Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,4,Mod(1,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.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: | \(127.444125612\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 1080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.87370\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 30.2207 | 1.63176 | 0.815882 | − | 0.578218i | \(-0.196252\pi\) | ||||
0.815882 | + | 0.578218i | \(0.196252\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −67.3185 | −1.84521 | −0.922604 | − | 0.385748i | \(-0.873944\pi\) | ||||
−0.922604 | + | 0.385748i | \(0.873944\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −60.7911 | −1.29696 | −0.648478 | − | 0.761234i | \(-0.724594\pi\) | ||||
−0.648478 | + | 0.761234i | \(0.724594\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 61.1347 | 0.872196 | 0.436098 | − | 0.899899i | \(-0.356360\pi\) | ||||
0.436098 | + | 0.899899i | \(0.356360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27.8771 | 0.336603 | 0.168301 | − | 0.985736i | \(-0.446172\pi\) | ||||
0.168301 | + | 0.985736i | \(0.446172\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.4655 | 0.366854 | 0.183427 | − | 0.983033i | \(-0.441281\pi\) | ||||
0.183427 | + | 0.983033i | \(0.441281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 212.108 | 1.35819 | 0.679095 | − | 0.734051i | \(-0.262373\pi\) | ||||
0.679095 | + | 0.734051i | \(0.262373\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −167.318 | −0.969394 | −0.484697 | − | 0.874682i | \(-0.661070\pi\) | ||||
−0.484697 | + | 0.874682i | \(0.661070\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 151.103 | 0.729747 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −366.539 | −1.62861 | −0.814305 | − | 0.580437i | \(-0.802882\pi\) | ||||
−0.814305 | + | 0.580437i | \(0.802882\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −363.385 | −1.38418 | −0.692088 | − | 0.721813i | \(-0.743309\pi\) | ||||
−0.692088 | + | 0.721813i | \(0.743309\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −153.839 | −0.545586 | −0.272793 | − | 0.962073i | \(-0.587947\pi\) | ||||
−0.272793 | + | 0.962073i | \(0.587947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 434.212 | 1.34758 | 0.673791 | − | 0.738922i | \(-0.264665\pi\) | ||||
0.673791 | + | 0.738922i | \(0.264665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 570.291 | 1.66265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.6550 | 0.206442 | 0.103221 | − | 0.994658i | \(-0.467085\pi\) | ||||
0.103221 | + | 0.994658i | \(0.467085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −336.593 | −0.825202 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −339.414 | −0.748948 | −0.374474 | − | 0.927237i | \(-0.622177\pi\) | ||||
−0.374474 | + | 0.927237i | \(0.622177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −525.856 | −1.10375 | −0.551877 | − | 0.833926i | \(-0.686088\pi\) | ||||
−0.551877 | + | 0.833926i | \(0.686088\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −303.956 | −0.580016 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −131.916 | −0.240539 | −0.120269 | − | 0.992741i | \(-0.538376\pi\) | ||||
−0.120269 | + | 0.992741i | \(0.538376\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 296.263 | 0.495210 | 0.247605 | − | 0.968861i | \(-0.420356\pi\) | ||||
0.247605 | + | 0.968861i | \(0.420356\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1230.34 | −1.97261 | −0.986305 | − | 0.164932i | \(-0.947259\pi\) | ||||
−0.986305 | + | 0.164932i | \(0.947259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2034.41 | −3.01095 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 621.772 | 0.885504 | 0.442752 | − | 0.896644i | \(-0.354002\pi\) | ||||
0.442752 | + | 0.896644i | \(0.354002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 76.3372 | 0.100953 | 0.0504765 | − | 0.998725i | \(-0.483926\pi\) | ||||
0.0504765 | + | 0.998725i | \(0.483926\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 305.673 | 0.390058 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −192.406 | −0.229157 | −0.114579 | − | 0.993414i | \(-0.536552\pi\) | ||||
−0.114579 | + | 0.993414i | \(0.536552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1837.15 | −2.11633 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 139.386 | 0.150533 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −874.771 | −0.915666 | −0.457833 | − | 0.889038i | \(-0.651374\pi\) | ||||
−0.457833 | + | 0.889038i | \(0.651374\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1093.02 | −1.07682 | −0.538412 | − | 0.842682i | \(-0.680975\pi\) | ||||
−0.538412 | + | 0.842682i | \(0.680975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −228.932 | −0.219003 | −0.109502 | − | 0.993987i | \(-0.534925\pi\) | ||||
−0.109502 | + | 0.993987i | \(0.534925\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −479.745 | −0.433446 | −0.216723 | − | 0.976233i | \(-0.569537\pi\) | ||||
−0.216723 | + | 0.976233i | \(0.569537\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −116.246 | −0.102150 | −0.0510751 | − | 0.998695i | \(-0.516265\pi\) | ||||
−0.0510751 | + | 0.998695i | \(0.516265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 741.222 | 0.617065 | 0.308532 | − | 0.951214i | \(-0.400162\pi\) | ||||
0.308532 | + | 0.951214i | \(0.400162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 202.327 | 0.164062 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1847.53 | 1.42322 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3200.78 | 2.40479 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2595.38 | 1.81340 | 0.906702 | − | 0.421771i | \(-0.138591\pi\) | ||||
0.906702 | + | 0.421771i | \(0.138591\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1405.62 | −0.937476 | −0.468738 | − | 0.883337i | \(-0.655291\pi\) | ||||
−0.468738 | + | 0.883337i | \(0.655291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 842.466 | 0.549256 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2457.39 | −1.53248 | −0.766239 | − | 0.642556i | \(-0.777874\pi\) | ||||
−0.766239 | + | 0.642556i | \(0.777874\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 585.391 | 0.357210 | 0.178605 | − | 0.983921i | \(-0.442842\pi\) | ||||
0.178605 | + | 0.983921i | \(0.442842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4092.37 | 2.39315 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1060.54 | 0.607401 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 926.505 | 0.509411 | 0.254705 | − | 0.967019i | \(-0.418021\pi\) | ||||
0.254705 | + | 0.967019i | \(0.418021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −411.900 | −0.221987 | −0.110993 | − | 0.993821i | \(-0.535403\pi\) | ||||
−0.110993 | + | 0.993821i | \(0.535403\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −836.590 | −0.433526 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2959.97 | −1.50466 | −0.752328 | − | 0.658789i | \(-0.771069\pi\) | ||||
−0.752328 | + | 0.658789i | \(0.771069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1222.89 | 0.598619 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2504.50 | −1.20348 | −0.601741 | − | 0.798691i | \(-0.705526\pi\) | ||||
−0.601741 | + | 0.798691i | \(0.705526\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2055.42 | −0.952413 | −0.476207 | − | 0.879333i | \(-0.657989\pi\) | ||||
−0.476207 | + | 0.879333i | \(0.657989\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1498.56 | 0.682093 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1724.17 | 0.757722 | 0.378861 | − | 0.925454i | \(-0.376316\pi\) | ||||
0.378861 | + | 0.925454i | \(0.376316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 755.517 | 0.326353 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3601.35 | 1.50379 | 0.751893 | − | 0.659285i | \(-0.229141\pi\) | ||||
0.751893 | + | 0.659285i | \(0.229141\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1257.17 | −0.516267 | −0.258134 | − | 0.966109i | \(-0.583107\pi\) | ||||
−0.258134 | + | 0.966109i | \(0.583107\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1832.69 | −0.728337 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4115.50 | −1.60938 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4677.47 | 1.77199 | 0.885994 | − | 0.463697i | \(-0.153477\pi\) | ||||
0.885994 | + | 0.463697i | \(0.153477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2647.88 | −0.987556 | −0.493778 | − | 0.869588i | \(-0.664384\pi\) | ||||
−0.493778 | + | 0.869588i | \(0.664384\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1368.91 | 0.495082 | 0.247541 | − | 0.968877i | \(-0.420378\pi\) | ||||
0.247541 | + | 0.968877i | \(0.420378\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5411.43 | 1.92767 | 0.963835 | − | 0.266501i | \(-0.0858675\pi\) | ||||
0.963835 | + | 0.266501i | \(0.0858675\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6410.06 | 2.21625 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1816.93 | −0.619022 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1876.65 | −0.621102 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1987.12 | −0.648337 | −0.324168 | − | 0.945999i | \(-0.605084\pi\) | ||||
−0.324168 | + | 0.945999i | \(0.605084\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −769.194 | −0.243993 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5056.47 | −1.58182 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3716.45 | −1.13120 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3687.95 | −1.10746 | −0.553730 | − | 0.832697i | \(-0.686796\pi\) | ||||
−0.553730 | + | 0.832697i | \(0.686796\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 859.424 | 0.251286 | 0.125643 | − | 0.992076i | \(-0.459901\pi\) | ||||
0.125643 | + | 0.992076i | \(0.459901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1862.67 | −0.537504 | −0.268752 | − | 0.963209i | \(-0.586611\pi\) | ||||
−0.268752 | + | 0.963209i | \(0.586611\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5011.22 | −1.40900 | −0.704498 | − | 0.709706i | \(-0.748828\pi\) | ||||
−0.704498 | + | 0.709706i | \(0.748828\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2171.06 | 0.602657 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5057.92 | 1.36891 | 0.684455 | − | 0.729055i | \(-0.260040\pi\) | ||||
0.684455 | + | 0.729055i | \(0.260040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7276.37 | −1.94486 | −0.972431 | − | 0.233189i | \(-0.925084\pi\) | ||||
−0.972431 | + | 0.233189i | \(0.925084\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2851.45 | 0.743562 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1694.68 | −0.436559 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 204.208 | 0.0513525 | 0.0256762 | − | 0.999670i | \(-0.491826\pi\) | ||||
0.0256762 | + | 0.999670i | \(0.491826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2724.07 | −0.676921 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4591.80 | −1.11451 | −0.557254 | − | 0.830342i | \(-0.688145\pi\) | ||||
−0.557254 | + | 0.830342i | \(0.688145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11077.1 | −2.65751 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7689.01 | −1.80276 | −0.901378 | − | 0.433033i | \(-0.857443\pi\) | ||||
−0.901378 | + | 0.433033i | \(0.857443\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 398.275 | 0.0923239 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5790.73 | −1.31252 | −0.656258 | − | 0.754536i | \(-0.727862\pi\) | ||||
−0.656258 | + | 0.754536i | \(0.727862\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6146.43 | −1.37775 | −0.688873 | − | 0.724882i | \(-0.741894\pi\) | ||||
−0.688873 | + | 0.724882i | \(0.741894\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1682.96 | −0.369042 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4811.02 | 1.04356 | 0.521781 | − | 0.853080i | \(-0.325268\pi\) | ||||
0.521781 | + | 0.853080i | \(0.325268\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2333.19 | −0.495325 | −0.247663 | − | 0.968846i | \(-0.579662\pi\) | ||||
−0.247663 | + | 0.968846i | \(0.579662\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8697.84 | −1.82697 | −0.913486 | − | 0.406870i | \(-0.866620\pi\) | ||||
−0.913486 | + | 0.406870i | \(0.866620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10981.8 | −2.25865 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1175.55 | −0.239273 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1838.13 | 0.366501 | 0.183251 | − | 0.983066i | \(-0.441338\pi\) | ||||
0.183251 | + | 0.983066i | \(0.441338\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1697.07 | −0.334940 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2459.94 | −0.475793 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4649.12 | −0.890268 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2629.28 | −0.493614 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4152.70 | 0.772010 | 0.386005 | − | 0.922497i | \(-0.373855\pi\) | ||||
0.386005 | + | 0.922497i | \(0.373855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2861.14 | 0.521674 | 0.260837 | − | 0.965383i | \(-0.416001\pi\) | ||||
0.260837 | + | 0.965383i | \(0.416001\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −438.494 | −0.0791858 | −0.0395929 | − | 0.999216i | \(-0.512606\pi\) | ||||
−0.0395929 | + | 0.999216i | \(0.512606\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6279.80 | 1.11265 | 0.556323 | − | 0.830966i | \(-0.312212\pi\) | ||||
0.556323 | + | 0.830966i | \(0.312212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14278.8 | −2.50614 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1704.26 | 0.293584 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1519.78 | −0.259391 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13122.2 | 2.19894 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7564.20 | 1.25609 | 0.628046 | − | 0.778176i | \(-0.283855\pi\) | ||||
0.628046 | + | 0.778176i | \(0.283855\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −659.580 | −0.107572 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3468.51 | 0.560658 | 0.280329 | − | 0.959904i | \(-0.409556\pi\) | ||||
0.280329 | + | 0.959904i | \(0.409556\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11263.6 | 1.78873 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6868.88 | 1.08130 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6415.10 | −0.992452 | −0.496226 | − | 0.868193i | \(-0.665281\pi\) | ||||
−0.496226 | + | 0.868193i | \(0.665281\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2248.97 | −0.344941 | −0.172470 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172470 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7197.94 | 1.08529 | 0.542645 | − | 0.839962i | \(-0.317423\pi\) | ||||
0.542645 | + | 0.839962i | \(0.317423\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1481.31 | 0.221465 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8618.50 | −1.26704 | −0.633520 | − | 0.773726i | \(-0.718391\pi\) | ||||
−0.633520 | + | 0.773726i | \(0.718391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6081.87 | −0.886699 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6151.70 | −0.882178 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9025.95 | 1.28379 | 0.641895 | − | 0.766793i | \(-0.278149\pi\) | ||||
0.641895 | + | 0.766793i | \(0.278149\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2407.23 | 0.336865 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7549.69 | 1.04801 | 0.524005 | − | 0.851715i | \(-0.324437\pi\) | ||||
0.524005 | + | 0.851715i | \(0.324437\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12894.3 | −1.76151 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11849.7 | −1.60601 | −0.803007 | − | 0.595970i | \(-0.796768\pi\) | ||||
−0.803007 | + | 0.595970i | \(0.796768\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8613.06 | −1.14910 | −0.574552 | − | 0.818468i | \(-0.694824\pi\) | ||||
−0.574552 | + | 0.818468i | \(0.694824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10172.1 | −1.34654 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2529.23 | 0.329658 | 0.164829 | − | 0.986322i | \(-0.447293\pi\) | ||||
0.164829 | + | 0.986322i | \(0.447293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2473.84 | 0.319968 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3108.86 | 0.396009 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14195.7 | −1.79461 | −0.897306 | − | 0.441410i | \(-0.854479\pi\) | ||||
−0.897306 | + | 0.441410i | \(0.854479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11005.5 | 1.37054 | 0.685270 | − | 0.728289i | \(-0.259684\pi\) | ||||
0.685270 | + | 0.728289i | \(0.259684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10171.4 | 1.25726 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24674.8 | 3.00513 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14339.1 | 1.73356 | 0.866779 | − | 0.498692i | \(-0.166186\pi\) | ||||
0.866779 | + | 0.498692i | \(0.166186\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10257.3 | −1.22211 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 381.686 | 0.0451475 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5352.51 | 0.624075 | 0.312037 | − | 0.950070i | \(-0.398989\pi\) | ||||
0.312037 | + | 0.950070i | \(0.398989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2683.89 | −0.310701 | −0.155350 | − | 0.987859i | \(-0.549651\pi\) | ||||
−0.155350 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1528.37 | 0.174439 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15891.7 | −1.80107 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10019.0 | −1.11972 | −0.559861 | − | 0.828587i | \(-0.689145\pi\) | ||||
−0.559861 | + | 0.828587i | \(0.689145\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5292.20 | −0.587361 | −0.293680 | − | 0.955904i | \(-0.594880\pi\) | ||||
−0.293680 | + | 0.955904i | \(0.594880\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1128.06 | 0.123484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9453.33 | −1.02775 | −0.513875 | − | 0.857865i | \(-0.671791\pi\) | ||||
−0.513875 | + | 0.857865i | \(0.671791\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2858.23 | 0.306543 | 0.153272 | − | 0.988184i | \(-0.451019\pi\) | ||||
0.153272 | + | 0.988184i | \(0.451019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −962.030 | −0.102482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9322.81 | 0.979890 | 0.489945 | − | 0.871753i | \(-0.337017\pi\) | ||||
0.489945 | + | 0.871753i | \(0.337017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 24462.5 | 2.55409 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9185.75 | −0.946449 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4960.54 | 0.507755 | 0.253878 | − | 0.967236i | \(-0.418294\pi\) | ||||
0.253878 | + | 0.967236i | \(0.418294\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5235.83 | 0.528974 | 0.264487 | − | 0.964389i | \(-0.414797\pi\) | ||||
0.264487 | + | 0.964389i | \(0.414797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7121.96 | −0.714871 | −0.357436 | − | 0.933938i | \(-0.616349\pi\) | ||||
−0.357436 | + | 0.933938i | \(0.616349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1991.23 | 0.197308 | 0.0986541 | − | 0.995122i | \(-0.468546\pi\) | ||||
0.0986541 | + | 0.995122i | \(0.468546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3986.59 | −0.392503 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10356.2 | 1.00672 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 696.928 | 0.0673205 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9377.15 | −0.894474 | −0.447237 | − | 0.894415i | \(-0.647592\pi\) | ||||
−0.447237 | + | 0.894415i | \(0.647592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22282.3 | 2.11224 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4373.86 | −0.409498 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4855.98 | 0.451838 | 0.225919 | − | 0.974146i | \(-0.427461\pi\) | ||||
0.225919 | + | 0.974146i | \(0.427461\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4048.75 | −0.372133 | −0.186067 | − | 0.982537i | \(-0.559574\pi\) | ||||
−0.186067 | + | 0.982537i | \(0.559574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12967.2 | 1.18461 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8953.27 | 0.808066 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6259.64 | −0.561563 | −0.280781 | − | 0.959772i | \(-0.590594\pi\) | ||||
−0.280781 | + | 0.959772i | \(0.590594\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9127.86 | −0.809128 | −0.404564 | − | 0.914510i | \(-0.632577\pi\) | ||||
−0.404564 | + | 0.914510i | \(0.632577\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5465.08 | −0.481570 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9495.89 | −0.826911 | −0.413456 | − | 0.910524i | \(-0.635678\pi\) | ||||
−0.413456 | + | 0.910524i | \(0.635678\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −37181.8 | −3.21883 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1144.66 | −0.0979412 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −29230.5 | −2.48657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12282.6 | −1.03284 | −0.516421 | − | 0.856335i | \(-0.672736\pi\) | ||||
−0.516421 | + | 0.856335i | \(0.672736\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8010.57 | −0.669747 | −0.334873 | − | 0.942263i | \(-0.608694\pi\) | ||||
−0.334873 | + | 0.942263i | \(0.608694\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10228.9 | −0.845502 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10529.5 | −0.865418 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22090.6 | 1.79521 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2398.73 | −0.193843 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −38391.1 | −3.06794 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15476.8 | −1.22995 | −0.614974 | − | 0.788548i | \(-0.710833\pi\) | ||||
−0.614974 | + | 0.788548i | \(0.710833\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −581.231 | −0.0456829 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22837.0 | 1.78508 | 0.892540 | − | 0.450968i | \(-0.148921\pi\) | ||||
0.892540 | + | 0.450968i | \(0.148921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5912.96 | 0.457170 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18790.4 | 1.44493 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15800.3 | 1.20194 | 0.600971 | − | 0.799271i | \(-0.294781\pi\) | ||||
0.600971 | + | 0.799271i | \(0.294781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9352.03 | 0.707601 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13515.7 | 1.01176 | 0.505879 | − | 0.862605i | \(-0.331168\pi\) | ||||
0.505879 | + | 0.862605i | \(0.331168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3706.11 | 0.275960 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19632.0 | −1.44642 | −0.723211 | − | 0.690627i | \(-0.757335\pi\) | ||||
−0.723211 | + | 0.690627i | \(0.757335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12800.7 | 0.938166 | 0.469083 | − | 0.883154i | \(-0.344584\pi\) | ||||
0.469083 | + | 0.883154i | \(0.344584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1011.64 | 0.0733707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9214.08 | −0.664796 | −0.332398 | − | 0.943139i | \(-0.607858\pi\) | ||||
−0.332398 | + | 0.943139i | \(0.607858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2306.96 | 0.164731 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5362.25 | −0.380929 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −275.136 | −0.0193460 | −0.00967298 | − | 0.999953i | \(-0.503079\pi\) | ||||
−0.00967298 | + | 0.999953i | \(0.503079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4664.34 | −0.326300 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15753.5 | 1.09093 | 0.545464 | − | 0.838135i | \(-0.316354\pi\) | ||||
0.545464 | + | 0.838135i | \(0.316354\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9237.66 | 0.636483 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13557.3 | −0.924770 | −0.462385 | − | 0.886679i | \(-0.653006\pi\) | ||||
−0.462385 | + | 0.886679i | \(0.653006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23976.7 | 1.62734 | 0.813668 | − | 0.581330i | \(-0.197467\pi\) | ||||
0.813668 | + | 0.581330i | \(0.197467\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16003.9 | 1.07546 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12766.6 | 0.853677 | 0.426839 | − | 0.904328i | \(-0.359627\pi\) | ||||
0.426839 | + | 0.904328i | \(0.359627\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26396.2 | −1.74775 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16776.3 | −1.10537 | −0.552684 | − | 0.833391i | \(-0.686396\pi\) | ||||
−0.552684 | + | 0.833391i | \(0.686396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17941.4 | 1.17065 | 0.585327 | − | 0.810798i | \(-0.300966\pi\) | ||||
0.585327 | + | 0.810798i | \(0.300966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 987.096 | 0.0640949 | 0.0320475 | − | 0.999486i | \(-0.489797\pi\) | ||||
0.0320475 | + | 0.999486i | \(0.489797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5814.64 | −0.373930 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22408.2 | −1.42047 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18504.9 | −1.16746 | −0.583730 | − | 0.811948i | \(-0.698407\pi\) | ||||
−0.583730 | + | 0.811948i | \(0.698407\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12976.9 | 0.810979 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34668.6 | −2.15639 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10260.2 | 0.632219 | 0.316110 | − | 0.948723i | \(-0.397623\pi\) | ||||
0.316110 | + | 0.948723i | \(0.397623\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6221.29 | −0.381561 | −0.190781 | − | 0.981633i | \(-0.561102\pi\) | ||||
−0.190781 | + | 0.981633i | \(0.561102\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21446.7 | 1.30318 | 0.651590 | − | 0.758572i | \(-0.274102\pi\) | ||||
0.651590 | + | 0.758572i | \(0.274102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22848.8 | 1.38196 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25051.0 | −1.50126 | −0.750628 | − | 0.660725i | \(-0.770249\pi\) | ||||
−0.750628 | + | 0.660725i | \(0.770249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7028.09 | −0.419252 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7125 | −0.00122435 | −0.000612174 | − | 1.00000i | \(-0.500195\pi\) | ||||
−0.000612174 | 1.00000i | \(0.500195\pi\) | ||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23294.7 | 1.37074 | 0.685371 | − | 0.728194i | \(-0.259640\pi\) | ||||
0.685371 | + | 0.728194i | \(0.259640\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4212.33 | 0.245635 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8583.05 | 0.498257 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35399.9 | 2.03666 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25764.3 | 1.47569 | 0.737845 | − | 0.674970i | \(-0.235843\pi\) | ||||
0.737845 | + | 0.674970i | \(0.235843\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26667.3 | 1.51390 | 0.756948 | − | 0.653475i | \(-0.226689\pi\) | ||||
0.756948 | + | 0.653475i | \(0.226689\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26436.2 | −1.49415 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.8616 | −0.000832599 0 | −0.000416299 | − | 1.00000i | \(-0.500133\pi\) | ||||
−0.000416299 | 1.00000i | \(0.500133\pi\) | ||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12287.0 | −0.685345 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4842.31 | −0.267747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26645.5 | −1.46692 | −0.733460 | − | 0.679733i | \(-0.762096\pi\) | ||||
−0.733460 | + | 0.679733i | \(0.762096\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2926.96 | 0.159749 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22215.4 | −1.20727 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −431.952 | −0.0232733 | −0.0116367 | − | 0.999932i | \(-0.503704\pi\) | ||||
−0.0116367 | + | 0.999932i | \(0.503704\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10218.0 | −0.548195 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33031.7 | −1.75712 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35463.0 | 1.87848 | 0.939240 | − | 0.343261i | \(-0.111532\pi\) | ||||
0.939240 | + | 0.343261i | \(0.111532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6770.60 | −0.355626 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20461.8 | 1.07025 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26340.5 | 1.36625 | 0.683125 | − | 0.730302i | \(-0.260621\pi\) | ||||
0.683125 | + | 0.730302i | \(0.260621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6918.48 | −0.357362 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5302.70 | 0.271638 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38279.1 | 1.95281 | 0.976404 | − | 0.215952i | \(-0.0692853\pi\) | ||||
0.976404 | + | 0.215952i | \(0.0692853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9404.89 | −0.475858 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16445.7 | −0.828700 | −0.414350 | − | 0.910118i | \(-0.635991\pi\) | ||||
−0.414350 | + | 0.910118i | \(0.635991\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8880.39 | 0.443844 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5150.65 | 0.256387 | 0.128193 | − | 0.991749i | \(-0.459082\pi\) | ||||
0.128193 | + | 0.991749i | \(0.459082\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8844.91 | 0.436727 | 0.218364 | − | 0.975868i | \(-0.429928\pi\) | ||||
0.218364 | + | 0.975868i | \(0.429928\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4632.52 | 0.227816 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14498.2 | −0.707282 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5774.81 | −0.280594 | −0.140297 | − | 0.990109i | \(-0.544806\pi\) | ||||
−0.140297 | + | 0.990109i | \(0.544806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2059.50 | −0.0992754 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14267.1 | 0.685003 | 0.342501 | − | 0.939517i | \(-0.388726\pi\) | ||||
0.342501 | + | 0.939517i | \(0.388726\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21823.0 | −1.03953 | −0.519765 | − | 0.854309i | \(-0.673980\pi\) | ||||
−0.519765 | + | 0.854309i | \(0.673980\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3513.04 | −0.166685 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20633.3 | 0.971352 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3080.07 | −0.144435 | −0.0722173 | − | 0.997389i | \(-0.523008\pi\) | ||||
−0.0722173 | + | 0.997389i | \(0.523008\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8834.10 | −0.411049 | −0.205524 | − | 0.978652i | \(-0.565890\pi\) | ||||
−0.205524 | + | 0.978652i | \(0.565890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4182.95 | −0.193879 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10130.1 | −0.465917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19944.0 | −0.913766 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14799.8 | −0.672903 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11060.1 | −0.500952 | −0.250476 | − | 0.968123i | \(-0.580587\pi\) | ||||
−0.250476 | + | 0.968123i | \(0.580587\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22400.3 | 1.00690 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31967.4 | 1.43152 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3379.95 | 0.150218 | 0.0751091 | − | 0.997175i | \(-0.476070\pi\) | ||||
0.0751091 | + | 0.997175i | \(0.476070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26545.4 | 1.17536 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 82824.7 | 3.63988 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6114.47 | 0.267710 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38358.8 | −1.66703 | −0.833513 | − | 0.552499i | \(-0.813674\pi\) | ||||
−0.833513 | + | 0.552499i | \(0.813674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9110.42 | 0.394464 | 0.197232 | − | 0.980357i | \(-0.436805\pi\) | ||||
0.197232 | + | 0.980357i | \(0.436805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12522.5 | −0.538214 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4288.58 | −0.183646 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8177.12 | 0.347605 | 0.173802 | − | 0.984781i | \(-0.444395\pi\) | ||||
0.173802 | + | 0.984781i | \(0.444395\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4238.40 | 0.179515 | 0.0897577 | − | 0.995964i | \(-0.471391\pi\) | ||||
0.0897577 | + | 0.995964i | \(0.471391\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12021.9 | 0.505492 | 0.252746 | − | 0.967533i | \(-0.418666\pi\) | ||||
0.252746 | + | 0.967533i | \(0.418666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6564.14 | 0.275009 | 0.137504 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137504 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 34864.5 | 1.45016 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10277.1 | −0.425932 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3645.41 | 0.150004 | 0.0750021 | − | 0.997183i | \(-0.476104\pi\) | ||||
0.0750021 | + | 0.997183i | \(0.476104\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20600.9 | 0.844679 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7492.79 | 0.305041 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 96729.9 | 3.92406 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14832.2 | −0.597462 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45697.7 | −1.83430 | −0.917151 | − | 0.398540i | \(-0.869517\pi\) | ||||
−0.917151 | + | 0.398540i | \(0.869517\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13766.3 | −0.548716 | −0.274358 | − | 0.961628i | \(-0.588465\pi\) | ||||
−0.274358 | + | 0.961628i | \(0.588465\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15422.0 | −0.612563 | −0.306282 | − | 0.951941i | \(-0.599085\pi\) | ||||
−0.306282 | + | 0.951941i | \(0.599085\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7382.54 | −0.291199 | −0.145599 | − | 0.989344i | \(-0.546511\pi\) | ||||
−0.145599 | + | 0.989344i | \(0.546511\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8620.83 | 0.338863 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −41856.8 | −1.63394 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8019.32 | 0.311968 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3777.59 | 0.145949 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12079.7 | −0.465112 | −0.232556 | − | 0.972583i | \(-0.574709\pi\) | ||||
−0.232556 | + | 0.972583i | \(0.574709\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25501.7 | −0.975227 | −0.487613 | − | 0.873060i | \(-0.662132\pi\) | ||||
−0.487613 | + | 0.873060i | \(0.662132\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29353.2 | 1.11870 | 0.559351 | − | 0.828931i | \(-0.311050\pi\) | ||||
0.559351 | + | 0.828931i | \(0.311050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17185.8 | 0.650556 | 0.325278 | − | 0.945618i | \(-0.394542\pi\) | ||||
0.325278 | + | 0.945618i | \(0.394542\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 78434.1 | 2.95905 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12104.6 | 0.453600 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18006.8 | 0.672513 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −35489.5 | −1.31662 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4869.68 | 0.180058 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6285.83 | −0.230882 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38511.6 | 1.40988 | 0.704938 | − | 0.709269i | \(-0.250975\pi\) | ||||
0.704938 | + | 0.709269i | \(0.250975\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11451.4 | −0.416467 | −0.208233 | − | 0.978079i | \(-0.566771\pi\) | ||||
−0.208233 | + | 0.978079i | \(0.566771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5138.90 | −0.186279 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −42478.8 | −1.52974 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14096.0 | −0.505968 | −0.252984 | − | 0.967470i | \(-0.581412\pi\) | ||||
−0.252984 | + | 0.967470i | \(0.581412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −18010.1 | −0.642265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9163.47 | −0.325722 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15020.3 | 0.530462 | 0.265231 | − | 0.964185i | \(-0.414552\pi\) | ||||
0.265231 | + | 0.964185i | \(0.414552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15898.1 | 0.559654 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20577.5 | −0.719739 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18430.5 | 0.642582 | 0.321291 | − | 0.946981i | \(-0.395883\pi\) | ||||
0.321291 | + | 0.946981i | \(0.395883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55141.3 | −1.91026 | −0.955131 | − | 0.296184i | \(-0.904286\pi\) | ||||
−0.955131 | + | 0.296184i | \(0.904286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14704.5 | −0.507790 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24231.3 | 0.831480 | 0.415740 | − | 0.909484i | \(-0.363523\pi\) | ||||
0.415740 | + | 0.909484i | \(0.363523\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 74793.8 | 2.55839 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19107.5 | 0.649479 | 0.324739 | − | 0.945804i | \(-0.394723\pi\) | ||||
0.324739 | + | 0.945804i | \(0.394723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23387.3 | 0.792457 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −74264.2 | −2.50064 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1795.67 | −0.0602756 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13239.4 | −0.441649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21993.6 | −0.731401 | −0.365701 | − | 0.930732i | \(-0.619171\pi\) | ||||
−0.365701 | + | 0.930732i | \(0.619171\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19409.3 | 0.641477 | 0.320738 | − | 0.947168i | \(-0.396069\pi\) | ||||
0.320738 | + | 0.947168i | \(0.396069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17690.9 | 0.582883 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −36384.1 | −1.19143 | −0.595717 | − | 0.803194i | \(-0.703132\pi\) | ||||
−0.595717 | + | 0.803194i | \(0.703132\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12952.5 | 0.422843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4202.43 | −0.136355 | −0.0681774 | − | 0.997673i | \(-0.521718\pi\) | ||||
−0.0681774 | + | 0.997673i | \(0.521718\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6844.57 | 0.221407 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6225.16 | −0.200150 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17753.0 | 0.569064 | 0.284532 | − | 0.958666i | \(-0.408162\pi\) | ||||
0.284532 | + | 0.958666i | \(0.408162\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27057.2 | 0.862080 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12519.0 | 0.397673 | 0.198837 | − | 0.980033i | \(-0.436284\pi\) | ||||
0.198837 | + | 0.980033i | \(0.436284\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2160.4.a.bs.1.3 | 3 | ||
3.2 | odd | 2 | 2160.4.a.bk.1.3 | 3 | |||
4.3 | odd | 2 | 1080.4.a.j.1.1 | yes | 3 | ||
12.11 | even | 2 | 1080.4.a.d.1.1 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.4.a.d.1.1 | ✓ | 3 | 12.11 | even | 2 | ||
1080.4.a.j.1.1 | yes | 3 | 4.3 | odd | 2 | ||
2160.4.a.bk.1.3 | 3 | 3.2 | odd | 2 | |||
2160.4.a.bs.1.3 | 3 | 1.1 | even | 1 | trivial |