Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(1,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1183.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 15 x^{10} + 46 x^{9} + 80 x^{8} - 246 x^{7} - 199 x^{6} + 562 x^{5} + 262 x^{4} - 542 x^{3} - 157 x^{2} + 183 x + 29 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.10989\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.10989 | 0.784809 | 0.392404 | − | 0.919793i | \(-0.371643\pi\) | ||||
0.392404 | + | 0.919793i | \(0.371643\pi\) | |||||||
\(3\) | 0.955760 | 0.551808 | 0.275904 | − | 0.961185i | \(-0.411023\pi\) | ||||
0.275904 | + | 0.961185i | \(0.411023\pi\) | |||||||
\(4\) | −0.768150 | −0.384075 | ||||||||
\(5\) | 3.55862 | 1.59146 | 0.795731 | − | 0.605650i | \(-0.207087\pi\) | ||||
0.795731 | + | 0.605650i | \(0.207087\pi\) | |||||||
\(6\) | 1.06079 | 0.433064 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −3.07233 | −1.08623 | ||||||||
\(9\) | −2.08652 | −0.695508 | ||||||||
\(10\) | 3.94966 | 1.24899 | ||||||||
\(11\) | 4.00483 | 1.20750 | 0.603751 | − | 0.797173i | \(-0.293672\pi\) | ||||
0.603751 | + | 0.797173i | \(0.293672\pi\) | |||||||
\(12\) | −0.734167 | −0.211936 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.10989 | −0.296630 | ||||||||
\(15\) | 3.40118 | 0.878182 | ||||||||
\(16\) | −1.87364 | −0.468411 | ||||||||
\(17\) | 1.86471 | 0.452258 | 0.226129 | − | 0.974097i | \(-0.427393\pi\) | ||||
0.226129 | + | 0.974097i | \(0.427393\pi\) | |||||||
\(18\) | −2.31581 | −0.545841 | ||||||||
\(19\) | 6.34660 | 1.45601 | 0.728005 | − | 0.685572i | \(-0.240448\pi\) | ||||
0.728005 | + | 0.685572i | \(0.240448\pi\) | |||||||
\(20\) | −2.73355 | −0.611241 | ||||||||
\(21\) | −0.955760 | −0.208564 | ||||||||
\(22\) | 4.44491 | 0.947658 | ||||||||
\(23\) | 4.50206 | 0.938744 | 0.469372 | − | 0.883001i | \(-0.344480\pi\) | ||||
0.469372 | + | 0.883001i | \(0.344480\pi\) | |||||||
\(24\) | −2.93641 | −0.599393 | ||||||||
\(25\) | 7.66376 | 1.53275 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.86149 | −0.935595 | ||||||||
\(28\) | 0.768150 | 0.145167 | ||||||||
\(29\) | 8.63110 | 1.60275 | 0.801377 | − | 0.598159i | \(-0.204101\pi\) | ||||
0.801377 | + | 0.598159i | \(0.204101\pi\) | |||||||
\(30\) | 3.77493 | 0.689205 | ||||||||
\(31\) | 3.22435 | 0.579110 | 0.289555 | − | 0.957161i | \(-0.406493\pi\) | ||||
0.289555 | + | 0.957161i | \(0.406493\pi\) | |||||||
\(32\) | 4.06514 | 0.718621 | ||||||||
\(33\) | 3.82766 | 0.666309 | ||||||||
\(34\) | 2.06962 | 0.354936 | ||||||||
\(35\) | −3.55862 | −0.601516 | ||||||||
\(36\) | 1.60276 | 0.267127 | ||||||||
\(37\) | −1.83406 | −0.301517 | −0.150758 | − | 0.988571i | \(-0.548172\pi\) | ||||
−0.150758 | + | 0.988571i | \(0.548172\pi\) | |||||||
\(38\) | 7.04401 | 1.14269 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.9333 | −1.72870 | ||||||||
\(41\) | −10.3590 | −1.61780 | −0.808899 | − | 0.587947i | \(-0.799936\pi\) | ||||
−0.808899 | + | 0.587947i | \(0.799936\pi\) | |||||||
\(42\) | −1.06079 | −0.163683 | ||||||||
\(43\) | −10.3318 | −1.57559 | −0.787793 | − | 0.615941i | \(-0.788776\pi\) | ||||
−0.787793 | + | 0.615941i | \(0.788776\pi\) | |||||||
\(44\) | −3.07631 | −0.463771 | ||||||||
\(45\) | −7.42514 | −1.10687 | ||||||||
\(46\) | 4.99678 | 0.736735 | ||||||||
\(47\) | 0.832988 | 0.121504 | 0.0607519 | − | 0.998153i | \(-0.480650\pi\) | ||||
0.0607519 | + | 0.998153i | \(0.480650\pi\) | |||||||
\(48\) | −1.79075 | −0.258473 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.50590 | 1.20292 | ||||||||
\(51\) | 1.78221 | 0.249560 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.53512 | 0.897667 | 0.448834 | − | 0.893615i | \(-0.351840\pi\) | ||||
0.448834 | + | 0.893615i | \(0.351840\pi\) | |||||||
\(54\) | −5.39571 | −0.734263 | ||||||||
\(55\) | 14.2517 | 1.92169 | ||||||||
\(56\) | 3.07233 | 0.410558 | ||||||||
\(57\) | 6.06582 | 0.803438 | ||||||||
\(58\) | 9.57955 | 1.25786 | ||||||||
\(59\) | −5.20780 | −0.677997 | −0.338999 | − | 0.940787i | \(-0.610088\pi\) | ||||
−0.338999 | + | 0.940787i | \(0.610088\pi\) | |||||||
\(60\) | −2.61262 | −0.337288 | ||||||||
\(61\) | −1.83794 | −0.235324 | −0.117662 | − | 0.993054i | \(-0.537540\pi\) | ||||
−0.117662 | + | 0.993054i | \(0.537540\pi\) | |||||||
\(62\) | 3.57866 | 0.454491 | ||||||||
\(63\) | 2.08652 | 0.262877 | ||||||||
\(64\) | 8.25913 | 1.03239 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.24827 | 0.522925 | ||||||||
\(67\) | −3.05008 | −0.372626 | −0.186313 | − | 0.982490i | \(-0.559654\pi\) | ||||
−0.186313 | + | 0.982490i | \(0.559654\pi\) | |||||||
\(68\) | −1.43238 | −0.173701 | ||||||||
\(69\) | 4.30289 | 0.518007 | ||||||||
\(70\) | −3.94966 | −0.472075 | ||||||||
\(71\) | −14.4391 | −1.71361 | −0.856805 | − | 0.515640i | \(-0.827554\pi\) | ||||
−0.856805 | + | 0.515640i | \(0.827554\pi\) | |||||||
\(72\) | 6.41050 | 0.755484 | ||||||||
\(73\) | −12.9055 | −1.51047 | −0.755235 | − | 0.655454i | \(-0.772477\pi\) | ||||
−0.755235 | + | 0.655454i | \(0.772477\pi\) | |||||||
\(74\) | −2.03559 | −0.236633 | ||||||||
\(75\) | 7.32471 | 0.845785 | ||||||||
\(76\) | −4.87514 | −0.559217 | ||||||||
\(77\) | −4.00483 | −0.456393 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0931919 | 0.0104849 | 0.00524245 | − | 0.999986i | \(-0.498331\pi\) | ||||
0.00524245 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(80\) | −6.66758 | −0.745458 | ||||||||
\(81\) | 1.61315 | 0.179239 | ||||||||
\(82\) | −11.4973 | −1.26966 | ||||||||
\(83\) | −3.17863 | −0.348900 | −0.174450 | − | 0.984666i | \(-0.555815\pi\) | ||||
−0.174450 | + | 0.984666i | \(0.555815\pi\) | |||||||
\(84\) | 0.734167 | 0.0801042 | ||||||||
\(85\) | 6.63578 | 0.719752 | ||||||||
\(86\) | −11.4671 | −1.23653 | ||||||||
\(87\) | 8.24926 | 0.884413 | ||||||||
\(88\) | −12.3042 | −1.31163 | ||||||||
\(89\) | −12.2290 | −1.29627 | −0.648137 | − | 0.761524i | \(-0.724451\pi\) | ||||
−0.648137 | + | 0.761524i | \(0.724451\pi\) | |||||||
\(90\) | −8.24106 | −0.868684 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.45826 | −0.360548 | ||||||||
\(93\) | 3.08170 | 0.319558 | ||||||||
\(94\) | 0.924522 | 0.0953572 | ||||||||
\(95\) | 22.5851 | 2.31718 | ||||||||
\(96\) | 3.88529 | 0.396541 | ||||||||
\(97\) | 13.1916 | 1.33941 | 0.669704 | − | 0.742628i | \(-0.266421\pi\) | ||||
0.669704 | + | 0.742628i | \(0.266421\pi\) | |||||||
\(98\) | 1.10989 | 0.112116 | ||||||||
\(99\) | −8.35617 | −0.839827 | ||||||||
\(100\) | −5.88692 | −0.588692 | ||||||||
\(101\) | −7.73025 | −0.769188 | −0.384594 | − | 0.923086i | \(-0.625659\pi\) | ||||
−0.384594 | + | 0.923086i | \(0.625659\pi\) | |||||||
\(102\) | 1.97806 | 0.195857 | ||||||||
\(103\) | −0.359154 | −0.0353885 | −0.0176943 | − | 0.999843i | \(-0.505633\pi\) | ||||
−0.0176943 | + | 0.999843i | \(0.505633\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.40118 | −0.331922 | ||||||||
\(106\) | 7.25324 | 0.704497 | ||||||||
\(107\) | −3.99044 | −0.385770 | −0.192885 | − | 0.981221i | \(-0.561784\pi\) | ||||
−0.192885 | + | 0.981221i | \(0.561784\pi\) | |||||||
\(108\) | 3.73436 | 0.359339 | ||||||||
\(109\) | 9.65395 | 0.924681 | 0.462341 | − | 0.886702i | \(-0.347010\pi\) | ||||
0.462341 | + | 0.886702i | \(0.347010\pi\) | |||||||
\(110\) | 15.8177 | 1.50816 | ||||||||
\(111\) | −1.75292 | −0.166379 | ||||||||
\(112\) | 1.87364 | 0.177043 | ||||||||
\(113\) | 2.08248 | 0.195904 | 0.0979518 | − | 0.995191i | \(-0.468771\pi\) | ||||
0.0979518 | + | 0.995191i | \(0.468771\pi\) | |||||||
\(114\) | 6.73238 | 0.630545 | ||||||||
\(115\) | 16.0211 | 1.49398 | ||||||||
\(116\) | −6.62998 | −0.615578 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.78007 | −0.532098 | ||||||||
\(119\) | −1.86471 | −0.170937 | ||||||||
\(120\) | −10.4496 | −0.953911 | ||||||||
\(121\) | 5.03866 | 0.458060 | ||||||||
\(122\) | −2.03991 | −0.184685 | ||||||||
\(123\) | −9.90068 | −0.892714 | ||||||||
\(124\) | −2.47678 | −0.222422 | ||||||||
\(125\) | 9.47929 | 0.847853 | ||||||||
\(126\) | 2.31581 | 0.206308 | ||||||||
\(127\) | 7.18287 | 0.637376 | 0.318688 | − | 0.947860i | \(-0.396758\pi\) | ||||
0.318688 | + | 0.947860i | \(0.396758\pi\) | |||||||
\(128\) | 1.03643 | 0.0916084 | ||||||||
\(129\) | −9.87472 | −0.869421 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.48085 | −0.129383 | −0.0646913 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646913 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(132\) | −2.94022 | −0.255913 | ||||||||
\(133\) | −6.34660 | −0.550320 | ||||||||
\(134\) | −3.38524 | −0.292440 | ||||||||
\(135\) | −17.3002 | −1.48896 | ||||||||
\(136\) | −5.72901 | −0.491258 | ||||||||
\(137\) | 4.43864 | 0.379219 | 0.189609 | − | 0.981860i | \(-0.439278\pi\) | ||||
0.189609 | + | 0.981860i | \(0.439278\pi\) | |||||||
\(138\) | 4.77572 | 0.406536 | ||||||||
\(139\) | 17.3529 | 1.47186 | 0.735929 | − | 0.677059i | \(-0.236746\pi\) | ||||
0.735929 | + | 0.677059i | \(0.236746\pi\) | |||||||
\(140\) | 2.73355 | 0.231027 | ||||||||
\(141\) | 0.796136 | 0.0670468 | ||||||||
\(142\) | −16.0258 | −1.34486 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.90940 | 0.325783 | ||||||||
\(145\) | 30.7148 | 2.55072 | ||||||||
\(146\) | −14.3236 | −1.18543 | ||||||||
\(147\) | 0.955760 | 0.0788297 | ||||||||
\(148\) | 1.40883 | 0.115805 | ||||||||
\(149\) | −23.1381 | −1.89554 | −0.947771 | − | 0.318950i | \(-0.896670\pi\) | ||||
−0.947771 | + | 0.318950i | \(0.896670\pi\) | |||||||
\(150\) | 8.12960 | 0.663779 | ||||||||
\(151\) | −10.8846 | −0.885778 | −0.442889 | − | 0.896576i | \(-0.646047\pi\) | ||||
−0.442889 | + | 0.896576i | \(0.646047\pi\) | |||||||
\(152\) | −19.4989 | −1.58157 | ||||||||
\(153\) | −3.89076 | −0.314549 | ||||||||
\(154\) | −4.44491 | −0.358181 | ||||||||
\(155\) | 11.4742 | 0.921632 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.2555 | 1.13771 | 0.568855 | − | 0.822438i | \(-0.307387\pi\) | ||||
0.568855 | + | 0.822438i | \(0.307387\pi\) | |||||||
\(158\) | 0.103432 | 0.00822865 | ||||||||
\(159\) | 6.24600 | 0.495340 | ||||||||
\(160\) | 14.4663 | 1.14366 | ||||||||
\(161\) | −4.50206 | −0.354812 | ||||||||
\(162\) | 1.79041 | 0.140668 | ||||||||
\(163\) | 2.01430 | 0.157772 | 0.0788861 | − | 0.996884i | \(-0.474864\pi\) | ||||
0.0788861 | + | 0.996884i | \(0.474864\pi\) | |||||||
\(164\) | 7.95724 | 0.621356 | ||||||||
\(165\) | 13.6212 | 1.06041 | ||||||||
\(166\) | −3.52792 | −0.273820 | ||||||||
\(167\) | 18.8978 | 1.46236 | 0.731178 | − | 0.682187i | \(-0.238971\pi\) | ||||
0.731178 | + | 0.682187i | \(0.238971\pi\) | |||||||
\(168\) | 2.93641 | 0.226549 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 7.36497 | 0.564867 | ||||||||
\(171\) | −13.2423 | −1.01267 | ||||||||
\(172\) | 7.93638 | 0.605143 | ||||||||
\(173\) | −12.4146 | −0.943868 | −0.471934 | − | 0.881634i | \(-0.656444\pi\) | ||||
−0.471934 | + | 0.881634i | \(0.656444\pi\) | |||||||
\(174\) | 9.15575 | 0.694095 | ||||||||
\(175\) | −7.66376 | −0.579325 | ||||||||
\(176\) | −7.50363 | −0.565607 | ||||||||
\(177\) | −4.97740 | −0.374125 | ||||||||
\(178\) | −13.5728 | −1.01733 | ||||||||
\(179\) | −9.37393 | −0.700641 | −0.350320 | − | 0.936630i | \(-0.613927\pi\) | ||||
−0.350320 | + | 0.936630i | \(0.613927\pi\) | |||||||
\(180\) | 5.70362 | 0.425123 | ||||||||
\(181\) | 5.83547 | 0.433747 | 0.216873 | − | 0.976200i | \(-0.430414\pi\) | ||||
0.216873 | + | 0.976200i | \(0.430414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.75663 | −0.129854 | ||||||||
\(184\) | −13.8318 | −1.01970 | ||||||||
\(185\) | −6.52670 | −0.479852 | ||||||||
\(186\) | 3.42034 | 0.250792 | ||||||||
\(187\) | 7.46784 | 0.546102 | ||||||||
\(188\) | −0.639860 | −0.0466666 | ||||||||
\(189\) | 4.86149 | 0.353622 | ||||||||
\(190\) | 25.0669 | 1.81855 | ||||||||
\(191\) | −16.3051 | −1.17980 | −0.589899 | − | 0.807477i | \(-0.700833\pi\) | ||||
−0.589899 | + | 0.807477i | \(0.700833\pi\) | |||||||
\(192\) | 7.89375 | 0.569682 | ||||||||
\(193\) | −21.2251 | −1.52782 | −0.763910 | − | 0.645323i | \(-0.776723\pi\) | ||||
−0.763910 | + | 0.645323i | \(0.776723\pi\) | |||||||
\(194\) | 14.6412 | 1.05118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.768150 | −0.0548679 | ||||||||
\(197\) | 16.0798 | 1.14564 | 0.572818 | − | 0.819683i | \(-0.305850\pi\) | ||||
0.572818 | + | 0.819683i | \(0.305850\pi\) | |||||||
\(198\) | −9.27441 | −0.659103 | ||||||||
\(199\) | −15.4383 | −1.09440 | −0.547198 | − | 0.837003i | \(-0.684305\pi\) | ||||
−0.547198 | + | 0.837003i | \(0.684305\pi\) | |||||||
\(200\) | −23.5456 | −1.66493 | ||||||||
\(201\) | −2.91514 | −0.205618 | ||||||||
\(202\) | −8.57970 | −0.603666 | ||||||||
\(203\) | −8.63110 | −0.605784 | ||||||||
\(204\) | −1.36901 | −0.0958497 | ||||||||
\(205\) | −36.8636 | −2.57466 | ||||||||
\(206\) | −0.398621 | −0.0277732 | ||||||||
\(207\) | −9.39365 | −0.652904 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.4170 | 1.75813 | ||||||||
\(210\) | −3.77493 | −0.260495 | ||||||||
\(211\) | 3.45377 | 0.237767 | 0.118884 | − | 0.992908i | \(-0.462068\pi\) | ||||
0.118884 | + | 0.992908i | \(0.462068\pi\) | |||||||
\(212\) | −5.01995 | −0.344772 | ||||||||
\(213\) | −13.8004 | −0.945584 | ||||||||
\(214\) | −4.42893 | −0.302756 | ||||||||
\(215\) | −36.7669 | −2.50748 | ||||||||
\(216\) | 14.9361 | 1.01628 | ||||||||
\(217\) | −3.22435 | −0.218883 | ||||||||
\(218\) | 10.7148 | 0.725698 | ||||||||
\(219\) | −12.3345 | −0.833490 | ||||||||
\(220\) | −10.9474 | −0.738075 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.94554 | −0.130576 | ||||||||
\(223\) | −15.6638 | −1.04893 | −0.524464 | − | 0.851433i | \(-0.675734\pi\) | ||||
−0.524464 | + | 0.851433i | \(0.675734\pi\) | |||||||
\(224\) | −4.06514 | −0.271613 | ||||||||
\(225\) | −15.9906 | −1.06604 | ||||||||
\(226\) | 2.31132 | 0.153747 | ||||||||
\(227\) | 8.05474 | 0.534612 | 0.267306 | − | 0.963612i | \(-0.413867\pi\) | ||||
0.267306 | + | 0.963612i | \(0.413867\pi\) | |||||||
\(228\) | −4.65947 | −0.308581 | ||||||||
\(229\) | 19.9670 | 1.31946 | 0.659730 | − | 0.751503i | \(-0.270671\pi\) | ||||
0.659730 | + | 0.751503i | \(0.270671\pi\) | |||||||
\(230\) | 17.7816 | 1.17248 | ||||||||
\(231\) | −3.82766 | −0.251841 | ||||||||
\(232\) | −26.5176 | −1.74097 | ||||||||
\(233\) | 12.1790 | 0.797871 | 0.398935 | − | 0.916979i | \(-0.369380\pi\) | ||||
0.398935 | + | 0.916979i | \(0.369380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.96428 | 0.193369 | ||||||||
\(236\) | 4.00037 | 0.260402 | ||||||||
\(237\) | 0.0890691 | 0.00578566 | ||||||||
\(238\) | −2.06962 | −0.134153 | ||||||||
\(239\) | −15.5704 | −1.00717 | −0.503584 | − | 0.863946i | \(-0.667986\pi\) | ||||
−0.503584 | + | 0.863946i | \(0.667986\pi\) | |||||||
\(240\) | −6.37261 | −0.411350 | ||||||||
\(241\) | −1.30581 | −0.0841148 | −0.0420574 | − | 0.999115i | \(-0.513391\pi\) | ||||
−0.0420574 | + | 0.999115i | \(0.513391\pi\) | |||||||
\(242\) | 5.59235 | 0.359490 | ||||||||
\(243\) | 16.1263 | 1.03450 | ||||||||
\(244\) | 1.41182 | 0.0903822 | ||||||||
\(245\) | 3.55862 | 0.227352 | ||||||||
\(246\) | −10.9886 | −0.700610 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9.90628 | −0.629049 | ||||||||
\(249\) | −3.03801 | −0.192526 | ||||||||
\(250\) | 10.5209 | 0.665402 | ||||||||
\(251\) | −20.2852 | −1.28039 | −0.640196 | − | 0.768212i | \(-0.721147\pi\) | ||||
−0.640196 | + | 0.768212i | \(0.721147\pi\) | |||||||
\(252\) | −1.60276 | −0.100965 | ||||||||
\(253\) | 18.0300 | 1.13353 | ||||||||
\(254\) | 7.97217 | 0.500219 | ||||||||
\(255\) | 6.34221 | 0.397165 | ||||||||
\(256\) | −15.3679 | −0.960496 | ||||||||
\(257\) | 17.3450 | 1.08195 | 0.540977 | − | 0.841038i | \(-0.318055\pi\) | ||||
0.540977 | + | 0.841038i | \(0.318055\pi\) | |||||||
\(258\) | −10.9598 | −0.682329 | ||||||||
\(259\) | 1.83406 | 0.113963 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.0090 | −1.11473 | ||||||||
\(262\) | −1.64358 | −0.101541 | ||||||||
\(263\) | −10.8891 | −0.671448 | −0.335724 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335724 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(264\) | −11.7598 | −0.723768 | ||||||||
\(265\) | 23.2560 | 1.42860 | ||||||||
\(266\) | −7.04401 | −0.431896 | ||||||||
\(267\) | −11.6880 | −0.715294 | ||||||||
\(268\) | 2.34292 | 0.143117 | ||||||||
\(269\) | 8.99414 | 0.548382 | 0.274191 | − | 0.961675i | \(-0.411590\pi\) | ||||
0.274191 | + | 0.961675i | \(0.411590\pi\) | |||||||
\(270\) | −19.2013 | −1.16855 | ||||||||
\(271\) | −4.94282 | −0.300255 | −0.150127 | − | 0.988667i | \(-0.547968\pi\) | ||||
−0.150127 | + | 0.988667i | \(0.547968\pi\) | |||||||
\(272\) | −3.49380 | −0.211843 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.92639 | 0.297614 | ||||||||
\(275\) | 30.6920 | 1.85080 | ||||||||
\(276\) | −3.30526 | −0.198954 | ||||||||
\(277\) | 19.4610 | 1.16930 | 0.584650 | − | 0.811286i | \(-0.301232\pi\) | ||||
0.584650 | + | 0.811286i | \(0.301232\pi\) | |||||||
\(278\) | 19.2598 | 1.15513 | ||||||||
\(279\) | −6.72768 | −0.402776 | ||||||||
\(280\) | 10.9333 | 0.653387 | ||||||||
\(281\) | 20.1468 | 1.20185 | 0.600927 | − | 0.799304i | \(-0.294798\pi\) | ||||
0.600927 | + | 0.799304i | \(0.294798\pi\) | |||||||
\(282\) | 0.883621 | 0.0526189 | ||||||||
\(283\) | −22.8282 | −1.35699 | −0.678496 | − | 0.734604i | \(-0.737368\pi\) | ||||
−0.678496 | + | 0.734604i | \(0.737368\pi\) | |||||||
\(284\) | 11.0914 | 0.658155 | ||||||||
\(285\) | 21.5859 | 1.27864 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.3590 | 0.611470 | ||||||||
\(288\) | −8.48200 | −0.499807 | ||||||||
\(289\) | −13.5229 | −0.795463 | ||||||||
\(290\) | 34.0899 | 2.00183 | ||||||||
\(291\) | 12.6080 | 0.739096 | ||||||||
\(292\) | 9.91334 | 0.580134 | ||||||||
\(293\) | −26.5717 | −1.55233 | −0.776166 | − | 0.630528i | \(-0.782838\pi\) | ||||
−0.776166 | + | 0.630528i | \(0.782838\pi\) | |||||||
\(294\) | 1.06079 | 0.0618663 | ||||||||
\(295\) | −18.5326 | −1.07901 | ||||||||
\(296\) | 5.63483 | 0.327518 | ||||||||
\(297\) | −19.4695 | −1.12973 | ||||||||
\(298\) | −25.6806 | −1.48764 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −5.62648 | −0.324845 | ||||||||
\(301\) | 10.3318 | 0.595515 | ||||||||
\(302\) | −12.0807 | −0.695167 | ||||||||
\(303\) | −7.38826 | −0.424444 | ||||||||
\(304\) | −11.8913 | −0.682011 | ||||||||
\(305\) | −6.54053 | −0.374510 | ||||||||
\(306\) | −4.31830 | −0.246861 | ||||||||
\(307\) | 7.16833 | 0.409118 | 0.204559 | − | 0.978854i | \(-0.434424\pi\) | ||||
0.204559 | + | 0.978854i | \(0.434424\pi\) | |||||||
\(308\) | 3.07631 | 0.175289 | ||||||||
\(309\) | −0.343265 | −0.0195277 | ||||||||
\(310\) | 12.7351 | 0.723305 | ||||||||
\(311\) | −13.6640 | −0.774817 | −0.387408 | − | 0.921908i | \(-0.626630\pi\) | ||||
−0.387408 | + | 0.921908i | \(0.626630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.5821 | 0.598137 | 0.299068 | − | 0.954232i | \(-0.403324\pi\) | ||||
0.299068 | + | 0.954232i | \(0.403324\pi\) | |||||||
\(314\) | 15.8219 | 0.892884 | ||||||||
\(315\) | 7.42514 | 0.418359 | ||||||||
\(316\) | −0.0715854 | −0.00402699 | ||||||||
\(317\) | 3.65041 | 0.205027 | 0.102514 | − | 0.994732i | \(-0.467311\pi\) | ||||
0.102514 | + | 0.994732i | \(0.467311\pi\) | |||||||
\(318\) | 6.93236 | 0.388747 | ||||||||
\(319\) | 34.5661 | 1.93533 | ||||||||
\(320\) | 29.3911 | 1.64301 | ||||||||
\(321\) | −3.81390 | −0.212871 | ||||||||
\(322\) | −4.99678 | −0.278459 | ||||||||
\(323\) | 11.8346 | 0.658492 | ||||||||
\(324\) | −1.23914 | −0.0688411 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.23565 | 0.123821 | ||||||||
\(327\) | 9.22686 | 0.510247 | ||||||||
\(328\) | 31.8262 | 1.75731 | ||||||||
\(329\) | −0.832988 | −0.0459241 | ||||||||
\(330\) | 15.1180 | 0.832216 | ||||||||
\(331\) | −21.7576 | −1.19590 | −0.597952 | − | 0.801532i | \(-0.704019\pi\) | ||||
−0.597952 | + | 0.801532i | \(0.704019\pi\) | |||||||
\(332\) | 2.44167 | 0.134004 | ||||||||
\(333\) | 3.82680 | 0.209707 | ||||||||
\(334\) | 20.9744 | 1.14767 | ||||||||
\(335\) | −10.8541 | −0.593021 | ||||||||
\(336\) | 1.79075 | 0.0976936 | ||||||||
\(337\) | −17.8877 | −0.974405 | −0.487202 | − | 0.873289i | \(-0.661983\pi\) | ||||
−0.487202 | + | 0.873289i | \(0.661983\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.99036 | 0.108101 | ||||||||
\(340\) | −5.09728 | −0.276439 | ||||||||
\(341\) | 12.9130 | 0.699276 | ||||||||
\(342\) | −14.6975 | −0.794749 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 31.7428 | 1.71145 | ||||||||
\(345\) | 15.3123 | 0.824388 | ||||||||
\(346\) | −13.7789 | −0.740756 | ||||||||
\(347\) | 11.2388 | 0.603331 | 0.301666 | − | 0.953414i | \(-0.402457\pi\) | ||||
0.301666 | + | 0.953414i | \(0.402457\pi\) | |||||||
\(348\) | −6.33667 | −0.339681 | ||||||||
\(349\) | 24.4183 | 1.30708 | 0.653542 | − | 0.756891i | \(-0.273282\pi\) | ||||
0.653542 | + | 0.756891i | \(0.273282\pi\) | |||||||
\(350\) | −8.50590 | −0.454660 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2802 | 0.867736 | ||||||||
\(353\) | 15.9072 | 0.846655 | 0.423327 | − | 0.905977i | \(-0.360862\pi\) | ||||
0.423327 | + | 0.905977i | \(0.360862\pi\) | |||||||
\(354\) | −5.52436 | −0.293616 | ||||||||
\(355\) | −51.3834 | −2.72715 | ||||||||
\(356\) | 9.39372 | 0.497866 | ||||||||
\(357\) | −1.78221 | −0.0943247 | ||||||||
\(358\) | −10.4040 | −0.549869 | ||||||||
\(359\) | −12.4456 | −0.656853 | −0.328427 | − | 0.944529i | \(-0.606518\pi\) | ||||
−0.328427 | + | 0.944529i | \(0.606518\pi\) | |||||||
\(360\) | 22.8125 | 1.20232 | ||||||||
\(361\) | 21.2793 | 1.11996 | ||||||||
\(362\) | 6.47671 | 0.340408 | ||||||||
\(363\) | 4.81575 | 0.252761 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.9256 | −2.40386 | ||||||||
\(366\) | −1.94966 | −0.101910 | ||||||||
\(367\) | −18.2038 | −0.950231 | −0.475115 | − | 0.879923i | \(-0.657594\pi\) | ||||
−0.475115 | + | 0.879923i | \(0.657594\pi\) | |||||||
\(368\) | −8.43525 | −0.439718 | ||||||||
\(369\) | 21.6142 | 1.12519 | ||||||||
\(370\) | −7.24390 | −0.376592 | ||||||||
\(371\) | −6.53512 | −0.339286 | ||||||||
\(372\) | −2.36721 | −0.122734 | ||||||||
\(373\) | 32.6828 | 1.69225 | 0.846126 | − | 0.532983i | \(-0.178929\pi\) | ||||
0.846126 | + | 0.532983i | \(0.178929\pi\) | |||||||
\(374\) | 8.28846 | 0.428586 | ||||||||
\(375\) | 9.05992 | 0.467852 | ||||||||
\(376\) | −2.55922 | −0.131982 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.39571 | 0.277525 | ||||||||
\(379\) | −8.81792 | −0.452946 | −0.226473 | − | 0.974017i | \(-0.572720\pi\) | ||||
−0.226473 | + | 0.974017i | \(0.572720\pi\) | |||||||
\(380\) | −17.3488 | −0.889973 | ||||||||
\(381\) | 6.86510 | 0.351710 | ||||||||
\(382\) | −18.0969 | −0.925916 | ||||||||
\(383\) | 2.54364 | 0.129974 | 0.0649870 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649870 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(384\) | 0.990579 | 0.0505502 | ||||||||
\(385\) | −14.2517 | −0.726332 | ||||||||
\(386\) | −23.5575 | −1.19905 | ||||||||
\(387\) | 21.5575 | 1.09583 | ||||||||
\(388\) | −10.1332 | −0.514433 | ||||||||
\(389\) | −0.516707 | −0.0261981 | −0.0130990 | − | 0.999914i | \(-0.504170\pi\) | ||||
−0.0130990 | + | 0.999914i | \(0.504170\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.39502 | 0.424555 | ||||||||
\(392\) | −3.07233 | −0.155176 | ||||||||
\(393\) | −1.41534 | −0.0713944 | ||||||||
\(394\) | 17.8467 | 0.899104 | ||||||||
\(395\) | 0.331634 | 0.0166863 | ||||||||
\(396\) | 6.41880 | 0.322557 | ||||||||
\(397\) | 25.8956 | 1.29967 | 0.649833 | − | 0.760077i | \(-0.274839\pi\) | ||||
0.649833 | + | 0.760077i | \(0.274839\pi\) | |||||||
\(398\) | −17.1348 | −0.858891 | ||||||||
\(399\) | −6.06582 | −0.303671 | ||||||||
\(400\) | −14.3591 | −0.717957 | ||||||||
\(401\) | 10.2493 | 0.511828 | 0.255914 | − | 0.966700i | \(-0.417624\pi\) | ||||
0.255914 | + | 0.966700i | \(0.417624\pi\) | |||||||
\(402\) | −3.23548 | −0.161371 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.93799 | 0.295426 | ||||||||
\(405\) | 5.74057 | 0.285251 | ||||||||
\(406\) | −9.57955 | −0.475425 | ||||||||
\(407\) | −7.34508 | −0.364082 | ||||||||
\(408\) | −5.47556 | −0.271080 | ||||||||
\(409\) | −20.5100 | −1.01416 | −0.507078 | − | 0.861900i | \(-0.669274\pi\) | ||||
−0.507078 | + | 0.861900i | \(0.669274\pi\) | |||||||
\(410\) | −40.9144 | −2.02062 | ||||||||
\(411\) | 4.24228 | 0.209256 | ||||||||
\(412\) | 0.275884 | 0.0135918 | ||||||||
\(413\) | 5.20780 | 0.256259 | ||||||||
\(414\) | −10.4259 | −0.512405 | ||||||||
\(415\) | −11.3115 | −0.555261 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.5852 | 0.812183 | ||||||||
\(418\) | 28.2101 | 1.37980 | ||||||||
\(419\) | 15.2380 | 0.744426 | 0.372213 | − | 0.928147i | \(-0.378599\pi\) | ||||
0.372213 | + | 0.928147i | \(0.378599\pi\) | |||||||
\(420\) | 2.61262 | 0.127483 | ||||||||
\(421\) | 26.3846 | 1.28590 | 0.642952 | − | 0.765906i | \(-0.277709\pi\) | ||||
0.642952 | + | 0.765906i | \(0.277709\pi\) | |||||||
\(422\) | 3.83329 | 0.186602 | ||||||||
\(423\) | −1.73805 | −0.0845068 | ||||||||
\(424\) | −20.0781 | −0.975077 | ||||||||
\(425\) | 14.2907 | 0.693199 | ||||||||
\(426\) | −15.3168 | −0.742103 | ||||||||
\(427\) | 1.83794 | 0.0889442 | ||||||||
\(428\) | 3.06526 | 0.148165 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −40.8071 | −1.96790 | ||||||||
\(431\) | −37.9100 | −1.82606 | −0.913031 | − | 0.407889i | \(-0.866265\pi\) | ||||
−0.913031 | + | 0.407889i | \(0.866265\pi\) | |||||||
\(432\) | 9.10871 | 0.438243 | ||||||||
\(433\) | 8.51058 | 0.408993 | 0.204496 | − | 0.978867i | \(-0.434444\pi\) | ||||
0.204496 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(434\) | −3.57866 | −0.171781 | ||||||||
\(435\) | 29.3559 | 1.40751 | ||||||||
\(436\) | −7.41569 | −0.355147 | ||||||||
\(437\) | 28.5728 | 1.36682 | ||||||||
\(438\) | −13.6899 | −0.654130 | ||||||||
\(439\) | 18.6101 | 0.888213 | 0.444107 | − | 0.895974i | \(-0.353521\pi\) | ||||
0.444107 | + | 0.895974i | \(0.353521\pi\) | |||||||
\(440\) | −43.7859 | −2.08741 | ||||||||
\(441\) | −2.08652 | −0.0993582 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.8582 | 1.27607 | 0.638035 | − | 0.770007i | \(-0.279747\pi\) | ||||
0.638035 | + | 0.770007i | \(0.279747\pi\) | |||||||
\(444\) | 1.34650 | 0.0639022 | ||||||||
\(445\) | −43.5184 | −2.06297 | ||||||||
\(446\) | −17.3851 | −0.823208 | ||||||||
\(447\) | −22.1144 | −1.04598 | ||||||||
\(448\) | −8.25913 | −0.390207 | ||||||||
\(449\) | −15.5278 | −0.732804 | −0.366402 | − | 0.930457i | \(-0.619411\pi\) | ||||
−0.366402 | + | 0.930457i | \(0.619411\pi\) | |||||||
\(450\) | −17.7478 | −0.836638 | ||||||||
\(451\) | −41.4859 | −1.95349 | ||||||||
\(452\) | −1.59966 | −0.0752418 | ||||||||
\(453\) | −10.4031 | −0.488780 | ||||||||
\(454\) | 8.93986 | 0.419568 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.6362 | −0.872722 | ||||||||
\(457\) | −33.5563 | −1.56970 | −0.784848 | − | 0.619688i | \(-0.787259\pi\) | ||||
−0.784848 | + | 0.619688i | \(0.787259\pi\) | |||||||
\(458\) | 22.1612 | 1.03552 | ||||||||
\(459\) | −9.06527 | −0.423130 | ||||||||
\(460\) | −12.3066 | −0.573799 | ||||||||
\(461\) | 4.34899 | 0.202553 | 0.101276 | − | 0.994858i | \(-0.467707\pi\) | ||||
0.101276 | + | 0.994858i | \(0.467707\pi\) | |||||||
\(462\) | −4.24827 | −0.197647 | ||||||||
\(463\) | −23.2754 | −1.08170 | −0.540850 | − | 0.841119i | \(-0.681897\pi\) | ||||
−0.540850 | + | 0.841119i | \(0.681897\pi\) | |||||||
\(464\) | −16.1716 | −0.750748 | ||||||||
\(465\) | 10.9666 | 0.508564 | ||||||||
\(466\) | 13.5173 | 0.626176 | ||||||||
\(467\) | 12.2510 | 0.566909 | 0.283454 | − | 0.958986i | \(-0.408520\pi\) | ||||
0.283454 | + | 0.958986i | \(0.408520\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.05008 | 0.140840 | ||||||||
\(470\) | 3.29002 | 0.151757 | ||||||||
\(471\) | 13.6248 | 0.627797 | ||||||||
\(472\) | 16.0001 | 0.736464 | ||||||||
\(473\) | −41.3771 | −1.90252 | ||||||||
\(474\) | 0.0988566 | 0.00454063 | ||||||||
\(475\) | 48.6388 | 2.23170 | ||||||||
\(476\) | 1.43238 | 0.0656529 | ||||||||
\(477\) | −13.6357 | −0.624334 | ||||||||
\(478\) | −17.2814 | −0.790434 | ||||||||
\(479\) | 0.683706 | 0.0312393 | 0.0156197 | − | 0.999878i | \(-0.495028\pi\) | ||||
0.0156197 | + | 0.999878i | \(0.495028\pi\) | |||||||
\(480\) | 13.8263 | 0.631080 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1.44930 | −0.0660140 | ||||||||
\(483\) | −4.30289 | −0.195788 | ||||||||
\(484\) | −3.87045 | −0.175930 | ||||||||
\(485\) | 46.9440 | 2.13162 | ||||||||
\(486\) | 17.8983 | 0.811885 | ||||||||
\(487\) | 2.18545 | 0.0990323 | 0.0495162 | − | 0.998773i | \(-0.484232\pi\) | ||||
0.0495162 | + | 0.998773i | \(0.484232\pi\) | |||||||
\(488\) | 5.64677 | 0.255617 | ||||||||
\(489\) | 1.92519 | 0.0870601 | ||||||||
\(490\) | 3.94966 | 0.178428 | ||||||||
\(491\) | 8.81707 | 0.397909 | 0.198954 | − | 0.980009i | \(-0.436245\pi\) | ||||
0.198954 | + | 0.980009i | \(0.436245\pi\) | |||||||
\(492\) | 7.60521 | 0.342870 | ||||||||
\(493\) | 16.0945 | 0.724859 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.7364 | −1.33655 | ||||||||
\(496\) | −6.04128 | −0.271262 | ||||||||
\(497\) | 14.4391 | 0.647684 | ||||||||
\(498\) | −3.37185 | −0.151096 | ||||||||
\(499\) | −16.3801 | −0.733275 | −0.366637 | − | 0.930364i | \(-0.619491\pi\) | ||||
−0.366637 | + | 0.930364i | \(0.619491\pi\) | |||||||
\(500\) | −7.28152 | −0.325639 | ||||||||
\(501\) | 18.0618 | 0.806940 | ||||||||
\(502\) | −22.5143 | −1.00486 | ||||||||
\(503\) | −11.5765 | −0.516168 | −0.258084 | − | 0.966122i | \(-0.583091\pi\) | ||||
−0.258084 | + | 0.966122i | \(0.583091\pi\) | |||||||
\(504\) | −6.41050 | −0.285546 | ||||||||
\(505\) | −27.5090 | −1.22413 | ||||||||
\(506\) | 20.0112 | 0.889608 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.51752 | −0.244800 | ||||||||
\(509\) | −13.3984 | −0.593874 | −0.296937 | − | 0.954897i | \(-0.595965\pi\) | ||||
−0.296937 | + | 0.954897i | \(0.595965\pi\) | |||||||
\(510\) | 7.03914 | 0.311698 | ||||||||
\(511\) | 12.9055 | 0.570904 | ||||||||
\(512\) | −19.1295 | −0.845414 | ||||||||
\(513\) | −30.8540 | −1.36224 | ||||||||
\(514\) | 19.2510 | 0.849127 | ||||||||
\(515\) | −1.27809 | −0.0563195 | ||||||||
\(516\) | 7.58527 | 0.333923 | ||||||||
\(517\) | 3.33597 | 0.146716 | ||||||||
\(518\) | 2.03559 | 0.0894389 | ||||||||
\(519\) | −11.8654 | −0.520834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0891 | 1.66871 | 0.834356 | − | 0.551226i | \(-0.185840\pi\) | ||||
0.834356 | + | 0.551226i | \(0.185840\pi\) | |||||||
\(522\) | −19.9879 | −0.874848 | ||||||||
\(523\) | 1.91936 | 0.0839276 | 0.0419638 | − | 0.999119i | \(-0.486639\pi\) | ||||
0.0419638 | + | 0.999119i | \(0.486639\pi\) | |||||||
\(524\) | 1.13752 | 0.0496927 | ||||||||
\(525\) | −7.32471 | −0.319677 | ||||||||
\(526\) | −12.0856 | −0.526959 | ||||||||
\(527\) | 6.01247 | 0.261907 | ||||||||
\(528\) | −7.17166 | −0.312107 | ||||||||
\(529\) | −2.73147 | −0.118760 | ||||||||
\(530\) | 25.8115 | 1.12118 | ||||||||
\(531\) | 10.8662 | 0.471552 | ||||||||
\(532\) | 4.87514 | 0.211364 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.9724 | −0.561369 | ||||||||
\(535\) | −14.2004 | −0.613938 | ||||||||
\(536\) | 9.37086 | 0.404760 | ||||||||
\(537\) | −8.95923 | −0.386619 | ||||||||
\(538\) | 9.98248 | 0.430375 | ||||||||
\(539\) | 4.00483 | 0.172500 | ||||||||
\(540\) | 13.2892 | 0.571874 | ||||||||
\(541\) | 7.49222 | 0.322116 | 0.161058 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161058 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(542\) | −5.48597 | −0.235642 | ||||||||
\(543\) | 5.57731 | 0.239345 | ||||||||
\(544\) | 7.58029 | 0.325002 | ||||||||
\(545\) | 34.3547 | 1.47159 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.7156 | 0.629192 | 0.314596 | − | 0.949226i | \(-0.398131\pi\) | ||||
0.314596 | + | 0.949226i | \(0.398131\pi\) | |||||||
\(548\) | −3.40955 | −0.145649 | ||||||||
\(549\) | 3.83491 | 0.163670 | ||||||||
\(550\) | 34.0647 | 1.45252 | ||||||||
\(551\) | 54.7781 | 2.33363 | ||||||||
\(552\) | −13.2199 | −0.562677 | ||||||||
\(553\) | −0.0931919 | −0.00396292 | ||||||||
\(554\) | 21.5995 | 0.917677 | ||||||||
\(555\) | −6.23796 | −0.264787 | ||||||||
\(556\) | −13.3297 | −0.565304 | ||||||||
\(557\) | 5.45353 | 0.231073 | 0.115537 | − | 0.993303i | \(-0.463141\pi\) | ||||
0.115537 | + | 0.993303i | \(0.463141\pi\) | |||||||
\(558\) | −7.46696 | −0.316102 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.66758 | 0.281757 | ||||||||
\(561\) | 7.13746 | 0.301344 | ||||||||
\(562\) | 22.3606 | 0.943226 | ||||||||
\(563\) | 36.8364 | 1.55247 | 0.776235 | − | 0.630444i | \(-0.217127\pi\) | ||||
0.776235 | + | 0.630444i | \(0.217127\pi\) | |||||||
\(564\) | −0.611552 | −0.0257510 | ||||||||
\(565\) | 7.41077 | 0.311773 | ||||||||
\(566\) | −25.3367 | −1.06498 | ||||||||
\(567\) | −1.61315 | −0.0677458 | ||||||||
\(568\) | 44.3619 | 1.86138 | ||||||||
\(569\) | 15.0251 | 0.629885 | 0.314942 | − | 0.949111i | \(-0.398015\pi\) | ||||
0.314942 | + | 0.949111i | \(0.398015\pi\) | |||||||
\(570\) | 23.9580 | 1.00349 | ||||||||
\(571\) | 33.2518 | 1.39155 | 0.695773 | − | 0.718262i | \(-0.255062\pi\) | ||||
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.5838 | −0.651023 | ||||||||
\(574\) | 11.4973 | 0.479887 | ||||||||
\(575\) | 34.5027 | 1.43886 | ||||||||
\(576\) | −17.2329 | −0.718036 | ||||||||
\(577\) | −34.7983 | −1.44867 | −0.724335 | − | 0.689448i | \(-0.757853\pi\) | ||||
−0.724335 | + | 0.689448i | \(0.757853\pi\) | |||||||
\(578\) | −15.0089 | −0.624286 | ||||||||
\(579\) | −20.2861 | −0.843063 | ||||||||
\(580\) | −23.5936 | −0.979670 | ||||||||
\(581\) | 3.17863 | 0.131872 | ||||||||
\(582\) | 13.9935 | 0.580049 | ||||||||
\(583\) | 26.1720 | 1.08393 | ||||||||
\(584\) | 39.6499 | 1.64072 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.4915 | −1.21828 | ||||||||
\(587\) | 19.7267 | 0.814210 | 0.407105 | − | 0.913381i | \(-0.366538\pi\) | ||||
0.407105 | + | 0.913381i | \(0.366538\pi\) | |||||||
\(588\) | −0.734167 | −0.0302766 | ||||||||
\(589\) | 20.4636 | 0.843190 | ||||||||
\(590\) | −20.5690 | −0.846814 | ||||||||
\(591\) | 15.3684 | 0.632171 | ||||||||
\(592\) | 3.43637 | 0.141234 | ||||||||
\(593\) | −7.56122 | −0.310502 | −0.155251 | − | 0.987875i | \(-0.549619\pi\) | ||||
−0.155251 | + | 0.987875i | \(0.549619\pi\) | |||||||
\(594\) | −21.6089 | −0.886624 | ||||||||
\(595\) | −6.63578 | −0.272041 | ||||||||
\(596\) | 17.7735 | 0.728031 | ||||||||
\(597\) | −14.7554 | −0.603896 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.48332 | 0.142325 | 0.0711623 | − | 0.997465i | \(-0.477329\pi\) | ||||
0.0711623 | + | 0.997465i | \(0.477329\pi\) | |||||||
\(600\) | −22.5040 | −0.918720 | ||||||||
\(601\) | −43.3614 | −1.76875 | −0.884374 | − | 0.466778i | \(-0.845415\pi\) | ||||
−0.884374 | + | 0.466778i | \(0.845415\pi\) | |||||||
\(602\) | 11.4671 | 0.467366 | ||||||||
\(603\) | 6.36406 | 0.259165 | ||||||||
\(604\) | 8.36103 | 0.340206 | ||||||||
\(605\) | 17.9307 | 0.728985 | ||||||||
\(606\) | −8.20013 | −0.333108 | ||||||||
\(607\) | −24.5108 | −0.994864 | −0.497432 | − | 0.867503i | \(-0.665724\pi\) | ||||
−0.497432 | + | 0.867503i | \(0.665724\pi\) | |||||||
\(608\) | 25.7998 | 1.04632 | ||||||||
\(609\) | −8.24926 | −0.334277 | ||||||||
\(610\) | −7.25925 | −0.293918 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.98869 | 0.120810 | ||||||||
\(613\) | 0.842003 | 0.0340082 | 0.0170041 | − | 0.999855i | \(-0.494587\pi\) | ||||
0.0170041 | + | 0.999855i | \(0.494587\pi\) | |||||||
\(614\) | 7.95604 | 0.321080 | ||||||||
\(615\) | −35.2327 | −1.42072 | ||||||||
\(616\) | 12.3042 | 0.495749 | ||||||||
\(617\) | −11.6951 | −0.470828 | −0.235414 | − | 0.971895i | \(-0.575645\pi\) | ||||
−0.235414 | + | 0.971895i | \(0.575645\pi\) | |||||||
\(618\) | −0.380986 | −0.0153255 | ||||||||
\(619\) | −30.4915 | −1.22556 | −0.612779 | − | 0.790254i | \(-0.709948\pi\) | ||||
−0.612779 | + | 0.790254i | \(0.709948\pi\) | |||||||
\(620\) | −8.81393 | −0.353976 | ||||||||
\(621\) | −21.8867 | −0.878284 | ||||||||
\(622\) | −15.1655 | −0.608083 | ||||||||
\(623\) | 12.2290 | 0.489945 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.58563 | −0.183425 | ||||||||
\(626\) | 11.7450 | 0.469423 | ||||||||
\(627\) | 24.2926 | 0.970153 | ||||||||
\(628\) | −10.9503 | −0.436966 | ||||||||
\(629\) | −3.41998 | −0.136363 | ||||||||
\(630\) | 8.24106 | 0.328332 | ||||||||
\(631\) | 19.0797 | 0.759552 | 0.379776 | − | 0.925078i | \(-0.376001\pi\) | ||||
0.379776 | + | 0.925078i | \(0.376001\pi\) | |||||||
\(632\) | −0.286317 | −0.0113891 | ||||||||
\(633\) | 3.30097 | 0.131202 | ||||||||
\(634\) | 4.05154 | 0.160907 | ||||||||
\(635\) | 25.5611 | 1.01436 | ||||||||
\(636\) | −4.79787 | −0.190248 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 38.3644 | 1.51886 | ||||||||
\(639\) | 30.1276 | 1.19183 | ||||||||
\(640\) | 3.68826 | 0.145791 | ||||||||
\(641\) | 26.9166 | 1.06314 | 0.531571 | − | 0.847014i | \(-0.321602\pi\) | ||||
0.531571 | + | 0.847014i | \(0.321602\pi\) | |||||||
\(642\) | −4.23300 | −0.167063 | ||||||||
\(643\) | 50.6462 | 1.99729 | 0.998646 | − | 0.0520237i | \(-0.0165671\pi\) | ||||
0.998646 | + | 0.0520237i | \(0.0165671\pi\) | |||||||
\(644\) | 3.45826 | 0.136274 | ||||||||
\(645\) | −35.1404 | −1.38365 | ||||||||
\(646\) | 13.1350 | 0.516790 | ||||||||
\(647\) | −38.2321 | −1.50306 | −0.751530 | − | 0.659699i | \(-0.770684\pi\) | ||||
−0.751530 | + | 0.659699i | \(0.770684\pi\) | |||||||
\(648\) | −4.95613 | −0.194695 | ||||||||
\(649\) | −20.8563 | −0.818683 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.08170 | −0.120781 | ||||||||
\(652\) | −1.54729 | −0.0605964 | ||||||||
\(653\) | −10.3427 | −0.404742 | −0.202371 | − | 0.979309i | \(-0.564865\pi\) | ||||
−0.202371 | + | 0.979309i | \(0.564865\pi\) | |||||||
\(654\) | 10.2408 | 0.400446 | ||||||||
\(655\) | −5.26979 | −0.205908 | ||||||||
\(656\) | 19.4090 | 0.757795 | ||||||||
\(657\) | 26.9275 | 1.05054 | ||||||||
\(658\) | −0.924522 | −0.0360416 | ||||||||
\(659\) | 12.8844 | 0.501904 | 0.250952 | − | 0.968000i | \(-0.419256\pi\) | ||||
0.250952 | + | 0.968000i | \(0.419256\pi\) | |||||||
\(660\) | −10.4631 | −0.407276 | ||||||||
\(661\) | 19.1895 | 0.746385 | 0.373192 | − | 0.927754i | \(-0.378263\pi\) | ||||
0.373192 | + | 0.927754i | \(0.378263\pi\) | |||||||
\(662\) | −24.1484 | −0.938555 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.76582 | 0.378987 | ||||||||
\(665\) | −22.5851 | −0.875813 | ||||||||
\(666\) | 4.24731 | 0.164580 | ||||||||
\(667\) | 38.8577 | 1.50458 | ||||||||
\(668\) | −14.5163 | −0.561654 | ||||||||
\(669\) | −14.9709 | −0.578807 | ||||||||
\(670\) | −12.0468 | −0.465408 | ||||||||
\(671\) | −7.36064 | −0.284154 | ||||||||
\(672\) | −3.88529 | −0.149878 | ||||||||
\(673\) | 11.1856 | 0.431172 | 0.215586 | − | 0.976485i | \(-0.430834\pi\) | ||||
0.215586 | + | 0.976485i | \(0.430834\pi\) | |||||||
\(674\) | −19.8533 | −0.764721 | ||||||||
\(675\) | −37.2573 | −1.43403 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.4527 | −0.632330 | −0.316165 | − | 0.948704i | \(-0.602395\pi\) | ||||
−0.316165 | + | 0.948704i | \(0.602395\pi\) | |||||||
\(678\) | 2.20907 | 0.0848388 | ||||||||
\(679\) | −13.1916 | −0.506248 | ||||||||
\(680\) | −20.3873 | −0.781819 | ||||||||
\(681\) | 7.69840 | 0.295003 | ||||||||
\(682\) | 14.3319 | 0.548798 | ||||||||
\(683\) | −13.5271 | −0.517600 | −0.258800 | − | 0.965931i | \(-0.583327\pi\) | ||||
−0.258800 | + | 0.965931i | \(0.583327\pi\) | |||||||
\(684\) | 10.1721 | 0.388940 | ||||||||
\(685\) | 15.7954 | 0.603512 | ||||||||
\(686\) | −1.10989 | −0.0423757 | ||||||||
\(687\) | 19.0837 | 0.728089 | ||||||||
\(688\) | 19.3581 | 0.738021 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16.9950 | 0.646987 | ||||||||
\(691\) | −20.5171 | −0.780507 | −0.390254 | − | 0.920707i | \(-0.627613\pi\) | ||||
−0.390254 | + | 0.920707i | \(0.627613\pi\) | |||||||
\(692\) | 9.53632 | 0.362516 | ||||||||
\(693\) | 8.35617 | 0.317425 | ||||||||
\(694\) | 12.4738 | 0.473500 | ||||||||
\(695\) | 61.7525 | 2.34241 | ||||||||
\(696\) | −25.3445 | −0.960680 | ||||||||
\(697\) | −19.3164 | −0.731662 | ||||||||
\(698\) | 27.1016 | 1.02581 | ||||||||
\(699\) | 11.6402 | 0.440272 | ||||||||
\(700\) | 5.88692 | 0.222505 | ||||||||
\(701\) | 46.6380 | 1.76149 | 0.880747 | − | 0.473587i | \(-0.157041\pi\) | ||||
0.880747 | + | 0.473587i | \(0.157041\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6400 | −0.439011 | ||||||||
\(704\) | 33.0764 | 1.24661 | ||||||||
\(705\) | 2.83314 | 0.106702 | ||||||||
\(706\) | 17.6552 | 0.664462 | ||||||||
\(707\) | 7.73025 | 0.290726 | ||||||||
\(708\) | 3.82339 | 0.143692 | ||||||||
\(709\) | −42.2314 | −1.58603 | −0.793017 | − | 0.609199i | \(-0.791491\pi\) | ||||
−0.793017 | + | 0.609199i | \(0.791491\pi\) | |||||||
\(710\) | −57.0297 | −2.14029 | ||||||||
\(711\) | −0.194447 | −0.00729233 | ||||||||
\(712\) | 37.5716 | 1.40806 | ||||||||
\(713\) | 14.5162 | 0.543636 | ||||||||
\(714\) | −1.97806 | −0.0740269 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.20059 | 0.269099 | ||||||||
\(717\) | −14.8816 | −0.555764 | ||||||||
\(718\) | −13.8132 | −0.515504 | ||||||||
\(719\) | 37.9404 | 1.41494 | 0.707469 | − | 0.706744i | \(-0.249837\pi\) | ||||
0.707469 | + | 0.706744i | \(0.249837\pi\) | |||||||
\(720\) | 13.9121 | 0.518472 | ||||||||
\(721\) | 0.359154 | 0.0133756 | ||||||||
\(722\) | 23.6176 | 0.878957 | ||||||||
\(723\) | −1.24804 | −0.0464152 | ||||||||
\(724\) | −4.48252 | −0.166591 | ||||||||
\(725\) | 66.1466 | 2.45662 | ||||||||
\(726\) | 5.34494 | 0.198369 | ||||||||
\(727\) | −16.5215 | −0.612748 | −0.306374 | − | 0.951911i | \(-0.599116\pi\) | ||||
−0.306374 | + | 0.951911i | \(0.599116\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.5734 | 0.391607 | ||||||||
\(730\) | −50.9722 | −1.88657 | ||||||||
\(731\) | −19.2658 | −0.712571 | ||||||||
\(732\) | 1.34936 | 0.0498737 | ||||||||
\(733\) | −17.6511 | −0.651957 | −0.325978 | − | 0.945377i | \(-0.605694\pi\) | ||||
−0.325978 | + | 0.945377i | \(0.605694\pi\) | |||||||
\(734\) | −20.2042 | −0.745750 | ||||||||
\(735\) | 3.40118 | 0.125455 | ||||||||
\(736\) | 18.3015 | 0.674601 | ||||||||
\(737\) | −12.2150 | −0.449947 | ||||||||
\(738\) | 23.9893 | 0.883060 | ||||||||
\(739\) | 0.370373 | 0.0136244 | 0.00681220 | − | 0.999977i | \(-0.497832\pi\) | ||||
0.00681220 | + | 0.999977i | \(0.497832\pi\) | |||||||
\(740\) | 5.01349 | 0.184299 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.25324 | −0.266275 | ||||||||
\(743\) | −17.5579 | −0.644137 | −0.322068 | − | 0.946716i | \(-0.604378\pi\) | ||||
−0.322068 | + | 0.946716i | \(0.604378\pi\) | |||||||
\(744\) | −9.46802 | −0.347115 | ||||||||
\(745\) | −82.3395 | −3.01668 | ||||||||
\(746\) | 36.2742 | 1.32809 | ||||||||
\(747\) | 6.63229 | 0.242663 | ||||||||
\(748\) | −5.73642 | −0.209744 | ||||||||
\(749\) | 3.99044 | 0.145807 | ||||||||
\(750\) | 10.0555 | 0.367175 | ||||||||
\(751\) | −15.0706 | −0.549933 | −0.274967 | − | 0.961454i | \(-0.588667\pi\) | ||||
−0.274967 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(752\) | −1.56072 | −0.0569137 | ||||||||
\(753\) | −19.3878 | −0.706530 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.7342 | −1.40968 | ||||||||
\(756\) | −3.73436 | −0.135817 | ||||||||
\(757\) | 39.8030 | 1.44666 | 0.723332 | − | 0.690500i | \(-0.242609\pi\) | ||||
0.723332 | + | 0.690500i | \(0.242609\pi\) | |||||||
\(758\) | −9.78689 | −0.355476 | ||||||||
\(759\) | 17.2323 | 0.625494 | ||||||||
\(760\) | −69.3890 | −2.51700 | ||||||||
\(761\) | −20.7066 | −0.750613 | −0.375306 | − | 0.926901i | \(-0.622462\pi\) | ||||
−0.375306 | + | 0.926901i | \(0.622462\pi\) | |||||||
\(762\) | 7.61948 | 0.276025 | ||||||||
\(763\) | −9.65395 | −0.349497 | ||||||||
\(764\) | 12.5248 | 0.453131 | ||||||||
\(765\) | −13.8457 | −0.500593 | ||||||||
\(766\) | 2.82315 | 0.102005 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −14.6881 | −0.530010 | ||||||||
\(769\) | 13.2638 | 0.478306 | 0.239153 | − | 0.970982i | \(-0.423130\pi\) | ||||
0.239153 | + | 0.970982i | \(0.423130\pi\) | |||||||
\(770\) | −15.8177 | −0.570031 | ||||||||
\(771\) | 16.5777 | 0.597031 | ||||||||
\(772\) | 16.3041 | 0.586798 | ||||||||
\(773\) | 11.6627 | 0.419478 | 0.209739 | − | 0.977757i | \(-0.432739\pi\) | ||||
0.209739 | + | 0.977757i | \(0.432739\pi\) | |||||||
\(774\) | 23.9264 | 0.860018 | ||||||||
\(775\) | 24.7106 | 0.887632 | ||||||||
\(776\) | −40.5291 | −1.45491 | ||||||||
\(777\) | 1.75292 | 0.0628855 | ||||||||
\(778\) | −0.573486 | −0.0205605 | ||||||||
\(779\) | −65.7442 | −2.35553 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −57.8263 | −2.06919 | ||||||||
\(782\) | 9.31753 | 0.333194 | ||||||||
\(783\) | −41.9600 | −1.49953 | ||||||||
\(784\) | −1.87364 | −0.0669159 | ||||||||
\(785\) | 50.7297 | 1.81062 | ||||||||
\(786\) | −1.57087 | −0.0560310 | ||||||||
\(787\) | 5.00642 | 0.178460 | 0.0892298 | − | 0.996011i | \(-0.471559\pi\) | ||||
0.0892298 | + | 0.996011i | \(0.471559\pi\) | |||||||
\(788\) | −12.3517 | −0.440010 | ||||||||
\(789\) | −10.4073 | −0.370511 | ||||||||
\(790\) | 0.368077 | 0.0130956 | ||||||||
\(791\) | −2.08248 | −0.0740446 | ||||||||
\(792\) | 25.6730 | 0.912249 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 28.7412 | 1.01999 | ||||||||
\(795\) | 22.2271 | 0.788315 | ||||||||
\(796\) | 11.8590 | 0.420330 | ||||||||
\(797\) | 9.95893 | 0.352763 | 0.176382 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176382 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(798\) | −6.73238 | −0.238324 | ||||||||
\(799\) | 1.55328 | 0.0549511 | ||||||||
\(800\) | 31.1542 | 1.10147 | ||||||||
\(801\) | 25.5161 | 0.901568 | ||||||||
\(802\) | 11.3756 | 0.401687 | ||||||||
\(803\) | −51.6842 | −1.82389 | ||||||||
\(804\) | 2.23927 | 0.0789729 | ||||||||
\(805\) | −16.0211 | −0.564670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.59623 | 0.302602 | ||||||||
\(808\) | 23.7499 | 0.835519 | ||||||||
\(809\) | 12.0200 | 0.422601 | 0.211300 | − | 0.977421i | \(-0.432230\pi\) | ||||
0.211300 | + | 0.977421i | \(0.432230\pi\) | |||||||
\(810\) | 6.37139 | 0.223868 | ||||||||
\(811\) | −2.91856 | −0.102484 | −0.0512422 | − | 0.998686i | \(-0.516318\pi\) | ||||
−0.0512422 | + | 0.998686i | \(0.516318\pi\) | |||||||
\(812\) | 6.62998 | 0.232667 | ||||||||
\(813\) | −4.72414 | −0.165683 | ||||||||
\(814\) | −8.15221 | −0.285735 | ||||||||
\(815\) | 7.16813 | 0.251089 | ||||||||
\(816\) | −3.33923 | −0.116897 | ||||||||
\(817\) | −65.5718 | −2.29407 | ||||||||
\(818\) | −22.7638 | −0.795919 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 28.3168 | 0.988865 | ||||||||
\(821\) | −12.9996 | −0.453689 | −0.226844 | − | 0.973931i | \(-0.572841\pi\) | ||||
−0.226844 | + | 0.973931i | \(0.572841\pi\) | |||||||
\(822\) | 4.70845 | 0.164226 | ||||||||
\(823\) | −39.6283 | −1.38136 | −0.690678 | − | 0.723163i | \(-0.742688\pi\) | ||||
−0.690678 | + | 0.723163i | \(0.742688\pi\) | |||||||
\(824\) | 1.10344 | 0.0384402 | ||||||||
\(825\) | 29.3342 | 1.02129 | ||||||||
\(826\) | 5.78007 | 0.201114 | ||||||||
\(827\) | 31.5319 | 1.09647 | 0.548237 | − | 0.836323i | \(-0.315299\pi\) | ||||
0.548237 | + | 0.836323i | \(0.315299\pi\) | |||||||
\(828\) | 7.21574 | 0.250764 | ||||||||
\(829\) | 36.2352 | 1.25850 | 0.629251 | − | 0.777202i | \(-0.283362\pi\) | ||||
0.629251 | + | 0.777202i | \(0.283362\pi\) | |||||||
\(830\) | −12.5545 | −0.435774 | ||||||||
\(831\) | 18.6001 | 0.645229 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.86471 | 0.0646083 | ||||||||
\(834\) | 18.4078 | 0.637408 | ||||||||
\(835\) | 67.2500 | 2.32728 | ||||||||
\(836\) | −19.5241 | −0.675256 | ||||||||
\(837\) | −15.6752 | −0.541813 | ||||||||
\(838\) | 16.9125 | 0.584232 | ||||||||
\(839\) | 12.0623 | 0.416438 | 0.208219 | − | 0.978082i | \(-0.433233\pi\) | ||||
0.208219 | + | 0.978082i | \(0.433233\pi\) | |||||||
\(840\) | 10.4496 | 0.360545 | ||||||||
\(841\) | 45.4959 | 1.56882 | ||||||||
\(842\) | 29.2839 | 1.00919 | ||||||||
\(843\) | 19.2555 | 0.663193 | ||||||||
\(844\) | −2.65301 | −0.0913204 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.92904 | −0.0663217 | ||||||||
\(847\) | −5.03866 | −0.173130 | ||||||||
\(848\) | −12.2445 | −0.420477 | ||||||||
\(849\) | −21.8182 | −0.748800 | ||||||||
\(850\) | 15.8610 | 0.544029 | ||||||||
\(851\) | −8.25702 | −0.283047 | ||||||||
\(852\) | 10.6007 | 0.363176 | ||||||||
\(853\) | 11.7255 | 0.401475 | 0.200738 | − | 0.979645i | \(-0.435666\pi\) | ||||
0.200738 | + | 0.979645i | \(0.435666\pi\) | |||||||
\(854\) | 2.03991 | 0.0698042 | ||||||||
\(855\) | −47.1244 | −1.61162 | ||||||||
\(856\) | 12.2600 | 0.419037 | ||||||||
\(857\) | 28.0128 | 0.956900 | 0.478450 | − | 0.878115i | \(-0.341199\pi\) | ||||
0.478450 | + | 0.878115i | \(0.341199\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.70001 | 0.194482 | 0.0972408 | − | 0.995261i | \(-0.468998\pi\) | ||||
0.0972408 | + | 0.995261i | \(0.468998\pi\) | |||||||
\(860\) | 28.2425 | 0.963063 | ||||||||
\(861\) | 9.90068 | 0.337414 | ||||||||
\(862\) | −42.0759 | −1.43311 | ||||||||
\(863\) | −41.0325 | −1.39676 | −0.698381 | − | 0.715726i | \(-0.746096\pi\) | ||||
−0.698381 | + | 0.715726i | \(0.746096\pi\) | |||||||
\(864\) | −19.7626 | −0.672339 | ||||||||
\(865\) | −44.1790 | −1.50213 | ||||||||
\(866\) | 9.44579 | 0.320981 | ||||||||
\(867\) | −12.9246 | −0.438943 | ||||||||
\(868\) | 2.47678 | 0.0840676 | ||||||||
\(869\) | 0.373218 | 0.0126605 | ||||||||
\(870\) | 32.5818 | 1.10463 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −29.6602 | −1.00442 | ||||||||
\(873\) | −27.5246 | −0.931568 | ||||||||
\(874\) | 31.7125 | 1.07269 | ||||||||
\(875\) | −9.47929 | −0.320458 | ||||||||
\(876\) | 9.47477 | 0.320123 | ||||||||
\(877\) | −10.7401 | −0.362668 | −0.181334 | − | 0.983422i | \(-0.558042\pi\) | ||||
−0.181334 | + | 0.983422i | \(0.558042\pi\) | |||||||
\(878\) | 20.6551 | 0.697077 | ||||||||
\(879\) | −25.3961 | −0.856590 | ||||||||
\(880\) | −26.7025 | −0.900142 | ||||||||
\(881\) | 37.5517 | 1.26515 | 0.632574 | − | 0.774500i | \(-0.281998\pi\) | ||||
0.632574 | + | 0.774500i | \(0.281998\pi\) | |||||||
\(882\) | −2.31581 | −0.0779772 | ||||||||
\(883\) | 47.1134 | 1.58549 | 0.792745 | − | 0.609553i | \(-0.208651\pi\) | ||||
0.792745 | + | 0.609553i | \(0.208651\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −17.7127 | −0.595405 | ||||||||
\(886\) | 29.8095 | 1.00147 | ||||||||
\(887\) | 5.06090 | 0.169928 | 0.0849642 | − | 0.996384i | \(-0.472922\pi\) | ||||
0.0849642 | + | 0.996384i | \(0.472922\pi\) | |||||||
\(888\) | 5.38555 | 0.180727 | ||||||||
\(889\) | −7.18287 | −0.240906 | ||||||||
\(890\) | −48.3005 | −1.61904 | ||||||||
\(891\) | 6.46038 | 0.216431 | ||||||||
\(892\) | 12.0322 | 0.402867 | ||||||||
\(893\) | 5.28664 | 0.176911 | ||||||||
\(894\) | −24.5445 | −0.820891 | ||||||||
\(895\) | −33.3582 | −1.11504 | ||||||||
\(896\) | −1.03643 | −0.0346247 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2342 | −0.575111 | ||||||||
\(899\) | 27.8297 | 0.928171 | ||||||||
\(900\) | 12.2832 | 0.409440 | ||||||||
\(901\) | 12.1861 | 0.405977 | ||||||||
\(902\) | −46.0447 | −1.53312 | ||||||||
\(903\) | 9.87472 | 0.328610 | ||||||||
\(904\) | −6.39809 | −0.212797 | ||||||||
\(905\) | 20.7662 | 0.690292 | ||||||||
\(906\) | −11.5463 | −0.383599 | ||||||||
\(907\) | −48.6215 | −1.61445 | −0.807226 | − | 0.590243i | \(-0.799032\pi\) | ||||
−0.807226 | + | 0.590243i | \(0.799032\pi\) | |||||||
\(908\) | −6.18726 | −0.205331 | ||||||||
\(909\) | 16.1293 | 0.534976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.76756 | 0.0585620 | 0.0292810 | − | 0.999571i | \(-0.490678\pi\) | ||||
0.0292810 | + | 0.999571i | \(0.490678\pi\) | |||||||
\(912\) | −11.3652 | −0.376339 | ||||||||
\(913\) | −12.7299 | −0.421297 | ||||||||
\(914\) | −37.2437 | −1.23191 | ||||||||
\(915\) | −6.25118 | −0.206658 | ||||||||
\(916\) | −15.3377 | −0.506772 | ||||||||
\(917\) | 1.48085 | 0.0489021 | ||||||||
\(918\) | −10.0614 | −0.332076 | ||||||||
\(919\) | 27.4163 | 0.904380 | 0.452190 | − | 0.891922i | \(-0.350643\pi\) | ||||
0.452190 | + | 0.891922i | \(0.350643\pi\) | |||||||
\(920\) | −49.2222 | −1.62281 | ||||||||
\(921\) | 6.85120 | 0.225755 | ||||||||
\(922\) | 4.82689 | 0.158965 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.94022 | 0.0967260 | ||||||||
\(925\) | −14.0557 | −0.462150 | ||||||||
\(926\) | −25.8331 | −0.848928 | ||||||||
\(927\) | 0.749383 | 0.0246130 | ||||||||
\(928\) | 35.0866 | 1.15177 | ||||||||
\(929\) | 31.0105 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330122\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330122\pi\) | |||||||
\(930\) | 12.1717 | 0.399125 | ||||||||
\(931\) | 6.34660 | 0.208001 | ||||||||
\(932\) | −9.35528 | −0.306442 | ||||||||
\(933\) | −13.0595 | −0.427550 | ||||||||
\(934\) | 13.5972 | 0.444915 | ||||||||
\(935\) | 26.5752 | 0.869101 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.5463 | −0.442537 | −0.221269 | − | 0.975213i | \(-0.571020\pi\) | ||||
−0.221269 | + | 0.975213i | \(0.571020\pi\) | |||||||
\(938\) | 3.38524 | 0.110532 | ||||||||
\(939\) | 10.1140 | 0.330057 | ||||||||
\(940\) | −2.27702 | −0.0742681 | ||||||||
\(941\) | 27.1579 | 0.885321 | 0.442661 | − | 0.896689i | \(-0.354035\pi\) | ||||
0.442661 | + | 0.896689i | \(0.354035\pi\) | |||||||
\(942\) | 15.1220 | 0.492701 | ||||||||
\(943\) | −46.6367 | −1.51870 | ||||||||
\(944\) | 9.75756 | 0.317581 | ||||||||
\(945\) | 17.3002 | 0.562775 | ||||||||
\(946\) | −45.9239 | −1.49312 | ||||||||
\(947\) | −30.1736 | −0.980511 | −0.490256 | − | 0.871579i | \(-0.663097\pi\) | ||||
−0.490256 | + | 0.871579i | \(0.663097\pi\) | |||||||
\(948\) | −0.0684184 | −0.00222213 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 53.9835 | 1.75146 | ||||||||
\(951\) | 3.48892 | 0.113136 | ||||||||
\(952\) | 5.72901 | 0.185678 | ||||||||
\(953\) | 13.0194 | 0.421738 | 0.210869 | − | 0.977514i | \(-0.432371\pi\) | ||||
0.210869 | + | 0.977514i | \(0.432371\pi\) | |||||||
\(954\) | −15.1341 | −0.489983 | ||||||||
\(955\) | −58.0237 | −1.87760 | ||||||||
\(956\) | 11.9604 | 0.386828 | ||||||||
\(957\) | 33.0369 | 1.06793 | ||||||||
\(958\) | 0.758836 | 0.0245169 | ||||||||
\(959\) | −4.43864 | −0.143331 | ||||||||
\(960\) | 28.0908 | 0.906627 | ||||||||
\(961\) | −20.6036 | −0.664632 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.32614 | 0.268306 | ||||||||
\(964\) | 1.00306 | 0.0323064 | ||||||||
\(965\) | −75.5322 | −2.43147 | ||||||||
\(966\) | −4.77572 | −0.153656 | ||||||||
\(967\) | −49.5415 | −1.59315 | −0.796573 | − | 0.604542i | \(-0.793356\pi\) | ||||
−0.796573 | + | 0.604542i | \(0.793356\pi\) | |||||||
\(968\) | −15.4805 | −0.497561 | ||||||||
\(969\) | 11.3110 | 0.363361 | ||||||||
\(970\) | 52.1025 | 1.67291 | ||||||||
\(971\) | −34.3718 | −1.10304 | −0.551522 | − | 0.834160i | \(-0.685953\pi\) | ||||
−0.551522 | + | 0.834160i | \(0.685953\pi\) | |||||||
\(972\) | −12.3874 | −0.397326 | ||||||||
\(973\) | −17.3529 | −0.556310 | ||||||||
\(974\) | 2.42561 | 0.0777214 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.44365 | 0.110228 | ||||||||
\(977\) | −10.8964 | −0.348607 | −0.174303 | − | 0.984692i | \(-0.555767\pi\) | ||||
−0.174303 | + | 0.984692i | \(0.555767\pi\) | |||||||
\(978\) | 2.13674 | 0.0683255 | ||||||||
\(979\) | −48.9751 | −1.56525 | ||||||||
\(980\) | −2.73355 | −0.0873202 | ||||||||
\(981\) | −20.1432 | −0.643123 | ||||||||
\(982\) | 9.78595 | 0.312282 | ||||||||
\(983\) | 17.8803 | 0.570293 | 0.285146 | − | 0.958484i | \(-0.407958\pi\) | ||||
0.285146 | + | 0.958484i | \(0.407958\pi\) | |||||||
\(984\) | 30.4182 | 0.969697 | ||||||||
\(985\) | 57.2217 | 1.82323 | ||||||||
\(986\) | 17.8631 | 0.568876 | ||||||||
\(987\) | −0.796136 | −0.0253413 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.5144 | −1.47907 | ||||||||
\(990\) | −33.0041 | −1.04894 | ||||||||
\(991\) | −43.2925 | −1.37523 | −0.687616 | − | 0.726074i | \(-0.741343\pi\) | ||||
−0.687616 | + | 0.726074i | \(0.741343\pi\) | |||||||
\(992\) | 13.1074 | 0.416161 | ||||||||
\(993\) | −20.7950 | −0.659909 | ||||||||
\(994\) | 16.0258 | 0.508308 | ||||||||
\(995\) | −54.9392 | −1.74169 | ||||||||
\(996\) | 2.33365 | 0.0739444 | ||||||||
\(997\) | 25.7004 | 0.813940 | 0.406970 | − | 0.913442i | \(-0.366585\pi\) | ||||
0.406970 | + | 0.913442i | \(0.366585\pi\) | |||||||
\(998\) | −18.1801 | −0.575480 | ||||||||
\(999\) | 8.91625 | 0.282098 |
(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 | 1183.2.a.q.1.9 | ✓ | 12 | |
7.6 | odd | 2 | 8281.2.a.cn.1.9 | 12 | |||
13.5 | odd | 4 | 1183.2.c.j.337.8 | 24 | |||
13.8 | odd | 4 | 1183.2.c.j.337.17 | 24 | |||
13.12 | even | 2 | 1183.2.a.r.1.4 | yes | 12 | ||
91.90 | odd | 2 | 8281.2.a.cq.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1183.2.a.q.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
1183.2.a.r.1.4 | yes | 12 | 13.12 | even | 2 | ||
1183.2.c.j.337.8 | 24 | 13.5 | odd | 4 | |||
1183.2.c.j.337.17 | 24 | 13.8 | odd | 4 | |||
8281.2.a.cn.1.9 | 12 | 7.6 | odd | 2 | |||
8281.2.a.cq.1.4 | 12 | 91.90 | odd | 2 |