Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} - 37096332 x^{4} + 27824160 x^{2} - 6889792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7\cdot 13^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.15064\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15064 | −0.406813 | −0.203406 | − | 0.979094i | \(-0.565201\pi\) | ||||
−0.203406 | + | 0.979094i | \(0.565201\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −6.67603 | −0.834503 | ||||||||
\(5\) | −21.2034 | −1.89649 | −0.948247 | − | 0.317534i | \(-0.897145\pi\) | ||||
−0.948247 | + | 0.317534i | \(0.897145\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.2668 | −1.68825 | −0.844124 | − | 0.536148i | \(-0.819879\pi\) | ||||
−0.844124 | + | 0.536148i | \(0.819879\pi\) | |||||||
\(8\) | 16.8868 | 0.746300 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 24.3975 | 0.771518 | ||||||||
\(11\) | −17.3811 | −0.476419 | −0.238209 | − | 0.971214i | \(-0.576560\pi\) | ||||
−0.238209 | + | 0.971214i | \(0.576560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 35.9768 | 0.686801 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 33.9775 | 0.530899 | ||||||||
\(17\) | −89.1071 | −1.27127 | −0.635637 | − | 0.771988i | \(-0.719262\pi\) | ||||
−0.635637 | + | 0.771988i | \(0.719262\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −80.6466 | −0.973769 | −0.486884 | − | 0.873466i | \(-0.661867\pi\) | ||||
−0.486884 | + | 0.873466i | \(0.661867\pi\) | |||||||
\(20\) | 141.555 | 1.58263 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 19.9994 | 0.193813 | ||||||||
\(23\) | 149.683 | 1.35700 | 0.678502 | − | 0.734599i | \(-0.262630\pi\) | ||||
0.678502 | + | 0.734599i | \(0.262630\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 324.586 | 2.59669 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 208.738 | 1.40885 | ||||||||
\(29\) | −6.30162 | −0.0403511 | −0.0201755 | − | 0.999796i | \(-0.506423\pi\) | ||||
−0.0201755 | + | 0.999796i | \(0.506423\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 78.3099 | 0.453706 | 0.226853 | − | 0.973929i | \(-0.427156\pi\) | ||||
0.226853 | + | 0.973929i | \(0.427156\pi\) | |||||||
\(32\) | −174.191 | −0.962276 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 102.530 | 0.517170 | ||||||||
\(35\) | 662.964 | 3.20175 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 39.2975 | 0.174607 | 0.0873037 | − | 0.996182i | \(-0.472175\pi\) | ||||
0.0873037 | + | 0.996182i | \(0.472175\pi\) | |||||||
\(38\) | 92.7953 | 0.396142 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −358.059 | −1.41535 | ||||||||
\(41\) | −330.647 | −1.25947 | −0.629737 | − | 0.776809i | \(-0.716837\pi\) | ||||
−0.629737 | + | 0.776809i | \(0.716837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −198.803 | −0.705052 | −0.352526 | − | 0.935802i | \(-0.614677\pi\) | ||||
−0.352526 | + | 0.935802i | \(0.614677\pi\) | |||||||
\(44\) | 116.037 | 0.397573 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −172.231 | −0.552046 | ||||||||
\(47\) | 246.612 | 0.765364 | 0.382682 | − | 0.923880i | \(-0.375000\pi\) | ||||
0.382682 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 634.613 | 1.85018 | ||||||||
\(50\) | −373.482 | −1.05637 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 600.345 | 1.55592 | 0.777960 | − | 0.628314i | \(-0.216255\pi\) | ||||
0.777960 | + | 0.628314i | \(0.216255\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 368.540 | 0.903525 | ||||||||
\(56\) | −527.997 | −1.25994 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.25090 | 0.0164153 | ||||||||
\(59\) | 709.534 | 1.56565 | 0.782826 | − | 0.622240i | \(-0.213777\pi\) | ||||
0.782826 | + | 0.622240i | \(0.213777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −472.354 | −0.991455 | −0.495727 | − | 0.868478i | \(-0.665098\pi\) | ||||
−0.495727 | + | 0.868478i | \(0.665098\pi\) | |||||||
\(62\) | −90.1066 | −0.184573 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −71.3895 | −0.139433 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −331.545 | −0.604547 | −0.302273 | − | 0.953221i | \(-0.597746\pi\) | ||||
−0.302273 | + | 0.953221i | \(0.597746\pi\) | |||||||
\(68\) | 594.881 | 1.06088 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −762.833 | −1.30251 | ||||||||
\(71\) | 472.765 | 0.790238 | 0.395119 | − | 0.918630i | \(-0.370703\pi\) | ||||
0.395119 | + | 0.918630i | \(0.370703\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 651.016 | 1.04378 | 0.521888 | − | 0.853014i | \(-0.325228\pi\) | ||||
0.521888 | + | 0.853014i | \(0.325228\pi\) | |||||||
\(74\) | −45.2173 | −0.0710325 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 538.399 | 0.812613 | ||||||||
\(77\) | 543.452 | 0.804313 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 240.920 | 0.343109 | 0.171555 | − | 0.985175i | \(-0.445121\pi\) | ||||
0.171555 | + | 0.985175i | \(0.445121\pi\) | |||||||
\(80\) | −720.441 | −1.00685 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 380.456 | 0.512370 | ||||||||
\(83\) | −538.031 | −0.711524 | −0.355762 | − | 0.934577i | \(-0.615779\pi\) | ||||
−0.355762 | + | 0.934577i | \(0.615779\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1889.38 | 2.41096 | ||||||||
\(86\) | 228.751 | 0.286824 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −293.512 | −0.355551 | ||||||||
\(89\) | 673.484 | 0.802126 | 0.401063 | − | 0.916050i | \(-0.368641\pi\) | ||||
0.401063 | + | 0.916050i | \(0.368641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −999.288 | −1.13242 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −283.762 | −0.311360 | ||||||||
\(95\) | 1709.99 | 1.84675 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −468.827 | −0.490744 | −0.245372 | − | 0.969429i | \(-0.578910\pi\) | ||||
−0.245372 | + | 0.969429i | \(0.578910\pi\) | |||||||
\(98\) | −730.211 | −0.752678 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2166.94 | −2.16694 | ||||||||
\(101\) | 305.731 | 0.301201 | 0.150601 | − | 0.988595i | \(-0.451879\pi\) | ||||
0.150601 | + | 0.988595i | \(0.451879\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1560.85 | −1.49315 | −0.746576 | − | 0.665300i | \(-0.768304\pi\) | ||||
−0.746576 | + | 0.665300i | \(0.768304\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −690.781 | −0.632968 | ||||||||
\(107\) | 707.803 | 0.639494 | 0.319747 | − | 0.947503i | \(-0.396402\pi\) | ||||
0.319747 | + | 0.947503i | \(0.396402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1714.25 | −1.50638 | −0.753192 | − | 0.657801i | \(-0.771487\pi\) | ||||
−0.753192 | + | 0.657801i | \(0.771487\pi\) | |||||||
\(110\) | −424.057 | −0.367566 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1062.37 | −0.896289 | ||||||||
\(113\) | −1263.51 | −1.05187 | −0.525935 | − | 0.850525i | \(-0.676285\pi\) | ||||
−0.525935 | + | 0.850525i | \(0.676285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3173.80 | −2.57355 | ||||||||
\(116\) | 42.0698 | 0.0336731 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −816.419 | −0.636928 | ||||||||
\(119\) | 2786.09 | 2.14623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1028.90 | −0.773025 | ||||||||
\(122\) | 543.510 | 0.403337 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −522.799 | −0.378619 | ||||||||
\(125\) | −4231.91 | −3.02811 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 893.935 | 0.624598 | 0.312299 | − | 0.949984i | \(-0.398901\pi\) | ||||
0.312299 | + | 0.949984i | \(0.398901\pi\) | |||||||
\(128\) | 1475.67 | 1.01900 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.87226 | 0.00658430 | 0.00329215 | − | 0.999995i | \(-0.498952\pi\) | ||||
0.00329215 | + | 0.999995i | \(0.498952\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2521.56 | 1.64396 | ||||||||
\(134\) | 381.489 | 0.245937 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1504.74 | −0.948751 | ||||||||
\(137\) | −1486.59 | −0.927063 | −0.463532 | − | 0.886080i | \(-0.653418\pi\) | ||||
−0.463532 | + | 0.886080i | \(0.653418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 530.179 | 0.323520 | 0.161760 | − | 0.986830i | \(-0.448283\pi\) | ||||
0.161760 | + | 0.986830i | \(0.448283\pi\) | |||||||
\(140\) | −4425.96 | −2.67187 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −543.983 | −0.321479 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 133.616 | 0.0765255 | ||||||||
\(146\) | −749.086 | −0.424622 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −262.351 | −0.145710 | ||||||||
\(149\) | 1796.65 | 0.987832 | 0.493916 | − | 0.869510i | \(-0.335565\pi\) | ||||
0.493916 | + | 0.869510i | \(0.335565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1818.69 | −0.980150 | −0.490075 | − | 0.871680i | \(-0.663031\pi\) | ||||
−0.490075 | + | 0.871680i | \(0.663031\pi\) | |||||||
\(152\) | −1361.87 | −0.726723 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −625.318 | −0.327205 | ||||||||
\(155\) | −1660.44 | −0.860450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −875.076 | −0.444832 | −0.222416 | − | 0.974952i | \(-0.571394\pi\) | ||||
−0.222416 | + | 0.974952i | \(0.571394\pi\) | |||||||
\(158\) | −277.213 | −0.139581 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3693.44 | 1.82495 | ||||||||
\(161\) | −4680.11 | −2.29096 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1777.39 | 0.854083 | 0.427042 | − | 0.904232i | \(-0.359556\pi\) | ||||
0.427042 | + | 0.904232i | \(0.359556\pi\) | |||||||
\(164\) | 2207.41 | 1.05103 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 619.080 | 0.289457 | ||||||||
\(167\) | 2526.37 | 1.17064 | 0.585319 | − | 0.810803i | \(-0.300969\pi\) | ||||
0.585319 | + | 0.810803i | \(0.300969\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −2173.99 | −0.980810 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1327.22 | 0.588368 | ||||||||
\(173\) | 204.999 | 0.0900913 | 0.0450457 | − | 0.998985i | \(-0.485657\pi\) | ||||
0.0450457 | + | 0.998985i | \(0.485657\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10148.8 | −4.38385 | ||||||||
\(176\) | −590.568 | −0.252930 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −774.939 | −0.326315 | ||||||||
\(179\) | 1768.15 | 0.738311 | 0.369156 | − | 0.929368i | \(-0.379647\pi\) | ||||
0.369156 | + | 0.929368i | \(0.379647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2542.64 | 1.04416 | 0.522079 | − | 0.852897i | \(-0.325157\pi\) | ||||
0.522079 | + | 0.852897i | \(0.325157\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2527.67 | 1.01273 | ||||||||
\(185\) | −833.243 | −0.331142 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1548.78 | 0.605659 | ||||||||
\(188\) | −1646.39 | −0.638699 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1967.58 | −0.751280 | ||||||||
\(191\) | −40.7190 | −0.0154258 | −0.00771289 | − | 0.999970i | \(-0.502455\pi\) | ||||
−0.00771289 | + | 0.999970i | \(0.502455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2774.70 | −1.03486 | −0.517428 | − | 0.855727i | \(-0.673110\pi\) | ||||
−0.517428 | + | 0.855727i | \(0.673110\pi\) | |||||||
\(194\) | 539.451 | 0.199641 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4236.69 | −1.54398 | ||||||||
\(197\) | 1171.74 | 0.423770 | 0.211885 | − | 0.977295i | \(-0.432040\pi\) | ||||
0.211885 | + | 0.977295i | \(0.432040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1940.97 | 0.691417 | 0.345708 | − | 0.938342i | \(-0.387639\pi\) | ||||
0.345708 | + | 0.938342i | \(0.387639\pi\) | |||||||
\(200\) | 5481.23 | 1.93791 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −351.786 | −0.122533 | ||||||||
\(203\) | 197.031 | 0.0681226 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7010.86 | 2.38858 | ||||||||
\(206\) | 1795.97 | 0.607434 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1401.73 | 0.463922 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1659.92 | 0.541580 | 0.270790 | − | 0.962638i | \(-0.412715\pi\) | ||||
0.270790 | + | 0.962638i | \(0.412715\pi\) | |||||||
\(212\) | −4007.92 | −1.29842 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −814.427 | −0.260155 | ||||||||
\(215\) | 4215.32 | 1.33713 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2448.50 | −0.765968 | ||||||||
\(218\) | 1972.49 | 0.612816 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2460.38 | −0.753995 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4619.40 | −1.38716 | −0.693582 | − | 0.720378i | \(-0.743969\pi\) | ||||
−0.693582 | + | 0.720378i | \(0.743969\pi\) | |||||||
\(224\) | 5446.38 | 1.62456 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1453.85 | 0.427914 | ||||||||
\(227\) | −1220.49 | −0.356859 | −0.178429 | − | 0.983953i | \(-0.557102\pi\) | ||||
−0.178429 | + | 0.983953i | \(0.557102\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3911.47 | −1.12872 | −0.564361 | − | 0.825528i | \(-0.690878\pi\) | ||||
−0.564361 | + | 0.825528i | \(0.690878\pi\) | |||||||
\(230\) | 3651.90 | 1.04695 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −106.414 | −0.0301140 | ||||||||
\(233\) | 4235.15 | 1.19079 | 0.595395 | − | 0.803433i | \(-0.296996\pi\) | ||||
0.595395 | + | 0.803433i | \(0.296996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5229.03 | −1.45151 | ||||||||
\(236\) | −4736.87 | −1.30654 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3205.79 | −0.873112 | ||||||||
\(239\) | −772.395 | −0.209046 | −0.104523 | − | 0.994522i | \(-0.533332\pi\) | ||||
−0.104523 | + | 0.994522i | \(0.533332\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1319.51 | 0.352684 | 0.176342 | − | 0.984329i | \(-0.443574\pi\) | ||||
0.176342 | + | 0.984329i | \(0.443574\pi\) | |||||||
\(242\) | 1183.89 | 0.314477 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3153.45 | 0.827372 | ||||||||
\(245\) | −13456.0 | −3.50886 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1322.41 | 0.338600 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4869.41 | 1.23187 | ||||||||
\(251\) | 2422.90 | 0.609292 | 0.304646 | − | 0.952466i | \(-0.401462\pi\) | ||||
0.304646 | + | 0.952466i | \(0.401462\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2601.66 | −0.646502 | ||||||||
\(254\) | −1028.60 | −0.254094 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1126.85 | −0.275109 | ||||||||
\(257\) | 3778.25 | 0.917047 | 0.458523 | − | 0.888682i | \(-0.348379\pi\) | ||||
0.458523 | + | 0.888682i | \(0.348379\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1228.71 | −0.294781 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11.3594 | −0.00267858 | ||||||||
\(263\) | −7343.43 | −1.72173 | −0.860866 | − | 0.508832i | \(-0.830077\pi\) | ||||
−0.860866 | + | 0.508832i | \(0.830077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12729.4 | −2.95079 | ||||||||
\(266\) | −2901.41 | −0.668786 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2213.40 | 0.504496 | ||||||||
\(269\) | 7812.34 | 1.77073 | 0.885365 | − | 0.464896i | \(-0.153908\pi\) | ||||
0.885365 | + | 0.464896i | \(0.153908\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5592.09 | −1.25349 | −0.626745 | − | 0.779225i | \(-0.715613\pi\) | ||||
−0.626745 | + | 0.779225i | \(0.715613\pi\) | |||||||
\(272\) | −3027.64 | −0.674918 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1710.53 | 0.377141 | ||||||||
\(275\) | −5641.67 | −1.23711 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3897.19 | 0.845342 | 0.422671 | − | 0.906283i | \(-0.361093\pi\) | ||||
0.422671 | + | 0.906283i | \(0.361093\pi\) | |||||||
\(278\) | −610.046 | −0.131612 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11195.4 | 2.38947 | ||||||||
\(281\) | 5921.18 | 1.25704 | 0.628519 | − | 0.777794i | \(-0.283661\pi\) | ||||
0.628519 | + | 0.777794i | \(0.283661\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4936.47 | −1.03690 | −0.518450 | − | 0.855108i | \(-0.673491\pi\) | ||||
−0.518450 | + | 0.855108i | \(0.673491\pi\) | |||||||
\(284\) | −3156.19 | −0.659456 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10338.3 | 2.12630 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3027.07 | 0.616136 | ||||||||
\(290\) | −153.744 | −0.0311316 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4346.20 | −0.871035 | ||||||||
\(293\) | 5575.98 | 1.11178 | 0.555891 | − | 0.831255i | \(-0.312377\pi\) | ||||
0.555891 | + | 0.831255i | \(0.312377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15044.6 | −2.96925 | ||||||||
\(296\) | 663.611 | 0.130309 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2067.29 | −0.401863 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6215.95 | 1.19030 | ||||||||
\(302\) | 2092.66 | 0.398738 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2740.17 | −0.516973 | ||||||||
\(305\) | 10015.5 | 1.88029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10168.3 | 1.89035 | 0.945175 | − | 0.326564i | \(-0.105891\pi\) | ||||
0.945175 | + | 0.326564i | \(0.105891\pi\) | |||||||
\(308\) | −3628.10 | −0.671202 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1910.57 | 0.350042 | ||||||||
\(311\) | −4680.41 | −0.853382 | −0.426691 | − | 0.904397i | \(-0.640321\pi\) | ||||
−0.426691 | + | 0.904397i | \(0.640321\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2990.32 | 0.540009 | 0.270004 | − | 0.962859i | \(-0.412975\pi\) | ||||
0.270004 | + | 0.962859i | \(0.412975\pi\) | |||||||
\(314\) | 1006.90 | 0.180963 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1608.39 | −0.286326 | ||||||||
\(317\) | 9081.93 | 1.60912 | 0.804561 | − | 0.593870i | \(-0.202401\pi\) | ||||
0.804561 | + | 0.593870i | \(0.202401\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 109.529 | 0.0192240 | ||||||||
\(320\) | 1513.70 | 0.264433 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5385.12 | 0.931991 | ||||||||
\(323\) | 7186.19 | 1.23793 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2045.13 | −0.347452 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5583.58 | −0.939945 | ||||||||
\(329\) | −7710.78 | −1.29213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5290.27 | 0.878488 | 0.439244 | − | 0.898368i | \(-0.355246\pi\) | ||||
0.439244 | + | 0.898368i | \(0.355246\pi\) | |||||||
\(332\) | 3591.91 | 0.593769 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2906.95 | −0.476231 | ||||||||
\(335\) | 7029.89 | 1.14652 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3313.51 | −0.535603 | −0.267802 | − | 0.963474i | \(-0.586297\pi\) | ||||
−0.267802 | + | 0.963474i | \(0.586297\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12613.5 | −2.01196 | ||||||||
\(341\) | −1361.11 | −0.216154 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9117.79 | −1.43532 | ||||||||
\(344\) | −3357.16 | −0.526180 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −235.880 | −0.0366503 | ||||||||
\(347\) | −4218.65 | −0.652649 | −0.326324 | − | 0.945258i | \(-0.605810\pi\) | ||||
−0.326324 | + | 0.945258i | \(0.605810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6552.91 | −1.00507 | −0.502535 | − | 0.864557i | \(-0.667599\pi\) | ||||
−0.502535 | + | 0.864557i | \(0.667599\pi\) | |||||||
\(350\) | 11677.6 | 1.78341 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3027.63 | 0.458447 | ||||||||
\(353\) | 3864.50 | 0.582681 | 0.291341 | − | 0.956619i | \(-0.405899\pi\) | ||||
0.291341 | + | 0.956619i | \(0.405899\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10024.2 | −1.49868 | ||||||||
\(356\) | −4496.20 | −0.669377 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2034.51 | −0.300355 | ||||||||
\(359\) | 588.511 | 0.0865192 | 0.0432596 | − | 0.999064i | \(-0.486226\pi\) | ||||
0.0432596 | + | 0.999064i | \(0.486226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −355.122 | −0.0517746 | ||||||||
\(362\) | −2925.66 | −0.424777 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13803.8 | −1.97952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11082.7 | 1.57633 | 0.788167 | − | 0.615462i | \(-0.211030\pi\) | ||||
0.788167 | + | 0.615462i | \(0.211030\pi\) | |||||||
\(368\) | 5085.86 | 0.720432 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 958.763 | 0.134713 | ||||||||
\(371\) | −18770.9 | −2.62678 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4106.52 | −0.570048 | −0.285024 | − | 0.958520i | \(-0.592001\pi\) | ||||
−0.285024 | + | 0.958520i | \(0.592001\pi\) | |||||||
\(374\) | −1782.09 | −0.246390 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4164.50 | 0.571191 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6169.89 | 0.836216 | 0.418108 | − | 0.908397i | \(-0.362693\pi\) | ||||
0.418108 | + | 0.908397i | \(0.362693\pi\) | |||||||
\(380\) | −11415.9 | −1.54112 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 46.8530 | 0.00627541 | ||||||||
\(383\) | −9133.11 | −1.21849 | −0.609243 | − | 0.792984i | \(-0.708527\pi\) | ||||
−0.609243 | + | 0.792984i | \(0.708527\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11523.1 | −1.52538 | ||||||||
\(386\) | 3192.68 | 0.420992 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3129.90 | 0.409527 | ||||||||
\(389\) | −12369.3 | −1.61221 | −0.806104 | − | 0.591774i | \(-0.798428\pi\) | ||||
−0.806104 | + | 0.591774i | \(0.798428\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13337.8 | −1.72512 | ||||||||
\(392\) | 10716.6 | 1.38079 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1348.25 | −0.172395 | ||||||||
\(395\) | −5108.34 | −0.650705 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2520.20 | −0.318603 | −0.159301 | − | 0.987230i | \(-0.550924\pi\) | ||||
−0.159301 | + | 0.987230i | \(0.550924\pi\) | |||||||
\(398\) | −2233.36 | −0.281277 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11028.6 | 1.37858 | ||||||||
\(401\) | 4400.92 | 0.548059 | 0.274029 | − | 0.961721i | \(-0.411643\pi\) | ||||
0.274029 | + | 0.961721i | \(0.411643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2041.07 | −0.251353 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −226.712 | −0.0277132 | ||||||||
\(407\) | −683.035 | −0.0831862 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6482.35 | −0.783696 | −0.391848 | − | 0.920030i | \(-0.628164\pi\) | ||||
−0.391848 | + | 0.920030i | \(0.628164\pi\) | |||||||
\(410\) | −8066.98 | −0.971707 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10420.2 | 1.24604 | ||||||||
\(413\) | −22184.9 | −2.64321 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11408.1 | 1.34940 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1612.89 | −0.188729 | ||||||||
\(419\) | 6293.72 | 0.733815 | 0.366908 | − | 0.930257i | \(-0.380417\pi\) | ||||
0.366908 | + | 0.930257i | \(0.380417\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8376.89 | 0.969749 | 0.484875 | − | 0.874584i | \(-0.338865\pi\) | ||||
0.484875 | + | 0.874584i | \(0.338865\pi\) | |||||||
\(422\) | −1909.97 | −0.220322 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10137.9 | 1.16118 | ||||||||
\(425\) | −28922.9 | −3.30110 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14769.0 | 1.67382 | ||||||||
\(428\) | −4725.31 | −0.533660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4850.32 | −0.543961 | ||||||||
\(431\) | 3392.05 | 0.379094 | 0.189547 | − | 0.981872i | \(-0.439298\pi\) | ||||
0.189547 | + | 0.981872i | \(0.439298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13767.3 | 1.52798 | 0.763991 | − | 0.645227i | \(-0.223237\pi\) | ||||
0.763991 | + | 0.645227i | \(0.223237\pi\) | |||||||
\(434\) | 2817.34 | 0.311606 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11444.4 | 1.25708 | ||||||||
\(437\) | −12071.4 | −1.32141 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6355.98 | −0.691013 | −0.345506 | − | 0.938416i | \(-0.612293\pi\) | ||||
−0.345506 | + | 0.938416i | \(0.612293\pi\) | |||||||
\(440\) | 6223.47 | 0.674301 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.2187 | −0.00216844 | −0.00108422 | − | 0.999999i | \(-0.500345\pi\) | ||||
−0.00108422 | + | 0.999999i | \(0.500345\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14280.2 | −1.52123 | ||||||||
\(446\) | 5315.26 | 0.564316 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2232.12 | 0.235397 | ||||||||
\(449\) | 10039.8 | 1.05525 | 0.527626 | − | 0.849477i | \(-0.323082\pi\) | ||||
0.527626 | + | 0.849477i | \(0.323082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5747.02 | 0.600037 | ||||||||
\(452\) | 8435.25 | 0.877789 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1404.35 | 0.145175 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14931.2 | 1.52834 | 0.764168 | − | 0.645017i | \(-0.223150\pi\) | ||||
0.764168 | + | 0.645017i | \(0.223150\pi\) | |||||||
\(458\) | 4500.70 | 0.459179 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 21188.3 | 2.14763 | ||||||||
\(461\) | −952.278 | −0.0962083 | −0.0481041 | − | 0.998842i | \(-0.515318\pi\) | ||||
−0.0481041 | + | 0.998842i | \(0.515318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 666.672 | 0.0669176 | 0.0334588 | − | 0.999440i | \(-0.489348\pi\) | ||||
0.0334588 | + | 0.999440i | \(0.489348\pi\) | |||||||
\(464\) | −214.113 | −0.0214223 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4873.14 | −0.484428 | ||||||||
\(467\) | −13525.2 | −1.34020 | −0.670098 | − | 0.742273i | \(-0.733748\pi\) | ||||
−0.670098 | + | 0.742273i | \(0.733748\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10366.3 | 1.02062 | ||||||||
\(470\) | 6016.74 | 0.590492 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11981.8 | 1.16845 | ||||||||
\(473\) | 3455.43 | 0.335900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26176.8 | −2.52857 | ||||||||
\(476\) | −18600.0 | −1.79103 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 888.749 | 0.0850427 | ||||||||
\(479\) | 5120.03 | 0.488393 | 0.244196 | − | 0.969726i | \(-0.421476\pi\) | ||||
0.244196 | + | 0.969726i | \(0.421476\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −1518.28 | −0.143476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6868.94 | 0.645092 | ||||||||
\(485\) | 9940.74 | 0.930692 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9776.37 | −0.909671 | −0.454835 | − | 0.890575i | \(-0.650302\pi\) | ||||
−0.454835 | + | 0.890575i | \(0.650302\pi\) | |||||||
\(488\) | −7976.56 | −0.739922 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15483.0 | 1.42745 | ||||||||
\(491\) | −10423.9 | −0.958097 | −0.479048 | − | 0.877788i | \(-0.659018\pi\) | ||||
−0.479048 | + | 0.877788i | \(0.659018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 561.519 | 0.0512972 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2660.78 | 0.240872 | ||||||||
\(497\) | −14781.8 | −1.33412 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10785.0 | 0.967544 | 0.483772 | − | 0.875194i | \(-0.339266\pi\) | ||||
0.483772 | + | 0.875194i | \(0.339266\pi\) | |||||||
\(500\) | 28252.3 | 2.52697 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2787.89 | −0.247868 | ||||||||
\(503\) | 2135.13 | 0.189266 | 0.0946330 | − | 0.995512i | \(-0.469832\pi\) | ||||
0.0946330 | + | 0.995512i | \(0.469832\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6482.54 | −0.571226 | ||||||||
\(506\) | 2993.58 | 0.263005 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5967.93 | −0.521229 | ||||||||
\(509\) | −13658.8 | −1.18942 | −0.594711 | − | 0.803939i | \(-0.702734\pi\) | ||||
−0.594711 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20355.2 | −1.76215 | ||||||||
\(512\) | −10508.7 | −0.907081 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4347.41 | −0.373066 | ||||||||
\(515\) | 33095.3 | 2.83175 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4286.40 | −0.364634 | ||||||||
\(518\) | 1413.80 | 0.119921 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14644.5 | −1.23146 | −0.615728 | − | 0.787958i | \(-0.711138\pi\) | ||||
−0.615728 | + | 0.787958i | \(0.711138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −810.895 | −0.0677973 | −0.0338986 | − | 0.999425i | \(-0.510792\pi\) | ||||
−0.0338986 | + | 0.999425i | \(0.510792\pi\) | |||||||
\(524\) | −65.9075 | −0.00549462 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8449.65 | 0.700422 | ||||||||
\(527\) | −6977.97 | −0.576784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10238.0 | 0.841458 | ||||||||
\(530\) | 14646.9 | 1.20042 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16834.0 | −1.37189 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15007.9 | −1.21280 | ||||||||
\(536\) | −5598.74 | −0.451173 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8989.19 | −0.720356 | ||||||||
\(539\) | −11030.3 | −0.881462 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23330.4 | −1.85407 | −0.927036 | − | 0.374971i | \(-0.877653\pi\) | ||||
−0.927036 | + | 0.374971i | \(0.877653\pi\) | |||||||
\(542\) | 6434.49 | 0.509935 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15521.6 | 1.22332 | ||||||||
\(545\) | 36348.1 | 2.85685 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24537.6 | 1.91801 | 0.959005 | − | 0.283390i | \(-0.0914589\pi\) | ||||
0.959005 | + | 0.283390i | \(0.0914589\pi\) | |||||||
\(548\) | 9924.49 | 0.773637 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6491.54 | 0.503273 | ||||||||
\(551\) | 508.204 | 0.0392926 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7532.81 | −0.579254 | ||||||||
\(554\) | −4484.27 | −0.343896 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3539.49 | −0.269978 | ||||||||
\(557\) | −4219.10 | −0.320950 | −0.160475 | − | 0.987040i | \(-0.551303\pi\) | ||||
−0.160475 | + | 0.987040i | \(0.551303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 22525.9 | 1.69981 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6813.15 | −0.511379 | ||||||||
\(563\) | −981.849 | −0.0734991 | −0.0367496 | − | 0.999325i | \(-0.511700\pi\) | ||||
−0.0367496 | + | 0.999325i | \(0.511700\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26790.8 | 1.99486 | ||||||||
\(566\) | 5680.11 | 0.421825 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7983.50 | 0.589754 | ||||||||
\(569\) | 2021.40 | 0.148930 | 0.0744652 | − | 0.997224i | \(-0.476275\pi\) | ||||
0.0744652 | + | 0.997224i | \(0.476275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11994.8 | 0.879099 | 0.439549 | − | 0.898218i | \(-0.355138\pi\) | ||||
0.439549 | + | 0.898218i | \(0.355138\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −11895.6 | −0.865008 | ||||||||
\(575\) | 48585.0 | 3.52371 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −176.997 | −0.0127703 | −0.00638516 | − | 0.999980i | \(-0.502032\pi\) | ||||
−0.00638516 | + | 0.999980i | \(0.502032\pi\) | |||||||
\(578\) | −3483.08 | −0.250652 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −892.024 | −0.0638608 | ||||||||
\(581\) | 16822.5 | 1.20123 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10434.7 | −0.741269 | ||||||||
\(584\) | 10993.6 | 0.778970 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6415.95 | −0.452288 | ||||||||
\(587\) | −10885.6 | −0.765413 | −0.382707 | − | 0.923870i | \(-0.625008\pi\) | ||||
−0.382707 | + | 0.923870i | \(0.625008\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6315.43 | −0.441804 | ||||||||
\(590\) | 17310.9 | 1.20793 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1335.23 | 0.0926989 | ||||||||
\(593\) | −6043.37 | −0.418502 | −0.209251 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209251 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −59074.8 | −4.07030 | ||||||||
\(596\) | −11994.5 | −0.824349 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23893.3 | 1.62981 | 0.814904 | − | 0.579596i | \(-0.196789\pi\) | ||||
0.814904 | + | 0.579596i | \(0.196789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −25840.1 | −1.75381 | −0.876905 | − | 0.480665i | \(-0.840395\pi\) | ||||
−0.876905 | + | 0.480665i | \(0.840395\pi\) | |||||||
\(602\) | −7152.32 | −0.484231 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12141.6 | 0.817939 | ||||||||
\(605\) | 21816.1 | 1.46604 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −395.714 | −0.0264605 | −0.0132303 | − | 0.999912i | \(-0.504211\pi\) | ||||
−0.0132303 | + | 0.999912i | \(0.504211\pi\) | |||||||
\(608\) | 14047.9 | 0.937034 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11524.3 | −0.764925 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20523.7 | 1.35228 | 0.676139 | − | 0.736774i | \(-0.263652\pi\) | ||||
0.676139 | + | 0.736774i | \(0.263652\pi\) | |||||||
\(614\) | −11700.1 | −0.769019 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9177.19 | 0.600259 | ||||||||
\(617\) | 2398.68 | 0.156511 | 0.0782556 | − | 0.996933i | \(-0.475065\pi\) | ||||
0.0782556 | + | 0.996933i | \(0.475065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17708.2 | 1.14984 | 0.574922 | − | 0.818208i | \(-0.305032\pi\) | ||||
0.574922 | + | 0.818208i | \(0.305032\pi\) | |||||||
\(620\) | 11085.1 | 0.718048 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 5385.47 | 0.347167 | ||||||||
\(623\) | −21057.7 | −1.35419 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49157.8 | 3.14610 | ||||||||
\(626\) | −3440.78 | −0.219682 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5842.03 | 0.371214 | ||||||||
\(629\) | −3501.69 | −0.221974 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18170.1 | 1.14634 | 0.573170 | − | 0.819437i | \(-0.305713\pi\) | ||||
0.573170 | + | 0.819437i | \(0.305713\pi\) | |||||||
\(632\) | 4068.38 | 0.256062 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10450.0 | −0.654612 | ||||||||
\(635\) | −18954.5 | −1.18455 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −126.029 | −0.00782058 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −31289.2 | −1.93253 | ||||||||
\(641\) | −30492.4 | −1.87891 | −0.939453 | − | 0.342678i | \(-0.888666\pi\) | ||||
−0.939453 | + | 0.342678i | \(0.888666\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22280.9 | 1.36652 | 0.683260 | − | 0.730175i | \(-0.260562\pi\) | ||||
0.683260 | + | 0.730175i | \(0.260562\pi\) | |||||||
\(644\) | 31244.5 | 1.91181 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8268.72 | −0.503604 | ||||||||
\(647\) | −16844.4 | −1.02353 | −0.511763 | − | 0.859127i | \(-0.671008\pi\) | ||||
−0.511763 | + | 0.859127i | \(0.671008\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12332.5 | −0.745906 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11865.9 | −0.712735 | ||||||||
\(653\) | −5880.96 | −0.352435 | −0.176217 | − | 0.984351i | \(-0.556386\pi\) | ||||
−0.176217 | + | 0.984351i | \(0.556386\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −209.326 | −0.0124871 | ||||||||
\(656\) | −11234.6 | −0.668653 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8872.34 | 0.525653 | ||||||||
\(659\) | 29655.1 | 1.75296 | 0.876479 | − | 0.481441i | \(-0.159886\pi\) | ||||
0.876479 | + | 0.481441i | \(0.159886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18713.4 | −1.10116 | −0.550581 | − | 0.834782i | \(-0.685594\pi\) | ||||
−0.550581 | + | 0.834782i | \(0.685594\pi\) | |||||||
\(662\) | −6087.20 | −0.357380 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9085.63 | −0.531010 | ||||||||
\(665\) | −53465.8 | −3.11777 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −943.245 | −0.0547565 | ||||||||
\(668\) | −16866.1 | −0.976901 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8088.87 | −0.466419 | ||||||||
\(671\) | 8210.05 | 0.472348 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7932.59 | 0.454352 | 0.227176 | − | 0.973854i | \(-0.427051\pi\) | ||||
0.227176 | + | 0.973854i | \(0.427051\pi\) | |||||||
\(674\) | 3812.66 | 0.217890 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14742.2 | −0.836910 | −0.418455 | − | 0.908238i | \(-0.637428\pi\) | ||||
−0.418455 | + | 0.908238i | \(0.637428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14658.7 | 0.828497 | ||||||||
\(680\) | 31905.6 | 1.79930 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1566.15 | 0.0879342 | ||||||||
\(683\) | 3081.46 | 0.172634 | 0.0863169 | − | 0.996268i | \(-0.472490\pi\) | ||||
0.0863169 | + | 0.996268i | \(0.472490\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31520.8 | 1.75817 | ||||||||
\(686\) | 10491.3 | 0.583906 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6754.85 | −0.374312 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11563.5 | −0.636607 | −0.318303 | − | 0.947989i | \(-0.603113\pi\) | ||||
−0.318303 | + | 0.947989i | \(0.603113\pi\) | |||||||
\(692\) | −1368.58 | −0.0751815 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4854.15 | 0.265506 | ||||||||
\(695\) | −11241.6 | −0.613553 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29463.0 | 1.60114 | ||||||||
\(698\) | 7540.04 | 0.408875 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 67753.4 | 3.65834 | ||||||||
\(701\) | −3283.53 | −0.176914 | −0.0884572 | − | 0.996080i | \(-0.528194\pi\) | ||||
−0.0884572 | + | 0.996080i | \(0.528194\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3169.21 | −0.170027 | ||||||||
\(704\) | 1240.83 | 0.0664283 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4446.65 | −0.237042 | ||||||||
\(707\) | −9559.22 | −0.508503 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22397.5 | −1.18640 | −0.593198 | − | 0.805056i | \(-0.702135\pi\) | ||||
−0.593198 | + | 0.805056i | \(0.702135\pi\) | |||||||
\(710\) | 11534.3 | 0.609683 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11373.0 | 0.598626 | ||||||||
\(713\) | 11721.7 | 0.615680 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11804.2 | −0.616123 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −677.164 | −0.0351971 | ||||||||
\(719\) | −21475.6 | −1.11392 | −0.556958 | − | 0.830540i | \(-0.688032\pi\) | ||||
−0.556958 | + | 0.830540i | \(0.688032\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 48802.6 | 2.52081 | ||||||||
\(722\) | 408.617 | 0.0210626 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −16974.7 | −0.871353 | ||||||||
\(725\) | −2045.42 | −0.104779 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2541.54 | −0.129657 | −0.0648285 | − | 0.997896i | \(-0.520650\pi\) | ||||
−0.0648285 | + | 0.997896i | \(0.520650\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15883.2 | 0.805293 | ||||||||
\(731\) | 17714.8 | 0.896314 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1921.91 | 0.0968447 | 0.0484224 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484224 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(734\) | −12752.3 | −0.641273 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26073.4 | −1.30581 | ||||||||
\(737\) | 5762.62 | 0.288017 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3501.37 | 0.174290 | 0.0871448 | − | 0.996196i | \(-0.472226\pi\) | ||||
0.0871448 | + | 0.996196i | \(0.472226\pi\) | |||||||
\(740\) | 5562.75 | 0.276339 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 21598.5 | 1.06861 | ||||||||
\(743\) | 38056.5 | 1.87908 | 0.939541 | − | 0.342437i | \(-0.111252\pi\) | ||||
0.939541 | + | 0.342437i | \(0.111252\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38095.1 | −1.87342 | ||||||||
\(746\) | 4725.13 | 0.231903 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10339.7 | −0.505424 | ||||||||
\(749\) | −22130.7 | −1.07963 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9334.53 | −0.453557 | −0.226779 | − | 0.973946i | \(-0.572819\pi\) | ||||
−0.226779 | + | 0.973946i | \(0.572819\pi\) | |||||||
\(752\) | 8379.28 | 0.406331 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38562.4 | 1.85885 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12334.1 | 0.592193 | 0.296097 | − | 0.955158i | \(-0.404315\pi\) | ||||
0.296097 | + | 0.955158i | \(0.404315\pi\) | |||||||
\(758\) | −7099.32 | −0.340183 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 28876.2 | 1.37823 | ||||||||
\(761\) | 16234.5 | 0.773326 | 0.386663 | − | 0.922221i | \(-0.373628\pi\) | ||||
0.386663 | + | 0.922221i | \(0.373628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53599.2 | 2.54315 | ||||||||
\(764\) | 271.841 | 0.0128729 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10508.9 | 0.495696 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2020.55 | 0.0947501 | 0.0473750 | − | 0.998877i | \(-0.484914\pi\) | ||||
0.0473750 | + | 0.998877i | \(0.484914\pi\) | |||||||
\(770\) | 13258.9 | 0.620542 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18523.9 | 0.863590 | ||||||||
\(773\) | 31025.1 | 1.44359 | 0.721795 | − | 0.692106i | \(-0.243317\pi\) | ||||
0.721795 | + | 0.692106i | \(0.243317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25418.3 | 1.17813 | ||||||||
\(776\) | −7917.00 | −0.366242 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14232.6 | 0.655867 | ||||||||
\(779\) | 26665.6 | 1.22644 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8217.19 | −0.376484 | ||||||||
\(782\) | 15347.0 | 0.701802 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 21562.6 | 0.982260 | ||||||||
\(785\) | 18554.6 | 0.843621 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31464.9 | −1.42516 | −0.712581 | − | 0.701590i | \(-0.752474\pi\) | ||||
−0.712581 | + | 0.701590i | \(0.752474\pi\) | |||||||
\(788\) | −7822.54 | −0.353638 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5877.86 | 0.264715 | ||||||||
\(791\) | 39506.0 | 1.77582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 2899.85 | 0.129612 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12958.0 | −0.576989 | ||||||||
\(797\) | −15051.4 | −0.668945 | −0.334473 | − | 0.942405i | \(-0.608558\pi\) | ||||
−0.334473 | + | 0.942405i | \(0.608558\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21974.9 | −0.972987 | ||||||||
\(800\) | −56539.8 | −2.49873 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5063.88 | −0.222957 | ||||||||
\(803\) | −11315.4 | −0.497275 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 99234.4 | 4.34479 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5162.82 | 0.224786 | ||||||||
\(809\) | −36468.2 | −1.58486 | −0.792432 | − | 0.609960i | \(-0.791185\pi\) | ||||
−0.792432 | + | 0.609960i | \(0.791185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21761.0 | 0.942210 | 0.471105 | − | 0.882077i | \(-0.343855\pi\) | ||||
0.471105 | + | 0.882077i | \(0.343855\pi\) | |||||||
\(812\) | −1315.39 | −0.0568486 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 785.928 | 0.0338412 | ||||||||
\(815\) | −37686.7 | −1.61976 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16032.8 | 0.686558 | ||||||||
\(818\) | 7458.86 | 0.318818 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −46804.7 | −1.99328 | ||||||||
\(821\) | 43320.0 | 1.84151 | 0.920754 | − | 0.390144i | \(-0.127575\pi\) | ||||
0.920754 | + | 0.390144i | \(0.127575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5819.88 | 0.246498 | 0.123249 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123249 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(824\) | −26357.7 | −1.11434 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 25526.8 | 1.07529 | ||||||||
\(827\) | 9099.01 | 0.382592 | 0.191296 | − | 0.981532i | \(-0.438731\pi\) | ||||
0.191296 | + | 0.981532i | \(0.438731\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6582.90 | 0.275794 | 0.137897 | − | 0.990447i | \(-0.455966\pi\) | ||||
0.137897 | + | 0.990447i | \(0.455966\pi\) | |||||||
\(830\) | −13126.6 | −0.548954 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −56548.5 | −2.35209 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −53567.8 | −2.22011 | ||||||||
\(836\) | −9357.98 | −0.387144 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7241.82 | −0.298526 | ||||||||
\(839\) | −28867.9 | −1.18788 | −0.593939 | − | 0.804510i | \(-0.702428\pi\) | ||||
−0.593939 | + | 0.804510i | \(0.702428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24349.3 | −0.998372 | ||||||||
\(842\) | −9638.78 | −0.394506 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11081.6 | −0.451950 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32170.3 | 1.30506 | ||||||||
\(848\) | 20398.2 | 0.826036 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 33279.9 | 1.34293 | ||||||||
\(851\) | 5882.17 | 0.236943 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17014.4 | 0.682958 | 0.341479 | − | 0.939889i | \(-0.389072\pi\) | ||||
0.341479 | + | 0.939889i | \(0.389072\pi\) | |||||||
\(854\) | −16993.8 | −0.680932 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11952.5 | 0.477254 | ||||||||
\(857\) | −6261.29 | −0.249570 | −0.124785 | − | 0.992184i | \(-0.539824\pi\) | ||||
−0.124785 | + | 0.992184i | \(0.539824\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29513.0 | 1.17226 | 0.586129 | − | 0.810218i | \(-0.300651\pi\) | ||||
0.586129 | + | 0.810218i | \(0.300651\pi\) | |||||||
\(860\) | −28141.6 | −1.11584 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3903.03 | −0.154220 | ||||||||
\(863\) | −7073.47 | −0.279008 | −0.139504 | − | 0.990222i | \(-0.544551\pi\) | ||||
−0.139504 | + | 0.990222i | \(0.544551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4346.69 | −0.170858 | ||||||||
\(866\) | −15841.3 | −0.621603 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 16346.2 | 0.639203 | ||||||||
\(869\) | −4187.47 | −0.163464 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −28948.3 | −1.12421 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13889.9 | 0.537565 | ||||||||
\(875\) | 132318. | 5.11220 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12567.8 | −0.483906 | −0.241953 | − | 0.970288i | \(-0.577788\pi\) | ||||
−0.241953 | + | 0.970288i | \(0.577788\pi\) | |||||||
\(878\) | 7313.45 | 0.281113 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 12522.1 | 0.479681 | ||||||||
\(881\) | −4722.06 | −0.180579 | −0.0902895 | − | 0.995916i | \(-0.528779\pi\) | ||||
−0.0902895 | + | 0.995916i | \(0.528779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20943.3 | 0.798185 | 0.399093 | − | 0.916911i | \(-0.369325\pi\) | ||||
0.399093 | + | 0.916911i | \(0.369325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.2645 | 0.000882151 0 | ||||||||
\(887\) | −36524.2 | −1.38260 | −0.691298 | − | 0.722570i | \(-0.742961\pi\) | ||||
−0.691298 | + | 0.722570i | \(0.742961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27950.5 | −1.05448 | ||||||||
\(890\) | 16431.4 | 0.618855 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30839.2 | 1.15759 | ||||||||
\(893\) | −19888.5 | −0.745288 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37490.9 | −1.40020 | ||||||||
\(896\) | −46139.4 | −1.72032 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11552.2 | −0.429290 | ||||||||
\(899\) | −493.479 | −0.0183075 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53495.0 | −1.97800 | ||||||||
\(902\) | −6612.76 | −0.244103 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −21336.7 | −0.785010 | ||||||||
\(905\) | −53912.6 | −1.98024 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19686.4 | −0.720701 | −0.360351 | − | 0.932817i | \(-0.617343\pi\) | ||||
−0.360351 | + | 0.932817i | \(0.617343\pi\) | |||||||
\(908\) | 8148.04 | 0.297800 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22339.4 | 0.812444 | 0.406222 | − | 0.913774i | \(-0.366846\pi\) | ||||
0.406222 | + | 0.913774i | \(0.366846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9351.58 | 0.338984 | ||||||||
\(914\) | −17180.4 | −0.621747 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26113.1 | 0.941923 | ||||||||
\(917\) | −308.674 | −0.0111159 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34118.9 | 1.22468 | 0.612338 | − | 0.790596i | \(-0.290229\pi\) | ||||
0.612338 | + | 0.790596i | \(0.290229\pi\) | |||||||
\(920\) | −53595.4 | −1.92064 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1095.73 | 0.0391388 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12755.4 | 0.453401 | ||||||||
\(926\) | −767.100 | −0.0272230 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1097.68 | 0.0388289 | ||||||||
\(929\) | 19596.3 | 0.692071 | 0.346035 | − | 0.938221i | \(-0.387528\pi\) | ||||
0.346035 | + | 0.938221i | \(0.387528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −51179.4 | −1.80165 | ||||||||
\(932\) | −28274.0 | −0.993718 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15562.6 | 0.545209 | ||||||||
\(935\) | −32839.5 | −1.14863 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52085.3 | 1.81596 | 0.907978 | − | 0.419017i | \(-0.137625\pi\) | ||||
0.907978 | + | 0.419017i | \(0.137625\pi\) | |||||||
\(938\) | −11927.9 | −0.415203 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 34909.2 | 1.21129 | ||||||||
\(941\) | −1090.90 | −0.0377921 | −0.0188960 | − | 0.999821i | \(-0.506015\pi\) | ||||
−0.0188960 | + | 0.999821i | \(0.506015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −49492.3 | −1.70911 | ||||||||
\(944\) | 24108.2 | 0.831203 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3975.96 | −0.136649 | ||||||||
\(947\) | 25306.1 | 0.868361 | 0.434181 | − | 0.900826i | \(-0.357038\pi\) | ||||
0.434181 | + | 0.900826i | \(0.357038\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 30120.0 | 1.02866 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 47048.3 | 1.60173 | ||||||||
\(953\) | −5321.09 | −0.180868 | −0.0904339 | − | 0.995902i | \(-0.528825\pi\) | ||||
−0.0904339 | + | 0.995902i | \(0.528825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 863.383 | 0.0292549 | ||||||||
\(956\) | 5156.53 | 0.174450 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5891.31 | −0.198684 | ||||||||
\(959\) | 46480.8 | 1.56511 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23658.6 | −0.794151 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8809.06 | −0.294316 | ||||||||
\(965\) | 58833.1 | 1.96260 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33045.4 | −1.09893 | −0.549466 | − | 0.835516i | \(-0.685169\pi\) | ||||
−0.549466 | + | 0.835516i | \(0.685169\pi\) | |||||||
\(968\) | −17374.8 | −0.576908 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11438.2 | −0.378618 | ||||||||
\(971\) | −53559.8 | −1.77015 | −0.885076 | − | 0.465447i | \(-0.845894\pi\) | ||||
−0.885076 | + | 0.465447i | \(0.845894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16577.0 | −0.546181 | ||||||||
\(974\) | 11249.1 | 0.370066 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16049.4 | −0.526362 | ||||||||
\(977\) | 31189.3 | 1.02132 | 0.510662 | − | 0.859782i | \(-0.329400\pi\) | ||||
0.510662 | + | 0.859782i | \(0.329400\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11705.9 | −0.382148 | ||||||||
\(980\) | 89832.4 | 2.92815 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11994.2 | 0.389766 | ||||||||
\(983\) | −6235.44 | −0.202319 | −0.101160 | − | 0.994870i | \(-0.532255\pi\) | ||||
−0.101160 | + | 0.994870i | \(0.532255\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24844.8 | −0.803677 | ||||||||
\(986\) | −646.106 | −0.0208684 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29757.5 | −0.956758 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24157.5 | 0.774357 | 0.387178 | − | 0.922005i | \(-0.373450\pi\) | ||||
0.387178 | + | 0.922005i | \(0.373450\pi\) | |||||||
\(992\) | −13640.8 | −0.436590 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 17008.6 | 0.542736 | ||||||||
\(995\) | −41155.3 | −1.31127 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35679.6 | −1.13339 | −0.566693 | − | 0.823929i | \(-0.691777\pi\) | ||||
−0.566693 | + | 0.823929i | \(0.691777\pi\) | |||||||
\(998\) | −12409.7 | −0.393609 | ||||||||
\(999\) | 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 | 1521.4.a.bm.1.8 | ✓ | 18 | |
3.2 | odd | 2 | inner | 1521.4.a.bm.1.11 | yes | 18 | |
13.12 | even | 2 | 1521.4.a.bn.1.11 | yes | 18 | ||
39.38 | odd | 2 | 1521.4.a.bn.1.8 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1521.4.a.bm.1.8 | ✓ | 18 | 1.1 | even | 1 | trivial | |
1521.4.a.bm.1.11 | yes | 18 | 3.2 | odd | 2 | inner | |
1521.4.a.bn.1.8 | yes | 18 | 39.38 | odd | 2 | ||
1521.4.a.bn.1.11 | yes | 18 | 13.12 | even | 2 |