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: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 540) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.79129\) 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 | ||||||||
\(7\) | 14.7477 | 0.796302 | 0.398151 | − | 0.917320i | \(-0.369652\pi\) | ||||
0.398151 | + | 0.917320i | \(0.369652\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.25227 | −0.198786 | −0.0993928 | − | 0.995048i | \(-0.531690\pi\) | ||||
−0.0993928 | + | 0.995048i | \(0.531690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.7386 | 1.31717 | 0.658585 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658585 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 108.234 | 1.54415 | 0.772077 | − | 0.635529i | \(-0.219218\pi\) | ||||
0.772077 | + | 0.635529i | \(0.219218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 56.2523 | 0.679219 | 0.339609 | − | 0.940567i | \(-0.389705\pi\) | ||||
0.339609 | + | 0.940567i | \(0.389705\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 46.9818 | 0.425930 | 0.212965 | − | 0.977060i | \(-0.431688\pi\) | ||||
0.212965 | + | 0.977060i | \(0.431688\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −214.225 | −1.37174 | −0.685872 | − | 0.727722i | \(-0.740579\pi\) | ||||
−0.685872 | + | 0.727722i | \(0.740579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 261.711 | 1.51628 | 0.758141 | − | 0.652091i | \(-0.226108\pi\) | ||||
0.758141 | + | 0.652091i | \(0.226108\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −73.7386 | −0.356117 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −286.000 | −1.27076 | −0.635380 | − | 0.772200i | \(-0.719156\pi\) | ||||
−0.635380 | + | 0.772200i | \(0.719156\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 255.702 | 0.974000 | 0.487000 | − | 0.873402i | \(-0.338091\pi\) | ||||
0.487000 | + | 0.873402i | \(0.338091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 361.234 | 1.28111 | 0.640554 | − | 0.767913i | \(-0.278705\pi\) | ||||
0.640554 | + | 0.767913i | \(0.278705\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.53182 | 0.0171681 | 0.00858403 | − | 0.999963i | \(-0.497268\pi\) | ||||
0.00858403 | + | 0.999963i | \(0.497268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −125.505 | −0.365902 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −595.693 | −1.54386 | −0.771932 | − | 0.635706i | \(-0.780709\pi\) | ||||
−0.771932 | + | 0.635706i | \(0.780709\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 36.2614 | 0.0888997 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −315.234 | −0.695593 | −0.347796 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347796 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 276.405 | 0.580164 | 0.290082 | − | 0.957002i | \(-0.406317\pi\) | ||||
0.290082 | + | 0.957002i | \(0.406317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −308.693 | −0.589057 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −117.405 | −0.214078 | −0.107039 | − | 0.994255i | \(-0.534137\pi\) | ||||
−0.107039 | + | 0.994255i | \(0.534137\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −192.784 | −0.322243 | −0.161122 | − | 0.986935i | \(-0.551511\pi\) | ||||
−0.161122 | + | 0.986935i | \(0.551511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −756.189 | −1.21240 | −0.606200 | − | 0.795312i | \(-0.707307\pi\) | ||||
−0.606200 | + | 0.795312i | \(0.707307\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −106.955 | −0.158294 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1150.70 | 1.63879 | 0.819393 | − | 0.573232i | \(-0.194311\pi\) | ||||
0.819393 | + | 0.573232i | \(0.194311\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −141.936 | −0.187705 | −0.0938526 | − | 0.995586i | \(-0.529918\pi\) | ||||
−0.0938526 | + | 0.995586i | \(0.529918\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −541.170 | −0.690567 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 719.107 | 0.856463 | 0.428231 | − | 0.903669i | \(-0.359137\pi\) | ||||
0.428231 | + | 0.903669i | \(0.359137\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 910.505 | 1.04887 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −281.261 | −0.303756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1043.82 | −1.09262 | −0.546308 | − | 0.837585i | \(-0.683967\pi\) | ||||
−0.546308 | + | 0.837585i | \(0.683967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 685.873 | 0.675712 | 0.337856 | − | 0.941198i | \(-0.390298\pi\) | ||||
0.337856 | + | 0.941198i | \(0.390298\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 370.055 | 0.354005 | 0.177003 | − | 0.984210i | \(-0.443360\pi\) | ||||
0.177003 | + | 0.984210i | \(0.443360\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1354.85 | 1.22409 | 0.612046 | − | 0.790822i | \(-0.290347\pi\) | ||||
0.612046 | + | 0.790822i | \(0.290347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 882.873 | 0.775815 | 0.387908 | − | 0.921698i | \(-0.373198\pi\) | ||||
0.387908 | + | 0.921698i | \(0.373198\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 986.559 | 0.821307 | 0.410653 | − | 0.911792i | \(-0.365301\pi\) | ||||
0.410653 | + | 0.911792i | \(0.365301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −234.909 | −0.190482 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1596.21 | 1.22961 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1278.40 | −0.960484 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 809.405 | 0.565536 | 0.282768 | − | 0.959188i | \(-0.408747\pi\) | ||||
0.282768 | + | 0.959188i | \(0.408747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1288.13 | −0.859116 | −0.429558 | − | 0.903039i | \(-0.641331\pi\) | ||||
−0.429558 | + | 0.903039i | \(0.641331\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 829.593 | 0.540864 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2300.16 | −1.43442 | −0.717212 | − | 0.696855i | \(-0.754582\pi\) | ||||
−0.717212 | + | 0.696855i | \(0.754582\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1359.89 | 0.829816 | 0.414908 | − | 0.909863i | \(-0.363814\pi\) | ||||
0.414908 | + | 0.909863i | \(0.363814\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −447.745 | −0.261835 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1071.12 | 0.613463 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 233.270 | 0.128257 | 0.0641284 | − | 0.997942i | \(-0.479573\pi\) | ||||
0.0641284 | + | 0.997942i | \(0.479573\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76.0000 | 0.0409589 | 0.0204794 | − | 0.999790i | \(-0.493481\pi\) | ||||
0.0204794 | + | 0.999790i | \(0.493481\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1308.56 | −0.678102 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1348.60 | 0.685543 | 0.342771 | − | 0.939419i | \(-0.388634\pi\) | ||||
0.342771 | + | 0.939419i | \(0.388634\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 692.875 | 0.339169 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −216.127 | −0.103855 | −0.0519276 | − | 0.998651i | \(-0.516537\pi\) | ||||
−0.0519276 | + | 0.998651i | \(0.516537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2601.55 | −1.20548 | −0.602738 | − | 0.797940i | \(-0.705923\pi\) | ||||
−0.602738 | + | 0.797940i | \(0.705923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1614.66 | 0.734938 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2563.64 | −1.12665 | −0.563323 | − | 0.826237i | \(-0.690477\pi\) | ||||
−0.563323 | + | 0.826237i | \(0.690477\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 368.693 | 0.159260 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3791.98 | 1.58338 | 0.791692 | − | 0.610921i | \(-0.209201\pi\) | ||||
0.791692 | + | 0.610921i | \(0.209201\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1245.18 | 0.511346 | 0.255673 | − | 0.966763i | \(-0.417703\pi\) | ||||
0.255673 | + | 0.966763i | \(0.417703\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1430.00 | 0.568301 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −784.943 | −0.306956 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3466.57 | 1.31326 | 0.656629 | − | 0.754213i | \(-0.271982\pi\) | ||||
0.656629 | + | 0.754213i | \(0.271982\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3572.51 | 1.33241 | 0.666205 | − | 0.745769i | \(-0.267918\pi\) | ||||
0.666205 | + | 0.745769i | \(0.267918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −761.048 | −0.275241 | −0.137620 | − | 0.990485i | \(-0.543945\pi\) | ||||
−0.137620 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −764.195 | −0.272223 | −0.136112 | − | 0.990694i | \(-0.543461\pi\) | ||||
−0.136112 | + | 0.990694i | \(0.543461\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3159.33 | −1.09232 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1278.51 | −0.435586 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −407.957 | −0.135019 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4213.38 | −1.37470 | −0.687349 | − | 0.726327i | \(-0.741226\pi\) | ||||
−0.687349 | + | 0.726327i | \(0.741226\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1806.17 | −0.572929 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3859.65 | 1.20742 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6682.22 | 2.03391 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3407.55 | 1.02326 | 0.511628 | − | 0.859207i | \(-0.329043\pi\) | ||||
0.511628 | + | 0.859207i | \(0.329043\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5638.40 | 1.64861 | 0.824304 | − | 0.566147i | \(-0.191567\pi\) | ||||
0.824304 | + | 0.566147i | \(0.191567\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −73.0863 | −0.0210903 | −0.0105452 | − | 0.999944i | \(-0.503357\pi\) | ||||
−0.0105452 | + | 0.999944i | \(0.503357\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1865.78 | 0.524598 | 0.262299 | − | 0.964987i | \(-0.415519\pi\) | ||||
0.262299 | + | 0.964987i | \(0.415519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −27.6591 | −0.00767779 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3147.60 | −0.851890 | −0.425945 | − | 0.904749i | \(-0.640058\pi\) | ||||
−0.425945 | + | 0.904749i | \(0.640058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5098.59 | 1.36278 | 0.681388 | − | 0.731923i | \(-0.261377\pi\) | ||||
0.681388 | + | 0.731923i | \(0.261377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 627.523 | 0.163637 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3472.94 | 0.894647 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6566.90 | −1.65139 | −0.825695 | − | 0.564117i | \(-0.809217\pi\) | ||||
−0.825695 | + | 0.564117i | \(0.809217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −340.725 | −0.0846688 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6118.62 | −1.48509 | −0.742547 | − | 0.669794i | \(-0.766382\pi\) | ||||
−0.742547 | + | 0.669794i | \(0.766382\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4217.85 | −1.01191 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7268.01 | 1.70405 | 0.852025 | − | 0.523502i | \(-0.175375\pi\) | ||||
0.852025 | + | 0.523502i | \(0.175375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2978.47 | 0.690437 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4292.72 | −0.972981 | −0.486491 | − | 0.873686i | \(-0.661723\pi\) | ||||
−0.486491 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3847.73 | 0.862483 | 0.431242 | − | 0.902237i | \(-0.358076\pi\) | ||||
0.431242 | + | 0.902237i | \(0.358076\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −181.307 | −0.0397571 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7770.26 | 1.68545 | 0.842725 | − | 0.538345i | \(-0.180950\pi\) | ||||
0.842725 | + | 0.538345i | \(0.180950\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6325.03 | 1.34278 | 0.671388 | − | 0.741106i | \(-0.265699\pi\) | ||||
0.671388 | + | 0.741106i | \(0.265699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2662.96 | −0.559352 | −0.279676 | − | 0.960094i | \(-0.590227\pi\) | ||||
−0.279676 | + | 0.960094i | \(0.590227\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3771.03 | 0.775598 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6801.62 | 1.38441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3510.32 | 0.699915 | 0.349958 | − | 0.936766i | \(-0.386196\pi\) | ||||
0.349958 | + | 0.936766i | \(0.386196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1576.17 | 0.311079 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2900.59 | 0.561022 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5327.38 | 1.02015 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1382.02 | −0.259457 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3451.19 | 0.641596 | 0.320798 | − | 0.947148i | \(-0.396049\pi\) | ||||
0.320798 | + | 0.947148i | \(0.396049\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9390.04 | −1.71209 | −0.856046 | − | 0.516900i | \(-0.827086\pi\) | ||||
−0.856046 | + | 0.516900i | \(0.827086\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7116.66 | 1.28517 | 0.642584 | − | 0.766216i | \(-0.277863\pi\) | ||||
0.642584 | + | 0.766216i | \(0.277863\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6219.53 | −1.10197 | −0.550984 | − | 0.834516i | \(-0.685747\pi\) | ||||
−0.550984 | + | 0.834516i | \(0.685747\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1553.62 | 0.272683 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6088.41 | 1.04882 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1543.47 | 0.263434 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 81.5818 | 0.0136710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8443.07 | 1.40203 | 0.701017 | − | 0.713145i | \(-0.252730\pi\) | ||||
0.701017 | + | 0.713145i | \(0.252730\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 587.023 | 0.0957387 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1647.83 | 0.266359 | 0.133180 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133180 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1898.00 | −0.301415 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6909.38 | −1.08767 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2462.48 | −0.380960 | −0.190480 | − | 0.981691i | \(-0.561004\pi\) | ||||
−0.190480 | + | 0.981691i | \(0.561004\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8126.99 | −1.24650 | −0.623249 | − | 0.782023i | \(-0.714188\pi\) | ||||
−0.623249 | + | 0.782023i | \(0.714188\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5376.64 | 0.810679 | 0.405340 | − | 0.914166i | \(-0.367153\pi\) | ||||
0.405340 | + | 0.914166i | \(0.367153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 963.920 | 0.144112 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4860.14 | −0.714508 | −0.357254 | − | 0.934007i | \(-0.616287\pi\) | ||||
−0.357254 | + | 0.934007i | \(0.616287\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3694.68 | −0.538662 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3780.94 | 0.542202 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 964.293 | 0.137154 | 0.0685772 | − | 0.997646i | \(-0.478154\pi\) | ||||
0.0685772 | + | 0.997646i | \(0.478154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8785.12 | −1.22938 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6114.13 | −0.848734 | −0.424367 | − | 0.905490i | \(-0.639503\pi\) | ||||
−0.424367 | + | 0.905490i | \(0.639503\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13226.0 | −1.80682 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12063.6 | 1.63501 | 0.817504 | − | 0.575924i | \(-0.195357\pi\) | ||||
0.817504 | + | 0.575924i | \(0.195357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9275.13 | 1.23743 | 0.618717 | − | 0.785614i | \(-0.287653\pi\) | ||||
0.618717 | + | 0.785614i | \(0.287653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 534.773 | 0.0707910 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11309.4 | −1.47406 | −0.737030 | − | 0.675860i | \(-0.763772\pi\) | ||||
−0.737030 | + | 0.675860i | \(0.763772\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5085.03 | 0.657701 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5753.51 | −0.732888 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6235.73 | −0.788319 | −0.394159 | − | 0.919042i | \(-0.628964\pi\) | ||||
−0.394159 | + | 0.919042i | \(0.628964\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13997.3 | 1.74313 | 0.871564 | − | 0.490282i | \(-0.163106\pi\) | ||||
0.871564 | + | 0.490282i | \(0.163106\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16157.7 | 1.99720 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2074.15 | 0.252609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6772.52 | 0.818776 | 0.409388 | − | 0.912360i | \(-0.365742\pi\) | ||||
0.409388 | + | 0.912360i | \(0.365742\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4648.99 | −0.553902 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 709.682 | 0.0839444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4636.81 | 0.540628 | 0.270314 | − | 0.962772i | \(-0.412873\pi\) | ||||
0.270314 | + | 0.962772i | \(0.412873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9177.47 | 1.06243 | 0.531215 | − | 0.847237i | \(-0.321736\pi\) | ||||
0.531215 | + | 0.847237i | \(0.321736\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2705.85 | 0.308831 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4076.34 | 0.461986 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16939.0 | −1.89310 | −0.946549 | − | 0.322561i | \(-0.895456\pi\) | ||||
−0.946549 | + | 0.322561i | \(0.895456\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7368.61 | 0.817812 | 0.408906 | − | 0.912576i | \(-0.365910\pi\) | ||||
0.408906 | + | 0.912576i | \(0.365910\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2642.83 | 0.289300 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7899.77 | −0.858850 | −0.429425 | − | 0.903102i | \(-0.641284\pi\) | ||||
−0.429425 | + | 0.903102i | \(0.641284\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3730.12 | 0.400053 | 0.200027 | − | 0.979790i | \(-0.435897\pi\) | ||||
0.200027 | + | 0.979790i | \(0.435897\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3595.53 | −0.383022 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 742.811 | 0.0780745 | 0.0390372 | − | 0.999238i | \(-0.487571\pi\) | ||||
0.0390372 | + | 0.999238i | \(0.487571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1854.42 | −0.193617 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4552.52 | −0.469067 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3281.02 | −0.335842 | −0.167921 | − | 0.985800i | \(-0.553705\pi\) | ||||
−0.167921 | + | 0.985800i | \(0.553705\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2708.55 | 0.273644 | 0.136822 | − | 0.990596i | \(-0.456311\pi\) | ||||
0.136822 | + | 0.990596i | \(0.456311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12296.2 | 1.23424 | 0.617120 | − | 0.786869i | \(-0.288299\pi\) | ||||
0.617120 | + | 0.786869i | \(0.288299\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 347.168 | 0.0344005 | 0.0172002 | − | 0.999852i | \(-0.494525\pi\) | ||||
0.0172002 | + | 0.999852i | \(0.494525\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1731.45 | −0.170471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2619.77 | −0.254666 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1406.31 | 0.135844 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11968.0 | 1.14162 | 0.570808 | − | 0.821084i | \(-0.306630\pi\) | ||||
0.570808 | + | 0.821084i | \(0.306630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17657.2 | −1.67381 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5219.09 | 0.488632 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 827.189 | 0.0769682 | 0.0384841 | − | 0.999259i | \(-0.487747\pi\) | ||||
0.0384841 | + | 0.999259i | \(0.487747\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10268.9 | 0.943848 | 0.471924 | − | 0.881639i | \(-0.343560\pi\) | ||||
0.471924 | + | 0.881639i | \(0.343560\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23186.4 | −2.11818 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2843.13 | −0.256603 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8313.30 | 0.745800 | 0.372900 | − | 0.927871i | \(-0.378363\pi\) | ||||
0.372900 | + | 0.927871i | \(0.378363\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7575.17 | −0.671492 | −0.335746 | − | 0.941953i | \(-0.608988\pi\) | ||||
−0.335746 | + | 0.941953i | \(0.608988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3429.36 | −0.302187 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10638.4 | −0.926401 | −0.463200 | − | 0.886254i | \(-0.653299\pi\) | ||||
−0.463200 | + | 0.886254i | \(0.653299\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11152.1 | −0.965437 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1850.27 | −0.158316 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.1183 | −0.00341277 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −289.152 | −0.0243148 | −0.0121574 | − | 0.999926i | \(-0.503870\pi\) | ||||
−0.0121574 | + | 0.999926i | \(0.503870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5708.40 | −0.477268 | −0.238634 | − | 0.971110i | \(-0.576700\pi\) | ||||
−0.238634 | + | 0.971110i | \(0.576700\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28326.1 | 2.34137 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9959.71 | −0.818584 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15786.7 | 1.28292 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6774.23 | −0.547431 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 910.193 | 0.0727362 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7904.89 | −0.628203 | −0.314101 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314101 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4414.36 | −0.346955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4563.11 | 0.356681 | 0.178340 | − | 0.983969i | \(-0.442927\pi\) | ||||
0.178340 | + | 0.983969i | \(0.442927\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12050.6 | −0.931714 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16970.2 | 1.30497 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1729.19 | 0.131540 | 0.0657702 | − | 0.997835i | \(-0.479050\pi\) | ||||
0.0657702 | + | 0.997835i | \(0.479050\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22302.1 | 1.68744 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15656.0 | −1.17198 | −0.585988 | − | 0.810320i | \(-0.699293\pi\) | ||||
−0.585988 | + | 0.810320i | \(0.699293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4932.80 | −0.367300 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15868.5 | 1.16914 | 0.584570 | − | 0.811343i | \(-0.301263\pi\) | ||||
0.584570 | + | 0.811343i | \(0.301263\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12989.1 | 0.951976 | 0.475988 | − | 0.879452i | \(-0.342091\pi\) | ||||
0.475988 | + | 0.879452i | \(0.342091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1174.55 | 0.0851860 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6404.62 | −0.462093 | −0.231046 | − | 0.972943i | \(-0.574215\pi\) | ||||
−0.231046 | + | 0.972943i | \(0.574215\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2093.24 | −0.149470 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4320.13 | 0.306898 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21081.5 | 1.48233 | 0.741165 | − | 0.671323i | \(-0.234274\pi\) | ||||
0.741165 | + | 0.671323i | \(0.234274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14721.9 | 1.02989 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1379.98 | −0.0955629 | −0.0477814 | − | 0.998858i | \(-0.515215\pi\) | ||||
−0.0477814 | + | 0.998858i | \(0.515215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7981.03 | −0.549900 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12952.1 | −0.883484 | −0.441742 | − | 0.897142i | \(-0.645639\pi\) | ||||
−0.441742 | + | 0.897142i | \(0.645639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23140.5 | 1.57059 | 0.785293 | − | 0.619124i | \(-0.212512\pi\) | ||||
0.785293 | + | 0.619124i | \(0.212512\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6392.02 | 0.429542 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1479.65 | 0.0989411 | 0.0494705 | − | 0.998776i | \(-0.484247\pi\) | ||||
0.0494705 | + | 0.998776i | \(0.484247\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 341.527 | 0.0226133 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20327.3 | 1.33934 | 0.669668 | − | 0.742661i | \(-0.266436\pi\) | ||||
0.669668 | + | 0.742661i | \(0.266436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14362.8 | −0.937158 | −0.468579 | − | 0.883422i | \(-0.655234\pi\) | ||||
−0.468579 | + | 0.883422i | \(0.655234\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3115.20 | −0.202278 | −0.101139 | − | 0.994872i | \(-0.532249\pi\) | ||||
−0.101139 | + | 0.994872i | \(0.532249\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10605.2 | 0.682003 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −30954.9 | −1.96225 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23024.2 | 1.45258 | 0.726292 | − | 0.687386i | \(-0.241242\pi\) | ||||
0.726292 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4047.02 | −0.252915 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7748.48 | −0.481956 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27234.2 | 1.67814 | 0.839068 | − | 0.544027i | \(-0.183101\pi\) | ||||
0.839068 | + | 0.544027i | \(0.183101\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2245.50 | −0.137720 | −0.0688600 | − | 0.997626i | \(-0.521936\pi\) | ||||
−0.0688600 | + | 0.997626i | \(0.521936\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7245.60 | 0.440269 | 0.220135 | − | 0.975470i | \(-0.429350\pi\) | ||||
0.220135 | + | 0.975470i | \(0.429350\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2286.16 | 0.138274 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12061.0 | −0.722795 | −0.361398 | − | 0.932412i | \(-0.617700\pi\) | ||||
−0.361398 | + | 0.932412i | \(0.617700\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6440.64 | 0.384208 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31632.7 | −1.86986 | −0.934929 | − | 0.354836i | \(-0.884537\pi\) | ||||
−0.934929 | + | 0.354836i | \(0.884537\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9312.26 | −0.547965 | −0.273983 | − | 0.961735i | \(-0.588341\pi\) | ||||
−0.273983 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4147.97 | −0.241882 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10064.7 | −0.584267 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2004.56 | −0.115328 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3761.02 | −0.215418 | −0.107709 | − | 0.994182i | \(-0.534352\pi\) | ||||
−0.107709 | + | 0.994182i | \(0.534352\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29897.7 | 1.69728 | 0.848642 | − | 0.528968i | \(-0.177421\pi\) | ||||
0.848642 | + | 0.528968i | \(0.177421\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15393.9 | −0.870052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7931.11 | −0.444327 | −0.222164 | − | 0.975009i | \(-0.571312\pi\) | ||||
−0.222164 | + | 0.975009i | \(0.571312\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11500.8 | 0.641494 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36777.3 | −2.03353 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19436.9 | −1.07007 | −0.535033 | − | 0.844831i | \(-0.679701\pi\) | ||||
−0.535033 | + | 0.844831i | \(0.679701\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6799.45 | −0.371105 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27675.7 | 1.50401 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26442.4 | 1.42470 | 0.712351 | − | 0.701823i | \(-0.247630\pi\) | ||||
0.712351 | + | 0.701823i | \(0.247630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16088.2 | −0.863124 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10115.1 | 0.538071 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22397.5 | 1.18640 | 0.593199 | − | 0.805056i | \(-0.297865\pi\) | ||||
0.593199 | + | 0.805056i | \(0.297865\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12295.7 | 0.645830 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2238.73 | 0.117096 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29828.0 | −1.54715 | −0.773573 | − | 0.633707i | \(-0.781533\pi\) | ||||
−0.773573 | + | 0.633707i | \(0.781533\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5457.46 | 0.281895 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5355.62 | −0.274349 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37300.9 | −1.90291 | −0.951454 | − | 0.307791i | \(-0.900410\pi\) | ||||
−0.951454 | + | 0.307791i | \(0.900410\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39097.8 | 1.97823 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15835.9 | −0.797969 | −0.398985 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398985 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 851.450 | 0.0425557 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26946.7 | −1.34134 | −0.670669 | − | 0.741756i | \(-0.733993\pi\) | ||||
−0.670669 | + | 0.741756i | \(0.733993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37380.0 | 1.84568 | 0.922839 | − | 0.385187i | \(-0.125863\pi\) | ||||
0.922839 | + | 0.385187i | \(0.125863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1166.35 | −0.0573582 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19980.9 | 0.974747 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39652.4 | −1.92668 | −0.963339 | − | 0.268285i | \(-0.913543\pi\) | ||||
−0.963339 | + | 0.268285i | \(0.913543\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −380.000 | −0.0183174 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27952.6 | −1.34208 | −0.671041 | − | 0.741420i | \(-0.734153\pi\) | ||||
−0.671041 | + | 0.741420i | \(0.734153\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25619.6 | −1.22038 | −0.610190 | − | 0.792255i | \(-0.708907\pi\) | ||||
−0.610190 | + | 0.792255i | \(0.708907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13020.4 | 0.617784 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19462.1 | −0.916214 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16666.0 | −0.781521 | −0.390761 | − | 0.920492i | \(-0.627788\pi\) | ||||
−0.390761 | + | 0.920492i | \(0.627788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4266.62 | 0.198525 | 0.0992623 | − | 0.995061i | \(-0.468352\pi\) | ||||
0.0992623 | + | 0.995061i | \(0.468352\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6542.78 | 0.303256 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14383.8 | 0.661559 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1398.12 | 0.0640573 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6743.01 | −0.306584 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12095.0 | 0.547829 | 0.273914 | − | 0.961754i | \(-0.411682\pi\) | ||||
0.273914 | + | 0.961754i | \(0.411682\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14549.5 | 0.654009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17064.8 | 0.764174 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15082.0 | 0.670303 | 0.335152 | − | 0.942164i | \(-0.391212\pi\) | ||||
0.335152 | + | 0.942164i | \(0.391212\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 598.732 | 0.0265101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5484.09 | 0.241008 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3464.38 | −0.151681 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29078.6 | −1.26372 | −0.631859 | − | 0.775083i | \(-0.717708\pi\) | ||||
−0.631859 | + | 0.775083i | \(0.717708\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10900.8 | −0.471985 | −0.235992 | − | 0.971755i | \(-0.575834\pi\) | ||||
−0.235992 | + | 0.971755i | \(0.575834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1080.64 | 0.0464455 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20320.2 | 0.870153 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24577.1 | 1.04476 | 0.522378 | − | 0.852714i | \(-0.325045\pi\) | ||||
0.522378 | + | 0.852714i | \(0.325045\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36000.8 | −1.52480 | −0.762399 | − | 0.647107i | \(-0.775979\pi\) | ||||
−0.762399 | + | 0.647107i | \(0.775979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31061.1 | −1.30605 | −0.653024 | − | 0.757337i | \(-0.726500\pi\) | ||||
−0.653024 | + | 0.757337i | \(0.726500\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30816.6 | −1.29108 | −0.645540 | − | 0.763727i | \(-0.723368\pi\) | ||||
−0.645540 | + | 0.763727i | \(0.723368\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13583.9 | −0.565010 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13007.8 | 0.539105 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27778.0 | 1.14303 | 0.571515 | − | 0.820592i | \(-0.306356\pi\) | ||||
0.571515 | + | 0.820592i | \(0.306356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21503.3 | 0.881682 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8073.30 | −0.328674 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18853.6 | −0.764836 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13436.8 | −0.541254 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46700.6 | −1.87456 | −0.937279 | − | 0.348580i | \(-0.886664\pi\) | ||||
−0.937279 | + | 0.348580i | \(0.886664\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25745.8 | 1.02621 | 0.513103 | − | 0.858327i | \(-0.328496\pi\) | ||||
0.513103 | + | 0.858327i | \(0.328496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9974.80 | −0.396200 | −0.198100 | − | 0.980182i | \(-0.563477\pi\) | ||||
−0.198100 | + | 0.980182i | \(0.563477\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9723.99 | 0.383555 | 0.191778 | − | 0.981438i | \(-0.438575\pi\) | ||||
0.191778 | + | 0.981438i | \(0.438575\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12818.2 | 0.503852 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8345.21 | −0.325767 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7248.40 | −0.281978 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1843.47 | −0.0712235 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13654.9 | −0.525763 | −0.262882 | − | 0.964828i | \(-0.584673\pi\) | ||||
−0.262882 | + | 0.964828i | \(0.584673\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9893.62 | 0.378348 | 0.189174 | − | 0.981944i | \(-0.439419\pi\) | ||||
0.189174 | + | 0.981944i | \(0.439419\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41598.9 | −1.58541 | −0.792703 | − | 0.609607i | \(-0.791327\pi\) | ||||
−0.792703 | + | 0.609607i | \(0.791327\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16369.6 | −0.619660 | −0.309830 | − | 0.950792i | \(-0.600272\pi\) | ||||
−0.309830 | + | 0.950792i | \(0.600272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11936.9 | 0.450337 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 311.177 | 0.0116609 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18959.9 | −0.708111 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −56065.1 | −2.07995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64474.3 | −2.38396 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6225.91 | −0.228681 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39211.0 | −1.43548 | −0.717740 | − | 0.696312i | \(-0.754823\pi\) | ||||
−0.717740 | + | 0.696312i | \(0.754823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10858.8 | −0.394917 | −0.197459 | − | 0.980311i | \(-0.563269\pi\) | ||||
−0.197459 | + | 0.980311i | \(0.563269\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1029.36 | 0.0373131 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18996.9 | −0.684116 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50169.6 | −1.80081 | −0.900403 | − | 0.435057i | \(-0.856728\pi\) | ||||
−0.900403 | + | 0.435057i | \(0.856728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11902.2 | −0.424449 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7150.00 | −0.254152 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12666.4 | −0.447330 | −0.223665 | − | 0.974666i | \(-0.571802\pi\) | ||||
−0.223665 | + | 0.974666i | \(0.571802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7059.92 | −0.248528 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3924.72 | 0.137275 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6348.26 | 0.221333 | 0.110666 | − | 0.993858i | \(-0.464702\pi\) | ||||
0.110666 | + | 0.993858i | \(0.464702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −39141.4 | −1.35598 | −0.677988 | − | 0.735073i | \(-0.737148\pi\) | ||||
−0.677988 | + | 0.735073i | \(0.737148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12013.4 | 0.414855 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26580.2 | 0.912082 | 0.456041 | − | 0.889959i | \(-0.349267\pi\) | ||||
0.456041 | + | 0.889959i | \(0.349267\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46686.1 | −1.59694 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −406.982 | −0.0138336 | −0.00691680 | − | 0.999976i | \(-0.502202\pi\) | ||||
−0.00691680 | + | 0.999976i | \(0.502202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17332.9 | −0.587307 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −33922.2 | −1.14224 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38701.8 | 1.29911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17862.6 | −0.595872 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 58873.6 | 1.95786 | 0.978928 | − | 0.204204i | \(-0.0654607\pi\) | ||||
0.978928 | + | 0.204204i | \(0.0654607\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52987.1 | 1.75122 | 0.875611 | − | 0.483016i | \(-0.160459\pi\) | ||||
0.875611 | + | 0.483016i | \(0.160459\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20055.3 | 0.660785 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6382.49 | −0.209001 | −0.104500 | − | 0.994525i | \(-0.533324\pi\) | ||||
−0.104500 | + | 0.994525i | \(0.533324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5215.16 | −0.170253 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25662.0 | −0.832646 | −0.416323 | − | 0.909217i | \(-0.636681\pi\) | ||||
−0.416323 | + | 0.909217i | \(0.636681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3805.24 | 0.123091 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16971.4 | 0.545662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49058.5 | 1.57255 | 0.786275 | − | 0.617877i | \(-0.212007\pi\) | ||||
0.786275 | + | 0.617877i | \(0.212007\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3820.98 | 0.121742 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4731.80 | −0.150309 | −0.0751543 | − | 0.997172i | \(-0.523945\pi\) | ||||
−0.0751543 | + | 0.997172i | \(0.523945\pi\) | |||||||
\(998\) | 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.x.1.2 | 2 | ||
3.2 | odd | 2 | 2160.4.a.bc.1.2 | 2 | |||
4.3 | odd | 2 | 540.4.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 540.4.a.h.1.1 | yes | 2 | ||
36.7 | odd | 6 | 1620.4.i.r.1081.2 | 4 | |||
36.11 | even | 6 | 1620.4.i.o.1081.2 | 4 | |||
36.23 | even | 6 | 1620.4.i.o.541.2 | 4 | |||
36.31 | odd | 6 | 1620.4.i.r.541.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.4.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
540.4.a.h.1.1 | yes | 2 | 12.11 | even | 2 | ||
1620.4.i.o.541.2 | 4 | 36.23 | even | 6 | |||
1620.4.i.o.1081.2 | 4 | 36.11 | even | 6 | |||
1620.4.i.r.541.2 | 4 | 36.31 | odd | 6 | |||
1620.4.i.r.1081.2 | 4 | 36.7 | odd | 6 | |||
2160.4.a.x.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2160.4.a.bc.1.2 | 2 | 3.2 | odd | 2 |