Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2312,4,Mod(1,2312)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2312, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2312.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2312 = 2^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2312.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: | \(136.412415933\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 92x^{4} + 123x^{3} + 2120x^{2} - 3573x - 261 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(6.22873\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2312.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −7.22873 | −1.39117 | −0.695585 | − | 0.718444i | \(-0.744855\pi\) | ||||
−0.695585 | + | 0.718444i | \(0.744855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 20.1017 | 1.79795 | 0.898975 | − | 0.437999i | \(-0.144313\pi\) | ||||
0.898975 | + | 0.437999i | \(0.144313\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.5412 | −0.677159 | −0.338580 | − | 0.940938i | \(-0.609946\pi\) | ||||
−0.338580 | + | 0.940938i | \(0.609946\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 25.2545 | 0.935352 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −69.4815 | −1.90450 | −0.952249 | − | 0.305324i | \(-0.901235\pi\) | ||||
−0.952249 | + | 0.305324i | \(0.901235\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.6090 | −0.653031 | −0.326515 | − | 0.945192i | \(-0.605874\pi\) | ||||
−0.326515 | + | 0.945192i | \(0.605874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −145.310 | −2.50125 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 141.932 | 1.71376 | 0.856882 | − | 0.515512i | \(-0.172398\pi\) | ||||
0.856882 | + | 0.515512i | \(0.172398\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 90.6567 | 0.942043 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −142.423 | −1.29118 | −0.645591 | − | 0.763683i | \(-0.723389\pi\) | ||||
−0.645591 | + | 0.763683i | \(0.723389\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 279.078 | 2.23263 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.6177 | 0.0899359 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 266.503 | 1.70650 | 0.853248 | − | 0.521505i | \(-0.174629\pi\) | ||||
0.853248 | + | 0.521505i | \(0.174629\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −64.8995 | −0.376010 | −0.188005 | − | 0.982168i | \(-0.560202\pi\) | ||||
−0.188005 | + | 0.982168i | \(0.560202\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 502.263 | 2.64948 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −252.099 | −1.21750 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 231.103 | 1.02684 | 0.513421 | − | 0.858137i | \(-0.328378\pi\) | ||||
0.513421 | + | 0.858137i | \(0.328378\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 221.264 | 0.908476 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 87.1044 | 0.331791 | 0.165895 | − | 0.986143i | \(-0.446949\pi\) | ||||
0.165895 | + | 0.986143i | \(0.446949\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.2977 | 0.153554 | 0.0767771 | − | 0.997048i | \(-0.475537\pi\) | ||||
0.0767771 | + | 0.997048i | \(0.475537\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 507.659 | 1.68172 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.4576 | −0.0355589 | −0.0177794 | − | 0.999842i | \(-0.505660\pi\) | ||||
−0.0177794 | + | 0.999842i | \(0.505660\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −185.719 | −0.541456 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −359.499 | −0.931716 | −0.465858 | − | 0.884860i | \(-0.654254\pi\) | ||||
−0.465858 | + | 0.884860i | \(0.654254\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1396.70 | −3.42419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1025.99 | −2.38414 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 88.5702 | 0.195438 | 0.0977191 | − | 0.995214i | \(-0.468845\pi\) | ||||
0.0977191 | + | 0.995214i | \(0.468845\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −331.042 | −0.694846 | −0.347423 | − | 0.937708i | \(-0.612943\pi\) | ||||
−0.347423 | + | 0.937708i | \(0.612943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −316.721 | −0.633382 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −615.292 | −1.17412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 701.651 | 1.27941 | 0.639704 | − | 0.768621i | \(-0.279057\pi\) | ||||
0.639704 | + | 0.768621i | \(0.279057\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1029.54 | 1.79625 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 115.400 | 0.192893 | 0.0964465 | − | 0.995338i | \(-0.469252\pi\) | ||||
0.0964465 | + | 0.995338i | \(0.469252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −253.087 | −0.405776 | −0.202888 | − | 0.979202i | \(-0.565033\pi\) | ||||
−0.202888 | + | 0.979202i | \(0.565033\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2017.38 | −3.10596 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 871.379 | 1.28965 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.0538 | 0.105465 | 0.0527323 | − | 0.998609i | \(-0.483207\pi\) | ||||
0.0527323 | + | 0.998609i | \(0.483207\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −773.081 | −1.06047 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 310.263 | 0.410311 | 0.205155 | − | 0.978729i | \(-0.434230\pi\) | ||||
0.205155 | + | 0.978729i | \(0.434230\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1926.48 | −2.37403 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 37.0798 | 0.0441623 | 0.0220812 | − | 0.999756i | \(-0.492971\pi\) | ||||
0.0220812 | + | 0.999756i | \(0.492971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 383.872 | 0.442206 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 469.141 | 0.523093 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2853.08 | 3.08126 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −847.155 | −0.886758 | −0.443379 | − | 0.896334i | \(-0.646220\pi\) | ||||
−0.443379 | + | 0.896334i | \(0.646220\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1754.72 | −1.78138 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1681.22 | 1.65631 | 0.828155 | − | 0.560499i | \(-0.189390\pi\) | ||||
0.828155 | + | 0.560499i | \(0.189390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −257.365 | −0.246203 | −0.123101 | − | 0.992394i | \(-0.539284\pi\) | ||||
−0.123101 | + | 0.992394i | \(0.539284\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1822.35 | 1.69375 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1339.74 | −1.21045 | −0.605224 | − | 0.796055i | \(-0.706916\pi\) | ||||
−0.605224 | + | 0.796055i | \(0.706916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1036.78 | −0.911060 | −0.455530 | − | 0.890221i | \(-0.650550\pi\) | ||||
−0.455530 | + | 0.890221i | \(0.650550\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1670.58 | −1.42851 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 649.092 | 0.540367 | 0.270184 | − | 0.962809i | \(-0.412916\pi\) | ||||
0.270184 | + | 0.962809i | \(0.412916\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2862.94 | −2.32148 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −773.014 | −0.610814 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3496.68 | 2.62711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −629.654 | −0.461577 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3097.24 | 2.21620 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1671.72 | 1.16804 | 0.584020 | − | 0.811739i | \(-0.301479\pi\) | ||||
0.584020 | + | 0.811739i | \(0.301479\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −312.987 | −0.213620 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −46.5186 | −0.0310256 | −0.0155128 | − | 0.999880i | \(-0.504938\pi\) | ||||
−0.0155128 | + | 0.999880i | \(0.504938\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1780.00 | −1.16049 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 253.636 | 0.161700 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2075.69 | −1.29444 | −0.647219 | − | 0.762304i | \(-0.724068\pi\) | ||||
−0.647219 | + | 0.762304i | \(0.724068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2285.72 | −1.39476 | −0.697382 | − | 0.716699i | \(-0.745652\pi\) | ||||
−0.697382 | + | 0.716699i | \(0.745652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 82.8241 | 0.0494684 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2126.76 | 1.24369 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5357.17 | 3.06820 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1342.51 | 0.753256 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2616.77 | 1.43876 | 0.719378 | − | 0.694619i | \(-0.244427\pi\) | ||||
0.719378 | + | 0.694619i | \(0.244427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −829.579 | −0.447087 | −0.223544 | − | 0.974694i | \(-0.571763\pi\) | ||||
−0.223544 | + | 0.974694i | \(0.571763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1304.59 | −0.676047 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −534.658 | −0.271786 | −0.135893 | − | 0.990724i | \(-0.543390\pi\) | ||||
−0.135893 | + | 0.990724i | \(0.543390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2598.72 | 1.29617 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1786.15 | 0.874336 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1302.98 | 0.626119 | 0.313060 | − | 0.949733i | \(-0.398646\pi\) | ||||
0.313060 | + | 0.949733i | \(0.398646\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10096.3 | 4.76363 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1397.37 | −0.647497 | −0.323748 | − | 0.946143i | \(-0.604943\pi\) | ||||
−0.323748 | + | 0.946143i | \(0.604943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1260.09 | −0.573551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3584.43 | 1.60297 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2226.77 | −0.978601 | −0.489301 | − | 0.872115i | \(-0.662748\pi\) | ||||
−0.489301 | + | 0.872115i | \(0.662748\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3499.97 | −1.51184 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −640.250 | −0.271888 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2723.06 | −1.13705 | −0.568523 | − | 0.822667i | \(-0.692485\pi\) | ||||
−0.568523 | + | 0.822667i | \(0.692485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2189.24 | −0.899034 | −0.449517 | − | 0.893272i | \(-0.648404\pi\) | ||||
−0.449517 | + | 0.893272i | \(0.648404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2393.01 | 0.966649 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4645.57 | 1.84621 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −158.240 | −0.0609009 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4759.50 | 1.80306 | 0.901532 | − | 0.432712i | \(-0.142443\pi\) | ||||
0.901532 | + | 0.432712i | \(0.142443\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4200.31 | −1.56656 | −0.783278 | − | 0.621672i | \(-0.786454\pi\) | ||||
−0.783278 | + | 0.621672i | \(0.786454\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4447.78 | 1.63340 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2682.70 | −0.970225 | −0.485113 | − | 0.874452i | \(-0.661221\pi\) | ||||
−0.485113 | + | 0.874452i | \(0.661221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2599.57 | −0.926024 | −0.463012 | − | 0.886352i | \(-0.653231\pi\) | ||||
−0.463012 | + | 0.886352i | \(0.653231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5072.05 | −1.77987 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3342.26 | −1.15557 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1750.95 | 0.596543 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3596.82 | −1.20771 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9861.68 | −3.26386 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1313.29 | −0.428486 | −0.214243 | − | 0.976780i | \(-0.568728\pi\) | ||||
−0.214243 | + | 0.976780i | \(0.568728\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −834.192 | −0.268347 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 870.357 | 0.276083 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 813.916 | 0.254618 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1829.50 | 0.564503 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3580.77 | −1.07527 | −0.537637 | − | 0.843176i | \(-0.680683\pi\) | ||||
−0.537637 | + | 0.843176i | \(0.680683\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7047.99 | 2.08829 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1317.19 | −0.385131 | −0.192565 | − | 0.981284i | \(-0.561681\pi\) | ||||
−0.192565 | + | 0.981284i | \(0.561681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −928.092 | −0.267817 | −0.133908 | − | 0.990994i | \(-0.542753\pi\) | ||||
−0.133908 | + | 0.990994i | \(0.542753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6298.96 | −1.79412 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1723.82 | −0.484682 | −0.242341 | − | 0.970191i | \(-0.577915\pi\) | ||||
−0.242341 | + | 0.970191i | \(0.577915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −230.318 | −0.0639331 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −535.315 | −0.146719 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4010.58 | −1.08545 | −0.542725 | − | 0.839910i | \(-0.682607\pi\) | ||||
−0.542725 | + | 0.839910i | \(0.682607\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3462.05 | 0.925353 | 0.462676 | − | 0.886527i | \(-0.346889\pi\) | ||||
0.462676 | + | 0.886527i | \(0.346889\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5247.72 | 1.38536 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3733.27 | −0.973510 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4344.40 | −1.11914 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2242.81 | −0.570812 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7169.18 | 1.80285 | 0.901423 | − | 0.432940i | \(-0.142524\pi\) | ||||
0.901423 | + | 0.432940i | \(0.142524\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9895.75 | 2.45905 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4618.01 | 1.12087 | 0.560435 | − | 0.828198i | \(-0.310634\pi\) | ||||
0.560435 | + | 0.828198i | \(0.310634\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2898.30 | −0.695335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6730.41 | 1.59618 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2669.24 | 0.625826 | 0.312913 | − | 0.949782i | \(-0.398695\pi\) | ||||
0.312913 | + | 0.949782i | \(0.398695\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7226.53 | −1.67518 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −268.040 | −0.0614373 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6903.18 | 1.56466 | 0.782332 | − | 0.622862i | \(-0.214030\pi\) | ||||
0.782332 | + | 0.622862i | \(0.214030\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 556.074 | 0.124646 | 0.0623231 | − | 0.998056i | \(-0.480149\pi\) | ||||
0.0623231 | + | 0.998056i | \(0.480149\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2774.91 | −0.615183 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −19390.8 | −4.25203 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1791.33 | −0.388558 | −0.194279 | − | 0.980946i | \(-0.562237\pi\) | ||||
−0.194279 | + | 0.980946i | \(0.562237\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1639.01 | −0.351702 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8844.03 | −1.87755 | −0.938773 | − | 0.344536i | \(-0.888036\pi\) | ||||
−0.938773 | + | 0.344536i | \(0.888036\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2003.30 | 0.420790 | 0.210395 | − | 0.977616i | \(-0.432525\pi\) | ||||
0.210395 | + | 0.977616i | \(0.432525\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −20624.2 | −4.28656 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1092.39 | −0.224675 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6123.85 | 1.23363 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4397.46 | −0.876800 | −0.438400 | − | 0.898780i | \(-0.644455\pi\) | ||||
−0.438400 | + | 0.898780i | \(0.644455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1780.41 | 0.351388 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −876.694 | −0.171283 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4359.41 | 0.843182 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −543.003 | −0.103981 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12153.1 | −2.30421 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6654.51 | −1.24930 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7093.45 | −1.31871 | −0.659356 | − | 0.751831i | \(-0.729171\pi\) | ||||
−0.659356 | + | 0.751831i | \(0.729171\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1860.42 | 0.342510 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 65.9674 | 0.0120279 | 0.00601394 | − | 0.999982i | \(-0.498086\pi\) | ||||
0.00601394 | + | 0.999982i | \(0.498086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2826.30 | 0.510390 | 0.255195 | − | 0.966890i | \(-0.417860\pi\) | ||||
0.255195 | + | 0.966890i | \(0.417860\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6366.63 | −1.13879 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −828.181 | −0.146736 | −0.0733680 | − | 0.997305i | \(-0.523375\pi\) | ||||
−0.0733680 | + | 0.997305i | \(0.523375\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18517.1 | −3.25002 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9684.64 | 1.68394 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8542.30 | −1.45797 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7494.60 | 1.26744 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 143.692 | 0.0240790 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 360.307 | 0.0598315 | 0.0299158 | − | 0.999552i | \(-0.490476\pi\) | ||||
0.0299158 | + | 0.999552i | \(0.490476\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5836.40 | 0.960459 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14104.4 | 2.30031 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3573.20 | 0.577581 | 0.288790 | − | 0.957392i | \(-0.406747\pi\) | ||||
0.288790 | + | 0.957392i | \(0.406747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4692.11 | −0.751742 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4509.32 | 0.716109 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6630.75 | 1.04381 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20695.4 | 3.22958 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4277.60 | −0.661769 | −0.330884 | − | 0.943671i | \(-0.607347\pi\) | ||||
−0.330884 | + | 0.943671i | \(0.607347\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5164.62 | 0.792136 | 0.396068 | − | 0.918221i | \(-0.370374\pi\) | ||||
0.396068 | + | 0.918221i | \(0.370374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −386.213 | −0.0587309 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11013.9 | −1.66066 | −0.830328 | − | 0.557275i | \(-0.811847\pi\) | ||||
−0.830328 | + | 0.557275i | \(0.811847\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2319.73 | 0.346812 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5734.19 | −0.843005 | −0.421503 | − | 0.906827i | \(-0.638497\pi\) | ||||
−0.421503 | + | 0.906827i | \(0.638497\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13285.8 | 1.93699 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25276.6 | −3.65476 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5087.48 | −0.729564 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6705.71 | −0.953775 | −0.476887 | − | 0.878964i | \(-0.658235\pi\) | ||||
−0.476887 | + | 0.878964i | \(0.658235\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2199.78 | 0.310341 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4508.53 | 0.630920 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 895.205 | 0.124268 | 0.0621340 | − | 0.998068i | \(-0.480209\pi\) | ||||
0.0621340 | + | 0.998068i | \(0.480209\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −22389.1 | −3.08311 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8157.39 | −1.11439 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5639.78 | 0.764370 | 0.382185 | − | 0.924086i | \(-0.375172\pi\) | ||||
0.382185 | + | 0.924086i | \(0.375172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12084.4 | −1.62494 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1924.52 | 0.256758 | 0.128379 | − | 0.991725i | \(-0.459023\pi\) | ||||
0.128379 | + | 0.991725i | \(0.459023\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17516.2 | 2.31872 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1093.46 | 0.143627 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4330.08 | −0.564380 | −0.282190 | − | 0.959359i | \(-0.591061\pi\) | ||||
−0.282190 | + | 0.959359i | \(0.591061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 336.270 | 0.0431618 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1488.61 | 0.189620 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 227.821 | 0.0288011 | 0.0144005 | − | 0.999896i | \(-0.495416\pi\) | ||||
0.0144005 | + | 0.999896i | \(0.495416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12867.1 | 1.61444 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11165.9 | −1.39052 | −0.695259 | − | 0.718759i | \(-0.744710\pi\) | ||||
−0.695259 | + | 0.718759i | \(0.744710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1986.51 | 0.245546 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −15540.2 | −1.90667 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16057.4 | −1.95562 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4583.25 | 0.554100 | 0.277050 | − | 0.960855i | \(-0.410643\pi\) | ||||
0.277050 | + | 0.960855i | \(0.410643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15004.6 | 1.80078 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1110.77 | −0.132343 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6236.82 | 0.737719 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16522.9 | 1.94035 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3560.30 | 0.415112 | 0.207556 | − | 0.978223i | \(-0.433449\pi\) | ||||
0.207556 | + | 0.978223i | \(0.433449\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14890.5 | −1.72380 | −0.861899 | − | 0.507080i | \(-0.830725\pi\) | ||||
−0.861899 | + | 0.507080i | \(0.830725\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −289.357 | −0.0332601 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4151.65 | 0.470521 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15373.8 | −1.73019 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9161.06 | −1.02383 | −0.511917 | − | 0.859035i | \(-0.671064\pi\) | ||||
−0.511917 | + | 0.859035i | \(0.671064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7039.80 | −0.781320 | −0.390660 | − | 0.920535i | \(-0.627753\pi\) | ||||
−0.390660 | + | 0.920535i | \(0.627753\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −38725.5 | −4.26838 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20214.4 | −2.21278 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2096.93 | −0.227975 | −0.113987 | − | 0.993482i | \(-0.536362\pi\) | ||||
−0.113987 | + | 0.993482i | \(0.536362\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4690.25 | −0.506452 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4869.32 | −0.522231 | −0.261116 | − | 0.965308i | \(-0.584090\pi\) | ||||
−0.261116 | + | 0.965308i | \(0.584090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 745.366 | 0.0794017 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18916.0 | −2.00155 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10282.6 | −1.08077 | −0.540384 | − | 0.841419i | \(-0.681721\pi\) | ||||
−0.540384 | + | 0.841419i | \(0.681721\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6052.15 | −0.631894 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5996.80 | 0.621974 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7716.48 | 0.795064 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5974.47 | −0.611540 | −0.305770 | − | 0.952105i | \(-0.598914\pi\) | ||||
−0.305770 | + | 0.952105i | \(0.598914\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5073.15 | −0.512538 | −0.256269 | − | 0.966605i | \(-0.582493\pi\) | ||||
−0.256269 | + | 0.966605i | \(0.582493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10175.2 | 1.02135 | 0.510673 | − | 0.859775i | \(-0.329396\pi\) | ||||
0.510673 | + | 0.859775i | \(0.329396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9430.53 | 0.940496 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16042.8 | 1.58966 | 0.794832 | − | 0.606829i | \(-0.207559\pi\) | ||||
0.794832 | + | 0.606829i | \(0.207559\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8799.52 | −0.866363 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3864.89 | 0.378100 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3008.39 | −0.292444 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 39610.3 | 3.82620 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9078.96 | −0.871482 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3112.53 | −0.296900 | −0.148450 | − | 0.988920i | \(-0.547428\pi\) | ||||
−0.148450 | + | 0.988920i | \(0.547428\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7073.83 | −0.670559 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12911.6 | −1.21635 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17029.3 | −1.59435 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14246.8 | −1.32563 | −0.662817 | − | 0.748782i | \(-0.730639\pi\) | ||||
−0.662817 | + | 0.748782i | \(0.730639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9418.90 | −0.871038 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12067.1 | −1.10913 | −0.554563 | − | 0.832141i | \(-0.687115\pi\) | ||||
−0.554563 | + | 0.832141i | \(0.687115\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −35272.9 | −3.20283 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1447.24 | −0.130619 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9899.84 | −0.888132 | −0.444066 | − | 0.895994i | \(-0.646464\pi\) | ||||
−0.444066 | + | 0.895994i | \(0.646464\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10101.2 | 0.900778 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6311.17 | 0.559446 | 0.279723 | − | 0.960081i | \(-0.409757\pi\) | ||||
0.279723 | + | 0.960081i | \(0.409757\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33795.3 | 2.97796 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9108.86 | 0.797907 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20723.8 | −1.80465 | −0.902323 | − | 0.431060i | \(-0.858140\pi\) | ||||
−0.902323 | + | 0.431060i | \(0.858140\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3174.01 | 0.274775 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1790.85 | 0.154129 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5173.47 | −0.442660 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 796.094 | 0.0677218 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16096.7 | 1.36140 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20086.3 | 1.68906 | 0.844528 | − | 0.535512i | \(-0.179881\pi\) | ||||
0.844528 | + | 0.535512i | \(0.179881\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1030.12 | −0.0861260 | −0.0430630 | − | 0.999072i | \(-0.513712\pi\) | ||||
−0.0430630 | + | 0.999072i | \(0.513712\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25300.3 | 2.10323 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8117.24 | 0.667152 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2236.80 | 0.182804 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2666.17 | −0.216669 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26931.1 | −2.17632 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19684.3 | 1.58182 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12904.1 | 1.03120 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17839.9 | −1.41774 | −0.708869 | − | 0.705340i | \(-0.750794\pi\) | ||||
−0.708869 | + | 0.705340i | \(0.750794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15825.4 | 1.25071 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20841.0 | −1.63804 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24222.2 | −1.89336 | −0.946679 | − | 0.322178i | \(-0.895585\pi\) | ||||
−0.946679 | + | 0.322178i | \(0.895585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8360.31 | −0.649926 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37825.4 | 2.92453 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −928.721 | −0.0714163 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −33581.6 | −2.56839 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5181.50 | −0.394160 | −0.197080 | − | 0.980387i | \(-0.563146\pi\) | ||||
−0.197080 | + | 0.980387i | \(0.563146\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1325.30 | −0.100276 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16423.8 | 1.22945 | 0.614727 | − | 0.788740i | \(-0.289266\pi\) | ||||
0.614727 | + | 0.788740i | \(0.289266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13047.9 | 0.971553 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9695.34 | 0.718106 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10895.9 | 0.802774 | 0.401387 | − | 0.915909i | \(-0.368528\pi\) | ||||
0.401387 | + | 0.915909i | \(0.368528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11768.7 | 0.862532 | 0.431266 | − | 0.902225i | \(-0.358067\pi\) | ||||
0.431266 | + | 0.902225i | \(0.358067\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −34405.1 | −2.50837 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39747.1 | −2.88273 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3354.51 | −0.242028 | −0.121014 | − | 0.992651i | \(-0.538615\pi\) | ||||
−0.121014 | + | 0.992651i | \(0.538615\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30362.9 | 2.17934 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3891.06 | −0.277846 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24978.5 | 1.77445 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15538.9 | −1.09821 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14249.2 | −1.00192 | −0.500961 | − | 0.865470i | \(-0.667020\pi\) | ||||
−0.500961 | + | 0.865470i | \(0.667020\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9211.35 | −0.644392 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19392.5 | 1.34975 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −21494.4 | −1.48848 | −0.744242 | − | 0.667910i | \(-0.767189\pi\) | ||||
−0.744242 | + | 0.667910i | \(0.767189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18791.6 | 1.28826 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −23890.0 | −1.62958 | −0.814789 | − | 0.579758i | \(-0.803147\pi\) | ||||
−0.814789 | + | 0.579758i | \(0.803147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19368.0 | 1.31454 | 0.657268 | − | 0.753657i | \(-0.271712\pi\) | ||||
0.657268 | + | 0.753657i | \(0.271712\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17719.9 | 1.19670 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 70289.3 | 4.72341 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9298.54 | −0.621773 | −0.310886 | − | 0.950447i | \(-0.600626\pi\) | ||||
−0.310886 | + | 0.950447i | \(0.600626\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24160.3 | 1.60759 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 350.706 | 0.0232210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14980.8 | 0.987062 | 0.493531 | − | 0.869728i | \(-0.335706\pi\) | ||||
0.493531 | + | 0.869728i | \(0.335706\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12657.1 | −0.829893 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1781.72 | −0.116255 | −0.0581275 | − | 0.998309i | \(-0.518513\pi\) | ||||
−0.0581275 | + | 0.998309i | \(0.518513\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1779.72 | −0.115562 | −0.0577812 | − | 0.998329i | \(-0.518403\pi\) | ||||
−0.0577812 | + | 0.998329i | \(0.518403\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1797.04 | −0.116124 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −465.023 | −0.0299049 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 27374.9 | 1.75199 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 71287.4 | 4.54058 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24432.5 | 1.54143 | 0.770716 | − | 0.637179i | \(-0.219899\pi\) | ||||
0.770716 | + | 0.637179i | \(0.219899\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9493.41 | 0.596097 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33604.4 | 2.10008 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5684.67 | 0.353587 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2914.36 | 0.180423 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21340.3 | 1.31496 | 0.657482 | − | 0.753471i | \(-0.271622\pi\) | ||||
0.657482 | + | 0.753471i | \(0.271622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28838.7 | −1.76872 | −0.884359 | − | 0.466807i | \(-0.845404\pi\) | ||||
−0.884359 | + | 0.466807i | \(0.845404\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6291.57 | −0.384078 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8229.72 | 0.500068 | 0.250034 | − | 0.968237i | \(-0.419558\pi\) | ||||
0.250034 | + | 0.968237i | \(0.419558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6153.99 | −0.372212 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5883.57 | −0.354217 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12819.1 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −935.103 | −0.0557824 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6391.59 | −0.379543 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7540.71 | −0.445743 | −0.222871 | − | 0.974848i | \(-0.571543\pi\) | ||||
−0.222871 | + | 0.974848i | \(0.571543\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2217.32 | 0.130474 | 0.0652372 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652372 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −35781.0 | −2.08651 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37956.1 | −2.20340 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 25884.4 | 1.49589 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23001.3 | 1.32333 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20231.7 | −1.15880 | −0.579402 | − | 0.815042i | \(-0.696714\pi\) | ||||
−0.579402 | + | 0.815042i | \(0.696714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3521.31 | 0.200793 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15767.4 | 0.895109 | 0.447554 | − | 0.894257i | \(-0.352295\pi\) | ||||
0.447554 | + | 0.894257i | \(0.352295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10624.3 | 0.600477 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9521.58 | 0.535782 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5108.40 | 0.286190 | 0.143095 | − | 0.989709i | \(-0.454295\pi\) | ||||
0.143095 | + | 0.989709i | \(0.454295\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41724.9 | −2.32734 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6708.92 | 0.372579 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11003.9 | 0.608439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10967.2 | 0.603782 | 0.301891 | − | 0.953342i | \(-0.402382\pi\) | ||||
0.301891 | + | 0.953342i | \(0.402382\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 22006.3 | 1.20628 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −45946.9 | −2.50772 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12461.0 | 0.674275 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9631.21 | 0.518924 | 0.259462 | − | 0.965753i | \(-0.416455\pi\) | ||||
0.259462 | + | 0.965753i | \(0.416455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 32801.1 | 1.75977 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1664.90 | 0.0889418 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21084.4 | −1.12159 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2497.09 | 0.132271 | 0.0661355 | − | 0.997811i | \(-0.478933\pi\) | ||||
0.0661355 | + | 0.997811i | \(0.478933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1870.19 | 0.0986466 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9243.17 | 0.485497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42751.4 | 2.23610 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 28991.4 | 1.51005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25801.7 | −1.33831 | −0.669153 | − | 0.743125i | \(-0.733343\pi\) | ||||
−0.669153 | + | 0.743125i | \(0.733343\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3227.65 | 0.166718 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25026.2 | −1.28732 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 74375.3 | 3.80997 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4794.66 | 0.244600 | 0.122300 | − | 0.992493i | \(-0.460973\pi\) | ||||
0.122300 | + | 0.992493i | \(0.460973\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17061.1 | −0.866796 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35417.8 | 1.78470 | 0.892351 | − | 0.451341i | \(-0.149054\pi\) | ||||
0.892351 | + | 0.451341i | \(0.149054\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26986.8 | 1.35432 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −48751.8 | −2.43663 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1824.26 | 0.0908073 | 0.0454036 | − | 0.998969i | \(-0.485543\pi\) | ||||
0.0454036 | + | 0.998969i | \(0.485543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31404.5 | 1.55691 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20648.4 | −1.01954 | −0.509768 | − | 0.860312i | \(-0.670269\pi\) | ||||
−0.509768 | + | 0.860312i | \(0.670269\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 52601.6 | 2.58681 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7835.54 | 0.383785 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16801.9 | 0.819666 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21345.1 | 1.03714 | 0.518571 | − | 0.855035i | \(-0.326464\pi\) | ||||
0.518571 | + | 0.855035i | \(0.326464\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −51824.0 | −2.50806 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16675.9 | −0.803841 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7073.26 | 0.339606 | 0.169803 | − | 0.985478i | \(-0.445687\pi\) | ||||
0.169803 | + | 0.985478i | \(0.445687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −71533.7 | −3.42096 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21558.9 | 1.02695 | 0.513476 | − | 0.858104i | \(-0.328358\pi\) | ||||
0.513476 | + | 0.858104i | \(0.328358\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13002.4 | 0.616932 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2711.04 | −0.127627 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21519.5 | −1.00912 | −0.504561 | − | 0.863376i | \(-0.668346\pi\) | ||||
−0.504561 | + | 0.863376i | \(0.668346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33382.3 | −1.55932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38270.0 | −1.78069 | −0.890347 | − | 0.455283i | \(-0.849538\pi\) | ||||
−0.890347 | + | 0.455283i | \(0.849538\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18112.0 | −0.839489 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20951.1 | 0.967329 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12362.9 | 0.568611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8018.14 | −0.367364 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3362.64 | 0.153475 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10747.5 | −0.488657 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13164.9 | 0.596288 | 0.298144 | − | 0.954521i | \(-0.403632\pi\) | ||||
0.298144 | + | 0.954521i | \(0.403632\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19295.2 | −0.870630 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8140.37 | −0.365914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10132.9 | 0.453756 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 52238.6 | 2.33046 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25617.3 | −1.13853 | −0.569267 | − | 0.822153i | \(-0.692773\pi\) | ||||
−0.569267 | + | 0.822153i | \(0.692773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 936.431 | 0.0413073 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17584.9 | 0.772798 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35904.6 | 1.57201 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −49901.2 | −2.17671 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13970.8 | −0.607155 | −0.303578 | − | 0.952807i | \(-0.598181\pi\) | ||||
−0.303578 | + | 0.952807i | \(0.598181\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6997.62 | −0.302984 | −0.151492 | − | 0.988459i | \(-0.548408\pi\) | ||||
−0.151492 | + | 0.988459i | \(0.548408\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4019.71 | −0.173404 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26192.2 | 1.12573 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6145.34 | 0.263156 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9694.50 | 0.413618 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33514.2 | 1.42467 | 0.712335 | − | 0.701840i | \(-0.247638\pi\) | ||||
0.712335 | + | 0.701840i | \(0.247638\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7392.06 | −0.313088 | −0.156544 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156544 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 140171. | 5.91530 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35535.6 | 1.49419 | 0.747095 | − | 0.664717i | \(-0.231448\pi\) | ||||
0.747095 | + | 0.664717i | \(0.231448\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22227.0 | 0.931211 | 0.465606 | − | 0.884992i | \(-0.345837\pi\) | ||||
0.465606 | + | 0.884992i | \(0.345837\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12949.0 | 0.540550 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28089.6 | −1.16417 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −818.880 | −0.0338167 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12905.7 | −0.531052 | −0.265526 | − | 0.964104i | \(-0.585546\pi\) | ||||
−0.265526 | + | 0.964104i | \(0.585546\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46635.0 | 1.91213 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 63931.1 | 2.61198 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25330.0 | −1.03122 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43852.5 | −1.77897 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14481.3 | −0.585391 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32914.4 | −1.32584 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38244.5 | −1.53513 | −0.767565 | − | 0.640971i | \(-0.778532\pi\) | ||||
−0.767565 | + | 0.640971i | \(0.778532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 72053.2 | 2.88207 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13499.9 | 0.538095 | 0.269047 | − | 0.963127i | \(-0.413291\pi\) | ||||
0.269047 | + | 0.963127i | \(0.413291\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17229.3 | −0.684349 | −0.342175 | − | 0.939636i | \(-0.611163\pi\) | ||||
−0.342175 | + | 0.939636i | \(0.611163\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7896.59 | 0.312561 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1566.04 | −0.0617712 | −0.0308856 | − | 0.999523i | \(-0.509833\pi\) | ||||
−0.0308856 | + | 0.999523i | \(0.509833\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44761.8 | −1.75948 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5145.37 | −0.200857 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21476.8 | −0.835493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21394.5 | −0.829432 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38842.9 | −1.50072 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34387.0 | −1.32402 | −0.662010 | − | 0.749495i | \(-0.730296\pi\) | ||||
−0.662010 | + | 0.749495i | \(0.730296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31788.0 | 1.21978 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27902.5 | 1.06704 | 0.533518 | − | 0.845789i | \(-0.320870\pi\) | ||||
0.533518 | + | 0.845789i | \(0.320870\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23855.6 | 0.909180 | 0.454590 | − | 0.890701i | \(-0.349786\pi\) | ||||
0.454590 | + | 0.890701i | \(0.349786\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12870.1 | −0.488841 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20476.4 | 0.775119 | 0.387560 | − | 0.921845i | \(-0.373318\pi\) | ||||
0.387560 | + | 0.921845i | \(0.373318\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20965.3 | −0.790949 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 53714.9 | 2.01966 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1626.21 | −0.0609395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −54738.2 | −2.04435 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −31513.0 | −1.17301 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17295.9 | −0.641659 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3925.22 | 0.144655 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −44007.5 | −1.61642 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −40323.7 | −1.47622 | −0.738108 | − | 0.674683i | \(-0.764280\pi\) | ||||
−0.738108 | + | 0.674683i | \(0.764280\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 42458.3 | 1.54923 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31332.9 | 1.13952 | 0.569761 | − | 0.821811i | \(-0.307036\pi\) | ||||
0.569761 | + | 0.821811i | \(0.307036\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21557.6 | −0.781436 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 48103.7 | 1.73799 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 583.397 | 0.0210092 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36056.5 | −1.29423 | −0.647113 | − | 0.762394i | \(-0.724024\pi\) | ||||
−0.647113 | + | 0.762394i | \(0.724024\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51276.6 | 1.83455 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3532.26 | −0.125965 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 64495.9 | 2.29255 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6499.62 | −0.230286 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13754.0 | −0.485740 | −0.242870 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242870 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26359.6 | −0.927927 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −476.860 | −0.0167328 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 54250.9 | 1.89146 | 0.945731 | − | 0.324951i | \(-0.105348\pi\) | ||||
0.945731 | + | 0.324951i | \(0.105348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20430.6 | −0.710039 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36296.2 | −1.25741 | −0.628705 | − | 0.777644i | \(-0.716415\pi\) | ||||
−0.628705 | + | 0.777644i | \(0.716415\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12405.6 | −0.428402 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3180.89 | −0.109497 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24725.5 | −0.848439 | −0.424220 | − | 0.905559i | \(-0.639452\pi\) | ||||
−0.424220 | + | 0.905559i | \(0.639452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7746.74 | 0.264984 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5986.70 | 0.204135 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −24482.5 | −0.832180 | −0.416090 | − | 0.909323i | \(-0.636600\pi\) | ||||
−0.416090 | + | 0.909323i | \(0.636600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 95674.0 | 3.24182 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 133855. | 4.52133 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26031.5 | 0.876541 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25579.1 | −0.858617 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33834.6 | −1.13219 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −84433.4 | −2.81659 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14361.7 | −0.477602 | −0.238801 | − | 0.971068i | \(-0.576754\pi\) | ||||
−0.238801 | + | 0.971068i | \(0.576754\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −45204.8 | −1.49402 | −0.747009 | − | 0.664814i | \(-0.768511\pi\) | ||||
−0.747009 | + | 0.664814i | \(0.768511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28665.6 | 0.944478 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 61749.9 | 2.02829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9862.31 | 0.322951 | 0.161476 | − | 0.986877i | \(-0.448375\pi\) | ||||
0.161476 | + | 0.986877i | \(0.448375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2576.36 | −0.0841070 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26183.4 | −0.852162 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17654.3 | 0.572824 | 0.286412 | − | 0.958107i | \(-0.407537\pi\) | ||||
0.286412 | + | 0.958107i | \(0.407537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −53926.8 | −1.74442 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1038.71 | −0.0334980 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6166.57 | −0.198267 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21299.8 | −0.682756 | −0.341378 | − | 0.939926i | \(-0.610894\pi\) | ||||
−0.341378 | + | 0.939926i | \(0.610894\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2604.56 | −0.0832358 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52255.8 | −1.66494 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26618.1 | −0.845541 | −0.422770 | − | 0.906237i | \(-0.638942\pi\) | ||||
−0.422770 | + | 0.906237i | \(0.638942\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2915.98 | 0.0923499 |
(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 | 2312.4.a.f.1.2 | ✓ | 6 | |
17.16 | even | 2 | 2312.4.a.j.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2312.4.a.f.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
2312.4.a.j.1.5 | yes | 6 | 17.16 | even | 2 |