Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 5.19615 | 0.464758 | 0.232379 | − | 0.972625i | \(-0.425349\pi\) | ||||
0.232379 | + | 0.972625i | \(0.425349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.3923 | 0.561132 | 0.280566 | − | 0.959835i | \(-0.409478\pi\) | ||||
0.280566 | + | 0.959835i | \(0.409478\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −51.9615 | −1.42427 | −0.712136 | − | 0.702042i | \(-0.752272\pi\) | ||||
−0.712136 | + | 0.702042i | \(0.752272\pi\) | |||||||
\(12\) | 24.0000 | 0.577350 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −15.5885 | −0.268328 | ||||||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | 117.000 | 1.66922 | 0.834608 | − | 0.550845i | \(-0.185694\pi\) | ||||
0.834608 | + | 0.550845i | \(0.185694\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.2487 | 0.292791 | 0.146396 | − | 0.989226i | \(-0.453233\pi\) | ||||
0.146396 | + | 0.989226i | \(0.453233\pi\) | |||||||
\(20\) | −41.5692 | −0.464758 | ||||||||
\(21\) | −31.1769 | −0.323970 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.0000 | −0.163185 | −0.0815926 | − | 0.996666i | \(-0.526001\pi\) | ||||
−0.0815926 | + | 0.996666i | \(0.526001\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −98.0000 | −0.784000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −83.1384 | −0.561132 | ||||||||
\(29\) | −99.0000 | −0.633925 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.990 | 1.12392 | 0.561961 | − | 0.827164i | \(-0.310047\pi\) | ||||
0.561961 | + | 0.827164i | \(0.310047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 155.885 | 0.822304 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 54.0000 | 0.260790 | ||||||||
\(36\) | −72.0000 | −0.333333 | ||||||||
\(37\) | −112.583 | −0.500232 | −0.250116 | − | 0.968216i | \(-0.580469\pi\) | ||||
−0.250116 | + | 0.968216i | \(0.580469\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −36.3731 | −0.138549 | −0.0692746 | − | 0.997598i | \(-0.522068\pi\) | ||||
−0.0692746 | + | 0.997598i | \(0.522068\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 82.0000 | 0.290811 | 0.145406 | − | 0.989372i | \(-0.453551\pi\) | ||||
0.145406 | + | 0.989372i | \(0.453551\pi\) | |||||||
\(44\) | 415.692 | 1.42427 | ||||||||
\(45\) | 46.7654 | 0.154919 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 72.7461 | 0.225768 | 0.112884 | − | 0.993608i | \(-0.463991\pi\) | ||||
0.112884 | + | 0.993608i | \(0.463991\pi\) | |||||||
\(48\) | −192.000 | −0.577350 | ||||||||
\(49\) | −235.000 | −0.685131 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −351.000 | −0.963722 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −261.000 | −0.676436 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −270.000 | −0.661942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −72.7461 | −0.169043 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −789.815 | −1.74280 | −0.871400 | − | 0.490574i | \(-0.836787\pi\) | ||||
−0.871400 | + | 0.490574i | \(0.836787\pi\) | |||||||
\(60\) | 124.708 | 0.268328 | ||||||||
\(61\) | −719.000 | −1.50916 | −0.754578 | − | 0.656210i | \(-0.772158\pi\) | ||||
−0.754578 | + | 0.656210i | \(0.772158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 93.5307 | 0.187044 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −703.213 | −1.28226 | −0.641128 | − | 0.767434i | \(-0.721533\pi\) | ||||
−0.641128 | + | 0.767434i | \(0.721533\pi\) | |||||||
\(68\) | −936.000 | −1.66922 | ||||||||
\(69\) | 54.0000 | 0.0942150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 467.654 | 0.781694 | 0.390847 | − | 0.920456i | \(-0.372182\pi\) | ||||
0.390847 | + | 0.920456i | \(0.372182\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −684.160 | −1.09692 | −0.548458 | − | 0.836178i | \(-0.684785\pi\) | ||||
−0.548458 | + | 0.836178i | \(0.684785\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 294.000 | 0.452643 | ||||||||
\(76\) | −193.990 | −0.292791 | ||||||||
\(77\) | −540.000 | −0.799204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −440.000 | −0.626631 | −0.313316 | − | 0.949649i | \(-0.601440\pi\) | ||||
−0.313316 | + | 0.949649i | \(0.601440\pi\) | |||||||
\(80\) | 332.554 | 0.464758 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1195.12 | 1.58049 | 0.790247 | − | 0.612789i | \(-0.209952\pi\) | ||||
0.790247 | + | 0.612789i | \(0.209952\pi\) | |||||||
\(84\) | 249.415 | 0.323970 | ||||||||
\(85\) | 607.950 | 0.775781 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 297.000 | 0.365997 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1517.28 | −1.80709 | −0.903545 | − | 0.428493i | \(-0.859045\pi\) | ||||
−0.903545 | + | 0.428493i | \(0.859045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 144.000 | 0.163185 | ||||||||
\(93\) | −581.969 | −0.648897 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 126.000 | 0.136077 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1157.01 | 1.21110 | 0.605549 | − | 0.795808i | \(-0.292953\pi\) | ||||
0.605549 | + | 0.795808i | \(0.292953\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −467.654 | −0.474757 | ||||||||
\(100\) | 784.000 | 0.784000 | ||||||||
\(101\) | −1575.00 | −1.55167 | −0.775833 | − | 0.630938i | \(-0.782670\pi\) | ||||
−0.775833 | + | 0.630938i | \(0.782670\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −794.000 | −0.759565 | −0.379782 | − | 0.925076i | \(-0.624001\pi\) | ||||
−0.379782 | + | 0.925076i | \(0.624001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −162.000 | −0.150567 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 450.000 | 0.406571 | 0.203286 | − | 0.979119i | \(-0.434838\pi\) | ||||
0.203286 | + | 0.979119i | \(0.434838\pi\) | |||||||
\(108\) | 216.000 | 0.192450 | ||||||||
\(109\) | 595.825 | 0.523576 | 0.261788 | − | 0.965125i | \(-0.415688\pi\) | ||||
0.261788 | + | 0.965125i | \(0.415688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 337.750 | 0.288809 | ||||||||
\(112\) | 665.108 | 0.561132 | ||||||||
\(113\) | −1701.00 | −1.41608 | −0.708038 | − | 0.706174i | \(-0.750420\pi\) | ||||
−0.708038 | + | 0.706174i | \(0.750420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −93.5307 | −0.0758416 | ||||||||
\(116\) | 792.000 | 0.633925 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1215.90 | 0.936650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1369.00 | 1.02855 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 109.119 | 0.0799914 | ||||||||
\(124\) | −1551.92 | −1.12392 | ||||||||
\(125\) | −1158.74 | −0.829128 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1664.00 | 1.16265 | 0.581323 | − | 0.813673i | \(-0.302535\pi\) | ||||
0.581323 | + | 0.813673i | \(0.302535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −246.000 | −0.167900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1476.00 | −0.984418 | −0.492209 | − | 0.870477i | \(-0.663810\pi\) | ||||
−0.492209 | + | 0.870477i | \(0.663810\pi\) | |||||||
\(132\) | −1247.08 | −0.822304 | ||||||||
\(133\) | 252.000 | 0.164295 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −140.296 | −0.0894427 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1013.25 | 0.631882 | 0.315941 | − | 0.948779i | \(-0.397680\pi\) | ||||
0.315941 | + | 0.948779i | \(0.397680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1124.00 | 0.685874 | 0.342937 | − | 0.939358i | \(-0.388578\pi\) | ||||
0.342937 | + | 0.939358i | \(0.388578\pi\) | |||||||
\(140\) | −432.000 | −0.260790 | ||||||||
\(141\) | −218.238 | −0.130347 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 576.000 | 0.333333 | ||||||||
\(145\) | −514.419 | −0.294622 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 705.000 | 0.395561 | ||||||||
\(148\) | 900.666 | 0.500232 | ||||||||
\(149\) | −3268.38 | −1.79702 | −0.898510 | − | 0.438952i | \(-0.855350\pi\) | ||||
−0.898510 | + | 0.438952i | \(0.855350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1638.52 | 0.883052 | 0.441526 | − | 0.897248i | \(-0.354437\pi\) | ||||
0.441526 | + | 0.897248i | \(0.354437\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1053.00 | 0.556405 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1008.00 | 0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1259.00 | 0.639995 | 0.319997 | − | 0.947418i | \(-0.396318\pi\) | ||||
0.319997 | + | 0.947418i | \(0.396318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 783.000 | 0.390540 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −187.061 | −0.0915684 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2951.41 | 1.41824 | 0.709118 | − | 0.705089i | \(-0.249093\pi\) | ||||
0.709118 | + | 0.705089i | \(0.249093\pi\) | |||||||
\(164\) | 290.985 | 0.138549 | ||||||||
\(165\) | 810.000 | 0.382172 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3138.48 | 1.45427 | 0.727133 | − | 0.686496i | \(-0.240852\pi\) | ||||
0.727133 | + | 0.686496i | \(0.240852\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 218.238 | 0.0975971 | ||||||||
\(172\) | −656.000 | −0.290811 | ||||||||
\(173\) | −4266.00 | −1.87479 | −0.937393 | − | 0.348273i | \(-0.886768\pi\) | ||||
−0.937393 | + | 0.348273i | \(0.886768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1018.45 | −0.439927 | ||||||||
\(176\) | −3325.54 | −1.42427 | ||||||||
\(177\) | 2369.45 | 1.00621 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3006.00 | −1.25519 | −0.627595 | − | 0.778540i | \(-0.715961\pi\) | ||||
−0.627595 | + | 0.778540i | \(0.715961\pi\) | |||||||
\(180\) | −374.123 | −0.154919 | ||||||||
\(181\) | 1873.00 | 0.769166 | 0.384583 | − | 0.923090i | \(-0.374345\pi\) | ||||
0.384583 | + | 0.923090i | \(0.374345\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2157.00 | 0.871312 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −585.000 | −0.232487 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6079.50 | −2.37742 | ||||||||
\(188\) | −581.969 | −0.225768 | ||||||||
\(189\) | −280.592 | −0.107990 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2736.00 | −1.03649 | −0.518246 | − | 0.855232i | \(-0.673415\pi\) | ||||
−0.518246 | + | 0.855232i | \(0.673415\pi\) | |||||||
\(192\) | 1536.00 | 0.577350 | ||||||||
\(193\) | 2603.27 | 0.970920 | 0.485460 | − | 0.874259i | \(-0.338652\pi\) | ||||
0.485460 | + | 0.874259i | \(0.338652\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1880.00 | 0.685131 | ||||||||
\(197\) | 3720.45 | 1.34554 | 0.672768 | − | 0.739853i | \(-0.265105\pi\) | ||||
0.672768 | + | 0.739853i | \(0.265105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1198.00 | −0.426754 | −0.213377 | − | 0.976970i | \(-0.568446\pi\) | ||||
−0.213377 | + | 0.976970i | \(0.568446\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2109.64 | 0.740310 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1028.84 | −0.355716 | ||||||||
\(204\) | 2808.00 | 0.963722 | ||||||||
\(205\) | −189.000 | −0.0643919 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −162.000 | −0.0543951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1260.00 | −0.417014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2392.00 | 0.780436 | 0.390218 | − | 0.920722i | \(-0.372400\pi\) | ||||
0.390218 | + | 0.920722i | \(0.372400\pi\) | |||||||
\(212\) | 2088.00 | 0.676436 | ||||||||
\(213\) | −1402.96 | −0.451311 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 426.084 | 0.135157 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2016.00 | 0.630668 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2052.48 | 0.633305 | ||||||||
\(220\) | 2160.00 | 0.661942 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2036.89 | −0.611661 | −0.305830 | − | 0.952086i | \(-0.598934\pi\) | ||||
−0.305830 | + | 0.952086i | \(0.598934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −882.000 | −0.261333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2151.21 | −0.628990 | −0.314495 | − | 0.949259i | \(-0.601835\pi\) | ||||
−0.314495 | + | 0.949259i | \(0.601835\pi\) | |||||||
\(228\) | 581.969 | 0.169043 | ||||||||
\(229\) | −3471.03 | −1.00162 | −0.500812 | − | 0.865556i | \(-0.666965\pi\) | ||||
−0.500812 | + | 0.865556i | \(0.666965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1620.00 | 0.461421 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1854.00 | 0.521286 | 0.260643 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260643 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 378.000 | 0.104928 | ||||||||
\(236\) | 6318.52 | 1.74280 | ||||||||
\(237\) | 1320.00 | 0.361786 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4458.30 | −1.20662 | −0.603312 | − | 0.797505i | \(-0.706153\pi\) | ||||
−0.603312 | + | 0.797505i | \(0.706153\pi\) | |||||||
\(240\) | −997.661 | −0.268328 | ||||||||
\(241\) | −417.424 | −0.111571 | −0.0557856 | − | 0.998443i | \(-0.517766\pi\) | ||||
−0.0557856 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 5752.00 | 1.50916 | ||||||||
\(245\) | −1221.10 | −0.318420 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3585.35 | −0.912498 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4104.00 | −1.03204 | −0.516020 | − | 0.856576i | \(-0.672587\pi\) | ||||
−0.516020 | + | 0.856576i | \(0.672587\pi\) | |||||||
\(252\) | −748.246 | −0.187044 | ||||||||
\(253\) | 935.307 | 0.232420 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1823.85 | −0.447898 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | −1989.00 | −0.482764 | −0.241382 | − | 0.970430i | \(-0.577601\pi\) | ||||
−0.241382 | + | 0.970430i | \(0.577601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1170.00 | −0.280696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −891.000 | −0.211308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 738.000 | 0.173031 | 0.0865153 | − | 0.996251i | \(-0.472427\pi\) | ||||
0.0865153 | + | 0.996251i | \(0.472427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1356.20 | −0.314379 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4551.83 | 1.04332 | ||||||||
\(268\) | 5625.70 | 1.28226 | ||||||||
\(269\) | −2106.00 | −0.477342 | −0.238671 | − | 0.971100i | \(-0.576712\pi\) | ||||
−0.238671 | + | 0.971100i | \(0.576712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −685.892 | −0.153745 | −0.0768727 | − | 0.997041i | \(-0.524493\pi\) | ||||
−0.0768727 | + | 0.997041i | \(0.524493\pi\) | |||||||
\(272\) | 7488.00 | 1.66922 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5092.23 | 1.11663 | ||||||||
\(276\) | −432.000 | −0.0942150 | ||||||||
\(277\) | −3665.00 | −0.794977 | −0.397488 | − | 0.917607i | \(-0.630118\pi\) | ||||
−0.397488 | + | 0.917607i | \(0.630118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1745.91 | 0.374641 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1719.93 | 0.365132 | 0.182566 | − | 0.983194i | \(-0.441560\pi\) | ||||
0.182566 | + | 0.983194i | \(0.441560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1826.00 | 0.383549 | 0.191775 | − | 0.981439i | \(-0.438576\pi\) | ||||
0.191775 | + | 0.981439i | \(0.438576\pi\) | |||||||
\(284\) | −3741.23 | −0.781694 | ||||||||
\(285\) | −378.000 | −0.0785642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −378.000 | −0.0777444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8776.00 | 1.78628 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3471.03 | −0.699228 | ||||||||
\(292\) | 5473.28 | 1.09692 | ||||||||
\(293\) | −504.027 | −0.100497 | −0.0502484 | − | 0.998737i | \(-0.516001\pi\) | ||||
−0.0502484 | + | 0.998737i | \(0.516001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4104.00 | −0.809980 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1402.96 | 0.274101 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −2352.00 | −0.452643 | ||||||||
\(301\) | 852.169 | 0.163183 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4725.00 | 0.895855 | ||||||||
\(304\) | 1551.92 | 0.292791 | ||||||||
\(305\) | −3736.03 | −0.701392 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1950.29 | −0.362570 | −0.181285 | − | 0.983431i | \(-0.558026\pi\) | ||||
−0.181285 | + | 0.983431i | \(0.558026\pi\) | |||||||
\(308\) | 4320.00 | 0.799204 | ||||||||
\(309\) | 2382.00 | 0.438535 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3798.00 | 0.692491 | 0.346246 | − | 0.938144i | \(-0.387456\pi\) | ||||
0.346246 | + | 0.938144i | \(0.387456\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1378.00 | 0.248847 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 486.000 | 0.0869302 | ||||||||
\(316\) | 3520.00 | 0.626631 | ||||||||
\(317\) | 7103.14 | 1.25852 | 0.629262 | − | 0.777193i | \(-0.283357\pi\) | ||||
0.629262 | + | 0.777193i | \(0.283357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5144.19 | 0.902882 | ||||||||
\(320\) | −2660.43 | −0.464758 | ||||||||
\(321\) | −1350.00 | −0.234734 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2837.10 | 0.488732 | ||||||||
\(324\) | −648.000 | −0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1787.48 | −0.302286 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 756.000 | 0.126686 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10073.6 | −1.67280 | −0.836398 | − | 0.548122i | \(-0.815343\pi\) | ||||
−0.836398 | + | 0.548122i | \(0.815343\pi\) | |||||||
\(332\) | −9560.92 | −1.58049 | ||||||||
\(333\) | −1013.25 | −0.166744 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3654.00 | −0.595938 | ||||||||
\(336\) | −1995.32 | −0.323970 | ||||||||
\(337\) | −9001.00 | −1.45494 | −0.727471 | − | 0.686138i | \(-0.759305\pi\) | ||||
−0.727471 | + | 0.686138i | \(0.759305\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5103.00 | 0.817572 | ||||||||
\(340\) | −4863.60 | −0.775781 | ||||||||
\(341\) | −10080.0 | −1.60077 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6006.75 | −0.945581 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 280.592 | 0.0437872 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3294.00 | 0.509600 | 0.254800 | − | 0.966994i | \(-0.417990\pi\) | ||||
0.254800 | + | 0.966994i | \(0.417990\pi\) | |||||||
\(348\) | −2376.00 | −0.365997 | ||||||||
\(349\) | 10544.7 | 1.61732 | 0.808662 | − | 0.588273i | \(-0.200192\pi\) | ||||
0.808662 | + | 0.588273i | \(0.200192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2478.56 | −0.373713 | −0.186856 | − | 0.982387i | \(-0.559830\pi\) | ||||
−0.186856 | + | 0.982387i | \(0.559830\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2430.00 | 0.363299 | ||||||||
\(356\) | 12138.2 | 1.80709 | ||||||||
\(357\) | −3647.70 | −0.540775 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5414.39 | 0.795991 | 0.397995 | − | 0.917387i | \(-0.369706\pi\) | ||||
0.397995 | + | 0.917387i | \(0.369706\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6271.00 | −0.914273 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4107.00 | −0.593834 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3555.00 | −0.509801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9946.00 | −1.41465 | −0.707326 | − | 0.706888i | \(-0.750099\pi\) | ||||
−0.707326 | + | 0.706888i | \(0.750099\pi\) | |||||||
\(368\) | −1152.00 | −0.163185 | ||||||||
\(369\) | −327.358 | −0.0461831 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2712.39 | −0.379570 | ||||||||
\(372\) | 4655.75 | 0.648897 | ||||||||
\(373\) | −7301.00 | −1.01349 | −0.506745 | − | 0.862096i | \(-0.669151\pi\) | ||||
−0.506745 | + | 0.862096i | \(0.669151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3476.23 | 0.478697 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3422.53 | −0.463862 | −0.231931 | − | 0.972732i | \(-0.574504\pi\) | ||||
−0.231931 | + | 0.972732i | \(0.574504\pi\) | |||||||
\(380\) | −1008.00 | −0.136077 | ||||||||
\(381\) | −4992.00 | −0.671254 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5778.12 | 0.770883 | 0.385442 | − | 0.922732i | \(-0.374049\pi\) | ||||
0.385442 | + | 0.922732i | \(0.374049\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2805.92 | −0.371436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 738.000 | 0.0969371 | ||||||||
\(388\) | −9256.08 | −1.21110 | ||||||||
\(389\) | −9153.00 | −1.19300 | −0.596498 | − | 0.802614i | \(-0.703442\pi\) | ||||
−0.596498 | + | 0.802614i | \(0.703442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2106.00 | −0.272391 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4428.00 | 0.568354 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2286.31 | −0.291232 | ||||||||
\(396\) | 3741.23 | 0.474757 | ||||||||
\(397\) | 2023.04 | 0.255751 | 0.127876 | − | 0.991790i | \(-0.459184\pi\) | ||||
0.127876 | + | 0.991790i | \(0.459184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −756.000 | −0.0948555 | ||||||||
\(400\) | −6272.00 | −0.784000 | ||||||||
\(401\) | −8308.65 | −1.03470 | −0.517349 | − | 0.855774i | \(-0.673081\pi\) | ||||
−0.517349 | + | 0.855774i | \(0.673081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 12600.0 | 1.55167 | ||||||||
\(405\) | 420.888 | 0.0516398 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5850.00 | 0.712466 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10418.3 | 1.25954 | 0.629769 | − | 0.776782i | \(-0.283150\pi\) | ||||
0.629769 | + | 0.776782i | \(0.283150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3039.75 | −0.364817 | ||||||||
\(412\) | 6352.00 | 0.759565 | ||||||||
\(413\) | −8208.00 | −0.977940 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6210.00 | 0.734547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3372.00 | −0.395989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4176.00 | 0.486900 | 0.243450 | − | 0.969913i | \(-0.421721\pi\) | ||||
0.243450 | + | 0.969913i | \(0.421721\pi\) | |||||||
\(420\) | 1296.00 | 0.150567 | ||||||||
\(421\) | 14471.3 | 1.67527 | 0.837633 | − | 0.546233i | \(-0.183939\pi\) | ||||
0.837633 | + | 0.546233i | \(0.183939\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 654.715 | 0.0752561 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11466.0 | −1.30867 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7472.07 | −0.846835 | ||||||||
\(428\) | −3600.00 | −0.406571 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6578.33 | −0.735190 | −0.367595 | − | 0.929986i | \(-0.619819\pi\) | ||||
−0.367595 | + | 0.929986i | \(0.619819\pi\) | |||||||
\(432\) | −1728.00 | −0.192450 | ||||||||
\(433\) | 6605.00 | 0.733062 | 0.366531 | − | 0.930406i | \(-0.380545\pi\) | ||||
0.366531 | + | 0.930406i | \(0.380545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1543.26 | 0.170100 | ||||||||
\(436\) | −4766.60 | −0.523576 | ||||||||
\(437\) | −436.477 | −0.0477792 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8542.00 | 0.928673 | 0.464336 | − | 0.885659i | \(-0.346293\pi\) | ||||
0.464336 | + | 0.885659i | \(0.346293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2115.00 | −0.228377 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14328.0 | −1.53667 | −0.768334 | − | 0.640049i | \(-0.778914\pi\) | ||||
−0.768334 | + | 0.640049i | \(0.778914\pi\) | |||||||
\(444\) | −2702.00 | −0.288809 | ||||||||
\(445\) | −7884.00 | −0.839859 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9805.14 | 1.03751 | ||||||||
\(448\) | −5320.86 | −0.561132 | ||||||||
\(449\) | 3013.77 | 0.316767 | 0.158384 | − | 0.987378i | \(-0.449372\pi\) | ||||
0.158384 | + | 0.987378i | \(0.449372\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1890.00 | 0.197332 | ||||||||
\(452\) | 13608.0 | 1.41608 | ||||||||
\(453\) | −4915.56 | −0.509830 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2887.33 | −0.295544 | −0.147772 | − | 0.989021i | \(-0.547210\pi\) | ||||
−0.147772 | + | 0.989021i | \(0.547210\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3159.00 | −0.321241 | ||||||||
\(460\) | 748.246 | 0.0758416 | ||||||||
\(461\) | −3600.93 | −0.363801 | −0.181900 | − | 0.983317i | \(-0.558225\pi\) | ||||
−0.181900 | + | 0.983317i | \(0.558225\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2677.75 | −0.268781 | −0.134391 | − | 0.990928i | \(-0.542908\pi\) | ||||
−0.134391 | + | 0.990928i | \(0.542908\pi\) | |||||||
\(464\) | −6336.00 | −0.633925 | ||||||||
\(465\) | −3024.00 | −0.301580 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13878.0 | −1.37515 | −0.687577 | − | 0.726111i | \(-0.741326\pi\) | ||||
−0.687577 | + | 0.726111i | \(0.741326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7308.00 | −0.719514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3777.00 | −0.369501 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4260.84 | −0.414194 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2376.37 | −0.229548 | ||||||||
\(476\) | −9727.20 | −0.936650 | ||||||||
\(477\) | −2349.00 | −0.225479 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1101.58 | −0.105079 | −0.0525393 | − | 0.998619i | \(-0.516731\pi\) | ||||
−0.0525393 | + | 0.998619i | \(0.516731\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 561.184 | 0.0528670 | ||||||||
\(484\) | −10952.0 | −1.02855 | ||||||||
\(485\) | 6012.00 | 0.562868 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17123.1 | 1.59326 | 0.796632 | − | 0.604464i | \(-0.206613\pi\) | ||||
0.796632 | + | 0.604464i | \(0.206613\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8854.24 | −0.818820 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −450.000 | −0.0413609 | −0.0206805 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206805 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(492\) | −872.954 | −0.0799914 | ||||||||
\(493\) | −11583.0 | −1.05816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2430.00 | −0.220647 | ||||||||
\(496\) | 12415.3 | 1.12392 | ||||||||
\(497\) | 4860.00 | 0.438633 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13219.0 | 1.18590 | 0.592950 | − | 0.805239i | \(-0.297963\pi\) | ||||
0.592950 | + | 0.805239i | \(0.297963\pi\) | |||||||
\(500\) | 9269.94 | 0.829128 | ||||||||
\(501\) | −9415.43 | −0.839621 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5346.00 | 0.473889 | 0.236945 | − | 0.971523i | \(-0.423854\pi\) | ||||
0.236945 | + | 0.971523i | \(0.423854\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8183.94 | −0.721150 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13312.0 | −1.16265 | ||||||||
\(509\) | −5866.46 | −0.510857 | −0.255428 | − | 0.966828i | \(-0.582217\pi\) | ||||
−0.255428 | + | 0.966828i | \(0.582217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7110.00 | −0.615514 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −654.715 | −0.0563477 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4125.75 | −0.353014 | ||||||||
\(516\) | 1968.00 | 0.167900 | ||||||||
\(517\) | −3780.00 | −0.321556 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12798.0 | 1.08241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9657.00 | −0.812055 | −0.406028 | − | 0.913861i | \(-0.633086\pi\) | ||||
−0.406028 | + | 0.913861i | \(0.633086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21626.0 | 1.80811 | 0.904053 | − | 0.427421i | \(-0.140578\pi\) | ||||
0.904053 | + | 0.427421i | \(0.140578\pi\) | |||||||
\(524\) | 11808.0 | 0.984418 | ||||||||
\(525\) | 3055.34 | 0.253992 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22696.8 | 1.87607 | ||||||||
\(528\) | 9976.61 | 0.822304 | ||||||||
\(529\) | −11843.0 | −0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7108.34 | −0.580933 | ||||||||
\(532\) | −2016.00 | −0.164295 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2338.27 | 0.188957 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9018.00 | 0.724684 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12211.0 | 0.975813 | ||||||||
\(540\) | 1122.37 | 0.0894427 | ||||||||
\(541\) | 5371.09 | 0.426841 | 0.213421 | − | 0.976960i | \(-0.431540\pi\) | ||||
0.213421 | + | 0.976960i | \(0.431540\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5619.00 | −0.444078 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3096.00 | 0.243336 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16946.0 | 1.32460 | 0.662302 | − | 0.749237i | \(-0.269579\pi\) | ||||
0.662302 | + | 0.749237i | \(0.269579\pi\) | |||||||
\(548\) | −8106.00 | −0.631882 | ||||||||
\(549\) | −6471.00 | −0.503052 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2400.62 | −0.185608 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4572.61 | −0.351623 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1755.00 | 0.134226 | ||||||||
\(556\) | −8992.00 | −0.685874 | ||||||||
\(557\) | −3860.74 | −0.293689 | −0.146845 | − | 0.989160i | \(-0.546912\pi\) | ||||
−0.146845 | + | 0.989160i | \(0.546912\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3456.00 | 0.260790 | ||||||||
\(561\) | 18238.5 | 1.37260 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21672.0 | −1.62232 | −0.811160 | − | 0.584825i | \(-0.801163\pi\) | ||||
−0.811160 | + | 0.584825i | \(0.801163\pi\) | |||||||
\(564\) | 1745.91 | 0.130347 | ||||||||
\(565\) | −8838.66 | −0.658133 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 841.777 | 0.0623480 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1386.00 | 0.102116 | 0.0510581 | − | 0.998696i | \(-0.483741\pi\) | ||||
0.0510581 | + | 0.998696i | \(0.483741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1162.00 | −0.0851632 | −0.0425816 | − | 0.999093i | \(-0.513558\pi\) | ||||
−0.0425816 | + | 0.999093i | \(0.513558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8208.00 | 0.598419 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1764.00 | 0.127937 | ||||||||
\(576\) | −4608.00 | −0.333333 | ||||||||
\(577\) | −8045.38 | −0.580474 | −0.290237 | − | 0.956955i | \(-0.593734\pi\) | ||||
−0.290237 | + | 0.956955i | \(0.593734\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7809.82 | −0.560561 | ||||||||
\(580\) | 4115.35 | 0.294622 | ||||||||
\(581\) | 12420.0 | 0.886865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13562.0 | 0.963429 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27622.7 | −1.94227 | −0.971135 | − | 0.238530i | \(-0.923335\pi\) | ||||
−0.971135 | + | 0.238530i | \(0.923335\pi\) | |||||||
\(588\) | −5640.00 | −0.395561 | ||||||||
\(589\) | 4704.00 | 0.329075 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11161.3 | −0.776846 | ||||||||
\(592\) | −7205.33 | −0.500232 | ||||||||
\(593\) | 275.396 | 0.0190711 | 0.00953555 | − | 0.999955i | \(-0.496965\pi\) | ||||
0.00953555 | + | 0.999955i | \(0.496965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6318.00 | 0.435316 | ||||||||
\(596\) | 26147.0 | 1.79702 | ||||||||
\(597\) | 3594.00 | 0.246386 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22356.0 | 1.52494 | 0.762472 | − | 0.647021i | \(-0.223986\pi\) | ||||
0.762472 | + | 0.647021i | \(0.223986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18083.0 | −1.22732 | −0.613661 | − | 0.789569i | \(-0.710304\pi\) | ||||
−0.613661 | + | 0.789569i | \(0.710304\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6328.91 | −0.427418 | ||||||||
\(604\) | −13108.2 | −0.883052 | ||||||||
\(605\) | 7113.53 | 0.478027 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5480.00 | 0.366435 | 0.183218 | − | 0.983072i | \(-0.441349\pi\) | ||||
0.183218 | + | 0.983072i | \(0.441349\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3086.51 | 0.205373 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −8424.00 | −0.556405 | ||||||||
\(613\) | 17737.9 | 1.16872 | 0.584362 | − | 0.811493i | \(-0.301345\pi\) | ||||
0.584362 | + | 0.811493i | \(0.301345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 567.000 | 0.0371767 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9867.49 | −0.643842 | −0.321921 | − | 0.946767i | \(-0.604328\pi\) | ||||
−0.321921 | + | 0.946767i | \(0.604328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4115.35 | −0.267221 | −0.133611 | − | 0.991034i | \(-0.542657\pi\) | ||||
−0.133611 | + | 0.991034i | \(0.542657\pi\) | |||||||
\(620\) | −8064.00 | −0.522352 | ||||||||
\(621\) | 486.000 | 0.0314050 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15768.0 | −1.01402 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6229.00 | 0.398656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3780.00 | 0.240763 | ||||||||
\(628\) | −10072.0 | −0.639995 | ||||||||
\(629\) | −13172.2 | −0.834995 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12664.8 | −0.799011 | −0.399506 | − | 0.916731i | \(-0.630818\pi\) | ||||
−0.399506 | + | 0.916731i | \(0.630818\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7176.00 | −0.450585 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8646.40 | 0.540349 | ||||||||
\(636\) | −6264.00 | −0.390540 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4208.88 | 0.260565 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3789.00 | 0.233473 | 0.116737 | − | 0.993163i | \(-0.462757\pi\) | ||||
0.116737 | + | 0.993163i | \(0.462757\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16911.7 | −1.03722 | −0.518611 | − | 0.855010i | \(-0.673551\pi\) | ||||
−0.518611 | + | 0.855010i | \(0.673551\pi\) | |||||||
\(644\) | 1496.49 | 0.0915684 | ||||||||
\(645\) | −1278.25 | −0.0780328 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27792.0 | 1.68874 | 0.844371 | − | 0.535759i | \(-0.179974\pi\) | ||||
0.844371 | + | 0.535759i | \(0.179974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41040.0 | 2.48222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6048.00 | −0.364116 | ||||||||
\(652\) | −23611.3 | −1.41824 | ||||||||
\(653\) | −594.000 | −0.0355973 | −0.0177986 | − | 0.999842i | \(-0.505666\pi\) | ||||
−0.0177986 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7669.52 | −0.457516 | ||||||||
\(656\) | −2327.88 | −0.138549 | ||||||||
\(657\) | −6157.44 | −0.365639 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17748.0 | 1.04911 | 0.524555 | − | 0.851376i | \(-0.324232\pi\) | ||||
0.524555 | + | 0.851376i | \(0.324232\pi\) | |||||||
\(660\) | −6480.00 | −0.382172 | ||||||||
\(661\) | −15791.1 | −0.929203 | −0.464601 | − | 0.885520i | \(-0.653802\pi\) | ||||
−0.464601 | + | 0.885520i | \(0.653802\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1309.43 | 0.0763572 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1782.00 | 0.103447 | ||||||||
\(668\) | −25107.8 | −1.45427 | ||||||||
\(669\) | 6110.68 | 0.353143 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37360.3 | 2.14945 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20933.0 | −1.19897 | −0.599486 | − | 0.800385i | \(-0.704628\pi\) | ||||
−0.599486 | + | 0.800385i | \(0.704628\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2646.00 | 0.150881 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3402.00 | 0.193131 | 0.0965653 | − | 0.995327i | \(-0.469214\pi\) | ||||
0.0965653 | + | 0.995327i | \(0.469214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12024.0 | 0.679586 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6453.62 | 0.363147 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 24983.1 | 1.39964 | 0.699818 | − | 0.714321i | \(-0.253264\pi\) | ||||
0.699818 | + | 0.714321i | \(0.253264\pi\) | |||||||
\(684\) | −1745.91 | −0.0975971 | ||||||||
\(685\) | 5265.00 | 0.293672 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10413.1 | 0.578288 | ||||||||
\(688\) | 5248.00 | 0.290811 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13866.8 | 0.763412 | 0.381706 | − | 0.924284i | \(-0.375337\pi\) | ||||
0.381706 | + | 0.924284i | \(0.375337\pi\) | |||||||
\(692\) | 34128.0 | 1.87479 | ||||||||
\(693\) | −4860.00 | −0.266401 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5840.48 | 0.318765 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4255.65 | −0.231269 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5562.00 | −0.300964 | ||||||||
\(700\) | 8147.57 | 0.439927 | ||||||||
\(701\) | 21906.0 | 1.18028 | 0.590141 | − | 0.807300i | \(-0.299072\pi\) | ||||
0.590141 | + | 0.807300i | \(0.299072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2730.00 | −0.146464 | ||||||||
\(704\) | 26604.3 | 1.42427 | ||||||||
\(705\) | −1134.00 | −0.0605800 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16367.9 | −0.870690 | ||||||||
\(708\) | −18955.6 | −1.00621 | ||||||||
\(709\) | −13057.9 | −0.691680 | −0.345840 | − | 0.938294i | \(-0.612406\pi\) | ||||
−0.345840 | + | 0.938294i | \(0.612406\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3960.00 | −0.208877 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3491.81 | −0.183407 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24048.0 | 1.25519 | ||||||||
\(717\) | 13374.9 | 0.696645 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14220.0 | 0.737575 | 0.368788 | − | 0.929514i | \(-0.379773\pi\) | ||||
0.368788 | + | 0.929514i | \(0.379773\pi\) | |||||||
\(720\) | 2992.98 | 0.154919 | ||||||||
\(721\) | −8251.49 | −0.426216 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1252.27 | 0.0644157 | ||||||||
\(724\) | −14984.0 | −0.769166 | ||||||||
\(725\) | 9702.00 | 0.496998 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5282.00 | 0.269462 | 0.134731 | − | 0.990882i | \(-0.456983\pi\) | ||||
0.134731 | + | 0.990882i | \(0.456983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9594.00 | 0.485427 | ||||||||
\(732\) | −17256.0 | −0.871312 | ||||||||
\(733\) | 11419.4 | 0.575424 | 0.287712 | − | 0.957717i | \(-0.407105\pi\) | ||||
0.287712 | + | 0.957717i | \(0.407105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3663.29 | 0.183840 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36540.0 | 1.82628 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20535.2 | 1.02219 | 0.511096 | − | 0.859524i | \(-0.329240\pi\) | ||||
0.511096 | + | 0.859524i | \(0.329240\pi\) | |||||||
\(740\) | 4680.00 | 0.232487 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20826.2 | −1.02832 | −0.514158 | − | 0.857696i | \(-0.671895\pi\) | ||||
−0.514158 | + | 0.857696i | \(0.671895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16983.0 | −0.835180 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10756.0 | 0.526831 | ||||||||
\(748\) | 48636.0 | 2.37742 | ||||||||
\(749\) | 4676.54 | 0.228140 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4834.00 | 0.234880 | 0.117440 | − | 0.993080i | \(-0.462531\pi\) | ||||
0.117440 | + | 0.993080i | \(0.462531\pi\) | |||||||
\(752\) | 4655.75 | 0.225768 | ||||||||
\(753\) | 12312.0 | 0.595849 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8514.00 | 0.410406 | ||||||||
\(756\) | 2244.74 | 0.107990 | ||||||||
\(757\) | 9046.00 | 0.434323 | 0.217161 | − | 0.976136i | \(-0.430320\pi\) | ||||
0.217161 | + | 0.976136i | \(0.430320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2805.92 | −0.134188 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12034.3 | −0.573249 | −0.286625 | − | 0.958043i | \(-0.592533\pi\) | ||||
−0.286625 | + | 0.958043i | \(0.592533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6192.00 | 0.293795 | ||||||||
\(764\) | 21888.0 | 1.03649 | ||||||||
\(765\) | 5471.55 | 0.258594 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −12288.0 | −0.577350 | ||||||||
\(769\) | 37543.9 | 1.76056 | 0.880279 | − | 0.474457i | \(-0.157355\pi\) | ||||
0.880279 | + | 0.474457i | \(0.157355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5967.00 | 0.278724 | ||||||||
\(772\) | −20826.2 | −0.970920 | ||||||||
\(773\) | 15713.2 | 0.731130 | 0.365565 | − | 0.930786i | \(-0.380876\pi\) | ||||
0.365565 | + | 0.930786i | \(0.380876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19011.0 | −0.881155 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3510.00 | 0.162060 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −882.000 | −0.0405660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24300.0 | −1.11334 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2673.00 | 0.121999 | ||||||||
\(784\) | −15040.0 | −0.685131 | ||||||||
\(785\) | 6541.96 | 0.297443 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3755.09 | −0.170082 | −0.0850409 | − | 0.996377i | \(-0.527102\pi\) | ||||
−0.0850409 | + | 0.996377i | \(0.527102\pi\) | |||||||
\(788\) | −29763.6 | −1.34554 | ||||||||
\(789\) | −2214.00 | −0.0998992 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17677.3 | −0.794605 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4068.59 | 0.181507 | ||||||||
\(796\) | 9584.00 | 0.426754 | ||||||||
\(797\) | 7830.00 | 0.347996 | 0.173998 | − | 0.984746i | \(-0.444331\pi\) | ||||
0.173998 | + | 0.984746i | \(0.444331\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8511.30 | 0.376856 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13655.5 | −0.602363 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35550.0 | 1.56231 | ||||||||
\(804\) | −16877.1 | −0.740310 | ||||||||
\(805\) | −972.000 | −0.0425571 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6318.00 | 0.275594 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6165.00 | −0.267923 | −0.133962 | − | 0.990987i | \(-0.542770\pi\) | ||||
−0.133962 | + | 0.990987i | \(0.542770\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29839.8 | −1.29201 | −0.646003 | − | 0.763335i | \(-0.723560\pi\) | ||||
−0.646003 | + | 0.763335i | \(0.723560\pi\) | |||||||
\(812\) | 8230.71 | 0.355716 | ||||||||
\(813\) | 2057.68 | 0.0887649 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15336.0 | 0.659137 | ||||||||
\(816\) | −22464.0 | −0.963722 | ||||||||
\(817\) | 1988.39 | 0.0851470 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1512.00 | 0.0643919 | ||||||||
\(821\) | −29763.6 | −1.26523 | −0.632616 | − | 0.774466i | \(-0.718019\pi\) | ||||
−0.632616 | + | 0.774466i | \(0.718019\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8920.00 | 0.377803 | 0.188901 | − | 0.981996i | \(-0.439507\pi\) | ||||
0.188901 | + | 0.981996i | \(0.439507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15276.7 | −0.644686 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18041.0 | 0.758583 | 0.379292 | − | 0.925277i | \(-0.376168\pi\) | ||||
0.379292 | + | 0.925277i | \(0.376168\pi\) | |||||||
\(828\) | 1296.00 | 0.0543951 | ||||||||
\(829\) | 21023.0 | 0.880771 | 0.440385 | − | 0.897809i | \(-0.354842\pi\) | ||||
0.440385 | + | 0.897809i | \(0.354842\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10995.0 | 0.458980 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27495.0 | −1.14363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16308.0 | 0.675882 | ||||||||
\(836\) | 10080.0 | 0.417014 | ||||||||
\(837\) | −5237.72 | −0.216299 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22073.3 | −0.908288 | −0.454144 | − | 0.890928i | \(-0.650055\pi\) | ||||
−0.454144 | + | 0.890928i | \(0.650055\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14588.0 | −0.598139 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5159.78 | −0.210809 | ||||||||
\(844\) | −19136.0 | −0.780436 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14227.1 | 0.577152 | ||||||||
\(848\) | −16704.0 | −0.676436 | ||||||||
\(849\) | −5478.00 | −0.221442 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2026.50 | 0.0816304 | ||||||||
\(852\) | 11223.7 | 0.451311 | ||||||||
\(853\) | 26609.5 | 1.06810 | 0.534051 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534051 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1134.00 | 0.0453590 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12771.0 | 0.509042 | 0.254521 | − | 0.967067i | \(-0.418082\pi\) | ||||
0.254521 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17134.0 | 0.680564 | 0.340282 | − | 0.940323i | \(-0.389477\pi\) | ||||
0.340282 | + | 0.940323i | \(0.389477\pi\) | |||||||
\(860\) | −3408.68 | −0.135157 | ||||||||
\(861\) | 1134.00 | 0.0448857 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7929.33 | −0.312766 | −0.156383 | − | 0.987696i | \(-0.549983\pi\) | ||||
−0.156383 | + | 0.987696i | \(0.549983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22166.8 | −0.871322 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26328.0 | −1.03131 | ||||||||
\(868\) | −16128.0 | −0.630668 | ||||||||
\(869\) | 22863.1 | 0.892493 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10413.1 | 0.403700 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12042.0 | −0.465250 | ||||||||
\(876\) | −16419.8 | −0.633305 | ||||||||
\(877\) | −9864.03 | −0.379800 | −0.189900 | − | 0.981803i | \(-0.560816\pi\) | ||||
−0.189900 | + | 0.981803i | \(0.560816\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1512.08 | 0.0580218 | ||||||||
\(880\) | −17280.0 | −0.661942 | ||||||||
\(881\) | −29169.0 | −1.11547 | −0.557735 | − | 0.830019i | \(-0.688329\pi\) | ||||
−0.557735 | + | 0.830019i | \(0.688329\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −928.000 | −0.0353677 | −0.0176839 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176839 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12312.0 | 0.467642 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14400.0 | −0.545101 | −0.272551 | − | 0.962141i | \(-0.587867\pi\) | ||||
−0.272551 | + | 0.962141i | \(0.587867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17292.8 | 0.652398 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4208.88 | −0.158252 | ||||||||
\(892\) | 16295.1 | 0.611661 | ||||||||
\(893\) | 1764.00 | 0.0661030 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15619.6 | −0.583360 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19205.0 | −0.712483 | ||||||||
\(900\) | 7056.00 | 0.261333 | ||||||||
\(901\) | −30537.0 | −1.12912 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2556.51 | −0.0942140 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9732.39 | 0.357476 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19684.0 | −0.720614 | −0.360307 | − | 0.932834i | \(-0.617328\pi\) | ||||
−0.360307 | + | 0.932834i | \(0.617328\pi\) | |||||||
\(908\) | 17209.7 | 0.628990 | ||||||||
\(909\) | −14175.0 | −0.517222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24480.0 | 0.890295 | 0.445147 | − | 0.895457i | \(-0.353151\pi\) | ||||
0.445147 | + | 0.895457i | \(0.353151\pi\) | |||||||
\(912\) | −4655.75 | −0.169043 | ||||||||
\(913\) | −62100.0 | −2.25105 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11208.1 | 0.404949 | ||||||||
\(916\) | 27768.2 | 1.00162 | ||||||||
\(917\) | −15339.0 | −0.552388 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38608.0 | 1.38581 | 0.692906 | − | 0.721028i | \(-0.256330\pi\) | ||||
0.692906 | + | 0.721028i | \(0.256330\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5850.87 | 0.209330 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12960.0 | −0.461421 | ||||||||
\(925\) | 11033.2 | 0.392182 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7146.00 | −0.253188 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10210.4 | −0.360596 | −0.180298 | − | 0.983612i | \(-0.557706\pi\) | ||||
−0.180298 | + | 0.983612i | \(0.557706\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5698.45 | −0.200600 | ||||||||
\(932\) | −14832.0 | −0.521286 | ||||||||
\(933\) | −11394.0 | −0.399810 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31590.0 | −1.10492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28495.0 | 0.993480 | 0.496740 | − | 0.867899i | \(-0.334530\pi\) | ||||
0.496740 | + | 0.867899i | \(0.334530\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4134.00 | −0.143672 | ||||||||
\(940\) | −3024.00 | −0.104928 | ||||||||
\(941\) | 10724.9 | 0.371541 | 0.185771 | − | 0.982593i | \(-0.440522\pi\) | ||||
0.185771 | + | 0.982593i | \(0.440522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 654.715 | 0.0226092 | ||||||||
\(944\) | −50548.2 | −1.74280 | ||||||||
\(945\) | −1458.00 | −0.0501891 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33962.1 | −1.16538 | −0.582692 | − | 0.812693i | \(-0.698001\pi\) | ||||
−0.582692 | + | 0.812693i | \(0.698001\pi\) | |||||||
\(948\) | −10560.0 | −0.361786 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21309.4 | −0.726609 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23814.0 | −0.809456 | −0.404728 | − | 0.914437i | \(-0.632634\pi\) | ||||
−0.404728 | + | 0.914437i | \(0.632634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14216.7 | −0.481718 | ||||||||
\(956\) | 35666.4 | 1.20662 | ||||||||
\(957\) | −15432.6 | −0.521279 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10530.0 | 0.354569 | ||||||||
\(960\) | 7981.29 | 0.268328 | ||||||||
\(961\) | 7841.00 | 0.263200 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4050.00 | 0.135524 | ||||||||
\(964\) | 3339.39 | 0.111571 | ||||||||
\(965\) | 13527.0 | 0.451243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51549.3 | 1.71429 | 0.857143 | − | 0.515079i | \(-0.172238\pi\) | ||||
0.857143 | + | 0.515079i | \(0.172238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8511.30 | −0.282170 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12312.0 | −0.406911 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(972\) | 1944.00 | 0.0641500 | ||||||||
\(973\) | 11681.0 | 0.384865 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46016.0 | −1.50916 | ||||||||
\(977\) | 21538.1 | 0.705285 | 0.352642 | − | 0.935758i | \(-0.385283\pi\) | ||||
0.352642 | + | 0.935758i | \(0.385283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78840.0 | 2.57379 | ||||||||
\(980\) | 9768.77 | 0.318420 | ||||||||
\(981\) | 5362.43 | 0.174525 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32611.1 | 1.05812 | 0.529060 | − | 0.848585i | \(-0.322545\pi\) | ||||
0.529060 | + | 0.848585i | \(0.322545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19332.0 | 0.625349 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2268.00 | −0.0731421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1476.00 | −0.0474561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22330.0 | −0.715778 | −0.357889 | − | 0.933764i | \(-0.616503\pi\) | ||||
−0.357889 | + | 0.933764i | \(0.616503\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30220.8 | 0.965789 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6224.99 | −0.198337 | ||||||||
\(996\) | 28682.8 | 0.912498 | ||||||||
\(997\) | −24931.0 | −0.791949 | −0.395974 | − | 0.918262i | \(-0.629593\pi\) | ||||
−0.395974 | + | 0.918262i | \(0.629593\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3039.75 | 0.0962697 |
(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 | 507.4.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 1521.4.a.m.1.1 | 2 | |||
13.2 | odd | 12 | 39.4.j.a.4.1 | ✓ | 2 | ||
13.5 | odd | 4 | 507.4.b.a.337.1 | 2 | |||
13.7 | odd | 12 | 39.4.j.a.10.1 | yes | 2 | ||
13.8 | odd | 4 | 507.4.b.a.337.2 | 2 | |||
13.12 | even | 2 | inner | 507.4.a.g.1.1 | 2 | ||
39.2 | even | 12 | 117.4.q.b.82.1 | 2 | |||
39.20 | even | 12 | 117.4.q.b.10.1 | 2 | |||
39.38 | odd | 2 | 1521.4.a.m.1.2 | 2 | |||
52.7 | even | 12 | 624.4.bv.a.49.1 | 2 | |||
52.15 | even | 12 | 624.4.bv.a.433.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.a.4.1 | ✓ | 2 | 13.2 | odd | 12 | ||
39.4.j.a.10.1 | yes | 2 | 13.7 | odd | 12 | ||
117.4.q.b.10.1 | 2 | 39.20 | even | 12 | |||
117.4.q.b.82.1 | 2 | 39.2 | even | 12 | |||
507.4.a.g.1.1 | 2 | 13.12 | even | 2 | inner | ||
507.4.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
507.4.b.a.337.1 | 2 | 13.5 | odd | 4 | |||
507.4.b.a.337.2 | 2 | 13.8 | odd | 4 | |||
624.4.bv.a.49.1 | 2 | 52.7 | even | 12 | |||
624.4.bv.a.433.1 | 2 | 52.15 | even | 12 | |||
1521.4.a.m.1.1 | 2 | 3.2 | odd | 2 | |||
1521.4.a.m.1.2 | 2 | 39.38 | odd | 2 |