Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,4,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(32.2740447731\) |
Analytic rank: | \(1\) |
Dimension: | \(65\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.89720 | −1.37787 | −0.688934 | − | 0.724824i | \(-0.741921\pi\) | ||||
−0.688934 | + | 0.724824i | \(0.741921\pi\) | |||||||
\(3\) | 3.45547 | 0.665006 | 0.332503 | − | 0.943102i | \(-0.392107\pi\) | ||||
0.332503 | + | 0.943102i | \(0.392107\pi\) | |||||||
\(4\) | 7.18817 | 0.898521 | ||||||||
\(5\) | −9.93922 | −0.888991 | −0.444495 | − | 0.895781i | \(-0.646617\pi\) | ||||
−0.444495 | + | 0.895781i | \(0.646617\pi\) | |||||||
\(6\) | −13.4667 | −0.916290 | ||||||||
\(7\) | 29.7950 | 1.60878 | 0.804389 | − | 0.594103i | \(-0.202493\pi\) | ||||
0.804389 | + | 0.594103i | \(0.202493\pi\) | |||||||
\(8\) | 3.16387 | 0.139824 | ||||||||
\(9\) | −15.0597 | −0.557768 | ||||||||
\(10\) | 38.7351 | 1.22491 | ||||||||
\(11\) | 35.6383 | 0.976852 | 0.488426 | − | 0.872605i | \(-0.337571\pi\) | ||||
0.488426 | + | 0.872605i | \(0.337571\pi\) | |||||||
\(12\) | 24.8385 | 0.597522 | ||||||||
\(13\) | −67.6663 | −1.44364 | −0.721818 | − | 0.692083i | \(-0.756693\pi\) | ||||
−0.721818 | + | 0.692083i | \(0.756693\pi\) | |||||||
\(14\) | −116.117 | −2.21668 | ||||||||
\(15\) | −34.3447 | −0.591184 | ||||||||
\(16\) | −69.8356 | −1.09118 | ||||||||
\(17\) | −113.010 | −1.61230 | −0.806148 | − | 0.591714i | \(-0.798452\pi\) | ||||
−0.806148 | + | 0.591714i | \(0.798452\pi\) | |||||||
\(18\) | 58.6908 | 0.768530 | ||||||||
\(19\) | 71.6030 | 0.864571 | 0.432286 | − | 0.901737i | \(-0.357707\pi\) | ||||
0.432286 | + | 0.901737i | \(0.357707\pi\) | |||||||
\(20\) | −71.4448 | −0.798777 | ||||||||
\(21\) | 102.956 | 1.06985 | ||||||||
\(22\) | −138.890 | −1.34597 | ||||||||
\(23\) | 178.047 | 1.61415 | 0.807075 | − | 0.590449i | \(-0.201049\pi\) | ||||
0.807075 | + | 0.590449i | \(0.201049\pi\) | |||||||
\(24\) | 10.9326 | 0.0929841 | ||||||||
\(25\) | −26.2119 | −0.209696 | ||||||||
\(26\) | 263.709 | 1.98914 | ||||||||
\(27\) | −145.336 | −1.03592 | ||||||||
\(28\) | 214.171 | 1.44552 | ||||||||
\(29\) | −193.459 | −1.23878 | −0.619388 | − | 0.785085i | \(-0.712619\pi\) | ||||
−0.619388 | + | 0.785085i | \(0.712619\pi\) | |||||||
\(30\) | 133.848 | 0.814573 | ||||||||
\(31\) | 226.450 | 1.31199 | 0.655995 | − | 0.754765i | \(-0.272249\pi\) | ||||
0.655995 | + | 0.754765i | \(0.272249\pi\) | |||||||
\(32\) | 246.852 | 1.36368 | ||||||||
\(33\) | 123.147 | 0.649612 | ||||||||
\(34\) | 440.424 | 2.22153 | ||||||||
\(35\) | −296.139 | −1.43019 | ||||||||
\(36\) | −108.252 | −0.501166 | ||||||||
\(37\) | −253.122 | −1.12467 | −0.562337 | − | 0.826908i | \(-0.690098\pi\) | ||||
−0.562337 | + | 0.826908i | \(0.690098\pi\) | |||||||
\(38\) | −279.051 | −1.19127 | ||||||||
\(39\) | −233.819 | −0.960026 | ||||||||
\(40\) | −31.4464 | −0.124303 | ||||||||
\(41\) | 235.725 | 0.897905 | 0.448952 | − | 0.893556i | \(-0.351797\pi\) | ||||
0.448952 | + | 0.893556i | \(0.351797\pi\) | |||||||
\(42\) | −401.239 | −1.47411 | ||||||||
\(43\) | 269.313 | 0.955113 | 0.477557 | − | 0.878601i | \(-0.341523\pi\) | ||||
0.477557 | + | 0.878601i | \(0.341523\pi\) | |||||||
\(44\) | 256.174 | 0.877722 | ||||||||
\(45\) | 149.682 | 0.495850 | ||||||||
\(46\) | −693.886 | −2.22409 | ||||||||
\(47\) | −570.540 | −1.77068 | −0.885339 | − | 0.464946i | \(-0.846074\pi\) | ||||
−0.885339 | + | 0.464946i | \(0.846074\pi\) | |||||||
\(48\) | −241.315 | −0.725641 | ||||||||
\(49\) | 544.741 | 1.58817 | ||||||||
\(50\) | 102.153 | 0.288933 | ||||||||
\(51\) | −390.504 | −1.07219 | ||||||||
\(52\) | −486.397 | −1.29714 | ||||||||
\(53\) | 168.825 | 0.437546 | 0.218773 | − | 0.975776i | \(-0.429795\pi\) | ||||
0.218773 | + | 0.975776i | \(0.429795\pi\) | |||||||
\(54\) | 566.404 | 1.42737 | ||||||||
\(55\) | −354.217 | −0.868412 | ||||||||
\(56\) | 94.2673 | 0.224946 | ||||||||
\(57\) | 247.422 | 0.574945 | ||||||||
\(58\) | 753.950 | 1.70687 | ||||||||
\(59\) | −636.666 | −1.40486 | −0.702431 | − | 0.711752i | \(-0.747902\pi\) | ||||
−0.702431 | + | 0.711752i | \(0.747902\pi\) | |||||||
\(60\) | −246.875 | −0.531191 | ||||||||
\(61\) | 95.0644 | 0.199537 | 0.0997685 | − | 0.995011i | \(-0.468190\pi\) | ||||
0.0997685 | + | 0.995011i | \(0.468190\pi\) | |||||||
\(62\) | −882.522 | −1.80775 | ||||||||
\(63\) | −448.704 | −0.897324 | ||||||||
\(64\) | −403.348 | −0.787789 | ||||||||
\(65\) | 672.550 | 1.28338 | ||||||||
\(66\) | −479.930 | −0.895079 | ||||||||
\(67\) | 259.671 | 0.473490 | 0.236745 | − | 0.971572i | \(-0.423919\pi\) | ||||
0.236745 | + | 0.971572i | \(0.423919\pi\) | |||||||
\(68\) | −812.337 | −1.44868 | ||||||||
\(69\) | 615.238 | 1.07342 | ||||||||
\(70\) | 1154.11 | 1.97061 | ||||||||
\(71\) | −542.632 | −0.907022 | −0.453511 | − | 0.891251i | \(-0.649829\pi\) | ||||
−0.453511 | + | 0.891251i | \(0.649829\pi\) | |||||||
\(72\) | −47.6470 | −0.0779896 | ||||||||
\(73\) | 56.5424 | 0.0906547 | 0.0453273 | − | 0.998972i | \(-0.485567\pi\) | ||||
0.0453273 | + | 0.998972i | \(0.485567\pi\) | |||||||
\(74\) | 986.466 | 1.54965 | ||||||||
\(75\) | −90.5746 | −0.139449 | ||||||||
\(76\) | 514.694 | 0.776836 | ||||||||
\(77\) | 1061.84 | 1.57154 | ||||||||
\(78\) | 911.240 | 1.32279 | ||||||||
\(79\) | 602.510 | 0.858071 | 0.429036 | − | 0.903288i | \(-0.358853\pi\) | ||||
0.429036 | + | 0.903288i | \(0.358853\pi\) | |||||||
\(80\) | 694.111 | 0.970050 | ||||||||
\(81\) | −95.5922 | −0.131128 | ||||||||
\(82\) | −918.668 | −1.23719 | ||||||||
\(83\) | −1241.39 | −1.64169 | −0.820846 | − | 0.571150i | \(-0.806498\pi\) | ||||
−0.820846 | + | 0.571150i | \(0.806498\pi\) | |||||||
\(84\) | 740.063 | 0.961279 | ||||||||
\(85\) | 1123.23 | 1.43332 | ||||||||
\(86\) | −1049.57 | −1.31602 | ||||||||
\(87\) | −668.493 | −0.823793 | ||||||||
\(88\) | 112.755 | 0.136588 | ||||||||
\(89\) | −404.559 | −0.481834 | −0.240917 | − | 0.970546i | \(-0.577448\pi\) | ||||
−0.240917 | + | 0.970546i | \(0.577448\pi\) | |||||||
\(90\) | −583.340 | −0.683216 | ||||||||
\(91\) | −2016.12 | −2.32249 | ||||||||
\(92\) | 1279.83 | 1.45035 | ||||||||
\(93\) | 782.492 | 0.872480 | ||||||||
\(94\) | 2223.51 | 2.43976 | ||||||||
\(95\) | −711.678 | −0.768596 | ||||||||
\(96\) | 852.991 | 0.906854 | ||||||||
\(97\) | −624.109 | −0.653285 | −0.326643 | − | 0.945148i | \(-0.605917\pi\) | ||||
−0.326643 | + | 0.945148i | \(0.605917\pi\) | |||||||
\(98\) | −2122.96 | −2.18828 | ||||||||
\(99\) | −536.704 | −0.544856 | ||||||||
\(100\) | −188.416 | −0.188416 | ||||||||
\(101\) | −1966.30 | −1.93717 | −0.968585 | − | 0.248682i | \(-0.920002\pi\) | ||||
−0.968585 | + | 0.248682i | \(0.920002\pi\) | |||||||
\(102\) | 1521.87 | 1.47733 | ||||||||
\(103\) | 934.025 | 0.893517 | 0.446759 | − | 0.894655i | \(-0.352578\pi\) | ||||
0.446759 | + | 0.894655i | \(0.352578\pi\) | |||||||
\(104\) | −214.087 | −0.201856 | ||||||||
\(105\) | −1023.30 | −0.951083 | ||||||||
\(106\) | −657.946 | −0.602881 | ||||||||
\(107\) | −151.988 | −0.137320 | −0.0686601 | − | 0.997640i | \(-0.521872\pi\) | ||||
−0.0686601 | + | 0.997640i | \(0.521872\pi\) | |||||||
\(108\) | −1044.70 | −0.930800 | ||||||||
\(109\) | −2196.56 | −1.93021 | −0.965104 | − | 0.261867i | \(-0.915662\pi\) | ||||
−0.965104 | + | 0.261867i | \(0.915662\pi\) | |||||||
\(110\) | 1380.46 | 1.19656 | ||||||||
\(111\) | −874.655 | −0.747915 | ||||||||
\(112\) | −2080.75 | −1.75547 | ||||||||
\(113\) | −1606.36 | −1.33729 | −0.668643 | − | 0.743583i | \(-0.733125\pi\) | ||||
−0.668643 | + | 0.743583i | \(0.733125\pi\) | |||||||
\(114\) | −964.253 | −0.792198 | ||||||||
\(115\) | −1769.65 | −1.43496 | ||||||||
\(116\) | −1390.62 | −1.11307 | ||||||||
\(117\) | 1019.04 | 0.805213 | ||||||||
\(118\) | 2481.21 | 1.93571 | ||||||||
\(119\) | −3367.14 | −2.59383 | ||||||||
\(120\) | −108.662 | −0.0826620 | ||||||||
\(121\) | −60.9081 | −0.0457611 | ||||||||
\(122\) | −370.485 | −0.274936 | ||||||||
\(123\) | 814.541 | 0.597112 | ||||||||
\(124\) | 1627.76 | 1.17885 | ||||||||
\(125\) | 1502.93 | 1.07541 | ||||||||
\(126\) | 1748.69 | 1.23639 | ||||||||
\(127\) | 130.605 | 0.0912546 | 0.0456273 | − | 0.998959i | \(-0.485471\pi\) | ||||
0.0456273 | + | 0.998959i | \(0.485471\pi\) | |||||||
\(128\) | −402.890 | −0.278209 | ||||||||
\(129\) | 930.604 | 0.635156 | ||||||||
\(130\) | −2621.06 | −1.76833 | ||||||||
\(131\) | −1228.07 | −0.819059 | −0.409529 | − | 0.912297i | \(-0.634307\pi\) | ||||
−0.409529 | + | 0.912297i | \(0.634307\pi\) | |||||||
\(132\) | 885.203 | 0.583690 | ||||||||
\(133\) | 2133.41 | 1.39090 | ||||||||
\(134\) | −1011.99 | −0.652407 | ||||||||
\(135\) | 1444.53 | 0.920927 | ||||||||
\(136\) | −357.550 | −0.225438 | ||||||||
\(137\) | −201.322 | −0.125548 | −0.0627739 | − | 0.998028i | \(-0.519995\pi\) | ||||
−0.0627739 | + | 0.998028i | \(0.519995\pi\) | |||||||
\(138\) | −2397.70 | −1.47903 | ||||||||
\(139\) | 2040.03 | 1.24484 | 0.622422 | − | 0.782682i | \(-0.286149\pi\) | ||||
0.622422 | + | 0.782682i | \(0.286149\pi\) | |||||||
\(140\) | −2128.70 | −1.28505 | ||||||||
\(141\) | −1971.49 | −1.17751 | ||||||||
\(142\) | 2114.74 | 1.24976 | ||||||||
\(143\) | −2411.52 | −1.41022 | ||||||||
\(144\) | 1051.70 | 0.608625 | ||||||||
\(145\) | 1922.83 | 1.10126 | ||||||||
\(146\) | −220.357 | −0.124910 | ||||||||
\(147\) | 1882.34 | 1.05614 | ||||||||
\(148\) | −1819.48 | −1.01054 | ||||||||
\(149\) | −3280.48 | −1.80368 | −0.901838 | − | 0.432074i | \(-0.857782\pi\) | ||||
−0.901838 | + | 0.432074i | \(0.857782\pi\) | |||||||
\(150\) | 352.987 | 0.192142 | ||||||||
\(151\) | 1152.01 | 0.620858 | 0.310429 | − | 0.950597i | \(-0.399527\pi\) | ||||
0.310429 | + | 0.950597i | \(0.399527\pi\) | |||||||
\(152\) | 226.542 | 0.120888 | ||||||||
\(153\) | 1701.90 | 0.899286 | ||||||||
\(154\) | −4138.22 | −2.16537 | ||||||||
\(155\) | −2250.74 | −1.16635 | ||||||||
\(156\) | −1680.73 | −0.862604 | ||||||||
\(157\) | −3328.26 | −1.69187 | −0.845936 | − | 0.533284i | \(-0.820958\pi\) | ||||
−0.845936 | + | 0.533284i | \(0.820958\pi\) | |||||||
\(158\) | −2348.10 | −1.18231 | ||||||||
\(159\) | 583.371 | 0.290970 | ||||||||
\(160\) | −2453.52 | −1.21230 | ||||||||
\(161\) | 5304.92 | 2.59681 | ||||||||
\(162\) | 372.542 | 0.180677 | ||||||||
\(163\) | 280.168 | 0.134628 | 0.0673142 | − | 0.997732i | \(-0.478557\pi\) | ||||
0.0673142 | + | 0.997732i | \(0.478557\pi\) | |||||||
\(164\) | 1694.43 | 0.806786 | ||||||||
\(165\) | −1223.99 | −0.577499 | ||||||||
\(166\) | 4837.95 | 2.26204 | ||||||||
\(167\) | 665.104 | 0.308188 | 0.154094 | − | 0.988056i | \(-0.450754\pi\) | ||||
0.154094 | + | 0.988056i | \(0.450754\pi\) | |||||||
\(168\) | 325.738 | 0.149591 | ||||||||
\(169\) | 2381.73 | 1.08408 | ||||||||
\(170\) | −4377.47 | −1.97492 | ||||||||
\(171\) | −1078.32 | −0.482230 | ||||||||
\(172\) | 1935.87 | 0.858189 | ||||||||
\(173\) | 1250.56 | 0.549587 | 0.274794 | − | 0.961503i | \(-0.411390\pi\) | ||||
0.274794 | + | 0.961503i | \(0.411390\pi\) | |||||||
\(174\) | 2605.25 | 1.13508 | ||||||||
\(175\) | −780.984 | −0.337353 | ||||||||
\(176\) | −2488.82 | −1.06592 | ||||||||
\(177\) | −2199.98 | −0.934241 | ||||||||
\(178\) | 1576.65 | 0.663903 | ||||||||
\(179\) | −2223.89 | −0.928609 | −0.464305 | − | 0.885676i | \(-0.653696\pi\) | ||||
−0.464305 | + | 0.885676i | \(0.653696\pi\) | |||||||
\(180\) | 1075.94 | 0.445532 | ||||||||
\(181\) | −1493.99 | −0.613520 | −0.306760 | − | 0.951787i | \(-0.599245\pi\) | ||||
−0.306760 | + | 0.951787i | \(0.599245\pi\) | |||||||
\(182\) | 7857.21 | 3.20008 | ||||||||
\(183\) | 328.492 | 0.132693 | ||||||||
\(184\) | 563.318 | 0.225698 | ||||||||
\(185\) | 2515.83 | 0.999826 | ||||||||
\(186\) | −3049.53 | −1.20216 | ||||||||
\(187\) | −4027.50 | −1.57497 | ||||||||
\(188\) | −4101.14 | −1.59099 | ||||||||
\(189\) | −4330.29 | −1.66657 | ||||||||
\(190\) | 2773.55 | 1.05902 | ||||||||
\(191\) | 2211.47 | 0.837780 | 0.418890 | − | 0.908037i | \(-0.362419\pi\) | ||||
0.418890 | + | 0.908037i | \(0.362419\pi\) | |||||||
\(192\) | −1393.76 | −0.523884 | ||||||||
\(193\) | −3108.68 | −1.15942 | −0.579710 | − | 0.814823i | \(-0.696834\pi\) | ||||
−0.579710 | + | 0.814823i | \(0.696834\pi\) | |||||||
\(194\) | 2432.28 | 0.900141 | ||||||||
\(195\) | 2323.98 | 0.853454 | ||||||||
\(196\) | 3915.69 | 1.42700 | ||||||||
\(197\) | 588.092 | 0.212689 | 0.106345 | − | 0.994329i | \(-0.466085\pi\) | ||||
0.106345 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(198\) | 2091.64 | 0.750740 | ||||||||
\(199\) | −2863.82 | −1.02015 | −0.510077 | − | 0.860129i | \(-0.670383\pi\) | ||||
−0.510077 | + | 0.860129i | \(0.670383\pi\) | |||||||
\(200\) | −82.9311 | −0.0293206 | ||||||||
\(201\) | 897.285 | 0.314874 | ||||||||
\(202\) | 7663.07 | 2.66917 | ||||||||
\(203\) | −5764.12 | −1.99292 | ||||||||
\(204\) | −2807.01 | −0.963382 | ||||||||
\(205\) | −2342.92 | −0.798229 | ||||||||
\(206\) | −3640.08 | −1.23115 | ||||||||
\(207\) | −2681.34 | −0.900321 | ||||||||
\(208\) | 4725.52 | 1.57527 | ||||||||
\(209\) | 2551.81 | 0.844558 | ||||||||
\(210\) | 3988.00 | 1.31047 | ||||||||
\(211\) | −579.519 | −0.189079 | −0.0945396 | − | 0.995521i | \(-0.530138\pi\) | ||||
−0.0945396 | + | 0.995521i | \(0.530138\pi\) | |||||||
\(212\) | 1213.54 | 0.393144 | ||||||||
\(213\) | −1875.05 | −0.603174 | ||||||||
\(214\) | 592.329 | 0.189209 | ||||||||
\(215\) | −2676.76 | −0.849087 | ||||||||
\(216\) | −459.824 | −0.144848 | ||||||||
\(217\) | 6747.08 | 2.11070 | ||||||||
\(218\) | 8560.45 | 2.65957 | ||||||||
\(219\) | 195.381 | 0.0602859 | ||||||||
\(220\) | −2546.17 | −0.780286 | ||||||||
\(221\) | 7647.00 | 2.32757 | ||||||||
\(222\) | 3408.71 | 1.03053 | ||||||||
\(223\) | 1754.27 | 0.526793 | 0.263396 | − | 0.964688i | \(-0.415157\pi\) | ||||
0.263396 | + | 0.964688i | \(0.415157\pi\) | |||||||
\(224\) | 7354.96 | 2.19386 | ||||||||
\(225\) | 394.745 | 0.116961 | ||||||||
\(226\) | 6260.30 | 1.84261 | ||||||||
\(227\) | 906.638 | 0.265091 | 0.132546 | − | 0.991177i | \(-0.457685\pi\) | ||||
0.132546 | + | 0.991177i | \(0.457685\pi\) | |||||||
\(228\) | 1778.51 | 0.516600 | ||||||||
\(229\) | 3291.34 | 0.949773 | 0.474886 | − | 0.880047i | \(-0.342489\pi\) | ||||
0.474886 | + | 0.880047i | \(0.342489\pi\) | |||||||
\(230\) | 6896.69 | 1.97719 | ||||||||
\(231\) | 3669.17 | 1.04508 | ||||||||
\(232\) | −612.080 | −0.173211 | ||||||||
\(233\) | 710.066 | 0.199648 | 0.0998240 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998240 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(234\) | −3971.39 | −1.10948 | ||||||||
\(235\) | 5670.72 | 1.57412 | ||||||||
\(236\) | −4576.46 | −1.26230 | ||||||||
\(237\) | 2081.95 | 0.570622 | ||||||||
\(238\) | 13122.4 | 3.57395 | ||||||||
\(239\) | 1172.59 | 0.317359 | 0.158679 | − | 0.987330i | \(-0.449276\pi\) | ||||
0.158679 | + | 0.987330i | \(0.449276\pi\) | |||||||
\(240\) | 2398.48 | 0.645088 | ||||||||
\(241\) | −4164.61 | −1.11314 | −0.556568 | − | 0.830802i | \(-0.687882\pi\) | ||||
−0.556568 | + | 0.830802i | \(0.687882\pi\) | |||||||
\(242\) | 237.371 | 0.0630528 | ||||||||
\(243\) | 3593.76 | 0.948723 | ||||||||
\(244\) | 683.339 | 0.179288 | ||||||||
\(245\) | −5414.30 | −1.41186 | ||||||||
\(246\) | −3174.43 | −0.822741 | ||||||||
\(247\) | −4845.11 | −1.24813 | ||||||||
\(248\) | 716.459 | 0.183448 | ||||||||
\(249\) | −4289.59 | −1.09173 | ||||||||
\(250\) | −5857.21 | −1.48177 | ||||||||
\(251\) | 5355.66 | 1.34680 | 0.673399 | − | 0.739279i | \(-0.264834\pi\) | ||||
0.673399 | + | 0.739279i | \(0.264834\pi\) | |||||||
\(252\) | −3225.36 | −0.806265 | ||||||||
\(253\) | 6345.32 | 1.57678 | ||||||||
\(254\) | −508.994 | −0.125737 | ||||||||
\(255\) | 3881.30 | 0.953163 | ||||||||
\(256\) | 4796.93 | 1.17112 | ||||||||
\(257\) | −899.111 | −0.218230 | −0.109115 | − | 0.994029i | \(-0.534802\pi\) | ||||
−0.109115 | + | 0.994029i | \(0.534802\pi\) | |||||||
\(258\) | −3626.75 | −0.875161 | ||||||||
\(259\) | −7541.76 | −1.80935 | ||||||||
\(260\) | 4834.41 | 1.15314 | ||||||||
\(261\) | 2913.44 | 0.690949 | ||||||||
\(262\) | 4786.02 | 1.12855 | ||||||||
\(263\) | −1950.08 | −0.457212 | −0.228606 | − | 0.973519i | \(-0.573417\pi\) | ||||
−0.228606 | + | 0.973519i | \(0.573417\pi\) | |||||||
\(264\) | 389.622 | 0.0908316 | ||||||||
\(265\) | −1677.99 | −0.388974 | ||||||||
\(266\) | −8314.32 | −1.91648 | ||||||||
\(267\) | −1397.94 | −0.320422 | ||||||||
\(268\) | 1866.56 | 0.425441 | ||||||||
\(269\) | 2126.86 | 0.482071 | 0.241035 | − | 0.970516i | \(-0.422513\pi\) | ||||
0.241035 | + | 0.970516i | \(0.422513\pi\) | |||||||
\(270\) | −5629.61 | −1.26892 | ||||||||
\(271\) | 1834.40 | 0.411188 | 0.205594 | − | 0.978637i | \(-0.434087\pi\) | ||||
0.205594 | + | 0.978637i | \(0.434087\pi\) | |||||||
\(272\) | 7892.14 | 1.75931 | ||||||||
\(273\) | −6966.63 | −1.54447 | ||||||||
\(274\) | 784.590 | 0.172988 | ||||||||
\(275\) | −934.150 | −0.204841 | ||||||||
\(276\) | 4422.43 | 0.964490 | ||||||||
\(277\) | 1157.49 | 0.251073 | 0.125536 | − | 0.992089i | \(-0.459935\pi\) | ||||
0.125536 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(278\) | −7950.42 | −1.71523 | ||||||||
\(279\) | −3410.28 | −0.731785 | ||||||||
\(280\) | −936.944 | −0.199975 | ||||||||
\(281\) | −1540.07 | −0.326949 | −0.163475 | − | 0.986548i | \(-0.552270\pi\) | ||||
−0.163475 | + | 0.986548i | \(0.552270\pi\) | |||||||
\(282\) | 7683.27 | 1.62245 | ||||||||
\(283\) | −7277.32 | −1.52859 | −0.764296 | − | 0.644865i | \(-0.776914\pi\) | ||||
−0.764296 | + | 0.644865i | \(0.776914\pi\) | |||||||
\(284\) | −3900.53 | −0.814978 | ||||||||
\(285\) | −2459.18 | −0.511120 | ||||||||
\(286\) | 9398.16 | 1.94309 | ||||||||
\(287\) | 7023.43 | 1.44453 | ||||||||
\(288\) | −3717.53 | −0.760616 | ||||||||
\(289\) | 7858.34 | 1.59950 | ||||||||
\(290\) | −7493.67 | −1.51739 | ||||||||
\(291\) | −2156.59 | −0.434438 | ||||||||
\(292\) | 406.437 | 0.0814551 | ||||||||
\(293\) | −3281.32 | −0.654256 | −0.327128 | − | 0.944980i | \(-0.606081\pi\) | ||||
−0.327128 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(294\) | −7335.84 | −1.45522 | ||||||||
\(295\) | 6327.96 | 1.24891 | ||||||||
\(296\) | −800.844 | −0.157257 | ||||||||
\(297\) | −5179.54 | −1.01194 | ||||||||
\(298\) | 12784.7 | 2.48523 | ||||||||
\(299\) | −12047.8 | −2.33024 | ||||||||
\(300\) | −651.065 | −0.125298 | ||||||||
\(301\) | 8024.18 | 1.53656 | ||||||||
\(302\) | −4489.63 | −0.855461 | ||||||||
\(303\) | −6794.49 | −1.28823 | ||||||||
\(304\) | −5000.44 | −0.943404 | ||||||||
\(305\) | −944.866 | −0.177386 | ||||||||
\(306\) | −6632.66 | −1.23910 | ||||||||
\(307\) | 4409.16 | 0.819688 | 0.409844 | − | 0.912156i | \(-0.365583\pi\) | ||||
0.409844 | + | 0.912156i | \(0.365583\pi\) | |||||||
\(308\) | 7632.71 | 1.41206 | ||||||||
\(309\) | 3227.50 | 0.594194 | ||||||||
\(310\) | 8771.58 | 1.60707 | ||||||||
\(311\) | −3722.70 | −0.678762 | −0.339381 | − | 0.940649i | \(-0.610218\pi\) | ||||
−0.339381 | + | 0.940649i | \(0.610218\pi\) | |||||||
\(312\) | −739.772 | −0.134235 | ||||||||
\(313\) | −6210.79 | −1.12158 | −0.560790 | − | 0.827958i | \(-0.689502\pi\) | ||||
−0.560790 | + | 0.827958i | \(0.689502\pi\) | |||||||
\(314\) | 12970.9 | 2.33118 | ||||||||
\(315\) | 4459.77 | 0.797713 | ||||||||
\(316\) | 4330.94 | 0.770995 | ||||||||
\(317\) | 2533.52 | 0.448885 | 0.224442 | − | 0.974487i | \(-0.427944\pi\) | ||||
0.224442 | + | 0.974487i | \(0.427944\pi\) | |||||||
\(318\) | −2273.51 | −0.400919 | ||||||||
\(319\) | −6894.57 | −1.21010 | ||||||||
\(320\) | 4008.97 | 0.700337 | ||||||||
\(321\) | −525.191 | −0.0913188 | ||||||||
\(322\) | −20674.3 | −3.57806 | ||||||||
\(323\) | −8091.88 | −1.39394 | ||||||||
\(324\) | −687.133 | −0.117821 | ||||||||
\(325\) | 1773.67 | 0.302724 | ||||||||
\(326\) | −1091.87 | −0.185500 | ||||||||
\(327\) | −7590.16 | −1.28360 | ||||||||
\(328\) | 745.803 | 0.125549 | ||||||||
\(329\) | −16999.2 | −2.84863 | ||||||||
\(330\) | 4770.12 | 0.795717 | ||||||||
\(331\) | 5686.83 | 0.944339 | 0.472170 | − | 0.881508i | \(-0.343471\pi\) | ||||
0.472170 | + | 0.881508i | \(0.343471\pi\) | |||||||
\(332\) | −8923.33 | −1.47509 | ||||||||
\(333\) | 3811.94 | 0.627307 | ||||||||
\(334\) | −2592.04 | −0.424642 | ||||||||
\(335\) | −2580.93 | −0.420928 | ||||||||
\(336\) | −7189.97 | −1.16740 | ||||||||
\(337\) | 1659.25 | 0.268205 | 0.134103 | − | 0.990967i | \(-0.457185\pi\) | ||||
0.134103 | + | 0.990967i | \(0.457185\pi\) | |||||||
\(338\) | −9282.09 | −1.49373 | ||||||||
\(339\) | −5550.72 | −0.889303 | ||||||||
\(340\) | 8074.00 | 1.28786 | ||||||||
\(341\) | 8070.32 | 1.28162 | ||||||||
\(342\) | 4202.43 | 0.664449 | ||||||||
\(343\) | 6010.86 | 0.946227 | ||||||||
\(344\) | 852.071 | 0.133548 | ||||||||
\(345\) | −6114.98 | −0.954259 | ||||||||
\(346\) | −4873.70 | −0.757259 | ||||||||
\(347\) | 107.939 | 0.0166988 | 0.00834939 | − | 0.999965i | \(-0.497342\pi\) | ||||
0.00834939 | + | 0.999965i | \(0.497342\pi\) | |||||||
\(348\) | −4805.24 | −0.740195 | ||||||||
\(349\) | 892.258 | 0.136852 | 0.0684262 | − | 0.997656i | \(-0.478202\pi\) | ||||
0.0684262 | + | 0.997656i | \(0.478202\pi\) | |||||||
\(350\) | 3043.65 | 0.464829 | ||||||||
\(351\) | 9834.36 | 1.49550 | ||||||||
\(352\) | 8797.41 | 1.33211 | ||||||||
\(353\) | 8396.01 | 1.26593 | 0.632966 | − | 0.774179i | \(-0.281837\pi\) | ||||
0.632966 | + | 0.774179i | \(0.281837\pi\) | |||||||
\(354\) | 8573.76 | 1.28726 | ||||||||
\(355\) | 5393.33 | 0.806334 | ||||||||
\(356\) | −2908.04 | −0.432938 | ||||||||
\(357\) | −11635.1 | −1.72491 | ||||||||
\(358\) | 8666.93 | 1.27950 | ||||||||
\(359\) | 5054.88 | 0.743138 | 0.371569 | − | 0.928405i | \(-0.378820\pi\) | ||||
0.371569 | + | 0.928405i | \(0.378820\pi\) | |||||||
\(360\) | 473.574 | 0.0693320 | ||||||||
\(361\) | −1732.01 | −0.252517 | ||||||||
\(362\) | 5822.36 | 0.845349 | ||||||||
\(363\) | −210.466 | −0.0304314 | ||||||||
\(364\) | −14492.2 | −2.08681 | ||||||||
\(365\) | −561.988 | −0.0805912 | ||||||||
\(366\) | −1280.20 | −0.182834 | ||||||||
\(367\) | 6389.49 | 0.908798 | 0.454399 | − | 0.890798i | \(-0.349854\pi\) | ||||
0.454399 | + | 0.890798i | \(0.349854\pi\) | |||||||
\(368\) | −12434.0 | −1.76133 | ||||||||
\(369\) | −3549.96 | −0.500822 | ||||||||
\(370\) | −9804.70 | −1.37763 | ||||||||
\(371\) | 5030.14 | 0.703914 | ||||||||
\(372\) | 5624.69 | 0.783942 | ||||||||
\(373\) | −4305.83 | −0.597714 | −0.298857 | − | 0.954298i | \(-0.596605\pi\) | ||||
−0.298857 | + | 0.954298i | \(0.596605\pi\) | |||||||
\(374\) | 15696.0 | 2.17011 | ||||||||
\(375\) | 5193.32 | 0.715152 | ||||||||
\(376\) | −1805.11 | −0.247584 | ||||||||
\(377\) | 13090.7 | 1.78834 | ||||||||
\(378\) | 16876.0 | 2.29632 | ||||||||
\(379\) | 10177.6 | 1.37938 | 0.689692 | − | 0.724103i | \(-0.257746\pi\) | ||||
0.689692 | + | 0.724103i | \(0.257746\pi\) | |||||||
\(380\) | −5115.66 | −0.690600 | ||||||||
\(381\) | 451.302 | 0.0606848 | ||||||||
\(382\) | −8618.52 | −1.15435 | ||||||||
\(383\) | 4254.81 | 0.567652 | 0.283826 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283826 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(384\) | −1392.17 | −0.185011 | ||||||||
\(385\) | −10553.9 | −1.39708 | ||||||||
\(386\) | 12115.2 | 1.59753 | ||||||||
\(387\) | −4055.78 | −0.532731 | ||||||||
\(388\) | −4486.20 | −0.586990 | ||||||||
\(389\) | 13055.6 | 1.70166 | 0.850832 | − | 0.525437i | \(-0.176098\pi\) | ||||
0.850832 | + | 0.525437i | \(0.176098\pi\) | |||||||
\(390\) | −9057.01 | −1.17595 | ||||||||
\(391\) | −20121.2 | −2.60249 | ||||||||
\(392\) | 1723.49 | 0.222064 | ||||||||
\(393\) | −4243.55 | −0.544679 | ||||||||
\(394\) | −2291.91 | −0.293058 | ||||||||
\(395\) | −5988.47 | −0.762817 | ||||||||
\(396\) | −3857.92 | −0.489565 | ||||||||
\(397\) | −5512.97 | −0.696947 | −0.348473 | − | 0.937319i | \(-0.613300\pi\) | ||||
−0.348473 | + | 0.937319i | \(0.613300\pi\) | |||||||
\(398\) | 11160.9 | 1.40564 | ||||||||
\(399\) | 7371.93 | 0.924958 | ||||||||
\(400\) | 1830.53 | 0.228816 | ||||||||
\(401\) | −2561.08 | −0.318938 | −0.159469 | − | 0.987203i | \(-0.550978\pi\) | ||||
−0.159469 | + | 0.987203i | \(0.550978\pi\) | |||||||
\(402\) | −3496.90 | −0.433854 | ||||||||
\(403\) | −15323.1 | −1.89404 | ||||||||
\(404\) | −14134.1 | −1.74059 | ||||||||
\(405\) | 950.111 | 0.116571 | ||||||||
\(406\) | 22463.9 | 2.74597 | ||||||||
\(407\) | −9020.84 | −1.09864 | ||||||||
\(408\) | −1235.50 | −0.149918 | ||||||||
\(409\) | −8140.79 | −0.984196 | −0.492098 | − | 0.870540i | \(-0.663770\pi\) | ||||
−0.492098 | + | 0.870540i | \(0.663770\pi\) | |||||||
\(410\) | 9130.84 | 1.09985 | ||||||||
\(411\) | −695.661 | −0.0834900 | ||||||||
\(412\) | 6713.93 | 0.802844 | ||||||||
\(413\) | −18969.4 | −2.26011 | ||||||||
\(414\) | 10449.7 | 1.24052 | ||||||||
\(415\) | 12338.5 | 1.45945 | ||||||||
\(416\) | −16703.6 | −1.96866 | ||||||||
\(417\) | 7049.28 | 0.827829 | ||||||||
\(418\) | −9944.92 | −1.16369 | ||||||||
\(419\) | −6967.71 | −0.812398 | −0.406199 | − | 0.913785i | \(-0.633146\pi\) | ||||
−0.406199 | + | 0.913785i | \(0.633146\pi\) | |||||||
\(420\) | −7355.65 | −0.854568 | ||||||||
\(421\) | −11309.5 | −1.30924 | −0.654622 | − | 0.755956i | \(-0.727172\pi\) | ||||
−0.654622 | + | 0.755956i | \(0.727172\pi\) | |||||||
\(422\) | 2258.50 | 0.260526 | ||||||||
\(423\) | 8592.18 | 0.987627 | ||||||||
\(424\) | 534.141 | 0.0611796 | ||||||||
\(425\) | 2962.22 | 0.338091 | ||||||||
\(426\) | 7307.44 | 0.831095 | ||||||||
\(427\) | 2832.44 | 0.321011 | ||||||||
\(428\) | −1092.52 | −0.123385 | ||||||||
\(429\) | −8332.92 | −0.937803 | ||||||||
\(430\) | 10431.9 | 1.16993 | ||||||||
\(431\) | −405.096 | −0.0452733 | −0.0226367 | − | 0.999744i | \(-0.507206\pi\) | ||||
−0.0226367 | + | 0.999744i | \(0.507206\pi\) | |||||||
\(432\) | 10149.6 | 1.13038 | ||||||||
\(433\) | −820.746 | −0.0910913 | −0.0455457 | − | 0.998962i | \(-0.514503\pi\) | ||||
−0.0455457 | + | 0.998962i | \(0.514503\pi\) | |||||||
\(434\) | −26294.7 | −2.90827 | ||||||||
\(435\) | 6644.30 | 0.732344 | ||||||||
\(436\) | −15789.3 | −1.73433 | ||||||||
\(437\) | 12748.7 | 1.39555 | ||||||||
\(438\) | −761.438 | −0.0830660 | ||||||||
\(439\) | −1206.67 | −0.131188 | −0.0655938 | − | 0.997846i | \(-0.520894\pi\) | ||||
−0.0655938 | + | 0.997846i | \(0.520894\pi\) | |||||||
\(440\) | −1120.70 | −0.121425 | ||||||||
\(441\) | −8203.65 | −0.885827 | ||||||||
\(442\) | −29801.9 | −3.20708 | ||||||||
\(443\) | 14106.9 | 1.51295 | 0.756476 | − | 0.654021i | \(-0.226919\pi\) | ||||
0.756476 | + | 0.654021i | \(0.226919\pi\) | |||||||
\(444\) | −6287.17 | −0.672018 | ||||||||
\(445\) | 4021.00 | 0.428346 | ||||||||
\(446\) | −6836.75 | −0.725851 | ||||||||
\(447\) | −11335.6 | −1.19945 | ||||||||
\(448\) | −12017.8 | −1.26738 | ||||||||
\(449\) | 3882.59 | 0.408086 | 0.204043 | − | 0.978962i | \(-0.434592\pi\) | ||||
0.204043 | + | 0.978962i | \(0.434592\pi\) | |||||||
\(450\) | −1538.40 | −0.161157 | ||||||||
\(451\) | 8400.86 | 0.877119 | ||||||||
\(452\) | −11546.8 | −1.20158 | ||||||||
\(453\) | 3980.75 | 0.412874 | ||||||||
\(454\) | −3533.35 | −0.365261 | ||||||||
\(455\) | 20038.6 | 2.06467 | ||||||||
\(456\) | 782.810 | 0.0803913 | ||||||||
\(457\) | −2328.16 | −0.238308 | −0.119154 | − | 0.992876i | \(-0.538018\pi\) | ||||
−0.119154 | + | 0.992876i | \(0.538018\pi\) | |||||||
\(458\) | −12827.0 | −1.30866 | ||||||||
\(459\) | 16424.5 | 1.67022 | ||||||||
\(460\) | −12720.6 | −1.28935 | ||||||||
\(461\) | −1481.31 | −0.149656 | −0.0748281 | − | 0.997196i | \(-0.523841\pi\) | ||||
−0.0748281 | + | 0.997196i | \(0.523841\pi\) | |||||||
\(462\) | −14299.5 | −1.43998 | ||||||||
\(463\) | −6262.08 | −0.628561 | −0.314280 | − | 0.949330i | \(-0.601763\pi\) | ||||
−0.314280 | + | 0.949330i | \(0.601763\pi\) | |||||||
\(464\) | 13510.3 | 1.35173 | ||||||||
\(465\) | −7777.36 | −0.775627 | ||||||||
\(466\) | −2767.27 | −0.275089 | ||||||||
\(467\) | −11953.6 | −1.18447 | −0.592234 | − | 0.805766i | \(-0.701754\pi\) | ||||
−0.592234 | + | 0.805766i | \(0.701754\pi\) | |||||||
\(468\) | 7325.01 | 0.723501 | ||||||||
\(469\) | 7736.89 | 0.761741 | ||||||||
\(470\) | −22099.9 | −2.16892 | ||||||||
\(471\) | −11500.7 | −1.12510 | ||||||||
\(472\) | −2014.33 | −0.196434 | ||||||||
\(473\) | 9597.88 | 0.933004 | ||||||||
\(474\) | −8113.79 | −0.786242 | ||||||||
\(475\) | −1876.85 | −0.181297 | ||||||||
\(476\) | −24203.6 | −2.33061 | ||||||||
\(477\) | −2542.46 | −0.244049 | ||||||||
\(478\) | −4569.83 | −0.437278 | ||||||||
\(479\) | −7020.73 | −0.669698 | −0.334849 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334849 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(480\) | −8478.06 | −0.806185 | ||||||||
\(481\) | 17127.8 | 1.62362 | ||||||||
\(482\) | 16230.3 | 1.53376 | ||||||||
\(483\) | 18331.0 | 1.72689 | ||||||||
\(484\) | −437.817 | −0.0411173 | ||||||||
\(485\) | 6203.15 | 0.580764 | ||||||||
\(486\) | −14005.6 | −1.30722 | ||||||||
\(487\) | 2152.74 | 0.200308 | 0.100154 | − | 0.994972i | \(-0.468066\pi\) | ||||
0.100154 | + | 0.994972i | \(0.468066\pi\) | |||||||
\(488\) | 300.771 | 0.0279001 | ||||||||
\(489\) | 968.112 | 0.0895287 | ||||||||
\(490\) | 21100.6 | 1.94536 | ||||||||
\(491\) | −15458.2 | −1.42082 | −0.710408 | − | 0.703790i | \(-0.751490\pi\) | ||||
−0.710408 | + | 0.703790i | \(0.751490\pi\) | |||||||
\(492\) | 5855.06 | 0.536517 | ||||||||
\(493\) | 21862.9 | 1.99727 | ||||||||
\(494\) | 18882.4 | 1.71975 | ||||||||
\(495\) | 5334.42 | 0.484372 | ||||||||
\(496\) | −15814.3 | −1.43162 | ||||||||
\(497\) | −16167.7 | −1.45920 | ||||||||
\(498\) | 16717.4 | 1.50427 | ||||||||
\(499\) | 8252.41 | 0.740338 | 0.370169 | − | 0.928964i | \(-0.379300\pi\) | ||||
0.370169 | + | 0.928964i | \(0.379300\pi\) | |||||||
\(500\) | 10803.3 | 0.966277 | ||||||||
\(501\) | 2298.25 | 0.204946 | ||||||||
\(502\) | −20872.1 | −1.85571 | ||||||||
\(503\) | 5936.35 | 0.526220 | 0.263110 | − | 0.964766i | \(-0.415252\pi\) | ||||
0.263110 | + | 0.964766i | \(0.415252\pi\) | |||||||
\(504\) | −1419.64 | −0.125468 | ||||||||
\(505\) | 19543.5 | 1.72213 | ||||||||
\(506\) | −24729.0 | −2.17260 | ||||||||
\(507\) | 8230.01 | 0.720922 | ||||||||
\(508\) | 938.812 | 0.0819942 | ||||||||
\(509\) | 6924.41 | 0.602985 | 0.301492 | − | 0.953469i | \(-0.402515\pi\) | ||||
0.301492 | + | 0.953469i | \(0.402515\pi\) | |||||||
\(510\) | −15126.2 | −1.31333 | ||||||||
\(511\) | 1684.68 | 0.145843 | ||||||||
\(512\) | −15471.5 | −1.33545 | ||||||||
\(513\) | −10406.5 | −0.895630 | ||||||||
\(514\) | 3504.01 | 0.300692 | ||||||||
\(515\) | −9283.48 | −0.794328 | ||||||||
\(516\) | 6689.34 | 0.570701 | ||||||||
\(517\) | −20333.1 | −1.72969 | ||||||||
\(518\) | 29391.7 | 2.49305 | ||||||||
\(519\) | 4321.28 | 0.365478 | ||||||||
\(520\) | 2127.86 | 0.179448 | ||||||||
\(521\) | 14323.1 | 1.20443 | 0.602215 | − | 0.798334i | \(-0.294285\pi\) | ||||
0.602215 | + | 0.798334i | \(0.294285\pi\) | |||||||
\(522\) | −11354.3 | −0.952037 | ||||||||
\(523\) | −3168.12 | −0.264880 | −0.132440 | − | 0.991191i | \(-0.542281\pi\) | ||||
−0.132440 | + | 0.991191i | \(0.542281\pi\) | |||||||
\(524\) | −8827.55 | −0.735941 | ||||||||
\(525\) | −2698.67 | −0.224342 | ||||||||
\(526\) | 7599.84 | 0.629979 | ||||||||
\(527\) | −25591.2 | −2.11532 | ||||||||
\(528\) | −8600.06 | −0.708844 | ||||||||
\(529\) | 19533.9 | 1.60548 | ||||||||
\(530\) | 6539.47 | 0.535955 | ||||||||
\(531\) | 9588.01 | 0.783586 | ||||||||
\(532\) | 15335.3 | 1.24976 | ||||||||
\(533\) | −15950.7 | −1.29625 | ||||||||
\(534\) | 5448.06 | 0.441499 | ||||||||
\(535\) | 1510.65 | 0.122076 | ||||||||
\(536\) | 821.564 | 0.0662055 | ||||||||
\(537\) | −7684.57 | −0.617530 | ||||||||
\(538\) | −8288.81 | −0.664230 | ||||||||
\(539\) | 19413.7 | 1.55140 | ||||||||
\(540\) | 10383.5 | 0.827472 | ||||||||
\(541\) | 8148.79 | 0.647585 | 0.323793 | − | 0.946128i | \(-0.395042\pi\) | ||||
0.323793 | + | 0.946128i | \(0.395042\pi\) | |||||||
\(542\) | −7149.03 | −0.566563 | ||||||||
\(543\) | −5162.42 | −0.407994 | ||||||||
\(544\) | −27896.9 | −2.19865 | ||||||||
\(545\) | 21832.1 | 1.71594 | ||||||||
\(546\) | 27150.4 | 2.12807 | ||||||||
\(547\) | 547.000 | 0.0427569 | ||||||||
\(548\) | −1447.13 | −0.112807 | ||||||||
\(549\) | −1431.64 | −0.111295 | ||||||||
\(550\) | 3640.57 | 0.282244 | ||||||||
\(551\) | −13852.3 | −1.07101 | ||||||||
\(552\) | 1946.53 | 0.150090 | ||||||||
\(553\) | 17951.8 | 1.38045 | ||||||||
\(554\) | −4510.99 | −0.345945 | ||||||||
\(555\) | 8693.39 | 0.664890 | ||||||||
\(556\) | 14664.1 | 1.11852 | ||||||||
\(557\) | −18207.3 | −1.38504 | −0.692520 | − | 0.721399i | \(-0.743500\pi\) | ||||
−0.692520 | + | 0.721399i | \(0.743500\pi\) | |||||||
\(558\) | 13290.5 | 1.00830 | ||||||||
\(559\) | −18223.4 | −1.37884 | ||||||||
\(560\) | 20681.0 | 1.56059 | ||||||||
\(561\) | −13916.9 | −1.04737 | ||||||||
\(562\) | 6001.95 | 0.450493 | ||||||||
\(563\) | 25323.1 | 1.89563 | 0.947816 | − | 0.318818i | \(-0.103286\pi\) | ||||
0.947816 | + | 0.318818i | \(0.103286\pi\) | |||||||
\(564\) | −14171.4 | −1.05802 | ||||||||
\(565\) | 15965.9 | 1.18884 | ||||||||
\(566\) | 28361.2 | 2.10620 | ||||||||
\(567\) | −2848.17 | −0.210955 | ||||||||
\(568\) | −1716.81 | −0.126824 | ||||||||
\(569\) | 5359.03 | 0.394837 | 0.197419 | − | 0.980319i | \(-0.436744\pi\) | ||||
0.197419 | + | 0.980319i | \(0.436744\pi\) | |||||||
\(570\) | 9583.92 | 0.704257 | ||||||||
\(571\) | 6668.17 | 0.488712 | 0.244356 | − | 0.969686i | \(-0.421424\pi\) | ||||
0.244356 | + | 0.969686i | \(0.421424\pi\) | |||||||
\(572\) | −17334.4 | −1.26711 | ||||||||
\(573\) | 7641.65 | 0.557129 | ||||||||
\(574\) | −27371.7 | −1.99037 | ||||||||
\(575\) | −4666.97 | −0.338480 | ||||||||
\(576\) | 6074.31 | 0.439403 | ||||||||
\(577\) | −7081.74 | −0.510948 | −0.255474 | − | 0.966816i | \(-0.582231\pi\) | ||||
−0.255474 | + | 0.966816i | \(0.582231\pi\) | |||||||
\(578\) | −30625.5 | −2.20390 | ||||||||
\(579\) | −10742.0 | −0.771020 | ||||||||
\(580\) | 13821.7 | 0.989506 | ||||||||
\(581\) | −36987.2 | −2.64112 | ||||||||
\(582\) | 8404.66 | 0.598599 | ||||||||
\(583\) | 6016.65 | 0.427417 | ||||||||
\(584\) | 178.893 | 0.0126757 | ||||||||
\(585\) | −10128.4 | −0.715827 | ||||||||
\(586\) | 12788.0 | 0.901478 | ||||||||
\(587\) | −21128.1 | −1.48561 | −0.742803 | − | 0.669510i | \(-0.766504\pi\) | ||||
−0.742803 | + | 0.669510i | \(0.766504\pi\) | |||||||
\(588\) | 13530.5 | 0.948963 | ||||||||
\(589\) | 16214.5 | 1.13431 | ||||||||
\(590\) | −24661.3 | −1.72083 | ||||||||
\(591\) | 2032.13 | 0.141440 | ||||||||
\(592\) | 17676.9 | 1.22722 | ||||||||
\(593\) | −27207.3 | −1.88410 | −0.942050 | − | 0.335474i | \(-0.891104\pi\) | ||||
−0.942050 | + | 0.335474i | \(0.891104\pi\) | |||||||
\(594\) | 20185.7 | 1.39433 | ||||||||
\(595\) | 33466.7 | 2.30589 | ||||||||
\(596\) | −23580.7 | −1.62064 | ||||||||
\(597\) | −9895.84 | −0.678408 | ||||||||
\(598\) | 46952.8 | 3.21077 | ||||||||
\(599\) | 17939.7 | 1.22370 | 0.611850 | − | 0.790974i | \(-0.290426\pi\) | ||||
0.611850 | + | 0.790974i | \(0.290426\pi\) | |||||||
\(600\) | −286.566 | −0.0194983 | ||||||||
\(601\) | 25217.0 | 1.71152 | 0.855758 | − | 0.517375i | \(-0.173091\pi\) | ||||
0.855758 | + | 0.517375i | \(0.173091\pi\) | |||||||
\(602\) | −31271.8 | −2.11718 | ||||||||
\(603\) | −3910.57 | −0.264098 | ||||||||
\(604\) | 8280.87 | 0.557854 | ||||||||
\(605\) | 605.378 | 0.0406812 | ||||||||
\(606\) | 26479.5 | 1.77501 | ||||||||
\(607\) | −21271.4 | −1.42237 | −0.711185 | − | 0.703004i | \(-0.751841\pi\) | ||||
−0.711185 | + | 0.703004i | \(0.751841\pi\) | |||||||
\(608\) | 17675.4 | 1.17900 | ||||||||
\(609\) | −19917.7 | −1.32530 | ||||||||
\(610\) | 3682.33 | 0.244415 | ||||||||
\(611\) | 38606.4 | 2.55621 | ||||||||
\(612\) | 12233.6 | 0.808028 | ||||||||
\(613\) | −2331.98 | −0.153651 | −0.0768253 | − | 0.997045i | \(-0.524478\pi\) | ||||
−0.0768253 | + | 0.997045i | \(0.524478\pi\) | |||||||
\(614\) | −17183.4 | −1.12942 | ||||||||
\(615\) | −8095.90 | −0.530827 | ||||||||
\(616\) | 3359.53 | 0.219739 | ||||||||
\(617\) | −4293.64 | −0.280155 | −0.140077 | − | 0.990141i | \(-0.544735\pi\) | ||||
−0.140077 | + | 0.990141i | \(0.544735\pi\) | |||||||
\(618\) | −12578.2 | −0.818721 | ||||||||
\(619\) | −19118.3 | −1.24141 | −0.620704 | − | 0.784045i | \(-0.713153\pi\) | ||||
−0.620704 | + | 0.784045i | \(0.713153\pi\) | |||||||
\(620\) | −16178.7 | −1.04799 | ||||||||
\(621\) | −25876.7 | −1.67214 | ||||||||
\(622\) | 14508.1 | 0.935245 | ||||||||
\(623\) | −12053.8 | −0.775163 | ||||||||
\(624\) | 16328.9 | 1.04756 | ||||||||
\(625\) | −11661.4 | −0.746332 | ||||||||
\(626\) | 24204.7 | 1.54539 | ||||||||
\(627\) | 8817.71 | 0.561636 | ||||||||
\(628\) | −23924.1 | −1.52018 | ||||||||
\(629\) | 28605.4 | 1.81331 | ||||||||
\(630\) | −17380.6 | −1.09914 | ||||||||
\(631\) | −5338.95 | −0.336831 | −0.168415 | − | 0.985716i | \(-0.553865\pi\) | ||||
−0.168415 | + | 0.985716i | \(0.553865\pi\) | |||||||
\(632\) | 1906.26 | 0.119979 | ||||||||
\(633\) | −2002.51 | −0.125739 | ||||||||
\(634\) | −9873.62 | −0.618504 | ||||||||
\(635\) | −1298.11 | −0.0811245 | ||||||||
\(636\) | 4193.37 | 0.261443 | ||||||||
\(637\) | −36860.6 | −2.29273 | ||||||||
\(638\) | 26869.5 | 1.66736 | ||||||||
\(639\) | 8171.88 | 0.505907 | ||||||||
\(640\) | 4004.41 | 0.247325 | ||||||||
\(641\) | −6625.69 | −0.408267 | −0.204134 | − | 0.978943i | \(-0.565438\pi\) | ||||
−0.204134 | + | 0.978943i | \(0.565438\pi\) | |||||||
\(642\) | 2046.78 | 0.125825 | ||||||||
\(643\) | 24100.7 | 1.47813 | 0.739067 | − | 0.673632i | \(-0.235267\pi\) | ||||
0.739067 | + | 0.673632i | \(0.235267\pi\) | |||||||
\(644\) | 38132.7 | 2.33329 | ||||||||
\(645\) | −9249.47 | −0.564647 | ||||||||
\(646\) | 31535.7 | 1.92067 | ||||||||
\(647\) | −2466.44 | −0.149870 | −0.0749349 | − | 0.997188i | \(-0.523875\pi\) | ||||
−0.0749349 | + | 0.997188i | \(0.523875\pi\) | |||||||
\(648\) | −302.441 | −0.0183349 | ||||||||
\(649\) | −22689.7 | −1.37234 | ||||||||
\(650\) | −6912.33 | −0.417114 | ||||||||
\(651\) | 23314.3 | 1.40363 | ||||||||
\(652\) | 2013.89 | 0.120967 | ||||||||
\(653\) | −31485.7 | −1.88688 | −0.943440 | − | 0.331544i | \(-0.892431\pi\) | ||||
−0.943440 | + | 0.331544i | \(0.892431\pi\) | |||||||
\(654\) | 29580.4 | 1.76863 | ||||||||
\(655\) | 12206.0 | 0.728135 | ||||||||
\(656\) | −16462.0 | −0.979776 | ||||||||
\(657\) | −851.513 | −0.0505642 | ||||||||
\(658\) | 66249.4 | 3.92503 | ||||||||
\(659\) | 14179.6 | 0.838175 | 0.419088 | − | 0.907946i | \(-0.362350\pi\) | ||||
0.419088 | + | 0.907946i | \(0.362350\pi\) | |||||||
\(660\) | −8798.23 | −0.518895 | ||||||||
\(661\) | 22865.9 | 1.34551 | 0.672754 | − | 0.739866i | \(-0.265111\pi\) | ||||
0.672754 | + | 0.739866i | \(0.265111\pi\) | |||||||
\(662\) | −22162.7 | −1.30118 | ||||||||
\(663\) | 26424.0 | 1.54785 | ||||||||
\(664\) | −3927.60 | −0.229549 | ||||||||
\(665\) | −21204.4 | −1.23650 | ||||||||
\(666\) | −14855.9 | −0.864347 | ||||||||
\(667\) | −34444.9 | −1.99957 | ||||||||
\(668\) | 4780.88 | 0.276913 | ||||||||
\(669\) | 6061.84 | 0.350320 | ||||||||
\(670\) | 10058.4 | 0.579984 | ||||||||
\(671\) | 3387.94 | 0.194918 | ||||||||
\(672\) | 25414.8 | 1.45893 | ||||||||
\(673\) | 31403.4 | 1.79868 | 0.899341 | − | 0.437248i | \(-0.144047\pi\) | ||||
0.899341 | + | 0.437248i | \(0.144047\pi\) | |||||||
\(674\) | −6466.44 | −0.369552 | ||||||||
\(675\) | 3809.54 | 0.217229 | ||||||||
\(676\) | 17120.3 | 0.974073 | ||||||||
\(677\) | −31721.6 | −1.80083 | −0.900414 | − | 0.435033i | \(-0.856737\pi\) | ||||
−0.900414 | + | 0.435033i | \(0.856737\pi\) | |||||||
\(678\) | 21632.3 | 1.22534 | ||||||||
\(679\) | −18595.3 | −1.05099 | ||||||||
\(680\) | 3553.76 | 0.200413 | ||||||||
\(681\) | 3132.86 | 0.176287 | ||||||||
\(682\) | −31451.6 | −1.76590 | ||||||||
\(683\) | 15444.2 | 0.865238 | 0.432619 | − | 0.901577i | \(-0.357590\pi\) | ||||
0.432619 | + | 0.901577i | \(0.357590\pi\) | |||||||
\(684\) | −7751.16 | −0.433294 | ||||||||
\(685\) | 2000.98 | 0.111611 | ||||||||
\(686\) | −23425.5 | −1.30378 | ||||||||
\(687\) | 11373.1 | 0.631604 | ||||||||
\(688\) | −18807.6 | −1.04220 | ||||||||
\(689\) | −11423.8 | −0.631657 | ||||||||
\(690\) | 23831.3 | 1.31484 | ||||||||
\(691\) | −24734.6 | −1.36172 | −0.680861 | − | 0.732413i | \(-0.738394\pi\) | ||||
−0.680861 | + | 0.732413i | \(0.738394\pi\) | |||||||
\(692\) | 8989.26 | 0.493816 | ||||||||
\(693\) | −15991.1 | −0.876552 | ||||||||
\(694\) | −420.661 | −0.0230087 | ||||||||
\(695\) | −20276.3 | −1.10666 | ||||||||
\(696\) | −2115.02 | −0.115186 | ||||||||
\(697\) | −26639.4 | −1.44769 | ||||||||
\(698\) | −3477.31 | −0.188564 | ||||||||
\(699\) | 2453.61 | 0.132767 | ||||||||
\(700\) | −5613.85 | −0.303119 | ||||||||
\(701\) | 25510.2 | 1.37448 | 0.687238 | − | 0.726433i | \(-0.258823\pi\) | ||||
0.687238 | + | 0.726433i | \(0.258823\pi\) | |||||||
\(702\) | −38326.5 | −2.06060 | ||||||||
\(703\) | −18124.3 | −0.972362 | ||||||||
\(704\) | −14374.7 | −0.769553 | ||||||||
\(705\) | 19595.0 | 1.04680 | ||||||||
\(706\) | −32720.9 | −1.74429 | ||||||||
\(707\) | −58585.9 | −3.11648 | ||||||||
\(708\) | −15813.8 | −0.839435 | ||||||||
\(709\) | 3299.69 | 0.174785 | 0.0873924 | − | 0.996174i | \(-0.472147\pi\) | ||||
0.0873924 | + | 0.996174i | \(0.472147\pi\) | |||||||
\(710\) | −21018.9 | −1.11102 | ||||||||
\(711\) | −9073.63 | −0.478604 | ||||||||
\(712\) | −1279.97 | −0.0673721 | ||||||||
\(713\) | 40318.9 | 2.11775 | ||||||||
\(714\) | 45344.1 | 2.37670 | ||||||||
\(715\) | 23968.6 | 1.25367 | ||||||||
\(716\) | −15985.7 | −0.834375 | ||||||||
\(717\) | 4051.86 | 0.211045 | ||||||||
\(718\) | −19699.9 | −1.02395 | ||||||||
\(719\) | 36828.1 | 1.91023 | 0.955117 | − | 0.296230i | \(-0.0957294\pi\) | ||||
0.955117 | + | 0.296230i | \(0.0957294\pi\) | |||||||
\(720\) | −10453.1 | −0.541062 | ||||||||
\(721\) | 27829.3 | 1.43747 | ||||||||
\(722\) | 6749.99 | 0.347935 | ||||||||
\(723\) | −14390.7 | −0.740242 | ||||||||
\(724\) | −10739.0 | −0.551260 | ||||||||
\(725\) | 5070.95 | 0.259766 | ||||||||
\(726\) | 820.228 | 0.0419305 | ||||||||
\(727\) | −18832.9 | −0.960759 | −0.480380 | − | 0.877061i | \(-0.659501\pi\) | ||||
−0.480380 | + | 0.877061i | \(0.659501\pi\) | |||||||
\(728\) | −6378.73 | −0.324741 | ||||||||
\(729\) | 14999.1 | 0.762034 | ||||||||
\(730\) | 2190.18 | 0.111044 | ||||||||
\(731\) | −30435.2 | −1.53993 | ||||||||
\(732\) | 2361.26 | 0.119228 | ||||||||
\(733\) | 28389.7 | 1.43055 | 0.715277 | − | 0.698841i | \(-0.246300\pi\) | ||||
0.715277 | + | 0.698841i | \(0.246300\pi\) | |||||||
\(734\) | −24901.1 | −1.25220 | ||||||||
\(735\) | −18708.9 | −0.938898 | ||||||||
\(736\) | 43951.4 | 2.20118 | ||||||||
\(737\) | 9254.24 | 0.462530 | ||||||||
\(738\) | 13834.9 | 0.690067 | ||||||||
\(739\) | 20926.6 | 1.04168 | 0.520838 | − | 0.853655i | \(-0.325619\pi\) | ||||
0.520838 | + | 0.853655i | \(0.325619\pi\) | |||||||
\(740\) | 18084.2 | 0.898364 | ||||||||
\(741\) | −16742.1 | −0.830011 | ||||||||
\(742\) | −19603.5 | −0.969901 | ||||||||
\(743\) | 3593.16 | 0.177416 | 0.0887081 | − | 0.996058i | \(-0.471726\pi\) | ||||
0.0887081 | + | 0.996058i | \(0.471726\pi\) | |||||||
\(744\) | 2475.70 | 0.121994 | ||||||||
\(745\) | 32605.5 | 1.60345 | ||||||||
\(746\) | 16780.7 | 0.823571 | ||||||||
\(747\) | 18695.0 | 0.915682 | ||||||||
\(748\) | −28950.4 | −1.41515 | ||||||||
\(749\) | −4528.49 | −0.220918 | ||||||||
\(750\) | −20239.4 | −0.985386 | ||||||||
\(751\) | 26375.6 | 1.28157 | 0.640786 | − | 0.767719i | \(-0.278608\pi\) | ||||
0.640786 | + | 0.767719i | \(0.278608\pi\) | |||||||
\(752\) | 39844.0 | 1.93213 | ||||||||
\(753\) | 18506.3 | 0.895628 | ||||||||
\(754\) | −51017.0 | −2.46410 | ||||||||
\(755\) | −11450.1 | −0.551937 | ||||||||
\(756\) | −31126.8 | −1.49745 | ||||||||
\(757\) | 19750.9 | 0.948294 | 0.474147 | − | 0.880446i | \(-0.342757\pi\) | ||||
0.474147 | + | 0.880446i | \(0.342757\pi\) | |||||||
\(758\) | −39664.0 | −1.90061 | ||||||||
\(759\) | 21926.1 | 1.04857 | ||||||||
\(760\) | −2251.65 | −0.107469 | ||||||||
\(761\) | 7056.82 | 0.336149 | 0.168075 | − | 0.985774i | \(-0.446245\pi\) | ||||
0.168075 | + | 0.985774i | \(0.446245\pi\) | |||||||
\(762\) | −1758.82 | −0.0836157 | ||||||||
\(763\) | −65446.6 | −3.10528 | ||||||||
\(764\) | 15896.4 | 0.752763 | ||||||||
\(765\) | −16915.6 | −0.799457 | ||||||||
\(766\) | −16581.8 | −0.782149 | ||||||||
\(767\) | 43080.8 | 2.02811 | ||||||||
\(768\) | 16575.6 | 0.778805 | ||||||||
\(769\) | −5780.19 | −0.271052 | −0.135526 | − | 0.990774i | \(-0.543272\pi\) | ||||
−0.135526 | + | 0.990774i | \(0.543272\pi\) | |||||||
\(770\) | 41130.7 | 1.92499 | ||||||||
\(771\) | −3106.85 | −0.145124 | ||||||||
\(772\) | −22345.7 | −1.04176 | ||||||||
\(773\) | −38813.6 | −1.80599 | −0.902994 | − | 0.429653i | \(-0.858636\pi\) | ||||
−0.902994 | + | 0.429653i | \(0.858636\pi\) | |||||||
\(774\) | 15806.2 | 0.734033 | ||||||||
\(775\) | −5935.70 | −0.275118 | ||||||||
\(776\) | −1974.60 | −0.0913452 | ||||||||
\(777\) | −26060.3 | −1.20323 | ||||||||
\(778\) | −50880.5 | −2.34467 | ||||||||
\(779\) | 16878.6 | 0.776302 | ||||||||
\(780\) | 16705.1 | 0.766847 | ||||||||
\(781\) | −19338.5 | −0.886025 | ||||||||
\(782\) | 78416.3 | 3.58589 | ||||||||
\(783\) | 28116.6 | 1.28328 | ||||||||
\(784\) | −38042.3 | −1.73298 | ||||||||
\(785\) | 33080.3 | 1.50406 | ||||||||
\(786\) | 16538.0 | 0.750495 | ||||||||
\(787\) | 39826.5 | 1.80389 | 0.901946 | − | 0.431849i | \(-0.142139\pi\) | ||||
0.901946 | + | 0.431849i | \(0.142139\pi\) | |||||||
\(788\) | 4227.30 | 0.191106 | ||||||||
\(789\) | −6738.43 | −0.304049 | ||||||||
\(790\) | 23338.3 | 1.05106 | ||||||||
\(791\) | −47861.4 | −2.15140 | ||||||||
\(792\) | −1698.06 | −0.0761842 | ||||||||
\(793\) | −6432.66 | −0.288059 | ||||||||
\(794\) | 21485.1 | 0.960301 | ||||||||
\(795\) | −5798.25 | −0.258670 | ||||||||
\(796\) | −20585.6 | −0.916630 | ||||||||
\(797\) | −15985.8 | −0.710471 | −0.355236 | − | 0.934777i | \(-0.615599\pi\) | ||||
−0.355236 | + | 0.934777i | \(0.615599\pi\) | |||||||
\(798\) | −28729.9 | −1.27447 | ||||||||
\(799\) | 64477.0 | 2.85486 | ||||||||
\(800\) | −6470.48 | −0.285957 | ||||||||
\(801\) | 6092.55 | 0.268751 | ||||||||
\(802\) | 9981.03 | 0.439454 | ||||||||
\(803\) | 2015.08 | 0.0885562 | ||||||||
\(804\) | 6449.84 | 0.282921 | ||||||||
\(805\) | −52726.7 | −2.30854 | ||||||||
\(806\) | 59717.0 | 2.60973 | ||||||||
\(807\) | 7349.31 | 0.320580 | ||||||||
\(808\) | −6221.11 | −0.270864 | ||||||||
\(809\) | −3314.23 | −0.144032 | −0.0720162 | − | 0.997403i | \(-0.522943\pi\) | ||||
−0.0720162 | + | 0.997403i | \(0.522943\pi\) | |||||||
\(810\) | −3702.77 | −0.160620 | ||||||||
\(811\) | −33298.1 | −1.44174 | −0.720872 | − | 0.693068i | \(-0.756259\pi\) | ||||
−0.720872 | + | 0.693068i | \(0.756259\pi\) | |||||||
\(812\) | −41433.5 | −1.79068 | ||||||||
\(813\) | 6338.72 | 0.273443 | ||||||||
\(814\) | 35156.0 | 1.51378 | ||||||||
\(815\) | −2784.65 | −0.119683 | ||||||||
\(816\) | 27271.1 | 1.16995 | ||||||||
\(817\) | 19283.6 | 0.825763 | ||||||||
\(818\) | 31726.3 | 1.35609 | ||||||||
\(819\) | 30362.2 | 1.29541 | ||||||||
\(820\) | −16841.3 | −0.717225 | ||||||||
\(821\) | −8056.63 | −0.342483 | −0.171241 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171241 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(822\) | 2711.13 | 0.115038 | ||||||||
\(823\) | 26454.6 | 1.12047 | 0.560237 | − | 0.828332i | \(-0.310710\pi\) | ||||
0.560237 | + | 0.828332i | \(0.310710\pi\) | |||||||
\(824\) | 2955.13 | 0.124936 | ||||||||
\(825\) | −3227.93 | −0.136221 | ||||||||
\(826\) | 73927.7 | 3.11413 | ||||||||
\(827\) | −10029.0 | −0.421695 | −0.210848 | − | 0.977519i | \(-0.567622\pi\) | ||||
−0.210848 | + | 0.977519i | \(0.567622\pi\) | |||||||
\(828\) | −19274.0 | −0.808957 | ||||||||
\(829\) | −5565.05 | −0.233151 | −0.116576 | − | 0.993182i | \(-0.537192\pi\) | ||||
−0.116576 | + | 0.993182i | \(0.537192\pi\) | |||||||
\(830\) | −48085.4 | −2.01093 | ||||||||
\(831\) | 3999.69 | 0.166965 | ||||||||
\(832\) | 27293.1 | 1.13728 | ||||||||
\(833\) | −61561.3 | −2.56059 | ||||||||
\(834\) | −27472.4 | −1.14064 | ||||||||
\(835\) | −6610.62 | −0.273976 | ||||||||
\(836\) | 18342.9 | 0.758853 | ||||||||
\(837\) | −32911.4 | −1.35912 | ||||||||
\(838\) | 27154.6 | 1.11938 | ||||||||
\(839\) | 36168.6 | 1.48830 | 0.744148 | − | 0.668015i | \(-0.232856\pi\) | ||||
0.744148 | + | 0.668015i | \(0.232856\pi\) | |||||||
\(840\) | −3237.58 | −0.132985 | ||||||||
\(841\) | 13037.5 | 0.534566 | ||||||||
\(842\) | 44075.4 | 1.80397 | ||||||||
\(843\) | −5321.66 | −0.217423 | ||||||||
\(844\) | −4165.68 | −0.169892 | ||||||||
\(845\) | −23672.6 | −0.963741 | ||||||||
\(846\) | −33485.4 | −1.36082 | ||||||||
\(847\) | −1814.75 | −0.0736195 | ||||||||
\(848\) | −11790.0 | −0.477442 | ||||||||
\(849\) | −25146.6 | −1.01652 | ||||||||
\(850\) | −11544.4 | −0.465845 | ||||||||
\(851\) | −45067.7 | −1.81539 | ||||||||
\(852\) | −13478.2 | −0.541965 | ||||||||
\(853\) | −17788.6 | −0.714034 | −0.357017 | − | 0.934098i | \(-0.616206\pi\) | ||||
−0.357017 | + | 0.934098i | \(0.616206\pi\) | |||||||
\(854\) | −11038.6 | −0.442310 | ||||||||
\(855\) | 10717.7 | 0.428698 | ||||||||
\(856\) | −480.871 | −0.0192007 | ||||||||
\(857\) | 19234.2 | 0.766661 | 0.383330 | − | 0.923611i | \(-0.374777\pi\) | ||||
0.383330 | + | 0.923611i | \(0.374777\pi\) | |||||||
\(858\) | 32475.1 | 1.29217 | ||||||||
\(859\) | −18203.3 | −0.723037 | −0.361519 | − | 0.932365i | \(-0.617742\pi\) | ||||
−0.361519 | + | 0.932365i | \(0.617742\pi\) | |||||||
\(860\) | −19241.0 | −0.762922 | ||||||||
\(861\) | 24269.2 | 0.960620 | ||||||||
\(862\) | 1578.74 | 0.0623807 | ||||||||
\(863\) | −1220.53 | −0.0481429 | −0.0240714 | − | 0.999710i | \(-0.507663\pi\) | ||||
−0.0240714 | + | 0.999710i | \(0.507663\pi\) | |||||||
\(864\) | −35876.6 | −1.41267 | ||||||||
\(865\) | −12429.6 | −0.488578 | ||||||||
\(866\) | 3198.61 | 0.125512 | ||||||||
\(867\) | 27154.2 | 1.06368 | ||||||||
\(868\) | 48499.2 | 1.89651 | ||||||||
\(869\) | 21472.4 | 0.838208 | ||||||||
\(870\) | −25894.2 | −1.00907 | ||||||||
\(871\) | −17571.0 | −0.683548 | ||||||||
\(872\) | −6949.64 | −0.269890 | ||||||||
\(873\) | 9398.91 | 0.364381 | ||||||||
\(874\) | −49684.3 | −1.92288 | ||||||||
\(875\) | 44779.7 | 1.73009 | ||||||||
\(876\) | 1404.43 | 0.0541681 | ||||||||
\(877\) | −5026.94 | −0.193555 | −0.0967774 | − | 0.995306i | \(-0.530853\pi\) | ||||
−0.0967774 | + | 0.995306i | \(0.530853\pi\) | |||||||
\(878\) | 4702.65 | 0.180759 | ||||||||
\(879\) | −11338.5 | −0.435084 | ||||||||
\(880\) | 24737.0 | 0.947594 | ||||||||
\(881\) | −26103.7 | −0.998246 | −0.499123 | − | 0.866531i | \(-0.666344\pi\) | ||||
−0.499123 | + | 0.866531i | \(0.666344\pi\) | |||||||
\(882\) | 31971.2 | 1.22055 | ||||||||
\(883\) | 34260.1 | 1.30571 | 0.652857 | − | 0.757481i | \(-0.273570\pi\) | ||||
0.652857 | + | 0.757481i | \(0.273570\pi\) | |||||||
\(884\) | 54967.9 | 2.09137 | ||||||||
\(885\) | 21866.1 | 0.830531 | ||||||||
\(886\) | −54977.3 | −2.08465 | ||||||||
\(887\) | −42206.8 | −1.59771 | −0.798854 | − | 0.601525i | \(-0.794560\pi\) | ||||
−0.798854 | + | 0.601525i | \(0.794560\pi\) | |||||||
\(888\) | −2767.29 | −0.104577 | ||||||||
\(889\) | 3891.38 | 0.146808 | ||||||||
\(890\) | −15670.7 | −0.590204 | ||||||||
\(891\) | −3406.75 | −0.128092 | ||||||||
\(892\) | 12610.0 | 0.473334 | ||||||||
\(893\) | −40852.4 | −1.53088 | ||||||||
\(894\) | 44177.2 | 1.65269 | ||||||||
\(895\) | 22103.7 | 0.825525 | ||||||||
\(896\) | −12004.1 | −0.447576 | ||||||||
\(897\) | −41630.9 | −1.54963 | ||||||||
\(898\) | −15131.2 | −0.562289 | ||||||||
\(899\) | −43808.9 | −1.62526 | ||||||||
\(900\) | 2837.49 | 0.105092 | ||||||||
\(901\) | −19079.0 | −0.705454 | ||||||||
\(902\) | −32739.8 | −1.20856 | ||||||||
\(903\) | 27727.3 | 1.02182 | ||||||||
\(904\) | −5082.30 | −0.186985 | ||||||||
\(905\) | 14849.0 | 0.545413 | ||||||||
\(906\) | −15513.8 | −0.568886 | ||||||||
\(907\) | −35714.2 | −1.30747 | −0.653733 | − | 0.756725i | \(-0.726798\pi\) | ||||
−0.653733 | + | 0.756725i | \(0.726798\pi\) | |||||||
\(908\) | 6517.07 | 0.238190 | ||||||||
\(909\) | 29611.9 | 1.08049 | ||||||||
\(910\) | −78094.5 | −2.84484 | ||||||||
\(911\) | −18645.2 | −0.678092 | −0.339046 | − | 0.940770i | \(-0.610104\pi\) | ||||
−0.339046 | + | 0.940770i | \(0.610104\pi\) | |||||||
\(912\) | −17278.9 | −0.627369 | ||||||||
\(913\) | −44241.1 | −1.60369 | ||||||||
\(914\) | 9073.31 | 0.328357 | ||||||||
\(915\) | −3264.96 | −0.117963 | ||||||||
\(916\) | 23658.7 | 0.853391 | ||||||||
\(917\) | −36590.2 | −1.31768 | ||||||||
\(918\) | −64009.5 | −2.30134 | ||||||||
\(919\) | −7917.55 | −0.284196 | −0.142098 | − | 0.989853i | \(-0.545385\pi\) | ||||
−0.142098 | + | 0.989853i | \(0.545385\pi\) | |||||||
\(920\) | −5598.94 | −0.200643 | ||||||||
\(921\) | 15235.7 | 0.545097 | ||||||||
\(922\) | 5772.97 | 0.206207 | ||||||||
\(923\) | 36717.9 | 1.30941 | ||||||||
\(924\) | 26374.6 | 0.939027 | ||||||||
\(925\) | 6634.81 | 0.235839 | ||||||||
\(926\) | 24404.6 | 0.866074 | ||||||||
\(927\) | −14066.2 | −0.498375 | ||||||||
\(928\) | −47755.9 | −1.68929 | ||||||||
\(929\) | 32441.3 | 1.14571 | 0.572856 | − | 0.819656i | \(-0.305836\pi\) | ||||
0.572856 | + | 0.819656i | \(0.305836\pi\) | |||||||
\(930\) | 30309.9 | 1.06871 | ||||||||
\(931\) | 39005.1 | 1.37308 | ||||||||
\(932\) | 5104.08 | 0.179388 | ||||||||
\(933\) | −12863.7 | −0.451381 | ||||||||
\(934\) | 46585.6 | 1.63204 | ||||||||
\(935\) | 40030.2 | 1.40014 | ||||||||
\(936\) | 3224.10 | 0.112589 | ||||||||
\(937\) | 52043.1 | 1.81449 | 0.907244 | − | 0.420605i | \(-0.138182\pi\) | ||||
0.907244 | + | 0.420605i | \(0.138182\pi\) | |||||||
\(938\) | −30152.2 | −1.04958 | ||||||||
\(939\) | −21461.2 | −0.745857 | ||||||||
\(940\) | 40762.1 | 1.41438 | ||||||||
\(941\) | 35207.1 | 1.21968 | 0.609840 | − | 0.792524i | \(-0.291234\pi\) | ||||
0.609840 | + | 0.792524i | \(0.291234\pi\) | |||||||
\(942\) | 44820.5 | 1.55025 | ||||||||
\(943\) | 41970.3 | 1.44935 | ||||||||
\(944\) | 44461.9 | 1.53296 | ||||||||
\(945\) | 43039.7 | 1.48157 | ||||||||
\(946\) | −37404.8 | −1.28556 | ||||||||
\(947\) | 29820.4 | 1.02327 | 0.511634 | − | 0.859204i | \(-0.329040\pi\) | ||||
0.511634 | + | 0.859204i | \(0.329040\pi\) | |||||||
\(948\) | 14965.4 | 0.512716 | ||||||||
\(949\) | −3826.02 | −0.130872 | ||||||||
\(950\) | 7314.47 | 0.249803 | ||||||||
\(951\) | 8754.49 | 0.298511 | ||||||||
\(952\) | −10653.2 | −0.362680 | ||||||||
\(953\) | 51897.8 | 1.76404 | 0.882022 | − | 0.471208i | \(-0.156182\pi\) | ||||
0.882022 | + | 0.471208i | \(0.156182\pi\) | |||||||
\(954\) | 9908.48 | 0.336267 | ||||||||
\(955\) | −21980.2 | −0.744779 | ||||||||
\(956\) | 8428.79 | 0.285153 | ||||||||
\(957\) | −23824.0 | −0.804723 | ||||||||
\(958\) | 27361.2 | 0.922755 | ||||||||
\(959\) | −5998.37 | −0.201979 | ||||||||
\(960\) | 13852.9 | 0.465728 | ||||||||
\(961\) | 21488.7 | 0.721317 | ||||||||
\(962\) | −66750.6 | −2.23714 | ||||||||
\(963\) | 2288.90 | 0.0765928 | ||||||||
\(964\) | −29935.9 | −1.00018 | ||||||||
\(965\) | 30897.9 | 1.03071 | ||||||||
\(966\) | −71439.5 | −2.37943 | ||||||||
\(967\) | 4411.28 | 0.146698 | 0.0733491 | − | 0.997306i | \(-0.476631\pi\) | ||||
0.0733491 | + | 0.997306i | \(0.476631\pi\) | |||||||
\(968\) | −192.705 | −0.00639852 | ||||||||
\(969\) | −27961.2 | −0.926981 | ||||||||
\(970\) | −24174.9 | −0.800217 | ||||||||
\(971\) | 37197.8 | 1.22939 | 0.614693 | − | 0.788766i | \(-0.289280\pi\) | ||||
0.614693 | + | 0.788766i | \(0.289280\pi\) | |||||||
\(972\) | 25832.6 | 0.852448 | ||||||||
\(973\) | 60782.8 | 2.00268 | ||||||||
\(974\) | −8389.65 | −0.275998 | ||||||||
\(975\) | 6128.85 | 0.201313 | ||||||||
\(976\) | −6638.88 | −0.217731 | ||||||||
\(977\) | −8254.57 | −0.270304 | −0.135152 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135152 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(978\) | −3772.93 | −0.123359 | ||||||||
\(979\) | −14417.8 | −0.470680 | ||||||||
\(980\) | −38918.9 | −1.26859 | ||||||||
\(981\) | 33079.6 | 1.07661 | ||||||||
\(982\) | 60243.9 | 1.95770 | ||||||||
\(983\) | −40483.9 | −1.31357 | −0.656783 | − | 0.754080i | \(-0.728083\pi\) | ||||
−0.656783 | + | 0.754080i | \(0.728083\pi\) | |||||||
\(984\) | 2577.10 | 0.0834908 | ||||||||
\(985\) | −5845.17 | −0.189079 | ||||||||
\(986\) | −85204.1 | −2.75198 | ||||||||
\(987\) | −58740.4 | −1.89435 | ||||||||
\(988\) | −34827.5 | −1.12147 | ||||||||
\(989\) | 47950.5 | 1.54170 | ||||||||
\(990\) | −20789.3 | −0.667401 | ||||||||
\(991\) | 39541.4 | 1.26748 | 0.633740 | − | 0.773546i | \(-0.281519\pi\) | ||||
0.633740 | + | 0.773546i | \(0.281519\pi\) | |||||||
\(992\) | 55899.8 | 1.78913 | ||||||||
\(993\) | 19650.7 | 0.627991 | ||||||||
\(994\) | 63008.8 | 2.01058 | ||||||||
\(995\) | 28464.1 | 0.906908 | ||||||||
\(996\) | −30834.3 | −0.980946 | ||||||||
\(997\) | 118.681 | 0.00376998 | 0.00188499 | − | 0.999998i | \(-0.499400\pi\) | ||||
0.00188499 | + | 0.999998i | \(0.499400\pi\) | |||||||
\(998\) | −32161.3 | −1.02009 | ||||||||
\(999\) | 36787.7 | 1.16508 |
(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 | 547.4.a.a.1.13 | ✓ | 65 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.4.a.a.1.13 | ✓ | 65 | 1.1 | even | 1 | trivial |