Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [232,4,Mod(1,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("232.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(13.6884431213\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.229.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.11491\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 232.1 |
$q$-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 | ||||||||
\(3\) | 2.92622 | 0.563151 | 0.281576 | − | 0.959539i | \(-0.409143\pi\) | ||||
0.281576 | + | 0.959539i | \(0.409143\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.3315 | 1.28185 | 0.640925 | − | 0.767603i | \(-0.278551\pi\) | ||||
0.640925 | + | 0.767603i | \(0.278551\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.8804 | 0.911454 | 0.455727 | − | 0.890120i | \(-0.349379\pi\) | ||||
0.455727 | + | 0.890120i | \(0.349379\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −18.4372 | −0.682860 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.5613 | 0.453948 | 0.226974 | − | 0.973901i | \(-0.427117\pi\) | ||||
0.226974 | + | 0.973901i | \(0.427117\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.3675 | 1.18124 | 0.590622 | − | 0.806948i | \(-0.298882\pi\) | ||||
0.590622 | + | 0.806948i | \(0.298882\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 41.9372 | 0.721876 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.28120 | 0.0896126 | 0.0448063 | − | 0.998996i | \(-0.485733\pi\) | ||||
0.0448063 | + | 0.998996i | \(0.485733\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −119.008 | −1.43696 | −0.718482 | − | 0.695545i | \(-0.755163\pi\) | ||||
−0.718482 | + | 0.695545i | \(0.755163\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 49.3957 | 0.513287 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 22.5433 | 0.204374 | 0.102187 | − | 0.994765i | \(-0.467416\pi\) | ||||
0.102187 | + | 0.994765i | \(0.467416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 80.3924 | 0.643139 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −132.959 | −0.947705 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 228.987 | 1.32669 | 0.663344 | − | 0.748314i | \(-0.269136\pi\) | ||||
0.663344 | + | 0.748314i | \(0.269136\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.4621 | 0.255642 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 241.921 | 1.16835 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 257.186 | 1.14273 | 0.571366 | − | 0.820696i | \(-0.306414\pi\) | ||||
0.571366 | + | 0.820696i | \(0.306414\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 162.017 | 0.665219 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 382.208 | 1.45588 | 0.727938 | − | 0.685643i | \(-0.240479\pi\) | ||||
0.727938 | + | 0.685643i | \(0.240479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −170.123 | −0.603337 | −0.301669 | − | 0.953413i | \(-0.597544\pi\) | ||||
−0.301669 | + | 0.953413i | \(0.597544\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −264.234 | −0.875325 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −172.889 | −0.536564 | −0.268282 | − | 0.963340i | \(-0.586456\pi\) | ||||
−0.268282 | + | 0.963340i | \(0.586456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −58.0532 | −0.169251 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.3802 | 0.0504654 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −69.2381 | −0.179445 | −0.0897224 | − | 0.995967i | \(-0.528598\pi\) | ||||
−0.0897224 | + | 0.995967i | \(0.528598\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 237.349 | 0.581893 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −348.244 | −0.809229 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −43.6860 | −0.0963971 | −0.0481986 | − | 0.998838i | \(-0.515348\pi\) | ||||
−0.0481986 | + | 0.998838i | \(0.515348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 684.892 | 1.43756 | 0.718782 | − | 0.695235i | \(-0.244700\pi\) | ||||
0.718782 | + | 0.695235i | \(0.244700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −311.227 | −0.622396 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 793.500 | 1.51418 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −528.585 | −0.963835 | −0.481917 | − | 0.876217i | \(-0.660059\pi\) | ||||
−0.481917 | + | 0.876217i | \(0.660059\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 65.9667 | 0.115094 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −488.054 | −0.815794 | −0.407897 | − | 0.913028i | \(-0.633738\pi\) | ||||
−0.407897 | + | 0.913028i | \(0.633738\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 80.3863 | 0.128884 | 0.0644418 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644418 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 235.246 | 0.362185 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 279.561 | 0.413753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −741.898 | −1.05658 | −0.528292 | − | 0.849063i | \(-0.677167\pi\) | ||||
−0.528292 | + | 0.849063i | \(0.677167\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 108.737 | 0.149159 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1360.29 | −1.79893 | −0.899466 | − | 0.436991i | \(-0.856044\pi\) | ||||
−0.899466 | + | 0.436991i | \(0.856044\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 90.0191 | 0.114870 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −84.8604 | −0.104575 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 957.563 | 1.14047 | 0.570233 | − | 0.821483i | \(-0.306853\pi\) | ||||
0.570233 | + | 0.821483i | \(0.306853\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 934.623 | 1.07665 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 670.068 | 0.747127 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1705.57 | −1.84197 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1111.59 | −1.16355 | −0.581776 | − | 0.813349i | \(-0.697642\pi\) | ||||
−0.581776 | + | 0.813349i | \(0.697642\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −305.345 | −0.309983 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1691.56 | −1.66650 | −0.833249 | − | 0.552898i | \(-0.813522\pi\) | ||||
−0.833249 | + | 0.552898i | \(0.813522\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −439.312 | −0.420259 | −0.210130 | − | 0.977674i | \(-0.567389\pi\) | ||||
−0.210130 | + | 0.977674i | \(0.567389\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 707.915 | 0.657957 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −861.531 | −0.778387 | −0.389193 | − | 0.921156i | \(-0.627246\pi\) | ||||
−0.389193 | + | 0.921156i | \(0.627246\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −459.780 | −0.404027 | −0.202013 | − | 0.979383i | \(-0.564748\pi\) | ||||
−0.202013 | + | 0.979383i | \(0.564748\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 752.582 | 0.643531 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.56230 | −0.00796058 | −0.00398029 | − | 0.999992i | \(-0.501267\pi\) | ||||
−0.00398029 | + | 0.999992i | \(0.501267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 323.080 | 0.261977 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1020.82 | −0.806625 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 106.029 | 0.0816777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1056.72 | −0.793931 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1118.43 | 0.819879 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −639.294 | −0.457442 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 905.522 | 0.632694 | 0.316347 | − | 0.948644i | \(-0.397544\pi\) | ||||
0.316347 | + | 0.948644i | \(0.397544\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −497.817 | −0.339770 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1039.43 | 0.693250 | 0.346625 | − | 0.938004i | \(-0.387328\pi\) | ||||
0.346625 | + | 0.938004i | \(0.387328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2008.90 | −1.30973 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1905.51 | −1.21482 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1146.58 | 0.715028 | 0.357514 | − | 0.933908i | \(-0.383624\pi\) | ||||
0.357514 | + | 0.933908i | \(0.383624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −573.043 | −0.349675 | −0.174838 | − | 0.984597i | \(-0.555940\pi\) | ||||
−0.174838 | + | 0.984597i | \(0.555940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −505.912 | −0.302167 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 916.959 | 0.536224 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −415.614 | −0.238034 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −169.877 | −0.0953142 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2324.32 | 1.27796 | 0.638979 | − | 0.769224i | \(-0.279357\pi\) | ||||
0.638979 | + | 0.769224i | \(0.279357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3188.68 | −1.71848 | −0.859242 | − | 0.511570i | \(-0.829064\pi\) | ||||
−0.859242 | + | 0.511570i | \(0.829064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −115.808 | −0.0611929 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3281.74 | 1.70062 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2960.71 | −1.50503 | −0.752516 | − | 0.658574i | \(-0.771160\pi\) | ||||
−0.752516 | + | 0.658574i | \(0.771160\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −202.606 | −0.101055 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 380.540 | 0.186278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3417.14 | 1.64203 | 0.821015 | − | 0.570907i | \(-0.193408\pi\) | ||||
0.821015 | + | 0.570907i | \(0.193408\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 694.536 | 0.327694 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −677.988 | −0.314158 | −0.157079 | − | 0.987586i | \(-0.550208\pi\) | ||||
−0.157079 | + | 0.987586i | \(0.550208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 868.556 | 0.395337 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2194.18 | 0.981246 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −773.271 | −0.339831 | −0.169915 | − | 0.985459i | \(-0.554349\pi\) | ||||
−0.169915 | + | 0.985459i | \(0.554349\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1357.05 | 0.586192 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −127.835 | −0.0542862 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1413.92 | 0.590399 | 0.295199 | − | 0.955436i | \(-0.404614\pi\) | ||||
0.295199 | + | 0.955436i | \(0.404614\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2160.51 | 0.887234 | 0.443617 | − | 0.896216i | \(-0.353695\pi\) | ||||
0.443617 | + | 0.896216i | \(0.353695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2004.15 | 0.809567 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3685.86 | 1.46481 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 104.025 | 0.0406795 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2244.40 | −0.863790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1586.39 | 0.600981 | 0.300490 | − | 0.953785i | \(-0.402850\pi\) | ||||
0.300490 | + | 0.953785i | \(0.402850\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1970.84 | −0.735047 | −0.367523 | − | 0.930014i | \(-0.619794\pi\) | ||||
−0.367523 | + | 0.930014i | \(0.619794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2321.96 | 0.852711 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4803.57 | 1.73726 | 0.868629 | − | 0.495463i | \(-0.165002\pi\) | ||||
0.868629 | + | 0.495463i | \(0.165002\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2692.85 | −0.959252 | −0.479626 | − | 0.877473i | \(-0.659228\pi\) | ||||
−0.479626 | + | 0.877473i | \(0.659228\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1546.76 | −0.542785 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −489.531 | −0.169253 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5477.63 | 1.86621 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −415.636 | −0.139559 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1970.93 | −0.652308 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −703.260 | −0.229452 | −0.114726 | − | 0.993397i | \(-0.536599\pi\) | ||||
−0.114726 | + | 0.993397i | \(0.536599\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1428.15 | −0.459415 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2438.12 | −0.773388 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3865.39 | 1.20922 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 235.228 | 0.0725810 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 347.774 | 0.105854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3965.95 | −1.19094 | −0.595469 | − | 0.803378i | \(-0.703034\pi\) | ||||
−0.595469 | + | 0.803378i | \(0.703034\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1482.21 | −0.439174 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3976.09 | 1.16256 | 0.581282 | − | 0.813702i | \(-0.302551\pi\) | ||||
0.581282 | + | 0.813702i | \(0.302551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −611.004 | −0.176316 | −0.0881578 | − | 0.996107i | \(-0.528098\pi\) | ||||
−0.0881578 | + | 0.996107i | \(0.528098\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 818.058 | 0.233006 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1051.90 | −0.295761 | −0.147880 | − | 0.989005i | \(-0.547245\pi\) | ||||
−0.147880 | + | 0.989005i | \(0.547245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2477.77 | −0.687794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2170.96 | −0.595017 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2085.97 | 0.564561 | 0.282280 | − | 0.959332i | \(-0.408909\pi\) | ||||
0.282280 | + | 0.959332i | \(0.408909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6064.55 | −1.62096 | −0.810481 | − | 0.585765i | \(-0.800794\pi\) | ||||
−0.810481 | + | 0.585765i | \(0.800794\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3908.09 | 1.03170 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −831.991 | −0.216955 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6589.18 | −1.69741 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3980.51 | −1.01307 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5169.26 | 1.29992 | 0.649962 | − | 0.759967i | \(-0.274785\pi\) | ||||
0.649962 | + | 0.759967i | \(0.274785\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 373.347 | 0.0927753 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 263.416 | 0.0646891 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7238.84 | −1.75699 | −0.878495 | − | 0.477751i | \(-0.841452\pi\) | ||||
−0.878495 | + | 0.477751i | \(0.841452\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4341.39 | 1.04155 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 534.680 | 0.126804 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4855.39 | 1.13839 | 0.569195 | − | 0.822203i | \(-0.307255\pi\) | ||||
0.569195 | + | 0.822203i | \(0.307255\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −992.286 | −0.230021 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2802.04 | 0.642255 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5559.70 | 1.26015 | 0.630076 | − | 0.776533i | \(-0.283024\pi\) | ||||
0.630076 | + | 0.776533i | \(0.283024\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2534.36 | 0.568087 | 0.284044 | − | 0.958811i | \(-0.408324\pi\) | ||||
0.284044 | + | 0.958811i | \(0.408324\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2734.91 | 0.606317 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1331.41 | 0.291952 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7540.72 | 1.63566 | 0.817831 | − | 0.575459i | \(-0.195177\pi\) | ||||
0.817831 | + | 0.575459i | \(0.195177\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4221.89 | −0.905943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5426.97 | 1.15212 | 0.576060 | − | 0.817407i | \(-0.304589\pi\) | ||||
0.576060 | + | 0.817407i | \(0.304589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1297.75 | 0.272590 | 0.136295 | − | 0.990668i | \(-0.456480\pi\) | ||||
0.136295 | + | 0.990668i | \(0.456480\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4990.87 | −1.03731 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6451.82 | 1.32696 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4873.55 | −0.991970 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3252.75 | −0.655256 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6201.84 | −1.23657 | −0.618285 | − | 0.785954i | \(-0.712172\pi\) | ||||
−0.618285 | + | 0.785954i | \(0.712172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −626.086 | −0.123567 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2201.98 | −0.430209 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1248.17 | 0.241416 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2871.74 | −0.549914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4949.87 | −0.938491 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9815.55 | 1.84274 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9181.06 | −1.70681 | −0.853406 | − | 0.521247i | \(-0.825467\pi\) | ||||
−0.853406 | + | 0.521247i | \(0.825467\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1285.52 | −0.236670 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3753.29 | 0.684339 | 0.342170 | − | 0.939638i | \(-0.388838\pi\) | ||||
0.342170 | + | 0.939638i | \(0.388838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2115.29 | 0.381991 | 0.190996 | − | 0.981591i | \(-0.438828\pi\) | ||||
0.190996 | + | 0.981591i | \(0.438828\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4460.36 | −0.797818 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4739.89 | −0.839807 | −0.419903 | − | 0.907569i | \(-0.637936\pi\) | ||||
−0.419903 | + | 0.907569i | \(0.637936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −480.279 | −0.0842961 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2521.03 | −0.438350 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −747.513 | −0.128770 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4451.12 | 0.759705 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1345.42 | −0.227528 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2918.43 | −0.489053 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6958.68 | −1.15554 | −0.577770 | − | 0.816200i | \(-0.696077\pi\) | ||||
−0.577770 | + | 0.816200i | \(0.696077\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4741.79 | −0.780326 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7575.42 | −1.23549 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2997.55 | 0.484530 | 0.242265 | − | 0.970210i | \(-0.422110\pi\) | ||||
0.242265 | + | 0.970210i | \(0.422110\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.9814 | −0.00448301 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3792.34 | 0.602248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6769.93 | −1.06572 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 945.404 | 0.147533 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7788.46 | 1.20492 | 0.602459 | − | 0.798150i | \(-0.294188\pi\) | ||||
0.602459 | + | 0.798150i | \(0.294188\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6404.16 | −0.982254 | −0.491127 | − | 0.871088i | \(-0.663415\pi\) | ||||
−0.491127 | + | 0.871088i | \(0.663415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7361.62 | −1.11947 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5869.46 | −0.884986 | −0.442493 | − | 0.896772i | \(-0.645906\pi\) | ||||
−0.442493 | + | 0.896772i | \(0.645906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6994.55 | −1.04572 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 310.264 | 0.0459969 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2761.48 | −0.405975 | −0.202988 | − | 0.979181i | \(-0.565065\pi\) | ||||
−0.202988 | + | 0.979181i | \(0.565065\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7303.93 | 1.06487 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3092.20 | −0.447103 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1152.06 | 0.165209 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3039.36 | 0.432298 | 0.216149 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216149 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7046.86 | −0.994160 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1168.76 | −0.163556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2051.57 | 0.284789 | 0.142394 | − | 0.989810i | \(-0.454520\pi\) | ||||
0.142394 | + | 0.989810i | \(0.454520\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1870.72 | −0.257609 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1605.66 | −0.219351 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1852.42 | −0.251062 | −0.125531 | − | 0.992090i | \(-0.540063\pi\) | ||||
−0.125531 | + | 0.992090i | \(0.540063\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2649.76 | 0.356302 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5723.43 | 0.763587 | 0.381793 | − | 0.924248i | \(-0.375307\pi\) | ||||
0.381793 | + | 0.924248i | \(0.375307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4006.54 | 0.530369 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3136.59 | 0.411995 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4946.70 | −0.644750 | −0.322375 | − | 0.946612i | \(-0.604481\pi\) | ||||
−0.322375 | + | 0.946612i | \(0.604481\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 141.599 | 0.0183145 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3041.61 | 0.390405 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10632.5 | −1.35438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9275.78 | 1.17264 | 0.586320 | − | 0.810080i | \(-0.300576\pi\) | ||||
0.586320 | + | 0.810080i | \(0.300576\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5878.49 | −0.737575 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5051.01 | 0.629016 | 0.314508 | − | 0.949255i | \(-0.398161\pi\) | ||||
0.314508 | + | 0.949255i | \(0.398161\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12678.4 | 1.56714 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1558.36 | 0.191199 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4259.34 | 0.518741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5049.42 | 0.610459 | 0.305229 | − | 0.952279i | \(-0.401267\pi\) | ||||
0.305229 | + | 0.952279i | \(0.401267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3355.14 | 0.402669 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −737.435 | −0.0878616 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19495.0 | −2.30596 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1676.85 | −0.196920 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5332.54 | 0.621746 | 0.310873 | − | 0.950451i | \(-0.399379\pi\) | ||||
0.310873 | + | 0.950451i | \(0.399379\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6195.89 | 0.717266 | 0.358633 | − | 0.933479i | \(-0.383243\pi\) | ||||
0.358633 | + | 0.933479i | \(0.383243\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3187.60 | 0.366398 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 504.961 | 0.0576334 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11561.2 | 1.31027 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2683.22 | 0.301975 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1399.50 | 0.156408 | 0.0782038 | − | 0.996937i | \(-0.475082\pi\) | ||||
0.0782038 | + | 0.996937i | \(0.475082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1689.45 | 0.187505 | 0.0937526 | − | 0.995596i | \(-0.470114\pi\) | ||||
0.0937526 | + | 0.995596i | \(0.470114\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1216.18 | −0.134049 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2682.84 | −0.293679 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12352.8 | −1.34298 | −0.671491 | − | 0.741013i | \(-0.734346\pi\) | ||||
−0.671491 | + | 0.741013i | \(0.734346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1070.34 | 0.115575 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13427.1 | −1.44005 | −0.720023 | − | 0.693950i | \(-0.755869\pi\) | ||||
−0.720023 | + | 0.693950i | \(0.755869\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13723.3 | 1.46191 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6801.47 | 0.719684 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2912.34 | 0.306107 | 0.153053 | − | 0.988218i | \(-0.451089\pi\) | ||||
0.153053 | + | 0.988218i | \(0.451089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6329.88 | 0.660892 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9330.78 | −0.967767 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13394.6 | 1.38010 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5906.26 | 0.604558 | 0.302279 | − | 0.953219i | \(-0.402253\pi\) | ||||
0.302279 | + | 0.953219i | \(0.402253\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −835.144 | −0.0849263 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2847.28 | 0.287659 | 0.143830 | − | 0.989602i | \(-0.454058\pi\) | ||||
0.143830 | + | 0.989602i | \(0.454058\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8561.02 | 0.859319 | 0.429659 | − | 0.902991i | \(-0.358634\pi\) | ||||
0.429659 | + | 0.902991i | \(0.358634\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9603.09 | 0.957704 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14998.9 | 1.48622 | 0.743112 | − | 0.669167i | \(-0.233349\pi\) | ||||
0.743112 | + | 0.669167i | \(0.233349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8922.71 | −0.878491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8663.68 | −0.847561 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2817.46 | −0.273884 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9567.35 | −0.924169 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1276.56 | 0.122536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8422.27 | −0.803389 | −0.401695 | − | 0.915774i | \(-0.631579\pi\) | ||||
−0.401695 | + | 0.915774i | \(0.631579\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14239.7 | 1.34984 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1113.54 | 0.104903 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15930.7 | −1.49150 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1773.91 | −0.165058 | −0.0825291 | − | 0.996589i | \(-0.526300\pi\) | ||||
−0.0825291 | + | 0.996589i | \(0.526300\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9999.30 | 0.924711 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2157.20 | −0.198275 | −0.0991375 | − | 0.995074i | \(-0.531608\pi\) | ||||
−0.0991375 | + | 0.995074i | \(0.531608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −182.155 | −0.0166406 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4376.06 | −0.397352 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8238.53 | −0.743558 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4303.31 | 0.386058 | 0.193029 | − | 0.981193i | \(-0.438169\pi\) | ||||
0.193029 | + | 0.981193i | \(0.438169\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1983.94 | −0.176918 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16020.5 | 1.42011 | 0.710057 | − | 0.704144i | \(-0.248669\pi\) | ||||
0.710057 | + | 0.704144i | \(0.248669\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24242.6 | −2.13620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2541.59 | 0.222635 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18269.6 | 1.59094 | 0.795469 | − | 0.605994i | \(-0.207224\pi\) | ||||
0.795469 | + | 0.605994i | \(0.207224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1356.95 | 0.117472 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 15823.2 | 1.36182 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6296.01 | −0.538709 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2863.28 | −0.243572 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2262.76 | −0.191376 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13128.7 | 1.10399 | 0.551996 | − | 0.833847i | \(-0.313866\pi\) | ||||
0.551996 | + | 0.833847i | \(0.313866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8295.67 | 0.693583 | 0.346792 | − | 0.937942i | \(-0.387271\pi\) | ||||
0.346792 | + | 0.937942i | \(0.387271\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3971.04 | 0.330115 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1438.31 | 0.118888 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11658.8 | −0.958231 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 805.449 | 0.0658258 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21161.9 | 1.71974 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12347.1 | −0.997775 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4137.44 | 0.332484 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −961.439 | −0.0768314 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23563.6 | 1.87261 | 0.936303 | − | 0.351194i | \(-0.114224\pi\) | ||||
0.936303 | + | 0.351194i | \(0.114224\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6322.13 | 0.499647 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6589.34 | −0.517902 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17151.4 | 1.34066 | 0.670330 | − | 0.742063i | \(-0.266152\pi\) | ||||
0.670330 | + | 0.742063i | \(0.266152\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12627.5 | −0.981656 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3451.23 | 0.266838 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12523.5 | −0.963027 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 10785.6 | 0.824910 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18572.6 | 1.41283 | 0.706415 | − | 0.707798i | \(-0.250311\pi\) | ||||
0.706415 | + | 0.707798i | \(0.250311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9419.27 | −0.712688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 304.400 | 0.0229087 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7835.40 | 0.586541 | 0.293270 | − | 0.956030i | \(-0.405256\pi\) | ||||
0.293270 | + | 0.956030i | \(0.405256\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −137.042 | −0.0102043 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1835.52 | 0.135951 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5891.09 | 0.434038 | 0.217019 | − | 0.976167i | \(-0.430367\pi\) | ||||
0.217019 | + | 0.976167i | \(0.430367\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20083.8 | −1.47195 | −0.735973 | − | 0.677010i | \(-0.763275\pi\) | ||||
−0.735973 | + | 0.677010i | \(0.763275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4642.13 | 0.338443 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1812.31 | 0.131441 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21008.9 | −1.51579 | −0.757896 | − | 0.652375i | \(-0.773773\pi\) | ||||
−0.757896 | + | 0.652375i | \(0.773773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5767.11 | −0.413943 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22962.2 | −1.63964 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1146.67 | −0.0814587 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14629.9 | −1.03397 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20222.3 | −1.42192 | −0.710958 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710958 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27251.4 | −1.90640 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14056.3 | 0.978339 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18803.0 | 1.30210 | 0.651051 | − | 0.759034i | \(-0.274328\pi\) | ||||
0.651051 | + | 0.759034i | \(0.274328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1519.55 | 0.104699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7879.87 | −0.540204 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10612.1 | 0.723872 | 0.361936 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361936 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27709.6 | 1.88070 | 0.940350 | − | 0.340210i | \(-0.110498\pi\) | ||||
0.940350 | + | 0.340210i | \(0.110498\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9745.64 | 0.658164 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15144.4 | −1.01770 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21945.0 | −1.46741 | −0.733707 | − | 0.679466i | \(-0.762212\pi\) | ||||
−0.733707 | + | 0.679466i | \(0.762212\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1432.47 | −0.0953150 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9572.44 | −0.633813 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11777.0 | −0.775971 | −0.387985 | − | 0.921665i | \(-0.626829\pi\) | ||||
−0.387985 | + | 0.921665i | \(0.626829\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 16028.7 | 1.05096 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27161.1 | −1.77223 | −0.886115 | − | 0.463465i | \(-0.846606\pi\) | ||||
−0.886115 | + | 0.463465i | \(0.846606\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10366.3 | −0.673116 | −0.336558 | − | 0.941663i | \(-0.609263\pi\) | ||||
−0.336558 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2997.35 | −0.193687 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16164.0 | 1.03948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19211.1 | −1.22951 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5767.38 | −0.367348 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1615.43 | 0.102403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11208.4 | −0.707132 | −0.353566 | − | 0.935410i | \(-0.615031\pi\) | ||||
−0.353566 | + | 0.935410i | \(0.615031\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2057.89 | −0.129216 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12977.5 | 0.811018 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3214.26 | −0.199927 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8998.36 | 0.557073 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 351.957 | 0.0216872 | 0.0108436 | − | 0.999941i | \(-0.496548\pi\) | ||||
0.0108436 | + | 0.999941i | \(0.496548\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27628.0 | 1.69447 | 0.847234 | − | 0.531220i | \(-0.178266\pi\) | ||||
0.847234 | + | 0.531220i | \(0.178266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7134.48 | −0.435534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10858.0 | −0.659771 | −0.329886 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329886 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −723.498 | −0.0437593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11311.0 | 0.680972 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9714.54 | −0.582174 | −0.291087 | − | 0.956697i | \(-0.594017\pi\) | ||||
−0.291087 | + | 0.956697i | \(0.594017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14896.7 | 0.888643 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1482.10 | −0.0880095 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1918.79 | 0.113422 | 0.0567111 | − | 0.998391i | \(-0.481939\pi\) | ||||
0.0567111 | + | 0.998391i | \(0.481939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12106.3 | −0.712375 | −0.356188 | − | 0.934414i | \(-0.615924\pi\) | ||||
−0.356188 | + | 0.934414i | \(0.615924\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1017.66 | 0.0596120 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −28790.6 | −1.67887 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −653.756 | −0.0379513 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11605.2 | −0.670679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11342.7 | 0.652580 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16348.0 | 0.936355 | 0.468178 | − | 0.883634i | \(-0.344911\pi\) | ||||
0.468178 | + | 0.883634i | \(0.344911\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10688.9 | −0.609507 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19298.2 | −1.09555 | −0.547776 | − | 0.836625i | \(-0.684525\pi\) | ||||
−0.547776 | + | 0.836625i | \(0.684525\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18764.0 | −1.06052 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11634.9 | 0.654700 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9938.38 | 0.556781 | 0.278390 | − | 0.960468i | \(-0.410199\pi\) | ||||
0.278390 | + | 0.960468i | \(0.410199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16432.2 | 0.916558 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1787.93 | −0.0992924 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3833.54 | −0.211968 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18610.4 | −1.02456 | −0.512282 | − | 0.858817i | \(-0.671200\pi\) | ||||
−0.512282 | + | 0.858817i | \(0.671200\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5154.34 | −0.282536 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8212.58 | −0.448231 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2400.73 | 0.130465 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3078.09 | −0.166558 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26877.8 | 1.44816 | 0.724080 | − | 0.689716i | \(-0.242265\pi\) | ||||
0.724080 | + | 0.689716i | \(0.242265\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30607.2 | −1.64206 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7250.49 | −0.387332 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28554.1 | −1.51894 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3141.28 | −0.166394 | −0.0831970 | − | 0.996533i | \(-0.526513\pi\) | ||||
−0.0831970 | + | 0.996533i | \(0.526513\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13678.6 | 0.721499 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5162.14 | 0.271141 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13141.4 | 0.687358 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6104.00 | 0.317933 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27198.6 | 1.41076 | 0.705379 | − | 0.708830i | \(-0.250777\pi\) | ||||
0.705379 | + | 0.708830i | \(0.250777\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7415.75 | −0.383047 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17746.2 | −0.912847 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2331.38 | −0.119428 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15713.1 | 0.801603 | 0.400802 | − | 0.916165i | \(-0.368732\pi\) | ||||
0.400802 | + | 0.916165i | \(0.368732\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8500.05 | 0.431847 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1068.58 | −0.0540666 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10977.4 | 0.553153 | 0.276576 | − | 0.960992i | \(-0.410800\pi\) | ||||
0.276576 | + | 0.960992i | \(0.410800\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2434.59 | −0.122178 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8754.07 | −0.437531 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12586.3 | 0.626515 | 0.313258 | − | 0.949668i | \(-0.398580\pi\) | ||||
0.313258 | + | 0.949668i | \(0.398580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19281.4 | −0.955897 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21237.6 | 1.04863 | 0.524315 | − | 0.851524i | \(-0.324321\pi\) | ||||
0.524315 | + | 0.851524i | \(0.324321\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33311.0 | 1.63815 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25080.0 | 1.22842 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14543.0 | −0.709464 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31114.2 | 1.51181 | 0.755907 | − | 0.654679i | \(-0.227196\pi\) | ||||
0.755907 | + | 0.654679i | \(0.227196\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15126.4 | 0.732054 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45698.6 | −2.20284 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12838.7 | 0.616423 | 0.308211 | − | 0.951318i | \(-0.400270\pi\) | ||||
0.308211 | + | 0.951318i | \(0.400270\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1092.50 | 0.0522466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11665.6 | −0.555689 | −0.277844 | − | 0.960626i | \(-0.589620\pi\) | ||||
−0.277844 | + | 0.960626i | \(0.589620\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7761.25 | −0.368252 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1659.70 | −0.0784401 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2418.78 | −0.113869 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33339.3 | −1.56339 | −0.781693 | − | 0.623663i | \(-0.785644\pi\) | ||||
−0.781693 | + | 0.623663i | \(0.785644\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21182.4 | −0.989452 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17895.2 | −0.832660 | −0.416330 | − | 0.909214i | \(-0.636684\pi\) | ||||
−0.416330 | + | 0.909214i | \(0.636684\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18408.9 | 0.853246 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12703.9 | 0.586549 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −45485.9 | −2.09204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8082.82 | −0.370328 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3855.82 | 0.175984 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −42431.4 | −1.92923 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15816.4 | −0.716384 | −0.358192 | − | 0.933648i | \(-0.616607\pi\) | ||||
−0.358192 | + | 0.933648i | \(0.616607\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14208.0 | 0.641086 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −161.415 | −0.00725570 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 37920.7 | 1.69811 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2903.65 | −0.129537 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21146.2 | 0.939822 | 0.469911 | − | 0.882714i | \(-0.344286\pi\) | ||||
0.469911 | + | 0.882714i | \(0.344286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1085.95 | −0.0480828 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17654.8 | −0.778779 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1331.30 | 0.0585065 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5453.71 | 0.238780 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16268.9 | 0.709657 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19190.2 | −0.833982 | −0.416991 | − | 0.908911i | \(-0.636915\pi\) | ||||
−0.416991 | + | 0.908911i | \(0.636915\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37890.9 | −1.64060 | −0.820302 | − | 0.571931i | \(-0.806194\pi\) | ||||
−0.820302 | + | 0.571931i | \(0.806194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7416.11 | 0.319919 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 48972.8 | 2.10484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20246.0 | 0.866974 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17231.9 | −0.735201 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11006.2 | −0.467868 | −0.233934 | − | 0.972252i | \(-0.575160\pi\) | ||||
−0.233934 | + | 0.972252i | \(0.575160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42361.2 | 1.79419 | 0.897094 | − | 0.441839i | \(-0.145674\pi\) | ||||
0.897094 | + | 0.441839i | \(0.145674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3895.99 | 0.164413 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1786.13 | −0.0751028 | −0.0375514 | − | 0.999295i | \(-0.511956\pi\) | ||||
−0.0375514 | + | 0.999295i | \(0.511956\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12070.8 | 0.505712 | 0.252856 | − | 0.967504i | \(-0.418630\pi\) | ||||
0.252856 | + | 0.967504i | \(0.418630\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22065.8 | 0.921125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −364.644 | −0.0151671 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9716.60 | −0.402703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −30446.0 | −1.25731 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39687.9 | −1.63311 | −0.816555 | − | 0.577267i | \(-0.804119\pi\) | ||||
−0.816555 | + | 0.577267i | \(0.804119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15880.5 | 0.648818 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12447.7 | 0.506763 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17837.9 | −0.723632 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3797.50 | 0.153510 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5797.82 | 0.233545 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36146.8 | 1.45093 | 0.725466 | − | 0.688258i | \(-0.241624\pi\) | ||||
0.725466 | + | 0.688258i | \(0.241624\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31445.9 | 1.25781 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1778.90 | 0.0709054 | 0.0354527 | − | 0.999371i | \(-0.488713\pi\) | ||||
0.0354527 | + | 0.999371i | \(0.488713\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37890.5 | 1.50501 | 0.752507 | − | 0.658584i | \(-0.228844\pi\) | ||||
0.752507 | + | 0.658584i | \(0.228844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18879.4 | 0.747282 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22754.4 | −0.897529 | −0.448764 | − | 0.893650i | \(-0.648136\pi\) | ||||
−0.448764 | + | 0.893650i | \(0.648136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11082.1 | −0.435612 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14261.1 | −0.558629 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12286.8 | −0.479634 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29266.4 | −1.13852 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20494.6 | 0.794543 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10791.5 | −0.416937 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28543.9 | 1.09904 | 0.549521 | − | 0.835480i | \(-0.314810\pi\) | ||||
0.549521 | + | 0.835480i | \(0.314810\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18147.9 | −0.696376 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46848.4 | 1.79156 | 0.895779 | − | 0.444499i | \(-0.146618\pi\) | ||||
0.895779 | + | 0.444499i | \(0.146618\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7020.06 | 0.267547 | 0.133773 | − | 0.991012i | \(-0.457291\pi\) | ||||
0.133773 | + | 0.991012i | \(0.457291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1832.07 | −0.0695867 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19200.5 | 0.726820 | 0.363410 | − | 0.931629i | \(-0.381612\pi\) | ||||
0.363410 | + | 0.931629i | \(0.381612\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15285.5 | 0.576671 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1800.83 | 0.0677104 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 20575.2 | 0.771023 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20263.6 | 0.756803 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3652.41 | 0.135954 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6640.63 | −0.246360 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −434.898 | −0.0160805 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8403.34 | −0.309685 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30963.4 | 1.13730 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36098.6 | −1.32154 | −0.660768 | − | 0.750590i | \(-0.729769\pi\) | ||||
−0.660768 | + | 0.750590i | \(0.729769\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31187.6 | 1.13799 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19193.8 | −0.698047 | −0.349023 | − | 0.937114i | \(-0.613487\pi\) | ||||
−0.349023 | + | 0.937114i | \(0.613487\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22528.2 | −0.816622 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28722.5 | 1.03774 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17546.0 | 0.631866 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49242.2 | 1.76752 | 0.883760 | − | 0.467941i | \(-0.155004\pi\) | ||||
0.883760 | + | 0.467941i | \(0.155004\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26865.8 | −0.961193 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −27022.3 | −0.963651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20675.8 | 0.734936 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8099.70 | 0.286978 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43350.9 | −1.53100 | −0.765498 | − | 0.643438i | \(-0.777507\pi\) | ||||
−0.765498 | + | 0.643438i | \(0.777507\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6908.80 | 0.243208 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10983.0 | 0.385387 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1490.84 | 0.0521450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39167.8 | 1.36559 | 0.682794 | − | 0.730611i | \(-0.260765\pi\) | ||||
0.682794 | + | 0.730611i | \(0.260765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6189.81 | 0.215119 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13329.9 | −0.461789 | −0.230895 | − | 0.972979i | \(-0.574165\pi\) | ||||
−0.230895 | + | 0.972979i | \(0.574165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8616.25 | 0.297544 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32165.7 | −1.10725 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19115.3 | −0.655926 | −0.327963 | − | 0.944690i | \(-0.606362\pi\) | ||||
−0.327963 | + | 0.944690i | \(0.606362\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4450.78 | 0.152243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13870.0 | −0.472938 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29008.4 | −0.986018 | −0.493009 | − | 0.870024i | \(-0.664103\pi\) | ||||
−0.493009 | + | 0.870024i | \(0.664103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22735.4 | 0.770367 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1405.40 | −0.0474715 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19354.7 | 0.651715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22644.2 | 0.760103 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15884.3 | 0.531529 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28245.1 | −0.942220 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55491.5 | 1.84538 | 0.922691 | − | 0.385539i | \(-0.125985\pi\) | ||||
0.922691 | + | 0.385539i | \(0.125985\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2187.39 | −0.0725171 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39721.0 | 1.31278 | 0.656389 | − | 0.754422i | \(-0.272083\pi\) | ||||
0.656389 | + | 0.754422i | \(0.272083\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9673.18 | −0.318713 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13025.0 | 0.427829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4352.89 | 0.142540 | 0.0712699 | − | 0.997457i | \(-0.477295\pi\) | ||||
0.0712699 | + | 0.997457i | \(0.477295\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15858.5 | 0.517712 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8477.07 | 0.275894 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10317.1 | −0.334754 | −0.167377 | − | 0.985893i | \(-0.553530\pi\) | ||||
−0.167377 | + | 0.985893i | \(0.553530\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 68842.4 | 2.22690 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8539.98 | −0.275411 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3835.13 | −0.123307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45439.0 | −1.45653 | −0.728264 | − | 0.685297i | \(-0.759672\pi\) | ||||
−0.728264 | + | 0.685297i | \(0.759672\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20362.6 | −0.650744 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38592.6 | −1.22962 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 31888.0 | 1.01294 | 0.506471 | − | 0.862257i | \(-0.330950\pi\) | ||||
0.506471 | + | 0.862257i | \(0.330950\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34195.2 | −1.08297 |
(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 | 232.4.a.b.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 2088.4.a.b.1.1 | 3 | |||
4.3 | odd | 2 | 464.4.a.g.1.2 | 3 | |||
8.3 | odd | 2 | 1856.4.a.u.1.2 | 3 | |||
8.5 | even | 2 | 1856.4.a.p.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.4.a.b.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
464.4.a.g.1.2 | 3 | 4.3 | odd | 2 | |||
1856.4.a.p.1.2 | 3 | 8.5 | even | 2 | |||
1856.4.a.u.1.2 | 3 | 8.3 | odd | 2 | |||
2088.4.a.b.1.1 | 3 | 3.2 | odd | 2 |