Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.8468.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 3x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.31743\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.31743 | 0.931564 | 0.465782 | − | 0.884899i | \(-0.345773\pi\) | ||||
0.465782 | + | 0.884899i | \(0.345773\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.264377 | −0.132188 | ||||||||
\(5\) | −0.264377 | −0.118233 | −0.0591164 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591164 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(6\) | 1.31743 | 0.537839 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.98316 | −1.05471 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.348298 | −0.110141 | ||||||||
\(11\) | 0.401352 | 0.121012 | 0.0605061 | − | 0.998168i | \(-0.480729\pi\) | ||||
0.0605061 | + | 0.998168i | \(0.480729\pi\) | |||||||
\(12\) | −0.264377 | −0.0763189 | ||||||||
\(13\) | −1.84618 | −0.512039 | −0.256020 | − | 0.966672i | \(-0.582411\pi\) | ||||
−0.256020 | + | 0.966672i | \(0.582411\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.264377 | −0.0682617 | ||||||||
\(16\) | −3.40135 | −0.850338 | ||||||||
\(17\) | 1.89924 | 0.460633 | 0.230316 | − | 0.973116i | \(-0.426024\pi\) | ||||
0.230316 | + | 0.973116i | \(0.426024\pi\) | |||||||
\(18\) | 1.31743 | 0.310521 | ||||||||
\(19\) | 6.30059 | 1.44545 | 0.722727 | − | 0.691133i | \(-0.242888\pi\) | ||||
0.722727 | + | 0.691133i | \(0.242888\pi\) | |||||||
\(20\) | 0.0698950 | 0.0156290 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.528753 | 0.112731 | ||||||||
\(23\) | −4.48105 | −0.934362 | −0.467181 | − | 0.884162i | \(-0.654730\pi\) | ||||
−0.467181 | + | 0.884162i | \(0.654730\pi\) | |||||||
\(24\) | −2.98316 | −0.608935 | ||||||||
\(25\) | −4.93011 | −0.986021 | ||||||||
\(26\) | −2.43222 | −0.476997 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.74965 | −0.510597 | −0.255299 | − | 0.966862i | \(-0.582174\pi\) | ||||
−0.255299 | + | 0.966862i | \(0.582174\pi\) | |||||||
\(30\) | −0.348298 | −0.0635902 | ||||||||
\(31\) | 5.89924 | 1.05953 | 0.529767 | − | 0.848143i | \(-0.322279\pi\) | ||||
0.529767 | + | 0.848143i | \(0.322279\pi\) | |||||||
\(32\) | 1.48527 | 0.262562 | ||||||||
\(33\) | 0.401352 | 0.0698664 | ||||||||
\(34\) | 2.50211 | 0.429109 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.264377 | −0.0440628 | ||||||||
\(37\) | −0.497886 | −0.0818520 | −0.0409260 | − | 0.999162i | \(-0.513031\pi\) | ||||
−0.0409260 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(38\) | 8.30059 | 1.34653 | ||||||||
\(39\) | −1.84618 | −0.295626 | ||||||||
\(40\) | 0.788677 | 0.124701 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.86556 | 0.894489 | 0.447244 | − | 0.894412i | \(-0.352405\pi\) | ||||
0.447244 | + | 0.894412i | \(0.352405\pi\) | |||||||
\(44\) | −0.106108 | −0.0159964 | ||||||||
\(45\) | −0.264377 | −0.0394109 | ||||||||
\(46\) | −5.90347 | −0.870419 | ||||||||
\(47\) | 13.1608 | 1.91970 | 0.959850 | − | 0.280514i | \(-0.0905049\pi\) | ||||
0.959850 | + | 0.280514i | \(0.0905049\pi\) | |||||||
\(48\) | −3.40135 | −0.490943 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −6.49507 | −0.918542 | ||||||||
\(51\) | 1.89924 | 0.265946 | ||||||||
\(52\) | 0.488088 | 0.0676856 | ||||||||
\(53\) | 8.75500 | 1.20259 | 0.601296 | − | 0.799027i | \(-0.294651\pi\) | ||||
0.601296 | + | 0.799027i | \(0.294651\pi\) | |||||||
\(54\) | 1.31743 | 0.179280 | ||||||||
\(55\) | −0.106108 | −0.0143076 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.30059 | 0.834533 | ||||||||
\(58\) | −3.62247 | −0.475654 | ||||||||
\(59\) | 2.50211 | 0.325747 | 0.162874 | − | 0.986647i | \(-0.447924\pi\) | ||||
0.162874 | + | 0.986647i | \(0.447924\pi\) | |||||||
\(60\) | 0.0698950 | 0.00902340 | ||||||||
\(61\) | −3.86556 | −0.494934 | −0.247467 | − | 0.968896i | \(-0.579598\pi\) | ||||
−0.247467 | + | 0.968896i | \(0.579598\pi\) | |||||||
\(62\) | 7.77184 | 0.987024 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.75945 | 1.09493 | ||||||||
\(65\) | 0.488088 | 0.0605398 | ||||||||
\(66\) | 0.528753 | 0.0650850 | ||||||||
\(67\) | 1.17319 | 0.143328 | 0.0716639 | − | 0.997429i | \(-0.477169\pi\) | ||||
0.0716639 | + | 0.997429i | \(0.477169\pi\) | |||||||
\(68\) | −0.502114 | −0.0608903 | ||||||||
\(69\) | −4.48105 | −0.539454 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.0292 | 1.78363 | 0.891817 | − | 0.452396i | \(-0.149431\pi\) | ||||
0.891817 | + | 0.452396i | \(0.149431\pi\) | |||||||
\(72\) | −2.98316 | −0.351569 | ||||||||
\(73\) | 7.37048 | 0.862650 | 0.431325 | − | 0.902197i | \(-0.358046\pi\) | ||||
0.431325 | + | 0.902197i | \(0.358046\pi\) | |||||||
\(74\) | −0.655930 | −0.0762503 | ||||||||
\(75\) | −4.93011 | −0.569279 | ||||||||
\(76\) | −1.66573 | −0.191072 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2.43222 | −0.275395 | ||||||||
\(79\) | 5.34103 | 0.600913 | 0.300456 | − | 0.953796i | \(-0.402861\pi\) | ||||
0.300456 | + | 0.953796i | \(0.402861\pi\) | |||||||
\(80\) | 0.899238 | 0.100538 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.31743 | 0.145486 | ||||||||
\(83\) | −0.106108 | −0.0116469 | −0.00582343 | − | 0.999983i | \(-0.501854\pi\) | ||||
−0.00582343 | + | 0.999983i | \(0.501854\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.502114 | −0.0544619 | ||||||||
\(86\) | 7.72746 | 0.833274 | ||||||||
\(87\) | −2.74965 | −0.294793 | ||||||||
\(88\) | −1.19730 | −0.127632 | ||||||||
\(89\) | −3.79848 | −0.402638 | −0.201319 | − | 0.979526i | \(-0.564523\pi\) | ||||
−0.201319 | + | 0.979526i | \(0.564523\pi\) | |||||||
\(90\) | −0.348298 | −0.0367138 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.18468 | 0.123512 | ||||||||
\(93\) | 5.89924 | 0.611722 | ||||||||
\(94\) | 17.3384 | 1.78832 | ||||||||
\(95\) | −1.66573 | −0.170900 | ||||||||
\(96\) | 1.48527 | 0.151590 | ||||||||
\(97\) | −9.72413 | −0.987336 | −0.493668 | − | 0.869651i | \(-0.664344\pi\) | ||||
−0.493668 | + | 0.869651i | \(0.664344\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.401352 | 0.0403374 | ||||||||
\(100\) | 1.30340 | 0.130340 | ||||||||
\(101\) | −0.656155 | −0.0652898 | −0.0326449 | − | 0.999467i | \(-0.510393\pi\) | ||||
−0.0326449 | + | 0.999467i | \(0.510393\pi\) | |||||||
\(102\) | 2.50211 | 0.247746 | ||||||||
\(103\) | 9.80716 | 0.966328 | 0.483164 | − | 0.875530i | \(-0.339488\pi\) | ||||
0.483164 | + | 0.875530i | \(0.339488\pi\) | |||||||
\(104\) | 5.50746 | 0.540051 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.5341 | 1.12029 | ||||||||
\(107\) | −12.6947 | −1.22724 | −0.613620 | − | 0.789601i | \(-0.710287\pi\) | ||||
−0.613620 | + | 0.789601i | \(0.710287\pi\) | |||||||
\(108\) | −0.264377 | −0.0254396 | ||||||||
\(109\) | −15.6320 | −1.49728 | −0.748639 | − | 0.662978i | \(-0.769292\pi\) | ||||
−0.748639 | + | 0.662978i | \(0.769292\pi\) | |||||||
\(110\) | −0.139790 | −0.0133285 | ||||||||
\(111\) | −0.497886 | −0.0472572 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.8027 | 1.20438 | 0.602189 | − | 0.798354i | \(-0.294296\pi\) | ||||
0.602189 | + | 0.798354i | \(0.294296\pi\) | |||||||
\(114\) | 8.30059 | 0.777421 | ||||||||
\(115\) | 1.18468 | 0.110472 | ||||||||
\(116\) | 0.726943 | 0.0674950 | ||||||||
\(117\) | −1.84618 | −0.170680 | ||||||||
\(118\) | 3.29636 | 0.303455 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.788677 | 0.0719961 | ||||||||
\(121\) | −10.8389 | −0.985356 | ||||||||
\(122\) | −5.09260 | −0.461062 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −1.55962 | −0.140058 | ||||||||
\(125\) | 2.62529 | 0.234813 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.889664 | 0.0789449 | 0.0394725 | − | 0.999221i | \(-0.487432\pi\) | ||||
0.0394725 | + | 0.999221i | \(0.487432\pi\) | |||||||
\(128\) | 8.56942 | 0.757437 | ||||||||
\(129\) | 5.86556 | 0.516433 | ||||||||
\(130\) | 0.643022 | 0.0563967 | ||||||||
\(131\) | −8.52171 | −0.744545 | −0.372273 | − | 0.928123i | \(-0.621421\pi\) | ||||
−0.372273 | + | 0.928123i | \(0.621421\pi\) | |||||||
\(132\) | −0.106108 | −0.00923552 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.54559 | 0.133519 | ||||||||
\(135\) | −0.264377 | −0.0227539 | ||||||||
\(136\) | −5.66573 | −0.485832 | ||||||||
\(137\) | 0.615489 | 0.0525848 | 0.0262924 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262924 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(138\) | −5.90347 | −0.502536 | ||||||||
\(139\) | 14.5428 | 1.23350 | 0.616751 | − | 0.787158i | \(-0.288448\pi\) | ||||
0.616751 | + | 0.787158i | \(0.288448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.1608 | 1.10834 | ||||||||
\(142\) | 19.7999 | 1.66157 | ||||||||
\(143\) | −0.740969 | −0.0619630 | ||||||||
\(144\) | −3.40135 | −0.283446 | ||||||||
\(145\) | 0.726943 | 0.0603693 | ||||||||
\(146\) | 9.71010 | 0.803614 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.131629 | 0.0108199 | ||||||||
\(149\) | 12.3623 | 1.01276 | 0.506381 | − | 0.862310i | \(-0.330983\pi\) | ||||
0.506381 | + | 0.862310i | \(0.330983\pi\) | |||||||
\(150\) | −6.49507 | −0.530320 | ||||||||
\(151\) | −1.89389 | −0.154123 | −0.0770614 | − | 0.997026i | \(-0.524554\pi\) | ||||
−0.0770614 | + | 0.997026i | \(0.524554\pi\) | |||||||
\(152\) | −18.7957 | −1.52453 | ||||||||
\(153\) | 1.89924 | 0.153544 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.55962 | −0.125272 | ||||||||
\(156\) | 0.488088 | 0.0390783 | ||||||||
\(157\) | 0.238855 | 0.0190627 | 0.00953136 | − | 0.999955i | \(-0.496966\pi\) | ||||
0.00953136 | + | 0.999955i | \(0.496966\pi\) | |||||||
\(158\) | 7.03644 | 0.559789 | ||||||||
\(159\) | 8.75500 | 0.694316 | ||||||||
\(160\) | −0.392671 | −0.0310434 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.31743 | 0.103507 | ||||||||
\(163\) | 8.12036 | 0.636036 | 0.318018 | − | 0.948085i | \(-0.396983\pi\) | ||||
0.318018 | + | 0.948085i | \(0.396983\pi\) | |||||||
\(164\) | −0.264377 | −0.0206443 | ||||||||
\(165\) | −0.106108 | −0.00826050 | ||||||||
\(166\) | −0.139790 | −0.0108498 | ||||||||
\(167\) | 8.14232 | 0.630072 | 0.315036 | − | 0.949080i | \(-0.397983\pi\) | ||||
0.315036 | + | 0.949080i | \(0.397983\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.59161 | −0.737816 | ||||||||
\(170\) | −0.661500 | −0.0507348 | ||||||||
\(171\) | 6.30059 | 0.481818 | ||||||||
\(172\) | −1.55072 | −0.118241 | ||||||||
\(173\) | −24.3045 | −1.84784 | −0.923920 | − | 0.382586i | \(-0.875033\pi\) | ||||
−0.923920 | + | 0.382586i | \(0.875033\pi\) | |||||||
\(174\) | −3.62247 | −0.274619 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.36514 | −0.102901 | ||||||||
\(177\) | 2.50211 | 0.188070 | ||||||||
\(178\) | −5.00423 | −0.375083 | ||||||||
\(179\) | 13.2924 | 0.993523 | 0.496761 | − | 0.867887i | \(-0.334522\pi\) | ||||
0.496761 | + | 0.867887i | \(0.334522\pi\) | |||||||
\(180\) | 0.0698950 | 0.00520966 | ||||||||
\(181\) | 16.4965 | 1.22617 | 0.613087 | − | 0.790015i | \(-0.289927\pi\) | ||||
0.613087 | + | 0.790015i | \(0.289927\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.86556 | −0.285750 | ||||||||
\(184\) | 13.3677 | 0.985478 | ||||||||
\(185\) | 0.131629 | 0.00967759 | ||||||||
\(186\) | 7.77184 | 0.569859 | ||||||||
\(187\) | 0.762263 | 0.0557422 | ||||||||
\(188\) | −3.47941 | −0.253762 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.19448 | −0.159204 | ||||||||
\(191\) | −8.49366 | −0.614580 | −0.307290 | − | 0.951616i | \(-0.599422\pi\) | ||||
−0.307290 | + | 0.951616i | \(0.599422\pi\) | |||||||
\(192\) | 8.75945 | 0.632159 | ||||||||
\(193\) | 4.08837 | 0.294288 | 0.147144 | − | 0.989115i | \(-0.452992\pi\) | ||||
0.147144 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(194\) | −12.8109 | −0.919766 | ||||||||
\(195\) | 0.488088 | 0.0349527 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.11034 | 0.649085 | 0.324542 | − | 0.945871i | \(-0.394790\pi\) | ||||
0.324542 | + | 0.945871i | \(0.394790\pi\) | |||||||
\(198\) | 0.528753 | 0.0375769 | ||||||||
\(199\) | 16.8400 | 1.19376 | 0.596879 | − | 0.802331i | \(-0.296407\pi\) | ||||
0.596879 | + | 0.802331i | \(0.296407\pi\) | |||||||
\(200\) | 14.7073 | 1.03996 | ||||||||
\(201\) | 1.17319 | 0.0827503 | ||||||||
\(202\) | −0.864438 | −0.0608217 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.502114 | −0.0351550 | ||||||||
\(205\) | −0.264377 | −0.0184649 | ||||||||
\(206\) | 12.9202 | 0.900196 | ||||||||
\(207\) | −4.48105 | −0.311454 | ||||||||
\(208\) | 6.27952 | 0.435406 | ||||||||
\(209\) | 2.52875 | 0.174918 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.4560 | 0.926352 | 0.463176 | − | 0.886266i | \(-0.346710\pi\) | ||||
0.463176 | + | 0.886266i | \(0.346710\pi\) | |||||||
\(212\) | −2.31462 | −0.158968 | ||||||||
\(213\) | 15.0292 | 1.02978 | ||||||||
\(214\) | −16.7244 | −1.14325 | ||||||||
\(215\) | −1.55072 | −0.105758 | ||||||||
\(216\) | −2.98316 | −0.202978 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.5941 | −1.39481 | ||||||||
\(219\) | 7.37048 | 0.498051 | ||||||||
\(220\) | 0.0280525 | 0.00189130 | ||||||||
\(221\) | −3.50634 | −0.235862 | ||||||||
\(222\) | −0.655930 | −0.0440232 | ||||||||
\(223\) | −3.78445 | −0.253425 | −0.126713 | − | 0.991939i | \(-0.540443\pi\) | ||||
−0.126713 | + | 0.991939i | \(0.540443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.93011 | −0.328674 | ||||||||
\(226\) | 16.8667 | 1.12195 | ||||||||
\(227\) | 20.1757 | 1.33911 | 0.669555 | − | 0.742763i | \(-0.266485\pi\) | ||||
0.669555 | + | 0.742763i | \(0.266485\pi\) | |||||||
\(228\) | −1.66573 | −0.110316 | ||||||||
\(229\) | 19.3384 | 1.27792 | 0.638960 | − | 0.769240i | \(-0.279365\pi\) | ||||
0.638960 | + | 0.769240i | \(0.279365\pi\) | |||||||
\(230\) | 1.56074 | 0.102912 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.20264 | 0.538530 | ||||||||
\(233\) | 9.29636 | 0.609025 | 0.304512 | − | 0.952508i | \(-0.401506\pi\) | ||||
0.304512 | + | 0.952508i | \(0.401506\pi\) | |||||||
\(234\) | −2.43222 | −0.158999 | ||||||||
\(235\) | −3.47941 | −0.226972 | ||||||||
\(236\) | −0.661500 | −0.0430600 | ||||||||
\(237\) | 5.34103 | 0.346937 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.8265 | 0.894364 | 0.447182 | − | 0.894443i | \(-0.352428\pi\) | ||||
0.447182 | + | 0.894443i | \(0.352428\pi\) | |||||||
\(240\) | 0.899238 | 0.0580456 | ||||||||
\(241\) | −17.5930 | −1.13327 | −0.566633 | − | 0.823970i | \(-0.691754\pi\) | ||||
−0.566633 | + | 0.823970i | \(0.691754\pi\) | |||||||
\(242\) | −14.2795 | −0.917922 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.02196 | 0.0654244 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.31743 | 0.0839963 | ||||||||
\(247\) | −11.6320 | −0.740129 | ||||||||
\(248\) | −17.5984 | −1.11750 | ||||||||
\(249\) | −0.106108 | −0.00672432 | ||||||||
\(250\) | 3.45863 | 0.218743 | ||||||||
\(251\) | 19.2253 | 1.21349 | 0.606747 | − | 0.794895i | \(-0.292474\pi\) | ||||
0.606747 | + | 0.794895i | \(0.292474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.79848 | −0.113069 | ||||||||
\(254\) | 1.17207 | 0.0735422 | ||||||||
\(255\) | −0.502114 | −0.0314436 | ||||||||
\(256\) | −6.22928 | −0.389330 | ||||||||
\(257\) | −12.3929 | −0.773048 | −0.386524 | − | 0.922279i | \(-0.626324\pi\) | ||||
−0.386524 | + | 0.922279i | \(0.626324\pi\) | |||||||
\(258\) | 7.72746 | 0.481091 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.129039 | −0.00800266 | ||||||||
\(261\) | −2.74965 | −0.170199 | ||||||||
\(262\) | −11.2268 | −0.693592 | ||||||||
\(263\) | 5.50323 | 0.339344 | 0.169672 | − | 0.985501i | \(-0.445729\pi\) | ||||
0.169672 | + | 0.985501i | \(0.445729\pi\) | |||||||
\(264\) | −1.19730 | −0.0736885 | ||||||||
\(265\) | −2.31462 | −0.142186 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.79848 | −0.232463 | ||||||||
\(268\) | −0.310164 | −0.0189463 | ||||||||
\(269\) | 23.9834 | 1.46229 | 0.731146 | − | 0.682221i | \(-0.238986\pi\) | ||||
0.731146 | + | 0.682221i | \(0.238986\pi\) | |||||||
\(270\) | −0.348298 | −0.0211967 | ||||||||
\(271\) | −4.44906 | −0.270261 | −0.135131 | − | 0.990828i | \(-0.543145\pi\) | ||||
−0.135131 | + | 0.990828i | \(0.543145\pi\) | |||||||
\(272\) | −6.45998 | −0.391694 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.810864 | 0.0489861 | ||||||||
\(275\) | −1.97871 | −0.119321 | ||||||||
\(276\) | 1.18468 | 0.0713096 | ||||||||
\(277\) | −31.7797 | −1.90946 | −0.954729 | − | 0.297477i | \(-0.903855\pi\) | ||||
−0.954729 | + | 0.297477i | \(0.903855\pi\) | |||||||
\(278\) | 19.1591 | 1.14909 | ||||||||
\(279\) | 5.89924 | 0.353178 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.6191 | 0.633485 | 0.316742 | − | 0.948512i | \(-0.397411\pi\) | ||||
0.316742 | + | 0.948512i | \(0.397411\pi\) | |||||||
\(282\) | 17.3384 | 1.03249 | ||||||||
\(283\) | 26.0778 | 1.55016 | 0.775081 | − | 0.631861i | \(-0.217709\pi\) | ||||
0.775081 | + | 0.631861i | \(0.217709\pi\) | |||||||
\(284\) | −3.97336 | −0.235776 | ||||||||
\(285\) | −1.66573 | −0.0986692 | ||||||||
\(286\) | −0.976176 | −0.0577225 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.48527 | 0.0875206 | ||||||||
\(289\) | −13.3929 | −0.787817 | ||||||||
\(290\) | 0.957697 | 0.0562379 | ||||||||
\(291\) | −9.72413 | −0.570038 | ||||||||
\(292\) | −1.94858 | −0.114032 | ||||||||
\(293\) | 4.81695 | 0.281409 | 0.140705 | − | 0.990052i | \(-0.455063\pi\) | ||||
0.140705 | + | 0.990052i | \(0.455063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.661500 | −0.0385140 | ||||||||
\(296\) | 1.48527 | 0.0863297 | ||||||||
\(297\) | 0.401352 | 0.0232888 | ||||||||
\(298\) | 16.2865 | 0.943452 | ||||||||
\(299\) | 8.27283 | 0.478430 | ||||||||
\(300\) | 1.30340 | 0.0752521 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.49507 | −0.143575 | ||||||||
\(303\) | −0.656155 | −0.0376951 | ||||||||
\(304\) | −21.4305 | −1.22912 | ||||||||
\(305\) | 1.02196 | 0.0585174 | ||||||||
\(306\) | 2.50211 | 0.143036 | ||||||||
\(307\) | −6.48076 | −0.369877 | −0.184938 | − | 0.982750i | \(-0.559209\pi\) | ||||
−0.184938 | + | 0.982750i | \(0.559209\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.80716 | 0.557910 | ||||||||
\(310\) | −2.05469 | −0.116699 | ||||||||
\(311\) | −26.6495 | −1.51115 | −0.755577 | − | 0.655060i | \(-0.772643\pi\) | ||||
−0.755577 | + | 0.655060i | \(0.772643\pi\) | |||||||
\(312\) | 5.50746 | 0.311799 | ||||||||
\(313\) | 5.80181 | 0.327938 | 0.163969 | − | 0.986466i | \(-0.447570\pi\) | ||||
0.163969 | + | 0.986466i | \(0.447570\pi\) | |||||||
\(314\) | 0.314675 | 0.0177581 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.41204 | −0.0794337 | ||||||||
\(317\) | 5.92921 | 0.333018 | 0.166509 | − | 0.986040i | \(-0.446751\pi\) | ||||
0.166509 | + | 0.986040i | \(0.446751\pi\) | |||||||
\(318\) | 11.5341 | 0.646800 | ||||||||
\(319\) | −1.10358 | −0.0617884 | ||||||||
\(320\) | −2.31579 | −0.129457 | ||||||||
\(321\) | −12.6947 | −0.708548 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.9663 | 0.665824 | ||||||||
\(324\) | −0.264377 | −0.0146876 | ||||||||
\(325\) | 9.10188 | 0.504881 | ||||||||
\(326\) | 10.6980 | 0.592508 | ||||||||
\(327\) | −15.6320 | −0.864454 | ||||||||
\(328\) | −2.98316 | −0.164717 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.139790 | −0.00769518 | ||||||||
\(331\) | −32.3045 | −1.77562 | −0.887809 | − | 0.460212i | \(-0.847773\pi\) | ||||
−0.887809 | + | 0.460212i | \(0.847773\pi\) | |||||||
\(332\) | 0.0280525 | 0.00153958 | ||||||||
\(333\) | −0.497886 | −0.0272840 | ||||||||
\(334\) | 10.7269 | 0.586952 | ||||||||
\(335\) | −0.310164 | −0.0169460 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.6750 | −0.744926 | −0.372463 | − | 0.928047i | \(-0.621487\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621487\pi\) | |||||||
\(338\) | −12.6363 | −0.687323 | ||||||||
\(339\) | 12.8027 | 0.695347 | ||||||||
\(340\) | 0.132747 | 0.00719923 | ||||||||
\(341\) | 2.36767 | 0.128217 | ||||||||
\(342\) | 8.30059 | 0.448844 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −17.4979 | −0.943423 | ||||||||
\(345\) | 1.18468 | 0.0637812 | ||||||||
\(346\) | −32.0195 | −1.72138 | ||||||||
\(347\) | −5.98236 | −0.321150 | −0.160575 | − | 0.987024i | \(-0.551335\pi\) | ||||
−0.160575 | + | 0.987024i | \(0.551335\pi\) | |||||||
\(348\) | 0.726943 | 0.0389682 | ||||||||
\(349\) | −3.24984 | −0.173960 | −0.0869800 | − | 0.996210i | \(-0.527722\pi\) | ||||
−0.0869800 | + | 0.996210i | \(0.527722\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.84618 | −0.0985420 | ||||||||
\(352\) | 0.596117 | 0.0317731 | ||||||||
\(353\) | −21.9770 | −1.16972 | −0.584859 | − | 0.811135i | \(-0.698850\pi\) | ||||
−0.584859 | + | 0.811135i | \(0.698850\pi\) | |||||||
\(354\) | 3.29636 | 0.175200 | ||||||||
\(355\) | −3.97336 | −0.210884 | ||||||||
\(356\) | 1.00423 | 0.0532240 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.5119 | 0.925530 | ||||||||
\(359\) | −35.8970 | −1.89457 | −0.947286 | − | 0.320388i | \(-0.896187\pi\) | ||||
−0.947286 | + | 0.320388i | \(0.896187\pi\) | |||||||
\(360\) | 0.788677 | 0.0415669 | ||||||||
\(361\) | 20.6974 | 1.08934 | ||||||||
\(362\) | 21.7330 | 1.14226 | ||||||||
\(363\) | −10.8389 | −0.568896 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.94858 | −0.101994 | ||||||||
\(366\) | −5.09260 | −0.266195 | ||||||||
\(367\) | 17.7309 | 0.925545 | 0.462772 | − | 0.886477i | \(-0.346855\pi\) | ||||
0.462772 | + | 0.886477i | \(0.346855\pi\) | |||||||
\(368\) | 15.2416 | 0.794524 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 0.173413 | 0.00901529 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.55962 | −0.0808626 | ||||||||
\(373\) | 2.88864 | 0.149568 | 0.0747840 | − | 0.997200i | \(-0.476173\pi\) | ||||
0.0747840 | + | 0.997200i | \(0.476173\pi\) | |||||||
\(374\) | 1.00423 | 0.0519274 | ||||||||
\(375\) | 2.62529 | 0.135569 | ||||||||
\(376\) | −39.2608 | −2.02472 | ||||||||
\(377\) | 5.07636 | 0.261446 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.8429 | −1.17336 | −0.586679 | − | 0.809819i | \(-0.699565\pi\) | ||||
−0.586679 | + | 0.809819i | \(0.699565\pi\) | |||||||
\(380\) | 0.440380 | 0.0225910 | ||||||||
\(381\) | 0.889664 | 0.0455789 | ||||||||
\(382\) | −11.1898 | −0.572520 | ||||||||
\(383\) | −29.0462 | −1.48419 | −0.742097 | − | 0.670293i | \(-0.766168\pi\) | ||||
−0.742097 | + | 0.670293i | \(0.766168\pi\) | |||||||
\(384\) | 8.56942 | 0.437306 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.38615 | 0.274148 | ||||||||
\(387\) | 5.86556 | 0.298163 | ||||||||
\(388\) | 2.57083 | 0.130514 | ||||||||
\(389\) | 5.68532 | 0.288257 | 0.144129 | − | 0.989559i | \(-0.453962\pi\) | ||||
0.144129 | + | 0.989559i | \(0.453962\pi\) | |||||||
\(390\) | 0.643022 | 0.0325607 | ||||||||
\(391\) | −8.51057 | −0.430398 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.52171 | −0.429863 | ||||||||
\(394\) | 12.0022 | 0.604664 | ||||||||
\(395\) | −1.41204 | −0.0710476 | ||||||||
\(396\) | −0.106108 | −0.00533213 | ||||||||
\(397\) | −34.9153 | −1.75235 | −0.876174 | − | 0.481995i | \(-0.839912\pi\) | ||||
−0.876174 | + | 0.481995i | \(0.839912\pi\) | |||||||
\(398\) | 22.1856 | 1.11206 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.7690 | 0.838451 | ||||||||
\(401\) | 0.456327 | 0.0227879 | 0.0113939 | − | 0.999935i | \(-0.496373\pi\) | ||||
0.0113939 | + | 0.999935i | \(0.496373\pi\) | |||||||
\(402\) | 1.54559 | 0.0770872 | ||||||||
\(403\) | −10.8911 | −0.542523 | ||||||||
\(404\) | 0.173472 | 0.00863055 | ||||||||
\(405\) | −0.264377 | −0.0131370 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.199827 | −0.00990508 | ||||||||
\(408\) | −5.66573 | −0.280495 | ||||||||
\(409\) | −19.8922 | −0.983606 | −0.491803 | − | 0.870707i | \(-0.663662\pi\) | ||||
−0.491803 | + | 0.870707i | \(0.663662\pi\) | |||||||
\(410\) | −0.348298 | −0.0172012 | ||||||||
\(411\) | 0.615489 | 0.0303598 | ||||||||
\(412\) | −2.59278 | −0.127737 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −5.90347 | −0.290140 | ||||||||
\(415\) | 0.0280525 | 0.00137704 | ||||||||
\(416\) | −2.74209 | −0.134442 | ||||||||
\(417\) | 14.5428 | 0.712163 | ||||||||
\(418\) | 3.33146 | 0.162947 | ||||||||
\(419\) | 13.5933 | 0.664076 | 0.332038 | − | 0.943266i | \(-0.392264\pi\) | ||||
0.332038 | + | 0.943266i | \(0.392264\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0224 | 1.21952 | 0.609759 | − | 0.792587i | \(-0.291266\pi\) | ||||
0.609759 | + | 0.792587i | \(0.291266\pi\) | |||||||
\(422\) | 17.7274 | 0.862957 | ||||||||
\(423\) | 13.1608 | 0.639900 | ||||||||
\(424\) | −26.1175 | −1.26838 | ||||||||
\(425\) | −9.36344 | −0.454194 | ||||||||
\(426\) | 19.7999 | 0.959308 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.35617 | 0.162227 | ||||||||
\(429\) | −0.740969 | −0.0357743 | ||||||||
\(430\) | −2.04296 | −0.0985203 | ||||||||
\(431\) | −15.8532 | −0.763620 | −0.381810 | − | 0.924241i | \(-0.624699\pi\) | ||||
−0.381810 | + | 0.924241i | \(0.624699\pi\) | |||||||
\(432\) | −3.40135 | −0.163648 | ||||||||
\(433\) | 23.5420 | 1.13136 | 0.565678 | − | 0.824627i | \(-0.308615\pi\) | ||||
0.565678 | + | 0.824627i | \(0.308615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.726943 | 0.0348542 | ||||||||
\(436\) | 4.13275 | 0.197923 | ||||||||
\(437\) | −28.2332 | −1.35058 | ||||||||
\(438\) | 9.71010 | 0.463967 | ||||||||
\(439\) | 31.5310 | 1.50489 | 0.752446 | − | 0.658654i | \(-0.228874\pi\) | ||||
0.752446 | + | 0.658654i | \(0.228874\pi\) | |||||||
\(440\) | 0.316537 | 0.0150903 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.61936 | −0.219721 | ||||||||
\(443\) | −17.5792 | −0.835214 | −0.417607 | − | 0.908628i | \(-0.637131\pi\) | ||||
−0.417607 | + | 0.908628i | \(0.637131\pi\) | |||||||
\(444\) | 0.131629 | 0.00624685 | ||||||||
\(445\) | 1.00423 | 0.0476050 | ||||||||
\(446\) | −4.98575 | −0.236082 | ||||||||
\(447\) | 12.3623 | 0.584718 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.3539 | −0.583015 | −0.291508 | − | 0.956569i | \(-0.594157\pi\) | ||||
−0.291508 | + | 0.956569i | \(0.594157\pi\) | |||||||
\(450\) | −6.49507 | −0.306181 | ||||||||
\(451\) | 0.401352 | 0.0188989 | ||||||||
\(452\) | −3.38474 | −0.159205 | ||||||||
\(453\) | −1.89389 | −0.0889828 | ||||||||
\(454\) | 26.5801 | 1.24747 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.7957 | −0.880187 | ||||||||
\(457\) | 3.59695 | 0.168258 | 0.0841291 | − | 0.996455i | \(-0.473189\pi\) | ||||
0.0841291 | + | 0.996455i | \(0.473189\pi\) | |||||||
\(458\) | 25.4771 | 1.19046 | ||||||||
\(459\) | 1.89924 | 0.0886488 | ||||||||
\(460\) | −0.313203 | −0.0146031 | ||||||||
\(461\) | 37.1077 | 1.72828 | 0.864139 | − | 0.503254i | \(-0.167864\pi\) | ||||
0.864139 | + | 0.503254i | \(0.167864\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7851 | 1.19833 | 0.599167 | − | 0.800624i | \(-0.295499\pi\) | ||||
0.599167 | + | 0.800624i | \(0.295499\pi\) | |||||||
\(464\) | 9.35253 | 0.434180 | ||||||||
\(465\) | −1.55962 | −0.0723257 | ||||||||
\(466\) | 12.2473 | 0.567346 | ||||||||
\(467\) | −7.64274 | −0.353664 | −0.176832 | − | 0.984241i | \(-0.556585\pi\) | ||||
−0.176832 | + | 0.984241i | \(0.556585\pi\) | |||||||
\(468\) | 0.488088 | 0.0225619 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.58388 | −0.211439 | ||||||||
\(471\) | 0.238855 | 0.0110059 | ||||||||
\(472\) | −7.46420 | −0.343568 | ||||||||
\(473\) | 2.35415 | 0.108244 | ||||||||
\(474\) | 7.03644 | 0.323194 | ||||||||
\(475\) | −31.0626 | −1.42525 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.75500 | 0.400864 | ||||||||
\(478\) | 18.2155 | 0.833157 | ||||||||
\(479\) | 5.64123 | 0.257755 | 0.128877 | − | 0.991661i | \(-0.458863\pi\) | ||||
0.128877 | + | 0.991661i | \(0.458863\pi\) | |||||||
\(480\) | −0.392671 | −0.0179229 | ||||||||
\(481\) | 0.919189 | 0.0419114 | ||||||||
\(482\) | −23.1776 | −1.05571 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.86556 | 0.130253 | ||||||||
\(485\) | 2.57083 | 0.116735 | ||||||||
\(486\) | 1.31743 | 0.0597599 | ||||||||
\(487\) | −13.0839 | −0.592886 | −0.296443 | − | 0.955050i | \(-0.595801\pi\) | ||||
−0.296443 | + | 0.955050i | \(0.595801\pi\) | |||||||
\(488\) | 11.5316 | 0.522010 | ||||||||
\(489\) | 8.12036 | 0.367215 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.0019 | 0.451378 | 0.225689 | − | 0.974199i | \(-0.427537\pi\) | ||||
0.225689 | + | 0.974199i | \(0.427537\pi\) | |||||||
\(492\) | −0.264377 | −0.0119190 | ||||||||
\(493\) | −5.22224 | −0.235198 | ||||||||
\(494\) | −15.3244 | −0.689478 | ||||||||
\(495\) | −0.106108 | −0.00476920 | ||||||||
\(496\) | −20.0654 | −0.900962 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.139790 | −0.00626414 | ||||||||
\(499\) | 19.9798 | 0.894420 | 0.447210 | − | 0.894429i | \(-0.352418\pi\) | ||||
0.447210 | + | 0.894429i | \(0.352418\pi\) | |||||||
\(500\) | −0.694065 | −0.0310395 | ||||||||
\(501\) | 8.14232 | 0.363772 | ||||||||
\(502\) | 25.3281 | 1.13045 | ||||||||
\(503\) | −3.15376 | −0.140619 | −0.0703095 | − | 0.997525i | \(-0.522399\pi\) | ||||
−0.0703095 | + | 0.997525i | \(0.522399\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.173472 | 0.00771940 | ||||||||
\(506\) | −2.36937 | −0.105331 | ||||||||
\(507\) | −9.59161 | −0.425978 | ||||||||
\(508\) | −0.235206 | −0.0104356 | ||||||||
\(509\) | 28.4331 | 1.26027 | 0.630136 | − | 0.776484i | \(-0.282999\pi\) | ||||
0.630136 | + | 0.776484i | \(0.282999\pi\) | |||||||
\(510\) | −0.661500 | −0.0292917 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −25.3455 | −1.12012 | ||||||||
\(513\) | 6.30059 | 0.278178 | ||||||||
\(514\) | −16.3268 | −0.720143 | ||||||||
\(515\) | −2.59278 | −0.114252 | ||||||||
\(516\) | −1.55072 | −0.0682665 | ||||||||
\(517\) | 5.28211 | 0.232307 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −24.3045 | −1.06685 | ||||||||
\(520\) | −1.45604 | −0.0638517 | ||||||||
\(521\) | −20.3003 | −0.889373 | −0.444686 | − | 0.895686i | \(-0.646685\pi\) | ||||
−0.444686 | + | 0.895686i | \(0.646685\pi\) | |||||||
\(522\) | −3.62247 | −0.158551 | ||||||||
\(523\) | 8.46561 | 0.370175 | 0.185088 | − | 0.982722i | \(-0.440743\pi\) | ||||
0.185088 | + | 0.982722i | \(0.440743\pi\) | |||||||
\(524\) | 2.25294 | 0.0984202 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.25013 | 0.316121 | ||||||||
\(527\) | 11.2041 | 0.488056 | ||||||||
\(528\) | −1.36514 | −0.0594100 | ||||||||
\(529\) | −2.92024 | −0.126967 | ||||||||
\(530\) | −3.04935 | −0.132455 | ||||||||
\(531\) | 2.50211 | 0.108582 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.84618 | −0.0799671 | ||||||||
\(534\) | −5.00423 | −0.216554 | ||||||||
\(535\) | 3.35617 | 0.145100 | ||||||||
\(536\) | −3.49981 | −0.151169 | ||||||||
\(537\) | 13.2924 | 0.573611 | ||||||||
\(538\) | 31.5964 | 1.36222 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.0698950 | 0.00300780 | ||||||||
\(541\) | −25.5874 | −1.10009 | −0.550044 | − | 0.835136i | \(-0.685389\pi\) | ||||
−0.550044 | + | 0.835136i | \(0.685389\pi\) | |||||||
\(542\) | −5.86133 | −0.251766 | ||||||||
\(543\) | 16.4965 | 0.707932 | ||||||||
\(544\) | 2.82089 | 0.120945 | ||||||||
\(545\) | 4.13275 | 0.177027 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.3531 | 1.34056 | 0.670282 | − | 0.742107i | \(-0.266173\pi\) | ||||
0.670282 | + | 0.742107i | \(0.266173\pi\) | |||||||
\(548\) | −0.162721 | −0.00695109 | ||||||||
\(549\) | −3.86556 | −0.164978 | ||||||||
\(550\) | −2.60681 | −0.111155 | ||||||||
\(551\) | −17.3244 | −0.738045 | ||||||||
\(552\) | 13.3677 | 0.568966 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −41.8676 | −1.77878 | ||||||||
\(555\) | 0.131629 | 0.00558736 | ||||||||
\(556\) | −3.84477 | −0.163055 | ||||||||
\(557\) | 31.0629 | 1.31618 | 0.658088 | − | 0.752941i | \(-0.271366\pi\) | ||||
0.658088 | + | 0.752941i | \(0.271366\pi\) | |||||||
\(558\) | 7.77184 | 0.329008 | ||||||||
\(559\) | −10.8289 | −0.458013 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.762263 | 0.0321828 | ||||||||
\(562\) | 13.9900 | 0.590132 | ||||||||
\(563\) | −1.99577 | −0.0841118 | −0.0420559 | − | 0.999115i | \(-0.513391\pi\) | ||||
−0.0420559 | + | 0.999115i | \(0.513391\pi\) | |||||||
\(564\) | −3.47941 | −0.146509 | ||||||||
\(565\) | −3.38474 | −0.142397 | ||||||||
\(566\) | 34.3557 | 1.44408 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −44.8344 | −1.88121 | ||||||||
\(569\) | −19.3295 | −0.810334 | −0.405167 | − | 0.914243i | \(-0.632787\pi\) | ||||
−0.405167 | + | 0.914243i | \(0.632787\pi\) | |||||||
\(570\) | −2.19448 | −0.0919167 | ||||||||
\(571\) | −30.3744 | −1.27113 | −0.635565 | − | 0.772047i | \(-0.719233\pi\) | ||||
−0.635565 | + | 0.772047i | \(0.719233\pi\) | |||||||
\(572\) | 0.195895 | 0.00819078 | ||||||||
\(573\) | −8.49366 | −0.354828 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.0920 | 0.921301 | ||||||||
\(576\) | 8.75945 | 0.364977 | ||||||||
\(577\) | 25.0275 | 1.04191 | 0.520954 | − | 0.853585i | \(-0.325576\pi\) | ||||
0.520954 | + | 0.853585i | \(0.325576\pi\) | |||||||
\(578\) | −17.6442 | −0.733902 | ||||||||
\(579\) | 4.08837 | 0.169907 | ||||||||
\(580\) | −0.192187 | −0.00798012 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.8109 | −0.531027 | ||||||||
\(583\) | 3.51383 | 0.145528 | ||||||||
\(584\) | −21.9873 | −0.909842 | ||||||||
\(585\) | 0.488088 | 0.0201799 | ||||||||
\(586\) | 6.34600 | 0.262151 | ||||||||
\(587\) | 0.853836 | 0.0352416 | 0.0176208 | − | 0.999845i | \(-0.494391\pi\) | ||||
0.0176208 | + | 0.999845i | \(0.494391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.1687 | 1.53151 | ||||||||
\(590\) | −0.871481 | −0.0358783 | ||||||||
\(591\) | 9.11034 | 0.374749 | ||||||||
\(592\) | 1.69349 | 0.0696018 | ||||||||
\(593\) | −1.16531 | −0.0478536 | −0.0239268 | − | 0.999714i | \(-0.507617\pi\) | ||||
−0.0239268 | + | 0.999714i | \(0.507617\pi\) | |||||||
\(594\) | 0.528753 | 0.0216950 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.26831 | −0.133875 | ||||||||
\(597\) | 16.8400 | 0.689217 | ||||||||
\(598\) | 10.8989 | 0.445688 | ||||||||
\(599\) | 27.7984 | 1.13581 | 0.567906 | − | 0.823093i | \(-0.307754\pi\) | ||||
0.567906 | + | 0.823093i | \(0.307754\pi\) | |||||||
\(600\) | 14.7073 | 0.600422 | ||||||||
\(601\) | −33.5231 | −1.36743 | −0.683717 | − | 0.729747i | \(-0.739638\pi\) | ||||
−0.683717 | + | 0.729747i | \(0.739638\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.17319 | 0.0477759 | ||||||||
\(604\) | 0.500701 | 0.0203732 | ||||||||
\(605\) | 2.86556 | 0.116501 | ||||||||
\(606\) | −0.864438 | −0.0351154 | ||||||||
\(607\) | −26.2691 | −1.06623 | −0.533116 | − | 0.846042i | \(-0.678979\pi\) | ||||
−0.533116 | + | 0.846042i | \(0.678979\pi\) | |||||||
\(608\) | 9.35810 | 0.379521 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.34636 | 0.0545127 | ||||||||
\(611\) | −24.2973 | −0.982962 | ||||||||
\(612\) | −0.502114 | −0.0202968 | ||||||||
\(613\) | −41.0477 | −1.65790 | −0.828951 | − | 0.559321i | \(-0.811062\pi\) | ||||
−0.828951 | + | 0.559321i | \(0.811062\pi\) | |||||||
\(614\) | −8.53795 | −0.344564 | ||||||||
\(615\) | −0.264377 | −0.0106607 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.9335 | −0.842750 | −0.421375 | − | 0.906887i | \(-0.638452\pi\) | ||||
−0.421375 | + | 0.906887i | \(0.638452\pi\) | |||||||
\(618\) | 12.9202 | 0.519729 | ||||||||
\(619\) | −44.6537 | −1.79478 | −0.897391 | − | 0.441236i | \(-0.854540\pi\) | ||||
−0.897391 | + | 0.441236i | \(0.854540\pi\) | |||||||
\(620\) | 0.412327 | 0.0165595 | ||||||||
\(621\) | −4.48105 | −0.179818 | ||||||||
\(622\) | −35.1089 | −1.40774 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.27952 | 0.251382 | ||||||||
\(625\) | 23.9565 | 0.958258 | ||||||||
\(626\) | 7.64348 | 0.305495 | ||||||||
\(627\) | 2.52875 | 0.100989 | ||||||||
\(628\) | −0.0631477 | −0.00251987 | ||||||||
\(629\) | −0.945604 | −0.0377037 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.9501 | −1.11268 | −0.556338 | − | 0.830956i | \(-0.687794\pi\) | ||||
−0.556338 | + | 0.830956i | \(0.687794\pi\) | |||||||
\(632\) | −15.9331 | −0.633786 | ||||||||
\(633\) | 13.4560 | 0.534830 | ||||||||
\(634\) | 7.81132 | 0.310227 | ||||||||
\(635\) | −0.235206 | −0.00933388 | ||||||||
\(636\) | −2.31462 | −0.0917805 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.45389 | −0.0575599 | ||||||||
\(639\) | 15.0292 | 0.594545 | ||||||||
\(640\) | −2.26555 | −0.0895539 | ||||||||
\(641\) | −23.4653 | −0.926825 | −0.463412 | − | 0.886143i | \(-0.653375\pi\) | ||||
−0.463412 | + | 0.886143i | \(0.653375\pi\) | |||||||
\(642\) | −16.7244 | −0.660058 | ||||||||
\(643\) | 37.8156 | 1.49130 | 0.745652 | − | 0.666336i | \(-0.232138\pi\) | ||||
0.745652 | + | 0.666336i | \(0.232138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.55072 | −0.0610594 | ||||||||
\(646\) | 15.7648 | 0.620258 | ||||||||
\(647\) | 21.2285 | 0.834580 | 0.417290 | − | 0.908773i | \(-0.362980\pi\) | ||||
0.417290 | + | 0.908773i | \(0.362980\pi\) | |||||||
\(648\) | −2.98316 | −0.117190 | ||||||||
\(649\) | 1.00423 | 0.0394194 | ||||||||
\(650\) | 11.9911 | 0.470329 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.14683 | −0.0840765 | ||||||||
\(653\) | −32.5672 | −1.27445 | −0.637227 | − | 0.770676i | \(-0.719919\pi\) | ||||
−0.637227 | + | 0.770676i | \(0.719919\pi\) | |||||||
\(654\) | −20.5941 | −0.805294 | ||||||||
\(655\) | 2.25294 | 0.0880297 | ||||||||
\(656\) | −3.40135 | −0.132800 | ||||||||
\(657\) | 7.37048 | 0.287550 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.3379 | −1.41552 | −0.707762 | − | 0.706451i | \(-0.750295\pi\) | ||||
−0.707762 | + | 0.706451i | \(0.750295\pi\) | |||||||
\(660\) | 0.0280525 | 0.00109194 | ||||||||
\(661\) | −18.8858 | −0.734573 | −0.367287 | − | 0.930108i | \(-0.619713\pi\) | ||||
−0.367287 | + | 0.930108i | \(0.619713\pi\) | |||||||
\(662\) | −42.5590 | −1.65410 | ||||||||
\(663\) | −3.50634 | −0.136175 | ||||||||
\(664\) | 0.316537 | 0.0122840 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.655930 | −0.0254168 | ||||||||
\(667\) | 12.3213 | 0.477083 | ||||||||
\(668\) | −2.15264 | −0.0832881 | ||||||||
\(669\) | −3.78445 | −0.146315 | ||||||||
\(670\) | −0.408619 | −0.0157863 | ||||||||
\(671\) | −1.55145 | −0.0598930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.43898 | 0.363846 | 0.181923 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181923 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(674\) | −18.0159 | −0.693946 | ||||||||
\(675\) | −4.93011 | −0.189760 | ||||||||
\(676\) | 2.53580 | 0.0975306 | ||||||||
\(677\) | −17.4852 | −0.672011 | −0.336006 | − | 0.941860i | \(-0.609076\pi\) | ||||
−0.336006 | + | 0.941860i | \(0.609076\pi\) | |||||||
\(678\) | 16.8667 | 0.647761 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.49789 | 0.0574413 | ||||||||
\(681\) | 20.1757 | 0.773135 | ||||||||
\(682\) | 3.11924 | 0.119442 | ||||||||
\(683\) | −37.9803 | −1.45328 | −0.726638 | − | 0.687021i | \(-0.758918\pi\) | ||||
−0.726638 | + | 0.687021i | \(0.758918\pi\) | |||||||
\(684\) | −1.66573 | −0.0636907 | ||||||||
\(685\) | −0.162721 | −0.00621725 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.3384 | 0.737808 | ||||||||
\(688\) | −19.9508 | −0.760618 | ||||||||
\(689\) | −16.1633 | −0.615774 | ||||||||
\(690\) | 1.56074 | 0.0594163 | ||||||||
\(691\) | −8.49462 | −0.323151 | −0.161575 | − | 0.986860i | \(-0.551657\pi\) | ||||
−0.161575 | + | 0.986860i | \(0.551657\pi\) | |||||||
\(692\) | 6.42555 | 0.244263 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.88134 | −0.299172 | ||||||||
\(695\) | −3.84477 | −0.145840 | ||||||||
\(696\) | 8.20264 | 0.310920 | ||||||||
\(697\) | 1.89924 | 0.0719388 | ||||||||
\(698\) | −4.28144 | −0.162055 | ||||||||
\(699\) | 9.29636 | 0.351621 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.9046 | 0.827325 | 0.413662 | − | 0.910430i | \(-0.364249\pi\) | ||||
0.413662 | + | 0.910430i | \(0.364249\pi\) | |||||||
\(702\) | −2.43222 | −0.0917982 | ||||||||
\(703\) | −3.13698 | −0.118313 | ||||||||
\(704\) | 3.51562 | 0.132500 | ||||||||
\(705\) | −3.47941 | −0.131042 | ||||||||
\(706\) | −28.9532 | −1.08967 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.661500 | −0.0248607 | ||||||||
\(709\) | 18.1981 | 0.683445 | 0.341723 | − | 0.939801i | \(-0.388990\pi\) | ||||
0.341723 | + | 0.939801i | \(0.388990\pi\) | |||||||
\(710\) | −5.23463 | −0.196452 | ||||||||
\(711\) | 5.34103 | 0.200304 | ||||||||
\(712\) | 11.3315 | 0.424664 | ||||||||
\(713\) | −26.4348 | −0.989989 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.195895 | 0.00732605 | ||||||||
\(716\) | −3.51421 | −0.131332 | ||||||||
\(717\) | 13.8265 | 0.516361 | ||||||||
\(718\) | −47.2918 | −1.76492 | ||||||||
\(719\) | 11.5476 | 0.430653 | 0.215327 | − | 0.976542i | \(-0.430918\pi\) | ||||
0.215327 | + | 0.976542i | \(0.430918\pi\) | |||||||
\(720\) | 0.899238 | 0.0335126 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 27.2674 | 1.01479 | ||||||||
\(723\) | −17.5930 | −0.654291 | ||||||||
\(724\) | −4.36128 | −0.162086 | ||||||||
\(725\) | 13.5561 | 0.503459 | ||||||||
\(726\) | −14.2795 | −0.529963 | ||||||||
\(727\) | −0.769589 | −0.0285425 | −0.0142712 | − | 0.999898i | \(-0.504543\pi\) | ||||
−0.0142712 | + | 0.999898i | \(0.504543\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −2.56712 | −0.0950135 | ||||||||
\(731\) | 11.1401 | 0.412031 | ||||||||
\(732\) | 1.02196 | 0.0377728 | ||||||||
\(733\) | −40.2110 | −1.48523 | −0.742613 | − | 0.669721i | \(-0.766414\pi\) | ||||
−0.742613 | + | 0.669721i | \(0.766414\pi\) | |||||||
\(734\) | 23.3592 | 0.862204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.65558 | −0.245328 | ||||||||
\(737\) | 0.470861 | 0.0173444 | ||||||||
\(738\) | 1.31743 | 0.0484953 | ||||||||
\(739\) | −33.7982 | −1.24329 | −0.621643 | − | 0.783300i | \(-0.713535\pi\) | ||||
−0.621643 | + | 0.783300i | \(0.713535\pi\) | |||||||
\(740\) | −0.0347997 | −0.00127926 | ||||||||
\(741\) | −11.6320 | −0.427314 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.8681 | 0.472084 | 0.236042 | − | 0.971743i | \(-0.424150\pi\) | ||||
0.236042 | + | 0.971743i | \(0.424150\pi\) | |||||||
\(744\) | −17.5984 | −0.645187 | ||||||||
\(745\) | −3.26831 | −0.119742 | ||||||||
\(746\) | 3.80558 | 0.139332 | ||||||||
\(747\) | −0.106108 | −0.00388229 | ||||||||
\(748\) | −0.201524 | −0.00736846 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.45863 | 0.126291 | ||||||||
\(751\) | 35.8029 | 1.30647 | 0.653233 | − | 0.757157i | \(-0.273412\pi\) | ||||
0.653233 | + | 0.757157i | \(0.273412\pi\) | |||||||
\(752\) | −44.7645 | −1.63239 | ||||||||
\(753\) | 19.2253 | 0.700611 | ||||||||
\(754\) | 6.68775 | 0.243553 | ||||||||
\(755\) | 0.500701 | 0.0182224 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.8364 | 0.975385 | 0.487693 | − | 0.873015i | \(-0.337839\pi\) | ||||
0.487693 | + | 0.873015i | \(0.337839\pi\) | |||||||
\(758\) | −30.0939 | −1.09306 | ||||||||
\(759\) | −1.79848 | −0.0652805 | ||||||||
\(760\) | 4.96913 | 0.180249 | ||||||||
\(761\) | 12.8992 | 0.467597 | 0.233799 | − | 0.972285i | \(-0.424884\pi\) | ||||
0.233799 | + | 0.972285i | \(0.424884\pi\) | |||||||
\(762\) | 1.17207 | 0.0424596 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.24552 | 0.0812402 | ||||||||
\(765\) | −0.502114 | −0.0181540 | ||||||||
\(766\) | −38.2664 | −1.38262 | ||||||||
\(767\) | −4.61936 | −0.166796 | ||||||||
\(768\) | −6.22928 | −0.224780 | ||||||||
\(769\) | −6.96424 | −0.251137 | −0.125568 | − | 0.992085i | \(-0.540075\pi\) | ||||
−0.125568 | + | 0.992085i | \(0.540075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.3929 | −0.446319 | ||||||||
\(772\) | −1.08087 | −0.0389014 | ||||||||
\(773\) | 6.90488 | 0.248351 | 0.124176 | − | 0.992260i | \(-0.460371\pi\) | ||||
0.124176 | + | 0.992260i | \(0.460371\pi\) | |||||||
\(774\) | 7.72746 | 0.277758 | ||||||||
\(775\) | −29.0839 | −1.04472 | ||||||||
\(776\) | 29.0086 | 1.04135 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.49002 | 0.268530 | ||||||||
\(779\) | 6.30059 | 0.225742 | ||||||||
\(780\) | −0.129039 | −0.00462034 | ||||||||
\(781\) | 6.03199 | 0.215841 | ||||||||
\(782\) | −11.2121 | −0.400943 | ||||||||
\(783\) | −2.74965 | −0.0982645 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.0631477 | −0.00225384 | ||||||||
\(786\) | −11.2268 | −0.400445 | ||||||||
\(787\) | −10.6169 | −0.378452 | −0.189226 | − | 0.981934i | \(-0.560598\pi\) | ||||
−0.189226 | + | 0.981934i | \(0.560598\pi\) | |||||||
\(788\) | −2.40856 | −0.0858014 | ||||||||
\(789\) | 5.50323 | 0.195920 | ||||||||
\(790\) | −1.86027 | −0.0661854 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.19730 | −0.0425441 | ||||||||
\(793\) | 7.13653 | 0.253425 | ||||||||
\(794\) | −45.9985 | −1.63242 | ||||||||
\(795\) | −2.31462 | −0.0820910 | ||||||||
\(796\) | −4.45211 | −0.157801 | ||||||||
\(797\) | −21.5437 | −0.763116 | −0.381558 | − | 0.924345i | \(-0.624612\pi\) | ||||
−0.381558 | + | 0.924345i | \(0.624612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.9955 | 0.884277 | ||||||||
\(800\) | −7.32255 | −0.258891 | ||||||||
\(801\) | −3.79848 | −0.134213 | ||||||||
\(802\) | 0.601179 | 0.0212284 | ||||||||
\(803\) | 2.95816 | 0.104391 | ||||||||
\(804\) | −0.310164 | −0.0109386 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.3482 | −0.505395 | ||||||||
\(807\) | 23.9834 | 0.844255 | ||||||||
\(808\) | 1.95741 | 0.0688616 | ||||||||
\(809\) | −8.78913 | −0.309009 | −0.154505 | − | 0.987992i | \(-0.549378\pi\) | ||||
−0.154505 | + | 0.987992i | \(0.549378\pi\) | |||||||
\(810\) | −0.348298 | −0.0122379 | ||||||||
\(811\) | −24.9708 | −0.876842 | −0.438421 | − | 0.898770i | \(-0.644462\pi\) | ||||
−0.438421 | + | 0.898770i | \(0.644462\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.44906 | −0.156035 | ||||||||
\(814\) | −0.263259 | −0.00922722 | ||||||||
\(815\) | −2.14683 | −0.0752003 | ||||||||
\(816\) | −6.45998 | −0.226144 | ||||||||
\(817\) | 36.9565 | 1.29294 | ||||||||
\(818\) | −26.2066 | −0.916292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.0698950 | 0.00244084 | ||||||||
\(821\) | 44.6324 | 1.55768 | 0.778841 | − | 0.627221i | \(-0.215808\pi\) | ||||
0.778841 | + | 0.627221i | \(0.215808\pi\) | |||||||
\(822\) | 0.810864 | 0.0282821 | ||||||||
\(823\) | 48.4771 | 1.68981 | 0.844903 | − | 0.534919i | \(-0.179658\pi\) | ||||
0.844903 | + | 0.534919i | \(0.179658\pi\) | |||||||
\(824\) | −29.2563 | −1.01919 | ||||||||
\(825\) | −1.97871 | −0.0688897 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.7051 | −0.789535 | −0.394768 | − | 0.918781i | \(-0.629175\pi\) | ||||
−0.394768 | + | 0.918781i | \(0.629175\pi\) | |||||||
\(828\) | 1.18468 | 0.0411706 | ||||||||
\(829\) | 16.2329 | 0.563793 | 0.281897 | − | 0.959445i | \(-0.409036\pi\) | ||||
0.281897 | + | 0.959445i | \(0.409036\pi\) | |||||||
\(830\) | 0.0369572 | 0.00128280 | ||||||||
\(831\) | −31.7797 | −1.10243 | ||||||||
\(832\) | −16.1716 | −0.560648 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 19.1591 | 0.663425 | ||||||||
\(835\) | −2.15264 | −0.0744951 | ||||||||
\(836\) | −0.668543 | −0.0231220 | ||||||||
\(837\) | 5.89924 | 0.203907 | ||||||||
\(838\) | 17.9082 | 0.618630 | ||||||||
\(839\) | 6.77718 | 0.233974 | 0.116987 | − | 0.993133i | \(-0.462676\pi\) | ||||
0.116987 | + | 0.993133i | \(0.462676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4394 | −0.739291 | ||||||||
\(842\) | 32.9653 | 1.13606 | ||||||||
\(843\) | 10.6191 | 0.365743 | ||||||||
\(844\) | −3.55746 | −0.122453 | ||||||||
\(845\) | 2.53580 | 0.0872340 | ||||||||
\(846\) | 17.3384 | 0.596108 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −29.7788 | −1.02261 | ||||||||
\(849\) | 26.0778 | 0.894987 | ||||||||
\(850\) | −12.3357 | −0.423111 | ||||||||
\(851\) | 2.23105 | 0.0764794 | ||||||||
\(852\) | −3.97336 | −0.136125 | ||||||||
\(853\) | −28.1364 | −0.963372 | −0.481686 | − | 0.876344i | \(-0.659975\pi\) | ||||
−0.481686 | + | 0.876344i | \(0.659975\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.66573 | −0.0569667 | ||||||||
\(856\) | 37.8702 | 1.29438 | ||||||||
\(857\) | 19.5239 | 0.666922 | 0.333461 | − | 0.942764i | \(-0.391783\pi\) | ||||
0.333461 | + | 0.942764i | \(0.391783\pi\) | |||||||
\(858\) | −0.976176 | −0.0333261 | ||||||||
\(859\) | 15.2479 | 0.520252 | 0.260126 | − | 0.965575i | \(-0.416236\pi\) | ||||
0.260126 | + | 0.965575i | \(0.416236\pi\) | |||||||
\(860\) | 0.409973 | 0.0139800 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.8854 | −0.711361 | ||||||||
\(863\) | 30.1625 | 1.02674 | 0.513372 | − | 0.858166i | \(-0.328396\pi\) | ||||
0.513372 | + | 0.858166i | \(0.328396\pi\) | |||||||
\(864\) | 1.48527 | 0.0505300 | ||||||||
\(865\) | 6.42555 | 0.218475 | ||||||||
\(866\) | 31.0149 | 1.05393 | ||||||||
\(867\) | −13.3929 | −0.454847 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.14363 | 0.0727178 | ||||||||
\(870\) | 0.957697 | 0.0324690 | ||||||||
\(871\) | −2.16592 | −0.0733894 | ||||||||
\(872\) | 46.6329 | 1.57919 | ||||||||
\(873\) | −9.72413 | −0.329112 | ||||||||
\(874\) | −37.1953 | −1.25815 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.94858 | −0.0658365 | ||||||||
\(877\) | −32.0072 | −1.08081 | −0.540403 | − | 0.841406i | \(-0.681728\pi\) | ||||
−0.540403 | + | 0.841406i | \(0.681728\pi\) | |||||||
\(878\) | 41.5399 | 1.40190 | ||||||||
\(879\) | 4.81695 | 0.162472 | ||||||||
\(880\) | 0.360911 | 0.0121663 | ||||||||
\(881\) | 1.10922 | 0.0373705 | 0.0186853 | − | 0.999825i | \(-0.494052\pi\) | ||||
0.0186853 | + | 0.999825i | \(0.494052\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.6523 | −0.392132 | −0.196066 | − | 0.980591i | \(-0.562817\pi\) | ||||
−0.196066 | + | 0.980591i | \(0.562817\pi\) | |||||||
\(884\) | 0.926995 | 0.0311782 | ||||||||
\(885\) | −0.661500 | −0.0222361 | ||||||||
\(886\) | −23.1594 | −0.778055 | ||||||||
\(887\) | −20.2080 | −0.678518 | −0.339259 | − | 0.940693i | \(-0.610176\pi\) | ||||
−0.339259 | + | 0.940693i | \(0.610176\pi\) | |||||||
\(888\) | 1.48527 | 0.0498425 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.32300 | 0.0443471 | ||||||||
\(891\) | 0.401352 | 0.0134458 | ||||||||
\(892\) | 1.00052 | 0.0334999 | ||||||||
\(893\) | 82.9208 | 2.77484 | ||||||||
\(894\) | 16.2865 | 0.544702 | ||||||||
\(895\) | −3.51421 | −0.117467 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.27283 | 0.276222 | ||||||||
\(898\) | −16.2754 | −0.543116 | ||||||||
\(899\) | −16.2208 | −0.540995 | ||||||||
\(900\) | 1.30340 | 0.0434468 | ||||||||
\(901\) | 16.6278 | 0.553953 | ||||||||
\(902\) | 0.528753 | 0.0176056 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.1925 | −1.27026 | ||||||||
\(905\) | −4.36128 | −0.144974 | ||||||||
\(906\) | −2.49507 | −0.0828932 | ||||||||
\(907\) | 26.3234 | 0.874054 | 0.437027 | − | 0.899448i | \(-0.356031\pi\) | ||||
0.437027 | + | 0.899448i | \(0.356031\pi\) | |||||||
\(908\) | −5.33399 | −0.177015 | ||||||||
\(909\) | −0.656155 | −0.0217633 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.3567 | −0.409396 | −0.204698 | − | 0.978825i | \(-0.565621\pi\) | ||||
−0.204698 | + | 0.978825i | \(0.565621\pi\) | |||||||
\(912\) | −21.4305 | −0.709635 | ||||||||
\(913\) | −0.0425867 | −0.00140941 | ||||||||
\(914\) | 4.73873 | 0.156743 | ||||||||
\(915\) | 1.02196 | 0.0337850 | ||||||||
\(916\) | −5.11263 | −0.168926 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.50211 | 0.0825821 | ||||||||
\(919\) | −52.1119 | −1.71901 | −0.859507 | − | 0.511124i | \(-0.829229\pi\) | ||||
−0.859507 | + | 0.511124i | \(0.829229\pi\) | |||||||
\(920\) | −3.53410 | −0.116516 | ||||||||
\(921\) | −6.48076 | −0.213548 | ||||||||
\(922\) | 48.8868 | 1.61000 | ||||||||
\(923\) | −27.7466 | −0.913291 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.45463 | 0.0807077 | ||||||||
\(926\) | 33.9700 | 1.11632 | ||||||||
\(927\) | 9.80716 | 0.322109 | ||||||||
\(928\) | −4.08398 | −0.134063 | ||||||||
\(929\) | −18.1288 | −0.594787 | −0.297394 | − | 0.954755i | \(-0.596117\pi\) | ||||
−0.297394 | + | 0.954755i | \(0.596117\pi\) | |||||||
\(930\) | −2.05469 | −0.0673760 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.45774 | −0.0805060 | ||||||||
\(933\) | −26.6495 | −0.872465 | ||||||||
\(934\) | −10.0688 | −0.329460 | ||||||||
\(935\) | −0.201524 | −0.00659055 | ||||||||
\(936\) | 5.50746 | 0.180017 | ||||||||
\(937\) | 3.93077 | 0.128413 | 0.0642064 | − | 0.997937i | \(-0.479548\pi\) | ||||
0.0642064 | + | 0.997937i | \(0.479548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.80181 | 0.189335 | ||||||||
\(940\) | 0.919874 | 0.0300030 | ||||||||
\(941\) | 30.4167 | 0.991557 | 0.495778 | − | 0.868449i | \(-0.334883\pi\) | ||||
0.495778 | + | 0.868449i | \(0.334883\pi\) | |||||||
\(942\) | 0.314675 | 0.0102527 | ||||||||
\(943\) | −4.48105 | −0.145923 | ||||||||
\(944\) | −8.51057 | −0.276995 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.10143 | 0.100836 | ||||||||
\(947\) | 16.0846 | 0.522679 | 0.261339 | − | 0.965247i | \(-0.415836\pi\) | ||||
0.261339 | + | 0.965247i | \(0.415836\pi\) | |||||||
\(948\) | −1.41204 | −0.0458610 | ||||||||
\(949\) | −13.6073 | −0.441711 | ||||||||
\(950\) | −40.9228 | −1.32771 | ||||||||
\(951\) | 5.92921 | 0.192268 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.7563 | 1.38501 | 0.692507 | − | 0.721411i | \(-0.256506\pi\) | ||||
0.692507 | + | 0.721411i | \(0.256506\pi\) | |||||||
\(954\) | 11.5341 | 0.373430 | ||||||||
\(955\) | 2.24552 | 0.0726635 | ||||||||
\(956\) | −3.65541 | −0.118224 | ||||||||
\(957\) | −1.10358 | −0.0356736 | ||||||||
\(958\) | 7.43194 | 0.240115 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.31579 | −0.0747419 | ||||||||
\(961\) | 3.80101 | 0.122613 | ||||||||
\(962\) | 1.21097 | 0.0390432 | ||||||||
\(963\) | −12.6947 | −0.409080 | ||||||||
\(964\) | 4.65118 | 0.149804 | ||||||||
\(965\) | −1.08087 | −0.0347944 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 54.8388 | 1.76350 | 0.881748 | − | 0.471720i | \(-0.156367\pi\) | ||||
0.881748 | + | 0.471720i | \(0.156367\pi\) | |||||||
\(968\) | 32.3342 | 1.03926 | ||||||||
\(969\) | 11.9663 | 0.384414 | ||||||||
\(970\) | 3.38689 | 0.108747 | ||||||||
\(971\) | −26.9195 | −0.863888 | −0.431944 | − | 0.901900i | \(-0.642172\pi\) | ||||
−0.431944 | + | 0.901900i | \(0.642172\pi\) | |||||||
\(972\) | −0.264377 | −0.00847988 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −17.2371 | −0.552312 | ||||||||
\(975\) | 9.10188 | 0.291493 | ||||||||
\(976\) | 13.1481 | 0.420861 | ||||||||
\(977\) | 55.3873 | 1.77200 | 0.885998 | − | 0.463689i | \(-0.153475\pi\) | ||||
0.885998 | + | 0.463689i | \(0.153475\pi\) | |||||||
\(978\) | 10.6980 | 0.342085 | ||||||||
\(979\) | −1.52453 | −0.0487240 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.6320 | −0.499093 | ||||||||
\(982\) | 13.1768 | 0.420487 | ||||||||
\(983\) | 34.7872 | 1.10954 | 0.554770 | − | 0.832004i | \(-0.312806\pi\) | ||||
0.554770 | + | 0.832004i | \(0.312806\pi\) | |||||||
\(984\) | −2.98316 | −0.0950996 | ||||||||
\(985\) | −2.40856 | −0.0767431 | ||||||||
\(986\) | −6.87994 | −0.219102 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.07524 | 0.0978364 | ||||||||
\(989\) | −26.2838 | −0.835777 | ||||||||
\(990\) | −0.139790 | −0.00444282 | ||||||||
\(991\) | 25.9053 | 0.822910 | 0.411455 | − | 0.911430i | \(-0.365021\pi\) | ||||
0.411455 | + | 0.911430i | \(0.365021\pi\) | |||||||
\(992\) | 8.76198 | 0.278193 | ||||||||
\(993\) | −32.3045 | −1.02515 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.45211 | −0.141141 | ||||||||
\(996\) | 0.0280525 | 0.000888877 0 | ||||||||
\(997\) | −36.1794 | −1.14581 | −0.572907 | − | 0.819620i | \(-0.694184\pi\) | ||||
−0.572907 | + | 0.819620i | \(0.694184\pi\) | |||||||
\(998\) | 26.3220 | 0.833210 | ||||||||
\(999\) | −0.497886 | −0.0157524 |
(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 | 6027.2.a.u.1.3 | 4 | ||
7.6 | odd | 2 | 861.2.a.i.1.3 | ✓ | 4 | ||
21.20 | even | 2 | 2583.2.a.o.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.a.i.1.3 | ✓ | 4 | 7.6 | odd | 2 | ||
2583.2.a.o.1.2 | 4 | 21.20 | even | 2 | |||
6027.2.a.u.1.3 | 4 | 1.1 | even | 1 | trivial |