Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, 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("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{137}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 34 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(6.35235\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-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 | ||||||||
\(5\) | −20.7047 | −1.85188 | −0.925942 | − | 0.377665i | \(-0.876727\pi\) | ||||
−0.925942 | + | 0.377665i | \(0.876727\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.11410 | −0.167588 | −0.0837941 | − | 0.996483i | \(-0.526704\pi\) | ||||
−0.0837941 | + | 0.996483i | \(0.526704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 22.8188 | 0.486830 | 0.243415 | − | 0.969922i | \(-0.421732\pi\) | ||||
0.243415 | + | 0.969922i | \(0.421732\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −62.1141 | −1.06919 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.70470 | −0.124188 | −0.0620941 | − | 0.998070i | \(-0.519778\pi\) | ||||
−0.0620941 | + | 0.998070i | \(0.519778\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 75.0470 | 0.906156 | 0.453078 | − | 0.891471i | \(-0.350326\pi\) | ||||
0.453078 | + | 0.891471i | \(0.350326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 178.570 | 1.61889 | 0.809446 | − | 0.587194i | \(-0.199767\pi\) | ||||
0.809446 | + | 0.587194i | \(0.199767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 303.685 | 2.42948 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −122.228 | −0.782662 | −0.391331 | − | 0.920250i | \(-0.627985\pi\) | ||||
−0.391331 | + | 0.920250i | \(0.627985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −102.591 | −0.594381 | −0.297191 | − | 0.954818i | \(-0.596050\pi\) | ||||
−0.297191 | + | 0.954818i | \(0.596050\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −18.3423 | −0.0967571 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 182.228 | 0.809679 | 0.404840 | − | 0.914388i | \(-0.367327\pi\) | ||||
0.404840 | + | 0.914388i | \(0.367327\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 68.4564 | 0.281072 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −488.208 | −1.85964 | −0.929821 | − | 0.368013i | \(-0.880038\pi\) | ||||
−0.929821 | + | 0.368013i | \(0.880038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −388.000 | −1.37603 | −0.688017 | − | 0.725695i | \(-0.741518\pi\) | ||||
−0.688017 | + | 0.725695i | \(0.741518\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −186.342 | −0.617295 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −254.550 | −0.790000 | −0.395000 | − | 0.918681i | \(-0.629255\pi\) | ||||
−0.395000 | + | 0.918681i | \(0.629255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −26.1141 | −0.0717001 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 610.228 | 1.58153 | 0.790767 | − | 0.612117i | \(-0.209682\pi\) | ||||
0.790767 | + | 0.612117i | \(0.209682\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 126.591 | 0.310354 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 225.141 | 0.523169 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 31.2752 | 0.0690116 | 0.0345058 | − | 0.999404i | \(-0.489014\pi\) | ||||
0.0345058 | + | 0.999404i | \(0.489014\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 587.503 | 1.23315 | 0.616575 | − | 0.787296i | \(-0.288520\pi\) | ||||
0.616575 | + | 0.787296i | \(0.288520\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −472.456 | −0.901554 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −689.597 | −1.25743 | −0.628714 | − | 0.777636i | \(-0.716419\pi\) | ||||
−0.628714 | + | 0.777636i | \(0.716419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 535.711 | 0.934668 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −563.940 | −0.942638 | −0.471319 | − | 0.881963i | \(-0.656222\pi\) | ||||
−0.471319 | + | 0.881963i | \(0.656222\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −275.315 | −0.441414 | −0.220707 | − | 0.975340i | \(-0.570836\pi\) | ||||
−0.220707 | + | 0.975340i | \(0.570836\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 911.054 | 1.40266 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −219.315 | −0.312341 | −0.156170 | − | 0.987730i | \(-0.549915\pi\) | ||||
−0.156170 | + | 0.987730i | \(0.549915\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1447.28 | −1.91396 | −0.956982 | − | 0.290146i | \(-0.906296\pi\) | ||||
−0.956982 | + | 0.290146i | \(0.906296\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 180.228 | 0.229982 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −366.685 | −0.451870 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1018.57 | −1.21313 | −0.606563 | − | 0.795035i | \(-0.707452\pi\) | ||||
−0.606563 | + | 0.795035i | \(0.707452\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −307.772 | −0.343166 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1553.83 | −1.67810 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −792.497 | −0.829545 | −0.414772 | − | 0.909925i | \(-0.636139\pi\) | ||||
−0.414772 | + | 0.909925i | \(0.636139\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −55.0269 | −0.0558627 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −509.658 | −0.502107 | −0.251054 | − | 0.967973i | \(-0.580777\pi\) | ||||
−0.251054 | + | 0.967973i | \(0.580777\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 217.490 | 0.208057 | 0.104029 | − | 0.994574i | \(-0.466827\pi\) | ||||
0.104029 | + | 0.994574i | \(0.466827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1897.31 | −1.71420 | −0.857102 | − | 0.515147i | \(-0.827737\pi\) | ||||
−0.857102 | + | 0.515147i | \(0.827737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 850.456 | 0.747330 | 0.373665 | − | 0.927564i | \(-0.378101\pi\) | ||||
0.373665 | + | 0.927564i | \(0.378101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 546.685 | 0.467469 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1527.48 | 1.27162 | 0.635809 | − | 0.771846i | \(-0.280666\pi\) | ||||
0.635809 | + | 0.771846i | \(0.280666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3697.25 | −2.99800 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 205.369 | 0.162277 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1293.62 | −0.971914 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1464.62 | −1.07366 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3699.61 | −2.64723 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1038.51 | 0.725613 | 0.362807 | − | 0.931864i | \(-0.381819\pi\) | ||||
0.362807 | + | 0.931864i | \(0.381819\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1164.00 | −0.794453 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 961.181 | 0.641059 | 0.320530 | − | 0.947238i | \(-0.396139\pi\) | ||||
0.320530 | + | 0.947238i | \(0.396139\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −559.027 | −0.356395 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1690.00 | −1.05392 | −0.526958 | − | 0.849891i | \(-0.676667\pi\) | ||||
−0.526958 | + | 0.849891i | \(0.676667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1732.30 | 1.05706 | 0.528530 | − | 0.848915i | \(-0.322743\pi\) | ||||
0.528530 | + | 0.848915i | \(0.322743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −763.651 | −0.456107 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −139.516 | −0.0815871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2530.70 | 1.44940 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2725.88 | 1.49874 | 0.749372 | − | 0.662150i | \(-0.230356\pi\) | ||||
0.749372 | + | 0.662150i | \(0.230356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1129.83 | 0.608900 | 0.304450 | − | 0.952528i | \(-0.401527\pi\) | ||||
0.304450 | + | 0.952528i | \(0.401527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −78.3423 | −0.0413961 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2124.11 | 1.10073 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 719.691 | 0.365845 | 0.182922 | − | 0.983127i | \(-0.441444\pi\) | ||||
0.182922 | + | 0.983127i | \(0.441444\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1830.68 | 0.913099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2469.25 | 1.18654 | 0.593271 | − | 0.805003i | \(-0.297836\pi\) | ||||
0.593271 | + | 0.805003i | \(0.297836\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 379.772 | 0.179183 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2419.03 | −1.12090 | −0.560451 | − | 0.828188i | \(-0.689372\pi\) | ||||
−0.560451 | + | 0.828188i | \(0.689372\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1676.30 | −0.762996 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 675.423 | 0.302052 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3559.16 | −1.56415 | −0.782075 | − | 0.623184i | \(-0.785839\pi\) | ||||
−0.782075 | + | 0.623184i | \(0.785839\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 93.8256 | 0.0398439 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3864.15 | 1.61352 | 0.806761 | − | 0.590878i | \(-0.201218\pi\) | ||||
0.806761 | + | 0.590878i | \(0.201218\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4100.46 | −1.68389 | −0.841946 | − | 0.539561i | \(-0.818590\pi\) | ||||
−0.841946 | + | 0.539561i | \(0.818590\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1762.51 | 0.711959 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3772.98 | −1.49943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 53.2214 | 0.0208125 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1120.17 | 0.424359 | 0.212179 | − | 0.977231i | \(-0.431944\pi\) | ||||
0.212179 | + | 0.977231i | \(0.431944\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1418.44 | −0.529025 | −0.264512 | − | 0.964382i | \(-0.585211\pi\) | ||||
−0.264512 | + | 0.964382i | \(0.585211\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1417.37 | −0.520512 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4611.01 | −1.66762 | −0.833809 | − | 0.552053i | \(-0.813844\pi\) | ||||
−0.833809 | + | 0.552053i | \(0.813844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5049.83 | −1.79886 | −0.899429 | − | 0.437067i | \(-0.856017\pi\) | ||||
−0.899429 | + | 0.437067i | \(0.856017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2068.79 | −0.725977 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10108.2 | 3.44384 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1607.13 | 0.539631 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −458.845 | −0.151861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1712.11 | −0.558608 | −0.279304 | − | 0.960203i | \(-0.590104\pi\) | ||||
−0.279304 | + | 0.960203i | \(0.590104\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1691.82 | −0.544233 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8033.42 | 2.54826 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −825.946 | −0.254851 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −198.631 | −0.0604586 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 161.906 | 0.0486190 | 0.0243095 | − | 0.999704i | \(-0.492261\pi\) | ||||
0.0243095 | + | 0.999704i | \(0.492261\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2733.16 | 0.809826 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3947.76 | −1.15428 | −0.577141 | − | 0.816645i | \(-0.695832\pi\) | ||||
−0.577141 | + | 0.816645i | \(0.695832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3584.78 | 1.03445 | 0.517225 | − | 0.855850i | \(-0.326965\pi\) | ||||
0.517225 | + | 0.855850i | \(0.326965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3448.85 | −0.969706 | −0.484853 | − | 0.874596i | \(-0.661127\pi\) | ||||
−0.484853 | + | 0.874596i | \(0.661127\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5270.39 | 1.46299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −657.946 | −0.180330 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3818.57 | 1.03348 | 0.516742 | − | 0.856141i | \(-0.327145\pi\) | ||||
0.516742 | + | 0.856141i | \(0.327145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1314.54 | 0.351356 | 0.175678 | − | 0.984448i | \(-0.443788\pi\) | ||||
0.175678 | + | 0.984448i | \(0.443788\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1712.48 | 0.441144 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4341.83 | −1.10503 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4829.66 | 1.21452 | 0.607262 | − | 0.794501i | \(-0.292268\pi\) | ||||
0.607262 | + | 0.794501i | \(0.292268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1091.80 | −0.271307 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 540.685 | 0.132780 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1479.93 | 0.359203 | 0.179602 | − | 0.983739i | \(-0.442519\pi\) | ||||
0.179602 | + | 0.983739i | \(0.442519\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1100.05 | −0.260887 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1191.01 | −0.279244 | −0.139622 | − | 0.990205i | \(-0.544589\pi\) | ||||
−0.139622 | + | 0.990205i | \(0.544589\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12634.6 | −2.92882 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3055.71 | −0.700399 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −558.772 | −0.126650 | −0.0633251 | − | 0.997993i | \(-0.520170\pi\) | ||||
−0.0633251 | + | 0.997993i | \(0.520170\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5992.31 | −1.34320 | −0.671599 | − | 0.740914i | \(-0.734392\pi\) | ||||
−0.671599 | + | 0.740914i | \(0.734392\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1856.76 | −0.407152 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7884.03 | 1.71013 | 0.855064 | − | 0.518523i | \(-0.173518\pi\) | ||||
0.855064 | + | 0.518523i | \(0.173518\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −923.315 | −0.198127 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −75.8256 | −0.0160974 | −0.00804871 | − | 0.999968i | \(-0.502562\pi\) | ||||
−0.00804871 | + | 0.999968i | \(0.502562\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −803.369 | −0.168747 | −0.0843733 | − | 0.996434i | \(-0.526889\pi\) | ||||
−0.0843733 | + | 0.996434i | \(0.526889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4661.48 | −0.968849 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4837.23 | −0.984577 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2377.49 | −0.478938 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2626.26 | 0.523645 | 0.261822 | − | 0.965116i | \(-0.415677\pi\) | ||||
0.261822 | + | 0.965116i | \(0.415677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −647.544 | −0.127802 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −165.081 | −0.0322524 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4074.76 | 0.788126 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1528.97 | −0.289892 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12164.1 | −2.28365 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4865.84 | 0.904587 | 0.452293 | − | 0.891869i | \(-0.350606\pi\) | ||||
0.452293 | + | 0.891869i | \(0.350606\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 652.469 | 0.120122 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6152.97 | −1.12187 | −0.560937 | − | 0.827859i | \(-0.689559\pi\) | ||||
−0.560937 | + | 0.827859i | \(0.689559\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7892.78 | −1.42532 | −0.712662 | − | 0.701508i | \(-0.752511\pi\) | ||||
−0.712662 | + | 0.701508i | \(0.752511\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3688.75 | −0.653568 | −0.326784 | − | 0.945099i | \(-0.605965\pi\) | ||||
−0.326784 | + | 0.945099i | \(0.605965\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 747.315 | 0.131165 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5691.93 | −0.989696 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −653.262 | −0.112534 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6929.72 | 1.18274 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2551.37 | 0.431471 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1981.80 | −0.329092 | −0.164546 | − | 0.986369i | \(-0.552616\pi\) | ||||
−0.164546 | + | 0.986369i | \(0.552616\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1640.05 | 0.269893 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14277.9 | 2.32861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1578.35 | 0.255128 | 0.127564 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127564 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4582.43 | 0.734169 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 627.249 | 0.0996113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11091.7 | −1.73090 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3213.51 | −0.497148 | −0.248574 | − | 0.968613i | \(-0.579962\pi\) | ||||
−0.248574 | + | 0.968613i | \(0.579962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 725.920 | 0.111340 | 0.0556699 | − | 0.998449i | \(-0.482271\pi\) | ||||
0.0556699 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 616.108 | 0.0936906 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 619.403 | 0.0933923 | 0.0466962 | − | 0.998909i | \(-0.485131\pi\) | ||||
0.0466962 | + | 0.998909i | \(0.485131\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11676.2 | 1.74566 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7912.05 | −1.16318 | −0.581590 | − | 0.813482i | \(-0.697569\pi\) | ||||
−0.581590 | + | 0.813482i | \(0.697569\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1226.95 | −0.178881 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3880.85 | −0.561135 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5700.32 | 0.817448 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2916.08 | −0.414764 | −0.207382 | − | 0.978260i | \(-0.566494\pi\) | ||||
−0.207382 | + | 0.978260i | \(0.566494\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4393.87 | −0.619880 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −53.1688 | −0.00738063 | −0.00369031 | − | 0.999993i | \(-0.501175\pi\) | ||||
−0.00369031 | + | 0.999993i | \(0.501175\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11098.8 | −1.52838 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2789.10 | −0.381024 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12650.6 | −1.71456 | −0.857281 | − | 0.514848i | \(-0.827848\pi\) | ||||
−0.857281 | + | 0.514848i | \(0.827848\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3115.53 | 0.418933 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10401.5 | 1.38770 | 0.693852 | − | 0.720118i | \(-0.255912\pi\) | ||||
0.693852 | + | 0.720118i | \(0.255912\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3492.00 | −0.458678 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2665.16 | 0.347375 | 0.173687 | − | 0.984801i | \(-0.444432\pi\) | ||||
0.173687 | + | 0.984801i | \(0.444432\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1554.40 | −0.201047 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2883.54 | 0.370116 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4540.86 | 0.578419 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10880.9 | −1.37556 | −0.687779 | − | 0.725920i | \(-0.741414\pi\) | ||||
−0.687779 | + | 0.725920i | \(0.741414\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12599.0 | −1.56899 | −0.784493 | − | 0.620137i | \(-0.787077\pi\) | ||||
−0.784493 | + | 0.620137i | \(0.787077\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2340.99 | −0.289363 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1677.08 | −0.205765 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1114.16 | −0.135693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5740.47 | 0.694005 | 0.347002 | − | 0.937864i | \(-0.387200\pi\) | ||||
0.347002 | + | 0.937864i | \(0.387200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5070.00 | −0.608478 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29965.4 | 3.54444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5196.89 | 0.610294 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3433.66 | 0.400347 | 0.200174 | − | 0.979760i | \(-0.435849\pi\) | ||||
0.200174 | + | 0.979760i | \(0.435849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4793.88 | −0.554963 | −0.277481 | − | 0.960731i | \(-0.589500\pi\) | ||||
−0.277481 | + | 0.960731i | \(0.589500\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2290.95 | −0.263333 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2643.48 | −0.301712 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −418.549 | −0.0471043 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5350.29 | 0.597945 | 0.298973 | − | 0.954262i | \(-0.403356\pi\) | ||||
0.298973 | + | 0.954262i | \(0.403356\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4440.03 | 0.492781 | 0.246390 | − | 0.969171i | \(-0.420755\pi\) | ||||
0.246390 | + | 0.969171i | \(0.420755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7592.09 | 0.836812 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13401.2 | 1.46697 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10376.0 | −1.12806 | −0.564030 | − | 0.825754i | \(-0.690750\pi\) | ||||
−0.564030 | + | 0.825754i | \(0.690750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4186.32 | −0.448979 | −0.224490 | − | 0.974476i | \(-0.572072\pi\) | ||||
−0.224490 | + | 0.974476i | \(0.572072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21089.2 | 2.24657 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8177.64 | 0.865300 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5216.36 | 0.548275 | 0.274137 | − | 0.961691i | \(-0.411608\pi\) | ||||
0.274137 | + | 0.961691i | \(0.411608\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2984.95 | 0.311654 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3389.48 | 0.351549 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9469.65 | 0.969303 | 0.484652 | − | 0.874707i | \(-0.338946\pi\) | ||||
0.484652 | + | 0.874707i | \(0.338946\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −235.027 | −0.0239000 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3455.07 | 0.349064 | 0.174532 | − | 0.984651i | \(-0.444159\pi\) | ||||
0.174532 | + | 0.984651i | \(0.444159\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10881.9 | −1.09228 | −0.546139 | − | 0.837695i | \(-0.683903\pi\) | ||||
−0.546139 | + | 0.837695i | \(0.683903\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6372.32 | 0.635504 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12053.6 | −1.19437 | −0.597186 | − | 0.802102i | \(-0.703715\pi\) | ||||
−0.597186 | + | 0.802102i | \(0.703715\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2159.07 | 0.211221 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2372.27 | 0.230607 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 22790.6 | 2.20148 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5492.05 | 0.527178 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7836.59 | 0.747522 | 0.373761 | − | 0.927525i | \(-0.378068\pi\) | ||||
0.373761 | + | 0.927525i | \(0.378068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4158.23 | 0.394177 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16408.4 | 1.53622 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8799.54 | 0.818779 | 0.409390 | − | 0.912360i | \(-0.365742\pi\) | ||||
0.409390 | + | 0.912360i | \(0.365742\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7407.75 | 0.685051 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11382.9 | −1.04623 | −0.523117 | − | 0.852261i | \(-0.675231\pi\) | ||||
−0.523117 | + | 0.852261i | \(0.675231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1063.96 | 0.0971974 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1139.32 | 0.103451 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17510.7 | 1.57092 | 0.785458 | − | 0.618915i | \(-0.212427\pi\) | ||||
0.785458 | + | 0.618915i | \(0.212427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7257.10 | −0.647153 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14573.9 | 1.29188 | 0.645940 | − | 0.763388i | \(-0.276465\pi\) | ||||
0.645940 | + | 0.763388i | \(0.276465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10552.3 | 0.929845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5028.91 | −0.440516 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17451.3 | −1.51968 | −0.759839 | − | 0.650112i | \(-0.774722\pi\) | ||||
−0.759839 | + | 0.650112i | \(0.774722\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2026.27 | 0.174390 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4503.06 | −0.385298 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1556.35 | 0.132395 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10677.5 | −0.903063 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3210.52 | 0.269972 | 0.134986 | − | 0.990848i | \(-0.456901\pi\) | ||||
0.134986 | + | 0.990848i | \(0.456901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16647.8 | 1.39188 | 0.695942 | − | 0.718098i | \(-0.254987\pi\) | ||||
0.695942 | + | 0.718098i | \(0.254987\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 893.020 | 0.0738151 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19720.4 | 1.62081 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 281.477 | 0.0230039 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11140.3 | −0.905330 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39283.2 | 3.17451 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11592.5 | 0.931568 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10709.9 | 0.851118 | 0.425559 | − | 0.904931i | \(-0.360078\pi\) | ||||
0.425559 | + | 0.904931i | \(0.360078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12301.4 | −0.972196 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17608.4 | −1.38397 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1263.05 | 0.0987277 | 0.0493638 | − | 0.998781i | \(-0.484281\pi\) | ||||
0.0493638 | + | 0.998781i | \(0.484281\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5287.53 | 0.411050 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9172.86 | −0.709214 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11318.9 | −0.865698 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24281.3 | −1.84710 | −0.923548 | − | 0.383483i | \(-0.874725\pi\) | ||||
−0.923548 | + | 0.383483i | \(0.874725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8853.69 | −0.669895 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 159.664 | 0.0120161 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5467.57 | 0.409291 | 0.204645 | − | 0.978836i | \(-0.434396\pi\) | ||||
0.204645 | + | 0.978836i | \(0.434396\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31625.9 | −2.35489 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6474.08 | 0.476991 | 0.238495 | − | 0.971144i | \(-0.423346\pi\) | ||||
0.238495 | + | 0.971144i | \(0.423346\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18112.8 | 1.32749 | 0.663747 | − | 0.747957i | \(-0.268965\pi\) | ||||
0.663747 | + | 0.747957i | \(0.268965\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3360.50 | 0.245004 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 54229.1 | 3.93306 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10175.8 | −0.734181 | −0.367090 | − | 0.930185i | \(-0.619646\pi\) | ||||
−0.367090 | + | 0.930185i | \(0.619646\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4255.33 | −0.305433 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3731.00 | −0.265046 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4252.11 | −0.300518 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11566.7 | −0.813304 | −0.406652 | − | 0.913583i | \(-0.633304\pi\) | ||||
−0.406652 | + | 0.913583i | \(0.633304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7699.12 | −0.538602 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13833.0 | −0.962799 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4736.73 | −0.328017 | −0.164009 | − | 0.986459i | \(-0.552443\pi\) | ||||
−0.164009 | + | 0.986459i | \(0.552443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15149.5 | −1.03857 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7774.56 | 0.530317 | 0.265158 | − | 0.964205i | \(-0.414576\pi\) | ||||
0.265158 | + | 0.964205i | \(0.414576\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16662.3 | 1.13089 | 0.565447 | − | 0.824784i | \(-0.308704\pi\) | ||||
0.565447 | + | 0.824784i | \(0.308704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6206.38 | −0.419143 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 26784.0 | 1.79987 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26523.4 | 1.77356 | 0.886781 | − | 0.462190i | \(-0.152936\pi\) | ||||
0.886781 | + | 0.462190i | \(0.152936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5808.53 | −0.384596 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6963.91 | −0.458841 | −0.229421 | − | 0.973327i | \(-0.573683\pi\) | ||||
−0.229421 | + | 0.973327i | \(0.573683\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 30324.6 | 1.98830 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22945.5 | −1.49716 | −0.748582 | − | 0.663042i | \(-0.769265\pi\) | ||||
−0.748582 | + | 0.663042i | \(0.769265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20783.6 | −1.34954 | −0.674769 | − | 0.738029i | \(-0.735757\pi\) | ||||
−0.674769 | + | 0.738029i | \(0.735757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4821.40 | 0.311556 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 38638.8 | 2.47288 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1376.53 | −0.0876770 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1586.24 | −0.100553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 909.976 | 0.0574098 | 0.0287049 | − | 0.999588i | \(-0.490862\pi\) | ||||
0.0287049 | + | 0.999588i | \(0.490862\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5136.32 | −0.322513 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −21502.0 | −1.34375 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5075.46 | −0.314213 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25103.9 | −1.54687 | −0.773437 | − | 0.633874i | \(-0.781464\pi\) | ||||
−0.773437 | + | 0.633874i | \(0.781464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23810.1 | 1.46031 | 0.730156 | − | 0.683281i | \(-0.239448\pi\) | ||||
0.730156 | + | 0.683281i | \(0.239448\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24100.3 | 1.47124 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10985.6 | 0.667527 | 0.333763 | − | 0.942657i | \(-0.391681\pi\) | ||||
0.333763 | + | 0.942657i | \(0.391681\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −191.220 | −0.0115655 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24506.4 | −1.46862 | −0.734309 | − | 0.678815i | \(-0.762494\pi\) | ||||
−0.734309 | + | 0.678815i | \(0.762494\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −19901.0 | −1.18717 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2477.84 | −0.147138 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22113.2 | 1.30714 | 0.653571 | − | 0.756865i | \(-0.273270\pi\) | ||||
0.653571 | + | 0.756865i | \(0.273270\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23937.9 | 1.40859 | 0.704294 | − | 0.709909i | \(-0.251264\pi\) | ||||
0.704294 | + | 0.709909i | \(0.251264\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −595.892 | −0.0349058 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21826.4 | −1.26705 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 485.718 | 0.0280702 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3592.05 | −0.206661 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15407.1 | −0.882468 | −0.441234 | − | 0.897392i | \(-0.645459\pi\) | ||||
−0.441234 | + | 0.897392i | \(0.645459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8199.48 | 0.467553 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5145.81 | 0.292126 | 0.146063 | − | 0.989275i | \(-0.453340\pi\) | ||||
0.146063 | + | 0.989275i | \(0.453340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11843.3 | −0.666425 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18247.7 | 1.02230 | 0.511148 | − | 0.859492i | \(-0.329220\pi\) | ||||
0.511148 | + | 0.859492i | \(0.329220\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34990.9 | 1.95173 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10754.3 | 0.597240 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13924.7 | 0.769939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10359.8 | 0.570338 | 0.285169 | − | 0.958477i | \(-0.407950\pi\) | ||||
0.285169 | + | 0.958477i | \(0.407950\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −35866.7 | −1.95755 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4249.70 | 0.230946 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10346.5 | −0.559860 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −369.772 | −0.0199231 | −0.00996155 | − | 0.999950i | \(-0.503171\pi\) | ||||
−0.00996155 | + | 0.999950i | \(0.503171\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13675.7 | 0.733696 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15811.2 | 0.844657 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16229.0 | −0.859652 | −0.429826 | − | 0.902912i | \(-0.641425\pi\) | ||||
−0.429826 | + | 0.902912i | \(0.641425\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1973.84 | −0.104114 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18319.7 | −0.962239 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2888.65 | 0.151090 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11455.7 | 0.596683 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27233.9 | −1.41259 | −0.706294 | − | 0.707918i | \(-0.749635\pi\) | ||||
−0.706294 | + | 0.707918i | \(0.749635\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3943.61 | 0.202855 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −37118.8 | −1.90146 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27653.4 | −1.41074 | −0.705370 | − | 0.708840i | \(-0.749219\pi\) | ||||
−0.705370 | + | 0.708840i | \(0.749219\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3377.42 | 0.170887 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20513.2 | 1.03366 | 0.516831 | − | 0.856088i | \(-0.327112\pi\) | ||||
0.516831 | + | 0.856088i | \(0.327112\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4216.27 | 0.210730 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5032.87 | −0.250524 | −0.125262 | − | 0.992124i | \(-0.539977\pi\) | ||||
−0.125262 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5137.45 | 0.254695 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6528.88 | −0.322371 | −0.161185 | − | 0.986924i | \(-0.551532\pi\) | ||||
−0.161185 | + | 0.986924i | \(0.551532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −56438.5 | −2.77550 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13025.5 | −0.637988 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11101.7 | 0.539423 | 0.269711 | − | 0.962941i | \(-0.413072\pi\) | ||||
0.269711 | + | 0.962941i | \(0.413072\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 14489.0 | 0.701206 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23392.7 | −1.12761 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6375.85 | −0.306122 | −0.153061 | − | 0.988217i | \(-0.548913\pi\) | ||||
−0.153061 | + | 0.988217i | \(0.548913\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3275.39 | −0.156639 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4038.93 | 0.192393 | 0.0961965 | − | 0.995362i | \(-0.469332\pi\) | ||||
0.0961965 | + | 0.995362i | \(0.469332\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1622.05 | 0.0766608 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 713.662 | 0.0335969 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18864.4 | −0.884614 | −0.442307 | − | 0.896864i | \(-0.645840\pi\) | ||||
−0.442307 | + | 0.896864i | \(0.645840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4439.78 | 0.207386 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10489.2 | −0.488060 | −0.244030 | − | 0.969768i | \(-0.578470\pi\) | ||||
−0.244030 | + | 0.969768i | \(0.578470\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −31155.2 | −1.44404 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36638.6 | −1.68513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3447.98 | 0.157975 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3300.16 | −0.150623 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14901.0 | −0.677502 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30948.6 | 1.40178 | 0.700888 | − | 0.713272i | \(-0.252787\pi\) | ||||
0.700888 | + | 0.713272i | \(0.252787\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3573.04 | −0.161221 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13406.1 | 0.600335 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −37903.8 | −1.69095 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38324.5 | 1.70329 | 0.851646 | − | 0.524117i | \(-0.175605\pi\) | ||||
0.851646 | + | 0.524117i | \(0.175605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2215.78 | 0.0981087 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9167.13 | −0.404375 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1683.31 | 0.0739758 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1676.31 | −0.0731215 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19368.1 | 0.841714 | 0.420857 | − | 0.907127i | \(-0.361729\pi\) | ||||
0.420857 | + | 0.907127i | \(0.361729\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5621.93 | 0.243419 | 0.121710 | − | 0.992566i | \(-0.461162\pi\) | ||||
0.121710 | + | 0.992566i | \(0.461162\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17976.9 | −0.775496 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −51125.1 | −2.19734 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29118.2 | −1.24690 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12512.3 | 0.531891 | 0.265945 | − | 0.963988i | \(-0.414316\pi\) | ||||
0.265945 | + | 0.963988i | \(0.414316\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26084.1 | 1.10478 | 0.552391 | − | 0.833585i | \(-0.313716\pi\) | ||||
0.552391 | + | 0.833585i | \(0.313716\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5570.27 | −0.235069 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22210.4 | −0.933895 | −0.466947 | − | 0.884285i | \(-0.654646\pi\) | ||||
−0.466947 | + | 0.884285i | \(0.654646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20945.2 | −0.877511 | −0.438755 | − | 0.898607i | \(-0.644581\pi\) | ||||
−0.438755 | + | 0.898607i | \(0.644581\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 23652.1 | 0.987343 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 50085.4 | 2.07578 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2769.95 | −0.114389 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1357.80 | −0.0558718 | −0.0279359 | − | 0.999610i | \(-0.508893\pi\) | ||||
−0.0279359 | + | 0.999610i | \(0.508893\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9449.27 | −0.387440 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −227.477 | −0.00929385 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34707.3 | 1.41298 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2410.11 | −0.0974259 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32540.6 | 1.31078 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24726.4 | 0.992516 | 0.496258 | − | 0.868175i | \(-0.334707\pi\) | ||||
0.496258 | + | 0.868175i | \(0.334707\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13984.4 | −0.559365 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20843.2 | −0.830792 | −0.415396 | − | 0.909641i | \(-0.636357\pi\) | ||||
−0.415396 | + | 0.909641i | \(0.636357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46160.3 | 1.83349 | 0.916745 | − | 0.399473i | \(-0.130807\pi\) | ||||
0.916745 | + | 0.399473i | \(0.130807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8635.84 | 0.340634 | 0.170317 | − | 0.985389i | \(-0.445521\pi\) | ||||
0.170317 | + | 0.985389i | \(0.445521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73691.4 | 2.89663 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14511.7 | −0.568446 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1340.92 | 0.0523446 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15735.8 | −0.612155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7132.47 | −0.276515 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23282.3 | −0.896453 | −0.448226 | − | 0.893920i | \(-0.647944\pi\) | ||||
−0.448226 | + | 0.893920i | \(0.647944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7878.79 | 0.302326 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7097.62 | −0.271424 | −0.135712 | − | 0.990748i | \(-0.543332\pi\) | ||||
−0.135712 | + | 0.990748i | \(0.543332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35486.1 | −1.35244 | −0.676219 | − | 0.736700i | \(-0.736383\pi\) | ||||
−0.676219 | + | 0.736700i | \(0.736383\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1942.63 | −0.0737862 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 45062.5 | 1.70581 | 0.852903 | − | 0.522070i | \(-0.174840\pi\) | ||||
0.852903 | + | 0.522070i | \(0.174840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −495.242 | −0.0186209 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −19103.2 | −0.715863 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −80006.2 | −2.98806 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12224.3 | 0.455025 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12539.5 | 0.465200 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5311.85 | −0.196408 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 84898.7 | 3.11837 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10899.4 | 0.399018 | 0.199509 | − | 0.979896i | \(-0.436065\pi\) | ||||
0.199509 | + | 0.979896i | \(0.436065\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4586.92 | −0.167369 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10217.7 | −0.371600 | −0.185800 | − | 0.982588i | \(-0.559488\pi\) | ||||
−0.185800 | + | 0.982588i | \(0.559488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8848.78 | 0.320758 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −36492.2 | −1.31847 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4396.64 | 0.157815 | 0.0789074 | − | 0.996882i | \(-0.474857\pi\) | ||||
0.0789074 | + | 0.996882i | \(0.474857\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14597.5 | 0.522263 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12868.4 | −0.458905 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 55339.9 | 1.96710 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1957.41 | 0.0693525 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42006.3 | 1.48351 | 0.741756 | − | 0.670670i | \(-0.233993\pi\) | ||||
0.741756 | + | 0.670670i | \(0.233993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18458.9 | −0.647714 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1101.93 | −0.0385423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39752.5 | −1.38597 | −0.692987 | − | 0.720950i | \(-0.743706\pi\) | ||||
−0.692987 | + | 0.720950i | \(0.743706\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23678.3 | −0.822911 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13609.1 | 0.471460 | 0.235730 | − | 0.971819i | \(-0.424252\pi\) | ||||
0.235730 | + | 0.971819i | \(0.424252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −87179.6 | −3.01056 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30929.7 | 1.06133 | 0.530665 | − | 0.847581i | \(-0.321942\pi\) | ||||
0.530665 | + | 0.847581i | \(0.321942\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6282.37 | −0.214894 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11066.3 | −0.377337 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26166.5 | −0.889418 | −0.444709 | − | 0.895675i | \(-0.646693\pi\) | ||||
−0.444709 | + | 0.895675i | \(0.646693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23192.7 | −0.785863 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2241.95 | 0.0757281 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19266.2 | −0.646711 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17075.8 | −0.571401 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 29368.4 | 0.979693 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55883.6 | −1.85842 | −0.929212 | − | 0.369546i | \(-0.879513\pi\) | ||||
−0.929212 | + | 0.369546i | \(0.879513\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1959.78 | −0.0649715 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10618.3 | −0.350933 | −0.175467 | − | 0.984485i | \(-0.556143\pi\) | ||||
−0.175467 | + | 0.984485i | \(0.556143\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20789.2 | 0.682857 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11493.1 | 0.376352 | 0.188176 | − | 0.982135i | \(-0.439743\pi\) | ||||
0.188176 | + | 0.982135i | \(0.439743\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6227.64 | 0.203306 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7654.11 | 0.249110 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25414.1 | −0.824602 | −0.412301 | − | 0.911048i | \(-0.635275\pi\) | ||||
−0.412301 | + | 0.911048i | \(0.635275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 95469.5 | 3.08824 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −69285.4 | −2.22765 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39966.1 | −1.28109 | −0.640547 | − | 0.767919i | \(-0.721292\pi\) | ||||
−0.640547 | + | 0.767919i | \(0.721292\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5945.40 | −0.190002 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 104555. | 3.33128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16507.7 | 0.524376 | 0.262188 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262188 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4920.16 | 0.155823 |
(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 | 1176.4.a.t.1.1 | yes | 2 | |
4.3 | odd | 2 | 2352.4.a.bm.1.1 | 2 | |||
7.6 | odd | 2 | 1176.4.a.s.1.2 | ✓ | 2 | ||
28.27 | even | 2 | 2352.4.a.ce.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.s.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
1176.4.a.t.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2352.4.a.bm.1.1 | 2 | 4.3 | odd | 2 | |||
2352.4.a.ce.1.2 | 2 | 28.27 | even | 2 |