Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8092,2,Mod(1,8092)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8092, 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("8092.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8092 = 2^{2} \cdot 7 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8092.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: | \(64.6149453156\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{8} - 2x^{7} - 7x^{6} + 12x^{5} + 15x^{4} - 16x^{3} - 13x^{2} + 2x + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 476) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.05350\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8092.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.98074 | −1.72093 | −0.860467 | − | 0.509507i | \(-0.829828\pi\) | ||||
−0.860467 | + | 0.509507i | \(0.829828\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.77152 | 0.792248 | 0.396124 | − | 0.918197i | \(-0.370355\pi\) | ||||
0.396124 | + | 0.918197i | \(0.370355\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.88484 | 1.96161 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.99979 | 0.904472 | 0.452236 | − | 0.891898i | \(-0.350626\pi\) | ||||
0.452236 | + | 0.891898i | \(0.350626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59917 | 0.720879 | 0.360440 | − | 0.932783i | \(-0.382627\pi\) | ||||
0.360440 | + | 0.932783i | \(0.382627\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.28045 | −1.36341 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.57015 | 1.04846 | 0.524232 | − | 0.851575i | \(-0.324352\pi\) | ||||
0.524232 | + | 0.851575i | \(0.324352\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.98074 | −0.650452 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.37363 | −0.911964 | −0.455982 | − | 0.889989i | \(-0.650712\pi\) | ||||
−0.455982 | + | 0.889989i | \(0.650712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.86172 | −0.372343 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −8.59896 | −1.65487 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.40860 | 0.447265 | 0.223633 | − | 0.974674i | \(-0.428208\pi\) | ||||
0.223633 | + | 0.974674i | \(0.428208\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.64427 | −0.474925 | −0.237463 | − | 0.971397i | \(-0.576316\pi\) | ||||
−0.237463 | + | 0.971397i | \(0.576316\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.94162 | −1.55654 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.77152 | 0.299442 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.526932 | −0.0866270 | −0.0433135 | − | 0.999062i | \(-0.513791\pi\) | ||||
−0.0433135 | + | 0.999062i | \(0.513791\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.74745 | −1.24059 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.0588 | −1.88326 | −0.941631 | − | 0.336646i | \(-0.890707\pi\) | ||||
−0.941631 | + | 0.336646i | \(0.890707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.63796 | −0.402285 | −0.201143 | − | 0.979562i | \(-0.564465\pi\) | ||||
−0.201143 | + | 0.979562i | \(0.564465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.4251 | 1.55408 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.67463 | −1.41119 | −0.705595 | − | 0.708616i | \(-0.749320\pi\) | ||||
−0.705595 | + | 0.708616i | \(0.749320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.88549 | 0.533713 | 0.266857 | − | 0.963736i | \(-0.414015\pi\) | ||||
0.266857 | + | 0.963736i | \(0.414015\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.31420 | 0.716566 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −13.6225 | −1.80434 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.63190 | −0.342645 | −0.171322 | − | 0.985215i | \(-0.554804\pi\) | ||||
−0.171322 | + | 0.985215i | \(0.554804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.36096 | −1.19855 | −0.599274 | − | 0.800544i | \(-0.704544\pi\) | ||||
−0.599274 | + | 0.800544i | \(0.704544\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.88484 | 0.741420 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.60448 | 0.571115 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9050 | −1.82093 | −0.910467 | − | 0.413581i | \(-0.864278\pi\) | ||||
−0.910467 | + | 0.413581i | \(0.864278\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.0367 | 1.56943 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.2979 | −1.69684 | −0.848422 | − | 0.529321i | \(-0.822447\pi\) | ||||
−0.848422 | + | 0.529321i | \(0.822447\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.15166 | 0.368874 | 0.184437 | − | 0.982844i | \(-0.440954\pi\) | ||||
0.184437 | + | 0.982844i | \(0.440954\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 5.54930 | 0.640778 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.99979 | 0.341858 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.3112 | −1.94766 | −0.973831 | − | 0.227273i | \(-0.927019\pi\) | ||||
−0.973831 | + | 0.227273i | \(0.927019\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.97679 | 0.886310 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.6749 | 1.39125 | 0.695624 | − | 0.718406i | \(-0.255128\pi\) | ||||
0.695624 | + | 0.718406i | \(0.255128\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.17941 | −0.769713 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.05547 | −0.217879 | −0.108940 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108940 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.59917 | 0.272467 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.88190 | 0.817314 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.09612 | 0.830644 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.19765 | 0.730811 | 0.365405 | − | 0.930849i | \(-0.380930\pi\) | ||||
0.365405 | + | 0.930849i | \(0.380930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.6533 | 1.77422 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.15980 | −0.115404 | −0.0577021 | − | 0.998334i | \(-0.518377\pi\) | ||||
−0.0577021 | + | 0.998334i | \(0.518377\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.73357 | −0.860545 | −0.430272 | − | 0.902699i | \(-0.641582\pi\) | ||||
−0.430272 | + | 0.902699i | \(0.641582\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.28045 | −0.515319 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.2202 | −1.27804 | −0.639022 | − | 0.769188i | \(-0.720661\pi\) | ||||
−0.639022 | + | 0.769188i | \(0.720661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.64129 | −0.444555 | −0.222277 | − | 0.974983i | \(-0.571349\pi\) | ||||
−0.222277 | + | 0.974983i | \(0.571349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.57065 | 0.149079 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.401281 | −0.0377494 | −0.0188747 | − | 0.999822i | \(-0.506008\pi\) | ||||
−0.0188747 | + | 0.999822i | \(0.506008\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.74797 | −0.722502 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 15.2957 | 1.41409 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00124 | −0.181931 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35.9441 | 3.24097 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1557 | −1.08724 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.350103 | 0.0310666 | 0.0155333 | − | 0.999879i | \(-0.495055\pi\) | ||||
0.0155333 | + | 0.999879i | \(0.495055\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.86309 | 0.692306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.88711 | −0.689100 | −0.344550 | − | 0.938768i | \(-0.611969\pi\) | ||||
−0.344550 | + | 0.938768i | \(0.611969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.57015 | 0.396282 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.2332 | −1.31107 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.64144 | 0.823724 | 0.411862 | − | 0.911246i | \(-0.364879\pi\) | ||||
0.411862 | + | 0.911246i | \(0.364879\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.9086 | 1.09489 | 0.547446 | − | 0.836841i | \(-0.315600\pi\) | ||||
0.547446 | + | 0.836841i | \(0.315600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.8376 | 2.42856 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.79696 | 0.652015 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.26688 | 0.354345 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.98074 | −0.245848 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.94430 | 0.323129 | 0.161565 | − | 0.986862i | \(-0.448346\pi\) | ||||
0.161565 | + | 0.986862i | \(0.448346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 23.8865 | 1.94385 | 0.971927 | − | 0.235281i | \(-0.0756012\pi\) | ||||
0.971927 | + | 0.235281i | \(0.0756012\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.68438 | −0.376258 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.4697 | 1.47404 | 0.737020 | − | 0.675871i | \(-0.236232\pi\) | ||||
0.737020 | + | 0.675871i | \(0.236232\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5817 | −0.918485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.37363 | −0.344690 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.3996 | −1.44117 | −0.720586 | − | 0.693366i | \(-0.756127\pi\) | ||||
−0.720586 | + | 0.693366i | \(0.756127\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.8403 | −1.23316 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.8278 | −1.84385 | −0.921925 | − | 0.387369i | \(-0.873384\pi\) | ||||
−0.921925 | + | 0.387369i | \(0.873384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.24433 | −0.480333 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 26.8946 | 2.05668 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.26854 | −0.476588 | −0.238294 | − | 0.971193i | \(-0.576588\pi\) | ||||
−0.238294 | + | 0.971193i | \(0.576588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.86172 | −0.140733 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.84503 | 0.589669 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.8732 | −0.962190 | −0.481095 | − | 0.876668i | \(-0.659761\pi\) | ||||
−0.481095 | + | 0.876668i | \(0.659761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.3869 | 1.58968 | 0.794838 | − | 0.606822i | \(-0.207556\pi\) | ||||
0.794838 | + | 0.606822i | \(0.207556\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.9026 | 2.06262 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.933470 | −0.0686301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.59896 | −0.625482 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.5198 | 1.26769 | 0.633846 | − | 0.773460i | \(-0.281475\pi\) | ||||
0.633846 | + | 0.773460i | \(0.281475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.15622 | −0.371153 | −0.185576 | − | 0.982630i | \(-0.559415\pi\) | ||||
−0.185576 | + | 0.982630i | \(0.559415\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.7248 | −0.982851 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.16634 | −0.653075 | −0.326537 | − | 0.945184i | \(-0.605882\pi\) | ||||
−0.326537 | + | 0.945184i | \(0.605882\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6411 | 0.825214 | 0.412607 | − | 0.910909i | \(-0.364618\pi\) | ||||
0.412607 | + | 0.910909i | \(0.364618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 44.4280 | 3.13371 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.40860 | 0.169050 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −21.3623 | −1.49201 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −25.7381 | −1.78892 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.7095 | 0.948307 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.56648 | 0.245526 | 0.122763 | − | 0.992436i | \(-0.460824\pi\) | ||||
0.122763 | + | 0.992436i | \(0.460824\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 42.6183 | 2.92015 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.67320 | −0.318710 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.64427 | −0.179505 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.39430 | −0.634808 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4094 | −1.43368 | −0.716840 | − | 0.697238i | \(-0.754412\pi\) | ||||
−0.716840 | + | 0.697238i | \(0.754412\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.9559 | −0.730393 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.0931 | −1.39999 | −0.699997 | − | 0.714145i | \(-0.746816\pi\) | ||||
−0.699997 | + | 0.714145i | \(0.746816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.2882 | 0.679866 | 0.339933 | − | 0.940450i | \(-0.389596\pi\) | ||||
0.339933 | + | 0.940450i | \(0.389596\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.94162 | −0.588315 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.4160 | 0.747888 | 0.373944 | − | 0.927451i | \(-0.378005\pi\) | ||||
0.373944 | + | 0.927451i | \(0.378005\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.1388 | −1.11801 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 51.6003 | 3.35180 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.00572125 | −0.000370077 0 | −0.000185039 | − | 1.00000i | \(-0.500059\pi\) | ||||
−0.000185039 | 1.00000i | \(0.500059\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.6937 | 1.65507 | 0.827537 | − | 0.561410i | \(-0.189741\pi\) | ||||
0.827537 | + | 0.561410i | \(0.189741\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.02010 | 0.129590 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.77152 | 0.113178 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.8786 | 0.755816 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −37.7805 | −2.39424 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.56127 | −0.540383 | −0.270191 | − | 0.962807i | \(-0.587087\pi\) | ||||
−0.270191 | + | 0.962807i | \(0.587087\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.1200 | −0.824846 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.3786 | −0.959291 | −0.479646 | − | 0.877462i | \(-0.659235\pi\) | ||||
−0.479646 | + | 0.877462i | \(0.659235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.526932 | −0.0327419 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.1742 | 0.877361 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.18787 | 0.0732471 | 0.0366236 | − | 0.999329i | \(-0.488340\pi\) | ||||
0.0366236 | + | 0.999329i | \(0.488340\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.88322 | 0.422833 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.12683 | 0.374956 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.48101 | 0.273212 | 0.136606 | − | 0.990625i | \(-0.456381\pi\) | ||||
0.136606 | + | 0.990625i | \(0.456381\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5763 | −0.946192 | −0.473096 | − | 0.881011i | \(-0.656864\pi\) | ||||
−0.473096 | + | 0.881011i | \(0.656864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.74745 | −0.468897 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.58477 | −0.336774 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.1491 | −1.09047 | −0.545237 | − | 0.838282i | \(-0.683560\pi\) | ||||
−0.545237 | + | 0.838282i | \(0.683560\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.5611 | −0.931619 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0114 | 1.61137 | 0.805683 | − | 0.592347i | \(-0.201798\pi\) | ||||
0.805683 | + | 0.592347i | \(0.201798\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.42153 | 0.381720 | 0.190860 | − | 0.981617i | \(-0.438872\pi\) | ||||
0.190860 | + | 0.981617i | \(0.438872\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −24.1324 | −1.42948 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0588 | −0.711806 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −21.4544 | −1.25768 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.4808 | −0.729134 | −0.364567 | − | 0.931177i | \(-0.618783\pi\) | ||||
−0.364567 | + | 0.931177i | \(0.618783\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.66247 | −0.271460 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −25.7951 | −1.49678 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.3678 | −0.657416 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.63796 | −0.152050 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.45706 | 0.198603 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.5831 | −0.949547 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.3966 | 1.67775 | 0.838877 | − | 0.544321i | \(-0.183213\pi\) | ||||
0.838877 | + | 0.544321i | \(0.183213\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.0325 | 1.48094 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.8689 | 0.899844 | 0.449922 | − | 0.893068i | \(-0.351452\pi\) | ||||
0.449922 | + | 0.893068i | \(0.351452\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.8643 | −1.85760 | −0.928801 | − | 0.370579i | \(-0.879159\pi\) | ||||
−0.928801 | + | 0.370579i | \(0.879159\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.4251 | 0.587388 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.5628 | −1.49191 | −0.745957 | − | 0.665994i | \(-0.768008\pi\) | ||||
−0.745957 | + | 0.665994i | \(0.768008\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.22529 | 0.404539 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 39.4060 | 2.19943 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.83891 | −0.268414 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.8345 | 0.765049 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.67463 | −0.533379 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.9872 | −0.988666 | −0.494333 | − | 0.869273i | \(-0.664588\pi\) | ||||
−0.494333 | + | 0.869273i | \(0.664588\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.10091 | −0.169929 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.4045 | −1.44263 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.0534 | 1.52816 | 0.764082 | − | 0.645119i | \(-0.223192\pi\) | ||||
0.764082 | + | 0.645119i | \(0.223192\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.19612 | 0.0649642 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.93227 | −0.429556 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.0947 | 1.24338 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.1197 | −1.02640 | −0.513199 | − | 0.858270i | \(-0.671540\pi\) | ||||
−0.513199 | + | 0.858270i | \(0.671540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.4741 | 0.667725 | 0.333863 | − | 0.942622i | \(-0.391648\pi\) | ||||
0.333863 | + | 0.942622i | \(0.391648\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.3501 | −1.19296 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.0136 | 1.70391 | 0.851956 | − | 0.523613i | \(-0.175416\pi\) | ||||
0.851956 | + | 0.523613i | \(0.175416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.3289 | −1.34432 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.5673 | 0.610501 | 0.305251 | − | 0.952272i | \(-0.401260\pi\) | ||||
0.305251 | + | 0.952272i | \(0.401260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.88628 | 0.0992781 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.96517 | 0.313090 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.58324 | 0.292240 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.64863 | −0.294856 | −0.147428 | − | 0.989073i | \(-0.547099\pi\) | ||||
−0.147428 | + | 0.989073i | \(0.547099\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −70.9638 | −3.69423 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.88549 | 0.201725 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0723 | −0.935750 | −0.467875 | − | 0.883795i | \(-0.654980\pi\) | ||||
−0.467875 | + | 0.883795i | \(0.654980\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 36.2329 | 1.87106 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.26034 | 0.322424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.27736 | −0.219713 | −0.109857 | − | 0.993947i | \(-0.535039\pi\) | ||||
−0.109857 | + | 0.993947i | \(0.535039\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.04357 | −0.0534636 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.28017 | 0.116511 | 0.0582557 | − | 0.998302i | \(-0.481446\pi\) | ||||
0.0582557 | + | 0.998302i | \(0.481446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.31420 | 0.270836 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −15.5240 | −0.789128 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.16537 | 0.160491 | 0.0802453 | − | 0.996775i | \(-0.474430\pi\) | ||||
0.0802453 | + | 0.996775i | \(0.474430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.5095 | 1.18590 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.6671 | −1.54303 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.47062 | 0.0738084 | 0.0369042 | − | 0.999319i | \(-0.488250\pi\) | ||||
0.0369042 | + | 0.999319i | \(0.488250\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.6225 | −0.681976 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.9273 | 1.64431 | 0.822155 | − | 0.569264i | \(-0.192772\pi\) | ||||
0.822155 | + | 0.569264i | \(0.192772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.87290 | −0.342364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.1310 | 0.702177 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.58069 | −0.0783517 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6136 | 0.574255 | 0.287128 | − | 0.957892i | \(-0.407300\pi\) | ||||
0.287128 | + | 0.957892i | \(0.407300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −28.7387 | −1.41757 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.63190 | −0.129508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.4538 | 1.10221 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.4772 | −1.88424 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.0454 | 1.66322 | 0.831612 | − | 0.555357i | \(-0.187418\pi\) | ||||
0.831612 | + | 0.555357i | \(0.187418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.4720 | −0.802797 | −0.401399 | − | 0.915903i | \(-0.631476\pi\) | ||||
−0.401399 | + | 0.915903i | \(0.631476\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −56.9336 | −2.76821 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.36096 | −0.453009 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.2408 | −1.12207 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.56754 | 0.171843 | 0.0859213 | − | 0.996302i | \(-0.472617\pi\) | ||||
0.0859213 | + | 0.996302i | \(0.472617\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.7012 | −0.658436 | −0.329218 | − | 0.944254i | \(-0.606785\pi\) | ||||
−0.329218 | + | 0.944254i | \(0.606785\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.7185 | −0.609804 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −19.9881 | −0.956162 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.1111 | −1.72349 | −0.861745 | − | 0.507341i | \(-0.830628\pi\) | ||||
−0.861745 | + | 0.507341i | \(0.830628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.88484 | 0.280230 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.17342 | 0.293308 | 0.146654 | − | 0.989188i | \(-0.453150\pi\) | ||||
0.146654 | + | 0.989188i | \(0.453150\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.64131 | −0.172615 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.7569 | −0.556084 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.1363 | −0.950290 | −0.475145 | − | 0.879907i | \(-0.657604\pi\) | ||||
−0.475145 | + | 0.879907i | \(0.657604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.1738 | −1.70336 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −71.1995 | −3.34524 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.60448 | 0.215861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.0583 | −0.610842 | −0.305421 | − | 0.952217i | \(-0.598797\pi\) | ||||
−0.305421 | + | 0.952217i | \(0.598797\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.0878 | −0.702710 | −0.351355 | − | 0.936242i | \(-0.614279\pi\) | ||||
−0.351355 | + | 0.936242i | \(0.614279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −30.0923 | −1.39851 | −0.699255 | − | 0.714873i | \(-0.746485\pi\) | ||||
−0.699255 | + | 0.714873i | \(0.746485\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.9629 | 0.647516 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.0220 | 0.602587 | 0.301294 | − | 0.953531i | \(-0.402582\pi\) | ||||
0.301294 | + | 0.953531i | \(0.402582\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.9050 | −0.688249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −55.0533 | −2.53672 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.91334 | −0.363856 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.50833 | −0.390389 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.8655 | 1.04694 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.5456 | 1.71550 | 0.857752 | − | 0.514064i | \(-0.171861\pi\) | ||||
0.857752 | + | 0.514064i | \(0.171861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.36958 | −0.0624476 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.0367 | 0.593189 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.7508 | 0.578983 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.4782 | −1.65298 | −0.826492 | − | 0.562948i | \(-0.809667\pi\) | ||||
−0.826492 | + | 0.562948i | \(0.809667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 54.8446 | 2.48016 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.2512 | −0.959053 | −0.479526 | − | 0.877527i | \(-0.659192\pi\) | ||||
−0.479526 | + | 0.877527i | \(0.659192\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.2732 | 1.40562 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.2979 | −0.641347 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0774 | 1.03309 | 0.516544 | − | 0.856261i | \(-0.327218\pi\) | ||||
0.516544 | + | 0.856261i | \(0.327218\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 71.0245 | 3.17314 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.650809 | −0.0290181 | −0.0145091 | − | 0.999895i | \(-0.504619\pi\) | ||||
−0.0145091 | + | 0.999895i | \(0.504619\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.05460 | −0.0914287 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.6128 | 0.826622 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.6793 | 1.13822 | 0.569108 | − | 0.822263i | \(-0.307289\pi\) | ||||
0.569108 | + | 0.822263i | \(0.307289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.15166 | 0.139421 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −39.2986 | −1.73507 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.4717 | −0.681765 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29.0219 | −1.27638 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.6849 | 0.820177 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.53401 | 0.373882 | 0.186941 | − | 0.982371i | \(-0.440143\pi\) | ||||
0.186941 | + | 0.982371i | \(0.440143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7723 | −0.820856 | −0.410428 | − | 0.911893i | \(-0.634621\pi\) | ||||
−0.410428 | + | 0.911893i | \(0.634621\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.54930 | 0.242191 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.87138 | −0.168321 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.4883 | −0.672136 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.3427 | −1.35760 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.4198 | −1.01253 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 38.3718 | 1.65587 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.99979 | 0.129210 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8125 | −0.593845 | −0.296923 | − | 0.954902i | \(-0.595960\pi\) | ||||
−0.296923 | + | 0.954902i | \(0.595960\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −63.7489 | −2.73573 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.22213 | −0.352197 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0774 | 0.430877 | 0.215438 | − | 0.976517i | \(-0.430882\pi\) | ||||
0.215438 | + | 0.976517i | \(0.430882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −55.0877 | −2.35109 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.0076 | 0.468942 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.3112 | −0.736147 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.78244 | 0.118108 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.0805 | −1.52878 | −0.764389 | − | 0.644756i | \(-0.776959\pi\) | ||||
−0.764389 | + | 0.644756i | \(0.776959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.85650 | −0.289999 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.6232 | −0.911309 | −0.455655 | − | 0.890157i | \(-0.650595\pi\) | ||||
−0.455655 | + | 0.890157i | \(0.650595\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.710878 | −0.0299069 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.97679 | 0.334994 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.92834 | 0.374296 | 0.187148 | − | 0.982332i | \(-0.440076\pi\) | ||||
0.187148 | + | 0.982332i | \(0.440076\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.8466 | 1.58383 | 0.791916 | − | 0.610631i | \(-0.209084\pi\) | ||||
0.791916 | + | 0.610631i | \(0.209084\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −52.2222 | −2.18161 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.14245 | 0.339564 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.3336 | 1.34607 | 0.673033 | − | 0.739612i | \(-0.264991\pi\) | ||||
0.673033 | + | 0.739612i | \(0.264991\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.3694 | 0.638729 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6749 | 0.525842 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6557 | 0.482729 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.0966 | 1.12031 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0489 | 0.744957 | 0.372478 | − | 0.928041i | \(-0.378508\pi\) | ||||
0.372478 | + | 0.928041i | \(0.378508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0847 | −0.497942 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.3225 | 1.12390 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.95732 | −0.367833 | −0.183917 | − | 0.982942i | \(-0.558878\pi\) | ||||
−0.183917 | + | 0.982942i | \(0.558878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −34.6991 | −1.42014 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.29732 | 0.0530070 | 0.0265035 | − | 0.999649i | \(-0.491563\pi\) | ||||
0.0265035 | + | 0.999649i | \(0.491563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.4326 | 1.28216 | 0.641082 | − | 0.767473i | \(-0.278486\pi\) | ||||
0.641082 | + | 0.767473i | \(0.278486\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −87.7134 | −3.57197 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.54523 | −0.144134 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.05652 | 0.0428830 | 0.0214415 | − | 0.999770i | \(-0.493174\pi\) | ||||
0.0214415 | + | 0.999770i | \(0.493174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.17941 | −0.290924 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.1460 | −1.01730 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.7088 | −1.03837 | −0.519183 | − | 0.854663i | \(-0.673764\pi\) | ||||
−0.519183 | + | 0.854663i | \(0.673764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 63.6757 | 2.56765 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.59660 | −0.305828 | −0.152914 | − | 0.988240i | \(-0.548866\pi\) | ||||
−0.152914 | + | 0.988240i | \(0.548866\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6467 | −0.709282 | −0.354641 | − | 0.935002i | \(-0.615397\pi\) | ||||
−0.354641 | + | 0.935002i | \(0.615397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.6087 | 1.50918 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.05547 | −0.0823507 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.2254 | −0.489017 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −40.8646 | −1.63197 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.2378 | −0.805653 | −0.402827 | − | 0.915276i | \(-0.631972\pi\) | ||||
−0.402827 | + | 0.915276i | \(0.631972\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.6308 | −0.422535 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.620215 | 0.0246125 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.59917 | 0.102983 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −84.1406 | −3.32855 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.2967 | −1.47313 | −0.736565 | − | 0.676367i | \(-0.763553\pi\) | ||||
−0.736565 | + | 0.676367i | \(0.763553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.6793 | 0.933820 | 0.466910 | − | 0.884305i | \(-0.345367\pi\) | ||||
0.466910 | + | 0.884305i | \(0.345367\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.9296 | 0.548478 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.2713 | −1.11146 | −0.555730 | − | 0.831363i | \(-0.687561\pi\) | ||||
−0.555730 | + | 0.831363i | \(0.687561\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.89517 | −0.309912 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.88190 | 0.308916 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.6863 | 0.535586 | 0.267793 | − | 0.963476i | \(-0.413706\pi\) | ||||
0.267793 | + | 0.963476i | \(0.413706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.9722 | −0.545938 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 18.5470 | 0.723588 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.7157 | 0.884878 | 0.442439 | − | 0.896799i | \(-0.354113\pi\) | ||||
0.442439 | + | 0.896799i | \(0.354113\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.6821 | 1.85462 | 0.927310 | − | 0.374294i | \(-0.122115\pi\) | ||||
0.927310 | + | 0.374294i | \(0.122115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8.09612 | 0.313954 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.5343 | −0.407890 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 63.8159 | 2.46727 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.0809 | −1.08405 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.7677 | 1.84131 | 0.920654 | − | 0.390380i | \(-0.127656\pi\) | ||||
0.920654 | + | 0.390380i | \(0.127656\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.0088 | 0.616180 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.8735 | −0.917532 | −0.458766 | − | 0.888557i | \(-0.651708\pi\) | ||||
−0.458766 | + | 0.888557i | \(0.651708\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.19765 | 0.276220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 62.8730 | 2.40930 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.8404 | −0.797434 | −0.398717 | − | 0.917074i | \(-0.630544\pi\) | ||||
−0.398717 | + | 0.917074i | \(0.630544\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.0800 | 0.652593 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.6666 | −1.17001 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0990 | 0.384743 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1028 | −0.422370 | −0.211185 | − | 0.977446i | \(-0.567732\pi\) | ||||
−0.211185 | + | 0.977446i | \(0.567732\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.6533 | 0.670593 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.8678 | 0.867427 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.0282 | −1.28707 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.3141 | −0.729482 | −0.364741 | − | 0.931109i | \(-0.618842\pi\) | ||||
−0.364741 | + | 0.931109i | \(0.618842\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.40816 | −0.0908254 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 51.0864 | 1.92402 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.15980 | −0.0436187 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.85560 | 0.257468 | 0.128734 | − | 0.991679i | \(-0.458909\pi\) | ||||
0.128734 | + | 0.991679i | \(0.458909\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −101.874 | −3.82056 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.5651 | 0.433115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.8125 | 0.516557 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.0170536 | 0.000636878 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.1354 | 0.601747 | 0.300874 | − | 0.953664i | \(-0.402722\pi\) | ||||
0.300874 | + | 0.953664i | \(0.402722\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.73357 | −0.325255 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −76.5863 | −2.84827 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.48412 | −0.166536 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.8301 | 0.401665 | 0.200832 | − | 0.979626i | \(-0.435635\pi\) | ||||
0.200832 | + | 0.979626i | \(0.435635\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9518 | −1.10933 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.4997 | −1.01573 | −0.507863 | − | 0.861438i | \(-0.669564\pi\) | ||||
−0.507863 | + | 0.861438i | \(0.669564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.28045 | −0.194772 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −44.7119 | −1.64698 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.42719 | −0.236428 | −0.118214 | − | 0.992988i | \(-0.537717\pi\) | ||||
−0.118214 | + | 0.992988i | \(0.537717\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.4070 | −1.30071 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.8081 | 1.02018 | 0.510090 | − | 0.860121i | \(-0.329612\pi\) | ||||
0.510090 | + | 0.860121i | \(0.329612\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.98740 | 0.255999 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 74.5895 | 2.72909 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.2202 | −0.483055 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.9244 | 0.654071 | 0.327035 | − | 0.945012i | \(-0.393950\pi\) | ||||
0.327035 | + | 0.945012i | \(0.393950\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.5190 | 0.929963 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.3154 | 1.54001 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.96117 | −0.362045 | −0.181023 | − | 0.983479i | \(-0.557941\pi\) | ||||
−0.181023 | + | 0.983479i | \(0.557941\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 39.1073 | 1.41951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.279750 | 0.0101409 | 0.00507046 | − | 0.999987i | \(-0.498386\pi\) | ||||
0.00507046 | + | 0.999987i | \(0.498386\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.64129 | −0.168026 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.84076 | −0.247005 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8011 | −0.677986 | −0.338993 | − | 0.940789i | \(-0.610086\pi\) | ||||
−0.338993 | + | 0.940789i | \(0.610086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.8397 | 1.65088 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.9445 | −0.537518 | −0.268759 | − | 0.963207i | \(-0.586613\pi\) | ||||
−0.268759 | + | 0.963207i | \(0.586613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.92288 | 0.176835 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.57065 | 0.0563467 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.1104 | −1.97453 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.8906 | −1.53475 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.7114 | −0.740166 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.7194 | 1.16780 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.8472 | 1.88380 | 0.941900 | − | 0.335894i | \(-0.109038\pi\) | ||||
0.941900 | + | 0.335894i | \(0.109038\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.54073 | −0.126053 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.401281 | −0.0142679 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.3307 | −0.864008 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −20.5171 | −0.727668 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.3791 | −0.757286 | −0.378643 | − | 0.925543i | \(-0.623609\pi\) | ||||
−0.378643 | + | 0.925543i | \(0.623609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.0961 | −0.427395 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.45434 | 0.333636 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.74797 | −0.273080 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.3567 | −0.470180 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.86433 | 0.241337 | 0.120668 | − | 0.992693i | \(-0.461496\pi\) | ||||
0.120668 | + | 0.992693i | \(0.461496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.3596 | 1.10118 | 0.550592 | − | 0.834775i | \(-0.314402\pi\) | ||||
0.550592 | + | 0.834775i | \(0.314402\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 46.4289 | 1.62833 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.5953 | −1.14176 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.0559 | −0.421782 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2957 | 0.534474 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.9312 | −0.905007 | −0.452503 | − | 0.891763i | \(-0.649469\pi\) | ||||
−0.452503 | + | 0.891763i | \(0.649469\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.0689 | 1.32700 | 0.663499 | − | 0.748177i | \(-0.269071\pi\) | ||||
0.663499 | + | 0.748177i | \(0.269071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.6468 | 0.579566 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.3710 | 0.917011 | 0.458505 | − | 0.888692i | \(-0.348385\pi\) | ||||
0.458505 | + | 0.888692i | \(0.348385\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7846 | 0.409298 | 0.204649 | − | 0.978835i | \(-0.434395\pi\) | ||||
0.204649 | + | 0.978835i | \(0.434395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 54.0979 | 1.87663 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.2114 | −1.46079 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.7380 | 0.785940 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.6807 | −1.47350 | −0.736750 | − | 0.676165i | \(-0.763641\pi\) | ||||
−0.736750 | + | 0.676165i | \(0.763641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.1987 | −0.799954 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −80.5141 | −2.77305 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0620 | −0.380543 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00124 | −0.0687633 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.1409 | −0.656915 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.30460 | 0.0790008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.93285 | 0.340094 | 0.170047 | − | 0.985436i | \(-0.445608\pi\) | ||||
0.170047 | + | 0.985436i | \(0.445608\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 47.6443 | 1.62940 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.1572 | 0.995990 | 0.497995 | − | 0.867180i | \(-0.334070\pi\) | ||||
0.497995 | + | 0.867180i | \(0.334070\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5644 | 0.872246 | 0.436123 | − | 0.899887i | \(-0.356351\pi\) | ||||
0.436123 | + | 0.899887i | \(0.356351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.9441 | 1.22497 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.40501 | 0.149948 | 0.0749741 | − | 0.997185i | \(-0.476113\pi\) | ||||
0.0749741 | + | 0.997185i | \(0.476113\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.1048 | −0.377576 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −51.9300 | −1.76161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.7406 | −1.31267 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 42.3570 | 1.43357 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.1557 | −0.410937 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.5494 | 0.862744 | 0.431372 | − | 0.902174i | \(-0.358030\pi\) | ||||
0.431372 | + | 0.902174i | \(0.358030\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.2020 | 1.25479 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.2495 | 1.32235 | 0.661174 | − | 0.750233i | \(-0.270059\pi\) | ||||
0.661174 | + | 0.750233i | \(0.270059\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.1225 | 1.11466 | 0.557330 | − | 0.830291i | \(-0.311826\pi\) | ||||
0.557330 | + | 0.830291i | \(0.311826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.8976 | 0.467164 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.1328 | 0.911030 | 0.455515 | − | 0.890228i | \(-0.349455\pi\) | ||||
0.455515 | + | 0.890228i | \(0.349455\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.350103 | 0.0117421 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23.9287 | 0.801643 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −44.2145 | −1.47958 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.8052 | −0.762293 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.8845 | 1.13137 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.36898 | −0.212417 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.86309 | 0.261667 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 37.8873 | 1.25942 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −56.2710 | −1.86845 | −0.934224 | − | 0.356687i | \(-0.883906\pi\) | ||||
−0.934224 | + | 0.356687i | \(0.883906\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.82522 | −0.226378 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.3479 | 1.50244 | 0.751221 | − | 0.660051i | \(-0.229465\pi\) | ||||
0.751221 | + | 0.660051i | \(0.229465\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.0220 | 1.25834 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 49.4301 | 1.63411 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.88711 | −0.260455 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.5827 | −1.00883 | −0.504415 | − | 0.863461i | \(-0.668292\pi\) | ||||
−0.504415 | + | 0.863461i | \(0.668292\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −87.6238 | −2.88730 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −37.1625 | −1.22322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.980997 | 0.0322550 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.3957 | −1.68805 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.4531 | −0.900707 | −0.450354 | − | 0.892850i | \(-0.648702\pi\) | ||||
−0.450354 | + | 0.892850i | \(0.648702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.57015 | 0.149781 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −47.3012 | −1.54857 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.3154 | 0.598337 | 0.299169 | − | 0.954200i | \(-0.403291\pi\) | ||||
0.299169 | + | 0.954200i | \(0.403291\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 97.9602 | 3.19681 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8433 | 1.00546 | 0.502731 | − | 0.864443i | \(-0.332329\pi\) | ||||
0.502731 | + | 0.864443i | \(0.332329\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.7405 | 1.71747 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.2332 | −0.495537 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7368 | −0.511379 | −0.255689 | − | 0.966759i | \(-0.582302\pi\) | ||||
−0.255689 | + | 0.966759i | \(0.582302\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.19170 | 0.265914 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 79.1768 | 2.56748 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.5074 | −1.66849 | −0.834244 | − | 0.551395i | \(-0.814096\pi\) | ||||
−0.834244 | + | 0.551395i | \(0.814096\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.0367 | 1.00433 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.5367 | −0.696184 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.64144 | 0.311338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.0078 | −0.774446 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −77.7987 | −2.50703 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.13434 | −0.294045 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.6915 | 0.697552 | 0.348776 | − | 0.937206i | \(-0.386597\pi\) | ||||
0.348776 | + | 0.937206i | \(0.386597\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.7980 | 0.474889 | 0.237444 | − | 0.971401i | \(-0.423690\pi\) | ||||
0.237444 | + | 0.971401i | \(0.423690\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.9086 | 0.413831 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4236 | 0.461924 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.5724 | 0.754147 | 0.377074 | − | 0.926183i | \(-0.376930\pi\) | ||||
0.377074 | + | 0.926183i | \(0.376930\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.16599 | −0.197066 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.3132 | −0.872044 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.0283 | −0.638803 | −0.319401 | − | 0.947620i | \(-0.603482\pi\) | ||||
−0.319401 | + | 0.947620i | \(0.603482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.2384 | −0.517397 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 28.8376 | 0.917910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.5375 | 0.366870 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.5094 | 0.492672 | 0.246336 | − | 0.969184i | \(-0.420773\pi\) | ||||
0.246336 | + | 0.969184i | \(0.420773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 53.6152 | 1.70143 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.6224 | 0.653774 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.4828 | −0.870388 | −0.435194 | − | 0.900337i | \(-0.643320\pi\) | ||||
−0.435194 | + | 0.900337i | \(0.643320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.53107 | 0.143357 |
(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 | 8092.2.a.s.1.1 | 8 | ||
17.8 | even | 8 | 476.2.l.a.421.8 | yes | 16 | ||
17.15 | even | 8 | 476.2.l.a.225.8 | ✓ | 16 | ||
17.16 | even | 2 | 8092.2.a.t.1.8 | 8 | |||
51.8 | odd | 8 | 4284.2.z.b.3277.4 | 16 | |||
51.32 | odd | 8 | 4284.2.z.b.4033.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.l.a.225.8 | ✓ | 16 | 17.15 | even | 8 | ||
476.2.l.a.421.8 | yes | 16 | 17.8 | even | 8 | ||
4284.2.z.b.3277.4 | 16 | 51.8 | odd | 8 | |||
4284.2.z.b.4033.4 | 16 | 51.32 | odd | 8 | |||
8092.2.a.s.1.1 | 8 | 1.1 | even | 1 | trivial | ||
8092.2.a.t.1.8 | 8 | 17.16 | even | 2 |