Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,4,Mod(1,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2240.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.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: | \(132.164278413\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 68x^{2} - 168x - 99 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 1120) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.914579\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1 |
$q$-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 | ||||||||
\(3\) | 4.75423 | 0.914953 | 0.457476 | − | 0.889222i | \(-0.348753\pi\) | ||||
0.457476 | + | 0.889222i | \(0.348753\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.39727 | −0.162862 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 47.7308 | 1.30831 | 0.654154 | − | 0.756361i | \(-0.273025\pi\) | ||||
0.654154 | + | 0.756361i | \(0.273025\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.7494 | −1.04005 | −0.520025 | − | 0.854151i | \(-0.674077\pi\) | ||||
−0.520025 | + | 0.854151i | \(0.674077\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −23.7712 | −0.409179 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 78.2159 | 1.11589 | 0.557945 | − | 0.829878i | \(-0.311590\pi\) | ||||
0.557945 | + | 0.829878i | \(0.311590\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.0153 | 0.277898 | 0.138949 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138949 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 33.2796 | 0.345820 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −32.9847 | −0.299034 | −0.149517 | − | 0.988759i | \(-0.547772\pi\) | ||||
−0.149517 | + | 0.988759i | \(0.547772\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −149.270 | −1.06396 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 158.595 | 1.01553 | 0.507763 | − | 0.861497i | \(-0.330472\pi\) | ||||
0.507763 | + | 0.861497i | \(0.330472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −55.9277 | −0.324029 | −0.162015 | − | 0.986788i | \(-0.551799\pi\) | ||||
−0.162015 | + | 0.986788i | \(0.551799\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 226.923 | 1.19704 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.0000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 165.083 | 0.733499 | 0.366750 | − | 0.930320i | \(-0.380471\pi\) | ||||
0.366750 | + | 0.930320i | \(0.380471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −231.766 | −0.951597 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 69.2477 | 0.263772 | 0.131886 | − | 0.991265i | \(-0.457897\pi\) | ||||
0.131886 | + | 0.991265i | \(0.457897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −221.017 | −0.783832 | −0.391916 | − | 0.920001i | \(-0.628188\pi\) | ||||
−0.391916 | + | 0.920001i | \(0.628188\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21.9863 | 0.0728340 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 83.8679 | 0.260285 | 0.130142 | − | 0.991495i | \(-0.458457\pi\) | ||||
0.130142 | + | 0.991495i | \(0.458457\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 371.857 | 1.02099 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −63.4374 | −0.164411 | −0.0822057 | − | 0.996615i | \(-0.526196\pi\) | ||||
−0.0822057 | + | 0.996615i | \(0.526196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −238.654 | −0.585093 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 109.420 | 0.254264 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 244.152 | 0.538743 | 0.269371 | − | 0.963036i | \(-0.413184\pi\) | ||||
0.269371 | + | 0.963036i | \(0.413184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −461.583 | −0.968846 | −0.484423 | − | 0.874834i | \(-0.660970\pi\) | ||||
−0.484423 | + | 0.874834i | \(0.660970\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −30.7809 | −0.0615560 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 243.747 | 0.465125 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 620.922 | 1.13220 | 0.566102 | − | 0.824335i | \(-0.308451\pi\) | ||||
0.566102 | + | 0.824335i | \(0.308451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −156.817 | −0.273602 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −293.354 | −0.490348 | −0.245174 | − | 0.969479i | \(-0.578845\pi\) | ||||
−0.245174 | + | 0.969479i | \(0.578845\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 993.671 | 1.59316 | 0.796578 | − | 0.604536i | \(-0.206641\pi\) | ||||
0.796578 | + | 0.604536i | \(0.206641\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 118.856 | 0.182991 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 334.116 | 0.494494 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −345.852 | −0.492549 | −0.246275 | − | 0.969200i | \(-0.579206\pi\) | ||||
−0.246275 | + | 0.969200i | \(0.579206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −590.938 | −0.810614 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 313.818 | 0.415013 | 0.207506 | − | 0.978234i | \(-0.433465\pi\) | ||||
0.207506 | + | 0.978234i | \(0.433465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −391.079 | −0.499041 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 753.995 | 0.929159 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 529.928 | 0.631148 | 0.315574 | − | 0.948901i | \(-0.397803\pi\) | ||||
0.315574 | + | 0.948901i | \(0.397803\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −341.246 | −0.393102 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −265.893 | −0.296471 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −115.076 | −0.124280 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 121.755 | 0.127447 | 0.0637234 | − | 0.997968i | \(-0.479702\pi\) | ||||
0.0637234 | + | 0.997968i | \(0.479702\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −209.885 | −0.213073 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 357.751 | 0.352451 | 0.176225 | − | 0.984350i | \(-0.443611\pi\) | ||||
0.176225 | + | 0.984350i | \(0.443611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −768.986 | −0.735635 | −0.367818 | − | 0.929898i | \(-0.619895\pi\) | ||||
−0.367818 | + | 0.929898i | \(0.619895\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −166.398 | −0.154655 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1110.71 | 1.00352 | 0.501761 | − | 0.865007i | \(-0.332686\pi\) | ||||
0.501761 | + | 0.865007i | \(0.332686\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 441.419 | 0.387892 | 0.193946 | − | 0.981012i | \(-0.437871\pi\) | ||||
0.193946 | + | 0.981012i | \(0.437871\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 784.843 | 0.671117 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −106.282 | −0.0884796 | −0.0442398 | − | 0.999021i | \(-0.514087\pi\) | ||||
−0.0442398 | + | 0.999021i | \(0.514087\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 164.924 | 0.133732 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 214.364 | 0.169384 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 547.511 | 0.421767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 947.232 | 0.711670 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 329.219 | 0.241339 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −160.779 | −0.112337 | −0.0561686 | − | 0.998421i | \(-0.517888\pi\) | ||||
−0.0561686 | + | 0.998421i | \(0.517888\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1050.77 | −0.717169 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2515.29 | 1.67757 | 0.838787 | − | 0.544459i | \(-0.183265\pi\) | ||||
0.838787 | + | 0.544459i | \(0.183265\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 161.107 | 0.105036 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 746.350 | 0.475819 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −989.039 | −0.616783 | −0.308392 | − | 0.951259i | \(-0.599791\pi\) | ||||
−0.308392 | + | 0.951259i | \(0.599791\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 405.360 | 0.247354 | 0.123677 | − | 0.992323i | \(-0.460531\pi\) | ||||
0.123677 | + | 0.992323i | \(0.460531\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 398.727 | 0.238148 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2326.85 | −1.36071 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −792.973 | −0.454157 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 232.957 | 0.130708 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3444.19 | 1.89368 | 0.946842 | − | 0.321699i | \(-0.104254\pi\) | ||||
0.946842 | + | 0.321699i | \(0.104254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1647.98 | −0.888153 | −0.444076 | − | 0.895989i | \(-0.646468\pi\) | ||||
−0.444076 | + | 0.895989i | \(0.646468\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −343.936 | −0.181736 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 279.638 | 0.144910 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2832.70 | 1.43996 | 0.719982 | − | 0.693992i | \(-0.244150\pi\) | ||||
0.719982 | + | 0.693992i | \(0.244150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −301.596 | −0.150429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −230.893 | −0.113024 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2464.41 | 1.18422 | 0.592109 | − | 0.805858i | \(-0.298295\pi\) | ||||
0.592109 | + | 0.805858i | \(0.298295\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1134.62 | −0.535332 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 799.488 | 0.370457 | 0.185228 | − | 0.982696i | \(-0.440698\pi\) | ||||
0.185228 | + | 0.982696i | \(0.440698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 179.505 | 0.0817048 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −101.204 | −0.0452590 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2338.71 | 1.02780 | 0.513899 | − | 0.857851i | \(-0.328200\pi\) | ||||
0.513899 | + | 0.857851i | \(0.328200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1160.75 | 0.492924 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1231.72 | 0.514319 | 0.257159 | − | 0.966369i | \(-0.417213\pi\) | ||||
0.257159 | + | 0.966369i | \(0.417213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3429.69 | −1.40844 | −0.704218 | − | 0.709984i | \(-0.748702\pi\) | ||||
−0.704218 | + | 0.709984i | \(0.748702\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2194.47 | −0.886448 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −825.415 | −0.328031 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3733.31 | 1.45993 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1044.89 | −0.402140 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 707.531 | 0.268038 | 0.134019 | − | 0.990979i | \(-0.457212\pi\) | ||||
0.134019 | + | 0.990979i | \(0.457212\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −768.906 | −0.286773 | −0.143386 | − | 0.989667i | \(-0.545799\pi\) | ||||
−0.143386 | + | 0.989667i | \(0.545799\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1158.83 | 0.425567 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3274.74 | 1.18434 | 0.592172 | − | 0.805811i | \(-0.298271\pi\) | ||||
0.592172 | + | 0.805811i | \(0.298271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2942.01 | −1.04801 | −0.524004 | − | 0.851716i | \(-0.675562\pi\) | ||||
−0.524004 | + | 0.851716i | \(0.675562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2952.01 | 1.03591 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1110.16 | 0.383833 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −346.238 | −0.117963 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 145.043 | 0.0487013 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1098.54 | 0.363577 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3340.88 | −1.09003 | −0.545014 | − | 0.838427i | \(-0.683476\pi\) | ||||
−0.545014 | + | 0.838427i | \(0.683476\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1394.67 | −0.448645 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1105.08 | 0.350540 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −391.494 | −0.122472 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4724.14 | 1.45766 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3812.98 | −1.16058 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 919.003 | 0.275969 | 0.137984 | − | 0.990434i | \(-0.455938\pi\) | ||||
0.137984 | + | 0.990434i | \(0.455938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −109.932 | −0.0325724 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3716.79 | 1.08675 | 0.543374 | − | 0.839491i | \(-0.317147\pi\) | ||||
0.543374 | + | 0.839491i | \(0.317147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5523.57 | 1.59392 | 0.796960 | − | 0.604032i | \(-0.206440\pi\) | ||||
0.796960 | + | 0.604032i | \(0.206440\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1588.46 | 0.452438 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2943.43 | −0.827599 | −0.413800 | − | 0.910368i | \(-0.635799\pi\) | ||||
−0.413800 | + | 0.910368i | \(0.635799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −419.339 | −0.116403 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1644.26 | −0.450659 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3642.42 | 0.985809 | 0.492905 | − | 0.870083i | \(-0.335935\pi\) | ||||
0.492905 | + | 0.870083i | \(0.335935\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3293.89 | 0.880407 | 0.440204 | − | 0.897898i | \(-0.354906\pi\) | ||||
0.440204 | + | 0.897898i | \(0.354906\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1220.83 | 0.322290 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −245.000 | −0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1121.98 | −0.289028 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1491.97 | 0.379717 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3165.71 | 0.796087 | 0.398043 | − | 0.917367i | \(-0.369689\pi\) | ||||
0.398043 | + | 0.917367i | \(0.369689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1574.39 | −0.391229 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1859.28 | −0.456599 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1392.66 | −0.338022 | −0.169011 | − | 0.985614i | \(-0.554057\pi\) | ||||
−0.169011 | + | 0.985614i | \(0.554057\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1155.58 | 0.277237 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −697.383 | −0.165390 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6122.99 | 1.43559 | 0.717794 | − | 0.696256i | \(-0.245152\pi\) | ||||
0.717794 | + | 0.696256i | \(0.245152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 317.187 | 0.0735270 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2519.40 | 0.577471 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −970.403 | −0.219950 | −0.109975 | − | 0.993934i | \(-0.535077\pi\) | ||||
−0.109975 | + | 0.993934i | \(0.535077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7522.49 | 1.68619 | 0.843097 | − | 0.537761i | \(-0.180730\pi\) | ||||
0.843097 | + | 0.537761i | \(0.180730\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1622.36 | −0.359670 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1193.27 | 0.261662 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3194.79 | −0.692982 | −0.346491 | − | 0.938053i | \(-0.612627\pi\) | ||||
−0.346491 | + | 0.938053i | \(0.612627\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 245.929 | 0.0527720 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −720.884 | −0.153040 | −0.0765201 | − | 0.997068i | \(-0.524381\pi\) | ||||
−0.0765201 | + | 0.997068i | \(0.524381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7815.32 | 1.64160 | 0.820799 | − | 0.571217i | \(-0.193528\pi\) | ||||
0.820799 | + | 0.571217i | \(0.193528\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −547.100 | −0.113710 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 484.734 | 0.0996966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1204.73 | 0.245212 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 578.852 | 0.116608 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4817.55 | 0.960561 | 0.480280 | − | 0.877115i | \(-0.340535\pi\) | ||||
0.480280 | + | 0.877115i | \(0.340535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1220.76 | −0.240933 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7124.78 | −1.39199 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1607.99 | 0.311011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1547.12 | −0.296261 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1700.83 | 0.322476 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2307.91 | 0.433281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5574.91 | −1.03641 | −0.518204 | − | 0.855257i | \(-0.673399\pi\) | ||||
−0.518204 | + | 0.855257i | \(0.673399\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3655.94 | −0.673071 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7028.07 | −1.28143 | −0.640716 | − | 0.767778i | \(-0.721362\pi\) | ||||
−0.640716 | + | 0.767778i | \(0.721362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8279.29 | −1.49512 | −0.747561 | − | 0.664193i | \(-0.768775\pi\) | ||||
−0.747561 | + | 0.664193i | \(0.768775\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 153.904 | 0.0275287 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9385.60 | −1.66293 | −0.831463 | − | 0.555580i | \(-0.812496\pi\) | ||||
−0.831463 | + | 0.555580i | \(0.812496\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7569.85 | 1.32862 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5280.59 | 0.918174 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1800.16 | 0.310104 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1218.74 | −0.208010 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2098.61 | 0.354903 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 587.075 | 0.0983784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4561.41 | −0.757455 | −0.378728 | − | 0.925508i | \(-0.623638\pi\) | ||||
−0.378728 | + | 0.925508i | \(0.623638\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −725.914 | −0.119459 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3104.61 | −0.506337 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5388.05 | −0.870936 | −0.435468 | − | 0.900204i | \(-0.643417\pi\) | ||||
−0.435468 | + | 0.900204i | \(0.643417\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −505.291 | −0.0809547 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2669.47 | −0.423930 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 784.085 | 0.122359 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12282.9 | −1.90024 | −0.950119 | − | 0.311886i | \(-0.899039\pi\) | ||||
−0.950119 | + | 0.311886i | \(0.899039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5073.63 | −0.778181 | −0.389090 | − | 0.921200i | \(-0.627211\pi\) | ||||
−0.389090 | + | 0.921200i | \(0.627211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7276.82 | 1.10658 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5728.69 | 0.863760 | 0.431880 | − | 0.901931i | \(-0.357850\pi\) | ||||
0.431880 | + | 0.901931i | \(0.357850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1466.77 | 0.219290 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2603.00 | 0.385897 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3277.22 | 0.481797 | 0.240899 | − | 0.970550i | \(-0.422558\pi\) | ||||
0.240899 | + | 0.970550i | \(0.422558\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6329.30 | −0.922773 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4503.36 | 0.651144 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4968.35 | −0.712481 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 619.243 | 0.0880769 | 0.0440385 | − | 0.999030i | \(-0.485978\pi\) | ||||
0.0440385 | + | 0.999030i | \(0.485978\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −304.500 | −0.0429584 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −444.062 | −0.0621416 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4043.42 | −0.561288 | −0.280644 | − | 0.959812i | \(-0.590548\pi\) | ||||
−0.280644 | + | 0.959812i | \(0.590548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −594.279 | −0.0818358 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7731.39 | −1.05620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5706.73 | 0.773444 | 0.386722 | − | 0.922196i | \(-0.373607\pi\) | ||||
0.386722 | + | 0.922196i | \(0.373607\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −764.381 | −0.102783 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2632.05 | −0.351152 | −0.175576 | − | 0.984466i | \(-0.556179\pi\) | ||||
−0.175576 | + | 0.984466i | \(0.556179\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1670.58 | −0.221144 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 971.871 | 0.127656 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11822.0 | 1.54088 | 0.770438 | − | 0.637515i | \(-0.220038\pi\) | ||||
0.770438 | + | 0.637515i | \(0.220038\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2579.93 | −0.333690 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11958.3 | 1.53490 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1729.26 | 0.220275 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −965.178 | −0.122017 | −0.0610087 | − | 0.998137i | \(-0.519432\pi\) | ||||
−0.0610087 | + | 0.998137i | \(0.519432\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 765.940 | 0.0961027 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14784.6 | 1.84116 | 0.920582 | − | 0.390550i | \(-0.127715\pi\) | ||||
0.920582 | + | 0.390550i | \(0.127715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2726.44 | 0.337007 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2954.69 | 0.362518 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7879.55 | 0.959643 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −587.656 | −0.0710457 | −0.0355229 | − | 0.999369i | \(-0.511310\pi\) | ||||
−0.0355229 | + | 0.999369i | \(0.511310\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4702.12 | −0.564327 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1709.06 | 0.203626 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1569.09 | −0.185599 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1927.17 | 0.226317 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9406.12 | −1.09670 | −0.548352 | − | 0.836248i | \(-0.684745\pi\) | ||||
−0.548352 | + | 0.836248i | \(0.684745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10083.1 | 1.16727 | 0.583633 | − | 0.812017i | \(-0.301631\pi\) | ||||
0.583633 | + | 0.812017i | \(0.301631\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −368.790 | −0.0423904 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1955.40 | 0.223178 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3231.08 | −0.366189 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11062.4 | −1.24498 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 254.372 | 0.0284284 | 0.0142142 | − | 0.999899i | \(-0.495475\pi\) | ||||
0.0142142 | + | 0.999899i | \(0.495475\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14730.1 | 1.63484 | 0.817418 | − | 0.576046i | \(-0.195405\pi\) | ||||
0.817418 | + | 0.576046i | \(0.195405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3769.98 | −0.415532 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −759.153 | −0.0831011 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −388.166 | −0.0422008 | −0.0211004 | − | 0.999777i | \(-0.506717\pi\) | ||||
−0.0211004 | + | 0.999777i | \(0.506717\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −215.466 | −0.0232660 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10172.9 | 1.09104 | 0.545518 | − | 0.838099i | \(-0.316333\pi\) | ||||
0.545518 | + | 0.838099i | \(0.316333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2649.64 | −0.282258 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16374.5 | 1.73263 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6441.31 | −0.677025 | −0.338513 | − | 0.940962i | \(-0.609924\pi\) | ||||
−0.338513 | + | 0.940962i | \(0.609924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3305.25 | 0.345095 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7834.90 | −0.812618 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1706.23 | 0.175801 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17815.4 | −1.82357 | −0.911785 | − | 0.410668i | \(-0.865296\pi\) | ||||
−0.911785 | + | 0.410668i | \(0.865296\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11675.3 | −1.18727 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2212.14 | 0.223491 | 0.111746 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111746 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9159.44 | 0.919385 | 0.459693 | − | 0.888078i | \(-0.347960\pi\) | ||||
0.459693 | + | 0.888078i | \(0.347960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1329.47 | 0.132586 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6387.57 | 0.632937 | 0.316468 | − | 0.948603i | \(-0.397503\pi\) | ||||
0.316468 | + | 0.948603i | \(0.397503\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4346.45 | 0.427933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13467.3 | 1.31750 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10549.3 | −1.02549 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 575.382 | 0.0555797 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 278.951 | 0.0267763 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10712.9 | 1.02189 | 0.510943 | − | 0.859615i | \(-0.329296\pi\) | ||||
0.510943 | + | 0.859615i | \(0.329296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8047.70 | −0.762876 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1097.72 | −0.103412 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −608.775 | −0.0569960 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11230.7 | 1.04499 | 0.522495 | − | 0.852643i | \(-0.325001\pi\) | ||||
0.522495 | + | 0.852643i | \(0.325001\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11716.4 | 1.08350 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19995.2 | −1.83782 | −0.918909 | − | 0.394470i | \(-0.870928\pi\) | ||||
−0.918909 | + | 0.394470i | \(0.870928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12404.6 | 1.13322 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1049.43 | 0.0952893 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2053.48 | −0.185334 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13856.6 | 1.24310 | 0.621548 | − | 0.783376i | \(-0.286504\pi\) | ||||
0.621548 | + | 0.783376i | \(0.286504\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3800.95 | 0.338950 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13761.4 | −1.21986 | −0.609931 | − | 0.792455i | \(-0.708803\pi\) | ||||
−0.609931 | + | 0.792455i | \(0.708803\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1788.75 | −0.157621 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 853.411 | 0.0747560 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14019.8 | 1.22086 | 0.610428 | − | 0.792072i | \(-0.290998\pi\) | ||||
0.610428 | + | 0.792072i | \(0.290998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6955.70 | 0.602156 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3435.49 | −0.295674 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3844.93 | 0.328986 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4003.08 | 0.340533 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11118.8 | 0.940387 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15380.3 | −1.29332 | −0.646661 | − | 0.762777i | \(-0.723835\pi\) | ||||
−0.646661 | + | 0.762777i | \(0.723835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3737.35 | 0.312472 | 0.156236 | − | 0.987720i | \(-0.450064\pi\) | ||||
0.156236 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 831.991 | 0.0691639 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4374.43 | −0.361581 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11079.0 | −0.910578 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1073.60 | −0.0877406 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3375.78 | −0.274337 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5553.57 | −0.448788 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5855.88 | 0.470577 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2338.81 | 0.186901 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5552.39 | 0.441249 | 0.220624 | − | 0.975359i | \(-0.429190\pi\) | ||||
0.220624 | + | 0.975359i | \(0.429190\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16305.6 | −1.28865 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2207.09 | −0.173471 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25025.1 | 1.95612 | 0.978058 | − | 0.208335i | \(-0.0668043\pi\) | ||||
0.978058 | + | 0.208335i | \(0.0668043\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2029.70 | 0.157788 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3650.10 | 0.282213 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2420.96 | −0.186166 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3924.21 | −0.300133 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14957.0 | −1.13779 | −0.568896 | − | 0.822409i | \(-0.692629\pi\) | ||||
−0.568896 | + | 0.822409i | \(0.692629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10774.4 | 0.815225 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17749.0 | 1.33577 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8173.82 | 0.611875 | 0.305937 | − | 0.952052i | \(-0.401030\pi\) | ||||
0.305937 | + | 0.952052i | \(0.401030\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 531.411 | 0.0395693 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4136.56 | −0.306383 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7344.79 | 0.541141 | 0.270571 | − | 0.962700i | \(-0.412788\pi\) | ||||
0.270571 | + | 0.962700i | \(0.412788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22283.4 | −1.63315 | −0.816576 | − | 0.577238i | \(-0.804131\pi\) | ||||
−0.816576 | + | 0.577238i | \(0.804131\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3363.77 | 0.245242 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −824.618 | −0.0598069 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9774.34 | −0.705218 | −0.352609 | − | 0.935771i | \(-0.614706\pi\) | ||||
−0.352609 | + | 0.935771i | \(0.614706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3655.56 | −0.262383 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2196.73 | 0.156860 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3027.92 | −0.215101 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1071.82 | −0.0757510 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26794.3 | −1.88402 | −0.942011 | − | 0.335582i | \(-0.891067\pi\) | ||||
−0.942011 | + | 0.335582i | \(0.891067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1287.19 | −0.0900471 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15568.9 | 1.08362 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3865.32 | −0.267672 | −0.133836 | − | 0.991003i | \(-0.542730\pi\) | ||||
−0.133836 | + | 0.991003i | \(0.542730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2737.56 | −0.188620 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13987.0 | −0.958878 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 509.159 | 0.0347306 | 0.0173653 | − | 0.999849i | \(-0.494472\pi\) | ||||
0.0173653 | + | 0.999849i | \(0.494472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11322.1 | 0.768450 | 0.384225 | − | 0.923240i | \(-0.374469\pi\) | ||||
0.384225 | + | 0.923240i | \(0.374469\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2730.36 | −0.184393 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4736.16 | −0.318268 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24447.3 | 1.63474 | 0.817368 | − | 0.576116i | \(-0.195432\pi\) | ||||
0.817368 | + | 0.576116i | \(0.195432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5277.97 | 0.351189 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4088.51 | −0.270709 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13210.2 | 0.870400 | 0.435200 | − | 0.900334i | \(-0.356678\pi\) | ||||
0.435200 | + | 0.900334i | \(0.356678\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1646.10 | −0.107930 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2283.50 | 0.148996 | 0.0744979 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744979 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4226.49 | 0.274438 | 0.137219 | − | 0.990541i | \(-0.456184\pi\) | ||||
0.137219 | + | 0.990541i | \(0.456184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4923.63 | 0.318162 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3709.49 | 0.238552 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5222.71 | 0.332655 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 12912.1 | 0.818505 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18142.7 | 1.14461 | 0.572305 | − | 0.820041i | \(-0.306049\pi\) | ||||
0.572305 | + | 0.820041i | \(0.306049\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15883.3 | −0.997324 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 803.895 | 0.0502388 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2388.72 | −0.148579 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1289.96 | 0.0798590 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14059.8 | −0.866350 | −0.433175 | − | 0.901310i | \(-0.642607\pi\) | ||||
−0.433175 | + | 0.901310i | \(0.642607\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29418.6 | −1.80429 | −0.902144 | − | 0.431436i | \(-0.858007\pi\) | ||||
−0.902144 | + | 0.431436i | \(0.858007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5253.83 | 0.320728 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4740.48 | −0.288049 | −0.144024 | − | 0.989574i | \(-0.546004\pi\) | ||||
−0.144024 | + | 0.989574i | \(0.546004\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11653.6 | 0.704842 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1861.25 | −0.112056 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14043.1 | −0.841573 | −0.420787 | − | 0.907160i | \(-0.638246\pi\) | ||||
−0.420787 | + | 0.907160i | \(0.638246\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12576.5 | −0.750234 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4369.44 | −0.259464 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3803.31 | −0.224819 | −0.112410 | − | 0.993662i | \(-0.535857\pi\) | ||||
−0.112410 | + | 0.993662i | \(0.535857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13101.4 | 0.770929 | 0.385464 | − | 0.922723i | \(-0.374041\pi\) | ||||
0.385464 | + | 0.922723i | \(0.374041\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18127.8 | −1.06188 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −805.535 | −0.0469734 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5231.20 | −0.303677 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4369.16 | 0.252498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22031.7 | −1.26755 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30039.1 | 1.72054 | 0.860268 | − | 0.509842i | \(-0.170296\pi\) | ||||
0.860268 | + | 0.509842i | \(0.170296\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3731.75 | −0.212793 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7794.32 | −0.442482 | −0.221241 | − | 0.975219i | \(-0.571011\pi\) | ||||
−0.221241 | + | 0.975219i | \(0.571011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 852.285 | 0.0481704 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17670.5 | 0.994323 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20258.0 | 1.13492 | 0.567461 | − | 0.823401i | \(-0.307926\pi\) | ||||
0.567461 | + | 0.823401i | \(0.307926\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4945.20 | 0.275834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26260.3 | 1.45836 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3092.54 | 0.170996 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22210.0 | −1.22273 | −0.611367 | − | 0.791347i | \(-0.709380\pi\) | ||||
−0.611367 | + | 0.791347i | \(0.709380\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1469.20 | −0.0805342 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2026.80 | −0.110620 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5416.27 | 0.294341 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13993.8 | −0.757214 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3033.60 | 0.163449 | 0.0817244 | − | 0.996655i | \(-0.473957\pi\) | ||||
0.0817244 | + | 0.996655i | \(0.473957\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3799.43 | 0.203838 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1993.64 | −0.106503 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2504.26 | 0.133214 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16465.4 | −0.872171 | −0.436086 | − | 0.899905i | \(-0.643636\pi\) | ||||
−0.436086 | + | 0.899905i | \(0.643636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1520.80 | 0.0802174 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1844.76 | 0.0968958 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11634.3 | 0.608526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17316.9 | 0.901969 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32975.7 | −1.71041 | −0.855206 | − | 0.518288i | \(-0.826570\pi\) | ||||
−0.855206 | + | 0.518288i | \(0.826570\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5382.90 | −0.278044 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15659.9 | 0.805531 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3964.86 | 0.203105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8657.41 | 0.441658 | 0.220829 | − | 0.975313i | \(-0.429124\pi\) | ||||
0.220829 | + | 0.975313i | \(0.429124\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21759.4 | 1.10549 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17287.0 | −0.874671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22964.1 | 1.15716 | 0.578580 | − | 0.815625i | \(-0.303607\pi\) | ||||
0.578580 | + | 0.815625i | \(0.303607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1164.79 | −0.0584542 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29637.1 | 1.48127 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19362.2 | 0.963803 | 0.481901 | − | 0.876226i | \(-0.339946\pi\) | ||||
0.481901 | + | 0.876226i | \(0.339946\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5334.16 | −0.264447 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14763.9 | −0.728986 | −0.364493 | − | 0.931206i | \(-0.618758\pi\) | ||||
−0.364493 | + | 0.931206i | \(0.618758\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −17220.9 | −0.846881 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1379.94 | −0.0675897 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7775.00 | 0.379295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28089.6 | 1.36485 | 0.682425 | − | 0.730956i | \(-0.260925\pi\) | ||||
0.682425 | + | 0.730956i | \(0.260925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15050.5 | 0.728382 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8239.92 | 0.397194 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19596.3 | −0.940871 | −0.470436 | − | 0.882434i | \(-0.655903\pi\) | ||||
−0.470436 | + | 0.882434i | \(0.655903\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7485.01 | −0.357956 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12978.5 | −0.618225 | −0.309113 | − | 0.951025i | \(-0.600032\pi\) | ||||
−0.309113 | + | 0.951025i | \(0.600032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3089.93 | 0.146610 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1719.68 | 0.0812748 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11902.2 | −0.560320 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14638.2 | 0.686433 | 0.343217 | − | 0.939256i | \(-0.388484\pi\) | ||||
0.343217 | + | 0.939256i | \(0.388484\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6621.03 | −0.309275 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16852.6 | 0.784147 | 0.392074 | − | 0.919934i | \(-0.371758\pi\) | ||||
0.392074 | + | 0.919934i | \(0.371758\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1398.19 | −0.0648058 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5493.90 | 0.253658 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1593.75 | 0.0733019 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14002.0 | −0.641526 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −23673.4 | −1.08048 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14163.5 | −0.643972 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13934.1 | −0.631126 | −0.315563 | − | 0.948905i | \(-0.602193\pi\) | ||||
−0.315563 | + | 0.948905i | \(0.602193\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29110.1 | 1.31349 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −743.976 | −0.0334422 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22501.9 | 1.00765 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1507.98 | 0.0672737 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36608.0 | −1.62701 | −0.813503 | − | 0.581561i | \(-0.802442\pi\) | ||||
−0.813503 | + | 0.581561i | \(0.802442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6559.80 | 0.290449 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2330.23 | −0.102790 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 47428.7 | 2.08434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1154.47 | 0.0505460 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4613.52 | −0.201244 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20466.8 | −0.889464 | −0.444732 | − | 0.895664i | \(-0.646701\pi\) | ||||
−0.444732 | + | 0.895664i | \(0.646701\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17371.6 | −0.752157 | −0.376078 | − | 0.926588i | \(-0.622728\pi\) | ||||
−0.376078 | + | 0.926588i | \(0.622728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35763.7 | 1.54279 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12322.1 | −0.529599 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5086.77 | −0.217826 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1500.55 | 0.0640213 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23358.9 | −0.992972 | −0.496486 | − | 0.868045i | \(-0.665377\pi\) | ||||
−0.496486 | + | 0.868045i | \(0.665377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 191.031 | 0.00809104 | 0.00404552 | − | 0.999992i | \(-0.498712\pi\) | ||||
0.00404552 | + | 0.999992i | \(0.498712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5673.09 | 0.239408 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42864.5 | 1.80235 | 0.901177 | − | 0.433452i | \(-0.142705\pi\) | ||||
0.901177 | + | 0.433452i | \(0.142705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8271.80 | 0.346552 | 0.173276 | − | 0.984873i | \(-0.444565\pi\) | ||||
0.173276 | + | 0.984873i | \(0.444565\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15188.8 | −0.634046 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3832.58 | 0.159413 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3997.44 | −0.165673 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8348.32 | 0.344755 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42316.8 | −1.74129 | −0.870643 | − | 0.491915i | \(-0.836297\pi\) | ||||
−0.870643 | + | 0.491915i | \(0.836297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 763.229 | 0.0312940 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3427.25 | −0.140025 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −897.527 | −0.0365395 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6630.62 | 0.268986 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37155.8 | 1.50198 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5445.21 | −0.219341 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33770.7 | −1.35555 | −0.677776 | − | 0.735268i | \(-0.737056\pi\) | ||||
−0.677776 | + | 0.735268i | \(0.737056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 506.022 | 0.0202404 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13518.3 | 0.538830 | 0.269415 | − | 0.963024i | \(-0.413170\pi\) | ||||
0.269415 | + | 0.963024i | \(0.413170\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −27385.8 | −1.08777 | −0.543883 | − | 0.839161i | \(-0.683046\pi\) | ||||
−0.543883 | + | 0.839161i | \(0.683046\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2304.54 | 0.0912176 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34154.1 | −1.34718 | −0.673592 | − | 0.739103i | \(-0.735249\pi\) | ||||
−0.673592 | + | 0.739103i | \(0.735249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11693.6 | −0.459646 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5727.55 | 0.224357 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16507.8 | −0.644406 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30269.6 | −1.17755 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −535.389 | −0.0207562 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −875.000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −43254.1 | −1.66544 | −0.832719 | − | 0.553697i | \(-0.813217\pi\) | ||||
−0.832719 | + | 0.553697i | \(0.813217\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22903.8 | 0.878868 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32955.0 | −1.26025 | −0.630125 | − | 0.776493i | \(-0.716997\pi\) | ||||
−0.630125 | + | 0.776493i | \(0.716997\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37636.3 | 1.43439 | 0.717193 | − | 0.696875i | \(-0.245427\pi\) | ||||
0.717193 | + | 0.696875i | \(0.245427\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5803.77 | −0.220442 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30670.1 | 1.16099 | 0.580496 | − | 0.814263i | \(-0.302859\pi\) | ||||
0.580496 | + | 0.814263i | \(0.302859\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1125.45 | −0.0424595 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28206.0 | −1.06053 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1930.24 | 0.0723327 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6158.60 | −0.230010 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7644.74 | 0.284560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8869.82 | −0.329060 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4961.82 | −0.183465 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7355.36 | −0.271064 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17148.5 | 0.629872 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24717.3 | −0.904877 | −0.452439 | − | 0.891795i | \(-0.649446\pi\) | ||||
−0.452439 | + | 0.891795i | \(0.649446\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1573.13 | −0.0574008 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25484.3 | −0.926821 | −0.463411 | − | 0.886144i | \(-0.653374\pi\) | ||||
−0.463411 | + | 0.886144i | \(0.653374\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14978.8 | 0.542964 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10972.4 | 0.396432 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17607.1 | 0.634064 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28510.6 | 1.02337 | 0.511686 | − | 0.859172i | \(-0.329021\pi\) | ||||
0.511686 | + | 0.859172i | \(0.329021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26504.4 | −0.948264 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14300.8 | 0.509987 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4127.07 | 0.146700 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3381.44 | 0.119807 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23929.6 | −0.845106 | −0.422553 | − | 0.906338i | \(-0.638866\pi\) | ||||
−0.422553 | + | 0.906338i | \(0.638866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1127.75 | 0.0396998 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33413.1 | −1.17245 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −18666.5 | −0.652900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24744.6 | 0.862721 | 0.431360 | − | 0.902180i | \(-0.358034\pi\) | ||||
0.431360 | + | 0.902180i | \(0.358034\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39361.7 | −1.36797 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16805.7 | −0.582199 | −0.291100 | − | 0.956693i | \(-0.594021\pi\) | ||||
−0.291100 | + | 0.956693i | \(0.594021\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2284.11 | −0.0788770 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5224.45 | 0.179843 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5212.41 | −0.178860 | −0.0894301 | − | 0.995993i | \(-0.528505\pi\) | ||||
−0.0894301 | + | 0.995993i | \(0.528505\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −48440.9 | −1.65696 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44621.3 | −1.52150 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28456.5 | −0.967257 | −0.483628 | − | 0.875273i | \(-0.660681\pi\) | ||||
−0.483628 | + | 0.875273i | \(0.660681\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3537.66 | −0.119870 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 35988.8 | 1.21563 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6923.27 | −0.233122 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26663.1 | −0.895005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4884.11 | −0.163435 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3844.53 | 0.128249 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50857.6 | −1.69128 | −0.845640 | − | 0.533753i | \(-0.820781\pi\) | ||||
−0.845640 | + | 0.533753i | \(0.820781\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8558.38 | 0.283731 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33639.8 | −1.11180 | −0.555898 | − | 0.831251i | \(-0.687625\pi\) | ||||
−0.555898 | + | 0.831251i | \(0.687625\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2837.52 | 0.0934909 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5794.15 | −0.190319 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36600.6 | −1.19852 | −0.599262 | − | 0.800553i | \(-0.704539\pi\) | ||||
−0.599262 | + | 0.800553i | \(0.704539\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25293.9 | 0.825736 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1941.04 | −0.0631728 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39139.4 | −1.26994 | −0.634971 | − | 0.772536i | \(-0.718988\pi\) | ||||
−0.634971 | + | 0.772536i | \(0.718988\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16373.7 | −0.529655 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2791.09 | 0.0900116 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7290.18 | 0.234393 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30319.0 | −0.971862 | −0.485931 | − | 0.873997i | \(-0.661519\pi\) | ||||
−0.485931 | + | 0.873997i | \(0.661519\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21686.0 | −0.693036 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14710.1 | 0.468684 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40669.9 | 1.29191 | 0.645953 | − | 0.763378i | \(-0.276460\pi\) | ||||
0.645953 | + | 0.763378i | \(0.276460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24641.9 | −0.780416 |
(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 | 2240.4.a.cl.1.3 | 4 | ||
4.3 | odd | 2 | 2240.4.a.ca.1.2 | 4 | |||
8.3 | odd | 2 | 1120.4.a.p.1.3 | yes | 4 | ||
8.5 | even | 2 | 1120.4.a.e.1.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.4.a.e.1.2 | ✓ | 4 | 8.5 | even | 2 | ||
1120.4.a.p.1.3 | yes | 4 | 8.3 | odd | 2 | ||
2240.4.a.ca.1.2 | 4 | 4.3 | odd | 2 | |||
2240.4.a.cl.1.3 | 4 | 1.1 | even | 1 | trivial |