Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 251) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-2.65791\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 2.62368 | 1.51478 | 0.757392 | − | 0.652960i | \(-0.226473\pi\) | ||||
0.757392 | + | 0.652960i | \(0.226473\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.15029 | 0.514426 | 0.257213 | − | 0.966355i | \(-0.417196\pi\) | ||||
0.257213 | + | 0.966355i | \(0.417196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.51426 | 0.950299 | 0.475150 | − | 0.879905i | \(-0.342394\pi\) | ||||
0.475150 | + | 0.879905i | \(0.342394\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.88372 | 1.29457 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.29973 | 1.89944 | 0.949720 | − | 0.313102i | \(-0.101368\pi\) | ||||
0.949720 | + | 0.313102i | \(0.101368\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.699407 | 0.193981 | 0.0969903 | − | 0.995285i | \(-0.469078\pi\) | ||||
0.0969903 | + | 0.995285i | \(0.469078\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.01800 | 0.779244 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.58455 | 1.11192 | 0.555958 | − | 0.831210i | \(-0.312352\pi\) | ||||
0.555958 | + | 0.831210i | \(0.312352\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.23032 | −1.65875 | −0.829375 | − | 0.558693i | \(-0.811303\pi\) | ||||
−0.829375 | + | 0.558693i | \(0.811303\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.59661 | 1.43950 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.43841 | 0.925472 | 0.462736 | − | 0.886496i | \(-0.346868\pi\) | ||||
0.462736 | + | 0.886496i | \(0.346868\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.67683 | −0.735366 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.31859 | 0.446213 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.16969 | 0.588597 | 0.294298 | − | 0.955714i | \(-0.404914\pi\) | ||||
0.294298 | + | 0.955714i | \(0.404914\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.86491 | −1.23297 | −0.616487 | − | 0.787365i | \(-0.711445\pi\) | ||||
−0.616487 | + | 0.787365i | \(0.711445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.5285 | 2.87724 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.89213 | 0.488858 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.34453 | 0.549838 | 0.274919 | − | 0.961467i | \(-0.411349\pi\) | ||||
0.274919 | + | 0.961467i | \(0.411349\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.83502 | 0.293839 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.17827 | 0.184016 | 0.0920078 | − | 0.995758i | \(-0.470672\pi\) | ||||
0.0920078 | + | 0.995758i | \(0.470672\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.14366 | −1.24190 | −0.620948 | − | 0.783851i | \(-0.713252\pi\) | ||||
−0.620948 | + | 0.783851i | \(0.713252\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.46740 | 0.665961 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.94801 | −1.15934 | −0.579668 | − | 0.814853i | \(-0.696818\pi\) | ||||
−0.579668 | + | 0.814853i | \(0.696818\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.678520 | −0.0969314 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0284 | 1.68431 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.14772 | 0.844455 | 0.422227 | − | 0.906490i | \(-0.361248\pi\) | ||||
0.422227 | + | 0.906490i | \(0.361248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.24652 | 0.977120 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.9701 | −2.51265 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.29675 | −0.429201 | −0.214600 | − | 0.976702i | \(-0.568845\pi\) | ||||
−0.214600 | + | 0.976702i | \(0.568845\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.51045 | 0.193394 | 0.0966968 | − | 0.995314i | \(-0.469172\pi\) | ||||
0.0966968 | + | 0.995314i | \(0.469172\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.76465 | 1.23023 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.804522 | 0.0997887 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.60689 | −0.562821 | −0.281411 | − | 0.959587i | \(-0.590802\pi\) | ||||
−0.281411 | + | 0.959587i | \(0.590802\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.6450 | 1.40189 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.22808 | 0.976494 | 0.488247 | − | 0.872706i | \(-0.337637\pi\) | ||||
0.488247 | + | 0.872706i | \(0.337637\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.16971 | −0.605069 | −0.302535 | − | 0.953138i | \(-0.597833\pi\) | ||||
−0.302535 | + | 0.953138i | \(0.597833\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.64684 | −1.11392 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.8391 | 1.80504 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.65353 | −0.973598 | −0.486799 | − | 0.873514i | \(-0.661836\pi\) | ||||
−0.486799 | + | 0.873514i | \(0.661836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.56790 | −0.618656 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.65024 | −0.510430 | −0.255215 | − | 0.966884i | \(-0.582146\pi\) | ||||
−0.255215 | + | 0.966884i | \(0.582146\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.27356 | 0.571998 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.31626 | 0.891597 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.59697 | 0.381279 | 0.190639 | − | 0.981660i | \(-0.438944\pi\) | ||||
0.190639 | + | 0.981660i | \(0.438944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.75849 | 0.184340 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.0113 | −1.86769 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.31697 | −0.853304 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.0684 | −1.83456 | −0.917282 | − | 0.398238i | \(-0.869622\pi\) | ||||
−0.917282 | + | 0.398238i | \(0.869622\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.4663 | 2.45896 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.97694 | −0.694231 | −0.347116 | − | 0.937822i | \(-0.612839\pi\) | ||||
−0.347116 | + | 0.937822i | \(0.612839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.85305 | −0.182587 | −0.0912933 | − | 0.995824i | \(-0.529100\pi\) | ||||
−0.0912933 | + | 0.995824i | \(0.529100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.58802 | 0.740515 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.70888 | −0.648572 | −0.324286 | − | 0.945959i | \(-0.605124\pi\) | ||||
−0.324286 | + | 0.945959i | \(0.605124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.8205 | −1.51533 | −0.757664 | − | 0.652645i | \(-0.773660\pi\) | ||||
−0.757664 | + | 0.652645i | \(0.773660\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.77500 | 0.832886 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.4826 | 1.55055 | 0.775275 | − | 0.631624i | \(-0.217612\pi\) | ||||
0.775275 | + | 0.631624i | \(0.217612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.10546 | 0.476087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.71630 | 0.251122 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.5267 | 1.05665 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.6866 | 2.60787 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.09142 | 0.278744 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.98088 | −0.892717 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.39892 | −0.479077 | −0.239538 | − | 0.970887i | \(-0.576996\pi\) | ||||
−0.239538 | + | 0.970887i | \(0.576996\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.3664 | −1.88121 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.4211 | −1.43472 | −0.717360 | − | 0.696703i | \(-0.754650\pi\) | ||||
−0.717360 | + | 0.696703i | \(0.754650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.1789 | −1.57631 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.66705 | 0.229543 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4638 | −0.979416 | −0.489708 | − | 0.871887i | \(-0.662897\pi\) | ||||
−0.489708 | + | 0.871887i | \(0.662897\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.63997 | 0.563195 | 0.281597 | − | 0.959533i | \(-0.409136\pi\) | ||||
0.281597 | + | 0.959533i | \(0.409136\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −20.8531 | −1.75614 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.40608 | 0.368455 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.64607 | 0.302789 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.78022 | −0.146830 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.1685 | 1.81611 | 0.908057 | − | 0.418846i | \(-0.137565\pi\) | ||||
0.908057 | + | 0.418846i | \(0.137565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.81459 | −0.391806 | −0.195903 | − | 0.980623i | \(-0.562764\pi\) | ||||
−0.195903 | + | 0.980623i | \(0.562764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.8051 | 1.43946 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.89664 | −0.634273 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.72414 | 0.776071 | 0.388035 | − | 0.921644i | \(-0.373154\pi\) | ||||
0.388035 | + | 0.921644i | \(0.373154\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.1297 | 1.27917 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.1593 | 0.879475 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2697 | 1.27434 | 0.637172 | − | 0.770721i | \(-0.280104\pi\) | ||||
0.637172 | + | 0.770721i | \(0.280104\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.0126 | 1.48013 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.4518 | 1.27308 | 0.636541 | − | 0.771243i | \(-0.280365\pi\) | ||||
0.636541 | + | 0.771243i | \(0.280365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5108 | −0.962371 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −28.0805 | −2.14737 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.0702 | 1.60194 | 0.800968 | − | 0.598708i | \(-0.204319\pi\) | ||||
0.800968 | + | 0.598708i | \(0.204319\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.24449 | −0.698818 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.64964 | −0.650147 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.45297 | −0.631804 | −0.315902 | − | 0.948792i | \(-0.602307\pi\) | ||||
−0.315902 | + | 0.948792i | \(0.602307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.28715 | 0.318662 | 0.159331 | − | 0.987225i | \(-0.449066\pi\) | ||||
0.159331 | + | 0.987225i | \(0.449066\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.96295 | 0.292950 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.84719 | 0.282851 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 28.8814 | 2.11202 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.82953 | 0.424036 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.3921 | 0.751947 | 0.375974 | − | 0.926630i | \(-0.377308\pi\) | ||||
0.375974 | + | 0.926630i | \(0.377308\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7332 | 0.916557 | 0.458278 | − | 0.888809i | \(-0.348466\pi\) | ||||
0.458278 | + | 0.888809i | \(0.348466\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.11081 | 0.151158 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.12368 | −0.293800 | −0.146900 | − | 0.989151i | \(-0.546930\pi\) | ||||
−0.146900 | + | 0.989151i | \(0.546930\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7296 | 0.973264 | 0.486632 | − | 0.873607i | \(-0.338225\pi\) | ||||
0.486632 | + | 0.873607i | \(0.338225\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0870 | −0.852553 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.96941 | 0.559343 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.35536 | 0.0946624 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.2375 | 1.19809 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −45.5491 | −3.15069 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.58825 | −0.315868 | −0.157934 | − | 0.987450i | \(-0.550483\pi\) | ||||
−0.157934 | + | 0.987450i | \(0.550483\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.5879 | 1.47918 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.36758 | −0.638864 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.2601 | −1.17169 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.5637 | −0.916549 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.20647 | 0.215690 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.0912325 | 0.00610938 | 0.00305469 | − | 0.999995i | \(-0.499028\pi\) | ||||
0.00305469 | + | 0.999995i | \(0.499028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.2798 | −0.951984 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.8140 | −0.850497 | −0.425249 | − | 0.905077i | \(-0.639813\pi\) | ||||
−0.425249 | + | 0.905077i | \(0.639813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.5635 | −1.09455 | −0.547275 | − | 0.836953i | \(-0.684335\pi\) | ||||
−0.547275 | + | 0.836953i | \(0.684335\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 41.5568 | 2.73424 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8233 | 1.16764 | 0.583820 | − | 0.811883i | \(-0.301557\pi\) | ||||
0.583820 | + | 0.811883i | \(0.301557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.14252 | −0.596392 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −22.7041 | −1.47479 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.8815 | 0.833234 | 0.416617 | − | 0.909082i | \(-0.363216\pi\) | ||||
0.416617 | + | 0.909082i | \(0.363216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.761335 | 0.0490419 | 0.0245210 | − | 0.999699i | \(-0.492194\pi\) | ||||
0.0245210 | + | 0.999699i | \(0.492194\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.5642 | −1.38334 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.780495 | −0.0498640 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.05694 | −0.321765 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.2007 | −0.773191 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.9608 | 1.75788 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.8362 | 0.866454 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.12039 | 0.381779 | 0.190890 | − | 0.981611i | \(-0.438863\pi\) | ||||
0.190890 | + | 0.981611i | \(0.438863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.40901 | 0.522511 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.3102 | 0.761981 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.47378 | −0.214202 | −0.107101 | − | 0.994248i | \(-0.534157\pi\) | ||||
−0.107101 | + | 0.994248i | \(0.534157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.07167 | 0.434409 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.43732 | 0.577555 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7931 | 0.658066 | 0.329033 | − | 0.944318i | \(-0.393277\pi\) | ||||
0.329033 | + | 0.944318i | \(0.393277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8686 | −0.842455 | −0.421227 | − | 0.906955i | \(-0.638401\pi\) | ||||
−0.421227 | + | 0.906955i | \(0.638401\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.61372 | 0.279235 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.1630 | −1.39678 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0135 | 1.20250 | 0.601248 | − | 0.799062i | \(-0.294670\pi\) | ||||
0.601248 | + | 0.799062i | \(0.294670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.6613 | −1.59617 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.4897 | 0.804726 | 0.402363 | − | 0.915480i | \(-0.368189\pi\) | ||||
0.402363 | + | 0.915480i | \(0.368189\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.9359 | 1.30396 | 0.651978 | − | 0.758238i | \(-0.273939\pi\) | ||||
0.651978 | + | 0.758238i | \(0.273939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −21.8211 | −1.29257 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.96248 | 0.174870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.01807 | 0.236357 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −47.4057 | −2.77897 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.14505 | 0.125315 | 0.0626576 | − | 0.998035i | \(-0.480042\pi\) | ||||
0.0626576 | + | 0.998035i | \(0.480042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.79223 | −0.220792 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 14.6065 | 0.847554 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.10425 | 0.179524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.4752 | −1.18017 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.3053 | −1.05161 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.73746 | 0.0994867 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.49142 | 0.0851200 | 0.0425600 | − | 0.999094i | \(-0.486449\pi\) | ||||
0.0425600 | + | 0.999094i | \(0.486449\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.86182 | −0.276579 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.70155 | −0.380010 | −0.190005 | − | 0.981783i | \(-0.560850\pi\) | ||||
−0.190005 | + | 0.981783i | \(0.560850\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.9053 | 1.18164 | 0.590818 | − | 0.806805i | \(-0.298805\pi\) | ||||
0.590818 | + | 0.806805i | \(0.298805\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.2322 | 0.632862 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.8281 | −0.720499 | −0.360249 | − | 0.932856i | \(-0.617308\pi\) | ||||
−0.360249 | + | 0.932856i | \(0.617308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.9682 | 1.11800 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.6020 | −0.982446 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.1478 | −1.84439 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.57160 | −0.142647 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −41.5080 | −2.29540 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.9833 | −1.10172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.3489 | −0.733723 | −0.366862 | − | 0.930275i | \(-0.619568\pi\) | ||||
−0.366862 | + | 0.930275i | \(0.619568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.9892 | 0.711805 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.29927 | −0.289530 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8628 | 0.700681 | 0.350340 | − | 0.936622i | \(-0.386066\pi\) | ||||
0.350340 | + | 0.936622i | \(0.386066\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.2450 | 2.34875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −43.2470 | −2.34196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.3058 | −1.04241 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.3951 | 0.721168 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.39781 | 0.128721 | 0.0643607 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643607 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.2451 | 1.88663 | 0.943313 | − | 0.331903i | \(-0.107691\pi\) | ||||
0.943313 | + | 0.331903i | \(0.107691\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.62164 | 0.0865566 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.5147 | −0.612868 | −0.306434 | − | 0.951892i | \(-0.599136\pi\) | ||||
−0.306434 | + | 0.951892i | \(0.599136\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.46469 | 0.502333 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.2425 | 1.60060 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.1553 | 0.852642 | 0.426321 | − | 0.904572i | \(-0.359809\pi\) | ||||
0.426321 | + | 0.904572i | \(0.359809\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.2776 | 1.75145 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 75.2645 | 3.95036 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.94668 | −0.311263 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.07079 | 0.0558946 | 0.0279473 | − | 0.999609i | \(-0.491103\pi\) | ||||
0.0279473 | + | 0.999609i | \(0.491103\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.57608 | 0.238221 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4569 | 0.802485 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7804 | −0.661742 | −0.330871 | − | 0.943676i | \(-0.607343\pi\) | ||||
−0.330871 | + | 0.943676i | \(0.607343\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −26.1867 | −1.35227 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.21690 | 0.114176 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.5543 | −0.901703 | −0.450851 | − | 0.892599i | \(-0.648880\pi\) | ||||
−0.450851 | + | 0.892599i | \(0.648880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1651 | −0.725698 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.9209 | 0.558030 | 0.279015 | − | 0.960287i | \(-0.409992\pi\) | ||||
0.279015 | + | 0.960287i | \(0.409992\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.2196 | 0.928557 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.6277 | −1.60772 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.85338 | −0.144672 | −0.0723361 | − | 0.997380i | \(-0.523045\pi\) | ||||
−0.0723361 | + | 0.997380i | \(0.523045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.3481 | 1.02905 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −43.0838 | −2.17329 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.95407 | −0.500844 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3951 | −0.923225 | −0.461613 | − | 0.887082i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887082i | \(0.652729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −47.6956 | −2.38777 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.0050 | −0.549564 | −0.274782 | − | 0.961506i | \(-0.588606\pi\) | ||||
−0.274782 | + | 0.961506i | \(0.588606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.80137 | −0.239173 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.40471 | −0.318252 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.0697 | 1.04438 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.5283 | −0.668930 | −0.334465 | − | 0.942408i | \(-0.608556\pi\) | ||||
−0.334465 | + | 0.942408i | \(0.608556\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.0773 | −1.48360 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.28888 | −0.407869 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.34912 | −0.262578 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.4212 | 0.853119 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.1141 | −0.689518 | −0.344759 | − | 0.938691i | \(-0.612039\pi\) | ||||
−0.344759 | + | 0.938691i | \(0.612039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.9882 | 1.85143 | 0.925716 | − | 0.378219i | \(-0.123463\pi\) | ||||
0.925716 | + | 0.378219i | \(0.123463\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.8678 | −1.50084 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.8566 | −0.817665 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.79766 | 0.183782 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.5601 | 0.558129 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.89014 | 0.0910450 | 0.0455225 | − | 0.998963i | \(-0.485505\pi\) | ||||
0.0455225 | + | 0.998963i | \(0.485505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.69728 | 0.417965 | 0.208982 | − | 0.977919i | \(-0.432985\pi\) | ||||
0.208982 | + | 0.977919i | \(0.432985\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.56612 | 0.458661 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.0911 | −1.53513 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2331 | −0.536129 | −0.268064 | − | 0.963401i | \(-0.586384\pi\) | ||||
−0.268064 | + | 0.963401i | \(0.586384\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.63518 | −0.125485 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.8903 | 0.897505 | 0.448753 | − | 0.893656i | \(-0.351868\pi\) | ||||
0.448753 | + | 0.893656i | \(0.351868\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.13757 | 0.196140 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 58.1631 | 2.75102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.47576 | −0.164031 | −0.0820157 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820157 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.42281 | 0.349526 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.6320 | −0.593501 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.02277 | 0.0948291 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.6495 | −0.685273 | −0.342637 | − | 0.939468i | \(-0.611320\pi\) | ||||
−0.342637 | + | 0.939468i | \(0.611320\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.6297 | 0.496151 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.0557 | −1.44641 | −0.723203 | − | 0.690635i | \(-0.757331\pi\) | ||||
−0.723203 | + | 0.690635i | \(0.757331\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.3099 | −0.572089 | −0.286045 | − | 0.958216i | \(-0.592341\pi\) | ||||
−0.286045 | + | 0.958216i | \(0.592341\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.7183 | −0.960787 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.59342 | 0.443930 | 0.221965 | − | 0.975055i | \(-0.428753\pi\) | ||||
0.221965 | + | 0.975055i | \(0.428753\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5829 | −0.534849 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.5131 | 1.17558 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −51.3028 | −2.35891 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.5847 | 1.21979 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.8760 | 1.09321 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.5463 | 0.664639 | 0.332320 | − | 0.943167i | \(-0.392169\pi\) | ||||
0.332320 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.33919 | 0.106658 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.2784 | 1.33222 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −20.7839 | −0.943747 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.1844 | 0.824015 | 0.412007 | − | 0.911180i | \(-0.364828\pi\) | ||||
0.412007 | + | 0.911180i | \(0.364828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 42.6867 | 1.93036 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.1596 | −1.22570 | −0.612848 | − | 0.790201i | \(-0.709976\pi\) | ||||
−0.612848 | + | 0.790201i | \(0.709976\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.5316 | 0.654470 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.1434 | 1.26495 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.6875 | 0.927961 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.4154 | −0.824386 | −0.412193 | − | 0.911096i | \(-0.635237\pi\) | ||||
−0.412193 | + | 0.911096i | \(0.635237\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 43.1644 | 1.92844 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.1500 | −1.79020 | −0.895100 | − | 0.445865i | \(-0.852896\pi\) | ||||
−0.895100 | + | 0.445865i | \(0.852896\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.02551 | −0.357130 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.8245 | −1.45779 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0878 | 0.491456 | 0.245728 | − | 0.969339i | \(-0.420973\pi\) | ||||
0.245728 | + | 0.969339i | \(0.420973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.9980 | −0.574997 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16.7641 | −0.740155 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.13155 | −0.0939273 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −50.0703 | −2.20209 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 55.2815 | 2.42659 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.2398 | −0.492423 | −0.246212 | − | 0.969216i | \(-0.579186\pi\) | ||||
−0.246212 | + | 0.969216i | \(0.579186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8526 | −0.562004 | −0.281002 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.2546 | −1.05856 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.4725 | −1.37096 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.30055 | −0.143502 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8037 | −0.555631 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.824094 | 0.0356955 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.71716 | −0.333642 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.1779 | −0.957047 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.27449 | −0.184115 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.7501 | 1.75198 | 0.875991 | − | 0.482328i | \(-0.160209\pi\) | ||||
0.875991 | + | 0.482328i | \(0.160209\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.2481 | 0.482704 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.1982 | −0.779524 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.4796 | 1.30321 | 0.651606 | − | 0.758558i | \(-0.274096\pi\) | ||||
0.651606 | + | 0.758558i | \(0.274096\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.86617 | 0.250362 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.9179 | −0.976335 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.7572 | −0.925209 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10.0938 | 0.428458 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.2478 | 0.730812 | 0.365406 | − | 0.930848i | \(-0.380930\pi\) | ||||
0.365406 | + | 0.930848i | \(0.380930\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.69574 | −0.240904 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 75.7756 | 3.19925 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.43193 | 0.313218 | 0.156609 | − | 0.987661i | \(-0.449944\pi\) | ||||
0.156609 | + | 0.987661i | \(0.449944\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.9597 | 0.797642 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −13.9991 | −0.587908 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.6087 | 1.07357 | 0.536786 | − | 0.843719i | \(-0.319638\pi\) | ||||
0.536786 | + | 0.843719i | \(0.319638\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.04995 | −0.211334 | −0.105667 | − | 0.994402i | \(-0.533698\pi\) | ||||
−0.105667 | + | 0.994402i | \(0.533698\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.2656 | 1.13904 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.3193 | −0.680561 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.2333 | −0.842322 | −0.421161 | − | 0.906986i | \(-0.638377\pi\) | ||||
−0.421161 | + | 0.906986i | \(0.638377\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 33.4079 | 1.38839 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11.6919 | −0.485061 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.7290 | 1.60399 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.12453 | 0.129184 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.6139 | 0.768279 | 0.384140 | − | 0.923275i | \(-0.374498\pi\) | ||||
0.384140 | + | 0.923275i | \(0.374498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.6355 | 2.04519 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.8192 | −0.445043 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.15937 | 0.0886748 | 0.0443374 | − | 0.999017i | \(-0.485882\pi\) | ||||
0.0443374 | + | 0.999017i | \(0.485882\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.2591 | 0.543569 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.0221 | 1.47429 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16.3514 | 0.668101 | 0.334050 | − | 0.942555i | \(-0.391584\pi\) | ||||
0.334050 | + | 0.942555i | \(0.391584\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.7825 | −1.62276 | −0.811380 | − | 0.584519i | \(-0.801283\pi\) | ||||
−0.811380 | + | 0.584519i | \(0.801283\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.8919 | −0.728613 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 32.9979 | 1.34156 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.5774 | 1.15992 | 0.579959 | − | 0.814645i | \(-0.303068\pi\) | ||||
0.579959 | + | 0.814645i | \(0.303068\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.9092 | 0.847284 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.55890 | −0.224889 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.3087 | −0.699093 | −0.349547 | − | 0.936919i | \(-0.613664\pi\) | ||||
−0.349547 | + | 0.936919i | \(0.613664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.55603 | 0.143393 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9753 | 0.482107 | 0.241054 | − | 0.970512i | \(-0.422507\pi\) | ||||
0.241054 | + | 0.970512i | \(0.422507\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.9447 | −1.32416 | −0.662080 | − | 0.749433i | \(-0.730326\pi\) | ||||
−0.662080 | + | 0.749433i | \(0.730326\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.2908 | 0.412957 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.04371 | 0.362329 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.90324 | 0.276130 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −119.506 | −4.77262 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.3332 | 0.611374 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.95086 | −0.117472 | −0.0587360 | − | 0.998274i | \(-0.518707\pi\) | ||||
−0.0587360 | + | 0.998274i | \(0.518707\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0381 | −0.478472 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.21033 | −0.246449 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.474562 | −0.0188028 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 31.9555 | 1.26414 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.1419 | 0.716560 | 0.358280 | − | 0.933614i | \(-0.383363\pi\) | ||||
0.358280 | + | 0.933614i | \(0.383363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 40.9334 | 1.61425 | 0.807127 | − | 0.590378i | \(-0.201021\pi\) | ||||
0.807127 | + | 0.590378i | \(0.201021\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.5776 | −0.967741 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.9579 | −0.509428 | −0.254714 | − | 0.967016i | \(-0.581981\pi\) | ||||
−0.254714 | + | 0.967016i | \(0.581981\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.7686 | −0.815241 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.2851 | −1.77486 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.0158713 | −0.000621093 0 | −0.000310546 | − | 1.00000i | \(-0.500099\pi\) | ||||
−0.000310546 | 1.00000i | \(0.500099\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.8891 | −0.738057 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.0777 | −0.783306 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.2333 | 1.13877 | 0.569385 | − | 0.822071i | \(-0.307182\pi\) | ||||
0.569385 | + | 0.822071i | \(0.307182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.7524 | 1.27392 | 0.636961 | − | 0.770896i | \(-0.280191\pi\) | ||||
0.636961 | + | 0.770896i | \(0.280191\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.41275 | 0.326724 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.9110 | −0.810894 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0684 | 0.544730 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.239365 | 0.00925439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.51544 | 0.367340 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0615 | −1.08169 | −0.540846 | − | 0.841122i | \(-0.681896\pi\) | ||||
−0.540846 | + | 0.841122i | \(0.681896\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.52506 | −0.328130 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.05737 | −0.0790713 | −0.0395357 | − | 0.999218i | \(-0.512588\pi\) | ||||
−0.0395357 | + | 0.999218i | \(0.512588\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.4285 | −1.74339 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.6200 | −1.28832 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 39.9521 | 1.52873 | 0.764363 | − | 0.644786i | \(-0.223054\pi\) | ||||
0.764363 | + | 0.644786i | \(0.223054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.1867 | −0.503837 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −43.4575 | −1.65801 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.29976 | 0.163808 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.9711 | −0.683654 | −0.341827 | − | 0.939763i | \(-0.611046\pi\) | ||||
−0.341827 | + | 0.939763i | \(0.611046\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 61.5146 | 2.33675 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.63790 | 0.289722 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.40186 | 0.204610 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.7626 | 1.76872 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.5074 | 1.75656 | 0.878281 | − | 0.478146i | \(-0.158691\pi\) | ||||
0.878281 | + | 0.478146i | \(0.158691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.1821 | −0.912044 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.9871 | −0.903406 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.5418 | −0.659727 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.0363 | −1.84160 | −0.920798 | − | 0.390041i | \(-0.872461\pi\) | ||||
−0.920798 | + | 0.390041i | \(0.872461\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −33.6078 | −1.26039 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −30.4692 | −1.14108 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.06827 | 0.189543 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.7969 | 1.26217 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.5201 | −0.989032 | −0.494516 | − | 0.869169i | \(-0.664655\pi\) | ||||
−0.494516 | + | 0.869169i | \(0.664655\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.65905 | −0.173512 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.99750 | 0.0742879 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.6544 | −0.432834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.6887 | −1.21236 | −0.606179 | − | 0.795329i | \(-0.707298\pi\) | ||||
−0.606179 | + | 0.795329i | \(0.707298\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.8739 | −1.47681 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.3350 | −1.38088 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.4066 | 0.458248 | 0.229124 | − | 0.973397i | \(-0.426414\pi\) | ||||
0.229124 | + | 0.973397i | \(0.426414\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.04777 | −0.0755332 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.0222 | −1.06904 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.1186 | 0.776862 | 0.388431 | − | 0.921478i | \(-0.373017\pi\) | ||||
0.388431 | + | 0.921478i | \(0.373017\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −13.2678 | −0.487405 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.8627 | 1.49911 | 0.749554 | − | 0.661944i | \(-0.230268\pi\) | ||||
0.749554 | + | 0.661944i | \(0.230268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.5002 | 0.934256 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.0602 | −0.660788 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.8678 | −0.616337 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.3790 | −0.524699 | −0.262349 | − | 0.964973i | \(-0.584497\pi\) | ||||
−0.262349 | + | 0.964973i | \(0.584497\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.62368 | −0.0956123 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.53818 | −0.201555 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.6835 | −0.679064 | −0.339532 | − | 0.940595i | \(-0.610269\pi\) | ||||
−0.339532 | + | 0.940595i | \(0.610269\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 73.3602 | 2.66281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.8685 | −0.792732 | −0.396366 | − | 0.918092i | \(-0.629729\pi\) | ||||
−0.396366 | + | 0.918092i | \(0.629729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −39.7768 | −1.44002 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 20.4810 | 0.740493 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.30577 | −0.0832567 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.85128 | 0.283124 | 0.141562 | − | 0.989929i | \(-0.454788\pi\) | ||||
0.141562 | + | 0.989929i | \(0.454788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.0580 | 0.578313 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.0681 | 1.47712 | 0.738558 | − | 0.674190i | \(-0.235507\pi\) | ||||
0.738558 | + | 0.674190i | \(0.235507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.2411 | 0.906687 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22.0626 | 0.791491 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.51931 | −0.305236 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.8347 | 1.85479 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.34921 | 0.262639 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.1856 | 0.399231 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.5345 | −1.51619 | −0.758096 | − | 0.652143i | \(-0.773870\pi\) | ||||
−0.758096 | + | 0.652143i | \(0.773870\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.11410 | −0.324470 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 41.4414 | 1.47349 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.05642 | 0.0375146 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 18.5538 | 0.658036 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.5901 | 1.18982 | 0.594912 | − | 0.803791i | \(-0.297187\pi\) | ||||
0.594912 | + | 0.803791i | \(0.297187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.4380 | −1.28908 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.9696 | 0.493592 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.5678 | −1.14929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.8364 | 0.452425 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.3176 | 0.996828 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4068 | −0.822940 | −0.411470 | − | 0.911423i | \(-0.634984\pi\) | ||||
−0.411470 | + | 0.911423i | \(0.634984\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.1515 | −0.496928 | −0.248464 | − | 0.968641i | \(-0.579926\pi\) | ||||
−0.248464 | + | 0.968641i | \(0.579926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −36.3867 | −1.27614 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.7149 | 0.655556 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 58.8813 | 2.06000 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.82947 | 0.238641 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.42484 | −0.259129 | −0.129564 | − | 0.991571i | \(-0.541358\pi\) | ||||
−0.129564 | + | 0.991571i | \(0.541358\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.63364 | 0.0569452 | 0.0284726 | − | 0.999595i | \(-0.490936\pi\) | ||||
0.0284726 | + | 0.999595i | \(0.490936\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −60.7725 | −2.11583 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46.8226 | −1.62818 | −0.814090 | − | 0.580739i | \(-0.802764\pi\) | ||||
−0.814090 | + | 0.580739i | \(0.802764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0372 | 0.348605 | 0.174303 | − | 0.984692i | \(-0.444233\pi\) | ||||
0.174303 | + | 0.984692i | \(0.444233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 52.5092 | 1.82152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.11071 | −0.107780 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.9244 | 0.654906 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.9169 | −0.550168 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.9971 | −0.517756 | −0.258878 | − | 0.965910i | \(-0.583353\pi\) | ||||
−0.258878 | + | 0.965910i | \(0.583353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9531 | −0.653554 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 35.3926 | 1.21899 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.3911 | −0.495069 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 72.1254 | 2.47826 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 57.5530 | 1.97521 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.8444 | 0.508860 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.8473 | 1.50130 | 0.750652 | − | 0.660698i | \(-0.229739\pi\) | ||||
0.750652 | + | 0.660698i | \(0.229739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.3008 | −1.10466 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.7227 | −0.434598 | −0.217299 | − | 0.976105i | \(-0.569725\pi\) | ||||
−0.217299 | + | 0.976105i | \(0.569725\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.7352 | −0.366281 | −0.183140 | − | 0.983087i | \(-0.558626\pi\) | ||||
−0.183140 | + | 0.983087i | \(0.558626\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.77262 | 0.264890 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.1108 | −0.582458 | −0.291229 | − | 0.956653i | \(-0.594064\pi\) | ||||
−0.291229 | + | 0.956653i | \(0.594064\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.2368 | 0.824077 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.5421 | 0.358030 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −54.5149 | −1.84929 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.22209 | −0.109176 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −70.1724 | −2.37498 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.0945 | −0.848348 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8816 | −0.907726 | −0.453863 | − | 0.891071i | \(-0.649954\pi\) | ||||
−0.453863 | + | 0.891071i | \(0.649954\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.62793 | 0.189825 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.8555 | 1.64598 | 0.822992 | − | 0.568053i | \(-0.192303\pi\) | ||||
0.822992 | + | 0.568053i | \(0.192303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.8833 | −0.904695 | −0.452347 | − | 0.891842i | \(-0.649413\pi\) | ||||
−0.452347 | + | 0.891842i | \(0.649413\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.94960 | −0.334452 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.58557 | 0.0868150 | 0.0434075 | − | 0.999057i | \(-0.486179\pi\) | ||||
0.0434075 | + | 0.999057i | \(0.486179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.5743 | −0.455266 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.0763 | −1.17510 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 57.4667 | 1.92305 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.72337 | −0.325016 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.14458 | 0.271940 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.7596 | −0.725724 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.1845 | 0.938963 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −53.7206 | −1.78771 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.93147 | 0.163928 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.0643 | 1.39672 | 0.698360 | − | 0.715746i | \(-0.253913\pi\) | ||||
0.698360 | + | 0.715746i | \(0.253913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.0964 | −0.898732 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.0365 | 1.95597 | 0.977983 | − | 0.208685i | \(-0.0669184\pi\) | ||||
0.977983 | + | 0.208685i | \(0.0669184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.2952 | −0.969530 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.55855 | 0.150701 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.2869 | −1.36341 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.57673 | −0.183959 | −0.0919797 | − | 0.995761i | \(-0.529319\pi\) | ||||
−0.0919797 | + | 0.995761i | \(0.529319\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.91302 | 0.128938 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.75478 | 0.189421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.2973 | −0.404332 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.19673 | −0.236372 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.9616 | −1.31110 | −0.655550 | − | 0.755152i | \(-0.727563\pi\) | ||||
−0.655550 | + | 0.755152i | \(0.727563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.90592 | 0.160785 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.5827 | −0.575633 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.2220 | 1.08648 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.0767 | −0.851888 | −0.425944 | − | 0.904749i | \(-0.640058\pi\) | ||||
−0.425944 | + | 0.904749i | \(0.640058\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.8489 | 1.78993 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.6025 | −1.48660 | −0.743299 | − | 0.668959i | \(-0.766740\pi\) | ||||
−0.743299 | + | 0.668959i | \(0.766740\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.22966 | 0.170301 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.70565 | 0.218135 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.2548 | 1.14563 | 0.572814 | − | 0.819685i | \(-0.305852\pi\) | ||||
0.572814 | + | 0.819685i | \(0.305852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.61574 | −0.117372 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −33.6569 | −1.09140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.6865 | −0.670103 | −0.335051 | − | 0.942200i | \(-0.608754\pi\) | ||||
−0.335051 | + | 0.942200i | \(0.608754\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.9540 | 0.386821 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 52.3902 | 1.69353 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.8228 | −0.930738 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1269 | 0.520224 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.0554 | −0.839622 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.6469 | 0.471500 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.8565 | −1.02444 | −0.512219 | − | 0.858855i | \(-0.671176\pi\) | ||||
−0.512219 | + | 0.858855i | \(0.671176\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −86.9692 | −2.79385 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.02520 | 0.0649919 | 0.0324960 | − | 0.999472i | \(-0.489654\pi\) | ||||
0.0324960 | + | 0.999472i | \(0.489654\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.6946 | 0.535204 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.74707 | −0.216079 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.33996 | −0.106855 | −0.0534274 | − | 0.998572i | \(-0.517015\pi\) | ||||
−0.0534274 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.6600 | 0.724215 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −61.4423 | −1.96170 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.40905 | −0.268207 | −0.134104 | − | 0.990967i | \(-0.542815\pi\) | ||||
−0.134104 | + | 0.990967i | \(0.542815\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.74343 | −0.151138 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −52.4299 | −1.66886 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.1449 | −1.14934 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.60494 | 0.0509825 | 0.0254912 | − | 0.999675i | \(-0.491885\pi\) | ||||
0.0254912 | + | 0.999675i | \(0.491885\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.0234 | −1.11143 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.7930 | 0.500672 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.8631 | −0.660742 | −0.330371 | − | 0.943851i | \(-0.607174\pi\) | ||||
−0.330371 | + | 0.943851i | \(0.607174\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.75460 | 0.245345 |
(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 | 4016.2.a.k.1.14 | 17 | ||
4.3 | odd | 2 | 251.2.a.b.1.1 | ✓ | 17 | ||
12.11 | even | 2 | 2259.2.a.k.1.17 | 17 | |||
20.19 | odd | 2 | 6275.2.a.e.1.17 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
251.2.a.b.1.1 | ✓ | 17 | 4.3 | odd | 2 | ||
2259.2.a.k.1.17 | 17 | 12.11 | even | 2 | |||
4016.2.a.k.1.14 | 17 | 1.1 | even | 1 | trivial | ||
6275.2.a.e.1.17 | 17 | 20.19 | odd | 2 |