Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2496,4,Mod(1,2496)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2496, 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("2496.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2496 = 2^{6} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2496.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: | \(147.268767374\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{43}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 43 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.55744\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2496.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.1149 | −1.70969 | −0.854843 | − | 0.518886i | \(-0.826347\pi\) | ||||
−0.854843 | + | 0.518886i | \(0.826347\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.1149 | 1.89603 | 0.948013 | − | 0.318233i | \(-0.103089\pi\) | ||||
0.948013 | + | 0.318233i | \(0.103089\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.0000 | −0.712663 | −0.356332 | − | 0.934360i | \(-0.615973\pi\) | ||||
−0.356332 | + | 0.934360i | \(0.615973\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 57.3446 | 0.987088 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −36.2298 | −0.516883 | −0.258441 | − | 0.966027i | \(-0.583209\pi\) | ||||
−0.258441 | + | 0.966027i | \(0.583209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 95.5744 | 1.15401 | 0.577007 | − | 0.816739i | \(-0.304221\pi\) | ||||
0.577007 | + | 0.816739i | \(0.304221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −105.345 | −1.09467 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −161.379 | −1.46303 | −0.731516 | − | 0.681824i | \(-0.761187\pi\) | ||||
−0.731516 | + | 0.681824i | \(0.761187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 240.379 | 1.92303 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 91.3785 | 0.585123 | 0.292561 | − | 0.956247i | \(-0.405492\pi\) | ||||
0.292561 | + | 0.956247i | \(0.405492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −266.723 | −1.54532 | −0.772660 | − | 0.634821i | \(-0.781074\pi\) | ||||
−0.772660 | + | 0.634821i | \(0.781074\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 78.0000 | 0.411456 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −671.217 | −3.24161 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 149.608 | 0.664742 | 0.332371 | − | 0.943149i | \(-0.392151\pi\) | ||||
0.332371 | + | 0.943149i | \(0.392151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −77.8041 | −0.296365 | −0.148183 | − | 0.988960i | \(-0.547342\pi\) | ||||
−0.148183 | + | 0.988960i | \(0.547342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −183.608 | −0.651163 | −0.325581 | − | 0.945514i | \(-0.605560\pi\) | ||||
−0.325581 | + | 0.945514i | \(0.605560\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −172.034 | −0.569896 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −60.6893 | −0.188350 | −0.0941749 | − | 0.995556i | \(-0.530021\pi\) | ||||
−0.0941749 | + | 0.995556i | \(0.530021\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 890.055 | 2.59491 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 108.689 | 0.298422 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −281.540 | −0.729671 | −0.364835 | − | 0.931072i | \(-0.618875\pi\) | ||||
−0.364835 | + | 0.931072i | \(0.618875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 496.987 | 1.21843 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −286.723 | −0.666270 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 542.527 | 1.19714 | 0.598568 | − | 0.801072i | \(-0.295737\pi\) | ||||
0.598568 | + | 0.801072i | \(0.295737\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −65.0810 | −0.136603 | −0.0683014 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683014 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 316.034 | 0.632008 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −248.493 | −0.474182 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1033.94 | 1.88531 | 0.942656 | − | 0.333767i | \(-0.108320\pi\) | ||||
0.942656 | + | 0.333767i | \(0.108320\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 484.136 | 0.844682 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1041.81 | 1.74141 | 0.870706 | − | 0.491803i | \(-0.163662\pi\) | ||||
0.870706 | + | 0.491803i | \(0.163662\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 483.311 | 0.774894 | 0.387447 | − | 0.921892i | \(-0.373357\pi\) | ||||
0.387447 | + | 0.921892i | \(0.373357\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −721.136 | −1.11026 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −912.987 | −1.35123 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1337.05 | −1.90418 | −0.952091 | − | 0.305815i | \(-0.901071\pi\) | ||||
−0.952091 | + | 0.305815i | \(0.901071\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −812.825 | −1.07493 | −0.537465 | − | 0.843286i | \(-0.680618\pi\) | ||||
−0.537465 | + | 0.843286i | \(0.680618\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 692.527 | 0.883707 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −274.136 | −0.337821 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 936.885 | 1.11584 | 0.557919 | − | 0.829895i | \(-0.311600\pi\) | ||||
0.557919 | + | 0.829895i | \(0.311600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 456.493 | 0.525863 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 800.169 | 0.892190 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1826.89 | −1.97300 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −954.068 | −0.998669 | −0.499335 | − | 0.866409i | \(-0.666422\pi\) | ||||
−0.499335 | + | 0.866409i | \(0.666422\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −234.000 | −0.237554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1401.15 | −1.38039 | −0.690196 | − | 0.723623i | \(-0.742476\pi\) | ||||
−0.690196 | + | 0.723623i | \(0.742476\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 954.960 | 0.913544 | 0.456772 | − | 0.889584i | \(-0.349005\pi\) | ||||
0.456772 | + | 0.889584i | \(0.349005\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2013.65 | 1.87154 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 924.595 | 0.835364 | 0.417682 | − | 0.908593i | \(-0.362843\pi\) | ||||
0.417682 | + | 0.908593i | \(0.362843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −172.893 | −0.151928 | −0.0759638 | − | 0.997111i | \(-0.524203\pi\) | ||||
−0.0759638 | + | 0.997111i | \(0.524203\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −448.825 | −0.383789 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1241.81 | 1.03380 | 0.516902 | − | 0.856045i | \(-0.327085\pi\) | ||||
0.516902 | + | 0.856045i | \(0.327085\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3084.73 | 2.50133 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1272.20 | −0.980023 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −655.000 | −0.492111 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 233.412 | 0.171106 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2205.45 | −1.57809 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1079.93 | −0.754555 | −0.377278 | − | 0.926100i | \(-0.623140\pi\) | ||||
−0.377278 | + | 0.926100i | \(0.623140\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 550.825 | 0.375949 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 918.026 | 0.612277 | 0.306139 | − | 0.951987i | \(-0.400963\pi\) | ||||
0.306139 | + | 0.951987i | \(0.400963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3356.08 | 2.18804 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 516.102 | 0.329029 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1311.06 | 0.817603 | 0.408801 | − | 0.912623i | \(-0.365947\pi\) | ||||
0.408801 | + | 0.912623i | \(0.365947\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 227.593 | 0.138879 | 0.0694396 | − | 0.997586i | \(-0.477879\pi\) | ||||
0.0694396 | + | 0.997586i | \(0.477879\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 182.068 | 0.108744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −338.000 | −0.197657 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1746.69 | −1.00038 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2670.16 | −1.49817 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1325.48 | −0.728776 | −0.364388 | − | 0.931247i | \(-0.618722\pi\) | ||||
−0.364388 | + | 0.931247i | \(0.618722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 252.426 | 0.136040 | 0.0680202 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680202 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −326.068 | −0.172294 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5098.38 | 2.64201 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2268.62 | 1.15322 | 0.576611 | − | 0.817019i | \(-0.304375\pi\) | ||||
0.576611 | + | 0.817019i | \(0.304375\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 844.621 | 0.421276 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5666.79 | −2.77395 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1083.45 | 0.520630 | 0.260315 | − | 0.965524i | \(-0.416174\pi\) | ||||
0.260315 | + | 0.965524i | \(0.416174\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1490.96 | −0.703461 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −796.041 | −0.368859 | −0.184430 | − | 0.982846i | \(-0.559044\pi\) | ||||
−0.184430 | + | 0.982846i | \(0.559044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 860.169 | 0.384671 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.09598 | 0.000481654 0 | 0.000240827 | − | 1.00000i | \(-0.499923\pi\) | ||||
0.000240827 | 1.00000i | \(0.499923\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8440.86 | 3.64611 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1627.58 | −0.691167 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3250.06 | −1.35710 | −0.678549 | − | 0.734555i | \(-0.737391\pi\) | ||||
−0.678549 | + | 0.734555i | \(0.737391\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2980.84 | −1.22411 | −0.612055 | − | 0.790815i | \(-0.709657\pi\) | ||||
−0.612055 | + | 0.790815i | \(0.709657\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 195.243 | 0.0788676 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2859.74 | −1.13650 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 941.974 | 0.368363 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −948.102 | −0.364890 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 612.595 | 0.232072 | 0.116036 | − | 0.993245i | \(-0.462981\pi\) | ||||
0.116036 | + | 0.993245i | \(0.462981\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4185.81 | −1.56115 | −0.780573 | − | 0.625064i | \(-0.785073\pi\) | ||||
−0.780573 | + | 0.625064i | \(0.785073\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 745.480 | 0.273769 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.06029 | −0.000745124 0 | −0.000372562 | − | 1.00000i | \(-0.500119\pi\) | ||||
−0.000372562 | 1.00000i | \(0.500119\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1492.39 | 0.531622 | 0.265811 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265811 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3101.82 | −1.08848 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3208.75 | 1.10941 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1487.22 | 0.506691 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1452.41 | −0.487678 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2484.93 | −0.822423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2748.27 | −0.896677 | −0.448338 | − | 0.893864i | \(-0.647984\pi\) | ||||
−0.448338 | + | 0.893864i | \(0.647984\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3125.43 | −1.00541 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3509.65 | 1.11328 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9365.95 | −2.92996 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1449.93 | −0.447385 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −470.987 | −0.143357 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 186.655 | 0.0560510 | 0.0280255 | − | 0.999607i | \(-0.491078\pi\) | ||||
0.0280255 | + | 0.999607i | \(0.491078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2163.41 | 0.641009 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3932.57 | −1.14984 | −0.574920 | − | 0.818210i | \(-0.694967\pi\) | ||||
−0.574920 | + | 0.818210i | \(0.694967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5951.00 | −1.71726 | −0.858632 | − | 0.512593i | \(-0.828685\pi\) | ||||
−0.858632 | + | 0.512593i | \(0.828685\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2738.96 | 0.780131 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6548.94 | 1.84135 | 0.920676 | − | 0.390327i | \(-0.127638\pi\) | ||||
0.920676 | + | 0.390327i | \(0.127638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1160.07 | 0.322019 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4011.16 | 1.09938 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3462.35 | −0.937076 | −0.468538 | − | 0.883443i | \(-0.655219\pi\) | ||||
−0.468538 | + | 0.883443i | \(0.655219\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4581.96 | 1.22469 | 0.612345 | − | 0.790591i | \(-0.290226\pi\) | ||||
0.612345 | + | 0.790591i | \(0.290226\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17013.3 | −4.43649 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1242.47 | 0.320066 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2438.47 | 0.620611 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4746.76 | −1.19368 | −0.596838 | − | 0.802362i | \(-0.703576\pi\) | ||||
−0.596838 | + | 0.802362i | \(0.703576\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4195.84 | 1.04265 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2077.58 | −0.510209 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3373.64 | −0.818840 | −0.409420 | − | 0.912346i | \(-0.634269\pi\) | ||||
−0.409420 | + | 0.912346i | \(0.634269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5253.48 | 1.26037 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 822.407 | 0.195041 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3527.19 | 0.826981 | 0.413491 | − | 0.910508i | \(-0.364309\pi\) | ||||
0.413491 | + | 0.910508i | \(0.364309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5381.61 | 1.24751 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2810.66 | −0.644230 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1144.30 | −0.259365 | −0.129682 | − | 0.991556i | \(-0.541396\pi\) | ||||
−0.129682 | + | 0.991556i | \(0.541396\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2254.25 | 0.505298 | 0.252649 | − | 0.967558i | \(-0.418698\pi\) | ||||
0.252649 | + | 0.967558i | \(0.418698\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1369.48 | −0.303607 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6249.84 | −1.37047 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7101.62 | −1.54042 | −0.770208 | − | 0.637793i | \(-0.779848\pi\) | ||||
−0.770208 | + | 0.637793i | \(0.779848\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2400.51 | −0.515106 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3831.81 | −0.813475 | −0.406738 | − | 0.913545i | \(-0.633334\pi\) | ||||
−0.406738 | + | 0.913545i | \(0.633334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3032.56 | 0.636985 | 0.318493 | − | 0.947925i | \(-0.396823\pi\) | ||||
0.318493 | + | 0.947925i | \(0.396823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5480.68 | 1.13911 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2732.08 | −0.561915 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3600.40 | −0.732832 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2862.20 | 0.576582 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2296.44 | 0.457882 | 0.228941 | − | 0.973440i | \(-0.426474\pi\) | ||||
0.228941 | + | 0.973440i | \(0.426474\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10370.3 | −2.04673 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 702.000 | 0.137152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2097.92 | −0.405772 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6447.38 | −1.23462 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4203.45 | 0.796969 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1244.01 | 0.233548 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5174.26 | −0.961925 | −0.480962 | − | 0.876741i | \(-0.659713\pi\) | ||||
−0.480962 | + | 0.876741i | \(0.659713\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2864.88 | −0.527435 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7481.54 | −1.36411 | −0.682057 | − | 0.731299i | \(-0.738914\pi\) | ||||
−0.682057 | + | 0.731299i | \(0.738914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4158.97 | −0.751051 | −0.375526 | − | 0.926812i | \(-0.622538\pi\) | ||||
−0.375526 | + | 0.926812i | \(0.622538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6040.95 | −1.08054 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 370.535 | 0.0656508 | 0.0328254 | − | 0.999461i | \(-0.489549\pi\) | ||||
0.0328254 | + | 0.999461i | \(0.489549\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2375.84 | −0.416996 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2773.79 | −0.482298 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3462.64 | −0.596490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3124.92 | 0.533352 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 518.678 | 0.0877154 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2131.10 | −0.357116 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1820.84 | −0.302364 | −0.151182 | − | 0.988506i | \(-0.548308\pi\) | ||||
−0.151182 | + | 0.988506i | \(0.548308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1346.47 | 0.221581 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19763.6 | −3.22329 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11838.2 | −1.91356 | −0.956781 | − | 0.290809i | \(-0.906076\pi\) | ||||
−0.956781 | + | 0.290809i | \(0.906076\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3725.43 | −0.596867 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6934.80 | 1.10129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19209.8 | 3.02399 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9254.19 | −1.44414 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10603.5 | −1.64043 | −0.820214 | − | 0.572057i | \(-0.806145\pi\) | ||||
−0.820214 | + | 0.572057i | \(0.806145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6398.72 | 0.981421 | 0.490710 | − | 0.871323i | \(-0.336737\pi\) | ||||
0.490710 | + | 0.871323i | \(0.336737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7031.27 | −1.06016 | −0.530080 | − | 0.847948i | \(-0.677838\pi\) | ||||
−0.530080 | + | 0.847948i | \(0.677838\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19914.1 | −2.97727 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3816.61 | 0.565816 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5053.75 | 0.742972 | 0.371486 | − | 0.928439i | \(-0.378848\pi\) | ||||
0.371486 | + | 0.928439i | \(0.378848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2275.46 | 0.331749 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1965.00 | 0.284121 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9238.43 | −1.32483 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −81.1902 | −0.0115479 | −0.00577397 | − | 0.999983i | \(-0.501838\pi\) | ||||
−0.00577397 | + | 0.999983i | \(0.501838\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −700.237 | −0.0987883 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9886.26 | −1.38347 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8295.79 | −1.15158 | −0.575790 | − | 0.817597i | \(-0.695305\pi\) | ||||
−0.575790 | + | 0.817597i | \(0.695305\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6616.34 | 0.911110 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1187.92 | 0.162284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6592.90 | 0.893548 | 0.446774 | − | 0.894647i | \(-0.352573\pi\) | ||||
0.446774 | + | 0.894647i | \(0.352573\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3239.80 | 0.435643 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7472.96 | −0.996999 | −0.498499 | − | 0.866890i | \(-0.666115\pi\) | ||||
−0.498499 | + | 0.866890i | \(0.666115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17451.6 | 2.31018 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1652.47 | −0.217054 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3175.88 | 0.413943 | 0.206971 | − | 0.978347i | \(-0.433639\pi\) | ||||
0.206971 | + | 0.978347i | \(0.433639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5846.70 | 0.756216 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2754.08 | −0.353499 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25557.6 | 3.25555 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11394.6 | −1.44050 | −0.720251 | − | 0.693713i | \(-0.755973\pi\) | ||||
−0.720251 | + | 0.693713i | \(0.755973\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10068.2 | −1.26327 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13046.7 | 1.62474 | 0.812370 | − | 0.583142i | \(-0.198177\pi\) | ||||
0.812370 | + | 0.583142i | \(0.198177\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3467.40 | −0.428594 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1548.31 | −0.189965 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3889.82 | −0.473737 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2888.77 | −0.349243 | −0.174622 | − | 0.984636i | \(-0.555870\pi\) | ||||
−0.174622 | + | 0.984636i | \(0.555870\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3933.19 | −0.472043 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19050.8 | 2.26980 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15537.0 | 1.83779 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −682.780 | −0.0801819 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14260.8 | 1.66273 | 0.831367 | − | 0.555724i | \(-0.187559\pi\) | ||||
0.831367 | + | 0.555724i | \(0.187559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −890.723 | −0.103114 | −0.0515572 | − | 0.998670i | \(-0.516418\pi\) | ||||
−0.0515572 | + | 0.998670i | \(0.516418\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −546.203 | −0.0627833 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8708.85 | −0.993980 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2285.31 | −0.259002 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1014.00 | 0.114117 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1323.12 | −0.147871 | −0.0739353 | − | 0.997263i | \(-0.523556\pi\) | ||||
−0.0739353 | + | 0.997263i | \(0.523556\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9399.47 | −1.04321 | −0.521605 | − | 0.853187i | \(-0.674666\pi\) | ||||
−0.521605 | + | 0.853187i | \(0.674666\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5240.07 | 0.577568 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −15423.7 | −1.68836 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6115.04 | −0.664817 | −0.332409 | − | 0.943135i | \(-0.607861\pi\) | ||||
−0.332409 | + | 0.943135i | \(0.607861\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8010.49 | 0.864970 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12931.1 | 1.38685 | 0.693425 | − | 0.720529i | \(-0.256101\pi\) | ||||
0.693425 | + | 0.720529i | \(0.256101\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17908.4 | −1.90773 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3976.44 | 0.420759 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2050.73 | −0.215546 | −0.107773 | − | 0.994176i | \(-0.534372\pi\) | ||||
−0.107773 | + | 0.994176i | \(0.534372\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2022.91 | 0.211208 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −757.277 | −0.0785430 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8725.82 | −0.899061 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11923.7 | −1.22049 | −0.610247 | − | 0.792211i | \(-0.708930\pi\) | ||||
−0.610247 | + | 0.792211i | \(0.708930\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 978.203 | 0.0994741 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1324.14 | −0.133777 | −0.0668886 | − | 0.997760i | \(-0.521307\pi\) | ||||
−0.0668886 | + | 0.997760i | \(0.521307\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6840.65 | −0.686635 | −0.343318 | − | 0.939219i | \(-0.611551\pi\) | ||||
−0.343318 | + | 0.939219i | \(0.611551\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15295.1 | −1.52537 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9041.73 | 0.895935 | 0.447967 | − | 0.894050i | \(-0.352148\pi\) | ||||
0.447967 | + | 0.894050i | \(0.352148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36306.7 | 3.57460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6805.86 | −0.665812 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4773.82 | 0.464060 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22974.0 | 2.21920 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2533.86 | −0.243224 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4650.71 | 0.443625 | 0.221812 | − | 0.975089i | \(-0.428803\pi\) | ||||
0.221812 | + | 0.975089i | \(0.428803\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1944.91 | 0.184366 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 17000.4 | 1.60154 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18236.9 | 1.70741 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19632.4 | −1.82675 | −0.913375 | − | 0.407120i | \(-0.866533\pi\) | ||||
−0.913375 | + | 0.407120i | \(0.866533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3250.36 | −0.300586 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14472.0 | 1.33017 | 0.665084 | − | 0.746769i | \(-0.268396\pi\) | ||||
0.665084 | + | 0.746769i | \(0.268396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3310.62 | −0.302440 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4472.88 | 0.406144 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 36583.1 | 3.30176 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7065.91 | 0.633895 | 0.316947 | − | 0.948443i | \(-0.397342\pi\) | ||||
0.316947 | + | 0.948443i | \(0.397342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2388.12 | 0.212961 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11955.1 | 1.05974 | 0.529871 | − | 0.848078i | \(-0.322240\pi\) | ||||
0.529871 | + | 0.848078i | \(0.322240\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26782.8 | 2.36004 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −507.000 | −0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8321.15 | 0.724614 | 0.362307 | − | 0.932059i | \(-0.381989\pi\) | ||||
0.362307 | + | 0.932059i | \(0.381989\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16971.4 | 1.46922 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2580.51 | −0.222090 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18254.0 | −1.56187 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1577.92 | 0.134230 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.28795 | −0.000278083 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20130.2 | −1.69274 | −0.846372 | − | 0.532592i | \(-0.821218\pi\) | ||||
−0.846372 | + | 0.532592i | \(0.821218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8810.52 | −0.736630 | −0.368315 | − | 0.929701i | \(-0.620065\pi\) | ||||
−0.368315 | + | 0.929701i | \(0.620065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −25322.6 | −2.10508 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9663.31 | 0.798749 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13876.0 | 1.14046 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4882.75 | 0.399045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1011.45 | −0.0821969 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17673.5 | −1.42821 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9750.17 | 0.783521 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23141.4 | −1.84930 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7765.62 | −0.617135 | −0.308567 | − | 0.951202i | \(-0.599850\pi\) | ||||
−0.308567 | + | 0.951202i | \(0.599850\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8942.52 | 0.706741 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3304.82 | 0.259749 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19782.4 | −1.54631 | −0.773156 | − | 0.634216i | \(-0.781323\pi\) | ||||
−0.773156 | + | 0.634216i | \(0.781323\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −585.729 | −0.0455342 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8733.45 | 0.675240 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −46950.5 | −3.61038 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8579.23 | 0.656159 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10153.9 | 0.772413 | 0.386206 | − | 0.922412i | \(-0.373785\pi\) | ||||
0.386206 | + | 0.922412i | \(0.373785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2386.91 | −0.180600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2825.92 | −0.212675 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18388.2 | −1.37650 | −0.688252 | − | 0.725472i | \(-0.741622\pi\) | ||||
−0.688252 | + | 0.725472i | \(0.741622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23737.1 | −1.76748 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2844.31 | 0.210669 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16365.0 | 1.20573 | 0.602863 | − | 0.797845i | \(-0.294027\pi\) | ||||
0.602863 | + | 0.797845i | \(0.294027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −544.241 | −0.0398875 | −0.0199437 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199437 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1837.79 | −0.133987 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38791.9 | −2.81345 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −798.738 | −0.0576289 | −0.0288145 | − | 0.999585i | \(-0.509173\pi\) | ||||
−0.0288145 | + | 0.999585i | \(0.509173\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12557.4 | 0.901328 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28542.2 | −2.03809 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7320.05 | 0.520010 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2236.44 | −0.158061 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9187.53 | −0.646013 | −0.323007 | − | 0.946397i | \(-0.604694\pi\) | ||||
−0.323007 | + | 0.946397i | \(0.604694\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25491.9 | −1.78332 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.18086 | 0.000430197 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4371.80 | −0.302746 | −0.151373 | − | 0.988477i | \(-0.548369\pi\) | ||||
−0.151373 | + | 0.988477i | \(0.548369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24318.0 | 1.67553 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4477.18 | −0.306932 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6780.78 | −0.462530 | −0.231265 | − | 0.972891i | \(-0.574286\pi\) | ||||
−0.231265 | + | 0.972891i | \(0.574286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21348.5 | −1.44895 | −0.724477 | − | 0.689299i | \(-0.757919\pi\) | ||||
−0.724477 | + | 0.689299i | \(0.757919\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9305.46 | 0.628437 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12520.2 | 0.841356 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11161.8 | 0.746362 | 0.373181 | − | 0.927758i | \(-0.378267\pi\) | ||||
0.373181 | + | 0.927758i | \(0.378267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9626.24 | −0.640517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −788.960 | −0.0522388 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12407.8 | −0.817528 | −0.408764 | − | 0.912640i | \(-0.634040\pi\) | ||||
−0.408764 | + | 0.912640i | \(0.634040\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4461.65 | −0.292538 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5035.01 | 0.328528 | 0.164264 | − | 0.986416i | \(-0.447475\pi\) | ||||
0.164264 | + | 0.986416i | \(0.447475\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1623.67 | 0.105430 | 0.0527148 | − | 0.998610i | \(-0.483213\pi\) | ||||
0.0527148 | + | 0.998610i | \(0.483213\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4357.22 | 0.281561 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32898.6 | 2.11566 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12109.5 | 0.775009 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7454.80 | 0.474826 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5420.27 | −0.343594 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24809.0 | 1.56519 | 0.782593 | − | 0.622534i | \(-0.213897\pi\) | ||||
0.782593 | + | 0.622534i | \(0.213897\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8244.81 | 0.517697 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20642.8 | 1.29005 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11570.7 | 0.719699 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9376.30 | 0.580471 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18076.6 | 1.11386 | 0.556928 | − | 0.830561i | \(-0.311980\pi\) | ||||
0.556928 | + | 0.830561i | \(0.311980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19954.2 | −1.22382 | −0.611910 | − | 0.790928i | \(-0.709598\pi\) | ||||
−0.611910 | + | 0.790928i | \(0.709598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10528.9 | −0.642755 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11206.1 | −0.680921 | −0.340461 | − | 0.940259i | \(-0.610583\pi\) | ||||
−0.340461 | + | 0.940259i | \(0.610583\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14105.7 | −0.853155 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28097.9 | 1.69162 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2456.10 | −0.147189 | −0.0735947 | − | 0.997288i | \(-0.523447\pi\) | ||||
−0.0735947 | + | 0.997288i | \(0.523447\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17548.0 | −1.04680 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4349.80 | 0.258298 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23280.8 | 1.37616 | 0.688081 | − | 0.725633i | \(-0.258453\pi\) | ||||
0.688081 | + | 0.725633i | \(0.258453\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6999.49 | 0.411874 | 0.205937 | − | 0.978565i | \(-0.433976\pi\) | ||||
0.205937 | + | 0.978565i | \(0.433976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1412.96 | 0.0827675 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −64151.1 | −3.74086 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14746.5 | −0.856054 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −559.966 | −0.0323610 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1692.11 | 0.0973517 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33166.1 | 1.89964 | 0.949820 | − | 0.312798i | \(-0.101266\pi\) | ||||
0.949820 | + | 0.312798i | \(0.101266\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6490.22 | −0.370087 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19998.6 | −1.13532 | −0.567658 | − | 0.823265i | \(-0.692150\pi\) | ||||
−0.567658 | + | 0.823265i | \(0.692150\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33502.0 | −1.89350 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11797.7 | 0.663861 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22857.9 | −1.28058 | −0.640289 | − | 0.768134i | \(-0.721185\pi\) | ||||
−0.640289 | + | 0.768134i | \(0.721185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25060.8 | −1.39784 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17853.0 | 0.991462 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3660.03 | −0.202374 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2866.56 | 0.157813 | 0.0789066 | − | 0.996882i | \(-0.474857\pi\) | ||||
0.0789066 | + | 0.996882i | \(0.474857\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8216.88 | −0.450409 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4350.42 | −0.237440 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2818.82 | 0.153186 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19646.8 | −1.06311 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30788.1 | −1.65885 | −0.829424 | − | 0.558620i | \(-0.811331\pi\) | ||||
−0.829424 | + | 0.558620i | \(0.811331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14298.7 | 0.767121 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3480.20 | −0.185918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −49201.2 | −2.61726 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4389.07 | 0.232489 | 0.116245 | − | 0.993221i | \(-0.462914\pi\) | ||||
0.116245 | + | 0.993221i | \(0.462914\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12033.5 | −0.634727 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 43043.4 | 2.26085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6460.83 | 0.337932 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10387.1 | 0.541021 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8729.09 | −0.452768 | −0.226384 | − | 0.974038i | \(-0.572690\pi\) | ||||
−0.226384 | + | 0.974038i | \(0.572690\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33533.3 | 1.73210 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13745.9 | −0.707075 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21965.4 | 1.12521 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1471.81 | 0.0750845 | 0.0375423 | − | 0.999295i | \(-0.488047\pi\) | ||||
0.0375423 | + | 0.999295i | \(0.488047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6652.08 | 0.336575 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14082.8 | 0.709632 | 0.354816 | − | 0.934936i | \(-0.384543\pi\) | ||||
0.354816 | + | 0.934936i | \(0.384543\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 51039.9 | 2.56141 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26882.4 | −1.34359 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12529.5 | −0.623687 | −0.311843 | − | 0.950133i | \(-0.600946\pi\) | ||||
−0.311843 | + | 0.950133i | \(0.600946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3727.40 | −0.184790 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19044.9 | −0.940363 | −0.470182 | − | 0.882570i | \(-0.655812\pi\) | ||||
−0.470182 | + | 0.882570i | \(0.655812\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25336.4 | 1.24598 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7315.42 | −0.358310 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 32467.0 | 1.58387 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22009.9 | −1.06944 | −0.534722 | − | 0.845028i | \(-0.679584\pi\) | ||||
−0.534722 | + | 0.845028i | \(0.679584\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14240.3 | 0.689169 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4825.08 | −0.232587 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8198.54 | 0.393634 | 0.196817 | − | 0.980440i | \(-0.436939\pi\) | ||||
0.196817 | + | 0.980440i | \(0.436939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12587.5 | −0.601974 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31929.6 | −1.52096 | −0.760478 | − | 0.649363i | \(-0.775036\pi\) | ||||
−0.760478 | + | 0.649363i | \(0.775036\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6071.10 | −0.288059 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6232.75 | 0.294569 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7052.85 | 0.332026 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26725.8 | −1.25326 | −0.626630 | − | 0.779317i | \(-0.715566\pi\) | ||||
−0.626630 | + | 0.779317i | \(0.715566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10120.9 | 0.472757 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23760.8 | −1.10558 | −0.552792 | − | 0.833320i | \(-0.686437\pi\) | ||||
−0.552792 | + | 0.833320i | \(0.686437\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −64114.5 | −2.97169 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15760.4 | −0.727673 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7436.08 | −0.342009 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27087.1 | −1.24104 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2467.22 | −0.112607 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −43364.4 | −1.97165 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23647.2 | 1.07107 | 0.535536 | − | 0.844513i | \(-0.320110\pi\) | ||||
0.535536 | + | 0.844513i | \(0.320110\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10581.6 | −0.477458 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43606.1 | 1.96012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −846.053 | −0.0378868 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16144.8 | −0.720249 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21067.5 | −0.936324 | −0.468162 | − | 0.883643i | \(-0.655084\pi\) | ||||
−0.468162 | + | 0.883643i | \(0.655084\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2198.76 | 0.0973547 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8431.97 | 0.371946 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12566.1 | −0.552238 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 108320. | 4.74258 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3432.89 | 0.149744 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1877.67 | 0.0816011 | 0.0408005 | − | 0.999167i | \(-0.487009\pi\) | ||||
0.0408005 | + | 0.999167i | \(0.487009\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2178.85 | −0.0943401 | −0.0471700 | − | 0.998887i | \(-0.515020\pi\) | ||||
−0.0471700 | + | 0.998887i | \(0.515020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6762.75 | −0.291734 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20710.1 | −0.890114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17548.2 | −0.751451 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4108.44 | 0.175288 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11731.4 | −0.498696 | −0.249348 | − | 0.968414i | \(-0.580216\pi\) | ||||
−0.249348 | + | 0.968414i | \(0.580216\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6925.69 | −0.293334 | −0.146667 | − | 0.989186i | \(-0.546855\pi\) | ||||
−0.146667 | + | 0.989186i | \(0.546855\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18749.5 | 0.791242 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35912.7 | 1.51004 | 0.755022 | − | 0.655700i | \(-0.227626\pi\) | ||||
0.755022 | + | 0.655700i | \(0.227626\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7107.67 | 0.297780 | 0.148890 | − | 0.988854i | \(-0.452430\pi\) | ||||
0.148890 | + | 0.988854i | \(0.452430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21304.9 | 0.889360 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −32246.5 | −1.34126 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15216.2 | 0.630634 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7201.53 | 0.297397 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37844.0 | 1.55724 | 0.778618 | − | 0.627498i | \(-0.215921\pi\) | ||||
0.778618 | + | 0.627498i | \(0.215921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16039.0 | −0.657631 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11495.4 | 0.469660 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3230.41 | −0.131514 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23000.2 | −0.933055 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9097.67 | −0.367764 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24143.6 | −0.972539 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23280.9 | −0.934492 | −0.467246 | − | 0.884127i | \(-0.654754\pi\) | ||||
−0.467246 | + | 0.884127i | \(0.654754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16442.0 | −0.657667 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10395.1 | 0.414342 | 0.207171 | − | 0.978305i | \(-0.433574\pi\) | ||||
0.207171 | + | 0.978305i | \(0.433574\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6698.89 | 0.266080 | 0.133040 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133040 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8196.25 | 0.324422 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31844.8 | 1.25609 | 0.628047 | − | 0.778175i | \(-0.283854\pi\) | ||||
0.628047 | + | 0.778175i | \(0.283854\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.9496 | −0.000823477 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10801.2 | 0.423101 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34763.4 | 1.35704 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13441.2 | 0.522891 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8586.61 | −0.332890 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −77444.0 | −2.99210 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20114.1 | 0.774465 | 0.387233 | − | 0.921982i | \(-0.373431\pi\) | ||||
0.387233 | + | 0.921982i | \(0.373431\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6889.32 | −0.264358 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2596.61 | −0.0992987 | −0.0496493 | − | 0.998767i | \(-0.515810\pi\) | ||||
−0.0496493 | + | 0.998767i | \(0.515810\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46374.7 | 1.76742 | 0.883710 | − | 0.468035i | \(-0.155038\pi\) | ||||
0.883710 | + | 0.468035i | \(0.155038\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 31111.0 | 1.18168 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −31863.1 | −1.20615 | −0.603077 | − | 0.797683i | \(-0.706059\pi\) | ||||
−0.603077 | + | 0.797683i | \(0.706059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37921.7 | −1.43066 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2106.00 | −0.0791848 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5800.34 | −0.217358 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 62124.4 | 2.32021 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6293.76 | 0.234273 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24372.8 | −0.904202 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10200.1 | 0.377154 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 19342.1 | 0.712809 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 56978.4 | 2.09285 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3004.29 | −0.109984 | −0.0549922 | − | 0.998487i | \(-0.517513\pi\) | ||||
−0.0549922 | + | 0.998487i | \(0.517513\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −12610.3 | −0.460130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9985.05 | −0.363139 | −0.181569 | − | 0.983378i | \(-0.558118\pi\) | ||||
−0.181569 | + | 0.983378i | \(0.558118\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21133.4 | 0.766062 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3732.04 | −0.134839 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 32236.4 | 1.16089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8216.29 | −0.294919 | −0.147459 | − | 0.989068i | \(-0.547110\pi\) | ||||
−0.147459 | + | 0.989068i | \(0.547110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15522.8 | 0.555367 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13543.6 | 0.482981 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 35962.6 | 1.27832 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8594.64 | 0.304515 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17832.8 | −0.629791 | −0.314896 | − | 0.949126i | \(-0.601970\pi\) | ||||
−0.314896 | + | 0.949126i | \(0.601970\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 85066.4 | 2.99456 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22444.6 | 0.787572 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18005.7 | −0.629786 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −444.289 | −0.0154902 | −0.00774509 | − | 0.999970i | \(-0.502465\pi\) | ||||
−0.00774509 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12476.9 | 0.433620 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30762.5 | −1.06571 | −0.532853 | − | 0.846208i | \(-0.678880\pi\) | ||||
−0.532853 | + | 0.846208i | \(0.678880\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12555.9 | 0.433592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18122.8 | 0.623848 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8791.45 | 0.301672 | 0.150836 | − | 0.988559i | \(-0.451803\pi\) | ||||
0.150836 | + | 0.988559i | \(0.451803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6283.04 | 0.214917 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1111.60 | −0.0379035 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1754.41 | 0.0596336 | 0.0298168 | − | 0.999555i | \(-0.490508\pi\) | ||||
0.0298168 | + | 0.999555i | \(0.490508\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11709.7 | −0.396771 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7127.52 | 0.240753 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 46037.8 | 1.55020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41350.2 | 1.38801 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8321.36 | 0.278455 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 80011.3 | 2.66907 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26655.9 | 0.886447 | 0.443224 | − | 0.896411i | \(-0.353835\pi\) | ||||
0.443224 | + | 0.896411i | \(0.353835\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10387.9 | 0.344384 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42151.7 | 1.39311 | 0.696556 | − | 0.717502i | \(-0.254715\pi\) | ||||
0.696556 | + | 0.717502i | \(0.254715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7991.91 | 0.263318 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9374.76 | −0.307931 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14594.7 | 0.477919 | 0.238959 | − | 0.971030i | \(-0.423194\pi\) | ||||
0.238959 | + | 0.971030i | \(0.423194\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24359.0 | −0.795217 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1556.03 | −0.0506425 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57077.8 | 1.85198 | 0.925991 | − | 0.377546i | \(-0.123232\pi\) | ||||
0.925991 | + | 0.377546i | \(0.123232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39.3821 | 0.00127393 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6393.29 | 0.206181 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29630.4 | 0.952672 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11986.6 | 0.384224 | 0.192112 | − | 0.981373i | \(-0.438466\pi\) | ||||
0.192112 | + | 0.981373i | \(0.438466\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5462.52 | 0.174570 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28526.9 | −0.908908 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32210.1 | −1.02317 | −0.511587 | − | 0.859231i | \(-0.670942\pi\) | ||||
−0.511587 | + | 0.859231i | \(0.670942\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4039.42 | −0.127930 |
(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 | 2496.4.a.u.1.1 | 2 | ||
4.3 | odd | 2 | 2496.4.a.bd.1.1 | 2 | |||
8.3 | odd | 2 | 624.4.a.l.1.2 | 2 | |||
8.5 | even | 2 | 312.4.a.f.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 936.4.a.c.1.1 | 2 | |||
24.11 | even | 2 | 1872.4.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.4.a.f.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
624.4.a.l.1.2 | 2 | 8.3 | odd | 2 | |||
936.4.a.c.1.1 | 2 | 24.5 | odd | 2 | |||
1872.4.a.v.1.1 | 2 | 24.11 | even | 2 | |||
2496.4.a.u.1.1 | 2 | 1.1 | even | 1 | trivial | ||
2496.4.a.bd.1.1 | 2 | 4.3 | odd | 2 |