Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,4,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("76.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(4.48414516044\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.35529.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 52x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.0768183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.1 |
$q$-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 | ||||||||
\(3\) | −8.47932 | −1.63185 | −0.815923 | − | 0.578161i | \(-0.803771\pi\) | ||||
−0.815923 | + | 0.578161i | \(0.803771\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.55614 | −0.496956 | −0.248478 | − | 0.968638i | \(-0.579930\pi\) | ||||
−0.248478 | + | 0.968638i | \(0.579930\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0355 | 1.72975 | 0.864876 | − | 0.501985i | \(-0.167397\pi\) | ||||
0.864876 | + | 0.501985i | \(0.167397\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 44.8989 | 1.66292 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 54.0539 | 1.48162 | 0.740812 | − | 0.671713i | \(-0.234441\pi\) | ||||
0.740812 | + | 0.671713i | \(0.234441\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −62.2771 | −1.32866 | −0.664329 | − | 0.747440i | \(-0.731283\pi\) | ||||
−0.664329 | + | 0.747440i | \(0.731283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.1123 | 0.810956 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 75.3355 | 1.07480 | 0.537398 | − | 0.843329i | \(-0.319407\pi\) | ||||
0.537398 | + | 0.843329i | \(0.319407\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −271.639 | −2.82269 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 114.160 | 1.03496 | 0.517479 | − | 0.855696i | \(-0.326870\pi\) | ||||
0.517479 | + | 0.855696i | \(0.326870\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −94.1293 | −0.753035 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −151.770 | −1.08179 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 171.178 | 1.09610 | 0.548051 | − | 0.836445i | \(-0.315370\pi\) | ||||
0.548051 | + | 0.836445i | \(0.315370\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 59.9028 | 0.347060 | 0.173530 | − | 0.984829i | \(-0.444483\pi\) | ||||
0.173530 | + | 0.984829i | \(0.444483\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −458.340 | −2.41778 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −177.993 | −0.859611 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 156.792 | 0.696660 | 0.348330 | − | 0.937372i | \(-0.386749\pi\) | ||||
0.348330 | + | 0.937372i | \(0.386749\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 528.067 | 2.16816 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 163.384 | 0.622349 | 0.311175 | − | 0.950353i | \(-0.399278\pi\) | ||||
0.311175 | + | 0.950353i | \(0.399278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −240.326 | −0.852310 | −0.426155 | − | 0.904650i | \(-0.640132\pi\) | ||||
−0.426155 | + | 0.904650i | \(0.640132\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −249.464 | −0.826399 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −292.877 | −0.908947 | −0.454474 | − | 0.890760i | \(-0.650173\pi\) | ||||
−0.454474 | + | 0.890760i | \(0.650173\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 683.271 | 1.99204 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −638.794 | −1.75390 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −214.708 | −0.556461 | −0.278230 | − | 0.960514i | \(-0.589748\pi\) | ||||
−0.278230 | + | 0.960514i | \(0.589748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −300.331 | −0.736302 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −161.107 | −0.374371 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 137.343 | 0.303061 | 0.151530 | − | 0.988453i | \(-0.451580\pi\) | ||||
0.151530 | + | 0.988453i | \(0.451580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.76203 | −0.00789637 | −0.00394818 | − | 0.999992i | \(-0.501257\pi\) | ||||
−0.00394818 | + | 0.999992i | \(0.501257\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1438.36 | 2.87644 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 346.020 | 0.660285 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 842.158 | 1.53561 | 0.767805 | − | 0.640683i | \(-0.221349\pi\) | ||||
0.767805 | + | 0.640683i | \(0.221349\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −968.001 | −1.68889 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1090.78 | 1.82327 | 0.911633 | − | 0.411005i | \(-0.134822\pi\) | ||||
0.911633 | + | 0.411005i | \(0.134822\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −954.887 | −1.53097 | −0.765487 | − | 0.643452i | \(-0.777502\pi\) | ||||
−0.765487 | + | 0.643452i | \(0.777502\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 798.153 | 1.22884 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1731.64 | 2.56284 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −363.816 | −0.518133 | −0.259066 | − | 0.965860i | \(-0.583415\pi\) | ||||
−0.259066 | + | 0.965860i | \(0.583415\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 74.6391 | 0.102386 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 131.966 | 0.174520 | 0.0872598 | − | 0.996186i | \(-0.472189\pi\) | ||||
0.0872598 | + | 0.996186i | \(0.472189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −418.574 | −0.534127 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1451.47 | −1.78867 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 55.5599 | 0.0661723 | 0.0330861 | − | 0.999453i | \(-0.489466\pi\) | ||||
0.0330861 | + | 0.999453i | \(0.489466\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1995.07 | −2.29825 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −507.935 | −0.566348 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −105.567 | −0.114010 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −470.657 | −0.492659 | −0.246330 | − | 0.969186i | \(-0.579225\pi\) | ||||
−0.246330 | + | 0.969186i | \(0.579225\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2426.96 | 2.46382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1444.43 | −1.42303 | −0.711517 | − | 0.702669i | \(-0.751991\pi\) | ||||
−0.711517 | + | 0.702669i | \(0.751991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1013.94 | −0.969965 | −0.484983 | − | 0.874524i | \(-0.661174\pi\) | ||||
−0.484983 | + | 0.874524i | \(0.661174\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1509.26 | 1.40275 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1636.57 | −1.47863 | −0.739314 | − | 0.673361i | \(-0.764850\pi\) | ||||
−0.739314 | + | 0.673361i | \(0.764850\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −87.1564 | −0.0765878 | −0.0382939 | − | 0.999267i | \(-0.512192\pi\) | ||||
−0.0382939 | + | 0.999267i | \(0.512192\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1329.49 | −1.13684 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 524.144 | 0.436348 | 0.218174 | − | 0.975910i | \(-0.429990\pi\) | ||||
0.218174 | + | 0.975910i | \(0.429990\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −634.290 | −0.514329 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2796.17 | −2.20945 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2413.41 | 1.85913 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1590.82 | 1.19521 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1385.39 | −1.01558 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1217.51 | 0.871181 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −795.847 | −0.556063 | −0.278032 | − | 0.960572i | \(-0.589682\pi\) | ||||
−0.278032 | + | 0.960572i | \(0.589682\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2037.80 | 1.39084 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1550.55 | 1.03414 | 0.517069 | − | 0.855944i | \(-0.327023\pi\) | ||||
0.517069 | + | 0.855944i | \(0.327023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 608.674 | 0.396832 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 843.257 | 0.537600 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −853.926 | −0.532524 | −0.266262 | − | 0.963901i | \(-0.585789\pi\) | ||||
−0.266262 | + | 0.963901i | \(0.585789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3041.73 | 1.85609 | 0.928044 | − | 0.372472i | \(-0.121490\pi\) | ||||
0.928044 | + | 0.372472i | \(0.121490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2483.40 | 1.48326 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3366.32 | −1.96857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −951.089 | −0.544715 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5793.67 | −3.25071 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1981.04 | −1.08921 | −0.544607 | − | 0.838692i | \(-0.683321\pi\) | ||||
−0.544607 | + | 0.838692i | \(0.683321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1753.69 | −0.945121 | −0.472561 | − | 0.881298i | \(-0.656670\pi\) | ||||
−0.472561 | + | 0.881298i | \(0.656670\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3382.48 | 1.78730 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −332.828 | −0.172473 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −727.595 | −0.369862 | −0.184931 | − | 0.982751i | \(-0.559206\pi\) | ||||
−0.184931 | + | 0.982751i | \(0.559206\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1820.58 | 0.908058 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3657.18 | 1.79022 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −937.248 | −0.450374 | −0.225187 | − | 0.974316i | \(-0.572299\pi\) | ||||
−0.225187 | + | 0.974316i | \(0.572299\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2546.60 | 1.20153 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3051.88 | 1.41414 | 0.707070 | − | 0.707144i | \(-0.250017\pi\) | ||||
0.707070 | + | 0.707144i | \(0.250017\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1681.43 | 0.765331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 853.079 | 0.381500 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2044.95 | 0.898698 | 0.449349 | − | 0.893356i | \(-0.351656\pi\) | ||||
0.449349 | + | 0.893356i | \(0.351656\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3015.48 | −1.30256 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1164.58 | −0.494548 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −846.452 | −0.353446 | −0.176723 | − | 0.984261i | \(-0.556550\pi\) | ||||
−0.176723 | + | 0.984261i | \(0.556550\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2698.93 | 1.10834 | 0.554171 | − | 0.832403i | \(-0.313035\pi\) | ||||
0.554171 | + | 0.832403i | \(0.313035\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 31.8994 | 0.0128857 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −871.157 | −0.346210 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4072.17 | 1.59244 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4862.03 | −1.87122 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2247.79 | 0.851540 | 0.425770 | − | 0.904831i | \(-0.360003\pi\) | ||||
0.425770 | + | 0.904831i | \(0.360003\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1859.21 | 0.693416 | 0.346708 | − | 0.937973i | \(-0.387300\pi\) | ||||
0.346708 | + | 0.937973i | \(0.387300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2934.01 | −1.07748 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2426.97 | −0.877740 | −0.438870 | − | 0.898551i | \(-0.644621\pi\) | ||||
−0.438870 | + | 0.898551i | \(0.644621\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3158.42 | −1.12510 | −0.562549 | − | 0.826764i | \(-0.690179\pi\) | ||||
−0.562549 | + | 0.826764i | \(0.690179\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7140.92 | −2.50588 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5483.77 | 1.89598 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −907.785 | −0.309280 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5125.67 | 1.72106 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1027.02 | 0.339908 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3223.50 | 1.05173 | 0.525864 | − | 0.850569i | \(-0.323742\pi\) | ||||
0.525864 | + | 0.850569i | \(0.323742\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9249.08 | −2.97529 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1335.28 | 0.423561 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1919.01 | 0.600327 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8096.79 | 2.49831 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4691.67 | −1.42804 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5068.34 | −1.52198 | −0.760989 | − | 0.648765i | \(-0.775286\pi\) | ||||
−0.760989 | + | 0.648765i | \(0.775286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4226.30 | −1.25224 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6443.84 | −1.88411 | −0.942054 | − | 0.335462i | \(-0.891108\pi\) | ||||
−0.942054 | + | 0.335462i | \(0.891108\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3897.61 | −1.12472 | −0.562361 | − | 0.826892i | \(-0.690107\pi\) | ||||
−0.562361 | + | 0.826892i | \(0.690107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14683.1 | −4.18216 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2901.11 | 0.815699 | 0.407849 | − | 0.913049i | \(-0.366279\pi\) | ||||
0.407849 | + | 0.913049i | \(0.366279\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1627.27 | 0.451707 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3084.91 | 0.845513 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1420.60 | −0.384482 | −0.192241 | − | 0.981348i | \(-0.561576\pi\) | ||||
−0.192241 | + | 0.981348i | \(0.561576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6149.55 | 1.64368 | 0.821841 | − | 0.569716i | \(-0.192947\pi\) | ||||
0.821841 | + | 0.569716i | \(0.192947\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3464.91 | 0.914708 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3796.35 | −0.989958 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1183.26 | −0.304815 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1118.98 | −0.284789 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3772.54 | 0.948688 | 0.474344 | − | 0.880340i | \(-0.342685\pi\) | ||||
0.474344 | + | 0.880340i | \(0.342685\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6170.80 | 1.53342 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3549.23 | 0.871612 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5930.61 | −1.43946 | −0.719730 | − | 0.694254i | \(-0.755735\pi\) | ||||
−0.719730 | + | 0.694254i | \(0.755735\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5022.90 | 1.20505 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7685.70 | 1.82273 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4559.86 | 1.06910 | 0.534549 | − | 0.845137i | \(-0.320481\pi\) | ||||
0.534549 | + | 0.845137i | \(0.320481\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1192.95 | 0.276537 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −471.110 | −0.107983 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4130.57 | −0.936227 | −0.468114 | − | 0.883668i | \(-0.655066\pi\) | ||||
−0.468114 | + | 0.883668i | \(0.655066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −569.640 | −0.127687 | −0.0638435 | − | 0.997960i | \(-0.520336\pi\) | ||||
−0.0638435 | + | 0.997960i | \(0.520336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16916.9 | 3.75039 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5088.05 | −1.11571 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3463.48 | −0.751265 | −0.375633 | − | 0.926769i | \(-0.622575\pi\) | ||||
−0.375633 | + | 0.926769i | \(0.622575\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2689.57 | 0.577133 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2951.55 | −0.626601 | −0.313300 | − | 0.949654i | \(-0.601435\pi\) | ||||
−0.313300 | + | 0.949654i | \(0.601435\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3104.67 | −0.652133 | −0.326066 | − | 0.945347i | \(-0.605723\pi\) | ||||
−0.326066 | + | 0.945347i | \(0.605723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 895.133 | 0.186046 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5234.09 | 1.07651 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 762.433 | 0.155187 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3990.85 | 0.803944 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1466.23 | −0.292348 | −0.146174 | − | 0.989259i | \(-0.546696\pi\) | ||||
−0.146174 | + | 0.989259i | \(0.546696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −763.099 | −0.150608 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8203.77 | −1.60280 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7109.56 | −1.37511 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7698.95 | −1.47429 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12247.8 | 2.32217 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 20.9023 | 0.00392415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2044.70 | 0.380121 | 0.190061 | − | 0.981772i | \(-0.439132\pi\) | ||||
0.190061 | + | 0.981772i | \(0.439132\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8597.51 | 1.58283 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4002.96 | −0.729862 | −0.364931 | − | 0.931035i | \(-0.618907\pi\) | ||||
−0.364931 | + | 0.931035i | \(0.618907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10350.4 | −1.86913 | −0.934564 | − | 0.355794i | \(-0.884211\pi\) | ||||
−0.934564 | + | 0.355794i | \(0.884211\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7991.70 | −1.42947 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7084.90 | −1.25529 | −0.627646 | − | 0.778499i | \(-0.715981\pi\) | ||||
−0.627646 | + | 0.778499i | \(0.715981\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9252.83 | 1.62401 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13877.0 | 2.41289 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1431.37 | 0.246575 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5862.10 | 1.00053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 739.027 | 0.124979 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9382.45 | −1.57225 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7837.56 | −1.30148 | −0.650742 | − | 0.759299i | \(-0.725542\pi\) | ||||
−0.650742 | + | 0.759299i | \(0.725542\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7039.78 | 1.15849 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4679.14 | −0.763131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1418.55 | 0.229298 | 0.114649 | − | 0.993406i | \(-0.463426\pi\) | ||||
0.114649 | + | 0.993406i | \(0.463426\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4444.38 | −0.712052 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3237.98 | 0.514212 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10900.7 | 1.71599 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5378.35 | 0.839306 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5558.78 | 0.859974 | 0.429987 | − | 0.902835i | \(-0.358518\pi\) | ||||
0.429987 | + | 0.902835i | \(0.358518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1077.94 | −0.165331 | −0.0826656 | − | 0.996577i | \(-0.526343\pi\) | ||||
−0.0826656 | + | 0.996577i | \(0.526343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9451.81 | 1.43732 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4498.87 | 0.678331 | 0.339166 | − | 0.940727i | \(-0.389855\pi\) | ||||
0.339166 | + | 0.940727i | \(0.389855\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6060.53 | −0.906083 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −20464.0 | −3.03382 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9060.02 | −1.33195 | −0.665974 | − | 0.745975i | \(-0.731984\pi\) | ||||
−0.665974 | + | 0.745975i | \(0.731984\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −13489.1 | −1.95039 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5305.48 | 0.760827 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2859.88 | 0.406770 | 0.203385 | − | 0.979099i | \(-0.434806\pi\) | ||||
0.203385 | + | 0.979099i | \(0.434806\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7335.76 | 1.03492 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6878.27 | −0.962539 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 335.799 | 0.0466140 | 0.0233070 | − | 0.999728i | \(-0.492580\pi\) | ||||
0.0233070 | + | 0.999728i | \(0.492580\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10323.7 | −1.42163 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10660.5 | −1.45634 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3507.13 | 0.475328 | 0.237664 | − | 0.971347i | \(-0.423618\pi\) | ||||
0.237664 | + | 0.971347i | \(0.423618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6748.24 | 0.907410 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5680.18 | 0.757816 | 0.378908 | − | 0.925434i | \(-0.376300\pi\) | ||||
0.378908 | + | 0.925434i | \(0.376300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9621.23 | −1.27362 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10790.4 | −1.41732 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3884.56 | 0.506311 | 0.253155 | − | 0.967426i | \(-0.418532\pi\) | ||||
0.253155 | + | 0.967426i | \(0.418532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8600.32 | 1.11237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13147.6 | −1.68755 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2021.41 | 0.257489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1328.04 | −0.167890 | −0.0839450 | − | 0.996470i | \(-0.526752\pi\) | ||||
−0.0839450 | + | 0.996470i | \(0.526752\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5161.14 | −0.647569 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2023.72 | 0.252020 | 0.126010 | − | 0.992029i | \(-0.459783\pi\) | ||||
0.126010 | + | 0.992029i | \(0.459783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3730.57 | −0.461124 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −414.705 | −0.0508811 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8475.21 | 1.03219 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3409.21 | 0.412163 | 0.206081 | − | 0.978535i | \(-0.433929\pi\) | ||||
0.206081 | + | 0.978535i | \(0.433929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7240.71 | 0.868997 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4399.86 | 0.524220 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −733.220 | −0.0867286 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25791.8 | −3.02885 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6306.05 | 0.735253 | 0.367626 | − | 0.929974i | \(-0.380171\pi\) | ||||
0.367626 | + | 0.929974i | \(0.380171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1989.12 | −0.230271 | −0.115135 | − | 0.993350i | \(-0.536730\pi\) | ||||
−0.115135 | + | 0.993350i | \(0.536730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13149.9 | −1.51151 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7091.28 | −0.809359 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −120.518 | −0.0136588 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28544.1 | 3.21240 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10688.9 | −1.19459 | −0.597293 | − | 0.802023i | \(-0.703757\pi\) | ||||
−0.597293 | + | 0.802023i | \(0.703757\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3581.70 | 0.397519 | 0.198759 | − | 0.980048i | \(-0.436309\pi\) | ||||
0.198759 | + | 0.980048i | \(0.436309\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8064.59 | 0.888890 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2169.04 | 0.237436 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14447.8 | −1.57074 | −0.785370 | − | 0.619027i | \(-0.787527\pi\) | ||||
−0.785370 | + | 0.619027i | \(0.787527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30678.1 | 3.31261 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14046.0 | 1.50643 | 0.753214 | − | 0.657776i | \(-0.228503\pi\) | ||||
0.753214 | + | 0.657776i | \(0.228503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −308.698 | −0.0328847 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16797.8 | 1.77743 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13791.0 | −1.44952 | −0.724761 | − | 0.689000i | \(-0.758050\pi\) | ||||
−0.724761 | + | 0.689000i | \(0.758050\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8831.55 | 0.922087 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14870.1 | 1.54229 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11084.9 | 1.14213 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15109.6 | 1.54661 | 0.773303 | − | 0.634036i | \(-0.218603\pi\) | ||||
0.773303 | + | 0.634036i | \(0.218603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11433.7 | −1.16270 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7351.36 | −0.742705 | −0.371352 | − | 0.928492i | \(-0.621106\pi\) | ||||
−0.371352 | + | 0.928492i | \(0.621106\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4793.20 | −0.481120 | −0.240560 | − | 0.970634i | \(-0.577331\pi\) | ||||
−0.240560 | + | 0.970634i | \(0.577331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2822.16 | 0.281450 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1821.63 | 0.180503 | 0.0902515 | − | 0.995919i | \(-0.471233\pi\) | ||||
0.0902515 | + | 0.995919i | \(0.471233\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26978.9 | 2.65623 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6169.51 | 0.603558 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12990.5 | −1.26280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1788.46 | −0.172758 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9640.15 | −0.925350 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −366.616 | −0.0349710 | −0.0174855 | − | 0.999847i | \(-0.505566\pi\) | ||||
−0.0174855 | + | 0.999847i | \(0.505566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9764.54 | −0.925623 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −31010.4 | −2.92137 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2615.04 | 0.244830 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3086.31 | −0.287175 | −0.143587 | − | 0.989638i | \(-0.545864\pi\) | ||||
−0.143587 | + | 0.989638i | \(0.545864\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7947.23 | 0.734941 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8230.71 | 0.756511 | 0.378255 | − | 0.925701i | \(-0.376524\pi\) | ||||
0.378255 | + | 0.925701i | \(0.376524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12895.8 | 1.17809 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13484.5 | −1.22441 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 34943.7 | 3.15380 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12825.9 | 1.15063 | 0.575315 | − | 0.817932i | \(-0.304879\pi\) | ||||
0.575315 | + | 0.817932i | \(0.304879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25877.8 | −2.30766 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −731.374 | −0.0648318 | −0.0324159 | − | 0.999474i | \(-0.510320\pi\) | ||||
−0.0324159 | + | 0.999474i | \(0.510320\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8025.47 | 0.707185 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14257.4 | −1.24890 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13268.0 | −1.15539 | −0.577695 | − | 0.816252i | \(-0.696048\pi\) | ||||
−0.577695 | + | 0.816252i | \(0.696048\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30590.2 | −2.64820 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2883.63 | −0.248179 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5633.59 | 0.482030 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15831.1 | −1.34672 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17339.8 | −1.46654 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12804.7 | −1.07675 | −0.538374 | − | 0.842706i | \(-0.680961\pi\) | ||||
−0.538374 | + | 0.842706i | \(0.680961\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3115.61 | −0.260490 | −0.130245 | − | 0.991482i | \(-0.541576\pi\) | ||||
−0.130245 | + | 0.991482i | \(0.541576\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25569.2 | 2.12558 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4512.80 | 0.373018 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 865.561 | 0.0711401 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6166.56 | 0.503966 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10175.1 | −0.826889 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9093.00 | 0.734813 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7177.34 | 0.576769 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36933.4 | 2.95146 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 664.570 | 0.0528135 | 0.0264068 | − | 0.999651i | \(-0.491593\pi\) | ||||
0.0264068 | + | 0.999651i | \(0.491593\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22885.1 | −1.80864 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 484.253 | 0.0380608 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11510.2 | −0.899709 | −0.449854 | − | 0.893102i | \(-0.648524\pi\) | ||||
−0.449854 | + | 0.893102i | \(0.648524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −168.911 | −0.0131310 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3252.38 | 0.251463 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11655.0 | −0.896241 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7386.82 | 0.564961 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13369.8 | 1.01705 | 0.508525 | − | 0.861047i | \(-0.330191\pi\) | ||||
0.508525 | + | 0.861047i | \(0.330191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14966.8 | 1.13243 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34529.3 | −2.59862 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9379.69 | 0.702143 | 0.351072 | − | 0.936349i | \(-0.385817\pi\) | ||||
0.351072 | + | 0.936349i | \(0.385817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2912.21 | −0.216846 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2391.10 | 0.177102 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3929.70 | 0.289528 | 0.144764 | − | 0.989466i | \(-0.453758\pi\) | ||||
0.144764 | + | 0.989466i | \(0.453758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19626.1 | −1.43840 | −0.719202 | − | 0.694802i | \(-0.755492\pi\) | ||||
−0.719202 | + | 0.694802i | \(0.755492\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19059.7 | −1.38958 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10745.8 | −0.779360 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4740.81 | −0.342049 | −0.171025 | − | 0.985267i | \(-0.554708\pi\) | ||||
−0.171025 | + | 0.985267i | \(0.554708\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15764.9 | −1.13155 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4227.58 | 0.301876 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11605.8 | −0.824465 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15535.9 | 1.09800 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22436.3 | 1.57759 | 0.788796 | − | 0.614656i | \(-0.210705\pi\) | ||||
0.788796 | + | 0.614656i | \(0.210705\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1138.15 | 0.0796210 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20579.1 | 1.43234 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16921.2 | −1.17179 | −0.585893 | − | 0.810389i | \(-0.699256\pi\) | ||||
−0.585893 | + | 0.810389i | \(0.699256\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13409.2 | −0.923907 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26781.3 | 1.83599 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5903.16 | −0.402665 | −0.201333 | − | 0.979523i | \(-0.564527\pi\) | ||||
−0.201333 | + | 0.979523i | \(0.564527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7880.39 | −0.534855 | −0.267428 | − | 0.963578i | \(-0.586174\pi\) | ||||
−0.267428 | + | 0.963578i | \(0.586174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 37811.9 | 2.55360 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8838.82 | −0.593966 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15127.6 | 1.01155 | 0.505774 | − | 0.862666i | \(-0.331207\pi\) | ||||
0.505774 | + | 0.862666i | \(0.331207\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −46498.6 | −3.09395 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18239.5 | 1.20768 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11225.2 | 0.739610 | 0.369805 | − | 0.929109i | \(-0.379425\pi\) | ||||
0.369805 | + | 0.929109i | \(0.379425\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7697.40 | 0.504698 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3338.12 | 0.217808 | 0.108904 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108904 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10482.7 | 0.680669 | 0.340334 | − | 0.940305i | \(-0.389460\pi\) | ||||
0.340334 | + | 0.940305i | \(0.389460\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17326.1 | −1.11960 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1779.89 | 0.114462 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5001.50 | 0.320096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8708.46 | −0.554677 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11812.0 | 0.748768 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27061.1 | −1.70727 | −0.853633 | − | 0.520875i | \(-0.825606\pi\) | ||||
−0.853633 | + | 0.520875i | \(0.825606\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27333.1 | −1.71626 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4421.84 | 0.276339 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −42552.1 | −2.64674 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48974.8 | 3.03195 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4000.76 | −0.246522 | −0.123261 | − | 0.992374i | \(-0.539335\pi\) | ||||
−0.123261 | + | 0.992374i | \(0.539335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5874.39 | 0.360285 | 0.180142 | − | 0.983641i | \(-0.442344\pi\) | ||||
0.180142 | + | 0.983641i | \(0.442344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11322.3 | −0.691186 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23424.1 | −1.42333 | −0.711666 | − | 0.702518i | \(-0.752059\pi\) | ||||
−0.711666 | + | 0.702518i | \(0.752059\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7423.94 | 0.449022 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16271.9 | −0.979642 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8096.54 | −0.485210 | −0.242605 | − | 0.970125i | \(-0.578002\pi\) | ||||
−0.242605 | + | 0.970125i | \(0.578002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8615.07 | −0.513921 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −42873.3 | −2.54589 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25418.1 | 1.50250 | 0.751250 | − | 0.660017i | \(-0.229451\pi\) | ||||
0.751250 | + | 0.660017i | \(0.229451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13421.9 | 0.789788 | 0.394894 | − | 0.918727i | \(-0.370781\pi\) | ||||
0.394894 | + | 0.918727i | \(0.370781\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 39782.2 | 2.33033 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3381.88 | −0.197208 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19541.7 | 1.13442 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42976.1 | 2.48363 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −203.352 | −0.0116994 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6406.65 | 0.366951 | 0.183476 | − | 0.983024i | \(-0.441265\pi\) | ||||
0.183476 | + | 0.983024i | \(0.441265\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14286.0 | 0.814622 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21258.3 | 1.20683 | 0.603414 | − | 0.797428i | \(-0.293806\pi\) | ||||
0.603414 | + | 0.797428i | \(0.293806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15077.7 | −0.852179 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54639.3 | 3.07457 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7604.89 | 0.426052 | 0.213026 | − | 0.977047i | \(-0.431668\pi\) | ||||
0.213026 | + | 0.977047i | \(0.431668\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4744.53 | 0.264641 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 33049.1 | 1.83537 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13371.4 | 0.739346 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 773.527 | 0.0425852 | 0.0212926 | − | 0.999773i | \(-0.493222\pi\) | ||||
0.0212926 | + | 0.999773i | \(0.493222\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 77748.7 | 4.26180 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16900.3 | −0.922394 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12308.6 | 0.668899 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −24599.4 | −1.33110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17527.6 | −0.944376 | −0.472188 | − | 0.881498i | \(-0.656536\pi\) | ||||
−0.472188 | + | 0.881498i | \(0.656536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2979.05 | 0.159825 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13798.1 | −0.737116 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −46273.0 | −2.46150 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18974.0 | −1.00506 | −0.502528 | − | 0.864561i | \(-0.667597\pi\) | ||||
−0.502528 | + | 0.864561i | \(0.667597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16334.9 | −0.861614 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6838.51 | 0.359193 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18703.7 | 0.978293 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12045.8 | 0.627416 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18481.4 | 0.958610 | 0.479305 | − | 0.877648i | \(-0.340889\pi\) | ||||
0.479305 | + | 0.877648i | \(0.340889\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32482.0 | −1.67780 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −52144.0 | −2.68224 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16112.9 | −0.825403 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7059.21 | 0.360126 | 0.180063 | − | 0.983655i | \(-0.442370\pi\) | ||||
0.180063 | + | 0.983655i | \(0.442370\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −31395.3 | −1.59505 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18105.1 | −0.916060 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1633.99 | −0.0823369 | −0.0411684 | − | 0.999152i | \(-0.513108\pi\) | ||||
−0.0411684 | + | 0.999152i | \(0.513108\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 32190.4 | 1.61546 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45521.9 | 2.27520 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26039.2 | −1.29617 | −0.648083 | − | 0.761569i | \(-0.724429\pi\) | ||||
−0.648083 | + | 0.761569i | \(0.724429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10033.3 | 0.497411 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33333.8 | −1.64589 | −0.822947 | − | 0.568119i | \(-0.807671\pi\) | ||||
−0.822947 | + | 0.568119i | \(0.807671\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11006.9 | 0.541291 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5925.12 | 0.290212 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −52428.2 | −2.55766 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15487.3 | 0.752517 | 0.376259 | − | 0.926515i | \(-0.377210\pi\) | ||||
0.376259 | + | 0.926515i | \(0.377210\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31988.6 | −1.54811 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9743.75 | 0.469684 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20858.3 | 1.00147 | 0.500733 | − | 0.865602i | \(-0.333064\pi\) | ||||
0.500733 | + | 0.865602i | \(0.333064\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −52324.2 | −2.50230 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32715.3 | 1.55838 | 0.779191 | − | 0.626786i | \(-0.215630\pi\) | ||||
0.779191 | + | 0.626786i | \(0.215630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2792.10 | −0.132478 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18793.5 | −0.888210 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8553.34 | −0.402664 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37273.2 | −1.74786 | −0.873932 | − | 0.486049i | \(-0.838438\pi\) | ||||
−0.873932 | + | 0.486049i | \(0.838438\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50287.5 | 2.34898 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13735.3 | −0.639098 | −0.319549 | − | 0.947570i | \(-0.603531\pi\) | ||||
−0.319549 | + | 0.947570i | \(0.603531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5638.61 | −0.261348 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −42590.8 | −1.96646 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3104.30 | 0.142777 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58960.9 | 2.70139 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −25979.7 | −1.18575 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4042.62 | 0.183805 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18769.2 | 0.850127 | 0.425064 | − | 0.905163i | \(-0.360252\pi\) | ||||
0.425064 | + | 0.905163i | \(0.360252\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38664.5 | −1.74460 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16791.2 | 0.754773 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 234.288 | 0.0104916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10115.4 | −0.451265 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34274.2 | 1.52328 | 0.761639 | − | 0.648001i | \(-0.224395\pi\) | ||||
0.761639 | + | 0.648001i | \(0.224395\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −22064.0 | −0.976933 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2494.58 | 0.110039 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −51615.3 | −2.26833 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20319.8 | −0.889662 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35024.4 | 1.52778 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33407.2 | 1.45184 | 0.725918 | − | 0.687781i | \(-0.241415\pi\) | ||||
0.725918 | + | 0.687781i | \(0.241415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13794.5 | 0.597275 | 0.298638 | − | 0.954367i | \(-0.403468\pi\) | ||||
0.298638 | + | 0.954367i | \(0.403468\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4830.16 | 0.208366 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5207.48 | 0.223816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4566.19 | −0.195533 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −89576.6 | −3.82181 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20672.7 | −0.878784 | −0.439392 | − | 0.898296i | \(-0.644806\pi\) | ||||
−0.439392 | + | 0.898296i | \(0.644806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13796.6 | 0.584347 | 0.292174 | − | 0.956365i | \(-0.405622\pi\) | ||||
0.292174 | + | 0.956365i | \(0.405622\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 43143.2 | 1.82067 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23226.2 | −0.976605 | −0.488303 | − | 0.872674i | \(-0.662384\pi\) | ||||
−0.488303 | + | 0.872674i | \(0.662384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9821.70 | −0.411486 | −0.205743 | − | 0.978606i | \(-0.565961\pi\) | ||||
−0.205743 | + | 0.978606i | \(0.565961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29368.0 | 1.22595 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 51474.5 | 2.14104 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16956.7 | −0.702765 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9091.46 | −0.375444 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12633.7 | 0.519862 | 0.259931 | − | 0.965627i | \(-0.416300\pi\) | ||||
0.259931 | + | 0.965627i | \(0.416300\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4912.91 | 0.201439 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25027.2 | 1.02252 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9342.27 | −0.380336 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 50962.7 | 2.06741 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26325.5 | 1.06418 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17899.4 | 0.721015 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1749.34 | −0.0702182 | −0.0351091 | − | 0.999383i | \(-0.511178\pi\) | ||||
−0.0351091 | + | 0.999383i | \(0.511178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4739.82 | −0.189589 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21953.5 | 0.875048 | 0.437524 | − | 0.899207i | \(-0.355856\pi\) | ||||
0.437524 | + | 0.899207i | \(0.355856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25690.7 | 1.02044 | 0.510219 | − | 0.860044i | \(-0.329564\pi\) | ||||
0.510219 | + | 0.860044i | \(0.329564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −44381.5 | −1.75670 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46400.0 | −1.83022 | −0.915108 | − | 0.403209i | \(-0.867895\pi\) | ||||
−0.915108 | + | 0.403209i | \(0.867895\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11362.0 | −0.446613 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6464.91 | −0.253241 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19665.7 | −0.767677 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52447.1 | −2.04030 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21132.0 | −0.819254 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 39003.6 | 1.50693 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24330.7 | 0.936818 | 0.468409 | − | 0.883512i | \(-0.344827\pi\) | ||||
0.468409 | + | 0.883512i | \(0.344827\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12432.6 | 0.477068 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31103.2 | 1.18944 | 0.594719 | − | 0.803934i | \(-0.297263\pi\) | ||||
0.594719 | + | 0.803934i | \(0.297263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22128.2 | 0.843344 | 0.421672 | − | 0.906748i | \(-0.361443\pi\) | ||||
0.421672 | + | 0.906748i | \(0.361443\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6470.56 | 0.245769 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20897.9 | −0.791076 | −0.395538 | − | 0.918450i | \(-0.629442\pi\) | ||||
−0.395538 | + | 0.918450i | \(0.629442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25495.3 | −0.961852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4034.53 | 0.151697 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5564.67 | −0.208527 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4703.00 | 0.175647 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 60284.3 | 2.24396 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10254.0 | 0.380413 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16175.1 | −0.598082 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 65281.8 | 2.40581 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14995.6 | −0.550798 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45089.0 | −1.65067 | −0.825334 | − | 0.564645i | \(-0.809013\pi\) | ||||
−0.825334 | + | 0.564645i | \(0.809013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −64853.4 | −2.36639 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26499.7 | 0.963749 | 0.481874 | − | 0.876240i | \(-0.339956\pi\) | ||||
0.481874 | + | 0.876240i | \(0.339956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7133.26 | 0.258572 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −177.238 | −0.00640360 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 49672.6 | 1.78880 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −19159.5 | −0.687718 | −0.343859 | − | 0.939021i | \(-0.611734\pi\) | ||||
−0.343859 | + | 0.939021i | \(0.611734\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17337.7 | −0.620299 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −67930.6 | −2.42250 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14758.7 | −0.524609 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45524.7 | −1.61298 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4702.46 | 0.166074 | 0.0830370 | − | 0.996546i | \(-0.473538\pi\) | ||||
0.0830370 | + | 0.996546i | \(0.473538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12982.1 | 0.457006 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33942.4 | 1.19102 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22625.6 | −0.791374 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37839.1 | 1.31926 | 0.659632 | − | 0.751589i | \(-0.270712\pi\) | ||||
0.659632 | + | 0.751589i | \(0.270712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 87764.1 | 3.05013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6041.39 | 0.209292 | 0.104646 | − | 0.994510i | \(-0.466629\pi\) | ||||
0.104646 | + | 0.994510i | \(0.466629\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18652.0 | 0.644106 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27014.1 | 0.929914 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1829.18 | −0.0627670 | −0.0313835 | − | 0.999507i | \(-0.509991\pi\) | ||||
−0.0313835 | + | 0.999507i | \(0.509991\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59467.6 | 2.03414 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 60075.1 | 2.04844 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2153.53 | 0.0732001 | 0.0366000 | − | 0.999330i | \(-0.488347\pi\) | ||||
0.0366000 | + | 0.999330i | \(0.488347\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12489.0 | −0.423178 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −78457.7 | −2.65013 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −27355.9 | −0.921135 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26202.7 | −0.879550 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −73480.1 | −2.45884 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10330.1 | −0.344597 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56520.9 | 1.87962 | 0.939808 | − | 0.341703i | \(-0.111004\pi\) | ||||
0.939808 | + | 0.341703i | \(0.111004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12137.1 | −0.402373 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27512.1 | −0.909275 | −0.454637 | − | 0.890677i | \(-0.650231\pi\) | ||||
−0.454637 | + | 0.890677i | \(0.650231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 97443.2 | 3.21057 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −49706.6 | −1.63270 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −27370.9 | −0.896286 | −0.448143 | − | 0.893962i | \(-0.647914\pi\) | ||||
−0.448143 | + | 0.893962i | \(0.647914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3003.23 | 0.0980424 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3913.22 | −0.127359 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 29069.1 | 0.943194 | 0.471597 | − | 0.881814i | \(-0.343678\pi\) | ||||
0.471597 | + | 0.881814i | \(0.343678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13484.6 | 0.436198 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 79556.8 | 2.56568 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27435.6 | −0.882106 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19874.2 | 0.637057 | 0.318529 | − | 0.947913i | \(-0.396811\pi\) | ||||
0.318529 | + | 0.947913i | \(0.396811\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 66457.1 | 2.12382 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17548.6 | 0.559124 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10809.0 | 0.343355 | 0.171677 | − | 0.985153i | \(-0.445081\pi\) | ||||
0.171677 | + | 0.985153i | \(0.445081\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23796.3 | −0.753637 |
(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 | 76.4.a.b.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 684.4.a.i.1.3 | 3 | |||
4.3 | odd | 2 | 304.4.a.h.1.3 | 3 | |||
5.2 | odd | 4 | 1900.4.c.c.1749.6 | 6 | |||
5.3 | odd | 4 | 1900.4.c.c.1749.1 | 6 | |||
5.4 | even | 2 | 1900.4.a.c.1.3 | 3 | |||
8.3 | odd | 2 | 1216.4.a.v.1.1 | 3 | |||
8.5 | even | 2 | 1216.4.a.t.1.3 | 3 | |||
19.18 | odd | 2 | 1444.4.a.e.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
304.4.a.h.1.3 | 3 | 4.3 | odd | 2 | |||
684.4.a.i.1.3 | 3 | 3.2 | odd | 2 | |||
1216.4.a.t.1.3 | 3 | 8.5 | even | 2 | |||
1216.4.a.v.1.1 | 3 | 8.3 | odd | 2 | |||
1444.4.a.e.1.3 | 3 | 19.18 | odd | 2 | |||
1900.4.a.c.1.3 | 3 | 5.4 | even | 2 | |||
1900.4.c.c.1749.1 | 6 | 5.3 | odd | 4 | |||
1900.4.c.c.1749.6 | 6 | 5.2 | odd | 4 |