Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{113})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 59x^{2} + 60x + 674 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 392) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-6.22929\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.63797 | 1.85483 | 0.927414 | − | 0.374037i | \(-0.122027\pi\) | ||||
0.927414 | + | 0.374037i | \(0.122027\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.91838 | 0.529356 | 0.264678 | − | 0.964337i | \(-0.414734\pi\) | ||||
0.264678 | + | 0.964337i | \(0.414734\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 65.8904 | 2.44039 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.3699 | 0.503520 | 0.251760 | − | 0.967790i | \(-0.418991\pi\) | ||||
0.251760 | + | 0.967790i | \(0.418991\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −90.9844 | −1.94112 | −0.970558 | − | 0.240866i | \(-0.922569\pi\) | ||||
−0.970558 | + | 0.240866i | \(0.922569\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 57.0412 | 0.981864 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 91.9239 | 1.31146 | 0.655730 | − | 0.754996i | \(-0.272361\pi\) | ||||
0.655730 | + | 0.754996i | \(0.272361\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 124.247 | 1.50023 | 0.750114 | − | 0.661309i | \(-0.229999\pi\) | ||||
0.750114 | + | 0.661309i | \(0.229999\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −65.0412 | −0.589653 | −0.294827 | − | 0.955551i | \(-0.595262\pi\) | ||||
−0.294827 | + | 0.955551i | \(0.595262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.9728 | −0.719782 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 374.825 | 2.67167 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 83.4110 | 0.534105 | 0.267052 | − | 0.963682i | \(-0.413950\pi\) | ||||
0.267052 | + | 0.963682i | \(0.413950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 165.308 | 0.957748 | 0.478874 | − | 0.877884i | \(-0.341045\pi\) | ||||
0.478874 | + | 0.877884i | \(0.341045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 177.048 | 0.933943 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 310.973 | 1.38172 | 0.690860 | − | 0.722989i | \(-0.257232\pi\) | ||||
0.690860 | + | 0.722989i | \(0.257232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −876.904 | −3.60044 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 181.504 | 0.691369 | 0.345685 | − | 0.938351i | \(-0.387647\pi\) | ||||
0.345685 | + | 0.938351i | \(0.387647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −82.3699 | −0.292123 | −0.146061 | − | 0.989276i | \(-0.546660\pi\) | ||||
−0.146061 | + | 0.989276i | \(0.546660\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 389.965 | 1.29183 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −367.909 | −1.14181 | −0.570904 | − | 0.821017i | \(-0.693407\pi\) | ||||
−0.570904 | + | 0.821017i | \(0.693407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 885.959 | 2.43253 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 52.6574 | 0.136473 | 0.0682363 | − | 0.997669i | \(-0.478263\pi\) | ||||
0.0682363 | + | 0.997669i | \(0.478263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 108.720 | 0.266541 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1197.49 | 2.78266 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −561.278 | −1.23851 | −0.619256 | − | 0.785189i | \(-0.712566\pi\) | ||||
−0.619256 | + | 0.785189i | \(0.712566\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 276.305 | 0.579954 | 0.289977 | − | 0.957034i | \(-0.406352\pi\) | ||||
0.289977 | + | 0.957034i | \(0.406352\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −538.480 | −1.02754 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.1368 | 0.109655 | 0.0548275 | − | 0.998496i | \(-0.482539\pi\) | ||||
0.0548275 | + | 0.998496i | \(0.482539\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −626.865 | −1.09370 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 155.534 | 0.259979 | 0.129989 | − | 0.991515i | \(-0.458506\pi\) | ||||
0.129989 | + | 0.991515i | \(0.458506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 731.478 | 1.17278 | 0.586391 | − | 0.810028i | \(-0.300548\pi\) | ||||
0.586391 | + | 0.810028i | \(0.300548\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −867.155 | −1.33507 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −290.384 | −0.413554 | −0.206777 | − | 0.978388i | \(-0.566297\pi\) | ||||
−0.206777 | + | 0.978388i | \(0.566297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1833.51 | 2.51510 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 43.5791 | 0.0576317 | 0.0288158 | − | 0.999585i | \(-0.490826\pi\) | ||||
0.0288158 | + | 0.999585i | \(0.490826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 544.041 | 0.694229 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 803.913 | 0.990672 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −393.093 | −0.468177 | −0.234089 | − | 0.972215i | \(-0.575211\pi\) | ||||
−0.234089 | + | 0.972215i | \(0.575211\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1593.23 | 1.77646 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 735.344 | 0.794155 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 521.748 | 0.546139 | 0.273070 | − | 0.961994i | \(-0.411961\pi\) | ||||
0.273070 | + | 0.961994i | \(0.411961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1210.40 | 1.22878 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −753.089 | −0.741932 | −0.370966 | − | 0.928646i | \(-0.620973\pi\) | ||||
−0.370966 | + | 0.928646i | \(0.620973\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −930.922 | −0.890548 | −0.445274 | − | 0.895394i | \(-0.646894\pi\) | ||||
−0.445274 | + | 0.895394i | \(0.646894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1683.04 | −1.52062 | −0.760308 | − | 0.649563i | \(-0.774952\pi\) | ||||
−0.760308 | + | 0.649563i | \(0.774952\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −783.905 | −0.688848 | −0.344424 | − | 0.938814i | \(-0.611926\pi\) | ||||
−0.344424 | + | 0.938814i | \(0.611926\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2997.15 | 2.56285 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −628.205 | −0.522979 | −0.261489 | − | 0.965206i | \(-0.584214\pi\) | ||||
−0.261489 | + | 0.965206i | \(0.584214\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −384.938 | −0.312136 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5995.00 | −4.73708 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −993.548 | −0.746468 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1749.33 | 1.28237 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1272.29 | −0.910377 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −328.466 | −0.229501 | −0.114751 | − | 0.993394i | \(-0.536607\pi\) | ||||
−0.114751 | + | 0.993394i | \(0.536607\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −793.878 | −0.541838 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2412.79 | −1.60921 | −0.804606 | − | 0.593809i | \(-0.797624\pi\) | ||||
−0.804606 | + | 0.593809i | \(0.797624\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2218.36 | 1.41426 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −175.699 | −0.109569 | −0.0547845 | − | 0.998498i | \(-0.517447\pi\) | ||||
−0.0547845 | + | 0.998498i | \(0.517447\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1489.47 | −0.908885 | −0.454442 | − | 0.890776i | \(-0.650161\pi\) | ||||
−0.454442 | + | 0.890776i | \(0.650161\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3545.89 | −2.11786 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1671.37 | −0.977391 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 493.658 | 0.282732 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3034.33 | 1.66834 | 0.834168 | − | 0.551511i | \(-0.185949\pi\) | ||||
0.834168 | + | 0.551511i | \(0.185949\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2114.82 | 1.13975 | 0.569873 | − | 0.821732i | \(-0.306992\pi\) | ||||
0.569873 | + | 0.821732i | \(0.306992\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6056.90 | 3.20047 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 978.356 | 0.506990 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −275.704 | −0.140150 | −0.0700752 | − | 0.997542i | \(-0.522324\pi\) | ||||
−0.0700752 | + | 0.997542i | \(0.522324\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 507.510 | 0.253133 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1219.25 | −0.585882 | −0.292941 | − | 0.956131i | \(-0.594634\pi\) | ||||
−0.292941 | + | 0.956131i | \(0.594634\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1047.84 | 0.494388 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2781.99 | −1.28908 | −0.644542 | − | 0.764569i | \(-0.722952\pi\) | ||||
−0.644542 | + | 0.764569i | \(0.722952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6081.15 | 2.76794 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8186.72 | 3.66114 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2707.05 | 1.18967 | 0.594835 | − | 0.803847i | \(-0.297217\pi\) | ||||
0.594835 | + | 0.803847i | \(0.297217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5409.58 | −2.29723 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1721.73 | 0.718926 | 0.359463 | − | 0.933159i | \(-0.382960\pi\) | ||||
0.359463 | + | 0.933159i | \(0.382960\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 624.549 | 0.256477 | 0.128238 | − | 0.991743i | \(-0.459068\pi\) | ||||
0.128238 | + | 0.991743i | \(0.459068\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2663.01 | 1.07571 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1840.46 | 0.731421 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1688.63 | 0.660346 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4789.78 | 1.81454 | 0.907269 | − | 0.420552i | \(-0.138164\pi\) | ||||
0.907269 | + | 0.420552i | \(0.138164\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1436.23 | −0.535660 | −0.267830 | − | 0.963466i | \(-0.586307\pi\) | ||||
−0.267830 | + | 0.963466i | \(0.586307\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5189.85 | −1.90591 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2508.66 | 0.907282 | 0.453641 | − | 0.891184i | \(-0.350125\pi\) | ||||
0.453641 | + | 0.891184i | \(0.350125\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4093.76 | −1.45829 | −0.729143 | − | 0.684361i | \(-0.760081\pi\) | ||||
−0.729143 | + | 0.684361i | \(0.760081\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 579.597 | 0.203391 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1074.21 | 0.365981 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4285.59 | −1.43898 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2282.41 | 0.755395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2308.68 | 0.753253 | 0.376626 | − | 0.926365i | \(-0.377084\pi\) | ||||
0.376626 | + | 0.926365i | \(0.377084\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1499.03 | 0.482215 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −487.496 | −0.154637 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7049.96 | 2.17531 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8363.64 | −2.54570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 775.802 | 0.232967 | 0.116483 | − | 0.993193i | \(-0.462838\pi\) | ||||
0.116483 | + | 0.993193i | \(0.462838\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5928.35 | −1.75655 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 178.238 | 0.0521150 | 0.0260575 | − | 0.999660i | \(-0.491705\pi\) | ||||
0.0260575 | + | 0.999660i | \(0.491705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2609.81 | −0.753106 | −0.376553 | − | 0.926395i | \(-0.622891\pi\) | ||||
−0.376553 | + | 0.926395i | \(0.622891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1575.84 | 0.443075 | 0.221538 | − | 0.975152i | \(-0.428892\pi\) | ||||
0.221538 | + | 0.975152i | \(0.428892\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2177.42 | −0.604423 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2798.71 | −0.767071 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −620.547 | −0.167949 | −0.0839746 | − | 0.996468i | \(-0.526761\pi\) | ||||
−0.0839746 | + | 0.996468i | \(0.526761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2552.79 | −0.682323 | −0.341161 | − | 0.940005i | \(-0.610820\pi\) | ||||
−0.341161 | + | 0.940005i | \(0.610820\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7551.02 | 1.99341 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11304.6 | −2.91212 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 420.014 | 0.106897 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4057.62 | 1.02038 | 0.510189 | − | 0.860062i | \(-0.329575\pi\) | ||||
0.510189 | + | 0.860062i | \(0.329575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1194.80 | −0.296902 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5243.45 | 1.28768 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5161.13 | 1.25269 | 0.626347 | − | 0.779545i | \(-0.284549\pi\) | ||||
0.626347 | + | 0.779545i | \(0.284549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5495.99 | 1.30342 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7119.65 | −1.66926 | −0.834632 | − | 0.550808i | \(-0.814320\pi\) | ||||
−0.834632 | + | 0.550808i | \(0.814320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 311.646 | 0.0722426 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3788.62 | −0.868389 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6002.71 | −1.36056 | −0.680282 | − | 0.732951i | \(-0.738143\pi\) | ||||
−0.680282 | + | 0.732951i | \(0.738143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 793.085 | 0.177773 | 0.0888864 | − | 0.996042i | \(-0.471669\pi\) | ||||
0.0888864 | + | 0.996042i | \(0.471669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1652.79 | −0.362425 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4054.33 | −0.879427 | −0.439713 | − | 0.898138i | \(-0.644920\pi\) | ||||
−0.439713 | + | 0.898138i | \(0.644920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10892.2 | 2.33728 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2990.91 | 0.634955 | 0.317478 | − | 0.948266i | \(-0.397164\pi\) | ||||
0.317478 | + | 0.948266i | \(0.397164\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5716.11 | −1.20066 | −0.600331 | − | 0.799752i | \(-0.704965\pi\) | ||||
−0.600331 | + | 0.799752i | \(0.704965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7087.22 | 1.47302 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3537.00 | 0.719927 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5028.59 | 1.01299 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5301.47 | −1.05705 | −0.528524 | − | 0.848918i | \(-0.677254\pi\) | ||||
−0.528524 | + | 0.848918i | \(0.677254\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3321.86 | −0.655613 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6885.48 | 1.34524 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5917.73 | 1.14459 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7258.25 | −1.37616 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1635.28 | 0.307002 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5978.40 | −1.11142 | −0.555709 | − | 0.831377i | \(-0.687553\pi\) | ||||
−0.555709 | + | 0.831377i | \(0.687553\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8972.19 | −1.65181 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4850.71 | −0.884433 | −0.442217 | − | 0.896908i | \(-0.645808\pi\) | ||||
−0.442217 | + | 0.896908i | \(0.645808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4455.34 | −0.804571 | −0.402285 | − | 0.915514i | \(-0.631784\pi\) | ||||
−0.402285 | + | 0.915514i | \(0.631784\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10261.9 | −1.81818 | −0.909091 | − | 0.416597i | \(-0.863223\pi\) | ||||
−0.909091 | + | 0.416597i | \(0.863223\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1532.25 | 0.268932 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16221.1 | −2.82048 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11421.3 | 1.96749 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8186.11 | 1.39718 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7555.25 | −1.27770 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3087.11 | 0.512638 | 0.256319 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256319 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20490.1 | 3.37193 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 355.912 | 0.0580465 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4588.57 | 0.741707 | 0.370853 | − | 0.928691i | \(-0.379065\pi\) | ||||
0.370853 | + | 0.928691i | \(0.379065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6054.62 | −0.970035 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3036.68 | 0.482245 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3710.02 | −0.578959 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9645.58 | 1.49222 | 0.746112 | − | 0.665820i | \(-0.231918\pi\) | ||||
0.746112 | + | 0.665820i | \(0.231918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2612.70 | 0.400730 | 0.200365 | − | 0.979721i | \(-0.435787\pi\) | ||||
0.200365 | + | 0.979721i | \(0.435787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −34103.2 | −5.18602 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8688.08 | −1.30997 | −0.654985 | − | 0.755642i | \(-0.727325\pi\) | ||||
−0.654985 | + | 0.755642i | \(0.727325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 920.509 | 0.137621 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2738.82 | 0.402645 | 0.201322 | − | 0.979525i | \(-0.435476\pi\) | ||||
0.201322 | + | 0.979525i | \(0.435476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8578.44 | 1.25068 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9575.79 | −1.38457 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4329.17 | 0.620819 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1968.59 | 0.279999 | 0.139999 | − | 0.990152i | \(-0.455290\pi\) | ||||
0.139999 | + | 0.990152i | \(0.455290\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11959.4 | 1.68721 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9915.60 | −1.37643 | −0.688217 | − | 0.725504i | \(-0.741607\pi\) | ||||
−0.688217 | + | 0.725504i | \(0.741607\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12262.3 | −1.68859 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7589.10 | −1.03676 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10933.4 | −1.48183 | −0.740913 | − | 0.671601i | \(-0.765607\pi\) | ||||
−0.740913 | + | 0.671601i | \(0.765607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3165.75 | −0.425685 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12009.7 | −1.60226 | −0.801131 | − | 0.598489i | \(-0.795768\pi\) | ||||
−0.801131 | + | 0.598489i | \(0.795768\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5427.39 | −0.712893 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9242.27 | 1.20463 | 0.602316 | − | 0.798258i | \(-0.294245\pi\) | ||||
0.602316 | + | 0.798258i | \(0.294245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5978.84 | −0.773306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −23254.4 | −2.98481 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1718.60 | −0.218917 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3702.46 | −0.468063 | −0.234032 | − | 0.972229i | \(-0.575192\pi\) | ||||
−0.234032 | + | 0.972229i | \(0.575192\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3194.78 | 0.397855 | 0.198927 | − | 0.980014i | \(-0.436254\pi\) | ||||
0.198927 | + | 0.980014i | \(0.436254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15040.4 | −1.85910 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10851.4 | 1.33138 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5712.52 | 0.695723 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6217.59 | −0.751687 | −0.375843 | − | 0.926683i | \(-0.622647\pi\) | ||||
−0.375843 | + | 0.926683i | \(0.622647\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1693.38 | −0.203231 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 257.918 | 0.0305077 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14355.4 | −1.68583 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −290.002 | −0.0338127 | −0.0169063 | − | 0.999857i | \(-0.505382\pi\) | ||||
−0.0169063 | + | 0.999857i | \(0.505382\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16109.3 | 1.86489 | 0.932445 | − | 0.361311i | \(-0.117671\pi\) | ||||
0.932445 | + | 0.361311i | \(0.117671\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −24241.7 | −2.78645 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8270.65 | −0.943965 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16108.6 | −1.81289 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 71.3997 | 0.00797958 | 0.00398979 | − | 0.999992i | \(-0.498730\pi\) | ||||
0.00398979 | + | 0.999992i | \(0.498730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2473.42 | 0.274515 | 0.137258 | − | 0.990535i | \(-0.456171\pi\) | ||||
0.137258 | + | 0.990535i | \(0.456171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4757.86 | 0.524418 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8081.20 | −0.884614 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13051.8 | 1.41898 | 0.709488 | − | 0.704718i | \(-0.248926\pi\) | ||||
0.709488 | + | 0.704718i | \(0.248926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5104.36 | −0.547439 | −0.273719 | − | 0.961810i | \(-0.588254\pi\) | ||||
−0.273719 | + | 0.961810i | \(0.588254\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2326.47 | −0.247833 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29244.8 | 3.09447 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7106.77 | −0.746969 | −0.373485 | − | 0.927636i | \(-0.621837\pi\) | ||||
−0.373485 | + | 0.927636i | \(0.621837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3334.20 | 0.348118 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20382.6 | 2.11403 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 942.949 | 0.0965192 | 0.0482596 | − | 0.998835i | \(-0.484633\pi\) | ||||
0.0482596 | + | 0.998835i | \(0.484633\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34455.4 | 3.50379 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1906.71 | 0.192634 | 0.0963172 | − | 0.995351i | \(-0.469294\pi\) | ||||
0.0963172 | + | 0.995351i | \(0.469294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4896.83 | 0.491523 | 0.245761 | − | 0.969330i | \(-0.420962\pi\) | ||||
0.245761 | + | 0.969330i | \(0.420962\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9429.36 | 0.940379 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 363.895 | 0.0360580 | 0.0180290 | − | 0.999837i | \(-0.494261\pi\) | ||||
0.0180290 | + | 0.999837i | \(0.494261\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2657.23 | −0.259955 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1513.12 | −0.147090 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11178.9 | −1.07984 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3469.62 | 0.333046 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5223.85 | −0.498296 | −0.249148 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249148 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28293.7 | −2.68208 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3087.90 | 0.289102 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12133.2 | −1.12896 | −0.564482 | − | 0.825445i | \(-0.690924\pi\) | ||||
−0.564482 | + | 0.825445i | \(0.690924\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11751.1 | −1.08671 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2875.76 | −0.264320 | −0.132160 | − | 0.991228i | \(-0.542191\pi\) | ||||
−0.132160 | + | 0.991228i | \(0.542191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7667.46 | 0.700457 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7163.59 | 0.650464 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15643.9 | −1.40344 | −0.701719 | − | 0.712454i | \(-0.747584\pi\) | ||||
−0.701719 | + | 0.712454i | \(0.747584\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −26812.8 | −2.39103 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3530.58 | −0.312964 | −0.156482 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156482 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4457.07 | −0.392746 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 58610.0 | 5.13404 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6053.60 | 0.527153 | 0.263577 | − | 0.964638i | \(-0.415098\pi\) | ||||
0.263577 | + | 0.964638i | \(0.415098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 46571.0 | 4.00811 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5509.55 | −0.471417 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6758.43 | −0.574923 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26090.4 | 2.20663 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20876.4 | −1.75549 | −0.877746 | − | 0.479126i | \(-0.840954\pi\) | ||||
−0.877746 | + | 0.479126i | \(0.840954\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19017.4 | 1.59000 | 0.795001 | − | 0.606608i | \(-0.207470\pi\) | ||||
0.795001 | + | 0.606608i | \(0.207470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15195.8 | 1.25605 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7936.65 | −0.652309 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36982.9 | −3.02245 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16514.0 | −1.34203 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9960.89 | −0.804947 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16593.9 | 1.33348 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14070.7 | 1.11820 | 0.559099 | − | 0.829101i | \(-0.311147\pi\) | ||||
0.559099 | + | 0.829101i | \(0.311147\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6019.38 | 0.475721 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4639.45 | −0.364646 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16099.5 | 1.25844 | 0.629218 | − | 0.777229i | \(-0.283375\pi\) | ||||
0.629218 | + | 0.777229i | \(0.283375\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 18205.8 | 1.41531 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10363.6 | 0.801279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 17738.2 | 1.35666 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12327.2 | 0.937740 | 0.468870 | − | 0.883267i | \(-0.344661\pi\) | ||||
0.468870 | + | 0.883267i | \(0.344661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7494.37 | 0.567045 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16274.9 | 1.22483 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4492.34 | −0.336287 | −0.168143 | − | 0.985763i | \(-0.553777\pi\) | ||||
−0.168143 | + | 0.985763i | \(0.553777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3717.96 | −0.276842 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16895.1 | −1.24478 | −0.622390 | − | 0.782707i | \(-0.713838\pi\) | ||||
−0.622390 | + | 0.782707i | \(0.713838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 88.1151 | 0.00645797 | 0.00322899 | − | 0.999995i | \(-0.498972\pi\) | ||||
0.00322899 | + | 0.999995i | \(0.498972\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 46163.8 | 3.36565 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5851.93 | 0.424422 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8172.92 | 0.589676 | 0.294838 | − | 0.955547i | \(-0.404734\pi\) | ||||
0.294838 | + | 0.955547i | \(0.404734\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13842.4 | −0.993557 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 967.308 | 0.0687167 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −35480.7 | −2.50760 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18301.4 | 1.28685 | 0.643425 | − | 0.765509i | \(-0.277513\pi\) | ||||
0.643425 | + | 0.765509i | \(0.277513\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20539.1 | 1.43684 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24178.4 | 1.68285 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2069.18 | −0.143290 | −0.0716452 | − | 0.997430i | \(-0.522825\pi\) | ||||
−0.0716452 | + | 0.997430i | \(0.522825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −39455.6 | −2.70487 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13615.6 | −0.928747 | −0.464373 | − | 0.885639i | \(-0.653720\pi\) | ||||
−0.464373 | + | 0.885639i | \(0.653720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1041.12 | −0.0706624 | −0.0353312 | − | 0.999376i | \(-0.511249\pi\) | ||||
−0.0353312 | + | 0.999376i | \(0.511249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3962.44 | 0.267600 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5880.20 | −0.395147 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15496.0 | 1.03618 | 0.518090 | − | 0.855326i | \(-0.326643\pi\) | ||||
0.518090 | + | 0.855326i | \(0.326643\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33473.9 | 2.21638 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 936.457 | 0.0617017 | 0.0308509 | − | 0.999524i | \(-0.490178\pi\) | ||||
0.0308509 | + | 0.999524i | \(0.490178\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10353.2 | 0.678831 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −798.142 | −0.0520778 | −0.0260389 | − | 0.999661i | \(-0.508289\pi\) | ||||
−0.0260389 | + | 0.999661i | \(0.508289\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 999.034 | 0.0648701 | 0.0324350 | − | 0.999474i | \(-0.489674\pi\) | ||||
0.0324350 | + | 0.999474i | \(0.489674\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24379.0 | −1.57536 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3716.70 | 0.237869 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21997.8 | 1.40113 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28585.8 | 1.81207 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25618.7 | −1.61626 | −0.808132 | − | 0.589001i | \(-0.799521\pi\) | ||||
−0.808132 | + | 0.589001i | \(0.799521\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22251.0 | 1.39715 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1943.99 | −0.121488 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10248.2 | 0.634448 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18351.4 | 1.13079 | 0.565394 | − | 0.824821i | \(-0.308724\pi\) | ||||
0.565394 | + | 0.824821i | \(0.308724\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22068.9 | −1.35352 | −0.676759 | − | 0.736205i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736205i | \(0.736616\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4698.47 | −0.286825 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6409.50 | −0.389464 | −0.194732 | − | 0.980856i | \(-0.562384\pi\) | ||||
−0.194732 | + | 0.980856i | \(0.562384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10310.6 | −0.623615 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21098.8 | 1.26441 | 0.632206 | − | 0.774800i | \(-0.282150\pi\) | ||||
0.632206 | + | 0.774800i | \(0.282150\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14279.8 | −0.851846 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 48197.4 | 2.86204 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29509.0 | 1.74432 | 0.872159 | − | 0.489222i | \(-0.162719\pi\) | ||||
0.872159 | + | 0.489222i | \(0.162719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21717.9 | −1.27795 | −0.638976 | − | 0.769226i | \(-0.720642\pi\) | ||||
−0.638976 | + | 0.769226i | \(0.720642\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −80608.5 | −4.72183 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5425.15 | −0.314937 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7477.16 | 0.432113 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5075.67 | 0.292018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3168.78 | 0.181497 | 0.0907486 | − | 0.995874i | \(-0.471074\pi\) | ||||
0.0907486 | + | 0.995874i | \(0.471074\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −33724.0 | −1.92302 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22586.8 | 1.28225 | 0.641124 | − | 0.767437i | \(-0.278468\pi\) | ||||
0.641124 | + | 0.767437i | \(0.278468\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1717.86 | 0.0966643 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7130.82 | 0.399492 | 0.199746 | − | 0.979848i | \(-0.435988\pi\) | ||||
0.199746 | + | 0.979848i | \(0.435988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1039.85 | −0.0580010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25153.3 | −1.39688 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4791.00 | −0.264909 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11414.6 | −0.628408 | −0.314204 | − | 0.949355i | \(-0.601738\pi\) | ||||
−0.314204 | + | 0.949355i | \(0.601738\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8815.24 | −0.481124 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16684.5 | 0.906703 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15187.9 | 0.821829 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10005.8 | 0.539106 | 0.269553 | − | 0.962986i | \(-0.413124\pi\) | ||||
0.269553 | + | 0.962986i | \(0.413124\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38637.6 | 2.07289 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −20985.9 | −1.12110 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9540.20 | −0.505345 | −0.252673 | − | 0.967552i | \(-0.581310\pi\) | ||||
−0.252673 | + | 0.967552i | \(0.581310\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −19133.5 | −1.00923 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10751.8 | −0.564739 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9891.80 | −0.517388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5980.81 | −0.311517 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5713.54 | 0.296355 | 0.148177 | − | 0.988961i | \(-0.452659\pi\) | ||||
0.148177 | + | 0.988961i | \(0.452659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24603.7 | −1.26559 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7504.72 | −0.384439 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18615.1 | −0.949649 | −0.474824 | − | 0.880081i | \(-0.657488\pi\) | ||||
−0.474824 | + | 0.880081i | \(0.657488\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23271.8 | 1.18233 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7571.76 | −0.383107 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26452.2 | −1.33293 | −0.666463 | − | 0.745538i | \(-0.732192\pi\) | ||||
−0.666463 | + | 0.745538i | \(0.732192\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1104.70 | 0.0552134 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22916.1 | 1.14071 | 0.570353 | − | 0.821400i | \(-0.306807\pi\) | ||||
0.570353 | + | 0.821400i | \(0.306807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −108953. | −5.40148 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24313.3 | 1.20050 | 0.600248 | − | 0.799814i | \(-0.295069\pi\) | ||||
0.600248 | + | 0.799814i | \(0.295069\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17958.3 | 0.883143 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2871.45 | 0.140644 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5618.48 | 0.272997 | 0.136499 | − | 0.990640i | \(-0.456415\pi\) | ||||
0.136499 | + | 0.990640i | \(0.456415\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 39107.3 | 1.89263 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12516.3 | 0.603332 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2786.08 | −0.133767 | −0.0668837 | − | 0.997761i | \(-0.521306\pi\) | ||||
−0.0668837 | + | 0.997761i | \(0.521306\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11515.4 | −0.550702 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6814.43 | 0.324603 | 0.162302 | − | 0.986741i | \(-0.448108\pi\) | ||||
0.162302 | + | 0.986741i | \(0.448108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 35847.1 | 1.69419 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 51067.5 | 2.40410 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13274.3 | −0.622474 | −0.311237 | − | 0.950332i | \(-0.600743\pi\) | ||||
−0.311237 | + | 0.950332i | \(0.600743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 49742.8 | 2.32353 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18651.4 | 0.867845 | 0.433922 | − | 0.900950i | \(-0.357129\pi\) | ||||
0.433922 | + | 0.900950i | \(0.357129\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14873.2 | −0.689370 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22551.4 | 1.03721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2857.13 | 0.130904 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 31264.5 | 1.42695 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1631.72 | −0.0741895 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35028.4 | −1.58657 | −0.793284 | − | 0.608852i | \(-0.791630\pi\) | ||||
−0.793284 | + | 0.608852i | \(0.791630\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −68618.9 | −3.09620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25139.4 | −1.12576 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3003.64 | 0.133998 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1170.81 | 0.0520352 | 0.0260176 | − | 0.999661i | \(-0.491717\pi\) | ||||
0.0260176 | + | 0.999661i | \(0.491717\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33819.6 | −1.49744 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −25901.1 | −1.14253 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13437.1 | 0.590519 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −57853.9 | −2.52361 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13354.8 | 0.580381 | 0.290190 | − | 0.956969i | \(-0.406281\pi\) | ||||
0.290190 | + | 0.956969i | \(0.406281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12327.2 | 0.533745 | 0.266872 | − | 0.963732i | \(-0.414010\pi\) | ||||
0.266872 | + | 0.963732i | \(0.414010\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7643.72 | 0.329738 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7215.96 | −0.310140 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10234.2 | −0.438251 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45453.9 | 1.93222 | 0.966109 | − | 0.258134i | \(-0.0831076\pi\) | ||||
0.966109 | + | 0.258134i | \(0.0831076\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9286.25 | −0.393315 | −0.196657 | − | 0.980472i | \(-0.563009\pi\) | ||||
−0.196657 | + | 0.980472i | \(0.563009\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15929.5 | −0.672235 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22224.4 | −0.934485 | −0.467242 | − | 0.884129i | \(-0.654752\pi\) | ||||
−0.467242 | + | 0.884129i | \(0.654752\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44036.7 | 1.84495 | 0.922473 | − | 0.386063i | \(-0.126165\pi\) | ||||
0.922473 | + | 0.386063i | \(0.126165\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −39075.5 | −1.63119 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16464.9 | −0.682384 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 61961.6 | 2.55879 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37521.9 | 1.54398 | 0.771991 | − | 0.635633i | \(-0.219261\pi\) | ||||
0.771991 | + | 0.635633i | \(0.219261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17431.6 | −0.714732 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28826.3 | 1.17773 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35990.6 | 1.46522 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −55091.7 | −2.22702 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20226.0 | −0.814735 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34441.3 | 1.38247 | 0.691235 | − | 0.722630i | \(-0.257067\pi\) | ||||
0.691235 | + | 0.722630i | \(0.257067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48452.1 | 1.93804 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24970.8 | −0.995318 | −0.497659 | − | 0.867373i | \(-0.665807\pi\) | ||||
−0.497659 | + | 0.867373i | \(0.665807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17355.5 | −0.689364 | −0.344682 | − | 0.938720i | \(-0.612013\pi\) | ||||
−0.344682 | + | 0.938720i | \(0.612013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26568.0 | −1.04795 | −0.523977 | − | 0.851732i | \(-0.675552\pi\) | ||||
−0.523977 | + | 0.851732i | \(0.675552\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16021.3 | 0.629760 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34089.5 | 1.33534 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5334.31 | −0.208232 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5471.51 | −0.212853 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 34378.2 | 1.33279 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 47235.3 | 1.81873 | 0.909363 | − | 0.416003i | \(-0.136569\pi\) | ||||
0.909363 | + | 0.416003i | \(0.136569\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −51095.4 | −1.96064 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29598.0 | 1.13188 | 0.565938 | − | 0.824448i | \(-0.308514\pi\) | ||||
0.565938 | + | 0.824448i | \(0.308514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42952.5 | −1.63700 | −0.818498 | − | 0.574509i | \(-0.805193\pi\) | ||||
−0.818498 | + | 0.574509i | \(0.805193\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32016.0 | −1.21605 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33497.9 | 1.26804 | 0.634018 | − | 0.773318i | \(-0.281404\pi\) | ||||
0.634018 | + | 0.773318i | \(0.281404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33681.3 | 1.26640 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45711.7 | −1.71297 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10189.8 | 0.380568 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 57034.9 | 2.12301 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13788.5 | 0.511538 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4840.47 | 0.178978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3696.32 | 0.135768 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13751.1 | −0.503417 | −0.251708 | − | 0.967803i | \(-0.580992\pi\) | ||||
−0.251708 | + | 0.967803i | \(0.580992\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −49621.4 | −1.81060 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38706.9 | −1.40770 | −0.703851 | − | 0.710348i | \(-0.748538\pi\) | ||||
−0.703851 | + | 0.710348i | \(0.748538\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 800.542 | 0.0290187 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 15760.7 | 0.569436 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23292.4 | 0.836068 | 0.418034 | − | 0.908431i | \(-0.362719\pi\) | ||||
0.418034 | + | 0.908431i | \(0.362719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −57619.6 | −2.06149 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14151.1 | −0.504649 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27979.1 | −0.994537 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −61338.8 | −2.17328 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42925.3 | 1.51597 | 0.757984 | − | 0.652273i | \(-0.226184\pi\) | ||||
0.757984 | + | 0.652273i | \(0.226184\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46751.0 | −1.64047 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9993.95 | 0.349558 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44869.6 | 1.56438 | 0.782191 | − | 0.623039i | \(-0.214102\pi\) | ||||
0.782191 | + | 0.623039i | \(0.214102\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42940.4 | −1.49234 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12243.4 | −0.424148 | −0.212074 | − | 0.977254i | \(-0.568022\pi\) | ||||
−0.212074 | + | 0.977254i | \(0.568022\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11805.2 | −0.407668 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42027.1 | 1.44213 | 0.721065 | − | 0.692868i | \(-0.243653\pi\) | ||||
0.721065 | + | 0.692868i | \(0.243653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66553.1 | −2.27651 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −98903.6 | −3.37242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15757.3 | 0.535601 | 0.267801 | − | 0.963474i | \(-0.413703\pi\) | ||||
0.267801 | + | 0.963474i | \(0.413703\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28347.8 | 0.960536 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14767.8 | 0.498823 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2464.25 | −0.0827180 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −110896. | −3.71089 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8500.17 | −0.283555 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25863.4 | 0.860093 | 0.430046 | − | 0.902807i | \(-0.358497\pi\) | ||||
0.430046 | + | 0.902807i | \(0.358497\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 110078. | 3.64935 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47845.6 | −1.58129 | −0.790647 | − | 0.612272i | \(-0.790256\pi\) | ||||
−0.790647 | + | 0.612272i | \(0.790256\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 78897.5 | 2.59153 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 54722.6 | 1.79195 | 0.895973 | − | 0.444108i | \(-0.146479\pi\) | ||||
0.895973 | + | 0.444108i | \(0.146479\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7221.06 | −0.235737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51651.8 | −1.68106 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30062.6 | −0.975430 | −0.487715 | − | 0.873003i | \(-0.662169\pi\) | ||||
−0.487715 | + | 0.873003i | \(0.662169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14847.2 | 0.480275 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5357.43 | 0.172251 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37286.6 | 1.19521 | 0.597603 | − | 0.801792i | \(-0.296120\pi\) | ||||
0.597603 | + | 0.801792i | \(0.296120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 29753.5 | 0.950855 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24228.4 | −0.771953 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 58934.5 | 1.87209 | 0.936045 | − | 0.351881i | \(-0.114458\pi\) | ||||
0.936045 | + | 0.351881i | \(0.114458\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 116560. | 3.69150 |
(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 | 784.4.a.bh.1.4 | 4 | ||
4.3 | odd | 2 | 392.4.a.n.1.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 784.4.a.bh.1.1 | 4 | ||
28.3 | even | 6 | 392.4.i.o.177.1 | 8 | |||
28.11 | odd | 6 | 392.4.i.o.177.4 | 8 | |||
28.19 | even | 6 | 392.4.i.o.361.1 | 8 | |||
28.23 | odd | 6 | 392.4.i.o.361.4 | 8 | |||
28.27 | even | 2 | 392.4.a.n.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.4.a.n.1.1 | ✓ | 4 | 4.3 | odd | 2 | ||
392.4.a.n.1.4 | yes | 4 | 28.27 | even | 2 | ||
392.4.i.o.177.1 | 8 | 28.3 | even | 6 | |||
392.4.i.o.177.4 | 8 | 28.11 | odd | 6 | |||
392.4.i.o.361.1 | 8 | 28.19 | even | 6 | |||
392.4.i.o.361.4 | 8 | 28.23 | odd | 6 | |||
784.4.a.bh.1.1 | 4 | 7.6 | odd | 2 | inner | ||
784.4.a.bh.1.4 | 4 | 1.1 | even | 1 | trivial |