Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,4,Mod(1,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, 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("1800.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.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: | \(106.203438010\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{181}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 45 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.22681\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −29.9072 | −1.61484 | −0.807420 | − | 0.589977i | \(-0.799137\pi\) | ||||
−0.807420 | + | 0.589977i | \(0.799137\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.9072 | −0.847171 | −0.423586 | − | 0.905856i | \(-0.639229\pi\) | ||||
−0.423586 | + | 0.905856i | \(0.639229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 46.8145 | 0.998770 | 0.499385 | − | 0.866380i | \(-0.333559\pi\) | ||||
0.499385 | + | 0.866380i | \(0.333559\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −26.9072 | −0.383880 | −0.191940 | − | 0.981407i | \(-0.561478\pi\) | ||||
−0.191940 | + | 0.981407i | \(0.561478\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 123.722 | 1.49388 | 0.746940 | − | 0.664892i | \(-0.231522\pi\) | ||||
0.746940 | + | 0.664892i | \(0.231522\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 144.722 | 1.31202 | 0.656012 | − | 0.754750i | \(-0.272242\pi\) | ||||
0.656012 | + | 0.754750i | \(0.272242\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −37.4638 | −0.239891 | −0.119946 | − | 0.992780i | \(-0.538272\pi\) | ||||
−0.119946 | + | 0.992780i | \(0.538272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −267.351 | −1.54896 | −0.774478 | − | 0.632601i | \(-0.781987\pi\) | ||||
−0.774478 | + | 0.632601i | \(0.781987\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 143.443 | 0.637350 | 0.318675 | − | 0.947864i | \(-0.396762\pi\) | ||||
0.318675 | + | 0.947864i | \(0.396762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 310.351 | 1.18216 | 0.591081 | − | 0.806612i | \(-0.298701\pi\) | ||||
0.591081 | + | 0.806612i | \(0.298701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.64926 | −0.0235815 | −0.0117907 | − | 0.999930i | \(-0.503753\pi\) | ||||
−0.0117907 | + | 0.999930i | \(0.503753\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 485.629 | 1.50715 | 0.753577 | − | 0.657359i | \(-0.228327\pi\) | ||||
0.753577 | + | 0.657359i | \(0.228327\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 551.443 | 1.60771 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 322.351 | 0.835439 | 0.417720 | − | 0.908576i | \(-0.362829\pi\) | ||||
0.417720 | + | 0.908576i | \(0.362829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −217.258 | −0.479400 | −0.239700 | − | 0.970847i | \(-0.577049\pi\) | ||||
−0.239700 | + | 0.970847i | \(0.577049\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −301.742 | −0.633346 | −0.316673 | − | 0.948535i | \(-0.602566\pi\) | ||||
−0.316673 | + | 0.948535i | \(0.602566\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −568.835 | −1.03723 | −0.518614 | − | 0.855009i | \(-0.673552\pi\) | ||||
−0.518614 | + | 0.855009i | \(0.673552\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −749.939 | −1.25354 | −0.626770 | − | 0.779204i | \(-0.715624\pi\) | ||||
−0.626770 | + | 0.779204i | \(0.715624\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52.9275 | −0.0848589 | −0.0424294 | − | 0.999099i | \(-0.513510\pi\) | ||||
−0.0424294 | + | 0.999099i | \(0.513510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 924.351 | 1.36805 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1010.14 | −1.43861 | −0.719305 | − | 0.694694i | \(-0.755540\pi\) | ||||
−0.719305 | + | 0.694694i | \(0.755540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1103.03 | −1.45872 | −0.729358 | − | 0.684132i | \(-0.760181\pi\) | ||||
−0.729358 | + | 0.684132i | \(0.760181\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1219.63 | −1.45259 | −0.726294 | − | 0.687384i | \(-0.758759\pi\) | ||||
−0.726294 | + | 0.687384i | \(0.758759\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1400.09 | −1.61285 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1116.03 | −1.16820 | −0.584102 | − | 0.811680i | \(-0.698553\pi\) | ||||
−0.584102 | + | 0.811680i | \(0.698553\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1256.12 | 1.23752 | 0.618758 | − | 0.785582i | \(-0.287636\pi\) | ||||
0.618758 | + | 0.785582i | \(0.287636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1724.99 | −1.65018 | −0.825090 | − | 0.565002i | \(-0.808875\pi\) | ||||
−0.825090 | + | 0.565002i | \(0.808875\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1636.91 | 1.47893 | 0.739466 | − | 0.673194i | \(-0.235078\pi\) | ||||
0.739466 | + | 0.673194i | \(0.235078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 294.113 | 0.258449 | 0.129224 | − | 0.991615i | \(-0.458751\pi\) | ||||
0.129224 | + | 0.991615i | \(0.458751\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1209.77 | 1.00713 | 0.503566 | − | 0.863957i | \(-0.332021\pi\) | ||||
0.503566 | + | 0.863957i | \(0.332021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 804.722 | 0.619905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −375.742 | −0.282301 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −673.072 | −0.470280 | −0.235140 | − | 0.971962i | \(-0.575555\pi\) | ||||
−0.235140 | + | 0.971962i | \(0.575555\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2224.79 | 1.48382 | 0.741910 | − | 0.670499i | \(-0.233920\pi\) | ||||
0.741910 | + | 0.670499i | \(0.233920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3700.18 | −2.41238 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1987.28 | −1.23931 | −0.619653 | − | 0.784876i | \(-0.712727\pi\) | ||||
−0.619653 | + | 0.784876i | \(0.712727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 183.217 | 0.111801 | 0.0559004 | − | 0.998436i | \(-0.482197\pi\) | ||||
0.0559004 | + | 0.998436i | \(0.482197\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1446.91 | −0.846129 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2179.81 | −1.19851 | −0.599253 | − | 0.800560i | \(-0.704536\pi\) | ||||
−0.599253 | + | 0.800560i | \(0.704536\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1456.32 | −0.784858 | −0.392429 | − | 0.919782i | \(-0.628365\pi\) | ||||
−0.392429 | + | 0.919782i | \(0.628365\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2743.00 | 1.39436 | 0.697182 | − | 0.716894i | \(-0.254437\pi\) | ||||
0.697182 | + | 0.716894i | \(0.254437\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4328.23 | −2.11871 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1093.46 | 0.525436 | 0.262718 | − | 0.964873i | \(-0.415381\pi\) | ||||
0.262718 | + | 0.964873i | \(0.415381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1120.79 | 0.519335 | 0.259668 | − | 0.965698i | \(-0.416387\pi\) | ||||
0.259668 | + | 0.965698i | \(0.416387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.40295 | −0.00245924 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1153.63 | −0.506989 | −0.253494 | − | 0.967337i | \(-0.581580\pi\) | ||||
−0.253494 | + | 0.967337i | \(0.581580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1385.22 | 0.578413 | 0.289207 | − | 0.957267i | \(-0.406608\pi\) | ||||
0.289207 | + | 0.957267i | \(0.406608\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −805.557 | −0.330810 | −0.165405 | − | 0.986226i | \(-0.552893\pi\) | ||||
−0.165405 | + | 0.986226i | \(0.552893\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 831.629 | 0.325212 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3322.50 | −1.25868 | −0.629339 | − | 0.777131i | \(-0.716674\pi\) | ||||
−0.629339 | + | 0.777131i | \(0.716674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 249.023 | 0.0928761 | 0.0464381 | − | 0.998921i | \(-0.485213\pi\) | ||||
0.0464381 | + | 0.998921i | \(0.485213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2727.20 | 0.986320 | 0.493160 | − | 0.869939i | \(-0.335842\pi\) | ||||
0.493160 | + | 0.869939i | \(0.335842\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3258.42 | −1.16072 | −0.580361 | − | 0.814360i | \(-0.697088\pi\) | ||||
−0.580361 | + | 0.814360i | \(0.697088\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1120.44 | 0.387386 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3823.90 | −1.26557 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3368.65 | −1.09909 | −0.549544 | − | 0.835465i | \(-0.685198\pi\) | ||||
−0.549544 | + | 0.835465i | \(0.685198\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7995.72 | 2.50131 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1259.65 | −0.383408 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5251.99 | 1.57713 | 0.788564 | − | 0.614953i | \(-0.210825\pi\) | ||||
0.788564 | + | 0.614953i | \(0.210825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6064.58 | −1.77322 | −0.886609 | − | 0.462520i | \(-0.846945\pi\) | ||||
−0.886609 | + | 0.462520i | \(0.846945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 595.354 | 0.171800 | 0.0858998 | − | 0.996304i | \(-0.472624\pi\) | ||||
0.0858998 | + | 0.996304i | \(0.472624\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2241.08 | 0.630119 | 0.315060 | − | 0.949072i | \(-0.397976\pi\) | ||||
0.315060 | + | 0.949072i | \(0.397976\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4579.17 | 1.23934 | 0.619670 | − | 0.784863i | \(-0.287267\pi\) | ||||
0.619670 | + | 0.784863i | \(0.287267\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5338.97 | −1.42702 | −0.713512 | − | 0.700643i | \(-0.752897\pi\) | ||||
−0.713512 | + | 0.700643i | \(0.752897\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5791.97 | 1.49204 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2698.93 | −0.678704 | −0.339352 | − | 0.940659i | \(-0.610208\pi\) | ||||
−0.339352 | + | 0.940659i | \(0.610208\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4472.95 | −1.11151 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7991.64 | 1.93971 | 0.969853 | − | 0.243690i | \(-0.0783580\pi\) | ||||
0.969853 | + | 0.243690i | \(0.0783580\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4290.00 | −1.02922 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7265.82 | −1.70353 | −0.851767 | − | 0.523921i | \(-0.824469\pi\) | ||||
−0.851767 | + | 0.523921i | \(0.824469\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6046.87 | 1.37057 | 0.685287 | − | 0.728273i | \(-0.259677\pi\) | ||||
0.685287 | + | 0.728273i | \(0.259677\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5106.39 | −1.14462 | −0.572309 | − | 0.820038i | \(-0.693952\pi\) | ||||
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8077.70 | 1.75214 | 0.876069 | − | 0.482186i | \(-0.160157\pi\) | ||||
0.876069 | + | 0.482186i | \(0.160157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8509.18 | −1.80646 | −0.903230 | − | 0.429157i | \(-0.858811\pi\) | ||||
−0.903230 | + | 0.429157i | \(0.858811\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6873.44 | −1.44376 | −0.721879 | − | 0.692019i | \(-0.756721\pi\) | ||||
−0.721879 | + | 0.692019i | \(0.756721\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9281.74 | −1.90900 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4189.00 | −0.852636 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4981.76 | −0.993301 | −0.496651 | − | 0.867950i | \(-0.665437\pi\) | ||||
−0.496651 | + | 0.867950i | \(0.665437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6775.08 | 1.31041 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 198.861 | 0.0380803 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7039.79 | −1.30874 | −0.654368 | − | 0.756176i | \(-0.727065\pi\) | ||||
−0.654368 | + | 0.756176i | \(0.727065\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2221.54 | −0.405055 | −0.202527 | − | 0.979277i | \(-0.564916\pi\) | ||||
−0.202527 | + | 0.979277i | \(0.564916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5381.48 | 0.971818 | 0.485909 | − | 0.874009i | \(-0.338489\pi\) | ||||
0.485909 | + | 0.874009i | \(0.338489\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6282.15 | −1.11306 | −0.556531 | − | 0.830827i | \(-0.687868\pi\) | ||||
−0.556531 | + | 0.830827i | \(0.687868\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1157.90 | 0.203229 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3329.01 | −0.573471 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14523.8 | −2.43381 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1727.72 | 0.286900 | 0.143450 | − | 0.989658i | \(-0.454180\pi\) | ||||
0.143450 | + | 0.989658i | \(0.454180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1033.97 | −0.167134 | −0.0835670 | − | 0.996502i | \(-0.526631\pi\) | ||||
−0.0835670 | + | 0.996502i | \(0.526631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8263.08 | 1.31223 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6233.97 | −0.981349 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9236.90 | 1.42900 | 0.714500 | − | 0.699636i | \(-0.246654\pi\) | ||||
0.714500 | + | 0.699636i | \(0.246654\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8658.79 | −1.32806 | −0.664032 | − | 0.747704i | \(-0.731156\pi\) | ||||
−0.664032 | + | 0.747704i | \(0.731156\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2572.10 | −0.387816 | −0.193908 | − | 0.981020i | \(-0.562116\pi\) | ||||
−0.193908 | + | 0.981020i | \(0.562116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1941.12 | −0.285371 | −0.142685 | − | 0.989768i | \(-0.545574\pi\) | ||||
−0.142685 | + | 0.989768i | \(0.545574\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8448.07 | 1.23168 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2614.98 | 0.371937 | 0.185968 | − | 0.982556i | \(-0.440458\pi\) | ||||
0.185968 | + | 0.982556i | \(0.440458\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9640.62 | −1.34910 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2258.81 | −0.313558 | −0.156779 | − | 0.987634i | \(-0.550111\pi\) | ||||
−0.156779 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1753.85 | −0.239596 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3319.24 | −0.449862 | −0.224931 | − | 0.974375i | \(-0.572216\pi\) | ||||
−0.224931 | + | 0.974375i | \(0.572216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4994.02 | 0.666273 | 0.333137 | − | 0.942879i | \(-0.391893\pi\) | ||||
0.333137 | + | 0.942879i | \(0.391893\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7076.79 | 0.922385 | 0.461192 | − | 0.887300i | \(-0.347422\pi\) | ||||
0.461192 | + | 0.887300i | \(0.347422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3894.06 | −0.503661 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9174.72 | 1.15986 | 0.579932 | − | 0.814665i | \(-0.303079\pi\) | ||||
0.579932 | + | 0.814665i | \(0.303079\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11194.8 | 1.39412 | 0.697058 | − | 0.717015i | \(-0.254492\pi\) | ||||
0.697058 | + | 0.717015i | \(0.254492\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12515.9 | −1.54705 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4433.44 | −0.539945 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11162.6 | −1.34952 | −0.674762 | − | 0.738036i | \(-0.735754\pi\) | ||||
−0.674762 | + | 0.738036i | \(0.735754\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6497.59 | 0.774154 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9135.55 | −1.06516 | −0.532579 | − | 0.846381i | \(-0.678777\pi\) | ||||
−0.532579 | + | 0.846381i | \(0.678777\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13668.3 | −1.58231 | −0.791155 | − | 0.611615i | \(-0.790520\pi\) | ||||
−0.791155 | + | 0.611615i | \(0.790520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9024.27 | 1.02275 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5806.70 | −0.648953 | −0.324477 | − | 0.945894i | \(-0.605188\pi\) | ||||
−0.324477 | + | 0.945894i | \(0.605188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5215.15 | −0.578809 | −0.289404 | − | 0.957207i | \(-0.593457\pi\) | ||||
−0.289404 | + | 0.957207i | \(0.593457\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17905.2 | 1.96001 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11398.7 | 1.23925 | 0.619625 | − | 0.784898i | \(-0.287285\pi\) | ||||
0.619625 | + | 0.784898i | \(0.287285\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5959.18 | −0.639118 | −0.319559 | − | 0.947566i | \(-0.603535\pi\) | ||||
−0.319559 | + | 0.947566i | \(0.603535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11864.6 | −1.24705 | −0.623526 | − | 0.781803i | \(-0.714300\pi\) | ||||
−0.623526 | + | 0.781803i | \(0.714300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9592.09 | −1.00149 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13452.6 | −1.37700 | −0.688499 | − | 0.725237i | \(-0.741730\pi\) | ||||
−0.688499 | + | 0.725237i | \(0.741730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11773.9 | 1.18951 | 0.594756 | − | 0.803906i | \(-0.297249\pi\) | ||||
0.594756 | + | 0.803906i | \(0.297249\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3269.36 | −0.328164 | −0.164082 | − | 0.986447i | \(-0.552466\pi\) | ||||
−0.164082 | + | 0.986447i | \(0.552466\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12407.6 | −1.22945 | −0.614726 | − | 0.788741i | \(-0.710733\pi\) | ||||
−0.614726 | + | 0.788741i | \(0.710733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17012.3 | 1.67496 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 205.510 | 0.0199775 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5046.09 | 0.481340 | 0.240670 | − | 0.970607i | \(-0.422633\pi\) | ||||
0.240670 | + | 0.970607i | \(0.422633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6715.23 | 0.636566 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8107.99 | −0.754432 | −0.377216 | − | 0.926125i | \(-0.623119\pi\) | ||||
−0.377216 | + | 0.926125i | \(0.623119\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13194.7 | −1.21276 | −0.606381 | − | 0.795174i | \(-0.707379\pi\) | ||||
−0.606381 | + | 0.795174i | \(0.707379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1008.05 | 0.0920895 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22428.6 | 2.02427 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16840.3 | 1.51077 | 0.755384 | − | 0.655282i | \(-0.227450\pi\) | ||||
0.755384 | + | 0.655282i | \(0.227450\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.3127 | 0.00153466 | 0.000767330 | − | 1.00000i | \(-0.499756\pi\) | ||||
0.000767330 | 1.00000i | \(0.499756\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7272.27 | 0.633276 | 0.316638 | − | 0.948546i | \(-0.397446\pi\) | ||||
0.316638 | + | 0.948546i | \(0.397446\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1582.92 | 0.137033 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15009.5 | −1.27682 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4830.58 | −0.406203 | −0.203101 | − | 0.979158i | \(-0.565102\pi\) | ||||
−0.203101 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15788.1 | 1.32001 | 0.660006 | − | 0.751261i | \(-0.270554\pi\) | ||||
0.660006 | + | 0.751261i | \(0.270554\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7193.67 | 0.594613 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8777.38 | 0.721409 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14528.9 | 1.18071 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17043.6 | −1.36200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19092.5 | −1.51729 | −0.758644 | − | 0.651506i | \(-0.774138\pi\) | ||||
−0.758644 | + | 0.651506i | \(0.774138\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6582.19 | −0.514504 | −0.257252 | − | 0.966344i | \(-0.582817\pi\) | ||||
−0.257252 | + | 0.966344i | \(0.582817\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4635.08 | −0.358369 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30210.7 | 2.32312 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14331.0 | 1.09017 | 0.545086 | − | 0.838380i | \(-0.316497\pi\) | ||||
0.545086 | + | 0.838380i | \(0.316497\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −311.282 | −0.0235525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7759.03 | −0.580824 | −0.290412 | − | 0.956902i | \(-0.593792\pi\) | ||||
−0.290412 | + | 0.956902i | \(0.593792\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14124.6 | 1.04066 | 0.520328 | − | 0.853967i | \(-0.325810\pi\) | ||||
0.520328 | + | 0.853967i | \(0.325810\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12036.6 | −0.882167 | −0.441083 | − | 0.897466i | \(-0.645406\pi\) | ||||
−0.441083 | + | 0.897466i | \(0.645406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14908.7 | −1.07566 | −0.537830 | − | 0.843053i | \(-0.680756\pi\) | ||||
−0.537830 | + | 0.843053i | \(0.680756\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32988.6 | 2.35559 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9962.97 | −0.707760 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14933.8 | −1.05006 | −0.525029 | − | 0.851084i | \(-0.675946\pi\) | ||||
−0.525029 | + | 0.851084i | \(0.675946\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33077.1 | −2.31395 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3451.38 | 0.239007 | 0.119503 | − | 0.992834i | \(-0.461870\pi\) | ||||
0.119503 | + | 0.992834i | \(0.461870\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 733.154 | 0.0500098 | 0.0250049 | − | 0.999687i | \(-0.492040\pi\) | ||||
0.0250049 | + | 0.999687i | \(0.492040\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19261.2 | 1.30729 | 0.653643 | − | 0.756803i | \(-0.273240\pi\) | ||||
0.653643 | + | 0.756803i | \(0.273240\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14402.2 | −0.963045 | −0.481523 | − | 0.876434i | \(-0.659916\pi\) | ||||
−0.481523 | + | 0.876434i | \(0.659916\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22734.5 | 1.50530 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2394.16 | 0.157748 | 0.0788738 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788738 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9171.17 | 0.598407 | 0.299204 | − | 0.954189i | \(-0.403279\pi\) | ||||
0.299204 | + | 0.954189i | \(0.403279\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20055.4 | 1.30225 | 0.651127 | − | 0.758969i | \(-0.274297\pi\) | ||||
0.651127 | + | 0.758969i | \(0.274297\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36475.7 | 2.34570 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3859.67 | −0.244666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3321.72 | 0.209565 | 0.104783 | − | 0.994495i | \(-0.466585\pi\) | ||||
0.104783 | + | 0.994495i | \(0.466585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25815.5 | 1.60573 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6189.65 | −0.381399 | −0.190699 | − | 0.981648i | \(-0.561076\pi\) | ||||
−0.190699 | + | 0.981648i | \(0.561076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5362.52 | −0.328891 | −0.164446 | − | 0.986386i | \(-0.552584\pi\) | ||||
−0.164446 | + | 0.986386i | \(0.552584\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12636.0 | −0.767809 | −0.383904 | − | 0.923373i | \(-0.625421\pi\) | ||||
−0.383904 | + | 0.923373i | \(0.625421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6714.85 | 0.406134 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10340.5 | 0.619687 | 0.309844 | − | 0.950788i | \(-0.399723\pi\) | ||||
0.309844 | + | 0.950788i | \(0.399723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5232.41 | 0.309296 | 0.154648 | − | 0.987970i | \(-0.450576\pi\) | ||||
0.154648 | + | 0.987970i | \(0.450576\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 602.256 | 0.0354388 | 0.0177194 | − | 0.999843i | \(-0.494359\pi\) | ||||
0.0177194 | + | 0.999843i | \(0.494359\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5421.82 | −0.314743 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9326.02 | 0.536553 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1870.31 | −0.107125 | −0.0535625 | − | 0.998565i | \(-0.517058\pi\) | ||||
−0.0535625 | + | 0.998565i | \(0.517058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2053.27 | 0.116563 | 0.0582817 | − | 0.998300i | \(-0.481438\pi\) | ||||
0.0582817 | + | 0.998300i | \(0.481438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33377.4 | 1.88646 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15169.3 | −0.849832 | −0.424916 | − | 0.905233i | \(-0.639696\pi\) | ||||
−0.424916 | + | 0.905233i | \(0.639696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15090.7 | 0.834411 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29469.8 | 1.62241 | 0.811204 | − | 0.584764i | \(-0.198813\pi\) | ||||
0.811204 | + | 0.584764i | \(0.198813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8350.68 | −0.453809 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6774.61 | 0.365012 | 0.182506 | − | 0.983205i | \(-0.441579\pi\) | ||||
0.182506 | + | 0.983205i | \(0.441579\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17747.1 | 0.952125 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37567.2 | −1.99839 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22501.2 | −1.19189 | −0.595944 | − | 0.803026i | \(-0.703222\pi\) | ||||
−0.595944 | + | 0.803026i | \(0.703222\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38691.5 | −2.03227 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10850.6 | 0.562809 | 0.281405 | − | 0.959589i | \(-0.409200\pi\) | ||||
0.281405 | + | 0.959589i | \(0.409200\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51589.7 | 2.66477 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27360.6 | −1.39580 | −0.697902 | − | 0.716193i | \(-0.745883\pi\) | ||||
−0.697902 | + | 0.716193i | \(0.745883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 178.913 | 0.00905246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −930.568 | −0.0468913 | −0.0234456 | − | 0.999725i | \(-0.507464\pi\) | ||||
−0.0234456 | + | 0.999725i | \(0.507464\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17581.1 | 0.878709 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16833.0 | −0.837903 | −0.418952 | − | 0.908009i | \(-0.637602\pi\) | ||||
−0.418952 | + | 0.908009i | \(0.637602\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1917.63 | 0.0946853 | 0.0473426 | − | 0.998879i | \(-0.484925\pi\) | ||||
0.0473426 | + | 0.998879i | \(0.484925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48955.4 | −2.38824 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30826.2 | 1.49782 | 0.748910 | − | 0.662671i | \(-0.230577\pi\) | ||||
0.748910 | + | 0.662671i | \(0.230577\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21934.2 | 1.05312 | 0.526559 | − | 0.850138i | \(-0.323482\pi\) | ||||
0.526559 | + | 0.850138i | \(0.323482\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8363.35 | −0.398385 | −0.199193 | − | 0.979960i | \(-0.563832\pi\) | ||||
−0.199193 | + | 0.979960i | \(0.563832\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8796.11 | −0.417353 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10170.8 | −0.478810 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 144.849 | 0.00679244 | 0.00339622 | − | 0.999994i | \(-0.498919\pi\) | ||||
0.00339622 | + | 0.999994i | \(0.498919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3894.51 | 0.181210 | 0.0906052 | − | 0.995887i | \(-0.471120\pi\) | ||||
0.0906052 | + | 0.995887i | \(0.471120\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38397.1 | 1.76601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23178.6 | 1.06196 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1312.46 | −0.0594461 | −0.0297231 | − | 0.999558i | \(-0.509463\pi\) | ||||
−0.0297231 | + | 0.999558i | \(0.509463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36181.0 | −1.62636 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14125.9 | −0.632567 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39493.7 | −1.75525 | −0.877627 | − | 0.479344i | \(-0.840875\pi\) | ||||
−0.877627 | + | 0.479344i | \(0.840875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13066.9 | −0.578567 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1635.84 | 0.0718900 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32500.1 | −1.41241 | −0.706207 | − | 0.708006i | \(-0.749595\pi\) | ||||
−0.706207 | + | 0.708006i | \(0.749595\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31191.9 | 1.35055 | 0.675274 | − | 0.737567i | \(-0.264025\pi\) | ||||
0.675274 | + | 0.737567i | \(0.264025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −822.658 | −0.0352279 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9882.99 | 0.420120 | 0.210060 | − | 0.977688i | \(-0.432634\pi\) | ||||
0.210060 | + | 0.977688i | \(0.432634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5785.39 | 0.245037 | 0.122519 | − | 0.992466i | \(-0.460903\pi\) | ||||
0.122519 | + | 0.992466i | \(0.460903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16531.6 | −0.695114 | −0.347557 | − | 0.937659i | \(-0.612989\pi\) | ||||
−0.347557 | + | 0.937659i | \(0.612989\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24870.4 | 1.04196 | 0.520980 | − | 0.853569i | \(-0.325567\pi\) | ||||
0.520980 | + | 0.853569i | \(0.325567\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14837.8 | −0.617167 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9771.47 | 0.402084 | 0.201042 | − | 0.979583i | \(-0.435567\pi\) | ||||
0.201042 | + | 0.979583i | \(0.435567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22985.5 | −0.942452 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11237.4 | 0.455870 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20759.4 | 0.836219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30223.3 | 1.21316 | 0.606581 | − | 0.795022i | \(-0.292541\pi\) | ||||
0.606581 | + | 0.795022i | \(0.292541\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12389.3 | 0.493826 | 0.246913 | − | 0.969038i | \(-0.420584\pi\) | ||||
0.246913 | + | 0.969038i | \(0.420584\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35118.3 | −1.39490 | −0.697450 | − | 0.716633i | \(-0.745682\pi\) | ||||
−0.697450 | + | 0.716633i | \(0.745682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8549.77 | 0.337239 | 0.168620 | − | 0.985681i | \(-0.446069\pi\) | ||||
0.168620 | + | 0.985681i | \(0.446069\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31220.8 | 1.21875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26629.7 | −1.03595 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25827.7 | −0.994457 | −0.497229 | − | 0.867620i | \(-0.665649\pi\) | ||||
−0.497229 | + | 0.867620i | \(0.665649\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22662.3 | −0.866641 | −0.433321 | − | 0.901240i | \(-0.642658\pi\) | ||||
−0.433321 | + | 0.901240i | \(0.642658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20406.2 | 0.777717 | 0.388859 | − | 0.921297i | \(-0.372869\pi\) | ||||
0.388859 | + | 0.921297i | \(0.372869\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21127.3 | −0.799758 | −0.399879 | − | 0.916568i | \(-0.630948\pi\) | ||||
−0.399879 | + | 0.916568i | \(0.630948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20129.7 | 0.759426 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 60082.9 | 2.25151 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10016.0 | 0.371581 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8673.57 | −0.320709 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5421.27 | 0.198468 | 0.0992338 | − | 0.995064i | \(-0.468361\pi\) | ||||
0.0992338 | + | 0.995064i | \(0.468361\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47003.1 | 1.70942 | 0.854711 | − | 0.519104i | \(-0.173734\pi\) | ||||
0.854711 | + | 0.519104i | \(0.173734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34091.7 | 1.23578 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −66537.2 | −2.39613 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6680.57 | −0.239795 | −0.119898 | − | 0.992786i | \(-0.538257\pi\) | ||||
−0.119898 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35108.0 | −1.25200 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39569.9 | 1.39747 | 0.698733 | − | 0.715383i | \(-0.253748\pi\) | ||||
0.698733 | + | 0.715383i | \(0.253748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68225.6 | 2.40172 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15386.6 | 0.536457 | 0.268228 | − | 0.963355i | \(-0.413562\pi\) | ||||
0.268228 | + | 0.963355i | \(0.413562\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11717.6 | −0.405934 | −0.202967 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202967 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 44914.5 | 1.55103 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9763.54 | 0.335029 | 0.167514 | − | 0.985870i | \(-0.446426\pi\) | ||||
0.167514 | + | 0.985870i | \(0.446426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2477.78 | −0.0847545 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13962.3 | 0.474590 | 0.237295 | − | 0.971438i | \(-0.423739\pi\) | ||||
0.237295 | + | 0.971438i | \(0.423739\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 59434.1 | 2.00128 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41685.4 | 1.39926 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24064.0 | 0.800255 | 0.400128 | − | 0.916459i | \(-0.368966\pi\) | ||||
0.400128 | + | 0.916459i | \(0.368966\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21872.0 | −0.722870 | −0.361435 | − | 0.932397i | \(-0.617713\pi\) | ||||
−0.361435 | + | 0.932397i | \(0.617713\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5479.53 | −0.180540 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3495.88 | 0.114476 | 0.0572381 | − | 0.998361i | \(-0.481771\pi\) | ||||
0.0572381 | + | 0.998361i | \(0.481771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37695.4 | 1.23059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −31582.7 | −1.02475 | −0.512376 | − | 0.858761i | \(-0.671235\pi\) | ||||
−0.512376 | + | 0.858761i | \(0.671235\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −962.293 | −0.0309395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20403.5 | −0.654025 | −0.327012 | − | 0.945020i | \(-0.606042\pi\) | ||||
−0.327012 | + | 0.945020i | \(0.606042\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14760.4 | 0.468874 | 0.234437 | − | 0.972131i | \(-0.424675\pi\) | ||||
0.234437 | + | 0.972131i | \(0.424675\pi\) | |||||||
\(998\) | 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 | 1800.4.a.bj.1.1 | 2 | ||
3.2 | odd | 2 | 600.4.a.r.1.1 | ✓ | 2 | ||
5.2 | odd | 4 | 1800.4.f.y.649.1 | 4 | |||
5.3 | odd | 4 | 1800.4.f.y.649.4 | 4 | |||
5.4 | even | 2 | 1800.4.a.bq.1.2 | 2 | |||
12.11 | even | 2 | 1200.4.a.bs.1.2 | 2 | |||
15.2 | even | 4 | 600.4.f.k.49.3 | 4 | |||
15.8 | even | 4 | 600.4.f.k.49.2 | 4 | |||
15.14 | odd | 2 | 600.4.a.w.1.2 | yes | 2 | ||
60.23 | odd | 4 | 1200.4.f.w.49.3 | 4 | |||
60.47 | odd | 4 | 1200.4.f.w.49.2 | 4 | |||
60.59 | even | 2 | 1200.4.a.bm.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.4.a.r.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
600.4.a.w.1.2 | yes | 2 | 15.14 | odd | 2 | ||
600.4.f.k.49.2 | 4 | 15.8 | even | 4 | |||
600.4.f.k.49.3 | 4 | 15.2 | even | 4 | |||
1200.4.a.bm.1.1 | 2 | 60.59 | even | 2 | |||
1200.4.a.bs.1.2 | 2 | 12.11 | even | 2 | |||
1200.4.f.w.49.2 | 4 | 60.47 | odd | 4 | |||
1200.4.f.w.49.3 | 4 | 60.23 | odd | 4 | |||
1800.4.a.bj.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1800.4.a.bq.1.2 | 2 | 5.4 | even | 2 | |||
1800.4.f.y.649.1 | 4 | 5.2 | odd | 4 | |||
1800.4.f.y.649.4 | 4 | 5.3 | odd | 4 |