Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1080,4,Mod(1,1080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1080, 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("1080.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1080.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: | \(63.7220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 8x + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.14974\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1080.1 |
$q$-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 | ||||||||
\(7\) | −3.85875 | −0.208353 | −0.104176 | − | 0.994559i | \(-0.533221\pi\) | ||||
−0.104176 | + | 0.994559i | \(0.533221\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 42.2783 | 1.15885 | 0.579427 | − | 0.815024i | \(-0.303276\pi\) | ||||
0.579427 | + | 0.815024i | \(0.303276\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.96700 | 0.105969 | 0.0529845 | − | 0.998595i | \(-0.483127\pi\) | ||||
0.0529845 | + | 0.998595i | \(0.483127\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.8876 | −0.369333 | −0.184666 | − | 0.982801i | \(-0.559120\pi\) | ||||
−0.184666 | + | 0.982801i | \(0.559120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.9958 | 0.350110 | 0.175055 | − | 0.984559i | \(-0.443990\pi\) | ||||
0.175055 | + | 0.984559i | \(0.443990\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −191.469 | −1.73583 | −0.867914 | − | 0.496715i | \(-0.834539\pi\) | ||||
−0.867914 | + | 0.496715i | \(0.834539\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 287.595 | 1.84155 | 0.920776 | − | 0.390092i | \(-0.127557\pi\) | ||||
0.920776 | + | 0.390092i | \(0.127557\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 52.6915 | 0.305280 | 0.152640 | − | 0.988282i | \(-0.451223\pi\) | ||||
0.152640 | + | 0.988282i | \(0.451223\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19.2937 | 0.0931782 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −225.550 | −1.00217 | −0.501084 | − | 0.865398i | \(-0.667065\pi\) | ||||
−0.501084 | + | 0.865398i | \(0.667065\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 73.9907 | 0.281839 | 0.140920 | − | 0.990021i | \(-0.454994\pi\) | ||||
0.140920 | + | 0.990021i | \(0.454994\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −275.370 | −0.976593 | −0.488297 | − | 0.872678i | \(-0.662382\pi\) | ||||
−0.488297 | + | 0.872678i | \(0.662382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −192.271 | −0.596715 | −0.298357 | − | 0.954454i | \(-0.596439\pi\) | ||||
−0.298357 | + | 0.954454i | \(0.596439\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −328.110 | −0.956589 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 275.204 | 0.713249 | 0.356624 | − | 0.934248i | \(-0.383928\pi\) | ||||
0.356624 | + | 0.934248i | \(0.383928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −211.392 | −0.518255 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 497.084 | 1.09686 | 0.548431 | − | 0.836196i | \(-0.315225\pi\) | ||||
0.548431 | + | 0.836196i | \(0.315225\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 44.0473 | 0.0924538 | 0.0462269 | − | 0.998931i | \(-0.485280\pi\) | ||||
0.0462269 | + | 0.998931i | \(0.485280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −24.8350 | −0.0473908 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 761.667 | 1.38884 | 0.694422 | − | 0.719568i | \(-0.255660\pi\) | ||||
0.694422 | + | 0.719568i | \(0.255660\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 264.284 | 0.441757 | 0.220879 | − | 0.975301i | \(-0.429108\pi\) | ||||
0.220879 | + | 0.975301i | \(0.429108\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 728.781 | 1.16846 | 0.584229 | − | 0.811589i | \(-0.301397\pi\) | ||||
0.584229 | + | 0.811589i | \(0.301397\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −163.141 | −0.241450 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 664.347 | 0.946137 | 0.473069 | − | 0.881026i | \(-0.343146\pi\) | ||||
0.473069 | + | 0.881026i | \(0.343146\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1491.33 | 1.97223 | 0.986113 | − | 0.166075i | \(-0.0531094\pi\) | ||||
0.986113 | + | 0.166075i | \(0.0531094\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 129.438 | 0.165171 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 106.783 | 0.127180 | 0.0635899 | − | 0.997976i | \(-0.479745\pi\) | ||||
0.0635899 | + | 0.997976i | \(0.479745\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −19.1664 | −0.0220789 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −144.979 | −0.156574 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −924.560 | −0.967782 | −0.483891 | − | 0.875128i | \(-0.660777\pi\) | ||||
−0.483891 | + | 0.875128i | \(0.660777\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 627.973 | 0.618670 | 0.309335 | − | 0.950953i | \(-0.399894\pi\) | ||||
0.309335 | + | 0.950953i | \(0.399894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −224.878 | −0.215125 | −0.107562 | − | 0.994198i | \(-0.534305\pi\) | ||||
−0.107562 | + | 0.994198i | \(0.534305\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −70.1076 | −0.0633417 | −0.0316708 | − | 0.999498i | \(-0.510083\pi\) | ||||
−0.0316708 | + | 0.999498i | \(0.510083\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −235.022 | −0.206523 | −0.103261 | − | 0.994654i | \(-0.532928\pi\) | ||||
−0.103261 | + | 0.994654i | \(0.532928\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1647.70 | 1.37170 | 0.685850 | − | 0.727743i | \(-0.259431\pi\) | ||||
0.685850 | + | 0.727743i | \(0.259431\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 957.344 | 0.776286 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 99.8936 | 0.0769515 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 456.458 | 0.342943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1282.64 | −0.896189 | −0.448095 | − | 0.893986i | \(-0.647897\pi\) | ||||
−0.448095 | + | 0.893986i | \(0.647897\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1070.64 | 0.714066 | 0.357033 | − | 0.934092i | \(-0.383788\pi\) | ||||
0.357033 | + | 0.934092i | \(0.383788\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −111.888 | −0.0729465 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2045.70 | 1.27574 | 0.637869 | − | 0.770145i | \(-0.279816\pi\) | ||||
0.637869 | + | 0.770145i | \(0.279816\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 784.256 | 0.478559 | 0.239280 | − | 0.970951i | \(-0.423089\pi\) | ||||
0.239280 | + | 0.970951i | \(0.423089\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 209.997 | 0.122803 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1437.97 | −0.823567 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1300.68 | 0.715140 | 0.357570 | − | 0.933886i | \(-0.383605\pi\) | ||||
0.357570 | + | 0.933886i | \(0.383605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1511.72 | 0.814718 | 0.407359 | − | 0.913268i | \(-0.366450\pi\) | ||||
0.407359 | + | 0.913268i | \(0.366450\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −263.458 | −0.136525 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 167.967 | 0.0853838 | 0.0426919 | − | 0.999088i | \(-0.486407\pi\) | ||||
0.0426919 | + | 0.999088i | \(0.486407\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 738.830 | 0.361664 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −67.1490 | −0.0322670 | −0.0161335 | − | 0.999870i | \(-0.505136\pi\) | ||||
−0.0161335 | + | 0.999870i | \(0.505136\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2568.36 | 1.19009 | 0.595046 | − | 0.803692i | \(-0.297134\pi\) | ||||
0.595046 | + | 0.803692i | \(0.297134\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2172.33 | −0.988771 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3012.46 | −1.32389 | −0.661945 | − | 0.749553i | \(-0.730269\pi\) | ||||
−0.661945 | + | 0.749553i | \(0.730269\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −96.4687 | −0.0416705 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2462.80 | 1.02837 | 0.514185 | − | 0.857679i | \(-0.328095\pi\) | ||||
0.514185 | + | 0.857679i | \(0.328095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3691.10 | −1.51578 | −0.757892 | − | 0.652380i | \(-0.773771\pi\) | ||||
−0.757892 | + | 0.652380i | \(0.773771\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1127.75 | 0.448183 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1094.48 | −0.428003 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1969.02 | 0.745932 | 0.372966 | − | 0.927845i | \(-0.378341\pi\) | ||||
0.372966 | + | 0.927845i | \(0.378341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 519.119 | 0.193612 | 0.0968058 | − | 0.995303i | \(-0.469137\pi\) | ||||
0.0968058 | + | 0.995303i | \(0.469137\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3286.33 | 1.18853 | 0.594267 | − | 0.804268i | \(-0.297442\pi\) | ||||
0.594267 | + | 0.804268i | \(0.297442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3626.47 | 1.29183 | 0.645914 | − | 0.763410i | \(-0.276476\pi\) | ||||
0.645914 | + | 0.763410i | \(0.276476\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1109.76 | −0.383692 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −369.954 | −0.126042 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1225.90 | 0.405727 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1410.39 | 0.460166 | 0.230083 | − | 0.973171i | \(-0.426100\pi\) | ||||
0.230083 | + | 0.973171i | \(0.426100\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1376.85 | 0.436746 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −203.323 | −0.0636059 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −128.584 | −0.0391379 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4026.25 | 1.20905 | 0.604524 | − | 0.796587i | \(-0.293363\pi\) | ||||
0.604524 | + | 0.796587i | \(0.293363\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2288.33 | 0.669083 | 0.334542 | − | 0.942381i | \(-0.391419\pi\) | ||||
0.334542 | + | 0.942381i | \(0.391419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2003.69 | 0.578200 | 0.289100 | − | 0.957299i | \(-0.406644\pi\) | ||||
0.289100 | + | 0.957299i | \(0.406644\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2837.72 | 0.797877 | 0.398939 | − | 0.916978i | \(-0.369379\pi\) | ||||
0.398939 | + | 0.916978i | \(0.369379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 961.355 | 0.266859 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1749.50 | −0.473496 | −0.236748 | − | 0.971571i | \(-0.576082\pi\) | ||||
−0.236748 | + | 0.971571i | \(0.576082\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3645.10 | 0.974279 | 0.487140 | − | 0.873324i | \(-0.338040\pi\) | ||||
0.487140 | + | 0.873324i | \(0.338040\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1640.55 | 0.427800 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 144.022 | 0.0371009 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1286.39 | −0.323491 | −0.161745 | − | 0.986833i | \(-0.551712\pi\) | ||||
−0.161745 | + | 0.986833i | \(0.551712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8094.99 | −2.01157 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2860.83 | −0.694372 | −0.347186 | − | 0.937796i | \(-0.612863\pi\) | ||||
−0.347186 | + | 0.937796i | \(0.612863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 870.341 | 0.208805 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4615.68 | 1.08219 | 0.541093 | − | 0.840963i | \(-0.318011\pi\) | ||||
0.541093 | + | 0.840963i | \(0.318011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1376.02 | −0.318974 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3053.54 | −0.692111 | −0.346055 | − | 0.938214i | \(-0.612479\pi\) | ||||
−0.346055 | + | 0.938214i | \(0.612479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5867.51 | −1.31523 | −0.657613 | − | 0.753356i | \(-0.728434\pi\) | ||||
−0.657613 | + | 0.753356i | \(0.728434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1056.96 | 0.231771 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7256.41 | −1.57399 | −0.786995 | − | 0.616959i | \(-0.788364\pi\) | ||||
−0.786995 | + | 0.616959i | \(0.788364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1318.05 | −0.279816 | −0.139908 | − | 0.990165i | \(-0.544681\pi\) | ||||
−0.139908 | + | 0.990165i | \(0.544681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4810.74 | 1.01049 | 0.505245 | − | 0.862976i | \(-0.331402\pi\) | ||||
0.505245 | + | 0.862976i | \(0.331402\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −285.511 | −0.0587220 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4242.83 | −0.863593 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1512.59 | 0.301593 | 0.150796 | − | 0.988565i | \(-0.451816\pi\) | ||||
0.150796 | + | 0.988565i | \(0.451816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2485.42 | −0.490531 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −951.026 | −0.183944 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1062.58 | 0.203476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −220.237 | −0.0413466 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3092.67 | 0.574945 | 0.287472 | − | 0.957789i | \(-0.407185\pi\) | ||||
0.287472 | + | 0.957789i | \(0.407185\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.7251 | 0.00396115 | 0.00198058 | − | 0.999998i | \(-0.499370\pi\) | ||||
0.00198058 | + | 0.999998i | \(0.499370\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 758.733 | 0.137016 | 0.0685082 | − | 0.997651i | \(-0.478176\pi\) | ||||
0.0685082 | + | 0.997651i | \(0.478176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1764.70 | −0.312668 | −0.156334 | − | 0.987704i | \(-0.549968\pi\) | ||||
−0.156334 | + | 0.987704i | \(0.549968\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12159.0 | 2.13409 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −750.632 | −0.129307 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 124.175 | 0.0211938 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 741.925 | 0.124327 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10098.1 | 1.67687 | 0.838433 | − | 0.545005i | \(-0.183472\pi\) | ||||
0.838433 | + | 0.545005i | \(0.183472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3808.34 | −0.621109 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4485.28 | −0.725012 | −0.362506 | − | 0.931981i | \(-0.618079\pi\) | ||||
−0.362506 | + | 0.931981i | \(0.618079\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2227.71 | 0.353775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2589.64 | 0.407661 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −585.137 | −0.0905239 | −0.0452620 | − | 0.998975i | \(-0.514412\pi\) | ||||
−0.0452620 | + | 0.998975i | \(0.514412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3461.97 | 0.530989 | 0.265494 | − | 0.964112i | \(-0.414465\pi\) | ||||
0.265494 | + | 0.964112i | \(0.414465\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6797.01 | −1.02484 | −0.512420 | − | 0.858735i | \(-0.671251\pi\) | ||||
−0.512420 | + | 0.858735i | \(0.671251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1321.42 | −0.197560 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4622.13 | −0.679518 | −0.339759 | − | 0.940513i | \(-0.610345\pi\) | ||||
−0.339759 | + | 0.940513i | \(0.610345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6018.24 | −0.877423 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3643.91 | −0.522550 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −147.843 | −0.0210281 | −0.0105141 | − | 0.999945i | \(-0.503347\pi\) | ||||
−0.0105141 | + | 0.999945i | \(0.503347\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1061.94 | −0.148607 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8840.27 | 1.22716 | 0.613582 | − | 0.789631i | \(-0.289728\pi\) | ||||
0.613582 | + | 0.789631i | \(0.289728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1428.48 | 0.195148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6063.51 | −0.821799 | −0.410899 | − | 0.911681i | \(-0.634785\pi\) | ||||
−0.410899 | + | 0.911681i | \(0.634785\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 496.589 | 0.0662520 | 0.0331260 | − | 0.999451i | \(-0.489454\pi\) | ||||
0.0331260 | + | 0.999451i | \(0.489454\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 815.707 | 0.107980 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3432.37 | −0.447373 | −0.223686 | − | 0.974661i | \(-0.571809\pi\) | ||||
−0.223686 | + | 0.974661i | \(0.571809\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4956.66 | 0.641098 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3321.73 | −0.423125 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15311.8 | −1.93571 | −0.967856 | − | 0.251506i | \(-0.919074\pi\) | ||||
−0.967856 | + | 0.251506i | \(0.919074\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7088.63 | 0.882766 | 0.441383 | − | 0.897319i | \(-0.354488\pi\) | ||||
0.441383 | + | 0.897319i | \(0.354488\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 261.719 | 0.0323502 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9535.89 | −1.16137 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9991.23 | 1.20791 | 0.603954 | − | 0.797019i | \(-0.293591\pi\) | ||||
0.603954 | + | 0.797019i | \(0.293591\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1918.12 | −0.228534 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7456.65 | −0.882006 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8172.83 | −0.952909 | −0.476455 | − | 0.879199i | \(-0.658078\pi\) | ||||
−0.476455 | + | 0.879199i | \(0.658078\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15475.1 | −1.79147 | −0.895734 | − | 0.444590i | \(-0.853350\pi\) | ||||
−0.895734 | + | 0.444590i | \(0.853350\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −647.189 | −0.0738666 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −169.968 | −0.0192630 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3426.00 | −0.382888 | −0.191444 | − | 0.981504i | \(-0.561317\pi\) | ||||
−0.191444 | + | 0.981504i | \(0.561317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1806.95 | −0.200546 | −0.100273 | − | 0.994960i | \(-0.531972\pi\) | ||||
−0.100273 | + | 0.994960i | \(0.531972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5551.80 | −0.607731 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7974.34 | 0.866957 | 0.433479 | − | 0.901164i | \(-0.357286\pi\) | ||||
0.433479 | + | 0.901164i | \(0.357286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3566.86 | −0.382544 | −0.191272 | − | 0.981537i | \(-0.561261\pi\) | ||||
−0.191272 | + | 0.981537i | \(0.561261\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −533.916 | −0.0568765 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13687.2 | 1.43862 | 0.719308 | − | 0.694692i | \(-0.244459\pi\) | ||||
0.719308 | + | 0.694692i | \(0.244459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3128.21 | 0.326611 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 95.8320 | 0.00987401 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1691.89 | 0.173180 | 0.0865902 | − | 0.996244i | \(-0.472403\pi\) | ||||
0.0865902 | + | 0.996244i | \(0.472403\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17881.6 | −1.80657 | −0.903285 | − | 0.429041i | \(-0.858851\pi\) | ||||
−0.903285 | + | 0.429041i | \(0.858851\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11459.6 | 1.15027 | 0.575135 | − | 0.818059i | \(-0.304950\pi\) | ||||
0.575135 | + | 0.818059i | \(0.304950\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18329.4 | −1.81624 | −0.908119 | − | 0.418711i | \(-0.862482\pi\) | ||||
−0.908119 | + | 0.418711i | \(0.862482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2939.08 | −0.289369 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11642.2 | −1.13173 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 724.896 | 0.0700221 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15475.4 | 1.47618 | 0.738090 | − | 0.674703i | \(-0.235728\pi\) | ||||
0.738090 | + | 0.674703i | \(0.235728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1120.31 | −0.106199 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4622.80 | 0.432805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16320.0 | −1.51854 | −0.759270 | − | 0.650776i | \(-0.774444\pi\) | ||||
−0.759270 | + | 0.650776i | \(0.774444\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6138.33 | −0.564193 | −0.282097 | − | 0.959386i | \(-0.591030\pi\) | ||||
−0.282097 | + | 0.959386i | \(0.591030\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7445.13 | −0.680146 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1019.81 | −0.0920413 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3272.20 | 0.293555 | 0.146777 | − | 0.989170i | \(-0.453110\pi\) | ||||
0.146777 | + | 0.989170i | \(0.453110\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4696.96 | −0.416356 | −0.208178 | − | 0.978091i | \(-0.566753\pi\) | ||||
−0.208178 | + | 0.978091i | \(0.566753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3139.87 | −0.276678 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10011.5 | 0.871815 | 0.435907 | − | 0.899992i | \(-0.356428\pi\) | ||||
0.435907 | + | 0.899992i | \(0.356428\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2812.18 | −0.243451 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1124.39 | 0.0962067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8128.89 | −0.691505 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19483.2 | −1.63833 | −0.819167 | − | 0.573554i | \(-0.805564\pi\) | ||||
−0.819167 | + | 0.573554i | \(0.805564\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5181.82 | −0.433241 | −0.216621 | − | 0.976256i | \(-0.569503\pi\) | ||||
−0.216621 | + | 0.976256i | \(0.569503\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1364.06 | −0.112750 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24493.3 | 2.01310 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 367.512 | 0.0298663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 350.538 | 0.0283273 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13871.9 | −1.10855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3178.24 | 0.252576 | 0.126288 | − | 0.991994i | \(-0.459694\pi\) | ||||
0.126288 | + | 0.991994i | \(0.459694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1175.11 | 0.0923599 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13887.9 | −1.08556 | −0.542781 | − | 0.839874i | \(-0.682629\pi\) | ||||
−0.542781 | + | 0.839874i | \(0.682629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8339.05 | 0.644747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2563.55 | −0.197130 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10574.5 | −0.804406 | −0.402203 | − | 0.915551i | \(-0.631755\pi\) | ||||
−0.402203 | + | 0.915551i | \(0.631755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1367.76 | −0.103489 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7815.91 | 0.585083 | 0.292541 | − | 0.956253i | \(-0.405499\pi\) | ||||
0.292541 | + | 0.956253i | \(0.405499\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8238.48 | −0.613443 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20024.0 | −1.47531 | −0.737655 | − | 0.675178i | \(-0.764067\pi\) | ||||
−0.737655 | + | 0.675178i | \(0.764067\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23886.5 | 1.75065 | 0.875323 | − | 0.483538i | \(-0.160649\pi\) | ||||
0.875323 | + | 0.483538i | \(0.160649\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4786.72 | −0.347165 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18777.2 | −1.35478 | −0.677389 | − | 0.735625i | \(-0.736888\pi\) | ||||
−0.677389 | + | 0.735625i | \(0.736888\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5754.67 | −0.410919 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11635.2 | 0.826551 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23209.8 | 1.63198 | 0.815988 | − | 0.578069i | \(-0.196194\pi\) | ||||
0.815988 | + | 0.578069i | \(0.196194\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1527.83 | 0.106882 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4204.44 | −0.291157 | −0.145578 | − | 0.989347i | \(-0.546504\pi\) | ||||
−0.145578 | + | 0.989347i | \(0.546504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −499.468 | −0.0344138 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26962.9 | −1.83919 | −0.919593 | − | 0.392872i | \(-0.871482\pi\) | ||||
−0.919593 | + | 0.392872i | \(0.871482\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13595.2 | 0.922727 | 0.461363 | − | 0.887211i | \(-0.347360\pi\) | ||||
0.461363 | + | 0.887211i | \(0.347360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2282.29 | −0.153369 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14337.5 | 0.958720 | 0.479360 | − | 0.877618i | \(-0.340869\pi\) | ||||
0.479360 | + | 0.877618i | \(0.340869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −955.010 | −0.0632333 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7963.62 | 0.524710 | 0.262355 | − | 0.964971i | \(-0.415501\pi\) | ||||
0.262355 | + | 0.964971i | \(0.415501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23594.2 | −1.53949 | −0.769745 | − | 0.638352i | \(-0.779617\pi\) | ||||
−0.769745 | + | 0.638352i | \(0.779617\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12132.6 | 0.787803 | 0.393901 | − | 0.919153i | \(-0.371125\pi\) | ||||
0.393901 | + | 0.919153i | \(0.371125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −412.049 | −0.0264982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5838.95 | 0.370134 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −614.270 | −0.0387539 | −0.0193769 | − | 0.999812i | \(-0.506168\pi\) | ||||
−0.0193769 | + | 0.999812i | \(0.506168\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6413.21 | 0.400788 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1629.72 | −0.101369 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2057.06 | 0.126754 | 0.0633769 | − | 0.997990i | \(-0.479813\pi\) | ||||
0.0633769 | + | 0.997990i | \(0.479813\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17827.2 | 1.09337 | 0.546684 | − | 0.837339i | \(-0.315890\pi\) | ||||
0.546684 | + | 0.837339i | \(0.315890\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17499.4 | 1.06333 | 0.531664 | − | 0.846955i | \(-0.321567\pi\) | ||||
0.531664 | + | 0.846955i | \(0.321567\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21015.9 | 1.27110 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6049.52 | −0.362536 | −0.181268 | − | 0.983434i | \(-0.558020\pi\) | ||||
−0.181268 | + | 0.983434i | \(0.558020\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5353.22 | −0.319340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1436.32 | −0.0849027 | −0.0424514 | − | 0.999099i | \(-0.513517\pi\) | ||||
−0.0424514 | + | 0.999099i | \(0.513517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9287.18 | 0.546489 | 0.273245 | − | 0.961945i | \(-0.411903\pi\) | ||||
0.273245 | + | 0.961945i | \(0.411903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 559.438 | 0.0326226 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −55065.4 | −3.19662 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1862.25 | 0.107141 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15014.9 | 0.860000 | 0.430000 | − | 0.902829i | \(-0.358514\pi\) | ||||
0.430000 | + | 0.902829i | \(0.358514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9147.19 | 0.519284 | 0.259642 | − | 0.965705i | \(-0.416396\pi\) | ||||
0.259642 | + | 0.965705i | \(0.416396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3567.64 | 0.201640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10388.4 | 0.581992 | 0.290996 | − | 0.956724i | \(-0.406013\pi\) | ||||
0.290996 | + | 0.956724i | \(0.406013\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10228.5 | −0.570527 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1366.94 | 0.0755823 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25955.9 | −1.42895 | −0.714477 | − | 0.699659i | \(-0.753335\pi\) | ||||
−0.714477 | + | 0.699659i | \(0.753335\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3921.28 | −0.214018 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1915.44 | −0.104093 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31771.2 | 1.71181 | 0.855906 | − | 0.517131i | \(-0.173000\pi\) | ||||
0.855906 | + | 0.517131i | \(0.173000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6540.02 | −0.350870 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2423.19 | −0.128902 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7002.47 | −0.370921 | −0.185461 | − | 0.982652i | \(-0.559378\pi\) | ||||
−0.185461 | + | 0.982652i | \(0.559378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10088.8 | −0.529913 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1049.98 | −0.0549191 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34634.3 | −1.79644 | −0.898221 | − | 0.439545i | \(-0.855140\pi\) | ||||
−0.898221 | + | 0.439545i | \(0.855140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 867.745 | 0.0448218 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7189.87 | 0.368310 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10821.6 | 0.552064 | 0.276032 | − | 0.961148i | \(-0.410980\pi\) | ||||
0.276032 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7128.66 | 0.360688 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5576.04 | −0.280977 | −0.140488 | − | 0.990082i | \(-0.544867\pi\) | ||||
−0.140488 | + | 0.990082i | \(0.544867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32202.0 | 1.60947 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29317.7 | 1.45936 | 0.729681 | − | 0.683788i | \(-0.239669\pi\) | ||||
0.729681 | + | 0.683788i | \(0.239669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7521.08 | −0.371361 | −0.185681 | − | 0.982610i | \(-0.559449\pi\) | ||||
−0.185681 | + | 0.982610i | \(0.559449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6503.40 | −0.319820 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 270.528 | 0.0131974 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37300.7 | −1.81241 | −0.906206 | − | 0.422837i | \(-0.861034\pi\) | ||||
−0.906206 | + | 0.422837i | \(0.861034\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7558.62 | −0.364353 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26432.1 | −1.26908 | −0.634538 | − | 0.772891i | \(-0.718810\pi\) | ||||
−0.634538 | + | 0.772891i | \(0.718810\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23440.4 | 1.11658 | 0.558288 | − | 0.829647i | \(-0.311458\pi\) | ||||
0.558288 | + | 0.829647i | \(0.311458\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 906.889 | 0.0430296 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2469.02 | 0.116233 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34075.2 | 1.59790 | 0.798948 | − | 0.601401i | \(-0.205390\pi\) | ||||
0.798948 | + | 0.601401i | \(0.205390\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14623.5 | −0.680427 | −0.340214 | − | 0.940348i | \(-0.610499\pi\) | ||||
−0.340214 | + | 0.940348i | \(0.610499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1317.29 | 0.0610560 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2145.42 | 0.0986749 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11173.5 | 0.511932 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −839.837 | −0.0381848 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33523.1 | −1.51839 | −0.759193 | − | 0.650865i | \(-0.774406\pi\) | ||||
−0.759193 | + | 0.650865i | \(0.774406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6358.04 | −0.285797 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 218.783 | 0.00979725 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29447.5 | 1.30876 | 0.654381 | − | 0.756165i | \(-0.272929\pi\) | ||||
0.654381 | + | 0.756165i | \(0.272929\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4977.43 | 0.220386 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30811.6 | 1.35407 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3694.15 | −0.161741 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26891.1 | 1.16866 | 0.584328 | − | 0.811518i | \(-0.301358\pi\) | ||||
0.584328 | + | 0.811518i | \(0.301358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14912.6 | 0.645687 | 0.322844 | − | 0.946452i | \(-0.395361\pi\) | ||||
0.322844 | + | 0.946452i | \(0.395361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 335.745 | 0.0144302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7984.58 | −0.341916 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42644.2 | −1.81278 | −0.906391 | − | 0.422439i | \(-0.861174\pi\) | ||||
−0.906391 | + | 0.422439i | \(0.861174\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25121.7 | −1.06402 | −0.532010 | − | 0.846738i | \(-0.678563\pi\) | ||||
−0.532010 | + | 0.846738i | \(0.678563\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4918.93 | −0.206830 | −0.103415 | − | 0.994638i | \(-0.532977\pi\) | ||||
−0.103415 | + | 0.994638i | \(0.532977\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22807.6 | −0.955538 | −0.477769 | − | 0.878486i | \(-0.658554\pi\) | ||||
−0.477769 | + | 0.878486i | \(0.658554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8493.97 | 0.353300 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12841.8 | −0.532225 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25772.5 | 1.06051 | 0.530255 | − | 0.847839i | \(-0.322096\pi\) | ||||
0.530255 | + | 0.847839i | \(0.322096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58321.7 | 2.39131 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10861.6 | 0.442192 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1761.35 | −0.0714532 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43185.9 | 1.73959 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41636.0 | 1.67126 | 0.835632 | − | 0.549289i | \(-0.185101\pi\) | ||||
0.835632 | + | 0.549289i | \(0.185101\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17941.6 | −0.715137 | −0.357569 | − | 0.933887i | \(-0.616394\pi\) | ||||
−0.357569 | + | 0.933887i | \(0.616394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23917.0 | 0.949985 | 0.474993 | − | 0.879990i | \(-0.342451\pi\) | ||||
0.474993 | + | 0.879990i | \(0.342451\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9786.53 | 0.386022 | 0.193011 | − | 0.981197i | \(-0.438175\pi\) | ||||
0.193011 | + | 0.981197i | \(0.438175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15062.3 | 0.592061 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28087.5 | 1.09644 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3783.20 | 0.147174 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 482.343 | 0.0186356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29186.8 | −1.12379 | −0.561897 | − | 0.827207i | \(-0.689928\pi\) | ||||
−0.561897 | + | 0.827207i | \(0.689928\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18426.6 | −0.704664 | −0.352332 | − | 0.935875i | \(-0.614611\pi\) | ||||
−0.352332 | + | 0.935875i | \(0.614611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3942.63 | 0.150261 | 0.0751303 | − | 0.997174i | \(-0.476063\pi\) | ||||
0.0751303 | + | 0.997174i | \(0.476063\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −436.876 | −0.0165376 | −0.00826881 | − | 0.999966i | \(-0.502632\pi\) | ||||
−0.00826881 | + | 0.999966i | \(0.502632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4949.39 | 0.186723 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5575.05 | −0.208916 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12314.0 | −0.459901 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 15153.8 | 0.562189 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7124.36 | −0.263426 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18455.5 | 0.677879 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −43243.2 | −1.58309 | −0.791547 | − | 0.611108i | \(-0.790724\pi\) | ||||
−0.791547 | + | 0.611108i | \(0.790724\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14141.5 | −0.514301 | −0.257150 | − | 0.966371i | \(-0.582784\pi\) | ||||
−0.257150 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 63051.0 | 2.28552 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4131.34 | −0.148778 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1506.36 | 0.0540697 | 0.0270349 | − | 0.999634i | \(-0.491393\pi\) | ||||
0.0270349 | + | 0.999634i | \(0.491393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1312.70 | 0.0468126 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5638.76 | −0.200434 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32173.3 | 1.13624 | 0.568122 | − | 0.822944i | \(-0.307670\pi\) | ||||
0.568122 | + | 0.822944i | \(0.307670\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9513.82 | −0.334912 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5472.42 | 0.191409 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34833.5 | 1.21447 | 0.607236 | − | 0.794522i | \(-0.292278\pi\) | ||||
0.607236 | + | 0.794522i | \(0.292278\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3709.66 | −0.128514 | −0.0642569 | − | 0.997933i | \(-0.520468\pi\) | ||||
−0.0642569 | + | 0.997933i | \(0.520468\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14166.9 | −0.489224 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32085.0 | 1.10097 | 0.550487 | − | 0.834844i | \(-0.314442\pi\) | ||||
0.550487 | + | 0.834844i | \(0.314442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3619.86 | 0.123820 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35654.2 | 1.21191 | 0.605956 | − | 0.795498i | \(-0.292791\pi\) | ||||
0.605956 | + | 0.795498i | \(0.292791\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9845.08 | −0.333591 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7893.84 | −0.265803 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27014.6 | −0.906804 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2595.60 | −0.0865857 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32345.4 | −1.07565 | −0.537827 | − | 0.843055i | \(-0.680755\pi\) | ||||
−0.537827 | + | 0.843055i | \(0.680755\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20137.4 | −0.665542 | −0.332771 | − | 0.943008i | \(-0.607984\pi\) | ||||
−0.332771 | + | 0.943008i | \(0.607984\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3026.25 | −0.0997091 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30087.1 | −0.985231 | −0.492615 | − | 0.870247i | \(-0.663959\pi\) | ||||
−0.492615 | + | 0.870247i | \(0.663959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4514.62 | 0.147383 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 59417.5 | 1.92790 | 0.963950 | − | 0.266084i | \(-0.0857299\pi\) | ||||
0.963950 | + | 0.266084i | \(0.0857299\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16431.6 | −0.531529 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 52724.8 | 1.69520 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20153.5 | −0.646011 | −0.323006 | − | 0.946397i | \(-0.604693\pi\) | ||||
−0.323006 | + | 0.946397i | \(0.604693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18132.4 | −0.577723 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20772.3 | −0.659846 | −0.329923 | − | 0.944008i | \(-0.607023\pi\) | ||||
−0.329923 | + | 0.944008i | \(0.607023\pi\) | |||||||
\(998\) | 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 | 1080.4.a.d.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 1080.4.a.j.1.2 | yes | 3 | ||
4.3 | odd | 2 | 2160.4.a.bk.1.2 | 3 | |||
12.11 | even | 2 | 2160.4.a.bs.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.d.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1080.4.a.j.1.2 | yes | 3 | 3.2 | odd | 2 | ||
2160.4.a.bk.1.2 | 3 | 4.3 | odd | 2 | |||
2160.4.a.bs.1.2 | 3 | 12.11 | even | 2 |