Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.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: | \(95.5830942093\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 151x^{4} - 212x^{3} + 4412x^{2} + 8656x - 19148 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(5.63924\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.5713 | 0.894766 | 0.447383 | − | 0.894343i | \(-0.352356\pi\) | ||||
0.447383 | + | 0.894343i | \(0.352356\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 72.5369 | 1.98824 | 0.994122 | − | 0.108266i | \(-0.0345298\pi\) | ||||
0.994122 | + | 0.108266i | \(0.0345298\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −59.8975 | −1.27789 | −0.638946 | − | 0.769252i | \(-0.720629\pi\) | ||||
−0.638946 | + | 0.769252i | \(0.720629\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −15.8529 | −0.226170 | −0.113085 | − | 0.993585i | \(-0.536073\pi\) | ||||
−0.113085 | + | 0.993585i | \(0.536073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −136.646 | −1.64993 | −0.824966 | − | 0.565182i | \(-0.808806\pi\) | ||||
−0.824966 | + | 0.565182i | \(0.808806\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −163.101 | −1.47864 | −0.739322 | − | 0.673352i | \(-0.764854\pi\) | ||||
−0.739322 | + | 0.673352i | \(0.764854\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −11.5985 | −0.0742683 | −0.0371342 | − | 0.999310i | \(-0.511823\pi\) | ||||
−0.0371342 | + | 0.999310i | \(0.511823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.0018 | −0.237553 | −0.118776 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118776 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 82.8565 | 0.400151 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −242.545 | −1.07768 | −0.538841 | − | 0.842408i | \(-0.681138\pi\) | ||||
−0.538841 | + | 0.842408i | \(0.681138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −57.8664 | −0.220420 | −0.110210 | − | 0.993908i | \(-0.535152\pi\) | ||||
−0.110210 | + | 0.993908i | \(0.535152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −264.504 | −0.938059 | −0.469029 | − | 0.883183i | \(-0.655396\pi\) | ||||
−0.469029 | + | 0.883183i | \(0.655396\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −599.889 | −1.86176 | −0.930882 | − | 0.365321i | \(-0.880959\pi\) | ||||
−0.930882 | + | 0.365321i | \(0.880959\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −68.3922 | −0.199394 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −592.285 | −1.53503 | −0.767516 | − | 0.641030i | \(-0.778507\pi\) | ||||
−0.767516 | + | 0.641030i | \(0.778507\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 362.684 | 0.889170 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −288.893 | −0.637468 | −0.318734 | − | 0.947844i | \(-0.603258\pi\) | ||||
−0.318734 | + | 0.947844i | \(0.603258\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 825.380 | 1.73244 | 0.866222 | − | 0.499660i | \(-0.166542\pi\) | ||||
0.866222 | + | 0.499660i | \(0.166542\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −299.488 | −0.571490 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 810.528 | 1.47794 | 0.738968 | − | 0.673741i | \(-0.235313\pi\) | ||||
0.738968 | + | 0.673741i | \(0.235313\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 966.126 | 1.61490 | 0.807451 | − | 0.589935i | \(-0.200847\pi\) | ||||
0.807451 | + | 0.589935i | \(0.200847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 802.840 | 1.28720 | 0.643598 | − | 0.765364i | \(-0.277441\pi\) | ||||
0.643598 | + | 0.765364i | \(0.277441\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1202.03 | 1.77901 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1162.00 | −1.65488 | −0.827440 | − | 0.561554i | \(-0.810204\pi\) | ||||
−0.827440 | + | 0.561554i | \(0.810204\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −502.375 | −0.664371 | −0.332186 | − | 0.943214i | \(-0.607786\pi\) | ||||
−0.332186 | + | 0.943214i | \(0.607786\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −79.2644 | −0.101146 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.76580 | −0.0104401 | −0.00522007 | − | 0.999986i | \(-0.501662\pi\) | ||||
−0.00522007 | + | 0.999986i | \(0.501662\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −992.580 | −1.14341 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −683.229 | −0.737872 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 138.364 | 0.144832 | 0.0724161 | − | 0.997375i | \(-0.476929\pi\) | ||||
0.0724161 | + | 0.997375i | \(0.476929\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1325.78 | 1.30614 | 0.653068 | − | 0.757299i | \(-0.273481\pi\) | ||||
0.653068 | + | 0.757299i | \(0.273481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 333.544 | 0.319078 | 0.159539 | − | 0.987192i | \(-0.448999\pi\) | ||||
0.159539 | + | 0.987192i | \(0.448999\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −584.004 | −0.527643 | −0.263821 | − | 0.964572i | \(-0.584983\pi\) | ||||
−0.263821 | + | 0.964572i | \(0.584983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1915.42 | −1.68315 | −0.841577 | − | 0.540137i | \(-0.818372\pi\) | ||||
−0.841577 | + | 0.540137i | \(0.818372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1237.32 | −1.03006 | −0.515030 | − | 0.857172i | \(-0.672219\pi\) | ||||
−0.515030 | + | 0.857172i | \(0.672219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −815.503 | −0.661270 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −262.703 | −0.202369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3930.59 | 2.95311 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1785.42 | −1.24749 | −0.623743 | − | 0.781629i | \(-0.714389\pi\) | ||||
−0.623743 | + | 0.781629i | \(0.714389\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −721.812 | −0.481413 | −0.240706 | − | 0.970598i | \(-0.577379\pi\) | ||||
−0.240706 | + | 0.970598i | \(0.577379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2264.40 | −1.47630 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1108.99 | 0.691585 | 0.345792 | − | 0.938311i | \(-0.387610\pi\) | ||||
0.345792 | + | 0.938311i | \(0.387610\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 436.770 | 0.266520 | 0.133260 | − | 0.991081i | \(-0.457455\pi\) | ||||
0.133260 | + | 0.991081i | \(0.457455\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4344.78 | −2.54076 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −57.9923 | −0.0332138 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 177.117 | 0.0973825 | 0.0486912 | − | 0.998814i | \(-0.484495\pi\) | ||||
0.0486912 | + | 0.998814i | \(0.484495\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 828.658 | 0.446591 | 0.223296 | − | 0.974751i | \(-0.428318\pi\) | ||||
0.223296 | + | 0.974751i | \(0.428318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −205.009 | −0.106237 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −866.524 | −0.440485 | −0.220242 | − | 0.975445i | \(-0.570685\pi\) | ||||
−0.220242 | + | 0.975445i | \(0.570685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2702.79 | −1.32304 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2984.70 | 1.43423 | 0.717116 | − | 0.696954i | \(-0.245462\pi\) | ||||
0.717116 | + | 0.696954i | \(0.245462\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1959.44 | −0.907940 | −0.453970 | − | 0.891017i | \(-0.649993\pi\) | ||||
−0.453970 | + | 0.891017i | \(0.649993\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1390.72 | 0.633007 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −506.945 | −0.222788 | −0.111394 | − | 0.993776i | \(-0.535532\pi\) | ||||
−0.111394 | + | 0.993776i | \(0.535532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 414.282 | 0.178953 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3122.26 | 1.30374 | 0.651869 | − | 0.758332i | \(-0.273985\pi\) | ||||
0.651869 | + | 0.758332i | \(0.273985\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2828.38 | −1.16150 | −0.580751 | − | 0.814082i | \(-0.697241\pi\) | ||||
−0.580751 | + | 0.814082i | \(0.697241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1212.73 | −0.481954 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1149.92 | −0.449681 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4078.64 | −1.54513 | −0.772565 | − | 0.634936i | \(-0.781027\pi\) | ||||
−0.772565 | + | 0.634936i | \(0.781027\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3043.12 | 1.13497 | 0.567483 | − | 0.823385i | \(-0.307917\pi\) | ||||
0.567483 | + | 0.823385i | \(0.307917\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1338.21 | −0.483978 | −0.241989 | − | 0.970279i | \(-0.577800\pi\) | ||||
−0.241989 | + | 0.970279i | \(0.577800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 453.645 | 0.161598 | 0.0807991 | − | 0.996730i | \(-0.474253\pi\) | ||||
0.0807991 | + | 0.996730i | \(0.474253\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −192.202 | −0.0664528 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −289.332 | −0.0985748 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9911.86 | −3.28047 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1905.96 | 0.621856 | 0.310928 | − | 0.950434i | \(-0.399360\pi\) | ||||
0.310928 | + | 0.950434i | \(0.399360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1322.52 | −0.419513 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −679.452 | −0.212554 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 949.548 | 0.289021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4455.51 | 1.33795 | 0.668976 | − | 0.743284i | \(-0.266733\pi\) | ||||
0.668976 | + | 0.743284i | \(0.266733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −171.235 | −0.0500672 | −0.0250336 | − | 0.999687i | \(-0.507969\pi\) | ||||
−0.0250336 | + | 0.999687i | \(0.507969\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4429.94 | 1.27834 | 0.639168 | − | 0.769067i | \(-0.279279\pi\) | ||||
0.639168 | + | 0.769067i | \(0.279279\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 762.810 | 0.214478 | 0.107239 | − | 0.994233i | \(-0.465799\pi\) | ||||
0.107239 | + | 0.994233i | \(0.465799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2999.45 | −0.832606 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3044.29 | −0.823927 | −0.411963 | − | 0.911200i | \(-0.635157\pi\) | ||||
−0.411963 | + | 0.911200i | \(0.635157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2018.31 | −0.539465 | −0.269733 | − | 0.962935i | \(-0.586935\pi\) | ||||
−0.269733 | + | 0.962935i | \(0.586935\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −341.961 | −0.0891718 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8184.75 | 2.10843 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3031.55 | −0.762351 | −0.381175 | − | 0.924503i | \(-0.624481\pi\) | ||||
−0.381175 | + | 0.924503i | \(0.624481\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11830.8 | −2.93990 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4754.62 | −1.15403 | −0.577013 | − | 0.816735i | \(-0.695782\pi\) | ||||
−0.577013 | + | 0.816735i | \(0.695782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4019.29 | −0.964272 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3964.86 | 0.929595 | 0.464798 | − | 0.885417i | \(-0.346127\pi\) | ||||
0.464798 | + | 0.885417i | \(0.346127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2961.43 | −0.686487 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3989.09 | −0.904161 | −0.452080 | − | 0.891977i | \(-0.649318\pi\) | ||||
−0.452080 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2684.00 | 0.601628 | 0.300814 | − | 0.953683i | \(-0.402742\pi\) | ||||
0.300814 | + | 0.953683i | \(0.402742\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1813.42 | 0.397649 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 53.5212 | 0.0116093 | 0.00580465 | − | 0.999983i | \(-0.498152\pi\) | ||||
0.00580465 | + | 0.999983i | \(0.498152\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3638.06 | −0.772344 | −0.386172 | − | 0.922427i | \(-0.626203\pi\) | ||||
−0.386172 | + | 0.922427i | \(0.626203\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7326.03 | 1.53882 | 0.769412 | − | 0.638752i | \(-0.220549\pi\) | ||||
0.769412 | + | 0.638752i | \(0.220549\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −958.922 | −0.197224 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4661.69 | −0.948847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2522.24 | −0.502903 | −0.251452 | − | 0.967870i | \(-0.580908\pi\) | ||||
−0.251452 | + | 0.967870i | \(0.580908\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1444.46 | −0.285084 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9769.32 | 1.88955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4383.18 | −0.839343 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4126.90 | 0.774772 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 640.204 | 0.119017 | 0.0595087 | − | 0.998228i | \(-0.481047\pi\) | ||||
0.0595087 | + | 0.998228i | \(0.481047\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4874.34 | 0.888741 | 0.444371 | − | 0.895843i | \(-0.353427\pi\) | ||||
0.444371 | + | 0.895843i | \(0.353427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5163.98 | −0.932541 | −0.466270 | − | 0.884642i | \(-0.654403\pi\) | ||||
−0.466270 | + | 0.884642i | \(0.654403\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7310.00 | −1.29517 | −0.647587 | − | 0.761991i | \(-0.724222\pi\) | ||||
−0.647587 | + | 0.761991i | \(0.724222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −841.316 | −0.147664 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2166.23 | 0.373165 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1497.44 | −0.255578 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9940.94 | −1.66584 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11735.6 | −1.94878 | −0.974390 | − | 0.224865i | \(-0.927806\pi\) | ||||
−0.974390 | + | 0.224865i | \(0.927806\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4052.64 | 0.660953 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2251.02 | 0.363860 | 0.181930 | − | 0.983311i | \(-0.441766\pi\) | ||||
0.181930 | + | 0.983311i | \(0.441766\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2974.14 | −0.472313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6817.30 | −1.07318 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6958.99 | −1.07659 | −0.538297 | − | 0.842755i | \(-0.680932\pi\) | ||||
−0.538297 | + | 0.842755i | \(0.680932\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2924.01 | −0.448477 | −0.224238 | − | 0.974534i | \(-0.571989\pi\) | ||||
−0.224238 | + | 0.974534i | \(0.571989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6552.47 | 0.987968 | 0.493984 | − | 0.869471i | \(-0.335540\pi\) | ||||
0.493984 | + | 0.869471i | \(0.335540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4830.63 | 0.722206 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1324.66 | 0.194743 | 0.0973717 | − | 0.995248i | \(-0.468956\pi\) | ||||
0.0973717 | + | 0.995248i | \(0.468956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11813.1 | 1.72228 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4014.20 | 0.575651 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3256.21 | −0.463141 | −0.231571 | − | 0.972818i | \(-0.574386\pi\) | ||||
−0.231571 | + | 0.972818i | \(0.574386\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9814.94 | −1.37349 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4544.66 | −0.630867 | −0.315433 | − | 0.948948i | \(-0.602150\pi\) | ||||
−0.315433 | + | 0.948948i | \(0.602150\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 694.720 | 0.0949069 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2484.30 | −0.336701 | −0.168351 | − | 0.985727i | \(-0.553844\pi\) | ||||
−0.168351 | + | 0.985727i | \(0.553844\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2828.87 | 0.377411 | 0.188705 | − | 0.982034i | \(-0.439571\pi\) | ||||
0.188705 | + | 0.982034i | \(0.439571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6010.15 | 0.795599 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2590.17 | −0.337601 | −0.168801 | − | 0.985650i | \(-0.553989\pi\) | ||||
−0.168801 | + | 0.985650i | \(0.553989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2585.61 | 0.334425 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5810.01 | −0.740085 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12207.4 | 1.54325 | 0.771625 | − | 0.636077i | \(-0.219444\pi\) | ||||
0.771625 | + | 0.636077i | \(0.219444\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9520.41 | −1.18560 | −0.592801 | − | 0.805349i | \(-0.701978\pi\) | ||||
−0.592801 | + | 0.805349i | \(0.701978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2455.91 | 0.303567 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17593.5 | −2.14269 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11246.7 | 1.35969 | 0.679846 | − | 0.733355i | \(-0.262047\pi\) | ||||
0.679846 | + | 0.733355i | \(0.262047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4787.32 | −0.570384 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2511.87 | −0.297116 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10682.0 | 1.24546 | 0.622731 | − | 0.782436i | \(-0.286023\pi\) | ||||
0.622731 | + | 0.782436i | \(0.286023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10824.0 | 1.25304 | 0.626518 | − | 0.779407i | \(-0.284479\pi\) | ||||
0.626518 | + | 0.779407i | \(0.284479\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −396.322 | −0.0452340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13677.6 | 1.55013 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 235.904 | 0.0263645 | 0.0131823 | − | 0.999913i | \(-0.495804\pi\) | ||||
0.0131823 | + | 0.999913i | \(0.495804\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11895.5 | −1.32024 | −0.660118 | − | 0.751162i | \(-0.729494\pi\) | ||||
−0.660118 | + | 0.751162i | \(0.729494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22287.0 | 2.43966 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3811.05 | 0.414331 | 0.207166 | − | 0.978306i | \(-0.433576\pi\) | ||||
0.207166 | + | 0.978306i | \(0.433576\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8032.23 | 0.861451 | 0.430725 | − | 0.902483i | \(-0.358258\pi\) | ||||
0.430725 | + | 0.902483i | \(0.358258\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.8290 | −0.00466897 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12271.3 | −1.28980 | −0.644898 | − | 0.764269i | \(-0.723100\pi\) | ||||
−0.644898 | + | 0.764269i | \(0.723100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4197.45 | −0.438249 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4962.90 | −0.511350 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9944.00 | 1.01786 | 0.508929 | − | 0.860809i | \(-0.330042\pi\) | ||||
0.508929 | + | 0.860809i | \(0.330042\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6749.48 | −0.681897 | −0.340949 | − | 0.940082i | \(-0.610748\pi\) | ||||
−0.340949 | + | 0.940082i | \(0.610748\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9560.15 | −0.959607 | −0.479804 | − | 0.877376i | \(-0.659292\pi\) | ||||
−0.479804 | + | 0.877376i | \(0.659292\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6517.56 | 0.645818 | 0.322909 | − | 0.946430i | \(-0.395339\pi\) | ||||
0.322909 | + | 0.946430i | \(0.395339\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13431.5 | 1.32241 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19186.3 | −1.86509 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3416.15 | −0.329986 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4752.73 | 0.453357 | 0.226678 | − | 0.973970i | \(-0.427213\pi\) | ||||
0.226678 | + | 0.973970i | \(0.427213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14527.9 | 1.37716 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 691.820 | 0.0647710 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8412.56 | −0.782771 | −0.391386 | − | 0.920227i | \(-0.628004\pi\) | ||||
−0.391386 | + | 0.920227i | \(0.628004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5570.45 | 0.511998 | 0.255999 | − | 0.966677i | \(-0.417596\pi\) | ||||
0.255999 | + | 0.966677i | \(0.417596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 183.869 | 0.0167973 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16010.0 | 1.44496 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15824.6 | −1.41966 | −0.709828 | − | 0.704375i | \(-0.751227\pi\) | ||||
−0.709828 | + | 0.704375i | \(0.751227\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15946.4 | 1.41354 | 0.706772 | − | 0.707441i | \(-0.250151\pi\) | ||||
0.706772 | + | 0.707441i | \(0.250151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6628.89 | 0.584122 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14638.7 | 1.27475 | 0.637375 | − | 0.770553i | \(-0.280020\pi\) | ||||
0.637375 | + | 0.770553i | \(0.280020\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13304.1 | 1.15174 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1667.72 | 0.142696 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −43514.1 | −3.70164 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13001.4 | 1.09329 | 0.546644 | − | 0.837365i | \(-0.315905\pi\) | ||||
0.546644 | + | 0.837365i | \(0.315905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1938.88 | −0.162106 | −0.0810531 | − | 0.996710i | \(-0.525828\pi\) | ||||
−0.0810531 | + | 0.996710i | \(0.525828\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 649.996 | 0.0537273 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14434.8 | 1.18639 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3466.06 | 0.281673 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2920.02 | −0.235969 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4960.96 | −0.396444 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7574.14 | −0.601918 | −0.300959 | − | 0.953637i | \(-0.597307\pi\) | ||||
−0.300959 | + | 0.953637i | \(0.597307\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9577.09 | −0.752729 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3141.87 | −0.245588 | −0.122794 | − | 0.992432i | \(-0.539185\pi\) | ||||
−0.122794 | + | 0.992432i | \(0.539185\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1584.88 | 0.122538 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19255.9 | −1.48073 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12191.5 | −0.927412 | −0.463706 | − | 0.885989i | \(-0.653481\pi\) | ||||
−0.463706 | + | 0.885989i | \(0.653481\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15843.2 | 1.19874 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2182.85 | 0.163403 | 0.0817016 | − | 0.996657i | \(-0.473965\pi\) | ||||
0.0817016 | + | 0.996657i | \(0.473965\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6186.58 | −0.460657 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1785.93 | 0.131582 | 0.0657911 | − | 0.997833i | \(-0.479043\pi\) | ||||
0.0657911 | + | 0.997833i | \(0.479043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3404.30 | 0.249502 | 0.124751 | − | 0.992188i | \(-0.460187\pi\) | ||||
0.124751 | + | 0.992188i | \(0.460187\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4077.51 | −0.295729 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4174.78 | −0.301210 | −0.150605 | − | 0.988594i | \(-0.548122\pi\) | ||||
−0.150605 | + | 0.988594i | \(0.548122\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8325.00 | −0.594457 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −42962.5 | −3.05202 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18616.9 | 1.30904 | 0.654518 | − | 0.756047i | \(-0.272872\pi\) | ||||
0.654518 | + | 0.756047i | \(0.272872\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5602.72 | 0.391946 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24181.4 | −1.67456 | −0.837278 | − | 0.546777i | \(-0.815855\pi\) | ||||
−0.837278 | + | 0.546777i | \(0.815855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1313.51 | −0.0905022 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5339.43 | −0.364212 | −0.182106 | − | 0.983279i | \(-0.558291\pi\) | ||||
−0.182106 | + | 0.983279i | \(0.558291\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9165.72 | 0.622093 | 0.311046 | − | 0.950395i | \(-0.399321\pi\) | ||||
0.311046 | + | 0.950395i | \(0.399321\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19653.0 | 1.32067 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11431.7 | 0.764413 | 0.382206 | − | 0.924077i | \(-0.375164\pi\) | ||||
0.382206 | + | 0.924077i | \(0.375164\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35931.9 | 2.37913 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29975.6 | 1.97505 | 0.987523 | − | 0.157477i | \(-0.0503361\pi\) | ||||
0.987523 | + | 0.157477i | \(0.0503361\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6112.72 | 0.398847 | 0.199424 | − | 0.979913i | \(-0.436093\pi\) | ||||
0.199424 | + | 0.979913i | \(0.436093\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1387.97 | 0.0901250 | 0.0450625 | − | 0.998984i | \(-0.485651\pi\) | ||||
0.0450625 | + | 0.998984i | \(0.485651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −145.261 | −0.00934148 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3845.04 | 0.243739 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18608.3 | 1.17399 | 0.586993 | − | 0.809592i | \(-0.300312\pi\) | ||||
0.586993 | + | 0.809592i | \(0.300312\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8927.12 | −0.557893 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4096.53 | 0.254804 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8039.55 | −0.495387 | −0.247693 | − | 0.968838i | \(-0.579673\pi\) | ||||
−0.247693 | + | 0.968838i | \(0.579673\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26661.4 | −1.63518 | −0.817592 | − | 0.575798i | \(-0.804692\pi\) | ||||
−0.817592 | + | 0.575798i | \(0.804692\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6303.13 | 0.383001 | 0.191501 | − | 0.981492i | \(-0.438665\pi\) | ||||
0.191501 | + | 0.981492i | \(0.438665\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20955.4 | −1.26744 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22598.3 | −1.35427 | −0.677136 | − | 0.735857i | \(-0.736779\pi\) | ||||
−0.677136 | + | 0.735857i | \(0.736779\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3609.06 | −0.215294 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2397.73 | 0.141733 | 0.0708667 | − | 0.997486i | \(-0.477423\pi\) | ||||
0.0708667 | + | 0.997486i | \(0.477423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5063.62 | −0.297961 | −0.148980 | − | 0.988840i | \(-0.547599\pi\) | ||||
−0.148980 | + | 0.988840i | \(0.547599\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11322.0 | −0.660223 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1891.72 | 0.109816 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59870.5 | 3.44452 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7281.32 | 0.417050 | 0.208525 | − | 0.978017i | \(-0.433134\pi\) | ||||
0.208525 | + | 0.978017i | \(0.433134\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28964.2 | −1.64429 | −0.822146 | − | 0.569277i | \(-0.807223\pi\) | ||||
−0.822146 | + | 0.569277i | \(0.807223\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2292.87 | 0.129591 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9158.42 | 0.513085 | 0.256543 | − | 0.966533i | \(-0.417417\pi\) | ||||
0.256543 | + | 0.966533i | \(0.417417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5544.93 | 0.309286 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 35476.4 | 1.96160 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10028.3 | 0.552090 | 0.276045 | − | 0.961145i | \(-0.410976\pi\) | ||||
0.276045 | + | 0.961145i | \(0.410976\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2183.85 | 0.119192 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 917.349 | 0.0498523 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27626.7 | 1.48851 | 0.744256 | − | 0.667894i | \(-0.232804\pi\) | ||||
0.744256 | + | 0.667894i | \(0.232804\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33142.8 | 1.77810 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21969.9 | 1.16869 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9703.69 | 0.514005 | 0.257003 | − | 0.966411i | \(-0.417265\pi\) | ||||
0.257003 | + | 0.966411i | \(0.417265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6687.41 | 0.351256 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21723.9 | −1.13626 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32045.4 | 1.66216 | 0.831080 | − | 0.556153i | \(-0.187723\pi\) | ||||
0.831080 | + | 0.556153i | \(0.187723\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5527.25 | 0.285500 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −289.962 | −0.0148537 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7447.26 | −0.379922 | −0.189961 | − | 0.981792i | \(-0.560836\pi\) | ||||
−0.189961 | + | 0.981792i | \(0.560836\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4193.15 | 0.212161 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18144.7 | −0.914312 | −0.457156 | − | 0.889386i | \(-0.651132\pi\) | ||||
−0.457156 | + | 0.889386i | \(0.651132\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58793.1 | 2.93850 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25920.2 | 1.29024 | 0.645121 | − | 0.764081i | \(-0.276807\pi\) | ||||
0.645121 | + | 0.764081i | \(0.276807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9313.10 | −0.459844 | −0.229922 | − | 0.973209i | \(-0.573847\pi\) | ||||
−0.229922 | + | 0.973209i | \(0.573847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 885.585 | 0.0435508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9677.69 | −0.472116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4984.29 | −0.242183 | −0.121091 | − | 0.992641i | \(-0.538639\pi\) | ||||
−0.121091 | + | 0.992641i | \(0.538639\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4143.29 | 0.199722 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10452.6 | −0.501857 | −0.250928 | − | 0.968006i | \(-0.580736\pi\) | ||||
−0.250928 | + | 0.968006i | \(0.580736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9405.94 | 0.448049 | 0.224024 | − | 0.974584i | \(-0.428080\pi\) | ||||
0.224024 | + | 0.974584i | \(0.428080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −31741.0 | −1.50603 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17304.0 | 0.814615 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23568.3 | −1.10519 | −0.552596 | − | 0.833449i | \(-0.686363\pi\) | ||||
−0.552596 | + | 0.833449i | \(0.686363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3172.70 | −0.147625 | −0.0738125 | − | 0.997272i | \(-0.523517\pi\) | ||||
−0.0738125 | + | 0.997272i | \(0.523517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1025.04 | −0.0475106 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7907.21 | 0.363678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 70079.7 | 3.21082 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4332.62 | −0.196991 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15442.4 | 0.699442 | 0.349721 | − | 0.936854i | \(-0.386276\pi\) | ||||
0.349721 | + | 0.936854i | \(0.386276\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20503.9 | −0.921663 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49438.2 | −2.21388 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9968.55 | −0.443042 | −0.221521 | − | 0.975156i | \(-0.571102\pi\) | ||||
−0.221521 | + | 0.975156i | \(0.571102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9509.97 | 0.421075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58235.5 | 2.55926 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13513.9 | −0.591681 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10439.0 | −0.453667 | −0.226833 | − | 0.973934i | \(-0.572837\pi\) | ||||
−0.226833 | + | 0.973934i | \(0.572837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17472.9 | 0.756544 | 0.378272 | − | 0.925694i | \(-0.376518\pi\) | ||||
0.378272 | + | 0.925694i | \(0.376518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14923.5 | 0.641408 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36143.4 | 1.54773 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19501.8 | −0.829009 | −0.414505 | − | 0.910047i | \(-0.636045\pi\) | ||||
−0.414505 | + | 0.910047i | \(0.636045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16592.4 | −0.702765 | −0.351383 | − | 0.936232i | \(-0.614288\pi\) | ||||
−0.351383 | + | 0.936232i | \(0.614288\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32449.4 | −1.36442 | −0.682210 | − | 0.731156i | \(-0.738981\pi\) | ||||
−0.682210 | + | 0.731156i | \(0.738981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7197.10 | 0.301527 | 0.150763 | − | 0.988570i | \(-0.451827\pi\) | ||||
0.150763 | + | 0.988570i | \(0.451827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1084.21 | 0.0450970 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9797.20 | −0.406043 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15431.9 | 0.635005 | 0.317503 | − | 0.948257i | \(-0.397156\pi\) | ||||
0.317503 | + | 0.948257i | \(0.397156\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24254.5 | −0.994484 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6953.58 | 0.283089 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 65135.0 | 2.64235 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39559.3 | 1.59351 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7914.74 | 0.317697 | 0.158848 | − | 0.987303i | \(-0.449222\pi\) | ||||
0.158848 | + | 0.987303i | \(0.449222\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26812.8 | −1.06874 | −0.534369 | − | 0.845252i | \(-0.679451\pi\) | ||||
−0.534369 | + | 0.845252i | \(0.679451\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1618.53 | 0.0642882 | 0.0321441 | − | 0.999483i | \(-0.489766\pi\) | ||||
0.0321441 | + | 0.999483i | \(0.489766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16678.5 | −0.657869 | −0.328935 | − | 0.944353i | \(-0.606690\pi\) | ||||
−0.328935 | + | 0.944353i | \(0.606690\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2534.72 | −0.0996338 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −84288.0 | −3.29030 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48548.6 | −1.88864 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2071.41 | 0.0800303 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2128.31 | −0.0819475 | −0.0409738 | − | 0.999160i | \(-0.513046\pi\) | ||||
−0.0409738 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2379.31 | −0.0909886 | −0.0454943 | − | 0.998965i | \(-0.514486\pi\) | ||||
−0.0454943 | + | 0.998965i | \(0.514486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36926.5 | −1.40733 | −0.703666 | − | 0.710531i | \(-0.748455\pi\) | ||||
−0.703666 | + | 0.710531i | \(0.748455\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4781.40 | 0.180996 | 0.0904981 | − | 0.995897i | \(-0.471154\pi\) | ||||
0.0904981 | + | 0.995897i | \(0.471154\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29586.8 | −1.11621 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 81972.4 | 3.07178 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15611.3 | 0.583049 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 475.558 | 0.0176426 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9389.43 | 0.347178 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14141.9 | −0.519439 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48064.8 | 1.75961 | 0.879804 | − | 0.475337i | \(-0.157674\pi\) | ||||
0.879804 | + | 0.475337i | \(0.157674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25634.4 | −0.932280 | −0.466140 | − | 0.884711i | \(-0.654356\pi\) | ||||
−0.466140 | + | 0.884711i | \(0.654356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36440.7 | −1.32093 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11961.4 | −0.430751 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9651.68 | −0.346441 | −0.173221 | − | 0.984883i | \(-0.555417\pi\) | ||||
−0.173221 | + | 0.984883i | \(0.555417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −57868.6 | −2.06367 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6063.63 | −0.215536 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −333.995 | −0.0117955 | −0.00589775 | − | 0.999983i | \(-0.501877\pi\) | ||||
−0.00589775 | + | 0.999983i | \(0.501877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9345.51 | 0.328987 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5749.59 | −0.201103 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11567.3 | 0.403295 | 0.201648 | − | 0.979458i | \(-0.435370\pi\) | ||||
0.201648 | + | 0.979458i | \(0.435370\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20261.7 | 0.701926 | 0.350963 | − | 0.936389i | \(-0.385854\pi\) | ||||
0.350963 | + | 0.936389i | \(0.385854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9438.04 | 0.325923 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27353.4 | −0.938614 | −0.469307 | − | 0.883035i | \(-0.655496\pi\) | ||||
−0.469307 | + | 0.883035i | \(0.655496\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48088.1 | −1.64490 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −45432.0 | −1.54427 | −0.772133 | − | 0.635460i | \(-0.780810\pi\) | ||||
−0.772133 | + | 0.635460i | \(0.780810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20393.2 | −0.691003 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18377.3 | 0.618806 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28109.9 | −0.943569 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15215.6 | 0.507572 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7134.19 | −0.237249 | −0.118625 | − | 0.992939i | \(-0.537849\pi\) | ||||
−0.118625 | + | 0.992939i | \(0.537849\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31719.4 | −1.04833 | −0.524163 | − | 0.851618i | \(-0.675622\pi\) | ||||
−0.524163 | + | 0.851618i | \(0.675622\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7237.84 | 0.238473 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17570.3 | 0.575357 | 0.287678 | − | 0.957727i | \(-0.407117\pi\) | ||||
0.287678 | + | 0.957727i | \(0.407117\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −635.843 | −0.0207575 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57987.3 | 1.88149 | 0.940746 | − | 0.339111i | \(-0.110126\pi\) | ||||
0.940746 | + | 0.339111i | \(0.110126\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6691.07 | −0.216442 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43140.8 | 1.38705 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20741.2 | 0.664851 | 0.332425 | − | 0.943130i | \(-0.392133\pi\) | ||||
0.332425 | + | 0.943130i | \(0.392133\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2268.22 | 0.0722689 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9921.41 | −0.315160 | −0.157580 | − | 0.987506i | \(-0.550369\pi\) | ||||
−0.157580 | + | 0.987506i | \(0.550369\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1620.4.a.j.1.5 | yes | 6 | |
3.2 | odd | 2 | 1620.4.a.i.1.5 | ✓ | 6 | ||
9.2 | odd | 6 | 1620.4.i.x.1081.2 | 12 | |||
9.4 | even | 3 | 1620.4.i.w.541.2 | 12 | |||
9.5 | odd | 6 | 1620.4.i.x.541.2 | 12 | |||
9.7 | even | 3 | 1620.4.i.w.1081.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.i.1.5 | ✓ | 6 | 3.2 | odd | 2 | ||
1620.4.a.j.1.5 | yes | 6 | 1.1 | even | 1 | trivial | |
1620.4.i.w.541.2 | 12 | 9.4 | even | 3 | |||
1620.4.i.w.1081.2 | 12 | 9.7 | even | 3 | |||
1620.4.i.x.541.2 | 12 | 9.5 | odd | 6 | |||
1620.4.i.x.1081.2 | 12 | 9.2 | odd | 6 |