Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,3,Mod(449,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.d (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: | \(109.864042590\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 8x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.3 | ||
Root | \(-1.16372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.449 |
Dual form | 4032.3.d.j.449.2 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | 6.06910i | 1.21382i | 0.794770 | + | 0.606910i | \(0.207591\pi\) | ||||
−0.794770 | + | 0.606910i | \(0.792409\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.64575 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 12.1382i | − 1.10347i | −0.834019 | − | 0.551736i | \(-0.813965\pi\) | ||||
0.834019 | − | 0.551736i | \(-0.186035\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18.5830 | 1.42946 | 0.714731 | − | 0.699399i | \(-0.246549\pi\) | ||||
0.714731 | + | 0.699399i | \(0.246549\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 10.9015i | − 0.641262i | −0.947204 | − | 0.320631i | \(-0.896105\pi\) | ||||
0.947204 | − | 0.320631i | \(-0.103895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 20.0000 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.1382i | 0.527748i | 0.964557 | + | 0.263874i | \(0.0850003\pi\) | ||||
−0.964557 | + | 0.263874i | \(0.915000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.8340 | −0.473360 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 41.8367i | − 1.44264i | −0.692600 | − | 0.721322i | \(-0.743535\pi\) | ||||
0.692600 | − | 0.721322i | \(-0.256465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −25.1660 | −0.811807 | −0.405903 | − | 0.913916i | \(-0.633043\pi\) | ||||
−0.405903 | + | 0.913916i | \(0.633043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.0573i | 0.458781i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −38.0000 | −1.02703 | −0.513514 | − | 0.858082i | \(-0.671656\pi\) | ||||
−0.513514 | + | 0.858082i | \(0.671656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 60.6337i | − 1.47887i | −0.673227 | − | 0.739435i | \(-0.735092\pi\) | ||||
0.673227 | − | 0.739435i | \(-0.264908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 83.4980 | 1.94181 | 0.970907 | − | 0.239455i | \(-0.0769689\pi\) | ||||
0.970907 | + | 0.239455i | \(0.0769689\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.9706i | 0.361076i | 0.983568 | + | 0.180538i | \(0.0577838\pi\) | ||||
−0.983568 | + | 0.180538i | \(0.942216\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 94.0424i | − 1.77439i | −0.461399 | − | 0.887193i | \(-0.652652\pi\) | ||||
0.461399 | − | 0.887193i | \(-0.347348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 73.6680 | 1.33942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 58.2175i | − 0.986738i | −0.869820 | − | 0.493369i | \(-0.835765\pi\) | ||||
0.869820 | − | 0.493369i | \(-0.164235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.6680 | −0.256852 | −0.128426 | − | 0.991719i | \(-0.540992\pi\) | ||||
−0.128426 | + | 0.991719i | \(0.540992\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 112.782i | 1.73511i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −132.664 | −1.98006 | −0.990030 | − | 0.140856i | \(-0.955015\pi\) | ||||
−0.990030 | + | 0.140856i | \(0.955015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1382i | 0.170961i | 0.996340 | + | 0.0854803i | \(0.0272425\pi\) | ||||
−0.996340 | + | 0.0854803i | \(0.972758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.9150 | −1.05363 | −0.526815 | − | 0.849980i | \(-0.676614\pi\) | ||||
−0.526815 | + | 0.849980i | \(0.676614\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 32.1147i | − 0.417074i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33.6680 | −0.426177 | −0.213088 | − | 0.977033i | \(-0.568352\pi\) | ||||
−0.213088 | + | 0.977033i | \(0.568352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 60.5764i | − 0.729836i | −0.931040 | − | 0.364918i | \(-0.881097\pi\) | ||||
0.931040 | − | 0.364918i | \(-0.118903\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 66.1621 | 0.778377 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 4.77506i | − 0.0536523i | −0.999640 | − | 0.0268262i | \(-0.991460\pi\) | ||||
0.999640 | − | 0.0268262i | \(-0.00854006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49.1660 | 0.540286 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 121.382i | 1.27771i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −188.413 | −1.94240 | −0.971201 | − | 0.238260i | \(-0.923423\pi\) | ||||
−0.971201 | + | 0.238260i | \(0.923423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 106.713i | − 1.05656i | −0.849069 | − | 0.528282i | \(-0.822836\pi\) | ||||
0.849069 | − | 0.528282i | \(-0.177164\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −131.498 | −1.27668 | −0.638340 | − | 0.769755i | \(-0.720379\pi\) | ||||
−0.638340 | + | 0.769755i | \(0.720379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 82.3793i | 0.769900i | 0.922937 | + | 0.384950i | \(0.125781\pi\) | ||||
−0.922937 | + | 0.384950i | \(0.874219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −33.8301 | −0.310367 | −0.155184 | − | 0.987886i | \(-0.549597\pi\) | ||||
−0.155184 | + | 0.987886i | \(0.549597\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 28.5190i | − 0.252381i | −0.992006 | − | 0.126190i | \(-0.959725\pi\) | ||||
0.992006 | − | 0.126190i | \(-0.0402750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −73.6680 | −0.640591 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 28.8426i | − 0.242374i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26.3360 | −0.217653 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 79.9059i | 0.639247i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −129.668 | −1.02101 | −0.510504 | − | 0.859875i | \(-0.670541\pi\) | ||||
−0.510504 | + | 0.859875i | \(0.670541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 148.017i | − 1.12990i | −0.825124 | − | 0.564952i | \(-0.808895\pi\) | ||||
0.825124 | − | 0.564952i | \(-0.191105\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 52.9150 | 0.397857 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 76.9573i | − 0.561732i | −0.959747 | − | 0.280866i | \(-0.909378\pi\) | ||||
0.959747 | − | 0.280866i | \(-0.0906216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 217.328 | 1.56351 | 0.781756 | − | 0.623585i | \(-0.214324\pi\) | ||||
0.781756 | + | 0.623585i | \(0.214324\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 225.564i | − 1.57737i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 253.911 | 1.75111 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 161.925i | − 1.08674i | −0.839492 | − | 0.543371i | \(-0.817148\pi\) | ||||
0.839492 | − | 0.543371i | \(-0.182852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 93.1660 | 0.616993 | 0.308497 | − | 0.951225i | \(-0.400174\pi\) | ||||
0.308497 | + | 0.951225i | \(0.400174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 152.735i | − 0.985388i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 184.996 | 1.17832 | 0.589159 | − | 0.808017i | \(-0.299459\pi\) | ||||
0.589159 | + | 0.808017i | \(0.299459\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 32.1147i | 0.199470i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 86.9961 | 0.533718 | 0.266859 | − | 0.963736i | \(-0.414014\pi\) | ||||
0.266859 | + | 0.963736i | \(0.414014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 60.5764i | − 0.362733i | −0.983416 | − | 0.181366i | \(-0.941948\pi\) | ||||
0.983416 | − | 0.181366i | \(-0.0580520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 176.328 | 1.04336 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 162.572i | − 0.939721i | −0.882741 | − | 0.469860i | \(-0.844304\pi\) | ||||
0.882741 | − | 0.469860i | \(-0.155696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −31.3098 | −0.178913 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 223.091i | 1.24632i | 0.782095 | + | 0.623159i | \(0.214151\pi\) | ||||
−0.782095 | + | 0.623159i | \(0.785849\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −188.915 | −1.04373 | −0.521865 | − | 0.853028i | \(-0.674763\pi\) | ||||
−0.521865 | + | 0.853028i | \(0.674763\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 230.626i | − 1.24663i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −132.324 | −0.707616 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 228.038i | 1.19391i | 0.802273 | + | 0.596957i | \(0.203624\pi\) | ||||
−0.802273 | + | 0.596957i | \(0.796376\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 134.000 | 0.694301 | 0.347150 | − | 0.937810i | \(-0.387149\pi\) | ||||
0.347150 | + | 0.937810i | \(0.387149\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 188.560i | 0.957157i | 0.878045 | + | 0.478579i | \(0.158848\pi\) | ||||
−0.878045 | + | 0.478579i | \(0.841152\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −102.494 | −0.515046 | −0.257523 | − | 0.966272i | \(-0.582906\pi\) | ||||
−0.257523 | + | 0.966272i | \(0.582906\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 110.689i | − 0.545268i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 367.992 | 1.79508 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 242.764i | − 1.16155i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −84.5020 | −0.400483 | −0.200242 | − | 0.979747i | \(-0.564173\pi\) | ||||
−0.200242 | + | 0.979747i | \(0.564173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 506.758i | 2.35701i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −66.5830 | −0.306834 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 202.582i | − 0.916660i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 158.494 | 0.710736 | 0.355368 | − | 0.934727i | \(-0.384356\pi\) | ||||
0.355368 | + | 0.934727i | \(0.384356\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 101.823i | 0.448561i | 0.974525 | + | 0.224281i | \(0.0720032\pi\) | ||||
−0.974525 | + | 0.224281i | \(0.927997\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 268.915 | 1.17430 | 0.587151 | − | 0.809478i | \(-0.300250\pi\) | ||||
0.587151 | + | 0.809478i | \(0.300250\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 26.2748i | − 0.112767i | −0.998409 | − | 0.0563836i | \(-0.982043\pi\) | ||||
0.998409 | − | 0.0563836i | \(-0.0179570\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −102.996 | −0.438281 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 92.2733i | − 0.386081i | −0.981191 | − | 0.193040i | \(-0.938165\pi\) | ||||
0.981191 | − | 0.193040i | \(-0.0618348\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 343.247 | 1.42426 | 0.712131 | − | 0.702047i | \(-0.247730\pi\) | ||||
0.712131 | + | 0.702047i | \(0.247730\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 42.4837i | 0.173403i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 371.660 | 1.50470 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 356.382i | 1.41985i | 0.704278 | + | 0.709924i | \(0.251271\pi\) | ||||
−0.704278 | + | 0.709924i | \(0.748729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 147.336 | 0.582356 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 254.730i | − 0.991169i | −0.868560 | − | 0.495584i | \(-0.834954\pi\) | ||||
0.868560 | − | 0.495584i | \(-0.165046\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −100.539 | −0.388180 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 261.979i | − 0.996117i | −0.867143 | − | 0.498059i | \(-0.834046\pi\) | ||||
0.867143 | − | 0.498059i | \(-0.165954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 570.753 | 2.15378 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 93.6246i | − 0.348047i | −0.984742 | − | 0.174023i | \(-0.944323\pi\) | ||||
0.984742 | − | 0.174023i | \(-0.0556768\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.16601 | −0.00430262 | −0.00215131 | − | 0.999998i | \(-0.500685\pi\) | ||||
−0.00215131 | + | 0.999998i | \(0.500685\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 143.643i | 0.522339i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.0000 | −0.115523 | −0.0577617 | − | 0.998330i | \(-0.518396\pi\) | ||||
−0.0577617 | + | 0.998330i | \(0.518396\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 166.757i | 0.593441i | 0.954964 | + | 0.296721i | \(0.0958930\pi\) | ||||
−0.954964 | + | 0.296721i | \(0.904107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.3399 | 0.0577381 | 0.0288691 | − | 0.999583i | \(-0.490809\pi\) | ||||
0.0288691 | + | 0.999583i | \(0.490809\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 160.422i | − 0.558961i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 170.158 | 0.588782 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 368.921i | − 1.25912i | −0.776953 | − | 0.629558i | \(-0.783236\pi\) | ||||
0.776953 | − | 0.629558i | \(-0.216764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 353.328 | 1.19772 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 225.564i | 0.754396i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 220.915 | 0.733937 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 95.0906i | − 0.311772i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −192.664 | −0.627570 | −0.313785 | − | 0.949494i | \(-0.601597\pi\) | ||||
−0.313785 | + | 0.949494i | \(0.601597\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 131.276i | − 0.422109i | −0.977474 | − | 0.211055i | \(-0.932310\pi\) | ||||
0.977474 | − | 0.211055i | \(-0.0676898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 43.3281 | 0.138428 | 0.0692142 | − | 0.997602i | \(-0.477951\pi\) | ||||
0.0692142 | + | 0.997602i | \(0.477951\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 251.724i | 0.794083i | 0.917801 | + | 0.397042i | \(0.129963\pi\) | ||||
−0.917801 | + | 0.397042i | \(0.870037\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −507.822 | −1.59192 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 218.029i | − 0.675013i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −219.911 | −0.676650 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 44.8999i | 0.136474i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 361.490 | 1.09212 | 0.546058 | − | 0.837748i | \(-0.316128\pi\) | ||||
0.546058 | + | 0.837748i | \(0.316128\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 805.151i | − 2.40344i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −298.834 | −0.886748 | −0.443374 | − | 0.896337i | \(-0.646219\pi\) | ||||
−0.443374 | + | 0.896337i | \(0.646219\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 305.470i | 0.895807i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 206.120i | 0.594006i | 0.954876 | + | 0.297003i | \(0.0959872\pi\) | ||||
−0.954876 | + | 0.297003i | \(0.904013\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −434.324 | −1.24448 | −0.622241 | − | 0.782826i | \(-0.713778\pi\) | ||||
−0.622241 | + | 0.782826i | \(0.713778\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 185.439i | − 0.525324i | −0.964888 | − | 0.262662i | \(-0.915400\pi\) | ||||
0.964888 | − | 0.262662i | \(-0.0846005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −73.6680 | −0.207515 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 516.767i | 1.43946i | 0.694254 | + | 0.719731i | \(0.255735\pi\) | ||||
−0.694254 | + | 0.719731i | \(0.744265\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.0000 | 0.108033 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 466.805i | − 1.27892i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 117.490 | 0.320137 | 0.160068 | − | 0.987106i | \(-0.448829\pi\) | ||||
0.160068 | + | 0.987106i | \(0.448829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 248.813i | − 0.670655i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 402.664 | 1.07953 | 0.539764 | − | 0.841816i | \(-0.318513\pi\) | ||||
0.539764 | + | 0.841816i | \(0.318513\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 777.451i | − 2.06221i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 398.834 | 1.05233 | 0.526166 | − | 0.850382i | \(-0.323629\pi\) | ||||
0.526166 | + | 0.850382i | \(0.323629\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 744.804i | − 1.94466i | −0.233614 | − | 0.972329i | \(-0.575055\pi\) | ||||
0.233614 | − | 0.972329i | \(-0.424945\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 194.907 | 0.506252 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 535.162i | 1.37574i | 0.725834 | + | 0.687869i | \(0.241454\pi\) | ||||
−0.725834 | + | 0.687869i | \(0.758546\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 132.324 | 0.338425 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 204.334i | − 0.517302i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 94.3241 | 0.237592 | 0.118796 | − | 0.992919i | \(-0.462096\pi\) | ||||
0.118796 | + | 0.992919i | \(0.462096\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 103.593i | − 0.258335i | −0.991623 | − | 0.129168i | \(-0.958769\pi\) | ||||
0.991623 | − | 0.129168i | \(-0.0412306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −467.660 | −1.16045 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 461.252i | 1.13330i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.75689 | −0.0238555 | −0.0119277 | − | 0.999929i | \(-0.503797\pi\) | ||||
−0.0119277 | + | 0.999929i | \(0.503797\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 154.029i | − 0.372952i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 367.644 | 0.885890 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 339.411i | 0.810051i | 0.914305 | + | 0.405025i | \(0.132737\pi\) | ||||
−0.914305 | + | 0.405025i | \(0.867263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 599.320 | 1.42356 | 0.711782 | − | 0.702401i | \(-0.247889\pi\) | ||||
0.711782 | + | 0.702401i | \(0.247889\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 129.008i | 0.303548i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.4536 | −0.0970810 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 710.978i | − 1.64960i | −0.565424 | − | 0.824800i | \(-0.691288\pi\) | ||||
0.565424 | − | 0.824800i | \(-0.308712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 377.984 | 0.872943 | 0.436471 | − | 0.899718i | \(-0.356228\pi\) | ||||
0.436471 | + | 0.899718i | \(0.356228\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 242.764i | 0.555524i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −528.146 | −1.20307 | −0.601533 | − | 0.798848i | \(-0.705443\pi\) | ||||
−0.601533 | + | 0.798848i | \(0.705443\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.6438i | 0.0827174i | 0.999144 | + | 0.0413587i | \(0.0131686\pi\) | ||||
−0.999144 | + | 0.0413587i | \(0.986831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.9803 | 0.0651243 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 397.612i | − 0.885550i | −0.896633 | − | 0.442775i | \(-0.853994\pi\) | ||||
0.896633 | − | 0.442775i | \(-0.146006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −735.984 | −1.63189 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 298.393i | 0.655810i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 344.324 | 0.753445 | 0.376722 | − | 0.926326i | \(-0.377051\pi\) | ||||
0.376722 | + | 0.926326i | \(0.377051\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 370.936i | 0.804634i | 0.915500 | + | 0.402317i | \(0.131795\pi\) | ||||
−0.915500 | + | 0.402317i | \(0.868205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −78.3320 | −0.169184 | −0.0845918 | − | 0.996416i | \(-0.526959\pi\) | ||||
−0.0845918 | + | 0.996416i | \(0.526959\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 399.758i | − 0.856014i | −0.903775 | − | 0.428007i | \(-0.859216\pi\) | ||||
0.903775 | − | 0.428007i | \(-0.140784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −350.996 | −0.748392 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 1013.52i | − 2.14274i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −236.680 | −0.498273 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 703.328i | 1.46833i | 0.678973 | + | 0.734163i | \(0.262425\pi\) | ||||
−0.678973 | + | 0.734163i | \(0.737575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −706.154 | −1.46810 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1143.50i | − 2.35773i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 82.5098 | 0.169425 | 0.0847124 | − | 0.996405i | \(-0.473003\pi\) | ||||
0.0847124 | + | 0.996405i | \(0.473003\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 184.203i | − 0.375158i | −0.982249 | − | 0.187579i | \(-0.939936\pi\) | ||||
0.982249 | − | 0.187579i | \(-0.0600641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −456.081 | −0.925114 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.1147i | 0.0646170i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 752.810 | 1.50864 | 0.754319 | − | 0.656508i | \(-0.227967\pi\) | ||||
0.754319 | + | 0.656508i | \(0.227967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 662.540i | 1.31718i | 0.752504 | + | 0.658588i | \(0.228846\pi\) | ||||
−0.752504 | + | 0.658588i | \(0.771154\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 647.652 | 1.28248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 949.115i | − 1.86467i | −0.361601 | − | 0.932333i | \(-0.617770\pi\) | ||||
0.361601 | − | 0.932333i | \(-0.382230\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −203.498 | −0.398235 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 798.075i | − 1.54966i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 205.992 | 0.398437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 714.344i | 1.37110i | 0.728025 | + | 0.685551i | \(0.240439\pi\) | ||||
−0.728025 | + | 0.685551i | \(0.759561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −232.000 | −0.443595 | −0.221797 | − | 0.975093i | \(-0.571192\pi\) | ||||
−0.221797 | + | 0.975093i | \(0.571192\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 274.346i | 0.520581i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 381.664 | 0.721482 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1126.76i | − 2.11399i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −499.969 | −0.934521 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 84.9674i | − 0.157639i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −165.668 | −0.306225 | −0.153113 | − | 0.988209i | \(-0.548930\pi\) | ||||
−0.153113 | + | 0.988209i | \(0.548930\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 205.318i | − 0.376730i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 295.676 | 0.540541 | 0.270270 | − | 0.962784i | \(-0.412887\pi\) | ||||
0.270270 | + | 0.962784i | \(0.412887\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 836.734i | − 1.51857i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −89.0771 | −0.161080 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 76.8426i | − 0.137958i | −0.997618 | − | 0.0689790i | \(-0.978026\pi\) | ||||
0.997618 | − | 0.0689790i | \(-0.0219742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1551.64 | 2.77575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1016.33i | 1.80521i | 0.430470 | + | 0.902605i | \(0.358348\pi\) | ||||
−0.430470 | + | 0.902605i | \(0.641652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 173.085 | 0.306345 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 586.533i | − 1.03081i | −0.856946 | − | 0.515406i | \(-0.827641\pi\) | ||||
0.856946 | − | 0.515406i | \(-0.172359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 951.644 | 1.66663 | 0.833314 | − | 0.552800i | \(-0.186441\pi\) | ||||
0.833314 | + | 0.552800i | \(0.186441\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 143.643i | − 0.249815i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −148.672 | −0.257664 | −0.128832 | − | 0.991666i | \(-0.541123\pi\) | ||||
−0.128832 | + | 0.991666i | \(0.541123\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 160.270i | − 0.275852i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1141.51 | −1.95799 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 332.564i | 0.566548i | 0.959039 | + | 0.283274i | \(0.0914206\pi\) | ||||
−0.959039 | + | 0.283274i | \(0.908579\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −503.320 | −0.854533 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 217.251i | 0.366359i | 0.983079 | + | 0.183180i | \(0.0586390\pi\) | ||||
−0.983079 | + | 0.183180i | \(0.941361\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 175.048 | 0.294199 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 172.179i | 0.287444i | 0.989618 | + | 0.143722i | \(0.0459072\pi\) | ||||
−0.989618 | + | 0.143722i | \(0.954093\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −418.000 | −0.695507 | −0.347754 | − | 0.937586i | \(-0.613055\pi\) | ||||
−0.347754 | + | 0.937586i | \(0.613055\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 159.836i | − 0.264191i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −627.158 | −1.03321 | −0.516605 | − | 0.856224i | \(-0.672804\pi\) | ||||
−0.516605 | + | 0.856224i | \(0.672804\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 315.364i | 0.516144i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 279.328 | 0.455674 | 0.227837 | − | 0.973699i | \(-0.426835\pi\) | ||||
0.227837 | + | 0.973699i | \(0.426835\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 358.380i | 0.580843i | 0.956899 | + | 0.290422i | \(0.0937955\pi\) | ||||
−0.956899 | + | 0.290422i | \(0.906204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −983.644 | −1.58909 | −0.794543 | − | 0.607208i | \(-0.792290\pi\) | ||||
−0.794543 | + | 0.607208i | \(0.792290\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 12.6336i | − 0.0202787i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −780.806 | −1.24929 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 414.256i | 0.658594i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 298.996 | 0.473845 | 0.236922 | − | 0.971529i | \(-0.423861\pi\) | ||||
0.236922 | + | 0.971529i | \(0.423861\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 786.968i | − 1.23932i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 130.081 | 0.204209 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 311.957i | − 0.486672i | −0.969942 | − | 0.243336i | \(-0.921758\pi\) | ||||
0.969942 | − | 0.243336i | \(-0.0782418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −604.000 | −0.939347 | −0.469673 | − | 0.882840i | \(-0.655628\pi\) | ||||
−0.469673 | + | 0.882840i | \(0.655628\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 179.600i | − 0.277588i | −0.990321 | − | 0.138794i | \(-0.955677\pi\) | ||||
0.990321 | − | 0.138794i | \(-0.0443226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −706.656 | −1.08884 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 481.892i | − 0.737966i | −0.929436 | − | 0.368983i | \(-0.879706\pi\) | ||||
0.929436 | − | 0.368983i | \(-0.120294\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 898.332 | 1.37150 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 877.408i | 1.33142i | 0.746209 | + | 0.665711i | \(0.231872\pi\) | ||||
−0.746209 | + | 0.665711i | \(0.768128\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 521.644 | 0.789175 | 0.394587 | − | 0.918858i | \(-0.370888\pi\) | ||||
0.394587 | + | 0.918858i | \(0.370888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 321.147i | 0.482927i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 507.822 | 0.761353 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 190.181i | 0.283429i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −659.992 | −0.980672 | −0.490336 | − | 0.871534i | \(-0.663126\pi\) | ||||
−0.490336 | + | 0.871534i | \(0.663126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1016.28i | − 1.50115i | −0.660787 | − | 0.750573i | \(-0.729778\pi\) | ||||
0.660787 | − | 0.750573i | \(-0.270222\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −498.494 | −0.734159 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 235.114i | − 0.344238i | −0.985076 | − | 0.172119i | \(-0.944939\pi\) | ||||
0.985076 | − | 0.172119i | \(-0.0550613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 467.061 | 0.681841 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 1747.59i | − 2.53642i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −50.9803 | −0.0737776 | −0.0368888 | − | 0.999319i | \(-0.511745\pi\) | ||||
−0.0368888 | + | 0.999319i | \(0.511745\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1318.99i | 1.89782i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −660.996 | −0.948344 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 141.530i | − 0.201898i | −0.994892 | − | 0.100949i | \(-0.967812\pi\) | ||||
0.994892 | − | 0.100949i | \(-0.0321879\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −760.000 | −1.08108 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 282.336i | − 0.399344i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 55.4980 | 0.0782765 | 0.0391382 | − | 0.999234i | \(-0.487539\pi\) | ||||
0.0391382 | + | 0.999234i | \(0.487539\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 305.470i | − 0.428429i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1368.97 | 1.91465 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1009.03i | 1.40338i | 0.712484 | + | 0.701688i | \(0.247570\pi\) | ||||
−0.712484 | + | 0.701688i | \(0.752430\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −347.911 | −0.482540 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 495.095i | 0.682890i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 365.182 | 0.502313 | 0.251157 | − | 0.967946i | \(-0.419189\pi\) | ||||
0.251157 | + | 0.967946i | \(0.419189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 910.251i | − 1.24521i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 353.077 | 0.481688 | 0.240844 | − | 0.970564i | \(-0.422576\pi\) | ||||
0.240844 | + | 0.970564i | \(0.422576\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1610.30i | 2.18494i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 329.684 | 0.446121 | 0.223061 | − | 0.974805i | \(-0.428395\pi\) | ||||
0.223061 | + | 0.974805i | \(0.428395\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 112.061i | 0.150822i | 0.997153 | + | 0.0754112i | \(0.0240270\pi\) | ||||
−0.997153 | + | 0.0754112i | \(0.975973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 982.737 | 1.31911 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 217.955i | 0.290995i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 144.826 | 0.192844 | 0.0964222 | − | 0.995341i | \(-0.469260\pi\) | ||||
0.0964222 | + | 0.995341i | \(0.469260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 565.434i | 0.748919i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −78.1699 | −0.103263 | −0.0516314 | − | 0.998666i | \(-0.516442\pi\) | ||||
−0.0516314 | + | 0.998666i | \(0.516442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1465.50i | 1.92576i | 0.269928 | + | 0.962880i | \(0.413000\pi\) | ||||
−0.269928 | + | 0.962880i | \(0.587000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −89.5059 | −0.117308 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 1081.86i | − 1.41050i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 729.320 | 0.948401 | 0.474200 | − | 0.880417i | \(-0.342737\pi\) | ||||
0.474200 | + | 0.880417i | \(0.342737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 434.559i | 0.562172i | 0.959683 | + | 0.281086i | \(0.0906947\pi\) | ||||
−0.959683 | + | 0.281086i | \(0.909305\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 297.814 | 0.384277 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1212.67i | − 1.55671i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 147.336 | 0.188650 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1122.76i | 1.43027i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3517 | −0.0195066 | −0.00975331 | − | 0.999952i | \(-0.503105\pi\) | ||||
−0.00975331 | + | 0.999952i | \(0.503105\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 75.4543i | − 0.0953910i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −291.158 | −0.367160 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1043.48i | 1.30927i | 0.755947 | + | 0.654633i | \(0.227177\pi\) | ||||
−0.755947 | + | 0.654633i | \(0.772823\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 185.004 | 0.231544 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 933.610i | 1.16265i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −194.907 | −0.242121 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1041.31i | 1.28716i | 0.765378 | + | 0.643581i | \(0.222552\pi\) | ||||
−0.765378 | + | 0.643581i | \(0.777448\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 502.316 | 0.619379 | 0.309689 | − | 0.950838i | \(-0.399775\pi\) | ||||
0.309689 | + | 0.950838i | \(0.399775\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 527.988i | 0.647838i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1669.96 | 2.04402 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.1137i | 0.0281531i | 0.999901 | + | 0.0140765i | \(0.00448085\pi\) | ||||
−0.999901 | + | 0.0140765i | \(0.995519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 600.664 | 0.729847 | 0.364923 | − | 0.931038i | \(-0.381095\pi\) | ||||
0.364923 | + | 0.931038i | \(0.381095\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1309.21i | − 1.58308i | −0.611118 | − | 0.791540i | \(-0.709280\pi\) | ||||
0.611118 | − | 0.791540i | \(-0.290720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 621.919 | 0.750204 | 0.375102 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375102 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 76.3102i | − 0.0916089i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 367.644 | 0.440293 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1190.30i | − 1.41871i | −0.704851 | − | 0.709355i | \(-0.748986\pi\) | ||||
0.704851 | − | 0.709355i | \(-0.251014\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −909.308 | −1.08122 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1070.15i | 1.26645i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −69.6784 | −0.0822649 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 461.252i | − 0.542011i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −137.012 | −0.160623 | −0.0803117 | − | 0.996770i | \(-0.525592\pi\) | ||||
−0.0803117 | + | 0.996770i | \(0.525592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 466.141i | 0.543922i | 0.962308 | + | 0.271961i | \(0.0876722\pi\) | ||||
−0.962308 | + | 0.271961i | \(0.912328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.9843 | 0.0279211 | 0.0139606 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139606 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 0.114603i | 0 0.000132796i | −1.00000 | 6.63982e-5i | \(-0.999979\pi\) | |||||
1.00000 | 6.63982e-5i | \(-2.11352e-5\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 986.664 | 1.14065 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 408.669i | 0.470275i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2465.30 | −2.83042 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 211.411i | 0.241613i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −997.304 | −1.13718 | −0.568589 | − | 0.822622i | \(-0.692510\pi\) | ||||
−0.568589 | + | 0.822622i | \(0.692510\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 935.649i | 1.06203i | 0.847362 | + | 0.531015i | \(0.178189\pi\) | ||||
−0.847362 | + | 0.531015i | \(0.821811\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1549.47 | −1.75478 | −0.877392 | − | 0.479774i | \(-0.840719\pi\) | ||||
−0.877392 | + | 0.479774i | \(0.840719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 894.493i | 1.00845i | 0.863573 | + | 0.504224i | \(0.168221\pi\) | ||||
−0.863573 | + | 0.504224i | \(0.831779\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −343.069 | −0.385905 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 339.411i | 0.380080i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1353.96 | −1.51281 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1052.86i | 1.17115i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1025.20 | −1.13785 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1146.54i | − 1.26690i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −135.838 | −0.149766 | −0.0748831 | − | 0.997192i | \(-0.523858\pi\) | ||||
−0.0748831 | + | 0.997192i | \(0.523858\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1242.01i | 1.36335i | 0.731655 | + | 0.681675i | \(0.238748\pi\) | ||||
−0.731655 | + | 0.681675i | \(0.761252\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −735.289 | −0.805355 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 391.617i | − 0.427063i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 388.162 | 0.422374 | 0.211187 | − | 0.977446i | \(-0.432267\pi\) | ||||
0.211187 | + | 0.977446i | \(0.432267\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 225.564i | 0.244382i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 449.692 | 0.486153 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 621.694i | − 0.669207i | −0.942359 | − | 0.334604i | \(-0.891398\pi\) | ||||
0.942359 | − | 0.334604i | \(-0.108602\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 140.000 | 0.150376 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 803.089i | − 0.858918i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1262.00 | 1.34685 | 0.673426 | − | 0.739255i | \(-0.264822\pi\) | ||||
0.673426 | + | 0.739255i | \(0.264822\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 672.410i | − 0.714569i | −0.933996 | − | 0.357285i | \(-0.883703\pi\) | ||||
0.933996 | − | 0.357285i | \(-0.116297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 735.984 | 0.780471 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1159.75i | 1.22465i | 0.790605 | + | 0.612327i | \(0.209766\pi\) | ||||
−0.790605 | + | 0.612327i | \(0.790234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1429.31 | −1.50612 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 163.104i | − 0.171148i | −0.996332 | − | 0.0855740i | \(-0.972728\pi\) | ||||
0.996332 | − | 0.0855740i | \(-0.0272724\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1383.98 | −1.44920 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 203.610i | − 0.212315i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −327.672 | −0.340970 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 813.260i | 0.842756i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −887.012 | −0.917282 | −0.458641 | − | 0.888622i | \(-0.651664\pi\) | ||||
−0.458641 | + | 0.888622i | \(0.651664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1416.32i | − 1.45862i | −0.684183 | − | 0.729310i | \(-0.739841\pi\) | ||||
0.684183 | − | 0.729310i | \(-0.260159\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 574.996 | 0.590952 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 339.051i | 0.347032i | 0.984831 | + | 0.173516i | \(0.0555129\pi\) | ||||
−0.984831 | + | 0.173516i | \(0.944487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57.9606 | −0.0592039 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 487.887i | 0.496324i | 0.968718 | + | 0.248162i | \(0.0798266\pi\) | ||||
−0.968718 | + | 0.248162i | \(0.920173\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1144.39 | −1.16182 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1013.52i | 1.02479i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 937.474 | 0.945988 | 0.472994 | − | 0.881066i | \(-0.343173\pi\) | ||||
0.472994 | + | 0.881066i | \(0.343173\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 622.047i | − 0.625173i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −461.012 | −0.462399 | −0.231200 | − | 0.972906i | \(-0.574265\pi\) | ||||
−0.231200 | + | 0.972906i | \(0.574265\pi\) | |||||||
\(998\) | 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 | 4032.3.d.j.449.3 | 4 | ||
3.2 | odd | 2 | inner | 4032.3.d.j.449.2 | 4 | ||
4.3 | odd | 2 | 4032.3.d.i.449.3 | 4 | |||
8.3 | odd | 2 | 126.3.b.a.71.1 | ✓ | 4 | ||
8.5 | even | 2 | 1008.3.d.a.449.2 | 4 | |||
12.11 | even | 2 | 4032.3.d.i.449.2 | 4 | |||
24.5 | odd | 2 | 1008.3.d.a.449.3 | 4 | |||
24.11 | even | 2 | 126.3.b.a.71.4 | yes | 4 | ||
40.3 | even | 4 | 3150.3.c.b.449.4 | 8 | |||
40.19 | odd | 2 | 3150.3.e.e.701.4 | 4 | |||
40.27 | even | 4 | 3150.3.c.b.449.6 | 8 | |||
56.3 | even | 6 | 882.3.s.i.863.3 | 8 | |||
56.11 | odd | 6 | 882.3.s.e.863.4 | 8 | |||
56.19 | even | 6 | 882.3.s.i.557.2 | 8 | |||
56.27 | even | 2 | 882.3.b.f.197.2 | 4 | |||
56.51 | odd | 6 | 882.3.s.e.557.1 | 8 | |||
72.11 | even | 6 | 1134.3.q.c.701.3 | 8 | |||
72.43 | odd | 6 | 1134.3.q.c.701.2 | 8 | |||
72.59 | even | 6 | 1134.3.q.c.1079.2 | 8 | |||
72.67 | odd | 6 | 1134.3.q.c.1079.3 | 8 | |||
120.59 | even | 2 | 3150.3.e.e.701.2 | 4 | |||
120.83 | odd | 4 | 3150.3.c.b.449.7 | 8 | |||
120.107 | odd | 4 | 3150.3.c.b.449.1 | 8 | |||
168.11 | even | 6 | 882.3.s.e.863.1 | 8 | |||
168.59 | odd | 6 | 882.3.s.i.863.2 | 8 | |||
168.83 | odd | 2 | 882.3.b.f.197.3 | 4 | |||
168.107 | even | 6 | 882.3.s.e.557.4 | 8 | |||
168.131 | odd | 6 | 882.3.s.i.557.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.3.b.a.71.1 | ✓ | 4 | 8.3 | odd | 2 | ||
126.3.b.a.71.4 | yes | 4 | 24.11 | even | 2 | ||
882.3.b.f.197.2 | 4 | 56.27 | even | 2 | |||
882.3.b.f.197.3 | 4 | 168.83 | odd | 2 | |||
882.3.s.e.557.1 | 8 | 56.51 | odd | 6 | |||
882.3.s.e.557.4 | 8 | 168.107 | even | 6 | |||
882.3.s.e.863.1 | 8 | 168.11 | even | 6 | |||
882.3.s.e.863.4 | 8 | 56.11 | odd | 6 | |||
882.3.s.i.557.2 | 8 | 56.19 | even | 6 | |||
882.3.s.i.557.3 | 8 | 168.131 | odd | 6 | |||
882.3.s.i.863.2 | 8 | 168.59 | odd | 6 | |||
882.3.s.i.863.3 | 8 | 56.3 | even | 6 | |||
1008.3.d.a.449.2 | 4 | 8.5 | even | 2 | |||
1008.3.d.a.449.3 | 4 | 24.5 | odd | 2 | |||
1134.3.q.c.701.2 | 8 | 72.43 | odd | 6 | |||
1134.3.q.c.701.3 | 8 | 72.11 | even | 6 | |||
1134.3.q.c.1079.2 | 8 | 72.59 | even | 6 | |||
1134.3.q.c.1079.3 | 8 | 72.67 | odd | 6 | |||
3150.3.c.b.449.1 | 8 | 120.107 | odd | 4 | |||
3150.3.c.b.449.4 | 8 | 40.3 | even | 4 | |||
3150.3.c.b.449.6 | 8 | 40.27 | even | 4 | |||
3150.3.c.b.449.7 | 8 | 120.83 | odd | 4 | |||
3150.3.e.e.701.2 | 4 | 120.59 | even | 2 | |||
3150.3.e.e.701.4 | 4 | 40.19 | odd | 2 | |||
4032.3.d.i.449.2 | 4 | 12.11 | even | 2 | |||
4032.3.d.i.449.3 | 4 | 4.3 | odd | 2 | |||
4032.3.d.j.449.2 | 4 | 3.2 | odd | 2 | inner | ||
4032.3.d.j.449.3 | 4 | 1.1 | even | 1 | trivial |