Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.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: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 80x^{3} + 121x^{2} + 1212x + 1044 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 460) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.72746\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-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 | ||||||||
\(3\) | 3.72746 | 0.717349 | 0.358675 | − | 0.933463i | \(-0.383229\pi\) | ||||
0.358675 | + | 0.933463i | \(0.383229\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.8626 | −0.640520 | −0.320260 | − | 0.947330i | \(-0.603770\pi\) | ||||
−0.320260 | + | 0.947330i | \(0.603770\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −13.1061 | −0.485410 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −64.0085 | −1.75448 | −0.877241 | − | 0.480051i | \(-0.840618\pi\) | ||||
−0.877241 | + | 0.480051i | \(0.840618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −77.5549 | −1.65460 | −0.827302 | − | 0.561757i | \(-0.810126\pi\) | ||||
−0.827302 | + | 0.561757i | \(0.810126\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.6373 | −0.320808 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.6338 | 0.365713 | 0.182856 | − | 0.983140i | \(-0.441466\pi\) | ||||
0.182856 | + | 0.983140i | \(0.441466\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −51.4669 | −0.621438 | −0.310719 | − | 0.950502i | \(-0.600570\pi\) | ||||
−0.310719 | + | 0.950502i | \(0.600570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −44.2173 | −0.459477 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −149.494 | −1.06556 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 68.3100 | 0.437409 | 0.218704 | − | 0.975791i | \(-0.429817\pi\) | ||||
0.218704 | + | 0.975791i | \(0.429817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 67.5033 | 0.391095 | 0.195547 | − | 0.980694i | \(-0.437352\pi\) | ||||
0.195547 | + | 0.980694i | \(0.437352\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −238.589 | −1.25858 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 59.3130 | 0.286449 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −149.346 | −0.663577 | −0.331789 | − | 0.943354i | \(-0.607652\pi\) | ||||
−0.331789 | + | 0.943354i | \(0.607652\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −289.083 | −1.18693 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −249.799 | −0.951512 | −0.475756 | − | 0.879577i | \(-0.657825\pi\) | ||||
−0.475756 | + | 0.879577i | \(0.657825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 534.186 | 1.89448 | 0.947240 | − | 0.320526i | \(-0.103860\pi\) | ||||
0.947240 | + | 0.320526i | \(0.103860\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 65.5303 | 0.217082 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −141.452 | −0.438998 | −0.219499 | − | 0.975613i | \(-0.570442\pi\) | ||||
−0.219499 | + | 0.975613i | \(0.570442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −202.279 | −0.589734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 95.5490 | 0.262344 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −76.1827 | −0.197443 | −0.0987217 | − | 0.995115i | \(-0.531475\pi\) | ||||
−0.0987217 | + | 0.995115i | \(0.531475\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 320.043 | 0.784628 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −191.841 | −0.445788 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 816.330 | 1.80131 | 0.900654 | − | 0.434537i | \(-0.143088\pi\) | ||||
0.900654 | + | 0.434537i | \(0.143088\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 356.152 | 0.747551 | 0.373775 | − | 0.927519i | \(-0.378063\pi\) | ||||
0.373775 | + | 0.927519i | \(0.378063\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 155.472 | 0.310915 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 387.775 | 0.739962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 671.800 | 1.22498 | 0.612489 | − | 0.790479i | \(-0.290168\pi\) | ||||
0.612489 | + | 0.790479i | \(0.290168\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 85.7315 | 0.149578 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 746.875 | 1.24842 | 0.624209 | − | 0.781257i | \(-0.285421\pi\) | ||||
0.624209 | + | 0.781257i | \(0.285421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −162.513 | −0.260558 | −0.130279 | − | 0.991477i | \(-0.541587\pi\) | ||||
−0.130279 | + | 0.991477i | \(0.541587\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 93.1864 | 0.143470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 759.307 | 1.12378 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −194.917 | −0.277593 | −0.138797 | − | 0.990321i | \(-0.544323\pi\) | ||||
−0.138797 | + | 0.990321i | \(0.544323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −203.367 | −0.278968 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −246.650 | −0.326185 | −0.163092 | − | 0.986611i | \(-0.552147\pi\) | ||||
−0.163092 | + | 0.986611i | \(0.552147\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −128.169 | −0.163552 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 254.623 | 0.313775 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −836.169 | −0.995884 | −0.497942 | − | 0.867210i | \(-0.665911\pi\) | ||||
−0.497942 | + | 0.867210i | \(0.665911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 920.003 | 1.05981 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 251.616 | 0.280552 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 257.335 | 0.277915 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −53.5771 | −0.0560817 | −0.0280409 | − | 0.999607i | \(-0.508927\pi\) | ||||
−0.0280409 | + | 0.999607i | \(0.508927\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 838.900 | 0.851642 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 888.956 | 0.875787 | 0.437893 | − | 0.899027i | \(-0.355725\pi\) | ||||
0.437893 | + | 0.899027i | \(0.355725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 152.873 | 0.146243 | 0.0731213 | − | 0.997323i | \(-0.476704\pi\) | ||||
0.0731213 | + | 0.997323i | \(0.476704\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 221.087 | 0.205484 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1376.40 | 1.24357 | 0.621783 | − | 0.783189i | \(-0.286409\pi\) | ||||
0.621783 | + | 0.783189i | \(0.286409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −383.902 | −0.337350 | −0.168675 | − | 0.985672i | \(-0.553949\pi\) | ||||
−0.168675 | + | 0.985672i | \(0.553949\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −556.681 | −0.476017 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1532.24 | −1.27558 | −0.637790 | − | 0.770210i | \(-0.720151\pi\) | ||||
−0.637790 | + | 0.770210i | \(0.720151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1016.44 | 0.803161 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −304.084 | −0.234246 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2766.09 | 2.07821 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −931.114 | −0.682567 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −897.249 | −0.626913 | −0.313457 | − | 0.949602i | \(-0.601487\pi\) | ||||
−0.313457 | + | 0.949602i | \(0.601487\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1991.16 | 1.35900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1770.30 | −1.18070 | −0.590350 | − | 0.807147i | \(-0.701010\pi\) | ||||
−0.590350 | + | 0.807147i | \(0.701010\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 610.531 | 0.398043 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 747.468 | 0.476532 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2984.69 | −1.86131 | −0.930655 | − | 0.365897i | \(-0.880762\pi\) | ||||
−0.930655 | + | 0.365897i | \(0.880762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3005.98 | −1.83427 | −0.917136 | − | 0.398574i | \(-0.869505\pi\) | ||||
−0.917136 | + | 0.398574i | \(0.869505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −527.256 | −0.314915 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4964.18 | 2.90297 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −341.550 | −0.195615 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −753.986 | −0.423045 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 770.968 | 0.423894 | 0.211947 | − | 0.977281i | \(-0.432020\pi\) | ||||
0.211947 | + | 0.977281i | \(0.432020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2232.13 | 1.20297 | 0.601484 | − | 0.798885i | \(-0.294576\pi\) | ||||
0.601484 | + | 0.798885i | \(0.294576\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −335.959 | −0.177521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −337.516 | −0.174903 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 665.093 | 0.338090 | 0.169045 | − | 0.985608i | \(-0.445932\pi\) | ||||
0.169045 | + | 0.985608i | \(0.445932\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −283.968 | −0.141636 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −272.840 | −0.133558 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 275.549 | 0.132409 | 0.0662045 | − | 0.997806i | \(-0.478911\pi\) | ||||
0.0662045 | + | 0.997806i | \(0.478911\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1192.95 | 0.562853 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −786.620 | −0.364494 | −0.182247 | − | 0.983253i | \(-0.558337\pi\) | ||||
−0.182247 | + | 0.983253i | \(0.558337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3817.76 | 1.73772 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 674.528 | 0.301652 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3134.38 | −1.37747 | −0.688735 | − | 0.725013i | \(-0.741834\pi\) | ||||
−0.688735 | + | 0.725013i | \(0.741834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −296.565 | −0.128104 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3042.84 | 1.29217 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −51.6322 | −0.0215596 | −0.0107798 | − | 0.999942i | \(-0.503431\pi\) | ||||
−0.0107798 | + | 0.999942i | \(0.503431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 188.767 | 0.0775192 | 0.0387596 | − | 0.999249i | \(-0.487659\pi\) | ||||
0.0387596 | + | 0.999249i | \(0.487659\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1327.54 | 0.536255 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 746.731 | 0.296761 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1640.78 | −0.641636 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1773.38 | 0.682511 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1976.70 | −0.748842 | −0.374421 | − | 0.927259i | \(-0.622158\pi\) | ||||
−0.374421 | + | 0.927259i | \(0.622158\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 89.0776 | 0.0332225 | 0.0166113 | − | 0.999862i | \(-0.494712\pi\) | ||||
0.0166113 | + | 0.999862i | \(0.494712\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1445.41 | 0.530811 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −958.216 | −0.346549 | −0.173274 | − | 0.984874i | \(-0.555435\pi\) | ||||
−0.173274 | + | 0.984874i | \(0.555435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3706.37 | −1.32029 | −0.660145 | − | 0.751138i | \(-0.729505\pi\) | ||||
−0.660145 | + | 0.751138i | \(0.729505\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2504.11 | 0.878737 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −810.334 | −0.280169 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1248.99 | 0.425529 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −301.439 | −0.101215 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3294.32 | 1.09030 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 890.496 | 0.290542 | 0.145271 | − | 0.989392i | \(-0.453595\pi\) | ||||
0.145271 | + | 0.989392i | \(0.453595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2783.94 | 0.895553 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2670.93 | −0.847237 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −800.764 | −0.250504 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −605.761 | −0.186911 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1988.03 | −0.605110 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1718.03 | 0.515910 | 0.257955 | − | 0.966157i | \(-0.416951\pi\) | ||||
0.257955 | + | 0.966157i | \(0.416951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −327.652 | −0.0970819 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −355.023 | −0.103805 | −0.0519025 | − | 0.998652i | \(-0.516528\pi\) | ||||
−0.0519025 | + | 0.998652i | \(0.516528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6681.36 | 1.92802 | 0.964011 | − | 0.265863i | \(-0.0856570\pi\) | ||||
0.964011 | + | 0.265863i | \(0.0856570\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2830.29 | 0.806143 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3719.27 | 1.04574 | 0.522870 | − | 0.852412i | \(-0.324861\pi\) | ||||
0.522870 | + | 0.852412i | \(0.324861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 707.260 | 0.196326 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −726.545 | −0.199132 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4963.49 | 1.34335 | 0.671677 | − | 0.740844i | \(-0.265574\pi\) | ||||
0.671677 | + | 0.740844i | \(0.265574\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5277.12 | −1.41050 | −0.705248 | − | 0.708961i | \(-0.749164\pi\) | ||||
−0.705248 | + | 0.708961i | \(0.749164\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3278.28 | 0.865441 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1011.39 | 0.263737 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3991.51 | 1.02823 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −919.377 | −0.233988 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 72.1196 | 0.0181360 | 0.00906802 | − | 0.999959i | \(-0.497114\pi\) | ||||
0.00906802 | + | 0.999959i | \(0.497114\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1472.20 | −0.365835 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −477.745 | −0.117324 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2930.92 | −0.711384 | −0.355692 | − | 0.934603i | \(-0.615755\pi\) | ||||
−0.355692 | + | 0.934603i | \(0.615755\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1771.63 | 0.425035 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −895.275 | −0.212322 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1684.95 | 0.395050 | 0.197525 | − | 0.980298i | \(-0.436710\pi\) | ||||
0.197525 | + | 0.980298i | \(0.436710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 380.914 | 0.0882994 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3116.78 | −0.714397 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 447.845 | 0.101508 | 0.0507538 | − | 0.998711i | \(-0.483838\pi\) | ||||
0.0507538 | + | 0.998711i | \(0.483838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1659.82 | 0.372055 | 0.186028 | − | 0.982545i | \(-0.440439\pi\) | ||||
0.186028 | + | 0.982545i | \(0.440439\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3429.27 | 0.760252 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1600.21 | −0.350896 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1449.27 | −0.314362 | −0.157181 | − | 0.987570i | \(-0.550241\pi\) | ||||
−0.157181 | + | 0.987570i | \(0.550241\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −884.702 | −0.189841 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1528.94 | −0.324586 | −0.162293 | − | 0.986743i | \(-0.551889\pi\) | ||||
−0.162293 | + | 0.986743i | \(0.551889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3481.74 | −0.731335 | −0.365667 | − | 0.930746i | \(-0.619159\pi\) | ||||
−0.365667 | + | 0.930746i | \(0.619159\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 959.203 | 0.199362 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2963.26 | 0.609463 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4255.91 | −0.866254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −199.706 | −0.0402302 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4602.57 | 0.917697 | 0.458848 | − | 0.888515i | \(-0.348262\pi\) | ||||
0.458848 | + | 0.888515i | \(0.348262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4081.65 | −0.805569 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9568.87 | 1.86950 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1783.76 | −0.345009 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6336.83 | −1.21345 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3313.55 | 0.628245 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1780.76 | −0.334315 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3004.50 | −0.558554 | −0.279277 | − | 0.960211i | \(-0.590095\pi\) | ||||
−0.279277 | + | 0.960211i | \(0.590095\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 569.827 | 0.104907 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9252.25 | −1.68697 | −0.843484 | − | 0.537155i | \(-0.819499\pi\) | ||||
−0.843484 | + | 0.537155i | \(0.819499\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2524.11 | −0.455818 | −0.227909 | − | 0.973682i | \(-0.573189\pi\) | ||||
−0.227909 | + | 0.973682i | \(0.573189\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −777.360 | −0.139045 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8948.50 | 1.58548 | 0.792741 | − | 0.609558i | \(-0.208653\pi\) | ||||
0.792741 | + | 0.609558i | \(0.208653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4372.42 | −0.767425 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5130.47 | 0.892072 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1319.29 | −0.227268 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1938.87 | −0.330921 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1430.98 | −0.241998 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1677.99 | 0.281187 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2848.38 | −0.472994 | −0.236497 | − | 0.971632i | \(-0.575999\pi\) | ||||
−0.236497 | + | 0.971632i | \(0.575999\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1957.34 | 0.322107 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3359.00 | −0.547827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11454.1 | −1.85147 | −0.925735 | − | 0.378173i | \(-0.876552\pi\) | ||||
−0.925735 | + | 0.378173i | \(0.876552\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5711.34 | −0.915037 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4320.78 | −0.686169 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6468.42 | 1.01826 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −428.658 | −0.0668932 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2858.52 | 0.442228 | 0.221114 | − | 0.975248i | \(-0.429031\pi\) | ||||
0.221114 | + | 0.975248i | \(0.429031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2586.61 | 0.396729 | 0.198364 | − | 0.980128i | \(-0.436437\pi\) | ||||
0.198364 | + | 0.980128i | \(0.436437\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11594.0 | 1.76308 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6506.44 | −0.981028 | −0.490514 | − | 0.871433i | \(-0.663191\pi\) | ||||
−0.490514 | + | 0.871433i | \(0.663191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3734.37 | −0.558310 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1133.46 | −0.168036 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9798.33 | 1.44049 | 0.720245 | − | 0.693720i | \(-0.244029\pi\) | ||||
0.720245 | + | 0.693720i | \(0.244029\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4210.16 | −0.613815 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10310.5 | 1.49080 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 812.566 | 0.116525 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4821.10 | 0.685720 | 0.342860 | − | 0.939386i | \(-0.388604\pi\) | ||||
0.342860 | + | 0.939386i | \(0.388604\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3273.88 | 0.461873 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 903.725 | 0.126466 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9742.30 | 1.35238 | 0.676190 | − | 0.736728i | \(-0.263630\pi\) | ||||
0.676190 | + | 0.736728i | \(0.263630\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −465.932 | −0.0641617 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5297.78 | −0.723738 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8403.84 | 1.13899 | 0.569494 | − | 0.821996i | \(-0.307139\pi\) | ||||
0.569494 | + | 0.821996i | \(0.307139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3344.46 | −0.449716 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14020.1 | 1.87048 | 0.935240 | − | 0.354013i | \(-0.115183\pi\) | ||||
0.935240 | + | 0.354013i | \(0.115183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3796.54 | −0.502570 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7001.08 | −0.919599 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13631.3 | 1.77670 | 0.888348 | − | 0.459170i | \(-0.151853\pi\) | ||||
0.888348 | + | 0.459170i | \(0.151853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 589.578 | 0.0762564 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6598.72 | −0.846975 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 974.585 | 0.124144 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11338.8 | −1.43345 | −0.716724 | − | 0.697357i | \(-0.754359\pi\) | ||||
−0.716724 | + | 0.697357i | \(0.754359\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2275.73 | 0.285536 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5482.78 | −0.682786 | −0.341393 | − | 0.939921i | \(-0.610899\pi\) | ||||
−0.341393 | + | 0.939921i | \(0.610899\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5235.21 | −0.647108 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1016.84 | 0.124758 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9559.43 | 1.16423 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14162.6 | 1.71221 | 0.856107 | − | 0.516799i | \(-0.172877\pi\) | ||||
0.856107 | + | 0.516799i | \(0.172877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11125.3 | −1.33521 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9683.80 | −1.15377 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1233.25 | 0.145874 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11204.7 | −1.31581 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9438.98 | 1.10054 | 0.550268 | − | 0.834988i | \(-0.314526\pi\) | ||||
0.550268 | + | 0.834988i | \(0.314526\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2888.29 | −0.334363 | −0.167181 | − | 0.985926i | \(-0.553467\pi\) | ||||
−0.167181 | + | 0.985926i | \(0.553467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1853.88 | 0.213094 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 640.846 | 0.0731425 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4224.89 | −0.478821 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18503.8 | 2.08245 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9881.73 | 1.10438 | 0.552188 | − | 0.833719i | \(-0.313793\pi\) | ||||
0.552188 | + | 0.833719i | \(0.313793\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −873.860 | −0.0969863 | −0.0484931 | − | 0.998824i | \(-0.515442\pi\) | ||||
−0.0484931 | + | 0.998824i | \(0.515442\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1273.11 | −0.140324 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1183.74 | −0.129579 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16959.1 | −1.84377 | −0.921883 | − | 0.387469i | \(-0.873350\pi\) | ||||
−0.921883 | + | 0.387469i | \(0.873350\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2651.08 | 0.286263 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8914.05 | 0.956025 | 0.478013 | − | 0.878353i | \(-0.341357\pi\) | ||||
0.478013 | + | 0.878353i | \(0.341357\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4180.84 | 0.445373 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2873.75 | 0.304080 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −864.502 | −0.0908650 | −0.0454325 | − | 0.998967i | \(-0.514467\pi\) | ||||
−0.0454325 | + | 0.998967i | \(0.514467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15989.2 | 1.66941 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8320.17 | 0.862949 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4600.01 | −0.473960 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19241.7 | 1.96956 | 0.984779 | − | 0.173812i | \(-0.0556086\pi\) | ||||
0.984779 | + | 0.173812i | \(0.0556086\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3832.09 | −0.389688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3935.04 | −0.397555 | −0.198778 | − | 0.980045i | \(-0.563697\pi\) | ||||
−0.198778 | + | 0.980045i | \(0.563697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1413.95 | 0.141926 | 0.0709631 | − | 0.997479i | \(-0.477393\pi\) | ||||
0.0709631 | + | 0.997479i | \(0.477393\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1258.08 | −0.125467 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7355.75 | 0.728873 | 0.364436 | − | 0.931228i | \(-0.381262\pi\) | ||||
0.364436 | + | 0.931228i | \(0.381262\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7969.30 | −0.784623 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2479.11 | 0.242529 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34192.5 | −3.32383 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1286.67 | −0.124288 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 998.455 | 0.0958409 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12770.7 | 1.21818 | 0.609090 | − | 0.793101i | \(-0.291535\pi\) | ||||
0.609090 | + | 0.793101i | \(0.291535\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11582.5 | 1.09796 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1017.00 | −0.0958075 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 267.885 | 0.0250805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12490.4 | 1.16221 | 0.581105 | − | 0.813829i | \(-0.302621\pi\) | ||||
0.581105 | + | 0.813829i | \(0.302621\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1027.10 | 0.0949836 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13347.7 | 1.22683 | 0.613415 | − | 0.789761i | \(-0.289795\pi\) | ||||
0.613415 | + | 0.789761i | \(0.289795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1751.05 | 0.159966 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4194.50 | −0.380866 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8859.87 | −0.799637 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15159.1 | 1.35995 | 0.679975 | − | 0.733235i | \(-0.261990\pi\) | ||||
0.679975 | + | 0.733235i | \(0.261990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2932.09 | −0.261470 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13114.9 | −1.16256 | −0.581278 | − | 0.813705i | \(-0.697447\pi\) | ||||
−0.581278 | + | 0.813705i | \(0.697447\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4444.78 | −0.391664 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14230.6 | 1.24655 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14089.6 | 1.22694 | 0.613469 | − | 0.789719i | \(-0.289774\pi\) | ||||
0.613469 | + | 0.789719i | \(0.289774\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1927.83 | 0.166893 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7693.97 | 0.662178 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −764.364 | −0.0654017 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9054.13 | 0.770213 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11683.3 | −0.988128 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5006.61 | −0.421005 | −0.210502 | − | 0.977593i | \(-0.567510\pi\) | ||||
−0.210502 | + | 0.977593i | \(0.567510\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7991.86 | −0.668183 | −0.334091 | − | 0.942541i | \(-0.608429\pi\) | ||||
−0.334091 | + | 0.942541i | \(0.608429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1105.43 | −0.0918953 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1730.37 | 0.143028 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10698.9 | −0.874372 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19373.1 | 1.57438 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6882.00 | −0.556140 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −192.457 | −0.0154658 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12947.6 | 1.03468 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9408.67 | −0.747708 | −0.373854 | − | 0.927488i | \(-0.621964\pi\) | ||||
−0.373854 | + | 0.927488i | \(0.621964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 703.622 | 0.0556083 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1919.51 | 0.150867 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7492.55 | −0.585664 | −0.292832 | − | 0.956164i | \(-0.594598\pi\) | ||||
−0.292832 | + | 0.956164i | \(0.594598\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4667.75 | −0.362868 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3515.70 | −0.271822 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2312.22 | 0.177804 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2783.41 | 0.212881 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6822.47 | 0.518990 | 0.259495 | − | 0.965744i | \(-0.416444\pi\) | ||||
0.259495 | + | 0.965744i | \(0.416444\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41428.8 | −3.13461 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6115.95 | −0.460277 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7654.32 | −0.572986 | −0.286493 | − | 0.958082i | \(-0.592490\pi\) | ||||
−0.286493 | + | 0.958082i | \(0.592490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7661.18 | 0.570457 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2412.47 | 0.178684 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −276.732 | −0.0203888 | −0.0101944 | − | 0.999948i | \(-0.503245\pi\) | ||||
−0.0101944 | + | 0.999948i | \(0.503245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15561.6 | −1.14051 | −0.570256 | − | 0.821467i | \(-0.693156\pi\) | ||||
−0.570256 | + | 0.821467i | \(0.693156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7368.06 | −0.537181 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21913.2 | 1.58103 | 0.790517 | − | 0.612440i | \(-0.209812\pi\) | ||||
0.790517 | + | 0.612440i | \(0.209812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 332.033 | 0.0238322 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2925.91 | 0.208928 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4876.34 | 0.346411 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5082.20 | −0.359185 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23731.6 | −1.66867 | −0.834336 | − | 0.551257i | \(-0.814148\pi\) | ||||
−0.834336 | + | 0.551257i | \(0.814148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3474.18 | −0.243041 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3571.71 | −0.248596 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18853.5 | −1.30560 | −0.652798 | − | 0.757532i | \(-0.726405\pi\) | ||||
−0.652798 | + | 0.757532i | \(0.726405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1520.42 | 0.104758 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13815.3 | −0.947109 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15886.8 | −1.08367 | −0.541835 | − | 0.840485i | \(-0.682270\pi\) | ||||
−0.541835 | + | 0.840485i | \(0.682270\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10870.6 | 0.737806 | 0.368903 | − | 0.929468i | \(-0.379733\pi\) | ||||
0.368903 | + | 0.929468i | \(0.379733\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8804.66 | −0.594616 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13830.5 | −0.929402 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26207.6 | −1.75244 | −0.876222 | − | 0.481908i | \(-0.839944\pi\) | ||||
−0.876222 | + | 0.481908i | \(0.839944\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3020.49 | −0.200979 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10970.3 | 0.726367 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25428.3 | 1.67543 | 0.837714 | − | 0.546109i | \(-0.183892\pi\) | ||||
0.837714 | + | 0.546109i | \(0.183892\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4655.57 | 0.305253 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25153.5 | 1.64124 | 0.820619 | − | 0.571476i | \(-0.193629\pi\) | ||||
0.820619 | + | 0.571476i | \(0.193629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19039.3 | 1.23628 | 0.618139 | − | 0.786069i | \(-0.287887\pi\) | ||||
0.618139 | + | 0.786069i | \(0.287887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3438.35 | −0.222184 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9919.13 | 0.637884 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12279.4 | 0.782127 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3828.31 | −0.242679 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29970.1 | −1.89079 | −0.945396 | − | 0.325924i | \(-0.894325\pi\) | ||||
−0.945396 | + | 0.325924i | \(0.894325\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3319.29 | 0.208420 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4486.25 | 0.280364 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15687.7 | 0.975777 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9788.59 | −0.605995 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9509.35 | 0.585955 | 0.292977 | − | 0.956119i | \(-0.405354\pi\) | ||||
0.292977 | + | 0.956119i | \(0.405354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22663.0 | 1.38996 | 0.694979 | − | 0.719030i | \(-0.255414\pi\) | ||||
0.694979 | + | 0.719030i | \(0.255414\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9955.78 | −0.607765 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25697.8 | 1.56149 | 0.780747 | − | 0.624848i | \(-0.214839\pi\) | ||||
0.780747 | + | 0.624848i | \(0.214839\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52252.1 | −3.16036 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2984.81 | −0.179699 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15010.3 | −0.899535 | −0.449768 | − | 0.893146i | \(-0.648493\pi\) | ||||
−0.449768 | + | 0.893146i | \(0.648493\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8851.50 | 0.528025 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2129.91 | 0.126477 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23949.7 | −1.41570 | −0.707850 | − | 0.706362i | \(-0.750335\pi\) | ||||
−0.707850 | + | 0.706362i | \(0.750335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24381.6 | 1.43470 | 0.717348 | − | 0.696715i | \(-0.245356\pi\) | ||||
0.717348 | + | 0.696715i | \(0.245356\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7410.29 | −0.434075 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3052.66 | −0.178010 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1571.13 | 0.0912060 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6403.89 | 0.370088 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22796.8 | −1.31156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9221.65 | 0.528185 | 0.264093 | − | 0.964497i | \(-0.414928\pi\) | ||||
0.264093 | + | 0.964497i | \(0.414928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3737.34 | −0.213112 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18144.6 | 1.03007 | 0.515033 | − | 0.857170i | \(-0.327779\pi\) | ||||
0.515033 | + | 0.857170i | \(0.327779\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 635.563 | 0.0359215 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1323.33 | −0.0744644 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14376.0 | −0.805390 | −0.402695 | − | 0.915334i | \(-0.631926\pi\) | ||||
−0.402695 | + | 0.915334i | \(0.631926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14923.5 | 0.832403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 24904.5 | 1.38307 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5908.34 | 0.326691 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29784.3 | −1.63972 | −0.819861 | − | 0.572563i | \(-0.805949\pi\) | ||||
−0.819861 | + | 0.572563i | \(0.805949\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9951.53 | −0.545494 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15029.9 | 0.820312 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6403.30 | −0.347980 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 13863.4 | 0.750161 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5784.80 | 0.311682 | 0.155841 | − | 0.987782i | \(-0.450191\pi\) | ||||
0.155841 | + | 0.987782i | \(0.450191\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7686.38 | 0.412372 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2636.28 | 0.140834 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10545.3 | −0.560959 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7136.17 | −0.378003 | −0.189002 | − | 0.981977i | \(-0.560525\pi\) | ||||
−0.189002 | + | 0.981977i | \(0.560525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2554.59 | 0.134747 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1552.58 | 0.0815489 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24820.9 | −1.29825 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18501.2 | 0.963654 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16973.2 | 0.880380 | 0.440190 | − | 0.897905i | \(-0.354911\pi\) | ||||
0.440190 | + | 0.897905i | \(0.354911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1813.47 | −0.0936714 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19670.2 | −1.01182 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1707.75 | 0.0874817 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18100.1 | −0.923378 | −0.461689 | − | 0.887042i | \(-0.652756\pi\) | ||||
−0.461689 | + | 0.887042i | \(0.652756\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17710.6 | 0.899791 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13693.2 | 0.692835 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26474.1 | −1.33403 | −0.667014 | − | 0.745045i | \(-0.732428\pi\) | ||||
−0.667014 | + | 0.745045i | \(0.732428\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3769.93 | 0.189192 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −43001.0 | −2.14920 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1455.63 | 0.0724575 | 0.0362288 | − | 0.999344i | \(-0.488466\pi\) | ||||
0.0362288 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14878.2 | 0.737603 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4845.16 | 0.239235 | 0.119617 | − | 0.992820i | \(-0.461833\pi\) | ||||
0.119617 | + | 0.992820i | \(0.461833\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3854.84 | −0.189571 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3232.61 | 0.158333 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16327.7 | −0.796529 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6411.21 | 0.311516 | 0.155758 | − | 0.987795i | \(-0.450218\pi\) | ||||
0.155758 | + | 0.987795i | \(0.450218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 268.823 | 0.0130099 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11160.7 | −0.537984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −546.716 | −0.0262493 | −0.0131247 | − | 0.999914i | \(-0.504178\pi\) | ||||
−0.0131247 | + | 0.999914i | \(0.504178\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5487.55 | −0.262431 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1981.09 | −0.0943686 | −0.0471843 | − | 0.998886i | \(-0.515025\pi\) | ||||
−0.0471843 | + | 0.998886i | \(0.515025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4554.07 | 0.216079 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1679.79 | 0.0793896 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −63310.4 | −2.98045 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12719.9 | 0.596478 | 0.298239 | − | 0.954491i | \(-0.403601\pi\) | ||||
0.298239 | + | 0.954491i | \(0.403601\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10924.9 | −0.510311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6926.77 | 0.322301 | 0.161150 | − | 0.986930i | \(-0.448480\pi\) | ||||
0.161150 | + | 0.986930i | \(0.448480\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1687.58 | 0.0782190 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6603.69 | 0.304898 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12856.4 | 0.591306 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47806.4 | −2.19033 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10211.9 | −0.466084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3325.46 | −0.151199 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4223.75 | 0.191309 | 0.0956546 | − | 0.995415i | \(-0.469506\pi\) | ||||
0.0956546 | + | 0.995415i | \(0.469506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6280.56 | 0.283389 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18176.3 | 0.817035 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27621.3 | −1.23690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1419.84 | 0.0633415 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27988.1 | −1.24390 | −0.621951 | − | 0.783056i | \(-0.713660\pi\) | ||||
−0.621951 | + | 0.783056i | \(0.713660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3625.95 | −0.160547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10958.9 | 0.483412 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10402.2 | 0.457144 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1364.20 | 0.0597288 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1669.32 | 0.0728165 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30980.6 | 1.34638 | 0.673190 | − | 0.739469i | \(-0.264924\pi\) | ||||
0.673190 | + | 0.739469i | \(0.264924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 389.244 | 0.0168535 | 0.00842677 | − | 0.999964i | \(-0.497318\pi\) | ||||
0.00842677 | + | 0.999964i | \(0.497318\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6186.91 | 0.266894 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1377.75 | −0.0592151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27492.9 | −1.17730 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12057.6 | −0.514441 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4469.51 | −0.189996 | −0.0949982 | − | 0.995477i | \(-0.530285\pi\) | ||||
−0.0949982 | + | 0.995477i | \(0.530285\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14661.6 | 0.620985 | 0.310492 | − | 0.950576i | \(-0.399506\pi\) | ||||
0.310492 | + | 0.950576i | \(0.399506\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5964.73 | −0.251715 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4882.54 | 0.205299 | 0.102650 | − | 0.994718i | \(-0.467268\pi\) | ||||
0.102650 | + | 0.994718i | \(0.467268\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35180.8 | −1.47392 | −0.736960 | − | 0.675936i | \(-0.763739\pi\) | ||||
−0.736960 | + | 0.675936i | \(0.763739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5402.10 | −0.225508 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5185.18 | −0.215673 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3933.10 | 0.163007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10091.3 | −0.416734 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9950.73 | 0.409460 | 0.204730 | − | 0.978818i | \(-0.434368\pi\) | ||||
0.204730 | + | 0.978818i | \(0.434368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19722.7 | −0.808674 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5699.04 | −0.232842 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19088.8 | −0.777131 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32813.0 | −1.33113 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12978.0 | −0.524622 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3434.96 | −0.138365 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36408.0 | 1.46141 | 0.730707 | − | 0.682691i | \(-0.239190\pi\) | ||||
0.730707 | + | 0.682691i | \(0.239190\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3372.64 | −0.134903 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22788.4 | −0.908329 | −0.454164 | − | 0.890918i | \(-0.650062\pi\) | ||||
−0.454164 | + | 0.890918i | \(0.650062\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21675.6 | 0.860956 | 0.430478 | − | 0.902601i | \(-0.358345\pi\) | ||||
0.430478 | + | 0.902601i | \(0.358345\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11045.4 | 0.437198 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16485.2 | 0.650248 | 0.325124 | − | 0.945671i | \(-0.394594\pi\) | ||||
0.325124 | + | 0.945671i | \(0.394594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15671.9 | 0.616024 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15863.7 | −0.621407 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12476.4 | 0.487033 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52101.4 | −2.02685 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 702.184 | 0.0272226 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1482.82 | 0.0572899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9325.23 | 0.359054 | 0.179527 | − | 0.983753i | \(-0.442543\pi\) | ||||
0.179527 | + | 0.983753i | \(0.442543\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17155.9 | 0.658309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18523.9 | −0.708384 | −0.354192 | − | 0.935173i | \(-0.615244\pi\) | ||||
−0.354192 | + | 0.935173i | \(0.615244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44162.2 | −1.68310 | −0.841549 | − | 0.540180i | \(-0.818356\pi\) | ||||
−0.841549 | + | 0.540180i | \(0.818356\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −15214.2 | −0.577875 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 31348.8 | 1.18669 | 0.593343 | − | 0.804950i | \(-0.297808\pi\) | ||||
0.593343 | + | 0.804950i | \(0.297808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10643.7 | 0.401551 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13017.3 | 0.489444 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7280.09 | 0.272810 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 258.161 | 0.00964176 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6648.90 | −0.247492 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4611.15 | 0.171068 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1952.85 | −0.0722076 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23620.3 | −0.870469 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −943.837 | −0.0346676 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12555.3 | 0.459639 | 0.229820 | − | 0.973233i | \(-0.426186\pi\) | ||||
0.229820 | + | 0.973233i | \(0.426186\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11650.7 | −0.425115 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21075.9 | −0.766495 | −0.383247 | − | 0.923646i | \(-0.625194\pi\) | ||||
−0.383247 | + | 0.923646i | \(0.625194\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15787.7 | 0.572285 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6637.71 | −0.239821 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21000.4 | 0.756263 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11091.1 | −0.398108 | −0.199054 | − | 0.979989i | \(-0.563787\pi\) | ||||
−0.199054 | + | 0.979989i | \(0.563787\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11199.2 | −0.400678 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57923.8 | −2.06564 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3733.65 | −0.132715 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2003.56 | −0.0709876 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −54912.1 | −1.93930 | −0.969648 | − | 0.244504i | \(-0.921375\pi\) | ||||
−0.969648 | + | 0.244504i | \(0.921375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10410.7 | 0.366483 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −34487.4 | −1.21015 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8203.92 | 0.286948 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20442.3 | −0.712721 | −0.356361 | − | 0.934348i | \(-0.615983\pi\) | ||||
−0.356361 | + | 0.934348i | \(0.615983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9408.50 | −0.326980 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32786.7 | −1.13583 | −0.567916 | − | 0.823087i | \(-0.692250\pi\) | ||||
−0.567916 | + | 0.823087i | \(0.692250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5745.37 | −0.198404 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8866.91 | −0.305228 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24034.5 | −0.824726 | −0.412363 | − | 0.911020i | \(-0.635297\pi\) | ||||
−0.412363 | + | 0.911020i | \(0.635297\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12603.7 | 0.431121 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33355.2 | 1.13735 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41931.0 | 1.42527 | 0.712633 | − | 0.701537i | \(-0.247502\pi\) | ||||
0.712633 | + | 0.701537i | \(0.247502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9883.49 | 0.334892 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16298.0 | −0.550512 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35406.2 | 1.19221 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25234.3 | −0.847045 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18039.2 | −0.603639 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −445.388 | −0.0148576 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52217.2 | 1.73650 | 0.868249 | − | 0.496129i | \(-0.165246\pi\) | ||||
0.868249 | + | 0.496129i | \(0.165246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4917.61 | −0.163030 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9432.54 | 0.311745 | 0.155873 | − | 0.987777i | \(-0.450181\pi\) | ||||
0.155873 | + | 0.987777i | \(0.450181\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35658.7 | 1.17489 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7227.07 | −0.237386 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6562.89 | 0.214908 | 0.107454 | − | 0.994210i | \(-0.465730\pi\) | ||||
0.107454 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 53521.9 | 1.74726 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5031.44 | 0.163753 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24052.6 | −0.780426 | −0.390213 | − | 0.920725i | \(-0.627599\pi\) | ||||
−0.390213 | + | 0.920725i | \(0.627599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4791.08 | 0.154981 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6254.63 | 0.201709 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12286.3 | 0.395026 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47681.8 | −1.52842 | −0.764209 | − | 0.644969i | \(-0.776870\pi\) | ||||
−0.764209 | + | 0.644969i | \(0.776870\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10617.2 | −0.339302 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 18531.9 | 0.590452 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6495.42 | −0.206331 | −0.103166 | − | 0.994664i | \(-0.532897\pi\) | ||||
−0.103166 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22326.3 | 0.707080 |
(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 | 1840.4.a.o.1.4 | 5 | ||
4.3 | odd | 2 | 460.4.a.b.1.2 | ✓ | 5 | ||
20.3 | even | 4 | 2300.4.c.d.1749.4 | 10 | |||
20.7 | even | 4 | 2300.4.c.d.1749.7 | 10 | |||
20.19 | odd | 2 | 2300.4.a.c.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
460.4.a.b.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
1840.4.a.o.1.4 | 5 | 1.1 | even | 1 | trivial | ||
2300.4.a.c.1.4 | 5 | 20.19 | odd | 2 | |||
2300.4.c.d.1749.4 | 10 | 20.3 | even | 4 | |||
2300.4.c.d.1749.7 | 10 | 20.7 | even | 4 |