Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(168,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.168");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.b (of order \(2\), degree \(1\), not 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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 168.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.168 |
Dual form | 169.4.b.a.168.1 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000i | 1.76777i | 0.467707 | + | 0.883883i | \(0.345080\pi\) | ||||
−0.467707 | + | 0.883883i | \(0.654920\pi\) | |||||||
\(3\) | −7.00000 | −1.34715 | −0.673575 | − | 0.739119i | \(-0.735242\pi\) | ||||
−0.673575 | + | 0.739119i | \(0.735242\pi\) | |||||||
\(4\) | −17.0000 | −2.12500 | ||||||||
\(5\) | 7.00000i | 0.626099i | 0.949737 | + | 0.313050i | \(0.101351\pi\) | ||||
−0.949737 | + | 0.313050i | \(0.898649\pi\) | |||||||
\(6\) | − 35.0000i | − 2.38145i | ||||||||
\(7\) | − 13.0000i | − 0.701934i | −0.936388 | − | 0.350967i | \(-0.885853\pi\) | ||||
0.936388 | − | 0.350967i | \(-0.114147\pi\) | |||||||
\(8\) | − 45.0000i | − 1.98874i | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | −35.0000 | −1.10680 | ||||||||
\(11\) | − 26.0000i | − 0.712663i | −0.934360 | − | 0.356332i | \(-0.884027\pi\) | ||||
0.934360 | − | 0.356332i | \(-0.115973\pi\) | |||||||
\(12\) | 119.000 | 2.86270 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 65.0000 | 1.24086 | ||||||||
\(15\) | − 49.0000i | − 0.843450i | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | −77.0000 | −1.09854 | −0.549272 | − | 0.835644i | \(-0.685095\pi\) | ||||
−0.549272 | + | 0.835644i | \(0.685095\pi\) | |||||||
\(18\) | 110.000i | 1.44040i | ||||||||
\(19\) | 126.000i | 1.52139i | 0.649110 | + | 0.760694i | \(0.275141\pi\) | ||||
−0.649110 | + | 0.760694i | \(0.724859\pi\) | |||||||
\(20\) | − 119.000i | − 1.33046i | ||||||||
\(21\) | 91.0000i | 0.945611i | ||||||||
\(22\) | 130.000 | 1.25982 | ||||||||
\(23\) | 96.0000 | 0.870321 | 0.435161 | − | 0.900353i | \(-0.356692\pi\) | ||||
0.435161 | + | 0.900353i | \(0.356692\pi\) | |||||||
\(24\) | 315.000i | 2.67913i | ||||||||
\(25\) | 76.0000 | 0.608000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | 221.000i | 1.49161i | ||||||||
\(29\) | −82.0000 | −0.525070 | −0.262535 | − | 0.964923i | \(-0.584558\pi\) | ||||
−0.262535 | + | 0.964923i | \(0.584558\pi\) | |||||||
\(30\) | 245.000 | 1.49102 | ||||||||
\(31\) | − 196.000i | − 1.13557i | −0.823177 | − | 0.567785i | \(-0.807801\pi\) | ||||
0.823177 | − | 0.567785i | \(-0.192199\pi\) | |||||||
\(32\) | 85.0000i | 0.469563i | ||||||||
\(33\) | 182.000i | 0.960065i | ||||||||
\(34\) | − 385.000i | − 1.94197i | ||||||||
\(35\) | 91.0000 | 0.439480 | ||||||||
\(36\) | −374.000 | −1.73148 | ||||||||
\(37\) | − 131.000i | − 0.582061i | −0.956714 | − | 0.291031i | \(-0.906002\pi\) | ||||
0.956714 | − | 0.291031i | \(-0.0939982\pi\) | |||||||
\(38\) | −630.000 | −2.68946 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 315.000 | 1.24515 | ||||||||
\(41\) | − 336.000i | − 1.27986i | −0.768432 | − | 0.639932i | \(-0.778963\pi\) | ||||
0.768432 | − | 0.639932i | \(-0.221037\pi\) | |||||||
\(42\) | −455.000 | −1.67162 | ||||||||
\(43\) | 201.000 | 0.712842 | 0.356421 | − | 0.934325i | \(-0.383997\pi\) | ||||
0.356421 | + | 0.934325i | \(0.383997\pi\) | |||||||
\(44\) | 442.000i | 1.51441i | ||||||||
\(45\) | 154.000i | 0.510155i | ||||||||
\(46\) | 480.000i | 1.53852i | ||||||||
\(47\) | − 105.000i | − 0.325869i | −0.986637 | − | 0.162934i | \(-0.947904\pi\) | ||||
0.986637 | − | 0.162934i | \(-0.0520959\pi\) | |||||||
\(48\) | −623.000 | −1.87338 | ||||||||
\(49\) | 174.000 | 0.507289 | ||||||||
\(50\) | 380.000i | 1.07480i | ||||||||
\(51\) | 539.000 | 1.47990 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −432.000 | −1.11962 | −0.559809 | − | 0.828622i | \(-0.689126\pi\) | ||||
−0.559809 | + | 0.828622i | \(0.689126\pi\) | |||||||
\(54\) | 175.000i | 0.441009i | ||||||||
\(55\) | 182.000 | 0.446198 | ||||||||
\(56\) | −585.000 | −1.39596 | ||||||||
\(57\) | − 882.000i | − 2.04954i | ||||||||
\(58\) | − 410.000i | − 0.928201i | ||||||||
\(59\) | − 294.000i | − 0.648738i | −0.945931 | − | 0.324369i | \(-0.894848\pi\) | ||||
0.945931 | − | 0.324369i | \(-0.105152\pi\) | |||||||
\(60\) | 833.000i | 1.79233i | ||||||||
\(61\) | −56.0000 | −0.117542 | −0.0587710 | − | 0.998271i | \(-0.518718\pi\) | ||||
−0.0587710 | + | 0.998271i | \(0.518718\pi\) | |||||||
\(62\) | 980.000 | 2.00742 | ||||||||
\(63\) | − 286.000i | − 0.571946i | ||||||||
\(64\) | 287.000 | 0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −910.000 | −1.69717 | ||||||||
\(67\) | − 478.000i | − 0.871597i | −0.900044 | − | 0.435798i | \(-0.856466\pi\) | ||||
0.900044 | − | 0.435798i | \(-0.143534\pi\) | |||||||
\(68\) | 1309.00 | 2.33441 | ||||||||
\(69\) | −672.000 | −1.17245 | ||||||||
\(70\) | 455.000i | 0.776899i | ||||||||
\(71\) | − 9.00000i | − 0.0150437i | −0.999972 | − | 0.00752186i | \(-0.997606\pi\) | ||||
0.999972 | − | 0.00752186i | \(-0.00239430\pi\) | |||||||
\(72\) | − 990.000i | − 1.62045i | ||||||||
\(73\) | 98.0000i | 0.157124i | 0.996909 | + | 0.0785619i | \(0.0250328\pi\) | ||||
−0.996909 | + | 0.0785619i | \(0.974967\pi\) | |||||||
\(74\) | 655.000 | 1.02895 | ||||||||
\(75\) | −532.000 | −0.819068 | ||||||||
\(76\) | − 2142.00i | − 3.23295i | ||||||||
\(77\) | −338.000 | −0.500243 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1304.00 | 1.85711 | 0.928554 | − | 0.371198i | \(-0.121053\pi\) | ||||
0.928554 | + | 0.371198i | \(0.121053\pi\) | |||||||
\(80\) | 623.000i | 0.870669i | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 1680.00 | 2.26250 | ||||||||
\(83\) | 308.000i | 0.407318i | 0.979042 | + | 0.203659i | \(0.0652834\pi\) | ||||
−0.979042 | + | 0.203659i | \(0.934717\pi\) | |||||||
\(84\) | − 1547.00i | − 2.00942i | ||||||||
\(85\) | − 539.000i | − 0.687797i | ||||||||
\(86\) | 1005.00i | 1.26014i | ||||||||
\(87\) | 574.000 | 0.707348 | ||||||||
\(88\) | −1170.00 | −1.41730 | ||||||||
\(89\) | − 1190.00i | − 1.41730i | −0.705560 | − | 0.708650i | \(-0.749304\pi\) | ||||
0.705560 | − | 0.708650i | \(-0.250696\pi\) | |||||||
\(90\) | −770.000 | −0.901835 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1632.00 | −1.84943 | ||||||||
\(93\) | 1372.00i | 1.52978i | ||||||||
\(94\) | 525.000 | 0.576060 | ||||||||
\(95\) | −882.000 | −0.952540 | ||||||||
\(96\) | − 595.000i | − 0.632572i | ||||||||
\(97\) | − 70.0000i | − 0.0732724i | −0.999329 | − | 0.0366362i | \(-0.988336\pi\) | ||||
0.999329 | − | 0.0366362i | \(-0.0116643\pi\) | |||||||
\(98\) | 870.000i | 0.896768i | ||||||||
\(99\) | − 572.000i | − 0.580689i | ||||||||
\(100\) | −1292.00 | −1.29200 | ||||||||
\(101\) | −420.000 | −0.413778 | −0.206889 | − | 0.978364i | \(-0.566334\pi\) | ||||
−0.206889 | + | 0.978364i | \(0.566334\pi\) | |||||||
\(102\) | 2695.00i | 2.61613i | ||||||||
\(103\) | −588.000 | −0.562499 | −0.281249 | − | 0.959635i | \(-0.590749\pi\) | ||||
−0.281249 | + | 0.959635i | \(0.590749\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −637.000 | −0.592046 | ||||||||
\(106\) | − 2160.00i | − 1.97922i | ||||||||
\(107\) | −684.000 | −0.617989 | −0.308994 | − | 0.951064i | \(-0.599992\pi\) | ||||
−0.308994 | + | 0.951064i | \(0.599992\pi\) | |||||||
\(108\) | −595.000 | −0.530129 | ||||||||
\(109\) | − 373.000i | − 0.327770i | −0.986479 | − | 0.163885i | \(-0.947597\pi\) | ||||
0.986479 | − | 0.163885i | \(-0.0524026\pi\) | |||||||
\(110\) | 910.000i | 0.788774i | ||||||||
\(111\) | 917.000i | 0.784124i | ||||||||
\(112\) | − 1157.00i | − 0.976127i | ||||||||
\(113\) | −1734.00 | −1.44355 | −0.721774 | − | 0.692128i | \(-0.756673\pi\) | ||||
−0.721774 | + | 0.692128i | \(0.756673\pi\) | |||||||
\(114\) | 4410.00 | 3.62311 | ||||||||
\(115\) | 672.000i | 0.544907i | ||||||||
\(116\) | 1394.00 | 1.11577 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1470.00 | 1.14682 | ||||||||
\(119\) | 1001.00i | 0.771105i | ||||||||
\(120\) | −2205.00 | −1.67740 | ||||||||
\(121\) | 655.000 | 0.492111 | ||||||||
\(122\) | − 280.000i | − 0.207787i | ||||||||
\(123\) | 2352.00i | 1.72417i | ||||||||
\(124\) | 3332.00i | 2.41308i | ||||||||
\(125\) | 1407.00i | 1.00677i | ||||||||
\(126\) | 1430.00 | 1.01107 | ||||||||
\(127\) | −1892.00 | −1.32195 | −0.660976 | − | 0.750407i | \(-0.729857\pi\) | ||||
−0.660976 | + | 0.750407i | \(0.729857\pi\) | |||||||
\(128\) | 2115.00i | 1.46048i | ||||||||
\(129\) | −1407.00 | −0.960306 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1435.00 | 0.957073 | 0.478536 | − | 0.878068i | \(-0.341167\pi\) | ||||
0.478536 | + | 0.878068i | \(0.341167\pi\) | |||||||
\(132\) | − 3094.00i | − 2.04014i | ||||||||
\(133\) | 1638.00 | 1.06791 | ||||||||
\(134\) | 2390.00 | 1.54078 | ||||||||
\(135\) | 245.000i | 0.156194i | ||||||||
\(136\) | 3465.00i | 2.18472i | ||||||||
\(137\) | − 1776.00i | − 1.10755i | −0.832667 | − | 0.553773i | \(-0.813187\pi\) | ||||
0.832667 | − | 0.553773i | \(-0.186813\pi\) | |||||||
\(138\) | − 3360.00i | − 2.07262i | ||||||||
\(139\) | −1869.00 | −1.14048 | −0.570239 | − | 0.821479i | \(-0.693150\pi\) | ||||
−0.570239 | + | 0.821479i | \(0.693150\pi\) | |||||||
\(140\) | −1547.00 | −0.933895 | ||||||||
\(141\) | 735.000i | 0.438994i | ||||||||
\(142\) | 45.0000 | 0.0265938 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1958.00 | 1.13310 | ||||||||
\(145\) | − 574.000i | − 0.328746i | ||||||||
\(146\) | −490.000 | −0.277758 | ||||||||
\(147\) | −1218.00 | −0.683394 | ||||||||
\(148\) | 2227.00i | 1.23688i | ||||||||
\(149\) | − 2466.00i | − 1.35586i | −0.735128 | − | 0.677928i | \(-0.762878\pi\) | ||||
0.735128 | − | 0.677928i | \(-0.237122\pi\) | |||||||
\(150\) | − 2660.00i | − 1.44792i | ||||||||
\(151\) | − 3323.00i | − 1.79087i | −0.445189 | − | 0.895437i | \(-0.646863\pi\) | ||||
0.445189 | − | 0.895437i | \(-0.353137\pi\) | |||||||
\(152\) | 5670.00 | 3.02564 | ||||||||
\(153\) | −1694.00 | −0.895110 | ||||||||
\(154\) | − 1690.00i | − 0.884312i | ||||||||
\(155\) | 1372.00 | 0.710979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2730.00 | −1.38776 | −0.693878 | − | 0.720092i | \(-0.744099\pi\) | ||||
−0.693878 | + | 0.720092i | \(0.744099\pi\) | |||||||
\(158\) | 6520.00i | 3.28293i | ||||||||
\(159\) | 3024.00 | 1.50829 | ||||||||
\(160\) | −595.000 | −0.293993 | ||||||||
\(161\) | − 1248.00i | − 0.610908i | ||||||||
\(162\) | − 4195.00i | − 2.03451i | ||||||||
\(163\) | − 544.000i | − 0.261407i | −0.991421 | − | 0.130704i | \(-0.958276\pi\) | ||||
0.991421 | − | 0.130704i | \(-0.0417236\pi\) | |||||||
\(164\) | 5712.00i | 2.71971i | ||||||||
\(165\) | −1274.00 | −0.601096 | ||||||||
\(166\) | −1540.00 | −0.720043 | ||||||||
\(167\) | 1624.00i | 0.752508i | 0.926516 | + | 0.376254i | \(0.122788\pi\) | ||||
−0.926516 | + | 0.376254i | \(0.877212\pi\) | |||||||
\(168\) | 4095.00 | 1.88057 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2695.00 | 1.21587 | ||||||||
\(171\) | 2772.00i | 1.23965i | ||||||||
\(172\) | −3417.00 | −1.51479 | ||||||||
\(173\) | 336.000 | 0.147662 | 0.0738312 | − | 0.997271i | \(-0.476477\pi\) | ||||
0.0738312 | + | 0.997271i | \(0.476477\pi\) | |||||||
\(174\) | 2870.00i | 1.25043i | ||||||||
\(175\) | − 988.000i | − 0.426776i | ||||||||
\(176\) | − 2314.00i | − 0.991047i | ||||||||
\(177\) | 2058.00i | 0.873948i | ||||||||
\(178\) | 5950.00 | 2.50546 | ||||||||
\(179\) | 3029.00 | 1.26479 | 0.632397 | − | 0.774645i | \(-0.282071\pi\) | ||||
0.632397 | + | 0.774645i | \(0.282071\pi\) | |||||||
\(180\) | − 2618.00i | − 1.08408i | ||||||||
\(181\) | 28.0000 | 0.0114985 | 0.00574924 | − | 0.999983i | \(-0.498170\pi\) | ||||
0.00574924 | + | 0.999983i | \(0.498170\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 392.000 | 0.158347 | ||||||||
\(184\) | − 4320.00i | − 1.73084i | ||||||||
\(185\) | 917.000 | 0.364428 | ||||||||
\(186\) | −6860.00 | −2.70430 | ||||||||
\(187\) | 2002.00i | 0.782892i | ||||||||
\(188\) | 1785.00i | 0.692471i | ||||||||
\(189\) | − 455.000i | − 0.175113i | ||||||||
\(190\) | − 4410.00i | − 1.68387i | ||||||||
\(191\) | 422.000 | 0.159868 | 0.0799342 | − | 0.996800i | \(-0.474529\pi\) | ||||
0.0799342 | + | 0.996800i | \(0.474529\pi\) | |||||||
\(192\) | −2009.00 | −0.755141 | ||||||||
\(193\) | 492.000i | 0.183497i | 0.995782 | + | 0.0917485i | \(0.0292456\pi\) | ||||
−0.995782 | + | 0.0917485i | \(0.970754\pi\) | |||||||
\(194\) | 350.000 | 0.129529 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2958.00 | −1.07799 | ||||||||
\(197\) | − 2991.00i | − 1.08173i | −0.841111 | − | 0.540863i | \(-0.818098\pi\) | ||||
0.841111 | − | 0.540863i | \(-0.181902\pi\) | |||||||
\(198\) | 2860.00 | 1.02652 | ||||||||
\(199\) | 70.0000 | 0.0249355 | 0.0124678 | − | 0.999922i | \(-0.496031\pi\) | ||||
0.0124678 | + | 0.999922i | \(0.496031\pi\) | |||||||
\(200\) | − 3420.00i | − 1.20915i | ||||||||
\(201\) | 3346.00i | 1.17417i | ||||||||
\(202\) | − 2100.00i | − 0.731463i | ||||||||
\(203\) | 1066.00i | 0.368564i | ||||||||
\(204\) | −9163.00 | −3.14480 | ||||||||
\(205\) | 2352.00 | 0.801321 | ||||||||
\(206\) | − 2940.00i | − 0.994367i | ||||||||
\(207\) | 2112.00 | 0.709150 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3276.00 | 1.08424 | ||||||||
\(210\) | − 3185.00i | − 1.04660i | ||||||||
\(211\) | 2851.00 | 0.930194 | 0.465097 | − | 0.885260i | \(-0.346019\pi\) | ||||
0.465097 | + | 0.885260i | \(0.346019\pi\) | |||||||
\(212\) | 7344.00 | 2.37919 | ||||||||
\(213\) | 63.0000i | 0.0202661i | ||||||||
\(214\) | − 3420.00i | − 1.09246i | ||||||||
\(215\) | 1407.00i | 0.446310i | ||||||||
\(216\) | − 1575.00i | − 0.496135i | ||||||||
\(217\) | −2548.00 | −0.797095 | ||||||||
\(218\) | 1865.00 | 0.579421 | ||||||||
\(219\) | − 686.000i | − 0.211669i | ||||||||
\(220\) | −3094.00 | −0.948170 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4585.00 | −1.38615 | ||||||||
\(223\) | − 217.000i | − 0.0651632i | −0.999469 | − | 0.0325816i | \(-0.989627\pi\) | ||||
0.999469 | − | 0.0325816i | \(-0.0103729\pi\) | |||||||
\(224\) | 1105.00 | 0.329602 | ||||||||
\(225\) | 1672.00 | 0.495407 | ||||||||
\(226\) | − 8670.00i | − 2.55186i | ||||||||
\(227\) | 2576.00i | 0.753194i | 0.926377 | + | 0.376597i | \(0.122906\pi\) | ||||
−0.926377 | + | 0.376597i | \(0.877094\pi\) | |||||||
\(228\) | 14994.0i | 4.35527i | ||||||||
\(229\) | 455.000i | 0.131298i | 0.997843 | + | 0.0656490i | \(0.0209118\pi\) | ||||
−0.997843 | + | 0.0656490i | \(0.979088\pi\) | |||||||
\(230\) | −3360.00 | −0.963269 | ||||||||
\(231\) | 2366.00 | 0.673902 | ||||||||
\(232\) | 3690.00i | 1.04423i | ||||||||
\(233\) | −3061.00 | −0.860656 | −0.430328 | − | 0.902673i | \(-0.641602\pi\) | ||||
−0.430328 | + | 0.902673i | \(0.641602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 735.000 | 0.204026 | ||||||||
\(236\) | 4998.00i | 1.37857i | ||||||||
\(237\) | −9128.00 | −2.50180 | ||||||||
\(238\) | −5005.00 | −1.36313 | ||||||||
\(239\) | 3477.00i | 0.941039i | 0.882389 | + | 0.470520i | \(0.155934\pi\) | ||||
−0.882389 | + | 0.470520i | \(0.844066\pi\) | |||||||
\(240\) | − 4361.00i | − 1.17292i | ||||||||
\(241\) | − 1610.00i | − 0.430329i | −0.976578 | − | 0.215164i | \(-0.930971\pi\) | ||||
0.976578 | − | 0.215164i | \(-0.0690287\pi\) | |||||||
\(242\) | 3275.00i | 0.869938i | ||||||||
\(243\) | 4928.00 | 1.30095 | ||||||||
\(244\) | 952.000 | 0.249777 | ||||||||
\(245\) | 1218.00i | 0.317613i | ||||||||
\(246\) | −11760.0 | −3.04793 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −8820.00 | −2.25835 | ||||||||
\(249\) | − 2156.00i | − 0.548719i | ||||||||
\(250\) | −7035.00 | −1.77973 | ||||||||
\(251\) | −1008.00 | −0.253484 | −0.126742 | − | 0.991936i | \(-0.540452\pi\) | ||||
−0.126742 | + | 0.991936i | \(0.540452\pi\) | |||||||
\(252\) | 4862.00i | 1.21539i | ||||||||
\(253\) | − 2496.00i | − 0.620246i | ||||||||
\(254\) | − 9460.00i | − 2.33690i | ||||||||
\(255\) | 3773.00i | 0.926566i | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | −6041.00 | −1.46625 | −0.733127 | − | 0.680092i | \(-0.761940\pi\) | ||||
−0.733127 | + | 0.680092i | \(0.761940\pi\) | |||||||
\(258\) | − 7035.00i | − 1.69760i | ||||||||
\(259\) | −1703.00 | −0.408569 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1804.00 | −0.427834 | ||||||||
\(262\) | 7175.00i | 1.69188i | ||||||||
\(263\) | −3708.00 | −0.869373 | −0.434686 | − | 0.900582i | \(-0.643141\pi\) | ||||
−0.434686 | + | 0.900582i | \(0.643141\pi\) | |||||||
\(264\) | 8190.00 | 1.90932 | ||||||||
\(265\) | − 3024.00i | − 0.700992i | ||||||||
\(266\) | 8190.00i | 1.88782i | ||||||||
\(267\) | 8330.00i | 1.90932i | ||||||||
\(268\) | 8126.00i | 1.85214i | ||||||||
\(269\) | 8344.00 | 1.89124 | 0.945618 | − | 0.325278i | \(-0.105458\pi\) | ||||
0.945618 | + | 0.325278i | \(0.105458\pi\) | |||||||
\(270\) | −1225.00 | −0.276115 | ||||||||
\(271\) | − 1617.00i | − 0.362457i | −0.983441 | − | 0.181228i | \(-0.941993\pi\) | ||||
0.983441 | − | 0.181228i | \(-0.0580073\pi\) | |||||||
\(272\) | −6853.00 | −1.52766 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8880.00 | 1.95788 | ||||||||
\(275\) | − 1976.00i | − 0.433299i | ||||||||
\(276\) | 11424.0 | 2.49146 | ||||||||
\(277\) | 3820.00 | 0.828598 | 0.414299 | − | 0.910141i | \(-0.364027\pi\) | ||||
0.414299 | + | 0.910141i | \(0.364027\pi\) | |||||||
\(278\) | − 9345.00i | − 2.01610i | ||||||||
\(279\) | − 4312.00i | − 0.925278i | ||||||||
\(280\) | − 4095.00i | − 0.874011i | ||||||||
\(281\) | − 6214.00i | − 1.31920i | −0.751615 | − | 0.659602i | \(-0.770725\pi\) | ||||
0.751615 | − | 0.659602i | \(-0.229275\pi\) | |||||||
\(282\) | −3675.00 | −0.776039 | ||||||||
\(283\) | 5292.00 | 1.11158 | 0.555789 | − | 0.831323i | \(-0.312416\pi\) | ||||
0.555789 | + | 0.831323i | \(0.312416\pi\) | |||||||
\(284\) | 153.000i | 0.0319679i | ||||||||
\(285\) | 6174.00 | 1.28321 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4368.00 | −0.898379 | ||||||||
\(288\) | 1870.00i | 0.382607i | ||||||||
\(289\) | 1016.00 | 0.206798 | ||||||||
\(290\) | 2870.00 | 0.581146 | ||||||||
\(291\) | 490.000i | 0.0987090i | ||||||||
\(292\) | − 1666.00i | − 0.333888i | ||||||||
\(293\) | − 903.000i | − 0.180047i | −0.995940 | − | 0.0900236i | \(-0.971306\pi\) | ||||
0.995940 | − | 0.0900236i | \(-0.0286942\pi\) | |||||||
\(294\) | − 6090.00i | − 1.20808i | ||||||||
\(295\) | 2058.00 | 0.406174 | ||||||||
\(296\) | −5895.00 | −1.15757 | ||||||||
\(297\) | − 910.000i | − 0.177790i | ||||||||
\(298\) | 12330.0 | 2.39684 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 9044.00 | 1.74052 | ||||||||
\(301\) | − 2613.00i | − 0.500368i | ||||||||
\(302\) | 16615.0 | 3.16585 | ||||||||
\(303\) | 2940.00 | 0.557421 | ||||||||
\(304\) | 11214.0i | 2.11568i | ||||||||
\(305\) | − 392.000i | − 0.0735930i | ||||||||
\(306\) | − 8470.00i | − 1.58235i | ||||||||
\(307\) | 2114.00i | 0.393004i | 0.980503 | + | 0.196502i | \(0.0629583\pi\) | ||||
−0.980503 | + | 0.196502i | \(0.937042\pi\) | |||||||
\(308\) | 5746.00 | 1.06302 | ||||||||
\(309\) | 4116.00 | 0.757770 | ||||||||
\(310\) | 6860.00i | 1.25684i | ||||||||
\(311\) | −3402.00 | −0.620288 | −0.310144 | − | 0.950690i | \(-0.600377\pi\) | ||||
−0.310144 | + | 0.950690i | \(0.600377\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10689.0 | −1.93028 | −0.965141 | − | 0.261732i | \(-0.915706\pi\) | ||||
−0.965141 | + | 0.261732i | \(0.915706\pi\) | |||||||
\(314\) | − 13650.0i | − 2.45323i | ||||||||
\(315\) | 2002.00 | 0.358095 | ||||||||
\(316\) | −22168.0 | −3.94635 | ||||||||
\(317\) | 7054.00i | 1.24982i | 0.780698 | + | 0.624909i | \(0.214864\pi\) | ||||
−0.780698 | + | 0.624909i | \(0.785136\pi\) | |||||||
\(318\) | 15120.0i | 2.66631i | ||||||||
\(319\) | 2132.00i | 0.374198i | ||||||||
\(320\) | 2009.00i | 0.350958i | ||||||||
\(321\) | 4788.00 | 0.832524 | ||||||||
\(322\) | 6240.00 | 1.07994 | ||||||||
\(323\) | − 9702.00i | − 1.67131i | ||||||||
\(324\) | 14263.0 | 2.44564 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2720.00 | 0.462107 | ||||||||
\(327\) | 2611.00i | 0.441555i | ||||||||
\(328\) | −15120.0 | −2.54531 | ||||||||
\(329\) | −1365.00 | −0.228738 | ||||||||
\(330\) | − 6370.00i | − 1.06260i | ||||||||
\(331\) | − 9704.00i | − 1.61142i | −0.592310 | − | 0.805710i | \(-0.701784\pi\) | ||||
0.592310 | − | 0.805710i | \(-0.298216\pi\) | |||||||
\(332\) | − 5236.00i | − 0.865551i | ||||||||
\(333\) | − 2882.00i | − 0.474272i | ||||||||
\(334\) | −8120.00 | −1.33026 | ||||||||
\(335\) | 3346.00 | 0.545706 | ||||||||
\(336\) | 8099.00i | 1.31499i | ||||||||
\(337\) | 10449.0 | 1.68900 | 0.844500 | − | 0.535555i | \(-0.179897\pi\) | ||||
0.844500 | + | 0.535555i | \(0.179897\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12138.0 | 1.94468 | ||||||||
\(340\) | 9163.00i | 1.46157i | ||||||||
\(341\) | −5096.00 | −0.809278 | ||||||||
\(342\) | −13860.0 | −2.19141 | ||||||||
\(343\) | − 6721.00i | − 1.05802i | ||||||||
\(344\) | − 9045.00i | − 1.41766i | ||||||||
\(345\) | − 4704.00i | − 0.734072i | ||||||||
\(346\) | 1680.00i | 0.261033i | ||||||||
\(347\) | −621.000 | −0.0960721 | −0.0480361 | − | 0.998846i | \(-0.515296\pi\) | ||||
−0.0480361 | + | 0.998846i | \(0.515296\pi\) | |||||||
\(348\) | −9758.00 | −1.50311 | ||||||||
\(349\) | 12481.0i | 1.91431i | 0.289584 | + | 0.957153i | \(0.406483\pi\) | ||||
−0.289584 | + | 0.957153i | \(0.593517\pi\) | |||||||
\(350\) | 4940.00 | 0.754440 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2210.00 | 0.334640 | ||||||||
\(353\) | 1400.00i | 0.211089i | 0.994415 | + | 0.105545i | \(0.0336586\pi\) | ||||
−0.994415 | + | 0.105545i | \(0.966341\pi\) | |||||||
\(354\) | −10290.0 | −1.54494 | ||||||||
\(355\) | 63.0000 | 0.00941885 | ||||||||
\(356\) | 20230.0i | 3.01176i | ||||||||
\(357\) | − 7007.00i | − 1.03879i | ||||||||
\(358\) | 15145.0i | 2.23586i | ||||||||
\(359\) | − 4968.00i | − 0.730365i | −0.930936 | − | 0.365182i | \(-0.881007\pi\) | ||||
0.930936 | − | 0.365182i | \(-0.118993\pi\) | |||||||
\(360\) | 6930.00 | 1.01456 | ||||||||
\(361\) | −9017.00 | −1.31462 | ||||||||
\(362\) | 140.000i | 0.0203266i | ||||||||
\(363\) | −4585.00 | −0.662948 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −686.000 | −0.0983750 | ||||||||
\(366\) | 1960.00i | 0.279920i | ||||||||
\(367\) | 8722.00 | 1.24056 | 0.620279 | − | 0.784381i | \(-0.287019\pi\) | ||||
0.620279 | + | 0.784381i | \(0.287019\pi\) | |||||||
\(368\) | 8544.00 | 1.21029 | ||||||||
\(369\) | − 7392.00i | − 1.04285i | ||||||||
\(370\) | 4585.00i | 0.644224i | ||||||||
\(371\) | 5616.00i | 0.785898i | ||||||||
\(372\) | − 23324.0i | − 3.25079i | ||||||||
\(373\) | 10012.0 | 1.38982 | 0.694908 | − | 0.719098i | \(-0.255445\pi\) | ||||
0.694908 | + | 0.719098i | \(0.255445\pi\) | |||||||
\(374\) | −10010.0 | −1.38397 | ||||||||
\(375\) | − 9849.00i | − 1.35627i | ||||||||
\(376\) | −4725.00 | −0.648067 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2275.00 | 0.309559 | ||||||||
\(379\) | 3372.00i | 0.457013i | 0.973542 | + | 0.228507i | \(0.0733843\pi\) | ||||
−0.973542 | + | 0.228507i | \(0.926616\pi\) | |||||||
\(380\) | 14994.0 | 2.02415 | ||||||||
\(381\) | 13244.0 | 1.78087 | ||||||||
\(382\) | 2110.00i | 0.282610i | ||||||||
\(383\) | 847.000i | 0.113002i | 0.998403 | + | 0.0565009i | \(0.0179944\pi\) | ||||
−0.998403 | + | 0.0565009i | \(0.982006\pi\) | |||||||
\(384\) | − 14805.0i | − 1.96749i | ||||||||
\(385\) | − 2366.00i | − 0.313201i | ||||||||
\(386\) | −2460.00 | −0.324380 | ||||||||
\(387\) | 4422.00 | 0.580834 | ||||||||
\(388\) | 1190.00i | 0.155704i | ||||||||
\(389\) | −11314.0 | −1.47466 | −0.737330 | − | 0.675533i | \(-0.763914\pi\) | ||||
−0.737330 | + | 0.675533i | \(0.763914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7392.00 | −0.956086 | ||||||||
\(392\) | − 7830.00i | − 1.00886i | ||||||||
\(393\) | −10045.0 | −1.28932 | ||||||||
\(394\) | 14955.0 | 1.91224 | ||||||||
\(395\) | 9128.00i | 1.16273i | ||||||||
\(396\) | 9724.00i | 1.23396i | ||||||||
\(397\) | 1862.00i | 0.235393i | 0.993050 | + | 0.117697i | \(0.0375510\pi\) | ||||
−0.993050 | + | 0.117697i | \(0.962449\pi\) | |||||||
\(398\) | 350.000i | 0.0440802i | ||||||||
\(399\) | −11466.0 | −1.43864 | ||||||||
\(400\) | 6764.00 | 0.845500 | ||||||||
\(401\) | 6820.00i | 0.849313i | 0.905355 | + | 0.424657i | \(0.139605\pi\) | ||||
−0.905355 | + | 0.424657i | \(0.860395\pi\) | |||||||
\(402\) | −16730.0 | −2.07566 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 7140.00 | 0.879278 | ||||||||
\(405\) | − 5873.00i | − 0.720572i | ||||||||
\(406\) | −5330.00 | −0.651536 | ||||||||
\(407\) | −3406.00 | −0.414814 | ||||||||
\(408\) | − 24255.0i | − 2.94314i | ||||||||
\(409\) | 12992.0i | 1.57069i | 0.619057 | + | 0.785346i | \(0.287515\pi\) | ||||
−0.619057 | + | 0.785346i | \(0.712485\pi\) | |||||||
\(410\) | 11760.0i | 1.41655i | ||||||||
\(411\) | 12432.0i | 1.49203i | ||||||||
\(412\) | 9996.00 | 1.19531 | ||||||||
\(413\) | −3822.00 | −0.455371 | ||||||||
\(414\) | 10560.0i | 1.25361i | ||||||||
\(415\) | −2156.00 | −0.255021 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13083.0 | 1.53640 | ||||||||
\(418\) | 16380.0i | 1.91668i | ||||||||
\(419\) | −7343.00 | −0.856155 | −0.428078 | − | 0.903742i | \(-0.640809\pi\) | ||||
−0.428078 | + | 0.903742i | \(0.640809\pi\) | |||||||
\(420\) | 10829.0 | 1.25810 | ||||||||
\(421\) | 5059.00i | 0.585655i | 0.956165 | + | 0.292827i | \(0.0945961\pi\) | ||||
−0.956165 | + | 0.292827i | \(0.905404\pi\) | |||||||
\(422\) | 14255.0i | 1.64437i | ||||||||
\(423\) | − 2310.00i | − 0.265523i | ||||||||
\(424\) | 19440.0i | 2.22663i | ||||||||
\(425\) | −5852.00 | −0.667915 | ||||||||
\(426\) | −315.000 | −0.0358258 | ||||||||
\(427\) | 728.000i | 0.0825068i | ||||||||
\(428\) | 11628.0 | 1.31323 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7035.00 | −0.788972 | ||||||||
\(431\) | − 3243.00i | − 0.362436i | −0.983443 | − | 0.181218i | \(-0.941996\pi\) | ||||
0.983443 | − | 0.181218i | \(-0.0580039\pi\) | |||||||
\(432\) | 3115.00 | 0.346922 | ||||||||
\(433\) | −11599.0 | −1.28733 | −0.643663 | − | 0.765309i | \(-0.722586\pi\) | ||||
−0.643663 | + | 0.765309i | \(0.722586\pi\) | |||||||
\(434\) | − 12740.0i | − 1.40908i | ||||||||
\(435\) | 4018.00i | 0.442870i | ||||||||
\(436\) | 6341.00i | 0.696511i | ||||||||
\(437\) | 12096.0i | 1.32410i | ||||||||
\(438\) | 3430.00 | 0.374182 | ||||||||
\(439\) | 17374.0 | 1.88887 | 0.944437 | − | 0.328692i | \(-0.106608\pi\) | ||||
0.944437 | + | 0.328692i | \(0.106608\pi\) | |||||||
\(440\) | − 8190.00i | − 0.887370i | ||||||||
\(441\) | 3828.00 | 0.413346 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 989.000 | 0.106070 | 0.0530348 | − | 0.998593i | \(-0.483111\pi\) | ||||
0.0530348 | + | 0.998593i | \(0.483111\pi\) | |||||||
\(444\) | − 15589.0i | − 1.66626i | ||||||||
\(445\) | 8330.00 | 0.887370 | ||||||||
\(446\) | 1085.00 | 0.115193 | ||||||||
\(447\) | 17262.0i | 1.82654i | ||||||||
\(448\) | − 3731.00i | − 0.393467i | ||||||||
\(449\) | − 14474.0i | − 1.52131i | −0.649154 | − | 0.760657i | \(-0.724877\pi\) | ||||
0.649154 | − | 0.760657i | \(-0.275123\pi\) | |||||||
\(450\) | 8360.00i | 0.875765i | ||||||||
\(451\) | −8736.00 | −0.912111 | ||||||||
\(452\) | 29478.0 | 3.06754 | ||||||||
\(453\) | 23261.0i | 2.41258i | ||||||||
\(454\) | −12880.0 | −1.33147 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39690.0 | −4.07600 | ||||||||
\(457\) | 1594.00i | 0.163160i | 0.996667 | + | 0.0815801i | \(0.0259966\pi\) | ||||
−0.996667 | + | 0.0815801i | \(0.974003\pi\) | |||||||
\(458\) | −2275.00 | −0.232104 | ||||||||
\(459\) | −2695.00 | −0.274056 | ||||||||
\(460\) | − 11424.0i | − 1.15793i | ||||||||
\(461\) | 5915.00i | 0.597590i | 0.954317 | + | 0.298795i | \(0.0965847\pi\) | ||||
−0.954317 | + | 0.298795i | \(0.903415\pi\) | |||||||
\(462\) | 11830.0i | 1.19130i | ||||||||
\(463\) | − 11072.0i | − 1.11136i | −0.831396 | − | 0.555680i | \(-0.812458\pi\) | ||||
0.831396 | − | 0.555680i | \(-0.187542\pi\) | |||||||
\(464\) | −7298.00 | −0.730175 | ||||||||
\(465\) | −9604.00 | −0.957795 | ||||||||
\(466\) | − 15305.0i | − 1.52144i | ||||||||
\(467\) | −1260.00 | −0.124852 | −0.0624260 | − | 0.998050i | \(-0.519884\pi\) | ||||
−0.0624260 | + | 0.998050i | \(0.519884\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6214.00 | −0.611804 | ||||||||
\(470\) | 3675.00i | 0.360670i | ||||||||
\(471\) | 19110.0 | 1.86952 | ||||||||
\(472\) | −13230.0 | −1.29017 | ||||||||
\(473\) | − 5226.00i | − 0.508016i | ||||||||
\(474\) | − 45640.0i | − 4.42260i | ||||||||
\(475\) | 9576.00i | 0.925004i | ||||||||
\(476\) | − 17017.0i | − 1.63860i | ||||||||
\(477\) | −9504.00 | −0.912281 | ||||||||
\(478\) | −17385.0 | −1.66354 | ||||||||
\(479\) | − 12033.0i | − 1.14781i | −0.818921 | − | 0.573906i | \(-0.805428\pi\) | ||||
0.818921 | − | 0.573906i | \(-0.194572\pi\) | |||||||
\(480\) | 4165.00 | 0.396053 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 8050.00 | 0.760721 | ||||||||
\(483\) | 8736.00i | 0.822985i | ||||||||
\(484\) | −11135.0 | −1.04574 | ||||||||
\(485\) | 490.000 | 0.0458758 | ||||||||
\(486\) | 24640.0i | 2.29978i | ||||||||
\(487\) | 2280.00i | 0.212149i | 0.994358 | + | 0.106075i | \(0.0338282\pi\) | ||||
−0.994358 | + | 0.106075i | \(0.966172\pi\) | |||||||
\(488\) | 2520.00i | 0.233760i | ||||||||
\(489\) | 3808.00i | 0.352155i | ||||||||
\(490\) | −6090.00 | −0.561466 | ||||||||
\(491\) | −16767.0 | −1.54111 | −0.770554 | − | 0.637375i | \(-0.780020\pi\) | ||||
−0.770554 | + | 0.637375i | \(0.780020\pi\) | |||||||
\(492\) | − 39984.0i | − 3.66386i | ||||||||
\(493\) | 6314.00 | 0.576812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4004.00 | 0.363569 | ||||||||
\(496\) | − 17444.0i | − 1.57915i | ||||||||
\(497\) | −117.000 | −0.0105597 | ||||||||
\(498\) | 10780.0 | 0.970007 | ||||||||
\(499\) | − 12840.0i | − 1.15190i | −0.817485 | − | 0.575949i | \(-0.804633\pi\) | ||||
0.817485 | − | 0.575949i | \(-0.195367\pi\) | |||||||
\(500\) | − 23919.0i | − 2.13938i | ||||||||
\(501\) | − 11368.0i | − 1.01374i | ||||||||
\(502\) | − 5040.00i | − 0.448100i | ||||||||
\(503\) | −2198.00 | −0.194839 | −0.0974195 | − | 0.995243i | \(-0.531059\pi\) | ||||
−0.0974195 | + | 0.995243i | \(0.531059\pi\) | |||||||
\(504\) | −12870.0 | −1.13745 | ||||||||
\(505\) | − 2940.00i | − 0.259066i | ||||||||
\(506\) | 12480.0 | 1.09645 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32164.0 | 2.80915 | ||||||||
\(509\) | 17066.0i | 1.48612i | 0.669223 | + | 0.743062i | \(0.266627\pi\) | ||||
−0.669223 | + | 0.743062i | \(0.733373\pi\) | |||||||
\(510\) | −18865.0 | −1.63795 | ||||||||
\(511\) | 1274.00 | 0.110290 | ||||||||
\(512\) | − 24475.0i | − 2.11260i | ||||||||
\(513\) | 4410.00i | 0.379544i | ||||||||
\(514\) | − 30205.0i | − 2.59200i | ||||||||
\(515\) | − 4116.00i | − 0.352180i | ||||||||
\(516\) | 23919.0 | 2.04065 | ||||||||
\(517\) | −2730.00 | −0.232235 | ||||||||
\(518\) | − 8515.00i | − 0.722254i | ||||||||
\(519\) | −2352.00 | −0.198924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2583.00 | 0.217204 | 0.108602 | − | 0.994085i | \(-0.465363\pi\) | ||||
0.108602 | + | 0.994085i | \(0.465363\pi\) | |||||||
\(522\) | − 9020.00i | − 0.756312i | ||||||||
\(523\) | 18620.0 | 1.55678 | 0.778390 | − | 0.627781i | \(-0.216037\pi\) | ||||
0.778390 | + | 0.627781i | \(0.216037\pi\) | |||||||
\(524\) | −24395.0 | −2.03378 | ||||||||
\(525\) | 6916.00i | 0.574931i | ||||||||
\(526\) | − 18540.0i | − 1.53685i | ||||||||
\(527\) | 15092.0i | 1.24747i | ||||||||
\(528\) | 16198.0i | 1.33509i | ||||||||
\(529\) | −2951.00 | −0.242541 | ||||||||
\(530\) | 15120.0 | 1.23919 | ||||||||
\(531\) | − 6468.00i | − 0.528601i | ||||||||
\(532\) | −27846.0 | −2.26932 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −41650.0 | −3.37523 | ||||||||
\(535\) | − 4788.00i | − 0.386922i | ||||||||
\(536\) | −21510.0 | −1.73338 | ||||||||
\(537\) | −21203.0 | −1.70387 | ||||||||
\(538\) | 41720.0i | 3.34327i | ||||||||
\(539\) | − 4524.00i | − 0.361526i | ||||||||
\(540\) | − 4165.00i | − 0.331913i | ||||||||
\(541\) | − 16833.0i | − 1.33772i | −0.743388 | − | 0.668861i | \(-0.766782\pi\) | ||||
0.743388 | − | 0.668861i | \(-0.233218\pi\) | |||||||
\(542\) | 8085.00 | 0.640739 | ||||||||
\(543\) | −196.000 | −0.0154902 | ||||||||
\(544\) | − 6545.00i | − 0.515836i | ||||||||
\(545\) | 2611.00 | 0.205216 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8615.00 | −0.673402 | −0.336701 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336701 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(548\) | 30192.0i | 2.35354i | ||||||||
\(549\) | −1232.00 | −0.0957750 | ||||||||
\(550\) | 9880.00 | 0.765972 | ||||||||
\(551\) | − 10332.0i | − 0.798835i | ||||||||
\(552\) | 30240.0i | 2.33170i | ||||||||
\(553\) | − 16952.0i | − 1.30357i | ||||||||
\(554\) | 19100.0i | 1.46477i | ||||||||
\(555\) | −6419.00 | −0.490939 | ||||||||
\(556\) | 31773.0 | 2.42352 | ||||||||
\(557\) | 8535.00i | 0.649263i | 0.945841 | + | 0.324632i | \(0.105240\pi\) | ||||
−0.945841 | + | 0.324632i | \(0.894760\pi\) | |||||||
\(558\) | 21560.0 | 1.63568 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 8099.00 | 0.611152 | ||||||||
\(561\) | − 14014.0i | − 1.05467i | ||||||||
\(562\) | 31070.0 | 2.33204 | ||||||||
\(563\) | 4641.00 | 0.347415 | 0.173708 | − | 0.984797i | \(-0.444425\pi\) | ||||
0.173708 | + | 0.984797i | \(0.444425\pi\) | |||||||
\(564\) | − 12495.0i | − 0.932862i | ||||||||
\(565\) | − 12138.0i | − 0.903804i | ||||||||
\(566\) | 26460.0i | 1.96501i | ||||||||
\(567\) | 10907.0i | 0.807850i | ||||||||
\(568\) | −405.000 | −0.0299180 | ||||||||
\(569\) | 4793.00 | 0.353134 | 0.176567 | − | 0.984289i | \(-0.443501\pi\) | ||||
0.176567 | + | 0.984289i | \(0.443501\pi\) | |||||||
\(570\) | 30870.0i | 2.26842i | ||||||||
\(571\) | 5563.00 | 0.407713 | 0.203857 | − | 0.979001i | \(-0.434652\pi\) | ||||
0.203857 | + | 0.979001i | \(0.434652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2954.00 | −0.215367 | ||||||||
\(574\) | − 21840.0i | − 1.58813i | ||||||||
\(575\) | 7296.00 | 0.529155 | ||||||||
\(576\) | 6314.00 | 0.456742 | ||||||||
\(577\) | − 24038.0i | − 1.73434i | −0.498011 | − | 0.867171i | \(-0.665936\pi\) | ||||
0.498011 | − | 0.867171i | \(-0.334064\pi\) | |||||||
\(578\) | 5080.00i | 0.365571i | ||||||||
\(579\) | − 3444.00i | − 0.247198i | ||||||||
\(580\) | 9758.00i | 0.698584i | ||||||||
\(581\) | 4004.00 | 0.285910 | ||||||||
\(582\) | −2450.00 | −0.174494 | ||||||||
\(583\) | 11232.0i | 0.797911i | ||||||||
\(584\) | 4410.00 | 0.312478 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4515.00 | 0.318281 | ||||||||
\(587\) | 21224.0i | 1.49235i | 0.665751 | + | 0.746174i | \(0.268111\pi\) | ||||
−0.665751 | + | 0.746174i | \(0.731889\pi\) | |||||||
\(588\) | 20706.0 | 1.45221 | ||||||||
\(589\) | 24696.0 | 1.72764 | ||||||||
\(590\) | 10290.0i | 0.718021i | ||||||||
\(591\) | 20937.0i | 1.45725i | ||||||||
\(592\) | − 11659.0i | − 0.809429i | ||||||||
\(593\) | 4354.00i | 0.301513i | 0.988571 | + | 0.150757i | \(0.0481710\pi\) | ||||
−0.988571 | + | 0.150757i | \(0.951829\pi\) | |||||||
\(594\) | 4550.00 | 0.314291 | ||||||||
\(595\) | −7007.00 | −0.482788 | ||||||||
\(596\) | 41922.0i | 2.88119i | ||||||||
\(597\) | −490.000 | −0.0335919 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7310.00 | 0.498629 | 0.249314 | − | 0.968423i | \(-0.419795\pi\) | ||||
0.249314 | + | 0.968423i | \(0.419795\pi\) | |||||||
\(600\) | 23940.0i | 1.62891i | ||||||||
\(601\) | −7595.00 | −0.515485 | −0.257743 | − | 0.966214i | \(-0.582979\pi\) | ||||
−0.257743 | + | 0.966214i | \(0.582979\pi\) | |||||||
\(602\) | 13065.0 | 0.884534 | ||||||||
\(603\) | − 10516.0i | − 0.710190i | ||||||||
\(604\) | 56491.0i | 3.80561i | ||||||||
\(605\) | 4585.00i | 0.308110i | ||||||||
\(606\) | 14700.0i | 0.985391i | ||||||||
\(607\) | −826.000 | −0.0552328 | −0.0276164 | − | 0.999619i | \(-0.508792\pi\) | ||||
−0.0276164 | + | 0.999619i | \(0.508792\pi\) | |||||||
\(608\) | −10710.0 | −0.714388 | ||||||||
\(609\) | − 7462.00i | − 0.496511i | ||||||||
\(610\) | 1960.00 | 0.130095 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 28798.0 | 1.90211 | ||||||||
\(613\) | − 14590.0i | − 0.961312i | −0.876909 | − | 0.480656i | \(-0.840398\pi\) | ||||
0.876909 | − | 0.480656i | \(-0.159602\pi\) | |||||||
\(614\) | −10570.0 | −0.694740 | ||||||||
\(615\) | −16464.0 | −1.07950 | ||||||||
\(616\) | 15210.0i | 0.994851i | ||||||||
\(617\) | − 4888.00i | − 0.318936i | −0.987203 | − | 0.159468i | \(-0.949022\pi\) | ||||
0.987203 | − | 0.159468i | \(-0.0509779\pi\) | |||||||
\(618\) | 20580.0i | 1.33956i | ||||||||
\(619\) | − 11004.0i | − 0.714520i | −0.934005 | − | 0.357260i | \(-0.883711\pi\) | ||||
0.934005 | − | 0.357260i | \(-0.116289\pi\) | |||||||
\(620\) | −23324.0 | −1.51083 | ||||||||
\(621\) | 3360.00 | 0.217121 | ||||||||
\(622\) | − 17010.0i | − 1.09653i | ||||||||
\(623\) | −15470.0 | −0.994851 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | − 53445.0i | − 3.41229i | ||||||||
\(627\) | −22932.0 | −1.46063 | ||||||||
\(628\) | 46410.0 | 2.94898 | ||||||||
\(629\) | 10087.0i | 0.639420i | ||||||||
\(630\) | 10010.0i | 0.633028i | ||||||||
\(631\) | − 4975.00i | − 0.313869i | −0.987609 | − | 0.156935i | \(-0.949839\pi\) | ||||
0.987609 | − | 0.156935i | \(-0.0501612\pi\) | |||||||
\(632\) | − 58680.0i | − 3.69330i | ||||||||
\(633\) | −19957.0 | −1.25311 | ||||||||
\(634\) | −35270.0 | −2.20939 | ||||||||
\(635\) | − 13244.0i | − 0.827673i | ||||||||
\(636\) | −51408.0 | −3.20513 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10660.0 | −0.661494 | ||||||||
\(639\) | − 198.000i | − 0.0122578i | ||||||||
\(640\) | −14805.0 | −0.914405 | ||||||||
\(641\) | −3950.00 | −0.243394 | −0.121697 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121697 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(642\) | 23940.0i | 1.47171i | ||||||||
\(643\) | 3682.00i | 0.225823i | 0.993605 | + | 0.112911i | \(0.0360176\pi\) | ||||
−0.993605 | + | 0.112911i | \(0.963982\pi\) | |||||||
\(644\) | 21216.0i | 1.29818i | ||||||||
\(645\) | − 9849.00i | − 0.601247i | ||||||||
\(646\) | 48510.0 | 2.95449 | ||||||||
\(647\) | −10402.0 | −0.632063 | −0.316032 | − | 0.948749i | \(-0.602351\pi\) | ||||
−0.316032 | + | 0.948749i | \(0.602351\pi\) | |||||||
\(648\) | 37755.0i | 2.28882i | ||||||||
\(649\) | −7644.00 | −0.462332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17836.0 | 1.07381 | ||||||||
\(652\) | 9248.00i | 0.555490i | ||||||||
\(653\) | −31680.0 | −1.89852 | −0.949260 | − | 0.314491i | \(-0.898166\pi\) | ||||
−0.949260 | + | 0.314491i | \(0.898166\pi\) | |||||||
\(654\) | −13055.0 | −0.780567 | ||||||||
\(655\) | 10045.0i | 0.599222i | ||||||||
\(656\) | − 29904.0i | − 1.77981i | ||||||||
\(657\) | 2156.00i | 0.128027i | ||||||||
\(658\) | − 6825.00i | − 0.404356i | ||||||||
\(659\) | 21940.0 | 1.29691 | 0.648453 | − | 0.761255i | \(-0.275416\pi\) | ||||
0.648453 | + | 0.761255i | \(0.275416\pi\) | |||||||
\(660\) | 21658.0 | 1.27733 | ||||||||
\(661\) | − 31374.0i | − 1.84615i | −0.384616 | − | 0.923077i | \(-0.625666\pi\) | ||||
0.384616 | − | 0.923077i | \(-0.374334\pi\) | |||||||
\(662\) | 48520.0 | 2.84862 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13860.0 | 0.810049 | ||||||||
\(665\) | 11466.0i | 0.668620i | ||||||||
\(666\) | 14410.0 | 0.838403 | ||||||||
\(667\) | −7872.00 | −0.456979 | ||||||||
\(668\) | − 27608.0i | − 1.59908i | ||||||||
\(669\) | 1519.00i | 0.0877847i | ||||||||
\(670\) | 16730.0i | 0.964681i | ||||||||
\(671\) | 1456.00i | 0.0837679i | ||||||||
\(672\) | −7735.00 | −0.444024 | ||||||||
\(673\) | −18013.0 | −1.03172 | −0.515862 | − | 0.856672i | \(-0.672528\pi\) | ||||
−0.515862 | + | 0.856672i | \(0.672528\pi\) | |||||||
\(674\) | 52245.0i | 2.98576i | ||||||||
\(675\) | 2660.00 | 0.151679 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10640.0 | −0.604030 | −0.302015 | − | 0.953303i | \(-0.597659\pi\) | ||||
−0.302015 | + | 0.953303i | \(0.597659\pi\) | |||||||
\(678\) | 60690.0i | 3.43774i | ||||||||
\(679\) | −910.000 | −0.0514324 | ||||||||
\(680\) | −24255.0 | −1.36785 | ||||||||
\(681\) | − 18032.0i | − 1.01467i | ||||||||
\(682\) | − 25480.0i | − 1.43062i | ||||||||
\(683\) | − 9336.00i | − 0.523034i | −0.965199 | − | 0.261517i | \(-0.915777\pi\) | ||||
0.965199 | − | 0.261517i | \(-0.0842227\pi\) | |||||||
\(684\) | − 47124.0i | − 2.63426i | ||||||||
\(685\) | 12432.0 | 0.693434 | ||||||||
\(686\) | 33605.0 | 1.87033 | ||||||||
\(687\) | − 3185.00i | − 0.176878i | ||||||||
\(688\) | 17889.0 | 0.991296 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 23520.0 | 1.29767 | ||||||||
\(691\) | − 4200.00i | − 0.231224i | −0.993294 | − | 0.115612i | \(-0.963117\pi\) | ||||
0.993294 | − | 0.115612i | \(-0.0368829\pi\) | |||||||
\(692\) | −5712.00 | −0.313783 | ||||||||
\(693\) | −7436.00 | −0.407605 | ||||||||
\(694\) | − 3105.00i | − 0.169833i | ||||||||
\(695\) | − 13083.0i | − 0.714052i | ||||||||
\(696\) | − 25830.0i | − 1.40673i | ||||||||
\(697\) | 25872.0i | 1.40599i | ||||||||
\(698\) | −62405.0 | −3.38405 | ||||||||
\(699\) | 21427.0 | 1.15943 | ||||||||
\(700\) | 16796.0i | 0.906899i | ||||||||
\(701\) | −9872.00 | −0.531898 | −0.265949 | − | 0.963987i | \(-0.585685\pi\) | ||||
−0.265949 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16506.0 | 0.885541 | ||||||||
\(704\) | − 7462.00i | − 0.399481i | ||||||||
\(705\) | −5145.00 | −0.274854 | ||||||||
\(706\) | −7000.00 | −0.373156 | ||||||||
\(707\) | 5460.00i | 0.290445i | ||||||||
\(708\) | − 34986.0i | − 1.85714i | ||||||||
\(709\) | 28450.0i | 1.50700i | 0.657449 | + | 0.753499i | \(0.271636\pi\) | ||||
−0.657449 | + | 0.753499i | \(0.728364\pi\) | |||||||
\(710\) | 315.000i | 0.0166503i | ||||||||
\(711\) | 28688.0 | 1.51320 | ||||||||
\(712\) | −53550.0 | −2.81864 | ||||||||
\(713\) | − 18816.0i | − 0.988310i | ||||||||
\(714\) | 35035.0 | 1.83635 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −51493.0 | −2.68769 | ||||||||
\(717\) | − 24339.0i | − 1.26772i | ||||||||
\(718\) | 24840.0 | 1.29111 | ||||||||
\(719\) | −32718.0 | −1.69705 | −0.848523 | − | 0.529159i | \(-0.822507\pi\) | ||||
−0.848523 | + | 0.529159i | \(0.822507\pi\) | |||||||
\(720\) | 13706.0i | 0.709434i | ||||||||
\(721\) | 7644.00i | 0.394837i | ||||||||
\(722\) | − 45085.0i | − 2.32395i | ||||||||
\(723\) | 11270.0i | 0.579718i | ||||||||
\(724\) | −476.000 | −0.0244343 | ||||||||
\(725\) | −6232.00 | −0.319242 | ||||||||
\(726\) | − 22925.0i | − 1.17194i | ||||||||
\(727\) | 22834.0 | 1.16488 | 0.582439 | − | 0.812874i | \(-0.302099\pi\) | ||||
0.582439 | + | 0.812874i | \(0.302099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | − 3430.00i | − 0.173904i | ||||||||
\(731\) | −15477.0 | −0.783088 | ||||||||
\(732\) | −6664.00 | −0.336487 | ||||||||
\(733\) | − 7875.00i | − 0.396821i | −0.980119 | − | 0.198410i | \(-0.936422\pi\) | ||||
0.980119 | − | 0.198410i | \(-0.0635779\pi\) | |||||||
\(734\) | 43610.0i | 2.19302i | ||||||||
\(735\) | − 8526.00i | − 0.427872i | ||||||||
\(736\) | 8160.00i | 0.408671i | ||||||||
\(737\) | −12428.0 | −0.621155 | ||||||||
\(738\) | 36960.0 | 1.84352 | ||||||||
\(739\) | − 2140.00i | − 0.106524i | −0.998581 | − | 0.0532620i | \(-0.983038\pi\) | ||||
0.998581 | − | 0.0532620i | \(-0.0169618\pi\) | |||||||
\(740\) | −15589.0 | −0.774410 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28080.0 | −1.38928 | ||||||||
\(743\) | − 31971.0i | − 1.57860i | −0.614006 | − | 0.789302i | \(-0.710443\pi\) | ||||
0.614006 | − | 0.789302i | \(-0.289557\pi\) | |||||||
\(744\) | 61740.0 | 3.04234 | ||||||||
\(745\) | 17262.0 | 0.848900 | ||||||||
\(746\) | 50060.0i | 2.45687i | ||||||||
\(747\) | 6776.00i | 0.331889i | ||||||||
\(748\) | − 34034.0i | − 1.66364i | ||||||||
\(749\) | 8892.00i | 0.433787i | ||||||||
\(750\) | 49245.0 | 2.39756 | ||||||||
\(751\) | 7432.00 | 0.361115 | 0.180558 | − | 0.983564i | \(-0.442210\pi\) | ||||
0.180558 | + | 0.983564i | \(0.442210\pi\) | |||||||
\(752\) | − 9345.00i | − 0.453161i | ||||||||
\(753\) | 7056.00 | 0.341481 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23261.0 | 1.12126 | ||||||||
\(756\) | 7735.00i | 0.372115i | ||||||||
\(757\) | 20176.0 | 0.968704 | 0.484352 | − | 0.874873i | \(-0.339055\pi\) | ||||
0.484352 | + | 0.874873i | \(0.339055\pi\) | |||||||
\(758\) | −16860.0 | −0.807893 | ||||||||
\(759\) | 17472.0i | 0.835564i | ||||||||
\(760\) | 39690.0i | 1.89435i | ||||||||
\(761\) | − 9478.00i | − 0.451481i | −0.974187 | − | 0.225741i | \(-0.927520\pi\) | ||||
0.974187 | − | 0.225741i | \(-0.0724802\pi\) | |||||||
\(762\) | 66220.0i | 3.14816i | ||||||||
\(763\) | −4849.00 | −0.230073 | ||||||||
\(764\) | −7174.00 | −0.339720 | ||||||||
\(765\) | − 11858.0i | − 0.560427i | ||||||||
\(766\) | −4235.00 | −0.199761 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 57953.0 | 2.72292 | ||||||||
\(769\) | 12096.0i | 0.567221i | 0.958940 | + | 0.283610i | \(0.0915323\pi\) | ||||
−0.958940 | + | 0.283610i | \(0.908468\pi\) | |||||||
\(770\) | 11830.0 | 0.553667 | ||||||||
\(771\) | 42287.0 | 1.97526 | ||||||||
\(772\) | − 8364.00i | − 0.389931i | ||||||||
\(773\) | − 17941.0i | − 0.834790i | −0.908725 | − | 0.417395i | \(-0.862943\pi\) | ||||
0.908725 | − | 0.417395i | \(-0.137057\pi\) | |||||||
\(774\) | 22110.0i | 1.02678i | ||||||||
\(775\) | − 14896.0i | − 0.690426i | ||||||||
\(776\) | −3150.00 | −0.145720 | ||||||||
\(777\) | 11921.0 | 0.550403 | ||||||||
\(778\) | − 56570.0i | − 2.60685i | ||||||||
\(779\) | 42336.0 | 1.94717 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −234.000 | −0.0107211 | ||||||||
\(782\) | − 36960.0i | − 1.69014i | ||||||||
\(783\) | −2870.00 | −0.130990 | ||||||||
\(784\) | 15486.0 | 0.705448 | ||||||||
\(785\) | − 19110.0i | − 0.868873i | ||||||||
\(786\) | − 50225.0i | − 2.27922i | ||||||||
\(787\) | 6664.00i | 0.301837i | 0.988546 | + | 0.150919i | \(0.0482232\pi\) | ||||
−0.988546 | + | 0.150919i | \(0.951777\pi\) | |||||||
\(788\) | 50847.0i | 2.29867i | ||||||||
\(789\) | 25956.0 | 1.17118 | ||||||||
\(790\) | −45640.0 | −2.05544 | ||||||||
\(791\) | 22542.0i | 1.01328i | ||||||||
\(792\) | −25740.0 | −1.15484 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9310.00 | −0.416120 | ||||||||
\(795\) | 21168.0i | 0.944342i | ||||||||
\(796\) | −1190.00 | −0.0529880 | ||||||||
\(797\) | 1442.00 | 0.0640882 | 0.0320441 | − | 0.999486i | \(-0.489798\pi\) | ||||
0.0320441 | + | 0.999486i | \(0.489798\pi\) | |||||||
\(798\) | − 57330.0i | − 2.54318i | ||||||||
\(799\) | 8085.00i | 0.357981i | ||||||||
\(800\) | 6460.00i | 0.285494i | ||||||||
\(801\) | − 26180.0i | − 1.15484i | ||||||||
\(802\) | −34100.0 | −1.50139 | ||||||||
\(803\) | 2548.00 | 0.111976 | ||||||||
\(804\) | − 56882.0i | − 2.49512i | ||||||||
\(805\) | 8736.00 | 0.382489 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −58408.0 | −2.54778 | ||||||||
\(808\) | 18900.0i | 0.822896i | ||||||||
\(809\) | 30207.0 | 1.31276 | 0.656379 | − | 0.754431i | \(-0.272087\pi\) | ||||
0.656379 | + | 0.754431i | \(0.272087\pi\) | |||||||
\(810\) | 29365.0 | 1.27380 | ||||||||
\(811\) | − 21140.0i | − 0.915322i | −0.889127 | − | 0.457661i | \(-0.848687\pi\) | ||||
0.889127 | − | 0.457661i | \(-0.151313\pi\) | |||||||
\(812\) | − 18122.0i | − 0.783199i | ||||||||
\(813\) | 11319.0i | 0.488284i | ||||||||
\(814\) | − 17030.0i | − 0.733294i | ||||||||
\(815\) | 3808.00 | 0.163667 | ||||||||
\(816\) | 47971.0 | 2.05799 | ||||||||
\(817\) | 25326.0i | 1.08451i | ||||||||
\(818\) | −64960.0 | −2.77662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −39984.0 | −1.70281 | ||||||||
\(821\) | − 569.000i | − 0.0241879i | −0.999927 | − | 0.0120939i | \(-0.996150\pi\) | ||||
0.999927 | − | 0.0120939i | \(-0.00384971\pi\) | |||||||
\(822\) | −62160.0 | −2.63757 | ||||||||
\(823\) | 8538.00 | 0.361623 | 0.180812 | − | 0.983518i | \(-0.442128\pi\) | ||||
0.180812 | + | 0.983518i | \(0.442128\pi\) | |||||||
\(824\) | 26460.0i | 1.11866i | ||||||||
\(825\) | 13832.0i | 0.583719i | ||||||||
\(826\) | − 19110.0i | − 0.804990i | ||||||||
\(827\) | − 32702.0i | − 1.37504i | −0.726164 | − | 0.687521i | \(-0.758699\pi\) | ||||
0.726164 | − | 0.687521i | \(-0.241301\pi\) | |||||||
\(828\) | −35904.0 | −1.50694 | ||||||||
\(829\) | 21154.0 | 0.886259 | 0.443130 | − | 0.896458i | \(-0.353868\pi\) | ||||
0.443130 | + | 0.896458i | \(0.353868\pi\) | |||||||
\(830\) | − 10780.0i | − 0.450818i | ||||||||
\(831\) | −26740.0 | −1.11625 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13398.0 | −0.557279 | ||||||||
\(834\) | 65415.0i | 2.71599i | ||||||||
\(835\) | −11368.0 | −0.471145 | ||||||||
\(836\) | −55692.0 | −2.30400 | ||||||||
\(837\) | − 6860.00i | − 0.283293i | ||||||||
\(838\) | − 36715.0i | − 1.51348i | ||||||||
\(839\) | − 2184.00i | − 0.0898690i | −0.998990 | − | 0.0449345i | \(-0.985692\pi\) | ||||
0.998990 | − | 0.0449345i | \(-0.0143079\pi\) | |||||||
\(840\) | 28665.0i | 1.17742i | ||||||||
\(841\) | −17665.0 | −0.724302 | ||||||||
\(842\) | −25295.0 | −1.03530 | ||||||||
\(843\) | 43498.0i | 1.77717i | ||||||||
\(844\) | −48467.0 | −1.97666 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11550.0 | 0.469382 | ||||||||
\(847\) | − 8515.00i | − 0.345430i | ||||||||
\(848\) | −38448.0 | −1.55697 | ||||||||
\(849\) | −37044.0 | −1.49746 | ||||||||
\(850\) | − 29260.0i | − 1.18072i | ||||||||
\(851\) | − 12576.0i | − 0.506580i | ||||||||
\(852\) | − 1071.00i | − 0.0430656i | ||||||||
\(853\) | 36687.0i | 1.47261i | 0.676648 | + | 0.736307i | \(0.263432\pi\) | ||||
−0.676648 | + | 0.736307i | \(0.736568\pi\) | |||||||
\(854\) | −3640.00 | −0.145853 | ||||||||
\(855\) | −19404.0 | −0.776144 | ||||||||
\(856\) | 30780.0i | 1.22902i | ||||||||
\(857\) | −36806.0 | −1.46706 | −0.733529 | − | 0.679658i | \(-0.762128\pi\) | ||||
−0.733529 | + | 0.679658i | \(0.762128\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4900.00 | 0.194628 | 0.0973142 | − | 0.995254i | \(-0.468975\pi\) | ||||
0.0973142 | + | 0.995254i | \(0.468975\pi\) | |||||||
\(860\) | − 23919.0i | − 0.948408i | ||||||||
\(861\) | 30576.0 | 1.21025 | ||||||||
\(862\) | 16215.0 | 0.640702 | ||||||||
\(863\) | 13697.0i | 0.540268i | 0.962823 | + | 0.270134i | \(0.0870680\pi\) | ||||
−0.962823 | + | 0.270134i | \(0.912932\pi\) | |||||||
\(864\) | 2975.00i | 0.117143i | ||||||||
\(865\) | 2352.00i | 0.0924513i | ||||||||
\(866\) | − 57995.0i | − 2.27569i | ||||||||
\(867\) | −7112.00 | −0.278588 | ||||||||
\(868\) | 43316.0 | 1.69383 | ||||||||
\(869\) | − 33904.0i | − 1.32349i | ||||||||
\(870\) | −20090.0 | −0.782891 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −16785.0 | −0.651848 | ||||||||
\(873\) | − 1540.00i | − 0.0597034i | ||||||||
\(874\) | −60480.0 | −2.34069 | ||||||||
\(875\) | 18291.0 | 0.706684 | ||||||||
\(876\) | 11662.0i | 0.449797i | ||||||||
\(877\) | − 6239.00i | − 0.240224i | −0.992760 | − | 0.120112i | \(-0.961675\pi\) | ||||
0.992760 | − | 0.120112i | \(-0.0383253\pi\) | |||||||
\(878\) | 86870.0i | 3.33909i | ||||||||
\(879\) | 6321.00i | 0.242551i | ||||||||
\(880\) | 16198.0 | 0.620494 | ||||||||
\(881\) | −133.000 | −0.00508613 | −0.00254307 | − | 0.999997i | \(-0.500809\pi\) | ||||
−0.00254307 | + | 0.999997i | \(0.500809\pi\) | |||||||
\(882\) | 19140.0i | 0.730700i | ||||||||
\(883\) | 26003.0 | 0.991020 | 0.495510 | − | 0.868602i | \(-0.334981\pi\) | ||||
0.495510 | + | 0.868602i | \(0.334981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14406.0 | −0.547178 | ||||||||
\(886\) | 4945.00i | 0.187506i | ||||||||
\(887\) | −31248.0 | −1.18287 | −0.591435 | − | 0.806353i | \(-0.701438\pi\) | ||||
−0.591435 | + | 0.806353i | \(0.701438\pi\) | |||||||
\(888\) | 41265.0 | 1.55942 | ||||||||
\(889\) | 24596.0i | 0.927923i | ||||||||
\(890\) | 41650.0i | 1.56866i | ||||||||
\(891\) | 21814.0i | 0.820198i | ||||||||
\(892\) | 3689.00i | 0.138472i | ||||||||
\(893\) | 13230.0 | 0.495773 | ||||||||
\(894\) | −86310.0 | −3.22890 | ||||||||
\(895\) | 21203.0i | 0.791886i | ||||||||
\(896\) | 27495.0 | 1.02516 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 72370.0 | 2.68933 | ||||||||
\(899\) | 16072.0i | 0.596253i | ||||||||
\(900\) | −28424.0 | −1.05274 | ||||||||
\(901\) | 33264.0 | 1.22995 | ||||||||
\(902\) | − 43680.0i | − 1.61240i | ||||||||
\(903\) | 18291.0i | 0.674071i | ||||||||
\(904\) | 78030.0i | 2.87084i | ||||||||
\(905\) | 196.000i | 0.00719918i | ||||||||
\(906\) | −116305. | −4.26487 | ||||||||
\(907\) | 38253.0 | 1.40041 | 0.700204 | − | 0.713943i | \(-0.253092\pi\) | ||||
0.700204 | + | 0.713943i | \(0.253092\pi\) | |||||||
\(908\) | − 43792.0i | − 1.60054i | ||||||||
\(909\) | −9240.00 | −0.337152 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36374.0 | 1.32286 | 0.661429 | − | 0.750007i | \(-0.269950\pi\) | ||||
0.661429 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(912\) | − 78498.0i | − 2.85014i | ||||||||
\(913\) | 8008.00 | 0.290281 | ||||||||
\(914\) | −7970.00 | −0.288429 | ||||||||
\(915\) | 2744.00i | 0.0991408i | ||||||||
\(916\) | − 7735.00i | − 0.279008i | ||||||||
\(917\) | − 18655.0i | − 0.671802i | ||||||||
\(918\) | − 13475.0i | − 0.484468i | ||||||||
\(919\) | −27648.0 | −0.992408 | −0.496204 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496204 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(920\) | 30240.0 | 1.08368 | ||||||||
\(921\) | − 14798.0i | − 0.529436i | ||||||||
\(922\) | −29575.0 | −1.05640 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −40222.0 | −1.43204 | ||||||||
\(925\) | − 9956.00i | − 0.353893i | ||||||||
\(926\) | 55360.0 | 1.96462 | ||||||||
\(927\) | −12936.0 | −0.458332 | ||||||||
\(928\) | − 6970.00i | − 0.246553i | ||||||||
\(929\) | − 756.000i | − 0.0266992i | −0.999911 | − | 0.0133496i | \(-0.995751\pi\) | ||||
0.999911 | − | 0.0133496i | \(-0.00424944\pi\) | |||||||
\(930\) | − 48020.0i | − 1.69316i | ||||||||
\(931\) | 21924.0i | 0.771783i | ||||||||
\(932\) | 52037.0 | 1.82889 | ||||||||
\(933\) | 23814.0 | 0.835622 | ||||||||
\(934\) | − 6300.00i | − 0.220709i | ||||||||
\(935\) | −14014.0 | −0.490168 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20846.0 | 0.726797 | 0.363399 | − | 0.931634i | \(-0.381616\pi\) | ||||
0.363399 | + | 0.931634i | \(0.381616\pi\) | |||||||
\(938\) | − 31070.0i | − 1.08153i | ||||||||
\(939\) | 74823.0 | 2.60038 | ||||||||
\(940\) | −12495.0 | −0.433555 | ||||||||
\(941\) | 41321.0i | 1.43148i | 0.698365 | + | 0.715742i | \(0.253911\pi\) | ||||
−0.698365 | + | 0.715742i | \(0.746089\pi\) | |||||||
\(942\) | 95550.0i | 3.30487i | ||||||||
\(943\) | − 32256.0i | − 1.11389i | ||||||||
\(944\) | − 26166.0i | − 0.902151i | ||||||||
\(945\) | 3185.00 | 0.109638 | ||||||||
\(946\) | 26130.0 | 0.898055 | ||||||||
\(947\) | 54966.0i | 1.88612i | 0.332624 | + | 0.943060i | \(0.392066\pi\) | ||||
−0.332624 | + | 0.943060i | \(0.607934\pi\) | |||||||
\(948\) | 155176. | 5.31633 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −47880.0 | −1.63519 | ||||||||
\(951\) | − 49378.0i | − 1.68369i | ||||||||
\(952\) | 45045.0 | 1.53353 | ||||||||
\(953\) | 44553.0 | 1.51439 | 0.757195 | − | 0.653189i | \(-0.226569\pi\) | ||||
0.757195 | + | 0.653189i | \(0.226569\pi\) | |||||||
\(954\) | − 47520.0i | − 1.61270i | ||||||||
\(955\) | 2954.00i | 0.100093i | ||||||||
\(956\) | − 59109.0i | − 1.99971i | ||||||||
\(957\) | − 14924.0i | − 0.504101i | ||||||||
\(958\) | 60165.0 | 2.02906 | ||||||||
\(959\) | −23088.0 | −0.777425 | ||||||||
\(960\) | − 14063.0i | − 0.472793i | ||||||||
\(961\) | −8625.00 | −0.289517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −15048.0 | −0.503546 | ||||||||
\(964\) | 27370.0i | 0.914448i | ||||||||
\(965\) | −3444.00 | −0.114887 | ||||||||
\(966\) | −43680.0 | −1.45485 | ||||||||
\(967\) | 27907.0i | 0.928054i | 0.885821 | + | 0.464027i | \(0.153596\pi\) | ||||
−0.885821 | + | 0.464027i | \(0.846404\pi\) | |||||||
\(968\) | − 29475.0i | − 0.978680i | ||||||||
\(969\) | 67914.0i | 2.25151i | ||||||||
\(970\) | 2450.00i | 0.0810977i | ||||||||
\(971\) | −16443.0 | −0.543441 | −0.271720 | − | 0.962376i | \(-0.587593\pi\) | ||||
−0.271720 | + | 0.962376i | \(0.587593\pi\) | |||||||
\(972\) | −83776.0 | −2.76452 | ||||||||
\(973\) | 24297.0i | 0.800541i | ||||||||
\(974\) | −11400.0 | −0.375030 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4984.00 | −0.163457 | ||||||||
\(977\) | 45414.0i | 1.48713i | 0.668666 | + | 0.743563i | \(0.266866\pi\) | ||||
−0.668666 | + | 0.743563i | \(0.733134\pi\) | |||||||
\(978\) | −19040.0 | −0.622528 | ||||||||
\(979\) | −30940.0 | −1.01006 | ||||||||
\(980\) | − 20706.0i | − 0.674927i | ||||||||
\(981\) | − 8206.00i | − 0.267072i | ||||||||
\(982\) | − 83835.0i | − 2.72432i | ||||||||
\(983\) | − 8981.00i | − 0.291403i | −0.989329 | − | 0.145702i | \(-0.953456\pi\) | ||||
0.989329 | − | 0.145702i | \(-0.0465440\pi\) | |||||||
\(984\) | 105840. | 3.42892 | ||||||||
\(985\) | 20937.0 | 0.677267 | ||||||||
\(986\) | 31570.0i | 1.01967i | ||||||||
\(987\) | 9555.00 | 0.308145 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19296.0 | 0.620402 | ||||||||
\(990\) | 20020.0i | 0.642704i | ||||||||
\(991\) | −17414.0 | −0.558198 | −0.279099 | − | 0.960262i | \(-0.590036\pi\) | ||||
−0.279099 | + | 0.960262i | \(0.590036\pi\) | |||||||
\(992\) | 16660.0 | 0.533221 | ||||||||
\(993\) | 67928.0i | 2.17083i | ||||||||
\(994\) | − 585.000i | − 0.0186671i | ||||||||
\(995\) | 490.000i | 0.0156121i | ||||||||
\(996\) | 36652.0i | 1.16603i | ||||||||
\(997\) | −23702.0 | −0.752909 | −0.376454 | − | 0.926435i | \(-0.622857\pi\) | ||||
−0.376454 | + | 0.926435i | \(0.622857\pi\) | |||||||
\(998\) | 64200.0 | 2.03629 | ||||||||
\(999\) | − 4585.00i | − 0.145208i |
(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 | 169.4.b.a.168.2 | 2 | ||
13.2 | odd | 12 | 169.4.c.a.22.1 | 2 | |||
13.3 | even | 3 | 169.4.e.e.147.1 | 4 | |||
13.4 | even | 6 | 169.4.e.e.23.1 | 4 | |||
13.5 | odd | 4 | 169.4.a.e.1.1 | 1 | |||
13.6 | odd | 12 | 169.4.c.a.146.1 | 2 | |||
13.7 | odd | 12 | 169.4.c.e.146.1 | 2 | |||
13.8 | odd | 4 | 13.4.a.a.1.1 | ✓ | 1 | ||
13.9 | even | 3 | 169.4.e.e.23.2 | 4 | |||
13.10 | even | 6 | 169.4.e.e.147.2 | 4 | |||
13.11 | odd | 12 | 169.4.c.e.22.1 | 2 | |||
13.12 | even | 2 | inner | 169.4.b.a.168.1 | 2 | ||
39.5 | even | 4 | 1521.4.a.a.1.1 | 1 | |||
39.8 | even | 4 | 117.4.a.b.1.1 | 1 | |||
52.47 | even | 4 | 208.4.a.g.1.1 | 1 | |||
65.8 | even | 4 | 325.4.b.b.274.2 | 2 | |||
65.34 | odd | 4 | 325.4.a.d.1.1 | 1 | |||
65.47 | even | 4 | 325.4.b.b.274.1 | 2 | |||
91.34 | even | 4 | 637.4.a.a.1.1 | 1 | |||
104.21 | odd | 4 | 832.4.a.r.1.1 | 1 | |||
104.99 | even | 4 | 832.4.a.a.1.1 | 1 | |||
143.21 | even | 4 | 1573.4.a.a.1.1 | 1 | |||
156.47 | odd | 4 | 1872.4.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.a.1.1 | ✓ | 1 | 13.8 | odd | 4 | ||
117.4.a.b.1.1 | 1 | 39.8 | even | 4 | |||
169.4.a.e.1.1 | 1 | 13.5 | odd | 4 | |||
169.4.b.a.168.1 | 2 | 13.12 | even | 2 | inner | ||
169.4.b.a.168.2 | 2 | 1.1 | even | 1 | trivial | ||
169.4.c.a.22.1 | 2 | 13.2 | odd | 12 | |||
169.4.c.a.146.1 | 2 | 13.6 | odd | 12 | |||
169.4.c.e.22.1 | 2 | 13.11 | odd | 12 | |||
169.4.c.e.146.1 | 2 | 13.7 | odd | 12 | |||
169.4.e.e.23.1 | 4 | 13.4 | even | 6 | |||
169.4.e.e.23.2 | 4 | 13.9 | even | 3 | |||
169.4.e.e.147.1 | 4 | 13.3 | even | 3 | |||
169.4.e.e.147.2 | 4 | 13.10 | even | 6 | |||
208.4.a.g.1.1 | 1 | 52.47 | even | 4 | |||
325.4.a.d.1.1 | 1 | 65.34 | odd | 4 | |||
325.4.b.b.274.1 | 2 | 65.47 | even | 4 | |||
325.4.b.b.274.2 | 2 | 65.8 | even | 4 | |||
637.4.a.a.1.1 | 1 | 91.34 | even | 4 | |||
832.4.a.a.1.1 | 1 | 104.99 | even | 4 | |||
832.4.a.r.1.1 | 1 | 104.21 | odd | 4 | |||
1521.4.a.a.1.1 | 1 | 39.5 | even | 4 | |||
1573.4.a.a.1.1 | 1 | 143.21 | even | 4 | |||
1872.4.a.k.1.1 | 1 | 156.47 | odd | 4 |