Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, 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("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.5054412.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 29x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.32750\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.32750 | −0.469343 | −0.234671 | − | 0.972075i | \(-0.575401\pi\) | ||||
−0.234671 | + | 0.972075i | \(0.575401\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −6.23774 | −0.779717 | ||||||||
\(5\) | −15.4241 | −1.37957 | −0.689785 | − | 0.724014i | \(-0.742295\pi\) | ||||
−0.689785 | + | 0.724014i | \(0.742295\pi\) | |||||||
\(6\) | 3.98251 | 0.270975 | ||||||||
\(7\) | 7.96501 | 0.430070 | 0.215035 | − | 0.976606i | \(-0.431013\pi\) | ||||
0.215035 | + | 0.976606i | \(0.431013\pi\) | |||||||
\(8\) | 18.9006 | 0.835297 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 20.4755 | 0.647491 | ||||||||
\(11\) | −12.7691 | −0.350002 | −0.175001 | − | 0.984568i | \(-0.555993\pi\) | ||||
−0.175001 | + | 0.984568i | \(0.555993\pi\) | |||||||
\(12\) | 18.7132 | 0.450170 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −10.5736 | −0.201850 | ||||||||
\(15\) | 46.2722 | 0.796496 | ||||||||
\(16\) | 24.8113 | 0.387677 | ||||||||
\(17\) | −54.0000 | −0.770407 | −0.385204 | − | 0.922832i | \(-0.625869\pi\) | ||||
−0.385204 | + | 0.922832i | \(0.625869\pi\) | |||||||
\(18\) | −11.9475 | −0.156448 | ||||||||
\(19\) | 84.5794 | 1.02126 | 0.510628 | − | 0.859802i | \(-0.329413\pi\) | ||||
0.510628 | + | 0.859802i | \(0.329413\pi\) | |||||||
\(20\) | 96.2113 | 1.07568 | ||||||||
\(21\) | −23.8950 | −0.248301 | ||||||||
\(22\) | 16.9510 | 0.164271 | ||||||||
\(23\) | 122.853 | 1.11376 | 0.556882 | − | 0.830591i | \(-0.311997\pi\) | ||||
0.556882 | + | 0.830591i | \(0.311997\pi\) | |||||||
\(24\) | −56.7019 | −0.482259 | ||||||||
\(25\) | 112.902 | 0.903215 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −49.6837 | −0.335333 | ||||||||
\(29\) | 140.853 | 0.901921 | 0.450961 | − | 0.892544i | \(-0.351081\pi\) | ||||
0.450961 | + | 0.892544i | \(0.351081\pi\) | |||||||
\(30\) | −61.4264 | −0.373829 | ||||||||
\(31\) | 116.439 | 0.674617 | 0.337309 | − | 0.941394i | \(-0.390483\pi\) | ||||
0.337309 | + | 0.941394i | \(0.390483\pi\) | |||||||
\(32\) | −184.142 | −1.01725 | ||||||||
\(33\) | 38.3072 | 0.202074 | ||||||||
\(34\) | 71.6851 | 0.361585 | ||||||||
\(35\) | −122.853 | −0.593312 | ||||||||
\(36\) | −56.1397 | −0.259906 | ||||||||
\(37\) | 433.898 | 1.92790 | 0.963951 | − | 0.266081i | \(-0.0857289\pi\) | ||||
0.963951 | + | 0.266081i | \(0.0857289\pi\) | |||||||
\(38\) | −112.279 | −0.479319 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −291.525 | −1.15235 | ||||||||
\(41\) | 205.823 | 0.784003 | 0.392002 | − | 0.919965i | \(-0.371783\pi\) | ||||
0.392002 | + | 0.919965i | \(0.371783\pi\) | |||||||
\(42\) | 31.7207 | 0.116538 | ||||||||
\(43\) | −418.853 | −1.48545 | −0.742726 | − | 0.669595i | \(-0.766468\pi\) | ||||
−0.742726 | + | 0.669595i | \(0.766468\pi\) | |||||||
\(44\) | 79.6501 | 0.272902 | ||||||||
\(45\) | −138.817 | −0.459857 | ||||||||
\(46\) | −163.087 | −0.522737 | ||||||||
\(47\) | −485.861 | −1.50787 | −0.753937 | − | 0.656947i | \(-0.771848\pi\) | ||||
−0.753937 | + | 0.656947i | \(0.771848\pi\) | |||||||
\(48\) | −74.4339 | −0.223825 | ||||||||
\(49\) | −279.559 | −0.815040 | ||||||||
\(50\) | −149.877 | −0.423918 | ||||||||
\(51\) | 162.000 | 0.444795 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −674.559 | −1.74826 | −0.874130 | − | 0.485693i | \(-0.838567\pi\) | ||||
−0.874130 | + | 0.485693i | \(0.838567\pi\) | |||||||
\(54\) | 35.8425 | 0.0903251 | ||||||||
\(55\) | 196.951 | 0.482852 | ||||||||
\(56\) | 150.544 | 0.359236 | ||||||||
\(57\) | −253.738 | −0.589622 | ||||||||
\(58\) | −186.982 | −0.423310 | ||||||||
\(59\) | −186.226 | −0.410925 | −0.205462 | − | 0.978665i | \(-0.565870\pi\) | ||||
−0.205462 | + | 0.978665i | \(0.565870\pi\) | |||||||
\(60\) | −288.634 | −0.621041 | ||||||||
\(61\) | −671.902 | −1.41030 | −0.705149 | − | 0.709059i | \(-0.749120\pi\) | ||||
−0.705149 | + | 0.709059i | \(0.749120\pi\) | |||||||
\(62\) | −154.574 | −0.316627 | ||||||||
\(63\) | 71.6851 | 0.143357 | ||||||||
\(64\) | 45.9584 | 0.0897626 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −50.8529 | −0.0948418 | ||||||||
\(67\) | −14.0364 | −0.0255944 | −0.0127972 | − | 0.999918i | \(-0.504074\pi\) | ||||
−0.0127972 | + | 0.999918i | \(0.504074\pi\) | |||||||
\(68\) | 336.838 | 0.600700 | ||||||||
\(69\) | −368.559 | −0.643033 | ||||||||
\(70\) | 163.087 | 0.278467 | ||||||||
\(71\) | 346.789 | 0.579665 | 0.289833 | − | 0.957077i | \(-0.406400\pi\) | ||||
0.289833 | + | 0.957077i | \(0.406400\pi\) | |||||||
\(72\) | 170.106 | 0.278432 | ||||||||
\(73\) | 832.900 | 1.33539 | 0.667695 | − | 0.744435i | \(-0.267281\pi\) | ||||
0.667695 | + | 0.744435i | \(0.267281\pi\) | |||||||
\(74\) | −576.000 | −0.904846 | ||||||||
\(75\) | −338.706 | −0.521472 | ||||||||
\(76\) | −527.584 | −0.796290 | ||||||||
\(77\) | −101.706 | −0.150525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −335.608 | −0.477960 | −0.238980 | − | 0.971025i | \(-0.576813\pi\) | ||||
−0.238980 | + | 0.971025i | \(0.576813\pi\) | |||||||
\(80\) | −382.691 | −0.534827 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −273.230 | −0.367966 | ||||||||
\(83\) | −568.797 | −0.752212 | −0.376106 | − | 0.926577i | \(-0.622737\pi\) | ||||
−0.376106 | + | 0.926577i | \(0.622737\pi\) | |||||||
\(84\) | 149.051 | 0.193605 | ||||||||
\(85\) | 832.900 | 1.06283 | ||||||||
\(86\) | 556.028 | 0.697186 | ||||||||
\(87\) | −422.559 | −0.520725 | ||||||||
\(88\) | −241.343 | −0.292355 | ||||||||
\(89\) | 236.671 | 0.281877 | 0.140939 | − | 0.990018i | \(-0.454988\pi\) | ||||
0.140939 | + | 0.990018i | \(0.454988\pi\) | |||||||
\(90\) | 184.279 | 0.215830 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −766.324 | −0.868422 | ||||||||
\(93\) | −349.318 | −0.389491 | ||||||||
\(94\) | 644.981 | 0.707710 | ||||||||
\(95\) | −1304.56 | −1.40889 | ||||||||
\(96\) | 552.426 | 0.587310 | ||||||||
\(97\) | 1278.94 | 1.33873 | 0.669365 | − | 0.742934i | \(-0.266566\pi\) | ||||
0.669365 | + | 0.742934i | \(0.266566\pi\) | |||||||
\(98\) | 371.115 | 0.382533 | ||||||||
\(99\) | −114.922 | −0.116667 | ||||||||
\(100\) | −704.253 | −0.704253 | ||||||||
\(101\) | 632.264 | 0.622898 | 0.311449 | − | 0.950263i | \(-0.399186\pi\) | ||||
0.311449 | + | 0.950263i | \(0.399186\pi\) | |||||||
\(102\) | −215.055 | −0.208761 | ||||||||
\(103\) | 1506.26 | 1.44094 | 0.720469 | − | 0.693487i | \(-0.243927\pi\) | ||||
0.720469 | + | 0.693487i | \(0.243927\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 368.559 | 0.342549 | ||||||||
\(106\) | 895.478 | 0.820533 | ||||||||
\(107\) | −1268.56 | −1.14613 | −0.573066 | − | 0.819509i | \(-0.694246\pi\) | ||||
−0.573066 | + | 0.819509i | \(0.694246\pi\) | |||||||
\(108\) | 168.419 | 0.150057 | ||||||||
\(109\) | −347.425 | −0.305296 | −0.152648 | − | 0.988281i | \(-0.548780\pi\) | ||||
−0.152648 | + | 0.988281i | \(0.548780\pi\) | |||||||
\(110\) | −261.453 | −0.226623 | ||||||||
\(111\) | −1301.69 | −1.11307 | ||||||||
\(112\) | 197.622 | 0.166728 | ||||||||
\(113\) | 659.706 | 0.549203 | 0.274601 | − | 0.961558i | \(-0.411454\pi\) | ||||
0.274601 | + | 0.961558i | \(0.411454\pi\) | |||||||
\(114\) | 336.838 | 0.276735 | ||||||||
\(115\) | −1894.89 | −1.53652 | ||||||||
\(116\) | −878.603 | −0.703244 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 247.215 | 0.192865 | ||||||||
\(119\) | −430.111 | −0.331329 | ||||||||
\(120\) | 874.574 | 0.665311 | ||||||||
\(121\) | −1167.95 | −0.877499 | ||||||||
\(122\) | 891.951 | 0.661913 | ||||||||
\(123\) | −617.469 | −0.452645 | ||||||||
\(124\) | −726.319 | −0.526011 | ||||||||
\(125\) | 186.602 | 0.133521 | ||||||||
\(126\) | −95.1621 | −0.0672834 | ||||||||
\(127\) | 275.019 | 0.192157 | 0.0960787 | − | 0.995374i | \(-0.469370\pi\) | ||||
0.0960787 | + | 0.995374i | \(0.469370\pi\) | |||||||
\(128\) | 1412.13 | 0.975121 | ||||||||
\(129\) | 1256.56 | 0.857626 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1183.97 | −0.789648 | −0.394824 | − | 0.918757i | \(-0.629195\pi\) | ||||
−0.394824 | + | 0.918757i | \(0.629195\pi\) | |||||||
\(132\) | −238.950 | −0.157560 | ||||||||
\(133\) | 673.676 | 0.439211 | ||||||||
\(134\) | 18.6334 | 0.0120125 | ||||||||
\(135\) | 416.450 | 0.265499 | ||||||||
\(136\) | −1020.63 | −0.643519 | ||||||||
\(137\) | −2557.36 | −1.59482 | −0.797410 | − | 0.603438i | \(-0.793797\pi\) | ||||
−0.797410 | + | 0.603438i | \(0.793797\pi\) | |||||||
\(138\) | 489.262 | 0.301803 | ||||||||
\(139\) | 545.736 | 0.333012 | 0.166506 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166506 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(140\) | 766.324 | 0.462616 | ||||||||
\(141\) | 1457.58 | 0.870571 | ||||||||
\(142\) | −460.362 | −0.272062 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 223.302 | 0.129226 | ||||||||
\(145\) | −2172.52 | −1.24426 | ||||||||
\(146\) | −1105.68 | −0.626756 | ||||||||
\(147\) | 838.676 | 0.470563 | ||||||||
\(148\) | −2706.54 | −1.50322 | ||||||||
\(149\) | −1376.78 | −0.756981 | −0.378491 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378491 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(150\) | 449.632 | 0.244749 | ||||||||
\(151\) | −2733.47 | −1.47316 | −0.736579 | − | 0.676352i | \(-0.763560\pi\) | ||||
−0.736579 | + | 0.676352i | \(0.763560\pi\) | |||||||
\(152\) | 1598.60 | 0.853052 | ||||||||
\(153\) | −486.000 | −0.256802 | ||||||||
\(154\) | 135.015 | 0.0706479 | ||||||||
\(155\) | −1795.97 | −0.930683 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1029.97 | 0.523570 | 0.261785 | − | 0.965126i | \(-0.415689\pi\) | ||||
0.261785 | + | 0.965126i | \(0.415689\pi\) | |||||||
\(158\) | 445.520 | 0.224327 | ||||||||
\(159\) | 2023.68 | 1.00936 | ||||||||
\(160\) | 2840.22 | 1.40337 | ||||||||
\(161\) | 978.524 | 0.478997 | ||||||||
\(162\) | −107.528 | −0.0521492 | ||||||||
\(163\) | 2882.91 | 1.38532 | 0.692660 | − | 0.721264i | \(-0.256439\pi\) | ||||
0.692660 | + | 0.721264i | \(0.256439\pi\) | |||||||
\(164\) | −1283.87 | −0.611301 | ||||||||
\(165\) | −590.853 | −0.278775 | ||||||||
\(166\) | 755.079 | 0.353045 | ||||||||
\(167\) | −1153.90 | −0.534679 | −0.267340 | − | 0.963602i | \(-0.586145\pi\) | ||||
−0.267340 | + | 0.963602i | \(0.586145\pi\) | |||||||
\(168\) | −451.631 | −0.207405 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1105.68 | −0.498832 | ||||||||
\(171\) | 761.215 | 0.340418 | ||||||||
\(172\) | 2612.69 | 1.15823 | ||||||||
\(173\) | −1688.85 | −0.742203 | −0.371101 | − | 0.928592i | \(-0.621020\pi\) | ||||
−0.371101 | + | 0.928592i | \(0.621020\pi\) | |||||||
\(174\) | 560.947 | 0.244398 | ||||||||
\(175\) | 899.265 | 0.388446 | ||||||||
\(176\) | −316.817 | −0.135687 | ||||||||
\(177\) | 558.678 | 0.237247 | ||||||||
\(178\) | −314.181 | −0.132297 | ||||||||
\(179\) | −942.793 | −0.393674 | −0.196837 | − | 0.980436i | \(-0.563067\pi\) | ||||
−0.196837 | + | 0.980436i | \(0.563067\pi\) | |||||||
\(180\) | 865.902 | 0.358558 | ||||||||
\(181\) | 482.030 | 0.197950 | 0.0989751 | − | 0.995090i | \(-0.468444\pi\) | ||||
0.0989751 | + | 0.995090i | \(0.468444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2015.71 | 0.814236 | ||||||||
\(184\) | 2322.00 | 0.930325 | ||||||||
\(185\) | −6692.47 | −2.65968 | ||||||||
\(186\) | 463.721 | 0.182805 | ||||||||
\(187\) | 689.530 | 0.269644 | ||||||||
\(188\) | 3030.67 | 1.17572 | ||||||||
\(189\) | −215.055 | −0.0827670 | ||||||||
\(190\) | 1731.80 | 0.661254 | ||||||||
\(191\) | 4223.32 | 1.59994 | 0.799971 | − | 0.600039i | \(-0.204848\pi\) | ||||
0.799971 | + | 0.600039i | \(0.204848\pi\) | |||||||
\(192\) | −137.875 | −0.0518244 | ||||||||
\(193\) | 229.092 | 0.0854424 | 0.0427212 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427212 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(194\) | −1697.80 | −0.628323 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1743.81 | 0.635501 | ||||||||
\(197\) | 228.335 | 0.0825798 | 0.0412899 | − | 0.999147i | \(-0.486853\pi\) | ||||
0.0412899 | + | 0.999147i | \(0.486853\pi\) | |||||||
\(198\) | 152.559 | 0.0547569 | ||||||||
\(199\) | 2939.02 | 1.04694 | 0.523471 | − | 0.852043i | \(-0.324637\pi\) | ||||
0.523471 | + | 0.852043i | \(0.324637\pi\) | |||||||
\(200\) | 2133.92 | 0.754453 | ||||||||
\(201\) | 42.1093 | 0.0147769 | ||||||||
\(202\) | −839.332 | −0.292352 | ||||||||
\(203\) | 1121.89 | 0.387889 | ||||||||
\(204\) | −1010.51 | −0.346814 | ||||||||
\(205\) | −3174.63 | −1.08159 | ||||||||
\(206\) | −1999.57 | −0.676294 | ||||||||
\(207\) | 1105.68 | 0.371255 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1080.00 | −0.357441 | ||||||||
\(210\) | −489.262 | −0.160773 | ||||||||
\(211\) | −1607.02 | −0.524321 | −0.262161 | − | 0.965024i | \(-0.584435\pi\) | ||||
−0.262161 | + | 0.965024i | \(0.584435\pi\) | |||||||
\(212\) | 4207.72 | 1.36315 | ||||||||
\(213\) | −1040.37 | −0.334670 | ||||||||
\(214\) | 1684.01 | 0.537929 | ||||||||
\(215\) | 6460.42 | 2.04929 | ||||||||
\(216\) | −510.317 | −0.160753 | ||||||||
\(217\) | 927.441 | 0.290133 | ||||||||
\(218\) | 461.207 | 0.143288 | ||||||||
\(219\) | −2498.70 | −0.770988 | ||||||||
\(220\) | −1228.53 | −0.376488 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1728.00 | 0.522413 | ||||||||
\(223\) | −130.867 | −0.0392981 | −0.0196490 | − | 0.999807i | \(-0.506255\pi\) | ||||
−0.0196490 | + | 0.999807i | \(0.506255\pi\) | |||||||
\(224\) | −1466.69 | −0.437489 | ||||||||
\(225\) | 1016.12 | 0.301072 | ||||||||
\(226\) | −875.761 | −0.257764 | ||||||||
\(227\) | −4325.19 | −1.26464 | −0.632319 | − | 0.774708i | \(-0.717897\pi\) | ||||
−0.632319 | + | 0.774708i | \(0.717897\pi\) | |||||||
\(228\) | 1582.75 | 0.459738 | ||||||||
\(229\) | 2621.57 | 0.756499 | 0.378250 | − | 0.925704i | \(-0.376526\pi\) | ||||
0.378250 | + | 0.925704i | \(0.376526\pi\) | |||||||
\(230\) | 2515.47 | 0.721153 | ||||||||
\(231\) | 305.117 | 0.0869058 | ||||||||
\(232\) | 2662.21 | 0.753373 | ||||||||
\(233\) | −4643.12 | −1.30550 | −0.652748 | − | 0.757575i | \(-0.726384\pi\) | ||||
−0.652748 | + | 0.757575i | \(0.726384\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7493.95 | 2.08022 | ||||||||
\(236\) | 1161.63 | 0.320405 | ||||||||
\(237\) | 1006.82 | 0.275950 | ||||||||
\(238\) | 570.972 | 0.155507 | ||||||||
\(239\) | −6696.69 | −1.81244 | −0.906219 | − | 0.422809i | \(-0.861044\pi\) | ||||
−0.906219 | + | 0.422809i | \(0.861044\pi\) | |||||||
\(240\) | 1148.07 | 0.308783 | ||||||||
\(241\) | −2301.47 | −0.615148 | −0.307574 | − | 0.951524i | \(-0.599517\pi\) | ||||
−0.307574 | + | 0.951524i | \(0.599517\pi\) | |||||||
\(242\) | 1550.46 | 0.411848 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 4191.15 | 1.09963 | ||||||||
\(245\) | 4311.93 | 1.12440 | ||||||||
\(246\) | 819.691 | 0.212445 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2200.78 | 0.563506 | ||||||||
\(249\) | 1706.39 | 0.434290 | ||||||||
\(250\) | −247.714 | −0.0626673 | ||||||||
\(251\) | 828.000 | 0.208219 | 0.104109 | − | 0.994566i | \(-0.466801\pi\) | ||||
0.104109 | + | 0.994566i | \(0.466801\pi\) | |||||||
\(252\) | −447.153 | −0.111778 | ||||||||
\(253\) | −1568.72 | −0.389820 | ||||||||
\(254\) | −365.088 | −0.0901877 | ||||||||
\(255\) | −2498.70 | −0.613626 | ||||||||
\(256\) | −2242.27 | −0.547429 | ||||||||
\(257\) | 884.763 | 0.214747 | 0.107374 | − | 0.994219i | \(-0.465756\pi\) | ||||
0.107374 | + | 0.994219i | \(0.465756\pi\) | |||||||
\(258\) | −1668.08 | −0.402521 | ||||||||
\(259\) | 3456.00 | 0.829133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1267.68 | 0.300640 | ||||||||
\(262\) | 1571.72 | 0.370616 | ||||||||
\(263\) | −8343.94 | −1.95631 | −0.978155 | − | 0.207878i | \(-0.933344\pi\) | ||||
−0.978155 | + | 0.207878i | \(0.933344\pi\) | |||||||
\(264\) | 724.030 | 0.168792 | ||||||||
\(265\) | 10404.4 | 2.41185 | ||||||||
\(266\) | −894.306 | −0.206141 | ||||||||
\(267\) | −710.013 | −0.162742 | ||||||||
\(268\) | 87.5556 | 0.0199564 | ||||||||
\(269\) | 2762.56 | 0.626157 | 0.313078 | − | 0.949727i | \(-0.398640\pi\) | ||||
0.313078 | + | 0.949727i | \(0.398640\pi\) | |||||||
\(270\) | −552.838 | −0.124610 | ||||||||
\(271\) | 3116.54 | 0.698585 | 0.349293 | − | 0.937014i | \(-0.386422\pi\) | ||||
0.349293 | + | 0.937014i | \(0.386422\pi\) | |||||||
\(272\) | −1339.81 | −0.298669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3394.91 | 0.748517 | ||||||||
\(275\) | −1441.65 | −0.316127 | ||||||||
\(276\) | 2298.97 | 0.501384 | ||||||||
\(277\) | −502.060 | −0.108902 | −0.0544510 | − | 0.998516i | \(-0.517341\pi\) | ||||
−0.0544510 | + | 0.998516i | \(0.517341\pi\) | |||||||
\(278\) | −724.465 | −0.156297 | ||||||||
\(279\) | 1047.96 | 0.224872 | ||||||||
\(280\) | −2322.00 | −0.495592 | ||||||||
\(281\) | −6607.56 | −1.40275 | −0.701377 | − | 0.712791i | \(-0.747431\pi\) | ||||
−0.701377 | + | 0.712791i | \(0.747431\pi\) | |||||||
\(282\) | −1934.94 | −0.408596 | ||||||||
\(283\) | −4368.98 | −0.917699 | −0.458850 | − | 0.888514i | \(-0.651738\pi\) | ||||
−0.458850 | + | 0.888514i | \(0.651738\pi\) | |||||||
\(284\) | −2163.18 | −0.451975 | ||||||||
\(285\) | 3913.68 | 0.813425 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1639.38 | 0.337176 | ||||||||
\(288\) | −1657.28 | −0.339084 | ||||||||
\(289\) | −1997.00 | −0.406473 | ||||||||
\(290\) | 2884.03 | 0.583986 | ||||||||
\(291\) | −3836.82 | −0.772916 | ||||||||
\(292\) | −5195.41 | −1.04123 | ||||||||
\(293\) | −5348.12 | −1.06635 | −0.533175 | − | 0.846005i | \(-0.679001\pi\) | ||||
−0.533175 | + | 0.846005i | \(0.679001\pi\) | |||||||
\(294\) | −1113.34 | −0.220856 | ||||||||
\(295\) | 2872.36 | 0.566900 | ||||||||
\(296\) | 8200.94 | 1.61037 | ||||||||
\(297\) | 344.765 | 0.0673579 | ||||||||
\(298\) | 1827.68 | 0.355284 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2112.76 | 0.406600 | ||||||||
\(301\) | −3336.17 | −0.638849 | ||||||||
\(302\) | 3628.69 | 0.691416 | ||||||||
\(303\) | −1896.79 | −0.359630 | ||||||||
\(304\) | 2098.53 | 0.395917 | ||||||||
\(305\) | 10363.5 | 1.94561 | ||||||||
\(306\) | 645.166 | 0.120528 | ||||||||
\(307\) | −4502.46 | −0.837032 | −0.418516 | − | 0.908210i | \(-0.637450\pi\) | ||||
−0.418516 | + | 0.908210i | \(0.637450\pi\) | |||||||
\(308\) | 634.414 | 0.117367 | ||||||||
\(309\) | −4518.79 | −0.831926 | ||||||||
\(310\) | 2384.15 | 0.436809 | ||||||||
\(311\) | −7447.20 | −1.35785 | −0.678926 | − | 0.734207i | \(-0.737554\pi\) | ||||
−0.678926 | + | 0.734207i | \(0.737554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6508.93 | −1.17542 | −0.587710 | − | 0.809072i | \(-0.699970\pi\) | ||||
−0.587710 | + | 0.809072i | \(0.699970\pi\) | |||||||
\(314\) | −1367.29 | −0.245734 | ||||||||
\(315\) | −1105.68 | −0.197771 | ||||||||
\(316\) | 2093.43 | 0.372673 | ||||||||
\(317\) | 2465.57 | 0.436846 | 0.218423 | − | 0.975854i | \(-0.429909\pi\) | ||||
0.218423 | + | 0.975854i | \(0.429909\pi\) | |||||||
\(318\) | −2686.43 | −0.473735 | ||||||||
\(319\) | −1798.56 | −0.315674 | ||||||||
\(320\) | −708.866 | −0.123834 | ||||||||
\(321\) | 3805.68 | 0.661720 | ||||||||
\(322\) | −1298.99 | −0.224814 | ||||||||
\(323\) | −4567.29 | −0.786782 | ||||||||
\(324\) | −505.257 | −0.0866353 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3827.07 | −0.650190 | ||||||||
\(327\) | 1042.27 | 0.176263 | ||||||||
\(328\) | 3890.18 | 0.654876 | ||||||||
\(329\) | −3869.89 | −0.648491 | ||||||||
\(330\) | 784.358 | 0.130841 | ||||||||
\(331\) | −4114.84 | −0.683300 | −0.341650 | − | 0.939827i | \(-0.610986\pi\) | ||||
−0.341650 | + | 0.939827i | \(0.610986\pi\) | |||||||
\(332\) | 3548.01 | 0.586513 | ||||||||
\(333\) | 3905.08 | 0.642634 | ||||||||
\(334\) | 1531.80 | 0.250948 | ||||||||
\(335\) | 216.499 | 0.0353092 | ||||||||
\(336\) | −592.867 | −0.0962605 | ||||||||
\(337\) | 4798.05 | 0.775568 | 0.387784 | − | 0.921750i | \(-0.373241\pi\) | ||||
0.387784 | + | 0.921750i | \(0.373241\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1979.12 | −0.317082 | ||||||||
\(340\) | −5195.41 | −0.828708 | ||||||||
\(341\) | −1486.82 | −0.236117 | ||||||||
\(342\) | −1010.51 | −0.159773 | ||||||||
\(343\) | −4958.69 | −0.780594 | ||||||||
\(344\) | −7916.58 | −1.24079 | ||||||||
\(345\) | 5684.67 | 0.887109 | ||||||||
\(346\) | 2241.96 | 0.348348 | ||||||||
\(347\) | −3314.76 | −0.512812 | −0.256406 | − | 0.966569i | \(-0.582538\pi\) | ||||
−0.256406 | + | 0.966569i | \(0.582538\pi\) | |||||||
\(348\) | 2635.81 | 0.406018 | ||||||||
\(349\) | −371.740 | −0.0570166 | −0.0285083 | − | 0.999594i | \(-0.509076\pi\) | ||||
−0.0285083 | + | 0.999594i | \(0.509076\pi\) | |||||||
\(350\) | −1193.78 | −0.182314 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2351.32 | 0.356039 | ||||||||
\(353\) | 7539.10 | 1.13673 | 0.568365 | − | 0.822776i | \(-0.307576\pi\) | ||||
0.568365 | + | 0.822776i | \(0.307576\pi\) | |||||||
\(354\) | −741.646 | −0.111350 | ||||||||
\(355\) | −5348.89 | −0.799689 | ||||||||
\(356\) | −1476.29 | −0.219785 | ||||||||
\(357\) | 1290.33 | 0.191293 | ||||||||
\(358\) | 1251.56 | 0.184768 | ||||||||
\(359\) | 12741.5 | 1.87317 | 0.936586 | − | 0.350437i | \(-0.113967\pi\) | ||||
0.936586 | + | 0.350437i | \(0.113967\pi\) | |||||||
\(360\) | −2623.72 | −0.384117 | ||||||||
\(361\) | 294.676 | 0.0429619 | ||||||||
\(362\) | −639.896 | −0.0929065 | ||||||||
\(363\) | 3503.85 | 0.506624 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12846.7 | −1.84227 | ||||||||
\(366\) | −2675.85 | −0.382156 | ||||||||
\(367\) | 7187.26 | 1.02227 | 0.511134 | − | 0.859501i | \(-0.329226\pi\) | ||||
0.511134 | + | 0.859501i | \(0.329226\pi\) | |||||||
\(368\) | 3048.14 | 0.431781 | ||||||||
\(369\) | 1852.41 | 0.261334 | ||||||||
\(370\) | 8884.26 | 1.24830 | ||||||||
\(371\) | −5372.87 | −0.751874 | ||||||||
\(372\) | 2178.96 | 0.303693 | ||||||||
\(373\) | −2087.99 | −0.289845 | −0.144922 | − | 0.989443i | \(-0.546293\pi\) | ||||
−0.144922 | + | 0.989443i | \(0.546293\pi\) | |||||||
\(374\) | −915.352 | −0.126555 | ||||||||
\(375\) | −559.805 | −0.0770886 | ||||||||
\(376\) | −9183.07 | −1.25952 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 285.486 | 0.0388461 | ||||||||
\(379\) | 3982.08 | 0.539699 | 0.269850 | − | 0.962902i | \(-0.413026\pi\) | ||||
0.269850 | + | 0.962902i | \(0.413026\pi\) | |||||||
\(380\) | 8137.50 | 1.09854 | ||||||||
\(381\) | −825.057 | −0.110942 | ||||||||
\(382\) | −5606.47 | −0.750921 | ||||||||
\(383\) | 8638.43 | 1.15249 | 0.576244 | − | 0.817278i | \(-0.304518\pi\) | ||||
0.576244 | + | 0.817278i | \(0.304518\pi\) | |||||||
\(384\) | −4236.38 | −0.562987 | ||||||||
\(385\) | 1568.72 | 0.207660 | ||||||||
\(386\) | −304.120 | −0.0401018 | ||||||||
\(387\) | −3769.68 | −0.495151 | ||||||||
\(388\) | −7977.70 | −1.04383 | ||||||||
\(389\) | −1275.74 | −0.166279 | −0.0831393 | − | 0.996538i | \(-0.526495\pi\) | ||||
−0.0831393 | + | 0.996538i | \(0.526495\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6634.06 | −0.858053 | ||||||||
\(392\) | −5283.83 | −0.680801 | ||||||||
\(393\) | 3551.91 | 0.455904 | ||||||||
\(394\) | −303.115 | −0.0387582 | ||||||||
\(395\) | 5176.44 | 0.659379 | ||||||||
\(396\) | 716.851 | 0.0909675 | ||||||||
\(397\) | −4622.65 | −0.584394 | −0.292197 | − | 0.956358i | \(-0.594386\pi\) | ||||
−0.292197 | + | 0.956358i | \(0.594386\pi\) | |||||||
\(398\) | −3901.55 | −0.491375 | ||||||||
\(399\) | −2021.03 | −0.253579 | ||||||||
\(400\) | 2801.24 | 0.350155 | ||||||||
\(401\) | −138.075 | −0.0171949 | −0.00859743 | − | 0.999963i | \(-0.502737\pi\) | ||||
−0.00859743 | + | 0.999963i | \(0.502737\pi\) | |||||||
\(402\) | −55.9001 | −0.00693544 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3943.90 | −0.485684 | ||||||||
\(405\) | −1249.35 | −0.153286 | ||||||||
\(406\) | −1489.32 | −0.182053 | ||||||||
\(407\) | −5540.47 | −0.674769 | ||||||||
\(408\) | 3061.90 | 0.371536 | ||||||||
\(409\) | −1204.64 | −0.145637 | −0.0728186 | − | 0.997345i | \(-0.523199\pi\) | ||||
−0.0728186 | + | 0.997345i | \(0.523199\pi\) | |||||||
\(410\) | 4214.32 | 0.507635 | ||||||||
\(411\) | 7672.09 | 0.920770 | ||||||||
\(412\) | −9395.68 | −1.12352 | ||||||||
\(413\) | −1483.29 | −0.176726 | ||||||||
\(414\) | −1467.79 | −0.174246 | ||||||||
\(415\) | 8773.16 | 1.03773 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1637.21 | −0.192265 | ||||||||
\(418\) | 1433.70 | 0.167762 | ||||||||
\(419\) | 5199.85 | 0.606275 | 0.303138 | − | 0.952947i | \(-0.401966\pi\) | ||||
0.303138 | + | 0.952947i | \(0.401966\pi\) | |||||||
\(420\) | −2298.97 | −0.267091 | ||||||||
\(421\) | −14136.5 | −1.63651 | −0.818256 | − | 0.574854i | \(-0.805059\pi\) | ||||
−0.818256 | + | 0.574854i | \(0.805059\pi\) | |||||||
\(422\) | 2133.32 | 0.246086 | ||||||||
\(423\) | −4372.75 | −0.502625 | ||||||||
\(424\) | −12749.6 | −1.46032 | ||||||||
\(425\) | −6096.70 | −0.695844 | ||||||||
\(426\) | 1381.09 | 0.157075 | ||||||||
\(427\) | −5351.71 | −0.606527 | ||||||||
\(428\) | 7912.94 | 0.893660 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8576.21 | −0.961818 | ||||||||
\(431\) | −2279.83 | −0.254793 | −0.127396 | − | 0.991852i | \(-0.540662\pi\) | ||||
−0.127396 | + | 0.991852i | \(0.540662\pi\) | |||||||
\(432\) | −669.905 | −0.0746084 | ||||||||
\(433\) | −13298.7 | −1.47597 | −0.737984 | − | 0.674819i | \(-0.764222\pi\) | ||||
−0.737984 | + | 0.674819i | \(0.764222\pi\) | |||||||
\(434\) | −1231.18 | −0.136172 | ||||||||
\(435\) | 6517.57 | 0.718376 | ||||||||
\(436\) | 2167.14 | 0.238045 | ||||||||
\(437\) | 10390.8 | 1.13744 | ||||||||
\(438\) | 3317.03 | 0.361858 | ||||||||
\(439\) | −10452.3 | −1.13635 | −0.568177 | − | 0.822907i | \(-0.692351\pi\) | ||||
−0.568177 | + | 0.822907i | \(0.692351\pi\) | |||||||
\(440\) | 3722.50 | 0.403325 | ||||||||
\(441\) | −2516.03 | −0.271680 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5363.50 | 0.575232 | 0.287616 | − | 0.957746i | \(-0.407137\pi\) | ||||
0.287616 | + | 0.957746i | \(0.407137\pi\) | |||||||
\(444\) | 8119.62 | 0.867883 | ||||||||
\(445\) | −3650.43 | −0.388870 | ||||||||
\(446\) | 173.726 | 0.0184443 | ||||||||
\(447\) | 4130.34 | 0.437043 | ||||||||
\(448\) | 366.059 | 0.0386042 | ||||||||
\(449\) | 9681.73 | 1.01762 | 0.508808 | − | 0.860880i | \(-0.330086\pi\) | ||||
0.508808 | + | 0.860880i | \(0.330086\pi\) | |||||||
\(450\) | −1348.90 | −0.141306 | ||||||||
\(451\) | −2628.17 | −0.274402 | ||||||||
\(452\) | −4115.07 | −0.428223 | ||||||||
\(453\) | 8200.42 | 0.850528 | ||||||||
\(454\) | 5741.69 | 0.593548 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4795.81 | −0.492510 | ||||||||
\(457\) | −3537.94 | −0.362139 | −0.181070 | − | 0.983470i | \(-0.557956\pi\) | ||||
−0.181070 | + | 0.983470i | \(0.557956\pi\) | |||||||
\(458\) | −3480.14 | −0.355057 | ||||||||
\(459\) | 1458.00 | 0.148265 | ||||||||
\(460\) | 11819.8 | 1.19805 | ||||||||
\(461\) | −15074.9 | −1.52302 | −0.761508 | − | 0.648156i | \(-0.775541\pi\) | ||||
−0.761508 | + | 0.648156i | \(0.775541\pi\) | |||||||
\(462\) | −405.044 | −0.0407886 | ||||||||
\(463\) | −11070.0 | −1.11116 | −0.555580 | − | 0.831463i | \(-0.687504\pi\) | ||||
−0.555580 | + | 0.831463i | \(0.687504\pi\) | |||||||
\(464\) | 3494.74 | 0.349654 | ||||||||
\(465\) | 5387.91 | 0.537330 | ||||||||
\(466\) | 6163.75 | 0.612725 | ||||||||
\(467\) | 13252.8 | 1.31320 | 0.656600 | − | 0.754239i | \(-0.271994\pi\) | ||||
0.656600 | + | 0.754239i | \(0.271994\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −111.800 | −0.0110074 | ||||||||
\(470\) | −9948.23 | −0.976335 | ||||||||
\(471\) | −3089.91 | −0.302284 | ||||||||
\(472\) | −3519.79 | −0.343244 | ||||||||
\(473\) | 5348.36 | 0.519911 | ||||||||
\(474\) | −1336.56 | −0.129515 | ||||||||
\(475\) | 9549.18 | 0.922413 | ||||||||
\(476\) | 2682.92 | 0.258343 | ||||||||
\(477\) | −6071.03 | −0.582753 | ||||||||
\(478\) | 8889.86 | 0.850654 | ||||||||
\(479\) | 12241.4 | 1.16769 | 0.583843 | − | 0.811866i | \(-0.301548\pi\) | ||||
0.583843 | + | 0.811866i | \(0.301548\pi\) | |||||||
\(480\) | −8520.66 | −0.810236 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3055.20 | 0.288715 | ||||||||
\(483\) | −2935.57 | −0.276549 | ||||||||
\(484\) | 7285.37 | 0.684201 | ||||||||
\(485\) | −19726.5 | −1.84687 | ||||||||
\(486\) | 322.583 | 0.0301084 | ||||||||
\(487\) | −13413.3 | −1.24808 | −0.624041 | − | 0.781392i | \(-0.714510\pi\) | ||||
−0.624041 | + | 0.781392i | \(0.714510\pi\) | |||||||
\(488\) | −12699.4 | −1.17802 | ||||||||
\(489\) | −8648.74 | −0.799815 | ||||||||
\(490\) | −5724.10 | −0.527731 | ||||||||
\(491\) | −737.885 | −0.0678214 | −0.0339107 | − | 0.999425i | \(-0.510796\pi\) | ||||
−0.0339107 | + | 0.999425i | \(0.510796\pi\) | |||||||
\(492\) | 3851.61 | 0.352935 | ||||||||
\(493\) | −7606.06 | −0.694847 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1772.56 | 0.160951 | ||||||||
\(496\) | 2889.01 | 0.261533 | ||||||||
\(497\) | 2762.17 | 0.249297 | ||||||||
\(498\) | −2265.24 | −0.203831 | ||||||||
\(499\) | 1865.65 | 0.167370 | 0.0836852 | − | 0.996492i | \(-0.473331\pi\) | ||||
0.0836852 | + | 0.996492i | \(0.473331\pi\) | |||||||
\(500\) | −1163.97 | −0.104109 | ||||||||
\(501\) | 3461.70 | 0.308697 | ||||||||
\(502\) | −1099.17 | −0.0977259 | ||||||||
\(503\) | −16632.0 | −1.47432 | −0.737161 | − | 0.675717i | \(-0.763834\pi\) | ||||
−0.737161 | + | 0.675717i | \(0.763834\pi\) | |||||||
\(504\) | 1354.89 | 0.119745 | ||||||||
\(505\) | −9752.09 | −0.859331 | ||||||||
\(506\) | 2082.47 | 0.182959 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1715.50 | −0.149829 | ||||||||
\(509\) | 4128.91 | 0.359549 | 0.179775 | − | 0.983708i | \(-0.442463\pi\) | ||||
0.179775 | + | 0.983708i | \(0.442463\pi\) | |||||||
\(510\) | 3317.03 | 0.288001 | ||||||||
\(511\) | 6634.06 | 0.574312 | ||||||||
\(512\) | −8320.40 | −0.718190 | ||||||||
\(513\) | −2283.64 | −0.196541 | ||||||||
\(514\) | −1174.52 | −0.100790 | ||||||||
\(515\) | −23232.7 | −1.98788 | ||||||||
\(516\) | −7838.08 | −0.668706 | ||||||||
\(517\) | 6203.99 | 0.527758 | ||||||||
\(518\) | −4587.85 | −0.389147 | ||||||||
\(519\) | 5066.56 | 0.428511 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −988.234 | −0.0831005 | −0.0415502 | − | 0.999136i | \(-0.513230\pi\) | ||||
−0.0415502 | + | 0.999136i | \(0.513230\pi\) | |||||||
\(522\) | −1682.84 | −0.141103 | ||||||||
\(523\) | −9441.62 | −0.789394 | −0.394697 | − | 0.918811i | \(-0.629150\pi\) | ||||
−0.394697 | + | 0.918811i | \(0.629150\pi\) | |||||||
\(524\) | 7385.30 | 0.615703 | ||||||||
\(525\) | −2697.79 | −0.224269 | ||||||||
\(526\) | 11076.6 | 0.918180 | ||||||||
\(527\) | −6287.73 | −0.519730 | ||||||||
\(528\) | 950.452 | 0.0783392 | ||||||||
\(529\) | 2925.83 | 0.240472 | ||||||||
\(530\) | −13811.9 | −1.13198 | ||||||||
\(531\) | −1676.03 | −0.136975 | ||||||||
\(532\) | −4202.21 | −0.342461 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 942.544 | 0.0763817 | ||||||||
\(535\) | 19566.3 | 1.58117 | ||||||||
\(536\) | −265.297 | −0.0213789 | ||||||||
\(537\) | 2828.38 | 0.227288 | ||||||||
\(538\) | −3667.30 | −0.293882 | ||||||||
\(539\) | 3569.70 | 0.285265 | ||||||||
\(540\) | −2597.71 | −0.207014 | ||||||||
\(541\) | 14001.5 | 1.11270 | 0.556351 | − | 0.830948i | \(-0.312201\pi\) | ||||
0.556351 | + | 0.830948i | \(0.312201\pi\) | |||||||
\(542\) | −4137.22 | −0.327876 | ||||||||
\(543\) | −1446.09 | −0.114287 | ||||||||
\(544\) | 9943.67 | 0.783697 | ||||||||
\(545\) | 5358.70 | 0.421177 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4244.85 | −0.331804 | −0.165902 | − | 0.986142i | \(-0.553053\pi\) | ||||
−0.165902 | + | 0.986142i | \(0.553053\pi\) | |||||||
\(548\) | 15952.2 | 1.24351 | ||||||||
\(549\) | −6047.12 | −0.470100 | ||||||||
\(550\) | 1913.80 | 0.148372 | ||||||||
\(551\) | 11913.3 | 0.921092 | ||||||||
\(552\) | −6965.99 | −0.537123 | ||||||||
\(553\) | −2673.12 | −0.205556 | ||||||||
\(554\) | 666.485 | 0.0511124 | ||||||||
\(555\) | 20077.4 | 1.53556 | ||||||||
\(556\) | −3404.16 | −0.259655 | ||||||||
\(557\) | −11732.2 | −0.892473 | −0.446236 | − | 0.894915i | \(-0.647236\pi\) | ||||
−0.446236 | + | 0.894915i | \(0.647236\pi\) | |||||||
\(558\) | −1391.16 | −0.105542 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3048.14 | −0.230013 | ||||||||
\(561\) | −2068.59 | −0.155679 | ||||||||
\(562\) | 8771.54 | 0.658372 | ||||||||
\(563\) | −9941.80 | −0.744222 | −0.372111 | − | 0.928188i | \(-0.621366\pi\) | ||||
−0.372111 | + | 0.928188i | \(0.621366\pi\) | |||||||
\(564\) | −9092.02 | −0.678800 | ||||||||
\(565\) | −10175.3 | −0.757664 | ||||||||
\(566\) | 5799.83 | 0.430716 | ||||||||
\(567\) | 645.166 | 0.0477856 | ||||||||
\(568\) | 6554.52 | 0.484193 | ||||||||
\(569\) | 3690.77 | 0.271925 | 0.135962 | − | 0.990714i | \(-0.456587\pi\) | ||||
0.135962 | + | 0.990714i | \(0.456587\pi\) | |||||||
\(570\) | −5195.41 | −0.381775 | ||||||||
\(571\) | −5685.09 | −0.416661 | −0.208331 | − | 0.978058i | \(-0.566803\pi\) | ||||
−0.208331 | + | 0.978058i | \(0.566803\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12670.0 | −0.923727 | ||||||||
\(574\) | −2176.28 | −0.158251 | ||||||||
\(575\) | 13870.3 | 1.00597 | ||||||||
\(576\) | 413.626 | 0.0299209 | ||||||||
\(577\) | 7746.50 | 0.558910 | 0.279455 | − | 0.960159i | \(-0.409846\pi\) | ||||
0.279455 | + | 0.960159i | \(0.409846\pi\) | |||||||
\(578\) | 2651.02 | 0.190775 | ||||||||
\(579\) | −687.275 | −0.0493302 | ||||||||
\(580\) | 13551.6 | 0.970175 | ||||||||
\(581\) | −4530.47 | −0.323504 | ||||||||
\(582\) | 5093.39 | 0.362762 | ||||||||
\(583\) | 8613.48 | 0.611894 | ||||||||
\(584\) | 15742.3 | 1.11545 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7099.64 | 0.500484 | ||||||||
\(587\) | −2766.54 | −0.194527 | −0.0972635 | − | 0.995259i | \(-0.531009\pi\) | ||||
−0.0972635 | + | 0.995259i | \(0.531009\pi\) | |||||||
\(588\) | −5231.44 | −0.366906 | ||||||||
\(589\) | 9848.38 | 0.688957 | ||||||||
\(590\) | −3813.07 | −0.266070 | ||||||||
\(591\) | −685.006 | −0.0476774 | ||||||||
\(592\) | 10765.6 | 0.747402 | ||||||||
\(593\) | −1440.79 | −0.0997743 | −0.0498871 | − | 0.998755i | \(-0.515886\pi\) | ||||
−0.0498871 | + | 0.998755i | \(0.515886\pi\) | |||||||
\(594\) | −457.676 | −0.0316139 | ||||||||
\(595\) | 6634.06 | 0.457092 | ||||||||
\(596\) | 8587.99 | 0.590231 | ||||||||
\(597\) | −8817.06 | −0.604452 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23837.5 | 1.62600 | 0.813001 | − | 0.582263i | \(-0.197832\pi\) | ||||
0.813001 | + | 0.582263i | \(0.197832\pi\) | |||||||
\(600\) | −6401.75 | −0.435584 | ||||||||
\(601\) | −6694.23 | −0.454348 | −0.227174 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227174 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(602\) | 4428.77 | 0.299839 | ||||||||
\(603\) | −126.328 | −0.00853145 | ||||||||
\(604\) | 17050.7 | 1.14865 | ||||||||
\(605\) | 18014.6 | 1.21057 | ||||||||
\(606\) | 2518.00 | 0.168790 | ||||||||
\(607\) | 3330.50 | 0.222703 | 0.111352 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111352 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(608\) | −15574.6 | −1.03887 | ||||||||
\(609\) | −3365.68 | −0.223948 | ||||||||
\(610\) | −13757.5 | −0.913156 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3031.54 | 0.200233 | ||||||||
\(613\) | −13490.3 | −0.888857 | −0.444428 | − | 0.895814i | \(-0.646593\pi\) | ||||
−0.444428 | + | 0.895814i | \(0.646593\pi\) | |||||||
\(614\) | 5977.02 | 0.392855 | ||||||||
\(615\) | 9523.88 | 0.624455 | ||||||||
\(616\) | −1922.30 | −0.125733 | ||||||||
\(617\) | 7470.76 | 0.487458 | 0.243729 | − | 0.969843i | \(-0.421629\pi\) | ||||
0.243729 | + | 0.969843i | \(0.421629\pi\) | |||||||
\(618\) | 5998.71 | 0.390458 | ||||||||
\(619\) | 24806.9 | 1.61078 | 0.805389 | − | 0.592746i | \(-0.201956\pi\) | ||||
0.805389 | + | 0.592746i | \(0.201956\pi\) | |||||||
\(620\) | 11202.8 | 0.725669 | ||||||||
\(621\) | −3317.03 | −0.214344 | ||||||||
\(622\) | 9886.17 | 0.637298 | ||||||||
\(623\) | 1885.09 | 0.121227 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16990.9 | −1.08742 | ||||||||
\(626\) | 8640.61 | 0.551675 | ||||||||
\(627\) | 3240.00 | 0.206369 | ||||||||
\(628\) | −6424.68 | −0.408237 | ||||||||
\(629\) | −23430.5 | −1.48527 | ||||||||
\(630\) | 1467.79 | 0.0928222 | ||||||||
\(631\) | 314.333 | 0.0198311 | 0.00991554 | − | 0.999951i | \(-0.496844\pi\) | ||||
0.00991554 | + | 0.999951i | \(0.496844\pi\) | |||||||
\(632\) | −6343.19 | −0.399238 | ||||||||
\(633\) | 4821.06 | 0.302717 | ||||||||
\(634\) | −3273.05 | −0.205031 | ||||||||
\(635\) | −4241.91 | −0.265095 | ||||||||
\(636\) | −12623.2 | −0.787014 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2387.59 | 0.148159 | ||||||||
\(639\) | 3121.10 | 0.193222 | ||||||||
\(640\) | −21780.7 | −1.34525 | ||||||||
\(641\) | 5550.41 | 0.342009 | 0.171005 | − | 0.985270i | \(-0.445299\pi\) | ||||
0.171005 | + | 0.985270i | \(0.445299\pi\) | |||||||
\(642\) | −5052.04 | −0.310573 | ||||||||
\(643\) | 5479.48 | 0.336065 | 0.168032 | − | 0.985781i | \(-0.446259\pi\) | ||||
0.168032 | + | 0.985781i | \(0.446259\pi\) | |||||||
\(644\) | −6103.78 | −0.373482 | ||||||||
\(645\) | −19381.2 | −1.18316 | ||||||||
\(646\) | 6063.08 | 0.369271 | ||||||||
\(647\) | 4724.83 | 0.287098 | 0.143549 | − | 0.989643i | \(-0.454149\pi\) | ||||
0.143549 | + | 0.989643i | \(0.454149\pi\) | |||||||
\(648\) | 1530.95 | 0.0928108 | ||||||||
\(649\) | 2377.93 | 0.143824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2782.32 | −0.167508 | ||||||||
\(652\) | −17982.9 | −1.08016 | ||||||||
\(653\) | 3463.91 | 0.207585 | 0.103793 | − | 0.994599i | \(-0.466902\pi\) | ||||
0.103793 | + | 0.994599i | \(0.466902\pi\) | |||||||
\(654\) | −1383.62 | −0.0827276 | ||||||||
\(655\) | 18261.6 | 1.08938 | ||||||||
\(656\) | 5106.73 | 0.303940 | ||||||||
\(657\) | 7496.10 | 0.445130 | ||||||||
\(658\) | 5137.28 | 0.304365 | ||||||||
\(659\) | −2606.35 | −0.154065 | −0.0770327 | − | 0.997029i | \(-0.524545\pi\) | ||||
−0.0770327 | + | 0.997029i | \(0.524545\pi\) | |||||||
\(660\) | 3685.59 | 0.217366 | ||||||||
\(661\) | −22436.7 | −1.32025 | −0.660127 | − | 0.751154i | \(-0.729498\pi\) | ||||
−0.660127 | + | 0.751154i | \(0.729498\pi\) | |||||||
\(662\) | 5462.46 | 0.320702 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10750.6 | −0.628321 | ||||||||
\(665\) | −10390.8 | −0.605923 | ||||||||
\(666\) | −5184.00 | −0.301615 | ||||||||
\(667\) | 17304.2 | 1.00453 | ||||||||
\(668\) | 7197.73 | 0.416899 | ||||||||
\(669\) | 392.600 | 0.0226888 | ||||||||
\(670\) | −287.403 | −0.0165721 | ||||||||
\(671\) | 8579.56 | 0.493607 | ||||||||
\(672\) | 4400.08 | 0.252584 | ||||||||
\(673\) | −633.970 | −0.0363117 | −0.0181558 | − | 0.999835i | \(-0.505779\pi\) | ||||
−0.0181558 | + | 0.999835i | \(0.505779\pi\) | |||||||
\(674\) | −6369.42 | −0.364007 | ||||||||
\(675\) | −3048.35 | −0.173824 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24457.4 | 1.38844 | 0.694221 | − | 0.719762i | \(-0.255749\pi\) | ||||
0.694221 | + | 0.719762i | \(0.255749\pi\) | |||||||
\(678\) | 2627.28 | 0.148820 | ||||||||
\(679\) | 10186.8 | 0.575747 | ||||||||
\(680\) | 15742.3 | 0.887780 | ||||||||
\(681\) | 12975.6 | 0.730139 | ||||||||
\(682\) | 1973.76 | 0.110820 | ||||||||
\(683\) | −12367.6 | −0.692875 | −0.346437 | − | 0.938073i | \(-0.612609\pi\) | ||||
−0.346437 | + | 0.938073i | \(0.612609\pi\) | |||||||
\(684\) | −4748.26 | −0.265430 | ||||||||
\(685\) | 39445.0 | 2.20017 | ||||||||
\(686\) | 6582.66 | 0.366366 | ||||||||
\(687\) | −7864.71 | −0.436765 | ||||||||
\(688\) | −10392.3 | −0.575875 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −7546.41 | −0.416358 | ||||||||
\(691\) | 1050.99 | 0.0578605 | 0.0289302 | − | 0.999581i | \(-0.490790\pi\) | ||||
0.0289302 | + | 0.999581i | \(0.490790\pi\) | |||||||
\(692\) | 10534.6 | 0.578709 | ||||||||
\(693\) | −915.352 | −0.0501751 | ||||||||
\(694\) | 4400.35 | 0.240685 | ||||||||
\(695\) | −8417.46 | −0.459414 | ||||||||
\(696\) | −7986.62 | −0.434960 | ||||||||
\(697\) | −11114.4 | −0.604002 | ||||||||
\(698\) | 493.486 | 0.0267603 | ||||||||
\(699\) | 13929.4 | 0.753729 | ||||||||
\(700\) | −5609.38 | −0.302878 | ||||||||
\(701\) | −24294.1 | −1.30895 | −0.654476 | − | 0.756083i | \(-0.727111\pi\) | ||||
−0.654476 | + | 0.756083i | \(0.727111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36698.8 | 1.96888 | ||||||||
\(704\) | −586.846 | −0.0314170 | ||||||||
\(705\) | −22481.8 | −1.20101 | ||||||||
\(706\) | −10008.2 | −0.533516 | ||||||||
\(707\) | 5035.99 | 0.267890 | ||||||||
\(708\) | −3484.89 | −0.184986 | ||||||||
\(709\) | −27465.9 | −1.45487 | −0.727436 | − | 0.686176i | \(-0.759288\pi\) | ||||
−0.727436 | + | 0.686176i | \(0.759288\pi\) | |||||||
\(710\) | 7100.66 | 0.375328 | ||||||||
\(711\) | −3020.47 | −0.159320 | ||||||||
\(712\) | 4473.23 | 0.235451 | ||||||||
\(713\) | 14304.9 | 0.751365 | ||||||||
\(714\) | −1712.92 | −0.0897820 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5880.90 | 0.306955 | ||||||||
\(717\) | 20090.1 | 1.04641 | ||||||||
\(718\) | −16914.3 | −0.879160 | ||||||||
\(719\) | 36433.5 | 1.88976 | 0.944882 | − | 0.327411i | \(-0.106176\pi\) | ||||
0.944882 | + | 0.327411i | \(0.106176\pi\) | |||||||
\(720\) | −3444.22 | −0.178276 | ||||||||
\(721\) | 11997.4 | 0.619704 | ||||||||
\(722\) | −391.183 | −0.0201639 | ||||||||
\(723\) | 6904.40 | 0.355156 | ||||||||
\(724\) | −3006.78 | −0.154345 | ||||||||
\(725\) | 15902.6 | 0.814629 | ||||||||
\(726\) | −4651.37 | −0.237780 | ||||||||
\(727\) | 551.608 | 0.0281403 | 0.0140701 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140701 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 17054.0 | 0.864654 | ||||||||
\(731\) | 22618.1 | 1.14440 | ||||||||
\(732\) | −12573.4 | −0.634874 | ||||||||
\(733\) | −20317.2 | −1.02379 | −0.511893 | − | 0.859049i | \(-0.671055\pi\) | ||||
−0.511893 | + | 0.859049i | \(0.671055\pi\) | |||||||
\(734\) | −9541.10 | −0.479794 | ||||||||
\(735\) | −12935.8 | −0.649175 | ||||||||
\(736\) | −22622.4 | −1.13298 | ||||||||
\(737\) | 179.232 | 0.00895807 | ||||||||
\(738\) | −2459.07 | −0.122655 | ||||||||
\(739\) | 29931.6 | 1.48992 | 0.744962 | − | 0.667107i | \(-0.232468\pi\) | ||||
0.744962 | + | 0.667107i | \(0.232468\pi\) | |||||||
\(740\) | 41745.9 | 2.07380 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7132.49 | 0.352887 | ||||||||
\(743\) | −24376.4 | −1.20361 | −0.601805 | − | 0.798643i | \(-0.705552\pi\) | ||||
−0.601805 | + | 0.798643i | \(0.705552\pi\) | |||||||
\(744\) | −6602.33 | −0.325340 | ||||||||
\(745\) | 21235.5 | 1.04431 | ||||||||
\(746\) | 2771.81 | 0.136037 | ||||||||
\(747\) | −5119.17 | −0.250737 | ||||||||
\(748\) | −4301.11 | −0.210246 | ||||||||
\(749\) | −10104.1 | −0.492917 | ||||||||
\(750\) | 743.142 | 0.0361810 | ||||||||
\(751\) | 22692.2 | 1.10260 | 0.551298 | − | 0.834308i | \(-0.314133\pi\) | ||||
0.551298 | + | 0.834308i | \(0.314133\pi\) | |||||||
\(752\) | −12054.8 | −0.584567 | ||||||||
\(753\) | −2484.00 | −0.120215 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42161.3 | 2.03232 | ||||||||
\(756\) | 1341.46 | 0.0645349 | ||||||||
\(757\) | −33063.5 | −1.58747 | −0.793734 | − | 0.608265i | \(-0.791866\pi\) | ||||
−0.793734 | + | 0.608265i | \(0.791866\pi\) | |||||||
\(758\) | −5286.22 | −0.253304 | ||||||||
\(759\) | 4706.15 | 0.225062 | ||||||||
\(760\) | −24657.0 | −1.17685 | ||||||||
\(761\) | 216.324 | 0.0103045 | 0.00515226 | − | 0.999987i | \(-0.498360\pi\) | ||||
0.00515226 | + | 0.999987i | \(0.498360\pi\) | |||||||
\(762\) | 1095.27 | 0.0520699 | ||||||||
\(763\) | −2767.24 | −0.131299 | ||||||||
\(764\) | −26344.0 | −1.24750 | ||||||||
\(765\) | 7496.10 | 0.354277 | ||||||||
\(766\) | −11467.5 | −0.540912 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 6726.80 | 0.316058 | ||||||||
\(769\) | −19214.4 | −0.901025 | −0.450512 | − | 0.892770i | \(-0.648759\pi\) | ||||
−0.450512 | + | 0.892770i | \(0.648759\pi\) | |||||||
\(770\) | −2082.47 | −0.0974638 | ||||||||
\(771\) | −2654.29 | −0.123984 | ||||||||
\(772\) | −1429.01 | −0.0666209 | ||||||||
\(773\) | −33175.6 | −1.54365 | −0.771826 | − | 0.635834i | \(-0.780656\pi\) | ||||
−0.771826 | + | 0.635834i | \(0.780656\pi\) | |||||||
\(774\) | 5004.25 | 0.232395 | ||||||||
\(775\) | 13146.2 | 0.609325 | ||||||||
\(776\) | 24172.8 | 1.11824 | ||||||||
\(777\) | −10368.0 | −0.478700 | ||||||||
\(778\) | 1693.54 | 0.0780416 | ||||||||
\(779\) | 17408.4 | 0.800667 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4428.17 | −0.202884 | ||||||||
\(782\) | 8806.72 | 0.402721 | ||||||||
\(783\) | −3803.03 | −0.173575 | ||||||||
\(784\) | −6936.21 | −0.315972 | ||||||||
\(785\) | −15886.3 | −0.722302 | ||||||||
\(786\) | −4715.17 | −0.213975 | ||||||||
\(787\) | 14887.9 | 0.674330 | 0.337165 | − | 0.941446i | \(-0.390532\pi\) | ||||
0.337165 | + | 0.941446i | \(0.390532\pi\) | |||||||
\(788\) | −1424.30 | −0.0643889 | ||||||||
\(789\) | 25031.8 | 1.12948 | ||||||||
\(790\) | −6871.73 | −0.309475 | ||||||||
\(791\) | 5254.56 | 0.236196 | ||||||||
\(792\) | −2172.09 | −0.0974518 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6136.58 | 0.274281 | ||||||||
\(795\) | −31213.3 | −1.39248 | ||||||||
\(796\) | −18332.8 | −0.816319 | ||||||||
\(797\) | 12954.5 | 0.575751 | 0.287876 | − | 0.957668i | \(-0.407051\pi\) | ||||
0.287876 | + | 0.957668i | \(0.407051\pi\) | |||||||
\(798\) | 2682.92 | 0.119015 | ||||||||
\(799\) | 26236.5 | 1.16168 | ||||||||
\(800\) | −20790.0 | −0.918796 | ||||||||
\(801\) | 2130.04 | 0.0939591 | ||||||||
\(802\) | 183.295 | 0.00807028 | ||||||||
\(803\) | −10635.4 | −0.467389 | ||||||||
\(804\) | −262.667 | −0.0115218 | ||||||||
\(805\) | −15092.8 | −0.660810 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8287.68 | −0.361512 | ||||||||
\(808\) | 11950.2 | 0.520305 | ||||||||
\(809\) | 8275.59 | 0.359647 | 0.179823 | − | 0.983699i | \(-0.442447\pi\) | ||||
0.179823 | + | 0.983699i | \(0.442447\pi\) | |||||||
\(810\) | 1658.51 | 0.0719435 | ||||||||
\(811\) | −26327.1 | −1.13991 | −0.569956 | − | 0.821675i | \(-0.693040\pi\) | ||||
−0.569956 | + | 0.821675i | \(0.693040\pi\) | |||||||
\(812\) | −6998.09 | −0.302444 | ||||||||
\(813\) | −9349.63 | −0.403328 | ||||||||
\(814\) | 7354.98 | 0.316698 | ||||||||
\(815\) | −44466.3 | −1.91115 | ||||||||
\(816\) | 4019.43 | 0.172437 | ||||||||
\(817\) | −35426.3 | −1.51703 | ||||||||
\(818\) | 1599.16 | 0.0683538 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 19802.5 | 0.843333 | ||||||||
\(821\) | 34439.0 | 1.46398 | 0.731992 | − | 0.681314i | \(-0.238591\pi\) | ||||
0.731992 | + | 0.681314i | \(0.238591\pi\) | |||||||
\(822\) | −10184.7 | −0.432157 | ||||||||
\(823\) | −13870.5 | −0.587479 | −0.293739 | − | 0.955886i | \(-0.594900\pi\) | ||||
−0.293739 | + | 0.955886i | \(0.594900\pi\) | |||||||
\(824\) | 28469.3 | 1.20361 | ||||||||
\(825\) | 4324.96 | 0.182516 | ||||||||
\(826\) | 1969.07 | 0.0829453 | ||||||||
\(827\) | −2132.30 | −0.0896583 | −0.0448292 | − | 0.998995i | \(-0.514274\pi\) | ||||
−0.0448292 | + | 0.998995i | \(0.514274\pi\) | |||||||
\(828\) | −6896.92 | −0.289474 | ||||||||
\(829\) | −6212.39 | −0.260272 | −0.130136 | − | 0.991496i | \(-0.541541\pi\) | ||||
−0.130136 | + | 0.991496i | \(0.541541\pi\) | |||||||
\(830\) | −11646.4 | −0.487051 | ||||||||
\(831\) | 1506.18 | 0.0628746 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15096.2 | 0.627913 | ||||||||
\(834\) | 2173.40 | 0.0902380 | ||||||||
\(835\) | 17797.8 | 0.737628 | ||||||||
\(836\) | 6736.76 | 0.278703 | ||||||||
\(837\) | −3143.87 | −0.129830 | ||||||||
\(838\) | −6902.81 | −0.284551 | ||||||||
\(839\) | 4550.52 | 0.187248 | 0.0936242 | − | 0.995608i | \(-0.470155\pi\) | ||||
0.0936242 | + | 0.995608i | \(0.470155\pi\) | |||||||
\(840\) | 6965.99 | 0.286130 | ||||||||
\(841\) | −4549.47 | −0.186538 | ||||||||
\(842\) | 18766.2 | 0.768085 | ||||||||
\(843\) | 19822.7 | 0.809880 | ||||||||
\(844\) | 10024.2 | 0.408822 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5804.83 | 0.235903 | ||||||||
\(847\) | −9302.74 | −0.377386 | ||||||||
\(848\) | −16736.7 | −0.677759 | ||||||||
\(849\) | 13106.9 | 0.529834 | ||||||||
\(850\) | 8093.38 | 0.326589 | ||||||||
\(851\) | 53305.6 | 2.14723 | ||||||||
\(852\) | 6489.53 | 0.260948 | ||||||||
\(853\) | −12262.8 | −0.492228 | −0.246114 | − | 0.969241i | \(-0.579154\pi\) | ||||
−0.246114 | + | 0.969241i | \(0.579154\pi\) | |||||||
\(854\) | 7104.40 | 0.284669 | ||||||||
\(855\) | −11741.0 | −0.469631 | ||||||||
\(856\) | −23976.5 | −0.957362 | ||||||||
\(857\) | −34949.1 | −1.39304 | −0.696521 | − | 0.717536i | \(-0.745270\pi\) | ||||
−0.696521 | + | 0.717536i | \(0.745270\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21762.1 | −0.864394 | −0.432197 | − | 0.901779i | \(-0.642261\pi\) | ||||
−0.432197 | + | 0.901779i | \(0.642261\pi\) | |||||||
\(860\) | −40298.4 | −1.59786 | ||||||||
\(861\) | −4918.14 | −0.194669 | ||||||||
\(862\) | 3026.48 | 0.119585 | ||||||||
\(863\) | 19811.5 | 0.781450 | 0.390725 | − | 0.920507i | \(-0.372224\pi\) | ||||
0.390725 | + | 0.920507i | \(0.372224\pi\) | |||||||
\(864\) | 4971.83 | 0.195770 | ||||||||
\(865\) | 26049.0 | 1.02392 | ||||||||
\(866\) | 17654.0 | 0.692735 | ||||||||
\(867\) | 5991.00 | 0.234677 | ||||||||
\(868\) | −5785.14 | −0.226222 | ||||||||
\(869\) | 4285.40 | 0.167287 | ||||||||
\(870\) | −8652.09 | −0.337165 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6566.54 | −0.255013 | ||||||||
\(873\) | 11510.5 | 0.446243 | ||||||||
\(874\) | −13793.8 | −0.533848 | ||||||||
\(875\) | 1486.28 | 0.0574235 | ||||||||
\(876\) | 15586.2 | 0.601153 | ||||||||
\(877\) | 25716.8 | 0.990186 | 0.495093 | − | 0.868840i | \(-0.335134\pi\) | ||||
0.495093 | + | 0.868840i | \(0.335134\pi\) | |||||||
\(878\) | 13875.4 | 0.533339 | ||||||||
\(879\) | 16044.4 | 0.615658 | ||||||||
\(880\) | 4886.61 | 0.187190 | ||||||||
\(881\) | 34709.6 | 1.32735 | 0.663676 | − | 0.748020i | \(-0.268995\pi\) | ||||
0.663676 | + | 0.748020i | \(0.268995\pi\) | |||||||
\(882\) | 3340.03 | 0.127511 | ||||||||
\(883\) | −3848.68 | −0.146680 | −0.0733400 | − | 0.997307i | \(-0.523366\pi\) | ||||
−0.0733400 | + | 0.997307i | \(0.523366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8617.09 | −0.327300 | ||||||||
\(886\) | −7120.06 | −0.269981 | ||||||||
\(887\) | 32804.8 | 1.24180 | 0.620900 | − | 0.783890i | \(-0.286767\pi\) | ||||
0.620900 | + | 0.783890i | \(0.286767\pi\) | |||||||
\(888\) | −24602.8 | −0.929748 | ||||||||
\(889\) | 2190.53 | 0.0826412 | ||||||||
\(890\) | 4845.95 | 0.182513 | ||||||||
\(891\) | −1034.29 | −0.0388891 | ||||||||
\(892\) | 816.311 | 0.0306414 | ||||||||
\(893\) | −41093.8 | −1.53992 | ||||||||
\(894\) | −5483.03 | −0.205123 | ||||||||
\(895\) | 14541.7 | 0.543101 | ||||||||
\(896\) | 11247.6 | 0.419371 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12852.5 | −0.477610 | ||||||||
\(899\) | 16400.8 | 0.608452 | ||||||||
\(900\) | −6338.27 | −0.234751 | ||||||||
\(901\) | 36426.2 | 1.34687 | ||||||||
\(902\) | 3488.90 | 0.128789 | ||||||||
\(903\) | 10008.5 | 0.368840 | ||||||||
\(904\) | 12468.8 | 0.458748 | ||||||||
\(905\) | −7434.86 | −0.273086 | ||||||||
\(906\) | −10886.1 | −0.399189 | ||||||||
\(907\) | −22262.2 | −0.814999 | −0.407500 | − | 0.913205i | \(-0.633599\pi\) | ||||
−0.407500 | + | 0.913205i | \(0.633599\pi\) | |||||||
\(908\) | 26979.4 | 0.986060 | ||||||||
\(909\) | 5690.38 | 0.207633 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13515.3 | −0.491528 | −0.245764 | − | 0.969330i | \(-0.579039\pi\) | ||||
−0.245764 | + | 0.969330i | \(0.579039\pi\) | |||||||
\(912\) | −6295.58 | −0.228583 | ||||||||
\(913\) | 7263.01 | 0.263275 | ||||||||
\(914\) | 4696.62 | 0.169968 | ||||||||
\(915\) | −31090.4 | −1.12330 | ||||||||
\(916\) | −16352.7 | −0.589855 | ||||||||
\(917\) | −9430.33 | −0.339604 | ||||||||
\(918\) | −1935.50 | −0.0695871 | ||||||||
\(919\) | 26600.6 | 0.954811 | 0.477405 | − | 0.878683i | \(-0.341577\pi\) | ||||
0.477405 | + | 0.878683i | \(0.341577\pi\) | |||||||
\(920\) | −35814.6 | −1.28345 | ||||||||
\(921\) | 13507.4 | 0.483260 | ||||||||
\(922\) | 20012.0 | 0.714816 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1903.24 | −0.0677620 | ||||||||
\(925\) | 48987.9 | 1.74131 | ||||||||
\(926\) | 14695.5 | 0.521515 | ||||||||
\(927\) | 13556.4 | 0.480313 | ||||||||
\(928\) | −25936.9 | −0.917480 | ||||||||
\(929\) | 32887.7 | 1.16148 | 0.580738 | − | 0.814090i | \(-0.302764\pi\) | ||||
0.580738 | + | 0.814090i | \(0.302764\pi\) | |||||||
\(930\) | −7152.46 | −0.252192 | ||||||||
\(931\) | −23644.9 | −0.832363 | ||||||||
\(932\) | 28962.6 | 1.01792 | ||||||||
\(933\) | 22341.6 | 0.783956 | ||||||||
\(934\) | −17593.1 | −0.616341 | ||||||||
\(935\) | −10635.4 | −0.371993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9261.78 | −0.322913 | −0.161456 | − | 0.986880i | \(-0.551619\pi\) | ||||
−0.161456 | + | 0.986880i | \(0.551619\pi\) | |||||||
\(938\) | 148.415 | 0.00516623 | ||||||||
\(939\) | 19526.8 | 0.678629 | ||||||||
\(940\) | −46745.3 | −1.62198 | ||||||||
\(941\) | −12054.9 | −0.417619 | −0.208810 | − | 0.977956i | \(-0.566959\pi\) | ||||
−0.208810 | + | 0.977956i | \(0.566959\pi\) | |||||||
\(942\) | 4101.86 | 0.141875 | ||||||||
\(943\) | 25285.9 | 0.873195 | ||||||||
\(944\) | −4620.51 | −0.159306 | ||||||||
\(945\) | 3317.03 | 0.114183 | ||||||||
\(946\) | −7099.96 | −0.244016 | ||||||||
\(947\) | −20221.4 | −0.693885 | −0.346942 | − | 0.937886i | \(-0.612780\pi\) | ||||
−0.346942 | + | 0.937886i | \(0.612780\pi\) | |||||||
\(948\) | −6280.30 | −0.215163 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12676.5 | −0.432928 | ||||||||
\(951\) | −7396.72 | −0.252213 | ||||||||
\(952\) | −8129.36 | −0.276758 | ||||||||
\(953\) | −20331.5 | −0.691083 | −0.345542 | − | 0.938403i | \(-0.612305\pi\) | ||||
−0.345542 | + | 0.938403i | \(0.612305\pi\) | |||||||
\(954\) | 8059.30 | 0.273511 | ||||||||
\(955\) | −65140.8 | −2.20723 | ||||||||
\(956\) | 41772.2 | 1.41319 | ||||||||
\(957\) | 5395.68 | 0.182254 | ||||||||
\(958\) | −16250.4 | −0.548045 | ||||||||
\(959\) | −20369.4 | −0.685885 | ||||||||
\(960\) | 2126.60 | 0.0714955 | ||||||||
\(961\) | −16232.9 | −0.544891 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11417.0 | −0.382044 | ||||||||
\(964\) | 14356.0 | 0.479641 | ||||||||
\(965\) | −3533.53 | −0.117874 | ||||||||
\(966\) | 3896.98 | 0.129796 | ||||||||
\(967\) | 11082.2 | 0.368541 | 0.184270 | − | 0.982876i | \(-0.441008\pi\) | ||||
0.184270 | + | 0.982876i | \(0.441008\pi\) | |||||||
\(968\) | −22075.0 | −0.732973 | ||||||||
\(969\) | 13701.9 | 0.454249 | ||||||||
\(970\) | 26186.9 | 0.866816 | ||||||||
\(971\) | −36694.1 | −1.21274 | −0.606369 | − | 0.795184i | \(-0.707374\pi\) | ||||
−0.606369 | + | 0.795184i | \(0.707374\pi\) | |||||||
\(972\) | 1515.77 | 0.0500189 | ||||||||
\(973\) | 4346.79 | 0.143219 | ||||||||
\(974\) | 17806.2 | 0.585778 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16670.8 | −0.546740 | ||||||||
\(977\) | −17155.3 | −0.561767 | −0.280883 | − | 0.959742i | \(-0.590627\pi\) | ||||
−0.280883 | + | 0.959742i | \(0.590627\pi\) | |||||||
\(978\) | 11481.2 | 0.375387 | ||||||||
\(979\) | −3022.07 | −0.0986575 | ||||||||
\(980\) | −26896.7 | −0.876718 | ||||||||
\(981\) | −3126.82 | −0.101765 | ||||||||
\(982\) | 979.544 | 0.0318315 | ||||||||
\(983\) | 38419.7 | 1.24659 | 0.623296 | − | 0.781986i | \(-0.285793\pi\) | ||||
0.623296 | + | 0.781986i | \(0.285793\pi\) | |||||||
\(984\) | −11670.5 | −0.378093 | ||||||||
\(985\) | −3521.86 | −0.113925 | ||||||||
\(986\) | 10097.1 | 0.326121 | ||||||||
\(987\) | 11609.7 | 0.374407 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −51457.3 | −1.65445 | ||||||||
\(990\) | −2353.07 | −0.0755410 | ||||||||
\(991\) | 51728.9 | 1.65815 | 0.829073 | − | 0.559140i | \(-0.188869\pi\) | ||||
0.829073 | + | 0.559140i | \(0.188869\pi\) | |||||||
\(992\) | −21441.4 | −0.686255 | ||||||||
\(993\) | 12344.5 | 0.394503 | ||||||||
\(994\) | −3666.79 | −0.117006 | ||||||||
\(995\) | −45331.6 | −1.44433 | ||||||||
\(996\) | −10644.0 | −0.338623 | ||||||||
\(997\) | −26846.8 | −0.852805 | −0.426403 | − | 0.904533i | \(-0.640219\pi\) | ||||
−0.426403 | + | 0.904533i | \(0.640219\pi\) | |||||||
\(998\) | −2476.65 | −0.0785541 | ||||||||
\(999\) | −11715.2 | −0.371025 |
(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 | 507.4.a.j.1.2 | 4 | ||
3.2 | odd | 2 | 1521.4.a.x.1.3 | 4 | |||
13.5 | odd | 4 | 39.4.b.a.25.3 | yes | 4 | ||
13.8 | odd | 4 | 39.4.b.a.25.2 | ✓ | 4 | ||
13.12 | even | 2 | inner | 507.4.a.j.1.3 | 4 | ||
39.5 | even | 4 | 117.4.b.d.64.2 | 4 | |||
39.8 | even | 4 | 117.4.b.d.64.3 | 4 | |||
39.38 | odd | 2 | 1521.4.a.x.1.2 | 4 | |||
52.31 | even | 4 | 624.4.c.e.337.4 | 4 | |||
52.47 | even | 4 | 624.4.c.e.337.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.a.25.2 | ✓ | 4 | 13.8 | odd | 4 | ||
39.4.b.a.25.3 | yes | 4 | 13.5 | odd | 4 | ||
117.4.b.d.64.2 | 4 | 39.5 | even | 4 | |||
117.4.b.d.64.3 | 4 | 39.8 | even | 4 | |||
507.4.a.j.1.2 | 4 | 1.1 | even | 1 | trivial | ||
507.4.a.j.1.3 | 4 | 13.12 | even | 2 | inner | ||
624.4.c.e.337.1 | 4 | 52.47 | even | 4 | |||
624.4.c.e.337.4 | 4 | 52.31 | even | 4 | |||
1521.4.a.x.1.2 | 4 | 39.38 | odd | 2 | |||
1521.4.a.x.1.3 | 4 | 3.2 | odd | 2 |