Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 21x^{5} - 12x^{4} + 93x^{3} + 18x^{2} - 120x + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(4.35097\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4020.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.772018 | 0.291795 | 0.145898 | − | 0.989300i | \(-0.453393\pi\) | ||||
0.145898 | + | 0.989300i | \(0.453393\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.49287 | 1.05314 | 0.526570 | − | 0.850132i | \(-0.323478\pi\) | ||||
0.526570 | + | 0.850132i | \(0.323478\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.80921 | −1.05649 | −0.528243 | − | 0.849093i | \(-0.677149\pi\) | ||||
−0.528243 | + | 0.849093i | \(0.677149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.47309 | −0.357276 | −0.178638 | − | 0.983915i | \(-0.557169\pi\) | ||||
−0.178638 | + | 0.983915i | \(0.557169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.60907 | 1.28681 | 0.643404 | − | 0.765526i | \(-0.277521\pi\) | ||||
0.643404 | + | 0.765526i | \(0.277521\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.772018 | 0.168468 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.75097 | 0.990646 | 0.495323 | − | 0.868709i | \(-0.335050\pi\) | ||||
0.495323 | + | 0.868709i | \(0.335050\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.97895 | −0.367482 | −0.183741 | − | 0.982975i | \(-0.558821\pi\) | ||||
−0.183741 | + | 0.982975i | \(0.558821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.171874 | −0.0308695 | −0.0154348 | − | 0.999881i | \(-0.504913\pi\) | ||||
−0.0154348 | + | 0.999881i | \(0.504913\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.49287 | 0.608031 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.772018 | 0.130495 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.95097 | 0.978333 | 0.489167 | − | 0.872190i | \(-0.337301\pi\) | ||||
0.489167 | + | 0.872190i | \(0.337301\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.80921 | −0.609962 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.79989 | −1.06197 | −0.530983 | − | 0.847383i | \(-0.678177\pi\) | ||||
−0.530983 | + | 0.847383i | \(0.678177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.90121 | 0.442430 | 0.221215 | − | 0.975225i | \(-0.428998\pi\) | ||||
0.221215 | + | 0.975225i | \(0.428998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.666440 | 0.0972103 | 0.0486051 | − | 0.998818i | \(-0.484522\pi\) | ||||
0.0486051 | + | 0.998818i | \(0.484522\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.40399 | −0.914856 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.47309 | −0.206273 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.18036 | 0.299495 | 0.149748 | − | 0.988724i | \(-0.452154\pi\) | ||||
0.149748 | + | 0.988724i | \(0.452154\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.49287 | 0.470979 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.60907 | 0.742940 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2262 | 1.33134 | 0.665668 | − | 0.746248i | \(-0.268147\pi\) | ||||
0.665668 | + | 0.746248i | \(0.268147\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.97755 | 1.14946 | 0.574729 | − | 0.818344i | \(-0.305108\pi\) | ||||
0.574729 | + | 0.818344i | \(0.305108\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.772018 | 0.0972651 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.80921 | −0.472475 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | −0.122169 | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.75097 | 0.571950 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.65305 | −1.14561 | −0.572803 | − | 0.819693i | \(-0.694144\pi\) | ||||
−0.572803 | + | 0.819693i | \(0.694144\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.54263 | −0.297592 | −0.148796 | − | 0.988868i | \(-0.547540\pi\) | ||||
−0.148796 | + | 0.988868i | \(0.547540\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.69656 | 0.307301 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.88724 | 0.774875 | 0.387437 | − | 0.921896i | \(-0.373360\pi\) | ||||
0.387437 | + | 0.921896i | \(0.373360\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.9668 | 1.42329 | 0.711647 | − | 0.702537i | \(-0.247949\pi\) | ||||
0.711647 | + | 0.702537i | \(0.247949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.47309 | −0.159779 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.97895 | −0.212166 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.2122 | −1.61249 | −0.806246 | − | 0.591580i | \(-0.798504\pi\) | ||||
−0.806246 | + | 0.591580i | \(0.798504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.94078 | −0.308277 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.171874 | −0.0178225 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.60907 | 0.575478 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.06150 | 0.107779 | 0.0538896 | − | 0.998547i | \(-0.482838\pi\) | ||||
0.0538896 | + | 0.998547i | \(0.482838\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.49287 | 0.351047 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.08976 | 0.605954 | 0.302977 | − | 0.952998i | \(-0.402020\pi\) | ||||
0.302977 | + | 0.952998i | \(0.402020\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.9586 | 1.47392 | 0.736959 | − | 0.675938i | \(-0.236261\pi\) | ||||
0.736959 | + | 0.675938i | \(0.236261\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.772018 | 0.0753412 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.67550 | 0.838692 | 0.419346 | − | 0.907826i | \(-0.362259\pi\) | ||||
0.419346 | + | 0.907826i | \(0.362259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.42094 | −0.423449 | −0.211725 | − | 0.977329i | \(-0.567908\pi\) | ||||
−0.211725 | + | 0.977329i | \(0.567908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.95097 | 0.564841 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.6417 | 1.75367 | 0.876834 | − | 0.480794i | \(-0.159651\pi\) | ||||
0.876834 | + | 0.480794i | \(0.159651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.75097 | 0.443030 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.80921 | −0.352162 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.13725 | −0.104251 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.20015 | 0.109104 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.79989 | −0.613126 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.47439 | 0.574509 | 0.287255 | − | 0.957854i | \(-0.407257\pi\) | ||||
0.287255 | + | 0.957854i | \(0.407257\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.90121 | 0.255437 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.5320 | −1.53177 | −0.765887 | − | 0.642975i | \(-0.777700\pi\) | ||||
−0.765887 | + | 0.642975i | \(0.777700\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.33030 | 0.375485 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.2289 | −1.21566 | −0.607828 | − | 0.794069i | \(-0.707959\pi\) | ||||
−0.607828 | + | 0.794069i | \(0.707959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.1873 | −1.88191 | −0.940953 | − | 0.338537i | \(-0.890068\pi\) | ||||
−0.940953 | + | 0.338537i | \(0.890068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.666440 | 0.0561244 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.3051 | −1.11263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.97895 | −0.164343 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.40399 | −0.528192 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.2572 | 1.57761 | 0.788805 | − | 0.614644i | \(-0.210700\pi\) | ||||
0.788805 | + | 0.614644i | \(0.210700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.3020 | −1.57077 | −0.785386 | − | 0.619006i | \(-0.787536\pi\) | ||||
−0.785386 | + | 0.619006i | \(0.787536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.47309 | −0.119092 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.171874 | −0.0138053 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.80650 | 0.303792 | 0.151896 | − | 0.988396i | \(-0.451462\pi\) | ||||
0.151896 | + | 0.988396i | \(0.451462\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.18036 | 0.172914 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.66783 | 0.289066 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.0767 | −1.41588 | −0.707938 | − | 0.706274i | \(-0.750375\pi\) | ||||
−0.707938 | + | 0.706274i | \(0.750375\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.49287 | 0.271920 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5459 | 1.51251 | 0.756254 | − | 0.654278i | \(-0.227027\pi\) | ||||
0.756254 | + | 0.654278i | \(0.227027\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.51010 | 0.116161 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.60907 | 0.428936 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3975 | 1.62682 | 0.813412 | − | 0.581689i | \(-0.197608\pi\) | ||||
0.813412 | + | 0.581689i | \(0.197608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.772018 | 0.0583591 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.2262 | 0.768648 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.270379 | 0.0202091 | 0.0101046 | − | 0.999949i | \(-0.496784\pi\) | ||||
0.0101046 | + | 0.999949i | \(0.496784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.43492 | 0.180986 | 0.0904930 | − | 0.995897i | \(-0.471156\pi\) | ||||
0.0904930 | + | 0.995897i | \(0.471156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.97755 | 0.663639 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.95097 | 0.437524 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.14530 | −0.376262 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.772018 | 0.0561560 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3834 | −0.823671 | −0.411835 | − | 0.911258i | \(-0.635112\pi\) | ||||
−0.411835 | + | 0.911258i | \(0.635112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.72764 | 0.556248 | 0.278124 | − | 0.960545i | \(-0.410287\pi\) | ||||
0.278124 | + | 0.960545i | \(0.410287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.80921 | −0.272783 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.9110 | −0.848624 | −0.424312 | − | 0.905516i | \(-0.639484\pi\) | ||||
−0.424312 | + | 0.905516i | \(0.639484\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.345159 | −0.0244677 | −0.0122338 | − | 0.999925i | \(-0.503894\pi\) | ||||
−0.0122338 | + | 0.999925i | \(0.503894\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.52779 | −0.107230 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.79989 | −0.474925 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.75097 | 0.330215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.5918 | 1.35519 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.5809 | 1.34800 | 0.674001 | − | 0.738730i | \(-0.264574\pi\) | ||||
0.674001 | + | 0.738730i | \(0.264574\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.65305 | −0.661416 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.90121 | 0.197861 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.132690 | −0.00900758 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.54263 | −0.171815 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.61130 | 0.377457 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.57499 | −0.239399 | −0.119700 | − | 0.992810i | \(-0.538193\pi\) | ||||
−0.119700 | + | 0.992810i | \(0.538193\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.8309 | −1.24985 | −0.624925 | − | 0.780685i | \(-0.714870\pi\) | ||||
−0.624925 | + | 0.780685i | \(0.714870\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.08710 | −0.600492 | −0.300246 | − | 0.953862i | \(-0.597069\pi\) | ||||
−0.300246 | + | 0.953862i | \(0.597069\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.69656 | 0.177421 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.280150 | −0.0183532 | −0.00917660 | − | 0.999958i | \(-0.502921\pi\) | ||||
−0.00917660 | + | 0.999958i | \(0.502921\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.666440 | 0.0434738 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.88724 | 0.447374 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.4729 | 1.38897 | 0.694483 | − | 0.719509i | \(-0.255633\pi\) | ||||
0.694483 | + | 0.719509i | \(0.255633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.38206 | −0.539936 | −0.269968 | − | 0.962869i | \(-0.587013\pi\) | ||||
−0.269968 | + | 0.962869i | \(0.587013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.40399 | −0.409136 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.3661 | −1.35949 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.9668 | 0.821739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.7462 | 1.05701 | 0.528506 | − | 0.848930i | \(-0.322753\pi\) | ||||
0.528506 | + | 0.848930i | \(0.322753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.5945 | 1.04329 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.47309 | −0.0922483 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0090 | 0.936233 | 0.468117 | − | 0.883667i | \(-0.344933\pi\) | ||||
0.468117 | + | 0.883667i | \(0.344933\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.59425 | 0.285473 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.97895 | −0.122494 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.86798 | 0.300172 | 0.150086 | − | 0.988673i | \(-0.452045\pi\) | ||||
0.150086 | + | 0.988673i | \(0.452045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.18036 | 0.133938 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.2122 | −0.930973 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.1049 | 0.677079 | 0.338540 | − | 0.940952i | \(-0.390067\pi\) | ||||
0.338540 | + | 0.940952i | \(0.390067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.4350 | 1.05910 | 0.529549 | − | 0.848279i | \(-0.322361\pi\) | ||||
0.529549 | + | 0.848279i | \(0.322361\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.94078 | −0.177984 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.49287 | 0.210628 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.6148 | −1.59913 | −0.799564 | − | 0.600581i | \(-0.794936\pi\) | ||||
−0.799564 | + | 0.600581i | \(0.794936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.171874 | −0.0102898 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.417408 | 0.0249005 | 0.0124502 | − | 0.999922i | \(-0.496037\pi\) | ||||
0.0124502 | + | 0.999922i | \(0.496037\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0097 | −0.892232 | −0.446116 | − | 0.894975i | \(-0.647193\pi\) | ||||
−0.446116 | + | 0.894975i | \(0.647193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.60907 | 0.332253 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.24964 | −0.309876 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.8300 | −0.872354 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.06150 | 0.0622264 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 29.6270 | 1.73083 | 0.865413 | − | 0.501059i | \(-0.167056\pi\) | ||||
0.865413 | + | 0.501059i | \(0.167056\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2262 | 0.595392 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.49287 | 0.202677 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.0975 | −1.04660 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.23979 | 0.129099 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.08976 | 0.349848 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.97755 | 0.514053 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.9483 | −1.36680 | −0.683402 | − | 0.730042i | \(-0.739500\pi\) | ||||
−0.683402 | + | 0.730042i | \(0.739500\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.9586 | 0.850967 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.17570 | 0.180078 | 0.0900388 | − | 0.995938i | \(-0.471301\pi\) | ||||
0.0900388 | + | 0.995938i | \(0.471301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.796458 | 0.0450185 | 0.0225092 | − | 0.999747i | \(-0.492834\pi\) | ||||
0.0225092 | + | 0.999747i | \(0.492834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.772018 | 0.0434983 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.80372 | −0.438301 | −0.219150 | − | 0.975691i | \(-0.570329\pi\) | ||||
−0.219150 | + | 0.975691i | \(0.570329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.91223 | −0.387011 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.67550 | 0.484219 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.26265 | −0.459746 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.80921 | −0.211297 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.42094 | −0.244478 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.514504 | 0.0283655 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.2554 | 1.66299 | 0.831494 | − | 0.555534i | \(-0.187486\pi\) | ||||
0.831494 | + | 0.555534i | \(0.187486\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.95097 | 0.326111 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.00000 | −0.0546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.93587 | 0.214401 | 0.107200 | − | 0.994237i | \(-0.465811\pi\) | ||||
0.107200 | + | 0.994237i | \(0.465811\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.6417 | 1.01248 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.600335 | −0.0325099 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.3481 | −0.558746 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.75097 | 0.255784 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0702 | −0.809009 | −0.404505 | − | 0.914536i | \(-0.632556\pi\) | ||||
−0.404505 | + | 0.914536i | \(0.632556\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.7710 | 1.64713 | 0.823567 | − | 0.567219i | \(-0.191981\pi\) | ||||
0.823567 | + | 0.567219i | \(0.191981\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.80921 | −0.203321 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.83282 | −0.204000 | −0.102000 | − | 0.994784i | \(-0.532524\pi\) | ||||
−0.102000 | + | 0.994784i | \(0.532524\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.65305 | −0.512331 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.13725 | −0.0601896 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6946 | 0.881109 | 0.440554 | − | 0.897726i | \(-0.354782\pi\) | ||||
0.440554 | + | 0.897726i | \(0.354782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4617 | 0.655877 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.20015 | 0.0629914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.54263 | −0.133087 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2371 | −0.690969 | −0.345484 | − | 0.938425i | \(-0.612285\pi\) | ||||
−0.345484 | + | 0.938425i | \(0.612285\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.79989 | −0.353988 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.68327 | 0.0873913 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.71691 | 0.451345 | 0.225672 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225672 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.53825 | 0.388240 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.6794 | −1.67863 | −0.839314 | − | 0.543647i | \(-0.817043\pi\) | ||||
−0.839314 | + | 0.543647i | \(0.817043\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.47439 | 0.331693 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.33406 | −0.425851 | −0.212925 | − | 0.977068i | \(-0.568299\pi\) | ||||
−0.212925 | + | 0.977068i | \(0.568299\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.69656 | 0.137429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.90121 | 0.147477 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −32.4917 | −1.64740 | −0.823698 | − | 0.567029i | \(-0.808093\pi\) | ||||
−0.823698 | + | 0.567029i | \(0.808093\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.99859 | −0.353934 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.5320 | −0.884370 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.88724 | 0.346534 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.60257 | 0.180808 | 0.0904038 | − | 0.995905i | \(-0.471184\pi\) | ||||
0.0904038 | + | 0.995905i | \(0.471184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.33030 | 0.216786 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.11208 | −0.255285 | −0.127642 | − | 0.991820i | \(-0.540741\pi\) | ||||
−0.127642 | + | 0.991820i | \(0.540741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.654705 | 0.0326132 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20.7860 | 1.03032 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.8869 | −0.785554 | −0.392777 | − | 0.919634i | \(-0.628486\pi\) | ||||
−0.392777 | + | 0.919634i | \(0.628486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.2289 | −0.701859 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.89480 | 0.388478 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.9668 | 0.636517 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.1873 | −1.08652 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.54463 | −0.319726 | −0.159863 | − | 0.987139i | \(-0.551105\pi\) | ||||
−0.159863 | + | 0.987139i | \(0.551105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.0622 | −1.61135 | −0.805675 | − | 0.592357i | \(-0.798197\pi\) | ||||
−0.805675 | + | 0.592357i | \(0.798197\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.666440 | 0.0324034 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.47309 | −0.0714552 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.93083 | 0.335406 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.3051 | −0.642376 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.91115 | −0.236562 | −0.118281 | − | 0.992980i | \(-0.537738\pi\) | ||||
−0.118281 | + | 0.992980i | \(0.537738\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.45669 | 0.358346 | 0.179173 | − | 0.983818i | \(-0.442658\pi\) | ||||
0.179173 | + | 0.983818i | \(0.442658\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.97895 | −0.0948836 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.6485 | 1.27477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.1708 | −1.24907 | −0.624533 | − | 0.780999i | \(-0.714710\pi\) | ||||
−0.624533 | + | 0.780999i | \(0.714710\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.40399 | −0.304952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3544 | 0.777019 | 0.388509 | − | 0.921445i | \(-0.372990\pi\) | ||||
0.388509 | + | 0.921445i | \(0.372990\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.2122 | −0.721128 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.2572 | 0.910834 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.8516 | −1.83352 | −0.916760 | − | 0.399438i | \(-0.869205\pi\) | ||||
−0.916760 | + | 0.399438i | \(0.869205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.7512 | −1.11840 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.3020 | −0.906886 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.94078 | −0.137866 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.434246 | 0.0203132 | 0.0101566 | − | 0.999948i | \(-0.496767\pi\) | ||||
0.0101566 | + | 0.999948i | \(0.496767\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.47309 | −0.0687578 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.2045 | 1.40676 | 0.703382 | − | 0.710812i | \(-0.251672\pi\) | ||||
0.703382 | + | 0.710812i | \(0.251672\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8061 | −0.920469 | −0.460235 | − | 0.887797i | \(-0.652235\pi\) | ||||
−0.460235 | + | 0.887797i | \(0.652235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.171874 | −0.00797048 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.4621 | −1.08570 | −0.542848 | − | 0.839831i | \(-0.682654\pi\) | ||||
−0.542848 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.772018 | −0.0356485 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.80650 | 0.175394 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.1336 | 0.465941 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.60907 | 0.257362 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.18036 | 0.0998317 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.57726 | 0.437596 | 0.218798 | − | 0.975770i | \(-0.429786\pi\) | ||||
0.218798 | + | 0.975770i | \(0.429786\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.6685 | −1.03359 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.66783 | 0.166892 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.06150 | 0.0482003 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −21.0897 | −0.955664 | −0.477832 | − | 0.878451i | \(-0.658577\pi\) | ||||
−0.477832 | + | 0.878451i | \(0.658577\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.0767 | −0.817457 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.41768 | −0.244497 | −0.122248 | − | 0.992500i | \(-0.539010\pi\) | ||||
−0.122248 | + | 0.992500i | \(0.539010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.91517 | 0.131293 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.49287 | 0.156993 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.45233 | −0.334283 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.7696 | 1.64603 | 0.823017 | − | 0.568016i | \(-0.192289\pi\) | ||||
0.823017 | + | 0.568016i | \(0.192289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.5459 | 0.873247 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.4158 | 1.66829 | 0.834145 | − | 0.551546i | \(-0.185962\pi\) | ||||
0.834145 | + | 0.551546i | \(0.185962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.08976 | 0.270991 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.51010 | 0.0670657 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.820242 | 0.0363566 | 0.0181783 | − | 0.999835i | \(-0.494213\pi\) | ||||
0.0181783 | + | 0.999835i | \(0.494213\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.96295 | −0.0868360 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.60907 | 0.247647 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.9586 | 0.659156 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.32779 | 0.102376 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.3975 | 0.939247 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0460 | 0.922042 | 0.461021 | − | 0.887389i | \(-0.347483\pi\) | ||||
0.461021 | + | 0.887389i | \(0.347483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.9849 | 1.13624 | 0.568120 | − | 0.822946i | \(-0.307671\pi\) | ||||
0.568120 | + | 0.822946i | \(0.307671\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.772018 | 0.0336936 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.253186 | 0.0110289 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.428270 | −0.0186204 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.2262 | 0.443779 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.9022 | 1.12195 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.67550 | 0.375075 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.270379 | 0.0116677 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −22.3683 | −0.963471 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.27257 | 0.398659 | 0.199330 | − | 0.979933i | \(-0.436124\pi\) | ||||
0.199330 | + | 0.979933i | \(0.436124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.43492 | 0.104492 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.42094 | −0.189372 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.6994 | 0.842284 | 0.421142 | − | 0.906995i | \(-0.361629\pi\) | ||||
0.421142 | + | 0.906995i | \(0.361629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.97755 | 0.383152 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.1001 | −0.472880 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.31707 | 0.226105 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.95097 | 0.252605 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.2284 | −1.66216 | −0.831081 | − | 0.556151i | \(-0.812278\pi\) | ||||
−0.831081 | + | 0.556151i | \(0.812278\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.0513 | −0.467421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.14530 | −0.217235 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5646 | −0.824552 | −0.412276 | − | 0.911059i | \(-0.635266\pi\) | ||||
−0.412276 | + | 0.911059i | \(0.635266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.6417 | 0.784264 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.772018 | 0.0324217 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −45.3427 | −1.90087 | −0.950433 | − | 0.310928i | \(-0.899360\pi\) | ||||
−0.950433 | + | 0.310928i | \(0.899360\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.8531 | −1.08192 | −0.540958 | − | 0.841049i | \(-0.681938\pi\) | ||||
−0.540958 | + | 0.841049i | \(0.681938\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.3834 | −0.475547 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.75097 | 0.198129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.9223 | 1.16242 | 0.581210 | − | 0.813754i | \(-0.302580\pi\) | ||||
0.581210 | + | 0.813754i | \(0.302580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.72764 | 0.321150 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0106 | 0.415311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.61571 | 0.315410 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.80921 | −0.157492 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.9344 | 0.451310 | 0.225655 | − | 0.974207i | \(-0.427548\pi\) | ||||
0.225655 | + | 0.974207i | \(0.427548\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.964055 | −0.0397232 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.9110 | −0.489953 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.0801 | 1.44057 | 0.720284 | − | 0.693680i | \(-0.244012\pi\) | ||||
0.720284 | + | 0.693680i | \(0.244012\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.13725 | −0.0466227 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.345159 | −0.0141264 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.23267 | 0.0503656 | 0.0251828 | − | 0.999683i | \(-0.491983\pi\) | ||||
0.0251828 | + | 0.999683i | \(0.491983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.1162 | −0.820556 | −0.410278 | − | 0.911960i | \(-0.634568\pi\) | ||||
−0.410278 | + | 0.911960i | \(0.634568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00000 | −0.0407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.20015 | 0.0487929 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −39.9333 | −1.62084 | −0.810421 | − | 0.585848i | \(-0.800761\pi\) | ||||
−0.810421 | + | 0.585848i | \(0.800761\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.52779 | −0.0619091 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.53861 | −0.102701 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0246 | −0.566450 | −0.283225 | − | 0.959053i | \(-0.591404\pi\) | ||||
−0.283225 | + | 0.959053i | \(0.591404\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.79989 | −0.274198 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.58743 | 0.224942 | 0.112471 | − | 0.993655i | \(-0.464124\pi\) | ||||
0.112471 | + | 0.993655i | \(0.464124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1025 | 0.526635 | 0.263317 | − | 0.964709i | \(-0.415183\pi\) | ||||
0.263317 | + | 0.964709i | \(0.415183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.75097 | 0.190650 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.7441 | −0.470518 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.5918 | 0.782419 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.76629 | −0.349535 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.1488 | −1.31963 | −0.659816 | − | 0.751427i | \(-0.729366\pi\) | ||||
−0.659816 | + | 0.751427i | \(0.729366\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.5809 | 0.778270 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.47439 | 0.256928 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.3941 | 0.966531 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.65305 | −0.381869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.08990 | −0.240537 | −0.120268 | − | 0.992741i | \(-0.538375\pi\) | ||||
−0.120268 | + | 0.992741i | \(0.538375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.23162 | 0.324624 | 0.162312 | − | 0.986740i | \(-0.448105\pi\) | ||||
0.162312 | + | 0.986740i | \(0.448105\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.90121 | 0.114235 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.8263 | −1.72299 | −0.861495 | − | 0.507767i | \(-0.830471\pi\) | ||||
−0.861495 | + | 0.507767i | \(0.830471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.7188 | 1.40208 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.132690 | −0.00520053 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.04576 | −0.314855 | −0.157428 | − | 0.987531i | \(-0.550320\pi\) | ||||
−0.157428 | + | 0.987531i | \(0.550320\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.5320 | −0.685030 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.54263 | −0.0991974 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.9610 | 0.738614 | 0.369307 | − | 0.929307i | \(-0.379595\pi\) | ||||
0.369307 | + | 0.929307i | \(0.379595\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.5682 | −1.77240 | −0.886199 | − | 0.463304i | \(-0.846664\pi\) | ||||
−0.886199 | + | 0.463304i | \(0.846664\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.61130 | 0.217925 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.33030 | 0.167922 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.40195 | −0.364045 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.57499 | −0.138217 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.3574 | 1.21054 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.4226 | 0.555951 | 0.277976 | − | 0.960588i | \(-0.410337\pi\) | ||||
0.277976 | + | 0.960588i | \(0.410337\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.31691 | 0.165912 | 0.0829561 | − | 0.996553i | \(-0.473564\pi\) | ||||
0.0829561 | + | 0.996553i | \(0.473564\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.819498 | 0.0314495 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.8309 | −0.721601 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.53346 | −0.135204 | −0.0676020 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676020 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.2289 | −0.543658 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.08710 | −0.346694 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.30544 | −0.316412 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1252 | −0.423224 | −0.211612 | − | 0.977354i | \(-0.567871\pi\) | ||||
−0.211612 | + | 0.977354i | \(0.567871\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.69656 | 0.102434 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.1873 | −0.841614 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0168 | 0.379415 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.280150 | −0.0105962 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.2127 | 1.66989 | 0.834946 | − | 0.550332i | \(-0.185499\pi\) | ||||
0.834946 | + | 0.550332i | \(0.185499\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.3794 | 1.25893 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.666440 | 0.0250996 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.70140 | 0.176814 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.44566 | −0.129405 | −0.0647023 | − | 0.997905i | \(-0.520610\pi\) | ||||
−0.0647023 | + | 0.997905i | \(0.520610\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.88724 | 0.258292 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.816570 | −0.0305808 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.3051 | −0.497582 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.4729 | 0.801920 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.51182 | −0.205556 | −0.102778 | − | 0.994704i | \(-0.532773\pi\) | ||||
−0.102778 | + | 0.994704i | \(0.532773\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5483 | 0.430082 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.38206 | −0.311732 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.97895 | −0.0734965 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.0730 | 0.929905 | 0.464953 | − | 0.885336i | \(-0.346071\pi\) | ||||
0.464953 | + | 0.885336i | \(0.346071\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.27373 | −0.158070 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4533 | 0.903204 | 0.451602 | − | 0.892220i | \(-0.350853\pi\) | ||||
0.451602 | + | 0.892220i | \(0.350853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.40399 | −0.236215 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.49287 | −0.128662 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35.2777 | −1.29771 | −0.648856 | − | 0.760911i | \(-0.724752\pi\) | ||||
−0.648856 | + | 0.760911i | \(0.724752\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.3661 | −0.784905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.1041 | −0.444056 | −0.222028 | − | 0.975040i | \(-0.571268\pi\) | ||||
−0.222028 | + | 0.975040i | \(0.571268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2572 | 0.705529 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.9668 | 0.474431 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.69764 | 0.244726 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.5005 | −1.36841 | −0.684206 | − | 0.729289i | \(-0.739851\pi\) | ||||
−0.684206 | + | 0.729289i | \(0.739851\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.7462 | 0.610266 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.3020 | −0.702471 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.8803 | −1.23140 | −0.615700 | − | 0.787980i | \(-0.711127\pi\) | ||||
−0.615700 | + | 0.787980i | \(0.711127\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.5945 | 0.602343 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.3139 | −1.49763 | −0.748814 | − | 0.662780i | \(-0.769377\pi\) | ||||
−0.748814 | + | 0.662780i | \(0.769377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.41304 | −0.123560 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.47309 | −0.0532596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38.9537 | −1.40654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.0009 | 0.937615 | 0.468807 | − | 0.883300i | \(-0.344684\pi\) | ||||
0.468807 | + | 0.883300i | \(0.344684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0090 | 0.540535 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.08729 | −0.182977 | −0.0914886 | − | 0.995806i | \(-0.529163\pi\) | ||||
−0.0914886 | + | 0.995806i | \(0.529163\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.171874 | −0.00617391 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.59425 | 0.164818 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.1411 | −1.36655 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.7169 | −1.20648 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.97895 | −0.0707220 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.80650 | 0.135860 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −47.8019 | −1.70395 | −0.851977 | − | 0.523580i | \(-0.824596\pi\) | ||||
−0.851977 | + | 0.523580i | \(0.824596\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.86798 | 0.173305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.3918 | 0.511712 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.1974 | −1.21438 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.18036 | 0.0773293 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −10.8864 | −0.385617 | −0.192808 | − | 0.981236i | \(-0.561760\pi\) | ||||
−0.192808 | + | 0.981236i | \(0.561760\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.981724 | −0.0347309 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.2122 | −0.537497 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.88107 | −0.313406 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.66783 | 0.129274 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.1049 | 0.390912 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.8878 | −0.804693 | −0.402346 | − | 0.915488i | \(-0.631805\pi\) | ||||
−0.402346 | + | 0.915488i | \(0.631805\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.4387 | −1.56045 | −0.780227 | − | 0.625496i | \(-0.784896\pi\) | ||||
−0.780227 | + | 0.625496i | \(0.784896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 17.4350 | 0.611471 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.0767 | −0.633199 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.2731 | 0.569324 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.94078 | −0.102759 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.47421 | 0.260852 | 0.130426 | − | 0.991458i | \(-0.458366\pi\) | ||||
0.130426 | + | 0.991458i | \(0.458366\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.8092 | −1.21337 | −0.606686 | − | 0.794942i | \(-0.707501\pi\) | ||||
−0.606686 | + | 0.794942i | \(0.707501\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.49287 | 0.121606 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.05105 | 0.245189 | 0.122595 | − | 0.992457i | \(-0.460879\pi\) | ||||
0.122595 | + | 0.992457i | \(0.460879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.8798 | −0.516796 | −0.258398 | − | 0.966038i | \(-0.583195\pi\) | ||||
−0.258398 | + | 0.966038i | \(0.583195\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.6148 | −0.923257 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.43363 | 0.326856 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.5459 | 0.676414 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.171874 | −0.00594084 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.99371 | 0.345021 | 0.172511 | − | 0.985008i | \(-0.444812\pi\) | ||||
0.172511 | + | 0.985008i | \(0.444812\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0837 | −0.864957 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.417408 | 0.0143763 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.51010 | 0.0519489 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.926535 | 0.0318361 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.0097 | −0.515130 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 28.2729 | 0.969182 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.8227 | −0.644477 | −0.322239 | − | 0.946658i | \(-0.604435\pi\) | ||||
−0.322239 | + | 0.946658i | \(0.604435\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.60907 | 0.191826 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.8679 | 0.439560 | 0.219780 | − | 0.975549i | \(-0.429466\pi\) | ||||
0.219780 | + | 0.975549i | \(0.429466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.0845 | −1.19707 | −0.598534 | − | 0.801097i | \(-0.704250\pi\) | ||||
−0.598534 | + | 0.801097i | \(0.704250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.24964 | −0.178907 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.6283 | 1.31492 | 0.657461 | − | 0.753489i | \(-0.271631\pi\) | ||||
0.657461 | + | 0.753489i | \(0.271631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.3975 | 0.727537 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.8300 | −0.503654 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.0562 | 0.816052 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.80921 | 0.129070 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.06150 | 0.0359264 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.772018 | 0.0260990 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.11218 | 0.0713232 | 0.0356616 | − | 0.999364i | \(-0.488646\pi\) | ||||
0.0356616 | + | 0.999364i | \(0.488646\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.6270 | 0.999293 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0148 | −0.606935 | −0.303468 | − | 0.952842i | \(-0.598144\pi\) | ||||
−0.303468 | + | 0.952842i | \(0.598144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.3114 | −0.347005 | −0.173502 | − | 0.984833i | \(-0.555508\pi\) | ||||
−0.173502 | + | 0.984833i | \(0.555508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.2262 | 0.343750 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 46.9685 | 1.57705 | 0.788524 | − | 0.615003i | \(-0.210845\pi\) | ||||
0.788524 | + | 0.615003i | \(0.210845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.99834 | 0.167639 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.49287 | 0.117016 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.73811 | 0.125091 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.270379 | 0.00903779 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18.0975 | −0.604257 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.340131 | 0.0113440 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.21186 | −0.107002 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.23979 | 0.0745354 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.43492 | 0.0809394 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −59.7785 | −1.98491 | −0.992457 | − | 0.122593i | \(-0.960879\pi\) | ||||
−0.992457 | + | 0.122593i | \(0.960879\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.08976 | 0.201985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.1299 | −0.766329 | −0.383164 | − | 0.923680i | \(-0.625166\pi\) | ||||
−0.383164 | + | 0.923680i | \(0.625166\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.2915 | 1.49893 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.97755 | 0.296789 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.5350 | −0.446965 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.7603 | 0.519886 | 0.259943 | − | 0.965624i | \(-0.416296\pi\) | ||||
0.259943 | + | 0.965624i | \(0.416296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.9483 | −0.789125 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.7705 | 1.21032 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.95097 | 0.195667 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.9586 | 0.491306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.4115 | 1.16181 | 0.580907 | − | 0.813970i | \(-0.302698\pi\) | ||||
0.580907 | + | 0.813970i | \(0.302698\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.9204 | −1.17724 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.17570 | 0.103968 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.14530 | −0.168269 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5869 | −0.378528 | −0.189264 | − | 0.981926i | \(-0.560610\pi\) | ||||
−0.189264 | + | 0.981926i | \(0.560610\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.796458 | 0.0259914 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.3078 | −0.922808 | −0.461404 | − | 0.887190i | \(-0.652654\pi\) | ||||
−0.461404 | + | 0.887190i | \(0.652654\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −32.3061 | −1.05203 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.772018 | 0.0251137 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 49.8955 | 1.62139 | 0.810693 | − | 0.585472i | \(-0.199091\pi\) | ||||
0.810693 | + | 0.585472i | \(0.199091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.68541 | 0.314402 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.80372 | −0.253053 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.1134 | 0.424784 | 0.212392 | − | 0.977184i | \(-0.431875\pi\) | ||||
0.212392 | + | 0.977184i | \(0.431875\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.3834 | −0.368357 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.91223 | −0.223441 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.9850 | −0.354723 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9705 | −0.999047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.67550 | 0.279564 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.72764 | 0.248762 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.5613 | −1.24005 | −0.620023 | − | 0.784583i | \(-0.712877\pi\) | ||||
−0.620023 | + | 0.784583i | \(0.712877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.26265 | −0.265434 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.8434 | −1.56746 | −0.783730 | − | 0.621102i | \(-0.786685\pi\) | ||||
−0.783730 | + | 0.621102i | \(0.786685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.1290 | −0.549131 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.80921 | −0.121992 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.47404 | −0.0791517 | −0.0395758 | − | 0.999217i | \(-0.512601\pi\) | ||||
−0.0395758 | + | 0.999217i | \(0.512601\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.1343 | −1.69818 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.42094 | −0.141150 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55.1656 | 1.75951 | 0.879754 | − | 0.475429i | \(-0.157707\pi\) | ||||
0.879754 | + | 0.475429i | \(0.157707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9110 | −0.379516 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.514504 | 0.0163768 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.7836 | 0.438292 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.86512 | −0.0910136 | −0.0455068 | − | 0.998964i | \(-0.514490\pi\) | ||||
−0.0455068 | + | 0.998964i | \(0.514490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.2554 | 0.960127 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.345159 | −0.0109423 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.19937 | −0.291347 | −0.145673 | − | 0.989333i | \(-0.546535\pi\) | ||||
−0.145673 | + | 0.989333i | \(0.546535\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.95097 | 0.188280 |
(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 | 4020.2.a.i.1.4 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.a.i.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial |