Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4011,2,Mod(1,4011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4011, 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("4011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4011 = 3 \cdot 7 \cdot 191 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4011.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: | \(32.0279962507\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23874 | −1.58303 | −0.791513 | − | 0.611152i | \(-0.790706\pi\) | ||||
−0.791513 | + | 0.611152i | \(0.790706\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.01194 | 1.50597 | ||||||||
\(5\) | 1.19635 | 0.535026 | 0.267513 | − | 0.963554i | \(-0.413798\pi\) | ||||
0.267513 | + | 0.963554i | \(0.413798\pi\) | |||||||
\(6\) | 2.23874 | 0.913961 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.26547 | −0.800966 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.67832 | −0.846960 | ||||||||
\(11\) | 4.91098 | 1.48072 | 0.740358 | − | 0.672213i | \(-0.234656\pi\) | ||||
0.740358 | + | 0.672213i | \(0.234656\pi\) | |||||||
\(12\) | −3.01194 | −0.869473 | ||||||||
\(13\) | 4.83040 | 1.33971 | 0.669856 | − | 0.742491i | \(-0.266356\pi\) | ||||
0.669856 | + | 0.742491i | \(0.266356\pi\) | |||||||
\(14\) | −2.23874 | −0.598328 | ||||||||
\(15\) | −1.19635 | −0.308897 | ||||||||
\(16\) | −0.952086 | −0.238022 | ||||||||
\(17\) | −6.57397 | −1.59442 | −0.797211 | − | 0.603701i | \(-0.793692\pi\) | ||||
−0.797211 | + | 0.603701i | \(0.793692\pi\) | |||||||
\(18\) | −2.23874 | −0.527675 | ||||||||
\(19\) | −2.90324 | −0.666049 | −0.333024 | − | 0.942918i | \(-0.608069\pi\) | ||||
−0.333024 | + | 0.942918i | \(0.608069\pi\) | |||||||
\(20\) | 3.60335 | 0.805734 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −10.9944 | −2.34401 | ||||||||
\(23\) | −6.64434 | −1.38544 | −0.692720 | − | 0.721206i | \(-0.743588\pi\) | ||||
−0.692720 | + | 0.721206i | \(0.743588\pi\) | |||||||
\(24\) | 2.26547 | 0.462438 | ||||||||
\(25\) | −3.56874 | −0.713747 | ||||||||
\(26\) | −10.8140 | −2.12080 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.01194 | 0.569204 | ||||||||
\(29\) | 5.61643 | 1.04294 | 0.521472 | − | 0.853268i | \(-0.325383\pi\) | ||||
0.521472 | + | 0.853268i | \(0.325383\pi\) | |||||||
\(30\) | 2.67832 | 0.488993 | ||||||||
\(31\) | 8.36935 | 1.50318 | 0.751590 | − | 0.659631i | \(-0.229287\pi\) | ||||
0.751590 | + | 0.659631i | \(0.229287\pi\) | |||||||
\(32\) | 6.66242 | 1.17776 | ||||||||
\(33\) | −4.91098 | −0.854892 | ||||||||
\(34\) | 14.7174 | 2.52401 | ||||||||
\(35\) | 1.19635 | 0.202221 | ||||||||
\(36\) | 3.01194 | 0.501990 | ||||||||
\(37\) | 6.18380 | 1.01661 | 0.508306 | − | 0.861177i | \(-0.330272\pi\) | ||||
0.508306 | + | 0.861177i | \(0.330272\pi\) | |||||||
\(38\) | 6.49959 | 1.05437 | ||||||||
\(39\) | −4.83040 | −0.773483 | ||||||||
\(40\) | −2.71031 | −0.428538 | ||||||||
\(41\) | 9.01478 | 1.40787 | 0.703936 | − | 0.710263i | \(-0.251424\pi\) | ||||
0.703936 | + | 0.710263i | \(0.251424\pi\) | |||||||
\(42\) | 2.23874 | 0.345445 | ||||||||
\(43\) | −0.0607989 | −0.00927174 | −0.00463587 | − | 0.999989i | \(-0.501476\pi\) | ||||
−0.00463587 | + | 0.999989i | \(0.501476\pi\) | |||||||
\(44\) | 14.7916 | 2.22992 | ||||||||
\(45\) | 1.19635 | 0.178342 | ||||||||
\(46\) | 14.8749 | 2.19319 | ||||||||
\(47\) | −7.86001 | −1.14650 | −0.573250 | − | 0.819381i | \(-0.694318\pi\) | ||||
−0.573250 | + | 0.819381i | \(0.694318\pi\) | |||||||
\(48\) | 0.952086 | 0.137422 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 7.98946 | 1.12988 | ||||||||
\(51\) | 6.57397 | 0.920540 | ||||||||
\(52\) | 14.5489 | 2.01757 | ||||||||
\(53\) | 0.959377 | 0.131781 | 0.0658903 | − | 0.997827i | \(-0.479011\pi\) | ||||
0.0658903 | + | 0.997827i | \(0.479011\pi\) | |||||||
\(54\) | 2.23874 | 0.304654 | ||||||||
\(55\) | 5.87527 | 0.792222 | ||||||||
\(56\) | −2.26547 | −0.302737 | ||||||||
\(57\) | 2.90324 | 0.384544 | ||||||||
\(58\) | −12.5737 | −1.65101 | ||||||||
\(59\) | 4.62990 | 0.602762 | 0.301381 | − | 0.953504i | \(-0.402552\pi\) | ||||
0.301381 | + | 0.953504i | \(0.402552\pi\) | |||||||
\(60\) | −3.60335 | −0.465191 | ||||||||
\(61\) | 1.52750 | 0.195577 | 0.0977883 | − | 0.995207i | \(-0.468823\pi\) | ||||
0.0977883 | + | 0.995207i | \(0.468823\pi\) | |||||||
\(62\) | −18.7368 | −2.37957 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −13.0112 | −1.62640 | ||||||||
\(65\) | 5.77887 | 0.716780 | ||||||||
\(66\) | 10.9944 | 1.35332 | ||||||||
\(67\) | 5.11522 | 0.624924 | 0.312462 | − | 0.949930i | \(-0.398846\pi\) | ||||
0.312462 | + | 0.949930i | \(0.398846\pi\) | |||||||
\(68\) | −19.8004 | −2.40115 | ||||||||
\(69\) | 6.64434 | 0.799885 | ||||||||
\(70\) | −2.67832 | −0.320121 | ||||||||
\(71\) | −7.71447 | −0.915539 | −0.457769 | − | 0.889071i | \(-0.651351\pi\) | ||||
−0.457769 | + | 0.889071i | \(0.651351\pi\) | |||||||
\(72\) | −2.26547 | −0.266989 | ||||||||
\(73\) | 5.82688 | 0.681984 | 0.340992 | − | 0.940066i | \(-0.389237\pi\) | ||||
0.340992 | + | 0.940066i | \(0.389237\pi\) | |||||||
\(74\) | −13.8439 | −1.60932 | ||||||||
\(75\) | 3.56874 | 0.412082 | ||||||||
\(76\) | −8.74439 | −1.00305 | ||||||||
\(77\) | 4.91098 | 0.559658 | ||||||||
\(78\) | 10.8140 | 1.22444 | ||||||||
\(79\) | 8.80672 | 0.990833 | 0.495417 | − | 0.868656i | \(-0.335015\pi\) | ||||
0.495417 | + | 0.868656i | \(0.335015\pi\) | |||||||
\(80\) | −1.13903 | −0.127348 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −20.1817 | −2.22870 | ||||||||
\(83\) | −3.10269 | −0.340564 | −0.170282 | − | 0.985395i | \(-0.554468\pi\) | ||||
−0.170282 | + | 0.985395i | \(0.554468\pi\) | |||||||
\(84\) | −3.01194 | −0.328630 | ||||||||
\(85\) | −7.86480 | −0.853057 | ||||||||
\(86\) | 0.136113 | 0.0146774 | ||||||||
\(87\) | −5.61643 | −0.602144 | ||||||||
\(88\) | −11.1257 | −1.18600 | ||||||||
\(89\) | −1.15416 | −0.122341 | −0.0611703 | − | 0.998127i | \(-0.519483\pi\) | ||||
−0.0611703 | + | 0.998127i | \(0.519483\pi\) | |||||||
\(90\) | −2.67832 | −0.282320 | ||||||||
\(91\) | 4.83040 | 0.506363 | ||||||||
\(92\) | −20.0124 | −2.08643 | ||||||||
\(93\) | −8.36935 | −0.867861 | ||||||||
\(94\) | 17.5965 | 1.81494 | ||||||||
\(95\) | −3.47330 | −0.356354 | ||||||||
\(96\) | −6.66242 | −0.679980 | ||||||||
\(97\) | 11.1893 | 1.13610 | 0.568050 | − | 0.822994i | \(-0.307698\pi\) | ||||
0.568050 | + | 0.822994i | \(0.307698\pi\) | |||||||
\(98\) | −2.23874 | −0.226147 | ||||||||
\(99\) | 4.91098 | 0.493572 | ||||||||
\(100\) | −10.7488 | −1.07488 | ||||||||
\(101\) | −7.91000 | −0.787074 | −0.393537 | − | 0.919309i | \(-0.628749\pi\) | ||||
−0.393537 | + | 0.919309i | \(0.628749\pi\) | |||||||
\(102\) | −14.7174 | −1.45724 | ||||||||
\(103\) | −0.523257 | −0.0515580 | −0.0257790 | − | 0.999668i | \(-0.508207\pi\) | ||||
−0.0257790 | + | 0.999668i | \(0.508207\pi\) | |||||||
\(104\) | −10.9431 | −1.07306 | ||||||||
\(105\) | −1.19635 | −0.116752 | ||||||||
\(106\) | −2.14779 | −0.208612 | ||||||||
\(107\) | −3.71914 | −0.359543 | −0.179771 | − | 0.983708i | \(-0.557536\pi\) | ||||
−0.179771 | + | 0.983708i | \(0.557536\pi\) | |||||||
\(108\) | −3.01194 | −0.289824 | ||||||||
\(109\) | −11.0066 | −1.05424 | −0.527119 | − | 0.849791i | \(-0.676728\pi\) | ||||
−0.527119 | + | 0.849791i | \(0.676728\pi\) | |||||||
\(110\) | −13.1532 | −1.25411 | ||||||||
\(111\) | −6.18380 | −0.586941 | ||||||||
\(112\) | −0.952086 | −0.0899637 | ||||||||
\(113\) | 2.50026 | 0.235204 | 0.117602 | − | 0.993061i | \(-0.462479\pi\) | ||||
0.117602 | + | 0.993061i | \(0.462479\pi\) | |||||||
\(114\) | −6.49959 | −0.608742 | ||||||||
\(115\) | −7.94899 | −0.741247 | ||||||||
\(116\) | 16.9164 | 1.57064 | ||||||||
\(117\) | 4.83040 | 0.446570 | ||||||||
\(118\) | −10.3651 | −0.954188 | ||||||||
\(119\) | −6.57397 | −0.602635 | ||||||||
\(120\) | 2.71031 | 0.247416 | ||||||||
\(121\) | 13.1177 | 1.19252 | ||||||||
\(122\) | −3.41967 | −0.309603 | ||||||||
\(123\) | −9.01478 | −0.812836 | ||||||||
\(124\) | 25.2080 | 2.26375 | ||||||||
\(125\) | −10.2512 | −0.916899 | ||||||||
\(126\) | −2.23874 | −0.199443 | ||||||||
\(127\) | 15.0444 | 1.33498 | 0.667489 | − | 0.744620i | \(-0.267369\pi\) | ||||
0.667489 | + | 0.744620i | \(0.267369\pi\) | |||||||
\(128\) | 15.8039 | 1.39688 | ||||||||
\(129\) | 0.0607989 | 0.00535304 | ||||||||
\(130\) | −12.9374 | −1.13468 | ||||||||
\(131\) | 16.1545 | 1.41142 | 0.705712 | − | 0.708499i | \(-0.250627\pi\) | ||||
0.705712 | + | 0.708499i | \(0.250627\pi\) | |||||||
\(132\) | −14.7916 | −1.28744 | ||||||||
\(133\) | −2.90324 | −0.251743 | ||||||||
\(134\) | −11.4516 | −0.989270 | ||||||||
\(135\) | −1.19635 | −0.102966 | ||||||||
\(136\) | 14.8932 | 1.27708 | ||||||||
\(137\) | −16.9693 | −1.44979 | −0.724895 | − | 0.688860i | \(-0.758112\pi\) | ||||
−0.724895 | + | 0.688860i | \(0.758112\pi\) | |||||||
\(138\) | −14.8749 | −1.26624 | ||||||||
\(139\) | −1.57636 | −0.133705 | −0.0668526 | − | 0.997763i | \(-0.521296\pi\) | ||||
−0.0668526 | + | 0.997763i | \(0.521296\pi\) | |||||||
\(140\) | 3.60335 | 0.304539 | ||||||||
\(141\) | 7.86001 | 0.661932 | ||||||||
\(142\) | 17.2707 | 1.44932 | ||||||||
\(143\) | 23.7220 | 1.98373 | ||||||||
\(144\) | −0.952086 | −0.0793405 | ||||||||
\(145\) | 6.71924 | 0.558002 | ||||||||
\(146\) | −13.0448 | −1.07960 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 18.6253 | 1.53099 | ||||||||
\(149\) | 22.4293 | 1.83748 | 0.918742 | − | 0.394859i | \(-0.129207\pi\) | ||||
0.918742 | + | 0.394859i | \(0.129207\pi\) | |||||||
\(150\) | −7.98946 | −0.652337 | ||||||||
\(151\) | 16.8263 | 1.36931 | 0.684654 | − | 0.728868i | \(-0.259953\pi\) | ||||
0.684654 | + | 0.728868i | \(0.259953\pi\) | |||||||
\(152\) | 6.57721 | 0.533483 | ||||||||
\(153\) | −6.57397 | −0.531474 | ||||||||
\(154\) | −10.9944 | −0.885953 | ||||||||
\(155\) | 10.0127 | 0.804240 | ||||||||
\(156\) | −14.5489 | −1.16484 | ||||||||
\(157\) | 11.6691 | 0.931294 | 0.465647 | − | 0.884970i | \(-0.345822\pi\) | ||||
0.465647 | + | 0.884970i | \(0.345822\pi\) | |||||||
\(158\) | −19.7159 | −1.56851 | ||||||||
\(159\) | −0.959377 | −0.0760835 | ||||||||
\(160\) | 7.97061 | 0.630132 | ||||||||
\(161\) | −6.64434 | −0.523647 | ||||||||
\(162\) | −2.23874 | −0.175892 | ||||||||
\(163\) | −19.6438 | −1.53862 | −0.769309 | − | 0.638877i | \(-0.779399\pi\) | ||||
−0.769309 | + | 0.638877i | \(0.779399\pi\) | |||||||
\(164\) | 27.1520 | 2.12022 | ||||||||
\(165\) | −5.87527 | −0.457389 | ||||||||
\(166\) | 6.94611 | 0.539122 | ||||||||
\(167\) | 2.58695 | 0.200184 | 0.100092 | − | 0.994978i | \(-0.468086\pi\) | ||||
0.100092 | + | 0.994978i | \(0.468086\pi\) | |||||||
\(168\) | 2.26547 | 0.174785 | ||||||||
\(169\) | 10.3327 | 0.794827 | ||||||||
\(170\) | 17.6072 | 1.35041 | ||||||||
\(171\) | −2.90324 | −0.222016 | ||||||||
\(172\) | −0.183123 | −0.0139630 | ||||||||
\(173\) | −9.38849 | −0.713793 | −0.356897 | − | 0.934144i | \(-0.616165\pi\) | ||||
−0.356897 | + | 0.934144i | \(0.616165\pi\) | |||||||
\(174\) | 12.5737 | 0.953210 | ||||||||
\(175\) | −3.56874 | −0.269771 | ||||||||
\(176\) | −4.67568 | −0.352442 | ||||||||
\(177\) | −4.62990 | −0.348005 | ||||||||
\(178\) | 2.58386 | 0.193668 | ||||||||
\(179\) | −21.6483 | −1.61807 | −0.809034 | − | 0.587762i | \(-0.800009\pi\) | ||||
−0.809034 | + | 0.587762i | \(0.800009\pi\) | |||||||
\(180\) | 3.60335 | 0.268578 | ||||||||
\(181\) | 14.7432 | 1.09586 | 0.547929 | − | 0.836525i | \(-0.315417\pi\) | ||||
0.547929 | + | 0.836525i | \(0.315417\pi\) | |||||||
\(182\) | −10.8140 | −0.801586 | ||||||||
\(183\) | −1.52750 | −0.112916 | ||||||||
\(184\) | 15.0526 | 1.10969 | ||||||||
\(185\) | 7.39802 | 0.543913 | ||||||||
\(186\) | 18.7368 | 1.37385 | ||||||||
\(187\) | −32.2846 | −2.36089 | ||||||||
\(188\) | −23.6739 | −1.72660 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 7.77581 | 0.564117 | ||||||||
\(191\) | −1.00000 | −0.0723575 | ||||||||
\(192\) | 13.0112 | 0.939004 | ||||||||
\(193\) | 24.6200 | 1.77219 | 0.886093 | − | 0.463507i | \(-0.153409\pi\) | ||||
0.886093 | + | 0.463507i | \(0.153409\pi\) | |||||||
\(194\) | −25.0499 | −1.79847 | ||||||||
\(195\) | −5.77887 | −0.413833 | ||||||||
\(196\) | 3.01194 | 0.215139 | ||||||||
\(197\) | −3.36933 | −0.240055 | −0.120027 | − | 0.992771i | \(-0.538298\pi\) | ||||
−0.120027 | + | 0.992771i | \(0.538298\pi\) | |||||||
\(198\) | −10.9944 | −0.781338 | ||||||||
\(199\) | −22.3704 | −1.58580 | −0.792900 | − | 0.609352i | \(-0.791429\pi\) | ||||
−0.792900 | + | 0.609352i | \(0.791429\pi\) | |||||||
\(200\) | 8.08488 | 0.571687 | ||||||||
\(201\) | −5.11522 | −0.360800 | ||||||||
\(202\) | 17.7084 | 1.24596 | ||||||||
\(203\) | 5.61643 | 0.394196 | ||||||||
\(204\) | 19.8004 | 1.38631 | ||||||||
\(205\) | 10.7849 | 0.753249 | ||||||||
\(206\) | 1.17143 | 0.0816177 | ||||||||
\(207\) | −6.64434 | −0.461814 | ||||||||
\(208\) | −4.59895 | −0.318880 | ||||||||
\(209\) | −14.2578 | −0.986230 | ||||||||
\(210\) | 2.67832 | 0.184822 | ||||||||
\(211\) | −11.9024 | −0.819394 | −0.409697 | − | 0.912222i | \(-0.634366\pi\) | ||||
−0.409697 | + | 0.912222i | \(0.634366\pi\) | |||||||
\(212\) | 2.88959 | 0.198458 | ||||||||
\(213\) | 7.71447 | 0.528587 | ||||||||
\(214\) | 8.32618 | 0.569166 | ||||||||
\(215\) | −0.0727370 | −0.00496062 | ||||||||
\(216\) | 2.26547 | 0.154146 | ||||||||
\(217\) | 8.36935 | 0.568148 | ||||||||
\(218\) | 24.6408 | 1.66889 | ||||||||
\(219\) | −5.82688 | −0.393744 | ||||||||
\(220\) | 17.6960 | 1.19306 | ||||||||
\(221\) | −31.7549 | −2.13607 | ||||||||
\(222\) | 13.8439 | 0.929143 | ||||||||
\(223\) | 22.0537 | 1.47682 | 0.738412 | − | 0.674350i | \(-0.235576\pi\) | ||||
0.738412 | + | 0.674350i | \(0.235576\pi\) | |||||||
\(224\) | 6.66242 | 0.445152 | ||||||||
\(225\) | −3.56874 | −0.237916 | ||||||||
\(226\) | −5.59742 | −0.372335 | ||||||||
\(227\) | 0.496506 | 0.0329542 | 0.0164771 | − | 0.999864i | \(-0.494755\pi\) | ||||
0.0164771 | + | 0.999864i | \(0.494755\pi\) | |||||||
\(228\) | 8.74439 | 0.579112 | ||||||||
\(229\) | −25.4168 | −1.67959 | −0.839796 | − | 0.542902i | \(-0.817326\pi\) | ||||
−0.839796 | + | 0.542902i | \(0.817326\pi\) | |||||||
\(230\) | 17.7957 | 1.17341 | ||||||||
\(231\) | −4.91098 | −0.323119 | ||||||||
\(232\) | −12.7239 | −0.835363 | ||||||||
\(233\) | −24.5871 | −1.61075 | −0.805377 | − | 0.592764i | \(-0.798037\pi\) | ||||
−0.805377 | + | 0.592764i | \(0.798037\pi\) | |||||||
\(234\) | −10.8140 | −0.706933 | ||||||||
\(235\) | −9.40335 | −0.613407 | ||||||||
\(236\) | 13.9450 | 0.907743 | ||||||||
\(237\) | −8.80672 | −0.572058 | ||||||||
\(238\) | 14.7174 | 0.953987 | ||||||||
\(239\) | 2.27952 | 0.147450 | 0.0737250 | − | 0.997279i | \(-0.476511\pi\) | ||||
0.0737250 | + | 0.997279i | \(0.476511\pi\) | |||||||
\(240\) | 1.13903 | 0.0735242 | ||||||||
\(241\) | 17.7901 | 1.14596 | 0.572979 | − | 0.819570i | \(-0.305788\pi\) | ||||
0.572979 | + | 0.819570i | \(0.305788\pi\) | |||||||
\(242\) | −29.3671 | −1.88779 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 4.60075 | 0.294533 | ||||||||
\(245\) | 1.19635 | 0.0764323 | ||||||||
\(246\) | 20.1817 | 1.28674 | ||||||||
\(247\) | −14.0238 | −0.892313 | ||||||||
\(248\) | −18.9605 | −1.20400 | ||||||||
\(249\) | 3.10269 | 0.196625 | ||||||||
\(250\) | 22.9498 | 1.45148 | ||||||||
\(251\) | 15.8080 | 0.997793 | 0.498896 | − | 0.866662i | \(-0.333739\pi\) | ||||
0.498896 | + | 0.866662i | \(0.333739\pi\) | |||||||
\(252\) | 3.01194 | 0.189735 | ||||||||
\(253\) | −32.6302 | −2.05144 | ||||||||
\(254\) | −33.6805 | −2.11330 | ||||||||
\(255\) | 7.86480 | 0.492513 | ||||||||
\(256\) | −9.35827 | −0.584892 | ||||||||
\(257\) | 2.60548 | 0.162525 | 0.0812627 | − | 0.996693i | \(-0.474105\pi\) | ||||
0.0812627 | + | 0.996693i | \(0.474105\pi\) | |||||||
\(258\) | −0.136113 | −0.00847400 | ||||||||
\(259\) | 6.18380 | 0.384243 | ||||||||
\(260\) | 17.4056 | 1.07945 | ||||||||
\(261\) | 5.61643 | 0.347648 | ||||||||
\(262\) | −36.1656 | −2.23432 | ||||||||
\(263\) | 10.6186 | 0.654772 | 0.327386 | − | 0.944891i | \(-0.393832\pi\) | ||||
0.327386 | + | 0.944891i | \(0.393832\pi\) | |||||||
\(264\) | 11.1257 | 0.684739 | ||||||||
\(265\) | 1.14775 | 0.0705060 | ||||||||
\(266\) | 6.49959 | 0.398515 | ||||||||
\(267\) | 1.15416 | 0.0706334 | ||||||||
\(268\) | 15.4068 | 0.941117 | ||||||||
\(269\) | 11.9894 | 0.731007 | 0.365503 | − | 0.930810i | \(-0.380897\pi\) | ||||
0.365503 | + | 0.930810i | \(0.380897\pi\) | |||||||
\(270\) | 2.67832 | 0.162998 | ||||||||
\(271\) | 24.2998 | 1.47611 | 0.738055 | − | 0.674741i | \(-0.235745\pi\) | ||||
0.738055 | + | 0.674741i | \(0.235745\pi\) | |||||||
\(272\) | 6.25899 | 0.379507 | ||||||||
\(273\) | −4.83040 | −0.292349 | ||||||||
\(274\) | 37.9899 | 2.29505 | ||||||||
\(275\) | −17.5260 | −1.05686 | ||||||||
\(276\) | 20.0124 | 1.20460 | ||||||||
\(277\) | 3.63746 | 0.218554 | 0.109277 | − | 0.994011i | \(-0.465147\pi\) | ||||
0.109277 | + | 0.994011i | \(0.465147\pi\) | |||||||
\(278\) | 3.52906 | 0.211659 | ||||||||
\(279\) | 8.36935 | 0.501060 | ||||||||
\(280\) | −2.71031 | −0.161972 | ||||||||
\(281\) | −27.9140 | −1.66521 | −0.832606 | − | 0.553866i | \(-0.813152\pi\) | ||||
−0.832606 | + | 0.553866i | \(0.813152\pi\) | |||||||
\(282\) | −17.5965 | −1.04786 | ||||||||
\(283\) | 5.72185 | 0.340129 | 0.170064 | − | 0.985433i | \(-0.445602\pi\) | ||||
0.170064 | + | 0.985433i | \(0.445602\pi\) | |||||||
\(284\) | −23.2355 | −1.37878 | ||||||||
\(285\) | 3.47330 | 0.205741 | ||||||||
\(286\) | −53.1073 | −3.14030 | ||||||||
\(287\) | 9.01478 | 0.532126 | ||||||||
\(288\) | 6.66242 | 0.392587 | ||||||||
\(289\) | 26.2171 | 1.54218 | ||||||||
\(290\) | −15.0426 | −0.883332 | ||||||||
\(291\) | −11.1893 | −0.655927 | ||||||||
\(292\) | 17.5502 | 1.02705 | ||||||||
\(293\) | −23.7777 | −1.38911 | −0.694553 | − | 0.719441i | \(-0.744398\pi\) | ||||
−0.694553 | + | 0.719441i | \(0.744398\pi\) | |||||||
\(294\) | 2.23874 | 0.130566 | ||||||||
\(295\) | 5.53901 | 0.322493 | ||||||||
\(296\) | −14.0092 | −0.814271 | ||||||||
\(297\) | −4.91098 | −0.284964 | ||||||||
\(298\) | −50.2134 | −2.90878 | ||||||||
\(299\) | −32.0948 | −1.85609 | ||||||||
\(300\) | 10.7488 | 0.620584 | ||||||||
\(301\) | −0.0607989 | −0.00350439 | ||||||||
\(302\) | −37.6698 | −2.16765 | ||||||||
\(303\) | 7.91000 | 0.454418 | ||||||||
\(304\) | 2.76413 | 0.158534 | ||||||||
\(305\) | 1.82743 | 0.104639 | ||||||||
\(306\) | 14.7174 | 0.841337 | ||||||||
\(307\) | −8.40496 | −0.479696 | −0.239848 | − | 0.970810i | \(-0.577098\pi\) | ||||
−0.239848 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(308\) | 14.7916 | 0.842829 | ||||||||
\(309\) | 0.523257 | 0.0297670 | ||||||||
\(310\) | −22.4158 | −1.27313 | ||||||||
\(311\) | 23.4356 | 1.32891 | 0.664455 | − | 0.747328i | \(-0.268664\pi\) | ||||
0.664455 | + | 0.747328i | \(0.268664\pi\) | |||||||
\(312\) | 10.9431 | 0.619533 | ||||||||
\(313\) | 20.2103 | 1.14235 | 0.571176 | − | 0.820828i | \(-0.306487\pi\) | ||||
0.571176 | + | 0.820828i | \(0.306487\pi\) | |||||||
\(314\) | −26.1240 | −1.47426 | ||||||||
\(315\) | 1.19635 | 0.0674069 | ||||||||
\(316\) | 26.5253 | 1.49217 | ||||||||
\(317\) | 13.1251 | 0.737177 | 0.368588 | − | 0.929593i | \(-0.379841\pi\) | ||||
0.368588 | + | 0.929593i | \(0.379841\pi\) | |||||||
\(318\) | 2.14779 | 0.120442 | ||||||||
\(319\) | 27.5822 | 1.54430 | ||||||||
\(320\) | −15.5660 | −0.870168 | ||||||||
\(321\) | 3.71914 | 0.207582 | ||||||||
\(322\) | 14.8749 | 0.828947 | ||||||||
\(323\) | 19.0858 | 1.06196 | ||||||||
\(324\) | 3.01194 | 0.167330 | ||||||||
\(325\) | −17.2384 | −0.956215 | ||||||||
\(326\) | 43.9772 | 2.43567 | ||||||||
\(327\) | 11.0066 | 0.608665 | ||||||||
\(328\) | −20.4228 | −1.12766 | ||||||||
\(329\) | −7.86001 | −0.433336 | ||||||||
\(330\) | 13.1532 | 0.724059 | ||||||||
\(331\) | 7.57883 | 0.416570 | 0.208285 | − | 0.978068i | \(-0.433212\pi\) | ||||
0.208285 | + | 0.978068i | \(0.433212\pi\) | |||||||
\(332\) | −9.34513 | −0.512880 | ||||||||
\(333\) | 6.18380 | 0.338870 | ||||||||
\(334\) | −5.79149 | −0.316896 | ||||||||
\(335\) | 6.11962 | 0.334350 | ||||||||
\(336\) | 0.952086 | 0.0519406 | ||||||||
\(337\) | 27.4532 | 1.49547 | 0.747736 | − | 0.663997i | \(-0.231141\pi\) | ||||
0.747736 | + | 0.663997i | \(0.231141\pi\) | |||||||
\(338\) | −23.1323 | −1.25823 | ||||||||
\(339\) | −2.50026 | −0.135795 | ||||||||
\(340\) | −23.6883 | −1.28468 | ||||||||
\(341\) | 41.1017 | 2.22578 | ||||||||
\(342\) | 6.49959 | 0.351458 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.137738 | 0.00742635 | ||||||||
\(345\) | 7.94899 | 0.427959 | ||||||||
\(346\) | 21.0183 | 1.12995 | ||||||||
\(347\) | 0.500520 | 0.0268693 | 0.0134347 | − | 0.999910i | \(-0.495723\pi\) | ||||
0.0134347 | + | 0.999910i | \(0.495723\pi\) | |||||||
\(348\) | −16.9164 | −0.906812 | ||||||||
\(349\) | −1.22673 | −0.0656656 | −0.0328328 | − | 0.999461i | \(-0.510453\pi\) | ||||
−0.0328328 | + | 0.999461i | \(0.510453\pi\) | |||||||
\(350\) | 7.98946 | 0.427055 | ||||||||
\(351\) | −4.83040 | −0.257828 | ||||||||
\(352\) | 32.7190 | 1.74393 | ||||||||
\(353\) | 19.9347 | 1.06102 | 0.530509 | − | 0.847679i | \(-0.322001\pi\) | ||||
0.530509 | + | 0.847679i | \(0.322001\pi\) | |||||||
\(354\) | 10.3651 | 0.550901 | ||||||||
\(355\) | −9.22924 | −0.489837 | ||||||||
\(356\) | −3.47626 | −0.184242 | ||||||||
\(357\) | 6.57397 | 0.347931 | ||||||||
\(358\) | 48.4648 | 2.56144 | ||||||||
\(359\) | 3.05808 | 0.161399 | 0.0806996 | − | 0.996738i | \(-0.474285\pi\) | ||||
0.0806996 | + | 0.996738i | \(0.474285\pi\) | |||||||
\(360\) | −2.71031 | −0.142846 | ||||||||
\(361\) | −10.5712 | −0.556379 | ||||||||
\(362\) | −33.0063 | −1.73477 | ||||||||
\(363\) | −13.1177 | −0.688502 | ||||||||
\(364\) | 14.5489 | 0.762569 | ||||||||
\(365\) | 6.97101 | 0.364879 | ||||||||
\(366\) | 3.41967 | 0.178749 | ||||||||
\(367\) | −7.70950 | −0.402432 | −0.201216 | − | 0.979547i | \(-0.564489\pi\) | ||||
−0.201216 | + | 0.979547i | \(0.564489\pi\) | |||||||
\(368\) | 6.32598 | 0.329765 | ||||||||
\(369\) | 9.01478 | 0.469291 | ||||||||
\(370\) | −16.5622 | −0.861029 | ||||||||
\(371\) | 0.959377 | 0.0498083 | ||||||||
\(372\) | −25.2080 | −1.30697 | ||||||||
\(373\) | −21.3810 | −1.10707 | −0.553534 | − | 0.832826i | \(-0.686721\pi\) | ||||
−0.553534 | + | 0.832826i | \(0.686721\pi\) | |||||||
\(374\) | 72.2768 | 3.73735 | ||||||||
\(375\) | 10.2512 | 0.529372 | ||||||||
\(376\) | 17.8066 | 0.918307 | ||||||||
\(377\) | 27.1296 | 1.39724 | ||||||||
\(378\) | 2.23874 | 0.115148 | ||||||||
\(379\) | 4.48857 | 0.230563 | 0.115281 | − | 0.993333i | \(-0.463223\pi\) | ||||
0.115281 | + | 0.993333i | \(0.463223\pi\) | |||||||
\(380\) | −10.4614 | −0.536658 | ||||||||
\(381\) | −15.0444 | −0.770749 | ||||||||
\(382\) | 2.23874 | 0.114544 | ||||||||
\(383\) | 3.51289 | 0.179500 | 0.0897501 | − | 0.995964i | \(-0.471393\pi\) | ||||
0.0897501 | + | 0.995964i | \(0.471393\pi\) | |||||||
\(384\) | −15.8039 | −0.806488 | ||||||||
\(385\) | 5.87527 | 0.299432 | ||||||||
\(386\) | −55.1177 | −2.80542 | ||||||||
\(387\) | −0.0607989 | −0.00309058 | ||||||||
\(388\) | 33.7015 | 1.71093 | ||||||||
\(389\) | 15.1081 | 0.766011 | 0.383006 | − | 0.923746i | \(-0.374889\pi\) | ||||
0.383006 | + | 0.923746i | \(0.374889\pi\) | |||||||
\(390\) | 12.9374 | 0.655109 | ||||||||
\(391\) | 43.6797 | 2.20898 | ||||||||
\(392\) | −2.26547 | −0.114424 | ||||||||
\(393\) | −16.1545 | −0.814886 | ||||||||
\(394\) | 7.54304 | 0.380013 | ||||||||
\(395\) | 10.5360 | 0.530121 | ||||||||
\(396\) | 14.7916 | 0.743306 | ||||||||
\(397\) | −5.62601 | −0.282361 | −0.141181 | − | 0.989984i | \(-0.545090\pi\) | ||||
−0.141181 | + | 0.989984i | \(0.545090\pi\) | |||||||
\(398\) | 50.0815 | 2.51036 | ||||||||
\(399\) | 2.90324 | 0.145344 | ||||||||
\(400\) | 3.39774 | 0.169887 | ||||||||
\(401\) | 31.9834 | 1.59717 | 0.798587 | − | 0.601880i | \(-0.205581\pi\) | ||||
0.798587 | + | 0.601880i | \(0.205581\pi\) | |||||||
\(402\) | 11.4516 | 0.571156 | ||||||||
\(403\) | 40.4273 | 2.01383 | ||||||||
\(404\) | −23.8245 | −1.18531 | ||||||||
\(405\) | 1.19635 | 0.0594473 | ||||||||
\(406\) | −12.5737 | −0.624022 | ||||||||
\(407\) | 30.3685 | 1.50531 | ||||||||
\(408\) | −14.8932 | −0.737321 | ||||||||
\(409\) | −11.1229 | −0.549991 | −0.274995 | − | 0.961446i | \(-0.588676\pi\) | ||||
−0.274995 | + | 0.961446i | \(0.588676\pi\) | |||||||
\(410\) | −24.1445 | −1.19241 | ||||||||
\(411\) | 16.9693 | 0.837036 | ||||||||
\(412\) | −1.57602 | −0.0776449 | ||||||||
\(413\) | 4.62990 | 0.227823 | ||||||||
\(414\) | 14.8749 | 0.731063 | ||||||||
\(415\) | −3.71192 | −0.182211 | ||||||||
\(416\) | 32.1821 | 1.57786 | ||||||||
\(417\) | 1.57636 | 0.0771947 | ||||||||
\(418\) | 31.9194 | 1.56123 | ||||||||
\(419\) | 27.1097 | 1.32440 | 0.662198 | − | 0.749329i | \(-0.269624\pi\) | ||||
0.662198 | + | 0.749329i | \(0.269624\pi\) | |||||||
\(420\) | −3.60335 | −0.175826 | ||||||||
\(421\) | 10.3542 | 0.504631 | 0.252316 | − | 0.967645i | \(-0.418808\pi\) | ||||
0.252316 | + | 0.967645i | \(0.418808\pi\) | |||||||
\(422\) | 26.6463 | 1.29712 | ||||||||
\(423\) | −7.86001 | −0.382167 | ||||||||
\(424\) | −2.17344 | −0.105552 | ||||||||
\(425\) | 23.4608 | 1.13801 | ||||||||
\(426\) | −17.2707 | −0.836766 | ||||||||
\(427\) | 1.52750 | 0.0739210 | ||||||||
\(428\) | −11.2018 | −0.541461 | ||||||||
\(429\) | −23.7220 | −1.14531 | ||||||||
\(430\) | 0.162839 | 0.00785279 | ||||||||
\(431\) | −15.8290 | −0.762457 | −0.381228 | − | 0.924481i | \(-0.624499\pi\) | ||||
−0.381228 | + | 0.924481i | \(0.624499\pi\) | |||||||
\(432\) | 0.952086 | 0.0458073 | ||||||||
\(433\) | 14.1026 | 0.677729 | 0.338864 | − | 0.940835i | \(-0.389957\pi\) | ||||
0.338864 | + | 0.940835i | \(0.389957\pi\) | |||||||
\(434\) | −18.7368 | −0.899394 | ||||||||
\(435\) | −6.71924 | −0.322163 | ||||||||
\(436\) | −33.1512 | −1.58765 | ||||||||
\(437\) | 19.2901 | 0.922771 | ||||||||
\(438\) | 13.0448 | 0.623307 | ||||||||
\(439\) | −6.85407 | −0.327127 | −0.163563 | − | 0.986533i | \(-0.552299\pi\) | ||||
−0.163563 | + | 0.986533i | \(0.552299\pi\) | |||||||
\(440\) | −13.3103 | −0.634543 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 71.0909 | 3.38145 | ||||||||
\(443\) | −25.6061 | −1.21658 | −0.608291 | − | 0.793714i | \(-0.708145\pi\) | ||||
−0.608291 | + | 0.793714i | \(0.708145\pi\) | |||||||
\(444\) | −18.6253 | −0.883916 | ||||||||
\(445\) | −1.38078 | −0.0654554 | ||||||||
\(446\) | −49.3724 | −2.33785 | ||||||||
\(447\) | −22.4293 | −1.06087 | ||||||||
\(448\) | −13.0112 | −0.614723 | ||||||||
\(449\) | −1.95832 | −0.0924188 | −0.0462094 | − | 0.998932i | \(-0.514714\pi\) | ||||
−0.0462094 | + | 0.998932i | \(0.514714\pi\) | |||||||
\(450\) | 7.98946 | 0.376627 | ||||||||
\(451\) | 44.2714 | 2.08466 | ||||||||
\(452\) | 7.53063 | 0.354211 | ||||||||
\(453\) | −16.8263 | −0.790571 | ||||||||
\(454\) | −1.11155 | −0.0521674 | ||||||||
\(455\) | 5.77887 | 0.270918 | ||||||||
\(456\) | −6.57721 | −0.308006 | ||||||||
\(457\) | −30.2629 | −1.41564 | −0.707820 | − | 0.706393i | \(-0.750321\pi\) | ||||
−0.707820 | + | 0.706393i | \(0.750321\pi\) | |||||||
\(458\) | 56.9016 | 2.65884 | ||||||||
\(459\) | 6.57397 | 0.306847 | ||||||||
\(460\) | −23.9419 | −1.11630 | ||||||||
\(461\) | 11.3263 | 0.527520 | 0.263760 | − | 0.964588i | \(-0.415037\pi\) | ||||
0.263760 | + | 0.964588i | \(0.415037\pi\) | |||||||
\(462\) | 10.9944 | 0.511505 | ||||||||
\(463\) | −37.7584 | −1.75478 | −0.877392 | − | 0.479775i | \(-0.840718\pi\) | ||||
−0.877392 | + | 0.479775i | \(0.840718\pi\) | |||||||
\(464\) | −5.34732 | −0.248243 | ||||||||
\(465\) | −10.0127 | −0.464328 | ||||||||
\(466\) | 55.0440 | 2.54986 | ||||||||
\(467\) | −28.9505 | −1.33967 | −0.669834 | − | 0.742511i | \(-0.733635\pi\) | ||||
−0.669834 | + | 0.742511i | \(0.733635\pi\) | |||||||
\(468\) | 14.5489 | 0.672522 | ||||||||
\(469\) | 5.11522 | 0.236199 | ||||||||
\(470\) | 21.0516 | 0.971039 | ||||||||
\(471\) | −11.6691 | −0.537683 | ||||||||
\(472\) | −10.4889 | −0.482792 | ||||||||
\(473\) | −0.298582 | −0.0137288 | ||||||||
\(474\) | 19.7159 | 0.905582 | ||||||||
\(475\) | 10.3609 | 0.475391 | ||||||||
\(476\) | −19.8004 | −0.907551 | ||||||||
\(477\) | 0.959377 | 0.0439268 | ||||||||
\(478\) | −5.10325 | −0.233417 | ||||||||
\(479\) | −36.1868 | −1.65342 | −0.826708 | − | 0.562631i | \(-0.809789\pi\) | ||||
−0.826708 | + | 0.562631i | \(0.809789\pi\) | |||||||
\(480\) | −7.97061 | −0.363807 | ||||||||
\(481\) | 29.8702 | 1.36197 | ||||||||
\(482\) | −39.8273 | −1.81408 | ||||||||
\(483\) | 6.64434 | 0.302328 | ||||||||
\(484\) | 39.5099 | 1.79590 | ||||||||
\(485\) | 13.3863 | 0.607843 | ||||||||
\(486\) | 2.23874 | 0.101551 | ||||||||
\(487\) | −20.5250 | −0.930079 | −0.465039 | − | 0.885290i | \(-0.653960\pi\) | ||||
−0.465039 | + | 0.885290i | \(0.653960\pi\) | |||||||
\(488\) | −3.46052 | −0.156650 | ||||||||
\(489\) | 19.6438 | 0.888322 | ||||||||
\(490\) | −2.67832 | −0.120994 | ||||||||
\(491\) | −17.9234 | −0.808872 | −0.404436 | − | 0.914566i | \(-0.632532\pi\) | ||||
−0.404436 | + | 0.914566i | \(0.632532\pi\) | |||||||
\(492\) | −27.1520 | −1.22411 | ||||||||
\(493\) | −36.9222 | −1.66289 | ||||||||
\(494\) | 31.3956 | 1.41256 | ||||||||
\(495\) | 5.87527 | 0.264074 | ||||||||
\(496\) | −7.96834 | −0.357789 | ||||||||
\(497\) | −7.71447 | −0.346041 | ||||||||
\(498\) | −6.94611 | −0.311262 | ||||||||
\(499\) | 17.5046 | 0.783612 | 0.391806 | − | 0.920048i | \(-0.371850\pi\) | ||||
0.391806 | + | 0.920048i | \(0.371850\pi\) | |||||||
\(500\) | −30.8762 | −1.38082 | ||||||||
\(501\) | −2.58695 | −0.115576 | ||||||||
\(502\) | −35.3900 | −1.57953 | ||||||||
\(503\) | −4.97229 | −0.221703 | −0.110852 | − | 0.993837i | \(-0.535358\pi\) | ||||
−0.110852 | + | 0.993837i | \(0.535358\pi\) | |||||||
\(504\) | −2.26547 | −0.100912 | ||||||||
\(505\) | −9.46316 | −0.421105 | ||||||||
\(506\) | 73.0505 | 3.24749 | ||||||||
\(507\) | −10.3327 | −0.458894 | ||||||||
\(508\) | 45.3130 | 2.01044 | ||||||||
\(509\) | 14.9079 | 0.660783 | 0.330391 | − | 0.943844i | \(-0.392819\pi\) | ||||
0.330391 | + | 0.943844i | \(0.392819\pi\) | |||||||
\(510\) | −17.6072 | −0.779661 | ||||||||
\(511\) | 5.82688 | 0.257766 | ||||||||
\(512\) | −10.6570 | −0.470979 | ||||||||
\(513\) | 2.90324 | 0.128181 | ||||||||
\(514\) | −5.83299 | −0.257282 | ||||||||
\(515\) | −0.626001 | −0.0275849 | ||||||||
\(516\) | 0.183123 | 0.00806153 | ||||||||
\(517\) | −38.6003 | −1.69764 | ||||||||
\(518\) | −13.8439 | −0.608267 | ||||||||
\(519\) | 9.38849 | 0.412109 | ||||||||
\(520\) | −13.0919 | −0.574117 | ||||||||
\(521\) | 41.2809 | 1.80855 | 0.904275 | − | 0.426950i | \(-0.140412\pi\) | ||||
0.904275 | + | 0.426950i | \(0.140412\pi\) | |||||||
\(522\) | −12.5737 | −0.550336 | ||||||||
\(523\) | −1.66264 | −0.0727022 | −0.0363511 | − | 0.999339i | \(-0.511573\pi\) | ||||
−0.0363511 | + | 0.999339i | \(0.511573\pi\) | |||||||
\(524\) | 48.6564 | 2.12556 | ||||||||
\(525\) | 3.56874 | 0.155752 | ||||||||
\(526\) | −23.7723 | −1.03652 | ||||||||
\(527\) | −55.0198 | −2.39670 | ||||||||
\(528\) | 4.67568 | 0.203483 | ||||||||
\(529\) | 21.1473 | 0.919446 | ||||||||
\(530\) | −2.56952 | −0.111613 | ||||||||
\(531\) | 4.62990 | 0.200921 | ||||||||
\(532\) | −8.74439 | −0.379118 | ||||||||
\(533\) | 43.5450 | 1.88614 | ||||||||
\(534\) | −2.58386 | −0.111815 | ||||||||
\(535\) | −4.44941 | −0.192365 | ||||||||
\(536\) | −11.5884 | −0.500543 | ||||||||
\(537\) | 21.6483 | 0.934192 | ||||||||
\(538\) | −26.8411 | −1.15720 | ||||||||
\(539\) | 4.91098 | 0.211531 | ||||||||
\(540\) | −3.60335 | −0.155064 | ||||||||
\(541\) | 1.33991 | 0.0576074 | 0.0288037 | − | 0.999585i | \(-0.490830\pi\) | ||||
0.0288037 | + | 0.999585i | \(0.490830\pi\) | |||||||
\(542\) | −54.4009 | −2.33672 | ||||||||
\(543\) | −14.7432 | −0.632693 | ||||||||
\(544\) | −43.7985 | −1.87785 | ||||||||
\(545\) | −13.1678 | −0.564045 | ||||||||
\(546\) | 10.8140 | 0.462796 | ||||||||
\(547\) | 18.8298 | 0.805103 | 0.402551 | − | 0.915397i | \(-0.368123\pi\) | ||||
0.402551 | + | 0.915397i | \(0.368123\pi\) | |||||||
\(548\) | −51.1107 | −2.18334 | ||||||||
\(549\) | 1.52750 | 0.0651922 | ||||||||
\(550\) | 39.2361 | 1.67303 | ||||||||
\(551\) | −16.3058 | −0.694652 | ||||||||
\(552\) | −15.0526 | −0.640680 | ||||||||
\(553\) | 8.80672 | 0.374500 | ||||||||
\(554\) | −8.14331 | −0.345976 | ||||||||
\(555\) | −7.39802 | −0.314029 | ||||||||
\(556\) | −4.74791 | −0.201356 | ||||||||
\(557\) | 34.8852 | 1.47813 | 0.739066 | − | 0.673633i | \(-0.235267\pi\) | ||||
0.739066 | + | 0.673633i | \(0.235267\pi\) | |||||||
\(558\) | −18.7368 | −0.793191 | ||||||||
\(559\) | −0.293683 | −0.0124215 | ||||||||
\(560\) | −1.13903 | −0.0481329 | ||||||||
\(561\) | 32.2846 | 1.36306 | ||||||||
\(562\) | 62.4922 | 2.63607 | ||||||||
\(563\) | 23.1043 | 0.973730 | 0.486865 | − | 0.873477i | \(-0.338140\pi\) | ||||
0.486865 | + | 0.873477i | \(0.338140\pi\) | |||||||
\(564\) | 23.6739 | 0.996851 | ||||||||
\(565\) | 2.99119 | 0.125840 | ||||||||
\(566\) | −12.8097 | −0.538432 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 17.4769 | 0.733315 | ||||||||
\(569\) | −18.0716 | −0.757602 | −0.378801 | − | 0.925478i | \(-0.623664\pi\) | ||||
−0.378801 | + | 0.925478i | \(0.623664\pi\) | |||||||
\(570\) | −7.77581 | −0.325693 | ||||||||
\(571\) | 38.6685 | 1.61823 | 0.809114 | − | 0.587652i | \(-0.199948\pi\) | ||||
0.809114 | + | 0.587652i | \(0.199948\pi\) | |||||||
\(572\) | 71.4493 | 2.98744 | ||||||||
\(573\) | 1.00000 | 0.0417756 | ||||||||
\(574\) | −20.1817 | −0.842369 | ||||||||
\(575\) | 23.7119 | 0.988854 | ||||||||
\(576\) | −13.0112 | −0.542134 | ||||||||
\(577\) | 20.5957 | 0.857410 | 0.428705 | − | 0.903445i | \(-0.358970\pi\) | ||||
0.428705 | + | 0.903445i | \(0.358970\pi\) | |||||||
\(578\) | −58.6932 | −2.44131 | ||||||||
\(579\) | −24.6200 | −1.02317 | ||||||||
\(580\) | 20.2380 | 0.840336 | ||||||||
\(581\) | −3.10269 | −0.128721 | ||||||||
\(582\) | 25.0499 | 1.03835 | ||||||||
\(583\) | 4.71148 | 0.195130 | ||||||||
\(584\) | −13.2006 | −0.546246 | ||||||||
\(585\) | 5.77887 | 0.238927 | ||||||||
\(586\) | 53.2320 | 2.19899 | ||||||||
\(587\) | 10.6936 | 0.441371 | 0.220685 | − | 0.975345i | \(-0.429171\pi\) | ||||
0.220685 | + | 0.975345i | \(0.429171\pi\) | |||||||
\(588\) | −3.01194 | −0.124210 | ||||||||
\(589\) | −24.2982 | −1.00119 | ||||||||
\(590\) | −12.4004 | −0.510515 | ||||||||
\(591\) | 3.36933 | 0.138596 | ||||||||
\(592\) | −5.88751 | −0.241975 | ||||||||
\(593\) | 15.1318 | 0.621387 | 0.310694 | − | 0.950510i | \(-0.399439\pi\) | ||||
0.310694 | + | 0.950510i | \(0.399439\pi\) | |||||||
\(594\) | 10.9944 | 0.451105 | ||||||||
\(595\) | −7.86480 | −0.322425 | ||||||||
\(596\) | 67.5559 | 2.76720 | ||||||||
\(597\) | 22.3704 | 0.915562 | ||||||||
\(598\) | 71.8518 | 2.93824 | ||||||||
\(599\) | −18.3890 | −0.751352 | −0.375676 | − | 0.926751i | \(-0.622589\pi\) | ||||
−0.375676 | + | 0.926751i | \(0.622589\pi\) | |||||||
\(600\) | −8.08488 | −0.330064 | ||||||||
\(601\) | −10.3429 | −0.421895 | −0.210947 | − | 0.977497i | \(-0.567655\pi\) | ||||
−0.210947 | + | 0.977497i | \(0.567655\pi\) | |||||||
\(602\) | 0.136113 | 0.00554754 | ||||||||
\(603\) | 5.11522 | 0.208308 | ||||||||
\(604\) | 50.6800 | 2.06214 | ||||||||
\(605\) | 15.6935 | 0.638030 | ||||||||
\(606\) | −17.7084 | −0.719355 | ||||||||
\(607\) | −45.1902 | −1.83421 | −0.917107 | − | 0.398641i | \(-0.869482\pi\) | ||||
−0.917107 | + | 0.398641i | \(0.869482\pi\) | |||||||
\(608\) | −19.3426 | −0.784446 | ||||||||
\(609\) | −5.61643 | −0.227589 | ||||||||
\(610\) | −4.09114 | −0.165646 | ||||||||
\(611\) | −37.9670 | −1.53598 | ||||||||
\(612\) | −19.8004 | −0.800385 | ||||||||
\(613\) | −14.7884 | −0.597299 | −0.298649 | − | 0.954363i | \(-0.596536\pi\) | ||||
−0.298649 | + | 0.954363i | \(0.596536\pi\) | |||||||
\(614\) | 18.8165 | 0.759372 | ||||||||
\(615\) | −10.7849 | −0.434888 | ||||||||
\(616\) | −11.1257 | −0.448267 | ||||||||
\(617\) | 18.6415 | 0.750479 | 0.375240 | − | 0.926928i | \(-0.377560\pi\) | ||||
0.375240 | + | 0.926928i | \(0.377560\pi\) | |||||||
\(618\) | −1.17143 | −0.0471220 | ||||||||
\(619\) | −27.6771 | −1.11244 | −0.556218 | − | 0.831037i | \(-0.687748\pi\) | ||||
−0.556218 | + | 0.831037i | \(0.687748\pi\) | |||||||
\(620\) | 30.1577 | 1.21116 | ||||||||
\(621\) | 6.64434 | 0.266628 | ||||||||
\(622\) | −52.4661 | −2.10370 | ||||||||
\(623\) | −1.15416 | −0.0462404 | ||||||||
\(624\) | 4.59895 | 0.184106 | ||||||||
\(625\) | 5.57956 | 0.223182 | ||||||||
\(626\) | −45.2455 | −1.80837 | ||||||||
\(627\) | 14.2578 | 0.569400 | ||||||||
\(628\) | 35.1466 | 1.40250 | ||||||||
\(629\) | −40.6521 | −1.62091 | ||||||||
\(630\) | −2.67832 | −0.106707 | ||||||||
\(631\) | −1.04580 | −0.0416327 | −0.0208163 | − | 0.999783i | \(-0.506627\pi\) | ||||
−0.0208163 | + | 0.999783i | \(0.506627\pi\) | |||||||
\(632\) | −19.9514 | −0.793624 | ||||||||
\(633\) | 11.9024 | 0.473077 | ||||||||
\(634\) | −29.3836 | −1.16697 | ||||||||
\(635\) | 17.9985 | 0.714248 | ||||||||
\(636\) | −2.88959 | −0.114580 | ||||||||
\(637\) | 4.83040 | 0.191387 | ||||||||
\(638\) | −61.7492 | −2.44467 | ||||||||
\(639\) | −7.71447 | −0.305180 | ||||||||
\(640\) | 18.9070 | 0.747367 | ||||||||
\(641\) | 39.2122 | 1.54879 | 0.774394 | − | 0.632703i | \(-0.218055\pi\) | ||||
0.774394 | + | 0.632703i | \(0.218055\pi\) | |||||||
\(642\) | −8.32618 | −0.328608 | ||||||||
\(643\) | 30.1716 | 1.18985 | 0.594927 | − | 0.803780i | \(-0.297181\pi\) | ||||
0.594927 | + | 0.803780i | \(0.297181\pi\) | |||||||
\(644\) | −20.0124 | −0.788598 | ||||||||
\(645\) | 0.0727370 | 0.00286402 | ||||||||
\(646\) | −42.7281 | −1.68112 | ||||||||
\(647\) | 36.8140 | 1.44731 | 0.723653 | − | 0.690164i | \(-0.242461\pi\) | ||||
0.723653 | + | 0.690164i | \(0.242461\pi\) | |||||||
\(648\) | −2.26547 | −0.0889962 | ||||||||
\(649\) | 22.7374 | 0.892520 | ||||||||
\(650\) | 38.5923 | 1.51371 | ||||||||
\(651\) | −8.36935 | −0.328021 | ||||||||
\(652\) | −59.1659 | −2.31711 | ||||||||
\(653\) | −19.7365 | −0.772348 | −0.386174 | − | 0.922426i | \(-0.626204\pi\) | ||||
−0.386174 | + | 0.922426i | \(0.626204\pi\) | |||||||
\(654\) | −24.6408 | −0.963532 | ||||||||
\(655\) | 19.3265 | 0.755148 | ||||||||
\(656\) | −8.58285 | −0.335104 | ||||||||
\(657\) | 5.82688 | 0.227328 | ||||||||
\(658\) | 17.5965 | 0.685982 | ||||||||
\(659\) | 20.3400 | 0.792333 | 0.396167 | − | 0.918179i | \(-0.370340\pi\) | ||||
0.396167 | + | 0.918179i | \(0.370340\pi\) | |||||||
\(660\) | −17.6960 | −0.688815 | ||||||||
\(661\) | −11.4093 | −0.443770 | −0.221885 | − | 0.975073i | \(-0.571221\pi\) | ||||
−0.221885 | + | 0.975073i | \(0.571221\pi\) | |||||||
\(662\) | −16.9670 | −0.659441 | ||||||||
\(663\) | 31.7549 | 1.23326 | ||||||||
\(664\) | 7.02906 | 0.272781 | ||||||||
\(665\) | −3.47330 | −0.134689 | ||||||||
\(666\) | −13.8439 | −0.536441 | ||||||||
\(667\) | −37.3175 | −1.44494 | ||||||||
\(668\) | 7.79174 | 0.301471 | ||||||||
\(669\) | −22.0537 | −0.852645 | ||||||||
\(670\) | −13.7002 | −0.529285 | ||||||||
\(671\) | 7.50153 | 0.289593 | ||||||||
\(672\) | −6.66242 | −0.257008 | ||||||||
\(673\) | 47.4217 | 1.82797 | 0.913985 | − | 0.405747i | \(-0.132989\pi\) | ||||
0.913985 | + | 0.405747i | \(0.132989\pi\) | |||||||
\(674\) | −61.4605 | −2.36737 | ||||||||
\(675\) | 3.56874 | 0.137361 | ||||||||
\(676\) | 31.1217 | 1.19699 | ||||||||
\(677\) | −15.0044 | −0.576667 | −0.288334 | − | 0.957530i | \(-0.593101\pi\) | ||||
−0.288334 | + | 0.957530i | \(0.593101\pi\) | |||||||
\(678\) | 5.59742 | 0.214967 | ||||||||
\(679\) | 11.1893 | 0.429405 | ||||||||
\(680\) | 17.8175 | 0.683270 | ||||||||
\(681\) | −0.496506 | −0.0190261 | ||||||||
\(682\) | −92.0159 | −3.52347 | ||||||||
\(683\) | −39.6557 | −1.51738 | −0.758691 | − | 0.651450i | \(-0.774161\pi\) | ||||
−0.758691 | + | 0.651450i | \(0.774161\pi\) | |||||||
\(684\) | −8.74439 | −0.334350 | ||||||||
\(685\) | −20.3014 | −0.775675 | ||||||||
\(686\) | −2.23874 | −0.0854754 | ||||||||
\(687\) | 25.4168 | 0.969713 | ||||||||
\(688\) | 0.0578857 | 0.00220687 | ||||||||
\(689\) | 4.63417 | 0.176548 | ||||||||
\(690\) | −17.7957 | −0.677470 | ||||||||
\(691\) | −30.5049 | −1.16046 | −0.580231 | − | 0.814452i | \(-0.697038\pi\) | ||||
−0.580231 | + | 0.814452i | \(0.697038\pi\) | |||||||
\(692\) | −28.2776 | −1.07495 | ||||||||
\(693\) | 4.91098 | 0.186553 | ||||||||
\(694\) | −1.12053 | −0.0425349 | ||||||||
\(695\) | −1.88589 | −0.0715357 | ||||||||
\(696\) | 12.7239 | 0.482297 | ||||||||
\(697\) | −59.2629 | −2.24474 | ||||||||
\(698\) | 2.74634 | 0.103950 | ||||||||
\(699\) | 24.5871 | 0.929969 | ||||||||
\(700\) | −10.7488 | −0.406268 | ||||||||
\(701\) | 36.0614 | 1.36202 | 0.681010 | − | 0.732274i | \(-0.261541\pi\) | ||||
0.681010 | + | 0.732274i | \(0.261541\pi\) | |||||||
\(702\) | 10.8140 | 0.408148 | ||||||||
\(703\) | −17.9531 | −0.677113 | ||||||||
\(704\) | −63.8979 | −2.40824 | ||||||||
\(705\) | 9.40335 | 0.354151 | ||||||||
\(706\) | −44.6286 | −1.67962 | ||||||||
\(707\) | −7.91000 | −0.297486 | ||||||||
\(708\) | −13.9450 | −0.524085 | ||||||||
\(709\) | 18.8618 | 0.708371 | 0.354186 | − | 0.935175i | \(-0.384758\pi\) | ||||
0.354186 | + | 0.935175i | \(0.384758\pi\) | |||||||
\(710\) | 20.6618 | 0.775425 | ||||||||
\(711\) | 8.80672 | 0.330278 | ||||||||
\(712\) | 2.61472 | 0.0979907 | ||||||||
\(713\) | −55.6088 | −2.08257 | ||||||||
\(714\) | −14.7174 | −0.550784 | ||||||||
\(715\) | 28.3799 | 1.06135 | ||||||||
\(716\) | −65.2034 | −2.43676 | ||||||||
\(717\) | −2.27952 | −0.0851303 | ||||||||
\(718\) | −6.84623 | −0.255499 | ||||||||
\(719\) | 1.43512 | 0.0535210 | 0.0267605 | − | 0.999642i | \(-0.491481\pi\) | ||||
0.0267605 | + | 0.999642i | \(0.491481\pi\) | |||||||
\(720\) | −1.13903 | −0.0424492 | ||||||||
\(721\) | −0.523257 | −0.0194871 | ||||||||
\(722\) | 23.6661 | 0.880762 | ||||||||
\(723\) | −17.7901 | −0.661619 | ||||||||
\(724\) | 44.4058 | 1.65033 | ||||||||
\(725\) | −20.0435 | −0.744399 | ||||||||
\(726\) | 29.3671 | 1.08992 | ||||||||
\(727\) | −9.78980 | −0.363084 | −0.181542 | − | 0.983383i | \(-0.558109\pi\) | ||||
−0.181542 | + | 0.983383i | \(0.558109\pi\) | |||||||
\(728\) | −10.9431 | −0.405580 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −15.6063 | −0.577613 | ||||||||
\(731\) | 0.399690 | 0.0147831 | ||||||||
\(732\) | −4.60075 | −0.170049 | ||||||||
\(733\) | −12.7193 | −0.469797 | −0.234898 | − | 0.972020i | \(-0.575476\pi\) | ||||
−0.234898 | + | 0.972020i | \(0.575476\pi\) | |||||||
\(734\) | 17.2595 | 0.637061 | ||||||||
\(735\) | −1.19635 | −0.0441282 | ||||||||
\(736\) | −44.2674 | −1.63172 | ||||||||
\(737\) | 25.1207 | 0.925335 | ||||||||
\(738\) | −20.1817 | −0.742900 | ||||||||
\(739\) | 33.0733 | 1.21662 | 0.608310 | − | 0.793700i | \(-0.291848\pi\) | ||||
0.608310 | + | 0.793700i | \(0.291848\pi\) | |||||||
\(740\) | 22.2824 | 0.819118 | ||||||||
\(741\) | 14.0238 | 0.515177 | ||||||||
\(742\) | −2.14779 | −0.0788479 | ||||||||
\(743\) | 26.9820 | 0.989874 | 0.494937 | − | 0.868929i | \(-0.335191\pi\) | ||||
0.494937 | + | 0.868929i | \(0.335191\pi\) | |||||||
\(744\) | 18.9605 | 0.695127 | ||||||||
\(745\) | 26.8334 | 0.983101 | ||||||||
\(746\) | 47.8665 | 1.75252 | ||||||||
\(747\) | −3.10269 | −0.113521 | ||||||||
\(748\) | −97.2395 | −3.55543 | ||||||||
\(749\) | −3.71914 | −0.135894 | ||||||||
\(750\) | −22.9498 | −0.838010 | ||||||||
\(751\) | 12.5210 | 0.456897 | 0.228449 | − | 0.973556i | \(-0.426635\pi\) | ||||
0.228449 | + | 0.973556i | \(0.426635\pi\) | |||||||
\(752\) | 7.48340 | 0.272892 | ||||||||
\(753\) | −15.8080 | −0.576076 | ||||||||
\(754\) | −60.7360 | −2.21187 | ||||||||
\(755\) | 20.1303 | 0.732616 | ||||||||
\(756\) | −3.01194 | −0.109543 | ||||||||
\(757\) | −9.61090 | −0.349314 | −0.174657 | − | 0.984629i | \(-0.555882\pi\) | ||||
−0.174657 | + | 0.984629i | \(0.555882\pi\) | |||||||
\(758\) | −10.0487 | −0.364987 | ||||||||
\(759\) | 32.6302 | 1.18440 | ||||||||
\(760\) | 7.86868 | 0.285427 | ||||||||
\(761\) | 31.2369 | 1.13234 | 0.566168 | − | 0.824290i | \(-0.308425\pi\) | ||||
0.566168 | + | 0.824290i | \(0.308425\pi\) | |||||||
\(762\) | 33.6805 | 1.22012 | ||||||||
\(763\) | −11.0066 | −0.398465 | ||||||||
\(764\) | −3.01194 | −0.108968 | ||||||||
\(765\) | −7.86480 | −0.284352 | ||||||||
\(766\) | −7.86444 | −0.284154 | ||||||||
\(767\) | 22.3643 | 0.807527 | ||||||||
\(768\) | 9.35827 | 0.337688 | ||||||||
\(769\) | −46.0230 | −1.65963 | −0.829816 | − | 0.558036i | \(-0.811555\pi\) | ||||
−0.829816 | + | 0.558036i | \(0.811555\pi\) | |||||||
\(770\) | −13.1532 | −0.474008 | ||||||||
\(771\) | −2.60548 | −0.0938341 | ||||||||
\(772\) | 74.1540 | 2.66886 | ||||||||
\(773\) | 26.2347 | 0.943596 | 0.471798 | − | 0.881707i | \(-0.343605\pi\) | ||||
0.471798 | + | 0.881707i | \(0.343605\pi\) | |||||||
\(774\) | 0.136113 | 0.00489247 | ||||||||
\(775\) | −29.8680 | −1.07289 | ||||||||
\(776\) | −25.3490 | −0.909977 | ||||||||
\(777\) | −6.18380 | −0.221843 | ||||||||
\(778\) | −33.8231 | −1.21262 | ||||||||
\(779\) | −26.1721 | −0.937712 | ||||||||
\(780\) | −17.4056 | −0.623221 | ||||||||
\(781\) | −37.8856 | −1.35565 | ||||||||
\(782\) | −97.7874 | −3.49687 | ||||||||
\(783\) | −5.61643 | −0.200715 | ||||||||
\(784\) | −0.952086 | −0.0340031 | ||||||||
\(785\) | 13.9604 | 0.498267 | ||||||||
\(786\) | 36.1656 | 1.28999 | ||||||||
\(787\) | 0.577184 | 0.0205744 | 0.0102872 | − | 0.999947i | \(-0.496725\pi\) | ||||
0.0102872 | + | 0.999947i | \(0.496725\pi\) | |||||||
\(788\) | −10.1482 | −0.361515 | ||||||||
\(789\) | −10.6186 | −0.378033 | ||||||||
\(790\) | −23.5872 | −0.839196 | ||||||||
\(791\) | 2.50026 | 0.0888989 | ||||||||
\(792\) | −11.1257 | −0.395334 | ||||||||
\(793\) | 7.37844 | 0.262016 | ||||||||
\(794\) | 12.5952 | 0.446985 | ||||||||
\(795\) | −1.14775 | −0.0407067 | ||||||||
\(796\) | −67.3785 | −2.38817 | ||||||||
\(797\) | 29.8531 | 1.05745 | 0.528726 | − | 0.848792i | \(-0.322670\pi\) | ||||
0.528726 | + | 0.848792i | \(0.322670\pi\) | |||||||
\(798\) | −6.49959 | −0.230083 | ||||||||
\(799\) | 51.6714 | 1.82800 | ||||||||
\(800\) | −23.7764 | −0.840623 | ||||||||
\(801\) | −1.15416 | −0.0407802 | ||||||||
\(802\) | −71.6024 | −2.52837 | ||||||||
\(803\) | 28.6157 | 1.00983 | ||||||||
\(804\) | −15.4068 | −0.543354 | ||||||||
\(805\) | −7.94899 | −0.280165 | ||||||||
\(806\) | −90.5061 | −3.18794 | ||||||||
\(807\) | −11.9894 | −0.422047 | ||||||||
\(808\) | 17.9199 | 0.630420 | ||||||||
\(809\) | 32.5113 | 1.14304 | 0.571519 | − | 0.820589i | \(-0.306354\pi\) | ||||
0.571519 | + | 0.820589i | \(0.306354\pi\) | |||||||
\(810\) | −2.67832 | −0.0941067 | ||||||||
\(811\) | −39.9287 | −1.40209 | −0.701044 | − | 0.713118i | \(-0.747282\pi\) | ||||
−0.701044 | + | 0.713118i | \(0.747282\pi\) | |||||||
\(812\) | 16.9164 | 0.593648 | ||||||||
\(813\) | −24.2998 | −0.852232 | ||||||||
\(814\) | −67.9872 | −2.38295 | ||||||||
\(815\) | −23.5009 | −0.823201 | ||||||||
\(816\) | −6.25899 | −0.219108 | ||||||||
\(817\) | 0.176514 | 0.00617543 | ||||||||
\(818\) | 24.9012 | 0.870649 | ||||||||
\(819\) | 4.83040 | 0.168788 | ||||||||
\(820\) | 32.4834 | 1.13437 | ||||||||
\(821\) | −7.86164 | −0.274373 | −0.137186 | − | 0.990545i | \(-0.543806\pi\) | ||||
−0.137186 | + | 0.990545i | \(0.543806\pi\) | |||||||
\(822\) | −37.9899 | −1.32505 | ||||||||
\(823\) | 9.55136 | 0.332939 | 0.166470 | − | 0.986047i | \(-0.446763\pi\) | ||||
0.166470 | + | 0.986047i | \(0.446763\pi\) | |||||||
\(824\) | 1.18542 | 0.0412962 | ||||||||
\(825\) | 17.5260 | 0.610177 | ||||||||
\(826\) | −10.3651 | −0.360649 | ||||||||
\(827\) | 5.44750 | 0.189428 | 0.0947141 | − | 0.995505i | \(-0.469806\pi\) | ||||
0.0947141 | + | 0.995505i | \(0.469806\pi\) | |||||||
\(828\) | −20.0124 | −0.695478 | ||||||||
\(829\) | 1.97167 | 0.0684790 | 0.0342395 | − | 0.999414i | \(-0.489099\pi\) | ||||
0.0342395 | + | 0.999414i | \(0.489099\pi\) | |||||||
\(830\) | 8.31001 | 0.288445 | ||||||||
\(831\) | −3.63746 | −0.126182 | ||||||||
\(832\) | −62.8494 | −2.17891 | ||||||||
\(833\) | −6.57397 | −0.227775 | ||||||||
\(834\) | −3.52906 | −0.122201 | ||||||||
\(835\) | 3.09491 | 0.107104 | ||||||||
\(836\) | −42.9435 | −1.48523 | ||||||||
\(837\) | −8.36935 | −0.289287 | ||||||||
\(838\) | −60.6915 | −2.09655 | ||||||||
\(839\) | −13.9047 | −0.480044 | −0.240022 | − | 0.970767i | \(-0.577155\pi\) | ||||
−0.240022 | + | 0.970767i | \(0.577155\pi\) | |||||||
\(840\) | 2.71031 | 0.0935146 | ||||||||
\(841\) | 2.54425 | 0.0877329 | ||||||||
\(842\) | −23.1803 | −0.798845 | ||||||||
\(843\) | 27.9140 | 0.961410 | ||||||||
\(844\) | −35.8493 | −1.23398 | ||||||||
\(845\) | 12.3616 | 0.425253 | ||||||||
\(846\) | 17.5965 | 0.604980 | ||||||||
\(847\) | 13.1177 | 0.450731 | ||||||||
\(848\) | −0.913409 | −0.0313666 | ||||||||
\(849\) | −5.72185 | −0.196373 | ||||||||
\(850\) | −52.5225 | −1.80151 | ||||||||
\(851\) | −41.0873 | −1.40845 | ||||||||
\(852\) | 23.2355 | 0.796036 | ||||||||
\(853\) | 44.1402 | 1.51133 | 0.755665 | − | 0.654958i | \(-0.227314\pi\) | ||||
0.755665 | + | 0.654958i | \(0.227314\pi\) | |||||||
\(854\) | −3.41967 | −0.117019 | ||||||||
\(855\) | −3.47330 | −0.118785 | ||||||||
\(856\) | 8.42562 | 0.287982 | ||||||||
\(857\) | 26.9020 | 0.918954 | 0.459477 | − | 0.888190i | \(-0.348037\pi\) | ||||
0.459477 | + | 0.888190i | \(0.348037\pi\) | |||||||
\(858\) | 53.1073 | 1.81305 | ||||||||
\(859\) | 28.6221 | 0.976574 | 0.488287 | − | 0.872683i | \(-0.337622\pi\) | ||||
0.488287 | + | 0.872683i | \(0.337622\pi\) | |||||||
\(860\) | −0.219080 | −0.00747055 | ||||||||
\(861\) | −9.01478 | −0.307223 | ||||||||
\(862\) | 35.4370 | 1.20699 | ||||||||
\(863\) | −32.7324 | −1.11422 | −0.557112 | − | 0.830438i | \(-0.688090\pi\) | ||||
−0.557112 | + | 0.830438i | \(0.688090\pi\) | |||||||
\(864\) | −6.66242 | −0.226660 | ||||||||
\(865\) | −11.2320 | −0.381898 | ||||||||
\(866\) | −31.5721 | −1.07286 | ||||||||
\(867\) | −26.2171 | −0.890379 | ||||||||
\(868\) | 25.2080 | 0.855615 | ||||||||
\(869\) | 43.2496 | 1.46714 | ||||||||
\(870\) | 15.0426 | 0.509992 | ||||||||
\(871\) | 24.7086 | 0.837217 | ||||||||
\(872\) | 24.9351 | 0.844409 | ||||||||
\(873\) | 11.1893 | 0.378700 | ||||||||
\(874\) | −43.1855 | −1.46077 | ||||||||
\(875\) | −10.2512 | −0.346555 | ||||||||
\(876\) | −17.5502 | −0.592967 | ||||||||
\(877\) | −35.4367 | −1.19661 | −0.598306 | − | 0.801268i | \(-0.704159\pi\) | ||||
−0.598306 | + | 0.801268i | \(0.704159\pi\) | |||||||
\(878\) | 15.3445 | 0.517850 | ||||||||
\(879\) | 23.7777 | 0.802001 | ||||||||
\(880\) | −5.59377 | −0.188566 | ||||||||
\(881\) | −12.3862 | −0.417300 | −0.208650 | − | 0.977990i | \(-0.566907\pi\) | ||||
−0.208650 | + | 0.977990i | \(0.566907\pi\) | |||||||
\(882\) | −2.23874 | −0.0753822 | ||||||||
\(883\) | −21.0202 | −0.707385 | −0.353692 | − | 0.935362i | \(-0.615074\pi\) | ||||
−0.353692 | + | 0.935362i | \(0.615074\pi\) | |||||||
\(884\) | −95.6439 | −3.21685 | ||||||||
\(885\) | −5.53901 | −0.186192 | ||||||||
\(886\) | 57.3253 | 1.92588 | ||||||||
\(887\) | 17.4206 | 0.584925 | 0.292463 | − | 0.956277i | \(-0.405525\pi\) | ||||
0.292463 | + | 0.956277i | \(0.405525\pi\) | |||||||
\(888\) | 14.0092 | 0.470120 | ||||||||
\(889\) | 15.0444 | 0.504574 | ||||||||
\(890\) | 3.09121 | 0.103618 | ||||||||
\(891\) | 4.91098 | 0.164524 | ||||||||
\(892\) | 66.4244 | 2.22405 | ||||||||
\(893\) | 22.8195 | 0.763625 | ||||||||
\(894\) | 50.2134 | 1.67939 | ||||||||
\(895\) | −25.8990 | −0.865708 | ||||||||
\(896\) | 15.8039 | 0.527971 | ||||||||
\(897\) | 32.0948 | 1.07161 | ||||||||
\(898\) | 4.38416 | 0.146301 | ||||||||
\(899\) | 47.0058 | 1.56773 | ||||||||
\(900\) | −10.7488 | −0.358294 | ||||||||
\(901\) | −6.30691 | −0.210114 | ||||||||
\(902\) | −99.1121 | −3.30007 | ||||||||
\(903\) | 0.0607989 | 0.00202326 | ||||||||
\(904\) | −5.66427 | −0.188391 | ||||||||
\(905\) | 17.6382 | 0.586312 | ||||||||
\(906\) | 37.6698 | 1.25149 | ||||||||
\(907\) | −24.3911 | −0.809894 | −0.404947 | − | 0.914340i | \(-0.632710\pi\) | ||||
−0.404947 | + | 0.914340i | \(0.632710\pi\) | |||||||
\(908\) | 1.49545 | 0.0496281 | ||||||||
\(909\) | −7.91000 | −0.262358 | ||||||||
\(910\) | −12.9374 | −0.428870 | ||||||||
\(911\) | −9.90018 | −0.328008 | −0.164004 | − | 0.986460i | \(-0.552441\pi\) | ||||
−0.164004 | + | 0.986460i | \(0.552441\pi\) | |||||||
\(912\) | −2.76413 | −0.0915296 | ||||||||
\(913\) | −15.2373 | −0.504279 | ||||||||
\(914\) | 67.7507 | 2.24099 | ||||||||
\(915\) | −1.82743 | −0.0604131 | ||||||||
\(916\) | −76.5541 | −2.52942 | ||||||||
\(917\) | 16.1545 | 0.533468 | ||||||||
\(918\) | −14.7174 | −0.485746 | ||||||||
\(919\) | 32.9140 | 1.08573 | 0.542867 | − | 0.839819i | \(-0.317339\pi\) | ||||
0.542867 | + | 0.839819i | \(0.317339\pi\) | |||||||
\(920\) | 18.0082 | 0.593713 | ||||||||
\(921\) | 8.40496 | 0.276953 | ||||||||
\(922\) | −25.3567 | −0.835077 | ||||||||
\(923\) | −37.2640 | −1.22656 | ||||||||
\(924\) | −14.7916 | −0.486608 | ||||||||
\(925\) | −22.0684 | −0.725603 | ||||||||
\(926\) | 84.5312 | 2.77787 | ||||||||
\(927\) | −0.523257 | −0.0171860 | ||||||||
\(928\) | 37.4190 | 1.22834 | ||||||||
\(929\) | 27.0441 | 0.887288 | 0.443644 | − | 0.896203i | \(-0.353686\pi\) | ||||
0.443644 | + | 0.896203i | \(0.353686\pi\) | |||||||
\(930\) | 22.4158 | 0.735044 | ||||||||
\(931\) | −2.90324 | −0.0951499 | ||||||||
\(932\) | −74.0549 | −2.42575 | ||||||||
\(933\) | −23.4356 | −0.767247 | ||||||||
\(934\) | 64.8125 | 2.12073 | ||||||||
\(935\) | −38.6239 | −1.26314 | ||||||||
\(936\) | −10.9431 | −0.357688 | ||||||||
\(937\) | 56.3376 | 1.84047 | 0.920235 | − | 0.391366i | \(-0.127997\pi\) | ||||
0.920235 | + | 0.391366i | \(0.127997\pi\) | |||||||
\(938\) | −11.4516 | −0.373909 | ||||||||
\(939\) | −20.2103 | −0.659537 | ||||||||
\(940\) | −28.3224 | −0.923774 | ||||||||
\(941\) | 6.90321 | 0.225038 | 0.112519 | − | 0.993650i | \(-0.464108\pi\) | ||||
0.112519 | + | 0.993650i | \(0.464108\pi\) | |||||||
\(942\) | 26.1240 | 0.851166 | ||||||||
\(943\) | −59.8973 | −1.95052 | ||||||||
\(944\) | −4.40807 | −0.143470 | ||||||||
\(945\) | −1.19635 | −0.0389174 | ||||||||
\(946\) | 0.668447 | 0.0217331 | ||||||||
\(947\) | −2.80736 | −0.0912270 | −0.0456135 | − | 0.998959i | \(-0.514524\pi\) | ||||
−0.0456135 | + | 0.998959i | \(0.514524\pi\) | |||||||
\(948\) | −26.5253 | −0.861503 | ||||||||
\(949\) | 28.1461 | 0.913662 | ||||||||
\(950\) | −23.1953 | −0.752556 | ||||||||
\(951\) | −13.1251 | −0.425609 | ||||||||
\(952\) | 14.8932 | 0.482690 | ||||||||
\(953\) | 5.51651 | 0.178697 | 0.0893486 | − | 0.996000i | \(-0.471521\pi\) | ||||
0.0893486 | + | 0.996000i | \(0.471521\pi\) | |||||||
\(954\) | −2.14779 | −0.0695373 | ||||||||
\(955\) | −1.19635 | −0.0387131 | ||||||||
\(956\) | 6.86579 | 0.222055 | ||||||||
\(957\) | −27.5822 | −0.891605 | ||||||||
\(958\) | 81.0127 | 2.61740 | ||||||||
\(959\) | −16.9693 | −0.547969 | ||||||||
\(960\) | 15.5660 | 0.502392 | ||||||||
\(961\) | 39.0460 | 1.25955 | ||||||||
\(962\) | −66.8716 | −2.15603 | ||||||||
\(963\) | −3.71914 | −0.119848 | ||||||||
\(964\) | 53.5826 | 1.72578 | ||||||||
\(965\) | 29.4542 | 0.948166 | ||||||||
\(966\) | −14.8749 | −0.478593 | ||||||||
\(967\) | −42.0701 | −1.35288 | −0.676442 | − | 0.736496i | \(-0.736479\pi\) | ||||
−0.676442 | + | 0.736496i | \(0.736479\pi\) | |||||||
\(968\) | −29.7179 | −0.955169 | ||||||||
\(969\) | −19.0858 | −0.613125 | ||||||||
\(970\) | −29.9685 | −0.962231 | ||||||||
\(971\) | 21.2806 | 0.682926 | 0.341463 | − | 0.939895i | \(-0.389078\pi\) | ||||
0.341463 | + | 0.939895i | \(0.389078\pi\) | |||||||
\(972\) | −3.01194 | −0.0966081 | ||||||||
\(973\) | −1.57636 | −0.0505358 | ||||||||
\(974\) | 45.9502 | 1.47234 | ||||||||
\(975\) | 17.2384 | 0.552071 | ||||||||
\(976\) | −1.45431 | −0.0465514 | ||||||||
\(977\) | 5.87114 | 0.187834 | 0.0939171 | − | 0.995580i | \(-0.470061\pi\) | ||||
0.0939171 | + | 0.995580i | \(0.470061\pi\) | |||||||
\(978\) | −43.9772 | −1.40624 | ||||||||
\(979\) | −5.66806 | −0.181152 | ||||||||
\(980\) | 3.60335 | 0.115105 | ||||||||
\(981\) | −11.0066 | −0.351413 | ||||||||
\(982\) | 40.1258 | 1.28047 | ||||||||
\(983\) | 0.809028 | 0.0258040 | 0.0129020 | − | 0.999917i | \(-0.495893\pi\) | ||||
0.0129020 | + | 0.999917i | \(0.495893\pi\) | |||||||
\(984\) | 20.4228 | 0.651054 | ||||||||
\(985\) | −4.03091 | −0.128435 | ||||||||
\(986\) | 82.6591 | 2.63240 | ||||||||
\(987\) | 7.86001 | 0.250187 | ||||||||
\(988\) | −42.2389 | −1.34380 | ||||||||
\(989\) | 0.403968 | 0.0128454 | ||||||||
\(990\) | −13.1532 | −0.418036 | ||||||||
\(991\) | −43.7490 | −1.38973 | −0.694867 | − | 0.719139i | \(-0.744537\pi\) | ||||
−0.694867 | + | 0.719139i | \(0.744537\pi\) | |||||||
\(992\) | 55.7601 | 1.77038 | ||||||||
\(993\) | −7.57883 | −0.240507 | ||||||||
\(994\) | 17.2707 | 0.547792 | ||||||||
\(995\) | −26.7630 | −0.848444 | ||||||||
\(996\) | 9.34513 | 0.296112 | ||||||||
\(997\) | −24.1816 | −0.765838 | −0.382919 | − | 0.923782i | \(-0.625081\pi\) | ||||
−0.382919 | + | 0.923782i | \(0.625081\pi\) | |||||||
\(998\) | −39.1881 | −1.24048 | ||||||||
\(999\) | −6.18380 | −0.195647 |
(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 | 4011.2.a.l.1.6 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4011.2.a.l.1.6 | ✓ | 28 | 1.1 | even | 1 | trivial |