Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,4,Mod(1,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("135.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.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: | \(7.96525785077\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1772.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 12x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.654334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.45876 | 1.92996 | 0.964981 | − | 0.262320i | \(-0.0844875\pi\) | ||||
0.964981 | + | 0.262320i | \(0.0844875\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 21.7980 | 2.72475 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.8065 | −0.637492 | −0.318746 | − | 0.947840i | \(-0.603262\pi\) | ||||
−0.318746 | + | 0.947840i | \(0.603262\pi\) | |||||||
\(8\) | 75.3201 | 3.32871 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 27.2938 | 0.863105 | ||||||||
\(11\) | −56.2376 | −1.54148 | −0.770740 | − | 0.637150i | \(-0.780113\pi\) | ||||
−0.770740 | + | 0.637150i | \(0.780113\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 34.5961 | 0.738094 | 0.369047 | − | 0.929411i | \(-0.379684\pi\) | ||||
0.369047 | + | 0.929411i | \(0.379684\pi\) | |||||||
\(14\) | −64.4489 | −1.23034 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 236.770 | 3.69953 | ||||||||
\(17\) | 39.2675 | 0.560221 | 0.280111 | − | 0.959968i | \(-0.409629\pi\) | ||||
0.280111 | + | 0.959968i | \(0.409629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −146.561 | −1.76965 | −0.884825 | − | 0.465924i | \(-0.845722\pi\) | ||||
−0.884825 | + | 0.465924i | \(0.845722\pi\) | |||||||
\(20\) | 108.990 | 1.21855 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −306.987 | −2.97500 | ||||||||
\(23\) | −23.5777 | −0.213752 | −0.106876 | − | 0.994272i | \(-0.534085\pi\) | ||||
−0.106876 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 188.851 | 1.42449 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −257.359 | −1.73701 | ||||||||
\(29\) | 161.003 | 1.03095 | 0.515473 | − | 0.856906i | \(-0.327616\pi\) | ||||
0.515473 | + | 0.856906i | \(0.327616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −29.5465 | −0.171184 | −0.0855921 | − | 0.996330i | \(-0.527278\pi\) | ||||
−0.0855921 | + | 0.996330i | \(0.527278\pi\) | |||||||
\(32\) | 689.908 | 3.81124 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 214.352 | 1.08121 | ||||||||
\(35\) | −59.0326 | −0.285095 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −217.688 | −0.967233 | −0.483617 | − | 0.875280i | \(-0.660677\pi\) | ||||
−0.483617 | + | 0.875280i | \(0.660677\pi\) | |||||||
\(38\) | −800.039 | −3.41536 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 376.600 | 1.48864 | ||||||||
\(41\) | 142.290 | 0.541999 | 0.270999 | − | 0.962580i | \(-0.412646\pi\) | ||||
0.270999 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −468.030 | −1.65986 | −0.829929 | − | 0.557869i | \(-0.811619\pi\) | ||||
−0.829929 | + | 0.557869i | \(0.811619\pi\) | |||||||
\(44\) | −1225.87 | −4.20015 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −128.705 | −0.412533 | ||||||||
\(47\) | 394.318 | 1.22377 | 0.611886 | − | 0.790946i | \(-0.290411\pi\) | ||||
0.611886 | + | 0.790946i | \(0.290411\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −203.606 | −0.593604 | ||||||||
\(50\) | 136.469 | 0.385992 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 754.126 | 2.01112 | ||||||||
\(53\) | −134.780 | −0.349311 | −0.174655 | − | 0.984630i | \(-0.555881\pi\) | ||||
−0.174655 | + | 0.984630i | \(0.555881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −281.188 | −0.689371 | ||||||||
\(56\) | −889.268 | −2.12203 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 878.875 | 1.98969 | ||||||||
\(59\) | −131.195 | −0.289495 | −0.144747 | − | 0.989469i | \(-0.546237\pi\) | ||||
−0.144747 | + | 0.989469i | \(0.546237\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 259.801 | 0.545313 | 0.272657 | − | 0.962111i | \(-0.412098\pi\) | ||||
0.272657 | + | 0.962111i | \(0.412098\pi\) | |||||||
\(62\) | −161.287 | −0.330379 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1871.88 | 3.65602 | ||||||||
\(65\) | 172.980 | 0.330086 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 445.244 | 0.811869 | 0.405935 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405935 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(68\) | 855.954 | 1.52647 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −322.245 | −0.550223 | ||||||||
\(71\) | 560.841 | 0.937459 | 0.468729 | − | 0.883342i | \(-0.344712\pi\) | ||||
0.468729 | + | 0.883342i | \(0.344712\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −88.6681 | −0.142162 | −0.0710809 | − | 0.997471i | \(-0.522645\pi\) | ||||
−0.0710809 | + | 0.997471i | \(0.522645\pi\) | |||||||
\(74\) | −1188.30 | −1.86672 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3194.74 | −4.82186 | ||||||||
\(77\) | 663.970 | 0.982681 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 450.342 | 0.641360 | 0.320680 | − | 0.947188i | \(-0.396089\pi\) | ||||
0.320680 | + | 0.947188i | \(0.396089\pi\) | |||||||
\(80\) | 1183.85 | 1.65448 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 776.726 | 1.04604 | ||||||||
\(83\) | 284.295 | 0.375969 | 0.187985 | − | 0.982172i | \(-0.439804\pi\) | ||||
0.187985 | + | 0.982172i | \(0.439804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 196.337 | 0.250539 | ||||||||
\(86\) | −2554.86 | −3.20346 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4235.82 | −5.13114 | ||||||||
\(89\) | 625.305 | 0.744744 | 0.372372 | − | 0.928083i | \(-0.378545\pi\) | ||||
0.372372 | + | 0.928083i | \(0.378545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −408.459 | −0.470529 | ||||||||
\(92\) | −513.948 | −0.582421 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2152.49 | 2.36183 | ||||||||
\(95\) | −732.804 | −0.791411 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −193.261 | −0.202296 | −0.101148 | − | 0.994871i | \(-0.532252\pi\) | ||||
−0.101148 | + | 0.994871i | \(0.532252\pi\) | |||||||
\(98\) | −1111.44 | −1.14563 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 544.951 | 0.544951 | ||||||||
\(101\) | 1374.86 | 1.35449 | 0.677245 | − | 0.735758i | \(-0.263174\pi\) | ||||
0.677245 | + | 0.735758i | \(0.263174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2029.60 | 1.94158 | 0.970789 | − | 0.239935i | \(-0.0771260\pi\) | ||||
0.970789 | + | 0.239935i | \(0.0771260\pi\) | |||||||
\(104\) | 2605.78 | 2.45690 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −735.732 | −0.674156 | ||||||||
\(107\) | −823.062 | −0.743630 | −0.371815 | − | 0.928307i | \(-0.621264\pi\) | ||||
−0.371815 | + | 0.928307i | \(0.621264\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −829.868 | −0.729238 | −0.364619 | − | 0.931157i | \(-0.618801\pi\) | ||||
−0.364619 | + | 0.931157i | \(0.618801\pi\) | |||||||
\(110\) | −1534.94 | −1.33046 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2795.43 | −2.35842 | ||||||||
\(113\) | −1503.37 | −1.25155 | −0.625773 | − | 0.780005i | \(-0.715216\pi\) | ||||
−0.625773 | + | 0.780005i | \(0.715216\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −117.889 | −0.0955928 | ||||||||
\(116\) | 3509.54 | 2.80908 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −716.164 | −0.558714 | ||||||||
\(119\) | −463.612 | −0.357137 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1831.67 | 1.37616 | ||||||||
\(122\) | 1418.19 | 1.05243 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −644.056 | −0.466435 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −576.348 | −0.402698 | −0.201349 | − | 0.979520i | \(-0.564532\pi\) | ||||
−0.201349 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(128\) | 4698.89 | 3.24474 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 944.257 | 0.637053 | ||||||||
\(131\) | 2390.04 | 1.59403 | 0.797017 | − | 0.603957i | \(-0.206410\pi\) | ||||
0.797017 | + | 0.603957i | \(0.206410\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1730.37 | 1.12814 | ||||||||
\(134\) | 2430.48 | 1.56688 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2957.63 | 1.86481 | ||||||||
\(137\) | 1002.46 | 0.625152 | 0.312576 | − | 0.949893i | \(-0.398808\pi\) | ||||
0.312576 | + | 0.949893i | \(0.398808\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 131.817 | 0.0804356 | 0.0402178 | − | 0.999191i | \(-0.487195\pi\) | ||||
0.0402178 | + | 0.999191i | \(0.487195\pi\) | |||||||
\(140\) | −1286.79 | −0.776814 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3061.50 | 1.80926 | ||||||||
\(143\) | −1945.60 | −1.13776 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 805.013 | 0.461053 | ||||||||
\(146\) | −484.017 | −0.274367 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4745.16 | −2.63547 | ||||||||
\(149\) | 1019.49 | 0.560533 | 0.280267 | − | 0.959922i | \(-0.409577\pi\) | ||||
0.280267 | + | 0.959922i | \(0.409577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2822.38 | 1.52107 | 0.760537 | − | 0.649295i | \(-0.224936\pi\) | ||||
0.760537 | + | 0.649295i | \(0.224936\pi\) | |||||||
\(152\) | −11039.0 | −5.89065 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3624.45 | 1.89654 | ||||||||
\(155\) | −147.733 | −0.0765559 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 476.499 | 0.242222 | 0.121111 | − | 0.992639i | \(-0.461354\pi\) | ||||
0.121111 | + | 0.992639i | \(0.461354\pi\) | |||||||
\(158\) | 2458.31 | 1.23780 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3449.54 | 1.70444 | ||||||||
\(161\) | 278.371 | 0.136265 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2242.26 | −1.07747 | −0.538734 | − | 0.842476i | \(-0.681097\pi\) | ||||
−0.538734 | + | 0.842476i | \(0.681097\pi\) | |||||||
\(164\) | 3101.64 | 1.47681 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1551.90 | 0.725607 | ||||||||
\(167\) | 95.0390 | 0.0440380 | 0.0220190 | − | 0.999758i | \(-0.492991\pi\) | ||||
0.0220190 | + | 0.999758i | \(0.492991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1000.11 | −0.455217 | ||||||||
\(170\) | 1071.76 | 0.483530 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10202.1 | −4.52270 | ||||||||
\(173\) | −2133.76 | −0.937727 | −0.468864 | − | 0.883271i | \(-0.655336\pi\) | ||||
−0.468864 | + | 0.883271i | \(0.655336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −295.163 | −0.127498 | ||||||||
\(176\) | −13315.4 | −5.70275 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3413.39 | 1.43733 | ||||||||
\(179\) | −1704.68 | −0.711808 | −0.355904 | − | 0.934523i | \(-0.615827\pi\) | ||||
−0.355904 | + | 0.934523i | \(0.615827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1360.98 | −0.558902 | −0.279451 | − | 0.960160i | \(-0.590152\pi\) | ||||
−0.279451 | + | 0.960160i | \(0.590152\pi\) | |||||||
\(182\) | −2229.68 | −0.908103 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1775.88 | −0.711518 | ||||||||
\(185\) | −1088.44 | −0.432560 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2208.31 | −0.863570 | ||||||||
\(188\) | 8595.36 | 3.33447 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4000.20 | −1.52739 | ||||||||
\(191\) | −1096.84 | −0.415522 | −0.207761 | − | 0.978180i | \(-0.566618\pi\) | ||||
−0.207761 | + | 0.978180i | \(0.566618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2867.27 | −1.06938 | −0.534691 | − | 0.845048i | \(-0.679572\pi\) | ||||
−0.534691 | + | 0.845048i | \(0.679572\pi\) | |||||||
\(194\) | −1054.97 | −0.390424 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4438.21 | −1.61742 | ||||||||
\(197\) | 724.139 | 0.261892 | 0.130946 | − | 0.991389i | \(-0.458199\pi\) | ||||
0.130946 | + | 0.991389i | \(0.458199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1693.65 | −0.603315 | −0.301658 | − | 0.953416i | \(-0.597540\pi\) | ||||
−0.301658 | + | 0.953416i | \(0.597540\pi\) | |||||||
\(200\) | 1883.00 | 0.665742 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7505.02 | 2.61411 | ||||||||
\(203\) | −1900.88 | −0.657220 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 711.449 | 0.242389 | ||||||||
\(206\) | 11079.1 | 3.74717 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8191.30 | 2.73060 | ||||||||
\(209\) | 8242.22 | 2.72788 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 947.452 | 0.309124 | 0.154562 | − | 0.987983i | \(-0.450603\pi\) | ||||
0.154562 | + | 0.987983i | \(0.450603\pi\) | |||||||
\(212\) | −2937.94 | −0.951785 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4492.89 | −1.43518 | ||||||||
\(215\) | −2340.15 | −0.742311 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 348.841 | 0.109129 | ||||||||
\(218\) | −4530.05 | −1.40740 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6129.34 | −1.87837 | ||||||||
\(221\) | 1358.50 | 0.413496 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 111.866 | 0.0335923 | 0.0167961 | − | 0.999859i | \(-0.494653\pi\) | ||||
0.0167961 | + | 0.999859i | \(0.494653\pi\) | |||||||
\(224\) | −8145.41 | −2.42964 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8206.51 | −2.41544 | ||||||||
\(227\) | 1200.70 | 0.351072 | 0.175536 | − | 0.984473i | \(-0.443834\pi\) | ||||
0.175536 | + | 0.984473i | \(0.443834\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 822.380 | 0.237312 | 0.118656 | − | 0.992935i | \(-0.462141\pi\) | ||||
0.118656 | + | 0.992935i | \(0.462141\pi\) | |||||||
\(230\) | −643.525 | −0.184490 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12126.7 | 3.43172 | ||||||||
\(233\) | −5329.21 | −1.49840 | −0.749202 | − | 0.662341i | \(-0.769563\pi\) | ||||
−0.749202 | + | 0.662341i | \(0.769563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1971.59 | 0.547287 | ||||||||
\(236\) | −2859.80 | −0.788802 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2530.75 | −0.689260 | ||||||||
\(239\) | −7085.61 | −1.91770 | −0.958850 | − | 0.283914i | \(-0.908367\pi\) | ||||
−0.958850 | + | 0.283914i | \(0.908367\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6560.09 | −1.75341 | −0.876707 | − | 0.481025i | \(-0.840265\pi\) | ||||
−0.876707 | + | 0.481025i | \(0.840265\pi\) | |||||||
\(242\) | 9998.63 | 2.65593 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5663.15 | 1.48584 | ||||||||
\(245\) | −1018.03 | −0.265468 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5070.42 | −1.30617 | ||||||||
\(248\) | −2225.45 | −0.569822 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 682.345 | 0.172621 | ||||||||
\(251\) | 714.222 | 0.179607 | 0.0898033 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898033 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1325.95 | 0.329494 | ||||||||
\(254\) | −3146.14 | −0.777191 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10675.0 | 2.60621 | ||||||||
\(257\) | 4396.59 | 1.06713 | 0.533563 | − | 0.845760i | \(-0.320853\pi\) | ||||
0.533563 | + | 0.845760i | \(0.320853\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2570.13 | 0.616604 | ||||||||
\(260\) | 3770.63 | 0.899402 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13046.6 | 3.07643 | ||||||||
\(263\) | −7550.31 | −1.77024 | −0.885118 | − | 0.465367i | \(-0.845922\pi\) | ||||
−0.885118 | + | 0.465367i | \(0.845922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −673.900 | −0.156216 | ||||||||
\(266\) | 9445.68 | 2.17726 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9705.45 | 2.21214 | ||||||||
\(269\) | −5536.86 | −1.25497 | −0.627487 | − | 0.778627i | \(-0.715917\pi\) | ||||
−0.627487 | + | 0.778627i | \(0.715917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3058.25 | 0.685518 | 0.342759 | − | 0.939423i | \(-0.388639\pi\) | ||||
0.342759 | + | 0.939423i | \(0.388639\pi\) | |||||||
\(272\) | 9297.36 | 2.07256 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5472.18 | 1.20652 | ||||||||
\(275\) | −1405.94 | −0.308296 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4070.19 | −0.882865 | −0.441433 | − | 0.897294i | \(-0.645530\pi\) | ||||
−0.441433 | + | 0.897294i | \(0.645530\pi\) | |||||||
\(278\) | 719.556 | 0.155238 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4446.34 | −0.948998 | ||||||||
\(281\) | 7446.19 | 1.58079 | 0.790396 | − | 0.612597i | \(-0.209875\pi\) | ||||
0.790396 | + | 0.612597i | \(0.209875\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −774.651 | −0.162715 | −0.0813573 | − | 0.996685i | \(-0.525925\pi\) | ||||
−0.0813573 | + | 0.996685i | \(0.525925\pi\) | |||||||
\(284\) | 12225.2 | 2.55434 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10620.6 | −2.19583 | ||||||||
\(287\) | −1679.95 | −0.345520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3371.06 | −0.686152 | ||||||||
\(290\) | 4394.37 | 0.889815 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1932.79 | −0.387356 | ||||||||
\(293\) | 6749.23 | 1.34571 | 0.672857 | − | 0.739772i | \(-0.265067\pi\) | ||||
0.672857 | + | 0.739772i | \(0.265067\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −655.977 | −0.129466 | ||||||||
\(296\) | −16396.3 | −3.21964 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5565.12 | 1.08181 | ||||||||
\(299\) | −815.696 | −0.157769 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5525.80 | 1.05815 | ||||||||
\(302\) | 15406.7 | 2.93561 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −34701.2 | −6.54687 | ||||||||
\(305\) | 1299.01 | 0.243872 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2204.39 | −0.409808 | −0.204904 | − | 0.978782i | \(-0.565688\pi\) | ||||
−0.204904 | + | 0.978782i | \(0.565688\pi\) | |||||||
\(308\) | 14473.2 | 2.67756 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −806.436 | −0.147750 | ||||||||
\(311\) | −6032.98 | −1.10000 | −0.549998 | − | 0.835166i | \(-0.685372\pi\) | ||||
−0.549998 | + | 0.835166i | \(0.685372\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5772.96 | −1.04251 | −0.521257 | − | 0.853400i | \(-0.674537\pi\) | ||||
−0.521257 | + | 0.853400i | \(0.674537\pi\) | |||||||
\(314\) | 2601.09 | 0.467479 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9816.57 | 1.74755 | ||||||||
\(317\) | −3302.07 | −0.585057 | −0.292528 | − | 0.956257i | \(-0.594497\pi\) | ||||
−0.292528 | + | 0.956257i | \(0.594497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9054.41 | −1.58918 | ||||||||
\(320\) | 9359.42 | 1.63502 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1519.56 | 0.262986 | ||||||||
\(323\) | −5755.07 | −0.991395 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 864.901 | 0.147619 | ||||||||
\(326\) | −12239.9 | −2.07947 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10717.3 | 1.80416 | ||||||||
\(329\) | −4655.53 | −0.780144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8053.15 | 1.33728 | 0.668642 | − | 0.743584i | \(-0.266876\pi\) | ||||
0.668642 | + | 0.743584i | \(0.266876\pi\) | |||||||
\(332\) | 6197.08 | 1.02442 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 518.795 | 0.0849916 | ||||||||
\(335\) | 2226.22 | 0.363079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3460.33 | 0.559335 | 0.279668 | − | 0.960097i | \(-0.409776\pi\) | ||||
0.279668 | + | 0.960097i | \(0.409776\pi\) | |||||||
\(338\) | −5459.37 | −0.878552 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4279.77 | 0.682656 | ||||||||
\(341\) | 1661.62 | 0.263877 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6453.51 | 1.01591 | ||||||||
\(344\) | −35252.0 | −5.52518 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11647.7 | −1.80978 | ||||||||
\(347\) | −9328.27 | −1.44314 | −0.721568 | − | 0.692344i | \(-0.756578\pi\) | ||||
−0.721568 | + | 0.692344i | \(0.756578\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8899.42 | 1.36497 | 0.682486 | − | 0.730899i | \(-0.260899\pi\) | ||||
0.682486 | + | 0.730899i | \(0.260899\pi\) | |||||||
\(350\) | −1611.22 | −0.246067 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −38798.8 | −5.87495 | ||||||||
\(353\) | 3722.45 | 0.561264 | 0.280632 | − | 0.959816i | \(-0.409456\pi\) | ||||
0.280632 | + | 0.959816i | \(0.409456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2804.21 | 0.419244 | ||||||||
\(356\) | 13630.4 | 2.02924 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9305.42 | −1.37376 | ||||||||
\(359\) | 11029.3 | 1.62145 | 0.810727 | − | 0.585425i | \(-0.199072\pi\) | ||||
0.810727 | + | 0.585425i | \(0.199072\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14621.1 | 2.13166 | ||||||||
\(362\) | −7429.29 | −1.07866 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8903.60 | −1.28208 | ||||||||
\(365\) | −443.340 | −0.0635767 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4853.11 | −0.690274 | −0.345137 | − | 0.938552i | \(-0.612167\pi\) | ||||
−0.345137 | + | 0.938552i | \(0.612167\pi\) | |||||||
\(368\) | −5582.49 | −0.790781 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5941.52 | −0.834824 | ||||||||
\(371\) | 1591.28 | 0.222683 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12373.8 | −1.71767 | −0.858834 | − | 0.512254i | \(-0.828811\pi\) | ||||
−0.858834 | + | 0.512254i | \(0.828811\pi\) | |||||||
\(374\) | −12054.6 | −1.66666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 29700.1 | 4.07358 | ||||||||
\(377\) | 5570.06 | 0.760935 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11150.6 | 1.51127 | 0.755634 | − | 0.654994i | \(-0.227329\pi\) | ||||
0.755634 | + | 0.654994i | \(0.227329\pi\) | |||||||
\(380\) | −15973.7 | −2.15640 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5987.39 | −0.801941 | ||||||||
\(383\) | 2199.59 | 0.293457 | 0.146728 | − | 0.989177i | \(-0.453126\pi\) | ||||
0.146728 | + | 0.989177i | \(0.453126\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3319.85 | 0.439468 | ||||||||
\(386\) | −15651.7 | −2.06386 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4212.72 | −0.551207 | ||||||||
\(389\) | 9218.92 | 1.20159 | 0.600794 | − | 0.799404i | \(-0.294851\pi\) | ||||
0.600794 | + | 0.799404i | \(0.294851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −925.838 | −0.119748 | ||||||||
\(392\) | −15335.6 | −1.97594 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3952.90 | 0.505442 | ||||||||
\(395\) | 2251.71 | 0.286825 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1119.36 | 0.141509 | 0.0707544 | − | 0.997494i | \(-0.477459\pi\) | ||||
0.0707544 | + | 0.997494i | \(0.477459\pi\) | |||||||
\(398\) | −9245.23 | −1.16438 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5919.25 | 0.739906 | ||||||||
\(401\) | 12296.9 | 1.53137 | 0.765683 | − | 0.643218i | \(-0.222401\pi\) | ||||
0.765683 | + | 0.643218i | \(0.222401\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1022.19 | −0.126350 | ||||||||
\(404\) | 29969.2 | 3.69065 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10376.4 | −1.26841 | ||||||||
\(407\) | 12242.2 | 1.49097 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2500.22 | 0.302269 | 0.151134 | − | 0.988513i | \(-0.451707\pi\) | ||||
0.151134 | + | 0.988513i | \(0.451707\pi\) | |||||||
\(410\) | 3883.63 | 0.467802 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 44241.3 | 5.29032 | ||||||||
\(413\) | 1548.96 | 0.184551 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1421.48 | 0.168139 | ||||||||
\(416\) | 23868.1 | 2.81305 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 44992.3 | 5.26470 | ||||||||
\(419\) | −8332.97 | −0.971581 | −0.485790 | − | 0.874075i | \(-0.661468\pi\) | ||||
−0.485790 | + | 0.874075i | \(0.661468\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11374.2 | 1.31673 | 0.658367 | − | 0.752697i | \(-0.271248\pi\) | ||||
0.658367 | + | 0.752697i | \(0.271248\pi\) | |||||||
\(422\) | 5171.91 | 0.596598 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10151.6 | −1.16275 | ||||||||
\(425\) | 981.687 | 0.112044 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3067.35 | −0.347633 | ||||||||
\(428\) | −17941.1 | −2.02621 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −12774.3 | −1.43263 | ||||||||
\(431\) | −10030.2 | −1.12097 | −0.560484 | − | 0.828165i | \(-0.689385\pi\) | ||||
−0.560484 | + | 0.828165i | \(0.689385\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7609.38 | 0.844535 | 0.422267 | − | 0.906471i | \(-0.361234\pi\) | ||||
0.422267 | + | 0.906471i | \(0.361234\pi\) | |||||||
\(434\) | 1904.24 | 0.210614 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −18089.5 | −1.98699 | ||||||||
\(437\) | 3455.57 | 0.378266 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12370.5 | −1.34490 | −0.672450 | − | 0.740143i | \(-0.734758\pi\) | ||||
−0.672450 | + | 0.740143i | \(0.734758\pi\) | |||||||
\(440\) | −21179.1 | −2.29471 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7415.72 | 0.798032 | ||||||||
\(443\) | −12084.4 | −1.29605 | −0.648023 | − | 0.761621i | \(-0.724404\pi\) | ||||
−0.648023 | + | 0.761621i | \(0.724404\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3126.53 | 0.333060 | ||||||||
\(446\) | 610.647 | 0.0648318 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22100.4 | −2.33068 | ||||||||
\(449\) | −625.550 | −0.0657495 | −0.0328747 | − | 0.999459i | \(-0.510466\pi\) | ||||
−0.0328747 | + | 0.999459i | \(0.510466\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8002.04 | −0.835480 | ||||||||
\(452\) | −32770.4 | −3.41016 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6554.33 | 0.677555 | ||||||||
\(455\) | −2042.29 | −0.210427 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1811.22 | 0.185395 | 0.0926974 | − | 0.995694i | \(-0.470451\pi\) | ||||
0.0926974 | + | 0.995694i | \(0.470451\pi\) | |||||||
\(458\) | 4489.17 | 0.458003 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2569.74 | −0.260467 | ||||||||
\(461\) | −11625.0 | −1.17447 | −0.587233 | − | 0.809418i | \(-0.699783\pi\) | ||||
−0.587233 | + | 0.809418i | \(0.699783\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7291.88 | 0.731928 | 0.365964 | − | 0.930629i | \(-0.380739\pi\) | ||||
0.365964 | + | 0.930629i | \(0.380739\pi\) | |||||||
\(464\) | 38120.6 | 3.81402 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29090.9 | −2.89186 | ||||||||
\(467\) | −11637.6 | −1.15316 | −0.576579 | − | 0.817042i | \(-0.695613\pi\) | ||||
−0.576579 | + | 0.817042i | \(0.695613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5256.78 | −0.517560 | ||||||||
\(470\) | 10762.4 | 1.05624 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9881.66 | −0.963644 | ||||||||
\(473\) | 26320.9 | 2.55864 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3664.02 | −0.353930 | ||||||||
\(476\) | −10105.8 | −0.973109 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −38678.6 | −3.70109 | ||||||||
\(479\) | 12041.4 | 1.14862 | 0.574309 | − | 0.818639i | \(-0.305271\pi\) | ||||
0.574309 | + | 0.818639i | \(0.305271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7531.14 | −0.713909 | ||||||||
\(482\) | −35810.0 | −3.38402 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39926.7 | 3.74969 | ||||||||
\(485\) | −966.307 | −0.0904695 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7037.81 | 0.654853 | 0.327427 | − | 0.944877i | \(-0.393819\pi\) | ||||
0.327427 | + | 0.944877i | \(0.393819\pi\) | |||||||
\(488\) | 19568.2 | 1.81519 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5557.18 | −0.512343 | ||||||||
\(491\) | 6603.07 | 0.606909 | 0.303454 | − | 0.952846i | \(-0.401860\pi\) | ||||
0.303454 | + | 0.952846i | \(0.401860\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6322.17 | 0.577558 | ||||||||
\(494\) | −27678.2 | −2.52085 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6995.72 | −0.633301 | ||||||||
\(497\) | −6621.58 | −0.597623 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.7047 | −0.00329284 | −0.00164642 | − | 0.999999i | \(-0.500524\pi\) | ||||
−0.00164642 | + | 0.999999i | \(0.500524\pi\) | |||||||
\(500\) | 2724.75 | 0.243709 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3898.76 | 0.346634 | ||||||||
\(503\) | 21242.5 | 1.88302 | 0.941508 | − | 0.336990i | \(-0.109409\pi\) | ||||
0.941508 | + | 0.336990i | \(0.109409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6874.29 | 0.605746 | ||||||||
\(506\) | 7238.06 | 0.635911 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12563.2 | −1.09725 | ||||||||
\(509\) | −11280.4 | −0.982309 | −0.491155 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491155 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1046.86 | 0.0906270 | ||||||||
\(512\) | 20681.3 | 1.78514 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23999.9 | 2.05951 | ||||||||
\(515\) | 10148.0 | 0.868300 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22175.5 | −1.88642 | ||||||||
\(518\) | 14029.7 | 1.19002 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13028.9 | 1.09876 | ||||||||
\(521\) | −10239.3 | −0.861023 | −0.430511 | − | 0.902585i | \(-0.641667\pi\) | ||||
−0.430511 | + | 0.902585i | \(0.641667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2822.00 | −0.235942 | −0.117971 | − | 0.993017i | \(-0.537639\pi\) | ||||
−0.117971 | + | 0.993017i | \(0.537639\pi\) | |||||||
\(524\) | 52098.1 | 4.34335 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −41215.3 | −3.41649 | ||||||||
\(527\) | −1160.22 | −0.0959010 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11611.1 | −0.954310 | ||||||||
\(530\) | −3678.66 | −0.301492 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 37718.7 | 3.07390 | ||||||||
\(533\) | 4922.67 | 0.400046 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4115.31 | −0.332561 | ||||||||
\(536\) | 33535.8 | 2.70248 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −30224.4 | −2.42205 | ||||||||
\(539\) | 11450.3 | 0.915028 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9409.63 | −0.747785 | −0.373892 | − | 0.927472i | \(-0.621977\pi\) | ||||
−0.373892 | + | 0.927472i | \(0.621977\pi\) | |||||||
\(542\) | 16694.2 | 1.32302 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 27091.0 | 2.13514 | ||||||||
\(545\) | −4149.34 | −0.326125 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3836.43 | −0.299879 | −0.149940 | − | 0.988695i | \(-0.547908\pi\) | ||||
−0.149940 | + | 0.988695i | \(0.547908\pi\) | |||||||
\(548\) | 21851.6 | 1.70339 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7674.69 | −0.594999 | ||||||||
\(551\) | −23596.7 | −1.82441 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5316.97 | −0.408862 | ||||||||
\(554\) | −22218.2 | −1.70390 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2873.35 | 0.219167 | ||||||||
\(557\) | 6145.92 | 0.467524 | 0.233762 | − | 0.972294i | \(-0.424896\pi\) | ||||
0.233762 | + | 0.972294i | \(0.424896\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16192.0 | −1.22513 | ||||||||
\(560\) | −13977.1 | −1.05472 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 40646.9 | 3.05087 | ||||||||
\(563\) | 13247.9 | 0.991707 | 0.495854 | − | 0.868406i | \(-0.334855\pi\) | ||||
0.495854 | + | 0.868406i | \(0.334855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7516.83 | −0.559709 | ||||||||
\(566\) | −4228.63 | −0.314033 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 42242.6 | 3.12053 | ||||||||
\(569\) | 6544.89 | 0.482208 | 0.241104 | − | 0.970499i | \(-0.422491\pi\) | ||||
0.241104 | + | 0.970499i | \(0.422491\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20362.1 | 1.49234 | 0.746170 | − | 0.665755i | \(-0.231890\pi\) | ||||
0.746170 | + | 0.665755i | \(0.231890\pi\) | |||||||
\(572\) | −42410.2 | −3.10011 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9170.43 | −0.666840 | ||||||||
\(575\) | −589.443 | −0.0427504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26247.4 | −1.89375 | −0.946876 | − | 0.321600i | \(-0.895779\pi\) | ||||
−0.946876 | + | 0.321600i | \(0.895779\pi\) | |||||||
\(578\) | −18401.8 | −1.32425 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17547.7 | 1.25626 | ||||||||
\(581\) | −3356.54 | −0.239677 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7579.71 | 0.538455 | ||||||||
\(584\) | −6678.49 | −0.473215 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36842.4 | 2.59718 | ||||||||
\(587\) | −14098.2 | −0.991301 | −0.495650 | − | 0.868522i | \(-0.665070\pi\) | ||||
−0.495650 | + | 0.868522i | \(0.665070\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4330.36 | 0.302936 | ||||||||
\(590\) | −3580.82 | −0.249865 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −51541.9 | −3.57831 | ||||||||
\(593\) | 3476.71 | 0.240761 | 0.120380 | − | 0.992728i | \(-0.461589\pi\) | ||||
0.120380 | + | 0.992728i | \(0.461589\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2318.06 | −0.159716 | ||||||||
\(596\) | 22222.8 | 1.52732 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4452.69 | −0.304488 | ||||||||
\(599\) | −16179.0 | −1.10360 | −0.551798 | − | 0.833978i | \(-0.686058\pi\) | ||||
−0.551798 | + | 0.833978i | \(0.686058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8112.16 | 0.550586 | 0.275293 | − | 0.961360i | \(-0.411225\pi\) | ||||
0.275293 | + | 0.961360i | \(0.411225\pi\) | |||||||
\(602\) | 30164.0 | 2.04218 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 61522.3 | 4.14455 | ||||||||
\(605\) | 9158.34 | 0.615437 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21139.2 | 1.41353 | 0.706765 | − | 0.707449i | \(-0.250154\pi\) | ||||
0.706765 | + | 0.707449i | \(0.250154\pi\) | |||||||
\(608\) | −101113. | −6.74456 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7090.95 | 0.470663 | ||||||||
\(611\) | 13641.9 | 0.903258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11440.3 | −0.753785 | −0.376892 | − | 0.926257i | \(-0.623007\pi\) | ||||
−0.376892 | + | 0.926257i | \(0.623007\pi\) | |||||||
\(614\) | −12033.2 | −0.790915 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 50010.3 | 3.27106 | ||||||||
\(617\) | 21566.2 | 1.40717 | 0.703584 | − | 0.710612i | \(-0.251582\pi\) | ||||
0.703584 | + | 0.710612i | \(0.251582\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15198.3 | −0.986866 | −0.493433 | − | 0.869784i | \(-0.664258\pi\) | ||||
−0.493433 | + | 0.869784i | \(0.664258\pi\) | |||||||
\(620\) | −3220.28 | −0.208596 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32932.6 | −2.12295 | ||||||||
\(623\) | −7382.68 | −0.474769 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −31513.2 | −2.01201 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10386.7 | 0.659994 | ||||||||
\(629\) | −8548.05 | −0.541865 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4929.66 | −0.311009 | −0.155504 | − | 0.987835i | \(-0.549700\pi\) | ||||
−0.155504 | + | 0.987835i | \(0.549700\pi\) | |||||||
\(632\) | 33919.8 | 2.13490 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18025.2 | −1.12914 | ||||||||
\(635\) | −2881.74 | −0.180092 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7043.97 | −0.438135 | ||||||||
\(638\) | −49425.8 | −3.06706 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23494.4 | 1.45109 | ||||||||
\(641\) | −7535.73 | −0.464342 | −0.232171 | − | 0.972675i | \(-0.574583\pi\) | ||||
−0.232171 | + | 0.972675i | \(0.574583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15997.2 | −0.981135 | −0.490568 | − | 0.871403i | \(-0.663211\pi\) | ||||
−0.490568 | + | 0.871403i | \(0.663211\pi\) | |||||||
\(644\) | 6067.93 | 0.371289 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31415.5 | −1.91336 | ||||||||
\(647\) | 6020.46 | 0.365825 | 0.182913 | − | 0.983129i | \(-0.441447\pi\) | ||||
0.182913 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7378.12 | 0.446250 | ||||||||
\(650\) | 4721.29 | 0.284899 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −48876.8 | −2.93583 | ||||||||
\(653\) | 10948.7 | 0.656133 | 0.328067 | − | 0.944655i | \(-0.393603\pi\) | ||||
0.328067 | + | 0.944655i | \(0.393603\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11950.2 | 0.712874 | ||||||||
\(656\) | 33690.0 | 2.00514 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −25413.4 | −1.50565 | ||||||||
\(659\) | −12338.3 | −0.729334 | −0.364667 | − | 0.931138i | \(-0.618817\pi\) | ||||
−0.364667 | + | 0.931138i | \(0.618817\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20016.8 | 1.17786 | 0.588928 | − | 0.808186i | \(-0.299550\pi\) | ||||
0.588928 | + | 0.808186i | \(0.299550\pi\) | |||||||
\(662\) | 43960.2 | 2.58091 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 21413.1 | 1.25149 | ||||||||
\(665\) | 8651.86 | 0.504518 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3796.08 | −0.220367 | ||||||||
\(668\) | 2071.66 | 0.119993 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12152.4 | 0.700729 | ||||||||
\(671\) | −14610.6 | −0.840589 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8419.22 | −0.482225 | −0.241112 | − | 0.970497i | \(-0.577512\pi\) | ||||
−0.241112 | + | 0.970497i | \(0.577512\pi\) | |||||||
\(674\) | 18889.1 | 1.07950 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21800.5 | −1.24036 | ||||||||
\(677\) | −25707.1 | −1.45938 | −0.729692 | − | 0.683776i | \(-0.760337\pi\) | ||||
−0.729692 | + | 0.683776i | \(0.760337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2281.74 | 0.128962 | ||||||||
\(680\) | 14788.2 | 0.833970 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9070.41 | 0.509272 | ||||||||
\(683\) | 19624.3 | 1.09942 | 0.549708 | − | 0.835357i | \(-0.314739\pi\) | ||||
0.549708 | + | 0.835357i | \(0.314739\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5012.30 | 0.279577 | ||||||||
\(686\) | 35228.2 | 1.96067 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −110815. | −6.14069 | ||||||||
\(689\) | −4662.86 | −0.257824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7273.23 | 0.400415 | 0.200207 | − | 0.979754i | \(-0.435838\pi\) | ||||
0.200207 | + | 0.979754i | \(0.435838\pi\) | |||||||
\(692\) | −46511.8 | −2.55508 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −50920.8 | −2.78520 | ||||||||
\(695\) | 659.084 | 0.0359719 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5587.37 | 0.303639 | ||||||||
\(698\) | 48579.8 | 2.63434 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6433.97 | −0.347402 | ||||||||
\(701\) | −17644.3 | −0.950664 | −0.475332 | − | 0.879807i | \(-0.657672\pi\) | ||||
−0.475332 | + | 0.879807i | \(0.657672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31904.5 | 1.71166 | ||||||||
\(704\) | −105270. | −5.63568 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20320.0 | 1.08322 | ||||||||
\(707\) | −16232.3 | −0.863476 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24304.4 | 1.28741 | 0.643703 | − | 0.765276i | \(-0.277397\pi\) | ||||
0.643703 | + | 0.765276i | \(0.277397\pi\) | |||||||
\(710\) | 15307.5 | 0.809126 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 47098.1 | 2.47904 | ||||||||
\(713\) | 696.639 | 0.0365909 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9728.00 | −0.508820 | ||||||||
\(716\) | −37158.6 | −1.93950 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 60206.0 | 3.12934 | ||||||||
\(719\) | 15170.2 | 0.786863 | 0.393431 | − | 0.919354i | \(-0.371288\pi\) | ||||
0.393431 | + | 0.919354i | \(0.371288\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23962.5 | −1.23774 | ||||||||
\(722\) | 79812.8 | 4.11402 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −29666.8 | −1.52287 | ||||||||
\(725\) | 4025.07 | 0.206189 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17487.0 | −0.892102 | −0.446051 | − | 0.895008i | \(-0.647170\pi\) | ||||
−0.446051 | + | 0.895008i | \(0.647170\pi\) | |||||||
\(728\) | −30765.2 | −1.56625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2420.09 | −0.122701 | ||||||||
\(731\) | −18378.4 | −0.929888 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18698.0 | 0.942194 | 0.471097 | − | 0.882082i | \(-0.343858\pi\) | ||||
0.471097 | + | 0.882082i | \(0.343858\pi\) | |||||||
\(734\) | −26492.0 | −1.33220 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16266.5 | −0.814660 | ||||||||
\(737\) | −25039.5 | −1.25148 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −35250.3 | −1.75467 | −0.877336 | − | 0.479876i | \(-0.840682\pi\) | ||||
−0.877336 | + | 0.479876i | \(0.840682\pi\) | |||||||
\(740\) | −23725.8 | −1.17862 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8686.43 | 0.429769 | ||||||||
\(743\) | 11133.6 | 0.549731 | 0.274866 | − | 0.961483i | \(-0.411367\pi\) | ||||
0.274866 | + | 0.961483i | \(0.411367\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5097.43 | 0.250678 | ||||||||
\(746\) | −67545.5 | −3.31503 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −48136.8 | −2.35301 | ||||||||
\(749\) | 9717.49 | 0.474058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17197.6 | 0.835619 | 0.417809 | − | 0.908535i | \(-0.362798\pi\) | ||||
0.417809 | + | 0.908535i | \(0.362798\pi\) | |||||||
\(752\) | 93362.7 | 4.52738 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30405.6 | 1.46858 | ||||||||
\(755\) | 14111.9 | 0.680245 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 804.647 | 0.0386333 | 0.0193166 | − | 0.999813i | \(-0.493851\pi\) | ||||
0.0193166 | + | 0.999813i | \(0.493851\pi\) | |||||||
\(758\) | 60868.7 | 2.91669 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −55194.8 | −2.63438 | ||||||||
\(761\) | 26208.9 | 1.24845 | 0.624225 | − | 0.781245i | \(-0.285415\pi\) | ||||
0.624225 | + | 0.781245i | \(0.285415\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9797.85 | 0.464883 | ||||||||
\(764\) | −23909.0 | −1.13219 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12007.0 | 0.566360 | ||||||||
\(767\) | −4538.85 | −0.213674 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36544.2 | 1.71367 | 0.856837 | − | 0.515587i | \(-0.172426\pi\) | ||||
0.856837 | + | 0.515587i | \(0.172426\pi\) | |||||||
\(770\) | 18122.3 | 0.848157 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −62500.8 | −2.91380 | ||||||||
\(773\) | −42387.4 | −1.97228 | −0.986139 | − | 0.165923i | \(-0.946940\pi\) | ||||
−0.986139 | + | 0.165923i | \(0.946940\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −738.663 | −0.0342368 | ||||||||
\(776\) | −14556.5 | −0.673385 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 50323.8 | 2.31902 | ||||||||
\(779\) | −20854.1 | −0.959148 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31540.4 | −1.44507 | ||||||||
\(782\) | −5053.92 | −0.231110 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −48207.8 | −2.19606 | ||||||||
\(785\) | 2382.50 | 0.108325 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26849.4 | 1.21611 | 0.608054 | − | 0.793896i | \(-0.291950\pi\) | ||||
0.608054 | + | 0.793896i | \(0.291950\pi\) | |||||||
\(788\) | 15784.8 | 0.713592 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12291.5 | 0.553561 | ||||||||
\(791\) | 17749.5 | 0.797851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8988.09 | 0.402492 | ||||||||
\(794\) | 6110.31 | 0.273107 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36918.3 | −1.64389 | ||||||||
\(797\) | −31307.0 | −1.39141 | −0.695704 | − | 0.718328i | \(-0.744908\pi\) | ||||
−0.695704 | + | 0.718328i | \(0.744908\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15483.9 | 0.685583 | ||||||||
\(800\) | 17247.7 | 0.762248 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 67125.7 | 2.95548 | ||||||||
\(803\) | 4986.48 | 0.219140 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1391.85 | 0.0609396 | ||||||||
\(806\) | −5579.90 | −0.243851 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 103554. | 4.50870 | ||||||||
\(809\) | −10011.9 | −0.435106 | −0.217553 | − | 0.976049i | \(-0.569807\pi\) | ||||
−0.217553 | + | 0.976049i | \(0.569807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4603.68 | 0.199331 | 0.0996653 | − | 0.995021i | \(-0.468223\pi\) | ||||
0.0996653 | + | 0.995021i | \(0.468223\pi\) | |||||||
\(812\) | −41435.5 | −1.79076 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 66827.4 | 2.87752 | ||||||||
\(815\) | −11211.3 | −0.481858 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 68594.8 | 2.93737 | ||||||||
\(818\) | 13648.1 | 0.583367 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15508.2 | 0.660451 | ||||||||
\(821\) | −35429.0 | −1.50607 | −0.753033 | − | 0.657983i | \(-0.771410\pi\) | ||||
−0.753033 | + | 0.657983i | \(0.771410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28297.6 | −1.19853 | −0.599265 | − | 0.800550i | \(-0.704541\pi\) | ||||
−0.599265 | + | 0.800550i | \(0.704541\pi\) | |||||||
\(824\) | 152870. | 6.46295 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8455.40 | 0.356176 | ||||||||
\(827\) | 41059.9 | 1.72647 | 0.863236 | − | 0.504800i | \(-0.168434\pi\) | ||||
0.863236 | + | 0.504800i | \(0.168434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9030.68 | 0.378345 | 0.189173 | − | 0.981944i | \(-0.439419\pi\) | ||||
0.189173 | + | 0.981944i | \(0.439419\pi\) | |||||||
\(830\) | 7759.49 | 0.324501 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 64759.8 | 2.69849 | ||||||||
\(833\) | −7995.10 | −0.332550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 475.195 | 0.0196944 | ||||||||
\(836\) | 179664. | 7.43280 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −45487.7 | −1.87511 | ||||||||
\(839\) | 5227.81 | 0.215118 | 0.107559 | − | 0.994199i | \(-0.465697\pi\) | ||||
0.107559 | + | 0.994199i | \(0.465697\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1532.87 | 0.0628508 | ||||||||
\(842\) | 62089.0 | 2.54125 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20652.6 | 0.842288 | ||||||||
\(845\) | −5000.56 | −0.203579 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21625.6 | −0.877290 | ||||||||
\(848\) | −31911.8 | −1.29228 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5358.79 | 0.216241 | ||||||||
\(851\) | 5132.58 | 0.206748 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30002.9 | −1.20432 | −0.602158 | − | 0.798377i | \(-0.705692\pi\) | ||||
−0.602158 | + | 0.798377i | \(0.705692\pi\) | |||||||
\(854\) | −16743.9 | −0.670918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −61993.1 | −2.47533 | ||||||||
\(857\) | 15671.7 | 0.624662 | 0.312331 | − | 0.949973i | \(-0.398890\pi\) | ||||
0.312331 | + | 0.949973i | \(0.398890\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31306.8 | −1.24351 | −0.621755 | − | 0.783212i | \(-0.713580\pi\) | ||||
−0.621755 | + | 0.783212i | \(0.713580\pi\) | |||||||
\(860\) | −51010.6 | −2.02261 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −54752.3 | −2.16342 | ||||||||
\(863\) | 13212.3 | 0.521150 | 0.260575 | − | 0.965454i | \(-0.416088\pi\) | ||||
0.260575 | + | 0.965454i | \(0.416088\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10668.8 | −0.419364 | ||||||||
\(866\) | 41537.8 | 1.62992 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7604.05 | 0.297348 | ||||||||
\(869\) | −25326.2 | −0.988643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15403.7 | 0.599236 | ||||||||
\(872\) | −62505.7 | −2.42742 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18863.1 | 0.730039 | ||||||||
\(875\) | −1475.81 | −0.0570190 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15440.6 | 0.594519 | 0.297260 | − | 0.954797i | \(-0.403927\pi\) | ||||
0.297260 | + | 0.954797i | \(0.403927\pi\) | |||||||
\(878\) | −67527.5 | −2.59561 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −66576.8 | −2.55035 | ||||||||
\(881\) | −27563.1 | −1.05406 | −0.527029 | − | 0.849847i | \(-0.676694\pi\) | ||||
−0.527029 | + | 0.849847i | \(0.676694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19897.7 | 0.758337 | 0.379169 | − | 0.925328i | \(-0.376210\pi\) | ||||
0.379169 | + | 0.925328i | \(0.376210\pi\) | |||||||
\(884\) | 29612.6 | 1.12667 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −65965.9 | −2.50132 | ||||||||
\(887\) | 40061.6 | 1.51650 | 0.758251 | − | 0.651963i | \(-0.226054\pi\) | ||||
0.758251 | + | 0.651963i | \(0.226054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6804.66 | 0.256716 | ||||||||
\(890\) | 17067.0 | 0.642793 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2438.45 | 0.0915306 | ||||||||
\(893\) | −57791.6 | −2.16565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8523.39 | −0.318330 | ||||||||
\(896\) | −55477.5 | −2.06850 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3414.72 | −0.126894 | ||||||||
\(899\) | −4757.07 | −0.176482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5292.47 | −0.195691 | ||||||||
\(902\) | −43681.2 | −1.61244 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −113234. | −4.16603 | ||||||||
\(905\) | −6804.92 | −0.249948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27839.6 | 1.01918 | 0.509591 | − | 0.860417i | \(-0.329797\pi\) | ||||
0.509591 | + | 0.860417i | \(0.329797\pi\) | |||||||
\(908\) | 26172.9 | 0.956584 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11148.4 | −0.406116 | ||||||||
\(911\) | 22251.0 | 0.809232 | 0.404616 | − | 0.914487i | \(-0.367405\pi\) | ||||
0.404616 | + | 0.914487i | \(0.367405\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15988.1 | −0.579549 | ||||||||
\(914\) | 9887.02 | 0.357805 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17926.3 | 0.646616 | ||||||||
\(917\) | −28218.0 | −1.01618 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29480.5 | 1.05819 | 0.529093 | − | 0.848564i | \(-0.322532\pi\) | ||||
0.529093 | + | 0.848564i | \(0.322532\pi\) | |||||||
\(920\) | −8879.38 | −0.318200 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −63457.9 | −2.26668 | ||||||||
\(923\) | 19402.9 | 0.691933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5442.19 | −0.193447 | ||||||||
\(926\) | 39804.6 | 1.41259 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 111077. | 3.92919 | ||||||||
\(929\) | 42351.8 | 1.49571 | 0.747857 | − | 0.663860i | \(-0.231083\pi\) | ||||
0.747857 | + | 0.663860i | \(0.231083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29840.7 | 1.05047 | ||||||||
\(932\) | −116166. | −4.08278 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −63526.9 | −2.22555 | ||||||||
\(935\) | −11041.5 | −0.386200 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35930.6 | −1.25272 | −0.626362 | − | 0.779532i | \(-0.715457\pi\) | ||||
−0.626362 | + | 0.779532i | \(0.715457\pi\) | |||||||
\(938\) | −28695.5 | −0.998872 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 42976.8 | 1.49122 | ||||||||
\(941\) | −21564.0 | −0.747041 | −0.373521 | − | 0.927622i | \(-0.621849\pi\) | ||||
−0.373521 | + | 0.927622i | \(0.621849\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3354.87 | −0.115853 | ||||||||
\(944\) | −31063.1 | −1.07099 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 143679. | 4.93807 | ||||||||
\(947\) | −16632.4 | −0.570729 | −0.285364 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285364 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3067.57 | −0.104929 | ||||||||
\(950\) | −20001.0 | −0.683071 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −34919.3 | −1.18880 | ||||||||
\(953\) | 39557.8 | 1.34460 | 0.672299 | − | 0.740279i | \(-0.265307\pi\) | ||||
0.672299 | + | 0.740279i | \(0.265307\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5484.21 | −0.185827 | ||||||||
\(956\) | −154452. | −5.22526 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 65731.4 | 2.21679 | ||||||||
\(959\) | −11835.5 | −0.398529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28918.0 | −0.970696 | ||||||||
\(962\) | −41110.6 | −1.37782 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −142997. | −4.77762 | ||||||||
\(965\) | −14336.3 | −0.478242 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10666.2 | −0.354707 | −0.177354 | − | 0.984147i | \(-0.556754\pi\) | ||||
−0.177354 | + | 0.984147i | \(0.556754\pi\) | |||||||
\(968\) | 137961. | 4.58083 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5274.83 | −0.174603 | ||||||||
\(971\) | 31821.8 | 1.05171 | 0.525855 | − | 0.850574i | \(-0.323746\pi\) | ||||
0.525855 | + | 0.850574i | \(0.323746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1556.30 | −0.0512771 | ||||||||
\(974\) | 38417.7 | 1.26384 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 61513.0 | 2.01740 | ||||||||
\(977\) | 11126.5 | 0.364347 | 0.182173 | − | 0.983266i | \(-0.441687\pi\) | ||||
0.182173 | + | 0.983266i | \(0.441687\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35165.7 | −1.14801 | ||||||||
\(980\) | −22191.1 | −0.723334 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36044.5 | 1.17131 | ||||||||
\(983\) | −991.225 | −0.0321619 | −0.0160810 | − | 0.999871i | \(-0.505119\pi\) | ||||
−0.0160810 | + | 0.999871i | \(0.505119\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3620.69 | 0.117122 | ||||||||
\(986\) | 34511.2 | 1.11467 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −110525. | −3.55898 | ||||||||
\(989\) | 11035.1 | 0.354798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −48714.9 | −1.56153 | −0.780767 | − | 0.624822i | \(-0.785171\pi\) | ||||
−0.780767 | + | 0.624822i | \(0.785171\pi\) | |||||||
\(992\) | −20384.4 | −0.652424 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −36145.6 | −1.15339 | ||||||||
\(995\) | −8468.25 | −0.269811 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42207.2 | −1.34074 | −0.670369 | − | 0.742028i | \(-0.733864\pi\) | ||||
−0.670369 | + | 0.742028i | \(0.733864\pi\) | |||||||
\(998\) | −200.362 | −0.00635505 | ||||||||
\(999\) | 0 | 0 |
(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 | 135.4.a.h.1.3 | yes | 3 | |
3.2 | odd | 2 | 135.4.a.e.1.1 | ✓ | 3 | ||
4.3 | odd | 2 | 2160.4.a.bq.1.2 | 3 | |||
5.2 | odd | 4 | 675.4.b.n.649.6 | 6 | |||
5.3 | odd | 4 | 675.4.b.n.649.1 | 6 | |||
5.4 | even | 2 | 675.4.a.p.1.1 | 3 | |||
9.2 | odd | 6 | 405.4.e.v.271.3 | 6 | |||
9.4 | even | 3 | 405.4.e.q.136.1 | 6 | |||
9.5 | odd | 6 | 405.4.e.v.136.3 | 6 | |||
9.7 | even | 3 | 405.4.e.q.271.1 | 6 | |||
12.11 | even | 2 | 2160.4.a.bi.1.2 | 3 | |||
15.2 | even | 4 | 675.4.b.m.649.1 | 6 | |||
15.8 | even | 4 | 675.4.b.m.649.6 | 6 | |||
15.14 | odd | 2 | 675.4.a.s.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.e.1.1 | ✓ | 3 | 3.2 | odd | 2 | ||
135.4.a.h.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
405.4.e.q.136.1 | 6 | 9.4 | even | 3 | |||
405.4.e.q.271.1 | 6 | 9.7 | even | 3 | |||
405.4.e.v.136.3 | 6 | 9.5 | odd | 6 | |||
405.4.e.v.271.3 | 6 | 9.2 | odd | 6 | |||
675.4.a.p.1.1 | 3 | 5.4 | even | 2 | |||
675.4.a.s.1.3 | 3 | 15.14 | odd | 2 | |||
675.4.b.m.649.1 | 6 | 15.2 | even | 4 | |||
675.4.b.m.649.6 | 6 | 15.8 | even | 4 | |||
675.4.b.n.649.1 | 6 | 5.3 | odd | 4 | |||
675.4.b.n.649.6 | 6 | 5.2 | odd | 4 | |||
2160.4.a.bi.1.2 | 3 | 12.11 | even | 2 | |||
2160.4.a.bq.1.2 | 3 | 4.3 | odd | 2 |