Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [440,2,Mod(1,440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(440, 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("440.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 440 = 2^{3} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 440.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: | \(3.51341768894\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 440.1 |
$q$-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 | ||||||||
\(3\) | 2.56155 | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235083\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.56155 | 1.72410 | 0.862052 | − | 0.506819i | \(-0.169179\pi\) | ||||
0.862052 | + | 0.506819i | \(0.169179\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.12311 | −0.311493 | −0.155747 | − | 0.987797i | \(-0.549778\pi\) | ||||
−0.155747 | + | 0.987797i | \(0.549778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.56155 | −0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.68466 | −1.86380 | −0.931902 | − | 0.362711i | \(-0.881851\pi\) | ||||
−0.931902 | + | 0.362711i | \(0.881851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.43845 | 0.330002 | 0.165001 | − | 0.986293i | \(-0.447237\pi\) | ||||
0.165001 | + | 0.986293i | \(0.447237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.6847 | 2.54980 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.12311 | 0.234184 | 0.117092 | − | 0.993121i | \(-0.462643\pi\) | ||||
0.117092 | + | 0.993121i | \(0.462643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845 | 0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.56155 | 1.58984 | 0.794920 | − | 0.606714i | \(-0.207513\pi\) | ||||
0.794920 | + | 0.606714i | \(0.207513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.43845 | −0.258353 | −0.129176 | − | 0.991622i | \(-0.541233\pi\) | ||||
−0.129176 | + | 0.991622i | \(0.541233\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.56155 | −0.445909 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.56155 | −0.771043 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.43845 | 1.22287 | 0.611437 | − | 0.791293i | \(-0.290592\pi\) | ||||
0.611437 | + | 0.791293i | \(0.290592\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.87689 | −0.460672 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.2462 | −1.91254 | −0.956268 | − | 0.292490i | \(-0.905516\pi\) | ||||
−0.956268 | + | 0.292490i | \(0.905516\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.12311 | −0.476269 | −0.238135 | − | 0.971232i | \(-0.576536\pi\) | ||||
−0.238135 | + | 0.971232i | \(0.576536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.56155 | −0.530925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3693 | −1.65839 | −0.829193 | − | 0.558963i | \(-0.811199\pi\) | ||||
−0.829193 | + | 0.558963i | \(0.811199\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.8078 | 1.97254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.6847 | −2.75640 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.68466 | 1.33029 | 0.665145 | − | 0.746714i | \(-0.268370\pi\) | ||||
0.665145 | + | 0.746714i | \(0.268370\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.68466 | 0.488045 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.12311 | 0.146216 | 0.0731079 | − | 0.997324i | \(-0.476708\pi\) | ||||
0.0731079 | + | 0.997324i | \(0.476708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.5616 | −1.60834 | −0.804171 | − | 0.594398i | \(-0.797390\pi\) | ||||
−0.804171 | + | 0.594398i | \(0.797390\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.2462 | 2.04683 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.12311 | 0.139304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.87689 | 0.346337 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68466 | 0.437289 | 0.218644 | − | 0.975805i | \(-0.429837\pi\) | ||||
0.218644 | + | 0.975805i | \(0.429837\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.12311 | 0.131450 | 0.0657248 | − | 0.997838i | \(-0.479064\pi\) | ||||
0.0657248 | + | 0.997838i | \(0.479064\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.56155 | 0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.56155 | −0.519837 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.3693 | −1.27915 | −0.639574 | − | 0.768729i | \(-0.720889\pi\) | ||||
−0.639574 | + | 0.768729i | \(0.720889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.68466 | 0.833518 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.9309 | 2.35124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.68466 | 1.02657 | 0.513286 | − | 0.858218i | \(-0.328428\pi\) | ||||
0.513286 | + | 0.858218i | \(0.328428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.12311 | −0.537047 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.68466 | −0.382081 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.43845 | −0.147582 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.87689 | −0.495174 | −0.247587 | − | 0.968866i | \(-0.579638\pi\) | ||||
−0.247587 | + | 0.968866i | \(0.579638\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.56155 | −0.357950 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.00000 | −0.199007 | −0.0995037 | − | 0.995037i | \(-0.531726\pi\) | ||||
−0.0995037 | + | 0.995037i | \(0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.6847 | −1.14031 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.12311 | 0.688617 | 0.344308 | − | 0.938857i | \(-0.388113\pi\) | ||||
0.344308 | + | 0.938857i | \(0.388113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.24621 | −0.406713 | −0.203357 | − | 0.979105i | \(-0.565185\pi\) | ||||
−0.203357 | + | 0.979105i | \(0.565185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.0540 | 1.80852 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.876894 | 0.0824913 | 0.0412456 | − | 0.999149i | \(-0.486867\pi\) | ||||
0.0412456 | + | 0.999149i | \(0.486867\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.12311 | −0.104730 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | −0.369800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −35.0540 | −3.21339 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −31.3693 | −2.82848 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.87689 | 0.432754 | 0.216377 | − | 0.976310i | \(-0.430576\pi\) | ||||
0.216377 | + | 0.976310i | \(0.430576\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | −0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.8078 | −1.46850 | −0.734251 | − | 0.678879i | \(-0.762466\pi\) | ||||
−0.734251 | + | 0.678879i | \(0.762466\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.56155 | 0.568959 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.43845 | −0.123802 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.12311 | −0.608568 | −0.304284 | − | 0.952581i | \(-0.598417\pi\) | ||||
−0.304284 | + | 0.952581i | \(0.598417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.1231 | −2.45261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.12311 | 0.0939188 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.56155 | −0.710998 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 35.3693 | 2.91721 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.68466 | 0.138013 | 0.0690063 | − | 0.997616i | \(-0.478017\pi\) | ||||
0.0690063 | + | 0.997616i | \(0.478017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.87689 | 0.559634 | 0.279817 | − | 0.960053i | \(-0.409726\pi\) | ||||
0.279817 | + | 0.960053i | \(0.409726\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.3693 | −2.21268 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.43845 | 0.115539 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.6847 | 1.73062 | 0.865312 | − | 0.501233i | \(-0.167120\pi\) | ||||
0.865312 | + | 0.501233i | \(0.167120\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.8078 | 1.96738 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.12311 | 0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.8078 | 1.62979 | 0.814895 | − | 0.579609i | \(-0.196795\pi\) | ||||
0.814895 | + | 0.579609i | \(0.196795\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.56155 | 0.199417 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.68466 | −0.130363 | −0.0651814 | − | 0.997873i | \(-0.520763\pi\) | ||||
−0.0651814 | + | 0.997873i | \(0.520763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7386 | −0.902972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.12311 | 0.391774 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8769 | 0.826955 | 0.413477 | − | 0.910514i | \(-0.364314\pi\) | ||||
0.413477 | + | 0.910514i | \(0.364314\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.56155 | 0.344821 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.87689 | 0.216241 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.2462 | 1.06481 | 0.532406 | − | 0.846489i | \(-0.321288\pi\) | ||||
0.532406 | + | 0.846489i | \(0.321288\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.24621 | −0.612936 | −0.306468 | − | 0.951881i | \(-0.599147\pi\) | ||||
−0.306468 | + | 0.951881i | \(0.599147\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −32.1771 | −2.37860 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.43845 | −0.546886 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.68466 | 0.561958 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.56155 | 0.477283 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.2462 | 0.741390 | 0.370695 | − | 0.928755i | \(-0.379120\pi\) | ||||
0.370695 | + | 0.928755i | \(0.379120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.4384 | −1.54317 | −0.771587 | − | 0.636124i | \(-0.780537\pi\) | ||||
−0.771587 | + | 0.636124i | \(0.780537\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.87689 | 0.206019 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.7386 | 1.62006 | 0.810030 | − | 0.586388i | \(-0.199451\pi\) | ||||
0.810030 | + | 0.586388i | \(0.199451\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.31534 | −0.305906 | −0.152953 | − | 0.988233i | \(-0.548878\pi\) | ||||
−0.152953 | + | 0.988233i | \(0.548878\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 39.0540 | 2.74105 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.2462 | 0.855312 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.00000 | 0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.43845 | −0.0994995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.6847 | 1.35515 | 0.677574 | − | 0.735455i | \(-0.263031\pi\) | ||||
0.677574 | + | 0.735455i | \(0.263031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.43845 | 0.646712 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.12311 | 0.212994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.56155 | −0.445427 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.87689 | 0.194403 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.63068 | 0.580563 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.1231 | 1.68237 | 0.841184 | − | 0.540749i | \(-0.181859\pi\) | ||||
0.841184 | + | 0.540749i | \(0.181859\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.24621 | 0.547320 | 0.273660 | − | 0.961826i | \(-0.411766\pi\) | ||||
0.273660 | + | 0.961826i | \(0.411766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.2462 | 1.07358 | 0.536790 | − | 0.843716i | \(-0.319637\pi\) | ||||
0.536790 | + | 0.843716i | \(0.319637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6847 | −0.768794 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.0540 | 1.77236 | 0.886182 | − | 0.463336i | \(-0.153348\pi\) | ||||
0.886182 | + | 0.463336i | \(0.153348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.3693 | 0.741652 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.1231 | −1.89175 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6155 | −1.39819 | −0.699096 | − | 0.715028i | \(-0.746414\pi\) | ||||
−0.699096 | + | 0.715028i | \(0.746414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.4924 | 1.19120 | 0.595601 | − | 0.803281i | \(-0.296914\pi\) | ||||
0.595601 | + | 0.803281i | \(0.296914\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2462 | −1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.8078 | −0.882146 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.61553 | −0.102794 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.3693 | −0.973991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.3693 | −1.72754 | −0.863768 | − | 0.503890i | \(-0.831902\pi\) | ||||
−0.863768 | + | 0.503890i | \(0.831902\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.12311 | −0.0706090 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.6847 | 1.23270 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.49242 | 0.404986 | 0.202493 | − | 0.979284i | \(-0.435096\pi\) | ||||
0.202493 | + | 0.979284i | \(0.435096\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 33.9309 | 2.10836 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.4924 | 1.88743 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.0540 | −1.79154 | −0.895772 | − | 0.444513i | \(-0.853377\pi\) | ||||
−0.895772 | + | 0.444513i | \(0.853377\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.68466 | −0.594924 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.8078 | 1.51821 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.876894 | 0.0534652 | 0.0267326 | − | 0.999643i | \(-0.491490\pi\) | ||||
0.0267326 | + | 0.999643i | \(0.491490\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.1231 | −0.794246 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.2462 | −1.33665 | −0.668323 | − | 0.743872i | \(-0.732987\pi\) | ||||
−0.668323 | + | 0.743872i | \(0.732987\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.12311 | −0.306712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.24621 | 0.491928 | 0.245964 | − | 0.969279i | \(-0.420896\pi\) | ||||
0.245964 | + | 0.969279i | \(0.420896\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | −0.356663 | −0.178331 | − | 0.983970i | \(-0.557070\pi\) | ||||
−0.178331 | + | 0.983970i | \(0.557070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.68466 | −0.218260 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −55.8617 | −3.29741 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.0540 | 2.47376 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4924 | −0.732319 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.1231 | 1.00034 | 0.500171 | − | 0.865927i | \(-0.333270\pi\) | ||||
0.500171 | + | 0.865927i | \(0.333270\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.12311 | −0.0653897 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.43845 | −0.0834672 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.26137 | −0.0729467 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.2462 | −0.821138 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.12311 | −0.294315 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.5616 | 0.719272 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0000 | 1.02731 | 0.513657 | − | 0.857996i | \(-0.328290\pi\) | ||||
0.513657 | + | 0.857996i | \(0.328290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.43845 | −0.535205 | −0.267603 | − | 0.963529i | \(-0.586231\pi\) | ||||
−0.267603 | + | 0.963529i | \(0.586231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.7386 | 1.39831 | 0.699155 | − | 0.714970i | \(-0.253560\pi\) | ||||
0.699155 | + | 0.714970i | \(0.253560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −16.2462 | −0.915370 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.31534 | 0.354705 | 0.177352 | − | 0.984147i | \(-0.443247\pi\) | ||||
0.177352 | + | 0.984147i | \(0.443247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.56155 | −0.479355 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.2462 | 1.01840 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.0540 | −0.615060 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.12311 | −0.0622987 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8769 | −0.601494 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −51.8617 | −2.85923 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7386 | −1.02997 | −0.514984 | − | 0.857200i | \(-0.672202\pi\) | ||||
−0.514984 | + | 0.857200i | \(0.672202\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.4924 | 1.45178 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.80776 | −0.261896 | −0.130948 | − | 0.991389i | \(-0.541802\pi\) | ||||
−0.130948 | + | 0.991389i | \(0.541802\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.24621 | 0.121997 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.43845 | 0.0778963 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 31.0540 | 1.67676 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.87689 | −0.154887 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0000 | −0.751559 | −0.375780 | − | 0.926709i | \(-0.622625\pi\) | ||||
−0.375780 | + | 0.926709i | \(0.622625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.4924 | 0.775762 | 0.387881 | − | 0.921710i | \(-0.373207\pi\) | ||||
0.387881 | + | 0.921710i | \(0.373207\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.61553 | −0.0862305 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0000 | 0.532246 | 0.266123 | − | 0.963939i | \(-0.414257\pi\) | ||||
0.266123 | + | 0.963939i | \(0.414257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.68466 | −0.195561 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −89.7926 | −4.75233 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.7386 | 0.988987 | 0.494494 | − | 0.869181i | \(-0.335354\pi\) | ||||
0.494494 | + | 0.869181i | \(0.335354\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9309 | −0.891098 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.56155 | 0.134447 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.12311 | −0.0587860 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4924 | 0.860897 | 0.430449 | − | 0.902615i | \(-0.358355\pi\) | ||||
0.430449 | + | 0.902615i | \(0.358355\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −43.6155 | −2.27053 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 44.1771 | 2.29356 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.3693 | 1.21002 | 0.605009 | − | 0.796219i | \(-0.293170\pi\) | ||||
0.605009 | + | 0.796219i | \(0.293170\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.56155 | −0.132278 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.61553 | −0.495225 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8769 | −0.764175 | −0.382087 | − | 0.924126i | \(-0.624795\pi\) | ||||
−0.382087 | + | 0.924126i | \(0.624795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.4924 | 0.640006 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.630683 | −0.0322264 | −0.0161132 | − | 0.999870i | \(-0.505129\pi\) | ||||
−0.0161132 | + | 0.999870i | \(0.505129\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.56155 | 0.232478 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.1231 | −0.565419 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.4924 | −0.734795 | −0.367397 | − | 0.930064i | \(-0.619751\pi\) | ||||
−0.367397 | + | 0.930064i | \(0.619751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.63068 | −0.436472 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −43.0540 | −2.17179 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.3693 | 0.572052 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 16.8078 | 0.841441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.8078 | 1.53847 | 0.769233 | − | 0.638968i | \(-0.220638\pi\) | ||||
0.769233 | + | 0.638968i | \(0.220638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.61553 | 0.0804752 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.00000 | 0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.43845 | −0.368710 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3693 | 0.858857 | 0.429429 | − | 0.903101i | \(-0.358715\pi\) | ||||
0.429429 | + | 0.903101i | \(0.358715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.2462 | −0.900019 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.12311 | 0.252092 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2462 | −0.501759 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.492423 | 0.0240564 | 0.0120282 | − | 0.999928i | \(-0.496171\pi\) | ||||
0.0120282 | + | 0.999928i | \(0.496171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6155 | 1.34590 | 0.672949 | − | 0.739689i | \(-0.265027\pi\) | ||||
0.672949 | + | 0.739689i | \(0.265027\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −40.4924 | −1.96881 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.68466 | −0.372761 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −57.3002 | −2.77295 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.87689 | 0.138898 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | 0.385346 | 0.192673 | − | 0.981263i | \(-0.438284\pi\) | ||||
0.192673 | + | 0.981263i | \(0.438284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.87689 | −0.234369 | −0.117184 | − | 0.993110i | \(-0.537387\pi\) | ||||
−0.117184 | + | 0.993110i | \(0.537387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.9309 | −1.05150 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.61553 | 0.0772812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2462 | 0.489025 | 0.244512 | − | 0.969646i | \(-0.421372\pi\) | ||||
0.244512 | + | 0.969646i | \(0.421372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 49.1771 | 2.34177 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.0000 | −0.570137 | −0.285069 | − | 0.958507i | \(-0.592016\pi\) | ||||
−0.285069 | + | 0.958507i | \(0.592016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.68466 | −0.459097 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.31534 | 0.204109 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.246211 | 0.0116194 | 0.00580971 | − | 0.999983i | \(-0.498151\pi\) | ||||
0.00580971 | + | 0.999983i | \(0.498151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2462 | 0.576652 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.6155 | 0.827650 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.12311 | 0.240175 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.68466 | 0.172361 | 0.0861805 | − | 0.996280i | \(-0.472534\pi\) | ||||
0.0861805 | + | 0.996280i | \(0.472534\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.0540 | −0.515955 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.0540 | −0.980581 | −0.490291 | − | 0.871559i | \(-0.663109\pi\) | ||||
−0.490291 | + | 0.871559i | \(0.663109\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.3693 | −1.27196 | −0.635980 | − | 0.771706i | \(-0.719404\pi\) | ||||
−0.635980 | + | 0.771706i | \(0.719404\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.68466 | 0.170872 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.8078 | 1.51816 | 0.759081 | − | 0.650996i | \(-0.225649\pi\) | ||||
0.759081 | + | 0.650996i | \(0.225649\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 55.5464 | 2.55944 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.12311 | 0.143601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.43845 | 0.0660005 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.4924 | 1.57930 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.2462 | 0.650926 | 0.325463 | − | 0.945555i | \(-0.394480\pi\) | ||||
0.325463 | + | 0.945555i | \(0.394480\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.35416 | −0.380917 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.1231 | 0.597122 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.87689 | 0.221448 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.2462 | −1.37059 | −0.685293 | − | 0.728267i | \(-0.740326\pi\) | ||||
−0.685293 | + | 0.728267i | \(0.740326\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 53.3002 | 2.41032 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.3153 | −0.736301 | −0.368151 | − | 0.929766i | \(-0.620009\pi\) | ||||
−0.368151 | + | 0.929766i | \(0.620009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −65.7926 | −2.96315 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.56155 | 0.160080 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16.8078 | 0.753931 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7386 | −0.838856 | −0.419428 | − | 0.907789i | \(-0.637769\pi\) | ||||
−0.419428 | + | 0.907789i | \(0.637769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.31534 | −0.192795 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.12311 | −0.139252 | −0.0696262 | − | 0.997573i | \(-0.522181\pi\) | ||||
−0.0696262 | + | 0.997573i | \(0.522181\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.00000 | 0.0889988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.0691 | −1.33542 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.384472 | −0.0170414 | −0.00852071 | − | 0.999964i | \(-0.502712\pi\) | ||||
−0.00852071 | + | 0.999964i | \(0.502712\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.12311 | 0.226633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.06913 | 0.0913543 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3693 | 0.500022 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.8617 | 1.22299 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.4924 | −1.33590 | −0.667949 | − | 0.744207i | \(-0.732827\pi\) | ||||
−0.667949 | + | 0.744207i | \(0.732827\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.8769 | 1.08779 | 0.543895 | − | 0.839153i | \(-0.316949\pi\) | ||||
0.543895 | + | 0.839153i | \(0.316949\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.6847 | 0.509960 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.0540 | 0.481519 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7386 | −0.945158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.7538 | 0.595743 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.12311 | −0.307959 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.4924 | 1.57476 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.8078 | −0.594743 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.93087 | −0.340975 | −0.170487 | − | 0.985360i | \(-0.554534\pi\) | ||||
−0.170487 | + | 0.985360i | \(0.554534\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.1231 | −0.906479 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.24621 | 0.181888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.6307 | −0.454535 | −0.227268 | − | 0.973832i | \(-0.572979\pi\) | ||||
−0.227268 | + | 0.973832i | \(0.572979\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −44.7386 | −1.90940 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3153 | 0.524651 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −51.8617 | −2.20539 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.0540 | −0.808796 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.6307 | 0.704665 | 0.352332 | − | 0.935875i | \(-0.385389\pi\) | ||||
0.352332 | + | 0.935875i | \(0.385389\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.50758 | 0.148355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19.6847 | 0.831087 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −42.9848 | −1.81160 | −0.905798 | − | 0.423711i | \(-0.860727\pi\) | ||||
−0.905798 | + | 0.423711i | \(0.860727\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.876894 | −0.0368912 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31.9309 | −1.34097 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.61553 | 0.151571 | 0.0757854 | − | 0.997124i | \(-0.475854\pi\) | ||||
0.0757854 | + | 0.997124i | \(0.475854\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.3002 | 1.05878 | 0.529390 | − | 0.848379i | \(-0.322421\pi\) | ||||
0.529390 | + | 0.848379i | \(0.322421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.2462 | 1.09645 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.12311 | 0.0468367 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.7538 | −0.655839 | −0.327919 | − | 0.944706i | \(-0.606347\pi\) | ||||
−0.327919 | + | 0.944706i | \(0.606347\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −54.9157 | −2.28222 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.3693 | −1.13547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.68466 | −0.401098 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.00000 | 0.165380 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.05398 | −0.126051 | −0.0630255 | − | 0.998012i | \(-0.520075\pi\) | ||||
−0.0630255 | + | 0.998012i | \(0.520075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.06913 | −0.0852570 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 58.2462 | 2.39593 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.6155 | 0.887643 | 0.443822 | − | 0.896115i | \(-0.353622\pi\) | ||||
0.443822 | + | 0.896115i | \(0.353622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 35.0540 | 1.43707 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.0540 | −0.452409 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.9309 | −1.22294 | −0.611471 | − | 0.791267i | \(-0.709422\pi\) | ||||
−0.611471 | + | 0.791267i | \(0.709422\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.9848 | −1.10073 | −0.550367 | − | 0.834923i | \(-0.685512\pi\) | ||||
−0.550367 | + | 0.834923i | \(0.685512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.8078 | −0.601029 | −0.300514 | − | 0.953777i | \(-0.597158\pi\) | ||||
−0.300514 | + | 0.953777i | \(0.597158\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 100.039 | 4.05378 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.7689 | 0.516576 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.87689 | −0.116197 | −0.0580983 | − | 0.998311i | \(-0.518504\pi\) | ||||
−0.0580983 | + | 0.998311i | \(0.518504\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.3693 | 1.26493 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.6155 | −1.11176 | −0.555880 | − | 0.831263i | \(-0.687618\pi\) | ||||
−0.555880 | + | 0.831263i | \(0.687618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.7386 | −1.39626 | −0.698132 | − | 0.715969i | \(-0.745985\pi\) | ||||
−0.698132 | + | 0.715969i | \(0.745985\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.61553 | 0.0648289 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.1771 | 1.76992 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.68466 | −0.147151 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −57.1619 | −2.27920 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.8078 | −1.30606 | −0.653028 | − | 0.757334i | \(-0.726502\pi\) | ||||
−0.653028 | + | 0.757334i | \(0.726502\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 50.4233 | 2.00415 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.87689 | −0.193534 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.5076 | −0.614433 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1231 | 0.519142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.5616 | 0.812133 | 0.406066 | − | 0.913844i | \(-0.366900\pi\) | ||||
0.406066 | + | 0.913844i | \(0.366900\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.3002 | 0.997742 | 0.498871 | − | 0.866676i | \(-0.333748\pi\) | ||||
0.498871 | + | 0.866676i | \(0.333748\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.00000 | 0.315000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.1231 | 1.77397 | 0.886986 | − | 0.461796i | \(-0.152795\pi\) | ||||
0.886986 | + | 0.461796i | \(0.152795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.12311 | −0.0440858 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.8078 | −0.658748 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.5616 | 1.11770 | 0.558850 | − | 0.829269i | \(-0.311243\pi\) | ||||
0.558850 | + | 0.829269i | \(0.311243\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.8078 | 0.656734 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.9309 | −1.32176 | −0.660880 | − | 0.750492i | \(-0.729817\pi\) | ||||
−0.660880 | + | 0.750492i | \(0.729817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.49242 | 0.0969440 | 0.0484720 | − | 0.998825i | \(-0.484565\pi\) | ||||
0.0484720 | + | 0.998825i | \(0.484565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.1080 | 0.858602 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.56155 | −0.254446 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.61553 | 0.372315 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 64.3542 | 2.48808 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.5616 | 0.484933 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −41.9309 | −1.61632 | −0.808158 | − | 0.588966i | \(-0.799535\pi\) | ||||
−0.808158 | + | 0.588966i | \(0.799535\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.43845 | 0.0553659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 46.2462 | 1.77739 | 0.888693 | − | 0.458502i | \(-0.151614\pi\) | ||||
0.888693 | + | 0.458502i | \(0.151614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.2462 | −0.853731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.1231 | 0.809439 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 40.1771 | 1.53733 | 0.768667 | − | 0.639650i | \(-0.220921\pi\) | ||||
0.768667 | + | 0.639650i | \(0.220921\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.12311 | 0.272160 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.6155 | 1.58773 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.8769 | −0.414377 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.61553 | 0.213625 | 0.106812 | − | 0.994279i | \(-0.465936\pi\) | ||||
0.106812 | + | 0.994279i | \(0.465936\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.2462 | −0.617143 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 94.1080 | 3.56459 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 69.3002 | 2.62117 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.5616 | −0.776599 | −0.388300 | − | 0.921533i | \(-0.626937\pi\) | ||||
−0.388300 | + | 0.921533i | \(0.626937\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6998 | 0.403551 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 29.1231 | 1.09684 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.12311 | −0.343110 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.2462 | −1.21103 | −0.605516 | − | 0.795833i | \(-0.707033\pi\) | ||||
−0.605516 | + | 0.795833i | \(0.707033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.4924 | −1.51858 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.61553 | −0.0605020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.12311 | −0.0420018 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −55.3693 | −2.06781 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −48.1771 | −1.79670 | −0.898351 | − | 0.439278i | \(-0.855234\pi\) | ||||
−0.898351 | + | 0.439278i | \(0.855234\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.3693 | 1.76168 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.56155 | 0.317968 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.8769 | −0.403402 | −0.201701 | − | 0.979447i | \(-0.564647\pi\) | ||||
−0.201701 | + | 0.979447i | \(0.564647\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000 | 0.887672 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.7538 | −0.508008 | −0.254004 | − | 0.967203i | \(-0.581748\pi\) | ||||
−0.254004 | + | 0.967203i | \(0.581748\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −35.3693 | −1.30462 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.2462 | 0.818340 | 0.409170 | − | 0.912458i | \(-0.365818\pi\) | ||||
0.409170 | + | 0.912458i | \(0.365818\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.13826 | −0.152023 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.5616 | 0.754330 | 0.377165 | − | 0.926146i | \(-0.376899\pi\) | ||||
0.377165 | + | 0.926146i | \(0.376899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.68466 | −0.0617211 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.3693 | −0.781862 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32.4924 | 1.18725 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.1922 | −1.13822 | −0.569110 | − | 0.822261i | \(-0.692712\pi\) | ||||
−0.569110 | + | 0.822261i | \(0.692712\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −70.1080 | −2.55488 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.87689 | −0.250276 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.87689 | −0.104425 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.75379 | 0.281075 | 0.140537 | − | 0.990075i | \(-0.455117\pi\) | ||||
0.140537 | + | 0.990075i | \(0.455117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.3693 | −0.701216 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 27.3693 | 0.989540 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.26137 | −0.0455453 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.75379 | 0.135365 | 0.0676825 | − | 0.997707i | \(-0.478439\pi\) | ||||
0.0676825 | + | 0.997707i | \(0.478439\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6307 | 0.598939 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 43.9309 | 1.58008 | 0.790042 | − | 0.613053i | \(-0.210059\pi\) | ||||
0.790042 | + | 0.613053i | \(0.210059\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.43845 | −0.0516705 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 86.9157 | 3.11808 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.6155 | −0.631142 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.68466 | −0.131847 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 12.3153 | 0.440114 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.6847 | −0.773959 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.8617 | −0.636702 | −0.318351 | − | 0.947973i | \(-0.603129\pi\) | ||||
−0.318351 | + | 0.947973i | \(0.603129\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −74.4233 | −2.64954 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.00000 | 0.142224 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.1080 | 0.500988 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.8078 | −0.879841 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.2462 | 0.717158 | 0.358579 | − | 0.933499i | \(-0.383261\pi\) | ||||
0.358579 | + | 0.933499i | \(0.383261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87.3693 | 3.09090 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.4924 | 1.21873 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.12311 | −0.0396335 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.12311 | −0.180566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.24621 | 0.0790704 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −40.7386 | −1.43229 | −0.716147 | − | 0.697949i | \(-0.754096\pi\) | ||||
−0.716147 | + | 0.697949i | \(0.754096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.93087 | −0.0678020 | −0.0339010 | − | 0.999425i | \(-0.510793\pi\) | ||||
−0.0339010 | + | 0.999425i | \(0.510793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.2462 | −0.359350 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.8078 | −0.728864 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.49242 | −0.157170 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.2462 | −0.637574 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4924 | 0.505789 | 0.252895 | − | 0.967494i | \(-0.418617\pi\) | ||||
0.252895 | + | 0.967494i | \(0.418617\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.4924 | 0.435458 | 0.217729 | − | 0.976009i | \(-0.430135\pi\) | ||||
0.217729 | + | 0.976009i | \(0.430135\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.56155 | −0.0891818 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.8617 | 1.03839 | 0.519197 | − | 0.854654i | \(-0.326231\pi\) | ||||
0.519197 | + | 0.854654i | \(0.326231\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.8769 | −1.14186 | −0.570931 | − | 0.820998i | \(-0.693418\pi\) | ||||
−0.570931 | + | 0.820998i | \(0.693418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −56.9848 | −1.97678 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −106.108 | −3.67642 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.68466 | 0.0583000 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.06913 | −0.0715196 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.5076 | 0.673476 | 0.336738 | − | 0.941598i | \(-0.390676\pi\) | ||||
0.336738 | + | 0.941598i | \(0.390676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.3002 | 1.52759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.1231 | 0.727518 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.7386 | 0.403821 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.56155 | 0.156737 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.3693 | −0.527474 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.35416 | 0.286377 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.1231 | −1.27107 | −0.635535 | − | 0.772072i | \(-0.719221\pi\) | ||||
−0.635535 | + | 0.772072i | \(0.719221\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.12311 | −0.175207 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.8078 | 0.437505 | 0.218752 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218752 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.8617 | 0.814152 | 0.407076 | − | 0.913394i | \(-0.366548\pi\) | ||||
0.407076 | + | 0.913394i | \(0.366548\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −143.093 | −4.87659 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.1231 | 0.991362 | 0.495681 | − | 0.868505i | \(-0.334919\pi\) | ||||
0.495681 | + | 0.868505i | \(0.334919\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.8769 | −0.369826 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 107.723 | 3.65848 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.3693 | 0.385678 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.3693 | −0.587862 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.56155 | −0.154209 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6155 | −0.864975 | −0.432487 | − | 0.901640i | \(-0.642364\pi\) | ||||
−0.432487 | + | 0.901640i | \(0.642364\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 43.8617 | 1.47942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.50758 | 0.185555 | 0.0927775 | − | 0.995687i | \(-0.470425\pi\) | ||||
0.0927775 | + | 0.995687i | \(0.470425\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −27.5464 | −0.927010 | −0.463505 | − | 0.886094i | \(-0.653408\pi\) | ||||
−0.463505 | + | 0.886094i | \(0.653408\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.87689 | −0.0967057 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.1231 | −0.910705 | −0.455352 | − | 0.890311i | \(-0.650487\pi\) | ||||
−0.455352 | + | 0.890311i | \(0.650487\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.2462 | 0.746114 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.00000 | 0.234509 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −16.3542 | −0.547271 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2462 | −0.476198 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.23106 | −0.107882 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.3153 | −0.410740 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −74.4233 | −2.47940 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.4924 | −1.21439 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.24621 | 0.274113 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43.6847 | −1.45053 | −0.725263 | − | 0.688472i | \(-0.758282\pi\) | ||||
−0.725263 | + | 0.688472i | \(0.758282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.12311 | −0.236259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.4384 | 1.37292 | 0.686459 | − | 0.727169i | \(-0.259164\pi\) | ||||
0.686459 | + | 0.727169i | \(0.259164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.1771 | 1.06374 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −76.6695 | −2.53185 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.2311 | −1.16217 | −0.581083 | − | 0.813845i | \(-0.697371\pi\) | ||||
−0.581083 | + | 0.813845i | \(0.697371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 46.1080 | 1.51931 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.13826 | −0.136213 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.43845 | 0.244575 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33.5464 | 1.10062 | 0.550311 | − | 0.834960i | \(-0.314509\pi\) | ||||
0.550311 | + | 0.834960i | \(0.314509\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.8617 | 0.650942 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.1771 | −0.791522 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.68466 | −0.251315 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.6155 | −1.62087 | −0.810434 | − | 0.585829i | \(-0.800769\pi\) | ||||
−0.810434 | + | 0.585829i | \(0.800769\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 63.3693 | 2.06798 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.05398 | 0.295151 | 0.147576 | − | 0.989051i | \(-0.452853\pi\) | ||||
0.147576 | + | 0.989051i | \(0.452853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.7538 | −0.447885 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.56155 | −0.213447 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.9460 | 0.420689 | 0.210345 | − | 0.977627i | \(-0.432541\pi\) | ||||
0.210345 | + | 0.977627i | \(0.432541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.26137 | −0.0409457 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.1771 | 0.524578 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.56155 | −0.212550 | −0.106275 | − | 0.994337i | \(-0.533892\pi\) | ||||
−0.106275 | + | 0.994337i | \(0.533892\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.2462 | −0.331560 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −21.9309 | −0.708924 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.4924 | −1.04924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9309 | −0.933254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.3693 | 0.817515 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.4384 | 0.690128 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.5616 | −0.403952 | −0.201976 | − | 0.979390i | \(-0.564736\pi\) | ||||
−0.201976 | + | 0.979390i | \(0.564736\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.3153 | −0.909620 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.0000 | −0.898563 | −0.449281 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449281 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.2462 | −0.584947 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.87689 | −0.0921344 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.8617 | −0.699419 | −0.349710 | − | 0.936858i | \(-0.613720\pi\) | ||||
−0.349710 | + | 0.936858i | \(0.613720\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.68466 | −0.309523 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.1231 | −0.482844 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.6307 | −0.530436 | −0.265218 | − | 0.964188i | \(-0.585444\pi\) | ||||
−0.265218 | + | 0.964188i | \(0.585444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.7386 | −0.724513 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −132.847 | −4.22855 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.50758 | −0.111534 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.0000 | −1.52323 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.31534 | 0.136806 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.26137 | 0.0399479 | 0.0199739 | − | 0.999801i | \(-0.493642\pi\) | ||||
0.0199739 | + | 0.999801i | \(0.493642\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.6998 | 0.338527 |
(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 | 440.2.a.g.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3960.2.a.bf.1.2 | 2 | |||
4.3 | odd | 2 | 880.2.a.k.1.1 | 2 | |||
5.2 | odd | 4 | 2200.2.b.f.1849.1 | 4 | |||
5.3 | odd | 4 | 2200.2.b.f.1849.4 | 4 | |||
5.4 | even | 2 | 2200.2.a.l.1.1 | 2 | |||
8.3 | odd | 2 | 3520.2.a.br.1.2 | 2 | |||
8.5 | even | 2 | 3520.2.a.bm.1.1 | 2 | |||
11.10 | odd | 2 | 4840.2.a.m.1.2 | 2 | |||
12.11 | even | 2 | 7920.2.a.by.1.1 | 2 | |||
20.3 | even | 4 | 4400.2.b.w.4049.1 | 4 | |||
20.7 | even | 4 | 4400.2.b.w.4049.4 | 4 | |||
20.19 | odd | 2 | 4400.2.a.bt.1.2 | 2 | |||
44.43 | even | 2 | 9680.2.a.bm.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.a.g.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
880.2.a.k.1.1 | 2 | 4.3 | odd | 2 | |||
2200.2.a.l.1.1 | 2 | 5.4 | even | 2 | |||
2200.2.b.f.1849.1 | 4 | 5.2 | odd | 4 | |||
2200.2.b.f.1849.4 | 4 | 5.3 | odd | 4 | |||
3520.2.a.bm.1.1 | 2 | 8.5 | even | 2 | |||
3520.2.a.br.1.2 | 2 | 8.3 | odd | 2 | |||
3960.2.a.bf.1.2 | 2 | 3.2 | odd | 2 | |||
4400.2.a.bt.1.2 | 2 | 20.19 | odd | 2 | |||
4400.2.b.w.4049.1 | 4 | 20.3 | even | 4 | |||
4400.2.b.w.4049.4 | 4 | 20.7 | even | 4 | |||
4840.2.a.m.1.2 | 2 | 11.10 | odd | 2 | |||
7920.2.a.by.1.1 | 2 | 12.11 | even | 2 | |||
9680.2.a.bm.1.1 | 2 | 44.43 | even | 2 |