Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,4,Mod(1,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, 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("2352.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.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: | \(138.772492334\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.145408.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 24x^{2} + 142 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1176) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.25358\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1 |
$q$-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 | ||||||||
\(5\) | 6.95987 | 0.622510 | 0.311255 | − | 0.950326i | \(-0.399251\pi\) | ||||
0.311255 | + | 0.950326i | \(0.399251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −43.9023 | −1.20337 | −0.601684 | − | 0.798734i | \(-0.705503\pi\) | ||||
−0.601684 | + | 0.798734i | \(0.705503\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 83.5699 | 1.78293 | 0.891466 | − | 0.453088i | \(-0.149678\pi\) | ||||
0.891466 | + | 0.453088i | \(0.149678\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.8796 | 0.359406 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −10.4354 | −0.148880 | −0.0744401 | − | 0.997225i | \(-0.523717\pi\) | ||||
−0.0744401 | + | 0.997225i | \(0.523717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.27642 | 0.0516357 | 0.0258179 | − | 0.999667i | \(-0.491781\pi\) | ||||
0.0258179 | + | 0.999667i | \(0.491781\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −160.077 | −1.45123 | −0.725616 | − | 0.688100i | \(-0.758445\pi\) | ||||
−0.725616 | + | 0.688100i | \(0.758445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −76.5601 | −0.612481 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.93138 | 0.0635935 | 0.0317967 | − | 0.999494i | \(-0.489877\pi\) | ||||
0.0317967 | + | 0.999494i | \(0.489877\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −133.715 | −0.774710 | −0.387355 | − | 0.921931i | \(-0.626611\pi\) | ||||
−0.387355 | + | 0.921931i | \(0.626611\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −131.707 | −0.694765 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −357.606 | −1.58892 | −0.794460 | − | 0.607316i | \(-0.792246\pi\) | ||||
−0.794460 | + | 0.607316i | \(0.792246\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 250.710 | 1.02938 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 127.174 | 0.484420 | 0.242210 | − | 0.970224i | \(-0.422128\pi\) | ||||
0.242210 | + | 0.970224i | \(0.422128\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −343.250 | −1.21733 | −0.608664 | − | 0.793428i | \(-0.708294\pi\) | ||||
−0.608664 | + | 0.793428i | \(0.708294\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 62.6389 | 0.207503 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 77.4628 | 0.240406 | 0.120203 | − | 0.992749i | \(-0.461645\pi\) | ||||
0.120203 | + | 0.992749i | \(0.461645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −31.3063 | −0.0859560 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −460.812 | −1.19429 | −0.597145 | − | 0.802133i | \(-0.703698\pi\) | ||||
−0.597145 | + | 0.802133i | \(0.703698\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −305.555 | −0.749109 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.8293 | 0.0298119 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 272.735 | 0.601816 | 0.300908 | − | 0.953653i | \(-0.402710\pi\) | ||||
0.300908 | + | 0.953653i | \(0.402710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.3874 | 0.107860 | 0.0539302 | − | 0.998545i | \(-0.482825\pi\) | ||||
0.0539302 | + | 0.998545i | \(0.482825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 581.636 | 1.10989 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 327.081 | 0.596407 | 0.298204 | − | 0.954502i | \(-0.403613\pi\) | ||||
0.298204 | + | 0.954502i | \(0.403613\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −480.231 | −0.837869 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 571.877 | 0.955905 | 0.477953 | − | 0.878386i | \(-0.341379\pi\) | ||||
0.477953 | + | 0.878386i | \(0.341379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −206.313 | −0.330783 | −0.165391 | − | 0.986228i | \(-0.552889\pi\) | ||||
−0.165391 | + | 0.986228i | \(0.552889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −229.680 | −0.353616 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −923.918 | −1.31581 | −0.657904 | − | 0.753102i | \(-0.728557\pi\) | ||||
−0.657904 | + | 0.753102i | \(0.728557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1105.73 | −1.46229 | −0.731143 | − | 0.682224i | \(-0.761013\pi\) | ||||
−0.731143 | + | 0.682224i | \(0.761013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72.6293 | −0.0926794 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29.7941 | 0.0367157 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1532.57 | 1.82531 | 0.912655 | − | 0.408731i | \(-0.134029\pi\) | ||||
0.912655 | + | 0.408731i | \(0.134029\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −401.146 | −0.447279 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 29.7634 | 0.0321438 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −97.6059 | −0.102169 | −0.0510844 | − | 0.998694i | \(-0.516268\pi\) | ||||
−0.0510844 | + | 0.998694i | \(0.516268\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −395.121 | −0.401123 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1326.39 | 1.30674 | 0.653368 | − | 0.757040i | \(-0.273355\pi\) | ||||
0.653368 | + | 0.757040i | \(0.273355\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −780.354 | −0.746511 | −0.373255 | − | 0.927729i | \(-0.621758\pi\) | ||||
−0.373255 | + | 0.927729i | \(0.621758\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 436.263 | 0.394160 | 0.197080 | − | 0.980387i | \(-0.436854\pi\) | ||||
0.197080 | + | 0.980387i | \(0.436854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2092.32 | −1.83861 | −0.919304 | − | 0.393547i | \(-0.871248\pi\) | ||||
−0.919304 | + | 0.393547i | \(0.871248\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1072.82 | −0.917363 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 129.323 | 0.107661 | 0.0538303 | − | 0.998550i | \(-0.482857\pi\) | ||||
0.0538303 | + | 0.998550i | \(0.482857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1114.12 | −0.903407 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 752.129 | 0.594311 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 596.415 | 0.448096 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 381.522 | 0.279680 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1402.83 | −1.00379 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −392.568 | −0.274289 | −0.137145 | − | 0.990551i | \(-0.543793\pi\) | ||||
−0.137145 | + | 0.990551i | \(0.543793\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1029.75 | −0.702824 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −952.085 | −0.634993 | −0.317496 | − | 0.948259i | \(-0.602842\pi\) | ||||
−0.317496 | + | 0.948259i | \(0.602842\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 187.917 | 0.119802 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1850.66 | −1.15411 | −0.577053 | − | 0.816706i | \(-0.695798\pi\) | ||||
−0.577053 | + | 0.816706i | \(0.695798\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1874.96 | 1.14412 | 0.572059 | − | 0.820213i | \(-0.306145\pi\) | ||||
0.572059 | + | 0.820213i | \(0.306145\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 232.388 | 0.138799 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3668.91 | −2.14552 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 69.1211 | 0.0395876 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −956.162 | −0.525717 | −0.262859 | − | 0.964834i | \(-0.584665\pi\) | ||||
−0.262859 | + | 0.964834i | \(0.584665\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 512.503 | 0.276205 | 0.138102 | − | 0.990418i | \(-0.455900\pi\) | ||||
0.138102 | + | 0.990418i | \(0.455900\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −93.9189 | −0.0496267 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −930.643 | −0.482265 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −573.762 | −0.291663 | −0.145832 | − | 0.989309i | \(-0.546586\pi\) | ||||
−0.145832 | + | 0.989309i | \(0.546586\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1382.44 | −0.689524 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3889.78 | −1.86915 | −0.934573 | − | 0.355771i | \(-0.884218\pi\) | ||||
−0.934573 | + | 0.355771i | \(0.884218\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −916.664 | −0.432498 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 167.287 | 0.0775154 | 0.0387577 | − | 0.999249i | \(-0.487660\pi\) | ||||
0.0387577 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4786.92 | 2.17885 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 38.4878 | 0.0172119 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2559.23 | 1.12471 | 0.562355 | − | 0.826896i | \(-0.309896\pi\) | ||||
0.562355 | + | 0.826896i | \(0.309896\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 818.206 | 0.347458 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1214.50 | 0.507130 | 0.253565 | − | 0.967318i | \(-0.418397\pi\) | ||||
0.253565 | + | 0.967318i | \(0.418397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2555.03 | 1.04925 | 0.524625 | − | 0.851334i | \(-0.324206\pi\) | ||||
0.524625 | + | 0.851334i | \(0.324206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 154.162 | 0.0622732 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2488.89 | −0.989119 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 458.140 | 0.179158 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3256.32 | −1.23361 | −0.616804 | − | 0.787117i | \(-0.711573\pi\) | ||||
−0.616804 | + | 0.787117i | \(0.711573\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 96.0749 | 0.0358323 | 0.0179161 | − | 0.999839i | \(-0.494297\pi\) | ||||
0.0179161 | + | 0.999839i | \(0.494297\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1744.91 | 0.640797 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1335.35 | 0.482941 | 0.241471 | − | 0.970408i | \(-0.422370\pi\) | ||||
0.241471 | + | 0.970408i | \(0.422370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2907.06 | −1.03556 | −0.517778 | − | 0.855515i | \(-0.673241\pi\) | ||||
−0.517778 | + | 0.855515i | \(0.673241\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 981.242 | 0.344336 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 885.115 | 0.301557 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1440.69 | −0.483744 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −187.745 | −0.0621368 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −721.998 | −0.235566 | −0.117783 | − | 0.993039i | \(-0.537579\pi\) | ||||
−0.117783 | + | 0.993039i | \(0.537579\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1715.63 | 0.551892 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2388.98 | −0.757799 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −618.940 | −0.190978 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −872.088 | −0.265443 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5906.68 | −1.77373 | −0.886863 | − | 0.462033i | \(-0.847120\pi\) | ||||
−0.886863 | + | 0.462033i | \(0.847120\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −689.041 | −0.204160 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4877.87 | −1.42624 | −0.713118 | − | 0.701044i | \(-0.752717\pi\) | ||||
−0.713118 | + | 0.701044i | \(0.752717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4893.35 | 1.41206 | 0.706030 | − | 0.708182i | \(-0.250484\pi\) | ||||
0.706030 | + | 0.708182i | \(0.250484\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3155.44 | 0.887208 | 0.443604 | − | 0.896223i | \(-0.353700\pi\) | ||||
0.443604 | + | 0.896223i | \(0.353700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 539.131 | 0.149655 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2771.75 | −0.759682 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4165.43 | 1.12736 | 0.563680 | − | 0.825993i | \(-0.309385\pi\) | ||||
0.563680 | + | 0.825993i | \(0.309385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6240.57 | 1.66801 | 0.834006 | − | 0.551756i | \(-0.186042\pi\) | ||||
0.834006 | + | 0.551756i | \(0.186042\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 357.380 | 0.0920630 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3317.19 | −0.844252 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −387.084 | −0.0973407 | −0.0486703 | − | 0.998815i | \(-0.515498\pi\) | ||||
−0.0486703 | + | 0.998815i | \(0.515498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7027.75 | 1.74637 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −217.888 | −0.0535085 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4498.89 | −1.09196 | −0.545979 | − | 0.837799i | \(-0.683842\pi\) | ||||
−0.545979 | + | 0.837799i | \(0.683842\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 89.3824 | 0.0211978 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6791.57 | 1.59234 | 0.796171 | − | 0.605071i | \(-0.206855\pi\) | ||||
0.796171 | + | 0.605071i | \(0.206855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3207.19 | −0.743458 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4597.72 | 1.05384 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8537.49 | −1.93509 | −0.967546 | − | 0.252694i | \(-0.918683\pi\) | ||||
−0.967546 | + | 0.252694i | \(0.918683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4743.77 | 1.06333 | 0.531667 | − | 0.846953i | \(-0.321566\pi\) | ||||
0.531667 | + | 0.846953i | \(0.321566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3361.17 | 0.737040 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1004.32 | −0.217847 | −0.108924 | − | 0.994050i | \(-0.534740\pi\) | ||||
−0.108924 | + | 0.994050i | \(0.534740\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1203.44 | −0.258237 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4563.78 | 0.968869 | 0.484435 | − | 0.874828i | \(-0.339025\pi\) | ||||
0.484435 | + | 0.874828i | \(0.339025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5558.25 | −1.16750 | −0.583752 | − | 0.811932i | \(-0.698416\pi\) | ||||
−0.583752 | + | 0.811932i | \(0.698416\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 89.2901 | 0.0185582 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4804.10 | −0.977835 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −292.818 | −0.0589872 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2903.23 | −0.578868 | −0.289434 | − | 0.957198i | \(-0.593467\pi\) | ||||
−0.289434 | + | 0.957198i | \(0.593467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1898.20 | 0.374636 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1185.36 | −0.231588 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13377.6 | −2.58745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3979.16 | 0.754444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 357.650 | 0.0671442 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7974.96 | −1.48259 | −0.741295 | − | 0.671179i | \(-0.765788\pi\) | ||||
−0.741295 | + | 0.671179i | \(0.765788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2341.06 | −0.430998 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4744.75 | 0.865114 | 0.432557 | − | 0.901607i | \(-0.357611\pi\) | ||||
0.432557 | + | 0.901607i | \(0.357611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9872.97 | −1.78292 | −0.891459 | − | 0.453102i | \(-0.850317\pi\) | ||||
−0.891459 | + | 0.453102i | \(0.850317\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −311.027 | −0.0551073 | −0.0275537 | − | 0.999620i | \(-0.508772\pi\) | ||||
−0.0275537 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −436.011 | −0.0765263 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1308.79 | 0.227568 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −44.6263 | −0.00768754 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6398.12 | −1.09201 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6276.97 | −1.06152 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7451.30 | −1.23734 | −0.618671 | − | 0.785650i | \(-0.712329\pi\) | ||||
−0.618671 | + | 0.785650i | \(0.712329\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3218.45 | −0.529640 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2276.44 | 0.371269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4112.84 | 0.664808 | 0.332404 | − | 0.943137i | \(-0.392140\pi\) | ||||
0.332404 | + | 0.943137i | \(0.392140\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 387.968 | 0.0621578 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5870.42 | 0.932262 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3342.35 | −0.521582 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11459.5 | −1.77285 | −0.886423 | − | 0.462876i | \(-0.846817\pi\) | ||||
−0.886423 | + | 0.462876i | \(0.846817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1293.03 | 0.198322 | 0.0991610 | − | 0.995071i | \(-0.468384\pi\) | ||||
0.0991610 | + | 0.995071i | \(0.468384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2256.39 | 0.343125 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7265.01 | −1.09540 | −0.547702 | − | 0.836674i | \(-0.684497\pi\) | ||||
−0.547702 | + | 0.836674i | \(0.684497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3980.19 | 0.595061 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1381.80 | 0.203143 | 0.101572 | − | 0.994828i | \(-0.467613\pi\) | ||||
0.101572 | + | 0.994828i | \(0.467613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6840.71 | −0.997334 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1789.25 | 0.258708 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1435.91 | −0.205916 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4502.44 | 0.640397 | 0.320198 | − | 0.947351i | \(-0.396250\pi\) | ||||
0.320198 | + | 0.947351i | \(0.396250\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1144.57 | 0.161473 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11140.1 | 1.54642 | 0.773208 | − | 0.634152i | \(-0.218651\pi\) | ||||
0.773208 | + | 0.634152i | \(0.218651\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4208.50 | −0.579536 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 829.964 | 0.113383 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13060.7 | 1.77015 | 0.885073 | − | 0.465453i | \(-0.154108\pi\) | ||||
0.885073 | + | 0.465453i | \(0.154108\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1177.70 | −0.158361 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11248.6 | 1.50072 | 0.750362 | − | 0.661027i | \(-0.229879\pi\) | ||||
0.750362 | + | 0.661027i | \(0.229879\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3089.25 | −0.405776 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11873.8 | −1.54763 | −0.773813 | − | 0.633414i | \(-0.781653\pi\) | ||||
−0.773813 | + | 0.633414i | \(0.781653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1670.47 | 0.216060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2856.26 | −0.366613 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6430.35 | −0.819104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13921.3 | −1.75992 | −0.879960 | − | 0.475047i | \(-0.842431\pi\) | ||||
−0.879960 | + | 0.475047i | \(0.842431\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12830.2 | −1.59778 | −0.798891 | − | 0.601475i | \(-0.794580\pi\) | ||||
−0.798891 | + | 0.601475i | \(0.794580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11174.6 | −1.38126 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 563.750 | 0.0691678 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15699.7 | 1.91206 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5606.76 | 0.677840 | 0.338920 | − | 0.940815i | \(-0.389938\pi\) | ||||
0.338920 | + | 0.940815i | \(0.389938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5551.98 | −0.666324 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7695.75 | −0.910288 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5624.89 | 0.660556 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 77.6276 | 0.00905097 | 0.00452549 | − | 0.999990i | \(-0.498559\pi\) | ||||
0.00452549 | + | 0.999990i | \(0.498559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9742.15 | 1.12780 | 0.563900 | − | 0.825843i | \(-0.309301\pi\) | ||||
0.563900 | + | 0.825843i | \(0.309301\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 697.165 | 0.0801355 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 798.938 | 0.0911863 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11006.7 | −1.23872 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1306.54 | 0.146018 | 0.0730092 | − | 0.997331i | \(-0.476740\pi\) | ||||
0.0730092 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4039.33 | 0.448309 | 0.224154 | − | 0.974554i | \(-0.428038\pi\) | ||||
0.224154 | + | 0.974554i | \(0.428038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 207.363 | 0.0228559 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −684.557 | −0.0749355 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −58.3195 | −0.00634040 | −0.00317020 | − | 0.999995i | \(-0.501009\pi\) | ||||
−0.00317020 | + | 0.999995i | \(0.501009\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16369.5 | 1.75561 | 0.877806 | − | 0.479016i | \(-0.159006\pi\) | ||||
0.877806 | + | 0.479016i | \(0.159006\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10666.5 | 1.13627 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2868.49 | −0.303523 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1584.33 | 0.166523 | 0.0832617 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832617 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5583.23 | −0.582936 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1537.51 | 0.159467 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8530.39 | −0.873162 | −0.436581 | − | 0.899665i | \(-0.643811\pi\) | ||||
−0.436581 | + | 0.899665i | \(0.643811\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −281.757 | −0.0286520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2593.77 | −0.262048 | −0.131024 | − | 0.991379i | \(-0.541826\pi\) | ||||
−0.131024 | + | 0.991379i | \(0.541826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15296.9 | −1.53543 | −0.767717 | − | 0.640789i | \(-0.778607\pi\) | ||||
−0.767717 | + | 0.640789i | \(0.778607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2791.93 | −0.278436 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13942.1 | 1.38151 | 0.690754 | − | 0.723090i | \(-0.257279\pi\) | ||||
0.690754 | + | 0.723090i | \(0.257279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1721.28 | −0.168392 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15069.5 | 1.46489 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −327.404 | −0.0316259 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4147.31 | −0.398097 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1431.14 | −0.136515 | −0.0682574 | − | 0.997668i | \(-0.521744\pi\) | ||||
−0.0682574 | + | 0.997668i | \(0.521744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29885.1 | −2.83294 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −679.325 | −0.0636012 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7664.42 | −0.713158 | −0.356579 | − | 0.934265i | \(-0.616057\pi\) | ||||
−0.356579 | + | 0.934265i | \(0.616057\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11669.3 | −1.07915 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14761.3 | 1.35676 | 0.678380 | − | 0.734711i | \(-0.262682\pi\) | ||||
0.678380 | + | 0.734711i | \(0.262682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −103.638 | −0.00946781 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2749.99 | −0.249703 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11606.1 | −1.04121 | −0.520604 | − | 0.853798i | \(-0.674293\pi\) | ||||
−0.520604 | + | 0.853798i | \(0.674293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 501.862 | 0.0447535 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1650.23 | 0.146283 | 0.0731414 | − | 0.997322i | \(-0.476698\pi\) | ||||
0.0731414 | + | 0.997322i | \(0.476698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9231.48 | 0.813456 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 14360.8 | 1.25796 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3728.12 | 0.324649 | 0.162324 | − | 0.986737i | \(-0.448101\pi\) | ||||
0.162324 | + | 0.986737i | \(0.448101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 115.463 | 0.00993730 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5431.17 | −0.464710 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3400.80 | −0.289298 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7677.69 | 0.649351 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15803.9 | −1.32895 | −0.664473 | − | 0.747312i | \(-0.731344\pi\) | ||||
−0.664473 | + | 0.747312i | \(0.731344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9235.54 | 0.772164 | 0.386082 | − | 0.922464i | \(-0.373828\pi\) | ||||
0.386082 | + | 0.922464i | \(0.373828\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1395.38 | 0.115339 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13457.6 | 1.10607 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2454.62 | 0.200605 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10627.9 | 0.863688 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3036.34 | 0.245369 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3643.51 | 0.292792 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8399.16 | −0.667483 | −0.333741 | − | 0.942665i | \(-0.608311\pi\) | ||||
−0.333741 | + | 0.942665i | \(0.608311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7665.10 | 0.605784 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14562.3 | −1.14455 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18402.5 | −1.43846 | −0.719228 | − | 0.694774i | \(-0.755504\pi\) | ||||
−0.719228 | + | 0.694774i | \(0.755504\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 462.487 | 0.0359535 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.4708 | 0.00328370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7466.68 | −0.571068 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7803.37 | 0.593607 | 0.296804 | − | 0.954938i | \(-0.404079\pi\) | ||||
0.296804 | + | 0.954938i | \(0.404079\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28685.3 | −2.17041 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1374.42 | 0.103437 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −708.972 | −0.0530721 | −0.0265361 | − | 0.999648i | \(-0.508448\pi\) | ||||
−0.0265361 | + | 0.999648i | \(0.508448\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 900.069 | 0.0670198 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15799.2 | 1.16403 | 0.582017 | − | 0.813176i | \(-0.302264\pi\) | ||||
0.582017 | + | 0.813176i | \(0.302264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22721.9 | −1.66529 | −0.832647 | − | 0.553804i | \(-0.813176\pi\) | ||||
−0.832647 | + | 0.553804i | \(0.813176\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9768.97 | −0.712224 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12255.5 | 0.888852 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19216.2 | −1.38645 | −0.693226 | − | 0.720721i | \(-0.743811\pi\) | ||||
−0.693226 | + | 0.720721i | \(0.743811\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 288.225 | 0.0206878 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20230.7 | 1.43717 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5234.72 | 0.369964 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19262.1 | 1.35440 | 0.677201 | − | 0.735798i | \(-0.263193\pi\) | ||||
0.677201 | + | 0.735798i | \(0.263193\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −571.824 | −0.0400027 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4006.04 | 0.278826 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11871.8 | 0.822122 | 0.411061 | − | 0.911608i | \(-0.365158\pi\) | ||||
0.411061 | + | 0.911608i | \(0.365158\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8721.17 | −0.597879 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17021.1 | −1.16104 | −0.580520 | − | 0.814246i | \(-0.697151\pi\) | ||||
−0.580520 | + | 0.814246i | \(0.697151\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5518.23 | 0.374531 | 0.187266 | − | 0.982309i | \(-0.440037\pi\) | ||||
0.187266 | + | 0.982309i | \(0.440037\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2943.73 | 0.198802 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4150.97 | 0.278944 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20388.4 | 1.36333 | 0.681663 | − | 0.731667i | \(-0.261257\pi\) | ||||
0.681663 | + | 0.731667i | \(0.261257\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6473.55 | 0.428628 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14237.0 | −0.938053 | −0.469026 | − | 0.883184i | \(-0.655395\pi\) | ||||
−0.469026 | + | 0.883184i | \(0.655395\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2655.34 | 0.174104 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20383.4 | −1.32999 | −0.664997 | − | 0.746846i | \(-0.731567\pi\) | ||||
−0.664997 | + | 0.746846i | \(0.731567\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15997.5 | −1.03876 | −0.519380 | − | 0.854543i | \(-0.673837\pi\) | ||||
−0.519380 | + | 0.854543i | \(0.673837\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4322.08 | −0.279290 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −193.527 | −0.0123857 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −563.235 | −0.0358747 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3731.77 | 0.236559 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4857.90 | −0.306481 | −0.153241 | − | 0.988189i | \(-0.548971\pi\) | ||||
−0.153241 | + | 0.988189i | \(0.548971\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2165.99 | −0.136004 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2732.22 | −0.170748 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5146.89 | 0.318635 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24563.9 | 1.51360 | 0.756798 | − | 0.653649i | \(-0.226763\pi\) | ||||
0.756798 | + | 0.653649i | \(0.226763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6010.79 | 0.368650 | 0.184325 | − | 0.982865i | \(-0.440990\pi\) | ||||
0.184325 | + | 0.982865i | \(0.440990\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7166.93 | −0.437515 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16927.4 | −1.02857 | −0.514285 | − | 0.857619i | \(-0.671943\pi\) | ||||
−0.514285 | + | 0.857619i | \(0.671943\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11973.7 | −0.724206 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7702.96 | 0.461623 | 0.230812 | − | 0.972998i | \(-0.425862\pi\) | ||||
0.230812 | + | 0.972998i | \(0.425862\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6626.39 | −0.395290 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1856.82 | −0.110261 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5899.80 | 0.348746 | 0.174373 | − | 0.984680i | \(-0.444210\pi\) | ||||
0.174373 | + | 0.984680i | \(0.444210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25442.5 | 1.49713 | 0.748563 | − | 0.663064i | \(-0.230744\pi\) | ||||
0.748563 | + | 0.663064i | \(0.230744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2616.26 | −0.153254 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1589.78 | −0.0922889 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17720.1 | −1.02406 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2256.03 | −0.129796 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18424.7 | −1.05531 | −0.527654 | − | 0.849460i | \(-0.676928\pi\) | ||||
−0.527654 | + | 0.849460i | \(0.676928\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2067.12 | −0.117872 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1189.55 | 0.0675307 | 0.0337654 | − | 0.999430i | \(-0.489250\pi\) | ||||
0.0337654 | + | 0.999430i | \(0.489250\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14633.6 | −0.823437 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19938.4 | 1.11702 | 0.558509 | − | 0.829499i | \(-0.311374\pi\) | ||||
0.558509 | + | 0.829499i | \(0.311374\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12880.4 | −0.718443 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14680.1 | 0.815253 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −38510.0 | −2.12934 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5625.32 | 0.309692 | 0.154846 | − | 0.987939i | \(-0.450512\pi\) | ||||
0.154846 | + | 0.987939i | \(0.450512\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13049.5 | 0.712225 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1327.11 | −0.0721206 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9466.31 | 0.512230 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29961.0 | −1.61428 | −0.807140 | − | 0.590360i | \(-0.798986\pi\) | ||||
−0.807140 | + | 0.590360i | \(0.798986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1529.27 | −0.0820451 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1617.39 | 0.0864036 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14177.2 | 0.750968 | 0.375484 | − | 0.926829i | \(-0.377476\pi\) | ||||
0.375484 | + | 0.926829i | \(0.377476\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8315.26 | −0.438603 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 21404.8 | 1.12428 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25535.2 | −1.33561 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12496.3 | 0.650882 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 425.151 | 0.0220521 | 0.0110260 | − | 0.999939i | \(-0.496490\pi\) | ||||
0.0110260 | + | 0.999939i | \(0.496490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18721.7 | 0.963027 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −760.348 | −0.0389498 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12678.5 | 0.646793 | 0.323397 | − | 0.946264i | \(-0.395175\pi\) | ||||
0.323397 | + | 0.946264i | \(0.395175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3581.96 | 0.181236 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7973.30 | −0.401774 | −0.200887 | − | 0.979614i | \(-0.564382\pi\) | ||||
−0.200887 | + | 0.979614i | \(0.564382\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14359.6 | −0.717698 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12208.1 | −0.607687 | −0.303843 | − | 0.952722i | \(-0.598270\pi\) | ||||
−0.303843 | + | 0.952722i | \(0.598270\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1072.14 | 0.0531526 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13351.2 | −0.659232 | −0.329616 | − | 0.944115i | \(-0.606919\pi\) | ||||
−0.329616 | + | 0.944115i | \(0.606919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6654.77 | −0.327264 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9951.58 | −0.487429 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27971.9 | −1.35913 | −0.679567 | − | 0.733614i | \(-0.737832\pi\) | ||||
−0.679567 | + | 0.733614i | \(0.737832\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1161.25 | −0.0561997 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3566.96 | 0.171940 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20382.6 | 0.978623 | 0.489312 | − | 0.872109i | \(-0.337248\pi\) | ||||
0.489312 | + | 0.872109i | \(0.337248\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21083.2 | 1.00827 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24172.0 | 1.15143 | 0.575713 | − | 0.817652i | \(-0.304725\pi\) | ||||
0.575713 | + | 0.817652i | \(0.304725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −653.664 | −0.0308931 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22792.5 | 1.07300 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1320.89 | −0.0619409 | −0.0309705 | − | 0.999520i | \(-0.509860\pi\) | ||||
−0.0309705 | + | 0.999520i | \(0.509860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13496.7 | −0.630443 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28790.1 | −1.33960 | −0.669798 | − | 0.742544i | \(-0.733619\pi\) | ||||
−0.669798 | + | 0.742544i | \(0.733619\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10237.3 | 0.474495 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 543.850 | 0.0250134 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −25106.7 | −1.15031 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 268.147 | 0.0122386 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3993.31 | −0.181563 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38138.2 | 1.72742 | 0.863710 | − | 0.503989i | \(-0.168135\pi\) | ||||
0.863710 | + | 0.503989i | \(0.168135\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20374.7 | 0.919339 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4294.44 | 0.192308 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9621.58 | −0.429235 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29562.7 | 1.31388 | 0.656941 | − | 0.753942i | \(-0.271850\pi\) | ||||
0.656941 | + | 0.753942i | \(0.271850\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −808.357 | −0.0357918 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13793.2 | 0.608437 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9057.63 | 0.398054 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25612.5 | −1.11723 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28800.4 | 1.25163 | 0.625814 | − | 0.779972i | \(-0.284767\pi\) | ||||
0.625814 | + | 0.779972i | \(0.284767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23960.3 | −1.03743 | −0.518717 | − | 0.854946i | \(-0.673590\pi\) | ||||
−0.518717 | + | 0.854946i | \(0.673590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14231.3 | 0.613917 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27072.4 | −1.16356 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1467.88 | −0.0628576 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7480.81 | 0.318005 | 0.159003 | − | 0.987278i | \(-0.449172\pi\) | ||||
0.159003 | + | 0.987278i | \(0.449172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37456.0 | 1.58643 | 0.793217 | − | 0.608939i | \(-0.208405\pi\) | ||||
0.793217 | + | 0.608939i | \(0.208405\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10083.5 | 0.425531 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18855.9 | −0.792847 | −0.396423 | − | 0.918068i | \(-0.629749\pi\) | ||||
−0.396423 | + | 0.918068i | \(0.629749\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34027.1 | 1.42559 | 0.712793 | − | 0.701375i | \(-0.247430\pi\) | ||||
0.712793 | + | 0.701375i | \(0.247430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3012.95 | −0.125774 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1164.30 | 0.0482541 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3610.32 | −0.149093 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9279.70 | −0.381848 | −0.190924 | − | 0.981605i | \(-0.561148\pi\) | ||||
−0.190924 | + | 0.981605i | \(0.561148\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24290.4 | −0.995956 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13691.3 | 0.559377 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33316.4 | 1.35635 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16674.7 | −0.674059 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57244.4 | 2.30589 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29478.9 | 1.18328 | 0.591641 | − | 0.806201i | \(-0.298480\pi\) | ||||
0.591641 | + | 0.806201i | \(0.298480\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 267.870 | 0.0107146 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18935.8 | 0.754765 | 0.377383 | − | 0.926057i | \(-0.376824\pi\) | ||||
0.377383 | + | 0.926057i | \(0.376824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11678.8 | 0.463883 | 0.231941 | − | 0.972730i | \(-0.425492\pi\) | ||||
0.231941 | + | 0.972730i | \(0.425492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14625.7 | 0.576899 | 0.288450 | − | 0.957495i | \(-0.406860\pi\) | ||||
0.288450 | + | 0.957495i | \(0.406860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17811.9 | 0.700143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14412.3 | −0.564553 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40562.1 | 1.58340 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27334.1 | 1.06335 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −878.454 | −0.0340563 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26195.9 | 1.00863 | 0.504317 | − | 0.863519i | \(-0.331744\pi\) | ||||
0.504317 | + | 0.863519i | \(0.331744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8709.68 | −0.334210 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17065.6 | −0.652616 | −0.326308 | − | 0.945264i | \(-0.605805\pi\) | ||||
−0.326308 | + | 0.945264i | \(0.605805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20428.3 | 0.778557 | 0.389279 | − | 0.921120i | \(-0.372724\pi\) | ||||
0.389279 | + | 0.921120i | \(0.372724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5694.61 | 0.216296 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3679.59 | 0.139288 | 0.0696441 | − | 0.997572i | \(-0.477814\pi\) | ||||
0.0696441 | + | 0.997572i | \(0.477814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3556.09 | −0.133708 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 331.264 | 0.0124136 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8452.80 | 0.315694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −40132.8 | −1.49386 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1327.98 | −0.0492665 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4808.77 | 0.177806 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17782.7 | 0.653168 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25374.5 | 0.928938 | 0.464469 | − | 0.885589i | \(-0.346245\pi\) | ||||
0.464469 | + | 0.885589i | \(0.346245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11937.5 | 0.435579 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4890.79 | 0.177869 | 0.0889347 | − | 0.996037i | \(-0.471654\pi\) | ||||
0.0889347 | + | 0.996037i | \(0.471654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 48544.2 | 1.75967 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1072.95 | 0.0387657 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16590.3 | −0.595501 | −0.297750 | − | 0.954644i | \(-0.596236\pi\) | ||||
−0.297750 | + | 0.954644i | \(0.596236\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23924.9 | −0.855974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 47791.7 | 1.70431 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27378.4 | 0.973184 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7023.19 | −0.248837 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51991.9 | −1.83617 | −0.918083 | − | 0.396388i | \(-0.870263\pi\) | ||||
−0.918083 | + | 0.396388i | \(0.870263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14234.3 | 0.499474 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3188.60 | 0.111528 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26392.7 | −0.920182 | −0.460091 | − | 0.887872i | \(-0.652183\pi\) | ||||
−0.460091 | + | 0.887872i | \(0.652183\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −29618.9 | −1.02937 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40403.8 | 1.39971 | 0.699854 | − | 0.714286i | \(-0.253248\pi\) | ||||
0.699854 | + | 0.714286i | \(0.253248\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20357.6 | −0.703006 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18557.3 | 0.636782 | 0.318391 | − | 0.947959i | \(-0.396858\pi\) | ||||
0.318391 | + | 0.947959i | \(0.396858\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17241.6 | −0.589763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −933.081 | −0.0318162 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30432.6 | −1.03443 | −0.517213 | − | 0.855857i | \(-0.673031\pi\) | ||||
−0.517213 | + | 0.855857i | \(0.673031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22663.6 | −0.767934 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1308.03 | −0.0441825 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11911.2 | −0.399824 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3926.37 | 0.131387 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 668.670 | 0.0223059 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21280.5 | −0.707688 | −0.353844 | − | 0.935304i | \(-0.615126\pi\) | ||||
−0.353844 | + | 0.935304i | \(0.615126\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −133.879 | −0.00443840 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10383.6 | −0.343179 | −0.171589 | − | 0.985169i | \(-0.554890\pi\) | ||||
−0.171589 | + | 0.985169i | \(0.554890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19194.4 | −0.630473 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50807.3 | −1.66374 | −0.831868 | − | 0.554973i | \(-0.812728\pi\) | ||||
−0.831868 | + | 0.554973i | \(0.812728\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −67283.6 | −2.19652 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18830.9 | −0.612870 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21417.1 | −0.694913 | −0.347456 | − | 0.937696i | \(-0.612955\pi\) | ||||
−0.347456 | + | 0.937696i | \(0.612955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9293.84 | 0.300636 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54946.3 | 1.76663 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3420.14 | −0.109631 | −0.0548155 | − | 0.998497i | \(-0.517457\pi\) | ||||
−0.0548155 | + | 0.998497i | \(0.517457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22353.9 | −0.714380 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20232.7 | −0.644644 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45658.1 | 1.45036 | 0.725180 | − | 0.688560i | \(-0.241757\pi\) | ||||
0.725180 | + | 0.688560i | \(0.241757\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9655.36 | −0.305788 |
(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 | 2352.4.a.cr.1.3 | 4 | ||
4.3 | odd | 2 | 1176.4.a.bb.1.3 | ✓ | 4 | ||
7.6 | odd | 2 | 2352.4.a.ck.1.2 | 4 | |||
28.27 | even | 2 | 1176.4.a.bc.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1176.4.a.bb.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
1176.4.a.bc.1.2 | yes | 4 | 28.27 | even | 2 | ||
2352.4.a.ck.1.2 | 4 | 7.6 | odd | 2 | |||
2352.4.a.cr.1.3 | 4 | 1.1 | even | 1 | trivial |