Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, 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("225.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(13.2754297513\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.16228 | 1.11803 | 0.559017 | − | 0.829156i | \(-0.311179\pi\) | ||||
0.559017 | + | 0.829156i | \(0.311179\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.250000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.0000 | −0.809924 | −0.404962 | − | 0.914334i | \(-0.632715\pi\) | ||||
−0.404962 | + | 0.914334i | \(0.632715\pi\) | |||||||
\(8\) | −18.9737 | −0.838525 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −63.2456 | −1.73357 | −0.866784 | − | 0.498683i | \(-0.833817\pi\) | ||||
−0.866784 | + | 0.498683i | \(0.833817\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −35.0000 | −0.746712 | −0.373356 | − | 0.927688i | \(-0.621793\pi\) | ||||
−0.373356 | + | 0.927688i | \(0.621793\pi\) | |||||||
\(14\) | −47.4342 | −0.905522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −76.0000 | −1.18750 | ||||||||
\(17\) | 88.5438 | 1.26324 | 0.631618 | − | 0.775280i | \(-0.282391\pi\) | ||||
0.631618 | + | 0.775280i | \(0.282391\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 91.0000 | 1.09878 | 0.549390 | − | 0.835566i | \(-0.314860\pi\) | ||||
0.549390 | + | 0.835566i | \(0.314860\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −200.000 | −1.93819 | ||||||||
\(23\) | −113.842 | −1.03207 | −0.516037 | − | 0.856566i | \(-0.672593\pi\) | ||||
−0.516037 | + | 0.856566i | \(0.672593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −110.680 | −0.834849 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −30.0000 | −0.202481 | ||||||||
\(29\) | 63.2456 | 0.404979 | 0.202490 | − | 0.979284i | \(-0.435097\pi\) | ||||
0.202490 | + | 0.979284i | \(0.435097\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −147.000 | −0.851677 | −0.425838 | − | 0.904799i | \(-0.640021\pi\) | ||||
−0.425838 | + | 0.904799i | \(0.640021\pi\) | |||||||
\(32\) | −88.5438 | −0.489140 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 280.000 | 1.41234 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −370.000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 287.767 | 1.22847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 442.719 | 1.68637 | 0.843184 | − | 0.537625i | \(-0.180679\pi\) | ||||
0.843184 | + | 0.537625i | \(0.180679\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −335.000 | −1.18807 | −0.594035 | − | 0.804439i | \(-0.702466\pi\) | ||||
−0.594035 | + | 0.804439i | \(0.702466\pi\) | |||||||
\(44\) | −126.491 | −0.433392 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −360.000 | −1.15389 | ||||||||
\(47\) | −177.088 | −0.549593 | −0.274797 | − | 0.961502i | \(-0.588610\pi\) | ||||
−0.274797 | + | 0.961502i | \(0.588610\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −118.000 | −0.344023 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −70.0000 | −0.186678 | ||||||||
\(53\) | 88.5438 | 0.229480 | 0.114740 | − | 0.993396i | \(-0.463397\pi\) | ||||
0.114740 | + | 0.993396i | \(0.463397\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 284.605 | 0.679142 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 200.000 | 0.452781 | ||||||||
\(59\) | 885.438 | 1.95380 | 0.976900 | − | 0.213698i | \(-0.0685508\pi\) | ||||
0.976900 | + | 0.213698i | \(0.0685508\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 427.000 | 0.896258 | 0.448129 | − | 0.893969i | \(-0.352090\pi\) | ||||
0.448129 | + | 0.893969i | \(0.352090\pi\) | |||||||
\(62\) | −464.855 | −0.952204 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 328.000 | 0.640625 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.0000 | −0.0273514 | −0.0136757 | − | 0.999906i | \(-0.504353\pi\) | ||||
−0.0136757 | + | 0.999906i | \(0.504353\pi\) | |||||||
\(68\) | 177.088 | 0.315809 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 63.2456 | 0.105716 | 0.0528582 | − | 0.998602i | \(-0.483167\pi\) | ||||
0.0528582 | + | 0.998602i | \(0.483167\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70.0000 | 0.112231 | 0.0561156 | − | 0.998424i | \(-0.482128\pi\) | ||||
0.0561156 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(74\) | −1170.04 | −1.83804 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 182.000 | 0.274695 | ||||||||
\(77\) | 948.683 | 1.40406 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −876.000 | −1.24757 | −0.623783 | − | 0.781598i | \(-0.714405\pi\) | ||||
−0.623783 | + | 0.781598i | \(0.714405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1400.00 | 1.88542 | ||||||||
\(83\) | −531.263 | −0.702574 | −0.351287 | − | 0.936268i | \(-0.614256\pi\) | ||||
−0.351287 | + | 0.936268i | \(0.614256\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1059.36 | −1.32830 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1200.00 | 1.45364 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 525.000 | 0.604780 | ||||||||
\(92\) | −227.684 | −0.258018 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −560.000 | −0.614464 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1085.00 | 1.13572 | 0.567861 | − | 0.823124i | \(-0.307771\pi\) | ||||
0.567861 | + | 0.823124i | \(0.307771\pi\) | |||||||
\(98\) | −373.149 | −0.384630 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1328.16 | −1.30848 | −0.654240 | − | 0.756287i | \(-0.727011\pi\) | ||||
−0.654240 | + | 0.756287i | \(0.727011\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1540.00 | −1.47321 | −0.736605 | − | 0.676323i | \(-0.763572\pi\) | ||||
−0.736605 | + | 0.676323i | \(0.763572\pi\) | |||||||
\(104\) | 664.078 | 0.626137 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 280.000 | 0.256566 | ||||||||
\(107\) | 796.894 | 0.719987 | 0.359994 | − | 0.932955i | \(-0.382779\pi\) | ||||
0.359994 | + | 0.932955i | \(0.382779\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −811.000 | −0.712658 | −0.356329 | − | 0.934361i | \(-0.615972\pi\) | ||||
−0.356329 | + | 0.934361i | \(0.615972\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1140.00 | 0.961785 | ||||||||
\(113\) | −1619.09 | −1.34788 | −0.673942 | − | 0.738785i | \(-0.735400\pi\) | ||||
−0.673942 | + | 0.738785i | \(0.735400\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 126.491 | 0.101245 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2800.00 | 2.18441 | ||||||||
\(119\) | −1328.16 | −1.02313 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2669.00 | 2.00526 | ||||||||
\(122\) | 1350.29 | 1.00205 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −294.000 | −0.212919 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −260.000 | −0.181664 | −0.0908318 | − | 0.995866i | \(-0.528953\pi\) | ||||
−0.0908318 | + | 0.995866i | \(0.528953\pi\) | |||||||
\(128\) | 1745.58 | 1.20538 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1328.16 | 0.885814 | 0.442907 | − | 0.896568i | \(-0.353947\pi\) | ||||
0.442907 | + | 0.896568i | \(0.353947\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1365.00 | −0.889929 | ||||||||
\(134\) | −47.4342 | −0.0305798 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1680.00 | −1.05926 | ||||||||
\(137\) | −2656.31 | −1.65653 | −0.828263 | − | 0.560339i | \(-0.810671\pi\) | ||||
−0.828263 | + | 0.560339i | \(0.810671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −784.000 | −0.478403 | −0.239201 | − | 0.970970i | \(-0.576886\pi\) | ||||
−0.239201 | + | 0.970970i | \(0.576886\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 200.000 | 0.118195 | ||||||||
\(143\) | 2213.59 | 1.29448 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 221.359 | 0.125478 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −740.000 | −0.410997 | ||||||||
\(149\) | 2150.35 | 1.18230 | 0.591152 | − | 0.806560i | \(-0.298673\pi\) | ||||
0.591152 | + | 0.806560i | \(0.298673\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −797.000 | −0.429529 | −0.214765 | − | 0.976666i | \(-0.568898\pi\) | ||||
−0.214765 | + | 0.976666i | \(0.568898\pi\) | |||||||
\(152\) | −1726.60 | −0.921356 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3000.00 | 1.56978 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1225.00 | −0.622711 | −0.311356 | − | 0.950293i | \(-0.600783\pi\) | ||||
−0.311356 | + | 0.950293i | \(0.600783\pi\) | |||||||
\(158\) | −2770.16 | −1.39482 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1707.63 | 0.835901 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 275.000 | 0.132145 | 0.0660726 | − | 0.997815i | \(-0.478953\pi\) | ||||
0.0660726 | + | 0.997815i | \(0.478953\pi\) | |||||||
\(164\) | 885.438 | 0.421592 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1680.00 | −0.785502 | ||||||||
\(167\) | 265.631 | 0.123085 | 0.0615424 | − | 0.998104i | \(-0.480398\pi\) | ||||
0.0615424 | + | 0.998104i | \(0.480398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −972.000 | −0.442421 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −670.000 | −0.297018 | ||||||||
\(173\) | 3984.47 | 1.75106 | 0.875531 | − | 0.483162i | \(-0.160512\pi\) | ||||
0.875531 | + | 0.483162i | \(0.160512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4806.66 | 2.05861 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1770.88 | −0.739449 | −0.369725 | − | 0.929141i | \(-0.620548\pi\) | ||||
−0.369725 | + | 0.929141i | \(0.620548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1687.00 | −0.692783 | −0.346391 | − | 0.938090i | \(-0.612593\pi\) | ||||
−0.346391 | + | 0.938090i | \(0.612593\pi\) | |||||||
\(182\) | 1660.20 | 0.676164 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2160.00 | 0.865420 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5600.00 | −2.18991 | ||||||||
\(188\) | −354.175 | −0.137398 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2213.59 | −0.838587 | −0.419293 | − | 0.907851i | \(-0.637722\pi\) | ||||
−0.419293 | + | 0.907851i | \(0.637722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3625.00 | −1.35199 | −0.675993 | − | 0.736908i | \(-0.736285\pi\) | ||||
−0.675993 | + | 0.736908i | \(0.736285\pi\) | |||||||
\(194\) | 3431.07 | 1.26978 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −236.000 | −0.0860058 | ||||||||
\(197\) | −1745.58 | −0.631306 | −0.315653 | − | 0.948875i | \(-0.602224\pi\) | ||||
−0.315653 | + | 0.948875i | \(0.602224\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3199.00 | 1.13955 | 0.569777 | − | 0.821800i | \(-0.307030\pi\) | ||||
0.569777 | + | 0.821800i | \(0.307030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4200.00 | −1.46293 | ||||||||
\(203\) | −948.683 | −0.328003 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4869.91 | −1.64710 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2660.00 | 0.886720 | ||||||||
\(209\) | −5755.35 | −1.90481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 887.000 | 0.289401 | 0.144700 | − | 0.989476i | \(-0.453778\pi\) | ||||
0.144700 | + | 0.989476i | \(0.453778\pi\) | |||||||
\(212\) | 177.088 | 0.0573699 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2520.00 | 0.804970 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2205.00 | 0.689793 | ||||||||
\(218\) | −2564.61 | −0.796776 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3099.03 | −0.943274 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3535.00 | −1.06153 | −0.530765 | − | 0.847519i | \(-0.678095\pi\) | ||||
−0.530765 | + | 0.847519i | \(0.678095\pi\) | |||||||
\(224\) | 1328.16 | 0.396166 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5120.00 | −1.50698 | ||||||||
\(227\) | −88.5438 | −0.0258892 | −0.0129446 | − | 0.999916i | \(-0.504121\pi\) | ||||
−0.0129446 | + | 0.999916i | \(0.504121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5019.00 | −1.44832 | −0.724159 | − | 0.689633i | \(-0.757772\pi\) | ||||
−0.724159 | + | 0.689633i | \(0.757772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1200.00 | −0.339586 | ||||||||
\(233\) | −3605.00 | −1.01361 | −0.506805 | − | 0.862061i | \(-0.669174\pi\) | ||||
−0.506805 | + | 0.862061i | \(0.669174\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1770.88 | 0.488450 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4200.00 | −1.14389 | ||||||||
\(239\) | −442.719 | −0.119821 | −0.0599103 | − | 0.998204i | \(-0.519081\pi\) | ||||
−0.0599103 | + | 0.998204i | \(0.519081\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −623.000 | −0.166518 | −0.0832592 | − | 0.996528i | \(-0.526533\pi\) | ||||
−0.0832592 | + | 0.996528i | \(0.526533\pi\) | |||||||
\(242\) | 8440.12 | 2.24195 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 854.000 | 0.224065 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3185.00 | −0.820472 | ||||||||
\(248\) | 2789.13 | 0.714153 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2656.31 | −0.667988 | −0.333994 | − | 0.942575i | \(-0.608397\pi\) | ||||
−0.333994 | + | 0.942575i | \(0.608397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7200.00 | 1.78917 | ||||||||
\(254\) | −822.192 | −0.203106 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2896.00 | 0.707031 | ||||||||
\(257\) | 3718.84 | 0.902626 | 0.451313 | − | 0.892366i | \(-0.350956\pi\) | ||||
0.451313 | + | 0.892366i | \(0.350956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5550.00 | 1.33151 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4200.00 | 0.990370 | ||||||||
\(263\) | −2896.65 | −0.679144 | −0.339572 | − | 0.940580i | \(-0.610282\pi\) | ||||
−0.339572 | + | 0.940580i | \(0.610282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4316.51 | −0.994970 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −30.0000 | −0.00683784 | ||||||||
\(269\) | −442.719 | −0.100346 | −0.0501729 | − | 0.998741i | \(-0.515977\pi\) | ||||
−0.0501729 | + | 0.998741i | \(0.515977\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −308.000 | −0.0690394 | −0.0345197 | − | 0.999404i | \(-0.510990\pi\) | ||||
−0.0345197 | + | 0.999404i | \(0.510990\pi\) | |||||||
\(272\) | −6729.33 | −1.50009 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8400.00 | −1.85205 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7485.00 | 1.62357 | 0.811787 | − | 0.583953i | \(-0.198495\pi\) | ||||
0.811787 | + | 0.583953i | \(0.198495\pi\) | |||||||
\(278\) | −2479.23 | −0.534871 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 948.683 | 0.201401 | 0.100701 | − | 0.994917i | \(-0.467892\pi\) | ||||
0.100701 | + | 0.994917i | \(0.467892\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −525.000 | −0.110276 | −0.0551378 | − | 0.998479i | \(-0.517560\pi\) | ||||
−0.0551378 | + | 0.998479i | \(0.517560\pi\) | |||||||
\(284\) | 126.491 | 0.0264291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7000.00 | 1.44727 | ||||||||
\(287\) | −6640.78 | −1.36583 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2927.00 | 0.595766 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 140.000 | 0.0280578 | ||||||||
\(293\) | 6375.15 | 1.27113 | 0.635564 | − | 0.772048i | \(-0.280768\pi\) | ||||
0.635564 | + | 0.772048i | \(0.280768\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7020.26 | 1.37853 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6800.00 | 1.32186 | ||||||||
\(299\) | 3984.47 | 0.770662 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5025.00 | 0.962246 | ||||||||
\(302\) | −2520.34 | −0.480228 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6916.00 | −1.30480 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2695.00 | 0.501016 | 0.250508 | − | 0.968115i | \(-0.419402\pi\) | ||||
0.250508 | + | 0.968115i | \(0.419402\pi\) | |||||||
\(308\) | 1897.37 | 0.351015 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5312.63 | 0.968654 | 0.484327 | − | 0.874887i | \(-0.339064\pi\) | ||||
0.484327 | + | 0.874887i | \(0.339064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2555.00 | 0.461397 | 0.230698 | − | 0.973025i | \(-0.425899\pi\) | ||||
0.230698 | + | 0.973025i | \(0.425899\pi\) | |||||||
\(314\) | −3873.79 | −0.696212 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1752.00 | −0.311891 | ||||||||
\(317\) | 7462.98 | 1.32228 | 0.661140 | − | 0.750263i | \(-0.270073\pi\) | ||||
0.661140 | + | 0.750263i | \(0.270073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4000.00 | −0.702060 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5400.00 | 0.934566 | ||||||||
\(323\) | 8057.48 | 1.38802 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 869.626 | 0.147743 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8400.00 | −1.41406 | ||||||||
\(329\) | 2656.31 | 0.445129 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5088.00 | −0.844900 | −0.422450 | − | 0.906386i | \(-0.638830\pi\) | ||||
−0.422450 | + | 0.906386i | \(0.638830\pi\) | |||||||
\(332\) | −1062.53 | −0.175644 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 840.000 | 0.137613 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11485.0 | 1.85646 | 0.928231 | − | 0.372004i | \(-0.121329\pi\) | ||||
0.928231 | + | 0.372004i | \(0.121329\pi\) | |||||||
\(338\) | −3073.73 | −0.494642 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9297.10 | 1.47644 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6915.00 | 1.08856 | ||||||||
\(344\) | 6356.18 | 0.996227 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12600.0 | 1.95775 | ||||||||
\(347\) | −6400.45 | −0.990185 | −0.495092 | − | 0.868840i | \(-0.664866\pi\) | ||||
−0.495092 | + | 0.868840i | \(0.664866\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9674.00 | −1.48377 | −0.741887 | − | 0.670525i | \(-0.766069\pi\) | ||||
−0.741887 | + | 0.670525i | \(0.766069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5600.00 | 0.847957 | ||||||||
\(353\) | −5578.26 | −0.841078 | −0.420539 | − | 0.907274i | \(-0.638159\pi\) | ||||
−0.420539 | + | 0.907274i | \(0.638159\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5600.00 | −0.826730 | ||||||||
\(359\) | 8917.62 | 1.31101 | 0.655507 | − | 0.755189i | \(-0.272455\pi\) | ||||
0.655507 | + | 0.755189i | \(0.272455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1422.00 | 0.207319 | ||||||||
\(362\) | −5334.76 | −0.774555 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1050.00 | 0.151195 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8505.00 | −1.20969 | −0.604847 | − | 0.796342i | \(-0.706766\pi\) | ||||
−0.604847 | + | 0.796342i | \(0.706766\pi\) | |||||||
\(368\) | 8651.99 | 1.22559 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1328.16 | −0.185861 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6775.00 | 0.940472 | 0.470236 | − | 0.882541i | \(-0.344169\pi\) | ||||
0.470236 | + | 0.882541i | \(0.344169\pi\) | |||||||
\(374\) | −17708.8 | −2.44839 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3360.00 | 0.460848 | ||||||||
\(377\) | −2213.59 | −0.302403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9241.00 | 1.25245 | 0.626225 | − | 0.779643i | \(-0.284599\pi\) | ||||
0.626225 | + | 0.779643i | \(0.284599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7000.00 | −0.937568 | ||||||||
\(383\) | −9031.46 | −1.20493 | −0.602463 | − | 0.798147i | \(-0.705814\pi\) | ||||
−0.602463 | + | 0.798147i | \(0.705814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11463.3 | −1.51157 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2170.00 | 0.283931 | ||||||||
\(389\) | 4363.94 | 0.568794 | 0.284397 | − | 0.958707i | \(-0.408207\pi\) | ||||
0.284397 | + | 0.958707i | \(0.408207\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10080.0 | −1.30375 | ||||||||
\(392\) | 2238.89 | 0.288472 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5520.00 | −0.705821 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4795.00 | 0.606182 | 0.303091 | − | 0.952962i | \(-0.401981\pi\) | ||||
0.303091 | + | 0.952962i | \(0.401981\pi\) | |||||||
\(398\) | 10116.1 | 1.27406 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7020.26 | −0.874252 | −0.437126 | − | 0.899400i | \(-0.644004\pi\) | ||||
−0.437126 | + | 0.899400i | \(0.644004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5145.00 | 0.635957 | ||||||||
\(404\) | −2656.31 | −0.327120 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3000.00 | −0.366718 | ||||||||
\(407\) | 23400.9 | 2.84997 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6881.00 | 0.831891 | 0.415946 | − | 0.909389i | \(-0.363451\pi\) | ||||
0.415946 | + | 0.909389i | \(0.363451\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3080.00 | −0.368303 | ||||||||
\(413\) | −13281.6 | −1.58243 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3099.03 | 0.365247 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18200.0 | −2.12964 | ||||||||
\(419\) | −12838.8 | −1.49694 | −0.748471 | − | 0.663167i | \(-0.769212\pi\) | ||||
−0.748471 | + | 0.663167i | \(0.769212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6418.00 | 0.742979 | 0.371490 | − | 0.928437i | \(-0.378847\pi\) | ||||
0.371490 | + | 0.928437i | \(0.378847\pi\) | |||||||
\(422\) | 2804.94 | 0.323560 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1680.00 | −0.192425 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6405.00 | −0.725901 | ||||||||
\(428\) | 1593.79 | 0.179997 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1328.16 | −0.148434 | −0.0742170 | − | 0.997242i | \(-0.523646\pi\) | ||||
−0.0742170 | + | 0.997242i | \(0.523646\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8155.00 | 0.905091 | 0.452545 | − | 0.891741i | \(-0.350516\pi\) | ||||
0.452545 | + | 0.891741i | \(0.350516\pi\) | |||||||
\(434\) | 6972.82 | 0.771212 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1622.00 | −0.178164 | ||||||||
\(437\) | −10359.6 | −1.13402 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14749.0 | 1.60349 | 0.801744 | − | 0.597667i | \(-0.203906\pi\) | ||||
0.801744 | + | 0.597667i | \(0.203906\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9800.00 | −1.05461 | ||||||||
\(443\) | −11156.5 | −1.19653 | −0.598264 | − | 0.801299i | \(-0.704143\pi\) | ||||
−0.598264 | + | 0.801299i | \(0.704143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11178.7 | −1.18683 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4920.00 | −0.518857 | ||||||||
\(449\) | 9233.85 | 0.970540 | 0.485270 | − | 0.874364i | \(-0.338721\pi\) | ||||
0.485270 | + | 0.874364i | \(0.338721\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28000.0 | −2.92343 | ||||||||
\(452\) | −3238.17 | −0.336971 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −280.000 | −0.0289450 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1030.00 | 0.105430 | 0.0527148 | − | 0.998610i | \(-0.483213\pi\) | ||||
0.0527148 | + | 0.998610i | \(0.483213\pi\) | |||||||
\(458\) | −15871.5 | −1.61927 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9297.10 | −0.939282 | −0.469641 | − | 0.882858i | \(-0.655617\pi\) | ||||
−0.469641 | + | 0.882858i | \(0.655617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11940.0 | −1.19849 | −0.599243 | − | 0.800567i | \(-0.704532\pi\) | ||||
−0.599243 | + | 0.800567i | \(0.704532\pi\) | |||||||
\(464\) | −4806.66 | −0.480913 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11400.0 | −1.13325 | ||||||||
\(467\) | 12130.5 | 1.20200 | 0.600998 | − | 0.799250i | \(-0.294770\pi\) | ||||
0.600998 | + | 0.799250i | \(0.294770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 225.000 | 0.0221525 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16800.0 | −1.63831 | ||||||||
\(473\) | 21187.3 | 2.05960 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2656.31 | −0.255781 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1400.00 | −0.133963 | ||||||||
\(479\) | 2656.31 | 0.253382 | 0.126691 | − | 0.991942i | \(-0.459564\pi\) | ||||
0.126691 | + | 0.991942i | \(0.459564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12950.0 | 1.22759 | ||||||||
\(482\) | −1970.10 | −0.186173 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5338.00 | 0.501315 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14125.0 | −1.31430 | −0.657151 | − | 0.753759i | \(-0.728239\pi\) | ||||
−0.657151 | + | 0.753759i | \(0.728239\pi\) | |||||||
\(488\) | −8101.76 | −0.751535 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4047.72 | 0.372038 | 0.186019 | − | 0.982546i | \(-0.440441\pi\) | ||||
0.186019 | + | 0.982546i | \(0.440441\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5600.00 | 0.511585 | ||||||||
\(494\) | −10071.9 | −0.917316 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11172.0 | 1.01137 | ||||||||
\(497\) | −948.683 | −0.0856223 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1279.00 | 0.114741 | 0.0573706 | − | 0.998353i | \(-0.481728\pi\) | ||||
0.0573706 | + | 0.998353i | \(0.481728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8400.00 | −0.746833 | ||||||||
\(503\) | 16380.6 | 1.45204 | 0.726019 | − | 0.687675i | \(-0.241369\pi\) | ||||
0.726019 | + | 0.687675i | \(0.241369\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22768.4 | 2.00035 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −520.000 | −0.0454159 | ||||||||
\(509\) | −4427.19 | −0.385524 | −0.192762 | − | 0.981246i | \(-0.561745\pi\) | ||||
−0.192762 | + | 0.981246i | \(0.561745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1050.00 | −0.0908988 | ||||||||
\(512\) | −4806.66 | −0.414895 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11760.0 | 1.00917 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11200.0 | 0.952757 | ||||||||
\(518\) | 17550.6 | 1.48867 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11068.0 | 0.930704 | 0.465352 | − | 0.885126i | \(-0.345928\pi\) | ||||
0.465352 | + | 0.885126i | \(0.345928\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10745.0 | −0.898367 | −0.449184 | − | 0.893439i | \(-0.648285\pi\) | ||||
−0.449184 | + | 0.893439i | \(0.648285\pi\) | |||||||
\(524\) | 2656.31 | 0.221453 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9160.00 | −0.759306 | ||||||||
\(527\) | −13015.9 | −1.07587 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 793.000 | 0.0651763 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2730.00 | −0.222482 | ||||||||
\(533\) | −15495.2 | −1.25923 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 284.605 | 0.0229348 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1400.00 | −0.112190 | ||||||||
\(539\) | 7462.98 | 0.596388 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9423.00 | −0.748847 | −0.374424 | − | 0.927258i | \(-0.622159\pi\) | ||||
−0.374424 | + | 0.927258i | \(0.622159\pi\) | |||||||
\(542\) | −973.982 | −0.0771884 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7840.00 | −0.617899 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9080.00 | −0.709749 | −0.354875 | − | 0.934914i | \(-0.615476\pi\) | ||||
−0.354875 | + | 0.934914i | \(0.615476\pi\) | |||||||
\(548\) | −5312.63 | −0.414132 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5755.35 | 0.444984 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13140.0 | 1.01043 | ||||||||
\(554\) | 23669.6 | 1.81521 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1568.00 | −0.119601 | ||||||||
\(557\) | −8348.41 | −0.635069 | −0.317535 | − | 0.948247i | \(-0.602855\pi\) | ||||
−0.317535 | + | 0.948247i | \(0.602855\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11725.0 | 0.887146 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3000.00 | 0.225173 | ||||||||
\(563\) | 7703.31 | 0.576653 | 0.288327 | − | 0.957532i | \(-0.406901\pi\) | ||||
0.288327 | + | 0.957532i | \(0.406901\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1660.20 | −0.123292 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1200.00 | −0.0886459 | ||||||||
\(569\) | 6261.31 | 0.461314 | 0.230657 | − | 0.973035i | \(-0.425912\pi\) | ||||
0.230657 | + | 0.973035i | \(0.425912\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 587.000 | 0.0430213 | 0.0215107 | − | 0.999769i | \(-0.493152\pi\) | ||||
0.0215107 | + | 0.999769i | \(0.493152\pi\) | |||||||
\(572\) | 4427.19 | 0.323619 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −21000.0 | −1.52704 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15995.0 | 1.15404 | 0.577020 | − | 0.816730i | \(-0.304216\pi\) | ||||
0.577020 | + | 0.816730i | \(0.304216\pi\) | |||||||
\(578\) | 9255.99 | 0.666087 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7968.94 | 0.569032 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5600.00 | −0.397819 | ||||||||
\(584\) | −1328.16 | −0.0941088 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20160.0 | 1.42116 | ||||||||
\(587\) | −20453.6 | −1.43818 | −0.719089 | − | 0.694918i | \(-0.755441\pi\) | ||||
−0.719089 | + | 0.694918i | \(0.755441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13377.0 | −0.935806 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28120.0 | 1.95224 | ||||||||
\(593\) | 11599.2 | 0.803244 | 0.401622 | − | 0.915806i | \(-0.368447\pi\) | ||||
0.401622 | + | 0.915806i | \(0.368447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4300.70 | 0.295576 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12600.0 | 0.861626 | ||||||||
\(599\) | −19100.2 | −1.30286 | −0.651428 | − | 0.758710i | \(-0.725830\pi\) | ||||
−0.651428 | + | 0.758710i | \(0.725830\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3143.00 | 0.213321 | 0.106660 | − | 0.994296i | \(-0.465984\pi\) | ||||
0.106660 | + | 0.994296i | \(0.465984\pi\) | |||||||
\(602\) | 15890.4 | 1.07582 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1594.00 | −0.107382 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2660.00 | −0.177868 | −0.0889342 | − | 0.996038i | \(-0.528346\pi\) | ||||
−0.0889342 | + | 0.996038i | \(0.528346\pi\) | |||||||
\(608\) | −8057.48 | −0.537457 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6198.06 | 0.410388 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6670.00 | 0.439476 | 0.219738 | − | 0.975559i | \(-0.429480\pi\) | ||||
0.219738 | + | 0.975559i | \(0.429480\pi\) | |||||||
\(614\) | 8522.34 | 0.560152 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −18000.0 | −1.17734 | ||||||||
\(617\) | 11042.7 | 0.720521 | 0.360260 | − | 0.932852i | \(-0.382688\pi\) | ||||
0.360260 | + | 0.932852i | \(0.382688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5579.00 | 0.362260 | 0.181130 | − | 0.983459i | \(-0.442025\pi\) | ||||
0.181130 | + | 0.983459i | \(0.442025\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 16800.0 | 1.08299 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8079.62 | 0.515857 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2450.00 | −0.155678 | ||||||||
\(629\) | −32761.2 | −2.07675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23617.0 | 1.48998 | 0.744990 | − | 0.667075i | \(-0.232454\pi\) | ||||
0.744990 | + | 0.667075i | \(0.232454\pi\) | |||||||
\(632\) | 16620.9 | 1.04612 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 23600.0 | 1.47835 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4130.00 | 0.256886 | ||||||||
\(638\) | −12649.1 | −0.784926 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31496.3 | −1.94076 | −0.970381 | − | 0.241579i | \(-0.922335\pi\) | ||||
−0.970381 | + | 0.241579i | \(0.922335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14280.0 | 0.875814 | 0.437907 | − | 0.899020i | \(-0.355720\pi\) | ||||
0.437907 | + | 0.899020i | \(0.355720\pi\) | |||||||
\(644\) | 3415.26 | 0.208975 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25480.0 | 1.55185 | ||||||||
\(647\) | −12396.1 | −0.753234 | −0.376617 | − | 0.926369i | \(-0.622913\pi\) | ||||
−0.376617 | + | 0.926369i | \(0.622913\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −56000.0 | −3.38705 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 550.000 | 0.0330363 | ||||||||
\(653\) | −12042.0 | −0.721651 | −0.360825 | − | 0.932633i | \(-0.617505\pi\) | ||||
−0.360825 | + | 0.932633i | \(0.617505\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −33646.6 | −2.00256 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8400.00 | 0.497669 | ||||||||
\(659\) | −5755.35 | −0.340207 | −0.170104 | − | 0.985426i | \(-0.554410\pi\) | ||||
−0.170104 | + | 0.985426i | \(0.554410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25438.0 | 1.49686 | 0.748429 | − | 0.663215i | \(-0.230808\pi\) | ||||
0.748429 | + | 0.663215i | \(0.230808\pi\) | |||||||
\(662\) | −16089.7 | −0.944626 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10080.0 | 0.589126 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7200.00 | −0.417969 | ||||||||
\(668\) | 531.263 | 0.0307712 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27005.9 | −1.55372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15150.0 | −0.867741 | −0.433870 | − | 0.900975i | \(-0.642852\pi\) | ||||
−0.433870 | + | 0.900975i | \(0.642852\pi\) | |||||||
\(674\) | 36318.8 | 2.07559 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1944.00 | −0.110605 | ||||||||
\(677\) | 20984.9 | 1.19131 | 0.595653 | − | 0.803242i | \(-0.296893\pi\) | ||||
0.595653 | + | 0.803242i | \(0.296893\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16275.0 | −0.919849 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 29400.0 | 1.65071 | ||||||||
\(683\) | −1973.26 | −0.110549 | −0.0552743 | − | 0.998471i | \(-0.517603\pi\) | ||||
−0.0552743 | + | 0.998471i | \(0.517603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 21867.2 | 1.21704 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 25460.0 | 1.41083 | ||||||||
\(689\) | −3099.03 | −0.171355 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20552.0 | −1.13145 | −0.565727 | − | 0.824592i | \(-0.691404\pi\) | ||||
−0.565727 | + | 0.824592i | \(0.691404\pi\) | |||||||
\(692\) | 7968.94 | 0.437765 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20240.0 | −1.10706 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39200.0 | 2.13028 | ||||||||
\(698\) | −30591.9 | −1.65891 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8411.66 | 0.453215 | 0.226608 | − | 0.973986i | \(-0.427236\pi\) | ||||
0.226608 | + | 0.973986i | \(0.427236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33670.0 | −1.80638 | ||||||||
\(704\) | −20744.5 | −1.11057 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17640.0 | −0.940354 | ||||||||
\(707\) | 19922.3 | 1.05977 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17281.0 | 0.915376 | 0.457688 | − | 0.889113i | \(-0.348678\pi\) | ||||
0.457688 | + | 0.889113i | \(0.348678\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16734.8 | 0.878993 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3541.75 | −0.184862 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28200.0 | 1.46576 | ||||||||
\(719\) | 9297.10 | 0.482230 | 0.241115 | − | 0.970497i | \(-0.422487\pi\) | ||||
0.241115 | + | 0.970497i | \(0.422487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23100.0 | 1.19319 | ||||||||
\(722\) | 4496.76 | 0.231790 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −3374.00 | −0.173196 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30415.0 | −1.55162 | −0.775811 | − | 0.630965i | \(-0.782659\pi\) | ||||
−0.775811 | + | 0.630965i | \(0.782659\pi\) | |||||||
\(728\) | −9961.17 | −0.507123 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29662.2 | −1.50081 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18550.0 | −0.934734 | −0.467367 | − | 0.884063i | \(-0.654797\pi\) | ||||
−0.467367 | + | 0.884063i | \(0.654797\pi\) | |||||||
\(734\) | −26895.2 | −1.35248 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10080.0 | 0.504828 | ||||||||
\(737\) | 948.683 | 0.0474155 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24016.0 | 1.19546 | 0.597729 | − | 0.801699i | \(-0.296070\pi\) | ||||
0.597729 | + | 0.801699i | \(0.296070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4200.00 | −0.207799 | ||||||||
\(743\) | −12396.1 | −0.612072 | −0.306036 | − | 0.952020i | \(-0.599003\pi\) | ||||
−0.306036 | + | 0.952020i | \(0.599003\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 21424.4 | 1.05148 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11200.0 | −0.547477 | ||||||||
\(749\) | −11953.4 | −0.583135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7772.00 | −0.377636 | −0.188818 | − | 0.982012i | \(-0.560466\pi\) | ||||
−0.188818 | + | 0.982012i | \(0.560466\pi\) | |||||||
\(752\) | 13458.7 | 0.652642 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7000.00 | −0.338097 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3865.00 | 0.185569 | 0.0927846 | − | 0.995686i | \(-0.470423\pi\) | ||||
0.0927846 | + | 0.995686i | \(0.470423\pi\) | |||||||
\(758\) | 29222.6 | 1.40028 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15937.9 | 0.759195 | 0.379598 | − | 0.925152i | \(-0.376062\pi\) | ||||
0.379598 | + | 0.925152i | \(0.376062\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12165.0 | 0.577199 | ||||||||
\(764\) | −4427.19 | −0.209647 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28560.0 | −1.34715 | ||||||||
\(767\) | −30990.3 | −1.45893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7441.00 | −0.348933 | −0.174466 | − | 0.984663i | \(-0.555820\pi\) | ||||
−0.174466 | + | 0.984663i | \(0.555820\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7250.00 | −0.337996 | ||||||||
\(773\) | 25766.2 | 1.19890 | 0.599448 | − | 0.800413i | \(-0.295387\pi\) | ||||
0.599448 | + | 0.800413i | \(0.295387\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20586.4 | −0.952332 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13800.0 | 0.635931 | ||||||||
\(779\) | 40287.4 | 1.85295 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4000.00 | −0.183267 | ||||||||
\(782\) | −31875.8 | −1.45764 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8968.00 | 0.408528 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6125.00 | −0.277424 | −0.138712 | − | 0.990333i | \(-0.544296\pi\) | ||||
−0.138712 | + | 0.990333i | \(0.544296\pi\) | |||||||
\(788\) | −3491.15 | −0.157826 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24286.3 | 1.09168 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14945.0 | −0.669247 | ||||||||
\(794\) | 15163.1 | 0.677732 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6398.00 | 0.284888 | ||||||||
\(797\) | −20010.9 | −0.889363 | −0.444681 | − | 0.895689i | \(-0.646683\pi\) | ||||
−0.444681 | + | 0.895689i | \(0.646683\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15680.0 | −0.694266 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22200.0 | −0.977443 | ||||||||
\(803\) | −4427.19 | −0.194561 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16269.9 | 0.711022 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 25200.0 | 1.09719 | ||||||||
\(809\) | 2719.56 | 0.118189 | 0.0590943 | − | 0.998252i | \(-0.481179\pi\) | ||||
0.0590943 | + | 0.998252i | \(0.481179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28623.0 | 1.23932 | 0.619661 | − | 0.784870i | \(-0.287270\pi\) | ||||
0.619661 | + | 0.784870i | \(0.287270\pi\) | |||||||
\(812\) | −1897.37 | −0.0820006 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 74000.0 | 3.18636 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30485.0 | −1.30543 | ||||||||
\(818\) | 21759.6 | 0.930083 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26563.1 | 1.12918 | 0.564592 | − | 0.825370i | \(-0.309034\pi\) | ||||
0.564592 | + | 0.825370i | \(0.309034\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1135.00 | −0.0480724 | −0.0240362 | − | 0.999711i | \(-0.507652\pi\) | ||||
−0.0240362 | + | 0.999711i | \(0.507652\pi\) | |||||||
\(824\) | 29219.4 | 1.23532 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42000.0 | −1.76921 | ||||||||
\(827\) | 999.280 | 0.0420174 | 0.0210087 | − | 0.999779i | \(-0.493312\pi\) | ||||
0.0210087 | + | 0.999779i | \(0.493312\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1974.00 | −0.0827019 | −0.0413509 | − | 0.999145i | \(-0.513166\pi\) | ||||
−0.0413509 | + | 0.999145i | \(0.513166\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11480.0 | −0.478362 | ||||||||
\(833\) | −10448.2 | −0.434583 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11510.7 | −0.476203 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40600.0 | −1.67363 | ||||||||
\(839\) | −42058.3 | −1.73065 | −0.865324 | − | 0.501213i | \(-0.832887\pi\) | ||||
−0.865324 | + | 0.501213i | \(0.832887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20389.0 | −0.835992 | ||||||||
\(842\) | 20295.5 | 0.830676 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1774.00 | 0.0723502 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −40035.0 | −1.62411 | ||||||||
\(848\) | −6729.33 | −0.272507 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 42121.5 | 1.69672 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −36645.0 | −1.47093 | −0.735464 | − | 0.677564i | \(-0.763036\pi\) | ||||
−0.735464 | + | 0.677564i | \(0.763036\pi\) | |||||||
\(854\) | −20254.4 | −0.811582 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15120.0 | −0.603728 | ||||||||
\(857\) | −10802.3 | −0.430573 | −0.215286 | − | 0.976551i | \(-0.569069\pi\) | ||||
−0.215286 | + | 0.976551i | \(0.569069\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20104.0 | 0.798533 | 0.399266 | − | 0.916835i | \(-0.369265\pi\) | ||||
0.399266 | + | 0.916835i | \(0.369265\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4200.00 | −0.165954 | ||||||||
\(863\) | 2150.35 | 0.0848189 | 0.0424095 | − | 0.999100i | \(-0.486497\pi\) | ||||
0.0424095 | + | 0.999100i | \(0.486497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25788.4 | 1.01192 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4410.00 | 0.172448 | ||||||||
\(869\) | 55403.1 | 2.16274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 525.000 | 0.0204236 | ||||||||
\(872\) | 15387.6 | 0.597582 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −32760.0 | −1.26788 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21975.0 | 0.846115 | 0.423058 | − | 0.906103i | \(-0.360957\pi\) | ||||
0.423058 | + | 0.906103i | \(0.360957\pi\) | |||||||
\(878\) | 46640.4 | 1.79275 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 885.438 | 0.0338606 | 0.0169303 | − | 0.999857i | \(-0.494611\pi\) | ||||
0.0169303 | + | 0.999857i | \(0.494611\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34915.0 | −1.33067 | −0.665336 | − | 0.746544i | \(-0.731712\pi\) | ||||
−0.665336 | + | 0.746544i | \(0.731712\pi\) | |||||||
\(884\) | −6198.06 | −0.235818 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35280.0 | −1.33776 | ||||||||
\(887\) | 49407.4 | 1.87028 | 0.935140 | − | 0.354277i | \(-0.115273\pi\) | ||||
0.935140 | + | 0.354277i | \(0.115273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3900.00 | 0.147134 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7070.00 | −0.265382 | ||||||||
\(893\) | −16115.0 | −0.603882 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −26183.7 | −0.976266 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 29200.0 | 1.08510 | ||||||||
\(899\) | −9297.10 | −0.344912 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7840.00 | 0.289887 | ||||||||
\(902\) | −88543.8 | −3.26850 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 30720.0 | 1.13023 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17880.0 | −0.654571 | −0.327285 | − | 0.944926i | \(-0.606134\pi\) | ||||
−0.327285 | + | 0.944926i | \(0.606134\pi\) | |||||||
\(908\) | −177.088 | −0.00647231 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17329.3 | −0.630236 | −0.315118 | − | 0.949053i | \(-0.602044\pi\) | ||||
−0.315118 | + | 0.949053i | \(0.602044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33600.0 | 1.21796 | ||||||||
\(914\) | 3257.15 | 0.117874 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10038.0 | −0.362080 | ||||||||
\(917\) | −19922.3 | −0.717442 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25829.0 | −0.927117 | −0.463558 | − | 0.886066i | \(-0.653428\pi\) | ||||
−0.463558 | + | 0.886066i | \(0.653428\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29400.0 | −1.05015 | ||||||||
\(923\) | −2213.59 | −0.0789397 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −37757.6 | −1.33995 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5600.00 | −0.198092 | ||||||||
\(929\) | 3099.03 | 0.109447 | 0.0547233 | − | 0.998502i | \(-0.482572\pi\) | ||||
0.0547233 | + | 0.998502i | \(0.482572\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10738.0 | −0.378006 | ||||||||
\(932\) | −7209.99 | −0.253403 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38360.0 | 1.34387 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40005.0 | −1.39478 | −0.697389 | − | 0.716693i | \(-0.745655\pi\) | ||||
−0.697389 | + | 0.716693i | \(0.745655\pi\) | |||||||
\(938\) | 711.512 | 0.0247673 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30104.9 | −1.04292 | −0.521462 | − | 0.853275i | \(-0.674613\pi\) | ||||
−0.521462 | + | 0.853275i | \(0.674613\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −50400.0 | −1.74046 | ||||||||
\(944\) | −67293.3 | −2.32014 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 67000.0 | 2.30270 | ||||||||
\(947\) | 43297.9 | 1.48574 | 0.742868 | − | 0.669437i | \(-0.233465\pi\) | ||||
0.742868 | + | 0.669437i | \(0.233465\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2450.00 | −0.0838044 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 25200.0 | 0.857917 | ||||||||
\(953\) | −53682.8 | −1.82472 | −0.912360 | − | 0.409390i | \(-0.865742\pi\) | ||||
−0.912360 | + | 0.409390i | \(0.865742\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −885.438 | −0.0299551 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8400.00 | 0.283290 | ||||||||
\(959\) | 39844.7 | 1.34166 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8182.00 | −0.274647 | ||||||||
\(962\) | 40951.5 | 1.37248 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1246.00 | −0.0416296 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20540.0 | 0.683063 | 0.341531 | − | 0.939870i | \(-0.389054\pi\) | ||||
0.341531 | + | 0.939870i | \(0.389054\pi\) | |||||||
\(968\) | −50640.7 | −1.68146 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10625.3 | −0.351164 | −0.175582 | − | 0.984465i | \(-0.556181\pi\) | ||||
−0.175582 | + | 0.984465i | \(0.556181\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11760.0 | 0.387470 | ||||||||
\(974\) | −44667.2 | −1.46943 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −32452.0 | −1.06431 | ||||||||
\(977\) | 28359.3 | 0.928654 | 0.464327 | − | 0.885664i | \(-0.346296\pi\) | ||||
0.464327 | + | 0.885664i | \(0.346296\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12800.0 | 0.415952 | ||||||||
\(983\) | 35063.3 | 1.13769 | 0.568844 | − | 0.822446i | \(-0.307391\pi\) | ||||
0.568844 | + | 0.822446i | \(0.307391\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17708.8 | 0.571969 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6370.00 | −0.205118 | ||||||||
\(989\) | 38137.1 | 1.22618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18283.0 | −0.586053 | −0.293027 | − | 0.956104i | \(-0.594662\pi\) | ||||
−0.293027 | + | 0.956104i | \(0.594662\pi\) | |||||||
\(992\) | 13015.9 | 0.416589 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3000.00 | −0.0957286 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13230.0 | 0.420259 | 0.210130 | − | 0.977674i | \(-0.432611\pi\) | ||||
0.210130 | + | 0.977674i | \(0.432611\pi\) | |||||||
\(998\) | 4044.55 | 0.128285 | ||||||||
\(999\) | 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 | 225.4.a.l.1.2 | yes | 2 | |
3.2 | odd | 2 | inner | 225.4.a.l.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 225.4.b.i.199.3 | 4 | |||
5.3 | odd | 4 | 225.4.b.i.199.2 | 4 | |||
5.4 | even | 2 | 225.4.a.m.1.1 | yes | 2 | ||
15.2 | even | 4 | 225.4.b.i.199.1 | 4 | |||
15.8 | even | 4 | 225.4.b.i.199.4 | 4 | |||
15.14 | odd | 2 | 225.4.a.m.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.a.l.1.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
225.4.a.l.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
225.4.a.m.1.1 | yes | 2 | 5.4 | even | 2 | ||
225.4.a.m.1.2 | yes | 2 | 15.14 | odd | 2 | ||
225.4.b.i.199.1 | 4 | 15.2 | even | 4 | |||
225.4.b.i.199.2 | 4 | 5.3 | odd | 4 | |||
225.4.b.i.199.3 | 4 | 5.2 | odd | 4 | |||
225.4.b.i.199.4 | 4 | 15.8 | even | 4 |