010 | 0.196505 | − | 0.980503i | \(-0.437041\pi\) | ||||
0.196505 | + | 0.980503i | \(0.437041\pi\) | |||||||
\(992\) | −1.28797 | −0.0408932 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 47.1210 | 1.49459 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.73671 | −0.0866725 | −0.0433363 | − | 0.999061i | \(-0.513799\pi\) | ||||
−0.0433363 | + | 0.999061i | \(0.513799\pi\) | |||||||
\(998\) | −33.8969 | −1.07299 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8550.2.a.cs.1.3 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.cg.1.3 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cd.1.1 | ✓ | 3 | ||
15.14 | odd | 2 | 8550.2.a.cn.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8550.2.a.cd.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
8550.2.a.cg.1.3 | yes | 3 | 3.2 | odd | 2 | ||
8550.2.a.cn.1.1 | yes | 3 | 15.14 | odd | 2 | ||
8550.2.a.cs.1.3 | yes | 3 | 1.1 | even | 1 | trivial |