Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,4,Mod(1,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.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: | \(9.44030560092\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.1 |
$q$-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 | ||||||||
\(3\) | 4.47214 | 0.860663 | 0.430331 | − | 0.902671i | \(-0.358397\pi\) | ||||
0.430331 | + | 0.902671i | \(0.358397\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.3050 | −1.69031 | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.00000 | −0.259259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.94427 | −0.245164 | −0.122582 | − | 0.992458i | \(-0.539117\pi\) | ||||
−0.122582 | + | 0.992458i | \(0.539117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −62.0000 | −1.32275 | −0.661373 | − | 0.750057i | \(-0.730026\pi\) | ||||
−0.661373 | + | 0.750057i | \(0.730026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −22.3607 | −0.384900 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −46.0000 | −0.656273 | −0.328136 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328136 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 107.331 | 1.29597 | 0.647986 | − | 0.761652i | \(-0.275611\pi\) | ||||
0.647986 | + | 0.761652i | \(0.275611\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −140.000 | −1.45479 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 192.302 | 1.74338 | 0.871689 | − | 0.490059i | \(-0.163025\pi\) | ||||
0.871689 | + | 0.490059i | \(0.163025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −152.053 | −1.08380 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −90.0000 | −0.576296 | −0.288148 | − | 0.957586i | \(-0.593039\pi\) | ||||
−0.288148 | + | 0.957586i | \(0.593039\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −152.053 | −0.880950 | −0.440475 | − | 0.897765i | \(-0.645190\pi\) | ||||
−0.440475 | + | 0.897765i | \(0.645190\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −40.0000 | −0.211003 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 156.525 | 0.755929 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −214.000 | −0.950848 | −0.475424 | − | 0.879757i | \(-0.657705\pi\) | ||||
−0.475424 | + | 0.879757i | \(0.657705\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −277.272 | −1.13844 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −0.0380912 | −0.0190456 | − | 0.999819i | \(-0.506063\pi\) | ||||
−0.0190456 | + | 0.999819i | \(0.506063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −67.0820 | −0.237905 | −0.118953 | − | 0.992900i | \(-0.537954\pi\) | ||||
−0.118953 | + | 0.992900i | \(0.537954\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 35.0000 | 0.115944 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 398.020 | 1.23526 | 0.617630 | − | 0.786469i | \(-0.288093\pi\) | ||||
0.617630 | + | 0.786469i | \(0.288093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 637.000 | 1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −205.718 | −0.564830 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −678.000 | −1.75718 | −0.878589 | − | 0.477578i | \(-0.841515\pi\) | ||||
−0.878589 | + | 0.477578i | \(0.841515\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 44.7214 | 0.109640 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 480.000 | 1.11540 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −411.437 | −0.907872 | −0.453936 | − | 0.891034i | \(-0.649981\pi\) | ||||
−0.453936 | + | 0.891034i | \(0.649981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 250.000 | 0.524741 | 0.262371 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262371 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 219.135 | 0.438228 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 310.000 | 0.591550 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49.1935 | 0.0897006 | 0.0448503 | − | 0.998994i | \(-0.485719\pi\) | ||||
0.0448503 | + | 0.998994i | \(0.485719\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 860.000 | 1.50046 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −366.715 | −0.612973 | −0.306486 | − | 0.951875i | \(-0.599153\pi\) | ||||
−0.306486 | + | 0.951875i | \(0.599153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 522.000 | 0.836924 | 0.418462 | − | 0.908234i | \(-0.362569\pi\) | ||||
0.418462 | + | 0.908234i | \(0.362569\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 111.803 | 0.172133 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 280.000 | 0.414402 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 876.539 | 1.24833 | 0.624166 | − | 0.781291i | \(-0.285439\pi\) | ||||
0.624166 | + | 0.781291i | \(0.285439\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −491.000 | −0.673525 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 380.132 | 0.502709 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 230.000 | 0.293494 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −402.492 | −0.495997 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 970.000 | 1.15528 | 0.577639 | − | 0.816292i | \(-0.303974\pi\) | ||||
0.577639 | + | 0.816292i | \(0.303974\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1940.91 | 2.23585 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −680.000 | −0.758201 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −536.656 | −0.579577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −934.000 | −0.977663 | −0.488832 | − | 0.872378i | \(-0.662577\pi\) | ||||
−0.488832 | + | 0.872378i | \(0.662577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 62.6099 | 0.0635609 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −602.000 | −0.593082 | −0.296541 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296541 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1829.10 | −1.74978 | −0.874888 | − | 0.484325i | \(-0.839065\pi\) | ||||
−0.874888 | + | 0.484325i | \(0.839065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 700.000 | 0.650600 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1525.00 | −1.37782 | −0.688912 | − | 0.724845i | \(-0.741911\pi\) | ||||
−0.688912 | + | 0.724845i | \(0.741911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2154.00 | 1.89281 | 0.946403 | − | 0.322989i | \(-0.104688\pi\) | ||||
0.946403 | + | 0.322989i | \(0.104688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −957.037 | −0.818360 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2182.00 | −1.81651 | −0.908254 | − | 0.418420i | \(-0.862584\pi\) | ||||
−0.908254 | + | 0.418420i | \(0.862584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −961.509 | −0.779663 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 434.000 | 0.342934 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1440.03 | 1.10930 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1251.00 | −0.939895 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −44.7214 | −0.0327837 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1310.34 | 0.915539 | 0.457770 | − | 0.889071i | \(-0.348648\pi\) | ||||
0.457770 | + | 0.889071i | \(0.348648\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −300.000 | −0.204756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −205.718 | −0.137204 | −0.0686019 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686019 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3360.00 | −2.19059 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 760.263 | 0.484689 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2094.00 | −1.30586 | −0.652929 | − | 0.757419i | \(-0.726460\pi\) | ||||
−0.652929 | + | 0.757419i | \(0.726460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1377.42 | −0.840511 | −0.420256 | − | 0.907406i | \(-0.638060\pi\) | ||||
−0.420256 | + | 0.907406i | \(0.638060\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1780.00 | 1.06314 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 554.545 | 0.324289 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 450.000 | 0.257727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2848.75 | 1.59837 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −334.000 | −0.183640 | −0.0918200 | − | 0.995776i | \(-0.529268\pi\) | ||||
−0.0918200 | + | 0.995776i | \(0.529268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3139.44 | 1.69195 | 0.845973 | − | 0.533225i | \(-0.179020\pi\) | ||||
0.845973 | + | 0.533225i | \(0.179020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 322.000 | 0.170145 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 760.263 | 0.393973 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 834.000 | 0.423952 | 0.211976 | − | 0.977275i | \(-0.432010\pi\) | ||||
0.211976 | + | 0.977275i | \(0.432010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3032.11 | −1.51234 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6020.00 | −2.94685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3090.25 | −1.48495 | −0.742475 | − | 0.669874i | \(-0.766348\pi\) | ||||
−0.742475 | + | 0.669874i | \(0.766348\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 200.000 | 0.0943635 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.47214 | 0.00207224 | 0.00103612 | − | 0.999999i | \(-0.499670\pi\) | ||||
0.00103612 | + | 0.999999i | \(0.499670\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1647.00 | 0.749659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −751.319 | −0.335993 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1838.00 | −0.807749 | −0.403874 | − | 0.914814i | \(-0.632337\pi\) | ||||
−0.403874 | + | 0.914814i | \(0.632337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −782.624 | −0.338062 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1840.00 | −0.781372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1842.52 | 0.769365 | 0.384683 | − | 0.923049i | \(-0.374311\pi\) | ||||
0.384683 | + | 0.923049i | \(0.374311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1862.00 | 0.764648 | 0.382324 | − | 0.924028i | \(-0.375124\pi\) | ||||
0.382324 | + | 0.924028i | \(0.375124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1118.03 | 0.451625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1070.00 | 0.425232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 411.437 | 0.160894 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4760.00 | 1.83195 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2066.13 | −0.782721 | −0.391360 | − | 0.920237i | \(-0.627995\pi\) | ||||
−0.391360 | + | 0.920237i | \(0.627995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3378.00 | 1.25986 | 0.629932 | − | 0.776650i | \(-0.283083\pi\) | ||||
0.629932 | + | 0.776650i | \(0.283083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1386.36 | 0.509125 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 66.0000 | 0.0238696 | 0.0119348 | − | 0.999929i | \(-0.496201\pi\) | ||||
0.0119348 | + | 0.999929i | \(0.496201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1216.42 | −0.433316 | −0.216658 | − | 0.976248i | \(-0.569516\pi\) | ||||
−0.216658 | + | 0.976248i | \(0.569516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 220.000 | 0.0772020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2817.45 | 0.974118 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 50.0000 | 0.0170349 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1346.11 | −0.451987 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −960.000 | −0.317725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5286.06 | −1.72468 | −0.862341 | − | 0.506329i | \(-0.831002\pi\) | ||||
−0.862341 | + | 0.506329i | \(0.831002\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1640.00 | −0.527563 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 335.410 | 0.106394 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4760.00 | 1.48908 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2334.45 | 0.720310 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2852.00 | 0.868083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2965.03 | 0.890371 | 0.445186 | − | 0.895438i | \(-0.353138\pi\) | ||||
0.445186 | + | 0.895438i | \(0.353138\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −175.000 | −0.0518519 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4369.28 | −1.27753 | −0.638765 | − | 0.769402i | \(-0.720554\pi\) | ||||
−0.638765 | + | 0.769402i | \(0.720554\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3250.00 | −0.937843 | −0.468921 | − | 0.883240i | \(-0.655357\pi\) | ||||
−0.468921 | + | 0.883240i | \(0.655357\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1252.20 | 0.356661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3298.00 | 0.927293 | 0.463646 | − | 0.886020i | \(-0.346541\pi\) | ||||
0.463646 | + | 0.886020i | \(0.346541\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1990.10 | −0.552425 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3920.00 | 1.07439 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −554.545 | −0.150086 | −0.0750429 | − | 0.997180i | \(-0.523909\pi\) | ||||
−0.0750429 | + | 0.997180i | \(0.523909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5150.00 | 1.37652 | 0.688259 | − | 0.725465i | \(-0.258375\pi\) | ||||
0.688259 | + | 0.725465i | \(0.258375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1909.60 | 0.504119 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3185.00 | −0.830540 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6654.54 | −1.71424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1700.00 | 0.432663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1386.36 | 0.348631 | 0.174316 | − | 0.984690i | \(-0.444229\pi\) | ||||
0.174316 | + | 0.984690i | \(0.444229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1720.00 | −0.427413 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1028.59 | 0.252600 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4166.00 | −1.01116 | −0.505580 | − | 0.862780i | \(-0.668721\pi\) | ||||
−0.505580 | + | 0.862780i | \(0.668721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6699.26 | 1.60723 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 630.000 | 0.149410 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 961.509 | 0.225434 | 0.112717 | − | 0.993627i | \(-0.464045\pi\) | ||||
0.112717 | + | 0.993627i | \(0.464045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3390.00 | 0.785834 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4337.97 | 0.994305 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1494.00 | −0.338627 | −0.169314 | − | 0.985562i | \(-0.554155\pi\) | ||||
−0.169314 | + | 0.985562i | \(0.554155\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5017.74 | 1.12474 | 0.562372 | − | 0.826884i | \(-0.309889\pi\) | ||||
0.562372 | + | 0.826884i | \(0.309889\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8680.00 | 1.92431 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −223.607 | −0.0490327 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1006.00 | −0.218212 | −0.109106 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109106 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1064.37 | 0.228395 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3210.00 | −0.681468 | −0.340734 | − | 0.940160i | \(-0.610676\pi\) | ||||
−0.340734 | + | 0.940160i | \(0.610676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3635.85 | 0.763705 | 0.381853 | − | 0.924223i | \(-0.375286\pi\) | ||||
0.381853 | + | 0.924223i | \(0.375286\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2400.00 | −0.498820 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 313.050 | 0.0643858 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2797.00 | −0.569306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4176.97 | −0.841439 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3622.00 | −0.722183 | −0.361091 | − | 0.932530i | \(-0.617596\pi\) | ||||
−0.361091 | + | 0.932530i | \(0.617596\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2057.18 | 0.406013 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1360.00 | 0.265708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11922.7 | −2.30605 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2100.00 | 0.402133 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2692.23 | −0.510443 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1250.00 | −0.234671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2088.49 | 0.388261 | 0.194131 | − | 0.980976i | \(-0.437811\pi\) | ||||
0.194131 | + | 0.980976i | \(0.437811\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8180.00 | −1.50597 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8899.55 | −1.62266 | −0.811330 | − | 0.584589i | \(-0.801256\pi\) | ||||
−0.811330 | + | 0.584589i | \(0.801256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8778.00 | 1.58518 | 0.792591 | − | 0.609754i | \(-0.208732\pi\) | ||||
0.792591 | + | 0.609754i | \(0.208732\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1095.67 | −0.195982 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5046.00 | −0.894043 | −0.447021 | − | 0.894523i | \(-0.647515\pi\) | ||||
−0.447021 | + | 0.894523i | \(0.647515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 804.984 | 0.141287 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6820.00 | −1.18584 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4937.24 | −0.850512 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1550.00 | −0.264549 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9632.98 | 1.62907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12460.0 | −2.08797 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −313.050 | −0.0519842 | −0.0259921 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259921 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1498.00 | 0.246516 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −245.967 | −0.0401153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2574.00 | −0.416067 | −0.208034 | − | 0.978122i | \(-0.566706\pi\) | ||||
−0.208034 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9758.20 | −1.56340 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1360.00 | 0.215977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9203.66 | −1.44884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4300.00 | −0.671027 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2643.03 | 0.408892 | 0.204446 | − | 0.978878i | \(-0.434461\pi\) | ||||
0.204446 | + | 0.978878i | \(0.434461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10170.0 | −1.55985 | −0.779925 | − | 0.625873i | \(-0.784743\pi\) | ||||
−0.779925 | + | 0.625873i | \(0.784743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9427.26 | 1.43359 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −318.000 | −0.0479474 | −0.0239737 | − | 0.999713i | \(-0.507632\pi\) | ||||
−0.0239737 | + | 0.999713i | \(0.507632\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1833.58 | 0.274130 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6440.00 | 0.954737 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12378.9 | 1.81987 | 0.909933 | − | 0.414755i | \(-0.136133\pi\) | ||||
0.909933 | + | 0.414755i | \(0.136133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4661.00 | 0.679545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5594.64 | −0.808933 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2610.00 | −0.374284 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3072.36 | −0.436991 | −0.218496 | − | 0.975838i | \(-0.570115\pi\) | ||||
−0.218496 | + | 0.975838i | \(0.570115\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 70.0000 | 0.00987549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21224.8 | 2.97017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3278.00 | −0.455036 | −0.227518 | − | 0.973774i | \(-0.573061\pi\) | ||||
−0.227518 | + | 0.973774i | \(0.573061\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −559.017 | −0.0769800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5580.00 | 0.762293 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5116.12 | 0.693397 | 0.346699 | − | 0.937977i | \(-0.387303\pi\) | ||||
0.346699 | + | 0.937977i | \(0.387303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5860.00 | 0.787971 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1149.34 | −0.153338 | −0.0766690 | − | 0.997057i | \(-0.524428\pi\) | ||||
−0.0766690 | + | 0.997057i | \(0.524428\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1400.00 | −0.185326 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 469.574 | 0.0616791 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 834.000 | 0.108703 | 0.0543515 | − | 0.998522i | \(-0.482691\pi\) | ||||
0.0543515 | + | 0.998522i | \(0.482691\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8845.88 | −1.14413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −920.000 | −0.118086 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4382.69 | −0.558271 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8734.00 | −1.10415 | −0.552074 | − | 0.833795i | \(-0.686163\pi\) | ||||
−0.552074 | + | 0.833795i | \(0.686163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15026.4 | −1.88536 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 242.000 | 0.0301369 | 0.0150685 | − | 0.999886i | \(-0.495203\pi\) | ||||
0.0150685 | + | 0.999886i | \(0.495203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9427.26 | 1.16527 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2455.00 | 0.301210 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1914.07 | 0.233113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6514.00 | −0.787522 | −0.393761 | − | 0.919213i | \(-0.628826\pi\) | ||||
−0.393761 | + | 0.919213i | \(0.628826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9364.65 | −1.12390 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12880.0 | 1.53458 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1900.66 | −0.224818 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6160.00 | −0.723397 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16081.8 | 1.87505 | 0.937527 | − | 0.347913i | \(-0.113110\pi\) | ||||
0.937527 | + | 0.347913i | \(0.113110\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7250.00 | 0.839295 | 0.419648 | − | 0.907687i | \(-0.362154\pi\) | ||||
0.419648 | + | 0.907687i | \(0.362154\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2786.14 | −0.320252 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1150.00 | −0.131255 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7826.24 | −0.886975 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2480.00 | 0.279104 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4981.96 | 0.556781 | 0.278390 | − | 0.960468i | \(-0.410199\pi\) | ||||
0.278390 | + | 0.960468i | \(0.410199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11482.0 | 1.27434 | 0.637171 | − | 0.770723i | \(-0.280105\pi\) | ||||
0.637171 | + | 0.770723i | \(0.280105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2012.46 | 0.221816 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20640.0 | 2.25937 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3792.37 | 0.412301 | 0.206150 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206150 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4459.00 | −0.481481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −746.847 | −0.0800988 | −0.0400494 | − | 0.999198i | \(-0.512752\pi\) | ||||
−0.0400494 | + | 0.999198i | \(0.512752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4850.00 | −0.516656 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1493.69 | −0.158052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1306.00 | −0.137269 | −0.0686347 | − | 0.997642i | \(-0.521864\pi\) | ||||
−0.0686347 | + | 0.997642i | \(0.521864\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 89.4427 | 0.00933857 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14040.0 | 1.45620 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9704.54 | −0.999902 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9526.00 | −0.975071 | −0.487536 | − | 0.873103i | \(-0.662104\pi\) | ||||
−0.487536 | + | 0.873103i | \(0.662104\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6994.42 | 0.711267 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1518.00 | 0.153363 | 0.0766815 | − | 0.997056i | \(-0.475568\pi\) | ||||
0.0766815 | + | 0.997056i | \(0.475568\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17293.7 | 1.73587 | 0.867936 | − | 0.496676i | \(-0.165446\pi\) | ||||
0.867936 | + | 0.496676i | \(0.165446\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3400.00 | 0.339078 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16980.7 | −1.68260 | −0.841299 | − | 0.540570i | \(-0.818208\pi\) | ||||
−0.841299 | + | 0.540570i | \(0.818208\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1540.00 | −0.151622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3729.76 | 0.364880 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 600.000 | 0.0583256 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2683.28 | 0.259195 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4746.00 | 0.455565 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3810.26 | 0.363456 | 0.181728 | − | 0.983349i | \(-0.441831\pi\) | ||||
0.181728 | + | 0.983349i | \(0.441831\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13268.0 | 1.25773 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26922.3 | −2.53624 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4670.00 | 0.437224 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1310.34 | 0.121924 | 0.0609620 | − | 0.998140i | \(-0.480583\pi\) | ||||
0.0609620 | + | 0.998140i | \(0.480583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13820.0 | −1.27804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2960.55 | 0.272114 | 0.136057 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136057 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4140.00 | 0.378207 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −313.050 | −0.0284253 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11480.0 | 1.03611 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19319.6 | −1.73320 | −0.866598 | − | 0.499006i | \(-0.833699\pi\) | ||||
−0.866598 | + | 0.499006i | \(0.833699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.0000 | 0.00178350 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3072.36 | 0.272345 | 0.136173 | − | 0.990685i | \(-0.456520\pi\) | ||||
0.136173 | + | 0.990685i | \(0.456520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3010.00 | 0.265234 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7365.61 | 0.645203 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18550.0 | 1.61535 | 0.807676 | − | 0.589626i | \(-0.200725\pi\) | ||||
0.807676 | + | 0.589626i | \(0.200725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16341.2 | −1.41466 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16320.0 | −1.40457 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9145.52 | 0.782524 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3560.00 | −0.302841 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8219.79 | −0.695200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2102.00 | −0.176757 | −0.0883784 | − | 0.996087i | \(-0.528168\pi\) | ||||
−0.0883784 | + | 0.996087i | \(0.528168\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17696.2 | 1.47955 | 0.739773 | − | 0.672856i | \(-0.234933\pi\) | ||||
0.739773 | + | 0.672856i | \(0.234933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3500.00 | −0.290957 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6994.42 | 0.578144 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24813.0 | 2.03937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2880.06 | 0.235374 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 620.000 | 0.0503850 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7624.99 | 0.616182 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8240.00 | 0.662164 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5697.50 | −0.455304 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9922.00 | −0.788503 | −0.394251 | − | 0.919003i | \(-0.628996\pi\) | ||||
−0.394251 | + | 0.919003i | \(0.628996\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8327.12 | 0.658105 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10770.0 | −0.846488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3716.34 | 0.290493 | 0.145246 | − | 0.989396i | \(-0.453603\pi\) | ||||
0.145246 | + | 0.989396i | \(0.453603\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1750.00 | −0.136044 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9659.81 | −0.746864 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27440.0 | −2.11007 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4785.19 | 0.365982 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15094.0 | −1.14821 | −0.574105 | − | 0.818781i | \(-0.694650\pi\) | ||||
−0.574105 | + | 0.818781i | \(0.694650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4159.09 | 0.314688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1840.00 | 0.138476 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5657.25 | 0.423490 | 0.211745 | − | 0.977325i | \(-0.432085\pi\) | ||||
0.211745 | + | 0.977325i | \(0.432085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10910.0 | 0.812367 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15370.7 | 1.13847 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5906.00 | −0.435136 | −0.217568 | − | 0.976045i | \(-0.569812\pi\) | ||||
−0.217568 | + | 0.976045i | \(0.569812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4892.52 | −0.358573 | −0.179287 | − | 0.983797i | \(-0.557379\pi\) | ||||
−0.179287 | + | 0.983797i | \(0.557379\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9240.00 | −0.673659 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4807.55 | 0.348676 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13286.0 | −0.958585 | −0.479292 | − | 0.877655i | \(-0.659107\pi\) | ||||
−0.479292 | + | 0.877655i | \(0.659107\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15106.9 | 1.08432 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −11900.0 | −0.849734 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6064.22 | 0.430796 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2170.00 | −0.153365 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9029.24 | 0.634884 | 0.317442 | − | 0.948278i | \(-0.397176\pi\) | ||||
0.317442 | + | 0.948278i | \(0.397176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16320.0 | −1.14169 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 295.161 | 0.0205437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11442.0 | 0.792355 | 0.396178 | − | 0.918174i | \(-0.370336\pi\) | ||||
0.396178 | + | 0.918174i | \(0.370336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7200.14 | −0.496096 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5440.00 | −0.372939 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14149.8 | −0.965187 | −0.482593 | − | 0.875845i | \(-0.660305\pi\) | ||||
−0.482593 | + | 0.875845i | \(0.660305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3110.00 | 0.211081 | 0.105540 | − | 0.994415i | \(-0.466343\pi\) | ||||
0.105540 | + | 0.994415i | \(0.466343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −344.354 | −0.0232557 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6255.00 | 0.420334 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11193.8 | −0.748502 | −0.374251 | − | 0.927327i | \(-0.622100\pi\) | ||||
−0.374251 | + | 0.927327i | \(0.622100\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12600.0 | 0.838387 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24677.2 | −1.63394 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5342.00 | −0.351976 | −0.175988 | − | 0.984392i | \(-0.556312\pi\) | ||||
−0.175988 | + | 0.984392i | \(0.556312\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 223.607 | 0.0146613 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19714.0 | 1.28631 | 0.643157 | − | 0.765734i | \(-0.277624\pi\) | ||||
0.643157 | + | 0.765734i | \(0.277624\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13166.0 | −0.854903 | −0.427451 | − | 0.904038i | \(-0.640589\pi\) | ||||
−0.427451 | + | 0.904038i | \(0.640589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29240.0 | −1.88947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30365.8 | −1.95278 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4293.25 | −0.273454 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9844.00 | 0.624016 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12262.6 | 0.773639 | 0.386820 | − | 0.922155i | \(-0.373574\pi\) | ||||
0.386820 | + | 0.922155i | \(0.373574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23640.0 | −1.48437 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6551.68 | −0.409442 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −39494.0 | −2.45653 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2567.01 | 0.158919 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2690.00 | −0.165754 | −0.0828772 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828772 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12240.2 | 0.750712 | 0.375356 | − | 0.926881i | \(-0.377520\pi\) | ||||
0.375356 | + | 0.926881i | \(0.377520\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1500.00 | 0.0915697 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17973.5 | −1.09214 | −0.546068 | − | 0.837741i | \(-0.683876\pi\) | ||||
−0.546068 | + | 0.837741i | \(0.683876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3680.00 | 0.222577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21287.4 | 1.28159 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3478.00 | −0.208430 | −0.104215 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104215 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1028.59 | 0.0613594 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3654.00 | −0.216980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10572.1 | −0.624934 | −0.312467 | − | 0.949929i | \(-0.601155\pi\) | ||||
−0.312467 | + | 0.949929i | \(0.601155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −110.000 | −0.00647277 | −0.00323639 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323639 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12754.5 | 0.747127 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16800.0 | 0.979663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17307.2 | −1.00470 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13260.0 | 0.766310 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2236.07 | −0.128647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14278.0 | −0.817796 | −0.408898 | − | 0.912580i | \(-0.634087\pi\) | ||||
−0.408898 | + | 0.912580i | \(0.634087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3801.32 | −0.216760 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18386.0 | 1.04377 | 0.521884 | − | 0.853016i | \(-0.325229\pi\) | ||||
0.521884 | + | 0.853016i | \(0.325229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29238.8 | 1.65255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19540.0 | −1.09952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15317.1 | 0.858113 | 0.429057 | − | 0.903278i | \(-0.358846\pi\) | ||||
0.429057 | + | 0.903278i | \(0.358846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10470.0 | 0.583997 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14534.4 | −0.807167 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42036.0 | 2.32430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9507.76 | 0.523433 | 0.261717 | − | 0.965145i | \(-0.415711\pi\) | ||||
0.261717 | + | 0.965145i | \(0.415711\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1960.00 | −0.107438 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6887.09 | 0.375888 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 460.000 | 0.0249982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14749.1 | 0.798086 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15830.0 | −0.852911 | −0.426456 | − | 0.904508i | \(-0.640238\pi\) | ||||
−0.426456 | + | 0.904508i | \(0.640238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22968.9 | −1.23227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8900.00 | −0.475452 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18845.6 | 1.00249 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20050.0 | −1.06205 | −0.531025 | − | 0.847356i | \(-0.678193\pi\) | ||||
−0.531025 | + | 0.847356i | \(0.678193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6135.77 | −0.323642 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29240.0 | −1.53583 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2772.72 | −0.145027 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2480.00 | −0.129173 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21126.4 | 1.09580 | 0.547900 | − | 0.836544i | \(-0.315427\pi\) | ||||
0.547900 | + | 0.836544i | \(0.315427\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 57260.0 | 2.95766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 23031.5 | 1.18472 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2250.00 | −0.115259 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11336.9 | −0.578351 | −0.289175 | − | 0.957276i | \(-0.593381\pi\) | ||||
−0.289175 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21797.0 | 1.10740 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3085.77 | 0.156131 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17198.0 | −0.866607 | −0.433303 | − | 0.901248i | \(-0.642652\pi\) | ||||
−0.433303 | + | 0.901248i | \(0.642652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −14243.8 | −0.714815 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −440.000 | −0.0219913 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4597.36 | 0.228845 | 0.114423 | − | 0.993432i | \(-0.463498\pi\) | ||||
0.114423 | + | 0.993432i | \(0.463498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29760.0 | −1.47539 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2419.43 | −0.119462 | −0.0597309 | − | 0.998215i | \(-0.519024\pi\) | ||||
−0.0597309 | + | 0.998215i | \(0.519024\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1670.00 | 0.0821263 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2660.92 | −0.130332 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 47740.0 | 2.32895 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7432.69 | 0.361149 | 0.180574 | − | 0.983561i | \(-0.442204\pi\) | ||||
0.180574 | + | 0.983561i | \(0.442204\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6200.00 | 0.300054 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15697.2 | −0.756662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11474.0 | 0.550898 | 0.275449 | − | 0.961316i | \(-0.411174\pi\) | ||||
0.275449 | + | 0.961316i | \(0.411174\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7692.07 | −0.367858 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31802.0 | 1.51488 | 0.757439 | − | 0.652906i | \(-0.226450\pi\) | ||||
0.757439 | + | 0.652906i | \(0.226450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −67430.9 | −3.19942 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1610.00 | −0.0760911 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25509.1 | 1.20089 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5310.00 | −0.249003 | −0.124502 | − | 0.992219i | \(-0.539733\pi\) | ||||
−0.124502 | + | 0.992219i | \(0.539733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18630.9 | −0.870267 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37938.0 | 1.76525 | 0.882623 | − | 0.470082i | \(-0.155776\pi\) | ||||
0.882623 | + | 0.470082i | \(0.155776\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3801.32 | −0.176190 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 29960.0 | 1.38328 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1073.31 | −0.0493651 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3280.00 | 0.150279 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13684.7 | 0.624588 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4170.00 | −0.189597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37633.0 | 1.70454 | 0.852270 | − | 0.523103i | \(-0.175226\pi\) | ||||
0.852270 | + | 0.523103i | \(0.175226\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4300.00 | 0.194023 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 68307.4 | 3.07046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15500.0 | −0.694100 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15160.5 | 0.676338 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17526.0 | −0.778924 | −0.389462 | − | 0.921042i | \(-0.627339\pi\) | ||||
−0.389462 | + | 0.921042i | \(0.627339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18308.9 | −0.810667 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6790.00 | −0.299517 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4668.91 | −0.205183 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30100.0 | 1.31787 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6681.37 | −0.291444 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8970.00 | 0.389825 | 0.194912 | − | 0.980821i | \(-0.437558\pi\) | ||||
0.194912 | + | 0.980821i | \(0.437558\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3550.88 | −0.153746 | −0.0768731 | − | 0.997041i | \(-0.524494\pi\) | ||||
−0.0768731 | + | 0.997041i | \(0.524494\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22440.0 | 0.968026 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15451.2 | 0.664090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7200.00 | −0.308318 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13586.3 | −0.579665 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15550.0 | −0.661022 | −0.330511 | − | 0.943802i | \(-0.607221\pi\) | ||||
−0.330511 | + | 0.943802i | \(0.607221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26712.1 | −1.13138 | −0.565689 | − | 0.824619i | \(-0.691390\pi\) | ||||
−0.565689 | + | 0.824619i | \(0.691390\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1000.00 | −0.0422006 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −863.122 | −0.0362923 | −0.0181461 | − | 0.999835i | \(-0.505776\pi\) | ||||
−0.0181461 | + | 0.999835i | \(0.505776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19066.0 | 0.798781 | 0.399391 | − | 0.916781i | \(-0.369222\pi\) | ||||
0.399391 | + | 0.916781i | \(0.369222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4498.97 | −0.187807 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29302.0 | −1.21879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.3607 | −0.000926734 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23120.0 | 0.954772 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47744.5 | −1.96463 | −0.982315 | − | 0.187238i | \(-0.940047\pi\) | ||||
−0.982315 | + | 0.187238i | \(0.940047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16289.0 | −0.667883 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14355.6 | −0.586514 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8235.00 | −0.335258 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 39162.5 | 1.58871 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16260.0 | 0.657293 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −41152.6 | −1.65769 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14462.0 | −0.580503 | −0.290252 | − | 0.956950i | \(-0.593739\pi\) | ||||
−0.290252 | + | 0.956950i | \(0.593739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3756.59 | 0.150261 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29346.0 | 1.16971 | 0.584854 | − | 0.811138i | \(-0.301152\pi\) | ||||
0.584854 | + | 0.811138i | \(0.301152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22807.9 | 0.905932 | 0.452966 | − | 0.891528i | \(-0.350366\pi\) | ||||
0.452966 | + | 0.891528i | \(0.350366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1400.00 | 0.0554145 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24753.3 | 0.976375 | 0.488187 | − | 0.872739i | \(-0.337658\pi\) | ||||
0.488187 | + | 0.872739i | \(0.337658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9190.00 | 0.361236 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12508.6 | −0.489981 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7840.00 | −0.306046 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3050.00 | −0.118651 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6538.00 | 0.253468 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3913.12 | 0.151186 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32126.0 | −1.23696 | −0.618482 | − | 0.785799i | \(-0.712252\pi\) | ||||
−0.618482 | + | 0.785799i | \(0.712252\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16198.1 | −0.621556 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33570.0 | −1.28377 | −0.641885 | − | 0.766801i | \(-0.721848\pi\) | ||||
−0.641885 | + | 0.766801i | \(0.721848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6435.40 | −0.245265 | −0.122632 | − | 0.992452i | \(-0.539134\pi\) | ||||
−0.122632 | + | 0.992452i | \(0.539134\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9200.00 | 0.349440 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46827.7 | −1.77263 | −0.886314 | − | 0.463084i | \(-0.846743\pi\) | ||||
−0.886314 | + | 0.463084i | \(0.846743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41020.0 | −1.54754 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4391.64 | 0.165124 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42720.0 | 1.60086 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9212.60 | −0.344071 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −53320.0 | −1.98473 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13684.7 | 0.507688 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 31188.0 | 1.15319 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9391.49 | 0.346101 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9310.00 | −0.341961 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11980.9 | 0.438608 | 0.219304 | − | 0.975657i | \(-0.429621\pi\) | ||||
0.219304 | + | 0.975657i | \(0.429621\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4214.00 | 0.153762 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24194.3 | −0.879903 | −0.439951 | − | 0.898022i | \(-0.645004\pi\) | ||||
−0.439951 | + | 0.898022i | \(0.645004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3400.00 | −0.123246 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5590.17 | −0.201973 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6440.00 | 0.231917 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37512.3 | −1.34648 | −0.673240 | − | 0.739424i | \(-0.735098\pi\) | ||||
−0.673240 | + | 0.739424i | \(0.735098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9340.00 | 0.334162 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22736.3 | 0.810808 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5350.00 | −0.190170 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12803.7 | 0.453646 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21994.0 | −0.776749 | −0.388374 | − | 0.921502i | \(-0.626963\pi\) | ||||
−0.388374 | + | 0.921502i | \(0.626963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68370.0 | 2.40681 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39800.0 | −1.39656 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2057.18 | −0.0719541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16286.0 | −0.567813 | −0.283906 | − | 0.958852i | \(-0.591630\pi\) | ||||
−0.283906 | + | 0.958852i | \(0.591630\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39256.4 | 1.36431 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24302.0 | 0.841894 | 0.420947 | − | 0.907085i | \(-0.361698\pi\) | ||||
0.420947 | + | 0.907085i | \(0.361698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1923.02 | −0.0664073 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −23800.0 | −0.819274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19869.7 | 0.681815 | 0.340907 | − | 0.940097i | \(-0.389266\pi\) | ||||
0.340907 | + | 0.940097i | \(0.389266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32364.0 | −1.10704 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22566.4 | −0.769470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22422.0 | −0.762140 | −0.381070 | − | 0.924546i | \(-0.624444\pi\) | ||||
−0.381070 | + | 0.924546i | \(0.624444\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10330.6 | 0.350043 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3600.00 | 0.121600 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 65552.6 | 2.20730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6671.00 | −0.223927 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10675.0 | 0.357214 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16890.0 | −0.563428 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43777.7 | 1.45584 | 0.727920 | − | 0.685662i | \(-0.240487\pi\) | ||||
0.727920 | + | 0.685662i | \(0.240487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22080.0 | −0.732004 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25714.8 | −0.849873 | −0.424936 | − | 0.905223i | \(-0.639704\pi\) | ||||
−0.424936 | + | 0.905223i | \(0.639704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43120.0 | 1.42072 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6931.81 | −0.227688 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28986.0 | 0.949175 | 0.474588 | − | 0.880208i | \(-0.342597\pi\) | ||||
0.474588 | + | 0.880208i | \(0.342597\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8675.94 | −0.283232 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15078.0 | −0.490727 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32123.4 | 1.04229 | 0.521147 | − | 0.853467i | \(-0.325504\pi\) | ||||
0.521147 | + | 0.853467i | \(0.325504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −330.000 | −0.0106748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −55722.8 | −1.79704 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12900.0 | −0.414758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11994.3 | −0.384471 | −0.192235 | − | 0.981349i | \(-0.561574\pi\) | ||||
−0.192235 | + | 0.981349i | \(0.561574\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1400.00 | −0.0447408 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6082.10 | 0.193785 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −406.000 | −0.0128968 | −0.00644842 | − | 0.999979i | \(-0.502053\pi\) | ||||
−0.00644842 | + | 0.999979i | \(0.502053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32539.3 | 1.03053 |
(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 | 160.4.a.d.1.2 | yes | 2 | |
3.2 | odd | 2 | 1440.4.a.bb.1.1 | 2 | |||
4.3 | odd | 2 | inner | 160.4.a.d.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 800.4.c.l.449.1 | 4 | |||
5.3 | odd | 4 | 800.4.c.l.449.3 | 4 | |||
5.4 | even | 2 | 800.4.a.o.1.1 | 2 | |||
8.3 | odd | 2 | 320.4.a.q.1.2 | 2 | |||
8.5 | even | 2 | 320.4.a.q.1.1 | 2 | |||
12.11 | even | 2 | 1440.4.a.bb.1.2 | 2 | |||
16.3 | odd | 4 | 1280.4.d.v.641.2 | 4 | |||
16.5 | even | 4 | 1280.4.d.v.641.1 | 4 | |||
16.11 | odd | 4 | 1280.4.d.v.641.3 | 4 | |||
16.13 | even | 4 | 1280.4.d.v.641.4 | 4 | |||
20.3 | even | 4 | 800.4.c.l.449.2 | 4 | |||
20.7 | even | 4 | 800.4.c.l.449.4 | 4 | |||
20.19 | odd | 2 | 800.4.a.o.1.2 | 2 | |||
40.19 | odd | 2 | 1600.4.a.cg.1.1 | 2 | |||
40.29 | even | 2 | 1600.4.a.cg.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.d.1.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
160.4.a.d.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
320.4.a.q.1.1 | 2 | 8.5 | even | 2 | |||
320.4.a.q.1.2 | 2 | 8.3 | odd | 2 | |||
800.4.a.o.1.1 | 2 | 5.4 | even | 2 | |||
800.4.a.o.1.2 | 2 | 20.19 | odd | 2 | |||
800.4.c.l.449.1 | 4 | 5.2 | odd | 4 | |||
800.4.c.l.449.2 | 4 | 20.3 | even | 4 | |||
800.4.c.l.449.3 | 4 | 5.3 | odd | 4 | |||
800.4.c.l.449.4 | 4 | 20.7 | even | 4 | |||
1280.4.d.v.641.1 | 4 | 16.5 | even | 4 | |||
1280.4.d.v.641.2 | 4 | 16.3 | odd | 4 | |||
1280.4.d.v.641.3 | 4 | 16.11 | odd | 4 | |||
1280.4.d.v.641.4 | 4 | 16.13 | even | 4 | |||
1440.4.a.bb.1.1 | 2 | 3.2 | odd | 2 | |||
1440.4.a.bb.1.2 | 2 | 12.11 | even | 2 | |||
1600.4.a.cg.1.1 | 2 | 40.19 | odd | 2 | |||
1600.4.a.cg.1.2 | 2 | 40.29 | even | 2 |