Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,4,Mod(1,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, 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("1900.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.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: | \(112.103629011\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 76) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1 |
$q$-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 | ||||||||
\(3\) | 5.37228 | 1.03390 | 0.516948 | − | 0.856017i | \(-0.327068\pi\) | ||||
0.516948 | + | 0.856017i | \(0.327068\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.4891 | 1.43028 | 0.715139 | − | 0.698982i | \(-0.246363\pi\) | ||||
0.715139 | + | 0.698982i | \(0.246363\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.86141 | 0.0689410 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −49.8614 | −1.36671 | −0.683354 | − | 0.730088i | \(-0.739479\pi\) | ||||
−0.683354 | + | 0.730088i | \(0.739479\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 49.0951 | 1.04743 | 0.523713 | − | 0.851895i | \(-0.324547\pi\) | ||||
0.523713 | + | 0.851895i | \(0.324547\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −17.2337 | −0.245870 | −0.122935 | − | 0.992415i | \(-0.539231\pi\) | ||||
−0.122935 | + | 0.992415i | \(0.539231\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 142.307 | 1.47876 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −166.965 | −1.51368 | −0.756838 | − | 0.653603i | \(-0.773257\pi\) | ||||
−0.756838 | + | 0.653603i | \(0.773257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −135.052 | −0.962618 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −109.198 | −0.699228 | −0.349614 | − | 0.936894i | \(-0.613687\pi\) | ||||
−0.349614 | + | 0.936894i | \(0.613687\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −273.783 | −1.58622 | −0.793110 | − | 0.609079i | \(-0.791539\pi\) | ||||
−0.793110 | + | 0.609079i | \(0.791539\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −267.870 | −1.41303 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −167.022 | −0.742114 | −0.371057 | − | 0.928610i | \(-0.621005\pi\) | ||||
−0.371057 | + | 0.928610i | \(0.621005\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 263.753 | 1.08293 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15.1684 | 0.0577783 | 0.0288892 | − | 0.999583i | \(-0.490803\pi\) | ||||
0.0288892 | + | 0.999583i | \(0.490803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −413.557 | −1.46667 | −0.733335 | − | 0.679867i | \(-0.762037\pi\) | ||||
−0.733335 | + | 0.679867i | \(0.762037\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 161.438 | 0.501023 | 0.250512 | − | 0.968114i | \(-0.419401\pi\) | ||||
0.250512 | + | 0.968114i | \(0.419401\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 358.674 | 1.04570 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −92.5842 | −0.254204 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 490.791 | 1.27199 | 0.635993 | − | 0.771695i | \(-0.280591\pi\) | ||||
0.635993 | + | 0.771695i | \(0.280591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −102.073 | −0.237192 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −335.970 | −0.741349 | −0.370674 | − | 0.928763i | \(-0.620873\pi\) | ||||
−0.370674 | + | 0.928763i | \(0.620873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 725.149 | 1.52206 | 0.761032 | − | 0.648715i | \(-0.224693\pi\) | ||||
0.761032 | + | 0.648715i | \(0.224693\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 49.3070 | 0.0986048 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −497.709 | −0.907535 | −0.453768 | − | 0.891120i | \(-0.649920\pi\) | ||||
−0.453768 | + | 0.891120i | \(0.649920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −896.981 | −1.56498 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −798.554 | −1.33480 | −0.667401 | − | 0.744698i | \(-0.732593\pi\) | ||||
−0.667401 | + | 0.744698i | \(0.732593\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 311.174 | 0.498906 | 0.249453 | − | 0.968387i | \(-0.419749\pi\) | ||||
0.249453 | + | 0.968387i | \(0.419749\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1320.79 | −1.95477 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −665.723 | −0.948097 | −0.474049 | − | 0.880499i | \(-0.657208\pi\) | ||||
−0.474049 | + | 0.880499i | \(0.657208\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −775.793 | −1.06419 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 372.440 | 0.492537 | 0.246269 | − | 0.969202i | \(-0.420795\pi\) | ||||
0.246269 | + | 0.969202i | \(0.420795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −586.644 | −0.722929 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −673.783 | −0.802481 | −0.401240 | − | 0.915973i | \(-0.631421\pi\) | ||||
−0.401240 | + | 0.915973i | \(0.631421\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1300.49 | 1.49811 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1470.84 | −1.63999 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 960.505 | 1.00541 | 0.502704 | − | 0.864459i | \(-0.332339\pi\) | ||||
0.502704 | + | 0.864459i | \(0.332339\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −92.8124 | −0.0942221 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1889.68 | 1.86169 | 0.930845 | − | 0.365415i | \(-0.119073\pi\) | ||||
0.930845 | + | 0.365415i | \(0.119073\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −760.217 | −0.727247 | −0.363624 | − | 0.931546i | \(-0.618461\pi\) | ||||
−0.363624 | + | 0.931546i | \(0.618461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −681.730 | −0.615938 | −0.307969 | − | 0.951396i | \(-0.599649\pi\) | ||||
−0.307969 | + | 0.951396i | \(0.599649\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1310.76 | −1.15182 | −0.575910 | − | 0.817513i | \(-0.695352\pi\) | ||||
−0.575910 | + | 0.817513i | \(0.695352\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −897.288 | −0.767268 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 713.413 | 0.593914 | 0.296957 | − | 0.954891i | \(-0.404028\pi\) | ||||
0.296957 | + | 0.954891i | \(0.404028\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 91.3859 | 0.0722105 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −456.505 | −0.351662 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1155.16 | 0.867889 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 81.4891 | 0.0597368 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 107.847 | 0.0753535 | 0.0376768 | − | 0.999290i | \(-0.488004\pi\) | ||||
0.0376768 | + | 0.999290i | \(0.488004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2221.74 | −1.51638 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 373.247 | 0.248937 | 0.124469 | − | 0.992224i | \(-0.460277\pi\) | ||||
0.124469 | + | 0.992224i | \(0.460277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −503.293 | −0.328128 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3118.25 | 1.94460 | 0.972301 | − | 0.233732i | \(-0.0750940\pi\) | ||||
0.972301 | + | 0.233732i | \(0.0750940\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −56.3774 | −0.0344019 | −0.0172010 | − | 0.999852i | \(-0.505476\pi\) | ||||
−0.0172010 | + | 0.999852i | \(0.505476\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 867.288 | 0.518006 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2447.95 | −1.43152 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1926.90 | 1.08114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1810.51 | −0.995457 | −0.497728 | − | 0.867333i | \(-0.665832\pi\) | ||||
−0.497728 | + | 0.867333i | \(0.665832\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2894.72 | 1.56006 | 0.780029 | − | 0.625744i | \(-0.215204\pi\) | ||||
0.780029 | + | 0.625744i | \(0.215204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −32.0789 | −0.0169505 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1381.71 | −0.702371 | −0.351185 | − | 0.936306i | \(-0.614221\pi\) | ||||
−0.351185 | + | 0.936306i | \(0.614221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2636.67 | 1.31510 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4422.75 | −2.16498 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3740.83 | 1.79757 | 0.898785 | − | 0.438389i | \(-0.144451\pi\) | ||||
0.898785 | + | 0.438389i | \(0.144451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3085.17 | −1.42957 | −0.714783 | − | 0.699347i | \(-0.753474\pi\) | ||||
−0.714783 | + | 0.699347i | \(0.753474\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 213.328 | 0.0970998 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −35.3667 | −0.0158161 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −293.000 | −0.128765 | −0.0643827 | − | 0.997925i | \(-0.520508\pi\) | ||||
−0.0643827 | + | 0.997925i | \(0.520508\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1804.93 | −0.766478 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2996.32 | −1.25115 | −0.625574 | − | 0.780165i | \(-0.715135\pi\) | ||||
−0.625574 | + | 0.780165i | \(0.715135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3265.41 | −1.34097 | −0.670487 | − | 0.741922i | \(-0.733915\pi\) | ||||
−0.670487 | + | 0.741922i | \(0.733915\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3895.71 | 1.57365 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 859.296 | 0.336032 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3577.40 | −1.37681 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1502.27 | −0.569113 | −0.284556 | − | 0.958659i | \(-0.591846\pi\) | ||||
−0.284556 | + | 0.958659i | \(0.591846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4103.30 | 1.53037 | 0.765186 | − | 0.643809i | \(-0.222647\pi\) | ||||
0.765186 | + | 0.643809i | \(0.222647\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5420.95 | −1.96054 | −0.980271 | − | 0.197658i | \(-0.936666\pi\) | ||||
−0.980271 | + | 0.197658i | \(0.936666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1666.05 | 0.593484 | 0.296742 | − | 0.954958i | \(-0.404100\pi\) | ||||
0.296742 | + | 0.954958i | \(0.404100\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2673.83 | −0.938297 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2892.57 | −1.00009 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −310.789 | −0.104354 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 947.367 | 0.313544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5865.90 | 1.91386 | 0.956931 | − | 0.290314i | \(-0.0937598\pi\) | ||||
0.956931 | + | 0.290314i | \(0.0937598\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4290.06 | −1.38005 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7252.26 | −2.26873 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1671.71 | 0.515817 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −846.090 | −0.257530 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5402.94 | 1.62246 | 0.811229 | − | 0.584729i | \(-0.198799\pi\) | ||||
0.811229 | + | 0.584729i | \(0.198799\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2571.34 | 0.751833 | 0.375916 | − | 0.926654i | \(-0.377328\pi\) | ||||
0.375916 | + | 0.926654i | \(0.377328\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3256.08 | 0.939597 | 0.469799 | − | 0.882774i | \(-0.344327\pi\) | ||||
0.469799 | + | 0.882774i | \(0.344327\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7095.63 | −2.02103 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1205.58 | −0.338972 | −0.169486 | − | 0.985533i | \(-0.554211\pi\) | ||||
−0.169486 | + | 0.985533i | \(0.554211\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3576.45 | −0.980234 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3404.52 | −0.921424 | −0.460712 | − | 0.887550i | \(-0.652406\pi\) | ||||
−0.460712 | + | 0.887550i | \(0.652406\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3301.51 | 0.882443 | 0.441221 | − | 0.897398i | \(-0.354545\pi\) | ||||
0.441221 | + | 0.897398i | \(0.354545\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −521.386 | −0.137642 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −932.807 | −0.240296 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2000.85 | 0.509233 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5330.81 | −1.34055 | −0.670275 | − | 0.742113i | \(-0.733824\pi\) | ||||
−0.670275 | + | 0.742113i | \(0.733824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8325.09 | 2.06875 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3812.14 | −0.925272 | −0.462636 | − | 0.886548i | \(-0.653096\pi\) | ||||
−0.462636 | + | 0.886548i | \(0.653096\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4424.26 | −1.06143 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −203.262 | −0.0482055 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −899.159 | −0.210816 | −0.105408 | − | 0.994429i | \(-0.533615\pi\) | ||||
−0.105408 | + | 0.994429i | \(0.533615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3619.75 | −0.829682 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2645.77 | 0.599685 | 0.299842 | − | 0.953989i | \(-0.403066\pi\) | ||||
0.299842 | + | 0.953989i | \(0.403066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 516.529 | 0.115782 | 0.0578909 | − | 0.998323i | \(-0.481562\pi\) | ||||
0.0578909 | + | 0.998323i | \(0.481562\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6986.58 | 1.54889 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2365.14 | −0.513023 | −0.256512 | − | 0.966541i | \(-0.582573\pi\) | ||||
−0.256512 | + | 0.966541i | \(0.582573\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −509.621 | −0.109356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1526.54 | −0.324077 | −0.162038 | − | 0.986784i | \(-0.551807\pi\) | ||||
−0.162038 | + | 0.986784i | \(0.551807\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4764.01 | −1.00067 | −0.500337 | − | 0.865831i | \(-0.666791\pi\) | ||||
−0.500337 | + | 0.865831i | \(0.666791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 401.799 | 0.0826391 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4616.00 | −0.939548 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5160.10 | 1.03949 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3189.07 | −0.635862 | −0.317931 | − | 0.948114i | \(-0.602988\pi\) | ||||
−0.317931 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6733.86 | 1.31562 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8197.14 | −1.58546 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10954.8 | −2.09775 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10151.9 | 1.92479 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5998.56 | −1.11517 | −0.557583 | − | 0.830121i | \(-0.688271\pi\) | ||||
−0.557583 | + | 0.830121i | \(0.688271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4084.10 | −0.751898 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5114.96 | 0.932614 | 0.466307 | − | 0.884623i | \(-0.345584\pi\) | ||||
0.466307 | + | 0.884623i | \(0.345584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2131.63 | −0.384942 | −0.192471 | − | 0.981303i | \(-0.561650\pi\) | ||||
−0.192471 | + | 0.981303i | \(0.561650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4457.03 | −0.789691 | −0.394845 | − | 0.918748i | \(-0.629202\pi\) | ||||
−0.394845 | + | 0.918748i | \(0.629202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5444.78 | 0.955640 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3662.45 | −0.636816 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 327.440 | 0.0564064 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7041.79 | −1.19086 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4276.34 | 0.716602 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4143.68 | −0.688088 | −0.344044 | − | 0.938954i | \(-0.611797\pi\) | ||||
−0.344044 | + | 0.938954i | \(0.611797\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −310.895 | −0.0511620 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5148.60 | 0.832231 | 0.416115 | − | 0.909312i | \(-0.363391\pi\) | ||||
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3832.66 | 0.614045 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13651.2 | 2.16790 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 415.184 | 0.0653581 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5873.56 | 0.908672 | 0.454336 | − | 0.890830i | \(-0.349877\pi\) | ||||
0.454336 | + | 0.890830i | \(0.349877\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5167.58 | 0.792590 | 0.396295 | − | 0.918123i | \(-0.370296\pi\) | ||||
0.396295 | + | 0.918123i | \(0.370296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6630.37 | −1.00827 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7191.17 | −1.08427 | −0.542135 | − | 0.840291i | \(-0.682384\pi\) | ||||
−0.542135 | + | 0.840291i | \(0.682384\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2452.47 | −0.363582 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7049.62 | −1.03639 | −0.518196 | − | 0.855262i | \(-0.673396\pi\) | ||||
−0.518196 | + | 0.855262i | \(0.673396\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6205.84 | 0.897307 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6935.53 | −0.986463 | −0.493231 | − | 0.869898i | \(-0.664184\pi\) | ||||
−0.493231 | + | 0.869898i | \(0.664184\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.2346 | 0.00398330 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13000.6 | 1.81929 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6346.92 | 0.881048 | 0.440524 | − | 0.897741i | \(-0.354793\pi\) | ||||
0.440524 | + | 0.897741i | \(0.354793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5361.10 | −0.732389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11363.0 | 1.54004 | 0.770022 | − | 0.638017i | \(-0.220245\pi\) | ||||
0.770022 | + | 0.638017i | \(0.220245\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 579.386 | 0.0779077 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3848.09 | 0.513390 | 0.256695 | − | 0.966493i | \(-0.417366\pi\) | ||||
0.256695 | + | 0.966493i | \(0.417366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −769.798 | −0.101114 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1936.75 | 0.252435 | 0.126217 | − | 0.992003i | \(-0.459716\pi\) | ||||
0.126217 | + | 0.992003i | \(0.459716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2877.42 | 0.372167 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2005.19 | 0.257375 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3851.40 | −0.486892 | −0.243446 | − | 0.969914i | \(-0.578278\pi\) | ||||
−0.243446 | + | 0.969914i | \(0.578278\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2703.83 | −0.339251 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1381.47 | −0.172038 | −0.0860189 | − | 0.996294i | \(-0.527415\pi\) | ||||
−0.0860189 | + | 0.996294i | \(0.527415\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13441.4 | −1.66145 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8327.94 | 1.01425 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 368.878 | 0.0445962 | 0.0222981 | − | 0.999751i | \(-0.492902\pi\) | ||||
0.0222981 | + | 0.999751i | \(0.492902\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16752.1 | 2.01052 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8899.56 | −1.06034 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −302.875 | −0.0355680 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1814.85 | −0.211602 | −0.105801 | − | 0.994387i | \(-0.533741\pi\) | ||||
−0.105801 | + | 0.994387i | \(0.533741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4614.01 | 0.534141 | 0.267070 | − | 0.963677i | \(-0.413944\pi\) | ||||
0.267070 | + | 0.963677i | \(0.413944\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 300.501 | 0.0345410 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19208.6 | 2.17697 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13151.1 | −1.48005 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2739.14 | −0.306125 | −0.153062 | − | 0.988217i | \(-0.548914\pi\) | ||||
−0.153062 | + | 0.988217i | \(0.548914\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10827.9 | 1.20174 | 0.600872 | − | 0.799345i | \(-0.294820\pi\) | ||||
0.600872 | + | 0.799345i | \(0.294820\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3172.33 | 0.347261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10359.5 | −1.12627 | −0.563137 | − | 0.826364i | \(-0.690406\pi\) | ||||
−0.563137 | + | 0.826364i | \(0.690406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 667.638 | 0.0720913 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8040.36 | −0.862322 | −0.431161 | − | 0.902275i | \(-0.641896\pi\) | ||||
−0.431161 | + | 0.902275i | \(0.641896\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9726.59 | −1.02920 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14071.8 | −1.47904 | −0.739522 | − | 0.673132i | \(-0.764948\pi\) | ||||
−0.739522 | + | 0.673132i | \(0.764948\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −756.320 | −0.0789661 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15551.2 | 1.61294 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4372.74 | 0.447589 | 0.223795 | − | 0.974636i | \(-0.428155\pi\) | ||||
0.223795 | + | 0.974636i | \(0.428155\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2327.44 | 0.236679 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17819.4 | −1.80029 | −0.900146 | − | 0.435589i | \(-0.856540\pi\) | ||||
−0.900146 | + | 0.435589i | \(0.856540\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7114.51 | −0.714124 | −0.357062 | − | 0.934081i | \(-0.616222\pi\) | ||||
−0.357062 | + | 0.934081i | \(0.616222\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8208.41 | 0.813361 | 0.406681 | − | 0.913570i | \(-0.366686\pi\) | ||||
0.406681 | + | 0.913570i | \(0.366686\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13183.9 | −1.29803 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7422.92 | −0.726178 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20620.5 | 2.00451 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 913.561 | 0.0876920 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11889.5 | −1.13413 | −0.567064 | − | 0.823674i | \(-0.691921\pi\) | ||||
−0.567064 | + | 0.823674i | \(0.691921\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8199.95 | −0.777309 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23760.2 | −2.23836 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13922.4 | −1.29545 | −0.647725 | − | 0.761875i | \(-0.724279\pi\) | ||||
−0.647725 | + | 0.761875i | \(0.724279\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20096.8 | 1.85850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2718.22 | 0.249840 | 0.124920 | − | 0.992167i | \(-0.460133\pi\) | ||||
0.124920 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1881.89 | 0.171919 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21153.0 | −1.90914 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7830.51 | −0.702489 | −0.351244 | − | 0.936284i | \(-0.614241\pi\) | ||||
−0.351244 | + | 0.936284i | \(0.614241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16574.4 | −1.47802 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6554.35 | 0.581002 | 0.290501 | − | 0.956875i | \(-0.406178\pi\) | ||||
0.290501 | + | 0.956875i | \(0.406178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1146.06 | 0.100391 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12611.4 | 1.09821 | 0.549105 | − | 0.835753i | \(-0.314969\pi\) | ||||
0.549105 | + | 0.835753i | \(0.314969\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8242.73 | 0.713575 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2565.98 | 0.220840 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8049.50 | −0.684752 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1574.08 | −0.133130 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1695.01 | 0.142533 | 0.0712666 | − | 0.997457i | \(-0.477296\pi\) | ||||
0.0712666 | + | 0.997457i | \(0.477296\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21001.4 | 1.75589 | 0.877944 | − | 0.478764i | \(-0.158915\pi\) | ||||
0.877944 | + | 0.478764i | \(0.158915\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4718.28 | 0.390003 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15710.2 | 1.29121 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −625.377 | −0.0511093 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 744.696 | 0.0605185 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −16097.1 | −1.29356 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17884.0 | −1.42916 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −555.994 | −0.0441849 | −0.0220925 | − | 0.999756i | \(-0.507033\pi\) | ||||
−0.0220925 | + | 0.999756i | \(0.507033\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17542.7 | −1.38643 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2987.93 | 0.233555 | 0.116778 | − | 0.993158i | \(-0.462744\pi\) | ||||
0.116778 | + | 0.993158i | \(0.462744\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1349.80 | 0.104933 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2074.77 | 0.160414 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17634.4 | −1.35604 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4357.38 | 0.331469 | 0.165735 | − | 0.986170i | \(-0.447001\pi\) | ||||
0.165735 | + | 0.986170i | \(0.447001\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20303.6 | −1.53623 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4616.38 | 0.347422 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1669.67 | −0.124988 | −0.0624941 | − | 0.998045i | \(-0.519905\pi\) | ||||
−0.0624941 | + | 0.998045i | \(0.519905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20550.1 | −1.52209 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20440.1 | −1.50596 | −0.752982 | − | 0.658041i | \(-0.771385\pi\) | ||||
−0.752982 | + | 0.658041i | \(0.771385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6920.98 | −0.507240 | −0.253620 | − | 0.967304i | \(-0.581621\pi\) | ||||
−0.253620 | + | 0.967304i | \(0.581621\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8070.62 | −0.588403 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5021.59 | 0.362307 | 0.181154 | − | 0.983455i | \(-0.442017\pi\) | ||||
0.181154 | + | 0.983455i | \(0.442017\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22044.1 | 1.58225 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9865.61 | 0.704466 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24471.5 | −1.73843 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6784.80 | 0.477068 | 0.238534 | − | 0.971134i | \(-0.423333\pi\) | ||||
0.238534 | + | 0.971134i | \(0.423333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5201.87 | 0.363904 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29122.9 | −2.02700 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22058.5 | −1.52754 | −0.763771 | − | 0.645487i | \(-0.776654\pi\) | ||||
−0.763771 | + | 0.645487i | \(0.776654\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8950.51 | 0.613601 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15616.7 | −1.06524 | −0.532620 | − | 0.846354i | \(-0.678793\pi\) | ||||
−0.532620 | + | 0.846354i | \(0.678793\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26769.6 | 1.81690 | 0.908448 | − | 0.417998i | \(-0.137268\pi\) | ||||
0.908448 | + | 0.417998i | \(0.137268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −926.439 | −0.0625664 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5164.26 | −0.345323 | −0.172661 | − | 0.984981i | \(-0.555237\pi\) | ||||
−0.172661 | + | 0.984981i | \(0.555237\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15539.7 | −1.03399 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7925.79 | 0.524784 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4226.03 | −0.278447 | −0.139223 | − | 0.990261i | \(-0.544461\pi\) | ||||
−0.139223 | + | 0.990261i | \(0.544461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14233.5 | −0.928717 | −0.464358 | − | 0.885647i | \(-0.653715\pi\) | ||||
−0.464358 | + | 0.885647i | \(0.653715\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3737.82 | −0.242707 | −0.121353 | − | 0.992609i | \(-0.538723\pi\) | ||||
−0.121353 | + | 0.992609i | \(0.538723\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22548.8 | 1.45709 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17847.9 | −1.14777 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5089.52 | 0.324172 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2878.40 | 0.182463 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2893.31 | −0.182537 | −0.0912684 | − | 0.995826i | \(-0.529092\pi\) | ||||
−0.0912684 | + | 0.995826i | \(0.529092\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31513.3 | 1.97874 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17609.1 | 1.09529 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1486.43 | −0.0920226 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6867.26 | 0.423152 | 0.211576 | − | 0.977362i | \(-0.432140\pi\) | ||||
0.211576 | + | 0.977362i | \(0.432140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4975.32 | −0.305144 | −0.152572 | − | 0.988292i | \(-0.548756\pi\) | ||||
−0.152572 | + | 0.988292i | \(0.548756\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24033.2 | 1.46035 | 0.730174 | − | 0.683262i | \(-0.239439\pi\) | ||||
0.730174 | + | 0.683262i | \(0.239439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16751.9 | 1.01321 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −38961.2 | −2.34564 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25718.4 | 1.54125 | 0.770626 | − | 0.637288i | \(-0.219944\pi\) | ||||
0.770626 | + | 0.637288i | \(0.219944\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 579.221 | 0.0343951 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7970.84 | −0.471168 | −0.235584 | − | 0.971854i | \(-0.575700\pi\) | ||||
−0.235584 | + | 0.971854i | \(0.575700\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14207.8 | 0.836038 | 0.418019 | − | 0.908438i | \(-0.362725\pi\) | ||||
0.418019 | + | 0.908438i | \(0.362725\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4545.43 | −0.266259 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18232.2 | 1.05840 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 29026.1 | 1.67745 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36157.0 | −2.08021 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17080.0 | −0.978287 | −0.489143 | − | 0.872203i | \(-0.662691\pi\) | ||||
−0.489143 | + | 0.872203i | \(0.662691\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16410.9 | 0.931641 | 0.465821 | − | 0.884879i | \(-0.345759\pi\) | ||||
0.465821 | + | 0.884879i | \(0.345759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25442.9 | 1.43801 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13814.0 | 0.777317 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 183.169 | 0.0102617 | 0.00513086 | − | 0.999987i | \(-0.498367\pi\) | ||||
0.00513086 | + | 0.999987i | \(0.498367\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17492.6 | 0.971446 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24095.4 | 1.33231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14974.0 | 0.824366 | 0.412183 | − | 0.911101i | \(-0.364766\pi\) | ||||
0.412183 | + | 0.911101i | \(0.364766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2458.52 | −0.134764 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −261.408 | −0.0142059 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6476.74 | −0.350462 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4341.08 | 0.233895 | 0.116947 | − | 0.993138i | \(-0.462689\pi\) | ||||
0.116947 | + | 0.993138i | \(0.462689\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3173.41 | 0.170253 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50056.1 | 2.66273 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23931.9 | 1.26767 | 0.633837 | − | 0.773467i | \(-0.281479\pi\) | ||||
0.633837 | + | 0.773467i | \(0.281479\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1239.18 | −0.0653627 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45712.0 | 2.40102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18290.1 | −0.952656 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16258.6 | 0.843314 | 0.421657 | − | 0.906756i | \(-0.361449\pi\) | ||||
0.421657 | + | 0.906756i | \(0.361449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20137.5 | −1.04017 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17736.6 | 0.912354 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2608.95 | 0.133096 | 0.0665479 | − | 0.997783i | \(-0.478801\pi\) | ||||
0.0665479 | + | 0.997783i | \(0.478801\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 18145.4 | 0.921881 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7127.11 | 0.360610 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9843.63 | −0.496020 | −0.248010 | − | 0.968757i | \(-0.579777\pi\) | ||||
−0.248010 | + | 0.968757i | \(0.579777\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24816.5 | 1.24033 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2419.46 | 0.120435 | 0.0602174 | − | 0.998185i | \(-0.480821\pi\) | ||||
0.0602174 | + | 0.998185i | \(0.480821\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5011.30 | −0.248441 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10442.9 | −0.515631 | −0.257816 | − | 0.966194i | \(-0.583003\pi\) | ||||
−0.257816 | + | 0.966194i | \(0.583003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 693.262 | 0.0339560 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18058.4 | −0.880963 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29434.6 | 1.43021 | 0.715103 | − | 0.699019i | \(-0.246380\pi\) | ||||
0.715103 | + | 0.699019i | \(0.246380\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28638.6 | −1.38599 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20638.3 | 0.990902 | 0.495451 | − | 0.868636i | \(-0.335003\pi\) | ||||
0.495451 | + | 0.868636i | \(0.335003\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 44724.7 | 2.13887 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4103.09 | 0.195449 | 0.0977246 | − | 0.995213i | \(-0.468844\pi\) | ||||
0.0977246 | + | 0.995213i | \(0.468844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34721.0 | −1.64742 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16494.5 | −0.776508 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14020.0 | −0.657444 | −0.328722 | − | 0.944427i | \(-0.606618\pi\) | ||||
−0.328722 | + | 0.944427i | \(0.606618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20479.9 | −0.956635 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32823.8 | −1.52728 | −0.763642 | − | 0.645640i | \(-0.776591\pi\) | ||||
−0.763642 | + | 0.645640i | \(0.776591\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23768.4 | −1.09741 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −288.200 | −0.0132553 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39817.0 | 1.82428 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14747.4 | 0.673090 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33903.0 | −1.53559 | −0.767796 | − | 0.640694i | \(-0.778647\pi\) | ||||
−0.767796 | + | 0.640694i | \(0.778647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4830.54 | −0.217962 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18897.7 | 0.849462 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35601.3 | 1.59425 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20830.2 | −0.925778 | −0.462889 | − | 0.886416i | \(-0.653187\pi\) | ||||
−0.462889 | + | 0.886416i | \(0.653187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2782.16 | −0.123186 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1254.18 | −0.0553238 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15515.6 | −0.681859 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14213.8 | 0.620012 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26505.7 | −1.15190 | −0.575952 | − | 0.817484i | \(-0.695368\pi\) | ||||
−0.575952 | + | 0.817484i | \(0.695368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10829.0 | −0.468876 | −0.234438 | − | 0.972131i | \(-0.575325\pi\) | ||||
−0.234438 | + | 0.972131i | \(0.575325\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2774.94 | 0.119706 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7857.58 | 0.336477 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2420.73 | 0.103281 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42046.8 | 1.78738 | 0.893692 | − | 0.448681i | \(-0.148106\pi\) | ||||
0.893692 | + | 0.448681i | \(0.148106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12949.0 | 0.548448 | 0.274224 | − | 0.961666i | \(-0.411579\pi\) | ||||
0.274224 | + | 0.961666i | \(0.411579\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13874.0 | 0.583368 | 0.291684 | − | 0.956515i | \(-0.405784\pi\) | ||||
0.291684 | + | 0.956515i | \(0.405784\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2387.20 | −0.100013 | −0.0500065 | − | 0.998749i | \(-0.515924\pi\) | ||||
−0.0500065 | + | 0.998749i | \(0.515924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12706.2 | −0.530412 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6181.27 | −0.257105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36974.8 | 1.52692 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47308.8 | 1.94670 | 0.973350 | − | 0.229324i | \(-0.0736515\pi\) | ||||
0.973350 | + | 0.229324i | \(0.0736515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12464.7 | −0.511080 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8200.99 | −0.335062 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30599.2 | 1.24132 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25593.6 | −1.03459 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27886.7 | 1.12332 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18211.3 | 0.730998 | 0.365499 | − | 0.930812i | \(-0.380898\pi\) | ||||
0.365499 | + | 0.930812i | \(0.380898\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14824.5 | 0.590893 | 0.295447 | − | 0.955359i | \(-0.404532\pi\) | ||||
0.295447 | + | 0.955359i | \(0.404532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44191.1 | −1.75527 | −0.877637 | − | 0.479326i | \(-0.840881\pi\) | ||||
−0.877637 | + | 0.479326i | \(0.840881\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2158.58 | 0.0854403 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 34927.0 | 1.37767 | 0.688835 | − | 0.724918i | \(-0.258122\pi\) | ||||
0.688835 | + | 0.724918i | \(0.258122\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24798.5 | −0.971395 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33193.9 | 1.29577 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24435.1 | −0.950575 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1787.89 | 0.0693138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16914.8 | 0.651278 | 0.325639 | − | 0.945494i | \(-0.394421\pi\) | ||||
0.325639 | + | 0.945494i | \(0.394421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17132.6 | −0.657415 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12634.8 | 0.483177 | 0.241588 | − | 0.970379i | \(-0.422332\pi\) | ||||
0.241588 | + | 0.970379i | \(0.422332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47260.3 | 1.80117 | 0.900586 | − | 0.434678i | \(-0.143138\pi\) | ||||
0.900586 | + | 0.434678i | \(0.143138\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4758.84 | 0.180142 | 0.0900711 | − | 0.995935i | \(-0.471291\pi\) | ||||
0.0900711 | + | 0.995935i | \(0.471291\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2856.78 | 0.107777 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 38682.1 | 1.45443 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3067.31 | −0.114943 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44037.4 | −1.63920 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29896.6 | 1.10913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8458.13 | −0.312743 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −58852.1 | −2.16885 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4111.61 | 0.150522 | 0.0752612 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752612 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3517.47 | 0.128347 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35113.1 | −1.27700 | −0.638501 | − | 0.769621i | \(-0.720445\pi\) | ||||
−0.638501 | + | 0.769621i | \(0.720445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18570.4 | −0.673155 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9887.00 | 0.356049 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37509.1 | 1.34637 | 0.673184 | − | 0.739475i | \(-0.264926\pi\) | ||||
0.673184 | + | 0.739475i | \(0.264926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32226.0 | −1.15297 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −39205.1 | −1.39811 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1415.07 | −0.0501371 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18393.8 | 0.649604 | 0.324802 | − | 0.945782i | \(-0.394702\pi\) | ||||
0.324802 | + | 0.945782i | \(0.394702\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6814.80 | −0.239899 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 27479.0 | 0.964226 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17106.7 | 0.596427 | 0.298214 | − | 0.954499i | \(-0.403609\pi\) | ||||
0.298214 | + | 0.954499i | \(0.403609\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11451.7 | −0.397990 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38100.7 | −1.31992 | −0.659961 | − | 0.751300i | \(-0.729427\pi\) | ||||
−0.659961 | + | 0.751300i | \(0.729427\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2532.59 | −0.0874576 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52712.7 | 1.80880 | 0.904400 | − | 0.426686i | \(-0.140319\pi\) | ||||
0.904400 | + | 0.426686i | \(0.140319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15277.1 | 0.522567 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23944.4 | −0.816458 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6744.38 | 0.229246 | 0.114623 | − | 0.993409i | \(-0.463434\pi\) | ||||
0.114623 | + | 0.993409i | \(0.463434\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29250.9 | 0.988032 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 82599.8 | 2.78132 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45165.9 | 1.51609 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1268.98 | −0.0424634 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28449.8 | 0.946104 | 0.473052 | − | 0.881034i | \(-0.343152\pi\) | ||||
0.473052 | + | 0.881034i | \(0.343152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1759.10 | 0.0583183 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13018.7 | −0.430266 | −0.215133 | − | 0.976585i | \(-0.569019\pi\) | ||||
−0.215133 | + | 0.976585i | \(0.569019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1493.39 | −0.0492043 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20043.8 | 0.656355 | 0.328178 | − | 0.944616i | \(-0.393566\pi\) | ||||
0.328178 | + | 0.944616i | \(0.393566\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33595.7 | 1.09676 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2439.86 | −0.0794076 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1823.72 | 0.0591735 | 0.0295868 | − | 0.999562i | \(-0.490581\pi\) | ||||
0.0295868 | + | 0.999562i | \(0.490581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22973.7 | 0.740892 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 69049.4 | 2.22006 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26635.4 | −0.853786 | −0.426893 | − | 0.904302i | \(-0.640392\pi\) | ||||
−0.426893 | + | 0.904302i | \(0.640392\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −22261.0 | −0.711411 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50874.6 | −1.61606 | −0.808031 | − | 0.589139i | \(-0.799467\pi\) | ||||
−0.808031 | + | 0.589139i | \(0.799467\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22556.6 | 0.714372 |
(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 | 1900.4.a.b.1.2 | 2 | ||
5.2 | odd | 4 | 1900.4.c.b.1749.1 | 4 | |||
5.3 | odd | 4 | 1900.4.c.b.1749.4 | 4 | |||
5.4 | even | 2 | 76.4.a.a.1.1 | ✓ | 2 | ||
15.14 | odd | 2 | 684.4.a.g.1.1 | 2 | |||
20.19 | odd | 2 | 304.4.a.f.1.2 | 2 | |||
40.19 | odd | 2 | 1216.4.a.h.1.1 | 2 | |||
40.29 | even | 2 | 1216.4.a.o.1.2 | 2 | |||
95.94 | odd | 2 | 1444.4.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.4.a.a.1.1 | ✓ | 2 | 5.4 | even | 2 | ||
304.4.a.f.1.2 | 2 | 20.19 | odd | 2 | |||
684.4.a.g.1.1 | 2 | 15.14 | odd | 2 | |||
1216.4.a.h.1.1 | 2 | 40.19 | odd | 2 | |||
1216.4.a.o.1.2 | 2 | 40.29 | even | 2 | |||
1444.4.a.d.1.2 | 2 | 95.94 | odd | 2 | |||
1900.4.a.b.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1900.4.c.b.1749.1 | 4 | 5.2 | odd | 4 | |||
1900.4.c.b.1749.4 | 4 | 5.3 | odd | 4 |