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: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.1362828.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 23x^{2} + 48 \) |
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 | 1.3 | ||
Root | \(1.52356\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52356 | 0.538658 | 0.269329 | − | 0.963048i | \(-0.413198\pi\) | ||||
0.269329 | + | 0.963048i | \(0.413198\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −5.67878 | −0.709847 | ||||||||
\(5\) | −9.65841 | −0.863874 | −0.431937 | − | 0.901904i | \(-0.642170\pi\) | ||||
−0.431937 | + | 0.901904i | \(0.642170\pi\) | |||||||
\(6\) | 4.57067 | 0.310994 | ||||||||
\(7\) | −22.3639 | −1.20754 | −0.603769 | − | 0.797159i | \(-0.706335\pi\) | ||||
−0.603769 | + | 0.797159i | \(0.706335\pi\) | |||||||
\(8\) | −20.8404 | −0.921023 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −14.7151 | −0.465333 | ||||||||
\(11\) | 50.3050 | 1.37887 | 0.689433 | − | 0.724349i | \(-0.257860\pi\) | ||||
0.689433 | + | 0.724349i | \(0.257860\pi\) | |||||||
\(12\) | −17.0363 | −0.409831 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −34.0727 | −0.650450 | ||||||||
\(15\) | −28.9752 | −0.498758 | ||||||||
\(16\) | 13.6788 | 0.213731 | ||||||||
\(17\) | 86.1454 | 1.22902 | 0.614509 | − | 0.788910i | \(-0.289354\pi\) | ||||
0.614509 | + | 0.788910i | \(0.289354\pi\) | |||||||
\(18\) | 13.7120 | 0.179553 | ||||||||
\(19\) | −116.880 | −1.41127 | −0.705633 | − | 0.708578i | \(-0.749337\pi\) | ||||
−0.705633 | + | 0.708578i | \(0.749337\pi\) | |||||||
\(20\) | 54.8480 | 0.613219 | ||||||||
\(21\) | −67.0918 | −0.697173 | ||||||||
\(22\) | 76.6424 | 0.742737 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | −62.5211 | −0.531753 | ||||||||
\(25\) | −31.7151 | −0.253721 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 127.000 | 0.857168 | ||||||||
\(29\) | 14.1454 | 0.0905768 | 0.0452884 | − | 0.998974i | \(-0.485579\pi\) | ||||
0.0452884 | + | 0.998974i | \(0.485579\pi\) | |||||||
\(30\) | −44.1454 | −0.268660 | ||||||||
\(31\) | 196.215 | 1.13682 | 0.568408 | − | 0.822747i | \(-0.307559\pi\) | ||||
0.568408 | + | 0.822747i | \(0.307559\pi\) | |||||||
\(32\) | 187.563 | 1.03615 | ||||||||
\(33\) | 150.915 | 0.796089 | ||||||||
\(34\) | 131.247 | 0.662021 | ||||||||
\(35\) | 216.000 | 1.04316 | ||||||||
\(36\) | −51.1090 | −0.236616 | ||||||||
\(37\) | 154.424 | 0.686138 | 0.343069 | − | 0.939310i | \(-0.388533\pi\) | ||||
0.343069 | + | 0.939310i | \(0.388533\pi\) | |||||||
\(38\) | −178.073 | −0.760190 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 201.285 | 0.795648 | ||||||||
\(41\) | 265.726 | 1.01218 | 0.506091 | − | 0.862480i | \(-0.331090\pi\) | ||||
0.506091 | + | 0.862480i | \(0.331090\pi\) | |||||||
\(42\) | −102.218 | −0.375538 | ||||||||
\(43\) | 211.855 | 0.751338 | 0.375669 | − | 0.926754i | \(-0.377413\pi\) | ||||
0.375669 | + | 0.926754i | \(0.377413\pi\) | |||||||
\(44\) | −285.671 | −0.978785 | ||||||||
\(45\) | −86.9257 | −0.287958 | ||||||||
\(46\) | 109.696 | 0.351604 | ||||||||
\(47\) | −67.5535 | −0.209653 | −0.104827 | − | 0.994491i | \(-0.533429\pi\) | ||||
−0.104827 | + | 0.994491i | \(0.533429\pi\) | |||||||
\(48\) | 41.0363 | 0.123398 | ||||||||
\(49\) | 157.145 | 0.458150 | ||||||||
\(50\) | −48.3197 | −0.136669 | ||||||||
\(51\) | 258.436 | 0.709574 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 686.581 | 1.77942 | 0.889710 | − | 0.456527i | \(-0.150907\pi\) | ||||
0.889710 | + | 0.456527i | \(0.150907\pi\) | |||||||
\(54\) | 41.1360 | 0.103665 | ||||||||
\(55\) | −485.866 | −1.19117 | ||||||||
\(56\) | 466.073 | 1.11217 | ||||||||
\(57\) | −350.639 | −0.814795 | ||||||||
\(58\) | 21.5512 | 0.0487899 | ||||||||
\(59\) | 91.9304 | 0.202853 | 0.101426 | − | 0.994843i | \(-0.467659\pi\) | ||||
0.101426 | + | 0.994843i | \(0.467659\pi\) | |||||||
\(60\) | 164.544 | 0.354042 | ||||||||
\(61\) | 329.006 | 0.690572 | 0.345286 | − | 0.938498i | \(-0.387782\pi\) | ||||
0.345286 | + | 0.938498i | \(0.387782\pi\) | |||||||
\(62\) | 298.945 | 0.612355 | ||||||||
\(63\) | −201.275 | −0.402513 | ||||||||
\(64\) | 176.333 | 0.344400 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 229.927 | 0.428820 | ||||||||
\(67\) | −768.370 | −1.40106 | −0.700532 | − | 0.713621i | \(-0.747054\pi\) | ||||
−0.700532 | + | 0.713621i | \(0.747054\pi\) | |||||||
\(68\) | −489.201 | −0.872416 | ||||||||
\(69\) | 216.000 | 0.376860 | ||||||||
\(70\) | 329.088 | 0.561908 | ||||||||
\(71\) | −264.969 | −0.442902 | −0.221451 | − | 0.975171i | \(-0.571079\pi\) | ||||
−0.221451 | + | 0.975171i | \(0.571079\pi\) | |||||||
\(72\) | −187.563 | −0.307008 | ||||||||
\(73\) | −771.306 | −1.23664 | −0.618319 | − | 0.785927i | \(-0.712186\pi\) | ||||
−0.618319 | + | 0.785927i | \(0.712186\pi\) | |||||||
\(74\) | 235.273 | 0.369594 | ||||||||
\(75\) | −95.1454 | −0.146486 | ||||||||
\(76\) | 663.734 | 1.00178 | ||||||||
\(77\) | −1125.02 | −1.66503 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1226.86 | 1.74725 | 0.873624 | − | 0.486602i | \(-0.161764\pi\) | ||||
0.873624 | + | 0.486602i | \(0.161764\pi\) | |||||||
\(80\) | −132.115 | −0.184637 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 404.849 | 0.545220 | ||||||||
\(83\) | 514.019 | 0.679771 | 0.339885 | − | 0.940467i | \(-0.389612\pi\) | ||||
0.339885 | + | 0.940467i | \(0.389612\pi\) | |||||||
\(84\) | 381.000 | 0.494886 | ||||||||
\(85\) | −832.027 | −1.06172 | ||||||||
\(86\) | 322.772 | 0.404714 | ||||||||
\(87\) | 42.4361 | 0.0522945 | ||||||||
\(88\) | −1048.38 | −1.26997 | ||||||||
\(89\) | −527.889 | −0.628720 | −0.314360 | − | 0.949304i | \(-0.601790\pi\) | ||||
−0.314360 | + | 0.949304i | \(0.601790\pi\) | |||||||
\(90\) | −132.436 | −0.155111 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −408.872 | −0.463346 | ||||||||
\(93\) | 588.646 | 0.656341 | ||||||||
\(94\) | −102.921 | −0.112931 | ||||||||
\(95\) | 1128.87 | 1.21916 | ||||||||
\(96\) | 562.690 | 0.598222 | ||||||||
\(97\) | 74.2755 | 0.0777478 | 0.0388739 | − | 0.999244i | \(-0.487623\pi\) | ||||
0.0388739 | + | 0.999244i | \(0.487623\pi\) | |||||||
\(98\) | 239.420 | 0.246786 | ||||||||
\(99\) | 452.745 | 0.459622 | ||||||||
\(100\) | 180.103 | 0.180103 | ||||||||
\(101\) | 609.419 | 0.600390 | 0.300195 | − | 0.953878i | \(-0.402948\pi\) | ||||
0.300195 | + | 0.953878i | \(0.402948\pi\) | |||||||
\(102\) | 393.742 | 0.382218 | ||||||||
\(103\) | −32.4361 | −0.0310293 | −0.0155147 | − | 0.999880i | \(-0.504939\pi\) | ||||
−0.0155147 | + | 0.999880i | \(0.504939\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 648.000 | 0.602270 | ||||||||
\(106\) | 1046.04 | 0.958498 | ||||||||
\(107\) | −1725.45 | −1.55893 | −0.779467 | − | 0.626444i | \(-0.784510\pi\) | ||||
−0.779467 | + | 0.626444i | \(0.784510\pi\) | |||||||
\(108\) | −153.327 | −0.136610 | ||||||||
\(109\) | −1273.43 | −1.11902 | −0.559508 | − | 0.828825i | \(-0.689010\pi\) | ||||
−0.559508 | + | 0.828825i | \(0.689010\pi\) | |||||||
\(110\) | −740.244 | −0.641632 | ||||||||
\(111\) | 463.271 | 0.396142 | ||||||||
\(112\) | −305.911 | −0.258088 | ||||||||
\(113\) | 1114.73 | 0.928006 | 0.464003 | − | 0.885834i | \(-0.346413\pi\) | ||||
0.464003 | + | 0.885834i | \(0.346413\pi\) | |||||||
\(114\) | −534.218 | −0.438896 | ||||||||
\(115\) | −695.406 | −0.563886 | ||||||||
\(116\) | −80.3284 | −0.0642957 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 140.061 | 0.109268 | ||||||||
\(119\) | −1926.55 | −1.48409 | ||||||||
\(120\) | 603.855 | 0.459368 | ||||||||
\(121\) | 1199.59 | 0.901272 | ||||||||
\(122\) | 501.259 | 0.371982 | ||||||||
\(123\) | 797.179 | 0.584384 | ||||||||
\(124\) | −1114.26 | −0.806966 | ||||||||
\(125\) | 1513.62 | 1.08306 | ||||||||
\(126\) | −306.654 | −0.216817 | ||||||||
\(127\) | 1174.01 | 0.820289 | 0.410144 | − | 0.912021i | \(-0.365478\pi\) | ||||
0.410144 | + | 0.912021i | \(0.365478\pi\) | |||||||
\(128\) | −1231.85 | −0.850637 | ||||||||
\(129\) | 635.564 | 0.433785 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1445.16 | −0.963851 | −0.481925 | − | 0.876212i | \(-0.660062\pi\) | ||||
−0.481925 | + | 0.876212i | \(0.660062\pi\) | |||||||
\(132\) | −857.013 | −0.565102 | ||||||||
\(133\) | 2613.89 | 1.70416 | ||||||||
\(134\) | −1170.65 | −0.754695 | ||||||||
\(135\) | −260.777 | −0.166253 | ||||||||
\(136\) | −1795.30 | −1.13195 | ||||||||
\(137\) | −508.793 | −0.317293 | −0.158646 | − | 0.987335i | \(-0.550713\pi\) | ||||
−0.158646 | + | 0.987335i | \(0.550713\pi\) | |||||||
\(138\) | 329.088 | 0.202999 | ||||||||
\(139\) | −757.018 | −0.461938 | −0.230969 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230969 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(140\) | −1226.62 | −0.740486 | ||||||||
\(141\) | −202.661 | −0.121043 | ||||||||
\(142\) | −403.695 | −0.238573 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 123.109 | 0.0712436 | ||||||||
\(145\) | −136.622 | −0.0782470 | ||||||||
\(146\) | −1175.13 | −0.666125 | ||||||||
\(147\) | 471.436 | 0.264513 | ||||||||
\(148\) | −876.939 | −0.487054 | ||||||||
\(149\) | 3247.79 | 1.78570 | 0.892851 | − | 0.450352i | \(-0.148702\pi\) | ||||
0.892851 | + | 0.450352i | \(0.148702\pi\) | |||||||
\(150\) | −144.959 | −0.0789058 | ||||||||
\(151\) | −795.296 | −0.428611 | −0.214305 | − | 0.976767i | \(-0.568749\pi\) | ||||
−0.214305 | + | 0.976767i | \(0.568749\pi\) | |||||||
\(152\) | 2435.82 | 1.29981 | ||||||||
\(153\) | 775.308 | 0.409673 | ||||||||
\(154\) | −1714.03 | −0.896884 | ||||||||
\(155\) | −1895.13 | −0.982067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −65.2732 | −0.0331807 | −0.0165903 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165903 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(158\) | 1869.19 | 0.941169 | ||||||||
\(159\) | 2059.74 | 1.02735 | ||||||||
\(160\) | −1811.56 | −0.895104 | ||||||||
\(161\) | −1610.20 | −0.788210 | ||||||||
\(162\) | 123.408 | 0.0598509 | ||||||||
\(163\) | 1855.39 | 0.891568 | 0.445784 | − | 0.895140i | \(-0.352925\pi\) | ||||
0.445784 | + | 0.895140i | \(0.352925\pi\) | |||||||
\(164\) | −1509.00 | −0.718495 | ||||||||
\(165\) | −1457.60 | −0.687721 | ||||||||
\(166\) | 783.137 | 0.366164 | ||||||||
\(167\) | 3532.54 | 1.63686 | 0.818432 | − | 0.574604i | \(-0.194844\pi\) | ||||
0.818432 | + | 0.574604i | \(0.194844\pi\) | |||||||
\(168\) | 1398.22 | 0.642112 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1267.64 | −0.571903 | ||||||||
\(171\) | −1051.92 | −0.470422 | ||||||||
\(172\) | −1203.08 | −0.533335 | ||||||||
\(173\) | −3178.36 | −1.39680 | −0.698400 | − | 0.715708i | \(-0.746104\pi\) | ||||
−0.698400 | + | 0.715708i | \(0.746104\pi\) | |||||||
\(174\) | 64.6537 | 0.0281689 | ||||||||
\(175\) | 709.275 | 0.306378 | ||||||||
\(176\) | 688.111 | 0.294706 | ||||||||
\(177\) | 275.791 | 0.117117 | ||||||||
\(178\) | −804.267 | −0.338665 | ||||||||
\(179\) | 2741.16 | 1.14460 | 0.572302 | − | 0.820043i | \(-0.306050\pi\) | ||||
0.572302 | + | 0.820043i | \(0.306050\pi\) | |||||||
\(180\) | 493.632 | 0.204406 | ||||||||
\(181\) | 3871.09 | 1.58970 | 0.794850 | − | 0.606806i | \(-0.207550\pi\) | ||||
0.794850 | + | 0.606806i | \(0.207550\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 987.018 | 0.398702 | ||||||||
\(184\) | −1500.51 | −0.601189 | ||||||||
\(185\) | −1491.49 | −0.592737 | ||||||||
\(186\) | 896.834 | 0.353544 | ||||||||
\(187\) | 4333.54 | 1.69465 | ||||||||
\(188\) | 383.621 | 0.148822 | ||||||||
\(189\) | −603.826 | −0.232391 | ||||||||
\(190\) | 1719.90 | 0.656708 | ||||||||
\(191\) | −928.291 | −0.351669 | −0.175834 | − | 0.984420i | \(-0.556262\pi\) | ||||
−0.175834 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(192\) | 528.999 | 0.198840 | ||||||||
\(193\) | 2261.51 | 0.843456 | 0.421728 | − | 0.906722i | \(-0.361424\pi\) | ||||
0.421728 | + | 0.906722i | \(0.361424\pi\) | |||||||
\(194\) | 113.163 | 0.0418795 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −892.394 | −0.325216 | ||||||||
\(197\) | 2265.59 | 0.819374 | 0.409687 | − | 0.912226i | \(-0.365638\pi\) | ||||
0.409687 | + | 0.912226i | \(0.365638\pi\) | |||||||
\(198\) | 689.782 | 0.247579 | ||||||||
\(199\) | −260.895 | −0.0929366 | −0.0464683 | − | 0.998920i | \(-0.514797\pi\) | ||||
−0.0464683 | + | 0.998920i | \(0.514797\pi\) | |||||||
\(200\) | 660.955 | 0.233683 | ||||||||
\(201\) | −2305.11 | −0.808905 | ||||||||
\(202\) | 928.483 | 0.323405 | ||||||||
\(203\) | −316.346 | −0.109375 | ||||||||
\(204\) | −1467.60 | −0.503690 | ||||||||
\(205\) | −2566.49 | −0.874399 | ||||||||
\(206\) | −49.4181 | −0.0167142 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5879.63 | −1.94595 | ||||||||
\(210\) | 987.264 | 0.324417 | ||||||||
\(211\) | 5851.22 | 1.90907 | 0.954537 | − | 0.298092i | \(-0.0963502\pi\) | ||||
0.954537 | + | 0.298092i | \(0.0963502\pi\) | |||||||
\(212\) | −3898.94 | −1.26312 | ||||||||
\(213\) | −794.907 | −0.255710 | ||||||||
\(214\) | −2628.82 | −0.839732 | ||||||||
\(215\) | −2046.18 | −0.649062 | ||||||||
\(216\) | −562.690 | −0.177251 | ||||||||
\(217\) | −4388.15 | −1.37275 | ||||||||
\(218\) | −1940.15 | −0.602767 | ||||||||
\(219\) | −2313.92 | −0.713973 | ||||||||
\(220\) | 2759.13 | 0.845547 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 705.820 | 0.213385 | ||||||||
\(223\) | 3463.60 | 1.04009 | 0.520045 | − | 0.854139i | \(-0.325915\pi\) | ||||
0.520045 | + | 0.854139i | \(0.325915\pi\) | |||||||
\(224\) | −4194.65 | −1.25119 | ||||||||
\(225\) | −285.436 | −0.0845737 | ||||||||
\(226\) | 1698.35 | 0.499878 | ||||||||
\(227\) | −5329.15 | −1.55819 | −0.779093 | − | 0.626908i | \(-0.784320\pi\) | ||||
−0.779093 | + | 0.626908i | \(0.784320\pi\) | |||||||
\(228\) | 1991.20 | 0.578380 | ||||||||
\(229\) | −4773.95 | −1.37761 | −0.688803 | − | 0.724949i | \(-0.741863\pi\) | ||||
−0.688803 | + | 0.724949i | \(0.741863\pi\) | |||||||
\(230\) | −1059.49 | −0.303742 | ||||||||
\(231\) | −3375.05 | −0.961308 | ||||||||
\(232\) | −294.795 | −0.0834233 | ||||||||
\(233\) | −4813.78 | −1.35348 | −0.676741 | − | 0.736221i | \(-0.736608\pi\) | ||||
−0.676741 | + | 0.736221i | \(0.736608\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 652.459 | 0.181114 | ||||||||
\(236\) | −522.052 | −0.143995 | ||||||||
\(237\) | 3680.58 | 1.00877 | ||||||||
\(238\) | −2935.20 | −0.799416 | ||||||||
\(239\) | −1683.19 | −0.455549 | −0.227775 | − | 0.973714i | \(-0.573145\pi\) | ||||
−0.227775 | + | 0.973714i | \(0.573145\pi\) | |||||||
\(240\) | −396.346 | −0.106600 | ||||||||
\(241\) | 664.861 | 0.177707 | 0.0888537 | − | 0.996045i | \(-0.471680\pi\) | ||||
0.0888537 | + | 0.996045i | \(0.471680\pi\) | |||||||
\(242\) | 1827.65 | 0.485477 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1868.35 | −0.490201 | ||||||||
\(245\) | −1517.77 | −0.395784 | ||||||||
\(246\) | 1214.55 | 0.314783 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4089.20 | −1.04703 | ||||||||
\(249\) | 1542.06 | 0.392466 | ||||||||
\(250\) | 2306.08 | 0.583398 | ||||||||
\(251\) | 2142.04 | 0.538662 | 0.269331 | − | 0.963048i | \(-0.413198\pi\) | ||||
0.269331 | + | 0.963048i | \(0.413198\pi\) | |||||||
\(252\) | 1143.00 | 0.285723 | ||||||||
\(253\) | 3621.96 | 0.900042 | ||||||||
\(254\) | 1788.67 | 0.441855 | ||||||||
\(255\) | −2496.08 | −0.612983 | ||||||||
\(256\) | −3287.46 | −0.802603 | ||||||||
\(257\) | 3152.62 | 0.765194 | 0.382597 | − | 0.923915i | \(-0.375030\pi\) | ||||
0.382597 | + | 0.923915i | \(0.375030\pi\) | |||||||
\(258\) | 968.317 | 0.233662 | ||||||||
\(259\) | −3453.52 | −0.828539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 127.308 | 0.0301923 | ||||||||
\(262\) | −2201.79 | −0.519186 | ||||||||
\(263\) | −2167.71 | −0.508238 | −0.254119 | − | 0.967173i | \(-0.581786\pi\) | ||||
−0.254119 | + | 0.967173i | \(0.581786\pi\) | |||||||
\(264\) | −3145.13 | −0.733216 | ||||||||
\(265\) | −6631.28 | −1.53719 | ||||||||
\(266\) | 3982.40 | 0.917958 | ||||||||
\(267\) | −1583.67 | −0.362992 | ||||||||
\(268\) | 4363.40 | 0.994542 | ||||||||
\(269\) | −3248.98 | −0.736409 | −0.368204 | − | 0.929745i | \(-0.620027\pi\) | ||||
−0.368204 | + | 0.929745i | \(0.620027\pi\) | |||||||
\(270\) | −397.308 | −0.0895534 | ||||||||
\(271\) | 4897.70 | 1.09784 | 0.548919 | − | 0.835876i | \(-0.315040\pi\) | ||||
0.548919 | + | 0.835876i | \(0.315040\pi\) | |||||||
\(272\) | 1178.36 | 0.262679 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −775.175 | −0.170912 | ||||||||
\(275\) | −1595.43 | −0.349847 | ||||||||
\(276\) | −1226.62 | −0.267513 | ||||||||
\(277\) | 2900.33 | 0.629111 | 0.314555 | − | 0.949239i | \(-0.398145\pi\) | ||||
0.314555 | + | 0.949239i | \(0.398145\pi\) | |||||||
\(278\) | −1153.36 | −0.248827 | ||||||||
\(279\) | 1765.94 | 0.378939 | ||||||||
\(280\) | −4501.52 | −0.960776 | ||||||||
\(281\) | −4396.53 | −0.933364 | −0.466682 | − | 0.884425i | \(-0.654551\pi\) | ||||
−0.466682 | + | 0.884425i | \(0.654551\pi\) | |||||||
\(282\) | −308.764 | −0.0652009 | ||||||||
\(283\) | −559.151 | −0.117449 | −0.0587245 | − | 0.998274i | \(-0.518703\pi\) | ||||
−0.0587245 | + | 0.998274i | \(0.518703\pi\) | |||||||
\(284\) | 1504.70 | 0.314393 | ||||||||
\(285\) | 3386.62 | 0.703880 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5942.69 | −1.22225 | ||||||||
\(288\) | 1688.07 | 0.345384 | ||||||||
\(289\) | 2508.02 | 0.510487 | ||||||||
\(290\) | −208.151 | −0.0421484 | ||||||||
\(291\) | 222.827 | 0.0448877 | ||||||||
\(292\) | 4380.08 | 0.877825 | ||||||||
\(293\) | 6918.65 | 1.37950 | 0.689748 | − | 0.724050i | \(-0.257722\pi\) | ||||
0.689748 | + | 0.724050i | \(0.257722\pi\) | |||||||
\(294\) | 718.259 | 0.142482 | ||||||||
\(295\) | −887.901 | −0.175239 | ||||||||
\(296\) | −3218.25 | −0.631949 | ||||||||
\(297\) | 1358.24 | 0.265363 | ||||||||
\(298\) | 4948.19 | 0.961883 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 540.310 | 0.103983 | ||||||||
\(301\) | −4737.90 | −0.907270 | ||||||||
\(302\) | −1211.68 | −0.230875 | ||||||||
\(303\) | 1828.26 | 0.346635 | ||||||||
\(304\) | −1598.77 | −0.301631 | ||||||||
\(305\) | −3177.67 | −0.596567 | ||||||||
\(306\) | 1181.22 | 0.220674 | ||||||||
\(307\) | 8980.94 | 1.66961 | 0.834803 | − | 0.550548i | \(-0.185581\pi\) | ||||
0.834803 | + | 0.550548i | \(0.185581\pi\) | |||||||
\(308\) | 6388.73 | 1.18192 | ||||||||
\(309\) | −97.3082 | −0.0179148 | ||||||||
\(310\) | −2887.33 | −0.528998 | ||||||||
\(311\) | −7943.13 | −1.44827 | −0.724137 | − | 0.689656i | \(-0.757762\pi\) | ||||
−0.724137 | + | 0.689656i | \(0.757762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5059.57 | −0.913686 | −0.456843 | − | 0.889547i | \(-0.651020\pi\) | ||||
−0.456843 | + | 0.889547i | \(0.651020\pi\) | |||||||
\(314\) | −99.4473 | −0.0178730 | ||||||||
\(315\) | 1944.00 | 0.347721 | ||||||||
\(316\) | −6967.07 | −1.24028 | ||||||||
\(317\) | 8702.12 | 1.54183 | 0.770914 | − | 0.636939i | \(-0.219800\pi\) | ||||
0.770914 | + | 0.636939i | \(0.219800\pi\) | |||||||
\(318\) | 3138.13 | 0.553389 | ||||||||
\(319\) | 711.582 | 0.124893 | ||||||||
\(320\) | −1703.10 | −0.297519 | ||||||||
\(321\) | −5176.36 | −0.900051 | ||||||||
\(322\) | −2453.23 | −0.424576 | ||||||||
\(323\) | −10068.6 | −1.73447 | ||||||||
\(324\) | −459.981 | −0.0788719 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2826.79 | 0.480250 | ||||||||
\(327\) | −3820.30 | −0.646064 | ||||||||
\(328\) | −5537.84 | −0.932244 | ||||||||
\(329\) | 1510.76 | 0.253164 | ||||||||
\(330\) | −2220.73 | −0.370446 | ||||||||
\(331\) | 1737.65 | 0.288549 | 0.144275 | − | 0.989538i | \(-0.453915\pi\) | ||||
0.144275 | + | 0.989538i | \(0.453915\pi\) | |||||||
\(332\) | −2919.00 | −0.482533 | ||||||||
\(333\) | 1389.81 | 0.228713 | ||||||||
\(334\) | 5382.02 | 0.881710 | ||||||||
\(335\) | 7421.23 | 1.21034 | ||||||||
\(336\) | −917.734 | −0.149007 | ||||||||
\(337\) | 2917.47 | 0.471586 | 0.235793 | − | 0.971803i | \(-0.424231\pi\) | ||||
0.235793 | + | 0.971803i | \(0.424231\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3344.18 | 0.535785 | ||||||||
\(340\) | 4724.90 | 0.753658 | ||||||||
\(341\) | 9870.61 | 1.56752 | ||||||||
\(342\) | −1602.65 | −0.253397 | ||||||||
\(343\) | 4156.44 | 0.654305 | ||||||||
\(344\) | −4415.13 | −0.692000 | ||||||||
\(345\) | −2086.22 | −0.325560 | ||||||||
\(346\) | −4842.41 | −0.752397 | ||||||||
\(347\) | 5081.23 | 0.786095 | 0.393047 | − | 0.919518i | \(-0.371421\pi\) | ||||
0.393047 | + | 0.919518i | \(0.371421\pi\) | |||||||
\(348\) | −240.985 | −0.0371211 | ||||||||
\(349\) | −4266.14 | −0.654330 | −0.327165 | − | 0.944967i | \(-0.606093\pi\) | ||||
−0.327165 | + | 0.944967i | \(0.606093\pi\) | |||||||
\(350\) | 1080.62 | 0.165033 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9435.38 | 1.42871 | ||||||||
\(353\) | −3264.49 | −0.492213 | −0.246106 | − | 0.969243i | \(-0.579151\pi\) | ||||
−0.246106 | + | 0.969243i | \(0.579151\pi\) | |||||||
\(354\) | 420.183 | 0.0630861 | ||||||||
\(355\) | 2559.18 | 0.382612 | ||||||||
\(356\) | 2997.76 | 0.446295 | ||||||||
\(357\) | −5779.65 | −0.856838 | ||||||||
\(358\) | 4176.31 | 0.616550 | ||||||||
\(359\) | 4416.98 | 0.649357 | 0.324679 | − | 0.945824i | \(-0.394744\pi\) | ||||
0.324679 | + | 0.945824i | \(0.394744\pi\) | |||||||
\(360\) | 1811.56 | 0.265216 | ||||||||
\(361\) | 6801.87 | 0.991670 | ||||||||
\(362\) | 5897.82 | 0.856305 | ||||||||
\(363\) | 3598.78 | 0.520350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7449.59 | 1.06830 | ||||||||
\(366\) | 1503.78 | 0.214764 | ||||||||
\(367\) | −1740.22 | −0.247516 | −0.123758 | − | 0.992312i | \(-0.539495\pi\) | ||||
−0.123758 | + | 0.992312i | \(0.539495\pi\) | |||||||
\(368\) | 984.872 | 0.139511 | ||||||||
\(369\) | 2391.54 | 0.337394 | ||||||||
\(370\) | −2272.37 | −0.319283 | ||||||||
\(371\) | −15354.7 | −2.14872 | ||||||||
\(372\) | −3342.79 | −0.465902 | ||||||||
\(373\) | 1176.28 | 0.163285 | 0.0816427 | − | 0.996662i | \(-0.473983\pi\) | ||||
0.0816427 | + | 0.996662i | \(0.473983\pi\) | |||||||
\(374\) | 6602.39 | 0.912838 | ||||||||
\(375\) | 4540.86 | 0.625304 | ||||||||
\(376\) | 1407.84 | 0.193095 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −919.962 | −0.125179 | ||||||||
\(379\) | 7135.54 | 0.967092 | 0.483546 | − | 0.875319i | \(-0.339349\pi\) | ||||
0.483546 | + | 0.875319i | \(0.339349\pi\) | |||||||
\(380\) | −6410.62 | −0.865415 | ||||||||
\(381\) | 3522.04 | 0.473594 | ||||||||
\(382\) | −1414.30 | −0.189429 | ||||||||
\(383\) | −1942.87 | −0.259207 | −0.129603 | − | 0.991566i | \(-0.541370\pi\) | ||||
−0.129603 | + | 0.991566i | \(0.541370\pi\) | |||||||
\(384\) | −3695.56 | −0.491116 | ||||||||
\(385\) | 10865.9 | 1.43838 | ||||||||
\(386\) | 3445.53 | 0.454334 | ||||||||
\(387\) | 1906.69 | 0.250446 | ||||||||
\(388\) | −421.794 | −0.0551891 | ||||||||
\(389\) | −7545.92 | −0.983531 | −0.491766 | − | 0.870728i | \(-0.663648\pi\) | ||||
−0.491766 | + | 0.870728i | \(0.663648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6202.47 | 0.802231 | ||||||||
\(392\) | −3274.97 | −0.421967 | ||||||||
\(393\) | −4335.49 | −0.556480 | ||||||||
\(394\) | 3451.75 | 0.441362 | ||||||||
\(395\) | −11849.5 | −1.50940 | ||||||||
\(396\) | −2571.04 | −0.326262 | ||||||||
\(397\) | 415.922 | 0.0525806 | 0.0262903 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262903 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(398\) | −397.489 | −0.0500611 | ||||||||
\(399\) | 7841.67 | 0.983896 | ||||||||
\(400\) | −433.824 | −0.0542280 | ||||||||
\(401\) | −958.178 | −0.119324 | −0.0596622 | − | 0.998219i | \(-0.519002\pi\) | ||||
−0.0596622 | + | 0.998219i | \(0.519002\pi\) | |||||||
\(402\) | −3511.96 | −0.435723 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −3460.75 | −0.426185 | ||||||||
\(405\) | −782.331 | −0.0959860 | ||||||||
\(406\) | −481.970 | −0.0589157 | ||||||||
\(407\) | 7768.29 | 0.946093 | ||||||||
\(408\) | −5385.90 | −0.653534 | ||||||||
\(409\) | 4284.83 | 0.518022 | 0.259011 | − | 0.965874i | \(-0.416603\pi\) | ||||
0.259011 | + | 0.965874i | \(0.416603\pi\) | |||||||
\(410\) | −3910.20 | −0.471002 | ||||||||
\(411\) | −1526.38 | −0.183189 | ||||||||
\(412\) | 184.197 | 0.0220261 | ||||||||
\(413\) | −2055.92 | −0.244953 | ||||||||
\(414\) | 987.264 | 0.117201 | ||||||||
\(415\) | −4964.61 | −0.587236 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2271.05 | −0.266700 | ||||||||
\(418\) | −8957.95 | −1.04820 | ||||||||
\(419\) | −9949.01 | −1.16000 | −0.580001 | − | 0.814616i | \(-0.696948\pi\) | ||||
−0.580001 | + | 0.814616i | \(0.696948\pi\) | |||||||
\(420\) | −3679.85 | −0.427520 | ||||||||
\(421\) | −377.250 | −0.0436724 | −0.0218362 | − | 0.999762i | \(-0.506951\pi\) | ||||
−0.0218362 | + | 0.999762i | \(0.506951\pi\) | |||||||
\(422\) | 8914.66 | 1.02834 | ||||||||
\(423\) | −607.982 | −0.0698843 | ||||||||
\(424\) | −14308.6 | −1.63889 | ||||||||
\(425\) | −2732.11 | −0.311828 | ||||||||
\(426\) | −1211.08 | −0.137740 | ||||||||
\(427\) | −7357.86 | −0.833892 | ||||||||
\(428\) | 9798.47 | 1.10661 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3117.47 | −0.349622 | ||||||||
\(431\) | 2437.13 | 0.272373 | 0.136186 | − | 0.990683i | \(-0.456515\pi\) | ||||
0.136186 | + | 0.990683i | \(0.456515\pi\) | |||||||
\(432\) | 369.327 | 0.0411325 | ||||||||
\(433\) | 11215.1 | 1.24471 | 0.622357 | − | 0.782733i | \(-0.286175\pi\) | ||||
0.622357 | + | 0.782733i | \(0.286175\pi\) | |||||||
\(434\) | −6685.58 | −0.739443 | ||||||||
\(435\) | −409.865 | −0.0451759 | ||||||||
\(436\) | 7231.55 | 0.794331 | ||||||||
\(437\) | −8415.34 | −0.921191 | ||||||||
\(438\) | −3525.38 | −0.384588 | ||||||||
\(439\) | −1835.19 | −0.199519 | −0.0997596 | − | 0.995012i | \(-0.531807\pi\) | ||||
−0.0997596 | + | 0.995012i | \(0.531807\pi\) | |||||||
\(440\) | 10125.6 | 1.09709 | ||||||||
\(441\) | 1414.31 | 0.152717 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11610.1 | 1.24518 | 0.622588 | − | 0.782550i | \(-0.286081\pi\) | ||||
0.622588 | + | 0.782550i | \(0.286081\pi\) | |||||||
\(444\) | −2630.82 | −0.281201 | ||||||||
\(445\) | 5098.56 | 0.543135 | ||||||||
\(446\) | 5276.99 | 0.560253 | ||||||||
\(447\) | 9743.38 | 1.03098 | ||||||||
\(448\) | −3943.50 | −0.415877 | ||||||||
\(449\) | 14087.0 | 1.48064 | 0.740319 | − | 0.672255i | \(-0.234674\pi\) | ||||
0.740319 | + | 0.672255i | \(0.234674\pi\) | |||||||
\(450\) | −434.878 | −0.0455563 | ||||||||
\(451\) | 13367.4 | 1.39566 | ||||||||
\(452\) | −6330.29 | −0.658743 | ||||||||
\(453\) | −2385.89 | −0.247459 | ||||||||
\(454\) | −8119.26 | −0.839330 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7307.45 | 0.750445 | ||||||||
\(457\) | −2375.01 | −0.243103 | −0.121552 | − | 0.992585i | \(-0.538787\pi\) | ||||
−0.121552 | + | 0.992585i | \(0.538787\pi\) | |||||||
\(458\) | −7273.38 | −0.742058 | ||||||||
\(459\) | 2325.92 | 0.236525 | ||||||||
\(460\) | 3949.05 | 0.400273 | ||||||||
\(461\) | 6372.06 | 0.643766 | 0.321883 | − | 0.946779i | \(-0.395684\pi\) | ||||
0.321883 | + | 0.946779i | \(0.395684\pi\) | |||||||
\(462\) | −5142.08 | −0.517816 | ||||||||
\(463\) | 63.4732 | 0.00637117 | 0.00318558 | − | 0.999995i | \(-0.498986\pi\) | ||||
0.00318558 | + | 0.999995i | \(0.498986\pi\) | |||||||
\(464\) | 193.491 | 0.0193591 | ||||||||
\(465\) | −5685.38 | −0.566996 | ||||||||
\(466\) | −7334.06 | −0.729064 | ||||||||
\(467\) | −7855.78 | −0.778420 | −0.389210 | − | 0.921149i | \(-0.627252\pi\) | ||||
−0.389210 | + | 0.921149i | \(0.627252\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17183.8 | 1.69184 | ||||||||
\(470\) | 994.058 | 0.0975584 | ||||||||
\(471\) | −195.820 | −0.0191569 | ||||||||
\(472\) | −1915.86 | −0.186832 | ||||||||
\(473\) | 10657.3 | 1.03599 | ||||||||
\(474\) | 5607.57 | 0.543384 | ||||||||
\(475\) | 3706.85 | 0.358068 | ||||||||
\(476\) | 10940.4 | 1.05348 | ||||||||
\(477\) | 6179.23 | 0.593140 | ||||||||
\(478\) | −2564.43 | −0.245385 | ||||||||
\(479\) | 13033.3 | 1.24323 | 0.621613 | − | 0.783324i | \(-0.286477\pi\) | ||||
0.621613 | + | 0.783324i | \(0.286477\pi\) | |||||||
\(480\) | −5434.69 | −0.516789 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1012.95 | 0.0957235 | ||||||||
\(483\) | −4830.61 | −0.455073 | ||||||||
\(484\) | −6812.23 | −0.639766 | ||||||||
\(485\) | −717.384 | −0.0671643 | ||||||||
\(486\) | 370.224 | 0.0345549 | ||||||||
\(487\) | 69.8976 | 0.00650383 | 0.00325191 | − | 0.999995i | \(-0.498965\pi\) | ||||
0.00325191 | + | 0.999995i | \(0.498965\pi\) | |||||||
\(488\) | −6856.60 | −0.636033 | ||||||||
\(489\) | 5566.18 | 0.514747 | ||||||||
\(490\) | −2312.41 | −0.213192 | ||||||||
\(491\) | −2625.66 | −0.241333 | −0.120667 | − | 0.992693i | \(-0.538503\pi\) | ||||
−0.120667 | + | 0.992693i | \(0.538503\pi\) | |||||||
\(492\) | −4527.01 | −0.414823 | ||||||||
\(493\) | 1218.56 | 0.111321 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4372.80 | −0.397056 | ||||||||
\(496\) | 2683.99 | 0.242973 | ||||||||
\(497\) | 5925.75 | 0.534821 | ||||||||
\(498\) | 2349.41 | 0.211405 | ||||||||
\(499\) | −7631.34 | −0.684621 | −0.342310 | − | 0.939587i | \(-0.611209\pi\) | ||||
−0.342310 | + | 0.939587i | \(0.611209\pi\) | |||||||
\(500\) | −8595.51 | −0.768806 | ||||||||
\(501\) | 10597.6 | 0.945044 | ||||||||
\(502\) | 3263.51 | 0.290154 | ||||||||
\(503\) | −4320.14 | −0.382953 | −0.191477 | − | 0.981497i | \(-0.561328\pi\) | ||||
−0.191477 | + | 0.981497i | \(0.561328\pi\) | |||||||
\(504\) | 4194.65 | 0.370724 | ||||||||
\(505\) | −5886.01 | −0.518662 | ||||||||
\(506\) | 5518.26 | 0.484815 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6666.95 | −0.582280 | ||||||||
\(509\) | 12450.7 | 1.08422 | 0.542109 | − | 0.840308i | \(-0.317626\pi\) | ||||
0.542109 | + | 0.840308i | \(0.317626\pi\) | |||||||
\(510\) | −3802.92 | −0.330188 | ||||||||
\(511\) | 17249.4 | 1.49329 | ||||||||
\(512\) | 4846.21 | 0.418309 | ||||||||
\(513\) | −3155.75 | −0.271598 | ||||||||
\(514\) | 4803.18 | 0.412178 | ||||||||
\(515\) | 313.281 | 0.0268054 | ||||||||
\(516\) | −3609.23 | −0.307921 | ||||||||
\(517\) | −3398.28 | −0.289083 | ||||||||
\(518\) | −5261.63 | −0.446299 | ||||||||
\(519\) | −9535.08 | −0.806443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14373.1 | 1.20863 | 0.604314 | − | 0.796746i | \(-0.293447\pi\) | ||||
0.604314 | + | 0.796746i | \(0.293447\pi\) | |||||||
\(522\) | 193.961 | 0.0162633 | ||||||||
\(523\) | −16946.7 | −1.41688 | −0.708439 | − | 0.705772i | \(-0.750600\pi\) | ||||
−0.708439 | + | 0.705772i | \(0.750600\pi\) | |||||||
\(524\) | 8206.76 | 0.684187 | ||||||||
\(525\) | 2127.82 | 0.176887 | ||||||||
\(526\) | −3302.62 | −0.273767 | ||||||||
\(527\) | 16903.0 | 1.39717 | ||||||||
\(528\) | 2064.33 | 0.170149 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | −10103.1 | −0.828022 | ||||||||
\(531\) | 827.373 | 0.0676176 | ||||||||
\(532\) | −14843.7 | −1.20969 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2412.80 | −0.195528 | ||||||||
\(535\) | 16665.1 | 1.34672 | ||||||||
\(536\) | 16013.1 | 1.29041 | ||||||||
\(537\) | 8223.49 | 0.660837 | ||||||||
\(538\) | −4950.00 | −0.396673 | ||||||||
\(539\) | 7905.20 | 0.631727 | ||||||||
\(540\) | 1480.90 | 0.118014 | ||||||||
\(541\) | −815.667 | −0.0648212 | −0.0324106 | − | 0.999475i | \(-0.510318\pi\) | ||||
−0.0324106 | + | 0.999475i | \(0.510318\pi\) | |||||||
\(542\) | 7461.92 | 0.591359 | ||||||||
\(543\) | 11613.3 | 0.917814 | ||||||||
\(544\) | 16157.7 | 1.27345 | ||||||||
\(545\) | 12299.3 | 0.966689 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17971.4 | −1.40476 | −0.702378 | − | 0.711804i | \(-0.747878\pi\) | ||||
−0.702378 | + | 0.711804i | \(0.747878\pi\) | |||||||
\(548\) | 2889.32 | 0.225230 | ||||||||
\(549\) | 2961.05 | 0.230191 | ||||||||
\(550\) | −2430.72 | −0.188448 | ||||||||
\(551\) | −1653.31 | −0.127828 | ||||||||
\(552\) | −4501.52 | −0.347097 | ||||||||
\(553\) | −27437.4 | −2.10987 | ||||||||
\(554\) | 4418.81 | 0.338876 | ||||||||
\(555\) | −4474.47 | −0.342217 | ||||||||
\(556\) | 4298.94 | 0.327906 | ||||||||
\(557\) | −6760.83 | −0.514301 | −0.257151 | − | 0.966371i | \(-0.582784\pi\) | ||||
−0.257151 | + | 0.966371i | \(0.582784\pi\) | |||||||
\(558\) | 2690.50 | 0.204118 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2954.62 | 0.222956 | ||||||||
\(561\) | 13000.6 | 0.978408 | ||||||||
\(562\) | −6698.36 | −0.502764 | ||||||||
\(563\) | −12962.7 | −0.970359 | −0.485179 | − | 0.874415i | \(-0.661246\pi\) | ||||
−0.485179 | + | 0.874415i | \(0.661246\pi\) | |||||||
\(564\) | 1150.86 | 0.0859222 | ||||||||
\(565\) | −10766.5 | −0.801681 | ||||||||
\(566\) | −851.898 | −0.0632649 | ||||||||
\(567\) | −1811.48 | −0.134171 | ||||||||
\(568\) | 5522.05 | 0.407923 | ||||||||
\(569\) | −164.757 | −0.0121388 | −0.00606938 | − | 0.999982i | \(-0.501932\pi\) | ||||
−0.00606938 | + | 0.999982i | \(0.501932\pi\) | |||||||
\(570\) | 5159.70 | 0.379151 | ||||||||
\(571\) | 5216.55 | 0.382322 | 0.191161 | − | 0.981559i | \(-0.438775\pi\) | ||||
0.191161 | + | 0.981559i | \(0.438775\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2784.87 | −0.203036 | ||||||||
\(574\) | −9054.01 | −0.658375 | ||||||||
\(575\) | −2283.49 | −0.165614 | ||||||||
\(576\) | 1587.00 | 0.114800 | ||||||||
\(577\) | −12753.3 | −0.920151 | −0.460076 | − | 0.887880i | \(-0.652178\pi\) | ||||
−0.460076 | + | 0.887880i | \(0.652178\pi\) | |||||||
\(578\) | 3821.11 | 0.274978 | ||||||||
\(579\) | 6784.53 | 0.486970 | ||||||||
\(580\) | 775.844 | 0.0555434 | ||||||||
\(581\) | −11495.5 | −0.820849 | ||||||||
\(582\) | 339.489 | 0.0241791 | ||||||||
\(583\) | 34538.5 | 2.45358 | ||||||||
\(584\) | 16074.3 | 1.13897 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10540.9 | 0.743076 | ||||||||
\(587\) | −1575.38 | −0.110771 | −0.0553857 | − | 0.998465i | \(-0.517639\pi\) | ||||
−0.0553857 | + | 0.998465i | \(0.517639\pi\) | |||||||
\(588\) | −2677.18 | −0.187764 | ||||||||
\(589\) | −22933.6 | −1.60435 | ||||||||
\(590\) | −1352.77 | −0.0943941 | ||||||||
\(591\) | 6796.77 | 0.473066 | ||||||||
\(592\) | 2112.33 | 0.146649 | ||||||||
\(593\) | −3845.95 | −0.266331 | −0.133165 | − | 0.991094i | \(-0.542514\pi\) | ||||
−0.133165 | + | 0.991094i | \(0.542514\pi\) | |||||||
\(594\) | 2069.35 | 0.142940 | ||||||||
\(595\) | 18607.4 | 1.28207 | ||||||||
\(596\) | −18443.5 | −1.26758 | ||||||||
\(597\) | −782.686 | −0.0536570 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6107.20 | 0.416583 | 0.208292 | − | 0.978067i | \(-0.433210\pi\) | ||||
0.208292 | + | 0.978067i | \(0.433210\pi\) | |||||||
\(600\) | 1982.86 | 0.134917 | ||||||||
\(601\) | 9638.90 | 0.654208 | 0.327104 | − | 0.944988i | \(-0.393927\pi\) | ||||
0.327104 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(602\) | −7218.46 | −0.488708 | ||||||||
\(603\) | −6915.33 | −0.467022 | ||||||||
\(604\) | 4516.31 | 0.304248 | ||||||||
\(605\) | −11586.2 | −0.778586 | ||||||||
\(606\) | 2785.45 | 0.186718 | ||||||||
\(607\) | 11821.7 | 0.790489 | 0.395244 | − | 0.918576i | \(-0.370660\pi\) | ||||
0.395244 | + | 0.918576i | \(0.370660\pi\) | |||||||
\(608\) | −21922.4 | −1.46228 | ||||||||
\(609\) | −949.037 | −0.0631477 | ||||||||
\(610\) | −4841.36 | −0.321346 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4402.80 | −0.290805 | ||||||||
\(613\) | −8107.86 | −0.534214 | −0.267107 | − | 0.963667i | \(-0.586068\pi\) | ||||
−0.267107 | + | 0.963667i | \(0.586068\pi\) | |||||||
\(614\) | 13683.0 | 0.899347 | ||||||||
\(615\) | −7699.48 | −0.504834 | ||||||||
\(616\) | 23445.8 | 1.53354 | ||||||||
\(617\) | −27647.6 | −1.80397 | −0.901985 | − | 0.431768i | \(-0.857890\pi\) | ||||
−0.901985 | + | 0.431768i | \(0.857890\pi\) | |||||||
\(618\) | −148.254 | −0.00964995 | ||||||||
\(619\) | −29181.9 | −1.89486 | −0.947432 | − | 0.319956i | \(-0.896332\pi\) | ||||
−0.947432 | + | 0.319956i | \(0.896332\pi\) | |||||||
\(620\) | 10762.0 | 0.697118 | ||||||||
\(621\) | 1944.00 | 0.125620 | ||||||||
\(622\) | −12101.8 | −0.780125 | ||||||||
\(623\) | 11805.7 | 0.759204 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10654.8 | −0.681905 | ||||||||
\(626\) | −7708.53 | −0.492165 | ||||||||
\(627\) | −17638.9 | −1.12349 | ||||||||
\(628\) | 370.672 | 0.0235532 | ||||||||
\(629\) | 13302.9 | 0.843277 | ||||||||
\(630\) | 2961.79 | 0.187303 | ||||||||
\(631\) | 2209.34 | 0.139386 | 0.0696928 | − | 0.997569i | \(-0.477798\pi\) | ||||
0.0696928 | + | 0.997569i | \(0.477798\pi\) | |||||||
\(632\) | −25568.2 | −1.60926 | ||||||||
\(633\) | 17553.7 | 1.10220 | ||||||||
\(634\) | 13258.2 | 0.830518 | ||||||||
\(635\) | −11339.1 | −0.708627 | ||||||||
\(636\) | −11696.8 | −0.729260 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1084.13 | 0.0672748 | ||||||||
\(639\) | −2384.72 | −0.147634 | ||||||||
\(640\) | 11897.8 | 0.734844 | ||||||||
\(641\) | −18256.0 | −1.12491 | −0.562455 | − | 0.826828i | \(-0.690143\pi\) | ||||
−0.562455 | + | 0.826828i | \(0.690143\pi\) | |||||||
\(642\) | −7886.47 | −0.484820 | ||||||||
\(643\) | −1281.61 | −0.0786033 | −0.0393016 | − | 0.999227i | \(-0.512513\pi\) | ||||
−0.0393016 | + | 0.999227i | \(0.512513\pi\) | |||||||
\(644\) | 9143.99 | 0.559509 | ||||||||
\(645\) | −6138.54 | −0.374736 | ||||||||
\(646\) | −15340.1 | −0.934287 | ||||||||
\(647\) | 16393.2 | 0.996107 | 0.498054 | − | 0.867146i | \(-0.334048\pi\) | ||||
0.498054 | + | 0.867146i | \(0.334048\pi\) | |||||||
\(648\) | −1688.07 | −0.102336 | ||||||||
\(649\) | 4624.56 | 0.279707 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13164.4 | −0.792557 | ||||||||
\(652\) | −10536.4 | −0.632878 | ||||||||
\(653\) | 16759.2 | 1.00434 | 0.502172 | − | 0.864768i | \(-0.332534\pi\) | ||||
0.502172 | + | 0.864768i | \(0.332534\pi\) | |||||||
\(654\) | −5820.44 | −0.348008 | ||||||||
\(655\) | 13958.0 | 0.832646 | ||||||||
\(656\) | 3634.81 | 0.216335 | ||||||||
\(657\) | −6941.76 | −0.412213 | ||||||||
\(658\) | 2301.73 | 0.136369 | ||||||||
\(659\) | −29659.3 | −1.75320 | −0.876601 | − | 0.481217i | \(-0.840195\pi\) | ||||
−0.876601 | + | 0.481217i | \(0.840195\pi\) | |||||||
\(660\) | 8277.38 | 0.488177 | ||||||||
\(661\) | 10386.0 | 0.611147 | 0.305573 | − | 0.952169i | \(-0.401152\pi\) | ||||
0.305573 | + | 0.952169i | \(0.401152\pi\) | |||||||
\(662\) | 2647.40 | 0.155429 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10712.4 | −0.626084 | ||||||||
\(665\) | −25246.0 | −1.47218 | ||||||||
\(666\) | 2117.46 | 0.123198 | ||||||||
\(667\) | 1018.47 | 0.0591232 | ||||||||
\(668\) | −20060.5 | −1.16192 | ||||||||
\(669\) | 10390.8 | 0.600496 | ||||||||
\(670\) | 11306.7 | 0.651962 | ||||||||
\(671\) | 16550.6 | 0.952206 | ||||||||
\(672\) | −12584.0 | −0.722376 | ||||||||
\(673\) | −19449.6 | −1.11400 | −0.557002 | − | 0.830511i | \(-0.688049\pi\) | ||||
−0.557002 | + | 0.830511i | \(0.688049\pi\) | |||||||
\(674\) | 4444.92 | 0.254024 | ||||||||
\(675\) | −856.308 | −0.0488286 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6629.48 | −0.376354 | −0.188177 | − | 0.982135i | \(-0.560258\pi\) | ||||
−0.188177 | + | 0.982135i | \(0.560258\pi\) | |||||||
\(678\) | 5095.04 | 0.288605 | ||||||||
\(679\) | −1661.09 | −0.0938835 | ||||||||
\(680\) | 17339.8 | 0.977867 | ||||||||
\(681\) | −15987.5 | −0.899619 | ||||||||
\(682\) | 15038.4 | 0.844356 | ||||||||
\(683\) | 2526.40 | 0.141537 | 0.0707687 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707687 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(684\) | 5973.61 | 0.333928 | ||||||||
\(685\) | 4914.13 | 0.274101 | ||||||||
\(686\) | 6332.57 | 0.352447 | ||||||||
\(687\) | −14321.9 | −0.795361 | ||||||||
\(688\) | 2897.91 | 0.160584 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3178.47 | −0.175365 | ||||||||
\(691\) | −3808.76 | −0.209685 | −0.104842 | − | 0.994489i | \(-0.533434\pi\) | ||||
−0.104842 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(692\) | 18049.2 | 0.991515 | ||||||||
\(693\) | −10125.2 | −0.555011 | ||||||||
\(694\) | 7741.54 | 0.423436 | ||||||||
\(695\) | 7311.59 | 0.399056 | ||||||||
\(696\) | −884.384 | −0.0481645 | ||||||||
\(697\) | 22891.1 | 1.24399 | ||||||||
\(698\) | −6499.69 | −0.352460 | ||||||||
\(699\) | −14441.3 | −0.781433 | ||||||||
\(700\) | −4027.81 | −0.217482 | ||||||||
\(701\) | 33617.8 | 1.81131 | 0.905655 | − | 0.424015i | \(-0.139380\pi\) | ||||
0.905655 | + | 0.424015i | \(0.139380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18049.0 | −0.968323 | ||||||||
\(704\) | 8870.43 | 0.474882 | ||||||||
\(705\) | 1957.38 | 0.104566 | ||||||||
\(706\) | −4973.63 | −0.265134 | ||||||||
\(707\) | −13629.0 | −0.724994 | ||||||||
\(708\) | −1566.16 | −0.0831353 | ||||||||
\(709\) | −26606.5 | −1.40935 | −0.704675 | − | 0.709530i | \(-0.748907\pi\) | ||||
−0.704675 | + | 0.709530i | \(0.748907\pi\) | |||||||
\(710\) | 3899.05 | 0.206097 | ||||||||
\(711\) | 11041.7 | 0.582416 | ||||||||
\(712\) | 11001.4 | 0.579066 | ||||||||
\(713\) | 14127.5 | 0.742046 | ||||||||
\(714\) | −8805.61 | −0.461543 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15566.5 | −0.812494 | ||||||||
\(717\) | −5049.56 | −0.263011 | ||||||||
\(718\) | 6729.51 | 0.349781 | ||||||||
\(719\) | −16539.3 | −0.857877 | −0.428939 | − | 0.903334i | \(-0.641112\pi\) | ||||
−0.428939 | + | 0.903334i | \(0.641112\pi\) | |||||||
\(720\) | −1189.04 | −0.0615456 | ||||||||
\(721\) | 725.398 | 0.0374691 | ||||||||
\(722\) | 10363.0 | 0.534171 | ||||||||
\(723\) | 1994.58 | 0.102599 | ||||||||
\(724\) | −21983.1 | −1.12844 | ||||||||
\(725\) | −448.622 | −0.0229812 | ||||||||
\(726\) | 5482.94 | 0.280291 | ||||||||
\(727\) | −12757.5 | −0.650823 | −0.325411 | − | 0.945573i | \(-0.605503\pi\) | ||||
−0.325411 | + | 0.945573i | \(0.605503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 11349.9 | 0.575448 | ||||||||
\(731\) | 18250.3 | 0.923408 | ||||||||
\(732\) | −5605.06 | −0.283017 | ||||||||
\(733\) | 20523.4 | 1.03417 | 0.517087 | − | 0.855933i | \(-0.327016\pi\) | ||||
0.517087 | + | 0.855933i | \(0.327016\pi\) | |||||||
\(734\) | −2651.31 | −0.133327 | ||||||||
\(735\) | −4553.32 | −0.228506 | ||||||||
\(736\) | 13504.6 | 0.676338 | ||||||||
\(737\) | −38652.9 | −1.93188 | ||||||||
\(738\) | 3643.64 | 0.181740 | ||||||||
\(739\) | −7462.66 | −0.371473 | −0.185736 | − | 0.982600i | \(-0.559467\pi\) | ||||
−0.185736 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(740\) | 8469.84 | 0.420753 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23393.7 | −1.15742 | ||||||||
\(743\) | 18847.8 | 0.930632 | 0.465316 | − | 0.885145i | \(-0.345941\pi\) | ||||
0.465316 | + | 0.885145i | \(0.345941\pi\) | |||||||
\(744\) | −12267.6 | −0.604506 | ||||||||
\(745\) | −31368.5 | −1.54262 | ||||||||
\(746\) | 1792.13 | 0.0879549 | ||||||||
\(747\) | 4626.17 | 0.226590 | ||||||||
\(748\) | −24609.2 | −1.20294 | ||||||||
\(749\) | 38587.9 | 1.88247 | ||||||||
\(750\) | 6918.25 | 0.336825 | ||||||||
\(751\) | −20832.6 | −1.01224 | −0.506119 | − | 0.862464i | \(-0.668920\pi\) | ||||
−0.506119 | + | 0.862464i | \(0.668920\pi\) | |||||||
\(752\) | −924.050 | −0.0448093 | ||||||||
\(753\) | 6426.11 | 0.310996 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7681.29 | 0.370266 | ||||||||
\(756\) | 3429.00 | 0.164962 | ||||||||
\(757\) | −20860.9 | −1.00159 | −0.500795 | − | 0.865566i | \(-0.666959\pi\) | ||||
−0.500795 | + | 0.865566i | \(0.666959\pi\) | |||||||
\(758\) | 10871.4 | 0.520932 | ||||||||
\(759\) | 10865.9 | 0.519640 | ||||||||
\(760\) | −23526.1 | −1.12287 | ||||||||
\(761\) | −4464.86 | −0.212682 | −0.106341 | − | 0.994330i | \(-0.533914\pi\) | ||||
−0.106341 | + | 0.994330i | \(0.533914\pi\) | |||||||
\(762\) | 5366.01 | 0.255105 | ||||||||
\(763\) | 28479.0 | 1.35126 | ||||||||
\(764\) | 5271.56 | 0.249631 | ||||||||
\(765\) | −7488.24 | −0.353906 | ||||||||
\(766\) | −2960.08 | −0.139624 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −9862.38 | −0.463383 | ||||||||
\(769\) | 23797.7 | 1.11595 | 0.557977 | − | 0.829857i | \(-0.311578\pi\) | ||||
0.557977 | + | 0.829857i | \(0.311578\pi\) | |||||||
\(770\) | 16554.8 | 0.774795 | ||||||||
\(771\) | 9457.85 | 0.441785 | ||||||||
\(772\) | −12842.6 | −0.598725 | ||||||||
\(773\) | 29418.7 | 1.36885 | 0.684423 | − | 0.729085i | \(-0.260054\pi\) | ||||
0.684423 | + | 0.729085i | \(0.260054\pi\) | |||||||
\(774\) | 2904.95 | 0.134905 | ||||||||
\(775\) | −6222.99 | −0.288434 | ||||||||
\(776\) | −1547.93 | −0.0716075 | ||||||||
\(777\) | −10360.6 | −0.478357 | ||||||||
\(778\) | −11496.6 | −0.529787 | ||||||||
\(779\) | −31058.0 | −1.42846 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13329.3 | −0.610703 | ||||||||
\(782\) | 9449.80 | 0.432128 | ||||||||
\(783\) | 381.925 | 0.0174315 | ||||||||
\(784\) | 2149.56 | 0.0979208 | ||||||||
\(785\) | 630.435 | 0.0286640 | ||||||||
\(786\) | −6605.36 | −0.299752 | ||||||||
\(787\) | 23896.0 | 1.08234 | 0.541170 | − | 0.840913i | \(-0.317982\pi\) | ||||
0.541170 | + | 0.840913i | \(0.317982\pi\) | |||||||
\(788\) | −12865.8 | −0.581630 | ||||||||
\(789\) | −6503.13 | −0.293432 | ||||||||
\(790\) | −18053.4 | −0.813052 | ||||||||
\(791\) | −24929.7 | −1.12060 | ||||||||
\(792\) | −9435.38 | −0.423323 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 633.680 | 0.0283230 | ||||||||
\(795\) | −19893.9 | −0.887500 | ||||||||
\(796\) | 1481.57 | 0.0659708 | ||||||||
\(797\) | −1034.67 | −0.0459847 | −0.0229923 | − | 0.999736i | \(-0.507319\pi\) | ||||
−0.0229923 | + | 0.999736i | \(0.507319\pi\) | |||||||
\(798\) | 11947.2 | 0.529983 | ||||||||
\(799\) | −5819.42 | −0.257667 | ||||||||
\(800\) | −5948.59 | −0.262893 | ||||||||
\(801\) | −4751.00 | −0.209573 | ||||||||
\(802\) | −1459.84 | −0.0642751 | ||||||||
\(803\) | −38800.6 | −1.70516 | ||||||||
\(804\) | 13090.2 | 0.574199 | ||||||||
\(805\) | 15552.0 | 0.680914 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9746.95 | −0.425166 | ||||||||
\(808\) | −12700.5 | −0.552973 | ||||||||
\(809\) | 29557.9 | 1.28455 | 0.642275 | − | 0.766474i | \(-0.277991\pi\) | ||||
0.642275 | + | 0.766474i | \(0.277991\pi\) | |||||||
\(810\) | −1191.92 | −0.0517037 | ||||||||
\(811\) | −30268.9 | −1.31058 | −0.655292 | − | 0.755376i | \(-0.727454\pi\) | ||||
−0.655292 | + | 0.755376i | \(0.727454\pi\) | |||||||
\(812\) | 1796.46 | 0.0776396 | ||||||||
\(813\) | 14693.1 | 0.633837 | ||||||||
\(814\) | 11835.4 | 0.509621 | ||||||||
\(815\) | −17920.2 | −0.770203 | ||||||||
\(816\) | 3535.09 | 0.151658 | ||||||||
\(817\) | −24761.5 | −1.06034 | ||||||||
\(818\) | 6528.17 | 0.279037 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14574.6 | 0.620690 | ||||||||
\(821\) | −39292.7 | −1.67031 | −0.835156 | − | 0.550013i | \(-0.814623\pi\) | ||||
−0.835156 | + | 0.550013i | \(0.814623\pi\) | |||||||
\(822\) | −2325.52 | −0.0986763 | ||||||||
\(823\) | −25988.8 | −1.10074 | −0.550372 | − | 0.834920i | \(-0.685514\pi\) | ||||
−0.550372 | + | 0.834920i | \(0.685514\pi\) | |||||||
\(824\) | 675.980 | 0.0285787 | ||||||||
\(825\) | −4786.29 | −0.201984 | ||||||||
\(826\) | −3132.31 | −0.131946 | ||||||||
\(827\) | −19585.1 | −0.823508 | −0.411754 | − | 0.911295i | \(-0.635084\pi\) | ||||
−0.411754 | + | 0.911295i | \(0.635084\pi\) | |||||||
\(828\) | −3679.85 | −0.154449 | ||||||||
\(829\) | 666.472 | 0.0279222 | 0.0139611 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139611 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(830\) | −7563.86 | −0.316320 | ||||||||
\(831\) | 8700.98 | 0.363217 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13537.3 | 0.563075 | ||||||||
\(834\) | −3460.07 | −0.143660 | ||||||||
\(835\) | −34118.7 | −1.41404 | ||||||||
\(836\) | 33389.1 | 1.38133 | ||||||||
\(837\) | 5297.81 | 0.218780 | ||||||||
\(838\) | −15157.9 | −0.624845 | ||||||||
\(839\) | −36379.7 | −1.49698 | −0.748490 | − | 0.663146i | \(-0.769221\pi\) | ||||
−0.748490 | + | 0.663146i | \(0.769221\pi\) | |||||||
\(840\) | −13504.6 | −0.554704 | ||||||||
\(841\) | −24188.9 | −0.991796 | ||||||||
\(842\) | −574.762 | −0.0235245 | ||||||||
\(843\) | −13189.6 | −0.538878 | ||||||||
\(844\) | −33227.8 | −1.35515 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −926.293 | −0.0376438 | ||||||||
\(847\) | −26827.6 | −1.08832 | ||||||||
\(848\) | 9391.60 | 0.380317 | ||||||||
\(849\) | −1677.45 | −0.0678093 | ||||||||
\(850\) | −4162.52 | −0.167969 | ||||||||
\(851\) | 11118.5 | 0.447871 | ||||||||
\(852\) | 4514.10 | 0.181515 | ||||||||
\(853\) | −39951.4 | −1.60364 | −0.801822 | − | 0.597563i | \(-0.796136\pi\) | ||||
−0.801822 | + | 0.597563i | \(0.796136\pi\) | |||||||
\(854\) | −11210.1 | −0.449183 | ||||||||
\(855\) | 10159.8 | 0.406385 | ||||||||
\(856\) | 35959.1 | 1.43581 | ||||||||
\(857\) | 17226.4 | 0.686629 | 0.343314 | − | 0.939221i | \(-0.388450\pi\) | ||||
0.343314 | + | 0.939221i | \(0.388450\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33392.3 | −1.32634 | −0.663172 | − | 0.748467i | \(-0.730790\pi\) | ||||
−0.663172 | + | 0.748467i | \(0.730790\pi\) | |||||||
\(860\) | 11619.8 | 0.460735 | ||||||||
\(861\) | −17828.1 | −0.705666 | ||||||||
\(862\) | 3713.11 | 0.146716 | ||||||||
\(863\) | 17381.9 | 0.685614 | 0.342807 | − | 0.939406i | \(-0.388622\pi\) | ||||
0.342807 | + | 0.939406i | \(0.388622\pi\) | |||||||
\(864\) | 5064.21 | 0.199407 | ||||||||
\(865\) | 30697.9 | 1.20666 | ||||||||
\(866\) | 17086.8 | 0.670476 | ||||||||
\(867\) | 7524.07 | 0.294730 | ||||||||
\(868\) | 24919.3 | 0.974443 | ||||||||
\(869\) | 61717.2 | 2.40922 | ||||||||
\(870\) | −624.452 | −0.0243344 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 26538.8 | 1.03064 | ||||||||
\(873\) | 668.480 | 0.0259159 | ||||||||
\(874\) | −12821.2 | −0.496207 | ||||||||
\(875\) | −33850.5 | −1.30783 | ||||||||
\(876\) | 13140.2 | 0.506812 | ||||||||
\(877\) | −14335.6 | −0.551970 | −0.275985 | − | 0.961162i | \(-0.589004\pi\) | ||||
−0.275985 | + | 0.961162i | \(0.589004\pi\) | |||||||
\(878\) | −2796.02 | −0.107473 | ||||||||
\(879\) | 20756.0 | 0.796452 | ||||||||
\(880\) | −6646.06 | −0.254589 | ||||||||
\(881\) | 5436.53 | 0.207901 | 0.103951 | − | 0.994582i | \(-0.466852\pi\) | ||||
0.103951 | + | 0.994582i | \(0.466852\pi\) | |||||||
\(882\) | 2154.78 | 0.0822620 | ||||||||
\(883\) | 21185.9 | 0.807430 | 0.403715 | − | 0.914885i | \(-0.367719\pi\) | ||||
0.403715 | + | 0.914885i | \(0.367719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2663.70 | −0.101174 | ||||||||
\(886\) | 17688.6 | 0.670724 | ||||||||
\(887\) | −12661.4 | −0.479287 | −0.239644 | − | 0.970861i | \(-0.577031\pi\) | ||||
−0.239644 | + | 0.970861i | \(0.577031\pi\) | |||||||
\(888\) | −9654.75 | −0.364856 | ||||||||
\(889\) | −26255.5 | −0.990531 | ||||||||
\(890\) | 7767.94 | 0.292564 | ||||||||
\(891\) | 4074.71 | 0.153207 | ||||||||
\(892\) | −19669.0 | −0.738305 | ||||||||
\(893\) | 7895.63 | 0.295876 | ||||||||
\(894\) | 14844.6 | 0.555343 | ||||||||
\(895\) | −26475.3 | −0.988794 | ||||||||
\(896\) | 27549.1 | 1.02718 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21462.3 | 0.797558 | ||||||||
\(899\) | 2775.54 | 0.102969 | ||||||||
\(900\) | 1620.93 | 0.0600344 | ||||||||
\(901\) | 59145.8 | 2.18694 | ||||||||
\(902\) | 20365.9 | 0.751786 | ||||||||
\(903\) | −14213.7 | −0.523812 | ||||||||
\(904\) | −23231.3 | −0.854715 | ||||||||
\(905\) | −37388.6 | −1.37330 | ||||||||
\(906\) | −3635.03 | −0.133296 | ||||||||
\(907\) | 3545.27 | 0.129789 | 0.0648946 | − | 0.997892i | \(-0.479329\pi\) | ||||
0.0648946 | + | 0.997892i | \(0.479329\pi\) | |||||||
\(908\) | 30263.1 | 1.10607 | ||||||||
\(909\) | 5484.77 | 0.200130 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3913.88 | −0.142341 | −0.0711706 | − | 0.997464i | \(-0.522673\pi\) | ||||
−0.0711706 | + | 0.997464i | \(0.522673\pi\) | |||||||
\(912\) | −4796.32 | −0.174147 | ||||||||
\(913\) | 25857.7 | 0.937313 | ||||||||
\(914\) | −3618.46 | −0.130950 | ||||||||
\(915\) | −9533.02 | −0.344428 | ||||||||
\(916\) | 27110.2 | 0.977890 | ||||||||
\(917\) | 32319.5 | 1.16389 | ||||||||
\(918\) | 3543.67 | 0.127406 | ||||||||
\(919\) | 6917.79 | 0.248310 | 0.124155 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124155 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(920\) | 14492.5 | 0.519352 | ||||||||
\(921\) | 26942.8 | 0.963948 | ||||||||
\(922\) | 9708.18 | 0.346770 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 19166.2 | 0.682382 | ||||||||
\(925\) | −4897.57 | −0.174088 | ||||||||
\(926\) | 96.7050 | 0.00343188 | ||||||||
\(927\) | −291.925 | −0.0103431 | ||||||||
\(928\) | 2653.15 | 0.0938512 | ||||||||
\(929\) | 3753.03 | 0.132543 | 0.0662717 | − | 0.997802i | \(-0.478890\pi\) | ||||
0.0662717 | + | 0.997802i | \(0.478890\pi\) | |||||||
\(930\) | −8662.00 | −0.305417 | ||||||||
\(931\) | −18367.1 | −0.646571 | ||||||||
\(932\) | 27336.4 | 0.960765 | ||||||||
\(933\) | −23829.4 | −0.836162 | ||||||||
\(934\) | −11968.7 | −0.419302 | ||||||||
\(935\) | −41855.1 | −1.46397 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48189.0 | 1.68011 | 0.840056 | − | 0.542499i | \(-0.182522\pi\) | ||||
0.840056 | + | 0.542499i | \(0.182522\pi\) | |||||||
\(938\) | 26180.4 | 0.911323 | ||||||||
\(939\) | −15178.7 | −0.527517 | ||||||||
\(940\) | −3705.17 | −0.128563 | ||||||||
\(941\) | −26656.4 | −0.923456 | −0.461728 | − | 0.887022i | \(-0.652770\pi\) | ||||
−0.461728 | + | 0.887022i | \(0.652770\pi\) | |||||||
\(942\) | −298.342 | −0.0103190 | ||||||||
\(943\) | 19132.3 | 0.660693 | ||||||||
\(944\) | 1257.50 | 0.0433559 | ||||||||
\(945\) | 5832.00 | 0.200757 | ||||||||
\(946\) | 16237.1 | 0.558047 | ||||||||
\(947\) | −31258.9 | −1.07263 | −0.536314 | − | 0.844018i | \(-0.680184\pi\) | ||||
−0.536314 | + | 0.844018i | \(0.680184\pi\) | |||||||
\(948\) | −20901.2 | −0.716076 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 5647.60 | 0.192876 | ||||||||
\(951\) | 26106.4 | 0.890175 | ||||||||
\(952\) | 40150.0 | 1.36688 | ||||||||
\(953\) | 10602.4 | 0.360382 | 0.180191 | − | 0.983632i | \(-0.442328\pi\) | ||||
0.180191 | + | 0.983632i | \(0.442328\pi\) | |||||||
\(954\) | 9414.40 | 0.319499 | ||||||||
\(955\) | 8965.81 | 0.303798 | ||||||||
\(956\) | 9558.44 | 0.323370 | ||||||||
\(957\) | 2134.75 | 0.0721072 | ||||||||
\(958\) | 19856.9 | 0.669674 | ||||||||
\(959\) | 11378.6 | 0.383144 | ||||||||
\(960\) | −5109.29 | −0.171772 | ||||||||
\(961\) | 8709.45 | 0.292352 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15529.1 | −0.519645 | ||||||||
\(964\) | −3775.60 | −0.126145 | ||||||||
\(965\) | −21842.6 | −0.728640 | ||||||||
\(966\) | −7359.70 | −0.245129 | ||||||||
\(967\) | 4815.93 | 0.160155 | 0.0800774 | − | 0.996789i | \(-0.474483\pi\) | ||||
0.0800774 | + | 0.996789i | \(0.474483\pi\) | |||||||
\(968\) | −25000.0 | −0.830092 | ||||||||
\(969\) | −30205.9 | −1.00140 | ||||||||
\(970\) | −1092.97 | −0.0361786 | ||||||||
\(971\) | 56729.5 | 1.87491 | 0.937454 | − | 0.348109i | \(-0.113176\pi\) | ||||
0.937454 | + | 0.348109i | \(0.113176\pi\) | |||||||
\(972\) | −1379.94 | −0.0455367 | ||||||||
\(973\) | 16929.9 | 0.557808 | ||||||||
\(974\) | 106.493 | 0.00350334 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4500.40 | 0.147597 | ||||||||
\(977\) | 55246.2 | 1.80909 | 0.904546 | − | 0.426375i | \(-0.140210\pi\) | ||||
0.904546 | + | 0.426375i | \(0.140210\pi\) | |||||||
\(978\) | 8480.38 | 0.277273 | ||||||||
\(979\) | −26555.4 | −0.866921 | ||||||||
\(980\) | 8619.11 | 0.280946 | ||||||||
\(981\) | −11460.9 | −0.373005 | ||||||||
\(982\) | −4000.34 | −0.129996 | ||||||||
\(983\) | 22820.6 | 0.740451 | 0.370226 | − | 0.928942i | \(-0.379280\pi\) | ||||
0.370226 | + | 0.928942i | \(0.379280\pi\) | |||||||
\(984\) | −16613.5 | −0.538231 | ||||||||
\(985\) | −21882.0 | −0.707836 | ||||||||
\(986\) | 1856.54 | 0.0599637 | ||||||||
\(987\) | 4532.29 | 0.146164 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15253.5 | 0.490429 | ||||||||
\(990\) | −6662.20 | −0.213877 | ||||||||
\(991\) | −46490.4 | −1.49023 | −0.745115 | − | 0.666936i | \(-0.767605\pi\) | ||||
−0.745115 | + | 0.666936i | \(0.767605\pi\) | |||||||
\(992\) | 36802.8 | 1.17791 | ||||||||
\(993\) | 5212.94 | 0.166594 | ||||||||
\(994\) | 9028.21 | 0.288086 | ||||||||
\(995\) | 2519.84 | 0.0802856 | ||||||||
\(996\) | −8757.01 | −0.278591 | ||||||||
\(997\) | 24943.4 | 0.792344 | 0.396172 | − | 0.918176i | \(-0.370338\pi\) | ||||
0.396172 | + | 0.918176i | \(0.370338\pi\) | |||||||
\(998\) | −11626.8 | −0.368777 | ||||||||
\(999\) | 4169.44 | 0.132047 |
(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.l.1.3 | 4 | ||
3.2 | odd | 2 | 1521.4.a.w.1.2 | 4 | |||
13.5 | odd | 4 | 39.4.b.b.25.2 | ✓ | 4 | ||
13.8 | odd | 4 | 39.4.b.b.25.3 | yes | 4 | ||
13.12 | even | 2 | inner | 507.4.a.l.1.2 | 4 | ||
39.5 | even | 4 | 117.4.b.e.64.3 | 4 | |||
39.8 | even | 4 | 117.4.b.e.64.2 | 4 | |||
39.38 | odd | 2 | 1521.4.a.w.1.3 | 4 | |||
52.31 | even | 4 | 624.4.c.c.337.3 | 4 | |||
52.47 | even | 4 | 624.4.c.c.337.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.b.25.2 | ✓ | 4 | 13.5 | odd | 4 | ||
39.4.b.b.25.3 | yes | 4 | 13.8 | odd | 4 | ||
117.4.b.e.64.2 | 4 | 39.8 | even | 4 | |||
117.4.b.e.64.3 | 4 | 39.5 | even | 4 | |||
507.4.a.l.1.2 | 4 | 13.12 | even | 2 | inner | ||
507.4.a.l.1.3 | 4 | 1.1 | even | 1 | trivial | ||
624.4.c.c.337.2 | 4 | 52.47 | even | 4 | |||
624.4.c.c.337.3 | 4 | 52.31 | even | 4 | |||
1521.4.a.w.1.2 | 4 | 3.2 | odd | 2 | |||
1521.4.a.w.1.3 | 4 | 39.38 | odd | 2 |