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: | \(0\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.61662 | −1.27867 | −0.639335 | − | 0.768928i | \(-0.720790\pi\) | ||||
−0.639335 | + | 0.768928i | \(0.720790\pi\) | |||||||
\(3\) | 5.98739 | 1.15227 | 0.576137 | − | 0.817353i | \(-0.304560\pi\) | ||||
0.576137 | + | 0.817353i | \(0.304560\pi\) | |||||||
\(4\) | 5.07997 | 0.634996 | ||||||||
\(5\) | 14.5299 | 1.29959 | 0.649796 | − | 0.760108i | \(-0.274854\pi\) | ||||
0.649796 | + | 0.760108i | \(0.274854\pi\) | |||||||
\(6\) | −21.6541 | −1.47338 | ||||||||
\(7\) | 21.3024 | 1.15022 | 0.575112 | − | 0.818075i | \(-0.304959\pi\) | ||||
0.575112 | + | 0.818075i | \(0.304959\pi\) | |||||||
\(8\) | 10.5606 | 0.466719 | ||||||||
\(9\) | 8.84881 | 0.327734 | ||||||||
\(10\) | −52.5491 | −1.66175 | ||||||||
\(11\) | −54.2135 | −1.48600 | −0.743000 | − | 0.669292i | \(-0.766598\pi\) | ||||
−0.743000 | + | 0.669292i | \(0.766598\pi\) | |||||||
\(12\) | 30.4158 | 0.731689 | ||||||||
\(13\) | 40.7748 | 0.869914 | 0.434957 | − | 0.900451i | \(-0.356764\pi\) | ||||
0.434957 | + | 0.900451i | \(0.356764\pi\) | |||||||
\(14\) | −77.0429 | −1.47076 | ||||||||
\(15\) | 86.9961 | 1.49749 | ||||||||
\(16\) | −78.8337 | −1.23178 | ||||||||
\(17\) | 102.739 | 1.46576 | 0.732879 | − | 0.680359i | \(-0.238176\pi\) | ||||
0.732879 | + | 0.680359i | \(0.238176\pi\) | |||||||
\(18\) | −32.0028 | −0.419063 | ||||||||
\(19\) | 41.9049 | 0.505982 | 0.252991 | − | 0.967469i | \(-0.418586\pi\) | ||||
0.252991 | + | 0.967469i | \(0.418586\pi\) | |||||||
\(20\) | 73.8114 | 0.825237 | ||||||||
\(21\) | 127.546 | 1.32537 | ||||||||
\(22\) | 196.070 | 1.90010 | ||||||||
\(23\) | 52.3053 | 0.474192 | 0.237096 | − | 0.971486i | \(-0.423804\pi\) | ||||
0.237096 | + | 0.971486i | \(0.423804\pi\) | |||||||
\(24\) | 63.2307 | 0.537788 | ||||||||
\(25\) | 86.1176 | 0.688941 | ||||||||
\(26\) | −147.467 | −1.11233 | ||||||||
\(27\) | −108.678 | −0.774634 | ||||||||
\(28\) | 108.216 | 0.730388 | ||||||||
\(29\) | 196.430 | 1.25780 | 0.628899 | − | 0.777487i | \(-0.283506\pi\) | ||||
0.628899 | + | 0.777487i | \(0.283506\pi\) | |||||||
\(30\) | −314.632 | −1.91479 | ||||||||
\(31\) | 107.249 | 0.621371 | 0.310685 | − | 0.950513i | \(-0.399441\pi\) | ||||
0.310685 | + | 0.950513i | \(0.399441\pi\) | |||||||
\(32\) | 200.627 | 1.10832 | ||||||||
\(33\) | −324.597 | −1.71228 | ||||||||
\(34\) | −371.569 | −1.87422 | ||||||||
\(35\) | 309.522 | 1.49482 | ||||||||
\(36\) | 44.9517 | 0.208110 | ||||||||
\(37\) | −409.454 | −1.81929 | −0.909645 | − | 0.415386i | \(-0.863647\pi\) | ||||
−0.909645 | + | 0.415386i | \(0.863647\pi\) | |||||||
\(38\) | −151.554 | −0.646984 | ||||||||
\(39\) | 244.134 | 1.00238 | ||||||||
\(40\) | 153.445 | 0.606545 | ||||||||
\(41\) | −282.185 | −1.07487 | −0.537437 | − | 0.843304i | \(-0.680607\pi\) | ||||
−0.537437 | + | 0.843304i | \(0.680607\pi\) | |||||||
\(42\) | −461.286 | −1.69471 | ||||||||
\(43\) | 489.222 | 1.73501 | 0.867507 | − | 0.497425i | \(-0.165721\pi\) | ||||
0.867507 | + | 0.497425i | \(0.165721\pi\) | |||||||
\(44\) | −275.403 | −0.943604 | ||||||||
\(45\) | 128.572 | 0.425921 | ||||||||
\(46\) | −189.169 | −0.606335 | ||||||||
\(47\) | 107.610 | 0.333970 | 0.166985 | − | 0.985959i | \(-0.446597\pi\) | ||||
0.166985 | + | 0.985959i | \(0.446597\pi\) | |||||||
\(48\) | −472.008 | −1.41934 | ||||||||
\(49\) | 110.794 | 0.323013 | ||||||||
\(50\) | −311.455 | −0.880928 | ||||||||
\(51\) | 615.139 | 1.68895 | ||||||||
\(52\) | 207.135 | 0.552392 | ||||||||
\(53\) | 490.814 | 1.27205 | 0.636023 | − | 0.771670i | \(-0.280578\pi\) | ||||
0.636023 | + | 0.771670i | \(0.280578\pi\) | |||||||
\(54\) | 393.048 | 0.990502 | ||||||||
\(55\) | −787.716 | −1.93119 | ||||||||
\(56\) | 224.967 | 0.536831 | ||||||||
\(57\) | 250.901 | 0.583029 | ||||||||
\(58\) | −710.414 | −1.60831 | ||||||||
\(59\) | −715.166 | −1.57808 | −0.789040 | − | 0.614342i | \(-0.789421\pi\) | ||||
−0.789040 | + | 0.614342i | \(0.789421\pi\) | |||||||
\(60\) | 441.938 | 0.950898 | ||||||||
\(61\) | 37.2896 | 0.0782696 | 0.0391348 | − | 0.999234i | \(-0.487540\pi\) | ||||
0.0391348 | + | 0.999234i | \(0.487540\pi\) | |||||||
\(62\) | −387.880 | −0.794528 | ||||||||
\(63\) | 188.501 | 0.376967 | ||||||||
\(64\) | −94.9216 | −0.185394 | ||||||||
\(65\) | 592.453 | 1.13053 | ||||||||
\(66\) | 1173.95 | 2.18944 | ||||||||
\(67\) | −1004.20 | −1.83109 | −0.915545 | − | 0.402214i | \(-0.868241\pi\) | ||||
−0.915545 | + | 0.402214i | \(0.868241\pi\) | |||||||
\(68\) | 521.911 | 0.930751 | ||||||||
\(69\) | 313.172 | 0.546399 | ||||||||
\(70\) | −1119.42 | −1.91138 | ||||||||
\(71\) | −612.234 | −1.02336 | −0.511682 | − | 0.859175i | \(-0.670977\pi\) | ||||
−0.511682 | + | 0.859175i | \(0.670977\pi\) | |||||||
\(72\) | 93.4492 | 0.152960 | ||||||||
\(73\) | 488.999 | 0.784014 | 0.392007 | − | 0.919962i | \(-0.371781\pi\) | ||||
0.392007 | + | 0.919962i | \(0.371781\pi\) | |||||||
\(74\) | 1480.84 | 2.32627 | ||||||||
\(75\) | 515.620 | 0.793848 | ||||||||
\(76\) | 212.876 | 0.321297 | ||||||||
\(77\) | −1154.88 | −1.70923 | ||||||||
\(78\) | −882.942 | −1.28171 | ||||||||
\(79\) | 389.173 | 0.554245 | 0.277123 | − | 0.960835i | \(-0.410619\pi\) | ||||
0.277123 | + | 0.960835i | \(0.410619\pi\) | |||||||
\(80\) | −1145.44 | −1.60081 | ||||||||
\(81\) | −889.616 | −1.22032 | ||||||||
\(82\) | 1020.56 | 1.37441 | ||||||||
\(83\) | −605.759 | −0.801092 | −0.400546 | − | 0.916277i | \(-0.631180\pi\) | ||||
−0.400546 | + | 0.916277i | \(0.631180\pi\) | |||||||
\(84\) | 647.930 | 0.841606 | ||||||||
\(85\) | 1492.79 | 1.90489 | ||||||||
\(86\) | −1769.33 | −2.21851 | ||||||||
\(87\) | 1176.10 | 1.44933 | ||||||||
\(88\) | −572.530 | −0.693544 | ||||||||
\(89\) | 1598.67 | 1.90403 | 0.952015 | − | 0.306050i | \(-0.0990075\pi\) | ||||
0.952015 | + | 0.306050i | \(0.0990075\pi\) | |||||||
\(90\) | −464.998 | −0.544612 | ||||||||
\(91\) | 868.601 | 1.00060 | ||||||||
\(92\) | 265.710 | 0.301110 | ||||||||
\(93\) | 642.142 | 0.715989 | ||||||||
\(94\) | −389.186 | −0.427037 | ||||||||
\(95\) | 608.874 | 0.657570 | ||||||||
\(96\) | 1201.23 | 1.27708 | ||||||||
\(97\) | 372.859 | 0.390289 | 0.195145 | − | 0.980774i | \(-0.437482\pi\) | ||||
0.195145 | + | 0.980774i | \(0.437482\pi\) | |||||||
\(98\) | −400.698 | −0.413027 | ||||||||
\(99\) | −479.725 | −0.487012 | ||||||||
\(100\) | 437.475 | 0.437475 | ||||||||
\(101\) | 1418.88 | 1.39786 | 0.698931 | − | 0.715189i | \(-0.253660\pi\) | ||||
0.698931 | + | 0.715189i | \(0.253660\pi\) | |||||||
\(102\) | −2224.73 | −2.15961 | ||||||||
\(103\) | 736.959 | 0.704997 | 0.352499 | − | 0.935812i | \(-0.385332\pi\) | ||||
0.352499 | + | 0.935812i | \(0.385332\pi\) | |||||||
\(104\) | 430.608 | 0.406006 | ||||||||
\(105\) | 1853.23 | 1.72244 | ||||||||
\(106\) | −1775.09 | −1.62653 | ||||||||
\(107\) | −359.834 | −0.325107 | −0.162553 | − | 0.986700i | \(-0.551973\pi\) | ||||
−0.162553 | + | 0.986700i | \(0.551973\pi\) | |||||||
\(108\) | −552.082 | −0.491890 | ||||||||
\(109\) | −638.777 | −0.561319 | −0.280659 | − | 0.959807i | \(-0.590553\pi\) | ||||
−0.280659 | + | 0.959807i | \(0.590553\pi\) | |||||||
\(110\) | 2848.87 | 2.46936 | ||||||||
\(111\) | −2451.56 | −2.09632 | ||||||||
\(112\) | −1679.35 | −1.41682 | ||||||||
\(113\) | −221.620 | −0.184498 | −0.0922491 | − | 0.995736i | \(-0.529406\pi\) | ||||
−0.0922491 | + | 0.995736i | \(0.529406\pi\) | |||||||
\(114\) | −907.415 | −0.745502 | ||||||||
\(115\) | 759.991 | 0.616257 | ||||||||
\(116\) | 997.859 | 0.798697 | ||||||||
\(117\) | 360.808 | 0.285100 | ||||||||
\(118\) | 2586.49 | 2.01784 | ||||||||
\(119\) | 2188.59 | 1.68595 | ||||||||
\(120\) | 918.735 | 0.698905 | ||||||||
\(121\) | 1608.10 | 1.20819 | ||||||||
\(122\) | −134.863 | −0.100081 | ||||||||
\(123\) | −1689.55 | −1.23855 | ||||||||
\(124\) | 544.822 | 0.394568 | ||||||||
\(125\) | −564.957 | −0.404250 | ||||||||
\(126\) | −681.738 | −0.482016 | ||||||||
\(127\) | −2071.95 | −1.44768 | −0.723842 | − | 0.689966i | \(-0.757626\pi\) | ||||
−0.723842 | + | 0.689966i | \(0.757626\pi\) | |||||||
\(128\) | −1261.72 | −0.871258 | ||||||||
\(129\) | 2929.16 | 1.99921 | ||||||||
\(130\) | −2142.68 | −1.44558 | ||||||||
\(131\) | 1843.90 | 1.22979 | 0.614894 | − | 0.788610i | \(-0.289199\pi\) | ||||
0.614894 | + | 0.788610i | \(0.289199\pi\) | |||||||
\(132\) | −1648.95 | −1.08729 | ||||||||
\(133\) | 892.677 | 0.581992 | ||||||||
\(134\) | 3631.83 | 2.34136 | ||||||||
\(135\) | −1579.08 | −1.00671 | ||||||||
\(136\) | 1084.99 | 0.684097 | ||||||||
\(137\) | 997.082 | 0.621799 | 0.310900 | − | 0.950443i | \(-0.399370\pi\) | ||||
0.310900 | + | 0.950443i | \(0.399370\pi\) | |||||||
\(138\) | −1132.63 | −0.698664 | ||||||||
\(139\) | 2960.35 | 1.80643 | 0.903213 | − | 0.429192i | \(-0.141202\pi\) | ||||
0.903213 | + | 0.429192i | \(0.141202\pi\) | |||||||
\(140\) | 1572.36 | 0.949206 | ||||||||
\(141\) | 644.305 | 0.384824 | ||||||||
\(142\) | 2214.22 | 1.30854 | ||||||||
\(143\) | −2210.54 | −1.29269 | ||||||||
\(144\) | −697.584 | −0.403695 | ||||||||
\(145\) | 2854.11 | 1.63463 | ||||||||
\(146\) | −1768.53 | −1.00249 | ||||||||
\(147\) | 663.364 | 0.372199 | ||||||||
\(148\) | −2080.01 | −1.15524 | ||||||||
\(149\) | 1822.08 | 1.00181 | 0.500907 | − | 0.865501i | \(-0.333000\pi\) | ||||
0.500907 | + | 0.865501i | \(0.333000\pi\) | |||||||
\(150\) | −1864.80 | −1.01507 | ||||||||
\(151\) | −1262.32 | −0.680305 | −0.340152 | − | 0.940370i | \(-0.610479\pi\) | ||||
−0.340152 | + | 0.940370i | \(0.610479\pi\) | |||||||
\(152\) | 442.543 | 0.236151 | ||||||||
\(153\) | 909.119 | 0.480378 | ||||||||
\(154\) | 4176.77 | 2.18554 | ||||||||
\(155\) | 1558.32 | 0.807529 | ||||||||
\(156\) | 1240.20 | 0.636507 | ||||||||
\(157\) | −1307.15 | −0.664470 | −0.332235 | − | 0.943197i | \(-0.607803\pi\) | ||||
−0.332235 | + | 0.943197i | \(0.607803\pi\) | |||||||
\(158\) | −1407.49 | −0.708697 | ||||||||
\(159\) | 2938.69 | 1.46574 | ||||||||
\(160\) | 2915.08 | 1.44036 | ||||||||
\(161\) | 1114.23 | 0.545427 | ||||||||
\(162\) | 3217.41 | 1.56039 | ||||||||
\(163\) | 1061.31 | 0.509989 | 0.254995 | − | 0.966942i | \(-0.417926\pi\) | ||||
0.254995 | + | 0.966942i | \(0.417926\pi\) | |||||||
\(164\) | −1433.49 | −0.682541 | ||||||||
\(165\) | −4716.36 | −2.22526 | ||||||||
\(166\) | 2190.80 | 1.02433 | ||||||||
\(167\) | 1098.53 | 0.509023 | 0.254511 | − | 0.967070i | \(-0.418085\pi\) | ||||
0.254511 | + | 0.967070i | \(0.418085\pi\) | |||||||
\(168\) | 1346.97 | 0.618576 | ||||||||
\(169\) | −534.419 | −0.243249 | ||||||||
\(170\) | −5398.85 | −2.43572 | ||||||||
\(171\) | 370.809 | 0.165827 | ||||||||
\(172\) | 2485.23 | 1.10173 | ||||||||
\(173\) | 2018.58 | 0.887110 | 0.443555 | − | 0.896247i | \(-0.353717\pi\) | ||||
0.443555 | + | 0.896247i | \(0.353717\pi\) | |||||||
\(174\) | −4253.52 | −1.85321 | ||||||||
\(175\) | 1834.51 | 0.792436 | ||||||||
\(176\) | 4273.85 | 1.83042 | ||||||||
\(177\) | −4281.98 | −1.81838 | ||||||||
\(178\) | −5781.79 | −2.43463 | ||||||||
\(179\) | 359.017 | 0.149912 | 0.0749559 | − | 0.997187i | \(-0.476118\pi\) | ||||
0.0749559 | + | 0.997187i | \(0.476118\pi\) | |||||||
\(180\) | 653.143 | 0.270458 | ||||||||
\(181\) | −1169.86 | −0.480414 | −0.240207 | − | 0.970722i | \(-0.577215\pi\) | ||||
−0.240207 | + | 0.970722i | \(0.577215\pi\) | |||||||
\(182\) | −3141.41 | −1.27943 | ||||||||
\(183\) | 223.267 | 0.0901880 | ||||||||
\(184\) | 552.378 | 0.221314 | ||||||||
\(185\) | −5949.31 | −2.36434 | ||||||||
\(186\) | −2322.39 | −0.915514 | ||||||||
\(187\) | −5569.84 | −2.17811 | ||||||||
\(188\) | 546.657 | 0.212070 | ||||||||
\(189\) | −2315.11 | −0.891002 | ||||||||
\(190\) | −2202.07 | −0.840815 | ||||||||
\(191\) | 1398.55 | 0.529818 | 0.264909 | − | 0.964273i | \(-0.414658\pi\) | ||||
0.264909 | + | 0.964273i | \(0.414658\pi\) | |||||||
\(192\) | −568.332 | −0.213624 | ||||||||
\(193\) | 508.410 | 0.189617 | 0.0948086 | − | 0.995496i | \(-0.469776\pi\) | ||||
0.0948086 | + | 0.995496i | \(0.469776\pi\) | |||||||
\(194\) | −1348.49 | −0.499051 | ||||||||
\(195\) | 3547.24 | 1.30268 | ||||||||
\(196\) | 562.828 | 0.205112 | ||||||||
\(197\) | −2535.12 | −0.916852 | −0.458426 | − | 0.888733i | \(-0.651587\pi\) | ||||
−0.458426 | + | 0.888733i | \(0.651587\pi\) | |||||||
\(198\) | 1734.99 | 0.622728 | ||||||||
\(199\) | 201.425 | 0.0717520 | 0.0358760 | − | 0.999356i | \(-0.488578\pi\) | ||||
0.0358760 | + | 0.999356i | \(0.488578\pi\) | |||||||
\(200\) | 909.458 | 0.321542 | ||||||||
\(201\) | −6012.56 | −2.10992 | ||||||||
\(202\) | −5131.56 | −1.78740 | ||||||||
\(203\) | 4184.44 | 1.44675 | ||||||||
\(204\) | 3124.89 | 1.07248 | ||||||||
\(205\) | −4100.11 | −1.39690 | ||||||||
\(206\) | −2665.30 | −0.901459 | ||||||||
\(207\) | 462.840 | 0.155409 | ||||||||
\(208\) | −3214.42 | −1.07154 | ||||||||
\(209\) | −2271.81 | −0.751888 | ||||||||
\(210\) | −6702.43 | −2.20244 | ||||||||
\(211\) | −5431.97 | −1.77229 | −0.886143 | − | 0.463413i | \(-0.846625\pi\) | ||||
−0.886143 | + | 0.463413i | \(0.846625\pi\) | |||||||
\(212\) | 2493.32 | 0.807744 | ||||||||
\(213\) | −3665.68 | −1.17919 | ||||||||
\(214\) | 1301.38 | 0.415704 | ||||||||
\(215\) | 7108.33 | 2.25481 | ||||||||
\(216\) | −1147.71 | −0.361537 | ||||||||
\(217\) | 2284.67 | 0.714715 | ||||||||
\(218\) | 2310.22 | 0.717741 | ||||||||
\(219\) | 2927.83 | 0.903398 | ||||||||
\(220\) | −4001.58 | −1.22630 | ||||||||
\(221\) | 4189.16 | 1.27508 | ||||||||
\(222\) | 8866.36 | 2.68050 | ||||||||
\(223\) | −4297.52 | −1.29051 | −0.645253 | − | 0.763969i | \(-0.723248\pi\) | ||||
−0.645253 | + | 0.763969i | \(0.723248\pi\) | |||||||
\(224\) | 4273.83 | 1.27481 | ||||||||
\(225\) | 762.039 | 0.225789 | ||||||||
\(226\) | 801.518 | 0.235912 | ||||||||
\(227\) | −4846.60 | −1.41709 | −0.708547 | − | 0.705664i | \(-0.750649\pi\) | ||||
−0.708547 | + | 0.705664i | \(0.750649\pi\) | |||||||
\(228\) | 1274.57 | 0.370222 | ||||||||
\(229\) | −6080.26 | −1.75456 | −0.877282 | − | 0.479976i | \(-0.840645\pi\) | ||||
−0.877282 | + | 0.479976i | \(0.840645\pi\) | |||||||
\(230\) | −2748.60 | −0.787989 | ||||||||
\(231\) | −6914.71 | −1.96950 | ||||||||
\(232\) | 2074.43 | 0.587038 | ||||||||
\(233\) | −3629.10 | −1.02039 | −0.510193 | − | 0.860060i | \(-0.670426\pi\) | ||||
−0.510193 | + | 0.860060i | \(0.670426\pi\) | |||||||
\(234\) | −1304.91 | −0.364549 | ||||||||
\(235\) | 1563.57 | 0.434025 | ||||||||
\(236\) | −3633.02 | −1.00207 | ||||||||
\(237\) | 2330.13 | 0.638642 | ||||||||
\(238\) | −7915.31 | −2.15577 | ||||||||
\(239\) | 1384.17 | 0.374622 | 0.187311 | − | 0.982301i | \(-0.440023\pi\) | ||||
0.187311 | + | 0.982301i | \(0.440023\pi\) | |||||||
\(240\) | −6858.22 | −1.84457 | ||||||||
\(241\) | 2091.61 | 0.559055 | 0.279528 | − | 0.960138i | \(-0.409822\pi\) | ||||
0.279528 | + | 0.960138i | \(0.409822\pi\) | |||||||
\(242\) | −5815.91 | −1.54488 | ||||||||
\(243\) | −2392.17 | −0.631513 | ||||||||
\(244\) | 189.430 | 0.0497009 | ||||||||
\(245\) | 1609.82 | 0.419785 | ||||||||
\(246\) | 6110.46 | 1.58370 | ||||||||
\(247\) | 1708.66 | 0.440161 | ||||||||
\(248\) | 1132.62 | 0.290006 | ||||||||
\(249\) | −3626.91 | −0.923077 | ||||||||
\(250\) | 2043.24 | 0.516902 | ||||||||
\(251\) | 7043.45 | 1.77123 | 0.885614 | − | 0.464422i | \(-0.153738\pi\) | ||||
0.885614 | + | 0.464422i | \(0.153738\pi\) | |||||||
\(252\) | 957.581 | 0.239373 | ||||||||
\(253\) | −2835.66 | −0.704649 | ||||||||
\(254\) | 7493.47 | 1.85111 | ||||||||
\(255\) | 8937.89 | 2.19495 | ||||||||
\(256\) | 5322.53 | 1.29945 | ||||||||
\(257\) | 3219.14 | 0.781339 | 0.390670 | − | 0.920531i | \(-0.372244\pi\) | ||||
0.390670 | + | 0.920531i | \(0.372244\pi\) | |||||||
\(258\) | −10593.7 | −2.55633 | ||||||||
\(259\) | −8722.36 | −2.09259 | ||||||||
\(260\) | 3009.64 | 0.717885 | ||||||||
\(261\) | 1738.17 | 0.412223 | ||||||||
\(262\) | −6668.69 | −1.57249 | ||||||||
\(263\) | −2563.95 | −0.601141 | −0.300571 | − | 0.953760i | \(-0.597177\pi\) | ||||
−0.300571 | + | 0.953760i | \(0.597177\pi\) | |||||||
\(264\) | −3427.96 | −0.799152 | ||||||||
\(265\) | 7131.47 | 1.65314 | ||||||||
\(266\) | −3228.48 | −0.744176 | ||||||||
\(267\) | 9571.86 | 2.19396 | ||||||||
\(268\) | −5101.33 | −1.16274 | ||||||||
\(269\) | 5355.59 | 1.21389 | 0.606945 | − | 0.794744i | \(-0.292395\pi\) | ||||
0.606945 | + | 0.794744i | \(0.292395\pi\) | |||||||
\(270\) | 5710.95 | 1.28725 | ||||||||
\(271\) | −1304.50 | −0.292408 | −0.146204 | − | 0.989254i | \(-0.546706\pi\) | ||||
−0.146204 | + | 0.989254i | \(0.546706\pi\) | |||||||
\(272\) | −8099.30 | −1.80549 | ||||||||
\(273\) | 5200.65 | 1.15296 | ||||||||
\(274\) | −3606.07 | −0.795076 | ||||||||
\(275\) | −4668.74 | −1.02377 | ||||||||
\(276\) | 1590.91 | 0.346961 | ||||||||
\(277\) | −5109.26 | −1.10825 | −0.554126 | − | 0.832433i | \(-0.686947\pi\) | ||||
−0.554126 | + | 0.832433i | \(0.686947\pi\) | |||||||
\(278\) | −10706.5 | −2.30982 | ||||||||
\(279\) | 949.027 | 0.203644 | ||||||||
\(280\) | 3268.75 | 0.697662 | ||||||||
\(281\) | −3250.12 | −0.689986 | −0.344993 | − | 0.938605i | \(-0.612119\pi\) | ||||
−0.344993 | + | 0.938605i | \(0.612119\pi\) | |||||||
\(282\) | −2330.21 | −0.492063 | ||||||||
\(283\) | 8799.91 | 1.84841 | 0.924205 | − | 0.381896i | \(-0.124729\pi\) | ||||
0.924205 | + | 0.381896i | \(0.124729\pi\) | |||||||
\(284\) | −3110.13 | −0.649832 | ||||||||
\(285\) | 3645.57 | 0.757701 | ||||||||
\(286\) | 7994.70 | 1.65293 | ||||||||
\(287\) | −6011.22 | −1.23635 | ||||||||
\(288\) | 1775.31 | 0.363233 | ||||||||
\(289\) | 5642.31 | 1.14845 | ||||||||
\(290\) | −10322.2 | −2.09015 | ||||||||
\(291\) | 2232.45 | 0.449720 | ||||||||
\(292\) | 2484.10 | 0.497846 | ||||||||
\(293\) | 3169.56 | 0.631972 | 0.315986 | − | 0.948764i | \(-0.397665\pi\) | ||||
0.315986 | + | 0.948764i | \(0.397665\pi\) | |||||||
\(294\) | −2399.14 | −0.475920 | ||||||||
\(295\) | −10391.3 | −2.05086 | ||||||||
\(296\) | −4324.09 | −0.849098 | ||||||||
\(297\) | 5891.83 | 1.15111 | ||||||||
\(298\) | −6589.76 | −1.28099 | ||||||||
\(299\) | 2132.74 | 0.412506 | ||||||||
\(300\) | 2619.33 | 0.504091 | ||||||||
\(301\) | 10421.6 | 1.99565 | ||||||||
\(302\) | 4565.33 | 0.869885 | ||||||||
\(303\) | 8495.40 | 1.61072 | ||||||||
\(304\) | −3303.52 | −0.623256 | ||||||||
\(305\) | 541.814 | 0.101719 | ||||||||
\(306\) | −3287.94 | −0.614245 | ||||||||
\(307\) | 7647.86 | 1.42178 | 0.710890 | − | 0.703303i | \(-0.248292\pi\) | ||||
0.710890 | + | 0.703303i | \(0.248292\pi\) | |||||||
\(308\) | −5866.75 | −1.08536 | ||||||||
\(309\) | 4412.46 | 0.812349 | ||||||||
\(310\) | −5635.85 | −1.03256 | ||||||||
\(311\) | −8400.00 | −1.53158 | −0.765788 | − | 0.643093i | \(-0.777651\pi\) | ||||
−0.765788 | + | 0.643093i | \(0.777651\pi\) | |||||||
\(312\) | 2578.22 | 0.467829 | ||||||||
\(313\) | −5970.25 | −1.07814 | −0.539071 | − | 0.842260i | \(-0.681225\pi\) | ||||
−0.539071 | + | 0.842260i | \(0.681225\pi\) | |||||||
\(314\) | 4727.47 | 0.849638 | ||||||||
\(315\) | 2738.90 | 0.489904 | ||||||||
\(316\) | 1976.99 | 0.351944 | ||||||||
\(317\) | 2352.99 | 0.416899 | 0.208449 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208449 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(318\) | −10628.1 | −1.87420 | ||||||||
\(319\) | −10649.2 | −1.86909 | ||||||||
\(320\) | −1379.20 | −0.240936 | ||||||||
\(321\) | −2154.46 | −0.374612 | ||||||||
\(322\) | −4029.75 | −0.697421 | ||||||||
\(323\) | 4305.27 | 0.741647 | ||||||||
\(324\) | −4519.23 | −0.774902 | ||||||||
\(325\) | 3511.43 | 0.599319 | ||||||||
\(326\) | −3838.36 | −0.652108 | ||||||||
\(327\) | −3824.61 | −0.646793 | ||||||||
\(328\) | −2980.05 | −0.501664 | ||||||||
\(329\) | 2292.36 | 0.384140 | ||||||||
\(330\) | 17057.3 | 2.84538 | ||||||||
\(331\) | −8514.82 | −1.41395 | −0.706974 | − | 0.707240i | \(-0.749940\pi\) | ||||
−0.706974 | + | 0.707240i | \(0.749940\pi\) | |||||||
\(332\) | −3077.24 | −0.508691 | ||||||||
\(333\) | −3623.18 | −0.596243 | ||||||||
\(334\) | −3972.97 | −0.650872 | ||||||||
\(335\) | −14591.0 | −2.37967 | ||||||||
\(336\) | −10054.9 | −1.63256 | ||||||||
\(337\) | −3182.38 | −0.514407 | −0.257204 | − | 0.966357i | \(-0.582801\pi\) | ||||
−0.257204 | + | 0.966357i | \(0.582801\pi\) | |||||||
\(338\) | 1932.79 | 0.311036 | ||||||||
\(339\) | −1326.93 | −0.212592 | ||||||||
\(340\) | 7583.31 | 1.20960 | ||||||||
\(341\) | −5814.35 | −0.923357 | ||||||||
\(342\) | −1341.08 | −0.212038 | ||||||||
\(343\) | −4946.56 | −0.778686 | ||||||||
\(344\) | 5166.50 | 0.809764 | ||||||||
\(345\) | 4550.36 | 0.710096 | ||||||||
\(346\) | −7300.46 | −1.13432 | ||||||||
\(347\) | 7946.55 | 1.22938 | 0.614688 | − | 0.788771i | \(-0.289282\pi\) | ||||
0.614688 | + | 0.788771i | \(0.289282\pi\) | |||||||
\(348\) | 5974.57 | 0.920318 | ||||||||
\(349\) | −7110.75 | −1.09063 | −0.545314 | − | 0.838232i | \(-0.683590\pi\) | ||||
−0.545314 | + | 0.838232i | \(0.683590\pi\) | |||||||
\(350\) | −6634.75 | −1.01326 | ||||||||
\(351\) | −4431.33 | −0.673865 | ||||||||
\(352\) | −10876.7 | −1.64696 | ||||||||
\(353\) | 9352.21 | 1.41011 | 0.705054 | − | 0.709154i | \(-0.250923\pi\) | ||||
0.705054 | + | 0.709154i | \(0.250923\pi\) | |||||||
\(354\) | 15486.3 | 2.32511 | ||||||||
\(355\) | −8895.69 | −1.32996 | ||||||||
\(356\) | 8121.20 | 1.20905 | ||||||||
\(357\) | 13103.9 | 1.94267 | ||||||||
\(358\) | −1298.43 | −0.191688 | ||||||||
\(359\) | 14.1011 | 0.00207306 | 0.00103653 | − | 0.999999i | \(-0.499670\pi\) | ||||
0.00103653 | + | 0.999999i | \(0.499670\pi\) | |||||||
\(360\) | 1357.81 | 0.198785 | ||||||||
\(361\) | −5102.98 | −0.743982 | ||||||||
\(362\) | 4230.94 | 0.614290 | ||||||||
\(363\) | 9628.35 | 1.39217 | ||||||||
\(364\) | 4412.47 | 0.635374 | ||||||||
\(365\) | 7105.10 | 1.01890 | ||||||||
\(366\) | −807.474 | −0.115321 | ||||||||
\(367\) | −7009.17 | −0.996937 | −0.498468 | − | 0.866908i | \(-0.666104\pi\) | ||||
−0.498468 | + | 0.866908i | \(0.666104\pi\) | |||||||
\(368\) | −4123.42 | −0.584098 | ||||||||
\(369\) | −2497.00 | −0.352273 | ||||||||
\(370\) | 21516.4 | 3.02321 | ||||||||
\(371\) | 10455.5 | 1.46314 | ||||||||
\(372\) | 3262.06 | 0.454651 | ||||||||
\(373\) | −3331.77 | −0.462499 | −0.231250 | − | 0.972894i | \(-0.574281\pi\) | ||||
−0.231250 | + | 0.972894i | \(0.574281\pi\) | |||||||
\(374\) | 20144.0 | 2.78509 | ||||||||
\(375\) | −3382.61 | −0.465807 | ||||||||
\(376\) | 1136.43 | 0.155870 | ||||||||
\(377\) | 8009.39 | 1.09418 | ||||||||
\(378\) | 8372.88 | 1.13930 | ||||||||
\(379\) | 8291.57 | 1.12377 | 0.561886 | − | 0.827215i | \(-0.310076\pi\) | ||||
0.561886 | + | 0.827215i | \(0.310076\pi\) | |||||||
\(380\) | 3093.06 | 0.417555 | ||||||||
\(381\) | −12405.6 | −1.66813 | ||||||||
\(382\) | −5058.02 | −0.677463 | ||||||||
\(383\) | −6622.40 | −0.883521 | −0.441761 | − | 0.897133i | \(-0.645646\pi\) | ||||
−0.441761 | + | 0.897133i | \(0.645646\pi\) | |||||||
\(384\) | −7554.39 | −1.00393 | ||||||||
\(385\) | −16780.3 | −2.22130 | ||||||||
\(386\) | −1838.73 | −0.242458 | ||||||||
\(387\) | 4329.03 | 0.568623 | ||||||||
\(388\) | 1894.11 | 0.247832 | ||||||||
\(389\) | 12619.6 | 1.64484 | 0.822418 | − | 0.568883i | \(-0.192624\pi\) | ||||
0.822418 | + | 0.568883i | \(0.192624\pi\) | |||||||
\(390\) | −12829.0 | −1.66570 | ||||||||
\(391\) | 5373.80 | 0.695051 | ||||||||
\(392\) | 1170.05 | 0.150756 | ||||||||
\(393\) | 11040.1 | 1.41705 | ||||||||
\(394\) | 9168.58 | 1.17235 | ||||||||
\(395\) | 5654.64 | 0.720293 | ||||||||
\(396\) | −2436.99 | −0.309251 | ||||||||
\(397\) | 1074.44 | 0.135831 | 0.0679153 | − | 0.997691i | \(-0.478365\pi\) | ||||
0.0679153 | + | 0.997691i | \(0.478365\pi\) | |||||||
\(398\) | −728.479 | −0.0917471 | ||||||||
\(399\) | 5344.80 | 0.670614 | ||||||||
\(400\) | −6788.97 | −0.848621 | ||||||||
\(401\) | −3731.07 | −0.464640 | −0.232320 | − | 0.972639i | \(-0.574632\pi\) | ||||
−0.232320 | + | 0.972639i | \(0.574632\pi\) | |||||||
\(402\) | 21745.2 | 2.69789 | ||||||||
\(403\) | 4373.05 | 0.540539 | ||||||||
\(404\) | 7207.88 | 0.887637 | ||||||||
\(405\) | −12926.0 | −1.58592 | ||||||||
\(406\) | −15133.5 | −1.84991 | ||||||||
\(407\) | 22197.9 | 2.70346 | ||||||||
\(408\) | 6496.26 | 0.788267 | ||||||||
\(409\) | 4666.38 | 0.564150 | 0.282075 | − | 0.959392i | \(-0.408977\pi\) | ||||
0.282075 | + | 0.959392i | \(0.408977\pi\) | |||||||
\(410\) | 14828.6 | 1.78617 | ||||||||
\(411\) | 5969.92 | 0.716483 | ||||||||
\(412\) | 3743.73 | 0.447671 | ||||||||
\(413\) | −15234.8 | −1.81514 | ||||||||
\(414\) | −1673.92 | −0.198717 | ||||||||
\(415\) | −8801.61 | −1.04109 | ||||||||
\(416\) | 8180.50 | 0.964139 | ||||||||
\(417\) | 17724.7 | 2.08150 | ||||||||
\(418\) | 8216.30 | 0.961417 | ||||||||
\(419\) | −8102.57 | −0.944717 | −0.472359 | − | 0.881406i | \(-0.656597\pi\) | ||||
−0.472359 | + | 0.881406i | \(0.656597\pi\) | |||||||
\(420\) | 9414.34 | 1.09375 | ||||||||
\(421\) | −4283.67 | −0.495898 | −0.247949 | − | 0.968773i | \(-0.579757\pi\) | ||||
−0.247949 | + | 0.968773i | \(0.579757\pi\) | |||||||
\(422\) | 19645.4 | 2.26617 | ||||||||
\(423\) | 952.224 | 0.109453 | ||||||||
\(424\) | 5183.31 | 0.593688 | ||||||||
\(425\) | 8847.64 | 1.00982 | ||||||||
\(426\) | 13257.4 | 1.50780 | ||||||||
\(427\) | 794.359 | 0.0900275 | ||||||||
\(428\) | −1827.95 | −0.206442 | ||||||||
\(429\) | −13235.4 | −1.48953 | ||||||||
\(430\) | −25708.2 | −2.88316 | ||||||||
\(431\) | 8589.77 | 0.959987 | 0.479994 | − | 0.877272i | \(-0.340639\pi\) | ||||
0.479994 | + | 0.877272i | \(0.340639\pi\) | |||||||
\(432\) | 8567.50 | 0.954176 | ||||||||
\(433\) | −8146.55 | −0.904153 | −0.452077 | − | 0.891979i | \(-0.649317\pi\) | ||||
−0.452077 | + | 0.891979i | \(0.649317\pi\) | |||||||
\(434\) | −8262.78 | −0.913885 | ||||||||
\(435\) | 17088.6 | 1.88354 | ||||||||
\(436\) | −3244.97 | −0.356435 | ||||||||
\(437\) | 2191.85 | 0.239933 | ||||||||
\(438\) | −10588.8 | −1.15515 | ||||||||
\(439\) | −16379.0 | −1.78070 | −0.890351 | − | 0.455274i | \(-0.849541\pi\) | ||||
−0.890351 | + | 0.455274i | \(0.849541\pi\) | |||||||
\(440\) | −8318.79 | −0.901325 | ||||||||
\(441\) | 980.391 | 0.105862 | ||||||||
\(442\) | −15150.6 | −1.63041 | ||||||||
\(443\) | −4534.63 | −0.486335 | −0.243168 | − | 0.969984i | \(-0.578187\pi\) | ||||
−0.243168 | + | 0.969984i | \(0.578187\pi\) | |||||||
\(444\) | −12453.8 | −1.33116 | ||||||||
\(445\) | 23228.5 | 2.47446 | ||||||||
\(446\) | 15542.5 | 1.65013 | ||||||||
\(447\) | 10909.5 | 1.15436 | ||||||||
\(448\) | −2022.06 | −0.213244 | ||||||||
\(449\) | −17706.1 | −1.86103 | −0.930513 | − | 0.366258i | \(-0.880639\pi\) | ||||
−0.930513 | + | 0.366258i | \(0.880639\pi\) | |||||||
\(450\) | −2756.01 | −0.288710 | ||||||||
\(451\) | 15298.2 | 1.59726 | ||||||||
\(452\) | −1125.82 | −0.117156 | ||||||||
\(453\) | −7557.99 | −0.783897 | ||||||||
\(454\) | 17528.3 | 1.81199 | ||||||||
\(455\) | 12620.7 | 1.30037 | ||||||||
\(456\) | 2649.68 | 0.272111 | ||||||||
\(457\) | −7191.90 | −0.736156 | −0.368078 | − | 0.929795i | \(-0.619984\pi\) | ||||
−0.368078 | + | 0.929795i | \(0.619984\pi\) | |||||||
\(458\) | 21990.0 | 2.24351 | ||||||||
\(459\) | −11165.5 | −1.13543 | ||||||||
\(460\) | 3860.73 | 0.391321 | ||||||||
\(461\) | −9509.22 | −0.960713 | −0.480356 | − | 0.877073i | \(-0.659493\pi\) | ||||
−0.480356 | + | 0.877073i | \(0.659493\pi\) | |||||||
\(462\) | 25007.9 | 2.51834 | ||||||||
\(463\) | 1945.35 | 0.195265 | 0.0976327 | − | 0.995223i | \(-0.468873\pi\) | ||||
0.0976327 | + | 0.995223i | \(0.468873\pi\) | |||||||
\(464\) | −15485.3 | −1.54933 | ||||||||
\(465\) | 9330.25 | 0.930494 | ||||||||
\(466\) | 13125.1 | 1.30474 | ||||||||
\(467\) | 14631.5 | 1.44981 | 0.724907 | − | 0.688846i | \(-0.241883\pi\) | ||||
0.724907 | + | 0.688846i | \(0.241883\pi\) | |||||||
\(468\) | 1832.90 | 0.181038 | ||||||||
\(469\) | −21392.0 | −2.10616 | ||||||||
\(470\) | −5654.83 | −0.554974 | ||||||||
\(471\) | −7826.41 | −0.765651 | ||||||||
\(472\) | −7552.62 | −0.736520 | ||||||||
\(473\) | −26522.4 | −2.57823 | ||||||||
\(474\) | −8427.20 | −0.816612 | ||||||||
\(475\) | 3608.75 | 0.348592 | ||||||||
\(476\) | 11118.0 | 1.07057 | ||||||||
\(477\) | 4343.12 | 0.416892 | ||||||||
\(478\) | −5006.03 | −0.479018 | ||||||||
\(479\) | 2595.61 | 0.247592 | 0.123796 | − | 0.992308i | \(-0.460493\pi\) | ||||
0.123796 | + | 0.992308i | \(0.460493\pi\) | |||||||
\(480\) | 17453.7 | 1.65969 | ||||||||
\(481\) | −16695.4 | −1.58263 | ||||||||
\(482\) | −7564.56 | −0.714847 | ||||||||
\(483\) | 6671.33 | 0.628481 | ||||||||
\(484\) | 8169.13 | 0.767198 | ||||||||
\(485\) | 5417.59 | 0.507217 | ||||||||
\(486\) | 8651.57 | 0.807497 | ||||||||
\(487\) | −18820.5 | −1.75121 | −0.875603 | − | 0.483031i | \(-0.839536\pi\) | ||||
−0.875603 | + | 0.483031i | \(0.839536\pi\) | |||||||
\(488\) | 393.803 | 0.0365299 | ||||||||
\(489\) | 6354.48 | 0.587647 | ||||||||
\(490\) | −5822.10 | −0.536767 | ||||||||
\(491\) | −10108.6 | −0.929109 | −0.464555 | − | 0.885544i | \(-0.653786\pi\) | ||||
−0.464555 | + | 0.885544i | \(0.653786\pi\) | |||||||
\(492\) | −8582.86 | −0.786474 | ||||||||
\(493\) | 20181.0 | 1.84363 | ||||||||
\(494\) | −6179.60 | −0.562820 | ||||||||
\(495\) | −6970.35 | −0.632917 | ||||||||
\(496\) | −8454.84 | −0.765390 | ||||||||
\(497\) | −13042.1 | −1.17710 | ||||||||
\(498\) | 13117.2 | 1.18031 | ||||||||
\(499\) | −4987.03 | −0.447395 | −0.223698 | − | 0.974659i | \(-0.571813\pi\) | ||||
−0.223698 | + | 0.974659i | \(0.571813\pi\) | |||||||
\(500\) | −2869.96 | −0.256697 | ||||||||
\(501\) | 6577.33 | 0.586533 | ||||||||
\(502\) | −25473.5 | −2.26482 | ||||||||
\(503\) | 4958.41 | 0.439532 | 0.219766 | − | 0.975553i | \(-0.429471\pi\) | ||||
0.219766 | + | 0.975553i | \(0.429471\pi\) | |||||||
\(504\) | 1990.70 | 0.175938 | ||||||||
\(505\) | 20616.2 | 1.81665 | ||||||||
\(506\) | 10255.5 | 0.901013 | ||||||||
\(507\) | −3199.77 | −0.280290 | ||||||||
\(508\) | −10525.4 | −0.919274 | ||||||||
\(509\) | 13928.5 | 1.21291 | 0.606455 | − | 0.795118i | \(-0.292591\pi\) | ||||
0.606455 | + | 0.795118i | \(0.292591\pi\) | |||||||
\(510\) | −32325.0 | −2.80662 | ||||||||
\(511\) | 10416.9 | 0.901790 | ||||||||
\(512\) | −9155.85 | −0.790303 | ||||||||
\(513\) | −4554.15 | −0.391951 | ||||||||
\(514\) | −11642.4 | −0.999075 | ||||||||
\(515\) | 10707.9 | 0.916209 | ||||||||
\(516\) | 14880.0 | 1.26949 | ||||||||
\(517\) | −5833.93 | −0.496279 | ||||||||
\(518\) | 31545.5 | 2.67573 | ||||||||
\(519\) | 12086.0 | 1.02219 | ||||||||
\(520\) | 6256.68 | 0.527642 | ||||||||
\(521\) | −2042.22 | −0.171730 | −0.0858651 | − | 0.996307i | \(-0.527365\pi\) | ||||
−0.0858651 | + | 0.996307i | \(0.527365\pi\) | |||||||
\(522\) | −6286.32 | −0.527097 | ||||||||
\(523\) | −11834.7 | −0.989471 | −0.494735 | − | 0.869044i | \(-0.664735\pi\) | ||||
−0.494735 | + | 0.869044i | \(0.664735\pi\) | |||||||
\(524\) | 9366.95 | 0.780910 | ||||||||
\(525\) | 10983.9 | 0.913103 | ||||||||
\(526\) | 9272.86 | 0.768661 | ||||||||
\(527\) | 11018.7 | 0.910779 | ||||||||
\(528\) | 25589.2 | 2.10914 | ||||||||
\(529\) | −9431.15 | −0.775142 | ||||||||
\(530\) | −25791.8 | −2.11382 | ||||||||
\(531\) | −6328.37 | −0.517190 | ||||||||
\(532\) | 4534.77 | 0.369563 | ||||||||
\(533\) | −11506.0 | −0.935048 | ||||||||
\(534\) | −34617.8 | −2.80536 | ||||||||
\(535\) | −5228.34 | −0.422507 | ||||||||
\(536\) | −10605.0 | −0.854605 | ||||||||
\(537\) | 2149.58 | 0.172739 | ||||||||
\(538\) | −19369.2 | −1.55216 | ||||||||
\(539\) | −6006.51 | −0.479997 | ||||||||
\(540\) | −8021.69 | −0.639257 | ||||||||
\(541\) | 9265.77 | 0.736352 | 0.368176 | − | 0.929756i | \(-0.379982\pi\) | ||||
0.368176 | + | 0.929756i | \(0.379982\pi\) | |||||||
\(542\) | 4717.88 | 0.373894 | ||||||||
\(543\) | −7004.39 | −0.553568 | ||||||||
\(544\) | 20612.2 | 1.62452 | ||||||||
\(545\) | −9281.36 | −0.729486 | ||||||||
\(546\) | −18808.8 | −1.47425 | ||||||||
\(547\) | −547.000 | −0.0427569 | ||||||||
\(548\) | 5065.15 | 0.394840 | ||||||||
\(549\) | 329.969 | 0.0256516 | ||||||||
\(550\) | 16885.1 | 1.30906 | ||||||||
\(551\) | 8231.39 | 0.636423 | ||||||||
\(552\) | 3307.30 | 0.255015 | ||||||||
\(553\) | 8290.33 | 0.637506 | ||||||||
\(554\) | 18478.3 | 1.41709 | ||||||||
\(555\) | −35620.9 | −2.72436 | ||||||||
\(556\) | 15038.5 | 1.14707 | ||||||||
\(557\) | −3706.74 | −0.281974 | −0.140987 | − | 0.990011i | \(-0.545028\pi\) | ||||
−0.140987 | + | 0.990011i | \(0.545028\pi\) | |||||||
\(558\) | −3432.27 | −0.260394 | ||||||||
\(559\) | 19947.9 | 1.50931 | ||||||||
\(560\) | −24400.7 | −1.84129 | ||||||||
\(561\) | −33348.8 | −2.50978 | ||||||||
\(562\) | 11754.5 | 0.882265 | ||||||||
\(563\) | −9943.90 | −0.744379 | −0.372189 | − | 0.928157i | \(-0.621393\pi\) | ||||
−0.372189 | + | 0.928157i | \(0.621393\pi\) | |||||||
\(564\) | 3273.05 | 0.244362 | ||||||||
\(565\) | −3220.12 | −0.239772 | ||||||||
\(566\) | −31826.0 | −2.36351 | ||||||||
\(567\) | −18951.0 | −1.40365 | ||||||||
\(568\) | −6465.59 | −0.477623 | ||||||||
\(569\) | −6200.20 | −0.456812 | −0.228406 | − | 0.973566i | \(-0.573351\pi\) | ||||
−0.228406 | + | 0.973566i | \(0.573351\pi\) | |||||||
\(570\) | −13184.6 | −0.968849 | ||||||||
\(571\) | 10773.1 | 0.789562 | 0.394781 | − | 0.918775i | \(-0.370820\pi\) | ||||
0.394781 | + | 0.918775i | \(0.370820\pi\) | |||||||
\(572\) | −11229.5 | −0.820854 | ||||||||
\(573\) | 8373.65 | 0.610496 | ||||||||
\(574\) | 21740.3 | 1.58088 | ||||||||
\(575\) | 4504.41 | 0.326690 | ||||||||
\(576\) | −839.943 | −0.0607598 | ||||||||
\(577\) | 22073.6 | 1.59261 | 0.796305 | − | 0.604896i | \(-0.206785\pi\) | ||||
0.796305 | + | 0.604896i | \(0.206785\pi\) | |||||||
\(578\) | −20406.1 | −1.46848 | ||||||||
\(579\) | 3044.05 | 0.218491 | ||||||||
\(580\) | 14498.8 | 1.03798 | ||||||||
\(581\) | −12904.1 | −0.921435 | ||||||||
\(582\) | −8073.93 | −0.575043 | ||||||||
\(583\) | −26608.7 | −1.89026 | ||||||||
\(584\) | 5164.14 | 0.365914 | ||||||||
\(585\) | 5242.50 | 0.370514 | ||||||||
\(586\) | −11463.1 | −0.808083 | ||||||||
\(587\) | −12786.4 | −0.899066 | −0.449533 | − | 0.893264i | \(-0.648410\pi\) | ||||
−0.449533 | + | 0.893264i | \(0.648410\pi\) | |||||||
\(588\) | 3369.87 | 0.236345 | ||||||||
\(589\) | 4494.27 | 0.314402 | ||||||||
\(590\) | 37581.4 | 2.62237 | ||||||||
\(591\) | −15178.7 | −1.05646 | ||||||||
\(592\) | 32278.7 | 2.24096 | ||||||||
\(593\) | 23546.2 | 1.63057 | 0.815285 | − | 0.579060i | \(-0.196580\pi\) | ||||
0.815285 | + | 0.579060i | \(0.196580\pi\) | |||||||
\(594\) | −21308.5 | −1.47188 | ||||||||
\(595\) | 31800.0 | 2.19105 | ||||||||
\(596\) | 9256.09 | 0.636148 | ||||||||
\(597\) | 1206.01 | 0.0826779 | ||||||||
\(598\) | −7713.31 | −0.527459 | ||||||||
\(599\) | −15023.7 | −1.02480 | −0.512398 | − | 0.858748i | \(-0.671243\pi\) | ||||
−0.512398 | + | 0.858748i | \(0.671243\pi\) | |||||||
\(600\) | 5445.28 | 0.370504 | ||||||||
\(601\) | −9311.82 | −0.632008 | −0.316004 | − | 0.948758i | \(-0.602341\pi\) | ||||
−0.316004 | + | 0.948758i | \(0.602341\pi\) | |||||||
\(602\) | −37691.0 | −2.55178 | ||||||||
\(603\) | −8886.02 | −0.600111 | ||||||||
\(604\) | −6412.54 | −0.431991 | ||||||||
\(605\) | 23365.6 | 1.57016 | ||||||||
\(606\) | −30724.7 | −2.05958 | ||||||||
\(607\) | −3513.63 | −0.234948 | −0.117474 | − | 0.993076i | \(-0.537480\pi\) | ||||
−0.117474 | + | 0.993076i | \(0.537480\pi\) | |||||||
\(608\) | 8407.25 | 0.560788 | ||||||||
\(609\) | 25053.9 | 1.66705 | ||||||||
\(610\) | −1959.54 | −0.130065 | ||||||||
\(611\) | 4387.78 | 0.290525 | ||||||||
\(612\) | 4618.30 | 0.305039 | ||||||||
\(613\) | −7779.37 | −0.512570 | −0.256285 | − | 0.966601i | \(-0.582499\pi\) | ||||
−0.256285 | + | 0.966601i | \(0.582499\pi\) | |||||||
\(614\) | −27659.4 | −1.81799 | ||||||||
\(615\) | −24549.0 | −1.60961 | ||||||||
\(616\) | −12196.3 | −0.797730 | ||||||||
\(617\) | 9268.56 | 0.604762 | 0.302381 | − | 0.953187i | \(-0.402218\pi\) | ||||
0.302381 | + | 0.953187i | \(0.402218\pi\) | |||||||
\(618\) | −15958.2 | −1.03873 | ||||||||
\(619\) | −12797.5 | −0.830976 | −0.415488 | − | 0.909599i | \(-0.636389\pi\) | ||||
−0.415488 | + | 0.909599i | \(0.636389\pi\) | |||||||
\(620\) | 7916.20 | 0.512778 | ||||||||
\(621\) | −5684.45 | −0.367325 | ||||||||
\(622\) | 30379.7 | 1.95838 | ||||||||
\(623\) | 34055.6 | 2.19006 | ||||||||
\(624\) | −19246.0 | −1.23471 | ||||||||
\(625\) | −18973.5 | −1.21430 | ||||||||
\(626\) | 21592.2 | 1.37859 | ||||||||
\(627\) | −13602.2 | −0.866381 | ||||||||
\(628\) | −6640.28 | −0.421936 | ||||||||
\(629\) | −42066.9 | −2.66664 | ||||||||
\(630\) | −9905.58 | −0.626425 | ||||||||
\(631\) | 881.562 | 0.0556171 | 0.0278086 | − | 0.999613i | \(-0.491147\pi\) | ||||
0.0278086 | + | 0.999613i | \(0.491147\pi\) | |||||||
\(632\) | 4109.92 | 0.258677 | ||||||||
\(633\) | −32523.3 | −2.04216 | ||||||||
\(634\) | −8509.87 | −0.533076 | ||||||||
\(635\) | −30105.2 | −1.88140 | ||||||||
\(636\) | 14928.5 | 0.930742 | ||||||||
\(637\) | 4517.58 | 0.280994 | ||||||||
\(638\) | 38514.0 | 2.38994 | ||||||||
\(639\) | −5417.55 | −0.335391 | ||||||||
\(640\) | −18332.6 | −1.13228 | ||||||||
\(641\) | 4417.49 | 0.272200 | 0.136100 | − | 0.990695i | \(-0.456543\pi\) | ||||
0.136100 | + | 0.990695i | \(0.456543\pi\) | |||||||
\(642\) | 7791.89 | 0.479005 | ||||||||
\(643\) | −15534.9 | −0.952776 | −0.476388 | − | 0.879235i | \(-0.658054\pi\) | ||||
−0.476388 | + | 0.879235i | \(0.658054\pi\) | |||||||
\(644\) | 5660.26 | 0.346344 | ||||||||
\(645\) | 42560.4 | 2.59816 | ||||||||
\(646\) | −15570.6 | −0.948321 | ||||||||
\(647\) | −3809.34 | −0.231469 | −0.115735 | − | 0.993280i | \(-0.536922\pi\) | ||||
−0.115735 | + | 0.993280i | \(0.536922\pi\) | |||||||
\(648\) | −9394.93 | −0.569549 | ||||||||
\(649\) | 38771.7 | 2.34502 | ||||||||
\(650\) | −12699.5 | −0.766332 | ||||||||
\(651\) | 13679.2 | 0.823547 | ||||||||
\(652\) | 5391.43 | 0.323841 | ||||||||
\(653\) | 5394.29 | 0.323270 | 0.161635 | − | 0.986851i | \(-0.448323\pi\) | ||||
0.161635 | + | 0.986851i | \(0.448323\pi\) | |||||||
\(654\) | 13832.2 | 0.827034 | ||||||||
\(655\) | 26791.6 | 1.59822 | ||||||||
\(656\) | 22245.7 | 1.32400 | ||||||||
\(657\) | 4327.06 | 0.256948 | ||||||||
\(658\) | −8290.61 | −0.491188 | ||||||||
\(659\) | 5590.04 | 0.330436 | 0.165218 | − | 0.986257i | \(-0.447167\pi\) | ||||
0.165218 | + | 0.986257i | \(0.447167\pi\) | |||||||
\(660\) | −23959.0 | −1.41303 | ||||||||
\(661\) | −17701.4 | −1.04161 | −0.520805 | − | 0.853676i | \(-0.674368\pi\) | ||||
−0.520805 | + | 0.853676i | \(0.674368\pi\) | |||||||
\(662\) | 30794.9 | 1.80797 | ||||||||
\(663\) | 25082.1 | 1.46924 | ||||||||
\(664\) | −6397.20 | −0.373885 | ||||||||
\(665\) | 12970.5 | 0.756352 | ||||||||
\(666\) | 13103.7 | 0.762398 | ||||||||
\(667\) | 10274.3 | 0.596438 | ||||||||
\(668\) | 5580.50 | 0.323228 | ||||||||
\(669\) | −25730.9 | −1.48702 | ||||||||
\(670\) | 52770.1 | 3.04281 | ||||||||
\(671\) | −2021.60 | −0.116309 | ||||||||
\(672\) | 25589.1 | 1.46893 | ||||||||
\(673\) | 15556.0 | 0.890996 | 0.445498 | − | 0.895283i | \(-0.353027\pi\) | ||||
0.445498 | + | 0.895283i | \(0.353027\pi\) | |||||||
\(674\) | 11509.5 | 0.657757 | ||||||||
\(675\) | −9359.11 | −0.533677 | ||||||||
\(676\) | −2714.83 | −0.154462 | ||||||||
\(677\) | −30896.1 | −1.75396 | −0.876982 | − | 0.480523i | \(-0.840447\pi\) | ||||
−0.876982 | + | 0.480523i | \(0.840447\pi\) | |||||||
\(678\) | 4799.00 | 0.271835 | ||||||||
\(679\) | 7942.79 | 0.448920 | ||||||||
\(680\) | 15764.8 | 0.889047 | ||||||||
\(681\) | −29018.5 | −1.63288 | ||||||||
\(682\) | 21028.3 | 1.18067 | ||||||||
\(683\) | −16765.5 | −0.939260 | −0.469630 | − | 0.882863i | \(-0.655613\pi\) | ||||
−0.469630 | + | 0.882863i | \(0.655613\pi\) | |||||||
\(684\) | 1883.70 | 0.105300 | ||||||||
\(685\) | 14487.5 | 0.808085 | ||||||||
\(686\) | 17889.9 | 0.995682 | ||||||||
\(687\) | −36404.9 | −2.02174 | ||||||||
\(688\) | −38567.1 | −2.13715 | ||||||||
\(689\) | 20012.8 | 1.10657 | ||||||||
\(690\) | −16456.9 | −0.907978 | ||||||||
\(691\) | 24887.6 | 1.37014 | 0.685072 | − | 0.728475i | \(-0.259771\pi\) | ||||
0.685072 | + | 0.728475i | \(0.259771\pi\) | |||||||
\(692\) | 10254.3 | 0.563312 | ||||||||
\(693\) | −10219.3 | −0.560173 | ||||||||
\(694\) | −28739.7 | −1.57197 | ||||||||
\(695\) | 43013.5 | 2.34762 | ||||||||
\(696\) | 12420.4 | 0.676429 | ||||||||
\(697\) | −28991.4 | −1.57551 | ||||||||
\(698\) | 25716.9 | 1.39455 | ||||||||
\(699\) | −21728.8 | −1.17576 | ||||||||
\(700\) | 9319.28 | 0.503194 | ||||||||
\(701\) | −3157.12 | −0.170104 | −0.0850518 | − | 0.996377i | \(-0.527106\pi\) | ||||
−0.0850518 | + | 0.996377i | \(0.527106\pi\) | |||||||
\(702\) | 16026.4 | 0.861651 | ||||||||
\(703\) | −17158.1 | −0.920528 | ||||||||
\(704\) | 5146.03 | 0.275495 | ||||||||
\(705\) | 9361.67 | 0.500115 | ||||||||
\(706\) | −33823.4 | −1.80306 | ||||||||
\(707\) | 30225.6 | 1.60785 | ||||||||
\(708\) | −21752.3 | −1.15466 | ||||||||
\(709\) | 29588.2 | 1.56729 | 0.783644 | − | 0.621210i | \(-0.213359\pi\) | ||||
0.783644 | + | 0.621210i | \(0.213359\pi\) | |||||||
\(710\) | 32172.4 | 1.70057 | ||||||||
\(711\) | 3443.72 | 0.181645 | ||||||||
\(712\) | 16883.0 | 0.888648 | ||||||||
\(713\) | 5609.70 | 0.294649 | ||||||||
\(714\) | −47392.0 | −2.48404 | ||||||||
\(715\) | −32118.9 | −1.67997 | ||||||||
\(716\) | 1823.80 | 0.0951935 | ||||||||
\(717\) | 8287.57 | 0.431667 | ||||||||
\(718\) | −50.9983 | −0.00265075 | ||||||||
\(719\) | −9248.18 | −0.479693 | −0.239846 | − | 0.970811i | \(-0.577097\pi\) | ||||
−0.239846 | + | 0.970811i | \(0.577097\pi\) | |||||||
\(720\) | −10135.8 | −0.524639 | ||||||||
\(721\) | 15699.0 | 0.810904 | ||||||||
\(722\) | 18455.5 | 0.951308 | ||||||||
\(723\) | 12523.3 | 0.644185 | ||||||||
\(724\) | −5942.84 | −0.305061 | ||||||||
\(725\) | 16916.1 | 0.866549 | ||||||||
\(726\) | −34822.1 | −1.78012 | ||||||||
\(727\) | 6815.64 | 0.347700 | 0.173850 | − | 0.984772i | \(-0.444379\pi\) | ||||
0.173850 | + | 0.984772i | \(0.444379\pi\) | |||||||
\(728\) | 9172.99 | 0.466997 | ||||||||
\(729\) | 9696.81 | 0.492649 | ||||||||
\(730\) | −25696.5 | −1.30283 | ||||||||
\(731\) | 50262.2 | 2.54311 | ||||||||
\(732\) | 1134.19 | 0.0572690 | ||||||||
\(733\) | −4348.84 | −0.219138 | −0.109569 | − | 0.993979i | \(-0.534947\pi\) | ||||
−0.109569 | + | 0.993979i | \(0.534947\pi\) | |||||||
\(734\) | 25349.5 | 1.27475 | ||||||||
\(735\) | 9638.60 | 0.483708 | ||||||||
\(736\) | 10493.8 | 0.525555 | ||||||||
\(737\) | 54441.4 | 2.72100 | ||||||||
\(738\) | 9030.71 | 0.450440 | ||||||||
\(739\) | −25559.3 | −1.27228 | −0.636139 | − | 0.771574i | \(-0.719470\pi\) | ||||
−0.636139 | + | 0.771574i | \(0.719470\pi\) | |||||||
\(740\) | −30222.3 | −1.50135 | ||||||||
\(741\) | 10230.4 | 0.507185 | ||||||||
\(742\) | −37813.7 | −1.87087 | ||||||||
\(743\) | −36199.4 | −1.78738 | −0.893691 | − | 0.448682i | \(-0.851894\pi\) | ||||
−0.893691 | + | 0.448682i | \(0.851894\pi\) | |||||||
\(744\) | 6781.43 | 0.334166 | ||||||||
\(745\) | 26474.6 | 1.30195 | ||||||||
\(746\) | 12049.7 | 0.591384 | ||||||||
\(747\) | −5360.25 | −0.262545 | ||||||||
\(748\) | −28294.7 | −1.38309 | ||||||||
\(749\) | −7665.33 | −0.373946 | ||||||||
\(750\) | 12233.6 | 0.595613 | ||||||||
\(751\) | −20181.2 | −0.980590 | −0.490295 | − | 0.871556i | \(-0.663111\pi\) | ||||
−0.490295 | + | 0.871556i | \(0.663111\pi\) | |||||||
\(752\) | −8483.31 | −0.411376 | ||||||||
\(753\) | 42171.8 | 2.04094 | ||||||||
\(754\) | −28967.0 | −1.39909 | ||||||||
\(755\) | −18341.3 | −0.884119 | ||||||||
\(756\) | −11760.7 | −0.565783 | ||||||||
\(757\) | −3516.85 | −0.168854 | −0.0844269 | − | 0.996430i | \(-0.526906\pi\) | ||||
−0.0844269 | + | 0.996430i | \(0.526906\pi\) | |||||||
\(758\) | −29987.5 | −1.43693 | ||||||||
\(759\) | −16978.2 | −0.811948 | ||||||||
\(760\) | 6430.11 | 0.306901 | ||||||||
\(761\) | 9277.47 | 0.441929 | 0.220965 | − | 0.975282i | \(-0.429079\pi\) | ||||
0.220965 | + | 0.975282i | \(0.429079\pi\) | |||||||
\(762\) | 44866.3 | 2.13298 | ||||||||
\(763\) | −13607.5 | −0.645642 | ||||||||
\(764\) | 7104.58 | 0.336433 | ||||||||
\(765\) | 13209.4 | 0.624296 | ||||||||
\(766\) | 23950.7 | 1.12973 | ||||||||
\(767\) | −29160.7 | −1.37279 | ||||||||
\(768\) | 31868.0 | 1.49732 | ||||||||
\(769\) | −20386.4 | −0.955986 | −0.477993 | − | 0.878364i | \(-0.658636\pi\) | ||||
−0.477993 | + | 0.878364i | \(0.658636\pi\) | |||||||
\(770\) | 60687.9 | 2.84031 | ||||||||
\(771\) | 19274.2 | 0.900316 | ||||||||
\(772\) | 2582.71 | 0.120406 | ||||||||
\(773\) | −30068.2 | −1.39907 | −0.699533 | − | 0.714601i | \(-0.746608\pi\) | ||||
−0.699533 | + | 0.714601i | \(0.746608\pi\) | |||||||
\(774\) | −15656.5 | −0.727081 | ||||||||
\(775\) | 9236.03 | 0.428088 | ||||||||
\(776\) | 3937.63 | 0.182155 | ||||||||
\(777\) | −52224.1 | −2.41124 | ||||||||
\(778\) | −45640.5 | −2.10320 | ||||||||
\(779\) | −11824.9 | −0.543867 | ||||||||
\(780\) | 18019.9 | 0.827200 | ||||||||
\(781\) | 33191.4 | 1.52072 | ||||||||
\(782\) | −19435.0 | −0.888740 | ||||||||
\(783\) | −21347.7 | −0.974334 | ||||||||
\(784\) | −8734.26 | −0.397880 | ||||||||
\(785\) | −18992.7 | −0.863541 | ||||||||
\(786\) | −39928.0 | −1.81194 | ||||||||
\(787\) | −12502.9 | −0.566305 | −0.283152 | − | 0.959075i | \(-0.591380\pi\) | ||||
−0.283152 | + | 0.959075i | \(0.591380\pi\) | |||||||
\(788\) | −12878.3 | −0.582198 | ||||||||
\(789\) | −15351.4 | −0.692679 | ||||||||
\(790\) | −20450.7 | −0.921017 | ||||||||
\(791\) | −4721.05 | −0.212214 | ||||||||
\(792\) | −5066.21 | −0.227298 | ||||||||
\(793\) | 1520.48 | 0.0680878 | ||||||||
\(794\) | −3885.85 | −0.173682 | ||||||||
\(795\) | 42698.8 | 1.90487 | ||||||||
\(796\) | 1023.23 | 0.0455622 | ||||||||
\(797\) | −9870.48 | −0.438683 | −0.219342 | − | 0.975648i | \(-0.570391\pi\) | ||||
−0.219342 | + | 0.975648i | \(0.570391\pi\) | |||||||
\(798\) | −19330.2 | −0.857494 | ||||||||
\(799\) | 11055.8 | 0.489519 | ||||||||
\(800\) | 17277.5 | 0.763564 | ||||||||
\(801\) | 14146.3 | 0.624015 | ||||||||
\(802\) | 13493.9 | 0.594121 | ||||||||
\(803\) | −26510.3 | −1.16504 | ||||||||
\(804\) | −30543.6 | −1.33979 | ||||||||
\(805\) | 16189.6 | 0.708832 | ||||||||
\(806\) | −15815.7 | −0.691171 | ||||||||
\(807\) | 32066.0 | 1.39873 | ||||||||
\(808\) | 14984.3 | 0.652409 | ||||||||
\(809\) | −24562.1 | −1.06744 | −0.533720 | − | 0.845662i | \(-0.679206\pi\) | ||||
−0.533720 | + | 0.845662i | \(0.679206\pi\) | |||||||
\(810\) | 46748.6 | 2.02787 | ||||||||
\(811\) | 22676.5 | 0.981849 | 0.490924 | − | 0.871202i | \(-0.336659\pi\) | ||||
0.490924 | + | 0.871202i | \(0.336659\pi\) | |||||||
\(812\) | 21256.8 | 0.918680 | ||||||||
\(813\) | −7810.54 | −0.336935 | ||||||||
\(814\) | −80281.5 | −3.45684 | ||||||||
\(815\) | 15420.7 | 0.662778 | ||||||||
\(816\) | −48493.6 | −2.08041 | ||||||||
\(817\) | 20500.8 | 0.877885 | ||||||||
\(818\) | −16876.5 | −0.721362 | ||||||||
\(819\) | 7686.09 | 0.327929 | ||||||||
\(820\) | −20828.4 | −0.887026 | ||||||||
\(821\) | −9836.99 | −0.418165 | −0.209082 | − | 0.977898i | \(-0.567048\pi\) | ||||
−0.209082 | + | 0.977898i | \(0.567048\pi\) | |||||||
\(822\) | −21590.9 | −0.916145 | ||||||||
\(823\) | −29849.3 | −1.26425 | −0.632127 | − | 0.774865i | \(-0.717818\pi\) | ||||
−0.632127 | + | 0.774865i | \(0.717818\pi\) | |||||||
\(824\) | 7782.76 | 0.329036 | ||||||||
\(825\) | −27953.5 | −1.17966 | ||||||||
\(826\) | 55098.5 | 2.32097 | ||||||||
\(827\) | −32963.1 | −1.38602 | −0.693011 | − | 0.720927i | \(-0.743716\pi\) | ||||
−0.693011 | + | 0.720927i | \(0.743716\pi\) | |||||||
\(828\) | 2351.22 | 0.0986840 | ||||||||
\(829\) | 7716.35 | 0.323281 | 0.161641 | − | 0.986850i | \(-0.448321\pi\) | ||||
0.161641 | + | 0.986850i | \(0.448321\pi\) | |||||||
\(830\) | 31832.1 | 1.33121 | ||||||||
\(831\) | −30591.1 | −1.27701 | ||||||||
\(832\) | −3870.40 | −0.161277 | ||||||||
\(833\) | 11382.8 | 0.473459 | ||||||||
\(834\) | −64103.7 | −2.66155 | ||||||||
\(835\) | 15961.5 | 0.661522 | ||||||||
\(836\) | −11540.8 | −0.477446 | ||||||||
\(837\) | −11655.6 | −0.481335 | ||||||||
\(838\) | 29304.0 | 1.20798 | ||||||||
\(839\) | −29201.2 | −1.20159 | −0.600797 | − | 0.799402i | \(-0.705150\pi\) | ||||
−0.600797 | + | 0.799402i | \(0.705150\pi\) | |||||||
\(840\) | 19571.3 | 0.803897 | ||||||||
\(841\) | 14195.8 | 0.582056 | ||||||||
\(842\) | 15492.4 | 0.634090 | ||||||||
\(843\) | −19459.8 | −0.795053 | ||||||||
\(844\) | −27594.2 | −1.12539 | ||||||||
\(845\) | −7765.05 | −0.316125 | ||||||||
\(846\) | −3443.84 | −0.139954 | ||||||||
\(847\) | 34256.5 | 1.38969 | ||||||||
\(848\) | −38692.6 | −1.56688 | ||||||||
\(849\) | 52688.5 | 2.12987 | ||||||||
\(850\) | −31998.6 | −1.29123 | ||||||||
\(851\) | −21416.6 | −0.862693 | ||||||||
\(852\) | −18621.6 | −0.748784 | ||||||||
\(853\) | −20411.2 | −0.819303 | −0.409652 | − | 0.912242i | \(-0.634350\pi\) | ||||
−0.409652 | + | 0.912242i | \(0.634350\pi\) | |||||||
\(854\) | −2872.90 | −0.115115 | ||||||||
\(855\) | 5387.81 | 0.215508 | ||||||||
\(856\) | −3800.08 | −0.151734 | ||||||||
\(857\) | −15868.0 | −0.632484 | −0.316242 | − | 0.948679i | \(-0.602421\pi\) | ||||
−0.316242 | + | 0.948679i | \(0.602421\pi\) | |||||||
\(858\) | 47867.4 | 1.90462 | ||||||||
\(859\) | 10889.4 | 0.432530 | 0.216265 | − | 0.976335i | \(-0.430613\pi\) | ||||
0.216265 | + | 0.976335i | \(0.430613\pi\) | |||||||
\(860\) | 36110.1 | 1.43180 | ||||||||
\(861\) | −35991.5 | −1.42461 | ||||||||
\(862\) | −31066.0 | −1.22751 | ||||||||
\(863\) | 25076.0 | 0.989104 | 0.494552 | − | 0.869148i | \(-0.335332\pi\) | ||||
0.494552 | + | 0.869148i | \(0.335332\pi\) | |||||||
\(864\) | −21803.7 | −0.858539 | ||||||||
\(865\) | 29329.8 | 1.15288 | ||||||||
\(866\) | 29463.0 | 1.15611 | ||||||||
\(867\) | 33782.7 | 1.32332 | ||||||||
\(868\) | 11606.0 | 0.453842 | ||||||||
\(869\) | −21098.4 | −0.823608 | ||||||||
\(870\) | −61803.2 | −2.40842 | ||||||||
\(871\) | −40946.2 | −1.59289 | ||||||||
\(872\) | −6745.90 | −0.261978 | ||||||||
\(873\) | 3299.36 | 0.127911 | ||||||||
\(874\) | −7927.11 | −0.306795 | ||||||||
\(875\) | −12034.9 | −0.464978 | ||||||||
\(876\) | 14873.3 | 0.573654 | ||||||||
\(877\) | 47178.1 | 1.81652 | 0.908262 | − | 0.418402i | \(-0.137410\pi\) | ||||
0.908262 | + | 0.418402i | \(0.137410\pi\) | |||||||
\(878\) | 59236.8 | 2.27693 | ||||||||
\(879\) | 18977.4 | 0.728204 | ||||||||
\(880\) | 62098.6 | 2.37880 | ||||||||
\(881\) | 16533.0 | 0.632248 | 0.316124 | − | 0.948718i | \(-0.397618\pi\) | ||||
0.316124 | + | 0.948718i | \(0.397618\pi\) | |||||||
\(882\) | −3545.71 | −0.135363 | ||||||||
\(883\) | 6961.19 | 0.265303 | 0.132652 | − | 0.991163i | \(-0.457651\pi\) | ||||
0.132652 | + | 0.991163i | \(0.457651\pi\) | |||||||
\(884\) | 21280.8 | 0.809673 | ||||||||
\(885\) | −62216.6 | −2.36315 | ||||||||
\(886\) | 16400.0 | 0.621862 | ||||||||
\(887\) | 46916.1 | 1.77597 | 0.887987 | − | 0.459869i | \(-0.152104\pi\) | ||||
0.887987 | + | 0.459869i | \(0.152104\pi\) | |||||||
\(888\) | −25890.0 | −0.978393 | ||||||||
\(889\) | −44137.6 | −1.66516 | ||||||||
\(890\) | −84008.8 | −3.16402 | ||||||||
\(891\) | 48229.2 | 1.81340 | ||||||||
\(892\) | −21831.3 | −0.819467 | ||||||||
\(893\) | 4509.40 | 0.168983 | ||||||||
\(894\) | −39455.5 | −1.47605 | ||||||||
\(895\) | 5216.48 | 0.194824 | ||||||||
\(896\) | −26877.6 | −1.00214 | ||||||||
\(897\) | 12769.5 | 0.475320 | ||||||||
\(898\) | 64036.2 | 2.37964 | ||||||||
\(899\) | 21066.9 | 0.781559 | ||||||||
\(900\) | 3871.14 | 0.143375 | ||||||||
\(901\) | 50425.7 | 1.86451 | ||||||||
\(902\) | −55327.9 | −2.04237 | ||||||||
\(903\) | 62398.2 | 2.29954 | ||||||||
\(904\) | −2340.45 | −0.0861088 | ||||||||
\(905\) | −16997.9 | −0.624342 | ||||||||
\(906\) | 27334.4 | 1.00235 | ||||||||
\(907\) | −16314.1 | −0.597245 | −0.298623 | − | 0.954371i | \(-0.596527\pi\) | ||||
−0.298623 | + | 0.954371i | \(0.596527\pi\) | |||||||
\(908\) | −24620.6 | −0.899849 | ||||||||
\(909\) | 12555.4 | 0.458127 | ||||||||
\(910\) | −45644.3 | −1.66274 | ||||||||
\(911\) | 29827.8 | 1.08479 | 0.542393 | − | 0.840125i | \(-0.317518\pi\) | ||||
0.542393 | + | 0.840125i | \(0.317518\pi\) | |||||||
\(912\) | −19779.5 | −0.718162 | ||||||||
\(913\) | 32840.3 | 1.19042 | ||||||||
\(914\) | 26010.4 | 0.941300 | ||||||||
\(915\) | 3244.05 | 0.117208 | ||||||||
\(916\) | −30887.6 | −1.11414 | ||||||||
\(917\) | 39279.5 | 1.41453 | ||||||||
\(918\) | 40381.4 | 1.45184 | ||||||||
\(919\) | 17571.6 | 0.630722 | 0.315361 | − | 0.948972i | \(-0.397874\pi\) | ||||
0.315361 | + | 0.948972i | \(0.397874\pi\) | |||||||
\(920\) | 8025.99 | 0.287619 | ||||||||
\(921\) | 45790.7 | 1.63828 | ||||||||
\(922\) | 34391.3 | 1.22843 | ||||||||
\(923\) | −24963.7 | −0.890239 | ||||||||
\(924\) | −35126.5 | −1.25063 | ||||||||
\(925\) | −35261.2 | −1.25338 | ||||||||
\(926\) | −7035.59 | −0.249680 | ||||||||
\(927\) | 6521.21 | 0.231051 | ||||||||
\(928\) | 39409.1 | 1.39404 | ||||||||
\(929\) | −45309.8 | −1.60018 | −0.800089 | − | 0.599881i | \(-0.795215\pi\) | ||||
−0.800089 | + | 0.599881i | \(0.795215\pi\) | |||||||
\(930\) | −33744.0 | −1.18979 | ||||||||
\(931\) | 4642.80 | 0.163439 | ||||||||
\(932\) | −18435.7 | −0.647941 | ||||||||
\(933\) | −50294.1 | −1.76480 | ||||||||
\(934\) | −52916.5 | −1.85383 | ||||||||
\(935\) | −80929.2 | −2.83066 | ||||||||
\(936\) | 3810.37 | 0.133062 | ||||||||
\(937\) | 8210.91 | 0.286274 | 0.143137 | − | 0.989703i | \(-0.454281\pi\) | ||||
0.143137 | + | 0.989703i | \(0.454281\pi\) | |||||||
\(938\) | 77366.8 | 2.69309 | ||||||||
\(939\) | −35746.2 | −1.24232 | ||||||||
\(940\) | 7942.87 | 0.275604 | ||||||||
\(941\) | 49966.4 | 1.73099 | 0.865493 | − | 0.500922i | \(-0.167006\pi\) | ||||
0.865493 | + | 0.500922i | \(0.167006\pi\) | |||||||
\(942\) | 28305.2 | 0.979015 | ||||||||
\(943\) | −14759.8 | −0.509697 | ||||||||
\(944\) | 56379.2 | 1.94384 | ||||||||
\(945\) | −33638.3 | −1.15794 | ||||||||
\(946\) | 95921.6 | 3.29670 | ||||||||
\(947\) | −42167.2 | −1.44694 | −0.723468 | − | 0.690358i | \(-0.757453\pi\) | ||||
−0.723468 | + | 0.690358i | \(0.757453\pi\) | |||||||
\(948\) | 11837.0 | 0.405535 | ||||||||
\(949\) | 19938.8 | 0.682024 | ||||||||
\(950\) | −13051.5 | −0.445733 | ||||||||
\(951\) | 14088.3 | 0.480382 | ||||||||
\(952\) | 23112.9 | 0.786864 | ||||||||
\(953\) | 8537.38 | 0.290192 | 0.145096 | − | 0.989418i | \(-0.453651\pi\) | ||||
0.145096 | + | 0.989418i | \(0.453651\pi\) | |||||||
\(954\) | −15707.4 | −0.533068 | ||||||||
\(955\) | 20320.7 | 0.688548 | ||||||||
\(956\) | 7031.55 | 0.237884 | ||||||||
\(957\) | −63760.7 | −2.15370 | ||||||||
\(958\) | −9387.34 | −0.316588 | ||||||||
\(959\) | 21240.3 | 0.715208 | ||||||||
\(960\) | −8257.80 | −0.277624 | ||||||||
\(961\) | −18288.6 | −0.613898 | ||||||||
\(962\) | 60380.9 | 2.02366 | ||||||||
\(963\) | −3184.10 | −0.106549 | ||||||||
\(964\) | 10625.3 | 0.354998 | ||||||||
\(965\) | 7387.13 | 0.246425 | ||||||||
\(966\) | −24127.7 | −0.803619 | ||||||||
\(967\) | 17713.6 | 0.589069 | 0.294534 | − | 0.955641i | \(-0.404835\pi\) | ||||
0.294534 | + | 0.955641i | \(0.404835\pi\) | |||||||
\(968\) | 16982.6 | 0.563887 | ||||||||
\(969\) | 25777.3 | 0.854580 | ||||||||
\(970\) | −19593.4 | −0.648563 | ||||||||
\(971\) | 30230.2 | 0.999107 | 0.499554 | − | 0.866283i | \(-0.333497\pi\) | ||||
0.499554 | + | 0.866283i | \(0.333497\pi\) | |||||||
\(972\) | −12152.1 | −0.401008 | ||||||||
\(973\) | 63062.6 | 2.07779 | ||||||||
\(974\) | 68066.6 | 2.23921 | ||||||||
\(975\) | 21024.3 | 0.690580 | ||||||||
\(976\) | −2939.68 | −0.0964106 | ||||||||
\(977\) | 37908.1 | 1.24134 | 0.620668 | − | 0.784073i | \(-0.286861\pi\) | ||||
0.620668 | + | 0.784073i | \(0.286861\pi\) | |||||||
\(978\) | −22981.8 | −0.751407 | ||||||||
\(979\) | −86669.5 | −2.82939 | ||||||||
\(980\) | 8177.82 | 0.266562 | ||||||||
\(981\) | −5652.42 | −0.183963 | ||||||||
\(982\) | 36558.8 | 1.18802 | ||||||||
\(983\) | −36870.4 | −1.19632 | −0.598160 | − | 0.801377i | \(-0.704101\pi\) | ||||
−0.598160 | + | 0.801377i | \(0.704101\pi\) | |||||||
\(984\) | −17842.7 | −0.578054 | ||||||||
\(985\) | −36835.0 | −1.19153 | ||||||||
\(986\) | −72987.2 | −2.35739 | ||||||||
\(987\) | 13725.3 | 0.442634 | ||||||||
\(988\) | 8679.96 | 0.279500 | ||||||||
\(989\) | 25588.9 | 0.822730 | ||||||||
\(990\) | 25209.2 | 0.809292 | ||||||||
\(991\) | −13385.1 | −0.429053 | −0.214526 | − | 0.976718i | \(-0.568821\pi\) | ||||
−0.214526 | + | 0.976718i | \(0.568821\pi\) | |||||||
\(992\) | 21517.0 | 0.688675 | ||||||||
\(993\) | −50981.5 | −1.62925 | ||||||||
\(994\) | 47168.3 | 1.50512 | ||||||||
\(995\) | 2926.68 | 0.0932483 | ||||||||
\(996\) | −18424.6 | −0.586151 | ||||||||
\(997\) | −25690.0 | −0.816058 | −0.408029 | − | 0.912969i | \(-0.633784\pi\) | ||||
−0.408029 | + | 0.912969i | \(0.633784\pi\) | |||||||
\(998\) | 18036.2 | 0.572071 | ||||||||
\(999\) | 44498.7 | 1.40929 |
(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.b.1.14 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.4.a.b.1.14 | ✓ | 71 | 1.1 | even | 1 | trivial |