Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(1,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(95.5830942093\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.438516.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 20x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 180) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.58654\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.61161 | 0.410988 | 0.205494 | − | 0.978658i | \(-0.434120\pi\) | ||||
0.205494 | + | 0.978658i | \(0.434120\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.5749 | 0.344680 | 0.172340 | − | 0.985038i | \(-0.444867\pi\) | ||||
0.172340 | + | 0.985038i | \(0.444867\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −20.3581 | −0.434333 | −0.217166 | − | 0.976135i | \(-0.569681\pi\) | ||||
−0.217166 | + | 0.976135i | \(0.569681\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.6483 | −0.323119 | −0.161559 | − | 0.986863i | \(-0.551652\pi\) | ||||
−0.161559 | + | 0.986863i | \(0.551652\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.8592 | −0.227716 | −0.113858 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113858 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.29244 | −0.0570463 | −0.0285232 | − | 0.999593i | \(-0.509080\pi\) | ||||
−0.0285232 | + | 0.999593i | \(0.509080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 206.960 | 1.32522 | 0.662612 | − | 0.748963i | \(-0.269448\pi\) | ||||
0.662612 | + | 0.748963i | \(0.269448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33.7288 | 0.195415 | 0.0977077 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977077 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −38.0580 | −0.183800 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.4727 | 0.0598623 | 0.0299312 | − | 0.999552i | \(-0.490471\pi\) | ||||
0.0299312 | + | 0.999552i | \(0.490471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −290.559 | −1.10677 | −0.553387 | − | 0.832924i | \(-0.686665\pi\) | ||||
−0.553387 | + | 0.832924i | \(0.686665\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −338.477 | −1.20040 | −0.600200 | − | 0.799850i | \(-0.704912\pi\) | ||||
−0.600200 | + | 0.799850i | \(0.704912\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 263.145 | 0.816674 | 0.408337 | − | 0.912831i | \(-0.366109\pi\) | ||||
0.408337 | + | 0.912831i | \(0.366109\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −285.063 | −0.831089 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 240.338 | 0.622887 | 0.311444 | − | 0.950265i | \(-0.399188\pi\) | ||||
0.311444 | + | 0.950265i | \(0.399188\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −62.8746 | −0.154146 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −373.694 | −0.824590 | −0.412295 | − | 0.911050i | \(-0.635273\pi\) | ||||
−0.412295 | + | 0.911050i | \(0.635273\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −454.553 | −0.954091 | −0.477045 | − | 0.878879i | \(-0.658292\pi\) | ||||
−0.477045 | + | 0.878879i | \(0.658292\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 101.791 | 0.194240 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 442.622 | 0.807088 | 0.403544 | − | 0.914960i | \(-0.367778\pi\) | ||||
0.403544 | + | 0.914960i | \(0.367778\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 371.467 | 0.620917 | 0.310458 | − | 0.950587i | \(-0.399517\pi\) | ||||
0.310458 | + | 0.950587i | \(0.399517\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 901.209 | 1.44491 | 0.722456 | − | 0.691417i | \(-0.243013\pi\) | ||||
0.722456 | + | 0.691417i | \(0.243013\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 95.7154 | 0.141660 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1034.81 | −1.47373 | −0.736866 | − | 0.676039i | \(-0.763695\pi\) | ||||
−0.736866 | + | 0.676039i | \(0.763695\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 34.6531 | 0.0458273 | 0.0229137 | − | 0.999737i | \(-0.492706\pi\) | ||||
0.0229137 | + | 0.999737i | \(0.492706\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 113.241 | 0.144503 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1070.24 | 1.27467 | 0.637333 | − | 0.770588i | \(-0.280037\pi\) | ||||
0.637333 | + | 0.770588i | \(0.280037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −154.958 | −0.178506 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 94.2962 | 0.101838 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1382.50 | −1.44713 | −0.723567 | − | 0.690254i | \(-0.757499\pi\) | ||||
−0.723567 | + | 0.690254i | \(0.757499\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 138.480 | 0.136429 | 0.0682144 | − | 0.997671i | \(-0.478270\pi\) | ||||
0.0682144 | + | 0.997671i | \(0.478270\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −51.1086 | −0.0488920 | −0.0244460 | − | 0.999701i | \(-0.507782\pi\) | ||||
−0.0244460 | + | 0.999701i | \(0.507782\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1519.23 | −1.37261 | −0.686304 | − | 0.727315i | \(-0.740768\pi\) | ||||
−0.686304 | + | 0.727315i | \(0.740768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1692.75 | 1.48748 | 0.743742 | − | 0.668467i | \(-0.233049\pi\) | ||||
0.743742 | + | 0.668467i | \(0.233049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1308.17 | −1.08905 | −0.544523 | − | 0.838746i | \(-0.683289\pi\) | ||||
−0.544523 | + | 0.838746i | \(0.683289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.4622 | 0.0255119 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −172.390 | −0.132798 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1172.87 | −0.881196 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1977.69 | −1.38182 | −0.690912 | − | 0.722939i | \(-0.742791\pi\) | ||||
−0.690912 | + | 0.722939i | \(0.742791\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1947.63 | −1.29897 | −0.649486 | − | 0.760374i | \(-0.725016\pi\) | ||||
−0.649486 | + | 0.760374i | \(0.725016\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −143.549 | −0.0935886 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1260.91 | 0.786325 | 0.393163 | − | 0.919469i | \(-0.371381\pi\) | ||||
0.393163 | + | 0.919469i | \(0.371381\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −661.071 | −0.403391 | −0.201695 | − | 0.979448i | \(-0.564645\pi\) | ||||
−0.201695 | + | 0.979448i | \(0.564645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −256.002 | −0.149706 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1034.80 | −0.592658 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −86.9994 | −0.0478340 | −0.0239170 | − | 0.999714i | \(-0.507614\pi\) | ||||
−0.0239170 | + | 0.999714i | \(0.507614\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1348.25 | 0.726618 | 0.363309 | − | 0.931669i | \(-0.381647\pi\) | ||||
0.363309 | + | 0.931669i | \(0.381647\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −168.644 | −0.0873924 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −516.367 | −0.262488 | −0.131244 | − | 0.991350i | \(-0.541897\pi\) | ||||
−0.131244 | + | 0.991350i | \(0.541897\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −47.8956 | −0.0234454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2464.89 | −1.18445 | −0.592224 | − | 0.805774i | \(-0.701750\pi\) | ||||
−0.592224 | + | 0.805774i | \(0.701750\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2981.02 | 1.38131 | 0.690653 | − | 0.723187i | \(-0.257323\pi\) | ||||
0.690653 | + | 0.723187i | \(0.257323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1782.55 | −0.811355 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1026.45 | 0.451096 | 0.225548 | − | 0.974232i | \(-0.427583\pi\) | ||||
0.225548 | + | 0.974232i | \(0.427583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 190.290 | 0.0821977 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 492.431 | 0.205620 | 0.102810 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102810 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3523.74 | −1.44706 | −0.723529 | − | 0.690294i | \(-0.757481\pi\) | ||||
−0.723529 | + | 0.690294i | \(0.757481\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −67.3637 | −0.0267712 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −284.801 | −0.111373 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2981.86 | −1.12963 | −0.564816 | − | 0.825217i | \(-0.691053\pi\) | ||||
−0.564816 | + | 0.825217i | \(0.691053\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3252.42 | −1.21303 | −0.606514 | − | 0.795073i | \(-0.707432\pi\) | ||||
−0.606514 | + | 0.795073i | \(0.707432\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4300.46 | −1.55531 | −0.777653 | − | 0.628694i | \(-0.783590\pi\) | ||||
−0.777653 | + | 0.628694i | \(0.783590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1549.59 | −0.551997 | −0.275998 | − | 0.961158i | \(-0.589008\pi\) | ||||
−0.275998 | + | 0.961158i | \(0.589008\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1575.30 | 0.544652 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1452.80 | 0.494964 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −237.153 | −0.0784892 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2564.99 | −0.836877 | −0.418439 | − | 0.908245i | \(-0.637422\pi\) | ||||
−0.418439 | + | 0.908245i | \(0.637422\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1692.38 | 0.536835 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 256.731 | 0.0803134 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 461.077 | 0.140341 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2499.47 | −0.750570 | −0.375285 | − | 0.926909i | \(-0.622455\pi\) | ||||
−0.375285 | + | 0.926909i | \(0.622455\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2917.54 | −0.853057 | −0.426528 | − | 0.904474i | \(-0.640264\pi\) | ||||
−0.426528 | + | 0.904474i | \(0.640264\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3904.29 | −1.12665 | −0.563324 | − | 0.826236i | \(-0.690478\pi\) | ||||
−0.563324 | + | 0.826236i | \(0.690478\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 529.427 | 0.148858 | 0.0744290 | − | 0.997226i | \(-0.476287\pi\) | ||||
0.0744290 | + | 0.997226i | \(0.476287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1315.73 | −0.365228 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3854.43 | 1.04319 | 0.521595 | − | 0.853193i | \(-0.325337\pi\) | ||||
0.521595 | + | 0.853193i | \(0.325337\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1713.23 | 0.457921 | 0.228960 | − | 0.973436i | \(-0.426467\pi\) | ||||
0.228960 | + | 0.973436i | \(0.426467\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1425.32 | 0.371674 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 383.939 | 0.0989046 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7789.93 | 1.95895 | 0.979474 | − | 0.201573i | \(-0.0646053\pi\) | ||||
0.979474 | + | 0.201573i | \(0.0646053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −79.1270 | −0.0196627 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4350.88 | 1.05603 | 0.528016 | − | 0.849234i | \(-0.322936\pi\) | ||||
0.528016 | + | 0.849234i | \(0.322936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 102.549 | 0.0246027 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6189.73 | −1.45124 | −0.725618 | − | 0.688098i | \(-0.758446\pi\) | ||||
−0.725618 | + | 0.688098i | \(0.758446\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1201.69 | −0.278564 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5497.65 | −1.24609 | −0.623044 | − | 0.782187i | \(-0.714104\pi\) | ||||
−0.623044 | + | 0.782187i | \(0.714104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6473.63 | −1.45109 | −0.725545 | − | 0.688175i | \(-0.758412\pi\) | ||||
−0.725545 | + | 0.688175i | \(0.758412\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 314.373 | 0.0689360 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6639.69 | −1.44022 | −0.720109 | − | 0.693861i | \(-0.755908\pi\) | ||||
−0.720109 | + | 0.693861i | \(0.755908\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2423.44 | −0.514486 | −0.257243 | − | 0.966347i | \(-0.582814\pi\) | ||||
−0.257243 | + | 0.966347i | \(0.582814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2182.30 | 0.458390 | 0.229195 | − | 0.973380i | \(-0.426391\pi\) | ||||
0.229195 | + | 0.973380i | \(0.426391\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2211.62 | −0.454871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4400.05 | −0.895594 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5783.64 | 1.15319 | 0.576594 | − | 0.817031i | \(-0.304382\pi\) | ||||
0.576594 | + | 0.817031i | \(0.304382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1868.47 | 0.368768 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 128.102 | 0.0247771 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2576.35 | −0.493351 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2272.76 | 0.426682 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3781.94 | 0.703084 | 0.351542 | − | 0.936172i | \(-0.385657\pi\) | ||||
0.351542 | + | 0.936172i | \(0.385657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5358.79 | −0.977072 | −0.488536 | − | 0.872544i | \(-0.662469\pi\) | ||||
−0.488536 | + | 0.872544i | \(0.662469\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1146.63 | −0.207066 | −0.103533 | − | 0.994626i | \(-0.533015\pi\) | ||||
−0.103533 | + | 0.994626i | \(0.533015\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1328.96 | 0.235464 | 0.117732 | − | 0.993045i | \(-0.462438\pi\) | ||||
0.117732 | + | 0.993045i | \(0.462438\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2602.51 | 0.456779 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 427.129 | 0.0735793 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −508.953 | −0.0868666 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2002.96 | 0.335643 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10544.9 | 1.75106 | 0.875528 | − | 0.483167i | \(-0.160514\pi\) | ||||
0.875528 | + | 0.483167i | \(0.160514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2213.11 | −0.360941 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3318.42 | −0.536398 | −0.268199 | − | 0.963364i | \(-0.586428\pi\) | ||||
−0.268199 | + | 0.963364i | \(0.586428\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 424.138 | 0.0673558 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4780.57 | −0.752556 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5230.96 | −0.809258 | −0.404629 | − | 0.914481i | \(-0.632599\pi\) | ||||
−0.404629 | + | 0.914481i | \(0.632599\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2859.66 | −0.438608 | −0.219304 | − | 0.975657i | \(-0.570379\pi\) | ||||
−0.219304 | + | 0.975657i | \(0.570379\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10993.4 | 1.65757 | 0.828784 | − | 0.559569i | \(-0.189033\pi\) | ||||
0.828784 | + | 0.559569i | \(0.189033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1857.34 | −0.277682 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3419.15 | −0.502662 | −0.251331 | − | 0.967901i | \(-0.580868\pi\) | ||||
−0.251331 | + | 0.967901i | \(0.580868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6503.33 | −0.948145 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4506.05 | −0.646184 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7785.47 | −1.10735 | −0.553676 | − | 0.832732i | \(-0.686775\pi\) | ||||
−0.553676 | + | 0.832732i | \(0.686775\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1829.36 | 0.255999 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9123.79 | −1.26652 | −0.633260 | − | 0.773939i | \(-0.718284\pi\) | ||||
−0.633260 | + | 0.773939i | \(0.718284\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4213.32 | −0.575589 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2117.60 | 0.287003 | 0.143501 | − | 0.989650i | \(-0.454164\pi\) | ||||
0.143501 | + | 0.989650i | \(0.454164\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3239.27 | 0.432165 | 0.216082 | − | 0.976375i | \(-0.430672\pi\) | ||||
0.216082 | + | 0.976375i | \(0.430672\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −478.577 | −0.0633521 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6103.04 | 0.795466 | 0.397733 | − | 0.917501i | \(-0.369797\pi\) | ||||
0.397733 | + | 0.917501i | \(0.369797\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 142.513 | 0.0184327 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5174.03 | 0.659073 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9935.69 | 1.25607 | 0.628033 | − | 0.778187i | \(-0.283860\pi\) | ||||
0.628033 | + | 0.778187i | \(0.283860\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11715.9 | −1.45902 | −0.729508 | − | 0.683973i | \(-0.760251\pi\) | ||||
−0.729508 | + | 0.683973i | \(0.760251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −686.656 | −0.0848753 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 169.419 | 0.0206334 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7690.95 | 0.929812 | 0.464906 | − | 0.885360i | \(-0.346088\pi\) | ||||
0.464906 | + | 0.885360i | \(0.346088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2844.41 | −0.338897 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −173.265 | −0.0204946 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4633.54 | 0.540246 | 0.270123 | − | 0.962826i | \(-0.412936\pi\) | ||||
0.270123 | + | 0.962826i | \(0.412936\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3867.10 | 0.447675 | 0.223837 | − | 0.974626i | \(-0.428142\pi\) | ||||
0.223837 | + | 0.974626i | \(0.428142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −566.207 | −0.0646237 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3459.88 | −0.392120 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5735.22 | 0.640965 | 0.320482 | − | 0.947254i | \(-0.396155\pi\) | ||||
0.320482 | + | 0.947254i | \(0.396155\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2696.51 | 0.299274 | 0.149637 | − | 0.988741i | \(-0.452189\pi\) | ||||
0.149637 | + | 0.988741i | \(0.452189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 118.671 | 0.0129904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9039.61 | −0.982773 | −0.491386 | − | 0.870942i | \(-0.663510\pi\) | ||||
−0.491386 | + | 0.870942i | \(0.663510\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8959.37 | 0.960886 | 0.480443 | − | 0.877026i | \(-0.340476\pi\) | ||||
0.480443 | + | 0.877026i | \(0.340476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5351.21 | −0.570048 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10716.1 | −1.12634 | −0.563169 | − | 0.826342i | \(-0.690418\pi\) | ||||
−0.563169 | + | 0.826342i | \(0.690418\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3653.76 | −0.381483 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 774.790 | 0.0798302 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15370.6 | −1.57331 | −0.786657 | − | 0.617390i | \(-0.788190\pi\) | ||||
−0.786657 | + | 0.617390i | \(0.788190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7155.35 | −0.722902 | −0.361451 | − | 0.932391i | \(-0.617719\pi\) | ||||
−0.361451 | + | 0.932391i | \(0.617719\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18448.9 | 1.85182 | 0.925911 | − | 0.377743i | \(-0.123300\pi\) | ||||
0.925911 | + | 0.377743i | \(0.123300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3276.70 | 0.324684 | 0.162342 | − | 0.986735i | \(-0.448095\pi\) | ||||
0.162342 | + | 0.986735i | \(0.448095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3369.07 | 0.331704 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4256.32 | −0.413754 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −471.481 | −0.0455432 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7742.87 | −0.738582 | −0.369291 | − | 0.929314i | \(-0.620399\pi\) | ||||
−0.369291 | + | 0.929314i | \(0.620399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −274.280 | −0.0260002 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6912.52 | 0.647178 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18292.5 | 1.70208 | 0.851041 | − | 0.525099i | \(-0.175972\pi\) | ||||
0.851041 | + | 0.525099i | \(0.175972\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19322.1 | −1.77596 | −0.887979 | − | 0.459883i | \(-0.847891\pi\) | ||||
−0.887979 | + | 0.459883i | \(0.847891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4687.29 | −0.428205 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2827.47 | 0.255189 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2480.64 | 0.222543 | 0.111271 | − | 0.993790i | \(-0.464508\pi\) | ||||
0.111271 | + | 0.993790i | \(0.464508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5598.09 | 0.496236 | 0.248118 | − | 0.968730i | \(-0.420188\pi\) | ||||
0.248118 | + | 0.968730i | \(0.420188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −692.402 | −0.0610128 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8550.84 | −0.744616 | −0.372308 | − | 0.928109i | \(-0.621433\pi\) | ||||
−0.372308 | + | 0.928109i | \(0.621433\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6859.65 | 0.593842 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 255.543 | 0.0218652 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3309.03 | 0.281491 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9207.53 | 0.774260 | 0.387130 | − | 0.922025i | \(-0.373467\pi\) | ||||
0.387130 | + | 0.922025i | \(0.373467\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4862.02 | 0.406503 | 0.203252 | − | 0.979127i | \(-0.434849\pi\) | ||||
0.203252 | + | 0.979127i | \(0.434849\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −763.901 | −0.0631424 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12127.4 | −0.996746 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5915.24 | 0.480708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7596.13 | 0.613849 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3584.65 | −0.286460 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5654.94 | 0.449399 | 0.224700 | − | 0.974428i | \(-0.427860\pi\) | ||||
0.224700 | + | 0.974428i | \(0.427860\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8463.74 | −0.665223 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3574.52 | −0.279407 | −0.139703 | − | 0.990193i | \(-0.544615\pi\) | ||||
−0.139703 | + | 0.990193i | \(0.544615\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3903.11 | −0.301775 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7876.55 | −0.605687 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10361.8 | −0.788230 | −0.394115 | − | 0.919061i | \(-0.628949\pi\) | ||||
−0.394115 | + | 0.919061i | \(0.628949\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6890.75 | 0.521373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12751.9 | 0.954580 | 0.477290 | − | 0.878746i | \(-0.341619\pi\) | ||||
0.477290 | + | 0.878746i | \(0.341619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6540.84 | 0.487036 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5557.24 | 0.409441 | 0.204720 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204720 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1543.35 | 0.113112 | 0.0565562 | − | 0.998399i | \(-0.481988\pi\) | ||||
0.0565562 | + | 0.998399i | \(0.481988\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −157.311 | −0.0114093 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4507.17 | 0.325192 | 0.162596 | − | 0.986693i | \(-0.448013\pi\) | ||||
0.162596 | + | 0.986693i | \(0.448013\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 263.766 | 0.0188345 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3022.24 | 0.214697 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1968.90 | −0.138442 | −0.0692208 | − | 0.997601i | \(-0.522051\pi\) | ||||
−0.0692208 | + | 0.997601i | \(0.522051\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −636.100 | −0.0444992 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18751.9 | 1.29857 | 0.649283 | − | 0.760547i | \(-0.275069\pi\) | ||||
0.649283 | + | 0.760547i | \(0.275069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 861.950 | 0.0593891 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2736.59 | 0.186668 | 0.0933340 | − | 0.995635i | \(-0.470248\pi\) | ||||
0.0933340 | + | 0.995635i | \(0.470248\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6214.47 | −0.421786 | −0.210893 | − | 0.977509i | \(-0.567637\pi\) | ||||
−0.210893 | + | 0.977509i | \(0.567637\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5864.36 | 0.394083 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15237.7 | 1.01891 | 0.509457 | − | 0.860496i | \(-0.329846\pi\) | ||||
0.509457 | + | 0.860496i | \(0.329846\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5357.14 | −0.354708 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9390.77 | 0.618743 | 0.309371 | − | 0.950941i | \(-0.399881\pi\) | ||||
0.309371 | + | 0.950941i | \(0.399881\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9597.64 | 0.626234 | 0.313117 | − | 0.949715i | \(-0.398627\pi\) | ||||
0.313117 | + | 0.949715i | \(0.398627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20136.4 | 1.30751 | 0.653756 | − | 0.756705i | \(-0.273192\pi\) | ||||
0.653756 | + | 0.756705i | \(0.273192\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8146.26 | 0.523873 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −305.135 | −0.0193426 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6466.60 | −0.407974 | −0.203987 | − | 0.978974i | \(-0.565390\pi\) | ||||
−0.203987 | + | 0.978974i | \(0.565390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9888.45 | 0.617971 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5803.36 | 0.360969 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22555.5 | −1.38984 | −0.694921 | − | 0.719086i | \(-0.744560\pi\) | ||||
−0.694921 | + | 0.719086i | \(0.744560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18114.3 | 1.11098 | 0.555488 | − | 0.831525i | \(-0.312532\pi\) | ||||
0.555488 | + | 0.831525i | \(0.312532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23680.5 | −1.43891 | −0.719456 | − | 0.694538i | \(-0.755609\pi\) | ||||
−0.719456 | + | 0.694538i | \(0.755609\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4699.17 | −0.284220 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10761.9 | 0.644939 | 0.322469 | − | 0.946580i | \(-0.395487\pi\) | ||||
0.322469 | + | 0.946580i | \(0.395487\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9738.15 | 0.580918 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3650.17 | 0.215767 | 0.107883 | − | 0.994164i | \(-0.465593\pi\) | ||||
0.107883 | + | 0.994164i | \(0.465593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3031.97 | −0.178411 | −0.0892056 | − | 0.996013i | \(-0.528433\pi\) | ||||
−0.0892056 | + | 0.996013i | \(0.528433\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 717.746 | 0.0418541 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1302.28 | −0.0755992 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5715.97 | −0.328856 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7852.53 | 0.449766 | 0.224883 | − | 0.974386i | \(-0.427800\pi\) | ||||
0.224883 | + | 0.974386i | \(0.427800\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1629.74 | −0.0925202 | −0.0462601 | − | 0.998929i | \(-0.514730\pi\) | ||||
−0.0462601 | + | 0.998929i | \(0.514730\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10523.1 | −0.594755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14384.1 | 0.805847 | 0.402923 | − | 0.915234i | \(-0.367994\pi\) | ||||
0.402923 | + | 0.915234i | \(0.367994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6304.54 | −0.351655 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4892.84 | −0.270540 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33385.6 | 1.83799 | 0.918993 | − | 0.394273i | \(-0.129004\pi\) | ||||
0.918993 | + | 0.394273i | \(0.129004\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3305.36 | 0.180402 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6580.67 | 0.357619 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13436.1 | −0.723929 | −0.361965 | − | 0.932192i | \(-0.617894\pi\) | ||||
−0.361965 | + | 0.932192i | \(0.617894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −254.086 | −0.0136316 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1054.06 | 0.0560707 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25316.2 | 1.34100 | 0.670501 | − | 0.741908i | \(-0.266079\pi\) | ||||
0.670501 | + | 0.741908i | \(0.266079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −212.237 | −0.0111477 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1280.01 | 0.0669505 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1384.99 | −0.0718378 | −0.0359189 | − | 0.999355i | \(-0.511436\pi\) | ||||
−0.0359189 | + | 0.999355i | \(0.511436\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −389.019 | −0.0200940 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5174.00 | 0.265045 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34360.0 | 1.75288 | 0.876439 | − | 0.481513i | \(-0.159912\pi\) | ||||
0.876439 | + | 0.481513i | \(0.159912\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7665.92 | 0.387872 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12812.9 | −0.645642 | −0.322821 | − | 0.946460i | \(-0.604631\pi\) | ||||
−0.322821 | + | 0.946460i | \(0.604631\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5565.94 | 0.278187 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32839.5 | 1.63467 | 0.817335 | − | 0.576163i | \(-0.195450\pi\) | ||||
0.817335 | + | 0.576163i | \(0.195450\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25350.6 | 1.25172 | 0.625858 | − | 0.779937i | \(-0.284749\pi\) | ||||
0.625858 | + | 0.779937i | \(0.284749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 434.997 | 0.0213920 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11563.8 | −0.564126 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3471.46 | 0.168675 | 0.0843377 | − | 0.996437i | \(-0.473123\pi\) | ||||
0.0843377 | + | 0.996437i | \(0.473123\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6741.27 | −0.324954 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33545.9 | −1.61063 | −0.805316 | − | 0.592846i | \(-0.798004\pi\) | ||||
−0.805316 | + | 0.592846i | \(0.798004\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5998.42 | −0.285733 | −0.142866 | − | 0.989742i | \(-0.545632\pi\) | ||||
−0.142866 | + | 0.989742i | \(0.545632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12884.5 | 0.611339 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7607.71 | 0.358146 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24208.1 | 1.13520 | 0.567598 | − | 0.823306i | \(-0.307873\pi\) | ||||
0.567598 | + | 0.823306i | \(0.307873\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2134.55 | −0.0993199 | −0.0496600 | − | 0.998766i | \(-0.515814\pi\) | ||||
−0.0496600 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 843.221 | 0.0390831 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5479.72 | 0.252030 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4671.18 | 0.214018 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2581.84 | 0.117388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15744.3 | 0.713117 | 0.356558 | − | 0.934273i | \(-0.383950\pi\) | ||||
0.356558 | + | 0.934273i | \(0.383950\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9957.27 | −0.447585 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9253.84 | 0.414393 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30160.5 | 1.34045 | 0.670226 | − | 0.742157i | \(-0.266197\pi\) | ||||
0.670226 | + | 0.742157i | \(0.266197\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5959.79 | −0.263883 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11332.6 | 0.498032 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 239.478 | 0.0104851 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31677.9 | 1.37668 | 0.688340 | − | 0.725388i | \(-0.258340\pi\) | ||||
0.688340 | + | 0.725388i | \(0.258340\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14294.2 | 0.618912 | 0.309456 | − | 0.950914i | \(-0.399853\pi\) | ||||
0.309456 | + | 0.950914i | \(0.399853\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12324.4 | 0.529701 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6383.41 | 0.273350 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25274.3 | −1.07440 | −0.537198 | − | 0.843456i | \(-0.680517\pi\) | ||||
−0.537198 | + | 0.843456i | \(0.680517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1414.08 | −0.0598928 | −0.0299464 | − | 0.999552i | \(-0.509534\pi\) | ||||
−0.0299464 | + | 0.999552i | \(0.509534\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19366.4 | −0.814311 | −0.407155 | − | 0.913359i | \(-0.633479\pi\) | ||||
−0.407155 | + | 0.913359i | \(0.633479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14280.3 | −0.598283 | −0.299141 | − | 0.954209i | \(-0.596700\pi\) | ||||
−0.299141 | + | 0.954209i | \(0.596700\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6456.20 | 0.268540 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14905.1 | −0.617739 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26112.9 | −1.07451 | −0.537257 | − | 0.843418i | \(-0.680540\pi\) | ||||
−0.537257 | + | 0.843418i | \(0.680540\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18443.4 | 0.756220 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8912.73 | 0.362849 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8927.44 | −0.362161 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −84.7765 | −0.00341493 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21239.0 | 0.852534 | 0.426267 | − | 0.904597i | \(-0.359828\pi\) | ||||
0.426267 | + | 0.904597i | \(0.359828\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41563.4 | −1.65669 | −0.828343 | − | 0.560222i | \(-0.810716\pi\) | ||||
−0.828343 | + | 0.560222i | \(0.810716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5885.90 | −0.233788 | −0.116894 | − | 0.993144i | \(-0.537294\pi\) | ||||
−0.116894 | + | 0.993144i | \(0.537294\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11237.9 | 0.443272 | 0.221636 | − | 0.975130i | \(-0.428860\pi\) | ||||
0.221636 | + | 0.975130i | \(0.428860\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5132.25 | −0.201736 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13012.6 | −0.507966 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9010.96 | −0.350545 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −951.451 | −0.0367599 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9433.27 | −0.363214 | −0.181607 | − | 0.983371i | \(-0.558130\pi\) | ||||
−0.181607 | + | 0.983371i | \(0.558130\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29845.4 | −1.14134 | −0.570668 | − | 0.821181i | \(-0.693315\pi\) | ||||
−0.570668 | + | 0.821181i | \(0.693315\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10785.9 | 0.411070 | 0.205535 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205535 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30705.7 | −1.16234 | −0.581171 | − | 0.813782i | \(-0.697405\pi\) | ||||
−0.581171 | + | 0.813782i | \(0.697405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15053.4 | −0.567914 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4962.72 | −0.185970 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2462.15 | −0.0919561 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6980.52 | 0.258969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5443.26 | −0.201267 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17618.7 | 0.647144 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7062.97 | 0.258569 | 0.129285 | − | 0.991608i | \(-0.458732\pi\) | ||||
0.129285 | + | 0.991608i | \(0.458732\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5057.09 | −0.183918 | −0.0919588 | − | 0.995763i | \(-0.529313\pi\) | ||||
−0.0919588 | + | 0.995763i | \(0.529313\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 435.760 | 0.0157958 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14824.6 | −0.533862 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48440.1 | 1.73873 | 0.869364 | − | 0.494173i | \(-0.164529\pi\) | ||||
0.869364 | + | 0.494173i | \(0.164529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7562.38 | −0.269684 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 336.819 | 0.0119725 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10086.5 | −0.356220 | −0.178110 | − | 0.984011i | \(-0.556998\pi\) | ||||
−0.178110 | + | 0.984011i | \(0.556998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5376.08 | 0.189252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1424.00 | 0.0498074 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22271.7 | −0.776504 | −0.388252 | − | 0.921553i | \(-0.626921\pi\) | ||||
−0.388252 | + | 0.921553i | \(0.626921\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18339.1 | 0.635322 | 0.317661 | − | 0.948204i | \(-0.397103\pi\) | ||||
0.317661 | + | 0.948204i | \(0.397103\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1828.33 | 0.0631374 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10141.9 | −0.348012 | −0.174006 | − | 0.984745i | \(-0.555671\pi\) | ||||
−0.174006 | + | 0.984745i | \(0.555671\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18346.9 | −0.627573 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46973.4 | 1.59666 | 0.798331 | − | 0.602219i | \(-0.205717\pi\) | ||||
0.798331 | + | 0.602219i | \(0.205717\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14909.3 | 0.505187 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9597.53 | 0.323171 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28653.4 | −0.961813 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16262.1 | 0.542482 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3021.79 | −0.100490 | −0.0502452 | − | 0.998737i | \(-0.516000\pi\) | ||||
−0.0502452 | + | 0.998737i | \(0.516000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13426.4 | −0.443743 | −0.221871 | − | 0.975076i | \(-0.571217\pi\) | ||||
−0.221871 | + | 0.975076i | \(0.571217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5031.82 | −0.165789 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −56527.9 | −1.85106 | −0.925531 | − | 0.378672i | \(-0.876381\pi\) | ||||
−0.925531 | + | 0.378672i | \(0.876381\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13458.2 | 0.439352 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 45626.5 | 1.48043 | 0.740213 | − | 0.672372i | \(-0.234725\pi\) | ||||
0.740213 | + | 0.672372i | \(0.234725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21502.3 | 0.695554 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2129.85 | 0.0684784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55864.3 | 1.79071 | 0.895353 | − | 0.445358i | \(-0.146924\pi\) | ||||
0.895353 | + | 0.445358i | \(0.146924\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7747.94 | 0.246860 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19012.0 | 0.603927 | 0.301963 | − | 0.953320i | \(-0.402358\pi\) | ||||
0.301963 | + | 0.953320i | \(0.402358\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.a.g.1.3 | 4 | ||
3.2 | odd | 2 | 1620.4.a.h.1.3 | 4 | |||
9.2 | odd | 6 | 540.4.i.b.361.2 | 8 | |||
9.4 | even | 3 | 180.4.i.b.61.4 | ✓ | 8 | ||
9.5 | odd | 6 | 540.4.i.b.181.2 | 8 | |||
9.7 | even | 3 | 180.4.i.b.121.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.4.i.b.61.4 | ✓ | 8 | 9.4 | even | 3 | ||
180.4.i.b.121.4 | yes | 8 | 9.7 | even | 3 | ||
540.4.i.b.181.2 | 8 | 9.5 | odd | 6 | |||
540.4.i.b.361.2 | 8 | 9.2 | odd | 6 | |||
1620.4.a.g.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1620.4.a.h.1.3 | 4 | 3.2 | odd | 2 |