Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5 x^{9} - 192 x^{8} + 762 x^{7} + 12246 x^{6} - 33828 x^{5} - 298243 x^{4} + 383603 x^{3} + 2423016 x^{2} + 864576 x + 57408 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-7.60722\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 7.60722 | 1.46401 | 0.732005 | − | 0.681299i | \(-0.238585\pi\) | ||||
0.732005 | + | 0.681299i | \(0.238585\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.6846 | 1.11686 | 0.558431 | − | 0.829551i | \(-0.311404\pi\) | ||||
0.558431 | + | 0.829551i | \(0.311404\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 30.8698 | 1.14332 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 65.9547 | 1.80783 | 0.903914 | − | 0.427715i | \(-0.140681\pi\) | ||||
0.903914 | + | 0.427715i | \(0.140681\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −73.2440 | −1.56263 | −0.781316 | − | 0.624135i | \(-0.785451\pi\) | ||||
−0.781316 | + | 0.624135i | \(0.785451\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 38.0361 | 0.654725 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 70.9305 | 1.01195 | 0.505975 | − | 0.862548i | \(-0.331133\pi\) | ||||
0.505975 | + | 0.862548i | \(0.331133\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 79.5074 | 0.960014 | 0.480007 | − | 0.877265i | \(-0.340634\pi\) | ||||
0.480007 | + | 0.877265i | \(0.340634\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 157.352 | 1.63510 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.4382 | 0.209829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −244.561 | −1.56600 | −0.782998 | − | 0.622024i | \(-0.786311\pi\) | ||||
−0.782998 | + | 0.622024i | \(0.786311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 283.927 | 1.64499 | 0.822496 | − | 0.568770i | \(-0.192581\pi\) | ||||
0.822496 | + | 0.568770i | \(0.192581\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 501.732 | 2.64668 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 103.423 | 0.499476 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −296.020 | −1.31528 | −0.657639 | − | 0.753333i | \(-0.728445\pi\) | ||||
−0.657639 | + | 0.753333i | \(0.728445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −557.183 | −2.28771 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 366.935 | 1.39770 | 0.698849 | − | 0.715270i | \(-0.253696\pi\) | ||||
0.698849 | + | 0.715270i | \(0.253696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 343.529 | 1.21832 | 0.609158 | − | 0.793049i | \(-0.291507\pi\) | ||||
0.609158 | + | 0.793049i | \(0.291507\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 154.349 | 0.511310 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −309.611 | −0.960881 | −0.480441 | − | 0.877027i | \(-0.659523\pi\) | ||||
−0.480441 | + | 0.877027i | \(0.659523\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 84.8511 | 0.247379 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 539.584 | 1.48151 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −477.489 | −1.23751 | −0.618756 | − | 0.785583i | \(-0.712363\pi\) | ||||
−0.618756 | + | 0.785583i | \(0.712363\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 329.774 | 0.808485 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 604.830 | 1.40547 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 251.707 | 0.555415 | 0.277708 | − | 0.960666i | \(-0.410425\pi\) | ||||
0.277708 | + | 0.960666i | \(0.410425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −60.6199 | −0.127239 | −0.0636195 | − | 0.997974i | \(-0.520264\pi\) | ||||
−0.0636195 | + | 0.997974i | \(0.520264\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 638.528 | 1.27694 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −366.220 | −0.698830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −433.850 | −0.791093 | −0.395546 | − | 0.918446i | \(-0.629445\pi\) | ||||
−0.395546 | + | 0.918446i | \(0.629445\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 174.966 | 0.305267 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1119.80 | 1.87178 | 0.935888 | − | 0.352299i | \(-0.114600\pi\) | ||||
0.935888 | + | 0.352299i | \(0.114600\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −583.370 | −0.935318 | −0.467659 | − | 0.883909i | \(-0.654903\pi\) | ||||
−0.467659 | + | 0.883909i | \(0.654903\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 190.180 | 0.292802 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1364.24 | 2.01909 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 804.524 | 1.14577 | 0.572886 | − | 0.819635i | \(-0.305824\pi\) | ||||
0.572886 | + | 0.819635i | \(0.305824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −609.541 | −0.836133 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −892.200 | −1.17990 | −0.589950 | − | 0.807440i | \(-0.700852\pi\) | ||||
−0.589950 | + | 0.807440i | \(0.700852\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 354.652 | 0.452558 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1860.43 | −2.29263 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 911.783 | 1.08594 | 0.542971 | − | 0.839752i | \(-0.317299\pi\) | ||||
0.542971 | + | 0.839752i | \(0.317299\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1515.02 | −1.74524 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2159.89 | 2.40829 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 397.537 | 0.429331 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 53.3224 | 0.0558151 | 0.0279076 | − | 0.999611i | \(-0.491116\pi\) | ||||
0.0279076 | + | 0.999611i | \(0.491116\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2036.01 | 2.06693 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 134.300 | 0.132311 | 0.0661554 | − | 0.997809i | \(-0.478927\pi\) | ||||
0.0661554 | + | 0.997809i | \(0.478927\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −253.628 | −0.242628 | −0.121314 | − | 0.992614i | \(-0.538711\pi\) | ||||
−0.121314 | + | 0.992614i | \(0.538711\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 786.760 | 0.731237 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1966.06 | −1.77632 | −0.888161 | − | 0.459532i | \(-0.848017\pi\) | ||||
−0.888161 | + | 0.459532i | \(0.848017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −468.098 | −0.411336 | −0.205668 | − | 0.978622i | \(-0.565937\pi\) | ||||
−0.205668 | + | 0.978622i | \(0.565937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2251.89 | −1.92558 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 62.6915 | 0.0521904 | 0.0260952 | − | 0.999659i | \(-0.491693\pi\) | ||||
0.0260952 | + | 0.999659i | \(0.491693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2261.02 | −1.78660 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1467.17 | 1.13021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3019.03 | 2.26824 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2791.35 | 2.04624 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2199.61 | −1.53688 | −0.768442 | − | 0.639920i | \(-0.778968\pi\) | ||||
−0.768442 | + | 0.639920i | \(0.778968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2613.30 | 1.78363 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1375.91 | −0.917662 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1644.58 | 1.07220 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 147.191 | 0.0938383 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.01310 | 0.00374988 | 0.00187494 | − | 0.999998i | \(-0.499403\pi\) | ||||
0.00187494 | + | 0.999998i | \(0.499403\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1522.15 | 0.928827 | 0.464414 | − | 0.885618i | \(-0.346265\pi\) | ||||
0.464414 | + | 0.885618i | \(0.346265\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2355.28 | −1.40674 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4830.79 | −2.82497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1222.81 | −0.700335 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 645.481 | 0.362166 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −440.008 | −0.241925 | −0.120963 | − | 0.992657i | \(-0.538598\pi\) | ||||
−0.120963 | + | 0.992657i | \(0.538598\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2902.27 | 1.56413 | 0.782065 | − | 0.623197i | \(-0.214167\pi\) | ||||
0.782065 | + | 0.623197i | \(0.214167\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2189.61 | 1.15699 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1419.63 | 0.735663 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.9338 | 0.0116581 | 0.00582904 | − | 0.999983i | \(-0.498145\pi\) | ||||
0.00582904 | + | 0.999983i | \(0.498145\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3632.36 | −1.81173 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 475.745 | 0.232882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1666.89 | −0.800989 | −0.400494 | − | 0.916299i | \(-0.631162\pi\) | ||||
−0.400494 | + | 0.916299i | \(0.631162\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2508.66 | 1.18363 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1048.90 | 0.486025 | 0.243012 | − | 0.970023i | \(-0.421864\pi\) | ||||
0.243012 | + | 0.970023i | \(0.421864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3167.68 | 1.44182 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2454.38 | 1.09761 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1273.69 | 0.559752 | 0.279876 | − | 0.960036i | \(-0.409707\pi\) | ||||
0.279876 | + | 0.960036i | \(0.409707\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 517.114 | 0.223372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1914.79 | 0.813133 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2408.10 | −1.00553 | −0.502765 | − | 0.864423i | \(-0.667684\pi\) | ||||
−0.502765 | + | 0.864423i | \(0.667684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1038.18 | 0.426339 | 0.213170 | − | 0.977015i | \(-0.431621\pi\) | ||||
0.213170 | + | 0.977015i | \(0.431621\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −461.149 | −0.186279 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1480.10 | −0.588211 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4678.20 | 1.82943 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 608.916 | 0.234350 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 890.919 | 0.337511 | 0.168756 | − | 0.985658i | \(-0.446025\pi\) | ||||
0.168756 | + | 0.985658i | \(0.446025\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −136.087 | −0.0507552 | −0.0253776 | − | 0.999678i | \(-0.508079\pi\) | ||||
−0.0253776 | + | 0.999678i | \(0.508079\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2785.91 | −1.02309 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1473.55 | 0.532926 | 0.266463 | − | 0.963845i | \(-0.414145\pi\) | ||||
0.266463 | + | 0.963845i | \(0.414145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 287.628 | 0.102459 | 0.0512296 | − | 0.998687i | \(-0.483686\pi\) | ||||
0.0512296 | + | 0.998687i | \(0.483686\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3300.39 | −1.15817 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5058.64 | −1.74900 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1834.67 | 0.625069 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 710.005 | 0.238400 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5243.89 | 1.73554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4392.16 | 1.43303 | 0.716513 | − | 0.697573i | \(-0.245737\pi\) | ||||
0.716513 | + | 0.697573i | \(0.245737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8518.58 | 2.74030 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1717.64 | 0.544848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5872.90 | 1.83723 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4437.82 | −1.36932 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5195.23 | −1.58131 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5397.64 | 1.62087 | 0.810433 | − | 0.585832i | \(-0.199232\pi\) | ||||
0.810433 | + | 0.585832i | \(0.199232\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 771.744 | 0.228665 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2518.70 | 0.736441 | 0.368220 | − | 0.929739i | \(-0.379967\pi\) | ||||
0.368220 | + | 0.929739i | \(0.379967\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4753.03 | −1.37157 | −0.685785 | − | 0.727805i | \(-0.740541\pi\) | ||||
−0.685785 | + | 0.727805i | \(0.740541\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10378.1 | 2.95597 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1194.30 | −0.335799 | −0.167900 | − | 0.985804i | \(-0.553698\pi\) | ||||
−0.167900 | + | 0.985804i | \(0.553698\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1548.06 | −0.429719 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6120.19 | 1.67742 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5851.02 | −1.58356 | −0.791780 | − | 0.610806i | \(-0.790845\pi\) | ||||
−0.791780 | + | 0.610806i | \(0.790845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 658.076 | 0.175894 | 0.0879469 | − | 0.996125i | \(-0.471969\pi\) | ||||
0.0879469 | + | 0.996125i | \(0.471969\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5431.74 | −1.43394 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 424.255 | 0.110631 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5823.44 | −1.50015 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6787.16 | −1.72738 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2724.99 | 0.685259 | 0.342629 | − | 0.939471i | \(-0.388682\pi\) | ||||
0.342629 | + | 0.939471i | \(0.388682\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1516.96 | 0.376958 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2697.92 | 0.662550 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3320.88 | −0.806035 | −0.403018 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403018 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6123.03 | −1.46898 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7549.55 | −1.79044 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −432.404 | −0.101381 | −0.0506904 | − | 0.998714i | \(-0.516142\pi\) | ||||
−0.0506904 | + | 0.998714i | \(0.516142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2387.44 | −0.553432 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6936.13 | 1.58983 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4408.43 | −0.999207 | −0.499603 | − | 0.866254i | \(-0.666521\pi\) | ||||
−0.499603 | + | 0.866254i | \(0.666521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8604.93 | −1.92883 | −0.964414 | − | 0.264398i | \(-0.914827\pi\) | ||||
−0.964414 | + | 0.264398i | \(0.914827\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11525.1 | −2.55505 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1648.87 | 0.361565 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6830.24 | −1.48155 | −0.740775 | − | 0.671753i | \(-0.765541\pi\) | ||||
−0.740775 | + | 0.671753i | \(0.765541\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8764.76 | 1.88076 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8532.12 | −1.81133 | −0.905665 | − | 0.423994i | \(-0.860628\pi\) | ||||
−0.905665 | + | 0.423994i | \(0.860628\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6759.86 | 1.41990 | 0.709950 | − | 0.704252i | \(-0.248717\pi\) | ||||
0.709950 | + | 0.704252i | \(0.248717\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3024.15 | 0.628545 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7589.88 | 1.56103 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 118.130 | 0.0240444 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 405.635 | 0.0817139 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5067.26 | −1.01035 | −0.505175 | − | 0.863017i | \(-0.668572\pi\) | ||||
−0.505175 | + | 0.863017i | \(0.668572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1258.54 | 0.248389 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1941.59 | 0.379334 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1684.61 | −0.325831 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7105.74 | 1.36069 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1021.65 | 0.193704 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −303.100 | −0.0569031 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4246.60 | 0.789467 | 0.394734 | − | 0.918796i | \(-0.370837\pi\) | ||||
0.394734 | + | 0.918796i | \(0.370837\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1929.40 | −0.355210 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 918.593 | 0.167487 | 0.0837437 | − | 0.996487i | \(-0.473312\pi\) | ||||
0.0837437 | + | 0.996487i | \(0.473312\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 530.478 | 0.0957967 | 0.0478984 | − | 0.998852i | \(-0.484748\pi\) | ||||
0.0478984 | + | 0.998852i | \(0.484748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3192.64 | 0.571063 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7854.64 | 1.39167 | 0.695837 | − | 0.718200i | \(-0.255034\pi\) | ||||
0.695837 | + | 0.718200i | \(0.255034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16130.0 | −2.83105 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14956.3 | −2.60055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5639.50 | 0.971487 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1831.10 | −0.312526 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3560.92 | −0.602200 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6404.17 | −1.07317 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11622.4 | 1.92998 | 0.964992 | − | 0.262280i | \(-0.0844746\pi\) | ||||
0.964992 | + | 0.262280i | \(0.0844746\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9138.06 | −1.50379 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2169.25 | −0.353787 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4454.29 | −0.720002 | −0.360001 | − | 0.932952i | \(-0.617224\pi\) | ||||
−0.360001 | + | 0.932952i | \(0.617224\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 476.908 | 0.0764073 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18726.3 | 2.97386 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5339.70 | −0.840573 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 874.830 | 0.136520 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7319.54 | −1.13237 | −0.566187 | − | 0.824277i | \(-0.691582\pi\) | ||||
−0.566187 | + | 0.824277i | \(0.691582\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7826.29 | 1.20038 | 0.600189 | − | 0.799858i | \(-0.295092\pi\) | ||||
0.600189 | + | 0.799858i | \(0.295092\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2156.17 | −0.327885 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7775.30 | 1.17234 | 0.586172 | − | 0.810187i | \(-0.300634\pi\) | ||||
0.586172 | + | 0.810187i | \(0.300634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5599.01 | 0.837083 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11161.0 | 1.65464 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 737.788 | 0.108465 | 0.0542325 | − | 0.998528i | \(-0.482729\pi\) | ||||
0.0542325 | + | 0.998528i | \(0.482729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −537.567 | −0.0783740 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22966.4 | 3.32073 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2916.85 | −0.418287 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10394.4 | 1.47843 | 0.739214 | − | 0.673471i | \(-0.235197\pi\) | ||||
0.739214 | + | 0.673471i | \(0.235197\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11327.2 | 1.59802 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9876.64 | −1.38213 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12595.6 | 1.74846 | 0.874232 | − | 0.485508i | \(-0.161365\pi\) | ||||
0.874232 | + | 0.485508i | \(0.161365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 950.902 | 0.130945 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17912.6 | 2.44708 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 596.932 | 0.0809033 | 0.0404516 | − | 0.999181i | \(-0.487120\pi\) | ||||
0.0404516 | + | 0.999181i | \(0.487120\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16732.9 | −2.25001 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7790.02 | −1.03930 | −0.519650 | − | 0.854380i | \(-0.673937\pi\) | ||||
−0.519650 | + | 0.854380i | \(0.673937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6821.22 | 0.902966 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10604.6 | 1.39293 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6802.65 | 0.886653 | 0.443327 | − | 0.896360i | \(-0.353798\pi\) | ||||
0.443327 | + | 0.896360i | \(0.353798\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1631.40 | 0.211006 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10466.8 | −1.34347 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4022.62 | 0.512405 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5352.36 | −0.676643 | −0.338322 | − | 0.941031i | \(-0.609859\pi\) | ||||
−0.338322 | + | 0.941031i | \(0.609859\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12510.7 | 1.56971 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6144.61 | −0.765205 | −0.382602 | − | 0.923913i | \(-0.624972\pi\) | ||||
−0.382602 | + | 0.923913i | \(0.624972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20795.9 | −2.57052 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3047.71 | −0.373930 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −19523.9 | −2.37780 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9226.12 | 1.11541 | 0.557705 | − | 0.830039i | \(-0.311682\pi\) | ||||
0.557705 | + | 0.830039i | \(0.311682\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 45.7430 | 0.00548986 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5206.45 | 0.620322 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4461.00 | −0.527667 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11579.3 | 1.35981 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 756.386 | 0.0881907 | 0.0440953 | − | 0.999027i | \(-0.485959\pi\) | ||||
0.0440953 | + | 0.999027i | \(0.485959\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2628.98 | −0.304344 | −0.152172 | − | 0.988354i | \(-0.548627\pi\) | ||||
−0.152172 | + | 0.988354i | \(0.548627\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9557.62 | −1.09860 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1773.26 | 0.202390 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1253.90 | −0.142108 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −36748.8 | −4.13578 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8492.79 | 0.949149 | 0.474575 | − | 0.880215i | \(-0.342602\pi\) | ||||
0.474575 | + | 0.880215i | \(0.342602\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5737.33 | −0.636763 | −0.318381 | − | 0.947963i | \(-0.603139\pi\) | ||||
−0.318381 | + | 0.947963i | \(0.603139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9302.16 | −1.02530 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1828.67 | 0.200177 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6974.82 | 0.758292 | 0.379146 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379146 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2619.33 | 0.282835 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2755.57 | 0.295533 | 0.147766 | − | 0.989022i | \(-0.452792\pi\) | ||||
0.147766 | + | 0.989022i | \(0.452792\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4558.92 | 0.485648 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3347.23 | −0.354181 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2242.66 | −0.235719 | −0.117860 | − | 0.993030i | \(-0.537603\pi\) | ||||
−0.117860 | + | 0.993030i | \(0.537603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24201.1 | 2.52680 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22078.2 | 2.28990 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7575.10 | −0.780497 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8098.67 | −0.828971 | −0.414486 | − | 0.910056i | \(-0.636038\pi\) | ||||
−0.414486 | + | 0.910056i | \(0.636038\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2088.06 | 0.212337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6133.87 | −0.619703 | −0.309851 | − | 0.950785i | \(-0.600279\pi\) | ||||
−0.309851 | + | 0.950785i | \(0.600279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15671.6 | −1.57305 | −0.786523 | − | 0.617560i | \(-0.788121\pi\) | ||||
−0.786523 | + | 0.617560i | \(0.788121\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10799.5 | 1.07702 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10231.3 | 1.01381 | 0.506906 | − | 0.862002i | \(-0.330789\pi\) | ||||
0.506906 | + | 0.862002i | \(0.330789\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8974.00 | −0.883541 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 174.463 | 0.0170676 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22657.3 | 2.20251 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1987.69 | 0.192003 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14740.0 | −1.41488 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13756.0 | 1.31216 | 0.656082 | − | 0.754690i | \(-0.272213\pi\) | ||||
0.656082 | + | 0.754690i | \(0.272213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21681.6 | 2.05530 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3619.10 | 0.340941 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 266.612 | 0.0249613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19708.6 | 1.83384 | 0.916920 | − | 0.399071i | \(-0.130667\pi\) | ||||
0.916920 | + | 0.399071i | \(0.130667\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12680.4 | −1.17266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13139.1 | 1.20766 | 0.603828 | − | 0.797115i | \(-0.293641\pi\) | ||||
0.603828 | + | 0.797115i | \(0.293641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17346.9 | −1.58471 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10180.0 | 0.924361 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 23162.6 | 2.09051 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21342.8 | −1.91470 | −0.957350 | − | 0.288932i | \(-0.906700\pi\) | ||||
−0.957350 | + | 0.288932i | \(0.906700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7979.19 | 0.711545 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4725.75 | 0.418909 | 0.209454 | − | 0.977818i | \(-0.432831\pi\) | ||||
0.209454 | + | 0.977818i | \(0.432831\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 671.502 | 0.0591712 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24097.2 | 2.11084 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16423.9 | −1.43021 | −0.715105 | − | 0.699017i | \(-0.753621\pi\) | ||||
−0.715105 | + | 0.699017i | \(0.753621\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12066.7 | −1.04462 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2340.55 | 0.201439 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1268.14 | −0.108507 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20420.3 | −1.73711 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9689.27 | 0.819483 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3724.80 | 0.313218 | 0.156609 | − | 0.987661i | \(-0.449944\pi\) | ||||
0.156609 | + | 0.987661i | \(0.449944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2905.97 | 0.242963 | 0.121481 | − | 0.992594i | \(-0.461236\pi\) | ||||
0.121481 | + | 0.992594i | \(0.461236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3933.80 | 0.327019 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20139.1 | 1.66465 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7770.14 | 0.635020 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26875.8 | −2.18409 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9830.31 | −0.794395 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18318.9 | −1.47211 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5596.33 | 0.447219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −772.962 | −0.0614274 | −0.0307137 | − | 0.999528i | \(-0.509778\pi\) | ||||
−0.0307137 | + | 0.999528i | \(0.509778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7897.67 | 0.624165 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2340.49 | −0.183955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3226.14 | 0.252175 | 0.126088 | − | 0.992019i | \(-0.459758\pi\) | ||||
0.126088 | + | 0.992019i | \(0.459758\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1871.32 | −0.145476 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19444.4 | −1.50338 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16641.2 | 1.27967 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −11259.4 | −0.861146 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3527.96 | −0.268374 | −0.134187 | − | 0.990956i | \(-0.542842\pi\) | ||||
−0.134187 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25161.4 | −1.90378 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35588.1 | 2.67831 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3414.29 | −0.255586 | −0.127793 | − | 0.991801i | \(-0.540789\pi\) | ||||
−0.127793 | + | 0.991801i | \(0.540789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 313.457 | 0.0233403 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12608.1 | −0.933845 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9661.15 | −0.711804 | −0.355902 | − | 0.934523i | \(-0.615826\pi\) | ||||
−0.355902 | + | 0.934523i | \(0.615826\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16580.1 | −1.21516 | −0.607578 | − | 0.794260i | \(-0.707859\pi\) | ||||
−0.607578 | + | 0.794260i | \(0.707859\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6777.41 | 0.494120 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4587.53 | −0.330990 | −0.165495 | − | 0.986211i | \(-0.552922\pi\) | ||||
−0.165495 | + | 0.986211i | \(0.552922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1035.24 | −0.0743061 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18454.8 | −1.31778 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31492.6 | −2.23721 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11305.1 | −0.798990 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21730.5 | 1.52796 | 0.763980 | − | 0.645240i | \(-0.223243\pi\) | ||||
0.763980 | + | 0.645240i | \(0.223243\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22574.3 | 1.57922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11209.6 | 0.780209 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3557.48 | −0.246354 | −0.123177 | − | 0.992385i | \(-0.539308\pi\) | ||||
−0.123177 | + | 0.992385i | \(0.539308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7335.83 | 0.505445 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2188.05 | 0.150001 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4940.46 | 0.336998 | 0.168499 | − | 0.985702i | \(-0.446108\pi\) | ||||
0.168499 | + | 0.985702i | \(0.446108\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24459.7 | −1.66012 | −0.830060 | − | 0.557675i | \(-0.811694\pi\) | ||||
−0.830060 | + | 0.557675i | \(0.811694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13392.8 | −0.904476 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15095.1 | 1.01439 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4098.17 | −0.274035 | −0.137018 | − | 0.990569i | \(-0.543752\pi\) | ||||
−0.137018 | + | 0.990569i | \(0.543752\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −38482.2 | −2.56056 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22677.1 | 1.50150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10486.4 | −0.690936 | −0.345468 | − | 0.938431i | \(-0.612280\pi\) | ||||
−0.345468 | + | 0.938431i | \(0.612280\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13956.8 | 0.915107 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6366.64 | −0.415415 | −0.207708 | − | 0.978191i | \(-0.566600\pi\) | ||||
−0.207708 | + | 0.978191i | \(0.566600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21614.5 | −1.40349 | −0.701746 | − | 0.712427i | \(-0.747596\pi\) | ||||
−0.701746 | + | 0.712427i | \(0.747596\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 677.078 | 0.0437524 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18859.8 | 1.21285 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 39891.4 | 2.54085 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20996.8 | −1.33100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20515.5 | −1.29431 | −0.647154 | − | 0.762359i | \(-0.724041\pi\) | ||||
−0.647154 | + | 0.762359i | \(0.724041\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 33412.1 | 2.09797 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10998.1 | −0.687315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6214.83 | −0.386563 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34568.0 | 2.14005 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14561.7 | 0.897275 | 0.448637 | − | 0.893714i | \(-0.351909\pi\) | ||||
0.448637 | + | 0.893714i | \(0.351909\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14571.0 | −0.893659 | −0.446830 | − | 0.894619i | \(-0.647447\pi\) | ||||
−0.446830 | + | 0.894619i | \(0.647447\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13066.5 | 0.797662 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9034.71 | −0.548981 | −0.274491 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274491 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16601.3 | 1.00409 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 44676.5 | 2.68972 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10412.8 | 0.624018 | 0.312009 | − | 0.950079i | \(-0.398998\pi\) | ||||
0.312009 | + | 0.950079i | \(0.398998\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6879.55 | −0.410391 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −18008.5 | −1.06937 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19212.5 | −1.13568 | −0.567840 | − | 0.823139i | \(-0.692221\pi\) | ||||
−0.567840 | + | 0.823139i | \(0.692221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17563.2 | 1.03348 | 0.516739 | − | 0.856143i | \(-0.327146\pi\) | ||||
0.516739 | + | 0.856143i | \(0.327146\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −39521.2 | −2.31505 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 8222.88 | 0.479503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5624.91 | −0.326533 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 41061.1 | 2.37296 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3998.17 | −0.230026 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11984.7 | −0.686445 | −0.343222 | − | 0.939254i | \(-0.611518\pi\) | ||||
−0.343222 | + | 0.939254i | \(0.611518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 735.955 | 0.0419658 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23516.9 | 1.33505 | 0.667525 | − | 0.744587i | \(-0.267354\pi\) | ||||
0.667525 | + | 0.744587i | \(0.267354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1102.95 | 0.0623378 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19160.3 | 1.07816 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7449.33 | 0.417336 | 0.208668 | − | 0.977987i | \(-0.433087\pi\) | ||||
0.208668 | + | 0.977987i | \(0.433087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.0655 | 0.00167700 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −36157.4 | −2.00799 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34973.2 | 1.93378 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21369.7 | 1.17647 | 0.588236 | − | 0.808689i | \(-0.299823\pi\) | ||||
0.588236 | + | 0.808689i | \(0.299823\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 42113.9 | 2.30848 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7610.75 | 0.415384 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26026.9 | 1.41440 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9085.30 | −0.491613 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1166.89 | 0.0628713 | 0.0314357 | − | 0.999506i | \(-0.489992\pi\) | ||||
0.0314357 | + | 0.999506i | \(0.489992\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23535.8 | −1.26269 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −11776.4 | −0.629113 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2777.95 | 0.147773 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31306.3 | −1.65830 | −0.829149 | − | 0.559028i | \(-0.811174\pi\) | ||||
−0.829149 | + | 0.559028i | \(0.811174\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24835.5 | 1.30999 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6530.32 | 0.343005 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24153.9 | −1.26336 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −44510.0 | −2.31835 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25017.0 | 1.29760 | 0.648802 | − | 0.760957i | \(-0.275270\pi\) | ||||
0.648802 | + | 0.760957i | \(0.275270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5246.18 | −0.270982 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5006.13 | 0.257510 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6114.03 | −0.313199 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22380.1 | −1.14172 | −0.570861 | − | 0.821047i | \(-0.693391\pi\) | ||||
−0.570861 | + | 0.821047i | \(0.693391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24862.8 | −1.26316 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24366.6 | 1.23288 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11655.7 | −0.587333 | −0.293666 | − | 0.955908i | \(-0.594875\pi\) | ||||
−0.293666 | + | 0.955908i | \(0.594875\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3227.40 | 0.161965 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −28614.5 | −1.43016 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11983.0 | −0.596484 | −0.298242 | − | 0.954490i | \(-0.596400\pi\) | ||||
−0.298242 | + | 0.954490i | \(0.596400\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −44300.2 | −2.19623 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8516.73 | 0.420523 | 0.210262 | − | 0.977645i | \(-0.432568\pi\) | ||||
0.210262 | + | 0.977645i | \(0.432568\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2200.04 | −0.108192 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −27542.0 | −1.34901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −40667.1 | −1.98391 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3530.23 | 0.171531 | 0.0857655 | − | 0.996315i | \(-0.472666\pi\) | ||||
0.0857655 | + | 0.996315i | \(0.472666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20729.6 | 1.00323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14511.4 | 0.699500 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28421.2 | −1.36458 | −0.682290 | − | 0.731081i | \(-0.739016\pi\) | ||||
−0.682290 | + | 0.731081i | \(0.739016\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11539.8 | 0.551870 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15456.9 | −0.736286 | −0.368143 | − | 0.929769i | \(-0.620006\pi\) | ||||
−0.368143 | + | 0.929769i | \(0.620006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9682.40 | −0.459405 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10948.0 | 0.517421 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −18436.0 | −0.867910 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10820.0 | −0.507385 | −0.253692 | − | 0.967285i | \(-0.581645\pi\) | ||||
−0.253692 | + | 0.967285i | \(0.581645\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25262.7 | −1.18004 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −29863.4 | −1.38954 | −0.694769 | − | 0.719233i | \(-0.744494\pi\) | ||||
−0.694769 | + | 0.719233i | \(0.744494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7098.17 | 0.328999 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −46579.3 | −2.15061 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29174.0 | 1.34181 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 73856.2 | 3.38385 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7199.44 | −0.328591 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 114.669 | 0.00521365 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1588.27 | 0.0719388 | 0.0359694 | − | 0.999353i | \(-0.488548\pi\) | ||||
0.0359694 | + | 0.999353i | \(0.488548\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3289.39 | −0.148423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1296.75 | 0.0582895 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4440.04 | 0.198828 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18161.8 | −0.810230 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38280.0 | −1.70131 | −0.850656 | − | 0.525723i | \(-0.823795\pi\) | ||||
−0.850656 | + | 0.525723i | \(0.823795\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21960.9 | −0.972365 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28146.5 | 1.24158 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −38476.0 | −1.69089 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2378.72 | 0.104148 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33535.9 | −1.46285 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21369.6 | −0.928694 | −0.464347 | − | 0.885653i | \(-0.653711\pi\) | ||||
−0.464347 | + | 0.885653i | \(0.653711\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16291.7 | −0.705401 | −0.352700 | − | 0.935736i | \(-0.614736\pi\) | ||||
−0.352700 | + | 0.935736i | \(0.614736\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −65459.6 | −2.82382 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8334.46 | −0.358213 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27313.1 | 1.16960 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −46768.3 | −1.99538 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45046.6 | −1.91491 | −0.957454 | − | 0.288587i | \(-0.906814\pi\) | ||||
−0.957454 | + | 0.288587i | \(0.906814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14521.8 | −0.615064 | −0.307532 | − | 0.951538i | \(-0.599503\pi\) | ||||
−0.307532 | + | 0.951538i | \(0.599503\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12543.3 | 0.529335 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27039.3 | −1.13694 | −0.568470 | − | 0.822704i | \(-0.692465\pi\) | ||||
−0.568470 | + | 0.822704i | \(0.692465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8102.50 | −0.339459 | −0.169730 | − | 0.985491i | \(-0.554289\pi\) | ||||
−0.169730 | + | 0.985491i | \(0.554289\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −51959.1 | −2.16900 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6018.53 | 0.250336 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5244.49 | 0.217357 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8358.29 | 0.345167 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −868.168 | −0.0357241 | −0.0178620 | − | 0.999840i | \(-0.505686\pi\) | ||||
−0.0178620 | + | 0.999840i | \(0.505686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35421.3 | 1.45235 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −64905.7 | −2.65181 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15838.4 | 0.644802 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 62447.3 | 2.53331 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 51423.7 | 2.07875 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6808.45 | −0.274255 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14481.6 | 0.581291 | 0.290645 | − | 0.956831i | \(-0.406130\pi\) | ||||
0.290645 | + | 0.956831i | \(0.406130\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12271.9 | 0.490865 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45840.2 | 1.82716 | 0.913578 | − | 0.406664i | \(-0.133308\pi\) | ||||
0.913578 | + | 0.406664i | \(0.133308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12096.4 | −0.480469 | −0.240235 | − | 0.970715i | \(-0.577224\pi\) | ||||
−0.240235 | + | 0.970715i | \(0.577224\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 57737.9 | 2.28537 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3013.77 | 0.118876 | 0.0594380 | − | 0.998232i | \(-0.481069\pi\) | ||||
0.0594380 | + | 0.998232i | \(0.481069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6368.47 | 0.250329 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 898.643 | 0.0352013 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53062.2 | 2.07136 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31776.9 | 1.23619 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1646.05 | 0.0638148 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2585.57 | 0.0998951 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1553.17 | 0.0598027 | 0.0299013 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0299013 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −38547.8 | −1.47916 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12466.6 | −0.476743 | −0.238372 | − | 0.971174i | \(-0.576614\pi\) | ||||
−0.238372 | + | 0.971174i | \(0.576614\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12283.0 | −0.468126 | −0.234063 | − | 0.972221i | \(-0.575202\pi\) | ||||
−0.234063 | + | 0.972221i | \(0.575202\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9573.96 | 0.363644 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5256.94 | 0.198997 | 0.0994987 | − | 0.995038i | \(-0.468276\pi\) | ||||
0.0994987 | + | 0.995038i | \(0.468276\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −45498.1 | −1.71649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40202.1 | −1.51158 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24616.4 | −0.922459 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12040.5 | −0.449687 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12815.2 | −0.477020 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −69437.6 | −2.57605 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33868.5 | −1.25230 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 54054.9 | 1.99206 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5190.91 | 0.190665 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28669.8 | 1.04958 | 0.524788 | − | 0.851233i | \(-0.324144\pi\) | ||||
0.524788 | + | 0.851233i | \(0.324144\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4145.82 | 0.151274 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10069.9 | 0.366225 | 0.183113 | − | 0.983092i | \(-0.441383\pi\) | ||||
0.183113 | + | 0.983092i | \(0.441383\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −58844.8 | −2.13305 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2305.74 | −0.0833066 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28460.1 | −1.02490 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −49898.4 | −1.79108 | −0.895538 | − | 0.444986i | \(-0.853209\pi\) | ||||
−0.895538 | + | 0.444986i | \(0.853209\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32304.8 | 1.15579 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −82018.7 | −2.92490 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7400.49 | −0.263056 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7829.43 | −0.277403 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8573.05 | −0.302769 | −0.151385 | − | 0.988475i | \(-0.548373\pi\) | ||||
−0.151385 | + | 0.988475i | \(0.548373\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6746.29 | 0.237487 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6987.93 | 0.245203 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 23391.0 | 0.818147 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3952.76 | 0.137813 | 0.0689066 | − | 0.997623i | \(-0.478049\pi\) | ||||
0.0689066 | + | 0.997623i | \(0.478049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4035.46 | 0.140247 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1708.81 | −0.0591982 | −0.0295991 | − | 0.999562i | \(-0.509423\pi\) | ||||
−0.0295991 | + | 0.999562i | \(0.509423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8439.50 | 0.291440 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3044.58 | 0.104804 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25389.4 | −0.871219 | −0.435609 | − | 0.900136i | \(-0.643467\pi\) | ||||
−0.435609 | + | 0.900136i | \(0.643467\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 42728.3 | 1.46156 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59752.0 | 2.03742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11245.0 | −0.382228 | −0.191114 | − | 0.981568i | \(-0.561210\pi\) | ||||
−0.191114 | + | 0.981568i | \(0.561210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4454.59 | 0.150940 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −122704. | −4.14469 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 124.378 | 0.00418810 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50823.5 | 1.70600 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −60691.9 | −2.03091 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −680.435 | −0.0226984 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3022.48 | 0.100513 | 0.0502566 | − | 0.998736i | \(-0.483996\pi\) | ||||
0.0502566 | + | 0.998736i | \(0.483996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42900.9 | 1.42227 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50953.9 | −1.68403 | −0.842013 | − | 0.539457i | \(-0.818630\pi\) | ||||
−0.842013 | + | 0.539457i | \(0.818630\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31485.0 | 1.03737 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13929.6 | −0.457542 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38184.7 | 1.25040 | 0.625199 | − | 0.780466i | \(-0.285018\pi\) | ||||
0.625199 | + | 0.780466i | \(0.285018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 60136.4 | 1.96320 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14450.1 | −0.470291 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13378.9 | 0.434099 | 0.217050 | − | 0.976161i | \(-0.430357\pi\) | ||||
0.217050 | + | 0.976161i | \(0.430357\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7367.77 | 0.238332 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −48717.9 | −1.57113 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7901.16 | 0.254037 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22011.7 | −0.705576 | −0.352788 | − | 0.935703i | \(-0.614766\pi\) | ||||
−0.352788 | + | 0.935703i | \(0.614766\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 88414.1 | 2.82551 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1438.14 | 0.0458212 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6203.59 | 0.197061 | 0.0985304 | − | 0.995134i | \(-0.468586\pi\) | ||||
0.0985304 | + | 0.995134i | \(0.468586\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8714.28 | −0.275984 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1840.4.a.ba.1.9 | 10 | ||
4.3 | odd | 2 | 920.4.a.h.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.h.1.2 | ✓ | 10 | 4.3 | odd | 2 | ||
1840.4.a.ba.1.9 | 10 | 1.1 | even | 1 | trivial |