Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
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: | \( x^{12} - 2 x^{11} - 15 x^{10} + 30 x^{9} + 74 x^{8} - 149 x^{7} - 140 x^{6} + 278 x^{5} + 126 x^{4} + \cdots + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.467496\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.467496 | 0.330569 | 0.165285 | − | 0.986246i | \(-0.447146\pi\) | ||||
0.165285 | + | 0.986246i | \(0.447146\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.78145 | −0.890724 | ||||||||
\(5\) | 2.48991 | 1.11352 | 0.556762 | − | 0.830672i | \(-0.312044\pi\) | ||||
0.556762 | + | 0.830672i | \(0.312044\pi\) | |||||||
\(6\) | 0.467496 | 0.190854 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.76781 | −0.625016 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.16402 | 0.368097 | ||||||||
\(11\) | 5.31632 | 1.60293 | 0.801466 | − | 0.598041i | \(-0.204054\pi\) | ||||
0.801466 | + | 0.598041i | \(0.204054\pi\) | |||||||
\(12\) | −1.78145 | −0.514260 | ||||||||
\(13\) | 3.14130 | 0.871240 | 0.435620 | − | 0.900131i | \(-0.356529\pi\) | ||||
0.435620 | + | 0.900131i | \(0.356529\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.48991 | 0.642893 | ||||||||
\(16\) | 2.73645 | 0.684113 | ||||||||
\(17\) | 5.72132 | 1.38762 | 0.693812 | − | 0.720156i | \(-0.255930\pi\) | ||||
0.693812 | + | 0.720156i | \(0.255930\pi\) | |||||||
\(18\) | 0.467496 | 0.110190 | ||||||||
\(19\) | −1.29973 | −0.298179 | −0.149090 | − | 0.988824i | \(-0.547634\pi\) | ||||
−0.149090 | + | 0.988824i | \(0.547634\pi\) | |||||||
\(20\) | −4.43565 | −0.991842 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.48536 | 0.529880 | ||||||||
\(23\) | −7.14975 | −1.49083 | −0.745413 | − | 0.666603i | \(-0.767748\pi\) | ||||
−0.745413 | + | 0.666603i | \(0.767748\pi\) | |||||||
\(24\) | −1.76781 | −0.360853 | ||||||||
\(25\) | 1.19967 | 0.239935 | ||||||||
\(26\) | 1.46854 | 0.288005 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.64170 | 1.23333 | 0.616666 | − | 0.787225i | \(-0.288483\pi\) | ||||
0.616666 | + | 0.787225i | \(0.288483\pi\) | |||||||
\(30\) | 1.16402 | 0.212521 | ||||||||
\(31\) | −3.31751 | −0.595842 | −0.297921 | − | 0.954591i | \(-0.596293\pi\) | ||||
−0.297921 | + | 0.954591i | \(0.596293\pi\) | |||||||
\(32\) | 4.81490 | 0.851162 | ||||||||
\(33\) | 5.31632 | 0.925453 | ||||||||
\(34\) | 2.67469 | 0.458706 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.78145 | −0.296908 | ||||||||
\(37\) | 0.130411 | 0.0214394 | 0.0107197 | − | 0.999943i | \(-0.496588\pi\) | ||||
0.0107197 | + | 0.999943i | \(0.496588\pi\) | |||||||
\(38\) | −0.607620 | −0.0985690 | ||||||||
\(39\) | 3.14130 | 0.503011 | ||||||||
\(40\) | −4.40170 | −0.695970 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.82425 | 1.04069 | 0.520344 | − | 0.853957i | \(-0.325804\pi\) | ||||
0.520344 | + | 0.853957i | \(0.325804\pi\) | |||||||
\(44\) | −9.47075 | −1.42777 | ||||||||
\(45\) | 2.48991 | 0.371175 | ||||||||
\(46\) | −3.34248 | −0.492822 | ||||||||
\(47\) | −0.120892 | −0.0176339 | −0.00881697 | − | 0.999961i | \(-0.502807\pi\) | ||||
−0.00881697 | + | 0.999961i | \(0.502807\pi\) | |||||||
\(48\) | 2.73645 | 0.394973 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.560843 | 0.0793152 | ||||||||
\(51\) | 5.72132 | 0.801145 | ||||||||
\(52\) | −5.59606 | −0.776034 | ||||||||
\(53\) | 9.92571 | 1.36340 | 0.681701 | − | 0.731631i | \(-0.261241\pi\) | ||||
0.681701 | + | 0.731631i | \(0.261241\pi\) | |||||||
\(54\) | 0.467496 | 0.0636181 | ||||||||
\(55\) | 13.2372 | 1.78490 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.29973 | −0.172154 | ||||||||
\(58\) | 3.10496 | 0.407702 | ||||||||
\(59\) | −12.4957 | −1.62680 | −0.813400 | − | 0.581705i | \(-0.802386\pi\) | ||||
−0.813400 | + | 0.581705i | \(0.802386\pi\) | |||||||
\(60\) | −4.43565 | −0.572640 | ||||||||
\(61\) | −2.10795 | −0.269896 | −0.134948 | − | 0.990853i | \(-0.543087\pi\) | ||||
−0.134948 | + | 0.990853i | \(0.543087\pi\) | |||||||
\(62\) | −1.55092 | −0.196967 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.22196 | −0.402744 | ||||||||
\(65\) | 7.82157 | 0.970146 | ||||||||
\(66\) | 2.48536 | 0.305927 | ||||||||
\(67\) | 6.29580 | 0.769154 | 0.384577 | − | 0.923093i | \(-0.374347\pi\) | ||||
0.384577 | + | 0.923093i | \(0.374347\pi\) | |||||||
\(68\) | −10.1922 | −1.23599 | ||||||||
\(69\) | −7.14975 | −0.860729 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.99477 | −0.236735 | −0.118368 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118368 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(72\) | −1.76781 | −0.208339 | ||||||||
\(73\) | 13.8293 | 1.61860 | 0.809298 | − | 0.587398i | \(-0.199848\pi\) | ||||
0.809298 | + | 0.587398i | \(0.199848\pi\) | |||||||
\(74\) | 0.0609666 | 0.00708722 | ||||||||
\(75\) | 1.19967 | 0.138526 | ||||||||
\(76\) | 2.31541 | 0.265596 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.46854 | 0.166280 | ||||||||
\(79\) | −17.0137 | −1.91419 | −0.957095 | − | 0.289774i | \(-0.906420\pi\) | ||||
−0.957095 | + | 0.289774i | \(0.906420\pi\) | |||||||
\(80\) | 6.81353 | 0.761776 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.467496 | −0.0516263 | ||||||||
\(83\) | −10.1178 | −1.11057 | −0.555286 | − | 0.831660i | \(-0.687391\pi\) | ||||
−0.555286 | + | 0.831660i | \(0.687391\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.2456 | 1.54515 | ||||||||
\(86\) | 3.19031 | 0.344020 | ||||||||
\(87\) | 6.64170 | 0.712064 | ||||||||
\(88\) | −9.39825 | −1.00186 | ||||||||
\(89\) | 0.414652 | 0.0439530 | 0.0219765 | − | 0.999758i | \(-0.493004\pi\) | ||||
0.0219765 | + | 0.999758i | \(0.493004\pi\) | |||||||
\(90\) | 1.16402 | 0.122699 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.7369 | 1.32791 | ||||||||
\(93\) | −3.31751 | −0.344009 | ||||||||
\(94\) | −0.0565166 | −0.00582924 | ||||||||
\(95\) | −3.23623 | −0.332030 | ||||||||
\(96\) | 4.81490 | 0.491419 | ||||||||
\(97\) | −7.26249 | −0.737394 | −0.368697 | − | 0.929550i | \(-0.620196\pi\) | ||||
−0.368697 | + | 0.929550i | \(0.620196\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.31632 | 0.534311 | ||||||||
\(100\) | −2.13716 | −0.213716 | ||||||||
\(101\) | 8.23179 | 0.819094 | 0.409547 | − | 0.912289i | \(-0.365687\pi\) | ||||
0.409547 | + | 0.912289i | \(0.365687\pi\) | |||||||
\(102\) | 2.67469 | 0.264834 | ||||||||
\(103\) | −1.06395 | −0.104834 | −0.0524168 | − | 0.998625i | \(-0.516692\pi\) | ||||
−0.0524168 | + | 0.998625i | \(0.516692\pi\) | |||||||
\(104\) | −5.55322 | −0.544538 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.64023 | 0.450699 | ||||||||
\(107\) | −13.9713 | −1.35066 | −0.675329 | − | 0.737517i | \(-0.735998\pi\) | ||||
−0.675329 | + | 0.737517i | \(0.735998\pi\) | |||||||
\(108\) | −1.78145 | −0.171420 | ||||||||
\(109\) | 13.7027 | 1.31248 | 0.656241 | − | 0.754552i | \(-0.272146\pi\) | ||||
0.656241 | + | 0.754552i | \(0.272146\pi\) | |||||||
\(110\) | 6.18833 | 0.590034 | ||||||||
\(111\) | 0.130411 | 0.0123781 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.05734 | 0.569827 | 0.284914 | − | 0.958553i | \(-0.408035\pi\) | ||||
0.284914 | + | 0.958553i | \(0.408035\pi\) | |||||||
\(114\) | −0.607620 | −0.0569088 | ||||||||
\(115\) | −17.8023 | −1.66007 | ||||||||
\(116\) | −11.8318 | −1.09856 | ||||||||
\(117\) | 3.14130 | 0.290413 | ||||||||
\(118\) | −5.84168 | −0.537770 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −4.40170 | −0.401818 | ||||||||
\(121\) | 17.2633 | 1.56939 | ||||||||
\(122\) | −0.985458 | −0.0892192 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 5.90996 | 0.530730 | ||||||||
\(125\) | −9.46249 | −0.846350 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.27309 | −0.290439 | −0.145220 | − | 0.989399i | \(-0.546389\pi\) | ||||
−0.145220 | + | 0.989399i | \(0.546389\pi\) | |||||||
\(128\) | −11.1361 | −0.984297 | ||||||||
\(129\) | 6.82425 | 0.600842 | ||||||||
\(130\) | 3.65655 | 0.320701 | ||||||||
\(131\) | 12.9751 | 1.13364 | 0.566821 | − | 0.823841i | \(-0.308173\pi\) | ||||
0.566821 | + | 0.823841i | \(0.308173\pi\) | |||||||
\(132\) | −9.47075 | −0.824323 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.94326 | 0.254259 | ||||||||
\(135\) | 2.48991 | 0.214298 | ||||||||
\(136\) | −10.1142 | −0.867286 | ||||||||
\(137\) | −19.3260 | −1.65113 | −0.825566 | − | 0.564306i | \(-0.809144\pi\) | ||||
−0.825566 | + | 0.564306i | \(0.809144\pi\) | |||||||
\(138\) | −3.34248 | −0.284531 | ||||||||
\(139\) | 5.34559 | 0.453407 | 0.226703 | − | 0.973964i | \(-0.427205\pi\) | ||||
0.226703 | + | 0.973964i | \(0.427205\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.120892 | −0.0101810 | ||||||||
\(142\) | −0.932545 | −0.0782574 | ||||||||
\(143\) | 16.7002 | 1.39654 | ||||||||
\(144\) | 2.73645 | 0.228038 | ||||||||
\(145\) | 16.5373 | 1.37334 | ||||||||
\(146\) | 6.46514 | 0.535058 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.232320 | −0.0190966 | ||||||||
\(149\) | 0.427636 | 0.0350333 | 0.0175166 | − | 0.999847i | \(-0.494424\pi\) | ||||
0.0175166 | + | 0.999847i | \(0.494424\pi\) | |||||||
\(150\) | 0.560843 | 0.0457926 | ||||||||
\(151\) | −4.05095 | −0.329662 | −0.164831 | − | 0.986322i | \(-0.552708\pi\) | ||||
−0.164831 | + | 0.986322i | \(0.552708\pi\) | |||||||
\(152\) | 2.29768 | 0.186367 | ||||||||
\(153\) | 5.72132 | 0.462541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.26031 | −0.663484 | ||||||||
\(156\) | −5.59606 | −0.448043 | ||||||||
\(157\) | −19.7473 | −1.57601 | −0.788005 | − | 0.615669i | \(-0.788886\pi\) | ||||
−0.788005 | + | 0.615669i | \(0.788886\pi\) | |||||||
\(158\) | −7.95383 | −0.632773 | ||||||||
\(159\) | 9.92571 | 0.787160 | ||||||||
\(160\) | 11.9887 | 0.947789 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.467496 | 0.0367299 | ||||||||
\(163\) | −3.41869 | −0.267772 | −0.133886 | − | 0.990997i | \(-0.542746\pi\) | ||||
−0.133886 | + | 0.990997i | \(0.542746\pi\) | |||||||
\(164\) | 1.78145 | 0.139108 | ||||||||
\(165\) | 13.2372 | 1.03051 | ||||||||
\(166\) | −4.73002 | −0.367121 | ||||||||
\(167\) | −5.10863 | −0.395318 | −0.197659 | − | 0.980271i | \(-0.563334\pi\) | ||||
−0.197659 | + | 0.980271i | \(0.563334\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.13223 | −0.240941 | ||||||||
\(170\) | 6.65976 | 0.510780 | ||||||||
\(171\) | −1.29973 | −0.0993931 | ||||||||
\(172\) | −12.1570 | −0.926966 | ||||||||
\(173\) | 10.7996 | 0.821075 | 0.410537 | − | 0.911844i | \(-0.365341\pi\) | ||||
0.410537 | + | 0.911844i | \(0.365341\pi\) | |||||||
\(174\) | 3.10496 | 0.235387 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 14.5479 | 1.09659 | ||||||||
\(177\) | −12.4957 | −0.939233 | ||||||||
\(178\) | 0.193848 | 0.0145295 | ||||||||
\(179\) | 0.632276 | 0.0472585 | 0.0236293 | − | 0.999721i | \(-0.492478\pi\) | ||||
0.0236293 | + | 0.999721i | \(0.492478\pi\) | |||||||
\(180\) | −4.43565 | −0.330614 | ||||||||
\(181\) | −3.24632 | −0.241297 | −0.120649 | − | 0.992695i | \(-0.538497\pi\) | ||||
−0.120649 | + | 0.992695i | \(0.538497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.10795 | −0.155824 | ||||||||
\(184\) | 12.6394 | 0.931790 | ||||||||
\(185\) | 0.324712 | 0.0238733 | ||||||||
\(186\) | −1.55092 | −0.113719 | ||||||||
\(187\) | 30.4164 | 2.22427 | ||||||||
\(188\) | 0.215363 | 0.0157070 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.51292 | −0.109759 | ||||||||
\(191\) | −2.69791 | −0.195214 | −0.0976071 | − | 0.995225i | \(-0.531119\pi\) | ||||
−0.0976071 | + | 0.995225i | \(0.531119\pi\) | |||||||
\(192\) | −3.22196 | −0.232525 | ||||||||
\(193\) | −1.09647 | −0.0789256 | −0.0394628 | − | 0.999221i | \(-0.512565\pi\) | ||||
−0.0394628 | + | 0.999221i | \(0.512565\pi\) | |||||||
\(194\) | −3.39518 | −0.243760 | ||||||||
\(195\) | 7.82157 | 0.560114 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0471 | 0.858317 | 0.429158 | − | 0.903229i | \(-0.358810\pi\) | ||||
0.429158 | + | 0.903229i | \(0.358810\pi\) | |||||||
\(198\) | 2.48536 | 0.176627 | ||||||||
\(199\) | 18.7422 | 1.32860 | 0.664298 | − | 0.747468i | \(-0.268731\pi\) | ||||
0.664298 | + | 0.747468i | \(0.268731\pi\) | |||||||
\(200\) | −2.12080 | −0.149963 | ||||||||
\(201\) | 6.29580 | 0.444071 | ||||||||
\(202\) | 3.84833 | 0.270767 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −10.1922 | −0.713599 | ||||||||
\(205\) | −2.48991 | −0.173903 | ||||||||
\(206\) | −0.497390 | −0.0346548 | ||||||||
\(207\) | −7.14975 | −0.496942 | ||||||||
\(208\) | 8.59601 | 0.596026 | ||||||||
\(209\) | −6.90981 | −0.477961 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.3366 | 1.46887 | 0.734435 | − | 0.678679i | \(-0.237447\pi\) | ||||
0.734435 | + | 0.678679i | \(0.237447\pi\) | |||||||
\(212\) | −17.6821 | −1.21441 | ||||||||
\(213\) | −1.99477 | −0.136679 | ||||||||
\(214\) | −6.53153 | −0.446486 | ||||||||
\(215\) | 16.9918 | 1.15883 | ||||||||
\(216\) | −1.76781 | −0.120284 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.40596 | 0.433866 | ||||||||
\(219\) | 13.8293 | 0.934497 | ||||||||
\(220\) | −23.5814 | −1.58986 | ||||||||
\(221\) | 17.9724 | 1.20895 | ||||||||
\(222\) | 0.0609666 | 0.00409181 | ||||||||
\(223\) | 19.7146 | 1.32019 | 0.660093 | − | 0.751184i | \(-0.270517\pi\) | ||||
0.660093 | + | 0.751184i | \(0.270517\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.19967 | 0.0799783 | ||||||||
\(226\) | 2.83178 | 0.188367 | ||||||||
\(227\) | −15.8988 | −1.05524 | −0.527621 | − | 0.849480i | \(-0.676916\pi\) | ||||
−0.527621 | + | 0.849480i | \(0.676916\pi\) | |||||||
\(228\) | 2.31541 | 0.153342 | ||||||||
\(229\) | 26.3058 | 1.73833 | 0.869167 | − | 0.494518i | \(-0.164655\pi\) | ||||
0.869167 | + | 0.494518i | \(0.164655\pi\) | |||||||
\(230\) | −8.32249 | −0.548769 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.7413 | −0.770852 | ||||||||
\(233\) | 13.3645 | 0.875538 | 0.437769 | − | 0.899087i | \(-0.355769\pi\) | ||||
0.437769 | + | 0.899087i | \(0.355769\pi\) | |||||||
\(234\) | 1.46854 | 0.0960018 | ||||||||
\(235\) | −0.301011 | −0.0196358 | ||||||||
\(236\) | 22.2604 | 1.44903 | ||||||||
\(237\) | −17.0137 | −1.10516 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.72975 | −0.499996 | −0.249998 | − | 0.968246i | \(-0.580430\pi\) | ||||
−0.249998 | + | 0.968246i | \(0.580430\pi\) | |||||||
\(240\) | 6.81353 | 0.439811 | ||||||||
\(241\) | 18.1506 | 1.16918 | 0.584590 | − | 0.811329i | \(-0.301255\pi\) | ||||
0.584590 | + | 0.811329i | \(0.301255\pi\) | |||||||
\(242\) | 8.07052 | 0.518792 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.75520 | 0.240402 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.467496 | −0.0298064 | ||||||||
\(247\) | −4.08285 | −0.259786 | ||||||||
\(248\) | 5.86472 | 0.372410 | ||||||||
\(249\) | −10.1178 | −0.641189 | ||||||||
\(250\) | −4.42367 | −0.279778 | ||||||||
\(251\) | −2.70780 | −0.170915 | −0.0854575 | − | 0.996342i | \(-0.527235\pi\) | ||||
−0.0854575 | + | 0.996342i | \(0.527235\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.0104 | −2.38969 | ||||||||
\(254\) | −1.53015 | −0.0960104 | ||||||||
\(255\) | 14.2456 | 0.892094 | ||||||||
\(256\) | 1.23785 | 0.0773658 | ||||||||
\(257\) | −4.77854 | −0.298077 | −0.149039 | − | 0.988831i | \(-0.547618\pi\) | ||||
−0.149039 | + | 0.988831i | \(0.547618\pi\) | |||||||
\(258\) | 3.19031 | 0.198620 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −13.9337 | −0.864132 | ||||||||
\(261\) | 6.64170 | 0.411111 | ||||||||
\(262\) | 6.06582 | 0.374747 | ||||||||
\(263\) | −14.7301 | −0.908299 | −0.454150 | − | 0.890925i | \(-0.650057\pi\) | ||||
−0.454150 | + | 0.890925i | \(0.650057\pi\) | |||||||
\(264\) | −9.39825 | −0.578423 | ||||||||
\(265\) | 24.7142 | 1.51818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.414652 | 0.0253763 | ||||||||
\(268\) | −11.2156 | −0.685104 | ||||||||
\(269\) | 12.5726 | 0.766563 | 0.383282 | − | 0.923631i | \(-0.374794\pi\) | ||||
0.383282 | + | 0.923631i | \(0.374794\pi\) | |||||||
\(270\) | 1.16402 | 0.0708403 | ||||||||
\(271\) | 16.3050 | 0.990461 | 0.495230 | − | 0.868762i | \(-0.335084\pi\) | ||||
0.495230 | + | 0.868762i | \(0.335084\pi\) | |||||||
\(272\) | 15.6561 | 0.949291 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.03482 | −0.545814 | ||||||||
\(275\) | 6.37786 | 0.384599 | ||||||||
\(276\) | 12.7369 | 0.766672 | ||||||||
\(277\) | 19.0119 | 1.14232 | 0.571158 | − | 0.820840i | \(-0.306495\pi\) | ||||
0.571158 | + | 0.820840i | \(0.306495\pi\) | |||||||
\(278\) | 2.49904 | 0.149883 | ||||||||
\(279\) | −3.31751 | −0.198614 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3779 | −0.738404 | −0.369202 | − | 0.929349i | \(-0.620369\pi\) | ||||
−0.369202 | + | 0.929349i | \(0.620369\pi\) | |||||||
\(282\) | −0.0565166 | −0.00336552 | ||||||||
\(283\) | 25.5514 | 1.51888 | 0.759438 | − | 0.650580i | \(-0.225474\pi\) | ||||
0.759438 | + | 0.650580i | \(0.225474\pi\) | |||||||
\(284\) | 3.55357 | 0.210866 | ||||||||
\(285\) | −3.23623 | −0.191698 | ||||||||
\(286\) | 7.80726 | 0.461653 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.81490 | 0.283721 | ||||||||
\(289\) | 15.7335 | 0.925499 | ||||||||
\(290\) | 7.73110 | 0.453986 | ||||||||
\(291\) | −7.26249 | −0.425735 | ||||||||
\(292\) | −24.6362 | −1.44172 | ||||||||
\(293\) | 34.1011 | 1.99221 | 0.996104 | − | 0.0881812i | \(-0.0281054\pi\) | ||||
0.996104 | + | 0.0881812i | \(0.0281054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.1132 | −1.81148 | ||||||||
\(296\) | −0.230542 | −0.0134000 | ||||||||
\(297\) | 5.31632 | 0.308484 | ||||||||
\(298\) | 0.199918 | 0.0115809 | ||||||||
\(299\) | −22.4595 | −1.29887 | ||||||||
\(300\) | −2.13716 | −0.123389 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.89380 | −0.108976 | ||||||||
\(303\) | 8.23179 | 0.472904 | ||||||||
\(304\) | −3.55666 | −0.203988 | ||||||||
\(305\) | −5.24862 | −0.300535 | ||||||||
\(306\) | 2.67469 | 0.152902 | ||||||||
\(307\) | 16.5266 | 0.943223 | 0.471611 | − | 0.881806i | \(-0.343672\pi\) | ||||
0.471611 | + | 0.881806i | \(0.343672\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.06395 | −0.0605258 | ||||||||
\(310\) | −3.86166 | −0.219327 | ||||||||
\(311\) | 7.64063 | 0.433260 | 0.216630 | − | 0.976254i | \(-0.430493\pi\) | ||||
0.216630 | + | 0.976254i | \(0.430493\pi\) | |||||||
\(312\) | −5.55322 | −0.314389 | ||||||||
\(313\) | 19.2853 | 1.09007 | 0.545034 | − | 0.838414i | \(-0.316517\pi\) | ||||
0.545034 | + | 0.838414i | \(0.316517\pi\) | |||||||
\(314\) | −9.23180 | −0.520981 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 30.3090 | 1.70501 | ||||||||
\(317\) | 4.94086 | 0.277506 | 0.138753 | − | 0.990327i | \(-0.455691\pi\) | ||||
0.138753 | + | 0.990327i | \(0.455691\pi\) | |||||||
\(318\) | 4.64023 | 0.260211 | ||||||||
\(319\) | 35.3094 | 1.97695 | ||||||||
\(320\) | −8.02239 | −0.448465 | ||||||||
\(321\) | −13.9713 | −0.779802 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.43619 | −0.413761 | ||||||||
\(324\) | −1.78145 | −0.0989693 | ||||||||
\(325\) | 3.76854 | 0.209041 | ||||||||
\(326\) | −1.59822 | −0.0885174 | ||||||||
\(327\) | 13.7027 | 0.757761 | ||||||||
\(328\) | 1.76781 | 0.0976110 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.18833 | 0.340656 | ||||||||
\(331\) | −28.0809 | −1.54347 | −0.771734 | − | 0.635946i | \(-0.780610\pi\) | ||||
−0.771734 | + | 0.635946i | \(0.780610\pi\) | |||||||
\(332\) | 18.0243 | 0.989213 | ||||||||
\(333\) | 0.130411 | 0.00714647 | ||||||||
\(334\) | −2.38826 | −0.130680 | ||||||||
\(335\) | 15.6760 | 0.856472 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2575 | 0.940074 | 0.470037 | − | 0.882647i | \(-0.344241\pi\) | ||||
0.470037 | + | 0.882647i | \(0.344241\pi\) | |||||||
\(338\) | −1.46431 | −0.0796478 | ||||||||
\(339\) | 6.05734 | 0.328990 | ||||||||
\(340\) | −25.3778 | −1.37630 | ||||||||
\(341\) | −17.6369 | −0.955093 | ||||||||
\(342\) | −0.607620 | −0.0328563 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.0640 | −0.650446 | ||||||||
\(345\) | −17.8023 | −0.958442 | ||||||||
\(346\) | 5.04875 | 0.271422 | ||||||||
\(347\) | −22.6422 | −1.21550 | −0.607749 | − | 0.794129i | \(-0.707927\pi\) | ||||
−0.607749 | + | 0.794129i | \(0.707927\pi\) | |||||||
\(348\) | −11.8318 | −0.634253 | ||||||||
\(349\) | 10.6177 | 0.568351 | 0.284175 | − | 0.958772i | \(-0.408280\pi\) | ||||
0.284175 | + | 0.958772i | \(0.408280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.14130 | 0.167670 | ||||||||
\(352\) | 25.5976 | 1.36436 | ||||||||
\(353\) | −26.6357 | −1.41767 | −0.708837 | − | 0.705372i | \(-0.750780\pi\) | ||||
−0.708837 | + | 0.705372i | \(0.750780\pi\) | |||||||
\(354\) | −5.84168 | −0.310482 | ||||||||
\(355\) | −4.96680 | −0.263610 | ||||||||
\(356\) | −0.738681 | −0.0391500 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.295586 | 0.0156222 | ||||||||
\(359\) | 14.2091 | 0.749927 | 0.374964 | − | 0.927040i | \(-0.377655\pi\) | ||||
0.374964 | + | 0.927040i | \(0.377655\pi\) | |||||||
\(360\) | −4.40170 | −0.231990 | ||||||||
\(361\) | −17.3107 | −0.911089 | ||||||||
\(362\) | −1.51764 | −0.0797655 | ||||||||
\(363\) | 17.2633 | 0.906088 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.4338 | 1.80234 | ||||||||
\(366\) | −0.985458 | −0.0515107 | ||||||||
\(367\) | −3.29888 | −0.172200 | −0.0861000 | − | 0.996286i | \(-0.527440\pi\) | ||||
−0.0861000 | + | 0.996286i | \(0.527440\pi\) | |||||||
\(368\) | −19.5649 | −1.01989 | ||||||||
\(369\) | −1.00000 | −0.0520579 | ||||||||
\(370\) | 0.151802 | 0.00789179 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.90996 | 0.306417 | ||||||||
\(373\) | −31.7746 | −1.64523 | −0.822614 | − | 0.568600i | \(-0.807485\pi\) | ||||
−0.822614 | + | 0.568600i | \(0.807485\pi\) | |||||||
\(374\) | 14.2195 | 0.735274 | ||||||||
\(375\) | −9.46249 | −0.488641 | ||||||||
\(376\) | 0.213715 | 0.0110215 | ||||||||
\(377\) | 20.8636 | 1.07453 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.74760 | −0.243868 | −0.121934 | − | 0.992538i | \(-0.538910\pi\) | ||||
−0.121934 | + | 0.992538i | \(0.538910\pi\) | |||||||
\(380\) | 5.76517 | 0.295747 | ||||||||
\(381\) | −3.27309 | −0.167685 | ||||||||
\(382\) | −1.26126 | −0.0645319 | ||||||||
\(383\) | 22.2893 | 1.13893 | 0.569464 | − | 0.822016i | \(-0.307151\pi\) | ||||
0.569464 | + | 0.822016i | \(0.307151\pi\) | |||||||
\(384\) | −11.1361 | −0.568284 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.512595 | −0.0260904 | ||||||||
\(387\) | 6.82425 | 0.346896 | ||||||||
\(388\) | 12.9377 | 0.656814 | ||||||||
\(389\) | −26.7971 | −1.35867 | −0.679334 | − | 0.733830i | \(-0.737731\pi\) | ||||
−0.679334 | + | 0.733830i | \(0.737731\pi\) | |||||||
\(390\) | 3.65655 | 0.185157 | ||||||||
\(391\) | −40.9060 | −2.06871 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9751 | 0.654508 | ||||||||
\(394\) | 5.63195 | 0.283733 | ||||||||
\(395\) | −42.3626 | −2.13150 | ||||||||
\(396\) | −9.47075 | −0.475923 | ||||||||
\(397\) | −20.5329 | −1.03052 | −0.515258 | − | 0.857035i | \(-0.672304\pi\) | ||||
−0.515258 | + | 0.857035i | \(0.672304\pi\) | |||||||
\(398\) | 8.76188 | 0.439193 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.28285 | 0.164143 | ||||||||
\(401\) | 4.04841 | 0.202168 | 0.101084 | − | 0.994878i | \(-0.467769\pi\) | ||||
0.101084 | + | 0.994878i | \(0.467769\pi\) | |||||||
\(402\) | 2.94326 | 0.146796 | ||||||||
\(403\) | −10.4213 | −0.519121 | ||||||||
\(404\) | −14.6645 | −0.729586 | ||||||||
\(405\) | 2.48991 | 0.123725 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.693307 | 0.0343659 | ||||||||
\(408\) | −10.1142 | −0.500728 | ||||||||
\(409\) | −31.2232 | −1.54389 | −0.771943 | − | 0.635691i | \(-0.780715\pi\) | ||||
−0.771943 | + | 0.635691i | \(0.780715\pi\) | |||||||
\(410\) | −1.16402 | −0.0574871 | ||||||||
\(411\) | −19.3260 | −0.953281 | ||||||||
\(412\) | 1.89536 | 0.0933779 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.34248 | −0.164274 | ||||||||
\(415\) | −25.1924 | −1.23665 | ||||||||
\(416\) | 15.1250 | 0.741567 | ||||||||
\(417\) | 5.34559 | 0.261775 | ||||||||
\(418\) | −3.23031 | −0.157999 | ||||||||
\(419\) | −5.92612 | −0.289510 | −0.144755 | − | 0.989468i | \(-0.546239\pi\) | ||||
−0.144755 | + | 0.989468i | \(0.546239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.82299 | −0.235058 | −0.117529 | − | 0.993069i | \(-0.537497\pi\) | ||||
−0.117529 | + | 0.993069i | \(0.537497\pi\) | |||||||
\(422\) | 9.97475 | 0.485563 | ||||||||
\(423\) | −0.120892 | −0.00587798 | ||||||||
\(424\) | −17.5468 | −0.852147 | ||||||||
\(425\) | 6.86372 | 0.332939 | ||||||||
\(426\) | −0.932545 | −0.0451819 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 24.8891 | 1.20306 | ||||||||
\(429\) | 16.7002 | 0.806292 | ||||||||
\(430\) | 7.94359 | 0.383074 | ||||||||
\(431\) | 32.8146 | 1.58062 | 0.790311 | − | 0.612706i | \(-0.209919\pi\) | ||||
0.790311 | + | 0.612706i | \(0.209919\pi\) | |||||||
\(432\) | 2.73645 | 0.131658 | ||||||||
\(433\) | −24.1095 | −1.15863 | −0.579315 | − | 0.815103i | \(-0.696680\pi\) | ||||
−0.579315 | + | 0.815103i | \(0.696680\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.5373 | 0.792901 | ||||||||
\(436\) | −24.4107 | −1.16906 | ||||||||
\(437\) | 9.29278 | 0.444534 | ||||||||
\(438\) | 6.46514 | 0.308916 | ||||||||
\(439\) | −10.4952 | −0.500910 | −0.250455 | − | 0.968128i | \(-0.580580\pi\) | ||||
−0.250455 | + | 0.968128i | \(0.580580\pi\) | |||||||
\(440\) | −23.4008 | −1.11559 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.40201 | 0.399643 | ||||||||
\(443\) | −25.9121 | −1.23112 | −0.615561 | − | 0.788089i | \(-0.711070\pi\) | ||||
−0.615561 | + | 0.788089i | \(0.711070\pi\) | |||||||
\(444\) | −0.232320 | −0.0110254 | ||||||||
\(445\) | 1.03245 | 0.0489427 | ||||||||
\(446\) | 9.21648 | 0.436413 | ||||||||
\(447\) | 0.427636 | 0.0202265 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.5623 | −0.734432 | −0.367216 | − | 0.930136i | \(-0.619689\pi\) | ||||
−0.367216 | + | 0.930136i | \(0.619689\pi\) | |||||||
\(450\) | 0.560843 | 0.0264384 | ||||||||
\(451\) | −5.31632 | −0.250336 | ||||||||
\(452\) | −10.7908 | −0.507558 | ||||||||
\(453\) | −4.05095 | −0.190330 | ||||||||
\(454\) | −7.43264 | −0.348831 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.29768 | 0.107599 | ||||||||
\(457\) | −25.3788 | −1.18717 | −0.593584 | − | 0.804772i | \(-0.702288\pi\) | ||||
−0.593584 | + | 0.804772i | \(0.702288\pi\) | |||||||
\(458\) | 12.2978 | 0.574640 | ||||||||
\(459\) | 5.72132 | 0.267048 | ||||||||
\(460\) | 31.7138 | 1.47866 | ||||||||
\(461\) | 2.41621 | 0.112534 | 0.0562671 | − | 0.998416i | \(-0.482080\pi\) | ||||
0.0562671 | + | 0.998416i | \(0.482080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.9928 | −1.71920 | −0.859600 | − | 0.510968i | \(-0.829287\pi\) | ||||
−0.859600 | + | 0.510968i | \(0.829287\pi\) | |||||||
\(464\) | 18.1747 | 0.843738 | ||||||||
\(465\) | −8.26031 | −0.383063 | ||||||||
\(466\) | 6.24785 | 0.289426 | ||||||||
\(467\) | −13.9352 | −0.644845 | −0.322422 | − | 0.946596i | \(-0.604497\pi\) | ||||
−0.322422 | + | 0.946596i | \(0.604497\pi\) | |||||||
\(468\) | −5.59606 | −0.258678 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.140722 | −0.00649100 | ||||||||
\(471\) | −19.7473 | −0.909910 | ||||||||
\(472\) | 22.0900 | 1.01678 | ||||||||
\(473\) | 36.2799 | 1.66815 | ||||||||
\(474\) | −7.95383 | −0.365332 | ||||||||
\(475\) | −1.55926 | −0.0715437 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.92571 | 0.454467 | ||||||||
\(478\) | −3.61362 | −0.165283 | ||||||||
\(479\) | −35.5586 | −1.62471 | −0.812357 | − | 0.583160i | \(-0.801816\pi\) | ||||
−0.812357 | + | 0.583160i | \(0.801816\pi\) | |||||||
\(480\) | 11.9887 | 0.547206 | ||||||||
\(481\) | 0.409660 | 0.0186789 | ||||||||
\(482\) | 8.48532 | 0.386496 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −30.7536 | −1.39789 | ||||||||
\(485\) | −18.0830 | −0.821106 | ||||||||
\(486\) | 0.467496 | 0.0212060 | ||||||||
\(487\) | −37.2431 | −1.68764 | −0.843822 | − | 0.536623i | \(-0.819700\pi\) | ||||
−0.843822 | + | 0.536623i | \(0.819700\pi\) | |||||||
\(488\) | 3.72646 | 0.168689 | ||||||||
\(489\) | −3.41869 | −0.154598 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.7187 | 0.889892 | 0.444946 | − | 0.895557i | \(-0.353223\pi\) | ||||
0.444946 | + | 0.895557i | \(0.353223\pi\) | |||||||
\(492\) | 1.78145 | 0.0803139 | ||||||||
\(493\) | 37.9993 | 1.71140 | ||||||||
\(494\) | −1.90872 | −0.0858772 | ||||||||
\(495\) | 13.2372 | 0.594967 | ||||||||
\(496\) | −9.07819 | −0.407623 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.73002 | −0.211957 | ||||||||
\(499\) | 35.7234 | 1.59920 | 0.799599 | − | 0.600534i | \(-0.205045\pi\) | ||||
0.799599 | + | 0.600534i | \(0.205045\pi\) | |||||||
\(500\) | 16.8569 | 0.753864 | ||||||||
\(501\) | −5.10863 | −0.228237 | ||||||||
\(502\) | −1.26589 | −0.0564993 | ||||||||
\(503\) | 32.8860 | 1.46631 | 0.733157 | − | 0.680059i | \(-0.238046\pi\) | ||||
0.733157 | + | 0.680059i | \(0.238046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.4965 | 0.912080 | ||||||||
\(506\) | −17.7697 | −0.789960 | ||||||||
\(507\) | −3.13223 | −0.139107 | ||||||||
\(508\) | 5.83083 | 0.258701 | ||||||||
\(509\) | −25.7759 | −1.14250 | −0.571248 | − | 0.820778i | \(-0.693540\pi\) | ||||
−0.571248 | + | 0.820778i | \(0.693540\pi\) | |||||||
\(510\) | 6.65976 | 0.294899 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.8508 | 1.00987 | ||||||||
\(513\) | −1.29973 | −0.0573847 | ||||||||
\(514\) | −2.23395 | −0.0985352 | ||||||||
\(515\) | −2.64913 | −0.116735 | ||||||||
\(516\) | −12.1570 | −0.535184 | ||||||||
\(517\) | −0.642702 | −0.0282660 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.7996 | 0.474048 | ||||||||
\(520\) | −13.8271 | −0.606356 | ||||||||
\(521\) | −4.35424 | −0.190763 | −0.0953813 | − | 0.995441i | \(-0.530407\pi\) | ||||
−0.0953813 | + | 0.995441i | \(0.530407\pi\) | |||||||
\(522\) | 3.10496 | 0.135901 | ||||||||
\(523\) | −35.4249 | −1.54902 | −0.774511 | − | 0.632560i | \(-0.782004\pi\) | ||||
−0.774511 | + | 0.632560i | \(0.782004\pi\) | |||||||
\(524\) | −23.1145 | −1.00976 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.88628 | −0.300256 | ||||||||
\(527\) | −18.9805 | −0.826804 | ||||||||
\(528\) | 14.5479 | 0.633114 | ||||||||
\(529\) | 28.1190 | 1.22256 | ||||||||
\(530\) | 11.5538 | 0.501864 | ||||||||
\(531\) | −12.4957 | −0.542267 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.14130 | −0.136065 | ||||||||
\(534\) | 0.193848 | 0.00838863 | ||||||||
\(535\) | −34.7874 | −1.50399 | ||||||||
\(536\) | −11.1298 | −0.480733 | ||||||||
\(537\) | 0.632276 | 0.0272847 | ||||||||
\(538\) | 5.87763 | 0.253402 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.43565 | −0.190880 | ||||||||
\(541\) | 9.81032 | 0.421779 | 0.210889 | − | 0.977510i | \(-0.432364\pi\) | ||||
0.210889 | + | 0.977510i | \(0.432364\pi\) | |||||||
\(542\) | 7.62254 | 0.327416 | ||||||||
\(543\) | −3.24632 | −0.139313 | ||||||||
\(544\) | 27.5476 | 1.18109 | ||||||||
\(545\) | 34.1186 | 1.46148 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.28690 | −0.311565 | −0.155783 | − | 0.987791i | \(-0.549790\pi\) | ||||
−0.155783 | + | 0.987791i | \(0.549790\pi\) | |||||||
\(548\) | 34.4283 | 1.47070 | ||||||||
\(549\) | −2.10795 | −0.0899652 | ||||||||
\(550\) | 2.98162 | 0.127137 | ||||||||
\(551\) | −8.63244 | −0.367754 | ||||||||
\(552\) | 12.6394 | 0.537969 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.88799 | 0.377615 | ||||||||
\(555\) | 0.324712 | 0.0137833 | ||||||||
\(556\) | −9.52289 | −0.403860 | ||||||||
\(557\) | 35.4329 | 1.50134 | 0.750669 | − | 0.660678i | \(-0.229731\pi\) | ||||
0.750669 | + | 0.660678i | \(0.229731\pi\) | |||||||
\(558\) | −1.55092 | −0.0656557 | ||||||||
\(559\) | 21.4370 | 0.906689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.4164 | 1.28418 | ||||||||
\(562\) | −5.78662 | −0.244094 | ||||||||
\(563\) | 28.7535 | 1.21181 | 0.605907 | − | 0.795535i | \(-0.292810\pi\) | ||||
0.605907 | + | 0.795535i | \(0.292810\pi\) | |||||||
\(564\) | 0.215363 | 0.00906843 | ||||||||
\(565\) | 15.0823 | 0.634516 | ||||||||
\(566\) | 11.9452 | 0.502094 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.52637 | 0.147963 | ||||||||
\(569\) | 29.3434 | 1.23014 | 0.615070 | − | 0.788473i | \(-0.289128\pi\) | ||||
0.615070 | + | 0.788473i | \(0.289128\pi\) | |||||||
\(570\) | −1.51292 | −0.0633693 | ||||||||
\(571\) | 5.28258 | 0.221069 | 0.110535 | − | 0.993872i | \(-0.464744\pi\) | ||||
0.110535 | + | 0.993872i | \(0.464744\pi\) | |||||||
\(572\) | −29.7505 | −1.24393 | ||||||||
\(573\) | −2.69791 | −0.112707 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.57738 | −0.357701 | ||||||||
\(576\) | −3.22196 | −0.134248 | ||||||||
\(577\) | 14.4751 | 0.602606 | 0.301303 | − | 0.953528i | \(-0.402578\pi\) | ||||
0.301303 | + | 0.953528i | \(0.402578\pi\) | |||||||
\(578\) | 7.35534 | 0.305942 | ||||||||
\(579\) | −1.09647 | −0.0455677 | ||||||||
\(580\) | −29.4603 | −1.22327 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.39518 | −0.140735 | ||||||||
\(583\) | 52.7683 | 2.18544 | ||||||||
\(584\) | −24.4476 | −1.01165 | ||||||||
\(585\) | 7.82157 | 0.323382 | ||||||||
\(586\) | 15.9421 | 0.658563 | ||||||||
\(587\) | −32.6688 | −1.34839 | −0.674193 | − | 0.738556i | \(-0.735508\pi\) | ||||
−0.674193 | + | 0.738556i | \(0.735508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.31188 | 0.177668 | ||||||||
\(590\) | −14.5453 | −0.598820 | ||||||||
\(591\) | 12.0471 | 0.495549 | ||||||||
\(592\) | 0.356863 | 0.0146670 | ||||||||
\(593\) | −14.8785 | −0.610988 | −0.305494 | − | 0.952194i | \(-0.598822\pi\) | ||||
−0.305494 | + | 0.952194i | \(0.598822\pi\) | |||||||
\(594\) | 2.48536 | 0.101976 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.761811 | −0.0312050 | ||||||||
\(597\) | 18.7422 | 0.767065 | ||||||||
\(598\) | −10.4997 | −0.429366 | ||||||||
\(599\) | −8.72721 | −0.356584 | −0.178292 | − | 0.983978i | \(-0.557057\pi\) | ||||
−0.178292 | + | 0.983978i | \(0.557057\pi\) | |||||||
\(600\) | −2.12080 | −0.0865812 | ||||||||
\(601\) | −8.13308 | −0.331755 | −0.165878 | − | 0.986146i | \(-0.553046\pi\) | ||||
−0.165878 | + | 0.986146i | \(0.553046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.29580 | 0.256385 | ||||||||
\(604\) | 7.21656 | 0.293638 | ||||||||
\(605\) | 42.9841 | 1.74755 | ||||||||
\(606\) | 3.84833 | 0.156328 | ||||||||
\(607\) | 42.1210 | 1.70964 | 0.854820 | − | 0.518925i | \(-0.173667\pi\) | ||||
0.854820 | + | 0.518925i | \(0.173667\pi\) | |||||||
\(608\) | −6.25809 | −0.253799 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.45371 | −0.0993477 | ||||||||
\(611\) | −0.379759 | −0.0153634 | ||||||||
\(612\) | −10.1922 | −0.411996 | ||||||||
\(613\) | −37.0682 | −1.49717 | −0.748585 | − | 0.663039i | \(-0.769266\pi\) | ||||
−0.748585 | + | 0.663039i | \(0.769266\pi\) | |||||||
\(614\) | 7.72612 | 0.311801 | ||||||||
\(615\) | −2.48991 | −0.100403 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 40.4266 | 1.62751 | 0.813757 | − | 0.581205i | \(-0.197418\pi\) | ||||
0.813757 | + | 0.581205i | \(0.197418\pi\) | |||||||
\(618\) | −0.497390 | −0.0200080 | ||||||||
\(619\) | 7.12931 | 0.286551 | 0.143276 | − | 0.989683i | \(-0.454236\pi\) | ||||
0.143276 | + | 0.989683i | \(0.454236\pi\) | |||||||
\(620\) | 14.7153 | 0.590981 | ||||||||
\(621\) | −7.14975 | −0.286910 | ||||||||
\(622\) | 3.57196 | 0.143223 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 8.59601 | 0.344116 | ||||||||
\(625\) | −29.5592 | −1.18237 | ||||||||
\(626\) | 9.01579 | 0.360343 | ||||||||
\(627\) | −6.90981 | −0.275951 | ||||||||
\(628\) | 35.1789 | 1.40379 | ||||||||
\(629\) | 0.746122 | 0.0297498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.9305 | 0.833230 | 0.416615 | − | 0.909083i | \(-0.363216\pi\) | ||||
0.416615 | + | 0.909083i | \(0.363216\pi\) | |||||||
\(632\) | 30.0770 | 1.19640 | ||||||||
\(633\) | 21.3366 | 0.848052 | ||||||||
\(634\) | 2.30983 | 0.0917351 | ||||||||
\(635\) | −8.14970 | −0.323411 | ||||||||
\(636\) | −17.6821 | −0.701142 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 16.5070 | 0.653518 | ||||||||
\(639\) | −1.99477 | −0.0789117 | ||||||||
\(640\) | −27.7278 | −1.09604 | ||||||||
\(641\) | 12.4115 | 0.490227 | 0.245113 | − | 0.969494i | \(-0.421175\pi\) | ||||
0.245113 | + | 0.969494i | \(0.421175\pi\) | |||||||
\(642\) | −6.53153 | −0.257779 | ||||||||
\(643\) | 18.4629 | 0.728107 | 0.364053 | − | 0.931378i | \(-0.381393\pi\) | ||||
0.364053 | + | 0.931378i | \(0.381393\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.9918 | 0.669051 | ||||||||
\(646\) | −3.47639 | −0.136777 | ||||||||
\(647\) | −22.7620 | −0.894865 | −0.447433 | − | 0.894318i | \(-0.647662\pi\) | ||||
−0.447433 | + | 0.894318i | \(0.647662\pi\) | |||||||
\(648\) | −1.76781 | −0.0694462 | ||||||||
\(649\) | −66.4311 | −2.60765 | ||||||||
\(650\) | 1.76178 | 0.0691025 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.09022 | 0.238511 | ||||||||
\(653\) | −39.7604 | −1.55594 | −0.777972 | − | 0.628299i | \(-0.783751\pi\) | ||||
−0.777972 | + | 0.628299i | \(0.783751\pi\) | |||||||
\(654\) | 6.40596 | 0.250493 | ||||||||
\(655\) | 32.3070 | 1.26234 | ||||||||
\(656\) | −2.73645 | −0.106840 | ||||||||
\(657\) | 13.8293 | 0.539532 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.6201 | −0.452656 | −0.226328 | − | 0.974051i | \(-0.572672\pi\) | ||||
−0.226328 | + | 0.974051i | \(0.572672\pi\) | |||||||
\(660\) | −23.5814 | −0.917903 | ||||||||
\(661\) | −42.6438 | −1.65865 | −0.829325 | − | 0.558766i | \(-0.811275\pi\) | ||||
−0.829325 | + | 0.558766i | \(0.811275\pi\) | |||||||
\(662\) | −13.1277 | −0.510223 | ||||||||
\(663\) | 17.9724 | 0.697989 | ||||||||
\(664\) | 17.8863 | 0.694125 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0609666 | 0.00236241 | ||||||||
\(667\) | −47.4865 | −1.83868 | ||||||||
\(668\) | 9.10076 | 0.352119 | ||||||||
\(669\) | 19.7146 | 0.762210 | ||||||||
\(670\) | 7.32847 | 0.283123 | ||||||||
\(671\) | −11.2065 | −0.432624 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0452 | −1.77491 | −0.887455 | − | 0.460894i | \(-0.847529\pi\) | ||||
−0.887455 | + | 0.460894i | \(0.847529\pi\) | |||||||
\(674\) | 8.06779 | 0.310760 | ||||||||
\(675\) | 1.19967 | 0.0461755 | ||||||||
\(676\) | 5.57991 | 0.214612 | ||||||||
\(677\) | −11.8928 | −0.457077 | −0.228538 | − | 0.973535i | \(-0.573395\pi\) | ||||
−0.228538 | + | 0.973535i | \(0.573395\pi\) | |||||||
\(678\) | 2.83178 | 0.108754 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −25.1835 | −0.965744 | ||||||||
\(681\) | −15.8988 | −0.609244 | ||||||||
\(682\) | −8.24519 | −0.315725 | ||||||||
\(683\) | −2.72867 | −0.104410 | −0.0522049 | − | 0.998636i | \(-0.516625\pi\) | ||||
−0.0522049 | + | 0.998636i | \(0.516625\pi\) | |||||||
\(684\) | 2.31541 | 0.0885318 | ||||||||
\(685\) | −48.1201 | −1.83857 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.3058 | 1.00363 | ||||||||
\(688\) | 18.6742 | 0.711948 | ||||||||
\(689\) | 31.1796 | 1.18785 | ||||||||
\(690\) | −8.32249 | −0.316832 | ||||||||
\(691\) | −34.2991 | −1.30480 | −0.652399 | − | 0.757876i | \(-0.726237\pi\) | ||||
−0.652399 | + | 0.757876i | \(0.726237\pi\) | |||||||
\(692\) | −19.2388 | −0.731351 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.5851 | −0.401807 | ||||||||
\(695\) | 13.3101 | 0.504879 | ||||||||
\(696\) | −11.7413 | −0.445051 | ||||||||
\(697\) | −5.72132 | −0.216710 | ||||||||
\(698\) | 4.96372 | 0.187879 | ||||||||
\(699\) | 13.3645 | 0.505492 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.14489 | 0.0810113 | 0.0405057 | − | 0.999179i | \(-0.487103\pi\) | ||||
0.0405057 | + | 0.999179i | \(0.487103\pi\) | |||||||
\(702\) | 1.46854 | 0.0554266 | ||||||||
\(703\) | −0.169500 | −0.00639279 | ||||||||
\(704\) | −17.1290 | −0.645572 | ||||||||
\(705\) | −0.301011 | −0.0113367 | ||||||||
\(706\) | −12.4521 | −0.468640 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 22.2604 | 0.836598 | ||||||||
\(709\) | −14.7175 | −0.552728 | −0.276364 | − | 0.961053i | \(-0.589130\pi\) | ||||
−0.276364 | + | 0.961053i | \(0.589130\pi\) | |||||||
\(710\) | −2.32196 | −0.0871415 | ||||||||
\(711\) | −17.0137 | −0.638063 | ||||||||
\(712\) | −0.733026 | −0.0274713 | ||||||||
\(713\) | 23.7193 | 0.888297 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.5820 | 1.55508 | ||||||||
\(716\) | −1.12637 | −0.0420943 | ||||||||
\(717\) | −7.72975 | −0.288673 | ||||||||
\(718\) | 6.64269 | 0.247903 | ||||||||
\(719\) | −0.753231 | −0.0280908 | −0.0140454 | − | 0.999901i | \(-0.504471\pi\) | ||||
−0.0140454 | + | 0.999901i | \(0.504471\pi\) | |||||||
\(720\) | 6.81353 | 0.253925 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.09268 | −0.301178 | ||||||||
\(723\) | 18.1506 | 0.675027 | ||||||||
\(724\) | 5.78315 | 0.214929 | ||||||||
\(725\) | 7.96787 | 0.295919 | ||||||||
\(726\) | 8.07052 | 0.299525 | ||||||||
\(727\) | 5.76563 | 0.213835 | 0.106918 | − | 0.994268i | \(-0.465902\pi\) | ||||
0.106918 | + | 0.994268i | \(0.465902\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.0976 | 0.595800 | ||||||||
\(731\) | 39.0437 | 1.44408 | ||||||||
\(732\) | 3.75520 | 0.138796 | ||||||||
\(733\) | 46.2479 | 1.70820 | 0.854102 | − | 0.520106i | \(-0.174107\pi\) | ||||
0.854102 | + | 0.520106i | \(0.174107\pi\) | |||||||
\(734\) | −1.54221 | −0.0569241 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.4254 | −1.26894 | ||||||||
\(737\) | 33.4705 | 1.23290 | ||||||||
\(738\) | −0.467496 | −0.0172088 | ||||||||
\(739\) | −32.5856 | −1.19868 | −0.599340 | − | 0.800494i | \(-0.704570\pi\) | ||||
−0.599340 | + | 0.800494i | \(0.704570\pi\) | |||||||
\(740\) | −0.578458 | −0.0212645 | ||||||||
\(741\) | −4.08285 | −0.149987 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.01713 | 0.147374 | 0.0736871 | − | 0.997281i | \(-0.476523\pi\) | ||||
0.0736871 | + | 0.997281i | \(0.476523\pi\) | |||||||
\(744\) | 5.86472 | 0.215011 | ||||||||
\(745\) | 1.06478 | 0.0390104 | ||||||||
\(746\) | −14.8545 | −0.543862 | ||||||||
\(747\) | −10.1178 | −0.370191 | ||||||||
\(748\) | −54.1852 | −1.98121 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −4.42367 | −0.161530 | ||||||||
\(751\) | 33.4781 | 1.22163 | 0.610816 | − | 0.791772i | \(-0.290841\pi\) | ||||
0.610816 | + | 0.791772i | \(0.290841\pi\) | |||||||
\(752\) | −0.330816 | −0.0120636 | ||||||||
\(753\) | −2.70780 | −0.0986779 | ||||||||
\(754\) | 9.75363 | 0.355206 | ||||||||
\(755\) | −10.0865 | −0.367086 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.4372 | −1.72413 | −0.862067 | − | 0.506794i | \(-0.830831\pi\) | ||||
−0.862067 | + | 0.506794i | \(0.830831\pi\) | |||||||
\(758\) | −2.21949 | −0.0806153 | ||||||||
\(759\) | −38.0104 | −1.37969 | ||||||||
\(760\) | 5.72104 | 0.207524 | ||||||||
\(761\) | −41.1769 | −1.49266 | −0.746331 | − | 0.665575i | \(-0.768186\pi\) | ||||
−0.746331 | + | 0.665575i | \(0.768186\pi\) | |||||||
\(762\) | −1.53015 | −0.0554316 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.80619 | 0.173882 | ||||||||
\(765\) | 14.2456 | 0.515051 | ||||||||
\(766\) | 10.4201 | 0.376495 | ||||||||
\(767\) | −39.2527 | −1.41733 | ||||||||
\(768\) | 1.23785 | 0.0446672 | ||||||||
\(769\) | −26.5898 | −0.958853 | −0.479426 | − | 0.877582i | \(-0.659155\pi\) | ||||
−0.479426 | + | 0.877582i | \(0.659155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.77854 | −0.172095 | ||||||||
\(772\) | 1.95330 | 0.0703009 | ||||||||
\(773\) | −20.9554 | −0.753712 | −0.376856 | − | 0.926272i | \(-0.622995\pi\) | ||||
−0.376856 | + | 0.926272i | \(0.622995\pi\) | |||||||
\(774\) | 3.19031 | 0.114673 | ||||||||
\(775\) | −3.97993 | −0.142963 | ||||||||
\(776\) | 12.8387 | 0.460883 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.5275 | −0.449134 | ||||||||
\(779\) | 1.29973 | 0.0465678 | ||||||||
\(780\) | −13.9337 | −0.498907 | ||||||||
\(781\) | −10.6048 | −0.379470 | ||||||||
\(782\) | −19.1234 | −0.683851 | ||||||||
\(783\) | 6.64170 | 0.237355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.1692 | −1.75492 | ||||||||
\(786\) | 6.06582 | 0.216361 | ||||||||
\(787\) | −16.9981 | −0.605917 | −0.302959 | − | 0.953004i | \(-0.597974\pi\) | ||||
−0.302959 | + | 0.953004i | \(0.597974\pi\) | |||||||
\(788\) | −21.4612 | −0.764523 | ||||||||
\(789\) | −14.7301 | −0.524407 | ||||||||
\(790\) | −19.8044 | −0.704607 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −9.39825 | −0.333952 | ||||||||
\(793\) | −6.62171 | −0.235144 | ||||||||
\(794\) | −9.59905 | −0.340657 | ||||||||
\(795\) | 24.7142 | 0.876521 | ||||||||
\(796\) | −33.3882 | −1.18341 | ||||||||
\(797\) | −15.3946 | −0.545306 | −0.272653 | − | 0.962112i | \(-0.587901\pi\) | ||||
−0.272653 | + | 0.962112i | \(0.587901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.691663 | −0.0244693 | ||||||||
\(800\) | 5.77632 | 0.204224 | ||||||||
\(801\) | 0.414652 | 0.0146510 | ||||||||
\(802\) | 1.89261 | 0.0668305 | ||||||||
\(803\) | 73.5210 | 2.59450 | ||||||||
\(804\) | −11.2156 | −0.395545 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.87191 | −0.171606 | ||||||||
\(807\) | 12.5726 | 0.442576 | ||||||||
\(808\) | −14.5523 | −0.511946 | ||||||||
\(809\) | −35.4587 | −1.24666 | −0.623332 | − | 0.781958i | \(-0.714221\pi\) | ||||
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(810\) | 1.16402 | 0.0408997 | ||||||||
\(811\) | 18.1260 | 0.636490 | 0.318245 | − | 0.948009i | \(-0.396907\pi\) | ||||
0.318245 | + | 0.948009i | \(0.396907\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.3050 | 0.571843 | ||||||||
\(814\) | 0.324118 | 0.0113603 | ||||||||
\(815\) | −8.51225 | −0.298171 | ||||||||
\(816\) | 15.6561 | 0.548073 | ||||||||
\(817\) | −8.86971 | −0.310312 | ||||||||
\(818\) | −14.5967 | −0.510362 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.43565 | 0.154900 | ||||||||
\(821\) | 52.7592 | 1.84131 | 0.920654 | − | 0.390381i | \(-0.127657\pi\) | ||||
0.920654 | + | 0.390381i | \(0.127657\pi\) | |||||||
\(822\) | −9.03482 | −0.315126 | ||||||||
\(823\) | 25.4878 | 0.888448 | 0.444224 | − | 0.895916i | \(-0.353479\pi\) | ||||
0.444224 | + | 0.895916i | \(0.353479\pi\) | |||||||
\(824\) | 1.88086 | 0.0655227 | ||||||||
\(825\) | 6.37786 | 0.222049 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.2046 | 1.18941 | 0.594706 | − | 0.803943i | \(-0.297269\pi\) | ||||
0.594706 | + | 0.803943i | \(0.297269\pi\) | |||||||
\(828\) | 12.7369 | 0.442638 | ||||||||
\(829\) | −2.43288 | −0.0844973 | −0.0422487 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422487 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(830\) | −11.7774 | −0.408798 | ||||||||
\(831\) | 19.0119 | 0.659516 | ||||||||
\(832\) | −10.1211 | −0.350887 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.49904 | 0.0865347 | ||||||||
\(835\) | −12.7201 | −0.440196 | ||||||||
\(836\) | 12.3095 | 0.425731 | ||||||||
\(837\) | −3.31751 | −0.114670 | ||||||||
\(838\) | −2.77044 | −0.0957032 | ||||||||
\(839\) | −3.85230 | −0.132996 | −0.0664981 | − | 0.997787i | \(-0.521183\pi\) | ||||
−0.0664981 | + | 0.997787i | \(0.521183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.1121 | 0.521107 | ||||||||
\(842\) | −2.25473 | −0.0777031 | ||||||||
\(843\) | −12.3779 | −0.426317 | ||||||||
\(844\) | −38.0100 | −1.30836 | ||||||||
\(845\) | −7.79900 | −0.268294 | ||||||||
\(846\) | −0.0565166 | −0.00194308 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 27.1612 | 0.932720 | ||||||||
\(849\) | 25.5514 | 0.876923 | ||||||||
\(850\) | 3.20876 | 0.110060 | ||||||||
\(851\) | −0.932406 | −0.0319625 | ||||||||
\(852\) | 3.55357 | 0.121743 | ||||||||
\(853\) | 34.7837 | 1.19097 | 0.595486 | − | 0.803366i | \(-0.296960\pi\) | ||||
0.595486 | + | 0.803366i | \(0.296960\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.23623 | −0.110677 | ||||||||
\(856\) | 24.6986 | 0.844182 | ||||||||
\(857\) | 22.5815 | 0.771369 | 0.385685 | − | 0.922631i | \(-0.373965\pi\) | ||||
0.385685 | + | 0.922631i | \(0.373965\pi\) | |||||||
\(858\) | 7.80726 | 0.266535 | ||||||||
\(859\) | −51.2667 | −1.74920 | −0.874599 | − | 0.484847i | \(-0.838875\pi\) | ||||
−0.874599 | + | 0.484847i | \(0.838875\pi\) | |||||||
\(860\) | −30.2700 | −1.03220 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.3407 | 0.522505 | ||||||||
\(863\) | 37.0308 | 1.26054 | 0.630272 | − | 0.776374i | \(-0.282943\pi\) | ||||
0.630272 | + | 0.776374i | \(0.282943\pi\) | |||||||
\(864\) | 4.81490 | 0.163806 | ||||||||
\(865\) | 26.8900 | 0.914286 | ||||||||
\(866\) | −11.2711 | −0.383008 | ||||||||
\(867\) | 15.7335 | 0.534337 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −90.4503 | −3.06832 | ||||||||
\(870\) | 7.73110 | 0.262109 | ||||||||
\(871\) | 19.7770 | 0.670118 | ||||||||
\(872\) | −24.2238 | −0.820321 | ||||||||
\(873\) | −7.26249 | −0.245798 | ||||||||
\(874\) | 4.34433 | 0.146949 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.6362 | −0.832379 | ||||||||
\(877\) | 13.4630 | 0.454612 | 0.227306 | − | 0.973823i | \(-0.427008\pi\) | ||||
0.227306 | + | 0.973823i | \(0.427008\pi\) | |||||||
\(878\) | −4.90647 | −0.165585 | ||||||||
\(879\) | 34.1011 | 1.15020 | ||||||||
\(880\) | 36.2229 | 1.22107 | ||||||||
\(881\) | 46.4466 | 1.56482 | 0.782412 | − | 0.622761i | \(-0.213989\pi\) | ||||
0.782412 | + | 0.622761i | \(0.213989\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4619 | −0.823207 | −0.411604 | − | 0.911363i | \(-0.635031\pi\) | ||||
−0.411604 | + | 0.911363i | \(0.635031\pi\) | |||||||
\(884\) | −32.0168 | −1.07684 | ||||||||
\(885\) | −31.1132 | −1.04586 | ||||||||
\(886\) | −12.1138 | −0.406971 | ||||||||
\(887\) | 4.40051 | 0.147755 | 0.0738773 | − | 0.997267i | \(-0.476463\pi\) | ||||
0.0738773 | + | 0.997267i | \(0.476463\pi\) | |||||||
\(888\) | −0.230542 | −0.00773648 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.482665 | 0.0161790 | ||||||||
\(891\) | 5.31632 | 0.178104 | ||||||||
\(892\) | −35.1205 | −1.17592 | ||||||||
\(893\) | 0.157128 | 0.00525808 | ||||||||
\(894\) | 0.199918 | 0.00668626 | ||||||||
\(895\) | 1.57431 | 0.0526235 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.4595 | −0.749902 | ||||||||
\(898\) | −7.27533 | −0.242781 | ||||||||
\(899\) | −22.0339 | −0.734871 | ||||||||
\(900\) | −2.13716 | −0.0712386 | ||||||||
\(901\) | 56.7881 | 1.89189 | ||||||||
\(902\) | −2.48536 | −0.0827534 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.7082 | −0.356151 | ||||||||
\(905\) | −8.08307 | −0.268690 | ||||||||
\(906\) | −1.89380 | −0.0629174 | ||||||||
\(907\) | −26.4356 | −0.877780 | −0.438890 | − | 0.898541i | \(-0.644628\pi\) | ||||
−0.438890 | + | 0.898541i | \(0.644628\pi\) | |||||||
\(908\) | 28.3229 | 0.939929 | ||||||||
\(909\) | 8.23179 | 0.273031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.5097 | 1.04396 | 0.521982 | − | 0.852957i | \(-0.325193\pi\) | ||||
0.521982 | + | 0.852957i | \(0.325193\pi\) | |||||||
\(912\) | −3.55666 | −0.117773 | ||||||||
\(913\) | −53.7894 | −1.78017 | ||||||||
\(914\) | −11.8645 | −0.392442 | ||||||||
\(915\) | −5.24862 | −0.173514 | ||||||||
\(916\) | −46.8624 | −1.54838 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.67469 | 0.0882780 | ||||||||
\(919\) | −41.0251 | −1.35329 | −0.676647 | − | 0.736307i | \(-0.736568\pi\) | ||||
−0.676647 | + | 0.736307i | \(0.736568\pi\) | |||||||
\(920\) | 31.4711 | 1.03757 | ||||||||
\(921\) | 16.5266 | 0.544570 | ||||||||
\(922\) | 1.12957 | 0.0372004 | ||||||||
\(923\) | −6.26616 | −0.206253 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.156451 | 0.00514407 | ||||||||
\(926\) | −17.2940 | −0.568315 | ||||||||
\(927\) | −1.06395 | −0.0349446 | ||||||||
\(928\) | 31.9791 | 1.04977 | ||||||||
\(929\) | −19.3736 | −0.635627 | −0.317814 | − | 0.948153i | \(-0.602949\pi\) | ||||
−0.317814 | + | 0.948153i | \(0.602949\pi\) | |||||||
\(930\) | −3.86166 | −0.126629 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −23.8082 | −0.779863 | ||||||||
\(933\) | 7.64063 | 0.250143 | ||||||||
\(934\) | −6.51465 | −0.213166 | ||||||||
\(935\) | 75.7342 | 2.47677 | ||||||||
\(936\) | −5.55322 | −0.181513 | ||||||||
\(937\) | 9.08010 | 0.296634 | 0.148317 | − | 0.988940i | \(-0.452614\pi\) | ||||
0.148317 | + | 0.988940i | \(0.452614\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.2853 | 0.629351 | ||||||||
\(940\) | 0.536236 | 0.0174901 | ||||||||
\(941\) | −4.13494 | −0.134795 | −0.0673976 | − | 0.997726i | \(-0.521470\pi\) | ||||
−0.0673976 | + | 0.997726i | \(0.521470\pi\) | |||||||
\(942\) | −9.23180 | −0.300788 | ||||||||
\(943\) | 7.14975 | 0.232828 | ||||||||
\(944\) | −34.1938 | −1.11291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.9607 | 0.551440 | ||||||||
\(947\) | −12.7363 | −0.413875 | −0.206937 | − | 0.978354i | \(-0.566350\pi\) | ||||
−0.206937 | + | 0.978354i | \(0.566350\pi\) | |||||||
\(948\) | 30.3090 | 0.984391 | ||||||||
\(949\) | 43.4419 | 1.41019 | ||||||||
\(950\) | −0.728947 | −0.0236501 | ||||||||
\(951\) | 4.94086 | 0.160218 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.07352 | −0.131954 | −0.0659772 | − | 0.997821i | \(-0.521016\pi\) | ||||
−0.0659772 | + | 0.997821i | \(0.521016\pi\) | |||||||
\(954\) | 4.64023 | 0.150233 | ||||||||
\(955\) | −6.71758 | −0.217376 | ||||||||
\(956\) | 13.7701 | 0.445358 | ||||||||
\(957\) | 35.3094 | 1.14139 | ||||||||
\(958\) | −16.6235 | −0.537081 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.02239 | −0.258922 | ||||||||
\(961\) | −19.9942 | −0.644973 | ||||||||
\(962\) | 0.191514 | 0.00617467 | ||||||||
\(963\) | −13.9713 | −0.450219 | ||||||||
\(964\) | −32.3343 | −1.04142 | ||||||||
\(965\) | −2.73012 | −0.0878855 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.6737 | −0.439717 | −0.219858 | − | 0.975532i | \(-0.570560\pi\) | ||||
−0.219858 | + | 0.975532i | \(0.570560\pi\) | |||||||
\(968\) | −30.5182 | −0.980893 | ||||||||
\(969\) | −7.43619 | −0.238885 | ||||||||
\(970\) | −8.45371 | −0.271432 | ||||||||
\(971\) | 39.9822 | 1.28309 | 0.641545 | − | 0.767085i | \(-0.278294\pi\) | ||||
0.641545 | + | 0.767085i | \(0.278294\pi\) | |||||||
\(972\) | −1.78145 | −0.0571400 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.4110 | −0.557884 | ||||||||
\(975\) | 3.76854 | 0.120690 | ||||||||
\(976\) | −5.76831 | −0.184639 | ||||||||
\(977\) | −35.2159 | −1.12666 | −0.563329 | − | 0.826233i | \(-0.690480\pi\) | ||||
−0.563329 | + | 0.826233i | \(0.690480\pi\) | |||||||
\(978\) | −1.59822 | −0.0511055 | ||||||||
\(979\) | 2.20442 | 0.0704537 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.7027 | 0.437494 | ||||||||
\(982\) | 9.21841 | 0.294171 | ||||||||
\(983\) | 43.1205 | 1.37533 | 0.687666 | − | 0.726027i | \(-0.258635\pi\) | ||||
0.687666 | + | 0.726027i | \(0.258635\pi\) | |||||||
\(984\) | 1.76781 | 0.0563558 | ||||||||
\(985\) | 29.9961 | 0.955756 | ||||||||
\(986\) | 17.7645 | 0.565737 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.27339 | 0.231397 | ||||||||
\(989\) | −48.7917 | −1.55149 | ||||||||
\(990\) | 6.18833 | 0.196678 | ||||||||
\(991\) | −57.1493 | −1.81541 | −0.907703 | − | 0.419613i | \(-0.862166\pi\) | ||||
−0.907703 | + | 0.419613i | \(0.862166\pi\) | |||||||
\(992\) | −15.9735 | −0.507158 | ||||||||
\(993\) | −28.0809 | −0.891121 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.6664 | 1.47942 | ||||||||
\(996\) | 18.0243 | 0.571122 | ||||||||
\(997\) | −46.4135 | −1.46993 | −0.734964 | − | 0.678106i | \(-0.762801\pi\) | ||||
−0.734964 | + | 0.678106i | \(0.762801\pi\) | |||||||
\(998\) | 16.7005 | 0.528646 | ||||||||
\(999\) | 0.130411 | 0.00412602 |
(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 | 6027.2.a.bg.1.8 | 12 | ||
7.2 | even | 3 | 861.2.i.e.739.5 | yes | 24 | ||
7.4 | even | 3 | 861.2.i.e.247.5 | ✓ | 24 | ||
7.6 | odd | 2 | 6027.2.a.bf.1.8 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.e.247.5 | ✓ | 24 | 7.4 | even | 3 | ||
861.2.i.e.739.5 | yes | 24 | 7.2 | even | 3 | ||
6027.2.a.bf.1.8 | 12 | 7.6 | odd | 2 | |||
6027.2.a.bg.1.8 | 12 | 1.1 | even | 1 | trivial |