Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(865,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.865");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.2261390379264.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 8x^{6} + 38x^{5} - 38x^{4} + 8x^{3} + 325x^{2} - 322x + 2122 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 865.7 | ||
Root | \(-2.75792 + 0.460416i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.865 |
Dual form | 1728.4.d.e.865.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 16.7850i | 1.50130i | 0.660701 | + | 0.750649i | \(0.270259\pi\) | ||||
−0.660701 | + | 0.750649i | \(0.729741\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.3100 | −1.20463 | −0.602314 | − | 0.798259i | \(-0.705755\pi\) | ||||
−0.602314 | + | 0.798259i | \(0.705755\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 51.9124i | 1.42293i | 0.702724 | + | 0.711463i | \(0.251967\pi\) | ||||
−0.702724 | + | 0.711463i | \(0.748033\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 28.0451i | 0.598331i | 0.954201 | + | 0.299165i | \(0.0967082\pi\) | ||||
−0.954201 | + | 0.299165i | \(0.903292\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −60.9124 | −0.869025 | −0.434513 | − | 0.900666i | \(-0.643079\pi\) | ||||
−0.434513 | + | 0.900666i | \(0.643079\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 162.737i | 1.96497i | 0.186335 | + | 0.982486i | \(0.440339\pi\) | ||||
−0.186335 | + | 0.982486i | \(0.559661\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 83.2950 | 0.755140 | 0.377570 | − | 0.925981i | \(-0.376760\pi\) | ||||
0.377570 | + | 0.925981i | \(0.376760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −156.737 | −1.25390 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 217.575i | 1.39320i | 0.717461 | + | 0.696598i | \(0.245304\pi\) | ||||
−0.717461 | + | 0.696598i | \(0.754696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −174.005 | −1.00814 | −0.504069 | − | 0.863663i | \(-0.668164\pi\) | ||||
−0.504069 | + | 0.863663i | \(0.668164\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 374.474i | − 1.80851i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 407.946i | 1.81259i | 0.422645 | + | 0.906295i | \(0.361102\pi\) | ||||
−0.422645 | + | 0.906295i | \(0.638898\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 196.562 | 0.748728 | 0.374364 | − | 0.927282i | \(-0.377861\pi\) | ||||
0.374364 | + | 0.927282i | \(0.377861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 345.474i | − 1.22522i | −0.790386 | − | 0.612609i | \(-0.790120\pi\) | ||||
0.790386 | − | 0.612609i | \(-0.209880\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 335.701 | 1.04185 | 0.520925 | − | 0.853602i | \(-0.325587\pi\) | ||||
0.520925 | + | 0.853602i | \(0.325587\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 154.737 | 0.451129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 234.360i | 0.607394i | 0.952769 | + | 0.303697i | \(0.0982210\pi\) | ||||
−0.952769 | + | 0.303697i | \(0.901779\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −871.351 | −2.13624 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 321.124i | 0.708590i | 0.935134 | + | 0.354295i | \(0.115279\pi\) | ||||
−0.935134 | + | 0.354295i | \(0.884721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 739.381i | 1.55194i | 0.630772 | + | 0.775968i | \(0.282738\pi\) | ||||
−0.630772 | + | 0.775968i | \(0.717262\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −470.737 | −0.898273 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.0000i | 0.0364685i | 0.999834 | + | 0.0182342i | \(0.00580446\pi\) | ||||
−0.999834 | + | 0.0182342i | \(0.994196\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 418.996 | 0.700361 | 0.350180 | − | 0.936682i | \(-0.386120\pi\) | ||||
0.350180 | + | 0.936682i | \(0.386120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 397.212 | 0.636851 | 0.318425 | − | 0.947948i | \(-0.396846\pi\) | ||||
0.318425 | + | 0.947948i | \(0.396846\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1158.17i | − 1.71410i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −95.6053 | −0.136157 | −0.0680787 | − | 0.997680i | \(-0.521687\pi\) | ||||
−0.0680787 | + | 0.997680i | \(0.521687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 348.263i | − 0.460564i | −0.973124 | − | 0.230282i | \(-0.926035\pi\) | ||||
0.973124 | − | 0.230282i | \(-0.0739649\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 1022.42i | − 1.30467i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1492.42 | −1.77749 | −0.888745 | − | 0.458403i | \(-0.848422\pi\) | ||||
−0.888745 | + | 0.458403i | \(0.848422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 625.686i | − 0.720766i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2731.55 | −2.95001 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 881.949 | 0.923179 | 0.461589 | − | 0.887094i | \(-0.347279\pi\) | ||||
0.461589 | + | 0.887094i | \(0.347279\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 642.242i | 0.632727i | 0.948638 | + | 0.316364i | \(0.102462\pi\) | ||||
−0.948638 | + | 0.316364i | \(0.897538\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1322.03 | 1.26469 | 0.632345 | − | 0.774687i | \(-0.282092\pi\) | ||||
0.632345 | + | 0.774687i | \(0.282092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1671.77i | − 1.51043i | −0.655475 | − | 0.755217i | \(-0.727531\pi\) | ||||
0.655475 | − | 0.755217i | \(-0.272469\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1667.52i | 1.46531i | 0.680598 | + | 0.732657i | \(0.261720\pi\) | ||||
−0.680598 | + | 0.732657i | \(0.738280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −418.314 | −0.348245 | −0.174122 | − | 0.984724i | \(-0.555709\pi\) | ||||
−0.174122 | + | 0.984724i | \(0.555709\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1398.11i | 1.13369i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1358.96 | 1.04685 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1363.90 | −1.02472 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 532.710i | − 0.381176i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −106.509 | −0.0744185 | −0.0372093 | − | 0.999307i | \(-0.511847\pi\) | ||||
−0.0372093 | + | 0.999307i | \(0.511847\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 1814.47i | − 1.21016i | −0.796163 | − | 0.605082i | \(-0.793140\pi\) | ||||
0.796163 | − | 0.605082i | \(-0.206860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 3630.67i | − 2.36706i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 401.197 | 0.250194 | 0.125097 | − | 0.992145i | \(-0.460076\pi\) | ||||
0.125097 | + | 0.992145i | \(0.460076\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 381.474i | 0.232779i | 0.993204 | + | 0.116389i | \(0.0371320\pi\) | ||||
−0.993204 | + | 0.116389i | \(0.962868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1455.89 | −0.851380 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3652.01 | −2.09160 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 3021.94i | − 1.66152i | −0.556630 | − | 0.830760i | \(-0.687906\pi\) | ||||
0.556630 | − | 0.830760i | \(-0.312094\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2165.27 | 1.16693 | 0.583467 | − | 0.812137i | \(-0.301696\pi\) | ||||
0.583467 | + | 0.812137i | \(0.301696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2920.69i | − 1.51352i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 1478.89i | − 0.751773i | −0.926666 | − | 0.375886i | \(-0.877338\pi\) | ||||
0.926666 | − | 0.375886i | \(-0.122662\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1858.31 | −0.909662 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1140.21i | 0.547903i | 0.961743 | + | 0.273952i | \(0.0883309\pi\) | ||||
−0.961743 | + | 0.273952i | \(0.911669\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −646.653 | −0.299638 | −0.149819 | − | 0.988713i | \(-0.547869\pi\) | ||||
−0.149819 | + | 0.988713i | \(0.547869\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1410.47 | 0.642000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4036.37i | 1.77387i | 0.461894 | + | 0.886935i | \(0.347170\pi\) | ||||
−0.461894 | + | 0.886935i | \(0.652830\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3496.81 | 1.51048 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1592.17i | 0.664828i | 0.943134 | + | 0.332414i | \(0.107863\pi\) | ||||
−0.943134 | + | 0.332414i | \(0.892137\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 3849.93i | − 1.58101i | −0.612456 | − | 0.790505i | \(-0.709818\pi\) | ||||
0.612456 | − | 0.790505i | \(-0.290182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6847.38 | −2.72124 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3162.11i | − 1.23656i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4049.60 | 1.53413 | 0.767065 | − | 0.641569i | \(-0.221716\pi\) | ||||
0.767065 | + | 0.641569i | \(0.221716\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3421.96 | 1.27626 | 0.638129 | − | 0.769930i | \(-0.279709\pi\) | ||||
0.638129 | + | 0.769930i | \(0.279709\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1955.03i | 0.707055i | 0.935424 | + | 0.353528i | \(0.115018\pi\) | ||||
−0.935424 | + | 0.353528i | \(0.884982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 109.030 | 0.0388387 | 0.0194194 | − | 0.999811i | \(-0.493818\pi\) | ||||
0.0194194 | + | 0.999811i | \(0.493818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4854.11i | − 1.67828i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3299.30i | 1.12406i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8448.08 | −2.79601 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 1491.58i | − 0.486658i | −0.969944 | − | 0.243329i | \(-0.921761\pi\) | ||||
0.969944 | − | 0.243329i | \(-0.0782395\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5798.80 | 1.83942 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3882.07 | 1.21443 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1708.29i | − 0.519965i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2183.67 | −0.655737 | −0.327869 | − | 0.944723i | \(-0.606330\pi\) | ||||
−0.327869 | + | 0.944723i | \(0.606330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 4868.07i | − 1.42337i | −0.702498 | − | 0.711686i | \(-0.747932\pi\) | ||||
0.702498 | − | 0.711686i | \(-0.252068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1619.18i | 0.467242i | 0.972328 | + | 0.233621i | \(0.0750575\pi\) | ||||
−0.972328 | + | 0.233621i | \(0.924943\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4354.61 | 1.22438 | 0.612189 | − | 0.790711i | \(-0.290289\pi\) | ||||
0.612189 | + | 0.790711i | \(0.290289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5634.74i | 1.56413i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2102.54 | −0.569046 | −0.284523 | − | 0.958669i | \(-0.591835\pi\) | ||||
−0.284523 | + | 0.958669i | \(0.591835\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −664.744 | −0.177676 | −0.0888381 | − | 0.996046i | \(-0.528315\pi\) | ||||
−0.0888381 | + | 0.996046i | \(0.528315\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2597.27i | 0.677279i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4563.98 | −1.17570 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4513.82i | − 1.13510i | −0.823339 | − | 0.567550i | \(-0.807891\pi\) | ||||
0.823339 | − | 0.567550i | \(-0.192109\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4324.04i | 1.07451i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −942.446 | −0.228748 | −0.114374 | − | 0.993438i | \(-0.536486\pi\) | ||||
−0.114374 | + | 0.993438i | \(0.536486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 9101.28i | − 2.18350i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1570.46 | −0.368208 | −0.184104 | − | 0.982907i | \(-0.558938\pi\) | ||||
−0.184104 | + | 0.982907i | \(0.558938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3933.74 | −0.911879 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3268.67i | 0.740871i | 0.928858 | + | 0.370436i | \(0.120792\pi\) | ||||
−0.928858 | + | 0.370436i | \(0.879208\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1081.79 | 0.242486 | 0.121243 | − | 0.992623i | \(-0.461312\pi\) | ||||
0.121243 | + | 0.992623i | \(0.461312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8136.61i | − 1.78420i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1402.51i | − 0.304219i | −0.988364 | − | 0.152109i | \(-0.951393\pi\) | ||||
0.988364 | − | 0.152109i | \(-0.0486066\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −432.416 | −0.0918000 | −0.0459000 | − | 0.998946i | \(-0.514616\pi\) | ||||
−0.0459000 | + | 0.998946i | \(0.514616\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3529.48i | 0.741364i | 0.928760 | + | 0.370682i | \(0.120876\pi\) | ||||
−0.928760 | + | 0.370682i | \(0.879124\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4385.30 | −0.901938 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1202.68 | −0.244795 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 985.906i | 0.196578i | 0.995158 | + | 0.0982888i | \(0.0313369\pi\) | ||||
−0.995158 | + | 0.0982888i | \(0.968663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5390.08 | −1.06380 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2336.01i | 0.451823i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7707.54i | 1.47593i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12410.5 | −2.32992 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1061.90i | − 0.197414i | −0.995117 | − | 0.0987070i | \(-0.968529\pi\) | ||||
0.995117 | − | 0.0987070i | \(-0.0314707\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2470.09 | −0.450373 | −0.225187 | − | 0.974316i | \(-0.572299\pi\) | ||||
−0.225187 | + | 0.974316i | \(0.572299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3270.89 | 0.590676 | 0.295338 | − | 0.955393i | \(-0.404568\pi\) | ||||
0.295338 | + | 0.955393i | \(0.404568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7925.23i | − 1.40418i | −0.712088 | − | 0.702090i | \(-0.752250\pi\) | ||||
0.712088 | − | 0.702090i | \(-0.247750\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11294.9 | −1.98242 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 9912.71i | − 1.70761i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4395.71i | − 0.750246i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7489.49 | −1.25504 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5577.08i | 0.926115i | 0.886328 | + | 0.463057i | \(0.153248\pi\) | ||||
−0.886328 | + | 0.463057i | \(0.846752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −335.701 | −0.0547501 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5957.59 | −0.962999 | −0.481499 | − | 0.876446i | \(-0.659908\pi\) | ||||
−0.481499 | + | 0.876446i | \(0.659908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 9033.04i | − 1.43451i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4200.15 | 0.661186 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3873.30i | 0.599221i | 0.954062 | + | 0.299610i | \(0.0968567\pi\) | ||||
−0.954062 | + | 0.299610i | \(0.903143\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11789.8i | 1.80830i | 0.427218 | + | 0.904148i | \(0.359494\pi\) | ||||
−0.427218 | + | 0.904148i | \(0.640506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6449.61 | −0.972460 | −0.486230 | − | 0.873831i | \(-0.661628\pi\) | ||||
−0.486230 | + | 0.873831i | \(0.661628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7032.85i | 1.05145i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4333.86 | −0.637138 | −0.318569 | − | 0.947900i | \(-0.603202\pi\) | ||||
−0.318569 | + | 0.947900i | \(0.603202\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19624.4 | −2.86112 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6667.21i | 0.956103i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1773.77 | 0.252289 | 0.126144 | − | 0.992012i | \(-0.459740\pi\) | ||||
0.126144 | + | 0.992012i | \(0.459740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 5228.58i | − 0.731683i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8187.21i | 1.13651i | 0.822853 | + | 0.568254i | \(0.192381\pi\) | ||||
−0.822853 | + | 0.568254i | \(0.807619\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6101.91 | −0.833593 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4548.20i | 0.616426i | 0.951317 | + | 0.308213i | \(0.0997310\pi\) | ||||
−0.951317 | + | 0.308213i | \(0.900269\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14304.4 | 1.90841 | 0.954204 | − | 0.299155i | \(-0.0967049\pi\) | ||||
0.954204 | + | 0.299155i | \(0.0967049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19439.9 | 2.57337 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 9949.97i | − 1.29687i | −0.761269 | − | 0.648436i | \(-0.775423\pi\) | ||||
0.761269 | − | 0.648436i | \(-0.224577\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5073.70 | −0.656235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1604.74i | − 0.204413i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8804.08i | − 1.11301i | −0.830845 | − | 0.556504i | \(-0.812143\pi\) | ||||
0.830845 | − | 0.556504i | \(-0.187857\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5447.33 | 0.678370 | 0.339185 | − | 0.940720i | \(-0.389849\pi\) | ||||
0.339185 | + | 0.940720i | \(0.389849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4879.99i | − 0.603200i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21177.4 | −2.57918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11192.0 | 1.35307 | 0.676537 | − | 0.736408i | \(-0.263480\pi\) | ||||
0.676537 | + | 0.736408i | \(0.263480\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7164.29i | − 0.853587i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5845.60 | 0.691444 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8012.23i | 0.934184i | 0.884209 | + | 0.467092i | \(0.154698\pi\) | ||||
−0.884209 | + | 0.467092i | \(0.845302\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 5895.02i | − 0.682436i | −0.939984 | − | 0.341218i | \(-0.889161\pi\) | ||||
0.939984 | − | 0.341218i | \(-0.110839\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9547.24 | 1.08967 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 16495.6i | − 1.86951i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3869.38 | −0.432439 | −0.216220 | − | 0.976345i | \(-0.569373\pi\) | ||||
−0.216220 | + | 0.976345i | \(0.569373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2257.93 | −0.250599 | −0.125300 | − | 0.992119i | \(-0.539989\pi\) | ||||
−0.125300 | + | 0.992119i | \(0.539989\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13555.2i | 1.48383i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13979.2 | 1.51979 | 0.759897 | − | 0.650043i | \(-0.225249\pi\) | ||||
0.759897 | + | 0.650043i | \(0.225249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 16551.5i | − 1.77513i | −0.460679 | − | 0.887567i | \(-0.652394\pi\) | ||||
0.460679 | − | 0.887567i | \(-0.347606\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 25050.4i | − 2.66854i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4494.66 | −0.472419 | −0.236210 | − | 0.971702i | \(-0.575905\pi\) | ||||
−0.236210 | + | 0.971702i | \(0.575905\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10204.0i | 1.06538i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10502.2 | 1.08209 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16034.1 | 1.64123 | 0.820615 | − | 0.571482i | \(-0.193631\pi\) | ||||
0.820615 | + | 0.571482i | \(0.193631\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1432.00i | − 0.144674i | −0.997380 | − | 0.0723370i | \(-0.976954\pi\) | ||||
0.997380 | − | 0.0723370i | \(-0.0230457\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12090.6 | 1.21360 | 0.606800 | − | 0.794855i | \(-0.292453\pi\) | ||||
0.606800 | + | 0.794855i | \(0.292453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2767.50i | − 0.274229i | −0.990555 | − | 0.137114i | \(-0.956217\pi\) | ||||
0.990555 | − | 0.137114i | \(-0.0437828\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 446.200i | − 0.0439310i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17934.4 | 1.74339 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 25507.0i | − 2.46387i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14484.6 | 1.38167 | 0.690834 | − | 0.723013i | \(-0.257243\pi\) | ||||
0.690834 | + | 0.723013i | \(0.257243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11440.9 | −1.08453 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14803.5i | 1.38597i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3300.69 | −0.307122 | −0.153561 | − | 0.988139i | \(-0.549074\pi\) | ||||
−0.153561 | + | 0.988139i | \(0.549074\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 8400.25i | − 0.772094i | −0.922479 | − | 0.386047i | \(-0.873840\pi\) | ||||
0.922479 | − | 0.386047i | \(-0.126160\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 13253.0i | − 1.21072i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9347.80 | −0.843675 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5884.85i | 0.527940i | 0.964531 | + | 0.263970i | \(0.0850319\pi\) | ||||
−0.964531 | + | 0.263970i | \(0.914968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15361.0 | 1.36166 | 0.680828 | − | 0.732443i | \(-0.261620\pi\) | ||||
0.680828 | + | 0.732443i | \(0.261620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10780.1 | −0.949913 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4734.24i | 0.412262i | 0.978524 | + | 0.206131i | \(0.0660873\pi\) | ||||
−0.978524 | + | 0.206131i | \(0.933913\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8861.80 | −0.767168 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22190.3i | 1.89868i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17427.0i | 1.48248i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1802.84 | −0.151600 | −0.0758002 | − | 0.997123i | \(-0.524151\pi\) | ||||
−0.0758002 | + | 0.997123i | \(0.524151\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14334.3i | 1.19846i | 0.800576 | + | 0.599231i | \(0.204527\pi\) | ||||
−0.800576 | + | 0.599231i | \(0.795473\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10599.1 | 0.876098 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5228.94 | −0.429764 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5512.59i | 0.447987i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28060.8 | 2.26761 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8032.78i | 0.641923i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 80.7842i | − 0.00641993i | −0.999995 | − | 0.00320997i | \(-0.998978\pi\) | ||||
0.999995 | − | 0.00320997i | \(-0.00102177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −27989.3 | −2.19987 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16156.2i | − 1.26287i | −0.775429 | − | 0.631435i | \(-0.782466\pi\) | ||||
0.775429 | − | 0.631435i | \(-0.217534\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35407.6 | −2.73759 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2132.96 | 0.164019 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11647.7i | 0.886050i | 0.896509 | + | 0.443025i | \(0.146095\pi\) | ||||
−0.896509 | + | 0.443025i | \(0.853905\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9688.85 | 0.733085 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15422.5i | 1.15450i | 0.816568 | + | 0.577249i | \(0.195874\pi\) | ||||
−0.816568 | + | 0.577249i | \(0.804126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 7021.41i | − 0.522819i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22141.8 | 1.63134 | 0.815669 | − | 0.578519i | \(-0.196369\pi\) | ||||
0.815669 | + | 0.578519i | \(0.196369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22320.5i | 1.63587i | 0.575309 | + | 0.817936i | \(0.304882\pi\) | ||||
−0.575309 | + | 0.817936i | \(0.695118\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13055.4 | −0.946868 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1412.77 | 0.101932 | 0.0509658 | − | 0.998700i | \(-0.483770\pi\) | ||||
0.0509658 | + | 0.998700i | \(0.483770\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7769.75i | 0.554808i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12166.2 | −0.864276 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20519.0i | 1.44278i | 0.692531 | + | 0.721388i | \(0.256495\pi\) | ||||
−0.692531 | + | 0.721388i | \(0.743505\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 28317.2i | − 1.98096i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15003.2 | 1.03897 | 0.519483 | − | 0.854480i | \(-0.326124\pi\) | ||||
0.519483 | + | 0.854480i | \(0.326124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22810.1i | 1.57164i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15673.9 | 1.06915 | 0.534573 | − | 0.845123i | \(-0.320473\pi\) | ||||
0.534573 | + | 0.845123i | \(0.320473\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8395.61 | 0.569824 | 0.284912 | − | 0.958554i | \(-0.408036\pi\) | ||||
0.284912 | + | 0.958554i | \(0.408036\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 22893.1i | − 1.53841i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5507.73 | −0.368290 | −0.184145 | − | 0.982899i | \(-0.558952\pi\) | ||||
−0.184145 | + | 0.982899i | \(0.558952\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9414.74i | 0.623371i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22607.4i | 1.48956i | 0.667308 | + | 0.744782i | \(0.267446\pi\) | ||||
−0.667308 | + | 0.744782i | \(0.732554\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28342.0 | 1.84928 | 0.924639 | − | 0.380844i | \(-0.124366\pi\) | ||||
0.924639 | + | 0.380844i | \(0.124366\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 22779.4i | − 1.47913i | −0.673086 | − | 0.739564i | \(-0.735032\pi\) | ||||
0.673086 | − | 0.739564i | \(-0.264968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33296.0 | 2.14121 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10650.6 | −0.681638 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 24848.9i | − 1.57519i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19354.6 | −1.22107 | −0.610536 | − | 0.791989i | \(-0.709046\pi\) | ||||
−0.610536 | + | 0.791989i | \(0.709046\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1787.76i | − 0.111724i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4339.61i | 0.269924i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1458.61 | 0.0898775 | 0.0449387 | − | 0.998990i | \(-0.485691\pi\) | ||||
0.0449387 | + | 0.998990i | \(0.485691\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14874.5i | 0.912278i | 0.889909 | + | 0.456139i | \(0.150768\pi\) | ||||
−0.889909 | + | 0.456139i | \(0.849232\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13724.8 | 0.833966 | 0.416983 | − | 0.908914i | \(-0.363087\pi\) | ||||
0.416983 | + | 0.908914i | \(0.363087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16670.3 | −1.00827 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14706.2i | 0.881311i | 0.897676 | + | 0.440656i | \(0.145254\pi\) | ||||
−0.897676 | + | 0.440656i | \(0.854746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30456.0 | 1.81682 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 14302.2i | − 0.845426i | −0.906264 | − | 0.422713i | \(-0.861078\pi\) | ||||
0.906264 | − | 0.422713i | \(-0.138922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18402.5i | 1.08287i | 0.840743 | + | 0.541434i | \(0.182118\pi\) | ||||
−0.840743 | + | 0.541434i | \(0.817882\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 60940.9 | 3.55367 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18122.9i | 1.05206i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38383.1 | −2.20829 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20057.4 | 1.14882 | 0.574411 | − | 0.818567i | \(-0.305231\pi\) | ||||
0.574411 | + | 0.818567i | \(0.305231\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 3332.38i | − 0.189178i | −0.995516 | − | 0.0945891i | \(-0.969846\pi\) | ||||
0.995516 | − | 0.0945891i | \(-0.0301537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19676.3 | −1.11209 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25093.2i | 1.40581i | 0.711286 | + | 0.702903i | \(0.248113\pi\) | ||||
−0.711286 | + | 0.702903i | \(0.751887\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6734.10i | 0.375616i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6572.65 | −0.363422 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 5265.23i | − 0.289868i | −0.989441 | − | 0.144934i | \(-0.953703\pi\) | ||||
0.989441 | − | 0.144934i | \(-0.0462970\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6403.06 | −0.349470 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11973.1 | −0.650663 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 20984.1i | − 1.13061i | −0.824882 | − | 0.565306i | \(-0.808758\pi\) | ||||
0.824882 | − | 0.565306i | \(-0.191242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −66387.9 | −3.56169 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 14328.4i | − 0.762201i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12441.7i | 0.659036i | 0.944149 | + | 0.329518i | \(0.106886\pi\) | ||||
−0.944149 | + | 0.329518i | \(0.893114\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14493.8 | −0.761285 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 24437.1i | − 1.27818i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34573.7 | −1.79330 | −0.896650 | − | 0.442740i | \(-0.854006\pi\) | ||||
−0.896650 | + | 0.442740i | \(0.854006\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29494.4 | −1.52348 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 34102.1i | − 1.74693i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20704.6 | −1.05624 | −0.528122 | − | 0.849168i | \(-0.677104\pi\) | ||||
−0.528122 | + | 0.849168i | \(0.677104\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21043.7i | 1.06474i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11999.1i | 0.604633i | 0.953208 | + | 0.302317i | \(0.0977600\pi\) | ||||
−0.953208 | + | 0.302317i | \(0.902240\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1038.25 | −0.0518919 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 4576.46i | − 0.227805i | −0.993492 | − | 0.113902i | \(-0.963665\pi\) | ||||
0.993492 | − | 0.113902i | \(-0.0363351\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −457.260 | −0.0225777 | −0.0112889 | − | 0.999936i | \(-0.503593\pi\) | ||||
−0.0112889 | + | 0.999936i | \(0.503593\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50723.3 | 2.49444 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37297.3i | 1.81951i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15889.2 | 0.772045 | 0.386022 | − | 0.922489i | \(-0.373849\pi\) | ||||
0.386022 | + | 0.922489i | \(0.373849\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 36344.1i | 1.75192i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34433.6i | 1.65325i | 0.562754 | + | 0.826624i | \(0.309742\pi\) | ||||
−0.562754 | + | 0.826624i | \(0.690258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21391.1 | 1.01896 | 0.509480 | − | 0.860483i | \(-0.329838\pi\) | ||||
0.509480 | + | 0.860483i | \(0.329838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 37202.3i | − 1.76516i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9005.94 | −0.423971 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23915.1 | 1.12146 | 0.560728 | − | 0.828000i | \(-0.310521\pi\) | ||||
0.560728 | + | 0.828000i | \(0.310521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19446.0i | 0.904818i | 0.891811 | + | 0.452409i | \(0.149435\pi\) | ||||
−0.891811 | + | 0.452409i | \(0.850565\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27273.1 | 1.26410 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31988.0i | 1.47123i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21751.1i | 0.996561i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 24823.2 | 1.12864 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 29340.7i | − 1.32895i | −0.747310 | − | 0.664475i | \(-0.768655\pi\) | ||||
0.747310 | − | 0.664475i | \(-0.231345\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9332.59 | 0.419506 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20736.0 | −0.928571 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 33505.7i | − 1.48913i | −0.667552 | − | 0.744563i | \(-0.732658\pi\) | ||||
0.667552 | − | 0.744563i | \(-0.267342\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20448.3 | −0.905394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20620.2i | 0.906191i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 31191.9i | − 1.36568i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19418.0 | 0.843882 | 0.421941 | − | 0.906623i | \(-0.361349\pi\) | ||||
0.421941 | + | 0.906623i | \(0.361349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24228.8i | 1.04906i | 0.851391 | + | 0.524531i | \(0.175759\pi\) | ||||
−0.851391 | + | 0.524531i | \(0.824241\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19138.5 | −0.822567 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 56221.5 | 2.40752 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 16355.5i | − 0.695263i | −0.937631 | − | 0.347631i | \(-0.886986\pi\) | ||||
0.937631 | − | 0.347631i | \(-0.113014\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3280.51 | −0.138945 | −0.0694724 | − | 0.997584i | \(-0.522132\pi\) | ||||
−0.0694724 | + | 0.997584i | \(0.522132\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23480.5i | 0.987298i | 0.869661 | + | 0.493649i | \(0.164337\pi\) | ||||
−0.869661 | + | 0.493649i | \(0.835663\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 16306.2i | − 0.683160i | −0.939853 | − | 0.341580i | \(-0.889038\pi\) | ||||
0.939853 | − | 0.341580i | \(-0.110962\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9425.42 | −0.392042 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 10854.1i | − 0.449846i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29259.0 | 1.20397 | 0.601986 | − | 0.798506i | \(-0.294376\pi\) | ||||
0.601986 | + | 0.798506i | \(0.294376\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22950.0 | −0.940998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23674.9i | 0.963834i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30428.6 | 1.23440 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33979.8i | 1.36876i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14076.0i | 0.565008i | 0.959266 | + | 0.282504i | \(0.0911651\pi\) | ||||
−0.959266 | + | 0.282504i | \(0.908835\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43553.3 | 1.73600 | 0.868000 | − | 0.496565i | \(-0.165405\pi\) | ||||
0.868000 | + | 0.496565i | \(0.165405\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43728.9i | 1.73692i | 0.495761 | + | 0.868459i | \(0.334889\pi\) | ||||
−0.495761 | + | 0.868459i | \(0.665111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21807.9 | 0.860198 | 0.430099 | − | 0.902782i | \(-0.358479\pi\) | ||||
0.430099 | + | 0.902782i | \(0.358479\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −67750.6 | −2.66311 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4963.10i | − 0.193742i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −560.901 | −0.0218202 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11884.8i | 0.459176i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6228.27i | − 0.239810i | −0.992785 | − | 0.119905i | \(-0.961741\pi\) | ||||
0.992785 | − | 0.119905i | \(-0.0382591\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −40608.1 | −1.55292 | −0.776459 | − | 0.630168i | \(-0.782986\pi\) | ||||
−0.776459 | + | 0.630168i | \(0.782986\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 78.9699i | − 0.00300968i | −0.999999 | − | 0.00150484i | \(-0.999521\pi\) | ||||
0.999999 | − | 0.00150484i | \(-0.000479006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33039.9 | −1.25070 | −0.625351 | − | 0.780344i | \(-0.715044\pi\) | ||||
−0.625351 | + | 0.780344i | \(0.715044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2376.22 | 0.0896467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 54631.0i | 2.04721i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26724.6 | −0.998105 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 37859.3i | − 1.40454i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 14275.4i | − 0.527840i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 64621.1 | 2.37357 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23459.7i | 0.858838i | 0.903105 | + | 0.429419i | \(0.141282\pi\) | ||||
−0.903105 | + | 0.429419i | \(0.858718\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36386.3 | 1.32331 | 0.661653 | − | 0.749811i | \(-0.269855\pi\) | ||||
0.661653 | + | 0.749811i | \(0.269855\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18079.2 | 0.655348 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 40481.0i | 1.45780i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19058.6 | 0.684097 | 0.342049 | − | 0.939682i | \(-0.388879\pi\) | ||||
0.342049 | + | 0.939682i | \(0.388879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11750.8i | 0.419048i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 63940.3i | − 2.27280i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 27020.7 | 0.954274 | 0.477137 | − | 0.878829i | \(-0.341674\pi\) | ||||
0.477137 | + | 0.878829i | \(0.341674\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25181.5i | 0.886456i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 53076.1 | 1.85644 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11862.3 | 0.413581 | 0.206791 | − | 0.978385i | \(-0.433698\pi\) | ||||
0.206791 | + | 0.978385i | \(0.433698\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 53659.9i | − 1.85894i | −0.368897 | − | 0.929470i | \(-0.620265\pi\) | ||||
0.368897 | − | 0.929470i | \(-0.379735\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16372.6 | 0.565394 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1063.85i | 0.0365052i | 0.999833 | + | 0.0182526i | \(0.00581030\pi\) | ||||
−0.999833 | + | 0.0182526i | \(0.994190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11139.8i | 0.381047i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5715.17 | 0.194263 | 0.0971314 | − | 0.995272i | \(-0.469033\pi\) | ||||
0.0971314 | + | 0.995272i | \(0.469033\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 67972.7i | 2.30319i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8950.71 | −0.301391 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 486.886 | 0.0163434 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57437.6i | 1.91604i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 124.600 | 0.00414360 | 0.00207180 | − | 0.999998i | \(-0.499341\pi\) | ||||
0.00207180 | + | 0.999998i | \(0.499341\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 40767.0i | − 1.34735i | −0.739028 | − | 0.673674i | \(-0.764715\pi\) | ||||
0.739028 | − | 0.673674i | \(-0.235285\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 8510.70i | − 0.280412i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11600.1 | −0.379856 | −0.189928 | − | 0.981798i | \(-0.560825\pi\) | ||||
−0.189928 | + | 0.981798i | \(0.560825\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 77475.3i | − 2.52923i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16979.6 | 0.550930 | 0.275465 | − | 0.961311i | \(-0.411168\pi\) | ||||
0.275465 | + | 0.961311i | \(0.411168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32815.2 | −1.06150 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 28776.3i | − 0.925210i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15762.5 | 0.505259 | 0.252630 | − | 0.967563i | \(-0.418705\pi\) | ||||
0.252630 | + | 0.967563i | \(0.418705\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1830.07i | 0.0583085i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8861.70i | 0.281497i | 0.990045 | + | 0.140749i | \(0.0449509\pi\) | ||||
−0.990045 | + | 0.140749i | \(0.955049\pi\) | |||||||
\(998\) | 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 | 1728.4.d.e.865.7 | yes | 8 | |
3.2 | odd | 2 | 1728.4.d.h.865.1 | yes | 8 | ||
4.3 | odd | 2 | inner | 1728.4.d.e.865.8 | yes | 8 | |
8.3 | odd | 2 | inner | 1728.4.d.e.865.2 | yes | 8 | |
8.5 | even | 2 | inner | 1728.4.d.e.865.1 | ✓ | 8 | |
12.11 | even | 2 | 1728.4.d.h.865.2 | yes | 8 | ||
24.5 | odd | 2 | 1728.4.d.h.865.7 | yes | 8 | ||
24.11 | even | 2 | 1728.4.d.h.865.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.d.e.865.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
1728.4.d.e.865.2 | yes | 8 | 8.3 | odd | 2 | inner | |
1728.4.d.e.865.7 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.4.d.e.865.8 | yes | 8 | 4.3 | odd | 2 | inner | |
1728.4.d.h.865.1 | yes | 8 | 3.2 | odd | 2 | ||
1728.4.d.h.865.2 | yes | 8 | 12.11 | even | 2 | ||
1728.4.d.h.865.7 | yes | 8 | 24.5 | odd | 2 | ||
1728.4.d.h.865.8 | yes | 8 | 24.11 | even | 2 |